LMFDB - Embedded newform 400.2.u.f.321.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(81,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("400.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.u (of order $5$, degree $4$, not 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 13 x^{10} - 24 x^{9} + 93 x^{8} - 6 x^{7} + 342 x^{6} + 786 x^{5} + 1473 x^{4} + \cdots + 16 $ x^12 - 3x^11 + 13x^10 - 24x^9 + 93x^8 - 6x^7 + 342x^6 + 786x^5 + 1473x^4 + 84x^3 + 688x^2 + 168*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 100)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			321.2
Root			$0.213831 - 0.658105i$ of defining polynomial
Character	$\chi$	$=$	400.321
Dual form			400.2.u.f.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.559818 - 0.406731i) q^{3} +(-0.463031 + 2.18760i) q^{5} -3.25686 q^{7} +(-0.779086 - 2.39778i) q^{9} +O(q^{10})$	\(q+(-0.559818 - 0.406731i) q^{3} +(-0.463031 + 2.18760i) q^{5} -3.25686 q^{7} +(-0.779086 - 2.39778i) q^{9} +(0.967992 - 2.97917i) q^{11} +(-1.87219 - 5.76202i) q^{13} +(1.14898 - 1.03633i) q^{15} +(0.772048 - 0.560925i) q^{17} +(4.69307 - 3.40972i) q^{19} +(1.82325 + 1.32467i) q^{21} +(-0.660440 + 2.03262i) q^{23} +(-4.57121 - 2.02585i) q^{25} +(-1.18060 + 3.63351i) q^{27} +(-5.01851 - 3.64616i) q^{29} +(-2.25179 + 1.63602i) q^{31} +(-1.75362 + 1.27408i) q^{33} +(1.50803 - 7.12472i) q^{35} +(0.459265 + 1.41347i) q^{37} +(-1.29551 + 3.98716i) q^{39} +(2.49665 + 7.68391i) q^{41} -7.86497 q^{43} +(5.60613 - 0.594084i) q^{45} +(-2.18825 - 1.58986i) q^{47} +3.60716 q^{49} -0.660352 q^{51} +(0.984166 + 0.715038i) q^{53} +(6.06903 + 3.49703i) q^{55} -4.01411 q^{57} +(-4.35884 - 13.4151i) q^{59} +(1.03830 - 3.19554i) q^{61} +(2.53738 + 7.80924i) q^{63} +(13.4719 - 1.42762i) q^{65} +(-3.44114 + 2.50014i) q^{67} +(1.19646 - 0.869278i) q^{69} +(8.07600 + 5.86756i) q^{71} +(-3.26304 + 10.0426i) q^{73} +(1.73506 + 2.99336i) q^{75} +(-3.15262 + 9.70276i) q^{77} +(3.05745 + 2.22137i) q^{79} +(-3.98023 + 2.89181i) q^{81} +(13.0656 - 9.49272i) q^{83} +(0.869600 + 1.94866i) q^{85} +(1.32644 + 4.08237i) q^{87} +(3.35954 - 10.3396i) q^{89} +(6.09748 + 18.7661i) q^{91} +1.92601 q^{93} +(5.28607 + 11.8454i) q^{95} +(-3.89763 - 2.83180i) q^{97} -7.89755 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} - 4 q^{5} + 2 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q - 2 * q^3 - 4 * q^5 + 2 * q^7 - 3 * q^9	$ 12 q - 2 q^{3} - 4 q^{5} + 2 q^{7} - 3 q^{9} + 5 q^{11} - 2 q^{13} - 18 q^{15} + q^{17} + 8 q^{19} + 2 q^{21} + 6 q^{23} - 26 q^{25} + 34 q^{27} - 18 q^{29} - 12 q^{31} - 35 q^{33} + 3 q^{35} + 13 q^{37} - 22 q^{39} - 23 q^{41} - 50 q^{43} + 71 q^{45} - q^{47} + 34 q^{49} - 14 q^{51} + 21 q^{53} - 5 q^{55} + 72 q^{57} - 9 q^{59} - 26 q^{61} + 32 q^{63} - 18 q^{65} + 37 q^{67} - 44 q^{69} - 21 q^{71} + 18 q^{73} + 73 q^{75} - 60 q^{77} + 24 q^{79} + 18 q^{81} + 46 q^{83} - 16 q^{85} - 57 q^{87} - 2 q^{89} + 32 q^{91} + 22 q^{93} - 6 q^{95} - 7 q^{97} - 40 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 - 4 * q^5 + 2 * q^7 - 3 * q^9 + 5 * q^11 - 2 * q^13 - 18 * q^15 + q^17 + 8 * q^19 + 2 * q^21 + 6 * q^23 - 26 * q^25 + 34 * q^27 - 18 * q^29 - 12 * q^31 - 35 * q^33 + 3 * q^35 + 13 * q^37 - 22 * q^39 - 23 * q^41 - 50 * q^43 + 71 * q^45 - q^47 + 34 * q^49 - 14 * q^51 + 21 * q^53 - 5 * q^55 + 72 * q^57 - 9 * q^59 - 26 * q^61 + 32 * q^63 - 18 * q^65 + 37 * q^67 - 44 * q^69 - 21 * q^71 + 18 * q^73 + 73 * q^75 - 60 * q^77 + 24 * q^79 + 18 * q^81 + 46 * q^83 - 16 * q^85 - 57 * q^87 - 2 * q^89 + 32 * q^91 + 22 * q^93 - 6 * q^95 - 7 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.559818	−	0.406731i	−0.323211	−	0.234826i	0.414333	−	0.910125i	$-0.364015\pi$
$3$	−0.559818	−	0.406731i	−0.323211	−	0.234826i	−0.737544	+	0.675299i	$0.764015\pi$
$4$		0			0
$5$	−0.463031	+	2.18760i	−0.207074	+	0.978325i
$5$	−0.463031	+	2.18760i	−0.207074	+	0.978325i
$6$		0			0
$7$	−3.25686			−1.23098			−0.615489	−	0.788145i	$-0.711042\pi$
$7$	−3.25686			−1.23098			−0.615489	+	0.788145i	$0.711042\pi$
$8$		0			0
$9$	−0.779086	−	2.39778i	−0.259695	−	0.799260i
$10$		0			0
$11$	0.967992	−	2.97917i	0.291861	−	0.898254i	−0.692397	−	0.721516i	$-0.743445\pi$
$11$	0.967992	−	2.97917i	0.291861	−	0.898254i	0.984258	−	0.176738i	$-0.0565545\pi$
$12$		0			0
$13$	−1.87219	−	5.76202i	−0.519253	−	1.59810i	−0.775407	−	0.631462i	$-0.782455\pi$
$13$	−1.87219	−	5.76202i	−0.519253	−	1.59810i	0.256154	−	0.966636i	$-0.417545\pi$
$14$		0			0
$15$	1.14898	−	1.03633i	0.296665	−	0.267579i
$16$		0			0
$17$	0.772048	−	0.560925i	0.187249	−	0.136044i	−0.490211	−	0.871604i	$-0.663080\pi$
$17$	0.772048	−	0.560925i	0.187249	−	0.136044i	0.677461	+	0.735559i	$0.263080\pi$
$18$		0			0
$19$	4.69307	−	3.40972i	1.07667	−	0.782243i	0.0995667	−	0.995031i	$-0.468254\pi$
$19$	4.69307	−	3.40972i	1.07667	−	0.782243i	0.977098	+	0.212788i	$0.0682543\pi$
$20$		0			0
$21$	1.82325	+	1.32467i	0.397866	+	0.289066i
$22$		0			0
$23$	−0.660440	+	2.03262i	−0.137711	+	0.423832i	−0.996002	−	0.0893323i	$-0.971527\pi$
$23$	−0.660440	+	2.03262i	−0.137711	+	0.423832i	0.858291	+	0.513164i	$0.171527\pi$
$24$		0			0
$25$	−4.57121	−	2.02585i	−0.914241	−	0.405171i
$26$		0			0
$27$	−1.18060	+	3.63351i	−0.227207	+	0.699270i
$28$		0			0
$29$	−5.01851	−	3.64616i	−0.931915	−	0.677076i	0.0145463	−	0.999894i	$-0.495370\pi$
$29$	−5.01851	−	3.64616i	−0.931915	−	0.677076i	−0.946461	+	0.322819i	$0.895370\pi$
$30$		0			0
$31$	−2.25179	+	1.63602i	−0.404434	+	0.293838i	−0.771344	−	0.636418i	$-0.780415\pi$
$31$	−2.25179	+	1.63602i	−0.404434	+	0.293838i	0.366911	+	0.930256i	$0.380415\pi$
$32$		0			0
$33$	−1.75362	+	1.27408i	−0.305266	+	0.221789i
$34$		0			0
$35$	1.50803	−	7.12472i	0.254903	−	1.20430i
$36$		0			0
$37$	0.459265	+	1.41347i	0.0755027	+	0.232373i	0.981684	−	0.190516i	$-0.0610160\pi$
$37$	0.459265	+	1.41347i	0.0755027	+	0.232373i	−0.906181	+	0.422889i	$0.861016\pi$
$38$		0			0
$39$	−1.29551	+	3.98716i	−0.207447	+	0.638457i
$40$		0			0
$41$	2.49665	+	7.68391i	0.389912	+	1.20003i	0.932854	+	0.360255i	$0.117310\pi$
$41$	2.49665	+	7.68391i	0.389912	+	1.20003i	−0.542942	+	0.839770i	$0.682690\pi$
$42$		0			0
$43$	−7.86497			−1.19940			−0.599699	−	0.800226i	$-0.704713\pi$
$43$	−7.86497			−1.19940			−0.599699	+	0.800226i	$0.704713\pi$
$44$		0			0
$45$	5.60613	−	0.594084i	0.835712	−	0.0885608i
$46$		0			0
$47$	−2.18825	−	1.58986i	−0.319189	−	0.231904i	0.416640	−	0.909071i	$-0.363207\pi$
$47$	−2.18825	−	1.58986i	−0.319189	−	0.231904i	−0.735829	+	0.677167i	$0.763207\pi$
$48$		0			0
$49$	3.60716			0.515309
$50$		0			0
$51$	−0.660352			−0.0924678
$52$		0			0
$53$	0.984166	+	0.715038i	0.135186	+	0.0982181i	0.653323	−	0.757079i	$-0.273374\pi$
$53$	0.984166	+	0.715038i	0.135186	+	0.0982181i	−0.518137	+	0.855297i	$0.673374\pi$
$54$		0			0
$55$	6.06903	+	3.49703i	0.818349	+	0.471539i
$56$		0			0
$57$	−4.01411			−0.531681
$58$		0			0
$59$	−4.35884	−	13.4151i	−0.567472	−	1.74650i	−0.660489	−	0.750836i	$-0.729651\pi$
$59$	−4.35884	−	13.4151i	−0.567472	−	1.74650i	0.0930161	−	0.995665i	$-0.470349\pi$
