LMFDB - Embedded newform 670.2.k.a.411.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(81,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([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("670.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.k (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:	$5.34997693543$
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			411.1
Character	$\chi$	$=$	670.411
Dual form			670.2.k.a.551.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 + 0.540641i) q^{2} +(-1.57680 - 0.462990i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-1.07618 - 1.24197i) q^{6} +(-0.776855 - 0.499255i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.251829 - 0.161841i) q^{9} +O(q^{10})$	\(q+(0.841254 + 0.540641i) q^{2} +(-1.57680 - 0.462990i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-1.07618 - 1.24197i) q^{6} +(-0.776855 - 0.499255i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.251829 - 0.161841i) q^{9} +(-0.959493 + 0.281733i) q^{10} +(4.00973 - 4.62747i) q^{11} +(-0.233875 - 1.62664i) q^{12} +(-0.274824 - 1.91144i) q^{13} +(-0.383615 - 0.839999i) q^{14} +(1.38249 - 0.888470i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-0.640958 + 1.40350i) q^{17} +(-0.124355 - 0.272299i) q^{18} +(3.67698 - 2.36305i) q^{19} +(-0.959493 - 0.281733i) q^{20} +(0.993794 + 1.14690i) q^{21} +(5.87500 - 1.72506i) q^{22} +(4.35736 + 1.27944i) q^{23} +(0.682679 - 1.49486i) q^{24} +(-0.142315 - 0.989821i) q^{25} +(0.802208 - 1.75659i) q^{26} +(3.55068 + 4.09770i) q^{27} +(0.131421 - 0.914050i) q^{28} -0.963711 q^{29} +1.64337 q^{30} +(0.637396 - 4.43319i) q^{31} +(-0.959493 + 0.281733i) q^{32} +(-8.46500 + 5.44013i) q^{33} +(-1.29800 + 0.834173i) q^{34} +(0.886043 - 0.260166i) q^{35} +(0.0426020 - 0.296303i) q^{36} +11.4866 q^{37} +4.37084 q^{38} +(-0.451637 + 3.14120i) q^{39} +(-0.654861 - 0.755750i) q^{40} +(4.63207 - 10.1428i) q^{41} +(0.215972 + 1.50212i) q^{42} +(0.0242783 - 0.0531621i) q^{43} +(5.87500 + 1.72506i) q^{44} +(0.287224 - 0.0843367i) q^{45} +(2.97393 + 3.43209i) q^{46} +(-9.38421 - 2.75545i) q^{47} +(1.38249 - 0.888470i) q^{48} +(-2.55366 - 5.59173i) q^{49} +(0.415415 - 0.909632i) q^{50} +(1.66047 - 1.91628i) q^{51} +(1.62454 - 1.04403i) q^{52} +(-3.77141 - 8.25823i) q^{53} +(0.771636 + 5.36685i) q^{54} +(0.871397 + 6.06070i) q^{55} +(0.604731 - 0.697897i) q^{56} +(-6.89193 + 2.02365i) q^{57} +(-0.810726 - 0.521022i) q^{58} +(-1.71644 + 11.9381i) q^{59} +(1.38249 + 0.888470i) q^{60} +(-8.96088 - 10.3414i) q^{61} +(2.93297 - 3.38483i) q^{62} +(0.114835 + 0.251454i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(1.62454 + 1.04403i) q^{65} -10.0624 q^{66} +(-1.84776 + 7.97407i) q^{67} -1.54293 q^{68} +(-6.27830 - 4.03482i) q^{69} +(0.886043 + 0.260166i) q^{70} +(1.16326 + 2.54719i) q^{71} +(0.196033 - 0.226234i) q^{72} +(3.29739 + 3.80539i) q^{73} +(9.66311 + 6.21010i) q^{74} +(-0.233875 + 1.62664i) q^{75} +(3.67698 + 2.36305i) q^{76} +(-5.42527 + 1.59300i) q^{77} +(-2.07820 + 2.39837i) q^{78} +(0.856146 + 5.95462i) q^{79} +(-0.142315 - 0.989821i) q^{80} +(-3.32845 - 7.28828i) q^{81} +(9.38037 - 6.02840i) q^{82} +(5.80916 - 6.70413i) q^{83} +(-0.630419 + 1.38043i) q^{84} +(-0.640958 - 1.40350i) q^{85} +(0.0491658 - 0.0315969i) q^{86} +(1.51958 + 0.446188i) q^{87} +(4.00973 + 4.62747i) q^{88} +(10.9945 - 3.22826i) q^{89} +(0.287224 + 0.0843367i) q^{90} +(-0.740799 + 1.62212i) q^{91} +(0.646296 + 4.49509i) q^{92} +(-3.05756 + 6.69513i) q^{93} +(-6.40479 - 7.39152i) q^{94} +(-0.622035 + 4.32635i) q^{95} +1.64337 q^{96} -16.6493 q^{97} +(0.874844 - 6.08467i) q^{98} +(-1.75868 + 0.516396i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} + 6 q^{3} - 4 q^{4} - 4 q^{5} + 6 q^{6} + 13 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 + 6 * q^3 - 4 * q^4 - 4 * q^5 + 6 * q^6 + 13 * q^7 - 4 * q^8 + 4 * q^9	\( 40 q - 4 q^{2} + 6 q^{3} - 4 q^{4} - 4 q^{5} + 6 q^{6} + 13 q^{7} - 4 q^{8} + 4 q^{9} - 4 q^{10} - 14 q^{11} - 5 q^{12} - 6 q^{13} - 9 q^{14} + 6 q^{15} - 4 q^{16} - 24 q^{17} + 4 q^{18} + 24 q^{19} - 4 q^{20} - 10 q^{21} + 19 q^{22} - 15 q^{23} - 5 q^{24} - 4 q^{25} + 16 q^{26} + 54 q^{27} + 2 q^{28} - 40 q^{29} - 16 q^{30} + 15 q^{31} - 4 q^{32} - 40 q^{33} - 2 q^{34} - 9 q^{35} + 4 q^{36} - 6 q^{37} - 20 q^{38} + 21 q^{39} - 4 q^{40} + 8 q^{41} + 23 q^{42} - 54 q^{43} + 19 q^{44} - 7 q^{45} + 7 q^{46} - 23 q^{47} + 6 q^{48} - 7 q^{49} - 4 q^{50} + 61 q^{51} - 6 q^{52} + 17 q^{53} - 12 q^{54} - 3 q^{55} + 2 q^{56} - 18 q^{57} - 18 q^{58} - q^{59} + 6 q^{60} - 6 q^{61} - 7 q^{62} - 43 q^{63} - 4 q^{64} - 6 q^{65} - 18 q^{66} + 44 q^{67} - 2 q^{68} - 45 q^{69} - 9 q^{70} - 14 q^{71} - 7 q^{72} - 26 q^{73} + 38 q^{74} - 5 q^{75} + 24 q^{76} + 21 q^{77} - 45 q^{78} + 2 q^{79} - 4 q^{80} + 4 q^{81} + 8 q^{82} - 11 q^{83} - 10 q^{84} - 24 q^{85} + 45 q^{86} - 7 q^{87} - 14 q^{88} + 61 q^{89} - 7 q^{90} + 70 q^{91} + 18 q^{92} + 10 q^{93} + 43 q^{94} + 13 q^{95} - 16 q^{96} - 18 q^{97} + 26 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 + 6 * q^3 - 4 * q^4 - 4 * q^5 + 6 * q^6 + 13 * q^7 - 4 * q^8 + 4 * q^9 - 4 * q^10 - 14 * q^11 - 5 * q^12 - 6 * q^13 - 9 * q^14 + 6 * q^15 - 4 * q^16 - 24 * q^17 + 4 * q^18 + 24 * q^19 - 4 * q^20 - 10 * q^21 + 19 * q^22 - 15 * q^23 - 5 * q^24 - 4 * q^25 + 16 * q^26 + 54 * q^27 + 2 * q^28 - 40 * q^29 - 16 * q^30 + 15 * q^31 - 4 * q^32 - 40 * q^33 - 2 * q^34 - 9 * q^35 + 4 * q^36 - 6 * q^37 - 20 * q^38 + 21 * q^39 - 4 * q^40 + 8 * q^41 + 23 * q^42 - 54 * q^43 + 19 * q^44 - 7 * q^45 + 7 * q^46 - 23 * q^47 + 6 * q^48 - 7 * q^49 - 4 * q^50 + 61 * q^51 - 6 * q^52 + 17 * q^53 - 12 * q^54 - 3 * q^55 + 2 * q^56 - 18 * q^57 - 18 * q^58 - q^59 + 6 * q^60 - 6 * q^61 - 7 * q^62 - 43 * q^63 - 4 * q^64 - 6 * q^65 - 18 * q^66 + 44 * q^67 - 2 * q^68 - 45 * q^69 - 9 * q^70 - 14 * q^71 - 7 * q^72 - 26 * q^73 + 38 * q^74 - 5 * q^75 + 24 * q^76 + 21 * q^77 - 45 * q^78 + 2 * q^79 - 4 * q^80 + 4 * q^81 + 8 * q^82 - 11 * q^83 - 10 * q^84 - 24 * q^85 + 45 * q^86 - 7 * q^87 - 14 * q^88 + 61 * q^89 - 7 * q^90 + 70 * q^91 + 18 * q^92 + 10 * q^93 + 43 * q^94 + 13 * q^95 - 16 * q^96 - 18 * q^97 + 26 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	0.841254	+	0.540641i	0.594856	+	0.382291i
$2$	0.841254	+	0.540641i	0.594856	+	0.382291i
$3$	−1.57680	−	0.462990i	−0.910364	−	0.267307i	−0.207170	−	0.978305i	$-0.566425\pi$
$3$	−1.57680	−	0.462990i	−0.910364	−	0.267307i	−0.703194	+	0.710998i	$0.748244\pi$
$4$	0.415415	+	0.909632i	0.207708	+	0.454816i
$5$	−0.654861	+	0.755750i	−0.292863	+	0.337981i
$5$	−0.654861	+	0.755750i	−0.292863	+	0.337981i
$6$	−1.07618	−	1.24197i	−0.439347	−	0.507033i
$7$	−0.776855	−	0.499255i	−0.293624	−	0.188700i	0.385533	−	0.922694i	$-0.374018\pi$
$7$	−0.776855	−	0.499255i	−0.293624	−	0.188700i	−0.679156	+	0.733994i	$0.737654\pi$
$8$	−0.142315	+	0.989821i	−0.0503159	+	0.349955i
$9$	−0.251829	−	0.161841i	−0.0839431	−	0.0539470i
$10$	−0.959493	+	0.281733i	−0.303418	+	0.0890917i
$11$	4.00973	−	4.62747i	1.20898	−	1.39524i	0.313823	−	0.949481i	$-0.398390\pi$
$11$	4.00973	−	4.62747i	1.20898	−	1.39524i	0.895155	−	0.445754i	$-0.147064\pi$
$12$	−0.233875	−	1.62664i	−0.0675140	−	0.469570i
$13$	−0.274824	−	1.91144i	−0.0762225	−	0.530139i	−0.991780	−	0.127953i	$-0.959159\pi$
$13$	−0.274824	−	1.91144i	−0.0762225	−	0.530139i	0.915558	−	0.402187i	$-0.131750\pi$
$14$	−0.383615	−	0.839999i	−0.102525	−	0.224499i
$15$	1.38249	−	0.888470i	0.356957	−	0.229402i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	−0.640958	+	1.40350i	−0.155455	+	0.340399i	−0.971295	−	0.237879i	$-0.923548\pi$
$17$	−0.640958	+	1.40350i	−0.155455	+	0.340399i	0.815840	+	0.578278i	$0.196275\pi$
$18$	−0.124355	−	0.272299i	−0.0293107	−	0.0641814i
$19$	3.67698	−	2.36305i	0.843558	−	0.542122i	−0.0460015	−	0.998941i	$-0.514648\pi$
$19$	3.67698	−	2.36305i	0.843558	−	0.542122i	0.889559	+	0.456820i	$0.151012\pi$
$20$	−0.959493	−	0.281733i	−0.214549	−	0.0629973i
$21$	0.993794	+	1.14690i	0.216864	+	0.250274i
$22$	5.87500	−	1.72506i	1.25255	−	0.367783i
$23$	4.35736	+	1.27944i	0.908572	+	0.266781i	0.702440	−	0.711743i	$-0.252094\pi$
$23$	4.35736	+	1.27944i	0.908572	+	0.266781i	0.206132	+	0.978524i	$0.433912\pi$
$24$	0.682679	−	1.49486i	0.139351	−	0.305137i
$25$	−0.142315	−	0.989821i	−0.0284630	−	0.197964i
$26$	0.802208	−	1.75659i	0.157326	−	0.344496i
$27$	3.55068	+	4.09770i	0.683329	+	0.788603i
$28$	0.131421	−	0.914050i	0.0248362	−	0.172739i
$29$	−0.963711			−0.178957			−0.0894784	−	0.995989i	$-0.528520\pi$
$29$	−0.963711			−0.178957			−0.0894784	+	0.995989i	$0.528520\pi$
$30$	1.64337			0.300036
$31$	0.637396	−	4.43319i	0.114480	−	0.796224i	−0.848990	−	0.528408i	$-0.822789\pi$
$31$	0.637396	−	4.43319i	0.114480	−	0.796224i	0.963470	−	0.267816i	$-0.0863018\pi$
$32$	−0.959493	+	0.281733i	−0.169616	+	0.0498038i
$33$	−8.46500	+	5.44013i	−1.47357	+	0.947004i
$34$	−1.29800	+	0.834173i	−0.222605	+	0.143059i
$35$	0.886043	−	0.260166i	0.149769	−	0.0439761i
$36$	0.0426020	−	0.296303i	0.00710033	−	0.0493839i
$37$	11.4866			1.88838			0.944189	−	0.329403i	$-0.106848\pi$
$37$	11.4866			1.88838			0.944189	+	0.329403i	$0.106848\pi$
$38$	4.37084			0.709044
$39$	−0.451637	+	3.14120i	−0.0723197	+	0.502995i
$40$	−0.654861	−	0.755750i	−0.103543	−	0.119494i
$41$	4.63207	−	10.1428i	0.723408	−	1.58404i	−0.0856586	−	0.996325i	$-0.527299\pi$
$41$	4.63207	−	10.1428i	0.723408	−	1.58404i	0.809066	−	0.587717i	$-0.199973\pi$
$42$	0.215972	+	1.50212i	0.0333252	+	0.231782i
$43$	0.0242783	−	0.0531621i	0.00370241	−	0.00810714i	−0.907772	−	0.419464i	$-0.862218\pi$
$43$	0.0242783	−	0.0531621i	0.00370241	−	0.00810714i	0.911474	+	0.411357i	$0.134945\pi$
$44$	5.87500	+	1.72506i	0.885689	+	0.260062i
$45$	0.287224	−	0.0843367i	0.0428169	−	0.0125722i
$46$	2.97393	+	3.43209i	0.438482	+	0.506035i
$47$	−9.38421	−	2.75545i	−1.36883	−	0.401924i	−0.486961	−	0.873424i	$-0.661895\pi$
