LMFDB - Embedded newform 1232.2.q.f.177.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,2,Mod(177,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1232.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.q (of order $3$, degree $2$, 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:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1232.177
Dual form			1232.2.q.f.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20711 - 2.09077i) q^{3} +(0.292893 - 0.507306i) q^{5} +(-1.62132 - 2.09077i) q^{7} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})$	\(q+(-1.20711 - 2.09077i) q^{3} +(0.292893 - 0.507306i) q^{5} +(-1.62132 - 2.09077i) q^{7} +(-1.41421 + 2.44949i) q^{9} +(0.500000 + 0.866025i) q^{11} -3.82843 q^{13} -1.41421 q^{15} +(-1.82843 - 3.16693i) q^{17} +(-0.292893 + 0.507306i) q^{19} +(-2.41421 + 5.91359i) q^{21} +(-3.12132 + 5.40629i) q^{23} +(2.32843 + 4.03295i) q^{25} -0.414214 q^{27} +2.65685 q^{29} +(-2.00000 - 3.46410i) q^{31} +(1.20711 - 2.09077i) q^{33} +(-1.53553 + 0.210133i) q^{35} +(4.70711 - 8.15295i) q^{37} +(4.62132 + 8.00436i) q^{39} -5.41421 q^{41} +5.65685 q^{43} +(0.828427 + 1.43488i) q^{45} +(-5.24264 + 9.08052i) q^{47} +(-1.74264 + 6.77962i) q^{49} +(-4.41421 + 7.64564i) q^{51} +(-3.94975 - 6.84116i) q^{53} +0.585786 q^{55} +1.41421 q^{57} +(-2.79289 - 4.83743i) q^{59} +(-5.91421 + 10.2437i) q^{61} +(7.41421 - 1.01461i) q^{63} +(-1.12132 + 1.94218i) q^{65} +(1.37868 + 2.38794i) q^{67} +15.0711 q^{69} +11.0711 q^{71} +(4.70711 + 8.15295i) q^{73} +(5.62132 - 9.73641i) q^{75} +(1.00000 - 2.44949i) q^{77} +(-6.62132 + 11.4685i) q^{79} +(4.74264 + 8.21449i) q^{81} +12.1421 q^{83} -2.14214 q^{85} +(-3.20711 - 5.55487i) q^{87} +(-6.24264 + 10.8126i) q^{89} +(6.20711 + 8.00436i) q^{91} +(-4.82843 + 8.36308i) q^{93} +(0.171573 + 0.297173i) q^{95} -3.82843 q^{97} -2.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 4 q^{5} + 2 q^{7}+O(q^{10}) $ 4 * q - 2 * q^3 + 4 * q^5 + 2 * q^7	$ 4 q - 2 q^{3} + 4 q^{5} + 2 q^{7} + 2 q^{11} - 4 q^{13} + 4 q^{17} - 4 q^{19} - 4 q^{21} - 4 q^{23} - 2 q^{25} + 4 q^{27} - 12 q^{29} - 8 q^{31} + 2 q^{33} + 8 q^{35} + 16 q^{37} + 10 q^{39} - 16 q^{41} - 8 q^{45} - 4 q^{47} + 10 q^{49} - 12 q^{51} + 4 q^{53} + 8 q^{55} - 14 q^{59} - 18 q^{61} + 24 q^{63} + 4 q^{65} + 14 q^{67} + 32 q^{69} + 16 q^{71} + 16 q^{73} + 14 q^{75} + 4 q^{77} - 18 q^{79} + 2 q^{81} - 8 q^{83} + 48 q^{85} - 10 q^{87} - 8 q^{89} + 22 q^{91} - 8 q^{93} + 12 q^{95} - 4 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 + 4 * q^5 + 2 * q^7 + 2 * q^11 - 4 * q^13 + 4 * q^17 - 4 * q^19 - 4 * q^21 - 4 * q^23 - 2 * q^25 + 4 * q^27 - 12 * q^29 - 8 * q^31 + 2 * q^33 + 8 * q^35 + 16 * q^37 + 10 * q^39 - 16 * q^41 - 8 * q^45 - 4 * q^47 + 10 * q^49 - 12 * q^51 + 4 * q^53 + 8 * q^55 - 14 * q^59 - 18 * q^61 + 24 * q^63 + 4 * q^65 + 14 * q^67 + 32 * q^69 + 16 * q^71 + 16 * q^73 + 14 * q^75 + 4 * q^77 - 18 * q^79 + 2 * q^81 - 8 * q^83 + 48 * q^85 - 10 * q^87 - 8 * q^89 + 22 * q^91 - 8 * q^93 + 12 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	−1.20711	−	2.09077i	−0.696923	−	1.20711i	−0.969528	−	0.244981i	$-0.921218\pi$
$3$	−1.20711	−	2.09077i	−0.696923	−	1.20711i	0.272605	−	0.962126i	$-0.412115\pi$
$4$		0			0
$5$	0.292893	−	0.507306i	0.130986	−	0.226874i	−0.793071	−	0.609129i	$-0.791519\pi$
$5$	0.292893	−	0.507306i	0.130986	−	0.226874i	0.924057	+	0.382255i	$0.124852\pi$
$6$		0			0
$7$	−1.62132	−	2.09077i	−0.612801	−	0.790237i
$7$	−1.62132	−	2.09077i	−0.612801	−	0.790237i
$8$		0			0
$9$	−1.41421	+	2.44949i	−0.471405	+	0.816497i
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$		0			0
$13$	−3.82843			−1.06181			−0.530907	−	0.847430i	$-0.678149\pi$
$13$	−3.82843			−1.06181			−0.530907	+	0.847430i	$0.678149\pi$
$14$		0			0
$15$	−1.41421			−0.365148
$16$		0			0
$17$	−1.82843	−	3.16693i	−0.443459	−	0.768093i	0.554485	−	0.832194i	$-0.312915\pi$
$17$	−1.82843	−	3.16693i	−0.443459	−	0.768093i	−0.997943	+	0.0641009i	$0.979582\pi$
$18$		0			0
$19$	−0.292893	+	0.507306i	−0.0671943	+	0.116384i	−0.897665	−	0.440678i	$-0.854738\pi$
$19$	−0.292893	+	0.507306i	−0.0671943	+	0.116384i	0.830471	+	0.557062i	$0.188071\pi$
$20$		0			0
$21$	−2.41421	+	5.91359i	−0.526825	+	1.29045i
$22$		0			0
$23$	−3.12132	+	5.40629i	−0.650840	+	1.12729i	0.332079	+	0.943252i	$0.392250\pi$
$23$	−3.12132	+	5.40629i	−0.650840	+	1.12729i	−0.982919	+	0.184037i	$0.941083\pi$
$24$		0			0
$25$	2.32843	+	4.03295i	0.465685	+	0.806591i
$26$		0			0
$27$	−0.414214			−0.0797154
$28$		0			0
$29$	2.65685			0.493365			0.246683	−	0.969096i	$-0.420659\pi$
$29$	2.65685			0.493365			0.246683	+	0.969096i	$0.420659\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$		0			0
$33$	1.20711	−	2.09077i	0.210130	−	0.363956i
$34$		0			0
$35$	−1.53553	+	0.210133i	−0.259553	+	0.0355190i
$36$		0			0
$37$	4.70711	−	8.15295i	0.773844	−	1.34034i	−0.161599	−	0.986857i	$-0.551665\pi$
$37$	4.70711	−	8.15295i	0.773844	−	1.34034i	0.935442	−	0.353480i	$-0.115002\pi$
$38$		0			0
$39$	4.62132	+	8.00436i	0.740003	+	1.28172i
$40$		0			0
$41$	−5.41421			−0.845558			−0.422779	−	0.906233i	$-0.638945\pi$
$41$	−5.41421			−0.845558			−0.422779	+	0.906233i	$0.638945\pi$
$42$		0			0
$43$	5.65685			0.862662			0.431331	−	0.902194i	$-0.358044\pi$
$43$	5.65685			0.862662			0.431331	+	0.902194i	$0.358044\pi$
$44$		0			0
$45$	0.828427	+	1.43488i	0.123495	+	0.213899i
$46$		0			0
$47$	−5.24264	+	9.08052i	−0.764718	+	1.32453i	0.175678	+	0.984448i	$0.443788\pi$
$47$	−5.24264	+	9.08052i	−0.764718	+	1.32453i	−0.940396	+	0.340082i	$0.889545\pi$
$48$		0			0
$49$	−1.74264	+	6.77962i	−0.248949	+	0.968517i
$50$		0			0
$51$	−4.41421	+	7.64564i	−0.618114	+	1.07060i
$52$		0			0
$53$	−3.94975	−	6.84116i	−0.542540	−	0.939706i	−0.998757	−	0.0498379i	$-0.984130\pi$
$53$	−3.94975	−	6.84116i	−0.542540	−	0.939706i	0.456218	−	0.889868i	$-0.349204\pi$
$54$		0			0
$55$	0.585786			0.0789874
$56$		0			0
$57$	1.41421			0.187317
$58$		0			0
$59$	−2.79289	−	4.83743i	−0.363604	−	0.629780i	0.624947	−	0.780667i	$-0.285120\pi$
$59$	−2.79289	−	4.83743i	−0.363604	−	0.629780i	−0.988551	+	0.150887i	$0.951787\pi$
$60$		0			0
$61$	−5.91421	+	10.2437i	−0.757237	+	1.31157i	0.187017	+	0.982357i	$0.440118\pi$
$61$	−5.91421	+	10.2437i	−0.757237	+	1.31157i	−0.944254	+	0.329217i	$0.893215\pi$
$62$		0			0
$63$	7.41421	−	1.01461i	0.934103	−	0.127829i
$64$		0			0
$65$	−1.12132	+	1.94218i	−0.139083	+	0.240898i
$66$		0			0
$67$	1.37868	+	2.38794i	0.168433	+	0.291734i	0.937869	−	0.346990i	$-0.112796\pi$
$67$	1.37868	+	2.38794i	0.168433	+	0.291734i	−0.769436	+	0.638723i	$0.779463\pi$
$68$		0			0
