LMFDB - Embedded newform 322.2.i.c.127.2

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:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 9 x^{19} + 41 x^{18} - 119 x^{17} + 245 x^{16} - 404 x^{15} + 623 x^{14} - 898 x^{13} + \cdots + 1 $ x^20 - 9x^19 + 41x^18 - 119x^17 + 245x^16 - 404x^15 + 623x^14 - 898x^13 + 1048x^12 - 693x^11 + 859x^10 - 935x^9 + 620x^8 + 679x^7 + 1220x^6 + 2241x^5 + 1750x^4 + 1079x^3 + 534x^2 + 38*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			127.2
Root			$-0.753480 + 0.869562i$ of defining polynomial
Character	$\chi$	$=$	322.127
Dual form			322.2.i.c.71.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 - 0.540641i) q^{2} +(0.306062 - 2.12871i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.500990 + 0.147104i) q^{5} +(-0.893390 - 1.95625i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-1.55924 - 0.457833i) q^{9} +O(q^{10})$	\(q+(0.841254 - 0.540641i) q^{2} +(0.306062 - 2.12871i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.500990 + 0.147104i) q^{5} +(-0.893390 - 1.95625i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-1.55924 - 0.457833i) q^{9} +(-0.341929 + 0.394607i) q^{10} +(-1.56822 - 1.00784i) q^{11} +(-1.80920 - 1.16270i) q^{12} +(1.97894 - 2.28382i) q^{13} +(-0.959493 - 0.281733i) q^{14} +(0.159807 + 1.11148i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(0.725896 + 1.58949i) q^{17} +(-1.55924 + 0.457833i) q^{18} +(-0.0859639 + 0.188235i) q^{19} +(-0.0743083 + 0.516825i) q^{20} +(-1.80920 + 1.16270i) q^{21} -1.86415 q^{22} +(2.92383 + 3.80148i) q^{23} -2.15060 q^{24} +(-3.97692 + 2.55581i) q^{25} +(0.430065 - 2.99117i) q^{26} +(1.22836 - 2.68972i) q^{27} +(-0.959493 + 0.281733i) q^{28} +(2.73503 + 5.98888i) q^{29} +(0.735351 + 0.848640i) q^{30} +(-0.971867 - 6.75948i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-2.62536 + 3.02983i) q^{33} +(1.47001 + 0.944715i) q^{34} +(0.439252 + 0.282290i) q^{35} +(-1.06419 + 1.22814i) q^{36} +(7.21088 + 2.11731i) q^{37} +(0.0294499 + 0.204829i) q^{38} +(-4.25590 - 4.91157i) q^{39} +(0.216905 + 0.474955i) q^{40} +(6.01689 - 1.76672i) q^{41} +(-0.893390 + 1.95625i) q^{42} +(-0.481627 + 3.34979i) q^{43} +(-1.56822 + 1.00784i) q^{44} +0.848509 q^{45} +(4.51492 + 1.61726i) q^{46} +0.462510 q^{47} +(-1.80920 + 1.16270i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(-1.96382 + 4.30017i) q^{50} +(3.60572 - 1.05874i) q^{51} +(-1.25535 - 2.74884i) q^{52} +(1.49007 + 1.71963i) q^{53} +(-0.420816 - 2.92684i) q^{54} +(0.933920 + 0.274224i) q^{55} +(-0.654861 + 0.755750i) q^{56} +(0.374386 + 0.240603i) q^{57} +(5.53869 + 3.55950i) q^{58} +(5.71117 - 6.59104i) q^{59} +(1.07743 + 0.316361i) q^{60} +(0.231596 + 1.61079i) q^{61} +(-4.47204 - 5.16101i) q^{62} +(0.675075 + 1.47821i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(-0.655470 + 1.43528i) q^{65} +(-0.570545 + 3.96823i) q^{66} +(-0.278441 + 0.178943i) q^{67} +1.74740 q^{68} +(8.98710 - 5.06049i) q^{69} +0.522140 q^{70} +(-2.28603 + 1.46914i) q^{71} +(-0.231270 + 1.60852i) q^{72} +(-0.560506 + 1.22734i) q^{73} +(7.21088 - 2.11731i) q^{74} +(4.22338 + 9.24792i) q^{75} +(0.135514 + 0.156391i) q^{76} +(0.265296 + 1.84518i) q^{77} +(-6.23569 - 1.83096i) q^{78} +(0.735399 - 0.848696i) q^{79} +(0.439252 + 0.282290i) q^{80} +(-9.45094 - 6.07375i) q^{81} +(4.10657 - 4.73924i) q^{82} +(1.82966 + 0.537237i) q^{83} +(0.306062 + 2.12871i) q^{84} +(-0.597486 - 0.689536i) q^{85} +(1.40586 + 3.07841i) q^{86} +(13.5857 - 3.98911i) q^{87} +(-0.774396 + 1.69569i) q^{88} +(-2.58306 + 17.9656i) q^{89} +(0.713812 - 0.458739i) q^{90} -3.02193 q^{91} +(4.67255 - 1.08042i) q^{92} -14.6864 q^{93} +(0.389088 - 0.250052i) q^{94} +(0.0153770 - 0.106949i) q^{95} +(-0.893390 + 1.95625i) q^{96} +(-11.9000 + 3.49416i) q^{97} +(0.415415 + 0.909632i) q^{98} +(1.98381 + 2.28944i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 5 q^{5} + 4 q^{6} - 2 q^{7} - 2 q^{8} - 12 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 5 * q^5 + 4 * q^6 - 2 * q^7 - 2 * q^8 - 12 * q^9	\( 20 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 5 q^{5} + 4 q^{6} - 2 q^{7} - 2 q^{8} - 12 q^{9} + 6 q^{10} + 6 q^{11} + 4 q^{12} + 14 q^{13} - 2 q^{14} + 13 q^{15} - 2 q^{16} + 7 q^{17} - 12 q^{18} - 2 q^{19} + 6 q^{20} + 4 q^{21} - 16 q^{22} + 9 q^{23} - 18 q^{24} + 23 q^{25} + 3 q^{26} - 47 q^{27} - 2 q^{28} + 2 q^{29} - 20 q^{30} + 28 q^{31} - 2 q^{32} + 26 q^{33} + 18 q^{34} - 5 q^{35} + 10 q^{36} - 17 q^{37} + 9 q^{38} + 36 q^{39} - 5 q^{40} - 7 q^{41} + 4 q^{42} - 17 q^{43} + 6 q^{44} + 90 q^{45} + 9 q^{46} - 68 q^{47} + 4 q^{48} - 2 q^{49} - 43 q^{50} - 15 q^{51} + 14 q^{52} - 35 q^{53} + 19 q^{54} + 8 q^{55} - 2 q^{56} - 20 q^{57} + 24 q^{58} - 60 q^{59} + 13 q^{60} - 48 q^{61} - 5 q^{62} + 10 q^{63} - 2 q^{64} + 40 q^{65} - 29 q^{66} - 57 q^{67} + 18 q^{68} + 4 q^{69} + 6 q^{70} - 39 q^{71} - q^{72} - 30 q^{73} - 17 q^{74} + 57 q^{75} - 2 q^{76} + 6 q^{77} - 19 q^{78} - 18 q^{79} - 5 q^{80} - 90 q^{81} + 26 q^{82} + 28 q^{83} + 4 q^{84} - 13 q^{85} - 6 q^{86} + 13 q^{87} + 6 q^{88} + 34 q^{89} - 20 q^{90} - 30 q^{91} - 2 q^{92} - 16 q^{93} + 9 q^{94} + 110 q^{95} + 4 q^{96} - 2 q^{98} - 28 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 5 * q^5 + 4 * q^6 - 2 * q^7 - 2 * q^8 - 12 * q^9 + 6 * q^10 + 6 * q^11 + 4 * q^12 + 14 * q^13 - 2 * q^14 + 13 * q^15 - 2 * q^16 + 7 * q^17 - 12 * q^18 - 2 * q^19 + 6 * q^20 + 4 * q^21 - 16 * q^22 + 9 * q^23 - 18 * q^24 + 23 * q^25 + 3 * q^26 - 47 * q^27 - 2 * q^28 + 2 * q^29 - 20 * q^30 + 28 * q^31 - 2 * q^32 + 26 * q^33 + 18 * q^34 - 5 * q^35 + 10 * q^36 - 17 * q^37 + 9 * q^38 + 36 * q^39 - 5 * q^40 - 7 * q^41 + 4 * q^42 - 17 * q^43 + 6 * q^44 + 90 * q^45 + 9 * q^46 - 68 * q^47 + 4 * q^48 - 2 * q^49 - 43 * q^50 - 15 * q^51 + 14 * q^52 - 35 * q^53 + 19 * q^54 + 8 * q^55 - 2 * q^56 - 20 * q^57 + 24 * q^58 - 60 * q^59 + 13 * q^60 - 48 * q^61 - 5 * q^62 + 10 * q^63 - 2 * q^64 + 40 * q^65 - 29 * q^66 - 57 * q^67 + 18 * q^68 + 4 * q^69 + 6 * q^70 - 39 * q^71 - q^72 - 30 * q^73 - 17 * q^74 + 57 * q^75 - 2 * q^76 + 6 * q^77 - 19 * q^78 - 18 * q^79 - 5 * q^80 - 90 * q^81 + 26 * q^82 + 28 * q^83 + 4 * q^84 - 13 * q^85 - 6 * q^86 + 13 * q^87 + 6 * q^88 + 34 * q^89 - 20 * q^90 - 30 * q^91 - 2 * q^92 - 16 * q^93 + 9 * q^94 + 110 * q^95 + 4 * q^96 - 2 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{10}{11}\right)$

Coefficient data

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

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

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

$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$3$	0.306062	−	2.12871i	0.176705	−	1.22901i	−0.687619	−	0.726072i	$-0.741344\pi$
$3$	0.306062	−	2.12871i	0.176705	−	1.22901i	0.864323	−	0.502937i	$-0.167747\pi$
$4$	0.415415	−	0.909632i	0.207708	−	0.454816i
$5$	−0.500990	+	0.147104i	−0.224049	+	0.0657868i	−0.391830	−	0.920037i	$-0.628158\pi$
$5$	−0.500990	+	0.147104i	−0.224049	+	0.0657868i	0.167781	+	0.985824i	$0.446340\pi$
$6$	−0.893390	−	1.95625i	−0.364725	−	0.798636i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$8$	−0.142315	−	0.989821i	−0.0503159	−	0.349955i
$9$	−1.55924	−	0.457833i	−0.519745	−	0.152611i
$10$	−0.341929	+	0.394607i	−0.108127	+	0.124786i
$11$	−1.56822	−	1.00784i	−0.472837	−	0.303874i	0.282434	−	0.959287i	$-0.408858\pi$
$11$	−1.56822	−	1.00784i	−0.472837	−	0.303874i	−0.755271	+	0.655413i	$0.772495\pi$
$12$	−1.80920	−	1.16270i	−0.522270	−	0.335643i
$13$	1.97894	−	2.28382i	0.548859	−	0.633417i	−0.411758	−	0.911293i	$-0.635085\pi$
$13$	1.97894	−	2.28382i	0.548859	−	0.633417i	0.960617	+	0.277876i	$0.0896304\pi$
$14$	−0.959493	−	0.281733i	−0.256435	−	0.0752962i
$15$	0.159807	+	1.11148i	0.0412620	+	0.286983i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	0.725896	+	1.58949i	0.176056	+	0.385508i	0.977003	−	0.213227i	$-0.0683975\pi$
$17$	0.725896	+	1.58949i	0.176056	+	0.385508i	−0.800947	+	0.598735i	$0.795670\pi$
$18$	−1.55924	+	0.457833i	−0.367515	+	0.107912i
$19$	−0.0859639	+	0.188235i	−0.0197215	+	0.0431840i	−0.919236	−	0.393706i	$-0.871193\pi$
$19$	−0.0859639	+	0.188235i	−0.0197215	+	0.0431840i	0.899515	+	0.436890i	$0.143920\pi$
$20$	−0.0743083	+	0.516825i	−0.0166158	+	0.115566i
$21$	−1.80920	+	1.16270i	−0.394799	+	0.253722i
$22$	−1.86415			−0.397438
$23$	2.92383	+	3.80148i	0.609661	+	0.792663i
$23$	2.92383	+	3.80148i	0.609661	+	0.792663i
$24$	−2.15060			−0.438988
$25$	−3.97692	+	2.55581i	−0.795383	+	0.511162i
$26$	0.430065	−	2.99117i	0.0843427	−	0.586616i
$27$	1.22836	−	2.68972i	0.236397	−	0.517638i
$28$	−0.959493	+	0.281733i	−0.181327	+	0.0532424i
$29$	2.73503	+	5.98888i	0.507883	+	1.11211i	0.973826	+	0.227293i	$0.0729877\pi$
$29$	2.73503	+	5.98888i	0.507883	+	1.11211i	−0.465944	+	0.884814i	$0.654285\pi$
$30$	0.735351	+	0.848640i	0.134256	+	0.154940i
$31$	−0.971867	−	6.75948i	−0.174552	−	1.21404i	−0.869116	−	0.494608i	$-0.835312\pi$
$31$	−0.971867	−	6.75948i	−0.174552	−	1.21404i	0.694564	−	0.719431i	$-0.255597\pi$
$32$	−0.959493	−	0.281733i	−0.169616	−	0.0498038i
$33$	−2.62536	+	3.02983i	−0.457016	+	0.527425i
$34$	1.47001	+	0.944715i	0.252104	+	0.162017i
$35$	0.439252	+	0.282290i	0.0742471	+	0.0477157i
$36$	−1.06419	+	1.22814i	−0.177365	+	0.204690i
$37$	7.21088	+	2.11731i	1.18546	+	0.348083i	0.814277	−	0.580476i	$-0.197134\pi$
$37$	7.21088	+	2.11731i	1.18546	+	0.348083i	0.371184	+	0.928559i	$0.378952\pi$
$38$	0.0294499	+	0.204829i	0.00477741	+	0.0332276i
$39$	−4.25590	−	4.91157i	−0.681490	−	0.786481i
$40$	0.216905	+	0.474955i	0.0342957	+	0.0750970i
$41$	6.01689	−	1.76672i	0.939681	−	0.275915i	0.224196	−	0.974544i	$-0.428024\pi$
$41$	6.01689	−	1.76672i	0.939681	−	0.275915i	0.715484	+	0.698629i	$0.246206\pi$
$42$	−0.893390	+	1.95625i	−0.137853	+	0.301856i
$43$	−0.481627	+	3.34979i	−0.0734475	+	0.510838i	0.919575	+	0.392914i	$0.128533\pi$
$43$	−0.481627	+	3.34979i	−0.0734475	+	0.510838i	−0.993023	+	0.117924i	$0.962376\pi$
