LMFDB - Embedded newform 230.2.g.b.71.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(31,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("230.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.g (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:	$1.83655924649$
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} - 5 x^{19} + 12 x^{18} + 16 x^{17} - 49 x^{16} + 59 x^{15} - 197 x^{14} + 42 x^{13} + 1625 x^{12} + \cdots + 529 $ x^20 - 5x^19 + 12x^18 + 16x^17 - 49x^16 + 59x^15 - 197x^14 + 42x^13 + 1625x^12 - 5910x^11 + 14651x^10 - 22501x^9 + 26003x^8 - 19607x^7 + 13040x^6 + 348x^5 + 7193x^4 + 10771x^3 + 8781x^2 + 3105*x + 529
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			71.2
Root			$0.212636 - 1.47891i$ of defining polynomial
Character	$\chi$	$=$	230.71
Dual form			230.2.g.b.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841254 - 0.540641i) q^{2} +(0.0390478 + 0.271583i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(0.113980 - 0.249581i) q^{6} +(-0.365070 + 0.421313i) q^{7} +(0.142315 - 0.989821i) q^{8} +(2.80625 - 0.823988i) q^{9} +O(q^{10})$	\(q+(-0.841254 - 0.540641i) q^{2} +(0.0390478 + 0.271583i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(0.113980 - 0.249581i) q^{6} +(-0.365070 + 0.421313i) q^{7} +(0.142315 - 0.989821i) q^{8} +(2.80625 - 0.823988i) q^{9} +(0.654861 + 0.755750i) q^{10} +(4.26584 - 2.74149i) q^{11} +(-0.230820 + 0.148339i) q^{12} +(2.67167 + 3.08328i) q^{13} +(0.534895 - 0.157059i) q^{14} +(0.0390478 - 0.271583i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-0.242471 + 0.530937i) q^{17} +(-2.80625 - 0.823988i) q^{18} +(-0.100630 - 0.220348i) q^{19} +(-0.142315 - 0.989821i) q^{20} +(-0.128677 - 0.0826955i) q^{21} -5.07081 q^{22} +(4.35089 - 2.01736i) q^{23} +0.274376 q^{24} +(0.841254 + 0.540641i) q^{25} +(-0.580610 - 4.03823i) q^{26} +(0.675299 + 1.47870i) q^{27} +(-0.534895 - 0.157059i) q^{28} +(0.883401 - 1.93438i) q^{29} +(-0.179678 + 0.207360i) q^{30} +(0.336901 - 2.34320i) q^{31} +(0.959493 - 0.281733i) q^{32} +(0.911114 + 1.05148i) q^{33} +(0.491025 - 0.315563i) q^{34} +(0.468979 - 0.301395i) q^{35} +(1.91528 + 2.21035i) q^{36} +(-9.46472 + 2.77909i) q^{37} +(-0.0344742 + 0.239773i) q^{38} +(-0.733043 + 0.845977i) q^{39} +(-0.415415 + 0.909632i) q^{40} +(0.750956 + 0.220501i) q^{41} +(0.0635411 + 0.139136i) q^{42} +(-0.472974 - 3.28960i) q^{43} +(4.26584 + 2.74149i) q^{44} -2.92472 q^{45} +(-4.75087 - 0.655153i) q^{46} -11.3769 q^{47} +(-0.230820 - 0.148339i) q^{48} +(0.951975 + 6.62113i) q^{49} +(-0.415415 - 0.909632i) q^{50} +(-0.153661 - 0.0451191i) q^{51} +(-1.69479 + 3.71108i) q^{52} +(1.08813 - 1.25577i) q^{53} +(0.231347 - 1.60905i) q^{54} +(-4.86541 + 1.42861i) q^{55} +(0.365070 + 0.421313i) q^{56} +(0.0559136 - 0.0359335i) q^{57} +(-1.78897 + 1.14970i) q^{58} +(1.22817 + 1.41738i) q^{59} +(0.263262 - 0.0773006i) q^{60} +(-1.90259 + 13.2328i) q^{61} +(-1.55025 + 1.78908i) q^{62} +(-0.677318 + 1.48312i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-1.69479 - 3.71108i) q^{65} +(-0.198004 - 1.37715i) q^{66} +(-5.19967 - 3.34163i) q^{67} -0.583683 q^{68} +(0.717775 + 1.10286i) q^{69} -0.557477 q^{70} +(2.45727 + 1.57919i) q^{71} +(-0.416231 - 2.89495i) q^{72} +(3.30108 + 7.22836i) q^{73} +(9.46472 + 2.77909i) q^{74} +(-0.113980 + 0.249581i) q^{75} +(0.158633 - 0.183072i) q^{76} +(-0.402304 + 2.79809i) q^{77} +(1.07405 - 0.315368i) q^{78} +(-9.00256 - 10.3895i) q^{79} +(0.841254 - 0.540641i) q^{80} +(7.00607 - 4.50253i) q^{81} +(-0.512533 - 0.591494i) q^{82} +(-3.65782 + 1.07403i) q^{83} +(0.0217682 - 0.151401i) q^{84} +(0.382231 - 0.441118i) q^{85} +(-1.38060 + 3.02310i) q^{86} +(0.559840 + 0.164384i) q^{87} +(-2.10649 - 4.61257i) q^{88} +(-2.21153 - 15.3815i) q^{89} +(2.46043 + 1.58122i) q^{90} -2.27437 q^{91} +(3.64248 + 3.11966i) q^{92} +0.649529 q^{93} +(9.57090 + 6.15084i) q^{94} +(0.0344742 + 0.239773i) q^{95} +(0.113980 + 0.249581i) q^{96} +(7.91120 + 2.32294i) q^{97} +(2.77880 - 6.08473i) q^{98} +(9.71204 - 11.2083i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9} + 2 q^{10} + 7 q^{11} + 8 q^{12} + 8 q^{13} + 3 q^{14} - 3 q^{15} - 2 q^{16} + 8 q^{17} + 27 q^{18} - q^{19} - 2 q^{20} - 31 q^{21} - 18 q^{22} - 9 q^{23} - 8 q^{24} - 2 q^{25} - 8 q^{26} - 18 q^{27} - 3 q^{28} + 20 q^{29} + 3 q^{30} - 17 q^{31} + 2 q^{32} + 17 q^{33} + 3 q^{34} - 3 q^{35} + 17 q^{36} + 6 q^{37} - 21 q^{38} - 75 q^{39} + 2 q^{40} - 2 q^{41} + 42 q^{42} - 18 q^{43} + 7 q^{44} + 28 q^{45} - 2 q^{46} + 42 q^{47} + 8 q^{48} - 19 q^{49} + 2 q^{50} + 26 q^{51} + 19 q^{52} + 19 q^{53} - 26 q^{54} - 15 q^{55} - 19 q^{56} + 7 q^{57} - 9 q^{58} + 25 q^{59} - 3 q^{60} - 49 q^{61} - 38 q^{62} - 87 q^{63} - 2 q^{64} + 19 q^{65} - 6 q^{66} + 19 q^{67} - 36 q^{68} + 36 q^{69} + 14 q^{70} + 7 q^{71} - 17 q^{72} - 10 q^{73} - 6 q^{74} - 3 q^{75} - q^{76} - 29 q^{77} - 2 q^{78} - 33 q^{79} - 2 q^{80} + 72 q^{81} + 2 q^{82} - 41 q^{83} + 13 q^{84} - 14 q^{85} - 48 q^{86} - 16 q^{87} - 7 q^{88} + 55 q^{89} + 5 q^{90} + 13 q^{92} + 10 q^{93} + 13 q^{94} + 21 q^{95} + 3 q^{96} - 9 q^{97} + 41 q^{98} + 59 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9 + 2 * q^10 + 7 * q^11 + 8 * q^12 + 8 * q^13 + 3 * q^14 - 3 * q^15 - 2 * q^16 + 8 * q^17 + 27 * q^18 - q^19 - 2 * q^20 - 31 * q^21 - 18 * q^22 - 9 * q^23 - 8 * q^24 - 2 * q^25 - 8 * q^26 - 18 * q^27 - 3 * q^28 + 20 * q^29 + 3 * q^30 - 17 * q^31 + 2 * q^32 + 17 * q^33 + 3 * q^34 - 3 * q^35 + 17 * q^36 + 6 * q^37 - 21 * q^38 - 75 * q^39 + 2 * q^40 - 2 * q^41 + 42 * q^42 - 18 * q^43 + 7 * q^44 + 28 * q^45 - 2 * q^46 + 42 * q^47 + 8 * q^48 - 19 * q^49 + 2 * q^50 + 26 * q^51 + 19 * q^52 + 19 * q^53 - 26 * q^54 - 15 * q^55 - 19 * q^56 + 7 * q^57 - 9 * q^58 + 25 * q^59 - 3 * q^60 - 49 * q^61 - 38 * q^62 - 87 * q^63 - 2 * q^64 + 19 * q^65 - 6 * q^66 + 19 * q^67 - 36 * q^68 + 36 * q^69 + 14 * q^70 + 7 * q^71 - 17 * q^72 - 10 * q^73 - 6 * q^74 - 3 * q^75 - q^76 - 29 * q^77 - 2 * q^78 - 33 * q^79 - 2 * q^80 + 72 * q^81 + 2 * q^82 - 41 * q^83 + 13 * q^84 - 14 * q^85 - 48 * q^86 - 16 * q^87 - 7 * q^88 + 55 * q^89 + 5 * q^90 + 13 * q^92 + 10 * q^93 + 13 * q^94 + 21 * q^95 + 3 * q^96 - 9 * q^97 + 41 * q^98 + 59 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{1}{11}\right)$

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
$3$	0.0390478	+	0.271583i	0.0225442	+	0.156799i	0.997984	−	0.0634684i	$-0.0202162\pi$
$3$	0.0390478	+	0.271583i	0.0225442	+	0.156799i	−0.975440	+	0.220267i	$0.929307\pi$
$4$	0.415415	+	0.909632i	0.207708	+	0.454816i
$5$	−0.959493	−	0.281733i	−0.429098	−	0.125995i
$5$	−0.959493	−	0.281733i	−0.429098	−	0.125995i
$6$	0.113980	−	0.249581i	0.0465321	−	0.101891i
$7$	−0.365070	+	0.421313i	−0.137983	+	0.159241i	−0.820535	−	0.571596i	$-0.806325\pi$
$7$	−0.365070	+	0.421313i	−0.137983	+	0.159241i	0.682552	+	0.730837i	$0.260870\pi$
$8$	0.142315	−	0.989821i	0.0503159	−	0.349955i
$9$	2.80625	−	0.823988i	0.935415	−	0.274663i
$10$	0.654861	+	0.755750i	0.207085	+	0.238989i
$11$	4.26584	−	2.74149i	1.28620	−	0.826590i	0.294560	−	0.955633i	$-0.404827\pi$
$11$	4.26584	−	2.74149i	1.28620	−	0.826590i	0.991639	+	0.129043i	$0.0411905\pi$
$12$	−0.230820	+	0.148339i	−0.0666319	+	0.0428217i
$13$	2.67167	+	3.08328i	0.740989	+	0.855147i	0.993663	−	0.112404i	$-0.0358552\pi$
$13$	2.67167	+	3.08328i	0.740989	+	0.855147i	−0.252673	+	0.967552i	$0.581310\pi$
$14$	0.534895	−	0.157059i	0.142957	−	0.0419759i
$15$	0.0390478	−	0.271583i	0.0100821	−	0.0701225i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	−0.242471	+	0.530937i	−0.0588078	+	0.128771i	−0.936754	−	0.349988i	$-0.886186\pi$
$17$	−0.242471	+	0.530937i	−0.0588078	+	0.128771i	0.877947	+	0.478759i	$0.158913\pi$
$18$	−2.80625	−	0.823988i	−0.661439	−	0.194216i
$19$	−0.100630	−	0.220348i	−0.0230860	−	0.0505514i	0.897738	−	0.440530i	$-0.145210\pi$
$19$	−0.100630	−	0.220348i	−0.0230860	−	0.0505514i	−0.920824	+	0.389979i	$0.872482\pi$
$20$	−0.142315	−	0.989821i	−0.0318226	−	0.221331i
$21$	−0.128677	−	0.0826955i	−0.0280795	−	0.0180456i
$22$	−5.07081			−1.08110
$23$	4.35089	−	2.01736i	0.907223	−	0.420650i
$23$	4.35089	−	2.01736i	0.907223	−	0.420650i
$24$	0.274376			0.0560068
$25$	0.841254	+	0.540641i	0.168251	+	0.108128i
$26$	−0.580610	−	4.03823i	−0.113867	−	0.791963i
$27$	0.675299	+	1.47870i	0.129961	+	0.284576i
$28$	−0.534895	−	0.157059i	−0.101086	−	0.0296814i
$29$	0.883401	−	1.93438i	0.164043	−	0.359205i	−0.809703	−	0.586840i	$-0.800372\pi$
$29$	0.883401	−	1.93438i	0.164043	−	0.359205i	0.973747	+	0.227635i	$0.0730991\pi$
$30$	−0.179678	+	0.207360i	−0.0328046	+	0.0378585i
$31$	0.336901	−	2.34320i	0.0605092	−	0.420851i	−0.936941	−	0.349487i	$-0.886356\pi$
$31$	0.336901	−	2.34320i	0.0605092	−	0.420851i	0.997450	−	0.0713638i	$-0.0227351\pi$
$32$	0.959493	−	0.281733i	0.169616	−	0.0498038i
$33$	0.911114	+	1.05148i	0.158605	+	0.183039i
$34$	0.491025	−	0.315563i	0.0842101	−	0.0541186i
$35$	0.468979	−	0.301395i	0.0792720	−	0.0509450i
$36$	1.91528	+	2.21035i	0.319214	+	0.368392i
$37$	−9.46472	+	2.77909i	−1.55599	+	0.456880i	−0.942884	−	0.333120i	$-0.891898\pi$
$37$	−9.46472	+	2.77909i	−1.55599	+	0.456880i	−0.613106	+	0.790000i	$0.710080\pi$
$38$	−0.0344742	+	0.239773i	−0.00559245	+	0.0388964i
$39$	−0.733043	+	0.845977i	−0.117381	+	0.135465i
$40$	−0.415415	+	0.909632i	−0.0656829	+	0.143825i
$41$	0.750956	+	0.220501i	0.117280	+	0.0344364i	0.339846	−	0.940481i	$-0.389625\pi$
$41$	0.750956	+	0.220501i	0.117280	+	0.0344364i	−0.222566	+	0.974918i	$0.571443\pi$
$42$	0.0635411	+	0.139136i	0.00980461	+	0.0214691i
$43$	−0.472974	−	3.28960i	−0.0721278	−	0.501660i	−0.993577	−	0.113160i	$-0.963903\pi$
$43$	−0.472974	−	3.28960i	−0.0721278	−	0.501660i	0.921449	−	0.388500i	$-0.127006\pi$
$44$	4.26584	+	2.74149i	0.643100	+	0.413295i
$45$	−2.92472			−0.435991
$46$	−4.75087	−	0.655153i	−0.700478	−	0.0965971i
$47$	−11.3769			−1.65950			−0.829749	−	0.558136i	$-0.811517\pi$
