LMFDB - Embedded newform 322.2.i.b.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			29.1
Root			$0.959493 - 0.281733i$ of defining polynomial
Character	$\chi$	$=$	322.29
Dual form			322.2.i.b.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 + 0.909632i) q^{2} +(2.30075 + 0.675560i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(1.74412 - 1.12088i) q^{5} +(-1.57028 + 1.81219i) q^{6} +(0.142315 - 0.989821i) q^{7} +(0.959493 - 0.281733i) q^{8} +(2.31329 + 1.48666i) q^{9} +O(q^{10})$	\(q+(-0.415415 + 0.909632i) q^{2} +(2.30075 + 0.675560i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(1.74412 - 1.12088i) q^{5} +(-1.57028 + 1.81219i) q^{6} +(0.142315 - 0.989821i) q^{7} +(0.959493 - 0.281733i) q^{8} +(2.31329 + 1.48666i) q^{9} +(0.295053 + 2.05214i) q^{10} +(-0.100702 - 0.220506i) q^{11} +(-0.996114 - 2.18119i) q^{12} +(0.220047 + 1.53046i) q^{13} +(0.841254 + 0.540641i) q^{14} +(4.77001 - 1.40060i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(1.47459 - 1.70177i) q^{17} +(-2.31329 + 1.48666i) q^{18} +(-0.686393 - 0.792140i) q^{19} +(-1.98926 - 0.584100i) q^{20} +(0.996114 - 2.18119i) q^{21} +0.242413 q^{22} +(-3.74217 + 2.99936i) q^{23} +2.39788 q^{24} +(-0.291482 + 0.638257i) q^{25} +(-1.48357 - 0.435615i) q^{26} +(-0.392858 - 0.453382i) q^{27} +(-0.841254 + 0.540641i) q^{28} +(-2.84950 + 3.28850i) q^{29} +(-0.707501 + 4.92078i) q^{30} +(1.89491 - 0.556396i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(-0.0827241 - 0.575359i) q^{33} +(0.935418 + 2.04828i) q^{34} +(-0.861256 - 1.88589i) q^{35} +(-0.391340 - 2.72183i) q^{36} +(0.372092 + 0.239129i) q^{37} +(1.00569 - 0.295298i) q^{38} +(-0.527646 + 3.66986i) q^{39} +(1.35769 - 1.56685i) q^{40} +(-8.15464 + 5.24067i) q^{41} +(1.57028 + 1.81219i) q^{42} +(-7.00617 - 2.05720i) q^{43} +(-0.100702 + 0.220506i) q^{44} +5.70104 q^{45} +(-1.17376 - 4.64998i) q^{46} +5.57944 q^{47} +(-0.996114 + 2.18119i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(-0.459493 - 0.530283i) q^{50} +(4.54231 - 2.91917i) q^{51} +(1.01255 - 1.16854i) q^{52} +(-1.23916 + 8.61852i) q^{53} +(0.575610 - 0.169014i) q^{54} +(-0.422797 - 0.271715i) q^{55} +(-0.142315 - 0.989821i) q^{56} +(-1.04408 - 2.28621i) q^{57} +(-1.80760 - 3.95809i) q^{58} +(-0.149697 - 1.04117i) q^{59} +(-4.18219 - 2.68773i) q^{60} +(13.7257 - 4.03022i) q^{61} +(-0.281059 + 1.95481i) q^{62} +(1.80075 - 2.07817i) q^{63} +(0.841254 - 0.540641i) q^{64} +(2.09925 + 2.42267i) q^{65} +(0.557730 + 0.163764i) q^{66} +(0.663423 - 1.45269i) q^{67} -2.25177 q^{68} +(-10.6360 + 4.37270i) q^{69} +2.07324 q^{70} +(0.842376 - 1.84455i) q^{71} +(2.63843 + 0.774713i) q^{72} +(-7.49726 - 8.65230i) q^{73} +(-0.372092 + 0.239129i) q^{74} +(-1.10181 + 1.27155i) q^{75} +(-0.149167 + 1.03748i) q^{76} +(-0.232593 + 0.0682955i) q^{77} +(-3.11903 - 2.00448i) q^{78} +(-1.78907 - 12.4432i) q^{79} +(0.861256 + 1.88589i) q^{80} +(-4.02452 - 8.81248i) q^{81} +(-1.37952 - 9.59478i) q^{82} +(-10.9763 - 7.05402i) q^{83} +(-2.30075 + 0.675560i) q^{84} +(0.664391 - 4.62094i) q^{85} +(4.78176 - 5.51845i) q^{86} +(-8.77756 + 5.64100i) q^{87} +(-0.158746 - 0.183203i) q^{88} +(1.64765 + 0.483793i) q^{89} +(-2.36830 + 5.18584i) q^{90} +1.54620 q^{91} +(4.71737 + 0.863983i) q^{92} +4.73559 q^{93} +(-2.31778 + 5.07524i) q^{94} +(-2.08505 - 0.612225i) q^{95} +(-1.57028 - 1.81219i) q^{96} +(-0.815998 + 0.524410i) q^{97} +(0.654861 - 0.755750i) q^{98} +(0.0948656 - 0.659805i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} + 5 q^{3} - q^{4} + 8 q^{5} - 5 q^{6} + q^{7} + q^{8}+O(q^{10}) $ 10 * q + q^2 + 5 * q^3 - q^4 + 8 * q^5 - 5 * q^6 + q^7 + q^8	\( 10 q + q^{2} + 5 q^{3} - q^{4} + 8 q^{5} - 5 q^{6} + q^{7} + q^{8} + 3 q^{10} + 11 q^{11} + 5 q^{12} - 6 q^{13} - q^{14} + 4 q^{15} - q^{16} - 2 q^{17} - 3 q^{19} + 8 q^{20} - 5 q^{21} - 21 q^{23} + 6 q^{24} - 15 q^{25} - 5 q^{26} - 4 q^{27} + q^{28} + 2 q^{29} - 4 q^{30} + 3 q^{31} + q^{32} - 11 q^{33} + 2 q^{34} + 3 q^{35} - 6 q^{37} - 8 q^{38} + 8 q^{39} + 14 q^{40} - 23 q^{41} + 5 q^{42} - q^{43} + 11 q^{44} - 22 q^{45} - q^{46} + 38 q^{47} + 5 q^{48} - q^{49} + 4 q^{50} + 21 q^{51} + 5 q^{52} - 49 q^{53} + 4 q^{54} + 11 q^{55} - q^{56} - 7 q^{57} - 13 q^{58} + 9 q^{59} + 4 q^{60} + 16 q^{61} - 14 q^{62} - q^{64} + 15 q^{65} + 7 q^{67} - 2 q^{68} - 16 q^{69} + 8 q^{70} - 16 q^{71} + 11 q^{72} - 9 q^{73} + 6 q^{74} - 2 q^{75} - 14 q^{76} + 11 q^{77} - 8 q^{78} + 6 q^{79} - 3 q^{80} - 24 q^{81} - 43 q^{82} - 19 q^{83} - 5 q^{84} + 49 q^{85} + 23 q^{86} - 21 q^{87} - 11 q^{88} + 25 q^{89} - 11 q^{90} + 6 q^{91} + q^{92} - 4 q^{93} - 5 q^{94} + 24 q^{95} - 5 q^{96} + 16 q^{97} + q^{98} - 33 q^{99}+O(q^{100}) \) 10 * q + q^2 + 5 * q^3 - q^4 + 8 * q^5 - 5 * q^6 + q^7 + q^8 + 3 * q^10 + 11 * q^11 + 5 * q^12 - 6 * q^13 - q^14 + 4 * q^15 - q^16 - 2 * q^17 - 3 * q^19 + 8 * q^20 - 5 * q^21 - 21 * q^23 + 6 * q^24 - 15 * q^25 - 5 * q^26 - 4 * q^27 + q^28 + 2 * q^29 - 4 * q^30 + 3 * q^31 + q^32 - 11 * q^33 + 2 * q^34 + 3 * q^35 - 6 * q^37 - 8 * q^38 + 8 * q^39 + 14 * q^40 - 23 * q^41 + 5 * q^42 - q^43 + 11 * q^44 - 22 * q^45 - q^46 + 38 * q^47 + 5 * q^48 - q^49 + 4 * q^50 + 21 * q^51 + 5 * q^52 - 49 * q^53 + 4 * q^54 + 11 * q^55 - q^56 - 7 * q^57 - 13 * q^58 + 9 * q^59 + 4 * q^60 + 16 * q^61 - 14 * q^62 - q^64 + 15 * q^65 + 7 * q^67 - 2 * q^68 - 16 * q^69 + 8 * q^70 - 16 * q^71 + 11 * q^72 - 9 * q^73 + 6 * q^74 - 2 * q^75 - 14 * q^76 + 11 * q^77 - 8 * q^78 + 6 * q^79 - 3 * q^80 - 24 * q^81 - 43 * q^82 - 19 * q^83 - 5 * q^84 + 49 * q^85 + 23 * q^86 - 21 * q^87 - 11 * q^88 + 25 * q^89 - 11 * q^90 + 6 * q^91 + q^92 - 4 * q^93 - 5 * q^94 + 24 * q^95 - 5 * q^96 + 16 * q^97 + q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$3$	2.30075	+	0.675560i	1.32834	+	0.390035i	0.867494	−	0.497447i	$-0.165729\pi$
$3$	2.30075	+	0.675560i	1.32834	+	0.390035i	0.460842	+	0.887482i	$0.347547\pi$
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	1.74412	−	1.12088i	0.779995	−	0.501273i	−0.0890367	−	0.996028i	$-0.528379\pi$
$5$	1.74412	−	1.12088i	0.779995	−	0.501273i	0.869032	+	0.494756i	$0.164742\pi$
$6$	−1.57028	+	1.81219i	−0.641062	+	0.739825i
$7$	0.142315	−	0.989821i	0.0537900	−	0.374117i
$7$	0.142315	−	0.989821i	0.0537900	−	0.374117i
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$	2.31329	+	1.48666i	0.771097	+	0.495554i
$10$	0.295053	+	2.05214i	0.0933040	+	0.648944i
$11$	−0.100702	−	0.220506i	−0.0303627	−	0.0664851i	0.893843	−	0.448380i	$-0.147999\pi$
$11$	−0.100702	−	0.220506i	−0.0303627	−	0.0664851i	−0.924206	+	0.381895i	$0.875272\pi$
$12$	−0.996114	−	2.18119i	−0.287553	−	0.629654i
$13$	0.220047	+	1.53046i	0.0610301	+	0.424474i	0.997315	+	0.0732321i	$0.0233314\pi$
$13$	0.220047	+	1.53046i	0.0610301	+	0.424474i	−0.936285	+	0.351242i	$0.885760\pi$
$14$	0.841254	+	0.540641i	0.224834	+	0.144492i
$15$	4.77001	−	1.40060i	1.23161	−	0.361633i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	1.47459	−	1.70177i	0.357641	−	0.412740i	−0.548207	−	0.836343i	$-0.684689\pi$
$17$	1.47459	−	1.70177i	0.357641	−	0.412740i	0.905848	+	0.423603i	$0.139235\pi$
$18$	−2.31329	+	1.48666i	−0.545248	+	0.350410i
$19$	−0.686393	−	0.792140i	−0.157469	−	0.181729i	0.671533	−	0.740975i	$-0.265636\pi$
$19$	−0.686393	−	0.792140i	−0.157469	−	0.181729i	−0.829002	+	0.559246i	$0.811091\pi$
$20$	−1.98926	−	0.584100i	−0.444812	−	0.130609i
$21$	0.996114	−	2.18119i	0.217370	−	0.475974i
$22$	0.242413			0.0516825
$23$	−3.74217	+	2.99936i	−0.780297	+	0.625409i
$23$	−3.74217	+	2.99936i	−0.780297	+	0.625409i
$24$	2.39788			0.489465
$25$	−0.291482	+	0.638257i	−0.0582964	+	0.127651i
$26$	−1.48357	−	0.435615i	−0.290952	−	0.0854311i
$27$	−0.392858	−	0.453382i	−0.0756055	−	0.0872534i
$28$	−0.841254	+	0.540641i	−0.158982	+	0.102172i
$29$	−2.84950	+	3.28850i	−0.529139	+	0.610659i	−0.955895	−	0.293708i	$-0.905111\pi$
$29$	−2.84950	+	3.28850i	−0.529139	+	0.610659i	0.426756	+	0.904367i	$0.359656\pi$
$30$	−0.707501	+	4.92078i	−0.129171	+	0.898407i
$31$	1.89491	−	0.556396i	0.340336	−	0.0999317i	−0.107098	−	0.994248i	$-0.534156\pi$
$31$	1.89491	−	0.556396i	0.340336	−	0.0999317i	0.447434	+	0.894317i	$0.352338\pi$
$32$	−0.841254	−	0.540641i	−0.148714	−	0.0955727i
$33$	−0.0827241	−	0.575359i	−0.0144004	−	0.100157i
$34$	0.935418	+	2.04828i	0.160423	+	0.351277i
$35$	−0.861256	−	1.88589i	−0.145579	−	0.318773i
$36$	−0.391340	−	2.72183i	−0.0652233	−	0.453638i
$37$	0.372092	+	0.239129i	0.0611715	+	0.0393126i	0.570869	−	0.821041i	$-0.306606\pi$
$37$	0.372092	+	0.239129i	0.0611715	+	0.0393126i	−0.509698	+	0.860354i	$0.670243\pi$
$38$	1.00569	−	0.295298i	0.163145	−	0.0479037i
$39$	−0.527646	+	3.66986i	−0.0844910	+	0.587648i
$40$	1.35769	−	1.56685i	0.214669	−	0.247741i
$41$	−8.15464	+	5.24067i	−1.27354	+	0.818455i	−0.990077	−	0.140527i	$-0.955120\pi$
$41$	−8.15464	+	5.24067i	−1.27354	+	0.818455i	−0.283465	+	0.958983i	$0.591484\pi$
$42$	1.57028	+	1.81219i	0.242299	+	0.279628i
$43$	−7.00617	−	2.05720i	−1.06843	−	0.313720i	−0.300189	−	0.953880i	$-0.597050\pi$
$43$	−7.00617	−	2.05720i	−1.06843	−	0.313720i	−0.768242	+	0.640160i	$0.778868\pi$
$44$	−0.100702	+	0.220506i	−0.0151814	+	0.0332426i
$45$	5.70104			0.849860
$46$	−1.17376	−	4.64998i	−0.173061	−	0.685602i
$47$	5.57944			0.813845			0.406922	−	0.913463i	$-0.366602\pi$
$47$	5.57944			0.813845			0.406922	+	0.913463i	$0.366602\pi$
$48$	−0.996114	+	2.18119i	−0.143777	+	0.314827i
$49$	−0.959493	−	0.281733i	−0.137070	−	0.0402475i
$50$	−0.459493	−	0.530283i	−0.0649821	−	0.0749934i
$51$	4.54231	−	2.91917i	0.636051	−	0.408765i
$52$	1.01255	−	1.16854i	0.140415	−	0.162047i
$53$	−1.23916	+	8.61852i	−0.170211	+	1.18385i	0.708225	+	0.705986i	$0.249496\pi$
$53$	−1.23916	+	8.61852i	−0.170211	+	1.18385i	−0.878437	+	0.477859i	$0.841413\pi$
$54$	0.575610	−	0.169014i	0.0783306	−	0.0229999i
