LMFDB - Embedded newform 966.2.q.i.127.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (of order $11$, degree $10$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			127.3
Character	$\chi$	$=$	966.127
Dual form			966.2.q.i.715.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 - 0.540641i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(2.16398 - 0.635401i) q^{5} +(0.415415 + 0.909632i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(0.841254 - 0.540641i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(2.16398 - 0.635401i) q^{5} +(0.415415 + 0.909632i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(1.47693 - 1.70447i) q^{10} +(-5.26843 - 3.38582i) q^{11} +(0.841254 + 0.540641i) q^{12} +(3.13522 - 3.61823i) q^{13} +(-0.959493 - 0.281733i) q^{14} +(0.320967 + 2.23238i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-0.662658 - 1.45102i) q^{17} +(-0.959493 + 0.281733i) q^{18} +(1.67247 - 3.66219i) q^{19} +(0.320967 - 2.23238i) q^{20} +(0.841254 - 0.540641i) q^{21} -6.26260 q^{22} +(1.62006 - 4.51391i) q^{23} +1.00000 q^{24} +(0.0727884 - 0.0467782i) q^{25} +(0.681348 - 4.73888i) q^{26} +(0.415415 - 0.909632i) q^{27} +(-0.959493 + 0.281733i) q^{28} +(3.50240 + 7.66918i) q^{29} +(1.47693 + 1.70447i) q^{30} +(0.768825 + 5.34730i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(4.10113 - 4.73296i) q^{33} +(-1.34194 - 0.862414i) q^{34} +(-1.89731 - 1.21932i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(1.64122 + 0.481907i) q^{37} +(-0.572961 - 3.98503i) q^{38} +(3.13522 + 3.61823i) q^{39} +(-0.936899 - 2.05152i) q^{40} +(2.81636 - 0.826958i) q^{41} +(0.415415 - 0.909632i) q^{42} +(0.800998 - 5.57107i) q^{43} +(-5.26843 + 3.38582i) q^{44} -2.25533 q^{45} +(-1.07752 - 4.67322i) q^{46} +0.112309 q^{47} +(0.841254 - 0.540641i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(0.0359432 - 0.0787047i) q^{50} +(1.53056 - 0.449412i) q^{51} +(-1.98884 - 4.35496i) q^{52} +(7.99920 + 9.23157i) q^{53} +(-0.142315 - 0.989821i) q^{54} +(-13.5521 - 3.97926i) q^{55} +(-0.654861 + 0.755750i) q^{56} +(3.38690 + 2.17663i) q^{57} +(7.09267 + 4.55818i) q^{58} +(-6.22111 + 7.17954i) q^{59} +(2.16398 + 0.635401i) q^{60} +(0.462535 + 3.21700i) q^{61} +(3.53774 + 4.08277i) q^{62} +(0.415415 + 0.909632i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(4.48551 - 9.82189i) q^{65} +(0.891261 - 6.19885i) q^{66} +(5.54138 - 3.56123i) q^{67} -1.59517 q^{68} +(4.23741 + 2.24597i) q^{69} -2.25533 q^{70} +(5.46928 - 3.51489i) q^{71} +(-0.142315 + 0.989821i) q^{72} +(-0.296033 + 0.648221i) q^{73} +(1.64122 - 0.481907i) q^{74} +(0.0359432 + 0.0787047i) q^{75} +(-2.63648 - 3.04266i) q^{76} +(0.891261 + 6.19885i) q^{77} +(4.59368 + 1.34883i) q^{78} +(-2.01595 + 2.32653i) q^{79} +(-1.89731 - 1.21932i) q^{80} +(0.841254 + 0.540641i) q^{81} +(1.92219 - 2.21832i) q^{82} +(-16.7586 - 4.92078i) q^{83} +(-0.142315 - 0.989821i) q^{84} +(-2.35595 - 2.71892i) q^{85} +(-2.33810 - 5.11973i) q^{86} +(-8.08956 + 2.37531i) q^{87} +(-2.60158 + 5.69666i) q^{88} +(0.707632 - 4.92169i) q^{89} +(-1.89731 + 1.21932i) q^{90} -4.78761 q^{91} +(-3.43300 - 3.34881i) q^{92} -5.40229 q^{93} +(0.0944807 - 0.0607191i) q^{94} +(1.29222 - 8.98758i) q^{95} +(0.415415 - 0.909632i) q^{96} +(13.6389 - 4.00475i) q^{97} +(0.415415 + 0.909632i) q^{98} +(4.10113 + 4.73296i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 4 q^{10} - q^{11} - 4 q^{12} - 8 q^{13} - 4 q^{14} - 7 q^{15} - 4 q^{16} - 7 q^{17} - 4 q^{18} + 20 q^{19} - 7 q^{20} - 4 q^{21} + 10 q^{22} + 2 q^{23} + 40 q^{24} - 22 q^{25} + 14 q^{26} - 4 q^{27} - 4 q^{28} + 15 q^{29} + 4 q^{30} - 16 q^{31} - 4 q^{32} - q^{33} - 7 q^{34} - 7 q^{35} - 4 q^{36} - 16 q^{37} - 13 q^{38} - 8 q^{39} + 4 q^{40} - 17 q^{41} - 4 q^{42} + 26 q^{43} - q^{44} + 4 q^{45} - 20 q^{46} + 72 q^{47} - 4 q^{48} - 4 q^{49} + 11 q^{50} - 7 q^{51} - 19 q^{52} + 6 q^{53} - 4 q^{54} + 49 q^{55} - 4 q^{56} + 9 q^{57} - 7 q^{58} - 51 q^{59} + 4 q^{60} - 42 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{64} + 8 q^{65} - 12 q^{66} + 54 q^{67} + 4 q^{68} + 2 q^{69} + 4 q^{70} - 59 q^{71} - 4 q^{72} - 27 q^{73} - 16 q^{74} + 11 q^{75} - 2 q^{76} - 12 q^{77} - 8 q^{78} - 6 q^{79} - 7 q^{80} - 4 q^{81} - 6 q^{82} - 24 q^{83} - 4 q^{84} + 35 q^{85} - 7 q^{86} - 29 q^{87} - q^{88} + 22 q^{89} - 7 q^{90} + 36 q^{91} - 9 q^{92} + 50 q^{93} - 16 q^{94} + 22 q^{95} - 4 q^{96} + 16 q^{97} - 4 q^{98} - q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 4 * q^10 - q^11 - 4 * q^12 - 8 * q^13 - 4 * q^14 - 7 * q^15 - 4 * q^16 - 7 * q^17 - 4 * q^18 + 20 * q^19 - 7 * q^20 - 4 * q^21 + 10 * q^22 + 2 * q^23 + 40 * q^24 - 22 * q^25 + 14 * q^26 - 4 * q^27 - 4 * q^28 + 15 * q^29 + 4 * q^30 - 16 * q^31 - 4 * q^32 - q^33 - 7 * q^34 - 7 * q^35 - 4 * q^36 - 16 * q^37 - 13 * q^38 - 8 * q^39 + 4 * q^40 - 17 * q^41 - 4 * q^42 + 26 * q^43 - q^44 + 4 * q^45 - 20 * q^46 + 72 * q^47 - 4 * q^48 - 4 * q^49 + 11 * q^50 - 7 * q^51 - 19 * q^52 + 6 * q^53 - 4 * q^54 + 49 * q^55 - 4 * q^56 + 9 * q^57 - 7 * q^58 - 51 * q^59 + 4 * q^60 - 42 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^64 + 8 * q^65 - 12 * q^66 + 54 * q^67 + 4 * q^68 + 2 * q^69 + 4 * q^70 - 59 * q^71 - 4 * q^72 - 27 * q^73 - 16 * q^74 + 11 * q^75 - 2 * q^76 - 12 * q^77 - 8 * q^78 - 6 * q^79 - 7 * q^80 - 4 * q^81 - 6 * q^82 - 24 * q^83 - 4 * q^84 + 35 * q^85 - 7 * q^86 - 29 * q^87 - q^88 + 22 * q^89 - 7 * q^90 + 36 * q^91 - 9 * q^92 + 50 * q^93 - 16 * q^94 + 22 * q^95 - 4 * q^96 + 16 * q^97 - 4 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{10}{11}\right)$

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 $

$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$4$	0.415415	−	0.909632i	0.207708	−	0.454816i
$5$	2.16398	−	0.635401i	0.967759	−	0.284160i	0.240597	−	0.970625i	$-0.422657\pi$
$5$	2.16398	−	0.635401i	0.967759	−	0.284160i	0.727162	+	0.686465i	$0.240839\pi$
$6$	0.415415	+	0.909632i	0.169592	+	0.371356i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$8$	−0.142315	−	0.989821i	−0.0503159	−	0.349955i
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$	1.47693	−	1.70447i	0.467046	−	0.539000i
$11$	−5.26843	−	3.38582i	−1.58849	−	1.02086i	−0.972439	−	0.233158i	$-0.925094\pi$
$11$	−5.26843	−	3.38582i	−1.58849	−	1.02086i	−0.616054	−	0.787704i	$-0.711270\pi$
$12$	0.841254	+	0.540641i	0.242849	+	0.156070i
$13$	3.13522	−	3.61823i	0.869553	−	1.00352i	−0.130375	−	0.991465i	$-0.541618\pi$
$13$	3.13522	−	3.61823i	0.869553	−	1.00352i	0.999927	−	0.0120527i	$-0.00383657\pi$
$14$	−0.959493	−	0.281733i	−0.256435	−	0.0752962i
$15$	0.320967	+	2.23238i	0.0828734	+	0.576397i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−0.662658	−	1.45102i	−0.160718	−	0.351924i	0.812091	−	0.583530i	$-0.198329\pi$
$17$	−0.662658	−	1.45102i	−0.160718	−	0.351924i	−0.972810	+	0.231607i	$0.925602\pi$
$18$	−0.959493	+	0.281733i	−0.226155	+	0.0664050i
$19$	1.67247	−	3.66219i	0.383690	−	0.840164i	−0.614977	−	0.788545i	$-0.710835\pi$
$19$	1.67247	−	3.66219i	0.383690	−	0.840164i	0.998667	−	0.0516189i	$-0.0164381\pi$
$20$	0.320967	−	2.23238i	0.0717705	−	0.499175i
$21$	0.841254	−	0.540641i	0.183577	−	0.117977i
$22$	−6.26260			−1.33519
$23$	1.62006	−	4.51391i	0.337807	−	0.941216i
$23$	1.62006	−	4.51391i	0.337807	−	0.941216i
$24$	1.00000			0.204124
$25$	0.0727884	−	0.0467782i	0.0145577	−	0.00935565i
$26$	0.681348	−	4.73888i	0.133623	−	0.929371i
$27$	0.415415	−	0.909632i	0.0799467	−	0.175059i
$28$	−0.959493	+	0.281733i	−0.181327	+	0.0532424i
$29$	3.50240	+	7.66918i	0.650379	+	1.42413i	0.891222	+	0.453567i	$0.149849\pi$
$29$	3.50240	+	7.66918i	0.650379	+	1.42413i	−0.240844	+	0.970564i	$0.577424\pi$
$30$	1.47693	+	1.70447i	0.269649	+	0.311192i
$31$	0.768825	+	5.34730i	0.138085	+	0.960403i	0.934579	+	0.355756i	$0.115777\pi$
$31$	0.768825	+	5.34730i	0.138085	+	0.960403i	−0.796494	+	0.604647i	$0.793314\pi$
$32$	−0.959493	−	0.281733i	−0.169616	−	0.0498038i
$33$	4.10113	−	4.73296i	0.713915	−	0.823902i
$34$	−1.34194	−	0.862414i	−0.230141	−	0.147903i
$35$	−1.89731	−	1.21932i	−0.320703	−	0.206103i
$36$	−0.654861	+	0.755750i	−0.109143	+	0.125958i
$37$	1.64122	+	0.481907i	0.269815	+	0.0792250i	0.413842	−	0.910349i	$-0.364187\pi$
$37$	1.64122	+	0.481907i	0.269815	+	0.0792250i	−0.144026	+	0.989574i	$0.546005\pi$
$38$	−0.572961	−	3.98503i	−0.0929466	−	0.646458i
$39$	3.13522	+	3.61823i	0.502037	+	0.579381i
$40$	−0.936899	−	2.05152i	−0.148137	−	0.324374i
$41$	2.81636	−	0.826958i	0.439842	−	0.129149i	−0.0543115	−	0.998524i	$-0.517296\pi$
$41$	2.81636	−	0.826958i	0.439842	−	0.129149i	0.494153	+	0.869375i	$0.335478\pi$
$42$	0.415415	−	0.909632i	0.0640999	−	0.140359i
$43$	0.800998	−	5.57107i	0.122151	−	0.849580i	−0.832960	−	0.553333i	$-0.813356\pi$
$43$	0.800998	−	5.57107i	0.122151	−	0.849580i	0.955111	−	0.296247i	$-0.0957351\pi$
$44$	−5.26843	+	3.38582i	−0.794246	+	0.510431i
$45$	−2.25533			−0.336205
$46$	−1.07752	−	4.67322i	−0.158872	−	0.689028i
$47$	0.112309			0.0163820			0.00819101	−	0.999966i	$-0.497393\pi$
$47$	0.112309			0.0163820			0.00819101	+	0.999966i	$0.497393\pi$
$48$	0.841254	−	0.540641i	0.121424	−	0.0780348i
$49$	−0.142315	+	0.989821i	−0.0203307	+	0.141403i
$50$	0.0359432	−	0.0787047i	0.00508314	−	0.0111305i
$51$	1.53056	−	0.449412i	0.214321	−	0.0629302i
$52$	−1.98884	−	4.35496i	−0.275803	−	0.603925i
$53$	7.99920	+	9.23157i	1.09877	+	1.26805i	0.960687	+	0.277634i	$0.0895502\pi$
$53$	7.99920	+	9.23157i	1.09877	+	1.26805i	0.138088	+	0.990420i	$0.455904\pi$
$54$	−0.142315	−	0.989821i	−0.0193666	−	0.134698i
$55$	−13.5521	−	3.97926i	−1.82737	−	0.536563i
$56$	−0.654861	+	0.755750i	−0.0875094	+	0.100991i
$57$	3.38690	+	2.17663i	0.448606	+	0.288301i