$60$		0			0
$61$	1.03830	−	3.19554i	0.132940	−	0.409148i	−0.862324	−	0.506357i	$-0.830992\pi$
$61$	1.03830	−	3.19554i	0.132940	−	0.409148i	0.995264	+	0.0972096i	$0.0309917\pi$
$62$		0			0
$63$	2.53738	+	7.80924i	0.319679	+	0.983872i
$64$		0			0
$65$	13.4719	−	1.42762i	1.67098	−	0.177075i
$66$		0			0
$67$	−3.44114	+	2.50014i	−0.420402	+	0.305440i	−0.777800	−	0.628512i	$-0.783664\pi$
$67$	−3.44114	+	2.50014i	−0.420402	+	0.305440i	0.357397	+	0.933952i	$0.383664\pi$
$68$		0			0
$69$	1.19646	−	0.869278i	0.144037	−	0.104649i
$70$		0			0
$71$	8.07600	+	5.86756i	0.958445	+	0.696351i	0.952789	−	0.303633i	$-0.0981997\pi$
$71$	8.07600	+	5.86756i	0.958445	+	0.696351i	0.00565579	+	0.999984i	$0.498200\pi$
$72$		0			0
$73$	−3.26304	+	10.0426i	−0.381910	+	1.17540i	0.556787	+	0.830655i	$0.312034\pi$
$73$	−3.26304	+	10.0426i	−0.381910	+	1.17540i	−0.938697	+	0.344743i	$0.887966\pi$
$74$		0			0
$75$	1.73506	+	2.99336i	0.200348	+	0.345644i
$76$		0			0
$77$	−3.15262	+	9.70276i	−0.359274	+	1.10573i
$78$		0			0
$79$	3.05745	+	2.22137i	0.343990	+	0.249923i	0.746343	−	0.665561i	$-0.231808\pi$
$79$	3.05745	+	2.22137i	0.343990	+	0.249923i	−0.402354	+	0.915484i	$0.631808\pi$
$80$		0			0
$81$	−3.98023	+	2.89181i	−0.442248	+	0.321312i
$82$		0			0
$83$	13.0656	−	9.49272i	1.43414	−	1.04196i	0.444908	−	0.895576i	$-0.353236\pi$
$83$	13.0656	−	9.49272i	1.43414	−	1.04196i	0.989228	−	0.146385i	$-0.0467638\pi$
$84$		0			0
$85$	0.869600	+	1.94866i	0.0943214	+	0.211362i
$86$		0			0
$87$	1.32644	+	4.08237i	0.142210	+	0.437676i
$88$		0			0
$89$	3.35954	−	10.3396i	0.356110	−	1.09600i	−0.599252	−	0.800560i	$-0.704535\pi$
$89$	3.35954	−	10.3396i	0.356110	−	1.09600i	0.955363	−	0.295435i	$-0.0954646\pi$
$90$		0			0
$91$	6.09748	+	18.7661i	0.639190	+	1.96722i
$92$		0			0
$93$	1.92601			0.199718
$94$		0			0
$95$	5.28607	+	11.8454i	0.542339	+	1.21531i
$96$		0			0
$97$	−3.89763	−	2.83180i	−0.395745	−	0.287525i	0.372061	−	0.928208i	$-0.378651\pi$
$97$	−3.89763	−	2.83180i	−0.395745	−	0.287525i	−0.767806	+	0.640683i	$0.778651\pi$
$98$		0			0
$99$	−7.89755			−0.793733
$100$		0			0
$101$	0.856639			0.0852388			0.0426194	−	0.999091i	$-0.486430\pi$
$101$	0.856639			0.0852388			0.0426194	+	0.999091i	$0.486430\pi$
$102$		0			0
$103$	−16.1249	−	11.7154i	−1.58884	−	1.15436i	−0.905579	−	0.424179i	$-0.860563\pi$
$103$	−16.1249	−	11.7154i	−1.58884	−	1.15436i	−0.683257	−	0.730178i	$-0.739437\pi$
$104$		0			0
$105$	−3.74207	+	3.37518i	−0.365188	+	0.329384i
$106$		0			0
$107$	14.2140			1.37412			0.687059	−	0.726602i	$-0.258901\pi$
$107$	14.2140			1.37412			0.687059	+	0.726602i	$0.258901\pi$
$108$		0			0
$109$	2.54037	+	7.81846i	0.243324	+	0.748873i	0.995908	+	0.0903767i	$0.0288071\pi$
$109$	2.54037	+	7.81846i	0.243324	+	0.748873i	−0.752584	+	0.658496i	$0.771193\pi$
$110$		0			0
$111$	0.317799	−	0.978084i	0.0301641	−	0.0928356i
$112$		0			0
$113$	−3.83971	−	11.8174i	−0.361210	−	1.11169i	−0.952321	−	0.305099i	$-0.901310\pi$
$113$	−3.83971	−	11.8174i	−0.361210	−	1.11169i	0.591111	−	0.806590i	$-0.298690\pi$
$114$		0			0
$115$	−4.14077	−	2.38595i	−0.386129	−	0.222491i
$116$		0			0
$117$	−12.3575	+	8.97822i	−1.14245	+	0.830036i
$118$		0			0
$119$	−2.51445	+	1.82686i	−0.230500	+	0.167468i
$120$		0			0
$121$	0.960724	+	0.698007i	0.0873385	+	0.0634552i
$122$		0			0
$123$	1.72762	−	5.31706i	0.155774	−	0.479423i
$124$		0			0
$125$	6.54837	−	9.06195i	0.585704	−	0.810525i
$126$		0			0
$127$	−1.85787	+	5.71793i	−0.164859	+	0.507384i	−0.999026	−	0.0441281i	$-0.985949\pi$
$127$	−1.85787	+	5.71793i	−0.164859	+	0.507384i	0.834167	+	0.551512i	$0.185949\pi$
$128$		0			0
$129$	4.40295	+	3.19893i	0.387658	+	0.281650i
$130$		0			0
$131$	−3.67460	+	2.66975i	−0.321051	+	0.233257i	−0.736624	−	0.676303i	$-0.763581\pi$
$131$	−3.67460	+	2.66975i	−0.321051	+	0.233257i	0.415573	+	0.909560i	$0.363581\pi$
$132$		0			0
$133$	−15.2847	+	11.1050i	−1.32535	+	0.962924i
$134$		0			0
$135$	−7.40203	−	4.26511i	−0.637065	−	0.367082i
$136$		0			0
$137$	0.269732	+	0.830149i	0.0230447	+	0.0709244i	0.961918	−	0.273340i	$-0.0881284\pi$
$137$	0.269732	+	0.830149i	0.0230447	+	0.0709244i	−0.938873	+	0.344264i	$0.888128\pi$
$138$		0			0
$139$	2.26431	−	6.96882i	0.192056	−	0.591088i	−0.807942	−	0.589262i	$-0.799419\pi$
$139$	2.26431	−	6.96882i	0.192056	−	0.591088i	0.999998	−	0.00182613i	$-0.000581277\pi$
$140$		0			0
$141$	0.578376	+	1.78006i	0.0487081	+	0.149908i
$142$		0			0
$143$	−18.9783			−1.58705
$144$		0			0
$145$	10.3001	−	9.29022i	0.855375	−	0.771511i
$146$		0			0
$147$	−2.01935	−	1.46715i	−0.166553	−	0.121008i
$148$		0			0
$149$	15.4590			1.26645			0.633227	−	0.773966i	$-0.281730\pi$
$149$	15.4590			1.26645			0.633227	+	0.773966i	$0.281730\pi$
$150$		0			0
$151$	14.2497			1.15962			0.579811	−	0.814751i	$-0.303126\pi$
$151$	14.2497			1.15962			0.579811	+	0.814751i	$0.303126\pi$
$152$		0			0
$153$	−1.94647	−	1.41419i	−0.157362	−	0.114331i
$154$		0			0
$155$	−2.53632	−	5.68355i	−0.203722	−	0.456514i
$156$		0			0
$157$	22.1897			1.77093			0.885464	−	0.464708i	$-0.153841\pi$
$157$	22.1897			1.77093			0.885464	+	0.464708i	$0.153841\pi$
$158$		0			0
$159$	−0.260125	−	0.800582i	−0.0206292	−	0.0634903i
$160$		0			0
$161$	2.15096	−	6.61998i	0.169520	−	0.521728i
$162$		0			0
$163$	−1.43050	−	4.40264i	−0.112046	−	0.344841i	0.879274	−	0.476317i	$-0.158029\pi$
$163$	−1.43050	−	4.40264i	−0.112046	−	0.344841i	−0.991319	+	0.131476i	$0.958029\pi$
$164$		0			0
$165$	−1.97520	−	4.42617i	−0.153769	−	0.344577i
$166$		0			0
$167$	−0.522198	+	0.379399i	−0.0404089	+	0.0293588i	−0.607806	−	0.794085i	$-0.707950\pi$
$167$	−0.522198	+	0.379399i	−0.0404089	+	0.0293588i	0.567397	+	0.823444i	$0.307950\pi$
$168$		0			0
$169$	−19.1786	+	13.9340i	−1.47527	+	1.07185i
$170$		0			0
$171$	−11.8321	−	8.59649i	−0.904820	−	0.657390i
$172$		0			0
$173$	3.32744	−	10.2408i	0.252981	−	0.778595i	−0.741240	−	0.671240i	$-0.765762\pi$
$173$	3.32744	−	10.2408i	0.252981	−	0.778595i	0.994221	−	0.107355i	$-0.0342380\pi$
$174$		0			0
$175$	14.8878	+	6.59793i	1.12541	+	0.498757i
$176$		0			0
$177$	−3.01620	+	9.28290i	−0.226711	+	0.697746i
$178$		0			0
$179$	4.85895	+	3.53023i	0.363175	+	0.263862i	0.754375	−	0.656443i	$-0.227940\pi$
$179$	4.85895	+	3.53023i	0.363175	+	0.263862i	−0.391200	+	0.920306i	$0.627940\pi$
$180$		0			0
$181$	−1.26278	+	0.917460i	−0.0938614	+	0.0681943i	−0.633726	−	0.773557i	$-0.718475\pi$
$181$	−1.26278	+	0.917460i	−0.0938614	+	0.0681943i	0.539865	+	0.841752i	$0.318475\pi$
$182$		0			0
$183$	−1.88098	+	1.36662i	−0.139046	+	0.101023i
$184$		0			0
$185$	−3.30477	+	0.350208i	−0.242971	+	0.0257478i
$186$		0			0
$187$	−0.923758	−	2.84303i	−0.0675519	−	0.207903i
$188$		0			0
$189$	3.84505	−	11.8339i	0.279686	−	0.860786i
$190$		0			0
$191$	−5.15092	−	15.8529i	−0.372707	−	1.14708i	−0.945012	−	0.327034i	$-0.893951\pi$
$191$	−5.15092	−	15.8529i	−0.372707	−	1.14708i	0.572305	−	0.820041i	$-0.306049\pi$
$192$		0			0
$193$	7.64238			0.550110			0.275055	−	0.961428i	$-0.411304\pi$
$193$	7.64238			0.550110			0.275055	+	0.961428i	$0.411304\pi$
