LMFDB - Embedded newform 945.2.do.a.473.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(2,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9, 12]))

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

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

chi := DirichletCharacter("945.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.do (of order $36$, degree $12$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$1680$
Relative dimension:	$140$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			473.19
Character	$\chi$	$=$	945.473
Dual form			945.2.do.a.2.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.19767 - 0.192271i) q^{2} +(0.295033 - 1.70674i) q^{3} +(2.82316 + 0.497800i) q^{4} +(0.351401 + 2.20828i) q^{5} +(-0.976541 + 3.69412i) q^{6} +(-0.166853 - 2.64048i) q^{7} +(-1.84688 - 0.494869i) q^{8} +(-2.82591 - 1.00709i) q^{9} +O(q^{10})$	\(q+(-2.19767 - 0.192271i) q^{2} +(0.295033 - 1.70674i) q^{3} +(2.82316 + 0.497800i) q^{4} +(0.351401 + 2.20828i) q^{5} +(-0.976541 + 3.69412i) q^{6} +(-0.166853 - 2.64048i) q^{7} +(-1.84688 - 0.494869i) q^{8} +(-2.82591 - 1.00709i) q^{9} +(-0.347674 - 4.92064i) q^{10} +(-4.18808 + 0.738472i) q^{11} +(1.68254 - 4.67153i) q^{12} +(0.104503 - 0.0731741i) q^{13} +(-0.141002 + 5.83499i) q^{14} +(3.87264 + 0.0517672i) q^{15} +(-1.42399 - 0.518289i) q^{16} +(-0.492925 + 1.83962i) q^{17} +(6.01678 + 2.75659i) q^{18} +(2.22549 + 1.28489i) q^{19} +(-0.107221 + 6.40927i) q^{20} +(-4.55584 - 0.494256i) q^{21} +(9.34601 - 0.817670i) q^{22} +(5.28668 - 0.462525i) q^{23} +(-1.38950 + 3.00613i) q^{24} +(-4.75303 + 1.55199i) q^{25} +(-0.243733 + 0.140719i) q^{26} +(-2.55257 + 4.52597i) q^{27} +(0.843380 - 7.53758i) q^{28} +(0.465271 + 2.63868i) q^{29} +(-8.50082 - 0.858363i) q^{30} +(-0.0315243 + 0.178783i) q^{31} +(6.49557 + 3.02893i) q^{32} +(0.0247558 + 7.36584i) q^{33} +(1.43699 - 3.94810i) q^{34} +(5.77231 - 1.29633i) q^{35} +(-7.47668 - 4.24991i) q^{36} +(0.606980 - 0.606980i) q^{37} +(-4.64385 - 3.25166i) q^{38} +(-0.0940571 - 0.199949i) q^{39} +(0.443817 - 4.25233i) q^{40} +(-10.1168 - 1.78386i) q^{41} +(9.91720 + 1.96217i) q^{42} +(-12.2381 - 1.07069i) q^{43} -12.1913 q^{44} +(1.23091 - 6.59431i) q^{45} -11.7073 q^{46} +(-2.23386 + 3.19029i) q^{47} +(-1.30471 + 2.27746i) q^{48} +(-6.94432 + 0.881145i) q^{49} +(10.7440 - 2.49688i) q^{50} +(2.99432 + 1.38404i) q^{51} +(0.331456 - 0.154561i) q^{52} +(2.84198 + 10.6064i) q^{53} +(6.47992 - 9.45579i) q^{54} +(-3.10245 - 8.98898i) q^{55} +(-0.998538 + 4.95922i) q^{56} +(2.84956 - 3.41925i) q^{57} +(-0.515169 - 5.88840i) q^{58} +(-3.88857 + 1.41532i) q^{59} +(10.9073 + 2.07395i) q^{60} +(0.393991 + 2.23444i) q^{61} +(0.103655 - 0.386845i) q^{62} +(-2.18769 + 7.62981i) q^{63} +(-11.0680 - 6.39013i) q^{64} +(0.198312 + 0.205060i) q^{65} +(1.36183 - 16.1924i) q^{66} +(13.4841 - 1.17970i) q^{67} +(-2.30737 + 4.94817i) q^{68} +(0.770337 - 9.15944i) q^{69} +(-12.9349 + 1.73905i) q^{70} +(3.39061 + 1.95757i) q^{71} +(4.72073 + 3.25842i) q^{72} +(4.68183 + 4.68183i) q^{73} +(-1.45065 + 1.21724i) q^{74} +(1.24653 + 8.57007i) q^{75} +(5.64331 + 4.73530i) q^{76} +(2.64872 + 10.9354i) q^{77} +(0.168262 + 0.457506i) q^{78} +(8.13529 + 9.69526i) q^{79} +(0.644139 - 3.32670i) q^{80} +(6.97155 + 5.69188i) q^{81} +(21.8903 + 5.86550i) q^{82} +(2.43111 + 1.70228i) q^{83} +(-12.6158 - 3.66326i) q^{84} +(-4.23562 - 0.442073i) q^{85} +(26.6894 + 4.70605i) q^{86} +(4.64081 - 0.0155972i) q^{87} +(8.10032 + 0.708686i) q^{88} +(-8.23114 + 14.2567i) q^{89} +(-3.97302 + 14.2554i) q^{90} +(-0.210652 - 0.263731i) q^{91} +(15.1554 + 1.32593i) q^{92} +(0.295836 + 0.106551i) q^{93} +(5.52269 - 6.58168i) q^{94} +(-2.05536 + 5.36603i) q^{95} +(7.08601 - 10.1926i) q^{96} +(-0.505228 + 5.77479i) q^{97} +(15.4307 - 0.601272i) q^{98} +(12.5789 + 2.13091i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1680 q - 6 q^{2} - 6 q^{3} - 6 q^{5} - 36 q^{6} - 12 q^{7} - 36 q^{8}+O(q^{10}) $ 1680 * q - 6 * q^2 - 6 * q^3 - 6 * q^5 - 36 * q^6 - 12 * q^7 - 36 * q^8	$ 1680 q - 6 q^{2} - 6 q^{3} - 6 q^{5} - 36 q^{6} - 12 q^{7} - 36 q^{8} + 6 q^{10} + 12 q^{11} - 6 q^{12} - 24 q^{13} - 24 q^{15} - 12 q^{16} - 18 q^{17} - 6 q^{18} - 24 q^{20} - 24 q^{21} - 24 q^{22} + 42 q^{23} - 6 q^{25} - 24 q^{27} - 24 q^{28} + 30 q^{30} - 12 q^{31} + 90 q^{32} - 6 q^{33} - 18 q^{35} - 84 q^{36} - 12 q^{37} - 30 q^{38} - 54 q^{40} - 72 q^{41} - 108 q^{42} - 24 q^{43} - 6 q^{45} - 24 q^{46} - 6 q^{47} - 96 q^{48} - 72 q^{50} - 12 q^{51} - 30 q^{52} - 90 q^{53} - 48 q^{55} - 72 q^{56} - 24 q^{57} - 6 q^{58} + 186 q^{60} + 24 q^{61} - 36 q^{62} - 54 q^{63} + 138 q^{65} - 12 q^{66} - 6 q^{67} + 114 q^{68} - 12 q^{70} - 72 q^{71} + 18 q^{72} - 12 q^{73} - 150 q^{75} - 156 q^{77} - 84 q^{78} + 12 q^{81} - 12 q^{82} - 24 q^{83} - 24 q^{85} - 120 q^{86} - 102 q^{87} - 6 q^{88} + 30 q^{90} - 12 q^{91} + 108 q^{92} + 138 q^{93} - 66 q^{95} - 444 q^{96} - 24 q^{97} - 360 q^{98}+O(q^{100}) $ 1680 * q - 6 * q^2 - 6 * q^3 - 6 * q^5 - 36 * q^6 - 12 * q^7 - 36 * q^8 + 6 * q^10 + 12 * q^11 - 6 * q^12 - 24 * q^13 - 24 * q^15 - 12 * q^16 - 18 * q^17 - 6 * q^18 - 24 * q^20 - 24 * q^21 - 24 * q^22 + 42 * q^23 - 6 * q^25 - 24 * q^27 - 24 * q^28 + 30 * q^30 - 12 * q^31 + 90 * q^32 - 6 * q^33 - 18 * q^35 - 84 * q^36 - 12 * q^37 - 30 * q^38 - 54 * q^40 - 72 * q^41 - 108 * q^42 - 24 * q^43 - 6 * q^45 - 24 * q^46 - 6 * q^47 - 96 * q^48 - 72 * q^50 - 12 * q^51 - 30 * q^52 - 90 * q^53 - 48 * q^55 - 72 * q^56 - 24 * q^57 - 6 * q^58 + 186 * q^60 + 24 * q^61 - 36 * q^62 - 54 * q^63 + 138 * q^65 - 12 * q^66 - 6 * q^67 + 114 * q^68 - 12 * q^70 - 72 * q^71 + 18 * q^72 - 12 * q^73 - 150 * q^75 - 156 * q^77 - 84 * q^78 + 12 * q^81 - 12 * q^82 - 24 * q^83 - 24 * q^85 - 120 * q^86 - 102 * q^87 - 6 * q^88 + 30 * q^90 - 12 * q^91 + 108 * q^92 + 138 * q^93 - 66 * q^95 - 444 * q^96 - 24 * q^97 - 360 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−2.19767	−	0.192271i	−1.55399	−	0.135956i	−0.722449	−	0.691425i	$-0.756983\pi$
$2$	−2.19767	−	0.192271i	−1.55399	−	0.135956i	−0.831538	+	0.555468i	$0.812539\pi$
$3$	0.295033	−	1.70674i	0.170337	−	0.985386i
$3$	0.295033	−	1.70674i	0.170337	−	0.985386i
$4$	2.82316	+	0.497800i	1.41158	+	0.248900i
$5$	0.351401	+	2.20828i	0.157151	+	0.987575i
$5$	0.351401	+	2.20828i	0.157151	+	0.987575i
$6$	−0.976541	+	3.69412i	−0.398671	+	1.50812i
$7$	−0.166853	−	2.64048i	−0.0630644	−	0.998009i
$7$	−0.166853	−	2.64048i	−0.0630644	−	0.998009i
$8$	−1.84688	−	0.494869i	−0.652970	−	0.174963i
$9$	−2.82591	−	1.00709i	−0.941970	−	0.335696i
$10$	−0.347674	−	4.92064i	−0.109944	−	1.55604i
$11$	−4.18808	+	0.738472i	−1.26275	+	0.222658i	−0.764643	−	0.644455i	$-0.777084\pi$
$11$	−4.18808	+	0.738472i	−1.26275	+	0.222658i	−0.498112	+	0.867112i	$0.665973\pi$
$12$	1.68254	−	4.67153i	0.485708	−	1.34856i
$13$	0.104503	−	0.0731741i	0.0289840	−	0.0202948i	−0.558995	−	0.829171i	$-0.688813\pi$
$13$	0.104503	−	0.0731741i	0.0289840	−	0.0202948i	0.587979	+	0.808876i	$0.299924\pi$
$14$	−0.141002	+	5.83499i	−0.0376843	+	1.55947i
$15$	3.87264	+	0.0517672i	0.999911	+	0.0133662i
$16$	−1.42399	−	0.518289i	−0.355997	−	0.129572i
$17$	−0.492925	+	1.83962i	−0.119552	+	0.446173i	−0.999587	−	0.0287350i	$-0.990852\pi$
$17$	−0.492925	+	1.83962i	−0.119552	+	0.446173i	0.880035	+	0.474908i	$0.157519\pi$
$18$	6.01678	+	2.75659i	1.41817	+	0.649734i
$19$	2.22549	+	1.28489i	0.510563	+	0.294774i	0.733065	−	0.680159i	$-0.238089\pi$
$19$	2.22549	+	1.28489i	0.510563	+	0.294774i	−0.222502	+	0.974932i	$0.571422\pi$
$20$	−0.107221	+	6.40927i	−0.0239754	+	1.43316i
$21$	−4.55584	−	0.494256i	−0.994167	−	0.107856i
$22$	9.34601	−	0.817670i	1.99258	−	0.174328i
$23$	5.28668	−	0.462525i	1.10235	−	0.0964431i	0.478574	−	0.878047i	$-0.341154\pi$
$23$	5.28668	−	0.462525i	1.10235	−	0.0964431i	0.623775	+	0.781604i	$0.285598\pi$
$24$	−1.38950	+	3.00613i	−0.283631	+	0.613624i
$25$	−4.75303	+	1.55199i	−0.950607	+	0.310397i
$26$	−0.243733	+	0.140719i	−0.0478000	+	0.0275974i
$27$	−2.55257	+	4.52597i	−0.491243	+	0.871023i
$28$	0.843380	−	7.53758i	0.159384	−	1.42447i
$29$	0.465271	+	2.63868i	0.0863986	+	0.489991i	0.997046	+	0.0768065i	$0.0244724\pi$
$29$	0.465271	+	2.63868i	0.0863986	+	0.489991i	−0.910647	+	0.413184i	$0.864417\pi$
$30$	−8.50082	−	0.858363i	−1.55203	−	0.156715i
$31$	−0.0315243	+	0.178783i	−0.00566193	+	0.0321104i	−0.987508	−	0.157570i	$-0.949634\pi$
$31$	−0.0315243	+	0.178783i	−0.00566193	+	0.0321104i	0.981846	+	0.189680i	$0.0607452\pi$
$32$	6.49557	+	3.02893i	1.14827	+	0.535445i
$33$	0.0247558	+	7.36584i	0.00430943	+	1.28223i
$34$	1.43699	−	3.94810i	0.246442	−	0.677093i
$35$	5.77231	−	1.29633i	0.975698	−	0.219119i
$36$	−7.47668	−	4.24991i	−1.24611	−	0.708319i
$37$	0.606980	−	0.606980i	0.0997869	−	0.0997869i	−0.655451	−	0.755238i	$-0.727521\pi$
$37$	0.606980	−	0.606980i	0.0997869	−	0.0997869i	0.755238	+	0.655451i	$0.227521\pi$
$38$	−4.64385	−	3.25166i	−0.753331	−	0.527488i
$39$	−0.0940571	−	0.199949i	−0.0150612	−	0.0320174i
$40$	0.443817	−	4.25233i	0.0701737	−	0.672352i
$41$	−10.1168	−	1.78386i	−1.57997	−	0.278592i	−0.686304	−	0.727315i	$-0.740768\pi$
$41$	−10.1168	−	1.78386i	−1.57997	−	0.278592i	−0.893671	+	0.448723i	$0.851879\pi$
$42$	9.91720	+	1.96217i	1.53026	+	0.302769i
$43$	−12.2381	−	1.07069i	−1.86629	−	0.163279i	−0.902630	−	0.430418i	$-0.858366\pi$
$43$	−12.2381	−	1.07069i	−1.86629	−	0.163279i	−0.963658	+	0.267139i	$0.913922\pi$
$44$	−12.1913			−1.83790
$45$	1.23091	−	6.59431i	0.183493	−	0.983021i
$46$	−11.7073			−1.72615
$47$	−2.23386	+	3.19029i	−0.325842	+	0.465351i	−0.948333	−	0.317276i	$-0.897232\pi$
$47$	−2.23386	+	3.19029i	−0.325842	+	0.465351i	0.622491	+	0.782627i	$0.286121\pi$
$48$	−1.30471	+	2.27746i	−0.188318	+	0.328723i
$49$	−6.94432	+	0.881145i	−0.992046	+	0.125878i
$50$	10.7440	−	2.49688i	1.51943	−	0.353112i
$51$	2.99432	+	1.38404i	0.419289	+	0.193805i
$52$	0.331456	−	0.154561i	0.0459647	−	0.0214337i
