LMFDB - Embedded newform 675.2.ba.b.443.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(32,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("675.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.ba (of order $36$, degree $12$, 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			443.4
Character	$\chi$	$=$	675.443
Dual form			675.2.ba.b.32.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.153697 - 1.75676i) q^{2} +(-1.70488 - 0.305576i) q^{3} +(-1.09297 + 0.192720i) q^{4} +(-0.274789 + 3.04204i) q^{6} +(1.93217 + 2.75943i) q^{7} +(-0.406292 - 1.51630i) q^{8} +(2.81325 + 1.04194i) q^{9} +O(q^{10})$	\(q+(-0.153697 - 1.75676i) q^{2} +(-1.70488 - 0.305576i) q^{3} +(-1.09297 + 0.192720i) q^{4} +(-0.274789 + 3.04204i) q^{6} +(1.93217 + 2.75943i) q^{7} +(-0.406292 - 1.51630i) q^{8} +(2.81325 + 1.04194i) q^{9} +(-1.11880 - 3.07388i) q^{11} +(1.92227 + 0.00542048i) q^{12} +(-5.79013 - 0.506571i) q^{13} +(4.55068 - 3.81848i) q^{14} +(-4.68713 + 1.70598i) q^{16} +(-0.298295 + 1.11325i) q^{17} +(1.39806 - 5.10234i) q^{18} +(-6.40749 - 3.69937i) q^{19} +(-2.45091 - 5.29492i) q^{21} +(-5.22812 + 2.43791i) q^{22} +(-1.56820 - 1.09807i) q^{23} +(0.229334 + 2.70927i) q^{24} +10.2497i q^{26} +(-4.47786 - 2.63605i) q^{27} +(-2.64360 - 2.64360i) q^{28} +(-0.381851 - 0.320411i) q^{29} +(0.573116 + 3.25030i) q^{31} +(2.39054 + 5.12653i) q^{32} +(0.968121 + 5.58249i) q^{33} +(2.00157 + 0.352930i) q^{34} +(-3.27559 - 0.596642i) q^{36} +(-4.40348 - 1.17991i) q^{37} +(-5.51409 + 11.8250i) q^{38} +(9.71669 + 2.63297i) q^{39} +(-1.39279 - 1.65986i) q^{41} +(-8.92522 + 5.11947i) q^{42} +(3.62184 + 1.68889i) q^{43} +(1.81521 + 3.14404i) q^{44} +(-1.68801 + 2.92372i) q^{46} +(4.06724 - 2.84791i) q^{47} +(8.51231 - 1.47621i) q^{48} +(-1.48701 + 4.08553i) q^{49} +(0.848742 - 1.80681i) q^{51} +(6.42605 - 0.562207i) q^{52} +(1.25033 - 1.25033i) q^{53} +(-3.94268 + 8.27168i) q^{54} +(3.39910 - 4.05089i) q^{56} +(9.79358 + 8.26496i) q^{57} +(-0.504196 + 0.720066i) q^{58} +(-9.92422 - 3.61212i) q^{59} +(-1.82504 + 10.3503i) q^{61} +(5.62192 - 1.50639i) q^{62} +(2.56051 + 9.77616i) q^{63} +(-0.000691655 + 0.000399327i) q^{64} +(9.65830 - 2.55877i) q^{66} +(0.509729 - 5.82623i) q^{67} +(0.111481 - 1.27424i) q^{68} +(2.33806 + 2.35128i) q^{69} +(-6.62671 + 3.82593i) q^{71} +(0.436900 - 4.68906i) q^{72} +(-6.89704 + 1.84806i) q^{73} +(-1.39602 + 7.91721i) q^{74} +(7.71612 + 2.80844i) q^{76} +(6.32044 - 9.02653i) q^{77} +(3.13207 - 17.4746i) q^{78} +(5.08874 - 6.06452i) q^{79} +(6.82871 + 5.86248i) q^{81} +(-2.70191 + 2.70191i) q^{82} +(6.22270 - 0.544416i) q^{83} +(3.69920 + 5.31485i) q^{84} +(2.41031 - 6.62228i) q^{86} +(0.553100 + 0.662947i) q^{87} +(-4.20637 + 2.94533i) q^{88} +(-0.260380 + 0.450992i) q^{89} +(-9.78968 - 16.9562i) q^{91} +(1.92562 + 0.897929i) q^{92} +(0.0161196 - 5.71652i) q^{93} +(-5.62822 - 6.70745i) q^{94} +(-2.50905 - 9.47063i) q^{96} +(-1.99563 + 4.27963i) q^{97} +(7.40585 + 1.98439i) q^{98} +(0.0553442 - 9.81332i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8}+O(q^{10}) $ 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8	$ 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31} + 48 q^{32} + 6 q^{33} + 12 q^{36} + 6 q^{37} - 12 q^{38} + 24 q^{41} + 24 q^{42} + 12 q^{43} - 12 q^{46} + 6 q^{47} - 12 q^{48} + 144 q^{51} - 12 q^{52} + 180 q^{56} + 12 q^{57} + 12 q^{58} - 60 q^{61} + 18 q^{62} + 54 q^{63} + 72 q^{66} - 24 q^{67} + 60 q^{68} - 36 q^{71} - 180 q^{72} + 6 q^{73} - 72 q^{76} - 132 q^{77} - 78 q^{78} + 12 q^{81} + 24 q^{82} - 48 q^{83} + 12 q^{86} - 144 q^{87} + 48 q^{88} - 12 q^{91} - 258 q^{92} - 180 q^{93} - 12 q^{96} - 24 q^{97} - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.153697	−	1.75676i	−0.108680	−	1.24222i	−0.833203	−	0.552967i	$-0.813496\pi$
$2$	−0.153697	−	1.75676i	−0.108680	−	1.24222i	0.724523	−	0.689250i	$-0.242060\pi$
$3$	−1.70488	−	0.305576i	−0.984314	−	0.176424i
$3$	−1.70488	−	0.305576i	−0.984314	−	0.176424i
$4$	−1.09297	+	0.192720i	−0.546484	+	0.0963599i
$5$		0			0
$5$		0			0
$6$	−0.274789	+	3.04204i	−0.112182	+	1.24191i
$7$	1.93217	+	2.75943i	0.730292	+	1.04297i	0.996863	+	0.0791502i	$0.0252207\pi$
$7$	1.93217	+	2.75943i	0.730292	+	1.04297i	−0.266570	+	0.963815i	$0.585890\pi$
$8$	−0.406292	−	1.51630i	−0.143646	−	0.536093i
$9$	2.81325	+	1.04194i	0.937749	+	0.347314i
$10$		0			0
$11$	−1.11880	−	3.07388i	−0.337332	−	0.926811i	−0.986148	−	0.165866i	$-0.946958\pi$
$11$	−1.11880	−	3.07388i	−0.337332	−	0.926811i	0.648817	−	0.760945i	$-0.275264\pi$
$12$	1.92227	+	0.00542048i	0.554912	+	0.00156476i
$13$	−5.79013	−	0.506571i	−1.60589	−	0.140497i	−0.751359	−	0.659893i	$-0.770601\pi$
$13$	−5.79013	−	0.506571i	−1.60589	−	0.140497i	−0.854534	+	0.519396i	$0.826157\pi$
$14$	4.55068	−	3.81848i	1.21622	−	1.02053i
$15$		0			0
$16$	−4.68713	+	1.70598i	−1.17178	+	0.426494i
$17$	−0.298295	+	1.11325i	−0.0723472	+	0.270003i	−0.992619	−	0.121277i	$-0.961301\pi$
$17$	−0.298295	+	1.11325i	−0.0723472	+	0.270003i	0.920271	+	0.391280i	$0.127968\pi$
$18$	1.39806	−	5.10234i	0.329525	−	1.20263i
$19$	−6.40749	−	3.69937i	−1.46998	−	0.848693i	−0.470546	−	0.882375i	$-0.655943\pi$
$19$	−6.40749	−	3.69937i	−1.46998	−	0.848693i	−0.999433	+	0.0336827i	$0.989276\pi$
$20$		0			0
$21$	−2.45091	−	5.29492i	−0.534833	−	1.15545i
$22$	−5.22812	+	2.43791i	−1.11464	+	0.519765i
$23$	−1.56820	−	1.09807i	−0.326993	−	0.228963i	0.398539	−	0.917151i	$-0.369517\pi$
$23$	−1.56820	−	1.09807i	−0.326993	−	0.228963i	−0.725532	+	0.688189i	$0.758406\pi$
$24$	0.229334	+	2.70927i	0.0468126	+	0.553027i
$25$		0			0
$26$			10.2497i			2.01014i
$27$	−4.47786	−	2.63605i	−0.861765	−	0.507308i
$28$	−2.64360	−	2.64360i	−0.499593	−	0.499593i
$29$	−0.381851	−	0.320411i	−0.0709079	−	0.0594988i	0.606645	−	0.794973i	$-0.292515\pi$
$29$	−0.381851	−	0.320411i	−0.0709079	−	0.0594988i	−0.677553	+	0.735474i	$0.736959\pi$
$30$		0			0
$31$	0.573116	+	3.25030i	0.102935	+	0.583772i	0.992025	+	0.126040i	$0.0402269\pi$
$31$	0.573116	+	3.25030i	0.102935	+	0.583772i	−0.889090	+	0.457732i	$0.848662\pi$
$32$	2.39054	+	5.12653i	0.422592	+	0.906251i
$33$	0.968121	+	5.58249i	0.168528	+	0.971787i
$34$	2.00157	+	0.352930i	0.343266	+	0.0605270i
$35$		0			0
$36$	−3.27559	−	0.596642i	−0.545932	−	0.0994403i
$37$	−4.40348	−	1.17991i	−0.723928	−	0.193976i	−0.122004	−	0.992530i	$-0.538932\pi$
$37$	−4.40348	−	1.17991i	−0.723928	−	0.193976i	−0.601924	+	0.798554i	$0.705599\pi$
$38$	−5.51409	+	11.8250i	−0.894503	+	1.91827i
$39$	9.71669	+	2.63297i	1.55592	+	0.421612i
$40$		0			0
$41$	−1.39279	−	1.65986i	−0.217517	−	0.259226i	0.646241	−	0.763133i	$-0.276340\pi$
$41$	−1.39279	−	1.65986i	−0.217517	−	0.259226i	−0.863758	+	0.503907i	$0.831895\pi$
$42$	−8.92522	+	5.11947i	−1.37719	+	0.789952i
$43$	3.62184	+	1.68889i	0.552325	+	0.257554i	0.678683	−	0.734431i	$-0.262551\pi$
$43$	3.62184	+	1.68889i	0.552325	+	0.257554i	−0.126358	+	0.991985i	$0.540329\pi$
$44$	1.81521	+	3.14404i	0.273654	+	0.473982i
$45$		0			0
$46$	−1.68801	+	2.92372i	−0.248884	+	0.431080i
$47$	4.06724	−	2.84791i	0.593268	−	0.415410i	−0.238014	−	0.971262i	$-0.576496\pi$
$47$	4.06724	−	2.84791i	0.593268	−	0.415410i	0.831282	+	0.555851i	$0.187608\pi$
$48$	8.51231	−	1.47621i	1.22865	−	0.213073i
$49$	−1.48701	+	4.08553i	−0.212430	+	0.583647i
$50$		0			0
$51$	0.848742	−	1.80681i	0.118848	−	0.253004i
$52$	6.42605	−	0.562207i	0.891133	−	0.0779641i
$53$	1.25033	−	1.25033i	0.171746	−	0.171746i	−0.616000	−	0.787746i	$-0.711248\pi$
$53$	1.25033	−	1.25033i	0.171746	−	0.171746i	0.787746	+	0.616000i	$0.211248\pi$
$54$	−3.94268	+	8.27168i	−0.536530	+	1.12563i
$55$		0			0
$56$	3.39910	−	4.05089i	0.454223	−	0.541322i
$57$	9.79358	+	8.26496i	1.29719	+	1.09472i
$58$	−0.504196	+	0.720066i	−0.0662041	+	0.0945493i
$59$	−9.92422	−	3.61212i	−1.29202	−	0.470258i	−0.397633	−	0.917545i	$-0.630168\pi$
$59$	−9.92422	−	3.61212i	−1.29202	−	0.470258i	−0.894391	+	0.447286i	$0.852391\pi$
$60$		0			0
$61$	−1.82504	+	10.3503i	−0.233672	+	1.32522i	0.611720	+	0.791074i	$0.290478\pi$
$61$	−1.82504	+	10.3503i	−0.233672	+	1.32522i	−0.845392	+	0.534146i	$0.820633\pi$
$62$	5.62192	−	1.50639i	0.713985	−	0.191312i
$63$	2.56051	+	9.77616i	0.322594	+	1.23168i
$64$	−0.000691655	0	0.000399327i	−8.64569e−5	0	4.99159e-5i
$65$		0			0
$66$	9.65830	−	2.55877i	1.18885	−	0.314962i
$67$	0.509729	−	5.82623i	0.0622733	−	0.711787i	−0.899317	−	0.437298i	$-0.855936\pi$
$67$	0.509729	−	5.82623i	0.0622733	−	0.711787i	0.961590	−	0.274490i	$-0.0885089\pi$
$68$	0.111481	−	1.27424i	0.0135191	−	0.154524i
$69$	2.33806	+	2.35128i	0.281469	+	0.283061i