$55$	−0.422797	−	0.271715i	−0.0570100	−	0.0366381i
$56$	−0.142315	−	0.989821i	−0.0190176	−	0.132270i
$57$	−1.04408	−	2.28621i	−0.138292	−	0.302816i
$58$	−1.80760	−	3.95809i	−0.237349	−	0.519723i
$59$	−0.149697	−	1.04117i	−0.0194889	−	0.135548i	0.977754	−	0.209755i	$-0.0672666\pi$
$59$	−0.149697	−	1.04117i	−0.0194889	−	0.135548i	−0.997243	+	0.0742067i	$0.976358\pi$
$60$	−4.18219	−	2.68773i	−0.539919	−	0.346985i
$61$	13.7257	−	4.03022i	1.75739	−	0.516016i	0.765536	−	0.643393i	$-0.222474\pi$
$61$	13.7257	−	4.03022i	1.75739	−	0.516016i	0.991854	+	0.127377i	$0.0406557\pi$
$62$	−0.281059	+	1.95481i	−0.0356945	+	0.248261i
$63$	1.80075	−	2.07817i	0.226873	−	0.261825i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	2.09925	+	2.42267i	0.260380	+	0.300495i
$66$	0.557730	+	0.163764i	0.0686518	+	0.0201580i
$67$	0.663423	−	1.45269i	0.0810501	−	0.177475i	−0.864768	−	0.502171i	$-0.832535\pi$
$67$	0.663423	−	1.45269i	0.0810501	−	0.177475i	0.945818	+	0.324696i	$0.105262\pi$
$68$	−2.25177			−0.273067
$69$	−10.6360	+	4.37270i	−1.28043	+	0.526411i
$70$	2.07324			0.247800
$71$	0.842376	−	1.84455i	0.0999716	−	0.218907i	−0.853037	−	0.521850i	$-0.825242\pi$
$71$	0.842376	−	1.84455i	0.0999716	−	0.218907i	0.953009	+	0.302943i	$0.0979692\pi$
$72$	2.63843	+	0.774713i	0.310942	+	0.0913008i
$73$	−7.49726	−	8.65230i	−0.877488	−	1.01268i	−0.999796	−	0.0201834i	$-0.993575\pi$
$73$	−7.49726	−	8.65230i	−0.877488	−	1.01268i	0.122308	−	0.992492i	$-0.460970\pi$
$74$	−0.372092	+	0.239129i	−0.0432548	+	0.0277982i
$75$	−1.10181	+	1.27155i	−0.127226	+	0.146826i
$76$	−0.149167	+	1.03748i	−0.0171107	+	0.119007i
$77$	−0.232593	+	0.0682955i	−0.0265064	+	0.00778300i
$78$	−3.11903	−	2.00448i	−0.353161	−	0.226963i
$79$	−1.78907	−	12.4432i	−0.201286	−	1.39997i	−0.800475	−	0.599366i	$-0.795420\pi$
$79$	−1.78907	−	12.4432i	−0.201286	−	1.39997i	0.599190	−	0.800607i	$-0.295490\pi$
$80$	0.861256	+	1.88589i	0.0962914	+	0.210849i
$81$	−4.02452	−	8.81248i	−0.447169	−	0.979164i
$82$	−1.37952	−	9.59478i	−0.152343	−	1.05957i
$83$	−10.9763	−	7.05402i	−1.20480	−	0.774280i	−0.225022	−	0.974354i	$-0.572245\pi$
$83$	−10.9763	−	7.05402i	−1.20480	−	0.774280i	−0.979781	+	0.200074i	$0.935882\pi$
$84$	−2.30075	+	0.675560i	−0.251032	+	0.0737097i
$85$	0.664391	−	4.62094i	0.0720633	−	0.501211i
$86$	4.78176	−	5.51845i	0.515630	−	0.595069i
$87$	−8.77756	+	5.64100i	−0.941053	+	0.604778i
$88$	−0.158746	−	0.183203i	−0.0169224	−	0.0195295i
$89$	1.64765	+	0.483793i	0.174650	+	0.0512820i	0.367889	−	0.929870i	$-0.380081\pi$
$89$	1.64765	+	0.483793i	0.174650	+	0.0512820i	−0.193238	+	0.981152i	$0.561899\pi$
$90$	−2.36830	+	5.18584i	−0.249640	+	0.546636i
$91$	1.54620			0.162086
$92$	4.71737	+	0.863983i	0.491819	+	0.0900765i
$93$	4.73559			0.491058
$94$	−2.31778	+	5.07524i	−0.239061	+	0.523471i
$95$	−2.08505	−	0.612225i	−0.213921	−	0.0628129i
$96$	−1.57028	−	1.81219i	−0.160266	−	0.184956i
$97$	−0.815998	+	0.524410i	−0.0828520	+	0.0532458i	−0.581411	−	0.813610i	$-0.697499\pi$
$97$	−0.815998	+	0.524410i	−0.0828520	+	0.0532458i	0.498559	+	0.866856i	$0.333863\pi$
$98$	0.654861	−	0.755750i	0.0661509	−	0.0763422i
$99$	0.0948656	−	0.659805i	0.00953436	−	0.0663129i
$100$	0.673243	−	0.197682i	0.0673243	−	0.0197682i
$101$	−1.00326	−	0.644754i	−0.0998277	−	0.0641554i	0.489774	−	0.871849i	$-0.337079\pi$
$101$	−1.00326	−	0.644754i	−0.0998277	−	0.0641554i	−0.589602	+	0.807694i	$0.700715\pi$
$102$	0.768423	+	5.34450i	0.0760852	+	0.529184i
$103$	2.93116	+	6.41834i	0.288816	+	0.632418i	0.997310	−	0.0732983i	$-0.0233525\pi$
$103$	2.93116	+	6.41834i	0.288816	+	0.632418i	−0.708494	+	0.705716i	$0.750625\pi$
$104$	0.642315	+	1.40647i	0.0629842	+	0.137916i
$105$	−0.707501	−	4.92078i	−0.0690451	−	0.480219i
$106$	−7.32492	−	4.70744i	−0.711459	−	0.457227i
$107$	8.49477	−	2.49429i	0.821221	−	0.241132i	0.155979	−	0.987760i	$-0.450147\pi$
$107$	8.49477	−	2.49429i	0.821221	−	0.241132i	0.665242	+	0.746628i	$0.268329\pi$
$108$	−0.0853762	+	0.593804i	−0.00821533	+	0.0571389i
$109$	5.53434	−	6.38697i	0.530094	−	0.611761i	−0.426035	−	0.904706i	$-0.640090\pi$
$109$	5.53434	−	6.38697i	0.530094	−	0.611761i	0.956129	+	0.292946i	$0.0946356\pi$
$110$	0.422797	−	0.271715i	0.0403121	−	0.0259070i
$111$	0.694543	+	0.801546i	0.0659231	+	0.0760793i
$112$	0.959493	+	0.281733i	0.0906636	+	0.0266212i
$113$	−4.49706	+	9.84719i	−0.423048	+	0.926346i	0.571356	+	0.820702i	$0.306418\pi$
$113$	−4.49706	+	9.84719i	−0.423048	+	0.926346i	−0.994404	+	0.105643i	$0.966310\pi$
$114$	2.51334			0.235396
$115$	−3.16489	+	9.42577i	−0.295127	+	0.878958i
$116$	4.35131			0.404009
$117$	−1.76625	+	3.86754i	−0.163290	+	0.357554i
$118$	1.00926	+	0.296347i	0.0929103	+	0.0272809i
$119$	−1.47459	−	1.70177i	−0.135176	−	0.156001i
$120$	4.18219	−	2.68773i	0.381780	−	0.245355i
$121$	7.16499	−	8.26883i	0.651362	−	0.751712i
$122$	−2.03583	+	14.1595i	−0.184315	+	1.28194i
$123$	−22.3022	+	6.54850i	−2.01092	+	0.590459i
$124$	−1.66140	−	1.06772i	−0.149198	−	0.0958837i
$125$	1.68229	+	11.7006i	0.150469	+	1.04653i
$126$	1.14231	+	2.50132i	0.101765	+	0.222835i
$127$	−3.57683	−	7.83218i	−0.317393	−	0.694993i	0.681944	−	0.731404i	$-0.261135\pi$
$127$	−3.57683	−	7.83218i	−0.317393	−	0.694993i	−0.999337	+	0.0364111i	$0.988407\pi$
$128$	0.142315	+	0.989821i	0.0125790	+	0.0874887i
$129$	−14.7297	−	9.46618i	−1.29687	−	0.833450i
$130$	−3.07580	+	0.903136i	−0.269765	+	0.0792102i
$131$	−1.78627	+	12.4238i	−0.156067	+	1.08547i	0.749725	+	0.661749i	$0.230186\pi$
$131$	−1.78627	+	12.4238i	−0.156067	+	1.08547i	−0.905792	+	0.423722i	$0.860723\pi$
$132$	−0.380655	+	0.439299i	−0.0331317	+	0.0382361i
$133$	−0.881761	+	0.566673i	−0.0764583	+	0.0491368i
$134$	1.04582	+	1.20694i	0.0903452	+	0.104264i
$135$	−1.19338	−	0.350408i	−0.102710	−	0.0301583i
$136$	0.935418	−	2.04828i	0.0802114	−	0.175638i
$137$	22.8150			1.94922			0.974610	−	0.223908i	$-0.0718816\pi$
$137$	22.8150			1.94922			0.974610	+	0.223908i	$0.0718816\pi$
$138$	0.440822	−	11.4914i	0.0375252	−	0.978210i
$139$	−8.54084			−0.724424			−0.362212	−	0.932096i	$-0.617978\pi$
$139$	−8.54084			−0.724424			−0.362212	+	0.932096i	$0.617978\pi$
$140$	−0.861256	+	1.88589i	−0.0727894	+	0.159387i
$141$	12.8369	+	3.76925i	1.08106	+	0.317428i
$142$	1.32792	+	1.53250i	0.111437	+	0.128605i
$143$	0.315317	−	0.202642i	0.0263682	−	0.0169458i
$144$	−1.80075	+	2.07817i	−0.150062	+	0.173181i
$145$	−1.28387	+	8.92950i	−0.106619	+	0.741554i
$146$	10.9849	−	3.22545i	0.909116	−	0.266941i
$147$	−2.01722	−	1.29639i	−0.166378	−	0.106924i
$148$	−0.0629468	−	0.437804i	−0.00517419	−	0.0359873i
$149$	1.72417	+	3.77541i	0.141250	+	0.309294i	0.967015	−	0.254721i	$-0.0819835\pi$
$149$	1.72417	+	3.77541i	0.141250	+	0.309294i	−0.825765	+	0.564014i	$0.809256\pi$
$150$	−0.698939	−	1.53046i	−0.0570681	−	0.124962i
$151$	0.173415	+	1.20613i	0.0141123	+	0.0981531i	0.995660	−	0.0930632i	$-0.0296659\pi$
$151$	0.173415	+	1.20613i	0.0141123	+	0.0981531i	−0.981548	+	0.191216i	$0.938757\pi$
$152$	−0.881761	−	0.566673i	−0.0715202	−	0.0459633i
$153$	5.94113	−	1.74447i	0.480312	−	0.141032i
$154$	0.0344989	−	0.239945i	0.00278000	−	0.0193353i
$155$	2.68130	−	3.09439i	0.215367	−	0.248547i
$156$	3.11903	−	2.00448i	0.249722	−	0.160487i
$157$	11.1958	+	12.9206i	0.893518	+	1.03118i	0.999323	+	0.0367884i	$0.0117127\pi$
$157$	11.1958	+	12.9206i	0.893518	+	1.03118i	−0.105805	+	0.994387i	$0.533742\pi$
$158$	12.0620	+	3.54171i	0.959598	+	0.281763i
$159$	−8.67331	+	18.9919i	−0.687839	+	1.50616i
$160$	−2.07324			−0.163904
$161$	2.43626	+	4.13094i	0.192004	+	0.325563i
$162$	9.68796			0.761158
$163$	7.18627	−	15.7357i	0.562872	−	1.23252i	−0.387635	−	0.921813i	$-0.626708\pi$
$163$	7.18627	−	15.7357i	0.562872	−	1.23252i	0.950507	−	0.310704i	$-0.100565\pi$
$164$	9.30079	+	2.73096i	0.726270	+	0.213252i
$165$	−0.789189	−	0.910773i	−0.0614383	−	0.0709036i
$166$	10.9763	−	7.05402i	0.851924	−	0.547498i
$167$	−8.89236	+	10.2623i	−0.688112	+	0.794123i	−0.987095	−	0.160135i	$-0.948807\pi$
$167$	−8.89236	+	10.2623i	−0.688112	+	0.794123i	0.298983	+	0.954258i	$0.403352\pi$
$168$	0.341254	−	2.37347i	0.0263283	−	0.183117i
$169$	10.1795	−	2.98898i	0.783040	−	0.229921i
$170$	3.92736	+	2.52396i	0.301215	+	0.193579i
$171$	−0.410183	−	2.85288i	−0.0313675	−	0.218166i
$172$	3.03334	+	6.64209i	0.231290	+	0.506454i
$173$	7.58560	+	16.6102i	0.576723	+	1.26285i	0.943140	+	0.332396i	$0.107857\pi$
$173$	7.58560	+	16.6102i	0.576723	+	1.26285i	−0.366417	+	0.930451i	$0.619416\pi$
$174$	−1.48490	−	10.3277i	−0.112570	−	0.782941i
$175$	0.590278	+	0.379349i	0.0446208	+	0.0286761i
$176$	0.232593	−	0.0682955i	0.0175324	−	0.00514797i
$177$	0.358955	−	2.49659i	0.0269807	−	0.187655i
$178$	−1.12453	+	1.29778i	−0.0842872	+	0.0972727i
$179$	−18.9458	+	12.1757i	−1.41608	+	0.910058i	−0.416077	+	0.909329i	$0.636595\pi$
$179$	−18.9458	+	12.1757i	−1.41608	+	0.910058i	−1.00000		0.000728387i	$0.999768\pi$
$180$	−3.73338	−	4.30856i	−0.278270	−	0.321141i
$181$	11.3277	+	3.32613i	0.841985	+	0.247229i	0.674158	−	0.738587i	$-0.264507\pi$
$181$	11.3277	+	3.32613i	0.841985	+	0.247229i	0.167827	+	0.985816i	$0.446325\pi$
$182$	−0.642315	+	1.40647i	−0.0476115	+	0.104255i
$183$	34.3019			2.53567
$184$	−2.74557	+	3.93215i	−0.202406	+	0.289882i
$185$	0.917009			0.0674198
$186$	−1.96723	+	4.30764i	−0.144245	+	0.315852i
$187$	−0.523745	−	0.153786i	−0.0383001	−	0.0112459i
$188$	−3.65375	−	4.21666i	−0.266477	−	0.307531i
$189$	−0.504677	+	0.324336i	−0.0367098	+	0.0235920i
$190$	1.42306	−	1.64230i	0.103240	−	0.119145i
$191$	2.98464	−	20.7586i	0.215961	−	1.50204i	−0.536780	−	0.843722i	$-0.680359\pi$
$191$	2.98464	−	20.7586i	0.215961	−	1.50204i	0.752741	−	0.658317i	$-0.228731\pi$
$192$	2.30075	−	0.675560i	0.166042	−	0.0487544i
$193$	7.55600	+	4.85595i	0.543893	+	0.349539i	0.783560	−	0.621316i	$-0.213402\pi$