$53$	2.84198	+	10.6064i	0.390375	+	1.45690i	0.829516	+	0.558483i	$0.188616\pi$
$53$	2.84198	+	10.6064i	0.390375	+	1.45690i	−0.439141	+	0.898418i	$0.644717\pi$
$54$	6.47992	−	9.45579i	0.881806	−	1.28677i
$55$	−3.10245	−	8.98898i	−0.418335	−	1.21207i
$56$	−0.998538	+	4.95922i	−0.133435	+	0.662704i
$57$	2.84956	−	3.41925i	0.377434	−	0.452890i
$58$	−0.515169	−	5.88840i	−0.0676450	−	0.773185i
$59$	−3.88857	+	1.41532i	−0.506249	+	0.184259i	−0.582502	−	0.812829i	$-0.697926\pi$
$59$	−3.88857	+	1.41532i	−0.506249	+	0.184259i	0.0762537	+	0.997088i	$0.475704\pi$
$60$	10.9073	+	2.07395i	1.40813	+	0.267745i
$61$	0.393991	+	2.23444i	0.0504454	+	0.286090i	0.999586	−	0.0287615i	$-0.00915633\pi$
$61$	0.393991	+	2.23444i	0.0504454	+	0.286090i	−0.949141	+	0.314852i	$0.898045\pi$
$62$	0.103655	−	0.386845i	0.0131642	−	0.0491294i
$63$	−2.18769	+	7.62981i	−0.275623	+	0.961266i
$64$	−11.0680	−	6.39013i	−1.38350	−	0.798766i
$65$	0.198312	+	0.205060i	0.0245976	+	0.0254345i
$66$	1.36183	−	16.1924i	0.167630	−	1.99315i
$67$	13.4841	−	1.17970i	1.64734	−	0.144124i	0.774648	−	0.632393i	$-0.217927\pi$
$67$	13.4841	−	1.17970i	1.64734	−	0.144124i	0.872693	+	0.488269i	$0.162372\pi$
$68$	−2.30737	+	4.94817i	−0.279810	+	0.600053i
$69$	0.770337	−	9.15944i	0.0927377	−	1.10267i
$70$	−12.9349	+	1.73905i	−1.54601	+	0.207856i
$71$	3.39061	+	1.95757i	0.402391	+	0.232321i	0.687515	−	0.726170i	$-0.258701\pi$
$71$	3.39061	+	1.95757i	0.402391	+	0.232321i	−0.285124	+	0.958491i	$0.592035\pi$
$72$	4.72073	+	3.25842i	0.556344	+	0.384009i
$73$	4.68183	+	4.68183i	0.547967	+	0.547967i	0.925852	−	0.377886i	$-0.123349\pi$
$73$	4.68183	+	4.68183i	0.547967	+	0.547967i	−0.377886	+	0.925852i	$0.623349\pi$
$74$	−1.45065	+	1.21724i	−0.168634	+	0.141501i
$75$	1.24653	+	8.57007i	0.143937	+	0.989587i
$76$	5.64331	+	4.73530i	0.647332	+	0.543176i
$77$	2.64872	+	10.9354i	0.301850	+	1.24620i
$78$	0.168262	+	0.457506i	0.0190519	+	0.0518023i
$79$	8.13529	+	9.69526i	0.915292	+	1.09080i	0.995569	+	0.0940299i	$0.0299749\pi$
$79$	8.13529	+	9.69526i	0.915292	+	1.09080i	−0.0802774	+	0.996773i	$0.525581\pi$
$80$	0.644139	−	3.32670i	0.0720169	−	0.371936i
$81$	6.97155	+	5.69188i	0.774616	+	0.632432i
$82$	21.8903	+	5.86550i	2.41738	+	0.647736i
$83$	2.43111	+	1.70228i	0.266849	+	0.186850i	0.699341	−	0.714788i	$-0.253477\pi$
$83$	2.43111	+	1.70228i	0.266849	+	0.186850i	−0.432492	+	0.901638i	$0.642366\pi$
$84$	−12.6158	−	3.66326i	−1.37650	−	0.399695i
$85$	−4.23562	−	0.442073i	−0.459417	−	0.0479496i
$86$	26.6894	+	4.70605i	2.87799	+	0.507467i
$87$	4.64081	−	0.0155972i	0.497547	−	0.00167220i
$88$	8.10032	+	0.708686i	0.863497	+	0.0755462i
$89$	−8.23114	+	14.2567i	−0.872499	+	1.51121i	−0.0130953	+	0.999914i	$0.504168\pi$
$89$	−8.23114	+	14.2567i	−0.872499	+	1.51121i	−0.859403	+	0.511298i	$0.829165\pi$
$90$	−3.97302	+	14.2554i	−0.418793	+	1.50265i
$91$	−0.210652	−	0.263731i	−0.0220823	−	0.0276465i
$92$	15.1554	+	1.32593i	1.58006	+	0.138237i
$93$	0.295836	+	0.106551i	0.0306767	+	0.0110488i
$94$	5.52269	−	6.58168i	0.569622	−	0.678849i
$95$	−2.05536	+	5.36603i	−0.210875	+	0.550543i
$96$	7.08601	−	10.1926i	0.723213	−	1.04028i
$97$	−0.505228	+	5.77479i	−0.0512982	+	0.586341i	0.926430	+	0.376467i	$0.122861\pi$
$97$	−0.505228	+	5.77479i	−0.0512982	+	0.586341i	−0.977728	+	0.209874i	$0.932695\pi$
$98$	15.4307	−	0.601272i	1.55874	−	0.0607377i
$99$	12.5789	+	2.13091i	1.26422	+	0.214165i
$100$	−14.1912	+	2.01545i	−1.41912	+	0.201545i
$101$	−6.53154	−	7.78399i	−0.649913	−	0.774536i	0.335988	−	0.941866i	$-0.390930\pi$
$101$	−6.53154	−	7.78399i	−0.649913	−	0.774536i	−0.985901	+	0.167331i	$0.946485\pi$
$102$	−6.31441	−	3.61739i	−0.625220	−	0.358175i
$103$	3.44582	−	2.41279i	0.339527	−	0.237739i	−0.391360	−	0.920237i	$-0.627995\pi$
$103$	3.44582	−	2.41279i	0.339527	−	0.237739i	0.730887	+	0.682498i	$0.239107\pi$
$104$	−0.229217	+	0.0834280i	−0.0224765	+	0.00818079i
$105$	−0.509470	−	10.2343i	−0.0497192	−	0.998763i
$106$	−4.20642	−	23.8558i	−0.408563	−	2.31708i
$107$	−1.05984	+	3.95536i	−0.102458	+	0.382379i	−0.998044	−	0.0625089i	$-0.980090\pi$
$107$	−1.05984	+	3.95536i	−0.102458	+	0.382379i	0.895586	+	0.444888i	$0.146756\pi$
$108$	−9.45935	+	11.5069i	−0.910227	+	1.10725i
$109$	−2.74723	−	1.58611i	−0.263137	−	0.151922i	0.362628	−	0.931934i	$-0.381880\pi$
$109$	−2.74723	−	1.58611i	−0.263137	−	0.151922i	−0.625765	+	0.780012i	$0.715213\pi$
$110$	5.08984	+	20.3513i	0.485297	+	1.94042i
$111$	−0.856877	−	1.21504i	−0.0813312	−	0.115326i
$112$	−1.13094	+	3.84650i	−0.106864	+	0.363460i
$113$	−2.75320	+	0.240874i	−0.259000	+	0.0226595i	−0.215916	−	0.976412i	$-0.569274\pi$
$113$	−2.75320	+	0.240874i	−0.259000	+	0.0226595i	−0.0430836	+	0.999071i	$0.513718\pi$
$114$	−6.91981	+	6.96648i	−0.648100	+	0.652471i
$115$	2.87913	+	11.5120i	0.268480	+	1.07350i
$116$			7.68104i			0.713167i
$117$	−0.369010	+	0.101539i	−0.0341150	+	0.00938731i
$118$	8.81791	−	2.36275i	0.811755	−	0.217509i
$119$	4.93973	+	0.994614i	0.452825	+	0.0911761i
$120$	−7.12667	−	2.01206i	−0.650573	−	0.183675i
$121$	6.65809	−	2.42335i	0.605281	−	0.220304i
$122$	−0.436245	−	4.98630i	−0.0394958	−	0.451439i
$123$	−6.02937	+	16.7404i	−0.543650	+	1.50943i
$124$	−0.177997	+	0.489041i	−0.0159846	+	0.0439172i
$125$	−5.09745	−	9.95068i	−0.455929	−	0.890016i
$126$	6.27481	−	16.3472i	0.559004	−	1.45632i
$127$	−7.16793	−	1.92064i	−0.636051	−	0.170429i	−0.0736371	−	0.997285i	$-0.523461\pi$
$127$	−7.16793	−	1.92064i	−0.636051	−	0.170429i	−0.562414	+	0.826856i	$0.690127\pi$
$128$	11.3534	+	7.94972i	1.00351	+	0.702663i
$129$	−5.43803	+	20.5713i	−0.478791	+	1.81120i
$130$	−0.396397	−	0.488783i	−0.0347663	−	0.0428691i
$131$	−5.06210	+	6.03277i	−0.442277	+	0.527086i	−0.940423	−	0.340008i	$-0.889570\pi$
$131$	−5.06210	+	6.03277i	−0.442277	+	0.527086i	0.498145	+	0.867094i	$0.334015\pi$
$132$	−3.59682	+	20.8073i	−0.313063	+	1.81104i
$133$	3.02140	−	6.09076i	0.261988	−	0.528136i
$134$	−29.8603			−2.57954
$135$	−10.8916	−	4.04638i	−0.937399	−	0.348257i
$136$	1.82074	−	3.15362i	0.156127	−	0.270420i
$137$	−6.73011	−	14.4328i	−0.574992	−	1.23308i	−0.951782	−	0.306776i	$-0.900750\pi$
$137$	−6.73011	−	14.4328i	−0.574992	−	1.23308i	0.376789	−	0.926299i	$-0.377028\pi$
$138$	−3.45404	+	19.9813i	−0.294028	+	1.70092i
$139$	7.80023	+	21.4310i	0.661607	+	1.81775i	0.569485	+	0.822002i	$0.307143\pi$
$139$	7.80023	+	21.4310i	0.661607	+	1.81775i	0.0921223	+	0.995748i	$0.470635\pi$
$140$	16.9415	−	0.786289i	1.43182	−	0.0664536i
$141$	4.78592	+	4.75386i	0.403047	+	0.400347i
$142$	−7.07505	−	4.95400i	−0.593725	−	0.415731i
$143$	−0.383632	+	0.383632i	−0.0320809	+	0.0320809i
$144$	3.50210	+	2.89872i	0.291842	+	0.241560i
$145$	−5.66346	+	1.95468i	−0.470325	+	0.162328i
$146$	−9.38893	−	11.1893i	−0.777033	−	0.926032i
$147$	−0.544920	+	12.1121i	−0.0449443	+	0.998989i
$148$	2.01576	−	1.41145i	0.165694	−	0.116020i
$149$	1.52867	−	0.556392i	0.125234	−	0.0455814i	−0.278643	−	0.960395i	$-0.589885\pi$
$149$	1.52867	−	0.556392i	0.125234	−	0.0455814i	0.403877	+	0.914813i	$0.367662\pi$
$150$	−1.09169	−	19.0739i	−0.0891358	−	1.55737i
$151$	−0.258696	−	1.46714i	−0.0210524	−	0.119394i	0.972471	−	0.233026i	$-0.0748627\pi$
$151$	−0.258696	−	1.46714i	−0.0210524	−	0.119394i	−0.993523	+	0.113632i	$0.963752\pi$
$152$	−3.47436	−	3.47436i	−0.281808	−	0.281808i
$153$	3.24562	−	4.70218i	0.262393	−	0.380149i
$154$	−3.71845	−	24.5416i	−0.299641	−	1.97762i
$155$	−0.405882	−	0.00679003i	−0.0326012	−	0.000545388i
$156$	−0.166004	−	0.611310i	−0.0132910	−	0.0489440i
$157$	3.75395	−	8.05037i	0.299598	−	0.642490i	−0.697665	−	0.716424i	$-0.745778\pi$
$157$	3.75395	−	8.05037i	0.299598	−	0.642490i	0.997263	+	0.0739342i	$0.0235555\pi$
$158$	−16.0146	−	22.8712i	−1.27405	−	1.81953i
$159$	18.9408	−	1.72127i	1.50210	−	0.136506i
$160$	−4.40620	+	15.4084i	−0.348341	+	1.21814i
$161$	−2.10339	−	13.8822i	−0.165770	−	1.09407i
$162$	−14.2268	−	13.8493i	−1.11776	−	1.08810i
$163$	0.0449382	−	0.167712i	0.00351983	−	0.0131362i	−0.964144	−	0.265381i	$-0.914502\pi$
$163$	0.0449382	−	0.167712i	0.00351983	−	0.0131362i	0.967663	+	0.252245i	$0.0811689\pi$
$164$	−27.6733	−	10.0723i	−2.16092	−	0.786511i
$165$	−16.2572	+	2.64303i	−1.26562	+	0.205760i
$166$	−5.01548	−	4.20849i	−0.389277	−	0.326642i
$167$	2.00334	+	22.8982i	0.155023	+	1.77192i	0.533011	+	0.846109i	$0.321061\pi$
$167$	2.00334	+	22.8982i	0.155023	+	1.77192i	−0.377988	+	0.925811i	$0.623384\pi$
$168$	8.16949	+	3.16738i	0.630290	+	0.244368i
$169$	−4.44070	+	12.2007i	−0.341592	+	0.938516i
$170$	9.22348	+	1.78592i	0.707409	+	0.136974i
$171$	−4.99505	−	5.87225i	−0.381981	−	0.449062i
$172$	−34.0171	−	9.11485i	−2.59378	−	0.695001i
$173$	5.97312	−	2.78531i	0.454128	−	0.211763i	−0.182076	−	0.983285i	$-0.558282\pi$
$173$	5.97312	−	2.78531i	0.454128	−	0.211763i	0.636204	+	0.771521i	$0.280504\pi$
$174$	−10.2020	−	0.858016i	−0.773408	−	0.0650460i
$175$	4.89105	+	12.2914i	0.369729	+	0.929140i
$176$	6.34652	+	1.11906i	0.478387	+	0.0843526i
$177$	1.26833	+	7.05434i	0.0953336	+	0.530236i
$178$	20.8305	−	29.7490i	1.56131	−	2.22978i
$179$	−5.03410	−	8.71932i	−0.376266	−	0.651713i	0.614249	−	0.789112i	$-0.289459\pi$
$179$	−5.03410	−	8.71932i	−0.376266	−	0.651713i	−0.990516	+	0.137399i	$0.956126\pi$
$180$	6.75770	−	18.0041i	0.503689	−	1.34194i
$181$	1.31310	+	2.27436i	0.0976020	+	0.169052i	0.910692	−	0.413087i	$-0.135549\pi$
$181$	1.31310	+	2.27436i	0.0976020	+	0.169052i	−0.813090	+	0.582139i	$0.802216\pi$
$182$	0.412235	+	0.620094i	0.0305569	+	0.0459645i
$183$	3.92984	−	0.0132078i	0.290502	−	0.000976345i
$184$	−9.99274	−	1.76199i	−0.736674	−	0.129896i
$185$	1.55368	+	1.12709i	0.114229	+	0.0828654i
$186$	−0.629662	−	0.291044i	−0.0461690	−	0.0213404i
$187$	0.705902	−	8.06849i	0.0516206	−	0.590027i
$188$	−7.89468	+	7.89468i	−0.575779	+	0.575779i
$189$	12.3766	+	5.98486i	0.900269	+	0.435335i
$190$	5.54873	−	11.3976i	0.402547	−	0.826866i
$191$	5.27702	+	6.28891i	0.381832	+	0.455049i	0.922391	−	0.386256i	$-0.126232\pi$
$191$	5.27702	+	6.28891i	0.381832	+	0.455049i	−0.540560	+	0.841306i	$0.681788\pi$
