LMFDB - Embedded newform 336.4.bc.d.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,4,Mod(17,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("336.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.bc (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 29x^{9} + 6x^{8} - 49x^{7} + 1564x^{6} - 441x^{5} + 486x^{4} - 21141x^{3} - 59049x + 531441 $ x^12 - x^11 - 29x^9 + 6x^8 - 49x^7 + 1564x^6 - 441x^5 + 486x^4 - 21141x^3 - 59049x + 531441
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.1
Root			$-2.59957 + 1.49740i$ of defining polynomial
Character	$\chi$	$=$	336.17
Dual form			336.4.bc.d.257.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.19615 + 0.00519496i) q^{3} +(8.05907 + 13.9587i) q^{5} +(5.67909 + 17.6280i) q^{7} +(26.9999 - 0.0539876i) q^{9} +O(q^{10})$	\(q+(-5.19615 + 0.00519496i) q^{3} +(8.05907 + 13.9587i) q^{5} +(5.67909 + 17.6280i) q^{7} +(26.9999 - 0.0539876i) q^{9} +(30.8296 + 17.7995i) q^{11} -7.40831i q^{13} +(-41.9486 - 72.4897i) q^{15} +(14.4601 - 25.0457i) q^{17} +(-30.4580 + 17.5849i) q^{19} +(-29.6010 - 91.5685i) q^{21} +(48.0017 - 27.7138i) q^{23} +(-67.3971 + 116.735i) q^{25} +(-140.295 + 0.420792i) q^{27} +68.1510i q^{29} +(154.734 + 89.3356i) q^{31} +(-160.288 - 92.3286i) q^{33} +(-200.297 + 221.338i) q^{35} +(116.838 + 202.370i) q^{37} +(0.0384859 + 38.4947i) q^{39} -370.068 q^{41} +187.068 q^{43} +(218.348 + 376.449i) q^{45} +(-87.3726 - 151.334i) q^{47} +(-278.496 + 200.222i) q^{49} +(-75.0068 + 130.216i) q^{51} +(235.715 + 136.090i) q^{53} +573.789i q^{55} +(158.173 - 91.5321i) q^{57} +(-48.4354 + 83.8926i) q^{59} +(-333.882 + 192.767i) q^{61} +(154.287 + 475.650i) q^{63} +(103.411 - 59.7041i) q^{65} +(-509.009 + 881.630i) q^{67} +(-249.280 + 144.254i) q^{69} -125.333i q^{71} +(195.346 + 112.783i) q^{73} +(349.599 - 606.924i) q^{75} +(-138.686 + 644.550i) q^{77} +(-532.154 - 921.718i) q^{79} +(728.994 - 2.91533i) q^{81} -601.040 q^{83} +466.140 q^{85} +(-0.354042 - 354.123i) q^{87} +(-752.606 - 1303.55i) q^{89} +(130.594 - 42.0725i) q^{91} +(-804.484 - 463.397i) q^{93} +(-490.926 - 283.436i) q^{95} +327.463i q^{97} +(833.358 + 478.920i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 + 56 * q^7 - 3 * q^9	$ 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9} - 6 q^{15} - 300 q^{19} + 357 q^{21} - 42 q^{25} + 930 q^{31} - 855 q^{33} + 764 q^{37} + 426 q^{39} + 1012 q^{43} + 2367 q^{45} - 336 q^{49} + 1341 q^{51} + 270 q^{57} + 2358 q^{61} - 1071 q^{63} - 792 q^{67} - 2904 q^{73} + 2418 q^{75} - 1674 q^{79} + 837 q^{81} + 348 q^{85} - 1638 q^{87} + 1218 q^{91} - 1479 q^{93} + 3354 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 + 56 * q^7 - 3 * q^9 - 6 * q^15 - 300 * q^19 + 357 * q^21 - 42 * q^25 + 930 * q^31 - 855 * q^33 + 764 * q^37 + 426 * q^39 + 1012 * q^43 + 2367 * q^45 - 336 * q^49 + 1341 * q^51 + 270 * q^57 + 2358 * q^61 - 1071 * q^63 - 792 * q^67 - 2904 * q^73 + 2418 * q^75 - 1674 * q^79 + 837 * q^81 + 348 * q^85 - 1638 * q^87 + 1218 * q^91 - 1479 * q^93 + 3354 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	−5.19615	+	0.00519496i	−1.00000	+	0.000999771i
$3$	−5.19615	+	0.00519496i	−1.00000	+	0.000999771i
$4$		0			0
$5$	8.05907	+	13.9587i	0.720825	+	1.24851i	0.960670	+	0.277694i	$0.0895701\pi$
$5$	8.05907	+	13.9587i	0.720825	+	1.24851i	−0.239845	+	0.970811i	$0.577097\pi$
$6$		0			0
$7$	5.67909	+	17.6280i	0.306642	+	0.951825i
$7$	5.67909	+	17.6280i	0.306642	+	0.951825i
$8$		0			0
$9$	26.9999	−	0.0539876i	0.999998	−	0.00199954i
$10$		0			0
$11$	30.8296	+	17.7995i	0.845043	+	0.487886i	0.858975	−	0.512017i	$-0.171102\pi$
$11$	30.8296	+	17.7995i	0.845043	+	0.487886i	−0.0139322	+	0.999903i	$0.504435\pi$
$12$		0			0
$13$		−	7.40831i		−	0.158054i	−0.996872	−	0.0790268i	$-0.974819\pi$
$13$		−	7.40831i		−	0.158054i	0.996872	−	0.0790268i	$-0.0251813\pi$
$14$		0			0
$15$	−41.9486	−	72.4897i	−0.722073	−	1.24778i
$16$		0			0
$17$	14.4601	−	25.0457i	0.206300	−	0.357322i	−0.744246	−	0.667905i	$-0.767191\pi$
$17$	14.4601	−	25.0457i	0.206300	−	0.357322i	0.950546	+	0.310584i	$0.100524\pi$
$18$		0			0
$19$	−30.4580	+	17.5849i	−0.367765	+	0.212329i	−0.672482	−	0.740114i	$-0.734772\pi$
$19$	−30.4580	+	17.5849i	−0.367765	+	0.212329i	0.304716	+	0.952443i	$0.401438\pi$
$20$		0			0
$21$	−29.6010	−	91.5685i	−0.307593	−	0.951518i
$22$		0			0
$23$	48.0017	−	27.7138i	0.435175	−	0.251249i	−0.266374	−	0.963870i	$-0.585825\pi$
$23$	48.0017	−	27.7138i	0.435175	−	0.251249i	0.701549	+	0.712621i	$0.252492\pi$
$24$		0			0
$25$	−67.3971	+	116.735i	−0.539177	+	0.933881i
$26$		0			0
$27$	−140.295	+	0.420792i	−0.999996	+	0.00299931i
$28$		0			0
$29$			68.1510i			0.436390i	0.975905	+	0.218195i	$0.0700169\pi$
$29$			68.1510i			0.436390i	−0.975905	+	0.218195i	$0.929983\pi$
$30$		0			0
$31$	154.734	+	89.3356i	0.896484	+	0.517585i	0.876058	−	0.482206i	$-0.160164\pi$
$31$	154.734	+	89.3356i	0.896484	+	0.517585i	0.0204262	+	0.999791i	$0.493498\pi$
$32$		0			0
$33$	−160.288	−	92.3286i	−0.845530	−	0.487041i
$34$		0			0
$35$	−200.297	+	221.338i	−0.967323	+	1.06894i
$36$		0			0
$37$	116.838	+	202.370i	0.519137	+	0.899172i	0.999753	+	0.0222405i	$0.00707996\pi$
$37$	116.838	+	202.370i	0.519137	+	0.899172i	−0.480615	+	0.876931i	$0.659587\pi$
$38$		0			0
$39$	0.0384859	+	38.4947i	0.000158017	+	0.158053i
$40$		0			0
$41$	−370.068			−1.40963			−0.704816	−	0.709390i	$-0.748970\pi$
$41$	−370.068			−1.40963			−0.704816	+	0.709390i	$0.748970\pi$
$42$		0			0
$43$	187.068			0.663432			0.331716	−	0.943379i	$-0.392372\pi$
$43$	187.068			0.663432			0.331716	+	0.943379i	$0.392372\pi$
