LMFDB - Embedded newform 690.2.j.a.643.7

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			643.7
Character	$\chi$	$=$	690.643
Dual form			690.2.j.a.367.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-2.22154 + 0.254460i) q^{5} -1.00000 q^{6} +(2.54671 + 2.54671i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-2.22154 + 0.254460i) q^{5} -1.00000 q^{6} +(2.54671 + 2.54671i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(-1.39094 + 1.75080i) q^{10} +3.50160i q^{11} +(-0.707107 + 0.707107i) q^{12} +(2.40571 + 2.40571i) q^{13} +3.60159 q^{14} +(1.75080 + 1.39094i) q^{15} -1.00000 q^{16} +(1.37206 + 1.37206i) q^{17} +(0.707107 + 0.707107i) q^{18} +2.31155 q^{19} +(0.254460 + 2.22154i) q^{20} -3.60159i q^{21} +(2.47600 + 2.47600i) q^{22} +(-2.27923 - 4.21961i) q^{23} +1.00000i q^{24} +(4.87050 - 1.13059i) q^{25} +3.40219 q^{26} +(0.707107 - 0.707107i) q^{27} +(2.54671 - 2.54671i) q^{28} +0.113162i q^{29} +(2.22154 - 0.254460i) q^{30} +1.27272 q^{31} +(-0.707107 + 0.707107i) q^{32} +(2.47600 - 2.47600i) q^{33} +1.94038 q^{34} +(-6.30566 - 5.00959i) q^{35} +1.00000 q^{36} +(3.74806 + 3.74806i) q^{37} +(1.63451 - 1.63451i) q^{38} -3.40219i q^{39} +(1.75080 + 1.39094i) q^{40} +5.08960 q^{41} +(-2.54671 - 2.54671i) q^{42} +(-2.71117 + 2.71117i) q^{43} +3.50160 q^{44} +(-0.254460 - 2.22154i) q^{45} +(-4.59537 - 1.37206i) q^{46} +(-0.775445 + 0.775445i) q^{47} +(0.707107 + 0.707107i) q^{48} +5.97146i q^{49} +(2.64452 - 4.24341i) q^{50} -1.94038i q^{51} +(2.40571 - 2.40571i) q^{52} +(-2.61742 + 2.61742i) q^{53} -1.00000i q^{54} +(-0.891017 - 7.77894i) q^{55} -3.60159i q^{56} +(-1.63451 - 1.63451i) q^{57} +(0.0800174 + 0.0800174i) q^{58} +13.2983i q^{59} +(1.39094 - 1.75080i) q^{60} -0.841493i q^{61} +(0.899946 - 0.899946i) q^{62} +(-2.54671 + 2.54671i) q^{63} +1.00000i q^{64} +(-5.95656 - 4.73224i) q^{65} -3.50160i q^{66} +(5.33351 + 5.33351i) q^{67} +(1.37206 - 1.37206i) q^{68} +(-1.37206 + 4.59537i) q^{69} +(-8.00109 + 0.916462i) q^{70} +14.2568 q^{71} +(0.707107 - 0.707107i) q^{72} +(-7.88793 - 7.88793i) q^{73} +5.30056 q^{74} +(-4.24341 - 2.64452i) q^{75} -2.31155i q^{76} +(-8.91755 + 8.91755i) q^{77} +(-2.40571 - 2.40571i) q^{78} +2.37992 q^{79} +(2.22154 - 0.254460i) q^{80} -1.00000 q^{81} +(3.59889 - 3.59889i) q^{82} +(1.02759 - 1.02759i) q^{83} -3.60159 q^{84} +(-3.39722 - 2.69895i) q^{85} +3.83417i q^{86} +(0.0800174 - 0.0800174i) q^{87} +(2.47600 - 2.47600i) q^{88} -14.7757 q^{89} +(-1.75080 - 1.39094i) q^{90} +12.2533i q^{91} +(-4.21961 + 2.27923i) q^{92} +(-0.899946 - 0.899946i) q^{93} +1.09665i q^{94} +(-5.13520 + 0.588197i) q^{95} +1.00000 q^{96} +(-4.66285 - 4.66285i) q^{97} +(4.22246 + 4.22246i) q^{98} -3.50160 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
$5$	−2.22154	+	0.254460i	−0.993504	+	0.113798i
$5$	−2.22154	+	0.254460i	−0.993504	+	0.113798i
$6$	−1.00000			−0.408248
$7$	2.54671	+	2.54671i	0.962566	+	0.962566i	0.999324	−	0.0367582i	$-0.0117032\pi$
$7$	2.54671	+	2.54671i	0.962566	+	0.962566i	−0.0367582	+	0.999324i	$0.511703\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$			1.00000i			0.333333i
$10$	−1.39094	+	1.75080i	−0.439853	+	0.553651i
$11$			3.50160i			1.05577i	0.849316	+	0.527886i	$0.177015\pi$
$11$			3.50160i			1.05577i	−0.849316	+	0.527886i	$0.822985\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	2.40571	+	2.40571i	0.667225	+	0.667225i	0.957073	−	0.289848i	$-0.0936046\pi$
$13$	2.40571	+	2.40571i	0.667225	+	0.667225i	−0.289848	+	0.957073i	$0.593605\pi$
$14$	3.60159			0.962566
$15$	1.75080	+	1.39094i	0.452054	+	0.359138i
$16$	−1.00000			−0.250000
$17$	1.37206	+	1.37206i	0.332773	+	0.332773i	0.853639	−	0.520866i	$-0.174391\pi$
$17$	1.37206	+	1.37206i	0.332773	+	0.332773i	−0.520866	+	0.853639i	$0.674391\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	2.31155			0.530305			0.265153	−	0.964206i	$-0.414578\pi$
$19$	2.31155			0.530305			0.265153	+	0.964206i	$0.414578\pi$
$20$	0.254460	+	2.22154i	0.0568991	+	0.496752i
$21$		−	3.60159i		−	0.785932i
$22$	2.47600	+	2.47600i	0.527886	+	0.527886i
$23$	−2.27923	−	4.21961i	−0.475252	−	0.879850i
$23$	−2.27923	−	4.21961i	−0.475252	−	0.879850i
$24$			1.00000i			0.204124i
$25$	4.87050	−	1.13059i	0.974100	−	0.226118i
$26$	3.40219			0.667225
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	2.54671	−	2.54671i	0.481283	−	0.481283i
$29$			0.113162i			0.0210136i	0.999945	+	0.0105068i	$0.00334448\pi$
$29$			0.113162i			0.0210136i	−0.999945	+	0.0105068i	$0.996656\pi$
$30$	2.22154	−	0.254460i	0.405596	−	0.0464579i
$31$	1.27272			0.228586			0.114293	−	0.993447i	$-0.463540\pi$
$31$	1.27272			0.228586			0.114293	+	0.993447i	$0.463540\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	2.47600	−	2.47600i	0.431017	−	0.431017i
$34$	1.94038			0.332773
$35$	−6.30566	−	5.00959i	−1.06585	−	0.846775i
$36$	1.00000			0.166667
$37$	3.74806	+	3.74806i	0.616178	+	0.616178i	0.944549	−	0.328371i	$-0.106500\pi$
$37$	3.74806	+	3.74806i	0.616178	+	0.616178i	−0.328371	+	0.944549i	$0.606500\pi$
$38$	1.63451	−	1.63451i	0.265153	−	0.265153i
$39$		−	3.40219i		−	0.544787i
$40$	1.75080	+	1.39094i	0.276826	+	0.219926i
$41$	5.08960			0.794863			0.397431	−	0.917632i	$-0.369902\pi$
$41$	5.08960			0.794863			0.397431	+	0.917632i	$0.369902\pi$
$42$	−2.54671	−	2.54671i	−0.392966	−	0.392966i
$43$	−2.71117	+	2.71117i	−0.413449	+	0.413449i	−0.882938	−	0.469489i	$-0.844438\pi$
$43$	−2.71117	+	2.71117i	−0.413449	+	0.413449i	0.469489	+	0.882938i	$0.344438\pi$
$44$	3.50160			0.527886
$45$	−0.254460	−	2.22154i	−0.0379327	−	0.331168i
$46$	−4.59537	−	1.37206i	−0.677551	−	0.202299i
$47$	−0.775445	+	0.775445i	−0.113110	+	0.113110i	−0.761397	−	0.648286i	$-0.775486\pi$
$47$	−0.775445	+	0.775445i	−0.113110	+	0.113110i	0.648286	+	0.761397i	$0.275486\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$			5.97146i			0.853066i
$50$	2.64452	−	4.24341i	0.373991	−	0.600109i
$51$		−	1.94038i		−	0.271708i
$52$	2.40571	−	2.40571i	0.333613	−	0.333613i
$53$	−2.61742	+	2.61742i	−0.359530	+	0.359530i	−0.863640	−	0.504110i	$-0.831821\pi$
$53$	−2.61742	+	2.61742i	−0.359530	+	0.359530i	0.504110	+	0.863640i	$0.331821\pi$
$54$		−	1.00000i		−	0.136083i
$55$	−0.891017	−	7.77894i	−0.120145	−	1.04891i
$56$		−	3.60159i		−	0.481283i
$57$	−1.63451	−	1.63451i	−0.216496	−	0.216496i
$58$	0.0800174	+	0.0800174i	0.0105068	+	0.0105068i
$59$			13.2983i			1.73128i	0.500663	+	0.865642i	$0.333090\pi$
$59$			13.2983i			1.73128i	−0.500663	+	0.865642i	$0.666910\pi$
$60$	1.39094	−	1.75080i	0.179569	−	0.226027i
$61$		−	0.841493i		−	0.107742i	−0.998548	−	0.0538710i	$-0.982844\pi$
$61$		−	0.841493i		−	0.107742i	0.998548	−	0.0538710i	$-0.0171560\pi$
$62$	0.899946	−	0.899946i	0.114293	−	0.114293i
$63$	−2.54671	+	2.54671i	−0.320855	+	0.320855i
$64$			1.00000i			0.125000i
$65$	−5.95656	−	4.73224i	−0.738820	−	0.586962i
$66$		−	3.50160i		−	0.431017i
$67$	5.33351	+	5.33351i	0.651592	+	0.651592i	0.953376	−	0.301784i	$-0.0975822\pi$
$67$	5.33351	+	5.33351i	0.651592	+	0.651592i	−0.301784	+	0.953376i	$0.597582\pi$
$68$	1.37206	−	1.37206i	0.166386	−	0.166386i
$69$	−1.37206	+	4.59537i	−0.165176	+	0.553218i
$70$	−8.00109	+	0.916462i	−0.956313	+	0.109538i
$71$	14.2568			1.69198			0.845988	−	0.533203i	$-0.179012\pi$
$71$	14.2568			1.69198			0.845988	+	0.533203i	$0.179012\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	−7.88793	−	7.88793i	−0.923212	−	0.923212i	0.0740430	−	0.997255i	$-0.476410\pi$
$73$	−7.88793	−	7.88793i	−0.923212	−	0.923212i	−0.997255	+	0.0740430i	$0.976410\pi$
$74$	5.30056			0.616178
$75$	−4.24341	−	2.64452i	−0.489987	−	0.305362i
$76$		−	2.31155i		−	0.265153i
$77$	−8.91755	+	8.91755i	−1.01625	+	1.01625i
$78$	−2.40571	−	2.40571i	−0.272394	−	0.272394i
$79$	2.37992			0.267761			0.133881	−	0.990997i	$-0.457256\pi$
$79$	2.37992			0.267761			0.133881	+	0.990997i	$0.457256\pi$
$80$	2.22154	−	0.254460i	0.248376	−	0.0284495i
$81$	−1.00000			−0.111111
$82$	3.59889	−	3.59889i	0.397431	−	0.397431i
$83$	1.02759	−	1.02759i	0.112793	−	0.112793i	−0.648458	−	0.761251i	$-0.724586\pi$
$83$	1.02759	−	1.02759i	0.112793	−	0.112793i	0.761251	+	0.648458i	$0.224586\pi$
