LMFDB - Embedded newform 322.2.i.d.141.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			141.1
Character	$\chi$	$=$	322.141
Dual form			322.2.i.d.169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{2} +(-1.08968 + 2.38606i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(0.443664 - 0.512016i) q^{5} +(2.51685 + 0.739013i) q^{6} +(-0.841254 + 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-2.54129 - 2.93281i) q^{9} +O(q^{10})$	\(q+(-0.142315 - 0.989821i) q^{2} +(-1.08968 + 2.38606i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(0.443664 - 0.512016i) q^{5} +(2.51685 + 0.739013i) q^{6} +(-0.841254 + 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-2.54129 - 2.93281i) q^{9} +(-0.569944 - 0.366281i) q^{10} +(-0.529744 + 3.68445i) q^{11} +(0.373306 - 2.59640i) q^{12} +(0.0806711 + 0.0518442i) q^{13} +(0.654861 + 0.755750i) q^{14} +(0.738248 + 1.61654i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-7.52455 - 2.20941i) q^{17} +(-2.54129 + 2.93281i) q^{18} +(-7.32649 + 2.15125i) q^{19} +(-0.281441 + 0.616270i) q^{20} +(-0.373306 - 2.59640i) q^{21} +3.72234 q^{22} +(4.07836 + 2.52329i) q^{23} -2.62310 q^{24} +(0.646252 + 4.49478i) q^{25} +(0.0398358 - 0.0872282i) q^{26} +(2.21648 - 0.650818i) q^{27} +(0.654861 - 0.755750i) q^{28} +(-3.73821 - 1.09764i) q^{29} +(1.49502 - 0.960791i) q^{30} +(-0.242071 - 0.530062i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(-8.21406 - 5.27886i) q^{33} +(-1.11606 + 7.76239i) q^{34} +(-0.0964174 + 0.670598i) q^{35} +(3.26462 + 2.09804i) q^{36} +(4.26340 + 4.92023i) q^{37} +(3.17202 + 6.94576i) q^{38} +(-0.211608 + 0.135992i) q^{39} +(0.650051 + 0.190872i) q^{40} +(3.00717 - 3.47046i) q^{41} +(-2.51685 + 0.739013i) q^{42} +(0.547621 - 1.19912i) q^{43} +(-0.529744 - 3.68445i) q^{44} -2.62912 q^{45} +(1.91719 - 4.39595i) q^{46} +10.6453 q^{47} +(0.373306 + 2.59640i) q^{48} +(0.415415 - 0.909632i) q^{49} +(4.35706 - 1.27935i) q^{50} +(13.4711 - 15.5465i) q^{51} +(-0.0920095 - 0.0270164i) q^{52} +(4.71732 - 3.03164i) q^{53} +(-0.959632 - 2.10130i) q^{54} +(1.65147 + 1.90590i) q^{55} +(-0.841254 - 0.540641i) q^{56} +(2.85049 - 19.8256i) q^{57} +(-0.554463 + 3.85637i) q^{58} +(-0.235727 - 0.151492i) q^{59} +(-1.16378 - 1.34307i) q^{60} +(2.64493 + 5.79159i) q^{61} +(-0.490216 + 0.315043i) q^{62} +(3.72346 + 1.09331i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(0.0623359 - 0.0183035i) q^{65} +(-4.05614 + 8.88171i) q^{66} +(2.21596 + 15.4123i) q^{67} +7.84221 q^{68} +(-10.4648 + 6.98163i) q^{69} +0.677494 q^{70} +(-0.800042 - 5.56441i) q^{71} +(1.61208 - 3.52997i) q^{72} +(-4.11569 + 1.20848i) q^{73} +(4.26340 - 4.92023i) q^{74} +(-11.4290 - 3.35586i) q^{75} +(6.42364 - 4.12822i) q^{76} +(-1.54632 - 3.38596i) q^{77} +(0.164723 + 0.190101i) q^{78} +(-12.7745 - 8.20965i) q^{79} +(0.0964174 - 0.670598i) q^{80} +(0.794468 - 5.52565i) q^{81} +(-3.86310 - 2.48266i) q^{82} +(10.1788 + 11.7470i) q^{83} +(1.08968 + 2.38606i) q^{84} +(-4.46962 + 2.87245i) q^{85} +(-1.26485 - 0.371394i) q^{86} +(6.69246 - 7.72351i) q^{87} +(-3.57156 + 1.04870i) q^{88} +(0.279223 - 0.611413i) q^{89} +(0.374163 + 2.60236i) q^{90} -0.0958939 q^{91} +(-4.62405 - 1.27207i) q^{92} +1.52854 q^{93} +(-1.51498 - 10.5369i) q^{94} +(-2.14903 + 4.70571i) q^{95} +(2.51685 - 0.739013i) q^{96} +(-4.10798 + 4.74086i) q^{97} +(-0.959493 - 0.281733i) q^{98} +(12.1520 - 7.80963i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$3$	−1.08968	+	2.38606i	−0.629124	+	1.37759i	0.279569	+	0.960126i	$0.409809\pi$
$3$	−1.08968	+	2.38606i	−0.629124	+	1.37759i	−0.908693	+	0.417465i	$0.862919\pi$
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	0.443664	−	0.512016i	0.198413	−	0.228980i	−0.647821	−	0.761793i	$-0.724319\pi$
$5$	0.443664	−	0.512016i	0.198413	−	0.228980i	0.846233	+	0.532812i	$0.178865\pi$
$6$	2.51685	+	0.739013i	1.02750	+	0.301701i
$7$	−0.841254	+	0.540641i	−0.317964	+	0.204343i
$7$	−0.841254	+	0.540641i	−0.317964	+	0.204343i
$8$	0.415415	+	0.909632i	0.146871	+	0.321603i
$9$	−2.54129	−	2.93281i	−0.847097	−	0.977602i
$10$	−0.569944	−	0.366281i	−0.180232	−	0.115828i
$11$	−0.529744	+	3.68445i	−0.159724	+	1.11090i	0.739418	+	0.673247i	$0.235101\pi$
$11$	−0.529744	+	3.68445i	−0.159724	+	1.11090i	−0.899142	+	0.437657i	$0.855808\pi$
$12$	0.373306	−	2.59640i	0.107764	−	0.749517i
$13$	0.0806711	+	0.0518442i	0.0223741	+	0.0143790i	0.551780	−	0.833990i	$-0.313949\pi$
$13$	0.0806711	+	0.0518442i	0.0223741	+	0.0143790i	−0.529406	+	0.848369i	$0.677585\pi$
$14$	0.654861	+	0.755750i	0.175019	+	0.201983i
$15$	0.738248	+	1.61654i	0.190615	+	0.417388i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−7.52455	−	2.20941i	−1.82497	−	0.535860i	−0.825383	−	0.564572i	$-0.809041\pi$
$17$	−7.52455	−	2.20941i	−1.82497	−	0.535860i	−0.999588	+	0.0287126i	$0.990859\pi$
$18$	−2.54129	+	2.93281i	−0.598988	+	0.691269i
$19$	−7.32649	+	2.15125i	−1.68081	+	0.493531i	−0.976347	−	0.216208i	$-0.930631\pi$
$19$	−7.32649	+	2.15125i	−1.68081	+	0.493531i	−0.704465	+	0.709739i	$0.748813\pi$
$20$	−0.281441	+	0.616270i	−0.0629321	+	0.137802i
$21$	−0.373306	−	2.59640i	−0.0814621	−	0.566581i
$22$	3.72234			0.793606
$23$	4.07836	+	2.52329i	0.850397	+	0.526142i
$23$	4.07836	+	2.52329i	0.850397	+	0.526142i
$24$	−2.62310			−0.535438
$25$	0.646252	+	4.49478i	0.129250	+	0.898956i
$26$	0.0398358	−	0.0872282i	0.00781244	−	0.0171069i
$27$	2.21648	−	0.650818i	0.426562	−	0.125250i
$28$	0.654861	−	0.755750i	0.123757	−	0.142823i
$29$	−3.73821	−	1.09764i	−0.694168	−	0.203826i	−0.0844305	−	0.996429i	$-0.526907\pi$
$29$	−3.73821	−	1.09764i	−0.694168	−	0.203826i	−0.609738	+	0.792603i	$0.708725\pi$
$30$	1.49502	−	0.960791i	0.272952	−	0.175416i
$31$	−0.242071	−	0.530062i	−0.0434772	−	0.0952019i	0.886647	−	0.462447i	$-0.153028\pi$
$31$	−0.242071	−	0.530062i	−0.0434772	−	0.0952019i	−0.930124	+	0.367245i	$0.880301\pi$
$32$	−0.654861	−	0.755750i	−0.115764	−	0.133599i
$33$	−8.21406	−	5.27886i	−1.42988	−	0.918931i
$34$	−1.11606	+	7.76239i	−0.191403	+	1.33124i
$35$	−0.0964174	+	0.670598i	−0.0162975	+	0.113352i
$36$	3.26462	+	2.09804i	0.544103	+	0.349674i
$37$	4.26340	+	4.92023i	0.700899	+	0.808880i	0.988874	−	0.148757i	$-0.0475274\pi$
$37$	4.26340	+	4.92023i	0.700899	+	0.808880i	−0.287975	+	0.957638i	$0.592982\pi$
$38$	3.17202	+	6.94576i	0.514570	+	1.12675i
$39$	−0.211608	+	0.135992i	−0.0338845	+	0.0217762i
$40$	0.650051	+	0.190872i	0.102782	+	0.0301795i
$41$	3.00717	−	3.47046i	0.469641	−	0.541994i	−0.470671	−	0.882309i	$-0.655988\pi$
$41$	3.00717	−	3.47046i	0.469641	−	0.541994i	0.940312	+	0.340315i	$0.110534\pi$
$42$	−2.51685	+	0.739013i	−0.388358	+	0.114032i
$43$	0.547621	−	1.19912i	0.0835114	−	0.182864i	−0.863269	−	0.504743i	$-0.831587\pi$
$43$	0.547621	−	1.19912i	0.0835114	−	0.182864i	0.946781	+	0.321879i	$0.104314\pi$
$44$	−0.529744	−	3.68445i	−0.0798620	−	0.555452i
$45$	−2.62912			−0.391926
$46$	1.91719	−	4.39595i	0.282675	−	0.648147i
$47$	10.6453			1.55277			0.776386	−	0.630258i	$-0.217051\pi$
$47$	10.6453			1.55277			0.776386	+	0.630258i	$0.217051\pi$
$48$	0.373306	+	2.59640i	0.0538821	+	0.374758i
$49$	0.415415	−	0.909632i	0.0593450	−	0.129947i
$50$	4.35706	−	1.27935i	0.616181	−	0.180927i
$51$	13.4711	−	15.5465i	1.88633	−	2.17694i
$52$	−0.0920095	−	0.0270164i	−0.0127594	−	0.00374651i
$53$	4.71732	−	3.03164i	0.647973	−	0.416427i	−0.174952	−	0.984577i	$-0.555977\pi$
$53$	4.71732	−	3.03164i	0.647973	−	0.416427i	0.822925	+	0.568150i	$0.192341\pi$
$54$	−0.959632	−	2.10130i	−0.130589	−	0.285951i
$55$	1.65147	+	1.90590i	0.222684	+	0.256991i
$56$	−0.841254	−	0.540641i	−0.112417	−	0.0722462i
$57$	2.85049	−	19.8256i	0.377556	−	2.62596i
$58$	−0.554463	+	3.85637i	−0.0728045	+	0.506366i
$59$	−0.235727	−	0.151492i	−0.0306890	−	0.0197226i	0.525206	−	0.850975i	$-0.323988\pi$
$59$	−0.235727	−	0.151492i	−0.0306890	−	0.0197226i	−0.555895	+	0.831252i	$0.687624\pi$
$60$	−1.16378	−	1.34307i	−0.150243	−	0.173389i
$61$	2.64493	+	5.79159i	0.338649	+	0.741537i	0.999963	−	0.00857161i	$-0.00272846\pi$
$61$	2.64493	+	5.79159i	0.338649	+	0.741537i	−0.661315	+	0.750109i	$0.730001\pi$
$62$	−0.490216	+	0.315043i	−0.0622575	+	0.0400105i
$63$	3.72346	+	1.09331i	0.469112	+	0.137744i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	0.0623359	−	0.0183035i	0.00773182	−	0.00227027i
$66$	−4.05614	+	8.88171i	−0.499277	+	1.09326i
$67$	2.21596	+	15.4123i	0.270722	+	1.88292i	0.440982	+	0.897516i	$0.354630\pi$
$67$	2.21596	+	15.4123i	0.270722	+	1.88292i	−0.170259	+	0.985399i	$0.554461\pi$
$68$	7.84221			0.951008
$69$	−10.4648	+	6.98163i	−1.25981	+	0.840490i
$70$	0.677494			0.0809760
$71$	−0.800042	−	5.56441i	−0.0949475	−	0.660374i	−0.980599	−	0.196024i	$-0.937197\pi$
$71$	−0.800042	−	5.56441i	−0.0949475	−	0.660374i	0.885652	−	0.464350i	$-0.153712\pi$
$72$	1.61208	−	3.52997i	0.189986	−	0.416011i
$73$	−4.11569	+	1.20848i	−0.481705	+	0.141441i	−0.513565	−	0.858051i	$-0.671675\pi$
$73$	−4.11569	+	1.20848i	−0.481705	+	0.141441i	0.0318593	+	0.999492i	$0.489857\pi$
$74$	4.26340	−	4.92023i	0.495610	−	0.571965i
$75$	−11.4290	−	3.35586i	−1.31971	−	0.387501i
$76$	6.42364	−	4.12822i	0.736842	−	0.473539i
$77$	−1.54632	−	3.38596i	−0.176219	−	0.385866i
$78$	0.164723	+	0.190101i	0.0186512	+	0.0215247i