$47$	−9.38421	−	2.75545i	−1.36883	−	0.401924i	−0.881866	+	0.471500i	$0.843713\pi$
$48$	1.38249	−	0.888470i	0.199545	−	0.128240i
$49$	−2.55366	−	5.59173i	−0.364808	−	0.798818i
$50$	0.415415	−	0.909632i	0.0587486	−	0.128641i
$51$	1.66047	−	1.91628i	0.232512	−	0.268333i
$52$	1.62454	−	1.04403i	0.225284	−	0.144781i
$53$	−3.77141	−	8.25823i	−0.518042	−	1.13435i	−0.970175	−	0.242404i	$-0.922064\pi$
$53$	−3.77141	−	8.25823i	−0.518042	−	1.13435i	0.452133	−	0.891951i	$-0.350663\pi$
$54$	0.771636	+	5.36685i	0.105006	+	0.730336i
$55$	0.871397	+	6.06070i	0.117499	+	0.817225i
$56$	0.604731	−	0.697897i	0.0808106	−	0.0932604i
$57$	−6.89193	+	2.02365i	−0.912858	+	0.268039i
$58$	−0.810726	−	0.521022i	−0.106453	−	0.0684135i
$59$	−1.71644	+	11.9381i	−0.223461	+	1.55420i	0.501343	+	0.865249i	$0.332840\pi$
$59$	−1.71644	+	11.9381i	−0.223461	+	1.55420i	−0.724804	+	0.688956i	$0.758069\pi$
$60$	1.38249	+	0.888470i	0.178478	+	0.114701i
$61$	−8.96088	−	10.3414i	−1.14732	−	1.32408i	−0.938160	−	0.346201i	$-0.887471\pi$
$61$	−8.96088	−	10.3414i	−1.14732	−	1.32408i	−0.209163	−	0.977881i	$-0.567074\pi$
$62$	2.93297	−	3.38483i	0.372488	−	0.429874i
$63$	0.114835	+	0.251454i	0.0144679	+	0.0316802i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	1.62454	+	1.04403i	0.201500	+	0.129496i
$66$	−10.0624			−1.23859
$67$	−1.84776	+	7.97407i	−0.225740	+	0.974188i
$67$	−1.84776	+	7.97407i	−0.225740	+	0.974188i
$68$	−1.54293			−0.187108
$69$	−6.27830	−	4.03482i	−0.755819	−	0.485735i
$70$	0.886043	+	0.260166i	0.105902	+	0.0310958i
$71$	1.16326	+	2.54719i	0.138054	+	0.302295i	0.966013	−	0.258492i	$-0.0832257\pi$
$71$	1.16326	+	2.54719i	0.138054	+	0.302295i	−0.827960	+	0.560788i	$0.810498\pi$
$72$	0.196033	−	0.226234i	0.0231027	−	0.0266619i
$73$	3.29739	+	3.80539i	0.385930	+	0.445387i	0.915160	−	0.403092i	$-0.132064\pi$
$73$	3.29739	+	3.80539i	0.385930	+	0.445387i	−0.529230	+	0.848479i	$0.677519\pi$
$74$	9.66311	+	6.21010i	1.12331	+	0.721910i
$75$	−0.233875	+	1.62664i	−0.0270056	+	0.187828i
$76$	3.67698	+	2.36305i	0.421779	+	0.271061i
$77$	−5.42527	+	1.59300i	−0.618266	+	0.181539i
$78$	−2.07820	+	2.39837i	−0.235310	+	0.271562i
$79$	0.856146	+	5.95462i	0.0963239	+	0.669948i	0.979580	+	0.201056i	$0.0644374\pi$
$79$	0.856146	+	5.95462i	0.0963239	+	0.669948i	−0.883256	+	0.468891i	$0.844654\pi$
$80$	−0.142315	−	0.989821i	−0.0159113	−	0.110665i
$81$	−3.32845	−	7.28828i	−0.369827	−	0.809809i
$82$	9.38037	−	6.02840i	1.03589	−	0.665725i
$83$	5.80916	−	6.70413i	0.637639	−	0.735874i	−0.341317	−	0.939948i	$-0.610873\pi$
$83$	5.80916	−	6.70413i	0.637639	−	0.735874i	0.978955	+	0.204074i	$0.0654184\pi$
$84$	−0.630419	+	1.38043i	−0.0687844	+	0.150617i
$85$	−0.640958	−	1.40350i	−0.0695216	−	0.152231i
$86$	0.0491658	−	0.0315969i	0.00530168	−	0.00340719i
$87$	1.51958	+	0.446188i	0.162916	+	0.0478364i
$88$	4.00973	+	4.62747i	0.427438	+	0.493290i
$89$	10.9945	−	3.22826i	1.16541	−	0.342195i	0.358877	−	0.933385i	$-0.383160\pi$
$89$	10.9945	−	3.22826i	1.16541	−	0.342195i	0.806533	+	0.591189i	$0.201341\pi$
$90$	0.287224	+	0.0843367i	0.0302761	+	0.00888987i
$91$	−0.740799	+	1.62212i	−0.0776568	+	0.170045i
$92$	0.646296	+	4.49509i	0.0673810	+	0.468645i
$93$	−3.05756	+	6.69513i	−0.317055	+	0.694253i
$94$	−6.40479	−	7.39152i	−0.660604	−	0.762377i
$95$	−0.622035	+	4.32635i	−0.0638195	+	0.443874i
$96$	1.64337			0.167725
$97$	−16.6493			−1.69048			−0.845238	−	0.534390i	$-0.820541\pi$
$97$	−16.6493			−1.69048			−0.845238	+	0.534390i	$0.820541\pi$
$98$	0.874844	−	6.08467i	0.0883725	−	0.614645i
$99$	−1.75868	+	0.516396i	−0.176754	+	0.0518997i
$100$	0.841254	−	0.540641i	0.0841254	−	0.0540641i
$101$	−12.3687	+	7.94887i	−1.23073	+	0.790942i	−0.984005	−	0.178143i	$-0.942991\pi$
$101$	−12.3687	+	7.94887i	−1.23073	+	0.790942i	−0.246726	+	0.969085i	$0.579355\pi$
$102$	2.43289	−	0.714362i	0.240892	−	0.0707324i
$103$	−0.721442	+	5.01774i	−0.0710858	+	0.494413i	0.922912	+	0.385011i	$0.125802\pi$
$103$	−0.721442	+	5.01774i	−0.0710858	+	0.494413i	−0.993998	+	0.109401i	$0.965107\pi$
$104$	1.93110			0.189360
$105$	−1.51757			−0.148099
$106$	1.29203	−	8.98624i	0.125493	−	0.872821i
$107$	1.89361	+	2.18534i	0.183062	+	0.211265i	0.839862	−	0.542800i	$-0.182636\pi$
$107$	1.89361	+	2.18534i	0.183062	+	0.211265i	−0.656800	+	0.754065i	$0.728090\pi$
$108$	−2.25240	+	4.93206i	−0.216737	+	0.474588i
$109$	0.404161	+	2.81100i	0.0387117	+	0.269245i	0.999980	−	0.00636971i	$-0.00202756\pi$
$109$	0.404161	+	2.81100i	0.0387117	+	0.269245i	−0.961268	+	0.275615i	$0.911118\pi$
$110$	−2.54360	+	5.56970i	−0.242522	+	0.531050i
$111$	−18.1120	−	5.31816i	−1.71911	−	0.504777i
$112$	0.886043	−	0.260166i	0.0837232	−	0.0245834i
$113$	10.1381	+	11.7000i	0.953711	+	1.10064i	0.994837	+	0.101487i	$0.0323600\pi$
$113$	10.1381	+	11.7000i	0.953711	+	1.10064i	−0.0411260	+	0.999154i	$0.513095\pi$
$114$	−6.89193	−	2.02365i	−0.645488	−	0.189532i
$115$	−3.82039	+	2.45522i	−0.356254	+	0.228950i
$116$	−0.400340	−	0.876623i	−0.0371707	−	0.0813924i
$117$	−0.240141	+	0.525836i	−0.0222011	+	0.0486135i
$118$	−7.89817	+	9.11497i	−0.727085	+	0.839101i
$119$	1.19864	−	0.770317i	0.109879	−	0.0706148i
$120$	0.682679	+	1.49486i	0.0623197	+	0.136461i
$121$	−3.77012	−	26.2218i	−0.342739	−	2.38380i
$122$	−1.94739	−	13.5444i	−0.176308	−	1.22625i
$123$	−11.9999	+	13.8486i	−1.08199	+	1.24868i
$124$	4.29735	−	1.26182i	0.385914	−	0.113314i
$125$	0.841254	+	0.540641i	0.0752440	+	0.0483564i
$126$	−0.0393408	+	0.273621i	−0.00350476	+	0.0243761i
$127$	−2.19582	−	1.41117i	−0.194847	−	0.125221i	0.439580	−	0.898204i	$-0.355127\pi$
$127$	−2.19582	−	1.41117i	−0.194847	−	0.125221i	−0.634427	+	0.772983i	$0.718764\pi$
$128$	−0.654861	−	0.755750i	−0.0578821	−	0.0667995i
$129$	−0.0628955	+	0.0725852i	−0.00553764	+	0.00639077i
$130$	0.802208	+	1.75659i	0.0703583	+	0.154063i
$131$	18.1501	+	5.32934i	1.58578	+	0.465627i	0.951544	−	0.307513i	$-0.0994968\pi$
$131$	18.1501	+	5.32934i	1.58578	+	0.465627i	0.634235	+	0.773140i	$0.281315\pi$
$132$	−8.46500	−	5.44013i	−0.736784	−	0.473502i
$133$	−4.03625			−0.349987
$134$	−5.86554	+	5.70924i	−0.506706	+	0.493203i
$135$	−5.42204			−0.466655
$136$	−1.29800	−	0.834173i	−0.111302	−	0.0715297i
$137$	4.29444	+	1.26096i	0.366899	+	0.107731i	0.459984	−	0.887927i	$-0.347855\pi$
$137$	4.29444	+	1.26096i	0.366899	+	0.107731i	−0.0930860	+	0.995658i	$0.529673\pi$
$138$	−3.10026	−	6.78861i	−0.263911	−	0.577885i
$139$	−4.73712	+	5.46693i	−0.401798	+	0.463699i	−0.920206	−	0.391434i	$-0.871979\pi$
$139$	−4.73712	+	5.46693i	−0.401798	+	0.463699i	0.518409	+	0.855133i	$0.326525\pi$
$140$	0.604731	+	0.697897i	0.0511091	+	0.0589830i
$141$	13.5213	+	8.68958i	1.13869	+	0.731795i
$142$	−0.398515	+	2.77174i	−0.0334427	+	0.232599i
$143$	−9.94713	−	6.39263i	−0.831821	−	0.534579i
$144$	0.287224	−	0.0843367i	0.0239354	−	0.00702806i
$145$	0.631097	−	0.728324i	0.0524097	−	0.0604841i
$146$	0.716590	+	4.98400i	0.0593055	+	0.412478i
$147$	1.43769	+	9.99934i	0.118578	+	0.824731i
$148$	4.77169	+	10.4485i	0.392230	+	0.858865i
$149$	−10.0493	+	6.45830i	−0.823272	+	0.529085i	−0.883133	−	0.469122i	$-0.844570\pi$
$149$	−10.0493	+	6.45830i	−0.823272	+	0.529085i	0.0598614	+	0.998207i	$0.480934\pi$
$150$	−1.07618	+	1.24197i	−0.0878694	+	0.101407i
$151$	3.60639	−	7.89690i	0.293484	−	0.642640i	−0.704248	−	0.709954i	$-0.748716\pi$
$151$	3.60639	−	7.89690i	0.293484	−	0.642640i	0.997732	+	0.0673138i	$0.0214429\pi$
$152$	1.81571	+	3.97585i	0.147274	+	0.322484i
$153$	0.388556	−	0.249710i	0.0314129	−	0.0201878i
$154$	−5.42527	−	1.59300i	−0.437180	−	0.128368i
$155$	2.93297	+	3.38483i	0.235582	+	0.271876i
$156$	−3.04495	+	0.894079i	−0.243791	+	0.0715836i
$157$	−10.7680	−	3.16177i	−0.859380	−	0.252337i	−0.177788	−	0.984069i	$-0.556894\pi$
$157$	−10.7680	−	3.16177i	−0.859380	−	0.252337i	−0.681592	+	0.731732i	$0.738712\pi$
$158$	−2.49908	+	5.47222i	−0.198816	+	0.435346i
$159$	2.12327	+	14.7677i	0.168386	+	1.17115i
$160$	0.415415	−	0.909632i	0.0328414	−	0.0719127i
$161$	−2.74627	−	3.16937i	−0.216437	−	0.249781i
$162$	1.14027	−	7.93078i	0.0895884	−	0.623101i
$163$	−17.3092			−1.35576			−0.677882	−	0.735171i	$-0.737102\pi$
$163$	−17.3092			−1.35576			−0.677882	+	0.735171i	$0.737102\pi$
$164$	11.1505			0.870705
$165$	1.43202	−	9.95995i	0.111483	−	0.775381i
$166$	8.51151	−	2.49920i	0.660621	−	0.193976i
$167$	14.7593	−	9.48522i	1.14211	−	0.733988i	0.174055	−	0.984736i	$-0.444313\pi$
$167$	14.7593	−	9.48522i	1.14211	−	0.733988i	0.968052	+	0.250748i	$0.0806765\pi$
$168$	−1.27666	+	0.820458i	−0.0984962	+	0.0632997i
$169$	8.89532	−	2.61190i	0.684255	−	0.200915i
$170$	0.219582	−	1.52723i	0.0168412	−	0.117133i
$171$	−1.30841			−0.100057
$172$	0.0584435			0.00445627
$173$	−3.46970	+	24.1323i	−0.263796	+	1.83474i	0.239821	+	0.970817i	$0.422911\pi$
$173$	−3.46970	+	24.1323i	−0.263796	+	1.83474i	−0.503618	+	0.863927i	$0.667998\pi$
$174$	1.03712	+	1.19690i	0.0786241	+	0.0907370i
$175$	−0.383615	+	0.839999i	−0.0289986	+	0.0634980i
$176$	0.871397	+	6.06070i	0.0656840	+	0.456843i
$177$	8.23367	−	18.0292i	0.618881	−	1.35516i
$178$	10.9945	+	3.22826i	0.824069	+	0.241969i
$179$	14.7263	−	4.32404i	1.10070	−	0.323194i	0.319568	−	0.947563i	$-0.396462\pi$
$179$	14.7263	−	4.32404i	1.10070	−	0.323194i	0.781129	+	0.624369i	$0.214644\pi$
$180$	0.196033	+	0.226234i	0.0146114	+	0.0168625i
$181$	−8.50634	−	2.49769i	−0.632271	−	0.185652i	−0.0501345	−	0.998742i	$-0.515965\pi$
$181$	−8.50634	−	2.49769i	−0.632271	−	0.185652i	−0.582137	+	0.813091i	$0.697783\pi$
$182$	−1.50019	+	0.964111i	−0.111201	+	0.0714646i
$183$	9.34153	+	20.4551i	0.690546	+	1.51208i
$184$	−1.88653	+	4.13092i	−0.139077	+	0.304536i
$185$	−7.52210	+	8.68096i	−0.553035	+	0.638237i
$186$	−6.19185	+	3.97926i	−0.454008	+	0.291773i
$187$	3.92460	+	8.59368i	0.286995	+	0.628432i
$188$	−1.39189	−	9.68083i	−0.101514	−	0.706047i
$189$	−0.712567	−	4.95602i	−0.0518317	−	0.360497i
