LMFDB - Embedded newform 864.2.v.b.109.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(109,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

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

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

chi := DirichletCharacter("864.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.v (of order $8$, degree $4$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			109.13
Character	$\chi$	$=$	864.109
Dual form			864.2.v.b.325.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.463875 - 1.33597i) q^{2} +(-1.56964 + 1.23945i) q^{4} +(-0.137547 + 0.0569738i) q^{5} +(0.385875 - 0.385875i) q^{7} +(2.38398 + 1.52205i) q^{8} +O(q^{10})$	\(q+(-0.463875 - 1.33597i) q^{2} +(-1.56964 + 1.23945i) q^{4} +(-0.137547 + 0.0569738i) q^{5} +(0.385875 - 0.385875i) q^{7} +(2.38398 + 1.52205i) q^{8} +(0.139920 + 0.157330i) q^{10} +(1.66259 + 4.01386i) q^{11} +(-5.30371 - 2.19687i) q^{13} +(-0.694516 - 0.336521i) q^{14} +(0.927543 - 3.89097i) q^{16} +4.41571i q^{17} +(-7.14906 - 2.96124i) q^{19} +(0.145283 - 0.259911i) q^{20} +(4.59117 - 4.08311i) q^{22} +(-5.04601 - 5.04601i) q^{23} +(-3.51986 + 3.51986i) q^{25} +(-0.474698 + 8.10468i) q^{26} +(-0.127414 + 1.08396i) q^{28} +(1.66821 - 4.02742i) q^{29} +0.274792 q^{31} +(-5.62849 + 0.565751i) q^{32} +(5.89927 - 2.04834i) q^{34} +(-0.0310912 + 0.0750608i) q^{35} +(-1.49115 + 0.617653i) q^{37} +(-0.639862 + 10.9246i) q^{38} +(-0.414626 - 0.0735285i) q^{40} +(0.482993 + 0.482993i) q^{41} +(-0.554390 - 1.33842i) q^{43} +(-7.58464 - 4.23962i) q^{44} +(-4.40061 + 9.08204i) q^{46} +12.2231i q^{47} +6.70220i q^{49} +(6.33521 + 3.06966i) q^{50} +(11.0478 - 3.12537i) q^{52} +(2.13483 + 5.15392i) q^{53} +(-0.457370 - 0.457370i) q^{55} +(1.50724 - 0.332599i) q^{56} +(-6.15436 - 0.360466i) q^{58} +(-8.90946 + 3.69042i) q^{59} +(4.31381 - 10.4145i) q^{61} +(-0.127469 - 0.367114i) q^{62} +(3.36674 + 7.25707i) q^{64} +0.854674 q^{65} +(-4.38272 + 10.5808i) q^{67} +(-5.47304 - 6.93108i) q^{68} +(0.114702 + 0.00671816i) q^{70} +(-6.62943 + 6.62943i) q^{71} +(-4.79216 - 4.79216i) q^{73} +(1.51687 + 1.70562i) q^{74} +(14.8918 - 4.21280i) q^{76} +(2.19040 + 0.907295i) q^{77} +3.60122i q^{79} +(0.0941028 + 0.588037i) q^{80} +(0.421217 - 0.869313i) q^{82} +(-9.62080 - 3.98506i) q^{83} +(-0.251580 - 0.607368i) q^{85} +(-1.53092 + 1.36151i) q^{86} +(-2.14569 + 12.0995i) q^{88} +(10.0686 - 10.0686i) q^{89} +(-2.89429 + 1.19885i) q^{91} +(14.1747 + 1.66616i) q^{92} +(16.3297 - 5.66998i) q^{94} +1.15205 q^{95} -6.06867 q^{97} +(8.95395 - 3.10898i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) $ 128 * q + 16 * q^10 - 32 * q^16 - 16 * q^22 - 32 * q^40 - 32 * q^46 - 80 * q^52 + 32 * q^55 - 32 * q^58 + 64 * q^61 + 48 * q^64 + 64 * q^67 - 96 * q^70 + 32 * q^76 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 48 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.463875	−	1.33597i	−0.328009	−	0.944675i
$2$	−0.463875	−	1.33597i	−0.328009	−	0.944675i
$3$		0			0
$3$		0			0
$4$	−1.56964	+	1.23945i	−0.784820	+	0.619723i
$5$	−0.137547	+	0.0569738i	−0.0615129	+	0.0254795i	−0.413228	−	0.910628i	$-0.635599\pi$
$5$	−0.137547	+	0.0569738i	−0.0615129	+	0.0254795i	0.351715	+	0.936107i	$0.385599\pi$
$6$		0			0
$7$	0.385875	−	0.385875i	0.145847	−	0.145847i	−0.630413	−	0.776260i	$-0.717114\pi$
$7$	0.385875	−	0.385875i	0.145847	−	0.145847i	0.776260	+	0.630413i	$0.217114\pi$
$8$	2.38398	+	1.52205i	0.842865	+	0.538125i
$9$		0			0
$10$	0.139920	+	0.157330i	0.0442466	+	0.0497522i
$11$	1.66259	+	4.01386i	0.501291	+	1.21022i	0.948781	+	0.315935i	$0.102318\pi$
$11$	1.66259	+	4.01386i	0.501291	+	1.21022i	−0.447490	+	0.894289i	$0.647682\pi$
$12$		0			0
$13$	−5.30371	−	2.19687i	−1.47099	−	0.609302i	−0.503902	−	0.863761i	$-0.668103\pi$
$13$	−5.30371	−	2.19687i	−1.47099	−	0.609302i	−0.967084	+	0.254459i	$0.918103\pi$
$14$	−0.694516	−	0.336521i	−0.185617	−	0.0899390i
$15$		0			0
$16$	0.927543	−	3.89097i	0.231886	−	0.972743i
$17$			4.41571i			1.07097i	0.844545	+	0.535484i	$0.179871\pi$
$17$			4.41571i			1.07097i	−0.844545	+	0.535484i	$0.820129\pi$
$18$		0			0
$19$	−7.14906	−	2.96124i	−1.64011	−	0.679355i	−0.643798	−	0.765195i	$-0.722642\pi$
$19$	−7.14906	−	2.96124i	−1.64011	−	0.679355i	−0.996309	+	0.0858404i	$0.972642\pi$
$20$	0.145283	−	0.259911i	0.0324863	−	0.0581178i
$21$		0			0
$22$	4.59117	−	4.08311i	0.978840	−	0.870521i
$23$	−5.04601	−	5.04601i	−1.05217	−	1.05217i	−0.998562	−	0.0536038i	$-0.982929\pi$
$23$	−5.04601	−	5.04601i	−1.05217	−	1.05217i	−0.0536038	−	0.998562i	$-0.517071\pi$
$24$		0			0
$25$	−3.51986	+	3.51986i	−0.703972	+	0.703972i
$26$	−0.474698	+	8.10468i	−0.0930960	+	1.58946i
$27$		0			0
$28$	−0.127414	+	1.08396i	−0.0240789	+	0.204849i
$29$	1.66821	−	4.02742i	0.309779	−	0.747873i	−0.689933	−	0.723874i	$-0.742360\pi$
$29$	1.66821	−	4.02742i	0.309779	−	0.747873i	0.999712	−	0.0239999i	$-0.00764014\pi$
$30$		0			0
$31$	0.274792			0.0493541			0.0246770	−	0.999695i	$-0.492144\pi$
$31$	0.274792			0.0493541			0.0246770	+	0.999695i	$0.492144\pi$
$32$	−5.62849	+	0.565751i	−0.994986	+	0.100012i
$33$		0			0
$34$	5.89927	−	2.04834i	1.01172	−	0.351287i
$35$	−0.0310912	+	0.0750608i	−0.00525537	+	0.0126876i
$36$		0			0
$37$	−1.49115	+	0.617653i	−0.245143	+	0.101542i	−0.501872	−	0.864942i	$-0.667355\pi$
$37$	−1.49115	+	0.617653i	−0.245143	+	0.101542i	0.256729	+	0.966483i	$0.417355\pi$
$38$	−0.639862	+	10.9246i	−0.103799	+	1.77220i
$39$		0			0
$40$	−0.414626	−	0.0735285i	−0.0655582	−	0.0116259i
$41$	0.482993	+	0.482993i	0.0754308	+	0.0754308i	0.743816	−	0.668385i	$-0.233014\pi$
$41$	0.482993	+	0.482993i	0.0754308	+	0.0754308i	−0.668385	+	0.743816i	$0.733014\pi$
$42$		0			0
$43$	−0.554390	−	1.33842i	−0.0845437	−	0.204107i	0.875954	−	0.482395i	$-0.160233\pi$
$43$	−0.554390	−	1.33842i	−0.0845437	−	0.204107i	−0.960498	+	0.278288i	$0.910233\pi$
$44$	−7.58464	−	4.23962i	−1.14343	−	0.639147i
$45$		0			0
$46$	−4.40061	+	9.08204i	−0.648835	+	1.33907i
$47$			12.2231i			1.78292i	0.453100	+	0.891460i	$0.350318\pi$
$47$			12.2231i			1.78292i	−0.453100	+	0.891460i	$0.649682\pi$
$48$		0			0
$49$			6.70220i			0.957457i
$50$	6.33521	+	3.06966i	0.895934	+	0.434116i
$51$		0			0
$52$	11.0478	−	3.12537i	1.53206	−	0.433411i
$53$	2.13483	+	5.15392i	0.293241	+	0.707946i	1.00000		0.000491566i	$0.000156470\pi$
$53$	2.13483	+	5.15392i	0.293241	+	0.707946i	−0.706759	+	0.707454i	$0.749844\pi$
$54$		0			0
$55$	−0.457370	−	0.457370i	−0.0616717	−	0.0616717i
$56$	1.50724	−	0.332599i	0.201414	−	0.0444455i
$57$		0			0
$58$	−6.15436	−	0.360466i	−0.808107	−	0.0473315i
$59$	−8.90946	+	3.69042i	−1.15991	+	0.480451i	−0.877846	−	0.478943i	$-0.841020\pi$
$59$	−8.90946	+	3.69042i	−1.15991	+	0.480451i	−0.282067	+	0.959395i	$0.591020\pi$
$60$		0			0
$61$	4.31381	−	10.4145i	0.552327	−	1.33344i	−0.363399	−	0.931634i	$-0.618384\pi$
$61$	4.31381	−	10.4145i	0.552327	−	1.33344i	0.915726	−	0.401803i	$-0.131616\pi$
$62$	−0.127469	−	0.367114i	−0.0161886	−	0.0466235i
$63$		0			0
$64$	3.36674	+	7.25707i	0.420843	+	0.907134i
$65$	0.854674			0.106009
$66$		0			0
$67$	−4.38272	+	10.5808i	−0.535434	+	1.29265i	0.392447	+	0.919775i	$0.371629\pi$
$67$	−4.38272	+	10.5808i	−0.535434	+	1.29265i	−0.927881	+	0.372877i	$0.878371\pi$
$68$	−5.47304	−	6.93108i	−0.663704	−	0.840517i
$69$		0			0
$70$	0.114702	+	0.00671816i	0.0137095	+	0.000802974i
$71$	−6.62943	+	6.62943i	−0.786768	+	0.786768i	−0.980963	−	0.194195i	$-0.937791\pi$
$71$	−6.62943	+	6.62943i	−0.786768	+	0.786768i	0.194195	+	0.980963i	$0.437791\pi$
