LMFDB - Embedded newform 1050.2.s.i.551.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(101,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("1050.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.s (of order $6$, degree $2$, 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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.11007531417600000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{12} + 48x^{8} - 7x^{4} + 1 $ x^16 - 7x^12 + 48x^8 - 7*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			551.3
Root			$0.596975 + 0.159959i$ of defining polynomial
Character	$\chi$	$=$	1050.551
Dual form			1050.2.s.i.101.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.178197 + 1.72286i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.707107 - 1.58114i) q^{6} +(2.23607 - 1.41421i) q^{7} -1.00000i q^{8} +(-2.93649 + 0.614017i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.178197 + 1.72286i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.707107 - 1.58114i) q^{6} +(2.23607 - 1.41421i) q^{7} -1.00000i q^{8} +(-2.93649 + 0.614017i) q^{9} +(0.184829 - 0.106711i) q^{11} +(-1.40294 + 1.01575i) q^{12} -6.70141i q^{13} +(-2.64360 + 0.106711i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.58114 - 2.73861i) q^{17} +(2.85008 + 0.936492i) q^{18} +(-4.23861 - 2.44716i) q^{19} +(2.83495 + 3.60042i) q^{21} -0.213422 q^{22} +(-5.60944 - 3.23861i) q^{23} +(1.72286 - 0.178197i) q^{24} +(-3.35071 + 5.80359i) q^{26} +(-1.58114 - 4.94975i) q^{27} +(2.34278 + 1.22938i) q^{28} +2.02265i q^{29} +(-0.261387 + 0.150912i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.216784 + 0.299418i) q^{33} +3.16228i q^{34} +(-2.00000 - 2.23607i) q^{36} +(3.56752 - 6.17913i) q^{37} +(2.44716 + 4.23861i) q^{38} +(11.5456 - 1.19417i) q^{39} -6.70141 q^{41} +(-0.654929 - 4.53553i) q^{42} -2.02265 q^{43} +(0.184829 + 0.106711i) q^{44} +(3.23861 + 5.60944i) q^{46} +(-3.87739 + 6.71584i) q^{47} +(-1.58114 - 0.707107i) q^{48} +(3.00000 - 6.32456i) q^{49} +(4.43649 - 3.21209i) q^{51} +(5.80359 - 3.35071i) q^{52} +(-4.33013 + 2.50000i) q^{53} +(-1.10557 + 5.07718i) q^{54} +(-1.41421 - 2.23607i) q^{56} +(3.46081 - 7.73861i) q^{57} +(1.01132 - 1.75166i) q^{58} +(2.45877 + 4.25871i) q^{59} +(3.00000 + 1.73205i) q^{61} +0.301824 q^{62} +(-5.69784 + 5.52581i) q^{63} -1.00000 q^{64} +(-0.0380311 - 0.367696i) q^{66} +(-2.66291 - 4.61230i) q^{67} +(1.58114 - 2.73861i) q^{68} +(4.58009 - 10.2414i) q^{69} +2.02265i q^{71} +(0.614017 + 2.93649i) q^{72} +(10.3824 - 5.99430i) q^{73} +(-6.17913 + 3.56752i) q^{74} -4.89433i q^{76} +(0.262377 - 0.500000i) q^{77} +(-10.5959 - 4.73861i) q^{78} +(0.261387 - 0.452736i) q^{79} +(8.24597 - 3.60611i) q^{81} +(5.80359 + 3.35071i) q^{82} +16.7169 q^{83} +(-1.70058 + 4.25535i) q^{84} +(1.75166 + 1.01132i) q^{86} +(-3.48474 + 0.360429i) q^{87} +(-0.106711 - 0.184829i) q^{88} +(5.28720 - 9.15769i) q^{89} +(-9.47723 - 14.9848i) q^{91} -6.47723i q^{92} +(-0.306579 - 0.423441i) q^{93} +(6.71584 - 3.87739i) q^{94} +(1.01575 + 1.40294i) q^{96} -3.50333i q^{97} +(-5.76035 + 3.97723i) q^{98} +(-0.477226 + 0.426844i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 16 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 - 16 * q^9	$ 16 q + 8 q^{4} - 16 q^{9} - 8 q^{16} - 24 q^{19} + 8 q^{21} - 48 q^{31} - 32 q^{36} + 16 q^{39} + 8 q^{46} + 48 q^{49} + 40 q^{51} + 48 q^{61} - 16 q^{64} + 24 q^{66} + 48 q^{79} + 8 q^{81} - 8 q^{84} - 64 q^{91} - 24 q^{94} + 80 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 - 16 * q^9 - 8 * q^16 - 24 * q^19 + 8 * q^21 - 48 * q^31 - 32 * q^36 + 16 * q^39 + 8 * q^46 + 48 * q^49 + 40 * q^51 + 48 * q^61 - 16 * q^64 + 24 * q^66 + 48 * q^79 + 8 * q^81 - 8 * q^84 - 64 * q^91 - 24 * q^94 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.178197	+	1.72286i	0.102882	+	0.994694i
$3$	0.178197	+	1.72286i	0.102882	+	0.994694i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	0.707107	−	1.58114i	0.288675	−	0.645497i
$7$	2.23607	−	1.41421i	0.845154	−	0.534522i
$7$	2.23607	−	1.41421i	0.845154	−	0.534522i
$8$		−	1.00000i		−	0.353553i
$9$	−2.93649	+	0.614017i	−0.978831	+	0.204672i
$10$		0			0
$11$	0.184829	−	0.106711i	0.0557279	−	0.0321745i	−0.471877	−	0.881664i	$-0.656423\pi$
$11$	0.184829	−	0.106711i	0.0557279	−	0.0321745i	0.527605	+	0.849490i	$0.323090\pi$
$12$	−1.40294	+	1.01575i	−0.404994	+	0.293223i
$13$		−	6.70141i		−	1.85864i	−0.369279	−	0.929318i	$-0.620395\pi$
$13$		−	6.70141i		−	1.85864i	0.369279	−	0.929318i	$-0.379605\pi$
$14$	−2.64360	+	0.106711i	−0.706531	+	0.0285197i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.58114	−	2.73861i	−0.383482	−	0.664211i	0.608075	−	0.793880i	$-0.291942\pi$
$17$	−1.58114	−	2.73861i	−0.383482	−	0.664211i	−0.991557	+	0.129668i	$0.958609\pi$
$18$	2.85008	+	0.936492i	0.671771	+	0.220733i
$19$	−4.23861	−	2.44716i	−0.972404	−	0.561418i	−0.0724360	−	0.997373i	$-0.523077\pi$
$19$	−4.23861	−	2.44716i	−0.972404	−	0.561418i	−0.899968	+	0.435955i	$0.856411\pi$
$20$		0			0
$21$	2.83495	+	3.60042i	0.618637	+	0.785677i
$22$	−0.213422			−0.0455017
$23$	−5.60944	−	3.23861i	−1.16965	−	0.675297i	−0.216052	−	0.976382i	$-0.569318\pi$
$23$	−5.60944	−	3.23861i	−1.16965	−	0.675297i	−0.953597	+	0.301084i	$0.902651\pi$
$24$	1.72286	−	0.178197i	0.351677	−	0.0363743i
$25$		0			0
$26$	−3.35071	+	5.80359i	−0.657127	+	1.13818i
$27$	−1.58114	−	4.94975i	−0.304290	−	0.952579i
$28$	2.34278	+	1.22938i	0.442744	+	0.232332i
$29$			2.02265i			0.375596i	0.982208	+	0.187798i	$0.0601350\pi$
$29$			2.02265i			0.375596i	−0.982208	+	0.187798i	$0.939865\pi$
$30$		0			0
$31$	−0.261387	+	0.150912i	−0.0469465	+	0.0271046i	−0.523290	−	0.852155i	$-0.675295\pi$
$31$	−0.261387	+	0.150912i	−0.0469465	+	0.0271046i	0.476343	+	0.879260i	$0.341962\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	0.216784	+	0.299418i	0.0377372	+	0.0521220i
$34$			3.16228i			0.542326i
$35$		0			0
$36$	−2.00000	−	2.23607i	−0.333333	−	0.372678i
$37$	3.56752	−	6.17913i	0.586497	−	1.01584i	−0.408190	−	0.912897i	$-0.633840\pi$
$37$	3.56752	−	6.17913i	0.586497	−	1.01584i	0.994687	−	0.102946i	$-0.0328269\pi$
$38$	2.44716	+	4.23861i	0.396982	+	0.687594i
$39$	11.5456	−	1.19417i	1.84877	−	0.191220i
$40$		0			0
$41$	−6.70141			−1.04658			−0.523292	−	0.852153i	$-0.675296\pi$
$41$	−6.70141			−1.04658			−0.523292	+	0.852153i	$0.675296\pi$
$42$	−0.654929	−	4.53553i	−0.101058	−	0.699848i
$43$	−2.02265			−0.308451			−0.154225	−	0.988036i	$-0.549288\pi$
$43$	−2.02265			−0.308451			−0.154225	+	0.988036i	$0.549288\pi$
$44$	0.184829	+	0.106711i	0.0278640	+	0.0160873i
$45$		0			0
$46$	3.23861	+	5.60944i	0.477507	+	0.827067i
$47$	−3.87739	+	6.71584i	−0.565576	+	0.979606i	0.431420	+	0.902151i	$0.358013\pi$
$47$	−3.87739	+	6.71584i	−0.565576	+	0.979606i	−0.996996	+	0.0774546i	$0.975321\pi$
$48$	−1.58114	−	0.707107i	−0.228218	−	0.102062i
$49$	3.00000	−	6.32456i	0.428571	−	0.903508i
$50$		0			0
$51$	4.43649	−	3.21209i	0.621233	−	0.449783i
$52$	5.80359	−	3.35071i	0.804813	−	0.464659i
$53$	−4.33013	+	2.50000i	−0.594789	+	0.343401i	−0.766989	−	0.641661i	$-0.778246\pi$
$53$	−4.33013	+	2.50000i	−0.594789	+	0.343401i	0.172200	+	0.985062i	$0.444912\pi$
$54$	−1.10557	+	5.07718i	−0.150449	+	0.690916i
$55$		0			0
$56$	−1.41421	−	2.23607i	−0.188982	−	0.298807i
$57$	3.46081	−	7.73861i	0.458396	−	1.02500i
$58$	1.01132	−	1.75166i	0.132793	−	0.230005i
$59$	2.45877	+	4.25871i	0.320105	+	0.554437i	0.980509	−	0.196472i	$-0.0629486\pi$
$59$	2.45877	+	4.25871i	0.320105	+	0.554437i	−0.660405	+	0.750910i	$0.729615\pi$
$60$		0			0
$61$	3.00000	+	1.73205i	0.384111	+	0.221766i	0.679605	−	0.733578i	$-0.262151\pi$
$61$	3.00000	+	1.73205i	0.384111	+	0.221766i	−0.295495	+	0.955344i	$0.595484\pi$
$62$	0.301824			0.0383317
$63$	−5.69784	+	5.52581i	−0.717861	+	0.696187i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−0.0380311	−	0.367696i	−0.00468131	−	0.0452602i
$67$	−2.66291	−	4.61230i	−0.325326	−	0.563482i	0.656252	−	0.754542i	$-0.272141\pi$
$67$	−2.66291	−	4.61230i	−0.325326	−	0.563482i	−0.981578	+	0.191060i	$0.938808\pi$
$68$	1.58114	−	2.73861i	0.191741	−	0.332106i
$69$	4.58009	−	10.2414i	0.551378	−	1.23292i
$70$		0			0