$44$		0			0
$45$	218.348	+	376.449i	0.723320	+	1.24706i
$46$		0			0
$47$	−87.3726	−	151.334i	−0.271162	−	0.469666i	0.697998	−	0.716100i	$-0.254075\pi$
$47$	−87.3726	−	151.334i	−0.271162	−	0.469666i	−0.969160	+	0.246434i	$0.920741\pi$
$48$		0			0
$49$	−278.496	+	200.222i	−0.811942	+	0.583739i
$50$		0			0
$51$	−75.0068	+	130.216i	−0.205942	+	0.357528i
$52$		0			0
$53$	235.715	+	136.090i	0.610905	+	0.352706i	0.773319	−	0.634017i	$-0.218595\pi$
$53$	235.715	+	136.090i	0.610905	+	0.352706i	−0.162415	+	0.986723i	$0.551928\pi$
$54$		0			0
$55$			573.789i			1.40672i
$56$		0			0
$57$	158.173	−	91.5321i	0.367553	−	0.212697i
$58$		0			0
$59$	−48.4354	+	83.8926i	−0.106877	+	0.185117i	−0.914504	−	0.404578i	$-0.867419\pi$
$59$	−48.4354	+	83.8926i	−0.106877	+	0.185117i	0.807626	+	0.589695i	$0.200752\pi$
$60$		0			0
$61$	−333.882	+	192.767i	−0.700807	+	0.404611i	−0.807648	−	0.589665i	$-0.799260\pi$
$61$	−333.882	+	192.767i	−0.700807	+	0.404611i	0.106841	+	0.994276i	$0.465927\pi$
$62$		0			0
$63$	154.287	+	475.650i	0.308544	+	0.951210i
$64$		0			0
$65$	103.411	−	59.7041i	0.197331	−	0.113929i
$66$		0			0
$67$	−509.009	+	881.630i	−0.928140	+	1.60759i	−0.141708	+	0.989908i	$0.545259\pi$
$67$	−509.009	+	881.630i	−0.928140	+	1.60759i	−0.786432	+	0.617677i	$0.788074\pi$
$68$		0			0
$69$	−249.280	+	144.254i	−0.434924	+	0.251684i
$70$		0			0
$71$		−	125.333i		−	0.209497i	−0.994499	−	0.104749i	$-0.966596\pi$
$71$		−	125.333i		−	0.209497i	0.994499	−	0.104749i	$-0.0334038\pi$
$72$		0			0
$73$	195.346	+	112.783i	0.313199	+	0.180825i	0.648357	−	0.761337i	$-0.275456\pi$
$73$	195.346	+	112.783i	0.313199	+	0.180825i	−0.335158	+	0.942162i	$0.608790\pi$
$74$		0			0
$75$	349.599	−	606.924i	0.538243	−	0.934420i
$76$		0			0
$77$	−138.686	+	644.550i	−0.205256	+	0.953939i
$78$		0			0
$79$	−532.154	−	921.718i	−0.757874	−	1.31268i	−0.943933	−	0.330138i	$-0.892905\pi$
$79$	−532.154	−	921.718i	−0.757874	−	1.31268i	0.186059	−	0.982539i	$-0.440428\pi$
$80$		0			0
$81$	728.994	−	2.91533i	0.999992	−	0.00399908i
$82$		0			0
$83$	−601.040			−0.794852			−0.397426	−	0.917634i	$-0.630096\pi$
$83$	−601.040			−0.794852			−0.397426	+	0.917634i	$0.630096\pi$
$84$		0			0
$85$	466.140			0.594824
$86$		0			0
$87$	−0.354042	−	354.123i	−0.000436290	−	0.436390i
$88$		0			0
$89$	−752.606	−	1303.55i	−0.896360	−	1.55254i	−0.832112	−	0.554607i	$-0.812869\pi$
$89$	−752.606	−	1303.55i	−0.896360	−	1.55254i	−0.0642474	−	0.997934i	$-0.520465\pi$
$90$		0			0
$91$	130.594	−	42.0725i	0.150439	−	0.0484658i
$92$		0			0
$93$	−804.484	−	463.397i	−0.897001	−	0.516689i
$94$		0			0
$95$	−490.926	−	283.436i	−0.530189	−	0.306105i
$96$		0			0
$97$			327.463i			0.342771i	0.985204	+	0.171386i	$0.0548244\pi$
$97$			327.463i			0.342771i	−0.985204	+	0.171386i	$0.945176\pi$
$98$		0			0
$99$	833.358	+	478.920i	0.846017	+	0.486195i
$100$		0			0
$101$	547.845	−	948.895i	0.539729	−	0.934837i	−0.459190	−	0.888338i	$-0.651860\pi$
$101$	547.845	−	948.895i	0.539729	−	0.934837i	0.998918	−	0.0464990i	$-0.0148064\pi$
$102$		0			0
$103$	−179.848	+	103.835i	−0.172048	+	0.0993318i	−0.583551	−	0.812076i	$-0.698337\pi$
$103$	−179.848	+	103.835i	−0.172048	+	0.0993318i	0.411503	+	0.911408i	$0.365004\pi$
$104$		0			0
$105$	1039.62	−	1151.15i	0.966254	−	1.06991i
$106$		0			0
$107$	1561.25	−	901.391i	1.41058	−	0.814399i	0.415138	−	0.909759i	$-0.363733\pi$
$107$	1561.25	−	901.391i	1.41058	−	0.814399i	0.995443	+	0.0953593i	$0.0304000\pi$
$108$		0			0
$109$	−141.825	+	245.647i	−0.124627	+	0.215860i	−0.921587	−	0.388172i	$-0.873107\pi$
$109$	−141.825	+	245.647i	−0.124627	+	0.215860i	0.796960	+	0.604032i	$0.206440\pi$
$110$		0			0
$111$	−608.160	−	1050.94i	−0.520036	−	0.898652i
$112$		0			0
$113$			1037.39i			0.863627i	0.901963	+	0.431814i	$0.142126\pi$
$113$			1037.39i			0.863627i	−0.901963	+	0.431814i	$0.857874\pi$
$114$		0			0
$115$	773.697	+	446.694i	0.627371	+	0.362213i
$116$		0			0
$117$	−0.399957	−	200.024i	−0.000316035	−	0.158053i
$118$		0			0
$119$	523.626	+	112.667i	0.403368	+	0.0867915i
$120$		0			0
$121$	−31.8573	−	55.1785i	−0.0239349	−	0.0414564i
$122$		0			0
$123$	1922.93	−	1.92249i	1.40963	−	0.00140931i
$124$		0			0
$125$	−157.864			−0.112958
$126$		0			0
$127$	−1645.81			−1.14994			−0.574968	−	0.818176i	$-0.694985\pi$
$127$	−1645.81			−1.14994			−0.574968	+	0.818176i	$0.694985\pi$
$128$		0			0
$129$	−972.033	+	0.971811i	−0.663432	+	0.000663281i
$130$		0			0
$131$	314.185	+	544.184i	0.209545	+	0.362943i	0.951571	−	0.307428i	$-0.0994683\pi$
$131$	314.185	+	544.184i	0.209545	+	0.362943i	−0.742026	+	0.670371i	$0.766135\pi$
$132$		0			0
$133$	−482.961	−	437.048i	−0.314873	−	0.284939i
$134$		0			0
$135$	−1136.52	−	1954.95i	−0.724566	−	1.24634i
$136$		0			0
$137$	−432.079	−	249.461i	−0.269453	−	0.155569i	0.359186	−	0.933266i	$-0.383054\pi$
$137$	−432.079	−	249.461i	−0.269453	−	0.155569i	−0.628639	+	0.777697i	$0.716388\pi$
$138$		0			0
$139$			1216.65i			0.742410i	0.928551	+	0.371205i	$0.121055\pi$
$139$			1216.65i			0.742410i	−0.928551	+	0.371205i	$0.878945\pi$
$140$		0			0
$141$	454.788	+	785.900i	0.271631	+	0.469395i
$142$		0			0
$143$	131.864	−	228.395i	0.0771121	−	0.133562i
$144$		0			0
$145$	−951.300	+	549.233i	−0.544835	+	0.314561i
$146$		0			0
$147$	1446.07	−	1041.83i	0.811358	−	0.584550i
$148$		0			0
$149$	2010.18	−	1160.58i	1.10524	−	0.638111i	0.167648	−	0.985847i	$-0.446383\pi$
$149$	2010.18	−	1160.58i	1.10524	−	0.638111i	0.937592	+	0.347736i	$0.113050\pi$
$150$		0			0
$151$	488.726	−	846.497i	0.263390	−	0.456205i	−0.703750	−	0.710447i	$-0.748493\pi$
