LMFDB - Embedded newform 825.2.ct.b.707.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(218,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 15, 12]))

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

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

chi := DirichletCharacter("825.218");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.ct (of order $20$, degree $8$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			707.7
Character	$\chi$	$=$	825.707
Dual form			825.2.ct.b.818.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.149735 + 0.945387i) q^{2} +(-0.913834 + 1.47136i) q^{3} +(1.03078 + 0.334920i) q^{4} +(-1.25417 - 1.08424i) q^{6} +(-0.821076 + 0.418359i) q^{7} +(-1.34007 + 2.63003i) q^{8} +(-1.32982 - 2.68916i) q^{9} +O(q^{10})$	\(q+(-0.149735 + 0.945387i) q^{2} +(-0.913834 + 1.47136i) q^{3} +(1.03078 + 0.334920i) q^{4} +(-1.25417 - 1.08424i) q^{6} +(-0.821076 + 0.418359i) q^{7} +(-1.34007 + 2.63003i) q^{8} +(-1.32982 - 2.68916i) q^{9} +(0.392844 + 3.29328i) q^{11} +(-1.43475 + 1.21059i) q^{12} +(0.142038 - 0.896795i) q^{13} +(-0.272568 - 0.838878i) q^{14} +(-0.532077 - 0.386576i) q^{16} +(-1.56555 + 0.247959i) q^{17} +(2.74142 - 0.854531i) q^{18} +(-5.01090 + 1.62814i) q^{19} +(0.134769 - 1.59041i) q^{21} +(-3.17224 - 0.121728i) q^{22} +(-2.25932 - 2.25932i) q^{23} +(-2.64513 - 4.37513i) q^{24} +(0.826550 + 0.268563i) q^{26} +(5.17196 + 0.500803i) q^{27} +(-0.986463 + 0.156240i) q^{28} +(-2.40096 + 7.38940i) q^{29} +(4.53969 - 3.29827i) q^{31} +(-3.72927 + 3.72927i) q^{32} +(-5.20460 - 2.43149i) q^{33} -1.51718i q^{34} +(-0.470091 - 3.21731i) q^{36} +(-7.40678 + 3.77394i) q^{37} +(-0.788918 - 4.98103i) q^{38} +(1.18971 + 1.02851i) q^{39} +(-4.98402 + 1.61941i) q^{41} +(1.48338 + 0.365548i) q^{42} +(7.44106 - 7.44106i) q^{43} +(-0.698048 + 3.52620i) q^{44} +(2.47423 - 1.79763i) q^{46} +(-1.94269 - 0.989848i) q^{47} +(1.05502 - 0.429611i) q^{48} +(-3.61536 + 4.97611i) q^{49} +(1.06581 - 2.53008i) q^{51} +(0.446764 - 0.876824i) q^{52} +(3.30793 + 0.523924i) q^{53} +(-1.24787 + 4.81452i) q^{54} -2.72008i q^{56} +(2.18354 - 8.86070i) q^{57} +(-6.62633 - 3.37629i) q^{58} +(3.57773 - 11.0111i) q^{59} +(4.04491 + 2.93880i) q^{61} +(2.43840 + 4.78563i) q^{62} +(2.21692 + 1.65167i) q^{63} +(-3.74035 - 5.14815i) q^{64} +(3.07801 - 4.55628i) q^{66} +(2.52797 + 2.52797i) q^{67} +(-1.69678 - 0.268743i) q^{68} +(5.38891 - 1.25963i) q^{69} +(2.53621 - 3.49079i) q^{71} +(8.85460 + 0.106199i) q^{72} +(5.62549 + 11.0406i) q^{73} +(-2.45879 - 7.56737i) q^{74} -5.71042 q^{76} +(-1.70033 - 2.53968i) q^{77} +(-1.15048 + 0.970734i) q^{78} +(-6.22215 - 8.56405i) q^{79} +(-5.46318 + 7.15218i) q^{81} +(-0.784685 - 4.95431i) q^{82} +(-0.0187595 - 0.118443i) q^{83} +(0.671577 - 1.59422i) q^{84} +(5.92050 + 8.14886i) q^{86} +(-8.67840 - 10.2854i) q^{87} +(-9.18784 - 3.38001i) q^{88} -10.7445 q^{89} +(0.258558 + 0.795760i) q^{91} +(-1.57216 - 3.08554i) q^{92} +(0.704441 + 9.69360i) q^{93} +(1.22668 - 1.68838i) q^{94} +(-2.07917 - 8.89503i) q^{96} +(11.0231 + 1.74588i) q^{97} +(-4.16301 - 4.16301i) q^{98} +(8.33374 - 5.43588i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{3} - 12 q^{6} + 20 q^{7}+O(q^{10}) $ 160 * q + 8 * q^3 - 12 * q^6 + 20 * q^7	$ 160 q + 8 q^{3} - 12 q^{6} + 20 q^{7} + 68 q^{12} + 4 q^{13} - 8 q^{16} - 2 q^{18} - 24 q^{21} + 20 q^{22} + 14 q^{27} - 8 q^{28} - 8 q^{31} - 38 q^{33} - 124 q^{36} - 16 q^{37} - 74 q^{42} - 34 q^{48} - 116 q^{51} - 12 q^{52} - 30 q^{57} - 112 q^{58} + 14 q^{63} - 20 q^{66} - 128 q^{67} - 92 q^{72} + 80 q^{73} - 176 q^{76} - 20 q^{78} + 52 q^{81} - 12 q^{82} + 36 q^{87} + 276 q^{88} + 128 q^{91} + 8 q^{93} + 152 q^{96} + 96 q^{97}+O(q^{100}) $ 160 * q + 8 * q^3 - 12 * q^6 + 20 * q^7 + 68 * q^12 + 4 * q^13 - 8 * q^16 - 2 * q^18 - 24 * q^21 + 20 * q^22 + 14 * q^27 - 8 * q^28 - 8 * q^31 - 38 * q^33 - 124 * q^36 - 16 * q^37 - 74 * q^42 - 34 * q^48 - 116 * q^51 - 12 * q^52 - 30 * q^57 - 112 * q^58 + 14 * q^63 - 20 * q^66 - 128 * q^67 - 92 * q^72 + 80 * q^73 - 176 * q^76 - 20 * q^78 + 52 * q^81 - 12 * q^82 + 36 * q^87 + 276 * q^88 + 128 * q^91 + 8 * q^93 + 152 * q^96 + 96 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.149735	+	0.945387i	−0.105878	+	0.668490i	0.876474	+	0.481449i	$0.159889\pi$
$2$	−0.149735	+	0.945387i	−0.105878	+	0.668490i	−0.982352	+	0.187040i	$0.940111\pi$
$3$	−0.913834	+	1.47136i	−0.527602	+	0.849492i
$3$	−0.913834	+	1.47136i	−0.527602	+	0.849492i
$4$	1.03078	+	0.334920i	0.515388	+	0.167460i
$5$		0			0
$5$		0			0
$6$	−1.25417	−	1.08424i	−0.512015	−	0.442639i
$7$	−0.821076	+	0.418359i	−0.310338	+	0.158125i	−0.602222	−	0.798329i	$-0.705718\pi$
$7$	−0.821076	+	0.418359i	−0.310338	+	0.158125i	0.291884	+	0.956454i	$0.405718\pi$
$8$	−1.34007	+	2.63003i	−0.473785	+	0.929855i
$9$	−1.32982	−	2.68916i	−0.443272	−	0.896387i
$10$		0			0
$11$	0.392844	+	3.29328i	0.118447	+	0.992960i
$11$	0.392844	+	3.29328i	0.118447	+	0.992960i
$12$	−1.43475	+	1.21059i	−0.414176	+	0.349466i
$13$	0.142038	−	0.896795i	0.0393944	−	0.248726i	−0.960130	−	0.279553i	$-0.909814\pi$
$13$	0.142038	−	0.896795i	0.0393944	−	0.248726i	0.999525	+	0.0308263i	$0.00981388\pi$
$14$	−0.272568	−	0.838878i	−0.0728468	−	0.224200i
$15$		0			0
$16$	−0.532077	−	0.386576i	−0.133019	−	0.0966441i
$17$	−1.56555	+	0.247959i	−0.379702	+	0.0601388i	−0.343368	−	0.939201i	$-0.611568\pi$
$17$	−1.56555	+	0.247959i	−0.379702	+	0.0601388i	−0.0363334	+	0.999340i	$0.511568\pi$
$18$	2.74142	−	0.854531i	0.646158	−	0.201415i
$19$	−5.01090	+	1.62814i	−1.14958	+	0.373521i	−0.820985	−	0.570950i	$-0.806575\pi$
$19$	−5.01090	+	1.62814i	−1.14958	+	0.373521i	−0.328595	+	0.944471i	$0.606575\pi$
$20$		0			0
$21$	0.134769	−	1.59041i	0.0294090	−	0.347056i
$22$	−3.17224	−	0.121728i	−0.676325	−	0.0259524i
$23$	−2.25932	−	2.25932i	−0.471100	−	0.471100i	0.431171	−	0.902270i	$-0.358101\pi$
$23$	−2.25932	−	2.25932i	−0.471100	−	0.471100i	−0.902270	+	0.431171i	$0.858101\pi$
$24$	−2.64513	−	4.37513i	−0.539934	−	0.893069i
$25$		0			0
$26$	0.826550	+	0.268563i	0.162100	+	0.0526694i
$27$	5.17196	+	0.500803i	0.995345	+	0.0963796i
$28$	−0.986463	+	0.156240i	−0.186424	+	0.0295267i
$29$	−2.40096	+	7.38940i	−0.445847	+	1.37218i	0.435705	+	0.900090i	$0.356499\pi$
$29$	−2.40096	+	7.38940i	−0.445847	+	1.37218i	−0.881552	+	0.472087i	$0.843501\pi$
$30$		0			0
$31$	4.53969	−	3.29827i	0.815352	−	0.592388i	−0.100026	−	0.994985i	$-0.531892\pi$
$31$	4.53969	−	3.29827i	0.815352	−	0.592388i	0.915377	+	0.402597i	$0.131892\pi$
$32$	−3.72927	+	3.72927i	−0.659247	+	0.659247i
$33$	−5.20460	−	2.43149i	−0.906004	−	0.423268i
$34$		−	1.51718i		−	0.260194i
$35$		0			0
$36$	−0.470091	−	3.21731i	−0.0783485	−	0.536218i
$37$	−7.40678	+	3.77394i	−1.21767	+	0.620432i	−0.940305	−	0.340333i	$-0.889460\pi$
$37$	−7.40678	+	3.77394i	−1.21767	+	0.620432i	−0.277362	+	0.960765i	$0.589460\pi$
$38$	−0.788918	−	4.98103i	−0.127979	−	0.808030i
$39$	1.18971	+	1.02851i	0.190506	+	0.164694i
$40$		0			0
$41$	−4.98402	+	1.61941i	−0.778373	+	0.252909i	−0.671145	−	0.741326i	$-0.734197\pi$
$41$	−4.98402	+	1.61941i	−0.778373	+	0.252909i	−0.107227	+	0.994235i	$0.534197\pi$
$42$	1.48338	+	0.365548i	0.228890	+	0.0564053i
$43$	7.44106	−	7.44106i	1.13475	−	1.13475i	0.145374	−	0.989377i	$-0.453562\pi$
$43$	7.44106	−	7.44106i	1.13475	−	1.13475i	0.989377	−	0.145374i	$-0.0464385\pi$
$44$	−0.698048	+	3.52620i	−0.105235	+	0.531595i
$45$		0			0
$46$	2.47423	−	1.79763i	0.364805	−	0.265046i
$47$	−1.94269	−	0.989848i	−0.283370	−	0.144384i	0.306529	−	0.951861i	$-0.400832\pi$
$47$	−1.94269	−	0.989848i	−0.283370	−	0.144384i	−0.589899	+	0.807477i	$0.700832\pi$
$48$	1.05502	−	0.429611i	0.152280	−	0.0620091i
$49$	−3.61536	+	4.97611i	−0.516479	+	0.710873i
$50$		0			0
$51$	1.06581	−	2.53008i	0.149244	−	0.354283i
$52$	0.446764	−	0.876824i	0.0619550	−	0.121594i
$53$	3.30793	+	0.523924i	0.454379	+	0.0719665i	0.379429	−	0.925221i	$-0.376120\pi$
$53$	3.30793	+	0.523924i	0.454379	+	0.0719665i	0.0749496	+	0.997187i	$0.476120\pi$
$54$	−1.24787	+	4.81452i	−0.169814	+	0.655173i
$55$		0			0
$56$		−	2.72008i		−	0.363486i
$57$	2.18354	−	8.86070i	0.289218	−	1.17363i
$58$	−6.62633	−	3.37629i	−0.870080	−	0.443328i
$59$	3.57773	−	11.0111i	0.465781	−	1.43353i	−0.392216	−	0.919873i	$-0.628291\pi$
$59$	3.57773	−	11.0111i	0.465781	−	1.43353i	0.857997	−	0.513654i	$-0.171709\pi$
$60$		0			0
$61$	4.04491	+	2.93880i	0.517898	+	0.376275i	0.815811	−	0.578318i	$-0.196291\pi$
$61$	4.04491	+	2.93880i	0.517898	+	0.376275i	−0.297913	+	0.954593i	$0.596291\pi$
$62$	2.43840	+	4.78563i	0.309677	+	0.607775i
$63$	2.21692	+	1.65167i	0.279305	+	0.208090i
$64$	−3.74035	−	5.14815i	−0.467544	−	0.643519i
$65$		0			0
