LMFDB - Embedded newform 690.2.j.a.367.2

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			367.2
Character	$\chi$	$=$	690.367
Dual form			690.2.j.a.643.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-0.899538 - 2.04715i) q^{5} -1.00000 q^{6} +(-1.80902 + 1.80902i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(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} +(4.36621 - 1.98398i) 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} +(1.98398 + 4.36621i) 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

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

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	$-0.910627\pi$
$7$	−1.80902	+	1.80902i	−0.683744	+	0.683744i	0.277098	+	0.960842i	$0.410627\pi$
$8$	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	−0.993984	−	0.109530i	$-0.965066\pi$
$13$	−3.18894	+	3.18894i	−0.884454	+	0.884454i	0.109530	+	0.993984i	$0.465066\pi$
$14$	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	$-0.843285\pi$
$17$	−1.68449	+	1.68449i	−0.408549	+	0.408549i	0.472683	+	0.881232i	$0.343285\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	−5.24101			−1.20237			−0.601185	−	0.799110i	$-0.705304\pi$
$19$	−5.24101			−1.20237			−0.601185	+	0.799110i	$0.705304\pi$
$20$	2.04715	−	0.899538i	0.457757	−	0.201143i
$21$			2.55834i			0.558275i
$22$	2.94669	−	2.94669i	0.628236	−	0.628236i
$23$	4.36621	−	1.98398i	0.910418	−	0.413689i
$23$	4.36621	−	1.98398i	0.910418	−	0.413689i
$24$		−	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	$0.104762\pi$
$29$			3.48107i			0.646418i	−0.946328	+	0.323209i	$0.895238\pi$
$30$	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	$-0.969044\pi$
$37$	−5.46339	+	5.46339i	−0.898175	+	0.898175i	0.0970994	+	0.995275i	$0.469044\pi$
$38$	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	$-0.491437\pi$
$43$	−6.37868	−	6.37868i	−0.972739	−	0.972739i	−0.999638	+	0.0268989i	$0.991437\pi$
$44$	−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	−0.908477	−	0.417935i	$-0.862754\pi$
$47$	−9.09342	−	9.09342i	−1.32641	−	1.32641i	−0.417935	−	0.908477i	$-0.637246\pi$
$48$	−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	$-0.0299180\pi$
$53$	6.56472	+	6.56472i	0.901734	+	0.901734i	−0.0938519	+	0.995586i	$0.529918\pi$
$54$			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	$0.146052\pi$
$59$			6.80402i			0.885808i	−0.896569	+	0.442904i	$0.853948\pi$
$60$	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	$-0.805867\pi$
$67$	−2.02126	+	2.02126i	−0.246937	+	0.246937i	0.572776	+	0.819712i	$0.305867\pi$
$68$	−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	−0.959270	−	0.282492i	$-0.908839\pi$
$73$	−5.78239	+	5.78239i	−0.676778	+	0.676778i	0.282492	+	0.959270i	$0.408839\pi$
$74$	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	$-0.374090\pi$
$79$	6.84964			0.770645			0.385322	+	0.922782i	$0.374090\pi$
$80$	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	$-0.190134\pi$
$83$	2.40890	+	2.40890i	0.264411	+	0.264411i	−0.562432	+	0.826843i	$0.690134\pi$
$84$	−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	$-0.439101\pi$
$89$	3.58782			0.380308			0.190154	+	0.981754i	$0.439101\pi$
$90$	2.08362	+	0.811485i	0.219633	+	0.0855381i
$91$		−	11.5377i		−	1.20948i
$92$	1.98398	+	4.36621i	0.206844	+	0.455209i
$93$	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	$-0.843501\pi$
$97$	−4.03278	+	4.03278i	−0.409467	+	0.409467i	0.472086	+	0.881553i	$0.343501\pi$
$98$	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	$-0.294482\pi$
