LMFDB - Embedded newform 690.2.j.a.643.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(367,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("690.367");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.j (of order $4$, degree $2$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			643.5
Character	$\chi$	$=$	690.643
Dual form			690.2.j.a.367.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(0.899538 - 2.04715i) q^{5} -1.00000 q^{6} +(1.80902 + 1.80902i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(0.899538 - 2.04715i) q^{5} -1.00000 q^{6} +(1.80902 + 1.80902i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(0.811485 + 2.08362i) q^{10} +4.16725i q^{11} +(0.707107 - 0.707107i) q^{12} +(-3.18894 - 3.18894i) q^{13} -2.55834 q^{14} +(2.08362 - 0.811485i) q^{15} -1.00000 q^{16} +(1.68449 + 1.68449i) q^{17} +(-0.707107 - 0.707107i) q^{18} +5.24101 q^{19} +(-2.04715 - 0.899538i) q^{20} +2.55834i q^{21} +(-2.94669 - 2.94669i) q^{22} +(1.98398 + 4.36621i) q^{23} +1.00000i q^{24} +(-3.38166 - 3.68298i) q^{25} +4.50985 q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.80902 - 1.80902i) q^{28} -3.48107i q^{29} +(-0.899538 + 2.04715i) q^{30} +7.27142 q^{31} +(0.707107 - 0.707107i) q^{32} +(-2.94669 + 2.94669i) q^{33} -2.38223 q^{34} +(5.33061 - 2.07605i) q^{35} +1.00000 q^{36} +(5.46339 + 5.46339i) q^{37} +(-3.70595 + 3.70595i) q^{38} -4.50985i q^{39} +(2.08362 - 0.811485i) q^{40} +4.53754 q^{41} +(-1.80902 - 1.80902i) q^{42} +(6.37868 - 6.37868i) q^{43} +4.16725 q^{44} +(2.04715 + 0.899538i) q^{45} +(-4.49027 - 1.68449i) q^{46} +(-9.09342 + 9.09342i) q^{47} +(-0.707107 - 0.707107i) q^{48} -0.454913i q^{49} +(4.99546 + 0.213067i) q^{50} +2.38223i q^{51} +(-3.18894 + 3.18894i) q^{52} +(-6.56472 + 6.56472i) q^{53} -1.00000i q^{54} +(8.53099 + 3.74860i) q^{55} +2.55834i q^{56} +(3.70595 + 3.70595i) q^{57} +(2.46149 + 2.46149i) q^{58} -6.80402i q^{59} +(-0.811485 - 2.08362i) q^{60} -0.759260i q^{61} +(-5.14167 + 5.14167i) q^{62} +(-1.80902 + 1.80902i) q^{63} +1.00000i q^{64} +(-9.39683 + 3.65967i) q^{65} -4.16725i q^{66} +(2.02126 + 2.02126i) q^{67} +(1.68449 - 1.68449i) q^{68} +(-1.68449 + 4.49027i) q^{69} +(-2.30132 + 5.23730i) q^{70} -9.56406 q^{71} +(-0.707107 + 0.707107i) q^{72} +(-5.78239 - 5.78239i) q^{73} -7.72640 q^{74} +(0.213067 - 4.99546i) q^{75} -5.24101i q^{76} +(-7.53863 + 7.53863i) q^{77} +(3.18894 + 3.18894i) q^{78} -6.84964 q^{79} +(-0.899538 + 2.04715i) q^{80} -1.00000 q^{81} +(-3.20853 + 3.20853i) q^{82} +(-2.40890 + 2.40890i) q^{83} +2.55834 q^{84} +(4.96367 - 1.93314i) q^{85} +9.02081i q^{86} +(2.46149 - 2.46149i) q^{87} +(-2.94669 + 2.94669i) q^{88} -3.58782 q^{89} +(-2.08362 + 0.811485i) q^{90} -11.5377i q^{91} +(4.36621 - 1.98398i) q^{92} +(5.14167 + 5.14167i) q^{93} -12.8600i q^{94} +(4.71449 - 10.7291i) q^{95} +1.00000 q^{96} +(4.03278 + 4.03278i) q^{97} +(0.321672 + 0.321672i) q^{98} -4.16725 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{6}+O(q^{10}) $ 24 * q - 24 * q^6	$ 24 q - 24 q^{6} - 24 q^{16} - 8 q^{23} - 16 q^{25} - 16 q^{26} + 16 q^{31} - 16 q^{35} + 24 q^{36} - 8 q^{46} - 8 q^{47} + 24 q^{50} + 24 q^{55} + 16 q^{58} - 56 q^{62} - 32 q^{70} - 16 q^{71} - 48 q^{73} - 24 q^{81} + 24 q^{82} + 16 q^{87} - 8 q^{92} + 56 q^{93} + 24 q^{95} + 24 q^{96} - 32 q^{98}+O(q^{100}) $ 24 * q - 24 * q^6 - 24 * q^16 - 8 * q^23 - 16 * q^25 - 16 * q^26 + 16 * q^31 - 16 * q^35 + 24 * q^36 - 8 * q^46 - 8 * q^47 + 24 * q^50 + 24 * q^55 + 16 * q^58 - 56 * q^62 - 32 * q^70 - 16 * q^71 - 48 * q^73 - 24 * q^81 + 24 * q^82 + 16 * q^87 - 8 * q^92 + 56 * q^93 + 24 * q^95 + 24 * q^96 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	0.899538	−	2.04715i	0.402286	−	0.915514i
$5$	0.899538	−	2.04715i	0.402286	−	0.915514i
$6$	−1.00000			−0.408248
$7$	1.80902	+	1.80902i	0.683744	+	0.683744i	0.960842	−	0.277098i	$-0.0893725\pi$
$7$	1.80902	+	1.80902i	0.683744	+	0.683744i	−0.277098	+	0.960842i	$0.589373\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$			1.00000i			0.333333i
$10$	0.811485	+	2.08362i	0.256614	+	0.658900i
$11$			4.16725i			1.25647i	0.778022	+	0.628236i	$0.216223\pi$
$11$			4.16725i			1.25647i	−0.778022	+	0.628236i	$0.783777\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	−3.18894	−	3.18894i	−0.884454	−	0.884454i	0.109530	−	0.993984i	$-0.465066\pi$
$13$	−3.18894	−	3.18894i	−0.884454	−	0.884454i	−0.993984	+	0.109530i	$0.965066\pi$
$14$	−2.55834			−0.683744
$15$	2.08362	−	0.811485i	0.537990	−	0.209525i
$16$	−1.00000			−0.250000
$17$	1.68449	+	1.68449i	0.408549	+	0.408549i	0.881232	−	0.472683i	$-0.156715\pi$
$17$	1.68449	+	1.68449i	0.408549	+	0.408549i	−0.472683	+	0.881232i	$0.656715\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	5.24101			1.20237			0.601185	−	0.799110i	$-0.294696\pi$
$19$	5.24101			1.20237			0.601185	+	0.799110i	$0.294696\pi$
$20$	−2.04715	−	0.899538i	−0.457757	−	0.201143i
$21$			2.55834i			0.558275i
$22$	−2.94669	−	2.94669i	−0.628236	−	0.628236i
$23$	1.98398	+	4.36621i	0.413689	+	0.910418i
$23$	1.98398	+	4.36621i	0.413689	+	0.910418i
$24$			1.00000i			0.204124i
$25$	−3.38166	−	3.68298i	−0.676332	−	0.736597i
$26$	4.50985			0.884454
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	1.80902	−	1.80902i	0.341872	−	0.341872i
$29$		−	3.48107i		−	0.646418i	−0.946328	−	0.323209i	$-0.895238\pi$
$29$		−	3.48107i		−	0.646418i	0.946328	−	0.323209i	$-0.104762\pi$
$30$	−0.899538	+	2.04715i	−0.164232	+	0.373757i
$31$	7.27142			1.30599			0.652993	−	0.757364i	$-0.273513\pi$
$31$	7.27142			1.30599			0.652993	+	0.757364i	$0.273513\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−2.94669	+	2.94669i	−0.512953	+	0.512953i
$34$	−2.38223			−0.408549
$35$	5.33061	−	2.07605i	0.901038	−	0.350917i
$36$	1.00000			0.166667
$37$	5.46339	+	5.46339i	0.898175	+	0.898175i	0.995275	−	0.0970994i	$-0.0309565\pi$
$37$	5.46339	+	5.46339i	0.898175	+	0.898175i	−0.0970994	+	0.995275i	$0.530956\pi$
$38$	−3.70595	+	3.70595i	−0.601185	+	0.601185i
$39$		−	4.50985i		−	0.722154i
$40$	2.08362	−	0.811485i	0.329450	−	0.128307i
$41$	4.53754			0.708645			0.354322	−	0.935123i	$-0.384712\pi$
$41$	4.53754			0.708645			0.354322	+	0.935123i	$0.384712\pi$
$42$	−1.80902	−	1.80902i	−0.279137	−	0.279137i
$43$	6.37868	−	6.37868i	0.972739	−	0.972739i	−0.0268989	−	0.999638i	$-0.508563\pi$
$43$	6.37868	−	6.37868i	0.972739	−	0.972739i	0.999638	+	0.0268989i	$0.00856321\pi$
$44$	4.16725			0.628236
$45$	2.04715	+	0.899538i	0.305171	+	0.134095i
$46$	−4.49027	−	1.68449i	−0.662054	−	0.248365i
$47$	−9.09342	+	9.09342i	−1.32641	+	1.32641i	−0.417935	+	0.908477i	$0.637246\pi$
$47$	−9.09342	+	9.09342i	−1.32641	+	1.32641i	−0.908477	+	0.417935i	$0.862754\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$		−	0.454913i		−	0.0649875i
$50$	4.99546	+	0.213067i	0.706464	+	0.0301322i
$51$			2.38223i			0.333579i
$52$	−3.18894	+	3.18894i	−0.442227	+	0.442227i
$53$	−6.56472	+	6.56472i	−0.901734	+	0.901734i	−0.995586	−	0.0938519i	$-0.970082\pi$
$53$	−6.56472	+	6.56472i	−0.901734	+	0.901734i	0.0938519	+	0.995586i	$0.470082\pi$
$54$		−	1.00000i		−	0.136083i
$55$	8.53099	+	3.74860i	1.15032	+	0.505461i
$56$			2.55834i			0.341872i
$57$	3.70595	+	3.70595i	0.490865	+	0.490865i
$58$	2.46149	+	2.46149i	0.323209	+	0.323209i
$59$		−	6.80402i		−	0.885808i	−0.896569	−	0.442904i	$-0.853948\pi$
$59$		−	6.80402i		−	0.885808i	0.896569	−	0.442904i	$-0.146052\pi$
$60$	−0.811485	−	2.08362i	−0.104762	−	0.268995i
$61$		−	0.759260i		−	0.0972133i	−0.998818	−	0.0486066i	$-0.984522\pi$
$61$		−	0.759260i		−	0.0972133i	0.998818	−	0.0486066i	$-0.0154781\pi$
$62$	−5.14167	+	5.14167i	−0.652993	+	0.652993i
$63$	−1.80902	+	1.80902i	−0.227915	+	0.227915i
$64$			1.00000i			0.125000i
$65$	−9.39683	+	3.65967i	−1.16553	+	0.453927i
$66$		−	4.16725i		−	0.512953i
$67$	2.02126	+	2.02126i	0.246937	+	0.246937i	0.819712	−	0.572776i	$-0.194133\pi$
$67$	2.02126	+	2.02126i	0.246937	+	0.246937i	−0.572776	+	0.819712i	$0.694133\pi$
$68$	1.68449	−	1.68449i	0.204275	−	0.204275i
$69$	−1.68449	+	4.49027i	−0.202789	+	0.540565i
$70$	−2.30132	+	5.23730i	−0.275061	+	0.625978i
$71$	−9.56406			−1.13504			−0.567522	−	0.823358i	$-0.692098\pi$
$71$	−9.56406			−1.13504			−0.567522	+	0.823358i	$0.692098\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	−5.78239	−	5.78239i	−0.676778	−	0.676778i	0.282492	−	0.959270i	$-0.408839\pi$