$71$			2.02265i			0.240044i	0.992771	+	0.120022i	$0.0382965\pi$
$71$			2.02265i			0.240044i	−0.992771	+	0.120022i	$0.961703\pi$
$72$	0.614017	+	2.93649i	0.0723626	+	0.346069i
$73$	10.3824	−	5.99430i	1.21517	−	0.701580i	0.251291	−	0.967912i	$-0.419145\pi$
$73$	10.3824	−	5.99430i	1.21517	−	0.701580i	0.963882	+	0.266331i	$0.0858116\pi$
$74$	−6.17913	+	3.56752i	−0.718310	+	0.414716i
$75$		0			0
$76$		−	4.89433i		−	0.561418i
$77$	0.262377	−	0.500000i	0.0299007	−	0.0569803i
$78$	−10.5959	−	4.73861i	−1.19974	−	0.536542i
$79$	0.261387	−	0.452736i	0.0294084	−	0.0509368i	−0.850947	−	0.525252i	$-0.823971\pi$
$79$	0.261387	−	0.452736i	0.0294084	−	0.0509368i	0.880355	+	0.474315i	$0.157304\pi$
$80$		0			0
$81$	8.24597	−	3.60611i	0.916219	−	0.400679i
$82$	5.80359	+	3.35071i	0.640899	+	0.370023i
$83$	16.7169			1.83491			0.917457	−	0.397835i	$-0.130238\pi$
$83$	16.7169			1.83491			0.917457	+	0.397835i	$0.130238\pi$
$84$	−1.70058	+	4.25535i	−0.185549	+	0.464297i
$85$		0			0
$86$	1.75166	+	1.01132i	0.188887	+	0.109054i
$87$	−3.48474	+	0.360429i	−0.373603	+	0.0386421i
$88$	−0.106711	−	0.184829i	−0.0113754	−	0.0197028i
$89$	5.28720	−	9.15769i	0.560442	−	0.970714i	−0.437016	−	0.899454i	$-0.643965\pi$
$89$	5.28720	−	9.15769i	0.560442	−	0.970714i	0.997458	−	0.0712599i	$-0.0227020\pi$
$90$		0			0
$91$	−9.47723	−	14.9848i	−0.993483	−	1.57083i
$92$		−	6.47723i		−	0.675297i
$93$	−0.306579	−	0.423441i	−0.0317907	−	0.0439088i
$94$	6.71584	−	3.87739i	0.692686	−	0.399922i
$95$		0			0
$96$	1.01575	+	1.40294i	0.103670	+	0.143187i
$97$		−	3.50333i		−	0.355709i	−0.984057	−	0.177854i	$-0.943084\pi$
$97$		−	3.50333i		−	0.355709i	0.984057	−	0.177854i	$-0.0569156\pi$
$98$	−5.76035	+	3.97723i	−0.581884	+	0.401760i
$99$	−0.477226	+	0.426844i	−0.0479630	+	0.0428994i
$100$		0			0
$101$	−5.65685	−	9.79796i	−0.562878	−	0.974933i	−0.997244	−	0.0741967i	$-0.976361\pi$
$101$	−5.65685	−	9.79796i	−0.562878	−	0.974933i	0.434366	−	0.900737i	$-0.356973\pi$
$102$	−5.44816	+	0.563508i	−0.539448	+	0.0557956i
$103$	9.15769	+	5.28720i	0.902334	+	0.520963i	0.877957	−	0.478740i	$-0.158906\pi$
$103$	9.15769	+	5.28720i	0.902334	+	0.520963i	0.0243776	+	0.999703i	$0.492240\pi$
$104$	−6.70141			−0.657127
$105$		0			0
$106$	5.00000			0.485643
$107$	−4.74342	−	2.73861i	−0.458563	−	0.264752i	0.252877	−	0.967499i	$-0.418623\pi$
$107$	−4.74342	−	2.73861i	−0.458563	−	0.264752i	−0.711440	+	0.702747i	$0.751957\pi$
$108$	3.49604	−	3.84418i	0.336406	−	0.369906i
$109$	6.21584	+	10.7661i	0.595369	+	1.03121i	0.993495	+	0.113879i	$0.0363276\pi$
$109$	6.21584	+	10.7661i	0.595369	+	1.03121i	−0.398125	+	0.917331i	$0.630339\pi$
$110$		0			0
$111$	11.2815	+	5.04524i	1.07079	+	0.478873i
$112$	0.106711	+	2.64360i	0.0100832	+	0.249797i
$113$		−	6.52277i		−	0.613611i	−0.951772	−	0.306806i	$-0.900740\pi$
$113$		−	6.52277i		−	0.613611i	0.951772	−	0.306806i	$-0.0992601\pi$
$114$	−6.86646	+	4.97143i	−0.643103	+	0.465617i
$115$		0			0
$116$	−1.75166	+	1.01132i	−0.162638	+	0.0938990i
$117$	4.11478	+	19.6786i	0.380411	+	1.81929i
$118$		−	4.91754i		−	0.452696i
$119$	−7.40852	−	3.88766i	−0.679138	−	0.356381i
$120$		0			0
$121$	−5.47723	+	9.48683i	−0.497930	+	0.862439i
$122$	−1.73205	−	3.00000i	−0.156813	−	0.271607i
$123$	−1.19417	−	11.5456i	−0.107675	−	1.04103i
$124$	−0.261387	−	0.150912i	−0.0234733	−	0.0135523i
$125$		0			0
$126$	7.69738	−	1.93657i	0.685737	−	0.172523i
$127$	−13.6298			−1.20945			−0.604726	−	0.796434i	$-0.706717\pi$
$127$	−13.6298			−1.20945			−0.604726	+	0.796434i	$0.706717\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−0.360429	−	3.48474i	−0.0317340	−	0.306814i
$130$		0			0
$131$	3.01326	−	5.21911i	0.263269	−	0.455996i	−0.703839	−	0.710359i	$-0.748533\pi$
$131$	3.01326	−	5.21911i	0.263269	−	0.455996i	0.967109	+	0.254363i	$0.0818659\pi$
$132$	−0.150912	+	0.337449i	−0.0131352	+	0.0293712i
$133$	−12.9386	+	0.522278i	−1.12192	+	0.0452873i
$134$			5.32582i			0.460081i
$135$		0			0
$136$	−2.73861	+	1.58114i	−0.234834	+	0.135582i
$137$	6.47547	−	3.73861i	0.553237	−	0.319411i	−0.197190	−	0.980365i	$-0.563182\pi$
$137$	6.47547	−	3.73861i	0.553237	−	0.319411i	0.750426	+	0.660954i	$0.229848\pi$
$138$	−9.08717	+	6.57926i	−0.773551	+	0.560064i
$139$			7.53185i			0.638843i	0.947613	+	0.319422i	$0.103489\pi$
$139$			7.53185i			0.638843i	−0.947613	+	0.319422i	$0.896511\pi$
$140$		0			0
$141$	−12.2614	−	5.48346i	−1.03260	−	0.461791i
$142$	1.01132	−	1.75166i	0.0848683	−	0.146996i
$143$	−0.715113	−	1.23861i	−0.0598008	−	0.103578i
$144$	0.936492	−	2.85008i	0.0780410	−	0.237507i
$145$		0			0
$146$	−11.9886			−0.992184
$147$	11.4309	+	4.04156i	0.942806	+	0.333342i
$148$	7.13505			0.586497
$149$	−2.12132	−	1.22474i	−0.173785	−	0.100335i	0.410584	−	0.911823i	$-0.365325\pi$
$149$	−2.12132	−	1.22474i	−0.173785	−	0.100335i	−0.584370	+	0.811488i	$0.698658\pi$
$150$		0			0
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	0.903842	−	0.427865i	$-0.140734\pi$
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	−0.822464	+	0.568818i	$0.807401\pi$
$152$	−2.44716	+	4.23861i	−0.198491	+	0.343797i
$153$	6.32456	+	7.07107i	0.511310	+	0.571662i
$154$	−0.477226	+	0.301824i	−0.0384559	+	0.0243217i
$155$		0			0
$156$	6.80698	+	9.40169i	0.544994	+	0.752738i
$157$	−7.61282	+	4.39526i	−0.607569	+	0.350780i	−0.772013	−	0.635606i	$-0.780750\pi$
$157$	−7.61282	+	4.39526i	−0.607569	+	0.350780i	0.164445	+	0.986386i	$0.447417\pi$
$158$	−0.452736	+	0.261387i	−0.0360177	+	0.0207949i
$159$	−5.07877	−	7.01471i	−0.402772	−	0.556303i
$160$		0			0
$161$	−17.1232	+	0.691190i	−1.34950	+	0.0544734i
$162$	−8.94427	−	1.00000i	−0.702728	−	0.0785674i
$163$	−7.34847	+	12.7279i	−0.575577	+	0.996928i	0.420402	+	0.907338i	$0.361889\pi$
$163$	−7.34847	+	12.7279i	−0.575577	+	0.996928i	−0.995979	+	0.0895899i	$0.971444\pi$
$164$	−3.35071	−	5.80359i	−0.261646	−	0.453184i
$165$		0			0
$166$	−14.4772	−	8.35843i	−1.12365	−	0.648740i
$167$	14.6830			1.13620			0.568102	−	0.822958i	$-0.307678\pi$
$167$	14.6830			1.13620			0.568102	+	0.822958i	$0.307678\pi$
$168$	3.60042	−	2.83495i	0.277779	−	0.218721i
$169$	−31.9089			−2.45453
$170$		0			0
$171$	13.9493	+	4.58350i	1.06673	+	0.350509i
$172$	−1.01132	−	1.75166i	−0.0771127	−	0.133563i
$173$	−5.76035	+	9.97723i	−0.437952	+	0.758554i	−0.997531	−	0.0702221i	$-0.977629\pi$
$173$	−5.76035	+	9.97723i	−0.437952	+	0.758554i	0.559580	+	0.828776i	$0.310963\pi$
$174$	3.19808	+	1.43023i	0.242446	+	0.108425i
$175$		0			0
$176$			0.213422i			0.0160873i
$177$	−6.89902	+	4.99501i	−0.518562	+	0.375448i
$178$	−9.15769	+	5.28720i	−0.686398	+	0.396292i
$179$	12.9128	−	7.45518i	0.965144	−	0.557226i	0.0673918	−	0.997727i	$-0.478532\pi$
$179$	12.9128	−	7.45518i	0.965144	−	0.557226i	0.897752	+	0.440500i	$0.145199\pi$
$180$		0			0
$181$			3.16228i			0.235050i	0.993070	+	0.117525i	$0.0374961\pi$
$181$			3.16228i			0.235050i	−0.993070	+	0.117525i	$0.962504\pi$
$182$	0.715113	+	17.7158i	0.0530077	+	1.31319i
$183$	−2.44949	+	5.47723i	−0.181071	+	0.404888i
$184$	−3.23861	+	5.60944i	−0.238754	+	0.413534i
$185$		0			0
$186$	0.0537841	+	0.520000i	0.00394364	+	0.0381283i
$187$	−0.584480	−	0.337449i	−0.0427414	−	0.0246767i
$188$	−7.75478			−0.565576
$189$	−10.5355	−	8.83190i	−0.766347	−	0.642426i
$190$		0			0
$191$	−1.38201	−	0.797901i	−0.0999984	−	0.0577341i	0.449167	−	0.893448i	$-0.351721\pi$
$191$	−1.38201	−	0.797901i	−0.0999984	−	0.0577341i	−0.549165	+	0.835714i	$0.685054\pi$
$192$	−0.178197	−	1.72286i	−0.0128603	−	0.124337i
$193$	3.67423	+	6.36396i	0.264477	+	0.458088i	0.967427	−	0.253152i	$-0.0814673\pi$
$193$	3.67423	+	6.36396i	0.264477	+	0.458088i	−0.702949	+	0.711240i	$0.748134\pi$
$194$	−1.75166	+	3.03397i	−0.125762	+	0.217826i
$195$		0			0
$196$	6.97723	−	0.564201i	0.498373	−	0.0403001i
$197$			9.00000i			0.641223i	0.947211	+	0.320612i	$0.103888\pi$
$197$			9.00000i			0.641223i	−0.947211	+	0.320612i	$0.896112\pi$
$198$	0.626711	−	0.131045i	0.0445384	−	0.00931293i
$199$	19.4317	−	11.2189i	1.37748	−	0.795286i	0.385620	−	0.922658i	$-0.373988\pi$
$199$	19.4317	−	11.2189i	1.37748	−	0.795286i	0.991855	+	0.127372i	$0.0406542\pi$
$200$		0			0
$201$	7.47182	−	5.40972i	0.527022	−	0.381572i
$202$			11.3137i			0.796030i
$203$	2.86045	+	4.52277i	0.200764	+	0.317437i