$193$	7.55600	+	4.85595i	0.543893	+	0.349539i	−0.239667	+	0.970855i	$0.577038\pi$
$194$	−0.138042	−	0.960105i	−0.00991086	−	0.0689315i
$195$	3.19319	+	6.99212i	0.228669	+	0.500716i
$196$	0.415415	+	0.909632i	0.0296725	+	0.0649737i
$197$	2.37706	+	16.5328i	0.169359	+	1.17792i	0.880214	+	0.474577i	$0.157399\pi$
$197$	2.37706	+	16.5328i	0.169359	+	1.17792i	−0.710855	+	0.703338i	$0.751692\pi$
$198$	0.560771	+	0.360386i	0.0398523	+	0.0256115i
$199$	−23.0414	+	6.76555i	−1.63336	+	0.479597i	−0.964564	−	0.263850i	$-0.915008\pi$
$199$	−23.0414	+	6.76555i	−1.63336	+	0.479597i	−0.668795	+	0.743447i	$0.733190\pi$
$200$	−0.0998574	+	0.694523i	−0.00706098	+	0.0491102i
$201$	2.50775	−	2.89410i	0.176883	−	0.204134i
$202$	1.00326	−	0.644754i	0.0705889	−	0.0453647i
$203$	2.84950	+	3.28850i	0.199996	+	0.230807i
$204$	−5.18074	−	1.52120i	−0.362725	−	0.106506i
$205$	−8.34854	+	18.2807i	−0.583087	+	1.27678i
$206$	−7.05598			−0.491613
$207$	−13.1158	+	1.37504i	−0.911609	+	0.0955721i
$208$	−1.54620			−0.107210
$209$	−0.105551	+	0.231124i	−0.00730109	+	0.0159872i
$210$	4.77001	+	1.40060i	0.329162	+	0.0966506i
$211$	−12.6282	−	14.5737i	−0.869360	−	1.00329i	−0.999930	−	0.0118558i	$-0.996226\pi$
$211$	−12.6282	−	14.5737i	−0.869360	−	1.00329i	0.130570	−	0.991439i	$-0.458319\pi$
$212$	7.32492	−	4.70744i	0.503078	−	0.323308i
$213$	3.18420	−	3.67476i	0.218177	−	0.251790i
$214$	−1.25997	+	8.76328i	−0.0861298	+	0.599046i
$215$	−14.5255	+	4.26507i	−0.990630	+	0.290875i
$216$	−0.504677	−	0.324336i	−0.0343389	−	0.0220683i
$217$	−0.281059	−	1.95481i	−0.0190795	−	0.132701i
$218$	3.51074	+	7.68745i	0.237778	+	0.520660i
$219$	−11.4042	−	24.9716i	−0.770621	−	1.68743i
$220$	0.0715246	+	0.497465i	0.00482219	+	0.0335390i
$221$	2.92898	+	1.88234i	0.197024	+	0.126620i
$222$	−1.01764	+	0.298805i	−0.0682992	+	0.0200545i
$223$	−2.40202	+	16.7064i	−0.160851	+	1.11874i	0.736184	+	0.676782i	$0.236626\pi$
$223$	−2.40202	+	16.7064i	−0.160851	+	1.11874i	−0.897034	+	0.441961i	$0.854283\pi$
$224$	−0.654861	+	0.755750i	−0.0437547	+	0.0504956i
$225$	−1.62316	+	1.04314i	−0.108210	+	0.0695426i
$226$	−7.08917	−	8.18134i	−0.471565	−	0.544215i
$227$	9.35713	+	2.74750i	0.621054	+	0.182358i	0.577097	−	0.816675i	$-0.304185\pi$
$227$	9.35713	+	2.74750i	0.621054	+	0.182358i	0.0439570	+	0.999033i	$0.486004\pi$
$228$	−1.04408	+	2.28621i	−0.0691458	+	0.151408i
$229$	2.83339			0.187235			0.0936177	−	0.995608i	$-0.470157\pi$
$229$	2.83339			0.187235			0.0936177	+	0.995608i	$0.470157\pi$
$230$	−7.25924	−	6.79449i	−0.478660	−	0.448015i
$231$	−0.581276			−0.0382451
$232$	−1.80760	+	3.95809i	−0.118675	+	0.259861i
$233$	−13.4849	−	3.95954i	−0.883428	−	0.259398i	−0.191611	−	0.981471i	$-0.561371\pi$
$233$	−13.4849	−	3.95954i	−0.883428	−	0.259398i	−0.691817	+	0.722073i	$0.743189\pi$
$234$	−2.78431	−	3.21327i	−0.182016	−	0.210058i
$235$	9.73122	−	6.25388i	0.634795	−	0.407958i
$236$	−0.688830	+	0.794952i	−0.0448390	+	0.0517470i
$237$	4.28996	−	29.8373i	0.278663	−	1.93814i
$238$	2.16055	−	0.634396i	0.140048	−	0.0411218i
$239$	2.77164	+	1.78122i	0.179282	+	0.115218i	0.627204	−	0.778855i	$-0.284199\pi$
$239$	2.77164	+	1.78122i	0.179282	+	0.115218i	−0.447922	+	0.894073i	$0.647836\pi$
$240$	0.707501	+	4.92078i	0.0456690	+	0.317635i
$241$	−1.58884	−	3.47909i	−0.102346	−	0.224108i	0.851531	−	0.524305i	$-0.175675\pi$
$241$	−1.58884	−	3.47909i	−0.102346	−	0.224108i	−0.953877	+	0.300197i	$0.902947\pi$
$242$	4.54515	+	9.95250i	0.292174	+	0.639771i
$243$	−3.04992	−	21.2127i	−0.195653	−	1.36079i
$244$	−12.0342	−	7.73393i	−0.770413	−	0.495114i
$245$	−1.98926	+	0.584100i	−0.127089	+	0.0373168i
$246$	3.30792	−	23.0071i	0.210905	−	1.46688i
$247$	1.06130	−	1.22481i	0.0675290	−	0.0779326i
$248$	1.66140	−	1.06772i	0.105499	−	0.0678000i
$249$	−20.4882	−	23.6447i	−1.29839	−	1.49842i
$250$	−11.3421	−	3.33034i	−0.717338	−	0.210629i
$251$	−1.36526	+	2.98951i	−0.0861745	+	0.188696i	−0.947813	−	0.318826i	$-0.896711\pi$
$251$	−1.36526	+	2.98951i	−0.0861745	+	0.188696i	0.861639	+	0.507522i	$0.169439\pi$
$252$	−2.74982			−0.173222
$253$	1.03822	+	0.523131i	0.0652724	+	0.0328890i
$254$	8.61027			0.540256
$255$	4.65032	−	10.1828i	0.291214	−	0.637670i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	−18.5114	−	21.3632i	−1.15471	−	1.33260i	−0.934005	−	0.357261i	$-0.883711\pi$
$257$	−18.5114	−	21.3632i	−1.15471	−	1.33260i	−0.220702	−	0.975341i	$-0.570835\pi$
$258$	14.7297	−	9.46618i	0.917029	−	0.589338i
$259$	0.289649	−	0.334273i	0.0179979	−	0.0207707i
$260$	0.456211	−	3.17302i	0.0282930	−	0.196782i
$261$	−11.4806	+	3.37101i	−0.710633	+	0.208661i
$262$	−10.5590	−	6.78587i	−0.652339	−	0.419233i
$263$	−0.0136783	−	0.0951347i	−0.000843440	−	0.00586626i	0.989395	−	0.145247i	$-0.0463978\pi$
$263$	−0.0136783	−	0.0951347i	−0.000843440	−	0.00586626i	−0.990239	+	0.139381i	$0.955489\pi$
$264$	−0.241471	−	0.528747i	−0.0148615	−	0.0325421i
$265$	7.49908	+	16.4207i	0.460665	+	1.00872i
$266$	−0.149167	−	1.03748i	−0.00914604	−	0.0636121i
$267$	3.46399	+	2.22617i	0.211993	+	0.136240i
$268$	−1.53232	+	0.449931i	−0.0936015	+	0.0274839i
$269$	2.62166	−	18.2341i	0.159846	−	1.11175i	−0.739070	−	0.673629i	$-0.764735\pi$
$269$	2.62166	−	18.2341i	0.159846	−	1.11175i	0.898916	−	0.438122i	$-0.144356\pi$
$270$	0.814490	−	0.939971i	0.0495683	−	0.0572048i
$271$	−0.769104	+	0.494273i	−0.0467197	+	0.0300249i	−0.563792	−	0.825917i	$-0.690658\pi$
$271$	−0.769104	+	0.494273i	−0.0467197	+	0.0300249i	0.517072	+	0.855942i	$0.327022\pi$
$272$	1.47459	+	1.70177i	0.0894104	+	0.103185i
$273$	3.55742	+	1.04455i	0.215305	+	0.0632191i
$274$	−9.47771	+	20.7533i	−0.572569	+	1.25375i
$275$	0.170092			0.0102570
$276$	10.2698	+	5.17467i	0.618169	+	0.311479i
$277$	−0.308692			−0.0185475			−0.00927377	−	0.999957i	$-0.502952\pi$
$277$	−0.308692			−0.0185475			−0.00927377	+	0.999957i	$0.502952\pi$
$278$	3.54799	−	7.76902i	0.212794	−	0.465955i
$279$	5.21066	+	1.52999i	0.311954	+	0.0915979i
$280$	−1.35769	−	1.56685i	−0.0811372	−	0.0936373i
$281$	−3.91687	+	2.51722i	−0.233661	+	0.150165i	−0.652232	−	0.758019i	$-0.726167\pi$
$281$	−3.91687	+	2.51722i	−0.233661	+	0.150165i	0.418571	+	0.908184i	$0.362531\pi$
$282$	−8.76126	+	10.1110i	−0.521725	+	0.602103i
$283$	0.751923	−	5.22974i	0.0446972	−	0.310876i	−0.955192	−	0.295987i	$-0.904351\pi$
$283$	0.751923	−	5.22974i	0.0446972	−	0.310876i	0.999889	−	0.0148888i	$-0.00473943\pi$
$284$	−1.94565	+	0.571296i	−0.115453	+	0.0339002i
$285$	−4.38357	−	2.81715i	−0.259660	−	0.166873i
$286$	0.0533422	+	0.371003i	0.00315419	+	0.0219379i
$287$	4.02680	+	8.81747i	0.237695	+	0.520479i
$288$	−1.14231	−	2.50132i	−0.0673115	−	0.147392i
$289$	1.69775	+	11.8081i	0.0998677	+	0.694595i
$290$	−7.58922	−	4.87729i	−0.445654	−	0.286405i
$291$	−2.23167	+	0.655279i	−0.130823	+	0.0384131i
$292$	−1.62931	+	11.3321i	−0.0953482	+	0.663162i
$293$	4.34405	−	5.01330i	0.253782	−	0.292880i	−0.614535	−	0.788889i	$-0.710656\pi$
$293$	4.34405	−	5.01330i	0.253782	−	0.292880i	0.868317	+	0.496009i	$0.165202\pi$
$294$	2.01722	−	1.29639i	0.117647	−	0.0756070i
$295$	−1.42811	−	1.64813i	−0.0831479	−	0.0959578i
$296$	0.424390	+	0.124612i	0.0246672	+	0.00724293i
$297$	−0.0604121	+	0.132284i	−0.00350546	+	0.00767590i
$298$	−4.15048			−0.240431
$299$	−5.41386	−	5.06725i	−0.313092	−	0.293047i
$300$	1.68251			0.0971396
$301$	−3.03334	+	6.64209i	−0.174839	+	0.382844i
$302$	−1.16917	−	0.343299i	−0.0672782	−	0.0197547i
$303$	−1.87267	−	2.16117i	−0.107582	−	0.124156i
$304$	0.881761	−	0.566673i	0.0505724	−	0.0325009i
$305$	19.4218	−	22.4140i	1.11209	−	1.28342i
$306$	−0.881205	+	6.12892i	−0.0503752	+	0.350367i
$307$	21.8969	−	6.42952i	1.24972	−	0.366952i	0.411064	−	0.911607i	$-0.365157\pi$
$307$	21.8969	−	6.42952i	1.24972	−	0.366952i	0.838660	+	0.544655i	$0.183339\pi$
$308$	0.203930	+	0.131058i	0.0116200	+	0.00746773i
$309$	2.40788	+	16.7472i	0.136979	+	0.952712i
$310$	1.70090	+	3.72446i	0.0966047	+	0.211535i
$311$	1.61552	+	3.53750i	0.0916078	+	0.200593i	0.949890	−	0.312586i	$-0.101195\pi$
$311$	1.61552	+	3.53750i	0.0916078	+	0.200593i	−0.858282	+	0.513179i	$0.828468\pi$
$312$	0.527646	+	3.66986i	0.0298721	+	0.207765i
$313$	23.0745	+	14.8291i	1.30425	+	0.838190i	0.993668	−	0.112357i	$-0.0358402\pi$
$313$	23.0745	+	14.8291i	1.30425	+	0.838190i	0.310581	+	0.950547i	$0.399477\pi$
$314$	−16.4039	+	4.81661i	−0.925724	+	0.271817i
$315$	0.811342	−	5.64301i	0.0457139	−	0.317947i
$316$	−8.23238	+	9.50067i	−0.463107	+	0.534454i
$317$	−11.5938	+	7.45091i	−0.651175	+	0.418485i	−0.824096	−	0.566451i	$-0.808316\pi$
$317$	−11.5938	+	7.45091i	−0.651175	+	0.418485i	0.172920	+	0.984936i	$0.444680\pi$
$318$	−13.6726	−	15.7790i	−0.766723	−	0.884845i
$319$	1.01208	+	0.297175i	0.0566659	+	0.0166386i
$320$	0.861256	−	1.88589i	0.0481457	−	0.105424i
$321$	21.2294			1.18491
$322$	−4.76969	+	0.500049i	−0.265804	+	0.0278667i
$323$	−2.36019			−0.131325
$324$	−4.02452	+	8.81248i	−0.223585	+	0.489582i
$325$	−1.04097	−	0.305656i	−0.0577425	−	0.0169547i
$326$	11.3284	+	13.0737i	0.627424	+	0.724086i
$327$	17.0479	−	10.9560i	0.942751	−	0.605869i
$328$	−6.34786	+	7.32582i	−0.350502	+	0.404501i
$329$	0.794037	−	5.52265i	0.0437767	−	0.304473i
$330$	1.15631	−	0.339523i	0.0636527	−	0.0186901i
$331$	10.4673	+	6.72691i	0.575333	+	0.369744i	0.795717	−	0.605669i	$-0.207094\pi$
$331$	10.4673	+	6.72691i	0.575333	+	0.369744i	−0.220383	+	0.975413i	$0.570731\pi$
$332$	1.85686	+	12.9147i	0.101908	+	0.708787i
$333$	0.505253	+	1.10635i	0.0276877	+	0.0606276i
$334$	−5.64093	−	12.3519i	−0.308658	−	0.675866i
$335$	−0.471204	−	3.27730i	−0.0257446	−	0.179058i
$336$	2.01722	+	1.29639i	0.110049	+	0.0707239i
$337$	−10.8763	+	3.19357i	−0.592470	+	0.173965i	−0.564204	−	0.825636i	$-0.690817\pi$
$337$	−10.8763	+	3.19357i	−0.592470	+	0.173965i	−0.0282660	+	0.999600i	$0.508999\pi$
$338$	−1.50986	+	10.5013i	−0.0821253	+	0.571194i
