LMFDB - Embedded newform 460.2.m.a.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(41,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("460.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.m (of order $11$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			41.1
Character	$\chi$	$=$	460.41
Dual form			460.2.m.a.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26886 + 1.46434i) q^{3} +(-0.142315 + 0.989821i) q^{5} +(0.0191296 + 0.0418879i) q^{7} +(-0.107349 - 0.746632i) q^{9} +O(q^{10})$	\(q+(-1.26886 + 1.46434i) q^{3} +(-0.142315 + 0.989821i) q^{5} +(0.0191296 + 0.0418879i) q^{7} +(-0.107349 - 0.746632i) q^{9} +(0.229658 - 0.0674336i) q^{11} +(-1.75005 + 3.83208i) q^{13} +(-1.26886 - 1.46434i) q^{15} +(-0.597021 + 0.383682i) q^{17} +(-3.34165 - 2.14755i) q^{19} +(-0.0856110 - 0.0251377i) q^{21} +(-4.35746 + 2.00313i) q^{23} +(-0.959493 - 0.281733i) q^{25} +(-3.66051 - 2.35247i) q^{27} +(-0.590543 + 0.379519i) q^{29} +(-3.43965 - 3.96957i) q^{31} +(-0.192658 + 0.421862i) q^{33} +(-0.0441840 + 0.0129736i) q^{35} +(0.347733 + 2.41854i) q^{37} +(-3.39091 - 7.42506i) q^{39} +(-0.510902 + 3.55340i) q^{41} +(-3.44042 + 3.97045i) q^{43} +0.754310 q^{45} -0.0114334 q^{47} +(4.58264 - 5.28864i) q^{49} +(0.195694 - 1.36108i) q^{51} +(5.16162 + 11.3024i) q^{53} +(0.0340635 + 0.236917i) q^{55} +(7.38483 - 2.16838i) q^{57} +(-2.03273 + 4.45105i) q^{59} +(3.47877 + 4.01472i) q^{61} +(0.0292213 - 0.0187794i) q^{63} +(-3.54402 - 2.27760i) q^{65} +(2.04121 + 0.599352i) q^{67} +(2.59574 - 8.92251i) q^{69} +(7.02708 + 2.06334i) q^{71} +(-0.786056 - 0.505167i) q^{73} +(1.63002 - 1.04755i) q^{75} +(0.00721790 + 0.00832991i) q^{77} +(4.12602 - 9.03472i) q^{79} +(10.2608 - 3.01283i) q^{81} +(1.46896 + 10.2168i) q^{83} +(-0.294812 - 0.645548i) q^{85} +(0.193571 - 1.34631i) q^{87} +(1.17192 - 1.35246i) q^{89} -0.193996 q^{91} +10.1773 q^{93} +(2.60125 - 3.00201i) q^{95} +(-0.0699118 + 0.486247i) q^{97} +(-0.0750017 - 0.164231i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) $ 30 * q - 3 * q^5 + q^7 + 21 * q^9	$ 30 q - 3 q^{5} + q^{7} + 21 q^{9} + 2 q^{13} + 10 q^{17} + 3 q^{19} + 39 q^{21} + 10 q^{23} - 3 q^{25} + 21 q^{27} + 14 q^{29} - 2 q^{31} - 50 q^{33} - 10 q^{35} + 9 q^{37} + 38 q^{39} - 3 q^{41} - 50 q^{43} + 10 q^{45} - 6 q^{47} - 36 q^{49} - 36 q^{51} - 5 q^{53} - 11 q^{55} + 23 q^{57} + 14 q^{59} - 16 q^{61} - 52 q^{63} + 2 q^{65} + 27 q^{67} + 42 q^{69} + 19 q^{71} + 24 q^{73} - 10 q^{77} - 22 q^{79} + 35 q^{81} + 36 q^{83} + 10 q^{85} - 3 q^{87} - 28 q^{89} - 98 q^{91} - 60 q^{93} - 19 q^{95} - 2 q^{97} - 14 q^{99}+O(q^{100}) $ 30 * q - 3 * q^5 + q^7 + 21 * q^9 + 2 * q^13 + 10 * q^17 + 3 * q^19 + 39 * q^21 + 10 * q^23 - 3 * q^25 + 21 * q^27 + 14 * q^29 - 2 * q^31 - 50 * q^33 - 10 * q^35 + 9 * q^37 + 38 * q^39 - 3 * q^41 - 50 * q^43 + 10 * q^45 - 6 * q^47 - 36 * q^49 - 36 * q^51 - 5 * q^53 - 11 * q^55 + 23 * q^57 + 14 * q^59 - 16 * q^61 - 52 * q^63 + 2 * q^65 + 27 * q^67 + 42 * q^69 + 19 * q^71 + 24 * q^73 - 10 * q^77 - 22 * q^79 + 35 * q^81 + 36 * q^83 + 10 * q^85 - 3 * q^87 - 28 * q^89 - 98 * q^91 - 60 * q^93 - 19 * q^95 - 2 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.26886	+	1.46434i	−0.732577	+	0.845439i	−0.992759	−	0.120120i	$-0.961672\pi$
$3$	−1.26886	+	1.46434i	−0.732577	+	0.845439i	0.260182	+	0.965560i	$0.416217\pi$
$4$		0			0
$5$	−0.142315	+	0.989821i	−0.0636451	+	0.442662i
$5$	−0.142315	+	0.989821i	−0.0636451	+	0.442662i
$6$		0			0
$7$	0.0191296	+	0.0418879i	0.00723030	+	0.0158321i	0.913213	−	0.407483i	$-0.133594\pi$
$7$	0.0191296	+	0.0418879i	0.00723030	+	0.0158321i	−0.905982	+	0.423315i	$0.860866\pi$
$8$		0			0
$9$	−0.107349	−	0.746632i	−0.0357831	−	0.248877i
$10$		0			0
$11$	0.229658	−	0.0674336i	0.0692444	−	0.0203320i	−0.246927	−	0.969034i	$-0.579421\pi$
$11$	0.229658	−	0.0674336i	0.0692444	−	0.0203320i	0.316171	+	0.948702i	$0.397603\pi$
$12$		0			0
$13$	−1.75005	+	3.83208i	−0.485378	+	1.06283i	0.495572	+	0.868567i	$0.334958\pi$
$13$	−1.75005	+	3.83208i	−0.485378	+	1.06283i	−0.980950	+	0.194262i	$0.937769\pi$
$14$		0			0
$15$	−1.26886	−	1.46434i	−0.327618	−	0.378092i
$16$		0			0
$17$	−0.597021	+	0.383682i	−0.144799	+	0.0930566i	−0.611034	−	0.791604i	$-0.709246\pi$
$17$	−0.597021	+	0.383682i	−0.144799	+	0.0930566i	0.466235	+	0.884661i	$0.345610\pi$
$18$		0			0
$19$	−3.34165	−	2.14755i	−0.766626	−	0.492681i	0.0979444	−	0.995192i	$-0.468773\pi$
$19$	−3.34165	−	2.14755i	−0.766626	−	0.492681i	−0.864571	+	0.502511i	$0.832410\pi$
$20$		0			0
$21$	−0.0856110	−	0.0251377i	−0.0186819	−	0.00548549i
$22$		0			0
$23$	−4.35746	+	2.00313i	−0.908593	+	0.417682i
$23$	−4.35746	+	2.00313i	−0.908593	+	0.417682i
$24$		0			0
$25$	−0.959493	−	0.281733i	−0.191899	−	0.0563465i
$26$		0			0
$27$	−3.66051	−	2.35247i	−0.704466	−	0.452733i
$28$		0			0
$29$	−0.590543	+	0.379519i	−0.109661	+	0.0704749i	−0.594322	−	0.804227i	$-0.702579\pi$
$29$	−0.590543	+	0.379519i	−0.109661	+	0.0704749i	0.484661	+	0.874702i	$0.338943\pi$
$30$		0			0
$31$	−3.43965	−	3.96957i	−0.617780	−	0.712956i	0.357504	−	0.933912i	$-0.383628\pi$
$31$	−3.43965	−	3.96957i	−0.617780	−	0.712956i	−0.975284	+	0.220955i	$0.929082\pi$
$32$		0			0
$33$	−0.192658	+	0.421862i	−0.0335374	+	0.0734367i
$34$		0			0
$35$	−0.0441840	+	0.0129736i	−0.00746845	+	0.00219294i
$36$		0			0
$37$	0.347733	+	2.41854i	0.0571670	+	0.397605i	0.998235	+	0.0593878i	$0.0189148\pi$
$37$	0.347733	+	2.41854i	0.0571670	+	0.397605i	−0.941068	+	0.338217i	$0.890176\pi$
$38$		0			0
$39$	−3.39091	−	7.42506i	−0.542980	−	1.18896i
$40$		0			0
$41$	−0.510902	+	3.55340i	−0.0797895	+	0.554948i	0.910239	+	0.414083i	$0.135898\pi$
$41$	−0.510902	+	3.55340i	−0.0797895	+	0.554948i	−0.990029	+	0.140866i	$0.955011\pi$
$42$		0			0
$43$	−3.44042	+	3.97045i	−0.524659	+	0.605488i	−0.954791	−	0.297277i	$-0.903921\pi$
$43$	−3.44042	+	3.97045i	−0.524659	+	0.605488i	0.430132	+	0.902766i	$0.358467\pi$
$44$		0			0
$45$	0.754310			0.112446
$46$		0			0
$47$	−0.0114334			−0.00166774			−0.000833869	−	1.00000i	$-0.500265\pi$
$47$	−0.0114334			−0.00166774			−0.000833869		1.00000i	$0.500265\pi$
$48$		0			0
$49$	4.58264	−	5.28864i	0.654662	−	0.755521i
$50$		0			0
$51$	0.195694	−	1.36108i	0.0274027	−	0.190590i
$52$		0			0
$53$	5.16162	+	11.3024i	0.709003	+	1.55250i	0.828702	+	0.559690i	$0.189080\pi$
$53$	5.16162	+	11.3024i	0.709003	+	1.55250i	−0.119699	+	0.992810i	$0.538193\pi$
$54$		0			0
$55$	0.0340635	+	0.236917i	0.00459312	+	0.0319459i
$56$		0			0
$57$	7.38483	−	2.16838i	0.978145	−	0.287209i
$58$		0			0
$59$	−2.03273	+	4.45105i	−0.264638	+	0.579477i	−0.994573	−	0.104040i	$-0.966823\pi$
$59$	−2.03273	+	4.45105i	−0.264638	+	0.579477i	0.729935	+	0.683517i	$0.239550\pi$
$60$		0			0
$61$	3.47877	+	4.01472i	0.445411	+	0.514032i	0.933410	−	0.358813i	$-0.116818\pi$
$61$	3.47877	+	4.01472i	0.445411	+	0.514032i	−0.487999	+	0.872844i	$0.662273\pi$
$62$		0			0
$63$	0.0292213	−	0.0187794i	0.00368154	−	0.00236598i
$64$		0			0
$65$	−3.54402	−	2.27760i	−0.439582	−	0.282502i
$66$		0			0