$44$	−1.56822	+	1.00784i	−0.236419	+	0.151937i
$45$	0.848509			0.126488
$46$	4.51492	+	1.61726i	0.665688	+	0.238453i
$47$	0.462510			0.0674640			0.0337320	−	0.999431i	$-0.489261\pi$
$47$	0.462510			0.0674640			0.0337320	+	0.999431i	$0.489261\pi$
$48$	−1.80920	+	1.16270i	−0.261135	+	0.167821i
$49$	−0.142315	+	0.989821i	−0.0203307	+	0.141403i
$50$	−1.96382	+	4.30017i	−0.277726	+	0.608135i
$51$	3.60572	−	1.05874i	0.504902	−	0.148253i
$52$	−1.25535	−	2.74884i	−0.174086	−	0.381196i
$53$	1.49007	+	1.71963i	0.204676	+	0.236209i	0.848802	−	0.528710i	$-0.177324\pi$
$53$	1.49007	+	1.71963i	0.204676	+	0.236209i	−0.644126	+	0.764919i	$0.722779\pi$
$54$	−0.420816	−	2.92684i	−0.0572658	−	0.398292i
$55$	0.933920	+	0.274224i	0.125930	+	0.0369763i
$56$	−0.654861	+	0.755750i	−0.0875094	+	0.100991i
$57$	0.374386	+	0.240603i	0.0495886	+	0.0318687i
$58$	5.53869	+	3.55950i	0.727266	+	0.467385i
$59$	5.71117	−	6.59104i	0.743531	−	0.858080i	−0.250394	−	0.968144i	$-0.580560\pi$
$59$	5.71117	−	6.59104i	0.743531	−	0.858080i	0.993925	+	0.110064i	$0.0351055\pi$
$60$	1.07743	+	0.316361i	0.139095	+	0.0408420i
$61$	0.231596	+	1.61079i	0.0296529	+	0.206240i	0.999262	−	0.0384203i	$-0.0122326\pi$
$61$	0.231596	+	1.61079i	0.0296529	+	0.206240i	−0.969609	+	0.244661i	$0.921323\pi$
$62$	−4.47204	−	5.16101i	−0.567949	−	0.655448i
$63$	0.675075	+	1.47821i	0.0850514	+	0.186237i
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	−0.655470	+	1.43528i	−0.0813011	+	0.178024i
$66$	−0.570545	+	3.96823i	−0.0702292	+	0.488455i
$67$	−0.278441	+	0.178943i	−0.0340170	+	0.0218614i	−0.557539	−	0.830151i	$-0.688254\pi$
$67$	−0.278441	+	0.178943i	−0.0340170	+	0.0218614i	0.523522	+	0.852012i	$0.324618\pi$
$68$	1.74740			0.211903
$69$	8.98710	−	5.06049i	1.08192	−	0.609211i
$70$	0.522140			0.0624077
$71$	−2.28603	+	1.46914i	−0.271301	+	0.174355i	−0.669217	−	0.743067i	$-0.733370\pi$
$71$	−2.28603	+	1.46914i	−0.271301	+	0.174355i	0.397915	+	0.917422i	$0.369734\pi$
$72$	−0.231270	+	1.60852i	−0.0272555	+	0.189566i
$73$	−0.560506	+	1.22734i	−0.0656023	+	0.143649i	−0.939593	−	0.342293i	$-0.888796\pi$
$73$	−0.560506	+	1.22734i	−0.0656023	+	0.143649i	0.873991	+	0.485943i	$0.161524\pi$
$74$	7.21088	−	2.11731i	0.838248	−	0.246132i
$75$	4.22338	+	9.24792i	0.487674	+	1.06786i
$76$	0.135514	+	0.156391i	0.0155445	+	0.0179393i
$77$	0.265296	+	1.84518i	0.0302333	+	0.210277i
$78$	−6.23569	−	1.83096i	−0.706053	−	0.207316i
$79$	0.735399	−	0.848696i	0.0827389	−	0.0954857i	−0.712871	−	0.701296i	$-0.752605\pi$
$79$	0.735399	−	0.848696i	0.0827389	−	0.0954857i	0.795609	+	0.605810i	$0.207151\pi$
$80$	0.439252	+	0.282290i	0.0491099	+	0.0315610i
$81$	−9.45094	−	6.07375i	−1.05010	−	0.674861i
$82$	4.10657	−	4.73924i	0.453495	−	0.523361i
$83$	1.82966	+	0.537237i	0.200831	+	0.0589694i	0.380601	−	0.924739i	$-0.375717\pi$
$83$	1.82966	+	0.537237i	0.200831	+	0.0589694i	−0.179770	+	0.983709i	$0.557535\pi$
$84$	0.306062	+	2.12871i	0.0333941	+	0.232261i
$85$	−0.597486	−	0.689536i	−0.0648065	−	0.0747907i
$86$	1.40586	+	3.07841i	0.151598	+	0.331954i
$87$	13.5857	−	3.98911i	1.45654	−	0.427677i
$88$	−0.774396	+	1.69569i	−0.0825509	+	0.180761i
$89$	−2.58306	+	17.9656i	−0.273804	+	1.90435i	0.133486	+	0.991051i	$0.457383\pi$
$89$	−2.58306	+	17.9656i	−0.273804	+	1.90435i	−0.407290	+	0.913299i	$0.633526\pi$
$90$	0.713812	−	0.458739i	0.0752423	−	0.0483553i
$91$	−3.02193			−0.316784
$92$	4.67255	−	1.08042i	0.487147	−	0.112641i
$93$	−14.6864			−1.52291
$94$	0.389088	−	0.250052i	0.0401314	−	0.0257909i
$95$	0.0153770	−	0.106949i	0.00157764	−	0.0109728i
$96$	−0.893390	+	1.95625i	−0.0911812	+	0.199659i
$97$	−11.9000	+	3.49416i	−1.20826	+	0.354779i	−0.823007	−	0.568031i	$-0.807705\pi$
$97$	−11.9000	+	3.49416i	−1.20826	+	0.354779i	−0.385257	+	0.922809i	$0.625887\pi$
$98$	0.415415	+	0.909632i	0.0419633	+	0.0918867i
$99$	1.98381	+	2.28944i	0.199380	+	0.230097i
$100$	0.672775	+	4.67925i	0.0672775	+	0.467925i
$101$	−6.72446	−	1.97448i	−0.669108	−	0.196468i	−0.0705024	−	0.997512i	$-0.522460\pi$
$101$	−6.72446	−	1.97448i	−0.669108	−	0.196468i	−0.598606	+	0.801044i	$0.704278\pi$
$102$	2.46093	−	2.84007i	0.243669	−	0.281209i
$103$	−5.62320	−	3.61381i	−0.554071	−	0.356080i	0.233449	−	0.972369i	$-0.424999\pi$
$103$	−5.62320	−	3.61381i	−0.554071	−	0.356080i	−0.787520	+	0.616289i	$0.788635\pi$
$104$	−2.54221	−	1.63378i	−0.249284	−	0.160205i
$105$	0.735351	−	0.848640i	0.0717629	−	0.0828188i
$106$	2.18322	+	0.641052i	0.212053	+	0.0622645i
$107$	1.75042	+	12.1744i	0.169219	+	1.17695i	0.880503	+	0.474041i	$0.157205\pi$
$107$	1.75042	+	12.1744i	0.169219	+	1.17695i	−0.711283	+	0.702905i	$0.751886\pi$
$108$	−1.93638	−	2.23470i	−0.186328	−	0.215034i
$109$	1.15387	+	2.52663i	0.110521	+	0.242007i	0.956808	−	0.290720i	$-0.0938947\pi$
$109$	1.15387	+	2.52663i	0.110521	+	0.242007i	−0.846287	+	0.532727i	$0.821167\pi$
$110$	0.933920	−	0.274224i	0.0890458	−	0.0261462i
$111$	6.71410	−	14.7018i	0.637274	−	1.39543i
$112$	−0.142315	+	0.989821i	−0.0134475	+	0.0935293i
$113$	−16.5426	+	10.6313i	−1.55620	+	1.00011i	−0.572579	+	0.819850i	$0.694057\pi$
$113$	−16.5426	+	10.6313i	−1.55620	+	1.00011i	−0.983619	+	0.180258i	$0.942307\pi$
$114$	0.445033			0.0416812
$115$	−2.02402	−	1.47439i	−0.188741	−	0.137488i
$116$	6.58385			0.611295
$117$	−4.13124	+	2.65499i	−0.381933	+	0.245454i
$118$	1.24116	−	8.63243i	0.114258	−	0.794679i
$119$	0.725896	−	1.58949i	0.0665427	−	0.145708i
$120$	1.07743	−	0.316361i	0.0983551	−	0.0288797i
$121$	−3.12597	−	6.84493i	−0.284179	−	0.622266i
$122$	1.06569	+	1.22987i	0.0964830	+	0.111347i
$123$	−1.91928	−	13.3489i	−0.173056	−	1.20363i
$124$	−6.55237	−	1.92395i	−0.588420	−	0.172776i
$125$	3.32607	−	3.83849i	0.297493	−	0.343325i
$126$	1.36709	+	0.878575i	0.121790	+	0.0782696i
$127$	−4.86285	−	3.12516i	−0.431508	−	0.277313i	0.306804	−	0.951773i	$-0.400740\pi$
$127$	−4.86285	−	3.12516i	−0.431508	−	0.277313i	−0.738312	+	0.674459i	$0.764377\pi$
$128$	−0.654861	+	0.755750i	−0.0578821	+	0.0667995i
$129$	6.98331	+	2.05049i	0.614846	+	0.180535i
$130$	0.224554	+	1.56181i	0.0196947	+	0.136980i
$131$	6.22991	+	7.18970i	0.544310	+	0.628167i	0.959548	−	0.281546i	$-0.0908472\pi$
$131$	6.22991	+	7.18970i	0.544310	+	0.628167i	−0.415238	+	0.909713i	$0.636302\pi$
$132$	1.66541	+	3.64675i	0.144956	+	0.317408i
$133$	0.198553	−	0.0583003i	0.0172167	−	0.00505528i
$134$	−0.137496	+	0.301074i	−0.0118778	+	0.0260088i
$135$	−0.219725	+	1.52822i	−0.0189109	+	0.131528i
$136$	1.47001	−	0.944715i	0.126052	−	0.0810086i
$137$	15.5818			1.33124			0.665620	−	0.746291i	$-0.268167\pi$
$137$	15.5818			1.33124			0.665620	+	0.746291i	$0.268167\pi$
$138$	4.82452	−	9.11594i	0.410690	−	0.776001i
$139$	−12.4603			−1.05687			−0.528435	−	0.848974i	$-0.677221\pi$
$139$	−12.4603			−1.05687			−0.528435	+	0.848974i	$0.677221\pi$
$140$	0.439252	−	0.282290i	0.0371236	−	0.0238579i
$141$	0.141557	−	0.984547i	0.0119212	−	0.0829138i
$142$	−1.12885	+	2.47184i	−0.0947311	+	0.207432i
$143$	−5.40514	+	1.58709i	−0.452000	+	0.132719i
$144$	0.675075	+	1.47821i	0.0562562	+	0.123184i
$145$	−2.25121	−	2.59803i	−0.186953	−	0.215755i
$146$	0.192021	+	1.33553i	0.0158918	+	0.110530i
$147$	2.06348	+	0.605893i	0.170193	+	0.0499732i
$148$	4.92148	−	5.67969i	0.404543	−	0.466868i
$149$	−16.2227	−	10.4257i	−1.32902	−	0.854107i	−0.332970	−	0.942937i	$-0.608051\pi$
$149$	−16.2227	−	10.4257i	−1.32902	−	0.854107i	−0.996047	+	0.0888304i	$0.971687\pi$
$150$	8.55274	+	5.49651i	0.698328	+	0.448788i
$151$	6.15432	−	7.10246i	0.500831	−	0.577990i	−0.447896	−	0.894086i	$-0.647827\pi$
$151$	6.15432	−	7.10246i	0.500831	−	0.577990i	0.948727	+	0.316096i	$0.102372\pi$
$152$	0.198553	+	0.0583003i	0.0161047	+	0.00472878i
$153$	−0.404122	−	2.81073i	−0.0326713	−	0.227234i
$154$	1.22076	+	1.40883i	0.0983716	+	0.113527i
$155$	1.48124	+	3.24346i	0.118976	+	0.260521i
$156$	−6.23569	+	1.83096i	−0.499255	+	0.146594i
$157$	0.241775	−	0.529414i	0.0192958	−	0.0422518i	−0.899739	−	0.436429i	$-0.856243\pi$
$157$	0.241775	−	0.529414i	0.0192958	−	0.0422518i	0.919035	+	0.394177i	$0.128970\pi$
$158$	0.159818	−	1.11156i	0.0127144	−	0.0884306i
$159$	4.11663	−	2.64560i	0.326470	−	0.209810i
$160$	0.522140			0.0412788
$161$	0.958263	−	4.69912i	0.0755217	−	0.370343i
$162$	−11.2344			−0.882655
$163$	−9.93619	+	6.38560i	−0.778263	+	0.500159i	−0.868457	−	0.495765i	$-0.834888\pi$
$163$	−9.93619	+	6.38560i	−0.778263	+	0.500159i	0.0901940	+	0.995924i	$0.471251\pi$
$164$	0.892443	−	6.20708i	0.0696881	−	0.484691i
$165$	0.869579	−	1.90411i	0.0676966	−	0.148235i
$166$	1.82966	−	0.537237i	0.142009	−	0.0416977i
$167$	1.39213	+	3.04833i	0.107726	+	0.235887i	0.955816	−	0.293965i	$-0.0949748\pi$
$167$	1.39213	+	3.04833i	0.107726	+	0.235887i	−0.848090	+	0.529852i	$0.822248\pi$
$168$	1.40834	+	1.62531i	0.108656	+	0.125396i
$169$	0.550469	+	3.82859i	0.0423437	+	0.294507i
$170$	−0.875429	−	0.257049i	−0.0671423	−	0.0197148i
$171$	0.220218	−	0.254145i	0.0168405	−	0.0194350i
$172$	2.84700	+	1.82966i	0.217082	+	0.139510i
$173$	−2.76340	−	1.77593i	−0.210097	−	0.135021i	0.431361	−	0.902180i	$-0.358034\pi$
$173$	−2.76340	−	1.77593i	−0.210097	−	0.135021i	−0.641458	+	0.767158i	$0.721670\pi$
$174$	9.27231	−	10.7008i	0.702932	−	0.811227i
$175$	4.53588	+	1.33185i	0.342880	+	0.100679i
$176$	0.265296	+	1.84518i	0.0199975	+	0.139085i
$177$	−12.2824	−	14.1747i	−0.923203	−	1.06543i
$178$	7.53992	+	16.5101i	0.565141	+	1.23749i
$179$	15.9594	−	4.68609i	1.19286	−	0.350255i	0.375741	−	0.926725i	$-0.377388\pi$
$179$	15.9594	−	4.68609i	1.19286	−	0.350255i	0.817118	+	0.576470i	$0.195570\pi$
$180$	0.352484	−	0.771831i	0.0262726	−	0.0575289i
$181$	1.82787	−	12.7131i	0.135864	−	0.944957i	−0.801844	−	0.597534i	$-0.796147\pi$
$181$	1.82787	−	12.7131i	0.135864	−	0.944957i	0.937708	−	0.347424i	$-0.112943\pi$
$182$	−2.54221	+	1.63378i	−0.188441	+	0.121104i
$183$	3.49978			0.258711
$184$	3.34668	−	3.43508i	0.246720	−	0.253237i
$185$	−3.92404			−0.288501