$70$		0			0
$71$	−6.62671	+	3.82593i	−0.786446	+	0.454055i	−0.838710	−	0.544579i	$-0.816690\pi$
$71$	−6.62671	+	3.82593i	−0.786446	+	0.454055i	0.0522640	+	0.998633i	$0.483356\pi$
$72$	0.436900	−	4.68906i	0.0514892	−	0.552611i
$73$	−6.89704	+	1.84806i	−0.807238	+	0.216299i	−0.638759	−	0.769407i	$-0.720552\pi$
$73$	−6.89704	+	1.84806i	−0.807238	+	0.216299i	−0.168478	+	0.985705i	$0.553885\pi$
$74$	−1.39602	+	7.91721i	−0.162284	+	0.920357i
$75$		0			0
$76$	7.71612	+	2.80844i	0.885100	+	0.322150i
$77$	6.32044	−	9.02653i	0.720281	−	1.02867i
$78$	3.13207	−	17.4746i	0.354637	−	1.97861i
$79$	5.08874	−	6.06452i	0.572528	−	0.682312i	−0.399620	−	0.916681i	$-0.630858\pi$
$79$	5.08874	−	6.06452i	0.572528	−	0.682312i	0.972148	+	0.234369i	$0.0753024\pi$
$80$		0			0
$81$	6.82871	+	5.86248i	0.758746	+	0.651387i
$82$	−2.70191	+	2.70191i	−0.298375	+	0.298375i
$83$	6.22270	−	0.544416i	0.683031	−	0.0597574i	0.259641	−	0.965705i	$-0.416396\pi$
$83$	6.22270	−	0.544416i	0.683031	−	0.0597574i	0.423389	+	0.905948i	$0.360840\pi$
$84$	3.69920	+	5.31485i	0.403616	+	0.579897i
$85$		0			0
$86$	2.41031	−	6.62228i	0.259911	−	0.714099i
$87$	0.553100	+	0.662947i	0.0592986	+	0.0710754i
$88$	−4.20637	+	2.94533i	−0.448401	+	0.313974i
$89$	−0.260380	+	0.450992i	−0.0276002	+	0.0478050i	−0.879496	−	0.475907i	$-0.842120\pi$
$89$	−0.260380	+	0.450992i	−0.0276002	+	0.0478050i	0.851895	+	0.523712i	$0.175453\pi$
$90$		0			0
$91$	−9.78968	−	16.9562i	−1.02624	−	1.77750i
$92$	1.92562	+	0.897929i	0.200759	+	0.0936156i
$93$	0.0161196	−	5.71652i	0.00167153	−	0.592775i
$94$	−5.62822	−	6.70745i	−0.580506	−	0.691820i
$95$		0			0
$96$	−2.50905	−	9.47063i	−0.256078	−	0.966592i
$97$	−1.99563	+	4.27963i	−0.202625	+	0.434531i	−0.981193	−	0.193029i	$-0.938169\pi$
$97$	−1.99563	+	4.27963i	−0.202625	+	0.434531i	0.778568	+	0.627560i	$0.215946\pi$
$98$	7.40585	+	1.98439i	0.748103	+	0.200454i
$99$	0.0553442	−	9.81332i	0.00556230	−	0.986276i
$100$		0			0
$101$	−6.92843	−	1.22167i	−0.689404	−	0.121561i	−0.182038	−	0.983291i	$-0.558270\pi$
$101$	−6.92843	−	1.22167i	−0.689404	−	0.121561i	−0.507366	+	0.861731i	$0.669381\pi$
$102$	−3.30459	−	1.21333i	−0.327203	−	0.120138i
$103$	−2.95859	−	6.34471i	−0.291518	−	0.625163i	0.704938	−	0.709268i	$-0.250975\pi$
$103$	−2.95859	−	6.34471i	−0.291518	−	0.625163i	−0.996457	+	0.0841052i	$0.973197\pi$
$104$	1.58437	+	8.98539i	0.155360	+	0.881090i
$105$		0			0
$106$	−2.38870	−	2.00436i	−0.232011	−	0.194680i
$107$	−3.17818	−	3.17818i	−0.307247	−	0.307247i	0.536594	−	0.843841i	$-0.319711\pi$
$107$	−3.17818	−	3.17818i	−0.307247	−	0.307247i	−0.843841	+	0.536594i	$0.819711\pi$
$108$	5.40218	+	2.01815i	0.519825	+	0.194196i
$109$			3.14715i			0.301442i	0.988576	+	0.150721i	$0.0481595\pi$
$109$			3.14715i			0.301442i	−0.988576	+	0.150721i	$0.951840\pi$
$110$		0			0
$111$	7.14687	+	3.35721i	0.678351	+	0.318652i
$112$	−13.7639	−	9.63755i	−1.30056	−	0.910663i
$113$	0.408788	−	0.190621i	0.0384556	−	0.0179321i	−0.403295	−	0.915070i	$-0.632135\pi$
$113$	0.408788	−	0.190621i	0.0384556	−	0.0179321i	0.441751	+	0.897138i	$0.354357\pi$
$114$	13.0143	−	18.4753i	1.21890	−	1.73037i
$115$		0			0
$116$	0.479100	+	0.276609i	0.0444833	+	0.0256825i
$117$	−15.7612	−	7.45809i	−1.45713	−	0.689501i
$118$	−4.82031	+	17.9897i	−0.443746	+	1.65608i
$119$	−3.64830	+	1.32787i	−0.334439	+	0.121726i
$120$		0			0
$121$	0.229444	−	0.192526i	0.0208585	−	0.0175024i
$122$	18.4635	+	1.61535i	1.67161	+	0.146247i
$123$	1.86732	+	3.25546i	0.168371	+	0.293535i
$124$	−1.25280	−	3.44203i	−0.112504	−	0.309103i
$125$		0			0
$126$	16.7808	−	6.00077i	1.49496	−	0.534591i
$127$	0.143092	+	0.534026i	0.0126973	+	0.0473871i	0.971984	−	0.235048i	$-0.0755246\pi$
$127$	0.143092	+	0.534026i	0.0126973	+	0.0473871i	−0.959287	+	0.282435i	$0.908858\pi$
$128$	6.48968	+	9.26822i	0.573612	+	0.819203i
$129$	−5.65873	−	3.98611i	−0.498223	−	0.350957i
$130$		0			0
$131$	14.1236	−	2.49037i	1.23398	−	0.217585i	0.481648	−	0.876365i	$-0.340038\pi$
$131$	14.1236	−	2.49037i	1.23398	−	0.217585i	0.752336	+	0.658780i	$0.228927\pi$
$132$	−2.13398	−	5.91491i	−0.185739	−	0.514827i
$133$	−2.17224	−	24.8288i	−0.188357	−	2.15293i
$134$	−10.3136			−0.890962
$135$		0			0
$136$	1.80922			0.155139
$137$	0.295060	+	3.37255i	0.0252087	+	0.288136i	0.998327	+	0.0578286i	$0.0184177\pi$
$137$	0.295060	+	3.37255i	0.0252087	+	0.288136i	−0.973118	+	0.230308i	$0.926027\pi$
$138$	3.77128	−	4.46879i	0.321033	−	0.380409i
$139$	−5.42140	+	0.955940i	−0.459837	+	0.0810818i	−0.398768	−	0.917052i	$-0.630562\pi$
$139$	−5.42140	+	0.955940i	−0.459837	+	0.0810818i	−0.0610693	+	0.998134i	$0.519451\pi$
$140$		0			0
$141$	−7.80442	+	3.61250i	−0.657250	+	0.304227i
$142$	7.73975	+	11.0535i	0.649505	+	0.927590i
$143$	4.92087	+	18.3649i	0.411504	+	1.53575i
$144$	−14.9636	−	0.0843901i	−1.24696	−	0.00703251i
$145$		0			0
$146$	4.30665	+	11.8324i	0.356420	+	0.979257i
$147$	3.78362	−	6.51095i	0.312068	−	0.537014i
$148$	5.04026	+	0.440966i	0.414307	+	0.0362472i
$149$	10.1897	−	8.55016i	0.834771	−	0.700456i	−0.121610	−	0.992578i	$-0.538806\pi$
$149$	10.1897	−	8.55016i	0.834771	−	0.700456i	0.956381	+	0.292122i	$0.0943613\pi$
$150$		0			0
$151$	13.7660	−	5.01040i	1.12026	−	0.407741i	0.285512	−	0.958375i	$-0.407836\pi$
$151$	13.7660	−	5.01040i	1.12026	−	0.407741i	0.834747	+	0.550634i	$0.185614\pi$
$152$	−3.00604	+	11.2187i	−0.243822	+	0.909957i
$153$	−1.99912	+	2.82105i	−0.161620	+	0.228068i
$154$	−16.8289	−	9.71616i	−1.35611	−	0.782950i
$155$		0			0
$156$	−11.1275	−	1.00515i	−0.890910	−	0.0804766i
$157$	5.03036	−	2.34570i	0.401467	−	0.187207i	−0.211389	−	0.977402i	$-0.567799\pi$
$157$	5.03036	−	2.34570i	0.401467	−	0.187207i	0.612855	+	0.790195i	$0.290021\pi$
$158$	−11.4360	−	8.00759i	−0.909802	−	0.637050i
$159$	−2.51373	+	1.74959i	−0.199352	+	0.138752i
$160$		0			0
$161$		−	6.44900i		−	0.508252i
$162$	9.24943	−	12.8975i	0.726704	−	1.01332i
$163$	−5.06235	−	5.06235i	−0.396514	−	0.396514i	0.480488	−	0.877002i	$-0.340460\pi$
$163$	−5.06235	−	5.06235i	−0.396514	−	0.396514i	−0.877002	+	0.480488i	$0.840460\pi$
$164$	1.84216	+	1.54575i	0.143848	+	0.120703i
$165$		0			0
$166$	−1.91282	−	10.8481i	−0.148463	−	0.841978i
$167$	−5.92432	−	12.7047i	−0.458438	−	0.983123i	−0.990639	−	0.136505i	$-0.956413\pi$
$167$	−5.92432	−	12.7047i	−0.458438	−	0.983123i	0.532202	−	0.846618i	$-0.321365\pi$
$168$	−7.03291	+	5.86760i	−0.542601	+	0.452695i
$169$	20.4665	+	3.60879i	1.57434	+	0.277599i
$170$		0			0
$171$	−14.1713	−	17.0835i	−1.08371	−	1.30641i
$172$	−4.28404	−	1.14791i	−0.326655	−	0.0875269i
$173$	4.13731	−	8.87248i	0.314554	−	0.674563i	−0.683934	−	0.729544i	$-0.739732\pi$
$173$	4.13731	−	8.87248i	0.314554	−	0.674563i	0.998487	+	0.0549816i	$0.0175100\pi$
$174$	1.07963	−	1.07356i	0.0818465	−	0.0813862i
$175$		0			0
$176$	10.4879	+	12.4990i	0.790558	+	0.942151i
$177$	15.8159	+	9.19085i	1.18879	+	0.690827i
$178$	0.832304	+	0.388110i	0.0623838	+	0.0290900i
$179$	−5.82103	−	10.0823i	−0.435084	−	0.753588i	0.562218	−	0.826989i	$-0.309948\pi$
$179$	−5.82103	−	10.0823i	−0.435084	−	0.753588i	−0.997303	+	0.0734009i	$0.976615\pi$
$180$		0			0
$181$	−10.5182	+	18.2180i	−0.781810	+	1.35413i	0.149076	+	0.988826i	$0.452370\pi$
$181$	−10.5182	+	18.2180i	−0.781810	+	1.35413i	−0.930886	+	0.365309i	$0.880963\pi$
$182$	−28.2834	+	19.8042i	−2.09650	+	1.46799i
$183$	6.27428	−	17.0884i	0.463808	−	1.26321i
$184$	−1.02785	+	2.82400i	−0.0757743	+	0.208188i
$185$		0			0
$186$	−10.0450	+	0.850291i	−0.736537	+	0.0623464i
$187$	3.75574	−	0.328585i	0.274647	−	0.0240285i
$188$	−3.89651	+	3.89651i	−0.284182	+	0.284182i
$189$	−1.37801	−	17.4496i	−0.100235	−	1.26927i
$190$		0			0
$191$	16.1454	−	19.2414i	1.16824	−	1.39226i	0.264388	−	0.964416i	$-0.414830\pi$
$191$	16.1454	−	19.2414i	1.16824	−	1.39226i	0.903854	−	0.427841i	$-0.140726\pi$
$192$	0.00130122		0.000469453i	9.39072e−5		3.38798e-5i
$193$	−2.29216	+	3.27354i	−0.164993	+	0.235635i	−0.893132	−	0.449795i	$-0.851497\pi$
$193$	−2.29216	+	3.27354i	−0.164993	+	0.235635i	0.728138	+	0.685430i	$0.240386\pi$
$194$	7.82501	+	2.84807i	0.561803	+	0.204480i
$195$		0			0
$196$	0.837894	−	4.75193i	0.0598496	−	0.339424i
$197$	−10.0136	+	2.68314i	−0.713441	+	0.191166i	−0.597243	−	0.802060i	$-0.703737\pi$
$197$	−10.0136	+	2.68314i	−0.713441	+	0.191166i	−0.116198	+	0.993226i	$0.537071\pi$
$198$	−17.2482	+	1.41105i	−1.22577	+	0.100279i
$199$	10.6933	−	6.17378i	0.758027	−	0.437647i	−0.0705597	−	0.997508i	$-0.522479\pi$
$199$	10.6933	−	6.17378i	0.758027	−	0.437647i	0.828587	+	0.559860i	$0.189145\pi$
$200$		0			0
$201$	−2.64938	+	9.77727i	−0.186873	+	0.689636i