$339$	−16.9990	+	19.6179i	−0.923257	+	1.06550i
$340$	−3.92736	+	2.52396i	−0.212991	+	0.136881i
$341$	−0.313510	−	0.361809i	−0.0169775	−	0.0195931i
$342$	2.76547	+	0.812016i	0.149540	+	0.0439088i
$343$	−0.415415	+	0.909632i	−0.0224303	+	0.0491155i
$344$	−7.30195			−0.393695
$345$	−13.6493	+	19.5482i	−0.734853	+	1.05244i
$346$	−18.2603			−0.981680
$347$	11.7621	−	25.7554i	0.631422	−	1.38262i	−0.275490	−	0.961304i	$-0.588840\pi$
$347$	11.7621	−	25.7554i	0.631422	−	1.38262i	0.906913	−	0.421319i	$-0.138433\pi$
$348$	10.0113	+	2.93957i	0.536660	+	0.157578i
$349$	5.60439	+	6.46781i	0.299996	+	0.346214i	0.885655	−	0.464343i	$-0.153710\pi$
$349$	5.60439	+	6.46781i	0.299996	+	0.346214i	−0.585659	+	0.810558i	$0.699164\pi$
$350$	−0.590278	+	0.379349i	−0.0315517	+	0.0202770i
$351$	0.607437	−	0.701020i	0.0324226	−	0.0374177i
$352$	−0.0344989	+	0.239945i	−0.00183880	+	0.0127891i
$353$	23.2345	−	6.82228i	1.23665	−	0.363113i	0.402894	−	0.915247i	$-0.368004\pi$
$353$	23.2345	−	6.82228i	1.23665	−	0.363113i	0.833756	+	0.552134i	$0.186186\pi$
$354$	2.12186	+	1.36364i	0.112776	+	0.0724765i
$355$	−0.598307	−	4.16132i	−0.0317548	−	0.220860i
$356$	−0.713354	−	1.56203i	−0.0378077	−	0.0827873i
$357$	−2.24302	−	4.91152i	−0.118713	−	0.259945i
$358$	−3.20506	−	22.2917i	−0.169393	−	1.17815i
$359$	12.1471	+	7.80645i	0.641098	+	0.412009i	0.820404	−	0.571785i	$-0.193749\pi$
$359$	12.1471	+	7.80645i	0.641098	+	0.412009i	−0.179305	+	0.983793i	$0.557385\pi$
$360$	5.47010	−	1.60617i	0.288300	−	0.0846525i
$361$	2.54763	−	17.7192i	0.134086	−	0.932588i
$362$	−7.73127	+	8.92236i	−0.406346	+	0.468949i
$363$	22.0709	−	14.1841i	1.15842	−	0.744473i
$364$	−1.01255	−	1.16854i	−0.0530718	−	0.0612482i
$365$	−22.7743	−	6.68715i	−1.19206	−	0.350021i
$366$	−14.2495	+	31.2021i	−0.744835	+	1.63096i
$367$	16.5536			0.864092			0.432046	−	0.901852i	$-0.357792\pi$
$367$	16.5536			0.864092			0.432046	+	0.901852i	$0.357792\pi$
$368$	−2.43626	−	4.13094i	−0.126999	−	0.215340i
$369$	−26.6552			−1.38761
$370$	−0.380939	+	0.834140i	−0.0198041	+	0.0433649i
$371$	8.35445	+	2.45309i	0.433741	+	0.127358i
$372$	−3.10115	−	3.57892i	−0.160787	−	0.185558i
$373$	−16.3815	+	10.5277i	−0.848200	+	0.545105i	−0.891013	−	0.453978i	$-0.850004\pi$
$373$	−16.3815	+	10.5277i	−0.848200	+	0.545105i	0.0428128	+	0.999083i	$0.486368\pi$
$374$	0.357460	−	0.412531i	0.0184838	−	0.0213315i
$375$	−4.03394	+	28.0566i	−0.208312	+	1.44884i
$376$	5.35343	−	1.57191i	0.276082	−	0.0810650i
$377$	−5.65995	−	3.63743i	−0.291502	−	0.187337i
$378$	−0.0853762	−	0.593804i	−0.00439128	−	0.0305420i
$379$	−3.53003	−	7.72970i	−0.181326	−	0.397048i	0.797041	−	0.603925i	$-0.206397\pi$
$379$	−3.53003	−	7.72970i	−0.181326	−	0.397048i	−0.978367	+	0.206877i	$0.933670\pi$
$380$	0.902726	+	1.97669i	0.0463089	+	0.101402i
$381$	−2.93828	−	20.4362i	−0.150533	−	1.04698i
$382$	17.6428	+	11.3384i	0.902685	+	0.580121i
$383$	−6.52063	+	1.91463i	−0.333189	+	0.0978331i	−0.444048	−	0.896003i	$-0.646458\pi$
$383$	−6.52063	+	1.91463i	−0.333189	+	0.0978331i	0.110859	+	0.993836i	$0.464640\pi$
$384$	−0.341254	+	2.37347i	−0.0174145	+	0.121121i
$385$	−0.329120	+	0.379825i	−0.0167735	+	0.0193577i
$386$	−7.55600	+	4.85595i	−0.384590	+	0.247161i
$387$	−13.1490	−	15.1747i	−0.668399	−	0.771374i
$388$	0.930687	+	0.273274i	0.0472485	+	0.0138734i
$389$	14.5530	−	31.8665i	0.737865	−	1.61570i	−0.0491711	−	0.998790i	$-0.515658\pi$
$389$	14.5530	−	31.8665i	0.737865	−	1.61570i	0.787036	−	0.616908i	$-0.211615\pi$
$390$	−7.68675			−0.389234
$391$	−0.413961	+	10.7912i	−0.0209349	+	0.545732i
$392$	−1.00000			−0.0505076
$393$	−12.5028	+	27.3772i	−0.630681	+	1.38100i
$394$	−16.0263	−	4.70573i	−0.807391	−	0.237071i
$395$	−17.0677	−	19.6972i	−0.858770	−	0.991073i
$396$	−0.560771	+	0.360386i	−0.0281798	+	0.0181101i
$397$	23.9035	−	27.5861i	1.19968	−	1.38451i	0.296622	−	0.954995i	$-0.404140\pi$
$397$	23.9035	−	27.5861i	1.19968	−	1.38451i	0.903061	−	0.429513i	$-0.141315\pi$
$398$	3.41756	−	23.7697i	0.171307	−	1.19147i
$399$	−2.41153	+	0.708089i	−0.120727	+	0.0354488i
$400$	−0.590278	−	0.379349i	−0.0295139	−	0.0189674i
$401$	4.88005	+	33.9415i	0.243698	+	1.69496i	0.633245	+	0.773952i	$0.281723\pi$
$401$	4.88005	+	33.9415i	0.243698	+	1.69496i	−0.389546	+	0.921007i	$0.627368\pi$
$402$	1.59081	+	3.48338i	0.0793423	+	0.173735i
$403$	1.26851	+	2.77766i	0.0631891	+	0.138365i
$404$	0.169721	+	1.18043i	0.00844393	+	0.0587288i
$405$	−16.8970	−	10.8590i	−0.839618	−	0.539590i
$406$	−4.17505	+	1.22591i	−0.207204	+	0.0608407i
$407$	0.0152591	−	0.106129i	0.000756365	−	0.00526063i
$408$	3.53589	−	4.08064i	0.175053	−	0.202022i
$409$	−18.3329	+	11.7818i	−0.906504	+	0.582574i	−0.908712	−	0.417423i	$-0.862933\pi$
$409$	−18.3329	+	11.7818i	−0.906504	+	0.582574i	0.00220870	+	0.999998i	$0.499297\pi$
$410$	−13.1606	−	15.1882i	−0.649958	−	0.750091i
$411$	52.4916	+	15.4129i	2.58922	+	0.760264i
$412$	2.93116	−	6.41834i	0.144408	−	0.316209i
$413$	−1.05187			−0.0517593
$414$	4.19771	−	12.5017i	0.206306	−	0.614427i
$415$	−27.0507			−1.32787
$416$	0.642315	−	1.40647i	0.0314921	−	0.0689580i
$417$	−19.6503	−	5.76985i	−0.962279	−	0.282551i
$418$	−0.166390	−	0.192025i	−0.00813841	−	0.00939223i
$419$	−9.75675	+	6.27028i	−0.476649	+	0.306323i	−0.756816	−	0.653628i	$-0.773246\pi$
$419$	−9.75675	+	6.27028i	−0.476649	+	0.306323i	0.280168	+	0.959951i	$0.409610\pi$
$420$	−3.25556	+	3.75712i	−0.158855	+	0.183329i
$421$	1.30473	−	9.07457i	0.0635885	−	0.442268i	−0.933010	−	0.359852i	$-0.882827\pi$
$421$	1.30473	−	9.07457i	0.0635885	−	0.442268i	0.996598	−	0.0824160i	$-0.0262636\pi$
$422$	18.5026	−	5.43287i	0.900695	−	0.264468i
$423$	12.9069	+	8.29474i	0.627554	+	0.403304i
$424$	1.23916	+	8.61852i	0.0601788	+	0.418552i
$425$	0.656350	+	1.43721i	0.0318376	+	0.0697147i
$426$	2.01991	+	4.42300i	0.0978652	+	0.214295i
$427$	−2.03583	−	14.1595i	−0.0985207	−	0.685227i
$428$	−7.44795	−	4.78651i	−0.360010	−	0.231365i
$429$	0.862362	−	0.253212i	0.0416352	−	0.0122252i
$430$	2.15446	−	14.9846i	0.103897	−	0.722623i
$431$	13.8114	−	15.9392i	0.665272	−	0.767765i	−0.318356	−	0.947971i	$-0.603131\pi$
$431$	13.8114	−	15.9392i	0.665272	−	0.767765i	0.983629	+	0.180206i	$0.0576763\pi$
$432$	0.504677	−	0.324336i	0.0242813	−	0.0156046i
$433$	0.545611	+	0.629669i	0.0262204	+	0.0302599i	0.768708	−	0.639600i	$-0.220900\pi$
$433$	0.545611	+	0.629669i	0.0262204	+	0.0302599i	−0.742488	+	0.669859i	$0.766354\pi$
$434$	1.89491	+	0.556396i	0.0909586	+	0.0267079i
$435$	−8.98626	+	19.6772i	−0.430858	+	0.943448i
$436$	−8.45117			−0.404738
$437$	4.94451	+	0.905585i	0.236528	+	0.0433200i
$438$	27.4524			1.31173
$439$	−16.5698	+	36.2829i	−0.790836	+	1.73169i	−0.116592	+	0.993180i	$0.537197\pi$
$439$	−16.5698	+	36.2829i	−0.790836	+	1.73169i	−0.674244	+	0.738509i	$0.735530\pi$
$440$	−0.482222	−	0.141593i	−0.0229890	−	0.00675019i
$441$	−1.80075	−	2.07817i	−0.0857498	−	0.0989606i
$442$	−2.92898	+	1.88234i	−0.139317	+	0.0895338i
$443$	23.1099	−	26.6703i	1.09799	−	1.26714i	0.136993	−	0.990572i	$-0.456256\pi$
$443$	23.1099	−	26.6703i	1.09799	−	1.26714i	0.960993	−	0.276571i	$-0.0891982\pi$
$444$	0.150939	−	1.04980i	0.00716323	−	0.0498214i
$445$	3.41598	−	1.00302i	0.161933	−	0.0475478i
$446$	−14.1988	−	9.12504i	−0.672334	−	0.432083i
$447$	1.41637	+	9.85105i	0.0669919	+	0.465939i
$448$	−0.415415	−	0.909632i	−0.0196265	−	0.0429761i
$449$	0.208145	+	0.455773i	0.00982295	+	0.0215093i	0.914480	−	0.404631i	$-0.132600\pi$
$449$	0.208145	+	0.455773i	0.00982295	+	0.0215093i	−0.904657	+	0.426141i	$0.859873\pi$
$450$	−0.274589	−	1.90981i	−0.0129443	−	0.0900294i
$451$	1.97679	+	1.27040i	0.0930833	+	0.0598210i
$452$	10.3870	−	3.04989i	0.488561	−	0.143455i
$453$	−0.415827	+	2.89214i	−0.0195373	+	0.135885i
$454$	−6.38630	+	7.37019i	−0.299724	+	0.345900i
$455$	2.69676	−	1.73310i	0.126426	−	0.0812492i
$456$	−1.64589	−	1.89945i	−0.0770757	−	0.0889501i
$457$	−4.61530	−	1.35517i	−0.215894	−	0.0633923i	0.171997	−	0.985098i	$-0.444978\pi$
$457$	−4.61530	−	1.35517i	−0.215894	−	0.0633923i	−0.387891	+	0.921705i	$0.626796\pi$
$458$	−1.17703	+	2.57734i	−0.0549990	+	0.120431i
$459$	−1.35086			−0.0630527
$460$	9.19608	−	3.78071i	0.428770	−	0.176276i
$461$	−39.2880			−1.82983			−0.914913	−	0.403650i	$-0.867741\pi$
$461$	−39.2880			−1.82983			−0.914913	+	0.403650i	$0.867741\pi$
$462$	0.241471	−	0.528747i	0.0112342	−	0.0245995i
$463$	40.5831	+	11.9163i	1.88606	+	0.553796i	0.994997	+	0.0999095i	$0.0318553\pi$
$463$	40.5831	+	11.9163i	1.88606	+	0.553796i	0.891059	+	0.453887i	$0.149963\pi$
$464$	−2.84950	−	3.28850i	−0.132285	−	0.152665i
$465$	8.25945	−	5.30802i	0.383023	−	0.246154i
$466$	9.20357	−	10.6215i	0.426347	−	0.492031i
$467$	−0.511907	+	3.56039i	−0.0236882	+	0.164755i	−0.998232	−	0.0594435i	$-0.981067\pi$
$467$	−0.511907	+	3.56039i	−0.0236882	+	0.164755i	0.974543	+	0.224199i	$0.0719765\pi$
$468$	4.07954	−	1.19786i	0.188577	−	0.0553711i
$469$	−1.34349	−	0.863411i	−0.0620368	−	0.0398686i
$470$	1.64623	+	11.4498i	0.0759350	+	0.528139i
$471$	17.0300	+	37.2904i	0.784699	+	1.71825i
$472$	−0.436964	−	0.956817i	−0.0201129	−	0.0440411i
$473$	0.251909	+	1.75207i	0.0115828	+	0.0805601i
$474$	25.3589	+	16.2972i	1.16477	+	0.748554i
$475$	0.705660	−	0.207200i	0.0323779	−	0.00950701i
$476$	−0.320460	+	2.22885i	−0.0146882	+	0.102159i
$477$	−15.6794	+	18.0950i	−0.717909	+	0.828511i
$478$	−2.77164	+	1.78122i	−0.126772	+	0.0814713i
$479$	8.61027	+	9.93678i	0.393413	+	0.454023i	0.917556	−	0.397608i	$-0.130159\pi$
$479$	8.61027	+	9.93678i	0.393413	+	0.454023i	−0.524142	+	0.851631i	$0.675614\pi$
$480$	−4.77001	−	1.40060i	−0.217720	−	0.0639284i
$481$	−0.284100	+	0.622092i	−0.0129538	+	0.0283650i
$482$	3.82472			0.174211
$483$	2.81453	+	11.1501i	0.128065	+	0.507346i
$484$	−10.9412			−0.497329
$485$	−0.835400	+	1.82927i	−0.0379335	+	0.0830629i
$486$	20.5627	+	6.03776i	0.932743	+	0.273878i
