LMFDB - Embedded newform 207.2.o.a.11.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(5,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("207.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.o (of order $66$, degree $20$, 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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			11.22
Character	$\chi$	$=$	207.11
Dual form			207.2.o.a.113.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.70946 - 0.129067i) q^{2} +(-1.70554 + 0.301886i) q^{3} +(5.33355 - 0.509292i) q^{4} +(-0.312243 - 0.297723i) q^{5} +(-4.58212 + 1.03808i) q^{6} +(-0.00342569 - 0.0177741i) q^{7} +(9.01544 - 1.29622i) q^{8} +(2.81773 - 1.02976i) q^{9} +O(q^{10})$	\(q+(2.70946 - 0.129067i) q^{2} +(-1.70554 + 0.301886i) q^{3} +(5.33355 - 0.509292i) q^{4} +(-0.312243 - 0.297723i) q^{5} +(-4.58212 + 1.03808i) q^{6} +(-0.00342569 - 0.0177741i) q^{7} +(9.01544 - 1.29622i) q^{8} +(2.81773 - 1.02976i) q^{9} +(-0.884435 - 0.766367i) q^{10} +(-3.01443 + 1.55405i) q^{11} +(-8.94283 + 2.47874i) q^{12} +(-4.11460 - 0.793024i) q^{13} +(-0.0115758 - 0.0477161i) q^{14} +(0.622421 + 0.413517i) q^{15} +(13.7377 - 2.64772i) q^{16} +(2.53006 + 5.54006i) q^{17} +(7.50161 - 3.15375i) q^{18} +(-4.12200 - 1.88245i) q^{19} +(-1.81699 - 1.42890i) q^{20} +(0.0112084 + 0.0292803i) q^{21} +(-7.96690 + 4.59969i) q^{22} +(-3.07331 - 3.68168i) q^{23} +(-14.9849 + 4.93239i) q^{24} +(-0.229053 - 4.80841i) q^{25} +(-11.2507 - 1.61760i) q^{26} +(-4.49488 + 2.60692i) q^{27} +(-0.0273233 - 0.0930546i) q^{28} +(0.00670806 - 0.0702500i) q^{29} +(1.73979 + 1.04007i) q^{30} +(-0.0649439 + 0.0510724i) q^{31} +(19.1771 - 4.65230i) q^{32} +(4.67209 - 3.56051i) q^{33} +(7.57013 + 14.6840i) q^{34} +(-0.00422212 + 0.00656975i) q^{35} +(14.5041 - 6.92730i) q^{36} +(-2.34304 + 7.97966i) q^{37} +(-11.4113 - 4.56841i) q^{38} +(7.25702 + 0.110396i) q^{39} +(-3.20092 - 2.27937i) q^{40} +(2.49878 - 2.62064i) q^{41} +(0.0341478 + 0.0778871i) q^{42} +(0.343465 - 0.436751i) q^{43} +(-15.2862 + 9.82382i) q^{44} +(-1.18640 - 0.517369i) q^{45} +(-8.80218 - 9.57868i) q^{46} +(5.27123 + 3.04334i) q^{47} +(-22.6308 + 8.66299i) q^{48} +(6.49827 - 2.60152i) q^{49} +(-1.24122 - 12.9986i) q^{50} +(-5.98759 - 8.68501i) q^{51} +(-22.3493 - 2.13410i) q^{52} +(6.52711 + 7.53268i) q^{53} +(-11.8422 + 7.64348i) q^{54} +(1.40391 + 0.412226i) q^{55} +(-0.0539233 - 0.155801i) q^{56} +(7.59852 + 1.96623i) q^{57} +(0.00910822 - 0.191205i) q^{58} +(-1.53541 + 7.96646i) q^{59} +(3.53031 + 1.88852i) q^{60} +(4.17225 - 10.4218i) q^{61} +(-0.169371 + 0.146761i) q^{62} +(-0.0279557 - 0.0465551i) q^{63} +(24.5114 - 7.19719i) q^{64} +(1.04865 + 1.47263i) q^{65} +(12.1993 - 10.2500i) q^{66} +(5.96686 - 11.5741i) q^{67} +(16.3157 + 28.2597i) q^{68} +(6.35310 + 5.35146i) q^{69} +(-0.0105917 + 0.0183454i) q^{70} +(3.48365 + 5.42067i) q^{71} +(24.0683 - 12.9361i) q^{72} +(2.29911 - 5.03436i) q^{73} +(-5.31845 + 21.9230i) q^{74} +(1.84225 + 8.13179i) q^{75} +(-22.9436 - 7.94086i) q^{76} +(0.0379484 + 0.0482553i) q^{77} +(19.6768 - 0.637532i) q^{78} +(-10.0257 + 3.46994i) q^{79} +(-5.07778 - 3.26329i) q^{80} +(6.87921 - 5.80315i) q^{81} +(6.43209 - 7.42303i) q^{82} +(2.44718 - 2.33338i) q^{83} +(0.0746928 + 0.150460i) q^{84} +(0.859410 - 2.48310i) q^{85} +(0.874233 - 1.22769i) q^{86} +(0.00976660 + 0.121839i) q^{87} +(-25.1621 + 17.9178i) q^{88} +(0.962501 - 6.69434i) q^{89} +(-3.28127 - 1.24866i) q^{90} +0.0758502i q^{91} +(-18.2667 - 18.0712i) q^{92} +(0.0953463 - 0.106712i) q^{93} +(14.6749 + 7.56546i) q^{94} +(0.726615 + 1.81500i) q^{95} +(-31.3028 + 13.7240i) q^{96} +(4.13449 + 1.00302i) q^{97} +(17.2710 - 7.88740i) q^{98} +(-6.89357 + 7.48302i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	2.70946	−	0.129067i	1.91587	−	0.0912644i	0.944456	−	0.328638i	$-0.106590\pi$
$2$	2.70946	−	0.129067i	1.91587	−	0.0912644i	0.971418	+	0.237373i	$0.0762865\pi$
$3$	−1.70554	+	0.301886i	−0.984694	+	0.174294i
$3$	−1.70554	+	0.301886i	−0.984694	+	0.174294i
$4$	5.33355	−	0.509292i	2.66677	−	0.254646i
$5$	−0.312243	−	0.297723i	−0.139639	−	0.133146i	0.617041	−	0.786931i	$-0.288331\pi$
$5$	−0.312243	−	0.297723i	−0.139639	−	0.133146i	−0.756680	+	0.653785i	$0.773180\pi$
$6$	−4.58212	+	1.03808i	−1.87064	+	0.423792i
$7$	−0.00342569	−	0.0177741i	−0.00129479	−	0.00671799i	0.981276	−	0.192609i	$-0.0616949\pi$
$7$	−0.00342569	−	0.0177741i	−0.00129479	−	0.00671799i	−0.982570	+	0.185891i	$0.940483\pi$
$8$	9.01544	−	1.29622i	3.18744	−	0.458285i
$9$	2.81773	−	1.02976i	0.939243	−	0.343252i
$10$	−0.884435	−	0.766367i	−0.279683	−	0.242346i
$11$	−3.01443	+	1.55405i	−0.908886	+	0.468563i	−0.848250	−	0.529597i	$-0.822343\pi$
$11$	−3.01443	+	1.55405i	−0.908886	+	0.468563i	−0.0606363	+	0.998160i	$0.519313\pi$
$12$	−8.94283	+	2.47874i	−2.58157	+	0.715550i
$13$	−4.11460	−	0.793024i	−1.14119	−	0.219945i	−0.416573	−	0.909102i	$-0.636769\pi$
$13$	−4.11460	−	0.793024i	−1.14119	−	0.219945i	−0.724612	+	0.689157i	$0.757981\pi$
$14$	−0.0115758	−	0.0477161i	−0.00309376	−	0.0127527i
$15$	0.622421	+	0.413517i	0.160708	+	0.106770i
$16$	13.7377	−	2.64772i	3.43442	−	0.661930i
$17$	2.53006	+	5.54006i	0.613630	+	1.34366i	0.920063	+	0.391771i	$0.128137\pi$
$17$	2.53006	+	5.54006i	0.613630	+	1.34366i	−0.306433	+	0.951892i	$0.599135\pi$
$18$	7.50161	−	3.15375i	1.76815	−	0.743347i
$19$	−4.12200	−	1.88245i	−0.945652	−	0.431865i	−0.117941	−	0.993021i	$-0.537630\pi$
$19$	−4.12200	−	1.88245i	−0.945652	−	0.431865i	−0.827710	+	0.561156i	$0.810357\pi$
$20$	−1.81699	−	1.42890i	−0.406291	−	0.319511i
$21$	0.0112084	+	0.0292803i	0.00244587	+	0.00638949i
$22$	−7.96690	+	4.59969i	−1.69855	+	0.980657i
$23$	−3.07331	−	3.68168i	−0.640830	−	0.767683i
$23$	−3.07331	−	3.68168i	−0.640830	−	0.767683i
$24$	−14.9849	+	4.93239i	−3.05878	+	1.00682i
$25$	−0.229053	−	4.80841i	−0.0458106	−	0.961683i
$26$	−11.2507	−	1.61760i	−2.20644	−	0.317238i
$27$	−4.49488	+	2.60692i	−0.865040	+	0.501702i
$28$	−0.0273233	−	0.0930546i	−0.00516362	−	0.0175857i
$29$	0.00670806	−	0.0702500i	0.00124566	−	0.0130451i	−0.994828	−	0.101577i	$-0.967611\pi$
$29$	0.00670806	−	0.0702500i	0.00124566	−	0.0130451i	0.996073	+	0.0885315i	$0.0282174\pi$
$30$	1.73979	+	1.04007i	0.317641	+	0.189890i
$31$	−0.0649439	+	0.0510724i	−0.0116643	+	0.00917288i	−0.623974	−	0.781445i	$-0.714483\pi$
$31$	−0.0649439	+	0.0510724i	−0.0116643	+	0.00917288i	0.612310	+	0.790618i	$0.290241\pi$
$32$	19.1771	−	4.65230i	3.39006	−	0.822419i
$33$	4.67209	−	3.56051i	0.813307	−	0.619804i
$34$	7.57013	+	14.6840i	1.29827	+	2.51829i
$35$	−0.00422212	+	0.00656975i	−0.000713669	+	0.00111049i
$36$	14.5041	−	6.92730i	2.41734	−	1.15455i
$37$	−2.34304	+	7.97966i	−0.385193	+	1.31185i	0.507682	+	0.861545i	$0.330503\pi$
$37$	−2.34304	+	7.97966i	−0.385193	+	1.31185i	−0.892875	+	0.450304i	$0.851316\pi$
$38$	−11.4113	−	4.56841i	−1.85116	−	0.741094i
$39$	7.25702	+	0.110396i	1.16205	+	0.0176774i
$40$	−3.20092	−	2.27937i	−0.506110	−	0.360400i
$41$	2.49878	−	2.62064i	0.390244	−	0.409276i	−0.499079	−	0.866557i	$-0.666328\pi$
$41$	2.49878	−	2.62064i	0.390244	−	0.409276i	0.889322	+	0.457281i	$0.151177\pi$
$42$	0.0341478	+	0.0778871i	0.00526912	+	0.0120182i
$43$	0.343465	−	0.436751i	0.0523779	−	0.0666039i	−0.759158	−	0.650906i	$-0.774389\pi$
$43$	0.343465	−	0.436751i	0.0523779	−	0.0666039i	0.811536	+	0.584302i	$0.198632\pi$
$44$	−15.2862	+	9.82382i	−2.30448	+	1.48100i
$45$	−1.18640	−	0.517369i	−0.176858	−	0.0771248i
$46$	−8.80218	−	9.57868i	−1.29781	−	1.41230i
$47$	5.27123	+	3.04334i	0.768887	+	0.443917i	0.832478	−	0.554059i	$-0.186922\pi$
$47$	5.27123	+	3.04334i	0.768887	+	0.443917i	−0.0635903	+	0.997976i	$0.520255\pi$
$48$	−22.6308	+	8.66299i	−3.26648	+	1.25040i
$49$	6.49827	−	2.60152i	0.928324	−	0.371645i
$50$	−1.24122	−	12.9986i	−0.175535	−	1.83828i
$51$	−5.98759	−	8.68501i	−0.838430	−	1.21614i
$52$	−22.3493	−	2.13410i	−3.09929	−	0.295946i
$53$	6.52711	+	7.53268i	0.896567	+	1.03469i	0.999201	+	0.0399744i	$0.0127276\pi$
$53$	6.52711	+	7.53268i	0.896567	+	1.03469i	−0.102634	+	0.994719i	$0.532727\pi$
$54$	−11.8422	+	7.64348i	−1.61152	+	1.04015i
$55$	1.40391	+	0.412226i	0.189303	+	0.0555845i
$56$	−0.0539233	−	0.155801i	−0.00720581	−	0.0208198i
$57$	7.59852	+	1.96623i	1.00645	+	0.260433i
$58$	0.00910822	−	0.191205i	0.00119597	−	0.0251064i
$59$	−1.53541	+	7.96646i	−0.199893	+	1.03714i	0.733880	+	0.679279i	$0.237707\pi$
$59$	−1.53541	+	7.96646i	−0.199893	+	1.03714i	−0.933773	+	0.357865i	$0.883505\pi$
$60$	3.53031	+	1.88852i	0.455761	+	0.243807i
$61$	4.17225	−	10.4218i	0.534202	−	1.33437i	−0.378445	−	0.925624i	$-0.623541\pi$
$61$	4.17225	−	10.4218i	0.534202	−	1.33437i	0.912647	−	0.408749i	$-0.134035\pi$
$62$	−0.169371	+	0.146761i	−0.0215101	+	0.0186386i
$63$	−0.0279557	−	0.0465551i	−0.00352208	−	0.00586539i
$64$	24.5114	−	7.19719i	3.06392	−	0.899648i
$65$	1.04865	+	1.47263i	0.130069	+	0.182657i
$66$	12.1993	−	10.2500i	1.50163	−	1.26169i
$67$	5.96686	−	11.5741i	0.728968	−	1.41400i	−0.174198	−	0.984711i	$-0.555733\pi$
$67$	5.96686	−	11.5741i	0.728968	−	1.41400i	0.903167	−	0.429290i	$-0.141236\pi$
$68$	16.3157	+	28.2597i	1.97857	+	3.42699i
$69$	6.35310	+	5.35146i	0.764823	+	0.644240i
$70$	−0.0105917	+	0.0183454i	−0.00126595	+	0.00219269i
$71$	3.48365	+	5.42067i	0.413433	+	0.643315i	0.984048	−	0.177903i	$-0.0569314\pi$
$71$	3.48365	+	5.42067i	0.413433	+	0.643315i	−0.570615	+	0.821218i	$0.693295\pi$
$72$	24.0683	−	12.9361i	2.83647	−	1.52454i
$73$	2.29911	−	5.03436i	0.269091	−	0.589227i	−0.726055	−	0.687636i	$-0.758648\pi$
$73$	2.29911	−	5.03436i	0.269091	−	0.589227i	0.995146	+	0.0984098i	$0.0313756\pi$
