LMFDB - Embedded newform 1110.2.u.f.401.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(191,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("1110.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.u (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			401.1
Character	$\chi$	$=$	1110.401
Dual form			1110.2.u.f.191.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.169604 + 1.72373i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.33879 - 1.09893i) q^{6} +1.82689 q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.94247 + 0.584702i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.169604 + 1.72373i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.33879 - 1.09893i) q^{6} +1.82689 q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.94247 + 0.584702i) q^{9} -1.00000 q^{10} +5.15936 q^{11} +(1.72373 - 0.169604i) q^{12} +(-3.16917 + 3.16917i) q^{13} +(-1.29181 + 1.29181i) q^{14} +(-1.09893 + 1.33879i) q^{15} -1.00000 q^{16} +(-2.98694 - 2.98694i) q^{17} +(1.66719 - 2.49409i) q^{18} +(-2.92931 + 2.92931i) q^{19} +(0.707107 - 0.707107i) q^{20} +(0.309848 + 3.14906i) q^{21} +(-3.64822 + 3.64822i) q^{22} +(3.68979 + 3.68979i) q^{23} +(-1.09893 + 1.33879i) q^{24} +1.00000i q^{25} -4.48188i q^{26} +(-1.50692 - 4.97285i) q^{27} -1.82689i q^{28} +(4.89488 - 4.89488i) q^{29} +(-0.169604 - 1.72373i) q^{30} +(6.21752 + 6.21752i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.875047 + 8.89332i) q^{33} +4.22417 q^{34} +(1.29181 + 1.29181i) q^{35} +(0.584702 + 2.94247i) q^{36} +(0.159948 + 6.08066i) q^{37} -4.14267i q^{38} +(-6.00028 - 4.92527i) q^{39} +1.00000i q^{40} -0.816209 q^{41} +(-2.44582 - 2.00763i) q^{42} +(-2.69720 + 2.69720i) q^{43} -5.15936i q^{44} +(-2.49409 - 1.66719i) q^{45} -5.21815 q^{46} +6.46196i q^{47} +(-0.169604 - 1.72373i) q^{48} -3.66246 q^{49} +(-0.707107 - 0.707107i) q^{50} +(4.64208 - 5.65527i) q^{51} +(3.16917 + 3.16917i) q^{52} +12.1785i q^{53} +(4.58189 + 2.45078i) q^{54} +(3.64822 + 3.64822i) q^{55} +(1.29181 + 1.29181i) q^{56} +(-5.54615 - 4.55251i) q^{57} +6.92241i q^{58} +(-0.207760 - 0.207760i) q^{59} +(1.33879 + 1.09893i) q^{60} +(-8.45738 - 8.45738i) q^{61} -8.79291 q^{62} +(-5.37558 + 1.06819i) q^{63} +1.00000i q^{64} -4.48188 q^{65} +(-6.90728 - 5.66978i) q^{66} +12.0378i q^{67} +(-2.98694 + 2.98694i) q^{68} +(-5.73439 + 6.98599i) q^{69} -1.82689 q^{70} -11.3303i q^{71} +(-2.49409 - 1.66719i) q^{72} -10.9001i q^{73} +(-4.41278 - 4.18658i) q^{74} +(-1.72373 + 0.169604i) q^{75} +(2.92931 + 2.92931i) q^{76} +9.42559 q^{77} +(7.72553 - 0.760144i) q^{78} +(5.32048 - 5.32048i) q^{79} +(-0.707107 - 0.707107i) q^{80} +(8.31625 - 3.44093i) q^{81} +(0.577147 - 0.577147i) q^{82} -14.3723i q^{83} +(3.14906 - 0.309848i) q^{84} -4.22417i q^{85} -3.81442i q^{86} +(9.26763 + 7.60725i) q^{87} +(3.64822 + 3.64822i) q^{88} +(-6.37672 + 6.37672i) q^{89} +(2.94247 - 0.584702i) q^{90} +(-5.78973 + 5.78973i) q^{91} +(3.68979 - 3.68979i) q^{92} +(-9.66280 + 11.7718i) q^{93} +(-4.56930 - 4.56930i) q^{94} -4.14267 q^{95} +(1.33879 + 1.09893i) q^{96} +(-8.32365 + 8.32365i) q^{97} +(2.58975 - 2.58975i) q^{98} +(-15.1812 + 3.01668i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 24 q^{7} - 8 q^{9}+O(q^{10}) $ 40 * q + 24 * q^7 - 8 * q^9	$ 40 q + 24 q^{7} - 8 q^{9} - 40 q^{10} + 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 16 q^{22} - 8 q^{31} + 24 q^{33} + 24 q^{34} + 32 q^{37} + 16 q^{39} + 12 q^{42} + 32 q^{43} + 8 q^{45} - 56 q^{46} - 32 q^{49} - 44 q^{51} - 16 q^{52} - 24 q^{54} + 16 q^{55} + 8 q^{57} - 72 q^{61} + 24 q^{63} - 28 q^{66} + 16 q^{69} - 24 q^{70} + 8 q^{72} - 16 q^{76} - 48 q^{79} + 120 q^{81} - 24 q^{82} - 24 q^{84} + 20 q^{87} + 16 q^{88} + 8 q^{90} - 92 q^{93} - 8 q^{94} - 40 q^{97}+O(q^{100}) $ 40 * q + 24 * q^7 - 8 * q^9 - 40 * q^10 + 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 16 * q^22 - 8 * q^31 + 24 * q^33 + 24 * q^34 + 32 * q^37 + 16 * q^39 + 12 * q^42 + 32 * q^43 + 8 * q^45 - 56 * q^46 - 32 * q^49 - 44 * q^51 - 16 * q^52 - 24 * q^54 + 16 * q^55 + 8 * q^57 - 72 * q^61 + 24 * q^63 - 28 * q^66 + 16 * q^69 - 24 * q^70 + 8 * q^72 - 16 * q^76 - 48 * q^79 + 120 * q^81 - 24 * q^82 - 24 * q^84 + 20 * q^87 + 16 * q^88 + 8 * q^90 - 92 * q^93 - 8 * q^94 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	0.169604	+	1.72373i	0.0979209	+	0.995194i
$3$	0.169604	+	1.72373i	0.0979209	+	0.995194i
$4$		−	1.00000i		−	0.500000i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$	−1.33879	−	1.09893i	−0.546558	−	0.448637i
$7$	1.82689			0.690501			0.345250	−	0.938511i	$-0.387794\pi$
$7$	1.82689			0.690501			0.345250	+	0.938511i	$0.387794\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.94247	+	0.584702i	−0.980823	+	0.194901i
$10$	−1.00000			−0.316228
$11$	5.15936			1.55560			0.777802	−	0.628509i	$-0.216335\pi$
$11$	5.15936			1.55560			0.777802	+	0.628509i	$0.216335\pi$
$12$	1.72373	−	0.169604i	0.497597	−	0.0489604i
$13$	−3.16917	+	3.16917i	−0.878968	+	0.878968i	−0.993428	−	0.114459i	$-0.963486\pi$
$13$	−3.16917	+	3.16917i	−0.878968	+	0.878968i	0.114459	+	0.993428i	$0.463486\pi$
$14$	−1.29181	+	1.29181i	−0.345250	+	0.345250i
$15$	−1.09893	+	1.33879i	−0.283743	+	0.345673i
$16$	−1.00000			−0.250000
$17$	−2.98694	−	2.98694i	−0.724440	−	0.724440i	0.245066	−	0.969506i	$-0.421190\pi$
$17$	−2.98694	−	2.98694i	−0.724440	−	0.724440i	−0.969506	+	0.245066i	$0.921190\pi$
$18$	1.66719	−	2.49409i	0.392961	−	0.587862i
$19$	−2.92931	+	2.92931i	−0.672030	+	0.672030i	−0.958184	−	0.286154i	$-0.907623\pi$
$19$	−2.92931	+	2.92931i	−0.672030	+	0.672030i	0.286154	+	0.958184i	$0.407623\pi$
$20$	0.707107	−	0.707107i	0.158114	−	0.158114i
$21$	0.309848	+	3.14906i	0.0676144	+	0.687182i
$22$	−3.64822	+	3.64822i	−0.777802	+	0.777802i
$23$	3.68979	+	3.68979i	0.769374	+	0.769374i	0.977996	−	0.208622i	$-0.0668979\pi$
$23$	3.68979	+	3.68979i	0.769374	+	0.769374i	−0.208622	+	0.977996i	$0.566898\pi$
$24$	−1.09893	+	1.33879i	−0.224318	+	0.273279i
$25$			1.00000i			0.200000i
$26$		−	4.48188i		−	0.878968i
$27$	−1.50692	−	4.97285i	−0.290007	−	0.957025i
$28$		−	1.82689i		−	0.345250i
$29$	4.89488	−	4.89488i	0.908957	−	0.908957i	−0.0872311	−	0.996188i	$-0.527802\pi$
$29$	4.89488	−	4.89488i	0.908957	−	0.908957i	0.996188	+	0.0872311i	$0.0278018\pi$
$30$	−0.169604	−	1.72373i	−0.0309653	−	0.314708i
$31$	6.21752	+	6.21752i	1.11670	+	1.11670i	0.992222	+	0.124478i	$0.0397255\pi$
$31$	6.21752	+	6.21752i	1.11670	+	1.11670i	0.124478	+	0.992222i	$0.460274\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	0.875047	+	8.89332i	0.152326	+	1.54813i
$34$	4.22417			0.724440
$35$	1.29181	+	1.29181i	0.218355	+	0.218355i
$36$	0.584702	+	2.94247i	0.0974503	+	0.490412i
$37$	0.159948	+	6.08066i	0.0262952	+	0.999654i
$37$	0.159948	+	6.08066i	0.0262952	+	0.999654i
$38$		−	4.14267i		−	0.672030i
$39$	−6.00028	−	4.92527i	−0.960814	−	0.788675i
$40$			1.00000i			0.158114i
$41$	−0.816209			−0.127471			−0.0637353	−	0.997967i	$-0.520301\pi$
$41$	−0.816209			−0.127471			−0.0637353	+	0.997967i	$0.520301\pi$
$42$	−2.44582	−	2.00763i	−0.377398	−	0.309784i
$43$	−2.69720	+	2.69720i	−0.411319	+	0.411319i	−0.882198	−	0.470879i	$-0.843937\pi$
$43$	−2.69720	+	2.69720i	−0.411319	+	0.411319i	0.470879	+	0.882198i	$0.343937\pi$
$44$		−	5.15936i		−	0.777802i
$45$	−2.49409	−	1.66719i	−0.371796	−	0.248531i
$46$	−5.21815			−0.769374
$47$			6.46196i			0.942574i	0.881980	+	0.471287i	$0.156210\pi$
$47$			6.46196i			0.942574i	−0.881980	+	0.471287i	$0.843790\pi$
$48$	−0.169604	−	1.72373i	−0.0244802	−	0.248799i
$49$	−3.66246			−0.523209
$50$	−0.707107	−	0.707107i	−0.100000	−	0.100000i
$51$	4.64208	−	5.65527i	0.650021	−	0.791896i
$52$	3.16917	+	3.16917i	0.439484	+	0.439484i
$53$			12.1785i			1.67285i	0.548079	+	0.836426i	$0.315359\pi$
$53$			12.1785i			1.67285i	−0.548079	+	0.836426i	$0.684641\pi$
$54$	4.58189	+	2.45078i	0.623516	+	0.333509i
$55$	3.64822	+	3.64822i	0.491925	+	0.491925i
$56$	1.29181	+	1.29181i	0.172625	+	0.172625i
$57$	−5.54615	−	4.55251i	−0.734606	−	0.602994i
$58$			6.92241i			0.908957i
$59$	−0.207760	−	0.207760i	−0.0270481	−	0.0270481i	0.693453	−	0.720501i	$-0.256088\pi$
$59$	−0.207760	−	0.207760i	−0.0270481	−	0.0270481i	−0.720501	+	0.693453i	$0.756088\pi$
$60$	1.33879	+	1.09893i	0.172837	+	0.141871i
$61$	−8.45738	−	8.45738i	−1.08286	−	1.08286i	−0.996242	−	0.0866145i	$-0.972395\pi$
$61$	−8.45738	−	8.45738i	−1.08286	−	1.08286i	−0.0866145	−	0.996242i	$-0.527605\pi$
$62$	−8.79291			−1.11670
$63$	−5.37558	+	1.06819i	−0.677259	+	0.134579i
$64$			1.00000i			0.125000i
$65$	−4.48188			−0.555908
$66$	−6.90728	−	5.66978i	−0.850227	−	0.697901i