$487$	15.8222	+	18.2598i	0.716973	+	0.827431i	0.990940	−	0.134308i	$-0.0428813\pi$
$487$	15.8222	+	18.2598i	0.716973	+	0.827431i	−0.273967	+	0.961739i	$0.588336\pi$
$488$	12.0342	−	7.73393i	0.544764	−	0.350099i
$489$	27.1642	−	31.3492i	1.22841	−	1.41766i
$490$	0.295053	−	2.05214i	0.0133291	−	0.0927062i
$491$	−25.1491	+	7.38445i	−1.13496	+	0.333256i	−0.794657	−	0.607058i	$-0.792349\pi$
$491$	−25.1491	+	7.38445i	−1.13496	+	0.333256i	−0.340308	+	0.940314i	$0.610531\pi$
$492$	19.5538	+	12.5665i	0.881555	+	0.566541i
$493$	1.39442	+	9.69840i	0.0628015	+	0.436794i
$494$	0.673243	+	1.47420i	0.0302906	+	0.0663272i
$495$	−0.574105	−	1.25711i	−0.0258041	−	0.0565031i
$496$	0.281059	+	1.95481i	0.0126199	+	0.0877734i
$497$	−1.70589	−	1.09631i	−0.0765196	−	0.0491761i
$498$	30.0190	−	8.81439i	1.34519	−	0.394982i
$499$	−0.199259	+	1.38588i	−0.00892006	+	0.0620404i	−0.993795	−	0.111225i	$-0.964523\pi$
$499$	−0.199259	+	1.38588i	−0.00892006	+	0.0620404i	0.984875	+	0.173265i	$0.0554318\pi$
$500$	7.74107	−	8.93367i	0.346191	−	0.399526i
$501$	−27.3919	+	17.6037i	−1.22378	+	0.786475i
$502$	−2.15220	−	2.48377i	−0.0960574	−	0.110856i
$503$	10.9962	+	3.22878i	0.490298	+	0.143964i	0.517530	−	0.855665i	$-0.326851\pi$
$503$	10.9962	+	3.22878i	0.490298	+	0.143964i	−0.0272330	+	0.999629i	$0.508670\pi$
$504$	1.14231	−	2.50132i	0.0508827	−	0.111418i
$505$	−2.47249			−0.110024
$506$	−0.907150	+	0.727082i	−0.0403277	+	0.0323227i
$507$	25.4397			1.12982
$508$	−3.57683	+	7.83218i	−0.158696	+	0.347497i
$509$	−20.6302	−	6.05758i	−0.914419	−	0.268498i	−0.209519	−	0.977805i	$-0.567190\pi$
$509$	−20.6302	−	6.05758i	−0.914419	−	0.268498i	−0.704900	+	0.709307i	$0.749008\pi$
$510$	7.33077	+	8.46016i	0.324612	+	0.374622i
$511$	−9.63121	+	6.18960i	−0.426060	+	0.273812i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$	−0.0894871	+	0.622397i	−0.00395095	+	0.0274795i
$514$	27.1226	−	7.96391i	1.19633	−	0.351273i
$515$	12.3065	+	7.90890i	0.542289	+	0.348508i
$516$	2.49182	+	17.3310i	0.109696	+	0.762953i
$517$	−0.561860	−	1.23030i	−0.0247106	−	0.0541086i
$518$	0.183741	+	0.402336i	0.00807311	+	0.0176776i
$519$	6.23139	+	43.3403i	0.273528	+	1.90243i
$520$	2.69676	+	1.73310i	0.118261	+	0.0760017i
$521$	−1.19547	+	0.351022i	−0.0523746	+	0.0153786i	−0.307815	−	0.951446i	$-0.599598\pi$
$521$	−1.19547	+	0.351022i	−0.0523746	+	0.0153786i	0.255440	+	0.966825i	$0.417780\pi$
$522$	1.70284	−	11.8435i	0.0745313	−	0.518376i
$523$	26.3225	−	30.3778i	1.15100	−	1.32833i	0.214886	−	0.976639i	$-0.431062\pi$
$523$	26.3225	−	30.3778i	1.15100	−	1.32833i	0.936117	−	0.351689i	$-0.114393\pi$
$524$	10.5590	−	6.78587i	0.461273	−	0.296442i
$525$	1.10181	+	1.27155i	0.0480868	+	0.0554952i
$526$	0.0922197	+	0.0270782i	0.00402097	+	0.00118066i
$527$	1.84736	−	4.04516i	0.0804724	−	0.176210i
$528$	0.581276			0.0252968
$529$	5.00771	−	22.4482i	0.217726	−	0.976010i
$530$	−18.0520			−0.784130
$531$	1.20157	−	2.63107i	0.0521437	−	0.114179i
$532$	1.00569	+	0.295298i	0.0436023	+	0.0128028i
$533$	−9.81506	−	11.3272i	−0.425137	−	0.490635i
$534$	−3.46399	+	2.22617i	−0.149902	+	0.0963359i
$535$	12.0201	−	13.8720i	0.519675	−	0.599737i
$536$	0.227279	−	1.58076i	0.00981695	−	0.0682784i
$537$	−51.8150	+	15.2143i	−2.23598	+	0.656543i
$538$	15.4972	+	9.95945i	0.668132	+	0.429383i
$539$	0.0344989	+	0.239945i	0.00148597	+	0.0103352i
$540$	0.516677	+	1.13136i	0.0222342	+	0.0486862i
$541$	−6.72502	−	14.7257i	−0.289131	−	0.633109i	0.708209	−	0.706003i	$-0.249504\pi$
$541$	−6.72502	−	14.7257i	−0.289131	−	0.633109i	−0.997340	+	0.0728946i	$0.976776\pi$
$542$	−0.130109	−	0.904930i	−0.00558867	−	0.0388701i
$543$	23.8153	+	15.3051i	1.02201	+	0.656807i
$544$	−2.16055	+	0.634396i	−0.0926330	+	0.0271995i
$545$	2.49354	−	17.3430i	0.106812	−	0.742892i
$546$	−2.42796	+	2.80202i	−0.103907	+	0.119915i
$547$	3.70481	−	2.38094i	0.158406	−	0.101801i	−0.459036	−	0.888418i	$-0.651805\pi$
$547$	3.70481	−	2.38094i	0.158406	−	0.101801i	0.617442	+	0.786616i	$0.288169\pi$
$548$	−14.9407	−	17.2425i	−0.638234	−	0.736561i
$549$	37.7430	+	11.0824i	1.61083	+	0.472983i
$550$	−0.0706590	+	0.154722i	−0.00301291	+	0.00659735i
$551$	4.56083			0.194298
$552$	−8.97327	+	7.19209i	−0.381928	+	0.306116i
$553$	−12.5712			−0.534581
$554$	0.128235	−	0.280797i	0.00544820	−	0.0119299i
$555$	2.10980	+	0.619494i	0.0895562	+	0.0262961i
$556$	5.59306	+	6.45473i	0.237198	+	0.273742i
$557$	26.1174	−	16.7846i	1.10663	−	0.711188i	0.146074	−	0.989274i	$-0.453336\pi$
$557$	26.1174	−	16.7846i	1.10663	−	0.711188i	0.960556	+	0.278085i	$0.0896998\pi$
$558$	−3.55631	+	4.10420i	−0.150551	+	0.173745i
$559$	1.60677	−	11.1754i	0.0679593	−	0.472667i
$560$	1.98926	−	0.584100i	0.0840616	−	0.0246827i
$561$	−1.10111	−	0.707643i	−0.0464891	−	0.0298767i
$562$	−0.662617	−	4.60860i	−0.0279508	−	0.194402i
$563$	−10.6710	−	23.3661i	−0.449727	−	0.984765i	−0.989710	−	0.143089i	$-0.954297\pi$
$563$	−10.6710	−	23.3661i	−0.449727	−	0.984765i	0.539983	−	0.841676i	$-0.318431\pi$
$564$	−5.55776	−	12.1698i	−0.234024	−	0.512441i
$565$	3.19409	+	22.2154i	0.134376	+	0.934608i
$566$	4.44478	+	2.85649i	0.186828	+	0.120067i
$567$	−9.29553	+	2.72941i	−0.390376	+	0.114625i
$568$	0.288585	−	2.00715i	0.0121088	−	0.0842183i
$569$	6.08497	−	7.02243i	0.255095	−	0.294396i	−0.613728	−	0.789517i	$-0.710331\pi$
$569$	6.08497	−	7.02243i	0.255095	−	0.294396i	0.868824	+	0.495122i	$0.164876\pi$
$570$	4.38357	−	2.81715i	0.183607	−	0.117997i
$571$	−29.2777	−	33.7883i	−1.22523	−	1.41400i	−0.879659	−	0.475604i	$-0.842229\pi$
$571$	−29.2777	−	33.7883i	−1.22523	−	1.41400i	−0.345575	−	0.938391i	$-0.612316\pi$
$572$	−0.359636	−	0.105599i	−0.0150371	−	0.00441530i
$573$	20.8906	−	45.7440i	0.872716	−	1.91098i
$574$	−9.69344			−0.404597
$575$	−0.823585	−	3.26273i	−0.0343459	−	0.136065i
$576$	2.74982			0.114576
$577$	−10.6264	+	23.2685i	−0.442381	+	0.968680i	0.548774	+	0.835971i	$0.315095\pi$
$577$	−10.6264	+	23.2685i	−0.442381	+	0.968680i	−0.991155	+	0.132709i	$0.957632\pi$
$578$	−11.4463	−	3.36094i	−0.476104	−	0.139797i
$579$	14.1040	+	16.2768i	0.586141	+	0.676442i
$580$	7.58922	−	4.87729i	0.315125	−	0.202519i
$581$	−8.54431	+	9.86066i	−0.354478	+	0.409089i
$582$	0.331009	−	2.30221i	0.0137207	−	0.0954299i
$583$	2.02522	−	0.594659i	0.0838762	−	0.0246283i
$584$	−9.63121	−	6.18960i	−0.398542	−	0.256128i
$585$	1.25450	+	8.72522i	0.0518671	+	0.360743i
$586$	2.75568	+	6.03409i	0.113836	+	0.249266i
$587$	−0.722064	−	1.58110i	−0.0298028	−	0.0652589i	0.894145	−	0.447777i	$-0.147784\pi$
$587$	−0.722064	−	1.58110i	−0.0298028	−	0.0652589i	−0.923948	+	0.382518i	$0.875057\pi$
$588$	0.341254	+	2.37347i	0.0140731	+	0.0978803i
$589$	−1.74140	−	1.11913i	−0.0717530	−	0.0461128i
$590$	2.09245	−	0.614399i	0.0861448	−	0.0252944i
$591$	−5.69990	+	39.6437i	−0.234463	+	1.63072i
$592$	−0.289649	+	0.334273i	−0.0119045	+	0.0137385i
$593$	−27.9875	+	17.9865i	−1.14931	+	0.738616i	−0.969501	−	0.245086i	$-0.921184\pi$
$593$	−27.9875	+	17.9865i	−1.14931	+	0.738616i	−0.179808	+	0.983702i	$0.557548\pi$
$594$	−0.0952337	−	0.109906i	−0.00390749	−	0.00450948i
$595$	−4.47935	−	1.31526i	−0.183636	−	0.0539203i
$596$	1.72417	−	3.77541i	0.0706249	−	0.154647i
$597$	−57.5829			−2.35671
$598$	6.85833	−	2.81961i	0.280458	−	0.115302i
$599$	1.03096			0.0421238			0.0210619	−	0.999778i	$-0.493295\pi$
$599$	1.03096			0.0421238			0.0210619	+	0.999778i	$0.493295\pi$
$600$	−0.698939	+	1.53046i	−0.0285341	+	0.0624809i
$601$	31.8204	+	9.34330i	1.29798	+	0.381121i	0.856499	−	0.516149i	$-0.172635\pi$
$601$	31.8204	+	9.34330i	1.29798	+	0.381121i	0.441481	+	0.897270i	$0.354453\pi$
$602$	−4.78176	−	5.51845i	−0.194890	−	0.224915i
$603$	3.69436	−	2.37422i	0.150446	−	0.0966857i
$604$	0.797967	−	0.920903i	0.0324688	−	0.0374710i
$605$	3.22825	−	22.4529i	0.131247	−	0.912842i
$606$	2.74381	−	0.805655i	0.111460	−	0.0327275i
$607$	−25.9407	−	16.6710i	−1.05290	−	0.676657i	−0.104755	−	0.994498i	$-0.533406\pi$
$607$	−25.9407	−	16.6710i	−1.05290	−	0.676657i	−0.948144	+	0.317841i	$0.897042\pi$
$608$	0.149167	+	1.03748i	0.00604954	+	0.0420755i
$609$	4.33440	+	9.49101i	0.175639	+	0.384595i
$610$	12.3204	+	26.9778i	0.498837	+	1.09230i
$611$	1.22774	+	8.53912i	0.0496690	+	0.345456i
$612$	−5.20899	−	3.34762i	−0.210561	−	0.135319i
$613$	−25.3505	+	7.44358i	−1.02390	+	0.300643i	−0.750227	−	0.661180i	$-0.770056\pi$
$613$	−25.3505	+	7.44358i	−1.02390	+	0.300643i	−0.273670	+	0.961824i	$0.588238\pi$
$614$	−3.24782	+	22.5891i	−0.131071	+	0.911621i
$615$	−31.5576	+	36.4194i	−1.27253	+	1.46857i
$616$	−0.203930	+	0.131058i	−0.00821659	+	0.00528048i
$617$	17.1749	+	19.8209i	0.691435	+	0.797958i	0.987569	−	0.157188i	$-0.0502430\pi$
$617$	17.1749	+	19.8209i	0.691435	+	0.797958i	−0.296134	+	0.955146i	$0.595698\pi$
$618$	−16.2340	−	4.76674i	−0.653028	−	0.191746i
$619$	−4.13882	+	9.06275i	−0.166353	+	0.364263i	−0.974388	−	0.224872i	$-0.927804\pi$
$619$	−4.13882	+	9.06275i	−0.166353	+	0.364263i	0.808035	+	0.589134i	$0.200531\pi$
$620$	−4.09446			−0.164438
$621$	2.83000	+	0.518313i	0.113564	+	0.0207992i
$622$	−3.88893			−0.155932
$623$	0.713354	−	1.56203i	0.0285799	−	0.0625813i
$624$	−3.55742	−	1.04455i	−0.142411	−	0.0418155i
$625$	13.7516	+	15.8702i	0.550066	+	0.634810i
$626$	−23.0745	+	14.8291i	−0.922243	+	0.592690i
$627$	−0.398983	+	0.460451i	−0.0159339	+	0.0183887i
$628$	2.43307	−	16.9224i	0.0970901	−	0.675276i
$629$	0.955627	−	0.280597i	0.0381033	−	0.0111882i
$630$	4.79602	+	3.08221i	0.191078	+	0.122798i
$631$	−6.14096	−	42.7113i	−0.244468	−	1.70031i	−0.629168	−	0.777270i	$-0.716604\pi$
$631$	−6.14096	−	42.7113i	−0.244468	−	1.70031i	0.384700	−	0.923042i	$-0.374305\pi$
$632$	−5.22226	−	11.4352i	−0.207730	−	0.454866i
$633$	−19.2088	−	42.0615i	−0.763483	−	1.67179i
$634$	−1.96133	−	13.6414i	−0.0778944	−	0.541767i
$635$	−15.0174	−	9.65107i	−0.595946	−	0.382991i
$636$	20.0329	−	5.88220i	0.794358	−	0.233244i