$194$		0			0
$195$	−8.12247	−	4.68023i	−0.581662	−	0.335158i
$196$		0			0
$197$	−18.2797	−	13.2810i	−1.30238	−	0.946233i	−0.302402	−	0.953181i	$-0.597788\pi$
$197$	−18.2797	−	13.2810i	−1.30238	−	0.946233i	−0.999976	+	0.00694775i	$0.997788\pi$
$198$		0			0
$199$	0.532017			0.0377137			0.0188568	−	0.999822i	$-0.493997\pi$
$199$	0.532017			0.0377137			0.0188568	+	0.999822i	$0.493997\pi$
$200$		0			0
$201$	2.94330			0.207604
$202$		0			0
$203$	16.3446	+	11.8751i	1.14717	+	0.833466i
$204$		0			0
$205$	−17.9654	+	1.90380i	−1.25476	+	0.132967i
$206$		0			0
$207$	5.38832			0.374514
$208$		0			0
$209$	−5.61528	−	17.2821i	−0.388417	−	1.19543i
$210$		0			0
$211$	−2.62958	+	8.09300i	−0.181027	+	0.557145i	−0.999857	−	0.0168911i	$-0.994623\pi$
$211$	−2.62958	+	8.09300i	−0.181027	+	0.557145i	0.818830	+	0.574036i	$0.194623\pi$
$212$		0			0
$213$	−2.13457	−	6.56952i	−0.146258	−	0.450136i
$214$		0			0
$215$	3.64172	−	17.2054i	0.248364	−	1.17340i
$216$		0			0
$217$	7.33377	−	5.32830i	0.497849	−	0.361709i
$218$		0			0
$219$	5.91135	−	4.29485i	0.399452	−	0.290219i
$220$		0			0
$221$	−4.67749	−	3.39839i	−0.314642	−	0.228601i
$222$		0			0
$223$	0.0768927	−	0.236651i	0.00514912	−	0.0158473i	−0.948449	−	0.316930i	$-0.897348\pi$
$223$	0.0768927	−	0.236651i	0.00514912	−	0.0158473i	0.953598	+	0.301083i	$0.0973480\pi$
$224$		0			0
$225$	−1.29619	+	12.5391i	−0.0864126	+	0.835937i
$226$		0			0
$227$	−6.19661	+	19.0712i	−0.411284	+	1.26580i	0.504249	+	0.863558i	$0.331769\pi$
$227$	−6.19661	+	19.0712i	−0.411284	+	1.26580i	−0.915533	+	0.402243i	$0.868231\pi$
$228$		0			0
$229$	−11.0981	−	8.06325i	−0.733384	−	0.532835i	0.157248	−	0.987559i	$-0.449738\pi$
$229$	−11.0981	−	8.06325i	−0.733384	−	0.532835i	−0.890632	+	0.454724i	$0.849738\pi$
$230$		0			0
$231$	5.71131	−	4.14951i	0.375776	−	0.273018i
$232$		0			0
$233$	1.56613	−	1.13786i	0.102601	−	0.0745438i	−0.535302	−	0.844661i	$-0.679802\pi$
$233$	1.56613	−	1.13786i	0.102601	−	0.0745438i	0.637903	+	0.770117i	$0.279802\pi$
$234$		0			0
$235$	4.49120	−	4.05087i	0.292974	−	0.264249i
$236$		0			0
$237$	−0.808114	−	2.48712i	−0.0524927	−	0.161556i
$238$		0			0
$239$	−1.43722	+	4.42332i	−0.0929663	+	0.286121i	−0.986718	−	0.162440i	$-0.948063\pi$
$239$	−1.43722	+	4.42332i	−0.0929663	+	0.286121i	0.893752	+	0.448561i	$0.148063\pi$
$240$		0			0
$241$	−0.239428	−	0.736883i	−0.0154229	−	0.0474668i	0.943049	−	0.332654i	$-0.107944\pi$
$241$	−0.239428	−	0.736883i	−0.0154229	−	0.0474668i	−0.958472	+	0.285187i	$0.907944\pi$
$242$		0			0
$243$	14.8659			0.953648
$244$		0			0
$245$	−1.67023	+	7.89103i	−0.106707	+	0.504140i
$246$		0			0
$247$	−28.4332	−	20.6579i	−1.80916	−	1.31443i
$248$		0			0
$249$	−11.1753			−0.708208
$250$		0			0
$251$	−10.8691			−0.686053			−0.343027	−	0.939326i	$-0.611452\pi$
$251$	−10.8691			−0.686053			−0.343027	+	0.939326i	$0.611452\pi$
$252$		0			0
$253$	5.41624	+	3.93513i	0.340516	+	0.247399i
$254$		0			0
$255$	0.305763	−	1.44459i	0.0191476	−	0.0904636i
$256$		0			0
$257$	12.7119			0.792944			0.396472	−	0.918047i	$-0.370234\pi$
$257$	12.7119			0.792944			0.396472	+	0.918047i	$0.370234\pi$
$258$		0			0
$259$	−1.49576	−	4.60348i	−0.0929422	−	0.286047i
$260$		0			0
$261$	−4.83284	+	14.8740i	−0.299145	+	0.920675i
$262$		0			0
$263$	5.53061	+	17.0215i	0.341032	+	1.04959i	0.963674	+	0.267082i	$0.0860594\pi$
$263$	5.53061	+	17.0215i	0.341032	+	1.04959i	−0.622642	+	0.782507i	$0.713941\pi$
$264$		0			0
$265$	−2.01992	+	1.82188i	−0.124083	+	0.111917i
$266$		0			0
$267$	−6.08617	+	4.42186i	−0.372467	+	0.270613i
$268$		0			0
$269$	4.10292	−	2.98095i	0.250159	−	0.181751i	−0.455638	−	0.890165i	$-0.650589\pi$
$269$	4.10292	−	2.98095i	0.250159	−	0.181751i	0.705797	+	0.708414i	$0.250589\pi$
$270$		0			0
$271$	−14.2920	−	10.3838i	−0.868180	−	0.630769i	0.0619182	−	0.998081i	$-0.480278\pi$
$271$	−14.2920	−	10.3838i	−0.868180	−	0.630769i	−0.930098	+	0.367312i	$0.880278\pi$
$272$		0			0
$273$	4.21929	−	12.9856i	0.255363	−	0.785927i
$274$		0			0
$275$	−10.4603	+	11.6574i	−0.630777	+	0.702968i
$276$		0			0
$277$	2.86080	−	8.80465i	0.171889	−	0.529020i	−0.827589	−	0.561335i	$-0.810288\pi$
$277$	2.86080	−	8.80465i	0.171889	−	0.529020i	0.999478	+	0.0323150i	$0.0102880\pi$
$278$		0			0
$279$	5.67715	+	4.12469i	0.339882	+	0.246939i
$280$		0			0
$281$	−8.77443	+	6.37500i	−0.523439	+	0.380301i	−0.817898	−	0.575364i	$-0.804861\pi$
$281$	−8.77443	+	6.37500i	−0.523439	+	0.380301i	0.294459	+	0.955664i	$0.404861\pi$
$282$		0			0
$283$	−16.3781	+	11.8994i	−0.973575	+	0.707343i	−0.956263	−	0.292507i	$-0.905511\pi$
$283$	−16.3781	+	11.8994i	−0.973575	+	0.707343i	−0.0173113	+	0.999850i	$0.505511\pi$
$284$		0			0
$285$	1.85865	−	8.78127i	0.110097	−	0.520157i
$286$		0			0
$287$	−8.13126	−	25.0255i	−0.479973	−	1.47721i
$288$		0			0
$289$	−4.97187	+	15.3018i	−0.292463	+	0.900108i
$290$		0			0
$291$	1.03018	+	3.17058i	0.0603905	+	0.185863i
$292$		0			0
$293$	0.0888185			0.00518883			0.00259442	−	0.999997i	$-0.499174\pi$
$293$	0.0888185			0.00518883			0.00259442	+	0.999997i	$0.499174\pi$
$294$		0			0
$295$	31.3652	−	3.32379i	1.82615	−	0.193519i
$296$		0			0
$297$	9.68205	+	7.03442i	0.561810	+	0.408179i
$298$		0			0
$299$	12.9485			0.748831
$300$		0			0
$301$	25.6152			1.47643
$302$		0			0
$303$	−0.479562	−	0.348422i	−0.0275501	−	0.0200163i
$304$		0			0
$305$	6.50982	+	3.75101i	0.372751	+	0.214782i
$306$		0			0
$307$	15.6142			0.891148			0.445574	−	0.895245i	$-0.353000\pi$
$307$	15.6142			0.891148			0.445574	+	0.895245i	$0.353000\pi$
$308$		0			0
$309$	4.26198	+	13.1170i	0.242455	+	0.746201i
$310$		0			0
$311$	5.54210	−	17.0568i	0.314264	−	0.967204i	−0.661793	−	0.749687i	$-0.730204\pi$
$311$	5.54210	−	17.0568i	0.314264	−	0.967204i	0.976056	−	0.217517i	$-0.0697959\pi$
$312$		0			0
$313$	3.66886	+	11.2916i	0.207376	+	0.638238i	0.999607	+	0.0280172i	$0.00891932\pi$
$313$	3.66886	+	11.2916i	0.207376	+	0.638238i	−0.792231	+	0.610221i	$0.791081\pi$
$314$		0			0
$315$	−18.2584	+	1.93485i	−1.02874	+	0.109017i
$316$		0			0
$317$	20.0342	−	14.5557i	1.12523	−	0.817528i	0.140237	−	0.990118i	$-0.455214\pi$
$317$	20.0342	−	14.5557i	1.12523	−	0.817528i	0.984994	+	0.172590i	$0.0552137\pi$
$318$		0			0
$319$	−15.7204	+	11.4216i	−0.880175	+	0.639485i
$320$		0			0
$321$	−7.95724	−	5.78127i	−0.444130	−	0.322679i
$322$		0			0
$323$	1.71068	−	5.26493i	0.0951847	−	0.292949i
$324$		0			0
$325$	−3.11483	+	30.1322i	−0.172780	+	1.67143i
$326$		0			0
$327$	1.75787	−	5.41016i	0.0972103	−	0.299183i
$328$		0			0
$329$	7.12683	+	5.17795i	0.392915	+	0.285469i
$330$		0			0
$331$	−15.4888	+	11.2533i	−0.851342	+	0.618536i	−0.925516	−	0.378709i	$-0.876368\pi$
$331$	−15.4888	+	11.2533i	−0.851342	+	0.618536i	0.0741734	+	0.997245i	$0.476368\pi$
$332$		0			0
$333$	3.03139	−	2.20243i	0.166119	−	0.120692i
$334$		0			0
$335$	−3.87595	−	8.68549i	−0.211766	−	0.474539i
$336$		0			0
$337$	−9.53733	−	29.3529i	−0.519531	−	1.59895i	−0.774883	−	0.632105i	$-0.782191\pi$
$337$	−9.53733	−	29.3529i	−0.519531	−	1.59895i	0.255351	−	0.966848i	$-0.417809\pi$
$338$		0			0
