LMFDB - Embedded newform 966.2.q.b.547.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			547.1
Root			$0.654861 + 0.755750i$ of defining polynomial
Character	$\chi$	$=$	966.547
Dual form			966.2.q.b.883.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 - 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.273100 + 1.89945i) q^{5} +(0.841254 - 0.540641i) q^{6} +(-0.415415 - 0.909632i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.273100 + 1.89945i) q^{5} +(0.841254 - 0.540641i) q^{6} +(-0.415415 - 0.909632i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.797176 - 1.74557i) q^{10} +(0.992543 - 0.291437i) q^{11} +(-0.959493 + 0.281733i) q^{12} +(-0.929067 + 2.03437i) q^{13} +(0.142315 + 0.989821i) q^{14} +(-1.25667 - 1.45027i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-2.87958 + 1.85060i) q^{17} +(-0.142315 + 0.989821i) q^{18} +(0.629769 + 0.404728i) q^{19} +(-1.25667 + 1.45027i) q^{20} +(0.959493 + 0.281733i) q^{21} -1.03445 q^{22} +(2.94881 + 3.78213i) q^{23} +1.00000 q^{24} +(1.26413 + 0.371181i) q^{25} +(1.46458 - 1.69022i) q^{26} +(0.841254 + 0.540641i) q^{27} +(0.142315 - 0.989821i) q^{28} +(-7.27468 + 4.67515i) q^{29} +(0.797176 + 1.74557i) q^{30} +(-2.57574 - 2.97257i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(-0.429724 + 0.940965i) q^{33} +(3.28431 - 0.964362i) q^{34} +(1.84125 - 0.540641i) q^{35} +(0.415415 - 0.909632i) q^{36} +(-0.937128 - 6.51787i) q^{37} +(-0.490234 - 0.565760i) q^{38} +(-0.929067 - 2.03437i) q^{39} +(1.61435 - 1.03748i) q^{40} +(-0.732593 + 5.09530i) q^{41} +(-0.841254 - 0.540641i) q^{42} +(0.387886 - 0.447644i) q^{43} +(0.992543 + 0.291437i) q^{44} +1.91899 q^{45} +(-1.76381 - 4.45971i) q^{46} -12.5451 q^{47} +(-0.959493 - 0.281733i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(-1.10835 - 0.712290i) q^{50} +(0.487139 - 3.38813i) q^{51} +(-1.88145 + 1.20913i) q^{52} +(-5.36381 - 11.7451i) q^{53} +(-0.654861 - 0.755750i) q^{54} +(0.282507 + 1.96488i) q^{55} +(-0.415415 + 0.909632i) q^{56} +(-0.718284 + 0.210907i) q^{57} +(8.29715 - 2.43626i) q^{58} +(-1.96392 + 4.30040i) q^{59} +(-0.273100 - 1.89945i) q^{60} +(-1.59040 - 1.83541i) q^{61} +(1.63394 + 3.57783i) q^{62} +(-0.841254 + 0.540641i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-3.61047 - 2.32031i) q^{65} +(0.677418 - 0.781782i) q^{66} +(-7.94784 - 2.33370i) q^{67} -3.42297 q^{68} +(-4.78940 - 0.248210i) q^{69} -1.91899 q^{70} +(10.1604 + 2.98335i) q^{71} +(-0.654861 + 0.755750i) q^{72} +(-10.9057 - 7.00866i) q^{73} +(-0.937128 + 6.51787i) q^{74} +(-1.10835 + 0.712290i) q^{75} +(0.310983 + 0.680958i) q^{76} +(-0.677418 - 0.781782i) q^{77} +(0.318284 + 2.21371i) q^{78} +(1.02242 - 2.23879i) q^{79} +(-1.84125 + 0.540641i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(2.13843 - 4.68251i) q^{82} +(2.02695 + 14.0978i) q^{83} +(0.654861 + 0.755750i) q^{84} +(-2.72871 - 5.97504i) q^{85} +(-0.498290 + 0.320231i) q^{86} +(1.23066 - 8.55941i) q^{87} +(-0.870231 - 0.559264i) q^{88} +(-7.63502 + 8.81128i) q^{89} +(-1.84125 - 0.540641i) q^{90} +2.23648 q^{91} +(0.435919 + 4.77598i) q^{92} +3.93327 q^{93} +(12.0370 + 3.53437i) q^{94} +(-0.940752 + 1.08569i) q^{95} +(0.841254 + 0.540641i) q^{96} +(0.221983 - 1.54392i) q^{97} +(0.841254 - 0.540641i) q^{98} +(-0.429724 - 0.940965i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{3} - q^{4} + 2 q^{5} - q^{6} + q^{7} - q^{8} - q^{9}+O(q^{10}) $ 10 * q - q^2 - q^3 - q^4 + 2 * q^5 - q^6 + q^7 - q^8 - q^9	\( 10 q - q^{2} - q^{3} - q^{4} + 2 q^{5} - q^{6} + q^{7} - q^{8} - q^{9} + 2 q^{10} + 7 q^{11} - q^{12} - 2 q^{13} + q^{14} + 2 q^{15} - q^{16} - 6 q^{17} - q^{18} + 11 q^{19} + 2 q^{20} + q^{21} + 18 q^{22} + 21 q^{23} + 10 q^{24} + q^{25} - 2 q^{26} - q^{27} + q^{28} - 20 q^{29} + 2 q^{30} + 18 q^{31} - q^{32} - 15 q^{33} + 5 q^{34} + 9 q^{35} - q^{36} + 5 q^{37} - 22 q^{38} - 2 q^{39} + 2 q^{40} + 6 q^{41} + q^{42} - 12 q^{43} + 7 q^{44} + 2 q^{45} + 21 q^{46} - 32 q^{47} - q^{48} - q^{49} + 12 q^{50} - 17 q^{51} + 9 q^{52} - 39 q^{53} - q^{54} + 8 q^{55} + q^{56} + 22 q^{57} + 13 q^{58} + 15 q^{59} + 2 q^{60} + 21 q^{61} - 4 q^{62} + q^{63} - q^{64} - 7 q^{65} - 4 q^{66} - 26 q^{67} - 6 q^{68} - 12 q^{69} - 2 q^{70} + 27 q^{71} - q^{72} - 2 q^{73} + 5 q^{74} + 12 q^{75} + 4 q^{77} - 2 q^{78} + 47 q^{79} - 9 q^{80} - q^{81} + 6 q^{82} + 5 q^{83} + q^{84} + q^{85} - 12 q^{86} - 9 q^{87} - 4 q^{88} + 5 q^{89} - 9 q^{90} + 24 q^{91} + 10 q^{92} - 26 q^{93} + 23 q^{94} - 11 q^{95} - q^{96} + 2 q^{97} - q^{98} - 15 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^3 - q^4 + 2 * q^5 - q^6 + q^7 - q^8 - q^9 + 2 * q^10 + 7 * q^11 - q^12 - 2 * q^13 + q^14 + 2 * q^15 - q^16 - 6 * q^17 - q^18 + 11 * q^19 + 2 * q^20 + q^21 + 18 * q^22 + 21 * q^23 + 10 * q^24 + q^25 - 2 * q^26 - q^27 + q^28 - 20 * q^29 + 2 * q^30 + 18 * q^31 - q^32 - 15 * q^33 + 5 * q^34 + 9 * q^35 - q^36 + 5 * q^37 - 22 * q^38 - 2 * q^39 + 2 * q^40 + 6 * q^41 + q^42 - 12 * q^43 + 7 * q^44 + 2 * q^45 + 21 * q^46 - 32 * q^47 - q^48 - q^49 + 12 * q^50 - 17 * q^51 + 9 * q^52 - 39 * q^53 - q^54 + 8 * q^55 + q^56 + 22 * q^57 + 13 * q^58 + 15 * q^59 + 2 * q^60 + 21 * q^61 - 4 * q^62 + q^63 - q^64 - 7 * q^65 - 4 * q^66 - 26 * q^67 - 6 * q^68 - 12 * q^69 - 2 * q^70 + 27 * q^71 - q^72 - 2 * q^73 + 5 * q^74 + 12 * q^75 + 4 * q^77 - 2 * q^78 + 47 * q^79 - 9 * q^80 - q^81 + 6 * q^82 + 5 * q^83 + q^84 + q^85 - 12 * q^86 - 9 * q^87 - 4 * q^88 + 5 * q^89 - 9 * q^90 + 24 * q^91 + 10 * q^92 - 26 * q^93 + 23 * q^94 - 11 * q^95 - q^96 + 2 * q^97 - q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

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 $

$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$4$	0.841254	+	0.540641i	0.420627	+	0.270320i
$5$	−0.273100	+	1.89945i	−0.122134	+	0.849461i	0.832997	+	0.553278i	$0.186623\pi$
$5$	−0.273100	+	1.89945i	−0.122134	+	0.849461i	−0.955131	+	0.296184i	$0.904286\pi$
$6$	0.841254	−	0.540641i	0.343440	−	0.220716i
$7$	−0.415415	−	0.909632i	−0.157012	−	0.343809i
$7$	−0.415415	−	0.909632i	−0.157012	−	0.343809i
$8$	−0.654861	−	0.755750i	−0.231528	−	0.267198i
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$	0.797176	−	1.74557i	0.252089	−	0.551998i
$11$	0.992543	−	0.291437i	0.299263	−	0.0878716i	−0.128654	−	0.991690i	$-0.541066\pi$
$11$	0.992543	−	0.291437i	0.299263	−	0.0878716i	0.427917	+	0.903818i	$0.359248\pi$
$12$	−0.959493	+	0.281733i	−0.276982	+	0.0813292i
$13$	−0.929067	+	2.03437i	−0.257677	+	0.564233i	−0.993616	−	0.112814i	$-0.964014\pi$
$13$	−0.929067	+	2.03437i	−0.257677	+	0.564233i	0.735939	+	0.677047i	$0.236741\pi$
$14$	0.142315	+	0.989821i	0.0380352	+	0.264541i
$15$	−1.25667	−	1.45027i	−0.324470	−	0.374459i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	−2.87958	+	1.85060i	−0.698402	+	0.448836i	−0.841064	−	0.540936i	$-0.818070\pi$
$17$	−2.87958	+	1.85060i	−0.698402	+	0.448836i	0.142662	+	0.989771i	$0.454434\pi$
$18$	−0.142315	+	0.989821i	−0.0335439	+	0.233303i
$19$	0.629769	+	0.404728i	0.144479	+	0.0928510i	0.610883	−	0.791721i	$-0.290814\pi$
$19$	0.629769	+	0.404728i	0.144479	+	0.0928510i	−0.466404	+	0.884572i	$0.654451\pi$
$20$	−1.25667	+	1.45027i	−0.281000	+	0.324291i
$21$	0.959493	+	0.281733i	0.209379	+	0.0614791i
$22$	−1.03445			−0.220545
$23$	2.94881	+	3.78213i	0.614869	+	0.788629i
$23$	2.94881	+	3.78213i	0.614869	+	0.788629i
$24$	1.00000			0.204124
$25$	1.26413	+	0.371181i	0.252825	+	0.0742361i
$26$	1.46458	−	1.69022i	0.287228	−	0.331479i
$27$	0.841254	+	0.540641i	0.161899	+	0.104046i
$28$	0.142315	−	0.989821i	0.0268950	−	0.187059i
$29$	−7.27468	+	4.67515i	−1.35087	+	0.868154i	−0.997725	−	0.0674125i	$-0.978526\pi$
$29$	−7.27468	+	4.67515i	−1.35087	+	0.868154i	−0.353149	+	0.935567i	$0.614889\pi$
$30$	0.797176	+	1.74557i	0.145544	+	0.318696i
$31$	−2.57574	−	2.97257i	−0.462617	−	0.533889i	0.475726	−	0.879593i	$-0.342185\pi$
$31$	−2.57574	−	2.97257i	−0.462617	−	0.533889i	−0.938343	+	0.345705i	$0.887640\pi$
$32$	−0.142315	−	0.989821i	−0.0251579	−	0.174977i
$33$	−0.429724	+	0.940965i	−0.0748054	+	0.163801i
$34$	3.28431	−	0.964362i	0.563255	−	0.165387i
$35$	1.84125	−	0.540641i	0.311229	−	0.0913850i
$36$	0.415415	−	0.909632i	0.0692358	−	0.151605i
$37$	−0.937128	−	6.51787i	−0.154063	−	1.07153i	−0.909319	−	0.416100i	$-0.863396\pi$
$37$	−0.937128	−	6.51787i	−0.154063	−	1.07153i	0.755256	−	0.655430i	$-0.227513\pi$
$38$	−0.490234	−	0.565760i	−0.0795264	−	0.0917784i
$39$	−0.929067	−	2.03437i	−0.148770	−	0.325760i
$40$	1.61435	−	1.03748i	0.255252	−	0.164040i
$41$	−0.732593	+	5.09530i	−0.114412	+	0.795752i	0.849128	+	0.528187i	$0.177128\pi$
$41$	−0.732593	+	5.09530i	−0.114412	+	0.795752i	−0.963540	+	0.267565i	$0.913781\pi$
$42$	−0.841254	−	0.540641i	−0.129808	−	0.0834227i
$43$	0.387886	−	0.447644i	0.0591521	−	0.0682651i	−0.725402	−	0.688325i	$-0.758346\pi$
$43$	0.387886	−	0.447644i	0.0591521	−	0.0682651i	0.784554	+	0.620060i	$0.212892\pi$
$44$	0.992543	+	0.291437i	0.149632	+	0.0439358i
$45$	1.91899			0.286066
$46$	−1.76381	−	4.45971i	−0.260060	−	0.657548i
$47$	−12.5451			−1.82989			−0.914947	−	0.403574i	$-0.867768\pi$
$47$	−12.5451			−1.82989			−0.914947	+	0.403574i	$0.867768\pi$
$48$	−0.959493	−	0.281733i	−0.138491	−	0.0406646i
$49$	−0.654861	+	0.755750i	−0.0935515	+	0.107964i
$50$	−1.10835	−	0.712290i	−0.156744	−	0.100733i
$51$	0.487139	−	3.38813i	0.0682131	−	0.474433i
$52$	−1.88145	+	1.20913i	−0.260910	+	0.167676i
$53$	−5.36381	−	11.7451i	−0.736776	−	1.61331i	−0.788786	−	0.614668i	$-0.789290\pi$
$53$	−5.36381	−	11.7451i	−0.736776	−	1.61331i	0.0520099	−	0.998647i	$-0.483437\pi$
$54$	−0.654861	−	0.755750i	−0.0891153	−	0.102844i
$55$	0.282507	+	1.96488i	0.0380933	+	0.264945i
$56$	−0.415415	+	0.909632i	−0.0555122	+	0.121555i