$151$	488.726	−	846.497i	0.263390	−	0.456205i	0.967141	+	0.254242i	$0.0818260\pi$
$152$		0			0
$153$	389.070	−	677.012i	0.205585	−	0.357733i
$154$		0			0
$155$			2879.85i			1.49235i
$156$		0			0
$157$	−143.752	−	82.9950i	−0.0730740	−	0.0421893i	0.463018	−	0.886349i	$-0.346767\pi$
$157$	−143.752	−	82.9950i	−0.0730740	−	0.0421893i	−0.536092	+	0.844160i	$0.680100\pi$
$158$		0			0
$159$	−1225.52	−	705.920i	−0.611257	−	0.352095i
$160$		0			0
$161$	761.145	+	688.786i	0.372588	+	0.337168i
$162$		0			0
$163$	488.511	+	846.127i	0.234743	+	0.406587i	0.959198	−	0.282735i	$-0.0912417\pi$
$163$	488.511	+	846.127i	0.234743	+	0.406587i	−0.724455	+	0.689322i	$0.757908\pi$
$164$		0			0
$165$	−2.98081	−	2981.49i	−0.00140640	−	1.40672i
$166$		0			0
$167$	1.00709			0.000466651			0.000233326	−	1.00000i	$-0.499926\pi$
$167$	1.00709			0.000466651			0.000233326		1.00000i	$0.499926\pi$
$168$		0			0
$169$	2142.12			0.975019
$170$		0			0
$171$	−821.414	+	476.436i	−0.367340	+	0.213064i
$172$		0			0
$173$	1978.27	+	3426.47i	0.869395	+	1.50584i	0.862616	+	0.505860i	$0.168825\pi$
$173$	1978.27	+	3426.47i	0.869395	+	1.50584i	0.00677983	+	0.999977i	$0.497842\pi$
$174$		0			0
$175$	−2440.57	−	525.130i	−1.05423	−	0.226835i
$176$		0			0
$177$	251.242	−	436.170i	0.106692	−	0.185224i
$178$		0			0
$179$	−2423.54	−	1399.23i	−1.01198	−	0.584266i	−0.100208	−	0.994967i	$-0.531951\pi$
$179$	−2423.54	−	1399.23i	−1.01198	−	0.584266i	−0.911770	+	0.410701i	$0.865284\pi$
$180$		0			0
$181$			1506.74i			0.618758i	0.950939	+	0.309379i	$0.100121\pi$
$181$			1506.74i			0.618758i	−0.950939	+	0.309379i	$0.899879\pi$
$182$		0			0
$183$	1733.90	−	1003.38i	0.700403	−	0.405312i
$184$		0			0
$185$	−1883.21	+	3261.82i	−0.748414	+	1.29629i
$186$		0			0
$187$	891.599	−	514.765i	0.348664	−	0.201301i
$188$		0			0
$189$	−804.168	−	2470.75i	−0.309495	−	0.950901i
$190$		0			0
$191$	3184.51	−	1838.58i	1.20640	−	0.696518i	0.244433	−	0.969666i	$-0.421398\pi$
$191$	3184.51	−	1838.58i	1.20640	−	0.696518i	0.961972	+	0.273148i	$0.0880650\pi$
$192$		0			0
$193$	64.7335	−	112.122i	0.0241431	−	0.0418171i	−0.853701	−	0.520763i	$-0.825648\pi$
$193$	64.7335	−	112.122i	0.0241431	−	0.0418171i	0.877845	+	0.478946i	$0.158981\pi$
$194$		0			0
$195$	−537.026	+	310.769i	−0.197217	+	0.114126i
$196$		0			0
$197$		−	3044.81i		−	1.10119i	−0.834774	−	0.550593i	$-0.814402\pi$
$197$		−	3044.81i		−	1.10119i	0.834774	−	0.550593i	$-0.185598\pi$
$198$		0			0
$199$	−3458.29	−	1996.64i	−1.23192	−	0.711248i	−0.264488	−	0.964389i	$-0.585203\pi$
$199$	−3458.29	−	1996.64i	−1.23192	−	0.711248i	−0.967429	+	0.253141i	$0.918536\pi$
$200$		0			0
$201$	2640.31	−	4583.73i	0.926532	−	1.60851i
$202$		0			0
$203$	−1201.37	+	387.035i	−0.415367	+	0.133815i
$204$		0			0
$205$	−2982.40	−	5165.67i	−1.01610	−	1.75993i
$206$		0			0
$207$	1294.55	−	750.862i	0.434672	−	0.252118i
$208$		0			0
$209$	−1252.01			−0.414370
$210$		0			0
$211$	4383.67			1.43026			0.715129	−	0.698992i	$-0.246368\pi$
$211$	4383.67			1.43026			0.715129	+	0.698992i	$0.246368\pi$
$212$		0			0
$213$	0.651100	+	651.249i	0.000209449	+	0.209497i
$214$		0			0
$215$	1507.59	+	2611.23i	0.478219	+	0.828299i
$216$		0			0
$217$	−696.065	+	3235.00i	−0.217751	+	1.01201i
$218$		0			0
$219$	−1015.63	−	585.022i	−0.313379	−	0.180512i
$220$		0			0
$221$	−185.546	−	107.125i	−0.0564759	−	0.0326064i
$222$		0			0
$223$			4851.53i			1.45687i	0.685114	+	0.728436i	$0.259753\pi$
$223$			4851.53i			1.45687i	−0.685114	+	0.728436i	$0.740247\pi$
$224$		0			0
$225$	−1813.42	+	3155.48i	−0.537308	+	0.934958i
$226$		0			0
$227$	−1184.05	+	2050.83i	−0.346203	+	0.599642i	−0.985572	−	0.169259i	$-0.945863\pi$
$227$	−1184.05	+	2050.83i	−0.346203	+	0.599642i	0.639368	+	0.768901i	$0.279196\pi$
$228$		0			0
$229$	−3737.27	+	2157.72i	−1.07845	+	0.622646i	−0.930479	−	0.366345i	$-0.880609\pi$
$229$	−3737.27	+	2157.72i	−1.07845	+	0.622646i	−0.147975	+	0.988991i	$0.547276\pi$
$230$		0			0
$231$	717.285	−	3349.90i	0.204303	−	0.954144i
$232$		0			0
$233$	4826.98	−	2786.86i	1.35719	−	0.783576i	0.367949	−	0.929846i	$-0.380060\pi$
$233$	4826.98	−	2786.86i	1.35719	−	0.783576i	0.989245	+	0.146270i	$0.0467267\pi$
$234$		0			0
$235$	1408.28	−	2439.22i	0.390920	−	0.677094i
$236$		0			0
$237$	2769.94	+	4786.62i	0.759186	+	1.31192i
$238$		0			0
$239$		−	4683.70i		−	1.26763i	−0.773485	−	0.633814i	$-0.781488\pi$
$239$		−	4683.70i		−	1.26763i	0.773485	−	0.633814i	$-0.218512\pi$
$240$		0			0
$241$	−1896.77	−	1095.10i	−0.506977	−	0.292703i	0.224613	−	0.974448i	$-0.427888\pi$
$241$	−1896.77	−	1095.10i	−0.506977	−	0.292703i	−0.731590	+	0.681745i	$0.761222\pi$
$242$		0			0
$243$	−3787.95	+	18.9356i	−0.999988	+	0.00499884i
$244$		0			0
$245$	−5039.26	−	2273.84i	−1.31407	−	0.592940i
$246$		0			0
$247$	130.275	+	225.642i	0.0335594	+	0.0581266i
$248$		0			0
$249$	3123.09	−	3.12238i	0.794851	−	0.000794670i
$250$		0			0
$251$	2240.70			0.563473			0.281736	−	0.959492i	$-0.409090\pi$
$251$	2240.70			0.563473			0.281736	+	0.959492i	$0.409090\pi$
$252$		0			0
$253$	1973.16			0.490323
$254$		0			0
$255$	−2422.13	+	2.42158i	−0.594823	+	0.000594688i
$256$		0			0
$257$	555.785	+	962.648i	0.134898	+	0.233651i	0.925559	−	0.378604i	$-0.123596\pi$
$257$	555.785	+	962.648i	0.134898	+	0.233651i	−0.790660	+	0.612255i	$0.790263\pi$
$258$		0			0
$259$	−2903.85	+	3208.90i	−0.696665	+	0.769851i
$260$		0			0
$261$	3.67931	+	1840.07i	0.000872580	+	0.436389i
$262$		0			0
$263$	1782.86	+	1029.34i	0.418007	+	0.241337i	0.694224	−	0.719759i	$-0.255748\pi$
$263$	1782.86	+	1029.34i	0.418007	+	0.241337i	−0.276217	+	0.961095i	$0.589081\pi$
$264$		0			0