$58$	7.09267	+	4.55818i	0.931314	+	0.598519i
$59$	−6.22111	+	7.17954i	−0.809919	+	0.934696i	−0.998881	−	0.0472881i	$-0.984942\pi$
$59$	−6.22111	+	7.17954i	−0.809919	+	0.934696i	0.188962	+	0.981984i	$0.439488\pi$
$60$	2.16398	+	0.635401i	0.279368	+	0.0820299i
$61$	0.462535	+	3.21700i	0.0592215	+	0.411895i	0.997770	+	0.0667470i	$0.0212621\pi$
$61$	0.462535	+	3.21700i	0.0592215	+	0.411895i	−0.938548	+	0.345148i	$0.887829\pi$
$62$	3.53774	+	4.08277i	0.449294	+	0.518513i
$63$	0.415415	+	0.909632i	0.0523374	+	0.114603i
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	4.48551	−	9.82189i	0.556359	−	1.21826i
$66$	0.891261	−	6.19885i	0.109707	−	0.763026i
$67$	5.54138	−	3.56123i	0.676988	−	0.435074i	−0.156451	−	0.987686i	$-0.550005\pi$
$67$	5.54138	−	3.56123i	0.676988	−	0.435074i	0.833439	+	0.552612i	$0.186369\pi$
$68$	−1.59517			−0.193443
$69$	4.23741	+	2.24597i	0.510124	+	0.270383i
$70$	−2.25533			−0.269564
$71$	5.46928	−	3.51489i	0.649084	−	0.417141i	−0.174248	−	0.984702i	$-0.555749\pi$
$71$	5.46928	−	3.51489i	0.649084	−	0.417141i	0.823331	+	0.567561i	$0.192113\pi$
$72$	−0.142315	+	0.989821i	−0.0167720	+	0.116652i
$73$	−0.296033	+	0.648221i	−0.0346480	+	0.0758685i	−0.926165	−	0.377119i	$-0.876915\pi$
$73$	−0.296033	+	0.648221i	−0.0346480	+	0.0758685i	0.891517	+	0.452988i	$0.149642\pi$
$74$	1.64122	−	0.481907i	0.190788	−	0.0560205i
$75$	0.0359432	+	0.0787047i	0.00415037	+	0.00908804i
$76$	−2.63648	−	3.04266i	−0.302425	−	0.349017i
$77$	0.891261	+	6.19885i	0.101569	+	0.706425i
$78$	4.59368	+	1.34883i	0.520132	+	0.152724i
$79$	−2.01595	+	2.32653i	−0.226812	+	0.261755i	−0.857737	−	0.514089i	$-0.828130\pi$
$79$	−2.01595	+	2.32653i	−0.226812	+	0.261755i	0.630925	+	0.775844i	$0.282676\pi$
$80$	−1.89731	−	1.21932i	−0.212125	−	0.136325i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	1.92219	−	2.21832i	0.212270	−	0.244973i
$83$	−16.7586	−	4.92078i	−1.83950	−	0.540126i	−0.839504	−	0.543353i	$-0.817155\pi$
$83$	−16.7586	−	4.92078i	−1.83950	−	0.540126i	−0.999995	+	0.00322730i	$0.998973\pi$
$84$	−0.142315	−	0.989821i	−0.0155278	−	0.107998i
$85$	−2.35595	−	2.71892i	−0.255539	−	0.294908i
$86$	−2.33810	−	5.11973i	−0.252124	−	0.552075i
$87$	−8.08956	+	2.37531i	−0.867292	+	0.254660i
$88$	−2.60158	+	5.69666i	−0.277329	+	0.607266i
$89$	0.707632	−	4.92169i	0.0750089	−	0.521698i	−0.917328	−	0.398133i	$-0.869658\pi$
$89$	0.707632	−	4.92169i	0.0750089	−	0.521698i	0.992336	−	0.123565i	$-0.0394327\pi$
$90$	−1.89731	+	1.21932i	−0.199994	+	0.128528i
$91$	−4.78761			−0.501878
$92$	−3.43300	−	3.34881i	−0.357915	−	0.349137i
$93$	−5.40229			−0.560191
$94$	0.0944807	−	0.0607191i	0.00974495	−	0.00626270i
$95$	1.29222	−	8.98758i	0.132579	−	0.922106i
$96$	0.415415	−	0.909632i	0.0423981	−	0.0928389i
$97$	13.6389	−	4.00475i	1.38482	−	0.406621i	0.497379	−	0.867534i	$-0.334296\pi$
$97$	13.6389	−	4.00475i	1.38482	−	0.406621i	0.887446	+	0.460913i	$0.152478\pi$
$98$	0.415415	+	0.909632i	0.0419633	+	0.0918867i
$99$	4.10113	+	4.73296i	0.412179	+	0.475680i
$100$	−0.0123136	−	0.0856430i	−0.00123136	−	0.00856430i
$101$	−9.22935	−	2.70998i	−0.918355	−	0.269653i	−0.211801	−	0.977313i	$-0.567933\pi$
$101$	−9.22935	−	2.70998i	−0.918355	−	0.269653i	−0.706554	+	0.707660i	$0.749751\pi$
$102$	1.04461	−	1.20555i	0.103432	−	0.119367i
$103$	12.4932	+	8.02889i	1.23099	+	0.791110i	0.984045	−	0.177919i	$-0.0569365\pi$
$103$	12.4932	+	8.02889i	1.23099	+	0.791110i	0.246946	+	0.969029i	$0.420573\pi$
$104$	−4.02759	−	2.58838i	−0.394938	−	0.253811i
$105$	1.47693	−	1.70447i	0.144133	−	0.166339i
$106$	11.7203	+	3.44140i	1.13838	+	0.334258i
$107$	−1.28398	−	8.93025i	−0.124127	−	0.863320i	−0.952802	−	0.303591i	$-0.901814\pi$
$107$	−1.28398	−	8.93025i	−0.124127	−	0.863320i	0.828676	−	0.559729i	$-0.189095\pi$
$108$	−0.654861	−	0.755750i	−0.0630140	−	0.0727220i
$109$	−6.93994	−	15.1963i	−0.664725	−	1.45555i	−0.878052	−	0.478565i	$-0.841157\pi$
$109$	−6.93994	−	15.1963i	−0.664725	−	1.45555i	0.213327	−	0.976981i	$-0.431570\pi$
$110$	−13.5521	+	3.97926i	−1.29214	+	0.379407i
$111$	−0.710572	+	1.55594i	−0.0674445	+	0.147683i
$112$	−0.142315	+	0.989821i	−0.0134475	+	0.0935293i
$113$	−6.55058	+	4.20980i	−0.616227	+	0.396025i	−0.811188	−	0.584786i	$-0.801178\pi$
$113$	−6.55058	+	4.20980i	−0.616227	+	0.396025i	0.194961	+	0.980811i	$0.437542\pi$
$114$	4.02601			0.377071
$115$	0.637636	−	10.7974i	0.0594598	−	1.00686i
$116$	8.43108			0.782806
$117$	−4.02759	+	2.58838i	−0.372351	+	0.239296i
$118$	−1.35198	+	9.40320i	−0.124459	+	0.865634i
$119$	−0.662658	+	1.45102i	−0.0607458	+	0.133015i
$120$	2.16398	−	0.635401i	0.197543	−	0.0580039i
$121$	11.7231	+	25.6699i	1.06573	+	2.33363i
$122$	2.12835	+	2.45625i	0.192692	+	0.222378i
$123$	0.417731	+	2.90538i	0.0376655	+	0.261970i
$124$	5.18345	+	1.52200i	0.465488	+	0.136680i
$125$	−7.25685	+	8.37486i	−0.649073	+	0.749070i
$126$	0.841254	+	0.540641i	0.0749448	+	0.0481641i
$127$	12.5774	+	8.08299i	1.11606	+	0.717249i	0.962606	−	0.270906i	$-0.0873233\pi$
$127$	12.5774	+	8.08299i	1.11606	+	0.717249i	0.153456	+	0.988155i	$0.450960\pi$
$128$	−0.654861	+	0.755750i	−0.0578821	+	0.0667995i
$129$	5.40037	+	1.58569i	0.475476	+	0.139612i
$130$	−1.53667	−	10.6877i	−0.134775	−	0.937377i
$131$	−0.964864	−	1.11351i	−0.0843006	−	0.0972880i	0.712032	−	0.702147i	$-0.247775\pi$
$131$	−0.964864	−	1.11351i	−0.0843006	−	0.0972880i	−0.796333	+	0.604859i	$0.793230\pi$
$132$	−2.60158	−	5.69666i	−0.226438	−	0.495831i
$133$	−3.86293	+	1.13426i	−0.334959	+	0.0983527i
$134$	2.73636	−	5.99180i	0.236386	−	0.517612i
$135$	0.320967	−	2.23238i	0.0276245	−	0.192132i
$136$	−1.34194	+	0.862414i	−0.115071	+	0.0739514i
$137$	−7.97434			−0.681294			−0.340647	−	0.940191i	$-0.610646\pi$
$137$	−7.97434			−0.681294			−0.340647	+	0.940191i	$0.610646\pi$
$138$	4.77900	−	0.401485i	0.406815	−	0.0341767i
$139$	6.80800			0.577447			0.288723	−	0.957413i	$-0.406769\pi$
$139$	6.80800			0.577447			0.288723	+	0.957413i	$0.406769\pi$
$140$	−1.89731	+	1.21932i	−0.160352	+	0.103052i
$141$	−0.0159833	+	0.111166i	−0.00134604	+	0.00936189i
$142$	2.70075	−	5.91383i	0.226642	−	0.496277i
$143$	−28.7684	+	8.44715i	−2.40573	+	0.706386i
$144$	0.415415	+	0.909632i	0.0346179	+	0.0758027i
$145$	12.4521	+	14.3705i	1.03409	+	1.19340i
$146$	0.101416	+	0.705366i	0.00839327	+	0.0583765i
$147$	−0.959493	−	0.281733i	−0.0791376	−	0.0232369i
$148$	1.12015	−	1.29272i	0.0920755	−	0.106261i
$149$	16.6336	+	10.6898i	1.36268	+	0.875740i	0.998455	−	0.0555715i	$-0.0176981\pi$
$149$	16.6336	+	10.6898i	1.36268	+	0.875740i	0.364223	+	0.931312i	$0.381334\pi$
$150$	0.0727884	+	0.0467782i	0.00594314	+	0.00381943i
$151$	−2.42147	+	2.79453i	−0.197056	+	0.227415i	−0.845675	−	0.533699i	$-0.820802\pi$
$151$	−2.42147	+	2.79453i	−0.197056	+	0.227415i	0.648618	+	0.761114i	$0.275347\pi$
$152$	−3.86293	−	1.13426i	−0.313325	−	0.0920006i
$153$	0.227016	+	1.57893i	0.0183532	+	0.127649i
$154$	4.10113	+	4.73296i	0.330478	+	0.381392i
$155$	5.06139	+	11.0829i	0.406541	+	0.890201i
$156$	4.59368	−	1.34883i	0.367789	−	0.107992i
$157$	−5.14516	+	11.2663i	−0.410628	+	0.899151i	0.585453	+	0.810706i	$0.300917\pi$
$157$	−5.14516	+	11.2663i	−0.410628	+	0.899151i	−0.996081	+	0.0884441i	$0.971811\pi$
$158$	−0.438107	+	3.04710i	−0.0348539	+	0.242415i
$159$	−10.2760	+	6.60399i	−0.814941	+	0.523731i
$160$	−2.25533			−0.178300
$161$	−4.47230	+	1.73162i	−0.352467	+	0.136471i
$162$	1.00000			0.0785674
$163$	−2.44089	+	1.56867i	−0.191185	+	0.122867i	−0.632732	−	0.774371i	$-0.718066\pi$
$163$	−2.44089	+	1.56867i	−0.191185	+	0.122867i	0.441546	+	0.897238i	$0.354430\pi$
$164$	0.417731	−	2.90538i	0.0326193	−	0.226872i
$165$	5.86742	−	12.8479i	0.456778	−	1.00020i
$166$	−16.7586	+	4.92078i	−1.30072	+	0.381927i
$167$	1.82016	+	3.98559i	0.140848	+	0.308415i	0.966890	−	0.255195i	$-0.0821396\pi$
$167$	1.82016	+	3.98559i	0.140848	+	0.308415i	−0.826041	+	0.563609i	$0.809412\pi$
$168$	−0.654861	−	0.755750i	−0.0505236	−	0.0583073i
$169$	−1.41193	−	9.82022i	−0.108610	−	0.755402i
$170$	−3.45191	−	1.01357i	−0.264749	−	0.0777375i
$171$	−2.63648	+	3.04266i	−0.201617	+	0.232678i
$172$	−4.73487	−	3.04292i	−0.361031	−	0.232020i
$173$	−17.4375	−	11.2064i	−1.32575	−	0.852005i	−0.329985	−	0.943986i	$-0.607044\pi$
$173$	−17.4375	−	11.2064i	−1.32575	−	0.852005i	−0.995761	+	0.0919810i	$0.970680\pi$
$174$	−5.52118	+	6.37178i	−0.418560	+	0.483044i
$175$	−0.0830189	−	0.0243765i	−0.00627564	−	0.00184269i
$176$	0.891261	+	6.19885i	0.0671813	+	0.467256i
$177$	−6.22111	−	7.17954i	−0.467607	−	0.539647i
$178$	−2.06557	−	4.52296i	−0.154821	−	0.339011i
$179$	2.99157	−	0.878405i	0.223601	−	0.0656551i	−0.168013	−	0.985785i	$-0.553735\pi$
$179$	2.99157	−	0.878405i	0.223601	−	0.0656551i	0.391614	+	0.920130i	$0.371917\pi$
$180$	−0.936899	+	2.05152i	−0.0698323	+	0.152911i
$181$	−1.05375	+	7.32902i	−0.0783249	+	0.544762i	0.912444	+	0.409201i	$0.134193\pi$
$181$	−1.05375	+	7.32902i	−0.0783249	+	0.544762i	−0.990769	+	0.135560i	$0.956716\pi$
$182$	−4.02759	+	2.58838i	−0.298545	+	0.191863i
$183$	−3.25008			−0.240253
$184$	−4.69853	−	0.961177i	−0.346380	−	0.0708589i
$185$	3.85777			0.283629
$186$	−4.54469	+	2.92070i	−0.333233	+	0.214156i
$187$	−1.42171	+	9.88823i	−0.103966	+	0.723099i
$188$	0.0466550	−	0.102160i	0.00340267	−	0.00745081i
$189$	−0.959493	+	0.281733i	−0.0697928	+	0.0204930i
$190$	−3.77197	−	8.25946i	−0.273647	−	0.599204i
$191$	14.2756	+	16.4749i	1.03294	+	1.19208i	0.981115	+	0.193425i	$0.0619598\pi$
$191$	14.2756	+	16.4749i	1.03294	+	1.19208i	0.0518294	+	0.998656i	$0.483495\pi$
$192$	−0.142315	−	0.989821i	−0.0102707	−	0.0714342i
$193$	16.4822	+	4.83961i	1.18641	+	0.348362i	0.814643	−	0.579962i	$-0.196933\pi$
$193$	16.4822	+	4.83961i	1.18641	+	0.348362i	0.371770	+	0.928325i	$0.378751\pi$