$190$	−2.86229	+	3.30326i	−0.207652	+	0.239644i
$191$	13.8701	−	4.07262i	1.00360	−	0.294685i	0.261670	−	0.965157i	$-0.415727\pi$
$191$	13.8701	−	4.07262i	1.00360	−	0.294685i	0.741934	+	0.670473i	$0.233909\pi$
$192$	1.38249	+	0.888470i	0.0997724	+	0.0641198i
$193$	1.09990	−	7.64997i	0.0791725	−	0.550657i	−0.911172	−	0.412027i	$-0.864821\pi$
$193$	1.09990	−	7.64997i	0.0791725	−	0.550657i	0.990344	−	0.138630i	$-0.0442699\pi$
$194$	−14.0062	−	9.00127i	−1.00559	−	0.646253i
$195$	−2.07820	−	2.39837i	−0.148823	−	0.171751i
$196$	4.02559	−	4.64577i	0.287542	−	0.331841i
$197$	−8.41290	−	18.4217i	−0.599395	−	1.31249i	−0.929596	−	0.368580i	$-0.879844\pi$
$197$	−8.41290	−	18.4217i	−0.599395	−	1.31249i	0.330201	−	0.943911i	$-0.392883\pi$
$198$	−1.75868	−	0.516396i	−0.124984	−	0.0366986i
$199$	−14.9668	−	9.61859i	−1.06097	−	0.681844i	−0.110884	−	0.993833i	$-0.535368\pi$
$199$	−14.9668	−	9.61859i	−1.06097	−	0.681844i	−0.950086	+	0.311990i	$0.899005\pi$
$200$	1.00000			0.0707107
$201$	6.60545	−	11.7180i	0.465913	−	0.826524i
$202$	−14.7027			−1.03448
$203$	0.748664	+	0.481137i	0.0525459	+	0.0337692i
$204$	2.43289	+	0.714362i	0.170337	+	0.0500154i
$205$	4.63207	+	10.1428i	0.323518	+	0.708405i
$206$	−3.31971	+	3.83115i	−0.231295	+	0.266929i
$207$	−0.890246	−	1.02740i	−0.0618763	−	0.0714091i
$208$	1.62454	+	1.04403i	0.112642	+	0.0723906i
$209$	3.80874	−	26.4903i	0.263456	−	1.83238i
$210$	−1.27666	−	0.820458i	−0.0880977	−	0.0566170i
$211$	8.41127	−	2.46977i	0.579056	−	0.170026i	0.0209278	−	0.999781i	$-0.493338\pi$
$211$	8.41127	−	2.46977i	0.579056	−	0.170026i	0.558128	+	0.829755i	$0.311520\pi$
$212$	5.94525	−	6.86118i	0.408321	−	0.471228i
$213$	−0.654906	−	4.55497i	−0.0448734	−	0.312102i
$214$	0.411521	+	2.86219i	0.0281310	+	0.195655i
$215$	0.0242783	+	0.0531621i	0.00165577	+	0.00362562i
$216$	−4.56131	+	2.93138i	−0.310358	+	0.199455i
$217$	−2.70845	+	3.12572i	−0.183862	+	0.212188i
$218$	−1.17974	+	2.58327i	−0.0799022	+	0.174961i
$219$	−3.43746	−	7.52698i	−0.232282	−	0.508626i
$220$	−5.15102	+	3.31036i	−0.347281	+	0.223184i
$221$	2.85887	+	0.839439i	0.192308	+	0.0564668i
$222$	−12.3616	−	14.2660i	−0.829653	−	0.957471i
$223$	−0.423373	+	0.124314i	−0.0283512	+	0.00832465i	−0.295877	−	0.955226i	$-0.595612\pi$
$223$	−0.423373	+	0.124314i	−0.0283512	+	0.00832465i	0.267526	+	0.963551i	$0.413794\pi$
$224$	0.886043	+	0.260166i	0.0592013	+	0.0173831i
$225$	−0.124355	+	0.272299i	−0.00829030	+	0.0181532i
$226$	2.20322	+	15.3237i	0.146556	+	1.01932i
$227$	−1.81647	+	3.97752i	−0.120564	+	0.263997i	−0.960285	−	0.279019i	$-0.909991\pi$
$227$	−1.81647	+	3.97752i	−0.120564	+	0.263997i	0.839722	+	0.543017i	$0.182718\pi$
$228$	−4.70379	−	5.42846i	−0.311516	−	0.359509i
$229$	−0.394933	+	2.74682i	−0.0260979	+	0.181515i	−0.998701	−	0.0509579i	$-0.983773\pi$
$229$	−0.394933	+	2.74682i	−0.0260979	+	0.181515i	0.972603	+	0.232473i	$0.0746817\pi$
$230$	−4.54131			−0.299445
$231$	9.29209			0.611375
$232$	0.137150	−	0.953902i	0.00900437	−	0.0626267i
$233$	5.53330	−	1.62472i	0.362498	−	0.106439i	−0.0954112	−	0.995438i	$-0.530417\pi$
$233$	5.53330	−	1.62472i	0.362498	−	0.106439i	0.457909	+	0.888999i	$0.348598\pi$
$234$	−0.486308	+	0.312531i	−0.0317909	+	0.0204308i
$235$	8.22778	−	5.28767i	0.536721	−	0.344930i
$236$	−11.5723	+	3.39793i	−0.753292	+	0.221186i
$237$	1.40696	−	9.78562i	0.0913919	−	0.635645i
$238$	1.42482			0.0923575
$239$	28.9870			1.87501			0.937505	−	0.347971i	$-0.113129\pi$
$239$	28.9870			1.87501			0.937505	+	0.347971i	$0.113129\pi$
$240$	−0.233875	+	1.62664i	−0.0150966	+	0.104999i
$241$	6.97470	+	8.04923i	0.449280	+	0.518497i	0.934533	−	0.355877i	$-0.115818\pi$
$241$	6.97470	+	8.04923i	0.449280	+	0.518497i	−0.485253	+	0.874374i	$0.661272\pi$
$242$	11.0049	−	24.0975i	0.707424	−	1.54904i
$243$	−0.441021	−	3.06737i	−0.0282915	−	0.196772i
$244$	5.68439	−	12.4471i	0.363906	−	0.796843i
$245$	5.89823	+	1.73188i	0.376824	+	0.110646i
$246$	−17.5820	+	5.16255i	−1.12099	+	0.329152i
$247$	−5.52737	−	6.37892i	−0.351698	−	0.405881i
$248$	4.29735	+	1.26182i	0.272882	+	0.0801254i
$249$	−12.2638	+	7.88148i	−0.777188	+	0.499468i
$250$	0.415415	+	0.909632i	0.0262732	+	0.0575302i
$251$	1.55690	−	3.40914i	0.0982707	−	0.215183i	−0.854111	−	0.520090i	$-0.825898\pi$
$251$	1.55690	−	3.40914i	0.0982707	−	0.215183i	0.952382	+	0.304907i	$0.0986255\pi$
$252$	−0.181026	+	0.208916i	−0.0114036	+	0.0131604i
$253$	23.3924	−	15.0334i	1.47067	−	0.945139i
$254$	−1.08431	−	2.37430i	−0.0680354	−	0.148977i
$255$	0.360854	+	2.50980i	0.0225976	+	0.157169i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−12.1338	+	14.0032i	−0.756886	+	0.873493i	−0.995217	−	0.0976914i	$-0.968854\pi$
$257$	−12.1338	+	14.0032i	−0.756886	+	0.873493i	0.238331	+	0.971184i	$0.423400\pi$
$258$	−0.0921536	+	0.0270587i	−0.00573723	+	0.00168460i
$259$	−8.92339	−	5.73472i	−0.554473	−	0.356338i
$260$	−0.274824	+	1.91144i	−0.0170439	+	0.118543i
$261$	0.242691	+	0.155968i	0.0150222	+	0.00965417i
$262$	12.3876	+	14.2960i	0.765306	+	0.883210i
$263$	2.15915	−	2.49179i	0.133139	−	0.153651i	−0.685265	−	0.728294i	$-0.740314\pi$
$263$	2.15915	−	2.49179i	0.133139	−	0.153651i	0.818404	+	0.574643i	$0.194859\pi$
$264$	−4.18006	−	9.15305i	−0.257265	−	0.563331i
$265$	8.71090	+	2.55775i	0.535106	+	0.157121i
$266$	−3.39551	−	2.18216i	−0.208192	−	0.133797i
$267$	−18.8307			−1.15242
$268$	−8.02106	+	1.63177i	−0.489964	+	0.0996761i
$269$	−11.6175			−0.708329			−0.354164	−	0.935183i	$-0.615235\pi$
$269$	−11.6175			−0.708329			−0.354164	+	0.935183i	$0.615235\pi$
$270$	−4.56131	−	2.93138i	−0.277592	−	0.178398i
$271$	15.3786	+	4.51558i	0.934186	+	0.274302i	0.713188	−	0.700973i	$-0.247251\pi$
$271$	15.3786	+	4.51558i	0.934186	+	0.274302i	0.220998	+	0.975274i	$0.429069\pi$
$272$	−0.640958	−	1.40350i	−0.0388638	−	0.0850998i
$273$	1.91912	−	2.21478i	0.116150	−	0.134044i
$274$	2.93098	+	3.38254i	0.177067	+	0.204346i
$275$	−5.15102	−	3.31036i	−0.310618	−	0.199622i
$276$	1.06210	−	7.38707i	0.0639309	−	0.444649i
$277$	1.80799	+	1.16193i	0.108632	+	0.0698134i	0.593829	−	0.804592i	$-0.297616\pi$
$277$	1.80799	+	1.16193i	0.108632	+	0.0698134i	−0.485197	+	0.874405i	$0.661252\pi$
$278$	−6.94077	+	2.03799i	−0.416280	+	0.122231i
$279$	−0.877986	+	1.01325i	−0.0525637	+	0.0606617i
$280$	0.131421	+	0.914050i	0.00785388	+	0.0546250i
$281$	3.67183	+	25.5381i	0.219043	+	1.52348i	0.741583	+	0.670861i	$0.234075\pi$
$281$	3.67183	+	25.5381i	0.219043	+	1.52348i	−0.522540	+	0.852615i	$0.675015\pi$
$282$	6.67686	+	14.6203i	0.397601	+	0.870625i
$283$	3.37506	−	2.16902i	0.200627	−	0.128935i	−0.436470	−	0.899719i	$-0.643772\pi$
$283$	3.37506	−	2.16902i	0.200627	−	0.128935i	0.637097	+	0.770784i	$0.280135\pi$
$284$	−1.83377	+	2.11628i	−0.108814	+	0.125578i
$285$	2.98388	−	6.53378i	0.176750	−	0.387028i
$286$	−4.91194	−	10.7556i	−0.290449	−	0.635995i
$287$	−8.66230	+	5.56692i	−0.511319	+	0.328605i
$288$	0.287224	+	0.0843367i	0.0169249	+	0.00496959i
$289$	9.57364	+	11.0486i	0.563155	+	0.649916i
$290$	0.924674	−	0.271509i	0.0542987	−	0.0159436i
$291$	26.2525	+	7.70843i	1.53895	+	0.451876i
$292$	−2.09172	+	4.58022i	−0.122409	+	0.268037i
$293$	1.72304	+	11.9840i	0.100661	+	0.700114i	0.976185	+	0.216939i	$0.0696074\pi$
$293$	1.72304	+	11.9840i	0.100661	+	0.700114i	−0.875524	+	0.483175i	$0.839483\pi$
$294$	−4.19659	+	9.18925i	−0.244750	+	0.535928i
$295$	−7.89817	−	9.11497i	−0.459849	−	0.530694i
$296$	−1.63471	+	11.3696i	−0.0950155	+	0.660847i
$297$	33.1993			1.92642
$298$	−11.9456			−0.691993
$299$	1.24806	−	8.68047i	0.0721773	−	0.502004i
$300$	−1.57680	+	0.462990i	−0.0910364	+	0.0267307i
$301$	−0.0454021	+	0.0291782i	−0.00261694	+	0.00168180i
$302$	7.30328	−	4.69353i	0.420256	−	0.270082i
$303$	23.1832	−	6.80719i	1.33184	−	0.391063i
$304$	−0.622035	+	4.32635i	−0.0356762	+	0.248133i
$305$	13.6836			0.783523
$306$	0.461878			0.0264038
$307$	−1.65836	+	11.5342i	−0.0946477	+	0.658289i	0.886170	+	0.463361i	$0.153357\pi$
$307$	−1.65836	+	11.5342i	−0.0946477	+	0.658289i	−0.980817	+	0.194928i	$0.937553\pi$
$308$	−3.70278	−	4.27324i	−0.210986	−	0.243490i
$309$	3.46073	−	7.57794i	0.196874	−	0.431094i
$310$	0.637396	+	4.43319i	0.0362017	+	0.251788i
$311$	−5.68484	+	12.4481i	−0.322357	+	0.705864i	−0.999552	−	0.0299400i	$-0.990468\pi$
$311$	−5.68484	+	12.4481i	−0.322357	+	0.705864i	0.677194	+	0.735804i	$0.263196\pi$
$312$	−3.04495	−	0.894079i	−0.172387	−	0.0506173i
$313$	5.39596	−	1.58440i	0.304998	−	0.0895554i	−0.125652	−	0.992074i	$-0.540102\pi$
$313$	5.39596	−	1.58440i	0.304998	−	0.0895554i	0.430650	+	0.902519i	$0.358284\pi$
$314$	−7.34924	−	8.48147i	−0.414742	−	0.478637i
$315$	−0.265237	−	0.0778807i	−0.0149444	−	0.00438808i
$316$	−5.06086	+	3.25242i	−0.284696	+	0.182963i
$317$	3.81937	+	8.36326i	0.214517	+	0.469728i	0.986047	−	0.166465i	$-0.0532354\pi$
$317$	3.81937	+	8.36326i	0.214517	+	0.469728i	−0.771530	+	0.636193i	$0.780508\pi$
$318$	−6.19780	+	13.5713i	−0.347555	+	0.761040i
$319$	−3.86422	+	4.45955i	−0.216355	+	0.249687i
$320$	0.841254	−	0.540641i	0.0470275	−	0.0302227i
$321$	−1.97405	−	4.32256i	−0.110181	−	0.241262i
$322$	−0.596822	−	4.15099i	−0.0332596	−	0.231325i
$323$	0.959759	+	6.67527i	0.0534024	+	0.371422i
$324$	5.24697	−	6.05532i	0.291498	−	0.336407i
$325$	−1.85288	+	0.544054i	−0.102779	+	0.0301787i
$326$	−14.5615	−	9.35808i	−0.806485	−	0.518296i
$327$	0.664185	−	4.61951i	0.0367295	−	0.255459i
$328$	9.38037	+	6.02840i	0.517944	+	0.332862i
$329$	5.91450	+	6.82570i	0.326077	+	0.376313i
$330$	6.58945	−	7.60463i	0.362737	−	0.418621i
$331$	2.87149	+	6.28768i	0.157831	+	0.345602i	0.971983	−	0.235049i	$-0.0755252\pi$
$331$	2.87149	+	6.28768i	0.157831	+	0.345602i	−0.814152	+	0.580651i	$0.802798\pi$
$332$	8.51151	+	2.49920i	0.467130	+	0.137162i
$333$	−2.89265	−	1.85900i	−0.158516	−	0.101872i
$334$	17.5444			0.959987
$335$	−4.81638	−	6.61835i	−0.263147	−	0.361599i
$336$	−1.51757			−0.0827900