$73$	−5.78239	−	5.78239i	−0.676778	−	0.676778i	−0.959270	+	0.282492i	$0.908839\pi$
$74$	−7.72640			−0.898175
$75$	0.213067	−	4.99546i	0.0246029	−	0.576826i
$76$		−	5.24101i		−	0.601185i
$77$	−7.53863	+	7.53863i	−0.859106	+	0.859106i
$78$	3.18894	+	3.18894i	0.361077	+	0.361077i
$79$	−6.84964			−0.770645			−0.385322	−	0.922782i	$-0.625910\pi$
$79$	−6.84964			−0.770645			−0.385322	+	0.922782i	$0.625910\pi$
$80$	−0.899538	+	2.04715i	−0.100571	+	0.228879i
$81$	−1.00000			−0.111111
$82$	−3.20853	+	3.20853i	−0.354322	+	0.354322i
$83$	−2.40890	+	2.40890i	−0.264411	+	0.264411i	−0.826843	−	0.562432i	$-0.809866\pi$
$83$	−2.40890	+	2.40890i	−0.264411	+	0.264411i	0.562432	+	0.826843i	$0.309866\pi$
$84$	2.55834			0.279137
$85$	4.96367	−	1.93314i	0.538386	−	0.209679i
$86$			9.02081i			0.972739i
$87$	2.46149	−	2.46149i	0.263899	−	0.263899i
$88$	−2.94669	+	2.94669i	−0.314118	+	0.314118i
$89$	−3.58782			−0.380308			−0.190154	−	0.981754i	$-0.560899\pi$
$89$	−3.58782			−0.380308			−0.190154	+	0.981754i	$0.560899\pi$
$90$	−2.08362	+	0.811485i	−0.219633	+	0.0855381i
$91$		−	11.5377i		−	1.20948i
$92$	4.36621	−	1.98398i	0.455209	−	0.206844i
$93$	5.14167	+	5.14167i	0.533166	+	0.533166i
$94$		−	12.8600i		−	1.32641i
$95$	4.71449	−	10.7291i	0.483696	−	1.10079i
$96$	1.00000			0.102062
$97$	4.03278	+	4.03278i	0.409467	+	0.409467i	0.881553	−	0.472086i	$-0.156499\pi$
$97$	4.03278	+	4.03278i	0.409467	+	0.409467i	−0.472086	+	0.881553i	$0.656499\pi$
$98$	0.321672	+	0.321672i	0.0324938	+	0.0324938i
$99$	−4.16725			−0.418824
$100$	−3.68298	+	3.38166i	−0.368298	+	0.338166i
$101$	6.36488			0.633329			0.316665	−	0.948538i	$-0.397437\pi$
$101$	6.36488			0.633329			0.316665	+	0.948538i	$0.397437\pi$
$102$	−1.68449	−	1.68449i	−0.166789	−	0.166789i
$103$	1.99918	−	1.99918i	0.196985	−	0.196985i	−0.601721	−	0.798706i	$-0.705518\pi$
$103$	1.99918	−	1.99918i	0.196985	−	0.196985i	0.798706	+	0.601721i	$0.205518\pi$
$104$		−	4.50985i		−	0.442227i
$105$	5.23730	+	2.30132i	0.511109	+	0.224586i
$106$		−	9.28392i		−	0.901734i
$107$	6.26821	+	6.26821i	0.605971	+	0.605971i	0.941891	−	0.335920i	$-0.109047\pi$
$107$	6.26821	+	6.26821i	0.605971	+	0.605971i	−0.335920	+	0.941891i	$0.609047\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$	1.53597			0.147119			0.0735595	−	0.997291i	$-0.476564\pi$
$109$	1.53597			0.147119			0.0735595	+	0.997291i	$0.476564\pi$
$110$	−8.68298	+	3.38166i	−0.827890	+	0.322429i
$111$			7.72640i			0.733357i
$112$	−1.80902	−	1.80902i	−0.170936	−	0.170936i
$113$	14.0619	−	14.0619i	1.32283	−	1.32283i	0.411360	−	0.911473i	$-0.365054\pi$
$113$	14.0619	−	14.0619i	1.32283	−	1.32283i	0.911473	−	0.411360i	$-0.134946\pi$
$114$	−5.24101			−0.490865
$115$	10.7230	−	0.133937i	0.999922	−	0.0124897i
$116$	−3.48107			−0.323209
$117$	3.18894	−	3.18894i	0.294818	−	0.294818i
$118$	4.81117	+	4.81117i	0.442904	+	0.442904i
$119$			6.09455i			0.558686i
$120$	2.04715	+	0.899538i	0.186879	+	0.0821162i
$121$	−6.36597			−0.578724
$122$	0.536878	+	0.536878i	0.0486066	+	0.0486066i
$123$	3.20853	+	3.20853i	0.289303	+	0.289303i
$124$		−	7.27142i		−	0.652993i
$125$	−10.5816	+	3.60979i	−0.946444	+	0.322869i
$126$		−	2.55834i		−	0.227915i
$127$	−7.12493	+	7.12493i	−0.632235	+	0.632235i	−0.948628	−	0.316393i	$-0.897528\pi$
$127$	−7.12493	+	7.12493i	−0.632235	+	0.632235i	0.316393	+	0.948628i	$0.397528\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	9.02081			0.794238
$130$	4.05678	−	9.23234i	0.355803	−	0.809730i
$131$	1.98524			0.173451			0.0867257	−	0.996232i	$-0.472360\pi$
$131$	1.98524			0.173451			0.0867257	+	0.996232i	$0.472360\pi$
$132$	2.94669	+	2.94669i	0.256476	+	0.256476i
$133$	9.48107	+	9.48107i	0.822113	+	0.822113i
$134$	−2.85850			−0.246937
$135$	0.811485	+	2.08362i	0.0698415	+	0.179330i
$136$			2.38223i			0.204275i
$137$	−13.6901	−	13.6901i	−1.16962	−	1.16962i	−0.982298	−	0.187325i	$-0.940018\pi$
$137$	−13.6901	−	13.6901i	−1.16962	−	1.16962i	−0.187325	−	0.982298i	$-0.559982\pi$
$138$	−1.98398	−	4.36621i	−0.168888	−	0.371677i
$139$		−	19.4321i		−	1.64821i	−0.566438	−	0.824104i	$-0.691679\pi$
$139$		−	19.4321i		−	1.64821i	0.566438	−	0.824104i	$-0.308321\pi$
$140$	−2.07605	−	5.33061i	−0.175458	−	0.450519i
$141$	−12.8600			−1.08301
$142$	6.76281	−	6.76281i	0.567522	−	0.567522i
$143$	13.2891	−	13.2891i	1.11129	−	1.11129i
$144$		−	1.00000i		−	0.0833333i
$145$	−7.12628	−	3.13136i	−0.591805	−	0.260045i
$146$	8.17754			0.676778
$147$	0.321672	−	0.321672i	0.0265310	−	0.0265310i
$148$	5.46339	−	5.46339i	0.449088	−	0.449088i
$149$	3.37276			0.276307			0.138154	−	0.990411i	$-0.455883\pi$
$149$	3.37276			0.276307			0.138154	+	0.990411i	$0.455883\pi$
$150$	3.38166	+	3.68298i	0.276111	+	0.300714i
$151$	−18.7035			−1.52207			−0.761035	−	0.648710i	$-0.775309\pi$
$151$	−18.7035			−1.52207			−0.761035	+	0.648710i	$0.775309\pi$
$152$	3.70595	+	3.70595i	0.300592	+	0.300592i
$153$	−1.68449	+	1.68449i	−0.136183	+	0.136183i
$154$		−	10.6612i		−	0.859106i
$155$	6.54092	−	14.8857i	0.525379	−	1.19565i
$156$	−4.50985			−0.361077
$157$	−11.8389	−	11.8389i	−0.944844	−	0.944844i	0.0537126	−	0.998556i	$-0.482895\pi$
$157$	−11.8389	−	11.8389i	−0.944844	−	0.944844i	−0.998556	+	0.0537126i	$0.982895\pi$
$158$	4.84343	−	4.84343i	0.385322	−	0.385322i
$159$	−9.28392			−0.736263
$160$	−0.811485	−	2.08362i	−0.0641535	−	0.164725i
$161$	−4.30950	+	11.4876i	−0.339636	+	0.905351i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−8.37789	−	8.37789i	−0.656207	−	0.656207i	0.298274	−	0.954480i	$-0.403589\pi$
$163$	−8.37789	−	8.37789i	−0.656207	−	0.656207i	−0.954480	+	0.298274i	$0.903589\pi$
$164$		−	4.53754i		−	0.354322i
$165$	3.38166	+	8.68298i	0.263262	+	0.675969i
$166$		−	3.40670i		−	0.264411i
$167$	−13.2847	+	13.2847i	−1.02800	+	1.02800i	−0.0284037	+	0.999597i	$0.509042\pi$
$167$	−13.2847	+	13.2847i	−1.02800	+	1.02800i	−0.999597	+	0.0284037i	$0.990958\pi$
$168$	−1.80902	+	1.80902i	−0.139569	+	0.139569i
$169$			7.33872i			0.564517i
$170$	−2.14291	+	4.87679i	−0.164354	+	0.374033i
$171$			5.24101i			0.400790i
$172$	−6.37868	−	6.37868i	−0.486370	−	0.486370i
$173$	13.3807	+	13.3807i	1.01732	+	1.01732i	0.999847	+	0.0174703i	$0.00556124\pi$
$173$	13.3807	+	13.3807i	1.01732	+	1.01732i	0.0174703	+	0.999847i	$0.494439\pi$
$174$			3.48107i			0.263899i
$175$	0.545097	−	12.7801i	0.0412055	−	0.966082i
$176$		−	4.16725i		−	0.314118i
$177$	4.81117	−	4.81117i	0.361630	−	0.361630i
$178$	2.53697	−	2.53697i	0.190154	−	0.190154i
$179$		−	17.1255i		−	1.28002i	−0.768367	−	0.640010i	$-0.778930\pi$
$179$		−	17.1255i		−	1.28002i	0.768367	−	0.640010i	$-0.221070\pi$
$180$	0.899538	−	2.04715i	0.0670476	−	0.152586i
$181$		−	7.02770i		−	0.522365i	−0.965289	−	0.261183i	$-0.915888\pi$
$181$		−	7.02770i		−	0.522365i	0.965289	−	0.261183i	$-0.0841124\pi$
$182$	8.15839	+	8.15839i	0.604740	+	0.604740i
$183$	0.536878	−	0.536878i	0.0396872	−	0.0396872i
$184$	−1.68449	+	4.49027i	−0.124182	+	0.331027i
$185$	16.0989	−	6.26986i	1.18362	−	0.460969i
$186$	−7.27142			−0.533166
$187$	−7.01970	+	7.01970i	−0.513331	+	0.513331i
$188$	9.09342	+	9.09342i	0.663206	+	0.663206i
$189$	−2.55834			−0.186092
$190$	4.25300	+	10.9203i	0.308545	+	0.792241i
$191$		−	22.3085i		−	1.61419i	−0.590422	−	0.807094i	$-0.701039\pi$
$191$		−	22.3085i		−	1.61419i	0.590422	−	0.807094i	$-0.298961\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	−12.5386	−	12.5386i	−0.902550	−	0.902550i	0.0931061	−	0.995656i	$-0.470320\pi$
$193$	−12.5386	−	12.5386i	−0.902550	−	0.902550i	−0.995656	+	0.0931061i	$0.970320\pi$
$194$	−5.70322			−0.409467
$195$	−9.23234	−	4.05678i	−0.661142	−	0.290512i
$196$	−0.454913			−0.0324938
$197$	−2.02769	+	2.02769i	−0.144467	+	0.144467i	−0.775641	−	0.631174i	$-0.782573\pi$
$197$	−2.02769	+	2.02769i	−0.144467	+	0.144467i	0.631174	+	0.775641i	$0.282573\pi$
$198$	2.94669	−	2.94669i	0.209412	−	0.209412i
$199$	4.87669			0.345699			0.172850	−	0.984948i	$-0.444703\pi$
$199$	4.87669			0.345699			0.172850	+	0.984948i	$0.444703\pi$
$200$	0.213067	−	4.99546i	0.0150661	−	0.353232i
$201$			2.85850i			0.201623i
$202$	−4.50065	+	4.50065i	−0.316665	+	0.316665i
$203$	6.29731	−	6.29731i	0.441985	−	0.441985i
$204$	2.38223			0.166789
$205$	4.08169	−	9.28903i	0.285078	−	0.648774i