$204$	5.00000	+	2.23607i	0.350070	+	0.156556i
$205$		0			0
$206$	−5.28720	−	9.15769i	−0.368376	−	0.638047i
$207$	18.4606	+	6.06587i	1.28310	+	0.421607i
$208$	5.80359	+	3.35071i	0.402407	+	0.232330i
$209$	−1.04456			−0.0722535
$210$		0			0
$211$	13.5228			0.930946			0.465473	−	0.885062i	$-0.345884\pi$
$211$	13.5228			0.930946			0.465473	+	0.885062i	$0.345884\pi$
$212$	−4.33013	−	2.50000i	−0.297394	−	0.171701i
$213$	−3.48474	+	0.360429i	−0.238770	+	0.0246962i
$214$	2.73861	+	4.74342i	0.187208	+	0.324253i
$215$		0			0
$216$	−4.94975	+	1.58114i	−0.336788	+	0.107583i
$217$	−0.371058	+	0.707107i	−0.0251890	+	0.0480015i
$218$		−	12.4317i		−	0.841979i
$219$	12.1775	+	16.8193i	0.822877	+	1.13654i
$220$		0			0
$221$	−18.3526	+	10.5959i	−1.23453	+	0.712755i
$222$	−7.24745	−	10.0101i	−0.486417	−	0.671831i
$223$		−	6.39617i		−	0.428319i	−0.976799	−	0.214160i	$-0.931299\pi$
$223$		−	6.39617i		−	0.428319i	0.976799	−	0.214160i	$-0.0687013\pi$
$224$	1.22938	−	2.34278i	0.0821417	−	0.156533i
$225$		0			0
$226$	−3.26139	+	5.64889i	−0.216944	+	0.375758i
$227$	5.19615	+	9.00000i	0.344881	+	0.597351i	0.985332	−	0.170648i	$-0.0545860\pi$
$227$	5.19615	+	9.00000i	0.344881	+	0.597351i	−0.640451	+	0.767999i	$0.721253\pi$
$228$	8.43224	−	0.872155i	0.558439	−	0.0577598i
$229$	6.26139	+	3.61501i	0.413764	+	0.238887i	0.692406	−	0.721508i	$-0.256551\pi$
$229$	6.26139	+	3.61501i	0.413764	+	0.238887i	−0.278642	+	0.960395i	$0.589884\pi$
$230$		0			0
$231$	0.908185	+	0.362941i	0.0597542	+	0.0238798i
$232$	2.02265			0.132793
$233$	−3.46410	−	2.00000i	−0.226941	−	0.131024i	0.382219	−	0.924072i	$-0.375160\pi$
$233$	−3.46410	−	2.00000i	−0.226941	−	0.131024i	−0.609160	+	0.793047i	$0.708493\pi$
$234$	6.27582	−	19.0996i	0.410263	−	1.24858i
$235$		0			0
$236$	−2.45877	+	4.25871i	−0.160052	+	0.277219i
$237$	0.826579	+	0.369657i	0.0536921	+	0.0240118i
$238$	4.47214	+	7.07107i	0.289886	+	0.458349i
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$	3.45445	−	1.99443i	0.222521	−	0.128472i	−0.384596	−	0.923085i	$-0.625659\pi$
$241$	3.45445	−	1.99443i	0.222521	−	0.128472i	0.607117	+	0.794613i	$0.292326\pi$
$242$	9.48683	−	5.47723i	0.609837	−	0.352089i
$243$	7.68223	+	13.5640i	0.492815	+	0.870134i
$244$			3.46410i			0.221766i
$245$		0			0
$246$	−4.73861	+	10.5959i	−0.302123	+	0.675567i
$247$	−16.3995	+	28.4047i	−1.04347	+	1.80735i
$248$	0.150912	+	0.261387i	0.00958292	+	0.0165981i
$249$	2.97889	+	28.8008i	0.188780	+	1.82518i
$250$		0			0
$251$	16.6009			1.04784			0.523920	−	0.851768i	$-0.324469\pi$
$251$	16.6009			1.04784			0.523920	+	0.851768i	$0.324469\pi$
$252$	−7.63441	−	2.17157i	−0.480923	−	0.136796i
$253$	−1.38238			−0.0869095
$254$	11.8038	+	6.81491i	0.740635	+	0.427606i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	11.8225	−	20.4772i	0.737469	−	1.27733i	−0.216162	−	0.976357i	$-0.569354\pi$
$257$	11.8225	−	20.4772i	0.737469	−	1.27733i	0.953631	−	0.300977i	$-0.0973127\pi$
$258$	−1.43023	+	3.19808i	−0.0890420	+	0.199104i
$259$	−0.761387	−	18.8622i	−0.0473103	−	1.17204i
$260$		0			0
$261$	−1.24194	−	5.93948i	−0.0768741	−	0.367645i
$262$	−5.21911	+	3.01326i	−0.322438	+	0.186160i
$263$	1.73205	−	1.00000i	0.106803	−	0.0616626i	−0.445647	−	0.895209i	$-0.647026\pi$
$263$	1.73205	−	1.00000i	0.106803	−	0.0616626i	0.552450	+	0.833546i	$0.313693\pi$
$264$	0.299418	−	0.216784i	0.0184279	−	0.0133421i
$265$		0			0
$266$	11.4663	+	6.01701i	0.703046	+	0.368927i
$267$	16.7196	+	7.47723i	1.02322	+	0.457599i
$268$	2.66291	−	4.61230i	0.162663	−	0.281741i
$269$	−14.4474	−	25.0236i	−0.880872	−	1.52572i	−0.850373	−	0.526180i	$-0.823624\pi$
$269$	−14.4474	−	25.0236i	−0.880872	−	1.52572i	−0.0304992	−	0.999535i	$-0.509710\pi$
$270$		0			0
$271$	5.47723	+	3.16228i	0.332718	+	0.192095i	0.657047	−	0.753850i	$-0.271805\pi$
$271$	5.47723	+	3.16228i	0.332718	+	0.192095i	−0.324329	+	0.945944i	$0.605139\pi$
$272$	3.16228			0.191741
$273$	24.1279	−	18.9982i	1.46029	−	1.14982i
$274$	−7.47723			−0.451716
$275$		0			0
$276$	11.1594	−	1.15422i	0.671714	−	0.0694760i
$277$	4.89898	+	8.48528i	0.294351	+	0.509831i	0.974834	−	0.222933i	$-0.0715631\pi$
$277$	4.89898	+	8.48528i	0.294351	+	0.509831i	−0.680483	+	0.732764i	$0.738230\pi$
$278$	3.76593	−	6.52277i	0.225865	−	0.391210i
$279$	0.674899	−	0.603648i	0.0404051	−	0.0361395i
$280$		0			0
$281$			11.6072i			0.692427i	0.938156	+	0.346213i	$0.112533\pi$
$281$			11.6072i			0.692427i	−0.938156	+	0.346213i	$0.887467\pi$
$282$	7.87694	+	10.8795i	0.469065	+	0.647865i
$283$	−21.4051	+	12.3583i	−1.27240	+	0.734623i	−0.975440	−	0.220266i	$-0.929307\pi$
$283$	−21.4051	+	12.3583i	−1.27240	+	0.734623i	−0.296964	+	0.954889i	$0.595974\pi$
$284$	−1.75166	+	1.01132i	−0.103942	+	0.0600110i
$285$		0			0
$286$			1.43023i			0.0845711i
$287$	−14.9848	+	9.47723i	−0.884525	+	0.559423i
$288$	−2.23607	+	2.00000i	−0.131762	+	0.117851i
$289$	3.50000	−	6.06218i	0.205882	−	0.356599i
$290$		0			0
$291$	6.03574	−	0.624282i	0.353821	−	0.0365961i
$292$	10.3824	+	5.99430i	0.607586	+	0.350790i
$293$	4.59250			0.268297			0.134148	−	0.990961i	$-0.457170\pi$
$293$	4.59250			0.268297			0.134148	+	0.990961i	$0.457170\pi$
$294$	−7.87868	−	9.21555i	−0.459494	−	0.537462i
$295$		0			0
$296$	−6.17913	−	3.56752i	−0.359155	−	0.207358i
$297$	−0.820432	−	0.746131i	−0.0476063	−	0.0432949i
$298$	1.22474	+	2.12132i	0.0709476	+	0.122885i
$299$	−21.7033	+	37.5912i	−1.25513	+	2.17395i
$300$		0			0
$301$	−4.52277	+	2.86045i	−0.260688	+	0.164874i
$302$		−	2.00000i		−	0.115087i
$303$	15.8725	−	11.4919i	0.911850	−	0.660194i
$304$	4.23861	−	2.44716i	0.243101	−	0.140354i
$305$		0			0
$306$	−1.94169	−	9.28600i	−0.110999	−	0.530845i
$307$			3.50333i			0.199945i	0.994990	+	0.0999727i	$0.0318755\pi$
$307$			3.50333i			0.199945i	−0.994990	+	0.0999727i	$0.968124\pi$
$308$	0.564201	−	0.0227744i	0.0321484	−	0.00129769i
$309$	−7.47723	+	16.7196i	−0.425365	+	0.951144i
$310$		0			0
$311$	14.4474	+	25.0236i	0.819236	+	1.41896i	0.906246	+	0.422750i	$0.138935\pi$
$311$	14.4474	+	25.0236i	0.819236	+	1.41896i	−0.0870106	+	0.996207i	$0.527731\pi$
$312$	−1.19417	−	11.5456i	−0.0676066	−	0.653640i
$313$	−20.1246	−	11.6190i	−1.13751	−	0.656742i	−0.191697	−	0.981454i	$-0.561399\pi$
$313$	−20.1246	−	11.6190i	−1.13751	−	0.656742i	−0.945813	+	0.324712i	$0.894733\pi$
$314$	8.79052			0.496078
$315$		0			0
$316$	0.522774			0.0294084
$317$	−29.3660	−	16.9545i	−1.64936	−	0.952257i	−0.977328	−	0.211733i	$-0.932089\pi$
$317$	−29.3660	−	16.9545i	−1.64936	−	0.952257i	−0.672030	−	0.740524i	$-0.734577\pi$
$318$	0.890985	+	8.61430i	0.0499640	+	0.483066i
$319$	0.215838	+	0.373843i	0.0120846	+	0.0209312i
$320$		0			0
$321$	3.87298	−	8.66025i	0.216169	−	0.483368i
$322$	15.1747	+	7.96300i	0.845653	+	0.443761i
$323$			15.4772i			0.861176i
$324$	7.24597	+	5.33816i	0.402554	+	0.296565i
$325$		0			0
$326$	12.7279	−	7.34847i	0.704934	−	0.406994i
$327$	−17.4409	+	12.6275i	−0.964485	+	0.698303i
$328$			6.70141i			0.370023i
$329$	0.827520	+	20.5005i	0.0456226	+	1.13023i
$330$		0			0
$331$	5.71584	−	9.90012i	0.314171	−	0.544160i	−0.665090	−	0.746763i	$-0.731607\pi$
$331$	5.71584	−	9.90012i	0.314171	−	0.544160i	0.979261	+	0.202603i	$0.0649402\pi$
$332$	8.35843	+	14.4772i	0.458728	+	0.794541i
$333$	−6.68191	+	20.3355i	−0.366167	+	1.11438i
$334$	−12.7158	−	7.34149i	−0.695780	−	0.401709i
$335$		0			0
$336$	−4.53553	+	0.654929i	−0.247434	+	0.0357293i
$337$	−17.1464			−0.934025			−0.467013	−	0.884251i	$-0.654670\pi$
$337$	−17.1464			−0.934025			−0.467013	+	0.884251i	$0.654670\pi$
$338$	27.6339	+	15.9545i	1.50309	+	0.867808i
$339$	11.2378	−	1.16234i	0.610355	−	0.0631296i
$340$		0			0
$341$	−0.0322079	+	0.0557857i	−0.00174416	+	0.00302097i
$342$	−9.78866	−	10.9441i	−0.529310	−	0.591787i
$343$	−2.23607	−	18.3848i	−0.120736	−	0.992685i
$344$			2.02265i			0.109054i
$345$		0			0
$346$	9.97723	−	5.76035i	0.536379	−	0.309679i
$347$	−5.64889	+	3.26139i	−0.303248	+	0.175080i	−0.643901	−	0.765109i	$-0.722685\pi$
$347$	−5.64889	+	3.26139i	−0.303248	+	0.175080i	0.340653	+	0.940189i	$0.389352\pi$
$348$	−2.05451	−	2.83766i	−0.110133	−	0.152114i
$349$			32.5282i			1.74120i	0.491994	+	0.870599i	$0.336268\pi$
$349$			32.5282i			1.74120i	−0.491994	+	0.870599i	$0.663732\pi$
$350$		0			0