$337$	−16.5741	−	10.6515i	−0.902848	−	0.580225i	0.00478579	−	0.999989i	$-0.498477\pi$
$337$	−16.5741	−	10.6515i	−0.902848	−	0.580225i	−0.907633	+	0.419764i	$0.862113\pi$
$338$	8.89532	+	2.61190i	0.483841	+	0.142069i
$339$	−10.5687	−	23.1423i	−0.574015	−	1.25692i
$340$	1.01041	−	1.16607i	0.0547970	−	0.0632391i
$341$	−17.9587	−	20.7254i	−0.972516	−	1.12234i
$342$	−1.10071	−	0.707381i	−0.0595193	−	0.0382508i
$343$	−1.72782	+	12.0172i	−0.0932934	+	0.648870i
$344$	0.0491658	+	0.0315969i	0.00265084	+	0.00170359i
$345$	7.16073	−	2.10258i	0.385521	−	0.113199i
$346$	−15.9658	+	18.4255i	−0.858327	+	0.990562i
$347$	3.57564	+	24.8691i	0.191950	+	1.33504i	0.826838	+	0.562440i	$0.190137\pi$
$347$	3.57564	+	24.8691i	0.191950	+	1.33504i	−0.634888	+	0.772604i	$0.718954\pi$
$348$	0.225388	+	1.56761i	0.0120821	+	0.0840327i
$349$	−3.03809	−	6.65249i	−0.162625	−	0.356100i	0.810724	−	0.585429i	$-0.199074\pi$
$349$	−3.03809	−	6.65249i	−0.162625	−	0.356100i	−0.973349	+	0.229329i	$0.926347\pi$
$350$	−0.776855	+	0.499255i	−0.0415247	+	0.0266863i
$351$	6.85672	−	7.91308i	0.365985	−	0.422369i
$352$	−2.54360	+	5.56970i	−0.135574	+	0.296866i
$353$	−0.289575	−	0.634081i	−0.0154125	−	0.0337487i	0.901769	−	0.432218i	$-0.142269\pi$
$353$	−0.289575	−	0.634081i	−0.0154125	−	0.0337487i	−0.917182	+	0.398469i	$0.869542\pi$
$354$	16.6739	−	10.7157i	0.886210	−	0.569533i
$355$	−2.68681	−	0.788918i	−0.142601	−	0.0418714i
$356$	7.50379	+	8.65984i	0.397700	+	0.458971i
$357$	−2.24666	+	0.659678i	−0.118906	+	0.0349138i
$358$	14.7263	+	4.32404i	0.778311	+	0.228533i
$359$	−2.21284	+	4.84545i	−0.116789	+	0.255733i	−0.958995	−	0.283424i	$-0.908530\pi$
$359$	−2.21284	+	4.84545i	−0.116789	+	0.255733i	0.842205	+	0.539157i	$0.181257\pi$
$360$	0.0426020	+	0.296303i	0.00224532	+	0.0156166i
$361$	0.0432977	−	0.0948086i	0.00227882	−	0.00498993i
$362$	−5.80564	−	6.70006i	−0.305137	−	0.352147i
$363$	−6.19569	+	43.0920i	−0.325189	+	2.26174i
$364$	−1.78327			−0.0934690
$365$	−5.03525			−0.263557
$366$	−3.20027	+	22.2583i	−0.167281	+	1.16346i
$367$	−2.31270	+	0.679069i	−0.120722	+	0.0354471i	−0.341535	−	0.939869i	$-0.610947\pi$
$367$	−2.31270	+	0.679069i	−0.120722	+	0.0354471i	0.220814	+	0.975316i	$0.429129\pi$
$368$	−3.82039	+	2.45522i	−0.199152	+	0.127987i
$369$	−2.80801	+	1.80460i	−0.146179	+	0.0939438i
$370$	−11.0213	+	3.23614i	−0.572969	+	0.168239i
$371$	−1.19312	+	8.29834i	−0.0619438	+	0.430828i
$372$	−7.36026			−0.381612
$373$	−18.3251			−0.948838			−0.474419	−	0.880299i	$-0.657342\pi$
$373$	−18.3251			−0.948838			−0.474419	+	0.880299i	$0.657342\pi$
$374$	−1.34451	+	9.35126i	−0.0695229	+	0.483542i
$375$	−1.07618	−	1.24197i	−0.0555735	−	0.0641352i
$376$	4.06292	−	8.89655i	0.209529	−	0.458804i
$377$	0.264851	+	1.84208i	0.0136405	+	0.0948720i
$378$	2.07997	−	4.55451i	0.106982	−	0.234259i
$379$	−6.91110	−	2.02928i	−0.354999	−	0.104237i	0.0993702	−	0.995051i	$-0.468317\pi$
$379$	−6.91110	−	2.02928i	−0.354999	−	0.104237i	−0.454369	+	0.890813i	$0.650135\pi$
$380$	−4.19379	+	1.23141i	−0.215137	+	0.0631699i
$381$	2.80900	+	3.24176i	0.143910	+	0.166081i
$382$	13.8701	+	4.07262i	0.709655	+	0.208374i
$383$	11.9575	−	7.68462i	0.611000	−	0.392666i	−0.198232	−	0.980155i	$-0.563520\pi$
$383$	11.9575	−	7.68462i	0.611000	−	0.392666i	0.809232	+	0.587489i	$0.199884\pi$
$384$	0.682679	+	1.49486i	0.0348378	+	0.0762841i
$385$	2.34888	−	5.14334i	0.119710	−	0.262129i
$386$	5.06118	−	5.84091i	0.257607	−	0.297295i
$387$	−0.0147178	+	0.00945855i	−0.000748147	+	0.000480805i
$388$	−6.91635	−	15.1447i	−0.351125	−	0.768855i
$389$	0.673623	+	4.68515i	0.0341540	+	0.237546i	0.999747	−	0.0225133i	$-0.00716681\pi$
$389$	0.673623	+	4.68515i	0.0341540	+	0.237546i	−0.965593	+	0.260060i	$0.916258\pi$
$390$	−0.451637	−	3.14120i	−0.0228695	−	0.159061i
$391$	−4.58857	+	5.29549i	−0.232054	+	0.267805i
$392$	5.89823	−	1.73188i	0.297906	−	0.0874730i
$393$	−26.1516	−	16.8066i	−1.31917	−	0.847780i
$394$	2.88213	−	20.0457i	0.145200	−	1.00989i
$395$	−5.06086	−	3.25242i	−0.254640	−	0.163647i
$396$	−1.20031	−	1.38523i	−0.0603180	−	0.0696107i
$397$	−7.57009	+	8.73635i	−0.379932	+	0.438465i	−0.913219	−	0.407470i	$-0.866411\pi$
$397$	−7.57009	+	8.73635i	−0.379932	+	0.438465i	0.533287	+	0.845934i	$0.320957\pi$
$398$	−7.39069	−	16.1833i	−0.370462	−	0.811198i
$399$	6.36435	+	1.86874i	0.318616	+	0.0935541i
$400$	0.841254	+	0.540641i	0.0420627	+	0.0270320i
$401$	31.7950			1.58777			0.793884	−	0.608069i	$-0.208056\pi$
$401$	31.7950			1.58777			0.793884	+	0.608069i	$0.208056\pi$
$402$	11.8921	−	6.28663i	0.593123	−	0.313549i
$403$	−8.64896			−0.430836
$404$	−12.3687	−	7.94887i	−0.615365	−	0.395471i
$405$	7.68778	+	2.25734i	0.382009	+	0.112168i
$406$	0.369694	+	0.809517i	0.0183476	+	0.0401757i
$407$	46.0580	−	53.1537i	2.28301	−	2.63473i
$408$	1.66047	+	1.91628i	0.0822054	+	0.0948701i
$409$	0.558652	+	0.359024i	0.0276235	+	0.0177526i	0.554380	−	0.832264i	$-0.312956\pi$
$409$	0.558652	+	0.359024i	0.0276235	+	0.0177526i	−0.526756	+	0.850016i	$0.676592\pi$
$410$	−1.58688	+	11.0370i	−0.0783702	+	0.545077i
$411$	−6.18765	−	3.97656i	−0.305214	−	0.196149i
$412$	−4.86400	+	1.42820i	−0.239632	+	0.0703623i
$413$	7.29356	−	8.41722i	0.358893	−	0.414184i
$414$	−0.193469	−	1.34561i	−0.00950847	−	0.0661329i
$415$	1.26245	+	8.78055i	0.0619713	+	0.431020i
$416$	0.802208	+	1.75659i	0.0393315	+	0.0861239i
$417$	10.0006	−	6.42701i	0.489732	−	0.314732i
$418$	17.5259	−	20.2259i	0.857219	−	0.989283i
$419$	−8.55237	+	18.7271i	−0.417811	+	0.914878i	0.577339	+	0.816505i	$0.304091\pi$
$419$	−8.55237	+	18.7271i	−0.417811	+	0.914878i	−0.995150	+	0.0983732i	$0.968636\pi$
$420$	−0.630419	−	1.38043i	−0.0307613	−	0.0673579i
$421$	2.57314	−	1.65365i	0.125407	−	0.0805942i	−0.476433	−	0.879211i	$-0.658071\pi$
$421$	2.57314	−	1.65365i	0.125407	−	0.0805942i	0.601840	+	0.798616i	$0.294434\pi$
$422$	8.41127	+	2.46977i	0.409454	+	0.120227i
$423$	1.91727	+	2.21265i	0.0932211	+	0.107583i
$424$	8.71090	−	2.55775i	0.423039	−	0.124215i
$425$	1.48043	+	0.434695i	0.0718116	+	0.0210858i
$426$	1.91166	−	4.18596i	0.0926204	−	0.202810i
$427$	1.79831	+	12.5075i	0.0870265	+	0.605282i
$428$	−1.20122	+	2.63031i	−0.0580633	+	0.127141i
$429$	12.7249	+	14.6853i	0.614363	+	0.709013i
$430$	−0.00831738	+	0.0578486i	−0.000401100	+	0.00278971i
$431$	19.2312			0.926332			0.463166	−	0.886271i	$-0.346713\pi$
$431$	19.2312			0.926332			0.463166	+	0.886271i	$0.346713\pi$
$432$	−5.42204			−0.260868
$433$	5.05196	−	35.1371i	0.242782	−	1.68858i	−0.395250	−	0.918573i	$-0.629342\pi$
$433$	5.05196	−	35.1371i	0.242782	−	1.68858i	0.638032	−	0.770010i	$-0.279749\pi$
$434$	−3.96839	+	1.16522i	−0.190489	+	0.0559325i
$435$	−1.33232	+	0.856229i	−0.0638798	+	0.0410530i
$436$	−2.38909	+	1.53537i	−0.114416	+	0.0735310i
$437$	19.0453	−	5.59221i	0.911060	−	0.267511i
$438$	1.17762	−	8.19053i	0.0562689	−	0.391359i
$439$	−27.7048			−1.32228			−0.661140	−	0.750263i	$-0.729927\pi$
$439$	−27.7048			−1.32228			−0.661140	+	0.750263i	$0.729927\pi$
$440$	−6.12302			−0.291904
$441$	−0.261885	+	1.82145i	−0.0124707	+	0.0867356i
$442$	1.95120	+	2.25180i	0.0928090	+	0.107107i
$443$	−2.54814	+	5.57966i	−0.121066	+	0.265098i	−0.960456	−	0.278432i	$-0.910185\pi$
$443$	−2.54814	+	5.57966i	−0.121066	+	0.265098i	0.839390	+	0.543530i	$0.182913\pi$
$444$	−2.68642	−	18.6845i	−0.127492	−	0.886726i
$445$	−4.76008	+	10.4231i	−0.225649	+	0.494103i
$446$	−0.423373	−	0.124314i	−0.0200473	−	0.00588642i
$447$	18.8359	−	5.53071i	0.890906	−	0.261594i
$448$	0.604731	+	0.697897i	0.0285709	+	0.0329725i
$449$	−23.5245	−	6.90742i	−1.11019	−	0.325981i	−0.325297	−	0.945612i	$-0.605464\pi$
$449$	−23.5245	−	6.90742i	−1.11019	−	0.325981i	−0.784894	+	0.619631i	$0.787282\pi$
$450$	−0.251829	+	0.161841i	−0.0118714	+	0.00762925i
$451$	−28.3623	−	62.1047i	−1.33553	−	2.92440i
$452$	−6.43116	+	14.0823i	−0.302496	+	0.662374i
$453$	−9.34273	+	10.7821i	−0.438960	+	0.506587i
$454$	−3.67852	+	2.36404i	−0.172642	+	0.110950i
$455$	−0.740799	−	1.62212i	−0.0347292	−	0.0760463i
$456$	−1.02223	−	7.10977i	−0.0478704	−	0.332946i
$457$	1.10596	+	7.69210i	0.0517345	+	0.359821i	0.999201	+	0.0399663i	$0.0127250\pi$
$457$	1.10596	+	7.69210i	0.0517345	+	0.359821i	−0.947467	+	0.319855i	$0.896366\pi$
$458$	−1.81728	+	2.09725i	−0.0849160	+	0.0979982i
$459$	−8.02697	+	2.35693i	−0.374667	+	0.110012i
$460$	−3.82039	−	2.45522i	−0.178127	−	0.114475i
$461$	0.633004	−	4.40264i	0.0294819	−	0.205051i	−0.969756	−	0.244075i	$-0.921516\pi$
$461$	0.633004	−	4.40264i	0.0294819	−	0.205051i	0.999238	+	0.0390237i	$0.0124248\pi$
$462$	7.81700	+	5.02368i	0.363680	+	0.233723i
$463$	19.8834	+	22.9466i	0.924059	+	1.06642i	0.997608	+	0.0691294i	$0.0220221\pi$
$463$	19.8834	+	22.9466i	0.924059	+	1.06642i	−0.0735487	+	0.997292i	$0.523432\pi$
$464$	0.631097	−	0.728324i	0.0292979	−	0.0338116i
$465$	−3.05756	−	6.69513i	−0.141791	−	0.310479i
$466$	5.53330	+	1.62472i	0.256325	+	0.0752638i
$467$	6.20357	+	3.98679i	0.287067	+	0.184487i	0.676247	−	0.736675i	$-0.263605\pi$
$467$	6.20357	+	3.98679i	0.287067	+	0.184487i	−0.389180	+	0.921162i	$0.627242\pi$
$468$	−0.578075			−0.0267215
$469$	5.41653	−	5.27220i	0.250112	−	0.243447i
$470$	9.78038			0.451135
$471$	15.5151	+	9.97095i	0.714898	+	0.459437i
$472$	−11.5723	−	3.39793i	−0.532658	−	0.156402i
$473$	−0.148657	−	0.325513i	−0.00683524	−	0.0149671i
$474$	6.47412	−	7.47153i	0.297366	−	0.343179i
$475$	−2.86229	−	3.30326i	−0.131331	−	0.151564i
$476$	1.19864	+	0.770317i	0.0549394	+	0.0353074i
$477$	−0.386768	+	2.69003i	−0.0177089	+	0.123168i
$478$	24.3854	+	15.6715i	1.11536	+	0.716799i
$479$	−21.8961	+	6.42928i	−1.00046	+	0.293761i	−0.740645	−	0.671897i	$-0.765480\pi$
$479$	−21.8961	+	6.42928i	−1.00046	+	0.293761i	−0.259815	+	0.965658i	$0.583662\pi$
$480$	−1.07618	+	1.24197i	−0.0491205	+	0.0566880i
$481$	−3.15678	−	21.9559i	−0.143937	−	1.00110i
$482$	1.51575	+	10.5423i	0.0690404	+	0.480186i