$67$			12.0378i			1.47065i	0.677716	+	0.735323i	$0.262970\pi$
$67$			12.0378i			1.47065i	−0.677716	+	0.735323i	$0.737030\pi$
$68$	−2.98694	+	2.98694i	−0.362220	+	0.362220i
$69$	−5.73439	+	6.98599i	−0.690339	+	0.841015i
$70$	−1.82689			−0.218355
$71$		−	11.3303i		−	1.34466i	−0.740253	−	0.672329i	$-0.765294\pi$
$71$		−	11.3303i		−	1.34466i	0.740253	−	0.672329i	$-0.234706\pi$
$72$	−2.49409	−	1.66719i	−0.293931	−	0.196481i
$73$		−	10.9001i		−	1.27576i	−0.770138	−	0.637878i	$-0.779813\pi$
$73$		−	10.9001i		−	1.27576i	0.770138	−	0.637878i	$-0.220187\pi$
$74$	−4.41278	−	4.18658i	−0.512975	−	0.486680i
$75$	−1.72373	+	0.169604i	−0.199039	+	0.0195842i
$76$	2.92931	+	2.92931i	0.336015	+	0.336015i
$77$	9.42559			1.07415
$78$	7.72553	−	0.760144i	0.874744	−	0.0860693i
$79$	5.32048	−	5.32048i	0.598601	−	0.598601i	−0.341339	−	0.939940i	$-0.610881\pi$
$79$	5.32048	−	5.32048i	0.598601	−	0.598601i	0.939940	+	0.341339i	$0.110881\pi$
$80$	−0.707107	−	0.707107i	−0.0790569	−	0.0790569i
$81$	8.31625	−	3.44093i	0.924028	−	0.382326i
$82$	0.577147	−	0.577147i	0.0637353	−	0.0637353i
$83$		−	14.3723i		−	1.57756i	−0.614673	−	0.788782i	$-0.710712\pi$
$83$		−	14.3723i		−	1.57756i	0.614673	−	0.788782i	$-0.289288\pi$
$84$	3.14906	−	0.309848i	0.343591	−	0.0338072i
$85$		−	4.22417i		−	0.458176i
$86$		−	3.81442i		−	0.411319i
$87$	9.26763	+	7.60725i	0.993595	+	0.815583i
$88$	3.64822	+	3.64822i	0.388901	+	0.388901i
$89$	−6.37672	+	6.37672i	−0.675931	+	0.675931i	−0.959077	−	0.283146i	$-0.908622\pi$
$89$	−6.37672	+	6.37672i	−0.675931	+	0.675931i	0.283146	+	0.959077i	$0.408622\pi$
$90$	2.94247	−	0.584702i	0.310163	−	0.0616330i
$91$	−5.78973	+	5.78973i	−0.606928	+	0.606928i
$92$	3.68979	−	3.68979i	0.384687	−	0.384687i
$93$	−9.66280	+	11.7718i	−1.00199	+	1.22068i
$94$	−4.56930	−	4.56930i	−0.471287	−	0.471287i
$95$	−4.14267			−0.425029
$96$	1.33879	+	1.09893i	0.136639	+	0.112159i
$97$	−8.32365	+	8.32365i	−0.845139	+	0.845139i	−0.989522	−	0.144383i	$-0.953880\pi$
$97$	−8.32365	+	8.32365i	−0.845139	+	0.845139i	0.144383	+	0.989522i	$0.453880\pi$
$98$	2.58975	−	2.58975i	0.261604	−	0.261604i
$99$	−15.1812	+	3.01668i	−1.52577	+	0.303188i
$100$	1.00000			0.100000
$101$	8.26384			0.822283			0.411141	−	0.911572i	$-0.365130\pi$
$101$	8.26384			0.822283			0.411141	+	0.911572i	$0.365130\pi$
$102$	0.716437	+	7.28132i	0.0709378	+	0.720959i
$103$	−8.51882	−	8.51882i	−0.839384	−	0.839384i	0.149394	−	0.988778i	$-0.452268\pi$
$103$	−8.51882	−	8.51882i	−0.839384	−	0.839384i	−0.988778	+	0.149394i	$0.952268\pi$
$104$	−4.48188			−0.439484
$105$	−2.00763	+	2.44582i	−0.195925	+	0.238688i
$106$	−8.61154	−	8.61154i	−0.836426	−	0.836426i
$107$		−	7.75936i		−	0.750126i	−0.926999	−	0.375063i	$-0.877621\pi$
$107$		−	7.75936i		−	0.750126i	0.926999	−	0.375063i	$-0.122379\pi$
$108$	−4.97285	+	1.50692i	−0.478512	+	0.145003i
$109$	0.985941	−	0.985941i	0.0944360	−	0.0944360i	−0.658310	−	0.752747i	$-0.728729\pi$
$109$	0.985941	−	0.985941i	0.0944360	−	0.0944360i	0.752747	+	0.658310i	$0.228729\pi$
$110$	−5.15936			−0.491925
$111$	−10.4543	+	1.30701i	−0.992275	+	0.124056i
$112$	−1.82689			−0.172625
$113$	4.37433	−	4.37433i	0.411502	−	0.411502i	−0.470759	−	0.882262i	$-0.656020\pi$
$113$	4.37433	−	4.37433i	0.411502	−	0.411502i	0.882262	+	0.470759i	$0.156020\pi$
$114$	7.14083	−	0.702613i	0.668800	−	0.0658057i
$115$			5.21815i			0.486595i
$116$	−4.89488	−	4.89488i	−0.454479	−	0.454479i
$117$	7.47216	−	11.1782i	0.690801	−	1.03342i
$118$	0.293817			0.0270481
$119$	−5.45682	−	5.45682i	−0.500226	−	0.500226i
$120$	−1.72373	+	0.169604i	−0.157354	+	0.0154826i
$121$	15.6189			1.41990
$122$	11.9605			1.08286
$123$	−0.138432	−	1.40692i	−0.0124820	−	0.126858i
$124$	6.21752	−	6.21752i	0.558350	−	0.558350i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$	3.04578	−	4.55643i	0.271340	−	0.405919i
$127$	2.09841			0.186203			0.0931017	−	0.995657i	$-0.470322\pi$
$127$	2.09841			0.186203			0.0931017	+	0.995657i	$0.470322\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−5.10669	−	4.19178i	−0.449619	−	0.369066i
$130$	3.16917	−	3.16917i	0.277954	−	0.277954i
$131$	−13.8897	+	13.8897i	−1.21355	+	1.21355i	−0.243698	+	0.969851i	$0.578361\pi$
$131$	−13.8897	+	13.8897i	−1.21355	+	1.21355i	−0.969851	+	0.243698i	$0.921639\pi$
$132$	8.89332	−	0.875047i	0.774064	−	0.0761630i
$133$	−5.35154	+	5.35154i	−0.464037	+	0.464037i
$134$	−8.51198	−	8.51198i	−0.735323	−	0.735323i
$135$	2.45078	−	4.58189i	0.210929	−	0.394346i
$136$		−	4.22417i		−	0.362220i
$137$			6.46639i			0.552461i	0.961091	+	0.276231i	$0.0890853\pi$
$137$			6.46639i			0.552461i	−0.961091	+	0.276231i	$0.910915\pi$
$138$	−0.885019	−	8.99467i	−0.0753378	−	0.765677i
$139$			1.28795i			0.109243i	0.998507	+	0.0546213i	$0.0173952\pi$
$139$			1.28795i			0.109243i	−0.998507	+	0.0546213i	$0.982605\pi$
$140$	1.29181	−	1.29181i	0.109178	−	0.109178i
$141$	−11.1387	+	1.09597i	−0.938044	+	0.0922977i
$142$	8.01172	+	8.01172i	0.672329	+	0.672329i
$143$	−16.3509	+	16.3509i	−1.36733	+	1.36733i
$144$	2.94247	−	0.584702i	0.245206	−	0.0487251i
$145$	6.92241			0.574875
$146$	7.70750	+	7.70750i	0.637878	+	0.637878i
$147$	−0.621168	−	6.31308i	−0.0512331	−	0.520694i
$148$	6.08066	−	0.159948i	0.499827	−	0.0131476i
$149$			5.06286i			0.414766i	0.978260	+	0.207383i	$0.0664946\pi$
$149$			5.06286i			0.414766i	−0.978260	+	0.207383i	$0.933505\pi$
$150$	1.09893	−	1.33879i	0.0897273	−	0.109312i
$151$		−	0.958969i		−	0.0780398i	−0.999238	−	0.0390199i	$-0.987576\pi$
$151$		−	0.958969i		−	0.0780398i	0.999238	−	0.0390199i	$-0.0124236\pi$
$152$	−4.14267			−0.336015
$153$	10.5355	+	7.04252i	0.851741	+	0.569354i
$154$	−6.66490	+	6.66490i	−0.537073	+	0.537073i
$155$			8.79291i			0.706263i
$156$	−4.92527	+	6.00028i	−0.394337	+	0.480407i
$157$	23.5311			1.87799			0.938995	−	0.343932i	$-0.111759\pi$
$157$	23.5311			1.87799			0.938995	+	0.343932i	$0.111759\pi$
$158$			7.52430i			0.598601i
$159$	−20.9925	+	2.06553i	−1.66481	+	0.163807i
$160$	1.00000			0.0790569
$161$	6.74085	+	6.74085i	0.531253	+	0.531253i
$162$	−3.44737	+	8.31358i	−0.270851	+	0.653177i
$163$	1.12493	+	1.12493i	0.0881116	+	0.0881116i	0.749789	−	0.661677i	$-0.230155\pi$
$163$	1.12493	+	1.12493i	0.0881116	+	0.0881116i	−0.661677	+	0.749789i	$0.730155\pi$
$164$			0.816209i			0.0637353i
$165$	−5.66978	+	6.90728i	−0.441391	+	0.537731i
$166$	10.1627	+	10.1627i	0.788782	+	0.788782i
$167$	−5.15136	−	5.15136i	−0.398624	−	0.398624i	0.479123	−	0.877748i	$-0.340955\pi$
$167$	−5.15136	−	5.15136i	−0.398624	−	0.398624i	−0.877748	+	0.479123i	$0.840955\pi$
$168$	−2.00763	+	2.44582i	−0.154892	+	0.188699i
$169$		−	7.08722i		−	0.545171i
$170$	2.98694	+	2.98694i	0.229088	+	0.229088i
$171$	6.90663	−	10.3322i	0.528163	−	0.790121i
$172$	2.69720	+	2.69720i	0.205660	+	0.205660i
$173$	10.8091			0.821800			0.410900	−	0.911680i	$-0.365215\pi$
$173$	10.8091			0.821800			0.410900	+	0.911680i	$0.365215\pi$
$174$	−11.9323	+	1.17407i	−0.904589	+	0.0890059i
$175$			1.82689i			0.138100i
$176$	−5.15936			−0.388901
$177$	0.322885	−	0.393359i	0.0242695	−	0.0295667i
$178$		−	9.01804i		−	0.675931i
$179$	8.35712	−	8.35712i	0.624640	−	0.624640i	−0.322074	−	0.946714i	$-0.604380\pi$
$179$	8.35712	−	8.35712i	0.624640	−	0.624640i	0.946714	+	0.322074i	$0.104380\pi$
$180$	−1.66719	+	2.49409i	−0.124265	+	0.185898i
$181$	25.7306			1.91254			0.956270	−	0.292484i	$-0.0944819\pi$
$181$	25.7306			1.91254			0.956270	+	0.292484i	$0.0944819\pi$
$182$		−	8.18791i		−	0.606928i
$183$	13.1438	−	16.0126i	0.971618	−	1.18369i
$184$			5.21815i			0.384687i
$185$	−4.18658	+	4.41278i	−0.307803	+	0.324434i
$186$	−1.49131	−	15.1566i	−0.109348	−	1.11133i
$187$	−15.4107	−	15.4107i	−1.12694	−	1.12694i
$188$	6.46196			0.471287
$189$	−2.75298	−	9.08486i	−0.200250	−	0.660826i
$190$	2.92931	−	2.92931i	0.212514	−	0.212514i
$191$	−7.19370	−	7.19370i	−0.520518	−	0.520518i	0.397210	−	0.917728i	$-0.369978\pi$
$191$	−7.19370	−	7.19370i	−0.520518	−	0.520518i	−0.917728	+	0.397210i	$0.869978\pi$
$192$	−1.72373	+	0.169604i	−0.124399	+	0.0122401i
$193$	2.35783	−	2.35783i	0.169720	−	0.169720i	−0.617136	−	0.786856i	$-0.711707\pi$
$193$	2.35783	−	2.35783i	0.169720	−	0.169720i	0.786856	+	0.617136i	$0.211707\pi$
$194$		−	11.7714i		−	0.845139i
$195$	−0.760144	−	7.72553i	−0.0544350	−	0.553237i
$196$			3.66246i			0.261604i
$197$			12.5331i			0.892949i	0.894796	+	0.446474i	$0.147321\pi$
$197$			12.5331i			0.892949i	−0.894796	+	0.446474i	$0.852679\pi$
$198$	8.60164	−	12.8679i	0.611292	−	0.914480i
$199$	0.389611	+	0.389611i	0.0276188	+	0.0276188i	0.720781	−	0.693163i	$-0.243783\pi$
$199$	0.389611	+	0.389611i	0.0276188	+	0.0276188i	−0.693163	+	0.720781i	$0.743783\pi$