$66$	3.07801	−	4.55628i	0.378877	−	0.560840i
$67$	2.52797	+	2.52797i	0.308841	+	0.308841i	0.844460	−	0.535619i	$-0.179922\pi$
$67$	2.52797	+	2.52797i	0.308841	+	0.308841i	−0.535619	+	0.844460i	$0.679922\pi$
$68$	−1.69678	−	0.268743i	−0.205765	−	0.0325899i
$69$	5.38891	−	1.25963i	0.648749	−	0.151642i
$70$		0			0
$71$	2.53621	−	3.49079i	0.300992	−	0.414280i	−0.631553	−	0.775332i	$-0.717582\pi$
$71$	2.53621	−	3.49079i	0.300992	−	0.414280i	0.932546	+	0.361052i	$0.117582\pi$
$72$	8.85460	+	0.106199i	1.04353	+	0.0125157i
$73$	5.62549	+	11.0406i	0.658413	+	1.29221i	0.942755	+	0.333486i	$0.108225\pi$
$73$	5.62549	+	11.0406i	0.658413	+	1.29221i	−0.284342	+	0.958723i	$0.591775\pi$
$74$	−2.45879	−	7.56737i	−0.285828	−	0.879688i
$75$		0			0
$76$	−5.71042			−0.655030
$77$	−1.70033	−	2.53968i	−0.193770	−	0.289424i
$78$	−1.15048	+	0.970734i	−0.130266	+	0.109914i
$79$	−6.22215	−	8.56405i	−0.700046	−	0.963531i	−0.999954	−	0.00956273i	$-0.996956\pi$
$79$	−6.22215	−	8.56405i	−0.700046	−	0.963531i	0.299908	−	0.953968i	$-0.403044\pi$
$80$		0			0
$81$	−5.46318	+	7.15218i	−0.607020	+	0.794687i
$82$	−0.784685	−	4.95431i	−0.0866540	−	0.547112i
$83$	−0.0187595	−	0.118443i	−0.00205913	−	0.0130008i	0.986637	−	0.162931i	$-0.0520950\pi$
$83$	−0.0187595	−	0.118443i	−0.00205913	−	0.0130008i	−0.988697	+	0.149931i	$0.952095\pi$
$84$	0.671577	−	1.59422i	0.0732750	−	0.173944i
$85$		0			0
$86$	5.92050	+	8.14886i	0.638424	+	0.878715i
$87$	−8.67840	−	10.2854i	−0.930423	−	1.10271i
$88$	−9.18784	−	3.38001i	−0.979427	−	0.360311i
$89$	−10.7445			−1.13891			−0.569457	−	0.822021i	$-0.692847\pi$
$89$	−10.7445			−1.13891			−0.569457	+	0.822021i	$0.692847\pi$
$90$		0			0
$91$	0.258558	+	0.795760i	0.0271043	+	0.0834183i
$92$	−1.57216	−	3.08554i	−0.163909	−	0.321690i
$93$	0.704441	+	9.69360i	0.0730472	+	1.00518i
$94$	1.22668	−	1.68838i	0.126522	−	0.174143i
$95$		0			0
$96$	−2.07917	−	8.89503i	−0.212205	−	0.907845i
$97$	11.0231	+	1.74588i	1.11922	+	0.177268i	0.688514	−	0.725223i	$-0.258263\pi$
$97$	11.0231	+	1.74588i	1.11922	+	0.177268i	0.430710	+	0.902490i	$0.358263\pi$
$98$	−4.16301	−	4.16301i	−0.420527	−	0.420527i
$99$	8.33374	−	5.43588i	0.837573	−	0.546326i
$100$		0			0
$101$	−3.11015	−	4.28075i	−0.309471	−	0.425951i	0.625745	−	0.780028i	$-0.284795\pi$
$101$	−3.11015	−	4.28075i	−0.309471	−	0.425951i	−0.935216	+	0.354077i	$0.884795\pi$
$102$	2.23232	+	1.38645i	0.221033	+	0.137279i
$103$	0.649175	+	1.27408i	0.0639652	+	0.125539i	0.920775	−	0.390093i	$-0.127557\pi$
$103$	0.649175	+	1.27408i	0.0639652	+	0.125539i	−0.856810	+	0.515632i	$0.827557\pi$
$104$	2.16825	+	1.57533i	0.212615	+	0.154474i
$105$		0			0
$106$	−0.990622	+	3.04882i	−0.0962177	+	0.296128i
$107$	5.04348	+	2.56978i	0.487572	+	0.248430i	0.680453	−	0.732792i	$-0.261783\pi$
$107$	5.04348	+	2.56978i	0.487572	+	0.248430i	−0.192881	+	0.981222i	$0.561783\pi$
$108$	5.16341	+	2.24841i	0.496849	+	0.216353i
$109$			8.51522i			0.815611i	0.913069	+	0.407805i	$0.133706\pi$
$109$			8.51522i			0.815611i	−0.913069	+	0.407805i	$0.866294\pi$
$110$		0			0
$111$	1.21573	−	14.3468i	0.115392	−	1.36174i
$112$	0.598603	+	0.0948095i	0.0565627	+	0.00895865i
$113$	−0.453174	+	0.889404i	−0.0426310	+	0.0836681i	−0.911339	−	0.411656i	$-0.864951\pi$
$113$	−0.453174	+	0.889404i	−0.0426310	+	0.0836681i	0.868708	+	0.495324i	$0.164951\pi$
$114$	8.04984	+	3.39105i	0.753937	+	0.317601i
$115$		0			0
$116$	−4.94971	+	6.81269i	−0.459569	+	0.632542i
$117$	−2.60051	+	0.810609i	−0.240417	+	0.0749408i
$118$	9.87408	+	5.03109i	0.908982	+	0.463150i
$119$	1.18170	−	0.858555i	0.108326	−	0.0787036i
$120$		0			0
$121$	−10.6913	+	2.58749i	−0.971941	+	0.235226i
$122$	−3.38397	+	3.38397i	−0.306370	+	0.306370i
$123$	2.17183	−	8.81316i	0.195827	−	0.794656i
$124$	5.78406	−	1.87935i	0.519424	−	0.168771i
$125$		0			0
$126$	−1.89341	+	1.84853i	−0.168679	+	0.164680i
$127$	1.96005	+	12.3753i	0.173927	+	1.09813i	0.907973	+	0.419030i	$0.137630\pi$
$127$	1.96005	+	12.3753i	0.173927	+	1.09813i	−0.734046	+	0.679100i	$0.762370\pi$
$128$	−3.97124	+	2.02345i	−0.351011	+	0.178849i
$129$	4.14861	+	17.7484i	0.365264	+	1.56266i
$130$		0			0
$131$			7.72546i			0.674976i	0.941330	+	0.337488i	$0.109577\pi$
$131$			7.72546i			0.674976i	−0.941330	+	0.337488i	$0.890423\pi$
$132$	−4.55043	−	4.24945i	−0.396064	−	0.369867i
$133$	3.43319	−	3.43319i	0.297695	−	0.297695i
$134$	−2.76843	+	2.01139i	−0.239156	+	0.173757i
$135$		0			0
$136$	1.44580	−	4.44972i	0.123976	−	0.381560i
$137$	−16.2879	+	2.57976i	−1.39157	+	0.220403i	−0.806815	−	0.590805i	$-0.798810\pi$
$137$	−16.2879	+	2.57976i	−1.39157	+	0.220403i	−0.584758	+	0.811208i	$0.698810\pi$
$138$	0.383936	+	5.28322i	0.0326828	+	0.449737i
$139$	8.71297	+	2.83102i	0.739025	+	0.240124i	0.654252	−	0.756277i	$-0.272984\pi$
$139$	8.71297	+	2.83102i	0.739025	+	0.240124i	0.0847727	+	0.996400i	$0.472984\pi$
$140$		0			0
$141$	3.23172	−	1.95384i	0.272160	−	0.164543i
$142$	2.92039	+	2.92039i	0.245074	+	0.245074i
$143$	3.00919	+	0.115471i	0.251641	+	0.00965616i
$144$	−0.332002	+	1.94492i	−0.0276668	+	0.162076i
$145$		0			0
$146$	−11.2800	+	3.66510i	−0.933540	+	0.303326i
$147$	−4.01783	−	9.86683i	−0.331385	−	0.813803i
$148$	−8.89870	+	1.40942i	−0.731469	+	0.115853i
$149$	14.8244	+	10.7706i	1.21446	+	0.882360i	0.995629	−	0.0934013i	$-0.0297740\pi$
$149$	14.8244	+	10.7706i	1.21446	+	0.882360i	0.218836	+	0.975762i	$0.429774\pi$
$150$		0			0
$151$	4.94120	+	15.2075i	0.402109	+	1.23757i	0.923285	+	0.384116i	$0.125494\pi$
$151$	4.94120	+	15.2075i	0.402109	+	1.23757i	−0.521176	+	0.853449i	$0.674506\pi$
$152$	2.43288	−	15.3606i	0.197333	−	1.24591i
$153$	2.74869	+	3.88028i	0.222219	+	0.313702i
$154$	2.65558	−	1.22719i	0.213993	−	0.0988898i
$155$		0			0
$156$	0.881858	+	1.45862i	0.0706052	+	0.116783i
$157$	7.69283	−	15.0980i	0.613955	−	1.20495i	−0.349463	−	0.936950i	$-0.613636\pi$
$157$	7.69283	−	15.0980i	0.613955	−	1.20495i	0.963418	−	0.268004i	$-0.0863641\pi$
$158$	9.02801	−	4.60000i	0.718230	−	0.365957i
$159$	−3.79378	+	4.38838i	−0.300866	+	0.348021i
$160$		0			0
$161$	2.80028	+	0.909865i	0.220693	+	0.0717074i
$162$	−5.94355	−	6.23575i	−0.466970	−	0.489926i
$163$	−3.40276	+	21.4842i	−0.266524	+	1.68277i	0.384039	+	0.923317i	$0.374533\pi$
$163$	−3.40276	+	21.4842i	−0.266524	+	1.68277i	−0.650563	+	0.759452i	$0.725467\pi$
$164$	−5.67978			−0.443516
$165$		0			0
$166$	0.114783			0.00890892
$167$	−3.19153	+	20.1506i	−0.246968	+	1.55930i	0.482880	+	0.875687i	$0.339591\pi$
$167$	−3.19153	+	20.1506i	−0.246968	+	1.55930i	−0.729848	+	0.683610i	$0.760409\pi$
$168$	4.00223	+	2.48570i	0.308778	+	0.191776i
$169$	11.5797	+	3.76246i	0.890744	+	0.289420i
$170$		0			0
$171$	11.0419	+	11.3100i	0.844396	+	0.864897i
$172$	10.1622	−	5.17791i	0.774862	−	0.394812i
$173$	2.26013	−	4.43575i	0.171834	−	0.337244i	−0.788988	−	0.614408i	$-0.789395\pi$
$173$	2.26013	−	4.43575i	0.171834	−	0.337244i	0.960822	+	0.277165i	$0.0893947\pi$
$174$	11.0231	−	6.66438i	0.835660	−	0.505225i
$175$		0			0
$176$	1.06408	−	1.90414i	0.0802080	−	0.143530i
$177$	12.9319	+	15.3265i	0.972023	+	1.15201i
$178$	1.60882	−	10.1577i	0.120586	−	0.761352i
$179$	1.26602	+	3.89640i	0.0946266	+	0.291231i	0.987156	−	0.159758i	$-0.0510714\pi$
$179$	1.26602	+	3.89640i	0.0946266	+	0.291231i	−0.892530	+	0.450989i	$0.851071\pi$
$180$		0			0
$181$	−0.565059	−	0.410539i	−0.0420005	−	0.0305151i	0.566587	−	0.824002i	$-0.308264\pi$
$181$	−0.565059	−	0.410539i	−0.0420005	−	0.0305151i	−0.608587	+	0.793487i	$0.708264\pi$
$182$	−0.791017	+	0.125285i	−0.0586341	+	0.00928672i
$183$	−8.02042	+	3.26596i	−0.592886	+	0.241427i
$184$	8.96969	−	2.91443i	0.661254	−	0.214854i
$185$		0			0
$186$	−9.26968	−	0.785497i	−0.679686	−	0.0575955i
$187$	−1.43161	−	5.05838i	−0.104690	−	0.369905i
$188$	−1.67096	−	1.67096i	−0.121867	−	0.121867i
$189$	−4.45609	+	1.75254i	−0.324133	+	0.127479i
$190$		0			0
$191$	21.4085	+	6.95604i	1.54906	+	0.503322i	0.953860	−	0.300253i	$-0.0970710\pi$
$191$	21.4085	+	6.95604i	1.54906	+	0.503322i	0.595205	+	0.803574i	$0.297071\pi$
$192$	10.9929	−	0.798860i	0.793341	−	0.0576528i
$193$	8.47373	−	1.34211i	0.609953	−	0.0966070i	0.156186	−	0.987728i	$-0.450080\pi$
$193$	8.47373	−	1.34211i	0.609953	−	0.0966070i	0.453766	+	0.891121i	$0.350080\pi$
$194$	−3.30107	+	10.1597i	−0.237003	+	0.729421i
$195$		0			0
$196$	−5.39322	+	3.91840i	−0.385230	+	0.279886i
$197$	−4.23275	+	4.23275i	−0.301571	+	0.301571i	−0.841628	−	0.540057i	$-0.818403\pi$
$197$	−4.23275	+	4.23275i	−0.301571	+	0.301571i	0.540057	+	0.841628i	$0.318403\pi$
$198$	3.89116	+	8.69255i	0.276533	+	0.617753i
$199$		−	1.35667i		−	0.0961715i	−0.998843	−	0.0480858i	$-0.984688\pi$
$199$		−	1.35667i		−	0.0961715i	0.998843	−	0.0480858i	$-0.0153121\pi$