$47$	−11.3769			−1.65950			−0.829749	+	0.558136i	$0.811517\pi$
$48$	−0.230820	−	0.148339i	−0.0333160	−	0.0214109i
$49$	0.951975	+	6.62113i	0.135996	+	0.945876i
$50$	−0.415415	−	0.909632i	−0.0587486	−	0.128641i
$51$	−0.153661	−	0.0451191i	−0.0215169	−	0.00631793i
$52$	−1.69479	+	3.71108i	−0.235026	+	0.514634i
$53$	1.08813	−	1.25577i	0.149466	−	0.172493i	−0.676079	−	0.736829i	$-0.736322\pi$
$53$	1.08813	−	1.25577i	0.149466	−	0.172493i	0.825545	+	0.564336i	$0.190868\pi$
$54$	0.231347	−	1.60905i	0.0314823	−	0.218965i
$55$	−4.86541	+	1.42861i	−0.656052	+	0.192634i
$56$	0.365070	+	0.421313i	0.0487845	+	0.0563003i
$57$	0.0559136	−	0.0359335i	0.00740593	−	0.00475950i
$58$	−1.78897	+	1.14970i	−0.234903	+	0.150963i
$59$	1.22817	+	1.41738i	0.159894	+	0.184528i	0.830044	−	0.557699i	$-0.188315\pi$
$59$	1.22817	+	1.41738i	0.159894	+	0.184528i	−0.670149	+	0.742226i	$0.733770\pi$
$60$	0.263262	−	0.0773006i	0.0339870	−	0.00997947i
$61$	−1.90259	+	13.2328i	−0.243601	+	1.69428i	0.390153	+	0.920750i	$0.372422\pi$
$61$	−1.90259	+	13.2328i	−0.243601	+	1.69428i	−0.633754	+	0.773534i	$0.718487\pi$
$62$	−1.55025	+	1.78908i	−0.196882	+	0.227214i
$63$	−0.677318	+	1.48312i	−0.0853341	+	0.186856i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	−1.69479	−	3.71108i	−0.210213	−	0.460303i
$66$	−0.198004	−	1.37715i	−0.0243726	−	0.169515i
$67$	−5.19967	−	3.34163i	−0.635241	−	0.408245i	0.183005	−	0.983112i	$-0.441417\pi$
$67$	−5.19967	−	3.34163i	−0.635241	−	0.408245i	−0.818247	+	0.574867i	$0.805054\pi$
$68$	−0.583683			−0.0707819
$69$	0.717775	+	1.10286i	0.0864100	+	0.132768i
$70$	−0.557477			−0.0666312
$71$	2.45727	+	1.57919i	0.291624	+	0.187415i	0.678270	−	0.734813i	$-0.262730\pi$
$71$	2.45727	+	1.57919i	0.291624	+	0.187415i	−0.386646	+	0.922228i	$0.626366\pi$
$72$	−0.416231	−	2.89495i	−0.0490533	−	0.341173i
$73$	3.30108	+	7.22836i	0.386362	+	0.846016i	0.998473	+	0.0552435i	$0.0175935\pi$
$73$	3.30108	+	7.22836i	0.386362	+	0.846016i	−0.612110	+	0.790772i	$0.709679\pi$
$74$	9.46472	+	2.77909i	1.10025	+	0.323063i
$75$	−0.113980	+	0.249581i	−0.0131613	+	0.0288192i
$76$	0.158633	−	0.183072i	0.0181964	−	0.0209998i
$77$	−0.402304	+	2.79809i	−0.0458468	+	0.318872i
$78$	1.07405	−	0.315368i	0.121612	−	0.0357084i
$79$	−9.00256	−	10.3895i	−1.01287	−	1.16891i	−0.985567	−	0.169284i	$-0.945854\pi$
$79$	−9.00256	−	10.3895i	−1.01287	−	1.16891i	−0.0273001	−	0.999627i	$-0.508691\pi$
$80$	0.841254	−	0.540641i	0.0940550	−	0.0604455i
$81$	7.00607	−	4.50253i	0.778452	−	0.500281i
$82$	−0.512533	−	0.591494i	−0.0565998	−	0.0653196i
$83$	−3.65782	+	1.07403i	−0.401498	+	0.117890i	−0.476246	−	0.879312i	$-0.658003\pi$
$83$	−3.65782	+	1.07403i	−0.401498	+	0.117890i	0.0747484	+	0.997202i	$0.476185\pi$
$84$	0.0217682	−	0.151401i	0.00237511	−	0.0165192i
$85$	0.382231	−	0.441118i	0.0414588	−	0.0478460i
$86$	−1.38060	+	3.02310i	−0.148874	+	0.325989i
$87$	0.559840	+	0.164384i	0.0600211	+	0.0176238i
$88$	−2.10649	−	4.61257i	−0.224553	−	0.491702i
$89$	−2.21153	−	15.3815i	−0.234421	−	1.63044i	−0.678607	−	0.734502i	$-0.737416\pi$
$89$	−2.21153	−	15.3815i	−0.234421	−	1.63044i	0.444185	−	0.895935i	$-0.353493\pi$
$90$	2.46043	+	1.58122i	0.259352	+	0.166675i
$91$	−2.27437			−0.238419
$92$	3.64248	+	3.11966i	0.379755	+	0.325248i
$93$	0.649529			0.0673530
$94$	9.57090	+	6.15084i	0.987163	+	0.634411i
$95$	0.0344742	+	0.239773i	0.00353698	+	0.0246002i
$96$	0.113980	+	0.249581i	0.0116330	+	0.0254728i
$97$	7.91120	+	2.32294i	0.803260	+	0.235859i	0.657493	−	0.753460i	$-0.271617\pi$
$97$	7.91120	+	2.32294i	0.803260	+	0.235859i	0.145767	+	0.989319i	$0.453435\pi$
$98$	2.77880	−	6.08473i	0.280701	−	0.614650i
$99$	9.71204	−	11.2083i	0.976097	−	1.12648i
$100$	−0.142315	+	0.989821i	−0.0142315	+	0.0989821i
$101$	−9.09276	+	2.66988i	−0.904764	+	0.265663i	−0.700835	−	0.713323i	$-0.747189\pi$
$101$	−9.09276	+	2.66988i	−0.904764	+	0.265663i	−0.203929	+	0.978986i	$0.565371\pi$
$102$	0.104875	+	0.121032i	0.0103842	+	0.0119840i
$103$	7.89742	−	5.07536i	0.778156	−	0.500090i	−0.0902654	−	0.995918i	$-0.528772\pi$
$103$	7.89742	−	5.07536i	0.778156	−	0.500090i	0.868421	+	0.495828i	$0.165135\pi$
$104$	3.43211	−	2.20568i	0.336546	−	0.216285i
$105$	0.100166	+	0.115598i	0.00977523	+	0.0112812i
$106$	−1.59431	+	0.468132i	−0.154853	+	0.0454690i
$107$	2.13724	−	14.8648i	0.206615	−	1.43704i	−0.577484	−	0.816402i	$-0.695966\pi$
$107$	2.13724	−	14.8648i	0.206615	−	1.43704i	0.784099	−	0.620636i	$-0.213125\pi$
$108$	−1.06454	+	1.22855i	−0.102436	+	0.118217i
$109$	−5.47381	+	11.9860i	−0.524296	+	1.14805i	0.443491	+	0.896279i	$0.353740\pi$
$109$	−5.47381	+	11.9860i	−0.524296	+	1.14805i	−0.967787	+	0.251770i	$0.918987\pi$
$110$	4.86541	+	1.42861i	0.463899	+	0.136213i
$111$	−1.12433	−	2.46194i	−0.106717	−	0.233677i
$112$	−0.0793372	−	0.551802i	−0.00749666	−	0.0521404i
$113$	5.85212	+	3.76093i	0.550521	+	0.353798i	0.786141	−	0.618047i	$-0.212076\pi$
$113$	5.85212	+	3.76093i	0.550521	+	0.353798i	−0.235620	+	0.971845i	$0.575712\pi$
$114$	−0.0664646			−0.00622498
$115$	−4.74301	+	0.709860i	−0.442288	+	0.0661948i
$116$	2.12655			0.197445
$117$	10.0380	+	6.45101i	0.928010	+	0.596396i
$118$	−0.266907	−	1.85638i	−0.0245708	−	0.170893i
$119$	−0.135172	−	0.295985i	−0.0123912	−	0.0271329i
$120$	−0.263262	−	0.0773006i	−0.0240324	−	0.00705655i
$121$	6.11206	−	13.3836i	0.555642	−	1.21669i
$122$	8.75474	−	10.1035i	0.792617	−	0.914729i
$123$	−0.0305611	+	0.212557i	−0.00275560	+	0.0191656i
$124$	2.27140	−	0.666944i	0.203978	−	0.0598934i
$125$	−0.654861	−	0.755750i	−0.0585725	−	0.0675963i
$126$	1.37163	−	0.881494i	0.122195	−	0.0785298i
$127$	8.43745	−	5.42242i	0.748703	−	0.481162i	−0.109811	−	0.993952i	$-0.535025\pi$
$127$	8.43745	−	5.42242i	0.748703	−	0.481162i	0.858514	+	0.512790i	$0.171388\pi$
$128$	0.654861	+	0.755750i	0.0578821	+	0.0667995i
$129$	0.874933	−	0.256903i	0.0770335	−	0.0226191i
$130$	−0.580610	+	4.03823i	−0.0509229	+	0.354177i
$131$	−10.8418	+	12.5122i	−0.947257	+	1.09319i	0.0482818	+	0.998834i	$0.484625\pi$
$131$	−10.8418	+	12.5122i	−0.947257	+	1.09319i	−0.995538	+	0.0943585i	$0.969920\pi$
$132$	−0.577971	+	1.26558i	−0.0503059	+	0.110155i
$133$	0.129572	+	0.0380459i	0.0112354	+	0.00329900i
$134$	2.56762	+	5.62231i	0.221809	+	0.485694i
$135$	−0.231347	−	1.60905i	−0.0199112	−	0.138485i
$136$	0.491025	+	0.315563i	0.0421051	+	0.0270593i
$137$	−11.0893			−0.947420			−0.473710	−	0.880681i	$-0.657085\pi$
$137$	−11.0893			−0.947420			−0.473710	+	0.880681i	$0.657085\pi$
$138$	−0.00758225	−	1.31584i	−0.000645444	−	0.112012i
$139$	−4.19223			−0.355581			−0.177790	−	0.984068i	$-0.556895\pi$
$139$	−4.19223			−0.355581			−0.177790	+	0.984068i	$0.556895\pi$
$140$	0.468979	+	0.301395i	0.0396360	+	0.0254725i
$141$	−0.444244	−	3.08979i	−0.0374121	−	0.260207i
$142$	−1.21341	−	2.65700i	−0.101827	−	0.222970i
$143$	19.8497	+	5.82840i	1.65992	+	0.487395i
$144$	−1.21497	+	2.66042i	−0.101248	+	0.221701i
$145$	−1.39259	+	1.60714i	−0.115649	+	0.133466i
$146$	1.13090	−	7.86558i	0.0935940	−	0.650960i
$147$	−1.76102	+	0.517081i	−0.145246	+	0.0426481i
$148$	−6.45974	−	7.45494i	−0.530987	−	0.612792i
$149$	−8.02781	+	5.15916i	−0.657664	+	0.422655i	−0.826459	−	0.562996i	$-0.809649\pi$
$149$	−8.02781	+	5.15916i	−0.657664	+	0.422655i	0.168796	+	0.985651i	$0.446012\pi$
$150$	0.230820	−	0.148339i	0.0188464	−	0.0121118i
$151$	6.30246	+	7.27342i	0.512887	+	0.591903i	0.951835	−	0.306609i	$-0.0991945\pi$
$151$	6.30246	+	7.27342i	0.512887	+	0.591903i	−0.438949	+	0.898512i	$0.644649\pi$
$152$	−0.232427	+	0.0682466i	−0.0188523	+	0.00553553i
$153$	−0.242947	+	1.68973i	−0.0196411	+	0.136607i
$154$	1.85120	−	2.13640i	0.149174	−	0.172156i
$155$	−0.983410	+	2.15337i	−0.0789894	+	0.172963i
$156$	−1.07405	−	0.315368i	−0.0859924	−	0.0252497i
$157$	4.20314	+	9.20360i	0.335447	+	0.734527i	0.999918	−	0.0127869i	$-0.00407030\pi$
$157$	4.20314	+	9.20360i	0.335447	+	0.734527i	−0.664471	+	0.747314i	$0.731343\pi$
$158$	1.95644	+	13.6074i	0.155646	+	1.08254i
$159$	0.383535	+	0.246483i	0.0304163	+	0.0195473i
$160$	−1.00000			−0.0790569
$161$	−0.738436	+	2.56956i	−0.0581969	+	0.202510i
$162$	−8.32813			−0.654320
$163$	−15.4445	−	9.92559i	−1.20971	−	0.777432i	−0.229099	−	0.973403i	$-0.573578\pi$
$163$	−15.4445	−	9.92559i	−1.20971	−	0.777432i	−0.980610	+	0.195971i	$0.937214\pi$
$164$	0.111384	+	0.774693i	0.00869763	+	0.0604933i
$165$	−0.577971	−	1.26558i	−0.0449950	−	0.0985252i
$166$	3.65782	+	1.07403i	0.283902	+	0.0833611i
$167$	6.10622	−	13.3707i	0.472513	−	1.03466i	−0.511941	−	0.859020i	$-0.671074\pi$
$167$	6.10622	−	13.3707i	0.472513	−	1.03466i	0.984455	−	0.175639i	$-0.0561992\pi$
$168$	−0.100166	+	0.115598i	−0.00772800	+	0.00891859i
$169$	−0.518658	+	3.60735i	−0.0398968	+	0.277488i
$170$	−0.560040	+	0.164442i	−0.0429531	+	0.0126122i
$171$	−0.463956	−	0.535434i	−0.0354796	−	0.0409457i
$172$	2.79585	−	1.79678i	0.213181	−	0.137003i
$173$	−0.845262	+	0.543217i	−0.0642641	+	0.0413000i	−0.572378	−	0.819990i	$-0.693979\pi$
$173$	−0.845262	+	0.543217i	−0.0642641	+	0.0413000i	0.508114	+	0.861290i	$0.330343\pi$
$174$	−0.382095	−	0.440961i	−0.0289665	−	0.0334291i
$175$	−0.534895	+	0.157059i	−0.0404343	+	0.0118726i
$176$	−0.721652	+	5.01920i	−0.0543966	+	0.378336i
$177$	−0.336980	+	0.388896i	−0.0253290	+	0.0292312i
$178$	−6.45542	+	14.1354i	−0.483854	+	1.05949i
$179$	−2.07432	−	0.609076i	−0.155042	−	0.0455245i	0.203290	−	0.979118i	$-0.434836\pi$
$179$	−2.07432	−	0.609076i	−0.155042	−	0.0455245i	−0.358333	+	0.933594i	$0.616655\pi$
$180$	−1.21497	−	2.66042i	−0.0905586	−	0.198296i
$181$	−2.83121	−	19.6915i	−0.210442	−	1.46366i	−0.771685	−	0.636005i	$-0.780586\pi$
$181$	−2.83121	−	19.6915i	−0.210442	−	1.46366i	0.561243	−	0.827651i	$-0.310323\pi$
$182$	1.91332	+	1.22962i	0.141825	+	0.0911454i
$183$	−3.66809			−0.271153
$184$	−1.37763	−	4.59370i	−0.101561	−	0.338652i
$185$	9.86429			0.725237
$186$	−0.546419	−	0.351162i	−0.0400654	−	0.0257484i
$187$	0.421216	+	2.92962i	0.0308024	+	0.214235i