$200$	−0.707107	+	0.707107i	−0.0500000	+	0.0500000i
$201$	−20.7498	+	2.04165i	−1.46358	+	0.144007i
$202$	−5.84342	+	5.84342i	−0.411141	+	0.411141i
$203$	8.94243	−	8.94243i	0.627635	−	0.627635i
$204$	−5.65527	−	4.64208i	−0.395948	−	0.325010i
$205$	−0.577147	−	0.577147i	−0.0403097	−	0.0403097i
$206$	12.0474			0.839384
$207$	−13.0145	−	8.69967i	−0.904571	−	0.604669i
$208$	3.16917	−	3.16917i	0.219742	−	0.219742i
$209$	−15.1133	+	15.1133i	−1.04541	+	1.04541i
$210$	−0.309848	−	3.14906i	−0.0213816	−	0.217306i
$211$	11.3256			0.779683			0.389842	−	0.920882i	$-0.372530\pi$
$211$	11.3256			0.779683			0.389842	+	0.920882i	$0.372530\pi$
$212$	12.1785			0.836426
$213$	19.5303	−	1.92166i	1.33820	−	0.131670i
$214$	5.48670	+	5.48670i	0.375063	+	0.375063i
$215$	−3.81442			−0.260141
$216$	2.45078	−	4.58189i	0.166754	−	0.311758i
$217$	11.3587	+	11.3587i	0.771082	+	0.771082i
$218$			1.39433i			0.0944360i
$219$	18.7887	−	1.84869i	1.26962	−	0.124923i
$220$	3.64822	−	3.64822i	0.245963	−	0.245963i
$221$	18.9322			1.27352
$222$	6.46809	−	8.31648i	0.434110	−	0.558166i
$223$	5.35541			0.358625			0.179313	−	0.983792i	$-0.442613\pi$
$223$	5.35541			0.358625			0.179313	+	0.983792i	$0.442613\pi$
$224$	1.29181	−	1.29181i	0.0863126	−	0.0863126i
$225$	−0.584702	−	2.94247i	−0.0389801	−	0.196165i
$226$			6.18624i			0.411502i
$227$	11.4661	+	11.4661i	0.761032	+	0.761032i	0.976509	−	0.215477i	$-0.0691305\pi$
$227$	11.4661	+	11.4661i	0.761032	+	0.761032i	−0.215477	+	0.976509i	$0.569130\pi$
$228$	−4.55251	+	5.54615i	−0.301497	+	0.367303i
$229$	−20.8218			−1.37595			−0.687973	−	0.725737i	$-0.741499\pi$
$229$	−20.8218			−1.37595			−0.687973	+	0.725737i	$0.741499\pi$
$230$	−3.68979	−	3.68979i	−0.243298	−	0.243298i
$231$	1.59862	+	16.2471i	0.105181	+	1.06898i
$232$	6.92241			0.454479
$233$	30.2639			1.98265			0.991327	−	0.131420i	$-0.0419537\pi$
$233$	30.2639			1.98265			0.991327	+	0.131420i	$0.0419537\pi$
$234$	2.62056	+	13.1878i	0.171311	+	0.862112i
$235$	−4.56930	+	4.56930i	−0.298068	+	0.298068i
$236$	−0.207760	+	0.207760i	−0.0135240	+	0.0135240i
$237$	10.0734	+	8.26868i	0.654340	+	0.537109i
$238$	7.71712			0.500226
$239$	−14.0684	−	14.0684i	−0.910008	−	0.910008i	0.0862646	−	0.996272i	$-0.472507\pi$
$239$	−14.0684	−	14.0684i	−0.910008	−	0.910008i	−0.996272	+	0.0862646i	$0.972507\pi$
$240$	1.09893	−	1.33879i	0.0709357	−	0.0864183i
$241$	0.972895	−	0.972895i	0.0626697	−	0.0626697i	−0.675077	−	0.737747i	$-0.735890\pi$
$241$	0.972895	−	0.972895i	0.0626697	−	0.0626697i	0.737747	+	0.675077i	$0.235890\pi$
$242$	−11.0443	+	11.0443i	−0.709952	+	0.709952i
$243$	7.34170	+	13.7513i	0.470970	+	0.882149i
$244$	−8.45738	+	8.45738i	−0.541428	+	0.541428i
$245$	−2.58975	−	2.58975i	−0.165453	−	0.165453i
$246$	1.09273	+	0.896958i	0.0696700	+	0.0571879i
$247$		−	18.5669i		−	1.18139i
$248$			8.79291i			0.558350i
$249$	24.7739	−	2.43760i	1.56998	−	0.154476i
$250$		−	1.00000i		−	0.0632456i
$251$	2.10725	−	2.10725i	0.133009	−	0.133009i	−0.637468	−	0.770477i	$-0.720018\pi$
$251$	2.10725	−	2.10725i	0.133009	−	0.133009i	0.770477	+	0.637468i	$0.220018\pi$
$252$	1.06819	+	5.37558i	0.0672895	+	0.338629i
$253$	19.0369	+	19.0369i	1.19684	+	1.19684i
$254$	−1.48380	+	1.48380i	−0.0931017	+	0.0931017i
$255$	7.28132	−	0.716437i	0.455974	−	0.0448650i
$256$	1.00000			0.0625000
$257$	0.195695	+	0.195695i	0.0122071	+	0.0122071i	0.713184	−	0.700977i	$-0.247252\pi$
$257$	0.195695	+	0.195695i	0.0122071	+	0.0122071i	−0.700977	+	0.713184i	$0.747252\pi$
$258$	6.57501	−	0.646940i	0.409342	−	0.0402767i
$259$	0.292207	+	11.1087i	0.0181569	+	0.690262i
$260$			4.48188i			0.277954i
$261$	−11.5410	+	17.2651i	−0.714370	+	1.06868i
$262$		−	19.6430i		−	1.21355i
$263$	−8.71623			−0.537466			−0.268733	−	0.963215i	$-0.586605\pi$
$263$	−8.71623			−0.537466			−0.268733	+	0.963215i	$0.586605\pi$
$264$	−5.66978	+	6.90728i	−0.348951	+	0.425114i
$265$	−8.61154	+	8.61154i	−0.529002	+	0.529002i
$266$		−	7.56821i		−	0.464037i
$267$	−12.0732	−	9.91021i	−0.738870	−	0.606495i
$268$	12.0378			0.735323
$269$		−	21.2276i		−	1.29427i	−0.762376	−	0.647134i	$-0.775967\pi$
$269$		−	21.2276i		−	1.29427i	0.762376	−	0.647134i	$-0.224033\pi$
$270$	1.50692	+	4.97285i	0.0917082	+	0.302638i
$271$	16.3350			0.992282			0.496141	−	0.868242i	$-0.334750\pi$
$271$	16.3350			0.992282			0.496141	+	0.868242i	$0.334750\pi$
$272$	2.98694	+	2.98694i	0.181110	+	0.181110i
$273$	−10.9619	−	8.99795i	−0.663442	−	0.544581i
$274$	−4.57243	−	4.57243i	−0.276231	−	0.276231i
$275$			5.15936i			0.311121i
$276$	6.98599	+	5.73439i	0.420507	+	0.345170i
$277$	14.7587	+	14.7587i	0.886767	+	0.886767i	0.994211	−	0.107444i	$-0.0342667\pi$
$277$	14.7587	+	14.7587i	0.886767	+	0.886767i	−0.107444	+	0.994211i	$0.534267\pi$
$278$	−0.910719	−	0.910719i	−0.0546213	−	0.0546213i
$279$	−21.9303	−	14.6595i	−1.31293	−	0.877640i
$280$			1.82689i			0.109178i
$281$	2.73296	+	2.73296i	0.163035	+	0.163035i	0.783910	−	0.620875i	$-0.213223\pi$
$281$	2.73296	+	2.73296i	0.163035	+	0.163035i	−0.620875	+	0.783910i	$0.713223\pi$
$282$	7.10125	−	8.65119i	0.422873	−	0.515171i
$283$	18.4473	+	18.4473i	1.09658	+	1.09658i	0.994808	+	0.101772i	$0.0324511\pi$
$283$	18.4473	+	18.4473i	1.09658	+	1.09658i	0.101772	+	0.994808i	$0.467549\pi$
$284$	−11.3303			−0.672329
$285$	−0.702613	−	7.14083i	−0.0416192	−	0.422986i
$286$		−	23.1236i		−	1.36733i
$287$	−1.49113			−0.0880185
$288$	−1.66719	+	2.49409i	−0.0982403	+	0.146965i
$289$			0.843654i			0.0496267i
$290$	−4.89488	+	4.89488i	−0.287437	+	0.287437i
$291$	−15.7594	−	12.9360i	−0.923834	−	0.758320i
$292$	−10.9001			−0.637878
$293$		−	17.4763i		−	1.02098i	−0.859884	−	0.510490i	$-0.829464\pi$
$293$		−	17.4763i		−	1.02098i	0.859884	−	0.510490i	$-0.170536\pi$
$294$	4.90326	+	4.02479i	0.285964	+	0.234731i
$295$		−	0.293817i		−	0.0171067i
$296$	−4.18658	+	4.41278i	−0.243340	+	0.256487i
$297$	−7.77474	−	25.6567i	−0.451136	−	1.48875i
$298$	−3.57999	−	3.57999i	−0.207383	−	0.207383i
$299$	−23.3871			−1.35251
$300$	0.169604	+	1.72373i	0.00979209	+	0.0995194i
$301$	−4.92749	+	4.92749i	−0.284016	+	0.284016i
$302$	0.678093	+	0.678093i	0.0390199	+	0.0390199i
$303$	1.40158	+	14.2446i	0.0805186	+	0.818331i
$304$	2.92931	−	2.92931i	0.168007	−	0.168007i
$305$		−	11.9605i		−	0.684859i
$306$	−12.4295	+	2.46988i	−0.710547	+	0.141194i
$307$		−	1.88574i		−	0.107625i	−0.998551	−	0.0538125i	$-0.982863\pi$
$307$		−	1.88574i		−	0.107625i	0.998551	−	0.0538125i	$-0.0171373\pi$
$308$		−	9.42559i		−	0.537073i
$309$	13.2393	−	16.1289i	0.753157	−	0.917543i
$310$	−6.21752	−	6.21752i	−0.353132	−	0.353132i
$311$	11.7011	−	11.7011i	0.663511	−	0.663511i	−0.292695	−	0.956206i	$-0.594552\pi$
$311$	11.7011	−	11.7011i	0.663511	−	0.663511i	0.956206	+	0.292695i	$0.0945521\pi$
$312$	−0.760144	−	7.72553i	−0.0430347	−	0.437372i
$313$	−11.8759	+	11.8759i	−0.671265	+	0.671265i	−0.958008	−	0.286743i	$-0.907428\pi$
$313$	−11.8759	+	11.8759i	−0.671265	+	0.671265i	0.286743	+	0.958008i	$0.407428\pi$
$314$	−16.6390	+	16.6390i	−0.938995	+	0.938995i
$315$	−4.55643	−	3.04578i	−0.256726	−	0.171610i
$316$	−5.32048	−	5.32048i	−0.299300	−	0.299300i
$317$	15.5170			0.871524			0.435762	−	0.900062i	$-0.356479\pi$
$317$	15.5170			0.871524			0.435762	+	0.900062i	$0.356479\pi$
$318$	13.3834	−	16.3045i	0.750503	−	0.914310i
$319$	25.2544	−	25.2544i	1.41398	−	1.41398i
$320$	−0.707107	+	0.707107i	−0.0395285	+	0.0395285i
$321$	13.3750	−	1.31602i	0.746521	−	0.0734530i
$322$	−9.53300			−0.531253
$323$	17.4994			0.973690
$324$	−3.44093	−	8.31625i	−0.191163	−	0.462014i
$325$	−3.16917	−	3.16917i	−0.175794	−	0.175794i
$326$	−1.59090			−0.0881116
$327$	1.86671	+	1.53227i	0.103229	+	0.0847349i
$328$	−0.577147	−	0.577147i	−0.0318676	−	0.0318676i
$329$			11.8053i			0.650848i
$330$	−0.875047	−	8.89332i	−0.0481697	−	0.489561i
$331$	14.6764	−	14.6764i	0.806690	−	0.806690i	−0.177441	−	0.984131i	$-0.556782\pi$
$331$	14.6764	−	14.6764i	0.806690	−	0.806690i	0.984131	+	0.177441i	$0.0567819\pi$
$332$	−14.3723			−0.788782
$333$	−4.02601	−	17.7986i	−0.220624	−	0.975359i
$334$	7.28513			0.398624
$335$	−8.51198	+	8.51198i	−0.465059	+	0.465059i
$336$	−0.309848	−	3.14906i	−0.0169036	−	0.171796i
$337$		−	4.00664i		−	0.218255i	−0.994028	−	0.109128i	$-0.965194\pi$
$337$		−	4.00664i		−	0.218255i	0.994028	−	0.109128i	$-0.0348057\pi$
$338$	5.01142	+	5.01142i	0.272585	+	0.272585i
$339$	8.28206	+	6.79825i	0.449820	+	0.369230i
$340$	−4.22417			−0.229088
$341$	32.0784	+	32.0784i	1.73714	+	1.73714i
$342$	2.42223	+	12.1897i	0.130979	+	0.659142i
$343$	−19.4792			−1.05178
$344$	−3.81442			−0.205660
$345$	−8.99467	+	0.885019i	−0.484257	+	0.0476478i