$72$		0			0
$73$	−4.79216	−	4.79216i	−0.560879	−	0.560879i	0.368678	−	0.929557i	$-0.379811\pi$
$73$	−4.79216	−	4.79216i	−0.560879	−	0.560879i	−0.929557	+	0.368678i	$0.879811\pi$
$74$	1.51687	+	1.70562i	0.176333	+	0.198274i
$75$		0			0
$76$	14.8918	−	4.21280i	1.70820	−	0.483241i
$77$	2.19040	+	0.907295i	0.249620	+	0.103396i
$78$		0			0
$79$			3.60122i			0.405169i	0.979265	+	0.202584i	$0.0649340\pi$
$79$			3.60122i			0.405169i	−0.979265	+	0.202584i	$0.935066\pi$
$80$	0.0941028	+	0.588037i	0.0105210	+	0.0657446i
$81$		0			0
$82$	0.421217	−	0.869313i	0.0465156	−	0.0959996i
$83$	−9.62080	−	3.98506i	−1.05602	−	0.437418i	−0.213983	−	0.976837i	$-0.568644\pi$
$83$	−9.62080	−	3.98506i	−1.05602	−	0.437418i	−0.842037	+	0.539420i	$0.818644\pi$
$84$		0			0
$85$	−0.251580	−	0.607368i	−0.0272877	−	0.0658783i
$86$	−1.53092	+	1.36151i	−0.165083	+	0.146815i
$87$		0			0
$88$	−2.14569	+	12.0995i	−0.228731	+	1.28981i
$89$	10.0686	−	10.0686i	1.06727	−	1.06727i	0.0697058	−	0.997568i	$-0.477794\pi$
$89$	10.0686	−	10.0686i	1.06727	−	1.06727i	0.997568	−	0.0697058i	$-0.0222060\pi$
$90$		0			0
$91$	−2.89429	+	1.19885i	−0.303404	+	0.125674i
$92$	14.1747	+	1.66616i	1.47781	+	0.173709i
$93$		0			0
$94$	16.3297	−	5.66998i	1.68428	−	0.584813i
$95$	1.15205			0.118197
$96$		0			0
$97$	−6.06867			−0.616180			−0.308090	−	0.951357i	$-0.599690\pi$
$97$	−6.06867			−0.616180			−0.308090	+	0.951357i	$0.599690\pi$
$98$	8.95395	−	3.10898i	0.904486	−	0.314054i
$99$		0			0
$100$	1.16224	−	9.88760i	0.116224	−	0.988760i
$101$	11.1272	−	4.60905i	1.10720	−	0.458618i	0.247229	−	0.968957i	$-0.420480\pi$
$101$	11.1272	−	4.60905i	1.10720	−	0.458618i	0.859973	+	0.510339i	$0.170480\pi$
$102$		0			0
$103$	−3.41073	+	3.41073i	−0.336069	+	0.336069i	−0.854886	−	0.518817i	$-0.826373\pi$
$103$	−3.41073	+	3.41073i	−0.336069	+	0.336069i	0.518817	+	0.854886i	$0.326373\pi$
$104$	−9.30022	−	13.3098i	−0.911962	−	1.30513i
$105$		0			0
$106$	5.89520	−	5.24284i	0.572593	−	0.509230i
$107$	0.0209570	+	0.0505946i	0.00202599	+	0.00489116i	0.924889	−	0.380237i	$-0.124157\pi$
$107$	0.0209570	+	0.0505946i	0.00202599	+	0.00489116i	−0.922863	+	0.385128i	$0.874157\pi$
$108$		0			0
$109$	2.85064	+	1.18077i	0.273042	+	0.113098i	0.515003	−	0.857188i	$-0.327791\pi$
$109$	2.85064	+	1.18077i	0.273042	+	0.113098i	−0.241961	+	0.970286i	$0.577791\pi$
$110$	−0.398871	+	0.823196i	−0.0380309	+	0.0784886i
$111$		0			0
$112$	−1.14351	−	1.85935i	−0.108052	−	0.175692i
$113$		−	10.0925i		−	0.949425i	−0.880141	−	0.474712i	$-0.842552\pi$
$113$		−	10.0925i		−	0.949425i	0.880141	−	0.474712i	$-0.157448\pi$
$114$		0			0
$115$	0.981554	+	0.406573i	0.0915304	+	0.0379131i
$116$	2.37328	+	8.38927i	0.220354	+	0.778924i
$117$		0			0
$118$	9.06316	+	10.1909i	0.834332	+	0.938147i
$119$	1.70391	+	1.70391i	0.156198	+	0.156198i
$120$		0			0
$121$	−5.56867	+	5.56867i	−0.506243	+	0.506243i
$122$	−15.9145	−	0.932126i	−1.44083	−	0.0843907i
$123$		0			0
$124$	−0.431324	+	0.340590i	−0.0387341	+	0.0305859i
$125$	0.568475	−	1.37242i	0.0508460	−	0.122753i
$126$		0			0
$127$	7.31493			0.649095			0.324548	−	0.945869i	$-0.394788\pi$
$127$	7.31493			0.649095			0.324548	+	0.945869i	$0.394788\pi$
$128$	8.13349	−	7.86424i	0.718906	−	0.695107i
$129$		0			0
$130$	−0.396462	−	1.14182i	−0.0347720	−	0.100144i
$131$	1.54246	−	3.72384i	0.134766	−	0.325353i	−0.842062	−	0.539381i	$-0.818658\pi$
$131$	1.54246	−	3.72384i	0.134766	−	0.325353i	0.976828	+	0.214028i	$0.0686583\pi$
$132$		0			0
$133$	−3.90132	+	1.61598i	−0.338287	+	0.140123i
$134$	16.1687	+	0.947014i	1.39676	+	0.0818096i
$135$		0			0
$136$	−6.72093	+	10.5270i	−0.576315	+	0.902681i
$137$	11.0330	+	11.0330i	0.942613	+	0.942613i	0.998440	−	0.0558274i	$-0.0177797\pi$
$137$	11.0330	+	11.0330i	0.942613	+	0.942613i	−0.0558274	+	0.998440i	$0.517780\pi$
$138$		0			0
$139$	−4.43699	−	10.7118i	−0.376340	−	0.908566i	−0.992645	−	0.121058i	$-0.961371\pi$
$139$	−4.43699	−	10.7118i	−0.376340	−	0.908566i	0.616305	−	0.787507i	$-0.288629\pi$
$140$	−0.0442319	−	0.156354i	−0.00373827	−	0.0132144i
$141$		0			0
$142$	11.9319	+	5.78150i	1.00131	+	0.485173i
$143$		−	24.9409i		−	2.08566i
$144$		0			0
$145$			0.649004i			0.0538969i
$146$	−4.17923	+	8.62515i	−0.345875	+	0.713822i
$147$		0			0
$148$	1.57502	−	2.81769i	0.129466	−	0.231613i
$149$	−0.376981	−	0.910112i	−0.0308835	−	0.0745593i	0.907685	−	0.419651i	$-0.137848\pi$
$149$	−0.376981	−	0.910112i	−0.0308835	−	0.0745593i	−0.938569	+	0.345092i	$0.887848\pi$
$150$		0			0
$151$	−5.16130	−	5.16130i	−0.420021	−	0.420021i	0.465190	−	0.885211i	$-0.345986\pi$
$151$	−5.16130	−	5.16130i	−0.420021	−	0.420021i	−0.885211	+	0.465190i	$0.845986\pi$
$152$	−12.5361	−	17.9408i	−1.01681	−	1.45519i
$153$		0			0
$154$	0.196048	−	3.34719i	0.0157980	−	0.269724i
$155$	−0.0377968	+	0.0156559i	−0.00303591	+	0.00125752i
$156$		0			0
$157$	−5.35913	+	12.9381i	−0.427705	+	1.03257i	0.552308	+	0.833640i	$0.313747\pi$
$157$	−5.35913	+	12.9381i	−0.427705	+	1.03257i	−0.980013	+	0.198932i	$0.936253\pi$
$158$	4.81112	−	1.67051i	0.382752	−	0.132899i
$159$		0			0
$160$	0.741949	−	0.398494i	0.0586562	−	0.0315037i
$161$	−3.89426			−0.306911
$162$		0			0
$163$	4.12757	−	9.96484i	0.323296	−	0.780506i	−0.675762	−	0.737120i	$-0.736185\pi$
$163$	4.12757	−	9.96484i	0.323296	−	0.780506i	0.999058	−	0.0433866i	$-0.0138147\pi$
$164$	−1.35677	−	0.159481i	−0.105946	−	0.0124534i
$165$		0			0
$166$	−0.861090	+	14.7017i	−0.0668335	+	1.14107i
$167$	−8.52303	+	8.52303i	−0.659532	+	0.659532i	−0.955269	−	0.295737i	$-0.904435\pi$
$167$	−8.52303	+	8.52303i	−0.659532	+	0.659532i	0.295737	+	0.955269i	$0.404435\pi$
$168$		0			0
$169$	14.1108	+	14.1108i	1.08544	+	1.08544i
$170$	−0.694725	+	0.617847i	−0.0532830	+	0.0473867i
$171$		0			0
$172$	2.52909	+	1.41370i	0.192841	+	0.107793i
$173$	3.44529	+	1.42708i	0.261940	+	0.108499i	0.509789	−	0.860300i	$-0.329724\pi$
$173$	3.44529	+	1.42708i	0.261940	+	0.108499i	−0.247849	+	0.968799i	$0.579724\pi$
$174$		0			0
$175$			2.71646i			0.205345i
$176$	17.1599	−	2.74608i	1.29348	−	0.206994i
$177$		0			0
$178$	−18.1220	−	8.78083i	−1.35830	−	0.658151i
$179$	−4.16062	−	1.72339i	−0.310979	−	0.128812i	0.221735	−	0.975107i	$-0.428828\pi$
$179$	−4.16062	−	1.72339i	−0.310979	−	0.128812i	−0.532714	+	0.846295i	$0.678828\pi$
$180$		0			0
$181$	−7.88463	−	19.0352i	−0.586060	−	1.41487i	−0.887241	−	0.461307i	$-0.847381\pi$
$181$	−7.88463	−	19.0352i	−0.586060	−	1.41487i	0.301181	−	0.953567i	$-0.402619\pi$
$182$	2.94422	+	3.31057i	0.218240	+	0.245396i
$183$		0			0
$184$	−4.34933	−	19.7099i	−0.320637	−	1.45303i
$185$	0.169913	−	0.169913i	0.0124922	−	0.0124922i
$186$		0			0
$187$	−17.7241	+	7.34154i	−1.29611	+	0.536867i
$188$	−15.1499	−	19.1858i	−1.10492	−	1.39927i
$189$		0			0
$190$	−0.534405	−	1.53910i	−0.0387698	−	0.111658i
$191$	2.32788			0.168439			0.0842196	−	0.996447i	$-0.473160\pi$
$191$	2.32788			0.168439			0.0842196	+	0.996447i	$0.473160\pi$
$192$		0			0
$193$	2.60192			0.187290			0.0936451	−	0.995606i	$-0.470148\pi$
$193$	2.60192			0.187290			0.0936451	+	0.995606i	$0.470148\pi$
$194$	2.81510	+	8.10757i	0.202112	+	0.582089i
$195$		0			0
$196$	−8.30702	−	10.5200i	−0.593359	−	0.751432i
$197$	−9.45596	+	3.91679i	−0.673710	+	0.279060i	−0.693195	−	0.720751i	$-0.743797\pi$
$197$	−9.45596	+	3.91679i	−0.673710	+	0.279060i	0.0194850	+	0.999810i	$0.493797\pi$
$198$		0			0
$199$	13.9255	−	13.9255i	0.987152	−	0.987152i	−0.0127667	−	0.999919i	$-0.504064\pi$
$199$	13.9255	−	13.9255i	0.987152	−	0.987152i	0.999919	+	0.0127667i	$0.00406387\pi$