$483$	2.86293	+	6.26894i	0.130268	+	0.285247i
$484$	22.2860	−	14.3223i	1.01300	−	0.651016i
$485$	10.9029	−	12.5827i	0.495077	−	0.571350i
$486$	1.28734	−	2.81887i	0.0583947	−	0.127867i
$487$	−5.34779	−	11.7100i	−0.242332	−	0.530632i	0.748913	−	0.662668i	$-0.230576\pi$
$487$	−5.34779	−	11.7100i	−0.242332	−	0.530632i	−0.991245	+	0.132036i	$0.957849\pi$
$488$	11.5114	−	7.39794i	0.521097	−	0.334889i
$489$	27.2932	+	8.01400i	1.23424	+	0.362405i
$490$	4.02559	+	4.64577i	0.181857	+	0.209875i
$491$	31.5686	−	9.26937i	1.42467	−	0.418321i	0.523589	−	0.851971i	$-0.324593\pi$
$491$	31.5686	−	9.26937i	1.42467	−	0.418321i	0.901081	+	0.433650i	$0.142775\pi$
$492$	−17.5820	−	5.16255i	−0.792659	−	0.232746i
$493$	0.617698	−	1.35257i	0.0278197	−	0.0609167i
$494$	−1.20121	−	8.35461i	−0.0540451	−	0.375892i
$495$	0.761426	−	1.66729i	0.0342236	−	0.0749391i
$496$	2.93297	+	3.38483i	0.131694	+	0.151983i
$497$	0.368009	−	2.55956i	0.0165075	−	0.114812i
$498$	−14.5780			−0.653257
$499$	9.66846			0.432820			0.216410	−	0.976303i	$-0.430565\pi$
$499$	9.66846			0.432820			0.216410	+	0.976303i	$0.430565\pi$
$500$	−0.142315	+	0.989821i	−0.00636451	+	0.0442662i
$501$	−27.6640	+	8.12287i	−1.23593	+	0.362903i
$502$	3.15287	−	2.02623i	0.140719	−	0.0904349i
$503$	2.71276	−	1.74339i	0.120956	−	0.0777337i	−0.478764	−	0.877944i	$-0.658915\pi$
$503$	2.71276	−	1.74339i	0.120956	−	0.0777337i	0.599720	+	0.800210i	$0.295279\pi$
$504$	−0.265237	+	0.0778807i	−0.0118146	+	0.00346908i
$505$	2.09241	−	14.5530i	0.0931110	−	0.647601i
$506$	27.8066			1.23615
$507$	−15.2354			−0.676628
$508$	0.371466	−	2.58361i	0.0164812	−	0.114629i
$509$	27.9117	+	32.2119i	1.23717	+	1.42777i	0.866633	+	0.498946i	$0.166279\pi$
$509$	27.9117	+	32.2119i	1.23717	+	1.42777i	0.370533	+	0.928819i	$0.379175\pi$
$510$	−1.05333	+	2.30647i	−0.0466421	+	0.102132i
$511$	−0.661735	−	4.60247i	−0.0292734	−	0.203601i
$512$	0.415415	−	0.909632i	0.0183589	−	0.0402004i
$513$	22.7389	+	6.67674i	1.00395	+	0.294785i
$514$	−17.7783	+	5.22017i	−0.784166	+	0.230252i
$515$	−3.31971	−	3.83115i	−0.146284	−	0.168821i
$516$	−0.0921536	−	0.0270587i	−0.00405683	−	0.00119119i
$517$	−50.3789	+	32.3766i	−2.21566	+	1.42392i
$518$	−4.40641	−	9.64870i	−0.193607	−	0.423940i
$519$	16.6440	−	36.4453i	0.730591	−	1.59977i
$520$	−1.26460	+	1.45943i	−0.0554565	+	0.0640002i
$521$	−23.1921	+	14.9047i	−1.01607	+	0.652986i	−0.938956	−	0.344036i	$-0.888206\pi$
$521$	−23.1921	+	14.9047i	−1.01607	+	0.652986i	−0.0771099	+	0.997023i	$0.524569\pi$
$522$	0.119842	+	0.262417i	0.00524534	+	0.0114857i
$523$	−1.61515	−	11.2336i	−0.0706257	−	0.491213i	−0.994179	−	0.107742i	$-0.965638\pi$
$523$	−1.61515	−	11.2336i	−0.0706257	−	0.491213i	0.923553	−	0.383471i	$-0.125271\pi$
$524$	2.69207	+	18.7238i	0.117604	+	0.817952i
$525$	0.993794	−	1.14690i	0.0433727	−	0.0500548i
$526$	3.16356	−	0.928905i	0.137938	−	0.0405022i
$527$	5.81344	+	3.73607i	0.253238	+	0.162746i
$528$	1.43202	−	9.95995i	0.0623208	−	0.433451i
$529$	−1.99923	−	1.28483i	−0.0869230	−	0.0558620i
$530$	5.94525	+	6.86118i	0.258245	+	0.298031i
$531$	2.36432	−	2.72857i	0.102603	−	0.118410i
$532$	−1.67672	−	3.67150i	−0.0726950	−	0.159180i
$533$	−20.6604	−	6.06645i	−0.894903	−	0.262767i
$534$	−15.8414	−	10.1806i	−0.685524	−	0.440559i
$535$	−2.89162			−0.125016
$536$	−7.62994	−	2.96378i	−0.329563	−	0.128016i
$537$	−25.2224			−1.08843
$538$	−9.77322	−	6.28087i	−0.421354	−	0.270788i
$539$	−36.1150	−	10.6043i	−1.55558	−	0.456761i
$540$	−2.25240	−	4.93206i	−0.0969277	−	0.212242i
$541$	−1.03334	+	1.19254i	−0.0444267	+	0.0512712i	−0.777528	−	0.628848i	$-0.783527\pi$
$541$	−1.03334	+	1.19254i	−0.0444267	+	0.0512712i	0.733101	+	0.680119i	$0.238072\pi$
$542$	10.4960	+	12.1131i	0.450843	+	0.520301i
$543$	12.2564	+	7.87669i	0.525971	+	0.338021i
$544$	0.219582	−	1.52723i	0.00941452	−	0.0654794i
$545$	−2.38909	−	1.53537i	−0.102337	−	0.0657681i
$546$	2.81186	−	0.825637i	0.120337	−	0.0353340i
$547$	−9.13688	+	10.5445i	−0.390665	+	0.450851i	−0.916679	−	0.399625i	$-0.869140\pi$
$547$	−9.13688	+	10.5445i	−0.390665	+	0.450851i	0.526014	+	0.850476i	$0.323686\pi$
$548$	0.636964	+	4.43018i	0.0272097	+	0.189248i
$549$	0.582950	+	4.05451i	0.0248797	+	0.173042i
$550$	−2.54360	−	5.56970i	−0.108459	−	0.237493i
$551$	−3.54355	+	2.27730i	−0.150960	+	0.0970163i
$552$	4.88725	−	5.64019i	0.208015	−	0.240062i
$553$	2.30777	−	5.05332i	0.0981364	−	0.214889i
$554$	0.892796	+	1.95495i	0.0379313	+	0.0830579i
$555$	15.8800	−	10.2055i	0.674069	−	0.433198i
$556$	−6.94077	−	2.03799i	−0.294354	−	0.0864302i
$557$	14.9461	+	17.2487i	0.633286	+	0.730850i	0.978173	−	0.207794i	$-0.0666283\pi$
$557$	14.9461	+	17.2487i	0.633286	+	0.730850i	−0.344887	+	0.938644i	$0.612083\pi$
$558$	−1.28641	+	0.377725i	−0.0544582	+	0.0159904i
$559$	−0.108289	−	0.0317964i	−0.00458012	−	0.00134484i
$560$	−0.383615	+	0.839999i	−0.0162107	+	0.0354965i
$561$	−2.20952	−	15.3675i	−0.0932859	−	0.648818i
$562$	−10.7180	+	23.4692i	−0.452112	+	0.989987i
$563$	−1.67880	−	1.93744i	−0.0707529	−	0.0816532i	0.719270	−	0.694731i	$-0.244477\pi$
$563$	−1.67880	−	1.93744i	−0.0707529	−	0.0816532i	−0.790022	+	0.613078i	$0.789931\pi$
$564$	−2.28739	+	15.9091i	−0.0963165	+	0.669896i
$565$	−15.4813			−0.651303
$566$	4.01194			0.168634
$567$	−1.05299	+	7.32368i	−0.0442213	+	0.307566i
$568$	−2.68681	+	0.788918i	−0.112736	+	0.0331023i
$569$	20.9269	−	13.4489i	0.877300	−	0.563806i	−0.0226778	−	0.999743i	$-0.507219\pi$
$569$	20.9269	−	13.4489i	0.877300	−	0.563806i	0.899977	+	0.435937i	$0.143583\pi$
$570$	6.04263	−	3.88336i	0.253098	−	0.162656i
$571$	−32.3253	+	9.49157i	−1.35277	+	0.397210i	−0.876210	−	0.481930i	$-0.839936\pi$
$571$	−32.3253	+	9.49157i	−1.35277	+	0.397210i	−0.476563	+	0.879140i	$0.658118\pi$
$572$	1.68276	−	11.7038i	0.0703595	−	0.489361i
$573$	−23.7559			−0.992417
$574$	−10.2969			−0.429784
$575$	0.646296	−	4.49509i	0.0269524	−	0.187458i
$576$	0.196033	+	0.226234i	0.00816803	+	0.00942641i
$577$	2.34195	−	5.12817i	0.0974969	−	0.213488i	−0.854599	−	0.519289i	$-0.826197\pi$
$577$	2.34195	−	5.12817i	0.0974969	−	0.213488i	0.952096	+	0.305801i	$0.0989241\pi$
$578$	2.08055	+	14.4706i	0.0865395	+	0.601896i
$579$	−5.27618	+	11.5532i	−0.219270	+	0.480135i
$580$	0.924674	+	0.271509i	0.0383950	+	0.0112738i
$581$	−7.85995	+	2.30789i	−0.326086	+	0.0957474i
$582$	17.9175	+	20.6779i	0.742705	+	0.857127i
$583$	−53.3370	−	15.6612i	−2.20899	−	0.648619i
$584$	−4.23592	+	2.72226i	−0.175284	+	0.112648i
$585$	−0.240141	−	0.525836i	−0.00992861	−	0.0217406i
$586$	−5.02954	+	11.0132i	−0.207768	+	0.454949i
$587$	12.4503	−	14.3685i	0.513881	−	0.593050i	−0.438207	−	0.898874i	$-0.644386\pi$
$587$	12.4503	−	14.3685i	0.513881	−	0.593050i	0.952088	+	0.305824i	$0.0989319\pi$
$588$	−8.49848	+	5.46164i	−0.350471	+	0.225234i
$589$	−8.13216	−	17.8070i	−0.335080	−	0.733723i
$590$	−1.71644	−	11.9381i	−0.0706645	−	0.491483i
$591$	4.73640	+	32.9424i	0.194829	+	1.35507i
$592$	−7.52210	+	8.68096i	−0.309156	+	0.356785i
$593$	24.2219	−	7.11219i	0.994675	−	0.292063i	0.256406	−	0.966569i	$-0.417462\pi$
$593$	24.2219	−	7.11219i	0.994675	−	0.292063i	0.738269	+	0.674506i	$0.235644\pi$
$594$	27.9290	+	17.9489i	1.14594	+	0.736452i
$595$	−0.202773	+	1.41032i	−0.00831289	+	0.0578174i
$596$	−10.0493	−	6.45830i	−0.411636	−	0.264542i
$597$	19.1463	+	22.0961i	0.783607	+	0.904331i
$598$	5.74295	−	6.62772i	0.234847	−	0.271028i
$599$	−9.12321	−	19.9771i	−0.372764	−	0.816240i	−0.999320	−	0.0368637i	$-0.988263\pi$
$599$	−9.12321	−	19.9771i	−0.372764	−	0.816240i	0.626556	−	0.779377i	$-0.284464\pi$
$600$	−1.57680	−	0.462990i	−0.0643725	−	0.0189015i
$601$	−14.9970	−	9.63798i	−0.611740	−	0.393142i	0.197769	−	0.980249i	$-0.436630\pi$
$601$	−14.9970	−	9.63798i	−0.611740	−	0.393142i	−0.809509	+	0.587107i	$0.800267\pi$
$602$	−0.0539696			−0.00219964
$603$	1.75585	−	1.70906i	0.0715038	−	0.0695984i
$604$	8.68142			0.353242
$605$	22.2860	+	14.3223i	0.906055	+	0.582286i
$606$	23.1832	+	6.80719i	0.941751	+	0.276523i
$607$	3.74979	+	8.21089i	0.152199	+	0.333270i	0.970338	−	0.241750i	$-0.0777215\pi$
$607$	3.74979	+	8.21089i	0.152199	+	0.333270i	−0.818139	+	0.575020i	$0.804994\pi$
$608$	−2.86229	+	3.30326i	−0.116081	+	0.133965i
$609$	−0.957730	−	1.10528i	−0.0388092	−	0.0447882i
$610$	11.5114	+	7.39794i	0.466084	+	0.299534i
$611$	−2.68789	+	18.6947i	−0.108740	+	0.756305i
$612$	0.388556	+	0.249710i	0.0157064	+	0.0100939i
$613$	11.7632	−	3.45398i	0.475111	−	0.139505i	−0.0354058	−	0.999373i	$-0.511272\pi$
$613$	11.7632	−	3.45398i	0.475111	−	0.139505i	0.510517	+	0.859868i	$0.329454\pi$
$614$	−7.63094	+	8.80657i	−0.307960	+	0.355404i
$615$	−2.60782	−	18.1378i	−0.105157	−	0.731385i
$616$	−0.804691	−	5.59675i	−0.0324219	−	0.225500i
$617$	−7.25365	−	15.8833i	−0.292021	−	0.639437i	0.705582	−	0.708628i	$-0.250686\pi$
$617$	−7.25365	−	15.8833i	−0.292021	−	0.639437i	−0.997603	+	0.0691909i	$0.977958\pi$
$618$	7.00830	−	4.50396i	0.281915	−	0.181176i
$619$	−5.69511	+	6.57251i	−0.228906	+	0.264171i	−0.858570	−	0.512696i	$-0.828647\pi$
$619$	−5.69511	+	6.57251i	−0.228906	+	0.264171i	0.629665	+	0.776867i	$0.283192\pi$
$620$	−1.86055	+	4.07404i	−0.0747215	+	0.163617i
$621$	10.2288	+	22.3980i	0.410469	+	0.898802i
$622$	−11.5123	+	7.39851i	−0.461602	+	0.296653i
$623$	−10.1528	−	2.98114i	−0.406764	−	0.119437i
$624$	−2.07820	−	2.39837i	−0.0831947	−	0.0960118i
$625$	−0.959493	+	0.281733i	−0.0383797	+	0.0112693i
$626$	5.39596	+	1.58440i	0.215666	+	0.0633253i
$627$	−18.2704	+	40.0065i	−0.729648	+	1.59771i
$628$	−1.59714	−	11.1084i	−0.0637329	−	0.443272i
$629$	−7.36240	+	16.1214i	−0.293558	+	0.642803i
$630$	−0.181026	−	0.208916i	−0.00721226	−	0.00832339i
$631$	−0.231695	+	1.61147i	−0.00922362	+	0.0641517i	−0.993913	−	0.110164i	$-0.964862\pi$
$631$	−0.231695	+	1.61147i	−0.00922362	+	0.0641517i	0.984690	+	0.174316i	$0.0557714\pi$
$632$	−6.01586			−0.239298
$633$	−14.4064			−0.572601