$103$	−1.99918	−	1.99918i	−0.196985	−	0.196985i	−0.798706	+	0.601721i	$0.794482\pi$
$104$			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	$-0.890953\pi$
$107$	−6.26821	+	6.26821i	−0.605971	+	0.605971i	0.335920	+	0.941891i	$0.390953\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	−1.53597			−0.147119			−0.0735595	−	0.997291i	$-0.523436\pi$
$109$	−1.53597			−0.147119			−0.0735595	+	0.997291i	$0.523436\pi$
$110$	−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	−0.911473	−	0.411360i	$-0.865054\pi$
$113$	−14.0619	−	14.0619i	−1.32283	−	1.32283i	−0.411360	−	0.911473i	$-0.634946\pi$
$114$	5.24101			0.490865
$115$	−7.98909	−	7.15363i	−0.744986	−	0.667080i
$116$	−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	0.316393	−	0.948628i	$-0.397528\pi$
$127$	−7.12493	−	7.12493i	−0.632235	−	0.632235i	−0.948628	+	0.316393i	$0.897528\pi$
$128$	−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	0.187325	−	0.982298i	$-0.440018\pi$
$137$	13.6901	−	13.6901i	1.16962	−	1.16962i	0.982298	−	0.187325i	$-0.0599819\pi$
$138$	−4.36621	+	1.98398i	−0.371677	+	0.168888i
$139$			19.4321i			1.64821i	0.566438	+	0.824104i	$0.308321\pi$
$139$			19.4321i			1.64821i	−0.566438	+	0.824104i	$0.691679\pi$
$140$	−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	$-0.544117\pi$
$149$	−3.37276			−0.276307			−0.138154	+	0.990411i	$0.544117\pi$
$150$	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	$-0.517105\pi$
$157$	11.8389	−	11.8389i	0.944844	−	0.944844i	0.998556	+	0.0537126i	$0.0171055\pi$
$158$	−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	−0.954480	−	0.298274i	$-0.903589\pi$
$163$	−8.37789	+	8.37789i	−0.656207	+	0.656207i	0.298274	+	0.954480i	$0.403589\pi$
$164$			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	−0.999597	−	0.0284037i	$-0.990958\pi$
$167$	−13.2847	−	13.2847i	−1.02800	−	1.02800i	−0.0284037	−	0.999597i	$-0.509042\pi$
$168$	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	0.0174703	−	0.999847i	$-0.494439\pi$
$173$	13.3807	−	13.3807i	1.01732	−	1.01732i	0.999847	−	0.0174703i	$-0.00556124\pi$
$174$		−	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	$0.221070\pi$
$179$			17.1255i			1.28002i	−0.768367	+	0.640010i	$0.778930\pi$
$180$	−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	−0.995656	−	0.0931061i	$-0.970320\pi$
$193$	−12.5386	+	12.5386i	−0.902550	+	0.902550i	0.0931061	+	0.995656i	$0.470320\pi$
$194$	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	0.631174	−	0.775641i	$-0.282573\pi$
$197$	−2.02769	−	2.02769i	−0.144467	−	0.144467i	−0.775641	+	0.631174i	$0.782573\pi$
$198$	−2.94669	−	2.94669i	−0.209412	−	0.209412i
$199$	−4.87669			−0.345699			−0.172850	−	0.984948i	$-0.555297\pi$
$199$	−4.87669			−0.345699			−0.172850	+	0.984948i	$0.555297\pi$
$200$	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
$207$	−1.98398	−	4.36621i	−0.137896	−	0.303473i
$208$	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	−0.185308	−	0.982681i	$-0.559328\pi$
$223$	11.9073	−	11.9073i	0.797373	−	0.797373i	0.982681	+	0.185308i	$0.0593282\pi$
$224$	−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	$-0.753619\pi$
$227$	−0.242263	+	0.242263i	−0.0160796	+	0.0160796i	0.699021	+	0.715101i	$0.253619\pi$
$228$	−3.70595	−	3.70595i	−0.245433	−	0.245433i
$229$	5.80623			0.383687			0.191843	−	0.981426i	$-0.438553\pi$
$229$	5.80623			0.383687			0.191843	+	0.981426i	$0.438553\pi$
$230$	0.590758	+	10.7075i	0.0389534	+	0.706033i
$231$	−10.6612			−0.701457
$232$	2.46149	+	2.46149i	0.161605	+	0.161605i