$74$	−5.31845	+	21.9230i	−0.618257	+	2.54849i
$75$	1.84225	+	8.13179i	0.212725	+	0.938978i
$76$	−22.9436	−	7.94086i	−2.63181	−	0.910879i
$77$	0.0379484	+	0.0482553i	0.00432462	+	0.00549920i
$78$	19.6768	−	0.637532i	2.22796	−	0.0721863i
$79$	−10.0257	+	3.46994i	−1.12798	+	0.390399i	−0.826424	−	0.563048i	$-0.809629\pi$
$79$	−10.0257	+	3.46994i	−1.12798	+	0.390399i	−0.301560	+	0.953447i	$0.597507\pi$
$80$	−5.07778	−	3.26329i	−0.567713	−	0.364847i
$81$	6.87921	−	5.80315i	0.764356	−	0.644794i
$82$	6.43209	−	7.42303i	0.710306	−	0.819737i
$83$	2.44718	−	2.33338i	0.268612	−	0.256121i	−0.543786	−	0.839224i	$-0.683010\pi$
$83$	2.44718	−	2.33338i	0.268612	−	0.256121i	0.812399	+	0.583102i	$0.198161\pi$
$84$	0.0746928	+	0.150460i	0.00814965	+	0.0164165i
$85$	0.859410	−	2.48310i	0.0932162	−	0.269330i
$86$	0.874233	−	1.22769i	0.0942709	−	0.132385i
$87$	0.00976660	+	0.121839i	0.00104709	+	0.0130625i
$88$	−25.1621	+	17.9178i	−2.68228	+	1.91005i
$89$	0.962501	−	6.69434i	0.102025	−	0.709599i	−0.873035	−	0.487657i	$-0.837852\pi$
$89$	0.962501	−	6.69434i	0.102025	−	0.709599i	0.975060	−	0.221941i	$-0.0712394\pi$
$90$	−3.28127	−	1.24866i	−0.345876	−	0.131621i
$91$			0.0758502i			0.00795126i
$92$	−18.2667	−	18.0712i	−1.90444	−	1.88405i
$93$	0.0953463	−	0.106712i	0.00988695	−	0.0110655i
$94$	14.6749	+	7.56546i	1.51361	+	0.780318i
$95$	0.726615	+	1.81500i	0.0745491	+	0.186215i
$96$	−31.3028	+	13.7240i	−3.19483	+	1.40070i
$97$	4.13449	+	1.00302i	0.419793	+	0.101841i	0.440091	−	0.897953i	$-0.354946\pi$
$97$	4.13449	+	1.00302i	0.419793	+	0.101841i	−0.0202975	+	0.999794i	$0.506461\pi$
$98$	17.2710	−	7.88740i	1.74464	−	0.796748i
$99$	−6.89357	+	7.48302i	−0.692830	+	0.752072i
$100$	−3.67055	−	25.5292i	−0.367055	−	2.55292i
$101$	1.09415	+	1.14751i	0.108872	+	0.114182i	0.775915	−	0.630838i	$-0.217289\pi$
$101$	1.09415	+	1.14751i	0.108872	+	0.114182i	−0.667043	+	0.745019i	$0.732440\pi$
$102$	−17.3441	−	22.7588i	−1.71732	−	2.25346i
$103$	−9.67815	−	0.461027i	−0.953616	−	0.0454263i	−0.434997	−	0.900432i	$-0.643251\pi$
$103$	−9.67815	−	0.461027i	−0.953616	−	0.0454263i	−0.518619	+	0.855005i	$0.673554\pi$
$104$	−38.1229	−	1.81602i	−3.73826	−	0.178075i
$105$	0.00521769	−	0.0124796i	0.000509194	−	0.00121788i
$106$	18.6571	+	19.5670i	1.81214	+	1.90052i
$107$	1.97441	+	13.7323i	0.190873	+	1.32755i	0.829704	+	0.558204i	$0.188509\pi$
$107$	1.97441	+	13.7323i	0.190873	+	1.32755i	−0.638831	+	0.769347i	$0.720582\pi$
$108$	−22.6460	+	16.1933i	−2.17911	+	1.55821i
$109$	0.797258	−	0.364095i	0.0763635	−	0.0348740i	−0.376867	−	0.926267i	$-0.622999\pi$
$109$	0.797258	−	0.364095i	0.0763635	−	0.0348740i	0.453231	+	0.891393i	$0.350271\pi$
$110$	3.85704	+	0.935708i	0.367754	+	0.0892163i
$111$	1.58720	−	14.3170i	0.150651	−	1.35891i
$112$	−0.0941218	−	0.235105i	−0.00889368	−	0.0222153i
$113$	−9.52551	−	4.91074i	−0.896085	−	0.461964i	−0.0522912	−	0.998632i	$-0.516652\pi$
$113$	−9.52551	−	4.91074i	−0.896085	−	0.461964i	−0.843793	+	0.536668i	$0.819683\pi$
$114$	20.8416	+	4.34669i	1.95200	+	0.407104i
$115$	−0.136501	+	2.06457i	−0.0127288	+	0.192522i
$116$		−	0.378098i		−	0.0351055i
$117$	−12.4105	+	2.00251i	−1.14735	+	0.185132i
$118$	−3.13191	+	21.7829i	−0.288316	+	2.00528i
$119$	0.0898027	−	0.0639482i	0.00823220	−	0.00586212i
$120$	6.14741	+	2.92124i	0.561179	+	0.266671i
$121$	0.291117	−	0.408817i	0.0264652	−	0.0371652i
$122$	9.95942	−	28.7759i	0.901684	−	2.60524i
$123$	−3.47063	+	5.22396i	−0.312936	+	0.471028i
$124$	−0.320370	+	0.305473i	−0.0287701	+	0.0274323i
$125$	−2.77270	+	3.19986i	−0.247998	+	0.286205i
$126$	−0.0817534	−	0.122531i	−0.00728317	−	0.0109159i
$127$	3.08082	+	1.97992i	0.273378	+	0.175690i	0.670146	−	0.742230i	$-0.266232\pi$
$127$	3.08082	+	1.97992i	0.273378	+	0.175690i	−0.396767	+	0.917919i	$0.629868\pi$
$128$	28.1876	−	9.75581i	2.49145	−	0.862300i
$129$	−0.453944	+	0.848584i	−0.0399676	+	0.0747136i
$130$	3.03135	+	3.85467i	0.265867	+	0.338077i
$131$	−5.99311	−	2.07424i	−0.523621	−	0.181227i	0.0524549	−	0.998623i	$-0.483295\pi$
$131$	−5.99311	−	2.07424i	−0.523621	−	0.181227i	−0.576076	+	0.817396i	$0.695417\pi$
$132$	23.1055	−	21.3696i	2.01107	−	1.85998i
$133$	−0.0193383	+	0.0797137i	−0.00167685	+	0.00691205i
$134$	14.6731	−	32.1296i	1.26756	−	2.77558i
$135$	2.17964	+	0.524237i	0.187593	+	0.0451191i
$136$	29.9908	+	46.6666i	2.57169	+	4.00163i
$137$	−3.54890	+	6.14687i	−0.303203	+	0.525163i	−0.976860	−	0.213882i	$-0.931389\pi$
$137$	−3.54890	+	6.14687i	−0.303203	+	0.525163i	0.673657	+	0.739044i	$0.264723\pi$
$138$	17.9041	+	13.6796i	1.52410	+	1.16448i
$139$	−9.32203	−	16.1462i	−0.790684	−	1.36950i	−0.925544	−	0.378640i	$-0.876392\pi$
$139$	−9.32203	−	16.1462i	−0.790684	−	1.36950i	0.134860	−	0.990865i	$-0.456942\pi$
$140$	−0.0191730	+	0.0371904i	−0.00162041	+	0.00314316i
$141$	−9.90903	−	3.59924i	−0.834490	−	0.303110i
$142$	10.1384	+	14.2374i	0.850798	+	1.19478i
$143$	13.6356	−	4.00377i	1.14027	−	0.334812i
$144$	35.9825	−	21.6070i	2.99854	−	1.80058i
$145$	−0.0230096	+	0.0199379i	−0.00191084	+	0.00165575i
$146$	5.57957	−	13.9371i	0.461769	−	1.15344i
$147$	−10.2977	+	6.39872i	−0.849340	+	0.527758i
$148$	−8.43274	+	43.7532i	−0.693167	+	3.59649i
$149$	0.817132	−	17.1537i	0.0669421	−	1.40529i	−0.676478	−	0.736463i	$-0.736495\pi$
$149$	0.817132	−	17.1537i	0.0669421	−	1.40529i	0.743420	−	0.668825i	$-0.233202\pi$
$150$	6.04104	+	21.7950i	0.493249	+	1.77955i
$151$	−2.07407	−	5.99264i	−0.168786	−	0.487674i	0.828608	−	0.559830i	$-0.189133\pi$
$151$	−2.07407	−	5.99264i	−0.168786	−	0.487674i	−0.997393	+	0.0721555i	$0.977012\pi$
$152$	−39.6017	−	11.6281i	−3.21212	−	0.943165i
$153$	12.8339	+	13.0051i	1.03756	+	1.05140i
$154$	0.109048	+	0.125848i	0.00878731	+	0.0101411i
$155$	0.0354837	+	0.00338828i	0.00285012	+	0.000272153i
$156$	38.7619	−	3.10714i	3.10343	−	0.248770i
$157$	0.690350	+	7.22967i	0.0550959	+	0.576991i	0.980299	+	0.197519i	$0.0632883\pi$
$157$	0.690350	+	7.22967i	0.0550959	+	0.576991i	−0.925203	+	0.379472i	$0.876106\pi$
$158$	−26.7165	+	10.6957i	−2.12545	+	0.850901i
$159$	−13.4062	−	10.8768i	−1.06318	−	0.862590i
$160$	−7.37300	−	4.25680i	−0.582887	−	0.336530i
$161$	−0.0549105	+	0.0672377i	−0.00432755	+	0.00529908i
$162$	17.8899	−	16.6113i	1.40556	−	1.30510i
$163$	−3.42857	+	2.20341i	−0.268547	+	0.172584i	−0.667983	−	0.744176i	$-0.732842\pi$
$163$	−3.42857	+	2.20341i	−0.268547	+	0.172584i	0.399437	+	0.916761i	$0.369206\pi$
$164$	11.9927	−	15.2499i	0.936472	−	1.19082i
$165$	−2.51887	−	0.279246i	−0.196094	−	0.0217393i
$166$	6.32935	−	6.63803i	0.491253	−	0.515211i
$167$	9.80197	+	6.97995i	0.758499	+	0.540125i	0.892604	−	0.450842i	$-0.148876\pi$
$167$	9.80197	+	6.97995i	0.758499	+	0.540125i	−0.134104	+	0.990967i	$0.542816\pi$
$168$	0.139003	+	0.249447i	0.0107243	+	0.0192452i
$169$	4.23227	+	1.69435i	0.325560	+	0.130334i
$170$	2.00805	−	6.83878i	0.154010	−	0.524511i
$171$	−13.5531	−	1.05960i	−1.03644	−	0.0810293i
$172$	1.60945	−	2.50436i	0.122720	−	0.190955i
$173$	7.03457	+	13.6452i	0.534828	+	1.03742i	0.989195	+	0.146607i	$0.0468353\pi$
$173$	7.03457	+	13.6452i	0.534828	+	1.03742i	−0.454367	+	0.890815i	$0.650134\pi$
$174$	0.0421876	+	0.328857i	0.00319823	+	0.0249306i
$175$	−0.0846808	+	0.0205433i	−0.00640126	+	0.00155293i
$176$	−37.2966	+	29.3304i	−2.81134	+	2.21086i
$177$	0.213742	−	14.0506i	0.0160658	−	1.05611i
$178$	1.74383	−	18.2622i	0.130706	−	1.36881i
$179$	1.28680	+	4.38243i	0.0961798	+	0.327558i	0.993502	−	0.113819i	$-0.0363083\pi$
$179$	1.28680	+	4.38243i	0.0961798	+	0.327558i	−0.897322	+	0.441377i	$0.854490\pi$
$180$	−6.59120	−	2.15519i	−0.491279	−	0.160638i
$181$	6.66775	+	0.958678i	0.495610	+	0.0712580i	0.385588	−	0.922671i	$-0.373999\pi$
$181$	6.66775	+	0.958678i	0.495610	+	0.0712580i	0.110022	+	0.993929i	$0.464908\pi$
$182$	0.00978977	+	0.205513i	0.000725666	+	0.0152336i
$183$	−3.96976	+	19.0343i	−0.293453	+	1.40706i
$184$	−32.4795	−	29.2083i	−2.39442	−	2.15326i
$185$	3.10733	−	1.79402i	0.228455	−	0.131899i
$186$	0.244564	−	0.301437i	0.0179323	−	0.0221024i
$187$	−16.2362	−	12.7683i	−1.18731	−	0.933712i
$188$	29.6643	+	13.5472i	2.16349	+	0.988033i
$189$	0.0617338	+	0.0709622i	0.00449048	+	0.00516174i
$190$	2.20299	+	4.82387i	0.159822	+	0.349960i
$191$	−22.3907	+	4.31545i	−1.62013	+	0.312255i	−0.917025	−	0.398829i	$-0.869417\pi$
$191$	−22.3907	+	4.31545i	−1.62013	+	0.312255i	−0.703107	+	0.711084i	$0.748205\pi$
$192$	−39.6324	+	19.6747i	−2.86022	+	1.41990i
$193$	5.74423	+	23.6780i	0.413479	+	1.70438i	0.673845	+	0.738872i	$0.264641\pi$
$193$	5.74423	+	23.6780i	0.413479	+	1.70438i	−0.260367	+	0.965510i	$0.583843\pi$
$194$	11.3317	+	2.18400i	0.813566	+	0.156802i
$195$	−2.23308	−	2.19505i	−0.159915	−	0.157191i
$196$	33.3339	−	17.1848i	2.38099	−	1.22749i
$197$	−10.2133	−	8.84991i	−0.727671	−	0.630530i	0.210143	−	0.977671i	$-0.432607\pi$
$197$	−10.2133	−	8.84991i	−0.727671	−	0.630530i	−0.937813	+	0.347141i	$0.887153\pi$
$198$	−17.7120	+	21.1646i	−1.25874	+	1.50411i
$199$	5.81617	−	0.836239i	0.412297	−	0.0592794i	0.0669545	−	0.997756i	$-0.478672\pi$
$199$	5.81617	−	0.836239i	0.412297	−	0.0592794i	0.345343	+	0.938477i	$0.387763\pi$
$200$	−8.29780	−	43.0531i	−0.586743	−	3.04431i
$201$	−6.68266	+	21.5414i	−0.471359	+	1.51941i
$202$	3.11266	+	2.96791i	0.219006	+	0.208821i
$203$	−0.00127161		0.000121424i	−8.92497e−5		8.52232e-6i
$204$	−36.3583	−	43.2725i	−2.54559	−	3.02968i
$205$	−1.56045	+	0.0743335i	−0.108987	+	0.00519168i
$206$	−26.2820			−1.83115
$207$	−12.4510	−	7.20922i	−0.865404	−	0.501075i
$208$	−58.6247			−4.06489
$209$	15.3509	−	0.731254i	1.06185	−	0.0505819i