$206$			2.82727i			0.196985i
$207$	−4.36621	+	1.98398i	−0.303473	+	0.137896i
$208$	3.18894	+	3.18894i	0.221113	+	0.221113i
$209$			21.8406i			1.51074i
$210$	−5.33061	+	2.07605i	−0.367847	+	0.143261i
$211$	−10.4399			−0.718710			−0.359355	−	0.933201i	$-0.617003\pi$
$211$	−10.4399			−0.718710			−0.359355	+	0.933201i	$0.617003\pi$
$212$	6.56472	+	6.56472i	0.450867	+	0.450867i
$213$	−6.76281	−	6.76281i	−0.463380	−	0.463380i
$214$	−8.86459			−0.605971
$215$	−7.32026	−	18.7960i	−0.499237	−	1.28188i
$216$	−1.00000			−0.0680414
$217$	13.1541	+	13.1541i	0.892960	+	0.892960i
$218$	−1.08609	+	1.08609i	−0.0735595	+	0.0735595i
$219$		−	8.17754i		−	0.552587i
$220$	3.74860	−	8.53099i	0.252731	−	0.575159i
$221$		−	10.7435i		−	0.722686i
$222$	−5.46339	−	5.46339i	−0.366679	−	0.366679i
$223$	11.9073	+	11.9073i	0.797373	+	0.797373i	0.982681	−	0.185308i	$-0.0593282\pi$
$223$	11.9073	+	11.9073i	0.797373	+	0.797373i	−0.185308	+	0.982681i	$0.559328\pi$
$224$	2.55834			0.170936
$225$	3.68298	−	3.38166i	0.245532	−	0.225444i
$226$			19.8865i			1.32283i
$227$	0.242263	+	0.242263i	0.0160796	+	0.0160796i	0.715101	−	0.699021i	$-0.246381\pi$
$227$	0.242263	+	0.242263i	0.0160796	+	0.0160796i	−0.699021	+	0.715101i	$0.746381\pi$
$228$	3.70595	−	3.70595i	0.245433	−	0.245433i
$229$	−5.80623			−0.383687			−0.191843	−	0.981426i	$-0.561447\pi$
$229$	−5.80623			−0.383687			−0.191843	+	0.981426i	$0.561447\pi$
$230$	−7.48758	+	7.67699i	−0.493716	+	0.506206i
$231$	−10.6612			−0.701457
$232$	2.46149	−	2.46149i	0.161605	−	0.161605i
$233$	−11.2922	−	11.2922i	−0.739779	−	0.739779i	0.232756	−	0.972535i	$-0.425226\pi$
$233$	−11.2922	−	11.2922i	−0.739779	−	0.739779i	−0.972535	+	0.232756i	$0.925226\pi$
$234$			4.50985i			0.294818i
$235$	10.4357	+	26.7955i	0.680752	+	1.74795i
$236$	−6.80402			−0.442904
$237$	−4.84343	−	4.84343i	−0.314614	−	0.314614i
$238$	−4.30950	−	4.30950i	−0.279343	−	0.279343i
$239$		−	0.457589i		−	0.0295990i	−0.999890	−	0.0147995i	$-0.995289\pi$
$239$		−	0.457589i		−	0.0295990i	0.999890	−	0.0147995i	$-0.00471099\pi$
$240$	−2.08362	+	0.811485i	−0.134497	+	0.0523811i
$241$			22.2609i			1.43395i	0.697098	+	0.716976i	$0.254474\pi$
$241$			22.2609i			1.43395i	−0.697098	+	0.716976i	$0.745526\pi$
$242$	4.50142	−	4.50142i	0.289362	−	0.289362i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−0.759260			−0.0486066
$245$	−0.931275	−	0.409211i	−0.0594970	−	0.0261436i
$246$	−4.53754			−0.289303
$247$	−16.7133	−	16.7133i	−1.06344	−	1.06344i
$248$	5.14167	+	5.14167i	0.326496	+	0.326496i
$249$	−3.40670			−0.215891
$250$	4.92979	−	10.0348i	0.311787	−	0.634656i
$251$		−	26.7068i		−	1.68572i	−0.538135	−	0.842858i	$-0.680871\pi$
$251$		−	26.7068i		−	1.68572i	0.538135	−	0.842858i	$-0.319129\pi$
$252$	1.80902	+	1.80902i	0.113957	+	0.113957i
$253$	−18.1951	+	8.26775i	−1.14392	+	0.519789i
$254$		−	10.0762i		−	0.632235i
$255$	4.87679	+	2.14291i	0.305396	+	0.134194i
$256$	1.00000			0.0625000
$257$	−5.33827	+	5.33827i	−0.332992	+	0.332992i	−0.853722	−	0.520729i	$-0.825660\pi$
$257$	−5.33827	+	5.33827i	−0.332992	+	0.332992i	0.520729	+	0.853722i	$0.325660\pi$
$258$	−6.37868	+	6.37868i	−0.397119	+	0.397119i
$259$			19.7667i			1.22824i
$260$	3.65967	+	9.39683i	0.226963	+	0.582767i
$261$	3.48107			0.215473
$262$	−1.40378	+	1.40378i	−0.0867257	+	0.0867257i
$263$	−19.5204	+	19.5204i	−1.20368	+	1.20368i	−0.230639	+	0.973039i	$0.574082\pi$
$263$	−19.5204	+	19.5204i	−1.20368	+	1.20368i	−0.973039	+	0.230639i	$0.925918\pi$
$264$	−4.16725			−0.256476
$265$	7.53377	+	19.3442i	0.462796	+	1.18831i
$266$	−13.4083			−0.822113
$267$	−2.53697	−	2.53697i	−0.155260	−	0.155260i
$268$	2.02126	−	2.02126i	0.123468	−	0.123468i
$269$		−	4.38872i		−	0.267585i	−0.991009	−	0.133793i	$-0.957284\pi$
$269$		−	4.38872i		−	0.267585i	0.991009	−	0.133793i	$-0.0427156\pi$
$270$	−2.04715	−	0.899538i	−0.124586	−	0.0547442i
$271$	18.9023			1.14823			0.574117	−	0.818773i	$-0.305345\pi$
$271$	18.9023			1.14823			0.574117	+	0.818773i	$0.305345\pi$
$272$	−1.68449	−	1.68449i	−0.102137	−	0.102137i
$273$	8.15839	−	8.15839i	0.493768	−	0.493768i
$274$	19.3607			1.16962
$275$	15.3479	−	14.0922i	0.925514	−	0.849793i
$276$	4.49027	+	1.68449i	0.270282	+	0.101394i
$277$	2.44423	−	2.44423i	0.146860	−	0.146860i	−0.629854	−	0.776714i	$-0.716885\pi$
$277$	2.44423	−	2.44423i	0.146860	−	0.146860i	0.776714	+	0.629854i	$0.216885\pi$
$278$	13.7406	+	13.7406i	0.824104	+	0.824104i
$279$			7.27142i			0.435328i
$280$	5.23730	+	2.30132i	0.312989	+	0.137530i
$281$		−	2.33823i		−	0.139487i	−0.997565	−	0.0697436i	$-0.977782\pi$
$281$		−	2.33823i		−	0.139487i	0.997565	−	0.0697436i	$-0.0222181\pi$
$282$	9.09342	−	9.09342i	0.541505	−	0.541505i
$283$	−21.6132	+	21.6132i	−1.28477	+	1.28477i	−0.346850	+	0.937921i	$0.612749\pi$
$283$	−21.6132	+	21.6132i	−1.28477	+	1.28477i	−0.937921	+	0.346850i	$0.887251\pi$
$284$			9.56406i			0.567522i
$285$	10.9203	−	4.25300i	0.646862	−	0.251926i
$286$			18.7937i			1.11129i
$287$	8.20849	+	8.20849i	0.484532	+	0.484532i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$		−	11.3250i		−	0.666175i
$290$	7.25324	−	2.82484i	0.425925	−	0.165880i
$291$			5.70322i			0.334328i
$292$	−5.78239	+	5.78239i	−0.338389	+	0.338389i
$293$	−21.4487	+	21.4487i	−1.25305	+	1.25305i	−0.298699	+	0.954347i	$0.596553\pi$
$293$	−21.4487	+	21.4487i	−1.25305	+	1.25305i	−0.954347	+	0.298699i	$0.903447\pi$
$294$			0.454913i			0.0265310i
$295$	−13.9289	−	6.12048i	−0.810970	−	0.356348i
$296$			7.72640i			0.449088i
$297$	−2.94669	−	2.94669i	−0.170984	−	0.170984i
$298$	−2.38490	+	2.38490i	−0.138154	+	0.138154i
$299$	7.59680	−	20.2504i	0.439334	−	1.17111i
$300$	−4.99546	−	0.213067i	−0.288413	−	0.0123014i
$301$	23.0783			1.33021
$302$	13.2254	−	13.2254i	0.761035	−	0.761035i
$303$	4.50065	+	4.50065i	0.258556	+	0.258556i
$304$	−5.24101			−0.300592
$305$	−1.55432	−	0.682984i	−0.0890001	−	0.0391075i
$306$		−	2.38223i		−	0.136183i
$307$	12.0002	−	12.0002i	0.684889	−	0.684889i	−0.276209	−	0.961098i	$-0.589078\pi$
$307$	12.0002	−	12.0002i	0.684889	−	0.684889i	0.961098	+	0.276209i	$0.0890781\pi$
$308$	7.53863	+	7.53863i	0.429553	+	0.429553i
$309$	2.82727			0.160838
$310$	5.90065	+	15.1509i	0.335134	+	0.860514i
$311$	1.56616			0.0888087			0.0444043	−	0.999014i	$-0.485861\pi$
$311$	1.56616			0.0888087			0.0444043	+	0.999014i	$0.485861\pi$
$312$	3.18894	−	3.18894i	0.180538	−	0.180538i
$313$	8.94733	−	8.94733i	0.505733	−	0.505733i	−0.407481	−	0.913214i	$-0.633593\pi$
$313$	8.94733	−	8.94733i	0.505733	−	0.505733i	0.913214	+	0.407481i	$0.133593\pi$
$314$	16.7427			0.944844
$315$	2.07605	+	5.33061i	0.116972	+	0.300346i
$316$			6.84964i			0.385322i
$317$	8.43391	−	8.43391i	0.473695	−	0.473695i	−0.429413	−	0.903108i	$-0.641279\pi$
$317$	8.43391	−	8.43391i	0.473695	−	0.473695i	0.903108	+	0.429413i	$0.141279\pi$
$318$	6.56472	−	6.56472i	0.368131	−	0.368131i
$319$	14.5065			0.812207
$320$	2.04715	+	0.899538i	0.114439	+	0.0502857i
$321$			8.86459i			0.494773i
$322$	−5.07570	−	11.1702i	−0.282857	−	0.622493i
$323$	8.82843	+	8.82843i	0.491227	+	0.491227i
$324$			1.00000i			0.0555556i
$325$	−0.960900	+	22.5288i	−0.0533011	+	1.24967i
$326$	11.8481			0.656207
$327$	1.08609	+	1.08609i	0.0600611	+	0.0600611i
$328$	3.20853	+	3.20853i	0.177161	+	0.177161i
$329$	−32.9003			−1.81385
$330$	−8.53099	−	3.74860i	−0.469616	−	0.206354i
$331$	12.9490			0.711741			0.355870	−	0.934535i	$-0.384184\pi$
$331$	12.9490			0.711741			0.355870	+	0.934535i	$0.384184\pi$
$332$	2.40890	+	2.40890i	0.132206	+	0.132206i
$333$	−5.46339	+	5.46339i	−0.299392	+	0.299392i
$334$		−	18.7874i		−	1.02800i
$335$	5.95604	−	2.31963i	0.325413	−	0.126735i
$336$		−	2.55834i		−	0.139569i
$337$	4.75471	+	4.75471i	0.259006	+	0.259006i	0.824650	−	0.565644i	$-0.191372\pi$
$337$	4.75471	+	4.75471i	0.259006	+	0.259006i	−0.565644	+	0.824650i	$0.691372\pi$
$338$	−5.18926	−	5.18926i	−0.282259	−	0.282259i
$339$	19.8865			1.08009
$340$	−1.93314	−	4.96367i	−0.104839	−	0.269193i
$341$			30.3018i			1.64094i
$342$	−3.70595	−	3.70595i	−0.200395	−	0.200395i
$343$	13.4861	−	13.4861i	0.728179	−	0.728179i
$344$	9.02081			0.486370
$345$	7.67699	+	7.48758i	0.413315	+	0.403118i
$346$	−18.9232			−1.01732
$347$	−3.12333	+	3.12333i	−0.167669	+	0.167669i	−0.785954	−	0.618285i	$-0.787828\pi$
$347$	−3.12333	+	3.12333i	−0.167669	+	0.167669i	0.618285	+	0.785954i	$0.287828\pi$