$265$			4387.04i			1.01696i
$266$		0			0
$267$	3917.42	+	6769.54i	0.897912	+	1.55164i
$268$		0			0
$269$	2414.62	−	4182.24i	0.547294	−	0.947940i	−0.451165	−	0.892441i	$-0.648991\pi$
$269$	2414.62	−	4182.24i	0.547294	−	0.947940i	0.998459	−	0.0554999i	$-0.0176752\pi$
$270$		0			0
$271$	191.772	−	110.720i	0.0429865	−	0.0248183i	−0.478353	−	0.878168i	$-0.658766\pi$
$271$	191.772	−	110.720i	0.0429865	−	0.0248183i	0.521339	+	0.853350i	$0.325433\pi$
$272$		0			0
$273$	−678.368	+	219.293i	−0.150391	+	0.0486162i
$274$		0			0
$275$	−4155.65	+	2399.27i	−0.911255	+	0.526113i
$276$		0			0
$277$	−1233.58	+	2136.62i	−0.267576	+	0.463455i	−0.968235	−	0.250041i	$-0.919556\pi$
$277$	−1233.58	+	2136.62i	−0.267576	+	0.463455i	0.700660	+	0.713496i	$0.252889\pi$
$278$		0			0
$279$	4182.63	+	2403.70i	0.897517	+	0.515792i
$280$		0			0
$281$			4174.76i			0.886282i	0.896452	+	0.443141i	$0.146136\pi$
$281$			4174.76i			0.886282i	−0.896452	+	0.443141i	$0.853864\pi$
$282$		0			0
$283$	5628.39	+	3249.55i	1.18224	+	0.682565i	0.956531	−	0.291630i	$-0.0941977\pi$
$283$	5628.39	+	3249.55i	1.18224	+	0.682565i	0.225706	+	0.974195i	$0.427531\pi$
$284$		0			0
$285$	2552.40	+	1470.23i	0.530494	+	0.305574i
$286$		0			0
$287$	−2101.65	−	6523.57i	−0.432252	−	1.34172i
$288$		0			0
$289$	2038.31	+	3530.46i	0.414881	+	0.718595i
$290$		0			0
$291$	−1.70116	−	1701.55i	−0.000342693	−	0.342771i
$292$		0			0
$293$	−5637.32			−1.12401			−0.562007	−	0.827133i	$-0.689970\pi$
$293$	−5637.32			−1.12401			−0.562007	+	0.827133i	$0.689970\pi$
$294$		0			0
$295$	−1561.38			−0.308159
$296$		0			0
$297$	−4332.74	−	2484.21i	−0.846503	−	0.485349i
$298$		0			0
$299$	−205.312	−	355.611i	−0.0397108	−	0.0687810i
$300$		0			0
$301$	1062.38	+	3297.64i	0.203436	+	0.631472i
$302$		0			0
$303$	−2841.75	+	4933.45i	−0.538794	+	0.935376i
$304$		0			0
$305$	−5381.56	−	3107.05i	−1.01032	−	0.583308i
$306$		0			0
$307$			3442.95i			0.640064i	0.947407	+	0.320032i	$0.103694\pi$
$307$			3442.95i			0.640064i	−0.947407	+	0.320032i	$0.896306\pi$
$308$		0			0
$309$	933.976	−	540.477i	0.171948	−	0.0995037i
$310$		0			0
$311$	−75.7324	+	131.172i	−0.0138083	+	0.0239167i	−0.872847	−	0.487994i	$-0.837729\pi$
$311$	−75.7324	+	131.172i	−0.0138083	+	0.0239167i	0.859039	+	0.511911i	$0.171062\pi$
$312$		0			0
$313$	8335.31	−	4812.40i	1.50524	−	0.869050i	0.505257	−	0.862969i	$-0.331398\pi$
$313$	8335.31	−	4812.40i	1.50524	−	0.869050i	0.999982	−	0.00608123i	$-0.00193573\pi$
$314$		0			0
$315$	−5396.05	+	5986.94i	−0.965184	+	1.07087i
$316$		0			0
$317$	−7866.93	+	4541.98i	−1.39385	+	0.804741i	−0.993739	−	0.111726i	$-0.964362\pi$
$317$	−7866.93	+	4541.98i	−1.39385	+	0.804741i	−0.400112	+	0.916466i	$0.631029\pi$
$318$		0			0
$319$	−1213.05	+	2101.07i	−0.212909	+	0.368768i
$320$		0			0
$321$	−8107.83	+	4691.87i	−1.40977	+	0.815809i
$322$		0			0
$323$			1017.12i			0.175214i
$324$		0			0
$325$	864.811	+	499.299i	0.147603	+	0.0852188i
$326$		0			0
$327$	735.666	−	1277.16i	0.124411	−	0.215985i
$328$		0			0
$329$	2171.52	−	2399.65i	0.363890	−	0.402118i
$330$		0			0
$331$	−702.788	−	1217.26i	−0.116703	−	0.202136i	0.801756	−	0.597651i	$-0.203899\pi$
$331$	−702.788	−	1217.26i	−0.116703	−	0.202136i	−0.918459	+	0.395516i	$0.870566\pi$
$332$		0			0
$333$	3165.55	+	5457.66i	0.520934	+	0.898132i
$334$		0			0
$335$	−16408.6			−2.67611
$336$		0			0
$337$	7983.35			1.29045			0.645223	−	0.763994i	$-0.276764\pi$
$337$	7983.35			1.29045			0.645223	+	0.763994i	$0.276764\pi$
$338$		0			0
$339$	−5.38923	−	5390.46i	−0.000863430	−	0.863627i
$340$		0			0
$341$	3180.25	+	5508.36i	0.505045	+	0.874764i
$342$		0			0
$343$	−5111.13	−	3772.26i	−0.804592	−	0.593828i
$344$		0			0
$345$	−4022.57	−	2317.07i	−0.627732	−	0.361585i
$346$		0			0
$347$	2268.41	+	1309.67i	0.350935	+	0.202612i	0.665097	−	0.746757i	$-0.268390\pi$
$347$	2268.41	+	1309.67i	0.350935	+	0.202612i	−0.314162	+	0.949369i	$0.601724\pi$
$348$		0			0
$349$		−	6032.33i		−	0.925224i	−0.886561	−	0.462612i	$-0.846912\pi$
$349$		−	6032.33i		−	0.925224i	0.886561	−	0.462612i	$-0.153088\pi$
$350$		0			0
$351$	3.11736	+	1039.35i	0.000474052	+	0.158053i
$352$		0			0
$353$	2658.15	−	4604.06i	0.400791	−	0.694190i	−0.593031	−	0.805180i	$-0.702069\pi$
$353$	2658.15	−	4604.06i	0.400791	−	0.694190i	0.993822	+	0.110990i	$0.0354020\pi$
$354$		0			0
$355$	1749.49	−	1010.07i	0.261558	−	0.151011i
$356$		0			0
$357$	−2721.43	−	582.715i	−0.403454	−	0.0863881i
$358$		0			0
$359$	1612.51	−	930.982i	0.237061	−	0.136867i	−0.376764	−	0.926309i	$-0.622963\pi$
$359$	1612.51	−	930.982i	0.237061	−	0.136867i	0.613825	+	0.789442i	$0.289630\pi$
$360$		0			0
$361$	−2811.04	+	4868.87i	−0.409832	+	0.709851i
$362$		0			0
$363$	165.822	+	286.550i	0.0239763	+	0.0414325i
$364$		0			0
$365$			3635.70i			0.521373i
$366$		0			0
$367$	1675.89	+	967.574i	0.238367	+	0.137621i	0.614426	−	0.788975i	$-0.289388\pi$
$367$	1675.89	+	967.574i	0.238367	+	0.137621i	−0.376059	+	0.926596i	$0.622721\pi$
$368$		0			0
$369$	−9991.81	+	19.9791i	−1.40963	+	0.00281862i
$370$		0			0
$371$	−1060.36	+	4928.06i	−0.148385	+	0.689629i
$372$		0			0
$373$	−3871.04	−	6704.83i	−0.537359	−	0.930732i	−0.999045	−	0.0436892i	$-0.986089\pi$
$373$	−3871.04	−	6704.83i	−0.537359	−	0.930732i	0.461687	−	0.887043i	$-0.347244\pi$
$374$		0			0
$375$	820.284	−	0.820097i	0.112958	−	0.000112932i
$376$		0			0
$377$	504.884			0.0689730
$378$		0			0
$379$	3722.15			0.504470			0.252235	−	0.967666i	$-0.418834\pi$
$379$	3722.15			0.504470			0.252235	+	0.967666i	$0.418834\pi$
$380$		0			0
$381$	8551.86	−	8.54991i	1.14994	−	0.00114967i
$382$		0			0