$186$	−12.3550	+	7.94006i	−0.905911	+	0.582194i
$187$	0.463578	−	3.22426i	0.0339002	−	0.235781i
$188$	0.192134	−	0.420714i	0.0140128	−	0.0306837i
$189$	−2.83716	+	0.833065i	−0.206373	+	0.0605966i
$190$	−0.0448852	−	0.0982848i	−0.00325631	−	0.00713033i
$191$	−2.65193	−	3.06049i	−0.191887	−	0.221449i	0.651651	−	0.758519i	$-0.274077\pi$
$191$	−2.65193	−	3.06049i	−0.191887	−	0.221449i	−0.843538	+	0.537070i	$0.819531\pi$
$192$	0.306062	+	2.12871i	0.0220881	+	0.153626i
$193$	−25.1573	−	7.38685i	−1.81086	−	0.531717i	−0.812198	−	0.583381i	$-0.801729\pi$
$193$	−25.1573	−	7.38685i	−1.81086	−	0.531717i	−0.998665	+	0.0516639i	$0.983548\pi$
$194$	−8.12185	+	9.37312i	−0.583115	+	0.672951i
$195$	2.85467	+	1.83459i	0.204427	+	0.131377i
$196$	0.841254	+	0.540641i	0.0600895	+	0.0386172i
$197$	2.45222	−	2.83001i	0.174713	−	0.201630i	−0.661639	−	0.749823i	$-0.730139\pi$
$197$	2.45222	−	2.83001i	0.174713	−	0.201630i	0.836352	+	0.548193i	$0.184684\pi$
$198$	2.90665	+	0.853469i	0.206567	+	0.0606534i
$199$	−1.35586	−	9.43020i	−0.0961142	−	0.668489i	−0.979737	−	0.200289i	$-0.935812\pi$
$199$	−1.35586	−	9.43020i	−0.0961142	−	0.668489i	0.883623	−	0.468200i	$-0.155097\pi$
$200$	3.09577	+	3.57271i	0.218904	+	0.252629i
$201$	0.295698	+	0.647487i	0.0208569	+	0.0456702i
$202$	−6.72446	+	1.97448i	−0.473131	+	0.138924i
$203$	2.73503	−	5.98888i	0.191962	−	0.420337i
$204$	0.534812	−	3.71970i	0.0374443	−	0.260431i
$205$	−2.75451	+	1.77022i	−0.192383	+	0.123637i
$206$	−6.68431			−0.465718
$207$	−2.81850	−	7.26602i	−0.195899	−	0.505023i
$208$	−3.02193			−0.209533
$209$	0.324520	−	0.208557i	0.0224475	−	0.0144262i
$210$	0.159807	−	1.11148i	0.0110277	−	0.0766996i
$211$	−3.49234	+	7.64717i	−0.240423	+	0.526453i	−0.990925	−	0.134415i	$-0.957084\pi$
$211$	−3.49234	+	7.64717i	−0.240423	+	0.526453i	0.750502	+	0.660868i	$0.229812\pi$
$212$	2.18322	−	0.641052i	0.149944	−	0.0440277i
$213$	2.42770	+	5.31592i	0.166343	+	0.364241i
$214$	8.05454	+	9.29544i	0.550597	+	0.635423i
$215$	−0.251477	−	1.74906i	−0.0171506	−	0.119285i
$216$	−2.83716	−	0.833065i	−0.193044	−	0.0566829i
$217$	−4.47204	+	5.16101i	−0.303582	+	0.350352i
$218$	2.33670	+	1.50170i	0.158261	+	0.101708i
$219$	2.44109	+	1.56879i	0.164954	+	0.106009i
$220$	0.637407	−	0.735607i	0.0429740	−	0.0495946i
$221$	5.06661	+	1.48769i	0.340817	+	0.100073i
$222$	−2.30015	−	15.9979i	−0.154376	−	1.07371i
$223$	−15.9970	−	18.4615i	−1.07124	−	1.23628i	−0.970433	−	0.241370i	$-0.922403\pi$
$223$	−15.9970	−	18.4615i	−1.07124	−	1.23628i	−0.100806	−	0.994906i	$-0.532142\pi$
$224$	0.415415	+	0.909632i	0.0277561	+	0.0607773i
$225$	7.37108	−	2.16434i	0.491405	−	0.144290i
$226$	−8.16882	+	17.8872i	−0.543382	+	1.18984i
$227$	−1.24153	+	8.63500i	−0.0824029	+	0.573125i	0.906231	+	0.422783i	$0.138947\pi$
$227$	−1.24153	+	8.63500i	−0.0824029	+	0.573125i	−0.988634	+	0.150342i	$0.951962\pi$
$228$	0.374386	−	0.240603i	0.0247943	−	0.0159343i
$229$	18.5768			1.22759			0.613796	−	0.789465i	$-0.289642\pi$
$229$	18.5768			1.22759			0.613796	+	0.789465i	$0.289642\pi$
$230$	−2.49983	−	0.146071i	−0.164834	−	0.00963164i
$231$	4.00903			0.263775
$232$	5.53869	−	3.55950i	0.363633	−	0.233693i
$233$	−1.39074	+	9.67280i	−0.0911103	+	0.633686i	0.892185	+	0.451670i	$0.149171\pi$
$233$	−1.39074	+	9.67280i	−0.0911103	+	0.633686i	−0.983296	+	0.182016i	$0.941738\pi$
$234$	−2.04003	+	4.46703i	−0.133361	+	0.292019i
$235$	−0.231713	+	0.0680369i	−0.0151153	+	0.00443824i
$236$	−3.62292	−	7.93308i	−0.235832	−	0.516400i
$237$	−1.58155	−	1.82520i	−0.102732	−	0.118560i
$238$	−0.248681	−	1.72961i	−0.0161196	−	0.112114i
$239$	11.1479	+	3.27332i	0.721097	+	0.211733i	0.621634	−	0.783308i	$-0.286469\pi$
$239$	11.1479	+	3.27332i	0.721097	+	0.211733i	0.0994635	+	0.995041i	$0.468287\pi$
$240$	0.735351	−	0.848640i	0.0474667	−	0.0547795i
$241$	−6.92327	−	4.44932i	−0.445967	−	0.286606i	0.298319	−	0.954466i	$-0.403574\pi$
$241$	−6.92327	−	4.44932i	−0.445967	−	0.286606i	−0.744287	+	0.667860i	$0.767210\pi$
$242$	−6.33038	−	4.06829i	−0.406932	−	0.261520i
$243$	−10.0127	+	11.5552i	−0.642312	+	0.741268i
$244$	1.56143	+	0.458478i	0.0999605	+	0.0293511i
$245$	−0.0743083	−	0.516825i	−0.00474738	−	0.0330188i
$246$	−8.83157	−	10.1922i	−0.563081	−	0.649830i
$247$	0.259777	+	0.568831i	0.0165292	+	0.0361939i
$248$	−6.55237	+	1.92395i	−0.416076	+	0.122171i
$249$	1.70361	−	3.73038i	0.107962	−	0.236403i
$250$	0.722824	−	5.02735i	0.0457154	−	0.317958i
$251$	−4.83407	+	3.10667i	−0.305124	+	0.196091i	−0.684238	−	0.729259i	$-0.739865\pi$
$251$	−4.83407	+	3.10667i	−0.305124	+	0.196091i	0.379114	+	0.925350i	$0.376229\pi$
$252$	1.62506			0.102369
$253$	−0.753954	−	8.90830i	−0.0474007	−	0.560060i
$254$	−5.78048			−0.362699
$255$	−1.65069	+	1.06083i	−0.103370	+	0.0664319i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−11.8257	+	25.8947i	−0.737668	+	1.61527i	0.0496837	+	0.998765i	$0.484179\pi$
$257$	−11.8257	+	25.8947i	−0.737668	+	1.61527i	−0.787352	+	0.616504i	$0.788549\pi$
$258$	6.98331	−	2.05049i	0.434762	−	0.127658i
$259$	−3.12197	−	6.83616i	−0.193990	−	0.424778i
$260$	1.03328	+	1.19247i	0.0640815	+	0.0739540i
$261$	−1.52265	−	10.5903i	−0.0942497	−	0.655521i
$262$	9.12798	+	2.68022i	0.563928	+	0.165584i
$263$	0.277459	−	0.320205i	0.0171089	−	0.0197447i	−0.747131	−	0.664677i	$-0.768569\pi$
$263$	0.277459	−	0.320205i	0.0171089	−	0.0197447i	0.764240	+	0.644933i	$0.223115\pi$
$264$	3.37261	+	2.16745i	0.207570	+	0.133397i
$265$	−0.999471	−	0.642321i	−0.0613970	−	0.0394575i
$266$	0.135514	−	0.156391i	0.00830887	−	0.00958895i
$267$	37.4529	+	10.9972i	2.29208	+	0.673015i
$268$	0.0471039	+	0.327615i	0.00287733	+	0.0200123i
$269$	5.29298	+	6.10843i	0.322719	+	0.372437i	0.893807	−	0.448451i	$-0.148024\pi$
$269$	5.29298	+	6.10843i	0.322719	+	0.372437i	−0.571089	+	0.820888i	$0.693479\pi$
$270$	0.641374	+	1.40441i	0.0390328	+	0.0854698i
$271$	21.5084	−	6.31543i	1.30654	−	0.383635i	0.446923	−	0.894573i	$-0.352520\pi$
$271$	21.5084	−	6.31543i	1.30654	−	0.383635i	0.859618	+	0.510938i	$0.170702\pi$
$272$	0.725896	−	1.58949i	0.0440139	−	0.0963770i
$273$	−0.924896	+	6.43279i	−0.0559772	+	0.389330i
$274$	13.1082	−	8.42414i	0.791896	−	0.508921i
$275$	8.81253			0.531416
$276$	−0.869806	−	10.2772i	−0.0523562	−	0.618612i
$277$	28.3907			1.70583			0.852916	−	0.522048i	$-0.174832\pi$
$277$	28.3907			1.70583			0.852916	+	0.522048i	$0.174832\pi$
$278$	−10.4823	+	6.73655i	−0.628685	+	0.404031i
$279$	−1.57934	+	10.9846i	−0.0945528	+	0.657629i
$280$	0.216905	−	0.474955i	0.0129625	−	0.0283840i
$281$	−14.0196	+	4.11653i	−0.836340	+	0.245571i	−0.671738	−	0.740789i	$-0.734452\pi$
$281$	−14.0196	+	4.11653i	−0.836340	+	0.245571i	−0.164601	+	0.986360i	$0.552634\pi$
$282$	−0.413201	−	0.904785i	−0.0246058	−	0.0538792i
$283$	−11.6714	−	13.4695i	−0.693791	−	0.800678i	0.294108	−	0.955772i	$-0.404977\pi$
$283$	−11.6714	−	13.4695i	−0.693791	−	0.800678i	−0.987900	+	0.155094i	$0.950432\pi$
$284$	0.386727	+	2.68975i	0.0229480	+	0.159607i
$285$	−0.222957	−	0.0654661i	−0.0132068	−	0.00387788i
$286$	−3.68904	+	4.25738i	−0.218138	+	0.251744i
$287$	−5.27542	−	3.39031i	−0.311398	−	0.200124i
$288$	1.36709	+	0.878575i	0.0805565	+	0.0517705i
$289$	9.13308	−	10.5401i	0.537240	−	0.620008i
$290$	−3.29844	−	0.968510i	−0.193691	−	0.0568729i
$291$	3.79590	+	26.4011i	0.222520	+	1.54766i
$292$	0.883583	+	1.01971i	0.0517078	+	0.0596740i
$293$	11.3561	+	24.8664i	0.663432	+	1.45271i	0.879289	+	0.476288i	$0.158018\pi$
$293$	11.3561	+	24.8664i	0.663432	+	1.45271i	−0.215858	+	0.976425i	$0.569255\pi$
$294$	2.06348	−	0.605893i	0.120345	−	0.0353364i
$295$	−1.89167	+	4.14218i	−0.110137	+	0.241167i
$296$	1.06954	−	7.43881i	0.0621657	−	0.432372i
$297$	−4.63714	+	2.98011i	−0.269074	+	0.172923i
$298$	−19.2840			−1.11709
$299$	14.4680	+	0.845397i	0.836704	+	0.0488906i
$300$	10.1667			0.586972
$301$	2.84700	−	1.82966i	0.164099	−	0.105460i
$302$	1.33746	−	9.30225i	0.0769622	−	0.535284i
$303$	−6.26118	+	13.7101i	−0.359695	+	0.787623i
$304$	0.198553	−	0.0583003i	0.0113878	−	0.00334375i
$305$	−0.352980	−	0.772919i	−0.0202116	−	0.0442572i
$306$	−1.85956	−	2.14605i	−0.106304	−	0.122681i
$307$	4.73405	+	32.9260i	0.270186	+	1.87919i	0.446397	+	0.894835i	$0.352707\pi$
$307$	4.73405	+	32.9260i	0.270186	+	1.87919i	−0.176211	+	0.984353i	$0.556384\pi$
$308$	1.78864	+	0.525192i	0.101917	+	0.0299256i
$309$	−9.41379	+	10.8641i	−0.535532	+	0.618037i
$310$	2.99965	+	1.92776i	0.170369	+	0.109489i
$311$	−26.0507	−	16.7417i	−1.47720	−	0.949337i	−0.997408	−	0.0719533i	$-0.977077\pi$
$311$	−26.0507	−	16.7417i	−1.47720	−	0.949337i	−0.479789	−	0.877384i	$-0.659287\pi$
$312$	−4.25590	+	4.91157i	−0.240943	+	0.278063i
$313$	6.36899	+	1.87010i	0.359996	+	0.105704i	0.456729	−	0.889606i	$-0.349021\pi$
$313$	6.36899	+	1.87010i	0.359996	+	0.105704i	−0.0967325	+	0.995310i	$0.530839\pi$
$314$	−0.0828285	−	0.576085i	−0.00467428	−	0.0325103i
$315$	−0.555655	−	0.641261i	−0.0313076	−	0.0361309i
$316$	−0.466505	−	1.02150i	−0.0262430	−	0.0574641i
$317$	16.6614	−	4.89224i	0.935799	−	0.274776i	0.221937	−	0.975061i	$-0.428762\pi$
$317$	16.6614	−	4.89224i	0.935799	−	0.274776i	0.713863	+	0.700286i	$0.246944\pi$
$318$	2.03281	−	4.45124i	0.113994	−	0.249613i
$319$	1.74667	−	12.1484i	0.0977949	−	0.680178i
$320$	0.439252	−	0.282290i	0.0245549	−	0.0157805i
$321$	26.4515			1.47638
$322$	−1.73439	−	4.47123i	−0.0966540	−	0.249172i
$323$	−0.361598			−0.0201198
$324$	−9.45094	+	6.07375i	−0.525052	+	0.337431i
$325$	−2.03308	+	14.1404i	−0.112775	+	0.784366i
$326$	−4.90654	+	10.7438i	−0.271748	+	0.595045i
$327$	5.73160	−	1.68295i	0.316958	−	0.0930674i
$328$	−2.60503	−	5.70422i	−0.143839	−	0.314963i
$329$	−0.302879	−	0.349542i	−0.0166983	−	0.0192708i
$330$	−0.297904	−	2.07197i	−0.0163991	−	0.114058i
$331$	13.1146	+	3.85078i	0.720841	+	0.211658i	0.621521	−	0.783398i	$-0.286515\pi$
$331$	13.1146	+	3.85078i	0.720841	+	0.211658i	0.0993201	+	0.995056i	$0.468333\pi$
$332$	1.24876	−	1.44114i	0.0685344	−	0.0790929i