$348$	−2.46149	−	2.46149i	−0.131950	−	0.131950i
$349$		−	16.1446i		−	0.864201i	−0.901825	−	0.432101i	$-0.857773\pi$
$349$		−	16.1446i		−	0.864201i	0.901825	−	0.432101i	$-0.142227\pi$
$350$	8.65143	+	9.42231i	0.462438	+	0.503644i
$351$	4.50985			0.240718
$352$	2.94669	+	2.94669i	0.157059	+	0.157059i
$353$	−10.2236	−	10.2236i	−0.544146	−	0.544146i	0.380596	−	0.924742i	$-0.375719\pi$
$353$	−10.2236	−	10.2236i	−0.544146	−	0.544146i	−0.924742	+	0.380596i	$0.875719\pi$
$354$			6.80402i			0.361630i
$355$	−8.60324	+	19.5791i	−0.456612	+	1.03915i
$356$			3.58782i			0.190154i
$357$	−4.30950	+	4.30950i	−0.228083	+	0.228083i
$358$	12.1096	+	12.1096i	0.640010	+	0.640010i
$359$	18.2877			0.965188			0.482594	−	0.875844i	$-0.339695\pi$
$359$	18.2877			0.965188			0.482594	+	0.875844i	$0.339695\pi$
$360$	0.811485	+	2.08362i	0.0427690	+	0.109817i
$361$	8.46813			0.445691
$362$	4.96934	+	4.96934i	0.261183	+	0.261183i
$363$	−4.50142	−	4.50142i	−0.236263	−	0.236263i
$364$	−11.5377			−0.604740
$365$	−17.0389	+	6.63595i	−0.891858	+	0.347341i
$366$			0.759260i			0.0396872i
$367$	−7.66636	−	7.66636i	−0.400181	−	0.400181i	0.478116	−	0.878297i	$-0.341320\pi$
$367$	−7.66636	−	7.66636i	−0.400181	−	0.400181i	−0.878297	+	0.478116i	$0.841320\pi$
$368$	−1.98398	−	4.36621i	−0.103422	−	0.227605i
$369$			4.53754i			0.236215i
$370$	−6.95019	+	15.8171i	−0.361323	+	0.822292i
$371$	−23.7514			−1.23311
$372$	5.14167	−	5.14167i	0.266583	−	0.266583i
$373$	−18.9572	+	18.9572i	−0.981564	+	0.981564i	−0.999833	−	0.0182689i	$-0.994185\pi$
$373$	−18.9572	+	18.9572i	−0.981564	+	0.981564i	0.0182689	+	0.999833i	$0.494185\pi$
$374$		−	9.92735i		−	0.513331i
$375$	−10.0348	−	4.92979i	−0.518195	−	0.254573i
$376$	−12.8600			−0.663206
$377$	−11.1009	+	11.1009i	−0.571727	+	0.571727i
$378$	1.80902	−	1.80902i	0.0930458	−	0.0930458i
$379$	−21.8702			−1.12340			−0.561699	−	0.827341i	$-0.689852\pi$
$379$	−21.8702			−1.12340			−0.561699	+	0.827341i	$0.689852\pi$
$380$	−10.7291	−	4.71449i	−0.550393	−	0.241848i
$381$	−10.0762			−0.516218
$382$	15.7745	+	15.7745i	0.807094	+	0.807094i
$383$	20.5841	−	20.5841i	1.05180	−	1.05180i	0.0532143	−	0.998583i	$-0.483053\pi$
$383$	20.5841	−	20.5841i	1.05180	−	1.05180i	0.998583	−	0.0532143i	$-0.0169466\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	8.65143	+	22.2140i	0.440918	+	1.13213i
$386$	17.7323			0.902550
$387$	6.37868	+	6.37868i	0.324246	+	0.324246i
$388$	4.03278	−	4.03278i	0.204734	−	0.204734i
$389$	2.71068			0.137437			0.0687184	−	0.997636i	$-0.478109\pi$
$389$	2.71068			0.137437			0.0687184	+	0.997636i	$0.478109\pi$
$390$	9.39683	−	3.65967i	0.475827	−	0.185315i
$391$	−4.01285	+	10.6968i	−0.202938	+	0.540963i
$392$	0.321672	−	0.321672i	0.0162469	−	0.0162469i
$393$	1.40378	+	1.40378i	0.0708113	+	0.0708113i
$394$		−	2.86759i		−	0.144467i
$395$	−6.16152	+	14.0223i	−0.310020	+	0.705536i
$396$			4.16725i			0.209412i
$397$	26.9536	−	26.9536i	1.35276	−	1.35276i	0.470203	−	0.882558i	$-0.344181\pi$
$397$	26.9536	−	26.9536i	1.35276	−	1.35276i	0.882558	−	0.470203i	$-0.155819\pi$
$398$	−3.44834	+	3.44834i	−0.172850	+	0.172850i
$399$			13.4083i			0.671252i
$400$	3.38166	+	3.68298i	0.169083	+	0.184149i
$401$			9.86390i			0.492580i	0.969196	+	0.246290i	$0.0792115\pi$
$401$			9.86390i			0.492580i	−0.969196	+	0.246290i	$0.920788\pi$
$402$	−2.02126	−	2.02126i	−0.100812	−	0.100812i
$403$	−23.1881	−	23.1881i	−1.15508	−	1.15508i
$404$		−	6.36488i		−	0.316665i
$405$	−0.899538	+	2.04715i	−0.0446984	+	0.101724i
$406$			8.90575i			0.441985i
$407$	−22.7673	+	22.7673i	−1.12853	+	1.12853i
$408$	−1.68449	+	1.68449i	−0.0833947	+	0.0833947i
$409$			30.0925i			1.48798i	0.668191	+	0.743990i	$0.267069\pi$
$409$			30.0925i			1.48798i	−0.668191	+	0.743990i	$0.732931\pi$
$410$	3.68215	+	9.45453i	0.181848	+	0.466926i
$411$		−	19.3607i		−	0.954993i
$412$	−1.99918	−	1.99918i	−0.0984926	−	0.0984926i
$413$	12.3086	−	12.3086i	0.605666	−	0.605666i
$414$	1.68449	−	4.49027i	0.0827882	−	0.220685i
$415$	2.76449	+	7.09828i	0.135703	+	0.348441i
$416$	−4.50985			−0.221113
$417$	13.7406	−	13.7406i	0.672878	−	0.672878i
$418$	−15.4436	−	15.4436i	−0.755372	−	0.755372i
$419$	−7.59626			−0.371102			−0.185551	−	0.982635i	$-0.559407\pi$
$419$	−7.59626			−0.371102			−0.185551	+	0.982635i	$0.559407\pi$
$420$	2.30132	−	5.23730i	0.112293	−	0.255554i
$421$			23.4653i			1.14363i	0.820382	+	0.571816i	$0.193761\pi$
$421$			23.4653i			1.14363i	−0.820382	+	0.571816i	$0.806239\pi$
$422$	7.38210	−	7.38210i	0.359355	−	0.359355i
$423$	−9.09342	−	9.09342i	−0.442137	−	0.442137i
$424$	−9.28392			−0.450867
$425$	0.507575	−	11.9003i	0.0246210	−	0.577251i
$426$	9.56406			0.463380
$427$	1.37351	−	1.37351i	0.0664690	−	0.0664690i
$428$	6.26821	−	6.26821i	0.302985	−	0.302985i
$429$	18.7937			0.907366
$430$	18.4670	+	8.11457i	0.890557	+	0.391319i
$431$		−	21.7988i		−	1.05001i	−0.851099	−	0.525005i	$-0.824063\pi$
$431$		−	21.7988i		−	1.05001i	0.851099	−	0.525005i	$-0.175937\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	−17.0890	+	17.0890i	−0.821245	+	0.821245i	−0.986287	−	0.165041i	$-0.947224\pi$
$433$	−17.0890	+	17.0890i	−0.821245	+	0.821245i	0.165041	+	0.986287i	$0.447224\pi$
$434$	−18.6027			−0.892960
$435$	−2.82484	−	7.25324i	−0.135441	−	0.347766i
$436$		−	1.53597i		−	0.0735595i
$437$	10.3981	+	22.8833i	0.497407	+	1.09466i
$438$	5.78239	+	5.78239i	0.276293	+	0.276293i
$439$			18.6384i			0.889563i	0.895639	+	0.444781i	$0.146719\pi$
$439$			18.6384i			0.889563i	−0.895639	+	0.444781i	$0.853281\pi$
$440$	3.38166	+	8.68298i	0.161214	+	0.413945i
$441$	0.454913			0.0216625
$442$	7.59680	+	7.59680i	0.361343	+	0.361343i
$443$	7.32527	+	7.32527i	0.348034	+	0.348034i	0.859377	−	0.511343i	$-0.170852\pi$
$443$	7.32527	+	7.32527i	0.348034	+	0.348034i	−0.511343	+	0.859377i	$0.670852\pi$
$444$	7.72640			0.366679
$445$	−3.22738	+	7.34481i	−0.152993	+	0.348177i
$446$	−16.8395			−0.797373
$447$	2.38490	+	2.38490i	0.112802	+	0.112802i
$448$	−1.80902	+	1.80902i	−0.0854680	+	0.0854680i
$449$		−	12.9705i		−	0.612116i	−0.952013	−	0.306058i	$-0.900990\pi$
$449$		−	12.9705i		−	0.612116i	0.952013	−	0.306058i	$-0.0990102\pi$
$450$	−0.213067	+	4.99546i	−0.0100441	+	0.235488i
$451$			18.9091i			0.890393i
$452$	−14.0619	−	14.0619i	−0.661417	−	0.661417i
$453$	−13.2254	−	13.2254i	−0.621383	−	0.621383i
$454$	−0.342612			−0.0160796
$455$	−23.6194	−	10.3786i	−1.10730	−	0.486557i
$456$			5.24101i			0.245433i
$457$	27.4401	+	27.4401i	1.28360	+	1.28360i	0.938607	+	0.344988i	$0.112117\pi$
$457$	27.4401	+	27.4401i	1.28360	+	1.28360i	0.344988	+	0.938607i	$0.387883\pi$
$458$	4.10563	−	4.10563i	0.191843	−	0.191843i
$459$	−2.38223			−0.111193
$460$	−0.133937	−	10.7230i	−0.00624484	−	0.499961i
$461$	10.2068			0.475376			0.237688	−	0.971342i	$-0.423610\pi$
$461$	10.2068			0.475376			0.237688	+	0.971342i	$0.423610\pi$
$462$	7.53863	−	7.53863i	0.350729	−	0.350729i
$463$	−8.13895	−	8.13895i	−0.378249	−	0.378249i	0.492221	−	0.870470i	$-0.336185\pi$
$463$	−8.13895	−	8.13895i	−0.378249	−	0.378249i	−0.870470	+	0.492221i	$0.836185\pi$
$464$			3.48107i			0.161605i
$465$	15.1509	−	5.90065i	0.702607	−	0.273636i
$466$	15.9696			0.739779
$467$	20.9496	+	20.9496i	0.969434	+	0.969434i	0.999547	−	0.0301128i	$-0.00958666\pi$
$467$	20.9496	+	20.9496i	0.969434	+	0.969434i	−0.0301128	+	0.999547i	$0.509587\pi$
$468$	−3.18894	−	3.18894i	−0.147409	−	0.147409i
$469$			7.31300i			0.337683i
$470$	−26.3265	−	11.5681i	−1.21435	−	0.533597i
$471$		−	16.7427i		−	0.771462i
$472$	4.81117	−	4.81117i	0.221452	−	0.221452i
$473$	26.5815	+	26.5815i	1.22222	+	1.22222i
$474$	6.84964			0.314614
$475$	−17.7233	−	19.3025i	−0.813201	−	0.885661i
$476$	6.09455			0.279343
$477$	−6.56472	−	6.56472i	−0.300578	−	0.300578i
$478$	0.323564	+	0.323564i	0.0147995	+	0.0147995i
$479$	−23.4064			−1.06947			−0.534733	−	0.845021i	$-0.679588\pi$
$479$	−23.4064			−1.06947			−0.534733	+	0.845021i	$0.679588\pi$
$480$	0.899538	−	2.04715i	0.0410581	−	0.0934393i
$481$		−	34.8449i		−	1.58879i
$482$	−15.7409	−	15.7409i	−0.716976	−	0.716976i
$483$	−11.1702	+	5.07570i	−0.508264	+	0.230952i
$484$			6.36597i			0.289362i
$485$	11.8834	−	4.62808i	0.539596	−	0.210150i
$486$	1.00000			0.0453609
$487$	22.9383	−	22.9383i	1.03943	−	1.03943i	0.0402440	−	0.999190i	$-0.487186\pi$