$84$	−3.60159			−0.392966
$85$	−3.39722	−	2.69895i	−0.368480	−	0.292742i
$86$			3.83417i			0.413449i
$87$	0.0800174	−	0.0800174i	0.00857877	−	0.00857877i
$88$	2.47600	−	2.47600i	0.263943	−	0.263943i
$89$	−14.7757			−1.56622			−0.783109	−	0.621885i	$-0.786367\pi$
$89$	−14.7757			−1.56622			−0.783109	+	0.621885i	$0.786367\pi$
$90$	−1.75080	−	1.39094i	−0.184550	−	0.146618i
$91$			12.2533i			1.28450i
$92$	−4.21961	+	2.27923i	−0.439925	+	0.237626i
$93$	−0.899946	−	0.899946i	−0.0933200	−	0.0933200i
$94$			1.09665i			0.113110i
$95$	−5.13520	+	0.588197i	−0.526860	+	0.0603477i
$96$	1.00000			0.102062
$97$	−4.66285	−	4.66285i	−0.473441	−	0.473441i	0.429585	−	0.903026i	$-0.358660\pi$
$97$	−4.66285	−	4.66285i	−0.473441	−	0.473441i	−0.903026	+	0.429585i	$0.858660\pi$
$98$	4.22246	+	4.22246i	0.426533	+	0.426533i
$99$	−3.50160			−0.351924
$100$	−1.13059	−	4.87050i	−0.113059	−	0.487050i
$101$	0.433231			0.0431081			0.0215541	−	0.999768i	$-0.493139\pi$
$101$	0.433231			0.0431081			0.0215541	+	0.999768i	$0.493139\pi$
$102$	−1.37206	−	1.37206i	−0.135854	−	0.135854i
$103$	−8.99956	+	8.99956i	−0.886753	+	0.886753i	−0.994210	−	0.107457i	$-0.965729\pi$
$103$	−8.99956	+	8.99956i	−0.886753	+	0.886753i	0.107457	+	0.994210i	$0.465729\pi$
$104$		−	3.40219i		−	0.333613i
$105$	0.916462	+	8.00109i	0.0894376	+	0.780826i
$106$			3.70159i			0.359530i
$107$	−13.7709	−	13.7709i	−1.33128	−	1.33128i	−0.904225	−	0.427056i	$-0.859551\pi$
$107$	−13.7709	−	13.7709i	−1.33128	−	1.33128i	−0.427056	−	0.904225i	$-0.640449\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	3.09267			0.296224			0.148112	−	0.988971i	$-0.452680\pi$
$109$	3.09267			0.296224			0.148112	+	0.988971i	$0.452680\pi$
$110$	−6.13059	−	4.87050i	−0.584529	−	0.464384i
$111$		−	5.30056i		−	0.503107i
$112$	−2.54671	−	2.54671i	−0.240641	−	0.240641i
$113$	2.36212	−	2.36212i	0.222209	−	0.222209i	−0.587219	−	0.809428i	$-0.699777\pi$
$113$	2.36212	−	2.36212i	0.222209	−	0.222209i	0.809428	+	0.587219i	$0.199777\pi$
$114$	−2.31155			−0.216496
$115$	6.13713	+	8.79407i	0.572290	+	0.820051i
$116$	0.113162			0.0105068
$117$	−2.40571	+	2.40571i	−0.222408	+	0.222408i
$118$	9.40328	+	9.40328i	0.865642	+	0.865642i
$119$			6.98846i			0.640631i
$120$	−0.254460	−	2.22154i	−0.0232289	−	0.202798i
$121$	−1.26118			−0.114653
$122$	−0.595025	−	0.595025i	−0.0538710	−	0.0538710i
$123$	−3.59889	−	3.59889i	−0.324501	−	0.324501i
$124$		−	1.27272i		−	0.114293i
$125$	−10.5323	+	3.75100i	−0.942040	+	0.335500i
$126$			3.60159i			0.320855i
$127$	8.49034	−	8.49034i	0.753396	−	0.753396i	−0.221715	−	0.975111i	$-0.571166\pi$
$127$	8.49034	−	8.49034i	0.753396	−	0.753396i	0.975111	+	0.221715i	$0.0711656\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	3.83417			0.337580
$130$	−7.55812	+	0.865724i	−0.662891	+	0.0759290i
$131$	18.8562			1.64747			0.823736	−	0.566973i	$-0.191886\pi$
$131$	18.8562			1.64747			0.823736	+	0.566973i	$0.191886\pi$
$132$	−2.47600	−	2.47600i	−0.215508	−	0.215508i
$133$	5.88684	+	5.88684i	0.510454	+	0.510454i
$134$	7.54272			0.651592
$135$	−1.39094	+	1.75080i	−0.119713	+	0.150685i
$136$		−	1.94038i		−	0.166386i
$137$	−3.49960	−	3.49960i	−0.298991	−	0.298991i	0.541628	−	0.840618i	$-0.317808\pi$
$137$	−3.49960	−	3.49960i	−0.298991	−	0.298991i	−0.840618	+	0.541628i	$0.817808\pi$
$138$	2.27923	+	4.21961i	0.194021	+	0.359197i
$139$			14.4705i			1.22737i	0.789552	+	0.613684i	$0.210313\pi$
$139$			14.4705i			1.22737i	−0.789552	+	0.613684i	$0.789687\pi$
$140$	−5.00959	+	6.30566i	−0.423387	+	0.532926i
$141$	1.09665			0.0923542
$142$	10.0811	−	10.0811i	0.845988	−	0.845988i
$143$	−8.42384	+	8.42384i	−0.704437	+	0.704437i
$144$		−	1.00000i		−	0.0833333i
$145$	−0.0287952	−	0.251394i	−0.00239131	−	0.0208771i
$146$	−11.1552			−0.923212
$147$	4.22246	−	4.22246i	0.348263	−	0.348263i
$148$	3.74806	−	3.74806i	0.308089	−	0.308089i
$149$	−2.64129			−0.216383			−0.108192	−	0.994130i	$-0.534506\pi$
$149$	−2.64129			−0.216383			−0.108192	+	0.994130i	$0.534506\pi$
$150$	−4.87050	+	1.13059i	−0.397675	+	0.0923122i
$151$	21.1977			1.72505			0.862524	−	0.506016i	$-0.168882\pi$
$151$	21.1977			1.72505			0.862524	+	0.506016i	$0.168882\pi$
$152$	−1.63451	−	1.63451i	−0.132576	−	0.132576i
$153$	−1.37206	+	1.37206i	−0.110924	+	0.110924i
$154$			12.6113i			1.01625i
$155$	−2.82739	+	0.323856i	−0.227102	+	0.0260127i
$156$	−3.40219			−0.272394
$157$	−17.0584	−	17.0584i	−1.36141	−	1.36141i	−0.872128	−	0.489278i	$-0.837260\pi$
$157$	−17.0584	−	17.0584i	−1.36141	−	1.36141i	−0.489278	−	0.872128i	$-0.662740\pi$
$158$	1.68285	−	1.68285i	0.133881	−	0.133881i
$159$	3.70159			0.293555
$160$	1.39094	−	1.75080i	0.109963	−	0.138413i
$161$	4.94159	−	16.5507i	0.389452	−	1.30437i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	2.81143	+	2.81143i	0.220208	+	0.220208i	0.808586	−	0.588378i	$-0.200233\pi$
$163$	2.81143	+	2.81143i	0.220208	+	0.220208i	−0.588378	+	0.808586i	$0.700233\pi$
$164$		−	5.08960i		−	0.397431i
$165$	−4.87050	+	6.13059i	−0.379168	+	0.477266i
$166$		−	1.45324i		−	0.112793i
$167$	−8.40826	+	8.40826i	−0.650651	+	0.650651i	−0.953150	−	0.302499i	$-0.902179\pi$
$167$	−8.40826	+	8.40826i	−0.650651	+	0.650651i	0.302499	+	0.953150i	$0.402179\pi$
$168$	−2.54671	+	2.54671i	−0.196483	+	0.196483i
$169$		−	1.42507i		−	0.109621i
$170$	−4.31064	+	0.493750i	−0.330611	+	0.0378689i
$171$			2.31155i			0.176768i
$172$	2.71117	+	2.71117i	0.206724	+	0.206724i
$173$	−8.59500	−	8.59500i	−0.653466	−	0.653466i	0.300360	−	0.953826i	$-0.402893\pi$
$173$	−8.59500	−	8.59500i	−0.653466	−	0.653466i	−0.953826	+	0.300360i	$0.902893\pi$
$174$		−	0.113162i		−	0.00857877i
$175$	15.2830	+	9.52447i	1.15529	+	0.719982i
$176$		−	3.50160i		−	0.263943i
$177$	9.40328	−	9.40328i	0.706794	−	0.706794i
$178$	−10.4480	+	10.4480i	−0.783109	+	0.783109i
$179$		−	22.1597i		−	1.65629i	−0.560511	−	0.828147i	$-0.689395\pi$
$179$		−	22.1597i		−	1.65629i	0.560511	−	0.828147i	$-0.310605\pi$
$180$	−2.22154	+	0.254460i	−0.165584	+	0.0189664i
$181$			7.71976i			0.573805i	0.957960	+	0.286903i	$0.0926256\pi$
$181$			7.71976i			0.573805i	−0.957960	+	0.286903i	$0.907374\pi$
$182$	8.66440	+	8.66440i	0.642248	+	0.642248i
$183$	−0.595025	+	0.595025i	−0.0439855	+	0.0439855i
$184$	−1.37206	+	4.59537i	−0.101149	+	0.338775i
$185$	−9.28022	−	7.37275i	−0.682295	−	0.542055i
$186$	−1.27272			−0.0933200
$187$	−4.80439	+	4.80439i	−0.351332	+	0.351332i
$188$	0.775445	+	0.775445i	0.0565552	+	0.0565552i
$189$	3.60159			0.261977
$190$	−3.21522	+	4.04705i	−0.233256	+	0.293604i
$191$		−	22.6783i		−	1.64094i	−0.571689	−	0.820471i	$-0.693711\pi$
$191$		−	22.6783i		−	1.64094i	0.571689	−	0.820471i	$-0.306289\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	−13.9176	−	13.9176i	−1.00181	−	1.00181i	−0.999998	−	0.00180888i	$-0.999424\pi$
$193$	−13.9176	−	13.9176i	−1.00181	−	1.00181i	−0.00180888	−	0.999998i	$-0.500576\pi$
$194$	−6.59427			−0.473441
$195$	0.865724	+	7.55812i	0.0619958	+	0.541248i
$196$	5.97146			0.426533
$197$	−3.68741	+	3.68741i	−0.262717	+	0.262717i	−0.826157	−	0.563440i	$-0.809478\pi$
$197$	−3.68741	+	3.68741i	−0.262717	+	0.262717i	0.563440	+	0.826157i	$0.309478\pi$
$198$	−2.47600	+	2.47600i	−0.175962	+	0.175962i
$199$	11.8404			0.839343			0.419672	−	0.907676i	$-0.362145\pi$
$199$	11.8404			0.839343			0.419672	+	0.907676i	$0.362145\pi$
$200$	−4.24341	−	2.64452i	−0.300054	−	0.186996i
$201$		−	7.54272i		−	0.532023i
$202$	0.306341	−	0.306341i	0.0215541	−	0.0215541i
$203$	−0.288190	+	0.288190i	−0.0202270	+	0.0202270i
$204$	−1.94038			−0.135854
$205$	−11.3068	+	1.29510i	−0.789699	+	0.0904539i
$206$			12.7273i			0.886753i
$207$	4.21961	−	2.27923i	0.293283	−	0.158417i
$208$	−2.40571	−	2.40571i	−0.166806	−	0.166806i
$209$			8.09410i			0.559881i
$210$	6.30566	+	5.00959i	0.435132	+	0.345694i
$211$	−24.3012			−1.67296			−0.836482	−	0.547994i	$-0.815392\pi$
$211$	−24.3012			−1.67296			−0.836482	+	0.547994i	$0.815392\pi$
$212$	2.61742	+	2.61742i	0.179765	+	0.179765i
$213$	−10.0811	−	10.0811i	−0.690746	−	0.690746i
$214$	−19.4750			−1.33128
$215$	5.33309	−	6.71285i	0.363713	−	0.457813i
$216$	−1.00000			−0.0680414
$217$	3.24124	+	3.24124i	0.220030	+	0.220030i