$383$	3546.73	+	6143.12i	0.473184	+	0.819578i	0.999529	−	0.0306926i	$-0.00977131\pi$
$383$	3546.73	+	6143.12i	0.473184	+	0.819578i	−0.526345	+	0.850271i	$0.676438\pi$
$384$		0			0
$385$	−10114.8	+	3258.60i	−1.33895	+	0.431359i
$386$		0			0
$387$	5050.82	−	10.0994i	0.663431	−	0.00132656i
$388$		0			0
$389$	6173.12	+	3564.05i	0.804601	+	0.464537i	0.845077	−	0.534644i	$-0.179554\pi$
$389$	6173.12	+	3564.05i	0.804601	+	0.464537i	−0.0404765	+	0.999180i	$0.512888\pi$
$390$		0			0
$391$		−	1602.98i		−	0.207330i
$392$		0			0
$393$	−1635.38	−	2826.03i	−0.209908	−	0.362733i
$394$		0			0
$395$	8577.33	−	14856.4i	1.09259	−	1.89242i
$396$		0			0
$397$	7738.99	−	4468.11i	0.978360	−	0.564857i	0.0765855	−	0.997063i	$-0.475598\pi$
$397$	7738.99	−	4468.11i	0.978360	−	0.564857i	0.901775	+	0.432206i	$0.142265\pi$
$398$		0			0
$399$	2511.81	+	2268.46i	0.315157	+	0.284624i
$400$		0			0
$401$	7719.60	−	4456.91i	0.961343	−	0.555032i	0.0647568	−	0.997901i	$-0.479373\pi$
$401$	7719.60	−	4456.91i	0.961343	−	0.555032i	0.896586	+	0.442869i	$0.146039\pi$
$402$		0			0
$403$	661.826	−	1146.32i	0.0818062	−	0.141692i
$404$		0			0
$405$	5915.71	+	10152.3i	0.725812	+	1.24561i
$406$		0			0
$407$			8318.63i			1.01312i
$408$		0			0
$409$	−2680.13	−	1547.37i	−0.324019	−	0.187073i	0.329163	−	0.944273i	$-0.393233\pi$
$409$	−2680.13	−	1547.37i	−0.324019	−	0.187073i	−0.653183	+	0.757200i	$0.726567\pi$
$410$		0			0
$411$	2246.44	+	1293.99i	0.269608	+	0.155299i
$412$		0			0
$413$	−1753.93	−	377.389i	−0.208972	−	0.0449639i
$414$		0			0
$415$	−4843.82	−	8389.74i	−0.572949	−	0.992377i
$416$		0			0
$417$	−6.32046	−	6321.90i	−0.000742240	−	0.742409i
$418$		0			0
$419$	7234.25			0.843476			0.421738	−	0.906718i	$-0.361420\pi$
$419$	7234.25			0.843476			0.421738	+	0.906718i	$0.361420\pi$
$420$		0			0
$421$	406.124			0.0470148			0.0235074	−	0.999724i	$-0.492517\pi$
$421$	406.124			0.0470148			0.0235074	+	0.999724i	$0.492517\pi$
$422$		0			0
$423$	−2367.23	−	4081.29i	−0.272101	−	0.469123i
$424$		0			0
$425$	1949.14	+	3376.01i	0.222464	+	0.385319i
$426$		0			0
$427$	−5294.25	−	4790.95i	−0.600016	−	0.542975i
$428$		0			0
$429$	−683.999	+	1187.46i	−0.0769785	+	0.133639i
$430$		0			0
$431$	10590.4	+	6114.37i	1.18358	+	0.683338i	0.956839	−	0.290618i	$-0.0938609\pi$
$431$	10590.4	+	6114.37i	1.18358	+	0.683338i	0.226737	+	0.973956i	$0.427194\pi$
$432$		0			0
$433$		−	3252.79i		−	0.361014i	−0.983574	−	0.180507i	$-0.942226\pi$
$433$		−	3252.79i		−	0.361014i	0.983574	−	0.180507i	$-0.0577738\pi$
$434$		0			0
$435$	4940.24	−	2858.84i	0.544521	−	0.315105i
$436$		0			0
$437$	−974.689	+	1688.21i	−0.106695	+	0.184801i
$438$		0			0
$439$	13036.8	−	7526.81i	1.41734	−	0.818303i	0.421278	−	0.906932i	$-0.361582\pi$
$439$	13036.8	−	7526.81i	1.41734	−	0.818303i	0.996065	+	0.0886287i	$0.0282485\pi$
$440$		0			0
$441$	−7508.57	+	5421.03i	−0.810773	+	0.585361i
$442$		0			0
$443$	204.373	−	117.995i	0.0219189	−	0.0126549i	−0.489001	−	0.872283i	$-0.662638\pi$
$443$	204.373	−	117.995i	0.0219189	−	0.0126549i	0.510919	+	0.859629i	$0.329305\pi$
$444$		0			0
$445$	12130.6	−	21010.8i	1.29224	−	2.23822i
$446$		0			0
$447$	−10439.2	+	6040.99i	−1.10460	+	0.639215i
$448$		0			0
$449$		−	5874.66i		−	0.617466i	−0.951149	−	0.308733i	$-0.900095\pi$
$449$		−	5874.66i		−	0.617466i	0.951149	−	0.308733i	$-0.0999049\pi$
$450$		0			0
$451$	−11409.0	−	6587.02i	−1.19120	−	0.687739i
$452$		0			0
$453$	−2535.09	+	4401.07i	−0.262934	+	0.456468i
$454$		0			0
$455$	1639.74	+	1483.86i	0.168950	+	0.152889i
$456$		0			0
$457$	−153.883	−	266.533i	−0.0157513	−	0.0272821i	0.858042	−	0.513579i	$-0.171681\pi$
$457$	−153.883	−	266.533i	−0.0157513	−	0.0272821i	−0.873794	+	0.486297i	$0.838347\pi$
$458$		0			0
$459$	−2018.15	+	3519.88i	−0.205227	+	0.357939i
$460$		0			0
$461$	4752.26			0.480119			0.240060	−	0.970758i	$-0.422833\pi$
$461$	4752.26			0.480119			0.240060	+	0.970758i	$0.422833\pi$
$462$		0			0
$463$	9529.43			0.956523			0.478261	−	0.878218i	$-0.341267\pi$
$463$	9529.43			0.956523			0.478261	+	0.878218i	$0.341267\pi$
$464$		0			0
$465$	−14.9607	−	14964.1i	−0.00149201	−	1.49235i
$466$		0			0
$467$	−3269.28	−	5662.56i	−0.323949	−	0.561097i	0.657350	−	0.753586i	$-0.271677\pi$
$467$	−3269.28	−	5662.56i	−0.323949	−	0.561097i	−0.981299	+	0.192489i	$0.938344\pi$
$468$		0			0
$469$	−18432.1	−	3965.99i	−1.81475	−	0.390474i
$470$		0			0
$471$	747.386	+	430.508i	0.0731162	+	0.0421162i
$472$		0			0
$473$	5767.23	+	3329.71i	0.560629	+	0.323679i
$474$		0			0
$475$		−	4740.69i		−	0.457932i
$476$		0			0
$477$	6371.64	+	3661.70i	0.611609	+	0.351484i
$478$		0			0
$479$	3671.28	−	6358.85i	0.350199	−	0.606562i	−0.636085	−	0.771619i	$-0.719447\pi$
$479$	3671.28	−	6358.85i	0.350199	−	0.606562i	0.986284	+	0.165057i	$0.0527807\pi$
$480$		0			0
$481$	1499.22	−	865.574i	0.142117	−	0.0820515i
$482$		0			0
$483$	−3958.60	−	3575.08i	−0.372925	−	0.336795i
$484$		0			0
$485$	−4570.96	+	2639.05i	−0.427952	+	0.247078i
$486$		0			0
$487$	3508.78	−	6077.39i	0.326485	−	0.565489i	−0.655327	−	0.755345i	$-0.727469\pi$
$487$	3508.78	−	6077.39i	0.326485	−	0.565489i	0.981812	+	0.189857i	$0.0608024\pi$
$488$		0			0
$489$	−2542.77	−	4394.06i	−0.235150	−	0.406352i
$490$		0			0
$491$			224.222i			0.0206089i	0.999947	+	0.0103045i	$0.00328007\pi$
$491$			224.222i			0.0206089i	−0.999947	+	0.0103045i	$0.996720\pi$
$492$		0			0
$493$	1706.89	+	985.471i	0.155932	+	0.0900272i
$494$		0			0
$495$	30.9775	+	15492.3i	0.00281280	+	1.40672i
$496$		0			0
$497$	2209.38	−	711.777i	0.199405	−	0.0642406i
$498$		0			0
$499$	−10396.1	−	18006.6i	−0.932651	−	1.61540i	−0.778770	−	0.627309i	$-0.784156\pi$