$188$	−4.72615	−	10.3488i	−0.344690	−	0.754766i
$189$	−0.869526	−	0.255316i	−0.0632487	−	0.0185715i
$190$	0.100630	−	0.220348i	0.00730045	−	0.0159857i
$191$	−12.6043	+	14.5461i	−0.912013	+	1.05252i	0.0864030	+	0.996260i	$0.472463\pi$
$191$	−12.6043	+	14.5461i	−0.912013	+	1.05252i	−0.998416	+	0.0562591i	$0.982083\pi$
$192$	0.0390478	−	0.271583i	0.00281803	−	0.0195998i
$193$	−13.6610	+	4.01124i	−0.983342	+	0.288735i	−0.733603	−	0.679578i	$-0.762163\pi$
$193$	−13.6610	+	4.01124i	−0.983342	+	0.288735i	−0.249738	+	0.968313i	$0.580345\pi$
$194$	−5.39945	−	6.23130i	−0.387658	−	0.447381i
$195$	0.941689	−	0.605187i	0.0674358	−	0.0433383i
$196$	−5.62733	+	3.61647i	−0.401952	+	0.258319i
$197$	14.9447	+	17.2470i	1.06476	+	1.22880i	0.972460	+	0.233070i	$0.0748772\pi$
$197$	14.9447	+	17.2470i	1.06476	+	1.22880i	0.0923026	+	0.995731i	$0.470577\pi$
$198$	−14.2300	+	4.17829i	−1.01128	+	0.296938i
$199$	0.169585	−	1.17949i	0.0120215	−	0.0836116i	−0.982927	−	0.183994i	$-0.941097\pi$
$199$	0.169585	−	1.17949i	0.0120215	−	0.0836116i	0.994949	+	0.100382i	$0.0320065\pi$
$200$	0.654861	−	0.755750i	0.0463056	−	0.0534396i
$201$	0.704494	−	1.54263i	0.0496912	−	0.108809i
$202$	9.09276	+	2.66988i	0.639765	+	0.187852i
$203$	0.492476	+	1.07837i	0.0345650	+	0.0756868i
$204$	−0.0227915	−	0.158518i	−0.00159573	−	0.0110985i
$205$	−0.658415	−	0.423137i	−0.0459857	−	0.0295532i
$206$	−9.38768			−0.654070
$207$	10.5474	−	9.24630i	0.733094	−	0.642663i
$208$	−4.07976			−0.282880
$209$	−1.03335	−	0.664096i	−0.0714785	−	0.0459364i
$210$	−0.0217682	−	0.151401i	−0.00150215	−	0.0104477i
$211$	8.69340	+	19.0359i	0.598478	+	1.31049i	0.930181	+	0.367101i	$0.119650\pi$
$211$	8.69340	+	19.0359i	0.598478	+	1.31049i	−0.331703	+	0.943384i	$0.607623\pi$
$212$	1.59431	+	0.468132i	0.109498	+	0.0321514i
$213$	−0.332930	+	0.729016i	−0.0228120	+	0.0499513i
$214$	−9.83450	+	11.3496i	−0.672272	+	0.775844i
$215$	−0.472974	+	3.28960i	−0.0322565	+	0.224349i
$216$	1.55975	−	0.457985i	0.106128	−	0.0311619i
$217$	0.864228	+	0.997372i	0.0586676	+	0.0677060i
$218$	11.0850	−	7.12388i	0.750769	−	0.482490i
$219$	−1.83420	+	1.17877i	−0.123944	+	0.0796539i
$220$	−3.32068	−	3.83227i	−0.223880	−	0.258371i
$221$	−2.28483	+	0.670886i	−0.153694	+	0.0451287i
$222$	−0.385179	+	2.67898i	−0.0258515	+	0.179801i
$223$	−14.4160	+	16.6370i	−0.965367	+	1.11409i	0.0280575	+	0.999606i	$0.491068\pi$
$223$	−14.4160	+	16.6370i	−0.965367	+	1.11409i	−0.993425	+	0.114487i	$0.963478\pi$
$224$	−0.231584	+	0.507099i	−0.0154734	+	0.0338820i
$225$	2.80625	+	0.823988i	0.187083	+	0.0549325i
$226$	−2.88980	−	6.32779i	−0.192227	−	0.420918i
$227$	0.527150	+	3.66641i	0.0349882	+	0.243348i	0.999809	−	0.0195614i	$-0.00622698\pi$
$227$	0.527150	+	3.66641i	0.0349882	+	0.243348i	−0.964820	+	0.262910i	$0.915318\pi$
$228$	0.0559136	+	0.0359335i	0.00370297	+	0.00237975i
$229$	−24.1493			−1.59583			−0.797914	−	0.602771i	$-0.794063\pi$
$229$	−24.1493			−1.59583			−0.797914	+	0.602771i	$0.794063\pi$
$230$	4.37385	+	1.96709i	0.288403	+	0.129706i
$231$	−0.775623			−0.0510322
$232$	−1.78897	−	1.14970i	−0.117452	−	0.0754815i
$233$	−2.58055	−	17.9481i	−0.169057	−	1.17582i	−0.880838	−	0.473417i	$-0.843020\pi$
$233$	−2.58055	−	17.9481i	−0.169057	−	1.17582i	0.711781	−	0.702401i	$-0.247889\pi$
$234$	−4.95679	−	10.8539i	−0.324036	−	0.709539i
$235$	10.9161	+	3.20526i	0.712088	+	0.209088i
$236$	−0.779097	+	1.70599i	−0.0507149	+	0.111050i
$237$	2.47009	−	2.85063i	0.160449	−	0.185168i
$238$	−0.0463078	+	0.322078i	−0.00300169	+	0.0208772i
$239$	−18.4453	+	5.41604i	−1.19313	+	0.350334i	−0.817222	−	0.576323i	$-0.804487\pi$
$239$	−18.4453	+	5.41604i	−1.19313	+	0.350334i	−0.375907	+	0.926657i	$0.622669\pi$
$240$	0.179678	+	0.207360i	0.0115982	+	0.0133850i
$241$	22.7555	−	14.6241i	1.46581	−	0.942020i	0.467497	−	0.883995i	$-0.345156\pi$
$241$	22.7555	−	14.6241i	1.46581	−	0.942020i	0.998315	−	0.0580256i	$-0.0184805\pi$
$242$	−12.3775	+	7.95453i	−0.795655	+	0.511337i
$243$	4.69001	+	5.41256i	0.300864	+	0.347216i
$244$	−12.8273	+	3.76644i	−0.821185	+	0.241122i
$245$	0.951975	−	6.62113i	0.0608195	−	0.423009i
$246$	0.140627	−	0.162292i	0.00896603	−	0.0103474i
$247$	0.410545	−	0.898968i	0.0261224	−	0.0572000i
$248$	−2.27140	−	0.666944i	−0.144234	−	0.0423510i
$249$	−0.434519	−	0.951463i	−0.0275365	−	0.0602965i
$250$	0.142315	+	0.989821i	0.00900078	+	0.0626018i
$251$	−10.4009	−	6.68423i	−0.656497	−	0.421905i	0.169538	−	0.985524i	$-0.445772\pi$
$251$	−10.4009	−	6.68423i	−0.656497	−	0.421905i	−0.826035	+	0.563619i	$0.809409\pi$
$252$	−1.63046			−0.102709
$253$	13.0296	−	20.5337i	0.819165	−	1.29094i
$254$	−10.0296			−0.629314
$255$	0.134726	+	0.0865829i	0.00843684	+	0.00542203i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−0.0808766	−	0.177095i	−0.00504494	−	0.0110469i	0.907093	−	0.420931i	$-0.138296\pi$
$257$	−0.0808766	−	0.177095i	−0.00504494	−	0.0110469i	−0.912138	+	0.409884i	$0.865569\pi$
$258$	−0.874933	−	0.256903i	−0.0544709	−	0.0159941i
$259$	2.28441	−	5.00217i	0.141947	−	0.310820i
$260$	2.67167	−	3.08328i	0.165690	−	0.191217i
$261$	0.885136	−	6.15626i	0.0547885	−	0.381063i
$262$	15.8853	−	4.66435i	0.981399	−	0.288165i
$263$	4.03035	+	4.65128i	0.248522	+	0.286810i	0.866280	−	0.499558i	$-0.166504\pi$
$263$	4.03035	+	4.65128i	0.248522	+	0.286810i	−0.617758	+	0.786368i	$0.711959\pi$
$264$	1.17044	−	0.752199i	0.0720359	−	0.0462946i
$265$	−1.39784	+	0.898339i	−0.0858688	+	0.0551845i
$266$	−0.0884341	−	0.102058i	−0.00542224	−	0.00625760i
$267$	4.09101	−	1.20123i	0.250365	−	0.0735139i
$268$	0.879629	−	6.11795i	0.0537319	−	0.373713i
$269$	−9.98468	+	11.5229i	−0.608777	+	0.702566i	−0.973535	−	0.228536i	$-0.926606\pi$
$269$	−9.98468	+	11.5229i	−0.608777	+	0.702566i	0.364759	+	0.931102i	$0.381151\pi$
$270$	−0.675299	+	1.47870i	−0.0410974	+	0.0899907i
$271$	25.8391	+	7.58705i	1.56961	+	0.460880i	0.946889	−	0.321560i	$-0.104207\pi$
$271$	25.8391	+	7.58705i	1.56961	+	0.460880i	0.622725	+	0.782441i	$0.286025\pi$
$272$	−0.242471	−	0.530937i	−0.0147019	−	0.0321928i
$273$	−0.0888091	−	0.617681i	−0.00537497	−	0.0373838i
$274$	9.32888	+	5.99531i	0.563578	+	0.362190i
$275$	5.07081			0.305782
$276$	−0.705018	+	1.11105i	−0.0424371	+	0.0668776i
$277$	4.57420			0.274837			0.137419	−	0.990513i	$-0.456119\pi$
$277$	4.57420			0.274837			0.137419	+	0.990513i	$0.456119\pi$
$278$	3.52673	+	2.26649i	0.211519	+	0.135935i
$279$	−0.985341	−	6.85320i	−0.0589908	−	0.410290i
$280$	−0.231584	−	0.507099i	−0.0138398	−	0.0303049i
$281$	−7.04276	−	2.06794i	−0.420136	−	0.123363i	0.0648297	−	0.997896i	$-0.479350\pi$
$281$	−7.04276	−	2.06794i	−0.420136	−	0.123363i	−0.484965	+	0.874533i	$0.661168\pi$
$282$	−1.29674	+	2.83947i	−0.0772199	+	0.169088i
$283$	2.11718	−	2.44335i	0.125853	−	0.145242i	−0.689326	−	0.724451i	$-0.742093\pi$
$283$	2.11718	−	2.44335i	0.125853	−	0.145242i	0.815179	+	0.579209i	$0.196639\pi$
$284$	−0.415696	+	2.89123i	−0.0246670	+	0.171563i
$285$	−0.0637723	+	0.0187252i	−0.00377754	+	0.00110919i
$286$	−13.5476	−	15.6347i	−0.801084	−	0.924501i
$287$	−0.367051	+	0.235889i	−0.0216663	+	0.0139241i
$288$	2.46043	−	1.58122i	0.144982	−	0.0931744i
$289$	10.9095	+	12.5903i	0.641737	+	0.740604i
$290$	2.04041	−	0.599119i	0.119817	−	0.0351815i
$291$	−0.321956	+	2.23925i	−0.0188734	+	0.131267i
$292$	−5.20383	+	6.00554i	−0.304531	+	0.351448i
$293$	−2.80852	+	6.14981i	−0.164076	+	0.359276i	−0.973756	−	0.227596i	$-0.926913\pi$
$293$	−2.80852	+	6.14981i	−0.164076	+	0.359276i	0.809680	+	0.586872i	$0.199641\pi$
$294$	1.76102	+	0.517081i	0.102705	+	0.0301568i
$295$	−0.779097	−	1.70599i	−0.0453608	−	0.0993263i
$296$	1.40384	+	9.76389i	0.0815963	+	0.567515i
$297$	6.93455	+	4.45657i	0.402383	+	0.258596i
$298$	9.54267			0.552792
$299$	17.8443	+	8.02526i	1.03196	+	0.464113i
$300$	−0.274376			−0.0158411
$301$	1.55862	+	1.00166i	0.0898374	+	0.0577350i
$302$	−1.36965	−	9.52616i	−0.0788148	−	0.548169i
$303$	−1.08015	−	2.36519i	−0.0620528	−	0.135877i
$304$	0.232427	+	0.0682466i	0.0133306	+	0.00391421i
$305$	5.55362	−	12.1607i	0.318000	−	0.696322i
$306$	1.11792	−	1.29015i	0.0639071	−	0.0737527i
$307$	1.36340	−	9.48267i	0.0778134	−	0.541204i	−0.913207	−	0.407495i	$-0.866402\pi$
$307$	1.36340	−	9.48267i	0.0778134	−	0.541204i	0.991021	−	0.133709i	$-0.0426887\pi$
$308$	−2.71235	+	0.796419i	−0.154551	+	0.0453802i
$309$	1.68676	+	1.94662i	0.0959564	+	0.110740i
$310$	1.99150	−	1.27986i	0.113109	−	0.0726910i
$311$	−10.0589	+	6.46448i	−0.570390	+	0.366567i	−0.793820	−	0.608153i	$-0.791911\pi$
$311$	−10.0589	+	6.46448i	−0.570390	+	0.366567i	0.223430	+	0.974720i	$0.428274\pi$
$312$	0.733043	+	0.845977i	0.0415004	+	0.0478940i
$313$	6.00377	−	1.76286i	0.339353	−	0.0996430i	−0.107616	−	0.994193i	$-0.534322\pi$
$313$	6.00377	−	1.76286i	0.339353	−	0.0996430i	0.446969	+	0.894550i	$0.352503\pi$
$314$	1.43993	−	10.0150i	0.0812601	−	0.565176i
$315$	1.06773	−	1.23222i	0.0601595	−	0.0694278i
$316$	5.71083	−	12.5050i	0.321259	−	0.703460i
$317$	−24.0731	−	7.06851i	−1.35208	−	0.397007i	−0.476118	−	0.879382i	$-0.657956\pi$
$317$	−24.0731	−	7.06851i	−1.35208	−	0.397007i	−0.875965	+	0.482374i	$0.839775\pi$
$318$	−0.189391	−	0.414709i	−0.0106205	−	0.0232557i
$319$	−1.53463	−	10.6736i	−0.0859228	−	0.597606i
$320$	0.841254	+	0.540641i	0.0470275	+	0.0302227i
$321$	4.12049			0.229984
$322$	2.01042	−	1.76243i	0.112037	−	0.0982162i
$323$	0.141391			0.00786719
$324$	7.00607	+	4.50253i	0.389226	+	0.250140i
$325$	0.580610	+	4.03823i	0.0322065	+	0.224001i
$326$	7.62658	+	16.6999i	0.422397	+	0.924921i
$327$	−3.46893	−	1.01857i	−0.191832	−	0.0563271i
$328$	0.325128	−	0.711932i	0.0179522	−	0.0393099i
$329$	4.15338	−	4.79325i	0.228983	−	0.264261i
$330$	−0.198004	+	1.37715i	−0.0108998	+	0.0758095i
$331$	1.65168	−	0.484978i	0.0907847	−	0.0266568i	−0.236025	−	0.971747i	$-0.575845\pi$
$331$	1.65168	−	0.484978i	0.0907847	−	0.0266568i	0.326809	+	0.945090i	$0.394026\pi$
$332$	−2.49649	−	2.88110i	−0.137012	−	0.158121i