$233$	−11.2922	+	11.2922i	−0.739779	+	0.739779i	−0.972535	−	0.232756i	$-0.925226\pi$
$233$	−11.2922	+	11.2922i	−0.739779	+	0.739779i	0.232756	+	0.972535i	$0.425226\pi$
$234$		−	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	$0.00471099\pi$
$239$			0.457589i			0.0295990i	−0.999890	+	0.0147995i	$0.995289\pi$
$240$	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
$253$	8.26775	+	18.1951i	0.519789	+	1.14392i
$254$			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	0.520729	−	0.853722i	$-0.325660\pi$
$257$	−5.33827	−	5.33827i	−0.332992	−	0.332992i	−0.853722	+	0.520729i	$0.825660\pi$
$258$	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	0.973039	+	0.230639i	$0.0740817\pi$
$263$	19.5204	+	19.5204i	1.20368	+	1.20368i	0.230639	+	0.973039i	$0.425918\pi$
$264$	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	$0.0427156\pi$
$269$			4.38872i			0.267585i	−0.991009	+	0.133793i	$0.957284\pi$
$270$	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	0.776714	−	0.629854i	$-0.216885\pi$
$277$	2.44423	+	2.44423i	0.146860	+	0.146860i	−0.629854	+	0.776714i	$0.716885\pi$
$278$	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	0.937921	+	0.346850i	$0.112749\pi$
$283$	21.6132	+	21.6132i	1.28477	+	1.28477i	0.346850	+	0.937921i	$0.387251\pi$
$284$		−	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	0.954347	+	0.298699i	$0.0965528\pi$
$293$	21.4487	+	21.4487i	1.25305	+	1.25305i	0.298699	+	0.954347i	$0.403447\pi$
$294$		−	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	0.961098	−	0.276209i	$-0.0890781\pi$
$307$	12.0002	+	12.0002i	0.684889	+	0.684889i	−0.276209	+	0.961098i	$0.589078\pi$
$308$	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	$-0.366407\pi$
$313$	−8.94733	−	8.94733i	−0.505733	−	0.505733i	−0.913214	+	0.407481i	$0.866407\pi$
$314$	−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	0.903108	−	0.429413i	$-0.141279\pi$
$317$	8.43391	+	8.43391i	0.473695	+	0.473695i	−0.429413	+	0.903108i	$0.641279\pi$
$318$	−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
$322$	11.1702	−	5.07570i	0.622493	−	0.282857i
$323$	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	$-0.808628\pi$
$337$	−4.75471	+	4.75471i	−0.259006	+	0.259006i	0.565644	+	0.824650i	$0.308628\pi$
$338$	−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
$345$	−10.7075	+	0.590758i	−0.576474	+	0.0318053i
$346$	−18.9232			−1.01732
$347$	−3.12333	−	3.12333i	−0.167669	−	0.167669i	0.618285	−	0.785954i	$-0.287828\pi$
$347$	−3.12333	−	3.12333i	−0.167669	−	0.167669i	−0.785954	+	0.618285i	$0.787828\pi$
$348$	−2.46149	+	2.46149i	−0.131950	+	0.131950i
$349$			16.1446i			0.864201i	0.901825	+	0.432101i	$0.142227\pi$
$349$			16.1446i			0.864201i	−0.901825	+	0.432101i	$0.857773\pi$
$350$	−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	−0.924742	−	0.380596i	$-0.875719\pi$
$353$	−10.2236	+	10.2236i	−0.544146	+	0.544146i	0.380596	+	0.924742i	$0.375719\pi$
$354$		−	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	$-0.660305\pi$
$359$	−18.2877			−0.965188			−0.482594	+	0.875844i	$0.660305\pi$
$360$	−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	$-0.658680\pi$
$367$	7.66636	−	7.66636i	0.400181	−	0.400181i	0.878297	+	0.478116i	$0.158680\pi$
$368$	−4.36621	+	1.98398i	−0.227605	+	0.103422i
$369$		−	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	$-0.00581550\pi$
$373$	18.9572	+	18.9572i	0.981564	+	0.981564i	−0.0182689	+	0.999833i	$0.505815\pi$
$374$			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	$-0.310148\pi$