$499$	−10396.1	−	18006.6i	−0.932651	−	1.61540i	−0.153881	−	0.988089i	$-0.549177\pi$
$500$		0			0
$501$	−5.23298	+	0.00523178i	−0.000466651	+	4.66545e-7i
$502$		0			0
$503$	−7341.52			−0.650780			−0.325390	−	0.945580i	$-0.605496\pi$
$503$	−7341.52			−0.650780			−0.325390	+	0.945580i	$0.605496\pi$
$504$		0			0
$505$	17660.5			1.55620
$506$		0			0
$507$	−11130.8	+	11.1282i	−0.975019	+	0.000974796i
$508$		0			0
$509$	−9956.11	−	17244.5i	−0.866988	−	1.50167i	−0.865060	−	0.501669i	$-0.832720\pi$
$509$	−9956.11	−	17244.5i	−0.866988	−	1.50167i	−0.00192778	−	0.999998i	$-0.500614\pi$
$510$		0			0
$511$	−878.757	+	4084.07i	−0.0760742	+	0.353559i
$512$		0			0
$513$	4265.72	−	2479.90i	0.367127	−	0.213431i
$514$		0			0
$515$	−2898.81	−	1673.63i	−0.248032	−	0.143202i
$516$		0			0
$517$		−	6220.75i		−	0.529184i
$518$		0			0
$519$	−10297.2	−	17794.2i	−0.870900	−	1.50497i
$520$		0			0
$521$	−3745.90	+	6488.08i	−0.314992	+	0.545582i	−0.979436	−	0.201756i	$-0.935335\pi$
$521$	−3745.90	+	6488.08i	−0.314992	+	0.545582i	0.664444	+	0.747338i	$0.268668\pi$
$522$		0			0
$523$	−249.515	+	144.058i	−0.0208614	+	0.0120444i	−0.510394	−	0.859940i	$-0.670501\pi$
$523$	−249.515	+	144.058i	−0.0208614	+	0.0120444i	0.489533	+	0.871985i	$0.337167\pi$
$524$		0			0
$525$	12684.3	+	2715.97i	1.05445	+	0.225781i
$526$		0			0
$527$	4474.94	−	2583.61i	0.369889	−	0.213555i
$528$		0			0
$529$	−4547.39	+	7876.32i	−0.373748	+	0.647351i
$530$		0			0
$531$	−1303.23	+	2267.71i	−0.106507	+	0.185330i
$532$		0			0
$533$			2741.58i			0.222797i
$534$		0			0
$535$	25164.5	+	14528.7i	2.03356	+	1.17408i
$536$		0			0
$537$	12600.4	+	7258.03i	1.01256	+	0.583254i
$538$		0			0
$539$	−12149.8	+	1215.69i	−0.970923	+	0.0971496i
$540$		0			0
$541$	−7400.87	−	12818.7i	−0.588149	−	1.01870i	−0.994475	−	0.104975i	$-0.966524\pi$
$541$	−7400.87	−	12818.7i	−0.588149	−	1.01870i	0.406326	−	0.913728i	$-0.366810\pi$
$542$		0			0
$543$	−7.82747	−	7829.25i	−0.000618616	−	0.618758i
$544$		0			0
$545$	−4571.90			−0.359337
$546$		0			0
$547$	4036.80			0.315541			0.157771	−	0.987476i	$-0.449569\pi$
$547$	4036.80			0.315541			0.157771	+	0.987476i	$0.449569\pi$
$548$		0			0
$549$	−9004.40	+	5222.73i	−0.699997	+	0.406012i
$550$		0			0
$551$	−1198.43	−	2075.74i	−0.0926585	−	0.160489i
$552$		0			0
$553$	13225.9	−	14615.4i	1.01704	−	1.12388i
$554$		0			0
$555$	9768.51	−	16958.7i	0.747117	−	1.29704i
$556$		0			0
$557$	14891.1	+	8597.36i	1.13277	+	0.654007i	0.944631	−	0.328135i	$-0.106420\pi$
$557$	14891.1	+	8597.36i	1.13277	+	0.654007i	0.188142	+	0.982142i	$0.439754\pi$
$558$		0			0
$559$		−	1385.86i		−	0.104858i
$560$		0			0
$561$	−4630.21	+	2679.43i	−0.348463	+	0.201650i
$562$		0			0
$563$	−9453.63	+	16374.2i	−0.707678	+	1.22573i	0.258038	+	0.966135i	$0.416924\pi$
$563$	−9453.63	+	16374.2i	−0.707678	+	1.22573i	−0.965716	+	0.259600i	$0.916409\pi$
$564$		0			0
$565$	−14480.7	+	8360.43i	−1.07824	+	0.622524i
$566$		0			0
$567$	4191.41	+	12834.2i	0.310446	+	0.950591i
$568$		0			0
$569$	−6255.57	+	3611.66i	−0.460891	+	0.266096i	−0.712419	−	0.701754i	$-0.752400\pi$
$569$	−6255.57	+	3611.66i	−0.460891	+	0.266096i	0.251528	+	0.967850i	$0.419067\pi$
$570$		0			0
$571$	−4965.17	+	8599.93i	−0.363898	+	0.630290i	−0.988599	−	0.150574i	$-0.951888\pi$
$571$	−4965.17	+	8599.93i	−0.363898	+	0.630290i	0.624700	+	0.780865i	$0.285221\pi$
$572$		0			0
$573$	−16537.7	+	9570.08i	−1.20571	+	0.697724i
$574$		0			0
$575$			7471.31i			0.541870i
$576$		0			0
$577$	7254.16	+	4188.19i	0.523388	+	0.302178i	0.738320	−	0.674451i	$-0.235620\pi$
$577$	7254.16	+	4188.19i	0.523388	+	0.302178i	−0.214932	+	0.976629i	$0.568953\pi$
$578$		0			0
$579$	−335.782	+	582.937i	−0.0241013	+	0.0418412i
$580$		0			0
$581$	−3413.36	−	10595.2i	−0.243735	−	0.756560i
$582$		0			0
$583$	4844.67	+	8391.21i	0.344161	+	0.596104i
$584$		0			0
$585$	2788.85	−	1617.59i	0.197102	−	0.114323i
$586$		0			0
$587$	21277.2			1.49609			0.748043	−	0.663650i	$-0.230994\pi$
$587$	21277.2			1.49609			0.748043	+	0.663650i	$0.230994\pi$
$588$		0			0
$589$	−6283.84			−0.439594
$590$		0			0
$591$	15.8177	+	15821.3i	0.00110093	+	1.10118i
$592$		0			0
$593$	−1424.49	−	2467.29i	−0.0986454	−	0.170859i	0.812479	−	0.582991i	$-0.198118\pi$
$593$	−1424.49	−	2467.29i	−0.0986454	−	0.170859i	−0.911124	+	0.412132i	$0.864784\pi$
$594$		0			0
$595$	2647.25	+	8217.14i	0.182398	+	0.566168i
$596$		0			0
$597$	17980.2	+	10356.9i	1.23263	+	0.710016i
$598$		0			0
$599$	−3844.40	−	2219.57i	−0.262234	−	0.151401i	0.363119	−	0.931743i	$-0.381712\pi$
$599$	−3844.40	−	2219.57i	−0.262234	−	0.151401i	−0.625353	+	0.780342i	$0.715045\pi$
$600$		0			0
$601$			7868.29i			0.534033i	0.963692	+	0.267017i	$0.0860379\pi$
$601$			7868.29i			0.534033i	−0.963692	+	0.267017i	$0.913962\pi$
$602$		0			0
$603$	−13695.6	+	23831.4i	−0.924924	+	1.60944i
$604$		0			0
$605$	513.480	−	889.374i	0.0345057	−	0.0597656i
$606$		0			0
$607$	15144.9	−	8743.92i	1.01271	−	0.584686i	0.100724	−	0.994914i	$-0.467884\pi$
$607$	15144.9	−	8743.92i	1.01271	−	0.584686i	0.911983	+	0.410228i	$0.134551\pi$
$608$		0			0
$609$	6240.48	−	2017.33i	0.415233	−	0.134231i
$610$		0			0
$611$	−1121.13	+	647.284i	−0.0742324	+	0.0428581i
$612$		0			0
$613$	−6422.07	+	11123.3i	−0.423140	+	0.732900i	−0.996245	−	0.0865820i	$-0.972406\pi$
$613$	−6422.07	+	11123.3i	−0.423140	+	0.732900i	0.573105	+	0.819482i	$0.305739\pi$
$614$		0			0
$615$	15523.8	+	26826.1i	1.01786	+	1.75892i
$616$		0			0
$617$			23625.5i			1.54153i	0.637117	+	0.770767i	$0.280127\pi$
$617$			23625.5i			1.54153i	−0.637117	+	0.770767i	$0.719873\pi$