$79$	−12.7745	−	8.20965i	−1.43724	−	0.923658i	−0.999701	−	0.0244591i	$-0.992214\pi$
$79$	−12.7745	−	8.20965i	−1.43724	−	0.923658i	−0.437540	−	0.899199i	$-0.644150\pi$
$80$	0.0964174	−	0.670598i	0.0107798	−	0.0749751i
$81$	0.794468	−	5.52565i	0.0882742	−	0.613961i
$82$	−3.86310	−	2.48266i	−0.426608	−	0.274164i
$83$	10.1788	+	11.7470i	1.11727	+	1.28940i	0.952994	+	0.302988i	$0.0979841\pi$
$83$	10.1788	+	11.7470i	1.11727	+	1.28940i	0.164279	+	0.986414i	$0.447470\pi$
$84$	1.08968	+	2.38606i	0.118893	+	0.260340i
$85$	−4.46962	+	2.87245i	−0.484799	+	0.311561i
$86$	−1.26485	−	0.371394i	−0.136392	−	0.0400484i
$87$	6.69246	−	7.72351i	0.717507	−	0.828048i
$88$	−3.57156	+	1.04870i	−0.380730	+	0.111792i
$89$	0.279223	−	0.611413i	0.0295976	−	0.0648096i	−0.894256	−	0.447556i	$-0.852294\pi$
$89$	0.279223	−	0.611413i	0.0295976	−	0.0648096i	0.923853	+	0.382747i	$0.125022\pi$
$90$	0.374163	+	2.60236i	0.0394402	+	0.274313i
$91$	−0.0958939			−0.0100524
$92$	−4.62405	−	1.27207i	−0.482091	−	0.132623i
$93$	1.52854			0.158502
$94$	−1.51498	−	10.5369i	−0.156258	−	1.08680i
$95$	−2.14903	+	4.70571i	−0.220485	+	0.482796i
$96$	2.51685	−	0.739013i	0.256875	−	0.0754252i
$97$	−4.10798	+	4.74086i	−0.417102	+	0.481362i	−0.924952	−	0.380084i	$-0.875895\pi$
$97$	−4.10798	+	4.74086i	−0.417102	+	0.481362i	0.507850	+	0.861446i	$0.330440\pi$
$98$	−0.959493	−	0.281733i	−0.0969234	−	0.0284593i
$99$	12.1520	−	7.80963i	1.22132	−	0.784897i
$100$	−1.88640	−	4.13064i	−0.188640	−	0.413064i
$101$	−4.77271	−	5.50800i	−0.474902	−	0.548067i	0.466866	−	0.884328i	$-0.345383\pi$
$101$	−4.77271	−	5.50800i	−0.474902	−	0.548067i	−0.941769	+	0.336261i	$0.890837\pi$
$102$	−17.3054	−	11.1215i	−1.71349	−	1.10119i
$103$	−0.0810879	+	0.563979i	−0.00798983	+	0.0555705i	−0.993426	−	0.114474i	$-0.963482\pi$
$103$	−0.0810879	+	0.563979i	−0.00798983	+	0.0555705i	0.985436	+	0.170044i	$0.0543910\pi$
$104$	−0.0136471	+	0.0949179i	−0.00133821	+	0.00930746i
$105$	−1.49502	−	0.960791i	−0.145899	−	0.0937636i
$106$	−3.67212	−	4.23785i	−0.356668	−	0.411617i
$107$	2.45072	+	5.36634i	0.236920	+	0.518783i	0.990324	−	0.138775i	$-0.0443165\pi$
$107$	2.45072	+	5.36634i	0.236920	+	0.518783i	−0.753404	+	0.657558i	$0.771589\pi$
$108$	−1.94334	+	1.24891i	−0.186998	+	0.120176i
$109$	4.53904	+	1.33278i	0.434761	+	0.127657i	0.491787	−	0.870715i	$-0.336344\pi$
$109$	4.53904	+	1.33278i	0.434761	+	0.127657i	−0.0570264	+	0.998373i	$0.518162\pi$
$110$	1.65147	−	1.90590i	0.157461	−	0.181720i
$111$	−16.3857	+	4.81127i	−1.55526	+	0.456665i
$112$	−0.415415	+	0.909632i	−0.0392530	+	0.0859521i
$113$	0.453426	+	3.15365i	0.0426548	+	0.296670i	0.999971	+	0.00762749i	$0.00242793\pi$
$113$	0.453426	+	3.15365i	0.0426548	+	0.296670i	−0.957316	+	0.289043i	$0.906663\pi$
$114$	−20.0295			−1.87593
$115$	3.10138	−	0.968691i	0.289206	−	0.0903309i
$116$	3.89603			0.361737
$117$	−0.0529598	−	0.368344i	−0.00489614	−	0.0340534i
$118$	−0.116403	+	0.254887i	−0.0107158	+	0.0234643i
$119$	7.52455	−	2.20941i	0.689774	−	0.202536i
$120$	−1.16378	+	1.34307i	−0.106238	+	0.122605i
$121$	−2.74014	−	0.804577i	−0.249103	−	0.0731433i
$122$	5.35623	−	3.44224i	0.484930	−	0.311646i
$123$	5.00387	+	10.9569i	0.451183	+	0.987954i
$124$	0.381601	+	0.440391i	0.0342688	+	0.0395483i
$125$	5.43784	+	3.49469i	0.486375	+	0.312574i
$126$	0.552275	−	3.84116i	0.0492006	−	0.342198i
$127$	−0.648257	+	4.50873i	−0.0575235	+	0.400085i	0.940635	+	0.339421i	$0.110231\pi$
$127$	−0.648257	+	4.50873i	−0.0575235	+	0.400085i	−0.998158	+	0.0606643i	$0.980678\pi$
$128$	0.841254	+	0.540641i	0.0743570	+	0.0477863i
$129$	2.26445	+	2.61331i	0.199373	+	0.230089i
$130$	−0.0269885	−	0.0590965i	−0.00236705	−	0.00518311i
$131$	8.43297	−	5.41954i	0.736792	−	0.473508i	−0.117649	−	0.993055i	$-0.537536\pi$
$131$	8.43297	−	5.41954i	0.736792	−	0.473508i	0.854442	+	0.519547i	$0.173899\pi$
$132$	9.36856	+	2.75086i	0.815429	+	0.239431i
$133$	5.00038	−	5.77075i	0.433588	−	0.500387i
$134$	14.9401	−	4.38681i	1.29063	−	0.378962i
$135$	0.650144	−	1.42362i	0.0559555	−	0.122526i
$136$	−1.11606	−	7.76239i	−0.0957016	−	0.665620i
$137$	14.2070			1.21379			0.606893	−	0.794783i	$-0.292416\pi$
$137$	14.2070			1.21379			0.606893	+	0.794783i	$0.292416\pi$
$138$	8.39986	+	9.36469i	0.715044	+	0.797175i
$139$	−16.2309			−1.37669			−0.688344	−	0.725385i	$-0.741662\pi$
$139$	−16.2309			−1.37669			−0.688344	+	0.725385i	$0.741662\pi$
$140$	−0.0964174	−	0.670598i	−0.00814876	−	0.0566759i
$141$	−11.5999	+	25.4002i	−0.976886	+	2.13908i
$142$	−5.39392	+	1.58380i	−0.452647	+	0.132909i
$143$	−0.233752	+	0.269765i	−0.0195474	+	0.0225589i
$144$	−3.72346	−	1.09331i	−0.310289	−	0.0911090i
$145$	−2.22052	+	1.42704i	−0.184404	+	0.118509i
$146$	1.78190	+	3.90182i	0.147471	+	0.322917i
$147$	1.71777	+	1.98241i	0.141679	+	0.163506i
$148$	−5.47689	−	3.51979i	−0.450198	−	0.289325i
$149$	−0.312315	+	2.17220i	−0.0255858	+	0.177953i	−0.998607	−	0.0527620i	$-0.983198\pi$
$149$	−0.312315	+	2.17220i	−0.0255858	+	0.177953i	0.973021	+	0.230715i	$0.0741066\pi$
$150$	−1.69518	+	11.7903i	−0.138411	+	0.962671i
$151$	15.0888	+	9.69700i	1.22791	+	0.789131i	0.983565	−	0.180557i	$-0.0577900\pi$
$151$	15.0888	+	9.69700i	1.22791	+	0.789131i	0.244347	+	0.969688i	$0.421426\pi$
$152$	−5.00038	−	5.77075i	−0.405584	−	0.468069i
$153$	12.6423	+	27.6828i	1.02207	+	2.23802i
$154$	−3.13143	+	2.01245i	−0.252338	+	0.162168i
$155$	−0.378798	−	0.111225i	−0.0304258	−	0.00893382i
$156$	0.164723	−	0.190101i	0.0131884	−	0.0152202i
$157$	1.36000	−	0.399332i	0.108540	−	0.0318701i	−0.227012	−	0.973892i	$-0.572896\pi$
$157$	1.36000	−	0.399332i	0.108540	−	0.0318701i	0.335551	+	0.942022i	$0.391077\pi$
$158$	−6.30810	+	13.8128i	−0.501845	+	1.09889i
$159$	2.09331	+	14.5593i	0.166010	+	1.15463i
$160$	−0.677494			−0.0535606
$161$	−4.79513	+	0.0822024i	−0.377909	+	0.00647845i
$162$	−5.58247			−0.438600
$163$	−1.03473	−	7.19674i	−0.0810467	−	0.563692i	−0.989370	−	0.145422i	$-0.953546\pi$
$163$	−1.03473	−	7.19674i	−0.0810467	−	0.563692i	0.908323	−	0.418269i	$-0.137363\pi$
$164$	−1.90762	+	4.17709i	−0.148960	+	0.326176i
$165$	−6.34714	+	1.86369i	−0.494124	+	0.145088i
$166$	10.1788	−	11.7470i	0.790031	−	0.911745i
$167$	−15.5619	−	4.56939i	−1.20422	−	0.353590i	−0.382753	−	0.923851i	$-0.625024\pi$
$167$	−15.5619	−	4.56939i	−1.20422	−	0.353590i	−0.821464	+	0.570261i	$0.806842\pi$
$168$	2.20669	−	1.41816i	0.170250	−	0.109413i
$169$	−5.39658	−	11.8169i	−0.415121	−	0.908989i
$170$	3.47931	+	4.01534i	0.266851	+	0.307962i
$171$	24.9279	+	16.0202i	1.90629	+	1.22510i
$172$	−0.187607	+	1.30483i	−0.0143049	+	0.0994925i
$173$	−1.00482	+	6.98867i	−0.0763950	+	0.531339i	0.915305	+	0.402762i	$0.131950\pi$
$173$	−1.00482	+	6.98867i	−0.0763950	+	0.531339i	−0.991700	+	0.128576i	$0.958959\pi$
$174$	−8.59734	−	5.52517i	−0.651762	−	0.418862i
$175$	−2.97372	−	3.43186i	−0.224792	−	0.259424i
$176$	1.54632	+	3.38596i	0.116558	+	0.255226i
$177$	0.618335	−	0.397380i	0.0464769	−	0.0298689i
$178$	−0.644927	−	0.189368i	−0.0483393	−	0.0141937i
$179$	9.55574	−	11.0279i	0.714229	−	0.824265i	−0.276371	−	0.961051i	$-0.589132\pi$
$179$	9.55574	−	11.0279i	0.714229	−	0.824265i	0.990601	+	0.136786i	$0.0436773\pi$
$180$	2.52262	−	0.740709i	0.188025	−	0.0552092i
$181$	−5.11014	+	11.1896i	−0.379834	+	0.831720i	0.619089	+	0.785321i	$0.287502\pi$
$181$	−5.11014	+	11.1896i	−0.379834	+	0.831720i	−0.998923	+	0.0463991i	$0.985225\pi$
$182$	0.0136471	+	0.0949179i	0.00101159	+	0.00703578i
$183$	−16.7012			−1.23459
$184$	−0.601052	+	4.75802i	−0.0443101	+	0.350766i
$185$	4.41075			0.324285
$186$	−0.217533	−	1.51298i	−0.0159503	−	0.110937i
$187$	12.1265	−	26.5534i	0.886781	−	1.94178i
$188$	−10.2141	+	2.99912i	−0.744936	+	0.218733i
$189$	−1.51276	+	1.74582i	−0.110037	+	0.126990i
$190$	4.96365	+	1.45746i	0.360101	+	0.105735i
$191$	−6.13848	+	3.94496i	−0.444164	+	0.285447i	−0.743544	−	0.668687i	$-0.766857\pi$
$191$	−6.13848	+	3.94496i	−0.444164	+	0.285447i	0.299380	+	0.954134i	$0.403220\pi$
$192$	−1.08968	−	2.38606i	−0.0786406	−	0.172199i
$193$	−2.40661	−	2.77737i	−0.173231	−	0.199920i	0.662494	−	0.749067i	$-0.269498\pi$
$193$	−2.40661	−	2.77737i	−0.173231	−	0.199920i	−0.835725	+	0.549148i	$0.814953\pi$
$194$	5.27723	+	3.39147i	0.378883	+	0.243493i
$195$	−0.0242528	+	0.168682i	−0.00173678	+	0.0120796i
$196$	−0.142315	+	0.989821i	−0.0101653	+	0.0707015i
$197$	9.14505	+	5.87717i	0.651558	+	0.418731i	0.824235	−	0.566247i	$-0.191605\pi$
$197$	9.14505	+	5.87717i	0.651558	+	0.418731i	−0.172677	+	0.984978i	$0.555242\pi$
$198$	−9.45955	−	10.9169i	−0.672261	−	0.775830i
$199$	9.19779	+	20.1404i	0.652014	+	1.42771i	0.889780	+	0.456389i	$0.150858\pi$
$199$	9.19779	+	20.1404i	0.652014	+	1.42771i	−0.237766	+	0.971322i	$0.576415\pi$
$200$	−3.82013	+	2.45505i	−0.270124	+	0.173598i
$201$	−39.1894	−	11.5070i	−2.76420	−	0.811644i
$202$	−4.77271	+	5.50800i	−0.335807	+	0.387542i
$203$	3.73821	−	1.09764i	0.262371	−	0.0770391i
$204$	−8.54547	+	18.7120i	−0.598302	+	1.31010i
$205$	−0.442756	−	3.07943i	−0.0309234	−	0.215077i
$206$	0.569778			0.0396983
$207$	−2.96398	−	18.3734i	−0.206011	−	1.27704i
$208$	0.0958939			0.00664905
$209$	−4.04502	−	28.1337i	−0.279800	−	1.94605i
$210$	−0.738248	+	1.61654i	−0.0509440	+	0.111552i