$333$	−24.2704	+	15.5976i	−1.33001	+	0.854745i
$334$	−12.3656	+	7.94692i	−0.676618	+	0.434836i
$335$	4.04761	+	4.67119i	0.221144	+	0.255214i
$336$	0.146762	−	0.0430933i	0.00800654	−	0.00235093i
$337$	−1.27732	+	8.88396i	−0.0695801	+	0.483940i	0.925000	+	0.379967i	$0.124065\pi$
$337$	−1.27732	+	8.88396i	−0.0695801	+	0.483940i	−0.994580	+	0.103973i	$0.966844\pi$
$338$	2.38660	−	2.75429i	0.129814	−	0.149813i
$339$	−0.792893	+	1.73619i	−0.0430640	+	0.0942970i
$340$	0.560040	+	0.164442i	0.0303724	+	0.00891815i
$341$	−4.98669	−	10.9193i	−0.270044	−	0.591315i
$342$	0.100827	+	0.701269i	0.00545212	+	0.0379203i
$343$	−6.41996	−	4.12586i	−0.346645	−	0.222775i
$344$	−3.32343			−0.179187
$345$	−0.377990	−	1.26040i	−0.0203503	−	0.0678578i
$346$	1.00476			0.0540165
$347$	27.7725	+	17.8483i	1.49091	+	0.958147i	0.996014	+	0.0891925i	$0.0284286\pi$
$347$	27.7725	+	17.8483i	1.49091	+	0.958147i	0.494892	+	0.868955i	$0.335208\pi$
$348$	0.0830371	+	0.577536i	0.00445126	+	0.0309592i
$349$	−1.60731	−	3.51951i	−0.0860372	−	0.188395i	0.861723	−	0.507379i	$-0.169386\pi$
$349$	−1.60731	−	3.51951i	−0.0860372	−	0.188395i	−0.947760	+	0.318984i	$0.896658\pi$
$350$	0.534895	+	0.157059i	0.0285913	+	0.00839518i
$351$	−2.75506	+	6.03273i	−0.147054	+	0.322003i
$352$	3.32068	−	3.83227i	0.176993	−	0.204260i
$353$	−2.82676	+	19.6606i	−0.150453	+	1.04643i	0.765008	+	0.644021i	$0.222735\pi$
$353$	−2.82676	+	19.6606i	−0.150453	+	1.04643i	−0.915462	+	0.402406i	$0.868174\pi$
$354$	0.493739	−	0.144975i	0.0262419	−	0.00770533i
$355$	−1.91282	−	2.20751i	−0.101522	−	0.117163i
$356$	13.0728	−	8.40139i	0.692858	−	0.445273i
$357$	0.0751064	−	0.0482679i	0.00397505	−	0.00255461i
$358$	1.41574	+	1.63385i	0.0748242	+	0.0863517i
$359$	4.42347	−	1.29885i	0.233462	−	0.0685505i	−0.162909	−	0.986641i	$-0.552088\pi$
$359$	4.42347	−	1.29885i	0.233462	−	0.0685505i	0.396371	+	0.918091i	$0.370270\pi$
$360$	−0.416231	+	2.89495i	−0.0219373	+	0.152577i
$361$	12.4039	−	14.3149i	0.652838	−	0.753416i
$362$	−8.26425	+	18.0962i	−0.434360	+	0.951115i
$363$	3.87341	+	1.13734i	0.203301	+	0.0596947i
$364$	−0.944808	−	2.06884i	−0.0495214	−	0.108437i
$365$	−1.13090	−	7.86558i	−0.0591940	−	0.411704i
$366$	3.08580	+	1.98312i	0.161297	+	0.103659i
$367$	14.0677			0.734326			0.367163	−	0.930157i	$-0.380329\pi$
$367$	14.0677			0.734326			0.367163	+	0.930157i	$0.380329\pi$
$368$	−1.32460	+	4.60928i	−0.0690498	+	0.240275i
$369$	2.28906			0.119164
$370$	−8.29837	−	5.33304i	−0.431412	−	0.277252i
$371$	0.131828	+	0.916885i	0.00684418	+	0.0476023i
$372$	0.269824	+	0.590832i	0.0139897	+	0.0306332i
$373$	6.13295	+	1.80080i	0.317552	+	0.0932417i	0.436624	−	0.899644i	$-0.356174\pi$
$373$	6.13295	+	1.80080i	0.317552	+	0.0932417i	−0.119072	+	0.992886i	$0.537992\pi$
$374$	1.22952	−	2.69228i	0.0635771	−	0.139215i
$375$	0.179678	−	0.207360i	0.00927854	−	0.0107080i
$376$	−1.61911	+	11.2611i	−0.0834991	+	0.580749i
$377$	8.32439	−	2.44426i	0.428728	−	0.125886i
$378$	0.593457	+	0.684886i	0.0305242	+	0.0352267i
$379$	−3.71040	+	2.38453i	−0.190590	+	0.122485i	−0.632456	−	0.774596i	$-0.717953\pi$
$379$	−3.71040	+	2.38453i	−0.190590	+	0.122485i	0.441866	+	0.897081i	$0.354317\pi$
$380$	−0.203784	+	0.130964i	−0.0104539	+	0.00671833i
$381$	1.80210	+	2.07974i	0.0923245	+	0.106548i
$382$	18.4676	−	5.42258i	0.944885	−	0.277443i
$383$	3.37732	−	23.4898i	0.172573	−	1.20027i	−0.700849	−	0.713309i	$-0.747196\pi$
$383$	3.37732	−	23.4898i	0.172573	−	1.20027i	0.873423	−	0.486963i	$-0.161895\pi$
$384$	−0.179678	+	0.207360i	−0.00916916	+	0.0105818i
$385$	1.17432	−	2.57140i	0.0598489	−	0.131051i
$386$	13.6610	+	4.01124i	0.695327	+	0.204167i
$387$	−4.03788	−	8.84171i	−0.205257	−	0.449450i
$388$	1.17341	+	8.16126i	0.0595710	+	0.414325i
$389$	1.77301	+	1.13945i	0.0898953	+	0.0577722i	0.584816	−	0.811166i	$-0.301167\pi$
$389$	1.77301	+	1.13945i	0.0898953	+	0.0577722i	−0.494921	+	0.868938i	$0.664803\pi$
$390$	−1.11939			−0.0566824
$391$	0.0161298	+	2.79920i	0.000815719	+	0.141562i
$392$	6.68922			0.337857
$393$	−3.82144	−	2.45589i	−0.192766	−	0.123883i
$394$	−3.24778	−	22.5888i	−0.163621	−	1.13801i
$395$	5.71083	+	12.5050i	0.287343	+	0.629194i
$396$	14.2300	+	4.17829i	0.715082	+	0.209967i
$397$	7.79840	−	17.0761i	0.391390	−	0.857025i	−0.606681	−	0.794945i	$-0.707499\pi$
$397$	7.79840	−	17.0761i	0.391390	−	0.857025i	0.998071	−	0.0620797i	$-0.0197733\pi$
$398$	−0.780342	+	0.900563i	−0.0391150	+	0.0451411i
$399$	−0.00527311	+	0.0366753i	−0.000263986	+	0.00183606i
$400$	−0.959493	+	0.281733i	−0.0479746	+	0.0140866i
$401$	−24.6035	−	28.3940i	−1.22864	−	1.41793i	−0.876099	−	0.482131i	$-0.839863\pi$
$401$	−24.6035	−	28.3940i	−1.22864	−	1.41793i	−0.352541	−	0.935796i	$-0.614682\pi$
$402$	−1.42667	+	0.916862i	−0.0711556	+	0.0457289i
$403$	8.12482	−	5.22151i	0.404726	−	0.260102i
$404$	−6.20588	−	7.16196i	−0.308754	−	0.356321i
$405$	−7.99078	+	2.34630i	−0.397065	+	0.116589i
$406$	0.168715	−	1.17344i	0.00837317	−	0.0582367i
$407$	−32.7561	+	37.8026i	−1.62366	+	1.87380i
$408$	−0.0665281	+	0.145676i	−0.00329363	+	0.00721205i
$409$	16.6086	+	4.87671i	0.821240	+	0.241138i	0.665250	−	0.746621i	$-0.268325\pi$
$409$	16.6086	+	4.87671i	0.821240	+	0.241138i	0.155990	+	0.987759i	$0.450143\pi$
$410$	0.325128	+	0.711932i	0.0160569	+	0.0351598i
$411$	−0.433011	−	3.01166i	−0.0213589	−	0.148554i
$412$	7.89742	+	5.07536i	0.389078	+	0.250045i
$413$	−1.04553			−0.0514471
$414$	−13.8720	+	2.07614i	−0.681769	+	0.102037i
$415$	3.81224			0.187135
$416$	3.43211	+	2.20568i	0.168273	+	0.108143i
$417$	−0.163697	−	1.13854i	−0.00801629	−	0.0557546i
$418$	0.510275	+	1.11735i	0.0249583	+	0.0546512i
$419$	−28.7813	−	8.45094i	−1.40606	−	0.412855i	−0.511297	−	0.859404i	$-0.670835\pi$
$419$	−28.7813	−	8.45094i	−1.40606	−	0.412855i	−0.894759	+	0.446549i	$0.852653\pi$
$420$	−0.0635411	+	0.139136i	−0.00310049	+	0.00678913i
$421$	1.28507	−	1.48305i	0.0626306	−	0.0722796i	−0.723570	−	0.690251i	$-0.757500\pi$
$421$	1.28507	−	1.48305i	0.0626306	−	0.0722796i	0.786200	+	0.617972i	$0.212045\pi$
$422$	2.97823	−	20.7140i	0.144978	−	1.00834i
$423$	−31.9265	+	9.37447i	−1.55232	+	0.455802i
$424$	−1.08813	−	1.25577i	−0.0528442	−	0.0609855i
$425$	−0.491025	+	0.315563i	−0.0238182	+	0.0153070i
$426$	0.674215	−	0.433291i	0.0326658	−	0.0209930i
$427$	−4.88056	−	5.63247i	−0.236187	−	0.272574i
$428$	14.4094	−	4.23097i	0.696503	−	0.204512i
$429$	−0.807809	+	5.61843i	−0.0390014	+	0.271261i
$430$	2.17638	−	2.51168i	0.104955	−	0.121124i
$431$	5.65657	−	12.3862i	0.272467	−	0.596620i	−0.723093	−	0.690751i	$-0.757280\pi$
$431$	5.65657	−	12.3862i	0.272467	−	0.596620i	0.995560	+	0.0941311i	$0.0300073\pi$
$432$	−1.55975	−	0.457985i	−0.0750436	−	0.0220348i
$433$	−10.8539	−	23.7666i	−0.521603	−	1.14215i	−0.968829	−	0.247731i	$-0.920315\pi$
$433$	−10.8539	−	23.7666i	−0.521603	−	1.14215i	0.447226	−	0.894421i	$-0.352412\pi$
$434$	−0.187815	−	1.30628i	−0.00901539	−	0.0627034i
$435$	−0.490850	−	0.315450i	−0.0235345	−	0.0151247i
$436$	−13.1767			−0.631051
$437$	−0.882352	−	0.755704i	−0.0422086	−	0.0361502i
$438$	2.18032			0.104180
$439$	20.6030	+	13.2407i	0.983325	+	0.631945i	0.930358	−	0.366652i	$-0.119496\pi$
$439$	20.6030	+	13.2407i	0.983325	+	0.631945i	0.0529669	+	0.998596i	$0.483132\pi$
$440$	0.721652	+	5.01920i	0.0344034	+	0.239281i
$441$	8.12721	+	17.7961i	0.387010	+	0.847434i
$442$	2.28483	+	0.670886i	0.108678	+	0.0319108i
$443$	1.75534	−	3.84366i	0.0833987	−	0.182618i	−0.863338	−	0.504626i	$-0.831631\pi$
$443$	1.75534	−	3.84366i	0.0833987	−	0.182618i	0.946737	+	0.322008i	$0.104358\pi$
$444$	1.77240	−	2.04546i	0.0841142	−	0.0970730i
$445$	−2.21153	+	15.3815i	−0.104836	+	0.729154i
$446$	21.1221	−	6.20202i	1.00016	−	0.293674i
$447$	−1.71461	−	1.97876i	−0.0810982	−	0.0935924i
$448$	0.468979	−	0.301395i	0.0221572	−	0.0142396i
$449$	22.4655	−	14.4377i	1.06021	−	0.681356i	0.110307	−	0.993898i	$-0.464817\pi$
$449$	22.4655	−	14.4377i	1.06021	−	0.681356i	0.949904	+	0.312541i	$0.101180\pi$
$450$	−1.91528	−	2.21035i	−0.0902873	−	0.104197i
$451$	3.80796	−	1.11812i	0.179310	−	0.0526501i
$452$	−0.990002	+	6.88562i	−0.0465658	+	0.323872i
$453$	−1.72924	+	1.99565i	−0.0812469	+	0.0937639i
$454$	1.53874	−	3.36938i	0.0722169	−	0.158133i
$455$	2.18224	+	0.640765i	0.102305	+	0.0300395i
$456$	−0.0276104	−	0.0604583i	−0.00129297	−	0.00283122i
$457$	−2.91174	−	20.2516i	−0.136205	−	0.947329i	−0.937234	−	0.348702i	$-0.886623\pi$
$457$	−2.91174	−	20.2516i	−0.136205	−	0.947329i	0.801028	−	0.598626i	$-0.204287\pi$
$458$	20.3157	+	13.0561i	0.949288	+	0.610071i
$459$	−0.948835			−0.0442878
$460$	−2.61603	−	4.01950i	−0.121973	−	0.187410i
$461$	−39.8465			−1.85584			−0.927918	−	0.372783i	$-0.878404\pi$
$461$	−39.8465			−1.85584			−0.927918	+	0.372783i	$0.878404\pi$
$462$	0.652495	+	0.419333i	0.0303568	+	0.0195092i
$463$	2.10655	+	14.6514i	0.0978998	+	0.680908i	0.978379	+	0.206822i	$0.0663122\pi$
$463$	2.10655	+	14.6514i	0.0978998	+	0.680908i	−0.880479	+	0.474086i	$0.842779\pi$
$464$	0.883401	+	1.93438i	0.0410109	+	0.0898013i
$465$	−0.623218	−	0.182993i	−0.0289011	−	0.00848612i
$466$	−7.53258	+	16.4940i	−0.348940	+	0.764072i
$467$	−7.59362	+	8.76351i	−0.351391	+	0.405527i	−0.903737	−	0.428088i	$-0.859187\pi$
$467$	−7.59362	+	8.76351i	−0.351391	+	0.405527i	0.552346	+	0.833615i	$0.313733\pi$
$468$	−1.69812	+	11.8107i	−0.0784957	+	0.545950i
$469$	3.30611	−	0.970763i	0.152662	−	0.0448257i
$470$	−7.45032	−	8.59812i	−0.343657	−	0.396602i
$471$	−2.33542	+	1.50088i	−0.107610	+	0.0691571i
$472$	1.57774	−	1.01395i	0.0726215	−	0.0466710i
$473$	−11.0360	−	12.7363i	−0.507438	−	0.585614i
$474$	−3.61914	+	1.06267i	−0.166232	+	0.0488103i
$475$	0.0344742	−	0.239773i	0.00158178	−	0.0110016i
$476$	0.213085	−	0.245913i	0.00976673	−	0.0112714i
$477$	2.01882	−	4.42060i	0.0924354	−	0.202405i
$478$	18.4453	+	5.41604i	0.843669	+	0.247724i
$479$	13.2183	+	28.9441i	0.603961	+	1.32249i	0.926629	+	0.375977i	$0.122693\pi$