$192$	−14.1717	+	17.0049i	−1.02276	+	1.22722i
$193$	−8.92462	+	6.24909i	−0.642409	+	0.449819i	−0.848846	−	0.528641i	$-0.822702\pi$
$193$	−8.92462	+	6.24909i	−0.642409	+	0.449819i	0.206437	+	0.978460i	$0.433813\pi$
$194$	2.22065	−	12.5939i	0.159433	−	0.904191i
$195$	0.408492	−	0.277967i	0.0292527	−	0.0199056i
$196$	−20.0436	−	0.969266i	−1.43168	−	0.0692333i
$197$	5.71010	−	21.3104i	0.406828	−	1.51830i	−0.393832	−	0.919182i	$-0.628851\pi$
$197$	5.71010	−	21.3104i	0.406828	−	1.51830i	0.800660	−	0.599119i	$-0.204482\pi$
$198$	−27.2345	−	7.10159i	−1.93547	−	0.504688i
$199$	3.52436	−	2.03479i	0.249835	−	0.144242i	−0.369854	−	0.929090i	$-0.620592\pi$
$199$	3.52436	−	2.03479i	0.249835	−	0.144242i	0.619689	+	0.784848i	$0.287259\pi$
$200$	9.54630	−	0.514196i	0.675025	−	0.0363592i
$201$	1.96480	−	23.3618i	0.138586	−	1.64782i
$202$	12.8575	+	18.3624i	0.904652	+	1.29198i
$203$	6.88977	−	1.66881i	0.483567	−	0.117128i
$204$	7.76448	+	5.39795i	0.543622	+	0.377932i
$205$	0.384226	−	22.9676i	0.0268355	−	1.60412i
$206$	−8.03668	+	4.63998i	−0.559942	+	0.323283i
$207$	−15.4055	−	4.01710i	−1.07076	−	0.279208i
$208$	−0.186737	+	0.0500360i	−0.0129479	+	0.00346937i
$209$	−10.2694	−	3.73776i	−0.710349	−	0.258546i
$210$	−0.848109	+	22.5895i	−0.0585251	+	1.55882i
$211$	7.13070	+	5.98336i	0.490897	+	0.411912i	0.854348	−	0.519702i	$-0.173957\pi$
$211$	7.13070	+	5.98336i	0.490897	+	0.411912i	−0.363450	+	0.931614i	$0.618401\pi$
$212$	2.74350	+	31.3583i	0.188424	+	2.15370i
$213$	4.34140	−	5.20933i	0.297468	−	0.356938i
$214$	3.08967	−	8.48879i	0.211205	−	0.580282i
$215$	−1.93608	−	27.4014i	−0.132039	−	1.86876i
$216$	6.95405	−	7.09571i	0.473163	−	0.482802i
$217$	0.477334	+	0.0534090i	0.0324036	+	0.00362564i
$218$	5.73254	+	4.01396i	0.388256	+	0.271860i
$219$	9.37195	−	6.60936i	0.633298	−	0.446619i
$220$	−4.28402	−	26.9218i	−0.288828	−	1.81506i
$221$	0.0831002	+	0.228316i	0.00558992	+	0.0153582i
$222$	1.64952	+	2.83500i	0.110708	+	0.190273i
$223$	6.49943	+	13.9381i	0.435234	+	0.933362i	0.994536	+	0.104398i	$0.0332915\pi$
$223$	6.49943	+	13.9381i	0.435234	+	0.933362i	−0.559302	+	0.828964i	$0.688931\pi$
$224$	6.91405	−	17.6568i	0.461965	−	1.17975i
$225$	14.9946	+	0.400951i	0.999643	+	0.0267301i
$226$	6.09694			0.405563
$227$	14.6744	−	20.9572i	0.973974	−	1.39098i	0.0541997	−	0.998530i	$-0.482739\pi$
$227$	14.6744	−	20.9572i	0.973974	−	1.39098i	0.919774	−	0.392449i	$-0.128372\pi$
$228$	9.74688	−	8.23458i	0.645503	−	0.545348i
$229$	−1.14999	−	3.15958i	−0.0759937	−	0.208791i	0.895879	−	0.444298i	$-0.146547\pi$
$229$	−1.14999	−	3.15958i	−0.0759937	−	0.208791i	−0.971873	+	0.235508i	$0.924325\pi$
$230$	−4.11396	−	25.8531i	−0.271266	−	1.70470i
$231$	19.4453	−	1.29438i	1.27940	−	0.0851638i
$232$	0.446504	−	5.10357i	0.0293144	−	0.335066i
$233$	−13.6426	+	13.6426i	−0.893759	+	0.893759i	−0.994875	−	0.101116i	$-0.967759\pi$
$233$	−13.6426	+	13.6426i	−0.893759	+	0.893759i	0.101116	+	0.994875i	$0.467759\pi$
$234$	0.830485	−	0.152200i	0.0542905	−	0.00994961i
$235$	−7.83004	−	3.81193i	−0.510775	−	0.248663i
$236$	−11.6826	+	2.05996i	−0.760473	+	0.134092i
$237$	18.9475	−	11.0244i	1.23077	−	0.716111i
$238$	−10.6647	−	3.13560i	−0.691287	−	0.203251i
$239$	−26.0992	+	9.49934i	−1.68822	+	0.614461i	−0.994399	−	0.105688i	$-0.966295\pi$
$239$	−26.0992	+	9.49934i	−1.68822	+	0.614461i	−0.693819	+	0.720149i	$0.744073\pi$
$240$	−5.48776	−	2.08086i	−0.354233	−	0.134319i
$241$	−14.4196	−	5.24830i	−0.928848	−	0.338073i	−0.167095	−	0.985941i	$-0.553439\pi$
$241$	−14.4196	−	5.24830i	−0.928848	−	0.338073i	−0.761753	+	0.647868i	$0.775661\pi$
$242$	−15.0982	+	4.04556i	−0.970550	+	0.260058i
$243$	11.7714	−	10.2193i	0.755135	−	0.655569i
$244$			6.50431i			0.416396i
$245$	−4.38606	−	15.0254i	−0.280215	−	0.959937i
$246$	16.4692	−	35.6306i	1.05004	−	2.27172i
$247$	0.326592	−	0.0285731i	0.0207806	−	0.00181806i
$248$	0.146696	−	0.314590i	0.00931519	−	0.0199765i
$249$	3.62261	−	3.64705i	0.229574	−	0.231122i
$250$	9.28927	+	22.8484i	0.587505	+	1.44506i
$251$	−12.5196	+	7.22819i	−0.790230	+	0.456240i	−0.840044	−	0.542519i	$-0.817471\pi$
$251$	−12.5196	+	7.22819i	−0.790230	+	0.456240i	0.0498135	+	0.998759i	$0.484137\pi$
$252$	−9.97432	+	20.4512i	−0.628323	+	1.28830i
$253$	−21.7995	+	5.84116i	−1.37052	+	0.367231i
$254$	15.3835	+	5.59912i	0.965244	+	0.351320i
$255$	−2.00415	+	7.09866i	−0.125505	+	0.444535i
$256$	−3.84197	−	3.22379i	−0.240123	−	0.201487i
$257$	−18.9616	−	8.84196i	−1.18280	−	0.551546i	−0.271155	−	0.962536i	$-0.587406\pi$
$257$	−18.9616	−	8.84196i	−1.18280	−	0.551546i	−0.911640	+	0.410989i	$0.865183\pi$
$258$	15.9062	−	44.1633i	0.990279	−	2.74949i
$259$	−1.70400	−	1.50145i	−0.105881	−	0.0932953i
$260$	0.457788	+	0.677637i	0.0283908	+	0.0420253i
$261$	1.34257	−	7.92525i	0.0831031	−	0.490560i
$262$	12.2847	−	12.2847i	0.758954	−	0.758954i
$263$	2.68274	−	30.6639i	0.165425	−	1.89082i	−0.231303	−	0.972882i	$-0.574299\pi$
$263$	2.68274	−	30.6639i	0.165425	−	1.89082i	0.396728	−	0.917936i	$-0.370146\pi$
$264$	3.59940	−	13.6160i	0.221528	−	0.838010i
$265$	−22.4233	+	10.0030i	−1.37745	+	0.614479i
$266$	−7.81111	+	12.8046i	−0.478930	+	0.785097i
$267$	21.9041	+	18.2546i	1.34051	+	1.11716i
$268$	38.6550	+	3.38187i	2.36123	+	0.206581i
$269$	−9.42540	+	16.3253i	−0.574677	+	0.995369i	0.421400	+	0.906875i	$0.361539\pi$
$269$	−9.42540	+	16.3253i	−0.574677	+	0.995369i	−0.996077	+	0.0884943i	$0.971794\pi$
$270$	23.1581	+	10.9867i	1.40936	+	0.668631i
$271$	−8.64270	−	14.9696i	−0.525007	−	0.909339i	−0.999576	−	0.0291203i	$-0.990729\pi$
$271$	−8.64270	−	14.9696i	−0.525007	−	0.909339i	0.474569	−	0.880218i	$-0.342604\pi$
$272$	1.65537	−	2.36412i	0.100372	−	0.143346i
$273$	−0.512268	+	0.281718i	−0.0310039	+	0.0170504i
$274$	12.0156	+	33.0125i	0.725886	+	1.99436i
$275$	18.7600	−	10.0098i	1.13127	−	0.603616i
$276$	6.73436	−	25.4751i	0.405361	−	1.53342i
$277$	−1.44937	+	16.5664i	−0.0870843	+	0.995378i	0.819423	+	0.573189i	$0.194294\pi$
$277$	−1.44937	+	16.5664i	−0.0870843	+	0.995378i	−0.906508	+	0.422189i	$0.861262\pi$
$278$	−13.0218	−	48.5979i	−0.780994	−	2.91471i
$279$	0.269135	−	0.473478i	0.0161127	−	0.0283464i
$280$	−11.3023	−	0.462380i	−0.675439	−	0.0276325i
$281$	−10.1467	−	12.0923i	−0.605298	−	0.721367i	0.373170	−	0.927763i	$-0.378271\pi$
$281$	−10.1467	−	12.0923i	−0.605298	−	0.721367i	−0.978468	+	0.206396i	$0.933826\pi$
$282$	−9.60384	−	11.3676i	−0.571900	−	0.676931i
$283$	−0.670926	−	7.66872i	−0.0398824	−	0.455858i	−0.989710	−	0.143085i	$-0.954298\pi$
$283$	−0.670926	−	7.66872i	−0.0398824	−	0.455858i	0.949828	−	0.312773i	$-0.101258\pi$
$284$	8.59776	+	7.21438i	0.510183	+	0.428095i
$285$	8.55201	+	5.09111i	0.506577	+	0.301572i
$286$	0.916858	−	0.769335i	0.0542149	−	0.0454917i
$287$	−3.02224	+	27.0108i	−0.178397	+	1.59440i
$288$	−15.3055	−	15.1011i	−0.901885	−	0.889842i
$289$	11.5812	+	6.68641i	0.681247	+	0.393318i
$290$	12.8222	−	3.20683i	0.752948	−	0.188311i
$291$	9.70699	+	2.56605i	0.569034	+	0.150424i
$292$	10.8870	+	15.5482i	0.637111	+	0.909888i
$293$	12.4030	−	26.5984i	0.724593	−	1.55389i	−0.104337	−	0.994542i	$-0.533272\pi$
$293$	12.4030	−	26.5984i	0.724593	−	1.55389i	0.828930	−	0.559353i	$-0.188950\pi$
$294$	3.52636	−	26.5136i	0.205662	−	1.54631i
$295$	−4.49188	−	8.08972i	−0.261528	−	0.471002i
$296$	−1.42139	+	0.820642i	−0.0826168	+	0.0476988i
$297$	7.34809	−	20.8401i	0.426379	−	1.20927i
$298$	−3.46650	+	0.928845i	−0.200809	+	0.0538065i
$299$	0.518632	−	0.435184i	0.0299932	−	0.0251673i
$300$	−0.747019	+	24.8152i	−0.0431292	+	1.43271i
$301$	−0.785190	+	32.4931i	−0.0452576	+	1.87287i
$302$	0.286440	+	3.27402i	0.0164828	+	0.188399i
$303$	−15.2122	+	8.85110i	−0.873921	+	0.508482i
$304$	−2.50313	−	2.98311i	−0.143564	−	0.171093i
$305$	−4.79582	+	1.65523i	−0.274608	+	0.0947781i
$306$	−8.03689	+	9.70980i	−0.459438	+	0.555072i
$307$	−7.32095	−	27.3222i	−0.417829	−	1.55936i	−0.779102	−	0.626898i	$-0.784324\pi$
$307$	−7.32095	−	27.3222i	−0.417829	−	1.55936i	0.361273	−	0.932460i	$-0.382342\pi$
$308$	2.03415	+	32.1908i	0.115906	+	1.83424i
$309$	−3.10137	−	6.59297i	−0.176431	−	0.375061i
$310$	0.890688	+	0.0929616i	0.0505877	+	0.00527986i
$311$	17.5739	−	20.9437i	0.996524	−	1.18761i	0.0142999	−	0.999898i	$-0.495448\pi$
$311$	17.5739	−	20.9437i	0.996524	−	1.18761i	0.982224	−	0.187713i	$-0.0601075\pi$
$312$	0.0747633	+	0.415827i	0.00423264	+	0.0235416i
$313$	8.28614	+	17.7697i	0.468360	+	1.00440i	0.988626	+	0.150397i	$0.0480553\pi$
$313$	8.28614	+	17.7697i	0.468360	+	1.00440i	−0.520265	+	0.854005i	$0.674167\pi$
$314$	−9.79779	+	16.9703i	−0.552921	+	0.957688i
$315$	−17.6175	−	2.14992i	−0.992636	−	0.121134i
$316$	18.1410	+	31.4211i	1.02051	+	1.76757i
$317$	−4.65248	+	6.64443i	−0.261309	+	0.373188i	−0.928271	−	0.371903i	$-0.878705\pi$
$317$	−4.65248	+	6.64443i	−0.261309	+	0.373188i	0.666962	+	0.745091i	$0.267594\pi$
$318$	−41.9566	+	0.141012i	−2.35281	+	0.00790753i
$319$	−3.89719	−	10.7074i	−0.218201	−	0.599501i
$320$	10.2219	−	26.6868i	0.571422	−	1.49184i
$321$	6.43808	+	2.97582i	0.359338	+	0.166094i
$322$	1.95340	+	30.9130i	0.108859	+	1.72271i
$323$	−3.46070	+	3.46070i	−0.192559	+	0.192559i
$324$	16.8484	+	19.5395i	0.936022	+	1.08553i
$325$	−0.383143	+	0.509987i	−0.0212530	+	0.0282890i
$326$	−0.131005	+	0.359934i	−0.00725571	+	0.0199349i
$327$	−3.51760	+	4.22085i	−0.194524	+	0.233413i
$328$	17.8017	+	8.30105i	0.982932	+	0.458349i
$329$	8.79663	+	5.36617i	0.484974	+	0.295847i
$330$	36.2360	−	2.68272i	1.99473	−	0.147679i
$331$	2.11914	+	12.0182i	0.116478	+	0.660581i	0.986008	+	0.166700i	$0.0533111\pi$
$331$	2.11914	+	12.0182i	0.116478	+	0.660581i	−0.869529	+	0.493881i	$0.835578\pi$
$332$	6.01604	+	6.01604i	0.330173	+	0.330173i
$333$	−2.32655	+	1.10399i	−0.127494	+	0.0604982i
$334$		−	50.7079i		−	2.77461i
$335$	7.34343	+	29.3621i	0.401214	+	1.60422i
$336$	6.23130	+	3.06506i	0.339945	+	0.167213i
$337$	−17.7527	−	25.3535i	−0.967051	−	1.38109i	−0.924157	−	0.382012i	$-0.875231\pi$