$202$	−1.08130	+	12.3593i	−0.0760802	+	0.869601i
$203$	0.146349	−	1.67278i	0.0102717	−	0.117406i
$204$	−0.579439	+	2.13836i	−0.0405689	+	0.149715i
$205$		0			0
$206$	−10.6914	+	6.17269i	−0.744906	+	0.430072i
$207$	−3.26762	−	4.72311i	−0.227115	−	0.328279i
$208$	28.0033	−	7.50345i	1.94168	−	0.520271i
$209$	−4.20271	+	23.8347i	−0.290707	+	1.64868i
$210$		0			0
$211$	8.83540	+	3.21582i	0.608254	+	0.221386i	0.627739	−	0.778424i	$-0.283980\pi$
$211$	8.83540	+	3.21582i	0.608254	+	0.221386i	−0.0194850	+	0.999810i	$0.506203\pi$
$212$	−1.12561	+	1.60753i	−0.0773070	+	0.110406i
$213$	12.4669	−	4.49780i	0.854216	−	0.308184i
$214$	−5.09483	+	6.07178i	−0.348275	+	0.415058i
$215$		0			0
$216$	−2.17773	+	7.86079i	−0.148176	+	0.534859i
$217$	−7.86162	+	7.86162i	−0.533682	+	0.533682i
$218$	5.52878	−	0.483706i	0.374456	−	0.0327607i
$219$	12.3234	−	1.04315i	0.832736	−	0.0704894i
$220$		0			0
$221$	2.29111	−	6.29477i	0.154117	−	0.423432i
$222$	4.79936	−	13.0713i	0.322112	−	0.877290i
$223$	11.5379	−	8.07893i	0.772635	−	0.541005i	−0.119467	−	0.992838i	$-0.538119\pi$
$223$	11.5379	−	8.07893i	0.772635	−	0.541005i	0.892102	+	0.451833i	$0.149230\pi$
$224$	−9.52736	+	16.5019i	−0.636573	+	1.10258i
$225$		0			0
$226$	−0.397705	−	0.688845i	−0.0264549	−	0.0458213i
$227$	−23.9686	−	11.1767i	−1.59085	−	0.741825i	−0.592866	−	0.805301i	$-0.702004\pi$
$227$	−23.9686	−	11.1767i	−1.59085	−	0.741825i	−0.997983	+	0.0634761i	$0.979781\pi$
$228$	−12.2969	−	7.14592i	−0.814382	−	0.473250i
$229$	6.42008	+	7.65115i	0.424251	+	0.505602i	0.935254	−	0.353976i	$-0.115171\pi$
$229$	6.42008	+	7.65115i	0.424251	+	0.505602i	−0.511004	+	0.859579i	$0.670726\pi$
$230$		0			0
$231$	−13.5339	+	13.4578i	−0.890465	+	0.885458i
$232$	−0.330696	+	0.709181i	−0.0217113	+	0.0465600i
$233$	−26.1766	−	7.01401i	−1.71489	−	0.459503i	−0.738274	−	0.674500i	$-0.764359\pi$
$233$	−26.1766	−	7.01401i	−1.71489	−	0.459503i	−0.976615	+	0.214997i	$0.931026\pi$
$234$	−10.6796	+	28.8350i	−0.698149	+	1.88500i
$235$		0			0
$236$	11.5430	+	2.03534i	0.751385	+	0.132489i
$237$	−10.5289	+	8.78430i	−0.683924	+	0.570601i
$238$	2.89348	+	6.20510i	0.187557	+	0.402217i
$239$	−4.31982	−	24.4989i	−0.279426	−	1.58470i	−0.724543	−	0.689230i	$-0.757949\pi$
$239$	−4.31982	−	24.4989i	−0.279426	−	1.58470i	0.445117	−	0.895472i	$-0.353162\pi$
$240$		0			0
$241$	−21.8499	−	18.3342i	−1.40747	−	1.18101i	−0.957665	−	0.287885i	$-0.907048\pi$
$241$	−21.8499	−	18.3342i	−1.40747	−	1.18101i	−0.449808	−	0.893125i	$-0.648508\pi$
$242$	−0.373487	−	0.373487i	−0.0240087	−	0.0240087i
$243$	−9.85071	−	12.0815i	−0.631924	−	0.775031i
$244$		−	11.6643i		−	0.746728i
$245$		0			0
$246$	5.43207	−	3.78079i	0.346336	−	0.241054i
$247$	35.2262	+	24.6656i	2.24139	+	1.56944i
$248$	4.69559	−	2.18959i	0.298170	−	0.139039i
$249$	−10.7753	−	0.973345i	−0.682859	−	0.0616832i
$250$		0			0
$251$	9.61601	+	5.55181i	0.606957	+	0.350427i	0.771774	−	0.635897i	$-0.219370\pi$
$251$	9.61601	+	5.55181i	0.606957	+	0.350427i	−0.164816	+	0.986324i	$0.552703\pi$
$252$	−4.68262	−	10.1916i	−0.294977	−	0.642009i
$253$	−1.62082	+	6.04899i	−0.101900	+	0.380297i
$254$	0.916163	−	0.333456i	0.0574852	−	0.0209229i
$255$		0			0
$256$	15.2834	−	12.8243i	0.955211	−	0.801518i
$257$	28.1062	+	2.45897i	1.75321	+	0.153386i	0.918011	−	0.396555i	$-0.129794\pi$
$257$	28.1062	+	2.45897i	1.75321	+	0.153386i	0.835203	+	0.549941i	$0.185350\pi$
$258$	−6.13291	+	10.5537i	−0.381818	+	0.657043i
$259$	−5.25241	−	14.4309i	−0.326369	−	0.896691i
$260$		0			0
$261$	−0.740390	−	1.29926i	−0.0458290	−	0.0804222i
$262$	−6.54573	−	24.4290i	−0.404397	−	1.50923i
$263$	−1.41742	−	2.02429i	−0.0874019	−	0.124823i	0.773070	−	0.634321i	$-0.218720\pi$
$263$	−1.41742	−	2.02429i	−0.0874019	−	0.124823i	−0.860472	+	0.509498i	$0.829831\pi$
$264$	8.07139	−	3.73608i	0.496760	−	0.229940i
$265$		0			0
$266$	−43.2844	+	7.63221i	−2.65394	+	0.467961i
$267$	0.581730	−	0.689321i	0.0356013	−	0.0421858i
$268$	0.565712	+	6.46612i	0.0345564	+	0.394981i
$269$	−2.07465			−0.126494			−0.0632468	−	0.997998i	$-0.520146\pi$
$269$	−2.07465			−0.126494			−0.0632468	+	0.997998i	$0.520146\pi$
$270$		0			0
$271$	−18.0921			−1.09901			−0.549507	−	0.835489i	$-0.685184\pi$
$271$	−18.0921			−1.09901			−0.549507	+	0.835489i	$0.685184\pi$
$272$	−0.501034	−	5.72684i	−0.0303796	−	0.347241i
$273$	11.5088	+	31.8999i	0.696546	+	1.93067i
$274$	5.87941	−	1.03670i	0.355188	−	0.0626293i
$275$		0			0
$276$	−3.00856	−	2.11929i	−0.181094	−	0.127566i
$277$	14.7543	+	21.0713i	0.886497	+	1.26605i	0.963143	+	0.268991i	$0.0866901\pi$
$277$	14.7543	+	21.0713i	0.886497	+	1.26605i	−0.0766456	+	0.997058i	$0.524421\pi$
$278$	2.51261	+	9.37718i	0.150696	+	0.562406i
$279$	−1.77431	+	9.74106i	−0.106225	+	0.583182i
$280$		0			0
$281$	0.952631	+	2.61733i	0.0568292	+	0.156137i	0.964859	−	0.262769i	$-0.0846358\pi$
$281$	0.952631	+	2.61733i	0.0568292	+	0.156137i	−0.908029	+	0.418906i	$0.862414\pi$
$282$	7.54581	+	13.1553i	0.449346	+	0.783384i
$283$	−20.4164	−	1.78620i	−1.21363	−	0.106179i	−0.537694	−	0.843140i	$-0.680704\pi$
$283$	−20.4164	−	1.78620i	−1.21363	−	0.106179i	−0.675935	+	0.736962i	$0.736260\pi$
$284$	6.50545	−	5.45872i	0.386028	−	0.323916i
$285$		0			0
$286$	31.5065	−	11.4674i	1.86302	−	0.678083i
$287$	1.88915	−	7.05042i	0.111513	−	0.416173i
$288$	1.38363	+	16.9130i	0.0815311	+	0.996608i
$289$	13.5721	+	7.83584i	0.798358	+	0.460932i
$290$		0			0
$291$	4.71006	−	6.68646i	0.276109	−	0.391967i
$292$	7.18209	−	3.34907i	0.420300	−	0.195989i
$293$	25.6873	+	17.9864i	1.50067	+	1.05078i	0.980455	+	0.196743i	$0.0630364\pi$
$293$	25.6873	+	17.9864i	1.50067	+	1.05078i	0.520213	+	0.854036i	$0.325852\pi$
$294$	−12.0197	−	5.64620i	−0.701004	−	0.329293i
$295$		0			0
$296$			7.15639i			0.415957i
$297$	−3.09307	+	16.7136i	−0.179478	+	0.969824i
$298$	−16.5867	−	16.5867i	−0.960842	−	0.960842i
$299$	8.52385	+	7.15236i	0.492947	+	0.413631i
$300$		0			0
$301$	2.33764	+	13.2574i	0.134740	+	0.764146i
$302$	−10.9179	−	23.4134i	−0.628252	−	1.34729i
$303$	11.4388	+	4.19996i	0.657144	+	0.241282i
$304$	36.3437	+	6.40838i	2.08446	+	0.367546i
$305$		0			0
$306$	5.26316	+	3.07840i	0.300875	+	0.175980i
$307$	9.29823	+	2.49145i	0.530678	+	0.142195i	0.514201	−	0.857669i	$-0.328088\pi$
$307$	9.29823	+	2.49145i	0.530678	+	0.142195i	0.0164767	+	0.999864i	$0.494755\pi$
$308$	−5.16845	+	11.0838i	−0.294500	+	0.631557i
$309$	3.10525	+	11.7211i	0.176652	+	0.666788i
$310$		0			0
$311$	−0.00272616	−	0.00324891i	−0.000154586	−	0.000184229i	0.765967	−	0.642880i	$-0.222260\pi$
$311$	−0.00272616	−	0.00324891i	−0.000154586	−	0.000184229i	−0.766122	+	0.642695i	$0.777816\pi$
$312$	0.0445623	−	15.8032i	0.00252284	−	0.894679i
$313$	21.5265	+	10.0379i	1.21675	+	0.567378i	0.921625	−	0.388081i	$-0.126862\pi$
$313$	21.5265	+	10.0379i	1.21675	+	0.567378i	0.295122	+	0.955460i	$0.404640\pi$
$314$	−4.89398	−	8.47662i	−0.276183	−	0.478363i
$315$		0			0
$316$	−4.39308	+	7.60903i	−0.247130	+	0.428041i
$317$	−0.650197	+	0.455273i	−0.0365187	+	0.0255707i	−0.591693	−	0.806163i	$-0.701540\pi$
$317$	−0.650197	+	0.455273i	−0.0365187	+	0.0255707i	0.555175	+	0.831734i	$0.312651\pi$
$318$	3.45997	+	4.14712i	0.194025	+	0.232559i
$319$	−0.557690	+	1.53224i	−0.0312246	+	0.0857890i
$320$		0			0
$321$	4.44725	+	6.38960i	0.248221	+	0.356633i
$322$	−11.3293	+	0.991189i	−0.631359	+	0.0552368i
$323$	6.02965	−	6.02965i	0.335499	−	0.335499i
$324$	−8.59338	−	5.09148i	−0.477410	−	0.282860i
$325$		0			0
$326$	−8.11527	+	9.67140i	−0.449463	+	0.535649i
$327$	0.961693	−	5.36552i	0.0531817	−	0.296714i
$328$	−1.95097	+	2.78627i	−0.107724	+	0.153846i
$329$	15.7172	+	5.72060i	0.866518	+	0.315387i
$330$		0			0
$331$	−0.994980	+	5.64281i	−0.0546891	+	0.310157i	−0.999865	−	0.0164031i	$-0.994778\pi$
$331$	−0.994980	+	5.64281i	−0.0546891	+	0.310157i	0.945176	+	0.326560i	$0.105890\pi$
$332$	−6.69630	+	1.79427i	−0.367507	+	0.0984733i
$333$	−11.1587	−	7.90755i	−0.611492	−	0.433331i
$334$	−21.4086	+	12.3603i	−1.17143	+	0.676325i
$335$		0			0
$336$	20.5207	+	20.6368i	1.11950	+	1.12583i
$337$	2.22568	−	25.4396i	0.121240	−	1.38578i	−0.655135	−	0.755512i	$-0.727388\pi$
$337$	2.22568	−	25.4396i	0.121240	−	1.38578i	0.776375	−	0.630271i	$-0.217056\pi$
$338$	3.19415	−	36.5094i	0.173739	−	1.98585i
$339$	−0.755185	+	0.200071i	−0.0410160	+	0.0108663i
$340$		0			0
$341$	9.34986	−	5.39814i	0.506323	−	0.292326i
$342$	−27.8335	+	27.5213i	−1.50506	+	1.48818i
$343$	8.63010	−	2.31243i	0.465982	−	0.124859i
$344$	1.08934	−	6.17798i	0.0587335	−	0.333094i
$345$		0			0
$346$	−16.2227	−	5.90459i	−0.872139	−	0.317433i