$200$	−13.7487	+	3.03389i	−0.972179	+	0.214528i
$201$		0			0
$202$	−11.3192	−	12.7277i	−0.796417	−	0.895515i
$203$	−0.910361	−	2.19781i	−0.0638948	−	0.154256i
$204$		0			0
$205$	−0.0939522	−	0.0389163i	−0.00656191	−	0.00271803i
$206$	6.13878	+	2.97448i	0.427709	+	0.207242i
$207$		0			0
$208$	−13.4674	+	18.5989i	−0.933795	+	1.28960i
$209$		−	33.6187i		−	2.32545i
$210$		0			0
$211$	−20.8380	−	8.63137i	−1.43455	−	0.594208i	−0.476076	−	0.879404i	$-0.657941\pi$
$211$	−20.8380	−	8.63137i	−1.43455	−	0.594208i	−0.958469	+	0.285196i	$0.907941\pi$
$212$	−9.73892	−	5.44381i	−0.668872	−	0.373882i
$213$		0			0
$214$	0.0578715	−	0.0514674i	0.00395601	−	0.00351824i
$215$	0.152509	+	0.152509i	0.0104011	+	0.0104011i
$216$		0			0
$217$	0.106035	−	0.106035i	0.00719815	−	0.00719815i
$218$	0.255141	−	4.35611i	0.0172803	−	0.295033i
$219$		0			0
$220$	1.28479	+	0.151021i	0.0866207	+	0.0101818i
$221$	9.70075	−	23.4197i	0.652543	−	1.57538i
$222$		0			0
$223$	11.1452			0.746339			0.373169	−	0.927763i	$-0.378271\pi$
$223$	11.1452			0.746339			0.373169	+	0.927763i	$0.378271\pi$
$224$	−1.95359	+	2.39021i	−0.130530	+	0.159702i
$225$		0			0
$226$	−13.4833	+	4.68166i	−0.896897	+	0.311420i
$227$	−4.36068	+	10.5276i	−0.289429	+	0.698743i	−0.999988	−	0.00489452i	$-0.998442\pi$
$227$	−4.36068	+	10.5276i	−0.289429	+	0.698743i	0.710559	+	0.703637i	$0.248442\pi$
$228$		0			0
$229$	9.55651	−	3.95844i	0.631512	−	0.261581i	−0.0438834	−	0.999037i	$-0.513973\pi$
$229$	9.55651	−	3.95844i	0.631512	−	0.261581i	0.675395	+	0.737456i	$0.263973\pi$
$230$	0.0878520	−	1.49993i	0.00579279	−	0.0989023i
$231$		0			0
$232$	10.1069	−	7.06220i	0.663552	−	0.463656i
$233$	16.9630	+	16.9630i	1.11128	+	1.11128i	0.992977	+	0.118307i	$0.0377466\pi$
$233$	16.9630	+	16.9630i	1.11128	+	1.11128i	0.118307	+	0.992977i	$0.462253\pi$
$234$		0			0
$235$	−0.696396	−	1.68125i	−0.0454278	−	0.109672i
$236$	9.41057	−	16.8354i	0.612576	−	1.09589i
$237$		0			0
$238$	1.48598	−	3.06679i	0.0963217	−	0.198790i
$239$			4.48971i			0.290415i	0.989401	+	0.145208i	$0.0463850\pi$
$239$			4.48971i			0.290415i	−0.989401	+	0.145208i	$0.953615\pi$
$240$		0			0
$241$			15.6739i			1.00965i	0.863223	+	0.504823i	$0.168442\pi$
$241$			15.6739i			1.00965i	−0.863223	+	0.504823i	$0.831558\pi$
$242$	10.0227	+	4.85642i	0.644287	+	0.312182i
$243$		0			0
$244$	6.13704	+	21.6937i	0.392884	+	1.38880i
$245$	−0.381850	−	0.921868i	−0.0243955	−	0.0588960i
$246$		0			0
$247$	31.4111	+	31.4111i	1.99864	+	1.99864i
$248$	0.655099	+	0.418246i	0.0415988	+	0.0265587i
$249$		0			0
$250$	−2.09722	−	0.122836i	−0.132640	−	0.00776882i
$251$	−12.1909	+	5.04964i	−0.769483	+	0.318730i	−0.732663	−	0.680592i	$-0.761723\pi$
$251$	−12.1909	+	5.04964i	−0.769483	+	0.318730i	−0.0368199	+	0.999322i	$0.511723\pi$
$252$		0			0
$253$	11.8645	−	28.6435i	0.745915	−	1.80080i
$254$	−3.39321	−	9.77254i	−0.212909	−	0.613184i
$255$		0			0
$256$	−14.2793	−	7.21809i	−0.892458	−	0.451131i
$257$	2.45880			0.153376			0.0766879	−	0.997055i	$-0.475565\pi$
$257$	2.45880			0.153376			0.0766879	+	0.997055i	$0.475565\pi$
$258$		0			0
$259$	−0.337060	+	0.813734i	−0.0209439	+	0.0505630i
$260$	−1.34153	+	1.05932i	−0.0831982	+	0.0656964i
$261$		0			0
$262$	−5.69045	−	0.333295i	−0.351557	−	0.0205910i
$263$	−13.1192	+	13.1192i	−0.808963	+	0.808963i	−0.984477	−	0.175514i	$-0.943841\pi$
$263$	−13.1192	+	13.1192i	−0.808963	+	0.808963i	0.175514	+	0.984477i	$0.443841\pi$
$264$		0			0
$265$	−0.587278	−	0.587278i	−0.0360762	−	0.0360762i
$266$	3.96862	+	4.46244i	0.243332	+	0.273610i
$267$		0			0
$268$	−6.23507	−	22.0402i	−0.380867	−	1.34632i
$269$	22.8082	+	9.44745i	1.39064	+	0.576021i	0.947304	−	0.320336i	$-0.103796\pi$
$269$	22.8082	+	9.44745i	1.39064	+	0.576021i	0.443334	+	0.896357i	$0.353796\pi$
$270$		0			0
$271$		−	12.8280i		−	0.779246i	−0.920974	−	0.389623i	$-0.872605\pi$
$271$		−	12.8280i		−	0.779246i	0.920974	−	0.389623i	$-0.127395\pi$
$272$	17.1814	+	4.09577i	1.04178	+	0.248342i
$273$		0			0
$274$	9.62185	−	19.8577i	0.581277	−	1.19965i
$275$	−19.9803	−	8.27612i	−1.20486	−	0.499069i
$276$		0			0
$277$	−10.7416	−	25.9326i	−0.645403	−	1.55814i	−0.819293	−	0.573376i	$-0.805634\pi$
$277$	−10.7416	−	25.9326i	−0.645403	−	1.55814i	0.173890	−	0.984765i	$-0.444366\pi$
$278$	−12.2525	+	10.8966i	−0.734856	+	0.653537i
$279$		0			0
$280$	−0.188367	+	0.131621i	−0.0112571	+	0.00786588i
$281$	6.82980	−	6.82980i	0.407432	−	0.407432i	−0.473410	−	0.880842i	$-0.656977\pi$
$281$	6.82980	−	6.82980i	0.407432	−	0.407432i	0.880842	+	0.473410i	$0.156977\pi$
$282$		0			0
$283$	−23.9755	+	9.93099i	−1.42520	+	0.590336i	−0.956161	−	0.292843i	$-0.905399\pi$
$283$	−23.9755	+	9.93099i	−1.42520	+	0.590336i	−0.469037	+	0.883179i	$0.655399\pi$
$284$	2.18900	−	18.6226i	0.129893	−	1.10505i
$285$		0			0
$286$	−33.3203	+	11.5694i	−1.97027	+	0.684115i
$287$	0.372750			0.0220027
$288$		0			0
$289$	−2.49852			−0.146972
$290$	0.867051	−	0.301057i	0.0509150	−	0.0176787i
$291$		0			0
$292$	13.4616	+	1.58234i	0.787780	+	0.0925995i
$293$	−17.4843	+	7.24222i	−1.02144	+	0.423095i	−0.829616	−	0.558334i	$-0.811441\pi$
$293$	−17.4843	+	7.24222i	−1.02144	+	0.423095i	−0.191825	+	0.981429i	$0.561441\pi$
$294$		0			0
$295$	1.01521	−	1.01521i	0.0591079	−	0.0591079i
$296$	−4.49497	−	0.797122i	−0.261265	−	0.0463318i
$297$		0			0
$298$	−1.04101	+	0.925813i	−0.0603042	+	0.0536309i
$299$	15.6772	+	37.8480i	0.906634	+	2.18881i
$300$		0			0
$301$	−0.730388	−	0.302536i	−0.0420988	−	0.0174379i
$302$	−4.50115	+	9.28955i	−0.259012	+	0.534553i
$303$		0			0
$304$	−18.1532	+	25.0701i	−1.04116	+	1.43787i
$305$			1.67825i			0.0960965i
$306$		0			0
$307$	9.33032	+	3.86475i	0.532510	+	0.220573i	0.632702	−	0.774395i	$-0.281946\pi$
$307$	9.33032	+	3.86475i	0.532510	+	0.220573i	−0.100192	+	0.994968i	$0.531946\pi$
$308$	−4.56269	+	1.29076i	−0.259983	+	0.0735480i
$309$		0			0
$310$	0.0384489	+	0.0432331i	0.00218375	+	0.00245547i
$311$	−15.3735	−	15.3735i	−0.871750	−	0.871750i	0.120913	−	0.992663i	$-0.461418\pi$
$311$	−15.3735	−	15.3735i	−0.871750	−	0.871750i	−0.992663	+	0.120913i	$0.961418\pi$
$312$		0			0
$313$	−16.8462	+	16.8462i	−0.952204	+	0.952204i	−0.998909	−	0.0467048i	$-0.985128\pi$
$313$	−16.8462	+	16.8462i	−0.952204	+	0.952204i	0.0467048	+	0.998909i	$0.485128\pi$
$314$	19.7709	+	1.15800i	1.11574	+	0.0653496i
$315$		0			0
$316$	−4.46352	−	5.65262i	−0.251092	−	0.317985i
$317$	12.6409	−	30.5179i	0.709986	−	1.71406i	0.00995073	−	0.999950i	$-0.496833\pi$
$317$	12.6409	−	30.5179i	0.709986	−	1.71406i	0.700036	−	0.714108i	$-0.253167\pi$
$318$		0			0
$319$	18.9391			1.06038
$320$	−0.876548	−	0.806372i	−0.0490005	−	0.0450776i
$321$		0			0
$322$	1.80645	+	5.20262i	0.100670	+	0.289931i
$323$	13.0760	−	31.5682i	0.727567	−	1.75650i
$324$		0			0
$325$	26.4010	−	10.9357i	1.46446	−	0.606601i
$326$	−15.2274	−	0.891882i	−0.843369	−	0.0493968i
$327$		0			0
$328$	0.416308	+	1.88658i	0.0229868	+	0.104169i
$329$	4.71658	+	4.71658i	0.260034	+	0.260034i
$330$		0			0
$331$	8.80743	+	21.2630i	0.484100	+	1.16872i	0.957645	+	0.287951i	$0.0929741\pi$
$331$	8.80743	+	21.2630i	0.484100	+	1.16872i	−0.473545	+	0.880770i	$0.657026\pi$
$332$	20.0405	−	5.66935i	1.09986	−	0.311146i
$333$		0			0
$334$	15.3401	+	7.43291i	0.839375	+	0.406711i
$335$		−	1.70506i		−	0.0931573i
$336$		0			0
$337$			4.98345i			0.271466i	0.990745	+	0.135733i	$0.0433389\pi$
$337$			4.98345i			0.271466i	−0.990745	+	0.135733i	$0.956661\pi$
$338$	12.3060	−	25.3972i	0.669356	−	1.38143i
$339$		0			0
$340$	1.14769	+	0.641530i	0.0622423	+	0.0347918i
$341$	0.456868	+	1.10298i	0.0247408	+	0.0597295i