$618$		0			0
$619$	−16529.1	−	9543.05i	−1.07328	−	0.619657i	−0.144202	−	0.989548i	$-0.546062\pi$
$619$	−16529.1	−	9543.05i	−1.07328	−	0.619657i	−0.929075	+	0.369891i	$0.879395\pi$
$620$		0			0
$621$	−6722.75	+	3908.32i	−0.434420	+	0.252553i
$622$		0			0
$623$	18704.9	−	20669.9i	1.20289	−	1.32925i
$624$		0			0
$625$	7152.40	+	12388.3i	0.457754	+	0.792853i
$626$		0			0
$627$	6505.63	−	6.50415i	0.414370	−	0.000414275i
$628$		0			0
$629$	6757.98			0.428391
$630$		0			0
$631$	−32.3893			−0.00204342			−0.00102171	−	0.999999i	$-0.500325\pi$
$631$	−32.3893			−0.00204342			−0.00102171	+	0.999999i	$0.500325\pi$
$632$		0			0
$633$	−22778.2	+	22.7730i	−1.43026	+	0.00142993i
$634$		0			0
$635$	−13263.7	−	22973.4i	−0.828902	−	1.43570i
$636$		0			0
$637$	1483.31	+	2063.19i	0.0922620	+	0.128330i
$638$		0			0
$639$	−6.76643	−	3383.98i	−0.000418898	−	0.209497i
$640$		0			0
$641$	−18742.7	−	10821.1i	−1.15490	−	0.666784i	−0.204827	−	0.978798i	$-0.565663\pi$
$641$	−18742.7	−	10821.1i	−1.15490	−	0.666784i	−0.950078	+	0.312014i	$0.898996\pi$
$642$		0			0
$643$		−	19867.3i		−	1.21849i	−0.792982	−	0.609246i	$-0.791472\pi$
$643$		−	19867.3i		−	1.21849i	0.792982	−	0.609246i	$-0.208528\pi$
$644$		0			0
$645$	−7847.24	−	13560.5i	−0.479046	−	0.827820i
$646$		0			0
$647$	−11212.2	+	19420.1i	−0.681294	+	1.18004i	0.293293	+	0.956023i	$0.405249\pi$
$647$	−11212.2	+	19420.1i	−0.681294	+	1.18004i	−0.974586	+	0.224012i	$0.928084\pi$
$648$		0			0
$649$	−2986.49	+	1724.25i	−0.180632	+	0.104288i
$650$		0			0
$651$	3600.05	−	16813.2i	0.216739	−	1.01223i
$652$		0			0
$653$	17358.5	−	10021.9i	1.04026	−	0.600594i	0.120353	−	0.992731i	$-0.461597\pi$
$653$	17358.5	−	10021.9i	1.04026	−	0.600594i	0.919907	+	0.392137i	$0.128264\pi$
$654$		0			0
$655$	−5064.07	+	8771.22i	−0.302091	+	0.523237i
$656$		0			0
$657$	5280.41	+	3034.59i	0.313559	+	0.180199i
$658$		0			0
$659$		−	13217.9i		−	0.781327i	−0.920533	−	0.390664i	$-0.872246\pi$
$659$		−	13217.9i		−	0.781327i	0.920533	−	0.390664i	$-0.127754\pi$
$660$		0			0
$661$	8470.90	+	4890.68i	0.498457	+	0.287784i	0.728076	−	0.685496i	$-0.240415\pi$
$661$	8470.90	+	4890.68i	0.498457	+	0.287784i	−0.229619	+	0.973281i	$0.573748\pi$
$662$		0			0
$663$	964.682	+	555.674i	0.0565085	+	0.0325499i
$664$		0			0
$665$	2208.41	−	10263.7i	0.128780	−	0.598511i
$666$		0			0
$667$	1888.72	+	3271.36i	0.109642	+	0.189906i
$668$		0			0
$669$	−25.2035	−	25209.3i	−0.00145654	−	1.45687i
$670$		0			0
$671$	−13724.6			−0.789617
$672$		0			0
$673$	−4670.73			−0.267524			−0.133762	−	0.991014i	$-0.542706\pi$
$673$	−4670.73			−0.267524			−0.133762	+	0.991014i	$0.542706\pi$
$674$		0			0
$675$	9406.39	−	16405.8i	0.536373	−	0.935494i
$676$		0			0
$677$	−13521.0	−	23419.1i	−0.767584	−	1.32949i	−0.938870	−	0.344273i	$-0.888125\pi$
$677$	−13521.0	−	23419.1i	−0.767584	−	1.32949i	0.171286	−	0.985221i	$-0.445208\pi$
$678$		0			0
$679$	−5772.53	+	1859.69i	−0.326258	+	0.105108i
$680$		0			0
$681$	6141.85	−	10662.6i	0.345604	−	0.599988i
$682$		0			0
$683$	−11596.9	−	6695.45i	−0.649694	−	0.375101i	0.138645	−	0.990342i	$-0.455725\pi$
$683$	−11596.9	−	6695.45i	−0.649694	−	0.375101i	−0.788339	+	0.615241i	$0.789059\pi$
$684$		0			0
$685$		−	8041.69i		−	0.448551i
$686$		0			0
$687$	19408.2	−	11231.2i	1.07783	−	0.623724i
$688$		0			0
$689$	1008.20	−	1746.25i	0.0557464	−	0.0965557i
$690$		0			0
$691$	−26837.3	+	15494.6i	−1.47748	+	0.853025i	−0.999676	−	0.0254396i	$-0.991901\pi$
$691$	−26837.3	+	15494.6i	−1.47748	+	0.853025i	−0.477807	+	0.878465i	$0.658568\pi$
$692$		0			0
$693$	−3709.72	+	17410.3i	−0.203348	+	0.954348i
$694$		0			0
$695$	−16982.9	+	9805.07i	−0.926903	+	0.535147i
$696$		0			0
$697$	−5351.23	+	9268.60i	−0.290807	+	0.503692i
$698$		0			0
$699$	−25067.3	+	14506.0i	−1.35641	+	0.784933i
$700$		0			0
$701$			2892.67i			0.155855i	0.996959	+	0.0779277i	$0.0248303\pi$
$701$			2892.67i			0.155855i	−0.996959	+	0.0779277i	$0.975170\pi$
$702$		0			0
$703$	−7117.31	−	4109.18i	−0.381841	−	0.220456i
$704$		0			0
$705$	−7304.98	+	12681.9i	−0.390243	+	0.677485i
$706$		0			0
$707$	19838.4	+	4268.57i	1.05530	+	0.227067i
$708$		0			0
$709$	−7965.19	−	13796.1i	−0.421917	−	0.730781i	0.574210	−	0.818708i	$-0.305309\pi$
$709$	−7965.19	−	13796.1i	−0.421917	−	0.730781i	−0.996127	+	0.0879267i	$0.971976\pi$
$710$		0			0
$711$	−14417.9	−	24857.6i	−0.760497	−	1.31116i
$712$		0			0
$713$	9903.30			0.520171
$714$		0			0
$715$	4250.81			0.222337
$716$		0			0
$717$	24.3316	+	24337.2i	0.00126734	+	1.26763i
$718$		0			0
$719$	5938.87	+	10286.4i	0.308042	+	0.533545i	0.977934	−	0.208914i	$-0.0669928\pi$
$719$	5938.87	+	10286.4i	0.308042	+	0.533545i	−0.669892	+	0.742459i	$0.733659\pi$
$720$		0			0
$721$	−2851.78	−	2580.67i	−0.147303	−	0.133300i
$722$		0			0
$723$	9861.57	+	5680.44i	0.507270	+	0.292196i
$724$		0			0
$725$	−7955.61	−	4593.18i	−0.407537	−	0.235291i
$726$		0			0
$727$			16795.8i			0.856839i	0.903580	+	0.428419i	$0.140929\pi$
$727$			16795.8i			0.856839i	−0.903580	+	0.428419i	$0.859071\pi$
$728$		0			0
$729$	19682.6	−	118.070i	0.999982	−	0.00599859i
$730$		0			0
$731$	2705.03	−	4685.24i	0.136866	−	0.237059i
$732$		0			0
$733$	22048.4	−	12729.7i	1.11102	−	0.641447i	0.171926	−	0.985110i	$-0.445001\pi$
$733$	22048.4	−	12729.7i	1.11102	−	0.641447i	0.939093	+	0.343663i	$0.111668\pi$
$734$		0			0
$735$	26196.6	+	11789.0i	1.31466	+	0.591626i
$736$		0			0
$737$	−31385.1	+	18120.2i	−1.56864	+	0.905653i
$738$		0			0
$739$	−9319.48	+	16141.8i	−0.463901	+	0.803499i	−0.999151	−	0.0411940i	$-0.986884\pi$
$739$	−9319.48	+	16141.8i	−0.463901	+	0.803499i	0.535251	+	0.844693i	$0.320217\pi$