$479$	13.2183	+	28.9441i	0.603961	+	1.32249i	−0.322668	+	0.946512i	$0.604580\pi$
$480$	−0.0390478	−	0.271583i	−0.00178228	−	0.0123960i
$481$	−33.8554	−	21.7575i	−1.54367	−	0.992058i
$482$	−27.0495			−1.23207
$483$	−0.726685	−	0.100211i	−0.0330653	−	0.00455976i
$484$	14.7132			0.668780
$485$	−6.93629	−	4.45768i	−0.314961	−	0.202413i
$486$	−1.01924	−	7.08894i	−0.0462335	−	0.321561i
$487$	−15.6137	−	34.1892i	−0.707523	−	1.54926i	−0.830605	−	0.556863i	$-0.812005\pi$
$487$	−15.6137	−	34.1892i	−0.707523	−	1.54926i	0.123082	−	0.992397i	$-0.460722\pi$
$488$	12.8273	+	3.76644i	0.580666	+	0.170499i
$489$	2.09255	−	4.58205i	0.0946284	−	0.207207i
$490$	−4.38051	+	5.05537i	−0.197891	+	0.228379i
$491$	−5.57766	+	38.7935i	−0.251716	+	1.75073i	0.336188	+	0.941795i	$0.390862\pi$
$491$	−5.57766	+	38.7935i	−0.251716	+	1.75073i	−0.587904	+	0.808931i	$0.700047\pi$
$492$	−0.206044	+	0.0605001i	−0.00928919	+	0.00272755i
$493$	0.812834	+	0.938060i	0.0366082	+	0.0422481i
$494$	−0.831392	+	0.534303i	−0.0374061	+	0.0240394i
$495$	−12.4764	+	8.01808i	−0.560772	+	0.360386i
$496$	1.55025	+	1.78908i	0.0696082	+	0.0803322i
$497$	−1.56241	+	0.458764i	−0.0700835	+	0.0205784i
$498$	−0.148859	+	1.03534i	−0.00667055	+	0.0463947i
$499$	−0.0683537	+	0.0788844i	−0.00305993	+	0.00353135i	−0.757277	−	0.653093i	$-0.773471\pi$
$499$	−0.0683537	+	0.0788844i	−0.00305993	+	0.00353135i	0.754218	+	0.656625i	$0.228016\pi$
$500$	0.415415	−	0.909632i	0.0185779	−	0.0406800i
$501$	3.86970	+	1.13625i	0.172886	+	0.0507638i
$502$	5.13600	+	11.2463i	0.229231	+	0.501946i
$503$	−1.88569	−	13.1153i	−0.0840790	−	0.584782i	−0.987690	−	0.156427i	$-0.950002\pi$
$503$	−1.88569	−	13.1153i	−0.0840790	−	0.584782i	0.903611	−	0.428355i	$-0.140907\pi$
$504$	1.37163	+	0.881494i	0.0610974	+	0.0392649i
$505$	9.47663			0.421705
$506$	−22.0626	+	10.2297i	−0.980800	+	0.454765i
$507$	−0.999948			−0.0444092
$508$	8.43745	+	5.42242i	0.374351	+	0.240581i
$509$	−1.79372	−	12.4756i	−0.0795052	−	0.552971i	−0.990175	−	0.139835i	$-0.955343\pi$
$509$	−1.79372	−	12.4756i	−0.0795052	−	0.552971i	0.910670	−	0.413135i	$-0.135566\pi$
$510$	−0.0665281	−	0.145676i	−0.00294591	−	0.00645065i
$511$	−4.25053	−	1.24807i	−0.188032	−	0.0552112i
$512$	−0.415415	+	0.909632i	−0.0183589	+	0.0402004i
$513$	0.257874	−	0.297602i	0.0113854	−	0.0131394i
$514$	−0.0277071	+	0.192707i	−0.00122211	+	0.00849994i
$515$	−9.00741	+	2.64481i	−0.396914	+	0.116544i
$516$	0.597148	+	0.689145i	0.0262880	+	0.0303379i
$517$	−48.5322	+	31.1898i	−2.13445	+	1.37172i
$518$	−4.62615	+	2.97305i	−0.203261	+	0.130628i
$519$	−0.180534	−	0.208348i	−0.00792457	−	0.00914544i
$520$	−3.91450	+	1.14940i	−0.171662	+	0.0504046i
$521$	−2.05635	+	14.3022i	−0.0900905	+	0.626593i	0.893886	+	0.448294i	$0.147968\pi$
$521$	−2.05635	+	14.3022i	−0.0900905	+	0.626593i	−0.983976	+	0.178299i	$0.942941\pi$
$522$	−4.07295	+	4.70043i	−0.178268	+	0.205732i
$523$	−12.6646	+	27.7315i	−0.553783	+	1.21261i	0.401210	+	0.915986i	$0.368590\pi$
$523$	−12.6646	+	27.7315i	−0.553783	+	1.21261i	−0.954993	+	0.296629i	$0.904138\pi$
$524$	−15.8853	−	4.66435i	−0.693954	−	0.203763i
$525$	−0.0635411	−	0.139136i	−0.00277316	−	0.00607238i
$526$	−0.875880	−	6.09188i	−0.0381902	−	0.265618i
$527$	1.16240	+	0.747030i	0.0506350	+	0.0325412i
$528$	−1.39131			−0.0605490
$529$	14.8605	−	17.5547i	0.646108	−	0.763246i
$530$	1.66162			0.0721761
$531$	4.61445	+	2.96553i	0.200250	+	0.128693i
$532$	0.0192186	+	0.133668i	0.000833231	+	0.00579525i
$533$	1.32645	+	2.90451i	0.0574547	+	0.125808i
$534$	−4.09101	−	1.20123i	−0.177035	−	0.0519822i
$535$	−6.23857	+	13.6606i	−0.269717	+	0.590598i
$536$	−4.04761	+	4.67119i	−0.174830	+	0.201765i
$537$	0.0844172	−	0.587135i	0.00364287	−	0.0253367i
$538$	14.6294	−	4.29558i	0.630719	−	0.185196i
$539$	22.2127	+	25.6349i	0.956770	+	1.10417i
$540$	1.36754	−	0.878866i	0.0588496	−	0.0378204i
$541$	22.3026	−	14.3330i	0.958863	−	0.616224i	0.0351800	−	0.999381i	$-0.488800\pi$
$541$	22.3026	−	14.3330i	0.958863	−	0.616224i	0.923683	+	0.383157i	$0.125163\pi$
$542$	−17.6354	−	20.3523i	−0.757504	−	0.874207i
$543$	5.23732	−	1.53782i	0.224755	−	0.0659940i
$544$	−0.0830667	+	0.577742i	−0.00356146	+	0.0247705i
$545$	8.62893	−	9.95831i	0.369623	−	0.426567i
$546$	−0.259233	+	0.567640i	−0.0110941	+	0.0242928i
$547$	−31.1989	−	9.16083i	−1.33397	−	0.391689i	−0.464455	−	0.885596i	$-0.653750\pi$
$547$	−31.1989	−	9.16083i	−1.33397	−	0.391689i	−0.869514	+	0.493908i	$0.835568\pi$
$548$	−4.60665	−	10.0872i	−0.196786	−	0.430902i
$549$	5.56453	+	38.7022i	0.237488	+	1.65177i
$550$	−4.26584	−	2.74149i	−0.181896	−	0.116897i
$551$	−0.515134			−0.0219454
$552$	1.19378	−	0.553516i	0.0508106	−	0.0235592i
$553$	7.66380			0.325898
$554$	−3.84806	−	2.47300i	−0.163489	−	0.105068i
$555$	0.385179	+	2.67898i	0.0163499	+	0.113716i
$556$	−1.74152	−	3.81339i	−0.0738568	−	0.161724i
$557$	−20.1073	−	5.90405i	−0.851975	−	0.250163i	−0.173544	−	0.984826i	$-0.555522\pi$
$557$	−20.1073	−	5.90405i	−0.851975	−	0.250163i	−0.678432	+	0.734664i	$0.737340\pi$
$558$	−2.87620	+	6.29799i	−0.121759	+	0.266615i
$559$	8.87913	−	10.2471i	0.375547	−	0.433405i
$560$	−0.0793372	+	0.551802i	−0.00335261	+	0.0233179i
$561$	−0.779189	+	0.228790i	−0.0328974	+	0.00965954i
$562$	4.80673	+	5.54726i	0.202760	+	0.233997i
$563$	9.14553	−	5.87747i	0.385438	−	0.247706i	−0.333544	−	0.942734i	$-0.608245\pi$
$563$	9.14553	−	5.87747i	0.385438	−	0.247706i	0.718982	+	0.695029i	$0.244608\pi$
$564$	2.62602	−	1.68764i	0.110576	−	0.0710626i
$565$	−4.55549	−	5.25731i	−0.191651	−	0.221177i
$566$	−3.10206	+	0.910846i	−0.130389	+	0.0382857i
$567$	−0.660730	+	4.59548i	−0.0277481	+	0.192992i
$568$	1.91282	−	2.20751i	0.0802601	−	0.0926251i
$569$	10.1927	−	22.3189i	0.427300	−	0.935656i	−0.566457	−	0.824091i	$-0.691686\pi$
$569$	10.1927	−	22.3189i	0.427300	−	0.935656i	0.993757	−	0.111565i	$-0.0355863\pi$
$570$	0.0637723	+	0.0187252i	0.00267113	+	0.000784314i
$571$	14.8081	+	32.4252i	0.619699	+	1.35695i	0.915738	+	0.401776i	$0.131607\pi$
$571$	14.8081	+	32.4252i	0.619699	+	1.35695i	−0.296039	+	0.955176i	$0.595666\pi$
$572$	2.94417	+	20.4771i	0.123102	+	0.856192i
$573$	−4.44265	−	2.85512i	−0.185594	−	0.119274i
$574$	0.436314			0.0182114
$575$	4.75087	+	0.655153i	0.198125	+	0.0273218i
$576$	−2.92472			−0.121863
$577$	4.43135	+	2.84785i	0.184479	+	0.118558i	0.629621	−	0.776903i	$-0.283210\pi$
$577$	4.43135	+	2.84785i	0.184479	+	0.118558i	−0.445141	+	0.895460i	$0.646847\pi$
$578$	−2.37087	−	16.4897i	−0.0986151	−	0.685883i
$579$	−1.62282	−	3.55347i	−0.0674420	−	0.147677i
$580$	−2.04041	−	0.599119i	−0.0847235	−	0.0248770i
$581$	0.882855	−	1.93318i	0.0366270	−	0.0802019i
$582$	1.48148	−	1.70972i	0.0614093	−	0.0708701i
$583$	1.19911	−	8.34000i	0.0496621	−	0.345407i
$584$	7.62458	−	2.23878i	0.315507	−	0.0926413i
$585$	−7.81389	−	9.01772i	−0.323065	−	0.372837i
$586$	5.68752	−	3.65514i	0.234949	−	0.150993i
$587$	18.6345	−	11.9757i	0.769130	−	0.494290i	−0.0962802	−	0.995354i	$-0.530694\pi$
$587$	18.6345	−	11.9757i	0.769130	−	0.494290i	0.865410	+	0.501065i	$0.167058\pi$
$588$	−1.20191	−	1.38707i	−0.0495658	−	0.0572019i
$589$	−0.550222	+	0.161560i	−0.0226715	+	0.00665696i
$590$	−0.266907	+	1.85638i	−0.0109884	+	0.0764259i
$591$	−4.10045	+	4.73218i	−0.168670	+	0.194656i
$592$	4.09778	−	8.97288i	0.168418	−	0.368783i
$593$	10.7550	+	3.15796i	0.441656	+	0.129682i	0.494998	−	0.868894i	$-0.335169\pi$
$593$	10.7550	+	3.15796i	0.441656	+	0.129682i	−0.0533413	+	0.998576i	$0.516987\pi$
$594$	−3.42431	−	7.49820i	−0.140501	−	0.307655i
$595$	0.0463078	+	0.322078i	0.00189843	+	0.0132039i
$596$	−8.02781	−	5.15916i	−0.328832	−	0.211327i
$597$	0.326951			0.0133812
$598$	−10.6728	−	16.3986i	−0.436442	−	0.670589i
$599$	36.0050			1.47112			0.735562	−	0.677457i	$-0.236918\pi$
$599$	36.0050			1.47112			0.735562	+	0.677457i	$0.236918\pi$
$600$	0.230820	+	0.148339i	0.00942318	+	0.00605591i
$601$	5.52368	+	38.4180i	0.225316	+	1.56710i	0.717465	+	0.696594i	$0.245302\pi$
$601$	5.52368	+	38.4180i	0.225316	+	1.56710i	−0.492150	+	0.870511i	$0.663789\pi$
$602$	−0.769654	−	1.68531i	−0.0313688	−	0.0686880i
$603$	−17.3450	−	5.09296i	−0.706344	−	0.207401i
$604$	−3.99800	+	8.75440i	−0.162676	+	0.356212i
$605$	−9.63507	+	11.1195i	−0.391721	+	0.452070i
$606$	−0.370041	+	2.57370i	−0.0150319	+	0.104549i
$607$	24.9645	−	7.33023i	1.01328	−	0.297525i	0.267383	−	0.963590i	$-0.413841\pi$
$607$	24.9645	−	7.33023i	1.01328	−	0.297525i	0.745893	+	0.666065i	$0.232023\pi$
$608$	−0.158633	−	0.183072i	−0.00643341	−	0.00742455i
$609$	−0.273637	+	0.175856i	−0.0110884	+	0.00712605i
$610$	−11.2466	+	7.22775i	−0.455362	+	0.292643i
$611$	−30.3955	−	35.0783i	−1.22967	−	1.41912i
$612$	−1.63796	+	0.480948i	−0.0662105	+	0.0194412i
$613$	2.39010	−	16.6235i	0.0965354	−	0.671418i	−0.882885	−	0.469589i	$-0.844402\pi$
$613$	2.39010	−	16.6235i	0.0965354	−	0.671418i	0.979421	−	0.201830i	$-0.0646887\pi$
$614$	−6.27368	+	7.24022i	−0.253185	+	0.292191i
$615$	0.0892074	−	0.195337i	0.00359719	−	0.00787675i
$616$	2.71235	+	0.796419i	0.109284	+	0.0320886i
$617$	7.87771	+	17.2498i	0.317145	+	0.694450i	0.999325	−	0.0367338i	$-0.0116954\pi$
$617$	7.87771	+	17.2498i	0.317145	+	0.694450i	−0.682180	+	0.731184i	$0.738968\pi$
$618$	−0.366568	−	2.54954i	−0.0147455	−	0.102557i
$619$	−4.15253	−	2.66867i	−0.166904	−	0.107263i	0.454522	−	0.890735i	$-0.349810\pi$
$619$	−4.15253	−	2.66867i	−0.166904	−	0.107263i	−0.621426	+	0.783473i	$0.713446\pi$
$620$	−2.36730			−0.0950729
$621$	5.92122	+	5.07133i	0.237611	+	0.203505i
$622$	11.9571			0.479435
$623$	7.28779	+	4.68358i	0.291979	+	0.187644i
$624$	−0.159306	−	1.10799i	−0.00637733	−	0.0443553i
$625$	0.415415	+	0.909632i	0.0166166	+	0.0363853i
$626$	−6.00377	−	1.76286i	−0.239959	−	0.0704582i
$627$	0.140007	−	0.306573i	0.00559134	−	0.0122433i
$628$	−6.62584	+	7.64663i	−0.264400	+	0.305134i
$629$	0.819395	−	5.69902i	0.0326714	−	0.227235i
$630$	−1.56442	+	0.459354i	−0.0623279	+	0.0183011i