$210$	0.0125264	−	0.0344863i	0.000864403	−	0.00237978i
$211$	22.2843	−	2.12789i	1.53412	−	0.146490i	0.706471	−	0.707742i	$-0.250286\pi$
$211$	22.2843	−	2.12789i	1.53412	−	0.146490i	0.827645	+	0.561252i	$0.189680\pi$
$212$	38.6490	+	36.8517i	2.65442	+	2.53099i
$213$	−7.57792	−	8.19350i	−0.519231	−	0.561409i
$214$	7.12195	+	36.9522i	0.486847	+	2.52600i
$215$	−0.237275	+	0.0341150i	−0.0161820	+	0.00232663i
$216$	−37.1442	+	29.3289i	−2.52734	+	1.99558i
$217$	0.00113025		0.000979364i	7.67261e−5		6.64835e-5i
$218$	2.11314	−	1.08940i	0.143120	−	0.0737835i
$219$	−2.40143	+	9.28036i	−0.162274	+	0.627109i
$220$	7.69777	+	1.48362i	0.518984	+	0.100026i
$221$	−6.01679	−	24.8016i	−0.404733	−	1.66833i
$222$	2.45260	−	38.9960i	0.164608	−	2.61724i
$223$	−5.81556	+	1.12086i	−0.389439	+	0.0750581i	−0.380212	−	0.924899i	$-0.624149\pi$
$223$	−5.81556	+	1.12086i	−0.389439	+	0.0750581i	−0.00922642	+	0.999957i	$0.502937\pi$
$224$	−0.148385	−	0.324918i	−0.00991441	−	0.0217095i
$225$	−5.59690	−	13.3129i	−0.373127	−	0.887529i
$226$	−26.4428	−	12.0760i	−1.75895	−	0.803284i
$227$	−12.4245	−	9.77075i	−0.824644	−	0.648507i	0.113967	−	0.993485i	$-0.463644\pi$
$227$	−12.4245	−	9.77075i	−0.824644	−	0.648507i	−0.938611	+	0.344977i	$0.887887\pi$
$228$	41.5284	+	6.61710i	2.75029	+	0.438228i
$229$	−20.7134	+	11.9589i	−1.36878	+	0.790265i	−0.990772	−	0.135538i	$-0.956724\pi$
$229$	−20.7134	+	11.9589i	−1.36878	+	0.790265i	−0.378007	+	0.925803i	$0.623391\pi$
$230$	−0.103374	+	5.61149i	−0.00681629	+	0.370011i
$231$	−0.0792900	−	0.0708452i	−0.00521690	−	0.00466127i
$232$	−0.0305836	−	0.642030i	−0.00200791	−	0.0421513i
$233$	−11.3323	−	1.62934i	−0.742405	−	0.106742i	−0.239274	−	0.970952i	$-0.576910\pi$
$233$	−11.3323	−	1.62934i	−0.742405	−	0.106742i	−0.503131	+	0.864210i	$0.667819\pi$
$234$	−33.3671	+	7.02748i	−2.18128	+	0.459401i
$235$	−0.739829	−	2.51963i	−0.0482611	−	0.164362i
$236$	−4.13192	+	43.2715i	−0.268965	+	2.81673i
$237$	16.0518	−	8.94476i	1.04268	−	0.581024i
$238$	0.235063	−	0.184855i	0.0152369	−	0.0119824i
$239$	−2.01695	+	0.489306i	−0.130466	+	0.0316506i	−0.300460	−	0.953794i	$-0.597140\pi$
$239$	−2.01695	+	0.489306i	−0.130466	+	0.0316506i	0.169994	+	0.985445i	$0.445625\pi$
$240$	9.64549	+	4.03276i	0.622614	+	0.260314i
$241$	−3.36010	−	6.51768i	−0.216443	−	0.419841i	0.755469	−	0.655184i	$-0.227409\pi$
$241$	−3.36010	−	6.51768i	−0.216443	−	0.419841i	−0.971912	+	0.235343i	$0.924379\pi$
$242$	0.736004	−	1.14525i	0.0473122	−	0.0736191i
$243$	−9.98087	+	11.9742i	−0.640273	+	0.768147i
$244$	16.9452	−	57.7100i	1.08480	−	3.69450i
$245$	−2.80357	−	1.12238i	−0.179114	−	0.0717062i
$246$	−8.72928	+	14.6020i	−0.556559	+	0.930991i
$247$	15.4676	+	11.0144i	0.984177	+	0.700829i
$248$	−0.519296	+	0.544622i	−0.0329754	+	0.0345836i
$249$	−3.46934	+	4.71843i	−0.219861	+	0.299019i
$250$	−7.09951	+	9.02776i	−0.449012	+	0.570965i
$251$	20.0948	−	12.9142i	1.26837	−	0.815134i	0.278966	−	0.960301i	$-0.410008\pi$
$251$	20.0948	−	12.9142i	1.26837	−	0.815134i	0.989407	+	0.145167i	$0.0463719\pi$
$252$	−0.172813	−	0.234066i	−0.0108862	−	0.0147448i
$253$	14.9858	+	6.32210i	0.942149	+	0.397467i
$254$	8.60288	+	4.96688i	0.539793	+	0.311650i
$255$	−0.716145	+	4.49447i	−0.0448468	+	0.281455i
$256$	27.6813	−	11.0819i	1.73008	−	0.692620i
$257$	0.391408	+	4.09901i	0.0244153	+	0.255689i	0.999436	+	0.0335756i	$0.0106895\pi$
$257$	0.391408	+	4.09901i	0.0244153	+	0.255689i	−0.975021	+	0.222113i	$0.928704\pi$
$258$	−1.12042	+	2.35779i	−0.0697541	+	0.146790i
$259$	0.149858	+	0.0143097i	0.00931173	+	0.000889163i
$260$	6.34304	+	7.32026i	0.393379	+	0.453983i
$261$	−0.0534388	−	0.204853i	−0.00330778	−	0.0126801i
$262$	−16.5058	−	4.84654i	−1.01973	−	0.299420i
$263$	2.38979	+	6.90485i	0.147361	+	0.425771i	0.994390	−	0.105775i	$-0.0337324\pi$
$263$	2.38979	+	6.90485i	0.147361	+	0.425771i	−0.847029	+	0.531546i	$0.821611\pi$
$264$	37.5057	−	38.1556i	2.30832	−	2.34832i
$265$	0.204610	−	4.29530i	0.0125691	−	0.263858i
$266$	−0.0421079	+	0.218477i	−0.00258180	+	0.0133957i
$267$	0.379342	+	11.7080i	0.0232153	+	0.716520i
$268$	25.9299	−	64.7699i	1.58392	−	3.95645i
$269$	4.95781	−	4.29596i	0.302283	−	0.261930i	−0.490490	−	0.871447i	$-0.663182\pi$
$269$	4.95781	−	4.29596i	0.302283	−	0.261930i	0.792773	+	0.609517i	$0.208637\pi$
$270$	5.97329	+	1.13908i	0.363523	+	0.0693220i
$271$	13.6516	−	4.00847i	0.829276	−	0.243497i	0.160570	−	0.987024i	$-0.448667\pi$
$271$	13.6516	−	4.00847i	0.829276	−	0.243497i	0.668706	+	0.743527i	$0.266849\pi$
$272$	49.4257	+	69.4087i	2.99687	+	4.20852i
$273$	−0.0228981	−	0.129365i	−0.00138585	−	0.00782955i
$274$	−8.82223	+	17.1127i	−0.532970	+	1.03382i
$275$	8.16297	+	14.1387i	0.492246	+	0.852595i
$276$	36.6100	+	25.3067i	2.20366	+	1.52328i
$277$	−6.97117	+	12.0744i	−0.418857	+	0.725482i	−0.995825	−	0.0912853i	$-0.970902\pi$
$277$	−6.97117	+	12.0744i	−0.418857	+	0.725482i	0.576968	+	0.816767i	$0.304236\pi$
$278$	−27.3416	−	42.5443i	−1.63984	−	2.55164i
$279$	−0.130402	+	0.210785i	−0.00780698	+	0.0126193i
$280$	−0.0295484	+	0.0647021i	−0.00176586	+	0.00386669i
$281$	4.52905	−	18.6690i	0.270181	−	1.11370i	−0.661362	−	0.750067i	$-0.730021\pi$
$281$	4.52905	−	18.6690i	0.270181	−	1.11370i	0.931542	−	0.363633i	$-0.118464\pi$
$282$	−27.3126	−	8.47304i	−1.62644	−	0.504562i
$283$	2.05308	+	0.710578i	0.122043	+	0.0422395i	0.387407	−	0.921909i	$-0.373371\pi$
$283$	2.05308	+	0.710578i	0.122043	+	0.0422395i	−0.265364	+	0.964148i	$0.585492\pi$
$284$	21.3409	+	27.1372i	1.26635	+	1.61030i
$285$	−1.78719	−	2.87619i	−0.105864	−	0.170371i
$286$	36.4283	−	12.6079i	2.15405	−	0.745524i
$287$	−0.0551397	−	0.0354362i	−0.00325480	−	0.00209173i
$288$	49.2450	−	32.8566i	2.90179	−	1.93610i
$289$	−13.1585	+	15.1857i	−0.774027	+	0.893275i
$290$	−0.0597701	+	0.0569907i	−0.00350982	+	0.00334661i
$291$	−7.35433	−	0.462541i	−0.431118	−	0.0271146i
$292$	9.69847	−	28.0219i	0.567560	−	1.63986i
$293$	0.109504	−	0.153776i	0.00639727	−	0.00898370i	−0.811365	−	0.584540i	$-0.801275\pi$
$293$	0.109504	−	0.153776i	0.00639727	−	0.00898370i	0.817762	+	0.575556i	$0.195214\pi$
$294$	−27.0753	+	18.6661i	−1.57906	+	1.08863i
$295$	2.85122	−	2.03034i	0.166004	−	0.118211i
$296$	−10.7801	+	74.9773i	−0.626581	+	4.35797i
$297$	9.49824	−	14.8437i	0.551144	−	0.861316i
$298$		−	46.5827i		−	2.69846i
$299$	9.72579	+	17.5859i	0.562457	+	1.01702i
$300$	13.9672	+	42.4331i	0.806396	+	2.44987i
$301$	−0.00893948	−	0.00460862i	−0.000515263	−	0.000265637i
$302$	−6.39306	−	15.9691i	−0.367879	−	0.918918i
$303$	−2.21253	−	1.62682i	−0.127107	−	0.0934582i
$304$	−61.6109	−	14.9466i	−3.53363	−	0.857248i
$305$	−4.40556	+	2.01195i	−0.252262	+	0.115204i
$306$	36.4515	+	33.5802i	2.08380	+	1.91965i
$307$	−1.36305	−	9.48019i	−0.0777931	−	0.541063i	−0.991031	−	0.133635i	$-0.957335\pi$
$307$	−1.36305	−	9.48019i	−0.0777931	−	0.541063i	0.913237	−	0.407428i	$-0.133574\pi$
$308$	0.226976	+	0.238045i	0.0129331	+	0.0135639i
$309$	16.6456	−	2.13539i	0.946937	−	0.121478i
$310$	0.0965788	+	0.00460062i	0.00548531	+	0.000261297i
$311$	−17.1358	−	0.816278i	−0.971681	−	0.0462869i	−0.444266	−	0.895895i	$-0.646536\pi$
$311$	−17.1358	−	0.816278i	−0.971681	−	0.0462869i	−0.527415	+	0.849608i	$0.676839\pi$
$312$	65.5683	−	8.41146i	3.71208	−	0.476205i
$313$	−9.57423	−	10.0412i	−0.541168	−	0.567560i	0.395194	−	0.918598i	$-0.370677\pi$
$313$	−9.57423	−	10.0412i	−0.541168	−	0.567560i	−0.936361	+	0.351038i	$0.885829\pi$
$314$	2.80359	+	19.4994i	0.158216	+	1.10041i
$315$	−0.00513157	+	0.0228596i	−0.000289131	+	0.00128799i
$316$	−51.7056	+	23.6131i	−2.90867	+	1.32834i
$317$	−24.2602	−	5.88547i	−1.36259	−	0.330561i	−0.513175	−	0.858284i	$-0.671531\pi$
$317$	−24.2602	−	5.88547i	−1.36259	−	0.330561i	−0.849416	+	0.527723i	$0.823046\pi$
$318$	−37.7275	−	27.7400i	−2.11565	−	1.55558i
$319$	0.0889509	+	0.222189i	0.00498029	+	0.0124402i
$320$	−9.79627	−	5.05033i	−0.547628	−	0.282322i
$321$	−7.51301	−	22.8249i	−0.419335	−	1.27396i
$322$	−0.140099	+	0.189265i	−0.00780743	+	0.0105473i
$323$		−	27.5989i		−	1.53564i
$324$	33.7351	−	34.4549i	1.87417	−	1.91416i
$325$	−2.87073	+	19.9663i	−0.159239	+	1.10753i
$326$	−9.00518	+	6.41256i	−0.498751	+	0.355159i
$327$	−1.24984	+	0.861660i	−0.0691163	+	0.0476499i
$328$	19.1307	−	26.8652i	1.05631	−	1.48339i
$329$	0.0360353	−	0.104117i	0.00198669	−	0.00574016i
$330$	−6.86081	−	0.431502i	−0.377675	−	0.0237534i
$331$	−13.8020	+	13.1602i	−0.758627	+	0.723350i	−0.967021	−	0.254695i	$-0.918025\pi$
$331$	−13.8020	+	13.1602i	−0.758627	+	0.723350i	0.208394	+	0.978045i	$0.433176\pi$
$332$	11.8638	−	13.6915i	0.651108	−	0.751419i
$333$	1.61505	+	24.8973i	0.0885041	+	1.36436i
$334$	27.4589	+	17.6468i	1.50248	+	0.965588i
$335$	−5.30898	+	1.83746i	−0.290061	+	0.100391i
$336$	0.231503	+	0.372567i	0.0126295	+	0.0203252i
$337$	5.12699	+	6.51950i	0.279285	+	0.355140i	0.905376	−	0.424610i	$-0.139589\pi$
$337$	5.12699	+	6.51950i	0.279285	+	0.355140i	−0.626091	+	0.779750i	$0.715346\pi$
$338$	11.6858	+	4.04451i	0.635626	+	0.219992i
$339$	17.7286	+	5.49985i	0.962886	+	0.298711i
$340$	3.31908	−	13.6814i	0.180002	−	0.741980i
$341$	0.116400	−	0.254880i	0.00630341	−	0.0138025i
$342$	−36.8584	−	1.12166i	−1.99308	−	0.0606523i
$343$	−0.137005	−	0.213183i	−0.00739756	−	0.0115108i
$344$	2.53036	−	4.38271i	0.136428	−	0.236300i
$345$	−0.390457	−	3.56242i	−0.0210215	−	0.191794i
$346$	20.8210	+	36.0630i	1.11934	+	1.93876i
$347$	9.11747	−	17.6854i	0.489452	−	0.949404i	−0.506730	−	0.862105i	$-0.669146\pi$
$347$	9.11747	−	17.6854i	0.489452	−	0.949404i	0.996182	−	0.0872992i	$-0.0278236\pi$
$348$	0.114142	+	0.644861i	0.00611867	+	0.0345682i