$351$	−33.1703	+	10.5959i	−1.77050	+	0.565565i
$352$	0.106711	−	0.184829i	0.00568771	−	0.00985140i
$353$	−6.62638	−	11.4772i	−0.352687	−	0.610871i	0.634033	−	0.773306i	$-0.281398\pi$
$353$	−6.62638	−	11.4772i	−0.352687	−	0.610871i	−0.986719	+	0.162435i	$0.948065\pi$
$354$	8.47223	−	0.876291i	0.450294	−	0.0465743i
$355$		0			0
$356$	10.5744			0.560442
$357$	5.37771	−	13.4566i	0.284619	−	0.712199i
$358$	−14.9104			−0.788037
$359$	−5.62465	−	3.24739i	−0.296857	−	0.171391i	0.344173	−	0.938906i	$-0.388159\pi$
$359$	−5.62465	−	3.24739i	−0.296857	−	0.171391i	−0.641030	+	0.767516i	$0.721493\pi$
$360$		0			0
$361$	2.47723	+	4.29068i	0.130380	+	0.225825i
$362$	1.58114	−	2.73861i	0.0831028	−	0.143938i
$363$	−17.3205	−	7.74597i	−0.909091	−	0.406558i
$364$	8.23861	−	15.6999i	0.431821	−	0.822900i
$365$		0			0
$366$	4.85993	−	3.51867i	0.254033	−	0.183924i
$367$	7.02834	−	4.05781i	0.366876	−	0.211816i	−0.305217	−	0.952283i	$-0.598729\pi$
$367$	7.02834	−	4.05781i	0.366876	−	0.211816i	0.672093	+	0.740467i	$0.265396\pi$
$368$	5.60944	−	3.23861i	0.292412	−	0.168824i
$369$	19.6786	−	4.11478i	1.02443	−	0.214207i
$370$		0			0
$371$	−6.14692	+	11.7139i	−0.319132	+	0.608155i
$372$	0.213422	−	0.477226i	0.0110654	−	0.0247430i
$373$	−1.80922	+	3.13367i	−0.0936781	+	0.162255i	−0.909056	−	0.416674i	$-0.863196\pi$
$373$	−1.80922	+	3.13367i	−0.0936781	+	0.162255i	0.815378	+	0.578929i	$0.196529\pi$
$374$	0.337449	+	0.584480i	0.0174491	+	0.0302227i
$375$		0			0
$376$	6.71584	+	3.87739i	0.346343	+	0.199961i
$377$	13.5546			0.698097
$378$	4.70809	+	12.9164i	0.242158	+	0.664349i
$379$	9.52277			0.489152			0.244576	−	0.969630i	$-0.421351\pi$
$379$	9.52277			0.489152			0.244576	+	0.969630i	$0.421351\pi$
$380$		0			0
$381$	−2.42879	−	23.4823i	−0.124431	−	1.20303i
$382$	0.797901	+	1.38201i	0.0408242	+	0.0707096i
$383$	−0.413289	+	0.715838i	−0.0211181	+	0.0365776i	−0.876391	−	0.481600i	$-0.840056\pi$
$383$	−0.413289	+	0.715838i	−0.0211181	+	0.0365776i	0.855273	+	0.518177i	$0.173389\pi$
$384$	−0.707107	+	1.58114i	−0.0360844	+	0.0806872i
$385$		0			0
$386$		−	7.34847i		−	0.374027i
$387$	5.93948	−	1.24194i	0.301921	−	0.0631313i
$388$	3.03397	−	1.75166i	0.154026	−	0.0889272i
$389$	6.36396	−	3.67423i	0.322666	−	0.186291i	−0.329914	−	0.944011i	$-0.607020\pi$
$389$	6.36396	−	3.67423i	0.322666	−	0.186291i	0.652580	+	0.757720i	$0.273687\pi$
$390$		0			0
$391$			20.4828i			1.03586i
$392$	−6.32456	−	3.00000i	−0.319438	−	0.151523i
$393$	9.52875	+	4.26139i	0.480662	+	0.214959i
$394$	4.50000	−	7.79423i	0.226707	−	0.392668i
$395$		0			0
$396$	−0.608270	−	0.199868i	−0.0305667	−	0.0100437i
$397$	−26.3041	−	15.1867i	−1.32017	−	0.762198i	−0.336411	−	0.941715i	$-0.609213\pi$
$397$	−26.3041	−	15.1867i	−1.32017	−	0.762198i	−0.983755	+	0.179517i	$0.942547\pi$
$398$	−22.4378			−1.12470
$399$	−3.20544	−	22.1984i	−0.160473	−	1.11131i
$400$		0			0
$401$	−26.2834	−	15.1747i	−1.31253	−	0.757789i	−0.330014	−	0.943976i	$-0.607054\pi$
$401$	−26.2834	−	15.1747i	−1.31253	−	0.757789i	−0.982514	+	0.186187i	$0.940387\pi$
$402$	−9.17565	+	0.949046i	−0.457640	+	0.0473341i
$403$	1.01132	+	1.75166i	0.0503776	+	0.0872565i
$404$	5.65685	−	9.79796i	0.281439	−	0.487467i
$405$		0			0
$406$	−0.215838	−	5.34706i	−0.0107119	−	0.265370i
$407$		−	1.52277i		−	0.0754811i
$408$	−3.21209	−	4.43649i	−0.159022	−	0.219639i
$409$	19.4317	−	11.2189i	0.960835	−	0.554738i	0.0644048	−	0.997924i	$-0.479485\pi$
$409$	19.4317	−	11.2189i	0.960835	−	0.554738i	0.896430	+	0.443186i	$0.146152\pi$
$410$		0			0
$411$	7.59501	+	10.4901i	0.374634	+	0.517439i
$412$			10.5744i			0.520963i
$413$	11.5207	+	6.04555i	0.566897	+	0.297482i
$414$	−12.9545	−	14.4835i	−0.636677	−	0.711826i
$415$		0			0
$416$	−3.35071	−	5.80359i	−0.164282	−	0.284544i
$417$	−12.9763	+	1.34215i	−0.635453	+	0.0657255i
$418$	0.904612	+	0.522278i	0.0442460	+	0.0255455i
$419$	16.6009			0.811007			0.405504	−	0.914093i	$-0.367096\pi$
$419$	16.6009			0.811007			0.405504	+	0.914093i	$0.367096\pi$
$420$		0			0
$421$	−2.95445			−0.143991			−0.0719956	−	0.997405i	$-0.522937\pi$
$421$	−2.95445			−0.143991			−0.0719956	+	0.997405i	$0.522937\pi$
$422$	−11.7111	−	6.76139i	−0.570086	−	0.329139i
$423$	7.26229	−	22.1018i	0.353105	−	1.07463i
$424$	2.50000	+	4.33013i	0.121411	+	0.210290i
$425$		0			0
$426$	3.19808	+	1.43023i	0.154948	+	0.0692947i
$427$	9.15769	−	0.369657i	0.443172	−	0.0178890i
$428$		−	5.47723i		−	0.264752i
$429$	2.00653	−	1.45276i	0.0968759	−	0.0701398i
$430$		0			0
$431$	32.0928	−	18.5288i	1.54586	−	0.892501i	0.547406	−	0.836867i	$-0.315615\pi$
$431$	32.0928	−	18.5288i	1.54586	−	0.892501i	0.998451	−	0.0556344i	$-0.0177181\pi$
$432$	5.07718	+	1.10557i	0.244276	+	0.0531916i
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$	0.674899	−	0.426844i	0.0323962	−	0.0204891i
$435$		0			0
$436$	−6.21584	+	10.7661i	−0.297685	+	0.515605i
$437$	15.8508	+	27.4545i	0.758248	+	1.31332i
$438$	−2.13633	−	20.6547i	−0.102078	−	0.986919i
$439$	−19.6931	−	11.3698i	−0.939899	−	0.542651i	−0.0499701	−	0.998751i	$-0.515913\pi$
$439$	−19.6931	−	11.3698i	−0.939899	−	0.542651i	−0.889929	+	0.456100i	$0.849246\pi$
$440$		0			0
$441$	−4.92609	+	20.4141i	−0.234576	+	0.972098i
$442$	21.1917			1.00799
$443$	−32.0035	−	18.4772i	−1.52053	−	0.877879i	−0.999707	−	0.0242161i	$-0.992291\pi$
$443$	−32.0035	−	18.4772i	−1.52053	−	0.877879i	−0.520825	−	0.853663i	$-0.674376\pi$
$444$	1.27144	+	12.2927i	0.0603401	+	0.583385i
$445$		0			0
$446$	−3.19808	+	5.53924i	−0.151434	+	0.262291i
$447$	1.73205	−	3.87298i	0.0819232	−	0.183186i
$448$	−2.23607	+	1.41421i	−0.105644	+	0.0668153i
$449$			3.51660i			0.165959i	0.996551	+	0.0829793i	$0.0264435\pi$
$449$			3.51660i			0.165959i	−0.996551	+	0.0829793i	$0.973556\pi$
$450$		0			0
$451$	−1.23861	+	0.715113i	−0.0583240	+	0.0336734i
$452$	5.64889	−	3.26139i	0.265701	−	0.153403i
$453$	−2.80588	+	2.03151i	−0.131832	+	0.0954485i
$454$		−	10.3923i		−	0.487735i
$455$		0			0
$456$	−7.73861	−	3.46081i	−0.362394	−	0.162067i
$457$	18.9557	−	32.8322i	0.886708	−	1.53582i	0.0429646	−	0.999077i	$-0.486320\pi$
$457$	18.9557	−	32.8322i	0.886708	−	1.53582i	0.843743	−	0.536747i	$-0.180347\pi$
$458$	−3.61501	−	6.26139i	−0.168918	−	0.292575i
$459$	−11.0554	+	12.1564i	−0.516024	+	0.567411i
$460$		0			0
$461$	−16.2957			−0.758965			−0.379482	−	0.925199i	$-0.623898\pi$
$461$	−16.2957			−0.758965			−0.379482	+	0.925199i	$0.623898\pi$
$462$	−0.605041	−	0.768409i	−0.0281490	−	0.0357496i
$463$	17.6751			0.821433			0.410716	−	0.911763i	$-0.365279\pi$
$463$	17.6751			0.821433			0.410716	+	0.911763i	$0.365279\pi$
$464$	−1.75166	−	1.01132i	−0.0813189	−	0.0469495i
$465$		0			0
$466$	2.00000	+	3.46410i	0.0926482	+	0.160471i
$467$	17.1696	−	29.7386i	0.794514	−	1.37614i	−0.128633	−	0.991692i	$-0.541059\pi$
$467$	17.1696	−	29.7386i	0.794514	−	1.37614i	0.923147	−	0.384447i	$-0.125608\pi$
$468$	−14.9848	+	13.4028i	−0.692673	+	0.619546i
$469$	−12.4772	−	6.54749i	−0.576145	−	0.302335i
$470$		0			0
$471$	−8.92900	−	12.3326i	−0.411427	−	0.568256i
$472$	4.25871	−	2.45877i	0.196023	−	0.113174i
$473$	−0.373843	+	0.215838i	−0.0171893	+	0.00992426i
$474$	−0.531010	−	0.733422i	−0.0243901	−	0.0336872i
$475$		0			0
$476$	−0.337449	−	8.35979i	−0.0154670	−	0.383170i
$477$	11.1803	−	10.0000i	0.511913	−	0.457869i
$478$		0			0
$479$	−5.68906	−	9.85374i	−0.259940	−	0.450229i	0.706286	−	0.707927i	$-0.250369\pi$
$479$	−5.68906	−	9.85374i	−0.259940	−	0.450229i	−0.966226	+	0.257698i	$0.917036\pi$
$480$		0			0
$481$	−41.4089	−	23.9074i	−1.88808	−	1.09009i
$482$	−3.98886			−0.181687
$483$	−4.24212	−	29.3777i	−0.193023	−	1.33673i
$484$	−10.9545			−0.497930
$485$		0			0
$486$	0.129018	−	15.5879i	0.00585235	−	0.707083i
$487$	−18.3154	−	31.7232i	−0.829949	−	1.43751i	−0.898077	−	0.439838i	$-0.855036\pi$
$487$	−18.3154	−	31.7232i	−0.829949	−	1.43751i	0.0681277	−	0.997677i	$-0.478297\pi$
$488$	1.73205	−	3.00000i	0.0784063	−	0.135804i
$489$	−23.2379	−	10.3923i	−1.05085	−	0.469956i
$490$		0			0
$491$		−	4.04529i		−	0.182561i	−0.995825	−	0.0912807i	$-0.970904\pi$
$491$		−	4.04529i		−	0.182561i	0.995825	−	0.0912807i	$-0.0290961\pi$
$492$	9.40169	−	6.80698i	0.423861	−	0.306882i
$493$	5.53924	−	3.19808i	0.249475	−	0.144034i