$200$		0			0
$201$	−6.02970	+	1.40942i	−0.425303	+	0.0994126i
$202$	4.51266	−	2.29932i	0.317510	−	0.161779i
$203$	−1.12005	−	7.07172i	−0.0786122	−	0.496338i
$204$	1.94599	−	2.25099i	0.136247	−	0.157601i
$205$		0			0
$206$	−1.30170	+	0.422948i	−0.0906938	+	0.0294682i
$207$	−3.07119	+	9.08014i	−0.213462	+	0.631113i
$208$	−0.422255	+	0.422255i	−0.0292781	+	0.0292781i
$209$	−7.33042	−	15.8627i	−0.507056	−	1.09724i
$210$		0			0
$211$	−5.53696	+	4.02283i	−0.381180	+	0.276943i	−0.761832	−	0.647775i	$-0.775700\pi$
$211$	−5.53696	+	4.02283i	−0.381180	+	0.276943i	0.380652	+	0.924718i	$0.375700\pi$
$212$	3.23426	+	1.64794i	0.222130	+	0.113181i
$213$	2.81855	+	6.92168i	0.193124	+	0.474266i
$214$	−3.18462	+	4.38326i	−0.217696	+	0.299633i
$215$		0			0
$216$	−8.24789	+	12.9313i	−0.561198	+	0.879863i
$217$	−2.34756	+	4.60735i	−0.159363	+	0.312768i
$218$	−8.05018	−	1.27502i	−0.545227	−	0.0863555i
$219$	−21.3855	−	1.81218i	−1.44510	−	0.122455i
$220$		0			0
$221$			1.43920i			0.0968108i
$222$	13.3813	+	3.29755i	0.898091	+	0.221317i
$223$	−3.76420	−	1.91796i	−0.252069	−	0.128436i	0.323391	−	0.946265i	$-0.395177\pi$
$223$	−3.76420	−	1.91796i	−0.252069	−	0.128436i	−0.575460	+	0.817830i	$0.695177\pi$
$224$	1.50184	−	4.62219i	0.100346	−	0.308833i
$225$		0			0
$226$	−0.772976	−	0.561600i	−0.0514176	−	0.0373571i
$227$	9.37641	+	18.4022i	0.622334	+	1.22140i	0.959965	+	0.280121i	$0.0903744\pi$
$227$	9.37641	+	18.4022i	0.622334	+	1.22140i	−0.337631	+	0.941279i	$0.609626\pi$
$228$	5.21837	−	8.40210i	0.345595	−	0.556442i
$229$	17.3082	+	23.8227i	1.14376	+	1.57425i	0.758812	+	0.651310i	$0.225780\pi$
$229$	17.3082	+	23.8227i	1.14376	+	1.57425i	0.384946	+	0.922939i	$0.374220\pi$
$230$		0			0
$231$	5.29061	−	0.180953i	0.348097	−	0.0119059i
$232$	−16.2169	−	16.2169i	−1.06469	−	1.06469i
$233$	−17.0946	−	2.70752i	−1.11990	−	0.177375i	−0.431086	−	0.902311i	$-0.641870\pi$
$233$	−17.0946	−	2.70752i	−1.11990	−	0.177375i	−0.688817	+	0.724935i	$0.741870\pi$
$234$	−0.376953	−	2.57987i	−0.0246422	−	0.168651i
$235$		0			0
$236$	7.37569	−	10.1518i	0.480117	−	0.660824i
$237$	18.2868	−	1.32892i	1.18786	−	0.0863225i
$238$	0.634726	+	1.24572i	0.0411431	+	0.0807480i
$239$	−6.19241	−	19.0583i	−0.400553	−	1.23278i	−0.924551	−	0.381057i	$-0.875560\pi$
$239$	−6.19241	−	19.0583i	−0.400553	−	1.23278i	0.523998	−	0.851720i	$-0.324440\pi$
$240$		0			0
$241$	5.99679			0.386287			0.193144	−	0.981171i	$-0.438132\pi$
$241$	5.99679			0.386287			0.193144	+	0.981171i	$0.438132\pi$
$242$	−0.845316	−	10.4949i	−0.0543390	−	0.674638i
$243$	−5.53102	−	14.5742i	−0.354815	−	0.934936i
$244$	3.18514	+	4.38397i	0.203908	+	0.280655i
$245$		0			0
$246$	8.00665	+	3.37286i	0.510486	+	0.215045i
$247$	0.748368	+	4.72501i	0.0476175	+	0.300645i
$248$	2.59107	+	16.3594i	0.164533	+	1.03882i
$249$	0.191416	+	0.0806351i	0.0121305	+	0.00511004i
$250$		0			0
$251$	−6.28262	−	8.64729i	−0.396556	−	0.545812i	0.563320	−	0.826239i	$-0.309524\pi$
$251$	−6.28262	−	8.64729i	−0.396556	−	0.545812i	−0.959875	+	0.280427i	$0.909524\pi$
$252$	1.73197	+	2.44499i	0.109104	+	0.154020i
$253$	6.55299	−	8.32811i	0.411983	−	0.523584i
$254$	−11.9929			−0.752503
$255$		0			0
$256$	−5.25115	−	16.1614i	−0.328197	−	1.01009i
$257$	0.00197549	+	0.00387711i	0.000123227	+	0.000241848i	0.891068	−	0.453870i	$-0.149957\pi$
$257$	0.00197549	+	0.00387711i	0.000123227	+	0.000241848i	−0.890945	+	0.454111i	$0.849957\pi$
$258$	−17.4003	+	1.26449i	−1.08329	+	0.0787238i
$259$	4.50267	−	6.19739i	0.279782	−	0.385087i
$260$		0			0
$261$	23.0641	−	3.36997i	1.42763	−	0.208596i
$262$	−7.30355	−	1.15677i	−0.451215	−	0.0714654i
$263$	−1.07601	−	1.07601i	−0.0663495	−	0.0663495i	0.673153	−	0.739503i	$-0.264939\pi$
$263$	−1.07601	−	1.07601i	−0.0663495	−	0.0663495i	−0.739503	+	0.673153i	$0.764939\pi$
$264$	13.3694	−	10.4299i	0.822829	−	0.641915i
$265$		0			0
$266$	2.73162	+	3.75976i	0.167487	+	0.230525i
$267$	9.81868	−	15.8090i	0.600893	−	0.967498i
$268$	1.75911	+	3.45244i	0.107454	+	0.210891i
$269$	3.67944	+	2.67327i	0.224339	+	0.162992i	0.694278	−	0.719707i	$-0.255724\pi$
$269$	3.67944	+	2.67327i	0.224339	+	0.162992i	−0.469938	+	0.882699i	$0.655724\pi$
$270$		0			0
$271$	6.88331	−	21.1847i	0.418131	−	1.28688i	−0.491288	−	0.870997i	$-0.663474\pi$
$271$	6.88331	−	21.1847i	0.418131	−	1.28688i	0.909420	−	0.415879i	$-0.136526\pi$
$272$	0.928847	+	0.473271i	0.0563196	+	0.0286963i
$273$	−1.40713	−	0.346760i	−0.0851634	−	0.0209868i
$274$		−	15.7847i		−	0.953588i
$275$		0			0
$276$	5.97664	+	0.506450i	0.359751	+	0.0304847i
$277$	−11.3736	−	1.80139i	−0.683371	−	0.108235i	−0.194910	−	0.980821i	$-0.562441\pi$
$277$	−11.3736	−	1.80139i	−0.683371	−	0.108235i	−0.488461	+	0.872586i	$0.662441\pi$
$278$	−3.98104	+	7.81323i	−0.238767	+	0.468606i
$279$	−14.9065	−	7.82185i	−0.892431	−	0.468282i
$280$		0			0
$281$	−13.8388	+	19.0475i	−0.825554	+	1.13628i	0.163180	+	0.986596i	$0.447825\pi$
$281$	−13.8388	+	19.0475i	−0.825554	+	1.13628i	−0.988734	+	0.149682i	$0.952175\pi$
$282$	1.36323	+	3.34778i	0.0811794	+	0.199357i
$283$	−15.7061	−	8.00265i	−0.933630	−	0.475708i	−0.0801201	−	0.996785i	$-0.525530\pi$
$283$	−15.7061	−	8.00265i	−0.933630	−	0.475708i	−0.853510	+	0.521077i	$0.825530\pi$
$284$	3.78340	−	2.74880i	0.224503	−	0.163111i
$285$		0			0
$286$	−0.559745	+	2.82756i	−0.0330984	+	0.167197i
$287$	3.41476	−	3.41476i	0.201567	−	0.201567i
$288$	14.9878	+	5.06936i	0.883167	+	0.298715i
$289$	−13.7785	+	4.47691i	−0.810500	+	0.263347i
$290$		0			0
$291$	−12.6421	+	14.6235i	−0.741092	+	0.857245i
$292$	2.10089	+	13.2645i	0.122945	+	0.776247i
$293$	13.7114	−	6.98629i	0.801026	−	0.408143i	−0.00502635	−	0.999987i	$-0.501600\pi$
$293$	13.7114	−	6.98629i	0.801026	−	0.408143i	0.806052	+	0.591844i	$0.201600\pi$
$294$	9.92959	−	2.32100i	0.579105	−	0.135363i
$295$		0			0
$296$		−	24.5374i		−	1.42620i
$297$	0.382493	+	17.2294i	0.0221945	+	0.999754i
$298$	−12.4021	+	12.4021i	−0.718434	+	0.718434i
$299$	−2.34705	+	1.70523i	−0.135734	+	0.0986162i
$300$		0			0
$301$	−2.99664	+	9.22271i	−0.172723	+	0.531588i
$302$	−15.1168	+	2.39427i	−0.869874	+	0.137775i
$303$	9.14069	−	0.664261i	0.525119	−	0.0381608i
$304$	3.29559	+	1.07080i	0.189015	+	0.0614146i
$305$		0			0
$306$	−4.07994	+	2.01757i	−0.233234	+	0.115337i
$307$	−3.46654	−	3.46654i	−0.197846	−	0.197846i	0.601230	−	0.799076i	$-0.294678\pi$
$307$	−3.46654	−	3.46654i	−0.197846	−	0.197846i	−0.799076	+	0.601230i	$0.794678\pi$
$308$	−0.902069	−	3.18732i	−0.0514002	−	0.181614i
$309$	−2.46787	−	0.209123i	−0.140392	−	0.0118966i
$310$		0			0
$311$	10.2027	−	3.31506i	0.578542	−	0.187980i	−0.00510536	−	0.999987i	$-0.501625\pi$
$311$	10.2027	−	3.31506i	0.578542	−	0.187980i	0.583647	+	0.812007i	$0.301625\pi$
$312$	−4.29930	+	1.75070i	−0.243400	+	0.0991138i
$313$	−0.225375	+	0.0356958i	−0.0127389	+	0.00201765i	−0.162801	−	0.986659i	$-0.552053\pi$
$313$	−0.225375	+	0.0356958i	−0.0127389	+	0.00201765i	0.150062	+	0.988677i	$0.452053\pi$
$314$	13.1216	+	9.53340i	0.740495	+	0.538001i
$315$		0			0
$316$	−3.54537	−	10.9115i	−0.199443	−	0.613822i
$317$	3.60259	−	22.7459i	0.202342	−	1.27753i	−0.652158	−	0.758083i	$-0.726136\pi$
$317$	3.60259	−	22.7459i	0.202342	−	1.27753i	0.854500	−	0.519452i	$-0.173864\pi$
$318$	−3.58066	−	4.24368i	−0.200793	−	0.237974i
$319$	−25.2785	−	5.00414i	−1.41533	−	0.280178i
$320$		0			0
$321$	−8.38999	+	5.07244i	−0.468283	+	0.283116i
$322$	−1.27947	+	2.51111i	−0.0713022	+	0.139938i
$323$	7.44110	−	3.79143i	0.414034	−	0.210961i
$324$	−8.02672	+	5.54258i	−0.445929	+	0.307921i
$325$		0			0
$326$	−19.8013	−	6.43384i	−1.09669	−	0.356338i
$327$	−12.5290	−	7.78150i	−0.692854	−	0.430318i
$328$	2.41983	−	15.2782i	0.133613	−	0.843598i
$329$	2.00921			0.110771
$330$		0			0
$331$	−11.4437			−0.629004			−0.314502	−	0.949257i	$-0.601838\pi$
$331$	−11.4437			−0.629004			−0.314502	+	0.949257i	$0.601838\pi$
$332$	0.0203320	−	0.128371i	0.00111586	−	0.00704529i
$333$	19.9984	+	14.8994i	1.09591	+	0.816481i
$334$	−18.5722	−	6.03447i	−1.01622	−	0.330191i
$335$		0			0
$336$	−0.686523	+	0.794123i	−0.0374529	+	0.0433229i
$337$	7.15983	−	3.64812i	0.390021	−	0.198726i	−0.247973	−	0.968767i	$-0.579764\pi$
$337$	7.15983	−	3.64812i	0.390021	−	0.198726i	0.637994	+	0.770041i	$0.279764\pi$
$338$	−5.29086	+	10.3839i	−0.287785	+	0.564810i
$339$	−0.894511	−	1.47955i	−0.0485832	−	0.0803582i
$340$		0			0
$341$	12.6455	+	13.6547i	0.684793	+	0.739445i
$342$	−12.3457	+	8.74539i	−0.667578	+	0.472896i
$343$	1.89578	−	11.9695i	0.102362	−	0.646291i
$344$	9.59867	+	29.5417i	0.517526	+	1.59278i
$345$		0			0
$346$	3.85508	+	2.80088i	0.207250	+	0.150576i
$347$	22.6950	−	3.59454i	1.21833	−	0.192965i	0.486028	−	0.873943i	$-0.338445\pi$