$634$	−1.30846	+	9.10054i	−0.0519656	+	0.361428i
$635$	2.50444	−	0.735371i	0.0993858	−	0.0291823i
$636$	−12.5511	+	8.06611i	−0.497684	+	0.319842i
$637$	−9.98647	+	6.41791i	−0.395678	+	0.254287i
$638$	−5.66180	+	1.66246i	−0.224153	+	0.0658172i
$639$	0.119296	−	0.829720i	0.00471926	−	0.0328232i
$640$	1.00000			0.0395285
$641$	−18.6493			−0.736603			−0.368301	−	0.929706i	$-0.620061\pi$
$641$	−18.6493			−0.736603			−0.368301	+	0.929706i	$0.620061\pi$
$642$	0.676279	−	4.70362i	0.0266906	−	0.185637i
$643$	19.2738	+	22.2432i	0.760085	+	0.877185i	0.995505	−	0.0947084i	$-0.0301919\pi$
$643$	19.2738	+	22.2432i	0.760085	+	0.877185i	−0.235420	+	0.971894i	$0.575646\pi$
$644$	1.74211	−	3.81470i	0.0686489	−	0.150320i
$645$	−0.0136685	−	0.0950664i	−0.000538196	−	0.00374324i
$646$	−2.80152	+	6.13448i	−0.110224	+	0.241358i
$647$	−5.59248	−	1.64210i	−0.219863	−	0.0645577i	0.169946	−	0.985453i	$-0.445641\pi$
$647$	−5.59248	−	1.64210i	−0.219863	−	0.0645577i	−0.389809	+	0.920896i	$0.627459\pi$
$648$	7.68778	−	2.25734i	0.302005	−	0.0886766i
$649$	48.3607	+	55.8112i	1.89832	+	2.19078i
$650$	−1.85288	−	0.544054i	−0.0726758	−	0.0213395i
$651$	5.71786	−	3.67464i	0.224101	−	0.144021i
$652$	−7.19052	−	15.7450i	−0.281602	−	0.616623i
$653$	12.4384	−	27.2364i	0.486754	−	1.06584i	−0.493797	−	0.869577i	$-0.664391\pi$
$653$	12.4384	−	27.2364i	0.486754	−	1.06584i	0.980551	−	0.196265i	$-0.0628812\pi$
$654$	3.05624	−	3.52709i	0.119509	−	0.137920i
$655$	−15.9134	+	10.2269i	−0.621789	+	0.399599i
$656$	4.63207	+	10.1428i	0.180852	+	0.396010i
$657$	−0.214511	−	1.49196i	−0.00836889	−	0.0582069i
$658$	1.28534	+	8.93976i	0.0501079	+	0.348508i
$659$	−32.2242	+	37.1887i	−1.25527	+	1.44866i	−0.411999	+	0.911185i	$0.635169\pi$
$659$	−32.2242	+	37.1887i	−1.25527	+	1.44866i	−0.843276	+	0.537480i	$0.819376\pi$
$660$	9.65477	−	2.83490i	0.375811	−	0.110348i
$661$	−39.4324	−	25.3417i	−1.53374	−	0.985677i	−0.989139	−	0.146984i	$-0.953043\pi$
$661$	−39.4324	−	25.3417i	−1.53374	−	0.985677i	−0.544605	−	0.838693i	$-0.683320\pi$
$662$	−0.983727	+	6.84197i	−0.0382337	+	0.265921i
$663$	−4.11920	−	2.64725i	−0.159977	−	0.102811i
$664$	5.80916	+	6.70413i	0.225439	+	0.260171i
$665$	2.64318	−	3.05039i	0.102498	−	0.118289i
$666$	−1.42841	−	3.12777i	−0.0553496	−	0.121199i
$667$	−4.19923	−	1.23301i	−0.162595	−	0.0477422i
$668$	14.7593	+	9.48522i	0.571054	+	0.366994i
$669$	0.725129			0.0280351
$670$	−0.473644	−	8.17164i	−0.0182985	−	0.315698i
$671$	−83.7853			−3.23450
$672$	−1.27666	−	0.820458i	−0.0492481	−	0.0316498i
$673$	−31.7385	−	9.31927i	−1.22343	−	0.359232i	−0.394664	−	0.918826i	$-0.629139\pi$
$673$	−31.7385	−	9.31927i	−1.22343	−	0.359232i	−0.828767	+	0.559594i	$0.810957\pi$
$674$	−8.18436	−	17.9212i	−0.315250	−	0.690301i
$675$	3.55068	−	4.09770i	0.136666	−	0.157721i
$676$	6.07112	+	7.00644i	0.233504	+	0.269479i
$677$	−22.5241	−	14.4754i	−0.865671	−	0.556333i	0.0307547	−	0.999527i	$-0.490209\pi$
$677$	−22.5241	−	14.4754i	−0.865671	−	0.556333i	−0.896426	+	0.443194i	$0.853845\pi$
$678$	3.62069	−	25.1825i	0.139052	−	0.967126i
$679$	12.9341	+	8.31222i	0.496364	+	0.318994i
$680$	1.48043	−	0.434695i	0.0567721	−	0.0166698i
$681$	4.70576	−	5.43074i	0.180325	−	0.208106i
$682$	−3.90279	−	27.1445i	−0.149446	−	1.03942i
$683$	−4.07742	−	28.3590i	−0.156018	−	1.08513i	−0.905880	−	0.423535i	$-0.860789\pi$
$683$	−4.07742	−	28.3590i	−0.156018	−	1.08513i	0.749862	−	0.661594i	$-0.230120\pi$
$684$	−0.543534	−	1.19017i	−0.0207825	−	0.0455074i
$685$	−3.76523	+	2.41977i	−0.143862	+	0.0924545i
$686$	−7.95054	+	9.17542i	−0.303553	+	0.350319i
$687$	1.89448	−	4.14833i	0.0722788	−	0.158269i
$688$	0.0242783	+	0.0531621i	0.000925602	+	0.00202679i
$689$	−14.7487	+	9.47840i	−0.561880	+	0.361098i
$690$	7.16073	+	2.10258i	0.272604	+	0.0800438i
$691$	29.5682	+	34.1235i	1.12483	+	1.29812i	0.949556	+	0.313597i	$0.101534\pi$
$691$	29.5682	+	34.1235i	1.12483	+	1.29812i	0.175270	+	0.984520i	$0.443920\pi$
$692$	−23.3929	+	6.86877i	−0.889263	+	0.261111i
$693$	1.62405	+	0.476865i	0.0616927	+	0.0181146i
$694$	−10.4372	+	22.8544i	−0.396192	+	0.867540i
$695$	−1.02948	−	7.16016i	−0.0390502	−	0.271600i
$696$	−0.657905	+	1.44061i	−0.0249378	+	0.0546062i
$697$	11.2665	+	13.0022i	0.426749	+	0.492495i
$698$	1.04080	−	7.23895i	0.0393950	−	0.273998i
$699$	−9.47712			−0.358457
$700$	−0.923450			−0.0349031
$701$	−3.12934	+	21.7651i	−0.118194	+	0.822055i	0.841349	+	0.540492i	$0.181762\pi$
$701$	−3.12934	+	21.7651i	−0.118194	+	0.822055i	−0.959543	+	0.281563i	$0.909147\pi$
$702$	10.0464	−	2.94988i	0.379176	−	0.111336i
$703$	42.2359	−	27.1434i	1.59296	−	1.02373i
$704$	−5.15102	+	3.31036i	−0.194136	+	0.124764i
$705$	−15.4217	+	4.52821i	−0.580814	+	0.170542i
$706$	0.0992040	−	0.689979i	0.00373359	−	0.0259677i
$707$	13.5772			0.510623
$708$	19.8204			0.744895
$709$	−4.14259	+	28.8123i	−0.155578	+	1.08207i	0.751082	+	0.660208i	$0.229532\pi$
$709$	−4.14259	+	28.8123i	−0.155578	+	1.08207i	−0.906661	+	0.421861i	$0.861377\pi$
$710$	−1.83377	−	2.11628i	−0.0688200	−	0.0794225i
$711$	0.748099	−	1.63811i	0.0280559	−	0.0614339i
$712$	1.63073	+	11.3420i	0.0611142	+	0.425059i
$713$	8.44934	−	18.5015i	0.316430	−	0.692885i
$714$	−2.24666	−	0.659678i	−0.0840790	−	0.0246878i
$715$	11.3452	−	3.33126i	0.424287	−	0.124582i
$716$	10.0508	+	11.5993i	0.375617	+	0.433485i
$717$	−45.7066	−	13.4207i	−1.70694	−	0.501204i
$718$	−4.48121	+	2.87990i	−0.167237	+	0.107477i
$719$	4.59190	+	10.0549i	0.171249	+	0.374983i	0.975724	−	0.219003i	$-0.0702806\pi$
$719$	4.59190	+	10.0549i	0.171249	+	0.374983i	−0.804475	+	0.593986i	$0.797553\pi$
$720$	−0.124355	+	0.272299i	−0.00463442	+	0.0101480i
$721$	3.06559	−	3.53788i	0.114168	−	0.131757i
$722$	0.0876817	−	0.0563496i	0.00326318	−	0.00209712i
$723$	−7.27098	−	15.9212i	−0.270411	−	0.592117i
$724$	−1.26169	−	8.77522i	−0.0468902	−	0.326128i
$725$	0.137150	+	0.953902i	0.00509364	+	0.0354270i
$726$	−28.5094	+	32.9016i	−1.05808	+	1.22109i
$727$	−47.8139	+	14.0394i	−1.77332	+	0.520694i	−0.994330	−	0.106341i	$-0.966087\pi$
$727$	−47.8139	+	14.0394i	−1.77332	+	0.520694i	−0.778991	+	0.627035i	$0.784268\pi$
$728$	−1.50019	−	0.964111i	−0.0556006	−	0.0357323i
$729$	−4.14558	+	28.8332i	−0.153540	+	1.06790i
$730$	−4.23592	−	2.72226i	−0.156778	−	0.100755i
$731$	0.0590517	+	0.0681493i	0.00218411	+	0.00252059i
$732$	−14.7260	+	16.9947i	−0.544289	+	0.628143i
$733$	18.8411	+	41.2562i	0.695910	+	1.52383i	0.844861	+	0.534986i	$0.179683\pi$
$733$	18.8411	+	41.2562i	0.695910	+	1.52383i	−0.148951	+	0.988845i	$0.547590\pi$
$734$	−2.31270	−	0.679069i	−0.0853632	−	0.0250649i
$735$	−8.49848	−	5.46164i	−0.313471	−	0.201456i
$736$	−4.54131			−0.167395
$737$	29.4908	+	40.5243i	1.08631	+	1.49273i
$738$	−3.33789			−0.122870
$739$	−16.0983	−	10.3457i	−0.592186	−	0.380575i	0.209954	−	0.977711i	$-0.432669\pi$
$739$	−16.0983	−	10.3457i	−0.592186	−	0.380575i	−0.802139	+	0.597137i	$0.796305\pi$
$740$	−11.0213	−	3.23614i	−0.405150	−	0.118963i
$741$	5.76217	+	12.6174i	0.211679	+	0.463511i
$742$	−5.49014	+	6.33596i	−0.201549	+	0.232600i
$743$	−22.8762	−	26.4005i	−0.839245	−	0.968541i	0.160584	−	0.987022i	$-0.448662\pi$
$743$	−22.8762	−	26.4005i	−0.839245	−	0.968541i	−0.999829	+	0.0184815i	$0.994117\pi$
$744$	−6.19185	−	3.97926i	−0.227004	−	0.145887i
$745$	1.70004	−	11.8241i	0.0622847	−	0.433200i
$746$	−15.4161	−	9.90730i	−0.564422	−	0.362732i
$747$	−2.54792	+	0.748137i	−0.0932236	+	0.0273729i
$748$	−6.18675	+	7.13988i	−0.226210	+	0.261060i
$749$	−0.380019	−	2.64309i	−0.0138856	−	0.0965763i
$750$	−0.233875	−	1.62664i	−0.00853992	−	0.0593964i
$751$	18.4403	+	40.3785i	0.672895	+	1.47343i	0.870000	+	0.493052i	$0.164119\pi$
$751$	18.4403	+	40.3785i	0.672895	+	1.47343i	−0.197105	+	0.980382i	$0.563154\pi$
$752$	8.22778	−	5.28767i	0.300036	−	0.192822i
$753$	−4.03331	+	4.65469i	−0.146982	+	0.169626i
$754$	−0.773097	+	1.69285i	−0.0281545	+	0.0616498i
$755$	3.60639	+	7.89690i	0.131250	+	0.287398i
$756$	4.21214	−	2.70698i	0.153194	−	0.0984518i
$757$	−33.8455	−	9.93794i	−1.23014	−	0.361200i	−0.398835	−	0.917023i	$-0.630585\pi$
$757$	−33.8455	−	9.93794i	−1.23014	−	0.361200i	−0.831301	+	0.555822i	$0.812403\pi$
$758$	−4.71687	−	5.44356i	−0.171325	−	0.197719i
$759$	−43.8453	+	12.8741i	−1.59148	+	0.467302i
$760$	−4.19379	−	1.23141i	−0.152125	−	0.0446678i
$761$	−3.57945	+	7.83790i	−0.129755	+	0.284124i	−0.963348	−	0.268256i	$-0.913553\pi$
$761$	−3.57945	+	7.83790i	−0.129755	+	0.284124i	0.833593	+	0.552379i	$0.186280\pi$
$762$	0.610455	+	4.24581i	0.0221144	+	0.153809i
$763$	1.08943	−	2.38552i	0.0394401	−	0.0863618i
$764$	9.46643	+	10.9248i	0.342483	+	0.395247i
$765$	−0.0657320	+	0.457176i	−0.00237655	+	0.0165292i
$766$	14.2139			0.513569
$767$	23.2907			0.840978
$768$	−0.233875	+	1.62664i	−0.00843925	+	0.0586963i
$769$	6.58636	−	1.93393i	0.237510	−	0.0697393i	−0.160811	−	0.986985i	$-0.551411\pi$
$769$	6.58636	−	1.93393i	0.237510	−	0.0697393i	0.398322	+	0.917246i	$0.369593\pi$
$770$	4.75670	−	3.05695i	0.171420	−	0.110165i
$771$	25.6159	−	16.4623i	0.922533	−	0.592876i
$772$	7.41557	−	2.17741i	0.266892	−	0.0783667i
$773$	−1.61918	+	11.2616i	−0.0582379	+	0.405053i	0.939762	+	0.341831i	$0.111047\pi$
$773$	−1.61918	+	11.2616i	−0.0582379	+	0.405053i	−0.997999	+	0.0632226i	$0.979862\pi$
$774$	−0.0174951			−0.000628847
$775$	−4.47877			−0.160882
$776$	2.36944	−	16.4798i	0.0850578	−	0.591590i
$777$	11.4153	+	13.1739i	0.409521	+	0.472612i
$778$	−1.96630	+	4.30559i	−0.0704951	+	0.154363i
$779$	−6.93598	−	48.2408i	−0.248507	−	1.72841i
$780$	1.31832	−	2.88672i	0.0472035	−	0.103361i
$781$	16.4514	+	4.83057i	0.588677	+	0.172851i
$782$	−6.72311	+	1.97408i	−0.240418	+	0.0705931i
$783$	−3.42183	−	3.94900i	−0.122286	−	0.141126i
$784$	5.89823	+	1.73188i	0.210651	+	0.0618528i
$785$	9.44105	−	6.06739i	0.336966	−	0.216555i
$786$	−12.9138	−	28.2772i	−0.460619	−	1.00861i
$787$	9.18358	−	20.1092i	0.327359	−	0.716817i	−0.672367	−	0.740218i	$-0.734722\pi$