$67$	2.04121	+	0.599352i	0.249373	+	0.0732225i	0.404030	−	0.914746i	$-0.367609\pi$
$67$	2.04121	+	0.599352i	0.249373	+	0.0732225i	−0.154657	+	0.987968i	$0.549427\pi$
$68$		0			0
$69$	2.59574	−	8.92251i	0.312490	−	1.07414i
$70$		0			0
$71$	7.02708	+	2.06334i	0.833961	+	0.244873i	0.670717	−	0.741713i	$-0.265986\pi$
$71$	7.02708	+	2.06334i	0.833961	+	0.244873i	0.163243	+	0.986586i	$0.447805\pi$
$72$		0			0
$73$	−0.786056	−	0.505167i	−0.0920008	−	0.0591254i	0.493832	−	0.869558i	$-0.335596\pi$
$73$	−0.786056	−	0.505167i	−0.0920008	−	0.0591254i	−0.585832	+	0.810432i	$0.699232\pi$
$74$		0			0
$75$	1.63002	−	1.04755i	0.188218	−	0.120960i
$76$		0			0
$77$	0.00721790	+	0.00832991i	0.000822557	+	0.000949281i
$78$		0			0
$79$	4.12602	−	9.03472i	0.464213	−	1.01649i	−0.522294	−	0.852766i	$-0.674924\pi$
$79$	4.12602	−	9.03472i	0.464213	−	1.01649i	0.986507	−	0.163720i	$-0.0523492\pi$
$80$		0			0
$81$	10.2608	−	3.01283i	1.14009	−	0.334759i
$82$		0			0
$83$	1.46896	+	10.2168i	0.161239	+	1.12144i	0.896303	+	0.443443i	$0.146243\pi$
$83$	1.46896	+	10.2168i	0.161239	+	1.12144i	−0.735064	+	0.677998i	$0.762848\pi$
$84$		0			0
$85$	−0.294812	−	0.645548i	−0.0319768	−	0.0700195i
$86$		0			0
$87$	0.193571	−	1.34631i	0.0207530	−	0.144340i
$88$		0			0
$89$	1.17192	−	1.35246i	0.124223	−	0.143361i	−0.690231	−	0.723589i	$-0.742491\pi$
$89$	1.17192	−	1.35246i	0.124223	−	0.143361i	0.814454	+	0.580228i	$0.197037\pi$
$90$		0			0
$91$	−0.193996			−0.0203363
$92$		0			0
$93$	10.1773			1.05533
$94$		0			0
$95$	2.60125	−	3.00201i	0.266883	−	0.307999i
$96$		0			0
$97$	−0.0699118	+	0.486247i	−0.00709846	+	0.0493709i	−0.993063	−	0.117585i	$-0.962485\pi$
$97$	−0.0699118	+	0.486247i	−0.00709846	+	0.0493709i	0.985964	+	0.166956i	$0.0533938\pi$
$98$		0			0
$99$	−0.0750017	−	0.164231i	−0.00753795	−	0.0165058i
$100$		0			0
$101$	1.45265	+	10.1034i	0.144544	+	1.00533i	0.924960	+	0.380065i	$0.124098\pi$
$101$	1.45265	+	10.1034i	0.144544	+	1.00533i	−0.780416	+	0.625261i	$0.784993\pi$
$102$		0			0
$103$	2.91739	−	0.856624i	0.287459	−	0.0844057i	−0.134824	−	0.990870i	$-0.543047\pi$
$103$	2.91739	−	0.856624i	0.287459	−	0.0844057i	0.422283	+	0.906464i	$0.361229\pi$
$104$		0			0
$105$	0.0370655	−	0.0811622i	0.00361722	−	0.00792062i
$106$		0			0
$107$	5.29220	+	6.10753i	0.511616	+	0.590437i	0.951512	−	0.307612i	$-0.0995299\pi$
$107$	5.29220	+	6.10753i	0.511616	+	0.590437i	−0.439895	+	0.898049i	$0.644984\pi$
$108$		0			0
$109$	7.93159	−	5.09733i	0.759709	−	0.488235i	−0.102534	−	0.994729i	$-0.532695\pi$
$109$	7.93159	−	5.09733i	0.759709	−	0.488235i	0.862243	+	0.506494i	$0.169059\pi$
$110$		0			0
$111$	−3.98280	−	2.55959i	−0.378030	−	0.242945i
$112$		0			0
$113$	3.73369	+	1.09631i	0.351236	+	0.103132i	0.452591	−	0.891718i	$-0.350500\pi$
$113$	3.73369	+	1.09631i	0.351236	+	0.103132i	−0.101355	+	0.994850i	$0.532318\pi$
$114$		0			0
$115$	−1.36261	−	4.59818i	−0.127064	−	0.428783i
$116$		0			0
$117$	3.04902	+	0.895274i	0.281882	+	0.0827681i
$118$		0			0
$119$	−0.0274924	−	0.0176683i	−0.00252022	−	0.00161965i
$120$		0			0
$121$	−9.20559	+	5.91608i	−0.836872	+	0.537825i
$122$		0			0
$123$	−4.55514	−	5.25691i	−0.410723	−	0.474000i
$124$		0			0
$125$	0.415415	−	0.909632i	0.0371558	−	0.0813600i
$126$		0			0
$127$	9.59424	−	2.81712i	0.851351	−	0.249979i	0.173186	−	0.984889i	$-0.444594\pi$
$127$	9.59424	−	2.81712i	0.851351	−	0.249979i	0.678165	+	0.734910i	$0.262776\pi$
$128$		0			0
$129$	−1.44870	−	10.0759i	−0.127551	−	0.887134i
$130$		0			0
$131$	−0.970457	−	2.12500i	−0.0847892	−	0.185662i	0.862488	−	0.506077i	$-0.168905\pi$
$131$	−0.970457	−	2.12500i	−0.0847892	−	0.185662i	−0.947277	+	0.320415i	$0.896178\pi$
$132$		0			0
$133$	0.0260320	−	0.181056i	0.00225726	−	0.0156996i
$134$		0			0
$135$	2.84947	−	3.28846i	0.245243	−	0.283026i
$136$		0			0
$137$	−11.2818			−0.963869			−0.481934	−	0.876207i	$-0.660066\pi$
$137$	−11.2818			−0.963869			−0.481934	+	0.876207i	$0.660066\pi$
$138$		0			0
$139$	−15.9060			−1.34913			−0.674566	−	0.738215i	$-0.735669\pi$
$139$	−15.9060			−1.34913			−0.674566	+	0.738215i	$0.735669\pi$
$140$		0			0
$141$	0.0145074	−	0.0167425i	0.00122175	−	0.00140997i
$142$		0			0
$143$	−0.143502	+	0.998080i	−0.0120003	+	0.0834637i
$144$		0			0
$145$	−0.291613	−	0.638543i	−0.0242171	−	0.0530281i
$146$		0			0
$147$	1.92966	+	13.4211i	0.159156	+	1.10695i
$148$		0			0
$149$	18.7291	−	5.49936i	1.53435	−	0.450525i	0.597969	−	0.801519i	$-0.295974\pi$
$149$	18.7291	−	5.49936i	1.53435	−	0.450525i	0.936378	+	0.350994i	$0.114156\pi$
$150$		0			0
$151$	−1.09678	+	2.40160i	−0.0892543	+	0.195440i	−0.948995	−	0.315291i	$-0.897898\pi$
$151$	−1.09678	+	2.40160i	−0.0892543	+	0.195440i	0.859741	+	0.510731i	$0.170625\pi$
$152$		0			0
$153$	0.350559	+	0.404567i	0.0283410	+	0.0327073i
$154$		0			0
$155$	4.41868	−	2.83971i	0.354917	−	0.228091i
$156$		0			0
$157$	−16.1462	−	10.3765i	−1.28860	−	0.828136i	−0.296681	−	0.954977i	$-0.595880\pi$
$157$	−16.1462	−	10.3765i	−1.28860	−	0.828136i	−0.991923	+	0.126841i	$0.959516\pi$
$158$		0			0
$159$	−23.0999	−	6.78275i	−1.83194	−	0.537907i
$160$		0			0
$161$	−0.167263	−	0.144206i	−0.0131822	−	0.0113650i
$162$		0			0
$163$	16.3285	+	4.79449i	1.27895	+	0.375534i	0.849515	−	0.527564i	$-0.176895\pi$
$163$	16.3285	+	4.79449i	1.27895	+	0.375534i	0.429435	+	0.903098i	$0.358713\pi$
$164$		0			0
$165$	−0.390150	−	0.250734i	−0.0303731	−	0.0195196i
$166$		0			0
$167$	−8.11436	+	5.21478i	−0.627908	+	0.403532i	−0.815534	−	0.578709i	$-0.803557\pi$
$167$	−8.11436	+	5.21478i	−0.627908	+	0.403532i	0.187627	+	0.982240i	$0.439921\pi$
$168$		0			0
$169$	−3.10899	−	3.58796i	−0.239153	−	0.275997i
$170$		0			0
$171$	−1.24470	+	2.72552i	−0.0951848	+	0.208426i
$172$		0			0
$173$	20.9509	−	6.15175i	1.59287	−	0.467709i	0.639320	−	0.768941i	$-0.279216\pi$
$173$	20.9509	−	6.15175i	1.59287	−	0.467709i	0.953551	+	0.301232i	$0.0973979\pi$
$174$		0			0
$175$	−0.00655350	−	0.0455806i	−0.000495398	−	0.00344557i
$176$		0			0
$177$	−3.93862	−	8.62437i	−0.296045	−	0.648247i
$178$		0			0
$179$	−0.746126	+	5.18942i	−0.0557681	+	0.387876i	0.942752	+	0.333494i	$0.108228\pi$
$179$	−0.746126	+	5.18942i	−0.0557681	+	0.387876i	−0.998520	+	0.0543813i	$0.982681\pi$
$180$		0			0
$181$	−17.0099	+	19.6305i	−1.26434	+	1.45912i	−0.434943	+	0.900458i	$0.643231\pi$
$181$	−17.0099	+	19.6305i	−1.26434	+	1.45912i	−0.829394	+	0.558664i	$0.811314\pi$
$182$		0			0
$183$	−10.2930			−0.760880
$184$		0			0
$185$	−2.44341			−0.179643
$186$		0			0
$187$	−0.111237	+	0.128375i	−0.00813449	+	0.00938770i
$188$		0			0
$189$	0.0285160	−	0.198333i	0.00207423	−	0.0144266i
$190$		0			0
$191$	6.58771	+	14.4251i	0.476670	+	1.04376i	0.983366	+	0.181637i	$0.0581396\pi$
$191$	6.58771	+	14.4251i	0.476670	+	1.04376i	−0.506695	+	0.862125i	$0.669133\pi$
$192$		0			0
$193$	−1.77680	−	12.3579i	−0.127897	−	0.889544i	−0.948213	−	0.317634i	$-0.897112\pi$
$193$	−1.77680	−	12.3579i	−0.127897	−	0.889544i	0.820316	−	0.571910i	$-0.193797\pi$
$194$		0			0
$195$	7.83206	−	2.29970i	0.560866	−	0.164685i
$196$		0			0
$197$	−1.08988	+	2.38652i	−0.0776511	+	0.170032i	−0.944476	−	0.328581i	$-0.893430\pi$