$347$	22.6950	−	3.59454i	1.21833	−	0.192965i	0.732304	+	0.680978i	$0.238445\pi$
$348$	−5.50073	−	13.5085i	−0.294870	−	0.724130i
$349$	0.562363	−	0.182723i	0.0301026	−	0.00978093i	−0.293927	−	0.955828i	$-0.594962\pi$
$349$	0.562363	−	0.182723i	0.0301026	−	0.00978093i	0.324030	+	0.946047i	$0.394962\pi$
$350$		0			0
$351$	1.18374	−	4.56706i	0.0631831	−	0.243771i
$352$	−13.7465	−	10.8165i	−0.732692	−	0.576521i
$353$	−0.963205	−	0.963205i	−0.0512662	−	0.0512662i	0.681009	−	0.732275i	$-0.261541\pi$
$353$	−0.963205	−	0.963205i	−0.0512662	−	0.0512662i	−0.732275	+	0.681009i	$0.761541\pi$
$354$	−16.4258	+	9.93077i	−0.873023	+	0.527814i
$355$		0			0
$356$	−11.0752	−	3.59854i	−0.586983	−	0.190722i
$357$	0.183369	+	2.52329i	0.00970492	+	0.133546i
$358$	−3.87317	+	0.613450i	−0.204704	+	0.0324219i
$359$	−4.53802	+	13.9666i	−0.239508	+	0.737128i	0.756984	+	0.653434i	$0.226672\pi$
$359$	−4.53802	+	13.9666i	−0.239508	+	0.737128i	−0.996491	+	0.0836949i	$0.973328\pi$
$360$		0			0
$361$	7.08698	−	5.14899i	0.372999	−	0.270999i
$362$	0.472727	−	0.472727i	0.0248460	−	0.0248460i
$363$	5.96297	−	18.0954i	0.312975	−	0.949761i
$364$			0.906847i			0.0475317i
$365$		0			0
$366$	−1.88666	−	8.07143i	−0.0986174	−	0.421900i
$367$	0.00458024	−	0.00233375i	0.000239086	−	0.000121821i	−0.453871	−	0.891067i	$-0.649957\pi$
$367$	0.00458024	−	0.00233375i	0.000239086	−	0.000121821i	0.454110	+	0.890946i	$0.349957\pi$
$368$	0.328731	+	2.07553i	0.0171363	+	0.108194i
$369$	10.9827	+	11.2493i	0.571735	+	0.585616i
$370$		0			0
$371$	−2.93525	+	0.953720i	−0.152391	+	0.0495147i
$372$	−2.52045	+	10.2279i	−0.130679	+	0.530290i
$373$	−23.5389	+	23.5389i	−1.21880	+	1.21880i	−0.250748	+	0.968052i	$0.580677\pi$
$373$	−23.5389	+	23.5389i	−1.21880	+	1.21880i	−0.968052	+	0.250748i	$0.919323\pi$
$374$	4.99649	−	0.596015i	0.258362	−	0.0308192i
$375$		0			0
$376$	5.20665	−	3.78285i	0.268513	−	0.195086i
$377$	6.28575	+	3.20275i	0.323732	+	0.164950i
$378$	−0.989598	−	4.47515i	−0.0508994	−	0.230177i
$379$	15.8233	−	21.7790i	0.812790	−	1.11871i	−0.178096	−	0.984013i	$-0.556994\pi$
$379$	15.8233	−	21.7790i	0.812790	−	1.11871i	0.990887	−	0.134697i	$-0.0430061\pi$
$380$		0			0
$381$	−19.9997	−	8.42501i	−1.02462	−	0.431626i
$382$	−9.78175	+	19.1978i	−0.500478	+	0.982243i
$383$	22.0945	+	3.49943i	1.12898	+	0.178812i	0.692856	−	0.721076i	$-0.256352\pi$
$383$	22.0945	+	3.49943i	1.12898	+	0.178812i	0.436121	+	0.899888i	$0.356352\pi$
$384$	0.651827	−	7.69223i	0.0332634	−	0.392542i
$385$		0			0
$386$			8.21192i			0.417976i
$387$	−29.9054	−	10.1150i	−1.52018	−	0.514172i
$388$	10.7776	+	5.49146i	0.547150	+	0.278787i
$389$	6.06342	−	18.6613i	0.307428	−	0.946165i	−0.671332	−	0.741156i	$-0.734278\pi$
$389$	6.06342	−	18.6613i	0.307428	−	0.946165i	0.978760	−	0.205009i	$-0.0657223\pi$
$390$		0			0
$391$	4.09729	+	2.97685i	0.207209	+	0.150546i
$392$	−8.24249	−	16.1768i	−0.416308	−	0.817051i
$393$	−11.3670	−	7.05978i	−0.573387	−	0.356119i
$394$	−3.36780	−	4.63538i	−0.169667	−	0.233527i
$395$		0			0
$396$	10.4108	−	2.81204i	0.523163	−	0.141310i
$397$	15.7123	+	15.7123i	0.788577	+	0.788577i	0.981261	−	0.192684i	$-0.0617191\pi$
$397$	15.7123	+	15.7123i	0.788577	+	0.788577i	−0.192684	+	0.981261i	$0.561719\pi$
$398$	1.28258	+	0.203140i	0.0642897	+	0.0101825i
$399$	1.91410	+	8.18882i	0.0958249	+	0.409954i
$400$		0			0
$401$	0.341341	−	0.469815i	0.0170457	−	0.0234615i	−0.800409	−	0.599454i	$-0.795384\pi$
$401$	0.341341	−	0.469815i	0.0170457	−	0.0234615i	0.817455	+	0.575993i	$0.195384\pi$
$402$	−0.429589	−	5.91144i	−0.0214260	−	0.294836i
$403$	−2.31307	−	4.53965i	−0.115222	−	0.226136i
$404$	−1.77216	−	5.45415i	−0.0881682	−	0.271354i
$405$		0			0
$406$	6.85323			0.340120
$407$	−15.3384	−	22.9100i	−0.760294	−	1.13561i
$408$	5.22593	+	6.19360i	0.258722	+	0.306629i
$409$	7.56410	+	10.4111i	0.374021	+	0.514795i	0.953988	−	0.299844i	$-0.0969347\pi$
$409$	7.56410	+	10.4111i	0.374021	+	0.514795i	−0.579967	+	0.814640i	$0.696935\pi$
$410$		0			0
$411$	11.0887	−	26.3229i	0.546965	−	1.29841i
$412$	0.242441	+	1.53071i	0.0119442	+	0.0754128i
$413$	1.66902	+	10.5378i	0.0821270	+	0.518529i
$414$	−8.12438	−	4.26307i	−0.399292	−	0.209519i
$415$		0			0
$416$	2.81469	+	3.87409i	0.138001	+	0.189943i
$417$	−12.1277	+	10.2329i	−0.593894	+	0.501106i
$418$	16.0940	−	4.55490i	0.787183	−	0.222787i
$419$	−1.75998			−0.0859806			−0.0429903	−	0.999075i	$-0.513688\pi$
$419$	−1.75998			−0.0859806			−0.0429903	+	0.999075i	$0.513688\pi$
$420$		0			0
$421$	2.42998	+	7.47872i	0.118430	+	0.364491i	0.992647	−	0.121045i	$-0.0386246\pi$
$421$	2.42998	+	7.47872i	0.118430	+	0.364491i	−0.874217	+	0.485536i	$0.838625\pi$
$422$	−2.97406	−	5.83693i	−0.144775	−	0.284137i
$423$	−0.0784448	+	6.54051i	−0.00381412	+	0.318011i
$424$	−5.81077	+	7.99784i	−0.282196	+	0.388410i
$425$		0			0
$426$	−6.96570	+	1.62820i	−0.337489	+	0.0788866i
$427$	−4.55066	−	0.720753i	−0.220222	−	0.0348797i
$428$	4.33803	+	4.33803i	0.209687	+	0.209687i
$429$	−2.91980	+	4.32209i	−0.140969	+	0.208673i
$430$		0			0
$431$	−17.2516	−	23.7449i	−0.830982	−	1.14375i	−0.987739	−	0.156112i	$-0.950104\pi$
$431$	−17.2516	−	23.7449i	−0.830982	−	1.14375i	0.156757	−	0.987637i	$-0.449896\pi$
$432$	−2.55828	−	2.26582i	−0.123085	−	0.109015i
$433$	−4.94511	−	9.70533i	−0.237647	−	0.466408i	0.741123	−	0.671369i	$-0.234293\pi$
$433$	−4.94511	−	9.70533i	−0.237647	−	0.466408i	−0.978770	+	0.204961i	$0.934293\pi$
$434$	−4.00422	−	2.90924i	−0.192209	−	0.139648i
$435$		0			0
$436$	−2.85192	+	8.77729i	−0.136582	+	0.420356i
$437$	14.9997	+	7.64272i	0.717533	+	0.365601i
$438$	4.91536	−	19.9463i	0.234865	−	0.953070i
$439$		−	21.4325i		−	1.02292i	−0.859308	−	0.511459i	$-0.829105\pi$
$439$		−	21.4325i		−	1.02292i	0.859308	−	0.511459i	$-0.170895\pi$
$440$		0			0
$441$	18.1893	+	3.10496i	0.866158	+	0.147855i
$442$	−1.36060	−	0.215498i	−0.0647171	−	0.0102502i
$443$	3.27160	−	6.42089i	0.155439	−	0.305066i	−0.800134	−	0.599821i	$-0.795238\pi$
$443$	3.27160	−	6.42089i	0.155439	−	0.305066i	0.955573	+	0.294756i	$0.0952383\pi$
$444$	6.05817	−	14.3812i	0.287508	−	0.682501i
$445$		0			0
$446$	2.37684	−	3.27144i	0.112547	−	0.154907i
$447$	−29.3945	+	11.9696i	−1.39031	+	0.566143i
$448$	5.22489	+	2.66222i	0.246853	+	0.125778i
$449$	14.8706	−	10.8042i	0.701789	−	0.509880i	−0.178725	−	0.983899i	$-0.557197\pi$
$449$	14.8706	−	10.8042i	0.701789	−	0.509880i	0.880514	+	0.474019i	$0.157197\pi$
$450$		0			0
$451$	−7.29109	−	15.7776i	−0.343324	−	0.742937i
$452$	−0.765000	+	0.765000i	−0.0359826	+	0.0359826i
$453$	−26.8911	−	6.62678i	−1.26346	−	0.311353i
$454$	−18.8012	+	6.10888i	−0.882384	+	0.286704i
$455$		0			0
$456$	20.3778	+	17.6167i	0.954278	+	0.824978i
$457$	−5.01276	−	31.6493i	−0.234487	−	1.48049i	−0.771127	−	0.636681i	$-0.780307\pi$
$457$	−5.01276	−	31.6493i	−0.234487	−	1.48049i	0.536640	−	0.843811i	$-0.319693\pi$
$458$	−25.1133	+	12.7959i	−1.17347	+	0.597912i
$459$	−8.22114	+	0.498401i	−0.383730	+	0.0232634i
$460$		0			0
$461$		−	24.3461i		−	1.13391i	−0.823749	−	0.566955i	$-0.808121\pi$
$461$		−	24.3461i		−	1.13391i	0.823749	−	0.566955i	$-0.191879\pi$
$462$	−0.621116	+	5.02877i	−0.0288970	+	0.233960i
$463$	17.2432	−	17.2432i	0.801359	−	0.801359i	−0.181949	−	0.983308i	$-0.558241\pi$
$463$	17.2432	−	17.2432i	0.801359	−	0.801359i	0.983308	+	0.181949i	$0.0582406\pi$
$464$	4.13406	−	3.00357i	0.191919	−	0.139437i
$465$		0			0
$466$	5.11930	−	15.7556i	0.237147	−	0.729863i
$467$	30.6642	−	4.85673i	1.41897	−	0.224743i	0.600653	−	0.799510i	$-0.294907\pi$
$467$	30.6642	−	4.85673i	1.41897	−	0.224743i	0.818317	+	0.574767i	$0.194907\pi$
$468$	−2.95204	−	0.0354058i	−0.136458	−	0.00163663i
$469$	−3.13326	−	1.01806i	−0.144680	−	0.0470095i
$470$		0			0
$471$	15.1847	+	25.1160i	0.699675	+	1.15729i
$472$	24.1652	+	24.1652i	1.11229	+	1.11229i
$473$	27.4286	+	21.5823i	1.26117	+	0.992355i
$474$	−1.48183	+	17.4871i	−0.0680627	+	0.803210i
$475$		0			0
$476$	1.50562	−	0.489204i	0.0690098	−	0.0224226i
$477$	−2.99002	−	9.59227i	−0.136904	−	0.439200i
$478$	18.9447	−	3.00054i	0.866508	−	0.137241i
$479$	23.5213	+	17.0892i	1.07472	+	0.780827i	0.976754	−	0.214363i	$-0.0687676\pi$
$479$	23.5213	+	17.0892i	1.07472	+	0.780827i	0.0979620	+	0.995190i	$0.468768\pi$
$480$		0			0
$481$	2.33241	+	7.17841i	0.106349	+	0.327307i
$482$	−0.897927	+	5.66929i	−0.0408994	+	0.258229i
$483$	−3.89773	+	3.28876i	−0.177353	+	0.149644i
$484$	−11.8870	−	0.913617i	−0.540318	−	0.0415280i
$485$		0			0
$486$	14.6065	−	3.04669i	0.662563	−	0.138201i
$487$	−5.46741	+	10.7304i	−0.247752	+	0.486241i	−0.981072	−	0.193643i	$-0.937970\pi$
$487$	−5.46741	+	10.7304i	−0.247752	+	0.486241i	0.733320	+	0.679884i	$0.237970\pi$
$488$	−13.1496	+	6.70004i	−0.595253	+	0.303297i