$787$	9.18358	−	20.1092i	0.327359	−	0.716817i	0.999726	+	0.0234013i	$0.00744953\pi$
$788$	13.2621	−	15.3053i	0.472443	−	0.545228i
$789$	−4.55822	+	2.92939i	−0.162277	+	0.104289i
$790$	−2.49908	−	5.47222i	−0.0889132	−	0.194693i
$791$	−2.03456	−	14.1507i	−0.0723406	−	0.503140i
$792$	−0.260853	−	1.81427i	−0.00926901	−	0.0644673i
$793$	−17.3044	+	19.9703i	−0.614496	+	0.709166i
$794$	−11.0916	+	3.25678i	−0.393626	+	0.115579i
$795$	−12.5511	−	8.06611i	−0.445142	−	0.286075i
$796$	2.53194	−	17.6100i	0.0897421	−	0.624170i
$797$	−5.18173	−	3.33010i	−0.183546	−	0.117958i	0.445641	−	0.895212i	$-0.352976\pi$
$797$	−5.18173	−	3.33010i	−0.183546	−	0.117958i	−0.629187	+	0.777254i	$0.716612\pi$
$798$	4.34371	+	5.01291i	0.153766	+	0.177455i
$799$	9.88217	−	11.4046i	0.349606	−	0.403467i
$800$	0.415415	+	0.909632i	0.0146871	+	0.0321603i
$801$	−3.29119	−	0.966381i	−0.116289	−	0.0341454i
$802$	26.7477	+	17.1897i	0.944494	+	0.606989i
$803$	30.8309			1.08800
$804$	13.4031	+	1.14070i	0.472690	+	0.0402292i
$805$	4.19367			0.147808
$806$	−7.27597	−	4.67598i	−0.256285	−	0.164704i
$807$	18.3184	+	5.37876i	0.644837	+	0.189341i
$808$	−6.10772	−	13.3740i	−0.214869	−	0.470497i
$809$	10.7939	−	12.4568i	0.379492	−	0.437958i	−0.533583	−	0.845747i	$-0.679155\pi$
$809$	10.7939	−	12.4568i	0.379492	−	0.437958i	0.913076	+	0.407790i	$0.133700\pi$
$810$	5.24697	+	6.05532i	0.184360	+	0.212762i
$811$	44.8140	+	28.8002i	1.57363	+	1.01131i	0.978139	+	0.207951i	$0.0666796\pi$
$811$	44.8140	+	28.8002i	1.57363	+	1.01131i	0.595493	+	0.803361i	$0.296957\pi$
$812$	−0.126652	+	0.880881i	−0.00444460	+	0.0309129i
$813$	−22.1583	−	14.2403i	−0.777127	−	0.499429i
$814$	67.4835	−	19.8149i	2.36530	−	0.694514i
$815$	11.3351	−	13.0815i	0.397053	−	0.458223i
$816$	0.360854	+	2.50980i	0.0126324	+	0.0878604i
$817$	−0.0363539	−	0.252847i	−0.00127186	−	0.00884600i
$818$	0.275865	+	0.604060i	0.00964539	+	0.0211205i
$819$	0.449081	−	0.288607i	0.0156922	−	0.0100847i
$820$	−7.30200	+	8.42696i	−0.254997	+	0.294282i
$821$	−13.4476	+	29.4462i	−0.469325	+	1.02768i	0.515937	+	0.856627i	$0.327444\pi$
$821$	−13.4476	+	29.4462i	−0.469325	+	1.02768i	−0.985262	+	0.171052i	$0.945283\pi$
$822$	−3.05549	−	6.69059i	−0.106572	−	0.233361i
$823$	13.3482	−	8.57834i	0.465288	−	0.299022i	−0.286913	−	0.957957i	$-0.592629\pi$
$823$	13.3482	−	8.57834i	0.465288	−	0.299022i	0.752200	+	0.658935i	$0.228993\pi$
$824$	−4.86400	−	1.42820i	−0.169445	−	0.0497536i
$825$	6.58945	+	7.60463i	0.229415	+	0.264759i
$826$	10.6864	−	3.13782i	0.371828	−	0.109179i
$827$	45.1927	+	13.2698i	1.57151	+	0.461436i	0.947439	−	0.319936i	$-0.103661\pi$
$827$	45.1927	+	13.2698i	1.57151	+	0.461436i	0.624066	+	0.781372i	$0.285480\pi$
$828$	0.564733	−	1.23659i	0.0196258	−	0.0429746i
$829$	−2.83355	−	19.7077i	−0.0984131	−	0.684478i	−0.977979	−	0.208702i	$-0.933076\pi$
$829$	−2.83355	−	19.7077i	−0.0984131	−	0.684478i	0.879566	−	0.475777i	$-0.157833\pi$
$830$	−3.68508	+	8.06920i	−0.127911	+	0.280086i
$831$	−2.31288	−	2.66921i	−0.0802329	−	0.0925937i
$832$	−0.274824	+	1.91144i	−0.00952782	+	0.0662674i
$833$	9.48479			0.328628
$834$	11.8878			0.411639
$835$	−2.49683	+	17.3658i	−0.0864063	+	0.600969i
$836$	25.6787	−	7.53994i	0.888115	−	0.260774i
$837$	20.4291	−	13.1290i	0.706132	−	0.453804i
$838$	−17.3193	+	11.1305i	−0.598287	+	0.384495i
$839$	15.2375	−	4.47413i	0.526056	−	0.154464i	−0.00791173	−	0.999969i	$-0.502518\pi$
$839$	15.2375	−	4.47413i	0.526056	−	0.154464i	0.533968	+	0.845505i	$0.320700\pi$
$840$	0.215972	−	1.50212i	0.00745174	−	0.0518280i
$841$	−28.0713			−0.967974
$842$	3.05869			0.105410
$843$	6.03415	−	41.9685i	0.207827	−	1.44547i
$844$	5.74075	+	6.62518i	0.197605	+	0.228048i
$845$	−3.85125	+	8.43306i	−0.132487	+	0.290106i
$846$	0.416664	+	2.89796i	0.0143252	+	0.0996339i
$847$	−10.1625	+	22.2528i	−0.349188	+	0.764615i
$848$	8.71090	+	2.55775i	0.299133	+	0.0878335i
$849$	−6.32602	+	1.85749i	−0.217108	+	0.0637488i
$850$	1.01041	+	1.16607i	0.0346567	+	0.0399959i
$851$	50.0510	+	14.6963i	1.71573	+	0.503783i
$852$	3.87129	−	2.48793i	0.132628	−	0.0852350i
$853$	−17.4051	−	38.1119i	−0.595940	−	1.30493i	−0.931785	−	0.363010i	$-0.881749\pi$
$853$	−17.4051	−	38.1119i	−0.595940	−	1.30493i	0.335845	−	0.941917i	$-0.390978\pi$
$854$	−5.24925	+	11.4943i	−0.179626	+	0.393325i
$855$	0.856827	−	0.988831i	0.0293029	−	0.0338173i
$856$	−2.43259	+	1.56333i	−0.0831441	+	0.0534335i
$857$	−23.0212	−	50.4094i	−0.786389	−	1.72195i	−0.686709	−	0.726932i	$-0.740945\pi$
$857$	−23.0212	−	50.4094i	−0.786389	−	1.72195i	−0.0996799	−	0.995020i	$-0.531782\pi$
$858$	2.76538	+	19.2337i	0.0944086	+	0.656626i
$859$	2.25177	+	15.6614i	0.0768294	+	0.534361i	0.991495	+	0.130148i	$0.0415453\pi$
$859$	2.25177	+	15.6614i	0.0768294	+	0.534361i	−0.914665	+	0.404212i	$0.867546\pi$
$860$	−0.0382724	+	0.0441686i	−0.00130508	+	0.00150614i
$861$	16.2361	−	4.76735i	0.553325	−	0.162471i
$862$	16.1783	+	10.3971i	0.551034	+	0.354128i
$863$	0.0457721	−	0.318352i	0.00155810	−	0.0108368i	−0.989028	−	0.147731i	$-0.952803\pi$
$863$	0.0457721	−	0.318352i	0.00155810	−	0.0108368i	0.990586	+	0.136894i	$0.0437121\pi$
$864$	−4.56131	−	2.93138i	−0.155179	−	0.0997274i
$865$	−15.9658	−	18.4255i	−0.542853	−	0.626486i
$866$	23.2466	−	26.8280i	0.789950	−	0.911651i
$867$	−9.98032	−	21.8539i	−0.338950	−	0.742196i
$868$	−3.96839	−	1.16522i	−0.134696	−	0.0395503i
$869$	30.9878	+	19.9146i	1.05119	+	0.675558i
$870$	−1.58373			−0.0536935
$871$	15.7498	+	1.34042i	0.533662	+	0.0454184i
$872$	−2.83991			−0.0961715
$873$	4.19277	+	2.69453i	0.141904	+	0.0911961i
$874$	19.0453	+	5.59221i	0.644217	+	0.189159i
$875$	−0.383615	−	0.839999i	−0.0129685	−	0.0283972i
$876$	5.41881	−	6.25364i	0.183085	−	0.211291i
$877$	18.8079	+	21.7055i	0.635098	+	0.732942i	0.978500	−	0.206247i	$-0.0661249\pi$
$877$	18.8079	+	21.7055i	0.635098	+	0.732942i	−0.343402	+	0.939188i	$0.611579\pi$
$878$	−23.3068	−	14.9784i	−0.786566	−	0.505495i
$879$	2.83159	−	19.6941i	0.0955072	−	0.664267i
$880$	−5.15102	−	3.31036i	−0.173641	−	0.111592i
$881$	−36.7690	+	10.7964i	−1.23878	+	0.363739i	−0.834557	−	0.550922i	$-0.814276\pi$
$881$	−36.7690	+	10.7964i	−1.23878	+	0.363739i	−0.404223	+	0.914660i	$0.632458\pi$
$882$	−1.20506	+	1.39071i	−0.0405765	+	0.0468278i
$883$	0.0200301	+	0.139312i	0.000674066	+	0.00468823i	0.990156	−	0.139970i	$-0.0447007\pi$
$883$	0.0200301	+	0.139312i	0.000674066	+	0.00468823i	−0.989482	+	0.144659i	$0.953792\pi$
$884$	0.424036	+	2.94923i	0.0142619	+	0.0991934i
$885$	8.23367	+	18.0292i	0.276772	+	0.606046i
$886$	−5.16023	+	3.31628i	−0.173361	+	0.111412i
$887$	16.1335	−	18.6191i	0.541711	−	0.625168i	−0.417220	−	0.908805i	$-0.636996\pi$
$887$	16.1335	−	18.6191i	0.541711	−	0.625168i	0.958932	+	0.283637i	$0.0915411\pi$
$888$	7.84163	−	17.1708i	0.263148	−	0.576213i
$889$	1.00130	+	2.19254i	0.0335826	+	0.0735356i
$890$	−9.63960	+	6.19499i	−0.323120	+	0.207657i
$891$	−47.0725	−	13.8217i	−1.57699	−	0.463045i
$892$	−0.288955	−	0.333472i	−0.00967493	−	0.0111655i
$893$	−41.0169	+	12.0436i	−1.37258	+	0.403025i
$894$	18.8359	+	5.53071i	0.629965	+	0.184975i
$895$	−6.37580	+	13.9611i	−0.213120	+	0.466667i
$896$	0.131421	+	0.914050i	0.00439045	+	0.0305363i
$897$	−5.98691	+	13.1095i	−0.199897	+	0.437713i
$898$	−16.0556	−	18.5292i	−0.535784	−	0.618328i
$899$	−0.614266	+	4.27231i	−0.0204869	+	0.142490i
$900$	−0.299350			−0.00997834
$901$	14.0078			0.466666
$902$	9.71648	−	67.5796i	0.323523	−	2.25016i
$903$	0.0850992	−	0.0249874i	0.00283192	−	0.000831528i
$904$	−13.0237	+	8.36981i	−0.433161	+	0.278376i
$905$	7.45809	−	4.79303i	0.247915	−	0.159326i
$906$	−13.6888	+	4.01941i	−0.454781	+	0.133536i
$907$	−2.50775	+	17.4418i	−0.0832685	+	0.579145i	0.904883	+	0.425661i	$0.139958\pi$
$907$	−2.50775	+	17.4418i	−0.0832685	+	0.579145i	−0.988151	+	0.153484i	$0.950951\pi$
$908$	−4.37267			−0.145112
$909$	4.40125			0.145980
$910$	0.253786	−	1.76512i	0.00841294	−	0.0585133i
$911$	−15.9281	−	18.3820i	−0.527722	−	0.609024i	0.427825	−	0.903861i	$-0.359280\pi$
$911$	−15.9281	−	18.3820i	−0.527722	−	0.609024i	−0.955547	+	0.294838i	$0.904734\pi$
$912$	2.98388	−	6.53378i	0.0988061	−	0.216355i
$913$	−7.73003	−	53.7635i	−0.255826	−	1.77931i
$914$	−3.22827	+	7.06893i	−0.106782	+	0.233819i
$915$	−21.5763	−	6.33539i	−0.713292	−	0.209441i
$916$	−2.66265	+	0.781826i	−0.0879766	+	0.0258323i
$917$	−11.4393	−	13.2016i	−0.377758	−	0.435956i
$918$	−8.02697	−	2.35693i	−0.264929	−	0.0777903i
$919$	7.21808	−	4.63878i	0.238103	−	0.153019i	−0.416148	−	0.909297i	$-0.636620\pi$
$919$	7.21808	−	4.63878i	0.238103	−	0.153019i	0.654251	+	0.756277i	$0.272984\pi$
$920$	−1.88653	−	4.13092i	−0.0621970	−	0.136192i
$921$	7.95509	−	17.4192i	0.262129	−	0.573983i
$922$	2.91276	−	3.36151i	0.0959267	−	0.110705i
$923$	4.54911	−	2.92354i	0.149736	−	0.0962294i
$924$	3.86007	+	8.45238i	0.126987	+	0.278063i
$925$	−1.63471	−	11.3696i	−0.0537489	−	0.373832i
$926$	4.32107	+	30.0537i	0.141999	+	0.987626i
$927$	0.993756	−	1.14686i	0.0326392	−	0.0376677i
$928$	0.924674	−	0.271509i	0.0303539	−	0.00891272i
$929$	29.0797	+	18.6884i	0.954075	+	0.613147i	0.922352	−	0.386350i	$-0.126264\pi$
$929$	29.0797	+	18.6884i	0.954075	+	0.613147i	0.0317228	+	0.999497i	$0.489901\pi$
$930$	1.04747	−	7.28535i	0.0343480	−	0.238896i
$931$	−22.6033	−	14.5263i	−0.740793	−	0.476079i
$932$	3.77651	+	4.35833i	0.123704	+	0.142762i
$933$	14.7272	−	16.9960i	0.482145	−	0.556425i
$934$	3.06335	+	6.70781i	0.100236	+	0.219486i
$935$	−9.06473	−	2.66165i	−0.296449	−	0.0870451i
$936$	−0.486308	−	0.312531i	−0.0158955	−	0.0102154i
$937$	38.1571			1.24654			0.623269	−	0.782007i	$-0.285804\pi$
$937$	38.1571			1.24654			0.623269	+	0.782007i	$0.285804\pi$
$938$	7.40704	−	1.50686i	0.241848	−	0.0492006i
$939$	−9.24190			−0.301598
$940$	8.22778	+	5.28767i	0.268361	+	0.172465i
$941$	48.0604	+	14.1118i	1.56672	+	0.460031i	0.946045	−	0.324034i	$-0.105039\pi$