$333$	−10.2741	−	6.60276i	−0.563017	−	0.361829i
$334$	2.81919	+	1.81178i	0.154259	+	0.0991362i
$335$	0.113173	−	0.130609i	0.00618330	−	0.00713591i
$336$	2.06348	+	0.605893i	0.112572	+	0.0330542i
$337$	−3.06900	−	21.3454i	−0.167179	−	1.16276i	−0.884680	−	0.466198i	$-0.845623\pi$
$337$	−3.06900	−	21.3454i	−0.167179	−	1.16276i	0.717501	−	0.696557i	$-0.245286\pi$
$338$	2.53298	+	2.92321i	0.137776	+	0.159002i
$339$	17.5678	+	38.4682i	0.954154	+	2.08930i
$340$	−0.875429	+	0.257049i	−0.0474768	+	0.0139404i
$341$	−5.28834	+	11.5799i	−0.286380	+	0.627084i
$342$	0.0478579	−	0.332859i	0.00258786	−	0.0179990i
$343$	0.841254	−	0.540641i	0.0454234	−	0.0291919i
$344$	3.38424			0.182466
$345$	−3.75802	+	3.85729i	−0.202325	+	0.207669i
$346$	−3.28486			−0.176595
$347$	−11.5921	+	7.44981i	−0.622298	+	0.399927i	−0.813451	−	0.581634i	$-0.802414\pi$
$347$	−11.5921	+	7.44981i	−0.622298	+	0.399927i	0.191153	+	0.981560i	$0.438777\pi$
$348$	2.01507	−	14.0151i	0.108019	−	0.751288i
$349$	−1.06227	+	2.32605i	−0.0568621	+	0.124511i	−0.935930	−	0.352186i	$-0.885439\pi$
$349$	−1.06227	+	2.32605i	−0.0568621	+	0.124511i	0.879068	+	0.476696i	$0.158166\pi$
$350$	4.53588	−	1.33185i	0.242453	−	0.0711906i
$351$	−3.71200	−	8.12815i	−0.198132	−	0.433848i
$352$	1.22076	+	1.40883i	0.0650667	+	0.0750910i
$353$	1.23980	+	8.62302i	0.0659881	+	0.458957i	0.995847	+	0.0910411i	$0.0290195\pi$
$353$	1.23980	+	8.62302i	0.0659881	+	0.458957i	−0.929859	+	0.367916i	$0.880071\pi$
$354$	−17.9960	−	5.28411i	−0.956478	−	0.280847i
$355$	0.929159	−	1.07231i	0.0493147	−	0.0569121i
$356$	15.2690	+	9.81282i	0.809257	+	0.520078i
$357$	−3.16139	−	2.03170i	−0.167318	−	0.107529i
$358$	10.8924	−	12.5705i	0.575680	−	0.664370i
$359$	27.8397	+	8.17447i	1.46932	+	0.431432i	0.915879	−	0.401455i	$-0.131495\pi$
$359$	27.8397	+	8.17447i	1.46932	+	0.431432i	0.553443	+	0.832887i	$0.313314\pi$
$360$	−0.120755	−	0.839873i	−0.00636437	−	0.0442652i
$361$	12.4143	+	14.3269i	0.653385	+	0.754046i
$362$	−5.33552	−	11.6832i	−0.280429	−	0.614053i
$363$	−15.5276	+	4.55931i	−0.814986	+	0.239302i
$364$	−1.25535	+	2.74884i	−0.0657984	+	0.144078i
$365$	0.100262	−	0.697336i	0.00524794	−	0.0365002i
$366$	2.94420	−	1.89212i	0.153896	−	0.0989028i
$367$	−36.1411			−1.88655			−0.943274	−	0.332014i	$-0.892272\pi$
$367$	−36.1411			−1.88655			−0.943274	+	0.332014i	$0.892272\pi$
$368$	0.958263	−	4.69912i	0.0499529	−	0.244959i
$369$	−10.1906			−0.530502
$370$	−3.30111	+	2.12150i	−0.171617	+	0.110291i
$371$	0.323822	−	2.25223i	0.0168120	−	0.116930i
$372$	−6.10095	+	13.3592i	−0.316319	+	0.692643i
$373$	18.4503	−	5.41749i	0.955319	−	0.280507i	0.233319	−	0.972400i	$-0.425041\pi$
$373$	18.4503	−	5.41749i	0.955319	−	0.280507i	0.722000	+	0.691893i	$0.243223\pi$
$374$	−1.35318	−	2.96305i	−0.0699712	−	0.153216i
$375$	−7.15303	−	8.25504i	−0.369381	−	0.426288i
$376$	−0.0658220	−	0.457802i	−0.00339451	−	0.0236093i
$377$	19.0900	+	5.60533i	0.983185	+	0.288689i
$378$	−1.93638	+	2.23470i	−0.0995967	+	0.114941i
$379$	5.98198	+	3.84439i	0.307274	+	0.197473i	0.685185	−	0.728369i	$-0.259721\pi$
$379$	5.98198	+	3.84439i	0.307274	+	0.197473i	−0.377911	+	0.925842i	$0.623358\pi$
$380$	−0.0908966	−	0.0584157i	−0.00466290	−	0.00299666i
$381$	−8.14088	+	9.39508i	−0.417070	+	0.481324i
$382$	−3.88557	−	1.14091i	−0.198803	−	0.0583738i
$383$	1.80732	+	12.5702i	0.0923495	+	0.642305i	0.982448	+	0.186537i	$0.0597264\pi$
$383$	1.80732	+	12.5702i	0.0923495	+	0.642305i	−0.890098	+	0.455768i	$0.849365\pi$
$384$	1.40834	+	1.62531i	0.0718691	+	0.0829413i
$385$	−0.404343	−	0.885388i	−0.0206072	−	0.0451236i
$386$	−25.1573	+	7.38685i	−1.28047	+	0.375981i
$387$	2.28461	−	5.00261i	0.116133	−	0.254297i
$388$	−1.76505	+	12.2762i	−0.0896067	+	0.623228i
$389$	20.5919	−	13.2336i	1.04405	−	0.670972i	0.0980672	−	0.995180i	$-0.468734\pi$
$389$	20.5919	−	13.2336i	1.04405	−	0.670972i	0.945986	+	0.324208i	$0.105098\pi$
$390$	3.39336			0.171829
$391$	−3.92001	+	7.40687i	−0.198244	+	0.374582i
$392$	1.00000			0.0505076
$393$	17.2115	−	11.0611i	0.868205	−	0.557961i
$394$	0.532918	−	3.70652i	0.0268480	−	0.186732i
$395$	−0.243581	+	0.533368i	−0.0122559	+	0.0268366i
$396$	2.90665	−	0.853469i	0.146065	−	0.0428884i
$397$	5.93369	+	12.9930i	0.297804	+	0.652099i	0.998091	−	0.0617623i	$-0.0196721\pi$
$397$	5.93369	+	12.9930i	0.297804	+	0.652099i	−0.700287	+	0.713861i	$0.746945\pi$
$398$	−6.23897	−	7.20015i	−0.312731	−	0.360911i
$399$	−0.0633349	−	0.440504i	−0.00317071	−	0.0220528i
$400$	4.53588	+	1.33185i	0.226794	+	0.0665927i
$401$	10.4556	−	12.0663i	0.522125	−	0.602565i	−0.432036	−	0.901856i	$-0.642205\pi$
$401$	10.4556	−	12.0663i	0.522125	−	0.602565i	0.954162	+	0.299291i	$0.0967503\pi$
$402$	0.598815	+	0.384835i	0.0298662	+	0.0191938i
$403$	−17.3607	−	11.1570i	−0.864798	−	0.555772i
$404$	−4.58949	+	5.29655i	−0.228336	+	0.263513i
$405$	5.62830	+	1.65262i	0.279672	+	0.0821192i
$406$	−0.936980	−	6.51684i	−0.0465015	−	0.323425i
$407$	−9.17438	−	10.5878i	−0.454757	−	0.524818i
$408$	−1.56111	−	3.41835i	−0.0772864	−	0.169234i
$409$	16.9167	−	4.96720i	0.836479	−	0.245612i	0.164681	−	0.986347i	$-0.447341\pi$
$409$	16.9167	−	4.96720i	0.836479	−	0.245612i	0.671798	+	0.740734i	$0.265522\pi$
$410$	−1.36019	+	2.97840i	−0.0671750	+	0.147093i
$411$	4.76898	−	33.1690i	0.235236	−	1.63611i
$412$	−5.62320	+	3.61381i	−0.277035	+	0.178040i
$413$	−8.72120			−0.429142
$414$	−6.29938	−	4.58877i	−0.309598	−	0.225526i
$415$	−0.995670			−0.0488755
$416$	−2.54221	+	1.63378i	−0.124642	+	0.0801025i
$417$	−3.81362	+	26.5243i	−0.186754	+	1.29890i
$418$	0.160250	−	0.350898i	0.00783807	−	0.0171630i
$419$	−21.1743	+	6.21734i	−1.03443	+	0.303737i	−0.754512	−	0.656286i	$-0.772127\pi$
$419$	−21.1743	+	6.21734i	−1.03443	+	0.303737i	−0.279921	+	0.960023i	$0.590308\pi$
$420$	−0.466474	−	1.02144i	−0.0227616	−	0.0498410i
$421$	−13.5368	−	15.6223i	−0.659741	−	0.761382i	0.322994	−	0.946401i	$-0.395311\pi$
$421$	−13.5368	−	15.6223i	−0.659741	−	0.761382i	−0.982735	+	0.185019i	$0.940765\pi$
$422$	1.19642	+	8.32131i	0.0582410	+	0.405075i
$423$	−0.721161	−	0.211752i	−0.0350641	−	0.0102957i
$424$	1.49007	−	1.71963i	0.0723640	−	0.0835125i
$425$	−6.94926	−	4.46602i	−0.337089	−	0.216634i
$426$	4.91632	+	3.15953i	0.238196	+	0.153080i
$427$	1.06569	−	1.22987i	0.0515723	−	0.0595176i
$428$	11.8014	+	3.46520i	0.570442	+	0.167497i
$429$	1.72414	+	11.9917i	0.0832425	+	0.578964i
$430$	−1.15717	−	1.33544i	−0.0558036	−	0.0644008i
$431$	−11.3176	−	24.7821i	−0.545151	−	1.19371i	−0.959010	−	0.283373i	$-0.908547\pi$
$431$	−11.3176	−	24.7821i	−0.545151	−	1.19371i	0.413859	−	0.910341i	$-0.364181\pi$
$432$	−2.83716	+	0.833065i	−0.136503	+	0.0400809i
$433$	0.441140	−	0.965962i	0.0211998	−	0.0464212i	−0.898736	−	0.438490i	$-0.855513\pi$
$433$	0.441140	−	0.965962i	0.0211998	−	0.0464212i	0.919936	+	0.392069i	$0.128241\pi$
$434$	−0.971867	+	6.75948i	−0.0466511	+	0.324465i
$435$	−6.21946	+	3.99700i	−0.298200	+	0.191642i
$436$	2.77764			0.133025
$437$	−0.966913	+	0.223576i	−0.0462537	+	0.0106951i
$438$	2.90173			0.138650
$439$	1.53197	−	0.984539i	0.0731171	−	0.0469895i	−0.503572	−	0.863954i	$-0.667981\pi$
$439$	1.53197	−	0.984539i	0.0731171	−	0.0469895i	0.576689	+	0.816964i	$0.304345\pi$
$440$	0.138522	−	0.963440i	0.00660377	−	0.0459302i
$441$	0.675075	−	1.47821i	0.0321464	−	0.0703909i
$442$	5.06661	−	1.48769i	0.240994	−	0.0707623i
$443$	−11.8767	−	26.0063i	−0.564279	−	1.23560i	−0.949788	−	0.312894i	$-0.898701\pi$
$443$	−11.8767	−	26.0063i	−0.564279	−	1.23560i	0.385509	−	0.922704i	$-0.374026\pi$
$444$	−10.5841	−	12.2147i	−0.502300	−	0.579685i
$445$	−1.34872	−	9.38055i	−0.0639355	−	0.444681i
$446$	−23.4386	−	6.88220i	−1.10985	−	0.325881i
$447$	−27.1584	+	31.3425i	−1.28455	+	1.48245i
$448$	0.841254	+	0.540641i	0.0397455	+	0.0255429i
$449$	−5.35279	−	3.44003i	−0.252614	−	0.162345i	0.408206	−	0.912890i	$-0.366155\pi$
$449$	−5.35279	−	3.44003i	−0.252614	−	0.162345i	−0.660819	+	0.750545i	$0.729791\pi$
$450$	5.03081	−	5.80587i	0.237155	−	0.273691i
$451$	−11.2164	−	3.29343i	−0.528159	−	0.155082i
$452$	2.79851	+	19.4641i	0.131631	+	0.915514i
$453$	−13.2354	−	15.2745i	−0.621856	−	0.717660i
$454$	3.62399	+	7.93544i	0.170082	+	0.372429i
$455$	1.51395	−	0.444537i	0.0709752	−	0.0208402i
$456$	0.184874	−	0.404817i	0.00865750	−	0.0189573i
$457$	4.58013	−	31.8555i	0.214250	−	1.49014i	−0.544502	−	0.838759i	$-0.683281\pi$
$457$	4.58013	−	31.8555i	0.214250	−	1.49014i	0.758752	−	0.651380i	$-0.225809\pi$
$458$	15.6278	−	10.0434i	0.730241	−	0.469297i
$459$	5.16695			0.241172
$460$	−2.18196	+	1.22863i	−0.101735	+	0.0572851i
$461$	−11.1262			−0.518199			−0.259100	−	0.965851i	$-0.583426\pi$
$461$	−11.1262			−0.518199			−0.259100	+	0.965851i	$0.583426\pi$
$462$	3.37261	−	2.16745i	0.156908	−	0.100839i
$463$	2.57527	−	17.9114i	0.119683	−	0.832412i	−0.838223	−	0.545328i	$-0.816405\pi$
$463$	2.57527	−	17.9114i	0.119683	−	0.832412i	0.957905	−	0.287084i	$-0.0926858\pi$
$464$	2.73503	−	5.98888i	0.126971	−	0.278027i
$465$	7.35773	−	2.16042i	0.341207	−	0.100187i
$466$	4.05955	+	8.88917i	0.188055	+	0.411783i
$467$	−15.4111	−	17.7854i	−0.713141	−	0.823009i	0.277324	−	0.960777i	$-0.410553\pi$
$467$	−15.4111	−	17.7854i	−0.713141	−	0.823009i	−0.990465	+	0.137768i	$0.956007\pi$
$468$	0.698882	+	4.86083i	0.0323058	+	0.224692i
$469$	0.317577	+	0.0932489i	0.0146643	+	0.00430584i
$470$	−0.158145	+	0.182510i	−0.00729471	+	0.00841854i
$471$	−1.05297	−	0.676702i	−0.0485182	−	0.0311808i
$472$	−7.33674	−	4.71504i	−0.337701	−	0.217027i
$473$	4.13134	−	4.76782i	0.189959	−	0.219225i
$474$	−2.31726	−	0.680409i	−0.106435	−	0.0312522i
$475$	−0.139221	−	0.968301i	−0.00638788	−	0.0444287i
$476$	−1.14430	−	1.32060i	−0.0524490	−	0.0605294i
$477$	−1.53606	−	3.36350i	−0.0703314	−	0.154004i
$478$	11.1479	−	3.27332i	0.509893	−	0.149718i
$479$	16.5861	−	36.3185i	0.757839	−	1.65944i	0.00609577	−	0.999981i	$-0.498060\pi$
$479$	16.5861	−	36.3185i	0.757839	−	1.65944i	0.751744	−	0.659455i	$-0.229213\pi$