$347$	−6.98065	+	9.96940i	−0.374741	+	0.535185i	−0.961582	−	0.274516i	$-0.911482\pi$
$347$	−6.98065	+	9.96940i	−0.374741	+	0.535185i	0.586842	+	0.809702i	$0.300371\pi$
$348$	−0.732284	−	0.617987i	−0.0392546	−	0.0331276i
$349$	0.0762364	−	0.0908550i	0.00408084	−	0.00486336i	−0.764000	−	0.645216i	$-0.776767\pi$
$349$	0.0762364	−	0.0908550i	0.00408084	−	0.00486336i	0.768081	+	0.640353i	$0.221212\pi$
$350$		0			0
$351$	24.5920	+	17.5314i	1.31263	+	0.935758i
$352$	13.0838	−	13.0838i	0.697370	−	0.697370i
$353$	−21.5499	+	1.88537i	−1.14699	+	0.100348i	−0.644758	−	0.764387i	$-0.723042\pi$
$353$	−21.5499	+	1.88537i	−1.14699	+	0.100348i	−0.502228	+	0.864735i	$0.667486\pi$
$354$	13.7153	−	29.1973i	0.728959	−	1.55182i
$355$		0			0
$356$	0.197672	−	0.543100i	0.0104766	−	0.0287842i
$357$	6.62569	−	1.14903i	0.350668	−	0.0608132i
$358$	−16.8175	+	11.7758i	−0.888835	+	0.622369i
$359$	−15.2804	+	26.4664i	−0.806468	+	1.39684i	0.108828	+	0.994061i	$0.465290\pi$
$359$	−15.2804	+	26.4664i	−0.806468	+	1.39684i	−0.915296	+	0.402782i	$0.868043\pi$
$360$		0			0
$361$	17.8706	+	30.9528i	0.940558	+	1.62910i
$362$	33.6213	+	15.6779i	1.76710	+	0.824011i
$363$	−0.450006	+	0.258122i	−0.0236192	+	0.0135479i
$364$	13.9676	+	16.6460i	0.732102	+	0.872485i
$365$		0			0
$366$	−30.9845	−	8.39598i	−1.61958	−	0.438865i
$367$	6.49863	−	13.9364i	0.339226	−	0.727472i	−0.660502	−	0.750825i	$-0.729656\pi$
$367$	6.49863	−	13.9364i	0.339226	−	0.727472i	0.999727	+	0.0233530i	$0.00743415\pi$
$368$	9.22364	+	2.47147i	0.480816	+	0.128834i
$369$	−2.18877	−	6.12079i	−0.113943	−	0.318636i
$370$		0			0
$371$	5.86604	+	1.03434i	0.304550	+	0.0537003i
$372$	1.08407	+	6.25108i	0.0562063	+	0.324103i
$373$	11.7743	+	25.2501i	0.609651	+	1.30740i	0.932575	+	0.360976i	$0.117556\pi$
$373$	11.7743	+	25.2501i	0.609651	+	1.30740i	−0.322924	+	0.946425i	$0.604666\pi$
$374$	−1.15449	−	6.54744i	−0.0596973	−	0.338560i
$375$		0			0
$376$	−5.97077	−	5.01007i	−0.307919	−	0.258375i
$377$	2.04865	+	2.04865i	0.105511	+	0.105511i
$378$	−30.4430	+	5.10278i	−1.56582	+	0.262459i
$379$			16.6622i			0.855880i	0.903807	+	0.427940i	$0.140760\pi$
$379$			16.6622i			0.855880i	−0.903807	+	0.427940i	$0.859240\pi$
$380$		0			0
$381$	−0.0807691	−	0.954176i	−0.00413793	−	0.0488839i
$382$	−36.2840	−	25.4063i	−1.85645	−	1.29990i
$383$	−28.8135	+	13.4360i	−1.47230	+	0.686546i	−0.982667	−	0.185381i	$-0.940648\pi$
$383$	−28.8135	+	13.4360i	−1.47230	+	0.686546i	−0.489636	+	0.871927i	$0.662870\pi$
$384$	−8.23199	−	17.7843i	−0.420087	−	0.907552i
$385$		0			0
$386$	6.10313	+	3.52364i	0.310641	+	0.179349i
$387$	8.42940	+	8.52502i	0.428490	+	0.433351i
$388$	1.35639	−	5.06210i	0.0688601	−	0.256989i
$389$	10.3645	−	3.77237i	0.525501	−	0.191267i	−0.0656273	−	0.997844i	$-0.520905\pi$
$389$	10.3645	−	3.77237i	0.525501	−	0.191267i	0.591128	+	0.806577i	$0.298683\pi$
$390$		0			0
$391$	1.69021	−	1.41826i	0.0854778	−	0.0717244i
$392$	6.79905	+	0.594840i	0.343404	+	0.0300440i
$393$	−24.8401	−	0.0700447i	−1.25301	−	0.00353329i
$394$	6.25270	+	17.1791i	0.315006	+	0.865473i
$395$		0			0
$396$	1.83073	+	10.7363i	0.0919978	+	0.539520i
$397$	−4.10710	−	15.3279i	−0.206129	−	0.769286i	−0.989102	−	0.147230i	$-0.952964\pi$
$397$	−4.10710	−	15.3279i	−0.206129	−	0.769286i	0.782973	−	0.622056i	$-0.213702\pi$
$398$	−12.4894	−	17.8367i	−0.626035	−	0.894071i
$399$	−3.88368	+	42.9940i	−0.194427	+	2.15239i
$400$		0			0
$401$	−18.2547	+	3.21880i	−0.911598	+	0.160739i	−0.609729	−	0.792610i	$-0.708722\pi$
$401$	−18.2547	+	3.21880i	−0.911598	+	0.160739i	−0.301869	+	0.953349i	$0.597611\pi$
$402$	17.5835	+	3.15160i	0.876987	+	0.157188i
$403$	−1.67191	−	19.1100i	−0.0832837	−	0.951937i
$404$	7.80799			0.388462
$405$		0			0
$406$	−2.96116			−0.146960
$407$	1.29972	+	14.8559i	0.0644248	+	0.736379i
$408$	−3.08451	−	0.552855i	−0.152706	−	0.0273704i
$409$	−15.3828	+	2.71240i	−0.760628	+	0.134119i	−0.540491	−	0.841350i	$-0.681762\pi$
$409$	−15.3828	+	2.71240i	−0.760628	+	0.134119i	−0.220137	+	0.975469i	$0.570650\pi$
$410$		0			0
$411$	0.527528	−	5.83996i	0.0260211	−	0.288064i
$412$	4.45640	+	6.36439i	0.219551	+	0.313551i
$413$	−9.20792	−	34.3644i	−0.453092	−	1.69096i
$414$	−7.79515	+	6.46635i	−0.383111	+	0.317804i
$415$		0			0
$416$	−11.2446	−	30.8943i	−0.551311	−	1.51472i
$417$	9.53497	+	0.0268870i	0.466929	+	0.00131666i
$418$	42.5179	+	3.71983i	2.07962	+	0.181943i
$419$	−8.40402	+	7.05181i	−0.410563	+	0.344503i	−0.824560	−	0.565775i	$-0.808577\pi$
$419$	−8.40402	+	7.05181i	−0.410563	+	0.344503i	0.413996	+	0.910279i	$0.364133\pi$
$420$		0			0
$421$	−4.13716	+	1.50580i	−0.201633	+	0.0733884i	−0.440863	−	0.897575i	$-0.645327\pi$
$421$	−4.13716	+	1.50580i	−0.201633	+	0.0733884i	0.239230	+	0.970963i	$0.423105\pi$
$422$	4.29146	−	16.0159i	0.208905	−	0.779644i
$423$	14.4095	−	3.77405i	0.700614	−	0.183500i
$424$	−2.40387	−	1.38788i	−0.116742	−	0.0674012i
$425$		0			0
$426$	−9.81767	−	21.2100i	−0.475668	−	1.02763i
$427$	−32.0872	+	14.9625i	−1.55281	+	0.724086i
$428$	4.08615	+	2.86115i	0.197512	+	0.138299i
$429$	−2.77762	−	32.8138i	−0.134105	−	1.58426i
$430$		0			0
$431$		−	22.9617i		−	1.10603i	−0.833173	−	0.553013i	$-0.813478\pi$
$431$		−	22.9617i		−	1.10603i	0.833173	−	0.553013i	$-0.186522\pi$
$432$	25.4853	+	4.71639i	1.22616	+	0.226917i
$433$	11.8168	+	11.8168i	0.567878	+	0.567878i	0.931534	−	0.363655i	$-0.118471\pi$
$433$	11.8168	+	11.8168i	0.567878	+	0.567878i	−0.363655	+	0.931534i	$0.618471\pi$
$434$	15.0193	+	12.6027i	0.720949	+	0.604948i
$435$		0			0
$436$	−0.606518	−	3.43973i	−0.0290469	−	0.164733i
$437$	5.98609	+	12.8372i	0.286353	+	0.614087i
$438$	−3.72662	−	21.4889i	−0.178065	−	1.02678i
$439$	−15.4676	−	2.72735i	−0.738226	−	0.130169i	−0.208124	−	0.978103i	$-0.566736\pi$
$439$	−15.4676	−	2.72735i	−0.738226	−	0.130169i	−0.530103	+	0.847933i	$0.677847\pi$
$440$		0			0
$441$	−8.44022	+	9.94422i	−0.401915	+	0.473534i
$442$	−11.4105	−	3.05744i	−0.542744	−	0.145428i
$443$	9.83716	−	21.0959i	0.467378	−	1.00229i	−0.521457	−	0.853278i	$-0.674611\pi$
$443$	9.83716	−	21.0959i	0.467378	−	1.00229i	0.988835	−	0.149017i	$-0.0476109\pi$
$444$	−8.45830	−	2.29198i	−0.401413	−	0.108772i
$445$		0			0
$446$	−15.9661	−	19.0276i	−0.756016	−	0.900984i
$447$	−19.9849	+	11.4633i	−0.945255	+	0.542195i
$448$	−0.00243831	−	0.00113700i	−0.000115199	−	5.37184e-5i
$449$	−15.4027	−	26.6783i	−0.726900	−	1.25903i	−0.958187	−	0.286142i	$-0.907627\pi$
$449$	−15.4027	−	26.6783i	−0.726900	−	1.25903i	0.231288	−	0.972885i	$-0.425706\pi$
$450$		0			0
$451$	−3.54396	+	6.13831i	−0.166878	+	0.289042i
$452$	−0.410056	+	0.287125i	−0.0192874	+	0.0135052i
$453$	−25.0004	+	4.33560i	−1.17462	+	0.203704i
$454$	−15.9509	+	43.8248i	−0.748615	+	2.05680i
$455$		0			0
$456$	8.55311	−	18.2080i	0.400536	−	0.852667i
$457$	−26.1420	+	2.28713i	−1.22287	+	0.106988i	−0.680245	−	0.732985i	$-0.738126\pi$
$457$	−26.1420	+	2.28713i	−1.22287	+	0.106988i	−0.542629	+	0.839973i	$0.682571\pi$
$458$	12.4545	−	12.4545i	0.581961	−	0.581961i
$459$	4.27032	−	4.19867i	0.199321	−	0.195977i
$460$		0			0
$461$	−12.6198	+	15.0397i	−0.587761	+	0.700467i	−0.975174	−	0.221440i	$-0.928924\pi$
$461$	−12.6198	+	15.0397i	−0.587761	+	0.700467i	0.387413	+	0.921906i	$0.373369\pi$
$462$	25.7222	+	21.7074i	1.19671	+	1.00992i
$463$	−4.80533	+	6.86273i	−0.223323	+	0.318938i	−0.915141	−	0.403134i	$-0.867921\pi$
$463$	−4.80533	+	6.86273i	−0.223323	+	0.318938i	0.691818	+	0.722072i	$0.256810\pi$
$464$	2.33640	+	0.850378i	0.108464	+	0.0394778i
$465$		0			0
$466$	−8.29867	+	47.0641i	−0.384429	+	2.18020i
$467$	1.89386	−	0.507459i	0.0876375	−	0.0234824i	−0.214734	−	0.976673i	$-0.568888\pi$
$467$	1.89386	−	0.507459i	0.0876375	−	0.0234824i	0.302371	+	0.953190i	$0.402222\pi$
$468$	18.6639	+	5.11395i	0.862737	+	0.236393i
$469$	17.0619	−	9.85072i	0.787847	−	0.454864i
$470$		0			0
$471$	−9.29296	+	2.46198i	−0.428197	+	0.113442i
$472$	−1.44494	+	16.5157i	−0.0665085	+	0.760196i
$473$	1.13933	−	13.0227i	0.0523867	−	0.598782i
$474$	17.0502	+	17.1466i	0.783140	+	0.787569i
$475$		0			0
$476$	3.73157	−	2.15442i	0.171036	−	0.0987478i
$477$	4.82025	−	2.21471i	0.220704	−	0.101405i
$478$	−42.3747	+	11.3543i	−1.93818	+	0.519333i
$479$	3.17060	−	17.9814i	0.144868	−	0.821589i	−0.822604	−	0.568614i	$-0.807480\pi$
$479$	3.17060	−	17.9814i	0.144868	−	0.821589i	0.967473	−	0.252975i	$-0.0814091\pi$
$480$		0			0
$481$	24.8990	+	9.06251i	1.13530	+	0.413215i
$482$	−28.8506	+	41.2029i	−1.31411	+	1.87674i
$483$	−1.97066	+	10.9948i	−0.0896681	+	0.500280i
$484$	−0.213671	+	0.254643i	−0.00971233	+	0.0115747i
$485$		0			0
$486$	−19.7103	+	19.1622i	−0.894079	+	0.869216i