$194$	9.30867	−	10.7428i	0.668324	−	0.771287i
$195$	9.08356	+	5.83765i	0.650487	+	0.418043i
$196$	0.841254	+	0.540641i	0.0600895	+	0.0386172i
$197$	−12.2775	+	14.1690i	−0.874735	+	1.00950i	0.125114	+	0.992142i	$0.460070\pi$
$197$	−12.2775	+	14.1690i	−0.874735	+	1.00950i	−0.999849	+	0.0173560i	$0.994475\pi$
$198$	6.00892	+	1.76438i	0.427035	+	0.125389i
$199$	0.673584	+	4.68488i	0.0477491	+	0.332102i	0.999668	+	0.0257531i	$0.00819838\pi$
$199$	0.673584	+	4.68488i	0.0477491	+	0.332102i	−0.951919	+	0.306349i	$0.900893\pi$
$200$	−0.0566610	−	0.0653902i	−0.00400654	−	0.00462379i
$201$	2.73636	+	5.99180i	0.193008	+	0.422629i
$202$	−9.22935	+	2.70998i	−0.649375	+	0.190674i
$203$	3.50240	−	7.66918i	0.245820	−	0.538271i
$204$	0.227016	−	1.57893i	0.0158943	−	0.110548i
$205$	5.56909	−	3.57903i	0.388962	−	0.249971i
$206$	14.8507			1.03470
$207$	−2.82616	+	3.87464i	−0.196431	+	0.269306i
$208$	−4.78761			−0.331961
$209$	−21.2108	+	13.6313i	−1.46718	+	0.942900i
$210$	0.320967	−	2.23238i	0.0221488	−	0.154049i
$211$	2.26004	−	4.94880i	0.155588	−	0.340689i	−0.815746	−	0.578411i	$-0.803673\pi$
$211$	2.26004	−	4.94880i	0.155588	−	0.340689i	0.971333	+	0.237721i	$0.0764005\pi$
$212$	11.7203	−	3.44140i	0.804955	−	0.236356i
$213$	2.70075	+	5.91383i	0.185053	+	0.405209i
$214$	−5.90821	−	6.81843i	−0.403877	−	0.466099i
$215$	−1.80652	−	12.5646i	−0.123203	−	0.856899i
$216$	−0.959493	−	0.281733i	−0.0652852	−	0.0191695i
$217$	3.53774	−	4.08277i	0.240158	−	0.277157i
$218$	−14.0540	−	9.03196i	−0.951858	−	0.611722i
$219$	−0.599493	−	0.385271i	−0.0405100	−	0.0260342i
$220$	−9.24941	+	10.6744i	−0.623595	+	0.719667i
$221$	−7.32770	−	2.15161i	−0.492914	−	0.144733i
$222$	0.243431	+	1.69310i	0.0163380	+	0.113633i
$223$	−7.16793	−	8.27224i	−0.480000	−	0.553950i	0.463166	−	0.886272i	$-0.346713\pi$
$223$	−7.16793	−	8.27224i	−0.480000	−	0.553950i	−0.943166	+	0.332322i	$0.892168\pi$
$224$	0.415415	+	0.909632i	0.0277561	+	0.0607773i
$225$	−0.0830189	+	0.0243765i	−0.00553459	+	0.00162510i
$226$	−3.23471	+	7.08303i	−0.215170	+	0.471156i
$227$	−1.93348	+	13.4476i	−0.128329	+	0.892551i	0.819342	+	0.573304i	$0.194339\pi$
$227$	−1.93348	+	13.4476i	−0.128329	+	0.892551i	−0.947672	+	0.319246i	$0.896570\pi$
$228$	3.38690	−	2.17663i	0.224303	−	0.144151i
$229$	27.1592			1.79473			0.897366	−	0.441287i	$-0.145478\pi$
$229$	27.1592			1.79473			0.897366	+	0.441287i	$0.145478\pi$
$230$	−5.30109	−	9.42807i	−0.349544	−	0.621668i
$231$	−6.26260			−0.412049
$232$	7.09267	−	4.55818i	0.465657	−	0.299259i
$233$	−2.42849	+	16.8906i	−0.159096	+	1.10654i	0.741208	+	0.671275i	$0.234253\pi$
$233$	−2.42849	+	16.8906i	−0.159096	+	1.10654i	−0.900304	+	0.435261i	$0.856656\pi$
$234$	−1.98884	+	4.35496i	−0.130015	+	0.284693i
$235$	0.243035	−	0.0713615i	0.0158539	−	0.00465511i
$236$	3.94640	+	8.64140i	0.256889	+	0.562508i
$237$	−2.01595	−	2.32653i	−0.130950	−	0.151124i
$238$	0.227016	+	1.57893i	0.0147153	+	0.102347i
$239$	−15.3186	−	4.49794i	−0.990876	−	0.290947i	−0.254169	−	0.967160i	$-0.581802\pi$
$239$	−15.3186	−	4.49794i	−0.990876	−	0.290947i	−0.736707	+	0.676213i	$0.763620\pi$
$240$	1.47693	−	1.70447i	0.0953353	−	0.110023i
$241$	−12.7539	−	8.19641i	−0.821549	−	0.527977i	0.0610334	−	0.998136i	$-0.480560\pi$
$241$	−12.7539	−	8.19641i	−0.821549	−	0.527977i	−0.882582	+	0.470159i	$0.844197\pi$
$242$	23.7403	+	15.2570i	1.52608	+	0.980755i
$243$	−0.654861	+	0.755750i	−0.0420093	+	0.0484814i
$244$	3.11843	+	0.915654i	0.199637	+	0.0586187i
$245$	0.320967	+	2.23238i	0.0205058	+	0.142621i
$246$	1.92219	+	2.21832i	0.122554	+	0.141435i
$247$	−8.00712	−	17.5331i	−0.509481	−	1.11561i
$248$	5.18345	−	1.52200i	0.329150	−	0.0966471i
$249$	7.25570	−	15.8878i	0.459811	−	1.00685i
$250$	−1.57706	+	10.9687i	−0.0997423	+	0.693723i
$251$	4.26591	−	2.74153i	0.269262	−	0.173044i	−0.399042	−	0.916933i	$-0.630657\pi$
$251$	4.26591	−	2.74153i	0.269262	−	0.173044i	0.668303	+	0.743889i	$0.267021\pi$
$252$	1.00000			0.0629941
$253$	−23.8185	+	18.2960i	−1.49745	+	1.15026i
$254$	14.9508			0.938094
$255$	3.02653	−	1.94503i	0.189529	−	0.121803i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	10.6988	−	23.4271i	0.667373	−	1.46134i	−0.208116	−	0.978104i	$-0.566733\pi$
$257$	10.6988	−	23.4271i	0.667373	−	1.46134i	0.875489	−	0.483238i	$-0.160540\pi$
$258$	5.40037	−	1.58569i	0.336212	−	0.0987208i
$259$	−0.710572	−	1.55594i	−0.0441528	−	0.0966811i
$260$	−7.07096	−	8.16032i	−0.438522	−	0.506082i
$261$	−1.19987	−	8.34526i	−0.0742699	−	0.516559i
$262$	−1.41371	−	0.415101i	−0.0873390	−	0.0256450i
$263$	4.21255	−	4.86154i	0.259757	−	0.299776i	−0.610858	−	0.791740i	$-0.709176\pi$
$263$	4.21255	−	4.86154i	0.259757	−	0.299776i	0.870615	+	0.491964i	$0.163721\pi$
$264$	−5.26843	−	3.38582i	−0.324250	−	0.208383i
$265$	23.1758	+	14.8942i	1.42368	+	0.914943i
$266$	−2.63648	+	3.04266i	−0.161653	+	0.186557i
$267$	4.77089	+	1.40086i	0.291974	+	0.0857312i
$268$	−0.937436	−	6.52001i	−0.0572630	−	0.398273i
$269$	7.95489	+	9.18043i	0.485018	+	0.559741i	0.944528	−	0.328432i	$-0.106520\pi$
$269$	7.95489	+	9.18043i	0.485018	+	0.559741i	−0.459509	+	0.888173i	$0.651975\pi$
$270$	−0.936899	−	2.05152i	−0.0570179	−	0.124852i
$271$	−9.11005	+	2.67495i	−0.553396	+	0.162492i	−0.546462	−	0.837484i	$-0.684026\pi$
$271$	−9.11005	+	2.67495i	−0.553396	+	0.162492i	−0.00693464	+	0.999976i	$0.502207\pi$
$272$	−0.662658	+	1.45102i	−0.0401795	+	0.0879809i
$273$	0.681348	−	4.73888i	0.0412370	−	0.286810i
$274$	−6.70844	+	4.31126i	−0.405272	+	0.260452i
$275$	−0.541863			−0.0326756
$276$	3.80329	−	2.92147i	0.228931	−	0.175852i
$277$	25.6461			1.54092			0.770462	−	0.637486i	$-0.220025\pi$
$277$	25.6461			1.54092			0.770462	+	0.637486i	$0.220025\pi$
$278$	5.72725	−	3.68068i	0.343498	−	0.220753i
$279$	0.768825	−	5.34730i	0.0460284	−	0.320134i
$280$	−0.936899	+	2.05152i	−0.0559904	+	0.122602i
$281$	−4.61331	+	1.35459i	−0.275207	+	0.0808081i	−0.416424	−	0.909171i	$-0.636717\pi$
$281$	−4.61331	+	1.35459i	−0.275207	+	0.0808081i	0.141217	+	0.989979i	$0.454899\pi$
$282$	0.0466550	+	0.102160i	0.00277827	+	0.00608356i
$283$	6.19367	+	7.14788i	0.368176	+	0.424897i	0.909362	−	0.416005i	$-0.136570\pi$
$283$	6.19367	+	7.14788i	0.368176	+	0.424897i	−0.541187	+	0.840903i	$0.682025\pi$
$284$	−0.925237	−	6.43517i	−0.0549027	−	0.381857i
$285$	8.71220	+	2.55813i	0.516066	+	0.151531i
$286$	−19.6346	+	22.6595i	−1.16102	+	1.33989i
$287$	−2.46930	−	1.58692i	−0.145758	−	0.0936730i
$288$	0.841254	+	0.540641i	0.0495713	+	0.0318576i
$289$	9.46629	−	10.9247i	0.556841	−	0.642629i
$290$	18.2446	+	5.35711i	1.07136	+	0.314580i
$291$	2.02297	+	14.0700i	0.118588	+	0.824801i
$292$	0.466666	+	0.538561i	0.0273096	+	0.0315169i
$293$	−7.58813	−	16.6157i	−0.443303	−	0.970699i	−0.990980	−	0.134009i	$-0.957215\pi$
$293$	−7.58813	−	16.6157i	−0.443303	−	0.970699i	0.547677	−	0.836690i	$-0.315512\pi$
$294$	−0.959493	+	0.281733i	−0.0559588	+	0.0164310i
$295$	−8.90044	+	19.4892i	−0.518203	+	1.13471i
$296$	0.243431	−	1.69310i	0.0141491	−	0.0984095i
$297$	−5.26843	+	3.38582i	−0.305706	+	0.196465i
$298$	19.7724			1.14538
$299$	−11.2531	−	20.0139i	−0.650786	−	1.15743i
$300$	0.0865237			0.00499545
$301$	−4.73487	+	3.04292i	−0.272914	+	0.175391i
$302$	−0.526236	+	3.66005i	−0.0302815	+	0.210612i
$303$	3.99587	−	8.74974i	0.229557	−	0.502659i
$304$	−3.86293	+	1.13426i	−0.221554	+	0.0650542i
$305$	3.04500	+	6.66761i	0.174356	+	0.381786i
$306$	1.04461	+	1.20555i	0.0597167	+	0.0689167i
$307$	−0.930376	−	6.47091i	−0.0530994	−	0.369314i	−0.998994	−	0.0448407i	$-0.985722\pi$
$307$	−0.930376	−	6.47091i	−0.0530994	−	0.369314i	0.945895	−	0.324473i	$-0.105187\pi$
$308$	6.00892	+	1.76438i	0.342390	+	0.100535i
$309$	−9.72514	+	11.2234i	−0.553244	+	0.638477i
$310$	10.2498	+	6.58714i	0.582149	+	0.374124i
$311$	−0.210725	−	0.135425i	−0.0119491	−	0.00767923i	0.534653	−	0.845072i	$-0.320442\pi$
$311$	−0.210725	−	0.135425i	−0.0119491	−	0.00767923i	−0.546602	+	0.837393i	$0.684079\pi$
$312$	3.13522	−	3.61823i	0.177497	−	0.204842i
$313$	−26.5599	−	7.79870i	−1.50126	−	0.440809i	−0.575143	−	0.818053i	$-0.695054\pi$
$313$	−26.5599	−	7.79870i	−1.50126	−	0.440809i	−0.926114	+	0.377244i	$0.876872\pi$
$314$	1.76265	+	12.2595i	0.0994722	+	0.691845i
$315$	1.47693	+	1.70447i	0.0832155	+	0.0960358i
$316$	1.27883	+	2.80024i	0.0719398	+	0.157526i
$317$	10.8519	−	3.18641i	0.609505	−	0.178967i	0.0376082	−	0.999293i	$-0.488026\pi$
$317$	10.8519	−	3.18641i	0.609505	−	0.178967i	0.571896	+	0.820326i	$0.306208\pi$
$318$	−5.07434	+	11.1113i	−0.284555	+	0.623089i
$319$	7.51429	−	52.2630i	0.420719	−	2.92617i
$320$	−1.89731	+	1.21932i	−0.106063	+	0.0681623i
$321$	9.02208			0.503563
$322$	−2.82616	+	3.87464i	−0.157495	+	0.215925i
$323$	−6.42218			−0.357340
$324$	0.841254	−	0.540641i	0.0467363	−	0.0300356i
$325$	0.0589527	−	0.410025i	0.00327011	−	0.0227441i
$326$	−1.20532	+	2.63929i	−0.0667567	+	0.146177i
$327$	16.0293	−	4.70663i	0.886423	−	0.260277i
$328$	−1.21935	−	2.67001i	−0.0673274	−	0.147426i
$329$	−0.0735471	−	0.0848778i	−0.00405478	−	0.00467947i
$330$	−2.01009	−	13.9805i	−0.110652	−	0.769600i
$331$	19.4319	+	5.70572i	1.06807	+	0.313615i	0.768098	−	0.640332i	$-0.221203\pi$
$331$	19.4319	+	5.70572i	1.06807	+	0.313615i	0.299976	+	0.953947i	$0.403021\pi$
$332$	−11.4379	+	13.2000i	−0.627736	+	0.724445i
$333$	−1.43897	−	0.924772i	−0.0788553	−	0.0506772i
$334$	3.68599	+	2.36884i	0.201688	+	0.129617i
$335$	9.72861	−	11.2274i	0.531531	−	0.613419i
$336$	−0.959493	−	0.281733i	−0.0523446	−	0.0153698i
$337$	0.757696	+	5.26989i	0.0412743	+	0.287069i	0.999996	+	0.00272412i	$0.000867114\pi$
$337$	0.757696	+	5.26989i	0.0412743	+	0.287069i	−0.958722	+	0.284345i	$0.908224\pi$
$338$	−6.49701	−	7.49795i	−0.353391	−	0.407834i