$487$	22.9383	−	22.9383i	1.03943	−	1.03943i	0.999190	−	0.0402440i	$-0.0128135\pi$
$488$	0.536878	−	0.536878i	0.0243033	−	0.0243033i
$489$		−	11.8481i		−	0.535791i
$490$	0.947867	−	0.369155i	0.0428203	−	0.0166767i
$491$	30.8377			1.39169			0.695844	−	0.718193i	$-0.255031\pi$
$491$	30.8377			1.39169			0.695844	+	0.718193i	$0.255031\pi$
$492$	3.20853	−	3.20853i	0.144651	−	0.144651i
$493$	5.86383	−	5.86383i	0.264094	−	0.264094i
$494$	23.6361			1.06344
$495$	−3.74860	+	8.53099i	−0.168487	+	0.383440i
$496$	−7.27142			−0.326496
$497$	−17.3015	−	17.3015i	−0.776080	−	0.776080i
$498$	2.40890	−	2.40890i	0.107945	−	0.107945i
$499$			25.4897i			1.14107i	0.821272	+	0.570537i	$0.193265\pi$
$499$			25.4897i			1.14107i	−0.821272	+	0.570537i	$0.806735\pi$
$500$	3.60979	+	10.5816i	0.161435	+	0.473222i
$501$	−18.7874			−0.839359
$502$	18.8845	+	18.8845i	0.842858	+	0.842858i
$503$	−3.49872	+	3.49872i	−0.156000	+	0.156000i	−0.780792	−	0.624792i	$-0.785184\pi$
$503$	−3.49872	+	3.49872i	−0.156000	+	0.156000i	0.624792	+	0.780792i	$0.285184\pi$
$504$	−2.55834			−0.113957
$505$	5.72545	−	13.0299i	0.254779	−	0.579822i
$506$	7.01970	−	18.7121i	0.312064	−	0.831852i
$507$	−5.18926	+	5.18926i	−0.230463	+	0.230463i
$508$	7.12493	+	7.12493i	0.316117	+	0.316117i
$509$			26.2453i			1.16330i	0.813439	+	0.581651i	$0.197593\pi$
$509$			26.2453i			1.16330i	−0.813439	+	0.581651i	$0.802407\pi$
$510$	−4.96367	+	1.93314i	−0.219795	+	0.0856011i
$511$		−	20.9209i		−	0.925486i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−3.70595	+	3.70595i	−0.163622	+	0.163622i
$514$		−	7.54946i		−	0.332992i
$515$	−2.29429	−	5.89097i	−0.101098	−	0.259587i
$516$		−	9.02081i		−	0.397119i
$517$	−37.8946	−	37.8946i	−1.66660	−	1.66660i
$518$	−13.9772	−	13.9772i	−0.614122	−	0.614122i
$519$			18.9232i			0.830636i
$520$	−9.23234	−	4.05678i	−0.404865	−	0.177902i
$521$			16.1892i			0.709263i	0.935006	+	0.354631i	$0.115394\pi$
$521$			16.1892i			0.709263i	−0.935006	+	0.354631i	$0.884606\pi$
$522$	−2.46149	+	2.46149i	−0.107736	+	0.107736i
$523$	−1.41722	+	1.41722i	−0.0619705	+	0.0619705i	−0.737413	−	0.675442i	$-0.763953\pi$
$523$	−1.41722	+	1.41722i	−0.0619705	+	0.0619705i	0.675442	+	0.737413i	$0.263953\pi$
$524$		−	1.98524i		−	0.0867257i
$525$	9.42231	−	8.65143i	0.411223	−	0.377579i
$526$		−	27.6060i		−	1.20368i
$527$	12.2486	+	12.2486i	0.533559	+	0.533559i
$528$	2.94669	−	2.94669i	0.128238	−	0.128238i
$529$	−15.1276	+	17.3250i	−0.657723	+	0.753260i
$530$	−19.0056	−	8.35125i	−0.825551	−	0.362755i
$531$	6.80402			0.295269
$532$	9.48107	−	9.48107i	0.411056	−	0.411056i
$533$	−14.4700	−	14.4700i	−0.626764	−	0.626764i
$534$	3.58782			0.155260
$535$	18.4705	−	7.19348i	0.798548	−	0.311001i
$536$			2.85850i			0.123468i
$537$	12.1096	−	12.1096i	0.522566	−	0.522566i
$538$	3.10329	+	3.10329i	0.133793	+	0.133793i
$539$	1.89573			0.0816551
$540$	2.08362	−	0.811485i	0.0896649	−	0.0349208i
$541$	−3.67997			−0.158214			−0.0791072	−	0.996866i	$-0.525207\pi$
$541$	−3.67997			−0.158214			−0.0791072	+	0.996866i	$0.525207\pi$
$542$	−13.3660	+	13.3660i	−0.574117	+	0.574117i
$543$	4.96934	−	4.96934i	0.213255	−	0.213255i
$544$	2.38223			0.102137
$545$	1.38166	−	3.14436i	0.0591839	−	0.134689i
$546$			11.5377i			0.493768i
$547$	−4.37686	+	4.37686i	−0.187141	+	0.187141i	−0.794459	−	0.607318i	$-0.792245\pi$
$547$	−4.37686	+	4.37686i	−0.187141	+	0.187141i	0.607318	+	0.794459i	$0.292245\pi$
$548$	−13.6901	+	13.6901i	−0.584812	+	0.584812i
$549$	0.759260			0.0324044
$550$	−0.887903	+	20.8173i	−0.0378603	+	0.887653i
$551$		−	18.2443i		−	0.777233i
$552$	−4.36621	+	1.98398i	−0.185838	+	0.0844439i
$553$	−12.3911	−	12.3911i	−0.526924	−	0.526924i
$554$			3.45666i			0.146860i
$555$	15.8171	+	6.95019i	0.671399	+	0.295019i
$556$	−19.4321			−0.824104
$557$	−3.04302	−	3.04302i	−0.128937	−	0.128937i	0.639693	−	0.768630i	$-0.279061\pi$
$557$	−3.04302	−	3.04302i	−0.128937	−	0.128937i	−0.768630	+	0.639693i	$0.779061\pi$
$558$	−5.14167	−	5.14167i	−0.217664	−	0.217664i
$559$	−40.6825			−1.72069
$560$	−5.33061	+	2.07605i	−0.225260	+	0.0877292i
$561$	−9.92735			−0.419133
$562$	1.65338	+	1.65338i	0.0697436	+	0.0697436i
$563$	27.0816	−	27.0816i	1.14135	−	1.14135i	0.153151	−	0.988203i	$-0.451058\pi$
$563$	27.0816	−	27.0816i	1.14135	−	1.14135i	0.988203	−	0.153151i	$-0.0489420\pi$
$564$			12.8600i			0.541505i
$565$	−16.1376	−	41.4361i	−0.678915	−	1.74323i
$566$		−	30.5657i		−	1.28477i
$567$	−1.80902	−	1.80902i	−0.0759716	−	0.0759716i
$568$	−6.76281	−	6.76281i	−0.283761	−	0.283761i
$569$	−34.6663			−1.45329			−0.726644	−	0.687014i	$-0.758921\pi$
$569$	−34.6663			−1.45329			−0.726644	+	0.687014i	$0.758921\pi$
$570$	−4.71449	+	10.7291i	−0.197468	+	0.449394i
$571$		−	9.50431i		−	0.397743i	−0.980026	−	0.198871i	$-0.936272\pi$
$571$		−	9.50431i		−	0.397743i	0.980026	−	0.198871i	$-0.0637276\pi$
$572$	−13.2891	−	13.2891i	−0.555646	−	0.555646i
$573$	15.7745	−	15.7745i	0.658990	−	0.658990i
$574$	−11.6086			−0.484532
$575$	9.37153	−	22.0720i	0.390820	−	0.920467i
$576$	−1.00000			−0.0416667
$577$	−5.16579	+	5.16579i	−0.215054	+	0.215054i	−0.806411	−	0.591356i	$-0.798593\pi$
$577$	−5.16579	+	5.16579i	−0.215054	+	0.215054i	0.591356	+	0.806411i	$0.298593\pi$
$578$	8.00797	+	8.00797i	0.333088	+	0.333088i
$579$		−	17.7323i		−	0.736929i
$580$	−3.13136	+	7.12628i	−0.130022	+	0.295903i
$581$	−8.71549			−0.361579
$582$	−4.03278	−	4.03278i	−0.167164	−	0.167164i
$583$	−27.3568	−	27.3568i	−1.13300	−	1.13300i
$584$		−	8.17754i		−	0.338389i
$585$	−3.65967	−	9.39683i	−0.151309	−	0.388511i
$586$		−	30.3330i		−	1.25305i
$587$	−3.80896	+	3.80896i	−0.157213	+	0.157213i	−0.781330	−	0.624118i	$-0.785459\pi$
$587$	−3.80896	+	3.80896i	−0.157213	+	0.157213i	0.624118	+	0.781330i	$0.285459\pi$
$588$	−0.321672	−	0.321672i	−0.0132655	−	0.0132655i
$589$	38.1095			1.57028
$590$	14.1770	−	5.52136i	0.583659	−	0.227311i
$591$	−2.86759			−0.117957
$592$	−5.46339	−	5.46339i	−0.224544	−	0.224544i
$593$	−1.75845	−	1.75845i	−0.0722109	−	0.0722109i	0.670079	−	0.742290i	$-0.266260\pi$
$593$	−1.75845	−	1.75845i	−0.0722109	−	0.0722109i	−0.742290	+	0.670079i	$0.766260\pi$
$594$	4.16725			0.170984
$595$	12.4765	+	5.48228i	0.511485	+	0.224752i
$596$		−	3.37276i		−	0.138154i
$597$	3.44834	+	3.44834i	0.141131	+	0.141131i
$598$	8.94746	+	19.6910i	0.365889	+	0.805223i
$599$		−	36.0972i		−	1.47489i	−0.675407	−	0.737445i	$-0.736032\pi$
$599$		−	36.0972i		−	1.47489i	0.675407	−	0.737445i	$-0.263968\pi$
$600$	3.68298	−	3.38166i	0.150357	−	0.138056i
$601$	24.9687			1.01849			0.509247	−	0.860620i	$-0.329924\pi$
$601$	24.9687			1.01849			0.509247	+	0.860620i	$0.329924\pi$
$602$	−16.3188	+	16.3188i	−0.665105	+	0.665105i
$603$	−2.02126	+	2.02126i	−0.0823122	+	0.0823122i
$604$			18.7035i			0.761035i
$605$	−5.72643	+	13.0321i	−0.232813	+	0.529830i
$606$	−6.36488			−0.258556
$607$	−25.6608	+	25.6608i	−1.04154	+	1.04154i	−0.0424416	+	0.999099i	$0.513514\pi$
$607$	−25.6608	+	25.6608i	−1.04154	+	1.04154i	−0.999099	+	0.0424416i	$0.986486\pi$
$608$	3.70595	−	3.70595i	0.150296	−	0.150296i
$609$	8.90575			0.360879
$610$	1.58201	−	0.616128i	0.0640538	−	0.0249463i
$611$	57.9968			2.34630
$612$	1.68449	+	1.68449i	0.0680915	+	0.0680915i
$613$	−27.1716	+	27.1716i	−1.09745	+	1.09745i	−0.102742	+	0.994708i	$0.532762\pi$
$613$	−27.1716	+	27.1716i	−1.09745	+	1.09745i	−0.994708	+	0.102742i	$0.967238\pi$
$614$			16.9709i			0.684889i
$615$	9.45453	−	3.68215i	0.381243	−	0.148478i
$616$	−10.6612			−0.429553
$617$	−20.6665	−	20.6665i	−0.832002	−	0.832002i	0.155789	−	0.987790i	$-0.450208\pi$
$617$	−20.6665	−	20.6665i	−0.832002	−	0.832002i	−0.987790	+	0.155789i	$0.950208\pi$
$618$	−1.99918	+	1.99918i	−0.0804189	+	0.0804189i
$619$	44.8826			1.80398			0.901991	−	0.431754i	$-0.142105\pi$
$619$	44.8826			1.80398			0.901991	+	0.431754i	$0.142105\pi$
$620$	−14.8857	−	6.54092i	−0.597824	−	0.262690i
$621$	−4.49027	−	1.68449i	−0.180188	−	0.0675963i
$622$	−1.10744	+	1.10744i	−0.0444043	+	0.0444043i
$623$	−6.49043	−	6.49043i	−0.260033	−	0.260033i
$624$			4.50985i			0.180538i
$625$	−2.12873	+	24.9092i	−0.0851494	+	0.996368i
$626$			12.6534i			0.505733i
$627$	−15.4436	+	15.4436i	−0.616759	+	0.616759i
$628$	−11.8389	+	11.8389i	−0.472422	+	0.472422i
$629$			18.4061i			0.733897i
$630$	−5.23730	−	2.30132i	−0.208659	−	0.0916869i