$197$	−1.08988	+	2.38652i	−0.0776511	+	0.170032i	0.866825	+	0.498613i	$0.166157\pi$
$198$		0			0
$199$	6.22737	+	7.18676i	0.441446	+	0.509456i	0.932250	−	0.361814i	$-0.117842\pi$
$199$	6.22737	+	7.18676i	0.441446	+	0.509456i	−0.490804	+	0.871270i	$0.663297\pi$
$200$		0			0
$201$	−3.46766	+	2.22853i	−0.244590	+	0.157188i
$202$		0			0
$203$	−0.0271941	−	0.0174766i	−0.00190865	−	0.00122662i
$204$		0			0
$205$	−3.44453	−	1.01140i	−0.240576	−	0.0706395i
$206$		0			0
$207$	1.96337	+	3.03838i	0.136464	+	0.211182i
$208$		0			0
$209$	−0.912252	−	0.267861i	−0.0631018	−	0.0185284i
$210$		0			0
$211$	−11.1386	−	7.15834i	−0.766812	−	0.492800i	0.0978210	−	0.995204i	$-0.468813\pi$
$211$	−11.1386	−	7.15834i	−0.766812	−	0.492800i	−0.864633	+	0.502404i	$0.832449\pi$
$212$		0			0
$213$	−11.9378	+	7.67197i	−0.817966	+	0.525675i
$214$		0			0
$215$	−3.44042	−	3.97045i	−0.234635	−	0.270783i
$216$		0			0
$217$	0.100478	−	0.220016i	0.00682089	−	0.0149357i
$218$		0			0
$219$	1.73713	−	0.510068i	0.117385	−	0.0344672i
$220$		0			0
$221$	−0.425483	−	2.95930i	−0.0286211	−	0.199064i
$222$		0			0
$223$	−4.35198	−	9.52951i	−0.291430	−	0.638143i	0.706120	−	0.708092i	$-0.250444\pi$
$223$	−4.35198	−	9.52951i	−0.291430	−	0.638143i	−0.997551	+	0.0699485i	$0.977717\pi$
$224$		0			0
$225$	−0.107349	+	0.746632i	−0.00715663	+	0.0497755i
$226$		0			0
$227$	−10.5348	+	12.1578i	−0.699221	+	0.806944i	−0.988647	−	0.150257i	$-0.951990\pi$
$227$	−10.5348	+	12.1578i	−0.699221	+	0.806944i	0.289426	+	0.957200i	$0.406535\pi$
$228$		0			0
$229$	4.12377			0.272507			0.136253	−	0.990674i	$-0.456494\pi$
$229$	4.12377			0.272507			0.136253	+	0.990674i	$0.456494\pi$
$230$		0			0
$231$	−0.0213564			−0.00140515
$232$		0			0
$233$	1.52329	−	1.75796i	0.0997937	−	0.115168i	−0.703656	−	0.710541i	$-0.748450\pi$
$233$	1.52329	−	1.75796i	0.0997937	−	0.115168i	0.803449	+	0.595373i	$0.202996\pi$
$234$		0			0
$235$	0.00162715	−	0.0113171i	0.000106143	−	0.000738244i
$236$		0			0
$237$	7.99459	+	17.5057i	0.519304	+	1.13712i
$238$		0			0
$239$	1.94337	+	13.5164i	0.125706	+	0.874304i	0.950910	+	0.309468i	$0.100151\pi$
$239$	1.94337	+	13.5164i	0.125706	+	0.874304i	−0.825204	+	0.564835i	$0.808940\pi$
$240$		0			0
$241$	−1.53832	+	0.451692i	−0.0990921	+	0.0290961i	−0.330903	−	0.943665i	$-0.607353\pi$
$241$	−1.53832	+	0.451692i	−0.0990921	+	0.0290961i	0.231811	+	0.972761i	$0.425535\pi$
$242$		0			0
$243$	−3.18493	+	6.97402i	−0.204313	+	0.447383i
$244$		0			0
$245$	4.58264	+	5.28864i	0.292774	+	0.337879i
$246$		0			0
$247$	14.0776	−	9.04715i	0.895739	−	0.575656i
$248$		0			0
$249$	−16.8248	−	10.8127i	−1.06623	−	0.685224i
$250$		0			0
$251$	−1.29461	−	0.380132i	−0.0817152	−	0.0239937i	0.240619	−	0.970620i	$-0.422649\pi$
$251$	−1.29461	−	0.380132i	−0.0817152	−	0.0239937i	−0.322335	+	0.946626i	$0.604468\pi$
$252$		0			0
$253$	−0.865646	+	0.753874i	−0.0544227	+	0.0473957i
$254$		0			0
$255$	1.31938	+	0.387405i	0.0826228	+	0.0242602i
$256$		0			0
$257$	−5.22941	−	3.36074i	−0.326202	−	0.209637i	0.367282	−	0.930110i	$-0.380289\pi$
$257$	−5.22941	−	3.36074i	−0.326202	−	0.209637i	−0.693483	+	0.720473i	$0.743925\pi$
$258$		0			0
$259$	−0.0946555	+	0.0608314i	−0.00588161	+	0.00377988i
$260$		0			0
$261$	0.346755	+	0.400177i	0.0214636	+	0.0247703i
$262$		0			0
$263$	−2.76648	+	6.05774i	−0.170588	+	0.373536i	−0.975546	−	0.219796i	$-0.929461\pi$
$263$	−2.76648	+	6.05774i	−0.170588	+	0.373536i	0.804958	+	0.593332i	$0.202188\pi$
$264$		0			0
$265$	−11.9219	+	3.50059i	−0.732357	+	0.215039i
$266$		0			0
$267$	0.493473	+	3.43218i	0.0302000	+	0.210046i
$268$		0			0
$269$	5.50695	+	12.0585i	0.335765	+	0.735222i	0.999923	−	0.0123695i	$-0.00393745\pi$
$269$	5.50695	+	12.0585i	0.335765	+	0.735222i	−0.664159	+	0.747591i	$0.731210\pi$
$270$		0			0
$271$	3.47947	−	24.2003i	0.211363	−	1.47006i	−0.557249	−	0.830345i	$-0.688143\pi$
$271$	3.47947	−	24.2003i	0.211363	−	1.47006i	0.768612	−	0.639715i	$-0.220948\pi$
$272$		0			0
$273$	0.246154	−	0.284076i	0.0148979	−	0.0171931i
$274$		0			0
$275$	−0.239353			−0.0144335
$276$		0			0
$277$	8.82711			0.530370			0.265185	−	0.964198i	$-0.414567\pi$
$277$	8.82711			0.530370			0.265185	+	0.964198i	$0.414567\pi$
$278$		0			0
$279$	−2.59456	+	2.99429i	−0.155333	+	0.179263i
$280$		0			0
$281$	−1.22925	+	8.54963i	−0.0733309	+	0.510028i	0.919742	+	0.392525i	$0.128398\pi$
$281$	−1.22925	+	8.54963i	−0.0733309	+	0.510028i	−0.993072	+	0.117503i	$0.962511\pi$
$282$		0			0
$283$	8.43440	+	18.4688i	0.501373	+	1.09785i	0.976021	+	0.217678i	$0.0698483\pi$
$283$	8.43440	+	18.4688i	0.501373	+	1.09785i	−0.474647	+	0.880176i	$0.657424\pi$
$284$		0			0
$285$	1.09534	+	7.61826i	0.0648823	+	0.451267i
$286$		0			0
$287$	−0.158618	+	0.0465744i	−0.00936292	+	0.00274920i
$288$		0			0
$289$	−6.85283	+	15.0056i	−0.403108	+	0.882683i
$290$		0			0
$291$	−0.623324	−	0.719355i	−0.0365399	−	0.0421693i
$292$		0			0
$293$	−24.0325	+	15.4448i	−1.40400	+	0.902294i	−0.999923	−	0.0124328i	$-0.996042\pi$
$293$	−24.0325	+	15.4448i	−1.40400	+	0.902294i	−0.404074	+	0.914726i	$0.632406\pi$
$294$		0			0
$295$	−4.11646	−	2.64549i	−0.239669	−	0.154026i
$296$		0			0
$297$	−0.999300	−	0.293421i	−0.0579853	−	0.0170260i
$298$		0			0
$299$	−0.0503797	−	20.2037i	−0.00291353	−	1.16841i
$300$		0			0
$301$	−0.232128	−	0.0681588i	−0.0133796	−	0.00392861i
$302$		0			0
$303$	−16.6381	−	10.6926i	−0.955832	−	0.614276i
$304$		0			0
$305$	−4.46893	+	2.87201i	−0.255890	+	0.164451i
$306$		0			0
$307$	−20.0401	−	23.1275i	−1.14375	−	1.31996i	−0.940094	−	0.340915i	$-0.889263\pi$
$307$	−20.0401	−	23.1275i	−1.14375	−	1.31996i	−0.203656	−	0.979043i	$-0.565282\pi$
$308$		0			0
$309$	−2.44738	+	5.35900i	−0.139226	+	0.304863i
$310$		0			0
$311$	26.7357	−	7.85031i	1.51604	−	0.445150i	0.585297	−	0.810819i	$-0.300978\pi$
$311$	26.7357	−	7.85031i	1.51604	−	0.445150i	0.930745	+	0.365668i	$0.119160\pi$
$312$		0			0
$313$	−2.90518	−	20.2060i	−0.164211	−	1.14211i	−0.890587	−	0.454813i	$-0.849706\pi$
$313$	−2.90518	−	20.2060i	−0.164211	−	1.14211i	0.726376	−	0.687297i	$-0.241203\pi$
$314$		0			0
$315$	0.0144296	+	0.0315964i	0.000813017	+	0.00178026i
$316$		0			0
$317$	3.21783	−	22.3805i	0.180731	−	1.25701i	−0.674308	−	0.738451i	$-0.735558\pi$
$317$	3.21783	−	22.3805i	0.180731	−	1.25701i	0.855039	−	0.518564i	$-0.173533\pi$
$318$		0			0
$319$	−0.110030	+	0.126982i	−0.00616052	+	0.00710962i
$320$		0			0
$321$	−15.6586			−0.873977
$322$		0			0
$323$	2.81901			0.156854
$324$		0			0
$325$	2.75879	−	3.18381i	0.153030	−	0.176606i
$326$		0			0
$327$	−2.59985	+	18.0824i	−0.143772	+	0.999958i
$328$		0			0
$329$	−0.000218717	0	0.000478923i	−1.20582e−5	0	2.64039e-5i
$330$		0			0
$331$	−2.81411	−	19.5725i	−0.154677	−	1.07580i	−0.908247	−	0.418435i	$-0.862579\pi$
$331$	−2.81411	−	19.5725i	−0.154677	−	1.07580i	0.753569	−	0.657368i	$-0.228330\pi$
$332$		0			0
$333$	1.76843	−	0.519257i	0.0969093	−	0.0284551i
$334$		0			0
$335$	−0.883745	+	1.93513i	−0.0482842	+	0.105728i
$336$		0			0
$337$	−4.78872	−	5.52647i	−0.260858	−	0.301046i	0.610179	−	0.792264i	$-0.291098\pi$