$339$	−3.23471	−	7.08303i	−0.175685	−	0.384697i
$340$	−3.45191	+	1.01357i	−0.187206	+	0.0549687i
$341$	14.0545	−	30.7750i	0.761092	−	1.66656i
$342$	−0.572961	+	3.98503i	−0.0309822	+	0.215486i
$343$	0.841254	−	0.540641i	0.0454234	−	0.0291919i
$344$	−5.62835			−0.303461
$345$	10.5967	+	2.16777i	0.570509	+	0.116709i
$346$	−20.7280			−1.11434
$347$	−9.43779	+	6.06530i	−0.506647	+	0.325602i	−0.768870	−	0.639405i	$-0.779181\pi$
$347$	−9.43779	+	6.06530i	−0.506647	+	0.325602i	0.262223	+	0.965007i	$0.415544\pi$
$348$	−1.19987	+	8.34526i	−0.0643196	+	0.447353i
$349$	3.77178	−	8.25904i	0.201899	−	0.442096i	−0.781416	−	0.624011i	$-0.785502\pi$
$349$	3.77178	−	8.25904i	0.201899	−	0.442096i	0.983314	+	0.181914i	$0.0582294\pi$
$350$	−0.0830189	+	0.0243765i	−0.00443755	+	0.00130298i
$351$	−1.98884	−	4.35496i	−0.106157	−	0.232451i
$352$	4.10113	+	4.73296i	0.218591	+	0.252267i
$353$	−2.14991	−	14.9529i	−0.114428	−	0.795864i	−0.963523	−	0.267625i	$-0.913761\pi$
$353$	−2.14991	−	14.9529i	−0.114428	−	0.795864i	0.849095	−	0.528240i	$-0.177148\pi$
$354$	−9.11508	−	2.67643i	−0.484461	−	0.142251i
$355$	9.60202	−	11.0813i	0.509622	−	0.588135i
$356$	−4.18297	−	2.68823i	−0.221697	−	0.142476i
$357$	−1.34194	−	0.862414i	−0.0710232	−	0.0456438i
$358$	2.04177	−	2.35633i	0.107911	−	0.124536i
$359$	−26.7125	−	7.84351i	−1.40983	−	0.413964i	−0.513784	−	0.857919i	$-0.671757\pi$
$359$	−26.7125	−	7.84351i	−1.40983	−	0.413964i	−0.896049	+	0.443955i	$0.853575\pi$
$360$	0.320967	+	2.23238i	0.0169165	+	0.117657i
$361$	1.82786	+	2.10946i	0.0962029	+	0.111024i
$362$	3.07589	+	6.73527i	0.161665	+	0.353998i
$363$	−27.0770	+	7.95053i	−1.42118	+	0.417295i
$364$	−1.98884	+	4.35496i	−0.104244	+	0.228262i
$365$	−0.228727	+	1.59083i	−0.0119721	+	0.0832680i
$366$	−2.73414	+	1.75713i	−0.142916	+	0.0918465i
$367$	16.4788			0.860184			0.430092	−	0.902785i	$-0.358481\pi$
$367$	16.4788			0.860184			0.430092	+	0.902785i	$0.358481\pi$
$368$	−4.47230	+	1.73162i	−0.233135	+	0.0902670i
$369$	−2.93526			−0.152803
$370$	3.24536	−	2.08567i	0.168718	−	0.108429i
$371$	1.73839	−	12.0908i	0.0902528	−	0.627722i
$372$	−2.24419	+	4.91409i	−0.116356	+	0.254784i
$373$	26.2154	−	7.69754i	1.35738	−	0.398563i	0.479543	−	0.877519i	$-0.340803\pi$
$373$	26.2154	−	7.69754i	1.35738	−	0.398563i	0.877839	+	0.478955i	$0.158984\pi$
$374$	4.14996	+	9.08715i	0.214589	+	0.469885i
$375$	−7.25685	−	8.37486i	−0.374742	−	0.432476i
$376$	−0.0159833	−	0.111166i	−0.000824276	−	0.00573297i
$377$	38.7296	+	11.3721i	1.99468	+	0.585690i
$378$	−0.654861	+	0.755750i	−0.0336824	+	0.0388716i
$379$	−6.91918	−	4.44668i	−0.355414	−	0.228411i	0.350734	−	0.936475i	$-0.385932\pi$
$379$	−6.91918	−	4.44668i	−0.355414	−	0.228411i	−0.706148	+	0.708064i	$0.749569\pi$
$380$	−7.63858	−	4.90902i	−0.391851	−	0.251827i
$381$	−9.79066	+	11.2990i	−0.501591	+	0.578867i
$382$	20.9164	+	6.14160i	1.07017	+	0.314232i
$383$	3.37523	+	23.4752i	0.172466	+	1.19953i	0.873653	+	0.486550i	$0.161745\pi$
$383$	3.37523	+	23.4752i	0.172466	+	1.19953i	−0.701186	+	0.712978i	$0.747346\pi$
$384$	−0.654861	−	0.755750i	−0.0334182	−	0.0385667i
$385$	5.86742	+	12.8479i	0.299032	+	0.654788i
$386$	16.4822	−	4.83961i	0.838921	−	0.246329i
$387$	−2.33810	+	5.11973i	−0.118852	+	0.260251i
$388$	2.02297	−	14.0700i	0.102701	−	0.714298i
$389$	26.1943	−	16.8340i	1.32810	−	0.853519i	0.332134	−	0.943232i	$-0.392231\pi$
$389$	26.1943	−	16.8340i	1.32810	−	0.853519i	0.995968	+	0.0897134i	$0.0285951\pi$
$390$	10.7976			0.546760
$391$	−7.62332	+	0.640437i	−0.385528	+	0.0323883i
$392$	1.00000			0.0505076
$393$	1.23949	−	0.796574i	0.0625241	−	0.0401818i
$394$	−2.66815	+	18.5574i	−0.134420	+	0.934909i
$395$	−2.88418	+	6.31548i	−0.145119	+	0.317766i
$396$	6.00892	−	1.76438i	0.301960	−	0.0886633i
$397$	1.23203	+	2.69776i	0.0618337	+	0.135397i	0.938026	−	0.346565i	$-0.112652\pi$
$397$	1.23203	+	2.69776i	0.0618337	+	0.135397i	−0.876192	+	0.481961i	$0.839925\pi$
$398$	3.09949	+	3.57700i	0.155363	+	0.179299i
$399$	−0.572961	−	3.98503i	−0.0286840	−	0.199501i
$400$	−0.0830189	−	0.0243765i	−0.00415094	−	0.00121883i
$401$	−6.44415	+	7.43695i	−0.321806	+	0.371383i	−0.893485	−	0.449094i	$-0.851747\pi$
$401$	−6.44415	+	7.43695i	−0.321806	+	0.371383i	0.571679	+	0.820477i	$0.306292\pi$
$402$	5.54138	+	3.56123i	0.276379	+	0.177618i
$403$	21.7582	+	13.9832i	1.08385	+	0.696550i
$404$	−6.29910	+	7.26955i	−0.313392	+	0.361673i
$405$	2.16398	+	0.635401i	0.107529	+	0.0315733i
$406$	−1.19987	−	8.34526i	−0.0595484	−	0.414168i
$407$	−7.01503	−	8.09577i	−0.347722	−	0.401293i
$408$	−0.662658	−	1.45102i	−0.0328065	−	0.0718361i
$409$	−10.9253	+	3.20797i	−0.540223	+	0.158624i	−0.540450	−	0.841376i	$-0.681746\pi$
$409$	−10.9253	+	3.20797i	−0.540223	+	0.158624i	0.000227038		1.00000i	$0.499928\pi$
$410$	2.75004	−	6.02175i	0.135815	−	0.297393i
$411$	1.13487	−	7.89318i	0.0559789	−	0.389342i
$412$	12.4932	−	8.02889i	0.615496	−	0.395555i
$413$	9.49989			0.467459
$414$	−0.282724	+	4.78749i	−0.0138951	+	0.235292i
$415$	−39.3919			−1.93367
$416$	−4.02759	+	2.58838i	−0.197469	+	0.126906i
$417$	−0.968879	+	6.73870i	−0.0474462	+	0.329996i
$418$	−10.4740	+	22.9348i	−0.512299	+	1.12178i
$419$	−21.1278	+	6.20370i	−1.03216	+	0.303070i	−0.753590	−	0.657345i	$-0.771680\pi$
$419$	−21.1278	+	6.20370i	−1.03216	+	0.303070i	−0.278573	+	0.960415i	$0.589861\pi$
$420$	−0.936899	−	2.05152i	−0.0457160	−	0.100104i
$421$	−2.52522	−	2.91425i	−0.123071	−	0.142032i	0.690870	−	0.722979i	$-0.257228\pi$
$421$	−2.52522	−	2.91425i	−0.123071	−	0.142032i	−0.813941	+	0.580947i	$0.802682\pi$
$422$	−0.774255	−	5.38506i	−0.0376902	−	0.262141i
$423$	−0.107760	−	0.0316412i	−0.00523948	−	0.00153845i
$424$	7.99920	−	9.23157i	0.388476	−	0.448325i
$425$	−0.116110	−	0.0746193i	−0.00563216	−	0.00361957i
$426$	5.46928	+	3.51489i	0.264987	+	0.170297i
$427$	2.12835	−	2.45625i	0.102998	−	0.118866i
$428$	−8.65662	−	2.54181i	−0.418434	−	0.122863i
$429$	−4.26701	−	29.6777i	−0.206013	−	1.43285i
$430$	−8.31268	−	9.59334i	−0.400873	−	0.462632i
$431$	11.2665	+	24.6702i	0.542689	+	1.18832i	0.960113	+	0.279612i	$0.0902057\pi$
$431$	11.2665	+	24.6702i	0.542689	+	1.18832i	−0.417424	+	0.908712i	$0.637067\pi$
$432$	−0.959493	+	0.281733i	−0.0461636	+	0.0135549i
$433$	11.4392	−	25.0483i	0.549731	−	1.20374i	−0.407176	−	0.913350i	$-0.633486\pi$
$433$	11.4392	−	25.0483i	0.549731	−	1.20374i	0.956907	−	0.290394i	$-0.0937864\pi$
$434$	0.768825	−	5.34730i	0.0369048	−	0.256678i
$435$	−15.9963	+	10.2802i	−0.766966	+	0.492899i
$436$	−16.7060			−0.800074
$437$	−13.8213	−	13.4823i	−0.661163	−	0.644948i
$438$	−0.712619			−0.0340503
$439$	−10.6595	+	6.85042i	−0.508748	+	0.326953i	−0.769707	−	0.638397i	$-0.779598\pi$
$439$	−10.6595	+	6.85042i	−0.508748	+	0.326953i	0.260959	+	0.965350i	$0.415961\pi$
$440$	−2.01009	+	13.9805i	−0.0958272	+	0.666493i
$441$	0.415415	−	0.909632i	0.0197817	−	0.0433158i
$442$	−7.32770	+	2.15161i	−0.348543	+	0.102342i
$443$	11.7569	+	25.7441i	0.558589	+	1.22314i	0.952654	+	0.304057i	$0.0983414\pi$
$443$	11.7569	+	25.7441i	0.558589	+	1.22314i	−0.394065	+	0.919083i	$0.628931\pi$
$444$	1.12015	+	1.29272i	0.0531598	+	0.0613497i
$445$	−1.59595	−	11.1000i	−0.0756551	−	0.526193i
$446$	−10.5024	−	3.08377i	−0.497301	−	0.146021i
$447$	−12.9482	+	14.9430i	−0.612428	+	0.706779i
$448$	0.841254	+	0.540641i	0.0397455	+	0.0255429i
$449$	−16.1261	−	10.3636i	−0.761036	−	0.489088i	0.101655	−	0.994820i	$-0.467586\pi$
$449$	−16.1261	−	10.3636i	−0.761036	−	0.489088i	−0.862691	+	0.505732i	$0.831223\pi$
$450$	−0.0566610	+	0.0653902i	−0.00267102	+	0.00308253i
$451$	−17.6377	−	5.17891i	−0.830529	−	0.243865i
$452$	1.10816	+	7.70744i	0.0521236	+	0.362527i
$453$	−2.42147	−	2.79453i	−0.113771	−	0.131298i
$454$	5.64379	+	12.3582i	0.264876	+	0.579998i
$455$	−10.3603	+	3.04205i	−0.485697	+	0.142613i
$456$	1.67247	−	3.66219i	0.0783204	−	0.171498i
$457$	−0.597679	+	4.15695i	−0.0279583	+	0.194454i	−0.999014	−	0.0443996i	$-0.985863\pi$
$457$	−0.597679	+	4.15695i	−0.0279583	+	0.194454i	0.971056	+	0.238854i	$0.0767716\pi$
$458$	22.8478	−	14.6834i	1.06761	−	0.686110i
$459$	−1.59517			−0.0744562
$460$	−9.55676	−	5.06541i	−0.445586	−	0.236176i
$461$	−15.8721			−0.739239			−0.369620	−	0.929183i	$-0.620512\pi$
$461$	−15.8721			−0.739239			−0.369620	+	0.929183i	$0.620512\pi$
$462$	−5.26843	+	3.38582i	−0.245110	+	0.157522i
$463$	−3.91347	+	27.2188i	−0.181874	+	1.26496i	0.670452	+	0.741953i	$0.266100\pi$
$463$	−3.91347	+	27.2188i	−0.181874	+	1.26496i	−0.852326	+	0.523010i	$0.824809\pi$
$464$	3.50240	−	7.66918i	0.162595	−	0.356033i
$465$	−11.6904	+	3.43261i	−0.542130	+	0.159184i
$466$	7.08874	+	15.5222i	0.328380	+	0.719051i
$467$	−13.4167	−	15.4837i	−0.620851	−	0.716500i	0.355017	−	0.934860i	$-0.384475\pi$
$467$	−13.4167	−	15.4837i	−0.620851	−	0.716500i	−0.975868	+	0.218360i	$0.929929\pi$
$468$	0.681348	+	4.73888i	0.0314953	+	0.219055i
$469$	−6.32023	−	1.85579i	−0.291841	−	0.0856923i
$470$	0.165873	−	0.191428i	0.00765115	−	0.00882990i
$471$	−10.4194	−	6.69615i	−0.480101	−	0.308542i
$472$	7.99182	+	5.13603i	0.367853	+	0.236405i
$473$	−23.0826	+	26.6388i	−1.06134	+	1.22485i
$474$	−2.95374	−	0.867296i	−0.135670	−	0.0398362i
$475$	−0.0495747	−	0.344800i	−0.00227465	−	0.0158205i
$476$	1.04461	+	1.20555i	0.0478798	+	0.0552563i
$477$	−5.07434	−	11.1113i	−0.232338	−	0.508750i
$478$	−15.3186	+	4.49794i	−0.700655	+	0.205731i
$479$	13.7415	−	30.0897i	0.627866	−	1.37483i	−0.281792	−	0.959475i	$-0.590929\pi$
$479$	13.7415	−	30.0897i	0.627866	−	1.37483i	0.909658	−	0.415358i	$-0.136344\pi$
$480$	0.320967	−	2.23238i	0.0146501	−	0.101894i
$481$	6.88924	−	4.42745i	0.314122	−	0.201874i
$482$	−15.1605			−0.690544
$483$	−1.07752	−	4.67322i	−0.0490289	−	0.212639i
$484$	28.2201			1.28273