$631$			39.6759i			1.57947i	0.613448	+	0.789735i	$0.289782\pi$
$631$			39.6759i			1.57947i	−0.613448	+	0.789735i	$0.710218\pi$
$632$	−4.84343	−	4.84343i	−0.192661	−	0.192661i
$633$	−7.38210	−	7.38210i	−0.293412	−	0.293412i
$634$			11.9273i			0.473695i
$635$	8.17666	+	20.9949i	0.324481	+	0.833159i
$636$			9.28392i			0.368131i
$637$	−1.45069	+	1.45069i	−0.0574785	+	0.0574785i
$638$	−10.2576	+	10.2576i	−0.406104	+	0.406104i
$639$		−	9.56406i		−	0.378348i
$640$	−2.08362	+	0.811485i	−0.0823625	+	0.0320768i
$641$		−	20.9245i		−	0.826466i	−0.910625	−	0.413233i	$-0.864399\pi$
$641$		−	20.9245i		−	0.826466i	0.910625	−	0.413233i	$-0.135601\pi$
$642$	−6.26821	−	6.26821i	−0.247387	−	0.247387i
$643$	19.5758	−	19.5758i	0.771994	−	0.771994i	−0.206461	−	0.978455i	$-0.566195\pi$
$643$	19.5758	−	19.5758i	0.771994	−	0.771994i	0.978455	+	0.206461i	$0.0661947\pi$
$644$	11.4876	+	4.30950i	0.452675	+	0.169818i
$645$	8.11457	−	18.4670i	0.319511	−	0.727136i
$646$	−12.4853			−0.491227
$647$	27.6953	−	27.6953i	1.08881	−	1.08881i	0.0931635	−	0.995651i	$-0.470302\pi$
$647$	27.6953	−	27.6953i	1.08881	−	1.08881i	0.995651	−	0.0931635i	$-0.0296979\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	28.3541			1.11299
$650$	−15.2508	−	16.6097i	−0.598185	−	0.651486i
$651$			18.6027i			0.729099i
$652$	−8.37789	+	8.37789i	−0.328103	+	0.328103i
$653$	−22.7542	−	22.7542i	−0.890442	−	0.890442i	0.104122	−	0.994564i	$-0.466797\pi$
$653$	−22.7542	−	22.7542i	−0.890442	−	0.890442i	−0.994564	+	0.104122i	$0.966797\pi$
$654$	−1.53597			−0.0600611
$655$	1.78580	−	4.06409i	0.0697771	−	0.158797i
$656$	−4.53754			−0.177161
$657$	5.78239	−	5.78239i	0.225593	−	0.225593i
$658$	23.2640	−	23.2640i	0.906927	−	0.906927i
$659$	16.1643			0.629673			0.314837	−	0.949146i	$-0.398050\pi$
$659$	16.1643			0.629673			0.314837	+	0.949146i	$0.398050\pi$
$660$	8.68298	−	3.38166i	0.337985	−	0.131631i
$661$		−	20.0621i		−	0.780326i	−0.920746	−	0.390163i	$-0.872419\pi$
$661$		−	20.0621i		−	0.780326i	0.920746	−	0.390163i	$-0.127581\pi$
$662$	−9.15632	+	9.15632i	−0.355870	+	0.355870i
$663$	7.59680	−	7.59680i	0.295035	−	0.295035i
$664$	−3.40670			−0.132206
$665$	27.9378	−	10.8806i	1.08338	−	0.421932i
$666$		−	7.72640i		−	0.299392i
$667$	15.1991	−	6.90638i	0.588511	−	0.267416i
$668$	13.2847	+	13.2847i	0.514000	+	0.514000i
$669$			16.8395i			0.651052i
$670$	−2.57133	+	5.85178i	−0.0993391	+	0.226074i
$671$	3.16403			0.122146
$672$	1.80902	+	1.80902i	0.0697844	+	0.0697844i
$673$	−24.4850	−	24.4850i	−0.943829	−	0.943829i	0.0546752	−	0.998504i	$-0.482588\pi$
$673$	−24.4850	−	24.4850i	−0.943829	−	0.943829i	−0.998504	+	0.0546752i	$0.982588\pi$
$674$	−6.72418			−0.259006
$675$	4.99546	+	0.213067i	0.192275	+	0.00820095i
$676$	7.33872			0.282259
$677$	−13.9941	−	13.9941i	−0.537836	−	0.537836i	0.385057	−	0.922893i	$-0.374182\pi$
$677$	−13.9941	−	13.9941i	−0.537836	−	0.537836i	−0.922893	+	0.385057i	$0.874182\pi$
$678$	−14.0619	+	14.0619i	−0.540044	+	0.540044i
$679$			14.5907i			0.559942i
$680$	4.87679	+	2.14291i	0.187016	+	0.0821768i
$681$			0.342612i			0.0131289i
$682$	−21.4266	−	21.4266i	−0.820468	−	0.820468i
$683$	2.28231	+	2.28231i	0.0873303	+	0.0873303i	0.749422	−	0.662092i	$-0.230331\pi$
$683$	2.28231	+	2.28231i	0.0873303	+	0.0873303i	−0.662092	+	0.749422i	$0.730331\pi$
$684$	5.24101			0.200395
$685$	−40.3405	+	15.7109i	−1.54133	+	0.600284i
$686$			19.0722i			0.728179i
$687$	−4.10563	−	4.10563i	−0.156639	−	0.156639i
$688$	−6.37868	+	6.37868i	−0.243185	+	0.243185i
$689$	41.8691			1.59508
$690$	−10.7230	+	0.133937i	−0.408216	+	0.00509889i
$691$	15.2845			0.581450			0.290725	−	0.956807i	$-0.406103\pi$
$691$	15.2845			0.581450			0.290725	+	0.956807i	$0.406103\pi$
$692$	13.3807	−	13.3807i	0.508659	−	0.508659i
$693$	−7.53863	−	7.53863i	−0.286369	−	0.286369i
$694$		−	4.41705i		−	0.167669i
$695$	−39.7805	−	17.4799i	−1.50896	−	0.663051i
$696$	3.48107			0.131950
$697$	7.64345	+	7.64345i	0.289516	+	0.289516i
$698$	11.4160	+	11.4160i	0.432101	+	0.432101i
$699$		−	15.9696i		−	0.604027i
$700$	−12.7801	−	0.545097i	−0.483041	−	0.0206027i
$701$			16.4549i			0.621493i	0.950493	+	0.310746i	$0.100579\pi$
$701$			16.4549i			0.621493i	−0.950493	+	0.310746i	$0.899421\pi$
$702$	−3.18894	+	3.18894i	−0.120359	+	0.120359i
$703$	28.6336	+	28.6336i	1.07994	+	1.07994i
$704$	−4.16725			−0.157059
$705$	−11.5681	+	26.3265i	−0.435680	+	0.991512i
$706$	14.4583			0.544146
$707$	11.5142	+	11.5142i	0.433035	+	0.433035i
$708$	−4.81117	−	4.81117i	−0.180815	−	0.180815i
$709$	45.9132			1.72431			0.862153	−	0.506648i	$-0.169116\pi$
$709$	45.9132			1.72431			0.862153	+	0.506648i	$0.169116\pi$
$710$	−7.76109	−	19.9279i	−0.291269	−	0.747881i
$711$		−	6.84964i		−	0.256882i
$712$	−2.53697	−	2.53697i	−0.0950770	−	0.0950770i
$713$	14.4264	+	31.7486i	0.540272	+	1.18899i
$714$		−	6.09455i		−	0.228083i
$715$	−15.2508	−	39.1589i	−0.570347	−	1.46446i
$716$	−17.1255			−0.640010
$717$	0.323564	−	0.323564i	0.0120837	−	0.0120837i
$718$	−12.9314	+	12.9314i	−0.482594	+	0.482594i
$719$			30.7995i			1.14863i	0.818635	+	0.574314i	$0.194731\pi$
$719$			30.7995i			1.14863i	−0.818635	+	0.574314i	$0.805269\pi$
$720$	−2.04715	−	0.899538i	−0.0762928	−	0.0335238i
$721$	7.23311			0.269375
$722$	−5.98787	+	5.98787i	−0.222846	+	0.222846i
$723$	−15.7409	+	15.7409i	−0.585409	+	0.585409i
$724$	−7.02770			−0.261183
$725$	−12.8207	+	11.7718i	−0.476150	+	0.437194i
$726$	6.36597			0.236263
$727$	−14.2480	−	14.2480i	−0.528429	−	0.528429i	0.391674	−	0.920104i	$-0.371896\pi$
$727$	−14.2480	−	14.2480i	−0.528429	−	0.528429i	−0.920104	+	0.391674i	$0.871896\pi$
$728$	8.15839	−	8.15839i	0.302370	−	0.302370i
$729$		−	1.00000i		−	0.0370370i
$730$	7.35601	−	16.7407i	0.272258	−	0.619600i
$731$	21.4897			0.794824
$732$	−0.536878	−	0.536878i	−0.0198436	−	0.0198436i
$733$	−4.70374	+	4.70374i	−0.173737	+	0.173737i	−0.788619	−	0.614882i	$-0.789203\pi$
$733$	−4.70374	+	4.70374i	−0.173737	+	0.173737i	0.614882	+	0.788619i	$0.289203\pi$
$734$	10.8419			0.400181
$735$	−0.369155	−	0.947867i	−0.0136165	−	0.0349626i
$736$	4.49027	+	1.68449i	0.165513	+	0.0620912i
$737$	−8.42311	+	8.42311i	−0.310269	+	0.310269i
$738$	−3.20853	−	3.20853i	−0.118107	−	0.118107i
$739$			35.3216i			1.29932i	0.760223	+	0.649662i	$0.225090\pi$
$739$			35.3216i			1.29932i	−0.760223	+	0.649662i	$0.774910\pi$
$740$	−6.26986	−	16.0989i	−0.230484	−	0.591808i
$741$		−	23.6361i		−	0.868295i
$742$	16.7948	−	16.7948i	0.616556	−	0.616556i
$743$	−18.5881	+	18.5881i	−0.681932	+	0.681932i	−0.960435	−	0.278503i	$-0.910162\pi$
$743$	−18.5881	+	18.5881i	−0.681932	+	0.681932i	0.278503	+	0.960435i	$0.410162\pi$
$744$			7.27142i			0.266583i
$745$	3.03393	−	6.90455i	0.111155	−	0.252963i
$746$		−	26.8095i		−	0.981564i
$747$	−2.40890	−	2.40890i	−0.0881371	−	0.0881371i
$748$	7.01970	+	7.01970i	0.256665	+	0.256665i
$749$			22.6786i			0.828658i
$750$	10.5816	−	3.60979i	0.386384	−	0.131811i
$751$			23.3137i			0.850727i	0.905022	+	0.425364i	$0.139854\pi$
$751$			23.3137i			0.850727i	−0.905022	+	0.425364i	$0.860146\pi$
$752$	9.09342	−	9.09342i	0.331603	−	0.331603i
$753$	18.8845	−	18.8845i	0.688191	−	0.688191i
$754$		−	15.6991i		−	0.571727i
$755$	−16.8245	+	38.2889i	−0.612307	+	1.39348i
$756$			2.55834i			0.0930458i
$757$	3.52220	+	3.52220i	0.128016	+	0.128016i	0.768212	−	0.640196i	$-0.221147\pi$
$757$	3.52220	+	3.52220i	0.128016	+	0.128016i	−0.640196	+	0.768212i	$0.721147\pi$
$758$	15.4646	−	15.4646i	0.561699	−	0.561699i
$759$	−18.7121	−	7.01970i	−0.679205	−	0.254799i
$760$	10.9203	−	4.25300i	0.396120	−	0.154272i
$761$	−14.8262			−0.537449			−0.268724	−	0.963217i	$-0.586602\pi$
$761$	−14.8262			−0.537449			−0.268724	+	0.963217i	$0.586602\pi$
$762$	7.12493	−	7.12493i	0.258109	−	0.258109i
$763$	2.77859	+	2.77859i	0.100592	+	0.100592i
$764$	−22.3085			−0.807094
$765$	1.93314	+	4.96367i	0.0698930	+	0.179462i
$766$			29.1103i			1.05180i
$767$	−21.6976	+	21.6976i	−0.783456	+	0.783456i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	14.2891			0.515277			0.257638	−	0.966241i	$-0.417056\pi$
$769$	14.2891			0.515277			0.257638	+	0.966241i	$0.417056\pi$
$770$	−21.8252	−	9.59018i	−0.786524	−	0.345606i
$771$	−7.54946			−0.271887
$772$	−12.5386	+	12.5386i	−0.451275	+	0.451275i
$773$	−0.499292	+	0.499292i	−0.0179583	+	0.0179583i	−0.716029	−	0.698071i	$-0.754042\pi$