$211$	−10.4232	+	3.06054i	−0.717566	+	0.210696i	−0.620078	−	0.784540i	$-0.712899\pi$
$211$	−10.4232	+	3.06054i	−0.717566	+	0.210696i	−0.0974879	+	0.995237i	$0.531081\pi$
$212$	−3.67212	+	4.23785i	−0.252202	+	0.291057i
$213$	14.1488	+	4.15446i	0.969459	+	0.284659i
$214$	4.96294	−	3.18949i	0.339260	−	0.218029i
$215$	−0.371010	−	0.812398i	−0.0253027	−	0.0554051i
$216$	1.51276	+	1.74582i	0.102931	+	0.118788i
$217$	0.490216	+	0.315043i	0.0332780	+	0.0213865i
$218$	0.673243	−	4.68251i	0.0455978	−	0.317140i
$219$	1.60128	−	11.1371i	0.108204	−	0.752577i
$220$	−2.12153	−	1.36342i	−0.143033	−	0.0919219i
$221$	−0.492469	−	0.568339i	−0.0331270	−	0.0382306i
$222$	7.09422	+	15.5342i	0.476133	+	1.04259i
$223$	−12.7891	+	8.21903i	−0.856419	+	0.550387i	−0.893571	−	0.448923i	$-0.851808\pi$
$223$	−12.7891	+	8.21903i	−0.856419	+	0.550387i	0.0371516	+	0.999310i	$0.488172\pi$
$224$	0.959493	+	0.281733i	0.0641088	+	0.0188240i
$225$	11.5400	−	13.3179i	0.769334	−	0.887858i
$226$	3.05702	−	0.897622i	0.203350	−	0.0597089i
$227$	1.10175	−	2.41250i	0.0731260	−	0.160124i	−0.869539	−	0.493865i	$-0.835584\pi$
$227$	1.10175	−	2.41250i	0.0731260	−	0.160124i	0.942665	+	0.333741i	$0.108311\pi$
$228$	2.85049	+	19.8256i	0.188778	+	1.31298i
$229$	−17.1599			−1.13396			−0.566980	−	0.823732i	$-0.691888\pi$
$229$	−17.1599			−1.13396			−0.566980	+	0.823732i	$0.691888\pi$
$230$	−1.40020	−	2.93196i	−0.0923268	−	0.193328i
$231$	9.76407			0.642429
$232$	−0.554463	−	3.85637i	−0.0364023	−	0.253183i
$233$	−8.22403	+	18.0081i	−0.538774	+	1.17975i	0.423056	+	0.906104i	$0.360957\pi$
$233$	−8.22403	+	18.0081i	−0.538774	+	1.17975i	−0.961830	+	0.273647i	$0.911770\pi$
$234$	−0.357058	+	0.104842i	−0.0233416	+	0.00685371i
$235$	4.72292	−	5.45054i	0.308089	−	0.355554i
$236$	0.268859	+	0.0789440i	0.0175012	+	0.00513882i
$237$	33.5087	−	21.5348i	2.17663	−	1.39883i
$238$	−3.25777	−	7.13353i	−0.211170	−	0.462398i
$239$	−16.1714	−	18.6628i	−1.04604	−	1.20720i	−0.977802	−	0.209530i	$-0.932807\pi$
$239$	−16.1714	−	18.6628i	−1.04604	−	1.20720i	−0.0682414	−	0.997669i	$-0.521739\pi$
$240$	1.49502	+	0.960791i	0.0965032	+	0.0620188i
$241$	−0.216450	+	1.50544i	−0.0139428	+	0.0969741i	−0.995605	−	0.0936569i	$-0.970144\pi$
$241$	−0.216450	+	1.50544i	−0.0139428	+	0.0969741i	0.981662	+	0.190631i	$0.0610534\pi$
$242$	−0.406425	+	2.82675i	−0.0261260	+	0.181710i
$243$	18.1488	+	11.6635i	1.16425	+	0.748216i
$244$	−4.16947	−	4.81183i	−0.266923	−	0.308046i
$245$	−0.281441	−	0.616270i	−0.0179806	−	0.0393720i
$246$	10.1333	−	6.51227i	0.646075	−	0.415207i
$247$	−0.702566	−	0.206292i	−0.0447032	−	0.0131260i
$248$	0.381601	−	0.440391i	0.0242317	−	0.0279649i
$249$	−39.1207	+	11.4869i	−2.47917	+	0.727950i
$250$	2.68523	−	5.87983i	0.169829	−	0.371873i
$251$	−4.14745	−	28.8462i	−0.261785	−	1.82075i	−0.519428	−	0.854514i	$-0.673855\pi$
$251$	−4.14745	−	28.8462i	−0.261785	−	1.82075i	0.257643	−	0.966240i	$-0.417054\pi$
$252$	−3.88066			−0.244458
$253$	−11.4574	+	13.6898i	−0.720322	+	0.860672i
$254$	4.55509			0.285812
$255$	−1.98339	−	13.7948i	−0.124205	−	0.863865i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	15.7856	−	4.63507i	0.984678	−	0.289128i	0.250524	−	0.968110i	$-0.419397\pi$
$257$	15.7856	−	4.63507i	0.984678	−	0.289128i	0.734154	+	0.678983i	$0.237579\pi$
$258$	2.26445	−	2.61331i	0.140978	−	0.162698i
$259$	−6.24668	−	1.83419i	−0.388150	−	0.113971i
$260$	−0.0546542	+	0.0351241i	−0.00338951	+	0.00217830i
$261$	6.28072	+	13.7529i	0.388767	+	0.851281i
$262$	−6.56452	−	7.57586i	−0.405557	−	0.468038i
$263$	−12.1119	−	7.78382i	−0.746850	−	0.479971i	0.111033	−	0.993817i	$-0.464584\pi$
$263$	−12.1119	−	7.78382i	−0.746850	−	0.479971i	−0.857883	+	0.513846i	$0.828220\pi$
$264$	1.38957	−	9.66469i	0.0855223	−	0.594821i
$265$	0.540659	−	3.76037i	0.0332124	−	0.230998i
$266$	−6.42364	−	4.12822i	−0.393858	−	0.253117i
$267$	1.15460	+	1.33248i	0.0706606	+	0.0815466i
$268$	−6.46835	−	14.1637i	−0.395117	−	0.865186i
$269$	16.9797	−	10.9122i	1.03527	−	0.665329i	0.0914593	−	0.995809i	$-0.470847\pi$
$269$	16.9797	−	10.9122i	1.03527	−	0.665329i	0.943813	+	0.330480i	$0.107211\pi$
$270$	−1.50165	−	0.440925i	−0.0913877	−	0.0268338i
$271$	−5.02903	+	5.80381i	−0.305492	+	0.352556i	−0.887650	−	0.460520i	$-0.847663\pi$
$271$	−5.02903	+	5.80381i	−0.305492	+	0.352556i	0.582158	+	0.813076i	$0.302209\pi$
$272$	−7.52455	+	2.20941i	−0.456243	+	0.133965i
$273$	0.104493	−	0.228808i	0.00632422	−	0.0138481i
$274$	−2.02187	−	14.0624i	−0.122145	−	0.849540i
$275$	−16.9032			−1.01930
$276$	8.07395	−	9.64710i	0.485994	−	0.580687i
$277$	−13.8016			−0.829257			−0.414628	−	0.909991i	$-0.636088\pi$
$277$	−13.8016			−0.829257			−0.414628	+	0.909991i	$0.636088\pi$
$278$	2.30990	+	16.0657i	0.138539	+	0.963557i
$279$	−0.939395	+	2.05699i	−0.0562401	+	0.123149i
$280$	−0.650051	+	0.190872i	−0.0388479	+	0.0114068i
$281$	−10.1452	+	11.7082i	−0.605213	+	0.698453i	−0.972829	−	0.231525i	$-0.925628\pi$
$281$	−10.1452	+	11.7082i	−0.605213	+	0.698453i	0.367616	+	0.929978i	$0.380174\pi$
$282$	26.7925	+	7.86699i	1.59547	+	0.468472i
$283$	3.95868	−	2.54409i	0.235319	−	0.151230i	−0.417667	−	0.908600i	$-0.637152\pi$
$283$	3.95868	−	2.54409i	0.235319	−	0.151230i	0.652986	+	0.757370i	$0.273516\pi$
$284$	2.33531	+	5.11362i	0.138575	+	0.303437i
$285$	−8.88635	−	10.2554i	−0.526382	−	0.607477i
$286$	0.300285	+	0.192982i	0.0177562	+	0.0114112i
$287$	−0.653520	+	4.54533i	−0.0385761	+	0.268302i
$288$	−0.552275	+	3.84116i	−0.0325431	+	0.226342i
$289$	37.4360	+	24.0587i	2.20212	+	1.41522i
$290$	1.72853	+	1.99483i	0.101503	+	0.117140i
$291$	−6.83560	−	14.9679i	−0.400710	−	0.877432i
$292$	3.60851	−	2.31905i	0.211172	−	0.135712i
$293$	5.31182	+	1.55969i	0.310320	+	0.0911181i	0.433184	−	0.901305i	$-0.357390\pi$
$293$	5.31182	+	1.55969i	0.310320	+	0.0911181i	−0.122865	+	0.992423i	$0.539208\pi$
$294$	1.71777	−	1.98241i	0.100182	−	0.115616i
$295$	−0.182150	+	0.0534841i	−0.0106052	+	0.00311396i
$296$	−2.70452	+	5.92206i	−0.157197	+	0.344213i
$297$	1.22374	+	8.51129i	0.0710085	+	0.493875i
$298$	2.19454			0.127126
$299$	0.198188	+	0.414996i	0.0114615	+	0.0239998i
$300$	11.9115			0.687711
$301$	0.187607	+	1.30483i	0.0108135	+	0.0752093i
$302$	7.45094	−	16.3153i	0.428753	−	0.938839i
$303$	18.3431	−	5.38602i	1.05378	−	0.309419i
$304$	−5.00038	+	5.77075i	−0.286792	+	0.330975i
$305$	4.13884	+	1.21527i	0.236990	+	0.0695864i
$306$	25.6018	−	16.4533i	1.46356	−	0.940572i
$307$	13.6767	+	29.9478i	0.780571	+	1.70921i	0.701861	+	0.712314i	$0.252353\pi$
$307$	13.6767	+	29.9478i	0.780571	+	1.70921i	0.0787097	+	0.996898i	$0.474920\pi$
$308$	2.43761	+	2.81316i	0.138896	+	0.160295i
$309$	−1.25733	−	0.808034i	−0.0715267	−	0.0459674i
$310$	−0.0561845	+	0.390771i	−0.00319106	+	0.0221943i
$311$	−4.54620	+	31.6195i	−0.257791	+	1.79298i	0.290691	+	0.956817i	$0.406115\pi$
$311$	−4.54620	+	31.6195i	−0.257791	+	1.79298i	−0.548483	+	0.836162i	$0.684794\pi$
$312$	−0.211608	−	0.135992i	−0.0119800	−	0.00769906i
$313$	−4.36257	−	5.03468i	−0.246587	−	0.284577i	0.618940	−	0.785438i	$-0.287562\pi$
$313$	−4.36257	−	5.03468i	−0.246587	−	0.284577i	−0.865528	+	0.500861i	$0.833017\pi$
$314$	−0.588815	−	1.28933i	−0.0332288	−	0.0727608i
$315$	2.21176	−	1.42141i	0.124618	−	0.0800874i
$316$	14.5699	+	4.27812i	0.819623	+	0.240663i
$317$	8.69588	−	10.0356i	0.488410	−	0.563655i	−0.457030	−	0.889451i	$-0.651087\pi$
$317$	8.69588	−	10.0356i	0.488410	−	0.563655i	0.945440	+	0.325796i	$0.105632\pi$
$318$	14.1132	−	4.14400i	0.791428	−	0.232384i
$319$	6.02449	−	13.1918i	0.337307	−	0.738599i
$320$	0.0964174	+	0.670598i	0.00538990	+	0.0374876i
$321$	−15.4749			−0.863723
$322$	0.763783	+	4.73462i	0.0425640	+	0.263850i
$323$	59.8815			3.33190
$324$	0.794468	+	5.52565i	0.0441371	+	0.306980i
$325$	−0.180894	+	0.396103i	−0.0100342	+	0.0219719i
$326$	−6.97623	+	2.04840i	−0.386377	+	0.113451i
$327$	−8.12617	+	9.37810i	−0.449378	+	0.518610i
$328$	4.40606	+	1.29374i	0.243284	+	0.0714346i
$329$	−8.95536	+	5.75526i	−0.493725	+	0.317298i
$330$	2.74801	+	6.01731i	0.151273	+	0.331242i
$331$	−11.8402	−	13.6643i	−0.650797	−	0.751059i	0.330448	−	0.943824i	$-0.392800\pi$
$331$	−11.8402	−	13.6643i	−0.650797	−	0.751059i	−0.981245	+	0.192765i	$0.938255\pi$
$332$	−13.0760	−	8.40346i	−0.717641	−	0.461200i
$333$	3.59553	−	25.0075i	0.197034	−	1.37040i
$334$	−2.30819	+	16.0538i	−0.126298	+	0.878425i
$335$	8.87449	+	5.70329i	0.484865	+	0.311604i
$336$	−1.71777	−	1.98241i	−0.0937118	−	0.108149i
$337$	−10.6023	−	23.2159i	−0.577545	−	1.26465i	−0.942681	−	0.333694i	$-0.891705\pi$
$337$	−10.6023	−	23.2159i	−0.577545	−	1.26465i	0.365136	−	0.930954i	$-0.381022\pi$
$338$	−10.9286	+	7.02336i	−0.594435	+	0.382020i
$339$	−8.01887	−	2.35455i	−0.435525	−	0.127882i
$340$	3.47931	−	4.01534i	0.188692	−	0.217762i
$341$	2.08122	−	0.611102i	0.112705	−	0.0330930i
$342$	12.3095	−	26.9541i	0.665624	−	1.45751i
$343$	0.142315	+	0.989821i	0.00768428	+	0.0534453i
$344$	1.31825			0.0710753
$345$	−1.06815	+	8.45564i	−0.0575073	+	0.455236i
$346$	7.06054			0.379577
$347$	2.12682	+	14.7923i	0.114174	+	0.794094i	0.963784	+	0.266684i	$0.0859279\pi$
$347$	2.12682	+	14.7923i	0.114174	+	0.794094i	−0.849611	+	0.527411i	$0.823163\pi$
$348$	−4.24541	+	9.29614i	−0.227578	+	0.498326i