$485$	26.9697	−	17.3324i	1.22463	−	0.787023i
$486$	−0.142315	+	0.989821i	−0.00645553	+	0.0448992i
$487$	−11.7887	+	25.8137i	−0.534199	+	1.16973i	0.429580	+	0.903029i	$0.358662\pi$
$487$	−11.7887	+	25.8137i	−0.534199	+	1.16973i	−0.963779	+	0.266704i	$0.914066\pi$
$488$	3.11843	−	0.915654i	0.141165	−	0.0414497i
$489$	−1.20532	−	2.63929i	−0.0545067	−	0.119353i
$490$	1.47693	+	1.70447i	0.0667208	+	0.0769999i
$491$	−2.26194	−	15.7321i	−0.102080	−	0.709982i	−0.975014	−	0.222143i	$-0.928695\pi$
$491$	−2.26194	−	15.7321i	−0.102080	−	0.709982i	0.872934	−	0.487838i	$-0.162214\pi$
$492$	2.81636	+	0.826958i	0.126971	+	0.0372821i
$493$	8.80723	−	10.1641i	0.396658	−	0.457767i
$494$	−16.2151	−	10.4208i	−0.729554	−	0.468856i
$495$	11.8821	+	7.63614i	0.534059	+	0.343219i
$496$	3.53774	−	4.08277i	0.158849	−	0.183322i
$497$	−6.23799	−	1.83164i	−0.279812	−	0.0821603i
$498$	−2.48569	−	17.2884i	−0.111386	−	0.774710i
$499$	−5.09725	−	5.88253i	−0.228184	−	0.263338i	0.630099	−	0.776515i	$-0.283014\pi$
$499$	−5.09725	−	5.88253i	−0.228184	−	0.263338i	−0.858283	+	0.513176i	$0.828469\pi$
$500$	4.60343	+	10.0801i	0.205872	+	0.450796i
$501$	−4.20406	+	1.23442i	−0.187824	+	0.0551500i
$502$	2.10652	−	4.61265i	0.0940188	−	0.205872i
$503$	−5.76135	+	40.0711i	−0.256886	+	1.78668i	0.297808	+	0.954626i	$0.403744\pi$
$503$	−5.76135	+	40.0711i	−0.256886	+	1.78668i	−0.554694	+	0.832054i	$0.687165\pi$
$504$	0.841254	−	0.540641i	0.0374724	−	0.0240821i
$505$	−21.6940			−0.965371
$506$	−10.1458	+	28.2688i	−0.451036	+	1.25670i
$507$	9.92120			0.440616
$508$	12.5774	−	8.08299i	0.558031	−	0.358625i
$509$	5.33393	−	37.0983i	0.236422	−	1.64435i	−0.432945	−	0.901420i	$-0.642526\pi$
$509$	5.33393	−	37.0983i	0.236422	−	1.64435i	0.669367	−	0.742931i	$-0.266565\pi$
$510$	1.49451	−	3.27253i	0.0661782	−	0.144910i
$511$	0.683753	−	0.200768i	0.0302474	−	0.00888145i
$512$	0.415415	+	0.909632i	0.0183589	+	0.0402004i
$513$	−2.63648	−	3.04266i	−0.116403	−	0.134337i
$514$	−3.66524	−	25.4923i	−0.161667	−	1.12442i
$515$	32.1365	+	9.43614i	1.41611	+	0.415806i
$516$	3.68579	−	4.25363i	0.162258	−	0.187255i
$517$	−0.591695	−	0.380259i	−0.0260227	−	0.0167238i
$518$	−1.43897	−	0.924772i	−0.0632249	−	0.0406322i
$519$	13.5739	−	15.6651i	0.595829	−	0.687623i
$520$	−10.3603	−	3.04205i	−0.454328	−	0.133403i
$521$	−4.22455	−	29.3824i	−0.185081	−	1.28726i	−0.844527	−	0.535513i	$-0.820118\pi$
$521$	−4.22455	−	29.3824i	−0.185081	−	1.28726i	0.659446	−	0.751752i	$-0.270791\pi$
$522$	−5.52118	−	6.37178i	−0.241656	−	0.278885i
$523$	3.95355	+	8.65707i	0.172877	+	0.378547i	0.976161	−	0.217049i	$-0.0696431\pi$
$523$	3.95355	+	8.65707i	0.172877	+	0.378547i	−0.803284	+	0.595596i	$0.796916\pi$
$524$	−1.41371	+	0.415101i	−0.0617580	+	0.0181338i
$525$	0.0359432	−	0.0787047i	0.00156869	−	0.00343496i
$526$	0.915475	−	6.36727i	0.0399166	−	0.277626i
$527$	7.24956	−	4.65901i	0.315796	−	0.202950i
$528$	−6.26260			−0.272545
$529$	−17.7508	−	14.6256i	−0.771773	−	0.635898i
$530$	27.5492			1.19666
$531$	7.99182	−	5.13603i	0.346815	−	0.222885i
$532$	−0.572961	+	3.98503i	−0.0248410	+	0.172773i
$533$	5.83777	−	12.7829i	0.252862	−	0.553691i
$534$	4.77089	−	1.40086i	0.206457	−	0.0606211i
$535$	−8.45278	−	18.5090i	−0.365445	−	0.800214i
$536$	−4.31360	−	4.97816i	−0.186319	−	0.215024i
$537$	0.443719	+	3.08613i	0.0191479	+	0.133176i
$538$	11.6554	+	3.42233i	0.502500	+	0.147547i
$539$	4.10113	−	4.73296i	0.176648	−	0.203863i
$540$	−1.89731	−	1.21932i	−0.0816471	−	0.0524714i
$541$	−28.0947	−	18.0554i	−1.20789	−	0.776262i	−0.227584	−	0.973759i	$-0.573083\pi$
$541$	−28.0947	−	18.0554i	−1.20789	−	0.776262i	−0.980304	+	0.197497i	$0.936719\pi$
$542$	−6.21767	+	7.17558i	−0.267072	+	0.308218i
$543$	−7.10446	−	2.08606i	−0.304881	−	0.0895212i
$544$	0.227016	+	1.57893i	0.00973325	+	0.0676963i
$545$	−24.6736	−	28.4749i	−1.05690	−	1.21973i
$546$	−1.98884	−	4.35496i	−0.0851147	−	0.186375i
$547$	7.92145	−	2.32595i	0.338697	−	0.0994503i	−0.107961	−	0.994155i	$-0.534432\pi$
$547$	7.92145	−	2.32595i	0.338697	−	0.0994503i	0.446658	+	0.894705i	$0.352614\pi$
$548$	−3.31266	+	7.25372i	−0.141510	+	0.309863i
$549$	0.462535	−	3.21700i	0.0197405	−	0.137298i
$550$	−0.455844	+	0.292953i	−0.0194373	+	0.0124916i
$551$	33.9436			1.44605
$552$	1.62006	−	4.51391i	0.0689545	−	0.192125i
$553$	3.07844			0.130908
$554$	21.5749	−	13.8653i	0.916628	−	0.589081i
$555$	−0.549018	+	3.81850i	−0.0233045	+	0.162086i
$556$	2.82814	−	6.19277i	0.119940	−	0.262632i
$557$	40.1673	−	11.7942i	1.70194	−	0.499736i	0.720822	−	0.693120i	$-0.243765\pi$
$557$	40.1673	−	11.7942i	1.70194	−	0.499736i	0.981123	+	0.193384i	$0.0619464\pi$
$558$	−2.24419	−	4.91409i	−0.0950042	−	0.208030i
$559$	−17.6461	−	20.3647i	−0.746351	−	0.861335i
$560$	0.320967	+	2.23238i	0.0135633	+	0.0943351i
$561$	−9.58525	−	2.81448i	−0.404690	−	0.118828i
$562$	−3.14862	+	3.63370i	−0.132817	+	0.153278i
$563$	−8.78657	−	5.64679i	−0.370310	−	0.237984i	0.342229	−	0.939617i	$-0.388818\pi$
$563$	−8.78657	−	5.64679i	−0.370310	−	0.237984i	−0.712539	+	0.701633i	$0.752455\pi$
$564$	0.0944807	+	0.0607191i	0.00397836	+	0.00255673i
$565$	−11.5004	+	13.2722i	−0.483825	+	0.558364i
$566$	9.07488	+	2.66463i	0.381446	+	0.112003i
$567$	−0.142315	−	0.989821i	−0.00597666	−	0.0415686i
$568$	−4.25747	−	4.91339i	−0.178640	−	0.206161i
$569$	−5.03882	−	11.0335i	−0.211239	−	0.462548i	0.774121	−	0.633038i	$-0.218192\pi$
$569$	−5.03882	−	11.0335i	−0.211239	−	0.462548i	−0.985359	+	0.170490i	$0.945465\pi$
$570$	8.71220	−	2.55813i	0.364914	−	0.107148i
$571$	4.17439	−	9.14064i	0.174693	−	0.382524i	−0.801951	−	0.597390i	$-0.796204\pi$
$571$	4.17439	−	9.14064i	0.174693	−	0.382524i	0.976643	+	0.214866i	$0.0689316\pi$
$572$	−4.26701	+	29.6777i	−0.178413	+	1.24089i
$573$	−18.3388	+	11.7856i	−0.766116	+	0.492353i
$574$	−2.93526			−0.122515
$575$	−0.0932311	−	0.404344i	−0.00388800	−	0.0168623i
$576$	1.00000			0.0416667
$577$	−26.8618	+	17.2630i	−1.11827	+	0.718669i	−0.963080	−	0.269216i	$-0.913235\pi$
$577$	−26.8618	+	17.2630i	−1.11827	+	0.718669i	−0.155190	+	0.987885i	$0.549599\pi$
$578$	2.05722	−	14.3083i	0.0855692	−	0.595147i
$579$	−7.13600	+	15.6257i	−0.296562	+	0.649381i
$580$	18.2446	−	5.35711i	0.757568	−	0.222442i
$581$	7.25570	+	15.8878i	0.301017	+	0.659135i
$582$	9.30867	+	10.7428i	0.385857	+	0.445302i
$583$	−10.8869	−	75.7197i	−0.450887	−	3.13599i
$584$	0.683753	+	0.200768i	0.0282939	+	0.00830784i
$585$	−7.07096	+	8.16032i	−0.292348	+	0.337388i
$586$	−15.3667	−	9.87556i	−0.634791	−	0.407955i
$587$	36.3230	+	23.3433i	1.49921	+	0.963483i	0.994997	+	0.0999031i	$0.0318533\pi$
$587$	36.3230	+	23.3433i	1.49921	+	0.963483i	0.504212	+	0.863580i	$0.331783\pi$
$588$	−0.654861	+	0.755750i	−0.0270060	+	0.0311666i
$589$	20.8687	+	6.12759i	0.859878	+	0.252483i
$590$	3.04915	+	21.2073i	0.125532	+	0.873092i
$591$	−12.2775	−	14.1690i	−0.505029	−	0.582834i
$592$	−0.710572	−	1.55594i	−0.0292043	−	0.0639486i
$593$	−25.1378	+	7.38112i	−1.03229	+	0.303106i	−0.753640	−	0.657288i	$-0.771704\pi$
$593$	−25.1378	+	7.38112i	−1.03229	+	0.303106i	−0.278646	+	0.960394i	$0.589886\pi$
$594$	−2.60158	+	5.69666i	−0.106744	+	0.233737i
$595$	−0.511998	+	3.56102i	−0.0209899	+	0.145988i
$596$	16.6336	−	10.6898i	0.681339	−	0.437870i
$597$	−4.73305			−0.193711
$598$	−20.2870	−	10.7528i	−0.829599	−	0.439716i
$599$	−12.0656			−0.492988			−0.246494	−	0.969144i	$-0.579279\pi$
$599$	−12.0656			−0.492988			−0.246494	+	0.969144i	$0.579279\pi$
$600$	0.0727884	−	0.0467782i	0.00297157	−	0.00190971i
$601$	−1.45056	+	10.0889i	−0.0591697	+	0.411534i	0.938613	+	0.344973i	$0.112112\pi$
$601$	−1.45056	+	10.0889i	−0.0591697	+	0.411534i	−0.997782	+	0.0665612i	$0.978797\pi$
$602$	−2.33810	+	5.11973i	−0.0952940	+	0.208665i
$603$	−6.32023	+	1.85579i	−0.257380	+	0.0755735i
$604$	1.53607	+	3.36353i	0.0625020	+	0.136860i
$605$	41.6791	+	48.1003i	1.69450	+	1.95555i
$606$	−1.36892	−	9.52108i	−0.0556088	−	0.386767i
$607$	21.7655	+	6.39094i	0.883435	+	0.259400i	0.691820	−	0.722070i	$-0.256809\pi$
$607$	21.7655	+	6.39094i	0.883435	+	0.259400i	0.191615	+	0.981470i	$0.438627\pi$
$608$	−2.63648	+	3.04266i	−0.106923	+	0.123396i
$609$	7.09267	+	4.55818i	0.287410	+	0.184707i
$610$	6.16640	+	3.96290i	0.249670	+	0.160453i
$611$	0.352115	−	0.406362i	0.0142450	−	0.0164396i
$612$	1.53056	+	0.449412i	0.0618690	+	0.0181664i
$613$	−2.90965	−	20.2370i	−0.117520	−	0.817366i	−0.960272	−	0.279065i	$-0.909975\pi$
$613$	−2.90965	−	20.2370i	−0.117520	−	0.817366i	0.842753	−	0.538301i	$-0.180934\pi$
$614$	−4.28112	−	4.94067i	−0.172772	−	0.199389i
$615$	2.75004	+	6.02175i	0.110892	+	0.242820i
$616$	6.00892	−	1.76438i	0.242106	−	0.0710888i
$617$	16.6010	−	36.3511i	0.668332	−	1.46344i	−0.206218	−	0.978506i	$-0.566116\pi$
$617$	16.6010	−	36.3511i	0.668332	−	1.46344i	0.874550	−	0.484936i	$-0.161157\pi$
$618$	−2.11347	+	14.6995i	−0.0850164	+	0.591302i
$619$	−8.74517	+	5.62018i	−0.351498	+	0.225894i	−0.704460	−	0.709744i	$-0.748811\pi$
$619$	−8.74517	+	5.62018i	−0.351498	+	0.225894i	0.352962	+	0.935638i	$0.385174\pi$
$620$	12.1839			0.489319
$621$	−3.43300	−	3.34881i	−0.137762	−	0.134383i
$622$	−0.250489			−0.0100437
$623$	−4.18297	+	2.68823i	−0.167587	+	0.107702i
$624$	0.681348	−	4.73888i	0.0272757	−	0.189707i
$625$	−10.5620	+	23.1275i	−0.422479	+	0.925101i
$626$	−26.5599	+	7.79870i	−1.06155	+	0.311699i
$627$	−10.4740	−	22.9348i	−0.418291	−	0.915929i
$628$	8.11083	+	9.36040i	0.323657	+	0.373521i
$629$	−0.388314	−	2.70078i	−0.0154831	−	0.107687i
$630$	2.16398	+	0.635401i	0.0862148	+	0.0253150i
$631$	18.1796	−	20.9804i	0.723718	−	0.835215i	−0.268031	−	0.963410i	$-0.586373\pi$
$631$	18.1796	−	20.9804i	0.723718	−	0.835215i	0.991749	+	0.128195i	$0.0409185\pi$
$632$	2.58975	+	1.66433i	0.103015	+	0.0662034i