$342$		0			0
$343$	5.28734	+	5.28734i	0.285490	+	0.285490i
$344$	0.715477	−	4.03457i	0.0385759	−	0.217529i
$345$		0			0
$346$	0.308363	−	5.26479i	0.0165777	−	0.283037i
$347$	28.7463	−	11.9071i	1.54318	−	0.639206i	0.561113	−	0.827739i	$-0.310373\pi$
$347$	28.7463	−	11.9071i	1.54318	−	0.639206i	0.982067	+	0.188533i	$0.0603732\pi$
$348$		0			0
$349$	1.28371	−	3.09915i	0.0687154	−	0.165894i	−0.885791	−	0.464085i	$-0.846383\pi$
$349$	1.28371	−	3.09915i	0.0687154	−	0.165894i	0.954506	+	0.298191i	$0.0963833\pi$
$350$	3.62911	−	1.26009i	0.193984	−	0.0673549i
$351$		0			0
$352$	−11.6287	−	21.6514i	−0.619814	−	1.15402i
$353$	−12.3729			−0.658544			−0.329272	−	0.944235i	$-0.606803\pi$
$353$	−12.3729			−0.658544			−0.329272	+	0.944235i	$0.606803\pi$
$354$		0			0
$355$	0.534154	−	1.28956i	0.0283499	−	0.0684428i
$356$	−3.32460	+	28.2837i	−0.176204	+	1.49903i
$357$		0			0
$358$	−0.372388	+	6.35791i	−0.0196813	+	0.336026i
$359$	−3.96377	+	3.96377i	−0.209200	+	0.209200i	−0.803927	−	0.594728i	$-0.797260\pi$
$359$	−3.96377	+	3.96377i	−0.209200	+	0.209200i	0.594728	+	0.803927i	$0.297260\pi$
$360$		0			0
$361$	28.9051	+	28.9051i	1.52132	+	1.52132i
$362$	−21.7730	+	19.3636i	−1.14436	+	1.01773i
$363$		0			0
$364$	3.05708	−	5.46909i	0.160235	−	0.286658i
$365$	0.932174	+	0.386119i	0.0487922	+	0.0202104i
$366$		0			0
$367$		−	13.6004i		−	0.709934i	−0.934879	−	0.354967i	$-0.884492\pi$
$367$		−	13.6004i		−	0.709934i	0.934879	−	0.354967i	$-0.115508\pi$
$368$	−24.3143	+	14.9535i	−1.26747	+	0.779505i
$369$		0			0
$370$	−0.305817	−	0.148180i	−0.0158987	−	0.00770353i
$371$	2.81255	+	1.16500i	0.146020	+	0.0604836i
$372$		0			0
$373$	9.80075	+	23.6611i	0.507463	+	1.22512i	0.945339	+	0.326089i	$0.105731\pi$
$373$	9.80075	+	23.6611i	0.507463	+	1.22512i	−0.437876	+	0.899036i	$0.644269\pi$
$374$	18.0298	+	20.2733i	0.932300	+	1.04831i
$375$		0			0
$376$	−18.6041	+	29.1396i	−0.959433	+	1.50276i
$377$	−17.6954	+	17.6954i	−0.911362	+	0.911362i
$378$		0			0
$379$	12.2315	−	5.06646i	0.628291	−	0.260247i	−0.0457357	−	0.998954i	$-0.514563\pi$
$379$	12.2315	−	5.06646i	0.628291	−	0.260247i	0.674027	+	0.738707i	$0.264563\pi$
$380$	−1.80830	+	1.42790i	−0.0927637	+	0.0732497i
$381$		0			0
$382$	−1.07984	−	3.10998i	−0.0552496	−	0.159120i
$383$	23.3749			1.19440			0.597200	−	0.802092i	$-0.296280\pi$
$383$	23.3749			1.19440			0.597200	+	0.802092i	$0.296280\pi$
$384$		0			0
$385$	−0.352976			−0.0179893
$386$	−1.20696	−	3.47609i	−0.0614329	−	0.176928i
$387$		0			0
$388$	9.52563	−	7.52179i	0.483590	−	0.381861i
$389$	−23.2589	+	9.63415i	−1.17927	+	0.488471i	−0.884247	−	0.467019i	$-0.845328\pi$
$389$	−23.2589	+	9.63415i	−1.17927	+	0.488471i	−0.295025	+	0.955490i	$0.595328\pi$
$390$		0			0
$391$	22.2817	−	22.2817i	1.12684	−	1.12684i
$392$	−10.2011	+	15.9779i	−0.515232	+	0.807007i
$393$		0			0
$394$	9.61910	+	10.8160i	0.484603	+	0.544902i
$395$	−0.205175	−	0.495337i	−0.0103235	−	0.0249231i
$396$		0			0
$397$	−11.9476	−	4.94886i	−0.599633	−	0.248376i	0.0621557	−	0.998066i	$-0.480202\pi$
$397$	−11.9476	−	4.94886i	−0.599633	−	0.248376i	−0.661789	+	0.749690i	$0.730202\pi$
$398$	−25.0637	−	12.1444i	−1.25633	−	0.608743i
$399$		0			0
$400$	10.4309	+	16.9605i	0.521543	+	0.848025i
$401$			33.9923i			1.69749i	0.528799	+	0.848747i	$0.322642\pi$
$401$			33.9923i			1.69749i	−0.528799	+	0.848747i	$0.677358\pi$
$402$		0			0
$403$	−1.45742	−	0.603682i	−0.0725991	−	0.0300715i
$404$	−11.7531	+	21.0262i	−0.584738	+	1.04609i
$405$		0			0
$406$	−2.51391	+	2.23572i	−0.124763	+	0.110957i
$407$	−4.95835	−	4.95835i	−0.245776	−	0.245776i
$408$		0			0
$409$	22.3819	−	22.3819i	1.10671	−	1.10671i	0.113135	−	0.993580i	$-0.463911\pi$
$409$	22.3819	−	22.3819i	1.10671	−	1.10671i	0.993580	−	0.113135i	$-0.0360892\pi$
$410$	−0.00840900	+	0.143570i	−0.000415291	+	0.00709040i
$411$		0			0
$412$	1.12620	−	9.58103i	0.0554839	−	0.472023i
$413$	−2.01390	+	4.86198i	−0.0990975	+	0.239242i
$414$		0			0
$415$	1.55036			0.0761040
$416$	31.0948	+	9.36448i	1.52455	+	0.459132i
$417$		0			0
$418$	−44.9136	+	15.5948i	−2.19680	+	0.762769i
$419$	−0.979835	+	2.36553i	−0.0478681	+	0.115564i	−0.946005	−	0.324152i	$-0.894921\pi$
$419$	−0.979835	+	2.36553i	−0.0478681	+	0.115564i	0.898137	+	0.439716i	$0.144921\pi$
$420$		0			0
$421$	29.1635	−	12.0799i	1.42134	−	0.588740i	0.466146	−	0.884708i	$-0.345642\pi$
$421$	29.1635	−	12.0799i	1.42134	−	0.588740i	0.955198	+	0.295968i	$0.0956420\pi$
$422$	−1.86506	+	31.8428i	−0.0907897	+	1.55008i
$423$		0			0
$424$	−2.75513	+	15.5362i	−0.133801	+	0.754503i
$425$	−15.5427	−	15.5427i	−0.753931	−	0.753931i
$426$		0			0
$427$	−2.35409	−	5.68328i	−0.113923	−	0.275033i
$428$	−0.0956042	−	0.0534403i	−0.00462120	−	0.00258313i
$429$		0			0
$430$	0.133003	−	0.274494i	0.00641398	−	0.0132373i
$431$			12.9230i			0.622481i	0.950331	+	0.311241i	$0.100745\pi$
$431$			12.9230i			0.622481i	−0.950331	+	0.311241i	$0.899255\pi$
$432$		0			0
$433$			9.19011i			0.441649i	0.975314	+	0.220824i	$0.0708747\pi$
$433$			9.19011i			0.441649i	−0.975314	+	0.220824i	$0.929125\pi$
$434$	−0.190847	−	0.0924732i	−0.00916097	−	0.00443885i
$435$		0			0
$436$	−5.93799	+	1.67983i	−0.284378	+	0.0804491i
$437$	21.1318	+	51.0167i	1.01087	+	2.44046i
$438$		0			0
$439$	4.05484	+	4.05484i	0.193527	+	0.193527i	0.797218	−	0.603691i	$-0.206304\pi$
$439$	4.05484	+	4.05484i	0.193527	+	0.193527i	−0.603691	+	0.797218i	$0.706304\pi$
$440$	−0.394223	−	1.78650i	−0.0187938	−	0.0851681i
$441$		0			0
$442$	−35.7880	−	2.09613i	−1.70226	−	0.0997028i
$443$	−12.8505	+	5.32283i	−0.610543	+	0.252895i	−0.666461	−	0.745540i	$-0.732192\pi$
$443$	−12.8505	+	5.32283i	−0.610543	+	0.252895i	0.0559175	+	0.998435i	$0.482192\pi$
$444$		0			0
$445$	−0.811262	+	1.95856i	−0.0384575	+	0.0928446i
$446$	−5.16998	−	14.8897i	−0.244806	−	0.705047i
$447$		0			0
$448$	4.09947	+	1.50118i	0.193682	+	0.0709241i
$449$	−39.2227			−1.85103			−0.925516	−	0.378709i	$-0.876368\pi$
$449$	−39.2227			−1.85103			−0.925516	+	0.378709i	$0.876368\pi$
$450$		0			0
$451$	−1.13564	+	2.74169i	−0.0534754	+	0.129101i
$452$	12.5091	+	15.8416i	0.588381	+	0.745128i
$453$		0			0
$454$	16.0874	+	0.942253i	0.755020	+	0.0442221i
$455$	0.329798	−	0.329798i	0.0154612	−	0.0154612i
$456$		0			0
$457$	−9.49718	−	9.49718i	−0.444259	−	0.444259i	0.449181	−	0.893441i	$-0.351716\pi$
$457$	−9.49718	−	9.49718i	−0.444259	−	0.444259i	−0.893441	+	0.449181i	$0.851716\pi$
$458$	−9.72138	−	10.9310i	−0.454250	−	0.510773i
$459$		0			0
$460$	−2.04461	+	0.578411i	−0.0953306	+	0.0269685i
$461$	−19.8471	−	8.22092i	−0.924370	−	0.382887i	−0.130830	−	0.991405i	$-0.541764\pi$
$461$	−19.8471	−	8.22092i	−0.924370	−	0.382887i	−0.793540	+	0.608518i	$0.791764\pi$
$462$		0			0
$463$			24.0727i			1.11875i	0.828914	+	0.559377i	$0.188959\pi$
$463$			24.0727i			1.11875i	−0.828914	+	0.559377i	$0.811041\pi$
$464$	−14.1232	−	10.2266i	−0.655655	−	0.474757i
$465$		0			0
$466$	14.7934	−	30.5308i	0.685291	−	1.41431i
$467$	−3.99564	−	1.65505i	−0.184896	−	0.0765866i	0.288315	−	0.957536i	$-0.406905\pi$
$467$	−3.99564	−	1.65505i	−0.184896	−	0.0765866i	−0.473211	+	0.880949i	$0.656905\pi$
$468$		0			0
$469$	2.39169	+	5.77406i	0.110438	+	0.266621i
$470$	−1.92306	+	1.71025i	−0.0887041	+	0.0788881i
$471$		0			0
$472$	−26.8570	−	4.76273i	−1.23619	−	0.219222i
$473$	4.45049	−	4.45049i	0.204634	−	0.204634i
$474$		0			0
$475$	35.5869	−	14.7406i	1.63284	−	0.676343i
$476$	−4.78645	−	0.562622i	−0.219386	−	0.0257878i
$477$		0			0
$478$	5.99813	−	2.08266i	0.274348	−	0.0952589i
$479$	10.4953			0.479544			0.239772	−	0.970829i	$-0.422927\pi$