$57$	−0.718284	+	0.210907i	−0.0951390	+	0.0279353i
$58$	8.29715	−	2.43626i	1.08947	−	0.319897i
$59$	−1.96392	+	4.30040i	−0.255681	+	0.559864i	−0.993328	−	0.115323i	$-0.963210\pi$
$59$	−1.96392	+	4.30040i	−0.255681	+	0.559864i	0.737647	+	0.675187i	$0.235937\pi$
$60$	−0.273100	−	1.89945i	−0.0352571	−	0.245218i
$61$	−1.59040	−	1.83541i	−0.203629	−	0.235001i	0.644745	−	0.764398i	$-0.276964\pi$
$61$	−1.59040	−	1.83541i	−0.203629	−	0.235001i	−0.848374	+	0.529397i	$0.822418\pi$
$62$	1.63394	+	3.57783i	0.207510	+	0.454385i
$63$	−0.841254	+	0.540641i	−0.105988	+	0.0681143i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	−3.61047	−	2.32031i	−0.447823	−	0.287799i
$66$	0.677418	−	0.781782i	0.0833844	−	0.0962307i
$67$	−7.94784	−	2.33370i	−0.970983	−	0.285106i	−0.242485	−	0.970155i	$-0.577963\pi$
$67$	−7.94784	−	2.33370i	−0.970983	−	0.285106i	−0.728497	+	0.685049i	$0.759781\pi$
$68$	−3.42297			−0.415096
$69$	−4.78940	−	0.248210i	−0.576576	−	0.0298810i
$70$	−1.91899			−0.229363
$71$	10.1604	+	2.98335i	1.20581	+	0.354058i	0.822073	−	0.569383i	$-0.192818\pi$
$71$	10.1604	+	2.98335i	1.20581	+	0.354058i	0.383740	+	0.923441i	$0.374636\pi$
$72$	−0.654861	+	0.755750i	−0.0771761	+	0.0890659i
$73$	−10.9057	−	7.00866i	−1.27641	−	0.820301i	−0.285973	−	0.958238i	$-0.592317\pi$
$73$	−10.9057	−	7.00866i	−1.27641	−	0.820301i	−0.990441	+	0.137937i	$0.955953\pi$
$74$	−0.937128	+	6.51787i	−0.108939	+	0.757687i
$75$	−1.10835	+	0.712290i	−0.127981	+	0.0822482i
$76$	0.310983	+	0.680958i	0.0356722	+	0.0781112i
$77$	−0.677418	−	0.781782i	−0.0771989	−	0.0890923i
$78$	0.318284	+	2.21371i	0.0360386	+	0.250654i
$79$	1.02242	−	2.23879i	0.115032	−	0.251884i	−0.843355	−	0.537356i	$-0.819423\pi$
$79$	1.02242	−	2.23879i	0.115032	−	0.251884i	0.958387	+	0.285472i	$0.0921504\pi$
$80$	−1.84125	+	0.540641i	−0.205858	+	0.0604455i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	2.13843	−	4.68251i	0.236150	−	0.517096i
$83$	2.02695	+	14.0978i	0.222487	+	1.54743i	0.728585	+	0.684955i	$0.240178\pi$
$83$	2.02695	+	14.0978i	0.222487	+	1.54743i	−0.506098	+	0.862476i	$0.668913\pi$
$84$	0.654861	+	0.755750i	0.0714512	+	0.0824590i
$85$	−2.72871	−	5.97504i	−0.295970	−	0.648084i
$86$	−0.498290	+	0.320231i	−0.0537320	+	0.0345314i
$87$	1.23066	−	8.55941i	0.131940	−	0.917665i
$88$	−0.870231	−	0.559264i	−0.0927669	−	0.0596177i
$89$	−7.63502	+	8.81128i	−0.809310	+	0.933994i	−0.998853	−	0.0478784i	$-0.984754\pi$
$89$	−7.63502	+	8.81128i	−0.809310	+	0.933994i	0.189543	+	0.981872i	$0.439299\pi$
$90$	−1.84125	−	0.540641i	−0.194085	−	0.0569885i
$91$	2.23648			0.234447
$92$	0.435919	+	4.77598i	0.0454477	+	0.497930i
$93$	3.93327			0.407861
$94$	12.0370	+	3.53437i	1.24152	+	0.364542i
$95$	−0.940752	+	1.08569i	−0.0965191	+	0.111389i
$96$	0.841254	+	0.540641i	0.0858601	+	0.0551789i
$97$	0.221983	−	1.54392i	0.0225389	−	0.156762i	−0.975444	−	0.220249i	$-0.929313\pi$
$97$	0.221983	−	1.54392i	0.0225389	−	0.156762i	0.997983	+	0.0634872i	$0.0202222\pi$
$98$	0.841254	−	0.540641i	0.0849794	−	0.0546130i
$99$	−0.429724	−	0.940965i	−0.0431889	−	0.0945705i
$100$	0.862774	+	0.995695i	0.0862774	+	0.0995695i
$101$	−0.267542	−	1.86080i	−0.0266215	−	0.185156i	0.972172	−	0.234269i	$-0.0752697\pi$
$101$	−0.267542	−	1.86080i	−0.0266215	−	0.185156i	−0.998793	+	0.0491128i	$0.984361\pi$
$102$	−1.42195	+	3.11364i	−0.140794	+	0.308297i
$103$	−4.91020	+	1.44176i	−0.483816	+	0.142061i	−0.514540	−	0.857467i	$-0.672037\pi$
$103$	−4.91020	+	1.44176i	−0.483816	+	0.142061i	0.0307233	+	0.999528i	$0.490219\pi$
$104$	2.14589	−	0.630089i	0.210421	−	0.0617853i
$105$	−0.797176	+	1.74557i	−0.0777964	+	0.170350i
$106$	1.83756	+	12.7805i	0.178480	+	1.24135i
$107$	8.93334	+	10.3096i	0.863619	+	0.996669i	0.999982	+	0.00601002i	$0.00191306\pi$
$107$	8.93334	+	10.3096i	0.863619	+	0.996669i	−0.136363	+	0.990659i	$0.543541\pi$
$108$	0.415415	+	0.909632i	0.0399733	+	0.0875294i
$109$	1.09782	−	0.705529i	0.105153	−	0.0675774i	−0.487008	−	0.873398i	$-0.661912\pi$
$109$	1.09782	−	0.705529i	0.105153	−	0.0675774i	0.592160	+	0.805820i	$0.298275\pi$
$110$	0.282507	−	1.96488i	0.0269360	−	0.187344i
$111$	5.53956	+	3.56006i	0.525792	+	0.337906i
$112$	0.654861	−	0.755750i	0.0618785	−	0.0714116i
$113$	−13.4666	−	3.95415i	−1.26683	−	0.371975i	−0.421799	−	0.906689i	$-0.638601\pi$
$113$	−13.4666	−	3.95415i	−1.26683	−	0.371975i	−0.845033	+	0.534714i	$0.820419\pi$
$114$	0.748608			0.0701135
$115$	−7.98931	+	4.56822i	−0.745007	+	0.425989i
$116$	−8.64743			−0.802894
$117$	2.14589	+	0.630089i	0.198387	+	0.0582517i
$118$	3.09593	−	3.57290i	0.285004	−	0.328912i
$119$	2.87958	+	1.85060i	0.263971	+	0.169644i
$120$	−0.273100	+	1.89945i	−0.0249305	+	0.173396i
$121$	−8.35358	+	5.36852i	−0.759417	+	0.488047i
$122$	1.00888	+	2.20913i	0.0913395	+	0.200006i
$123$	−3.37102	−	3.89037i	−0.303955	−	0.350783i
$124$	−0.559763	−	3.89323i	−0.0502682	−	0.349623i
$125$	−5.03615	+	11.0276i	−0.450447	+	0.986341i
$126$	0.959493	−	0.281733i	0.0854784	−	0.0250987i
$127$	−14.3999	+	4.22820i	−1.27779	+	0.375192i	−0.849086	−	0.528255i	$-0.822847\pi$
$127$	−14.3999	+	4.22820i	−1.27779	+	0.375192i	−0.428700	+	0.903447i	$0.641028\pi$
$128$	0.415415	−	0.909632i	0.0367178	−	0.0804009i
$129$	0.0842957	+	0.586289i	0.00742182	+	0.0516199i
$130$	2.81051	+	3.24350i	0.246498	+	0.284474i
$131$	−5.83903	−	12.7857i	−0.510159	−	1.11709i	−0.973033	−	0.230668i	$-0.925909\pi$
$131$	−5.83903	−	12.7857i	−0.510159	−	1.11709i	0.462874	−	0.886424i	$-0.346818\pi$
$132$	−0.870231	+	0.559264i	−0.0757439	+	0.0486776i
$133$	0.106538	−	0.740988i	0.00923802	−	0.0642518i
$134$	6.96841	+	4.47833i	0.601979	+	0.386869i
$135$	−1.25667	+	1.45027i	−0.108157	+	0.124820i
$136$	3.28431	+	0.964362i	0.281628	+	0.0826933i
$137$	−5.21446			−0.445502			−0.222751	−	0.974875i	$-0.571504\pi$
$137$	−5.21446			−0.445502			−0.222751	+	0.974875i	$0.571504\pi$
$138$	4.52547	+	1.58749i	0.385234	+	0.135136i
$139$	14.1861			1.20325			0.601626	−	0.798778i	$-0.294520\pi$
$139$	14.1861			1.20325			0.601626	+	0.798778i	$0.294520\pi$
$140$	1.84125	+	0.540641i	0.155614	+	0.0456925i
$141$	8.21531	−	9.48097i	0.691854	−	0.798442i
$142$	−8.90828	−	5.72501i	−0.747567	−	0.480432i
$143$	−0.329248	+	2.28997i	−0.0275331	+	0.191497i
$144$	0.841254	−	0.540641i	0.0701045	−	0.0450534i
$145$	−6.89352	−	15.0947i	−0.572476	−	1.25355i
$146$	8.48936	+	9.79724i	0.702584	+	0.810826i
$147$	−0.142315	−	0.989821i	−0.0117379	−	0.0816391i
$148$	2.73546	−	5.98983i	0.224854	−	0.492361i
$149$	10.2397	−	3.00665i	0.838871	−	0.246315i	0.166047	−	0.986118i	$-0.446899\pi$
$149$	10.2397	−	3.00665i	0.838871	−	0.246315i	0.672824	+	0.739803i	$0.265081\pi$
$150$	1.26413	−	0.371181i	0.103215	−	0.0303068i
$151$	−0.739908	+	1.62017i	−0.0602129	+	0.131848i	−0.937346	−	0.348399i	$-0.886726\pi$
$151$	−0.739908	+	1.62017i	−0.0602129	+	0.131848i	0.877134	+	0.480247i	$0.159453\pi$
$152$	−0.106538	−	0.740988i	−0.00864137	−	0.0601021i
$153$	2.24157	+	2.58691i	0.181220	+	0.209139i
$154$	0.429724	+	0.940965i	0.0346282	+	0.0758251i
$155$	6.34969	−	4.08070i	0.510019	−	0.327769i
$156$	0.318284	−	2.21371i	0.0254831	−	0.177239i
$157$	10.4917	+	6.74261i	0.837330	+	0.538119i	0.887599	−	0.460617i	$-0.152372\pi$
$157$	10.4917	+	6.74261i	0.837330	+	0.538119i	−0.0502696	+	0.998736i	$0.516008\pi$
$158$	−1.61175	+	1.86006i	−0.128224	+	0.147978i
$159$	12.3889	+	3.63771i	0.982504	+	0.288489i
$160$	1.91899			0.151709
$161$	2.21537	−	4.25348i	0.174596	−	0.335222i
$162$	1.00000			0.0785674
$163$	6.14144	+	1.80329i	0.481035	+	0.141245i	0.513255	−	0.858236i	$-0.328440\pi$
$163$	6.14144	+	1.80329i	0.481035	+	0.141245i	−0.0322199	+	0.999481i	$0.510258\pi$
$164$	−3.37102	+	3.89037i	−0.263233	+	0.303787i
$165$	−1.66996	−	1.07322i	−0.130006	−	0.0835500i
$166$	2.02695	−	14.0978i	0.157322	−	1.09420i
$167$	−12.1694	+	7.82080i	−0.941697	+	0.605192i	−0.918875	−	0.394548i	$-0.870901\pi$
$167$	−12.1694	+	7.82080i	−0.941697	+	0.605192i	−0.0228212	+	0.999740i	$0.507265\pi$
$168$	−0.415415	−	0.909632i	−0.0320500	−	0.0701796i
$169$	5.23768	+	6.04461i	0.402899	+	0.464970i
$170$	0.934813	+	6.50177i	0.0716969	+	0.498663i
$171$	0.310983	−	0.680958i	0.0237815	−	0.0520741i
$172$	0.568325	−	0.166875i	0.0433344	−	0.0127241i
$173$	8.85124	−	2.59896i	0.672947	−	0.197595i	0.0726321	−	0.997359i	$-0.476860\pi$
$173$	8.85124	−	2.59896i	0.672947	−	0.197595i	0.600315	+	0.799764i	$0.295042\pi$
$174$	−3.59227	+	7.86598i	−0.272330	+	0.596318i
$175$	−0.187499	−	1.30408i	−0.0141736	−	0.0985794i
$176$	0.677418	+	0.781782i	0.0510623	+	0.0589290i
$177$	−1.96392	−	4.30040i	−0.147618	−	0.323238i
$178$	9.80817	−	6.30333i	0.735154	−	0.472455i
$179$	2.67688	−	18.6181i	0.200079	−	1.39158i	−0.603964	−	0.797011i	$-0.706413\pi$
$179$	2.67688	−	18.6181i	0.200079	−	1.39158i	0.804044	−	0.594570i	$-0.202678\pi$
$180$	1.61435	+	1.03748i	0.120327	+	0.0773294i
$181$	4.59954	−	5.30815i	0.341881	−	0.394552i	−0.558607	−	0.829432i	$-0.688664\pi$
$181$	4.59954	−	5.30815i	0.341881	−	0.394552i	0.900488	+	0.434881i	$0.143209\pi$
$182$	−2.14589	−	0.630089i	−0.159064	−	0.0467053i
$183$	2.42860			0.179527
$184$	0.927287	−	4.70533i	0.0683605	−	0.346882i
$185$	12.6363			0.929040
$186$	−3.77394	−	1.10813i	−0.276719	−	0.0812520i
$187$	−2.31878	+	2.67602i	−0.169566	+	0.195690i
$188$	−10.5536	−	6.78240i	−0.769702	−	0.494658i
$189$	0.142315	−	0.989821i	0.0103519	−	0.0719989i
$190$	1.20852	−	0.776667i	0.0876751	−	0.0563454i
$191$	0.987156	+	2.16157i	0.0714281	+	0.156406i	0.941978	−	0.335674i	$-0.108964\pi$
$191$	0.987156	+	2.16157i	0.0714281	+	0.156406i	−0.870550	+	0.492080i	$0.836237\pi$
$192$	−0.654861	−	0.755750i	−0.0472605	−	0.0545415i
$193$	0.0419235	+	0.291584i	0.00301772	+	0.0209887i	0.991275	−	0.131812i	$-0.0420797\pi$