$941$	48.0604	+	14.1118i	1.56672	+	0.460031i	0.620678	+	0.784066i	$0.286857\pi$
$942$	7.66143	+	16.7762i	0.249623	+	0.546598i
$943$	33.1607	−	38.2694i	1.07986	−	1.24622i
$944$	−7.89817	−	9.11497i	−0.257063	−	0.296667i
$945$	4.21214	+	2.70698i	0.137021	+	0.0880580i
$946$	0.0509275	−	0.354209i	0.00165580	−	0.0115163i
$947$	−28.5315	−	18.3361i	−0.927150	−	0.595843i	−0.0124260	−	0.999923i	$-0.503955\pi$
$947$	−28.5315	−	18.3361i	−0.927150	−	0.595843i	−0.914724	+	0.404080i	$0.867592\pi$
$948$	9.48579	−	2.78528i	0.308084	−	0.0904616i
$949$	6.36758	−	7.34858i	0.206701	−	0.238545i
$950$	−0.622035	−	4.32635i	−0.0201815	−	0.140365i
$951$	−2.15028	−	14.9555i	−0.0697275	−	0.484965i
$952$	0.591892	+	1.29606i	0.0191833	+	0.0420057i
$953$	−8.91733	+	5.73082i	−0.288861	+	0.185639i	−0.677044	−	0.735943i	$-0.736739\pi$
$953$	−8.91733	+	5.73082i	−0.288861	+	0.185639i	0.388183	+	0.921582i	$0.373103\pi$
$954$	−1.77971	+	2.05390i	−0.0576203	+	0.0664974i
$955$	−6.00509	+	13.1493i	−0.194320	+	0.425502i
$956$	12.0416	+	26.3675i	0.389454	+	0.852785i
$957$	8.15782	−	5.24271i	0.263705	−	0.169473i
$958$	−21.8961	−	6.42928i	−0.707432	−	0.207721i
$959$	−2.70662	−	3.12360i	−0.0874012	−	0.100866i
$960$	−1.57680	+	0.462990i	−0.0508909	+	0.0149429i
$961$	10.4974	+	3.08232i	0.338626	+	0.0994296i
$962$	9.21461	−	20.1772i	0.297091	−	0.650538i
$963$	−0.123189	−	0.856797i	−0.00396970	−	0.0276099i
$964$	−4.42444	+	9.68818i	−0.142502	+	0.312035i
$965$	5.06118	+	5.84091i	0.162925	+	0.188026i
$966$	−0.980796	+	6.82159i	−0.0315566	+	0.219481i
$967$	−41.7390			−1.34223			−0.671117	−	0.741351i	$-0.734185\pi$
$967$	−41.7390			−1.34223			−0.671117	+	0.741351i	$0.734185\pi$
$968$	26.4914			0.851467
$969$	1.57723	−	10.9699i	0.0506681	−	0.352404i
$970$	15.9748	−	4.69064i	0.512921	−	0.150607i
$971$	−13.0361	+	8.37777i	−0.418347	+	0.268855i	−0.732835	−	0.680406i	$-0.761803\pi$
$971$	−13.0361	+	8.37777i	−0.418347	+	0.268855i	0.314488	+	0.949261i	$0.398167\pi$
$972$	2.60697	−	1.67540i	0.0836187	−	0.0537384i
$973$	6.40945	−	1.88198i	0.205478	−	0.0603336i
$974$	1.83207	−	12.7423i	0.0587034	−	0.408291i
$975$	3.17350			0.101633
$976$	13.6836			0.438003
$977$	7.05241	−	49.0506i	0.225626	−	1.56927i	−0.490591	−	0.871390i	$-0.663219\pi$
$977$	7.05241	−	49.0506i	0.225626	−	1.56927i	0.716218	−	0.697877i	$-0.245872\pi$
$978$	18.6278	+	21.4976i	0.595651	+	0.687418i
$979$	29.1461	−	63.8210i	0.931513	−	2.03973i
$980$	0.874844	+	6.08467i	0.0279459	+	0.194368i
$981$	0.353156	−	0.773304i	0.0112754	−	0.0246897i
$982$	31.5686	+	9.26937i	1.00739	+	0.295798i
$983$	−50.3459	+	14.7829i	−1.60579	+	0.471501i	−0.957149	−	0.289596i	$-0.906479\pi$
$983$	−50.3459	+	14.7829i	−1.60579	+	0.471501i	−0.648637	+	0.761098i	$0.724661\pi$
$984$	−11.9999	−	13.8486i	−0.382541	−	0.441476i
$985$	19.4315	+	5.70559i	0.619138	+	0.181795i
$986$	1.25090	−	0.803902i	0.0398366	−	0.0256015i
$987$	−6.16574	−	13.5011i	−0.196258	−	0.429745i
$988$	3.50632	−	7.67777i	0.111551	−	0.244263i
$989$	0.173807	−	0.200584i	0.00552673	−	0.00637819i
$990$	1.54196	−	0.990956i	0.0490066	−	0.0314946i
$991$	12.2334	+	26.7874i	0.388606	+	0.850928i	0.998300	+	0.0582913i	$0.0185652\pi$
$991$	12.2334	+	26.7874i	0.388606	+	0.850928i	−0.609694	+	0.792637i	$0.708708\pi$
$992$	0.637396	+	4.43319i	0.0202373	+	0.140754i
$993$	−1.61662	−	11.2439i	−0.0513020	−	0.356813i
$994$	1.69339	−	1.95428i	0.0537111	−	0.0619859i
$995$	17.0704	−	5.01233i	0.541169	−	0.158902i
$996$	−12.2638	−	7.88148i	−0.388594	−	0.249734i
$997$	−3.36016	+	23.3704i	−0.106417	+	0.740148i	0.864828	+	0.502068i	$0.167427\pi$
$997$	−3.36016	+	23.3704i	−0.106417	+	0.740148i	−0.971246	+	0.238080i	$0.923482\pi$
$998$	8.13363	+	5.22716i	0.257465	+	0.165463i
$999$	40.7851	+	47.0685i	1.29038	+	1.48918i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.k.a.411.1	✓	40
67.15	even	11	inner	670.2.k.a.551.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.k.a.411.1	✓	40	1.1	even	1	trivial
670.2.k.a.551.1	yes	40	67.15	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:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.k (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 + 0.540641i) q^{2} +(-1.57680 - 0.462990i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-1.07618 - 1.24197i) q^{6} +(-0.776855 - 0.499255i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.251829 - 0.161841i) q^{9} +O(q^{10})\)	\(q+(0.841254 + 0.540641i) q^{2} +(-1.57680 - 0.462990i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-1.07618 - 1.24197i) q^{6} +(-0.776855 - 0.499255i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.251829 - 0.161841i) q^{9} +(-0.959493 + 0.281733i) q^{10} +(4.00973 - 4.62747i) q^{11} +(-0.233875 - 1.62664i) q^{12} +(-0.274824 - 1.91144i) q^{13} +(-0.383615 - 0.839999i) q^{14} +(1.38249 - 0.888470i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-0.640958 + 1.40350i) q^{17} +(-0.124355 - 0.272299i) q^{18} +(3.67698 - 2.36305i) q^{19} +(-0.959493 - 0.281733i) q^{20} +(0.993794 + 1.14690i) q^{21} +(5.87500 - 1.72506i) q^{22} +(4.35736 + 1.27944i) q^{23} +(0.682679 - 1.49486i) q^{24} +(-0.142315 - 0.989821i) q^{25} +(0.802208 - 1.75659i) q^{26} +(3.55068 + 4.09770i) q^{27} +(0.131421 - 0.914050i) q^{28} -0.963711 q^{29} +1.64337 q^{30} +(0.637396 - 4.43319i) q^{31} +(-0.959493 + 0.281733i) q^{32} +(-8.46500 + 5.44013i) q^{33} +(-1.29800 + 0.834173i) q^{34} +(0.886043 - 0.260166i) q^{35} +(0.0426020 - 0.296303i) q^{36} +11.4866 q^{37} +4.37084 q^{38} +(-0.451637 + 3.14120i) q^{39} +(-0.654861 - 0.755750i) q^{40} +(4.63207 - 10.1428i) q^{41} +(0.215972 + 1.50212i) q^{42} +(0.0242783 - 0.0531621i) q^{43} +(5.87500 + 1.72506i) q^{44} +(0.287224 - 0.0843367i) q^{45} +(2.97393 + 3.43209i) q^{46} +(-9.38421 - 2.75545i) q^{47} +(1.38249 - 0.888470i) q^{48} +(-2.55366 - 5.59173i) q^{49} +(0.415415 - 0.909632i) q^{50} +(1.66047 - 1.91628i) q^{51} +(1.62454 - 1.04403i) q^{52} +(-3.77141 - 8.25823i) q^{53} +(0.771636 + 5.36685i) q^{54} +(0.871397 + 6.06070i) q^{55} +(0.604731 - 0.697897i) q^{56} +(-6.89193 + 2.02365i) q^{57} +(-0.810726 - 0.521022i) q^{58} +(-1.71644 + 11.9381i) q^{59} +(1.38249 + 0.888470i) q^{60} +(-8.96088 - 10.3414i) q^{61} +(2.93297 - 3.38483i) q^{62} +(0.114835 + 0.251454i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(1.62454 + 1.04403i) q^{65} -10.0624 q^{66} +(-1.84776 + 7.97407i) q^{67} -1.54293 q^{68} +(-6.27830 - 4.03482i) q^{69} +(0.886043 + 0.260166i) q^{70} +(1.16326 + 2.54719i) q^{71} +(0.196033 - 0.226234i) q^{72} +(3.29739 + 3.80539i) q^{73} +(9.66311 + 6.21010i) q^{74} +(-0.233875 + 1.62664i) q^{75} +(3.67698 + 2.36305i) q^{76} +(-5.42527 + 1.59300i) q^{77} +(-2.07820 + 2.39837i) q^{78} +(0.856146 + 5.95462i) q^{79} +(-0.142315 - 0.989821i) q^{80} +(-3.32845 - 7.28828i) q^{81} +(9.38037 - 6.02840i) q^{82} +(5.80916 - 6.70413i) q^{83} +(-0.630419 + 1.38043i) q^{84} +(-0.640958 - 1.40350i) q^{85} +(0.0491658 - 0.0315969i) q^{86} +(1.51958 + 0.446188i) q^{87} +(4.00973 + 4.62747i) q^{88} +(10.9945 - 3.22826i) q^{89} +(0.287224 + 0.0843367i) q^{90} +(-0.740799 + 1.62212i) q^{91} +(0.646296 + 4.49509i) q^{92} +(-3.05756 + 6.69513i) q^{93} +(-6.40479 - 7.39152i) q^{94} +(-0.622035 + 4.32635i) q^{95} +1.64337 q^{96} -16.6493 q^{97} +(0.874844 - 6.08467i) q^{98} +(-1.75868 + 0.516396i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} + 6 q^{3} - 4 q^{4} - 4 q^{5} + 6 q^{6} + 13 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 + 6 * q^3 - 4 * q^4 - 4 * q^5 + 6 * q^6 + 13 * q^7 - 4 * q^8 + 4 * q^9	\( 40 q - 4 q^{2} + 6 q^{3} - 4 q^{4} - 4 q^{5} + 6 q^{6} + 13 q^{7} - 4 q^{8} + 4 q^{9} - 4 q^{10} - 14 q^{11} - 5 q^{12} - 6 q^{13} - 9 q^{14} + 6 q^{15} - 4 q^{16} - 24 q^{17} + 4 q^{18} + 24 q^{19} - 4 q^{20} - 10 q^{21} + 19 q^{22} - 15 q^{23} - 5 q^{24} - 4 q^{25} + 16 q^{26} + 54 q^{27} + 2 q^{28} - 40 q^{29} - 16 q^{30} + 15 q^{31} - 4 q^{32} - 40 q^{33} - 2 q^{34} - 9 q^{35} + 4 q^{36} - 6 q^{37} - 20 q^{38} + 21 q^{39} - 4 q^{40} + 8 q^{41} + 23 q^{42} - 54 q^{43} + 19 q^{44} - 7 q^{45} + 7 q^{46} - 23 q^{47} + 6 q^{48} - 7 q^{49} - 4 q^{50} + 61 q^{51} - 6 q^{52} + 17 q^{53} - 12 q^{54} - 3 q^{55} + 2 q^{56} - 18 q^{57} - 18 q^{58} - q^{59} + 6 q^{60} - 6 q^{61} - 7 q^{62} - 43 q^{63} - 4 q^{64} - 6 q^{65} - 18 q^{66} + 44 q^{67} - 2 q^{68} - 45 q^{69} - 9 q^{70} - 14 q^{71} - 7 q^{72} - 26 q^{73} + 38 q^{74} - 5 q^{75} + 24 q^{76} + 21 q^{77} - 45 q^{78} + 2 q^{79} - 4 q^{80} + 4 q^{81} + 8 q^{82} - 11 q^{83} - 10 q^{84} - 24 q^{85} + 45 q^{86} - 7 q^{87} - 14 q^{88} + 61 q^{89} - 7 q^{90} + 70 q^{91} + 18 q^{92} + 10 q^{93} + 43 q^{94} + 13 q^{95} - 16 q^{96} - 18 q^{97} + 26 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 + 6 * q^3 - 4 * q^4 - 4 * q^5 + 6 * q^6 + 13 * q^7 - 4 * q^8 + 4 * q^9 - 4 * q^10 - 14 * q^11 - 5 * q^12 - 6 * q^13 - 9 * q^14 + 6 * q^15 - 4 * q^16 - 24 * q^17 + 4 * q^18 + 24 * q^19 - 4 * q^20 - 10 * q^21 + 19 * q^22 - 15 * q^23 - 5 * q^24 - 4 * q^25 + 16 * q^26 + 54 * q^27 + 2 * q^28 - 40 * q^29 - 16 * q^30 + 15 * q^31 - 4 * q^32 - 40 * q^33 - 2 * q^34 - 9 * q^35 + 4 * q^36 - 6 * q^37 - 20 * q^38 + 21 * q^39 - 4 * q^40 + 8 * q^41 + 23 * q^42 - 54 * q^43 + 19 * q^44 - 7 * q^45 + 7 * q^46 - 23 * q^47 + 6 * q^48 - 7 * q^49 - 4 * q^50 + 61 * q^51 - 6 * q^52 + 17 * q^53 - 12 * q^54 - 3 * q^55 + 2 * q^56 - 18 * q^57 - 18 * q^58 - q^59 + 6 * q^60 - 6 * q^61 - 7 * q^62 - 43 * q^63 - 4 * q^64 - 6 * q^65 - 18 * q^66 + 44 * q^67 - 2 * q^68 - 45 * q^69 - 9 * q^70 - 14 * q^71 - 7 * q^72 - 26 * q^73 + 38 * q^74 - 5 * q^75 + 24 * q^76 + 21 * q^77 - 45 * q^78 + 2 * q^79 - 4 * q^80 + 4 * q^81 + 8 * q^82 - 11 * q^83 - 10 * q^84 - 24 * q^85 + 45 * q^86 - 7 * q^87 - 14 * q^88 + 61 * q^89 - 7 * q^90 + 70 * q^91 + 18 * q^92 + 10 * q^93 + 43 * q^94 + 13 * q^95 - 16 * q^96 - 18 * q^97 + 26 * q^98 - 48 * q^99

Introduction

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