$637$	0.220047	−	1.53046i	0.00871859	−	0.0606391i
$638$	−0.690755	+	0.797174i	−0.0273472	+	0.0315604i
$639$	4.69088	−	3.01465i	0.185568	−	0.119258i
$640$	1.35769	+	1.56685i	0.0536672	+	0.0619353i
$641$	−31.1798	−	9.15521i	−1.23153	−	0.361609i	−0.399701	−	0.916646i	$-0.630886\pi$
$641$	−31.1798	−	9.15521i	−1.23153	−	0.361609i	−0.831826	+	0.555037i	$0.812704\pi$
$642$	−8.81900	+	19.3109i	−0.348058	+	0.762141i
$643$	17.8362			0.703389			0.351695	−	0.936115i	$-0.385606\pi$
$643$	17.8362			0.703389			0.351695	+	0.936115i	$0.385606\pi$
$644$	1.52654	−	4.54639i	0.0601541	−	0.179153i
$645$	−36.3008			−1.42934
$646$	0.980459	−	2.14691i	0.0385756	−	0.0844688i
$647$	32.4550	+	9.52966i	1.27594	+	0.374650i	0.848404	−	0.529349i	$-0.177564\pi$
$647$	32.4550	+	9.52966i	1.27594	+	0.374650i	0.427535	+	0.903999i	$0.359382\pi$
$648$	−6.34426	−	7.32167i	−0.249226	−	0.287622i
$649$	−0.214509	+	0.137856i	−0.00842021	+	0.00541134i
$650$	0.710468	−	0.819924i	0.0278669	−	0.0321601i
$651$	0.673944	−	4.68739i	0.0264140	−	0.183713i
$652$	−16.5983	+	4.87369i	−0.650038	+	0.190869i
$653$	13.2708	+	8.52859i	0.519325	+	0.333750i	0.773905	−	0.633302i	$-0.218301\pi$
$653$	13.2708	+	8.52859i	0.519325	+	0.333750i	−0.254580	+	0.967052i	$0.581937\pi$
$654$	2.88399	+	20.0586i	0.112773	+	0.784353i
$655$	10.8101	+	23.6708i	0.422385	+	0.924894i
$656$	−4.02680	−	8.81747i	−0.157220	−	0.344264i
$657$	−4.48031	−	31.1612i	−0.174793	−	1.21571i
$658$	4.69372	+	3.01647i	0.182980	+	0.117594i
$659$	−28.2985	+	8.30919i	−1.10235	+	0.323680i	−0.781787	−	0.623546i	$-0.785691\pi$
$659$	−28.2985	+	8.30919i	−1.10235	+	0.323680i	−0.320566	+	0.947226i	$0.603873\pi$
$660$	−0.171507	+	1.19286i	−0.00667591	+	0.0464320i
$661$	−18.9949	+	21.9212i	−0.738814	+	0.852637i	−0.993434	−	0.114404i	$-0.963504\pi$
$661$	−18.9949	+	21.9212i	−0.738814	+	0.852637i	0.254620	+	0.967041i	$0.418050\pi$
$662$	−10.4673	+	6.72691i	−0.406822	+	0.261449i
$663$	5.46720	+	6.30949i	0.212328	+	0.245040i
$664$	−12.5190	−	3.67591i	−0.485832	−	0.142653i
$665$	−0.902726	+	1.97669i	−0.0350062	+	0.0766529i
$666$	−1.21626			−0.0471292
$667$	0.799937	−	20.8528i	0.0309737	−	0.807424i
$668$	13.5790			0.525388
$669$	−16.8126	+	36.8145i	−0.650013	+	1.42333i
$670$	3.17688	+	0.932815i	0.122733	+	0.0360378i
$671$	−2.27089	−	2.62074i	−0.0876666	−	0.101173i
$672$	−2.01722	+	1.29639i	−0.0778161	+	0.0500093i
$673$	9.77691	−	11.2832i	0.376872	−	0.434934i	−0.535349	−	0.844631i	$-0.679820\pi$
$673$	9.77691	−	11.2832i	0.376872	−	0.434934i	0.912222	+	0.409697i	$0.134366\pi$
$674$	1.61320	−	11.2201i	0.0621383	−	0.432182i
$675$	0.403886	−	0.118591i	0.0155456	−	0.00456459i
$676$	−8.92508	−	5.73580i	−0.343272	−	0.220608i
$677$	−0.971617	−	6.75775i	−0.0373423	−	0.259721i	0.962595	−	0.270945i	$-0.0873363\pi$
$677$	−0.971617	−	6.75775i	−0.0373423	−	0.259721i	−0.999937	+	0.0112241i	$0.996427\pi$
$678$	−10.7834	−	23.6124i	−0.414134	−	0.906827i
$679$	0.402944	+	0.882323i	0.0154636	+	0.0338605i
$680$	−0.664391	−	4.62094i	−0.0254782	−	0.177205i
$681$	19.6723	+	12.6426i	0.753843	+	0.484466i
$682$	0.459350	−	0.134877i	0.0175894	−	0.00516472i
$683$	−4.78972	+	33.3132i	−0.183273	+	1.27469i	0.665684	+	0.746234i	$0.268140\pi$
$683$	−4.78972	+	33.3132i	−0.183273	+	1.27469i	−0.848958	+	0.528461i	$0.822769\pi$
$684$	−1.88745	+	2.17824i	−0.0721686	+	0.0832870i
$685$	39.7922	−	25.5729i	1.52038	−	0.977091i
$686$	−0.654861	−	0.755750i	−0.0250027	−	0.0288547i
$687$	6.51890	+	1.91412i	0.248712	+	0.0730283i
$688$	3.03334	−	6.64209i	0.115645	−	0.253227i
$689$	−13.4630			−0.512899
$690$	−12.1116	−	20.5365i	−0.461080	−	0.781810i
$691$	−24.3807			−0.927484			−0.463742	−	0.885970i	$-0.653494\pi$
$691$	−24.3807			−0.927484			−0.463742	+	0.885970i	$0.653494\pi$
$692$	7.58560	−	16.6102i	0.288361	−	0.631423i
$693$	−0.639588	−	0.187800i	−0.0242960	−	0.00713394i
$694$	18.5418	+	21.3984i	0.703837	+	0.812271i
$695$	−14.8963	+	9.57325i	−0.565048	+	0.363134i
$696$	−6.83275	+	7.88542i	−0.258995	+	0.298896i
$697$	−3.10636	+	21.6052i	−0.117662	+	0.818355i
$698$	−8.21148	+	2.41111i	−0.310809	+	0.0912618i
$699$	−28.3505	−	18.2198i	−1.07232	−	0.689135i
$700$	−0.0998574	−	0.694523i	−0.00377425	−	0.0262505i
$701$	−20.3017	−	44.4546i	−0.766786	−	1.67903i	−0.733604	−	0.679577i	$-0.762163\pi$
$701$	−20.3017	−	44.4546i	−0.766786	−	1.67903i	−0.0331810	−	0.999449i	$-0.510564\pi$
$702$	0.385331	+	0.843758i	0.0145434	+	0.0318456i
$703$	−0.0659777	−	0.458885i	−0.00248840	−	0.0173072i
$704$	−0.203930	−	0.131058i	−0.00768592	−	0.00493944i
$705$	26.6139	−	7.81456i	1.00234	−	0.294313i
$706$	−3.44622	+	23.9690i	−0.129700	+	0.902084i
$707$	−0.780969	+	0.901286i	−0.0293714	+	0.0338964i
$708$	−2.12186	+	1.36364i	−0.0797444	+	0.0512486i
$709$	0.127816	+	0.147507i	0.00480021	+	0.00553974i	0.758145	−	0.652086i	$-0.226106\pi$
$709$	0.127816	+	0.147507i	0.00480021	+	0.00553974i	−0.753344	+	0.657626i	$0.771561\pi$
$710$	4.03381	+	1.18443i	0.151386	+	0.0444510i
$711$	14.3603	−	31.4446i	0.538552	−	1.17926i
$712$	1.71721			0.0643551
$713$	−5.42225	+	7.76564i	−0.203065	+	0.290826i
$714$	5.39946			0.202070
$715$	0.322815	−	0.706865i	0.0120726	−	0.0264353i
$716$	21.6087	+	6.34488i	0.807554	+	0.237119i
$717$	5.17351	+	5.97055i	0.193208	+	0.222974i
$718$	−12.1471	+	7.80645i	−0.453325	+	0.291334i
$719$	2.77597	−	3.20364i	0.103526	−	0.119476i	−0.701622	−	0.712550i	$-0.747540\pi$
$719$	2.77597	−	3.20364i	0.103526	−	0.119476i	0.805148	+	0.593074i	$0.202086\pi$
$720$	−0.811342	+	5.64301i	−0.0302369	+	0.210302i
$721$	6.77016	−	1.98790i	0.252134	−	0.0740332i
$722$	15.0596	+	9.67822i	0.560460	+	0.360186i
$723$	−1.30520	−	9.07785i	−0.0485408	−	0.337609i
$724$	−4.90438	−	10.7391i	−0.182270	−	0.399115i
$725$	−1.26833	−	2.77725i	−0.0471046	−	0.103145i
$726$	3.73374	+	25.9687i	0.138572	+	0.963789i
$727$	−34.4373	−	22.1315i	−1.27721	−	0.820812i	−0.286667	−	0.958030i	$-0.592547\pi$
$727$	−34.4373	−	22.1315i	−1.27721	−	0.820812i	−0.990541	+	0.137218i	$0.956184\pi$
$728$	1.48357	−	0.435615i	0.0549847	−	0.0161450i
$729$	3.17712	−	22.0973i	0.117671	−	0.818420i
$730$	15.5436	−	17.9383i	0.575296	−	0.663927i
$731$	−13.8321	+	8.88937i	−0.511600	+	0.328785i
$732$	−22.4630	−	25.9237i	−0.830255	−	0.958166i
$733$	8.58778	+	2.52160i	0.317197	+	0.0931374i	0.436456	−	0.899726i	$-0.356234\pi$
$733$	8.58778	+	2.52160i	0.317197	+	0.0931374i	−0.119259	+	0.992863i	$0.538052\pi$
$734$	−6.87662	+	15.0577i	−0.253821	+	0.555790i
$735$	−4.97138			−0.183372
$736$	4.76969	−	0.500049i	0.175813	−	0.0184321i
$737$	−0.387136			−0.0142603
$738$	11.0730	−	24.2464i	0.407601	−	0.892523i
$739$	6.32588	+	1.85744i	0.232701	+	0.0683272i	0.396004	−	0.918249i	$-0.370397\pi$
$739$	6.32588	+	1.85744i	0.232701	+	0.0683272i	−0.163303	+	0.986576i	$0.552215\pi$
$740$	−0.600513	−	0.693029i	−0.0220753	−	0.0254762i
$741$	3.26921	−	2.10100i	0.120098	−	0.0771820i
$742$	−5.70197	+	6.58042i	−0.209326	+	0.241575i
$743$	5.54350	−	38.5559i	0.203371	−	1.41448i	−0.590816	−	0.806806i	$-0.701194\pi$
$743$	5.54350	−	38.5559i	0.203371	−	1.41448i	0.794188	−	0.607673i	$-0.207897\pi$
$744$	4.54376	−	1.33417i	0.166582	−	0.0489130i
$745$	7.23895	+	4.65219i	0.265215	+	0.170443i
$746$	−2.77125	−	19.2745i	−0.101463	−	0.705689i
$747$	−14.9044	−	32.6360i	−0.545323	−	1.19409i
$748$	0.226757	+	0.496529i	0.00829106	+	0.0181549i
$749$	−1.25997	−	8.76328i	−0.0460383	−	0.320203i
$750$	−23.8455	−	15.3245i	−0.870713	−	0.559573i
$751$	17.9238	−	5.26289i	0.654048	−	0.192046i	0.0621601	−	0.998066i	$-0.480201\pi$
$751$	17.9238	−	5.26289i	0.654048	−	0.192046i	0.591888	+	0.806020i	$0.298383\pi$
$752$	−0.794037	+	5.52265i	−0.0289555	+	0.201390i
$753$	−5.16071	+	5.95578i	−0.188067	+	0.217041i
$754$	5.65995	−	3.63743i	0.206123	−	0.132467i
$755$	1.65438	+	1.90925i	0.0602090	+	0.0694849i
$756$	0.575610	+	0.169014i	0.0209347	+	0.00614699i
$757$	−3.04304	+	6.66332i	−0.110601	+	0.242183i	−0.956837	−	0.290626i	$-0.906136\pi$
$757$	−3.04304	+	6.66332i	−0.110601	+	0.242183i	0.846236	+	0.532809i	$0.178864\pi$
$758$	8.49761			0.308647
$759$	2.03528	+	1.90497i	0.0738758	+	0.0691462i
$760$	−2.17307			−0.0788256
$761$	−8.16949	+	17.8887i	−0.296144	+	0.648465i	−0.997956	−	0.0638970i	$-0.979647\pi$
$761$	−8.16949	+	17.8887i	−0.296144	+	0.648465i	0.701813	+	0.712362i	$0.252374\pi$
$762$	19.8100	+	5.81675i	0.717642	+	0.210719i
$763$	−5.53434	−	6.38697i	−0.200357	−	0.231224i
$764$	−17.6428	+	11.3384i	−0.638295	+	0.410207i
$765$	8.40671	−	9.70186i	0.303945	−	0.350771i
$766$	0.967160	−	6.72674i	0.0349449	−	0.243047i
$767$	1.56052	−	0.458211i	0.0563473	−	0.0165451i
$768$	−2.01722	−	1.29639i	−0.0727903	−	0.0467795i
$769$	−0.284142	−	1.97625i	−0.0102464	−	0.0712653i	0.984057	−	0.177855i	$-0.0569159\pi$
$769$	−0.284142	−	1.97625i	−0.0102464	−	0.0712653i	−0.994303	+	0.106590i	$0.966007\pi$
$770$	−0.208779	−	0.457163i	−0.00752388	−	0.0164750i
$771$	−28.1578	−	61.6569i	−1.01408	−	2.22052i
$772$	−1.27825	−	8.89041i	−0.0460052	−	0.319973i
$773$	3.92853	+	2.52471i	0.141299	+	0.0908076i	0.609381	−	0.792878i	$-0.291418\pi$
$773$	3.92853	+	2.52471i	0.141299	+	0.0908076i	−0.468081	+	0.883685i	$0.655055\pi$
$774$	19.2657	−	5.65691i	0.692490	−	0.203334i
$775$	−0.197209	+	1.37162i	−0.00708396	+	0.0492700i
$776$	−0.635201	+	0.733061i	−0.0228024	+	0.0263153i
$777$	0.892231	−	0.573402i	0.0320086	−	0.0205707i
$778$	22.9413	+	26.4757i	0.822486	+	0.949199i
$779$	9.74863	+	2.86246i	0.349281	+	0.102558i
$780$	3.19319	−	6.99212i	0.114335	−	0.250358i
$781$	−0.491563			−0.0175895
$782$	−9.64401	−	4.85936i	−0.344869	−	0.173770i
$783$	2.61040			0.0932880
$784$	0.415415	−	0.909632i	0.0148363	−	0.0324869i
$785$	34.0092	+	9.98600i	1.21384	+	0.356416i
$786$	−19.7094	−	22.7458i	−0.703010	−	0.811317i
$787$	−33.7166	+	21.6684i	−1.20187	+	0.772394i	−0.979278	−	0.202518i	$-0.935087\pi$