$337$	−17.7527	−	25.3535i	−0.967051	−	1.38109i	−0.0428932	−	0.999080i	$-0.513658\pi$
$338$	12.1050	−	25.9593i	0.658426	−	1.41200i
$339$	−0.401177	+	4.77006i	−0.0217889	+	0.259074i
$340$	−11.7378	−	3.35653i	−0.636570	−	0.182034i
$341$		−	0.772039i		−	0.0418083i
$342$	9.84839	+	13.8657i	0.532540	+	0.749769i
$343$	3.48533	+	18.1894i	0.188190	+	0.982133i
$344$	22.0724	+	8.03368i	1.19006	+	0.433147i
$345$	20.4973	−	1.51751i	1.10354	−	0.0817002i
$346$	−13.6625	+	4.97274i	−0.734499	+	0.267336i
$347$	−25.2856	+	17.7052i	−1.35740	+	0.950463i	−0.357539	+	0.933898i	$0.616384\pi$
$347$	−25.2856	+	17.7052i	−1.35740	+	0.950463i	−0.999863	+	0.0165648i	$0.994727\pi$
$348$	13.1095	+	2.26616i	0.702744	+	0.121479i
$349$	22.8884	−	4.03584i	1.22519	−	0.216033i	0.476630	−	0.879104i	$-0.341858\pi$
$349$	22.8884	−	4.03584i	1.22519	−	0.216033i	0.748557	+	0.663071i	$0.230747\pi$
$350$	−8.38564	−	27.9527i	−0.448231	−	1.49414i
$351$	0.0644308	+	0.659761i	0.00343906	+	0.0352155i
$352$	−29.4408	−	7.88864i	−1.56920	−	0.420466i
$353$	−13.2363	+	6.17217i	−0.704495	+	0.328512i	−0.741640	−	0.670798i	$-0.765952\pi$
$353$	−13.2363	+	6.17217i	−0.704495	+	0.328512i	0.0371444	+	0.999310i	$0.488174\pi$
$354$	−1.43102	−	15.7470i	−0.0760581	−	0.836941i
$355$	−3.13140	+	8.17532i	−0.166198	+	0.433901i
$356$	−30.3348	+	36.1517i	−1.60774	+	1.91603i
$357$	3.15493	−	8.13739i	0.166977	−	0.430676i
$358$	9.38681	+	20.1301i	0.496109	+	1.06391i
$359$	−11.5318	+	19.9736i	−0.608623	+	1.05417i	0.382845	+	0.923813i	$0.374944\pi$
$359$	−11.5318	+	19.9736i	−0.608623	+	1.05417i	−0.991468	+	0.130353i	$0.958389\pi$
$360$	−5.53666	+	11.5697i	−0.291807	+	0.609778i
$361$	−6.19813	−	10.7355i	−0.326217	−	0.565025i
$362$	−2.44847	−	5.25075i	−0.128689	−	0.275973i
$363$	−2.17166	−	12.0786i	−0.113983	−	0.633961i
$364$	−0.463419	−	0.849417i	−0.0242898	−	0.0445215i
$365$	−8.69361	+	11.9840i	−0.455044	+	0.627271i
$366$	−8.63902	−	0.726568i	−0.451569	−	0.0379783i
$367$	7.30456	+	5.11471i	0.381295	+	0.266986i	0.748473	−	0.663165i	$-0.230787\pi$
$367$	7.30456	+	5.11471i	0.381295	+	0.266986i	−0.367178	+	0.930151i	$0.619676\pi$
$368$	−7.76789	−	2.08140i	−0.404929	−	0.108500i
$369$	26.7926	+	15.2295i	1.39477	+	0.792817i
$370$	−3.19776	−	2.77570i	−0.166244	−	0.144302i
$371$	27.5318	−	9.27390i	1.42938	−	0.481477i
$372$	0.782151	+	0.448077i	0.0405526	+	0.0232317i
$373$	−2.10929	+	1.47694i	−0.109215	+	0.0764731i	−0.626908	−	0.779093i	$-0.715680\pi$
$373$	−2.10929	+	1.47694i	−0.109215	+	0.0764731i	0.517693	+	0.855566i	$0.326791\pi$
$374$	−3.10268	+	17.5961i	−0.160436	+	0.909875i
$375$	−18.4871	+	5.76423i	−0.954671	+	0.297663i
$376$	5.70444	−	4.78660i	0.294184	−	0.246850i
$377$	0.241706	+	0.241706i	0.0124485	+	0.0124485i
$378$	−26.0491	−	15.5324i	−1.33982	−	0.798901i
$379$		−	9.42082i		−	0.483915i	−0.970287	−	0.241957i	$-0.922211\pi$
$379$		−	9.42082i		−	0.483915i	0.970287	−	0.241957i	$-0.0777894\pi$
$380$	−8.47382	+	14.1260i	−0.434698	+	0.724649i
$381$	−5.39281	+	11.6671i	−0.276282	+	0.597725i
$382$	−10.3880	−	14.8355i	−0.531494	−	0.759053i
$383$	−1.69129	−	2.41542i	−0.0864211	−	0.123422i	0.773614	−	0.633658i	$-0.218447\pi$
$383$	−1.69129	−	2.41542i	−0.0864211	−	0.123422i	−0.860035	+	0.510235i	$0.829558\pi$
$384$	16.9177	−	17.0318i	0.863328	−	0.869151i
$385$	−23.2176	+	9.69182i	−1.18328	+	0.493941i
$386$	20.8149	−	12.0175i	1.05945	−	0.611674i
$387$	33.5054	+	15.3505i	1.70318	+	0.780310i
$388$	−4.30103	+	16.0517i	−0.218352	+	0.814900i
$389$	1.28986	+	7.31519i	0.0653987	+	0.370895i	0.999889	+	0.0149057i	$0.00474482\pi$
$389$	1.28986	+	7.31519i	0.0653987	+	0.370895i	−0.934490	+	0.355989i	$0.884144\pi$
$390$	−0.951175	+	0.532338i	−0.0481646	+	0.0269560i
$391$	−1.75507	+	9.95347i	−0.0887575	+	0.503369i
$392$	13.2614	+	1.80916i	0.669800	+	0.0913766i
$393$	8.80288	+	10.4195i	0.444046	+	0.525596i
$394$	−16.6463	+	45.7352i	−0.838627	+	2.30411i
$395$	−18.5511	+	21.3720i	−0.933409	+	1.07534i
$396$	34.4514	+	12.2777i	1.73125	+	0.616976i
$397$	−5.64243	−	21.0579i	−0.283186	−	1.05686i	−0.950155	−	0.311778i	$-0.899075\pi$
$397$	−5.64243	−	21.0579i	−0.283186	−	1.05686i	0.666969	−	0.745085i	$-0.267591\pi$
$398$	−8.13661	+	3.79416i	−0.407851	+	0.190184i
$399$	−9.50393	−	6.95371i	−0.475791	−	0.348121i
$400$	7.57264	+	0.253437i	0.378632	+	0.0126719i
$401$	2.46029	−	2.93206i	0.122861	−	0.146420i	−0.701108	−	0.713055i	$-0.747311\pi$
$401$	2.46029	−	2.93206i	0.122861	−	0.146420i	0.823969	+	0.566635i	$0.191755\pi$
$402$	−8.80978	+	50.9638i	−0.439392	+	2.54184i
$403$	0.00978791	+	0.0209902i	0.000487570	+	0.00104560i
$404$	−14.5647	−	25.2269i	−0.724623	−	1.25508i
$405$	−10.1195	+	17.3953i	−0.502841	+	0.864379i
$406$	−15.4623	+	2.34279i	−0.767380	+	0.116271i
$407$	−2.09385	+	2.99032i	−0.103788	+	0.148225i
$408$	−4.84522	−	4.03795i	−0.239874	−	0.199908i
$409$	−22.6384	−	3.99177i	−1.11940	−	0.197380i	−0.416822	−	0.908988i	$-0.636856\pi$
$409$	−22.6384	−	3.99177i	−1.11940	−	0.197380i	−0.702576	+	0.711608i	$0.747967\pi$
$410$	−5.26040	+	50.4012i	−0.259793	+	2.48914i
$411$	−26.6186	+	7.22840i	−1.31300	+	0.356551i
$412$	10.9292	−	5.09637i	0.538443	−	0.251080i
$413$	4.38596	+	10.0316i	0.215819	+	0.493621i
$414$	33.0838	+	11.7903i	1.62598	+	0.579461i
$415$	−2.90483	+	5.96678i	−0.142593	+	0.292897i
$416$	0.900449	−	0.158774i	0.0441482	−	0.00778451i
$417$	38.8784	−	6.99011i	1.90388	−	0.342307i
$418$	21.8501	+	10.1889i	1.06872	+	0.498353i
$419$	5.17645	−	29.3571i	0.252886	−	1.43419i	−0.548556	−	0.836114i	$-0.684822\pi$
$419$	5.17645	−	29.3571i	0.252886	−	1.43419i	0.801442	−	0.598073i	$-0.204067\pi$
$420$	3.65630	−	29.1466i	0.178409	−	1.42221i
$421$	−13.7480	+	11.5360i	−0.670038	+	0.562229i	−0.913077	−	0.407788i	$-0.866300\pi$
$421$	−13.7480	+	11.5360i	−0.670038	+	0.562229i	0.243039	+	0.970017i	$0.421856\pi$
$422$	−14.5205	−	14.5205i	−0.706846	−	0.706846i
$423$	9.52560	−	6.76577i	0.463150	−	0.328963i
$424$		−	20.9951i		−	1.01961i
$425$	−0.512176	−	9.50879i	−0.0248442	−	0.461244i
$426$	−10.5426	+	10.6137i	−0.510789	+	0.514234i
$427$	5.83426	−	1.41315i	0.282339	−	0.0683871i
$428$	−4.96106	+	10.6390i	−0.239802	+	0.514257i
$429$	0.541576	+	0.767944i	0.0261475	+	0.0370767i
$430$	−1.01364	+	60.5914i	−0.0488820	+	2.92198i
$431$	−15.4453	−	8.91734i	−0.743973	−	0.429533i	0.0795389	−	0.996832i	$-0.474655\pi$
$431$	−15.4453	−	8.91734i	−0.743973	−	0.429533i	−0.823512	+	0.567299i	$0.807989\pi$
$432$	5.98059	−	5.12195i	0.287741	−	0.246430i
$433$	24.2832	+	24.2832i	1.16698	+	1.16698i	0.982915	+	0.184060i	$0.0589241\pi$
$433$	24.2832	+	24.2832i	1.16698	+	1.16698i	0.184060	+	0.982915i	$0.441076\pi$
$434$	−1.03875	−	0.209153i	−0.0498618	−	0.0100397i
$435$	1.66523	+	10.2427i	0.0798415	+	0.491102i
$436$	−6.96631	−	5.84543i	−0.333626	−	0.279945i
$437$	12.3598	+	5.76345i	0.591247	+	0.275703i
$438$	−21.8672	+	12.7232i	−1.04486	+	0.607939i
$439$	−1.45622	+	0.256770i	−0.0695014	+	0.0122550i	−0.208291	−	0.978067i	$-0.566790\pi$
$439$	−1.45622	+	0.256770i	−0.0695014	+	0.0122550i	0.138789	+	0.990322i	$0.455679\pi$
$440$	1.28148	+	18.1368i	0.0610922	+	0.864640i
$441$	20.5114	+	4.50351i	0.976734	+	0.214453i
$442$	−0.138728	−	0.517740i	−0.00659862	−	0.0246264i
$443$	0.187851	−	0.0875963i	0.00892506	−	0.00416182i	−0.418151	−	0.908378i	$-0.637322\pi$
$443$	0.187851	−	0.0875963i	0.00892506	−	0.00416182i	0.427076	+	0.904216i	$0.359544\pi$
$444$	−1.81426	−	3.85680i	−0.0861009	−	0.183035i
$445$	−34.3754	−	13.1669i	−1.62955	−	0.624169i
$446$	−11.6037	−	31.8809i	−0.549451	−	1.50960i
$447$	−0.498606	−	2.77320i	−0.0235832	−	0.131168i
$448$	−15.0263	+	30.2912i	−0.709926	+	1.43112i
$449$	−7.92140	+	13.7203i	−0.373834	+	0.647499i	−0.990152	−	0.139998i	$-0.955290\pi$
$449$	−7.92140	+	13.7203i	−0.373834	+	0.647499i	0.616318	+	0.787497i	$0.288624\pi$
$450$	−32.8762	−	3.76419i	−1.54980	−	0.177446i
$451$	43.6872			2.05715
$452$	−7.89265	−	0.690517i	−0.371239	−	0.0324792i
$453$	−2.58034	+	0.00867225i	−0.121235	+	0.000407458i
$454$	−36.2789	+	43.2355i	−1.70265	+	2.02914i
$455$	0.508369	−	0.557854i	0.0238327	−	0.0261526i
$456$	−6.95487	+	4.90477i	−0.325692	+	0.229687i
$457$	3.67409	−	41.9950i	0.171867	−	1.96445i	−0.0803278	−	0.996768i	$-0.525597\pi$
$457$	3.67409	−	41.9950i	0.171867	−	1.96445i	0.252194	−	0.967677i	$-0.418848\pi$
$458$	1.91981	+	7.16482i	0.0897067	+	0.334790i
$459$	−7.06783	−	6.92672i	−0.329898	−	0.323312i
$460$	2.39760	+	33.9334i	0.111789	+	1.58215i
$461$	−32.6444	+	5.75608i	−1.52040	+	0.268087i	−0.870590	−	0.492010i	$-0.836262\pi$
$461$	−32.6444	+	5.75608i	−1.52040	+	0.268087i	−0.649809	+	0.760097i	$0.725151\pi$
$462$	−42.9831	−	0.894145i	−1.99975	−	0.0415994i
$463$	−27.3328	−	12.7455i	−1.27026	−	0.592333i	−0.333648	−	0.942698i	$-0.608280\pi$
$463$	−27.3328	−	12.7455i	−1.27026	−	0.592333i	−0.936613	+	0.350365i	$0.886057\pi$
$464$	0.705060	−	3.99859i	0.0327316	−	0.185630i
$465$	−0.131337	+	0.690731i	−0.00609062	+	0.0320319i
$466$	32.6051	−	27.3589i	1.51040	−	1.26738i
$467$	−0.688006	+	0.184351i	−0.0318371	+	0.00853073i	−0.274702	−	0.961529i	$-0.588579\pi$
$467$	−0.688006	+	0.184351i	−0.0318371	+	0.00853073i	0.242865	+	0.970060i	$0.421913\pi$
$468$	−1.09232	+	0.102969i	−0.0504926	+	0.00475974i
$469$	−5.36484	−	35.4076i	−0.247725	−	1.63497i
$470$	16.4749	+	9.88285i	0.759931	+	0.455862i
$471$	−12.6323	−	8.78214i	−0.582068	−	0.404660i
$472$	7.88211	−	0.689595i	0.362803	−	0.0317412i
$473$	52.0447	−	4.55332i	2.39302	−	0.209362i
$474$	−43.7599	+	20.5849i	−2.00996	+	0.945496i
$475$	−12.5720	−	2.65319i	−0.576841	−	0.121737i
$476$	13.4506	+	5.26696i	0.616505	+	0.241410i
$477$	2.65041	−	32.8349i	0.121354	−	1.50340i
$478$	59.1839	−	15.8583i	2.70701	−	0.725341i
$479$	23.8128	−	19.9814i	1.08804	−	0.912971i	0.0914736	−	0.995807i	$-0.470842\pi$
$479$	23.8128	−	19.9814i	1.08804	−	0.912971i	0.996563	+	0.0828362i	$0.0263978\pi$
$480$	24.9982	+	12.0662i	1.14101	+	0.550745i
$481$	0.0190163	−	0.107847i	0.000867068	−	0.00491739i
$482$	30.6804	+	14.3065i	1.39745	+	0.651643i
$483$	−24.3139	−	0.505784i	−1.10632	−	0.0230140i