$379$	21.8702			1.12340			0.561699	+	0.827341i	$0.310148\pi$
$380$	−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	−0.998583	−	0.0532143i	$-0.983053\pi$
$383$	−20.5841	−	20.5841i	−1.05180	−	1.05180i	−0.0532143	−	0.998583i	$-0.516947\pi$
$384$			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	$-0.521891\pi$
$389$	−2.71068			−0.137437			−0.0687184	+	0.997636i	$0.521891\pi$
$390$	−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	0.882558	+	0.470203i	$0.155819\pi$
$397$	26.9536	+	26.9536i	1.35276	+	1.35276i	0.470203	+	0.882558i	$0.344181\pi$
$398$	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	$-0.732931\pi$
$409$		−	30.0925i		−	1.48798i	0.668191	−	0.743990i	$-0.267069\pi$
$410$	−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	$-0.440593\pi$
$419$	7.59626			0.371102			0.185551	+	0.982635i	$0.440593\pi$
$420$	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	$-0.0527757\pi$
$433$	17.0890	+	17.0890i	0.821245	+	0.821245i	−0.165041	+	0.986287i	$0.552776\pi$
$434$	18.6027			0.892960
$435$	2.82484	−	7.25324i	0.135441	−	0.347766i
$436$		−	1.53597i		−	0.0735595i
$437$	−22.8833	+	10.3981i	−1.09466	+	0.497407i
$438$	5.78239	−	5.78239i	0.276293	−	0.276293i
$439$		−	18.6384i		−	0.889563i	−0.895639	−	0.444781i	$-0.853281\pi$
$439$		−	18.6384i		−	0.889563i	0.895639	−	0.444781i	$-0.146719\pi$
$440$	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	−0.511343	−	0.859377i	$-0.670852\pi$
$443$	7.32527	−	7.32527i	0.348034	−	0.348034i	0.859377	+	0.511343i	$0.170852\pi$
$444$	−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	$0.0990102\pi$
$449$			12.9705i			0.612116i	−0.952013	+	0.306058i	$0.900990\pi$
$450$	−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	−0.344988	+	0.938607i	$0.612117\pi$
$457$	−27.4401	+	27.4401i	−1.28360	+	1.28360i	−0.938607	+	0.344988i	$0.887883\pi$
$458$	−4.10563	−	4.10563i	−0.191843	−	0.191843i
$459$	2.38223			0.111193
$460$	7.15363	−	7.98909i	0.333540	−	0.372493i
$461$	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	−0.870470	−	0.492221i	$-0.836185\pi$
$463$	−8.13895	+	8.13895i	−0.378249	+	0.378249i	0.492221	+	0.870470i	$0.336185\pi$
$464$		−	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	$-0.990413\pi$
$467$	−20.9496	+	20.9496i	−0.969434	+	0.969434i	0.0301128	+	0.999547i	$0.490413\pi$
$468$	−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	$-0.320412\pi$
$479$	23.4064			1.06947			0.534733	+	0.845021i	$0.320412\pi$
$480$	−0.899538	−	2.04715i	−0.0410581	−	0.0934393i
$481$		−	34.8449i		−	1.58879i
$482$	15.7409	−	15.7409i	0.716976	−	0.716976i
$483$	5.07570	+	11.1702i	0.230952	+	0.508264i
$484$		−	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	0.999190	+	0.0402440i	$0.0128135\pi$
$487$	22.9383	+	22.9383i	1.03943	+	1.03943i	0.0402440	+	0.999190i	$0.487186\pi$
$488$	−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	$-0.806735\pi$
$499$		−	25.4897i		−	1.14107i	0.821272	−	0.570537i	$-0.193265\pi$
$500$	−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	$-0.214816\pi$
$503$	3.49872	+	3.49872i	0.156000	+	0.156000i	−0.624792	+	0.780792i	$0.714816\pi$
$504$	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	$-0.802407\pi$
$509$		−	26.2453i		−	1.16330i	0.813439	−	0.581651i	$-0.197593\pi$
$510$	−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	$-0.236047\pi$
$523$	1.41722	+	1.41722i	0.0619705	+	0.0619705i	−0.675442	+	0.737413i	$0.736047\pi$
$524$			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	0.607318	−	0.794459i	$-0.292245\pi$