$337$	−4.78872	−	5.52647i	−0.260858	−	0.301046i	−0.871037	+	0.491217i	$0.836552\pi$
$338$		0			0
$339$	−6.34291	+	4.07634i	−0.344500	+	0.221396i
$340$		0			0
$341$	−1.05763	−	0.679695i	−0.0572736	−	0.0368075i
$342$		0			0
$343$	0.618482	+	0.181603i	0.0333949	+	0.00980562i
$344$		0			0
$345$	8.46228	+	3.83912i	0.455594	+	0.206691i
$346$		0			0
$347$	−1.22212	−	0.358846i	−0.0656067	−	0.0192639i	0.248764	−	0.968564i	$-0.419975\pi$
$347$	−1.22212	−	0.358846i	−0.0656067	−	0.0192639i	−0.314371	+	0.949300i	$0.601794\pi$
$348$		0			0
$349$	18.2910	+	11.7549i	0.979095	+	0.629226i	0.929219	−	0.369529i	$-0.120481\pi$
$349$	18.2910	+	11.7549i	0.979095	+	0.629226i	0.0498757	+	0.998755i	$0.484117\pi$
$350$		0			0
$351$	15.4209	−	9.91044i	0.823109	−	0.528980i
$352$		0			0
$353$	−8.72769	−	10.0723i	−0.464528	−	0.536094i	0.474353	−	0.880335i	$-0.342682\pi$
$353$	−8.72769	−	10.0723i	−0.464528	−	0.536094i	−0.938882	+	0.344240i	$0.888136\pi$
$354$		0			0
$355$	−3.04239	+	6.66191i	−0.161473	+	0.353577i
$356$		0			0
$357$	0.0607565	−	0.0178397i	0.00321557	−	0.000944178i
$358$		0			0
$359$	2.88625	+	20.0743i	0.152331	+	1.05948i	0.912300	+	0.409523i	$0.134305\pi$
$359$	2.88625	+	20.0743i	0.152331	+	1.05948i	−0.759969	+	0.649959i	$0.774786\pi$
$360$		0			0
$361$	−1.33823	−	2.93032i	−0.0704334	−	0.154228i
$362$		0			0
$363$	3.01745	−	20.9868i	0.158375	−	1.10152i
$364$		0			0
$365$	0.611893	−	0.706162i	0.0320279	−	0.0369622i
$366$		0			0
$367$	7.79349			0.406817			0.203409	−	0.979094i	$-0.434798\pi$
$367$	7.79349			0.406817			0.203409	+	0.979094i	$0.434798\pi$
$368$		0			0
$369$	2.70793			0.140969
$370$		0			0
$371$	−0.374693	+	0.432419i	−0.0194531	+	0.0224501i
$372$		0			0
$373$	−0.670096	+	4.66062i	−0.0346963	+	0.241318i	−0.999788	−	0.0205946i	$-0.993444\pi$
$373$	−0.670096	+	4.66062i	−0.0346963	+	0.241318i	0.965092	+	0.261912i	$0.0843532\pi$
$374$		0			0
$375$	0.804910	+	1.76251i	0.0415654	+	0.0910155i
$376$		0			0
$377$	−0.420866	−	2.92719i	−0.0216757	−	0.150758i
$378$		0			0
$379$	30.4775	−	8.94900i	1.56552	−	0.459679i	0.619830	−	0.784736i	$-0.287202\pi$
$379$	30.4775	−	8.94900i	1.56552	−	0.459679i	0.945694	+	0.325057i	$0.105384\pi$
$380$		0			0
$381$	−8.04852	+	17.6238i	−0.412338	+	0.902895i
$382$		0			0
$383$	−1.54744	−	1.78584i	−0.0790705	−	0.0912522i	0.714836	−	0.699292i	$-0.246501\pi$
$383$	−1.54744	−	1.78584i	−0.0790705	−	0.0912522i	−0.793906	+	0.608040i	$0.791956\pi$
$384$		0			0
$385$	−0.00927233	+	0.00595897i	−0.000472562	+	0.000303697i
$386$		0			0
$387$	3.33379	+	2.14250i	0.169466	+	0.108909i
$388$		0			0
$389$	−26.1000	−	7.66365i	−1.32332	−	0.388563i	−0.457632	−	0.889142i	$-0.651302\pi$
$389$	−26.1000	−	7.66365i	−1.32332	−	0.388563i	−0.865691	+	0.500579i	$0.833120\pi$
$390$		0			0
$391$	1.83293	−	2.86779i	0.0926953	−	0.145031i
$392$		0			0
$393$	4.34311	+	1.27525i	0.219081	+	0.0643280i
$394$		0			0
$395$	8.35556	+	5.36980i	0.420414	+	0.270184i
$396$		0			0
$397$	8.09079	−	5.19963i	0.406065	−	0.260962i	−0.321627	−	0.946867i	$-0.604230\pi$
$397$	8.09079	−	5.19963i	0.406065	−	0.260962i	0.727692	+	0.685904i	$0.240593\pi$
$398$		0			0
$399$	0.232098	+	0.267855i	0.0116194	+	0.0134095i
$400$		0			0
$401$	9.29488	−	20.3529i	0.464164	−	1.01638i	−0.522355	−	0.852728i	$-0.674946\pi$
$401$	9.29488	−	20.3529i	0.464164	−	1.01638i	0.986519	−	0.163649i	$-0.0523265\pi$
$402$		0			0
$403$	21.2313	−	6.23408i	1.05761	−	0.310541i
$404$		0			0
$405$	1.52191	+	10.5851i	0.0756242	+	0.525978i
$406$		0			0
$407$	0.242950	+	0.531987i	0.0120426	+	0.0263696i
$408$		0			0
$409$	−1.58012	+	10.9900i	−0.0781318	+	0.543419i	0.912733	+	0.408557i	$0.133968\pi$
$409$	−1.58012	+	10.9900i	−0.0781318	+	0.543419i	−0.990864	+	0.134861i	$0.956941\pi$
$410$		0			0
$411$	14.3150	−	16.5204i	0.706108	−	0.814892i
$412$		0			0
$413$	−0.225330			−0.0110878
$414$		0			0
$415$	−10.3219			−0.506681
$416$		0			0
$417$	20.1825	−	23.2919i	0.988343	−	1.14061i
$418$		0			0
$419$	−3.49551	+	24.3118i	−0.170767	+	1.18771i	0.706503	+	0.707710i	$0.250272\pi$
$419$	−3.49551	+	24.3118i	−0.170767	+	1.18771i	−0.877270	+	0.479998i	$0.840637\pi$
$420$		0			0
$421$	6.36290	+	13.9328i	0.310109	+	0.679043i	0.998947	−	0.0458714i	$-0.0146064\pi$
$421$	6.36290	+	13.9328i	0.310109	+	0.679043i	−0.688839	+	0.724915i	$0.741879\pi$
$422$		0			0
$423$	0.00122737	+	0.00853657i	5.96770e−5	+	0.000415062i
$424$		0			0
$425$	0.680934	−	0.199940i	0.0330301	−	0.00969852i
$426$		0			0
$427$	−0.101621	+	0.222518i	−0.00491777	+	0.0107684i
$428$		0			0
$429$	−1.27945	−	1.47656i	−0.0617723	−	0.0712891i
$430$		0			0
$431$	8.07327	−	5.18837i	0.388876	−	0.249915i	−0.331564	−	0.943433i	$-0.607576\pi$
$431$	8.07327	−	5.18837i	0.388876	−	0.249915i	0.720440	+	0.693517i	$0.243940\pi$
$432$		0			0
$433$	−12.2942	−	7.90103i	−0.590824	−	0.379699i	0.210799	−	0.977529i	$-0.432393\pi$
$433$	−12.2942	−	7.90103i	−0.590824	−	0.379699i	−0.801623	+	0.597830i	$0.796030\pi$
$434$		0			0
$435$	1.30506	+	0.383201i	0.0625730	+	0.0183731i
$436$		0			0
$437$	18.8629	+	2.66409i	0.902336	+	0.127441i
$438$		0			0
$439$	34.7250	+	10.1962i	1.65733	+	0.486637i	0.970685	−	0.240355i	$-0.0772637\pi$
$439$	34.7250	+	10.1962i	1.65733	+	0.486637i	0.686647	+	0.726991i	$0.259082\pi$
$440$		0			0
$441$	−4.44061	−	2.85381i	−0.211458	−	0.135896i
$442$		0			0
$443$	29.9543	−	19.2505i	1.42317	−	0.914617i	0.423209	−	0.906032i	$-0.360904\pi$
$443$	29.9543	−	19.2505i	1.42317	−	0.914617i	0.999963	−	0.00858525i	$-0.00273280\pi$
$444$		0			0
$445$	1.17192	+	1.35246i	0.0555542	+	0.0641130i
$446$		0			0
$447$	−15.7117	+	34.4037i	−0.743136	+	1.62724i
$448$		0			0
$449$	1.05131	−	0.308693i	0.0496144	−	0.0145681i	−0.256831	−	0.966456i	$-0.582678\pi$
$449$	1.05131	−	0.308693i	0.0496144	−	0.0145681i	0.306446	+	0.951888i	$0.400860\pi$
$450$		0			0
$451$	0.122286	+	0.850518i	0.00575823	+	0.0400494i
$452$		0			0
$453$	−2.12512	−	4.65336i	−0.0998467	−	0.218634i
$454$		0			0
$455$	0.0276085	−	0.192021i	0.00129431	−	0.00900209i
$456$		0			0
$457$	12.4649	−	14.3852i	0.583083	−	0.672913i	−0.385182	−	0.922841i	$-0.625861\pi$
$457$	12.4649	−	14.3852i	0.583083	−	0.672913i	0.968265	+	0.249927i	$0.0804068\pi$
$458$		0			0
$459$	3.08800			0.144136
$460$		0			0
$461$	32.9352			1.53395			0.766973	−	0.641679i	$-0.221762\pi$
$461$	32.9352			1.53395			0.766973	+	0.641679i	$0.221762\pi$
$462$		0			0
$463$	−22.0429	+	25.4389i	−1.02442	+	1.18225i	−0.0413269	+	0.999146i	$0.513158\pi$
$463$	−22.0429	+	25.4389i	−1.02442	+	1.18225i	−0.983094	+	0.183099i	$0.941387\pi$
$464$		0			0
$465$	−1.44838	+	10.0737i	−0.0671668	+	0.467155i
$466$		0			0
$467$	4.89251	+	10.7131i	0.226398	+	0.495743i	0.988408	−	0.151823i	$-0.0485142\pi$
$467$	4.89251	+	10.7131i	0.226398	+	0.495743i	−0.762009	+	0.647566i	$0.775787\pi$
$468$		0			0
$469$	0.0139418	+	0.0969671i	0.000643771	+	0.00447753i
$470$		0			0
$471$	35.6820	−	10.4772i	1.64414	−	0.482763i
$472$		0			0
$473$	−0.522377	+	1.14385i	−0.0240189	+	0.0525941i
$474$		0			0
$475$	2.60125	+	3.00201i	0.119354	+	0.137741i
$476$		0			0
$477$	7.88461	−	5.06713i	0.361012	−	0.232008i