$494$	28.4047	−	16.3995i	1.27799	−	0.737846i
$495$		0			0
$496$		−	0.301824i		−	0.0135523i
$497$	2.86045	+	4.52277i	0.128309	+	0.202874i
$498$	11.8206	−	26.4317i	0.529694	−	1.18443i
$499$	−20.9545	+	36.2942i	−0.938050	+	1.62475i	−0.168947	+	0.985625i	$0.554037\pi$
$499$	−20.9545	+	36.2942i	−0.938050	+	1.62475i	−0.769103	+	0.639125i	$0.779297\pi$
$500$		0			0
$501$	2.61646	+	25.2967i	0.116895	+	1.13017i
$502$	−14.3768	−	8.30045i	−0.641668	−	0.370467i
$503$	22.4378			1.00045			0.500225	−	0.865895i	$-0.333251\pi$
$503$	22.4378			1.00045			0.500225	+	0.865895i	$0.333251\pi$
$504$	5.52581	+	5.69784i	0.246139	+	0.253802i
$505$		0			0
$506$	1.19718	+	0.691190i	0.0532210	+	0.0307272i
$507$	−5.68607	−	54.9746i	−0.252527	−	2.44151i
$508$	−6.81491	−	11.8038i	−0.302363	−	0.523708i
$509$	−4.61230	+	7.98873i	−0.204437	+	0.354094i	−0.949953	−	0.312393i	$-0.898870\pi$
$509$	−4.61230	+	7.98873i	−0.204437	+	0.354094i	0.745517	+	0.666487i	$0.232203\pi$
$510$		0			0
$511$	14.7386	−	28.0867i	0.651998	−	1.24248i
$512$			1.00000i			0.0441942i
$513$	−5.41101	+	24.8494i	−0.238902	+	1.09713i
$514$	−20.4772	+	11.8225i	−0.903212	+	0.521470i
$515$		0			0
$516$	2.83766	−	2.05451i	0.124921	−	0.0904447i
$517$			1.65504i			0.0727885i
$518$	−8.77172	+	16.7158i	−0.385407	+	0.734452i
$519$	−18.2158	−	8.14637i	−0.799587	−	0.357586i
$520$		0			0
$521$	−9.31280	−	16.1302i	−0.408001	−	0.706679i	0.586664	−	0.809830i	$-0.300441\pi$
$521$	−9.31280	−	16.1302i	−0.408001	−	0.706679i	−0.994666	+	0.103151i	$0.967107\pi$
$522$	−1.89419	+	5.76471i	−0.0829065	+	0.252315i
$523$	12.1917	+	7.03886i	0.533104	+	0.307788i	0.742280	−	0.670090i	$-0.233745\pi$
$523$	12.1917	+	7.03886i	0.533104	+	0.307788i	−0.209175	+	0.977878i	$0.567078\pi$
$524$	6.02651			0.263269
$525$		0			0
$526$	−2.00000			−0.0872041
$527$	0.826579	+	0.477226i	0.0360063	+	0.0207883i
$528$	−0.367696	+	0.0380311i	−0.0160019	+	0.00165509i
$529$	9.47723	+	16.4150i	0.412053	+	0.713697i
$530$		0			0
$531$	−9.83508	−	10.9960i	−0.426806	−	0.477184i
$532$	−6.92163	−	10.9441i	−0.300091	−	0.474485i
$533$			44.9089i			1.94522i
$534$	−10.7410	−	14.8353i	−0.464807	−	0.641984i
$535$		0			0
$536$	−4.61230	+	2.66291i	−0.199221	+	0.115020i
$537$	15.1452	+	20.9184i	0.653565	+	0.902694i
$538$			28.8948i			1.24574i
$539$	−0.120413	−	1.48909i	−0.00518655	−	0.0641397i
$540$		0			0
$541$	−9.73861	+	16.8678i	−0.418696	+	0.725202i	−0.995809	−	0.0914622i	$-0.970846\pi$
$541$	−9.73861	+	16.8678i	−0.418696	+	0.725202i	0.577113	+	0.816664i	$0.304179\pi$
$542$	−3.16228	−	5.47723i	−0.135831	−	0.235267i
$543$	−5.44816	+	0.563508i	−0.233803	+	0.0241825i
$544$	−2.73861	−	1.58114i	−0.117417	−	0.0677908i
$545$		0			0
$546$	−30.3945	+	4.38895i	−1.30076	+	0.187830i
$547$	23.2144			0.992575			0.496287	−	0.868158i	$-0.334696\pi$
$547$	23.2144			0.992575			0.496287	+	0.868158i	$0.334696\pi$
$548$	6.47547	+	3.73861i	0.276618	+	0.159706i
$549$	−9.87298	−	3.24410i	−0.421369	−	0.138455i
$550$		0			0
$551$	4.94975	−	8.57321i	0.210866	−	0.365231i
$552$	−10.2414	−	4.58009i	−0.435903	−	0.194942i
$553$	−0.0557857	−	1.38201i	−0.00237225	−	0.0587689i
$554$		−	9.79796i		−	0.416275i
$555$		0			0
$556$	−6.52277	+	3.76593i	−0.276627	+	0.159711i
$557$	−32.7906	+	18.9317i	−1.38938	+	0.802161i	−0.993246	−	0.116030i	$-0.962983\pi$
$557$	−32.7906	+	18.9317i	−1.38938	+	0.802161i	−0.396138	+	0.918191i	$0.629650\pi$
$558$	−0.886304	+	0.185325i	−0.0375202	+	0.00784543i
$559$			13.5546i			0.573298i
$560$		0			0
$561$	0.477226	−	1.06711i	0.0201485	−	0.0450534i
$562$	5.80359	−	10.0521i	0.244810	−	0.424023i
$563$	−5.19615	−	9.00000i	−0.218992	−	0.379305i	0.735508	−	0.677516i	$-0.236943\pi$
$563$	−5.19615	−	9.00000i	−0.218992	−	0.379305i	−0.954500	+	0.298211i	$0.903610\pi$
$564$	−1.38188	−	13.3604i	−0.0581876	−	0.562574i
$565$		0			0
$566$	24.7165			1.03891
$567$	13.3387	−	19.7251i	0.560174	−	0.828375i
$568$	2.02265			0.0848683
$569$	−10.4218	−	6.01701i	−0.436903	−	0.252246i	0.265380	−	0.964144i	$-0.414503\pi$
$569$	−10.4218	−	6.01701i	−0.436903	−	0.252246i	−0.702283	+	0.711898i	$0.747836\pi$
$570$		0			0
$571$	3.47723	+	6.02273i	0.145517	+	0.252043i	0.929566	−	0.368656i	$-0.120182\pi$
$571$	3.47723	+	6.02273i	0.145517	+	0.252043i	−0.784048	+	0.620700i	$0.786849\pi$
$572$	0.715113	−	1.23861i	0.0299004	−	0.0517890i
$573$	1.12840	−	2.52319i	0.0471397	−	0.105408i
$574$	17.7158	−	0.715113i	0.739445	−	0.0298483i
$575$		0			0
$576$	2.93649	−	0.614017i	0.122354	−	0.0255840i
$577$	12.8319	−	7.40852i	0.534200	−	0.308421i	−0.208525	−	0.978017i	$-0.566866\pi$
$577$	12.8319	−	7.40852i	0.534200	−	0.308421i	0.742725	+	0.669596i	$0.233533\pi$
$578$	−6.06218	+	3.50000i	−0.252153	+	0.145581i
$579$	−10.3095	+	7.46423i	−0.428447	+	0.310203i
$580$		0			0
$581$	37.3800	−	23.6412i	1.55079	−	0.980803i
$582$	−5.53924	−	2.47723i	−0.229609	−	0.102684i
$583$	−0.533554	+	0.924143i	−0.0220976	+	0.0382741i
$584$	−5.99430	−	10.3824i	−0.248046	−	0.429628i
$585$		0			0
$586$	−3.97723	−	2.29625i	−0.164298	−	0.0948573i
$587$	−27.4110			−1.13137			−0.565686	−	0.824621i	$-0.691389\pi$
$587$	−27.4110			−1.13137			−0.565686	+	0.824621i	$0.691389\pi$
$588$	2.21536	+	11.9202i	0.0913599	+	0.491583i
$589$	1.47723			0.0608680
$590$		0			0
$591$	−15.5057	+	1.60377i	−0.637821	+	0.0659704i
$592$	3.56752	+	6.17913i	0.146624	+	0.253961i
$593$	18.1471	−	31.4317i	0.745212	−	1.29074i	−0.204884	−	0.978786i	$-0.565682\pi$
$593$	18.1471	−	31.4317i	0.745212	−	1.29074i	0.950096	−	0.311958i	$-0.100985\pi$
$594$	0.337449	+	1.05638i	0.0138457	+	0.0433440i
$595$		0			0
$596$		−	2.44949i		−	0.100335i
$597$	22.7912	+	31.4789i	0.932783	+	1.28834i
$598$	37.5912	−	21.7033i	1.53722	−	0.887513i
$599$	−4.98196	+	2.87633i	−0.203557	+	0.117524i	−0.598314	−	0.801262i	$-0.704162\pi$
$599$	−4.98196	+	2.87633i	−0.203557	+	0.117524i	0.394756	+	0.918786i	$0.370829\pi$
$600$		0			0
$601$			16.7169i			0.681895i	0.940082	+	0.340947i	$0.110748\pi$
$601$			16.7169i			0.681895i	−0.940082	+	0.340947i	$0.889252\pi$
$602$	5.34706	−	0.215838i	0.217930	−	0.00879691i
$603$	10.6516	+	11.9089i	0.433769	+	0.484968i
$604$	−1.00000	+	1.73205i	−0.0406894	+	0.0704761i
$605$		0			0
$606$	−19.4919	+	2.01607i	−0.791806	+	0.0818972i
$607$	22.8942	+	13.2180i	0.929248	+	0.536502i	0.886574	−	0.462587i	$-0.153079\pi$
$607$	22.8942	+	13.2180i	0.929248	+	0.536502i	0.0426745	+	0.999089i	$0.486412\pi$
$608$	−4.89433			−0.198491
$609$	−7.28238	+	5.73411i	−0.295097	+	0.232358i
$610$		0			0
$611$	45.0056	+	25.9840i	1.82073	+	1.05120i
$612$	−2.96145	+	9.01276i	−0.119709	+	0.364319i
$613$	−12.7252	−	22.0407i	−0.513967	−	0.890216i	−0.999869	−	0.0162031i	$-0.994842\pi$
$613$	−12.7252	−	22.0407i	−0.513967	−	0.890216i	0.485902	−	0.874013i	$-0.338491\pi$
$614$	1.75166	−	3.03397i	0.0706914	−	0.122441i
$615$		0			0
$616$	−0.500000	−	0.262377i	−0.0201456	−	0.0105715i
$617$			25.4772i			1.02567i	0.858486	+	0.512837i	$0.171406\pi$
$617$			25.4772i			1.02567i	−0.858486	+	0.512837i	$0.828594\pi$
$618$	14.8353	−	10.7410i	0.596762	−	0.432065i
$619$	23.1475	−	13.3642i	0.930377	−	0.537154i	0.0434463	−	0.999056i	$-0.486166\pi$
$619$	23.1475	−	13.3642i	0.930377	−	0.537154i	0.886931	+	0.461902i	$0.152833\pi$
$620$		0			0
$621$	−7.16101	+	32.8860i	−0.287361	+	1.31967i
$622$		−	28.8948i		−	1.15857i
$623$	−1.12840	−	27.9545i	−0.0452085	−	1.11997i
$624$	−4.73861	+	10.5959i	−0.189696	+	0.424174i
$625$		0			0
$626$	11.6190	+	20.1246i	0.464387	+	0.804341i
$627$	−0.186137	−	1.79962i	−0.00743359	−	0.0718701i
$628$	−7.61282	−	4.39526i	−0.303784	−	0.175390i
$629$	−22.5630			−0.899646
$630$		0			0
$631$	−7.47723			−0.297664			−0.148832	−	0.988863i	$-0.547551\pi$
$631$	−7.47723			−0.297664			−0.148832	+	0.988863i	$0.547551\pi$
$632$	−0.452736	−	0.261387i	−0.0180089	−	0.0103974i
$633$	2.40972	+	23.2978i	0.0957777	+	0.926006i
$634$	16.9545	+	29.3660i	0.673347	+	1.16627i
$635$		0			0
$636$	3.53553	−	7.90569i	0.140193	−	0.313481i
$637$	−42.3834	−	20.1042i	−1.67929	−	0.796559i
$638$		−	0.431677i		−	0.0170902i
$639$	−1.24194	−	5.93948i	−0.0491303	−	0.234962i
$640$		0			0
$641$	5.43982	−	3.14068i	0.214860	−	0.124049i	−0.388708	−	0.921361i	$-0.627079\pi$
$641$	5.43982	−	3.14068i	0.214860	−	0.124049i	0.603568	+	0.797312i	$0.293745\pi$