$547$	−4.37686	−	4.37686i	−0.187141	−	0.187141i	−0.794459	+	0.607318i	$0.792245\pi$
$548$	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
$552$	−1.98398	−	4.36621i	−0.0844439	−	0.185838i
$553$	−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	$-0.720939\pi$
$557$	3.04302	−	3.04302i	0.128937	−	0.128937i	0.768630	+	0.639693i	$0.220939\pi$
$558$	−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	−0.988203	−	0.153151i	$-0.951058\pi$
$563$	−27.0816	−	27.0816i	−1.14135	−	1.14135i	−0.153151	−	0.988203i	$-0.548942\pi$
$564$		−	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	$-0.241079\pi$
$569$	34.6663			1.45329			0.726644	+	0.687014i	$0.241079\pi$
$570$	−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
$575$	−7.45808	+	22.7898i	−0.311023	+	0.950402i
$576$	−1.00000			−0.0416667
$577$	−5.16579	−	5.16579i	−0.215054	−	0.215054i	0.591356	−	0.806411i	$-0.298593\pi$
$577$	−5.16579	−	5.16579i	−0.215054	−	0.215054i	−0.806411	+	0.591356i	$0.798593\pi$
$578$	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	0.624118	−	0.781330i	$-0.285459\pi$
$587$	−3.80896	−	3.80896i	−0.157213	−	0.157213i	−0.781330	+	0.624118i	$0.785459\pi$
$588$	−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	−0.742290	−	0.670079i	$-0.766260\pi$
$593$	−1.75845	+	1.75845i	−0.0722109	+	0.0722109i	0.670079	+	0.742290i	$0.266260\pi$
$594$	−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
$598$	19.6910	−	8.94746i	0.805223	−	0.365889i
$599$			36.0972i			1.47489i	0.675407	+	0.737445i	$0.263968\pi$
$599$			36.0972i			1.47489i	−0.675407	+	0.737445i	$0.736032\pi$
$600$	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	−0.999099	−	0.0424416i	$-0.986486\pi$
$607$	−25.6608	−	25.6608i	−1.04154	−	1.04154i	−0.0424416	−	0.999099i	$-0.513514\pi$
$608$	−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	0.994708	+	0.102742i	$0.0327615\pi$
$613$	27.1716	+	27.1716i	1.09745	+	1.09745i	0.102742	+	0.994708i	$0.467238\pi$
$614$		−	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	$-0.549792\pi$
$617$	20.6665	−	20.6665i	0.832002	−	0.832002i	0.987790	+	0.155789i	$0.0497919\pi$
$618$	1.99918	+	1.99918i	0.0804189	+	0.0804189i
$619$	−44.8826			−1.80398			−0.901991	−	0.431754i	$-0.857895\pi$
$619$	−44.8826			−1.80398			−0.901991	+	0.431754i	$0.857895\pi$
$620$	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	$-0.433805\pi$
$643$	−19.5758	−	19.5758i	−0.771994	−	0.771994i	−0.978455	+	0.206461i	$0.933805\pi$
$644$	−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	0.995651	+	0.0931635i	$0.0296979\pi$
$647$	27.6953	+	27.6953i	1.08881	+	1.08881i	0.0931635	+	0.995651i	$0.470302\pi$
$648$	−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	−0.994564	−	0.104122i	$-0.966797\pi$
$653$	−22.7542	+	22.7542i	−0.890442	+	0.890442i	0.104122	+	0.994564i	$0.466797\pi$
$654$	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	$-0.601950\pi$
$659$	−16.1643			−0.629673			−0.314837	+	0.949146i	$0.601950\pi$
$660$	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
$667$	6.90638	+	15.1991i	0.267416	+	0.588511i
$668$	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	−0.998504	−	0.0546752i	$-0.982588\pi$
$673$	−24.4850	+	24.4850i	−0.943829	+	0.943829i	0.0546752	+	0.998504i	$0.482588\pi$
$674$	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	$-0.625818\pi$
$677$	13.9941	−	13.9941i	0.537836	−	0.537836i	0.922893	+	0.385057i	$0.125818\pi$
$678$	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	−0.662092	−	0.749422i	$-0.730331\pi$