$218$	2.18685	−	2.18685i	0.148112	−	0.148112i
$219$			11.1552i			0.753799i
$220$	−7.77894	+	0.891017i	−0.524456	+	0.0600724i
$221$			6.60156i			0.444069i
$222$	−3.74806	−	3.74806i	−0.251554	−	0.251554i
$223$	−1.60241	−	1.60241i	−0.107306	−	0.107306i	0.651416	−	0.758721i	$-0.274175\pi$
$223$	−1.60241	−	1.60241i	−0.107306	−	0.107306i	−0.758721	+	0.651416i	$0.774175\pi$
$224$	−3.60159			−0.240641
$225$	1.13059	+	4.87050i	0.0753726	+	0.324700i
$226$		−	3.34054i		−	0.222209i
$227$	15.4161	+	15.4161i	1.02320	+	1.02320i	0.999724	+	0.0234786i	$0.00747416\pi$
$227$	15.4161	+	15.4161i	1.02320	+	1.02320i	0.0234786	+	0.999724i	$0.492526\pi$
$228$	−1.63451	+	1.63451i	−0.108248	+	0.108248i
$229$	12.8440			0.848754			0.424377	−	0.905486i	$-0.360493\pi$
$229$	12.8440			0.848754			0.424377	+	0.905486i	$0.360493\pi$
$230$	10.5580	+	1.87874i	0.696171	+	0.123881i
$231$	12.6113			0.829764
$232$	0.0800174	−	0.0800174i	0.00525340	−	0.00525340i
$233$	−12.2901	−	12.2901i	−0.805153	−	0.805153i	0.178743	−	0.983896i	$-0.442797\pi$
$233$	−12.2901	−	12.2901i	−0.805153	−	0.805153i	−0.983896	+	0.178743i	$0.942797\pi$
$234$			3.40219i			0.222408i
$235$	1.52536	−	1.92000i	0.0995038	−	0.125247i
$236$	13.2983			0.865642
$237$	−1.68285	−	1.68285i	−0.109313	−	0.109313i
$238$	4.94159	+	4.94159i	0.320316	+	0.320316i
$239$			18.1727i			1.17549i	0.809045	+	0.587747i	$0.199985\pi$
$239$			18.1727i			1.17549i	−0.809045	+	0.587747i	$0.800015\pi$
$240$	−1.75080	−	1.39094i	−0.113014	−	0.0897846i
$241$			11.7886i			0.759373i	0.925115	+	0.379687i	$0.123968\pi$
$241$			11.7886i			0.759373i	−0.925115	+	0.379687i	$0.876032\pi$
$242$	−0.891787	+	0.891787i	−0.0573263	+	0.0573263i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−0.841493			−0.0538710
$245$	−1.51950	−	13.2659i	−0.0970774	−	0.847525i
$246$	−5.08960			−0.324501
$247$	5.56092	+	5.56092i	0.353833	+	0.353833i
$248$	−0.899946	−	0.899946i	−0.0571466	−	0.0571466i
$249$	−1.45324			−0.0920950
$250$	−4.79513	+	10.0998i	−0.303270	+	0.638770i
$251$		−	12.8428i		−	0.810631i	−0.914177	−	0.405315i	$-0.867162\pi$
$251$		−	12.8428i		−	0.810631i	0.914177	−	0.405315i	$-0.132838\pi$
$252$	2.54671	+	2.54671i	0.160428	+	0.160428i
$253$	14.7754	−	7.98094i	0.928920	−	0.501757i
$254$		−	12.0072i		−	0.753396i
$255$	0.493750	+	4.31064i	0.0309198	+	0.269943i
$256$	1.00000			0.0625000
$257$	1.42623	−	1.42623i	0.0889659	−	0.0889659i	−0.661223	−	0.750189i	$-0.729962\pi$
$257$	1.42623	−	1.42623i	0.0889659	−	0.0889659i	0.750189	+	0.661223i	$0.229962\pi$
$258$	2.71117	−	2.71117i	0.168790	−	0.168790i
$259$			19.0905i			1.18622i
$260$	−4.73224	+	5.95656i	−0.293481	+	0.369410i
$261$	−0.113162			−0.00700453
$262$	13.3333	−	13.3333i	0.823736	−	0.823736i
$263$	18.6079	−	18.6079i	1.14741	−	1.14741i	0.160349	−	0.987060i	$-0.448738\pi$
$263$	18.6079	−	18.6079i	1.14741	−	1.14741i	0.987060	−	0.160349i	$-0.0512621\pi$
$264$	−3.50160			−0.215508
$265$	5.14867	−	6.48073i	0.316281	−	0.398108i
$266$	8.32525			0.510454
$267$	10.4480	+	10.4480i	0.639406	+	0.639406i
$268$	5.33351	−	5.33351i	0.325796	−	0.325796i
$269$			13.7120i			0.836034i	0.908439	+	0.418017i	$0.137275\pi$
$269$			13.7120i			0.836034i	−0.908439	+	0.418017i	$0.862725\pi$
$270$	0.254460	+	2.22154i	0.0154860	+	0.135199i
$271$	−11.6831			−0.709696			−0.354848	−	0.934924i	$-0.615467\pi$
$271$	−11.6831			−0.709696			−0.354848	+	0.934924i	$0.615467\pi$
$272$	−1.37206	−	1.37206i	−0.0831932	−	0.0831932i
$273$	8.66440	−	8.66440i	0.524394	−	0.524394i
$274$	−4.94918			−0.298991
$275$	3.95887	+	17.0545i	0.238729	+	1.02843i
$276$	4.59537	+	1.37206i	0.276609	+	0.0825881i
$277$	10.3117	−	10.3117i	0.619572	−	0.619572i	−0.325850	−	0.945422i	$-0.605650\pi$
$277$	10.3117	−	10.3117i	0.619572	−	0.619572i	0.945422	+	0.325850i	$0.105650\pi$
$278$	10.2322	+	10.2322i	0.613684	+	0.613684i
$279$			1.27272i			0.0761955i
$280$	0.916462	+	8.00109i	0.0547691	+	0.478157i
$281$		−	29.4216i		−	1.75514i	−0.479445	−	0.877572i	$-0.659162\pi$
$281$		−	29.4216i		−	1.75514i	0.479445	−	0.877572i	$-0.340838\pi$
$282$	0.775445	−	0.775445i	0.0461771	−	0.0461771i
$283$	−18.0041	+	18.0041i	−1.07023	+	1.07023i	−0.0728932	+	0.997340i	$0.523223\pi$
$283$	−18.0041	+	18.0041i	−1.07023	+	1.07023i	−0.997340	+	0.0728932i	$0.976777\pi$
$284$		−	14.2568i		−	0.845988i
$285$	4.04705	+	3.21522i	0.239727	+	0.190453i
$286$			11.9131i			0.704437i
$287$	12.9617	+	12.9617i	0.765108	+	0.765108i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$		−	13.2349i		−	0.778525i
$290$	−0.198123	−	0.157401i	−0.0116342	−	0.00924289i
$291$			6.59427i			0.386563i
$292$	−7.88793	+	7.88793i	−0.461606	+	0.461606i
$293$	−11.1818	+	11.1818i	−0.653249	+	0.653249i	−0.953774	−	0.300525i	$-0.902838\pi$
$293$	−11.1818	+	11.1818i	−0.653249	+	0.653249i	0.300525	+	0.953774i	$0.402838\pi$
$294$		−	5.97146i		−	0.348263i
$295$	−3.38388	−	29.5426i	−0.197017	−	1.72004i
$296$		−	5.30056i		−	0.308089i
$297$	2.47600	+	2.47600i	0.143672	+	0.143672i
$298$	−1.86768	+	1.86768i	−0.108192	+	0.108192i
$299$	4.66800	−	15.6344i	0.269958	−	0.904158i
$300$	−2.64452	+	4.24341i	−0.152681	+	0.244993i
$301$	−13.8091			−0.795944
$302$	14.9891	−	14.9891i	0.862524	−	0.862524i
$303$	−0.306341	−	0.306341i	−0.0175988	−	0.0175988i
$304$	−2.31155			−0.132576
$305$	0.214126	+	1.86941i	0.0122608	+	0.107042i
$306$			1.94038i			0.110924i
$307$	9.99514	−	9.99514i	0.570453	−	0.570453i	−0.361802	−	0.932255i	$-0.617838\pi$
$307$	9.99514	−	9.99514i	0.570453	−	0.570453i	0.932255	+	0.361802i	$0.117838\pi$
$308$	8.91755	+	8.91755i	0.508125	+	0.508125i
$309$	12.7273			0.724031
$310$	−1.77027	+	2.22827i	−0.100544	+	0.126557i
$311$	3.18731			0.180736			0.0903678	−	0.995908i	$-0.471196\pi$
$311$	3.18731			0.180736			0.0903678	+	0.995908i	$0.471196\pi$
$312$	−2.40571	+	2.40571i	−0.136197	+	0.136197i
$313$	19.6532	−	19.6532i	1.11086	−	1.11086i	0.117830	−	0.993034i	$-0.462406\pi$
$313$	19.6532	−	19.6532i	1.11086	−	1.11086i	0.993034	−	0.117830i	$-0.0375936\pi$
$314$	−24.1242			−1.36141
$315$	5.00959	−	6.30566i	0.282258	−	0.355284i
$316$		−	2.37992i		−	0.133881i
$317$	3.39018	−	3.39018i	0.190411	−	0.190411i	−0.605463	−	0.795874i	$-0.707012\pi$
$317$	3.39018	−	3.39018i	0.190411	−	0.190411i	0.795874	+	0.605463i	$0.207012\pi$
$318$	2.61742	−	2.61742i	0.146777	−	0.146777i
$319$	−0.396247			−0.0221856
$320$	−0.254460	−	2.22154i	−0.0142248	−	0.124188i
$321$			19.4750i			1.08699i
$322$	−8.20885	−	15.1973i	−0.457462	−	0.846913i
$323$	3.17157	+	3.17157i	0.176471	+	0.176471i
$324$			1.00000i			0.0555556i
$325$	14.4369	+	8.99716i	0.800816	+	0.499073i
$326$	3.97596			0.220208
$327$	−2.18685	−	2.18685i	−0.120933	−	0.120933i
$328$	−3.59889	−	3.59889i	−0.198716	−	0.198716i
$329$	−3.94967			−0.217752
$330$	0.891017	+	7.77894i	0.0490489	+	0.428217i
$331$	−2.32929			−0.128029			−0.0640146	−	0.997949i	$-0.520390\pi$
$331$	−2.32929			−0.128029			−0.0640146	+	0.997949i	$0.520390\pi$
$332$	−1.02759	−	1.02759i	−0.0563965	−	0.0563965i
$333$	−3.74806	+	3.74806i	−0.205393	+	0.205393i
$334$			11.8911i			0.650651i
$335$	−13.2058	−	10.4915i	−0.721509	−	0.573209i
$336$			3.60159i			0.196483i
$337$	−19.2106	−	19.2106i	−1.04647	−	1.04647i	−0.998866	−	0.0476036i	$-0.984842\pi$
$337$	−19.2106	−	19.2106i	−1.04647	−	1.04647i	−0.0476036	−	0.998866i	$-0.515158\pi$
$338$	−1.00768	−	1.00768i	−0.0548104	−	0.0548104i
$339$	−3.34054			−0.181433
$340$	−2.69895	+	3.39722i	−0.146371	+	0.184240i
$341$			4.45654i			0.241335i
$342$	1.63451	+	1.63451i	0.0883842	+	0.0883842i
$343$	2.61938	−	2.61938i	0.141433	−	0.141433i
$344$	3.83417			0.206724
$345$	1.87874	−	10.5580i	0.101148	−	0.568421i
$346$	−12.1552			−0.653466
$347$	−6.50382	+	6.50382i	−0.349143	+	0.349143i	−0.859790	−	0.510647i	$-0.829406\pi$
$347$	−6.50382	+	6.50382i	−0.349143	+	0.349143i	0.510647	+	0.859790i	$0.329406\pi$
$348$	−0.0800174	−	0.0800174i	−0.00428938	−	0.00428938i
$349$		−	4.27903i		−	0.229051i	−0.993420	−	0.114526i	$-0.963465\pi$
$349$		−	4.27903i		−	0.229051i	0.993420	−	0.114526i	$-0.0365348\pi$
$350$	17.5416	−	4.07192i	0.937635	−	0.217653i
$351$	3.40219			0.181596
$352$	−2.47600	−	2.47600i	−0.131971	−	0.131971i