$69$	15.0711			1.81434
$70$		0			0
$71$	11.0711			1.31389			0.656947	−	0.753937i	$-0.271848\pi$
$71$	11.0711			1.31389			0.656947	+	0.753937i	$0.271848\pi$
$72$		0			0
$73$	4.70711	+	8.15295i	0.550925	+	0.954230i	0.998208	+	0.0598379i	$0.0190584\pi$
$73$	4.70711	+	8.15295i	0.550925	+	0.954230i	−0.447283	+	0.894393i	$0.647608\pi$
$74$		0			0
$75$	5.62132	−	9.73641i	0.649094	−	1.12426i
$76$		0			0
$77$	1.00000	−	2.44949i	0.113961	−	0.279145i
$78$		0			0
$79$	−6.62132	+	11.4685i	−0.744957	+	1.29030i	0.205258	+	0.978708i	$0.434197\pi$
$79$	−6.62132	+	11.4685i	−0.744957	+	1.29030i	−0.950215	+	0.311595i	$0.899137\pi$
$80$		0			0
$81$	4.74264	+	8.21449i	0.526960	+	0.912722i
$82$		0			0
$83$	12.1421			1.33277			0.666386	−	0.745607i	$-0.267840\pi$
$83$	12.1421			1.33277			0.666386	+	0.745607i	$0.267840\pi$
$84$		0			0
$85$	−2.14214			−0.232347
$86$		0			0
$87$	−3.20711	−	5.55487i	−0.343838	−	0.595545i
$88$		0			0
$89$	−6.24264	+	10.8126i	−0.661719	+	1.14613i	0.318445	+	0.947941i	$0.396839\pi$
$89$	−6.24264	+	10.8126i	−0.661719	+	1.14613i	−0.980164	+	0.198189i	$0.936494\pi$
$90$		0			0
$91$	6.20711	+	8.00436i	0.650682	+	0.839085i
$92$		0			0
$93$	−4.82843	+	8.36308i	−0.500685	+	0.867211i
$94$		0			0
$95$	0.171573	+	0.297173i	0.0176030	+	0.0304893i
$96$		0			0
$97$	−3.82843			−0.388718			−0.194359	−	0.980930i	$-0.562263\pi$
$97$	−3.82843			−0.388718			−0.194359	+	0.980930i	$0.562263\pi$
$98$		0			0
$99$	−2.82843			−0.284268
$100$		0			0
$101$	−3.08579	−	5.34474i	−0.307047	−	0.531821i	0.670668	−	0.741758i	$-0.266008\pi$
$101$	−3.08579	−	5.34474i	−0.307047	−	0.531821i	−0.977715	+	0.209936i	$0.932674\pi$
$102$		0			0
$103$	6.70711	−	11.6170i	0.660871	−	1.14466i	−0.319516	−	0.947581i	$-0.603520\pi$
$103$	6.70711	−	11.6170i	0.660871	−	1.14466i	0.980387	−	0.197081i	$-0.0631462\pi$
$104$		0			0
$105$	2.29289	+	2.95680i	0.223763	+	0.288554i
$106$		0			0
$107$	−1.53553	+	2.65962i	−0.148446	+	0.257115i	−0.930653	−	0.365903i	$-0.880760\pi$
$107$	−1.53553	+	2.65962i	−0.148446	+	0.257115i	0.782207	+	0.623018i	$0.214094\pi$
$108$		0			0
$109$	−8.24264	−	14.2767i	−0.789502	−	1.36746i	−0.926272	−	0.376854i	$-0.877006\pi$
$109$	−8.24264	−	14.2767i	−0.789502	−	1.36746i	0.136771	−	0.990603i	$-0.456328\pi$
$110$		0			0
$111$	−22.7279			−2.15724
$112$		0			0
$113$	−8.17157			−0.768717			−0.384358	−	0.923184i	$-0.625577\pi$
$113$	−8.17157			−0.768717			−0.384358	+	0.923184i	$0.625577\pi$
$114$		0			0
$115$	1.82843	+	3.16693i	0.170502	+	0.295318i
$116$		0			0
$117$	5.41421	−	9.37769i	0.500544	−	0.866968i
$118$		0			0
$119$	−3.65685	+	8.95743i	−0.335223	+	0.821126i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	6.53553	+	11.3199i	0.589289	+	1.02068i
$124$		0			0
$125$	5.65685			0.505964
$126$		0			0
$127$	−15.7279			−1.39563			−0.697814	−	0.716279i	$-0.745844\pi$
$127$	−15.7279			−1.39563			−0.697814	+	0.716279i	$0.745844\pi$
$128$		0			0
$129$	−6.82843	−	11.8272i	−0.601209	−	1.04133i
$130$		0			0
$131$	−0.292893	+	0.507306i	−0.0255902	+	0.0443235i	−0.878537	−	0.477674i	$-0.841480\pi$
$131$	−0.292893	+	0.507306i	−0.0255902	+	0.0443235i	0.852947	+	0.521998i	$0.174813\pi$
$132$		0			0
$133$	1.53553	−	0.210133i	0.133148	−	0.0182208i
$134$		0			0
$135$	−0.121320	+	0.210133i	−0.0104416	+	0.0180854i
$136$		0			0
$137$	8.32843	+	14.4253i	0.711546	+	1.23243i	0.964277	+	0.264897i	$0.0853378\pi$
$137$	8.32843	+	14.4253i	0.711546	+	1.23243i	−0.252731	+	0.967537i	$0.581329\pi$
$138$		0			0
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		0			0
$141$	25.3137			2.13180
$142$		0			0
$143$	−1.91421	−	3.31552i	−0.160075	−	0.277257i
$144$		0			0
$145$	0.778175	−	1.34784i	0.0646239	−	0.111932i
$146$		0			0
$147$	16.2782	−	4.54026i	1.34260	−	0.374474i
$148$		0			0
$149$	−8.82843	+	15.2913i	−0.723253	+	1.25271i	0.236436	+	0.971647i	$0.424021\pi$
$149$	−8.82843	+	15.2913i	−0.723253	+	1.25271i	−0.959689	+	0.281064i	$0.909313\pi$
$150$		0			0
$151$	−7.86396	−	13.6208i	−0.639960	−	1.10844i	−0.985441	−	0.170018i	$-0.945618\pi$
$151$	−7.86396	−	13.6208i	−0.639960	−	1.10844i	0.345481	−	0.938426i	$-0.387716\pi$
$152$		0			0
$153$	10.3431			0.836194
$154$		0			0
$155$	−2.34315			−0.188206
$156$		0			0
$157$	−8.82843	−	15.2913i	−0.704585	−	1.22038i	−0.966841	−	0.255379i	$-0.917800\pi$
$157$	−8.82843	−	15.2913i	−0.704585	−	1.22038i	0.262256	−	0.964998i	$-0.415534\pi$
$158$		0			0
$159$	−9.53553	+	16.5160i	−0.756217	+	1.30981i
$160$		0			0
$161$	16.3640	−	2.23936i	1.28966	−	0.176486i
$162$		0			0
$163$	4.86396	−	8.42463i	0.380975	−	0.659868i	−0.610227	−	0.792227i	$-0.708922\pi$
$163$	4.86396	−	8.42463i	0.380975	−	0.659868i	0.991202	+	0.132359i	$0.0422551\pi$
$164$		0			0
$165$	−0.707107	−	1.22474i	−0.0550482	−	0.0953463i
$166$		0			0
$167$	−13.7279			−1.06230			−0.531149	−	0.847278i	$-0.678240\pi$
$167$	−13.7279			−1.06230			−0.531149	+	0.847278i	$0.678240\pi$
$168$		0			0
$169$	1.65685			0.127450
$170$		0			0
$171$	−0.828427	−	1.43488i	−0.0633514	−	0.109728i
$172$		0			0
$173$	4.91421	−	8.51167i	0.373621	−	0.647130i	−0.616499	−	0.787356i	$-0.711449\pi$
$173$	4.91421	−	8.51167i	0.373621	−	0.647130i	0.990120	+	0.140226i	$0.0447828\pi$
$174$		0			0
$175$	4.65685	−	11.4069i	0.352025	−	0.862282i
$176$		0			0
$177$	−6.74264	+	11.6786i	−0.506808	+	0.877817i
$178$		0			0
$179$	0.449747	+	0.778985i	0.0336157	+	0.0582241i	0.882344	−	0.470605i	$-0.155964\pi$
$179$	0.449747	+	0.778985i	0.0336157	+	0.0582241i	−0.848728	+	0.528829i	$0.822631\pi$
$180$		0			0
$181$	−7.65685			−0.569129			−0.284565	−	0.958657i	$-0.591849\pi$
$181$	−7.65685			−0.569129			−0.284565	+	0.958657i	$0.591849\pi$
$182$		0			0
$183$	28.5563			2.11095
$184$		0			0
$185$	−2.75736	−	4.77589i	−0.202725	−	0.351130i
$186$		0			0
$187$	1.82843	−	3.16693i	0.133708	−	0.231589i
$188$		0			0
$189$	0.671573	+	0.866025i	0.0488497	+	0.0629941i
$190$		0			0
$191$	−3.58579	+	6.21076i	−0.259458	+	0.449395i	−0.966097	−	0.258180i	$-0.916877\pi$
$191$	−3.58579	+	6.21076i	−0.259458	+	0.449395i	0.706639	+	0.707575i	$0.250211\pi$
$192$		0			0
$193$	−10.9497	−	18.9655i	−0.788180	−	1.36517i	−0.927081	−	0.374862i	$-0.877690\pi$
$193$	−10.9497	−	18.9655i	−0.788180	−	1.36517i	0.138901	−	0.990306i	$-0.455643\pi$
$194$		0			0
$195$	5.41421			0.387720
$196$		0			0
$197$	−0.514719			−0.0366722			−0.0183361	−	0.999832i	$-0.505837\pi$
$197$	−0.514719			−0.0366722			−0.0183361	+	0.999832i	$0.505837\pi$
$198$		0			0
$199$	0.0502525	+	0.0870399i	0.00356231	+	0.00617010i	0.867801	−	0.496912i	$-0.165533\pi$
$199$	0.0502525	+	0.0870399i	0.00356231	+	0.00617010i	−0.864239	+	0.503082i	$0.832199\pi$
$200$		0			0