$339$	−2.65698	+	8.17733i	−0.144307	+	0.444132i
$340$		0			0
$341$	2.69428	+	8.29213i	0.145903	+	0.449044i
$342$		0			0
$343$	11.0500			0.596645
$344$		0			0
$345$	1.34764	+	3.01988i	0.0725543	+	0.162585i
$346$		0			0
$347$	19.4481	+	14.1298i	1.04403	+	0.758529i	0.971067	−	0.238806i	$-0.0767559\pi$
$347$	19.4481	+	14.1298i	1.04403	+	0.758529i	0.0729587	+	0.997335i	$0.476756\pi$
$348$		0			0
$349$	−19.6167			−1.05006			−0.525030	−	0.851084i	$-0.675946\pi$
$349$	−19.6167			−1.05006			−0.525030	+	0.851084i	$0.675946\pi$
$350$		0			0
$351$	23.1467			1.23548
$352$		0			0
$353$	6.21914	+	4.51847i	0.331011	+	0.240494i	0.740860	−	0.671660i	$-0.234418\pi$
$353$	6.21914	+	4.51847i	0.331011	+	0.240494i	−0.409848	+	0.912154i	$0.634418\pi$
$354$		0			0
$355$	−16.5753	+	14.9502i	−0.879726	+	0.793475i
$356$		0			0
$357$	2.15068			0.113826
$358$		0			0
$359$	7.93332	+	24.4163i	0.418705	+	1.28864i	0.908895	+	0.417025i	$0.136927\pi$
$359$	7.93332	+	24.4163i	0.418705	+	1.28864i	−0.490190	+	0.871616i	$0.663073\pi$
$360$		0			0
$361$	4.52745	−	13.9340i	0.238287	−	0.733371i
$362$		0			0
$363$	−0.253929	−	0.781513i	−0.0133278	−	0.0410188i
$364$		0			0
$365$	−20.4583	−	11.7883i	−1.07084	−	0.617026i
$366$		0			0
$367$	21.4739	−	15.6017i	1.12093	−	0.814403i	0.136579	−	0.990629i	$-0.456389\pi$
$367$	21.4739	−	15.6017i	1.12093	−	0.814403i	0.984350	+	0.176226i	$0.0563891\pi$
$368$		0			0
$369$	16.4792	−	11.9729i	0.857874	−	0.623282i
$370$		0			0
$371$	−3.20529	−	2.32878i	−0.166411	−	0.120904i
$372$		0			0
$373$	−0.105851	+	0.325775i	−0.00548074	+	0.0168680i	−0.953759	−	0.300571i	$-0.902823\pi$
$373$	−0.105851	+	0.325775i	−0.00548074	+	0.0168680i	0.948279	+	0.317439i	$0.102823\pi$
$374$		0			0
$375$	−7.35167	+	2.40961i	−0.379639	+	0.124432i
$376$		0			0
$377$	−11.6136	+	35.7431i	−0.598133	+	1.84086i
$378$		0			0
$379$	−10.2668	−	7.45930i	−0.527372	−	0.383159i	0.292002	−	0.956418i	$-0.405679\pi$
$379$	−10.2668	−	7.45930i	−0.527372	−	0.383159i	−0.819374	+	0.573259i	$0.805679\pi$
$380$		0			0
$381$	3.36573	−	2.44534i	0.172431	−	0.125279i
$382$		0			0
$383$	0.660019	−	0.479532i	0.0337254	−	0.0245029i	−0.570795	−	0.821093i	$-0.693365\pi$
$383$	0.660019	−	0.479532i	0.0337254	−	0.0245029i	0.604520	+	0.796590i	$0.293365\pi$
$384$		0			0
$385$	−19.7660	−	11.3893i	−1.00737	−	0.580455i
$386$		0			0
$387$	6.12749	+	18.8585i	0.311478	+	0.958630i
$388$		0			0
$389$	−9.14323	+	28.1400i	−0.463580	+	1.42675i	0.397179	+	0.917741i	$0.369989\pi$
$389$	−9.14323	+	28.1400i	−0.463580	+	1.42675i	−0.860759	+	0.509012i	$0.830011\pi$
$390$		0			0
$391$	0.630260	+	1.93974i	0.0318736	+	0.0980969i
$392$		0			0
$393$	3.14298			0.158542
$394$		0			0
$395$	−6.27516	+	5.65992i	−0.315737	+	0.284781i
$396$		0			0
$397$	−2.40066	−	1.74418i	−0.120486	−	0.0875380i	0.525911	−	0.850540i	$-0.323725\pi$
$397$	−2.40066	−	1.74418i	−0.120486	−	0.0875380i	−0.646396	+	0.763002i	$0.723725\pi$
$398$		0			0
$399$	13.0734			0.654488
$400$		0			0
$401$	−4.01204			−0.200352			−0.100176	−	0.994970i	$-0.531941\pi$
$401$	−4.01204			−0.200352			−0.100176	+	0.994970i	$0.531941\pi$
$402$		0			0
$403$	13.6426	+	9.91192i	0.679585	+	0.493748i
$404$		0			0
$405$	−4.48316	−	10.0462i	−0.222770	−	0.499198i
$406$		0			0
$407$	4.65554			0.230767
$408$		0			0
$409$	4.93095	+	15.1759i	0.243820	+	0.750400i	0.995828	+	0.0912469i	$0.0290852\pi$
$409$	4.93095	+	15.1759i	0.243820	+	0.750400i	−0.752008	+	0.659153i	$0.770915\pi$
$410$		0			0
$411$	0.186647	−	0.574441i	0.00920662	−	0.0283351i
$412$		0			0
$413$	14.1961	+	43.6912i	0.698547	+	2.14991i
$414$		0			0
$415$	14.7165	+	32.9778i	0.722405	+	1.61881i
$416$		0			0
$417$	−4.10204	+	2.98031i	−0.200878	+	0.145946i
$418$		0			0
$419$	2.75537	−	2.00189i	0.134609	−	0.0977989i	−0.518443	−	0.855112i	$-0.673488\pi$
$419$	2.75537	−	2.00189i	0.134609	−	0.0977989i	0.653052	+	0.757313i	$0.273488\pi$
$420$		0			0
$421$	−30.5473	−	22.1939i	−1.48878	−	1.08166i	−0.974592	−	0.223988i	$-0.928092\pi$
$421$	−30.5473	−	22.1939i	−1.48878	−	1.08166i	−0.514191	−	0.857676i	$-0.671908\pi$
$422$		0			0
$423$	−2.10729	+	6.48557i	−0.102460	+	0.315339i
$424$		0			0
$425$	−4.66554	+	1.00005i	−0.226312	+	0.0485095i
$426$		0			0
$427$	−3.38159	+	10.4075i	−0.163646	+	0.503652i
$428$		0			0
$429$	10.6244	+	7.71908i	0.512951	+	0.372681i
$430$		0			0
$431$	3.60047	−	2.61589i	0.173429	−	0.126003i	−0.497685	−	0.867358i	$-0.665816\pi$
$431$	3.60047	−	2.61589i	0.173429	−	0.126003i	0.671113	+	0.741355i	$0.265816\pi$
$432$		0			0
$433$	15.3915	−	11.1826i	0.739669	−	0.537401i	−0.152938	−	0.988236i	$-0.548874\pi$
$433$	15.3915	−	11.1826i	0.739669	−	0.537401i	0.892607	+	0.450835i	$0.148874\pi$
$434$		0			0
$435$	−9.54479	+	1.01147i	−0.457638	+	0.0484961i
$436$		0			0
$437$	3.83118	+	11.7912i	0.183270	+	0.564048i
$438$		0			0
$439$	−2.03280	+	6.25631i	−0.0970202	+	0.298597i	−0.987775	−	0.155887i	$-0.950176\pi$
$439$	−2.03280	+	6.25631i	−0.0970202	+	0.298597i	0.890755	+	0.454484i	$0.150176\pi$
$440$		0			0
$441$	−2.81029	−	8.64917i	−0.133823	−	0.411865i
$442$		0			0
$443$	40.9446			1.94534			0.972668	−	0.232202i	$-0.0745929\pi$
$443$	40.9446			1.94534			0.972668	+	0.232202i	$0.0745929\pi$
$444$		0			0
$445$	21.0634	+	12.1369i	0.998499	+	0.575343i
$446$		0			0
$447$	−8.65425	−	6.28768i	−0.409332	−	0.297397i
$448$		0			0
$449$	29.4900			1.39172			0.695860	−	0.718177i	$-0.255023\pi$
$449$	29.4900			1.39172			0.695860	+	0.718177i	$0.255023\pi$
$450$		0			0
$451$	25.3084			1.19173
$452$		0			0
$453$	−7.97722	−	5.79579i	−0.374803	−	0.272310i
$454$		0			0
$455$	−43.8761	+	4.64958i	−2.05694	+	0.217975i
$456$		0			0
$457$	8.69841			0.406895			0.203447	−	0.979086i	$-0.434785\pi$
$457$	8.69841			0.406895			0.203447	+	0.979086i	$0.434785\pi$
$458$		0			0
$459$	1.12665	+	3.46747i	0.0525875	+	0.161848i
$460$		0			0
$461$	8.38622	−	25.8101i	0.390585	−	1.20210i	−0.541762	−	0.840532i	$-0.682242\pi$
$461$	8.38622	−	25.8101i	0.390585	−	1.20210i	0.932347	−	0.361565i	$-0.117758\pi$
$462$		0			0
$463$	−9.39445	−	28.9132i	−0.436597	−	1.34371i	−0.891441	−	0.453137i	$-0.850305\pi$
$463$	−9.39445	−	28.9132i	−0.436597	−	1.34371i	0.454844	−	0.890571i	$-0.349695\pi$
$464$		0			0
$465$	−0.891803	+	4.21335i	−0.0413564	+	0.195389i
$466$		0			0
$467$	12.6698	−	9.20515i	0.586288	−	0.425963i	−0.254697	−	0.967021i	$-0.581976\pi$
$467$	12.6698	−	9.20515i	0.586288	−	0.425963i	0.840986	+	0.541057i	$0.181976\pi$
$468$		0			0
$469$	11.2073	−	8.14260i	0.517506	−	0.375990i
$470$		0			0
$471$	−12.4222	−	9.02523i	−0.572383	−	0.415861i
$472$		0			0
$473$	−7.61323	+	23.4311i	−0.350057	+	1.07736i
$474$		0			0
$475$	−28.3606	+	6.07904i	−1.30127	+	0.278926i
$476$		0			0
$477$	0.947754	−	2.91689i	0.0433947	−	0.133555i
$478$		0			0
$479$	−23.9553	−	17.4045i	−1.09455	−	0.795234i	−0.114384	−	0.993437i	$-0.536490\pi$
$479$	−23.9553	−	17.4045i	−1.09455	−	0.795234i	−0.980161	+	0.198203i	$0.936490\pi$
$480$		0			0
$481$	7.28462	−	5.29259i	0.332150	−	0.241321i
$482$		0			0
$483$	−3.89670	+	2.83112i	−0.177306	+	0.128820i
$484$		0			0