$353$	16.8716	+	16.8716i	0.897983	+	0.897983i	0.995258	−	0.0972747i	$-0.0310125\pi$
$353$	16.8716	+	16.8716i	0.897983	+	0.897983i	−0.0972747	+	0.995258i	$0.531013\pi$
$354$		−	13.2983i		−	0.706794i
$355$	−31.6722	+	3.62780i	−1.68098	+	0.192544i
$356$			14.7757i			0.783109i
$357$	4.94159	−	4.94159i	0.261537	−	0.261537i
$358$	−15.6693	−	15.6693i	−0.828147	−	0.828147i
$359$	24.2841			1.28166			0.640832	−	0.767681i	$-0.278590\pi$
$359$	24.2841			1.28166			0.640832	+	0.767681i	$0.278590\pi$
$360$	−1.39094	+	1.75080i	−0.0733088	+	0.0922752i
$361$	−13.6568			−0.718777
$362$	5.45870	+	5.45870i	0.286903	+	0.286903i
$363$	0.891787	+	0.891787i	0.0468067	+	0.0468067i
$364$	12.2533			0.642248
$365$	19.5305	+	15.5162i	1.02227	+	0.812155i
$366$			0.841493i			0.0439855i
$367$	16.5877	+	16.5877i	0.865871	+	0.865871i	0.992012	−	0.126141i	$-0.0402593\pi$
$367$	16.5877	+	16.5877i	0.865871	+	0.865871i	−0.126141	+	0.992012i	$0.540259\pi$
$368$	2.27923	+	4.21961i	0.118813	+	0.219962i
$369$			5.08960i			0.264954i
$370$	−11.7754	+	1.34878i	−0.612175	+	0.0701199i
$371$	−13.3316			−0.692143
$372$	−0.899946	+	0.899946i	−0.0466600	+	0.0466600i
$373$	0.545949	−	0.545949i	0.0282682	−	0.0282682i	−0.692831	−	0.721100i	$-0.743637\pi$
$373$	0.545949	−	0.545949i	0.0282682	−	0.0282682i	0.721100	+	0.692831i	$0.243637\pi$
$374$			6.79443i			0.351332i
$375$	10.0998	+	4.79513i	0.521554	+	0.247619i
$376$	1.09665			0.0565552
$377$	−0.272235	+	0.272235i	−0.0140208	+	0.0140208i
$378$	2.54671	−	2.54671i	0.130989	−	0.130989i
$379$	11.6412			0.597971			0.298985	−	0.954258i	$-0.403352\pi$
$379$	11.6412			0.597971			0.298985	+	0.954258i	$0.403352\pi$
$380$	0.588197	+	5.13520i	0.0301739	+	0.263430i
$381$	−12.0072			−0.615145
$382$	−16.0360	−	16.0360i	−0.820471	−	0.820471i
$383$	15.6586	−	15.6586i	0.800116	−	0.800116i	−0.182997	−	0.983113i	$-0.558580\pi$
$383$	15.6586	−	15.6586i	0.800116	−	0.800116i	0.983113	+	0.182997i	$0.0585800\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	17.5416	−	22.0799i	0.894000	−	1.12529i
$386$	−19.6824			−1.00181
$387$	−2.71117	−	2.71117i	−0.137816	−	0.137816i
$388$	−4.66285	+	4.66285i	−0.236720	+	0.236720i
$389$	34.3765			1.74296			0.871478	−	0.490435i	$-0.163162\pi$
$389$	34.3765			1.74296			0.871478	+	0.490435i	$0.163162\pi$
$390$	5.95656	+	4.73224i	0.301622	+	0.239626i
$391$	2.66231	−	8.91678i	0.134639	−	0.450941i
$392$	4.22246	−	4.22246i	0.213267	−	0.213267i
$393$	−13.3333	−	13.3333i	−0.672578	−	0.672578i
$394$			5.21479i			0.262717i
$395$	−5.28708	+	0.605594i	−0.266022	+	0.0304707i
$396$			3.50160i			0.175962i
$397$	3.67637	−	3.67637i	0.184512	−	0.184512i	−0.608807	−	0.793318i	$-0.708352\pi$
$397$	3.67637	−	3.67637i	0.184512	−	0.184512i	0.793318	+	0.608807i	$0.208352\pi$
$398$	8.37242	−	8.37242i	0.419672	−	0.419672i
$399$		−	8.32525i		−	0.416784i
$400$	−4.87050	+	1.13059i	−0.243525	+	0.0565294i
$401$			8.61364i			0.430145i	0.976598	+	0.215072i	$0.0689988\pi$
$401$			8.61364i			0.430145i	−0.976598	+	0.215072i	$0.931001\pi$
$402$	−5.33351	−	5.33351i	−0.266011	−	0.266011i
$403$	3.06179	+	3.06179i	0.152519	+	0.152519i
$404$		−	0.433231i		−	0.0215541i
$405$	2.22154	−	0.254460i	0.110389	−	0.0126442i
$406$			0.407562i			0.0202270i
$407$	−13.1242	+	13.1242i	−0.650543	+	0.650543i
$408$	−1.37206	+	1.37206i	−0.0679269	+	0.0679269i
$409$			10.5576i			0.522038i	0.965334	+	0.261019i	$0.0840585\pi$
$409$			10.5576i			0.522038i	−0.965334	+	0.261019i	$0.915941\pi$
$410$	−7.07932	+	8.91087i	−0.349623	+	0.440077i
$411$			4.94918i			0.244125i
$412$	8.99956	+	8.99956i	0.443377	+	0.443377i
$413$	−33.8668	+	33.8668i	−1.66648	+	1.66648i
$414$	1.37206	−	4.59537i	0.0674329	−	0.225850i
$415$	−2.02136	+	2.54432i	−0.0992246	+	0.124896i
$416$	−3.40219			−0.166806
$417$	10.2322	−	10.2322i	0.501071	−	0.501071i
$418$	5.72339	+	5.72339i	0.279940	+	0.279940i
$419$	−31.5043			−1.53909			−0.769543	−	0.638594i	$-0.779516\pi$
$419$	−31.5043			−1.53909			−0.769543	+	0.638594i	$0.779516\pi$
$420$	8.00109	−	0.916462i	0.390413	−	0.0447188i
$421$		−	29.1199i		−	1.41922i	−0.704595	−	0.709609i	$-0.748871\pi$
$421$		−	29.1199i		−	1.41922i	0.704595	−	0.709609i	$-0.251129\pi$
$422$	−17.1835	+	17.1835i	−0.836482	+	0.836482i
$423$	−0.775445	−	0.775445i	−0.0377034	−	0.0377034i
$424$	3.70159			0.179765
$425$	8.23383	+	5.13137i	0.399400	+	0.248908i
$426$	−14.2568			−0.690746
$427$	2.14304	−	2.14304i	0.103709	−	0.103709i
$428$	−13.7709	+	13.7709i	−0.665641	+	0.665641i
$429$	11.9131			0.575170
$430$	−0.975644	−	8.51777i	−0.0470497	−	0.410763i
$431$			29.7497i			1.43299i	0.697592	+	0.716495i	$0.254255\pi$
$431$			29.7497i			1.43299i	−0.697592	+	0.716495i	$0.745745\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	15.2332	−	15.2332i	0.732060	−	0.732060i	−0.238967	−	0.971028i	$-0.576809\pi$
$433$	15.2332	−	15.2332i	0.732060	−	0.732060i	0.971028	+	0.238967i	$0.0768089\pi$
$434$	4.58380			0.220030
$435$	−0.157401	+	0.198123i	−0.00754679	+	0.00949929i
$436$		−	3.09267i		−	0.148112i
$437$	−5.26854	−	9.75383i	−0.252029	−	0.466589i
$438$	7.88793	+	7.88793i	0.376900	+	0.376900i
$439$		−	32.1103i		−	1.53254i	−0.642518	−	0.766271i	$-0.722110\pi$
$439$		−	32.1103i		−	1.53254i	0.642518	−	0.766271i	$-0.277890\pi$
$440$	−4.87050	+	6.13059i	−0.232192	+	0.292264i
$441$	−5.97146			−0.284355
$442$	4.66800	+	4.66800i	0.222034	+	0.222034i
$443$	5.81843	+	5.81843i	0.276442	+	0.276442i	0.831687	−	0.555245i	$-0.187375\pi$
$443$	5.81843	+	5.81843i	0.276442	+	0.276442i	−0.555245	+	0.831687i	$0.687375\pi$
$444$	−5.30056			−0.251554
$445$	32.8248	−	3.75982i	1.55604	−	0.178233i
$446$	−2.26616			−0.107306
$447$	1.86768	+	1.86768i	0.0883380	+	0.0883380i
$448$	−2.54671	+	2.54671i	−0.120321	+	0.120321i
$449$			9.11228i			0.430035i	0.976610	+	0.215018i	$0.0689809\pi$
$449$			9.11228i			0.430035i	−0.976610	+	0.215018i	$0.931019\pi$
$450$	4.24341	+	2.64452i	0.200036	+	0.124664i
$451$			17.8217i			0.839193i
$452$	−2.36212	−	2.36212i	−0.111105	−	0.111105i
$453$	−14.9891	−	14.9891i	−0.704248	−	0.704248i
$454$	21.8017			1.02320
$455$	−3.11798	−	27.2213i	−0.146173	−	1.27615i
$456$			2.31155i			0.108248i
$457$	−1.84839	−	1.84839i	−0.0864641	−	0.0864641i	0.662552	−	0.749016i	$-0.269473\pi$
$457$	−1.84839	−	1.84839i	−0.0864641	−	0.0864641i	−0.749016	+	0.662552i	$0.769473\pi$
$458$	9.08206	−	9.08206i	0.424377	−	0.424377i
$459$	1.94038			0.0905692
$460$	8.79407	−	6.13713i	0.410026	−	0.286145i
$461$	24.8093			1.15549			0.577743	−	0.816219i	$-0.303934\pi$
$461$	24.8093			1.15549			0.577743	+	0.816219i	$0.303934\pi$
$462$	8.91755	−	8.91755i	0.414882	−	0.414882i
$463$	−11.8812	−	11.8812i	−0.552166	−	0.552166i	0.374899	−	0.927065i	$-0.377677\pi$
$463$	−11.8812	−	11.8812i	−0.552166	−	0.552166i	−0.927065	+	0.374899i	$0.877677\pi$
$464$		−	0.113162i		−	0.00525340i
$465$	2.22827	+	1.77027i	0.103333	+	0.0820942i
$466$	−17.3809			−0.805153
$467$	−19.0071	−	19.0071i	−0.879542	−	0.879542i	0.113945	−	0.993487i	$-0.463651\pi$
$467$	−19.0071	−	19.0071i	−0.879542	−	0.879542i	−0.993487	+	0.113945i	$0.963651\pi$
$468$	2.40571	+	2.40571i	0.111204	+	0.111204i
$469$			27.1658i			1.25440i
$470$	−0.279053	−	2.43624i	−0.0128717	−	0.112376i
$471$			24.1242i			1.11158i
$472$	9.40328	−	9.40328i	0.432821	−	0.432821i
$473$	−9.49341	−	9.49341i	−0.436507	−	0.436507i
$474$	−2.37992			−0.109313
$475$	11.2584	−	2.61341i	0.516570	−	0.119911i
$476$	6.98846			0.320316
$477$	−2.61742	−	2.61742i	−0.119843	−	0.119843i
$478$	12.8500	+	12.8500i	0.587747	+	0.587747i
$479$	4.09469			0.187091			0.0935455	−	0.995615i	$-0.470180\pi$
$479$	4.09469			0.187091			0.0935455	+	0.995615i	$0.470180\pi$
$480$	−2.22154	+	0.254460i	−0.101399	+	0.0116145i
$481$			18.0335i			0.822259i
$482$	8.33583	+	8.33583i	0.379687	+	0.379687i
$483$	−15.1973	+	8.20885i	−0.691502	+	0.373516i
$484$			1.26118i			0.0573263i
$485$	11.5452	+	9.17221i	0.524242	+	0.416489i
$486$	1.00000			0.0453609
$487$	21.9539	−	21.9539i	0.994826	−	0.994826i	−0.00516029	−	0.999987i	$-0.501643\pi$
$487$	21.9539	−	21.9539i	0.994826	−	0.994826i	0.999987	+	0.00516029i	$0.00164258\pi$
$488$	−0.595025	+	0.595025i	−0.0269355	+	0.0269355i