$349$	4.45894	+	6.26170i	0.238681	+	0.335181i	0.916490	−	0.400057i	$-0.131010\pi$
$349$	4.45894	+	6.26170i	0.238681	+	0.335181i	−0.677809	+	0.735238i	$0.737070\pi$
$350$	−0.226787	+	0.0665908i	−0.0121223	+	0.00355943i
$351$	20.5620	−	7.16189i	1.09752	−	0.382273i
$352$	−50.5781	+	43.8261i	−2.69582	+	2.33594i
$353$	−5.68414	+	14.1983i	−0.302536	+	0.755699i	0.696728	+	0.717336i	$0.254639\pi$
$353$	−5.68414	+	14.1983i	−0.302536	+	0.755699i	−0.999264	+	0.0383632i	$0.987786\pi$
$354$	−1.23435	−	38.0971i	−0.0656051	−	2.02484i
$355$	0.526112	−	2.72973i	0.0279231	−	0.144879i
$356$	1.72417	−	36.1948i	0.0913808	−	1.91832i
$357$	−0.133857	+	0.136176i	−0.00708446	+	0.00720722i
$358$	4.05215	+	11.7079i	0.214163	+	0.618783i
$359$	16.5204	+	4.85083i	0.871914	+	0.256017i	0.686929	−	0.726724i	$-0.258958\pi$
$359$	16.5204	+	4.85083i	0.871914	+	0.256017i	0.184985	+	0.982741i	$0.440776\pi$
$360$	−11.3665	−	3.12647i	−0.599069	−	0.164780i
$361$	1.00489	+	1.15971i	0.0528891	+	0.0610372i
$362$	18.1897	+	1.73691i	0.956030	+	0.0912898i
$363$	−0.373096	+	0.785138i	−0.0195825	+	0.0412090i
$364$	0.0386299	+	0.404550i	0.00202476	+	0.0212042i
$365$	−2.21672	+	0.887443i	−0.116029	+	0.0464509i
$366$	−8.29917	+	52.0850i	−0.433805	+	2.72253i
$367$	21.7504	+	12.5576i	1.13536	+	0.655502i	0.945278	−	0.326265i	$-0.105790\pi$
$367$	21.7504	+	12.5576i	1.13536	+	0.655502i	0.190085	+	0.981768i	$0.439124\pi$
$368$	−51.9682	−	42.4404i	−2.70903	−	2.21236i
$369$	4.34226	−	9.95740i	0.226049	−	0.518362i
$370$	8.18762	−	5.26186i	0.425654	−	0.273551i
$371$	0.111527	−	0.141818i	0.00579020	−	0.00736284i
$372$	0.454187	−	0.617711i	0.0235485	−	0.0320268i
$373$	13.0447	−	13.6809i	0.675428	−	0.708369i	−0.293431	−	0.955980i	$-0.594797\pi$
$373$	13.0447	−	13.6809i	0.675428	−	0.708369i	0.968859	+	0.247612i	$0.0796457\pi$
$374$	−45.6393	−	32.4996i	−2.35995	−	1.68052i
$375$	3.76295	−	6.29453i	0.194318	−	0.325048i
$376$	51.4673	+	20.6044i	2.65422	+	1.06259i
$377$	−0.0833109	+	0.283731i	−0.00429073	+	0.0146129i
$378$	0.176424	+	0.184301i	0.00907427	+	0.00947942i
$379$	6.37326	−	9.91698i	0.327372	−	0.509401i	−0.638084	−	0.769967i	$-0.720273\pi$
$379$	6.37326	−	9.91698i	0.327372	−	0.509401i	0.965456	+	0.260566i	$0.0839091\pi$
$380$	4.79980	+	9.31031i	0.246225	+	0.477609i
$381$	−5.85217	−	2.44678i	−0.299816	−	0.125352i
$382$	−60.1096	+	14.5824i	−3.07547	+	0.746102i
$383$	21.3754	−	16.8098i	1.09223	−	0.858941i	0.101509	−	0.994835i	$-0.467633\pi$
$383$	21.3754	−	16.8098i	1.09223	−	0.858941i	0.990724	+	0.135893i	$0.0433904\pi$
$384$	−45.1299	+	25.1483i	−2.30302	+	1.28335i
$385$	0.00251760	−	0.0263655i	0.000128309	−	0.00134371i
$386$	18.6198	+	63.4132i	0.947723	+	3.22765i
$387$	0.518045	−	1.58433i	0.0263337	−	0.0805361i
$388$	22.5623	+	3.24397i	1.14543	+	0.164688i
$389$	0.426210	+	8.94724i	0.0216097	+	0.453643i	0.983578	+	0.180483i	$0.0577660\pi$
$389$	0.426210	+	8.94724i	0.0216097	+	0.453643i	−0.961968	+	0.273161i	$0.911931\pi$
$390$	−6.33375	−	5.65918i	−0.320722	−	0.286564i
$391$	12.6211	−	26.3412i	0.638275	−	1.33213i
$392$	55.2126	−	31.8770i	2.78866	−	1.61003i
$393$	10.8477	+	1.72846i	0.547193	+	0.0871892i
$394$	−28.8148	−	22.6602i	−1.45167	−	1.14161i
$395$	4.16355	+	1.90143i	0.209491	+	0.0956713i
$396$	−32.9561	+	43.4219i	−1.65611	+	2.18203i
$397$	7.99021	+	17.4961i	0.401017	+	0.878105i	0.997166	+	0.0752313i	$0.0239695\pi$
$397$	7.99021	+	17.4961i	0.401017	+	0.878105i	−0.596149	+	0.802874i	$0.703303\pi$
$398$	15.6507	−	3.01643i	0.784500	−	0.151200i
$399$	0.00891787	−	0.141793i	0.000446452	−	0.00709852i
$400$	−15.8780	−	65.4499i	−0.793899	−	3.27250i
$401$	−11.4954	−	2.21555i	−0.574052	−	0.110639i	−0.106040	−	0.994362i	$-0.533817\pi$
$401$	−11.4954	−	2.21555i	−0.574052	−	0.110639i	−0.468011	+	0.883722i	$0.655029\pi$
$402$	−15.3261	+	59.2279i	−0.764396	+	2.95402i
$403$	0.307720	−	0.158641i	0.0153286	−	0.00790245i
$404$	6.42012	+	5.56306i	0.319413	+	0.276773i
$405$	−3.87571	−	0.236106i	−0.192586	−	0.0117322i
$406$	−0.00342971		0.000493117i	−0.000170213		2.44730e-5i
$407$	−5.33784	−	27.6954i	−0.264587	−	1.37281i
$408$	−65.2385	−	70.5379i	−3.22979	−	3.49215i
$409$	0.138599	+	0.132154i	0.00685329	+	0.00653460i	0.693498	−	0.720459i	$-0.256069\pi$
$409$	0.138599	+	0.132154i	0.00685329	+	0.00653460i	−0.686645	+	0.726993i	$0.740917\pi$
$410$	−4.21838	+	0.402807i	−0.208331	+	0.0198932i
$411$	4.19714	−	11.5551i	0.207029	−	0.569971i
$412$	−51.8537	+	2.47009i	−2.55465	+	0.121693i
$413$	0.146857			0.00722635
$414$	−34.6659	−	17.9260i	−1.70374	−	0.881017i
$415$	−1.45881			−0.0716103
$416$	−82.5953	+	3.93450i	−4.04957	+	0.192905i
$417$	20.7734	+	24.7238i	1.01728	+	1.21073i
$418$	41.4983	−	3.96260i	2.02975	−	0.193817i
$419$	17.7445	+	16.9194i	0.866876	+	0.826565i	0.986074	−	0.166306i	$-0.0531838\pi$
$419$	17.7445	+	16.9194i	0.866876	+	0.826565i	−0.119198	+	0.992871i	$0.538032\pi$
$420$	0.0214730	−	0.0692177i	0.00104778	−	0.00337748i
$421$	−0.196429	−	1.01917i	−0.00957336	−	0.0496713i	0.976828	−	0.214026i	$-0.0686578\pi$
$421$	−0.196429	−	1.01917i	−0.00957336	−	0.0496713i	−0.986401	+	0.164355i	$0.947446\pi$
$422$	60.1037	−	8.64161i	2.92580	−	0.420667i
$423$	17.9868	+	3.14725i	0.874548	+	0.153024i
$424$	68.6088	+	59.4499i	3.33194	+	2.88714i
$425$	26.0594	−	13.4346i	1.26407	−	0.651672i
$426$	−21.5896	−	21.2219i	−1.04602	−	1.02820i
$427$	−0.199531	−	0.0384565i	−0.00965599	−	0.00186104i
$428$	17.5243	+	72.2363i	0.847071	+	3.49167i
$429$	−22.0474	+	10.9450i	−1.06446	+	0.528429i
$430$	−0.638484	+	0.123058i	−0.0307904	+	0.00593437i
$431$	−5.05894	−	11.0775i	−0.243680	−	0.533586i	0.747787	−	0.663938i	$-0.231116\pi$
$431$	−5.05894	−	11.0775i	−0.243680	−	0.533586i	−0.991468	+	0.130353i	$0.958389\pi$
$432$	−54.8468	+	47.7142i	−2.63882	+	2.29565i
$433$	8.54916	+	3.90427i	0.410846	+	0.187627i	0.610107	−	0.792319i	$-0.291127\pi$
$433$	8.54916	+	3.90427i	0.410846	+	0.187627i	−0.199260	+	0.979947i	$0.563854\pi$
$434$	0.00318875	+	0.00250766i	0.000153065	+	0.000120372i
$435$	0.0332248	−	0.0409512i	0.00159301	−	0.00196346i
$436$	4.06678	−	2.34796i	0.194764	−	0.112447i
$437$	5.73760	+	20.9612i	0.274466	+	1.00271i
$438$	−5.30877	+	25.4547i	−0.253663	+	1.21627i
$439$	0.919912	+	19.3113i	0.0439050	+	0.921679i	0.908159	+	0.418624i	$0.137488\pi$
$439$	0.919912	+	19.3113i	0.0439050	+	0.921679i	−0.864254	+	0.503055i	$0.832209\pi$
$440$	13.1912	+	1.89661i	0.628867	+	0.0904174i
$441$	15.6314	−	14.0220i	0.744355	−	0.667714i
$442$	−19.5033	−	66.4222i	−0.927678	−	3.15938i
$443$	−0.883272	+	9.25004i	−0.0419655	+	0.439483i	0.949933	+	0.312453i	$0.101151\pi$
$443$	−0.883272	+	9.25004i	−0.0419655	+	0.439483i	−0.991899	+	0.127030i	$0.959456\pi$
$444$	1.17391	−	77.1685i	0.0557112	−	3.66226i
$445$	−2.29359	+	1.80370i	−0.108727	+	0.0855037i
$446$	−15.6123	+	3.78751i	−0.739265	+	0.179344i
$447$	3.78481	+	29.5030i	0.179015	+	1.39545i
$448$	−0.211892	−	0.411013i	−0.0100110	−	0.0194186i
$449$	8.29060	−	12.9004i	0.391258	−	0.608809i	−0.588619	−	0.808410i	$-0.700328\pi$
$449$	8.29060	−	12.9004i	0.391258	−	0.608809i	0.979877	+	0.199601i	$0.0639647\pi$
$450$	−16.8828	−	35.3484i	−0.795864	−	1.66634i
$451$	−3.45980	+	11.7830i	−0.162915	+	0.554839i
$452$	−53.3058	−	21.3404i	−2.50729	−	1.00377i
$453$	5.34650	+	9.59455i	0.251201	+	0.450791i
$454$	−34.9248	−	24.8698i	−1.63910	−	1.16720i
$455$	0.0225823	−	0.0236837i	0.00105868	−	0.00111031i
$456$	71.0527	+	7.87702i	3.32735	+	0.368875i
$457$	13.1875	−	16.7693i	0.616885	−	0.784433i	−0.372767	−	0.927925i	$-0.621591\pi$
$457$	13.1875	−	16.7693i	0.616885	−	0.784433i	0.989651	+	0.143492i	$0.0458333\pi$
$458$	−54.5785	+	35.0755i	−2.55029	+	1.63897i
$459$	−25.8148	−	18.3063i	−1.20493	−	0.854463i
$460$	0.323437	+	11.0810i	0.0150803	+	0.516655i
$461$	−28.1270	−	16.2391i	−1.31001	−	0.756332i	−0.327909	−	0.944709i	$-0.606344\pi$
$461$	−28.1270	−	16.2391i	−1.31001	−	0.756332i	−0.982097	+	0.188377i	$0.939677\pi$
$462$	−0.223977	−	0.181718i	−0.0104203	−	0.00845430i
$463$	−15.2307	+	6.09747i	−0.707832	+	0.283373i	−0.697512	−	0.716573i	$-0.745709\pi$
$463$	−15.2307	+	6.09747i	−0.707832	+	0.283373i	−0.0103207	+	0.999947i	$0.503285\pi$
$464$	−0.0938491	−	0.982832i	−0.00435683	−	0.0456268i
$465$	−0.0615417	+	0.00493317i	−0.00285393	+	0.000228770i
$466$	−30.9147	−	2.95200i	−1.43210	−	0.136749i
$467$	1.83523	+	2.11797i	0.0849242	+	0.0980078i	0.796621	−	0.604479i	$-0.206619\pi$
$467$	1.83523	+	2.11797i	0.0849242	+	0.0980078i	−0.711697	+	0.702487i	$0.752073\pi$
$468$	−65.1719	+	17.0010i	−3.01257	+	0.785872i
$469$	−0.226160	−	0.0664066i	−0.0104431	−	0.00306637i
$470$	−2.32974	−	6.73133i	−0.107463	−	0.310493i
$471$	−3.35995	−	12.1221i	−0.154819	−	0.558556i
$472$	−3.51607	+	73.8114i	−0.161840	+	3.39744i
$473$	−0.356620	+	1.85032i	−0.0163974	+	0.0850777i
$474$	42.3371	−	26.3072i	1.94461	−	1.20833i
$475$	−8.10746	+	20.2515i	−0.371996	+	0.929201i
$476$	0.446399	−	0.386807i	0.0204606	−	0.0177293i
$477$	26.1485	+	14.5037i	1.19726	+	0.664081i
$478$	−5.40168	+	1.58608i	−0.247067	+	0.0725454i
$479$	−12.2254	−	17.1682i	−0.558593	−	0.784435i	0.434636	−	0.900606i	$-0.356877\pi$
$479$	−12.2254	−	17.1682i	−0.558593	−	0.784435i	−0.993229	+	0.116172i	$0.962938\pi$
$480$	13.8600	+	5.03434i	0.632620	+	0.229785i
$481$	15.9687	−	30.9750i	0.728112	−	1.41234i
$482$	−9.94526	−	17.2257i	−0.452994	−	0.784609i
$483$	0.0733539	−	0.131253i	0.00333772	−	0.00597223i
$484$	1.34448	−	2.32871i	0.0611128	−	0.105850i
$485$	−0.992343	−	1.54412i	−0.0450600	−	0.0701147i
$486$	−25.4972	+	33.7319i	−1.15658	+	1.53011i
$487$	3.79267	−	8.30479i	0.171862	−	0.376326i	−0.804027	−	0.594593i	$-0.797313\pi$