$683$	2.28231	−	2.28231i	0.0873303	−	0.0873303i	0.749422	+	0.662092i	$0.230331\pi$
$684$	−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
$690$	7.98909	+	7.15363i	0.304139	+	0.272334i
$691$	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	$-0.830884\pi$
$709$	−45.9132			−1.72431			−0.862153	+	0.506648i	$0.830884\pi$
$710$	7.76109	−	19.9279i	0.291269	−	0.747881i
$711$		−	6.84964i		−	0.256882i
$712$	2.53697	−	2.53697i	0.0950770	−	0.0950770i
$713$	31.7486	−	14.4264i	1.18899	−	0.540272i
$714$			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	$-0.805269\pi$
$719$		−	30.7995i		−	1.14863i	0.818635	−	0.574314i	$-0.194731\pi$
$720$	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	$-0.628104\pi$
$727$	14.2480	−	14.2480i	0.528429	−	0.528429i	0.920104	+	0.391674i	$0.128104\pi$
$728$	−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	$-0.210797\pi$
$733$	4.70374	+	4.70374i	0.173737	+	0.173737i	−0.614882	+	0.788619i	$0.710797\pi$
$734$	−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	$-0.774910\pi$
$739$		−	35.3216i		−	1.29932i	0.760223	−	0.649662i	$-0.225090\pi$
$740$	−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	$-0.0898383\pi$
$743$	18.5881	+	18.5881i	0.681932	+	0.681932i	−0.278503	+	0.960435i	$0.589838\pi$
$744$		−	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	$-0.778853\pi$
$757$	−3.52220	+	3.52220i	−0.128016	+	0.128016i	0.640196	+	0.768212i	$0.278853\pi$
$758$	−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	$-0.582944\pi$
$769$	−14.2891			−0.515277			−0.257638	+	0.966241i	$0.582944\pi$
$770$	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	$-0.245958\pi$
$773$	0.499292	+	0.499292i	0.0179583	+	0.0179583i	−0.698071	+	0.716029i	$0.745958\pi$
$774$	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
$782$	10.4013	−	4.72630i	0.371951	−	0.169012i
$783$	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	$-0.723736\pi$
$787$	3.26984	−	3.26984i	0.116557	−	0.116557i	0.762980	+	0.646422i	$0.223736\pi$
$788$	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	$-0.822032\pi$
$797$	−8.95785	+	8.95785i	−0.317303	+	0.317303i	0.530427	+	0.847730i	$0.322032\pi$
$798$	−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
$805$	27.3934	−	1.51136i	0.965492	−	0.0532683i
$806$	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	$0.139467\pi$
$809$			24.1346i			0.848529i	−0.905538	+	0.424264i	$0.860533\pi$
$810$	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	−0.735907	−	0.677083i	$-0.763244\pi$
$823$	−1.68756	+	1.68756i	−0.0588246	+	0.0588246i	0.677083	+	0.735907i	$0.263244\pi$
$824$	−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	−0.102728	+	0.994709i	$0.532757\pi$
$827$	−31.5597	+	31.5597i	−1.09744	+	1.09744i	−0.994709	+	0.102728i	$0.967243\pi$
$828$	4.36621	−	1.98398i	0.151736	−	0.0689482i
$829$		−	25.2130i		−	0.875684i	−0.899052	−	0.437842i	$-0.855743\pi$
$829$		−	25.2130i		−	0.875684i	0.899052	−	0.437842i	$-0.144257\pi$
$830$	−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	$-0.521798\pi$
$839$	−3.96404			−0.136854			−0.0684270	+	0.997656i	$0.521798\pi$
$840$	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	−0.724851	−	0.688905i	$-0.758092\pi$
$853$	−1.04985	+	1.04985i	−0.0359460	+	0.0359460i	0.688905	+	0.724851i	$0.258092\pi$
$854$		−	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	0.924119	+	0.382104i	$0.124800\pi$
$857$	38.2391	+	38.2391i	1.30622	+	1.30622i	0.382104	+	0.924119i	$0.375200\pi$
$858$	13.2891	+	13.2891i	0.453683	+	0.453683i