$642$	−7.68423	+	5.56351i	−0.303272	+	0.219574i
$643$			20.4095i			0.804871i	0.915448	+	0.402436i	$0.131836\pi$
$643$			20.4095i			0.804871i	−0.915448	+	0.402436i	$0.868164\pi$
$644$	−9.16018	−	14.4835i	−0.360962	−	0.570731i
$645$		0			0
$646$	7.73861	−	13.4037i	0.304472	−	0.527360i
$647$	−11.9340	−	20.6703i	−0.469174	−	0.812633i	0.530205	−	0.847869i	$-0.322115\pi$
$647$	−11.9340	−	20.6703i	−0.469174	−	0.812633i	−0.999379	+	0.0352364i	$0.988782\pi$
$648$	−3.60611	−	8.24597i	−0.141661	−	0.323932i
$649$	0.908902	+	0.524755i	0.0356775	+	0.0205984i
$650$		0			0
$651$	−1.28437	−	0.513276i	−0.0503383	−	0.0201169i
$652$	−14.6969			−0.575577
$653$	−22.3983	−	12.9317i	−0.876514	−	0.506056i	−0.00700659	−	0.999975i	$-0.502230\pi$
$653$	−22.3983	−	12.9317i	−0.876514	−	0.506056i	−0.869507	+	0.493920i	$0.835564\pi$
$654$	21.4180	−	2.21529i	0.837511	−	0.0866246i
$655$		0			0
$656$	3.35071	−	5.80359i	0.130823	−	0.226592i
$657$	−26.8073	+	23.9772i	−1.04585	+	0.935440i
$658$	9.53361	−	18.1677i	0.371659	−	0.708252i
$659$			34.2929i			1.33586i	0.744224	+	0.667930i	$0.232819\pi$
$659$			34.2929i			1.33586i	−0.744224	+	0.667930i	$0.767181\pi$
$660$		0			0
$661$	11.4772	−	6.62638i	0.446412	−	0.257736i	−0.259901	−	0.965635i	$-0.583690\pi$
$661$	11.4772	−	6.62638i	0.446412	−	0.257736i	0.706314	+	0.707899i	$0.250357\pi$
$662$	−9.90012	+	5.71584i	−0.384779	+	0.222152i
$663$	−21.5256	−	29.7308i	−0.835983	−	1.15465i
$664$		−	16.7169i		−	0.648740i
$665$		0			0
$666$	15.9545	−	14.2701i	0.618222	−	0.552955i
$667$	6.55057	−	11.3459i	0.253639	−	0.439316i
$668$	7.34149	+	12.7158i	0.284051	+	0.491991i
$669$	11.0197	−	1.13978i	0.426046	−	0.0440664i
$670$		0			0
$671$	0.739315			0.0285409
$672$	4.25535	+	1.70058i	0.164154	+	0.0656014i
$673$	48.4514			1.86766			0.933832	−	0.357713i	$-0.116443\pi$
$673$	48.4514			1.86766			0.933832	+	0.357713i	$0.116443\pi$
$674$	14.8492	+	8.57321i	0.571971	+	0.330228i
$675$		0			0
$676$	−15.9545	−	27.6339i	−0.613633	−	1.06284i
$677$	16.4545	−	28.5000i	0.632397	−	1.09534i	−0.354663	−	0.934994i	$-0.615404\pi$
$677$	16.4545	−	28.5000i	0.632397	−	1.09534i	0.987060	−	0.160350i	$-0.0512622\pi$
$678$	−10.3134	−	4.61230i	−0.396084	−	0.177134i
$679$	−4.95445	−	7.83368i	−0.190134	−	0.300629i
$680$		0			0
$681$	−14.5798	+	10.5560i	−0.558699	+	0.404507i
$682$	0.0557857	−	0.0322079i	0.00213615	−	0.00123330i
$683$	−2.55863	+	1.47723i	−0.0979032	+	0.0565245i	−0.548152	−	0.836379i	$-0.684669\pi$
$683$	−2.55863	+	1.47723i	−0.0979032	+	0.0565245i	0.450249	+	0.892903i	$0.351335\pi$
$684$	3.00520	+	14.3722i	0.114907	+	0.549533i
$685$		0			0
$686$	−7.25590	+	17.0397i	−0.277031	+	0.650579i
$687$	−5.11240	+	11.4317i	−0.195050	+	0.436146i
$688$	1.01132	−	1.75166i	0.0385563	−	0.0667815i
$689$	16.7535	+	29.0180i	0.638259	+	1.10550i
$690$		0			0
$691$	3.00000	+	1.73205i	0.114125	+	0.0658903i	0.555976	−	0.831198i	$-0.312345\pi$
$691$	3.00000	+	1.73205i	0.114125	+	0.0658903i	−0.441851	+	0.897089i	$0.645678\pi$
$692$	−11.5207			−0.437952
$693$	−0.463461	+	1.62935i	−0.0176054	+	0.0618939i
$694$	6.52277			0.247601
$695$		0			0
$696$	0.360429	+	3.48474i	0.0136620	+	0.132089i
$697$	10.5959	+	18.3526i	0.401347	+	0.695153i
$698$	16.2641	−	28.1703i	0.615606	−	1.06626i
$699$	2.82843	−	6.32456i	0.106981	−	0.239217i
$700$		0			0
$701$			7.03320i			0.265640i	0.991140	+	0.132820i	$0.0424033\pi$
$701$			7.03320i			0.265640i	−0.991140	+	0.132820i	$0.957597\pi$
$702$	34.0242	+	7.40886i	1.28416	+	0.279629i
$703$	−30.2427	+	17.4606i	−1.14063	+	0.658540i
$704$	−0.184829	+	0.106711i	−0.00696599	+	0.00402182i
$705$		0			0
$706$			13.2528i			0.498774i
$707$	−26.5055	−	13.9089i	−0.996843	−	0.523098i
$708$	−7.77531	−	3.47723i	−0.292214	−	0.130682i
$709$	5.21584	−	9.03410i	0.195885	−	0.339283i	−0.751305	−	0.659955i	$-0.770575\pi$
$709$	5.21584	−	9.03410i	0.195885	−	0.339283i	0.947190	+	0.320672i	$0.103909\pi$
$710$		0			0
$711$	−0.489574	+	1.48995i	−0.0183605	+	0.0558775i
$712$	−9.15769	−	5.28720i	−0.343199	−	0.198146i
$713$	1.95498			0.0732146
$714$	−11.3855	+	8.96491i	−0.426093	+	0.335503i
$715$		0			0
$716$	12.9128	+	7.45518i	0.482572	+	0.278613i
$717$		0			0
$718$	3.24739	+	5.62465i	0.121192	+	0.209910i
$719$	23.6398	−	40.9453i	0.881614	−	1.52700i	0.0320690	−	0.999486i	$-0.489790\pi$
$719$	23.6398	−	40.9453i	0.881614	−	1.52700i	0.849545	−	0.527515i	$-0.176876\pi$
$720$		0			0
$721$	27.9545	−	1.12840i	1.04108	−	0.0420239i
$722$		−	4.95445i		−	0.184386i
$723$	4.05169	+	5.59613i	0.150684	+	0.208122i
$724$	−2.73861	+	1.58114i	−0.101780	+	0.0587626i
$725$		0			0
$726$	11.1270	+	15.3685i	0.412962	+	0.570377i
$727$		−	23.6076i		−	0.875556i	−0.899083	−	0.437778i	$-0.855766\pi$
$727$		−	23.6076i		−	0.875556i	0.899083	−	0.437778i	$-0.144234\pi$
$728$	−14.9848	+	9.47723i	−0.555374	+	0.351249i
$729$	−22.0000	+	15.6525i	−0.814815	+	0.579721i
$730$		0			0
$731$	3.19808	+	5.53924i	0.118285	+	0.204876i
$732$	−5.96816	+	0.617292i	−0.220590	+	0.0228158i
$733$	−31.4674	−	18.1677i	−1.16228	−	0.671041i	−0.210428	−	0.977609i	$-0.567486\pi$
$733$	−31.4674	−	18.1677i	−1.16228	−	0.671041i	−0.951849	+	0.306569i	$0.900819\pi$
$734$	−8.11562			−0.299553
$735$		0			0
$736$	−6.47723			−0.238754
$737$	−0.984365	−	0.568323i	−0.0362595	−	0.0209345i
$738$	−19.0996	−	6.27582i	−0.703066	−	0.231016i
$739$	−2.23861	−	3.87739i	−0.0823487	−	0.142632i	0.821910	−	0.569618i	$-0.192909\pi$
$739$	−2.23861	−	3.87739i	−0.0823487	−	0.142632i	−0.904258	+	0.426986i	$0.859575\pi$
$740$		0			0
$741$	−51.8596	−	23.1923i	−1.90511	−	0.851991i
$742$	11.1803	−	7.07107i	0.410443	−	0.259587i
$743$			19.4317i			0.712879i	0.934318	+	0.356440i	$0.116009\pi$
$743$			19.4317i			0.712879i	−0.934318	+	0.356440i	$0.883991\pi$
$744$	−0.423441	+	0.306579i	−0.0155241	+	0.0112397i
$745$		0			0
$746$	3.13367	−	1.80922i	0.114732	−	0.0662404i
$747$	−49.0889	+	10.2644i	−1.79607	+	0.375556i
$748$		−	0.674899i		−	0.0246767i
$749$	−14.4796	+	0.584480i	−0.529073	+	0.0213564i
$750$		0			0
$751$	16.0000	−	27.7128i	0.583848	−	1.01125i	−0.411170	−	0.911559i	$-0.634880\pi$
$751$	16.0000	−	27.7128i	0.583848	−	1.01125i	0.995018	−	0.0996961i	$-0.0317870\pi$
$752$	−3.87739	−	6.71584i	−0.141394	−	0.244901i
$753$	2.95823	+	28.6010i	0.107804	+	1.04228i
$754$	−11.7386	−	6.77729i	−0.427495	−	0.246814i
$755$		0			0
$756$	2.38089	−	13.5400i	0.0865920	−	0.492445i
$757$	30.2476			1.09937			0.549683	−	0.835373i	$-0.314748\pi$
$757$	30.2476			1.09937			0.549683	+	0.835373i	$0.314748\pi$
$758$	−8.24696	−	4.76139i	−0.299543	−	0.172941i
$759$	−0.246336	−	2.38165i	−0.00894143	−	0.0864484i
$760$		0			0
$761$	4.76492	−	8.25308i	0.172728	−	0.299174i	−0.766645	−	0.642072i	$-0.778075\pi$
$761$	4.76492	−	8.25308i	0.172728	−	0.299174i	0.939373	+	0.342898i	$0.111408\pi$
$762$	−9.63774	+	21.5507i	−0.349139	+	0.780698i
$763$	29.1247	+	15.2833i	1.05438	+	0.553293i
$764$		−	1.59580i		−	0.0577341i
$765$		0			0
$766$	0.715838	−	0.413289i	0.0258643	−	0.0149328i
$767$	28.5394	−	16.4772i	1.03050	−	0.594958i
$768$	1.40294	−	1.01575i	0.0506243	−	0.0366528i
$769$		−	28.8412i		−	1.04004i	−0.854154	−	0.520020i	$-0.825924\pi$
$769$		−	28.8412i		−	1.04004i	0.854154	−	0.520020i	$-0.174076\pi$
$770$		0			0
$771$	37.3861	+	16.7196i	1.34643	+	0.602141i
$772$	−3.67423	+	6.36396i	−0.132239	+	0.229044i
$773$	14.4206	+	24.9772i	0.518673	+	0.898368i	0.999765	+	0.0216979i	$0.00690720\pi$
$773$	14.4206	+	24.9772i	0.518673	+	0.898368i	−0.481091	+	0.876670i	$0.659759\pi$
$774$	−5.76471	−	1.89419i	−0.207208	−	0.0680853i
$775$		0			0
$776$	−3.50333			−0.125762
$777$	32.3612	−	4.67295i	1.16095	−	0.167641i
$778$	−7.34847			−0.263455
$779$	28.4047	+	16.3995i	1.01770	+	0.587571i
$780$		0			0
$781$	0.215838	+	0.373843i	0.00772330	+	0.0133772i
$782$	10.2414	−	17.7386i	0.366231	−	0.634331i
$783$	10.0116	−	3.19808i	0.357785	−	0.114290i
$784$	3.97723	+	5.76035i	0.142044	+	0.205727i
$785$		0			0
$786$	−6.12145	−	8.45485i	−0.218345	−	0.301574i
$787$	−30.0341	+	17.3402i	−1.07060	+	0.618112i	−0.928346	−	0.371718i	$-0.878769\pi$
$787$	−30.0341	+	17.3402i	−1.07060	+	0.618112i	−0.142256	+	0.989830i	$0.545436\pi$
$788$	−7.79423	+	4.50000i	−0.277658	+	0.160306i
$789$	2.03151	+	2.80588i	0.0723235	+	0.0998921i
$790$		0			0