$487$	3.79267	−	8.30479i	0.171862	−	0.376326i	0.975889	+	0.218267i	$0.0700404\pi$
$488$	24.1057	−	99.3652i	1.09121	−	4.49805i
$489$	5.18239	−	4.79304i	0.234356	−	0.216749i
$490$	−7.74101	−	2.67919i	−0.349703	−	0.121033i
$491$	7.93135	+	10.0855i	0.357937	+	0.455154i	0.931357	−	0.364108i	$-0.118626\pi$
$491$	7.93135	+	10.0855i	0.357937	+	0.455154i	−0.573420	+	0.819262i	$0.694384\pi$
$492$	−15.8503	+	29.6298i	−0.714585	+	1.33581i
$493$	0.406161	−	0.140574i	0.0182926	−	0.00633112i
$494$	43.3302	+	27.8467i	1.94952	+	1.25288i
$495$	4.38034	−	0.284145i	0.196881	−	0.0127714i
$496$	−0.756952	+	0.873569i	−0.0339881	+	0.0392244i
$497$	0.0844138	−	0.0804884i	0.00378648	−	0.00361040i
$498$	−8.79103	+	13.2322i	−0.393936	+	0.592947i
$499$	−2.04825	+	5.91802i	−0.0916921	+	0.264927i	−0.981517	−	0.191375i	$-0.938705\pi$
$499$	−2.04825	+	5.91802i	−0.0916921	+	0.264927i	0.889825	+	0.456302i	$0.150826\pi$
$500$	−13.1587	+	18.4787i	−0.588473	+	0.826395i
$501$	−18.8248	−	8.94551i	−0.841030	−	0.399656i
$502$	52.7792	−	37.5839i	2.35565	−	1.67745i
$503$	−2.09184	+	14.5491i	−0.0932706	+	0.648711i	0.888533	+	0.458812i	$0.151725\pi$
$503$	−2.09184	+	14.5491i	−0.0932706	+	0.648711i	−0.981804	+	0.189899i	$0.939184\pi$
$504$	−0.312379	−	0.383478i	−0.0139145	−	0.0170815i
$505$		−	0.684056i		−	0.0304401i
$506$	41.4193	+	15.1953i	1.84131	+	0.675512i
$507$	−7.72981	−	1.61211i	−0.343293	−	0.0715965i
$508$	17.4400	+	8.99097i	0.773777	+	0.398910i
$509$	−1.14919	−	2.87054i	−0.0509371	−	0.127235i	0.900717	−	0.434406i	$-0.143042\pi$
$509$	−1.14919	−	2.87054i	−0.0509371	−	0.127235i	−0.951654	+	0.307171i	$0.900617\pi$
$510$	−1.36027	+	12.2700i	−0.0602340	+	0.543325i
$511$	−0.0973574	−	0.0236186i	−0.00430684	−	0.00104483i
$512$	19.3058	−	8.81666i	0.853203	−	0.389645i
$513$	23.4353	−	2.28432i	1.03469	−	0.100855i
$514$	1.58955	+	11.0556i	0.0701120	+	0.487640i
$515$	2.88467	+	3.02536i	0.127114	+	0.133313i
$516$	−1.98896	+	4.75715i	−0.0875589	+	0.209422i
$517$	−20.6193	−	0.982217i	−0.906834	−	0.0431978i
$518$	0.407881	+	0.0194298i	0.0179213	+	0.000853695i
$519$	−16.1170	−	21.1487i	−0.707458	−	0.928326i
$520$	11.3629	+	11.9171i	0.498297	+	0.522599i
$521$	0.784173	+	5.45404i	0.0343552	+	0.238946i	0.999762	−	0.0218014i	$-0.00694015\pi$
$521$	0.784173	+	5.45404i	0.0343552	+	0.238946i	−0.965407	+	0.260747i	$0.916031\pi$
$522$	−0.171230	−	0.548143i	−0.00749453	−	0.0239916i
$523$	14.2085	−	6.48880i	0.621293	−	0.283735i	−0.0797931	−	0.996811i	$-0.525426\pi$
$523$	14.2085	−	6.48880i	0.621293	−	0.283735i	0.701086	+	0.713076i	$0.252699\pi$
$524$	−33.0209	−	8.01080i	−1.44253	−	0.349953i
$525$	0.138225	−	0.0606014i	0.00603262	−	0.00264486i
$526$	7.36622	+	18.3999i	0.321183	+	0.802275i
$527$	−0.447257	−	0.230577i	−0.0194828	−	0.0100441i
$528$	54.7564	−	61.2834i	2.38297	−	2.66702i
$529$	−4.10952	+	22.6299i	−0.178675	+	0.983908i
$530$		−	11.6643i		−	0.506666i
$531$	3.87714	+	24.0284i	0.168253	+	1.04275i
$532$	−0.0625444	+	0.435006i	−0.00271164	+	0.0188599i
$533$	−12.3597	+	8.80132i	−0.535359	+	0.381227i
$534$	2.53893	+	31.6734i	0.109870	+	1.37064i
$535$	3.47193	−	4.87564i	0.150104	−	0.210792i
$536$	38.7913	−	112.080i	1.67553	−	4.84112i
$537$	−3.51768	−	7.08594i	−0.151799	−	0.305781i
$538$	12.8785	−	12.2796i	0.555231	−	0.529412i
$539$	−15.5457	+	17.9407i	−0.669602	+	0.772762i
$540$	11.8922	+	1.68597i	0.511758	+	0.0725527i
$541$	−5.56999	−	3.57961i	−0.239472	−	0.153900i	0.415400	−	0.909639i	$-0.363641\pi$
$541$	−5.56999	−	3.57961i	−0.239472	−	0.153900i	−0.654873	+	0.755739i	$0.727278\pi$
$542$	36.4711	−	12.6228i	1.56657	−	0.542194i
$543$	−11.6615	+	0.377835i	−0.500444	+	0.0162145i
$544$	74.2932	+	94.4715i	3.18530	+	4.05043i
$545$	−0.357338	−	0.123676i	−0.0153067	−	0.00529769i
$546$	−0.0787382	−	0.347555i	−0.00336968	−	0.0148740i
$547$	−0.0720489	+	0.296990i	−0.00308059	+	0.0126984i	−0.973331	−	0.229405i	$-0.926322\pi$
$547$	−0.0720489	+	0.296990i	−0.00308059	+	0.0126984i	0.970251	+	0.242103i	$0.0778372\pi$
$548$	−15.7977	+	34.5921i	−0.674843	+	1.47770i
$549$	1.02439	−	33.6622i	0.0437200	−	1.43667i
$550$	23.9421	+	37.2546i	1.02089	+	1.58854i
$551$	−0.159893	+	0.276943i	−0.00681167	+	0.0117982i
$552$	64.2127	+	40.0107i	2.73307	+	1.70297i
$553$	0.0960203	+	0.166312i	0.00408320	+	0.00707231i
$554$	−17.3297	+	33.6149i	−0.736267	+	1.42816i
$555$	−4.75808	+	3.99782i	−0.201969	+	0.169698i
$556$	−57.9426	−	81.3690i	−2.45731	−	3.45082i
$557$	−21.3007	+	6.25446i	−0.902541	+	0.265010i	−0.699898	−	0.714243i	$-0.746771\pi$
$557$	−21.3007	+	6.25446i	−0.902541	+	0.265010i	−0.202643	+	0.979253i	$0.564953\pi$
$558$	−0.326114	+	0.587942i	−0.0138055	+	0.0248896i
$559$	−1.75958	+	1.52468i	−0.0744221	+	0.0644871i
$560$	−0.0406073	+	0.101432i	−0.00171597	+	0.00428629i
$561$	31.5461	+	16.8754i	1.33188	+	0.712479i
$562$	9.86171	−	51.1674i	0.415991	−	2.15837i
$563$	−0.0900316	+	1.89000i	−0.00379438	+	0.0796539i	−0.999970	−	0.00771715i	$-0.997544\pi$
$563$	−0.0900316	+	1.89000i	−0.00379438	+	0.0796539i	0.996176	+	0.0873710i	$0.0278466\pi$
$564$	−54.6833	−	14.1501i	−2.30258	−	0.595827i
$565$	1.51223	+	4.36931i	0.0636201	+	0.183818i
$566$	5.65444	+	1.66029i	0.237674	+	0.0697873i
$567$	−0.126712	−	0.102392i	−0.00532140	−	0.00430007i
$568$	38.4330	+	44.3541i	1.61261	+	1.86106i
$569$	41.2657	+	3.94039i	1.72995	+	0.165190i	0.912023	−	0.410138i	$-0.134519\pi$
$569$	41.2657	+	3.94039i	1.72995	+	0.165190i	0.817923	+	0.575328i	$0.195126\pi$
$570$	−5.21354	−	7.56225i	−0.218371	−	0.316748i
$571$	−3.64400	−	38.1617i	−0.152497	−	1.59702i	−0.670680	−	0.741747i	$-0.733998\pi$
$571$	−3.64400	−	38.1617i	−0.152497	−	1.59702i	0.518184	−	0.855269i	$-0.326608\pi$
$572$	70.6870	−	28.2988i	2.95557	−	1.18323i
$573$	36.8854	−	14.1196i	1.54091	−	0.589854i
$574$	−0.153972	−	0.0888960i	−0.00642668	−	0.00371045i
$575$	−16.9991	+	15.6210i	−0.708911	+	0.651443i
$576$	61.6551	−	45.5205i	2.56896	−	1.89669i
$577$	−38.9818	+	25.0521i	−1.62283	+	1.04293i	−0.668705	+	0.743528i	$0.733151\pi$
$577$	−38.9818	+	25.0521i	−1.62283	+	1.04293i	−0.954127	+	0.299403i	$0.903213\pi$
$578$	−33.6923	+	42.8432i	−1.40141	+	1.78204i
$579$	−16.9451	−	38.6497i	−0.704213	−	1.60623i
$580$	−0.112568	+	0.118058i	−0.00467415	+	0.00490211i
$581$	−0.0498570	−	0.0355030i	−0.00206842	−	0.00147291i
$582$	−19.9859	−	0.304031i	−0.828443	−	0.0126025i
$583$	−31.3817	−	12.5633i	−1.29970	−	0.520320i
$584$	14.2019	−	48.3671i	0.587677	−	2.00144i
$585$	4.47127	+	3.06961i	0.184864	+	0.126913i
$586$	0.276848	−	0.430783i	0.0114365	−	0.0177955i
$587$	9.79321	+	18.9962i	0.404209	+	0.784056i	0.999815	−	0.0192203i	$-0.00611840\pi$
$587$	9.79321	+	18.9962i	0.404209	+	0.784056i	−0.595606	+	0.803277i	$0.703088\pi$
$588$	−51.6645	+	39.3724i	−2.13061	+	1.62369i
$589$	0.363840	−	0.0882667i	0.0149918	−	0.00363696i
$590$	7.46320	−	5.86913i	0.307255	−	0.241628i
$591$	20.0909	+	12.0106i	0.826430	+	0.494051i
$592$	−11.0600	+	115.826i	−0.454564	+	4.76041i
$593$	−5.71376	−	19.4593i	−0.234636	−	0.799097i	−0.989664	−	0.143404i	$-0.954195\pi$
$593$	−5.71376	−	19.4593i	−0.234636	−	0.799097i	0.755028	−	0.655692i	$-0.227623\pi$
$594$	23.8192	−	41.4441i	0.977315	−	1.70047i
$595$	−0.0470791	−	0.00676895i	−0.00193006	−	0.000277500i
$596$	−4.37804	−	91.9064i	−0.179331	−	3.76463i
$597$	−9.66726	+	3.18206i	−0.395655	+	0.130233i
$598$	28.6214	+	46.3928i	1.17041	+	1.89714i
$599$	−19.3247	+	11.1571i	−0.789586	+	0.455868i	−0.839817	−	0.542870i	$-0.817338\pi$
$599$	−19.3247	+	11.1571i	−0.789586	+	0.455868i	0.0502305	+	0.998738i	$0.484004\pi$
$600$	27.1493	+	70.9237i	1.10837	+	2.89545i
$601$	18.8286	+	14.8070i	0.768034	+	0.603989i	0.923387	−	0.383870i	$-0.125409\pi$
$601$	18.8286	+	14.8070i	0.768034	+	0.603989i	−0.155353	+	0.987859i	$0.549651\pi$
$602$	−0.0248160	−	0.0113331i	−0.00101142	−	0.000461901i
$603$	4.89451	−	38.7571i	0.199320	−	1.57831i
$604$	−14.1142	−	30.9057i	−0.574297	−	1.25754i
$605$	−0.212613	+	0.0409779i	−0.00864397	+	0.00166599i
$606$	−6.20473	−	4.12222i	−0.252050	−	0.167454i
$607$	7.40945	+	30.5422i	0.300740	+	1.23967i	0.898851	+	0.438255i	$0.144403\pi$
$607$	7.40945	+	30.5422i	0.300740	+	1.23967i	−0.598111	+	0.801413i	$0.704082\pi$
$608$	−87.8056	−	16.9231i	−3.56099	−	0.686324i
$609$	0.00213213		0.000590976i	8.63983e−5		2.39475e-5i
$610$	−11.6770	+	6.01991i	−0.472788	+	0.243739i
$611$	−19.2755	−	16.7024i	−0.779805	−	0.675705i
$612$	75.0738	+	62.8269i	3.03468	+	2.53963i
$613$	−42.8186	+	6.15639i	−1.72943	+	0.248654i	−0.933969	−	0.357354i	$-0.883679\pi$
$613$	−42.8186	+	6.15639i	−1.72943	+	0.248654i	−0.795458	+	0.606008i	$0.792770\pi$
$614$	−4.91669	−	25.5102i	−0.198422	−	1.02951i
$615$	2.63897	−	0.597857i	0.106414	−	0.0241079i
$616$	0.404671	+	0.385853i	0.0163047	+	0.0155465i
$617$	10.0958	−	0.964028i	0.406440	−	0.0388103i	0.110166	−	0.993913i	$-0.464862\pi$
$617$	10.0958	−	0.964028i	0.406440	−	0.0388103i	0.296274	+	0.955103i	$0.404256\pi$
$618$	44.8250	−	7.93416i	1.80313	−	0.319159i
$619$	3.28242	−	0.156361i	0.131931	−	0.00628467i	0.0184877	−	0.999829i	$-0.494115\pi$
$619$	3.28242	−	0.156361i	0.131931	−	0.00628467i	0.113444	+	0.993544i	$0.463812\pi$
$620$	0.190980			0.00766993
$621$	23.4120	+	8.53683i	0.939492	+	0.342571i
$622$	−46.5340			−1.86584
$623$	−0.122283	+	0.00582508i	−0.00489918	+	0.000233377i
$624$	99.9868	−	17.6980i	4.00268	−	0.708486i
$625$	−22.1419	+	2.11430i	−0.885676	+	0.0845718i
$626$	−27.2369	−	25.9704i	−1.08861	−	1.03798i
$627$	−25.9608	+	5.88140i	−1.03678	+	0.234881i
$628$	7.36403	+	38.2082i	0.293857	+	1.52467i
$629$	−50.1359	+	7.20845i	−1.99905	+	0.287420i