$859$			0.796740i			0.0271844i	0.999908	+	0.0135922i	$0.00432667\pi$
$859$			0.796740i			0.0271844i	−0.999908	+	0.0135922i	$0.995673\pi$
$860$	−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	−0.928778	−	0.370637i	$-0.879139\pi$
$863$	−16.3964	+	16.3964i	−0.558140	+	0.558140i	0.370637	+	0.928778i	$0.379139\pi$
$864$		−	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	0.999928	+	0.0119983i	$0.00381927\pi$
$877$	29.9674	+	29.9674i	1.01193	+	1.01193i	0.0119983	+	0.999928i	$0.496181\pi$
$878$	−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	−0.168495	−	0.985702i	$-0.553891\pi$
$883$	24.2836	−	24.2836i	0.817207	−	0.817207i	0.985702	+	0.168495i	$0.0538908\pi$
$884$	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	0.484457	−	0.874815i	$-0.339017\pi$
$887$	−11.6259	−	11.6259i	−0.390358	−	0.390358i	−0.874815	+	0.484457i	$0.839017\pi$
$888$	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
$897$	8.94746	+	19.6910i	0.298747	+	0.657462i
$898$	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	$-0.706223\pi$
$907$	5.83912	−	5.83912i	0.193885	−	0.193885i	0.797372	+	0.603488i	$0.206223\pi$
$908$	−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	$-0.604717\pi$
$919$	−19.5882			−0.646154			−0.323077	+	0.946373i	$0.604717\pi$
$920$	−10.7075	+	0.590758i	−0.353017	+	0.0194767i
$921$	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	$0.00561208\pi$
$929$			1.07470i			0.0352599i	−0.999845	+	0.0176300i	$0.994388\pi$
$930$	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	$-0.511714\pi$
$937$	29.4635	−	29.4635i	0.962529	−	0.962529i	0.999323	+	0.0367936i	$0.0117144\pi$
$938$	−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
$943$	19.8119	−	9.00240i	0.645163	−	0.293158i
$944$		−	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	0.790534	−	0.612418i	$-0.209803\pi$
$947$	5.48123	+	5.48123i	0.178116	+	0.178116i	−0.612418	+	0.790534i	$0.709803\pi$
$948$	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	$-0.351912\pi$
$953$	−13.7402	−	13.7402i	−0.445088	−	0.445088i	−0.893718	+	0.448630i	$0.851912\pi$
$954$	−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	0.406436	−	0.913679i	$-0.366771\pi$
$967$	−15.7735	−	15.7735i	−0.507243	−	0.507243i	−0.913679	+	0.406436i	$0.866771\pi$
$968$	−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	−0.135511	+	0.990776i	$0.543268\pi$
$977$	−35.2043	+	35.2043i	−1.12629	+	1.12629i	−0.990776	+	0.135511i	$0.956732\pi$
$978$	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	$-0.134433\pi$
$983$	15.7468	+	15.7468i	0.502245	+	0.502245i	−0.409890	+	0.912135i	$0.634433\pi$
$984$		−	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	0.696300	−	0.717751i	$-0.254829\pi$
$997$	−0.677346	−	0.677346i	−0.0214518	−	0.0214518i	−0.717751	+	0.696300i	$0.754829\pi$
$998$	−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.367.2	✓	24
5.3	odd	4	inner	690.2.j.a.643.5	yes	24
23.22	odd	2	inner	690.2.j.a.367.5	yes	24
115.68	even	4	inner	690.2.j.a.643.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.j.a.367.2	✓	24	1.1	even	1	trivial
690.2.j.a.367.5	yes	24	23.22	odd	2	inner
690.2.j.a.643.2	yes	24	115.68	even	4	inner
690.2.j.a.643.5	yes	24	5.3	odd	4	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
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} +(4.36621 - 1.98398i) 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} +(1.98398 + 4.36621i) 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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