$193$	0.0419235	+	0.291584i	0.00301772	+	0.0209887i	−0.988257	+	0.152801i	$0.951171\pi$
$194$	−0.647964	+	1.41884i	−0.0465211	+	0.101867i
$195$	4.11792	−	1.20913i	0.294891	−	0.0865877i
$196$	−0.959493	+	0.281733i	−0.0685352	+	0.0201238i
$197$	10.2057	−	22.3473i	0.727125	−	1.59218i	−0.0765158	−	0.997068i	$-0.524380\pi$
$197$	10.2057	−	22.3473i	0.727125	−	1.59218i	0.803641	−	0.595114i	$-0.202893\pi$
$198$	0.147217	+	1.02392i	0.0104623	+	0.0727666i
$199$	7.61745	+	8.79100i	0.539987	+	0.623178i	0.958521	−	0.285023i	$-0.0920014\pi$
$199$	7.61745	+	8.79100i	0.539987	+	0.623178i	−0.418534	+	0.908201i	$0.637456\pi$
$200$	−0.547306	−	1.19843i	−0.0387004	−	0.0847421i
$201$	6.96841	−	4.47833i	0.491514	−	0.315877i
$202$	−0.267542	+	1.86080i	−0.0188242	+	0.130925i
$203$	7.27468	+	4.67515i	0.510583	+	0.328132i
$204$	2.24157	−	2.58691i	0.156941	−	0.181120i
$205$	−9.47821	−	2.78305i	−0.661987	−	0.194377i
$206$	5.11749			0.356553
$207$	3.32398	−	3.45705i	0.231032	−	0.240281i
$208$	−2.23648			−0.155072
$209$	0.743026	+	0.218172i	0.0513962	+	0.0150913i
$210$	1.25667	−	1.45027i	0.0867184	−	0.100078i
$211$	18.4276	+	11.8427i	1.26861	+	0.815285i	0.989438	−	0.144957i	$-0.0463044\pi$
$211$	18.4276	+	11.8427i	1.26861	+	0.815285i	0.279170	+	0.960242i	$0.409941\pi$
$212$	1.83756	−	12.7805i	0.126204	−	0.877769i
$213$	−8.90828	+	5.72501i	−0.610386	+	0.392271i
$214$	−5.66692	−	12.4088i	−0.387383	−	0.848250i
$215$	0.744348	+	0.859023i	0.0507641	+	0.0585849i
$216$	−0.142315	−	0.989821i	−0.00968330	−	0.0673488i
$217$	−1.63394	+	3.57783i	−0.110919	+	0.242879i
$218$	−1.25213	+	0.367657i	−0.0848046	+	0.0249009i
$219$	12.4385	−	3.65227i	0.840515	−	0.246798i
$220$	−0.824635	+	1.80570i	−0.0555969	+	0.121740i
$221$	−1.08948	−	7.57748i	−0.0732861	−	0.509716i
$222$	−4.31219	−	4.97653i	−0.289415	−	0.334003i
$223$	9.47373	+	20.7446i	0.634408	+	1.38916i	0.904562	+	0.426343i	$0.140198\pi$
$223$	9.47373	+	20.7446i	0.634408	+	1.38916i	−0.270154	+	0.962817i	$0.587075\pi$
$224$	−0.841254	+	0.540641i	−0.0562086	+	0.0361231i
$225$	0.187499	−	1.30408i	0.0124999	−	0.0869389i
$226$	11.8071	+	7.58796i	0.785397	+	0.504744i
$227$	−15.7906	+	18.2233i	−1.04806	+	1.20953i	−0.0707973	+	0.997491i	$0.522554\pi$
$227$	−15.7906	+	18.2233i	−1.04806	+	1.20953i	−0.977262	+	0.212034i	$0.931991\pi$
$228$	−0.718284	−	0.210907i	−0.0475695	−	0.0139677i
$229$	12.8352			0.848173			0.424087	−	0.905622i	$-0.360595\pi$
$229$	12.8352			0.848173			0.424087	+	0.905622i	$0.360595\pi$
$230$	8.95270	−	2.13233i	0.590324	−	0.140602i
$231$	1.03445			0.0680615
$232$	8.29715	+	2.43626i	0.544735	+	0.159949i
$233$	−7.44884	+	8.59642i	−0.487990	+	0.563170i	−0.945327	−	0.326123i	$-0.894258\pi$
$233$	−7.44884	+	8.59642i	−0.487990	+	0.563170i	0.457338	+	0.889293i	$0.348803\pi$
$234$	−1.88145	−	1.20913i	−0.122994	−	0.0790434i
$235$	3.42607	−	23.8289i	0.223492	−	1.55442i
$236$	−3.97713	+	2.55595i	−0.258889	+	0.166378i
$237$	1.02242	+	2.23879i	0.0664135	+	0.145425i
$238$	−2.24157	−	2.58691i	−0.145299	−	0.167684i
$239$	1.64605	+	11.4485i	0.106474	+	0.740543i	0.971194	+	0.238289i	$0.0765865\pi$
$239$	1.64605	+	11.4485i	0.106474	+	0.740543i	−0.864720	+	0.502254i	$0.832504\pi$
$240$	0.797176	−	1.74557i	0.0514575	−	0.112676i
$241$	2.57994	−	0.757539i	0.166189	−	0.0487974i	−0.197580	−	0.980287i	$-0.563308\pi$
$241$	2.57994	−	0.757539i	0.166189	−	0.0487974i	0.363768	+	0.931489i	$0.381490\pi$
$242$	9.52769	−	2.79758i	0.612463	−	0.179835i
$243$	0.415415	−	0.909632i	0.0266489	−	0.0583529i
$244$	−0.345626	−	2.40388i	−0.0221264	−	0.153893i
$245$	−1.25667	−	1.45027i	−0.0802856	−	0.0926545i
$246$	2.13843	+	4.68251i	0.136341	+	0.298546i
$247$	−1.40846	+	0.905165i	−0.0896185	+	0.0575943i
$248$	−0.559763	+	3.89323i	−0.0355450	+	0.247221i
$249$	−11.9818	−	7.70020i	−0.759313	−	0.487981i
$250$	7.93899	−	9.16209i	0.502106	−	0.579461i
$251$	18.4668	+	5.42235i	1.16562	+	0.342256i	0.806613	−	0.591080i	$-0.201298\pi$
$251$	18.4668	+	5.42235i	1.16562	+	0.342256i	0.359004	+	0.933336i	$0.383116\pi$
$252$	−1.00000			−0.0629941
$253$	4.02907	+	2.89454i	0.253306	+	0.181978i
$254$	15.0078			0.941676
$255$	6.30255	+	1.85060i	0.394681	+	0.115889i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	−9.11343	−	5.85685i	−0.568480	−	0.365340i	0.224606	−	0.974450i	$-0.427891\pi$
$257$	−9.11343	−	5.85685i	−0.568480	−	0.365340i	−0.793086	+	0.609110i	$0.791527\pi$
$258$	0.0842957	−	0.586289i	0.00524802	−	0.0365008i
$259$	−5.53956	+	3.56006i	−0.344212	+	0.221211i
$260$	−1.78287	−	3.90393i	−0.110569	−	0.242112i
$261$	5.66286	+	6.53529i	0.350522	+	0.404524i
$262$	2.00036	+	13.9128i	0.123583	+	0.859538i
$263$	3.06579	−	6.71315i	0.189045	−	0.413951i	−0.791249	−	0.611494i	$-0.790569\pi$
$263$	3.06579	−	6.71315i	0.189045	−	0.413951i	0.980294	+	0.197543i	$0.0632962\pi$
$264$	0.992543	−	0.291437i	0.0610868	−	0.0179367i
$265$	23.7741	−	6.98072i	1.46043	−	0.428822i
$266$	−0.310983	+	0.680958i	−0.0190676	+	0.0417522i
$267$	−1.65925	−	11.5403i	−0.101544	−	0.706256i
$268$	−5.42445	−	6.26015i	−0.331351	−	0.382400i
$269$	−9.39673	−	20.5760i	−0.572929	−	1.25454i	−0.945223	−	0.326424i	$-0.894156\pi$
$269$	−9.39673	−	20.5760i	−0.572929	−	1.25454i	0.372295	−	0.928115i	$-0.378571\pi$
$270$	1.61435	−	1.03748i	0.0982464	−	0.0631392i
$271$	1.10259	−	7.66866i	0.0669774	−	0.465838i	−0.928538	−	0.371237i	$-0.878934\pi$
$271$	1.10259	−	7.66866i	0.0669774	−	0.465838i	0.995515	−	0.0946003i	$-0.0301573\pi$
$272$	−2.87958	−	1.85060i	−0.174600	−	0.112209i
$273$	−1.46458	+	1.69022i	−0.0886405	+	0.102297i
$274$	5.00324	+	1.46908i	0.302257	+	0.0887506i
$275$	1.36287			0.0821844
$276$	−3.89491	−	2.79816i	−0.234446	−	0.168429i
$277$	−20.3890			−1.22506			−0.612529	−	0.790448i	$-0.709848\pi$
$277$	−20.3890			−1.22506			−0.612529	+	0.790448i	$0.709848\pi$
$278$	−13.6115	−	3.99669i	−0.816363	−	0.239706i
$279$	−2.57574	+	2.97257i	−0.154206	+	0.177963i
$280$	−1.61435	−	1.03748i	−0.0964761	−	0.0620014i
$281$	−1.34386	+	9.34672i	−0.0801677	+	0.557579i	0.909665	+	0.415343i	$0.136338\pi$
$281$	−1.34386	+	9.34672i	−0.0801677	+	0.557579i	−0.989833	+	0.142236i	$0.954571\pi$
$282$	−10.5536	+	6.78240i	−0.628459	+	0.403886i
$283$	2.71690	+	5.94919i	0.161503	+	0.353643i	0.973032	−	0.230670i	$-0.0740916\pi$
$283$	2.71690	+	5.94919i	0.161503	+	0.353643i	−0.811529	+	0.584312i	$0.801364\pi$
$284$	6.93452	+	8.00286i	0.411488	+	0.474882i
$285$	−0.204445	−	1.42195i	−0.0121103	−	0.0842288i
$286$	0.961069	−	2.10445i	0.0568292	−	0.124439i
$287$	4.93918	−	1.45027i	0.291550	−	0.0856069i
$288$	−0.959493	+	0.281733i	−0.0565387	+	0.0166013i
$289$	−2.19475	+	4.80584i	−0.129103	+	0.282697i
$290$	2.36162	+	16.4254i	0.138679	+	0.964532i
$291$	1.02145	+	1.17882i	0.0598785	+	0.0691035i
$292$	−5.38528	−	11.7921i	−0.315150	−	0.690081i
$293$	8.78110	−	5.64327i	0.512998	−	0.329683i	−0.258399	−	0.966038i	$-0.583195\pi$
$293$	8.78110	−	5.64327i	0.512998	−	0.329683i	0.771397	+	0.636355i	$0.219559\pi$
$294$	−0.142315	+	0.989821i	−0.00829997	+	0.0577276i
$295$	−7.63205	−	4.90482i	−0.444355	−	0.285570i
$296$	−4.31219	+	4.97653i	−0.250641	+	0.289255i
$297$	0.992543	+	0.291437i	0.0575932	+	0.0169109i
$298$	−10.6720			−0.618213
$299$	−10.4339	+	2.48512i	−0.603409	+	0.143718i
$300$	−1.31749			−0.0760655
$301$	−0.568325	−	0.166875i	−0.0327577	−	0.00961854i
$302$	1.16639	−	1.34609i	0.0671183	−	0.0774587i
$303$	1.58150	+	1.01637i	0.0908548	+	0.0583889i
$304$	−0.106538	+	0.740988i	−0.00611037	+	0.0424986i
$305$	3.92062	−	2.51963i	0.224494	−	0.144274i
$306$	−1.42195	−	3.11364i	−0.0812876	−	0.177995i
$307$	10.5418	+	12.1659i	0.601655	+	0.694346i	0.972116	−	0.234502i	$-0.0753458\pi$
$307$	10.5418	+	12.1659i	0.601655	+	0.694346i	−0.370461	+	0.928848i	$0.620800\pi$
$308$	−0.147217	−	1.02392i	−0.00838847	−	0.0583431i
$309$	2.12588	−	4.65503i	0.120937	−	0.264816i
$310$	−7.24215	+	2.12649i	−0.411326	+	0.120776i
$311$	27.7845	−	8.15826i	1.57551	−	0.462613i	0.626914	−	0.779089i	$-0.284318\pi$
$311$	27.7845	−	8.15826i	1.57551	−	0.462613i	0.948601	+	0.316476i	$0.102500\pi$
$312$	−0.929067	+	2.03437i	−0.0525981	+	0.115174i
$313$	1.52855	+	10.6313i	0.0863987	+	0.600916i	0.986317	+	0.164858i	$0.0527166\pi$
$313$	1.52855	+	10.6313i	0.0863987	+	0.600916i	−0.899919	+	0.436058i	$0.856374\pi$
$314$	−8.16711	−	9.42535i	−0.460897	−	0.531903i
$315$	−0.797176	−	1.74557i	−0.0449158	−	0.0983518i
$316$	2.07050	−	1.33063i	0.116475	−	0.0748538i
$317$	0.387272	−	2.69353i	0.0217513	−	0.151284i	−0.976051	−	0.217541i	$-0.930197\pi$
$317$	0.387272	−	2.69353i	0.0217513	−	0.151284i	0.997803	+	0.0662567i	$0.0211056\pi$
$318$	−10.8622	−	6.98072i	−0.609122	−	0.391459i
$319$	−5.85792	+	6.76041i	−0.327981	+	0.378510i
$320$	−1.84125	−	0.540641i	−0.102929	−	0.0302227i
$321$	−13.6416			−0.761399
$322$	−3.32398	+	3.45705i	−0.185238	+	0.192654i
$323$	−2.56246			−0.142579
$324$	−0.959493	−	0.281733i	−0.0533052	−	0.0156518i
$325$	−1.92958	+	2.22685i	−0.107034	+	0.123523i
$326$	−5.38463	−	3.46049i	−0.298227	−	0.191659i
$327$	−0.185719	+	1.29170i	−0.0102703	+	0.0714314i
$328$	4.33052	−	2.78305i	0.239113	−	0.153668i
$329$	5.21143	+	11.4114i	0.287316	+	0.629133i
$330$	1.29996	+	1.50023i	0.0715602	+	0.0825849i
$331$	−0.463591	−	3.22435i	−0.0254813	−	0.177226i	0.973106	−	0.230357i	$-0.0739892\pi$
$331$	−0.463591	−	3.22435i	−0.0254813	−	0.177226i	−0.998588	+	0.0531303i	$0.983080\pi$
$332$	−5.91665	+	12.9556i	−0.324718	+	0.711034i
$333$	−6.31816	+	1.85518i	−0.346233	+	0.101663i
$334$	13.8798	−	4.07549i	0.759470	−	0.223001i
$335$	6.60330	−	14.4592i	0.360777	−	0.789991i
$336$	0.142315	+	0.989821i	0.00776391	+	0.0539992i
$337$	20.8206	+	24.0282i	1.13417	+	1.30890i	0.945043	+	0.326947i	$0.106020\pi$
$337$	20.8206	+	24.0282i	1.13417	+	1.30890i	0.189125	+	0.981953i	$0.439435\pi$
$338$	−3.32256	−	7.27538i	−0.180723	−	0.395729i