$631$	−24.8126	−	28.6353i	−0.987775	−	1.13995i	−0.990158	−	0.139956i	$-0.955304\pi$
$631$	−24.8126	−	28.6353i	−0.987775	−	1.13995i	0.00238282	−	0.999997i	$-0.499242\pi$
$632$	−11.5650	+	7.43235i	−0.460029	+	0.295643i
$633$	−4.83037	+	3.10429i	−0.191990	+	0.123385i
$634$	16.4301	+	18.9613i	0.652522	+	0.753051i
$635$	−9.62335	+	2.82567i	−0.381891	+	0.112133i
$636$	−0.0648825	+	0.451268i	−0.00257276	+	0.0178939i
$637$	−17.8714	+	20.6247i	−0.708091	+	0.817181i
$638$	−4.47956	+	9.80888i	−0.177348	+	0.388337i
$639$	8.19692	+	2.40683i	0.324265	+	0.0952129i
$640$	−0.415415	−	0.909632i	−0.0164207	−	0.0359564i
$641$	−0.602581	−	4.19105i	−0.0238005	−	0.165536i	0.974455	−	0.224585i	$-0.0721025\pi$
$641$	−0.602581	−	4.19105i	−0.0238005	−	0.165536i	−0.998255	+	0.0590482i	$0.981193\pi$
$642$	−3.46638	−	2.22771i	−0.136807	−	0.0879206i
$643$	7.49055			0.295398			0.147699	−	0.989032i	$-0.452813\pi$
$643$	7.49055			0.295398			0.147699	+	0.989032i	$0.452813\pi$
$644$	−2.64412	+	0.395730i	−0.104193	+	0.0155940i
$645$	−0.911870			−0.0359048
$646$	−0.118945	−	0.0764416i	−0.00467985	−	0.00300756i
$647$	−3.99949	−	27.8171i	−0.157236	−	1.09360i	−0.903697	−	0.428172i	$-0.859158\pi$
$647$	−3.99949	−	27.8171i	−0.157236	−	1.09360i	0.746461	−	0.665429i	$-0.231751\pi$
$648$	−3.45963	−	7.57553i	−0.135907	−	0.297595i
$649$	9.12492	+	2.67932i	0.358184	+	0.105172i
$650$	1.69479	−	3.71108i	0.0664753	−	0.145561i
$651$	−0.237123	+	0.273655i	−0.00929360	+	0.0107254i
$652$	2.61275	−	18.1721i	0.102323	−	0.711673i
$653$	27.5086	−	8.07724i	1.07649	−	0.316087i	0.305018	−	0.952346i	$-0.401337\pi$
$653$	27.5086	−	8.07724i	1.07649	−	0.316087i	0.771475	+	0.636260i	$0.219519\pi$
$654$	2.36757	+	2.73232i	0.0925793	+	0.106842i
$655$	13.9278	−	8.95083i	0.544203	−	0.349738i
$656$	−0.658415	+	0.423137i	−0.0257068	+	0.0165207i
$657$	15.2197	+	17.5645i	0.593778	+	0.685257i
$658$	−6.08547	+	1.78686i	−0.237236	+	0.0696589i
$659$	1.00453	−	6.98666i	0.0391309	−	0.272162i	−0.960857	−	0.277044i	$-0.910645\pi$
$659$	1.00453	−	6.98666i	0.0391309	−	0.272162i	0.999988	+	0.00488263i	$0.00155420\pi$
$660$	0.911114	−	1.05148i	0.0354651	−	0.0409289i
$661$	11.0797	−	24.2612i	0.430951	−	0.943650i	−0.562221	−	0.826987i	$-0.690053\pi$
$661$	11.0797	−	24.2612i	0.430951	−	0.943650i	0.993172	−	0.116663i	$-0.0372198\pi$
$662$	−1.65168	−	0.484978i	−0.0641945	−	0.0188492i
$663$	−0.271419	−	0.594324i	−0.0105410	−	0.0230816i
$664$	0.542538	+	3.77344i	0.0210546	+	0.146438i
$665$	−0.113605	−	0.0730095i	−0.00440542	−	0.00283119i
$666$	28.8503			1.11793
$667$	−0.0587662	−	10.1984i	−0.00227544	−	0.394884i
$668$	14.6991			0.568724
$669$	−5.08123	−	3.26551i	−0.196452	−	0.126252i
$670$	−0.879629	−	6.11795i	−0.0339830	−	0.236357i
$671$	28.1614	+	61.6649i	1.08716	+	2.38055i
$672$	−0.146762	−	0.0430933i	−0.00566148	−	0.00166236i
$673$	4.01440	−	8.79031i	0.154744	−	0.338841i	−0.816343	−	0.577567i	$-0.804002\pi$
$673$	4.01440	−	8.79031i	0.154744	−	0.338841i	0.971087	+	0.238725i	$0.0767296\pi$
$674$	5.87758	−	6.78309i	0.226396	−	0.261275i
$675$	−0.231347	+	1.60905i	−0.00890455	+	0.0619325i
$676$	−3.49682	+	1.02676i	−0.134493	+	0.0394907i
$677$	24.6642	+	28.4640i	0.947923	+	1.09396i	0.995468	+	0.0950923i	$0.0303146\pi$
$677$	24.6642	+	28.4640i	0.947923	+	1.09396i	−0.0475455	+	0.998869i	$0.515140\pi$
$678$	1.60568	−	1.03191i	0.0616658	−	0.0396302i
$679$	−3.86682	+	2.48506i	−0.148395	+	0.0953677i
$680$	−0.382231	−	0.441118i	−0.0146579	−	0.0169161i
$681$	−0.975152	+	0.286330i	−0.0373679	+	0.0109722i
$682$	−1.70836	+	11.8819i	−0.0654166	+	0.454983i
$683$	30.4239	−	35.1111i	1.16414	−	1.34349i	0.235778	−	0.971807i	$-0.424236\pi$
$683$	30.4239	−	35.1111i	1.16414	−	1.34349i	0.928361	−	0.371680i	$-0.121218\pi$
$684$	0.294314	−	0.644457i	0.0112534	−	0.0246414i
$685$	10.6401	+	3.12421i	0.406536	+	0.119370i
$686$	3.17021	+	6.94179i	0.121039	+	0.265039i
$687$	−0.942975	−	6.55854i	−0.0359767	−	0.250224i
$688$	2.79585	+	1.79678i	0.106591	+	0.0685017i
$689$	6.77901			0.258260
$690$	−0.363440	+	1.26467i	−0.0138359	+	0.0481453i
$691$	51.7450			1.96847			0.984237	−	0.176856i	$-0.0565927\pi$
$691$	51.7450			1.96847			0.984237	+	0.176856i	$0.0565927\pi$
$692$	−0.845262	−	0.543217i	−0.0321320	−	0.0206500i
$693$	1.17663	+	8.18362i	0.0446963	+	0.310870i
$694$	−13.7142	−	30.0299i	−0.520584	−	1.13992i
$695$	4.02242	+	1.18109i	0.152579	+	0.0448012i
$696$	0.242384	−	0.530747i	0.00918755	−	0.0201179i
$697$	−0.299157	+	0.345245i	−0.0113314	+	0.0130771i
$698$	−0.550639	+	3.82978i	−0.0208420	+	0.144959i
$699$	4.77364	−	1.40167i	0.180556	−	0.0530159i
$700$	−0.365070	−	0.421313i	−0.0137983	−	0.0159241i
$701$	31.2264	−	20.0680i	1.17941	−	0.757958i	0.204129	−	0.978944i	$-0.434564\pi$
$701$	31.2264	−	20.0680i	1.17941	−	0.757958i	0.975277	+	0.220986i	$0.0709275\pi$
$702$	5.57924	−	3.58556i	0.210575	−	0.135328i
$703$	1.56480	+	1.80588i	0.0590176	+	0.0681099i
$704$	−4.86541	+	1.42861i	−0.183372	+	0.0538429i
$705$	−0.444244	+	3.08979i	−0.0167312	+	0.116368i
$706$	13.0073	−	15.0113i	0.489537	−	0.564956i
$707$	2.19464	−	4.80559i	0.0825379	−	0.180733i
$708$	−0.493739	−	0.144975i	−0.0185558	−	0.00544849i
$709$	10.6458	+	23.3111i	0.399813	+	0.875468i	0.997289	+	0.0735813i	$0.0234429\pi$
$709$	10.6458	+	23.3111i	0.399813	+	0.875468i	−0.597476	+	0.801886i	$0.703830\pi$
$710$	0.415696	+	2.89123i	0.0156008	+	0.108506i
$711$	−33.8242	−	21.7375i	−1.26851	−	0.815221i
$712$	−15.5397			−0.582374
$713$	−3.26127	−	10.8747i	−0.122135	−	0.407259i
$714$	−0.0892791			−0.00334119
$715$	−17.4036	−	11.1846i	−0.650858	−	0.418281i
$716$	−0.307670	−	2.13989i	−0.0114982	−	0.0799715i
$717$	−2.19115	−	4.79796i	−0.0818301	−	0.179183i
$718$	−4.42347	−	1.29885i	−0.165082	−	0.0484725i
$719$	13.4996	−	29.5600i	0.503450	−	1.10240i	−0.471882	−	0.881662i	$-0.656425\pi$
$719$	13.4996	−	29.5600i	0.503450	−	1.10240i	0.975333	−	0.220741i	$-0.0708474\pi$
$720$	1.91528	−	2.21035i	0.0713784	−	0.0823750i
$721$	−0.744792	+	5.18014i	−0.0277375	+	0.192919i
$722$	−18.1741	+	5.33639i	−0.676369	+	0.198600i
$723$	4.86021	+	5.60898i	0.180753	+	0.208600i
$724$	16.7359	−	10.7555i	0.621984	−	0.399725i
$725$	1.78897	−	1.14970i	0.0664406	−	0.0426988i
$726$	−2.64363	−	3.05091i	−0.0981143	−	0.113230i
$727$	−3.11073	+	0.913392i	−0.115371	+	0.0338758i	−0.338908	−	0.940819i	$-0.610058\pi$
$727$	−3.11073	+	0.913392i	−0.115371	+	0.0338758i	0.223538	+	0.974695i	$0.428239\pi$
$728$	−0.323677	+	2.25122i	−0.0119963	+	0.0834358i
$729$	15.0745	−	17.3969i	0.558314	−	0.644328i
$730$	−3.30108	+	7.22836i	−0.122179	+	0.267534i
$731$	1.86125	+	0.546513i	0.0688409	+	0.0202135i
$732$	−1.52378	−	3.33662i	−0.0563206	−	0.123325i
$733$	6.96768	+	48.4613i	0.257357	+	1.78996i	0.551478	+	0.834189i	$0.314064\pi$
$733$	6.96768	+	48.4613i	0.257357	+	1.78996i	−0.294121	+	0.955768i	$0.595027\pi$
$734$	−11.8345	−	7.60555i	−0.436818	−	0.280726i
$735$	1.83536			0.0676983
$736$	3.60629	−	3.16143i	0.132930	−	0.116532i
$737$	−31.3420			−1.15450
$738$	−1.92568	−	1.23756i	−0.0708852	−	0.0455551i
$739$	−0.802154	−	5.57910i	−0.0295077	−	0.205231i	0.969734	−	0.244163i	$-0.0785133\pi$
$739$	−0.802154	−	5.57910i	−0.0295077	−	0.205231i	−0.999242	+	0.0389327i	$0.987604\pi$
$740$	4.09778	+	8.97288i	0.150637	+	0.329850i
$741$	0.260176	+	0.0763945i	0.00955779	+	0.00280642i
$742$	0.384805	−	0.842605i	0.0141266	−	0.0309330i
$743$	14.5812	−	16.8277i	0.534934	−	0.617347i	−0.422372	−	0.906422i	$-0.638803\pi$
$743$	14.5812	−	16.8277i	0.534934	−	0.617347i	0.957306	+	0.289076i	$0.0933480\pi$
$744$	0.0924376	−	0.642918i	0.00338893	−	0.0235705i
$745$	9.15613	−	2.68848i	0.335455	−	0.0984984i
$746$	−4.18578	−	4.83065i	−0.153252	−	0.176863i
$747$	−9.37975	+	6.02800i	−0.343187	+	0.220553i
$748$	−2.48990	+	1.60016i	−0.0910397	+	0.0585077i
$749$	5.48250	+	6.32715i	0.200326	+	0.231189i
$750$	−0.263262	+	0.0773006i	−0.00961296	+	0.00282262i
$751$	−2.59846	+	18.0727i	−0.0948192	+	0.659482i	0.885874	+	0.463927i	$0.153560\pi$
$751$	−2.59846	+	18.0727i	−0.0948192	+	0.659482i	−0.980693	+	0.195555i	$0.937349\pi$
$752$	7.45032	−	8.59812i	0.271685	−	0.313541i
$753$	1.40919	−	3.08571i	0.0513539	−	0.112449i
$754$	−8.32439	−	2.44426i	−0.303156	−	0.0890147i
$755$	−3.99800	−	8.75440i	−0.145502	−	0.318605i
$756$	−0.128971	−	0.897010i	−0.00469062	−	0.0326239i
$757$	11.0327	+	7.09027i	0.400989	+	0.257700i	0.725557	−	0.688162i	$-0.241582\pi$
$757$	11.0327	+	7.09027i	0.400989	+	0.257700i	−0.324567	+	0.945863i	$0.605219\pi$
$758$	4.41056			0.160199
$759$	6.08538	+	2.73683i	0.220885	+	0.0993407i
$760$	0.242239			0.00878693
$761$	−25.6896	−	16.5097i	−0.931249	−	0.598477i	−0.0153480	−	0.999882i	$-0.504886\pi$
$761$	−25.6896	−	16.5097i	−0.931249	−	0.598477i	−0.915901	+	0.401405i	$0.868522\pi$
$762$	−0.391634	−	2.72388i	−0.0141874	−	0.0986756i
$763$	−3.05152	−	6.68190i	−0.110473	−	0.241901i
$764$	−18.4676	−	5.42258i	−0.668135	−	0.196182i
$765$	0.709158	−	1.55284i	0.0256397	−	0.0561430i
$766$	−15.5407	+	17.9350i	−0.561509	+	0.648016i
$767$	−1.08892	+	7.57358i	−0.0393185	+	0.273466i
$768$	0.263262	−	0.0773006i	0.00949964	−	0.00278935i
$769$	18.5925	+	21.4569i	0.670462	+	0.773754i	0.984449	−	0.175673i	$-0.0562102\pi$
$769$	18.5925	+	21.4569i	0.670462	+	0.773754i	−0.313987	+	0.949427i	$0.601665\pi$
$770$	−2.37811	+	1.52832i	−0.0857010	+	0.0550767i
$771$	0.0449380	−	0.0288799i	0.00161840	−	0.00104008i
$772$	−9.32374	−	10.7602i	−0.335569	−	0.387267i
$773$	27.9059	−	8.19392i	1.00371	−	0.294715i	0.261731	−	0.965141i	$-0.415707\pi$
$773$	27.9059	−	8.19392i	1.00371	−	0.294715i	0.741976	+	0.670426i	$0.233889\pi$
$774$	−1.38331	+	9.62116i	−0.0497222	+	0.345826i
$775$	1.55025	−	1.78908i	0.0556866	−	0.0642657i
$776$	3.42517	−	7.50008i	0.122957	−	0.269237i
$777$	1.44771	+	0.425085i	0.0519362	+	0.0152498i
$778$	−0.875522	−	1.91713i	−0.0313890	−	0.0687323i
$779$	−0.0269816	−	0.187661i	−0.000966714	−	0.00672365i
$780$	0.941689	+	0.605187i	0.0337179	+	0.0216692i
$781$	14.8116			0.530002
$782$	1.49979	−	2.36356i	0.0536324	−	0.0845206i