$346$	−7.64318	+	7.64318i	−0.410900	+	0.410900i
$347$	4.04747	−	4.04747i	0.217280	−	0.217280i	−0.590071	−	0.807351i	$-0.700900\pi$
$347$	4.04747	−	4.04747i	0.217280	−	0.217280i	0.807351	+	0.590071i	$0.200900\pi$
$348$	7.60725	−	9.26763i	0.407791	−	0.496797i
$349$	−22.3766			−1.19779			−0.598897	−	0.800826i	$-0.704394\pi$
$349$	−22.3766			−1.19779			−0.598897	+	0.800826i	$0.704394\pi$
$350$	−1.29181	−	1.29181i	−0.0690501	−	0.0690501i
$351$	20.5355	+	10.9841i	1.09610	+	0.586287i
$352$	3.64822	−	3.64822i	0.194451	−	0.194451i
$353$	23.6622	−	23.6622i	1.25941	−	1.25941i	0.308038	−	0.951374i	$-0.400328\pi$
$353$	23.6622	−	23.6622i	1.25941	−	1.25941i	0.951374	−	0.308038i	$-0.0996724\pi$
$354$	0.0498326	+	0.506461i	0.00264857	+	0.0269181i
$355$	8.01172	−	8.01172i	0.425218	−	0.425218i
$356$	6.37672	+	6.37672i	0.337965	+	0.337965i
$357$	8.48058	−	10.3316i	0.448840	−	0.546805i
$358$			11.8187i			0.624640i
$359$		−	6.19534i		−	0.326977i	−0.986545	−	0.163489i	$-0.947725\pi$
$359$		−	6.19534i		−	0.326977i	0.986545	−	0.163489i	$-0.0522747\pi$
$360$	−0.584702	−	2.94247i	−0.0308165	−	0.155082i
$361$			1.83829i			0.0967521i
$362$	−18.1943	+	18.1943i	−0.956270	+	0.956270i
$363$	2.64903	+	26.9228i	0.139038	+	1.41308i
$364$	5.78973	+	5.78973i	0.303464	+	0.303464i
$365$	7.70750	−	7.70750i	0.403429	−	0.403429i
$366$	2.02855	+	20.6167i	0.106034	+	1.07765i
$367$	−33.1126			−1.72846			−0.864231	−	0.503095i	$-0.832194\pi$
$367$	−33.1126			−1.72846			−0.864231	+	0.503095i	$0.832194\pi$
$368$	−3.68979	−	3.68979i	−0.192344	−	0.192344i
$369$	2.40167	−	0.477239i	0.125026	−	0.0248441i
$370$	−0.159948	−	6.08066i	−0.00831528	−	0.316118i
$371$			22.2489i			1.15511i
$372$	11.7718	+	9.66280i	0.610341	+	0.500993i
$373$		−	31.8445i		−	1.64884i	−0.565976	−	0.824422i	$-0.691501\pi$
$373$		−	31.8445i		−	1.64884i	0.565976	−	0.824422i	$-0.308499\pi$
$374$	21.7940			1.12694
$375$	−1.33879	−	1.09893i	−0.0691347	−	0.0567485i
$376$	−4.56930	+	4.56930i	−0.235644	+	0.235644i
$377$			31.0254i			1.59789i
$378$	8.37062	+	4.47731i	0.430538	+	0.230288i
$379$	18.1662			0.933133			0.466567	−	0.884486i	$-0.345491\pi$
$379$	18.1662			0.933133			0.466567	+	0.884486i	$0.345491\pi$
$380$			4.14267i			0.212514i
$381$	0.355898	+	3.61708i	0.0182332	+	0.185309i
$382$	10.1734			0.520518
$383$	−18.6163	−	18.6163i	−0.951247	−	0.951247i	0.0476184	−	0.998866i	$-0.484837\pi$
$383$	−18.6163	−	18.6163i	−0.951247	−	0.951247i	−0.998866	+	0.0476184i	$0.984837\pi$
$384$	1.09893	−	1.33879i	0.0560796	−	0.0683197i
$385$	6.66490	+	6.66490i	0.339675	+	0.339675i
$386$			3.33448i			0.169720i
$387$	6.35937	−	9.51348i	0.323265	−	0.483598i
$388$	8.32365	+	8.32365i	0.422569	+	0.422569i
$389$	2.92340	+	2.92340i	0.148222	+	0.148222i	0.777323	−	0.629101i	$-0.216577\pi$
$389$	2.92340	+	2.92340i	0.148222	+	0.148222i	−0.629101	+	0.777323i	$0.716577\pi$
$390$	6.00028	+	4.92527i	0.303836	+	0.249401i
$391$		−	22.0424i		−	1.11473i
$392$	−2.58975	−	2.58975i	−0.130802	−	0.130802i
$393$	−26.2978	−	21.5863i	−1.32655	−	1.08889i
$394$	−8.86227	−	8.86227i	−0.446474	−	0.446474i
$395$	7.52430			0.378588
$396$	3.01668	+	15.1812i	0.151594	+	0.762886i
$397$		−	30.6306i		−	1.53730i	−0.639667	−	0.768652i	$-0.720928\pi$
$397$		−	30.6306i		−	1.53730i	0.639667	−	0.768652i	$-0.279072\pi$
$398$	−0.550993			−0.0276188
$399$	−10.1322	−	8.31694i	−0.507246	−	0.416368i
$400$		−	1.00000i		−	0.0500000i
$401$	0.362967	−	0.362967i	0.0181257	−	0.0181257i	−0.697986	−	0.716112i	$-0.745920\pi$
$401$	0.362967	−	0.362967i	0.0181257	−	0.0181257i	0.716112	+	0.697986i	$0.245920\pi$
$402$	13.2287	−	16.1160i	0.659786	−	0.803793i
$403$	−39.4087			−1.96309
$404$		−	8.26384i		−	0.411141i
$405$	8.31358	+	3.44737i	0.413105	+	0.171301i
$406$			12.6465i			0.627635i
$407$	0.825226	+	31.3723i	0.0409050	+	1.55507i
$408$	7.28132	−	0.716437i	0.360479	−	0.0354689i
$409$	15.8169	+	15.8169i	0.782097	+	0.782097i	0.980184	−	0.198087i	$-0.0634729\pi$
$409$	15.8169	+	15.8169i	0.782097	+	0.782097i	−0.198087	+	0.980184i	$0.563473\pi$
$410$	0.816209			0.0403097
$411$	−11.1463	+	1.09673i	−0.549806	+	0.0540975i
$412$	−8.51882	+	8.51882i	−0.419692	+	0.419692i
$413$	−0.379556	−	0.379556i	−0.0186767	−	0.0186767i
$414$	15.3542	−	3.05106i	0.754620	−	0.149951i
$415$	10.1627	−	10.1627i	0.498870	−	0.498870i
$416$			4.48188i			0.219742i
$417$	−2.22008	+	0.218442i	−0.108718	+	0.0106971i
$418$		−	21.3735i		−	1.04541i
$419$		−	31.1819i		−	1.52333i	−0.647969	−	0.761667i	$-0.724381\pi$
$419$		−	31.1819i		−	1.52333i	0.647969	−	0.761667i	$-0.275619\pi$
$420$	2.44582	+	2.00763i	0.119344	+	0.0979623i
$421$	−6.58898	−	6.58898i	−0.321127	−	0.321127i	0.528072	−	0.849200i	$-0.322915\pi$
$421$	−6.58898	−	6.58898i	−0.321127	−	0.321127i	−0.849200	+	0.528072i	$0.822915\pi$
$422$	−8.00838	+	8.00838i	−0.389842	+	0.389842i
$423$	−3.77832	−	19.0141i	−0.183708	−	0.924499i
$424$	−8.61154	+	8.61154i	−0.418213	+	0.418213i
$425$	2.98694	−	2.98694i	0.144888	−	0.144888i
$426$	−12.4512	+	15.1688i	−0.603263	+	0.734933i
$427$	−15.4507	−	15.4507i	−0.747713	−	0.747713i
$428$	−7.75936			−0.375063
$429$	−30.9576	−	25.4112i	−1.49465	−	1.22687i
$430$	2.69720	−	2.69720i	0.130071	−	0.130071i
$431$	14.4596	−	14.4596i	0.696496	−	0.696496i	−0.267157	−	0.963653i	$-0.586084\pi$
$431$	14.4596	−	14.4596i	0.696496	−	0.696496i	0.963653	+	0.267157i	$0.0860842\pi$
$432$	1.50692	+	4.97285i	0.0725017	+	0.239256i
$433$	−15.9254			−0.765327			−0.382663	−	0.923888i	$-0.624993\pi$
$433$	−15.9254			−0.765327			−0.382663	+	0.923888i	$0.624993\pi$
$434$	−16.0637			−0.771082
$435$	1.17407	+	11.9323i	0.0562922	+	0.572112i
$436$	−0.985941	−	0.985941i	−0.0472180	−	0.0472180i
$437$	−21.6171			−1.03408
$438$	−11.9784	+	14.5929i	−0.572351	+	0.697274i
$439$	22.9843	+	22.9843i	1.09698	+	1.09698i	0.994762	+	0.102218i	$0.0325940\pi$
$439$	22.9843	+	22.9843i	1.09698	+	1.09698i	0.102218	+	0.994762i	$0.467406\pi$
$440$			5.15936i			0.245963i
$441$	10.7767	−	2.14145i	0.513175	−	0.101974i
$442$	−13.3871	+	13.3871i	−0.636760	+	0.636760i
$443$	32.8593			1.56119			0.780595	−	0.625037i	$-0.214916\pi$
$443$	32.8593			1.56119			0.780595	+	0.625037i	$0.214916\pi$
$444$	1.30701	+	10.4543i	0.0620279	+	0.496138i
$445$	−9.01804			−0.427496
$446$	−3.78685	+	3.78685i	−0.179313	+	0.179313i
$447$	−8.72699	+	0.858681i	−0.412773	+	0.0406142i
$448$			1.82689i			0.0863126i
$449$	16.6345	+	16.6345i	0.785033	+	0.785033i	0.980675	−	0.195643i	$-0.0626793\pi$
$449$	16.6345	+	16.6345i	0.785033	+	0.785033i	−0.195643	+	0.980675i	$0.562679\pi$
$450$	2.49409	+	1.66719i	0.117572	+	0.0785922i
$451$	−4.21111			−0.198294
$452$	−4.37433	−	4.37433i	−0.205751	−	0.205751i
$453$	1.65300	−	0.162645i	0.0776647	−	0.00764172i
$454$	−16.2155			−0.761032
$455$	−8.18791			−0.383855
$456$	−0.702613	−	7.14083i	−0.0329029	−	0.334400i
$457$	5.71433	−	5.71433i	0.267305	−	0.267305i	−0.560708	−	0.828013i	$-0.689471\pi$
$457$	5.71433	−	5.71433i	0.267305	−	0.267305i	0.828013	+	0.560708i	$0.189471\pi$
$458$	14.7233	−	14.7233i	0.687973	−	0.687973i
$459$	−10.3525	+	19.3547i	−0.483214	+	0.903400i
$460$	5.21815			0.243298
$461$	−14.0336	−	14.0336i	−0.653612	−	0.653612i	0.300249	−	0.953861i	$-0.402930\pi$
$461$	−14.0336	−	14.0336i	−0.653612	−	0.653612i	−0.953861	+	0.300249i	$0.902930\pi$
$462$	−12.6189	−	10.3581i	−0.587082	−	0.481901i
$463$	−24.6253	+	24.6253i	−1.14443	+	1.14443i	−0.156805	+	0.987630i	$0.550120\pi$
$463$	−24.6253	+	24.6253i	−1.14443	+	1.14443i	−0.987630	+	0.156805i	$0.949880\pi$
$464$	−4.89488	+	4.89488i	−0.227239	+	0.227239i
$465$	−15.1566	+	1.49131i	−0.702869	+	0.0691579i
$466$	−21.3998	+	21.3998i	−0.991327	+	0.991327i
$467$	24.1276	+	24.1276i	1.11649	+	1.11649i	0.992252	+	0.124239i	$0.0396488\pi$
$467$	24.1276	+	24.1276i	1.11649	+	1.11649i	0.124239	+	0.992252i	$0.460351\pi$
$468$	−11.1782	−	7.47216i	−0.516712	−	0.345401i
$469$			21.9917i			1.01548i
$470$		−	6.46196i		−	0.298068i
$471$	3.99097	+	40.5613i	0.183894	+	1.86896i
$472$		−	0.293817i		−	0.0135240i
$473$	−13.9158	+	13.9158i	−0.639850	+	0.639850i
$474$	−12.9698	+	1.27615i	−0.595724	+	0.0586155i
$475$	−2.92931	−	2.92931i	−0.134406	−	0.134406i
$476$	−5.45682	+	5.45682i	−0.250113	+	0.250113i
$477$	−7.12082	−	35.8350i	−0.326040	−	1.64077i
$478$	19.8957			0.910008
$479$	9.10014	+	9.10014i	0.415796	+	0.415796i	0.883752	−	0.467956i	$-0.155009\pi$
$479$	9.10014	+	9.10014i	0.415796	+	0.415796i	−0.467956	+	0.883752i	$0.655009\pi$
$480$	0.169604	+	1.72373i	0.00774132	+	0.0786770i
$481$	−19.7775	−	18.7637i	−0.901777	−	0.855552i
$482$			1.37588i			0.0626697i
$483$	−10.4761	+	12.7627i	−0.476680	+	0.580721i
$484$		−	15.6189i		−	0.709952i
$485$	−11.7714			−0.534513