$787$	−33.7166	+	21.6684i	−1.20187	+	0.772394i	−0.222590	+	0.974912i	$0.571451\pi$
$788$	10.9380	−	12.6232i	0.389651	−	0.449682i
$789$	0.0327989	−	0.228121i	0.00116767	−	0.00812134i
$790$	25.0074	−	7.34283i	0.889723	−	0.261246i
$791$	9.10696	+	5.85269i	0.323806	+	0.208098i
$792$	−0.0948656	−	0.659805i	−0.00337090	−	0.0234451i
$793$	9.18839	+	20.1198i	0.326289	+	0.714474i
$794$	15.1633	+	33.2031i	0.538127	+	1.17833i
$795$	6.16032	+	42.8460i	0.218484	+	1.51959i
$796$	20.2019	+	12.9830i	0.716039	+	0.460170i
$797$	−2.07463	+	0.609165i	−0.0734870	+	0.0215777i	−0.318269	−	0.948000i	$-0.603102\pi$
$797$	−2.07463	+	0.609165i	−0.0734870	+	0.0215777i	0.244782	+	0.969578i	$0.421283\pi$
$798$	0.357685	−	2.48775i	0.0126619	−	0.0880656i
$799$	8.22740	−	9.49493i	0.291065	−	0.335906i
$800$	0.590278	−	0.379349i	0.0208695	−	0.0134120i
$801$	3.09226	+	3.56865i	0.109260	+	0.126092i
$802$	−32.9015	−	9.66076i	−1.16179	−	0.341133i
$803$	−1.15290	+	2.52450i	−0.0406849	+	0.0890875i
$804$	−3.82944			−0.135054
$805$	8.87942	+	4.47410i	0.312958	+	0.157691i
$806$	−3.05360			−0.107559
$807$	18.3500	−	40.1809i	0.645950	−	1.41443i
$808$	−1.14427	−	0.335987i	−0.0402551	−	0.0118200i
$809$	26.5535	+	30.6443i	0.933570	+	1.07740i	0.996843	+	0.0794009i	$0.0253007\pi$
$809$	26.5535	+	30.6443i	0.933570	+	1.07740i	−0.0632728	+	0.997996i	$0.520154\pi$
$810$	16.8970	−	10.8590i	0.593700	−	0.381548i
$811$	13.4793	−	15.5560i	0.473324	−	0.546244i	−0.468010	−	0.883723i	$-0.655029\pi$
$811$	13.4793	−	15.5560i	0.473324	−	0.546244i	0.941333	+	0.337479i	$0.109574\pi$
$812$	0.619256	−	4.30702i	0.0217316	−	0.151147i
$813$	−2.10342	+	0.617621i	−0.0737703	+	0.0216609i
$814$	0.0901998	+	0.0579679i	0.00316150	+	0.00203177i
$815$	−5.10413	−	35.5000i	−0.178790	−	1.24351i
$816$	2.24302	+	4.91152i	0.0785213	+	0.171938i
$817$	3.17940	+	6.96191i	0.111233	+	0.243566i
$818$	−3.10138	−	21.5705i	−0.108437	−	0.754196i
$819$	3.57681	+	2.29868i	0.124984	+	0.0803223i
$820$	19.2828	−	5.66194i	0.673384	−	0.197724i
$821$	3.46018	−	24.0661i	0.120761	−	0.839913i	−0.835936	−	0.548827i	$-0.815074\pi$
$821$	3.46018	−	24.0661i	0.120761	−	0.839913i	0.956697	−	0.291086i	$-0.0940164\pi$
$822$	−35.8259	+	41.3453i	−1.24957	+	1.44208i
$823$	−43.6332	+	28.0414i	−1.52096	+	0.977461i	−0.529319	+	0.848423i	$0.677553\pi$
$823$	−43.6332	+	28.0414i	−1.52096	+	0.977461i	−0.991640	+	0.129038i	$0.958811\pi$
$824$	4.62068	+	5.33255i	0.160969	+	0.185768i
$825$	0.391340	+	0.114908i	0.0136247	+	0.00400057i
$826$	0.436964	−	0.956817i	0.0152039	−	0.0332919i
$827$	−3.29116			−0.114445			−0.0572224	−	0.998361i	$-0.518224\pi$
$827$	−3.29116			−0.114445			−0.0572224	+	0.998361i	$0.518224\pi$
$828$	9.62819	+	9.01178i	0.334603	+	0.313181i
$829$	9.85063			0.342127			0.171063	−	0.985260i	$-0.445280\pi$
$829$	9.85063			0.342127			0.171063	+	0.985260i	$0.445280\pi$
$830$	11.2373	−	24.6062i	0.390051	−	0.854092i
$831$	−0.710223	−	0.208540i	−0.0246374	−	0.00723418i
$832$	1.01255	+	1.16854i	0.0351037	+	0.0405118i
$833$	−1.89431	+	1.21740i	−0.0656338	+	0.0421803i
$834$	13.4115	−	15.4777i	0.464401	−	0.535947i
$835$	−4.00653	+	27.8660i	−0.138652	+	0.964344i
$836$	0.243793	−	0.0715840i	0.00843175	−	0.00247578i
$837$	−0.996691	−	0.640534i	−0.0344507	−	0.0221401i
$838$	−1.65055	−	11.4798i	−0.0570173	−	0.396564i
$839$	9.86443	+	21.6001i	0.340558	+	0.745718i	0.999982	−	0.00605372i	$-0.00192697\pi$
$839$	9.86443	+	21.6001i	0.340558	+	0.745718i	−0.659424	+	0.751771i	$0.729200\pi$
$840$	−2.06519	−	4.52213i	−0.0712557	−	0.156028i
$841$	1.43256	+	9.96365i	0.0493985	+	0.343574i
$842$	7.71252	+	4.95653i	0.265791	+	0.170813i
$843$	−10.7123	+	3.14540i	−0.368950	+	0.108333i
$844$	−2.74437	+	19.0875i	−0.0944650	+	0.657018i
$845$	14.4040	−	16.6231i	0.495514	−	0.571854i
$846$	−12.9069	+	8.29474i	−0.443747	+	0.285179i
$847$	−7.16499	−	8.26883i	−0.246192	−	0.284121i
$848$	−8.35445	−	2.45309i	−0.286893	−	0.0842394i
$849$	5.26299	−	11.5243i	0.180625	−	0.395514i
$850$	−1.57999			−0.0541931
$851$	−2.10967	+	0.221175i	−0.0723184	+	0.00758178i
$852$	−4.86240			−0.166583
$853$	−8.59210	+	18.8141i	−0.294188	+	0.644181i	−0.997792	−	0.0664103i	$-0.978845\pi$
$853$	−8.59210	+	18.8141i	−0.294188	+	0.644181i	0.703605	+	0.710592i	$0.251573\pi$
$854$	13.7257	+	4.03022i	0.469682	+	0.137911i
$855$	−3.91315	−	4.51602i	−0.133827	−	0.154444i
$856$	7.44795	−	4.78651i	0.254566	−	0.163600i
$857$	−21.9116	+	25.2873i	−0.748485	+	0.863798i	−0.994421	−	0.105489i	$-0.966359\pi$
$857$	−21.9116	+	25.2873i	−0.748485	+	0.863798i	0.245936	+	0.969286i	$0.420905\pi$
$858$	−0.127908	+	0.889620i	−0.00436671	+	0.0303711i
$859$	−17.2870	+	5.07593i	−0.589826	+	0.173188i	−0.563007	−	0.826452i	$-0.690356\pi$
$859$	−17.2870	+	5.07593i	−0.589826	+	0.173188i	−0.0268183	+	0.999640i	$0.508538\pi$
$860$	12.7355	+	8.18461i	0.434277	+	0.279093i
$861$	3.30792	+	23.0071i	0.112734	+	0.784080i
$862$	8.76136	+	19.1847i	0.298413	+	0.653433i
$863$	12.8756	+	28.1937i	0.438291	+	0.959724i	0.991909	+	0.126953i	$0.0405197\pi$
$863$	12.8756	+	28.1937i	0.438291	+	0.959724i	−0.553618	+	0.832771i	$0.686753\pi$
$864$	0.0853762	+	0.593804i	0.00290456	+	0.0202016i
$865$	31.8482	+	20.4676i	1.08287	+	0.695919i
$866$	−0.799422	+	0.234731i	−0.0271655	+	0.00797650i
$867$	−4.07100	+	28.3144i	−0.138258	+	0.961608i
$868$	−1.29329	+	1.49254i	−0.0438971	+	0.0506600i
$869$	−2.56365	+	1.64756i	−0.0869658	+	0.0558895i
$870$	−14.1660	−	16.3484i	−0.480271	−	0.554262i
$871$	2.36928	+	0.695683i	0.0802799	+	0.0235723i
$872$	3.51074	−	7.68745i	0.118889	−	0.260330i
$873$	−2.66726			−0.0902731
$874$	−2.87777	+	4.12149i	−0.0973421	+	0.139412i
$875$	11.8209			0.399621
$876$	−11.4042	+	24.9716i	−0.385311	+	0.843713i
$877$	−19.6436	−	5.76787i	−0.663316	−	0.194767i	−0.0672913	−	0.997733i	$-0.521436\pi$
$877$	−19.6436	−	5.76787i	−0.663316	−	0.194767i	−0.596024	+	0.802966i	$0.703254\pi$
$878$	−26.1207	−	30.1449i	−0.881532	−	1.01734i
$879$	13.3813	−	8.59967i	0.451342	−	0.290060i
$880$	0.329120	−	0.379825i	0.0110946	−	0.0128039i
$881$	5.02468	−	34.9474i	0.169286	−	1.17741i	−0.711080	−	0.703111i	$-0.751794\pi$
$881$	5.02468	−	34.9474i	0.169286	−	1.17741i	0.880365	−	0.474296i	$-0.157297\pi$
$882$	2.63843	−	0.774713i	0.0888405	−	0.0260859i
$883$	9.27701	+	5.96197i	0.312196	+	0.200636i	0.687350	−	0.726326i	$-0.258774\pi$
$883$	9.27701	+	5.96197i	0.312196	+	0.200636i	−0.375154	+	0.926962i	$0.622410\pi$
$884$	−0.495495	−	3.44624i	−0.0166653	−	0.115910i
$885$	−2.17231	−	4.75670i	−0.0730215	−	0.159895i
$886$	14.6599	+	32.1008i	0.492510	+	1.07845i
$887$	4.98130	+	34.6457i	0.167256	+	1.16329i	0.884525	+	0.466493i	$0.154483\pi$
$887$	4.98130	+	34.6457i	0.167256	+	1.16329i	−0.717269	+	0.696796i	$0.754608\pi$
$888$	0.892231	+	0.573402i	0.0299413	+	0.0192421i
$889$	−8.26149	+	2.42579i	−0.277082	+	0.0813585i
$890$	−0.506668	+	3.52395i	−0.0169835	+	0.118123i
$891$	−1.53793	+	1.77487i	−0.0515226	+	0.0594602i
$892$	14.1988	−	9.12504i	0.475412	−	0.305529i
$893$	−3.82969	−	4.41969i	−0.128156	−	0.147899i
$894$	−9.54921	−	2.80390i	−0.319373	−	0.0937765i
$895$	−19.3963	+	42.4720i	−0.648347	+	1.41968i
$896$	1.00000			0.0334077
$897$	−9.03268	−	15.3159i	−0.301592	−	0.511381i
$898$	−0.501052			−0.0167203
$899$	−3.56984	+	7.81686i	−0.119061	+	0.260707i
$900$	1.85129	+	0.543589i	0.0617098	+	0.0181196i
$901$	12.8395	+	14.8176i	0.427746	+	0.493645i
$902$	−1.97679	+	1.27040i	−0.0658198	+	0.0422998i
$903$	−11.4661	+	13.2326i	−0.381567	+	0.440352i
$904$	−1.54062	+	10.7153i	−0.0512404	+	0.356385i
$905$	23.4852	−	6.89587i	0.780673	−	0.229226i
$906$	−2.45804	−	1.57969i	−0.0816631	−	0.0524817i
$907$	−4.30973	−	29.9749i	−0.143102	−	0.995299i	−0.927175	−	0.374629i	$-0.877770\pi$
$907$	−4.30973	−	29.9749i	−0.143102	−	0.995299i	0.784072	−	0.620670i	$-0.213139\pi$
$908$	−4.05119	−	8.87087i	−0.134444	−	0.294390i
$909$	−1.36229	−	2.98301i	−0.0451844	−	0.0989401i
$910$	0.456211	+	3.17302i	0.0151233	+	0.105185i
$911$	−27.2561	−	17.5165i	−0.903036	−	0.580346i	0.00465305	−	0.999989i	$-0.498519\pi$
$911$	−27.2561	−	17.5165i	−0.903036	−	0.580346i	−0.907689	+	0.419643i	$0.862155\pi$
$912$	2.41153	−	0.708089i	0.0798537	−	0.0234472i
$913$	−0.450125	+	3.13069i	−0.0148970	+	0.103611i
$914$	3.14997	−	3.63526i	0.104192	−	0.120244i
$915$	59.8267	−	38.4483i	1.97781	−	1.27106i
$916$	−1.85547	−	2.14133i	−0.0613066	−	0.0707515i
$917$	12.0431	+	3.53618i	0.397699	+	0.116775i
$918$	0.561167	−	1.22878i	0.0185213	−	0.0405559i
$919$	−18.6529			−0.615302			−0.307651	−	0.951499i	$-0.599543\pi$
$919$	−18.6529			−0.615302			−0.307651	+	0.951499i	$0.599543\pi$
$920$	−0.381141	+	9.93561i	−0.0125659	+	0.327568i
$921$	54.7228			1.80318
$922$	16.3208	−	35.7377i	0.537498	−	1.17696i
$923$	3.00837	+	0.883337i	0.0990217	+	0.0290754i
$924$	0.380655	+	0.439299i	0.0125226	+	0.0144519i
$925$	−0.261084	+	0.167788i	−0.00858439	+	0.00551685i
$926$	−27.6982	+	31.9655i	−0.910221	+	1.05045i
$927$	−2.76128	+	19.2051i	−0.0906925	+	0.630780i
$928$	4.17505	−	1.22591i	0.137053	−	0.0402423i
$929$	−30.3292	−	19.4914i	−0.995067	−	0.639491i	−0.0615803	−	0.998102i	$-0.519614\pi$
$929$	−30.3292	−	19.4914i	−0.995067	−	0.639491i	−0.933487	+	0.358611i	$0.883250\pi$
$930$	1.39725	+	9.71809i	0.0458176	+	0.318669i
$931$	0.435418	+	0.953431i	0.0142702	+	0.0312475i
$932$	5.83834	+	12.7842i	0.191241	+	0.418760i
$933$	1.32711	+	9.23027i	0.0434477	+	0.302185i
$934$	−3.02599	−	1.94469i	−0.0990134	−	0.0636321i
$935$	−1.08585	+	0.318835i	−0.0355111	+	0.0104270i
$936$	−0.605089	+	4.20849i	−0.0197780	+	0.137559i
$937$	−14.5396	+	16.7796i	−0.474989	+	0.548167i	−0.941793	−	0.336194i	$-0.890860\pi$
$937$	−14.5396	+	16.7796i	−0.474989	+	0.548167i	0.466804	+	0.884361i	$0.345406\pi$
$938$	1.34349	−	0.863411i	0.0438666	−	0.0281914i
$939$	43.0707	+	49.7062i	1.40556	+	1.62210i
$940$	−11.0990	−	3.25895i	−0.362008	−	0.106295i