$201$	3.32843	−	5.76500i	0.234769	−	0.406632i
$202$		0			0
$203$	−4.30761	−	5.55487i	−0.302335	−	0.389876i
$204$		0			0
$205$	−1.58579	+	2.74666i	−0.110756	+	0.191835i
$206$		0			0
$207$	−8.82843	−	15.2913i	−0.613618	−	1.06282i
$208$		0			0
$209$	−0.585786			−0.0405197
$210$		0			0
$211$	−7.41421			−0.510416			−0.255208	−	0.966886i	$-0.582144\pi$
$211$	−7.41421			−0.510416			−0.255208	+	0.966886i	$0.582144\pi$
$212$		0			0
$213$	−13.3640	−	23.1471i	−0.915684	−	1.58601i
$214$		0			0
$215$	1.65685	−	2.86976i	0.112997	−	0.195716i
$216$		0			0
$217$	−4.00000	+	9.79796i	−0.271538	+	0.665129i
$218$		0			0
$219$	11.3640	−	19.6830i	0.767905	−	1.33005i
$220$		0			0
$221$	7.00000	+	12.1244i	0.470871	+	0.815572i
$222$		0			0
$223$	−8.58579			−0.574947			−0.287473	−	0.957789i	$-0.592815\pi$
$223$	−8.58579			−0.574947			−0.287473	+	0.957789i	$0.592815\pi$
$224$		0			0
$225$	−13.1716			−0.878105
$226$		0			0
$227$	−14.4142	−	24.9662i	−0.956705	−	1.65706i	−0.730417	−	0.683001i	$-0.760674\pi$
$227$	−14.4142	−	24.9662i	−0.956705	−	1.65706i	−0.226288	−	0.974061i	$-0.572659\pi$
$228$		0			0
$229$	−11.6569	+	20.1903i	−0.770307	+	1.33421i	0.167088	+	0.985942i	$0.446564\pi$
$229$	−11.6569	+	20.1903i	−0.770307	+	1.33421i	−0.937395	+	0.348268i	$0.886770\pi$
$230$		0			0
$231$	−6.32843	+	0.866025i	−0.416380	+	0.0569803i
$232$		0			0
$233$	−0.707107	+	1.22474i	−0.0463241	+	0.0802357i	−0.888258	−	0.459345i	$-0.848084\pi$
$233$	−0.707107	+	1.22474i	−0.0463241	+	0.0802357i	0.841934	+	0.539581i	$0.181417\pi$
$234$		0			0
$235$	3.07107	+	5.31925i	0.200334	+	0.346989i
$236$		0			0
$237$	31.9706			2.07671
$238$		0			0
$239$	−20.2132			−1.30748			−0.653742	−	0.756718i	$-0.726802\pi$
$239$	−20.2132			−1.30748			−0.653742	+	0.756718i	$0.726802\pi$
$240$		0			0
$241$	−6.12132	−	10.6024i	−0.394309	−	0.682963i	0.598704	−	0.800971i	$-0.295683\pi$
$241$	−6.12132	−	10.6024i	−0.394309	−	0.682963i	−0.993013	+	0.118007i	$0.962349\pi$
$242$		0			0
$243$	10.8284	−	18.7554i	0.694644	−	1.20316i
$244$		0			0
$245$	2.92893	+	2.86976i	0.187123	+	0.183342i
$246$		0			0
$247$	1.12132	−	1.94218i	0.0713479	−	0.123578i
$248$		0			0
$249$	−14.6569	−	25.3864i	−0.928840	−	1.60880i
$250$		0			0
$251$	26.1421			1.65008			0.825038	−	0.565077i	$-0.191153\pi$
$251$	26.1421			1.65008			0.825038	+	0.565077i	$0.191153\pi$
$252$		0			0
$253$	−6.24264			−0.392471
$254$		0			0
$255$	2.58579	+	4.47871i	0.161928	+	0.280468i
$256$		0			0
$257$	12.5711	−	21.7737i	0.784162	−	1.35821i	−0.145337	−	0.989382i	$-0.546427\pi$
$257$	12.5711	−	21.7737i	0.784162	−	1.35821i	0.929499	−	0.368826i	$-0.120240\pi$
$258$		0			0
$259$	−24.6777	+	3.37706i	−1.53340	+	0.209840i
$260$		0			0
$261$	−3.75736	+	6.50794i	−0.232575	+	0.402831i
$262$		0			0
$263$	−8.52082	−	14.7585i	−0.525416	−	0.910047i	−0.999562	−	0.0296008i	$-0.990576\pi$
$263$	−8.52082	−	14.7585i	−0.525416	−	0.910047i	0.474146	−	0.880446i	$-0.342757\pi$
$264$		0			0
$265$	−4.62742			−0.284260
$266$		0			0
$267$	30.1421			1.84467
$268$		0			0
$269$	−1.17157	−	2.02922i	−0.0714321	−	0.123724i	0.828097	−	0.560585i	$-0.189424\pi$
$269$	−1.17157	−	2.02922i	−0.0714321	−	0.123724i	−0.899529	+	0.436861i	$0.856090\pi$
$270$		0			0
$271$	2.27817	−	3.94591i	0.138389	−	0.239697i	−0.788498	−	0.615038i	$-0.789141\pi$
$271$	2.27817	−	3.94591i	0.138389	−	0.239697i	0.926887	+	0.375340i	$0.122474\pi$
$272$		0			0
$273$	9.24264	−	22.6398i	0.559390	−	1.37022i
$274$		0			0
$275$	−2.32843	+	4.03295i	−0.140409	+	0.243196i
$276$		0			0
$277$	−0.914214	−	1.58346i	−0.0549298	−	0.0951412i	0.837253	−	0.546816i	$-0.184160\pi$
$277$	−0.914214	−	1.58346i	−0.0549298	−	0.0951412i	−0.892183	+	0.451675i	$0.850827\pi$
$278$		0			0
$279$	11.3137			0.677334
$280$		0			0
$281$	8.72792			0.520664			0.260332	−	0.965519i	$-0.416168\pi$
$281$	8.72792			0.520664			0.260332	+	0.965519i	$0.416168\pi$
$282$		0			0
$283$	−11.7071	−	20.2773i	−0.695915	−	1.20536i	−0.969871	−	0.243618i	$-0.921666\pi$
$283$	−11.7071	−	20.2773i	−0.695915	−	1.20536i	0.273956	−	0.961742i	$-0.411668\pi$
$284$		0			0
$285$	0.414214	−	0.717439i	0.0245359	−	0.0424974i
$286$		0			0
$287$	8.77817	+	11.3199i	0.518159	+	0.668191i
$288$		0			0
$289$	1.81371	−	3.14144i	0.106689	−	0.184790i
$290$		0			0
$291$	4.62132	+	8.00436i	0.270907	+	0.469224i
$292$		0			0
$293$	−10.8284			−0.632603			−0.316302	−	0.948659i	$-0.602441\pi$
$293$	−10.8284			−0.632603			−0.316302	+	0.948659i	$0.602441\pi$
$294$		0			0
$295$	−3.27208			−0.190508
$296$		0			0
$297$	−0.207107	−	0.358719i	−0.0120176	−	0.0208150i
$298$		0			0
$299$	11.9497	−	20.6976i	0.691072	−	1.19697i
$300$		0			0
$301$	−9.17157	−	11.8272i	−0.528641	−	0.681707i
$302$		0			0
$303$	−7.44975	+	12.9033i	−0.427977	+	0.741278i
$304$		0			0
$305$	3.46447	+	6.00063i	0.198375	+	0.343595i
$306$		0			0
$307$	−9.89949			−0.564994			−0.282497	−	0.959268i	$-0.591163\pi$
$307$	−9.89949			−0.564994			−0.282497	+	0.959268i	$0.591163\pi$
$308$		0			0
$309$	−32.3848			−1.84231
$310$		0			0
$311$	8.36396	+	14.4868i	0.474277	+	0.821471i	0.999566	−	0.0294522i	$-0.00937629\pi$
$311$	8.36396	+	14.4868i	0.474277	+	0.821471i	−0.525289	+	0.850924i	$0.676043\pi$
$312$		0			0
$313$	10.3284	−	17.8894i	0.583797	−	1.01117i	−0.411227	−	0.911533i	$-0.634900\pi$
$313$	10.3284	−	17.8894i	0.583797	−	1.01117i	0.995024	−	0.0996335i	$-0.0317670\pi$
$314$		0			0
$315$	1.65685	−	4.05845i	0.0933532	−	0.228668i
$316$		0			0
$317$	−4.34315	+	7.52255i	−0.243935	+	0.422508i	−0.961832	−	0.273642i	$-0.911772\pi$
$317$	−4.34315	+	7.52255i	−0.243935	+	0.422508i	0.717896	+	0.696150i	$0.245105\pi$
$318$		0			0
$319$	1.32843	+	2.30090i	0.0743776	+	0.128826i
$320$		0			0
$321$	7.41421			0.413821
$322$		0			0
$323$	2.14214			0.119192
$324$		0			0
$325$	−8.91421	−	15.4399i	−0.494472	−	0.856450i
$326$		0			0
$327$	−19.8995	+	34.4669i	−1.10044	+	1.90603i
$328$		0			0
$329$	27.4853	−	3.76127i	1.51531	−	0.207366i
$330$		0			0
$331$	−12.0355	+	20.8462i	−0.661533	+	1.14581i	0.318680	+	0.947862i	$0.396760\pi$
$331$	−12.0355	+	20.8462i	−0.661533	+	1.14581i	−0.980213	+	0.197946i	$0.936573\pi$
$332$		0			0
$333$	13.3137	+	23.0600i	0.729587	+	1.26368i
$334$		0			0
$335$	1.61522			0.0882491
$336$		0			0
$337$	−28.2426			−1.53847			−0.769237	−	0.638963i	$-0.779364\pi$
$337$	−28.2426			−1.53847			−0.769237	+	0.638963i	$0.779364\pi$
$338$		0			0
$339$	9.86396	+	17.0849i	0.535737	+	0.927923i
$340$		0			0
$341$	2.00000	−	3.46410i	0.108306	−	0.187592i
$342$		0			0
$343$	17.0000	−	7.34847i	0.917914	−	0.396780i
$344$		0			0
$345$	4.41421	−	7.64564i	0.237653	−	0.411628i
$346$		0			0
$347$	8.70711	+	15.0812i	0.467422	+	0.809599i	0.999307	−	0.0372179i	$-0.0118495\pi$