$486$	−14.9150	−	4.53231i	−0.676560	−	0.205590i
$487$	−3.65154	+	3.65154i	−0.165467	+	0.165467i	−0.784984	−	0.619517i	$-0.787329\pi$
$487$	−3.65154	+	3.65154i	−0.165467	+	0.165467i	0.619517	+	0.784984i	$0.287329\pi$
$488$		−	11.9605i		−	0.541428i
$489$	−1.74829	+	2.12987i	−0.0790602	+	0.0963162i
$490$	3.66246			0.165453
$491$			9.68790i			0.437209i	0.975814	+	0.218604i	$0.0701504\pi$
$491$			9.68790i			0.437209i	−0.975814	+	0.218604i	$0.929850\pi$
$492$	−1.40692	+	0.138432i	−0.0634290	+	0.00624101i
$493$	−29.2415			−1.31697
$494$	13.1288	+	13.1288i	0.590693	+	0.590693i
$495$	−12.8679	−	8.60164i	−0.578368	−	0.386615i
$496$	−6.21752	−	6.21752i	−0.279175	−	0.279175i
$497$		−	20.6992i		−	0.928487i
$498$	−15.7942	+	19.2414i	−0.707753	+	0.862230i
$499$	14.5609	+	14.5609i	0.651836	+	0.651836i	0.953435	−	0.301599i	$-0.0975203\pi$
$499$	14.5609	+	14.5609i	0.651836	+	0.651836i	−0.301599	+	0.953435i	$0.597520\pi$
$500$	0.707107	+	0.707107i	0.0316228	+	0.0316228i
$501$	8.00585	−	9.75323i	0.357675	−	0.435742i
$502$			2.98011i			0.133009i
$503$	−16.9725	−	16.9725i	−0.756766	−	0.756766i	0.218966	−	0.975732i	$-0.429732\pi$
$503$	−16.9725	−	16.9725i	−0.756766	−	0.756766i	−0.975732	+	0.218966i	$0.929732\pi$
$504$	−4.55643	−	3.04578i	−0.202959	−	0.135670i
$505$	5.84342	+	5.84342i	0.260029	+	0.260029i
$506$	−26.9223			−1.19684
$507$	12.2164	−	1.20202i	0.542551	−	0.0533836i
$508$		−	2.09841i		−	0.0931017i
$509$	−15.8798			−0.703858			−0.351929	−	0.936027i	$-0.614474\pi$
$509$	−15.8798			−0.703858			−0.351929	+	0.936027i	$0.614474\pi$
$510$	−4.64208	+	5.65527i	−0.205555	+	0.250420i
$511$		−	19.9132i		−	0.880910i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	18.9812	+	10.1528i	0.838042	+	0.448256i
$514$	−0.276755			−0.0122071
$515$		−	12.0474i		−	0.530873i
$516$	−4.19178	+	5.10669i	−0.184533	+	0.224810i
$517$			33.3396i			1.46627i
$518$	−8.06167	−	7.64843i	−0.354209	−	0.336053i
$519$	1.83326	+	18.6319i	0.0804714	+	0.817851i
$520$	−3.16917	−	3.16917i	−0.138977	−	0.138977i
$521$	−6.74121			−0.295338			−0.147669	−	0.989037i	$-0.547177\pi$
$521$	−6.74121			−0.295338			−0.147669	+	0.989037i	$0.547177\pi$
$522$	−4.04754	−	20.3690i	−0.177156	−	0.891526i
$523$	0.762505	−	0.762505i	0.0333420	−	0.0333420i	−0.690239	−	0.723581i	$-0.742495\pi$
$523$	0.762505	−	0.762505i	0.0333420	−	0.0333420i	0.723581	+	0.690239i	$0.242495\pi$
$524$	13.8897	+	13.8897i	0.606775	+	0.606775i
$525$	−3.14906	+	0.309848i	−0.137436	+	0.0135229i
$526$	6.16330	−	6.16330i	0.268733	−	0.268733i
$527$		−	37.1428i		−	1.61796i
$528$	−0.875047	−	8.89332i	−0.0380815	−	0.387032i
$529$			4.22909i			0.183874i
$530$		−	12.1785i		−	0.529002i
$531$	0.732806	+	0.489850i	0.0318011	+	0.0212577i
$532$	5.35154	+	5.35154i	0.232018	+	0.232018i
$533$	2.58670	−	2.58670i	0.112043	−	0.112043i
$534$	15.5446	−	1.52950i	0.672682	−	0.0661877i
$535$	5.48670	−	5.48670i	0.237211	−	0.237211i
$536$	−8.51198	+	8.51198i	−0.367662	+	0.367662i
$537$	15.8228	+	12.9880i	0.682804	+	0.560473i
$538$	15.0102	+	15.0102i	0.647134	+	0.647134i
$539$	−18.8959			−0.813906
$540$	−4.58189	−	2.45078i	−0.197173	−	0.105465i
$541$	−30.2618	+	30.2618i	−1.30106	+	1.30106i	−0.373379	+	0.927679i	$0.621801\pi$
$541$	−30.2618	+	30.2618i	−1.30106	+	1.30106i	−0.927679	+	0.373379i	$0.878199\pi$
$542$	−11.5506	+	11.5506i	−0.496141	+	0.496141i
$543$	4.36401	+	44.3525i	0.187278	+	1.90335i
$544$	−4.22417			−0.181110
$545$	1.39433			0.0597266
$546$	14.1137	−	1.38870i	0.604011	−	0.0594309i
$547$	−13.5953	−	13.5953i	−0.581292	−	0.581292i	0.353966	−	0.935258i	$-0.384833\pi$
$547$	−13.5953	−	13.5953i	−0.581292	−	0.581292i	−0.935258	+	0.353966i	$0.884833\pi$
$548$	6.46639			0.276231
$549$	29.8306	+	19.9405i	1.27314	+	0.851041i
$550$	−3.64822	−	3.64822i	−0.155560	−	0.155560i
$551$			28.6773i			1.22169i
$552$	−8.99467	+	0.885019i	−0.382838	+	0.0376689i
$553$	9.71995	−	9.71995i	0.413334	−	0.413334i
$554$	−20.8720			−0.886767
$555$	−8.31648	−	6.46809i	−0.353015	−	0.274555i
$556$	1.28795			0.0546213
$557$	−19.8919	+	19.8919i	−0.842846	+	0.842846i	−0.989228	−	0.146382i	$-0.953237\pi$
$557$	−19.8919	+	19.8919i	−0.842846	+	0.842846i	0.146382	+	0.989228i	$0.453237\pi$
$558$	25.8729	−	5.14123i	1.09529	−	0.217645i
$559$		−	17.0957i		−	0.723073i
$560$	−1.29181	−	1.29181i	−0.0545889	−	0.0545889i
$561$	23.9501	−	29.1776i	1.01117	−	1.23188i
$562$	−3.86499			−0.163035
$563$	−0.570464	−	0.570464i	−0.0240422	−	0.0240422i	0.694983	−	0.719026i	$-0.255412\pi$
$563$	−0.570464	−	0.570464i	−0.0240422	−	0.0240422i	−0.719026	+	0.694983i	$0.755412\pi$
$564$	1.09597	+	11.1387i	0.0461488	+	0.469022i
$565$	6.18624			0.260257
$566$	−26.0884			−1.09658
$567$	15.1929	−	6.28622i	0.638042	−	0.263996i
$568$	8.01172	−	8.01172i	0.336164	−	0.336164i
$569$	21.4414	−	21.4414i	0.898870	−	0.898870i	−0.0964667	−	0.995336i	$-0.530754\pi$
$569$	21.4414	−	21.4414i	0.898870	−	0.898870i	0.995336	+	0.0964667i	$0.0307541\pi$
$570$	5.54615	+	4.55251i	0.232303	+	0.190684i
$571$	−23.9185			−1.00096			−0.500480	−	0.865748i	$-0.666843\pi$
$571$	−23.9185			−1.00096			−0.500480	+	0.865748i	$0.666843\pi$
$572$	16.3509	+	16.3509i	0.683663	+	0.683663i
$573$	11.1799	−	13.6201i	0.467047	−	0.568986i
$574$	1.05439	−	1.05439i	0.0440092	−	0.0440092i
$575$	−3.68979	+	3.68979i	−0.153875	+	0.153875i
$576$	−0.584702	−	2.94247i	−0.0243626	−	0.122603i
$577$	−24.0238	+	24.0238i	−1.00012	+	1.00012i	−0.000123162		1.00000i	$0.500039\pi$
$577$	−24.0238	+	24.0238i	−1.00012	+	1.00012i	−1.00000		0.000123162i	$0.999961\pi$
$578$	−0.596554	−	0.596554i	−0.0248134	−	0.0248134i
$579$	4.46416	+	3.66436i	0.185524	+	0.152286i
$580$		−	6.92241i		−	0.287437i
$581$		−	26.2566i		−	1.08931i
$582$	20.2907	−	1.99648i	0.841077	−	0.0827567i
$583$			62.8335i			2.60230i
$584$	7.70750	−	7.70750i	0.318939	−	0.318939i
$585$	13.1878	−	2.62056i	0.545248	−	0.108347i
$586$	12.3576	+	12.3576i	0.510490	+	0.510490i
$587$	7.33897	−	7.33897i	0.302912	−	0.302912i	−0.539240	−	0.842152i	$-0.681289\pi$
$587$	7.33897	−	7.33897i	0.302912	−	0.302912i	0.842152	+	0.539240i	$0.181289\pi$
$588$	−6.31308	+	0.621168i	−0.260347	+	0.0256165i
$589$	−36.4261			−1.50091
$590$	0.207760	+	0.207760i	0.00855335	+	0.00855335i
$591$	−21.6037	+	2.12567i	−0.888658	+	0.0874383i
$592$	−0.159948	−	6.08066i	−0.00657380	−	0.249914i
$593$			4.63342i			0.190272i	0.995464	+	0.0951358i	$0.0303285\pi$
$593$			4.63342i			0.190272i	−0.995464	+	0.0951358i	$0.969671\pi$
$594$	23.6396	+	12.6444i	0.969944	+	0.518808i
$595$		−	7.71712i		−	0.316371i
$596$	5.06286			0.207383
$597$	−0.605504	+	0.737663i	−0.0247816	+	0.0301905i
$598$	16.5372	−	16.5372i	0.676256	−	0.676256i
$599$		−	3.41553i		−	0.139555i	−0.997563	−	0.0697773i	$-0.977771\pi$
$599$		−	3.41553i		−	0.139555i	0.997563	−	0.0697773i	$-0.0222289\pi$
$600$	−1.33879	−	1.09893i	−0.0546558	−	0.0448637i
$601$	39.9252			1.62858			0.814290	−	0.580458i	$-0.197126\pi$
$601$	39.9252			1.62858			0.814290	+	0.580458i	$0.197126\pi$
$602$		−	6.96853i		−	0.284016i
$603$	−7.03850	−	35.4207i	−0.286630	−	1.44244i
$604$	−0.958969			−0.0390199
$605$	11.0443	+	11.0443i	0.449013	+	0.449013i
$606$	−11.0635	−	9.08139i	−0.449425	−	0.368906i
$607$	−8.29532	−	8.29532i	−0.336697	−	0.336697i	0.518426	−	0.855123i	$-0.326518\pi$
$607$	−8.29532	−	8.29532i	−0.336697	−	0.336697i	−0.855123	+	0.518426i	$0.826518\pi$
$608$			4.14267i			0.168007i
$609$	16.9310	+	13.8976i	0.686078	+	0.563161i
$610$	8.45738	+	8.45738i	0.342429	+	0.342429i
$611$	−20.4790	−	20.4790i	−0.828493	−	0.828493i
$612$	7.04252	−	10.5355i	0.284677	−	0.425871i
$613$			2.23084i			0.0901029i	0.998985	+	0.0450515i	$0.0143452\pi$
$613$			2.23084i			0.0901029i	−0.998985	+	0.0450515i	$0.985655\pi$
$614$	1.33342	+	1.33342i	0.0538125	+	0.0538125i
$615$	0.896958	−	1.09273i	0.0361688	−	0.0440632i
$616$	6.66490	+	6.66490i	0.268536	+	0.268536i
$617$	−18.5224			−0.745682			−0.372841	−	0.927895i	$-0.621616\pi$
$617$	−18.5224			−0.745682			−0.372841	+	0.927895i	$0.621616\pi$
$618$	2.04329	+	20.7665i	0.0821932	+	0.835350i
$619$		−	20.8999i		−	0.840038i	−0.907515	−	0.420019i	$-0.862023\pi$
$619$		−	20.8999i		−	0.840038i	0.907515	−	0.420019i	$-0.137977\pi$
$620$	8.79291			0.353132
$621$	12.7885	−	23.9090i	0.513186	−	0.959434i
$622$			16.5479i			0.663511i
$623$	−11.6496	+	11.6496i	−0.466731	+	0.466731i
$624$	6.00028	+	4.92527i	0.240203	+	0.197169i
$625$	−1.00000			−0.0400000
$626$		−	16.7950i		−	0.671265i
$627$	−28.6146	−	23.4880i	−1.14276	−	0.938021i
$628$		−	23.5311i		−	0.938995i
$629$	17.6848	−	18.6403i	0.705140	−	0.743239i
$630$	5.37558	−	1.06819i	0.214168	−	0.0425576i
$631$	28.0515	+	28.0515i	1.11671	+	1.11671i	0.992221	+	0.124492i	$0.0397300\pi$