$487$	23.0616	−	23.0616i	1.04502	−	1.04502i	0.0460835	−	0.998938i	$-0.485326\pi$
$487$	23.0616	−	23.0616i	1.04502	−	1.04502i	0.998938	−	0.0460835i	$-0.0146740\pi$
$488$	16.4357	−	1.43793i	0.744008	−	0.0650922i
$489$	7.08378	+	10.1776i	0.320339	+	0.460249i
$490$		0			0
$491$	1.13497	−	3.11830i	0.0512204	−	0.140727i	−0.911444	−	0.411423i	$-0.865032\pi$
$491$	1.13497	−	3.11830i	0.0512204	−	0.140727i	0.962665	+	0.270697i	$0.0872540\pi$
$492$	−2.66832	−	3.19825i	−0.120297	−	0.144188i
$493$	0.470602	−	0.329519i	0.0211949	−	0.0148408i
$494$	37.9175	−	65.6750i	1.70599	−	2.95486i
$495$		0			0
$496$	−8.23121	−	14.2569i	−0.369592	−	0.640153i
$497$	−23.3613	−	10.8936i	−1.04790	−	0.488643i
$498$	−0.0538003	+	19.0793i	−0.00241085	+	0.854963i
$499$	−4.13042	−	4.92245i	−0.184903	−	0.220359i	0.665628	−	0.746284i	$-0.268164\pi$
$499$	−4.13042	−	4.92245i	−0.184903	−	0.220359i	−0.850531	+	0.525925i	$0.823719\pi$
$500$		0			0
$501$	6.21800	+	23.4704i	0.277800	+	1.04858i
$502$	8.27524	−	17.7463i	0.369342	−	0.792057i
$503$	−6.23303	−	1.67013i	−0.277917	−	0.0744676i	0.117168	−	0.993112i	$-0.462618\pi$
$503$	−6.23303	−	1.67013i	−0.277917	−	0.0744676i	−0.395085	+	0.918644i	$0.629285\pi$
$504$	13.7833	−	7.85448i	0.613956	−	0.349866i
$505$		0			0
$506$	10.8757	+	1.91769i	0.483486	+	0.0852516i
$507$	−33.7902	−	12.4066i	−1.50067	−	0.550998i
$508$	−0.259312	−	0.556097i	−0.0115051	−	0.0246728i
$509$	2.35893	+	13.3781i	0.104558	+	0.592976i	0.991396	+	0.130896i	$0.0417854\pi$
$509$	2.35893	+	13.3781i	0.104558	+	0.592976i	−0.886838	+	0.462080i	$0.847103\pi$
$510$		0			0
$511$	−18.4259	−	15.4611i	−0.815112	−	0.683960i
$512$	−8.87720	−	8.87720i	−0.392320	−	0.392320i
$513$	18.9401	+	33.4557i	0.836227	+	1.47711i
$514$		−	49.7537i		−	2.19454i
$515$		0			0
$516$	6.95301	+	3.26614i	0.306089	+	0.143784i
$517$	−13.3046	−	9.31597i	−0.585135	−	0.409716i
$518$	−24.5443	+	11.4452i	−1.07842	+	0.502874i
$519$	−9.76484	+	13.8623i	−0.428629	+	0.608487i
$520$		0			0
$521$	−26.9126	−	15.5380i	−1.17906	−	0.680731i	−0.223263	−	0.974758i	$-0.571671\pi$
$521$	−26.9126	−	15.5380i	−1.17906	−	0.680731i	−0.955797	+	0.294027i	$0.905004\pi$
$522$	−2.16869	+	1.50038i	−0.0949212	+	0.0656699i
$523$	1.02410	−	3.82198i	0.0447807	−	0.167124i	−0.939914	−	0.341411i	$-0.889095\pi$
$523$	1.02410	−	3.82198i	0.0447807	−	0.167124i	0.984695	+	0.174287i	$0.0557620\pi$
$524$	−14.9567	+	5.44379i	−0.653386	+	0.237813i
$525$		0			0
$526$	−3.33833	+	2.80120i	−0.145558	+	0.122138i
$527$	−3.78937	−	0.331527i	−0.165068	−	0.0144415i
$528$	−14.0613	−	24.5143i	−0.611939	−	1.06685i
$529$	−6.61296	−	18.1689i	−0.287520	−	0.789954i
$530$		0			0
$531$	−24.1557	−	20.5023i	−1.04827	−	0.889722i
$532$	7.15919	+	26.7185i	0.310390	+	1.15839i
$533$	7.22357	+	10.3163i	0.312888	+	0.446850i
$534$	−1.30038	−	0.916013i	−0.0562731	−	0.0396398i
$535$		0			0
$536$	−9.04142	+	1.59425i	−0.390530	+	0.0688609i
$537$	6.84325	+	18.9679i	0.295308	+	0.818527i
$538$	0.318866	+	3.64466i	0.0137473	+	0.157132i
$539$	14.2221			0.612590
$540$		0			0
$541$	43.8935			1.88713			0.943565	−	0.331186i	$-0.107449\pi$
$541$	43.8935			1.88713			0.943565	+	0.331186i	$0.107449\pi$
$542$	2.78069	+	31.7834i	0.119441	+	1.36521i
$543$	23.4993	−	27.8455i	1.00845	−	1.19496i
$544$	−6.42021	+	1.13206i	−0.275264	+	0.0485365i
$545$		0			0
$546$	54.2715	−	25.1212i	2.32261	−	1.07509i
$547$	−13.7979	−	19.7055i	−0.589957	−	0.842546i	0.407545	−	0.913185i	$-0.366385\pi$
$547$	−13.7979	−	19.7055i	−0.589957	−	0.842546i	−0.997502	+	0.0706388i	$0.977496\pi$
$548$	−0.972448	−	3.62923i	−0.0415409	−	0.155033i
$549$	−15.9187	+	27.2164i	−0.679393	+	1.16157i
$550$		0			0
$551$	1.26139	+	3.46563i	0.0537369	+	0.147641i
$552$	2.61532	−	4.50050i	0.111315	−	0.191554i
$553$	26.5669	+	2.32430i	1.12974	+	0.0988395i
$554$	34.7495	−	29.1583i	1.47636	−	1.23882i
$555$		0			0
$556$	5.74120	−	2.08962i	0.243481	−	0.0886198i
$557$	6.85604	−	25.5871i	0.290500	−	1.08416i	−0.654226	−	0.756299i	$-0.727006\pi$
$557$	6.85604	−	25.5871i	0.290500	−	1.08416i	0.944726	−	0.327861i	$-0.106328\pi$
$558$	17.3854	+	1.61987i	0.735983	+	0.0685748i
$559$	−20.1154	−	11.6136i	−0.850790	−	0.491204i
$560$		0			0
$561$	−6.50351	−	0.587467i	−0.274578	−	0.0248029i
$562$	4.45161	−	2.07582i	0.187780	−	0.0875632i
$563$	17.6610	+	12.3664i	0.744323	+	0.521181i	0.883124	−	0.469140i	$-0.155436\pi$
$563$	17.6610	+	12.3664i	0.744323	+	0.521181i	−0.138801	+	0.990320i	$0.544325\pi$
$564$	7.83378	−	5.45242i	0.329862	−	0.229588i
$565$		0			0
$566$			36.1412i			1.51913i
$567$	−2.98285	+	30.1707i	−0.125268	+	1.26705i
$568$	8.49364	+	8.49364i	0.356385	+	0.356385i
$569$	−8.77990	−	7.36721i	−0.368073	−	0.308850i	0.439926	−	0.898034i	$-0.355005\pi$
$569$	−8.77990	−	7.36721i	−0.368073	−	0.308850i	−0.807999	+	0.589184i	$0.799449\pi$
$570$		0			0
$571$	1.87072	+	10.6094i	0.0782872	+	0.443989i	0.998604	+	0.0528155i	$0.0168195\pi$
$571$	1.87072	+	10.6094i	0.0782872	+	0.443989i	−0.920317	+	0.391173i	$0.872069\pi$
$572$	−8.91764	−	19.1239i	−0.372865	−	0.799612i
$573$	−33.4058	+	27.8706i	−1.39555	+	1.16431i
$574$	−12.6763	−	2.23517i	−0.529097	−	0.0932940i
$575$		0			0
$576$	−0.00236187		0.000402741i	−9.84114e−5		1.67809e-5i
$577$	24.8368	+	6.65499i	1.03397	+	0.277051i	0.735612	−	0.677403i	$-0.236895\pi$
$577$	24.8368	+	6.65499i	1.03397	+	0.277051i	0.298357	+	0.954454i	$0.403561\pi$
$578$	11.6797	−	25.0472i	0.485812	−	1.04183i
$579$	4.90818	−	4.88058i	0.203977	−	0.202830i
$580$		0			0
$581$	13.5256	+	16.1192i	0.561137	+	0.668737i
$582$	−12.4704	−	7.24676i	−0.516916	−	0.300388i
$583$	−5.24223	−	2.44449i	−0.217111	−	0.101241i
$584$	5.60442	+	9.70714i	0.231913	+	0.401684i
$585$		0			0
$586$	27.6498	−	47.8909i	1.14220	−	1.97835i
$587$	30.2354	−	21.1711i	1.24795	−	0.873824i	0.252360	−	0.967633i	$-0.418793\pi$
$587$	30.2354	−	21.1711i	1.24795	−	0.873824i	0.995590	+	0.0938095i	$0.0299045\pi$
$588$	−2.88059	+	7.84544i	−0.118793	+	0.323541i
$589$	8.35183	−	22.9465i	0.344131	−	0.945492i
$590$		0			0
$591$	17.8920	−	1.51452i	0.735977	−	0.0622989i
$592$	22.6526	−	1.98184i	0.931016	−	0.0814533i
$593$	−21.8217	+	21.8217i	−0.896109	+	0.896109i	−0.995089	−	0.0989808i	$-0.968442\pi$
$593$	−21.8217	+	21.8217i	−0.896109	+	0.896109i	0.0989808	+	0.995089i	$0.468442\pi$
$594$	29.8373	+	2.86496i	1.22424	+	0.117551i
$595$		0			0
$596$	−9.48922	+	11.3088i	−0.388693	+	0.463227i
$597$	−20.1174	+	7.25794i	−0.823349	+	0.297048i
$598$	11.2549	−	16.0736i	0.460247	−	0.657300i
$599$	−16.2128	−	5.90099i	−0.662438	−	0.241108i	−0.0111496	−	0.999938i	$-0.503549\pi$
$599$	−16.2128	−	5.90099i	−0.662438	−	0.241108i	−0.651289	+	0.758830i	$0.725771\pi$
$600$		0			0
$601$	7.91812	−	44.9059i	0.322987	−	1.83175i	−0.200473	−	0.979699i	$-0.564248\pi$
$601$	7.91812	−	44.9059i	0.322987	−	1.83175i	0.523460	−	0.852050i	$-0.324641\pi$
$602$	22.9308	−	6.14430i	0.934592	−	0.250423i
$603$	7.50459	−	15.8595i	0.305611	−	0.645849i
$604$	−14.0802	+	8.12919i	−0.572914	+	0.330772i
$605$		0			0
$606$	5.62022	−	20.7408i	0.228306	−	0.842538i
$607$	−4.17395	+	47.7085i	−0.169416	+	1.93643i	0.149737	+	0.988726i	$0.452157\pi$
$607$	−4.17395	+	47.7085i	−0.169416	+	1.93643i	−0.319153	+	0.947703i	$0.603398\pi$
$608$	3.64755	−	41.6917i	0.147928	−	1.69082i
$609$	−0.760669	+	2.80717i	−0.0308239	+	0.113752i
$610$		0			0
$611$	−24.9925	+	14.4294i	−1.01109	+	0.583752i
$612$	1.64131	−	3.46859i	0.0663459	−	0.140209i
$613$	−15.4970	+	4.15240i	−0.625916	+	0.167714i	−0.557816	−	0.829965i	$-0.688360\pi$
$613$	−15.4970	+	4.15240i	−0.625916	+	0.167714i	−0.0681004	+	0.997678i	$0.521694\pi$
$614$	2.94778	−	16.7177i	0.118963	−	0.674671i
$615$		0			0
$616$	−16.2549	−	5.91629i	−0.654927	−	0.238374i
$617$	−14.6368	+	20.9035i	−0.589254	+	0.841541i	−0.997451	−	0.0713522i	$-0.977269\pi$
$617$	−14.6368	+	20.9035i	−0.589254	+	0.841541i	0.408198	+	0.912894i	$0.366157\pi$
$618$	20.1138	−	7.25667i	0.809097	−	0.291906i
$619$	−27.5321	+	32.8114i	−1.10661	+	1.31880i	−0.163414	+	0.986558i	$0.552251\pi$
$619$	−27.5321	+	32.8114i	−1.10661	+	1.31880i	−0.943193	+	0.332245i	$0.892194\pi$
$620$		0			0
$621$	4.12763	+	9.05085i	0.165636	+	0.363198i
$622$	−0.00528856	+	0.00528856i	−0.000212052	+	0.000212052i
$623$	−1.74758	+	0.152893i	−0.0700152	+	0.00612554i
$624$	−50.0352	+	4.23537i	−2.00301	+	0.169551i
$625$		0			0
$626$	14.3257	−	39.3596i	0.572571	−	1.57313i
$627$	14.4484	−	39.3512i	0.577015	−	1.57153i
$628$	−5.04597	+	3.53322i	−0.201356	+	0.140991i
$629$	2.62708	−	4.55023i	0.104748	−	0.181430i
$630$		0			0
$631$	−6.58555	−	11.4065i	−0.262167	−	0.454086i	0.704651	−	0.709554i	$-0.251104\pi$
$631$	−6.58555	−	11.4065i	−0.262167	−	0.454086i	−0.966817	+	0.255468i	$0.917770\pi$