$480$	0.159807	−	1.11148i	0.00729416	−	0.0507320i
$481$	19.1055	−	12.2783i	0.871134	−	0.559844i
$482$	−8.22971			−0.374853
$483$	−9.70976	−	3.47808i	−0.441809	−	0.158258i
$484$	−7.52494			−0.342043
$485$	5.44778	−	3.50108i	0.247371	−	0.158976i
$486$	−2.17596	+	15.1341i	−0.0987035	+	0.686498i
$487$	−17.1051	+	37.4550i	−0.775108	+	1.69725i	−0.0600394	+	0.998196i	$0.519123\pi$
$487$	−17.1051	+	37.4550i	−0.775108	+	1.69725i	−0.715069	+	0.699054i	$0.753605\pi$
$488$	1.56143	−	0.458478i	0.0706828	−	0.0207543i
$489$	10.5520	+	23.1056i	0.477177	+	1.04487i
$490$	−0.341929	−	0.394607i	−0.0154468	−	0.0178265i
$491$	2.99119	+	20.8042i	0.134991	+	0.938880i	0.938915	+	0.344149i	$0.111832\pi$
$491$	2.99119	+	20.8042i	0.134991	+	0.938880i	−0.803925	+	0.594731i	$0.797258\pi$
$492$	−12.9399	−	3.79950i	−0.583376	−	0.171295i
$493$	−7.53392	+	8.69461i	−0.339311	+	0.391586i
$494$	0.526071	+	0.338086i	0.0236691	+	0.0152112i
$495$	−1.33065	−	0.855158i	−0.0598084	−	0.0384365i
$496$	−4.47204	+	5.16101i	−0.200800	+	0.231736i
$497$	2.60733	+	0.765581i	0.116955	+	0.0343410i
$498$	−0.583630	−	4.05924i	−0.0261531	−	0.181899i
$499$	3.12816	+	3.61009i	0.140036	+	0.161610i	0.821435	−	0.570302i	$-0.193174\pi$
$499$	3.12816	+	3.61009i	0.140036	+	0.161610i	−0.681400	+	0.731912i	$0.738628\pi$
$500$	−2.10991	−	4.62006i	−0.0943582	−	0.206616i
$501$	6.91508	−	2.03045i	0.308943	−	0.0907139i
$502$	−2.38709	+	5.22699i	−0.106541	+	0.233292i
$503$	3.09083	−	21.4972i	0.137813	−	0.958513i	−0.797153	−	0.603777i	$-0.793662\pi$
$503$	3.09083	−	21.4972i	0.137813	−	0.958513i	0.934966	−	0.354736i	$-0.115429\pi$
$504$	1.36709	−	0.878575i	0.0608950	−	0.0391348i
$505$	3.65934			0.162838
$506$	−5.45046	−	7.08652i	−0.242302	−	0.315034i
$507$	8.31843			0.369434
$508$	−4.86285	+	3.12516i	−0.215754	+	0.138657i
$509$	0.0468588	−	0.325910i	0.00207698	−	0.0144457i	−0.988757	−	0.149534i	$-0.952223\pi$
$509$	0.0468588	−	0.325910i	0.00207698	−	0.0144457i	0.990834	+	0.135088i	$0.0431318\pi$
$510$	−0.815117	+	1.78486i	−0.0360940	+	0.0790348i
$511$	1.29461	−	0.380133i	0.0572703	−	0.0168161i
$512$	0.415415	+	0.909632i	0.0183589	+	0.0402004i
$513$	0.400705	+	0.462438i	0.0176916	+	0.0204172i
$514$	4.05131	+	28.1775i	0.178696	+	1.24286i
$515$	3.34877	+	0.983288i	0.147565	+	0.0433288i
$516$	4.76616	−	5.50044i	0.209819	−	0.242143i
$517$	−0.725319	−	0.466134i	−0.0318995	−	0.0205005i
$518$	−6.32228	−	4.06308i	−0.277785	−	0.178522i
$519$	−4.62620	+	5.33891i	−0.203067	+	0.234352i
$520$	1.51395	+	0.444537i	0.0663912	+	0.0194942i
$521$	−4.40601	−	30.6445i	−0.193031	−	1.34256i	−0.823929	−	0.566694i	$-0.808222\pi$
$521$	−4.40601	−	30.6445i	−0.193031	−	1.34256i	0.630898	−	0.775866i	$-0.282687\pi$
$522$	−7.00646	−	8.08589i	−0.306665	−	0.353910i
$523$	−14.7192	−	32.2305i	−0.643624	−	1.40934i	−0.897025	−	0.441979i	$-0.854277\pi$
$523$	−14.7192	−	32.2305i	−0.643624	−	1.40934i	0.253401	−	0.967361i	$-0.418451\pi$
$524$	9.12798	−	2.68022i	0.398757	−	0.117086i
$525$	4.22338	−	9.24792i	0.184324	−	0.403612i
$526$	0.0602976	−	0.419379i	0.00262910	−	0.0182858i
$527$	10.0387	−	6.45145i	0.437291	−	0.281030i
$528$	4.00903			0.174471
$529$	−5.90244	+	22.2297i	−0.256628	+	0.966510i
$530$	−1.18807			−0.0516066
$531$	−11.9227	+	7.66222i	−0.517399	+	0.332512i
$532$	0.0294499	−	0.204829i	0.00127682	−	0.00888045i
$533$	7.87220	−	17.2377i	0.340983	−	0.746649i
$534$	37.4529	−	10.9972i	1.62075	−	0.475894i
$535$	−2.66785	−	5.84177i	−0.115341	−	0.252562i
$536$	0.216748	+	0.250141i	0.00936210	+	0.0108044i
$537$	−5.09076	−	35.4070i	−0.219683	−	1.52793i
$538$	7.75521	+	2.27713i	0.334351	+	0.0981742i
$539$	1.22076	−	1.40883i	0.0525818	−	0.0606827i
$540$	1.29884	+	0.834714i	0.0558932	+	0.0359204i
$541$	−6.87852	−	4.42056i	−0.295731	−	0.190055i	0.384359	−	0.923184i	$-0.374423\pi$
$541$	−6.87852	−	4.42056i	−0.295731	−	0.190055i	−0.680089	+	0.733129i	$0.738059\pi$
$542$	14.6796	−	16.9412i	0.630543	−	0.727686i
$543$	−26.5030	−	7.78199i	−1.13735	−	0.333957i
$544$	−0.248681	−	1.72961i	−0.0106621	−	0.0741565i
$545$	−0.949755	−	1.09608i	−0.0406830	−	0.0469507i
$546$	2.69976	+	5.91164i	0.115539	+	0.252995i
$547$	37.2187	−	10.9284i	1.59136	−	0.467265i	0.638233	−	0.769843i	$-0.279665\pi$
$547$	37.2187	−	10.9284i	1.59136	−	0.467265i	0.953125	+	0.302578i	$0.0978473\pi$
$548$	6.47290	−	14.1737i	0.276509	−	0.605469i
$549$	0.376358	−	2.61763i	0.0160626	−	0.111718i
$550$	7.41357	−	4.76441i	0.316116	−	0.203155i
$551$	−1.36243			−0.0580415
$552$	−6.28798	−	8.17544i	−0.267634	−	0.347970i
$553$	−1.12299			−0.0477542
$554$	23.8838	−	15.3492i	1.01472	−	0.652124i
$555$	−1.20100	+	8.35313i	−0.0509795	+	0.354570i
$556$	−5.17620	+	11.3343i	−0.219520	+	0.480681i
$557$	22.6859	−	6.66117i	0.961231	−	0.282243i	0.236776	−	0.971564i	$-0.423909\pi$
$557$	22.6859	−	6.66117i	0.961231	−	0.282243i	0.724456	+	0.689321i	$0.242091\pi$
$558$	4.61008	+	10.0947i	0.195160	+	0.427341i
$559$	6.69721	+	7.72899i	0.283262	+	0.326901i
$560$	−0.0743083	−	0.516825i	−0.00314010	−	0.0218399i
$561$	−6.72161	−	1.97364i	−0.283787	−	0.0833273i
$562$	−9.56848	+	11.0426i	−0.403622	+	0.465805i
$563$	16.1969	+	10.4091i	0.682619	+	0.438693i	0.835455	−	0.549559i	$-0.185204\pi$
$563$	16.1969	+	10.4091i	0.682619	+	0.438693i	−0.152836	+	0.988252i	$0.548841\pi$
$564$	−0.836771	−	0.537760i	−0.0352344	−	0.0226438i
$565$	6.72377	−	7.75965i	0.282871	−	0.326451i
$566$	−17.1007	−	5.02123i	−0.718798	−	0.211058i
$567$	1.59882	+	11.1200i	0.0671440	+	0.466997i
$568$	1.77952	+	2.05368i	0.0746671	+	0.0861704i
$569$	−9.63197	−	21.0911i	−0.403793	−	0.884184i	−0.996872	−	0.0790391i	$-0.974815\pi$
$569$	−9.63197	−	21.0911i	−0.403793	−	0.884184i	0.593078	−	0.805145i	$-0.297912\pi$
$570$	−0.222957	+	0.0654661i	−0.00933865	+	0.00274207i
$571$	−12.9117	+	28.2726i	−0.540336	+	1.18317i	0.420814	+	0.907147i	$0.361744\pi$
$571$	−12.9117	+	28.2726i	−0.540336	+	1.18317i	−0.961151	+	0.276025i	$0.910983\pi$
$572$	−0.801706	+	5.57599i	−0.0335210	+	0.233144i
$573$	−7.32653	+	4.70847i	−0.306070	+	0.196699i
$574$	−6.27091			−0.261743
$575$	−21.3437	−	7.64540i	−0.890093	−	0.318835i
$576$	1.62506			0.0677109
$577$	27.8544	−	17.9009i	1.15959	−	0.745226i	0.188067	−	0.982156i	$-0.439778\pi$
$577$	27.8544	−	17.9009i	1.15959	−	0.745226i	0.971527	+	0.236930i	$0.0761413\pi$
$578$	1.98481	−	13.8046i	0.0825571	−	0.574197i
$579$	−23.4241	+	51.2917i	−0.973473	+	2.13161i
$580$	−3.29844	+	0.968510i	−0.136960	+	0.0402152i
$581$	−0.792156	−	1.73458i	−0.0328642	−	0.0719625i
$582$	17.4668	+	20.1578i	0.724023	+	0.835567i
$583$	−0.603654	−	4.19850i	−0.0250008	−	0.173884i
$584$	1.29461	+	0.380133i	0.0535715	+	0.0157300i
$585$	1.67915	−	1.93784i	0.0694243	−	0.0801199i
$586$	22.9972	+	14.7794i	0.950005	+	0.610531i
$587$	−26.9970	−	17.3499i	−1.11429	−	0.716109i	−0.152064	−	0.988371i	$-0.548592\pi$
$587$	−26.9970	−	17.3499i	−1.11429	−	0.716109i	−0.962223	+	0.272262i	$0.912228\pi$
$588$	1.40834	−	1.62531i	0.0580790	−	0.0670267i
$589$	1.35591	+	0.398132i	0.0558695	+	0.0164048i
$590$	0.648057	+	4.50734i	0.0266801	+	0.185564i
$591$	−5.27373	−	6.08620i	−0.216932	−	0.250353i
$592$	−3.12197	−	6.83616i	−0.128312	−	0.280965i
$593$	−8.50316	+	2.49675i	−0.349183	+	0.102529i	−0.451621	−	0.892210i	$-0.649154\pi$
$593$	−8.50316	+	2.49675i	−0.349183	+	0.102529i	0.102438	+	0.994739i	$0.467336\pi$
$594$	−2.28984	+	5.01405i	−0.0939533	+	0.205729i
$595$	−0.129846	+	0.903100i	−0.00532317	+	0.0370235i
$596$	−16.2227	+	10.4257i	−0.664508	+	0.427054i
$597$	−20.4891			−0.838562
$598$	12.6283	−	7.11078i	0.516409	−	0.290781i
$599$	19.2974			0.788470			0.394235	−	0.919010i	$-0.371010\pi$
$599$	19.2974			0.788470			0.394235	+	0.919010i	$0.371010\pi$
$600$	8.55274	−	5.49651i	0.349164	−	0.224394i
$601$	−4.21089	+	29.2874i	−0.171766	+	1.19466i	0.703386	+	0.710808i	$0.251671\pi$
$601$	−4.21089	+	29.2874i	−0.171766	+	1.19466i	−0.875152	+	0.483849i	$0.839239\pi$
$602$	1.40586	−	3.07841i	0.0572987	−	0.125467i
$603$	0.516082	−	0.151535i	0.0210165	−	0.00617099i
$604$	−3.90403	−	8.54863i	−0.158853	−	0.347839i
$605$	2.57300	+	2.96939i	0.104607	+	0.120723i
$606$	2.14498	+	14.9187i	0.0871341	+	0.606031i
$607$	12.1881	+	3.57875i	0.494700	+	0.145257i	0.519560	−	0.854434i	$-0.326096\pi$
$607$	12.1881	+	3.57875i	0.494700	+	0.145257i	−0.0248602	+	0.999691i	$0.507914\pi$
$608$	0.135514	−	0.156391i	0.00549580	−	0.00634249i
$609$	−11.9115	−	7.65505i	−0.482678	−	0.310198i
$610$	−0.714818	−	0.459386i	−0.0289421	−	0.0186000i
$611$	0.915279	−	1.05629i	0.0370282	−	0.0427329i
$612$	−2.72461	−	0.800016i	−0.110136	−	0.0323387i
$613$	5.10252	+	35.4888i	0.206089	+	1.43338i	0.785761	+	0.618530i	$0.212272\pi$
$613$	5.10252	+	35.4888i	0.206089	+	1.43338i	−0.579672	+	0.814850i	$0.696819\pi$
$614$	21.7837	+	25.1397i	0.879118	+	1.01456i
$615$	2.92522	+	6.40533i	0.117956	+	0.258288i
$616$	1.78864	−	0.525192i	0.0720663	−	0.0211606i
$617$	−14.7571	+	32.3135i	−0.594097	+	1.30089i	0.338837	+	0.940845i	$0.389966\pi$
$617$	−14.7571	+	32.3135i	−0.594097	+	1.30089i	−0.932935	+	0.360046i	$0.882761\pi$
$618$	−2.04581	+	14.2289i	−0.0822946	+	0.572372i
$619$	8.37076	−	5.37956i	0.336449	−	0.216223i	−0.361496	−	0.932374i	$-0.617734\pi$
$619$	8.37076	−	5.37956i	0.336449	−	0.216223i	0.697946	+	0.716151i	$0.254098\pi$
$620$	3.56569			0.143201
$621$	13.8164	−	3.19473i	0.554434	−	0.128200i
$622$	−30.9665			−1.24164
$623$	15.2690	−	9.81282i	0.611741	−	0.393142i
$624$	−0.924896	+	6.43279i	−0.0370255	+	0.257518i
$625$	8.71743	−	19.0885i	0.348697	−	0.763541i
$626$	6.36899	−	1.87010i	0.254556	−	0.0747444i
$627$	−0.344632	−	0.754639i	−0.0137633	−	0.0301374i
$628$	−0.381135	−	0.439853i	−0.0152089	−	0.0175520i
$629$	1.86891	+	12.9986i	0.0745184	+	0.518287i
$630$	−0.814139	−	0.239053i	−0.0324361	−	0.00952409i
$631$	−30.2046	+	34.8580i	−1.20243	+	1.38768i	−0.301637	+	0.953423i	$0.597533\pi$
$631$	−30.2046	+	34.8580i	−1.20243	+	1.38768i	−0.900791	+	0.434253i	$0.857012\pi$
$632$	−0.944716	−	0.607132i	−0.0375788	−	0.0241504i