$349$	17.6952	−	5.19577i	0.947201	−	0.278123i	0.228580	−	0.973525i	$-0.426592\pi$
$349$	17.6952	−	5.19577i	0.947201	−	0.278123i	0.718621	+	0.695402i	$0.244774\pi$
$350$	−2.97372	+	3.43186i	−0.158952	+	0.183441i
$351$	0.212547	+	0.0624095i	0.0113449	+	0.00333117i
$352$	3.13143	−	2.01245i	0.166906	−	0.107264i
$353$	−12.6734	−	27.7508i	−0.674536	−	1.47703i	−0.868331	−	0.495986i	$-0.834807\pi$
$353$	−12.6734	−	27.7508i	−0.674536	−	1.47703i	0.193795	−	0.981042i	$-0.437920\pi$
$354$	−0.481334	−	0.555489i	−0.0255826	−	0.0295239i
$355$	−3.20402	−	2.05910i	−0.170051	−	0.109285i
$356$	−0.0956575	+	0.665312i	−0.00506984	+	0.0352615i
$357$	−2.92755	+	20.3615i	−0.154942	+	1.07765i
$358$	−12.2756	−	7.88904i	−0.648785	−	0.416949i
$359$	−3.67603	−	4.24236i	−0.194013	−	0.223903i	0.650405	−	0.759588i	$-0.274599\pi$
$359$	−3.67603	−	4.24236i	−0.194013	−	0.223903i	−0.844418	+	0.535684i	$0.820054\pi$
$360$	−1.09218	−	2.39153i	−0.0575628	−	0.126045i
$361$	33.0657	−	21.2501i	1.74030	−	1.11842i
$362$	11.8030	+	3.46567i	0.620352	+	0.182152i
$363$	4.90563	−	5.66139i	0.257479	−	0.297146i
$364$	0.0920095	−	0.0270164i	0.00482261	−	0.00141605i
$365$	−1.20723	+	2.64346i	−0.0631891	+	0.138365i
$366$	2.37682	+	16.5312i	0.124239	+	0.864099i
$367$	1.98028			0.103370			0.0516848	−	0.998663i	$-0.483541\pi$
$367$	1.98028			0.103370			0.0516848	+	0.998663i	$0.483541\pi$
$368$	4.79513	−	0.0822024i	0.249963	−	0.00428509i
$369$	−17.8203			−0.927686
$370$	−0.627715	−	4.36586i	−0.0326334	−	0.226970i
$371$	−2.32943	+	5.10075i	−0.120938	+	0.264818i
$372$	−1.46662	+	0.430638i	−0.0760407	+	0.0223276i
$373$	21.0828	−	24.3309i	1.09163	−	1.25981i	0.128226	−	0.991745i	$-0.459072\pi$
$373$	21.0828	−	24.3309i	1.09163	−	1.25981i	0.963402	−	0.268061i	$-0.0863829\pi$
$374$	−28.0089	−	8.22416i	−1.44831	−	0.425261i
$375$	−14.2640	+	9.16691i	−0.736590	+	0.473377i
$376$	4.42220	+	9.68327i	0.228058	+	0.499377i
$377$	−0.244660	−	0.282352i	−0.0126006	−	0.0145419i
$378$	1.94334	+	1.24891i	0.0999547	+	0.0642370i
$379$	−2.47384	+	17.2060i	−0.127073	+	0.883811i	0.822164	+	0.569250i	$0.192766\pi$
$379$	−2.47384	+	17.2060i	−0.127073	+	0.883811i	−0.949237	+	0.314561i	$0.898143\pi$
$380$	0.736223	−	5.12055i	0.0377675	−	0.262678i
$381$	−10.0517	−	6.45983i	−0.514964	−	0.330947i
$382$	4.77840	+	5.51457i	0.244484	+	0.282150i
$383$	−9.11657	−	19.9625i	−0.465835	−	1.02004i	−0.986119	−	0.166043i	$-0.946901\pi$
$383$	−9.11657	−	19.9625i	−0.465835	−	1.02004i	0.520284	−	0.853994i	$-0.325826\pi$
$384$	−2.20669	+	1.41816i	−0.112610	+	0.0723699i
$385$	−2.41971	−	0.710491i	−0.123320	−	0.0362100i
$386$	−2.40661	+	2.77737i	−0.122493	+	0.141364i
$387$	−4.90846	+	1.44125i	−0.249511	+	0.0732630i
$388$	2.60592	−	5.70617i	0.132296	−	0.289687i
$389$	4.96169	+	34.5093i	0.251568	+	1.74969i	0.588807	+	0.808274i	$0.299598\pi$
$389$	4.96169	+	34.5093i	0.251568	+	1.74969i	−0.337239	+	0.941419i	$0.609493\pi$
$390$	0.170416			0.00862937
$391$	−25.1128	−	27.9974i	−1.27001	−	1.41589i
$392$	1.00000			0.0505076
$393$	3.74213	+	26.0271i	0.188766	+	1.31289i
$394$	4.51587	−	9.88838i	0.227506	−	0.498169i
$395$	−9.87105	+	2.89840i	−0.496666	+	0.145834i
$396$	−9.45955	+	10.9169i	−0.475360	+	0.548595i
$397$	14.2409	+	4.18152i	0.714732	+	0.209864i	0.618828	−	0.785526i	$-0.287608\pi$
$397$	14.2409	+	4.18152i	0.714732	+	0.209864i	0.0959040	+	0.995391i	$0.469426\pi$
$398$	18.6264	−	11.9704i	0.933656	−	0.600024i
$399$	8.32054	+	18.2194i	0.416548	+	0.912112i
$400$	2.97372	+	3.43186i	0.148686	+	0.171593i
$401$	−1.86770	−	1.20030i	−0.0932683	−	0.0599399i	0.493175	−	0.869930i	$-0.335836\pi$
$401$	−1.86770	−	1.20030i	−0.0932683	−	0.0599399i	−0.586444	+	0.809990i	$0.699472\pi$
$402$	−5.81268	+	40.4281i	−0.289910	+	2.01637i
$403$	0.00795247	−	0.0553106i	0.000396141	−	0.00275522i
$404$	6.13117	+	3.94026i	0.305037	+	0.196035i
$405$	−2.47674	−	2.85831i	−0.123070	−	0.142031i
$406$	−1.61847	−	3.54395i	−0.0803232	−	0.175883i
$407$	−20.3869	+	13.1018i	−1.01054	+	0.649434i
$408$	19.7377	+	5.79550i	0.977159	+	0.286920i
$409$	−2.47652	+	2.85806i	−0.122456	+	0.141322i	−0.813667	−	0.581331i	$-0.802532\pi$
$409$	−2.47652	+	2.85806i	−0.122456	+	0.141322i	0.691211	+	0.722653i	$0.257078\pi$
$410$	−2.98508	+	0.876498i	−0.147422	+	0.0432871i
$411$	−15.4810	+	33.8987i	−0.763623	+	1.67210i
$412$	−0.0810879	−	0.563979i	−0.00399491	−	0.0277852i
$413$	0.280209			0.0137882
$414$	−17.7646	+	5.54863i	−0.873083	+	0.272700i
$415$	10.5306			0.516929
$416$	−0.0136471	−	0.0949179i	−0.000669106	−	0.00465373i
$417$	17.6864	−	38.7279i	0.866108	−	1.89651i
$418$	−27.2717	+	8.00769i	−1.33390	+	0.391669i
$419$	−18.8992	+	21.8108i	−0.923284	+	1.06553i	0.0743809	+	0.997230i	$0.476302\pi$
$419$	−18.8992	+	21.8108i	−0.923284	+	1.06553i	−0.997665	+	0.0682968i	$0.978244\pi$
$420$	1.70515	+	0.500677i	0.0832027	+	0.0244305i
$421$	−6.77484	+	4.35393i	−0.330186	+	0.212197i	−0.695221	−	0.718796i	$-0.744693\pi$
$421$	−6.77484	+	4.35393i	−0.330186	+	0.212197i	0.365035	+	0.930994i	$0.381057\pi$
$422$	4.51277	+	9.88159i	0.219678	+	0.481028i
$423$	−27.0527	−	31.2205i	−1.31535	−	1.51799i
$424$	4.71732	+	3.03164i	0.229093	+	0.147229i
$425$	5.06805	−	35.2490i	0.245836	−	1.70983i
$426$	2.09859	−	14.5960i	0.101677	−	0.707179i
$427$	−5.35623	−	3.44224i	−0.259206	−	0.166582i
$428$	−3.86332	−	4.45851i	−0.186741	−	0.215510i
$429$	−0.388959	−	0.851702i	−0.0187791	−	0.0411206i
$430$	−0.751329	+	0.482850i	−0.0362323	+	0.0232851i
$431$	−11.2648	−	3.30764i	−0.542605	−	0.159323i	−0.00106699	−	0.999999i	$-0.500340\pi$
$431$	−11.2648	−	3.30764i	−0.542605	−	0.159323i	−0.541538	+	0.840676i	$0.682158\pi$
$432$	1.51276	−	1.74582i	0.0727829	−	0.0839960i
$433$	35.6650	−	10.4722i	1.71395	−	0.503261i	0.730265	−	0.683164i	$-0.239396\pi$
$433$	35.6650	−	10.4722i	1.71395	−	0.503261i	0.983684	+	0.179903i	$0.0575782\pi$
$434$	0.242071	−	0.530062i	0.0116198	−	0.0254438i
$435$	−0.985355	−	6.85329i	−0.0472441	−	0.328590i
$436$	−4.73066			−0.226558
$437$	−35.3083	−	9.71327i	−1.68902	−	0.464649i
$438$	−11.2516			−0.537624
$439$	5.17070	+	35.9630i	0.246784	+	1.71642i	0.616566	+	0.787303i	$0.288523\pi$
$439$	5.17070	+	35.9630i	0.246784	+	1.71642i	−0.369782	+	0.929118i	$0.620568\pi$
$440$	−1.04762	+	2.29397i	−0.0499433	+	0.109361i
$441$	−3.72346	+	1.09331i	−0.177308	+	0.0520623i
$442$	−0.492469	+	0.568339i	−0.0234244	+	0.0270331i
$443$	5.50159	+	1.61541i	0.261389	+	0.0767506i	0.409801	−	0.912175i	$-0.365598\pi$
$443$	5.50159	+	1.61541i	0.261389	+	0.0767506i	−0.148412	+	0.988926i	$0.547416\pi$
$444$	14.3664	−	9.23275i	0.681801	−	0.438167i
$445$	−0.189172	−	0.414228i	−0.00896760	−	0.0196363i
$446$	9.95545	+	11.4892i	0.471404	+	0.544029i
$447$	−4.84267	−	3.11219i	−0.229050	−	0.147202i
$448$	0.142315	−	0.989821i	0.00672374	−	0.0467647i
$449$	1.37224	−	9.54415i	0.0647601	−	0.450417i	−0.931481	−	0.363791i	$-0.881482\pi$
$449$	1.37224	−	9.54415i	0.0647601	−	0.450417i	0.996241	−	0.0866260i	$-0.0276085\pi$
$450$	−14.8246	−	9.52721i	−0.698840	−	0.449117i
$451$	11.1937	+	12.9182i	0.527091	+	0.608295i
$452$	−1.32355	−	2.89816i	−0.0622543	−	0.136318i
$453$	−39.5795	+	25.4362i	−1.85961	+	1.19510i
$454$	−2.54474	−	0.747205i	−0.119431	−	0.0350680i
$455$	−0.0425447	+	0.0490992i	−0.00199453	+	0.00230181i
$456$	19.2181	−	5.64295i	0.899971	−	0.264255i
$457$	−9.63635	+	21.1007i	−0.450770	+	0.987048i	0.538726	+	0.842481i	$0.318906\pi$
$457$	−9.63635	+	21.1007i	−0.450770	+	0.987048i	−0.989495	+	0.144566i	$0.953821\pi$
$458$	2.44211	+	16.9853i	0.114112	+	0.793669i
$459$	−18.1159			−0.845580
$460$	−2.70284	+	1.80321i	−0.126021	+	0.0840753i
$461$	9.40459			0.438015			0.219008	−	0.975723i	$-0.429718\pi$
$461$	9.40459			0.438015			0.219008	+	0.975723i	$0.429718\pi$
$462$	−1.38957	−	9.66469i	−0.0646488	−	0.449642i
$463$	7.29551	−	15.9749i	0.339051	−	0.742419i	−0.660916	−	0.750460i	$-0.729832\pi$
$463$	7.29551	−	15.9749i	0.339051	−	0.742419i	0.999968	+	0.00804076i	$0.00255948\pi$
$464$	−3.73821	+	1.09764i	−0.173542	+	0.0509566i
$465$	0.678157	−	0.782634i	0.0314488	−	0.0362938i
$466$	18.9952	+	5.57750i	0.879937	+	0.258373i
$467$	−23.5268	+	15.1198i	−1.08869	+	0.699660i	−0.956549	−	0.291571i	$-0.905822\pi$
$467$	−23.5268	+	15.1198i	−1.08869	+	0.699660i	−0.132143	+	0.991231i	$0.542186\pi$
$468$	0.154589	+	0.338503i	0.00714588	+	0.0156473i
$469$	−10.1967	−	11.7676i	−0.470841	−	0.543379i
$470$	−6.06720	−	3.89916i	−0.279859	−	0.179855i
$471$	−0.529129	+	3.68018i	−0.0243810	+	0.169574i
$472$	0.0398779	−	0.277357i	0.00183553	−	0.0127664i
$473$	4.12801	+	2.65291i	0.189806	+	0.121981i
$474$	−26.0843	−	30.1029i	−1.19809	−	1.38267i
$475$	−14.4042	−	31.5407i	−0.660908	−	1.44719i
$476$	−6.59729	+	4.23982i	−0.302386	+	0.194332i
$477$	−20.8793	−	6.13071i	−0.955996	−	0.280706i
$478$	−16.1714	+	18.6628i	−0.739665	+	0.853618i
$479$	−29.2423	+	8.58631i	−1.33611	+	0.392318i	−0.870281	−	0.492555i	$-0.836063\pi$
$479$	−29.2423	+	8.58631i	−1.33611	+	0.392318i	−0.465832	+	0.884873i	$0.654245\pi$
$480$	0.738248	−	1.61654i	0.0336963	−	0.0737845i
$481$	0.0888482	+	0.617953i	0.00405113	+	0.0281762i
$482$	1.52092			0.0692762
$483$	5.02899	−	11.5310i	0.228827	−	0.524679i
$484$	2.85582			0.129810
$485$	0.604832	+	4.20670i	0.0274640	+	0.191016i
$486$	8.96197	−	19.6240i	0.406523	−	0.890162i