$479$	10.4953			0.479544			0.239772	+	0.970829i	$0.422927\pi$
$480$		0			0
$481$	9.26552			0.422471
$482$	20.9399	−	7.27074i	0.953787	−	0.331173i
$483$		0			0
$484$	1.83874	−	15.6429i	0.0835791	−	0.711040i
$485$	0.834727	−	0.345755i	0.0379030	−	0.0156999i
$486$		0			0
$487$	−7.38326	+	7.38326i	−0.334568	+	0.334568i	−0.854318	−	0.519751i	$-0.826025\pi$
$487$	−7.38326	+	7.38326i	−0.334568	+	0.334568i	0.519751	+	0.854318i	$0.326025\pi$
$488$	26.1354	−	18.2621i	1.18309	−	0.826686i
$489$		0			0
$490$	−1.05446	+	0.937772i	−0.0476356	+	0.0423642i
$491$	14.5797	+	35.1986i	0.657974	+	1.58849i	0.800929	+	0.598760i	$0.204339\pi$
$491$	14.5797	+	35.1986i	0.657974	+	1.58849i	−0.142955	+	0.989729i	$0.545661\pi$
$492$		0			0
$493$	17.7839	+	7.36635i	0.800948	+	0.331764i
$494$	27.3936	−	56.5352i	1.23249	−	2.54364i
$495$		0			0
$496$	0.254881	−	1.06921i	0.0114445	−	0.0480088i
$497$			5.11627i			0.229496i
$498$		0			0
$499$	−11.7203	−	4.85470i	−0.524672	−	0.217326i	0.104596	−	0.994515i	$-0.466645\pi$
$499$	−11.7203	−	4.85470i	−0.524672	−	0.217326i	−0.629268	+	0.777188i	$0.716645\pi$
$500$	0.808741	+	2.85880i	0.0361680	+	0.127850i
$501$		0			0
$502$	12.4012	+	13.9443i	0.553494	+	0.622364i
$503$	−3.78430	−	3.78430i	−0.168734	−	0.168734i	0.617689	−	0.786423i	$-0.288069\pi$
$503$	−3.78430	−	3.78430i	−0.168734	−	0.168734i	−0.786423	+	0.617689i	$0.788069\pi$
$504$		0			0
$505$	−1.26792	+	1.26792i	−0.0564218	+	0.0564218i
$506$	−43.7705	−	2.56367i	−1.94584	−	0.113969i
$507$		0			0
$508$	−11.4818	+	9.06647i	−0.509423	+	0.402260i
$509$	2.41153	−	5.82194i	0.106889	−	0.258053i	−0.861381	−	0.507960i	$-0.830400\pi$
$509$	2.41153	−	5.82194i	0.106889	−	0.258053i	0.968270	+	0.249907i	$0.0803999\pi$
$510$		0			0
$511$	−3.69835			−0.163605
$512$	−3.01935	+	22.4251i	−0.133438	+	0.991057i
$513$		0			0
$514$	−1.14058	−	3.28489i	−0.0503086	−	0.144890i
$515$	0.274813	−	0.663457i	0.0121097	−	0.0292354i
$516$		0			0
$517$	−49.0617	+	20.3220i	−2.15773	+	0.893762i
$518$	1.24348	+	0.0728316i	0.0546353	+	0.00320004i
$519$		0			0
$520$	2.03753	+	1.30085i	0.0893515	+	0.0570463i
$521$	25.8212	+	25.8212i	1.13125	+	1.13125i	0.989970	+	0.141280i	$0.0451217\pi$
$521$	25.8212	+	25.8212i	1.13125	+	1.13125i	0.141280	+	0.989970i	$0.454878\pi$
$522$		0			0
$523$	−12.3573	−	29.8332i	−0.540347	−	1.30451i	−0.924478	−	0.381234i	$-0.875499\pi$
$523$	−12.3573	−	29.8332i	−0.540347	−	1.30451i	0.384132	−	0.923278i	$-0.374501\pi$
$524$	2.19439	+	7.75689i	0.0958622	+	0.338861i
$525$		0			0
$526$	23.6125	+	11.4412i	1.02955	+	0.498860i
$527$			1.21340i			0.0528566i
$528$		0			0
$529$			27.9245i			1.21411i
$530$	−0.512163	+	1.05701i	−0.0222469	+	0.0459136i
$531$		0			0
$532$	4.12075	−	7.37198i	0.178657	−	0.319616i
$533$	−1.50058	−	3.62273i	−0.0649975	−	0.156918i
$534$		0			0
$535$	−0.00576513	−	0.00576513i	−0.000249248	−	0.000249248i
$536$	−26.5528	+	18.5538i	−1.14691	+	0.801401i
$537$		0			0
$538$	2.04140	−	34.8535i	0.0880109	−	1.50264i
$539$	−26.9017	+	11.1430i	−1.15874	+	0.479965i
$540$		0			0
$541$	2.61842	−	6.32143i	0.112575	−	0.271780i	−0.857544	−	0.514411i	$-0.828011\pi$
$541$	2.61842	−	6.32143i	0.112575	−	0.271780i	0.970119	+	0.242631i	$0.0780106\pi$
$542$	−17.1379	+	5.95059i	−0.736134	+	0.255600i
$543$		0			0
$544$	−2.49820	−	24.8538i	−0.107109	−	1.06560i
$545$	−0.459370			−0.0196773
$546$		0			0
$547$	−1.98725	+	4.79764i	−0.0849685	+	0.205132i	−0.960653	−	0.277752i	$-0.910411\pi$
$547$	−1.98725	+	4.79764i	−0.0849685	+	0.205132i	0.875684	+	0.482884i	$0.160411\pi$
$548$	−30.9927	−	3.64303i	−1.32394	−	0.155623i
$549$		0			0
$550$	−1.78830	+	30.5322i	−0.0762533	+	1.30190i
$551$	−23.8523	+	23.8523i	−1.01614	+	1.01614i
$552$		0			0
$553$	1.38962	+	1.38962i	0.0590927	+	0.0590927i
$554$	−29.6625	+	26.3800i	−1.26024	+	1.12078i
$555$		0			0
$556$	20.2412	+	11.3143i	0.858419	+	0.479834i
$557$	−9.66691	−	4.00417i	−0.409600	−	0.169662i	0.168363	−	0.985725i	$-0.446152\pi$
$557$	−9.66691	−	4.00417i	−0.409600	−	0.169662i	−0.577963	+	0.816063i	$0.696152\pi$
$558$		0			0
$559$			8.31650i			0.351751i
$560$	0.263221	+	0.190597i	0.0111231	+	0.00805420i
$561$		0			0
$562$	−12.2926	−	5.95625i	−0.518532	−	0.251249i
$563$	−7.69307	−	3.18657i	−0.324224	−	0.134298i	0.214634	−	0.976695i	$-0.431144\pi$
$563$	−7.69307	−	3.18657i	−0.324224	−	0.134298i	−0.538858	+	0.842396i	$0.681144\pi$
$564$		0			0
$565$	0.575010	+	1.38820i	0.0241908	+	0.0584018i
$566$	24.3892	+	27.4239i	1.02515	+	1.15271i
$567$		0			0
$568$	−25.8947	+	5.71413i	−1.08652	+	0.239760i
$569$	27.4613	−	27.4613i	1.15124	−	1.15124i	0.164932	−	0.986305i	$-0.447260\pi$
$569$	27.4613	−	27.4613i	1.15124	−	1.15124i	0.986305	−	0.164932i	$-0.0527404\pi$
$570$		0			0
$571$	−8.82788	+	3.65663i	−0.369435	+	0.153025i	−0.559674	−	0.828713i	$-0.689074\pi$
$571$	−8.82788	+	3.65663i	−0.369435	+	0.153025i	0.190239	+	0.981738i	$0.439074\pi$
$572$	30.9129	+	39.1482i	1.29253	+	1.63687i
$573$		0			0
$574$	−0.172909	−	0.497984i	−0.00721710	−	0.0207854i
$575$	35.5225			1.48139
$576$		0			0
$577$	3.42329			0.142513			0.0712567	−	0.997458i	$-0.477299\pi$
$577$	3.42329			0.142513			0.0712567	+	0.997458i	$0.477299\pi$
$578$	1.15900	+	3.33795i	0.0482081	+	0.138841i
$579$		0			0
$580$	−0.804406	−	1.01870i	−0.0334012	−	0.0422994i
$581$	−5.25017	+	2.17469i	−0.217814	+	0.0902214i
$582$		0			0
$583$	−17.1378	+	17.1378i	−0.709774	+	0.709774i
$584$	−4.13053	−	18.7183i	−0.170922	−	0.774569i
$585$		0			0
$586$	17.7859	+	19.9990i	0.734729	+	0.826151i
$587$	−5.20465	−	12.5651i	−0.214819	−	0.518618i	0.779333	−	0.626610i	$-0.215558\pi$
$587$	−5.20465	−	12.5651i	−0.214819	−	0.518618i	−0.994152	+	0.107992i	$0.965558\pi$
$588$		0			0
$589$	−1.96450	−	0.813724i	−0.0809460	−	0.0335289i
$590$	−1.82723	−	0.885363i	−0.0752257	−	0.0364498i
$591$		0			0
$592$	1.02017	+	6.37491i	0.0419286	+	0.262007i
$593$		−	19.3756i		−	0.795659i	−0.917459	−	0.397830i	$-0.869763\pi$
$593$		−	19.3756i		−	0.795659i	0.917459	−	0.397830i	$-0.130237\pi$
$594$		0			0
$595$	−0.331447	−	0.137290i	−0.0135880	−	0.00562833i
$596$	1.71976	+	0.961301i	0.0704441	+	0.0393764i
$597$		0			0
$598$	43.2917	−	38.5010i	1.77033	−	1.57442i
$599$	5.09199	+	5.09199i	0.208053	+	0.208053i	0.803439	−	0.595387i	$-0.203001\pi$
$599$	5.09199	+	5.09199i	0.208053	+	0.208053i	−0.595387	+	0.803439i	$0.703001\pi$
$600$		0			0
$601$	−5.26774	+	5.26774i	−0.214876	+	0.214876i	−0.806335	−	0.591459i	$-0.798552\pi$
$601$	−5.26774	+	5.26774i	−0.214876	+	0.214876i	0.591459	+	0.806335i	$0.298552\pi$
$602$	−0.0653719	+	1.11612i	−0.00266436	+	0.0454895i
$603$		0			0
$604$	14.4985	+	1.70423i	0.589937	+	0.0693441i
$605$	0.448685	−	1.08322i	0.0182417	−	0.0440392i
$606$		0			0
$607$	36.0147			1.46179			0.730896	−	0.682488i	$-0.239102\pi$
$607$	36.0147			1.46179			0.730896	+	0.682488i	$0.239102\pi$
$608$	41.9138	+	12.6227i	1.69983	+	0.511919i
$609$		0			0
$610$	2.24210	−	0.778499i	0.0907799	−	0.0315205i
$611$	26.8525	−	64.8277i	1.08634	−	2.62265i
$612$		0			0
$613$	−7.51205	+	3.11159i	−0.303409	+	0.125676i	−0.529193	−	0.848501i	$-0.677505\pi$
$613$	−7.51205	+	3.11159i	−0.303409	+	0.125676i	0.225785	+	0.974177i	$0.427505\pi$
$614$	0.835092	−	14.2578i	0.0337016	−	0.575398i
$615$		0			0
$616$	3.84094	+	5.49687i	0.154756	+	0.221475i
$617$	1.22919	+	1.22919i	0.0494852	+	0.0494852i	0.731416	−	0.681931i	$-0.238860\pi$
$617$	1.22919	+	1.22919i	0.0494852	+	0.0494852i	−0.681931	+	0.731416i	$0.738860\pi$
$618$		0			0
$619$	−6.88508	−	16.6220i	−0.276735	−	0.668096i	0.723007	−	0.690841i	$-0.242760\pi$