$633$	15.2097	+	9.77468i	0.604531	+	0.388508i
$634$	11.3715	−	13.1235i	0.451622	−	0.521199i
$635$	2.89596	+	0.850330i	0.114923	+	0.0337443i
$636$	−0.696411	−	4.84364i	−0.0276145	−	0.192063i
$637$	1.97894	+	2.28382i	0.0784085	+	0.0904882i
$638$	−5.09851	−	11.1642i	−0.201852	−	0.441994i
$639$	4.23707	−	1.24412i	0.167616	−	0.0492165i
$640$	0.216905	−	0.474955i	0.00857391	−	0.0187743i
$641$	−0.839642	+	5.83984i	−0.0331638	+	0.230660i	−0.999662	−	0.0260157i	$-0.991718\pi$
$641$	−0.839642	+	5.83984i	−0.0331638	+	0.230660i	0.966498	+	0.256675i	$0.0826271\pi$
$642$	22.2524	−	14.3008i	0.878233	−	0.564406i
$643$	−38.0101			−1.49897			−0.749486	−	0.662020i	$-0.769699\pi$
$643$	−38.0101			−1.49897			−0.749486	+	0.662020i	$0.769699\pi$
$644$	−3.87639	−	2.82375i	−0.152751	−	0.111271i
$645$	−3.80020			−0.149633
$646$	−0.304196	+	0.195495i	−0.0119684	+	0.00769163i
$647$	−4.38688	+	30.5114i	−0.172466	+	1.19953i	0.701187	+	0.712978i	$0.252654\pi$
$647$	−4.38688	+	30.5114i	−0.172466	+	1.19953i	−0.873653	+	0.486550i	$0.838255\pi$
$648$	−4.66692	+	10.2191i	−0.183334	+	0.401445i
$649$	−15.5991	+	4.58030i	−0.612317	+	0.179793i
$650$	5.93452	+	12.9948i	0.232771	+	0.509697i
$651$	9.61754	+	11.0992i	0.376941	+	0.435013i
$652$	1.68091	+	11.6910i	0.0658293	+	0.457853i
$653$	−41.8854	−	12.2987i	−1.63910	−	0.481283i	−0.673042	−	0.739605i	$-0.735013\pi$
$653$	−41.8854	−	12.2987i	−1.63910	−	0.481283i	−0.966059	+	0.258321i	$0.916831\pi$
$654$	3.91186	−	4.51453i	0.152966	−	0.176532i
$655$	−4.17875	−	2.68552i	−0.163277	−	0.104932i
$656$	−5.27542	−	3.39031i	−0.205971	−	0.132369i
$657$	1.43588	−	1.65709i	0.0560189	−	0.0646492i
$658$	−0.443775	−	0.130304i	−0.0173001	−	0.00507978i
$659$	−0.888426	−	6.17914i	−0.0346082	−	0.240705i	0.965173	−	0.261611i	$-0.0842539\pi$
$659$	−0.888426	−	6.17914i	−0.0346082	−	0.240705i	−0.999781	+	0.0209063i	$0.993345\pi$
$660$	−1.37080	−	1.58199i	−0.0533585	−	0.0615790i
$661$	18.5532	+	40.6258i	0.721634	+	1.58016i	0.811600	+	0.584214i	$0.198597\pi$
$661$	18.5532	+	40.6258i	0.721634	+	1.58016i	−0.0899656	+	0.995945i	$0.528676\pi$
$662$	13.1146	−	3.85078i	0.509712	−	0.149665i
$663$	4.71755	−	10.3300i	0.183215	−	0.401184i
$664$	0.271381	−	1.88749i	0.0105316	−	0.0732490i
$665$	−0.0908966	+	0.0584157i	−0.00352482	+	0.00226526i
$666$	−12.2128			−0.473238
$667$	−14.7698	+	27.9076i	−0.571890	+	1.08059i
$668$	3.35117			0.129661
$669$	−44.1953	+	28.4026i	−1.70869	+	1.09811i
$670$	0.0245948	−	0.171061i	0.000950181	−	0.00660866i
$671$	1.26022	−	2.75949i	0.0486501	−	0.106529i
$672$	2.06348	−	0.605893i	0.0796005	−	0.0233728i
$673$	5.92354	+	12.9708i	0.228336	+	0.499986i	0.988773	−	0.149426i	$-0.0477425\pi$
$673$	5.92354	+	12.9708i	0.228336	+	0.499986i	−0.760437	+	0.649412i	$0.775015\pi$
$674$	−14.1220	−	16.2976i	−0.543958	−	0.627761i
$675$	1.98935	+	13.8363i	0.0765702	+	0.532558i
$676$	3.71128	+	1.08973i	0.142742	+	0.0419127i
$677$	−16.1591	+	18.6485i	−0.621043	+	0.716722i	−0.975905	−	0.218197i	$-0.929983\pi$
$677$	−16.1591	+	18.6485i	−0.621043	+	0.716722i	0.354862	+	0.934919i	$0.384528\pi$
$678$	35.5765	+	22.8636i	1.36631	+	0.878072i
$679$	10.4336	+	6.70525i	0.400404	+	0.257324i
$680$	−0.597486	+	0.689536i	−0.0229125	+	0.0264425i
$681$	18.0014	+	5.28568i	0.689815	+	0.202548i
$682$	1.81171	+	12.6007i	0.0693738	+	0.482505i
$683$	4.80319	+	5.54317i	0.183789	+	0.212104i	0.840166	−	0.542329i	$-0.182457\pi$
$683$	4.80319	+	5.54317i	0.183789	+	0.212104i	−0.656377	+	0.754433i	$0.727912\pi$
$684$	−0.139697	−	0.305893i	−0.00534143	−	0.0116961i
$685$	−7.80630	+	2.29214i	−0.298263	+	0.0875780i
$686$	0.415415	−	0.909632i	0.0158606	−	0.0347299i
$687$	5.68566	−	39.5446i	0.216921	−	1.50872i
$688$	2.84700	−	1.82966i	0.108541	−	0.0697550i
$689$	6.87607			0.261957
$690$	−1.07604	+	5.27670i	−0.0409643	+	0.200880i
$691$	2.46128			0.0936315			0.0468157	−	0.998904i	$-0.485093\pi$
$691$	2.46128			0.0936315			0.0468157	+	0.998904i	$0.485093\pi$
$692$	−2.76340	+	1.77593i	−0.105049	+	0.0675106i
$693$	0.431123	−	2.99853i	0.0163770	−	0.113905i
$694$	−5.72425	+	12.5344i	−0.217289	+	0.475798i
$695$	6.24248	−	1.83296i	0.236791	−	0.0695281i
$696$	−5.88195	−	12.8797i	−0.222955	−	0.488203i
$697$	7.17582	+	8.28133i	0.271803	+	0.313678i
$698$	0.363918	+	2.53111i	0.0137745	+	0.0958038i
$699$	20.1649	+	5.92095i	0.762706	+	0.223951i
$700$	3.09577	−	3.57271i	0.117009	−	0.135036i
$701$	−4.06746	−	2.61400i	−0.153626	−	0.0987293i	0.461569	−	0.887104i	$-0.347287\pi$
$701$	−4.06746	−	2.61400i	−0.153626	−	0.0987293i	−0.615195	+	0.788375i	$0.710923\pi$
$702$	−7.51714	−	4.83097i	−0.283716	−	0.182333i
$703$	−1.01843	+	1.17533i	−0.0384107	+	0.0443283i
$704$	1.78864	+	0.525192i	0.0674119	+	0.0197939i
$705$	0.0739123	+	0.514071i	0.00278370	+	0.0193610i
$706$	5.70495	+	6.58386i	0.214708	+	0.247787i
$707$	2.91137	+	6.37501i	0.109493	+	0.239757i
$708$	−17.9960	+	5.28411i	−0.676332	+	0.198589i
$709$	−14.6248	+	32.0238i	−0.549246	+	1.20268i	0.407887	+	0.913032i	$0.366266\pi$
$709$	−14.6248	+	32.0238i	−0.549246	+	1.20268i	−0.957133	+	0.289648i	$0.906462\pi$
$710$	0.201926	−	1.40442i	0.00757813	−	0.0527071i
$711$	−1.53522	+	0.986627i	−0.0575753	+	0.0370014i
$712$	18.1503			0.680213
$713$	22.8544	−	23.4581i	0.855905	−	0.878513i
$714$	−3.75795			−0.140638
$715$	2.47445	−	1.59023i	0.0925392	−	0.0594713i
$716$	2.36714	−	16.4638i	0.0884642	−	0.615282i
$717$	10.3799	−	22.7288i	0.387643	−	0.848821i
$718$	27.8397	−	8.17447i	1.03897	−	0.305068i
$719$	14.0616	+	30.7905i	0.524408	+	1.14829i	0.967744	+	0.251938i	$0.0810677\pi$
$719$	14.0616	+	30.7905i	0.524408	+	1.14829i	−0.443336	+	0.896356i	$0.646205\pi$
$720$	−0.555655	−	0.641261i	−0.0207081	−	0.0238984i
$721$	0.951277	+	6.61628i	0.0354274	+	0.246403i
$722$	18.1893	+	5.34085i	0.676935	+	0.198766i
$723$	−11.5902	+	13.3758i	−0.431045	+	0.497453i
$724$	−10.8049	−	6.94390i	−0.401562	−	0.258068i
$725$	−26.1834	−	16.8271i	−0.972428	−	0.624942i
$726$	−10.5977	+	12.2304i	−0.393317	+	0.453912i
$727$	−13.1428	−	3.85909i	−0.487441	−	0.143126i	0.0287717	−	0.999586i	$-0.490840\pi$
$727$	−13.1428	−	3.85909i	−0.487441	−	0.143126i	−0.516213	+	0.856460i	$0.672659\pi$
$728$	0.430065	+	2.99117i	0.0159393	+	0.110860i
$729$	−0.537641	−	0.620471i	−0.0199126	−	0.0229804i
$730$	−0.292663	−	0.640842i	−0.0108319	−	0.0237186i
$731$	−5.67407	+	1.66606i	−0.209863	+	0.0616214i
$732$	1.45386	−	3.18351i	0.0537362	−	0.117666i
$733$	6.01170	−	41.8123i	0.222047	−	1.54437i	−0.508230	−	0.861222i	$-0.669700\pi$
$733$	6.01170	−	41.8123i	0.222047	−	1.54437i	0.730277	−	0.683151i	$-0.239391\pi$
$734$	−30.4038	+	19.5393i	−1.12222	+	0.721210i
$735$	−1.12291			−0.0414192
$736$	−1.73439	−	4.47123i	−0.0639306	−	0.164812i
$737$	0.617004			0.0227276
$738$	−8.57289	+	5.50946i	−0.315572	+	0.202806i
$739$	−2.34266	+	16.2935i	−0.0861760	+	0.599367i	0.900276	+	0.435319i	$0.143364\pi$
$739$	−2.34266	+	16.2935i	−0.0861760	+	0.599367i	−0.986452	+	0.164048i	$0.947545\pi$
$740$	−1.63011	+	3.56943i	−0.0599239	+	0.131215i
$741$	1.29038	−	0.378890i	0.0474034	−	0.0139189i
$742$	−0.945233	−	2.06977i	−0.0347006	−	0.0759837i
$743$	−31.2867	−	36.1068i	−1.14780	−	1.32463i	−0.937899	−	0.346908i	$-0.887232\pi$
$743$	−31.2867	−	36.1068i	−1.14780	−	1.32463i	−0.209900	−	0.977723i	$-0.567314\pi$
$744$	2.09009	+	14.5369i	0.0766265	+	0.532949i
$745$	9.66107	+	2.83675i	0.353954	+	0.103930i
$746$	12.5924	−	14.5325i	0.461042	−	0.532071i
$747$	−2.60691	−	1.67536i	−0.0953817	−	0.0612981i
$748$	−2.74031	−	1.76109i	−0.100196	−	0.0643919i
$749$	8.05454	−	9.29544i	0.294307	−	0.339648i
$750$	−10.4805	−	3.07736i	−0.382695	−	0.112369i
$751$	0.407928	+	2.83720i	0.0148855	+	0.103531i	0.995910	−	0.0903546i	$-0.0288000\pi$
$751$	0.407928	+	2.83720i	0.0148855	+	0.103531i	−0.981024	+	0.193886i	$0.937891\pi$
$752$	−0.302879	−	0.349542i	−0.0110449	−	0.0127465i
$753$	5.13366	+	11.2411i	0.187081	+	0.409650i
$754$	19.0900	−	5.60533i	0.695217	−	0.204134i
$755$	−2.03845	+	4.46358i	−0.0741868	+	0.162446i
$756$	−0.420816	+	2.92684i	−0.0153049	+	0.106448i
$757$	17.4358	−	11.2053i	0.633714	−	0.407263i	−0.183969	−	0.982932i	$-0.558895\pi$
$757$	17.4358	−	11.2053i	0.633714	−	0.407263i	0.817683	+	0.575669i	$0.195258\pi$
$758$	7.11080			0.258276
$759$	−19.1939	−	1.12155i	−0.696695	−	0.0407095i
$760$	−0.108049			−0.00391935
$761$	39.7460	−	25.5432i	1.44079	−	0.925941i	0.441199	−	0.897409i	$-0.354553\pi$
$761$	39.7460	−	25.5432i	1.44079	−	0.925941i	0.999593	−	0.0285319i	$-0.00908321\pi$
$762$	−1.76918	+	12.3049i	−0.0640907	+	0.445761i
$763$	1.15387	−	2.52663i	0.0417730	−	0.0914701i
$764$	−3.88557	+	1.14091i	−0.140575	+	0.0412765i
$765$	0.615929	+	1.34870i	0.0222690	+	0.0487622i
$766$	8.31635	+	9.59758i	0.300482	+	0.346775i
$767$	−3.75068	−	26.0866i	−0.135429	−	0.941931i
$768$	2.06348	+	0.605893i	0.0744595	+	0.0218633i
$769$	19.1549	−	22.1059i	0.690742	−	0.797159i	−0.296728	−	0.954962i	$-0.595896\pi$
$769$	19.1549	−	22.1059i	0.690742	−	0.797159i	0.987471	+	0.157803i	$0.0504410\pi$
$770$	−0.818832	−	0.526231i	−0.0295087	−	0.0189641i
$771$	51.5028	+	33.0989i	1.85483	+	1.19203i
$772$	−17.1700	+	19.8153i	−0.617963	+	0.713168i
$773$	26.5853	+	7.80616i	0.956209	+	0.280768i	0.722370	−	0.691507i	$-0.243053\pi$
$773$	26.5853	+	7.80616i	0.956209	+	0.280768i	0.233839	+	0.972275i	$0.424871\pi$
$774$	−0.782674	−	5.44362i	−0.0281326	−	0.195667i
$775$	21.1410	+	24.3980i	0.759406	+	0.876401i
$776$	5.15215	+	11.2816i	0.184951	+	0.404987i
$777$	−15.5077	+	4.55347i	−0.556335	+	0.163355i
$778$	10.1684	−	22.2657i	0.364555	−	0.798264i
$779$	−0.184678	+	1.28446i	−0.00661677	+	0.0460206i
$780$	2.85467	−	1.83459i	0.102214	−	0.0656887i
$781$	5.06565			0.181263
$782$	0.706733	+	8.35038i	0.0252727	+	0.298609i
$783$	19.4680			0.695731
$784$	0.841254	−	0.540641i	0.0300448	−	0.0193086i
$785$	−0.0432481	+	0.300797i	−0.00154359	+	0.0107359i
$786$	8.49911	−	18.6105i	0.303153	−	0.663813i
$787$	−1.56528	+	0.459608i	−0.0557963	+	0.0163833i	−0.309512	−	0.950896i	$-0.600166\pi$