$631$	28.0515	+	28.0515i	1.11671	+	1.11671i	0.124492	+	0.992221i	$0.460270\pi$
$632$	7.52430			0.299300
$633$	1.92086	+	19.5222i	0.0763473	+	0.775936i
$634$	−10.9722	+	10.9722i	−0.435762	+	0.435762i
$635$	1.48380	+	1.48380i	0.0588827	+	0.0588827i
$636$	2.06553	+	20.9925i	0.0819036	+	0.832407i
$637$	11.6069	−	11.6069i	0.459884	−	0.459884i
$638$			35.7152i			1.41398i
$639$	6.62484	+	33.3390i	0.262075	+	1.31887i
$640$		−	1.00000i		−	0.0395285i
$641$		−	11.3698i		−	0.449079i	−0.974465	−	0.224540i	$-0.927912\pi$
$641$		−	11.3698i		−	0.449079i	0.974465	−	0.224540i	$-0.0720878\pi$
$642$	−8.52700	+	10.3881i	−0.336534	+	0.409987i
$643$	7.89477	+	7.89477i	0.311339	+	0.311339i	0.845428	−	0.534089i	$-0.179345\pi$
$643$	7.89477	+	7.89477i	0.311339	+	0.311339i	−0.534089	+	0.845428i	$0.679345\pi$
$644$	6.74085	−	6.74085i	0.265627	−	0.265627i
$645$	−0.646940	−	6.57501i	−0.0254732	−	0.258891i
$646$	−12.3739	+	12.3739i	−0.486845	+	0.486845i
$647$	−18.1698	+	18.1698i	−0.714327	+	0.714327i	−0.967437	−	0.253110i	$-0.918546\pi$
$647$	−18.1698	+	18.1698i	−0.714327	+	0.714327i	0.253110	+	0.967437i	$0.418546\pi$
$648$	8.31358	+	3.44737i	0.326588	+	0.135425i
$649$	−1.07191	−	1.07191i	−0.0420761	−	0.0420761i
$650$	4.48188			0.175794
$651$	−17.6529	+	21.5059i	−0.691871	+	0.842881i
$652$	1.12493	−	1.12493i	0.0440558	−	0.0440558i
$653$	−16.0946	+	16.0946i	−0.629832	+	0.629832i	−0.948026	−	0.318194i	$-0.896924\pi$
$653$	−16.0946	+	16.0946i	−0.629832	+	0.629832i	0.318194	+	0.948026i	$0.396924\pi$
$654$	−2.40345	+	0.236484i	−0.0939822	+	0.00924726i
$655$	−19.6430			−0.767516
$656$	0.816209			0.0318676
$657$	6.37328	+	32.0731i	0.248645	+	1.25129i
$658$	−8.34762	−	8.34762i	−0.325424	−	0.325424i
$659$	22.0332			0.858292			0.429146	−	0.903235i	$-0.358815\pi$
$659$	22.0332			0.858292			0.429146	+	0.903235i	$0.358815\pi$
$660$	6.90728	+	5.66978i	0.268865	+	0.220696i
$661$	−2.53133	−	2.53133i	−0.0984575	−	0.0984575i	0.656162	−	0.754620i	$-0.272179\pi$
$661$	−2.53133	−	2.53133i	−0.0984575	−	0.0984575i	−0.754620	+	0.656162i	$0.772179\pi$
$662$			20.7556i			0.806690i
$663$	3.21098	+	32.6340i	0.124704	+	1.26740i
$664$	10.1627	−	10.1627i	0.394391	−	0.394391i
$665$	−7.56821			−0.293483
$666$	15.4324	+	9.73871i	0.597992	+	0.377367i
$667$	36.1222			1.39866
$668$	−5.15136	+	5.15136i	−0.199312	+	0.199312i
$669$	0.908299	+	9.23127i	0.0351169	+	0.356902i
$670$		−	12.0378i		−	0.465059i
$671$	−43.6346	−	43.6346i	−1.68450	−	1.68450i
$672$	2.44582	+	2.00763i	0.0943496	+	0.0774460i
$673$	25.6452			0.988550			0.494275	−	0.869306i	$-0.335434\pi$
$673$	25.6452			0.988550			0.494275	+	0.869306i	$0.335434\pi$
$674$	2.83312	+	2.83312i	0.109128	+	0.109128i
$675$	4.97285	−	1.50692i	0.191405	−	0.0580014i
$676$	−7.08722			−0.272585
$677$	36.1424			1.38907			0.694533	−	0.719461i	$-0.255611\pi$
$677$	36.1424			1.38907			0.694533	+	0.719461i	$0.255611\pi$
$678$	−10.6634	+	1.04921i	−0.409525	+	0.0402947i
$679$	−15.2064	+	15.2064i	−0.583569	+	0.583569i
$680$	2.98694	−	2.98694i	0.114544	−	0.114544i
$681$	−17.8197	+	21.7091i	−0.682854	+	0.831896i
$682$	−45.3657			−1.73714
$683$	−13.8969	−	13.8969i	−0.531749	−	0.531749i	0.389344	−	0.921093i	$-0.372702\pi$
$683$	−13.8969	−	13.8969i	−0.531749	−	0.531749i	−0.921093	+	0.389344i	$0.872702\pi$
$684$	−10.3322	−	6.90663i	−0.395061	−	0.264082i
$685$	−4.57243	+	4.57243i	−0.174704	+	0.174704i
$686$	13.7739	−	13.7739i	0.525888	−	0.525888i
$687$	−3.53146	−	35.8911i	−0.134734	−	1.36933i
$688$	2.69720	−	2.69720i	0.102830	−	0.102830i
$689$	−38.5958	−	38.5958i	−1.47038	−	1.47038i
$690$	5.73439	−	6.98599i	0.218304	−	0.265952i
$691$		−	45.4792i		−	1.73011i	−0.501678	−	0.865055i	$-0.667284\pi$
$691$		−	45.4792i		−	1.73011i	0.501678	−	0.865055i	$-0.332716\pi$
$692$		−	10.8091i		−	0.410900i
$693$	−27.7345	+	5.51116i	−1.05355	+	0.209352i
$694$			5.72399i			0.217280i
$695$	−0.910719	+	0.910719i	−0.0345456	+	0.0345456i
$696$	1.17407	+	11.9323i	0.0445029	+	0.452294i
$697$	2.43797	+	2.43797i	0.0923447	+	0.0923447i
$698$	15.8227	−	15.8227i	0.598897	−	0.598897i
$699$	5.13287	+	52.1667i	0.194143	+	1.97313i
$700$	1.82689			0.0690501
$701$	−15.8539	−	15.8539i	−0.598793	−	0.598793i	0.341199	−	0.939991i	$-0.389167\pi$
$701$	−15.8539	−	15.8539i	−0.598793	−	0.598793i	−0.939991	+	0.341199i	$0.889167\pi$
$702$	−22.2877	+	6.75383i	−0.841194	+	0.254907i
$703$	−18.2807	−	17.3436i	−0.689469	−	0.654126i
$704$			5.15936i			0.194451i
$705$	−8.65119	−	7.10125i	−0.325823	−	0.267449i
$706$			33.4634i			1.25941i
$707$	15.0972			0.567787
$708$	−0.393359	−	0.322885i	−0.0147833	−	0.0121348i
$709$	−10.2894	+	10.2894i	−0.386425	+	0.386425i	−0.873410	−	0.486985i	$-0.838097\pi$
$709$	−10.2894	+	10.2894i	−0.386425	+	0.386425i	0.486985	+	0.873410i	$0.338097\pi$
$710$			11.3303i			0.425218i
$711$	−12.5445	+	18.7662i	−0.470454	+	0.703789i
$712$	−9.01804			−0.337965
$713$			45.8827i			1.71832i
$714$	1.30885	+	13.3022i	0.0489826	+	0.497822i
$715$	−23.1236			−0.864773
$716$	−8.35712	−	8.35712i	−0.312320	−	0.312320i
$717$	21.8640	−	26.6361i	0.816526	−	0.994743i
$718$	4.38077	+	4.38077i	0.163489	+	0.163489i
$719$		−	29.1987i		−	1.08893i	−0.838784	−	0.544464i	$-0.816733\pi$
$719$		−	29.1987i		−	1.08893i	0.838784	−	0.544464i	$-0.183267\pi$
$720$	2.49409	+	1.66719i	0.0929491	+	0.0621326i
$721$	−15.5630	−	15.5630i	−0.579595	−	0.579595i
$722$	−1.29987	−	1.29987i	−0.0483761	−	0.0483761i
$723$	1.84201	+	1.51200i	0.0685052	+	0.0562318i
$724$		−	25.7306i		−	0.956270i
$725$	4.89488	+	4.89488i	0.181791	+	0.181791i
$726$	−20.9104	−	17.1641i	−0.776059	−	0.637021i
$727$	−11.2358	−	11.2358i	−0.416714	−	0.416714i	0.467355	−	0.884070i	$-0.345207\pi$
$727$	−11.2358	−	11.2358i	−0.416714	−	0.416714i	−0.884070	+	0.467355i	$0.845207\pi$
$728$	−8.18791			−0.303464
$729$	−22.4584	+	14.9874i	−0.831792	+	0.555087i
$730$			10.9001i			0.403429i
$731$	16.1128			0.595952
$732$	−16.0126	−	13.1438i	−0.591843	−	0.485809i
$733$		−	29.6661i		−	1.09574i	−0.836562	−	0.547872i	$-0.815438\pi$
$733$		−	29.6661i		−	1.09574i	0.836562	−	0.547872i	$-0.184562\pi$
$734$	23.4141	−	23.4141i	0.864231	−	0.864231i
$735$	4.02479	−	4.90326i	0.148457	−	0.180859i
$736$	5.21815			0.192344
$737$			62.1071i			2.28774i
$738$	−1.36078	+	2.03570i	−0.0500910	+	0.0749350i
$739$			29.5097i			1.08553i	0.839883	+	0.542767i	$0.182623\pi$
$739$			29.5097i			1.08553i	−0.839883	+	0.542767i	$0.817377\pi$
$740$	4.41278	+	4.18658i	0.162217	+	0.153902i
$741$	32.0043	−	3.14902i	1.17571	−	0.115682i
$742$	−15.7324	−	15.7324i	−0.577553	−	0.577553i
$743$	21.3251			0.782344			0.391172	−	0.920318i	$-0.372070\pi$
$743$	21.3251			0.782344			0.391172	+	0.920318i	$0.372070\pi$
$744$	−15.1566	+	1.49131i	−0.555667	+	0.0546741i
$745$	−3.57999	+	3.57999i	−0.131161	+	0.131161i
$746$	22.5174	+	22.5174i	0.824422	+	0.824422i
$747$	8.40350	+	42.2900i	0.307468	+	1.54731i
$748$	−15.4107	+	15.4107i	−0.563471	+	0.563471i
$749$		−	14.1755i		−	0.517962i
$750$	1.72373	−	0.169604i	0.0629416	−	0.00619306i
$751$			6.67039i			0.243406i	0.992567	+	0.121703i	$0.0388355\pi$
$751$			6.67039i			0.243406i	−0.992567	+	0.121703i	$0.961164\pi$
$752$		−	6.46196i		−	0.235644i
$753$	3.98973	+	3.27493i	0.145394	+	0.119345i
$754$	−21.9383	−	21.9383i	−0.798945	−	0.798945i
$755$	0.678093	−	0.678093i	0.0246783	−	0.0246783i
$756$	−9.08486	+	2.75298i	−0.330413	+	0.100125i
$757$	−6.34809	+	6.34809i	−0.230725	+	0.230725i	−0.812995	−	0.582270i	$-0.802165\pi$
$757$	−6.34809	+	6.34809i	−0.230725	+	0.230725i	0.582270	+	0.812995i	$0.302165\pi$
$758$	−12.8454	+	12.8454i	−0.466567	+	0.466567i
$759$	−29.5857	+	36.0432i	−1.07389	+	1.30829i
$760$	−2.92931	−	2.92931i	−0.106257	−	0.106257i
$761$	29.4703			1.06830			0.534148	−	0.845391i	$-0.320633\pi$
$761$	29.4703			1.06830			0.534148	+	0.845391i	$0.320633\pi$
$762$	−2.80932	−	2.30600i	−0.101771	−	0.0835377i
$763$	1.80121	−	1.80121i	0.0652081	−	0.0652081i
$764$	−7.19370	+	7.19370i	−0.260259	+	0.260259i
$765$	2.46988	+	12.4295i	0.0892988	+	0.449390i
$766$	26.3274			0.951247
$767$	1.31685			0.0475488
$768$	0.169604	+	1.72373i	0.00612005	+	0.0621996i
$769$	−35.2222	−	35.2222i	−1.27014	−	1.27014i	−0.946012	−	0.324133i	$-0.894928\pi$
$769$	−35.2222	−	35.2222i	−1.27014	−	1.27014i	−0.324133	−	0.946012i	$-0.605072\pi$
$770$	−9.42559			−0.339675
$771$	−0.304135	+	0.370516i	−0.0109531	+	0.0133438i
$772$	−2.35783	−	2.35783i	−0.0848602	−	0.0848602i
$773$		−	22.3562i		−	0.804095i	−0.915619	−	0.402048i	$-0.868299\pi$
$773$		−	22.3562i		−	0.804095i	0.915619	−	0.402048i	$-0.131701\pi$
$774$	2.23030	+	11.2238i	0.0801663	+	0.403431i
$775$	−6.21752	+	6.21752i	−0.223340	+	0.223340i
$776$	−11.7714			−0.422569