$489$		−	3.97596i		−	0.179799i
$490$	−10.4548	−	8.30593i	−0.472301	−	0.375224i
$491$	27.8777			1.25810			0.629051	−	0.777364i	$-0.283444\pi$
$491$	27.8777			1.25810			0.629051	+	0.777364i	$0.283444\pi$
$492$	−3.59889	+	3.59889i	−0.162251	+	0.162251i
$493$	−0.155264	+	0.155264i	−0.00699275	+	0.00699275i
$494$	7.86433			0.353833
$495$	7.77894	−	0.891017i	0.349638	−	0.0400483i
$496$	−1.27272			−0.0571466
$497$	36.3080	+	36.3080i	1.62864	+	1.62864i
$498$	−1.02759	+	1.02759i	−0.0460475	+	0.0460475i
$499$		−	3.43975i		−	0.153984i	−0.997032	−	0.0769921i	$-0.975468\pi$
$499$		−	3.43975i		−	0.153984i	0.997032	−	0.0769921i	$-0.0245316\pi$
$500$	3.75100	+	10.5323i	0.167750	+	0.471020i
$501$	11.8911			0.531254
$502$	−9.08123	−	9.08123i	−0.405315	−	0.405315i
$503$	−10.5623	+	10.5623i	−0.470951	+	0.470951i	−0.902222	−	0.431271i	$-0.858065\pi$
$503$	−10.5623	+	10.5623i	−0.470951	+	0.470951i	0.431271	+	0.902222i	$0.358065\pi$
$504$	3.60159			0.160428
$505$	−0.962442	+	0.110240i	−0.0428281	+	0.00490562i
$506$	4.80439	−	16.0911i	0.213581	−	0.715339i
$507$	−1.00768	+	1.00768i	−0.0447525	+	0.0447525i
$508$	−8.49034	−	8.49034i	−0.376698	−	0.376698i
$509$		−	26.4803i		−	1.17372i	−0.809690	−	0.586858i	$-0.800364\pi$
$509$		−	26.4803i		−	1.17372i	0.809690	−	0.586858i	$-0.199636\pi$
$510$	3.39722	+	2.69895i	0.150431	+	0.119511i
$511$		−	40.1765i		−	1.77730i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	1.63451	−	1.63451i	0.0721654	−	0.0721654i
$514$		−	2.01700i		−	0.0889659i
$515$	17.7029	−	22.2829i	0.780082	−	0.981904i
$516$		−	3.83417i		−	0.168790i
$517$	−2.71530	−	2.71530i	−0.119419	−	0.119419i
$518$	13.4990	+	13.4990i	0.593112	+	0.593112i
$519$			12.1552i			0.533553i
$520$	0.865724	+	7.55812i	0.0379645	+	0.331445i
$521$			36.7888i			1.61175i	0.592089	+	0.805873i	$0.298304\pi$
$521$			36.7888i			1.61175i	−0.592089	+	0.805873i	$0.701696\pi$
$522$	−0.0800174	+	0.0800174i	−0.00350227	+	0.00350227i
$523$	0.561001	−	0.561001i	0.0245309	−	0.0245309i	−0.694735	−	0.719266i	$-0.744478\pi$
$523$	0.561001	−	0.561001i	0.0245309	−	0.0245309i	0.719266	+	0.694735i	$0.244478\pi$
$524$		−	18.8562i		−	0.823736i
$525$	−4.07192	−	17.5416i	−0.177713	−	0.765576i
$526$		−	26.3155i		−	1.14741i
$527$	1.74624	+	1.74624i	0.0760673	+	0.0760673i
$528$	−2.47600	+	2.47600i	−0.107754	+	0.107754i
$529$	−12.6102	+	19.2349i	−0.548271	+	0.836301i
$530$	−0.941907	−	8.22323i	−0.0409138	−	0.357194i
$531$	−13.2983			−0.577095
$532$	5.88684	−	5.88684i	0.255227	−	0.255227i
$533$	12.2441	+	12.2441i	0.530352	+	0.530352i
$534$	14.7757			0.639406
$535$	34.0967	+	27.0885i	1.47413	+	1.17114i
$536$		−	7.54272i		−	0.325796i
$537$	−15.6693	+	15.6693i	−0.676179	+	0.676179i
$538$	9.69584	+	9.69584i	0.418017	+	0.418017i
$539$	−20.9097			−0.900643
$540$	1.75080	+	1.39094i	0.0753424	+	0.0598564i
$541$	−34.6074			−1.48789			−0.743945	−	0.668241i	$-0.767047\pi$
$541$	−34.6074			−1.48789			−0.743945	+	0.668241i	$0.767047\pi$
$542$	−8.26118	+	8.26118i	−0.354848	+	0.354848i
$543$	5.45870	−	5.45870i	0.234255	−	0.234255i
$544$	−1.94038			−0.0831932
$545$	−6.87050	+	0.786962i	−0.294300	+	0.0337098i
$546$		−	12.2533i		−	0.524394i
$547$	−32.8328	+	32.8328i	−1.40383	+	1.40383i	−0.616378	+	0.787451i	$0.711401\pi$
$547$	−32.8328	+	32.8328i	−1.40383	+	1.40383i	−0.787451	+	0.616378i	$0.788599\pi$
$548$	−3.49960	+	3.49960i	−0.149495	+	0.149495i
$549$	0.841493			0.0359140
$550$	14.8587	+	9.26003i	0.633578	+	0.394849i
$551$			0.261579i			0.0111436i
$552$	4.21961	−	2.27923i	0.179599	−	0.0970104i
$553$	6.06095	+	6.06095i	0.257738	+	0.257738i
$554$		−	14.5830i		−	0.619572i
$555$	1.34878	+	11.7754i	0.0572527	+	0.499839i
$556$	14.4705			0.613684
$557$	1.66595	+	1.66595i	0.0705886	+	0.0705886i	0.741520	−	0.670931i	$-0.234105\pi$
$557$	1.66595	+	1.66595i	0.0705886	+	0.0705886i	−0.670931	+	0.741520i	$0.734105\pi$
$558$	0.899946	+	0.899946i	0.0380977	+	0.0380977i
$559$	−13.0446			−0.551727
$560$	6.30566	+	5.00959i	0.266463	+	0.211694i
$561$	6.79443			0.286861
$562$	−20.8042	−	20.8042i	−0.877572	−	0.877572i
$563$	4.02393	−	4.02393i	0.169588	−	0.169588i	−0.617210	−	0.786798i	$-0.711737\pi$
$563$	4.02393	−	4.02393i	0.169588	−	0.169588i	0.786798	+	0.617210i	$0.211737\pi$
$564$		−	1.09665i		−	0.0461771i
$565$	−4.64648	+	5.84861i	−0.195479	+	0.246053i
$566$			25.4617i			1.07023i
$567$	−2.54671	−	2.54671i	−0.106952	−	0.106952i
$568$	−10.0811	−	10.0811i	−0.422994	−	0.422994i
$569$	−21.4834			−0.900630			−0.450315	−	0.892870i	$-0.648688\pi$
$569$	−21.4834			−0.900630			−0.450315	+	0.892870i	$0.648688\pi$
$570$	5.13520	−	0.588197i	0.215090	−	0.0246369i
$571$			5.17146i			0.216419i	0.994128	+	0.108209i	$0.0345117\pi$
$571$			5.17146i			0.216419i	−0.994128	+	0.108209i	$0.965488\pi$
$572$	8.42384	+	8.42384i	0.352219	+	0.352219i
$573$	−16.0360	+	16.0360i	−0.669911	+	0.669911i
$574$	18.3307			0.765108
$575$	−15.8716	−	17.9747i	−0.661893	−	0.749599i
$576$	−1.00000			−0.0416667
$577$	−16.9864	+	16.9864i	−0.707152	+	0.707152i	−0.965935	−	0.258784i	$-0.916678\pi$
$577$	−16.9864	+	16.9864i	−0.707152	+	0.707152i	0.258784	+	0.965935i	$0.416678\pi$
$578$	−9.35850	−	9.35850i	−0.389262	−	0.389262i
$579$			19.6824i			0.817972i
$580$	−0.251394	+	0.0287952i	−0.0104385	+	0.00119565i
$581$	5.23396			0.217141
$582$	4.66285	+	4.66285i	0.193281	+	0.193281i
$583$	−9.16514	−	9.16514i	−0.379581	−	0.379581i
$584$			11.1552i			0.461606i
$585$	4.73224	−	5.95656i	0.195654	−	0.246273i
$586$			15.8135i			0.653249i
$587$	1.63768	−	1.63768i	0.0675943	−	0.0675943i	−0.672501	−	0.740096i	$-0.734780\pi$
$587$	1.63768	−	1.63768i	0.0675943	−	0.0675943i	0.740096	+	0.672501i	$0.234780\pi$
$588$	−4.22246	−	4.22246i	−0.174131	−	0.174131i
$589$	2.94194			0.121221
$590$	−23.2826	−	18.4970i	−0.958528	−	0.761511i
$591$	5.21479			0.214508
$592$	−3.74806	−	3.74806i	−0.154044	−	0.154044i
$593$	32.8241	+	32.8241i	1.34792	+	1.34792i	0.887914	+	0.460010i	$0.152154\pi$
$593$	32.8241	+	32.8241i	1.34792	+	1.34792i	0.460010	+	0.887914i	$0.347846\pi$
$594$	3.50160			0.143672
$595$	−1.77829	−	15.5252i	−0.0729026	−	0.636470i
$596$			2.64129i			0.108192i
$597$	−8.37242	−	8.37242i	−0.342660	−	0.342660i
$598$	−7.75438	−	14.3559i	−0.317100	−	0.587058i
$599$			7.24916i			0.296193i	0.988973	+	0.148096i	$0.0473146\pi$
$599$			7.24916i			0.296193i	−0.988973	+	0.148096i	$0.952685\pi$
$600$	1.13059	+	4.87050i	0.0461561	+	0.198837i
$601$	−36.4196			−1.48559			−0.742793	−	0.669522i	$-0.766499\pi$
$601$	−36.4196			−1.48559			−0.742793	+	0.669522i	$0.766499\pi$
$602$	−9.76452	+	9.76452i	−0.397972	+	0.397972i
$603$	−5.33351	+	5.33351i	−0.217197	+	0.217197i
$604$		−	21.1977i		−	0.862524i
$605$	2.80176	−	0.320920i	0.113908	−	0.0130472i
$606$	−0.433231			−0.0175988
$607$	−27.1733	+	27.1733i	−1.10293	+	1.10293i	−0.108877	+	0.994055i	$0.534725\pi$
$607$	−27.1733	+	27.1733i	−1.10293	+	1.10293i	−0.994055	+	0.108877i	$0.965275\pi$
$608$	−1.63451	+	1.63451i	−0.0662881	+	0.0662881i
$609$	0.407562			0.0165153
$610$	1.47328	+	1.17046i	0.0596515	+	0.0473907i
$611$	−3.73100			−0.150940
$612$	1.37206	+	1.37206i	0.0554621	+	0.0554621i
$613$	16.1170	−	16.1170i	0.650961	−	0.650961i	−0.302264	−	0.953224i	$-0.597742\pi$
$613$	16.1170	−	16.1170i	0.650961	−	0.650961i	0.953224	+	0.302264i	$0.0977423\pi$
$614$		−	14.1353i		−	0.570453i
$615$	8.91087	+	7.07932i	0.359321	+	0.285466i
$616$	12.6113			0.508125
$617$	−23.2043	−	23.2043i	−0.934171	−	0.934171i	0.0637926	−	0.997963i	$-0.479680\pi$
$617$	−23.2043	−	23.2043i	−0.934171	−	0.934171i	−0.997963	+	0.0637926i	$0.979680\pi$
$618$	8.99956	−	8.99956i	0.362016	−	0.362016i
$619$	−46.2965			−1.86081			−0.930407	−	0.366527i	$-0.880547\pi$
$619$	−46.2965			−1.86081			−0.930407	+	0.366527i	$0.880547\pi$
$620$	0.323856	+	2.82739i	0.0130064	+	0.113551i
$621$	−4.59537	−	1.37206i	−0.184406	−	0.0550587i
$622$	2.25377	−	2.25377i	0.0903678	−	0.0903678i
$623$	−37.6293	−	37.6293i	−1.50759	−	1.50759i
$624$			3.40219i			0.136197i
$625$	22.4435	−	11.0131i	0.897742	−	0.440523i
$626$		−	27.7938i		−	1.11086i
$627$	5.72339	−	5.72339i	0.228570	−	0.228570i
$628$	−17.0584	+	17.0584i	−0.680703	+	0.680703i
$629$			10.2851i			0.410094i