$484$	20.0032	−	3.52711i	0.909237	−	0.160323i
$485$	−12.9299	+	0.913578i	−0.587117	+	0.0414834i
$486$	−27.8345	+	20.1954i	−1.26260	+	0.916080i
$487$	−1.91036	−	7.12957i	−0.0865668	−	0.323072i	0.909040	−	0.416710i	$-0.136817\pi$
$487$	−1.91036	−	7.12957i	−0.0865668	−	0.323072i	−0.995606	+	0.0936384i	$0.970150\pi$
$488$	0.378100	−	4.32170i	0.0171158	−	0.195634i
$489$	−0.272982	−	0.126178i	−0.0123447	−	0.00570598i
$490$	6.75015	+	33.8641i	0.304941	+	1.52983i
$491$	14.5682	−	17.3617i	0.657453	−	0.783522i	−0.329565	−	0.944133i	$-0.606902\pi$
$491$	14.5682	−	17.3617i	0.657453	−	0.783522i	0.987018	+	0.160611i	$0.0513464\pi$
$492$	−25.3552	+	44.2594i	−1.14310	+	1.99537i
$493$	−5.08351	−	0.444750i	−0.228950	−	0.0200305i
$494$	−0.723235			−0.0325399
$495$	−0.285439	+	28.5265i	−0.0128295	+	1.28217i
$496$	0.137552	−	0.238246i	0.00617625	−	0.0106976i
$497$	4.60320	−	9.27948i	0.206482	−	0.416241i
$498$	−8.66252	+	7.31847i	−0.388177	+	0.327949i
$499$	−4.78722	−	13.1528i	−0.214305	−	0.588799i	0.785232	−	0.619201i	$-0.212543\pi$
$499$	−4.78722	−	13.1528i	−0.214305	−	0.588799i	−0.999538	+	0.0304022i	$0.990321\pi$
$500$	−9.43747	−	30.6299i	−0.422057	−	1.36981i
$501$	39.6724	+	3.33657i	1.77243	+	0.149067i
$502$	28.9037	−	13.4780i	1.29004	−	0.601553i
$503$	2.38649	+	8.90651i	0.106408	+	0.397122i	0.998501	−	0.0547308i	$-0.0174301\pi$
$503$	2.38649	+	8.90651i	0.106408	+	0.397122i	−0.892093	+	0.451852i	$0.850763\pi$
$504$	7.81615	−	13.0087i	0.348159	−	0.579454i
$505$	14.8941	−	17.1588i	0.662777	−	0.763556i
$506$	49.0312	−	8.64552i	2.17970	−	0.384340i
$507$	19.5133	+	11.1787i	0.866615	+	0.496464i
$508$	−19.2801	−	8.99048i	−0.855418	−	0.398888i
$509$	18.9535	+	15.9039i	0.840100	+	0.704928i	0.957586	−	0.288147i	$-0.0930390\pi$
$509$	18.9535	+	15.9039i	0.840100	+	0.704928i	−0.117486	+	0.993075i	$0.537483\pi$
$510$	5.76932	−	15.2152i	0.255470	−	0.673739i
$511$	11.5811	−	13.1435i	0.512319	−	0.581433i
$512$	−11.7774	−	11.7774i	−0.520490	−	0.520490i
$513$	−11.4961	+	6.79273i	−0.507565	+	0.299906i
$514$	39.9714	+	23.0775i	1.76306	+	1.01790i
$515$	6.53899	+	6.76149i	0.288142	+	0.297947i
$516$	−25.5928	+	55.3691i	−1.12666	+	2.43749i
$517$	6.99967	−	15.0108i	0.307845	−	0.660176i
$518$	3.45614	+	3.62731i	0.151854	+	0.159375i
$519$	−2.99153	−	11.0163i	−0.131314	−	0.483563i
$520$	−0.264780	−	0.476859i	−0.0116114	−	0.0209116i
$521$			36.8697i			1.61529i	0.589668	+	0.807646i	$0.299259\pi$
$521$			36.8697i			1.61529i	−0.589668	+	0.807646i	$0.700741\pi$
$522$	−4.47432	+	17.1589i	−0.195836	+	0.751026i
$523$	17.0612	+	17.0612i	0.746034	+	0.746034i	0.973732	−	0.227698i	$-0.0731198\pi$
$523$	17.0612	+	17.0612i	0.746034	+	0.746034i	−0.227698	+	0.973732i	$0.573120\pi$
$524$	−17.2942	+	14.5116i	−0.755502	+	0.633942i
$525$	22.4212	−	4.72139i	0.978540	−	0.206058i
$526$	−11.7916	+	66.8733i	−0.514137	+	2.91581i
$527$	−0.313354	−	0.146119i	−0.0136499	−	0.00636506i
$528$	3.78238	−	10.5017i	0.164607	−	0.457028i
$529$	5.08450	−	0.896534i	0.221065	−	0.0389797i
$530$	51.2022	−	17.6719i	2.22408	−	0.767618i
$531$	12.4141	−	0.0834458i	0.538726	−	0.00362124i
$532$	11.5619	−	15.6912i	0.501271	−	0.680298i
$533$	−1.18777	+	0.553866i	−0.0514480	+	0.0239906i
$534$	−44.6281	−	44.3291i	−1.93125	−	1.91831i
$535$	−9.10698	−	0.950500i	−0.393729	−	0.0410937i
$536$	−25.4872	−	4.49408i	−1.10088	−	0.194115i
$537$	−16.3668	+	6.01941i	−0.706281	+	0.259757i
$538$	23.8528	−	34.0653i	1.02837	−	1.46866i
$539$	28.4327	−	8.81850i	1.22468	−	0.379840i
$540$	−28.7345	−	16.8454i	−1.23653	−	0.724911i
$541$	−17.1878	−	29.7702i	−0.738962	−	1.27992i	−0.952963	−	0.303087i	$-0.901983\pi$
$541$	−17.1878	−	29.7702i	−0.738962	−	1.27992i	0.214001	−	0.976834i	$-0.431351\pi$
$542$	16.1156	+	34.5600i	0.692223	+	1.48448i
$543$	4.26914	−	1.57011i	0.183206	−	0.0673798i
$544$	−8.77391	+	10.4563i	−0.376178	+	0.448312i
$545$	2.53721	−	6.62402i	0.108682	−	0.283742i
$546$	1.17996	−	0.520629i	0.0504977	−	0.0222809i
$547$	−29.2636	+	13.6459i	−1.25122	+	0.583455i	−0.931391	−	0.364020i	$-0.881404\pi$
$547$	−29.2636	+	13.6459i	−1.25122	+	0.583455i	−0.319831	+	0.947475i	$0.603626\pi$
$548$	−11.8156	−	44.0963i	−0.504736	−	1.88370i
$549$	1.13689	−	6.71110i	0.0485213	−	0.286423i
$550$	−43.1529	+	18.3913i	−1.84005	+	0.784207i
$551$	−2.35495	+	6.47018i	−0.100324	+	0.275639i
$552$	−5.95544	+	16.5351i	−0.253480	+	0.703783i
$553$	24.2428	−	23.0988i	1.03091	−	0.982261i
$554$	6.37048	−	36.1288i	0.270656	−	1.53496i
$555$	2.38204	−	2.31919i	0.101112	−	0.0984442i
$556$	11.3530	+	64.3860i	0.481474	+	2.73058i
$557$	7.38790	−	27.5720i	0.313036	−	1.16826i	−0.612769	−	0.790262i	$-0.709944\pi$
$557$	7.38790	−	27.5720i	0.313036	−	1.16826i	0.925805	−	0.378002i	$-0.123389\pi$
$558$	−0.682506	+	0.988800i	−0.0288928	+	0.0418593i
$559$	−1.35727	+	0.783619i	−0.0574063	+	0.0331435i
$560$	−8.89157	−	1.14577i	−0.375737	−	0.0484176i
$561$	−13.5625	−	3.58526i	−0.572611	−	0.151370i
$562$	19.9740	+	28.5258i	0.842551	+	1.20329i
$563$	6.96962	+	9.95365i	0.293735	+	0.419496i	0.938711	−	0.344706i	$-0.112022\pi$
$563$	6.96962	+	9.95365i	0.293735	+	0.419496i	−0.644976	+	0.764203i	$0.723133\pi$
$564$	11.1450	+	15.8033i	0.469288	+	0.665441i
$565$	−1.49940	−	5.99521i	−0.0630801	−	0.252220i
$566$			16.9823i			0.713820i
$567$	13.8661	−	19.3580i	0.582322	−	0.812958i
$568$	−5.29330	−	5.29330i	−0.222102	−	0.222102i
$569$	6.95868	−	5.83903i	0.291723	−	0.244785i	−0.485166	−	0.874422i	$-0.661241\pi$
$569$	6.95868	−	5.83903i	0.291723	−	0.244785i	0.776889	+	0.629637i	$0.216796\pi$
$570$	−17.8156	−	12.8329i	−0.746213	−	0.537510i
$571$	−5.48737	+	31.1204i	−0.229639	+	1.30235i	0.623975	+	0.781444i	$0.285517\pi$
$571$	−5.48737	+	31.1204i	−0.229639	+	1.30235i	−0.853614	+	0.520905i	$0.825594\pi$
$572$	−1.27403	+	0.892084i	−0.0532698	+	0.0372999i
$573$	12.2904	−	7.15105i	0.513439	−	0.298740i
$574$	11.8353	−	58.7798i	0.493996	−	2.45342i
$575$	−24.4100	+	10.4033i	−1.01797	+	0.433846i
$576$	24.8418	+	29.2044i	1.03508	+	1.21685i
$577$	30.1401	+	8.07602i	1.25475	+	0.336209i	0.824170	−	0.566343i	$-0.191642\pi$
$577$	30.1401	+	8.07602i	1.25475	+	0.336209i	0.430580	+	0.902552i	$0.358309\pi$
$578$	−24.1660	−	16.9213i	−1.00518	−	0.703831i
$579$	8.03250	+	17.0757i	0.333819	+	0.709641i
$580$	−16.9619	+	2.69912i	−0.704305	+	0.112075i
$581$	4.08922	−	6.70335i	0.169649	−	0.278102i
$582$	−20.8394	−	7.50569i	−0.863820	−	0.311121i
$583$	−19.7350	−	42.3218i	−0.817339	−	1.75279i
$584$	−6.32987	−	10.9637i	−0.261932	−	0.453679i
$585$	−0.353898	−	0.779198i	−0.0146319	−	0.0322159i
$586$	−32.3719	+	56.0697i	−1.33727	+	2.31622i
$587$	−9.96163	−	21.3628i	−0.411161	−	0.881737i	−0.997432	−	0.0716220i	$-0.977182\pi$
$587$	−9.96163	−	21.3628i	−0.411161	−	0.881737i	0.586271	−	0.810115i	$-0.300595\pi$
$588$	−7.56780	+	33.9232i	−0.312091	+	1.39897i
$589$	−0.299874	+	0.357375i	−0.0123561	+	0.0147254i
$590$	8.31625	+	18.6422i	0.342375	+	0.767486i
$591$	−34.6866	−	16.0329i	−1.42681	−	0.659506i
$592$	−1.17892	+	0.549741i	−0.0484535	+	0.0225942i
$593$	−15.9873	−	4.28377i	−0.656518	−	0.175914i	−0.0848440	−	0.996394i	$-0.527039\pi$
$593$	−15.9873	−	4.28377i	−0.656518	−	0.175914i	−0.571674	+	0.820481i	$0.693706\pi$
$594$	−20.1556	+	44.3869i	−0.826995	+	1.82122i
$595$	−0.460563	+	11.2578i	−0.0188813	+	0.461526i
$596$	4.59267	−	0.809811i	0.188123	−	0.0331711i
$597$	−2.43305	−	6.61549i	−0.0995782	−	0.270754i
$598$	−1.22345	+	0.856672i	−0.0500307	+	0.0350319i
$599$	−11.8247	+	4.30385i	−0.483146	+	0.175851i	−0.572098	−	0.820185i	$-0.693870\pi$
$599$	−11.8247	+	4.30385i	−0.483146	+	0.175851i	0.0889523	+	0.996036i	$0.471648\pi$
$600$	1.93887	−	16.4447i	0.0791542	−	0.671354i
$601$	1.79328	+	0.652699i	0.0731493	+	0.0266242i	0.378336	−	0.925668i	$-0.376497\pi$
$601$	1.79328	+	0.652699i	0.0731493	+	0.0266242i	−0.305186	+	0.952293i	$0.598719\pi$
$602$	7.97307	−	71.2581i	0.324958	−	2.90426i
$603$	−39.2928	−	10.2459i	−1.60013	−	0.417246i
$604$		−	4.27075i		−	0.173774i
$605$	7.69110	+	13.8514i	0.312688	+	0.563139i
$606$	35.1333	−	16.5269i	1.42719	−	0.671359i
$607$	−4.03683	+	8.65700i	−0.163850	+	0.351377i	−0.971041	−	0.238913i	$-0.923209\pi$
$607$	−4.03683	+	8.65700i	−0.163850	+	0.351377i	0.807191	+	0.590290i	$0.200987\pi$
$608$	10.5640	+	15.0870i	0.428427	+	0.611857i
$609$	−0.815516	−	12.2514i	−0.0330464	−	0.496451i
$610$	10.8579	−	2.71554i	0.439622	−	0.109949i
$611$			0.496857i			0.0201007i
$612$	11.5037	−	11.6594i	0.465008	−	0.471302i
$613$	6.25210	+	6.25210i	0.252520	+	0.252520i	0.822003	−	0.569483i	$-0.192857\pi$
$613$	6.25210	+	6.25210i	0.252520	+	0.252520i	−0.569483	+	0.822003i	$0.692857\pi$
$614$	10.8358	+	61.4526i	0.437296	+	2.48003i
$615$	−39.0863	−	7.43196i	−1.57611	−	0.299686i
$616$	0.519714	−	21.5070i	0.0209399	−	0.866543i
$617$	−7.77786	−	3.62688i	−0.313125	−	0.146013i	0.259702	−	0.965689i	$-0.416376\pi$
$617$	−7.77786	−	3.62688i	−0.313125	−	0.146013i	−0.572827	+	0.819676i	$0.694153\pi$
$618$	5.54815	+	15.0855i	0.223179	+	0.606826i
$619$	2.59150	−	7.12010i	0.104161	−	0.286181i	−0.876654	−	0.481122i	$-0.840229\pi$
$619$	2.59150	−	7.12010i	0.104161	−	0.286181i	0.980815	+	0.194941i	$0.0624516\pi$
$620$	−1.14249	−	0.221217i	−0.0458835	−	0.00888430i
$621$	−11.4013	+	25.1080i	−0.457517	+	1.00755i
$622$	−42.6485	+	42.6485i	−1.71005	+	1.71005i
$623$	39.0181	+	19.3554i	1.56323	+	0.775458i
$624$	0.0303048	+	0.333473i	0.00121316	+	0.0133496i
$625$	20.1827	−	14.7533i	0.807307	−	0.590131i
$626$	−14.7936	−	40.6451i	−0.591271	−	1.62450i
$627$	−9.40918	+	16.4244i	−0.375767	+	0.655928i
$628$	14.6055	−	20.8588i	0.582822	−	0.832357i
$629$	0.817417	+	1.41581i	0.0325925	+	0.0564519i
$630$	38.3042	+	8.11215i	1.52607	+	0.323196i
$631$	−19.1622	+	33.1899i	−0.762836	+	1.32127i	0.178547	+	0.983931i	$0.442860\pi$
$631$	−19.1622	+	33.1899i	−0.762836	+	1.32127i	−0.941383	+	0.337339i	$0.890473\pi$
$632$	−10.2270	−	21.9319i	−0.406808	−	0.872403i
$633$	12.3158	−	10.4049i	0.489510	−	0.413559i
$634$	11.5021	−	13.7077i	0.456808	−	0.544403i