$633$	4.57679	+	2.94132i	0.181911	+	0.116907i
$634$	7.40651	−	8.54757i	0.294150	−	0.339467i
$635$	32.3531	+	9.49972i	1.28389	+	0.376985i
$636$	1.73839	+	12.0908i	0.0689317	+	0.479431i
$637$	3.13522	+	3.61823i	0.124222	+	0.143360i
$638$	−21.9341	−	48.0290i	−0.868379	−	1.90149i
$639$	−6.23799	+	1.83164i	−0.246771	+	0.0724585i
$640$	−0.936899	+	2.05152i	−0.0370342	+	0.0810935i
$641$	−3.37443	+	23.4697i	−0.133282	+	0.926997i	0.807954	+	0.589246i	$0.200575\pi$
$641$	−3.37443	+	23.4697i	−0.133282	+	0.926997i	−0.941236	+	0.337751i	$0.890334\pi$
$642$	7.58986	−	4.87770i	0.299548	−	0.192508i
$643$	−28.4964			−1.12379			−0.561895	−	0.827209i	$-0.689927\pi$
$643$	−28.4964			−1.12379			−0.561895	+	0.827209i	$0.689927\pi$
$644$	−0.282724	+	4.78749i	−0.0111409	+	0.188654i
$645$	12.6938			0.499818
$646$	−5.40268	+	3.47209i	−0.212566	+	0.136608i
$647$	−7.02865	+	48.8853i	−0.276325	+	1.92188i	0.0991993	+	0.995068i	$0.468372\pi$
$647$	−7.02865	+	48.8853i	−0.276325	+	1.92188i	−0.375524	+	0.926813i	$0.622537\pi$
$648$	0.415415	−	0.909632i	0.0163190	−	0.0357337i
$649$	57.0841	−	16.7614i	2.24075	−	0.657942i
$650$	−0.172082	−	0.376807i	−0.00674962	−	0.0147796i
$651$	3.53774	+	4.08277i	0.138655	+	0.160017i
$652$	0.412926	+	2.87196i	0.0161714	+	0.112475i
$653$	−12.3604	−	3.62935i	−0.483701	−	0.142027i	0.0307854	−	0.999526i	$-0.490199\pi$
$653$	−12.3604	−	3.62935i	−0.483701	−	0.142027i	−0.514486	+	0.857499i	$0.672017\pi$
$654$	10.9401	−	12.6256i	0.427793	−	0.493699i
$655$	−2.79547	−	1.79654i	−0.109228	−	0.0701966i
$656$	−2.46930	−	1.58692i	−0.0964099	−	0.0619589i
$657$	0.466666	−	0.538561i	0.0182064	−	0.0210113i
$658$	−0.107760	−	0.0316412i	−0.00420093	−	0.00123350i
$659$	4.72736	+	32.8795i	0.184152	+	1.28081i	0.846815	+	0.531888i	$0.178517\pi$
$659$	4.72736	+	32.8795i	0.184152	+	1.28081i	−0.662663	+	0.748918i	$0.730574\pi$
$660$	−9.24941	−	10.6744i	−0.360033	−	0.415500i
$661$	17.3189	+	37.9231i	0.673628	+	1.47504i	0.869256	+	0.494361i	$0.164598\pi$
$661$	17.3189	+	37.9231i	0.673628	+	1.47504i	−0.195628	+	0.980678i	$0.562675\pi$
$662$	19.4319	−	5.70572i	0.755243	−	0.221759i
$663$	3.17255	−	6.94691i	0.123212	−	0.269796i
$664$	−2.48569	+	17.2884i	−0.0964635	+	0.670918i
$665$	−7.63858	+	4.90902i	−0.296211	+	0.190364i
$666$	−1.71051			−0.0662810
$667$	40.2921	−	3.38495i	1.56012	−	0.131066i
$668$	4.38155			0.169527
$669$	9.20814	−	5.91771i	0.356007	−	0.228792i
$670$	2.11423	−	14.7048i	0.0816798	−	0.568095i
$671$	8.45534	−	18.5146i	0.326415	−	0.714749i
$672$	−0.959493	+	0.281733i	−0.0370132	+	0.0108681i
$673$	13.5628	+	29.6984i	0.522808	+	1.14479i	0.968366	+	0.249536i	$0.0802781\pi$
$673$	13.5628	+	29.6984i	0.522808	+	1.14479i	−0.445558	+	0.895253i	$0.646995\pi$
$674$	3.48653	+	4.02368i	0.134296	+	0.154986i
$675$	−0.0123136	−	0.0856430i	−0.000473951	−	0.00329640i
$676$	−9.51932	−	2.79513i	−0.366128	−	0.107505i
$677$	22.8938	−	26.4209i	0.879882	−	1.01544i	−0.119862	−	0.992791i	$-0.538245\pi$
$677$	22.8938	−	26.4209i	0.879882	−	1.01544i	0.999744	−	0.0226471i	$-0.00720940\pi$
$678$	−6.55058	−	4.20980i	−0.251574	−	0.161677i
$679$	−11.9582	−	7.68506i	−0.458913	−	0.294926i
$680$	−2.35595	+	2.71892i	−0.0903467	+	0.104266i
$681$	−13.0356	−	3.82759i	−0.499525	−	0.146674i
$682$	−4.81484	−	33.4880i	−0.184370	−	1.28232i
$683$	6.20351	+	7.15923i	0.237371	+	0.273940i	0.861919	−	0.507046i	$-0.169262\pi$
$683$	6.20351	+	7.15923i	0.237371	+	0.273940i	−0.624549	+	0.780986i	$0.714717\pi$
$684$	1.67247	+	3.66219i	0.0639484	+	0.140027i
$685$	−17.2563	+	5.06690i	−0.659329	+	0.193596i
$686$	0.415415	−	0.909632i	0.0158606	−	0.0347299i
$687$	−3.86516	+	26.8828i	−0.147465	+	1.02564i
$688$	−4.73487	+	3.04292i	−0.180515	+	0.116010i
$689$	58.4812			2.22796
$690$	10.0865	−	3.90538i	0.383988	−	0.148675i
$691$	13.0181			0.495233			0.247616	−	0.968858i	$-0.420353\pi$
$691$	13.0181			0.495233			0.247616	+	0.968858i	$0.420353\pi$
$692$	−17.4375	+	11.2064i	−0.662873	+	0.426003i
$693$	0.891261	−	6.19885i	0.0338562	−	0.235475i
$694$	−4.66042	+	10.2049i	−0.176907	+	0.387373i
$695$	14.7323	−	4.32580i	0.558829	−	0.164087i
$696$	3.50240	+	7.66918i	0.132758	+	0.290699i
$697$	−3.06622	−	3.53860i	−0.116141	−	0.134034i
$698$	−1.29215	−	8.98713i	−0.0489087	−	0.340168i
$699$	−16.3730	−	4.80755i	−0.619284	−	0.181838i
$700$	−0.0566610	+	0.0653902i	−0.00214158	+	0.00247152i
$701$	36.8123	+	23.6578i	1.39038	+	0.893544i	0.999637	−	0.0269546i	$-0.00858095\pi$
$701$	36.8123	+	23.6578i	1.39038	+	0.893544i	0.390745	+	0.920499i	$0.372217\pi$
$702$	−4.02759	−	2.58838i	−0.152012	−	0.0976920i
$703$	4.50973	−	5.20450i	0.170088	−	0.196291i
$704$	6.00892	+	1.76438i	0.226470	+	0.0664975i
$705$	0.0360477	+	0.250717i	0.00135763	+	0.00944255i
$706$	−9.89278	−	11.4169i	−0.372320	−	0.429680i
$707$	3.99587	+	8.74974i	0.150280	+	0.329068i
$708$	−9.11508	+	2.67643i	−0.342566	+	0.100586i
$709$	−7.79097	+	17.0598i	−0.292596	+	0.640696i	−0.997654	−	0.0684533i	$-0.978194\pi$
$709$	−7.79097	+	17.0598i	−0.292596	+	0.640696i	0.705058	+	0.709149i	$0.250921\pi$
$710$	2.08672	−	14.5134i	0.0783131	−	0.544680i
$711$	2.58975	−	1.66433i	0.0971231	−	0.0624172i
$712$	−4.97230			−0.186345
$713$	25.3828	+	5.19255i	0.950592	+	0.194463i
$714$	−1.59517			−0.0596978
$715$	−56.8867	+	36.5589i	−2.12744	+	1.36722i
$716$	0.443719	−	3.08613i	0.0165826	−	0.115334i
$717$	6.63221	−	14.5225i	0.247685	−	0.542353i
$718$	−26.7125	+	7.84351i	−0.996903	+	0.292717i
$719$	−14.9744	−	32.7894i	−0.558452	−	1.22284i	−0.952722	−	0.303845i	$-0.901730\pi$
$719$	−14.9744	−	32.7894i	−0.558452	−	1.22284i	0.394269	−	0.918995i	$-0.370998\pi$
$720$	1.47693	+	1.70447i	0.0550419	+	0.0635217i
$721$	−2.11347	−	14.6995i	−0.0787099	−	0.547439i
$722$	2.67815	+	0.786376i	0.0996704	+	0.0292659i
$723$	9.92805	−	11.4576i	0.369228	−	0.426112i
$724$	6.22897	+	4.00311i	0.231498	+	0.148775i
$725$	0.613684	+	0.394391i	0.0227917	+	0.0146473i
$726$	−18.4803	+	21.3274i	−0.685867	+	0.791533i
$727$	−27.3322	−	8.02545i	−1.01369	−	0.297648i	−0.267631	−	0.963522i	$-0.586241\pi$
$727$	−27.3322	−	8.02545i	−1.01369	−	0.297648i	−0.746064	+	0.665874i	$0.768059\pi$
$728$	0.681348	+	4.73888i	0.0252524	+	0.175635i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	0.667652	+	1.46195i	0.0247109	+	0.0541093i
$731$	−8.61451	+	2.52945i	−0.318619	+	0.0935550i
$732$	−1.35013	+	2.95638i	−0.0499023	+	0.109271i
$733$	2.64354	−	18.3862i	0.0976412	−	0.679110i	−0.880937	−	0.473234i	$-0.843087\pi$
$733$	2.64354	−	18.3862i	0.0976412	−	0.679110i	0.978578	−	0.205876i	$-0.0660043\pi$
$734$	13.8628	−	8.90909i	0.511686	−	0.328840i
$735$	−2.25533			−0.0831892
$736$	−2.82616	+	3.87464i	−0.104173	+	0.142821i
$737$	−41.2521			−1.51954
$738$	−2.46930	+	1.58692i	−0.0908961	+	0.0584154i
$739$	4.71624	−	32.8022i	0.173490	−	1.20665i	−0.697951	−	0.716146i	$-0.745904\pi$
$739$	4.71624	−	32.8022i	0.173490	−	1.20665i	0.871440	−	0.490502i	$-0.163186\pi$
$740$	1.60258	−	3.50915i	0.0589119	−	0.128999i
$741$	18.4942	−	5.43039i	0.679402	−	0.199490i
$742$	−5.07434	−	11.1113i	−0.186285	−	0.407907i
$743$	−8.94503	−	10.3231i	−0.328161	−	0.378718i	0.567562	−	0.823331i	$-0.307887\pi$
$743$	−8.94503	−	10.3231i	−0.328161	−	0.378718i	−0.895723	+	0.444613i	$0.853341\pi$
$744$	0.768825	+	5.34730i	0.0281865	+	0.196041i
$745$	42.7870	+	12.5634i	1.56759	+	0.460287i
$746$	17.8922	−	20.6487i	0.655080	−	0.756002i
$747$	14.6934	+	9.44291i	0.537605	+	0.345498i
$748$	8.40405	+	5.40096i	0.307283	+	0.197479i
$749$	−5.90821	+	6.81843i	−0.215881	+	0.249140i
$750$	−10.6326	−	3.12203i	−0.388249	−	0.114000i
$751$	−2.82169	−	19.6253i	−0.102965	−	0.716136i	−0.974268	−	0.225392i	$-0.927634\pi$
$751$	−2.82169	−	19.6253i	−0.102965	−	0.716136i	0.871303	−	0.490745i	$-0.163275\pi$
$752$	−0.0735471	−	0.0848778i	−0.00268199	−	0.00309518i
$753$	2.10652	+	4.61265i	0.0767660	+	0.168094i
$754$	38.7296	−	11.3721i	1.41045	−	0.414146i
$755$	−3.46436	+	7.58589i	−0.126081	+	0.276079i
$756$	−0.142315	+	0.989821i	−0.00517594	+	0.0359995i
$757$	−10.9286	+	7.02341i	−0.397208	+	0.255270i	−0.723963	−	0.689839i	$-0.757681\pi$
$757$	−10.9286	+	7.02341i	−0.397208	+	0.255270i	0.326755	+	0.945109i	$0.394045\pi$
$758$	−8.22484			−0.298740
$759$	−14.7201	−	26.1798i	−0.534304	−	0.950267i
$760$	−9.08000			−0.329366
$761$	−31.2243	+	20.0666i	−1.13188	+	0.727415i	−0.965951	−	0.258723i	$-0.916698\pi$
$761$	−31.2243	+	20.0666i	−1.13188	+	0.727415i	−0.165928	+	0.986138i	$0.553062\pi$
$762$	−2.12771	+	14.7986i	−0.0770790	+	0.536096i
$763$	−6.93994	+	15.1963i	−0.251243	+	0.550145i
$764$	20.9164	−	6.14160i	0.756728	−	0.222195i
$765$	1.49451	+	3.27253i	0.0540343	+	0.118319i
$766$	15.5311	+	17.9238i	0.561161	+	0.647614i
$767$	6.47273	+	45.0188i	0.233717	+	1.62554i
$768$	−0.959493	−	0.281733i	−0.0346227	−	0.0101661i
$769$	−4.54544	+	5.24571i	−0.163913	+	0.189165i	−0.831764	−	0.555129i	$-0.812669\pi$
$769$	−4.54544	+	5.24571i	−0.163913	+	0.189165i	0.667851	+	0.744295i	$0.267214\pi$
$770$	11.8821	+	7.63614i	0.428200	+	0.275187i
$771$	21.6660	+	13.9239i	0.780284	+	0.501458i
$772$	11.2492	−	12.9823i	0.404868	−	0.467242i
$773$	12.8549	+	3.77455i	0.462360	+	0.135761i	0.504613	−	0.863346i	$-0.331635\pi$
$773$	12.8549	+	3.77455i	0.462360	+	0.135761i	−0.0422528	+	0.999107i	$0.513453\pi$
$774$	0.800998	+	5.57107i	0.0287913	+	0.200248i
$775$	0.306099	+	0.353257i	0.0109954	+	0.0126894i
$776$	−5.90501	−	12.9302i	−0.211978	−	0.464166i
$777$	1.64122	−	0.481907i	0.0588786	−	0.0172883i
$778$	12.9348	−	28.3234i	0.463737	−	1.01544i
$779$	1.68179	−	11.6971i	0.0602564	−	0.419092i
$780$	9.08356	−	5.83765i	0.325244	−	0.209021i
$781$	−40.7153			−1.45691
$782$	−6.06690	+	4.66025i	−0.216952	+	0.166650i
$783$	8.43108			0.301302
$784$	0.841254	−	0.540641i	0.0300448	−	0.0193086i