$773$	−0.499292	+	0.499292i	−0.0179583	+	0.0179583i	0.698071	+	0.716029i	$0.254042\pi$
$774$	−9.02081			−0.324246
$775$	−24.5895	−	26.7805i	−0.883280	−	0.961985i
$776$			5.70322i			0.204734i
$777$	−13.9772	+	13.9772i	−0.501429	+	0.501429i
$778$	−1.91674	+	1.91674i	−0.0687184	+	0.0687184i
$779$	23.7813			0.852052
$780$	−4.05678	+	9.23234i	−0.145256	+	0.330571i
$781$		−	39.8558i		−	1.42615i
$782$	−4.72630	−	10.4013i	−0.169012	−	0.371951i
$783$	2.46149	+	2.46149i	0.0879664	+	0.0879664i
$784$			0.454913i			0.0162469i
$785$	−34.8855	+	13.5864i	−1.24512	+	0.484921i
$786$	−1.98524			−0.0708113
$787$	−3.26984	−	3.26984i	−0.116557	−	0.116557i	0.646422	−	0.762980i	$-0.276264\pi$
$787$	−3.26984	−	3.26984i	−0.116557	−	0.116557i	−0.762980	+	0.646422i	$0.776264\pi$
$788$	2.02769	+	2.02769i	0.0722335	+	0.0722335i
$789$	−27.6060			−0.982799
$790$	−5.55838	−	14.2721i	−0.197758	−	0.507778i
$791$	50.8765			1.80896
$792$	−2.94669	−	2.94669i	−0.104706	−	0.104706i
$793$	−2.42124	+	2.42124i	−0.0859807	+	0.0859807i
$794$			38.1181i			1.35276i
$795$	−8.35125	+	19.0056i	−0.296188	+	0.674059i
$796$		−	4.87669i		−	0.172850i
$797$	8.95785	+	8.95785i	0.317303	+	0.317303i	0.847730	−	0.530427i	$-0.177968\pi$
$797$	8.95785	+	8.95785i	0.317303	+	0.317303i	−0.530427	+	0.847730i	$0.677968\pi$
$798$	−9.48107	−	9.48107i	−0.335626	−	0.335626i
$799$	−30.6356			−1.08381
$800$	−4.99546	−	0.213067i	−0.176616	−	0.00753306i
$801$		−	3.58782i		−	0.126769i
$802$	−6.97483	−	6.97483i	−0.246290	−	0.246290i
$803$	24.0967	−	24.0967i	0.850353	−	0.850353i
$804$	2.85850			0.100812
$805$	19.6403	+	19.1557i	0.692231	+	0.675151i
$806$	32.7930			1.15508
$807$	3.10329	−	3.10329i	0.109241	−	0.109241i
$808$	4.50065	+	4.50065i	0.158332	+	0.158332i
$809$		−	24.1346i		−	0.848529i	−0.905538	−	0.424264i	$-0.860533\pi$
$809$		−	24.1346i		−	0.848529i	0.905538	−	0.424264i	$-0.139467\pi$
$810$	−0.811485	−	2.08362i	−0.0285127	−	0.0732111i
$811$	−32.8187			−1.15242			−0.576210	−	0.817302i	$-0.695469\pi$
$811$	−32.8187			−1.15242			−0.576210	+	0.817302i	$0.695469\pi$
$812$	−6.29731	−	6.29731i	−0.220992	−	0.220992i
$813$	13.3660	+	13.3660i	0.468765	+	0.468765i
$814$		−	32.1978i		−	1.12853i
$815$	−24.6870	+	9.61458i	−0.864749	+	0.336784i
$816$		−	2.38223i		−	0.0833947i
$817$	33.4307	−	33.4307i	1.16959	−	1.16959i
$818$	−21.2786	−	21.2786i	−0.743990	−	0.743990i
$819$	11.5377			0.403160
$820$	−9.28903	−	4.08169i	−0.324387	−	0.142539i
$821$	−25.3607			−0.885096			−0.442548	−	0.896745i	$-0.645925\pi$
$821$	−25.3607			−0.885096			−0.442548	+	0.896745i	$0.645925\pi$
$822$	13.6901	+	13.6901i	0.477497	+	0.477497i
$823$	−1.68756	−	1.68756i	−0.0588246	−	0.0588246i	0.677083	−	0.735907i	$-0.263244\pi$
$823$	−1.68756	−	1.68756i	−0.0588246	−	0.0588246i	−0.735907	+	0.677083i	$0.763244\pi$
$824$	2.82727			0.0984926
$825$	20.8173	+	0.887903i	0.724766	+	0.0309128i
$826$			17.4070i			0.605666i
$827$	31.5597	+	31.5597i	1.09744	+	1.09744i	0.994709	+	0.102728i	$0.0327573\pi$
$827$	31.5597	+	31.5597i	1.09744	+	1.09744i	0.102728	+	0.994709i	$0.467243\pi$
$828$	1.98398	+	4.36621i	0.0689482	+	0.151736i
$829$			25.2130i			0.875684i	0.899052	+	0.437842i	$0.144257\pi$
$829$			25.2130i			0.875684i	−0.899052	+	0.437842i	$0.855743\pi$
$830$	−6.97403	−	3.06446i	−0.242072	−	0.106369i
$831$	3.45666			0.119910
$832$	3.18894	−	3.18894i	0.110557	−	0.110557i
$833$	0.766297	−	0.766297i	0.0265506	−	0.0265506i
$834$			19.4321i			0.672878i
$835$	15.2457	+	39.1459i	0.527599	+	1.35470i
$836$	21.8406			0.755372
$837$	−5.14167	+	5.14167i	−0.177722	+	0.177722i
$838$	5.37137	−	5.37137i	0.185551	−	0.185551i
$839$	3.96404			0.136854			0.0684270	−	0.997656i	$-0.478202\pi$
$839$	3.96404			0.136854			0.0684270	+	0.997656i	$0.478202\pi$
$840$	2.07605	+	5.33061i	0.0716306	+	0.183924i
$841$	16.8822			0.582143
$842$	−16.5925	−	16.5925i	−0.571816	−	0.571816i
$843$	1.65338	−	1.65338i	0.0569454	−	0.0569454i
$844$			10.4399i			0.359355i
$845$	15.0235	+	6.60146i	0.516824	+	0.227097i
$846$	12.8600			0.442137
$847$	−11.5161	−	11.5161i	−0.395699	−	0.395699i
$848$	6.56472	−	6.56472i	0.225434	−	0.225434i
$849$	−30.5657			−1.04901
$850$	8.05590	+	8.77372i	0.276315	+	0.300936i
$851$	−13.0150	+	34.6936i	−0.446150	+	1.18928i
$852$	−6.76281	+	6.76281i	−0.231690	+	0.231690i
$853$	−1.04985	−	1.04985i	−0.0359460	−	0.0359460i	0.688905	−	0.724851i	$-0.258092\pi$
$853$	−1.04985	−	1.04985i	−0.0359460	−	0.0359460i	−0.724851	+	0.688905i	$0.758092\pi$
$854$			1.94244i			0.0664690i
$855$	10.7291	+	4.71449i	0.366929	+	0.161232i
$856$			8.86459i			0.302985i
$857$	38.2391	−	38.2391i	1.30622	−	1.30622i	0.382104	−	0.924119i	$-0.375200\pi$
$857$	38.2391	−	38.2391i	1.30622	−	1.30622i	0.924119	−	0.382104i	$-0.124800\pi$
$858$	−13.2891	+	13.2891i	−0.453683	+	0.453683i
$859$		−	0.796740i		−	0.0271844i	−0.999908	−	0.0135922i	$-0.995673\pi$
$859$		−	0.796740i		−	0.0271844i	0.999908	−	0.0135922i	$-0.00432667\pi$
$860$	−18.7960	+	7.32026i	−0.640938	+	0.249619i
$861$			11.6086i			0.395619i
$862$	15.4141	+	15.4141i	0.525005	+	0.525005i
$863$	−16.3964	−	16.3964i	−0.558140	−	0.558140i	0.370637	−	0.928778i	$-0.379139\pi$
$863$	−16.3964	−	16.3964i	−0.558140	−	0.558140i	−0.928778	+	0.370637i	$0.879139\pi$
$864$			1.00000i			0.0340207i
$865$	39.4289	−	15.3559i	1.34062	−	0.522116i
$866$		−	24.1675i		−	0.821245i
$867$	8.00797	−	8.00797i	0.271965	−	0.271965i
$868$	13.1541	−	13.1541i	0.446480	−	0.446480i
$869$		−	28.5442i		−	0.968295i
$870$	7.12628	+	3.13136i	0.241603	+	0.106163i
$871$		−	12.8914i		−	0.436808i
$872$	1.08609	+	1.08609i	0.0367797	+	0.0367797i
$873$	−4.03278	+	4.03278i	−0.136489	+	0.136489i
$874$	−23.5335	−	8.82843i	−0.796033	−	0.298626i
$875$	−25.6724	−	12.6121i	−0.867885	−	0.426365i
$876$	−8.17754			−0.276293
$877$	29.9674	−	29.9674i	1.01193	−	1.01193i	0.0119983	−	0.999928i	$-0.496181\pi$
$877$	29.9674	−	29.9674i	1.01193	−	1.01193i	0.999928	−	0.0119983i	$-0.00381927\pi$
$878$	−13.1793	−	13.1793i	−0.444781	−	0.444781i
$879$	−30.3330			−1.02311
$880$	−8.53099	−	3.74860i	−0.287580	−	0.126365i
$881$			5.14908i			0.173477i	0.996231	+	0.0867384i	$0.0276444\pi$
$881$			5.14908i			0.173477i	−0.996231	+	0.0867384i	$0.972356\pi$
$882$	−0.321672	+	0.321672i	−0.0108313	+	0.0108313i
$883$	24.2836	+	24.2836i	0.817207	+	0.817207i	0.985702	−	0.168495i	$-0.0538908\pi$
$883$	24.2836	+	24.2836i	0.817207	+	0.817207i	−0.168495	+	0.985702i	$0.553891\pi$
$884$	−10.7435			−0.361343
$885$	−5.52136	−	14.1770i	−0.185599	−	0.476556i
$886$	−10.3595			−0.348034
$887$	−11.6259	+	11.6259i	−0.390358	+	0.390358i	−0.874815	−	0.484457i	$-0.839017\pi$
$887$	−11.6259	+	11.6259i	−0.390358	+	0.390358i	0.484457	+	0.874815i	$0.339017\pi$
$888$	−5.46339	+	5.46339i	−0.183339	+	0.183339i
$889$	−25.7782			−0.864574
$890$	−2.91146	−	7.47567i	−0.0975924	−	0.250585i
$891$		−	4.16725i		−	0.139608i
$892$	11.9073	−	11.9073i	0.398686	−	0.398686i
$893$	−47.6587	+	47.6587i	−1.59484	+	1.59484i
$894$	−3.37276			−0.112802
$895$	−35.0585	−	15.4050i	−1.17188	−	0.514934i
$896$		−	2.55834i		−	0.0854680i
$897$	19.6910	−	8.94746i	0.657462	−	0.298747i
$898$	9.17153	+	9.17153i	0.306058	+	0.306058i
$899$		−	25.3123i		−	0.844213i
$900$	−3.38166	−	3.68298i	−0.112722	−	0.122766i
$901$	−22.1164			−0.736806
$902$	−13.3707	−	13.3707i	−0.445196	−	0.445196i
$903$	16.3188	+	16.3188i	0.543056	+	0.543056i
$904$	19.8865			0.661417
$905$	−14.3868	−	6.32169i	−0.478233	−	0.210140i
$906$	18.7035			0.621383
$907$	−5.83912	−	5.83912i	−0.193885	−	0.193885i	0.603488	−	0.797372i	$-0.293777\pi$
$907$	−5.83912	−	5.83912i	−0.193885	−	0.193885i	−0.797372	+	0.603488i	$0.793777\pi$
$908$	0.242263	−	0.242263i	0.00803978	−	0.00803978i
$909$			6.36488i			0.211110i
$910$	24.0403	−	9.36268i	0.796927	−	0.310370i
$911$		−	34.0829i		−	1.12922i	−0.825359	−	0.564608i	$-0.809027\pi$
$911$		−	34.0829i		−	1.12922i	0.825359	−	0.564608i	$-0.190973\pi$
$912$	−3.70595	−	3.70595i	−0.122716	−	0.122716i
$913$	−10.0385	−	10.0385i	−0.332225	−	0.332225i
$914$	−38.8062			−1.28360
$915$	−0.616128	−	1.58201i	−0.0203686	−	0.0522997i
$916$			5.80623i			0.191843i
$917$	3.59134	+	3.59134i	0.118596	+	0.118596i
$918$	1.68449	−	1.68449i	0.0555965	−	0.0555965i
$919$	19.5882			0.646154			0.323077	−	0.946373i	$-0.395283\pi$
$919$	19.5882			0.646154			0.323077	+	0.946373i	$0.395283\pi$