$339$	11.8071	−	7.58796i	0.641274	−	0.412122i
$340$	0.934813	−	6.50177i	0.0506974	−	0.352608i
$341$	−3.42285	−	2.19973i	−0.185358	−	0.119122i
$342$	−0.490234	+	0.565760i	−0.0265088	+	0.0305928i
$343$	0.959493	+	0.281733i	0.0518078	+	0.0152121i
$344$	−0.592318			−0.0319357
$345$	1.77945	−	9.02946i	0.0958024	−	0.486130i
$346$	−9.22491			−0.495934
$347$	11.7492	+	3.44986i	0.630728	+	0.185198i	0.581444	−	0.813586i	$-0.302488\pi$
$347$	11.7492	+	3.44986i	0.630728	+	0.185198i	0.0492838	+	0.998785i	$0.484306\pi$
$348$	5.66286	−	6.53529i	0.303561	−	0.350328i
$349$	16.6394	+	10.6935i	0.890686	+	0.572409i	0.904015	−	0.427502i	$-0.140606\pi$
$349$	16.6394	+	10.6935i	0.890686	+	0.572409i	−0.0133281	+	0.999911i	$0.504243\pi$
$350$	−0.187499	+	1.30408i	−0.0100222	+	0.0697062i
$351$	−1.88145	+	1.20913i	−0.100424	+	0.0645387i
$352$	−0.429724	−	0.940965i	−0.0229044	−	0.0501536i
$353$	−5.06403	−	5.84420i	−0.269531	−	0.311055i	0.604808	−	0.796372i	$-0.293250\pi$
$353$	−5.06403	−	5.84420i	−0.269531	−	0.311055i	−0.874339	+	0.485316i	$0.838705\pi$
$354$	0.672811	+	4.67950i	0.0357595	+	0.248713i
$355$	−8.44153	+	18.4844i	−0.448030	+	0.981049i
$356$	−11.1867	+	3.28472i	−0.592895	+	0.174090i
$357$	−3.28431	+	0.964362i	−0.173824	+	0.0510394i
$358$	−7.81377	+	17.1098i	−0.412971	+	0.904279i
$359$	1.85798	+	12.9225i	0.0980603	+	0.682024i	0.978254	+	0.207410i	$0.0665034\pi$
$359$	1.85798	+	12.9225i	0.0980603	+	0.682024i	−0.880194	+	0.474614i	$0.842588\pi$
$360$	−1.25667	−	1.45027i	−0.0662322	−	0.0764361i
$361$	−7.66008	−	16.7732i	−0.403162	−	0.882802i
$362$	−5.90871	+	3.79730i	−0.310555	+	0.199581i
$363$	1.41318	−	9.82885i	0.0741725	−	0.515881i
$364$	1.88145	+	1.20913i	0.0986146	+	0.0633757i
$365$	16.2910	−	18.8008i	0.852708	−	0.984077i
$366$	−2.33023	−	0.684216i	−0.121803	−	0.0357645i
$367$	−0.868333			−0.0453266			−0.0226633	−	0.999743i	$-0.507215\pi$
$367$	−0.868333			−0.0453266			−0.0226633	+	0.999743i	$0.507215\pi$
$368$	−2.21537	+	4.25348i	−0.115484	+	0.221728i
$369$	5.14769			0.267978
$370$	−12.1245	−	3.56006i	−0.630320	−	0.185079i
$371$	−8.45552	+	9.75819i	−0.438989	+	0.506620i
$372$	3.30888	+	2.12649i	0.171557	+	0.110253i
$373$	−1.41476	+	9.83988i	−0.0732535	+	0.509490i	0.919852	+	0.392266i	$0.128309\pi$
$373$	−1.41476	+	9.83988i	−0.0732535	+	0.509490i	−0.993106	+	0.117224i	$0.962600\pi$
$374$	2.97877	−	1.91434i	0.154029	−	0.0989883i
$375$	−5.03615	−	11.0276i	−0.260066	−	0.569464i
$376$	8.21531	+	9.48097i	0.423672	+	0.488944i
$377$	−2.75234	−	19.1429i	−0.141753	−	0.985912i
$378$	−0.415415	+	0.909632i	−0.0213666	+	0.0467864i
$379$	−19.1208	+	5.61437i	−0.982169	+	0.288391i	−0.733119	−	0.680100i	$-0.761936\pi$
$379$	−19.1208	+	5.61437i	−0.982169	+	0.288391i	−0.249049	+	0.968491i	$0.580118\pi$
$380$	−1.37838	+	0.404728i	−0.0707092	+	0.0207621i
$381$	6.23448	−	13.6516i	0.319402	−	0.699393i
$382$	−0.338184	−	2.35212i	−0.0173030	−	0.120345i
$383$	1.50587	+	1.73787i	0.0769466	+	0.0888011i	0.792917	−	0.609329i	$-0.208561\pi$
$383$	1.50587	+	1.73787i	0.0769466	+	0.0888011i	−0.715971	+	0.698130i	$0.754016\pi$
$384$	0.415415	+	0.909632i	0.0211991	+	0.0464195i
$385$	1.66996	−	1.07322i	0.0851091	−	0.0546963i
$386$	0.0419235	−	0.291584i	0.00213385	−	0.0148413i
$387$	−0.498290	−	0.320231i	−0.0253295	−	0.0162783i
$388$	1.02145	−	1.17882i	0.0518563	−	0.0598454i
$389$	−13.9486	−	4.09569i	−0.707224	−	0.207660i	−0.0917102	−	0.995786i	$-0.529233\pi$
$389$	−13.9486	−	4.09569i	−0.707224	−	0.207660i	−0.615514	+	0.788126i	$0.711052\pi$
$390$	−4.29177			−0.217322
$391$	−15.4905	−	5.43392i	−0.783391	−	0.274805i
$392$	1.00000			0.0505076
$393$	13.4865	+	3.96001i	0.680306	+	0.199756i
$394$	−16.0883	+	18.5668i	−0.810515	+	0.935384i
$395$	3.97326	+	2.55346i	0.199917	+	0.128479i
$396$	0.147217	−	1.02392i	0.00739793	−	0.0514537i
$397$	−19.5954	+	12.5932i	−0.983465	+	0.632035i	−0.930396	−	0.366556i	$-0.880537\pi$
$397$	−19.5954	+	12.5932i	−0.983465	+	0.632035i	−0.0530691	+	0.998591i	$0.516900\pi$
$398$	−4.83218	−	10.5810i	−0.242215	−	0.530377i
$399$	0.490234	+	0.565760i	0.0245424	+	0.0283234i
$400$	0.187499	+	1.30408i	0.00937494	+	0.0652041i
$401$	−7.49905	+	16.4206i	−0.374485	+	0.820007i	0.624748	+	0.780827i	$0.285202\pi$
$401$	−7.49905	+	16.4206i	−0.374485	+	0.820007i	−0.999232	+	0.0391800i	$0.987525\pi$
$402$	−7.94784	+	2.33370i	−0.396402	+	0.116394i
$403$	8.44035	−	2.47831i	0.420444	−	0.123453i
$404$	0.780953	−	1.71005i	0.0388538	−	0.0850781i
$405$	−0.273100	−	1.89945i	−0.0135705	−	0.0943846i
$406$	−5.66286	−	6.53529i	−0.281043	−	0.324341i
$407$	−2.82969	−	6.19615i	−0.140262	−	0.307132i
$408$	−2.87958	+	1.85060i	−0.142561	+	0.0916182i
$409$	−0.940095	+	6.53850i	−0.0464847	+	0.323308i	0.953290	+	0.302058i	$0.0976737\pi$
$409$	−0.940095	+	6.53850i	−0.0464847	+	0.323308i	−0.999774	+	0.0212499i	$0.993235\pi$
$410$	8.31020	+	5.34064i	0.410411	+	0.263755i
$411$	3.41475	−	3.94083i	0.168437	−	0.194387i
$412$	−4.91020	−	1.44176i	−0.241908	−	0.0710306i
$413$	4.72762			0.232631
$414$	−4.16330	+	2.38054i	−0.204615	+	0.116997i
$415$	−27.3316			−1.34166
$416$	2.14589	+	0.630089i	0.105211	+	0.0308927i
$417$	−9.28994	+	10.7212i	−0.454930	+	0.525017i
$418$	−0.651462	−	0.418669i	−0.0318640	−	0.0204778i
$419$	−2.89192	+	20.1137i	−0.141279	+	0.982620i	0.788640	+	0.614856i	$0.210786\pi$
$419$	−2.89192	+	20.1137i	−0.141279	+	0.982620i	−0.929919	+	0.367764i	$0.880123\pi$
$420$	−1.61435	+	1.03748i	−0.0787724	+	0.0506239i
$421$	−12.7113	−	27.8339i	−0.619512	−	1.35654i	−0.915873	−	0.401467i	$-0.868500\pi$
$421$	−12.7113	−	27.8339i	−0.619512	−	1.35654i	0.296361	−	0.955076i	$-0.404227\pi$
$422$	−14.3447	−	16.5546i	−0.698288	−	0.805867i
$423$	1.78536	+	12.4174i	0.0868070	+	0.603756i
$424$	−5.36381	+	11.7451i	−0.260490	+	0.570393i
$425$	−4.32706	+	1.27054i	−0.209893	+	0.0616302i
$426$	10.1604	−	2.98335i	0.492271	−	0.144544i
$427$	−1.00888	+	2.20913i	−0.0488230	+	0.106907i
$428$	1.94140	+	13.5027i	0.0938411	+	0.652679i
$429$	−1.51503	−	1.74844i	−0.0731464	−	0.0844154i
$430$	−0.472182	−	1.03393i	−0.0227706	−	0.0498607i
$431$	16.1700	−	10.3918i	0.778880	−	0.500556i	−0.0897820	−	0.995961i	$-0.528617\pi$
$431$	16.1700	−	10.3918i	0.778880	−	0.500556i	0.868662	+	0.495406i	$0.164981\pi$
$432$	−0.142315	+	0.989821i	−0.00684713	+	0.0476228i
$433$	7.40317	+	4.75773i	0.355774	+	0.228642i	0.706303	−	0.707910i	$-0.250362\pi$
$433$	7.40317	+	4.75773i	0.355774	+	0.228642i	−0.350529	+	0.936552i	$0.613998\pi$
$434$	2.57574	−	2.97257i	0.123640	−	0.142688i
$435$	15.9221	+	4.67515i	0.763407	+	0.224157i
$436$	1.30499			0.0624975
$437$	0.326333	+	3.57533i	0.0156106	+	0.171031i
$438$	−12.9636			−0.619425
$439$	6.10236	+	1.79181i	0.291250	+	0.0855186i	0.424094	−	0.905618i	$-0.360593\pi$
$439$	6.10236	+	1.79181i	0.291250	+	0.0855186i	−0.132844	+	0.991137i	$0.542411\pi$
$440$	1.29996	−	1.50023i	0.0619729	−	0.0715206i
$441$	0.841254	+	0.540641i	0.0400597	+	0.0257448i
$442$	−1.08948	+	7.57748i	−0.0518211	+	0.360424i
$443$	14.2474	−	9.15627i	0.676916	−	0.435027i	−0.156497	−	0.987678i	$-0.550020\pi$
$443$	14.2474	−	9.15627i	0.676916	−	0.435027i	0.833413	+	0.552651i	$0.186384\pi$
$444$	2.73546	+	5.98983i	0.129819	+	0.284265i
$445$	−14.6515	−	16.9087i	−0.694548	−	0.801551i
$446$	−3.24556	−	22.5733i	−0.153682	−	1.06888i
$447$	−4.43332	+	9.70761i	−0.209689	+	0.459154i
$448$	0.959493	−	0.281733i	0.0453318	−	0.0133106i
$449$	−13.0610	+	3.83505i	−0.616386	+	0.180987i	−0.574997	−	0.818156i	$-0.694997\pi$
$449$	−13.0610	+	3.83505i	−0.616386	+	0.180987i	−0.0413896	+	0.999143i	$0.513178\pi$
$450$	−0.547306	+	1.19843i	−0.0258003	+	0.0564947i
$451$	0.757828	+	5.27081i	0.0356847	+	0.248193i
$452$	−9.19106	−	10.6070i	−0.432311	−	0.498913i
$453$	−0.739908	−	1.62017i	−0.0347639	−	0.0761224i
$454$	20.2851	−	13.0364i	0.952026	−	0.611830i
$455$	−0.610783	+	4.24809i	−0.0286339	+	0.199153i
$456$	0.629769	+	0.404728i	0.0294916	+	0.0189531i
$457$	1.39275	−	1.60732i	0.0651500	−	0.0751871i	−0.722239	−	0.691644i	$-0.756887\pi$
$457$	1.39275	−	1.60732i	0.0651500	−	0.0751871i	0.787389	+	0.616456i	$0.211432\pi$
$458$	−12.3153	−	3.61609i	−0.575455	−	0.168969i
$459$	−3.42297			−0.159771
$460$	−9.19080	−	0.476312i	−0.428523	−	0.0222082i
$461$	−27.7062			−1.29041			−0.645204	−	0.764011i	$-0.723228\pi$
$461$	−27.7062			−1.29041			−0.645204	+	0.764011i	$0.723228\pi$
$462$	−0.992543	−	0.291437i	−0.0461773	−	0.0135589i
$463$	−9.39133	+	10.8382i	−0.436452	+	0.503692i	−0.930778	−	0.365584i	$-0.880869\pi$
$463$	−9.39133	+	10.8382i	−0.436452	+	0.503692i	0.494326	+	0.869276i	$0.335415\pi$
$464$	−7.27468	−	4.67515i	−0.337719	−	0.217039i
$465$	−1.07418	+	7.47106i	−0.0498137	+	0.346462i
$466$	9.56900	−	6.14962i	0.443275	−	0.284876i
$467$	−5.55896	−	12.1724i	−0.257238	−	0.563273i	0.736315	−	0.676639i	$-0.236564\pi$
$467$	−5.55896	−	12.1724i	−0.257238	−	0.563273i	−0.993553	+	0.113366i	$0.963837\pi$
$468$	1.46458	+	1.69022i	0.0677003	+	0.0781304i
$469$	1.17885	+	8.19906i	0.0544341	+	0.378597i
$470$	−10.0007	+	21.8984i	−0.461296	+	1.01010i
$471$	−11.9663	+	3.51363i	−0.551380	+	0.161900i
$472$	4.53612	−	1.33192i	0.208792	−	0.0613068i
$473$	0.254534	−	0.557351i	0.0117035	−	0.0256270i
$474$	−0.350267	−	2.43616i	−0.0160883	−	0.111896i
$475$	0.645880	+	0.745385i	0.0296350	+	0.0342006i
$476$	1.42195	+	3.11364i	0.0651751	+	0.142714i
$477$	−10.8622	+	6.98072i	−0.497346	+	0.319625i
$478$	1.64605	−	11.4485i	0.0752885	−	0.523643i
$479$	11.8168	+	7.59422i	0.539925	+	0.346989i	0.782010	−	0.623266i	$-0.214195\pi$
$479$	11.8168	+	7.59422i	0.539925	+	0.346989i	−0.242085	+	0.970255i	$0.577831\pi$
$480$	−1.25667	+	1.45027i	−0.0573588	+	0.0661956i
$481$	14.1304	+	4.14907i	0.644292	+	0.189181i
$482$	−2.68886			−0.122474
$483$	1.76381	+	4.45971i	0.0802562	+	0.202924i