$487$	−20.8432	+	6.12013i	−0.944497	+	0.277329i	−0.717494	−	0.696565i	$-0.754711\pi$
$487$	−20.8432	+	6.12013i	−0.944497	+	0.277329i	−0.227003	+	0.973894i	$0.572893\pi$
$488$	−4.16947	+	4.81183i	−0.188743	+	0.217821i
$489$	18.2993	+	5.37317i	0.827525	+	0.242983i
$490$	−0.569944	+	0.366281i	−0.0257474	+	0.0165469i
$491$	14.5230	+	31.8009i	0.655413	+	1.43515i	0.886736	+	0.462276i	$0.152967\pi$
$491$	14.5230	+	31.8009i	0.655413	+	1.43515i	−0.231323	+	0.972877i	$0.574306\pi$
$492$	−7.88810	−	9.10335i	−0.355623	−	0.410411i
$493$	25.7032	+	16.5185i	1.15762	+	0.743954i
$494$	−0.104207	+	0.724773i	−0.00468848	+	0.0326091i
$495$	1.39276	−	9.68687i	0.0626000	−	0.435393i
$496$	−0.490216	−	0.315043i	−0.0220114	−	0.0141458i
$497$	3.68139	+	4.24855i	0.165133	+	0.190573i
$498$	16.9374	+	37.0877i	0.758983	+	1.66194i
$499$	32.5554	−	20.9221i	1.45738	−	0.936601i	0.458529	−	0.888680i	$-0.348377\pi$
$499$	32.5554	−	20.9221i	1.45738	−	0.936601i	0.998851	−	0.0479214i	$-0.0152597\pi$
$500$	−6.20213	−	1.82111i	−0.277368	−	0.0814425i
$501$	27.8602	−	32.1524i	1.24470	−	1.43647i
$502$	−27.9623	+	8.21048i	−1.24802	+	0.366452i
$503$	12.0522	−	26.3907i	0.537382	−	1.17670i	−0.425047	−	0.905171i	$-0.639742\pi$
$503$	12.0522	−	26.3907i	0.537382	−	1.17670i	0.962429	−	0.271532i	$-0.0875303\pi$
$504$	0.552275	+	3.84116i	0.0246003	+	0.171099i
$505$	−4.93766			−0.219723
$506$	15.1810	+	9.39254i	0.674880	+	0.417549i
$507$	34.0762			1.51338
$508$	−0.648257	−	4.50873i	−0.0287618	−	0.200042i
$509$	15.9407	−	34.9052i	0.706558	−	1.54715i	−0.125277	−	0.992122i	$-0.539982\pi$
$509$	15.9407	−	34.9052i	0.706558	−	1.54715i	0.831835	−	0.555024i	$-0.187291\pi$
$510$	−13.3721	+	3.92641i	−0.592128	+	0.173865i
$511$	2.80899	−	3.24175i	0.124262	−	0.143406i
$512$	−0.959493	−	0.281733i	−0.0424040	−	0.0124509i
$513$	−14.8390	+	9.53642i	−0.655156	+	0.421043i
$514$	−6.83441	−	14.9653i	−0.301453	−	0.660090i
$515$	0.252790	+	0.291735i	0.0111393	+	0.0128554i
$516$	−2.90897	−	1.86948i	−0.128060	−	0.0822994i
$517$	−5.63927	+	39.2220i	−0.248015	+	1.72498i
$518$	−0.926526	+	6.44413i	−0.0407092	+	0.283139i
$519$	−15.5804	−	10.0129i	−0.683905	−	0.439519i
$520$	0.0425447	+	0.0490992i	0.00186571	+	0.00215314i
$521$	0.613092	+	1.34249i	0.0268601	+	0.0588153i	0.922587	−	0.385790i	$-0.126071\pi$
$521$	0.613092	+	1.34249i	0.0268601	+	0.0588153i	−0.895726	+	0.444606i	$0.853344\pi$
$522$	12.7190	−	8.17403i	0.556697	−	0.357768i
$523$	−1.52806	−	0.448680i	−0.0668175	−	0.0196194i	0.248153	−	0.968721i	$-0.420176\pi$
$523$	−1.52806	−	0.448680i	−0.0668175	−	0.0196194i	−0.314970	+	0.949101i	$0.601995\pi$
$524$	−6.56452	+	7.57586i	−0.286772	+	0.330953i
$525$	11.4290	−	3.35586i	0.498803	−	0.146462i
$526$	−5.98090	+	13.0963i	−0.260780	+	0.571028i
$527$	0.650354	+	4.52331i	0.0283298	+	0.197038i
$528$	−9.76407			−0.424927
$529$	10.2660	+	20.5818i	0.446349	+	0.894859i
$530$	−3.79904			−0.165020
$531$	0.154753	+	1.07633i	0.00671569	+	0.0467086i
$532$	−3.17202	+	6.94576i	−0.137525	+	0.301137i
$533$	0.422514	−	0.124061i	0.0183011	−	0.00537370i
$534$	1.15460	−	1.33248i	0.0499646	−	0.0576622i
$535$	3.83495	+	1.12604i	0.165799	+	0.0486830i
$536$	−13.0990	+	8.41822i	−0.565791	+	0.363612i
$537$	15.9006	+	34.8174i	0.686160	+	1.50248i
$538$	−13.2176	−	15.2539i	−0.569851	−	0.657644i
$539$	3.13143	+	2.01245i	0.134880	+	0.0866823i
$540$	−0.222730	+	1.54912i	−0.00958475	+	0.0666634i
$541$	−3.51573	+	24.4525i	−0.151153	+	1.05129i	0.763138	+	0.646236i	$0.223658\pi$
$541$	−3.51573	+	24.4525i	−0.151153	+	1.05129i	−0.914291	+	0.405058i	$0.867251\pi$
$542$	6.46044	+	4.15187i	0.277500	+	0.178338i
$543$	−21.1307	−	24.3862i	−0.906806	−	1.04651i
$544$	3.25777	+	7.13353i	0.139676	+	0.305848i
$545$	2.69621	−	1.73275i	0.115493	−	0.0742229i
$546$	−0.241350	−	0.0708668i	−0.0103288	−	0.00303282i
$547$	−12.2208	+	14.1035i	−0.522523	+	0.603023i	−0.954261	−	0.298976i	$-0.903355\pi$
$547$	−12.2208	+	14.1035i	−0.522523	+	0.603023i	0.431738	+	0.901999i	$0.357900\pi$
$548$	−13.6315	+	4.00258i	−0.582310	+	0.170982i
$549$	10.2641	−	22.4752i	0.438060	−	0.959217i
$550$	2.40557	+	16.7311i	0.102574	+	0.713417i
$551$	29.7493			1.26736
$552$	−10.6979	−	6.61884i	−0.455335	−	0.281717i
$553$	15.1850			0.645734
$554$	1.96417	+	13.6611i	0.0834496	+	0.580405i
$555$	−4.80629	+	10.5243i	−0.204016	+	0.446732i
$556$	15.5734	−	4.57278i	0.660461	−	0.193929i
$557$	−1.33791	+	1.54403i	−0.0566892	+	0.0654228i	−0.783386	−	0.621536i	$-0.786509\pi$
$557$	−1.33791	+	1.54403i	−0.0566892	+	0.0654228i	0.726697	+	0.686958i	$0.241055\pi$
$558$	2.16974	+	0.637093i	0.0918525	+	0.0269703i
$559$	0.106345	−	0.0683436i	0.00449790	−	0.00289063i
$560$	0.281441	+	0.616270i	0.0118931	+	0.0260422i
$561$	50.1440	+	57.8692i	2.11708	+	2.44324i
$562$	13.0328	+	8.37570i	0.549757	+	0.353307i
$563$	−4.54106	+	31.5838i	−0.191383	+	1.33110i	0.636969	+	0.770890i	$0.280188\pi$
$563$	−4.54106	+	31.5838i	−0.191383	+	1.33110i	−0.828352	+	0.560209i	$0.810721\pi$
$564$	3.97394	−	27.6394i	0.167333	−	1.16383i
$565$	1.81589	+	1.16700i	0.0763949	+	0.0490960i
$566$	−3.08157	−	3.55633i	−0.129528	−	0.149484i
$567$	2.31904	+	5.07799i	0.0973905	+	0.213256i
$568$	4.72922	−	3.03928i	0.198434	−	0.127526i
$569$	12.7568	+	3.74574i	0.534793	+	0.157029i	0.537968	−	0.842966i	$-0.319192\pi$
$569$	12.7568	+	3.74574i	0.534793	+	0.157029i	−0.00317442	+	0.999995i	$0.501010\pi$
$570$	−8.88635	+	10.2554i	−0.372208	+	0.429551i
$571$	−7.08002	+	2.07888i	−0.296290	+	0.0869985i	−0.426499	−	0.904488i	$-0.640253\pi$
$571$	−7.08002	+	2.07888i	−0.296290	+	0.0869985i	0.130209	+	0.991487i	$0.458435\pi$
$572$	0.148282	−	0.324693i	0.00619999	−	0.0135761i
$573$	−2.72395	−	18.9455i	−0.113795	−	0.791459i
$574$	4.59207			0.191669
$575$	−8.70598	+	19.9620i	−0.363065	+	0.832474i
$576$	3.88066			0.161694
$577$	0.408290	+	2.83972i	0.0169973	+	0.118219i	0.996554	−	0.0829513i	$-0.0264346\pi$
$577$	0.408290	+	2.83972i	0.0169973	+	0.118219i	−0.979556	+	0.201170i	$0.935526\pi$
$578$	18.4861	−	40.4789i	0.768920	−	1.68370i
$579$	9.24939	−	2.71586i	0.384391	−	0.112867i
$580$	1.72853	−	1.99483i	0.0717732	−	0.0828307i
$581$	−14.9139	−	4.37912i	−0.618733	−	0.181676i
$582$	−13.8427	+	8.89617i	−0.573799	+	0.368758i
$583$	8.67094	+	18.9867i	0.359114	+	0.786350i
$584$	−2.80899	−	3.24175i	−0.116237	−	0.134144i
$585$	−0.212094	−	0.136305i	−0.00876901	−	0.00563550i
$586$	0.787864	−	5.47972i	0.0325464	−	0.226365i
$587$	0.595187	−	4.13962i	0.0245660	−	0.170860i	−0.973845	−	0.227214i	$-0.927038\pi$
$587$	0.595187	−	4.13962i	0.0245660	−	0.170860i	0.998411	+	0.0563536i	$0.0179474\pi$
$588$	−2.20669	−	1.41816i	−0.0910025	−	0.0584837i
$589$	2.91383	+	3.36274i	0.120062	+	0.138559i
$590$	0.0788624	+	0.172684i	0.00324671	+	0.00710931i
$591$	−23.9884	+	15.4164i	−0.986751	+	0.634146i
$592$	6.24668	+	1.83419i	0.256737	+	0.0753847i
$593$	7.67256	−	8.85461i	0.315074	−	0.363615i	−0.576018	−	0.817437i	$-0.695394\pi$
$593$	7.67256	−	8.85461i	0.315074	−	0.363615i	0.891092	+	0.453822i	$0.149940\pi$
$594$	8.25050	−	2.42257i	0.338522	−	0.0993991i
$595$	2.20712	−	4.83292i	0.0904831	−	0.198130i
$596$	−0.312315	−	2.17220i	−0.0127929	−	0.0889767i
$597$	−58.0786			−2.37700
$598$	0.382566	−	0.255231i	0.0156443	−	0.0104372i
$599$	−39.6734			−1.62101			−0.810506	−	0.585731i	$-0.800808\pi$
$599$	−39.6734			−1.62101			−0.810506	+	0.585731i	$0.800808\pi$
$600$	−1.69518	−	11.7903i	−0.0692056	−	0.481336i
$601$	11.9173	−	26.0952i	0.486116	−	1.06445i	−0.494620	−	0.869109i	$-0.664693\pi$
$601$	11.9173	−	26.0952i	0.486116	−	1.06445i	0.980736	−	0.195336i	$-0.0625799\pi$
$602$	1.26485	−	0.371394i	0.0515515	−	0.0151369i
$603$	39.5700	−	45.6662i	1.61141	−	1.85967i
$604$	−17.2096	−	5.05319i	−0.700248	−	0.205611i
$605$	−1.62766	+	1.04603i	−0.0661736	+	0.0425272i
$606$	−7.94170	−	17.3899i	−0.322609	−	0.706416i
$607$	6.36359	+	7.34397i	0.258290	+	0.298083i	0.870053	−	0.492959i	$-0.164085\pi$
$607$	6.36359	+	7.34397i	0.258290	+	0.298083i	−0.611763	+	0.791041i	$0.709539\pi$
$608$	6.42364	+	4.12822i	0.260513	+	0.167421i
$609$	−1.45441	+	10.1157i	−0.0589357	+	0.409907i
$610$	0.613886	−	4.26967i	0.0248555	−	0.172874i
$611$	0.858765	+	0.551895i	0.0347419	+	0.0223273i
$612$	−19.9293	−	22.9997i	−0.805596	−	0.929707i
$613$	9.68888	+	21.2157i	0.391330	+	0.856894i	0.998076	+	0.0619981i	$0.0197473\pi$
$613$	9.68888	+	21.2157i	0.391330	+	0.856894i	−0.606746	+	0.794896i	$0.707525\pi$
$614$	27.6966	−	17.7995i	1.11774	−	0.718330i
$615$	7.83016	+	2.29914i	0.315743	+	0.0927104i
$616$	2.43761	−	2.81316i	0.0982143	−	0.113345i
$617$	−20.4005	+	5.99013i	−0.821293	+	0.241153i	−0.665273	−	0.746600i	$-0.731685\pi$
$617$	−20.4005	+	5.99013i	−0.821293	+	0.241153i	−0.156020	+	0.987754i	$0.549867\pi$
$618$	−0.620873	+	1.35952i	−0.0249752	+	0.0546880i
$619$	−2.16219	−	15.0384i	−0.0869059	−	0.604444i	−0.986007	−	0.166703i	$-0.946688\pi$
$619$	−2.16219	−	15.0384i	−0.0869059	−	0.604444i	0.899101	−	0.437741i	$-0.144221\pi$
$620$	0.394790			0.0158551
$621$	10.6818	+	2.93855i	0.428646	+	0.117920i
$622$	31.9447			1.28086
$623$	0.0956575	+	0.665312i	0.00383244	+	0.0266552i
$624$	−0.104493	+	0.228808i	−0.00418308	+	0.00915966i
$625$	−17.5834	+	5.16295i	−0.703336	+	0.206518i
$626$	−4.36257	+	5.03468i	−0.174364	+	0.201226i
$627$	71.5364	+	21.0050i	2.85689	+	0.838858i