$630$	−0.916462	−	8.00109i	−0.0365127	−	0.318771i
$631$		−	5.61950i		−	0.223709i	−0.993725	−	0.111854i	$-0.964321\pi$
$631$		−	5.61950i		−	0.223709i	0.993725	−	0.111854i	$-0.0356790\pi$
$632$	−1.68285	−	1.68285i	−0.0669403	−	0.0669403i
$633$	17.1835	+	17.1835i	0.682985	+	0.682985i
$634$		−	4.79443i		−	0.190411i
$635$	−16.7012	+	21.0221i	−0.662767	+	0.834237i
$636$		−	3.70159i		−	0.146777i
$637$	−14.3656	+	14.3656i	−0.569187	+	0.569187i
$638$	−0.280189	+	0.280189i	−0.0110928	+	0.0110928i
$639$			14.2568i			0.563992i
$640$	−1.75080	−	1.39094i	−0.0692064	−	0.0549816i
$641$			34.0178i			1.34362i	0.740723	+	0.671810i	$0.234483\pi$
$641$			34.0178i			1.34362i	−0.740723	+	0.671810i	$0.765517\pi$
$642$	13.7709	+	13.7709i	0.543493	+	0.543493i
$643$	−20.2441	+	20.2441i	−0.798350	+	0.798350i	−0.982835	−	0.184486i	$-0.940938\pi$
$643$	−20.2441	+	20.2441i	−0.798350	+	0.798350i	0.184486	+	0.982835i	$0.440938\pi$
$644$	−16.5507	−	4.94159i	−0.652187	−	0.194726i
$645$	−8.51777	+	0.975644i	−0.335387	+	0.0384159i
$646$	4.48528			0.176471
$647$	−14.0759	+	14.0759i	−0.553381	+	0.553381i	−0.927415	−	0.374034i	$-0.877974\pi$
$647$	−14.0759	+	14.0759i	−0.553381	+	0.553381i	0.374034	+	0.927415i	$0.377974\pi$
$648$	0.707107	+	0.707107i	0.0277778	+	0.0277778i
$649$	−46.5651			−1.82784
$650$	16.5704	−	3.84648i	0.649944	−	0.150871i
$651$		−	4.58380i		−	0.179653i
$652$	2.81143	−	2.81143i	0.110104	−	0.110104i
$653$	−1.54803	−	1.54803i	−0.0605792	−	0.0605792i	0.676168	−	0.736747i	$-0.263639\pi$
$653$	−1.54803	−	1.54803i	−0.0605792	−	0.0605792i	−0.736747	+	0.676168i	$0.763639\pi$
$654$	−3.09267			−0.120933
$655$	−41.8898	+	4.79815i	−1.63677	+	0.187479i
$656$	−5.08960			−0.198716
$657$	7.88793	−	7.88793i	0.307737	−	0.307737i
$658$	−2.79284	+	2.79284i	−0.108876	+	0.108876i
$659$	27.5842			1.07453			0.537264	−	0.843414i	$-0.319458\pi$
$659$	27.5842			1.07453			0.537264	+	0.843414i	$0.319458\pi$
$660$	6.13059	+	4.87050i	0.238633	+	0.189584i
$661$		−	41.5932i		−	1.61779i	−0.587954	−	0.808894i	$-0.700066\pi$
$661$		−	41.5932i		−	1.61779i	0.587954	−	0.808894i	$-0.299934\pi$
$662$	−1.64705	+	1.64705i	−0.0640146	+	0.0640146i
$663$	4.66800	−	4.66800i	0.181290	−	0.181290i
$664$	−1.45324			−0.0563965
$665$	−14.5758	−	11.5799i	−0.565226	−	0.449049i
$666$			5.30056i			0.205393i
$667$	0.477498	−	0.257921i	0.0184888	−	0.00998676i
$668$	8.40826	+	8.40826i	0.325325	+	0.325325i
$669$			2.26616i			0.0876147i
$670$	−16.7565	+	1.91932i	−0.647359	+	0.0741499i
$671$	2.94657			0.113751
$672$	2.54671	+	2.54671i	0.0982415	+	0.0982415i
$673$	−27.7520	−	27.7520i	−1.06976	−	1.06976i	−0.997377	−	0.0723860i	$-0.976939\pi$
$673$	−27.7520	−	27.7520i	−1.06976	−	1.06976i	−0.0723860	−	0.997377i	$-0.523061\pi$
$674$	−27.1679			−1.04647
$675$	2.64452	−	4.24341i	0.101787	−	0.163329i
$676$	−1.42507			−0.0548104
$677$	−0.758084	−	0.758084i	−0.0291355	−	0.0291355i	0.692389	−	0.721524i	$-0.256558\pi$
$677$	−0.758084	−	0.758084i	−0.0291355	−	0.0291355i	−0.721524	+	0.692389i	$0.756558\pi$
$678$	−2.36212	+	2.36212i	−0.0907165	+	0.0907165i
$679$		−	23.7499i		−	0.911436i
$680$	0.493750	+	4.31064i	0.0189345	+	0.165305i
$681$		−	21.8017i		−	0.835442i
$682$	3.15125	+	3.15125i	0.120667	+	0.120667i
$683$	29.8443	+	29.8443i	1.14196	+	1.14196i	0.988091	+	0.153870i	$0.0491737\pi$
$683$	29.8443	+	29.8443i	1.14196	+	1.14196i	0.153870	+	0.988091i	$0.450826\pi$
$684$	2.31155			0.0883842
$685$	8.66501	+	6.88400i	0.331073	+	0.263024i
$686$		−	3.70436i		−	0.141433i
$687$	−9.08206	−	9.08206i	−0.346502	−	0.346502i
$688$	2.71117	−	2.71117i	0.103362	−	0.103362i
$689$	−12.5935			−0.479775
$690$	−6.13713	−	8.79407i	−0.233636	−	0.334785i
$691$	29.2340			1.11211			0.556056	−	0.831145i	$-0.312314\pi$
$691$	29.2340			1.11211			0.556056	+	0.831145i	$0.312314\pi$
$692$	−8.59500	+	8.59500i	−0.326733	+	0.326733i
$693$	−8.91755	−	8.91755i	−0.338750	−	0.338750i
$694$			9.19779i			0.349143i
$695$	−3.68216	−	32.1467i	−0.139672	−	1.21940i
$696$	−0.113162			−0.00428938
$697$	6.98323	+	6.98323i	0.264509	+	0.264509i
$698$	−3.02573	−	3.02573i	−0.114526	−	0.114526i
$699$			17.3809i			0.657404i
$700$	9.52447	−	15.2830i	0.359991	−	0.577644i
$701$		−	14.5948i		−	0.551239i	−0.961267	−	0.275619i	$-0.911117\pi$
$701$		−	14.5948i		−	0.551239i	0.961267	−	0.275619i	$-0.0888830\pi$
$702$	2.40571	−	2.40571i	0.0907979	−	0.0907979i
$703$	8.66382	+	8.66382i	0.326762	+	0.326762i
$704$	−3.50160			−0.131971
$705$	−2.43624	+	0.279053i	−0.0917542	+	0.0105097i
$706$	23.8600			0.897983
$707$	1.10331	+	1.10331i	0.0414944	+	0.0414944i
$708$	−9.40328	−	9.40328i	−0.353397	−	0.353397i
$709$	−40.4789			−1.52022			−0.760109	−	0.649796i	$-0.774854\pi$
$709$	−40.4789			−1.52022			−0.760109	+	0.649796i	$0.774854\pi$
$710$	−19.8304	+	24.9608i	−0.744220	+	0.936764i
$711$			2.37992i			0.0892538i
$712$	10.4480	+	10.4480i	0.391554	+	0.391554i
$713$	−2.90081	−	5.37036i	−0.108636	−	0.201122i
$714$		−	6.98846i		−	0.261537i
$715$	16.5704	−	20.8575i	0.619697	−	0.780025i
$716$	−22.1597			−0.828147
$717$	12.8500	−	12.8500i	0.479893	−	0.479893i
$718$	17.1714	−	17.1714i	0.640832	−	0.640832i
$719$		−	34.5861i		−	1.28984i	−0.764249	−	0.644922i	$-0.776890\pi$
$719$		−	34.5861i		−	1.28984i	0.764249	−	0.644922i	$-0.223110\pi$
$720$	0.254460	+	2.22154i	0.00948318	+	0.0827920i
$721$	−45.8386			−1.70712
$722$	−9.65678	+	9.65678i	−0.359388	+	0.359388i
$723$	8.33583	−	8.33583i	0.310013	−	0.310013i
$724$	7.71976			0.286903
$725$	0.127939	+	0.551154i	0.00475155	+	0.0204693i
$726$	1.26118			0.0468067
$727$	28.3874	+	28.3874i	1.05283	+	1.05283i	0.998524	+	0.0543047i	$0.0172942\pi$
$727$	28.3874	+	28.3874i	1.05283	+	1.05283i	0.0543047	+	0.998524i	$0.482706\pi$
$728$	8.66440	−	8.66440i	0.321124	−	0.321124i
$729$		−	1.00000i		−	0.0370370i
$730$	24.7818	−	2.83856i	0.917215	−	0.105060i
$731$	−7.43975			−0.275169
$732$	0.595025	+	0.595025i	0.0219928	+	0.0219928i
$733$	−19.5867	+	19.5867i	−0.723452	+	0.723452i	−0.969307	−	0.245855i	$-0.920931\pi$
$733$	−19.5867	+	19.5867i	−0.723452	+	0.723452i	0.245855	+	0.969307i	$0.420931\pi$
$734$	23.4586			0.865871
$735$	−8.30593	+	10.4548i	−0.306369	+	0.385632i
$736$	4.59537	+	1.37206i	0.169388	+	0.0505747i
$737$	−18.6758	+	18.6758i	−0.687932	+	0.687932i
$738$	3.59889	+	3.59889i	0.132477	+	0.132477i
$739$		−	7.22496i		−	0.265775i	−0.991131	−	0.132887i	$-0.957575\pi$
$739$		−	7.22496i		−	0.265775i	0.991131	−	0.132887i	$-0.0424248\pi$
$740$	−7.37275	+	9.28022i	−0.271028	+	0.341148i
$741$		−	7.86433i		−	0.288903i
$742$	−9.42687	+	9.42687i	−0.346071	+	0.346071i
$743$	38.0467	−	38.0467i	1.39580	−	1.39580i	0.584157	−	0.811641i	$-0.301425\pi$
$743$	38.0467	−	38.0467i	1.39580	−	1.39580i	0.811641	−	0.584157i	$-0.198575\pi$
$744$			1.27272i			0.0466600i
$745$	5.86774	−	0.672104i	0.214977	−	0.0246240i
$746$		−	0.772089i		−	0.0282682i
$747$	1.02759	+	1.02759i	0.0375976	+	0.0375976i
$748$	4.80439	+	4.80439i	0.175666	+	0.175666i
$749$		−	70.1409i		−	2.56289i
$750$	10.5323	−	3.75100i	0.384586	−	0.136967i
$751$		−	14.7440i		−	0.538017i	−0.963138	−	0.269009i	$-0.913304\pi$
$751$		−	14.7440i		−	0.538017i	0.963138	−	0.269009i	$-0.0866960\pi$
$752$	0.775445	−	0.775445i	0.0282776	−	0.0282776i
$753$	−9.08123	+	9.08123i	−0.330939	+	0.330939i
$754$			0.384998i			0.0140208i
$755$	−47.0917	+	5.39399i	−1.71384	+	0.196307i
$756$		−	3.60159i		−	0.130989i
$757$	−5.21529	−	5.21529i	−0.189553	−	0.189553i	0.605950	−	0.795503i	$-0.292793\pi$
$757$	−5.21529	−	5.21529i	−0.189553	−	0.189553i	−0.795503	+	0.605950i	$0.792793\pi$
$758$	8.23160	−	8.23160i	0.298985	−	0.298985i
$759$	−16.0911	−	4.80439i	−0.584072	−	0.174388i
$760$	4.04705	+	3.21522i	0.146802	+	0.116628i
$761$	9.25446			0.335474			0.167737	−	0.985832i	$-0.446354\pi$
$761$	9.25446			0.335474			0.167737	+	0.985832i	$0.446354\pi$
$762$	−8.49034	+	8.49034i	−0.307573	+	0.307573i
$763$	7.87614	+	7.87614i	0.285135	+	0.285135i
$764$	−22.6783			−0.820471
$765$	2.69895	−	3.39722i	0.0975807	−	0.122827i
$766$		−	22.1446i		−	0.800116i
$767$	−31.9918	+	31.9918i	−1.15516	+	1.15516i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−13.1928			−0.475744			−0.237872	−	0.971296i	$-0.576450\pi$