$484$	−9.92992			−0.451360
$485$	2.87199	+	0.843291i	0.130410	+	0.0382919i
$486$	−0.654861	+	0.755750i	−0.0297051	+	0.0342815i
$487$	−19.2397	−	12.3646i	−0.871835	−	0.560294i	0.0264787	−	0.999649i	$-0.491571\pi$
$487$	−19.2397	−	12.3646i	−0.871835	−	0.560294i	−0.898313	+	0.439355i	$0.855207\pi$
$488$	−0.345626	+	2.40388i	−0.0156458	+	0.108819i
$489$	−5.38463	+	3.46049i	−0.243501	+	0.156489i
$490$	0.797176	+	1.74557i	0.0360127	+	0.0788569i
$491$	2.46195	+	2.84124i	0.111106	+	0.128223i	0.808578	−	0.588389i	$-0.200237\pi$
$491$	2.46195	+	2.84124i	0.111106	+	0.128223i	−0.697472	+	0.716612i	$0.745692\pi$
$492$	−0.732593	−	5.09530i	−0.0330278	−	0.229714i
$493$	12.2962	−	26.9250i	0.553795	−	1.21264i
$494$	1.60643	−	0.471689i	0.0722766	−	0.0212223i
$495$	1.90468	−	0.559264i	0.0856089	−	0.0251370i
$496$	1.63394	−	3.57783i	0.0733660	−	0.160649i
$497$	−1.50701	−	10.4815i	−0.0675988	−	0.470160i
$498$	9.32701	+	10.7639i	0.417953	+	0.482344i
$499$	−4.77559	−	10.4571i	−0.213785	−	0.468123i	0.772110	−	0.635489i	$-0.219201\pi$
$499$	−4.77559	−	10.4571i	−0.213785	−	0.468123i	−0.985895	+	0.167365i	$0.946474\pi$
$500$	−10.1987	+	6.55429i	−0.456098	+	0.293117i
$501$	2.05870	−	14.3186i	0.0919758	−	0.639706i
$502$	−16.1912	−	10.4054i	−0.722646	−	0.464417i
$503$	−7.80973	+	9.01291i	−0.348219	+	0.401866i	−0.902658	−	0.430358i	$-0.858387\pi$
$503$	−7.80973	+	9.01291i	−0.348219	+	0.401866i	0.554440	+	0.832224i	$0.312933\pi$
$504$	0.959493	+	0.281733i	0.0427392	+	0.0125494i
$505$	3.60757			0.160535
$506$	−3.05038	−	3.91241i	−0.135606	−	0.173928i
$507$	−7.99816			−0.355211
$508$	−14.3999	−	4.22820i	−0.638893	−	0.187596i
$509$	−5.30605	+	6.12351i	−0.235187	+	0.271420i	−0.861058	−	0.508506i	$-0.830198\pi$
$509$	−5.30605	+	6.12351i	−0.235187	+	0.271420i	0.625872	+	0.779926i	$0.284743\pi$
$510$	−5.52588	−	3.55127i	−0.244690	−	0.157253i
$511$	−1.84491	+	12.8317i	−0.0816142	+	0.567639i
$512$	0.841254	−	0.540641i	0.0371785	−	0.0238932i
$513$	0.310983	+	0.680958i	0.0137302	+	0.0300650i
$514$	7.09421	+	8.18716i	0.312912	+	0.361120i
$515$	−1.39759	−	9.72044i	−0.0615851	−	0.428334i
$516$	−0.246058	+	0.538792i	−0.0108321	+	0.0237190i
$517$	−12.4516	+	3.65611i	−0.547620	+	0.160796i
$518$	6.31816	−	1.85518i	0.277604	−	0.0815118i
$519$	−3.83217	+	8.39127i	−0.168213	+	0.368336i
$520$	0.610783	+	4.24809i	0.0267846	+	0.186291i
$521$	4.09879	+	4.73026i	0.179571	+	0.207236i	0.838398	−	0.545058i	$-0.183492\pi$
$521$	4.09879	+	4.73026i	0.179571	+	0.207236i	−0.658827	+	0.752295i	$0.728947\pi$
$522$	−3.59227	−	7.86598i	−0.157230	−	0.344285i
$523$	−10.3264	+	6.63638i	−0.451542	+	0.290189i	−0.746578	−	0.665298i	$-0.768305\pi$
$523$	−10.3264	+	6.63638i	−0.451542	+	0.290189i	0.295036	+	0.955486i	$0.404668\pi$
$524$	2.00036	−	13.9128i	0.0873863	−	0.607785i
$525$	1.10835	+	0.712290i	0.0483722	+	0.0310869i
$526$	−4.83292	+	5.57749i	−0.210725	+	0.243190i
$527$	12.9181	+	3.79310i	0.562721	+	0.165230i
$528$	−1.03445			−0.0450185
$529$	−5.60906	+	22.3056i	−0.243872	+	0.969807i
$530$	−24.7778			−1.07628
$531$	4.53612	+	1.33192i	0.196851	+	0.0578006i
$532$	0.490234	−	0.565760i	0.0212543	−	0.0245288i
$533$	−9.68511	−	6.22424i	−0.419509	−	0.269602i
$534$	−1.65925	+	11.5403i	−0.0718027	+	0.499399i
$535$	−22.0223	+	14.1529i	−0.952109	+	0.611883i
$536$	3.44104	+	7.53482i	0.148630	+	0.325455i
$537$	12.3176	+	14.2153i	0.531545	+	0.613436i
$538$	3.21918	+	22.3899i	0.138789	+	0.965295i
$539$	−0.429724	+	0.940965i	−0.0185095	+	0.0405302i
$540$	−1.84125	+	0.540641i	−0.0792349	+	0.0232655i
$541$	−0.239729	+	0.0703907i	−0.0103067	+	0.00302633i	−0.286882	−	0.957966i	$-0.592619\pi$
$541$	−0.239729	+	0.0703907i	−0.0103067	+	0.00302633i	0.276575	+	0.960992i	$0.410801\pi$
$542$	−3.21843	+	7.04739i	−0.138244	+	0.302711i
$543$	0.999576	+	6.95220i	0.0428959	+	0.298348i
$544$	2.24157	+	2.58691i	0.0961064	+	0.110913i
$545$	1.04030	+	2.27795i	0.0445617	+	0.0975765i
$546$	1.88145	−	1.20913i	0.0805184	−	0.0517461i
$547$	0.998871	−	6.94730i	0.0427087	−	0.297045i	−0.957261	−	0.289226i	$-0.906602\pi$
$547$	0.998871	−	6.94730i	0.0427087	−	0.297045i	0.999969	−	0.00781902i	$-0.00248890\pi$
$548$	−4.38669	−	2.81915i	−0.187390	−	0.120428i
$549$	−1.59040	+	1.83541i	−0.0678764	+	0.0783336i
$550$	−1.30767	−	0.383966i	−0.0557592	−	0.0163724i
$551$	−6.47353			−0.275782
$552$	2.94881	+	3.78213i	0.125510	+	0.160978i
$553$	−2.46121			−0.104661
$554$	19.5631	+	5.74426i	0.831158	+	0.244050i
$555$	−8.27503	+	9.54989i	−0.351255	+	0.405370i
$556$	11.9341	+	7.66960i	0.506120	+	0.325263i
$557$	−2.07370	+	14.4229i	−0.0878656	+	0.611118i	0.897545	+	0.440923i	$0.145349\pi$
$557$	−2.07370	+	14.4229i	−0.0878656	+	0.611118i	−0.985410	+	0.170195i	$0.945560\pi$
$558$	3.30888	−	2.12649i	0.140076	−	0.0900213i
$559$	0.550303	+	1.20500i	0.0232754	+	0.0509659i
$560$	1.25667	+	1.45027i	0.0531039	+	0.0612852i
$561$	−0.503919	−	3.50483i	−0.0212755	−	0.147974i
$562$	3.92270	−	8.58951i	0.165469	−	0.362326i
$563$	32.6458	−	9.58568i	1.37586	−	0.403988i	0.491533	−	0.870859i	$-0.336437\pi$
$563$	32.6458	−	9.58568i	1.37586	−	0.403988i	0.884326	+	0.466871i	$0.154619\pi$
$564$	12.0370	−	3.53437i	0.506847	−	0.148824i
$565$	11.1885	−	24.4993i	0.470702	−	1.03069i
$566$	−0.930770	−	6.47365i	−0.0391232	−	0.272108i
$567$	0.654861	+	0.755750i	0.0275016	+	0.0317385i
$568$	−4.39895	−	9.63236i	−0.184576	−	0.404165i
$569$	36.0054	−	23.1393i	1.50943	−	0.970049i	0.515875	−	0.856664i	$-0.327467\pi$
$569$	36.0054	−	23.1393i	1.50943	−	0.970049i	0.993551	−	0.113385i	$-0.0361695\pi$
$570$	−0.204445	+	1.42195i	−0.00856326	+	0.0595587i
$571$	29.2221	+	18.7799i	1.22291	+	0.785915i	0.982772	−	0.184824i	$-0.0591716\pi$
$571$	29.2221	+	18.7799i	1.22291	+	0.785915i	0.240136	+	0.970739i	$0.422808\pi$
$572$	−1.51503	+	1.74844i	−0.0633466	+	0.0731059i
$573$	−2.28005	−	0.669485i	−0.0952507	−	0.0279681i
$574$	−5.14769			−0.214861
$575$	2.32381	+	5.87563i	0.0969095	+	0.245031i
$576$	1.00000			0.0416667
$577$	−16.8564	−	4.94948i	−0.701740	−	0.206050i	−0.0886505	−	0.996063i	$-0.528255\pi$
$577$	−16.8564	−	4.94948i	−0.701740	−	0.206050i	−0.613090	+	0.790013i	$0.710074\pi$
$578$	3.45981	−	3.99284i	0.143909	−	0.166080i
$579$	−0.247819	−	0.159263i	−0.0102990	−	0.00661876i
$580$	2.36162	−	16.4254i	0.0980607	−	0.682027i
$581$	11.9818	−	7.70020i	0.497087	−	0.319458i
$582$	−0.647964	−	1.41884i	−0.0268590	−	0.0588129i
$583$	−8.74677	−	10.0943i	−0.362254	−	0.418064i
$584$	1.84491	+	12.8317i	0.0763431	+	0.530978i
$585$	−1.78287	+	3.90393i	−0.0737125	+	0.161408i
$586$	−10.0153	+	2.94076i	−0.413728	+	0.121482i
$587$	−2.81364	+	0.826159i	−0.116131	+	0.0340992i	−0.339282	−	0.940685i	$-0.610184\pi$
$587$	−2.81364	+	0.826159i	−0.116131	+	0.0340992i	0.223151	+	0.974784i	$0.428366\pi$
$588$	0.415415	−	0.909632i	0.0171314	−	0.0375126i
$589$	−0.419043	−	2.91451i	−0.0172664	−	0.120090i
$590$	5.94105	+	6.85634i	0.244589	+	0.282271i
$591$	10.2057	+	22.3473i	0.419806	+	0.919247i
$592$	5.53956	−	3.56006i	0.227675	−	0.146318i
$593$	−3.87282	+	26.9361i	−0.159038	+	1.10613i	0.741373	+	0.671093i	$0.234175\pi$
$593$	−3.87282	+	26.9361i	−0.159038	+	1.10613i	−0.900411	+	0.435040i	$0.856734\pi$
$594$	−0.870231	−	0.559264i	−0.0357060	−	0.0229469i
$595$	−4.30154	+	4.96424i	−0.176346	+	0.203514i
$596$	10.2397	+	3.00665i	0.419436	+	0.123157i
$597$	−11.6322			−0.476073
$598$	10.7114	+	0.555117i	0.438022	+	0.0227004i
$599$	24.7323			1.01054			0.505268	−	0.862963i	$-0.331394\pi$
$599$	24.7323			1.01054			0.505268	+	0.862963i	$0.331394\pi$
$600$	1.26413	+	0.371181i	0.0516077	+	0.0151534i
$601$	−30.5657	+	35.2747i	−1.24680	+	1.43888i	−0.391966	+	0.919980i	$0.628205\pi$
$601$	−30.5657	+	35.2747i	−1.24680	+	1.43888i	−0.854833	+	0.518904i	$0.826340\pi$
$602$	0.498290	+	0.320231i	0.0203088	+	0.0130517i
$603$	−1.17885	+	8.19906i	−0.0480063	+	0.333891i
$604$	−1.49838	+	0.962951i	−0.0609683	+	0.0391819i
$605$	−7.91589	−	17.3334i	−0.321827	−	0.704702i
$606$	−1.23109	−	1.42076i	−0.0500098	−	0.0577144i
$607$	0.927849	+	6.45333i	0.0376602	+	0.261933i	0.999949	−	0.0100973i	$-0.00321413\pi$
$607$	0.927849	+	6.45333i	0.0376602	+	0.261933i	−0.962289	+	0.272030i	$0.912305\pi$
$608$	0.310983	−	0.680958i	0.0126120	−	0.0276165i
$609$	−8.29715	+	2.43626i	−0.336217	+	0.0987224i
$610$	−4.47167	+	1.31300i	−0.181053	+	0.0531619i
$611$	11.6553	−	25.5215i	0.471521	−	1.03249i
$612$	0.487139	+	3.38813i	0.0196914	+	0.136957i
$613$	14.2044	+	16.3927i	0.573709	+	0.662095i	0.966240	−	0.257643i	$-0.0829460\pi$
$613$	14.2044	+	16.3927i	0.573709	+	0.662095i	−0.392531	+	0.919739i	$0.628400\pi$
$614$	−6.68728	−	14.6431i	−0.269877	−	0.590948i
$615$	8.31020	−	5.34064i	0.335100	−	0.215355i
$616$	−0.147217	+	1.02392i	−0.00593154	+	0.0412548i
$617$	−18.5220	−	11.9034i	−0.745669	−	0.479213i	0.111811	−	0.993730i	$-0.464335\pi$
$617$	−18.5220	−	11.9034i	−0.745669	−	0.479213i	−0.857480	+	0.514517i	$0.827971\pi$
$618$	−3.35124	+	3.86754i	−0.134807	+	0.155575i
$619$	−29.4996	−	8.66186i	−1.18569	−	0.348149i	−0.371324	−	0.928503i	$-0.621096\pi$
$619$	−29.4996	−	8.66186i	−1.18569	−	0.348149i	−0.814364	+	0.580354i	$0.802914\pi$
$620$	7.54789			0.303131
$621$	0.435919	+	4.77598i	0.0174928	+	0.191653i
$622$	−28.9575			−1.16109
$623$	11.1867	+	3.28472i	0.448187	+	0.131599i
$624$	1.46458	−	1.69022i	0.0586302	−	0.0676629i
$625$	−14.0294	−	9.01613i	−0.561175	−	0.360645i
$626$	1.52855	−	10.6313i	0.0610931	−	0.424912i
$627$	−0.651462	+	0.418669i	−0.0260169	+	0.0167200i
$628$	5.18086	+	11.3445i	0.206739	+	0.452695i
$629$	14.7605	+	17.0345i	0.588539	+	0.679210i
$630$	0.273100	+	1.89945i	0.0108806	+	0.0756760i
$631$	−11.7270	+	25.6785i	−0.466843	+	1.02224i	0.519031	+	0.854755i	$0.326293\pi$
$631$	−11.7270	+	25.6785i	−0.466843	+	1.02224i	−0.985874	+	0.167488i	$0.946434\pi$