$920$	7.67699	+	7.48758i	0.253103	+	0.246858i
$921$	16.9709			0.559210
$922$	−7.21726	+	7.21726i	−0.237688	+	0.237688i
$923$	30.4992	+	30.4992i	1.00389	+	1.00389i
$924$			10.6612i			0.350729i
$925$	1.64624	−	38.5969i	0.0541280	−	1.26906i
$926$	11.5102			0.378249
$927$	1.99918	+	1.99918i	0.0656617	+	0.0656617i
$928$	−2.46149	−	2.46149i	−0.0808023	−	0.0808023i
$929$		−	1.07470i		−	0.0352599i	−0.999845	−	0.0176300i	$-0.994388\pi$
$929$		−	1.07470i		−	0.0352599i	0.999845	−	0.0176300i	$-0.00561208\pi$
$930$	−6.54092	+	14.8857i	−0.214485	+	0.488121i
$931$		−	2.38420i		−	0.0781390i
$932$	−11.2922	+	11.2922i	−0.369890	+	0.369890i
$933$	1.10744	+	1.10744i	0.0362560	+	0.0362560i
$934$	−29.6273			−0.969434
$935$	8.05590	+	20.6849i	0.263456	+	0.676467i
$936$	4.50985			0.147409
$937$	−29.4635	−	29.4635i	−0.962529	−	0.962529i	0.0367936	−	0.999323i	$-0.488286\pi$
$937$	−29.4635	−	29.4635i	−0.962529	−	0.962529i	−0.999323	+	0.0367936i	$0.988286\pi$
$938$	−5.17107	−	5.17107i	−0.168842	−	0.168842i
$939$	12.6534			0.412929
$940$	26.7955	−	10.4357i	0.873973	−	0.340376i
$941$		−	6.28427i		−	0.204861i	−0.994740	−	0.102431i	$-0.967338\pi$
$941$		−	6.28427i		−	0.204861i	0.994740	−	0.102431i	$-0.0326620\pi$
$942$	11.8389	+	11.8389i	0.385731	+	0.385731i
$943$	9.00240	+	19.8119i	0.293158	+	0.645163i
$944$			6.80402i			0.221452i
$945$	−2.30132	+	5.23730i	−0.0748620	+	0.170370i
$946$	−37.5920			−1.22222
$947$	5.48123	−	5.48123i	0.178116	−	0.178116i	−0.612418	−	0.790534i	$-0.709803\pi$
$947$	5.48123	−	5.48123i	0.178116	−	0.178116i	0.790534	+	0.612418i	$0.209803\pi$
$948$	−4.84343	+	4.84343i	−0.157307	+	0.157307i
$949$			36.8794i			1.19716i
$950$	26.1812	+	1.11669i	0.849431	+	0.0362301i
$951$	11.9273			0.386771
$952$	−4.30950	+	4.30950i	−0.139672	+	0.139672i
$953$	13.7402	−	13.7402i	0.445088	−	0.445088i	−0.448630	−	0.893718i	$-0.648088\pi$
$953$	13.7402	−	13.7402i	0.445088	−	0.445088i	0.893718	+	0.448630i	$0.148088\pi$
$954$	9.28392			0.300578
$955$	−45.6690	−	20.0674i	−1.47781	−	0.649365i
$956$	−0.457589			−0.0147995
$957$	10.2576	+	10.2576i	0.331582	+	0.331582i
$958$	16.5508	−	16.5508i	0.534733	−	0.534733i
$959$		−	49.5312i		−	1.59945i
$960$	0.811485	+	2.08362i	0.0261906	+	0.0672487i
$961$	21.8735			0.705598
$962$	24.6390	+	24.6390i	0.794395	+	0.794395i
$963$	−6.26821	+	6.26821i	−0.201990	+	0.201990i
$964$	22.2609			0.716976
$965$	−36.9474	+	14.3895i	−1.18938	+	0.463214i
$966$	4.30950	−	11.4876i	0.138656	−	0.369608i
$967$	−15.7735	+	15.7735i	−0.507243	+	0.507243i	−0.913679	−	0.406436i	$-0.866771\pi$
$967$	−15.7735	+	15.7735i	−0.507243	+	0.507243i	0.406436	+	0.913679i	$0.366771\pi$
$968$	−4.50142	−	4.50142i	−0.144681	−	0.144681i
$969$			12.4853i			0.401085i
$970$	−5.13026	+	11.6753i	−0.164723	+	0.374873i
$971$			45.2891i			1.45340i	0.686957	+	0.726698i	$0.258946\pi$
$971$			45.2891i			1.45340i	−0.686957	+	0.726698i	$0.741054\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	35.1530	−	35.1530i	1.12695	−	1.12695i
$974$			32.4397i			1.03943i
$975$	−16.6097	+	15.2508i	−0.531936	+	0.488416i
$976$			0.759260i			0.0243033i
$977$	35.2043	+	35.2043i	1.12629	+	1.12629i	0.990776	+	0.135511i	$0.0432675\pi$
$977$	35.2043	+	35.2043i	1.12629	+	1.12629i	0.135511	+	0.990776i	$0.456732\pi$
$978$	8.37789	+	8.37789i	0.267895	+	0.267895i
$979$		−	14.9513i		−	0.477847i
$980$	−0.409211	+	0.931275i	−0.0130718	+	0.0297485i
$981$			1.53597i			0.0490396i
$982$	−21.8056	+	21.8056i	−0.695844	+	0.695844i
$983$	−15.7468	+	15.7468i	−0.502245	+	0.502245i	−0.912135	−	0.409890i	$-0.865567\pi$
$983$	−15.7468	+	15.7468i	−0.502245	+	0.502245i	0.409890	+	0.912135i	$0.365567\pi$
$984$			4.53754i			0.144651i
$985$	2.32701	+	5.97498i	0.0741446	+	0.190379i
$986$			8.29271i			0.264094i
$987$	−23.2640	−	23.2640i	−0.740503	−	0.740503i
$988$	−16.7133	+	16.7133i	−0.531720	+	0.531720i
$989$	40.5059	+	15.1955i	1.28801	+	0.483188i
$990$	−3.38166	−	8.68298i	−0.107476	−	0.275963i
$991$	8.94505			0.284149			0.142074	−	0.989856i	$-0.454623\pi$
$991$	8.94505			0.284149			0.142074	+	0.989856i	$0.454623\pi$
$992$	5.14167	−	5.14167i	0.163248	−	0.163248i
$993$	9.15632	+	9.15632i	0.290567	+	0.290567i
$994$	24.4681			0.776080
$995$	4.38677	−	9.98332i	0.139070	−	0.316493i
$996$			3.40670i			0.107945i
$997$	−0.677346	+	0.677346i	−0.0214518	+	0.0214518i	−0.717751	−	0.696300i	$-0.754829\pi$
$997$	−0.677346	+	0.677346i	−0.0214518	+	0.0214518i	0.696300	+	0.717751i	$0.254829\pi$
$998$	−18.0239	−	18.0239i	−0.570537	−	0.570537i
$999$	−7.72640			−0.244452

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.j.a.643.5	yes	24
5.2	odd	4	inner	690.2.j.a.367.2	✓	24
23.22	odd	2	inner	690.2.j.a.643.2	yes	24
115.22	even	4	inner	690.2.j.a.367.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.j.a.367.2	✓	24	5.2	odd	4	inner
690.2.j.a.367.5	yes	24	115.22	even	4	inner
690.2.j.a.643.2	yes	24	23.22	odd	2	inner
690.2.j.a.643.5	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(0.899538 - 2.04715i) q^{5} -1.00000 q^{6} +(1.80902 + 1.80902i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(0.899538 - 2.04715i) q^{5} -1.00000 q^{6} +(1.80902 + 1.80902i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(0.811485 + 2.08362i) q^{10} +4.16725i q^{11} +(0.707107 - 0.707107i) q^{12} +(-3.18894 - 3.18894i) q^{13} -2.55834 q^{14} +(2.08362 - 0.811485i) q^{15} -1.00000 q^{16} +(1.68449 + 1.68449i) q^{17} +(-0.707107 - 0.707107i) q^{18} +5.24101 q^{19} +(-2.04715 - 0.899538i) q^{20} +2.55834i q^{21} +(-2.94669 - 2.94669i) q^{22} +(1.98398 + 4.36621i) q^{23} +1.00000i q^{24} +(-3.38166 - 3.68298i) q^{25} +4.50985 q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.80902 - 1.80902i) q^{28} -3.48107i q^{29} +(-0.899538 + 2.04715i) q^{30} +7.27142 q^{31} +(0.707107 - 0.707107i) q^{32} +(-2.94669 + 2.94669i) q^{33} -2.38223 q^{34} +(5.33061 - 2.07605i) q^{35} +1.00000 q^{36} +(5.46339 + 5.46339i) q^{37} +(-3.70595 + 3.70595i) q^{38} -4.50985i q^{39} +(2.08362 - 0.811485i) q^{40} +4.53754 q^{41} +(-1.80902 - 1.80902i) q^{42} +(6.37868 - 6.37868i) q^{43} +4.16725 q^{44} +(2.04715 + 0.899538i) q^{45} +(-4.49027 - 1.68449i) q^{46} +(-9.09342 + 9.09342i) q^{47} +(-0.707107 - 0.707107i) q^{48} -0.454913i q^{49} +(4.99546 + 0.213067i) q^{50} +2.38223i q^{51} +(-3.18894 + 3.18894i) q^{52} +(-6.56472 + 6.56472i) q^{53} -1.00000i q^{54} +(8.53099 + 3.74860i) q^{55} +2.55834i q^{56} +(3.70595 + 3.70595i) q^{57} +(2.46149 + 2.46149i) q^{58} -6.80402i q^{59} +(-0.811485 - 2.08362i) q^{60} -0.759260i q^{61} +(-5.14167 + 5.14167i) q^{62} +(-1.80902 + 1.80902i) q^{63} +1.00000i q^{64} +(-9.39683 + 3.65967i) q^{65} -4.16725i q^{66} +(2.02126 + 2.02126i) q^{67} +(1.68449 - 1.68449i) q^{68} +(-1.68449 + 4.49027i) q^{69} +(-2.30132 + 5.23730i) q^{70} -9.56406 q^{71} +(-0.707107 + 0.707107i) q^{72} +(-5.78239 - 5.78239i) q^{73} -7.72640 q^{74} +(0.213067 - 4.99546i) q^{75} -5.24101i q^{76} +(-7.53863 + 7.53863i) q^{77} +(3.18894 + 3.18894i) q^{78} -6.84964 q^{79} +(-0.899538 + 2.04715i) q^{80} -1.00000 q^{81} +(-3.20853 + 3.20853i) q^{82} +(-2.40890 + 2.40890i) q^{83} +2.55834 q^{84} +(4.96367 - 1.93314i) q^{85} +9.02081i q^{86} +(2.46149 - 2.46149i) q^{87} +(-2.94669 + 2.94669i) q^{88} -3.58782 q^{89} +(-2.08362 + 0.811485i) q^{90} -11.5377i q^{91} +(4.36621 - 1.98398i) q^{92} +(5.14167 + 5.14167i) q^{93} -12.8600i q^{94} +(4.71449 - 10.7291i) q^{95} +1.00000 q^{96} +(4.03278 + 4.03278i) q^{97} +(0.321672 + 0.321672i) q^{98} -4.16725 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{6}+O(q^{10}) \) 24 * q - 24 * q^6	\( 24 q - 24 q^{6} - 24 q^{16} - 8 q^{23} - 16 q^{25} - 16 q^{26} + 16 q^{31} - 16 q^{35} + 24 q^{36} - 8 q^{46} - 8 q^{47} + 24 q^{50} + 24 q^{55} + 16 q^{58} - 56 q^{62} - 32 q^{70} - 16 q^{71} - 48 q^{73} - 24 q^{81} + 24 q^{82} + 16 q^{87} - 8 q^{92} + 56 q^{93} + 24 q^{95} + 24 q^{96} - 32 q^{98}+O(q^{100}) \) 24 * q - 24 * q^6 - 24 * q^16 - 8 * q^23 - 16 * q^25 - 16 * q^26 + 16 * q^31 - 16 * q^35 + 24 * q^36 - 8 * q^46 - 8 * q^47 + 24 * q^50 + 24 * q^55 + 16 * q^58 - 56 * q^62 - 32 * q^70 - 16 * q^71 - 48 * q^73 - 24 * q^81 + 24 * q^82 + 16 * q^87 - 8 * q^92 + 56 * q^93 + 24 * q^95 + 24 * q^96 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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