$785$	−3.97537	+	27.6493i	−0.141887	+	0.986845i
$786$	0.612067	−	1.34024i	0.0218317	−	0.0478048i
$787$	36.6115	−	10.7501i	1.30506	−	0.383200i	0.445980	−	0.895043i	$-0.352855\pi$
$787$	36.6115	−	10.7501i	1.30506	−	0.383200i	0.859079	+	0.511843i	$0.171037\pi$
$788$	7.78831	+	17.0540i	0.277447	+	0.607524i
$789$	4.21255	+	4.86154i	0.149971	+	0.173076i
$790$	0.988077	+	6.87223i	0.0351542	+	0.244503i
$791$	7.47128	+	2.19376i	0.265648	+	0.0780013i
$792$	4.10113	−	4.73296i	0.145727	−	0.168178i
$793$	13.0900	+	8.41244i	0.464840	+	0.298734i
$794$	2.49497	+	1.60342i	0.0885431	+	0.0569032i
$795$	−18.0409	+	20.8203i	−0.639843	+	0.738418i
$796$	4.54133	+	1.33346i	0.160963	+	0.0472631i
$797$	−5.36092	−	37.2860i	−0.189894	−	1.32074i	−0.832279	−	0.554357i	$-0.812964\pi$
$797$	−5.36092	−	37.2860i	−0.189894	−	1.32074i	0.642386	−	0.766382i	$-0.277945\pi$
$798$	−2.63648	−	3.04266i	−0.0933303	−	0.107709i
$799$	−0.0744228	−	0.162963i	−0.00263289	−	0.00576522i
$800$	−0.0830189	+	0.0243765i	−0.00293516	+	0.000861841i
$801$	−2.06557	+	4.52296i	−0.0729833	+	0.159811i
$802$	−1.40045	+	9.74033i	−0.0494515	+	0.343943i
$803$	3.75439	−	2.41280i	0.132489	−	0.0851458i
$804$	6.58705			0.232308
$805$	−8.57768	+	6.58889i	−0.302323	+	0.232228i
$806$	25.8640			0.911022
$807$	−10.2191	+	6.56741i	−0.359729	+	0.231184i
$808$	−1.36892	+	9.52108i	−0.0481586	+	0.334950i
$809$	−16.5875	+	36.3215i	−0.583185	+	1.27700i	0.356289	+	0.934376i	$0.384042\pi$
$809$	−16.5875	+	36.3215i	−0.583185	+	1.27700i	−0.939474	+	0.342621i	$0.888685\pi$
$810$	2.16398	−	0.635401i	0.0760343	−	0.0223257i
$811$	−12.3755	−	27.0986i	−0.434564	−	0.951562i	−0.992564	−	0.121721i	$-0.961159\pi$
$811$	−12.3755	−	27.0986i	−0.434564	−	0.951562i	0.558001	−	0.829841i	$-0.311569\pi$
$812$	−5.52118	−	6.37178i	−0.193755	−	0.223606i
$813$	−1.35123	−	9.39801i	−0.0473897	−	0.329603i
$814$	−10.2783	−	3.01799i	−0.360255	−	0.105780i
$815$	−4.28530	+	4.94550i	−0.150108	+	0.173233i
$816$	−1.34194	−	0.862414i	−0.0469774	−	0.0301905i
$817$	−19.0627	−	12.2508i	−0.666918	−	0.428602i
$818$	−7.45661	+	8.60539i	−0.260714	+	0.300880i
$819$	4.59368	+	1.34883i	0.160516	+	0.0471318i
$820$	−0.942122	−	6.55260i	−0.0329003	−	0.228827i
$821$	9.48696	+	10.9485i	0.331097	+	0.382106i	0.896750	−	0.442537i	$-0.145921\pi$
$821$	9.48696	+	10.9485i	0.331097	+	0.382106i	−0.565653	+	0.824643i	$0.691376\pi$
$822$	−3.31266	−	7.25372i	−0.115542	−	0.253002i
$823$	21.1457	−	6.20893i	0.737092	−	0.216430i	0.108425	−	0.994105i	$-0.465419\pi$
$823$	21.1457	−	6.20893i	0.737092	−	0.216430i	0.628667	+	0.777675i	$0.283601\pi$
$824$	6.16920	−	13.5087i	0.214914	−	0.470597i
$825$	0.0771152	−	0.536348i	0.00268481	−	0.0186732i
$826$	7.99182	−	5.13603i	0.278071	−	0.178705i
$827$	−47.5858			−1.65472			−0.827361	−	0.561671i	$-0.810159\pi$
$827$	−47.5858			−1.65472			−0.827361	+	0.561671i	$0.810159\pi$
$828$	2.35047	+	4.18035i	0.0816845	+	0.145277i
$829$	−44.9489			−1.56114			−0.780571	−	0.625068i	$-0.785071\pi$
$829$	−44.9489			−1.56114			−0.780571	+	0.625068i	$0.785071\pi$
$830$	−33.1386	+	21.2969i	−1.15026	+	0.739226i
$831$	−3.64982	+	25.3851i	−0.126611	+	0.880598i
$832$	−1.98884	+	4.35496i	−0.0689508	+	0.150981i
$833$	1.53056	−	0.449412i	0.0530306	−	0.0155712i
$834$	2.82814	+	6.19277i	0.0979306	+	0.214438i
$835$	6.47123	+	7.46820i	0.223946	+	0.258448i
$836$	3.58823	+	24.9567i	0.124101	+	0.863145i
$837$	5.18345	+	1.52200i	0.179166	+	0.0526080i
$838$	−14.4199	+	16.6415i	−0.498127	+	0.574870i
$839$	−1.56934	−	1.00855i	−0.0541796	−	0.0348191i	0.513271	−	0.858227i	$-0.328434\pi$
$839$	−1.56934	−	1.00855i	−0.0541796	−	0.0348191i	−0.567450	+	0.823408i	$0.692070\pi$
$840$	−1.89731	−	1.21932i	−0.0654633	−	0.0420707i
$841$	−27.5585	+	31.8043i	−0.950295	+	1.09670i
$842$	−3.69991	−	1.08639i	−0.127507	−	0.0374395i
$843$	−0.684260	−	4.75914i	−0.0235672	−	0.163913i
$844$	−3.56273	−	4.11161i	−0.122634	−	0.141527i
$845$	−9.29516	−	20.3536i	−0.319763	−	0.700184i
$846$	−0.107760	+	0.0316412i	−0.00370487	+	0.00108785i
$847$	11.7231	−	25.6699i	0.402810	−	0.882030i
$848$	1.73839	−	12.0908i	0.0596966	−	0.415199i
$849$	−7.95658	+	5.11338i	−0.273069	+	0.175491i
$850$	−0.138020			−0.00473405
$851$	4.83417	−	6.62762i	0.165713	−	0.227192i
$852$	6.50134			0.222732
$853$	30.8436	−	19.8220i	1.05607	−	0.678693i	0.107157	−	0.994242i	$-0.465825\pi$
$853$	30.8436	−	19.8220i	1.05607	−	0.678693i	0.948909	+	0.315550i	$0.102189\pi$
$854$	0.462535	−	3.21700i	0.0158276	−	0.110083i
$855$	−3.77197	+	8.25946i	−0.128999	+	0.282467i
$856$	−8.65662	+	2.54181i	−0.295877	+	0.0868774i
$857$	6.15805	+	13.4843i	0.210355	+	0.460613i	0.985171	−	0.171573i	$-0.0548849\pi$
$857$	6.15805	+	13.4843i	0.210355	+	0.460613i	−0.774816	+	0.632186i	$0.782158\pi$
$858$	−19.6346	−	22.6595i	−0.670314	−	0.773584i
$859$	0.389630	+	2.70994i	0.0132940	+	0.0924619i	0.995388	−	0.0959286i	$-0.0305820\pi$
$859$	0.389630	+	2.70994i	0.0132940	+	0.0924619i	−0.982094	+	0.188390i	$0.939673\pi$
$860$	−12.1796	−	3.57626i	−0.415322	−	0.121949i
$861$	1.92219	−	2.21832i	0.0655079	−	0.0756002i
$862$	22.8157	+	14.6628i	0.777107	+	0.499416i
$863$	31.1860	+	20.0420i	1.06158	+	0.682239i	0.950232	−	0.311542i	$-0.100846\pi$
$863$	31.1860	+	20.0420i	1.06158	+	0.682239i	0.111352	+	0.993781i	$0.464482\pi$
$864$	−0.654861	+	0.755750i	−0.0222788	+	0.0257111i
$865$	−44.8548	−	13.1706i	−1.52511	−	0.447812i
$866$	−3.91888	−	27.2564i	−0.133169	−	0.926212i
$867$	9.46629	+	10.9247i	0.321492	+	0.371022i
$868$	−2.24419	−	4.91409i	−0.0761728	−	0.166795i
$869$	18.4981	−	5.43153i	0.627504	−	0.184252i
$870$	−7.89907	+	17.2965i	−0.267803	+	0.586408i
$871$	4.48808	−	31.2153i	0.152073	−	1.05769i
$872$	−14.0540	+	9.03196i	−0.475929	+	0.305861i
$873$	−14.2147			−0.481096
$874$	−18.9163	−	3.86971i	−0.639854	−	0.130895i
$875$	11.0815			0.374624
$876$	−0.599493	+	0.385271i	−0.0202550	+	0.0130171i
$877$	−1.03183	+	7.17650i	−0.0348423	+	0.242333i	−0.999798	−	0.0200779i	$-0.993609\pi$
$877$	−1.03183	+	7.17650i	−0.0348423	+	0.242333i	0.964956	+	0.262411i	$0.0845177\pi$
$878$	−5.26369	+	11.5259i	−0.177641	+	0.388980i
$879$	17.5265	−	5.14624i	0.591153	−	0.173578i
$880$	5.86742	+	12.8479i	0.197791	+	0.433101i
$881$	30.9054	+	35.6668i	1.04123	+	1.20164i	0.979059	+	0.203579i	$0.0652572\pi$
$881$	30.9054	+	35.6668i	1.04123	+	1.20164i	0.0621719	+	0.998065i	$0.480197\pi$
$882$	−0.142315	−	0.989821i	−0.00479199	−	0.0333290i
$883$	−18.8196	−	5.52592i	−0.633329	−	0.185962i	−0.0507174	−	0.998713i	$-0.516151\pi$
$883$	−18.8196	−	5.52592i	−0.633329	−	0.185962i	−0.582611	+	0.812751i	$0.697969\pi$
$884$	−5.00121	+	5.77170i	−0.168209	+	0.194123i
$885$	−18.0242	−	11.5835i	−0.605877	−	0.389373i
$886$	23.8089	+	15.3010i	0.799875	+	0.514049i
$887$	−21.8077	+	25.1674i	−0.732230	+	0.845038i	−0.992721	−	0.120438i	$-0.961570\pi$
$887$	−21.8077	+	25.1674i	−0.732230	+	0.845038i	0.260491	+	0.965476i	$0.416116\pi$
$888$	1.64122	+	0.481907i	0.0550759	+	0.0161717i
$889$	−2.12771	−	14.7986i	−0.0713613	−	0.496328i
$890$	−7.34373	−	8.47512i	−0.246163	−	0.284087i
$891$	−2.60158	−	5.69666i	−0.0871561	−	0.190845i
$892$	−10.5024	+	3.08377i	−0.351645	+	0.103252i
$893$	0.187834	−	0.411299i	0.00628562	−	0.0137636i
$894$	−2.81391	+	19.5712i	−0.0941111	+	0.654557i
$895$	5.91555	−	3.80169i	0.197735	−	0.127077i
$896$	1.00000			0.0334077
$897$	21.4116	−	8.29033i	0.714914	−	0.276806i
$898$	−19.1691			−0.639680
$899$	−38.3166	+	24.6246i	−1.27793	+	0.821277i
$900$	−0.0123136	+	0.0856430i	−0.000410453	+	0.00285477i
$901$	8.09444	−	17.7244i	0.269665	−	0.590484i
$902$	−17.6377	+	5.17891i	−0.587272	+	0.172439i
$903$	−2.33810	−	5.11973i	−0.0778072	−	0.170374i
$904$	5.09920	+	5.88479i	0.169597	+	0.195725i
$905$	2.37657	+	16.5294i	0.0789997	+	0.549455i
$906$	−3.54790	−	1.04176i	−0.117871	−	0.0346101i
$907$	−20.1799	+	23.2889i	−0.670064	+	0.773295i	−0.984386	−	0.176021i	$-0.943677\pi$
$907$	−20.1799	+	23.2889i	−0.670064	+	0.773295i	0.314323	+	0.949316i	$0.398223\pi$
$908$	11.4292	+	7.34510i	0.379291	+	0.243756i
$909$	8.09201	+	5.20042i	0.268395	+	0.172487i
$910$	−7.07096	+	8.16032i	−0.234400	+	0.270512i
$911$	−22.8006	−	6.69487i	−0.755419	−	0.221811i	−0.118724	−	0.992927i	$-0.537880\pi$
$911$	−22.8006	−	6.69487i	−0.755419	−	0.221811i	−0.636694	+	0.771116i	$0.719699\pi$
$912$	−0.572961	−	3.98503i	−0.0189727	−	0.131958i
$913$	71.6309	+	82.6665i	2.37064	+	2.73586i
$914$	1.74462	+	3.82018i	0.0577068	+	0.126360i
$915$	−7.03310	+	2.06510i	−0.232507	+	0.0682702i
$916$	11.2824	−	24.7049i	0.372779	−	0.816273i
$917$	−0.209685	+	1.45839i	−0.00692441	+	0.0481603i
$918$	−1.34194	+	0.862414i	−0.0442907	+	0.0284639i
$919$	−49.0151			−1.61686			−0.808429	−	0.588593i	$-0.799682\pi$
$919$	−49.0151			−1.61686			−0.808429	+	0.588593i	$0.799682\pi$
$920$	−10.7782	+	0.905482i	−0.355348	+	0.0298529i
$921$	6.53745			0.215416
$922$	−13.3525	+	8.58112i	−0.439741	+	0.282604i
$923$	4.42967	−	30.8091i	0.145805	−	1.01409i
$924$	−2.60158	+	5.69666i	−0.0855856	+	0.187406i
$925$	0.142005	−	0.0416963i	0.00466909	−	0.00137097i
$926$	11.4234	+	25.0137i	0.375395	+	0.822000i
$927$	−9.72514	−	11.2234i	−0.319415	−	0.368625i
$928$	−1.19987	−	8.34526i	−0.0393876	−	0.273947i
$929$	−29.1449	−	8.55772i	−0.956214	−	0.280770i	−0.233842	−	0.972275i	$-0.575130\pi$
$929$	−29.1449	−	8.55772i	−0.956214	−	0.280770i	−0.722372	+	0.691505i	$0.756948\pi$
$930$	−7.97879	+	9.20801i	−0.261635	+	0.301943i
$931$	3.38690	+	2.17663i	0.111001	+	0.0713361i
$932$	14.3554	+	9.22562i	0.470225	+	0.302195i
$933$	0.164036	−	0.189307i	0.00537029	−	0.00619764i
$934$	−19.6580	−	5.77210i	−0.643228	−	0.188869i
$935$	3.20644	+	22.3012i	0.104862	+	0.729329i
$936$	3.13522	+	3.61823i	0.102478	+	0.118266i