$783$	3.45692			0.123540
$784$	−5.62733	−	3.61647i	−0.200976	−	0.129159i
$785$	−1.43993	−	10.0150i	−0.0513934	−	0.357449i
$786$	1.88705	+	4.13206i	0.0673087	+	0.147386i
$787$	−43.2040	−	12.6858i	−1.54005	−	0.452201i	−0.601945	−	0.798538i	$-0.705607\pi$
$787$	−43.2040	−	12.6858i	−1.54005	−	0.452201i	−0.938110	+	0.346337i	$0.887425\pi$
$788$	−9.48023	+	20.7588i	−0.337719	+	0.739502i
$789$	−1.10583	+	1.27620i	−0.0393687	+	0.0454339i
$790$	1.95644	−	13.6074i	0.0696071	−	0.484128i
$791$	−3.72096	+	1.09257i	−0.132302	+	0.0388474i
$792$	−9.71204	−	11.2083i	−0.345102	−	0.398269i
$793$	−45.8834	+	29.4875i	−1.62937	+	1.04713i
$794$	−15.7925	+	10.1492i	−0.560454	+	0.360182i
$795$	−0.298556	−	0.344553i	−0.0105887	−	0.0122200i
$796$	1.14335	−	0.335717i	0.0405248	−	0.0118992i
$797$	5.39418	−	37.5173i	0.191072	−	1.32893i	−0.638107	−	0.769948i	$-0.720282\pi$
$797$	5.39418	−	37.5173i	0.191072	−	1.32893i	0.829178	−	0.558984i	$-0.188809\pi$
$798$	0.0242642	−	0.0280024i	0.000858943	−	0.000991273i
$799$	2.75858	−	6.04044i	0.0975914	−	0.213695i
$800$	0.959493	+	0.281733i	0.0339232	+	0.00996075i
$801$	−18.8803	−	41.3420i	−0.667102	−	1.46075i
$802$	5.34685	+	37.1882i	0.188804	+	1.31316i
$803$	33.8984	+	21.7852i	1.19625	+	0.768781i
$804$	1.69588			0.0598091
$805$	1.43245	−	2.25744i	0.0504874	−	0.0795642i
$806$	−9.65800			−0.340188
$807$	−3.51932	−	2.26173i	−0.123886	−	0.0796165i
$808$	1.34867	+	9.38018i	0.0474459	+	0.329993i
$809$	18.6295	+	40.7930i	0.654979	+	1.43420i	0.887128	+	0.461524i	$0.152697\pi$
$809$	18.6295	+	40.7930i	0.654979	+	1.43420i	−0.232149	+	0.972680i	$0.574576\pi$
$810$	7.99078	+	2.34630i	0.280767	+	0.0824407i
$811$	−3.29293	+	7.21052i	−0.115631	+	0.253196i	−0.958595	−	0.284774i	$-0.908081\pi$
$811$	−3.29293	+	7.21052i	−0.115631	+	0.253196i	0.842964	+	0.537970i	$0.180809\pi$
$812$	−0.776339	+	0.895943i	−0.0272442	+	0.0314414i
$813$	−1.05156	+	7.31373i	−0.0368797	+	0.256504i
$814$	47.9938	−	14.0923i	1.68218	−	0.493934i
$815$	12.0225	+	13.8748i	0.421131	+	0.486012i
$816$	0.134726	−	0.0865829i	0.00471634	−	0.00303101i
$817$	−0.677264	+	0.435251i	−0.0236945	+	0.0152275i
$818$	−11.3355	−	13.0818i	−0.396335	−	0.457395i
$819$	−6.38245	+	1.87406i	−0.223021	+	0.0654848i
$820$	0.111384	−	0.774693i	0.00388970	−	0.0270534i
$821$	29.3939	−	33.9224i	1.02586	−	1.18390i	0.0430847	−	0.999071i	$-0.486281\pi$
$821$	29.3939	−	33.9224i	1.02586	−	1.18390i	0.982771	−	0.184829i	$-0.0591731\pi$
$822$	−1.26395	+	2.76767i	−0.0440854	+	0.0965336i
$823$	−39.1805	−	11.5044i	−1.36575	−	0.401019i	−0.484961	−	0.874536i	$-0.661166\pi$
$823$	−39.1805	−	11.5044i	−1.36575	−	0.401019i	−0.880785	+	0.473516i	$0.842984\pi$
$824$	−3.89978	−	8.53933i	−0.135855	−	0.297482i
$825$	0.198004	+	1.37715i	0.00689361	+	0.0479461i
$826$	0.879555	+	0.565256i	0.0306036	+	0.0196678i
$827$	19.7597			0.687112			0.343556	−	0.939132i	$-0.388369\pi$
$827$	19.7597			0.687112			0.343556	+	0.939132i	$0.388369\pi$
$828$	12.7923	+	5.75318i	0.444562	+	0.199937i
$829$	−37.8794			−1.31561			−0.657803	−	0.753190i	$-0.728514\pi$
$829$	−37.8794			−1.31561			−0.657803	+	0.753190i	$0.728514\pi$
$830$	−3.20706	−	2.06105i	−0.111319	−	0.0715402i
$831$	0.178612	+	1.24228i	0.00619600	+	0.0430941i
$832$	−1.69479	−	3.71108i	−0.0587564	−	0.128659i
$833$	−3.74623	−	1.09999i	−0.129799	−	0.0381125i
$834$	−0.477830	+	1.04630i	−0.0165459	+	0.0362305i
$835$	−9.62585	+	11.1088i	−0.333116	+	0.384436i
$836$	0.174812	−	1.21585i	0.00604601	−	0.0420509i
$837$	3.69239	−	1.08418i	0.127628	−	0.0374749i
$838$	19.6434	+	22.6697i	0.678570	+	0.783112i
$839$	−25.3442	+	16.2877i	−0.874980	+	0.562315i	−0.899272	−	0.437390i	$-0.855903\pi$
$839$	−25.3442	+	16.2877i	−0.874980	+	0.562315i	0.0242923	+	0.999705i	$0.492267\pi$
$840$	0.128677	−	0.0826955i	0.00443977	−	0.00285326i
$841$	16.0295	+	18.4991i	0.552743	+	0.637899i
$842$	−1.88287	+	0.552861i	−0.0648880	+	0.0190528i
$843$	0.286614	−	1.99344i	0.00987150	−	0.0686578i
$844$	−13.7043	+	15.8156i	−0.471721	+	0.544395i
$845$	1.51396	−	3.31510i	0.0520817	−	0.114043i
$846$	31.9265	+	9.37447i	1.09766	+	0.322301i
$847$	3.40733	+	7.46102i	0.117077	+	0.256364i
$848$	0.236473	+	1.64471i	0.00812052	+	0.0564794i
$849$	0.746244	+	0.479582i	0.0256110	+	0.0164592i
$850$	0.583683			0.0200202
$851$	−35.5735	+	31.1853i	−1.21944	+	1.06902i
$852$	−0.801440			−0.0274569
$853$	−26.2902	−	16.8957i	−0.900160	−	0.578498i	0.00667771	−	0.999978i	$-0.497874\pi$
$853$	−26.2902	−	16.8957i	−0.900160	−	0.578498i	−0.906838	+	0.421480i	$0.861511\pi$
$854$	1.06065	+	7.37697i	0.0362946	+	0.252435i
$855$	0.294314	+	0.644457i	0.0100653	+	0.0220400i
$856$	−14.4094	−	4.23097i	−0.492502	−	0.144612i
$857$	−22.2622	+	48.7473i	−0.760461	+	1.66518i	−0.0138610	+	0.999904i	$0.504412\pi$
$857$	−22.2622	+	48.7473i	−0.760461	+	1.66518i	−0.746600	+	0.665273i	$0.768315\pi$
$858$	3.71713	−	4.28979i	0.126901	−	0.146451i
$859$	3.37277	−	23.4581i	0.115077	−	0.800380i	−0.847776	−	0.530355i	$-0.822059\pi$
$859$	3.37277	−	23.4581i	0.115077	−	0.800380i	0.962853	−	0.270025i	$-0.0870321\pi$
$860$	−3.18881	+	0.936319i	−0.108737	+	0.0319282i
$861$	−0.0783961	−	0.0904739i	−0.00267173	−	0.00308334i
$862$	−11.4551	+	7.36172i	−0.390161	+	0.250741i
$863$	−27.5149	+	17.6828i	−0.936619	+	0.601928i	−0.917434	−	0.397888i	$-0.869743\pi$
$863$	−27.5149	+	17.6828i	−0.936619	+	0.601928i	−0.0191847	+	0.999816i	$0.506107\pi$
$864$	1.06454	+	1.22855i	0.0362164	+	0.0417960i
$865$	0.964065	−	0.283075i	0.0327792	−	0.00962483i
$866$	−3.71837	+	25.8618i	−0.126355	+	0.878820i
$867$	−2.99331	+	3.45447i	−0.101658	+	0.117320i
$868$	−0.548228	+	1.20045i	−0.0186081	+	0.0407460i
$869$	−66.8862	−	19.6396i	−2.26896	−	0.666227i
$870$	0.242384	+	0.530747i	0.00821759	+	0.0179940i
$871$	−3.58867	−	24.9598i	−0.121598	−	0.845730i
$872$	11.0850	+	7.12388i	0.375385	+	0.241245i
$873$	24.1148			0.816164
$874$	0.333717	+	1.11277i	0.0112881	+	0.0376402i
$875$	0.557477			0.0188462
$876$	−1.83420	−	1.17877i	−0.0619719	−	0.0398269i
$877$	2.50619	+	17.4309i	0.0846280	+	0.588601i	0.987372	+	0.158422i	$0.0506405\pi$
$877$	2.50619	+	17.4309i	0.0846280	+	0.588601i	−0.902744	+	0.430179i	$0.858450\pi$
$878$	−10.1738	−	22.2776i	−0.343350	−	0.751832i
$879$	−1.77985	−	0.522611i	−0.0600329	−	0.0176272i
$880$	2.10649	−	4.61257i	0.0710098	−	0.155490i
$881$	−18.7469	+	21.6350i	−0.631598	+	0.728903i	−0.977866	−	0.209233i	$-0.932903\pi$
$881$	−18.7469	+	21.6350i	−0.631598	+	0.728903i	0.346268	+	0.938136i	$0.387449\pi$
$882$	2.78426	−	19.3649i	0.0937509	−	0.652052i
$883$	−48.9909	+	14.3850i	−1.64868	+	0.484095i	−0.968513	−	0.248965i	$-0.919910\pi$
$883$	−48.9909	+	14.3850i	−1.64868	+	0.484095i	−0.680164	+	0.733060i	$0.738091\pi$
$884$	−1.55941	−	1.79966i	−0.0524487	−	0.0605290i
$885$	0.432895	−	0.278205i	0.0145516	−	0.00935175i
$886$	−3.55473	+	2.28448i	−0.119423	+	0.0767487i
$887$	−7.89626	−	9.11277i	−0.265130	−	0.305977i	0.607538	−	0.794291i	$-0.292157\pi$
$887$	−7.89626	−	9.11277i	−0.265130	−	0.305977i	−0.872668	+	0.488314i	$0.837612\pi$
$888$	−2.59689	+	0.762516i	−0.0871460	+	0.0255884i
$889$	−0.795722	+	5.53437i	−0.0266877	+	0.185617i
$890$	10.1763	−	11.7441i	0.341111	−	0.393663i
$891$	17.5431	−	38.4141i	0.587717	−	1.28692i
$892$	−21.1221	−	6.20202i	−0.707221	−	0.207659i
$893$	1.14486	+	2.50689i	0.0383112	+	0.0838899i
$894$	0.372620	+	2.59163i	0.0124623	+	0.0866771i
$895$	1.81870	+	1.16881i	0.0607925	+	0.0390690i
$896$	−0.557477			−0.0186240
$897$	−1.48275	+	5.15957i	−0.0495075	+	0.172273i
$898$	−26.7048			−0.891149
$899$	−4.23502	−	2.72168i	−0.141246	−	0.0907731i
$900$	0.416231	+	2.89495i	0.0138744	+	0.0964983i
$901$	0.402894	+	0.882214i	0.0134223	+	0.0293908i
$902$	−3.80796	−	1.11812i	−0.126791	−	0.0372292i
$903$	−0.211175	+	0.462408i	−0.00702745	+	0.0153880i
$904$	4.55549	−	5.25731i	0.151513	−	0.174856i
$905$	−2.83121	+	19.6915i	−0.0941125	+	0.654567i
$906$	2.53366	−	0.743950i	0.0841753	−	0.0247161i
$907$	35.9595	+	41.4994i	1.19401	+	1.37797i	0.907587	+	0.419865i	$0.137923\pi$
$907$	35.9595	+	41.4994i	1.19401	+	1.37797i	0.286428	+	0.958102i	$0.407532\pi$
$908$	−3.11610	+	2.00259i	−0.103411	+	0.0664584i
$909$	−23.3166	+	14.9847i	−0.773362	+	0.497010i
$910$	−1.48940	−	1.71886i	−0.0493730	−	0.0569795i
$911$	14.4629	−	4.24670i	0.479179	−	0.140700i	−0.0332186	−	0.999448i	$-0.510576\pi$
$911$	14.4629	−	4.24670i	0.479179	−	0.140700i	0.512397	+	0.858749i	$0.328758\pi$
$912$	−0.00945889	+	0.0657881i	−0.000313215	+	0.00217846i
$913$	−12.6592	+	14.6095i	−0.418959	+	0.483504i
$914$	−8.49932	+	18.6109i	−0.281132	+	0.615594i
$915$	3.51951	+	1.03342i	0.116351	+	0.0341639i
$916$	−10.0320	−	21.9669i	−0.331466	−	0.725808i
$917$	−1.31350	−	9.13562i	−0.0433757	−	0.301685i
$918$	0.798211	+	0.512979i	0.0263449	+	0.0169308i
$919$	−23.0078			−0.758958			−0.379479	−	0.925200i	$-0.623897\pi$
$919$	−23.0078			−0.758958			−0.379479	+	0.925200i	$0.623897\pi$
$920$	0.0276345	+	4.79575i	0.000911083	+	0.158111i
$921$	2.62857			0.0866144
$922$	33.5210	+	21.5426i	1.10396	+	0.709469i
$923$	1.69594	+	11.7955i	0.0558225	+	0.388254i
$924$	−0.322205	−	0.705531i	−0.0105998	−	0.0232103i
$925$	−9.46472	−	2.77909i	−0.311198	−	0.0913760i
$926$	6.14900	−	13.4644i	0.202069	−	0.442469i
$927$	17.9801	−	20.7501i	0.590543	−	0.681522i
$928$	0.302640	−	2.10491i	0.00993464	−	0.0690969i
$929$	−33.5046	+	9.83783i	−1.09925	+	0.322769i	−0.780554	−	0.625089i	$-0.785063\pi$
$929$	−33.5046	+	9.83783i	−1.09925	+	0.322769i	−0.318695	+	0.947857i	$0.603245\pi$
$930$	0.425351	+	0.490881i	0.0139478	+	0.0160966i
$931$	1.36316	−	0.876049i	0.0446757	−	0.0287113i
$932$	15.2542	−	9.80326i	0.499667	−	0.321116i
$933$	−2.14842	−	2.47941i	−0.0703362	−	0.0811723i
$934$	11.1261	−	3.26691i	0.364056	−	0.106897i
$935$	0.421216	−	2.92962i	0.0137752	−	0.0958089i
$936$	7.81389	−	9.01772i	0.255405	−	0.294753i
$937$	6.43476	−	14.0902i	0.210214	−	0.460305i	−0.774927	−	0.632051i	$-0.782213\pi$