$630$	−0.0109533	+	0.0625993i	−0.000436391	+	0.00249401i
$631$	−17.1290	−	14.8424i	−0.681895	−	0.590865i	0.243486	−	0.969904i	$-0.421709\pi$
$631$	−17.1290	−	14.8424i	−0.681895	−	0.590865i	−0.925381	+	0.379039i	$0.876255\pi$
$632$	−85.8887	+	44.2787i	−3.41647	+	1.76131i
$633$	−37.3644	+	10.3565i	−1.48510	+	0.411635i
$634$	−66.4917	−	12.8152i	−2.64072	−	0.508957i
$635$	−0.372495	−	1.53545i	−0.0147820	−	0.0609323i
$636$	−77.0424	−	51.1845i	−3.05493	−	2.02960i
$637$	−28.8009	+	5.55091i	−1.14113	+	0.219935i
$638$	0.269686	+	0.590529i	0.0106770	+	0.0233793i
$639$	15.3979	+	11.6867i	0.609133	+	0.462317i
$640$	−11.7059	−	5.34590i	−0.462716	−	0.211315i
$641$	−37.2493	−	29.2932i	−1.47126	−	1.15701i	−0.953464	−	0.301506i	$-0.902511\pi$
$641$	−37.2493	−	29.2932i	−1.47126	−	1.15701i	−0.517795	−	0.855505i	$-0.673247\pi$
$642$	−23.3021	−	60.8734i	−0.919661	−	2.40248i
$643$	−12.7367	+	7.35353i	−0.502286	+	0.289995i	−0.729657	−	0.683813i	$-0.760320\pi$
$643$	−12.7367	+	7.35353i	−0.502286	+	0.289995i	0.227371	+	0.973808i	$0.426987\pi$
$644$	−0.258624	+	0.386581i	−0.0101912	+	0.0152334i
$645$	0.394384	−	0.129815i	0.0155288	−	0.00511144i
$646$	−3.56211	−	74.7779i	−0.140149	−	2.94210i
$647$	−0.801125	−	0.115184i	−0.0314955	−	0.00452836i	0.126549	−	0.991960i	$-0.459610\pi$
$647$	−0.801125	−	0.115184i	−0.0314955	−	0.00452836i	−0.158045	+	0.987432i	$0.550519\pi$
$648$	54.4969	−	61.2349i	2.14084	−	2.40554i
$649$	−7.75188	−	26.4005i	−0.304288	−	1.03631i
$650$	−5.20111	+	54.4685i	−0.204004	+	2.13643i
$651$	−0.00222333	−	0.00132914i	−8.71394e−5	−	5.20930e-5i
$652$	−17.1643	+	13.4981i	−0.672205	+	0.528628i
$653$	−27.8957	+	6.76743i	−1.09164	+	0.264830i	−0.740883	−	0.671635i	$-0.765592\pi$
$653$	−27.8957	+	6.76743i	−1.09164	+	0.264830i	−0.350762	+	0.936465i	$0.614077\pi$
$654$	−3.27517	+	2.49594i	−0.128069	+	0.0975991i
$655$	1.25376	+	2.43195i	0.0489884	+	0.0950243i
$656$	27.3887	−	42.6176i	1.06935	−	1.66394i
$657$	1.29412	−	16.5530i	0.0504886	−	0.645793i
$658$	0.0841978	−	0.286751i	0.00328237	−	0.0111787i
$659$	43.1218	+	17.2634i	1.67979	+	0.672486i	0.998241	−	0.0592878i	$-0.0188830\pi$
$659$	43.1218	+	17.2634i	1.67979	+	0.672486i	0.681548	+	0.731774i	$0.261307\pi$
$660$	−13.5767	−	0.206533i	−0.528474	−	0.00803928i
$661$	−10.6788	−	7.60435i	−0.415358	−	0.295775i	0.353209	−	0.935544i	$-0.385090\pi$
$661$	−10.6788	−	7.60435i	−0.415358	−	0.295775i	−0.768567	+	0.639769i	$0.779030\pi$
$662$	−35.6974	+	37.4384i	−1.38742	+	1.45508i
$663$	17.7491	+	40.4837i	0.689318	+	1.57225i
$664$	19.0378	−	24.2085i	0.738809	−	0.939473i
$665$	0.0297709	−	0.0191326i	0.00115446	−	0.000741929i
$666$	7.58933	+	67.2497i	0.294080	+	2.60587i
$667$	−0.279254	+	0.191203i	−0.0108128	+	0.00740342i
$668$	55.8341	+	32.2359i	2.16029	+	1.24724i
$669$	9.58029	−	3.66730i	0.370396	−	0.141786i
$670$	−14.1473	+	5.66373i	−0.546558	+	0.218809i
$671$	3.61898	+	37.8997i	0.139709	+	1.46310i
$672$	0.351165	+	0.509366i	0.0135465	+	0.0196492i
$673$	39.7071	+	3.79157i	1.53060	+	0.146154i	0.826088	−	0.563541i	$-0.190561\pi$
$673$	39.7071	+	3.79157i	1.53060	+	0.146154i	0.704509	+	0.709695i	$0.251167\pi$
$674$	14.7328	+	17.0026i	0.567487	+	0.654914i
$675$	13.5647	+	21.0161i	0.522106	+	0.808911i
$676$	23.4360	+	6.88142i	0.901383	+	0.264670i
$677$	9.18593	+	26.5410i	0.353044	+	1.02005i	0.972072	+	0.234684i	$0.0754056\pi$
$677$	9.18593	+	26.5410i	0.353044	+	1.02005i	−0.619028	+	0.785369i	$0.712473\pi$
$678$	48.7448	+	12.6134i	1.87203	+	0.484415i
$679$	0.00366429	−	0.0769230i	0.000140623	−	0.00295203i
$680$	4.52930	−	23.5003i	0.173691	−	0.901194i
$681$	24.1402	+	12.9136i	0.925053	+	0.494851i
$682$	0.282484	−	0.705611i	0.0108169	−	0.0270192i
$683$	5.22882	−	4.53080i	0.200075	−	0.173366i	−0.549061	−	0.835782i	$-0.685014\pi$
$683$	5.22882	−	4.53080i	0.200075	−	0.173366i	0.749136	+	0.662416i	$0.230469\pi$
$684$	−72.8260	+	1.25111i	−2.78457	+	0.0478374i
$685$	2.93818	−	0.862729i	0.112262	−	0.0329632i
$686$	−0.398723	−	0.559928i	−0.0152233	−	0.0213782i
$687$	31.7173	−	26.6494i	1.21009	−	1.01674i
$688$	3.56201	−	6.90934i	0.135800	−	0.263416i
$689$	−20.8828	−	36.1701i	−0.795573	−	1.37797i
$690$	−1.51772	−	9.60182i	−0.0577786	−	0.365535i
$691$	25.8023	−	44.6909i	0.981565	−	1.70012i	0.325262	−	0.945624i	$-0.394547\pi$
$691$	25.8023	−	44.6909i	0.981565	−	1.70012i	0.656303	−	0.754497i	$-0.272119\pi$
$692$	44.4686	+	69.1944i	1.69044	+	2.63038i
$693$	0.156619	+	0.0968928i	0.00594948	+	0.00368065i
$694$	22.4208	−	49.0947i	0.851081	−	1.86361i
$695$	−1.89637	+	7.81693i	−0.0719332	+	0.296513i
$696$	0.245981	+	1.08577i	0.00932389	+	0.0411562i
$697$	20.8406	+	7.21300i	0.789394	+	0.273212i
$698$	12.8895	+	16.3903i	0.487874	+	0.620382i
$699$	19.8196	−	0.642158i	0.749646	−	0.0242886i
$700$	−0.441186	+	0.152696i	−0.0166753	+	0.00577137i
$701$	−0.530009	−	0.340616i	−0.0200181	−	0.0128649i	0.530593	−	0.847626i	$-0.321969\pi$
$701$	−0.530009	−	0.340616i	−0.0200181	−	0.0128649i	−0.550612	+	0.834762i	$0.685605\pi$
$702$	54.7875	−	22.0587i	2.06782	−	0.832552i
$703$	24.6794	−	28.4815i	0.930800	−	1.07420i
$704$	−62.7031	+	59.7873i	−2.36321	+	2.25332i
$705$	2.02245	+	4.07398i	0.0761698	+	0.153435i
$706$	−13.5684	+	39.2033i	−0.510653	+	1.47544i
$707$	0.0166478	−	0.0233786i	0.000626105	−	0.000879242i
$708$	−6.01587	−	75.0486i	−0.226090	−	2.82050i
$709$	−3.57859	+	2.54830i	−0.134397	+	0.0957035i	−0.645278	−	0.763948i	$-0.723259\pi$
$709$	−3.57859	+	2.54830i	−0.134397	+	0.0957035i	0.510881	+	0.859651i	$0.329319\pi$
$710$	1.07316	−	7.46398i	0.0402749	−	0.280118i
$711$	−24.6767	+	20.1014i	−0.925447	+	0.753863i
$712$		−	61.6001i		−	2.30856i
$713$	0.387625	+	0.0821410i	0.0145167	+	0.00307621i
$714$	−0.345104	+	0.386240i	−0.0129152	+	0.0144547i
$715$	−5.44963	−	2.80948i	−0.203805	−	0.105069i
$716$	9.09514	+	22.7186i	0.339901	+	0.849032i
$717$	3.29227	−	1.44342i	0.122952	−	0.0539055i
$718$	45.3874	+	11.0109i	1.69384	+	0.410922i
$719$	38.7950	−	17.7171i	1.44681	−	0.660735i	0.471558	−	0.881835i	$-0.343692\pi$
$719$	38.7950	−	17.7171i	1.44681	−	0.660735i	0.975251	+	0.221100i	$0.0709647\pi$
$720$	−17.6682	−	3.96620i	−0.658455	−	0.147811i
$721$	0.0249599	+	0.173600i	0.000929556	+	0.00646521i
$722$	2.87239	+	3.01248i	0.106899	+	0.112113i
$723$	7.69838	+	10.1018i	0.286306	+	0.375690i
$724$	36.0510	+	1.71732i	1.33983	+	0.0638238i
$725$	−0.339327	−	0.0161642i	−0.0126023	−	0.000600322i
$726$	−0.909552	+	2.17545i	−0.0337566	+	0.0807385i
$727$	−30.8500	−	32.3546i	−1.14416	−	1.19997i	−0.976819	−	0.214067i	$-0.931329\pi$
$727$	−30.8500	−	32.3546i	−1.14416	−	1.19997i	−0.167346	−	0.985898i	$-0.553520\pi$
$728$	0.0983189	+	0.683823i	0.00364394	+	0.0253442i
$729$	13.4079	−	23.4356i	0.496590	−	0.867985i
$730$	−5.89158	+	2.69059i	−0.218057	+	0.0995833i
$731$	3.28862	+	0.797810i	0.121634	+	0.0295081i
$732$	−11.4789	+	103.542i	−0.424271	+	3.82703i
$733$	5.12628	+	12.8048i	0.189343	+	0.472957i	0.992416	−	0.122924i	$-0.0392272\pi$
$733$	5.12628	+	12.8048i	0.189343	+	0.472957i	−0.803073	+	0.595881i	$0.796803\pi$
$734$	60.5526	+	31.2170i	2.23504	+	1.15224i
$735$	5.12043	+	1.06791i	0.188870	+	0.0393903i
$736$	−76.0654	−	56.3058i	−2.80381	−	2.07546i
$737$			44.1621i			1.62673i
$738$	10.4800	−	27.5396i	0.385774	−	1.01375i
$739$	−4.11571	+	28.6254i	−0.151399	+	1.05300i	0.762479	+	0.647013i	$0.223982\pi$
$739$	−4.11571	+	28.6254i	−0.151399	+	1.05300i	−0.913878	+	0.405989i	$0.866927\pi$
$740$	15.6594	−	11.1510i	0.575651	−	0.409919i
$741$	−29.7056	−	14.1161i	−1.09126	−	0.518566i
$742$	0.283874	−	0.398645i	0.0104213	−	0.0146347i
$743$	4.20523	−	12.1502i	0.154275	−	0.445748i	−0.841205	−	0.540716i	$-0.818154\pi$
$743$	4.20523	−	12.1502i	0.154275	−	0.445748i	0.995480	+	0.0949675i	$0.0302747\pi$
$744$	0.721267	−	1.08564i	0.0264429	−	0.0398016i
$745$	−5.36220	+	5.11285i	−0.196456	+	0.187320i
$746$	33.5782	−	38.7514i	1.22939	−	1.41879i
$747$	4.49267	−	9.09482i	0.164378	−	0.332762i
$748$	−93.0995	−	59.8314i	−3.40406	−	2.18765i
$749$	0.237316	−	0.0821359i	0.00867134	−	0.00300118i
$750$	9.38314	−	17.5404i	0.342624	−	0.640486i
$751$	−10.0999	−	12.8430i	−0.368549	−	0.468649i	0.566040	−	0.824378i	$-0.308475\pi$
$751$	−10.0999	−	12.8430i	−0.368549	−	0.468649i	−0.934589	+	0.355729i	$0.884232\pi$
$752$	80.4723	+	27.8517i	2.93452	+	1.01565i
$753$	−30.3739	+	28.0919i	−1.10689	+	1.02373i
$754$	−0.189107	+	0.779509i	−0.00688687	+	0.0283881i
$755$	−1.13653	+	2.48866i	−0.0413626	+	0.0905715i
$756$	0.365401	+	0.347040i	0.0132895	+	0.0126217i
$757$	1.28830	+	2.00463i	0.0468239	+	0.0728595i	0.863876	−	0.503704i	$-0.168030\pi$
$757$	1.28830	+	2.00463i	0.0468239	+	0.0728595i	−0.817052	+	0.576563i	$0.804393\pi$
$758$	15.9881	−	27.6922i	0.580714	−	1.00583i
$759$	−27.4674	−	6.25860i	−0.997004	−	0.227173i
$760$	8.90340	+	15.4211i	0.322960	+	0.559384i
$761$	−22.6524	+	43.9396i	−0.821151	+	1.59281i	−0.0159014	+	0.999874i	$0.505062\pi$
$761$	−22.6524	+	43.9396i	−0.821151	+	1.59281i	−0.805249	+	0.592936i	$0.797969\pi$
$762$	−16.1720	−	5.87412i	−0.585849	−	0.212797i
$763$	−0.00920264	−	0.0129233i	−0.000333158	−	0.000467855i
$764$	−117.224	+	34.4200i	−4.24101	+	1.24527i
$765$	−0.135403	−	7.88170i	−0.00489551	−	0.284963i
$766$	55.7462	−	48.3043i	2.01419	−	1.74531i
$767$	12.6352	−	31.5612i	0.456230	−	1.13961i
$768$	−43.8661	+	27.2572i	−1.58288	+	0.983561i
$769$	−3.94812	+	20.4848i	−0.142373	+	0.738700i	0.838629	+	0.544703i	$0.183357\pi$
$769$	−3.94812	+	20.4848i	−0.142373	+	0.738700i	−0.981002	+	0.193997i	$0.937855\pi$
$770$	0.00341840	−	0.0717610i	0.000123191	−	0.00258609i
$771$	−1.90499	−	6.87286i	−0.0686066	−	0.247520i
$772$	42.6962	+	123.362i	1.53667	+	4.43991i