$632$	−11.2631	−	5.25209i	−0.448024	−	0.208917i
$633$	−14.0806	−	8.18249i	−0.559655	−	0.325225i
$634$	0.899738	+	1.07227i	0.0357332	+	0.0425851i
$635$		0			0
$636$	2.41025	−	2.39670i	0.0955726	−	0.0950351i
$637$	10.6796	−	22.9025i	0.423141	−	0.907429i
$638$	2.77749	+	0.744227i	0.109962	+	0.0294642i
$639$	−22.6290	+	3.85864i	−0.895188	+	0.152645i
$640$		0			0
$641$	2.12742	+	0.375121i	0.0840278	+	0.0148164i	0.215504	−	0.976503i	$-0.430861\pi$
$641$	2.12742	+	0.375121i	0.0840278	+	0.0148164i	−0.131476	+	0.991319i	$0.541972\pi$
$642$	10.5415	−	8.79481i	0.416039	−	0.347104i
$643$	−1.89186	−	4.05710i	−0.0746075	−	0.159996i	0.865466	−	0.500967i	$-0.167022\pi$
$643$	−1.89186	−	4.05710i	−0.0746075	−	0.159996i	−0.940074	+	0.340970i	$0.889244\pi$
$644$	1.24285	+	7.04855i	0.0489751	+	0.277752i
$645$		0			0
$646$	−11.5194	−	9.66592i	−0.453224	−	0.380300i
$647$	−35.0743	−	35.0743i	−1.37891	−	1.37891i	−0.846461	−	0.532451i	$-0.821271\pi$
$647$	−35.0743	−	35.0743i	−1.37891	−	1.37891i	−0.532451	−	0.846461i	$-0.678729\pi$
$648$	6.11484	−	12.7363i	0.240214	−	0.500327i
$649$			34.5472i			1.35609i
$650$		0			0
$651$	15.8055	−	11.0008i	0.619465	−	0.431156i
$652$	6.50860	+	4.55737i	0.254897	+	0.178481i
$653$	2.90729	−	1.35569i	0.113771	−	0.0530523i	−0.364899	−	0.931047i	$-0.618897\pi$
$653$	2.90729	−	1.35569i	0.113771	−	0.0530523i	0.478670	+	0.877995i	$0.341119\pi$
$654$	−9.57373	−	0.864803i	−0.374363	−	0.0338165i
$655$		0			0
$656$	9.35984	+	5.40391i	0.365440	+	0.210987i
$657$	−21.3287	−	1.98728i	−0.832110	−	0.0775313i
$658$	7.63403	−	28.4906i	0.297606	−	1.11068i
$659$	16.5503	−	6.02381i	0.644708	−	0.234654i	0.00108739	−	0.999999i	$-0.499654\pi$
$659$	16.5503	−	6.02381i	0.644708	−	0.234654i	0.643620	+	0.765345i	$0.277432\pi$
$660$		0			0
$661$	−31.9596	+	26.8173i	−1.24309	+	1.04307i	−0.245809	+	0.969318i	$0.579054\pi$
$661$	−31.9596	+	26.8173i	−1.24309	+	1.04307i	−0.997276	+	0.0737542i	$0.976502\pi$
$662$	10.0660	+	0.880660i	0.391226	+	0.0342278i
$663$	−5.82960	+	10.0317i	−0.226403	+	0.389600i
$664$	−3.35373	−	9.21430i	−0.130150	−	0.357584i
$665$		0			0
$666$	−12.1766	+	20.8185i	−0.471835	+	0.806701i
$667$	0.246987	+	0.921766i	0.00956336	+	0.0356909i
$668$	8.92355	+	12.7441i	0.345263	+	0.493086i
$669$	−22.1395	+	10.2479i	−0.855962	+	0.396207i
$670$		0			0
$671$	33.8575	−	5.96999i	1.30705	−	0.230469i
$672$	21.2856	−	25.2224i	0.821110	−	0.972975i
$673$	0.657527	+	7.51557i	0.0253458	+	0.289704i	0.998280	+	0.0586226i	$0.0186708\pi$
$673$	0.657527	+	7.51557i	0.0253458	+	0.289704i	−0.972934	+	0.231081i	$0.925774\pi$
$674$	−45.0333			−1.73462
$675$		0			0
$676$	−23.0647			−0.887104
$677$	−1.83342	−	20.9561i	−0.0704639	−	0.805407i	−0.946404	−	0.322986i	$-0.895313\pi$
$677$	−1.83342	−	20.9561i	−0.0704639	−	0.805407i	0.875940	−	0.482420i	$-0.160242\pi$
$678$	0.467546	+	1.29593i	0.0179560	+	0.0497699i
$679$	−15.6652	+	2.76220i	−0.601177	+	0.106004i
$680$		0			0
$681$	37.4482	+	26.3792i	1.43502	+	1.01085i
$682$	−10.9203	−	15.5958i	−0.418159	−	0.597193i
$683$	−1.26489	−	4.72063i	−0.0483997	−	0.180630i	0.937494	−	0.348000i	$-0.113139\pi$
$683$	−1.26489	−	4.72063i	−0.0483997	−	0.180630i	−0.985894	+	0.167370i	$0.946472\pi$
$684$	18.7811	+	15.9406i	0.718114	+	0.609504i
$685$		0			0
$686$	−5.38880	−	14.8056i	−0.205745	−	0.565281i
$687$	−8.60747	−	15.0061i	−0.328395	−	0.572520i
$688$	−19.8572	−	1.73728i	−0.757050	−	0.0662333i
$689$	−7.87294	+	6.60618i	−0.299935	+	0.251676i
$690$		0			0
$691$	39.6616	−	14.4357i	1.50880	−	0.549158i	0.550478	−	0.834850i	$-0.314445\pi$
$691$	39.6616	−	14.4357i	1.50880	−	0.549158i	0.958322	+	0.285692i	$0.0922233\pi$
$692$	−2.81204	+	10.4947i	−0.106898	+	0.398948i
$693$	27.1861	−	18.8083i	1.03271	−	0.714469i
$694$	18.5867	+	10.7311i	0.705543	+	0.407346i
$695$		0			0
$696$	0.780507	−	1.10802i	0.0295850	−	0.0419993i
$697$	2.26330	−	1.05540i	0.0857287	−	0.0399759i
$698$	−0.171328	−	0.119965i	−0.00648485	−	0.00454074i
$699$	42.4848	+	19.9570i	1.60692	+	0.754844i
$700$		0			0
$701$		−	3.71261i		−	0.140223i	−0.997539	−	0.0701117i	$-0.977664\pi$
$701$		−	3.71261i		−	0.140223i	0.997539	−	0.0701117i	$-0.0223356\pi$
$702$	27.0188	−	45.8969i	1.01976	−	1.73226i
$703$	23.8504	+	23.8504i	0.899533	+	0.899533i
$704$	0.00200131	+	0.00167930i	7.54273e−5	+	6.32910e-5i
$705$		0			0
$706$	6.62429	+	37.5682i	0.249309	+	1.41390i
$707$	−10.0158	−	21.4790i	−0.376683	−	0.807800i
$708$	−19.0575	−	6.99728i	−0.716224	−	0.262974i
$709$	18.4462	+	3.25257i	0.692763	+	0.122153i	0.508934	−	0.860805i	$-0.330040\pi$
$709$	18.4462	+	3.25257i	0.692763	+	0.122153i	0.183829	+	0.982958i	$0.441151\pi$
$710$		0			0
$711$	20.6348	−	11.7588i	0.773864	−	0.440990i
$712$	0.789629	+	0.211580i	0.0295926	+	0.00792931i
$713$	2.67029	−	5.72646i	0.100003	−	0.214457i
$714$	−3.03692	−	11.4631i	−0.113654	−	0.428997i
$715$		0			0
$716$	8.30527	+	9.89783i	0.310382	+	0.369899i
$717$	−0.121500	+	43.0878i	−0.00453751	+	1.60914i
$718$	48.8436	+	22.7762i	1.82283	+	0.849999i
$719$	7.23920	+	12.5387i	0.269977	+	0.467613i	0.968856	−	0.247627i	$-0.0796506\pi$
$719$	7.23920	+	12.5387i	0.269977	+	0.467613i	−0.698879	+	0.715240i	$0.746317\pi$
$720$		0			0
$721$	11.7913	−	20.4231i	0.439130	−	0.760596i
$722$	51.6300	−	36.1517i	1.92147	−	1.34543i
$723$	31.6489	+	37.9345i	1.17704	+	1.41080i
$724$	7.98507	−	21.9388i	0.296763	−	0.815349i
$725$		0			0
$726$	0.522623	+	0.750880i	0.0193963	+	0.0278678i
$727$	−4.05790	+	0.355020i	−0.150499	+	0.0131670i	−0.162156	−	0.986765i	$-0.551845\pi$
$727$	−4.05790	+	0.355020i	−0.150499	+	0.0131670i	0.0116572	+	0.999932i	$0.496289\pi$
$728$	−21.7333	+	21.7333i	−0.805489	+	0.805489i
$729$	13.1025	+	23.6077i	0.485277	+	0.874361i
$730$		0			0
$731$	−2.96054	+	3.52824i	−0.109500	+	0.130497i
$732$	−3.56432	+	19.8862i	−0.131741	+	0.735015i
$733$	−0.167146	+	0.238710i	−0.00617370	+	0.00881695i	−0.822227	−	0.569160i	$-0.807269\pi$
$733$	−0.167146	+	0.238710i	−0.00617370	+	0.00881695i	0.816053	+	0.577977i	$0.196158\pi$
$734$	−25.4816	−	9.27456i	−0.940545	−	0.342330i
$735$		0			0
$736$	1.88042	−	10.6644i	0.0693133	−	0.393096i
$737$	−18.4794	+	4.95155i	−0.680699	+	0.182393i
$738$	−10.4164	+	4.78589i	−0.383431	+	0.176171i
$739$	−0.493834	+	0.285115i	−0.0181660	+	0.0104881i	−0.509055	−	0.860734i	$-0.670005\pi$
$739$	−0.493834	+	0.285115i	−0.0181660	+	0.0104881i	0.490890	+	0.871222i	$0.336672\pi$
$740$		0			0
$741$	−52.5193	−	52.8163i	−1.92934	−	1.94026i
$742$	0.915499	−	10.4642i	0.0336090	−	0.384153i
$743$	−3.96205	+	45.2865i	−0.145354	+	1.66140i	0.477179	+	0.878806i	$0.341659\pi$
$743$	−3.96205	+	45.2865i	−0.145354	+	1.66140i	−0.622533	+	0.782594i	$0.713896\pi$
$744$	−8.67451	+	2.29813i	−0.318023	+	0.0842536i
$745$		0			0
$746$	42.5487	−	24.5655i	1.55782	−	0.899407i
$747$	18.0733	+	4.95212i	0.661266	+	0.181189i
$748$	−4.04158	+	1.08294i	−0.147775	+	0.0395962i
$749$	2.62917	−	14.9108i	0.0960678	−	0.544827i
$750$		0			0
$751$	21.7741	+	7.92512i	0.794547	+	0.289192i	0.707225	−	0.706988i	$-0.249947\pi$
$751$	21.7741	+	7.92512i	0.794547	+	0.289192i	0.0873224	+	0.996180i	$0.472169\pi$
$752$	−14.2052	+	20.2871i	−0.518010	+	0.739795i
$753$	−14.6977	−	12.4036i	−0.535613	−	0.452012i
$754$	3.28412	−	3.91386i	0.119601	−	0.142535i
$755$		0			0
$756$	4.86901	+	18.8063i	0.177084	+	0.683980i
$757$	8.24491	−	8.24491i	0.299666	−	0.299666i	−0.541217	−	0.840883i	$-0.682036\pi$
$757$	8.24491	−	8.24491i	0.299666	−	0.299666i	0.840883	+	0.541217i	$0.182036\pi$
$758$	29.2715	−	2.56092i	1.06319	−	0.0930169i
$759$	4.61174	−	9.81753i	0.167396	−	0.356354i
$760$		0			0
$761$	13.7885	−	37.8835i	0.499832	−	1.37328i	−0.391605	−	0.920133i	$-0.628080\pi$
$761$	13.7885	−	37.8835i	0.499832	−	1.37328i	0.891437	−	0.453144i	$-0.149698\pi$
$762$	−1.66385	+	0.288546i	−0.0602748	+	0.0104529i
$763$	−8.68433	+	6.08083i	−0.314394	+	0.220141i
$764$	−13.9383	+	24.1418i	−0.504268	+	0.873418i
$765$		0			0
$766$	28.0323	+	48.5534i	1.01285	+	1.75431i
$767$	55.6327	+	25.9420i	2.00878	+	0.936710i
$768$	−29.9752	+	17.1937i	−1.08164	+	0.620422i
$769$	13.5646	+	16.1656i	0.489151	+	0.582947i	0.953001	−	0.302966i	$-0.0979769\pi$
$769$	13.5646	+	16.1656i	0.489151	+	0.582947i	−0.463850	+	0.885914i	$0.653532\pi$
$770$		0			0
$771$	−47.1663	−	12.7808i	−1.69865	−	0.460290i
$772$	1.87438	−	4.01963i	0.0674605	−	0.144669i
$773$	−22.6795	−	6.07695i	−0.815724	−	0.218573i	−0.173248	−	0.984878i	$-0.555426\pi$
$773$	−22.6795	−	6.07695i	−0.815724	−	0.218573i	−0.642476	+	0.766306i	$0.722093\pi$
$774$	13.6808	−	16.1187i	0.491748	−	0.579375i
$775$		0			0
$776$	7.30002	+	1.28719i	0.262055	+	0.0462074i