$635$	1.72250	−	16.5037i	0.0683555	−	0.654931i
$636$	54.3299	+	4.56931i	2.15432	+	0.181185i
$637$	−0.661229	+	0.600227i	−0.0261988	+	0.0237819i
$638$	6.50599	+	24.2807i	0.257575	+	0.961282i
$639$	−7.61011	−	8.94656i	−0.301051	−	0.353920i
$640$	−13.5657	+	27.8650i	−0.536229	+	1.10146i
$641$	−13.0508	−	15.5533i	−0.515475	−	0.614319i	0.444030	−	0.896012i	$-0.353549\pi$
$641$	−13.0508	−	15.5533i	−0.515475	−	0.614319i	−0.959505	+	0.281693i	$0.909104\pi$
$642$	−13.5766	−	7.77773i	−0.535825	−	0.306962i
$643$	2.52694	+	28.8830i	0.0996527	+	1.13904i	0.867172	+	0.498009i	$0.165936\pi$
$643$	2.52694	+	28.8830i	0.0996527	+	1.13904i	−0.767519	+	0.641026i	$0.778509\pi$
$644$	0.972366	−	40.2389i	0.0383166	−	1.58563i
$645$	−47.3382	−	4.77993i	−1.86394	−	0.188210i
$646$	8.27087	−	6.94009i	0.325413	−	0.273054i
$647$	21.4052	−	5.73550i	0.841524	−	0.225486i	0.187789	−	0.982209i	$-0.439868\pi$
$647$	21.4052	−	5.73550i	0.841524	−	0.225486i	0.653735	+	0.756724i	$0.273201\pi$
$648$	−10.0588	−	13.9622i	−0.395149	−	0.548487i
$649$	15.2405	−	8.79910i	0.598241	−	0.345395i
$650$	0.940078	−	1.04711i	0.0368729	−	0.0410712i
$651$	0.231985	−	0.798927i	0.00909219	−	0.0313124i
$652$	0.210355	−	0.451107i	0.00823812	−	0.0176667i
$653$	10.4866	+	14.9764i	0.410372	+	0.586072i	0.970130	−	0.242584i	$-0.0779949\pi$
$653$	10.4866	+	14.9764i	0.410372	+	0.586072i	−0.559758	+	0.828656i	$0.689106\pi$
$654$	8.54207	−	8.59969i	0.334022	−	0.336274i
$655$	−15.1009	−	9.05862i	−0.590041	−	0.353950i
$656$	13.4816	+	7.78361i	0.526368	+	0.303899i
$657$	−8.51542	−	17.9454i	−0.332218	−	0.700118i
$658$	−18.3003	−	13.4844i	−0.713420	−	0.525677i
$659$	31.4861	−	26.4200i	1.22653	−	1.02918i	0.228068	−	0.973645i	$-0.426759\pi$
$659$	31.4861	−	26.4200i	1.22653	−	1.02918i	0.998457	−	0.0555315i	$-0.0176853\pi$
$660$	−47.2123	−	0.631107i	−1.83774	−	0.0245658i
$661$	10.0061	+	8.39609i	0.389191	+	0.326570i	0.816298	−	0.577631i	$-0.196023\pi$
$661$	10.0061	+	8.39609i	0.389191	+	0.326570i	−0.427107	+	0.904201i	$0.640467\pi$
$662$	−2.34640	−	26.8195i	−0.0911955	−	1.04237i
$663$	0.414193	−	0.0744696i	0.0160859	−	0.00289216i
$664$	−3.64756	−	4.34699i	−0.141553	−	0.168696i
$665$	14.5119	+	4.53180i	0.562746	+	0.175736i
$666$	5.32526	−	1.97887i	0.206350	−	0.0766798i
$667$	3.68019	+	13.7347i	0.142498	+	0.531809i
$668$	−5.74299	+	65.6427i	−0.222203	+	2.53979i
$669$	25.7062	−	6.98063i	0.993858	−	0.269887i
$670$	−10.4929	−	65.9401i	−0.405378	−	2.54749i
$671$	−3.30014	−	9.06706i	−0.127400	−	0.350030i
$672$	−28.0957	−	17.0098i	−1.08382	−	0.656168i
$673$	16.7885	−	23.9765i	0.647149	−	0.924225i	−0.352785	−	0.935705i	$-0.614765\pi$
$673$	16.7885	−	23.9765i	0.647149	−	0.924225i	0.999934	+	0.0114794i	$0.00365410\pi$
$674$	34.1398	+	59.1318i	1.31502	+	2.27767i
$675$	5.10823	−	25.4736i	0.196616	−	0.980481i
$676$	−18.6103	+	32.2340i	−0.715781	+	1.23977i
$677$	−13.4647	−	1.17801i	−0.517492	−	0.0452747i	−0.174581	−	0.984643i	$-0.555857\pi$
$677$	−13.4647	−	1.17801i	−0.517492	−	0.0452747i	−0.342911	+	0.939368i	$0.611413\pi$
$678$	1.79880	−	10.4059i	0.0690825	−	0.399636i
$679$	15.3325	+	0.370508i	0.588409	+	0.0142188i
$680$	7.60389	+	2.91253i	0.291596	+	0.111690i
$681$	−31.4390	−	31.2284i	−1.20475	−	1.19668i
$682$	−0.148441	+	1.69669i	−0.00568409	+	0.0649695i
$683$	0.714300	−	0.714300i	0.0273319	−	0.0273319i	−0.693309	−	0.720641i	$-0.743848\pi$
$683$	0.714300	−	0.714300i	0.0273319	−	0.0273319i	0.720641	+	0.693309i	$0.243848\pi$
$684$	−11.1786	−	19.0648i	−0.427425	−	0.728962i
$685$	29.5067	−	19.9337i	1.12739	−	0.761627i
$686$	−4.16231	−	40.6443i	−0.158918	−	1.55181i
$687$	−5.73186	+	1.03056i	−0.218684	+	0.0393182i
$688$	16.8719	+	7.86751i	0.643236	+	0.299946i
$689$	1.07311	+	0.900446i	0.0408822	+	0.0343043i
$690$	−45.3381	−	0.606055i	−1.72599	−	0.0230721i
$691$	7.75384	+	2.82217i	0.294970	+	0.107360i	0.485266	−	0.874366i	$-0.338723\pi$
$691$	7.75384	+	2.82217i	0.294970	+	0.107360i	−0.190296	+	0.981727i	$0.560945\pi$
$692$	18.2496	−	4.88997i	0.693747	−	0.185889i
$693$	3.52783	−	33.5698i	0.134011	−	1.27521i
$694$	58.9735	−	34.0484i	2.23861	−	1.29246i
$695$	−44.5846	+	24.7560i	−1.69119	+	0.939048i
$696$	−8.57872	−	2.26779i	−0.325176	−	0.0859602i
$697$	8.26843	−	17.7317i	0.313189	−	0.671636i
$698$	−51.0770	+	4.46866i	−1.93329	+	0.169141i
$699$	19.2594	+	27.3094i	0.728457	+	1.03294i
$700$	7.68960	+	37.1353i	0.290640	+	1.40358i
$701$			25.3011i			0.955610i	0.878466	+	0.477805i	$0.158567\pi$
$701$			25.3011i			0.955610i	−0.878466	+	0.477805i	$0.841433\pi$
$702$	−0.0147446	−	1.46233i	−0.000556498	−	0.0551919i
$703$	2.13073	−	0.570928i	0.0803620	−	0.0215329i
$704$	51.0728	+	18.5890i	1.92488	+	0.700598i
$705$	−8.81609	+	12.2392i	−0.332033	+	0.460954i
$706$	30.2757	−	11.0194i	1.13944	−	0.414722i
$707$	−19.4637	+	18.5452i	−0.732007	+	0.697464i
$708$	0.0690559	+	20.5469i	0.00259528	+	0.772201i
$709$	28.5545	−	5.03493i	1.07239	−	0.189091i	0.390540	−	0.920586i	$-0.372288\pi$
$709$	28.5545	−	5.03493i	1.07239	−	0.189091i	0.681847	+	0.731495i	$0.261177\pi$
$710$	8.45367	−	17.3646i	0.317260	−	0.651680i
$711$	−13.2256	−	35.5909i	−0.496000	−	1.33476i
$712$	22.2571	−	22.2571i	0.834121	−	0.834121i
$713$	−0.0839673	+	0.959751i	−0.00314460	+	0.0359430i
$714$	−8.49807	+	17.2767i	−0.318032	+	0.646563i
$715$	−0.981978	−	0.712360i	−0.0367239	−	0.0266408i
$716$	−9.87161	−	27.1220i	−0.368920	−	1.01360i
$717$	8.51275	+	47.3472i	0.317915	+	1.76821i
$718$	29.1833	−	41.6781i	1.08911	−	1.55541i
$719$	−7.37478			−0.275033			−0.137516	−	0.990499i	$-0.543912\pi$
$719$	−7.37478			−0.275033			−0.137516	+	0.990499i	$0.543912\pi$
$720$	−5.17056	+	8.75224i	−0.192695	+	0.326177i
$721$	−6.94588	−	8.69606i	−0.258678	−	0.323858i
$722$	11.5573	+	24.7847i	0.430118	+	0.922392i
$723$	−13.2117	+	23.0621i	−0.491350	+	0.857687i
$724$	2.57492	+	7.07454i	0.0956962	+	0.262923i
$725$	−6.30664	−	11.8196i	−0.234223	−	0.438971i
$726$	2.45023	+	26.9623i	0.0909366	+	1.00066i
$727$	29.2018	+	20.4474i	1.08304	+	0.758350i	0.971886	−	0.235453i	$-0.0756575\pi$
$727$	29.2018	+	20.4474i	1.08304	+	0.758350i	0.111151	+	0.993804i	$0.464546\pi$
$728$	0.258536	+	0.591323i	0.00958198	+	0.0219159i
$729$	−13.9687	−	23.1057i	−0.517361	−	0.855767i
$730$	21.4098	−	24.6653i	0.792414	−	0.912905i
$731$	8.00211	−	21.9856i	0.295969	−	0.813167i
$732$	11.1011	+	1.91898i	0.410310	+	0.0709277i
$733$	2.38973	+	27.3148i	0.0882668	+	1.00889i	0.903166	+	0.429292i	$0.141237\pi$
$733$	2.38973	+	27.3148i	0.0882668	+	1.00889i	−0.814899	+	0.579603i	$0.803208\pi$
$734$	−15.0696	−	12.6449i	−0.556229	−	0.466732i
$735$	−26.9384	+	3.05287i	−0.993640	+	0.112607i
$736$	35.7410	+	13.0087i	1.31743	+	0.479505i
$737$	−55.6012	+	14.8983i	−2.04810	+	0.548786i
$738$	−55.9531	−	38.6209i	−2.05966	−	1.42165i
$739$	−28.1617	+	16.2592i	−1.03595	+	0.598103i	−0.918682	−	0.394997i	$-0.870745\pi$
$739$	−28.1617	+	16.2592i	−1.03595	+	0.598103i	−0.117263	+	0.993101i	$0.537412\pi$
$740$	3.82522	+	3.95538i	0.140618	+	0.145403i
$741$	0.0475886	−	0.565837i	0.00174821	−	0.0207866i
$742$	−62.2890	+	15.0874i	−2.28670	+	0.553875i
$743$	−18.1794	−	25.9629i	−0.666939	−	0.952487i	−0.999954	−	0.00956573i	$-0.996955\pi$
$743$	−18.1794	−	25.9629i	−0.666939	−	0.952487i	0.333016	−	0.942921i	$-0.391934\pi$
$744$	−0.493643	−	0.343186i	−0.0180978	−	0.0125818i
$745$	1.76585	+	3.18023i	0.0646957	+	0.116515i
$746$	4.91949	−	2.84027i	0.180115	−	0.103990i
$747$	−5.15576	−	7.25885i	−0.188639	−	0.265588i
$748$	6.00937	−	22.4273i	0.219724	−	0.820022i
$749$	10.6209	+	2.13852i	0.388079	+	0.0781397i
$750$	41.7369	−	9.11332i	1.52401	−	0.332771i
$751$	−1.60367	+	9.09488i	−0.0585188	+	0.331877i	−0.999986	−	0.00522694i	$-0.998336\pi$
$751$	−1.60367	+	9.09488i	−0.0585188	+	0.331877i	0.941468	+	0.337104i	$0.109447\pi$
$752$	4.83448	−	3.38514i	0.176295	−	0.123443i
$753$	8.64294	+	23.5002i	0.314966	+	0.856396i
$754$	−0.484716	−	0.577662i	−0.0176523	−	0.0210372i
$755$	3.14895	−	1.08683i	0.114602	−	0.0395537i
$756$	31.9620	+	23.0573i	1.16245	+	0.838587i
$757$	−26.4769	+	26.4769i	−0.962320	+	0.962320i	−0.999315	−	0.0369950i	$-0.988221\pi$
$757$	−26.4769	+	26.4769i	−0.962320	+	0.962320i	0.0369950	+	0.999315i	$0.488221\pi$
$758$	−1.81135	+	20.7038i	−0.0657912	+	0.751997i
$759$	3.53776	+	38.9294i	0.128412	+	1.41305i
$760$	6.45147	−	8.89326i	0.234020	−	0.322592i
$761$	44.4159	+	7.83173i	1.61008	+	0.283900i	0.905058	−	0.425289i	$-0.139827\pi$
$761$	44.4159	+	7.83173i	1.61008	+	0.283900i	0.705019	+	0.709189i	$0.250938\pi$
$762$	14.0949	−	24.6036i	0.510603	−	0.891295i
$763$	−3.72973	+	7.51866i	−0.135025	+	0.272194i
$764$	11.7673	+	20.3815i	0.425725	+	0.737377i
$765$	11.5243	+	5.51490i	0.416661	+	0.199392i
$766$	3.25249	+	5.63347i	0.117517	+	0.203546i
$767$	−0.302804	+	0.432449i	−0.0109336	+	0.0156148i
$768$	−6.63568	+	5.60611i	−0.239444	+	0.202293i
$769$	−28.3491	−	4.99871i	−1.02230	−	0.180258i	−0.362721	−	0.931898i	$-0.618152\pi$
$769$	−28.3491	−	4.99871i	−1.02230	−	0.180258i	−0.659574	+	0.751640i	$0.729263\pi$
$770$	52.8881	−	16.8353i	1.90595	−	0.606703i
$771$	−20.6852	+	29.7539i	−0.744960	+	1.07156i
$772$	−28.3065	+	13.1995i	−1.01877	+	0.475061i
$773$	1.61342	+	0.432314i	0.0580306	+	0.0155492i	0.287718	−	0.957715i	$-0.407104\pi$
$773$	1.61342	+	0.432314i	0.0580306	+	0.0155492i	−0.229687	+	0.973265i	$0.573770\pi$
$774$	−70.6823	−	40.1774i	−2.54062	−	1.44415i
$775$	−0.127633	−	0.898688i	−0.00458471	−	0.0322818i
$776$	3.79086	−	10.4153i	0.136084	−	0.373887i
$777$	−3.06531	+	2.46530i	−0.109967	+	0.0884422i
$778$	−1.42820	−	16.3244i	−0.0512033	−	0.585257i
$779$	−20.2227	−	16.9689i	−0.724555	−	0.607974i
$780$	1.29161	−	0.581399i	0.0462471	−	0.0208174i
$781$	−15.6458	−	5.69459i	−0.559849	−	0.203769i
$782$	5.77082	−	21.5370i	0.206364	−	0.770161i
$783$	−13.1302	−	4.62963i	−0.469236	−	0.165449i
$784$	10.3453	+	2.34443i	0.369476	+	0.0837295i
$785$	19.0967	+	5.46088i	0.681589	+	0.194907i
$786$	−17.3424	−	24.5912i	−0.618584	−	0.877140i
$787$	−25.6834	−	36.6797i	−0.915515	−	1.30749i	−0.951343	−	0.308132i	$-0.900296\pi$