$628$	−1.19240	+	0.766312i	−0.0475821	+	0.0305792i
$629$	−21.2094	−	46.4421i	−0.845674	−	1.85177i
$630$	−1.72171	−	1.98696i	−0.0685945	−	0.0791623i
$631$	18.1736	+	11.6795i	0.723479	+	0.464952i	0.849846	−	0.527032i	$-0.176695\pi$
$631$	18.1736	+	11.6795i	0.723479	+	0.464952i	−0.126366	+	0.991984i	$0.540331\pi$
$632$	2.16106	−	15.0305i	0.0859622	−	0.597880i
$633$	4.05533	−	28.2054i	0.161185	−	1.12107i
$634$	−11.1710	−	7.17916i	−0.443657	−	0.285121i
$635$	2.02093	+	2.33228i	0.0801982	+	0.0925536i
$636$	−6.11034	−	13.3798i	−0.242291	−	0.530543i
$637$	0.0806711	−	0.0518442i	0.00319631	−	0.00205414i
$638$	−13.9149	−	4.08578i	−0.550896	−	0.161758i
$639$	−14.2862	+	16.4872i	−0.565153	+	0.652222i
$640$	0.650051	−	0.190872i	0.0256955	−	0.00754488i
$641$	−8.86023	+	19.4012i	−0.349958	+	0.766301i	0.650022	+	0.759916i	$0.274760\pi$
$641$	−8.86023	+	19.4012i	−0.349958	+	0.766301i	−0.999980	+	0.00638539i	$0.997967\pi$
$642$	2.20230	+	15.3174i	0.0869180	+	0.604528i
$643$	−1.47922			−0.0583348			−0.0291674	−	0.999575i	$-0.509286\pi$
$643$	−1.47922			−0.0583348			−0.0291674	+	0.999575i	$0.509286\pi$
$644$	4.57773	−	1.42982i	0.180388	−	0.0563426i
$645$	2.34271			0.0922440
$646$	−8.52203	−	59.2720i	−0.335295	−	2.33203i
$647$	1.20529	−	2.63922i	0.0473849	−	0.103758i	−0.884459	−	0.466618i	$-0.845472\pi$
$647$	1.20529	−	2.63922i	0.0473849	−	0.103758i	0.931844	+	0.362860i	$0.118200\pi$
$648$	5.35634	−	1.57276i	0.210417	−	0.0617839i
$649$	0.683042	−	0.788272i	0.0268117	−	0.0309424i
$650$	0.417816	+	0.122682i	0.0163881	+	0.00481197i
$651$	−1.28589	+	0.826389i	−0.0503979	+	0.0323887i
$652$	3.02038	+	6.61370i	0.118287	+	0.259012i
$653$	−11.7646	−	13.5771i	−0.460386	−	0.531314i	0.477327	−	0.878726i	$-0.341606\pi$
$653$	−11.7646	−	13.5771i	−0.460386	−	0.531314i	−0.937712	+	0.347412i	$0.887060\pi$
$654$	10.4391	+	6.70881i	0.408202	+	0.262335i
$655$	0.966517	−	6.72227i	0.0377649	−	0.262661i
$656$	0.653520	−	4.54533i	0.0255157	−	0.177465i
$657$	14.0034	+	8.99944i	0.546324	+	0.351101i
$658$	6.97116	+	8.04515i	0.271764	+	0.313633i
$659$	−4.03489	−	8.83518i	−0.157177	−	0.344170i	0.814618	−	0.579998i	$-0.196947\pi$
$659$	−4.03489	−	8.83518i	−0.157177	−	0.344170i	−0.971795	+	0.235829i	$0.924220\pi$
$660$	5.56498	−	3.57639i	0.216616	−	0.139211i
$661$	18.6053	+	5.46301i	0.723663	+	0.212487i	0.622763	−	0.782410i	$-0.286010\pi$
$661$	18.6053	+	5.46301i	0.723663	+	0.212487i	0.100899	+	0.994897i	$0.467828\pi$
$662$	−11.8402	+	13.6643i	−0.460183	+	0.531079i
$663$	1.89272	−	0.555753i	0.0735072	−	0.0215837i
$664$	−6.45701	+	14.1389i	−0.250581	+	0.548695i
$665$	−0.736223	−	5.12055i	−0.0285495	−	0.198566i
$666$	−25.2646			−0.978984
$667$	−12.4761	−	13.9091i	−0.483077	−	0.538564i
$668$	16.2189			0.627528
$669$	−5.67515	−	39.4715i	−0.219414	−	1.52606i
$670$	4.38227	−	9.59583i	0.169302	−	0.370719i
$671$	−22.7400	+	6.67706i	−0.877867	+	0.257765i
$672$	−1.71777	+	1.98241i	−0.0662643	+	0.0764730i
$673$	26.6567	+	7.82711i	1.02754	+	0.301713i	0.751710	−	0.659494i	$-0.229229\pi$
$673$	26.6567	+	7.82711i	1.02754	+	0.301713i	0.275830	+	0.961207i	$0.411047\pi$
$674$	−21.4707	+	13.7984i	−0.827020	+	0.531493i
$675$	4.35769	+	9.54201i	0.167728	+	0.367272i
$676$	8.50717	+	9.81779i	0.327199	+	0.377607i
$677$	34.6919	+	22.2951i	1.33332	+	0.856872i	0.996409	−	0.0846655i	$-0.0269822\pi$
$677$	34.6919	+	22.2951i	1.33332	+	0.856872i	0.336909	+	0.941537i	$0.390619\pi$
$678$	−1.18938	+	8.27234i	−0.0456780	+	0.317697i
$679$	0.892749	−	6.20921i	0.0342606	−	0.238288i
$680$	−4.46962	−	2.87245i	−0.171402	−	0.110154i
$681$	4.55582	+	5.25769i	0.174579	+	0.201475i
$682$	−0.901071	−	1.97307i	−0.0345038	−	0.0755528i
$683$	14.4220	−	9.26847i	0.551843	−	0.354648i	−0.234812	−	0.972041i	$-0.575447\pi$
$683$	14.4220	−	9.26847i	0.551843	−	0.354648i	0.786655	+	0.617393i	$0.211811\pi$
$684$	−28.4316	−	8.34827i	−1.08711	−	0.319204i
$685$	6.30314	−	7.27421i	0.240830	−	0.277933i
$686$	0.959493	−	0.281733i	0.0366336	−	0.0107566i
$687$	18.6987	−	40.9445i	0.713402	−	1.56213i
$688$	−0.187607	−	1.30483i	−0.00715243	−	0.0497463i
$689$	0.537724			0.0204856
$690$	8.52159	−	0.146085i	0.324411	−	0.00556135i
$691$	3.70717			0.141027			0.0705137	−	0.997511i	$-0.477536\pi$
$691$	3.70717			0.141027			0.0705137	+	0.997511i	$0.477536\pi$
$692$	−1.00482	−	6.98867i	−0.0381975	−	0.265669i
$693$	−6.00072	+	13.1398i	−0.227949	+	0.499138i
$694$	14.3391	−	4.21034i	0.544305	−	0.159822i
$695$	−7.20107	+	8.31048i	−0.273152	+	0.315234i
$696$	9.80571	+	2.87921i	0.371684	+	0.109136i
$697$	−30.2952	+	19.4696i	−1.14751	+	0.737462i
$698$	−7.66117	−	16.7756i	−0.289980	−	0.634967i
$699$	−34.0069	−	39.2460i	−1.28626	−	1.48442i
$700$	3.82013	+	2.45505i	0.144387	+	0.0927922i
$701$	−3.55462	+	24.7230i	−0.134256	+	0.933773i	0.805662	+	0.592375i	$0.201810\pi$
$701$	−3.55462	+	24.7230i	−0.134256	+	0.933773i	−0.939919	+	0.341398i	$0.889100\pi$
$702$	0.0315256	−	0.219266i	0.00118986	−	0.00827564i
$703$	−41.8204	−	26.8763i	−1.57729	−	1.01366i
$704$	−2.43761	−	2.81316i	−0.0918711	−	0.106025i
$705$	7.85885	+	17.2085i	0.295981	+	0.648109i
$706$	−25.6648	+	16.4937i	−0.965906	+	0.620750i
$707$	6.99291	+	2.05330i	0.262995	+	0.0772224i
$708$	−0.481334	+	0.555489i	−0.0180896	+	0.0208765i
$709$	−4.10506	+	1.20535i	−0.154169	+	0.0452680i	−0.357906	−	0.933758i	$-0.616509\pi$
$709$	−4.10506	+	1.20535i	−0.154169	+	0.0452680i	0.203738	+	0.979026i	$0.434691\pi$
$710$	−1.58216	+	3.46444i	−0.0593773	+	0.130018i
$711$	8.38632	+	58.3282i	0.314512	+	2.18748i
$712$	0.672154			0.0251900
$713$	0.350246	−	2.77260i	0.0131168	−	0.103835i
$714$	20.5709			0.769847
$715$	0.0344162	+	0.239370i	0.00128709	+	0.00895192i
$716$	−6.06174	+	13.2734i	−0.226538	+	0.496049i
$717$	62.1522	−	18.2495i	2.32112	−	0.681541i
$718$	−3.67603	+	4.24236i	−0.137188	+	0.158324i
$719$	6.60181	+	1.93847i	0.246206	+	0.0722926i	0.402507	−	0.915417i	$-0.368139\pi$
$719$	6.60181	+	1.93847i	0.246206	+	0.0722926i	−0.156301	+	0.987709i	$0.549957\pi$
$720$	−2.21176	+	1.42141i	−0.0824274	+	0.0529728i
$721$	−0.236694	−	0.518288i	−0.00881496	−	0.0193021i
$722$	−25.7395	−	29.7050i	−0.957926	−	1.10551i
$723$	−3.35621	−	2.15691i	−0.124819	−	0.0802162i
$724$	1.75066	−	12.1761i	0.0650626	−	0.452520i
$725$	2.51782	−	17.5118i	0.0935093	−	0.650372i
$726$	−6.30191	−	4.04999i	−0.233886	−	0.150309i
$727$	20.4951	+	23.6527i	0.760123	+	0.877229i	0.995508	−	0.0946736i	$-0.0301807\pi$
$727$	20.4951	+	23.6527i	0.760123	+	0.877229i	−0.235386	+	0.971902i	$0.575635\pi$
$728$	−0.0398358	−	0.0872282i	−0.00147641	−	0.00323289i
$729$	−33.5174	+	21.5403i	−1.24138	+	0.797789i
$730$	2.78836	+	0.818735i	0.103202	+	0.0303027i
$731$	−6.76995	+	7.81294i	−0.250396	+	0.288972i
$732$	16.0247	−	4.70526i	0.592288	−	0.173912i
$733$	−20.1425	+	44.1059i	−0.743979	+	1.62909i	0.0329163	+	0.999458i	$0.489521\pi$
$733$	−20.1425	+	44.1059i	−0.743979	+	1.62909i	−0.776896	+	0.629629i	$0.783207\pi$
$734$	−0.281823	−	1.96012i	−0.0104023	−	0.0723494i
$735$	1.77713			0.0655506
$736$	−0.763783	−	4.73462i	−0.0281534	−	0.174520i
$737$	−57.9599			−2.13498
$738$	2.53609	+	17.6389i	0.0933547	+	0.649296i
$739$	9.21312	−	20.1739i	0.338910	−	0.742109i	−0.661056	−	0.750336i	$-0.729892\pi$
$739$	9.21312	−	20.1739i	0.338910	−	0.742109i	0.999966	+	0.00822706i	$0.00261878\pi$
$740$	−4.23209	+	1.24265i	−0.155575	+	0.0456808i
$741$	1.25779	−	1.45157i	0.0462062	−	0.0533248i
$742$	5.38034	+	1.57981i	0.197519	+	0.0579967i
$743$	38.2405	−	24.5756i	1.40291	−	0.901593i	0.402999	−	0.915201i	$-0.367968\pi$
$743$	38.2405	−	24.5756i	1.40291	−	0.901593i	0.999907	+	0.0136075i	$0.00433152\pi$
$744$	0.634977	+	1.39041i	0.0232794	+	0.0509747i
$745$	0.973636	+	1.12364i	0.0356713	+	0.0411669i
$746$	−27.0836	−	17.4056i	−0.991603	−	0.637264i
$747$	8.58430	−	59.7051i	0.314083	−	2.18450i
$748$	−4.15437	+	28.8943i	−0.151899	+	1.05648i
$749$	−4.96294	−	3.18949i	−0.181342	−	0.116541i
$750$	11.1036	+	12.8142i	0.405446	+	0.467909i
$751$	−14.8702	−	32.5611i	−0.542620	−	1.18817i	−0.960144	−	0.279506i	$-0.909829\pi$
$751$	−14.8702	−	32.5611i	−0.542620	−	1.18817i	0.417524	−	0.908666i	$-0.362898\pi$
$752$	8.95536	−	5.75526i	0.326569	−	0.209873i
$753$	73.3480	+	21.5369i	2.67295	+	0.784849i
$754$	−0.244660	+	0.282352i	−0.00890997	+	0.0102827i
$755$	11.6594	−	3.42351i	0.424329	−	0.124594i
$756$	0.959632	−	2.10130i	0.0349015	−	0.0764236i
$757$	−5.47895	−	38.1069i	−0.199136	−	1.38502i	−0.806799	−	0.590825i	$-0.798802\pi$
$757$	−5.47895	−	38.1069i	−0.199136	−	1.38502i	0.607664	−	0.794195i	$-0.292107\pi$
$758$	17.3829			0.631375
$759$	−20.1798	−	42.2555i	−0.732481	−	1.53378i
$760$	−5.17320			−0.187652
$761$	−0.407868	−	2.83678i	−0.0147852	−	0.102833i	0.981093	−	0.193539i	$-0.0619967\pi$
$761$	−0.407868	−	2.83678i	−0.0147852	−	0.102833i	−0.995878	+	0.0907061i	$0.971088\pi$
$762$	−4.96357	+	10.8687i	−0.179811	+	0.393732i
$763$	−4.53904	+	1.33278i	−0.164324	+	0.0482499i
$764$	4.77840	−	5.51457i	0.172876	−	0.199510i
$765$	19.7830	+	5.80880i	0.715254	+	0.210018i
$766$	−18.4619	+	11.8647i	−0.667055	+	0.428690i
$767$	−0.0111623	−	0.0244421i	−0.000403049	−	0.000882554i
$768$	1.71777	+	1.98241i	0.0619845	+	0.0715340i
$769$	33.4193	+	21.4773i	1.20513	+	0.774491i	0.979837	−	0.199800i	$-0.0640292\pi$