$777$	−19.0988	+	2.38777i	−0.685167	+	0.0856606i
$778$	−4.13431			−0.148222
$779$	2.39093	−	2.39093i	0.0856640	−	0.0856640i
$780$	−7.72553	+	0.760144i	−0.276618	+	0.0272175i
$781$		−	58.4570i		−	2.09176i
$782$	15.5863	+	15.5863i	0.557366	+	0.557366i
$783$	−31.7177	−	16.9653i	−1.13350	−	0.606290i
$784$	3.66246			0.130802
$785$	16.6390	+	16.6390i	0.593872	+	0.593872i
$786$	33.8592	−	3.33153i	1.20772	−	0.118832i
$787$	−37.4201			−1.33388			−0.666941	−	0.745110i	$-0.732397\pi$
$787$	−37.4201			−1.33388			−0.666941	+	0.745110i	$0.732397\pi$
$788$	12.5331			0.446474
$789$	−1.47831	−	15.0244i	−0.0526291	−	0.534883i
$790$	−5.32048	+	5.32048i	−0.189294	+	0.189294i
$791$	7.99143	−	7.99143i	0.284143	−	0.284143i
$792$	−12.8679	−	8.60164i	−0.457240	−	0.305646i
$793$	53.6057			1.90359
$794$	21.6591	+	21.6591i	0.768652	+	0.768652i
$795$	−16.3045	−	13.3834i	−0.578260	−	0.474660i
$796$	0.389611	−	0.389611i	0.0138094	−	0.0138094i
$797$	2.88337	−	2.88337i	0.102134	−	0.102134i	−0.654193	−	0.756328i	$-0.726992\pi$
$797$	2.88337	−	2.88337i	0.102134	−	0.102134i	0.756328	+	0.654193i	$0.226992\pi$
$798$	13.0455	−	1.28360i	0.461807	−	0.0454389i
$799$	19.3015	−	19.3015i	0.682839	−	0.682839i
$800$	0.707107	+	0.707107i	0.0250000	+	0.0250000i
$801$	15.0348	−	22.4918i	0.531229	−	0.794708i
$802$			0.513312i			0.0181257i
$803$		−	56.2373i		−	1.98457i
$804$	2.04165	+	20.7498i	0.0720035	+	0.731790i
$805$			9.53300i			0.335994i
$806$	27.8662	−	27.8662i	0.981544	−	0.981544i
$807$	36.5906	−	3.60028i	1.28805	−	0.126736i
$808$	5.84342	+	5.84342i	0.205571	+	0.205571i
$809$	−16.8471	+	16.8471i	−0.592311	+	0.592311i	−0.938255	−	0.345944i	$-0.887559\pi$
$809$	−16.8471	+	16.8471i	−0.592311	+	0.592311i	0.345944	+	0.938255i	$0.387559\pi$
$810$	−8.31625	+	3.44093i	−0.292203	+	0.120902i
$811$	8.62531			0.302876			0.151438	−	0.988467i	$-0.451610\pi$
$811$	8.62531			0.302876			0.151438	+	0.988467i	$0.451610\pi$
$812$	−8.94243	−	8.94243i	−0.313818	−	0.313818i
$813$	2.77048	+	28.1571i	0.0971651	+	0.987513i
$814$	−22.7671	−	21.6000i	−0.797986	−	0.757081i
$815$			1.59090i			0.0557267i
$816$	−4.64208	+	5.65527i	−0.162505	+	0.197974i
$817$		−	15.8019i		−	0.552837i
$818$	−22.3685			−0.782097
$819$	13.6508	−	20.4214i	0.476999	−	0.713580i
$820$	−0.577147	+	0.577147i	−0.0201549	+	0.0201549i
$821$			11.0703i			0.386357i	0.981164	+	0.193179i	$0.0618797\pi$
$821$			11.0703i			0.386357i	−0.981164	+	0.193179i	$0.938120\pi$
$822$	7.10612	−	8.65712i	0.247854	−	0.301952i
$823$	−16.3353			−0.569414			−0.284707	−	0.958615i	$-0.591896\pi$
$823$	−16.3353			−0.569414			−0.284707	+	0.958615i	$0.591896\pi$
$824$		−	12.0474i		−	0.419692i
$825$	−8.89332	+	0.875047i	−0.309626	+	0.0304652i
$826$	0.536773			0.0186767
$827$	−31.1180	−	31.1180i	−1.08208	−	1.08208i	−0.996316	−	0.0857621i	$-0.972668\pi$
$827$	−31.1180	−	31.1180i	−1.08208	−	1.08208i	−0.0857621	−	0.996316i	$-0.527332\pi$
$828$	−8.69967	+	13.0145i	−0.302334	+	0.452286i
$829$	19.9622	+	19.9622i	0.693314	+	0.693314i	0.962960	−	0.269645i	$-0.0869065\pi$
$829$	19.9622	+	19.9622i	0.693314	+	0.693314i	−0.269645	+	0.962960i	$0.586906\pi$
$830$			14.3723i			0.498870i
$831$	−22.9369	+	27.9432i	−0.795672	+	0.969338i
$832$	−3.16917	−	3.16917i	−0.109871	−	0.109871i
$833$	10.9396	+	10.9396i	0.379033	+	0.379033i
$834$	1.41537	−	1.72429i	0.0490102	−	0.0597074i
$835$		−	7.28513i		−	0.252112i
$836$	15.1133	+	15.1133i	0.522706	+	0.522706i
$837$	21.5495	−	40.2881i	0.744859	−	1.39256i
$838$	22.0489	+	22.0489i	0.761667	+	0.761667i
$839$	−22.8829			−0.790004			−0.395002	−	0.918680i	$-0.629256\pi$
$839$	−22.8829			−0.790004			−0.395002	+	0.918680i	$0.629256\pi$
$840$	−3.14906	+	0.309848i	−0.108653	+	0.0106908i
$841$		−	18.9198i		−	0.652406i
$842$	9.31823			0.321127
$843$	−4.24736	+	5.17440i	−0.146287	+	0.178216i
$844$		−	11.3256i		−	0.389842i
$845$	5.01142	−	5.01142i	0.172398	−	0.172398i
$846$	16.1167	+	10.7733i	0.554103	+	0.370395i
$847$	28.5341			0.980445
$848$		−	12.1785i		−	0.418213i
$849$	−28.6694	+	34.9269i	−0.983931	+	1.19869i
$850$			4.22417i			0.144888i
$851$	−21.8462	+	23.0265i	−0.748877	+	0.789339i
$852$	−1.92166	−	19.5303i	−0.0658350	−	0.669098i
$853$	−16.7337	−	16.7337i	−0.572951	−	0.572951i	0.360001	−	0.932952i	$-0.382776\pi$
$853$	−16.7337	−	16.7337i	−0.572951	−	0.572951i	−0.932952	+	0.360001i	$0.882776\pi$
$854$	21.8506			0.747713
$855$	12.1897	−	2.42223i	0.416878	−	0.0828384i
$856$	5.48670	−	5.48670i	0.187531	−	0.187531i
$857$	13.2229	+	13.2229i	0.451687	+	0.451687i	0.895914	−	0.444227i	$-0.146522\pi$
$857$	13.2229	+	13.2229i	0.451687	+	0.451687i	−0.444227	+	0.895914i	$0.646522\pi$
$858$	39.8588	−	3.92185i	1.36076	−	0.133890i
$859$	14.0520	−	14.0520i	0.479448	−	0.479448i	−0.425507	−	0.904955i	$-0.639904\pi$
$859$	14.0520	−	14.0520i	0.479448	−	0.479448i	0.904955	+	0.425507i	$0.139904\pi$
$860$			3.81442i			0.130071i
$861$	−0.252901	−	2.57030i	−0.00861884	−	0.0875955i
$862$			20.4490i			0.696496i
$863$			30.1029i			1.02472i	0.858772	+	0.512358i	$0.171228\pi$
$863$			30.1029i			1.02472i	−0.858772	+	0.512358i	$0.828772\pi$
$864$	−4.58189	−	2.45078i	−0.155879	−	0.0833772i
$865$	7.64318	+	7.64318i	0.259876	+	0.259876i
$866$	11.2610	−	11.2610i	0.382663	−	0.382663i
$867$	−1.45423	+	0.143087i	−0.0493882	+	0.00485949i
$868$	11.3587	−	11.3587i	0.385541	−	0.385541i
$869$	27.4502	−	27.4502i	0.931186	−	0.931186i
$870$	−9.26763	−	7.60725i	−0.314202	−	0.257910i
$871$	−38.1497	−	38.1497i	−1.29265	−	1.29265i
$872$	1.39433			0.0472180
$873$	19.6252	−	29.3589i	0.664213	−	0.993649i
$874$	15.2856	−	15.2856i	0.517042	−	0.517042i
$875$	−1.29181	+	1.29181i	−0.0436711	+	0.0436711i
$876$	−1.84869	−	18.7887i	−0.0624615	−	0.634812i
$877$	53.5570			1.80849			0.904246	−	0.427012i	$-0.140434\pi$
$877$	53.5570			1.80849			0.904246	+	0.427012i	$0.140434\pi$
$878$	−32.5047			−1.09698
$879$	30.1245	−	2.96406i	1.01607	−	0.0999752i
$880$	−3.64822	−	3.64822i	−0.122981	−	0.122981i
$881$	15.9670			0.537943			0.268971	−	0.963148i	$-0.413316\pi$
$881$	15.9670			0.537943			0.268971	+	0.963148i	$0.413316\pi$
$882$	−6.10603	+	9.13450i	−0.205601	+	0.307574i
$883$	−13.4861	−	13.4861i	−0.453844	−	0.453844i	0.442784	−	0.896628i	$-0.353991\pi$
$883$	−13.4861	−	13.4861i	−0.453844	−	0.453844i	−0.896628	+	0.442784i	$0.853991\pi$
$884$		−	18.9322i		−	0.636760i
$885$	0.506461	−	0.0498326i	0.0170245	−	0.00167510i
$886$	−23.2350	+	23.2350i	−0.780595	+	0.780595i
$887$	9.32351			0.313053			0.156526	−	0.987674i	$-0.449970\pi$
$887$	9.32351			0.313053			0.156526	+	0.987674i	$0.449970\pi$
$888$	−8.31648	−	6.46809i	−0.279083	−	0.217055i
$889$	3.83356			0.128574
$890$	6.37672	−	6.37672i	0.213748	−	0.213748i
$891$	42.9065	−	17.7530i	1.43742	−	0.594748i
$892$		−	5.35541i		−	0.179313i
$893$	−18.9291	−	18.9291i	−0.633438	−	0.633438i
$894$	5.56374	−	6.77810i	0.186079	−	0.226693i
$895$	11.8187			0.395057
$896$	−1.29181	−	1.29181i	−0.0431563	−	0.0431563i
$897$	−3.96654	−	40.3130i	−0.132439	−	1.34601i
$898$	−23.5248			−0.785033
$899$	60.8681			2.03006
$900$	−2.94247	+	0.584702i	−0.0980823	+	0.0194901i
$901$	36.3766	−	36.3766i	1.21188	−	1.21188i
$902$	2.97771	−	2.97771i	0.0991468	−	0.0991468i
$903$	−9.32938	−	7.65793i	−0.310462	−	0.254840i
$904$	6.18624			0.205751
$905$	18.1943	+	18.1943i	0.604798	+	0.604798i
$906$	−1.05384	+	1.28385i	−0.0350115	+	0.0426532i
$907$	1.70977	−	1.70977i	0.0567720	−	0.0567720i	−0.678151	−	0.734923i	$-0.737218\pi$
$907$	1.70977	−	1.70977i	0.0567720	−	0.0567720i	0.734923	+	0.678151i	$0.237218\pi$
$908$	11.4661	−	11.4661i	0.380516	−	0.380516i
$909$	−24.3161	+	4.83188i	−0.806514	+	0.160263i
$910$	5.78973	−	5.78973i	0.191928	−	0.191928i
$911$	−20.7053	−	20.7053i	−0.685996	−	0.685996i	0.275348	−	0.961345i	$-0.411207\pi$
$911$	−20.7053	−	20.7053i	−0.685996	−	0.685996i	−0.961345	+	0.275348i	$0.911207\pi$
$912$	5.54615	+	4.55251i	0.183651	+	0.150749i
$913$		−	74.1518i		−	2.45407i
$914$			8.08129i			0.267305i
$915$	20.6167	−	2.02855i	0.681567	−	0.0670619i
$916$			20.8218i			0.687973i
$917$	−25.3750	+	25.3750i	−0.837956	+	0.837956i
$918$	−6.36549	−	21.0062i	−0.210093	−	0.693307i
$919$	22.2778	+	22.2778i	0.734876	+	0.734876i	0.971581	−	0.236705i	$-0.0760676\pi$
$919$	22.2778	+	22.2778i	0.734876	+	0.734876i	−0.236705	+	0.971581i	$0.576068\pi$
$920$	−3.68979	+	3.68979i	−0.121649	+	0.121649i
$921$	3.25050	−	0.319829i	0.107108	−	0.0105387i
$922$	19.8466			0.653612
$923$	35.9076	+	35.9076i	1.18191	+	1.18191i
$924$	16.2471	−	1.59862i	0.534492	−	0.0525906i
$925$	−6.08066	+	0.159948i	−0.199931	+	0.00525904i
$926$		−	34.8254i		−	1.14443i
$927$	30.0473	+	20.0854i	0.986883	+	0.659691i
$928$		−	6.92241i		−	0.227239i