$619$	−6.88508	−	16.6220i	−0.276735	−	0.668096i	−0.999741	+	0.0227447i	$0.992760\pi$
$620$	0.0399227	−	0.0714213i	0.00160333	−	0.00286835i
$621$		0			0
$622$	−13.4072	+	27.6699i	−0.537578	+	1.10946i
$623$		−	7.77048i		−	0.311318i
$624$		0			0
$625$		−	24.6680i		−	0.986721i
$626$	30.3206	+	14.6915i	1.21185	+	0.587192i
$627$		0			0
$628$	−7.62416	−	26.9505i	−0.304237	−	1.07544i
$629$	−2.72738	−	6.58448i	−0.108748	−	0.262540i
$630$		0			0
$631$	−13.7065	−	13.7065i	−0.545649	−	0.545649i	0.379531	−	0.925179i	$-0.376085\pi$
$631$	−13.7065	−	13.7065i	−0.545649	−	0.545649i	−0.925179	+	0.379531i	$0.876085\pi$
$632$	−5.48122	+	8.58524i	−0.218031	+	0.341502i
$633$		0			0
$634$	−46.6349	−	2.73145i	−1.85211	−	0.108480i
$635$	−1.00615	+	0.416760i	−0.0399277	+	0.0165386i
$636$		0			0
$637$	14.7239	−	35.5466i	0.583381	−	1.40841i
$638$	−8.78535	−	25.3021i	−0.347815	−	1.00172i
$639$		0			0
$640$	−0.670681	+	1.54510i	−0.0265110	+	0.0610754i
$641$	−5.87778			−0.232159			−0.116079	−	0.993240i	$-0.537033\pi$
$641$	−5.87778			−0.232159			−0.116079	+	0.993240i	$0.537033\pi$
$642$		0			0
$643$	−1.28825	+	3.11010i	−0.0508034	+	0.122650i	−0.947244	−	0.320514i	$-0.896144\pi$
$643$	−1.28825	+	3.11010i	−0.0508034	+	0.122650i	0.896440	+	0.443165i	$0.146144\pi$
$644$	6.11259	−	4.82673i	0.240870	−	0.190200i
$645$		0			0
$646$	−48.2398	−	2.82545i	−1.89797	−	0.111166i
$647$	18.4608	−	18.4608i	0.725770	−	0.725770i	−0.244004	−	0.969774i	$-0.578461\pi$
$647$	18.4608	−	18.4608i	0.725770	−	0.725770i	0.969774	+	0.244004i	$0.0784611\pi$
$648$		0			0
$649$	−29.6256	−	29.6256i	−1.16291	−	1.16291i
$650$	−26.8565	−	30.1982i	−1.05340	−	1.18447i
$651$		0			0
$652$	5.87208	+	20.7571i	0.229969	+	0.812912i
$653$	−28.1167	−	11.6463i	−1.10029	−	0.455755i	−0.242706	−	0.970100i	$-0.578035\pi$
$653$	−28.1167	−	11.6463i	−1.10029	−	0.455755i	−0.857583	+	0.514345i	$0.828035\pi$
$654$		0			0
$655$			0.600083i			0.0234472i
$656$	2.32731	−	1.43131i	0.0908661	−	0.0558835i
$657$		0			0
$658$	4.11332	−	8.48913i	0.160354	−	0.330941i
$659$	18.6550	+	7.72713i	0.726694	+	0.301006i	0.715193	−	0.698927i	$-0.246339\pi$
$659$	18.6550	+	7.72713i	0.726694	+	0.301006i	0.0115011	+	0.999934i	$0.496339\pi$
$660$		0			0
$661$	−14.3561	−	34.6587i	−0.558388	−	1.34807i	−0.911042	−	0.412314i	$-0.864721\pi$
$661$	−14.3561	−	34.6587i	−0.558388	−	1.34807i	0.352654	−	0.935754i	$-0.385279\pi$
$662$	24.3212	−	21.6298i	0.945272	−	0.840668i
$663$		0			0
$664$	−16.8704	−	24.1436i	−0.654697	−	0.936955i
$665$	0.444546	−	0.444546i	0.0172387	−	0.0172387i
$666$		0			0
$667$	−28.7402	+	11.9046i	−1.11283	+	0.460948i
$668$	2.81425	−	23.9419i	0.108887	−	0.926341i
$669$		0			0
$670$	−2.27791	+	0.790934i	−0.0880034	+	0.0305564i
$671$	48.9743			1.89063
$672$		0			0
$673$	2.67411			0.103079			0.0515396	−	0.998671i	$-0.483587\pi$
$673$	2.67411			0.103079			0.0515396	+	0.998671i	$0.483587\pi$
$674$	6.65775	−	2.31170i	0.256447	−	0.0890432i
$675$		0			0
$676$	−39.6384	−	4.65929i	−1.52455	−	0.179203i
$677$	−35.1760	+	14.5704i	−1.35192	+	0.559985i	−0.936827	−	0.349793i	$-0.886252\pi$
$677$	−35.1760	+	14.5704i	−1.35192	+	0.559985i	−0.415096	+	0.909778i	$0.636252\pi$
$678$		0			0
$679$	−2.34175	+	2.34175i	−0.0898681	+	0.0898681i
$680$	0.324681	−	1.83087i	0.0124509	−	0.0702107i
$681$		0			0
$682$	1.26162	−	1.12200i	0.0483097	−	0.0429638i
$683$	8.17797	+	19.7434i	0.312921	+	0.755459i	0.999594	+	0.0284920i	$0.00907050\pi$
$683$	8.17797	+	19.7434i	0.312921	+	0.755459i	−0.686673	+	0.726967i	$0.740929\pi$
$684$		0			0
$685$	−2.14615	−	0.888964i	−0.0820001	−	0.0339656i
$686$	4.61108	−	9.51640i	0.176052	−	0.363338i
$687$		0			0
$688$	−5.72196	+	0.915678i	−0.218148	+	0.0349099i
$689$		−	32.0249i		−	1.22005i
$690$		0			0
$691$	13.5166	+	5.59878i	0.514197	+	0.212988i	0.624666	−	0.780892i	$-0.285235\pi$
$691$	13.5166	+	5.59878i	0.514197	+	0.212988i	−0.110469	+	0.993880i	$0.535235\pi$
$692$	−7.17666	+	2.03024i	−0.272816	+	0.0771781i
$693$		0			0
$694$	−29.2422	−	32.8808i	−1.11002	−	1.24814i
$695$	1.22059	+	1.22059i	0.0462995	+	0.0462995i
$696$		0			0
$697$	−2.13276	+	2.13276i	−0.0807840	+	0.0807840i
$698$	−4.73585	−	0.277383i	−0.179255	−	0.0104991i
$699$		0			0
$700$	−3.36690	−	4.26386i	−0.127257	−	0.161159i
$701$	−18.6513	+	45.0282i	−0.704450	+	1.70069i	0.00897497	+	0.999960i	$0.497143\pi$
$701$	−18.6513	+	45.0282i	−0.704450	+	1.70069i	−0.713425	+	0.700732i	$0.752857\pi$
$702$		0			0
$703$	12.4893			0.471044
$704$	−23.5313	+	25.5792i	−0.886870	+	0.964052i
$705$		0			0
$706$	5.73948	+	16.5299i	0.216008	+	0.622110i
$707$	2.51521	−	6.07225i	0.0945941	−	0.228370i
$708$		0			0
$709$	10.8844	−	4.50848i	0.408773	−	0.169319i	−0.168815	−	0.985648i	$-0.553994\pi$
$709$	10.8844	−	4.50848i	0.408773	−	0.169319i	0.577588	+	0.816328i	$0.303994\pi$
$710$	−1.97060	−	0.115420i	−0.0739552	−	0.00433162i
$711$		0			0
$712$	39.3284	−	8.67851i	1.47389	−	0.325241i
$713$	−1.38660	−	1.38660i	−0.0519287	−	0.0519287i
$714$		0			0
$715$	1.42098	+	3.43054i	0.0531415	+	0.128295i
$716$	8.66673	−	2.45177i	0.323891	−	0.0916270i
$717$		0			0
$718$	7.13417	+	3.45679i	0.266245	+	0.129006i
$719$		−	50.3818i		−	1.87892i	−0.342654	−	0.939462i	$-0.611326\pi$
$719$		−	50.3818i		−	1.87892i	0.342654	−	0.939462i	$-0.388674\pi$
$720$		0			0
$721$			2.63223i			0.0980294i
$722$	25.2081	−	52.0248i	0.938147	−	1.93616i
$723$		0			0
$724$	35.9691	+	20.1058i	1.33678	+	0.747227i
$725$	8.30409	+	20.0478i	0.308406	+	0.744558i
$726$		0			0
$727$	−18.1604	−	18.1604i	−0.673531	−	0.673531i	0.284997	−	0.958528i	$-0.408007\pi$
$727$	−18.1604	−	18.1604i	−0.673531	−	0.673531i	−0.958528	+	0.284997i	$0.908007\pi$
$728$	−8.72465	−	1.54720i	−0.323357	−	0.0573431i
$729$		0			0
$730$	0.0834323	−	1.42447i	0.00308797	−	0.0527220i
$731$	5.91006	−	2.44803i	0.218592	−	0.0905436i
$732$		0			0
$733$	−1.20884	+	2.91840i	−0.0446495	+	0.107794i	−0.944631	−	0.328135i	$-0.893580\pi$
$733$	−1.20884	+	2.91840i	−0.0446495	+	0.107794i	0.899981	+	0.435928i	$0.143580\pi$
$734$	−18.1697	+	6.30887i	−0.670657	+	0.232865i
$735$		0			0
$736$	31.2562	+	25.5466i	1.15212	+	0.941662i
$737$	−49.7566			−1.83281
$738$		0			0
$739$	−14.4733	+	34.9417i	−0.532411	+	1.28535i	0.397512	+	0.917597i	$0.369874\pi$
$739$	−14.4733	+	34.9417i	−0.532411	+	1.28535i	−0.929922	+	0.367756i	$0.880126\pi$
$740$	−0.0561041	+	0.477300i	−0.00206243	+	0.0175459i
$741$		0			0
$742$	0.251731	−	4.29790i	0.00924135	−	0.157781i
$743$	−0.0918786	+	0.0918786i	−0.00337070	+	0.00337070i	−0.708790	−	0.705419i	$-0.750759\pi$
$743$	−0.0918786	+	0.0918786i	−0.00337070	+	0.00337070i	0.705419	+	0.708790i	$0.250759\pi$
$744$		0			0
$745$	0.103705	+	0.103705i	0.00379946	+	0.00379946i
$746$	27.0642	−	24.0693i	0.990892	−	0.881240i
$747$		0			0
$748$	18.7209	−	33.4916i	0.684505	−	1.22457i
$749$	0.0276100	+	0.0114364i	0.00100885	+	0.000417878i
$750$		0			0
$751$			4.16103i			0.151838i	0.997114	+	0.0759191i	$0.0241891\pi$
$751$			4.16103i			0.151838i	−0.997114	+	0.0759191i	$0.975811\pi$
$752$	47.5596	+	11.3374i	1.73432	+	0.413434i
$753$		0			0
$754$	31.8491	+	15.4321i	1.15988	+	0.562006i
$755$	1.00398	+	0.415862i	0.0365386	+	0.0151348i
$756$		0			0
$757$	3.73221	+	9.01035i	0.135649	+	0.327487i	0.977078	−	0.212882i	$-0.0682849\pi$
$757$	3.73221	+	9.01035i	0.135649	+	0.327487i	−0.841429	+	0.540368i	$0.818285\pi$
$758$	−12.4425	−	13.9908i	−0.451934	−	0.508167i
$759$		0			0
$760$	2.74646	+	1.75347i	0.0996244	+	0.0636050i
$761$	−23.4333	+	23.4333i	−0.849457	+	0.849457i	−0.990065	−	0.140608i	$-0.955094\pi$
$761$	−23.4333	+	23.4333i	−0.849457	+	0.849457i	0.140608	+	0.990065i	$0.455094\pi$