$489$	−28.5014	−	24.6396i	−1.28888	−	1.11424i
$490$		0			0
$491$	14.4279	+	4.68790i	0.651121	+	0.211562i	0.615908	−	0.787818i	$-0.288789\pi$
$491$	14.4279	+	4.68790i	0.651121	+	0.211562i	0.0352125	+	0.999380i	$0.488789\pi$
$492$	5.19037	−	8.35702i	0.234000	−	0.376763i
$493$	1.92656	−	12.1638i	0.0867678	−	0.547830i
$494$	−4.57902			−0.206020
$495$		0			0
$496$	−3.69050			−0.165708
$497$	−0.622015	+	3.92725i	−0.0279012	+	0.176161i
$498$	−0.104893	+	0.168888i	−0.00470037	+	0.00756806i
$499$	−27.7992	−	9.03250i	−1.24446	−	0.404350i	−0.388529	−	0.921437i	$-0.627017\pi$
$499$	−27.7992	−	9.03250i	−1.24446	−	0.404350i	−0.855933	+	0.517086i	$0.827017\pi$
$500$		0			0
$501$	−26.7322	−	23.1102i	−1.19431	−	1.03249i
$502$	9.11576	−	4.64471i	0.406856	−	0.207304i
$503$	0.175970	−	0.345360i	0.00784611	−	0.0153989i	−0.887050	−	0.461673i	$-0.847249\pi$
$503$	0.175970	−	0.345360i	0.00784611	−	0.0153989i	0.894896	+	0.446274i	$0.147249\pi$
$504$	−7.31474	+	3.61721i	−0.325824	+	0.161123i
$505$		0			0
$506$	6.89208	+	7.44212i	0.306390	+	0.330843i
$507$	−16.1178	+	13.5996i	−0.715818	+	0.603981i
$508$	−2.12435	+	13.4126i	−0.0942528	+	0.595089i
$509$	−3.79640	−	11.6841i	−0.168272	−	0.517889i	0.830990	−	0.556287i	$-0.187775\pi$
$509$	−3.79640	−	11.6841i	−0.168272	−	0.517889i	−0.999263	+	0.0383979i	$0.987775\pi$
$510$		0			0
$511$	−9.23791	−	6.71173i	−0.408661	−	0.296910i
$512$	7.26073	−	1.14999i	0.320882	−	0.0508227i
$513$	−26.7316	+	5.91121i	−1.18023	+	0.260986i
$514$	−0.00396117	+	0.00128706i	−0.000174720	+	5.67699e-5i
$515$		0			0
$516$	−1.66799	+	19.6841i	−0.0734294	+	0.866543i
$517$	2.49667	−	6.78666i	0.109803	−	0.298477i
$518$	5.18473	+	5.18473i	0.227804	+	0.227804i
$519$	4.46122	+	7.37900i	0.195826	+	0.323902i
$520$		0			0
$521$	10.4299	+	3.38889i	0.456944	+	0.148470i	0.528440	−	0.848971i	$-0.322777\pi$
$521$	10.4299	+	3.38889i	0.456944	+	0.148470i	−0.0714958	+	0.997441i	$0.522777\pi$
$522$	−0.267568	+	22.3091i	−0.0117112	+	0.976444i
$523$	−37.0145	+	5.86253i	−1.61853	+	0.256350i	−0.898948	−	0.438055i	$-0.855668\pi$
$523$	−37.0145	+	5.86253i	−1.61853	+	0.256350i	−0.719584	+	0.694405i	$0.755668\pi$
$524$	−2.58741	+	7.96322i	−0.113031	+	0.347875i
$525$		0			0
$526$	1.17836	−	0.856128i	0.0513789	−	0.0373290i
$527$	−6.28927	+	6.28927i	−0.273965	+	0.273965i
$528$	1.82929	+	3.30571i	0.0796096	+	0.143863i
$529$		−	12.7910i		−	0.556130i
$530$		0			0
$531$	−34.3684	+	5.02168i	−1.49146	+	0.217923i
$532$	4.68869	−	2.38901i	0.203280	−	0.103577i
$533$	0.744353	+	4.69966i	0.0322415	+	0.203565i
$534$	13.4755	+	11.6496i	0.583141	+	0.504128i
$535$		0			0
$536$	−10.0363	+	3.26098i	−0.433501	+	0.140853i
$537$	−6.88995	−	1.69789i	−0.297323	−	0.0732694i
$538$	−3.07821	+	3.07821i	−0.132711	+	0.132711i
$539$	−17.8080	−	9.95153i	−0.767044	−	0.428643i
$540$		0			0
$541$	−24.5988	+	17.8721i	−1.05758	+	0.768380i	−0.973640	−	0.228090i	$-0.926752\pi$
$541$	−24.5988	+	17.8721i	−1.05758	+	0.768380i	−0.0839447	+	0.996470i	$0.526752\pi$
$542$	18.9970	+	9.67947i	0.815992	+	0.415769i
$543$	1.12042	−	0.456242i	0.0480819	−	0.0195792i
$544$	4.91365	−	6.76306i	0.210671	−	0.289964i
$545$		0			0
$546$	0.538518	−	1.27836i	0.0230465	−	0.0547088i
$547$	−8.98826	+	17.6404i	−0.384310	+	0.754251i	−0.999415	−	0.0341940i	$-0.989114\pi$
$547$	−8.98826	+	17.6404i	−0.384310	+	0.754251i	0.615105	+	0.788445i	$0.289114\pi$
$548$	−17.6532	−	2.79600i	−0.754109	−	0.119439i
$549$	2.52392	−	14.7855i	0.107718	−	0.631029i
$550$		0			0
$551$		−	40.9366i		−	1.74396i
$552$	−3.90862	+	15.8610i	−0.166362	+	0.675088i
$553$	8.69171	+	4.42865i	0.369609	+	0.188325i
$554$	3.40603	−	10.4827i	0.144708	−	0.445366i
$555$		0			0
$556$	8.03297	+	5.83629i	0.340674	+	0.247514i
$557$	3.94604	+	7.74454i	0.167199	+	0.328147i	0.959369	−	0.282154i	$-0.0910488\pi$
$557$	3.94604	+	7.74454i	0.167199	+	0.328147i	−0.792170	+	0.610300i	$0.791049\pi$
$558$	9.62670	−	12.9213i	0.407531	−	0.547000i
$559$	−5.61619	−	7.73002i	−0.237539	−	0.326945i
$560$		0			0
$561$	8.75097	+	2.51609i	0.369466	+	0.106230i
$562$	−15.9351	−	15.9351i	−0.672182	−	0.672182i
$563$	26.3809	+	4.17832i	1.11182	+	0.176095i	0.685215	−	0.728341i	$-0.259708\pi$
$563$	26.3809	+	4.17832i	1.11182	+	0.176095i	0.426608	+	0.904437i	$0.359708\pi$
$564$	3.98556	−	0.931607i	0.167822	−	0.0392277i
$565$		0			0
$566$	9.91735	−	13.6501i	0.416857	−	0.573755i
$567$	1.49350	−	8.15806i	0.0627212	−	0.342606i
$568$	5.78218	+	11.3482i	0.242615	+	0.476159i
$569$	2.88499	+	8.87908i	0.120945	+	0.372230i	0.993141	−	0.116927i	$-0.0373044\pi$
$569$	2.88499	+	8.87908i	0.120945	+	0.372230i	−0.872196	+	0.489157i	$0.837304\pi$
$570$		0			0
$571$	23.3540			0.977336			0.488668	−	0.872470i	$-0.337483\pi$
$571$	23.3540			0.977336			0.488668	+	0.872470i	$0.337483\pi$
$572$	3.06313	+	1.12686i	0.128076	+	0.0471165i
$573$	−29.7987	+	25.1430i	−1.24486	+	1.05036i
$574$	2.71697	+	3.73958i	0.113404	+	0.156087i
$575$		0			0
$576$	−8.87023	+	16.9045i	−0.369593	+	0.704355i
$577$	0.0571918	+	0.361095i	0.00238093	+	0.0150326i	0.988850	−	0.148914i	$-0.0475776\pi$
$577$	0.0571918	+	0.361095i	0.00238093	+	0.0150326i	−0.986469	+	0.163946i	$0.947578\pi$
$578$	−2.16929	−	13.6964i	−0.0902306	−	0.569694i
$579$	−5.76885	+	13.6944i	−0.239745	+	0.569120i
$580$		0			0
$581$	0.0649547	+	0.0894025i	0.00269478	+	0.00370904i
$582$	−11.9319	−	14.1413i	−0.494594	−	0.586176i
$583$	−0.425927	+	11.0997i	−0.0176401	+	0.459704i
$584$	−36.5757			−1.51351
$585$		0			0
$586$	4.55168	+	14.0086i	0.188028	+	0.578691i
$587$	−5.52538	−	10.8442i	−0.228057	−	0.447587i	0.748415	−	0.663230i	$-0.230815\pi$
$587$	−5.52538	−	10.8442i	−0.228057	−	0.447587i	−0.976472	+	0.215644i	$0.930815\pi$
$588$	−0.836888	−	11.5162i	−0.0345127	−	0.474918i
$589$	−17.3779	+	23.9186i	−0.716042	+	0.985548i
$590$		0			0
$591$	−2.35988	−	10.0959i	−0.0970726	−	0.415291i
$592$	5.39989	+	0.855259i	0.221934	+	0.0351509i
$593$	−30.2540	−	30.2540i	−1.24238	−	1.24238i	−0.959011	−	0.283370i	$-0.908547\pi$
$593$	−30.2540	−	30.2540i	−1.24238	−	1.24238i	−0.283370	−	0.959011i	$-0.591453\pi$
$594$	−16.3458	−	2.21824i	−0.670675	−	0.0910155i
$595$		0			0
$596$	11.6734	+	16.0671i	0.478161	+	0.658132i
$597$	1.99615	+	1.23977i	0.0816969	+	0.0507403i
$598$	−1.26067	−	2.47421i	−0.0515527	−	0.101178i
$599$	16.5529	+	12.0264i	0.676331	+	0.491384i	0.872139	−	0.489259i	$-0.162733\pi$
$599$	16.5529	+	12.0264i	0.676331	+	0.491384i	−0.195807	+	0.980642i	$0.562733\pi$
$600$		0			0
$601$	6.89696	−	21.2267i	0.281333	−	0.865853i	−0.706141	−	0.708071i	$-0.749566\pi$
$601$	6.89696	−	21.2267i	0.281333	−	0.865853i	0.987474	−	0.157782i	$-0.0504344\pi$
$602$	−8.27033	−	4.21394i	−0.337074	−	0.171748i
$603$	3.43638	−	10.1599i	0.139940	−	0.413741i
$604$			17.3304i			0.705164i
$605$		0			0
$606$	−0.740694	+	8.74096i	−0.0300886	+	0.355077i
$607$	−9.93754	−	1.57395i	−0.403352	−	0.0638848i	−0.0485376	−	0.998821i	$-0.515456\pi$
$607$	−9.93754	−	1.57395i	−0.403352	−	0.0638848i	−0.354815	+	0.934937i	$0.615456\pi$
$608$	12.6152	−	24.7588i	0.511615	−	1.00410i
$609$	11.4286	+	4.81438i	0.463111	+	0.195088i
$610$		0			0
$611$	−1.16363	+	1.60159i	−0.0470753	+	0.0647936i
$612$	1.53371	+	4.92029i	0.0619965	+	0.198891i
$613$	−29.8386	−	15.2035i	−1.20517	−	0.614065i	−0.268163	−	0.963373i	$-0.586417\pi$
$613$	−29.8386	−	15.2035i	−1.20517	−	0.614065i	−0.937008	+	0.349308i	$0.886417\pi$
$614$	3.79629	−	2.75816i	0.153206	−	0.111310i
$615$		0			0
$616$	8.95798	−	1.06857i	0.360927	−	0.0430538i
$617$	−17.5330	+	17.5330i	−0.705851	+	0.705851i	−0.965660	−	0.259809i	$-0.916340\pi$
$617$	−17.5330	+	17.5330i	−0.705851	+	0.705851i	0.259809	+	0.965660i	$0.416340\pi$
$618$	0.567228	−	2.30178i	0.0228173	−	0.0925912i
$619$	17.8095	−	5.78666i	0.715825	−	0.232586i	0.0716127	−	0.997433i	$-0.477185\pi$
$619$	17.8095	−	5.78666i	0.715825	−	0.232586i	0.644212	+	0.764847i	$0.277185\pi$
$620$		0			0
$621$	−10.5536	−	12.8166i	−0.423502	−	0.514311i
$622$	1.60632	+	10.1419i	0.0644074	+	0.406652i
$623$	8.82205	−	4.49506i	0.353448	−	0.180091i
$624$	−0.235420	−	1.00716i	−0.00942432	−	0.0403187i
$625$		0			0
$626$		−	0.218411i		−	0.00872946i
$627$	30.0385	+	3.71014i	1.19962	+	0.148169i
$628$	12.9862	−	12.9862i	0.518207	−	0.518207i
$629$	10.6599	−	7.74487i	0.425038	−	0.308808i
$630$		0			0
$631$	−5.10514	+	15.7120i	−0.203232	+	0.625484i	0.796549	+	0.604574i	$0.206657\pi$
$631$	−5.10514	+	15.7120i	−0.203232	+	0.625484i	−0.999781	+	0.0209106i	$0.993343\pi$
$632$	30.8618	−	4.88802i	1.22761	−	0.194435i
$633$	−0.859192	−	11.8231i	−0.0341498	−	0.469925i
$634$	20.9642	+	6.81168i	0.832595	+	0.270526i
$635$		0			0
$636$	−5.38029	+	3.25283i	−0.213342	+	0.128983i
$637$	3.94903	+	3.94903i	0.156466	+	0.156466i
$638$	8.51593	−	23.1487i	0.337149	−	0.916466i