$791$	−9.22460	−	14.5854i	−0.327989	−	0.518596i
$792$	0.426844	+	0.477226i	0.0151672	+	0.0169575i
$793$	11.6072	−	20.1042i	0.412183	−	0.713922i
$794$	15.1867	+	26.3041i	0.538956	+	0.933498i
$795$		0			0
$796$	19.4317	+	11.2189i	0.688738	+	0.397643i
$797$	28.9201			1.02440			0.512201	−	0.858865i	$-0.328830\pi$
$797$	28.9201			1.02440			0.512201	+	0.858865i	$0.328830\pi$
$798$	−8.32321	+	20.8271i	−0.294638	+	0.737271i
$799$	24.5228			0.867553
$800$		0			0
$801$	−9.90283	+	30.1379i	−0.349899	+	1.06487i
$802$	15.1747	+	26.2834i	0.535838	+	0.928098i
$803$	1.27931	−	2.21584i	0.0451460	−	0.0781952i
$804$	8.42087	+	3.76593i	0.296981	+	0.132814i
$805$		0			0
$806$		−	2.02265i		−	0.0712447i
$807$	40.5377	−	29.3499i	1.42699	−	1.03317i
$808$	−9.79796	+	5.65685i	−0.344691	+	0.199007i
$809$	34.7686	−	20.0737i	1.22240	−	0.705753i	0.256971	−	0.966419i	$-0.417275\pi$
$809$	34.7686	−	20.0737i	1.22240	−	0.705753i	0.965429	+	0.260666i	$0.0839421\pi$
$810$		0			0
$811$			6.70527i			0.235454i	0.993046	+	0.117727i	$0.0375608\pi$
$811$			6.70527i			0.235454i	−0.993046	+	0.117727i	$0.962439\pi$
$812$	−2.48661	+	4.73861i	−0.0872629	+	0.166293i
$813$	−4.47214	+	10.0000i	−0.156845	+	0.350715i
$814$	−0.761387	+	1.31876i	−0.0266866	+	0.0462226i
$815$		0			0
$816$	0.563508	+	5.44816i	0.0197267	+	0.190724i
$817$	8.57321	+	4.94975i	0.299939	+	0.173170i
$818$	−22.4378			−0.784518
$819$	37.0307	+	38.1836i	1.29396	+	1.33424i
$820$		0			0
$821$	44.0814	+	25.4504i	1.53845	+	0.888226i	0.998930	+	0.0462557i	$0.0147289\pi$
$821$	44.0814	+	25.4504i	1.53845	+	0.888226i	0.539523	+	0.841971i	$0.318604\pi$
$822$	−1.33242	−	12.8822i	−0.0464734	−	0.449319i
$823$	16.2927	+	28.2199i	0.567929	+	0.983682i	0.996771	+	0.0803025i	$0.0255886\pi$
$823$	16.2927	+	28.2199i	0.567929	+	0.983682i	−0.428841	+	0.903380i	$0.641078\pi$
$824$	5.28720	−	9.15769i	0.184188	−	0.319023i
$825$		0			0
$826$	−6.95445	−	10.9960i	−0.241976	−	0.382598i
$827$			39.9089i			1.38777i	0.720087	+	0.693884i	$0.244102\pi$
$827$			39.9089i			1.38777i	−0.720087	+	0.693884i	$0.755898\pi$
$828$	3.97713	+	19.0203i	0.138215	+	0.661002i
$829$	16.3069	−	9.41481i	0.566363	−	0.326990i	−0.189332	−	0.981913i	$-0.560632\pi$
$829$	16.3069	−	9.41481i	0.566363	−	0.326990i	0.755696	+	0.654923i	$0.227299\pi$
$830$		0			0
$831$	−13.7460	+	9.95231i	−0.476842	+	0.345242i
$832$			6.70141i			0.232330i
$833$	−22.0639	+	1.78416i	−0.764470	+	0.0618175i
$834$	11.9089	+	5.32582i	0.412372	+	0.184418i
$835$		0			0
$836$	−0.522278	−	0.904612i	−0.0180634	−	0.0312867i
$837$	1.16027	+	1.05519i	0.0401046	+	0.0364726i
$838$	−14.3768	−	8.30045i	−0.496639	−	0.286734i
$839$	37.3156			1.28828			0.644139	−	0.764908i	$-0.277216\pi$
$839$	37.3156			1.28828			0.644139	+	0.764908i	$0.277216\pi$
$840$		0			0
$841$	24.9089			0.858928
$842$	2.55863	+	1.47723i	0.0881762	+	0.0509086i
$843$	−19.9975	+	2.06837i	−0.688752	+	0.0712383i
$844$	6.76139	+	11.7111i	0.232737	+	0.403112i
$845$		0			0
$846$	−17.3402	+	15.5096i	−0.596169	+	0.533230i
$847$	1.16896	+	28.9592i	0.0401659	+	0.995049i
$848$		−	5.00000i		−	0.171701i
$849$	−25.1059	−	34.6759i	−0.861632	−	1.19007i
$850$		0			0
$851$	−40.0236	+	23.1077i	−1.37199	+	0.792120i
$852$	−2.05451	−	2.83766i	−0.0703863	−	0.0972165i
$853$		−	53.9165i		−	1.84607i	−0.384720	−	0.923033i	$-0.625702\pi$
$853$		−	53.9165i		−	1.84607i	0.384720	−	0.923033i	$-0.374298\pi$
$854$	−8.11562	−	4.25871i	−0.277711	−	0.145730i
$855$		0			0
$856$	−2.73861	+	4.74342i	−0.0936039	+	0.162127i
$857$	20.1810	+	34.9545i	0.689369	+	1.19402i	0.972042	+	0.234805i	$0.0754452\pi$
$857$	20.1810	+	34.9545i	0.689369	+	1.19402i	−0.282674	+	0.959216i	$0.591221\pi$
$858$	−2.46408	+	0.254862i	−0.0841223	+	0.00870085i
$859$	15.5228	+	8.96208i	0.529630	+	0.305782i	0.740866	−	0.671653i	$-0.234415\pi$
$859$	15.5228	+	8.96208i	0.529630	+	0.305782i	−0.211236	+	0.977435i	$0.567749\pi$
$860$		0			0
$861$	−18.9982	−	24.1279i	−0.647456	−	0.822277i
$862$	−37.0576			−1.26219
$863$	−13.4431	−	7.76139i	−0.457609	−	0.264201i	0.253429	−	0.967354i	$-0.418441\pi$
$863$	−13.4431	−	7.76139i	−0.457609	−	0.264201i	−0.711038	+	0.703153i	$0.751775\pi$
$864$	−3.84418	−	3.49604i	−0.130782	−	0.118938i
$865$		0			0
$866$		0			0
$867$	11.0680	+	4.94975i	0.375888	+	0.168102i
$868$	−0.797901	+	0.0322079i	−0.0270825	+	0.00109321i
$869$		−	0.111571i		−	0.00378480i
$870$		0			0
$871$	−30.9089	+	17.8453i	−1.04731	+	0.604664i
$872$	10.7661	−	6.21584i	0.364588	−	0.210495i
$873$	2.15110	+	10.2875i	0.0728037	+	0.348179i
$874$		−	31.7017i		−	1.07232i
$875$		0			0
$876$	−8.47723	+	18.9557i	−0.286419	+	0.640452i
$877$	−21.1408	+	36.6169i	−0.713874	+	1.23647i	0.249518	+	0.968370i	$0.419728\pi$
$877$	−21.1408	+	36.6169i	−0.713874	+	1.23647i	−0.963392	+	0.268096i	$0.913606\pi$
$878$	11.3698	+	19.6931i	0.383712	+	0.664609i
$879$	0.818370	+	7.91224i	0.0276029	+	0.266873i
$880$		0			0
$881$	26.5004			0.892821			0.446411	−	0.894828i	$-0.352702\pi$
$881$	26.5004			0.892821			0.446411	+	0.894828i	$0.352702\pi$
$882$	14.4731	−	15.2160i	0.487336	−	0.512351i
$883$	−29.2823			−0.985428			−0.492714	−	0.870191i	$-0.663995\pi$
$883$	−29.2823			−0.985428			−0.492714	+	0.870191i	$0.663995\pi$
$884$	−18.3526	−	10.5959i	−0.617264	−	0.356377i
$885$		0			0
$886$	18.4772	+	32.0035i	0.620755	+	1.07518i
$887$	−1.73205	+	3.00000i	−0.0581566	+	0.100730i	−0.893638	−	0.448789i	$-0.851856\pi$
$887$	−1.73205	+	3.00000i	−0.0581566	+	0.100730i	0.835481	+	0.549519i	$0.185189\pi$
$888$	5.04524	−	11.2815i	0.169307	−	0.378582i
$889$	−30.4772	+	19.2755i	−1.02217	+	0.646479i
$890$		0			0
$891$	1.13928	−	1.54645i	0.0381673	−	0.0518079i
$892$	5.53924	−	3.19808i	0.185468	−	0.107080i
$893$	32.8695	−	18.9772i	1.09994	−	0.635049i
$894$	−3.43649	+	2.48808i	−0.114933	+	0.0832137i
$895$		0			0
$896$	2.64360	−	0.106711i	0.0883164	−	0.00356496i
$897$	−68.6318	−	30.6931i	−2.29155	−	1.02481i
$898$	1.75830	−	3.04546i	0.0586752	−	0.101628i
$899$	−0.305242	−	0.528694i	−0.0101804	−	0.0176329i
$900$		0			0
$901$	13.6931	+	7.90569i	0.456182	+	0.263377i
$902$	1.43023			0.0476213
$903$	−5.73411	−	7.28238i	−0.190819	−	0.242342i
$904$	−6.52277			−0.216944
$905$		0			0
$906$	3.44572	−	0.356394i	0.114476	−	0.0118404i
$907$	4.89898	+	8.48528i	0.162668	+	0.281749i	0.935825	−	0.352466i	$-0.114657\pi$
$907$	4.89898	+	8.48528i	0.162668	+	0.281749i	−0.773157	+	0.634215i	$0.781323\pi$
$908$	−5.19615	+	9.00000i	−0.172440	+	0.298675i
$909$	22.6274	+	25.2982i	0.750504	+	0.839089i
$910$		0			0
$911$		−	15.1238i		−	0.501073i	−0.968107	−	0.250537i	$-0.919393\pi$
$911$		−	15.1238i		−	0.501073i	0.968107	−	0.250537i	$-0.0806071\pi$
$912$	4.97143	+	6.86646i	0.164620	+	0.227371i
$913$	3.08976	−	1.78387i	0.102256	−	0.0590375i
$914$	−32.8322	+	18.9557i	−1.08599	+	0.626997i
$915$		0			0
$916$			7.23003i			0.238887i
$917$	−0.643094	−	15.9317i	−0.0212368	−	0.526110i
$918$	15.6525	−	5.00000i	0.516609	−	0.165025i
$919$	−16.2158	+	28.0867i	−0.534911	+	0.926493i	0.464256	+	0.885701i	$0.346322\pi$
$919$	−16.2158	+	28.0867i	−0.534911	+	0.926493i	−0.999168	+	0.0407925i	$0.987012\pi$
$920$		0			0
$921$	−6.03574	+	0.624282i	−0.198884	+	0.0205708i
$922$	14.1125	+	8.14783i	0.464769	+	0.268335i
$923$	13.5546			0.446155
$924$	0.139776	+	0.967982i	0.00459830	+	0.0318443i
$925$		0			0
$926$	−15.3071	−	8.83756i	−0.503023	−	0.290420i
$927$	−30.1379	−	9.90283i	−0.989859	−	0.325252i
$928$	1.01132	+	1.75166i	0.0331983	+	0.0575012i
$929$	11.8360	−	20.5005i	0.388326	−	0.672601i	−0.603898	−	0.797061i	$-0.706387\pi$
$929$	11.8360	−	20.5005i	0.388326	−	0.672601i	0.992225	+	0.124461i	$0.0397201\pi$
$930$		0			0
$931$	−28.1931	+	19.4658i	−0.923990	+	0.637967i
$932$		−	4.00000i		−	0.131024i
$933$	−40.5377	+	29.3499i	−1.32714	+	0.960874i
$934$	−29.7386	+	17.1696i	−0.973077	+	0.561806i
$935$		0			0
$936$	19.6786	−	4.11478i	0.643216	−	0.134496i
$937$			22.6918i			0.741310i	0.928771	+	0.370655i	$0.120867\pi$
$937$			22.6918i			0.741310i	−0.928771	+	0.370655i	$0.879133\pi$
$938$	7.53185	+	11.9089i	0.245924	+	0.388839i
$939$	16.4317	−	36.7423i	0.536228	−	1.19904i
$940$		0			0
$941$	2.49098	+	4.31450i	0.0812036	+	0.140649i	0.903767	−	0.428024i	$-0.140790\pi$
$941$	2.49098	+	4.31450i	0.0812036	+	0.140649i	−0.822564	+	0.568673i	$0.807457\pi$