$787$	−25.6834	−	36.6797i	−0.915515	−	1.30749i	0.0358289	−	0.999358i	$-0.488593\pi$
$788$	26.7288	−	57.3202i	0.952175	−	2.04195i
$789$	−51.5438	−	13.6256i	−1.83501	−	0.485085i
$790$	44.8785	−	43.4016i	1.59670	−	1.54416i
$791$	1.09540	+	7.22960i	0.0389481	+	0.257055i
$792$	−22.1771	−	10.1604i	−0.788028	−	0.361035i
$793$	0.204676	+	0.204676i	0.00726827	+	0.00726827i
$794$	8.35138	+	47.3631i	0.296380	+	1.68085i
$795$	10.4569	+	41.2219i	0.370867	+	1.46199i
$796$	10.9628	−	3.99012i	0.388565	−	0.141426i
$797$	−5.56190	+	3.89448i	−0.197013	+	0.137950i	−0.667920	−	0.744233i	$-0.732815\pi$
$797$	−5.56190	+	3.89448i	−0.197013	+	0.137950i	0.470908	+	0.882182i	$0.343926\pi$
$798$	19.5495	+	17.1093i	0.692044	+	0.605662i
$799$	−4.76779	−	5.68203i	−0.168672	−	0.201016i
$800$	−35.5745	−	4.31560i	−1.25775	−	0.152579i
$801$	37.6183	−	31.9988i	1.32918	−	1.13062i
$802$	−5.97065	+	5.97065i	−0.210831	+	0.210831i
$803$	−23.0653	−	16.1505i	−0.813957	−	0.569938i
$804$	17.1765	−	64.9761i	0.605767	−	2.29153i
$805$	29.9168	−	9.52310i	1.05443	−	0.335645i
$806$	−0.0174748	−	0.0480115i	−0.000615522	−	0.00169113i
$807$	25.0822	+	20.9032i	0.882934	+	0.735827i
$808$	8.21089	+	17.6083i	0.288858	+	0.619459i
$809$	1.18960	−	2.06045i	0.0418241	−	0.0724415i	−0.844356	−	0.535783i	$-0.820016\pi$
$809$	1.18960	−	2.06045i	0.0418241	−	0.0724415i	0.886180	+	0.463342i	$0.153350\pi$
$810$	25.5839	−	36.2834i	0.898926	−	1.27487i
$811$	34.7681			1.22087			0.610436	−	0.792065i	$-0.290994\pi$
$811$	34.7681			1.22087			0.610436	+	0.792065i	$0.290994\pi$
$812$	20.2817	−	1.28160i	0.711747	−	0.0449755i
$813$	−28.0991	+	10.3343i	−0.985478	+	0.362440i
$814$	5.17653	−	6.16915i	0.181437	−	0.216229i
$815$	0.386146	+	0.0403023i	0.0135261	+	0.00141173i
$816$	−3.54654	−	3.52278i	−0.124154	−	0.123322i
$817$	−25.8600	−	18.1074i	−0.904727	−	0.633497i
$818$	48.9843	+	13.1253i	1.71269	+	0.458915i
$819$	0.329683	+	0.957424i	0.0115201	+	0.0334551i
$820$	12.5180	−	64.6499i	0.437147	−	2.25767i
$821$	0.124677	−	0.342546i	0.00435125	−	0.0119550i	−0.937498	−	0.347991i	$-0.886864\pi$
$821$	0.124677	−	0.342546i	0.00435125	−	0.0119550i	0.941849	+	0.336036i	$0.109086\pi$
$822$	59.8886	−	10.7676i	2.08886	−	0.375564i
$823$	−0.602540	−	6.88707i	−0.0210032	−	0.240068i	−0.999438	−	0.0335133i	$-0.989330\pi$
$823$	−0.602540	−	6.88707i	−0.0210032	−	0.240068i	0.978435	−	0.206555i	$-0.0662252\pi$
$824$	−7.55802	+	2.75089i	−0.263296	+	0.0958320i
$825$	−11.5493	−	34.9717i	−0.402096	−	1.21756i
$826$	−7.71011	−	22.8893i	−0.268269	−	0.796422i
$827$	14.5273	−	3.89257i	0.505162	−	0.135358i	0.00276736	−	0.999996i	$-0.499119\pi$
$827$	14.5273	−	3.89257i	0.505162	−	0.135358i	0.502395	+	0.864638i	$0.332452\pi$
$828$	−41.4925	−	19.0098i	−1.44196	−	0.660636i
$829$		−	20.0583i		−	0.696653i	−0.937373	−	0.348327i	$-0.886750\pi$
$829$		−	20.0583i		−	0.696653i	0.937373	−	0.348327i	$-0.113250\pi$
$830$	7.53110	−	12.5545i	0.261408	−	0.435772i
$831$	27.8469	+	7.36133i	0.965998	+	0.255362i
$832$	−1.62424	+	0.142103i	−0.0563104	+	0.00492652i
$833$	1.80205	−	13.2092i	0.0624375	−	0.457673i
$834$	−86.7857	+	7.88676i	−3.00514	+	0.273096i
$835$	−49.8618	+	12.4704i	−1.72554	+	0.431556i
$836$	−27.1315	−	15.6644i	−0.938364	−	0.541765i
$837$	−0.728699	−	0.599035i	−0.0251875	−	0.0207057i
$838$	−17.0206	+	63.5218i	−0.587968	+	2.19433i
$839$	4.67340	+	26.5041i	0.161344	+	0.915025i	0.952755	+	0.303741i	$0.0982356\pi$
$839$	4.67340	+	26.5041i	0.161344	+	0.915025i	−0.791411	+	0.611284i	$0.790653\pi$
$840$	−4.12370	+	19.1536i	−0.142281	+	0.660861i
$841$	20.5049	−	7.46318i	0.707066	−	0.257351i
$842$	32.4316	−	22.7089i	1.11767	−	0.782600i
$843$	−23.6320	+	13.7500i	−0.813929	+	0.473577i
$844$	17.1526	+	20.4417i	0.590417	+	0.703631i
$845$	−28.5031	−	5.51897i	−0.980536	−	0.189859i
$846$	−22.2350	+	13.0374i	−0.764454	+	0.448236i
$847$	−7.50973	−	17.1762i	−0.258037	−	0.590183i
$848$	1.45024	−	16.5763i	0.0498015	−	0.569234i
$849$	−13.2864	−	1.11743i	−0.455990	−	0.0383501i
$850$	−0.702672	+	20.9956i	−0.0241014	+	0.720144i
$851$	2.92817	−	3.48965i	0.100376	−	0.119624i
$852$	14.8497	−	12.5456i	0.508742	−	0.429807i
$853$	−15.1332	−	1.32398i	−0.518151	−	0.0453323i	−0.174919	−	0.984583i	$-0.555966\pi$
$853$	−15.1332	−	1.32398i	−0.518151	−	0.0453323i	−0.343232	+	0.939251i	$0.611522\pi$
$854$	−13.0935	+	1.98388i	−0.448049	+	0.0678869i
$855$	11.2123	−	13.0940i	0.383453	−	0.447805i
$856$	3.91477	−	6.78058i	0.133804	−	0.231755i
$857$	15.3912	+	1.34656i	0.525753	+	0.0459975i	0.346943	−	0.937886i	$-0.387220\pi$
$857$	15.3912	+	1.34656i	0.525753	+	0.0459975i	0.178810	+	0.983884i	$0.442775\pi$
$858$	−1.04255	−	1.79182i	−0.0355921	−	0.0611716i
$859$	26.2215	+	4.62355i	0.894664	+	0.157753i	0.602032	−	0.798472i	$-0.294358\pi$
$859$	26.2215	+	4.62355i	0.894664	+	0.157753i	0.292632	+	0.956225i	$0.405469\pi$
$860$	8.17454	−	78.3223i	0.278749	−	2.67077i
$861$	45.2088	+	13.1273i	1.54071	+	0.447376i
$862$	32.2291	+	22.5670i	1.09773	+	0.768636i
$863$	19.4925	+	5.22300i	0.663532	+	0.177793i	0.574840	−	0.818266i	$-0.305064\pi$
$863$	19.4925	+	5.22300i	0.663532	+	0.177793i	0.0886927	+	0.996059i	$0.471731\pi$
$864$	−30.2893	+	21.6672i	−1.03046	+	0.737132i
$865$	8.24972	+	12.2116i	0.280499	+	0.415207i
$866$	−48.6974	−	58.0353i	−1.65481	−	1.97212i
$867$	14.8288	−	17.7934i	0.503612	−	0.604295i
$868$	1.32101	+	0.388399i	0.0448379	+	0.0131831i
$869$	−41.2310	−	34.5969i	−1.39867	−	1.17362i
$870$	−1.69023	−	22.8303i	−0.0573043	−	0.774020i
$871$	1.32281	−	1.10997i	0.0448216	−	0.0376098i
$872$	4.28888	+	4.28888i	0.145240	+	0.145240i
$873$	7.24345	−	15.8102i	0.245154	−	0.535095i
$874$	−26.0545	−	15.0426i	−0.881307	−	0.508823i
$875$	−25.4241	+	15.1200i	−0.859491	+	0.511150i
$876$	29.7487	−	13.9940i	1.00511	−	0.472812i
$877$	21.4280	−	45.9525i	0.723573	−	1.55171i	−0.106664	−	0.994295i	$-0.534017\pi$
$877$	21.4280	−	45.9525i	0.723573	−	1.55171i	0.830237	−	0.557411i	$-0.188205\pi$
$878$	3.24965	−	0.284308i	0.109670	−	0.00959492i
$879$	−41.7372	−	29.0161i	−1.40776	−	0.978690i
$880$	−0.241035	+	14.4082i	−0.00812530	+	0.485699i
$881$	−0.590192	−	0.340747i	−0.0198841	−	0.0114801i	0.490025	−	0.871708i	$-0.336988\pi$
$881$	−0.590192	−	0.340747i	−0.0198841	−	0.0114801i	−0.509909	+	0.860228i	$0.670321\pi$
$882$	−44.2114	−	13.8410i	−1.48868	−	0.466050i
$883$	−8.29706	+	30.9651i	−0.279218	+	1.04206i	0.673743	+	0.738966i	$0.264685\pi$
$883$	−8.29706	+	30.9651i	−0.279218	+	1.04206i	−0.952961	+	0.303091i	$0.901981\pi$
$884$	0.120950	+	0.685940i	0.00406798	+	0.0230707i
$885$	−15.1323	+	5.27973i	−0.508666	+	0.177476i
$886$	−0.429676	+	0.156389i	−0.0144352	+	0.00525400i
$887$	2.47045	+	28.2374i	0.0829497	+	0.948119i	0.917643	+	0.397405i	$0.130089\pi$
$887$	2.47045	+	28.2374i	0.0829497	+	0.948119i	−0.834694	+	0.550714i	$0.814355\pi$
$888$	0.981263	+	2.66806i	0.0329290	+	0.0895343i
$889$	−3.87544	+	19.2473i	−0.129978	+	0.645533i
$890$	73.0141	+	35.5458i	2.44744	+	1.19150i
$891$	−33.4007	−	18.6898i	−1.11897	−	0.626132i
$892$	11.4106	+	42.5848i	0.382054	+	1.42585i
$893$	−9.07060	+	4.22969i	−0.303536	+	0.141541i
$894$	0.562564	+	6.19044i	0.0188150	+	0.207039i
$895$	17.4857	−	14.1807i	0.584484	−	0.474009i
$896$	19.0968	−	31.3049i	0.637978	−	1.04582i
$897$	−0.589731	−	1.01356i	−0.0196906	−	0.0338419i
$898$	20.0466	−	28.6295i	0.668964	−	0.955380i
$899$	−0.486419			−0.0162230
$900$	42.1327	+	8.59628i	1.40442	+	0.286543i
$901$	−20.9126			−0.696700
$902$	−96.0101	−	8.39979i	−3.19679	−	0.279683i
$903$	55.2255	+	10.9266i	1.83779	+	0.363616i
$904$	5.20403	+	0.917611i	0.173083	+	0.0305193i
$905$	−4.56100	+	3.69891i	−0.151613	+	0.122956i
$906$	5.67241	+	0.477067i	0.188453	+	0.0158495i
$907$	−22.0277	−	15.4240i	−0.731419	−	0.512145i	0.147532	−	0.989057i	$-0.452867\pi$
$907$	−22.0277	−	15.4240i	−0.731419	−	0.512145i	−0.878951	+	0.476912i	$0.841756\pi$
$908$	51.8607	−	51.8607i	1.72106	−	1.72106i
$909$	10.6184	+	28.5747i	0.352190	+	0.947763i
$910$	−1.22448	+	1.12823i	−0.0405913	+	0.0374006i
$911$	−13.4026	+	36.8233i	−0.444047	+	1.22001i	0.492761	+	0.870165i	$0.335988\pi$
$911$	−13.4026	+	36.8233i	−0.444047	+	1.22001i	−0.936808	+	0.349844i	$0.886234\pi$
$912$	−5.82990	+	3.39207i	−0.193047	+	0.112323i
$913$	−11.4388	−	5.33400i	−0.378569	−	0.176530i
$914$	−16.1489	+	91.5848i	−0.534157	+	3.02935i
$915$	1.41012	+	8.67356i	0.0466170	+	0.286739i
$916$	−1.67378	−	9.49247i	−0.0553032	−	0.313640i
$917$	16.7741	+	12.3598i	0.553929	+	0.408157i
$918$	14.2009	+	16.5816i	0.468701	+	0.547274i
$919$	9.23068	−	5.32934i	0.304492	−	0.175799i	−0.339967	−	0.940437i	$-0.610416\pi$
$919$	9.23068	−	5.32934i	0.304492	−	0.175799i	0.644459	+	0.764639i	$0.277083\pi$
$920$	0.379515	−	22.6860i	0.0125122	−	0.747934i
$921$	−48.7917	+	4.43401i	−1.60774	+	0.146105i
$922$	72.8482	−	6.37339i	2.39913	−	0.209896i
$923$	0.497574	−	0.0435321i	0.0163778	−	0.00143288i
$924$	55.5415	+	6.02560i	1.82718	+	0.198228i
$925$	−1.94297	+	3.82702i	−0.0638846	+	0.125832i
$926$	57.6178	+	33.2656i	1.89344	+	1.09318i
$927$	−12.1675	+	3.34808i	−0.399632	+	0.109965i
$928$	−4.97019	+	18.5490i	−0.163155	+	0.608901i
$929$	24.6459	+	8.97038i	0.808607	+	0.294309i	0.713048	−	0.701115i	$-0.247314\pi$
$929$	24.6459	+	8.97038i	0.808607	+	0.294309i	0.0955585	+	0.995424i	$0.469536\pi$
$930$	0.421443	−	1.49274i	0.0138197	−	0.0489490i
$931$	−16.5867	−	6.96169i	−0.543607	−	0.228160i
$932$	−45.3067	+	31.7241i	−1.48407	+	1.03916i
$933$	−30.5606	−	36.1731i	−1.00051	−	1.18425i
$934$	1.54745	−	0.272858i	0.0506343	−	0.00892818i
$935$	18.0656	−	1.27644i	0.590807	−	0.0417442i
$936$	0.731765	−	0.00491882i	0.0239185	−	0.000160777i
$937$	42.7407	+	11.4523i	1.39628	+	0.374131i	0.877006	−	0.480479i	$-0.159537\pi$
$937$	42.7407	+	11.4523i	1.39628	+	0.374131i	0.519270	+	0.854610i	$0.326204\pi$
$938$	4.98228	+	78.8457i	0.162677	+	2.57440i
$939$	32.7729	−	8.89963i	1.06950	−	0.290428i
$940$	−20.2079	−	14.6595i	−0.659109	−	0.478140i
$941$	−24.2520	−	4.27628i	−0.790592	−	0.139403i	−0.236251	−	0.971692i	$-0.575919\pi$