$347$	8.70711	+	15.0812i	0.467422	+	0.809599i	−0.531885	+	0.846816i	$0.678516\pi$
$348$		0			0
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$		0			0
$351$	1.58579			0.0846430
$352$		0			0
$353$	1.34315	+	2.32640i	0.0714884	+	0.123822i	0.899554	−	0.436810i	$-0.143892\pi$
$353$	1.34315	+	2.32640i	0.0714884	+	0.123822i	−0.828065	+	0.560632i	$0.810558\pi$
$354$		0			0
$355$	3.24264	−	5.61642i	0.172101	−	0.298089i
$356$		0			0
$357$	23.1421	−	3.16693i	1.22481	−	0.167612i
$358$		0			0
$359$	9.62132	−	16.6646i	0.507794	−	0.879525i	−0.492165	−	0.870502i	$-0.663794\pi$
$359$	9.62132	−	16.6646i	0.507794	−	0.879525i	0.999959	−	0.00902308i	$-0.00287218\pi$
$360$		0			0
$361$	9.32843	+	16.1573i	0.490970	+	0.850385i
$362$		0			0
$363$	2.41421			0.126713
$364$		0			0
$365$	5.51472			0.288654
$366$		0			0
$367$	−5.36396	−	9.29065i	−0.279996	−	0.484968i	0.691387	−	0.722485i	$-0.257000\pi$
$367$	−5.36396	−	9.29065i	−0.279996	−	0.484968i	−0.971384	+	0.237516i	$0.923667\pi$
$368$		0			0
$369$	7.65685	−	13.2621i	0.398600	−	0.690395i
$370$		0			0
$371$	−7.89949	+	19.3497i	−0.410121	+	1.00459i
$372$		0			0
$373$	9.98528	−	17.2950i	0.517018	−	0.895502i	−0.482786	−	0.875738i	$-0.660375\pi$
$373$	9.98528	−	17.2950i	0.517018	−	0.895502i	0.999805	−	0.0197638i	$-0.00629142\pi$
$374$		0			0
$375$	−6.82843	−	11.8272i	−0.352618	−	0.610753i
$376$		0			0
$377$	−10.1716			−0.523863
$378$		0			0
$379$	−27.8701			−1.43159			−0.715794	−	0.698311i	$-0.753935\pi$
$379$	−27.8701			−1.43159			−0.715794	+	0.698311i	$0.753935\pi$
$380$		0			0
$381$	18.9853	+	32.8835i	0.972645	+	1.68467i
$382$		0			0
$383$	−3.19239	+	5.52938i	−0.163123	+	0.282538i	−0.935987	−	0.352034i	$-0.885490\pi$
$383$	−3.19239	+	5.52938i	−0.163123	+	0.282538i	0.772864	+	0.634572i	$0.218824\pi$
$384$		0			0
$385$	−0.949747	−	1.22474i	−0.0484036	−	0.0624188i
$386$		0			0
$387$	−8.00000	+	13.8564i	−0.406663	+	0.704361i
$388$		0			0
$389$	11.3640	+	19.6830i	0.576176	+	0.997966i	0.995913	+	0.0903199i	$0.0287889\pi$
$389$	11.3640	+	19.6830i	0.576176	+	0.997966i	−0.419737	+	0.907646i	$0.637878\pi$
$390$		0			0
$391$	22.8284			1.15448
$392$		0			0
$393$	1.41421			0.0713376
$394$		0			0
$395$	3.87868	+	6.71807i	0.195158	+	0.338023i
$396$		0			0
$397$	−11.0000	+	19.0526i	−0.552074	+	0.956221i	0.446051	+	0.895008i	$0.352830\pi$
$397$	−11.0000	+	19.0526i	−0.552074	+	0.956221i	−0.998125	+	0.0612128i	$0.980503\pi$
$398$		0			0
$399$	−2.29289	−	2.95680i	−0.114788	−	0.148025i
$400$		0			0
$401$	−9.15685	+	15.8601i	−0.457271	+	0.792017i	−0.998816	−	0.0486549i	$-0.984507\pi$
$401$	−9.15685	+	15.8601i	−0.457271	+	0.792017i	0.541544	+	0.840672i	$0.317840\pi$
$402$		0			0
$403$	7.65685	+	13.2621i	0.381415	+	0.660630i
$404$		0			0
$405$	5.55635			0.276097
$406$		0			0
$407$	9.41421			0.466645
$408$		0			0
$409$	−1.36396	−	2.36245i	−0.0674435	−	0.116816i	0.830332	−	0.557269i	$-0.188151\pi$
$409$	−1.36396	−	2.36245i	−0.0674435	−	0.116816i	−0.897775	+	0.440454i	$0.854818\pi$
$410$		0			0
$411$	20.1066	−	34.8257i	0.991786	−	1.71782i
$412$		0			0
$413$	−5.58579	+	13.6823i	−0.274859	+	0.673263i
$414$		0			0
$415$	3.55635	−	6.15978i	0.174574	−	0.302372i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	26.1421			1.27713			0.638563	−	0.769569i	$-0.279529\pi$
$419$	26.1421			1.27713			0.638563	+	0.769569i	$0.279529\pi$
$420$		0			0
$421$	0.686292			0.0334478			0.0167239	−	0.999860i	$-0.494676\pi$
$421$	0.686292			0.0334478			0.0167239	+	0.999860i	$0.494676\pi$
$422$		0			0
$423$	−14.8284	−	25.6836i	−0.720983	−	1.24878i
$424$		0			0
$425$	8.51472	−	14.7479i	0.413025	−	0.715379i
$426$		0			0
$427$	31.0061	−	4.24309i	1.50049	−	0.205337i
$428$		0			0
$429$	−4.62132	+	8.00436i	−0.223119	+	0.386454i
$430$		0			0
$431$	−8.79289	−	15.2297i	−0.423539	−	0.733591i	0.572744	−	0.819734i	$-0.305879\pi$
$431$	−8.79289	−	15.2297i	−0.423539	−	0.733591i	−0.996283	+	0.0861437i	$0.972546\pi$
$432$		0			0
$433$	26.1421			1.25631			0.628155	−	0.778088i	$-0.283810\pi$
$433$	26.1421			1.25631			0.628155	+	0.778088i	$0.283810\pi$
$434$		0			0
$435$	−3.75736			−0.180152
$436$		0			0
$437$	−1.82843	−	3.16693i	−0.0874655	−	0.151495i
$438$		0			0
$439$	−13.6924	+	23.7159i	−0.653502	+	1.13190i	0.328765	+	0.944412i	$0.393368\pi$
$439$	−13.6924	+	23.7159i	−0.653502	+	1.13190i	−0.982267	+	0.187487i	$0.939966\pi$
$440$		0			0
$441$	−14.1421	−	13.8564i	−0.673435	−	0.659829i
$442$		0			0
$443$	6.31371	−	10.9357i	0.299973	−	0.519569i	−0.676156	−	0.736758i	$-0.736356\pi$
$443$	6.31371	−	10.9357i	0.299973	−	0.519569i	0.976130	+	0.217189i	$0.0696889\pi$
$444$		0			0
$445$	3.65685	+	6.33386i	0.173352	+	0.300254i
$446$		0			0
$447$	42.6274			2.01621
$448$		0			0
$449$	22.3431			1.05444			0.527219	−	0.849729i	$-0.323235\pi$
$449$	22.3431			1.05444			0.527219	+	0.849729i	$0.323235\pi$
$450$		0			0
$451$	−2.70711	−	4.68885i	−0.127473	−	0.220789i
$452$		0			0
$453$	−18.9853	+	32.8835i	−0.892006	+	1.54500i
$454$		0			0
$455$	5.87868	−	0.804479i	0.275597	−	0.0377146i
$456$		0			0
$457$	5.82843	−	10.0951i	0.272642	−	0.472230i	−0.696895	−	0.717173i	$-0.745436\pi$
$457$	5.82843	−	10.0951i	0.272642	−	0.472230i	0.969538	+	0.244943i	$0.0787691\pi$
$458$		0			0
$459$	0.757359	+	1.31178i	0.0353505	+	0.0612289i
$460$		0			0
$461$	−8.31371			−0.387208			−0.193604	−	0.981080i	$-0.562018\pi$
$461$	−8.31371			−0.387208			−0.193604	+	0.981080i	$0.562018\pi$
$462$		0			0
$463$	−12.8284			−0.596188			−0.298094	−	0.954537i	$-0.596351\pi$
$463$	−12.8284			−0.596188			−0.298094	+	0.954537i	$0.596351\pi$
$464$		0			0
$465$	2.82843	+	4.89898i	0.131165	+	0.227185i
$466$		0			0
$467$	−17.0000	+	29.4449i	−0.786666	+	1.36255i	0.141332	+	0.989962i	$0.454861\pi$
$467$	−17.0000	+	29.4449i	−0.786666	+	1.36255i	−0.927999	+	0.372584i	$0.878472\pi$
$468$		0			0
$469$	2.75736	−	6.75412i	0.127323	−	0.311876i
$470$		0			0
$471$	−21.3137	+	36.9164i	−0.982084	+	1.70102i
$472$		0			0
$473$	2.82843	+	4.89898i	0.130051	+	0.225255i
$474$		0			0
$475$	−2.72792			−0.125166
$476$		0			0
$477$	22.3431			1.02302
$478$		0			0
$479$	−5.96447	−	10.3308i	−0.272523	−	0.472024i	0.696984	−	0.717087i	$-0.254525\pi$
$479$	−5.96447	−	10.3308i	−0.272523	−	0.472024i	−0.969507	+	0.245062i	$0.921192\pi$
$480$		0			0
$481$	−18.0208	+	31.2130i	−0.821678	+	1.42319i
$482$		0			0
$483$	−24.4350	−	31.5101i	−1.11183	−	1.43376i
$484$		0			0
$485$	−1.12132	+	1.94218i	−0.0509165	+	0.0881900i
$486$		0			0
$487$	−4.82843	−	8.36308i	−0.218797	−	0.378967i	0.735644	−	0.677369i	$-0.236880\pi$
$487$	−4.82843	−	8.36308i	−0.218797	−	0.378967i	−0.954440	+	0.298402i	$0.903547\pi$