$769$	33.4193	+	21.4773i	1.20513	+	0.774491i	0.225295	+	0.974291i	$0.427666\pi$
$770$	−0.358898	+	2.49619i	−0.0129338	+	0.0899566i
$771$	−6.14164	+	42.7160i	−0.221186	+	1.53838i
$772$	3.09160	+	1.98685i	0.111269	+	0.0715083i
$773$	−18.0851	−	20.8713i	−0.650475	−	0.750688i	0.330715	−	0.943731i	$-0.392710\pi$
$773$	−18.0851	−	20.8713i	−0.650475	−	0.750688i	−0.981190	+	0.193042i	$0.938165\pi$
$774$	2.12513	+	4.65338i	0.0763862	+	0.167262i
$775$	2.22607	−	1.43061i	0.0799629	−	0.0513890i
$776$	−6.01896	−	1.76732i	−0.216068	−	0.0634433i
$777$	11.1833	−	12.9063i	0.401200	−	0.463009i
$778$	33.4520	−	9.82238i	1.19931	−	0.352149i
$779$	−14.5662	+	31.8954i	−0.521887	+	1.14277i
$780$	−0.0242528	−	0.168682i	−0.000868389	−	0.00603978i
$781$	20.9256			0.748778
$782$	−24.1385	+	28.8417i	−0.863190	+	1.03138i
$783$	−9.00004			−0.321635
$784$	−0.142315	−	0.989821i	−0.00508267	−	0.0353508i
$785$	0.398919	−	0.873510i	0.0142380	−	0.0311769i
$786$	25.2296	−	7.40808i	0.899911	−	0.264238i
$787$	5.89849	−	6.80722i	0.210258	−	0.242651i	−0.640818	−	0.767693i	$-0.721405\pi$
$787$	5.89849	−	6.80722i	0.210258	−	0.242651i	0.851077	+	0.525042i	$0.175950\pi$
$788$	−10.4304	−	3.06264i	−0.371568	−	0.109102i
$789$	31.7707	−	20.4178i	1.13107	−	0.726891i
$790$	4.27370	+	9.35809i	0.152051	+	0.332946i
$791$	−2.08644	−	2.40788i	−0.0741852	−	0.0856143i
$792$	12.1520	+	7.80963i	0.431803	+	0.277503i
$793$	−0.0868907	+	0.604338i	−0.00308558	+	0.0214607i
$794$	2.11226	−	14.6911i	0.0749613	−	0.521367i
$795$	8.38331	+	5.38762i	0.297325	+	0.191079i
$796$	−14.4994	−	16.7332i	−0.513918	−	0.593093i
$797$	13.9239	+	30.4891i	0.493210	+	1.07998i	0.978617	+	0.205691i	$0.0659443\pi$
$797$	13.9239	+	30.4891i	0.493210	+	1.07998i	−0.485407	+	0.874288i	$0.661328\pi$
$798$	16.8498	−	10.8287i	0.596478	−	0.383333i
$799$	−80.1008	−	23.5197i	−2.83376	−	0.832068i
$800$	2.97372	−	3.43186i	0.105137	−	0.121335i
$801$	−2.50274	+	0.734871i	−0.0884300	+	0.0259654i
$802$	−0.922278	+	2.01951i	−0.0325668	+	0.0713113i
$803$	−2.27231	−	15.8043i	−0.0801880	−	0.557720i
$804$	40.8438			1.44045
$805$	−2.08534	+	2.49165i	−0.0734985	+	0.0878191i
$806$	−0.0558794			−0.00196827
$807$	7.53475	+	52.4054i	0.265236	+	1.84476i
$808$	3.02760	−	6.62952i	0.106511	−	0.233226i
$809$	20.8929	−	6.13472i	0.734556	−	0.215685i	0.107003	−	0.994259i	$-0.465875\pi$
$809$	20.8929	−	6.13472i	0.734556	−	0.215685i	0.627553	+	0.778574i	$0.284056\pi$
$810$	−2.47674	+	2.85831i	−0.0870238	+	0.100431i
$811$	−11.7219	−	3.44186i	−0.411611	−	0.120860i	0.0693696	−	0.997591i	$-0.477901\pi$
$811$	−11.7219	−	3.44186i	−0.411611	−	0.120860i	−0.480981	+	0.876731i	$0.659719\pi$
$812$	−3.27755	+	2.10635i	−0.115019	+	0.0739185i
$813$	−8.36820	−	18.3238i	−0.293486	−	0.642644i
$814$	15.8698	+	18.3148i	0.556237	+	0.641932i
$815$	−4.14392	−	2.66313i	−0.145155	−	0.0932855i
$816$	2.92755	−	20.3615i	0.102485	−	0.712796i
$817$	−1.43252	+	9.96343i	−0.0501177	+	0.348576i
$818$	3.18141	+	2.04457i	0.111235	+	0.0714867i
$819$	0.243694	+	0.281238i	0.00851537	+	0.00982726i
$820$	1.29240	+	2.82996i	0.0451325	+	0.0988263i
$821$	9.81675	−	6.30884i	0.342607	−	0.220180i	−0.358010	−	0.933718i	$-0.616545\pi$
$821$	9.81675	−	6.30884i	0.342607	−	0.220180i	0.700617	+	0.713538i	$0.252908\pi$
$822$	35.7569	+	10.4992i	1.24716	+	0.366200i
$823$	12.8770	−	14.8609i	0.448864	−	0.518017i	−0.485548	−	0.874210i	$-0.661380\pi$
$823$	12.8770	−	14.8609i	0.448864	−	0.518017i	0.934412	+	0.356193i	$0.115925\pi$
$824$	−0.546698	+	0.160525i	−0.0190451	+	0.00559215i
$825$	18.4190	−	40.3319i	0.641266	−	1.40418i
$826$	−0.0398779	−	0.277357i	−0.00138753	−	0.00965048i
$827$	−12.4664			−0.433500			−0.216750	−	0.976227i	$-0.569546\pi$
$827$	−12.4664			−0.433500			−0.216750	+	0.976227i	$0.569546\pi$
$828$	8.02032	+	16.7941i	0.278725	+	0.583637i
$829$	30.4171			1.05643			0.528215	−	0.849111i	$-0.322862\pi$
$829$	30.4171			1.05643			0.528215	+	0.849111i	$0.322862\pi$
$830$	−1.49867	−	10.4235i	−0.0520195	−	0.361803i
$831$	15.0392	−	32.9314i	0.521706	−	1.14238i
$832$	−0.0920095	+	0.0270164i	−0.00318986	+	0.000936627i
$833$	−5.13556	+	5.92675i	−0.177937	+	0.205350i
$834$	−40.8507	−	11.9949i	−1.41454	−	0.415348i
$835$	−9.24386	+	5.94067i	−0.319897	+	0.205585i
$836$	11.8073	+	25.8545i	0.408366	+	0.894196i
$837$	−0.881520	−	1.01733i	−0.0304698	−	0.0351640i
$838$	24.2784	+	15.6028i	0.838684	+	0.538989i
$839$	4.46461	−	31.0520i	0.154135	−	1.07204i	−0.755057	−	0.655659i	$-0.772391\pi$
$839$	4.46461	−	31.0520i	0.154135	−	1.07204i	0.909192	−	0.416376i	$-0.136700\pi$
$840$	0.252913	−	1.75905i	0.00872631	−	0.0606928i
$841$	−11.6269	−	7.47218i	−0.400929	−	0.257661i
$842$	5.27377	+	6.08626i	0.181746	+	0.209746i
$843$	−16.8814	−	36.9652i	−0.581427	−	1.27315i
$844$	9.13877	−	5.87313i	0.314570	−	0.202162i
$845$	−8.44468	−	2.47958i	−0.290506	−	0.0853002i
$846$	−27.0527	+	31.2205i	−0.930091	+	1.07338i
$847$	2.74014	−	0.804577i	0.0941522	−	0.0276456i
$848$	2.32943	−	5.10075i	0.0799931	−	0.175160i
$849$	1.75666	+	12.2179i	0.0602886	+	0.419316i
$850$	−35.6115			−1.22146
$851$	4.97253	+	30.8243i	0.170456	+	1.05664i
$852$	−14.7461			−0.505193
$853$	0.727640	+	5.06085i	0.0249139	+	0.173280i	0.998479	−	0.0551285i	$-0.0175569\pi$
$853$	0.727640	+	5.06085i	0.0249139	+	0.173280i	−0.973565	+	0.228409i	$0.926648\pi$
$854$	−2.64493	+	5.79159i	−0.0905076	+	0.198184i
$855$	19.2622	−	5.65590i	0.658754	−	0.193428i
$856$	−3.86332	+	4.45851i	−0.132046	+	0.152389i
$857$	10.4775	+	3.07648i	0.357906	+	0.105091i	0.455742	−	0.890112i	$-0.349374\pi$
$857$	10.4775	+	3.07648i	0.357906	+	0.105091i	−0.0978361	+	0.995203i	$0.531192\pi$
$858$	−0.787679	+	0.506210i	−0.0268909	+	0.0172817i
$859$	−13.9449	−	30.5351i	−0.475794	−	1.04184i	−0.983599	−	0.180372i	$-0.942270\pi$
$859$	−13.9449	−	30.5351i	−0.475794	−	1.04184i	0.507804	−	0.861472i	$-0.330457\pi$
$860$	0.584860	+	0.674965i	0.0199436	+	0.0230161i
$861$	−10.1333	−	6.51227i	−0.345342	−	0.221938i
$862$	−1.67082	+	11.6208i	−0.0569085	+	0.395807i
$863$	7.11688	−	49.4990i	0.242261	−	1.68496i	−0.398456	−	0.917187i	$-0.630454\pi$
$863$	7.11688	−	49.4990i	0.242261	−	1.68496i	0.640718	−	0.767777i	$-0.278637\pi$
$864$	−1.94334	−	1.24891i	−0.0661138	−	0.0424888i
$865$	3.13251	+	3.61511i	0.106508	+	0.122917i
$866$	−15.4412	−	33.8116i	−0.524715	−	1.14897i
$867$	−98.1985	+	63.1084i	−3.33500	+	2.14327i
$868$	−0.559117	−	0.164171i	−0.0189777	−	0.00557234i
$869$	37.0153	−	42.7179i	1.25566	−	1.44911i
$870$	−6.64330	+	1.95065i	−0.225229	+	0.0661332i
$871$	−0.620276	+	1.35821i	−0.0210172	+	0.0460213i
$872$	0.673243	+	4.68251i	0.0227989	+	0.158570i
$873$	24.3436			0.823906
$874$	−4.58951	+	36.3312i	−0.155242	+	1.22892i
$875$	−6.46397			−0.218522
$876$	1.60128	+	11.1371i	0.0541021	+	0.376288i
$877$	2.56681	−	5.62053i	0.0866751	−	0.189792i	−0.861331	−	0.508044i	$-0.830369\pi$
$877$	2.56681	−	5.62053i	0.0866751	−	0.189792i	0.948006	+	0.318252i	$0.103096\pi$
$878$	34.8611	−	10.2361i	1.17651	−	0.345453i
$879$	−9.50966	+	10.9747i	−0.320753	+	0.370169i
$880$	2.41971	+	0.710491i	0.0815684	+	0.0239506i
$881$	−11.9152	+	7.65743i	−0.401433	+	0.257985i	−0.725744	−	0.687965i	$-0.758504\pi$
$881$	−11.9152	+	7.65743i	−0.401433	+	0.257985i	0.324310	+	0.945951i	$0.394868\pi$
$882$	1.61208	+	3.52997i	0.0542817	+	0.118860i
$883$	18.3639	+	21.1931i	0.617994	+	0.713204i	0.975325	−	0.220774i	$-0.0708585\pi$
$883$	18.3639	+	21.1931i	0.617994	+	0.713204i	−0.357331	+	0.933978i	$0.616313\pi$
$884$	0.632640	+	0.406573i	0.0212780	+	0.0136745i
$885$	0.0708684	−	0.492901i	0.00238222	−	0.0165687i
$886$	0.816013	−	5.67549i	0.0274145	−	0.190672i
$887$	29.5718	+	19.0047i	0.992925	+	0.638114i	0.932920	−	0.360084i	$-0.117252\pi$
$887$	29.5718	+	19.0047i	0.992925	+	0.638114i	0.0600053	+	0.998198i	$0.480888\pi$
$888$	−11.1833	−	12.9063i	−0.375288	−	0.433106i
$889$	−1.89225	−	4.14346i	−0.0634641	−	0.138967i
$890$	−0.383090	+	0.246197i	−0.0128412	+	0.00825255i
$891$	19.9381	+	5.85436i	0.667952	+	0.196128i
$892$	9.95545	−	11.4892i	0.333333	−	0.384687i
$893$	−77.9924	+	22.9006i	−2.60992	+	0.766341i
$894$	−2.39133	+	5.23629i	−0.0799781	+	0.175128i
$895$	−1.40692	−	9.78538i	−0.0470283	−	0.327089i
$896$	−1.00000			−0.0334077
$897$	−1.20616	+	0.0206771i	−0.0402726	+	0.000690390i
$898$	−9.64230			−0.321768
$899$	0.323097	+	2.24719i	0.0107759	+	0.0749480i
$900$	−7.32048	+	16.0296i	−0.244016	+	0.534320i
$901$	−42.1938	+	12.3892i	−1.40568	+	0.412745i
$902$	11.1937	−	12.9182i	0.372709	−	0.430130i
$903$	−3.31783	−	0.974204i	−0.110411	−	0.0324195i
$904$	−2.68030	+	1.72252i	−0.0891455	+	0.0572903i
$905$	3.46209	+	7.58091i	0.115084	+	0.251998i
$906$	30.8101	+	35.5567i	1.02360	+	1.18129i
$907$	−42.1736	−	27.1033i	−1.40035	−	0.899952i	−0.400486	−	0.916303i	$-0.631159\pi$
$907$	−42.1736	−	27.1033i	−1.40035	−	0.899952i	−0.999866	+	0.0163511i	$0.994795\pi$
$908$	−0.377444	+	2.62518i	−0.0125259	+	0.0871197i
$909$	−4.02505	+	27.9949i	−0.133503	+	0.928531i
$910$	0.0546542	+	0.0351241i	0.00181177	+	0.00116435i
$911$	−4.43860	−	5.12241i	−0.147057	−	0.169713i	0.677442	−	0.735576i	$-0.263089\pi$
$911$	−4.43860	−	5.12241i	−0.147057	−	0.169713i	−0.824499	+	0.565863i	$0.808543\pi$
$912$	−8.32054	−	18.2194i	−0.275520	−	0.603306i
$913$	−48.6735	+	31.2805i	−1.61086	+	1.03523i