$632$	−2.36151	+	0.693403i	−0.0939359	+	0.0275821i
$633$	−21.0176	+	6.17133i	−0.835375	+	0.245288i
$634$	−1.13044	+	2.47532i	−0.0448955	+	0.0983075i
$635$	−4.09864	−	28.5067i	−0.162650	−	1.13125i
$636$	8.45552	+	9.75819i	0.335283	+	0.386937i
$637$	−0.929067	−	2.03437i	−0.0368110	−	0.0806048i
$638$	7.52526	−	4.83619i	0.297928	−	0.191467i
$639$	1.50701	−	10.4815i	0.0596166	−	0.414642i
$640$	1.61435	+	1.03748i	0.0638129	+	0.0410101i
$641$	−15.0641	+	17.3849i	−0.594997	+	0.686663i	−0.970760	−	0.240053i	$-0.922835\pi$
$641$	−15.0641	+	17.3849i	−0.594997	+	0.686663i	0.375763	+	0.926716i	$0.377381\pi$
$642$	13.0890	+	3.84328i	0.516582	+	0.151682i
$643$	23.8887			0.942077			0.471039	−	0.882113i	$-0.343879\pi$
$643$	23.8887			0.942077			0.471039	+	0.882113i	$0.343879\pi$
$644$	4.16330	−	2.38054i	0.164057	−	0.0938064i
$645$	−1.13665			−0.0447556
$646$	2.45866	+	0.721929i	0.0967348	+	0.0284039i
$647$	26.5782	−	30.6728i	1.04490	−	1.20587i	0.0667899	−	0.997767i	$-0.478724\pi$
$647$	26.5782	−	30.6728i	1.04490	−	1.20587i	0.978106	−	0.208107i	$-0.0667303\pi$
$648$	0.841254	+	0.540641i	0.0330476	+	0.0212384i
$649$	−0.695986	+	4.84069i	−0.0273198	+	0.190014i
$650$	2.47879	−	1.59302i	0.0972262	−	0.0624835i
$651$	−1.63394	−	3.57783i	−0.0640391	−	0.140226i
$652$	4.19158	+	4.83734i	0.164155	+	0.189445i
$653$	0.957835	+	6.66189i	0.0374830	+	0.260700i	0.999942	−	0.0107254i	$-0.00341407\pi$
$653$	0.957835	+	6.66189i	0.0374830	+	0.260700i	−0.962459	+	0.271425i	$0.912505\pi$
$654$	0.542111	−	1.18706i	0.0211982	−	0.0464176i
$655$	25.8805	−	7.59920i	1.01123	−	0.296925i
$656$	−4.93918	+	1.45027i	−0.192842	+	0.0566236i
$657$	−5.38528	+	11.7921i	−0.210100	+	0.460054i
$658$	−1.78536	−	12.4174i	−0.0696005	−	0.484082i
$659$	−27.0892	−	31.2626i	−1.05525	−	1.21782i	−0.975269	−	0.221022i	$-0.929061\pi$
$659$	−27.0892	−	31.2626i	−1.05525	−	1.21782i	−0.0799772	−	0.996797i	$-0.525485\pi$
$660$	−0.824635	−	1.80570i	−0.0320989	−	0.0702867i
$661$	37.5005	−	24.1001i	1.45860	−	0.937387i	0.459822	−	0.888011i	$-0.347913\pi$
$661$	37.5005	−	24.1001i	1.45860	−	0.937387i	0.998780	−	0.0493753i	$-0.0157230\pi$
$662$	−0.463591	+	3.22435i	−0.0180180	+	0.125318i
$663$	6.44013	+	4.13882i	0.250114	+	0.160738i
$664$	9.32701	−	10.7639i	0.361958	−	0.417722i
$665$	1.37838	+	0.404728i	0.0534512	+	0.0156947i
$666$	6.58489			0.255159
$667$	−39.1337	−	13.7277i	−1.51526	−	0.531538i
$668$	−14.4658			−0.559698
$669$	−21.8817	−	6.42504i	−0.845995	−	0.248406i
$670$	−10.4095	+	12.0131i	−0.402152	+	0.464108i
$671$	−2.11344	−	1.35823i	−0.0815886	−	0.0524338i
$672$	0.142315	−	0.989821i	0.00548991	−	0.0381832i
$673$	18.6809	−	12.0055i	0.720095	−	0.462777i	−0.128575	−	0.991700i	$-0.541040\pi$
$673$	18.6809	−	12.0055i	0.720095	−	0.462777i	0.848670	+	0.528923i	$0.177404\pi$
$674$	−13.2077	−	28.9207i	−0.508740	−	1.11398i
$675$	0.862774	+	0.995695i	0.0332082	+	0.0383243i
$676$	1.13826	+	7.91675i	0.0437791	+	0.304490i
$677$	−0.376310	+	0.824003i	−0.0144628	+	0.0316690i	−0.916726	−	0.399518i	$-0.869178\pi$
$677$	−0.376310	+	0.824003i	−0.0144628	+	0.0316690i	0.902263	+	0.431187i	$0.141905\pi$
$678$	−13.4666	+	3.95415i	−0.517182	+	0.151858i
$679$	−1.49662	+	0.439446i	−0.0574349	+	0.0168644i
$680$	−2.72871	+	5.97504i	−0.104641	+	0.229132i
$681$	−3.43163	−	23.8675i	−0.131500	−	0.914604i
$682$	2.66447	+	3.07496i	0.102028	+	0.117746i
$683$	−8.56715	−	18.7595i	−0.327813	−	0.717810i	0.671927	−	0.740618i	$-0.265467\pi$
$683$	−8.56715	−	18.7595i	−0.327813	−	0.717810i	−0.999740	+	0.0228071i	$0.992740\pi$
$684$	0.629769	−	0.404728i	0.0240798	−	0.0154752i
$685$	1.42407	−	9.90463i	0.0544110	−	0.378436i
$686$	−0.841254	−	0.540641i	−0.0321192	−	0.0206418i
$687$	−8.40526	+	9.70019i	−0.320681	+	0.370085i
$688$	0.568325	+	0.166875i	0.0216672	+	0.00636206i
$689$	28.8773			1.10014
$690$	−4.25126	+	8.16238i	−0.161843	+	0.310736i
$691$	−0.605385			−0.0230299			−0.0115150	−	0.999934i	$-0.503665\pi$
$691$	−0.605385			−0.0230299			−0.0115150	+	0.999934i	$0.503665\pi$
$692$	8.85124	+	2.59896i	0.336474	+	0.0987975i
$693$	−0.677418	+	0.781782i	−0.0257330	+	0.0296974i
$694$	−10.3013	−	6.62024i	−0.391032	−	0.251301i
$695$	−3.87423	+	26.9459i	−0.146958	+	1.02212i
$696$	−7.27468	+	4.67515i	−0.275746	+	0.177211i
$697$	−7.31978	−	16.0281i	−0.277256	−	0.607107i
$698$	−12.9527	−	14.9482i	−0.490266	−	0.565797i
$699$	−1.61879	−	11.2589i	−0.0612282	−	0.425851i
$700$	0.547306	−	1.19843i	0.0206862	−	0.0452965i
$701$	−3.93708	+	1.15603i	−0.148701	+	0.0436626i	−0.355236	−	0.934777i	$-0.615600\pi$
$701$	−3.93708	+	1.15603i	−0.148701	+	0.0436626i	0.206535	+	0.978439i	$0.433781\pi$
$702$	2.14589	−	0.630089i	0.0809912	−	0.0237812i
$703$	2.04779	−	4.48403i	0.0772338	−	0.169118i
$704$	0.147217	+	1.02392i	0.00554845	+	0.0385903i
$705$	15.7651	+	18.1938i	0.593746	+	0.685220i
$706$	3.21240	+	7.03417i	0.120900	+	0.264735i
$707$	−1.58150	+	1.01637i	−0.0594785	+	0.0382245i
$708$	0.672811	−	4.67950i	0.0252858	−	0.175866i
$709$	0.829986	+	0.533399i	0.0311708	+	0.0200322i	0.556133	−	0.831093i	$-0.312284\pi$
$709$	0.829986	+	0.533399i	0.0311708	+	0.0200322i	−0.524963	+	0.851125i	$0.675921\pi$
$710$	13.3072	−	15.3574i	0.499412	−	0.576352i
$711$	−2.36151	−	0.693403i	−0.0885637	−	0.0260046i
$712$	11.6590			0.436939
$713$	3.64727	−	18.5073i	0.136591	−	0.693105i
$714$	3.42297			0.128101
$715$	−4.25977	−	1.25078i	−0.159306	−	0.0467766i
$716$	12.3176	−	14.2153i	0.460332	−	0.531251i
$717$	−9.73014	−	6.25318i	−0.363379	−	0.233529i
$718$	1.85798	−	12.9225i	0.0693391	−	0.482264i
$719$	3.32969	−	2.13986i	0.124177	−	0.0798034i	−0.477078	−	0.878861i	$-0.658304\pi$
$719$	3.32969	−	2.13986i	0.124177	−	0.0798034i	0.601255	+	0.799058i	$0.294668\pi$
$720$	0.797176	+	1.74557i	0.0297090	+	0.0650536i
$721$	3.35124	+	3.86754i	0.124807	+	0.144035i
$722$	2.62423	+	18.2519i	0.0976636	+	0.679265i
$723$	−1.11699	+	2.44587i	−0.0415414	+	0.0909629i
$724$	6.73918	−	1.97880i	0.250460	−	0.0735416i
$725$	−10.9314	+	3.20976i	−0.405983	+	0.119207i
$726$	−4.12504	+	9.03257i	−0.153095	+	0.335230i
$727$	−5.37843	−	37.4078i	−0.199475	−	1.38738i	−0.805813	−	0.592171i	$-0.798271\pi$
$727$	−5.37843	−	37.4078i	−0.199475	−	1.38738i	0.606338	−	0.795207i	$-0.292638\pi$
$728$	−1.46458	−	1.69022i	−0.0542810	−	0.0626436i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	−20.9279	+	13.4495i	−0.774575	+	0.497789i
$731$	−0.288542	+	2.00685i	−0.0106721	+	0.0742261i
$732$	2.04307	+	1.31300i	0.0755140	+	0.0485299i
$733$	−4.69667	+	5.42024i	−0.173475	+	0.200201i	−0.835829	−	0.548990i	$-0.815012\pi$
$733$	−4.69667	+	5.42024i	−0.173475	+	0.200201i	0.662353	+	0.749192i	$0.269558\pi$
$734$	0.833159	+	0.244638i	0.0307525	+	0.00902974i
$735$	1.91899			0.0707829
$736$	3.32398	−	3.45705i	0.122523	−	0.127428i
$737$	−8.56870			−0.315632
$738$	−4.93918	−	1.45027i	−0.181814	−	0.0533853i
$739$	9.30363	−	10.7370i	0.342240	−	0.394966i	−0.558372	−	0.829591i	$-0.688574\pi$
$739$	9.30363	−	10.7370i	0.342240	−	0.394966i	0.900611	+	0.434625i	$0.143119\pi$
$740$	10.6303	+	6.83171i	0.390779	+	0.251139i
$741$	0.238270	−	1.65720i	0.00875307	−	0.0608789i
$742$	10.8622	−	6.98072i	0.398764	−	0.256270i
$743$	−12.6704	−	27.7443i	−0.464832	−	1.01784i	−0.986359	−	0.164606i	$-0.947365\pi$
$743$	−12.6704	−	27.7443i	−0.464832	−	1.01784i	0.521527	−	0.853235i	$-0.325362\pi$
$744$	−2.57574	−	2.97257i	−0.0944314	−	0.108980i
$745$	2.91453	+	20.2710i	0.106780	+	0.742672i
$746$	4.12967	−	9.04271i	0.151198	−	0.331077i
$747$	13.6658	−	4.01264i	0.500006	−	0.146815i
$748$	−3.39745	+	0.997580i	−0.124223	+	0.0364751i
$749$	5.66692	−	12.4088i	0.207065	−	0.453409i
$750$	1.72531	+	11.9998i	0.0629994	+	0.438170i
$751$	35.2766	+	40.7113i	1.28726	+	1.48558i	0.782996	+	0.622027i	$0.213691\pi$
$751$	35.2766	+	40.7113i	1.28726	+	1.48558i	0.504264	+	0.863550i	$0.331764\pi$
$752$	−5.21143	−	11.4114i	−0.190041	−	0.416133i
$753$	−16.1912	+	10.4054i	−0.590038	+	0.379195i
$754$	−2.75234	+	19.1429i	−0.100234	+	0.697145i
$755$	−2.87537	−	1.84789i	−0.104646	−	0.0672516i
$756$	0.654861	−	0.755750i	0.0238171	−	0.0274863i
$757$	−18.3808	−	5.39708i	−0.668060	−	0.196160i	−0.0699211	−	0.997553i	$-0.522275\pi$
$757$	−18.3808	−	5.39708i	−0.668060	−	0.196160i	−0.598139	+	0.801392i	$0.704093\pi$
$758$	19.9280			0.723818
$759$	−4.82603	+	1.14945i	−0.175174	+	0.0417224i
$760$	1.43657			0.0521098
$761$	30.0609	+	8.82668i	1.08971	+	0.319967i	0.776755	−	0.629802i	$-0.216864\pi$
$761$	30.0609	+	8.82668i	1.08971	+	0.319967i	0.312951	+	0.949769i	$0.398682\pi$
$762$	−9.82804	+	11.3422i	−0.356032	+	0.410883i
$763$	−1.09782	−	0.705529i	−0.0397439	−	0.0255419i
$764$	−0.338184	+	2.35212i	−0.0122351	+	0.0850969i
$765$	−5.52588	+	3.55127i	−0.199789	+	0.128396i
$766$	−0.955261	−	2.09173i	−0.0345150	−	0.0755773i
$767$	−6.92399	−	7.99071i	−0.250011	−	0.288528i
$768$	−0.142315	−	0.989821i	−0.00513534	−	0.0357171i
$769$	−9.97931	+	21.8516i	−0.359863	+	0.787991i	0.639945	+	0.768420i	$0.278957\pi$
$769$	−9.97931	+	21.8516i	−0.359863	+	0.787991i	−0.999808	+	0.0195700i	$0.993770\pi$
$770$	−1.90468	+	0.559264i	−0.0686398	+	0.0201545i
$771$	10.3943	−	3.05205i	0.374343	−	0.109917i
$772$	−0.122374	+	0.267962i	−0.00440434	+	0.00964416i
$773$	2.13061	+	14.8187i	0.0766327	+	0.532992i	0.991588	+	0.129437i	$0.0413168\pi$
$773$	2.13061	+	14.8187i	0.0766327	+	0.532992i	−0.914955	+	0.403556i	$0.867774\pi$
$774$	0.387886	+	0.447644i	0.0139423	+	0.0160902i
$775$	−2.15270	−	4.71376i	−0.0773274	−	0.169323i
$776$	−1.31219	+	0.843291i	−0.0471047	+	0.0302724i
$777$	0.937128	−	6.51787i	0.0336193	−	0.233827i
$778$	12.2297	+	7.85957i	0.438457	+	0.281779i
$779$	−2.52357	+	2.91236i	−0.0904164	+	0.104346i
$780$	4.11792	+	1.20913i	0.147445	+	0.0432939i
$781$	10.9541			0.391967
$782$	13.3322	+	9.57800i	0.476757	+	0.342509i