$488$		0			0
$489$	−23.4853			−1.06204
$490$		0			0
$491$	−19.1716			−0.865201			−0.432600	−	0.901586i	$-0.642404\pi$
$491$	−19.1716			−0.865201			−0.432600	+	0.901586i	$0.642404\pi$
$492$		0			0
$493$	−4.85786	−	8.41407i	−0.218787	−	0.378951i
$494$		0			0
$495$	−0.828427	+	1.43488i	−0.0372350	+	0.0644930i
$496$		0			0
$497$	−17.9497	−	23.1471i	−0.805156	−	1.03829i
$498$		0			0
$499$	11.0711	−	19.1757i	0.495609	−	0.858420i	−0.504378	−	0.863483i	$-0.668278\pi$
$499$	11.0711	−	19.1757i	0.495609	−	0.858420i	0.999987	+	0.00506282i	$0.00161155\pi$
$500$		0			0
$501$	16.5711	+	28.7019i	0.740341	+	1.28231i
$502$		0			0
$503$	−4.21320			−0.187857			−0.0939287	−	0.995579i	$-0.529943\pi$
$503$	−4.21320			−0.187857			−0.0939287	+	0.995579i	$0.529943\pi$
$504$		0			0
$505$	−3.61522			−0.160875
$506$		0			0
$507$	−2.00000	−	3.46410i	−0.0888231	−	0.153846i
$508$		0			0
$509$	−4.65685	+	8.06591i	−0.206411	+	0.357515i	−0.950582	−	0.310475i	$-0.899512\pi$
$509$	−4.65685	+	8.06591i	−0.206411	+	0.357515i	0.744170	+	0.667990i	$0.232845\pi$
$510$		0			0
$511$	9.41421	−	23.0600i	0.416460	−	1.02012i
$512$		0			0
$513$	0.121320	−	0.210133i	0.00535642	−	0.00927760i
$514$		0			0
$515$	−3.92893	−	6.80511i	−0.173129	−	0.299869i
$516$		0			0
$517$	−10.4853			−0.461142
$518$		0			0
$519$	−23.7279			−1.04154
$520$		0			0
$521$	14.1421	+	24.4949i	0.619578	+	1.07314i	0.989563	+	0.144103i	$0.0460297\pi$
$521$	14.1421	+	24.4949i	0.619578	+	1.07314i	−0.369984	+	0.929038i	$0.620637\pi$
$522$		0			0
$523$	−6.36396	+	11.0227i	−0.278277	+	0.481989i	−0.970957	−	0.239256i	$-0.923097\pi$
$523$	−6.36396	+	11.0227i	−0.278277	+	0.481989i	0.692680	+	0.721245i	$0.256430\pi$
$524$		0			0
$525$	−29.4706	+	4.03295i	−1.28620	+	0.176013i
$526$		0			0
$527$	−7.31371	+	12.6677i	−0.318590	+	0.551814i
$528$		0			0
$529$	−7.98528	−	13.8309i	−0.347186	−	0.601344i
$530$		0			0
$531$	15.7990			0.685618
$532$		0			0
$533$	20.7279			0.897826
$534$		0			0
$535$	0.899495	+	1.55797i	0.0388886	+	0.0673570i
$536$		0			0
$537$	1.08579	−	1.88064i	0.0468551	−	0.0811555i
$538$		0			0
$539$	−6.74264	+	1.88064i	−0.290426	+	0.0810048i
$540$		0			0
$541$	6.42893	−	11.1352i	0.276401	−	0.478741i	−0.694086	−	0.719892i	$-0.744191\pi$
$541$	6.42893	−	11.1352i	0.276401	−	0.478741i	0.970488	+	0.241151i	$0.0775248\pi$
$542$		0			0
$543$	9.24264	+	16.0087i	0.396640	+	0.687000i
$544$		0			0
$545$	−9.65685			−0.413654
$546$		0			0
$547$	−34.8701			−1.49094			−0.745468	−	0.666541i	$-0.767774\pi$
$547$	−34.8701			−1.49094			−0.745468	+	0.666541i	$0.767774\pi$
$548$		0			0
$549$	−16.7279	−	28.9736i	−0.713930	−	1.23656i
$550$		0			0
$551$	−0.778175	+	1.34784i	−0.0331514	+	0.0574198i
$552$		0			0
$553$	34.7132	−	4.75039i	1.47616	−	0.202007i
$554$		0			0
$555$	−6.65685	+	11.5300i	−0.282568	+	0.489422i
$556$		0			0
$557$	−3.75736	−	6.50794i	−0.159204	−	0.275750i	0.775378	−	0.631498i	$-0.217560\pi$
$557$	−3.75736	−	6.50794i	−0.159204	−	0.275750i	−0.934582	+	0.355748i	$0.884226\pi$
$558$		0			0
$559$	−21.6569			−0.915987
$560$		0			0
$561$	−8.82843			−0.372736
$562$		0			0
$563$	4.53553	+	7.85578i	0.191150	+	0.331081i	0.945632	−	0.325240i	$-0.105445\pi$
$563$	4.53553	+	7.85578i	0.191150	+	0.331081i	−0.754482	+	0.656321i	$0.772112\pi$
$564$		0			0
$565$	−2.39340	+	4.14549i	−0.100691	+	0.174402i
$566$		0			0
$567$	9.48528	−	23.2341i	0.398344	−	0.975740i
$568$		0			0
$569$	2.00000	−	3.46410i	0.0838444	−	0.145223i	−0.821054	−	0.570851i	$-0.806613\pi$
$569$	2.00000	−	3.46410i	0.0838444	−	0.145223i	0.904898	+	0.425628i	$0.139947\pi$
$570$		0			0
$571$	13.1924	+	22.8499i	0.552084	+	0.956238i	0.998124	+	0.0612248i	$0.0195007\pi$
$571$	13.1924	+	22.8499i	0.552084	+	0.956238i	−0.446040	+	0.895013i	$0.647166\pi$
$572$		0			0
$573$	17.3137			0.723291
$574$		0			0
$575$	−29.0711			−1.21235
$576$		0			0
$577$	4.84315	+	8.38857i	0.201623	+	0.349221i	0.949051	−	0.315121i	$-0.102045\pi$
$577$	4.84315	+	8.38857i	0.201623	+	0.349221i	−0.747429	+	0.664342i	$0.768712\pi$
$578$		0			0
$579$	−26.4350	+	45.7868i	−1.09860	+	1.90284i
$580$		0			0
$581$	−19.6863	−	25.3864i	−0.816725	−	1.05321i
$582$		0			0
$583$	3.94975	−	6.84116i	0.163582	−	0.283332i
$584$		0			0
$585$	−3.17157	−	5.49333i	−0.131128	−	0.227121i
$586$		0			0
$587$	25.1005			1.03601			0.518004	−	0.855378i	$-0.326675\pi$
$587$	25.1005			1.03601			0.518004	+	0.855378i	$0.326675\pi$
$588$		0			0
$589$	2.34315			0.0965476
$590$		0			0
$591$	0.621320	+	1.07616i	0.0255577	+	0.0442672i
$592$		0			0
$593$	−11.8492	+	20.5235i	−0.486590	+	0.842799i	−0.999881	−	0.0154159i	$-0.995093\pi$
$593$	−11.8492	+	20.5235i	−0.486590	+	0.842799i	0.513291	+	0.858215i	$0.328426\pi$
$594$		0			0
$595$	3.47309	+	4.47871i	0.142383	+	0.183609i
$596$		0			0
$597$	0.121320	−	0.210133i	0.00496531	−	0.00860017i
$598$		0			0
$599$	21.3137	+	36.9164i	0.870855	+	1.50836i	0.861114	+	0.508412i	$0.169767\pi$
$599$	21.3137	+	36.9164i	0.870855	+	1.50836i	0.00974040	+	0.999953i	$0.496899\pi$
$600$		0			0
$601$	31.9411			1.30291			0.651453	−	0.758689i	$-0.274160\pi$
$601$	31.9411			1.30291			0.651453	+	0.758689i	$0.274160\pi$
$602$		0			0
$603$	−7.79899			−0.317599
$604$		0			0
$605$	0.292893	+	0.507306i	0.0119078	+	0.0206249i
$606$		0			0
$607$	−21.4853	+	37.2136i	−0.872061	+	1.51045i	−0.0121994	+	0.999926i	$0.503883\pi$
$607$	−21.4853	+	37.2136i	−0.872061	+	1.51045i	−0.859861	+	0.510528i	$0.829450\pi$
$608$		0			0
$609$	−6.41421	+	15.7116i	−0.259917	+	0.636664i
$610$		0			0
$611$	20.0711	−	34.7641i	0.811988	−	1.40641i
$612$		0			0
$613$	−14.3137	−	24.7921i	−0.578125	−	1.00134i	−0.995694	−	0.0926971i	$-0.970451\pi$
$613$	−14.3137	−	24.7921i	−0.578125	−	1.00134i	0.417569	−	0.908645i	$-0.362882\pi$
$614$		0			0
$615$	7.65685			0.308754
$616$		0			0
$617$	−41.9706			−1.68967			−0.844836	−	0.535026i	$-0.820302\pi$
$617$	−41.9706			−1.68967			−0.844836	+	0.535026i	$0.820302\pi$
$618$		0			0
$619$	−10.9706	−	19.0016i	−0.440944	−	0.763738i	0.556816	−	0.830636i	$-0.312023\pi$
$619$	−10.9706	−	19.0016i	−0.440944	−	0.763738i	−0.997760	+	0.0668984i	$0.978690\pi$
$620$		0			0
$621$	1.29289	−	2.23936i	0.0518820	−	0.0898623i
$622$		0			0
$623$	32.7279	−	4.47871i	1.31122	−	0.179436i
$624$		0			0
$625$	−9.98528	+	17.2950i	−0.399411	+	0.691801i
$626$		0			0
$627$	0.707107	+	1.22474i	0.0282391	+	0.0489116i
$628$		0			0
$629$	−34.4264			−1.37267
$630$		0			0
$631$	−23.2721			−0.926447			−0.463223	−	0.886242i	$-0.653307\pi$
$631$	−23.2721			−0.926447			−0.463223	+	0.886242i	$0.653307\pi$
$632$		0			0
$633$	8.94975	+	15.5014i	0.355721	+	0.616126i
$634$		0			0