$639$	−12.7600	−	2.17816i	−0.504777	−	0.0861667i
$640$		0			0
$641$	7.69319	−	2.49967i	0.303863	−	0.0987310i	−0.153117	−	0.988208i	$-0.548931\pi$
$641$	7.69319	−	2.49967i	0.303863	−	0.0987310i	0.456980	+	0.889477i	$0.348931\pi$
$642$	−3.53915	−	8.69130i	−0.139679	−	0.343018i
$643$	27.7341	−	4.39265i	1.09373	−	0.173229i	0.416595	−	0.909092i	$-0.363223\pi$
$643$	27.7341	−	4.39265i	1.09373	−	0.173229i	0.677131	+	0.735863i	$0.263223\pi$
$644$	2.58173	+	1.87573i	0.101734	+	0.0739143i
$645$		0			0
$646$	2.47018	+	7.60243i	0.0971879	+	0.299114i
$647$	2.83037	−	17.8703i	0.111273	−	0.702553i	−0.867474	−	0.497483i	$-0.834258\pi$
$647$	2.83037	−	17.8703i	0.111273	−	0.702553i	0.978747	−	0.205070i	$-0.0657423\pi$
$648$	−11.4894	−	23.9527i	−0.451347	−	0.940950i
$649$	37.6682	+	7.45681i	1.47861	+	0.292705i
$650$		0			0
$651$	−4.63381	−	7.66447i	−0.181613	−	0.300394i
$652$	−10.7029	+	21.0057i	−0.419160	+	0.822648i
$653$	33.3027	−	16.9686i	1.30323	−	0.664031i	0.341983	−	0.939706i	$-0.388901\pi$
$653$	33.3027	−	16.9686i	1.30323	−	0.664031i	0.961251	+	0.275675i	$0.0889015\pi$
$654$	9.23255	−	10.6796i	0.361021	−	0.417605i
$655$		0			0
$656$	3.27790	+	1.06506i	0.127981	+	0.0415834i
$657$	22.2092	−	29.8099i	0.866463	−	1.16299i
$658$	−0.300848	+	1.89948i	−0.0117283	+	0.0740493i
$659$	−11.0122			−0.428973			−0.214486	−	0.976727i	$-0.568808\pi$
$659$	−11.0122			−0.428973			−0.214486	+	0.976727i	$0.568808\pi$
$660$		0			0
$661$	−26.3535			−1.02503			−0.512516	−	0.858678i	$-0.671286\pi$
$661$	−26.3535			−1.02503			−0.512516	+	0.858678i	$0.671286\pi$
$662$	1.71352	−	10.8188i	0.0665980	−	0.420483i
$663$	−2.11758	−	1.31519i	−0.0822400	−	0.0510776i
$664$	0.336647	+	0.109383i	0.0130644	+	0.00424490i
$665$		0			0
$666$	−17.0801	+	16.6753i	−0.661842	+	0.646154i
$667$	22.1195	−	11.2704i	0.856471	−	0.436394i
$668$	−10.0386	+	19.7018i	−0.388404	+	0.762286i
$669$	6.26186	−	3.78581i	0.242097	−	0.146368i
$670$		0			0
$671$	−8.08927	+	14.4755i	−0.312283	+	0.558821i
$672$	5.42848	+	6.43366i	0.209408	+	0.248184i
$673$	−7.66853	+	48.4172i	−0.295600	+	1.86634i	0.175801	+	0.984426i	$0.443748\pi$
$673$	−7.66853	+	48.4172i	−0.295600	+	1.86634i	−0.471401	+	0.881919i	$0.656252\pi$
$674$	2.37681	+	7.31506i	0.0915512	+	0.281766i
$675$		0			0
$676$	10.6759	+	7.75652i	0.410613	+	0.298328i
$677$	11.0044	−	1.74292i	0.422932	−	0.0669859i	0.0586592	−	0.998278i	$-0.481317\pi$
$677$	11.0044	−	1.74292i	0.422932	−	0.0669859i	0.364273	+	0.931292i	$0.381317\pi$
$678$	1.53269	−	0.624119i	0.0588625	−	0.0239691i
$679$	−9.78120	+	3.17810i	−0.375368	+	0.121964i
$680$		0			0
$681$	−35.6448	−	3.02048i	−1.36591	−	0.115745i
$682$	−14.8025	+	9.91033i	−0.566816	+	0.379486i
$683$	1.18402	+	1.18402i	0.0453054	+	0.0453054i	0.729397	−	0.684091i	$-0.239801\pi$
$683$	1.18402	+	1.18402i	0.0453054	+	0.0453054i	−0.684091	+	0.729397i	$0.739801\pi$
$684$	7.59381	+	15.3562i	0.290356	+	0.587160i
$685$		0			0
$686$	11.0319	+	3.58449i	0.421201	+	0.136856i
$687$	−50.8687	+	3.69667i	−1.94076	+	0.141037i
$688$	−6.83575	+	1.08268i	−0.260611	+	0.0412767i
$689$	0.939705	−	2.89212i	0.0357999	−	0.110181i
$690$		0			0
$691$	18.4894	−	13.4334i	0.703371	−	0.511029i	−0.177657	−	0.984092i	$-0.556852\pi$
$691$	18.4894	−	13.4334i	0.703371	−	0.511029i	0.881028	+	0.473064i	$0.156852\pi$
$692$	3.81531	−	3.81531i	0.145036	−	0.145036i
$693$	−4.56849	+	7.94977i	−0.173543	+	0.301987i
$694$			21.9938i			0.834873i
$695$		0			0
$696$	38.6804	−	9.04137i	1.46618	−	0.342712i
$697$	7.40118	−	3.77109i	0.280340	−	0.142840i
$698$	0.0885386	+	0.559011i	0.00335123	+	0.0211589i
$699$	19.6053	−	22.6781i	0.741542	−	0.857765i
$700$		0			0
$701$	2.84035	−	0.922886i	0.107279	−	0.0348569i	−0.254886	−	0.966971i	$-0.582038\pi$
$701$	2.84035	−	0.922886i	0.107279	−	0.0348569i	0.362164	+	0.932114i	$0.382038\pi$
$702$	4.14039	+	1.80293i	0.156269	+	0.0680474i
$703$	30.9701	−	30.9701i	1.16806	−	1.16806i
$704$	15.4849	−	14.3404i	0.583610	−	0.540476i
$705$		0			0
$706$	1.05483	−	0.766377i	0.0396989	−	0.0288430i
$707$	4.34456	+	2.21366i	0.163394	+	0.0832534i
$708$	8.19678	+	20.1293i	0.308054	+	0.756507i
$709$	4.94786	−	6.81015i	0.185821	−	0.255761i	−0.705936	−	0.708276i	$-0.749473\pi$
$709$	4.94786	−	6.81015i	0.185821	−	0.255761i	0.891757	+	0.452515i	$0.149473\pi$
$710$		0			0
$711$	−14.7558	+	28.1210i	−0.553386	+	1.05462i
$712$	14.3983	−	28.2583i	0.539600	−	1.05902i
$713$	−17.7084	−	2.80474i	−0.663186	−	0.105038i
$714$	−2.41294	−	0.204468i	−0.0903019	−	0.00765204i
$715$		0			0
$716$			4.44033i			0.165943i
$717$	33.7005	+	8.30481i	1.25857	+	0.310149i
$718$	−12.5243	−	6.38147i	−0.467404	−	0.238154i
$719$	−5.04595	+	15.5298i	−0.188182	+	0.579165i	−0.999989	−	0.00476148i	$-0.998484\pi$
$719$	−5.04595	+	15.5298i	−0.188182	+	0.579165i	0.811807	+	0.583926i	$0.198484\pi$
$720$		0			0
$721$	−1.06605	−	0.774527i	−0.0397016	−	0.0288449i
$722$	3.80662	+	7.47092i	0.141668	+	0.278039i
$723$	−5.48007	+	8.82345i	−0.203806	+	0.328148i
$724$	−0.444952	−	0.612423i	−0.0165365	−	0.0227605i
$725$		0			0
$726$	16.2143	+	8.34682i	0.601768	+	0.309780i
$727$	−13.2721	−	13.2721i	−0.492234	−	0.492234i	0.416776	−	0.909009i	$-0.363160\pi$
$727$	−13.2721	−	13.2721i	−0.492234	−	0.492234i	−0.909009	+	0.416776i	$0.863160\pi$
$728$	−2.43935	−	0.386356i	−0.0904085	−	0.0143193i
$729$	26.4984	+	5.18027i	0.981422	+	0.191862i
$730$		0			0
$731$	−9.80427	+	13.4944i	−0.362624	+	0.499109i
$732$	−9.36110	+	0.680278i	−0.345996	+	0.0251438i
$733$	3.62697	+	7.11832i	0.133965	+	0.262921i	0.948238	−	0.317561i	$-0.102864\pi$
$733$	3.62697	+	7.11832i	0.133965	+	0.262921i	−0.814273	+	0.580483i	$0.802864\pi$
$734$	0.00152047	+	0.00467954i	5.61217e−5	+	0.000172725i
$735$		0			0
$736$	16.8512			0.621143
$737$	−7.33221	+	9.31840i	−0.270085	+	0.343248i
$738$	−12.2794	+	8.69846i	−0.452013	+	0.320195i
$739$	9.78590	+	13.4691i	0.359980	+	0.495470i	0.950143	−	0.311814i	$-0.100937\pi$
$739$	9.78590	+	13.4691i	0.359980	+	0.495470i	−0.590163	+	0.807284i	$0.700937\pi$
$740$		0			0
$741$	−7.63609	−	3.21675i	−0.280519	−	0.118170i
$742$	−0.462126	−	2.91775i	−0.0169652	−	0.107114i
$743$	7.53580	+	47.5792i	0.276462	+	1.74551i	0.600645	+	0.799516i	$0.294910\pi$
$743$	7.53580	+	47.5792i	0.276462	+	1.74551i	−0.324184	+	0.945994i	$0.605090\pi$
$744$	−26.4384	−	11.1374i	−0.969279	−	0.408315i
$745$		0			0
$746$	−18.7288	−	25.7780i	−0.685711	−	0.943800i
$747$	−0.293566	+	0.207955i	−0.0107410	+	0.00760867i
$748$	0.218476	−	5.69353i	0.00798828	−	0.208176i
$749$	−5.21618			−0.190595
$750$		0			0
$751$	8.83329	+	27.1861i	0.322331	+	0.992034i	0.972631	+	0.232356i	$0.0746435\pi$
$751$	8.83329	+	27.1861i	0.322331	+	0.992034i	−0.650299	+	0.759678i	$0.725357\pi$
$752$	0.651006	+	1.27767i	0.0237398	+	0.0465919i
$753$	18.4646	−	1.34183i	0.672886	−	0.0488992i
$754$	−3.96903	+	5.46290i	−0.144544	+	0.198947i
$755$		0			0
$756$	−5.18020	+	0.314046i	−0.188402	+	0.0114217i
$757$	11.3180	+	1.79260i	0.411361	+	0.0651532i	0.358685	−	0.933458i	$-0.383225\pi$
$757$	11.3180	+	1.79260i	0.411361	+	0.0651532i	0.0526756	+	0.998612i	$0.483225\pi$
$758$	18.2202	+	18.2202i	0.661789	+	0.661789i
$759$	6.26533	+	17.2523i	0.227417	+	0.626220i
$760$		0			0
$761$	−3.76279	−	5.17904i	−0.136401	−	0.187740i	0.735352	−	0.677685i	$-0.237017\pi$
$761$	−3.76279	−	5.17904i	−0.136401	−	0.187740i	−0.871753	+	0.489945i	$0.837017\pi$
$762$	10.9595	−	17.6459i	0.397022	−	0.639245i
$763$	−3.56242	−	6.99165i	−0.128968	−	0.253115i
$764$	19.7377	+	14.3403i	0.714084	+	0.518812i
$765$		0			0
$766$	−6.61663	+	20.3639i	−0.239068	+	0.735777i
$767$	−9.36656	−	4.77250i	−0.338207	−	0.172325i
$768$	28.5779	+	7.04246i	1.03122	+	0.254123i
$769$			33.1965i			1.19710i	0.801087	+	0.598548i	$0.204256\pi$
$769$			33.1965i			1.19710i	−0.801087	+	0.598548i	$0.795744\pi$
$770$		0			0
$771$	−0.00750990		0.000636377i	−0.000270463		2.29185e-5i
$772$	9.18402	+	1.45461i	0.330540	+	0.0523524i
$773$	−13.5457	+	26.5850i	−0.487207	+	0.956197i	0.508271	+	0.861197i	$0.330285\pi$
$773$	−13.5457	+	26.5850i	−0.487207	+	0.956197i	−0.995477	+	0.0949996i	$0.969715\pi$
$774$	14.0404	−	26.7577i	0.504673	−	0.961784i
$775$		0			0
$776$	−19.3634	+	26.6514i	−0.695104	+	0.956729i
$777$	5.00392	+	12.2884i	0.179515	+	0.440845i
$778$	16.7342	+	8.52653i	0.599952	+	0.305691i
$779$	22.3378	−	16.2294i	0.800335	−	0.581477i
$780$		0			0
$781$	12.4925	+	6.98109i	0.447016	+	0.249803i
$782$	−3.42778	+	3.42778i	−0.122577	+	0.122577i
$783$	−16.1183	+	37.0153i	−0.576021	+	1.32282i
$784$	3.84729	−	1.25006i	0.137403	−	0.0446450i
$785$		0			0
$786$	8.37625	−	9.68907i	0.298771	−	0.345598i
$787$	−3.68052	−	23.2379i	−0.131196	−	0.828340i	−0.962254	−	0.272154i	$-0.912264\pi$