$478$		0			0
$479$	27.9522	+	17.9638i	1.27717	+	0.820786i	0.990536	−	0.137254i	$-0.0438277\pi$
$479$	27.9522	+	17.9638i	1.27717	+	0.820786i	0.286633	+	0.958041i	$0.407464\pi$
$480$		0			0
$481$	−9.87659	−	2.90003i	−0.450334	−	0.132230i
$482$		0			0
$483$	0.423401	−	0.0619538i	0.0192654	−	0.00281900i
$484$		0			0
$485$	−0.471348	−	0.138400i	−0.0214028	−	0.00628443i
$486$		0			0
$487$	−1.66502	−	1.07004i	−0.0754492	−	0.0484883i	0.502372	−	0.864651i	$-0.332461\pi$
$487$	−1.66502	−	1.07004i	−0.0754492	−	0.0484883i	−0.577822	+	0.816163i	$0.696097\pi$
$488$		0			0
$489$	−27.7394	+	17.8271i	−1.25442	+	0.806167i
$490$		0			0
$491$	−17.3781	−	20.0554i	−0.784263	−	0.905088i	0.213146	−	0.977020i	$-0.431629\pi$
$491$	−17.3781	−	20.0554i	−0.784263	−	0.905088i	−0.997410	+	0.0719324i	$0.977083\pi$
$492$		0			0
$493$	0.206952	−	0.453162i	0.00932065	−	0.0204094i
$494$		0			0
$495$	0.173233	−	0.0508658i	0.00778625	−	0.00228625i
$496$		0			0
$497$	0.0479961	+	0.333820i	0.00215292	+	0.0149739i
$498$		0			0
$499$	13.2525	+	29.0188i	0.593261	+	1.29906i	0.933451	+	0.358704i	$0.116781\pi$
$499$	13.2525	+	29.0188i	0.593261	+	1.29906i	−0.340190	+	0.940357i	$0.610491\pi$
$500$		0			0
$501$	2.65976	−	18.4990i	0.118829	−	0.826476i
$502$		0			0
$503$	−11.6418	+	13.4354i	−0.519083	+	0.599054i	−0.953401	−	0.301706i	$-0.902444\pi$
$503$	−11.6418	+	13.4354i	−0.519083	+	0.599054i	0.434318	+	0.900760i	$0.356989\pi$
$504$		0			0
$505$	−10.2073			−0.454219
$506$		0			0
$507$	9.19888			0.408537
$508$		0			0
$509$	22.9708	−	26.5097i	1.01816	−	1.17502i	0.0336968	−	0.999432i	$-0.489272\pi$
$509$	22.9708	−	26.5097i	1.01816	−	1.17502i	0.984464	−	0.175588i	$-0.0561826\pi$
$510$		0			0
$511$	0.00612350	−	0.0425898i	0.000270888	−	0.00188406i
$512$		0			0
$513$	7.18011	+	15.7222i	0.317009	+	0.694154i
$514$		0			0
$515$	0.432717	+	3.00961i	0.0190678	+	0.132619i
$516$		0			0
$517$	−0.00262578		0.000770998i	−0.000115482		3.39085e-5i
$518$		0			0
$519$	−17.5756	+	38.4851i	−0.771481	+	1.68931i
$520$		0			0
$521$	−12.9674	−	14.9652i	−0.568113	−	0.655638i	0.396893	−	0.917865i	$-0.370089\pi$
$521$	−12.9674	−	14.9652i	−0.568113	−	0.655638i	−0.965006	+	0.262227i	$0.915543\pi$
$522$		0			0
$523$	17.1146	−	10.9989i	0.748370	−	0.480948i	−0.110030	−	0.993928i	$-0.535095\pi$
$523$	17.1146	−	10.9989i	0.748370	−	0.480948i	0.858401	+	0.512980i	$0.171458\pi$
$524$		0			0
$525$	0.0750611	+	0.0482388i	0.00327593	+	0.00210532i
$526$		0			0
$527$	3.57660	+	1.05019i	0.155799	+	0.0457468i
$528$		0			0
$529$	14.9749	−	17.4571i	0.651084	−	0.759006i
$530$		0			0
$531$	3.54151	+	1.03988i	0.153688	+	0.0451270i
$532$		0			0
$533$	−12.7228	−	8.17647i	−0.551087	−	0.354162i
$534$		0			0
$535$	−6.79852	+	4.36914i	−0.293926	+	0.188895i
$536$		0			0
$537$	−6.65236	−	7.67724i	−0.287071	−	0.331297i
$538$		0			0
$539$	0.695806	−	1.52360i	0.0299705	−	0.0656262i
$540$		0			0
$541$	−30.4712	+	8.94715i	−1.31006	+	0.384668i	−0.860895	−	0.508782i	$-0.830096\pi$
$541$	−30.4712	+	8.94715i	−1.31006	+	0.384668i	−0.449163	+	0.893450i	$0.648278\pi$
$542$		0			0
$543$	−7.16256	−	49.8167i	−0.307375	−	2.13784i
$544$		0			0
$545$	3.91666	+	8.57629i	0.167771	+	0.367368i
$546$		0			0
$547$	5.60991	−	39.0178i	0.239863	−	1.66828i	−0.412944	−	0.910757i	$-0.635499\pi$
$547$	5.60991	−	39.0178i	0.239863	−	1.66828i	0.652806	−	0.757525i	$-0.273592\pi$
$548$		0			0
$549$	2.62407	−	3.02834i	0.111993	−	0.129246i
$550$		0			0
$551$	2.78842			0.118791
$552$		0			0
$553$	0.457374			0.0194495
$554$		0			0
$555$	3.10035	−	3.57799i	0.131602	−	0.151877i
$556$		0			0
$557$	2.70975	−	18.8467i	0.114816	−	0.798562i	−0.848308	−	0.529503i	$-0.822378\pi$
$557$	2.70975	−	18.8467i	0.114816	−	0.798562i	0.963124	−	0.269059i	$-0.0867126\pi$
$558$		0			0
$559$	−9.19419	−	20.1325i	−0.388873	−	0.851513i
$560$		0			0
$561$	−0.0468401	−	0.325780i	−0.00197759	−	0.0137544i
$562$		0			0
$563$	−13.5459	+	3.97742i	−0.570890	+	0.167628i	−0.554421	−	0.832236i	$-0.687060\pi$
$563$	−13.5459	+	3.97742i	−0.570890	+	0.167628i	−0.0164681	+	0.999864i	$0.505242\pi$
$564$		0			0
$565$	−1.61651	+	3.53967i	−0.0680071	+	0.148915i
$566$		0			0
$567$	0.322485	+	0.372168i	0.0135431	+	0.0156296i
$568$		0			0
$569$	−38.3375	+	24.6380i	−1.60719	+	1.03288i	−0.643647	+	0.765322i	$0.722580\pi$
$569$	−38.3375	+	24.6380i	−1.60719	+	1.03288i	−0.963542	+	0.267556i	$0.913784\pi$
$570$		0			0
$571$	−2.38979	−	1.53583i	−0.100010	−	0.0642724i	0.489680	−	0.871902i	$-0.337114\pi$
$571$	−2.38979	−	1.53583i	−0.100010	−	0.0642724i	−0.589690	+	0.807630i	$0.700750\pi$
$572$		0			0
$573$	−29.4822	−	8.65674i	−1.23164	−	0.361641i
$574$		0			0
$575$	4.74530	−	0.694353i	0.197893	−	0.0289565i
$576$		0			0
$577$	11.4077	+	3.34962i	0.474911	+	0.139446i	0.510424	−	0.859923i	$-0.329488\pi$
$577$	11.4077	+	3.34962i	0.474911	+	0.139446i	−0.0355134	+	0.999369i	$0.511307\pi$
$578$		0			0
$579$	20.3508	+	13.0787i	0.845750	+	0.543531i
$580$		0			0
$581$	−0.399860	+	0.256974i	−0.0165890	+	0.0106611i
$582$		0			0
$583$	1.94757	+	2.24761i	0.0806599	+	0.0930865i
$584$		0			0
$585$	−1.32008	+	2.89058i	−0.0545787	+	0.119511i
$586$		0			0
$587$	−44.8430	+	13.1671i	−1.85087	+	0.543464i	−0.851038	+	0.525103i	$0.824027\pi$
$587$	−44.8430	+	13.1671i	−1.85087	+	0.543464i	−0.999831	+	0.0183611i	$0.994155\pi$
$588$		0			0
$589$	2.96927	+	20.6517i	0.122347	+	0.850940i
$590$		0			0
$591$	−2.11177	−	4.62412i	−0.0868664	−	0.190211i
$592$		0			0
$593$	4.84662	−	33.7090i	0.199027	−	1.38426i	−0.608089	−	0.793869i	$-0.708064\pi$
$593$	4.84662	−	33.7090i	0.199027	−	1.38426i	0.807116	−	0.590393i	$-0.201027\pi$
$594$		0			0
$595$	0.0214010	−	0.0246981i	0.000877357	−	0.00101252i
$596$		0			0
$597$	−18.4256			−0.754108
$598$		0			0
$599$	−15.3446			−0.626963			−0.313481	−	0.949594i	$-0.601495\pi$
$599$	−15.3446			−0.626963			−0.313481	+	0.949594i	$0.601495\pi$
$600$		0			0
$601$	−16.8981	+	19.5015i	−0.689290	+	0.795483i	−0.987264	−	0.159091i	$-0.949144\pi$
$601$	−16.8981	+	19.5015i	−0.689290	+	0.795483i	0.297974	+	0.954574i	$0.403689\pi$
$602$		0			0
$603$	0.228373	−	1.58837i	0.00930007	−	0.0646834i
$604$		0			0
$605$	−4.54577	−	9.95384i	−0.184812	−	0.404681i
$606$		0			0
$607$	4.45913	+	31.0140i	0.180991	+	1.25882i	0.854427	+	0.519572i	$0.173909\pi$
$607$	4.45913	+	31.0140i	0.180991	+	1.25882i	−0.673436	+	0.739246i	$0.735182\pi$
$608$		0			0
$609$	0.0600972	−	0.0176461i	0.00243526	−	0.000715057i
$610$		0			0
$611$	0.0200091	−	0.0438139i	0.000809483	−	0.00177252i
$612$		0			0
$613$	−9.24200	−	10.6658i	−0.373281	−	0.430789i	0.537765	−	0.843095i	$-0.319269\pi$
$613$	−9.24200	−	10.6658i	−0.373281	−	0.430789i	−0.911045	+	0.412306i	$0.864723\pi$
$614$		0			0
$615$	5.85167	−	3.76064i	0.235962	−	0.151644i
$616$		0			0
$617$	−35.2587	−	22.6594i	−1.41946	−	0.912232i	−0.999990	−	0.00446382i	$-0.998579\pi$
$617$	−35.2587	−	22.6594i	−1.41946	−	0.912232i	−0.419471	−	0.907769i	$-0.637785\pi$
$618$		0			0
$619$	−42.1529	−	12.3772i	−1.69427	−	0.497482i	−0.714841	−	0.699287i	$-0.753501\pi$
$619$	−42.1529	−	12.3772i	−1.69427	−	0.497482i	−0.979426	+	0.201805i	$0.935319\pi$