$787$	−1.56528	+	0.459608i	−0.0557963	+	0.0163833i	0.253715	+	0.967279i	$0.418347\pi$
$788$	−1.55558	−	3.40624i	−0.0554152	−	0.121342i
$789$	−0.596702	−	0.688631i	−0.0212432	−	0.0245159i
$790$	0.0834471	+	0.580387i	0.00296891	+	0.0206493i
$791$	18.8677	+	5.54006i	0.670858	+	0.196982i
$792$	1.98381	−	2.28944i	0.0704916	−	0.0813516i
$793$	4.13706	+	2.65873i	0.146911	+	0.0944143i
$794$	12.0163	+	7.72239i	0.426442	+	0.274057i
$795$	−1.67321	+	1.93099i	−0.0593427	+	0.0684852i
$796$	−9.14125	−	2.68411i	−0.324003	−	0.0951359i
$797$	−2.87036	−	19.9638i	−0.101674	−	0.707155i	−0.975353	−	0.220652i	$-0.929181\pi$
$797$	−2.87036	−	19.9638i	−0.101674	−	0.707155i	0.873679	−	0.486503i	$-0.161728\pi$
$798$	−0.291435	−	0.336334i	−0.0103167	−	0.0119061i
$799$	0.335734	+	0.735155i	0.0118774	+	0.0260079i
$800$	4.53588	−	1.33185i	0.160368	−	0.0470882i
$801$	12.2528	−	26.8300i	0.432933	−	0.947991i
$802$	2.27221	−	15.8036i	0.0802345	−	0.558043i
$803$	2.11595	−	1.35984i	0.0746704	−	0.0479878i
$804$	0.711813			0.0251037
$805$	0.211179	+	2.49517i	0.00744308	+	0.0879433i
$806$	−20.6367			−0.726897
$807$	14.6230	−	9.39765i	0.514755	−	0.330813i
$808$	−0.997391	+	6.93701i	−0.0350881	+	0.244043i
$809$	16.7130	−	36.5965i	0.587599	−	1.28666i	−0.349283	−	0.937017i	$-0.613575\pi$
$809$	16.7130	−	36.5965i	0.587599	−	1.28666i	0.936882	−	0.349645i	$-0.113698\pi$
$810$	5.62830	−	1.65262i	0.197758	−	0.0580670i
$811$	−3.67066	−	8.03763i	−0.128894	−	0.282239i	0.834172	−	0.551505i	$-0.185946\pi$
$811$	−3.67066	−	8.03763i	−0.128894	−	0.282239i	−0.963066	+	0.269266i	$0.913219\pi$
$812$	−4.31151	−	4.97574i	−0.151304	−	0.174614i
$813$	−6.86080	−	47.7179i	−0.240619	−	1.67354i
$814$	−13.4422	−	3.94698i	−0.471148	−	0.138341i
$815$	4.03858	−	4.66077i	0.141465	−	0.163260i
$816$	−3.16139	−	2.03170i	−0.110671	−	0.0711237i
$817$	−0.589144	−	0.378620i	−0.0206116	−	0.0132462i
$818$	11.5458	−	13.3246i	0.403689	−	0.465882i
$819$	4.71189	+	1.38354i	0.164647	+	0.0483447i
$820$	0.465980	+	3.24096i	0.0162727	+	0.113179i
$821$	−4.05305	−	4.67747i	−0.141452	−	0.163245i	0.680603	−	0.732653i	$-0.261718\pi$
$821$	−4.05305	−	4.67747i	−0.141452	−	0.163245i	−0.822055	+	0.569408i	$0.807173\pi$
$822$	−13.9206	−	30.4818i	−0.485536	−	1.06318i
$823$	−47.3658	+	13.9079i	−1.65107	+	0.484797i	−0.969117	−	0.246601i	$-0.920686\pi$
$823$	−47.3658	+	13.9079i	−1.65107	+	0.484797i	−0.681951	+	0.731398i	$0.738868\pi$
$824$	−2.77676	+	6.08027i	−0.0967332	+	0.211816i
$825$	2.69718	−	18.7593i	0.0939037	−	0.653114i
$826$	−7.33674	+	4.71504i	−0.255278	+	0.164057i
$827$	24.0485			0.836248			0.418124	−	0.908390i	$-0.362688\pi$
$827$	24.0485			0.836248			0.418124	+	0.908390i	$0.362688\pi$
$828$	−7.78025	−	0.454618i	−0.270382	−	0.0157991i
$829$	−34.4775			−1.19745			−0.598726	−	0.800954i	$-0.704326\pi$
$829$	−34.4775			−1.19745			−0.598726	+	0.800954i	$0.704326\pi$
$830$	−0.837611	+	0.538300i	−0.0290739	+	0.0186847i
$831$	8.68931	−	60.4354i	0.301429	−	2.09648i
$832$	−1.25535	+	2.74884i	−0.0435215	+	0.0952989i
$833$	−1.67662	+	0.492299i	−0.0580913	+	0.0170572i
$834$	11.1319	+	24.3755i	0.385466	+	0.844054i
$835$	−1.14586	−	1.32240i	−0.0396542	−	0.0457634i
$836$	−0.0548991	−	0.381832i	−0.00189872	−	0.0132059i
$837$	−19.3749	−	5.68899i	−0.669696	−	0.196640i
$838$	−14.4516	+	16.6781i	−0.499223	+	0.576134i
$839$	2.42638	+	1.55934i	0.0837680	+	0.0538344i	0.581854	−	0.813293i	$-0.302327\pi$
$839$	2.42638	+	1.55934i	0.0837680	+	0.0538344i	−0.498086	+	0.867127i	$0.665964\pi$
$840$	−0.944653	−	0.607092i	−0.0325936	−	0.0209467i
$841$	−9.39537	+	10.8428i	−0.323978	+	0.373891i
$842$	−19.8339	−	5.82375i	−0.683520	−	0.200700i
$843$	4.47201	+	31.1035i	0.154024	+	1.07126i
$844$	5.50533	+	6.35349i	0.189501	+	0.218696i
$845$	−0.838980	−	1.83711i	−0.0288618	−	0.0631985i
$846$	−0.721161	+	0.211752i	−0.0247940	+	0.00728019i
$847$	−3.12597	+	6.84493i	−0.107410	+	0.235195i
$848$	0.323822	−	2.25223i	0.0111201	−	0.0773420i
$849$	−32.2447	+	20.7224i	−1.10664	+	0.711192i
$850$	−8.26060			−0.283336
$851$	13.0345	+	33.6026i	0.446817	+	1.15188i
$852$	5.84404			0.200213
$853$	32.7303	−	21.0345i	1.12066	−	0.720207i	0.157073	−	0.987587i	$-0.449794\pi$
$853$	32.7303	−	21.0345i	1.12066	−	0.720207i	0.963591	+	0.267380i	$0.0861578\pi$
$854$	0.231596	−	1.61079i	0.00792507	−	0.0551200i
$855$	−0.0729412	+	0.159719i	−0.00249454	+	0.00546227i
$856$	11.8014	−	3.46520i	0.403364	−	0.118438i
$857$	−8.80830	−	19.2875i	−0.300886	−	0.658848i	0.697443	−	0.716640i	$-0.254321\pi$
$857$	−8.80830	−	19.2875i	−0.300886	−	0.658848i	−0.998329	+	0.0577926i	$0.981594\pi$
$858$	7.93364	+	9.15591i	0.270850	+	0.312578i
$859$	−2.34507	−	16.3103i	−0.0800127	−	0.556501i	−0.989913	−	0.141674i	$-0.954751\pi$
$859$	−2.34507	−	16.3103i	−0.0800127	−	0.556501i	0.909901	−	0.414826i	$-0.136158\pi$
$860$	−1.69547	−	0.497834i	−0.0578150	−	0.0169760i
$861$	−8.83157	+	10.1922i	−0.300979	+	0.347349i
$862$	−22.9192	−	14.7293i	−0.780632	−	0.501682i
$863$	6.92763	+	4.45212i	0.235819	+	0.151552i	0.653214	−	0.757174i	$-0.273420\pi$
$863$	6.92763	+	4.45212i	0.235819	+	0.151552i	−0.417395	+	0.908725i	$0.637057\pi$
$864$	−1.93638	+	2.23470i	−0.0658770	+	0.0760262i
$865$	1.64568	+	0.483215i	0.0559547	+	0.0164298i
$866$	−0.151128	−	1.05112i	−0.00513553	−	0.0357184i
$867$	−19.6416	−	22.6676i	−0.667062	−	0.769831i
$868$	2.83686	+	6.21187i	0.0962895	+	0.210845i
$869$	−2.00862	+	0.589783i	−0.0681376	+	0.0200070i
$870$	−3.07120	+	6.72499i	−0.104123	+	0.227998i
$871$	−0.142345	+	0.990028i	−0.00482316	+	0.0335458i
$872$	2.33670	−	1.50170i	0.0791306	−	0.0508541i
$873$	20.1547			0.682133
$874$	−0.692545	+	0.710837i	−0.0234257	+	0.0240444i
$875$	−5.07905			−0.171703
$876$	2.44109	−	1.56879i	0.0824768	−	0.0530046i
$877$	3.03035	−	21.0765i	0.102328	−	0.711704i	−0.872479	−	0.488652i	$-0.837489\pi$
$877$	3.03035	−	21.0765i	0.102328	−	0.711704i	0.974807	−	0.223052i	$-0.0716020\pi$
$878$	0.756496	−	1.65649i	0.0255305	−	0.0559040i
$879$	56.4090	−	16.5632i	1.90263	−	0.558662i
$880$	−0.404343	−	0.885388i	−0.0136304	−	0.0298464i
$881$	−5.76859	−	6.65731i	−0.194349	−	0.224291i	0.650208	−	0.759756i	$-0.274682\pi$
$881$	−5.76859	−	6.65731i	−0.194349	−	0.224291i	−0.844557	+	0.535465i	$0.820136\pi$
$882$	−0.231270	−	1.60852i	−0.00778728	−	0.0541617i
$883$	−6.80275	−	1.99747i	−0.228931	−	0.0672201i	0.165255	−	0.986251i	$-0.447155\pi$
$883$	−6.80275	−	1.99747i	−0.228931	−	0.0672201i	−0.394186	+	0.919031i	$0.628973\pi$
$884$	3.45800	−	3.99074i	0.116305	−	0.134223i
$885$	8.23851	+	5.29457i	0.276934	+	0.177975i
$886$	−24.0514	−	15.4569i	−0.808023	−	0.519285i
$887$	−31.4671	+	36.3150i	−1.05656	+	1.21934i	−0.0816719	+	0.996659i	$0.526026\pi$
$887$	−31.4671	+	36.3150i	−1.05656	+	1.21934i	−0.974892	+	0.222680i	$0.928519\pi$
$888$	−15.5077	−	4.55347i	−0.520404	−	0.152804i
$889$	0.822648	+	5.72164i	0.0275907	+	0.191898i
$890$	−6.20613	−	7.16225i	−0.208030	−	0.240079i
$891$	8.69985	+	19.0500i	0.291456	+	0.638199i
$892$	−23.4386	+	6.88220i	−0.784783	+	0.230433i
$893$	−0.0397591	+	0.0870604i	−0.00133049	+	0.00291336i
$894$	−5.90209	+	41.0499i	−0.197395	+	1.37291i
$895$	−7.30613	+	4.69537i	−0.244217	+	0.156949i
$896$	1.00000			0.0334077
$897$	6.22769	−	30.5393i	0.207937	−	1.01968i
$898$	−6.36287			−0.212332
$899$	37.8237	−	24.3078i	1.26149	−	0.810710i
$900$	1.09330	−	7.60407i	0.0364434	−	0.253469i
$901$	−1.65170	+	3.61671i	−0.0550260	+	0.120490i
$902$	−11.2164	+	3.29343i	−0.373465	+	0.109659i
$903$	−3.02344	−	6.62042i	−0.100614	−	0.220314i
$904$	12.8773	+	14.8612i	0.428294	+	0.494278i
$905$	0.954403	+	6.63802i	0.0317254	+	0.220655i
$906$	−19.3924	−	5.69412i	−0.644269	−	0.189175i
$907$	−17.5930	+	20.3034i	−0.584166	+	0.674163i	−0.968495	−	0.249033i	$-0.919887\pi$
$907$	−17.5930	+	20.3034i	−0.584166	+	0.674163i	0.384329	+	0.923196i	$0.374433\pi$
$908$	7.33892	+	4.71644i	0.243551	+	0.156521i
$909$	9.58103	+	6.15735i	0.317783	+	0.204226i
$910$	1.03328	−	1.19247i	0.0342530	−	0.0395301i
$911$	−25.1777	−	7.39283i	−0.834174	−	0.244935i	−0.163365	−	0.986566i	$-0.552235\pi$
$911$	−25.1777	−	7.39283i	−0.834174	−	0.244935i	−0.670809	+	0.741630i	$0.734053\pi$
$912$	−0.0633349	−	0.440504i	−0.00209723	−	0.0145865i
$913$	−2.32787	−	2.68650i	−0.0770412	−	0.0889103i
$914$	−13.3693	−	29.2748i	−0.442219	−	0.968324i
$915$	−1.75335	+	0.514830i	−0.0579640	+	0.0170198i
$916$	7.71710	−	16.8981i	0.254980	−	0.558329i
$917$	1.35389	−	9.41650i	0.0447093	−	0.310960i
$918$	4.34671	−	2.79346i	0.143463	−	0.0921980i
$919$	−1.29649			−0.0427671			−0.0213836	−	0.999771i	$-0.506807\pi$
$919$	−1.29649			−0.0427671			−0.0213836	+	0.999771i	$0.506807\pi$
$920$	−1.17134	+	2.21325i	−0.0386179	+	0.0729686i
$921$	71.5387			2.35728
$922$	−9.35996	+	6.01528i	−0.308254	+	0.198103i
$923$	−1.16866	+	8.12821i	−0.0384669	+	0.267543i
$924$	1.66541	−	3.64675i	0.0547881	−	0.119969i
$925$	−34.0885	+	10.0093i	−1.12082	+	0.329103i
$926$	−7.51716	−	16.4603i	−0.247029	−	0.540919i
$927$	7.11337	+	8.20927i	0.233634	+	0.269628i
$928$	−0.936980	−	6.51684i	−0.0307579	−	0.213926i
$929$	−43.7715	−	12.8525i	−1.43610	−	0.421676i	−0.531177	−	0.847261i	$-0.678250\pi$
$929$	−43.7715	−	12.8525i	−1.43610	−	0.421676i	−0.904918	+	0.425585i	$0.860068\pi$
$930$	5.02170	−	5.79535i	0.164668	−	0.190037i
$931$	−0.174085	−	0.111878i	−0.00570540	−	0.00366664i
$932$	8.22095	+	5.28329i	0.269286	+	0.173060i
$933$	−43.6113	+	50.3302i	−1.42777	+	1.64774i
$934$	−22.5801	−	6.63013i	−0.738845	−	0.216944i
$935$	0.242053	+	1.68351i	0.00791597	+	0.0550568i
$936$	3.21590	+	3.71135i	0.105115	+	0.121309i
$937$	23.9397	+	52.4207i	0.782077	+	1.71251i	0.698053	+	0.716046i	$0.254050\pi$
$937$	23.9397	+	52.4207i	0.782077	+	1.71251i	0.0840239	+	0.996464i	$0.473223\pi$
$938$	0.317577	−	0.0932489i	0.0103692	−	0.00304469i
$939$	5.93020	−	12.9853i	0.193525	−	0.423760i
$940$	−0.0343683	+	0.239037i	−0.00112097	+	0.00779652i
$941$	−39.6147	+	25.4588i	−1.29140	+	0.829935i	−0.992248	−	0.124270i	$-0.960341\pi$