$937$	6.43476	−	14.0902i	0.210214	−	0.460305i	0.985141	+	0.171746i	$0.0549407\pi$
$938$	−3.30611	−	0.970763i	−0.107948	−	0.0316965i
$939$	0.713198	+	1.56169i	0.0232743	+	0.0509637i
$940$	1.61911	+	11.2611i	0.0528095	+	0.367298i
$941$	22.9784	+	14.7673i	0.749073	+	0.481400i	0.858640	−	0.512579i	$-0.171310\pi$
$941$	22.9784	+	14.7673i	0.749073	+	0.481400i	−0.109567	+	0.993979i	$0.534946\pi$
$942$	2.77612			0.0904509
$943$	3.71216	−	0.555578i	0.120884	−	0.0180921i
$944$	−1.87547			−0.0610413
$945$	0.762373	+	0.489947i	0.0248000	+	0.0159380i
$946$	2.39836	+	16.6810i	0.0779775	+	0.542345i
$947$	−2.21777	−	4.85623i	−0.0720677	−	0.157806i	0.870170	−	0.492752i	$-0.164009\pi$
$947$	−2.21777	−	4.85623i	−0.0720677	−	0.157806i	−0.942237	+	0.334946i	$0.891282\pi$
$948$	3.61914	+	1.06267i	0.117544	+	0.0345141i
$949$	−13.4676	+	29.4900i	−0.437178	+	0.957285i
$950$	−0.158633	+	0.183072i	−0.00514673	+	0.00593964i
$951$	0.979687	−	6.81387i	0.0317685	−	0.220955i
$952$	−0.312209	+	0.0916729i	−0.0101188	+	0.00297113i
$953$	4.93851	+	5.69934i	0.159974	+	0.184620i	0.830078	−	0.557648i	$-0.188296\pi$
$953$	4.93851	+	5.69934i	0.159974	+	0.184620i	−0.670104	+	0.742267i	$0.733750\pi$
$954$	−4.08830	+	2.62739i	−0.132363	+	0.0850648i
$955$	16.1918	−	10.4059i	0.523955	−	0.336725i
$956$	−12.5891	−	14.5286i	−0.407159	−	0.469887i
$957$	2.83884	−	0.833560i	0.0917668	−	0.0269452i
$958$	4.52840	−	31.4957i	0.146306	−	1.01758i
$959$	4.04835	−	4.67205i	0.130728	−	0.150868i
$960$	−0.113980	+	0.249581i	−0.00367869	+	0.00805520i
$961$	24.3672	+	7.15486i	0.786039	+	0.230802i
$962$	16.7179	+	36.6072i	0.539008	+	1.18026i
$963$	−6.25082	−	43.4754i	−0.201430	−	1.40098i
$964$	22.7555	+	14.6241i	0.732906	+	0.471010i
$965$	14.2377			0.458329
$966$	0.557148	+	0.477178i	0.0179259	+	0.0153530i
$967$	1.49888			0.0482008			0.0241004	−	0.999710i	$-0.492328\pi$
$967$	1.49888			0.0482008			0.0241004	+	0.999710i	$0.492328\pi$
$968$	−12.3775	−	7.95453i	−0.397828	−	0.255668i
$969$	0.00552099	+	0.0383994i	0.000177360	+	0.00123357i
$970$	3.42517	+	7.50008i	0.109976	+	0.240813i
$971$	1.58965	+	0.466762i	0.0510141	+	0.0149791i	0.307140	−	0.951664i	$-0.400628\pi$
$971$	1.58965	+	0.466762i	0.0510141	+	0.0149791i	−0.256126	+	0.966643i	$0.582446\pi$
$972$	−2.97514	+	6.51464i	−0.0954275	+	0.208957i
$973$	1.53046	−	1.76624i	0.0490642	−	0.0566231i
$974$	−5.34900	+	37.2031i	−0.171393	+	1.19207i
$975$	−1.07405	+	0.315368i	−0.0343970	+	0.0100999i
$976$	−8.75474	−	10.1035i	−0.280232	−	0.323405i
$977$	−6.41297	+	4.12137i	−0.205169	+	0.131854i	−0.639191	−	0.769048i	$-0.720731\pi$
$977$	−6.41297	+	4.12137i	−0.205169	+	0.131854i	0.434022	+	0.900903i	$0.357094\pi$
$978$	−4.23761	+	2.72334i	−0.135504	+	0.0870829i
$979$	−51.6023	−	59.5522i	−1.64922	−	1.90330i
$980$	6.41826	−	1.88457i	0.205024	−	0.0602004i
$981$	−5.48456	+	38.1460i	−0.175109	+	1.21791i
$982$	25.6656	−	29.6196i	0.819021	−	0.945201i
$983$	−14.6576	+	32.0958i	−0.467506	+	1.02370i	0.518206	+	0.855256i	$0.326600\pi$
$983$	−14.6576	+	32.0958i	−0.467506	+	1.02370i	−0.985712	+	0.168440i	$0.946127\pi$
$984$	0.206044	+	0.0605001i	0.00656845	+	0.00192867i
$985$	−9.48023	−	20.7588i	−0.302065	−	0.661431i
$986$	−0.176646	−	1.22860i	−0.00562554	−	0.0391265i
$987$	1.46395	+	0.940822i	0.0465980	+	0.0299467i
$988$	0.988277			0.0314413
$989$	−8.69419	−	13.3585i	−0.276459	−	0.424777i
$990$	14.8307			0.471351
$991$	1.21065	+	0.778039i	0.0384576	+	0.0247152i	0.559728	−	0.828676i	$-0.310905\pi$
$991$	1.21065	+	0.778039i	0.0384576	+	0.0247152i	−0.521271	+	0.853391i	$0.674542\pi$
$992$	−0.336901	−	2.34320i	−0.0106966	−	0.0743967i
$993$	0.196206	+	0.429632i	0.00622642	+	0.0136340i
$994$	1.56241	+	0.458764i	0.0495565	+	0.0145511i
$995$	−0.495015	+	1.08393i	−0.0156930	+	0.0343629i
$996$	0.684976	−	0.790504i	0.0217043	−	0.0250481i
$997$	0.744382	−	5.17729i	0.0235748	−	0.163966i	−0.974633	−	0.223809i	$-0.928151\pi$
$997$	0.744382	−	5.17729i	0.0235748	−	0.163966i	0.998208	+	0.0598426i	$0.0190599\pi$
$998$	0.100151	−	0.0294070i	0.00317022	−	0.000930862i
$999$	−10.5010	−	12.1187i	−0.332235	−	0.383420i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.g.b.71.2	✓	20
23.9	even	11		5290.2.a.bj.1.4		10
23.12	even	11	inner	230.2.g.b.81.2	yes	20
23.14	odd	22		5290.2.a.bi.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.b.71.2	✓	20	1.1	even	1	trivial
230.2.g.b.81.2	yes	20	23.12	even	11	inner
5290.2.a.bi.1.4		10	23.14	odd	22
5290.2.a.bj.1.4		10	23.9	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.841254 - 0.540641i) q^{2} +(0.0390478 + 0.271583i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(0.113980 - 0.249581i) q^{6} +(-0.365070 + 0.421313i) q^{7} +(0.142315 - 0.989821i) q^{8} +(2.80625 - 0.823988i) q^{9} +O(q^{10})\)	\(q+(-0.841254 - 0.540641i) q^{2} +(0.0390478 + 0.271583i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(0.113980 - 0.249581i) q^{6} +(-0.365070 + 0.421313i) q^{7} +(0.142315 - 0.989821i) q^{8} +(2.80625 - 0.823988i) q^{9} +(0.654861 + 0.755750i) q^{10} +(4.26584 - 2.74149i) q^{11} +(-0.230820 + 0.148339i) q^{12} +(2.67167 + 3.08328i) q^{13} +(0.534895 - 0.157059i) q^{14} +(0.0390478 - 0.271583i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-0.242471 + 0.530937i) q^{17} +(-2.80625 - 0.823988i) q^{18} +(-0.100630 - 0.220348i) q^{19} +(-0.142315 - 0.989821i) q^{20} +(-0.128677 - 0.0826955i) q^{21} -5.07081 q^{22} +(4.35089 - 2.01736i) q^{23} +0.274376 q^{24} +(0.841254 + 0.540641i) q^{25} +(-0.580610 - 4.03823i) q^{26} +(0.675299 + 1.47870i) q^{27} +(-0.534895 - 0.157059i) q^{28} +(0.883401 - 1.93438i) q^{29} +(-0.179678 + 0.207360i) q^{30} +(0.336901 - 2.34320i) q^{31} +(0.959493 - 0.281733i) q^{32} +(0.911114 + 1.05148i) q^{33} +(0.491025 - 0.315563i) q^{34} +(0.468979 - 0.301395i) q^{35} +(1.91528 + 2.21035i) q^{36} +(-9.46472 + 2.77909i) q^{37} +(-0.0344742 + 0.239773i) q^{38} +(-0.733043 + 0.845977i) q^{39} +(-0.415415 + 0.909632i) q^{40} +(0.750956 + 0.220501i) q^{41} +(0.0635411 + 0.139136i) q^{42} +(-0.472974 - 3.28960i) q^{43} +(4.26584 + 2.74149i) q^{44} -2.92472 q^{45} +(-4.75087 - 0.655153i) q^{46} -11.3769 q^{47} +(-0.230820 - 0.148339i) q^{48} +(0.951975 + 6.62113i) q^{49} +(-0.415415 - 0.909632i) q^{50} +(-0.153661 - 0.0451191i) q^{51} +(-1.69479 + 3.71108i) q^{52} +(1.08813 - 1.25577i) q^{53} +(0.231347 - 1.60905i) q^{54} +(-4.86541 + 1.42861i) q^{55} +(0.365070 + 0.421313i) q^{56} +(0.0559136 - 0.0359335i) q^{57} +(-1.78897 + 1.14970i) q^{58} +(1.22817 + 1.41738i) q^{59} +(0.263262 - 0.0773006i) q^{60} +(-1.90259 + 13.2328i) q^{61} +(-1.55025 + 1.78908i) q^{62} +(-0.677318 + 1.48312i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-1.69479 - 3.71108i) q^{65} +(-0.198004 - 1.37715i) q^{66} +(-5.19967 - 3.34163i) q^{67} -0.583683 q^{68} +(0.717775 + 1.10286i) q^{69} -0.557477 q^{70} +(2.45727 + 1.57919i) q^{71} +(-0.416231 - 2.89495i) q^{72} +(3.30108 + 7.22836i) q^{73} +(9.46472 + 2.77909i) q^{74} +(-0.113980 + 0.249581i) q^{75} +(0.158633 - 0.183072i) q^{76} +(-0.402304 + 2.79809i) q^{77} +(1.07405 - 0.315368i) q^{78} +(-9.00256 - 10.3895i) q^{79} +(0.841254 - 0.540641i) q^{80} +(7.00607 - 4.50253i) q^{81} +(-0.512533 - 0.591494i) q^{82} +(-3.65782 + 1.07403i) q^{83} +(0.0217682 - 0.151401i) q^{84} +(0.382231 - 0.441118i) q^{85} +(-1.38060 + 3.02310i) q^{86} +(0.559840 + 0.164384i) q^{87} +(-2.10649 - 4.61257i) q^{88} +(-2.21153 - 15.3815i) q^{89} +(2.46043 + 1.58122i) q^{90} -2.27437 q^{91} +(3.64248 + 3.11966i) q^{92} +0.649529 q^{93} +(9.57090 + 6.15084i) q^{94} +(0.0344742 + 0.239773i) q^{95} +(0.113980 + 0.249581i) q^{96} +(7.91120 + 2.32294i) q^{97} +(2.77880 - 6.08473i) q^{98} +(9.71204 - 11.2083i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9} + 2 q^{10} + 7 q^{11} + 8 q^{12} + 8 q^{13} + 3 q^{14} - 3 q^{15} - 2 q^{16} + 8 q^{17} + 27 q^{18} - q^{19} - 2 q^{20} - 31 q^{21} - 18 q^{22} - 9 q^{23} - 8 q^{24} - 2 q^{25} - 8 q^{26} - 18 q^{27} - 3 q^{28} + 20 q^{29} + 3 q^{30} - 17 q^{31} + 2 q^{32} + 17 q^{33} + 3 q^{34} - 3 q^{35} + 17 q^{36} + 6 q^{37} - 21 q^{38} - 75 q^{39} + 2 q^{40} - 2 q^{41} + 42 q^{42} - 18 q^{43} + 7 q^{44} + 28 q^{45} - 2 q^{46} + 42 q^{47} + 8 q^{48} - 19 q^{49} + 2 q^{50} + 26 q^{51} + 19 q^{52} + 19 q^{53} - 26 q^{54} - 15 q^{55} - 19 q^{56} + 7 q^{57} - 9 q^{58} + 25 q^{59} - 3 q^{60} - 49 q^{61} - 38 q^{62} - 87 q^{63} - 2 q^{64} + 19 q^{65} - 6 q^{66} + 19 q^{67} - 36 q^{68} + 36 q^{69} + 14 q^{70} + 7 q^{71} - 17 q^{72} - 10 q^{73} - 6 q^{74} - 3 q^{75} - q^{76} - 29 q^{77} - 2 q^{78} - 33 q^{79} - 2 q^{80} + 72 q^{81} + 2 q^{82} - 41 q^{83} + 13 q^{84} - 14 q^{85} - 48 q^{86} - 16 q^{87} - 7 q^{88} + 55 q^{89} + 5 q^{90} + 13 q^{92} + 10 q^{93} + 13 q^{94} + 21 q^{95} + 3 q^{96} - 9 q^{97} + 41 q^{98} + 59 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9 + 2 * q^10 + 7 * q^11 + 8 * q^12 + 8 * q^13 + 3 * q^14 - 3 * q^15 - 2 * q^16 + 8 * q^17 + 27 * q^18 - q^19 - 2 * q^20 - 31 * q^21 - 18 * q^22 - 9 * q^23 - 8 * q^24 - 2 * q^25 - 8 * q^26 - 18 * q^27 - 3 * q^28 + 20 * q^29 + 3 * q^30 - 17 * q^31 + 2 * q^32 + 17 * q^33 + 3 * q^34 - 3 * q^35 + 17 * q^36 + 6 * q^37 - 21 * q^38 - 75 * q^39 + 2 * q^40 - 2 * q^41 + 42 * q^42 - 18 * q^43 + 7 * q^44 + 28 * q^45 - 2 * q^46 + 42 * q^47 + 8 * q^48 - 19 * q^49 + 2 * q^50 + 26 * q^51 + 19 * q^52 + 19 * q^53 - 26 * q^54 - 15 * q^55 - 19 * q^56 + 7 * q^57 - 9 * q^58 + 25 * q^59 - 3 * q^60 - 49 * q^61 - 38 * q^62 - 87 * q^63 - 2 * q^64 + 19 * q^65 - 6 * q^66 + 19 * q^67 - 36 * q^68 + 36 * q^69 + 14 * q^70 + 7 * q^71 - 17 * q^72 - 10 * q^73 - 6 * q^74 - 3 * q^75 - q^76 - 29 * q^77 - 2 * q^78 - 33 * q^79 - 2 * q^80 + 72 * q^81 + 2 * q^82 - 41 * q^83 + 13 * q^84 - 14 * q^85 - 48 * q^86 - 16 * q^87 - 7 * q^88 + 55 * q^89 + 5 * q^90 + 13 * q^92 + 10 * q^93 + 13 * q^94 + 21 * q^95 + 3 * q^96 - 9 * q^97 + 41 * q^98 + 59 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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