$783$	−8.64743			−0.309034
$784$	−0.959493	−	0.281733i	−0.0342676	−	0.0100619i
$785$	−15.6726	+	18.0871i	−0.559378	+	0.645556i
$786$	−11.8246	−	7.59920i	−0.421769	−	0.271054i
$787$	2.86016	−	19.8929i	0.101954	−	0.709104i	−0.873166	−	0.487424i	$-0.837937\pi$
$787$	2.86016	−	19.8929i	0.101954	−	0.709104i	0.975119	−	0.221680i	$-0.0711541\pi$
$788$	20.6675	−	13.2822i	0.736248	−	0.473158i
$789$	3.06579	+	6.71315i	0.109145	+	0.238995i
$790$	−3.09292	−	3.56942i	−0.110041	−	0.126994i
$791$	1.99741	+	13.8923i	0.0710196	+	0.493952i
$792$	−0.429724	+	0.940965i	−0.0152696	+	0.0334357i
$793$	5.21150	−	1.53023i	0.185066	−	0.0543402i
$794$	22.3496	−	6.56242i	0.793156	−	0.232892i
$795$	−10.2931	+	22.5387i	−0.365058	+	0.799365i
$796$	1.65543	+	11.5138i	0.0586752	+	0.408095i
$797$	−26.6340	−	30.7372i	−0.943423	−	1.08877i	−0.995928	−	0.0901475i	$-0.971266\pi$
$797$	−26.6340	−	30.7372i	−0.943423	−	1.08877i	0.0525055	−	0.998621i	$-0.483279\pi$
$798$	−0.310983	−	0.680958i	−0.0110087	−	0.0241056i
$799$	36.1247	−	23.2160i	1.27800	−	0.821322i
$800$	0.187499	−	1.30408i	0.00662908	−	0.0461063i
$801$	9.80817	+	6.30333i	0.346555	+	0.222717i
$802$	11.8215	−	13.6427i	0.417432	−	0.481742i
$803$	−12.8669	−	3.77808i	−0.454065	−	0.133325i
$804$	8.28337			0.292132
$805$	7.47428	+	5.36962i	0.263434	+	0.189254i
$806$	−8.79667			−0.309850
$807$	21.7038	+	6.37282i	0.764011	+	0.224334i
$808$	−1.23109	+	1.42076i	−0.0433098	+	0.0499821i
$809$	30.2304	+	19.4279i	1.06285	+	0.683049i	0.950533	−	0.310624i	$-0.100538\pi$
$809$	30.2304	+	19.4279i	1.06285	+	0.683049i	0.112312	+	0.993673i	$0.464174\pi$
$810$	−0.273100	+	1.89945i	−0.00959576	+	0.0667400i
$811$	39.8946	−	25.6387i	1.40089	−	0.900298i	0.401015	−	0.916072i	$-0.368658\pi$
$811$	39.8946	−	25.6387i	1.40089	−	0.900298i	0.999876	+	0.0157739i	$0.00502119\pi$
$812$	3.59227	+	7.86598i	0.126064	+	0.276042i
$813$	5.07354	+	5.85518i	0.177937	+	0.205350i
$814$	0.969408	+	6.74238i	0.0339777	+	0.236320i
$815$	−5.10250	+	11.1729i	−0.178733	+	0.391370i
$816$	3.28431	−	0.964362i	0.114974	−	0.0337594i
$817$	0.425453	−	0.124924i	0.0148847	−	0.00437054i
$818$	2.74412	−	6.00879i	0.0959460	−	0.210092i
$819$	−0.318284	−	2.21371i	−0.0111217	−	0.0773535i
$820$	−6.46894	−	7.46556i	−0.225905	−	0.260709i
$821$	−15.6763	−	34.3264i	−0.547108	−	1.19800i	−0.958120	−	0.286369i	$-0.907552\pi$
$821$	−15.6763	−	34.3264i	−0.547108	−	1.19800i	0.411012	−	0.911630i	$-0.365175\pi$
$822$	−4.38669	+	2.81915i	−0.153003	+	0.0983292i
$823$	5.66293	−	39.3865i	0.197397	−	1.37293i	−0.614403	−	0.788993i	$-0.710603\pi$
$823$	5.66293	−	39.3865i	0.197397	−	1.37293i	0.811800	−	0.583936i	$-0.198488\pi$
$824$	4.30511	+	2.76673i	0.149976	+	0.0963834i
$825$	−0.892493	+	1.02999i	−0.0310726	+	0.0358597i
$826$	−4.53612	−	1.33192i	−0.157832	−	0.0463436i
$827$	−23.8051			−0.827785			−0.413893	−	0.910326i	$-0.635831\pi$
$827$	−23.8051			−0.827785			−0.413893	+	0.910326i	$0.635831\pi$
$828$	4.66533	−	1.11118i	0.162131	−	0.0386160i
$829$	−43.8981			−1.52464			−0.762322	−	0.647197i	$-0.775941\pi$
$829$	−43.8981			−1.52464			−0.762322	+	0.647197i	$0.775941\pi$
$830$	26.2245	+	7.70020i	0.910265	+	0.267278i
$831$	13.3520	−	15.4090i	0.463175	−	0.534532i
$832$	−1.88145	−	1.20913i	−0.0652274	−	0.0419191i
$833$	0.487139	−	3.38813i	0.0168784	−	0.117392i
$834$	11.9341	−	7.66960i	0.413245	−	0.265577i
$835$	−11.5318	−	25.2511i	−0.399074	−	0.873849i
$836$	0.507120	+	0.585248i	0.0175391	+	0.0202412i
$837$	−0.559763	−	3.89323i	−0.0193482	−	0.134570i
$838$	8.44146	−	18.4842i	0.291606	−	0.638527i
$839$	−26.4879	+	7.77756i	−0.914465	+	0.268511i	−0.704919	−	0.709288i	$-0.749017\pi$
$839$	−26.4879	+	7.77756i	−0.914465	+	0.268511i	−0.209546	+	0.977799i	$0.567199\pi$
$840$	1.84125	−	0.540641i	0.0635293	−	0.0186539i
$841$	19.0169	−	41.6412i	0.655755	−	1.43590i
$842$	4.35471	+	30.2877i	0.150073	+	1.04378i
$843$	−6.18374	−	7.13642i	−0.212979	−	0.245791i
$844$	9.09963	+	19.9254i	0.313222	+	0.685861i
$845$	−12.9119	+	8.29795i	−0.444182	+	0.285458i
$846$	1.78536	−	12.4174i	0.0613818	−	0.426920i
$847$	8.35358	+	5.36852i	0.287032	+	0.184465i
$848$	8.45552	−	9.75819i	0.290364	−	0.335098i
$849$	−6.27529	−	1.84259i	−0.215367	−	0.0632376i
$850$	4.50974			0.154683
$851$	21.8880	−	22.7643i	0.750312	−	0.780349i
$852$	−10.5893			−0.362783
$853$	26.9474	+	7.91248i	0.922663	+	0.270918i	0.708362	−	0.705850i	$-0.249435\pi$
$853$	26.9474	+	7.91248i	0.922663	+	0.270918i	0.214301	+	0.976768i	$0.431253\pi$
$854$	1.59040	−	1.83541i	0.0544222	−	0.0628066i
$855$	1.20852	+	0.776667i	0.0413304	+	0.0265615i
$856$	1.94140	−	13.5027i	0.0663557	−	0.461514i
$857$	−29.2830	+	18.8190i	−1.00029	+	0.642846i	−0.934862	−	0.355011i	$-0.884477\pi$
$857$	−29.2830	+	18.8190i	−1.00029	+	0.642846i	−0.0654265	+	0.997857i	$0.520841\pi$
$858$	0.961069	+	2.10445i	0.0328104	+	0.0718447i
$859$	29.9666	+	34.5833i	1.02245	+	1.17997i	0.983534	+	0.180723i	$0.0578439\pi$
$859$	29.9666	+	34.5833i	1.02245	+	1.17997i	0.0389124	+	0.999243i	$0.487611\pi$
$860$	0.161762	+	1.12508i	0.00551605	+	0.0383649i
$861$	−2.13843	+	4.68251i	−0.0728775	+	0.159579i
$862$	−18.4427	+	5.41526i	−0.628160	+	0.184444i
$863$	31.9320	−	9.37607i	1.08698	−	0.319165i	0.311310	−	0.950308i	$-0.399232\pi$
$863$	31.9320	−	9.37607i	1.08698	−	0.319165i	0.775666	+	0.631143i	$0.217414\pi$
$864$	0.415415	−	0.909632i	0.0141327	−	0.0309463i
$865$	2.51932	+	17.5223i	0.0856596	+	0.595776i
$866$	−5.76288	−	6.65072i	−0.195831	−	0.226001i
$867$	−2.19475	−	4.80584i	−0.0745378	−	0.163215i
$868$	−3.30888	+	2.12649i	−0.112311	+	0.0721776i
$869$	0.362332	−	2.52007i	0.0122913	−	0.0854876i
$870$	−13.9600	−	8.97156i	−0.473289	−	0.304164i
$871$	12.1317	−	14.0007i	0.411066	−	0.474396i
$872$	−1.25213	−	0.367657i	−0.0424023	−	0.0124504i
$873$	−1.55980			−0.0527912
$874$	0.694174	−	3.52245i	0.0234808	−	0.119149i
$875$	12.1232			0.409838
$876$	12.4385	+	3.65227i	0.420258	+	0.123399i
$877$	−30.0487	+	34.6780i	−1.01467	+	1.17099i	−0.0294749	+	0.999566i	$0.509383\pi$
$877$	−30.0487	+	34.6780i	−1.01467	+	1.17099i	−0.985197	+	0.171428i	$0.945162\pi$
$878$	−5.35036	−	3.43847i	−0.180566	−	0.116043i
$879$	−1.48550	+	10.3319i	−0.0501046	+	0.348485i
$880$	−1.66996	+	1.07322i	−0.0562944	+	0.0361782i
$881$	6.47061	+	14.1687i	0.218000	+	0.477354i	0.986761	−	0.162183i	$-0.0518534\pi$
$881$	6.47061	+	14.1687i	0.218000	+	0.477354i	−0.768760	+	0.639537i	$0.779126\pi$
$882$	−0.654861	−	0.755750i	−0.0220503	−	0.0254474i
$883$	−3.68127	−	25.6038i	−0.123885	−	0.861637i	−0.953089	−	0.302691i	$-0.902115\pi$
$883$	−3.68127	−	25.6038i	−0.123885	−	0.861637i	0.829204	−	0.558946i	$-0.188794\pi$
$884$	3.18017	−	6.96360i	0.106961	−	0.234211i
$885$	8.70475	−	2.55595i	0.292607	−	0.0859172i
$886$	−16.2499	+	4.77141i	−0.545927	+	0.160299i
$887$	2.26713	−	4.96433i	0.0761229	−	0.166686i	−0.867744	−	0.497011i	$-0.834431\pi$
$887$	2.26713	−	4.96433i	0.0761229	−	0.166686i	0.943867	+	0.330325i	$0.107158\pi$
$888$	−0.937128	−	6.51787i	−0.0314479	−	0.218725i
$889$	9.82804	+	11.3422i	0.329622	+	0.380404i
$890$	9.29427	+	20.3516i	0.311545	+	0.682187i
$891$	−0.870231	+	0.559264i	−0.0291538	+	0.0187360i
$892$	−3.24556	+	22.5733i	−0.108669	+	0.755811i
$893$	−7.90053	−	5.07736i	−0.264381	−	0.169907i
$894$	6.98869	−	8.06537i	0.233737	−	0.269746i
$895$	34.6331	+	10.1692i	1.15766	+	0.339919i
$896$	−1.00000			−0.0334077
$897$	4.95463	−	9.51283i	0.165430	−	0.317624i
$898$	13.6124			0.454251
$899$	32.6349	+	9.58248i	1.08844	+	0.319594i
$900$	0.862774	−	0.995695i	0.0287591	−	0.0331898i
$901$	37.1810	+	23.8948i	1.23868	+	0.796051i
$902$	0.757828	−	5.27081i	0.0252329	−	0.175499i
$903$	0.498290	−	0.320231i	0.0165820	−	0.0106566i
$904$	5.83040	+	12.7668i	0.193916	+	0.424618i
$905$	8.82645	+	10.1863i	0.293401	+	0.338603i
$906$	0.253481	+	1.76300i	0.00842135	+	0.0585718i
$907$	−17.4166	+	38.1371i	−0.578310	+	1.26632i	0.363943	+	0.931421i	$0.381430\pi$
$907$	−17.4166	+	38.1371i	−0.578310	+	1.26632i	−0.942253	+	0.334901i	$0.891297\pi$
$908$	−23.1362	+	6.79340i	−0.767801	+	0.225447i
$909$	−1.80378	+	0.529639i	−0.0598277	+	0.0175670i
$910$	1.78287	−	3.90393i	0.0591014	−	0.129414i
$911$	−3.18509	−	22.1528i	−0.105527	−	0.733955i	−0.972042	−	0.234805i	$-0.924555\pi$
$911$	−3.18509	−	22.1528i	−0.105527	−	0.733955i	0.866516	−	0.499150i	$-0.166354\pi$
$912$	−0.490234	−	0.565760i	−0.0162333	−	0.0187342i
$913$	6.12045	+	13.4019i	0.202557	+	0.443539i
$914$	−1.78917	+	1.14983i	−0.0591804	+	0.0380329i
$915$	−0.663251	+	4.61302i	−0.0219264	+	0.152502i
$916$	10.7977	+	6.93923i	0.356764	+	0.229279i
$917$	−9.20466	+	10.6227i	−0.303965	+	0.350794i
$918$	3.28431	+	0.964362i	0.108399	+	0.0318287i
$919$	−16.0216			−0.528503			−0.264252	−	0.964454i	$-0.585125\pi$
$919$	−16.0216			−0.528503			−0.264252	+	0.964454i	$0.585125\pi$
$920$	8.68431	+	3.04637i	0.286313	+	0.100436i
$921$	−16.0978			−0.530442
$922$	26.5839	+	7.80575i	0.875495	+	0.257069i
$923$	−15.5089	+	17.8982i	−0.510482	+	0.589127i
$924$	0.870231	+	0.559264i	0.0286285	+	0.0183984i
$925$	1.23466	−	8.58724i	0.0405953	−	0.282347i
$926$	12.0644	−	7.75331i	0.396460	−	0.254789i
$927$	2.12588	+	4.65503i	0.0698232	+	0.152891i
$928$	5.66286	+	6.53529i	0.185893	+	0.214532i
$929$	−8.25729	−	57.4307i	−0.270913	−	1.88424i	−0.439027	−	0.898474i	$-0.644677\pi$
$929$	−8.25729	−	57.4307i	−0.270913	−	1.88424i	0.168114	−	0.985768i	$-0.446232\pi$
$930$	3.13551	−	6.86580i	0.102817	−	0.225139i
$931$	−0.718284	+	0.210907i	−0.0235408	+	0.00691220i
$932$	−10.9139	+	3.20462i	−0.357498	+	0.104971i
$933$	−12.0294	+	26.3406i	−0.393824	+	0.862354i
$934$	1.90442	+	13.2455i	0.0623144	+	0.433406i
$935$	−4.44971	−	5.13524i	−0.145521	−	0.167940i
$936$	−0.929067	−	2.03437i	−0.0303675	−	0.0664956i