$635$	−4.60660	+	7.97887i	−0.182807	+	0.316632i
$636$		0			0
$637$	6.67157	−	25.9553i	0.264337	−	1.02839i
$638$		0			0
$639$	−15.6569	+	27.1185i	−0.619376	+	1.07279i
$640$		0			0
$641$	−7.64214	−	13.2366i	−0.301846	−	0.522813i	0.674708	−	0.738085i	$-0.264270\pi$
$641$	−7.64214	−	13.2366i	−0.301846	−	0.522813i	−0.976554	+	0.215272i	$0.930936\pi$
$642$		0			0
$643$	−1.58579			−0.0625373			−0.0312687	−	0.999511i	$-0.509955\pi$
$643$	−1.58579			−0.0625373			−0.0312687	+	0.999511i	$0.509955\pi$
$644$		0			0
$645$	−8.00000			−0.315000
$646$		0			0
$647$	15.0919	+	26.1399i	0.593323	+	1.02767i	0.993781	+	0.111351i	$0.0355177\pi$
$647$	15.0919	+	26.1399i	0.593323	+	1.02767i	−0.400458	+	0.916315i	$0.631149\pi$
$648$		0			0
$649$	2.79289	−	4.83743i	0.109631	−	0.189886i
$650$		0			0
$651$	25.3137	−	3.46410i	0.992122	−	0.135769i
$652$		0			0
$653$	9.19239	−	15.9217i	0.359726	−	0.623064i	−0.628189	−	0.778061i	$-0.716204\pi$
$653$	9.19239	−	15.9217i	0.359726	−	0.623064i	0.987915	+	0.154997i	$0.0495369\pi$
$654$		0			0
$655$	0.171573	+	0.297173i	0.00670391	+	0.0116115i
$656$		0			0
$657$	−26.6274			−1.03883
$658$		0			0
$659$	12.0000			0.467454			0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000			0.467454			0.233727	+	0.972302i	$0.424908\pi$
$660$		0			0
$661$	−9.48528	−	16.4290i	−0.368935	−	0.639014i	0.620465	−	0.784234i	$-0.286944\pi$
$661$	−9.48528	−	16.4290i	−0.368935	−	0.639014i	−0.989399	+	0.145221i	$0.953611\pi$
$662$		0			0
$663$	16.8995	−	29.2708i	0.656322	−	1.13678i
$664$		0			0
$665$	0.343146	−	0.840532i	0.0133066	−	0.0325944i
$666$		0			0
$667$	−8.29289	+	14.3637i	−0.321102	+	0.556165i
$668$		0			0
$669$	10.3640	+	17.9509i	0.400694	+	0.694022i
$670$		0			0
$671$	−11.8284			−0.456631
$672$		0			0
$673$	5.55635			0.214182			0.107091	−	0.994249i	$-0.465846\pi$
$673$	5.55635			0.214182			0.107091	+	0.994249i	$0.465846\pi$
$674$		0			0
$675$	−0.964466	−	1.67050i	−0.0371223	−	0.0642977i
$676$		0			0
$677$	17.6569	−	30.5826i	0.678608	−	1.17538i	−0.296792	−	0.954942i	$-0.595917\pi$
$677$	17.6569	−	30.5826i	0.678608	−	1.17538i	0.975400	−	0.220441i	$-0.0707498\pi$
$678$		0			0
$679$	6.20711	+	8.00436i	0.238207	+	0.307179i
$680$		0			0
$681$	−34.7990	+	60.2736i	−1.33350	+	2.30969i
$682$		0			0
$683$	6.79289	+	11.7656i	0.259923	+	0.450200i	0.966221	−	0.257715i	$-0.0829695\pi$
$683$	6.79289	+	11.7656i	0.259923	+	0.450200i	−0.706298	+	0.707914i	$0.749636\pi$
$684$		0			0
$685$	9.75736			0.372810
$686$		0			0
$687$	56.2843			2.14738
$688$		0			0
$689$	15.1213	+	26.1909i	0.576076	+	0.997794i
$690$		0			0
$691$	14.0355	−	24.3103i	0.533937	−	0.924806i	−0.465277	−	0.885165i	$-0.654045\pi$
$691$	14.0355	−	24.3103i	0.533937	−	0.924806i	0.999214	−	0.0396407i	$-0.0126213\pi$
$692$		0			0
$693$	4.58579	+	5.91359i	0.174200	+	0.224639i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	9.89949	+	17.1464i	0.374970	+	0.649467i
$698$		0			0
$699$	3.41421			0.129137
$700$		0			0
$701$	−26.1127			−0.986263			−0.493132	−	0.869955i	$-0.664148\pi$
$701$	−26.1127			−0.986263			−0.493132	+	0.869955i	$0.664148\pi$
$702$		0			0
$703$	2.75736	+	4.77589i	0.103996	+	0.180126i
$704$		0			0
$705$	7.41421	−	12.8418i	0.279235	−	0.483650i
$706$		0			0
$707$	−6.17157	+	15.1172i	−0.232106	+	0.568541i
$708$		0			0
$709$	6.02082	−	10.4284i	0.226116	−	0.391645i	−0.730537	−	0.682873i	$-0.760730\pi$
$709$	6.02082	−	10.4284i	0.226116	−	0.391645i	0.956654	+	0.291228i	$0.0940637\pi$
$710$		0			0
$711$	−18.7279	−	32.4377i	−0.702352	−	1.21651i
$712$		0			0
$713$	24.9706			0.935155
$714$		0			0
$715$	−2.24264			−0.0838700
$716$		0			0
$717$	24.3995	+	42.2612i	0.911216	+	1.57827i
$718$		0			0
$719$	−0.757359	+	1.31178i	−0.0282447	+	0.0489213i	−0.879802	−	0.475340i	$-0.842325\pi$
$719$	−0.757359	+	1.31178i	−0.0282447	+	0.0489213i	0.851558	+	0.524261i	$0.175658\pi$
$720$		0			0
$721$	−35.1630	+	4.81194i	−1.30954	+	0.179206i
$722$		0			0
$723$	−14.7782	+	25.5965i	−0.549606	+	0.951946i
$724$		0			0
$725$	6.18629	+	10.7150i	0.229753	+	0.397944i
$726$		0			0
$727$	−36.4264			−1.35098			−0.675490	−	0.737369i	$-0.736068\pi$
$727$	−36.4264			−1.35098			−0.675490	+	0.737369i	$0.736068\pi$
$728$		0			0
$729$	−23.8284			−0.882534
$730$		0			0
$731$	−10.3431	−	17.9149i	−0.382555	−	0.662605i
$732$		0			0
$733$	6.50000	−	11.2583i	0.240083	−	0.415836i	−0.720655	−	0.693294i	$-0.756159\pi$
$733$	6.50000	−	11.2583i	0.240083	−	0.415836i	0.960738	+	0.277458i	$0.0894920\pi$
$734$		0			0
$735$	2.46447	−	9.58783i	0.0909032	−	0.353652i
$736$		0			0
$737$	−1.37868	+	2.38794i	−0.0507843	+	0.0879610i
$738$		0			0
$739$	−26.2132	−	45.4026i	−0.964268	−	1.67016i	−0.711568	−	0.702617i	$-0.752015\pi$
$739$	−26.2132	−	45.4026i	−0.964268	−	1.67016i	−0.252700	−	0.967545i	$-0.581319\pi$
$740$		0			0
$741$	−5.41421			−0.198896
$742$		0			0
$743$	13.3137			0.488433			0.244216	−	0.969721i	$-0.421469\pi$
$743$	13.3137			0.488433			0.244216	+	0.969721i	$0.421469\pi$
$744$		0			0
$745$	5.17157	+	8.95743i	0.189472	+	0.328175i
$746$		0			0
$747$	−17.1716	+	29.7420i	−0.628275	+	1.08820i
$748$		0			0
$749$	8.05025	−	1.10165i	0.294150	−	0.0402535i
$750$		0			0
$751$	22.8284	−	39.5400i	0.833021	−	1.44283i	−0.0626103	−	0.998038i	$-0.519943\pi$
$751$	22.8284	−	39.5400i	0.833021	−	1.44283i	0.895631	−	0.444797i	$-0.146724\pi$
$752$		0			0
$753$	−31.5563	−	54.6572i	−1.14998	−	1.99182i
$754$		0			0
$755$	−9.21320			−0.335303
$756$		0			0
$757$	8.34315			0.303237			0.151618	−	0.988439i	$-0.451552\pi$
$757$	8.34315			0.303237			0.151618	+	0.988439i	$0.451552\pi$
$758$		0			0
$759$	7.53553	+	13.0519i	0.273523	+	0.473755i
$760$		0			0
$761$	−15.4853	+	26.8213i	−0.561341	+	0.972271i	0.436039	+	0.899928i	$0.356381\pi$
$761$	−15.4853	+	26.8213i	−0.561341	+	0.972271i	−0.997380	+	0.0723433i	$0.976952\pi$
$762$		0			0
$763$	−16.4853	+	40.3805i	−0.596807	+	1.46187i
$764$		0			0
$765$	3.02944	−	5.24714i	0.109530	−	0.189711i
$766$		0			0
$767$	10.6924	+	18.5198i	0.386080	+	0.668710i
$768$		0			0
$769$	22.9706			0.828340			0.414170	−	0.910200i	$-0.364072\pi$
$769$	22.9706			0.828340			0.414170	+	0.910200i	$0.364072\pi$
$770$		0			0
$771$	−60.6985			−2.18600
$772$		0			0
$773$	10.9706	+	19.0016i	0.394584	+	0.683439i	0.993048	−	0.117710i	$-0.0375555\pi$
$773$	10.9706	+	19.0016i	0.394584	+	0.683439i	−0.598464	+	0.801150i	$0.704222\pi$
$774$		0			0
$775$	9.31371	−	16.1318i	0.334558	−	0.579472i
$776$		0			0
$777$	36.8492	+	47.5189i	1.32196	+	1.70473i
$778$		0			0
$779$	1.58579	−	2.74666i	0.0568167	−	0.0984094i
$780$		0			0
$781$	5.53553	+	9.58783i	0.198077	+	0.343079i
$782$		0			0
$783$	−1.10051			−0.0393288
$784$		0			0