$787$	−3.68052	−	23.2379i	−0.131196	−	0.828340i	0.831058	−	0.556186i	$-0.187736\pi$
$788$	−5.78065	+	2.94539i	−0.205927	+	0.104925i
$789$	2.56649	−	0.599906i	0.0913695	−	0.0213572i
$790$		0			0
$791$		−	0.919858i		−	0.0327064i
$792$	3.12874	+	29.2024i	0.111175	+	1.03766i
$793$	3.21004	−	3.21004i	0.113992	−	0.113992i
$794$	−17.2069	+	12.5015i	−0.610649	+	0.443663i
$795$		0			0
$796$	0.454374	−	1.39842i	0.0161049	−	0.0495657i
$797$	−12.0063	+	1.90161i	−0.425285	+	0.0673586i	−0.365409	−	0.930847i	$-0.619071\pi$
$797$	−12.0063	+	1.90161i	−0.425285	+	0.0673586i	−0.0598767	+	0.998206i	$0.519071\pi$
$798$	−8.02821	+	0.583417i	−0.284196	+	0.0206527i
$799$	3.28681	+	1.06795i	0.116279	+	0.0377814i
$800$		0			0
$801$	14.2882	+	28.8937i	0.504849	+	1.02091i
$802$	0.393047	+	0.393047i	0.0138790	+	0.0138790i
$803$	−34.1499	+	22.8635i	−1.20513	+	0.806837i
$804$	−6.68732	−	0.566672i	−0.235844	−	0.0199850i
$805$		0			0
$806$	4.63807	−	1.50700i	0.163369	−	0.0530818i
$807$	−7.29575	+	2.97087i	−0.256822	+	0.104579i
$808$	15.4263	−	2.44328i	0.542695	−	0.0859544i
$809$	−23.6748	−	17.2008i	−0.832362	−	0.604747i	0.0878643	−	0.996132i	$-0.471996\pi$
$809$	−23.6748	−	17.2008i	−0.832362	−	0.604747i	−0.920227	+	0.391386i	$0.871996\pi$
$810$		0			0
$811$	−2.84848	−	8.76671i	−0.100024	−	0.307841i	0.888507	−	0.458864i	$-0.151743\pi$
$811$	−2.84848	−	8.76671i	−0.100024	−	0.307841i	−0.988530	+	0.151023i	$0.951743\pi$
$812$	1.21394	−	7.66449i	0.0426008	−	0.268971i
$813$	24.8801	+	29.4871i	0.872584	+	1.03416i
$814$	23.9555	−	11.0703i	0.839640	−	0.388012i
$815$		0			0
$816$	−1.54517	+	0.934180i	−0.0540916	+	0.0327028i
$817$	−25.1713	+	49.4015i	−0.880633	+	1.72834i
$818$	−10.9751	+	5.59210i	−0.383736	+	0.195523i
$819$	1.79609	−	1.75352i	0.0627606	−	0.0612729i
$820$		0			0
$821$	−21.7290	−	7.06016i	−0.758346	−	0.246401i	−0.0957772	−	0.995403i	$-0.530534\pi$
$821$	−21.7290	−	7.06016i	−0.758346	−	0.246401i	−0.662568	+	0.749001i	$0.730534\pi$
$822$	23.2250	+	14.4246i	0.810065	+	0.503115i
$823$	−5.49378	+	34.6864i	−0.191501	+	1.20909i	0.685308	+	0.728253i	$0.259668\pi$
$823$	−5.49378	+	34.6864i	−0.191501	+	1.20909i	−0.876809	+	0.480838i	$0.840332\pi$
$824$	−4.22080			−0.147038
$825$		0			0
$826$	−10.2122			−0.355327
$827$	6.28582	−	39.6871i	0.218579	−	1.38006i	−0.597386	−	0.801954i	$-0.703794\pi$
$827$	6.28582	−	39.6871i	0.218579	−	1.38006i	0.815965	−	0.578101i	$-0.196206\pi$
$828$	−6.20683	+	8.33099i	−0.215702	+	0.289522i
$829$	41.9934	+	13.6445i	1.45849	+	0.473892i	0.927609	−	0.373553i	$-0.121861\pi$
$829$	41.9934	+	13.6445i	1.45849	+	0.473892i	0.530882	+	0.847446i	$0.321861\pi$
$830$		0			0
$831$	13.0440	−	15.0885i	0.452493	−	0.523413i
$832$	−5.14811	+	2.62309i	−0.178479	+	0.0909394i
$833$	4.42615	−	8.68680i	0.153357	−	0.300980i
$834$	−7.85809	−	12.9975i	−0.272103	−	0.450068i
$835$		0			0
$836$	−2.24331	−	18.8060i	−0.0775863	−	0.650419i
$837$	25.1309	−	14.7851i	0.868650	−	0.511047i
$838$	0.263530	−	1.66386i	0.00910348	−	0.0574771i
$839$	−1.45847	−	4.48872i	−0.0503521	−	0.154968i	0.922719	−	0.385474i	$-0.125962\pi$
$839$	−1.45847	−	4.48872i	−0.0503521	−	0.154968i	−0.973071	+	0.230506i	$0.925962\pi$
$840$		0			0
$841$	−25.3771	−	18.4375i	−0.875072	−	0.635777i
$842$	−7.43414	+	1.17745i	−0.256197	+	0.0405777i
$843$	−15.3794	−	37.7682i	−0.529695	−	1.30080i
$844$	−7.05469	+	2.29221i	−0.242833	+	0.0789011i
$845$		0			0
$846$	−6.17157	−	1.05350i	−0.212183	−	0.0362201i
$847$	7.69591	−	6.59735i	0.264435	−	0.226688i
$848$	−1.55753	−	1.55753i	−0.0534859	−	0.0534859i
$849$	26.1275	−	15.7963i	0.896695	−	0.542126i
$850$		0			0
$851$	25.2608	+	8.20773i	0.865928	+	0.281357i
$852$	0.587085	+	8.07869i	0.0201132	+	0.276771i
$853$	34.5131	−	5.46634i	1.18171	−	0.187164i	0.465497	−	0.885050i	$-0.345876\pi$
$853$	34.5131	−	5.46634i	1.18171	−	0.187164i	0.716209	+	0.697886i	$0.245876\pi$
$854$	1.36278	−	4.19421i	0.0466334	−	0.143523i
$855$		0			0
$856$	−13.5172	+	9.82081i	−0.462008	+	0.335669i
$857$	1.44170	−	1.44170i	0.0492477	−	0.0492477i	−0.682054	−	0.731302i	$-0.738913\pi$
$857$	1.44170	−	1.44170i	0.0492477	−	0.0492477i	0.731302	+	0.682054i	$0.238913\pi$
$858$	−3.64886	−	3.40751i	−0.124570	−	0.116330i
$859$		−	2.64556i		−	0.0902653i	−0.998981	−	0.0451326i	$-0.985629\pi$
$859$		−	2.64556i		−	0.0902653i	0.998981	−	0.0451326i	$-0.0143710\pi$
$860$		0			0
$861$	1.90383	+	8.14488i	0.0648824	+	0.277577i
$862$	25.0312	−	12.7541i	0.852568	−	0.434405i
$863$	−1.97663	−	12.4799i	−0.0672852	−	0.424822i	−0.998220	−	0.0596369i	$-0.981006\pi$
$863$	−1.97663	−	12.4799i	−0.0672852	−	0.424822i	0.930935	−	0.365185i	$-0.118994\pi$
$864$	−21.1553	+	17.4200i	−0.719716	+	0.592640i
$865$		0			0
$866$	9.91575	−	3.22182i	0.336951	−	0.109482i
$867$	6.00410	−	24.3643i	0.203910	−	0.827456i
$868$	−3.96291	+	3.96291i	−0.134510	+	0.134510i
$869$	25.7595	−	23.8556i	0.873830	−	0.809245i
$870$		0			0
$871$	2.62614	−	1.90800i	0.0889834	−	0.0646502i
$872$	−22.3953	−	11.4110i	−0.758399	−	0.386424i
$873$	−9.96371	−	31.9645i	−0.337220	−	1.08184i
$874$	−9.47131	+	13.0361i	−0.320372	+	0.440954i
$875$		0			0
$876$	−21.4368	−	9.03039i	−0.724282	−	0.305108i
$877$	−4.45016	+	8.73394i	−0.150271	+	0.294924i	−0.953855	−	0.300268i	$-0.902924\pi$
$877$	−4.45016	+	8.73394i	−0.150271	+	0.294924i	0.803584	+	0.595192i	$0.202924\pi$
$878$	20.2620	+	3.20919i	0.683810	+	0.108305i
$879$	−2.25054	+	26.5587i	−0.0759088	+	0.895802i
$880$		0			0
$881$			13.7752i			0.464098i	0.972704	+	0.232049i	$0.0745429\pi$
$881$			13.7752i			0.464098i	−0.972704	+	0.232049i	$0.925457\pi$
$882$	−5.65896	+	16.7310i	−0.190547	+	0.563363i
$883$	−29.7018	−	15.1338i	−0.999544	−	0.509293i	−0.123923	−	0.992292i	$-0.539548\pi$
$883$	−29.7018	−	15.1338i	−0.999544	−	0.509293i	−0.875621	+	0.482999i	$0.839548\pi$
$884$	−0.482015	+	1.48349i	−0.0162119	+	0.0498952i
$885$		0			0
$886$	5.58035	+	4.05436i	0.187476	+	0.136209i
$887$	9.76814	+	19.1711i	0.327982	+	0.643701i	0.994837	−	0.101487i	$-0.0323599\pi$
$887$	9.76814	+	19.1711i	0.327982	+	0.643701i	−0.666855	+	0.745188i	$0.732360\pi$
$888$	36.1034	+	22.4231i	1.21155	+	0.752469i
$889$	−6.78667	−	9.34105i	−0.227618	−	0.313289i
$890$		0			0
$891$	−25.7003	−	15.1821i	−0.860992	−	0.508618i
$892$	−3.23769	−	3.23769i	−0.108406	−	0.108406i
$893$	11.3462	+	1.79706i	0.379687	+	0.0601365i
$894$	−6.91453	−	29.5814i	−0.231257	−	0.989351i
$895$		0			0
$896$	2.41416	−	3.32281i	0.0806515	−	0.111007i
$897$	−0.364202	−	5.01166i	−0.0121603	−	0.167335i
$898$	7.98746	+	15.6763i	0.266545	+	0.523124i
$899$	13.4727	+	41.4646i	0.449338	+	1.38292i
$900$		0			0
$901$	−5.30863			−0.176856
$902$	16.0076	−	4.53046i	0.532996	−	0.150848i
$903$	−10.8315	−	12.8372i	−0.360451	−	0.427194i
$904$	−1.73187	−	2.38372i	−0.0576013	−	0.0792813i
$905$		0			0
$906$	10.2914	−	24.4303i	0.341909	−	0.811641i
$907$	−6.66623	−	42.0889i	−0.221348	−	1.39754i	−0.808707	−	0.588212i	$-0.799832\pi$
$907$	−6.66623	−	42.0889i	−0.221348	−	1.39754i	0.587358	−	0.809327i	$-0.300168\pi$
$908$	3.50171	+	22.1089i	0.116208	+	0.733711i
$909$	−7.37570	+	14.0563i	−0.244637	+	0.466218i
$910$		0			0
$911$	−4.51254	−	6.21098i	−0.149507	−	0.205779i	0.727694	−	0.685902i	$-0.240592\pi$
$911$	−4.51254	−	6.21098i	−0.149507	−	0.205779i	−0.877201	+	0.480123i	$0.840592\pi$
$912$	−4.58715	+	3.87047i	−0.151896	+	0.128164i
$913$	0.382696	−	0.108310i	0.0126654	−	0.00358454i
$914$	30.6714			1.01452
$915$		0			0
$916$	9.86220	+	30.3527i	0.325856	+	1.00288i
$917$	−3.23202	−	6.34319i	−0.106731	−	0.209471i
$918$	0.759808	−	7.84679i	0.0250774	−	0.258983i
$919$	24.7472	−	34.0616i	0.816335	−	1.12359i	−0.173979	−	0.984749i	$-0.555663\pi$
$919$	24.7472	−	34.0616i	0.816335	−	1.12359i	0.990315	−	0.138840i	$-0.0443374\pi$
$920$		0			0
$921$	8.26839	−	1.93270i	0.272453	−	0.0636846i
$922$	23.0165	+	3.64545i	0.758007	+	0.120057i
$923$	−2.77028	−	2.77028i	−0.0911850	−	0.0911850i
$924$	5.51404	+	1.58541i	0.181399	+	0.0521560i
$925$		0			0
$926$	13.7196	+	18.8834i	0.450854	+	0.620547i
$927$	2.56292	−	3.44003i	0.0841773	−	0.112985i
$928$	−18.6032	−	36.5108i	−0.610680	−	1.19853i
$929$	−16.9077	−	12.2842i	−0.554725	−	0.403031i	0.274800	−	0.961501i	$-0.411388\pi$
$929$	−16.9077	−	12.2842i	−0.554725	−	0.403031i	−0.829524	+	0.558470i	$0.811388\pi$
$930$		0			0
$931$	10.0144	−	30.8211i	0.328208	−	1.01012i
$932$	−16.7139	−	8.51615i	−0.547482	−	0.278956i
$933$	−4.44592	+	18.0413i	−0.145553	+	0.590645i
$934$			29.7168i			0.972362i
$935$		0			0
$936$	1.35293	−	7.92568i	0.0442220	−	0.259059i
$937$	−2.77883	−	0.440123i	−0.0907803	−	0.0143782i	0.110879	−	0.993834i	$-0.464633\pi$
$937$	−2.77883	−	0.440123i	−0.0907803	−	0.0143782i	−0.201659	+	0.979456i	$0.564633\pi$
$938$	1.43161	−	2.80970i	0.0467439	−	0.0917400i