$620$		0			0
$621$	20.6628	+	2.91830i	0.829171	+	0.117107i
$622$		0			0
$623$	0.0790702	+	0.0232171i	0.00316788	+	0.000930173i
$624$		0			0
$625$	0.841254	+	0.540641i	0.0336501	+	0.0216256i
$626$		0			0
$627$	1.54976	−	0.995971i	0.0618915	−	0.0397753i
$628$		0			0
$629$	−1.13555	−	1.31050i	−0.0452775	−	0.0522530i
$630$		0			0
$631$	−17.1909	+	37.6429i	−0.684361	+	1.49854i	0.173595	+	0.984817i	$0.444462\pi$
$631$	−17.1909	+	37.6429i	−0.684361	+	1.49854i	−0.857956	+	0.513724i	$0.828266\pi$
$632$		0			0
$633$	24.6156	−	7.22779i	0.978382	−	0.287279i
$634$		0			0
$635$	1.42305	+	9.89751i	0.0564719	+	0.392771i
$636$		0			0
$637$	12.2467	+	26.8165i	0.485231	+	1.06251i
$638$		0			0
$639$	0.786199	−	5.46814i	0.0311016	−	0.216316i
$640$		0			0
$641$	−5.16211	+	5.95739i	−0.203891	+	0.235303i	−0.848481	−	0.529225i	$-0.822483\pi$
$641$	−5.16211	+	5.95739i	−0.203891	+	0.235303i	0.644590	+	0.764528i	$0.277028\pi$
$642$		0			0
$643$	0.901584			0.0355550			0.0177775	−	0.999842i	$-0.494341\pi$
$643$	0.901584			0.0355550			0.0177775	+	0.999842i	$0.494341\pi$
$644$		0			0
$645$	10.1795			0.400818
$646$		0			0
$647$	−15.6444	+	18.0546i	−0.615043	+	0.709798i	−0.974758	−	0.223265i	$-0.928329\pi$
$647$	−15.6444	+	18.0546i	−0.615043	+	0.709798i	0.359715	+	0.933062i	$0.382874\pi$
$648$		0			0
$649$	−0.166681	+	1.15929i	−0.00654280	+	0.0455062i
$650$		0			0
$651$	0.194687	+	0.426304i	0.00763037	+	0.0167082i
$652$		0			0
$653$	−3.70623	−	25.7774i	−0.145036	−	1.00875i	−0.924195	−	0.381921i	$-0.875263\pi$
$653$	−3.70623	−	25.7774i	−0.145036	−	1.00875i	0.779159	−	0.626826i	$-0.215646\pi$
$654$		0			0
$655$	2.24149	−	0.658159i	0.0875821	−	0.0257164i
$656$		0			0
$657$	−0.292791	+	0.641124i	−0.0114229	+	0.0250126i
$658$		0			0
$659$	4.71790	+	5.44475i	0.183783	+	0.212097i	0.840164	−	0.542333i	$-0.182459\pi$
$659$	4.71790	+	5.44475i	0.183783	+	0.212097i	−0.656380	+	0.754430i	$0.727913\pi$
$660$		0			0
$661$	−29.2606	+	18.8047i	−1.13811	+	0.731417i	−0.967237	−	0.253877i	$-0.918294\pi$
$661$	−29.2606	+	18.8047i	−1.13811	+	0.731417i	−0.170870	+	0.985294i	$0.554658\pi$
$662$		0			0
$663$	4.87331	+	3.13189i	0.189264	+	0.121632i
$664$		0			0
$665$	0.175509	+	0.0515340i	0.00680593	+	0.00199840i
$666$		0			0
$667$	1.81304	−	2.83667i	0.0702012	−	0.109836i
$668$		0			0
$669$	19.4765	+	5.71883i	0.753007	+	0.221103i
$670$		0			0
$671$	1.06965	+	0.687424i	0.0412935	+	0.0265377i
$672$		0			0
$673$	35.5143	−	22.8237i	1.36898	−	0.879787i	0.370186	−	0.928958i	$-0.379294\pi$
$673$	35.5143	−	22.8237i	1.36898	−	0.879787i	0.998790	+	0.0491703i	$0.0156577\pi$
$674$		0			0
$675$	2.84947	+	3.28846i	0.109676	+	0.126573i
$676$		0			0
$677$	−6.87037	+	15.0440i	−0.264050	+	0.578189i	−0.994495	−	0.104783i	$-0.966585\pi$
$677$	−6.87037	+	15.0440i	−0.264050	+	0.578189i	0.730445	+	0.682971i	$0.239313\pi$
$678$		0			0
$679$	−0.0217052	+	0.00637324i	−0.000832971	+	0.000244582i
$680$		0			0
$681$	−4.43602	−	30.8532i	−0.169989	−	1.18230i
$682$		0			0
$683$	2.32613	+	5.09352i	0.0890070	+	0.194898i	0.948901	−	0.315575i	$-0.102197\pi$
$683$	2.32613	+	5.09352i	0.0890070	+	0.194898i	−0.859894	+	0.510473i	$0.829470\pi$
$684$		0			0
$685$	1.60557	−	11.1670i	0.0613456	−	0.426668i
$686$		0			0
$687$	−5.23249	+	6.03862i	−0.199632	+	0.230388i
$688$		0			0
$689$	−52.3447			−1.99418
$690$		0			0
$691$	−43.5246			−1.65575			−0.827876	−	0.560911i	$-0.810451\pi$
$691$	−43.5246			−1.65575			−0.827876	+	0.560911i	$0.810451\pi$
$692$		0			0
$693$	0.00544453	−	0.00628333i	0.000206821	−	0.000238684i
$694$		0			0
$695$	2.26366	−	15.7441i	0.0858656	−	0.597209i
$696$		0			0
$697$	−1.05836	−	2.31748i	−0.0400882	−	0.0877809i
$698$		0			0
$699$	0.641427	+	4.46123i	0.0242610	+	0.168739i
$700$		0			0
$701$	−26.6193	+	7.81613i	−1.00540	+	0.295211i	−0.742669	−	0.669659i	$-0.766440\pi$
$701$	−26.6193	+	7.81613i	−1.00540	+	0.295211i	−0.262728	+	0.964870i	$0.584622\pi$
$702$		0			0
$703$	4.03192	−	8.82867i	0.152067	−	0.332980i
$704$		0			0
$705$	0.0145074	+	0.0167425i	0.000546382	+	0.000630559i
$706$		0			0
$707$	−0.395422	+	0.254122i	−0.0148714	+	0.00955725i
$708$		0			0
$709$	30.9854	+	19.9131i	1.16368	+	0.747853i	0.972317	−	0.233666i	$-0.0750723\pi$
$709$	30.9854	+	19.9131i	1.16368	+	0.747853i	0.191365	+	0.981519i	$0.438709\pi$
$710$		0			0
$711$	−7.18853	−	2.11074i	−0.269591	−	0.0791591i
$712$		0			0
$713$	22.9397	+	10.4072i	0.859100	+	0.389752i
$714$		0			0
$715$	−0.967499	−	0.284083i	−0.0361824	−	0.0106241i
$716$		0			0
$717$	−22.2585	−	14.3047i	−0.831260	−	0.534218i
$718$		0			0
$719$	−3.43230	+	2.20580i	−0.128003	+	0.0822626i	−0.603075	−	0.797684i	$-0.706058\pi$
$719$	−3.43230	+	2.20580i	−0.128003	+	0.0822626i	0.475072	+	0.879947i	$0.342422\pi$
$720$		0			0
$721$	0.0916907	+	0.105817i	0.00341474	+	0.00394082i
$722$		0			0
$723$	1.29049	−	2.82577i	0.0479937	−	0.105091i
$724$		0			0
$725$	0.673545	−	0.197771i	0.0250148	−	0.00734501i
$726$		0			0
$727$	0.509197	+	3.54154i	0.0188851	+	0.131348i	0.997083	−	0.0763270i	$-0.0243193\pi$
$727$	0.509197	+	3.54154i	0.0188851	+	0.131348i	−0.978198	+	0.207675i	$0.933410\pi$
$728$		0			0
$729$	7.15615	+	15.6698i	0.265043	+	0.580362i
$730$		0			0
$731$	0.530610	−	3.69047i	0.0196253	−	0.136497i
$732$		0			0
$733$	−28.7430	+	33.1712i	−1.06165	+	1.22521i	−0.0882450	+	0.996099i	$0.528126\pi$
$733$	−28.7430	+	33.1712i	−1.06165	+	1.22521i	−0.973401	+	0.229106i	$0.926420\pi$
$734$		0			0
$735$	−13.5591			−0.500136
$736$		0			0
$737$	0.509195			0.0187564
$738$		0			0
$739$	−8.34413	+	9.62964i	−0.306944	+	0.354232i	−0.888174	−	0.459507i	$-0.848026\pi$
$739$	−8.34413	+	9.62964i	−0.306944	+	0.354232i	0.581230	+	0.813739i	$0.302572\pi$
$740$		0			0
$741$	−4.61443	+	32.0941i	−0.169515	+	1.17901i
$742$		0			0
$743$	4.84107	+	10.6005i	0.177602	+	0.388893i	0.977407	−	0.211366i	$-0.0677913\pi$
$743$	4.84107	+	10.6005i	0.177602	+	0.388893i	−0.799805	+	0.600259i	$0.795064\pi$
$744$		0			0
$745$	2.77795	+	19.3211i	0.101776	+	0.707870i
$746$		0			0
$747$	7.47050	−	2.19354i	0.273331	−	0.0802573i
$748$		0			0
$749$	−0.154594	+	0.338514i	−0.00564874	+	0.0123690i
$750$		0			0
$751$	−1.92446	−	2.22094i	−0.0702244	−	0.0810433i	0.719550	−	0.694440i	$-0.244348\pi$
$751$	−1.92446	−	2.22094i	−0.0702244	−	0.0810433i	−0.789775	+	0.613397i	$0.789803\pi$
$752$		0			0
$753$	2.19933	−	1.41342i	0.0801479	−	0.0515079i
$754$		0			0
$755$	−2.22107	−	1.42740i	−0.0808330	−	0.0519482i
$756$		0			0
$757$	49.8893	+	14.6488i	1.81326	+	0.532421i	0.998853	−	0.0478768i	$-0.0152455\pi$
$757$	49.8893	+	14.6488i	1.81326	+	0.532421i	0.814405	+	0.580297i	$0.197064\pi$
$758$		0			0
$759$	−0.00554614	−	2.22416i	−0.000201312	−	0.0807321i
$760$		0			0
$761$	30.7881	+	9.04020i	1.11607	+	0.327707i	0.787218	−	0.616675i	$-0.211521\pi$
$761$	30.7881	+	9.04020i	1.11607	+	0.327707i	0.328850	+	0.944382i	$0.393339\pi$
$762$		0			0
$763$	0.365244	+	0.234728i	0.0132227	+	0.00849773i
$764$		0			0
$765$	−0.450339	+	0.289415i	−0.0162820	+	0.0104638i
$766$		0			0
$767$	−13.4994	−	15.5791i	−0.487435	−	0.562530i