$773$	−32.2694	−	9.47515i	−1.16065	−	0.340798i	−0.355965	−	0.934499i	$-0.615848\pi$
$773$	−32.2694	−	9.47515i	−1.16065	−	0.340798i	−0.804685	+	0.593702i	$0.797666\pi$
$774$	1.19913	−	4.35954i	0.0431020	−	0.156700i
$775$	0.260453	+	0.300579i	0.00935574	+	0.0107971i
$776$	38.5744	+	3.68340i	1.38474	+	0.132227i
$777$	−0.259909	+	0.0208342i	−0.00932418	+	0.000747424i
$778$	2.30959	+	24.1872i	0.0828029	+	0.867151i
$779$	−15.2332	+	6.09846i	−0.545786	+	0.218500i
$780$	−13.0282	−	10.5701i	−0.466484	−	0.378471i
$781$	−18.9252	−	10.9265i	−0.677197	−	0.390980i
$782$	30.7964	−	72.9993i	1.10128	−	2.61045i
$783$	0.152984	+	0.333253i	0.00546721	+	0.0119095i
$784$	82.3830	−	52.9443i	2.94225	−	1.89087i
$785$	1.93688	−	2.46295i	0.0691303	−	0.0879064i
$786$	29.6144	+	3.28310i	1.05631	+	0.117104i
$787$	21.6774	−	22.7346i	0.772717	−	0.810403i	−0.213310	−	0.976984i	$-0.568425\pi$
$787$	21.6774	−	22.7346i	0.772717	−	0.810403i	0.986028	+	0.166582i	$0.0532730\pi$
$788$	−58.9805	−	41.9999i	−2.10109	−	1.49618i
$789$	−6.16036	−	11.0550i	−0.219314	−	0.393570i
$790$	11.5264	+	4.61446i	0.410090	+	0.164175i
$791$	−0.0546528	+	0.186130i	−0.00194323	+	0.00661804i
$792$	−52.4489	+	76.3983i	−1.86369	+	2.71470i
$793$	−25.4319	+	39.5728i	−0.903113	+	1.40527i
$794$	23.9073	+	46.3737i	0.848438	+	1.64574i
$795$	0.947718	+	7.38757i	0.0336121	+	0.262010i
$796$	30.5949	−	7.42225i	1.08441	−	0.263075i
$797$	−12.6189	+	9.92358i	−0.446983	+	0.351511i	−0.816138	−	0.577856i	$-0.803889\pi$
$797$	−12.6189	+	9.92358i	−0.446983	+	0.351511i	0.369156	+	0.929368i	$0.379647\pi$
$798$	0.00586177	−	0.385332i	0.000207504	−	0.0136406i
$799$	−3.52379	+	36.9028i	−0.124663	+	1.30553i
$800$	−26.7628	−	91.1456i	−0.946207	−	3.22248i
$801$	−4.18147	−	19.8540i	−0.147745	−	0.701506i
$802$	−31.4322	−	4.51927i	−1.10991	−	0.159581i
$803$	0.893109	+	18.7487i	0.0315171	+	0.661626i
$804$	−24.6715	+	118.295i	−0.870095	+	4.17196i
$805$	0.0371636	−	0.00464639i	0.00130985	−	0.000163764i
$806$	0.813278	−	0.469546i	0.0286465	−	0.0165391i
$807$	−7.15885	+	8.82363i	−0.252003	+	0.310606i
$808$	11.3517	+	8.92705i	0.399350	+	0.314053i
$809$	10.9555	+	5.00322i	0.385176	+	0.175904i	0.598586	−	0.801059i	$-0.295730\pi$
$809$	10.9555	+	5.00322i	0.385176	+	0.175904i	−0.213410	+	0.976963i	$0.568457\pi$
$810$	−10.5315	−	0.139492i	−0.370041	−	0.00490126i
$811$	−19.4381	−	42.5636i	−0.682566	−	1.49461i	−0.859902	−	0.510460i	$-0.829475\pi$
$811$	−19.4381	−	42.5636i	−0.682566	−	1.49461i	0.177336	−	0.984150i	$-0.443252\pi$
$812$	−0.00672037	+	0.00129524i	−0.000235839	+	4.54542e-5i
$813$	−22.0733	+	10.9578i	−0.774143	+	0.384308i
$814$	−18.0372	−	74.3504i	−0.632204	−	2.60598i
$815$	1.72655	+	0.332766i	0.0604785	+	0.0116563i
$816$	−105.251	−	103.458i	−3.68452	−	3.62177i
$817$	−2.23793	+	1.15373i	−0.0782951	+	0.0403639i
$818$	0.392585	+	0.340177i	0.0137264	+	0.0118940i
$819$	0.0781071	+	0.213725i	0.00272928	+	0.00746817i
$820$	−8.28489	+	1.19119i	−0.289321	+	0.0415981i
$821$	−0.180229	−	0.935119i	−0.00629005	−	0.0326359i	0.978648	−	0.205543i	$-0.0658961\pi$
$821$	−0.180229	−	0.935119i	−0.00629005	−	0.0326359i	−0.984938	+	0.172907i	$0.944684\pi$
$822$	9.88057	−	31.8497i	0.344624	−	1.11089i
$823$	0.976092	+	0.930701i	0.0340244	+	0.0324422i	0.706901	−	0.707313i	$-0.250093\pi$
$823$	0.976092	+	0.930701i	0.0340244	+	0.0324422i	−0.672876	+	0.739755i	$0.734941\pi$
$824$	−87.8504	+	8.38869i	−3.06041	+	0.292234i
$825$	−18.1905	−	21.6498i	−0.633313	−	0.753749i
$826$	0.397902	−	0.0189544i	0.0138448	−	0.000659508i
$827$	−14.2547			−0.495685			−0.247843	−	0.968800i	$-0.579722\pi$
$827$	−14.2547			−0.495685			−0.247843	+	0.968800i	$0.579722\pi$
$828$	−70.0796	−	32.1095i	−2.43543	−	1.11588i
$829$	−37.8425			−1.31432			−0.657162	−	0.753750i	$-0.728243\pi$
$829$	−37.8425			−1.31432			−0.657162	+	0.753750i	$0.728243\pi$
$830$	−3.95259	+	0.188285i	−0.137196	+	0.00653547i
$831$	8.24451	−	22.6979i	0.285999	−	0.787381i
$832$	−106.562	+	10.1754i	−3.69437	+	0.352770i
$833$	30.8536	+	29.4188i	1.06901	+	1.01930i
$834$	59.4756	+	64.3070i	2.05947	+	2.22677i
$835$	−0.982504	−	5.09771i	−0.0340009	−	0.176414i
$836$	81.5024	−	11.7183i	2.81882	−	0.405285i
$837$	0.158773	−	0.398868i	0.00548801	−	0.0137869i
$838$	50.2617	+	43.5520i	1.73626	+	1.50448i
$839$	0.591448	−	0.304913i	0.0204191	−	0.0105268i	−0.447987	−	0.894040i	$-0.647859\pi$
$839$	0.591448	−	0.304913i	0.0204191	−	0.0105268i	0.468406	+	0.883513i	$0.344829\pi$
$840$	0.0308634	−	0.119272i	0.00106489	−	0.00411528i
$841$	28.4710	+	5.48734i	0.981760	+	0.189219i
$842$	−0.663757	−	2.73604i	−0.0228746	−	0.0942903i
$843$	−2.08857	+	33.2080i	−0.0719343	+	1.14374i
$844$	117.771	−	22.6985i	4.05384	−	0.781313i
$845$	−0.817051	−	1.78909i	−0.0281074	−	0.0615467i
$846$	49.1406	+	6.20582i	1.68949	+	0.213360i
$847$	−0.00826365	−	0.00377388i	−0.000283942	−	0.000129672i
$848$	109.612	+	86.1996i	3.76408	+	2.96011i
$849$	−3.71612	−	0.592123i	−0.127537	−	0.0203216i
$850$	68.8728	−	39.7637i	2.36232	−	1.36389i
$851$	36.5794	−	15.8977i	1.25393	−	0.544965i
$852$	−44.5901	−	39.8410i	−1.52763	−	1.36493i
$853$	−2.74544	−	57.6340i	−0.0940022	−	1.97335i	−0.202594	−	0.979263i	$-0.564937\pi$
$853$	−2.74544	−	57.6340i	−0.0940022	−	1.97335i	0.108592	−	0.994086i	$-0.465366\pi$
$854$	−0.545584	−	0.0784431i	−0.0186695	−	0.00268427i
$855$	3.91641	+	4.36594i	0.133938	+	0.149312i
$856$	35.6003	+	121.243i	1.21679	+	4.14401i
$857$	3.32059	−	34.7748i	0.113429	−	1.18788i	−0.742158	−	0.670225i	$-0.766198\pi$
$857$	3.32059	−	34.7748i	0.113429	−	1.18788i	0.855587	−	0.517659i	$-0.173196\pi$
$858$	−58.3237	+	32.5005i	−1.99114	+	1.10955i
$859$	34.7482	−	27.3263i	1.18559	−	0.932361i	0.186846	−	0.982389i	$-0.440174\pi$
$859$	34.7482	−	27.3263i	1.18559	−	0.932361i	0.998748	+	0.0500281i	$0.0159311\pi$
$860$	−1.24815	+	0.302797i	−0.0425614	+	0.0103253i
$861$	0.104741	+	0.0437919i	0.00356955	+	0.00149242i
$862$	−15.1367	−	29.3611i	−0.515559	−	1.00004i
$863$	−4.82983	+	7.51536i	−0.164409	+	0.255826i	−0.913677	−	0.406442i	$-0.866769\pi$
$863$	−4.82983	+	7.51536i	−0.164409	+	0.255826i	0.749267	+	0.662268i	$0.230406\pi$
$864$	−74.0704	+	70.9046i	−2.51993	+	2.41222i
$865$	1.86598	−	6.35496i	0.0634453	−	0.216075i
$866$	23.6675	+	9.47503i	0.804254	+	0.321975i
$867$	17.8579	−	29.8721i	0.606488	−	1.01451i
$868$	0.00652700	+	0.00464786i	0.000221541	+	0.000157759i
$869$	24.8295	−	26.0404i	0.842283	−	0.883360i
$870$	0.0847356	−	0.115244i	0.00287281	−	0.00390712i
$871$	−33.7298	+	42.8909i	−1.14289	+	1.45330i
$872$	6.71568	−	4.31591i	0.227422	−	0.146155i
$873$	12.6827	−	1.43128i	0.429245	−	0.0484416i
$874$	18.2512	+	56.0530i	0.617355	+	1.89602i
$875$	0.0663732	+	0.0383206i	0.00224382	+	0.00129547i
$876$	−8.08172	+	50.7203i	−0.273056	+	1.71368i
$877$	−0.00120232		0.000481335i	−4.05994e−5		1.62535e-5i	−0.371683	−	0.928360i	$-0.621219\pi$
$877$	−0.00120232		0.000481335i	−4.05994e−5		1.62535e-5i	0.371642	+	0.928376i	$0.378795\pi$
$878$	4.98492	+	52.2044i	0.168233	+	1.76181i
$879$	−0.140340	+	0.295329i	−0.00473355	+	0.00996120i
$880$	20.3779	+	1.94586i	0.686940	+	0.0655948i
$881$	−2.18015	−	2.51603i	−0.0734511	−	0.0847671i	0.717835	−	0.696214i	$-0.245133\pi$
$881$	−2.18015	−	2.51603i	−0.0734511	−	0.0847671i	−0.791286	+	0.611447i	$0.790588\pi$
$882$	40.5429	−	40.0095i	1.36515	−	1.34719i
$883$	36.3355	+	10.6691i	1.22279	+	0.359043i	0.828523	−	0.559955i	$-0.189181\pi$
$883$	36.3355	+	10.6691i	1.22279	+	0.359043i	0.394264	+	0.918997i	$0.371000\pi$
$884$	−44.7221	−	129.216i	−1.50417	−	4.34600i
$885$	−4.24993	+	4.32357i	−0.142860	+	0.145335i
$886$	−1.19931	+	25.1766i	−0.0402915	+	0.845823i
$887$	−6.64010	+	34.4521i	−0.222953	+	1.15679i	0.682025	+	0.731329i	$0.261100\pi$
$887$	−6.64010	+	34.4521i	−0.222953	+	1.15679i	−0.904978	+	0.425459i	$0.860113\pi$
$888$	−4.24867	−	131.131i	−0.142576	−	4.40047i
$889$	0.0246375	−	0.0615415i	0.000826315	−	0.00206404i
$890$	−5.98159	+	5.18308i	−0.200503	+	0.173737i
$891$	−11.7185	+	28.1838i	−0.392586	+	0.944194i
$892$	−30.4467	+	8.93996i	−1.01943	+	0.299332i
$893$	−15.9990	−	22.4675i	−0.535387	−	0.751846i
$894$	14.0627	+	79.4487i	0.470325	+	2.65716i
$895$	0.902957	−	1.75149i	0.0301825	−	0.0585459i
$896$	−0.269963	−	0.467589i	−0.00901882	−	0.0156211i
$897$	−21.8966	−	27.0573i	−0.731107	−	0.903417i
$898$	20.7980	−	36.0232i	0.694038	−	1.20211i
$899$	0.00315219	+	0.00490490i	0.000105131	+	0.000163588i
$900$	−36.6315	−	68.1548i	−1.22105	−	2.27183i
$901$	−25.2176	+	55.2188i	−0.840119	+	1.83960i
$902$	−7.85337	+	32.3720i	−0.261489	+	1.07787i
$903$	0.0166379	+	0.00516149i	0.000553675	+	0.000171764i
$904$	−92.2421	−	31.9253i	−3.06793	−	1.06182i
$905$	−1.79654	−	2.28448i	−0.0597189	−	0.0759388i
$906$	15.7245	+	25.3060i	0.522410	+	0.840734i
$907$	23.3786	−	8.09141i	0.776273	−	0.268671i	0.0899296	−	0.995948i	$-0.471336\pi$
$907$	23.3786	−	8.09141i	0.776273	−	0.268671i	0.686344	+	0.727277i	$0.259215\pi$
$908$	−71.2429	−	45.7850i	−2.36428	−	1.51943i
$909$	4.26467	+	2.10667i	0.141450	+	0.0698738i
$910$	0.0581291	−	0.0670845i	0.00192696	−	0.00222383i
$911$	11.1781	−	10.6583i	0.370346	−	0.353125i	−0.481936	−	0.876206i	$-0.660066\pi$
$911$	11.1781	−	10.6583i	0.370346	−	0.353125i	0.852282	+	0.523082i	$0.175218\pi$
$912$	109.592	+	6.89264i	3.62895	+	0.228238i
$913$	−3.75067	+	10.8368i	−0.124129	+	0.358647i
$914$	33.5666	−	47.1376i	1.11028	−	1.55917i
$915$	6.90648	−	4.76144i	0.228321	−	0.157408i
$916$	−104.385	+	74.3324i	−3.44899	+	2.45601i
$917$	−0.0163373	+	0.113628i	−0.000539504	+	0.00375233i
$918$	−72.3069	−	46.2681i	−2.38648	−	1.52708i
$919$			13.2570i			0.437306i	0.975803	+	0.218653i	$0.0701664\pi$