$939$	0.153433	−	0.364228i	0.00500711	−	0.0118861i
$940$		0			0
$941$	9.03112	−	12.4303i	0.294406	−	0.405215i	−0.636033	−	0.771662i	$-0.719426\pi$
$941$	9.03112	−	12.4303i	0.294406	−	0.405215i	0.930439	+	0.366447i	$0.119426\pi$
$942$	−26.0181	+	10.5947i	−0.847714	+	0.345194i
$943$	14.9192	+	7.60172i	0.485836	+	0.247546i
$944$	−6.16027	+	4.47570i	−0.200500	+	0.145672i
$945$		0			0
$946$	−24.5106	+	22.6991i	−0.796909	+	0.738010i
$947$	2.87539	−	2.87539i	0.0934376	−	0.0934376i	−0.658843	−	0.752281i	$-0.728954\pi$
$947$	2.87539	−	2.87539i	0.0934376	−	0.0934376i	0.752281	+	0.658843i	$0.228954\pi$
$948$	19.2947	+	4.75480i	0.626663	+	0.154429i
$949$	10.7002	−	3.47671i	0.347344	−	0.112859i
$950$		0			0
$951$	30.1752	+	26.0866i	0.978499	+	0.845917i
$952$	0.674468	+	4.25842i	0.0218596	+	0.138016i
$953$	24.4694	−	12.4678i	0.792641	−	0.403871i	−0.0102867	−	0.999947i	$-0.503274\pi$
$953$	24.4694	−	12.4678i	0.792641	−	0.403871i	0.802928	+	0.596076i	$0.203274\pi$
$954$	9.51612	−	1.39043i	0.308096	−	0.0450169i
$955$		0			0
$956$		−	21.7188i		−	0.702435i
$957$	30.4633	−	32.6209i	0.984738	−	1.05449i
$958$	−19.6779	+	19.6779i	−0.635764	+	0.635764i
$959$	12.2944	−	8.93238i	0.397006	−	0.288442i
$960$		0			0
$961$	0.150603	−	0.463508i	0.00485815	−	0.0149519i
$962$	−7.13562	+	1.13017i	−0.230062	+	0.0364382i
$963$	0.203654	−	16.9801i	0.00656264	−	0.547175i
$964$	6.18135	+	2.00844i	0.199088	+	0.0646876i
$965$		0			0
$966$	−2.52552	−	4.17730i	−0.0812574	−	0.134402i
$967$	8.06213	+	8.06213i	0.259261	+	0.259261i	0.824753	−	0.565493i	$-0.191314\pi$
$967$	8.06213	+	8.06213i	0.259261	+	0.259261i	−0.565493	+	0.824753i	$0.691314\pi$
$968$	7.52193	−	31.5859i	0.241764	−	1.01521i
$969$	−1.22136	+	14.4133i	−0.0392357	+	0.463022i
$970$		0			0
$971$	−24.2107	+	7.86654i	−0.776959	+	0.252449i	−0.670541	−	0.741872i	$-0.733938\pi$
$971$	−24.2107	+	7.86654i	−0.776959	+	0.252449i	−0.106418	+	0.994322i	$0.533938\pi$
$972$	−0.820055	−	16.8752i	−0.0263033	−	0.541273i
$973$	−8.33840	+	1.32067i	−0.267317	+	0.0423388i
$974$	−9.32572	−	6.77553i	−0.298815	−	0.217102i
$975$		0			0
$976$	−1.01613	−	3.12734i	−0.0325256	−	0.100104i
$977$	−3.61057	+	22.7962i	−0.115512	+	0.729316i	0.860151	+	0.510040i	$0.170370\pi$
$977$	−3.61057	+	22.7962i	−0.115512	+	0.729316i	−0.975663	+	0.219276i	$0.929630\pi$
$978$	27.5616	−	23.2555i	0.881324	−	0.743629i
$979$	−4.22091	−	35.3846i	−0.134901	−	1.13090i
$980$		0			0
$981$	22.8988	−	11.3237i	0.731103	−	0.361537i
$982$	−6.59223	+	12.9380i	−0.210367	+	0.412868i
$983$	−7.92307	+	4.03701i	−0.252707	+	0.128761i	−0.575756	−	0.817622i	$-0.695292\pi$
$983$	−7.92307	+	4.03701i	−0.252707	+	0.128761i	0.323049	+	0.946382i	$0.395292\pi$
$984$	20.2685	+	17.5222i	0.646135	+	0.558587i
$985$		0			0
$986$	11.2110	+	3.64269i	0.357032	+	0.116007i
$987$	−1.83608	+	2.95627i	−0.0584430	+	0.0940991i
$988$	−0.811098	+	5.12107i	−0.0258045	+	0.162923i
$989$	−33.6234			−1.06916
$990$		0			0
$991$	11.3191			0.359563			0.179782	−	0.983707i	$-0.442461\pi$
$991$	11.3191			0.359563			0.179782	+	0.983707i	$0.442461\pi$
$992$	−4.62955	+	29.2298i	−0.146988	+	0.928048i
$993$	10.4577	−	16.8379i	0.331864	−	0.534334i
$994$	−3.61963	−	1.17609i	−0.114808	−	0.0373033i
$995$		0			0
$996$	0.170301	+	0.147226i	0.00539618	+	0.00466502i
$997$	49.7357	−	25.3416i	1.57515	−	0.802577i	0.575264	−	0.817968i	$-0.304899\pi$
$997$	49.7357	−	25.3416i	1.57515	−	0.802577i	0.999882	+	0.0153913i	$0.00489938\pi$
$998$	12.7017	−	24.9285i	0.402066	−	0.789098i
$999$	−40.1976	+	15.8094i	−1.27180	+	0.500186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.ct.b.707.7		160
3.2	odd	2	inner	825.2.ct.b.707.14		160
5.2	odd	4		165.2.v.a.113.7	yes	160
5.3	odd	4	inner	825.2.ct.b.443.14		160
5.4	even	2		165.2.v.a.47.14	yes	160
11.4	even	5	inner	825.2.ct.b.257.7		160
15.2	even	4		165.2.v.a.113.14	yes	160
15.8	even	4	inner	825.2.ct.b.443.7		160
15.14	odd	2		165.2.v.a.47.7	✓	160
33.26	odd	10	inner	825.2.ct.b.257.14		160
55.4	even	10		165.2.v.a.92.14	yes	160
55.37	odd	20		165.2.v.a.158.7	yes	160
55.48	odd	20	inner	825.2.ct.b.818.14		160
165.59	odd	10		165.2.v.a.92.7	yes	160
165.92	even	20		165.2.v.a.158.14	yes	160
165.158	even	20	inner	825.2.ct.b.818.7		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.v.a.47.7	✓	160	15.14	odd	2
165.2.v.a.47.14	yes	160	5.4	even	2
165.2.v.a.92.7	yes	160	165.59	odd	10
165.2.v.a.92.14	yes	160	55.4	even	10
165.2.v.a.113.7	yes	160	5.2	odd	4
165.2.v.a.113.14	yes	160	15.2	even	4
165.2.v.a.158.7	yes	160	55.37	odd	20
165.2.v.a.158.14	yes	160	165.92	even	20
825.2.ct.b.257.7		160	11.4	even	5	inner
825.2.ct.b.257.14		160	33.26	odd	10	inner
825.2.ct.b.443.7		160	15.8	even	4	inner
825.2.ct.b.443.14		160	5.3	odd	4	inner
825.2.ct.b.707.7		160	1.1	even	1	trivial
825.2.ct.b.707.14		160	3.2	odd	2	inner
825.2.ct.b.818.7		160	165.158	even	20	inner
825.2.ct.b.818.14		160	55.48	odd	20	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.ct (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.149735 + 0.945387i) q^{2} +(-0.913834 + 1.47136i) q^{3} +(1.03078 + 0.334920i) q^{4} +(-1.25417 - 1.08424i) q^{6} +(-0.821076 + 0.418359i) q^{7} +(-1.34007 + 2.63003i) q^{8} +(-1.32982 - 2.68916i) q^{9} +O(q^{10})\)	\(q+(-0.149735 + 0.945387i) q^{2} +(-0.913834 + 1.47136i) q^{3} +(1.03078 + 0.334920i) q^{4} +(-1.25417 - 1.08424i) q^{6} +(-0.821076 + 0.418359i) q^{7} +(-1.34007 + 2.63003i) q^{8} +(-1.32982 - 2.68916i) q^{9} +(0.392844 + 3.29328i) q^{11} +(-1.43475 + 1.21059i) q^{12} +(0.142038 - 0.896795i) q^{13} +(-0.272568 - 0.838878i) q^{14} +(-0.532077 - 0.386576i) q^{16} +(-1.56555 + 0.247959i) q^{17} +(2.74142 - 0.854531i) q^{18} +(-5.01090 + 1.62814i) q^{19} +(0.134769 - 1.59041i) q^{21} +(-3.17224 - 0.121728i) q^{22} +(-2.25932 - 2.25932i) q^{23} +(-2.64513 - 4.37513i) q^{24} +(0.826550 + 0.268563i) q^{26} +(5.17196 + 0.500803i) q^{27} +(-0.986463 + 0.156240i) q^{28} +(-2.40096 + 7.38940i) q^{29} +(4.53969 - 3.29827i) q^{31} +(-3.72927 + 3.72927i) q^{32} +(-5.20460 - 2.43149i) q^{33} -1.51718i q^{34} +(-0.470091 - 3.21731i) q^{36} +(-7.40678 + 3.77394i) q^{37} +(-0.788918 - 4.98103i) q^{38} +(1.18971 + 1.02851i) q^{39} +(-4.98402 + 1.61941i) q^{41} +(1.48338 + 0.365548i) q^{42} +(7.44106 - 7.44106i) q^{43} +(-0.698048 + 3.52620i) q^{44} +(2.47423 - 1.79763i) q^{46} +(-1.94269 - 0.989848i) q^{47} +(1.05502 - 0.429611i) q^{48} +(-3.61536 + 4.97611i) q^{49} +(1.06581 - 2.53008i) q^{51} +(0.446764 - 0.876824i) q^{52} +(3.30793 + 0.523924i) q^{53} +(-1.24787 + 4.81452i) q^{54} -2.72008i q^{56} +(2.18354 - 8.86070i) q^{57} +(-6.62633 - 3.37629i) q^{58} +(3.57773 - 11.0111i) q^{59} +(4.04491 + 2.93880i) q^{61} +(2.43840 + 4.78563i) q^{62} +(2.21692 + 1.65167i) q^{63} +(-3.74035 - 5.14815i) q^{64} +(3.07801 - 4.55628i) q^{66} +(2.52797 + 2.52797i) q^{67} +(-1.69678 - 0.268743i) q^{68} +(5.38891 - 1.25963i) q^{69} +(2.53621 - 3.49079i) q^{71} +(8.85460 + 0.106199i) q^{72} +(5.62549 + 11.0406i) q^{73} +(-2.45879 - 7.56737i) q^{74} -5.71042 q^{76} +(-1.70033 - 2.53968i) q^{77} +(-1.15048 + 0.970734i) q^{78} +(-6.22215 - 8.56405i) q^{79} +(-5.46318 + 7.15218i) q^{81} +(-0.784685 - 4.95431i) q^{82} +(-0.0187595 - 0.118443i) q^{83} +(0.671577 - 1.59422i) q^{84} +(5.92050 + 8.14886i) q^{86} +(-8.67840 - 10.2854i) q^{87} +(-9.18784 - 3.38001i) q^{88} -10.7445 q^{89} +(0.258558 + 0.795760i) q^{91} +(-1.57216 - 3.08554i) q^{92} +(0.704441 + 9.69360i) q^{93} +(1.22668 - 1.68838i) q^{94} +(-2.07917 - 8.89503i) q^{96} +(11.0231 + 1.74588i) q^{97} +(-4.16301 - 4.16301i) q^{98} +(8.33374 - 5.43588i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{3} - 12 q^{6} + 20 q^{7}+O(q^{10}) \) 160 * q + 8 * q^3 - 12 * q^6 + 20 * q^7	\( 160 q + 8 q^{3} - 12 q^{6} + 20 q^{7} + 68 q^{12} + 4 q^{13} - 8 q^{16} - 2 q^{18} - 24 q^{21} + 20 q^{22} + 14 q^{27} - 8 q^{28} - 8 q^{31} - 38 q^{33} - 124 q^{36} - 16 q^{37} - 74 q^{42} - 34 q^{48} - 116 q^{51} - 12 q^{52} - 30 q^{57} - 112 q^{58} + 14 q^{63} - 20 q^{66} - 128 q^{67} - 92 q^{72} + 80 q^{73} - 176 q^{76} - 20 q^{78} + 52 q^{81} - 12 q^{82} + 36 q^{87} + 276 q^{88} + 128 q^{91} + 8 q^{93} + 152 q^{96} + 96 q^{97}+O(q^{100}) \) 160 * q + 8 * q^3 - 12 * q^6 + 20 * q^7 + 68 * q^12 + 4 * q^13 - 8 * q^16 - 2 * q^18 - 24 * q^21 + 20 * q^22 + 14 * q^27 - 8 * q^28 - 8 * q^31 - 38 * q^33 - 124 * q^36 - 16 * q^37 - 74 * q^42 - 34 * q^48 - 116 * q^51 - 12 * q^52 - 30 * q^57 - 112 * q^58 + 14 * q^63 - 20 * q^66 - 128 * q^67 - 92 * q^72 + 80 * q^73 - 176 * q^76 - 20 * q^78 + 52 * q^81 - 12 * q^82 + 36 * q^87 + 276 * q^88 + 128 * q^91 + 8 * q^93 + 152 * q^96 + 96 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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