$941$	−39.6147	+	25.4588i	−1.29140	+	0.829935i	−0.299155	+	0.954204i	$0.596705\pi$
$942$	−1.25167			−0.0407815
$943$	24.3085	+	17.7075i	0.791594	+	0.576635i
$944$	−8.72120			−0.283851
$945$	1.29884	−	0.834714i	0.0422513	−	0.0271533i
$946$	0.897826	−	6.24452i	0.0291908	−	0.203027i
$947$	2.99119	−	6.54979i	0.0972006	−	0.212840i	−0.854785	−	0.518982i	$-0.826311\pi$
$947$	2.99119	−	6.54979i	0.0972006	−	0.212840i	0.951986	+	0.306143i	$0.0990384\pi$
$948$	−2.31726	+	0.680409i	−0.0752611	+	0.0220987i
$949$	1.69381	+	3.70892i	0.0549834	+	0.120397i
$950$	−0.640623	−	0.739318i	−0.0207846	−	0.0239867i
$951$	−5.31471	−	36.9646i	−0.172341	−	1.19866i
$952$	−1.67662	−	0.492299i	−0.0543395	−	0.0159555i
$953$	−18.0497	+	20.8304i	−0.584686	+	0.674764i	−0.968605	−	0.248603i	$-0.920029\pi$
$953$	−18.0497	+	20.8304i	−0.584686	+	0.674764i	0.383919	+	0.923367i	$0.374574\pi$
$954$	−3.11066	−	1.99910i	−0.100711	−	0.0647233i
$955$	1.77880	+	1.14316i	0.0575605	+	0.0369919i
$956$	7.60852	−	8.78070i	0.246077	−	0.283988i
$957$	−25.3257	−	7.43630i	−0.818664	−	0.240382i
$958$	−5.68215	−	39.5202i	−0.183582	−	1.27684i
$959$	−10.2039	−	11.7759i	−0.329501	−	0.380264i
$960$	−0.466474	−	1.02144i	−0.0150554	−	0.0329667i
$961$	−15.0018	+	4.40492i	−0.483928	+	0.142094i
$962$	9.43436	−	20.6584i	0.304176	−	0.666053i
$963$	2.84454	−	19.7842i	0.0916640	−	0.637537i
$964$	−6.92327	+	4.44932i	−0.222984	+	0.143303i
$965$	13.6902			0.440703
$966$	−10.0488	+	2.32354i	−0.323314	+	0.0747588i
$967$	24.3032			0.781538			0.390769	−	0.920489i	$-0.372209\pi$
$967$	24.3032			0.781538			0.390769	+	0.920489i	$0.372209\pi$
$968$	−6.33038	+	4.06829i	−0.203466	+	0.130760i
$969$	−0.110671	+	0.769736i	−0.00355527	+	0.0247275i
$970$	2.69014	−	5.89059i	0.0863753	−	0.189135i
$971$	−44.7505	+	13.1399i	−1.43611	+	0.421680i	−0.904924	−	0.425574i	$-0.860072\pi$
$971$	−44.7505	+	13.1399i	−1.43611	+	0.421680i	−0.531188	+	0.847254i	$0.678254\pi$
$972$	6.35159	+	13.9080i	0.203727	+	0.446101i
$973$	8.15976	+	9.41687i	0.261590	+	0.301891i
$974$	5.85996	+	40.7569i	0.187765	+	1.30594i
$975$	29.4784	+	8.65564i	0.944064	+	0.277202i
$976$	1.06569	−	1.22987i	0.0341119	−	0.0393672i
$977$	−28.6416	−	18.4068i	−0.916326	−	0.588887i	−0.00473633	−	0.999989i	$-0.501508\pi$
$977$	−28.6416	−	18.4068i	−0.916326	−	0.588887i	−0.911589	+	0.411102i	$0.865144\pi$
$978$	21.3687	+	13.7328i	0.683297	+	0.439128i
$979$	22.1572	−	25.5708i	0.708147	−	0.817245i
$980$	−0.500990	−	0.147104i	−0.0160035	−	0.00469906i
$981$	−0.642385	−	4.46789i	−0.0205098	−	0.142649i
$982$	13.7639	+	15.8844i	0.439225	+	0.506893i
$983$	6.75180	+	14.7844i	0.215349	+	0.471549i	0.986219	−	0.165444i	$-0.0529056\pi$
$983$	6.75180	+	14.7844i	0.215349	+	0.471549i	−0.770870	+	0.636992i	$0.780178\pi$
$984$	−12.9399	+	3.79950i	−0.412509	+	0.121124i
$985$	−0.812230	+	1.77854i	−0.0258798	+	0.0566688i
$986$	−1.63728	+	11.3875i	−0.0521415	+	0.362652i
$987$	−0.836771	+	0.537760i	−0.0266347	+	0.0171171i
$988$	0.625342			0.0198948
$989$	−14.1424	+	7.96333i	−0.449701	+	0.253219i
$990$	−1.58175			−0.0502713
$991$	−52.1543	+	33.5175i	−1.65673	+	1.06472i	−0.734102	+	0.679039i	$0.762397\pi$
$991$	−52.1543	+	33.5175i	−1.65673	+	1.06472i	−0.922633	+	0.385679i	$0.873967\pi$
$992$	−0.971867	+	6.75948i	−0.0308568	+	0.214614i
$993$	12.2110	−	26.7384i	0.387506	−	0.848519i
$994$	2.60733	−	0.765581i	0.0826995	−	0.0242828i
$995$	2.06649	+	4.52498i	0.0655121	+	0.143451i
$996$	−2.68557	−	3.09931i	−0.0850955	−	0.0982055i
$997$	−5.55173	−	38.6132i	−0.175825	−	1.22289i	−0.866296	−	0.499531i	$-0.833506\pi$
$997$	−5.55173	−	38.6132i	−0.175825	−	1.22289i	0.690471	−	0.723360i	$-0.257403\pi$
$998$	4.58334	+	1.34579i	0.145083	+	0.0426002i
$999$	14.5525	−	16.7945i	0.460421	−	0.531354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.c.127.2	yes	20
23.2	even	11	inner	322.2.i.c.71.2	✓	20
23.5	odd	22		7406.2.a.bo.1.3		10
23.18	even	11		7406.2.a.bp.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.c.71.2	✓	20	23.2	even	11	inner
322.2.i.c.127.2	yes	20	1.1	even	1	trivial
7406.2.a.bo.1.3		10	23.5	odd	22
7406.2.a.bp.1.3		10	23.18	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)

\(f(q)\)	\(=\)	\(q+(0.841254 - 0.540641i) q^{2} +(0.306062 - 2.12871i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.500990 + 0.147104i) q^{5} +(-0.893390 - 1.95625i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-1.55924 - 0.457833i) q^{9} +O(q^{10})\)	\(q+(0.841254 - 0.540641i) q^{2} +(0.306062 - 2.12871i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.500990 + 0.147104i) q^{5} +(-0.893390 - 1.95625i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-1.55924 - 0.457833i) q^{9} +(-0.341929 + 0.394607i) q^{10} +(-1.56822 - 1.00784i) q^{11} +(-1.80920 - 1.16270i) q^{12} +(1.97894 - 2.28382i) q^{13} +(-0.959493 - 0.281733i) q^{14} +(0.159807 + 1.11148i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(0.725896 + 1.58949i) q^{17} +(-1.55924 + 0.457833i) q^{18} +(-0.0859639 + 0.188235i) q^{19} +(-0.0743083 + 0.516825i) q^{20} +(-1.80920 + 1.16270i) q^{21} -1.86415 q^{22} +(2.92383 + 3.80148i) q^{23} -2.15060 q^{24} +(-3.97692 + 2.55581i) q^{25} +(0.430065 - 2.99117i) q^{26} +(1.22836 - 2.68972i) q^{27} +(-0.959493 + 0.281733i) q^{28} +(2.73503 + 5.98888i) q^{29} +(0.735351 + 0.848640i) q^{30} +(-0.971867 - 6.75948i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-2.62536 + 3.02983i) q^{33} +(1.47001 + 0.944715i) q^{34} +(0.439252 + 0.282290i) q^{35} +(-1.06419 + 1.22814i) q^{36} +(7.21088 + 2.11731i) q^{37} +(0.0294499 + 0.204829i) q^{38} +(-4.25590 - 4.91157i) q^{39} +(0.216905 + 0.474955i) q^{40} +(6.01689 - 1.76672i) q^{41} +(-0.893390 + 1.95625i) q^{42} +(-0.481627 + 3.34979i) q^{43} +(-1.56822 + 1.00784i) q^{44} +0.848509 q^{45} +(4.51492 + 1.61726i) q^{46} +0.462510 q^{47} +(-1.80920 + 1.16270i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(-1.96382 + 4.30017i) q^{50} +(3.60572 - 1.05874i) q^{51} +(-1.25535 - 2.74884i) q^{52} +(1.49007 + 1.71963i) q^{53} +(-0.420816 - 2.92684i) q^{54} +(0.933920 + 0.274224i) q^{55} +(-0.654861 + 0.755750i) q^{56} +(0.374386 + 0.240603i) q^{57} +(5.53869 + 3.55950i) q^{58} +(5.71117 - 6.59104i) q^{59} +(1.07743 + 0.316361i) q^{60} +(0.231596 + 1.61079i) q^{61} +(-4.47204 - 5.16101i) q^{62} +(0.675075 + 1.47821i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(-0.655470 + 1.43528i) q^{65} +(-0.570545 + 3.96823i) q^{66} +(-0.278441 + 0.178943i) q^{67} +1.74740 q^{68} +(8.98710 - 5.06049i) q^{69} +0.522140 q^{70} +(-2.28603 + 1.46914i) q^{71} +(-0.231270 + 1.60852i) q^{72} +(-0.560506 + 1.22734i) q^{73} +(7.21088 - 2.11731i) q^{74} +(4.22338 + 9.24792i) q^{75} +(0.135514 + 0.156391i) q^{76} +(0.265296 + 1.84518i) q^{77} +(-6.23569 - 1.83096i) q^{78} +(0.735399 - 0.848696i) q^{79} +(0.439252 + 0.282290i) q^{80} +(-9.45094 - 6.07375i) q^{81} +(4.10657 - 4.73924i) q^{82} +(1.82966 + 0.537237i) q^{83} +(0.306062 + 2.12871i) q^{84} +(-0.597486 - 0.689536i) q^{85} +(1.40586 + 3.07841i) q^{86} +(13.5857 - 3.98911i) q^{87} +(-0.774396 + 1.69569i) q^{88} +(-2.58306 + 17.9656i) q^{89} +(0.713812 - 0.458739i) q^{90} -3.02193 q^{91} +(4.67255 - 1.08042i) q^{92} -14.6864 q^{93} +(0.389088 - 0.250052i) q^{94} +(0.0153770 - 0.106949i) q^{95} +(-0.893390 + 1.95625i) q^{96} +(-11.9000 + 3.49416i) q^{97} +(0.415415 + 0.909632i) q^{98} +(1.98381 + 2.28944i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 5 q^{5} + 4 q^{6} - 2 q^{7} - 2 q^{8} - 12 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 5 * q^5 + 4 * q^6 - 2 * q^7 - 2 * q^8 - 12 * q^9	\( 20 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 5 q^{5} + 4 q^{6} - 2 q^{7} - 2 q^{8} - 12 q^{9} + 6 q^{10} + 6 q^{11} + 4 q^{12} + 14 q^{13} - 2 q^{14} + 13 q^{15} - 2 q^{16} + 7 q^{17} - 12 q^{18} - 2 q^{19} + 6 q^{20} + 4 q^{21} - 16 q^{22} + 9 q^{23} - 18 q^{24} + 23 q^{25} + 3 q^{26} - 47 q^{27} - 2 q^{28} + 2 q^{29} - 20 q^{30} + 28 q^{31} - 2 q^{32} + 26 q^{33} + 18 q^{34} - 5 q^{35} + 10 q^{36} - 17 q^{37} + 9 q^{38} + 36 q^{39} - 5 q^{40} - 7 q^{41} + 4 q^{42} - 17 q^{43} + 6 q^{44} + 90 q^{45} + 9 q^{46} - 68 q^{47} + 4 q^{48} - 2 q^{49} - 43 q^{50} - 15 q^{51} + 14 q^{52} - 35 q^{53} + 19 q^{54} + 8 q^{55} - 2 q^{56} - 20 q^{57} + 24 q^{58} - 60 q^{59} + 13 q^{60} - 48 q^{61} - 5 q^{62} + 10 q^{63} - 2 q^{64} + 40 q^{65} - 29 q^{66} - 57 q^{67} + 18 q^{68} + 4 q^{69} + 6 q^{70} - 39 q^{71} - q^{72} - 30 q^{73} - 17 q^{74} + 57 q^{75} - 2 q^{76} + 6 q^{77} - 19 q^{78} - 18 q^{79} - 5 q^{80} - 90 q^{81} + 26 q^{82} + 28 q^{83} + 4 q^{84} - 13 q^{85} - 6 q^{86} + 13 q^{87} + 6 q^{88} + 34 q^{89} - 20 q^{90} - 30 q^{91} - 2 q^{92} - 16 q^{93} + 9 q^{94} + 110 q^{95} + 4 q^{96} - 2 q^{98} - 28 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 5 * q^5 + 4 * q^6 - 2 * q^7 - 2 * q^8 - 12 * q^9 + 6 * q^10 + 6 * q^11 + 4 * q^12 + 14 * q^13 - 2 * q^14 + 13 * q^15 - 2 * q^16 + 7 * q^17 - 12 * q^18 - 2 * q^19 + 6 * q^20 + 4 * q^21 - 16 * q^22 + 9 * q^23 - 18 * q^24 + 23 * q^25 + 3 * q^26 - 47 * q^27 - 2 * q^28 + 2 * q^29 - 20 * q^30 + 28 * q^31 - 2 * q^32 + 26 * q^33 + 18 * q^34 - 5 * q^35 + 10 * q^36 - 17 * q^37 + 9 * q^38 + 36 * q^39 - 5 * q^40 - 7 * q^41 + 4 * q^42 - 17 * q^43 + 6 * q^44 + 90 * q^45 + 9 * q^46 - 68 * q^47 + 4 * q^48 - 2 * q^49 - 43 * q^50 - 15 * q^51 + 14 * q^52 - 35 * q^53 + 19 * q^54 + 8 * q^55 - 2 * q^56 - 20 * q^57 + 24 * q^58 - 60 * q^59 + 13 * q^60 - 48 * q^61 - 5 * q^62 + 10 * q^63 - 2 * q^64 + 40 * q^65 - 29 * q^66 - 57 * q^67 + 18 * q^68 + 4 * q^69 + 6 * q^70 - 39 * q^71 - q^72 - 30 * q^73 - 17 * q^74 + 57 * q^75 - 2 * q^76 + 6 * q^77 - 19 * q^78 - 18 * q^79 - 5 * q^80 - 90 * q^81 + 26 * q^82 + 28 * q^83 + 4 * q^84 - 13 * q^85 - 6 * q^86 + 13 * q^87 + 6 * q^88 + 34 * q^89 - 20 * q^90 - 30 * q^91 - 2 * q^92 - 16 * q^93 + 9 * q^94 + 110 * q^95 + 4 * q^96 - 2 * q^98 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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