$919$			13.2570i			0.437306i	−0.975803	+	0.218653i	$0.929834\pi$
$920$	1.44554	+	18.7900i	0.0476579	+	0.619487i
$921$	5.18666	+	15.7574i	0.170906	+	0.519223i
$922$	−78.3048	−	40.3689i	−2.57883	−	1.32948i
$923$	−10.0351	−	25.0665i	−0.330310	−	0.825074i
$924$	−0.458978	−	0.337475i	−0.0150993	−	0.0111021i
$925$	38.9062	+	9.43854i	1.27923	+	0.310337i
$926$	−40.4800	+	18.4866i	−1.33026	+	0.607508i
$927$	−27.7452	+	8.66708i	−0.911270	+	0.284664i
$928$	−0.198183	−	1.37840i	−0.00650569	−	0.0452481i
$929$	−40.9875	−	42.9864i	−1.34476	−	1.41034i	−0.835249	−	0.549872i	$-0.814677\pi$
$929$	−40.9875	−	42.9864i	−1.34476	−	1.41034i	−0.509506	−	0.860467i	$-0.670172\pi$
$930$	−0.166108	+	0.0213092i	−0.00544689	+	0.000698757i
$931$	−31.6831	−	1.50925i	−1.03837	−	0.0494637i
$932$	−61.2713	−	2.91871i	−2.00701	−	0.0956056i
$933$	29.4722	−	3.78085i	0.964875	−	0.123779i
$934$	5.24583	+	5.50167i	0.171649	+	0.180020i
$935$	1.26823	+	8.82072i	0.0414755	+	0.288468i
$936$	−109.290	+	34.1402i	−3.57226	+	1.11591i
$937$	44.2577	−	20.2118i	1.44584	−	0.660291i	0.470779	−	0.882251i	$-0.343973\pi$
$937$	44.2577	−	20.2118i	1.44584	−	0.660291i	0.975056	+	0.221960i	$0.0712455\pi$
$938$	−0.621342	−	0.150736i	−0.0202875	−	0.00492170i
$939$	19.3605	+	14.2353i	0.631806	+	0.464551i
$940$	−5.22914	−	13.0618i	−0.170556	−	0.426028i
$941$	35.2964	+	18.1965i	1.15063	+	0.593190i	0.924603	−	0.380931i	$-0.124396\pi$
$941$	35.2964	+	18.1965i	1.15063	+	0.593190i	0.226025	+	0.974121i	$0.427427\pi$
$942$	−10.6682	−	32.4106i	−0.347589	−	1.05599i
$943$	−17.3279	−	1.14565i	−0.564274	−	0.0373074i
$944$			113.506i			3.69430i
$945$	0.00185112	−	0.0405370i	6.02169e−5	−	0.00131867i
$946$	−0.727430	+	5.05938i	−0.0236508	+	0.164495i
$947$	2.00186	−	1.42551i	0.0650515	−	0.0463230i	−0.547069	−	0.837088i	$-0.684256\pi$
$947$	2.00186	−	1.42551i	0.0650515	−	0.0463230i	0.612120	+	0.790765i	$0.290317\pi$
$948$	81.0574	−	55.8823i	2.63262	−	1.81497i
$949$	−13.4523	+	18.8911i	−0.436680	+	0.613231i
$950$	−19.3530	+	55.9168i	−0.627894	+	1.81418i
$951$	43.1535	+	2.71409i	1.39935	+	0.0880103i
$952$	0.726720	−	0.692926i	0.0235531	−	0.0224579i
$953$	−0.794047	+	0.916379i	−0.0257217	+	0.0296844i	−0.768465	−	0.639892i	$-0.778979\pi$
$953$	−0.794047	+	0.916379i	−0.0257217	+	0.0296844i	0.742743	+	0.669577i	$0.233524\pi$
$954$	72.7200	+	35.9223i	2.35440	+	1.16303i
$955$	8.27614	+	5.31875i	0.267810	+	0.172111i
$956$	−10.5083	+	3.63695i	−0.339862	+	0.117627i
$957$	−0.218785	−	0.352098i	−0.00707231	−	0.0113817i
$958$	−35.3401	−	44.9386i	−1.14179	−	1.45190i
$959$	0.121413	+	0.0420214i	0.00392062	+	0.00135694i
$960$	18.2325	+	5.65618i	0.588453	+	0.182552i
$961$	−7.30692	+	30.1195i	−0.235707	+	0.971598i
$962$	39.2687	−	85.9866i	1.26608	−	2.77232i
$963$	19.7042	+	36.6607i	0.634961	+	1.18138i
$964$	−21.2407	−	33.0511i	−0.684115	−	1.06450i
$965$	5.25590	−	9.10349i	0.169193	−	0.293052i
$966$	0.181809	−	0.365093i	0.00584960	−	0.0117467i
$967$	3.42344	+	5.92957i	0.110090	+	0.190682i	0.915807	−	0.401620i	$-0.131553\pi$
$967$	3.42344	+	5.92957i	0.110090	+	0.190682i	−0.805716	+	0.592302i	$0.798219\pi$
$968$	2.09463	−	4.06302i	0.0673240	−	0.130590i
$969$	8.33170	+	47.0710i	0.267653	+	1.51214i
$970$	−2.88800	−	4.05564i	−0.0927282	−	0.130219i
$971$	17.6254	−	5.17528i	0.565625	−	0.166083i	0.0135965	−	0.999908i	$-0.495672\pi$
$971$	17.6254	−	5.17528i	0.565625	−	0.166083i	0.552029	+	0.833825i	$0.313854\pi$
$972$	−47.1351	+	68.9483i	−1.51186	+	2.21152i
$973$	−0.255051	+	0.221003i	−0.00817656	+	0.00708503i
$974$	9.20419	−	22.9910i	0.294921	−	0.736678i
$975$	−1.13141	−	34.9200i	−0.0362342	−	1.11834i
$976$	29.7231	−	154.218i	0.951412	−	4.93640i
$977$	0.404465	−	8.49077i	0.0129400	−	0.271644i	−0.983120	−	0.182962i	$-0.941432\pi$
$977$	0.404465	−	8.49077i	0.0129400	−	0.271644i	0.996060	−	0.0886819i	$-0.0282655\pi$
$978$	13.4228	−	13.6554i	0.429215	−	0.436652i
$979$	7.50194	+	21.6754i	0.239763	+	0.692749i
$980$	−15.5246	−	4.55843i	−0.495915	−	0.145614i
$981$	1.87153	−	1.84690i	0.0597533	−	0.0589671i
$982$	22.7914	+	26.3026i	0.727301	+	0.839351i
$983$	−9.21315	−	0.879749i	−0.293854	−	0.0280596i	−0.0529120	−	0.998599i	$-0.516850\pi$
$983$	−9.21315	−	0.879749i	−0.293854	−	0.0280596i	−0.240942	+	0.970540i	$0.577456\pi$
$984$	−24.5179	+	51.5950i	−0.781601	+	1.64479i
$985$	0.554221	+	5.80407i	0.0176590	+	0.184933i
$986$	1.08233	−	0.433301i	0.0344685	−	0.0137991i
$987$	−0.0300281	+	0.188454i	−0.000955806	+	0.00599857i
$988$	88.1065	+	50.8683i	2.80304	+	1.61834i
$989$	−2.66355	+	0.0777448i	−0.0846960	+	0.00247214i
$990$	11.8317	−	1.33524i	0.376035	−	0.0424366i
$991$	48.2208	−	30.9896i	1.53179	−	0.984419i	0.542235	−	0.840227i	$-0.317578\pi$
$991$	48.2208	−	30.9896i	1.53179	−	0.984419i	0.989550	−	0.144192i	$-0.0460583\pi$
$992$	−1.00783	+	1.28156i	−0.0319986	+	0.0406895i
$993$	19.5670	−	26.6119i	0.620940	−	0.844502i
$994$	0.218327	−	0.228975i	0.00692491	−	0.00726264i
$995$	−2.06502	−	1.47050i	−0.0654657	−	0.0466179i
$996$	−16.1008	+	26.9329i	−0.510175	+	0.853402i
$997$	−1.17699	−	0.471195i	−0.0372756	−	0.0149229i	0.352950	−	0.935642i	$-0.385179\pi$
$997$	−1.17699	−	0.471195i	−0.0372756	−	0.0149229i	−0.390225	+	0.920719i	$0.627603\pi$
$998$	−4.78581	+	16.2990i	−0.151492	+	0.515935i
$999$	−10.2707	−	41.9758i	−0.324949	−	1.32805i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.o.a.11.22	✓	440
3.2	odd	2		621.2.s.a.494.1		440
9.4	even	3		621.2.s.a.287.1		440
9.5	odd	6	inner	207.2.o.a.149.22	yes	440
23.21	odd	22	inner	207.2.o.a.182.22	yes	440
69.44	even	22		621.2.s.a.251.1		440
207.67	odd	66		621.2.s.a.44.1		440
207.113	even	66	inner	207.2.o.a.113.22	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.22	✓	440	1.1	even	1	trivial
207.2.o.a.113.22	yes	440	207.113	even	66	inner
207.2.o.a.149.22	yes	440	9.5	odd	6	inner
207.2.o.a.182.22	yes	440	23.21	odd	22	inner
621.2.s.a.44.1		440	207.67	odd	66
621.2.s.a.251.1		440	69.44	even	22
621.2.s.a.287.1		440	9.4	even	3
621.2.s.a.494.1		440	3.2	odd	2

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.o (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(2.70946 - 0.129067i) q^{2} +(-1.70554 + 0.301886i) q^{3} +(5.33355 - 0.509292i) q^{4} +(-0.312243 - 0.297723i) q^{5} +(-4.58212 + 1.03808i) q^{6} +(-0.00342569 - 0.0177741i) q^{7} +(9.01544 - 1.29622i) q^{8} +(2.81773 - 1.02976i) q^{9} +O(q^{10})\)	\(q+(2.70946 - 0.129067i) q^{2} +(-1.70554 + 0.301886i) q^{3} +(5.33355 - 0.509292i) q^{4} +(-0.312243 - 0.297723i) q^{5} +(-4.58212 + 1.03808i) q^{6} +(-0.00342569 - 0.0177741i) q^{7} +(9.01544 - 1.29622i) q^{8} +(2.81773 - 1.02976i) q^{9} +(-0.884435 - 0.766367i) q^{10} +(-3.01443 + 1.55405i) q^{11} +(-8.94283 + 2.47874i) q^{12} +(-4.11460 - 0.793024i) q^{13} +(-0.0115758 - 0.0477161i) q^{14} +(0.622421 + 0.413517i) q^{15} +(13.7377 - 2.64772i) q^{16} +(2.53006 + 5.54006i) q^{17} +(7.50161 - 3.15375i) q^{18} +(-4.12200 - 1.88245i) q^{19} +(-1.81699 - 1.42890i) q^{20} +(0.0112084 + 0.0292803i) q^{21} +(-7.96690 + 4.59969i) q^{22} +(-3.07331 - 3.68168i) q^{23} +(-14.9849 + 4.93239i) q^{24} +(-0.229053 - 4.80841i) q^{25} +(-11.2507 - 1.61760i) q^{26} +(-4.49488 + 2.60692i) q^{27} +(-0.0273233 - 0.0930546i) q^{28} +(0.00670806 - 0.0702500i) q^{29} +(1.73979 + 1.04007i) q^{30} +(-0.0649439 + 0.0510724i) q^{31} +(19.1771 - 4.65230i) q^{32} +(4.67209 - 3.56051i) q^{33} +(7.57013 + 14.6840i) q^{34} +(-0.00422212 + 0.00656975i) q^{35} +(14.5041 - 6.92730i) q^{36} +(-2.34304 + 7.97966i) q^{37} +(-11.4113 - 4.56841i) q^{38} +(7.25702 + 0.110396i) q^{39} +(-3.20092 - 2.27937i) q^{40} +(2.49878 - 2.62064i) q^{41} +(0.0341478 + 0.0778871i) q^{42} +(0.343465 - 0.436751i) q^{43} +(-15.2862 + 9.82382i) q^{44} +(-1.18640 - 0.517369i) q^{45} +(-8.80218 - 9.57868i) q^{46} +(5.27123 + 3.04334i) q^{47} +(-22.6308 + 8.66299i) q^{48} +(6.49827 - 2.60152i) q^{49} +(-1.24122 - 12.9986i) q^{50} +(-5.98759 - 8.68501i) q^{51} +(-22.3493 - 2.13410i) q^{52} +(6.52711 + 7.53268i) q^{53} +(-11.8422 + 7.64348i) q^{54} +(1.40391 + 0.412226i) q^{55} +(-0.0539233 - 0.155801i) q^{56} +(7.59852 + 1.96623i) q^{57} +(0.00910822 - 0.191205i) q^{58} +(-1.53541 + 7.96646i) q^{59} +(3.53031 + 1.88852i) q^{60} +(4.17225 - 10.4218i) q^{61} +(-0.169371 + 0.146761i) q^{62} +(-0.0279557 - 0.0465551i) q^{63} +(24.5114 - 7.19719i) q^{64} +(1.04865 + 1.47263i) q^{65} +(12.1993 - 10.2500i) q^{66} +(5.96686 - 11.5741i) q^{67} +(16.3157 + 28.2597i) q^{68} +(6.35310 + 5.35146i) q^{69} +(-0.0105917 + 0.0183454i) q^{70} +(3.48365 + 5.42067i) q^{71} +(24.0683 - 12.9361i) q^{72} +(2.29911 - 5.03436i) q^{73} +(-5.31845 + 21.9230i) q^{74} +(1.84225 + 8.13179i) q^{75} +(-22.9436 - 7.94086i) q^{76} +(0.0379484 + 0.0482553i) q^{77} +(19.6768 - 0.637532i) q^{78} +(-10.0257 + 3.46994i) q^{79} +(-5.07778 - 3.26329i) q^{80} +(6.87921 - 5.80315i) q^{81} +(6.43209 - 7.42303i) q^{82} +(2.44718 - 2.33338i) q^{83} +(0.0746928 + 0.150460i) q^{84} +(0.859410 - 2.48310i) q^{85} +(0.874233 - 1.22769i) q^{86} +(0.00976660 + 0.121839i) q^{87} +(-25.1621 + 17.9178i) q^{88} +(0.962501 - 6.69434i) q^{89} +(-3.28127 - 1.24866i) q^{90} +0.0758502i q^{91} +(-18.2667 - 18.0712i) q^{92} +(0.0953463 - 0.106712i) q^{93} +(14.6749 + 7.56546i) q^{94} +(0.726615 + 1.81500i) q^{95} +(-31.3028 + 13.7240i) q^{96} +(4.13449 + 1.00302i) q^{97} +(17.2710 - 7.88740i) q^{98} +(-6.89357 + 7.48302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Introduction

L-functions

Modular forms

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Database

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