$485$	7.99957	−	7.21526i	0.363242	−	0.327628i
$486$		0			0
$487$	−6.22948	−	19.1724i	−0.282285	−	0.868783i	−0.987199	−	0.159491i	$-0.949015\pi$
$487$	−6.22948	−	19.1724i	−0.282285	−	0.868783i	0.704914	−	0.709292i	$-0.250985\pi$
$488$		0			0
$489$	−0.989870	+	3.04651i	−0.0447635	+	0.137768i
$490$		0			0
$491$	3.73062	+	11.4817i	0.168360	+	0.518160i	0.999268	−	0.0382500i	$-0.0121783\pi$
$491$	3.73062	+	11.4817i	0.168360	+	0.518160i	−0.830908	+	0.556410i	$0.812178\pi$
$492$		0			0
$493$	−5.91976			−0.266612
$494$		0			0
$495$	3.65681	−	17.2767i	0.164361	−	0.776529i
$496$		0			0
$497$	−26.3024	−	19.1098i	−1.17983	−	0.857193i
$498$		0			0
$499$	−22.1701			−0.992468			−0.496234	−	0.868189i	$-0.665284\pi$
$499$	−22.1701			−0.992468			−0.496234	+	0.868189i	$0.665284\pi$
$500$		0			0
$501$	0.446649			0.0199548
$502$		0			0
$503$	−11.4345	−	8.30762i	−0.509837	−	0.370418i	0.302925	−	0.953014i	$-0.402037\pi$
$503$	−11.4345	−	8.30762i	−0.509837	−	0.370418i	−0.812762	+	0.582596i	$0.802037\pi$
$504$		0			0
$505$	−0.396650	+	1.87399i	−0.0176507	+	0.0833913i
$506$		0			0
$507$	16.4039			0.728524
$508$		0			0
$509$	−3.04767	−	9.37976i	−0.135086	−	0.415751i	0.860518	−	0.509421i	$-0.170140\pi$
$509$	−3.04767	−	9.37976i	−0.135086	−	0.415751i	−0.995603	+	0.0936698i	$0.970140\pi$
$510$		0			0
$511$	10.6273	−	32.7074i	0.470123	−	1.44689i
$512$		0			0
$513$	6.84861	+	21.0779i	0.302374	+	0.930610i
$514$		0			0
$515$	33.0951	−	29.8503i	1.45834	−	1.31536i
$516$		0			0
$517$	−6.85467	+	4.98021i	−0.301468	+	0.219029i
$518$		0			0
$519$	−6.02802	+	4.37961i	−0.264601	+	0.192244i
$520$		0			0
$521$	−15.2400	−	11.0725i	−0.667678	−	0.485096i	0.201569	−	0.979474i	$-0.435396\pi$
$521$	−15.2400	−	11.0725i	−0.667678	−	0.485096i	−0.869247	+	0.494378i	$0.835396\pi$
$522$		0			0
$523$	3.66065	−	11.2663i	0.160069	−	0.492642i	−0.838570	−	0.544794i	$-0.816608\pi$
$523$	3.66065	−	11.2663i	0.160069	−	0.492642i	0.998639	+	0.0521519i	$0.0166080\pi$
$524$		0			0
$525$	−5.65087	−	9.74897i	−0.246624	−	0.425480i
$526$		0			0
$527$	−0.820803	+	2.52617i	−0.0357548	+	0.110042i
$528$		0			0
$529$	14.9120	+	10.8342i	0.648348	+	0.471053i
$530$		0			0
$531$	−28.7706	+	20.9031i	−1.24854	+	0.907116i
$532$		0			0
$533$	39.6007	−	28.7716i	1.71529	−	1.24623i
$534$		0			0
$535$	−6.58151	+	31.0945i	−0.284544	+	1.34433i
$536$		0			0
$537$	−1.28427	−	3.95258i	−0.0554203	−	0.170566i
$538$		0			0
$539$	3.49170	−	10.7464i	0.150398	−	0.462878i
$540$		0			0
$541$	−4.50285	−	13.8584i	−0.193593	−	0.595817i	−0.999990	−	0.00444309i	$-0.998586\pi$
$541$	−4.50285	−	13.8584i	−0.193593	−	0.595817i	0.806397	−	0.591374i	$-0.201414\pi$
$542$		0			0
$543$	1.08008			0.0463509
$544$		0			0
$545$	−18.2800	+	1.93714i	−0.783027	+	0.0829778i
$546$		0			0
$547$	−9.66204	−	7.01988i	−0.413119	−	0.300148i	0.361744	−	0.932277i	$-0.382181\pi$
$547$	−9.66204	−	7.01988i	−0.413119	−	0.300148i	−0.774863	+	0.632129i	$0.782181\pi$
$548$		0			0
$549$	−8.47113			−0.361539
$550$		0			0
$551$	−35.9846			−1.53300
$552$		0			0
$553$	−9.95769	−	7.23469i	−0.423444	−	0.307650i
$554$		0			0
$555$	1.99251	+	1.14810i	0.0845772	+	0.0487341i
$556$		0			0
$557$	−2.77697			−0.117664			−0.0588319	−	0.998268i	$-0.518738\pi$
$557$	−2.77697			−0.117664			−0.0588319	+	0.998268i	$0.518738\pi$
$558$		0			0
$559$	14.7248	+	45.3182i	0.622791	+	1.91675i
$560$		0			0
$561$	−0.639215	+	1.96730i	−0.0269877	+	0.0830596i
$562$		0			0
$563$	−6.64446	−	20.4495i	−0.280030	−	0.861845i	−0.987844	−	0.155446i	$-0.950318\pi$
$563$	−6.64446	−	20.4495i	−0.280030	−	0.861845i	0.707814	−	0.706399i	$-0.249682\pi$
$564$		0			0
$565$	27.6297	−	2.92794i	1.16239	−	0.123179i
$566$		0			0
$567$	12.9631	−	9.41823i	0.544398	−	0.395528i
$568$		0			0
$569$	−11.6806	+	8.48646i	−0.489677	+	0.355771i	−0.805060	−	0.593193i	$-0.797867\pi$
$569$	−11.6806	+	8.48646i	−0.489677	+	0.355771i	0.315383	+	0.948964i	$0.397867\pi$
$570$		0			0
$571$	2.79917	+	2.03371i	0.117141	+	0.0851082i	0.644814	−	0.764340i	$-0.276935\pi$
$571$	2.79917	+	2.03371i	0.117141	+	0.0851082i	−0.527672	+	0.849448i	$0.676935\pi$
$572$		0			0
$573$	−3.56429	+	10.9698i	−0.148901	+	0.458269i
$574$		0			0
$575$	7.13681	−	7.95359i	0.297625	−	0.331688i
$576$		0			0
$577$	4.83279	−	14.8738i	0.201192	−	0.619204i	−0.798657	−	0.601787i	$-0.794456\pi$
$577$	4.83279	−	14.8738i	0.201192	−	0.619204i	0.999848	−	0.0174174i	$-0.00554441\pi$
$578$		0			0
$579$	−4.27834	−	3.10839i	−0.177802	−	0.129180i
$580$		0			0
$581$	−42.5529	+	30.9165i	−1.76539	+	1.28263i
$582$		0			0
$583$	3.08289	−	2.23985i	0.127680	−	0.0927650i
$584$		0			0
$585$	−13.9189	−	31.1904i	−0.575475	−	1.28956i
$586$		0			0
$587$	−8.45245	−	26.0140i	−0.348870	−	1.07371i	−0.959479	−	0.281779i	$-0.909075\pi$
$587$	−8.45245	−	26.0140i	−0.348870	−	1.07371i	0.610609	−	0.791932i	$-0.290925\pi$
$588$		0			0
$589$	−4.98945	+	15.3559i	−0.205587	+	0.632731i
$590$		0			0
$591$	4.83152	+	14.8699i	0.198742	+	0.611665i
$592$		0			0
$593$	−40.1657			−1.64941			−0.824703	−	0.565566i	$-0.808658\pi$
$593$	−40.1657			−1.64941			−0.824703	+	0.565566i	$0.808658\pi$
$594$		0			0
$595$	−2.83217	−	6.34652i	−0.116108	−	0.260182i
$596$		0			0
$597$	−0.297833	−	0.216388i	−0.0121895	−	0.00885617i
$598$		0			0
$599$	14.9834			0.612207			0.306103	−	0.951998i	$-0.400975\pi$
$599$	14.9834			0.612207			0.306103	+	0.951998i	$0.400975\pi$
$600$		0			0
$601$	0.360256			0.0146952			0.00734758	−	0.999973i	$-0.497661\pi$
$601$	0.360256			0.0146952			0.00734758	+	0.999973i	$0.497661\pi$
$602$		0			0
$603$	8.67572	+	6.30328i	0.353302	+	0.256689i
$604$		0			0
$605$	−1.97181	+	1.77848i	−0.0801653	+	0.0723056i
$606$		0			0
$607$	11.8460			0.480815			0.240408	−	0.970672i	$-0.422719\pi$
$607$	11.8460			0.480815			0.240408	+	0.970672i	$0.422719\pi$
$608$		0			0
$609$	−4.32005	−	13.2957i	−0.175057	−	0.538770i
$610$		0			0
$611$	−5.06396	+	15.5853i	−0.204866	+	0.630512i
$612$		0			0
$613$	−4.39289	−	13.5199i	−0.177427	−	0.546065i	0.822309	−	0.569042i	$-0.192686\pi$
$613$	−4.39289	−	13.5199i	−0.177427	−	0.546065i	−0.999736	+	0.0229766i	$0.992686\pi$
$614$		0			0
$615$	10.8317	+	6.24130i	0.436775	+	0.251673i
$616$		0			0
$617$	32.7431	−	23.7892i	1.31819	−	0.957718i	0.318233	−	0.948013i	$-0.396911\pi$
$617$	32.7431	−	23.7892i	1.31819	−	0.957718i	0.999953	−	0.00970534i	$-0.00308936\pi$
$618$		0			0
$619$	−7.22707	+	5.25077i	−0.290480	+	0.211046i	−0.723476	−	0.690350i	$-0.757457\pi$
$619$	−7.22707	+	5.25077i	−0.290480	+	0.211046i	0.432995	+	0.901396i	$0.357457\pi$
$620$		0			0
$621$	−6.60585	−	4.79943i	−0.265084	−	0.192595i
$622$		0			0
$623$	−10.9416	+	33.6747i	−0.438364	+	1.34915i
$624$		0			0
$625$	16.7918	+	18.5212i	0.671673	+	0.740847i
$626$		0			0
$627$	−3.88562	+	11.9587i	−0.155177	+	0.477585i
$628$		0			0
$629$	1.14743	+	0.833654i	0.0457509	+	0.0332400i
$630$		0			0
$631$	18.7106	−	13.5940i	0.744856	−	0.541169i	−0.149372	−	0.988781i	$-0.547725\pi$
$631$	18.7106	−	13.5940i	0.744856	−	0.541169i	0.894228	+	0.447612i	$0.147725\pi$
$632$		0			0
$633$	4.76376	−	3.46107i	0.189342	−	0.137565i
$634$		0			0