$785$	−10.3431			−0.369163
$786$		0			0
$787$	6.77817	+	11.7401i	0.241616	+	0.418491i	0.961175	−	0.275941i	$-0.0889893\pi$
$787$	6.77817	+	11.7401i	0.241616	+	0.418491i	−0.719559	+	0.694431i	$0.755656\pi$
$788$		0			0
$789$	−20.5711	+	35.6301i	−0.732349	+	1.26847i
$790$		0			0
$791$	13.2487	+	17.0849i	0.471071	+	0.607468i
$792$		0			0
$793$	22.6421	−	39.2173i	0.804046	−	1.39265i
$794$		0			0
$795$	5.58579	+	9.67487i	0.198107	+	0.343132i
$796$		0			0
$797$	−7.65685			−0.271220			−0.135610	−	0.990762i	$-0.543299\pi$
$797$	−7.65685			−0.271220			−0.135610	+	0.990762i	$0.543299\pi$
$798$		0			0
$799$	38.3431			1.35648
$800$		0			0
$801$	−17.6569	−	30.5826i	−0.623874	−	1.08058i
$802$		0			0
$803$	−4.70711	+	8.15295i	−0.166110	+	0.287711i
$804$		0			0
$805$	3.65685	−	8.95743i	0.128887	−	0.315708i
$806$		0			0
$807$	−2.82843	+	4.89898i	−0.0995654	+	0.172452i
$808$		0			0
$809$	23.3137	+	40.3805i	0.819666	+	1.41970i	0.905928	+	0.423431i	$0.139174\pi$
$809$	23.3137	+	40.3805i	0.819666	+	1.41970i	−0.0862619	+	0.996272i	$0.527492\pi$
$810$		0			0
$811$	24.2843			0.852736			0.426368	−	0.904550i	$-0.359793\pi$
$811$	24.2843			0.852736			0.426368	+	0.904550i	$0.359793\pi$
$812$		0			0
$813$	−11.0000			−0.385787
$814$		0			0
$815$	−2.84924	−	4.93503i	−0.0998046	−	0.172867i
$816$		0			0
$817$	−1.65685	+	2.86976i	−0.0579660	+	0.100400i
$818$		0			0
$819$	−28.3848	+	3.88437i	−0.991844	+	0.135731i
$820$		0			0
$821$	14.7426	−	25.5350i	0.514522	−	0.891178i	−0.485336	−	0.874328i	$-0.661303\pi$
$821$	14.7426	−	25.5350i	0.514522	−	0.891178i	0.999858	−	0.0168502i	$-0.00536384\pi$
$822$		0			0
$823$	−21.7279	−	37.6339i	−0.757388	−	1.31183i	−0.944178	−	0.329434i	$-0.893142\pi$
$823$	−21.7279	−	37.6339i	−0.757388	−	1.31183i	0.186791	−	0.982400i	$-0.440191\pi$
$824$		0			0
$825$	11.2426			0.391419
$826$		0			0
$827$	21.3553			0.742598			0.371299	−	0.928513i	$-0.378913\pi$
$827$	21.3553			0.742598			0.371299	+	0.928513i	$0.378913\pi$
$828$		0			0
$829$	−10.8787	−	18.8424i	−0.377832	−	0.654425i	0.612914	−	0.790149i	$-0.289997\pi$
$829$	−10.8787	−	18.8424i	−0.377832	−	0.654425i	−0.990747	+	0.135725i	$0.956664\pi$
$830$		0			0
$831$	−2.20711	+	3.82282i	−0.0765637	+	0.132612i
$832$		0			0
$833$	24.6569	−	6.87722i	0.854309	−	0.238281i
$834$		0			0
$835$	−4.02082	+	6.96426i	−0.139146	+	0.241008i
$836$		0			0
$837$	0.828427	+	1.43488i	0.0286346	+	0.0495966i
$838$		0			0
$839$	18.4853			0.638183			0.319091	−	0.947724i	$-0.396622\pi$
$839$	18.4853			0.638183			0.319091	+	0.947724i	$0.396622\pi$
$840$		0			0
$841$	−21.9411			−0.756591
$842$		0			0
$843$	−10.5355	−	18.2481i	−0.362863	−	0.628497i
$844$		0			0
$845$	0.485281	−	0.840532i	0.0166942	−	0.0289152i
$846$		0			0
$847$	2.62132	−	0.358719i	0.0900696	−	0.0123257i
$848$		0			0
$849$	−28.2635	+	48.9537i	−0.969999	+	1.68009i
$850$		0			0
$851$	29.3848	+	50.8959i	1.00730	+	1.74469i
$852$		0			0
$853$	14.0000			0.479351			0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000			0.479351			0.239675	+	0.970853i	$0.422959\pi$
$854$		0			0
$855$	−0.970563			−0.0331925
$856$		0			0
$857$	17.3137	+	29.9882i	0.591425	+	1.02438i	0.994041	+	0.109009i	$0.0347678\pi$
$857$	17.3137	+	29.9882i	0.591425	+	1.02438i	−0.402616	+	0.915369i	$0.631899\pi$
$858$		0			0
$859$	−2.86396	+	4.96053i	−0.0977171	+	0.169251i	−0.910739	−	0.412982i	$-0.864487\pi$
$859$	−2.86396	+	4.96053i	−0.0977171	+	0.169251i	0.813022	+	0.582233i	$0.197821\pi$
$860$		0			0
$861$	13.0711	−	32.0174i	0.445461	−	1.09115i
$862$		0			0
$863$	17.6066	−	30.4955i	0.599336	−	1.03808i	−0.393584	−	0.919289i	$-0.628765\pi$
$863$	17.6066	−	30.4955i	0.599336	−	1.03808i	0.992919	−	0.118791i	$-0.0379019\pi$
$864$		0			0
$865$	−2.87868	−	4.98602i	−0.0978780	−	0.169530i
$866$		0			0
$867$	−8.75736			−0.297416
$868$		0			0
$869$	−13.2426			−0.449226
$870$		0			0
$871$	−5.27817	−	9.14207i	−0.178844	−	0.309767i
$872$		0			0
$873$	5.41421	−	9.37769i	0.183243	−	0.317387i
$874$		0			0
$875$	−9.17157	−	11.8272i	−0.310056	−	0.399832i
$876$		0			0
$877$	−9.81371	+	16.9978i	−0.331385	+	0.573976i	−0.982784	−	0.184760i	$-0.940849\pi$
$877$	−9.81371	+	16.9978i	−0.331385	+	0.573976i	0.651398	+	0.758736i	$0.274183\pi$
$878$		0			0
$879$	13.0711	+	22.6398i	0.440876	+	0.763620i
$880$		0			0
$881$	6.45584			0.217503			0.108751	−	0.994069i	$-0.465315\pi$
$881$	6.45584			0.217503			0.108751	+	0.994069i	$0.465315\pi$
$882$		0			0
$883$	−15.7279			−0.529287			−0.264643	−	0.964346i	$-0.585254\pi$
$883$	−15.7279			−0.529287			−0.264643	+	0.964346i	$0.585254\pi$
$884$		0			0
$885$	3.94975	+	6.84116i	0.132769	+	0.229963i
$886$		0			0
$887$	−1.55025	+	2.68512i	−0.0520524	+	0.0901574i	−0.890878	−	0.454243i	$-0.849910\pi$
$887$	−1.55025	+	2.68512i	−0.0520524	+	0.0901574i	0.838825	+	0.544401i	$0.183243\pi$
$888$		0			0
$889$	25.5000	+	32.8835i	0.855243	+	1.10288i
$890$		0			0
$891$	−4.74264	+	8.21449i	−0.158884	+	0.275196i
$892$		0			0
$893$	−3.07107	−	5.31925i	−0.102769	−	0.178002i
$894$		0			0
$895$	0.526912			0.0176127
$896$		0			0
$897$	−57.6985			−1.92650
$898$		0			0
$899$	−5.31371	−	9.20361i	−0.177222	−	0.306958i
$900$		0			0
$901$	−14.4437	+	25.0171i	−0.481188	+	0.833442i
$902$		0			0
$903$	−13.6569	+	33.4523i	−0.454472	+	1.11322i
$904$		0			0
$905$	−2.24264	+	3.88437i	−0.0745479	+	0.129121i
$906$		0			0
$907$	5.34315	+	9.25460i	0.177416	+	0.307294i	0.940995	−	0.338421i	$-0.109893\pi$
$907$	5.34315	+	9.25460i	0.177416	+	0.307294i	−0.763579	+	0.645715i	$0.776559\pi$
$908$		0			0
$909$	17.4558			0.578974
$910$		0			0
$911$	30.4853			1.01002			0.505011	−	0.863113i	$-0.331488\pi$
$911$	30.4853			1.01002			0.505011	+	0.863113i	$0.331488\pi$
$912$		0			0
$913$	6.07107	+	10.5154i	0.200923	+	0.348009i
$914$		0			0
$915$	8.36396	−	14.4868i	0.276504	−	0.478919i
$916$		0			0
$917$	1.53553	−	0.210133i	0.0507078	−	0.00693920i
$918$		0			0
$919$	11.0711	−	19.1757i	0.365201	−	0.632546i	−0.623608	−	0.781738i	$-0.714334\pi$
$919$	11.0711	−	19.1757i	0.365201	−	0.632546i	0.988808	+	0.149191i	$0.0476670\pi$
$920$		0			0
$921$	11.9497	+	20.6976i	0.393758	+	0.682008i
$922$		0			0
$923$	−42.3848			−1.39511
$924$		0			0
$925$	43.8406			1.44147
$926$		0			0
$927$	18.9706	+	32.8580i	0.623075	+	1.07920i
$928$		0			0
$929$	20.2279	−	35.0358i	0.663657	−	1.14949i	−0.315991	−	0.948762i	$-0.602337\pi$
$929$	20.2279	−	35.0358i	0.663657	−	1.14949i	0.979648	−	0.200725i	$-0.0643297\pi$
$930$		0			0
$931$	−2.92893	−	2.86976i	−0.0959919	−	0.0940524i
$932$		0			0
$933$	20.1924	−	34.9742i	0.661069	−	1.14501i
$934$		0			0
$935$	−1.07107	−	1.85514i	−0.0350277	−	0.0606697i
$936$		0			0