$768$		0			0
$769$	−0.446350	+	0.977371i	−0.0160958	+	0.0352449i	−0.917509	−	0.397715i	$-0.869803\pi$
$769$	−0.446350	+	0.977371i	−0.0160958	+	0.0352449i	0.901413	+	0.432959i	$0.142531\pi$
$770$		0			0
$771$	11.5567	−	3.39334i	0.416203	−	0.122208i
$772$		0			0
$773$	−6.39658	−	44.4892i	−0.230069	−	1.60017i	−0.697799	−	0.716294i	$-0.745837\pi$
$773$	−6.39658	−	44.4892i	−0.230069	−	1.60017i	0.467729	−	0.883872i	$-0.345072\pi$
$774$		0			0
$775$	2.18197	+	4.77784i	0.0783785	+	0.171625i
$776$		0			0
$777$	0.0310266	−	0.215795i	0.00111307	−	0.00774159i
$778$		0			0
$779$	9.33835	−	10.7770i	0.334581	−	0.386127i
$780$		0			0
$781$	1.75296			0.0627259
$782$		0			0
$783$	3.05450			0.109159
$784$		0			0
$785$	12.5687	−	14.5051i	0.448597	−	0.517709i
$786$		0			0
$787$	−6.81375	+	47.3906i	−0.242884	+	1.68929i	0.394618	+	0.918845i	$0.370877\pi$
$787$	−6.81375	+	47.3906i	−0.242884	+	1.68929i	−0.637502	+	0.770449i	$0.720032\pi$
$788$		0			0
$789$	−5.36034	−	11.7375i	−0.190833	−	0.417866i
$790$		0			0
$791$	0.0255017	+	0.177368i	0.000906737	+	0.00630650i
$792$		0			0
$793$	−21.4728	+	6.30497i	−0.762520	+	0.223896i
$794$		0			0
$795$	10.0012	−	21.8995i	0.354705	−	0.776696i
$796$		0			0
$797$	−8.97210	−	10.3544i	−0.317808	−	0.366770i	0.574259	−	0.818674i	$-0.305290\pi$
$797$	−8.97210	−	10.3544i	−0.317808	−	0.366770i	−0.892067	+	0.451904i	$0.850745\pi$
$798$		0			0
$799$	0.00682601	−	0.00438681i	0.000241487	−	0.000155194i
$800$		0			0
$801$	−1.13560	−	0.729804i	−0.0401244	−	0.0257864i
$802$		0			0
$803$	−0.214589	−	0.0630090i	−0.00757268	−	0.00222354i
$804$		0			0
$805$	0.166542	−	0.145038i	0.00586984	−	0.00511192i
$806$		0			0
$807$	−24.6454	−	7.23654i	−0.867559	−	0.254738i
$808$		0			0
$809$	40.9902	+	26.3428i	1.44114	+	0.926164i	0.999581	+	0.0289317i	$0.00921052\pi$
$809$	40.9902	+	26.3428i	1.44114	+	0.926164i	0.441558	+	0.897233i	$0.354426\pi$
$810$		0			0
$811$	32.2755	−	20.7422i	1.13335	−	0.728357i	0.167090	−	0.985942i	$-0.446563\pi$
$811$	32.2755	−	20.7422i	1.13335	−	0.728357i	0.966256	+	0.257585i	$0.0829267\pi$
$812$		0			0
$813$	31.0225	+	35.8019i	1.08801	+	1.25563i
$814$		0			0
$815$	−7.06949	+	15.4800i	−0.247633	+	0.542241i
$816$		0			0
$817$	20.0234	−	5.87940i	0.700530	−	0.205694i
$818$		0			0
$819$	0.0208253	+	0.144843i	0.000727696	+	0.00506124i
$820$		0			0
$821$	2.18554	+	4.78566i	0.0762758	+	0.167021i	0.943928	−	0.330150i	$-0.107099\pi$
$821$	2.18554	+	4.78566i	0.0762758	+	0.167021i	−0.867653	+	0.497171i	$0.834372\pi$
$822$		0			0
$823$	3.56722	−	24.8106i	0.124346	−	0.864842i	−0.828197	−	0.560437i	$-0.810633\pi$
$823$	3.56722	−	24.8106i	0.124346	−	0.864842i	0.952543	−	0.304405i	$-0.0984577\pi$
$824$		0			0
$825$	0.303706	−	0.350495i	0.0105737	−	0.0122027i
$826$		0			0
$827$	−35.7629			−1.24360			−0.621799	−	0.783177i	$-0.713598\pi$
$827$	−35.7629			−1.24360			−0.621799	+	0.783177i	$0.713598\pi$
$828$		0			0
$829$	−12.4676			−0.433019			−0.216510	−	0.976281i	$-0.569467\pi$
$829$	−12.4676			−0.433019			−0.216510	+	0.976281i	$0.569467\pi$
$830$		0			0
$831$	−11.2004	+	12.9259i	−0.388537	+	0.448395i
$832$		0			0
$833$	−0.706772	+	4.91571i	−0.0244882	+	0.170319i
$834$		0			0
$835$	−4.00691	−	8.77391i	−0.138665	−	0.303634i
$836$		0			0
$837$	3.25260	+	22.6223i	0.112426	+	0.781943i
$838$		0			0
$839$	7.30334	−	2.14445i	0.252139	−	0.0740348i	−0.153220	−	0.988192i	$-0.548964\pi$
$839$	7.30334	−	2.14445i	0.252139	−	0.0740348i	0.405360	+	0.914157i	$0.367146\pi$
$840$		0			0
$841$	−11.8423	+	25.9311i	−0.408356	+	0.894175i
$842$		0			0
$843$	−10.9598	−	12.6483i	−0.377477	−	0.435632i
$844$		0			0
$845$	3.99390	−	2.56672i	0.137394	−	0.0882979i
$846$		0			0
$847$	−0.423911	−	0.272431i	−0.0145658	−	0.00936084i
$848$		0			0
$849$	−37.7467	−	11.0834i	−1.29546	−	0.380382i
$850$		0			0
$851$	−6.35989	−	9.84213i	−0.218014	−	0.337384i
$852$		0			0
$853$	11.4129	+	3.35112i	0.390769	+	0.114740i	0.471214	−	0.882019i	$-0.343816\pi$
$853$	11.4129	+	3.35112i	0.390769	+	0.114740i	−0.0804447	+	0.996759i	$0.525634\pi$
$854$		0			0
$855$	−2.52064	−	1.61991i	−0.0862040	−	0.0553999i
$856$		0			0
$857$	17.8535	−	11.4737i	0.609864	−	0.391936i	−0.198942	−	0.980011i	$-0.563751\pi$
$857$	17.8535	−	11.4737i	0.609864	−	0.391936i	0.808806	+	0.588075i	$0.200114\pi$
$858$		0			0
$859$	−31.0647	−	35.8505i	−1.05991	−	1.22320i	−0.973916	−	0.226909i	$-0.927138\pi$
$859$	−31.0647	−	35.8505i	−1.05991	−	1.22320i	−0.0859971	−	0.996295i	$-0.527408\pi$
$860$		0			0
$861$	0.133063	−	0.291368i	0.00453478	−	0.00992978i
$862$		0			0
$863$	14.4800	−	4.25171i	0.492905	−	0.144730i	−0.0258276	−	0.999666i	$-0.508222\pi$
$863$	14.4800	−	4.25171i	0.492905	−	0.144730i	0.518733	+	0.854936i	$0.326404\pi$
$864$		0			0
$865$	3.10751	+	21.6132i	0.105658	+	0.734870i
$866$		0			0
$867$	−13.2781	−	29.0749i	−0.450947	−	0.987436i
$868$		0			0
$869$	0.338328	−	2.35313i	0.0114770	−	0.0798243i
$870$		0			0
$871$	−5.86899	+	6.77317i	−0.198863	+	0.229500i
$872$		0			0
$873$	0.370552			0.0125413
$874$		0			0
$875$	0.0460493			0.00155675
$876$		0			0
$877$	16.3292	−	18.8449i	0.551399	−	0.636348i	−0.409810	−	0.912171i	$-0.634405\pi$
$877$	16.3292	−	18.8449i	0.551399	−	0.636348i	0.961208	+	0.275823i	$0.0889503\pi$
$878$		0			0
$879$	7.87749	−	54.7892i	0.265701	−	1.84799i
$880$		0			0
$881$	9.96248	+	21.8148i	0.335644	+	0.734959i	0.999922	−	0.0125276i	$-0.00398776\pi$
$881$	9.96248	+	21.8148i	0.335644	+	0.734959i	−0.664277	+	0.747486i	$0.731260\pi$
$882$		0			0
$883$	1.39878	+	9.72874i	0.0470728	+	0.327398i	0.999727	+	0.0233440i	$0.00743131\pi$
$883$	1.39878	+	9.72874i	0.0470728	+	0.327398i	−0.952655	+	0.304054i	$0.901660\pi$
$884$		0			0
$885$	9.09711	−	2.67115i	0.305796	−	0.0897898i
$886$		0			0
$887$	8.01369	−	17.5475i	0.269073	−	0.589188i	−0.726071	−	0.687620i	$-0.758655\pi$
$887$	8.01369	−	17.5475i	0.269073	−	0.589188i	0.995144	+	0.0984320i	$0.0313827\pi$
$888$		0			0
$889$	0.301537	+	0.347992i	0.0101132	+	0.0116713i
$890$		0			0
$891$	2.15330	−	1.38384i	0.0721382	−	0.0463604i
$892$		0			0
$893$	0.0382065	+	0.0245538i	0.00127853	+	0.000821663i
$894$		0			0
$895$	−5.03042	−	1.47706i	−0.168148	−	0.0493728i
$896$		0			0
$897$	29.6491	+	25.5620i	0.989956	+	0.853489i
$898$		0			0
$899$	3.53779	+	1.03879i	0.117992	+	0.0346456i
$900$		0			0
$901$	−7.41812	−	4.76733i	−0.247133	−	0.158823i
$902$		0			0
$903$	0.394346	−	0.253431i	0.0131230	−	0.00843364i
$904$		0			0
$905$	−17.0099	−	19.6305i	−0.565429	−	0.652539i
$906$		0			0
$907$	−5.71963	+	12.5243i	−0.189917	+	0.415861i	−0.980507	−	0.196486i	$-0.937047\pi$
$907$	−5.71963	+	12.5243i	−0.189917	+	0.415861i	0.790589	+	0.612347i	$0.209774\pi$
$908$		0			0
$909$	7.38758	−	2.16919i	0.245031	−	0.0719475i
$910$		0			0
$911$	−5.73056	−	39.8569i	−0.189862	−	1.32052i	−0.832362	−	0.554233i	$-0.813012\pi$
$911$	−5.73056	−	39.8569i	−0.189862	−	1.32052i	0.642500	−	0.766286i	$-0.277897\pi$
$912$		0			0
$913$	1.02631	+	2.24731i	0.0339660	+	0.0743752i
$914$		0			0
$915$	1.46485	−	10.1882i	0.0484263	−	0.336813i
$916$		0			0
$917$	0.0704476	−	0.0813008i	0.00232638	−	0.00268479i