$929$	15.4466			0.506786			0.253393	−	0.967363i	$-0.418453\pi$
$929$	15.4466			0.506786			0.253393	+	0.967363i	$0.418453\pi$
$930$	9.66280	−	11.7718i	0.316856	−	0.386013i
$931$	10.7285	−	10.7285i	0.351612	−	0.351612i
$932$		−	30.2639i		−	0.991327i
$933$	22.1541	+	18.1850i	0.725293	+	0.595350i
$934$	−34.1215			−1.11649
$935$		−	21.7940i		−	0.712741i
$936$	13.1878	−	2.62056i	0.431056	−	0.0856557i
$937$	−29.3568			−0.959044			−0.479522	−	0.877530i	$-0.659190\pi$
$937$	−29.3568			−0.959044			−0.479522	+	0.877530i	$0.659190\pi$
$938$	−15.5505	−	15.5505i	−0.507741	−	0.507741i
$939$	−22.4850	−	18.4566i	−0.733770	−	0.602308i
$940$	4.56930	+	4.56930i	0.149034	+	0.149034i
$941$		−	0.103311i		−	0.00336783i	−0.999999	−	0.00168392i	$-0.999464\pi$
$941$		−	0.103311i		−	0.00336783i	0.999999	−	0.00168392i	$-0.000536007\pi$
$942$	−31.5032	−	25.8591i	−1.02643	−	0.842535i
$943$	−3.01164	−	3.01164i	−0.0980725	−	0.0980725i
$944$	0.207760	+	0.207760i	0.00676202	+	0.00676202i
$945$	4.47731	−	8.37062i	0.145647	−	0.272296i
$946$		−	19.6799i		−	0.639850i
$947$	−3.45717	−	3.45717i	−0.112343	−	0.112343i	0.648701	−	0.761044i	$-0.275313\pi$
$947$	−3.45717	−	3.45717i	−0.112343	−	0.112343i	−0.761044	+	0.648701i	$0.775313\pi$
$948$	8.26868	−	10.0734i	0.268554	−	0.327170i
$949$	34.5441	+	34.5441i	1.12135	+	1.12135i
$950$	4.14267			0.134406
$951$	2.63175	+	26.7471i	0.0853404	+	0.867335i
$952$		−	7.71712i		−	0.250113i
$953$	−41.4662			−1.34322			−0.671611	−	0.740904i	$-0.734397\pi$
$953$	−41.4662			−1.34322			−0.671611	+	0.740904i	$0.734397\pi$
$954$	30.3744	+	20.3040i	0.983406	+	0.657366i
$955$		−	10.1734i		−	0.329204i
$956$	−14.0684	+	14.0684i	−0.455004	+	0.455004i
$957$	47.8150	+	39.2485i	1.54564	+	1.26872i
$958$	−12.8695			−0.415796
$959$			11.8134i			0.381475i
$960$	−1.33879	−	1.09893i	−0.0432092	−	0.0354678i
$961$			46.3152i			1.49404i
$962$	27.2528	−	0.716865i	0.878664	−	0.0231127i
$963$	4.53691	+	22.8317i	0.146200	+	0.735741i
$964$	−0.972895	−	0.972895i	−0.0313348	−	0.0313348i
$965$	3.33448			0.107341
$966$	−1.61683	−	16.4323i	−0.0520208	−	0.528700i
$967$	6.83266	−	6.83266i	0.219723	−	0.219723i	−0.588658	−	0.808382i	$-0.700344\pi$
$967$	6.83266	−	6.83266i	0.219723	−	0.219723i	0.808382	+	0.588658i	$0.200344\pi$
$968$	11.0443	+	11.0443i	0.354976	+	0.354976i
$969$	2.96796	+	30.1641i	0.0953446	+	0.969011i
$970$	8.32365	−	8.32365i	0.267256	−	0.267256i
$971$			16.5919i			0.532458i	0.963910	+	0.266229i	$0.0857777\pi$
$971$			16.5919i			0.532458i	−0.963910	+	0.266229i	$0.914222\pi$
$972$	13.7513	−	7.34170i	0.441075	−	0.235485i
$973$			2.35295i			0.0754321i
$974$		−	5.16405i		−	0.165467i
$975$	4.92527	−	6.00028i	0.157735	−	0.192163i
$976$	8.45738	+	8.45738i	0.270714	+	0.270714i
$977$	16.2413	−	16.2413i	0.519604	−	0.519604i	−0.397847	−	0.917452i	$-0.630243\pi$
$977$	16.2413	−	16.2413i	0.519604	−	0.519604i	0.917452	+	0.397847i	$0.130243\pi$
$978$	−0.269822	−	2.74227i	−0.00862797	−	0.0876882i
$979$	−32.8998	+	32.8998i	−1.05148	+	1.05148i
$980$	−2.58975	+	2.58975i	−0.0827266	+	0.0827266i
$981$	−2.32462	+	3.47758i	−0.0742194	+	0.111031i
$982$	−6.85038	−	6.85038i	−0.218604	−	0.218604i
$983$	−21.5109			−0.686093			−0.343046	−	0.939318i	$-0.611459\pi$
$983$	−21.5109			−0.686093			−0.343046	+	0.939318i	$0.611459\pi$
$984$	0.896958	−	1.09273i	0.0285940	−	0.0348350i
$985$	−8.86227	+	8.86227i	−0.282375	+	0.282375i
$986$	20.6768	−	20.6768i	0.658485	−	0.658485i
$987$	−20.3491	+	2.00223i	−0.647720	+	0.0637316i
$988$	−18.5669			−0.590693
$989$	−19.9042			−0.632917
$990$	15.1812	−	3.01668i	0.482492	−	0.0958765i
$991$	−0.323127	−	0.323127i	−0.0102645	−	0.0102645i	0.701956	−	0.712220i	$-0.252310\pi$
$991$	−0.323127	−	0.323127i	−0.0102645	−	0.0102645i	−0.712220	+	0.701956i	$0.752310\pi$
$992$	8.79291			0.279175
$993$	27.7874	+	22.8090i	0.881806	+	0.723822i
$994$	14.6366	+	14.6366i	0.464243	+	0.464243i
$995$			0.550993i			0.0174677i
$996$	−2.43760	−	24.7739i	−0.0772382	−	0.784991i
$997$	22.8759	−	22.8759i	0.724486	−	0.724486i	−0.245030	−	0.969516i	$-0.578798\pi$
$997$	22.8759	−	22.8759i	0.724486	−	0.724486i	0.969516	+	0.245030i	$0.0787977\pi$
$998$	−20.5922			−0.651836
$999$	29.9972	−	9.95846i	0.949068	−	0.315072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.u.f.401.1	yes	40
3.2	odd	2	inner	1110.2.u.f.401.18	yes	40
37.6	odd	4	inner	1110.2.u.f.191.18	yes	40
111.80	even	4	inner	1110.2.u.f.191.1	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.f.191.1	✓	40	111.80	even	4	inner
1110.2.u.f.191.18	yes	40	37.6	odd	4	inner
1110.2.u.f.401.1	yes	40	1.1	even	1	trivial
1110.2.u.f.401.18	yes	40	3.2	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.169604 + 1.72373i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.33879 - 1.09893i) q^{6} +1.82689 q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.94247 + 0.584702i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.169604 + 1.72373i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.33879 - 1.09893i) q^{6} +1.82689 q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.94247 + 0.584702i) q^{9} -1.00000 q^{10} +5.15936 q^{11} +(1.72373 - 0.169604i) q^{12} +(-3.16917 + 3.16917i) q^{13} +(-1.29181 + 1.29181i) q^{14} +(-1.09893 + 1.33879i) q^{15} -1.00000 q^{16} +(-2.98694 - 2.98694i) q^{17} +(1.66719 - 2.49409i) q^{18} +(-2.92931 + 2.92931i) q^{19} +(0.707107 - 0.707107i) q^{20} +(0.309848 + 3.14906i) q^{21} +(-3.64822 + 3.64822i) q^{22} +(3.68979 + 3.68979i) q^{23} +(-1.09893 + 1.33879i) q^{24} +1.00000i q^{25} -4.48188i q^{26} +(-1.50692 - 4.97285i) q^{27} -1.82689i q^{28} +(4.89488 - 4.89488i) q^{29} +(-0.169604 - 1.72373i) q^{30} +(6.21752 + 6.21752i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.875047 + 8.89332i) q^{33} +4.22417 q^{34} +(1.29181 + 1.29181i) q^{35} +(0.584702 + 2.94247i) q^{36} +(0.159948 + 6.08066i) q^{37} -4.14267i q^{38} +(-6.00028 - 4.92527i) q^{39} +1.00000i q^{40} -0.816209 q^{41} +(-2.44582 - 2.00763i) q^{42} +(-2.69720 + 2.69720i) q^{43} -5.15936i q^{44} +(-2.49409 - 1.66719i) q^{45} -5.21815 q^{46} +6.46196i q^{47} +(-0.169604 - 1.72373i) q^{48} -3.66246 q^{49} +(-0.707107 - 0.707107i) q^{50} +(4.64208 - 5.65527i) q^{51} +(3.16917 + 3.16917i) q^{52} +12.1785i q^{53} +(4.58189 + 2.45078i) q^{54} +(3.64822 + 3.64822i) q^{55} +(1.29181 + 1.29181i) q^{56} +(-5.54615 - 4.55251i) q^{57} +6.92241i q^{58} +(-0.207760 - 0.207760i) q^{59} +(1.33879 + 1.09893i) q^{60} +(-8.45738 - 8.45738i) q^{61} -8.79291 q^{62} +(-5.37558 + 1.06819i) q^{63} +1.00000i q^{64} -4.48188 q^{65} +(-6.90728 - 5.66978i) q^{66} +12.0378i q^{67} +(-2.98694 + 2.98694i) q^{68} +(-5.73439 + 6.98599i) q^{69} -1.82689 q^{70} -11.3303i q^{71} +(-2.49409 - 1.66719i) q^{72} -10.9001i q^{73} +(-4.41278 - 4.18658i) q^{74} +(-1.72373 + 0.169604i) q^{75} +(2.92931 + 2.92931i) q^{76} +9.42559 q^{77} +(7.72553 - 0.760144i) q^{78} +(5.32048 - 5.32048i) q^{79} +(-0.707107 - 0.707107i) q^{80} +(8.31625 - 3.44093i) q^{81} +(0.577147 - 0.577147i) q^{82} -14.3723i q^{83} +(3.14906 - 0.309848i) q^{84} -4.22417i q^{85} -3.81442i q^{86} +(9.26763 + 7.60725i) q^{87} +(3.64822 + 3.64822i) q^{88} +(-6.37672 + 6.37672i) q^{89} +(2.94247 - 0.584702i) q^{90} +(-5.78973 + 5.78973i) q^{91} +(3.68979 - 3.68979i) q^{92} +(-9.66280 + 11.7718i) q^{93} +(-4.56930 - 4.56930i) q^{94} -4.14267 q^{95} +(1.33879 + 1.09893i) q^{96} +(-8.32365 + 8.32365i) q^{97} +(2.58975 - 2.58975i) q^{98} +(-15.1812 + 3.01668i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{7} - 8 q^{9}+O(q^{10}) \) 40 * q + 24 * q^7 - 8 * q^9	\( 40 q + 24 q^{7} - 8 q^{9} - 40 q^{10} + 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 16 q^{22} - 8 q^{31} + 24 q^{33} + 24 q^{34} + 32 q^{37} + 16 q^{39} + 12 q^{42} + 32 q^{43} + 8 q^{45} - 56 q^{46} - 32 q^{49} - 44 q^{51} - 16 q^{52} - 24 q^{54} + 16 q^{55} + 8 q^{57} - 72 q^{61} + 24 q^{63} - 28 q^{66} + 16 q^{69} - 24 q^{70} + 8 q^{72} - 16 q^{76} - 48 q^{79} + 120 q^{81} - 24 q^{82} - 24 q^{84} + 20 q^{87} + 16 q^{88} + 8 q^{90} - 92 q^{93} - 8 q^{94} - 40 q^{97}+O(q^{100}) \) 40 * q + 24 * q^7 - 8 * q^9 - 40 * q^10 + 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 16 * q^22 - 8 * q^31 + 24 * q^33 + 24 * q^34 + 32 * q^37 + 16 * q^39 + 12 * q^42 + 32 * q^43 + 8 * q^45 - 56 * q^46 - 32 * q^49 - 44 * q^51 - 16 * q^52 - 24 * q^54 + 16 * q^55 + 8 * q^57 - 72 * q^61 + 24 * q^63 - 28 * q^66 + 16 * q^69 - 24 * q^70 + 8 * q^72 - 16 * q^76 - 48 * q^79 + 120 * q^81 - 24 * q^82 - 24 * q^84 + 20 * q^87 + 16 * q^88 + 8 * q^90 - 92 * q^93 - 8 * q^94 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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