$941$	17.5040	−	38.3285i	0.570615	−	1.24947i	−0.375854	−	0.926679i	$-0.622651\pi$
$941$	17.5040	−	38.3285i	0.570615	−	1.24947i	0.946469	−	0.322794i	$-0.104622\pi$
$942$	−40.9950			−1.33569
$943$	14.7974	−	44.0702i	0.481871	−	1.43512i
$944$	1.05187			0.0342355
$945$	−0.516677	+	1.13136i	−0.0168075	+	0.0368033i
$946$	−1.69838	−	0.498690i	−0.0552192	−	0.0162138i
$947$	1.43262	+	1.65333i	0.0465538	+	0.0537260i	0.778549	−	0.627584i	$-0.215956\pi$
$947$	1.43262	+	1.65333i	0.0465538	+	0.0537260i	−0.731995	+	0.681310i	$0.761411\pi$
$948$	−25.3589	+	16.2972i	−0.823618	+	0.529307i
$949$	11.5923	−	13.3782i	0.376301	−	0.434275i
$950$	−0.104666	+	0.727965i	−0.00339580	+	0.0236183i
$951$	−31.7080	+	9.31032i	−1.02820	+	0.301908i
$952$	−1.89431	−	1.21740i	−0.0613948	−	0.0394561i
$953$	1.70820	+	11.8808i	0.0553341	+	0.384857i	0.998604	+	0.0528290i	$0.0168238\pi$
$953$	1.70820	+	11.8808i	0.0553341	+	0.384857i	−0.943269	+	0.332028i	$0.892267\pi$
$954$	−9.94630	−	21.7794i	−0.322024	−	0.705133i
$955$	−18.0623	−	39.5510i	−0.584483	−	1.27984i
$956$	−0.468878	−	3.26112i	−0.0151646	−	0.105472i
$957$	2.12779	+	1.36745i	0.0687817	+	0.0442033i
$958$	−12.6156	+	3.70429i	−0.407593	+	0.119680i
$959$	3.24692	−	22.5828i	0.104848	−	0.729237i
$960$	3.25556	−	3.75712i	0.105073	−	0.121261i
$961$	−22.7977	+	14.6512i	−0.735411	+	0.472620i
$962$	−0.447856	−	0.516853i	−0.0144394	−	0.0166640i
$963$	23.3591	+	6.85884i	0.752735	+	0.221023i
$964$	−1.58884	+	3.47909i	−0.0511732	+	0.112054i
$965$	18.6215			0.599448
$966$	−11.3117	−	2.07173i	−0.363947	−	0.0666567i
$967$	36.4493			1.17213			0.586065	−	0.810264i	$-0.300676\pi$
$967$	36.4493			1.17213			0.586065	+	0.810264i	$0.300676\pi$
$968$	4.54515	−	9.95250i	0.146087	−	0.319885i
$969$	−5.43020	−	1.59445i	−0.174443	−	0.0512211i
$970$	−1.31693	−	1.51981i	−0.0422839	−	0.0487982i
$971$	18.1094	−	11.6382i	0.581159	−	0.373488i	−0.216785	−	0.976219i	$-0.569557\pi$
$971$	18.1094	−	11.6382i	0.581159	−	0.373488i	0.797944	+	0.602731i	$0.205921\pi$
$972$	−14.0342	+	16.1963i	−0.450147	+	0.519497i
$973$	−1.21549	+	8.45390i	−0.0389667	+	0.271020i
$974$	−23.1825	+	6.80699i	−0.742815	+	0.218110i
$975$	−2.18852	−	1.40647i	−0.0700886	−	0.0450432i
$976$	2.03583	+	14.1595i	0.0651653	+	0.453235i
$977$	16.5373	+	36.2117i	0.529076	+	1.15852i	0.965888	+	0.258962i	$0.0833805\pi$
$977$	16.5373	+	36.2117i	0.529076	+	1.15852i	−0.436811	+	0.899553i	$0.643892\pi$
$978$	17.2318	+	37.7323i	0.551012	+	1.20655i
$979$	−0.0592418	−	0.412036i	−0.00189338	−	0.0131687i
$980$	1.74412	+	1.12088i	0.0557140	+	0.0358052i
$981$	22.2978	−	6.54723i	0.711914	−	0.209037i
$982$	3.73019	−	25.9441i	0.119035	−	0.827909i
$983$	−1.93156	+	2.22914i	−0.0616072	+	0.0710985i	−0.785717	−	0.618587i	$-0.787706\pi$
$983$	−1.93156	+	2.22914i	−0.0616072	+	0.0710985i	0.724109	+	0.689685i	$0.242251\pi$
$984$	−19.5538	+	12.5665i	−0.623353	+	0.400605i
$985$	22.6772	+	26.1709i	0.722556	+	0.833874i
$986$	−9.40124	−	2.76045i	−0.299396	−	0.0879107i
$987$	5.55776	−	12.1698i	0.176905	−	0.387369i
$988$	−1.62065			−0.0515598
$989$	32.3886	−	13.3156i	1.02990	−	0.423412i
$990$	1.38200			0.0439229
$991$	14.9868	−	32.8165i	0.476072	−	1.04245i	−0.507453	−	0.861679i	$-0.669413\pi$
$991$	14.9868	−	32.8165i	0.476072	−	1.04245i	0.983525	−	0.180773i	$-0.0578598\pi$
$992$	−1.89491	−	0.556396i	−0.0601635	−	0.0176656i
$993$	19.5381	+	22.5482i	0.620023	+	0.715545i
$994$	1.70589	−	1.09631i	0.0541075	−	0.0347728i
$995$	−32.6036	+	37.6265i	−1.03360	+	1.19284i
$996$	−4.45251	+	30.9679i	−0.141083	+	0.981256i
$997$	54.8467	−	16.1044i	1.73701	−	0.510033i	0.748756	−	0.662846i	$-0.230651\pi$
$997$	54.8467	−	16.1044i	1.73701	−	0.510033i	0.988255	+	0.152813i	$0.0488333\pi$
$998$	−1.17786	−	0.756967i	−0.0372846	−	0.0239614i
$999$	−0.0377624	−	0.262644i	−0.00119475	−	0.00830967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.b.29.1	✓	10
23.2	even	11		7406.2.a.bf.1.1		5
23.4	even	11	inner	322.2.i.b.211.1	yes	10
23.21	odd	22		7406.2.a.be.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.b.29.1	✓	10	1.1	even	1	trivial
322.2.i.b.211.1	yes	10	23.4	even	11	inner
7406.2.a.be.1.1		5	23.21	odd	22
7406.2.a.bf.1.1		5	23.2	even	11

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.909632i) q^{2} +(2.30075 + 0.675560i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(1.74412 - 1.12088i) q^{5} +(-1.57028 + 1.81219i) q^{6} +(0.142315 - 0.989821i) q^{7} +(0.959493 - 0.281733i) q^{8} +(2.31329 + 1.48666i) q^{9} +O(q^{10})\)	\(q+(-0.415415 + 0.909632i) q^{2} +(2.30075 + 0.675560i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(1.74412 - 1.12088i) q^{5} +(-1.57028 + 1.81219i) q^{6} +(0.142315 - 0.989821i) q^{7} +(0.959493 - 0.281733i) q^{8} +(2.31329 + 1.48666i) q^{9} +(0.295053 + 2.05214i) q^{10} +(-0.100702 - 0.220506i) q^{11} +(-0.996114 - 2.18119i) q^{12} +(0.220047 + 1.53046i) q^{13} +(0.841254 + 0.540641i) q^{14} +(4.77001 - 1.40060i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(1.47459 - 1.70177i) q^{17} +(-2.31329 + 1.48666i) q^{18} +(-0.686393 - 0.792140i) q^{19} +(-1.98926 - 0.584100i) q^{20} +(0.996114 - 2.18119i) q^{21} +0.242413 q^{22} +(-3.74217 + 2.99936i) q^{23} +2.39788 q^{24} +(-0.291482 + 0.638257i) q^{25} +(-1.48357 - 0.435615i) q^{26} +(-0.392858 - 0.453382i) q^{27} +(-0.841254 + 0.540641i) q^{28} +(-2.84950 + 3.28850i) q^{29} +(-0.707501 + 4.92078i) q^{30} +(1.89491 - 0.556396i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(-0.0827241 - 0.575359i) q^{33} +(0.935418 + 2.04828i) q^{34} +(-0.861256 - 1.88589i) q^{35} +(-0.391340 - 2.72183i) q^{36} +(0.372092 + 0.239129i) q^{37} +(1.00569 - 0.295298i) q^{38} +(-0.527646 + 3.66986i) q^{39} +(1.35769 - 1.56685i) q^{40} +(-8.15464 + 5.24067i) q^{41} +(1.57028 + 1.81219i) q^{42} +(-7.00617 - 2.05720i) q^{43} +(-0.100702 + 0.220506i) q^{44} +5.70104 q^{45} +(-1.17376 - 4.64998i) q^{46} +5.57944 q^{47} +(-0.996114 + 2.18119i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(-0.459493 - 0.530283i) q^{50} +(4.54231 - 2.91917i) q^{51} +(1.01255 - 1.16854i) q^{52} +(-1.23916 + 8.61852i) q^{53} +(0.575610 - 0.169014i) q^{54} +(-0.422797 - 0.271715i) q^{55} +(-0.142315 - 0.989821i) q^{56} +(-1.04408 - 2.28621i) q^{57} +(-1.80760 - 3.95809i) q^{58} +(-0.149697 - 1.04117i) q^{59} +(-4.18219 - 2.68773i) q^{60} +(13.7257 - 4.03022i) q^{61} +(-0.281059 + 1.95481i) q^{62} +(1.80075 - 2.07817i) q^{63} +(0.841254 - 0.540641i) q^{64} +(2.09925 + 2.42267i) q^{65} +(0.557730 + 0.163764i) q^{66} +(0.663423 - 1.45269i) q^{67} -2.25177 q^{68} +(-10.6360 + 4.37270i) q^{69} +2.07324 q^{70} +(0.842376 - 1.84455i) q^{71} +(2.63843 + 0.774713i) q^{72} +(-7.49726 - 8.65230i) q^{73} +(-0.372092 + 0.239129i) q^{74} +(-1.10181 + 1.27155i) q^{75} +(-0.149167 + 1.03748i) q^{76} +(-0.232593 + 0.0682955i) q^{77} +(-3.11903 - 2.00448i) q^{78} +(-1.78907 - 12.4432i) q^{79} +(0.861256 + 1.88589i) q^{80} +(-4.02452 - 8.81248i) q^{81} +(-1.37952 - 9.59478i) q^{82} +(-10.9763 - 7.05402i) q^{83} +(-2.30075 + 0.675560i) q^{84} +(0.664391 - 4.62094i) q^{85} +(4.78176 - 5.51845i) q^{86} +(-8.77756 + 5.64100i) q^{87} +(-0.158746 - 0.183203i) q^{88} +(1.64765 + 0.483793i) q^{89} +(-2.36830 + 5.18584i) q^{90} +1.54620 q^{91} +(4.71737 + 0.863983i) q^{92} +4.73559 q^{93} +(-2.31778 + 5.07524i) q^{94} +(-2.08505 - 0.612225i) q^{95} +(-1.57028 - 1.81219i) q^{96} +(-0.815998 + 0.524410i) q^{97} +(0.654861 - 0.755750i) q^{98} +(0.0948656 - 0.659805i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} + 5 q^{3} - q^{4} + 8 q^{5} - 5 q^{6} + q^{7} + q^{8}+O(q^{10}) \) 10 * q + q^2 + 5 * q^3 - q^4 + 8 * q^5 - 5 * q^6 + q^7 + q^8	\( 10 q + q^{2} + 5 q^{3} - q^{4} + 8 q^{5} - 5 q^{6} + q^{7} + q^{8} + 3 q^{10} + 11 q^{11} + 5 q^{12} - 6 q^{13} - q^{14} + 4 q^{15} - q^{16} - 2 q^{17} - 3 q^{19} + 8 q^{20} - 5 q^{21} - 21 q^{23} + 6 q^{24} - 15 q^{25} - 5 q^{26} - 4 q^{27} + q^{28} + 2 q^{29} - 4 q^{30} + 3 q^{31} + q^{32} - 11 q^{33} + 2 q^{34} + 3 q^{35} - 6 q^{37} - 8 q^{38} + 8 q^{39} + 14 q^{40} - 23 q^{41} + 5 q^{42} - q^{43} + 11 q^{44} - 22 q^{45} - q^{46} + 38 q^{47} + 5 q^{48} - q^{49} + 4 q^{50} + 21 q^{51} + 5 q^{52} - 49 q^{53} + 4 q^{54} + 11 q^{55} - q^{56} - 7 q^{57} - 13 q^{58} + 9 q^{59} + 4 q^{60} + 16 q^{61} - 14 q^{62} - q^{64} + 15 q^{65} + 7 q^{67} - 2 q^{68} - 16 q^{69} + 8 q^{70} - 16 q^{71} + 11 q^{72} - 9 q^{73} + 6 q^{74} - 2 q^{75} - 14 q^{76} + 11 q^{77} - 8 q^{78} + 6 q^{79} - 3 q^{80} - 24 q^{81} - 43 q^{82} - 19 q^{83} - 5 q^{84} + 49 q^{85} + 23 q^{86} - 21 q^{87} - 11 q^{88} + 25 q^{89} - 11 q^{90} + 6 q^{91} + q^{92} - 4 q^{93} - 5 q^{94} + 24 q^{95} - 5 q^{96} + 16 q^{97} + q^{98} - 33 q^{99}+O(q^{100}) \) 10 * q + q^2 + 5 * q^3 - q^4 + 8 * q^5 - 5 * q^6 + q^7 + q^8 + 3 * q^10 + 11 * q^11 + 5 * q^12 - 6 * q^13 - q^14 + 4 * q^15 - q^16 - 2 * q^17 - 3 * q^19 + 8 * q^20 - 5 * q^21 - 21 * q^23 + 6 * q^24 - 15 * q^25 - 5 * q^26 - 4 * q^27 + q^28 + 2 * q^29 - 4 * q^30 + 3 * q^31 + q^32 - 11 * q^33 + 2 * q^34 + 3 * q^35 - 6 * q^37 - 8 * q^38 + 8 * q^39 + 14 * q^40 - 23 * q^41 + 5 * q^42 - q^43 + 11 * q^44 - 22 * q^45 - q^46 + 38 * q^47 + 5 * q^48 - q^49 + 4 * q^50 + 21 * q^51 + 5 * q^52 - 49 * q^53 + 4 * q^54 + 11 * q^55 - q^56 - 7 * q^57 - 13 * q^58 + 9 * q^59 + 4 * q^60 + 16 * q^61 - 14 * q^62 - q^64 + 15 * q^65 + 7 * q^67 - 2 * q^68 - 16 * q^69 + 8 * q^70 - 16 * q^71 + 11 * q^72 - 9 * q^73 + 6 * q^74 - 2 * q^75 - 14 * q^76 + 11 * q^77 - 8 * q^78 + 6 * q^79 - 3 * q^80 - 24 * q^81 - 43 * q^82 - 19 * q^83 - 5 * q^84 + 49 * q^85 + 23 * q^86 - 21 * q^87 - 11 * q^88 + 25 * q^89 - 11 * q^90 + 6 * q^91 + q^92 - 4 * q^93 - 5 * q^94 + 24 * q^95 - 5 * q^96 + 16 * q^97 + q^98 - 33 * q^99

Introduction

L-functions

Modular forms

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Database

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