$918$		0			0
$919$	4.08011			0.134590			0.0672952	−	0.997733i	$-0.478563\pi$
$919$	4.08011			0.134590			0.0672952	+	0.997733i	$0.478563\pi$
$920$		0			0
$921$	59.2948			1.95383
$922$		0			0
$923$	−20.2046	+	23.3174i	−0.665044	+	0.767501i
$924$		0			0
$925$	0.347733	−	2.41854i	0.0114334	−	0.0795210i
$926$		0			0
$927$	−0.952764	−	2.08626i	−0.0312929	−	0.0685218i
$928$		0			0
$929$	−5.85823	−	40.7449i	−0.192202	−	1.33680i	−0.826163	−	0.563431i	$-0.809481\pi$
$929$	−5.85823	−	40.7449i	−0.192202	−	1.33680i	0.633961	−	0.773365i	$-0.281428\pi$
$930$		0			0
$931$	−26.6712	+	7.83136i	−0.874112	+	0.256662i
$932$		0			0
$933$	−22.4283	+	49.1112i	−0.734271	+	1.60783i
$934$		0			0
$935$	−0.111237	−	0.128375i	−0.00363785	−	0.00419831i
$936$		0			0
$937$	4.35151	−	2.79654i	0.142158	−	0.0913591i	−0.467629	−	0.883925i	$-0.654892\pi$
$937$	4.35151	−	2.79654i	0.142158	−	0.0913591i	0.609786	+	0.792566i	$0.291255\pi$
$938$		0			0
$939$	33.2748	+	21.3844i	1.08588	+	0.697854i
$940$		0			0
$941$	11.9496	+	3.50871i	0.389545	+	0.114381i	0.470639	−	0.882326i	$-0.344023\pi$
$941$	11.9496	+	3.50871i	0.389545	+	0.114381i	−0.0810942	+	0.996706i	$0.525841\pi$
$942$		0			0
$943$	−4.89170	−	16.5072i	−0.159296	−	0.537549i
$944$		0			0
$945$	0.192256	+	0.0564514i	0.00625408	+	0.00183636i
$946$		0			0
$947$	−9.07236	−	5.83045i	−0.294812	−	0.189464i	0.384870	−	0.922971i	$-0.374246\pi$
$947$	−9.07236	−	5.83045i	−0.294812	−	0.189464i	−0.679683	+	0.733506i	$0.737882\pi$
$948$		0			0
$949$	3.31148	−	2.12816i	0.107495	−	0.0690830i
$950$		0			0
$951$	28.6898	+	33.1098i	0.930329	+	1.07366i
$952$		0			0
$953$	1.98816	−	4.35346i	0.0644027	−	0.141022i	−0.874694	−	0.484676i	$-0.838937\pi$
$953$	1.98816	−	4.35346i	0.0644027	−	0.141022i	0.939096	+	0.343654i	$0.111665\pi$
$954$		0			0
$955$	−15.2158	+	4.46776i	−0.492371	+	0.144573i
$956$		0			0
$957$	−0.0463318	−	0.322245i	−0.00149769	−	0.0104167i
$958$		0			0
$959$	−0.215816	−	0.472571i	−0.00696906	−	0.0152601i
$960$		0			0
$961$	0.485474	−	3.37655i	0.0156605	−	0.108921i
$962$		0			0
$963$	3.99196	−	4.60697i	0.128639	−	0.148457i
$964$		0			0
$965$	12.4850			0.401907
$966$		0			0
$967$	11.2050			0.360328			0.180164	−	0.983637i	$-0.442337\pi$
$967$	11.2050			0.360328			0.180164	+	0.983637i	$0.442337\pi$
$968$		0			0
$969$	−3.57693	+	4.12800i	−0.114908	+	0.132610i
$970$		0			0
$971$	3.80594	−	26.4709i	0.122138	−	0.849491i	−0.832988	−	0.553292i	$-0.813372\pi$
$971$	3.80594	−	26.4709i	0.122138	−	0.849491i	0.955126	−	0.296200i	$-0.0957193\pi$
$972$		0			0
$973$	−0.304275	−	0.666270i	−0.00975462	−	0.0213596i
$974$		0			0
$975$	1.16167	+	8.07962i	0.0372034	+	0.258755i
$976$		0			0
$977$	18.0299	−	5.29404i	0.576826	−	0.169371i	0.0197096	−	0.999806i	$-0.493726\pi$
$977$	18.0299	−	5.29404i	0.576826	−	0.169371i	0.557117	+	0.830434i	$0.311908\pi$
$978$		0			0
$979$	0.177938	−	0.389630i	0.00568693	−	0.0124526i
$980$		0			0
$981$	−4.65728	−	5.37479i	−0.148695	−	0.171604i
$982$		0			0
$983$	−23.7263	+	15.2480i	−0.756751	+	0.486334i	−0.861244	−	0.508191i	$-0.830314\pi$
$983$	−23.7263	+	15.2480i	−0.756751	+	0.486334i	0.104493	+	0.994526i	$0.466678\pi$
$984$		0			0
$985$	−2.20712	−	1.41843i	−0.0703246	−	0.0451949i
$986$		0			0
$987$	0.000978829	0	0.000287410i	3.11565e−5	0	9.14836e-6i
$988$		0			0
$989$	7.03814	−	24.1927i	0.223800	−	0.769283i
$990$		0			0
$991$	−16.6403	−	4.88603i	−0.528597	−	0.155210i	0.00653499	−	0.999979i	$-0.497920\pi$
$991$	−16.6403	−	4.88603i	−0.528597	−	0.155210i	−0.535132	+	0.844769i	$0.679738\pi$
$992$		0			0
$993$	32.2316	+	20.7140i	1.02284	+	0.657339i
$994$		0			0
$995$	−7.99986	+	5.14120i	−0.253613	+	0.162987i
$996$		0			0
$997$	20.1736	+	23.2815i	0.638903	+	0.737334i	0.979181	−	0.202991i	$-0.0650664\pi$
$997$	20.1736	+	23.2815i	0.638903	+	0.737334i	−0.340277	+	0.940325i	$0.610521\pi$
$998$		0			0
$999$	4.41665	−	9.67112i	0.139737	−	0.305981i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.m.a.41.1	✓	30
23.9	even	11	inner	460.2.m.a.101.1	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.m.a.41.1	✓	30	1.1	even	1	trivial
460.2.m.a.101.1	yes	30	23.9	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26886 + 1.46434i) q^{3} +(-0.142315 + 0.989821i) q^{5} +(0.0191296 + 0.0418879i) q^{7} +(-0.107349 - 0.746632i) q^{9} +O(q^{10})\)	\(q+(-1.26886 + 1.46434i) q^{3} +(-0.142315 + 0.989821i) q^{5} +(0.0191296 + 0.0418879i) q^{7} +(-0.107349 - 0.746632i) q^{9} +(0.229658 - 0.0674336i) q^{11} +(-1.75005 + 3.83208i) q^{13} +(-1.26886 - 1.46434i) q^{15} +(-0.597021 + 0.383682i) q^{17} +(-3.34165 - 2.14755i) q^{19} +(-0.0856110 - 0.0251377i) q^{21} +(-4.35746 + 2.00313i) q^{23} +(-0.959493 - 0.281733i) q^{25} +(-3.66051 - 2.35247i) q^{27} +(-0.590543 + 0.379519i) q^{29} +(-3.43965 - 3.96957i) q^{31} +(-0.192658 + 0.421862i) q^{33} +(-0.0441840 + 0.0129736i) q^{35} +(0.347733 + 2.41854i) q^{37} +(-3.39091 - 7.42506i) q^{39} +(-0.510902 + 3.55340i) q^{41} +(-3.44042 + 3.97045i) q^{43} +0.754310 q^{45} -0.0114334 q^{47} +(4.58264 - 5.28864i) q^{49} +(0.195694 - 1.36108i) q^{51} +(5.16162 + 11.3024i) q^{53} +(0.0340635 + 0.236917i) q^{55} +(7.38483 - 2.16838i) q^{57} +(-2.03273 + 4.45105i) q^{59} +(3.47877 + 4.01472i) q^{61} +(0.0292213 - 0.0187794i) q^{63} +(-3.54402 - 2.27760i) q^{65} +(2.04121 + 0.599352i) q^{67} +(2.59574 - 8.92251i) q^{69} +(7.02708 + 2.06334i) q^{71} +(-0.786056 - 0.505167i) q^{73} +(1.63002 - 1.04755i) q^{75} +(0.00721790 + 0.00832991i) q^{77} +(4.12602 - 9.03472i) q^{79} +(10.2608 - 3.01283i) q^{81} +(1.46896 + 10.2168i) q^{83} +(-0.294812 - 0.645548i) q^{85} +(0.193571 - 1.34631i) q^{87} +(1.17192 - 1.35246i) q^{89} -0.193996 q^{91} +10.1773 q^{93} +(2.60125 - 3.00201i) q^{95} +(-0.0699118 + 0.486247i) q^{97} +(-0.0750017 - 0.164231i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) \) 30 * q - 3 * q^5 + q^7 + 21 * q^9	\( 30 q - 3 q^{5} + q^{7} + 21 q^{9} + 2 q^{13} + 10 q^{17} + 3 q^{19} + 39 q^{21} + 10 q^{23} - 3 q^{25} + 21 q^{27} + 14 q^{29} - 2 q^{31} - 50 q^{33} - 10 q^{35} + 9 q^{37} + 38 q^{39} - 3 q^{41} - 50 q^{43} + 10 q^{45} - 6 q^{47} - 36 q^{49} - 36 q^{51} - 5 q^{53} - 11 q^{55} + 23 q^{57} + 14 q^{59} - 16 q^{61} - 52 q^{63} + 2 q^{65} + 27 q^{67} + 42 q^{69} + 19 q^{71} + 24 q^{73} - 10 q^{77} - 22 q^{79} + 35 q^{81} + 36 q^{83} + 10 q^{85} - 3 q^{87} - 28 q^{89} - 98 q^{91} - 60 q^{93} - 19 q^{95} - 2 q^{97} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^5 + q^7 + 21 * q^9 + 2 * q^13 + 10 * q^17 + 3 * q^19 + 39 * q^21 + 10 * q^23 - 3 * q^25 + 21 * q^27 + 14 * q^29 - 2 * q^31 - 50 * q^33 - 10 * q^35 + 9 * q^37 + 38 * q^39 - 3 * q^41 - 50 * q^43 + 10 * q^45 - 6 * q^47 - 36 * q^49 - 36 * q^51 - 5 * q^53 - 11 * q^55 + 23 * q^57 + 14 * q^59 - 16 * q^61 - 52 * q^63 + 2 * q^65 + 27 * q^67 + 42 * q^69 + 19 * q^71 + 24 * q^73 - 10 * q^77 - 22 * q^79 + 35 * q^81 + 36 * q^83 + 10 * q^85 - 3 * q^87 - 28 * q^89 - 98 * q^91 - 60 * q^93 - 19 * q^95 - 2 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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