$937$	−13.8193	−	30.2601i	−0.451457	−	0.988554i	−0.989352	−	0.145542i	$-0.953507\pi$
$937$	−13.8193	−	30.2601i	−0.451457	−	0.988554i	0.537895	−	0.843012i	$-0.319220\pi$
$938$	−6.32023	+	1.85579i	−0.206363	+	0.0605936i
$939$	11.4992	−	25.1797i	0.375262	−	0.821710i
$940$	0.0360477	−	0.250717i	0.00117575	−	0.00817749i
$941$	2.19885	−	1.41312i	0.0716805	−	0.0460663i	−0.504310	−	0.863523i	$-0.668253\pi$
$941$	2.19885	−	1.41312i	0.0716805	−	0.0460663i	0.575990	+	0.817457i	$0.304617\pi$
$942$	−12.3856			−0.403544
$943$	0.829867	−	14.0525i	0.0270242	−	0.457613i
$944$	9.49989			0.309195
$945$	−1.89731	+	1.21932i	−0.0617194	+	0.0396646i
$946$	−5.01633	+	34.8893i	−0.163095	+	1.13435i
$947$	−13.8786	+	30.3898i	−0.450993	+	0.987536i	0.538456	+	0.842653i	$0.319008\pi$
$947$	−13.8786	+	30.3898i	−0.450993	+	0.987536i	−0.989449	+	0.144882i	$0.953720\pi$
$948$	−2.95374	+	0.867296i	−0.0959330	+	0.0281685i
$949$	1.41729	+	3.10343i	0.0460071	+	0.100742i
$950$	−0.228118	−	0.263262i	−0.00740112	−	0.00854135i
$951$	1.60959	+	11.1949i	0.0521945	+	0.363021i
$952$	1.53056	+	0.449412i	0.0496056	+	0.0145655i
$953$	20.3268	−	23.4584i	0.658450	−	0.759891i	−0.324074	−	0.946032i	$-0.605053\pi$
$953$	20.3268	−	23.4584i	0.658450	−	0.759891i	0.982523	+	0.186141i	$0.0595980\pi$
$954$	−10.2760	−	6.60399i	−0.332698	−	0.213812i
$955$	41.3602	+	26.5806i	1.33838	+	0.860127i
$956$	−10.4550	+	12.0657i	−0.338140	+	0.390234i
$957$	50.6617	+	14.8756i	1.63766	+	0.480860i
$958$	−4.70763	−	32.7423i	−0.152097	−	1.05786i
$959$	5.22208	+	6.02661i	0.168630	+	0.194609i
$960$	−0.936899	−	2.05152i	−0.0302383	−	0.0662126i
$961$	1.74178	−	0.511434i	0.0561865	−	0.0164979i
$962$	3.40194	−	7.44921i	0.109683	−	0.240172i
$963$	−1.28398	+	8.93025i	−0.0413755	+	0.287773i
$964$	−12.7539	+	8.19641i	−0.410774	+	0.263989i
$965$	38.7421			1.24715
$966$	−3.43300	−	3.34881i	−0.110455	−	0.107746i
$967$	−41.8448			−1.34564			−0.672819	−	0.739807i	$-0.734917\pi$
$967$	−41.8448			−1.34564			−0.672819	+	0.739807i	$0.734917\pi$
$968$	23.7403	−	15.2570i	0.763042	−	0.490377i
$969$	0.913971	−	6.35681i	0.0293610	−	0.204210i
$970$	13.3178	−	29.1618i	0.427608	−	0.936330i
$971$	25.7434	−	7.55895i	0.826145	−	0.242578i	0.158785	−	0.987313i	$-0.449242\pi$
$971$	25.7434	−	7.55895i	0.826145	−	0.242578i	0.667360	+	0.744735i	$0.267424\pi$
$972$	0.415415	+	0.909632i	0.0133244	+	0.0291765i
$973$	−4.45829	−	5.14514i	−0.142926	−	0.164946i
$974$	4.03864	+	28.0894i	0.129406	+	0.900042i
$975$	0.397462	+	0.116705i	0.0127290	+	0.00373756i
$976$	2.12835	−	2.45625i	0.0681268	−	0.0786226i
$977$	14.1686	+	9.10559i	0.453293	+	0.291314i	0.747297	−	0.664491i	$-0.231351\pi$
$977$	14.1686	+	9.10559i	0.453293	+	0.291314i	−0.294004	+	0.955804i	$0.594988\pi$
$978$	−2.44089	−	1.56867i	−0.0780511	−	0.0501604i
$979$	−20.3921	+	23.5337i	−0.651733	+	0.752140i
$980$	2.16398	+	0.635401i	0.0691257	+	0.0202971i
$981$	2.37752	+	16.5360i	0.0759083	+	0.527953i
$982$	−10.4083	−	12.0118i	−0.332142	−	0.383313i
$983$	10.5093	+	23.0121i	0.335193	+	0.733971i	0.999914	−	0.0131211i	$-0.00417670\pi$
$983$	10.5093	+	23.0121i	0.335193	+	0.733971i	−0.664721	+	0.747092i	$0.731449\pi$
$984$	2.81636	−	0.826958i	0.0897823	−	0.0263625i
$985$	−17.5652	+	38.4625i	−0.559674	+	1.22552i
$986$	1.91399	−	13.3121i	0.0609540	−	0.423944i
$987$	0.0944807	−	0.0607191i	0.00300736	−	0.00193271i
$988$	−19.2750			−0.613219
$989$	−23.8496	−	12.6411i	−0.758374	−	0.401964i
$990$	14.1242			0.448898
$991$	−47.2435	+	30.3616i	−1.50074	+	0.964467i	−0.505945	+	0.862566i	$0.668856\pi$
$991$	−47.2435	+	30.3616i	−1.50074	+	0.964467i	−0.994795	+	0.101901i	$0.967508\pi$
$992$	0.768825	−	5.34730i	0.0244102	−	0.169777i
$993$	−8.41310	+	18.4221i	−0.266982	+	0.584608i
$994$	−6.23799	+	1.83164i	−0.197857	+	0.0580961i
$995$	4.43439	+	9.70997i	0.140580	+	0.307827i
$996$	−11.4379	−	13.2000i	−0.362423	−	0.418259i
$997$	0.569718	+	3.96247i	0.0180431	+	0.125493i	0.996852	−	0.0792822i	$-0.0252628\pi$
$997$	0.569718	+	3.96247i	0.0180431	+	0.125493i	−0.978809	+	0.204775i	$0.934354\pi$
$998$	−7.46841	−	2.19292i	−0.236409	−	0.0694158i
$999$	1.12015	−	1.29272i	0.0354399	−	0.0408998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.i.127.3	✓	40
23.2	even	11	inner	966.2.q.i.715.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.i.127.3	✓	40	1.1	even	1	trivial
966.2.q.i.715.3	yes	40	23.2	even	11	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 - 0.540641i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(2.16398 - 0.635401i) q^{5} +(0.415415 + 0.909632i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(0.841254 - 0.540641i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(2.16398 - 0.635401i) q^{5} +(0.415415 + 0.909632i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(1.47693 - 1.70447i) q^{10} +(-5.26843 - 3.38582i) q^{11} +(0.841254 + 0.540641i) q^{12} +(3.13522 - 3.61823i) q^{13} +(-0.959493 - 0.281733i) q^{14} +(0.320967 + 2.23238i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-0.662658 - 1.45102i) q^{17} +(-0.959493 + 0.281733i) q^{18} +(1.67247 - 3.66219i) q^{19} +(0.320967 - 2.23238i) q^{20} +(0.841254 - 0.540641i) q^{21} -6.26260 q^{22} +(1.62006 - 4.51391i) q^{23} +1.00000 q^{24} +(0.0727884 - 0.0467782i) q^{25} +(0.681348 - 4.73888i) q^{26} +(0.415415 - 0.909632i) q^{27} +(-0.959493 + 0.281733i) q^{28} +(3.50240 + 7.66918i) q^{29} +(1.47693 + 1.70447i) q^{30} +(0.768825 + 5.34730i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(4.10113 - 4.73296i) q^{33} +(-1.34194 - 0.862414i) q^{34} +(-1.89731 - 1.21932i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(1.64122 + 0.481907i) q^{37} +(-0.572961 - 3.98503i) q^{38} +(3.13522 + 3.61823i) q^{39} +(-0.936899 - 2.05152i) q^{40} +(2.81636 - 0.826958i) q^{41} +(0.415415 - 0.909632i) q^{42} +(0.800998 - 5.57107i) q^{43} +(-5.26843 + 3.38582i) q^{44} -2.25533 q^{45} +(-1.07752 - 4.67322i) q^{46} +0.112309 q^{47} +(0.841254 - 0.540641i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(0.0359432 - 0.0787047i) q^{50} +(1.53056 - 0.449412i) q^{51} +(-1.98884 - 4.35496i) q^{52} +(7.99920 + 9.23157i) q^{53} +(-0.142315 - 0.989821i) q^{54} +(-13.5521 - 3.97926i) q^{55} +(-0.654861 + 0.755750i) q^{56} +(3.38690 + 2.17663i) q^{57} +(7.09267 + 4.55818i) q^{58} +(-6.22111 + 7.17954i) q^{59} +(2.16398 + 0.635401i) q^{60} +(0.462535 + 3.21700i) q^{61} +(3.53774 + 4.08277i) q^{62} +(0.415415 + 0.909632i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(4.48551 - 9.82189i) q^{65} +(0.891261 - 6.19885i) q^{66} +(5.54138 - 3.56123i) q^{67} -1.59517 q^{68} +(4.23741 + 2.24597i) q^{69} -2.25533 q^{70} +(5.46928 - 3.51489i) q^{71} +(-0.142315 + 0.989821i) q^{72} +(-0.296033 + 0.648221i) q^{73} +(1.64122 - 0.481907i) q^{74} +(0.0359432 + 0.0787047i) q^{75} +(-2.63648 - 3.04266i) q^{76} +(0.891261 + 6.19885i) q^{77} +(4.59368 + 1.34883i) q^{78} +(-2.01595 + 2.32653i) q^{79} +(-1.89731 - 1.21932i) q^{80} +(0.841254 + 0.540641i) q^{81} +(1.92219 - 2.21832i) q^{82} +(-16.7586 - 4.92078i) q^{83} +(-0.142315 - 0.989821i) q^{84} +(-2.35595 - 2.71892i) q^{85} +(-2.33810 - 5.11973i) q^{86} +(-8.08956 + 2.37531i) q^{87} +(-2.60158 + 5.69666i) q^{88} +(0.707632 - 4.92169i) q^{89} +(-1.89731 + 1.21932i) q^{90} -4.78761 q^{91} +(-3.43300 - 3.34881i) q^{92} -5.40229 q^{93} +(0.0944807 - 0.0607191i) q^{94} +(1.29222 - 8.98758i) q^{95} +(0.415415 - 0.909632i) q^{96} +(13.6389 - 4.00475i) q^{97} +(0.415415 + 0.909632i) q^{98} +(4.10113 + 4.73296i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 4 q^{10} - q^{11} - 4 q^{12} - 8 q^{13} - 4 q^{14} - 7 q^{15} - 4 q^{16} - 7 q^{17} - 4 q^{18} + 20 q^{19} - 7 q^{20} - 4 q^{21} + 10 q^{22} + 2 q^{23} + 40 q^{24} - 22 q^{25} + 14 q^{26} - 4 q^{27} - 4 q^{28} + 15 q^{29} + 4 q^{30} - 16 q^{31} - 4 q^{32} - q^{33} - 7 q^{34} - 7 q^{35} - 4 q^{36} - 16 q^{37} - 13 q^{38} - 8 q^{39} + 4 q^{40} - 17 q^{41} - 4 q^{42} + 26 q^{43} - q^{44} + 4 q^{45} - 20 q^{46} + 72 q^{47} - 4 q^{48} - 4 q^{49} + 11 q^{50} - 7 q^{51} - 19 q^{52} + 6 q^{53} - 4 q^{54} + 49 q^{55} - 4 q^{56} + 9 q^{57} - 7 q^{58} - 51 q^{59} + 4 q^{60} - 42 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{64} + 8 q^{65} - 12 q^{66} + 54 q^{67} + 4 q^{68} + 2 q^{69} + 4 q^{70} - 59 q^{71} - 4 q^{72} - 27 q^{73} - 16 q^{74} + 11 q^{75} - 2 q^{76} - 12 q^{77} - 8 q^{78} - 6 q^{79} - 7 q^{80} - 4 q^{81} - 6 q^{82} - 24 q^{83} - 4 q^{84} + 35 q^{85} - 7 q^{86} - 29 q^{87} - q^{88} + 22 q^{89} - 7 q^{90} + 36 q^{91} - 9 q^{92} + 50 q^{93} - 16 q^{94} + 22 q^{95} - 4 q^{96} + 16 q^{97} - 4 q^{98} - q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 4 * q^10 - q^11 - 4 * q^12 - 8 * q^13 - 4 * q^14 - 7 * q^15 - 4 * q^16 - 7 * q^17 - 4 * q^18 + 20 * q^19 - 7 * q^20 - 4 * q^21 + 10 * q^22 + 2 * q^23 + 40 * q^24 - 22 * q^25 + 14 * q^26 - 4 * q^27 - 4 * q^28 + 15 * q^29 + 4 * q^30 - 16 * q^31 - 4 * q^32 - q^33 - 7 * q^34 - 7 * q^35 - 4 * q^36 - 16 * q^37 - 13 * q^38 - 8 * q^39 + 4 * q^40 - 17 * q^41 - 4 * q^42 + 26 * q^43 - q^44 + 4 * q^45 - 20 * q^46 + 72 * q^47 - 4 * q^48 - 4 * q^49 + 11 * q^50 - 7 * q^51 - 19 * q^52 + 6 * q^53 - 4 * q^54 + 49 * q^55 - 4 * q^56 + 9 * q^57 - 7 * q^58 - 51 * q^59 + 4 * q^60 - 42 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^64 + 8 * q^65 - 12 * q^66 + 54 * q^67 + 4 * q^68 + 2 * q^69 + 4 * q^70 - 59 * q^71 - 4 * q^72 - 27 * q^73 - 16 * q^74 + 11 * q^75 - 2 * q^76 - 12 * q^77 - 8 * q^78 - 6 * q^79 - 7 * q^80 - 4 * q^81 - 6 * q^82 - 24 * q^83 - 4 * q^84 + 35 * q^85 - 7 * q^86 - 29 * q^87 - q^88 + 22 * q^89 - 7 * q^90 + 36 * q^91 - 9 * q^92 + 50 * q^93 - 16 * q^94 + 22 * q^95 - 4 * q^96 + 16 * q^97 - 4 * q^98 - q^99

Introduction

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