$762$		0			0
$763$	1.55562	−	0.644361i	0.0563174	−	0.0233274i
$764$	−3.65393	+	2.88528i	−0.132195	+	0.104386i
$765$		0			0
$766$	−10.8430	−	31.2282i	−0.391774	−	1.12832i
$767$	55.3606			1.99895
$768$		0			0
$769$	8.92760			0.321938			0.160969	−	0.986959i	$-0.448538\pi$
$769$	8.92760			0.321938			0.160969	+	0.986959i	$0.448538\pi$
$770$	0.163736	+	0.471565i	0.00590065	+	0.0169940i
$771$		0			0
$772$	−4.08408	+	3.22494i	−0.146989	+	0.116068i
$773$	−6.20812	+	2.57149i	−0.223291	+	0.0924900i	−0.491524	−	0.870864i	$-0.663560\pi$
$773$	−6.20812	+	2.57149i	−0.223291	+	0.0924900i	0.268234	+	0.963354i	$0.413560\pi$
$774$		0			0
$775$	−0.967229	+	0.967229i	−0.0347439	+	0.0347439i
$776$	−14.4676	−	9.23680i	−0.519356	−	0.331582i
$777$		0			0
$778$	23.6602	+	26.6042i	0.848258	+	0.953806i
$779$	−2.02269	−	4.88320i	−0.0724704	−	0.174959i
$780$		0			0
$781$	−37.6316	−	15.5875i	−1.34657	−	0.557766i
$782$	−40.1037	−	19.4318i	−1.43411	−	0.694881i
$783$		0			0
$784$	26.0781	+	6.21658i	0.931360	+	0.222021i
$785$		−	2.08493i		−	0.0744142i
$786$		0			0
$787$	−36.9605	−	15.3095i	−1.31750	−	0.545726i	−0.390436	−	0.920630i	$-0.627676\pi$
$787$	−36.9605	−	15.3095i	−1.31750	−	0.545726i	−0.927064	+	0.374904i	$0.877676\pi$
$788$	9.98781	−	17.8681i	0.355801	−	0.636525i
$789$		0			0
$790$	−0.566580	+	0.503882i	−0.0201580	+	0.0179273i
$791$	−3.89446	−	3.89446i	−0.138471	−	0.138471i
$792$		0			0
$793$	−45.7585	+	45.7585i	−1.62493	+	1.62493i
$794$	−1.06935	+	18.2573i	−0.0379497	+	0.647928i
$795$		0			0
$796$	−4.59811	+	39.1179i	−0.162976	+	1.38650i
$797$	14.0977	−	34.0348i	0.499366	−	1.20558i	−0.450460	−	0.892796i	$-0.648740\pi$
$797$	14.0977	−	34.0348i	0.499366	−	1.20558i	0.949826	−	0.312779i	$-0.101260\pi$
$798$		0			0
$799$	−53.9736			−1.90945
$800$	17.8201	−	21.8029i	0.630037	−	0.770848i
$801$		0			0
$802$	45.4127	−	15.7682i	1.60358	−	0.556793i
$803$	11.2676	−	27.2025i	0.397626	−	0.959954i
$804$		0			0
$805$	0.535644	−	0.221871i	0.0188790	−	0.00781993i
$806$	−0.130443	+	2.22710i	−0.00459466	+	0.0784463i
$807$		0			0
$808$	33.5423	+	5.94829i	1.18002	+	0.209260i
$809$	36.6623	+	36.6623i	1.28898	+	1.28898i	0.935408	+	0.353569i	$0.115032\pi$
$809$	36.6623	+	36.6623i	1.28898	+	1.28898i	0.353569	+	0.935408i	$0.384968\pi$
$810$		0			0
$811$	19.1870	+	46.3215i	0.673747	+	1.62657i	0.775190	+	0.631728i	$0.217654\pi$
$811$	19.1870	+	46.3215i	0.673747	+	1.62657i	−0.101443	+	0.994841i	$0.532346\pi$
$812$	4.15300	+	2.32142i	0.145742	+	0.0814659i
$813$		0			0
$814$	−4.32416	+	8.92426i	−0.151562	+	0.312795i
$815$			1.60580i			0.0562486i
$816$		0			0
$817$			11.2101i			0.392192i
$818$	−40.2840	−	19.5192i	−1.40850	−	0.682473i
$819$		0			0
$820$	0.195706	−	0.0553642i	0.00683434	−	0.00193340i
$821$	−3.24487	−	7.83381i	−0.113247	−	0.273402i	0.857087	−	0.515172i	$-0.172272\pi$
$821$	−3.24487	−	7.83381i	−0.113247	−	0.273402i	−0.970334	+	0.241770i	$0.922272\pi$
$822$		0			0
$823$	−31.9621	−	31.9621i	−1.11413	−	1.11413i	−0.992586	−	0.121542i	$-0.961216\pi$
$823$	−31.9621	−	31.9621i	−1.11413	−	1.11413i	−0.121542	−	0.992586i	$-0.538784\pi$
$824$	−13.3224	+	2.93982i	−0.464108	+	0.102414i
$825$		0			0
$826$	7.42967	+	0.435162i	0.258511	+	0.0151412i
$827$	28.2175	−	11.6881i	0.981220	−	0.406435i	0.166343	−	0.986068i	$-0.446804\pi$
$827$	28.2175	−	11.6881i	0.981220	−	0.406435i	0.814877	+	0.579633i	$0.196804\pi$
$828$		0			0
$829$	−16.1706	+	39.0393i	−0.561628	+	1.35589i	0.346836	+	0.937926i	$0.387256\pi$
$829$	−16.1706	+	39.0393i	−0.561628	+	1.35589i	−0.908464	+	0.417964i	$0.862744\pi$
$830$	−0.719171	−	2.07123i	−0.0249628	−	0.0718935i
$831$		0			0
$832$	−1.91340	−	45.8857i	−0.0663353	−	1.59080i
$833$	−29.5950			−1.02541
$834$		0			0
$835$	0.686728	−	1.65791i	0.0237652	−	0.0573742i
$836$	41.6685	+	52.7692i	1.44114	+	1.82506i
$837$		0			0
$838$	3.61480	+	0.211722i	0.124871	+	0.00731381i
$839$	−15.2345	+	15.2345i	−0.525953	+	0.525953i	−0.919363	−	0.393410i	$-0.871295\pi$
$839$	−15.2345	+	15.2345i	−0.525953	+	0.525953i	0.393410	+	0.919363i	$0.371295\pi$
$840$		0			0
$841$	7.06890	+	7.06890i	0.243755	+	0.243755i
$842$	−29.6667	−	33.3581i	−1.02238	−	1.14960i
$843$		0			0
$844$	43.4063	−	12.2794i	1.49411	−	0.422675i
$845$	−2.74484	−	1.13695i	−0.0944253	−	0.0391122i
$846$		0			0
$847$			4.29762i			0.147668i
$848$	22.0339	−	3.52606i	0.756648	−	0.121085i
$849$		0			0
$850$	−13.5547	+	27.9745i	−0.464924	+	0.959516i
$851$	10.6410	+	4.40766i	0.364770	+	0.151093i
$852$		0			0
$853$	2.71834	+	6.56264i	0.0930740	+	0.224701i	0.963560	−	0.267493i	$-0.0861952\pi$
$853$	2.71834	+	6.56264i	0.0930740	+	0.224701i	−0.870486	+	0.492194i	$0.836195\pi$
$854$	−6.50070	+	5.78133i	−0.222449	+	0.197833i
$855$		0			0
$856$	−0.0270463	+	0.152514i	−0.000924424	+	0.00521282i
$857$	−34.9218	+	34.9218i	−1.19291	+	1.19291i	−0.216657	+	0.976248i	$0.569515\pi$
$857$	−34.9218	+	34.9218i	−1.19291	+	1.19291i	−0.976248	+	0.216657i	$0.930485\pi$
$858$		0			0
$859$	−9.27651	+	3.84246i	−0.316510	+	0.131103i	−0.535283	−	0.844673i	$-0.679795\pi$
$859$	−9.27651	+	3.84246i	−0.316510	+	0.131103i	0.218772	+	0.975776i	$0.429795\pi$
$860$	−0.428412	−	0.0503577i	−0.0146087	−	0.00171718i
$861$		0			0
$862$	17.2648	−	5.99467i	0.588042	−	0.204179i
$863$	−56.5468			−1.92487			−0.962437	−	0.271505i	$-0.912479\pi$
$863$	−56.5468			−1.92487			−0.962437	+	0.271505i	$0.912479\pi$
$864$		0			0
$865$	−0.555195			−0.0188772
$866$	12.2777	−	4.26306i	0.417214	−	0.144865i
$867$		0			0
$868$	−0.0350122	+	0.297863i	−0.00118839	+	0.0101101i
$869$	−14.4548	+	5.98736i	−0.490345	+	0.203107i
$870$		0			0
$871$	46.4894	−	46.4894i	1.57523	−	1.57523i
$872$	4.99868	+	7.15376i	0.169277	+	0.242257i
$873$		0			0
$874$	58.3543	−	51.8968i	1.97387	−	1.75544i
$875$	−0.310223	−	0.748944i	−0.0104874	−	0.0253189i
$876$		0			0
$877$	28.5580	+	11.8291i	0.964337	+	0.399441i	0.808601	−	0.588357i	$-0.200225\pi$
$877$	28.5580	+	11.8291i	0.964337	+	0.399441i	0.155736	+	0.987799i	$0.450225\pi$
$878$	3.53621	−	7.29809i	0.119341	−	0.246298i
$879$		0			0
$880$	−2.20384	+	1.35538i	−0.0742916	+	0.0456900i
$881$		−	2.82221i		−	0.0950828i	−0.998869	−	0.0475414i	$-0.984861\pi$
$881$		−	2.82221i		−	0.0950828i	0.998869	−	0.0475414i	$-0.0151386\pi$
$882$		0			0
$883$	−22.7749	−	9.43367i	−0.766437	−	0.317468i	−0.0350085	−	0.999387i	$-0.511146\pi$
$883$	−22.7749	−	9.43367i	−0.766437	−	0.317468i	−0.731428	+	0.681919i	$0.761146\pi$
$884$	13.8008	+	48.7840i	0.464170	+	1.64079i
$885$		0			0
$886$	13.0721	+	14.6987i	0.439167	+	0.493813i
$887$	−21.9937	−	21.9937i	−0.738475	−	0.738475i	0.233807	−	0.972283i	$-0.424881\pi$
$887$	−21.9937	−	21.9937i	−0.738475	−	0.738475i	−0.972283	+	0.233807i	$0.924881\pi$
$888$		0			0
$889$	2.82265	−	2.82265i	0.0946687	−	0.0946687i
$890$	2.99290	+	0.175297i	0.100322	+	0.00587596i
$891$		0			0
$892$	−17.4940	+	13.8139i	−0.585742	+	0.462523i
$893$	36.1954	−	87.3835i	1.21123	−	2.92418i
$894$		0			0
$895$	0.670469			0.0224113
$896$	0.103896	−	6.17313i	0.00347094	−	0.206230i
$897$		0			0
$898$	18.1944	+	52.4004i	0.607155	+	1.74862i
$899$	0.458411	−	1.10670i	0.0152889	−	0.0369106i
$900$		0			0
$901$	−22.7582	+	9.42677i	−0.758187	+	0.314051i
$902$	4.18961	+	0.245389i	0.139499	+	0.00817056i
$903$		0			0
$904$	15.3613	−	24.0604i	0.510909	−	0.800237i
$905$	2.16901	+	2.16901i	0.0721005	+	0.0721005i
$906$		0			0
$907$	5.70834	+	13.7812i	0.189542	+	0.457596i	0.989872	−	0.141965i	$-0.0453420\pi$
$907$	5.70834	+	13.7812i	0.189542	+	0.457596i	−0.800329	+	0.599561i	$0.795342\pi$