$942$	1.56644	+	15.1448i	0.0510375	+	0.493445i
$943$	37.5912	+	21.7033i	1.22414	+	0.706756i
$944$	−4.91754			−0.160052
$945$		0			0
$946$	0.431677			0.0140350
$947$	28.4605	+	16.4317i	0.924842	+	0.533958i	0.885177	−	0.465255i	$-0.154037\pi$
$947$	28.4605	+	16.4317i	0.924842	+	0.533958i	0.0396654	+	0.999213i	$0.487371\pi$
$948$	0.0931568	+	0.900667i	0.00302559	+	0.0292523i
$949$	−40.1703	−	69.5770i	−1.30398	−	2.25856i
$950$		0			0
$951$	23.9772	−	53.6147i	0.777514	−	1.73858i
$952$	−3.88766	+	7.40852i	−0.126000	+	0.240111i
$953$		−	25.0455i		−	0.811305i	−0.914027	−	0.405652i	$-0.867044\pi$
$953$		−	25.0455i		−	0.811305i	0.914027	−	0.405652i	$-0.132956\pi$
$954$	−14.6825	+	3.07008i	−0.475362	+	0.0993976i
$955$		0			0
$956$		0			0
$957$	−0.605617	+	0.438477i	−0.0195768	+	0.0141739i
$958$			11.3781i			0.367611i
$959$	9.19239	−	17.5175i	0.296838	−	0.565669i
$960$		0			0
$961$	−15.4545	+	26.7679i	−0.498531	+	0.863480i
$962$	23.9074	+	41.4089i	0.770807	+	1.33508i
$963$	15.6106	+	5.12938i	0.503043	+	0.165292i
$964$	3.45445	+	1.99443i	0.111260	+	0.0642362i
$965$		0			0
$966$	−11.0151	+	27.5629i	−0.354403	+	0.886821i
$967$	46.4287			1.49305			0.746524	−	0.665359i	$-0.231721\pi$
$967$	46.4287			1.49305			0.746524	+	0.665359i	$0.231721\pi$
$968$	9.48683	+	5.47723i	0.304918	+	0.176045i
$969$	−26.6651	+	2.75799i	−0.856606	+	0.0885996i
$970$		0			0
$971$	−0.490070	+	0.848827i	−0.0157271	+	0.0272401i	−0.873782	−	0.486318i	$-0.838340\pi$
$971$	−0.490070	+	0.848827i	−0.0157271	+	0.0272401i	0.858055	+	0.513558i	$0.171673\pi$
$972$	−7.90569	+	13.4350i	−0.253575	+	0.430929i
$973$	10.6516	+	16.8417i	0.341476	+	0.539921i
$974$			36.6308i			1.17373i
$975$		0			0
$976$	−3.00000	+	1.73205i	−0.0960277	+	0.0554416i
$977$	−34.5621	+	19.9545i	−1.10574	+	0.638399i	−0.937723	−	0.347385i	$-0.887070\pi$
$977$	−34.5621	+	19.9545i	−1.10574	+	0.638399i	−0.168018	+	0.985784i	$0.553737\pi$
$978$	14.9285	+	20.6190i	0.477359	+	0.659321i
$979$		−	2.25681i		−	0.0721278i
$980$		0			0
$981$	−24.8634	−	27.7981i	−0.793826	−	0.887524i
$982$	−2.02265	+	3.50333i	−0.0645452	+	0.111796i
$983$	16.9072	+	29.2842i	0.539257	+	0.934020i	0.998944	+	0.0459391i	$0.0146280\pi$
$983$	16.9072	+	29.2842i	0.539257	+	0.934020i	−0.459688	+	0.888081i	$0.652039\pi$
$984$	−11.5456	+	1.19417i	−0.368060	+	0.0380688i
$985$		0			0
$986$	−6.39617			−0.203696
$987$	−35.1721	+	5.07883i	−1.11954	+	0.161661i
$988$	−32.7989			−1.04347
$989$	11.3459	+	6.55057i	0.360779	+	0.208296i
$990$		0			0
$991$	−10.7386	−	18.5998i	−0.341123	−	0.590843i	0.643518	−	0.765431i	$-0.277474\pi$
$991$	−10.7386	−	18.5998i	−0.341123	−	0.590843i	−0.984642	+	0.174588i	$0.944141\pi$
$992$	−0.150912	+	0.261387i	−0.00479146	+	0.00829905i
$993$	18.0751	+	8.08342i	0.573595	+	0.256519i
$994$	−0.215838	−	5.34706i	−0.00684598	−	0.169599i
$995$		0			0
$996$	−23.4528	+	16.9802i	−0.743130	+	0.538038i
$997$	−13.4164	+	7.74597i	−0.424902	+	0.245317i	−0.697172	−	0.716904i	$-0.745559\pi$
$997$	−13.4164	+	7.74597i	−0.424902	+	0.245317i	0.272270	+	0.962221i	$0.412225\pi$
$998$	36.2942	−	20.9545i	1.14887	−	0.663302i
$999$	−36.2259	−	7.88828i	−1.14614	−	0.249574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.s.i.551.3		16
3.2	odd	2	inner	1050.2.s.i.551.5		16
5.2	odd	4		210.2.t.f.89.4	yes	8
5.3	odd	4		210.2.t.e.89.1	yes	8
5.4	even	2	inner	1050.2.s.i.551.6		16
7.3	odd	6	inner	1050.2.s.i.101.5		16
15.2	even	4		210.2.t.e.89.2	yes	8
15.8	even	4		210.2.t.f.89.3	yes	8
15.14	odd	2	inner	1050.2.s.i.551.4		16
21.17	even	6	inner	1050.2.s.i.101.3		16
35.2	odd	12		1470.2.d.e.1469.4		8
35.3	even	12		210.2.t.e.59.2	yes	8
35.12	even	12		1470.2.d.e.1469.5		8
35.17	even	12		210.2.t.f.59.3	yes	8
35.23	odd	12		1470.2.d.f.1469.5		8
35.24	odd	6	inner	1050.2.s.i.101.4		16
35.33	even	12		1470.2.d.f.1469.4		8
105.2	even	12		1470.2.d.f.1469.1		8
105.17	odd	12		210.2.t.e.59.1	✓	8
105.23	even	12		1470.2.d.e.1469.8		8
105.38	odd	12		210.2.t.f.59.4	yes	8
105.47	odd	12		1470.2.d.f.1469.8		8
105.59	even	6	inner	1050.2.s.i.101.6		16
105.68	odd	12		1470.2.d.e.1469.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.t.e.59.1	✓	8	105.17	odd	12
210.2.t.e.59.2	yes	8	35.3	even	12
210.2.t.e.89.1	yes	8	5.3	odd	4
210.2.t.e.89.2	yes	8	15.2	even	4
210.2.t.f.59.3	yes	8	35.17	even	12
210.2.t.f.59.4	yes	8	105.38	odd	12
210.2.t.f.89.3	yes	8	15.8	even	4
210.2.t.f.89.4	yes	8	5.2	odd	4
1050.2.s.i.101.3		16	21.17	even	6	inner
1050.2.s.i.101.4		16	35.24	odd	6	inner
1050.2.s.i.101.5		16	7.3	odd	6	inner
1050.2.s.i.101.6		16	105.59	even	6	inner
1050.2.s.i.551.3		16	1.1	even	1	trivial
1050.2.s.i.551.4		16	15.14	odd	2	inner
1050.2.s.i.551.5		16	3.2	odd	2	inner
1050.2.s.i.551.6		16	5.4	even	2	inner
1470.2.d.e.1469.1		8	105.68	odd	12
1470.2.d.e.1469.4		8	35.2	odd	12
1470.2.d.e.1469.5		8	35.12	even	12
1470.2.d.e.1469.8		8	105.23	even	12
1470.2.d.f.1469.1		8	105.2	even	12
1470.2.d.f.1469.4		8	35.33	even	12
1470.2.d.f.1469.5		8	35.23	odd	12
1470.2.d.f.1469.8		8	105.47	odd	12

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.178197 + 1.72286i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.707107 - 1.58114i) q^{6} +(2.23607 - 1.41421i) q^{7} -1.00000i q^{8} +(-2.93649 + 0.614017i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.178197 + 1.72286i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.707107 - 1.58114i) q^{6} +(2.23607 - 1.41421i) q^{7} -1.00000i q^{8} +(-2.93649 + 0.614017i) q^{9} +(0.184829 - 0.106711i) q^{11} +(-1.40294 + 1.01575i) q^{12} -6.70141i q^{13} +(-2.64360 + 0.106711i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.58114 - 2.73861i) q^{17} +(2.85008 + 0.936492i) q^{18} +(-4.23861 - 2.44716i) q^{19} +(2.83495 + 3.60042i) q^{21} -0.213422 q^{22} +(-5.60944 - 3.23861i) q^{23} +(1.72286 - 0.178197i) q^{24} +(-3.35071 + 5.80359i) q^{26} +(-1.58114 - 4.94975i) q^{27} +(2.34278 + 1.22938i) q^{28} +2.02265i q^{29} +(-0.261387 + 0.150912i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.216784 + 0.299418i) q^{33} +3.16228i q^{34} +(-2.00000 - 2.23607i) q^{36} +(3.56752 - 6.17913i) q^{37} +(2.44716 + 4.23861i) q^{38} +(11.5456 - 1.19417i) q^{39} -6.70141 q^{41} +(-0.654929 - 4.53553i) q^{42} -2.02265 q^{43} +(0.184829 + 0.106711i) q^{44} +(3.23861 + 5.60944i) q^{46} +(-3.87739 + 6.71584i) q^{47} +(-1.58114 - 0.707107i) q^{48} +(3.00000 - 6.32456i) q^{49} +(4.43649 - 3.21209i) q^{51} +(5.80359 - 3.35071i) q^{52} +(-4.33013 + 2.50000i) q^{53} +(-1.10557 + 5.07718i) q^{54} +(-1.41421 - 2.23607i) q^{56} +(3.46081 - 7.73861i) q^{57} +(1.01132 - 1.75166i) q^{58} +(2.45877 + 4.25871i) q^{59} +(3.00000 + 1.73205i) q^{61} +0.301824 q^{62} +(-5.69784 + 5.52581i) q^{63} -1.00000 q^{64} +(-0.0380311 - 0.367696i) q^{66} +(-2.66291 - 4.61230i) q^{67} +(1.58114 - 2.73861i) q^{68} +(4.58009 - 10.2414i) q^{69} +2.02265i q^{71} +(0.614017 + 2.93649i) q^{72} +(10.3824 - 5.99430i) q^{73} +(-6.17913 + 3.56752i) q^{74} -4.89433i q^{76} +(0.262377 - 0.500000i) q^{77} +(-10.5959 - 4.73861i) q^{78} +(0.261387 - 0.452736i) q^{79} +(8.24597 - 3.60611i) q^{81} +(5.80359 + 3.35071i) q^{82} +16.7169 q^{83} +(-1.70058 + 4.25535i) q^{84} +(1.75166 + 1.01132i) q^{86} +(-3.48474 + 0.360429i) q^{87} +(-0.106711 - 0.184829i) q^{88} +(5.28720 - 9.15769i) q^{89} +(-9.47723 - 14.9848i) q^{91} -6.47723i q^{92} +(-0.306579 - 0.423441i) q^{93} +(6.71584 - 3.87739i) q^{94} +(1.01575 + 1.40294i) q^{96} -3.50333i q^{97} +(-5.76035 + 3.97723i) q^{98} +(-0.477226 + 0.426844i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 16 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 - 16 * q^9	\( 16 q + 8 q^{4} - 16 q^{9} - 8 q^{16} - 24 q^{19} + 8 q^{21} - 48 q^{31} - 32 q^{36} + 16 q^{39} + 8 q^{46} + 48 q^{49} + 40 q^{51} + 48 q^{61} - 16 q^{64} + 24 q^{66} + 48 q^{79} + 8 q^{81} - 8 q^{84} - 64 q^{91} - 24 q^{94} + 80 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 - 16 * q^9 - 8 * q^16 - 24 * q^19 + 8 * q^21 - 48 * q^31 - 32 * q^36 + 16 * q^39 + 8 * q^46 + 48 * q^49 + 40 * q^51 + 48 * q^61 - 16 * q^64 + 24 * q^66 + 48 * q^79 + 8 * q^81 - 8 * q^84 - 64 * q^91 - 24 * q^94 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

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