$769$	−13.1928			−0.475744			−0.237872	+	0.971296i	$0.576450\pi$
$770$	−3.20908	−	28.0166i	−0.115647	−	1.00965i
$771$	−2.01700			−0.0726404
$772$	−13.9176	+	13.9176i	−0.500904	+	0.500904i
$773$	−15.6399	+	15.6399i	−0.562527	+	0.562527i	−0.930025	−	0.367497i	$-0.880215\pi$
$773$	−15.6399	+	15.6399i	−0.562527	+	0.562527i	0.367497	+	0.930025i	$0.380215\pi$
$774$	−3.83417			−0.137816
$775$	6.19876	−	1.43892i	0.222666	−	0.0516875i
$776$			6.59427i			0.236720i
$777$	13.4990	−	13.4990i	0.484274	−	0.484274i
$778$	24.3078	−	24.3078i	0.871478	−	0.871478i
$779$	11.7649			0.421520
$780$	7.55812	−	0.865724i	0.270624	−	0.0309979i
$781$			49.9217i			1.78634i
$782$	−4.42257	−	8.18765i	−0.158151	−	0.292790i
$783$	0.0800174	+	0.0800174i	0.00285959	+	0.00285959i
$784$		−	5.97146i		−	0.213267i
$785$	42.2366	+	33.5552i	1.50749	+	1.19764i
$786$	−18.8562			−0.672578
$787$	−21.0340	−	21.0340i	−0.749782	−	0.749782i	0.224656	−	0.974438i	$-0.427874\pi$
$787$	−21.0340	−	21.0340i	−0.749782	−	0.749782i	−0.974438	+	0.224656i	$0.927874\pi$
$788$	3.68741	+	3.68741i	0.131359	+	0.131359i
$789$	−26.3155			−0.936856
$790$	−3.31031	+	4.16675i	−0.117776	+	0.148246i
$791$	12.0312			0.427782
$792$	2.47600	+	2.47600i	0.0879809	+	0.0879809i
$793$	2.02439	−	2.02439i	0.0718882	−	0.0718882i
$794$		−	5.19917i		−	0.184512i
$795$	−8.22323	+	0.941907i	−0.291648	+	0.0334060i
$796$		−	11.8404i		−	0.419672i
$797$	20.3632	+	20.3632i	0.721300	+	0.721300i	0.968870	−	0.247570i	$-0.0796321\pi$
$797$	20.3632	+	20.3632i	0.721300	+	0.721300i	−0.247570	+	0.968870i	$0.579632\pi$
$798$	−5.88684	−	5.88684i	−0.208392	−	0.208392i
$799$	−2.12791			−0.0752800
$800$	−2.64452	+	4.24341i	−0.0934978	+	0.150027i
$801$		−	14.7757i		−	0.522072i
$802$	6.09077	+	6.09077i	0.215072	+	0.215072i
$803$	27.6203	−	27.6203i	0.974701	−	0.974701i
$804$	−7.54272			−0.266011
$805$	−6.76646	+	38.0254i	−0.238486	+	1.34022i
$806$	4.33003			0.152519
$807$	9.69584	−	9.69584i	0.341310	−	0.341310i
$808$	−0.306341	−	0.306341i	−0.0107770	−	0.0107770i
$809$			21.8823i			0.769340i	0.923054	+	0.384670i	$0.125685\pi$
$809$			21.8823i			0.769340i	−0.923054	+	0.384670i	$0.874315\pi$
$810$	1.39094	−	1.75080i	0.0488725	−	0.0615168i
$811$	8.99460			0.315843			0.157922	−	0.987452i	$-0.449521\pi$
$811$	8.99460			0.315843			0.157922	+	0.987452i	$0.449521\pi$
$812$	0.288190	+	0.288190i	0.0101135	+	0.0101135i
$813$	8.26118	+	8.26118i	0.289732	+	0.289732i
$814$			18.5604i			0.650543i
$815$	−6.96111	−	5.53031i	−0.243837	−	0.193718i
$816$			1.94038i			0.0679269i
$817$	−6.26699	+	6.26699i	−0.219254	+	0.219254i
$818$	7.46533	+	7.46533i	0.261019	+	0.261019i
$819$	−12.2533			−0.428166
$820$	1.29510	+	11.3068i	0.0452269	+	0.394850i
$821$	−29.3828			−1.02547			−0.512734	−	0.858548i	$-0.671367\pi$
$821$	−29.3828			−1.02547			−0.512734	+	0.858548i	$0.671367\pi$
$822$	3.49960	+	3.49960i	0.122062	+	0.122062i
$823$	21.1671	+	21.1671i	0.737838	+	0.737838i	0.972159	−	0.234321i	$-0.0752868\pi$
$823$	21.1671	+	21.1671i	0.737838	+	0.737838i	−0.234321	+	0.972159i	$0.575287\pi$
$824$	12.7273			0.443377
$825$	9.26003	−	14.8587i	0.322393	−	0.517314i
$826$			47.8949i			1.66648i
$827$	−17.5954	−	17.5954i	−0.611853	−	0.611853i	0.331576	−	0.943429i	$-0.392420\pi$
$827$	−17.5954	−	17.5954i	−0.611853	−	0.611853i	−0.943429	+	0.331576i	$0.892420\pi$
$828$	−2.27923	−	4.21961i	−0.0792087	−	0.146642i
$829$		−	52.8512i		−	1.83560i	−0.397045	−	0.917799i	$-0.629964\pi$
$829$		−	52.8512i		−	1.83560i	0.397045	−	0.917799i	$-0.370036\pi$
$830$	0.369791	+	3.22842i	0.0128356	+	0.112060i
$831$	−14.5830			−0.505878
$832$	−2.40571	+	2.40571i	−0.0834032	+	0.0834032i
$833$	−8.19319	+	8.19319i	−0.283877	+	0.283877i
$834$		−	14.4705i		−	0.501071i
$835$	16.5397	−	20.8189i	0.572381	−	0.720467i
$836$	8.09410			0.279940
$837$	0.899946	−	0.899946i	0.0311067	−	0.0311067i
$838$	−22.2769	+	22.2769i	−0.769543	+	0.769543i
$839$	14.3452			0.495250			0.247625	−	0.968856i	$-0.420350\pi$
$839$	14.3452			0.495250			0.247625	+	0.968856i	$0.420350\pi$
$840$	5.00959	−	6.30566i	0.172847	−	0.217566i
$841$	28.9872			0.999558
$842$	−20.5909	−	20.5909i	−0.709609	−	0.709609i
$843$	−20.8042	+	20.8042i	−0.716535	+	0.716535i
$844$			24.3012i			0.836482i
$845$	0.362624	+	3.16586i	0.0124747	+	0.108909i
$846$	−1.09665			−0.0377034
$847$	−3.21185	−	3.21185i	−0.110361	−	0.110361i
$848$	2.61742	−	2.61742i	0.0898825	−	0.0898825i
$849$	25.4617			0.873842
$850$	9.45063	−	2.19377i	0.324154	−	0.0752458i
$851$	7.27267	−	24.3581i	0.249304	−	0.834984i
$852$	−10.0811	+	10.0811i	−0.345373	+	0.345373i
$853$	15.6696	+	15.6696i	0.536515	+	0.536515i	0.922504	−	0.385988i	$-0.126140\pi$
$853$	15.6696	+	15.6696i	0.536515	+	0.536515i	−0.385988	+	0.922504i	$0.626140\pi$
$854$		−	3.03071i		−	0.103709i
$855$	−0.588197	−	5.13520i	−0.0201159	−	0.175620i
$856$			19.4750i			0.665641i
$857$	18.8824	−	18.8824i	0.645011	−	0.645011i	−0.306772	−	0.951783i	$-0.599249\pi$
$857$	18.8824	−	18.8824i	0.645011	−	0.645011i	0.951783	+	0.306772i	$0.0992488\pi$
$858$	8.42384	−	8.42384i	0.287585	−	0.287585i
$859$		−	27.2280i		−	0.929009i	−0.885571	−	0.464504i	$-0.846232\pi$
$859$		−	27.2280i		−	0.929009i	0.885571	−	0.464504i	$-0.153768\pi$
$860$	−6.71285	−	5.33309i	−0.228906	−	0.181857i
$861$		−	18.3307i		−	0.624708i
$862$	21.0362	+	21.0362i	0.716495	+	0.716495i
$863$	23.0409	+	23.0409i	0.784321	+	0.784321i	0.980557	−	0.196236i	$-0.0628718\pi$
$863$	23.0409	+	23.0409i	0.784321	+	0.784321i	−0.196236	+	0.980557i	$0.562872\pi$
$864$			1.00000i			0.0340207i
$865$	21.2813	+	16.9071i	0.723584	+	0.574858i
$866$		−	21.5430i		−	0.732060i
$867$	−9.35850	+	9.35850i	−0.317831	+	0.317831i
$868$	3.24124	−	3.24124i	0.110015	−	0.110015i
$869$			8.33350i			0.282695i
$870$	0.0287952	+	0.251394i	0.000976248	+	0.00852304i
$871$			25.6618i			0.869517i
$872$	−2.18685	−	2.18685i	−0.0740560	−	0.0740560i
$873$	4.66285	−	4.66285i	0.157814	−	0.157814i
$874$	−10.6224	−	3.17157i	−0.359309	−	0.107280i
$875$	−36.3755	−	17.2701i	−1.22972	−	0.583835i
$876$	11.1552			0.376900
$877$	28.0528	−	28.0528i	0.947275	−	0.947275i	−0.0514032	−	0.998678i	$-0.516369\pi$
$877$	28.0528	−	28.0528i	0.947275	−	0.947275i	0.998678	+	0.0514032i	$0.0163694\pi$
$878$	−22.7054	−	22.7054i	−0.766271	−	0.766271i
$879$	15.8135			0.533376
$880$	0.891017	+	7.77894i	0.0300362	+	0.262228i
$881$			2.20846i			0.0744050i	0.999308	+	0.0372025i	$0.0118447\pi$
$881$			2.20846i			0.0744050i	−0.999308	+	0.0372025i	$0.988155\pi$
$882$	−4.22246	+	4.22246i	−0.142178	+	0.142178i
$883$	10.1952	+	10.1952i	0.343097	+	0.343097i	0.857530	−	0.514433i	$-0.171998\pi$
$883$	10.1952	+	10.1952i	0.343097	+	0.343097i	−0.514433	+	0.857530i	$0.671998\pi$
$884$	6.60156			0.222034
$885$	−18.4970	+	23.2826i	−0.621771	+	0.782634i
$886$	8.22850			0.276442
$887$	−31.6815	+	31.6815i	−1.06376	+	1.06376i	−0.0659369	+	0.997824i	$0.521004\pi$
$887$	−31.6815	+	31.6815i	−1.06376	+	1.06376i	−0.997824	+	0.0659369i	$0.978996\pi$
$888$	−3.74806	+	3.74806i	−0.125777	+	0.125777i
$889$	43.2449			1.45039
$890$	20.5520	−	25.8692i	0.688905	−	0.867138i
$891$		−	3.50160i		−	0.117308i
$892$	−1.60241	+	1.60241i	−0.0536528	+	0.0536528i
$893$	−1.79248	+	1.79248i	−0.0599830	+	0.0599830i
$894$	2.64129			0.0883380
$895$	5.63877	+	49.2287i	0.188483	+	1.64554i
$896$			3.60159i			0.120321i
$897$	−14.3559	+	7.75438i	−0.479331	+	0.258911i
$898$	6.44336	+	6.44336i	0.215018	+	0.215018i
$899$			0.144023i			0.00480343i
$900$	4.87050	−	1.13059i	0.162350	−	0.0376863i
$901$	−7.18249			−0.239283
$902$	12.6019	+	12.6019i	0.419597	+	0.419597i
$903$	9.76452	+	9.76452i	0.324943	+	0.324943i
$904$	−3.34054			−0.111105
$905$	−1.96437	−	17.1498i	−0.0652980	−	0.570078i
$906$	−21.1977			−0.704248
$907$	−8.04728	−	8.04728i	−0.267205	−	0.267205i	0.560768	−	0.827973i	$-0.310506\pi$
$907$	−8.04728	−	8.04728i	−0.267205	−	0.267205i	−0.827973	+	0.560768i	$0.810506\pi$
$908$	15.4161	−	15.4161i	0.511601	−	0.511601i
$909$			0.433231i			0.0143694i
$910$	−21.4531	−	17.0436i	−0.711163	−	0.564990i
$911$			1.59474i			0.0528363i	0.999651	+	0.0264181i	$0.00841013\pi$
$911$			1.59474i			0.0528363i	−0.999651	+	0.0264181i	$0.991590\pi$