$937$	−19.4142			−0.634235			−0.317117	−	0.948386i	$-0.602715\pi$
$937$	−19.4142			−0.634235			−0.317117	+	0.948386i	$0.602715\pi$
$938$		0			0
$939$	−49.8701			−1.62745
$940$		0			0
$941$	−12.3284	−	21.3535i	−0.401895	−	0.696103i	0.592059	−	0.805894i	$-0.298315\pi$
$941$	−12.3284	−	21.3535i	−0.401895	−	0.696103i	−0.993955	+	0.109791i	$0.964982\pi$
$942$		0			0
$943$	16.8995	−	29.2708i	0.550323	−	0.953188i
$944$		0			0
$945$	0.636039	−	0.0870399i	0.0206903	−	0.00283141i
$946$		0			0
$947$	17.4142	−	30.1623i	0.565886	−	0.980143i	−0.431081	−	0.902313i	$-0.641868\pi$
$947$	17.4142	−	30.1623i	0.565886	−	0.980143i	0.996967	−	0.0778298i	$-0.0247991\pi$
$948$		0			0
$949$	−18.0208	−	31.2130i	−0.584980	−	1.01322i
$950$		0			0
$951$	20.9706			0.680017
$952$		0			0
$953$	5.55635			0.179988			0.0899939	−	0.995942i	$-0.471315\pi$
$953$	5.55635			0.179988			0.0899939	+	0.995942i	$0.471315\pi$
$954$		0			0
$955$	2.10051	+	3.63818i	0.0679707	+	0.117729i
$956$		0			0
$957$	3.20711	−	5.55487i	0.103671	−	0.179564i
$958$		0			0
$959$	16.6569	−	40.8008i	0.537878	−	1.31753i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$	−4.34315	−	7.52255i	−0.139956	−	0.242411i
$964$		0			0
$965$	−12.8284			−0.412962
$966$		0			0
$967$	36.2843			1.16682			0.583412	−	0.812177i	$-0.301717\pi$
$967$	36.2843			1.16682			0.583412	+	0.812177i	$0.301717\pi$
$968$		0			0
$969$	−2.58579	−	4.47871i	−0.0830674	−	0.143877i
$970$		0			0
$971$	11.1360	−	19.2882i	0.357372	−	0.618987i	−0.630149	−	0.776475i	$-0.717006\pi$
$971$	11.1360	−	19.2882i	0.357372	−	0.618987i	0.987521	+	0.157487i	$0.0503393\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−21.5208	+	37.2751i	−0.689218	+	1.19376i
$976$		0			0
$977$	−20.0000	−	34.6410i	−0.639857	−	1.10826i	−0.985464	−	0.169885i	$-0.945660\pi$
$977$	−20.0000	−	34.6410i	−0.639857	−	1.10826i	0.345607	−	0.938379i	$-0.387673\pi$
$978$		0			0
$979$	−12.4853			−0.399031
$980$		0			0
$981$	46.6274			1.48870
$982$		0			0
$983$	16.2132	+	28.0821i	0.517121	+	0.895680i	0.999802	+	0.0198836i	$0.00632957\pi$
$983$	16.2132	+	28.0821i	0.517121	+	0.895680i	−0.482681	+	0.875796i	$0.660337\pi$
$984$		0			0
$985$	−0.150758	+	0.261120i	−0.00480354	+	0.00831997i
$986$		0			0
$987$	−41.0416	−	52.9251i	−1.30637	−	1.68463i
$988$		0			0
$989$	−17.6569	+	30.5826i	−0.561455	+	0.972469i
$990$		0			0
$991$	−0.807612	−	1.39882i	−0.0256546	−	0.0444351i	0.852913	−	0.522053i	$-0.174834\pi$
$991$	−0.807612	−	1.39882i	−0.0256546	−	0.0444351i	−0.878568	+	0.477618i	$0.841500\pi$
$992$		0			0
$993$	58.1127			1.84415
$994$		0			0
$995$	0.0588745			0.00186645
$996$		0			0
$997$	−6.58579	−	11.4069i	−0.208574	−	0.361261i	0.742692	−	0.669634i	$-0.233549\pi$
$997$	−6.58579	−	11.4069i	−0.208574	−	0.361261i	−0.951266	+	0.308373i	$0.900216\pi$
$998$		0			0
$999$	−1.94975	+	3.37706i	−0.0616873	+	0.106846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.q.f.177.1		4
4.3	odd	2		154.2.e.e.23.2	✓	4
7.2	even	3		8624.2.a.cc.1.2		2
7.4	even	3	inner	1232.2.q.f.529.1		4
7.5	odd	6		8624.2.a.bh.1.1		2
12.11	even	2		1386.2.k.t.793.2		4
28.3	even	6		1078.2.e.m.67.1		4
28.11	odd	6		154.2.e.e.67.2	yes	4
28.19	even	6		1078.2.a.x.1.2		2
28.23	odd	6		1078.2.a.t.1.1		2
28.27	even	2		1078.2.e.m.177.1		4
84.11	even	6		1386.2.k.t.991.2		4
84.23	even	6		9702.2.a.cx.1.1		2
84.47	odd	6		9702.2.a.ch.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.e.e.23.2	✓	4	4.3	odd	2
154.2.e.e.67.2	yes	4	28.11	odd	6
1078.2.a.t.1.1		2	28.23	odd	6
1078.2.a.x.1.2		2	28.19	even	6
1078.2.e.m.67.1		4	28.3	even	6
1078.2.e.m.177.1		4	28.27	even	2
1232.2.q.f.177.1		4	1.1	even	1	trivial
1232.2.q.f.529.1		4	7.4	even	3	inner
1386.2.k.t.793.2		4	12.11	even	2
1386.2.k.t.991.2		4	84.11	even	6
8624.2.a.bh.1.1		2	7.5	odd	6
8624.2.a.cc.1.2		2	7.2	even	3
9702.2.a.ch.1.2		2	84.47	odd	6
9702.2.a.cx.1.1		2	84.23	even	6

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:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.20711 - 2.09077i) q^{3} +(0.292893 - 0.507306i) q^{5} +(-1.62132 - 2.09077i) q^{7} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})\)	\(q+(-1.20711 - 2.09077i) q^{3} +(0.292893 - 0.507306i) q^{5} +(-1.62132 - 2.09077i) q^{7} +(-1.41421 + 2.44949i) q^{9} +(0.500000 + 0.866025i) q^{11} -3.82843 q^{13} -1.41421 q^{15} +(-1.82843 - 3.16693i) q^{17} +(-0.292893 + 0.507306i) q^{19} +(-2.41421 + 5.91359i) q^{21} +(-3.12132 + 5.40629i) q^{23} +(2.32843 + 4.03295i) q^{25} -0.414214 q^{27} +2.65685 q^{29} +(-2.00000 - 3.46410i) q^{31} +(1.20711 - 2.09077i) q^{33} +(-1.53553 + 0.210133i) q^{35} +(4.70711 - 8.15295i) q^{37} +(4.62132 + 8.00436i) q^{39} -5.41421 q^{41} +5.65685 q^{43} +(0.828427 + 1.43488i) q^{45} +(-5.24264 + 9.08052i) q^{47} +(-1.74264 + 6.77962i) q^{49} +(-4.41421 + 7.64564i) q^{51} +(-3.94975 - 6.84116i) q^{53} +0.585786 q^{55} +1.41421 q^{57} +(-2.79289 - 4.83743i) q^{59} +(-5.91421 + 10.2437i) q^{61} +(7.41421 - 1.01461i) q^{63} +(-1.12132 + 1.94218i) q^{65} +(1.37868 + 2.38794i) q^{67} +15.0711 q^{69} +11.0711 q^{71} +(4.70711 + 8.15295i) q^{73} +(5.62132 - 9.73641i) q^{75} +(1.00000 - 2.44949i) q^{77} +(-6.62132 + 11.4685i) q^{79} +(4.74264 + 8.21449i) q^{81} +12.1421 q^{83} -2.14214 q^{85} +(-3.20711 - 5.55487i) q^{87} +(-6.24264 + 10.8126i) q^{89} +(6.20711 + 8.00436i) q^{91} +(-4.82843 + 8.36308i) q^{93} +(0.171573 + 0.297173i) q^{95} -3.82843 q^{97} -2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 4 q^{5} + 2 q^{7}+O(q^{10}) \) 4 * q - 2 * q^3 + 4 * q^5 + 2 * q^7	\( 4 q - 2 q^{3} + 4 q^{5} + 2 q^{7} + 2 q^{11} - 4 q^{13} + 4 q^{17} - 4 q^{19} - 4 q^{21} - 4 q^{23} - 2 q^{25} + 4 q^{27} - 12 q^{29} - 8 q^{31} + 2 q^{33} + 8 q^{35} + 16 q^{37} + 10 q^{39} - 16 q^{41} - 8 q^{45} - 4 q^{47} + 10 q^{49} - 12 q^{51} + 4 q^{53} + 8 q^{55} - 14 q^{59} - 18 q^{61} + 24 q^{63} + 4 q^{65} + 14 q^{67} + 32 q^{69} + 16 q^{71} + 16 q^{73} + 14 q^{75} + 4 q^{77} - 18 q^{79} + 2 q^{81} - 8 q^{83} + 48 q^{85} - 10 q^{87} - 8 q^{89} + 22 q^{91} - 8 q^{93} + 12 q^{95} - 4 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 + 4 * q^5 + 2 * q^7 + 2 * q^11 - 4 * q^13 + 4 * q^17 - 4 * q^19 - 4 * q^21 - 4 * q^23 - 2 * q^25 + 4 * q^27 - 12 * q^29 - 8 * q^31 + 2 * q^33 + 8 * q^35 + 16 * q^37 + 10 * q^39 - 16 * q^41 - 8 * q^45 - 4 * q^47 + 10 * q^49 - 12 * q^51 + 4 * q^53 + 8 * q^55 - 14 * q^59 - 18 * q^61 + 24 * q^63 + 4 * q^65 + 14 * q^67 + 32 * q^69 + 16 * q^71 + 16 * q^73 + 14 * q^75 + 4 * q^77 - 18 * q^79 + 2 * q^81 - 8 * q^83 + 48 * q^85 - 10 * q^87 - 8 * q^89 + 22 * q^91 - 8 * q^93 + 12 * q^95 - 4 * q^97

Introduction

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