$777$	4.54501	+	26.2080i	0.163051	+	0.940206i
$778$	−8.22014	−	17.6281i	−0.294706	−	0.632000i
$779$	2.78384	+	15.7879i	0.0997414	+	0.565662i
$780$		0			0
$781$	19.1745	+	16.0893i	0.686116	+	0.575720i
$782$	−2.75132	−	2.75132i	−0.0983870	−	0.0983870i
$783$	0.865255	+	2.44133i	0.0309217	+	0.0872461i
$784$		−	21.6862i		−	0.774507i
$785$		0			0
$786$	3.69478	+	43.6488i	0.131788	+	1.55690i
$787$	6.64580	+	4.65344i	0.236897	+	0.165877i	0.685997	−	0.727604i	$-0.259366\pi$
$787$	6.64580	+	4.65344i	0.236897	+	0.165877i	−0.449100	+	0.893482i	$0.648255\pi$
$788$	10.4275	−	4.86241i	0.371464	−	0.173216i
$789$	1.79796	+	3.88430i	0.0640092	+	0.138285i
$790$		0			0
$791$	1.31585	+	0.759709i	0.0467864	+	0.0270121i
$792$	−14.9024	+	3.90315i	−0.529535	+	0.138692i
$793$	15.8104	−	59.0051i	0.561442	−	2.09533i
$794$	−26.2962	+	9.57104i	−0.933218	+	0.339663i
$795$		0			0
$796$	−10.4976	+	8.80855i	−0.372078	+	0.312211i
$797$	−12.7075	−	1.11177i	−0.450124	−	0.0393807i	−0.140160	−	0.990129i	$-0.544762\pi$
$797$	−12.7075	−	1.11177i	−0.450124	−	0.0393807i	−0.309964	+	0.950748i	$0.600317\pi$
$798$	76.1270	+	0.214665i	2.69487	+	0.00759907i
$799$	1.95721	+	5.37738i	0.0692410	+	0.190238i
$800$		0			0
$801$	−1.20242	+	0.997449i	−0.0424854	+	0.0352431i
$802$	8.46035	+	31.5745i	0.298745	+	1.11493i
$803$	13.3971	+	19.1331i	0.472775	+	0.675192i
$804$	1.01142	−	11.1968i	0.0356700	−	0.394882i
$805$		0			0
$806$	−33.3147	+	5.87429i	−1.17346	+	0.206913i
$807$	3.53703	+	0.633963i	0.124509	+	0.0223166i
$808$	0.962544	+	11.0019i	0.0338622	+	0.387047i
$809$	−37.1510			−1.30616			−0.653080	−	0.757289i	$-0.726523\pi$
$809$	−37.1510			−1.30616			−0.653080	+	0.757289i	$0.726523\pi$
$810$		0			0
$811$	−4.94368			−0.173596			−0.0867981	−	0.996226i	$-0.527664\pi$
$811$	−4.94368			−0.173596			−0.0867981	+	0.996226i	$0.527664\pi$
$812$	0.162423	+	1.85650i	0.00569991	+	0.0651503i
$813$	30.8448	+	5.52850i	1.08178	+	0.193893i
$814$	25.8985	−	4.56660i	0.907741	−	0.160059i
$815$		0			0
$816$	−0.895783	+	9.91670i	−0.0313587	+	0.347154i
$817$	−16.9591	−	24.2201i	−0.593323	−	0.847353i
$818$	7.12931	+	26.6069i	0.249270	+	0.930290i
$819$	−9.87337	−	57.9023i	−0.345004	−	2.02327i
$820$		0			0
$821$	11.5751	+	31.8023i	0.403973	+	1.10991i	0.960306	+	0.278948i	$0.0899857\pi$
$821$	11.5751	+	31.8023i	0.403973	+	1.10991i	−0.556333	+	0.830959i	$0.687792\pi$
$822$	−10.3405	−	0.0291584i	−0.360666	−	0.00101702i
$823$	−16.3354	−	1.42916i	−0.569416	−	0.0498174i	−0.201187	−	0.979553i	$-0.564480\pi$
$823$	−16.3354	−	1.42916i	−0.569416	−	0.0498174i	−0.368229	+	0.929735i	$0.620036\pi$
$824$	−8.41844	+	7.06391i	−0.293270	+	0.246083i
$825$		0			0
$826$	−58.9548	+	21.4578i	−2.05130	+	0.746612i
$827$	−8.28983	+	30.9381i	−0.288266	+	1.07582i	0.658154	+	0.752883i	$0.271338\pi$
$827$	−8.28983	+	30.9381i	−0.288266	+	1.07582i	−0.946420	+	0.322939i	$0.895329\pi$
$828$	4.48164	+	4.53248i	0.155748	+	0.157514i
$829$	2.18006	+	1.25866i	0.0757168	+	0.0437151i	0.537380	−	0.843340i	$-0.319414\pi$
$829$	2.18006	+	1.25866i	0.0757168	+	0.0437151i	−0.461664	+	0.887055i	$0.652747\pi$
$830$		0			0
$831$	−18.7154	−	40.4326i	−0.649230	−	1.40259i
$832$	0.00420706	−	0.00196178i	0.000145854	−	6.80126e-5i
$833$	−4.10466	−	2.87411i	−0.142218	−	0.0995821i
$834$	−1.41826	−	16.7548i	−0.0491103	−	0.580171i
$835$		0			0
$836$		−	26.8606i		−	0.928992i
$837$	6.00163	−	16.0652i	0.207447	−	0.555294i
$838$	13.6800	+	13.6800i	0.472568	+	0.472568i
$839$	37.2023	+	31.2164i	1.28437	+	1.07771i	0.992627	+	0.121213i	$0.0386784\pi$
$839$	37.2023	+	31.2164i	1.28437	+	1.07771i	0.291739	+	0.956498i	$0.405766\pi$
$840$		0			0
$841$	−4.99265	−	28.3147i	−0.172160	−	0.976370i
$842$	3.28121	+	7.03657i	0.113078	+	0.242496i
$843$	−0.824329	−	4.75334i	−0.0283914	−	0.163714i
$844$	−10.2766	−	1.81204i	−0.353734	−	0.0623729i
$845$		0			0
$846$	−8.84479	−	24.7340i	−0.304090	−	0.850372i
$847$	0.974587	+	0.261140i	0.0334872	+	0.00897287i
$848$	−3.72742	+	7.99348i	−0.128000	+	0.274497i
$849$	34.2617	+	9.28403i	1.17586	+	0.318627i
$850$		0			0
$851$	5.60993	+	6.68566i	0.192306	+	0.229181i
$852$	−12.7591	+	7.31857i	−0.437119	+	0.250730i
$853$	−8.48753	−	3.95780i	−0.290607	−	0.135512i	0.271848	−	0.962340i	$-0.412365\pi$
$853$	−8.48753	−	3.95780i	−0.290607	−	0.135512i	−0.562455	+	0.826828i	$0.690143\pi$
$854$	31.2172	+	54.0698i	1.06823	+	1.85023i
$855$		0			0
$856$	−3.52781	+	6.11035i	−0.120578	+	0.208847i
$857$	−44.5570	+	31.1992i	−1.52204	+	1.06574i	−0.548798	+	0.835955i	$0.684914\pi$
$857$	−44.5570	+	31.1992i	−1.52204	+	1.06574i	−0.973241	+	0.229788i	$0.926197\pi$
$858$	−57.2190	+	9.92297i	−1.95342	+	0.338765i
$859$	10.1859	−	27.9855i	0.347538	−	0.954853i	−0.635605	−	0.772015i	$-0.719249\pi$
$859$	10.1859	−	27.9855i	0.347538	−	0.954853i	0.983143	−	0.182839i	$-0.0585286\pi$
$860$		0			0
$861$	−5.37523	+	11.4429i	−0.183187	+	0.389972i
$862$	−40.3382	+	3.52913i	−1.37392	+	0.120203i
$863$	19.0658	−	19.0658i	0.649007	−	0.649007i	−0.303746	−	0.952753i	$-0.598237\pi$
$863$	19.0658	−	19.0658i	0.649007	−	0.649007i	0.952753	+	0.303746i	$0.0982373\pi$
$864$	2.80929	−	29.2575i	0.0955738	−	0.995360i
$865$		0			0
$866$	18.9430	−	22.5754i	0.643711	−	0.767145i
$867$	−20.7444	−	17.5065i	−0.704515	−	0.594552i
$868$	7.07741	−	10.1076i	0.240223	−	0.343074i
$869$	−24.3349	−	8.85719i	−0.825506	−	0.300460i
$870$		0			0
$871$	−5.90279	+	33.4764i	−0.200009	+	1.13430i
$872$	4.77202	−	1.27866i	0.161601	−	0.0433009i
$873$	−10.0733	+	9.96034i	−0.340930	+	0.337106i
$874$	21.6319	−	12.4892i	0.731708	−	0.422452i
$875$		0			0
$876$	−13.2680	+	3.51509i	−0.448285	+	0.118764i
$877$	0.346028	−	3.95512i	0.0116845	−	0.133555i	−0.988112	−	0.153737i	$-0.950869\pi$
$877$	0.346028	−	3.95512i	0.0116845	−	0.133555i	0.999796	+	0.0201823i	$0.00642465\pi$
$878$	−2.41399	+	27.5920i	−0.0814681	+	0.931184i
$879$	−38.2976	−	38.5142i	−1.29175	−	1.29905i
$880$		0			0
$881$	11.0930	−	6.40454i	0.373732	−	0.215774i	−0.301355	−	0.953512i	$-0.597439\pi$
$881$	11.0930	−	6.40454i	0.373732	−	0.215774i	0.675088	+	0.737737i	$0.264106\pi$
$882$	18.7668	+	13.2990i	0.631913	+	0.447802i
$883$	−30.0010	+	8.03874i	−1.00961	+	0.270525i	−0.725468	−	0.688256i	$-0.758377\pi$
$883$	−30.0010	+	8.03874i	−1.00961	+	0.270525i	−0.284146	+	0.958781i	$0.591710\pi$
$884$	−1.29098	+	7.32153i	−0.0434205	+	0.246250i
$885$		0			0
$886$	−38.5723	−	14.0392i	−1.29586	−	0.471655i
$887$	19.7558	−	28.2142i	0.663335	−	0.947341i	−0.336649	−	0.941630i	$-0.609293\pi$
$887$	19.7558	−	28.2142i	0.663335	−	0.947341i	0.999984	−	0.00571031i	$-0.00181766\pi$
$888$	2.18682	−	12.2008i	0.0733850	−	0.409432i
$889$	−1.19713	+	1.42668i	−0.0401504	+	0.0478493i
$890$		0			0
$891$	10.3806	−	27.5496i	0.347764	−	0.922947i
$892$	−11.0536	+	11.0536i	−0.370102	+	0.370102i
$893$	−36.5962	+	3.20176i	−1.22465	+	0.107143i
$894$	23.2099	+	33.3469i	0.776254	+	1.11529i
$895$		0			0
$896$	−13.0358	+	35.8156i	−0.435496	+	1.19652i
$897$	−12.3466	−	14.7986i	−0.412240	−	0.494111i
$898$	−44.5000	+	31.1593i	−1.48499	+	1.03980i
$899$	0.822588	−	1.42476i	0.0274348	−	0.0475185i
$900$		0			0
$901$	1.01896	+	1.76490i	0.0339466	+	0.0587973i
$902$	11.3282	+	5.28245i	0.377189	+	0.175886i
$903$	0.0657491	−	23.3167i	0.00218799	−	0.775931i
$904$	−0.455126	−	0.542398i	−0.0151373	−	0.0180399i
$905$		0			0
$906$	11.4591	+	43.2534i	0.380703	+	1.43700i
$907$	−13.2190	+	28.3482i	−0.438929	+	0.941287i	0.555060	+	0.831810i	$0.312695\pi$
$907$	−13.2190	+	28.3482i	−0.438929	+	0.941287i	−0.993989	+	0.109477i	$0.965083\pi$
$908$	28.3509	+	7.59659i	0.940856	+	0.252102i
$909$	−18.2185	−	10.6559i	−0.604268	−	0.353433i
$910$		0			0
$911$	−14.8888	−	2.62530i	−0.493288	−	0.0869800i	−0.0785299	−	0.996912i	$-0.525023\pi$
$911$	−14.8888	−	2.62530i	−0.493288	−	0.0869800i	−0.414758	+	0.909932i	$0.636134\pi$
$912$	−60.0036	−	22.0313i	−1.98692	−	0.729530i
$913$	−8.63545	−	18.5188i	−0.285792	−	0.612882i
$914$	8.03589	+	45.5738i	0.265804	+	1.50745i
$915$		0			0
$916$	−8.49147	−	7.12519i	−0.280566	−	0.235423i
$917$	34.1612	+	34.1612i	1.12810	+	1.12810i
$918$	−8.03239	−	6.85660i	−0.265108	−	0.226301i
$919$		−	1.84099i		−	0.0607286i	−0.999539	−	0.0303643i	$-0.990333\pi$
$919$		−	1.84099i		−	0.0607286i	0.999539	−	0.0303643i	$-0.00966675\pi$
$920$		0			0
$921$	−15.0911	−	7.08895i	−0.497267	−	0.233589i
$922$	28.3607	+	19.8584i	0.934010	+	0.654001i
$923$	40.3076	−	18.7957i	1.32674	−	0.618670i
$924$	12.1985	−	17.3172i	0.401303	−	0.569694i
$925$		0			0
$926$	12.7947	+	7.38704i	0.420461	+	0.242753i
$927$	−1.71241	−	20.9319i	−0.0562430	−	0.687495i
$928$	0.729766	−	2.72352i	0.0239557	−	0.0894041i