$912$	1.63451	+	1.63451i	0.0541240	+	0.0541240i
$913$	3.59821	+	3.59821i	0.119084	+	0.119084i
$914$	−2.61402			−0.0864641
$915$	1.17046	−	1.47328i	0.0386943	−	0.0487053i
$916$		−	12.8440i		−	0.424377i
$917$	48.0212	+	48.0212i	1.58580	+	1.58580i
$918$	1.37206	−	1.37206i	0.0452846	−	0.0452846i
$919$	37.8146			1.24739			0.623695	−	0.781668i	$-0.285631\pi$
$919$	37.8146			1.24739			0.623695	+	0.781668i	$0.285631\pi$
$920$	1.87874	−	10.5580i	0.0619403	−	0.348085i
$921$	−14.1353			−0.465773
$922$	17.5428	−	17.5428i	0.577743	−	0.577743i
$923$	34.2979	+	34.2979i	1.12893	+	1.12893i
$924$		−	12.6113i		−	0.414882i
$925$	22.4925	+	14.0174i	0.739548	+	0.460890i
$926$	−16.8025			−0.552166
$927$	−8.99956	−	8.99956i	−0.295584	−	0.295584i
$928$	−0.0800174	−	0.0800174i	−0.00262670	−	0.00262670i
$929$		−	11.2022i		−	0.367532i	−0.982970	−	0.183766i	$-0.941171\pi$
$929$		−	11.2022i		−	0.367532i	0.982970	−	0.183766i	$-0.0588288\pi$
$930$	2.82739	−	0.323856i	0.0927138	−	0.0106196i
$931$			13.8033i			0.452385i
$932$	−12.2901	+	12.2901i	−0.402576	+	0.402576i
$933$	−2.25377	−	2.25377i	−0.0737850	−	0.0737850i
$934$	−26.8801			−0.879542
$935$	9.45063	−	11.8957i	0.309069	−	0.389030i
$936$	3.40219			0.111204
$937$	−0.0232922	−	0.0232922i	−0.000760923	−	0.000760923i	0.706726	−	0.707487i	$-0.250171\pi$
$937$	−0.0232922	−	0.0232922i	−0.000760923	−	0.000760923i	−0.707487	+	0.706726i	$0.750171\pi$
$938$	19.2091	+	19.2091i	0.627200	+	0.627200i
$939$	−27.7938			−0.907016
$940$	−1.92000	−	1.52536i	−0.0626236	−	0.0497519i
$941$			10.8405i			0.353389i	0.984266	+	0.176694i	$0.0565404\pi$
$941$			10.8405i			0.353389i	−0.984266	+	0.176694i	$0.943460\pi$
$942$	17.0584	+	17.0584i	0.555792	+	0.555792i
$943$	−11.6004	−	21.4762i	−0.377760	−	0.699360i
$944$		−	13.2983i		−	0.432821i
$945$	−8.00109	+	0.916462i	−0.260275	+	0.0298125i
$946$	−13.4257			−0.436507
$947$	3.30449	−	3.30449i	0.107382	−	0.107382i	−0.651375	−	0.758756i	$-0.725807\pi$
$947$	3.30449	−	3.30449i	0.107382	−	0.107382i	0.758756	+	0.651375i	$0.225807\pi$
$948$	−1.68285	+	1.68285i	−0.0546566	+	0.0546566i
$949$		−	37.9522i		−	1.23198i
$950$	6.11292	−	9.80884i	0.198329	−	0.318241i
$951$	−4.79443			−0.155470
$952$	4.94159	−	4.94159i	0.160158	−	0.160158i
$953$	7.79694	−	7.79694i	0.252568	−	0.252568i	−0.569455	−	0.822023i	$-0.692846\pi$
$953$	7.79694	−	7.79694i	0.252568	−	0.252568i	0.822023	+	0.569455i	$0.192846\pi$
$954$	−3.70159			−0.119843
$955$	5.77072	+	50.3807i	0.186736	+	1.63028i
$956$	18.1727			0.587747
$957$	0.280189	+	0.280189i	0.00905721	+	0.00905721i
$958$	2.89538	−	2.89538i	0.0935455	−	0.0935455i
$959$		−	17.8249i		−	0.575597i
$960$	−1.39094	+	1.75080i	−0.0448923	+	0.0565068i
$961$	−29.3802			−0.947748
$962$	12.7516	+	12.7516i	0.411129	+	0.411129i
$963$	13.7709	−	13.7709i	0.443760	−	0.443760i
$964$	11.7886			0.379687
$965$	34.4599	+	27.3770i	1.10930	+	0.881296i
$966$	−4.94159	+	16.5507i	−0.158993	+	0.532509i
$967$	−27.5837	+	27.5837i	−0.887033	+	0.887033i	−0.994237	−	0.107204i	$-0.965810\pi$
$967$	−27.5837	+	27.5837i	−0.887033	+	0.887033i	0.107204	+	0.994237i	$0.465810\pi$
$968$	0.891787	+	0.891787i	0.0286631	+	0.0286631i
$969$		−	4.48528i		−	0.144088i
$970$	14.6494	−	1.67798i	0.470365	−	0.0538767i
$971$		−	40.8842i		−	1.31204i	−0.754745	−	0.656019i	$-0.772239\pi$
$971$		−	40.8842i		−	1.31204i	0.754745	−	0.656019i	$-0.227761\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	−36.8521	+	36.8521i	−1.18142	+	1.18142i
$974$		−	31.0475i		−	0.994826i
$975$	−3.84648	−	16.5704i	−0.123186	−	0.530677i
$976$			0.841493i			0.0269355i
$977$	0.566178	+	0.566178i	0.0181136	+	0.0181136i	0.716106	−	0.697992i	$-0.245923\pi$
$977$	0.566178	+	0.566178i	0.0181136	+	0.0181136i	−0.697992	+	0.716106i	$0.745923\pi$
$978$	−2.81143	−	2.81143i	−0.0898996	−	0.0898996i
$979$		−	51.7384i		−	1.65357i
$980$	−13.2659	+	1.51950i	−0.423762	+	0.0485387i
$981$			3.09267i			0.0987414i
$982$	19.7125	−	19.7125i	0.629051	−	0.629051i
$983$	12.9460	−	12.9460i	0.412913	−	0.412913i	−0.469839	−	0.882752i	$-0.655688\pi$
$983$	12.9460	−	12.9460i	0.412913	−	0.412913i	0.882752	+	0.469839i	$0.155688\pi$
$984$			5.08960i			0.162251i
$985$	7.25344	−	9.13004i	0.231114	−	0.290907i
$986$			0.219577i			0.00699275i
$987$	2.79284	+	2.79284i	0.0888970	+	0.0888970i
$988$	5.56092	−	5.56092i	0.176916	−	0.176916i
$989$	17.6194	+	5.26070i	0.560265	+	0.167280i
$990$	4.87050	−	6.13059i	0.154795	−	0.194843i
$991$	57.4401			1.82464			0.912322	−	0.409473i	$-0.134287\pi$
$991$	57.4401			1.82464			0.912322	+	0.409473i	$0.134287\pi$
$992$	−0.899946	+	0.899946i	−0.0285733	+	0.0285733i
$993$	1.64705	+	1.64705i	0.0522677	+	0.0522677i
$994$	51.3473			1.62864
$995$	−26.3039	+	3.01291i	−0.833891	+	0.0955157i
$996$			1.45324i			0.0460475i
$997$	−7.80361	+	7.80361i	−0.247143	+	0.247143i	−0.819797	−	0.572654i	$-0.805914\pi$
$997$	−7.80361	+	7.80361i	−0.247143	+	0.247143i	0.572654	+	0.819797i	$0.305914\pi$
$998$	−2.43227	−	2.43227i	−0.0769921	−	0.0769921i
$999$	5.30056			0.167702

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.j.a.643.7	yes	24
5.2	odd	4	inner	690.2.j.a.367.12	yes	24
23.22	odd	2	inner	690.2.j.a.643.12	yes	24
115.22	even	4	inner	690.2.j.a.367.7	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.j.a.367.7	✓	24	115.22	even	4	inner
690.2.j.a.367.12	yes	24	5.2	odd	4	inner
690.2.j.a.643.7	yes	24	1.1	even	1	trivial
690.2.j.a.643.12	yes	24	23.22	odd	2	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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-2.22154 + 0.254460i) q^{5} -1.00000 q^{6} +(2.54671 + 2.54671i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-2.22154 + 0.254460i) q^{5} -1.00000 q^{6} +(2.54671 + 2.54671i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(-1.39094 + 1.75080i) q^{10} +3.50160i q^{11} +(-0.707107 + 0.707107i) q^{12} +(2.40571 + 2.40571i) q^{13} +3.60159 q^{14} +(1.75080 + 1.39094i) q^{15} -1.00000 q^{16} +(1.37206 + 1.37206i) q^{17} +(0.707107 + 0.707107i) q^{18} +2.31155 q^{19} +(0.254460 + 2.22154i) q^{20} -3.60159i q^{21} +(2.47600 + 2.47600i) q^{22} +(-2.27923 - 4.21961i) q^{23} +1.00000i q^{24} +(4.87050 - 1.13059i) q^{25} +3.40219 q^{26} +(0.707107 - 0.707107i) q^{27} +(2.54671 - 2.54671i) q^{28} +0.113162i q^{29} +(2.22154 - 0.254460i) q^{30} +1.27272 q^{31} +(-0.707107 + 0.707107i) q^{32} +(2.47600 - 2.47600i) q^{33} +1.94038 q^{34} +(-6.30566 - 5.00959i) q^{35} +1.00000 q^{36} +(3.74806 + 3.74806i) q^{37} +(1.63451 - 1.63451i) q^{38} -3.40219i q^{39} +(1.75080 + 1.39094i) q^{40} +5.08960 q^{41} +(-2.54671 - 2.54671i) q^{42} +(-2.71117 + 2.71117i) q^{43} +3.50160 q^{44} +(-0.254460 - 2.22154i) q^{45} +(-4.59537 - 1.37206i) q^{46} +(-0.775445 + 0.775445i) q^{47} +(0.707107 + 0.707107i) q^{48} +5.97146i q^{49} +(2.64452 - 4.24341i) q^{50} -1.94038i q^{51} +(2.40571 - 2.40571i) q^{52} +(-2.61742 + 2.61742i) q^{53} -1.00000i q^{54} +(-0.891017 - 7.77894i) q^{55} -3.60159i q^{56} +(-1.63451 - 1.63451i) q^{57} +(0.0800174 + 0.0800174i) q^{58} +13.2983i q^{59} +(1.39094 - 1.75080i) q^{60} -0.841493i q^{61} +(0.899946 - 0.899946i) q^{62} +(-2.54671 + 2.54671i) q^{63} +1.00000i q^{64} +(-5.95656 - 4.73224i) q^{65} -3.50160i q^{66} +(5.33351 + 5.33351i) q^{67} +(1.37206 - 1.37206i) q^{68} +(-1.37206 + 4.59537i) q^{69} +(-8.00109 + 0.916462i) q^{70} +14.2568 q^{71} +(0.707107 - 0.707107i) q^{72} +(-7.88793 - 7.88793i) q^{73} +5.30056 q^{74} +(-4.24341 - 2.64452i) q^{75} -2.31155i q^{76} +(-8.91755 + 8.91755i) q^{77} +(-2.40571 - 2.40571i) q^{78} +2.37992 q^{79} +(2.22154 - 0.254460i) q^{80} -1.00000 q^{81} +(3.59889 - 3.59889i) q^{82} +(1.02759 - 1.02759i) q^{83} -3.60159 q^{84} +(-3.39722 - 2.69895i) q^{85} +3.83417i q^{86} +(0.0800174 - 0.0800174i) q^{87} +(2.47600 - 2.47600i) q^{88} -14.7757 q^{89} +(-1.75080 - 1.39094i) q^{90} +12.2533i q^{91} +(-4.21961 + 2.27923i) q^{92} +(-0.899946 - 0.899946i) q^{93} +1.09665i q^{94} +(-5.13520 + 0.588197i) q^{95} +1.00000 q^{96} +(-4.66285 - 4.66285i) q^{97} +(4.22246 + 4.22246i) q^{98} -3.50160 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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