$914$	22.2573	+	6.53533i	0.736206	+	0.216169i
$915$	−7.40971	+	8.55126i	−0.244957	+	0.282696i
$916$	16.4648	−	4.83451i	0.544013	−	0.159737i
$917$	−4.16424	+	9.11842i	−0.137515	+	0.301117i
$918$	2.57817	+	17.9316i	0.0850922	+	0.591829i
$919$	40.8116			1.34625			0.673126	−	0.739528i	$-0.264951\pi$
$919$	40.8116			1.34625			0.673126	+	0.739528i	$0.264951\pi$
$920$	2.16951	+	2.41871i	0.0715268	+	0.0797425i
$921$	−86.3603			−2.84567
$922$	−1.33841	−	9.30886i	−0.0440783	−	0.306571i
$923$	0.223942	−	0.490365i	0.00737114	−	0.0161406i
$924$	−9.36856	+	2.75086i	−0.308203	+	0.0904966i
$925$	−19.3601	+	22.3428i	−0.636557	+	0.734626i
$926$	−16.8506	−	4.94778i	−0.553745	−	0.162594i
$927$	1.86011	−	1.19542i	0.0610939	−	0.0392627i
$928$	1.61847	+	3.54395i	0.0531288	+	0.116336i
$929$	22.2044	+	25.6252i	0.728501	+	0.840735i	0.992302	−	0.123842i	$-0.0395215\pi$
$929$	22.2044	+	25.6252i	0.728501	+	0.840735i	−0.263801	+	0.964577i	$0.584976\pi$
$930$	−0.871180	−	0.559873i	−0.0285671	−	0.0183590i
$931$	−1.08669	+	7.55807i	−0.0356147	+	0.247706i
$932$	2.81743	−	19.5956i	0.0922879	−	0.641876i
$933$	−70.4921	−	45.3025i	−2.30781	−	1.48314i
$934$	18.3141	+	21.1356i	0.599255	+	0.691578i
$935$	−8.21566	−	17.9898i	−0.268681	−	0.588329i
$936$	0.313057	−	0.201190i	0.0102326	−	0.00657608i
$937$	11.3895	+	3.34425i	0.372078	+	0.109252i	0.462425	−	0.886658i	$-0.346979\pi$
$937$	11.3895	+	3.34425i	0.372078	+	0.109252i	−0.0903469	+	0.995910i	$0.528798\pi$
$938$	−10.1967	+	11.7676i	−0.332935	+	0.384227i
$939$	16.7668	−	4.92318i	0.547165	−	0.160662i
$940$	−2.99601	+	6.56036i	−0.0977192	+	0.213975i
$941$	−2.86358	−	19.9166i	−0.0933500	−	0.649264i	−0.981748	−	0.190189i	$-0.939090\pi$
$941$	−2.86358	−	19.9166i	−0.0933500	−	0.649264i	0.888398	−	0.459075i	$-0.151819\pi$
$942$	3.71802			0.121140
$943$	21.0213	−	6.56582i	0.684547	−	0.213812i
$944$	−0.280209			−0.00912003
$945$	0.222730	+	1.54912i	0.00724539	+	0.0503928i
$946$	2.03843	−	4.46354i	0.0662751	−	0.145122i
$947$	−37.0508	+	10.8791i	−1.20399	+	0.353523i	−0.821377	−	0.570386i	$-0.806794\pi$
$947$	−37.0508	+	10.8791i	−1.20399	+	0.353523i	−0.382612	+	0.923909i	$0.624975\pi$
$948$	−26.0843	+	30.1029i	−0.847180	+	0.977698i
$949$	−0.394670	−	0.115886i	−0.0128115	−	0.00376180i
$950$	−29.1698	+	18.7463i	−0.946392	+	0.608209i
$951$	14.4698	+	31.6844i	0.469215	+	1.02744i
$952$	5.13556	+	5.92675i	0.166444	+	0.192087i
$953$	−4.39541	−	2.82476i	−0.142381	−	0.0915030i	0.467511	−	0.883987i	$-0.345151\pi$
$953$	−4.39541	−	2.82476i	−0.142381	−	0.0915030i	−0.609892	+	0.792484i	$0.708787\pi$
$954$	−3.09688	+	21.5392i	−0.100265	+	0.697359i
$955$	−0.703541	+	4.89323i	−0.0227660	+	0.158341i
$956$	20.7743	+	13.3508i	0.671889	+	0.431797i
$957$	24.9116	+	28.7495i	0.805278	+	0.929341i
$958$	12.6605	+	27.7227i	0.409043	+	0.895679i
$959$	−11.9517	+	7.68089i	−0.385940	+	0.248029i
$960$	−1.70515	−	0.500677i	−0.0550334	−	0.0161593i
$961$	20.0783	−	23.1716i	0.647688	−	0.747471i
$962$	0.599018	−	0.175888i	0.0193131	−	0.00567085i
$963$	9.51042	−	20.8249i	0.306469	−	0.671073i
$964$	−0.216450	−	1.50544i	−0.00697138	−	0.0484870i
$965$	−2.48978			−0.0801489
$966$	−12.1293	−	3.33677i	−0.390255	−	0.107359i
$967$	−44.4352			−1.42894			−0.714470	−	0.699666i	$-0.753332\pi$
$967$	−44.4352			−1.42894			−0.714470	+	0.699666i	$0.753332\pi$
$968$	−0.406425	−	2.82675i	−0.0130630	−	0.0908552i
$969$	−65.2514	+	142.881i	−2.09618	+	4.58999i
$970$	4.07780	−	1.19735i	0.130930	−	0.0384446i
$971$	18.0513	−	20.8323i	0.579294	−	0.668541i	−0.388159	−	0.921592i	$-0.626889\pi$
$971$	18.0513	−	20.8323i	0.579294	−	0.668541i	0.967453	+	0.253052i	$0.0814343\pi$
$972$	−20.6997	−	6.07797i	−0.663942	−	0.194951i
$973$	13.6543	−	8.77509i	0.437737	−	0.281317i
$974$	9.02413	+	19.7601i	0.289152	+	0.633154i
$975$	−0.748009	−	0.863248i	−0.0239555	−	0.0276461i
$976$	5.35623	+	3.44224i	0.171449	+	0.110183i
$977$	−0.156495	+	1.08845i	−0.00500672	+	0.0348225i	−0.992172	−	0.124882i	$-0.960145\pi$
$977$	−0.156495	+	1.08845i	−0.00500672	+	0.0348225i	0.987165	+	0.159704i	$0.0510540\pi$
$978$	2.71421	−	18.8778i	0.0867910	−	0.603644i
$979$	2.10480	+	1.35268i	0.0672698	+	0.0432317i
$980$	0.443664	+	0.512016i	0.0141723	+	0.0163557i
$981$	−7.62622	−	16.6991i	−0.243487	−	0.533161i
$982$	29.4103	−	18.9009i	0.938522	−	0.603151i
$983$	12.2746	+	3.60415i	0.391500	+	0.114955i	0.471557	−	0.881836i	$-0.343692\pi$
$983$	12.2746	+	3.60415i	0.391500	+	0.114955i	−0.0800573	+	0.996790i	$0.525510\pi$
$984$	−7.88810	+	9.10335i	−0.251463	+	0.290204i
$985$	7.06654	−	2.07492i	0.225159	−	0.0661125i
$986$	12.6924	−	27.7924i	0.404208	−	0.885091i
$987$	−3.97394	−	27.6394i	−0.126492	−	0.879771i
$988$	0.732226			0.0232952
$989$	5.25913	−	3.50865i	0.167231	−	0.111568i
$990$	−9.78649			−0.311035
$991$	4.59587	+	31.9650i	0.145993	+	1.01540i	0.922694	+	0.385532i	$0.125982\pi$
$991$	4.59587	+	31.9650i	0.145993	+	1.01540i	−0.776702	+	0.629868i	$0.783109\pi$
$992$	−0.242071	+	0.530062i	−0.00768576	+	0.0168295i
$993$	45.5058	−	13.3617i	1.44408	−	0.424021i
$994$	3.68139	−	4.24855i	0.116766	−	0.134756i
$995$	14.3929	+	4.22614i	0.456286	+	0.133978i
$996$	34.2998	−	22.0431i	1.08683	−	0.698463i
$997$	−2.41955	−	5.29807i	−0.0766278	−	0.167791i	0.867441	−	0.497540i	$-0.165763\pi$
$997$	−2.41955	−	5.29807i	−0.0766278	−	0.167791i	−0.944069	+	0.329749i	$0.893036\pi$
$998$	−25.3422	−	29.2465i	−0.802195	−	0.925782i
$999$	12.6519	+	8.13090i	0.400289	+	0.257250i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.d.141.1	✓	40
23.8	even	11	inner	322.2.i.d.169.1	yes	40
23.10	odd	22		7406.2.a.bv.1.2		20
23.13	even	11		7406.2.a.bu.1.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.d.141.1	✓	40	1.1	even	1	trivial
322.2.i.d.169.1	yes	40	23.8	even	11	inner
7406.2.a.bu.1.2		20	23.13	even	11
7406.2.a.bv.1.2		20	23.10	odd	22

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)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{2} +(-1.08968 + 2.38606i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(0.443664 - 0.512016i) q^{5} +(2.51685 + 0.739013i) q^{6} +(-0.841254 + 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-2.54129 - 2.93281i) q^{9} +O(q^{10})\)	\(q+(-0.142315 - 0.989821i) q^{2} +(-1.08968 + 2.38606i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(0.443664 - 0.512016i) q^{5} +(2.51685 + 0.739013i) q^{6} +(-0.841254 + 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-2.54129 - 2.93281i) q^{9} +(-0.569944 - 0.366281i) q^{10} +(-0.529744 + 3.68445i) q^{11} +(0.373306 - 2.59640i) q^{12} +(0.0806711 + 0.0518442i) q^{13} +(0.654861 + 0.755750i) q^{14} +(0.738248 + 1.61654i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-7.52455 - 2.20941i) q^{17} +(-2.54129 + 2.93281i) q^{18} +(-7.32649 + 2.15125i) q^{19} +(-0.281441 + 0.616270i) q^{20} +(-0.373306 - 2.59640i) q^{21} +3.72234 q^{22} +(4.07836 + 2.52329i) q^{23} -2.62310 q^{24} +(0.646252 + 4.49478i) q^{25} +(0.0398358 - 0.0872282i) q^{26} +(2.21648 - 0.650818i) q^{27} +(0.654861 - 0.755750i) q^{28} +(-3.73821 - 1.09764i) q^{29} +(1.49502 - 0.960791i) q^{30} +(-0.242071 - 0.530062i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(-8.21406 - 5.27886i) q^{33} +(-1.11606 + 7.76239i) q^{34} +(-0.0964174 + 0.670598i) q^{35} +(3.26462 + 2.09804i) q^{36} +(4.26340 + 4.92023i) q^{37} +(3.17202 + 6.94576i) q^{38} +(-0.211608 + 0.135992i) q^{39} +(0.650051 + 0.190872i) q^{40} +(3.00717 - 3.47046i) q^{41} +(-2.51685 + 0.739013i) q^{42} +(0.547621 - 1.19912i) q^{43} +(-0.529744 - 3.68445i) q^{44} -2.62912 q^{45} +(1.91719 - 4.39595i) q^{46} +10.6453 q^{47} +(0.373306 + 2.59640i) q^{48} +(0.415415 - 0.909632i) q^{49} +(4.35706 - 1.27935i) q^{50} +(13.4711 - 15.5465i) q^{51} +(-0.0920095 - 0.0270164i) q^{52} +(4.71732 - 3.03164i) q^{53} +(-0.959632 - 2.10130i) q^{54} +(1.65147 + 1.90590i) q^{55} +(-0.841254 - 0.540641i) q^{56} +(2.85049 - 19.8256i) q^{57} +(-0.554463 + 3.85637i) q^{58} +(-0.235727 - 0.151492i) q^{59} +(-1.16378 - 1.34307i) q^{60} +(2.64493 + 5.79159i) q^{61} +(-0.490216 + 0.315043i) q^{62} +(3.72346 + 1.09331i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(0.0623359 - 0.0183035i) q^{65} +(-4.05614 + 8.88171i) q^{66} +(2.21596 + 15.4123i) q^{67} +7.84221 q^{68} +(-10.4648 + 6.98163i) q^{69} +0.677494 q^{70} +(-0.800042 - 5.56441i) q^{71} +(1.61208 - 3.52997i) q^{72} +(-4.11569 + 1.20848i) q^{73} +(4.26340 - 4.92023i) q^{74} +(-11.4290 - 3.35586i) q^{75} +(6.42364 - 4.12822i) q^{76} +(-1.54632 - 3.38596i) q^{77} +(0.164723 + 0.190101i) q^{78} +(-12.7745 - 8.20965i) q^{79} +(0.0964174 - 0.670598i) q^{80} +(0.794468 - 5.52565i) q^{81} +(-3.86310 - 2.48266i) q^{82} +(10.1788 + 11.7470i) q^{83} +(1.08968 + 2.38606i) q^{84} +(-4.46962 + 2.87245i) q^{85} +(-1.26485 - 0.371394i) q^{86} +(6.69246 - 7.72351i) q^{87} +(-3.57156 + 1.04870i) q^{88} +(0.279223 - 0.611413i) q^{89} +(0.374163 + 2.60236i) q^{90} -0.0958939 q^{91} +(-4.62405 - 1.27207i) q^{92} +1.52854 q^{93} +(-1.51498 - 10.5369i) q^{94} +(-2.14903 + 4.70571i) q^{95} +(2.51685 - 0.739013i) q^{96} +(-4.10798 + 4.74086i) q^{97} +(-0.959493 - 0.281733i) q^{98} +(12.1520 - 7.80963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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