$635$	−11.6483	−	6.71185i	−0.462249	−	0.266352i
$636$		0			0
$637$	−6.75331	−	20.7845i	−0.267576	−	0.823514i
$638$		0			0
$639$	7.77721	−	23.9358i	0.307662	−	0.946885i
$640$		0			0
$641$	8.97395	+	27.6190i	0.354450	+	1.09088i	0.956328	+	0.292296i	$0.0944193\pi$
$641$	8.97395	+	27.6190i	0.354450	+	1.09088i	−0.601878	+	0.798588i	$0.705581\pi$
$642$		0			0
$643$	12.5971			0.496781			0.248391	−	0.968660i	$-0.420098\pi$
$643$	12.5971			0.496781			0.248391	+	0.968660i	$0.420098\pi$
$644$		0			0
$645$	−9.03669	+	8.15070i	−0.355819	+	0.320934i
$646$		0			0
$647$	8.55357	+	6.21453i	0.336275	+	0.244318i	0.743089	−	0.669193i	$-0.233360\pi$
$647$	8.55357	+	6.21453i	0.336275	+	0.244318i	−0.406813	+	0.913511i	$0.633360\pi$
$648$		0			0
$649$	−44.1853			−1.73442
$650$		0			0
$651$	−6.27276			−0.245849
$652$		0			0
$653$	−3.34660	−	2.43144i	−0.130962	−	0.0951497i	0.520376	−	0.853938i	$-0.325792\pi$
$653$	−3.34660	−	2.43144i	−0.130962	−	0.0951497i	−0.651338	+	0.758788i	$0.725792\pi$
$654$		0			0
$655$	−4.13890	−	9.27474i	−0.161720	−	0.362394i
$656$		0			0
$657$	26.6221			1.03863
$658$		0			0
$659$	−8.86311	−	27.2778i	−0.345258	−	1.06259i	−0.961446	−	0.274995i	$-0.911324\pi$
$659$	−8.86311	−	27.2778i	−0.345258	−	1.06259i	0.616188	−	0.787599i	$-0.288676\pi$
$660$		0			0
$661$	0.266949	−	0.821583i	0.0103831	−	0.0319559i	−0.945731	−	0.324951i	$-0.894652\pi$
$661$	0.266949	−	0.821583i	0.0103831	−	0.0319559i	0.956114	+	0.292995i	$0.0946521\pi$
$662$		0			0
$663$	1.23631	+	3.80496i	0.0480142	+	0.147772i
$664$		0			0
$665$	−17.2160	−	38.5788i	−0.667608	−	1.49602i
$666$		0			0
$667$	10.7257	−	7.79268i	0.415301	−	0.301734i
$668$		0			0
$669$	−0.139299	+	0.101207i	−0.00538563	+	0.00391289i
$670$		0			0
$671$	−8.51502	−	6.18652i	−0.328719	−	0.238828i
$672$		0			0
$673$	10.9384	−	33.6651i	0.421646	−	1.29769i	−0.484523	−	0.874779i	$-0.661007\pi$
$673$	10.9384	−	33.6651i	0.421646	−	1.29769i	0.906169	−	0.422915i	$-0.138993\pi$
$674$		0			0
$675$	12.7577	−	14.2178i	0.491045	−	0.547244i
$676$		0			0
$677$	−6.04948	+	18.6184i	−0.232500	+	0.715562i	0.764943	+	0.644098i	$0.222767\pi$
$677$	−6.04948	+	18.6184i	−0.232500	+	0.715562i	−0.997443	+	0.0714641i	$0.977233\pi$
$678$		0			0
$679$	12.6941	+	9.22278i	0.487153	+	0.353938i
$680$		0			0
$681$	11.2258	−	8.15605i	0.430175	−	0.312540i
$682$		0			0
$683$	−20.3975	+	14.8197i	−0.780490	+	0.567059i	−0.905126	−	0.425143i	$-0.860224\pi$
$683$	−20.3975	+	14.8197i	−0.780490	+	0.567059i	0.124636	+	0.992203i	$0.460224\pi$
$684$		0			0
$685$	−1.94093	+	0.205681i	−0.0741591	+	0.00785868i
$686$		0			0
$687$	2.93334	+	9.02791i	0.111914	+	0.344436i
$688$		0			0
$689$	2.27752	−	7.00948i	0.0867665	−	0.267040i
$690$		0			0
$691$	−13.3068	−	40.9540i	−0.506213	−	1.55796i	−0.798722	−	0.601700i	$-0.794490\pi$
$691$	−13.3068	−	40.9540i	−0.506213	−	1.55796i	0.292509	−	0.956263i	$-0.405510\pi$
$692$		0			0
$693$	25.7212			0.977069
$694$		0			0
$695$	14.1966	+	8.18018i	0.538506	+	0.310292i
$696$		0			0
$697$	6.23764	+	4.53191i	0.236267	+	0.171658i
$698$		0			0
$699$	−1.33955			−0.0506665
$700$		0			0
$701$	−1.71915			−0.0649316			−0.0324658	−	0.999473i	$-0.510336\pi$
$701$	−1.71915			−0.0649316			−0.0324658	+	0.999473i	$0.510336\pi$
$702$		0			0
$703$	6.97490	+	5.06756i	0.263063	+	0.191127i
$704$		0			0
$705$	−4.16187	+	0.441035i	−0.156745	+	0.0166103i
$706$		0			0
$707$	−2.78996			−0.104927
$708$		0			0
$709$	−7.44728	−	22.9204i	−0.279688	−	0.860793i	−0.987941	−	0.154833i	$-0.950516\pi$
$709$	−7.44728	−	22.9204i	−0.279688	−	0.860793i	0.708252	−	0.705960i	$-0.249484\pi$
$710$		0			0
$711$	2.94433	−	9.06172i	0.110421	−	0.339841i
$712$		0			0
$713$	−1.83825	−	5.65754i	−0.0688428	−	0.211877i
$714$		0			0
$715$	8.78755	−	41.5170i	0.328636	−	1.55265i
$716$		0			0
$717$	2.60369	−	1.89169i	0.0972365	−	0.0706464i
$718$		0			0
$719$	−22.9753	+	16.6925i	−0.856835	+	0.622527i	−0.927022	−	0.375007i	$-0.877640\pi$
$719$	−22.9753	+	16.6925i	−0.856835	+	0.622527i	0.0701871	+	0.997534i	$0.477640\pi$
$720$		0			0
$721$	52.5167	+	38.1556i	1.95582	+	1.42099i
$722$		0			0
$723$	−0.165678	+	0.509903i	−0.00616162	+	0.0189635i
$724$		0			0
$725$	15.5541	+	26.8341i	0.577663	+	0.996595i
$726$		0			0
$727$	−0.313284	+	0.964189i	−0.0116191	+	0.0357598i	−0.956698	−	0.291082i	$-0.905985\pi$
$727$	−0.313284	+	0.964189i	−0.0116191	+	0.0357598i	0.945079	+	0.326842i	$0.105985\pi$
$728$		0			0
$729$	3.61850	+	2.62900i	0.134019	+	0.0973703i
$730$		0			0
$731$	−6.07214	+	4.41166i	−0.224586	+	0.163171i
$732$		0			0
$733$	−8.83915	+	6.42202i	−0.326481	+	0.237203i	−0.738936	−	0.673775i	$-0.764671\pi$
$733$	−8.83915	+	6.42202i	−0.326481	+	0.237203i	0.412455	+	0.910978i	$0.364671\pi$
$734$		0			0
$735$	4.14455	−	3.73821i	0.152874	−	0.137886i
$736$		0			0
$737$	4.11734	+	12.6719i	0.151664	+	0.466774i
$738$		0			0
$739$	−2.65822	+	8.18116i	−0.0977842	+	0.300949i	−0.987969	−	0.154650i	$-0.950575\pi$
$739$	−2.65822	+	8.18116i	−0.0977842	+	0.300949i	0.890185	+	0.455599i	$0.150575\pi$
$740$		0			0
$741$	7.51519	+	23.1294i	0.276077	+	0.849678i
$742$		0			0
$743$	−35.1466			−1.28940			−0.644701	−	0.764435i	$-0.723018\pi$
$743$	−35.1466			−1.28940			−0.644701	+	0.764435i	$0.723018\pi$
$744$		0			0
$745$	−7.15801	+	33.8182i	−0.262249	+	1.23900i
$746$		0			0
$747$	−32.9407	−	23.9328i	−1.20524	−	0.875655i
$748$		0			0
$749$	−46.2930			−1.69151
$750$		0			0
$751$	13.0807			0.477320			0.238660	−	0.971103i	$-0.423292\pi$
$751$	13.0807			0.477320			0.238660	+	0.971103i	$0.423292\pi$
$752$		0			0
$753$	6.08473	+	4.42082i	0.221740	+	0.161103i
$754$		0			0
$755$	−6.59804	+	31.1726i	−0.240127	+	1.13449i
$756$		0			0
$757$	13.4496			0.488833			0.244416	−	0.969670i	$-0.421404\pi$
$757$	13.4496			0.488833			0.244416	+	0.969670i	$0.421404\pi$
$758$		0			0
$759$	−1.43157	−	4.40591i	−0.0519626	−	0.159924i
$760$		0			0
$761$	12.3135	−	37.8969i	0.446363	−	1.37376i	−0.434620	−	0.900614i	$-0.643117\pi$
$761$	12.3135	−	37.8969i	0.446363	−	1.37376i	0.880983	−	0.473149i	$-0.156883\pi$
$762$		0			0
$763$	−8.27365	−	25.4637i	−0.299526	−	0.921846i
$764$		0			0
$765$	3.99496	−	3.60328i	0.144438	−	0.130277i
$766$		0			0
$767$	−69.1377	+	50.2315i	−2.49642	+	1.81375i
$768$		0			0
$769$	21.8466	−	15.8725i	0.787809	−	0.572377i	−0.119503	−	0.992834i	$-0.538130\pi$
$769$	21.8466	−	15.8725i	0.787809	−	0.572377i	0.907313	+	0.420457i	$0.138130\pi$
$770$		0			0
$771$	−7.11632	−	5.17031i	−0.256288	−	0.186204i
$772$		0			0
$773$	2.80456	−	8.63154i	0.100873	−	0.310455i	−0.887867	−	0.460101i	$-0.847813\pi$
$773$	2.80456	−	8.63154i	0.100873	−	0.310455i	0.988740	+	0.149646i	$0.0478133\pi$
$774$		0			0
$775$	13.6077	−	2.91679i	0.488804	−	0.104774i
$776$		0			0
$777$	−1.03503	+	3.18549i	−0.0371314	+	0.114279i
$778$		0			0
$779$	37.9170	+	27.5483i	1.35852	+	0.987020i
$780$		0			0
$781$	25.2980	−	18.3801i	0.905233	−	0.657690i
$782$		0			0
$783$	19.1732	−	13.9302i	0.685196	−	0.497824i
$784$		0			0
$785$	−10.2745	+	48.5422i	−0.366712	+	1.73254i
$786$		0			0
$787$	7.41857	+	22.8320i	0.264443	+	0.813873i	0.991821	+	0.127636i	$0.0407389\pi$