$937$	24.8567	−	15.9744i	0.812032	−	0.521861i	−0.0674896	−	0.997720i	$-0.521499\pi$
$937$	24.8567	−	15.9744i	0.812032	−	0.521861i	0.879522	+	0.475859i	$0.157863\pi$
$938$	1.17885	−	8.19906i	0.0384907	−	0.267709i
$939$	−9.03558	−	5.80681i	−0.294865	−	0.189498i
$940$	15.7651	−	18.1938i	0.514200	−	0.593418i
$941$	29.5620	+	8.68019i	0.963694	+	0.282966i	0.725477	−	0.688246i	$-0.241619\pi$
$941$	29.5620	+	8.68019i	0.963694	+	0.282966i	0.238217	+	0.971212i	$0.423437\pi$
$942$	12.4715			0.406344
$943$	−21.4314	+	12.2543i	−0.697901	+	0.399055i
$944$	−4.72762			−0.153871
$945$	1.84125	+	0.540641i	0.0598960	+	0.0175870i
$946$	−0.401247	+	0.463064i	−0.0130457	+	0.0150555i
$947$	34.9575	+	22.4658i	1.13597	+	0.730042i	0.966797	−	0.255545i	$-0.0822549\pi$
$947$	34.9575	+	22.4658i	1.13597	+	0.730042i	0.169170	+	0.985587i	$0.445891\pi$
$948$	−0.350267	+	2.43616i	−0.0113761	+	0.0791227i
$949$	24.3903	−	15.6747i	0.791744	−	0.508823i
$950$	−0.409718	−	0.897157i	−0.0132930	−	0.0291076i
$951$	1.78203	+	2.05657i	0.0577862	+	0.0666888i
$952$	−0.487139	−	3.38813i	−0.0157883	−	0.109810i
$953$	−5.95456	+	13.0387i	−0.192887	+	0.422364i	−0.981222	−	0.192883i	$-0.938216\pi$
$953$	−5.95456	+	13.0387i	−0.192887	+	0.422364i	0.788335	+	0.615246i	$0.210944\pi$
$954$	12.3889	−	3.63771i	0.401106	−	0.117775i
$955$	−4.37539	+	1.28473i	−0.141584	+	0.0415729i
$956$	−4.80479	+	10.5210i	−0.155398	+	0.340274i
$957$	−1.27305	−	8.85425i	−0.0411518	−	0.286217i
$958$	−9.19863	−	10.6158i	−0.297194	−	0.342981i
$959$	2.16617	+	4.74324i	0.0699492	+	0.153167i
$960$	1.61435	−	1.03748i	0.0521030	−	0.0334846i
$961$	2.21006	−	15.3713i	0.0712923	−	0.495849i
$962$	−12.3891	−	7.96200i	−0.399441	−	0.256705i
$963$	8.93334	−	10.3096i	0.287873	−	0.332223i
$964$	2.57994	+	0.757539i	0.0830943	+	0.0243987i
$965$	−0.565300			−0.0181977
$966$	−0.435919	−	4.77598i	−0.0140255	−	0.153665i
$967$	−47.2341			−1.51895			−0.759473	−	0.650539i	$-0.774543\pi$
$967$	−47.2341			−1.51895			−0.759473	+	0.650539i	$0.774543\pi$
$968$	9.52769	+	2.79758i	0.306232	+	0.0899177i
$969$	1.67806	−	1.93658i	0.0539069	−	0.0622119i
$970$	−2.51807	−	1.61826i	−0.0808503	−	0.0519593i
$971$	−7.96401	+	55.3909i	−0.255577	+	1.77758i	0.307871	+	0.951428i	$0.400384\pi$
$971$	−7.96401	+	55.3909i	−0.255577	+	1.77758i	−0.563448	+	0.826152i	$0.690525\pi$
$972$	0.841254	−	0.540641i	0.0269832	−	0.0173411i
$973$	−5.89313	−	12.9042i	−0.188925	−	0.413688i
$974$	14.9769	+	17.2842i	0.479889	+	0.553822i
$975$	−0.419337	−	2.91655i	−0.0134295	−	0.0934045i
$976$	1.00888	−	2.20913i	0.0322934	−	0.0707126i
$977$	41.1177	−	12.0732i	1.31547	−	0.386257i	0.452615	−	0.891706i	$-0.350491\pi$
$977$	41.1177	−	12.0732i	1.31547	−	0.386257i	0.862857	+	0.505448i	$0.168673\pi$
$978$	6.14144	−	1.80329i	0.196382	−	0.0576629i
$979$	−5.01015	+	10.9707i	−0.160125	+	0.350625i
$980$	−0.273100	−	1.89945i	−0.00872387	−	0.0606758i
$981$	−0.854584	−	0.986243i	−0.0272848	−	0.0314883i
$982$	−1.56175	−	3.41976i	−0.0498375	−	0.109129i
$983$	46.7213	−	30.0260i	1.49018	−	0.957680i	0.494082	−	0.869415i	$-0.335504\pi$
$983$	46.7213	−	30.0260i	1.49018	−	0.957680i	0.996097	−	0.0882646i	$-0.0281321\pi$
$984$	−0.732593	+	5.09530i	−0.0233542	+	0.162432i
$985$	39.6606	+	25.4883i	1.26369	+	0.812125i
$986$	−19.3838	+	22.3701i	−0.617306	+	0.712409i
$987$	−12.0370	−	3.53437i	−0.383140	−	0.112500i
$988$	−1.67425			−0.0532648
$989$	2.83685	+	0.147019i	0.0902066	+	0.00467495i
$990$	−1.98509			−0.0630902
$991$	−53.3731	−	15.6717i	−1.69545	−	0.497829i	−0.715761	−	0.698346i	$-0.753920\pi$
$991$	−53.3731	−	15.6717i	−1.69545	−	0.497829i	−0.979690	+	0.200516i	$0.935738\pi$
$992$	−2.57574	+	2.97257i	−0.0817799	+	0.0943791i
$993$	2.74039	+	1.76114i	0.0869636	+	0.0558881i
$994$	−1.50701	+	10.4815i	−0.0477996	+	0.332453i
$995$	−18.7784	+	12.0682i	−0.595316	+	0.382587i
$996$	−5.91665	−	12.9556i	−0.187476	−	0.410515i
$997$	−15.5121	−	17.9019i	−0.491273	−	0.566959i	0.454933	−	0.890526i	$-0.349663\pi$
$997$	−15.5121	−	17.9019i	−0.491273	−	0.566959i	−0.946205	+	0.323567i	$0.895118\pi$
$998$	1.63604	+	11.3789i	0.0517881	+	0.360194i
$999$	2.73546	−	5.98983i	0.0865462	−	0.189510i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.b.547.1	✓	10
23.9	even	11	inner	966.2.q.b.883.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.b.547.1	✓	10	1.1	even	1	trivial
966.2.q.b.883.1	yes	10	23.9	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.273100 + 1.89945i) q^{5} +(0.841254 - 0.540641i) q^{6} +(-0.415415 - 0.909632i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.273100 + 1.89945i) q^{5} +(0.841254 - 0.540641i) q^{6} +(-0.415415 - 0.909632i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.797176 - 1.74557i) q^{10} +(0.992543 - 0.291437i) q^{11} +(-0.959493 + 0.281733i) q^{12} +(-0.929067 + 2.03437i) q^{13} +(0.142315 + 0.989821i) q^{14} +(-1.25667 - 1.45027i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-2.87958 + 1.85060i) q^{17} +(-0.142315 + 0.989821i) q^{18} +(0.629769 + 0.404728i) q^{19} +(-1.25667 + 1.45027i) q^{20} +(0.959493 + 0.281733i) q^{21} -1.03445 q^{22} +(2.94881 + 3.78213i) q^{23} +1.00000 q^{24} +(1.26413 + 0.371181i) q^{25} +(1.46458 - 1.69022i) q^{26} +(0.841254 + 0.540641i) q^{27} +(0.142315 - 0.989821i) q^{28} +(-7.27468 + 4.67515i) q^{29} +(0.797176 + 1.74557i) q^{30} +(-2.57574 - 2.97257i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(-0.429724 + 0.940965i) q^{33} +(3.28431 - 0.964362i) q^{34} +(1.84125 - 0.540641i) q^{35} +(0.415415 - 0.909632i) q^{36} +(-0.937128 - 6.51787i) q^{37} +(-0.490234 - 0.565760i) q^{38} +(-0.929067 - 2.03437i) q^{39} +(1.61435 - 1.03748i) q^{40} +(-0.732593 + 5.09530i) q^{41} +(-0.841254 - 0.540641i) q^{42} +(0.387886 - 0.447644i) q^{43} +(0.992543 + 0.291437i) q^{44} +1.91899 q^{45} +(-1.76381 - 4.45971i) q^{46} -12.5451 q^{47} +(-0.959493 - 0.281733i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(-1.10835 - 0.712290i) q^{50} +(0.487139 - 3.38813i) q^{51} +(-1.88145 + 1.20913i) q^{52} +(-5.36381 - 11.7451i) q^{53} +(-0.654861 - 0.755750i) q^{54} +(0.282507 + 1.96488i) q^{55} +(-0.415415 + 0.909632i) q^{56} +(-0.718284 + 0.210907i) q^{57} +(8.29715 - 2.43626i) q^{58} +(-1.96392 + 4.30040i) q^{59} +(-0.273100 - 1.89945i) q^{60} +(-1.59040 - 1.83541i) q^{61} +(1.63394 + 3.57783i) q^{62} +(-0.841254 + 0.540641i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-3.61047 - 2.32031i) q^{65} +(0.677418 - 0.781782i) q^{66} +(-7.94784 - 2.33370i) q^{67} -3.42297 q^{68} +(-4.78940 - 0.248210i) q^{69} -1.91899 q^{70} +(10.1604 + 2.98335i) q^{71} +(-0.654861 + 0.755750i) q^{72} +(-10.9057 - 7.00866i) q^{73} +(-0.937128 + 6.51787i) q^{74} +(-1.10835 + 0.712290i) q^{75} +(0.310983 + 0.680958i) q^{76} +(-0.677418 - 0.781782i) q^{77} +(0.318284 + 2.21371i) q^{78} +(1.02242 - 2.23879i) q^{79} +(-1.84125 + 0.540641i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(2.13843 - 4.68251i) q^{82} +(2.02695 + 14.0978i) q^{83} +(0.654861 + 0.755750i) q^{84} +(-2.72871 - 5.97504i) q^{85} +(-0.498290 + 0.320231i) q^{86} +(1.23066 - 8.55941i) q^{87} +(-0.870231 - 0.559264i) q^{88} +(-7.63502 + 8.81128i) q^{89} +(-1.84125 - 0.540641i) q^{90} +2.23648 q^{91} +(0.435919 + 4.77598i) q^{92} +3.93327 q^{93} +(12.0370 + 3.53437i) q^{94} +(-0.940752 + 1.08569i) q^{95} +(0.841254 + 0.540641i) q^{96} +(0.221983 - 1.54392i) q^{97} +(0.841254 - 0.540641i) q^{98} +(-0.429724 - 0.940965i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{3} - q^{4} + 2 q^{5} - q^{6} + q^{7} - q^{8} - q^{9}+O(q^{10}) \) 10 * q - q^2 - q^3 - q^4 + 2 * q^5 - q^6 + q^7 - q^8 - q^9	\( 10 q - q^{2} - q^{3} - q^{4} + 2 q^{5} - q^{6} + q^{7} - q^{8} - q^{9} + 2 q^{10} + 7 q^{11} - q^{12} - 2 q^{13} + q^{14} + 2 q^{15} - q^{16} - 6 q^{17} - q^{18} + 11 q^{19} + 2 q^{20} + q^{21} + 18 q^{22} + 21 q^{23} + 10 q^{24} + q^{25} - 2 q^{26} - q^{27} + q^{28} - 20 q^{29} + 2 q^{30} + 18 q^{31} - q^{32} - 15 q^{33} + 5 q^{34} + 9 q^{35} - q^{36} + 5 q^{37} - 22 q^{38} - 2 q^{39} + 2 q^{40} + 6 q^{41} + q^{42} - 12 q^{43} + 7 q^{44} + 2 q^{45} + 21 q^{46} - 32 q^{47} - q^{48} - q^{49} + 12 q^{50} - 17 q^{51} + 9 q^{52} - 39 q^{53} - q^{54} + 8 q^{55} + q^{56} + 22 q^{57} + 13 q^{58} + 15 q^{59} + 2 q^{60} + 21 q^{61} - 4 q^{62} + q^{63} - q^{64} - 7 q^{65} - 4 q^{66} - 26 q^{67} - 6 q^{68} - 12 q^{69} - 2 q^{70} + 27 q^{71} - q^{72} - 2 q^{73} + 5 q^{74} + 12 q^{75} + 4 q^{77} - 2 q^{78} + 47 q^{79} - 9 q^{80} - q^{81} + 6 q^{82} + 5 q^{83} + q^{84} + q^{85} - 12 q^{86} - 9 q^{87} - 4 q^{88} + 5 q^{89} - 9 q^{90} + 24 q^{91} + 10 q^{92} - 26 q^{93} + 23 q^{94} - 11 q^{95} - q^{96} + 2 q^{97} - q^{98} - 15 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^3 - q^4 + 2 * q^5 - q^6 + q^7 - q^8 - q^9 + 2 * q^10 + 7 * q^11 - q^12 - 2 * q^13 + q^14 + 2 * q^15 - q^16 - 6 * q^17 - q^18 + 11 * q^19 + 2 * q^20 + q^21 + 18 * q^22 + 21 * q^23 + 10 * q^24 + q^25 - 2 * q^26 - q^27 + q^28 - 20 * q^29 + 2 * q^30 + 18 * q^31 - q^32 - 15 * q^33 + 5 * q^34 + 9 * q^35 - q^36 + 5 * q^37 - 22 * q^38 - 2 * q^39 + 2 * q^40 + 6 * q^41 + q^42 - 12 * q^43 + 7 * q^44 + 2 * q^45 + 21 * q^46 - 32 * q^47 - q^48 - q^49 + 12 * q^50 - 17 * q^51 + 9 * q^52 - 39 * q^53 - q^54 + 8 * q^55 + q^56 + 22 * q^57 + 13 * q^58 + 15 * q^59 + 2 * q^60 + 21 * q^61 - 4 * q^62 + q^63 - q^64 - 7 * q^65 - 4 * q^66 - 26 * q^67 - 6 * q^68 - 12 * q^69 - 2 * q^70 + 27 * q^71 - q^72 - 2 * q^73 + 5 * q^74 + 12 * q^75 + 4 * q^77 - 2 * q^78 + 47 * q^79 - 9 * q^80 - q^81 + 6 * q^82 + 5 * q^83 + q^84 + q^85 - 12 * q^86 - 9 * q^87 - 4 * q^88 + 5 * q^89 - 9 * q^90 + 24 * q^91 + 10 * q^92 - 26 * q^93 + 23 * q^94 - 11 * q^95 - q^96 + 2 * q^97 - q^98 - 15 * q^99

Introduction

L-functions

Modular forms

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