$908$	−6.20372	−	21.9294i	−0.205878	−	0.727753i
$909$		0			0
$910$	−0.593585	−	0.287616i	−0.0196772	−	0.00953436i
$911$			10.1437i			0.336076i	0.985780	+	0.168038i	$0.0537432\pi$
$911$			10.1437i			0.336076i	−0.985780	+	0.168038i	$0.946257\pi$
$912$		0			0
$913$		−	45.2421i		−	1.49729i
$914$	−8.28246	+	17.0935i	−0.273959	+	0.565402i
$915$		0			0
$916$	−10.0940	+	18.0581i	−0.333516	+	0.596657i
$917$	−0.841739	−	2.03214i	−0.0277967	−	0.0671071i
$918$		0			0
$919$	26.8301	+	26.8301i	0.885042	+	0.885042i	0.994042	−	0.109000i	$-0.0347648\pi$
$919$	26.8301	+	26.8301i	0.885042	+	0.885042i	−0.109000	+	0.994042i	$0.534765\pi$
$920$	1.72118	+	2.46324i	0.0567458	+	0.0812105i
$921$		0			0
$922$	−1.77637	+	30.3286i	−0.0585017	+	0.998819i
$923$	49.7246	−	20.5966i	1.63670	−	0.677945i
$924$		0			0
$925$	3.07458	−	7.42268i	0.101091	−	0.244056i
$926$	32.1604	−	11.1667i	1.05686	−	0.366961i
$927$		0			0
$928$	−7.11100	+	23.6121i	−0.233430	+	0.775105i
$929$	−34.7269			−1.13935			−0.569676	−	0.821869i	$-0.692931\pi$
$929$	−34.7269			−1.13935			−0.569676	+	0.821869i	$0.692931\pi$
$930$		0			0
$931$	19.8468	−	47.9144i	0.650453	−	1.57033i
$932$	−47.6506	−	5.60108i	−1.56085	−	0.183470i
$933$		0			0
$934$	−0.357622	+	6.10580i	−0.0117017	+	0.199788i
$935$	2.01961	−	2.01961i	0.0660484	−	0.0660484i
$936$		0			0
$937$	8.52664	+	8.52664i	0.278553	+	0.278553i	0.832531	−	0.553978i	$-0.186891\pi$
$937$	8.52664	+	8.52664i	0.278553	+	0.278553i	−0.553978	+	0.832531i	$0.686891\pi$
$938$	6.60453	−	5.87367i	0.215646	−	0.191782i
$939$		0			0
$940$	3.17691	+	1.77581i	0.103619	+	0.0579205i
$941$	38.2362	+	15.8379i	1.24646	+	0.516302i	0.905729	−	0.423858i	$-0.139324\pi$
$941$	38.2362	+	15.8379i	1.24646	+	0.516302i	0.340734	+	0.940160i	$0.389324\pi$
$942$		0			0
$943$		−	4.87438i		−	0.158731i
$944$	6.09540	+	38.0895i	0.198388	+	1.23971i
$945$		0			0
$946$	−8.01020	−	3.88126i	−0.260434	−	0.126191i
$947$	−30.7868	−	12.7523i	−1.00044	−	0.414394i	−0.178479	−	0.983944i	$-0.557118\pi$
$947$	−30.7868	−	12.7523i	−1.00044	−	0.414394i	−0.821957	+	0.569550i	$0.807118\pi$
$948$		0			0
$949$	14.8885	+	35.9440i	0.483301	+	1.16679i
$950$	−36.2008	−	40.7053i	−1.17451	−	1.32065i
$951$		0			0
$952$	1.46866	+	6.65554i	0.0475997	+	0.215707i
$953$	27.3727	−	27.3727i	0.886690	−	0.886690i	−0.107514	−	0.994204i	$-0.534289\pi$
$953$	27.3727	−	27.3727i	0.886690	−	0.886690i	0.994204	+	0.107514i	$0.0342890\pi$
$954$		0			0
$955$	−0.320193	+	0.132628i	−0.0103612	+	0.00429174i
$956$	−5.56476	−	7.04724i	−0.179977	−	0.227924i
$957$		0			0
$958$	−4.86852	−	14.0215i	−0.157295	−	0.453013i
$959$	8.51473			0.274955
$960$		0			0
$961$	−30.9245			−0.997564
$962$	−4.29804	−	12.3785i	−0.138574	−	0.399098i
$963$		0			0
$964$	−19.4270	−	24.6024i	−0.625702	−	0.792391i
$965$	−0.357886	+	0.148241i	−0.0115208	+	0.00477206i
$966$		0			0
$967$	−16.1014	+	16.1014i	−0.517787	+	0.517787i	−0.916901	−	0.399114i	$-0.869318\pi$
$967$	−16.1014	+	16.1014i	−0.517787	+	0.517787i	0.399114	+	0.916901i	$0.369318\pi$
$968$	−21.7514	+	4.79983i	−0.699116	+	0.154272i
$969$		0			0
$970$	−0.849128	−	0.954784i	−0.0272639	−	0.0306563i
$971$	23.0343	+	55.6097i	0.739206	+	1.78460i	0.609087	+	0.793103i	$0.291536\pi$
$971$	23.0343	+	55.6097i	0.739206	+	1.78460i	0.130119	+	0.991498i	$0.458464\pi$
$972$		0			0
$973$	−5.84556	−	2.42131i	−0.187400	−	0.0776236i
$974$	13.2887	+	6.43892i	0.425799	+	0.206316i
$975$		0			0
$976$	−36.5212	−	26.4448i	−1.16901	−	0.846478i
$977$		−	16.7011i		−	0.534316i	−0.963653	−	0.267158i	$-0.913915\pi$
$977$		−	16.7011i		−	0.534316i	0.963653	−	0.267158i	$-0.0860846\pi$
$978$		0			0
$979$	57.1542	+	23.6740i	1.82665	+	0.756625i
$980$	1.74197	+	0.973718i	0.0556453	+	0.0311043i
$981$		0			0
$982$	40.2611	−	35.8058i	1.28478	−	1.14261i
$983$	0.562655	+	0.562655i	0.0179459	+	0.0179459i	0.716023	−	0.698077i	$-0.245961\pi$
$983$	0.562655	+	0.562655i	0.0179459	+	0.0179459i	−0.698077	+	0.716023i	$0.745961\pi$
$984$		0			0
$985$	1.07749	−	1.07749i	0.0343315	−	0.0343315i
$986$	1.59172	−	27.1759i	0.0506905	−	0.865457i
$987$		0			0
$988$	−88.2366	−	10.3718i	−2.80718	−	0.329970i
$989$	−3.95621	+	9.55113i	−0.125800	+	0.303708i
$990$		0			0
$991$	−30.1284			−0.957059			−0.478530	−	0.878071i	$-0.658830\pi$
$991$	−30.1284			−0.957059			−0.478530	+	0.878071i	$0.658830\pi$
$992$	−1.54666	+	0.155464i	−0.0491066	+	0.00493598i
$993$		0			0
$994$	6.83519	−	2.37331i	0.216799	−	0.0752767i
$995$	−1.12202	+	2.70880i	−0.0355705	+	0.0858747i
$996$		0			0
$997$	0.827894	−	0.342925i	0.0262197	−	0.0108605i	−0.369535	−	0.929217i	$-0.620483\pi$
$997$	0.827894	−	0.342925i	0.0262197	−	0.0108605i	0.395755	+	0.918356i	$0.370483\pi$
$998$	−1.04900	+	17.9100i	−0.0332055	+	0.566930i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.v.b.109.13	✓	128
3.2	odd	2	inner	864.2.v.b.109.20	yes	128
32.5	even	8	inner	864.2.v.b.325.13	yes	128
96.5	odd	8	inner	864.2.v.b.325.20	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.v.b.109.13	✓	128	1.1	even	1	trivial
864.2.v.b.109.20	yes	128	3.2	odd	2	inner
864.2.v.b.325.13	yes	128	32.5	even	8	inner
864.2.v.b.325.20	yes	128	96.5	odd	8	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.463875 - 1.33597i) q^{2} +(-1.56964 + 1.23945i) q^{4} +(-0.137547 + 0.0569738i) q^{5} +(0.385875 - 0.385875i) q^{7} +(2.38398 + 1.52205i) q^{8} +O(q^{10})\)	\(q+(-0.463875 - 1.33597i) q^{2} +(-1.56964 + 1.23945i) q^{4} +(-0.137547 + 0.0569738i) q^{5} +(0.385875 - 0.385875i) q^{7} +(2.38398 + 1.52205i) q^{8} +(0.139920 + 0.157330i) q^{10} +(1.66259 + 4.01386i) q^{11} +(-5.30371 - 2.19687i) q^{13} +(-0.694516 - 0.336521i) q^{14} +(0.927543 - 3.89097i) q^{16} +4.41571i q^{17} +(-7.14906 - 2.96124i) q^{19} +(0.145283 - 0.259911i) q^{20} +(4.59117 - 4.08311i) q^{22} +(-5.04601 - 5.04601i) q^{23} +(-3.51986 + 3.51986i) q^{25} +(-0.474698 + 8.10468i) q^{26} +(-0.127414 + 1.08396i) q^{28} +(1.66821 - 4.02742i) q^{29} +0.274792 q^{31} +(-5.62849 + 0.565751i) q^{32} +(5.89927 - 2.04834i) q^{34} +(-0.0310912 + 0.0750608i) q^{35} +(-1.49115 + 0.617653i) q^{37} +(-0.639862 + 10.9246i) q^{38} +(-0.414626 - 0.0735285i) q^{40} +(0.482993 + 0.482993i) q^{41} +(-0.554390 - 1.33842i) q^{43} +(-7.58464 - 4.23962i) q^{44} +(-4.40061 + 9.08204i) q^{46} +12.2231i q^{47} +6.70220i q^{49} +(6.33521 + 3.06966i) q^{50} +(11.0478 - 3.12537i) q^{52} +(2.13483 + 5.15392i) q^{53} +(-0.457370 - 0.457370i) q^{55} +(1.50724 - 0.332599i) q^{56} +(-6.15436 - 0.360466i) q^{58} +(-8.90946 + 3.69042i) q^{59} +(4.31381 - 10.4145i) q^{61} +(-0.127469 - 0.367114i) q^{62} +(3.36674 + 7.25707i) q^{64} +0.854674 q^{65} +(-4.38272 + 10.5808i) q^{67} +(-5.47304 - 6.93108i) q^{68} +(0.114702 + 0.00671816i) q^{70} +(-6.62943 + 6.62943i) q^{71} +(-4.79216 - 4.79216i) q^{73} +(1.51687 + 1.70562i) q^{74} +(14.8918 - 4.21280i) q^{76} +(2.19040 + 0.907295i) q^{77} +3.60122i q^{79} +(0.0941028 + 0.588037i) q^{80} +(0.421217 - 0.869313i) q^{82} +(-9.62080 - 3.98506i) q^{83} +(-0.251580 - 0.607368i) q^{85} +(-1.53092 + 1.36151i) q^{86} +(-2.14569 + 12.0995i) q^{88} +(10.0686 - 10.0686i) q^{89} +(-2.89429 + 1.19885i) q^{91} +(14.1747 + 1.66616i) q^{92} +(16.3297 - 5.66998i) q^{94} +1.15205 q^{95} -6.06867 q^{97} +(8.95395 - 3.10898i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) \) 128 * q + 16 * q^10 - 32 * q^16 - 16 * q^22 - 32 * q^40 - 32 * q^46 - 80 * q^52 + 32 * q^55 - 32 * q^58 + 64 * q^61 + 48 * q^64 + 64 * q^67 - 96 * q^70 + 32 * q^76 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 48 * q^94

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