$787$	7.41857	+	22.8320i	0.264443	+	0.813873i	−0.727378	+	0.686237i	$0.759261\pi$
$788$		0			0
$789$	3.82703	−	11.7784i	0.136246	−	0.419322i
$790$		0			0
$791$	12.5054	+	38.4877i	0.444642	+	1.36847i
$792$		0			0
$793$	−20.3567			−0.722887
$794$		0			0
$795$	1.87180	−	0.198356i	0.0663859	−	0.00703495i
$796$		0			0
$797$	12.0077	+	8.72413i	0.425336	+	0.309024i	0.779781	−	0.626052i	$-0.215330\pi$
$797$	12.0077	+	8.72413i	0.425336	+	0.309024i	−0.354445	+	0.935077i	$0.615330\pi$
$798$		0			0
$799$	−2.58122			−0.0913171
$800$		0			0
$801$	−27.4094			−0.968465
$802$		0			0
$803$	26.7601	+	19.4423i	0.944342	+	0.686105i
$804$		0			0
$805$	13.4859	+	7.77070i	0.475316	+	0.273881i
$806$		0			0
$807$	−3.50933			−0.123534
$808$		0			0
$809$	7.53093	+	23.1778i	0.264774	+	0.814889i	0.991745	+	0.128222i	$0.0409270\pi$
$809$	7.53093	+	23.1778i	0.264774	+	0.814889i	−0.726972	+	0.686667i	$0.759073\pi$
$810$		0			0
$811$	14.4170	−	44.3708i	0.506248	−	1.55807i	−0.292415	−	0.956292i	$-0.594459\pi$
$811$	14.4170	−	44.3708i	0.506248	−	1.55807i	0.798663	−	0.601779i	$-0.205541\pi$
$812$		0			0
$813$	3.77753	+	11.6260i	0.132484	+	0.407743i
$814$		0			0
$815$	10.2936	−	1.09082i	0.360569	−	0.0382097i
$816$		0			0
$817$	−36.9109	+	26.8173i	−1.29135	+	0.938220i
$818$		0			0
$819$	40.2465	−	29.2408i	1.40633	−	1.02176i
$820$		0			0
$821$	16.5688	+	12.0380i	0.578256	+	0.420128i	0.838095	−	0.545524i	$-0.183669\pi$
$821$	16.5688	+	12.0380i	0.578256	+	0.420128i	−0.259839	+	0.965652i	$0.583669\pi$
$822$		0			0
$823$	−12.1750	+	37.4708i	−0.424394	+	1.30615i	0.479179	+	0.877717i	$0.340934\pi$
$823$	−12.1750	+	37.4708i	−0.424394	+	1.30615i	−0.903573	+	0.428433i	$0.859066\pi$
$824$		0			0
$825$	10.5973	−	2.27150i	0.368950	−	0.0790836i
$826$		0			0
$827$	−5.47685	+	16.8560i	−0.190449	+	0.586141i	−1.00000		0.000908626i	$-0.999711\pi$
$827$	−5.47685	+	16.8560i	−0.190449	+	0.586141i	0.809551	+	0.587050i	$0.199711\pi$
$828$		0			0
$829$	13.2105	+	9.59799i	0.458820	+	0.333352i	0.793068	−	0.609133i	$-0.208482\pi$
$829$	13.2105	+	9.59799i	0.458820	+	0.333352i	−0.334248	+	0.942485i	$0.608482\pi$
$830$		0			0
$831$	−5.18265	+	3.76542i	−0.179784	+	0.130621i
$832$		0			0
$833$	2.78490	−	2.02335i	0.0964911	−	0.0701049i
$834$		0			0
$835$	−0.588180	−	1.31803i	−0.0203548	−	0.0456125i
$836$		0			0
$837$	−3.28604	−	10.1134i	−0.113582	−	0.349570i
$838$		0			0
$839$	2.09291	−	6.44132i	0.0722554	−	0.222379i	−0.908407	−	0.418087i	$-0.862701\pi$
$839$	2.09291	−	6.44132i	0.0722554	−	0.222379i	0.980662	+	0.195708i	$0.0627006\pi$
$840$		0			0
$841$	2.92948	+	9.01600i	0.101016	+	0.310897i
$842$		0			0
$843$	7.50499			0.258486
$844$		0			0
$845$	−21.6019	−	48.4070i	−0.743127	−	1.66525i
$846$		0			0
$847$	−3.12895	−	2.27331i	−0.107512	−	0.0781119i
$848$		0			0
$849$	14.0086			0.480773
$850$		0			0
$851$	−3.17637			−0.108885
$852$		0			0
$853$	−35.8258	−	26.0290i	−1.22665	−	0.891216i	−0.230018	−	0.973186i	$-0.573879\pi$
$853$	−35.8258	−	26.0290i	−1.22665	−	0.891216i	−0.996635	+	0.0819706i	$0.973879\pi$
$854$		0			0
$855$	24.2843	−	21.9034i	0.830506	−	0.749080i
$856$		0			0
$857$	1.65123			0.0564049			0.0282024	−	0.999602i	$-0.491022\pi$
$857$	1.65123			0.0564049			0.0282024	+	0.999602i	$0.491022\pi$
$858$		0			0
$859$	0.210413	+	0.647586i	0.00717921	+	0.0220953i	0.954582	−	0.297948i	$-0.0963024\pi$
$859$	0.210413	+	0.647586i	0.00717921	+	0.0220953i	−0.947403	+	0.320044i	$0.896302\pi$
$860$		0			0
$861$	−5.62661	+	17.3169i	−0.191754	+	0.590160i
$862$		0			0
$863$	7.60286	+	23.3992i	0.258804	+	0.796517i	0.993056	+	0.117640i	$0.0375330\pi$
$863$	7.60286	+	23.3992i	0.258804	+	0.796517i	−0.734252	+	0.678877i	$0.762467\pi$
$864$		0			0
$865$	20.8621	+	12.0209i	0.709333	+	0.408724i
$866$		0			0
$867$	9.00708	−	6.54403i	0.305896	−	0.222247i
$868$		0			0
$869$	9.57742	−	6.95840i	0.324892	−	0.236048i
$870$		0			0
$871$	20.8483	+	15.1472i	0.706419	+	0.513243i
$872$		0			0
$873$	−3.75343	+	11.5519i	−0.127034	+	0.390972i
$874$		0			0
$875$	−21.3271	+	29.5135i	−0.720989	+	0.997739i
$876$		0			0
$877$	−14.0950	+	43.3799i	−0.475954	+	1.46484i	0.368712	+	0.929544i	$0.379799\pi$
$877$	−14.0950	+	43.3799i	−0.475954	+	1.46484i	−0.844666	+	0.535293i	$0.820201\pi$
$878$		0			0
$879$	−0.0497222	−	0.0361253i	−0.00167709	−	0.00121848i
$880$		0			0
$881$	−40.9097	+	29.7226i	−1.37828	+	1.00138i	−0.381244	+	0.924475i	$0.624504\pi$
$881$	−40.9097	+	29.7226i	−1.37828	+	1.00138i	−0.997038	+	0.0769061i	$0.975496\pi$
$882$		0			0
$883$	−36.8222	+	26.7529i	−1.23917	+	0.900307i	−0.997543	−	0.0700628i	$-0.977680\pi$
$883$	−36.8222	+	26.7529i	−1.23917	+	0.900307i	−0.241624	+	0.970370i	$0.577680\pi$
$884$		0			0
$885$	−18.9107	−	10.8965i	−0.635676	−	0.366282i
$886$		0			0
$887$	1.12281	+	3.45567i	0.0377004	+	0.116030i	0.968136	−	0.250427i	$-0.0805709\pi$
$887$	1.12281	+	3.45567i	0.0377004	+	0.116030i	−0.930435	+	0.366456i	$0.880571\pi$
$888$		0			0
$889$	6.05082	−	18.6225i	0.202938	−	0.624579i
$890$		0			0
$891$	4.76236	+	14.6570i	0.159545	+	0.491030i
$892$		0			0
$893$	−15.6906			−0.525065
$894$		0			0
$895$	−9.97259	+	8.99485i	−0.333347	+	0.300665i
$896$		0			0
$897$	−7.24880	−	5.26656i	−0.242030	−	0.175845i
$898$		0			0
$899$	17.2658			0.575848
$900$		0			0
$901$	1.16091			0.0386754
$902$		0			0
$903$	−14.3398	−	10.4185i	−0.477199	−	0.346705i
$904$		0			0
$905$	−1.42233	−	3.18726i	−0.0472800	−	0.105948i
$906$		0			0
$907$	7.74465			0.257157			0.128578	−	0.991699i	$-0.458959\pi$
$907$	7.74465			0.257157			0.128578	+	0.991699i	$0.458959\pi$
$908$		0			0
$909$	−0.667395	−	2.05403i	−0.0221361	−	0.0681279i
$910$		0			0
$911$	−14.6994	+	45.2402i	−0.487014	+	1.49888i	0.342028	+	0.939690i	$0.388886\pi$
$911$	−14.6994	+	45.2402i	−0.487014	+	1.49888i	−0.829042	+	0.559186i	$0.811114\pi$
$912$		0			0
$913$	−15.6330	−	48.1136i	−0.517378	−	1.59233i
$914$		0			0
$915$	−2.11866	−	4.74763i	−0.0700406	−	0.156952i
$916$		0			0
$917$	11.9677	−	8.69502i	0.395207	−	0.287135i
$918$		0			0
$919$	4.41767	−	3.20962i	0.145725	−	0.105876i	−0.512534	−	0.858667i	$-0.671293\pi$
$919$	4.41767	−	3.20962i	0.145725	−	0.105876i	0.658259	+	0.752791i	$0.271293\pi$
$920$		0			0
$921$	−8.74110	−	6.35078i	−0.288029	−	0.209265i
$922$		0			0
$923$	18.6892	−	57.5193i	0.615161	−	1.89327i
$924$		0			0
$925$	0.764093	−	7.39167i	0.0251232	−	0.243037i
$926$		0			0
$927$	−15.5283	+	47.7913i	−0.510018	+	1.56967i
$928$		0			0
$929$	−35.6216	−	25.8806i	−1.16871	−	0.849114i	−0.177852	−	0.984057i	$-0.556915\pi$
$929$	−35.6216	−	25.8806i	−1.16871	−	0.849114i	−0.990853	+	0.134943i	$0.956915\pi$
$930$		0			0
$931$	16.9287	−	12.2994i	0.554815	−	0.403097i
$932$		0			0
$933$	−10.0401	+	7.29457i	−0.328699	+	0.238814i
$934$		0			0
$935$	6.64716	−	0.704403i	0.217385	−	0.0230364i
$936$		0			0
$937$	4.38581	+	13.4981i	0.143278	+	0.440965i	0.996786	−	0.0801161i	$-0.0255291\pi$
$937$	4.38581	+	13.4981i	0.143278	+	0.440965i	−0.853507	+	0.521081i	$0.825529\pi$
$938$		0			0
$939$	2.53875	−	7.81347i	0.0828490	−	0.254983i
$940$		0			0