$941$	−24.2520	−	4.27628i	−0.790592	−	0.139403i	−0.554341	+	0.832289i	$0.687030\pi$
$942$	26.0731	+	21.7291i	0.849509	+	0.707971i
$943$	−54.3093	−	4.75144i	−1.76855	−	0.154728i
$944$	6.27082			0.204098
$945$	−8.86710	+	29.4342i	−0.288447	+	0.957496i
$946$	−115.253			−3.74718
$947$	−27.9481	−	2.44515i	−0.908193	−	0.0794566i	−0.376522	−	0.926408i	$-0.622880\pi$
$947$	−27.9481	−	2.44515i	−0.908193	−	0.0794566i	−0.531671	+	0.846951i	$0.678436\pi$
$948$	58.9797	−	21.6916i	1.91557	−	0.704511i
$949$	0.831856	+	0.146679i	0.0270032	+	0.00476139i
$950$	27.1189	+	8.24805i	0.879853	+	0.267602i
$951$	9.96766	+	9.90089i	0.323224	+	0.321058i
$952$	−8.63087	−	4.28145i	−0.279728	−	0.138763i
$953$	−31.7286	−	8.50165i	−1.02779	−	0.275396i	−0.294745	−	0.955576i	$-0.595235\pi$
$953$	−31.7286	−	8.50165i	−1.02779	−	0.275396i	−0.733045	+	0.680180i	$0.761901\pi$
$954$	−12.1379	+	71.6505i	−0.392979	+	2.31977i
$955$	−12.0333	+	13.8631i	−0.389390	+	0.448599i
$956$	−78.4111	+	13.8260i	−2.53600	+	0.447165i
$957$	−19.4246	+	3.49243i	−0.627907	+	0.112894i
$958$	−56.1746	+	39.3339i	−1.81492	+	1.27082i
$959$	−36.9866	+	20.1789i	−1.19436	+	0.651611i
$960$	−42.5317	−	25.3196i	−1.37270	−	0.817187i
$961$	29.0995	+	10.5914i	0.938694	+	0.341657i
$962$	−0.0625273	+	0.233355i	−0.00201596	+	0.00752367i
$963$	6.97840	−	10.1101i	0.224876	−	0.325795i
$964$	−38.0963	−	21.9949i	−1.22700	−	0.708408i
$965$	−16.9359	−	17.5122i	−0.545185	−	0.563737i
$966$	53.3366	+	5.78641i	1.71608	+	0.186175i
$967$	−39.4566	+	3.45200i	−1.26884	+	0.111009i	−0.701615	−	0.712556i	$-0.747538\pi$
$967$	−39.4566	+	3.45200i	−1.26884	+	0.111009i	−0.567222	+	0.823565i	$0.691982\pi$
$968$	−13.4959	+	1.18074i	−0.433775	+	0.0379504i
$969$	4.88549	+	6.92754i	0.156945	+	0.222545i
$970$	28.5913	+	0.478306i	0.918011	+	0.0153575i
$971$	35.5260	−	20.5109i	1.14008	−	0.658228i	0.193632	−	0.981074i	$-0.437973\pi$
$971$	35.5260	−	20.5109i	1.14008	−	0.658228i	0.946451	+	0.322847i	$0.104640\pi$
$972$	38.3197	−	22.9910i	1.22911	−	0.737436i
$973$	55.2866	−	24.1722i	1.77241	−	0.774925i
$974$	2.82753	+	16.0357i	0.0906000	+	0.513818i
$975$	0.757374	+	0.804389i	0.0242554	+	0.0257610i
$976$	0.597045	−	3.38601i	0.0191109	−	0.108384i
$977$	30.9067	+	14.4120i	0.988792	+	0.461081i	0.848595	−	0.529042i	$-0.177449\pi$
$977$	30.9067	+	14.4120i	0.988792	+	0.461081i	0.140197	+	0.990124i	$0.455227\pi$
$978$	0.575663	+	0.329784i	0.0184077	+	0.0105453i
$979$	23.9445	−	65.7869i	0.765269	−	2.10256i
$980$	−4.90292	−	44.6025i	−0.156618	−	1.42478i
$981$	6.16607	+	7.24892i	0.196867	+	0.231440i
$982$	−35.3542	+	35.3542i	−1.12820	+	1.12820i
$983$	−12.3679	−	8.66009i	−0.394474	−	0.276214i	0.359464	−	0.933159i	$-0.382959\pi$
$983$	−12.3679	−	8.66009i	−0.394474	−	0.276214i	−0.753939	+	0.656945i	$0.771848\pi$
$984$	19.4198	−	27.9337i	0.619080	−	0.890493i
$985$	49.0659	+	5.12103i	1.56337	+	0.163170i
$986$	11.0864	+	1.95482i	0.353062	+	0.0622543i
$987$	11.7539	−	13.4303i	0.374132	−	0.427493i
$988$	0.936246	+	0.0819110i	0.0297860	+	0.00260593i
$989$	−65.1940			−2.07305
$990$	6.11212	−	62.6369i	0.194256	−	1.99073i
$991$	7.04356			0.223746			0.111873	−	0.993723i	$-0.464315\pi$
$991$	7.04356			0.223746			0.111873	+	0.993723i	$0.464315\pi$
$992$	−0.746291	+	1.06581i	−0.0236948	+	0.0338396i
$993$	21.1372	−	0.0710397i	0.670767	−	0.00225438i
$994$	−11.9005	+	19.5081i	−0.377460	+	0.618761i
$995$	5.73186	+	7.06776i	0.181712	+	0.224063i
$996$	12.0427	−	8.49287i	0.381588	−	0.269107i
$997$	13.2580	−	6.18229i	0.419884	−	0.195795i	−0.201181	−	0.979554i	$-0.564478\pi$
$997$	13.2580	−	6.18229i	0.419884	−	0.195795i	0.621065	+	0.783759i	$0.286700\pi$
$998$	7.99182	+	29.8259i	0.252977	+	0.944121i
$999$	1.19781	+	4.29653i	0.0378970	+	0.135936i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.do.a.473.19	yes	1680
5.2	odd	4	inner	945.2.do.a.662.122	yes	1680
7.2	even	3		945.2.dh.a.338.122	yes	1680
27.2	odd	18		945.2.dh.a.893.19	yes	1680
35.2	odd	12		945.2.dh.a.527.19	yes	1680
135.2	even	36		945.2.dh.a.137.122	✓	1680
189.2	odd	18	inner	945.2.do.a.758.122	yes	1680
945.2	even	36	inner	945.2.do.a.2.19	yes	1680

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.dh.a.137.122	✓	1680	135.2	even	36
945.2.dh.a.338.122	yes	1680	7.2	even	3
945.2.dh.a.527.19	yes	1680	35.2	odd	12
945.2.dh.a.893.19	yes	1680	27.2	odd	18
945.2.do.a.2.19	yes	1680	945.2	even	36	inner
945.2.do.a.473.19	yes	1680	1.1	even	1	trivial
945.2.do.a.662.122	yes	1680	5.2	odd	4	inner
945.2.do.a.758.122	yes	1680	189.2	odd	18	inner

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.do (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.19767 - 0.192271i) q^{2} +(0.295033 - 1.70674i) q^{3} +(2.82316 + 0.497800i) q^{4} +(0.351401 + 2.20828i) q^{5} +(-0.976541 + 3.69412i) q^{6} +(-0.166853 - 2.64048i) q^{7} +(-1.84688 - 0.494869i) q^{8} +(-2.82591 - 1.00709i) q^{9} +O(q^{10})\)	\(q+(-2.19767 - 0.192271i) q^{2} +(0.295033 - 1.70674i) q^{3} +(2.82316 + 0.497800i) q^{4} +(0.351401 + 2.20828i) q^{5} +(-0.976541 + 3.69412i) q^{6} +(-0.166853 - 2.64048i) q^{7} +(-1.84688 - 0.494869i) q^{8} +(-2.82591 - 1.00709i) q^{9} +(-0.347674 - 4.92064i) q^{10} +(-4.18808 + 0.738472i) q^{11} +(1.68254 - 4.67153i) q^{12} +(0.104503 - 0.0731741i) q^{13} +(-0.141002 + 5.83499i) q^{14} +(3.87264 + 0.0517672i) q^{15} +(-1.42399 - 0.518289i) q^{16} +(-0.492925 + 1.83962i) q^{17} +(6.01678 + 2.75659i) q^{18} +(2.22549 + 1.28489i) q^{19} +(-0.107221 + 6.40927i) q^{20} +(-4.55584 - 0.494256i) q^{21} +(9.34601 - 0.817670i) q^{22} +(5.28668 - 0.462525i) q^{23} +(-1.38950 + 3.00613i) q^{24} +(-4.75303 + 1.55199i) q^{25} +(-0.243733 + 0.140719i) q^{26} +(-2.55257 + 4.52597i) q^{27} +(0.843380 - 7.53758i) q^{28} +(0.465271 + 2.63868i) q^{29} +(-8.50082 - 0.858363i) q^{30} +(-0.0315243 + 0.178783i) q^{31} +(6.49557 + 3.02893i) q^{32} +(0.0247558 + 7.36584i) q^{33} +(1.43699 - 3.94810i) q^{34} +(5.77231 - 1.29633i) q^{35} +(-7.47668 - 4.24991i) q^{36} +(0.606980 - 0.606980i) q^{37} +(-4.64385 - 3.25166i) q^{38} +(-0.0940571 - 0.199949i) q^{39} +(0.443817 - 4.25233i) q^{40} +(-10.1168 - 1.78386i) q^{41} +(9.91720 + 1.96217i) q^{42} +(-12.2381 - 1.07069i) q^{43} -12.1913 q^{44} +(1.23091 - 6.59431i) q^{45} -11.7073 q^{46} +(-2.23386 + 3.19029i) q^{47} +(-1.30471 + 2.27746i) q^{48} +(-6.94432 + 0.881145i) q^{49} +(10.7440 - 2.49688i) q^{50} +(2.99432 + 1.38404i) q^{51} +(0.331456 - 0.154561i) q^{52} +(2.84198 + 10.6064i) q^{53} +(6.47992 - 9.45579i) q^{54} +(-3.10245 - 8.98898i) q^{55} +(-0.998538 + 4.95922i) q^{56} +(2.84956 - 3.41925i) q^{57} +(-0.515169 - 5.88840i) q^{58} +(-3.88857 + 1.41532i) q^{59} +(10.9073 + 2.07395i) q^{60} +(0.393991 + 2.23444i) q^{61} +(0.103655 - 0.386845i) q^{62} +(-2.18769 + 7.62981i) q^{63} +(-11.0680 - 6.39013i) q^{64} +(0.198312 + 0.205060i) q^{65} +(1.36183 - 16.1924i) q^{66} +(13.4841 - 1.17970i) q^{67} +(-2.30737 + 4.94817i) q^{68} +(0.770337 - 9.15944i) q^{69} +(-12.9349 + 1.73905i) q^{70} +(3.39061 + 1.95757i) q^{71} +(4.72073 + 3.25842i) q^{72} +(4.68183 + 4.68183i) q^{73} +(-1.45065 + 1.21724i) q^{74} +(1.24653 + 8.57007i) q^{75} +(5.64331 + 4.73530i) q^{76} +(2.64872 + 10.9354i) q^{77} +(0.168262 + 0.457506i) q^{78} +(8.13529 + 9.69526i) q^{79} +(0.644139 - 3.32670i) q^{80} +(6.97155 + 5.69188i) q^{81} +(21.8903 + 5.86550i) q^{82} +(2.43111 + 1.70228i) q^{83} +(-12.6158 - 3.66326i) q^{84} +(-4.23562 - 0.442073i) q^{85} +(26.6894 + 4.70605i) q^{86} +(4.64081 - 0.0155972i) q^{87} +(8.10032 + 0.708686i) q^{88} +(-8.23114 + 14.2567i) q^{89} +(-3.97302 + 14.2554i) q^{90} +(-0.210652 - 0.263731i) q^{91} +(15.1554 + 1.32593i) q^{92} +(0.295836 + 0.106551i) q^{93} +(5.52269 - 6.58168i) q^{94} +(-2.05536 + 5.36603i) q^{95} +(7.08601 - 10.1926i) q^{96} +(-0.505228 + 5.77479i) q^{97} +(15.4307 - 0.601272i) q^{98} +(12.5789 + 2.13091i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1680 q - 6 q^{2} - 6 q^{3} - 6 q^{5} - 36 q^{6} - 12 q^{7} - 36 q^{8}+O(q^{10}) \) 1680 * q - 6 * q^2 - 6 * q^3 - 6 * q^5 - 36 * q^6 - 12 * q^7 - 36 * q^8	\( 1680 q - 6 q^{2} - 6 q^{3} - 6 q^{5} - 36 q^{6} - 12 q^{7} - 36 q^{8} + 6 q^{10} + 12 q^{11} - 6 q^{12} - 24 q^{13} - 24 q^{15} - 12 q^{16} - 18 q^{17} - 6 q^{18} - 24 q^{20} - 24 q^{21} - 24 q^{22} + 42 q^{23} - 6 q^{25} - 24 q^{27} - 24 q^{28} + 30 q^{30} - 12 q^{31} + 90 q^{32} - 6 q^{33} - 18 q^{35} - 84 q^{36} - 12 q^{37} - 30 q^{38} - 54 q^{40} - 72 q^{41} - 108 q^{42} - 24 q^{43} - 6 q^{45} - 24 q^{46} - 6 q^{47} - 96 q^{48} - 72 q^{50} - 12 q^{51} - 30 q^{52} - 90 q^{53} - 48 q^{55} - 72 q^{56} - 24 q^{57} - 6 q^{58} + 186 q^{60} + 24 q^{61} - 36 q^{62} - 54 q^{63} + 138 q^{65} - 12 q^{66} - 6 q^{67} + 114 q^{68} - 12 q^{70} - 72 q^{71} + 18 q^{72} - 12 q^{73} - 150 q^{75} - 156 q^{77} - 84 q^{78} + 12 q^{81} - 12 q^{82} - 24 q^{83} - 24 q^{85} - 120 q^{86} - 102 q^{87} - 6 q^{88} + 30 q^{90} - 12 q^{91} + 108 q^{92} + 138 q^{93} - 66 q^{95} - 444 q^{96} - 24 q^{97} - 360 q^{98}+O(q^{100}) \) 1680 * q - 6 * q^2 - 6 * q^3 - 6 * q^5 - 36 * q^6 - 12 * q^7 - 36 * q^8 + 6 * q^10 + 12 * q^11 - 6 * q^12 - 24 * q^13 - 24 * q^15 - 12 * q^16 - 18 * q^17 - 6 * q^18 - 24 * q^20 - 24 * q^21 - 24 * q^22 + 42 * q^23 - 6 * q^25 - 24 * q^27 - 24 * q^28 + 30 * q^30 - 12 * q^31 + 90 * q^32 - 6 * q^33 - 18 * q^35 - 84 * q^36 - 12 * q^37 - 30 * q^38 - 54 * q^40 - 72 * q^41 - 108 * q^42 - 24 * q^43 - 6 * q^45 - 24 * q^46 - 6 * q^47 - 96 * q^48 - 72 * q^50 - 12 * q^51 - 30 * q^52 - 90 * q^53 - 48 * q^55 - 72 * q^56 - 24 * q^57 - 6 * q^58 + 186 * q^60 + 24 * q^61 - 36 * q^62 - 54 * q^63 + 138 * q^65 - 12 * q^66 - 6 * q^67 + 114 * q^68 - 12 * q^70 - 72 * q^71 + 18 * q^72 - 12 * q^73 - 150 * q^75 - 156 * q^77 - 84 * q^78 + 12 * q^81 - 12 * q^82 - 24 * q^83 - 24 * q^85 - 120 * q^86 - 102 * q^87 - 6 * q^88 + 30 * q^90 - 12 * q^91 + 108 * q^92 + 138 * q^93 - 66 * q^95 - 444 * q^96 - 24 * q^97 - 360 * q^98

Introduction

L-functions

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