$929$	43.8338	−	15.9542i	1.43814	−	0.523441i	0.498888	−	0.866666i	$-0.333742\pi$
$929$	43.8338	−	15.9542i	1.43814	−	0.523441i	0.939253	+	0.343226i	$0.111520\pi$
$930$		0			0
$931$	24.6419	−	20.6770i	0.807605	−	0.677661i
$932$	29.9620	+	2.62133i	0.981438	+	0.0858647i
$933$	0.00365499	+	0.00637206i	0.000119659	+	0.000208612i
$934$	−1.18256	−	3.24907i	−0.0386947	−	0.106313i
$935$		0			0
$936$	−4.90505	+	26.9289i	−0.160327	+	0.880200i
$937$	−1.71942	−	6.41697i	−0.0561711	−	0.209633i	0.932136	−	0.362107i	$-0.117943\pi$
$937$	−1.71942	−	6.41697i	−0.0561711	−	0.209633i	−0.988307	+	0.152474i	$0.951276\pi$
$938$	−19.9277	−	28.4597i	−0.650663	−	0.929243i
$939$	−33.6327	−	23.6915i	−1.09756	−	0.773143i
$940$		0			0
$941$	−42.6827	+	7.52611i	−1.39142	+	0.245344i	−0.818612	−	0.574347i	$-0.805256\pi$
$941$	−42.6827	+	7.52611i	−1.39142	+	0.245344i	−0.572805	+	0.819692i	$0.694145\pi$
$942$	5.75340	+	15.9471i	0.187456	+	0.519585i
$943$	0.361535	+	4.13236i	0.0117732	+	0.134568i
$944$	52.6783			1.71453
$945$		0			0
$946$	−23.0528			−0.749511
$947$	4.39613	+	50.2480i	0.142855	+	1.63284i	0.642270	+	0.766478i	$0.277993\pi$
$947$	4.39613	+	50.2480i	0.142855	+	1.63284i	−0.499415	+	0.866363i	$0.666452\pi$
$948$	9.81481	−	11.6301i	0.318770	−	0.377727i
$949$	40.8709	−	7.20665i	1.32673	−	0.233938i
$950$		0			0
$951$	1.24763	−	0.577501i	0.0404571	−	0.0187268i
$952$	3.49573	+	4.99241i	0.113297	+	0.161805i
$953$	−8.14030	−	30.3800i	−0.263690	−	0.984105i	−0.963047	−	0.269333i	$-0.913197\pi$
$953$	−8.14030	−	30.3800i	−0.263690	−	0.984105i	0.699357	−	0.714773i	$-0.253470\pi$
$954$	−4.63157	−	8.12763i	−0.149953	−	0.263142i
$955$		0			0
$956$	9.44285	+	25.9440i	0.305404	+	0.839089i
$957$	1.41901	−	2.44187i	0.0458701	−	0.0789345i
$958$	−32.0762	−	2.80631i	−1.03634	−	0.0906677i
$959$	−8.73620	+	7.33054i	−0.282107	+	0.236716i
$960$		0			0
$961$	18.8945	−	6.87702i	0.609498	−	0.221839i
$962$	12.0938	−	45.1345i	0.389918	−	1.45519i
$963$	−5.62953	−	12.2525i	−0.181409	−	0.394831i
$964$	27.4146	+	15.8278i	0.882964	+	0.509780i
$965$		0			0
$966$	19.6181	+	1.77212i	0.631201	+	0.0570169i
$967$	−7.78315	+	3.62934i	−0.250289	+	0.116712i	−0.543715	−	0.839270i	$-0.682983\pi$
$967$	−7.78315	+	3.62934i	−0.250289	+	0.116712i	0.293425	+	0.955982i	$0.405205\pi$
$968$	−0.385149	−	0.269684i	−0.0123791	−	0.00866797i
$969$	−12.1224	+	8.43733i	−0.389426	+	0.271046i
$970$		0			0
$971$			29.8892i			0.959189i	0.877490	+	0.479595i	$0.159216\pi$
$971$			29.8892i			0.959189i	−0.877490	+	0.479595i	$0.840784\pi$
$972$	13.0949	+	11.3063i	0.420018	+	0.362650i
$973$	−13.1129	−	13.1129i	−0.420381	−	0.420381i
$974$	−44.0582	−	36.9692i	−1.41172	−	1.18457i
$975$		0			0
$976$	−9.10317	−	51.6266i	−0.291385	−	1.65253i
$977$	−15.1861	−	32.5668i	−0.485848	−	1.04190i	−0.984546	−	0.175128i	$-0.943966\pi$
$977$	−15.1861	−	32.5668i	−0.485848	−	1.04190i	0.498698	−	0.866776i	$-0.333812\pi$
$978$	16.7909	−	14.0088i	0.536915	−	0.447951i
$979$	1.67761	+	0.295808i	0.0536166	+	0.00945406i
$980$		0			0
$981$	−3.27915	+	8.85370i	−0.104695	+	0.282677i
$982$	−5.65254	−	1.51459i	−0.180380	−	0.0483327i
$983$	−15.4891	+	33.2165i	−0.494026	+	1.05944i	0.488371	+	0.872636i	$0.337591\pi$
$983$	−15.4891	+	33.2165i	−0.494026	+	1.05944i	−0.982397	+	0.186806i	$0.940186\pi$
$984$	4.17758	−	4.15409i	0.133177	−	0.132428i
$985$		0			0
$986$	−0.651216	−	0.776090i	−0.0207390	−	0.0247157i
$987$	−25.0479	−	14.5557i	−0.797284	−	0.463314i
$988$	−43.2547	−	20.1700i	−1.37611	−	0.641693i
$989$	−3.82526	−	6.62555i	−0.121636	−	0.210680i
$990$		0			0
$991$	−19.5180	+	33.8061i	−0.620009	+	1.07389i	0.369474	+	0.929241i	$0.379538\pi$
$991$	−19.5180	+	33.8061i	−0.620009	+	1.07389i	−0.989483	+	0.144647i	$0.953795\pi$
$992$	−15.2927	+	10.7081i	−0.485545	+	0.339982i
$993$	3.42063	−	9.31629i	0.108551	−	0.295644i
$994$	−15.5468	+	42.7146i	−0.493115	+	1.35482i
$995$		0			0
$996$	11.9647	−	1.01279i	0.379116	−	0.0320914i
$997$	39.0397	−	3.41553i	1.23640	−	0.108171i	0.549856	−	0.835259i	$-0.314683\pi$
$997$	39.0397	−	3.41553i	1.23640	−	0.108171i	0.686544	+	0.727088i	$0.259127\pi$
$998$	−8.01273	+	8.01273i	−0.253638	+	0.253638i
$999$	16.6079	+	16.8913i	0.525450	+	0.534416i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.ba.b.443.4		192
5.2	odd	4	inner	675.2.ba.b.632.13		192
5.3	odd	4		135.2.q.a.92.4	yes	192
5.4	even	2		135.2.q.a.38.13	yes	192
15.8	even	4		405.2.r.a.197.13		192
15.14	odd	2		405.2.r.a.278.4		192
27.5	odd	18	inner	675.2.ba.b.518.13		192
135.32	even	36	inner	675.2.ba.b.32.4		192
135.49	even	18		405.2.r.a.368.13		192
135.59	odd	18		135.2.q.a.113.4	yes	192
135.103	odd	36		405.2.r.a.287.4		192
135.113	even	36		135.2.q.a.32.13	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.13	✓	192	135.113	even	36
135.2.q.a.38.13	yes	192	5.4	even	2
135.2.q.a.92.4	yes	192	5.3	odd	4
135.2.q.a.113.4	yes	192	135.59	odd	18
405.2.r.a.197.13		192	15.8	even	4
405.2.r.a.278.4		192	15.14	odd	2
405.2.r.a.287.4		192	135.103	odd	36
405.2.r.a.368.13		192	135.49	even	18
675.2.ba.b.32.4		192	135.32	even	36	inner
675.2.ba.b.443.4		192	1.1	even	1	trivial
675.2.ba.b.518.13		192	27.5	odd	18	inner
675.2.ba.b.632.13		192	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.153697 - 1.75676i) q^{2} +(-1.70488 - 0.305576i) q^{3} +(-1.09297 + 0.192720i) q^{4} +(-0.274789 + 3.04204i) q^{6} +(1.93217 + 2.75943i) q^{7} +(-0.406292 - 1.51630i) q^{8} +(2.81325 + 1.04194i) q^{9} +O(q^{10})\)	\(q+(-0.153697 - 1.75676i) q^{2} +(-1.70488 - 0.305576i) q^{3} +(-1.09297 + 0.192720i) q^{4} +(-0.274789 + 3.04204i) q^{6} +(1.93217 + 2.75943i) q^{7} +(-0.406292 - 1.51630i) q^{8} +(2.81325 + 1.04194i) q^{9} +(-1.11880 - 3.07388i) q^{11} +(1.92227 + 0.00542048i) q^{12} +(-5.79013 - 0.506571i) q^{13} +(4.55068 - 3.81848i) q^{14} +(-4.68713 + 1.70598i) q^{16} +(-0.298295 + 1.11325i) q^{17} +(1.39806 - 5.10234i) q^{18} +(-6.40749 - 3.69937i) q^{19} +(-2.45091 - 5.29492i) q^{21} +(-5.22812 + 2.43791i) q^{22} +(-1.56820 - 1.09807i) q^{23} +(0.229334 + 2.70927i) q^{24} +10.2497i q^{26} +(-4.47786 - 2.63605i) q^{27} +(-2.64360 - 2.64360i) q^{28} +(-0.381851 - 0.320411i) q^{29} +(0.573116 + 3.25030i) q^{31} +(2.39054 + 5.12653i) q^{32} +(0.968121 + 5.58249i) q^{33} +(2.00157 + 0.352930i) q^{34} +(-3.27559 - 0.596642i) q^{36} +(-4.40348 - 1.17991i) q^{37} +(-5.51409 + 11.8250i) q^{38} +(9.71669 + 2.63297i) q^{39} +(-1.39279 - 1.65986i) q^{41} +(-8.92522 + 5.11947i) q^{42} +(3.62184 + 1.68889i) q^{43} +(1.81521 + 3.14404i) q^{44} +(-1.68801 + 2.92372i) q^{46} +(4.06724 - 2.84791i) q^{47} +(8.51231 - 1.47621i) q^{48} +(-1.48701 + 4.08553i) q^{49} +(0.848742 - 1.80681i) q^{51} +(6.42605 - 0.562207i) q^{52} +(1.25033 - 1.25033i) q^{53} +(-3.94268 + 8.27168i) q^{54} +(3.39910 - 4.05089i) q^{56} +(9.79358 + 8.26496i) q^{57} +(-0.504196 + 0.720066i) q^{58} +(-9.92422 - 3.61212i) q^{59} +(-1.82504 + 10.3503i) q^{61} +(5.62192 - 1.50639i) q^{62} +(2.56051 + 9.77616i) q^{63} +(-0.000691655 + 0.000399327i) q^{64} +(9.65830 - 2.55877i) q^{66} +(0.509729 - 5.82623i) q^{67} +(0.111481 - 1.27424i) q^{68} +(2.33806 + 2.35128i) q^{69} +(-6.62671 + 3.82593i) q^{71} +(0.436900 - 4.68906i) q^{72} +(-6.89704 + 1.84806i) q^{73} +(-1.39602 + 7.91721i) q^{74} +(7.71612 + 2.80844i) q^{76} +(6.32044 - 9.02653i) q^{77} +(3.13207 - 17.4746i) q^{78} +(5.08874 - 6.06452i) q^{79} +(6.82871 + 5.86248i) q^{81} +(-2.70191 + 2.70191i) q^{82} +(6.22270 - 0.544416i) q^{83} +(3.69920 + 5.31485i) q^{84} +(2.41031 - 6.62228i) q^{86} +(0.553100 + 0.662947i) q^{87} +(-4.20637 + 2.94533i) q^{88} +(-0.260380 + 0.450992i) q^{89} +(-9.78968 - 16.9562i) q^{91} +(1.92562 + 0.897929i) q^{92} +(0.0161196 - 5.71652i) q^{93} +(-5.62822 - 6.70745i) q^{94} +(-2.50905 - 9.47063i) q^{96} +(-1.99563 + 4.27963i) q^{97} +(7.40585 + 1.98439i) q^{98} +(0.0553442 - 9.81332i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8}+O(q^{10}) \) 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8	\( 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31} + 48 q^{32} + 6 q^{33} + 12 q^{36} + 6 q^{37} - 12 q^{38} + 24 q^{41} + 24 q^{42} + 12 q^{43} - 12 q^{46} + 6 q^{47} - 12 q^{48} + 144 q^{51} - 12 q^{52} + 180 q^{56} + 12 q^{57} + 12 q^{58} - 60 q^{61} + 18 q^{62} + 54 q^{63} + 72 q^{66} - 24 q^{67} + 60 q^{68} - 36 q^{71} - 180 q^{72} + 6 q^{73} - 72 q^{76} - 132 q^{77} - 78 q^{78} + 12 q^{81} + 24 q^{82} - 48 q^{83} + 12 q^{86} - 144 q^{87} + 48 q^{88} - 12 q^{91} - 258 q^{92} - 180 q^{93} - 12 q^{96} - 24 q^{97} - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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