$941$	−2.07545	−	6.38758i	−0.0676577	−	0.208229i	0.911512	−	0.411274i	$-0.134916\pi$
$941$	−2.07545	−	6.38758i	−0.0676577	−	0.208229i	−0.979169	+	0.203045i	$0.934916\pi$
$942$		0			0
$943$	−17.2674			−0.562304
$944$		0			0
$945$	24.1074	+	13.8909i	0.784213	+	0.451870i
$946$		0			0
$947$	17.7763	+	12.9153i	0.577653	+	0.419690i	0.837877	−	0.545859i	$-0.183796\pi$
$947$	17.7763	+	12.9153i	0.577653	+	0.419690i	−0.260224	+	0.965548i	$0.583796\pi$
$948$		0			0
$949$	63.9748			2.07671
$950$		0			0
$951$	−17.1357			−0.555664
$952$		0			0
$953$	43.9673	+	31.9441i	1.42424	+	1.03477i	0.991053	+	0.133467i	$0.0426109\pi$
$953$	43.9673	+	31.9441i	1.42424	+	1.03477i	0.433187	+	0.901304i	$0.357389\pi$
$954$		0			0
$955$	37.0649	−	3.92778i	1.19939	−	0.127100i
$956$		0			0
$957$	13.4461			0.434650
$958$		0			0
$959$	−0.878480	−	2.70368i	−0.0283676	−	0.0873065i
$960$		0			0
$961$	−7.18553	+	22.1148i	−0.231791	+	0.713381i
$962$		0			0
$963$	−11.0739	−	34.0820i	−0.356852	−	1.09828i
$964$		0			0
$965$	−3.53865	+	16.7185i	−0.113913	+	0.538187i
$966$		0			0
$967$	25.8178	−	18.7577i	0.830243	−	0.603207i	−0.0893847	−	0.995997i	$-0.528490\pi$
$967$	25.8178	−	18.7577i	0.830243	−	0.603207i	0.919628	+	0.392790i	$0.128490\pi$
$968$		0			0
$969$	−3.09908	+	2.25161i	−0.0995568	+	0.0723323i
$970$		0			0
$971$	29.5803	+	21.4913i	0.949276	+	0.689689i	0.950636	−	0.310310i	$-0.100433\pi$
$971$	29.5803	+	21.4913i	0.949276	+	0.689689i	−0.00135957	+	0.999999i	$0.500433\pi$
$972$		0			0
$973$	−7.37454	+	22.6965i	−0.236417	+	0.727617i
$974$		0			0
$975$	13.9994	−	15.6016i	0.448341	−	0.499652i
$976$		0			0
$977$	−7.39316	+	22.7538i	−0.236528	+	0.727959i	0.760387	+	0.649470i	$0.225009\pi$
$977$	−7.39316	+	22.7538i	−0.236528	+	0.727959i	−0.996915	+	0.0784882i	$0.974991\pi$
$978$		0			0
$979$	−27.5514	−	20.0173i	−0.880548	−	0.639755i
$980$		0			0
$981$	16.7678	−	12.1825i	0.535354	−	0.388957i
$982$		0			0
$983$	29.3423	−	21.3184i	0.935875	−	0.679953i	−0.0115495	−	0.999933i	$-0.503676\pi$
$983$	29.3423	−	21.3184i	0.935875	−	0.679953i	0.947424	+	0.319981i	$0.103676\pi$
$984$		0			0
$985$	37.5176	−	33.8393i	1.19541	−	1.07821i
$986$		0			0
$987$	−1.88369	−	5.79741i	−0.0599586	−	0.184534i
$988$		0			0
$989$	5.19434	−	15.9865i	0.165170	−	0.508343i
$990$		0			0
$991$	7.69069	+	23.6695i	0.244303	+	0.751887i	0.995750	+	0.0920941i	$0.0293561\pi$
$991$	7.69069	+	23.6695i	0.244303	+	0.751887i	−0.751447	+	0.659793i	$0.770644\pi$
$992$		0			0
$993$	13.2480			0.420412
$994$		0			0
$995$	−0.246340	+	1.16384i	−0.00780951	+	0.0368963i
$996$		0			0
$997$	−33.8140	−	24.5673i	−1.07090	−	0.778055i	−0.0948267	−	0.995494i	$-0.530230\pi$
$997$	−33.8140	−	24.5673i	−1.07090	−	0.778055i	−0.976074	+	0.217439i	$0.930230\pi$
$998$		0			0
$999$	−5.67807			−0.179646

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.u.f.321.2		12
4.3	odd	2		100.2.g.a.21.2	✓	12
12.11	even	2		900.2.n.c.721.2		12
20.3	even	4		500.2.i.b.149.3		24
20.7	even	4		500.2.i.b.149.4		24
20.19	odd	2		500.2.g.a.101.2		12
25.6	even	5	inner	400.2.u.f.81.2		12
25.9	even	10		10000.2.a.bd.1.3		6
25.16	even	5		10000.2.a.bc.1.4		6
100.19	odd	10		500.2.g.a.401.2		12
100.31	odd	10		100.2.g.a.81.2	yes	12
100.59	odd	10		2500.2.a.c.1.4		6
100.63	even	20		2500.2.c.c.1249.5		12
100.67	even	20		500.2.i.b.349.3		24
100.83	even	20		500.2.i.b.349.4		24
100.87	even	20		2500.2.c.c.1249.8		12
100.91	odd	10		2500.2.a.d.1.3		6
300.131	even	10		900.2.n.c.181.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.2.g.a.21.2	✓	12	4.3	odd	2
100.2.g.a.81.2	yes	12	100.31	odd	10
400.2.u.f.81.2		12	25.6	even	5	inner
400.2.u.f.321.2		12	1.1	even	1	trivial
500.2.g.a.101.2		12	20.19	odd	2
500.2.g.a.401.2		12	100.19	odd	10
500.2.i.b.149.3		24	20.3	even	4
500.2.i.b.149.4		24	20.7	even	4
500.2.i.b.349.3		24	100.67	even	20
500.2.i.b.349.4		24	100.83	even	20
900.2.n.c.181.2		12	300.131	even	10
900.2.n.c.721.2		12	12.11	even	2
2500.2.a.c.1.4		6	100.59	odd	10
2500.2.a.d.1.3		6	100.91	odd	10
2500.2.c.c.1249.5		12	100.63	even	20
2500.2.c.c.1249.8		12	100.87	even	20
10000.2.a.bc.1.4		6	25.16	even	5
10000.2.a.bd.1.3		6	25.9	even	10

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.559818 - 0.406731i) q^{3} +(-0.463031 + 2.18760i) q^{5} -3.25686 q^{7} +(-0.779086 - 2.39778i) q^{9} +O(q^{10})\)	\(q+(-0.559818 - 0.406731i) q^{3} +(-0.463031 + 2.18760i) q^{5} -3.25686 q^{7} +(-0.779086 - 2.39778i) q^{9} +(0.967992 - 2.97917i) q^{11} +(-1.87219 - 5.76202i) q^{13} +(1.14898 - 1.03633i) q^{15} +(0.772048 - 0.560925i) q^{17} +(4.69307 - 3.40972i) q^{19} +(1.82325 + 1.32467i) q^{21} +(-0.660440 + 2.03262i) q^{23} +(-4.57121 - 2.02585i) q^{25} +(-1.18060 + 3.63351i) q^{27} +(-5.01851 - 3.64616i) q^{29} +(-2.25179 + 1.63602i) q^{31} +(-1.75362 + 1.27408i) q^{33} +(1.50803 - 7.12472i) q^{35} +(0.459265 + 1.41347i) q^{37} +(-1.29551 + 3.98716i) q^{39} +(2.49665 + 7.68391i) q^{41} -7.86497 q^{43} +(5.60613 - 0.594084i) q^{45} +(-2.18825 - 1.58986i) q^{47} +3.60716 q^{49} -0.660352 q^{51} +(0.984166 + 0.715038i) q^{53} +(6.06903 + 3.49703i) q^{55} -4.01411 q^{57} +(-4.35884 - 13.4151i) q^{59} +(1.03830 - 3.19554i) q^{61} +(2.53738 + 7.80924i) q^{63} +(13.4719 - 1.42762i) q^{65} +(-3.44114 + 2.50014i) q^{67} +(1.19646 - 0.869278i) q^{69} +(8.07600 + 5.86756i) q^{71} +(-3.26304 + 10.0426i) q^{73} +(1.73506 + 2.99336i) q^{75} +(-3.15262 + 9.70276i) q^{77} +(3.05745 + 2.22137i) q^{79} +(-3.98023 + 2.89181i) q^{81} +(13.0656 - 9.49272i) q^{83} +(0.869600 + 1.94866i) q^{85} +(1.32644 + 4.08237i) q^{87} +(3.35954 - 10.3396i) q^{89} +(6.09748 + 18.7661i) q^{91} +1.92601 q^{93} +(5.28607 + 11.8454i) q^{95} +(-3.89763 - 2.83180i) q^{97} -7.89755 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} - 4 q^{5} + 2 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q - 2 * q^3 - 4 * q^5 + 2 * q^7 - 3 * q^9	\( 12 q - 2 q^{3} - 4 q^{5} + 2 q^{7} - 3 q^{9} + 5 q^{11} - 2 q^{13} - 18 q^{15} + q^{17} + 8 q^{19} + 2 q^{21} + 6 q^{23} - 26 q^{25} + 34 q^{27} - 18 q^{29} - 12 q^{31} - 35 q^{33} + 3 q^{35} + 13 q^{37} - 22 q^{39} - 23 q^{41} - 50 q^{43} + 71 q^{45} - q^{47} + 34 q^{49} - 14 q^{51} + 21 q^{53} - 5 q^{55} + 72 q^{57} - 9 q^{59} - 26 q^{61} + 32 q^{63} - 18 q^{65} + 37 q^{67} - 44 q^{69} - 21 q^{71} + 18 q^{73} + 73 q^{75} - 60 q^{77} + 24 q^{79} + 18 q^{81} + 46 q^{83} - 16 q^{85} - 57 q^{87} - 2 q^{89} + 32 q^{91} + 22 q^{93} - 6 q^{95} - 7 q^{97} - 40 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 - 4 * q^5 + 2 * q^7 - 3 * q^9 + 5 * q^11 - 2 * q^13 - 18 * q^15 + q^17 + 8 * q^19 + 2 * q^21 + 6 * q^23 - 26 * q^25 + 34 * q^27 - 18 * q^29 - 12 * q^31 - 35 * q^33 + 3 * q^35 + 13 * q^37 - 22 * q^39 - 23 * q^41 - 50 * q^43 + 71 * q^45 - q^47 + 34 * q^49 - 14 * q^51 + 21 * q^53 - 5 * q^55 + 72 * q^57 - 9 * q^59 - 26 * q^61 + 32 * q^63 - 18 * q^65 + 37 * q^67 - 44 * q^69 - 21 * q^71 + 18 * q^73 + 73 * q^75 - 60 * q^77 + 24 * q^79 + 18 * q^81 + 46 * q^83 - 16 * q^85 - 57 * q^87 - 2 * q^89 + 32 * q^91 + 22 * q^93 - 6 * q^95 - 7 * q^97 - 40 * q^99

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