$740$		0			0
$741$	−678.099	−	1171.79i	−0.0336175	−	0.0580930i
$742$		0			0
$743$			14043.3i			0.693401i	0.937976	+	0.346700i	$0.112698\pi$
$743$			14043.3i			0.693401i	−0.937976	+	0.346700i	$0.887302\pi$
$744$		0			0
$745$	32400.4	+	18706.4i	1.59337	+	0.919932i
$746$		0			0
$747$	−16228.0	+	32.4487i	−0.794850	+	0.00158934i
$748$		0			0
$749$	24756.3	+	22402.8i	1.20771	+	1.09290i
$750$		0			0
$751$	8115.13	+	14055.8i	0.394308	+	0.682961i	0.993013	−	0.118009i	$-0.0376510\pi$
$751$	8115.13	+	14055.8i	0.394308	+	0.682961i	−0.598705	+	0.800970i	$0.704318\pi$
$752$		0			0
$753$	−11643.0	+	11.6404i	−0.563473	+	0.000563344i
$754$		0			0
$755$	15754.7			0.759433
$756$		0			0
$757$	−33345.7			−1.60102			−0.800508	−	0.599322i	$-0.795437\pi$
$757$	−33345.7			−1.60102			−0.800508	+	0.599322i	$0.795437\pi$
$758$		0			0
$759$	−10252.8	+	10.2505i	−0.490322	+	0.000490211i
$760$		0			0
$761$	5394.02	+	9342.71i	0.256942	+	0.445037i	0.965421	−	0.260695i	$-0.0839517\pi$
$761$	5394.02	+	9342.71i	0.256942	+	0.445037i	−0.708479	+	0.705732i	$0.750618\pi$
$762$		0			0
$763$	−5135.72	−	1105.04i	−0.243677	−	0.0524313i
$764$		0			0
$765$	12585.8	−	25.1658i	0.594822	−	0.00118937i
$766$		0			0
$767$	621.503	+	358.825i	0.0292584	+	0.0168923i
$768$		0			0
$769$			35799.6i			1.67876i	0.543543	+	0.839381i	$0.317082\pi$
$769$			35799.6i			1.67876i	−0.543543	+	0.839381i	$0.682918\pi$
$770$		0			0
$771$	−2892.94	−	4999.17i	−0.135132	−	0.233516i
$772$		0			0
$773$	−18306.3	+	31707.5i	−0.851788	+	1.47534i	0.0278053	+	0.999613i	$0.491148\pi$
$773$	−18306.3	+	31707.5i	−0.851788	+	1.47534i	−0.879593	+	0.475727i	$0.842185\pi$
$774$		0			0
$775$	−20857.2	+	12041.9i	−0.966727	+	0.558140i
$776$		0			0
$777$	15072.2	−	16689.0i	0.695895	−	0.770548i
$778$		0			0
$779$	11271.5	−	6507.62i	0.518414	−	0.299306i
$780$		0			0
$781$	2230.86	−	3863.97i	0.102211	−	0.177034i
$782$		0			0
$783$	−28.6773	−	9561.27i	−0.00130887	−	0.436388i
$784$		0			0
$785$		−	2675.45i		−	0.121644i
$786$		0			0
$787$	34874.9	+	20135.0i	1.57961	+	0.911990i	0.994913	+	0.100742i	$0.0321216\pi$
$787$	34874.9	+	20135.0i	1.57961	+	0.911990i	0.584701	+	0.811249i	$0.301212\pi$
$788$		0			0
$789$	−9269.36	−	5339.32i	−0.418248	−	0.240919i
$790$		0			0
$791$	−18287.2	+	5891.45i	−0.822022	+	0.264824i
$792$		0			0
$793$	1428.08	+	2473.51i	0.0639503	+	0.110765i
$794$		0			0
$795$	−22.7905	−	22795.7i	−0.00101672	−	1.01696i
$796$		0			0
$797$	−11444.6			−0.508645			−0.254323	−	0.967119i	$-0.581852\pi$
$797$	−11444.6			−0.508645			−0.254323	+	0.967119i	$0.581852\pi$
$798$		0			0
$799$	−5053.68			−0.223762
$800$		0			0
$801$	−20390.7	−	35155.2i	−0.899462	−	1.55075i
$802$		0			0
$803$	4014.95	+	6954.10i	0.176444	+	0.305610i
$804$		0			0
$805$	−3480.45	+	16175.6i	−0.152385	+	0.708216i
$806$		0			0
$807$	−12525.0	+	21744.1i	−0.546346	+	0.948487i
$808$		0			0
$809$	−2702.86	−	1560.50i	−0.117463	−	0.0678172i	0.440117	−	0.897940i	$-0.354937\pi$
$809$	−2702.86	−	1560.50i	−0.117463	−	0.0678172i	−0.557580	+	0.830123i	$0.688270\pi$
$810$		0			0
$811$		−	3571.23i		−	0.154628i	−0.997007	−	0.0773138i	$-0.975366\pi$
$811$		−	3571.23i		−	0.154628i	0.997007	−	0.0773138i	$-0.0246343\pi$
$812$		0			0
$813$	−995.903	+	576.313i	−0.0429617	+	0.0248612i
$814$		0			0
$815$	−7873.89	+	13638.0i	−0.338418	+	0.586157i
$816$		0			0
$817$	−5697.71	+	3289.58i	−0.243987	+	0.140866i
$818$		0			0
$819$	3523.76	−	1143.00i	0.150342	−	0.0487666i
$820$		0			0
$821$	24420.3	−	14099.1i	1.03809	−	0.599344i	0.118801	−	0.992918i	$-0.462095\pi$
$821$	24420.3	−	14099.1i	1.03809	−	0.599344i	0.919293	+	0.393574i	$0.128762\pi$
$822$		0			0
$823$	−5700.86	+	9874.18i	−0.241457	+	0.418217i	−0.961130	−	0.276097i	$-0.910959\pi$
$823$	−5700.86	+	9874.18i	−0.241457	+	0.418217i	0.719672	+	0.694314i	$0.244292\pi$
$824$		0			0
$825$	21580.9	−	12488.5i	0.910729	−	0.527024i
$826$		0			0
$827$			18948.2i			0.796726i	0.917228	+	0.398363i	$0.130422\pi$
$827$			18948.2i			0.796726i	−0.917228	+	0.398363i	$0.869578\pi$
$828$		0			0
$829$	663.246	+	382.925i	0.0277871	+	0.0160429i	0.513829	−	0.857893i	$-0.328227\pi$
$829$	663.246	+	382.925i	0.0277871	+	0.0160429i	−0.486042	+	0.873935i	$0.661560\pi$
$830$		0			0
$831$	6398.75	−	11108.6i	0.267112	−	0.463722i
$832$		0			0
$833$	987.617	+	9870.36i	0.0410791	+	0.410549i
$834$		0			0
$835$	8.11618	+	14.0576i	0.000336374	+	0.000582617i
$836$		0			0
$837$	−21746.0	−	12468.3i	−0.898032	−	0.514894i
$838$		0			0
$839$	5355.68			0.220380			0.110190	−	0.993911i	$-0.464854\pi$
$839$	5355.68			0.220380			0.110190	+	0.993911i	$0.464854\pi$
$840$		0			0
$841$	19744.4			0.809564
$842$		0			0
$843$	−21.6877	−	21692.7i	−0.000886080	−	0.886282i
$844$		0			0
$845$	17263.5	+	29901.2i	0.702818	+	1.21732i
$846$		0			0
$847$	791.768	−	874.946i	0.0321198	−	0.0354941i
$848$		0			0
$849$	−29262.9	−	16855.9i	−1.18292	−	0.681383i
$850$		0			0
$851$	11216.8	+	6476.05i	0.451832	+	0.260865i
$852$		0			0
$853$		−	8591.74i		−	0.344872i	−0.985021	−	0.172436i	$-0.944836\pi$
$853$		−	8591.74i		−	0.344872i	0.985021	−	0.172436i	$-0.0551638\pi$
$854$		0			0
$855$	−13270.3	−	7626.26i	−0.530800	−	0.305044i
$856$		0			0
$857$	20273.3	−	35114.5i	0.808080	−	1.39964i	−0.106112	−	0.994354i	$-0.533840\pi$
$857$	20273.3	−	35114.5i	0.808080	−	1.39964i	0.914192	−	0.405281i	$-0.132826\pi$
$858$		0			0
$859$	8352.92	−	4822.56i	0.331779	−	0.191553i	−0.324852	−	0.945765i	$-0.605314\pi$
$859$	8352.92	−	4822.56i	0.331779	−	0.191553i	0.656631	+	0.754212i	$0.271981\pi$
$860$		0			0
$861$	10954.4	+	33886.6i	0.433593	+	1.34129i
$862$		0			0
$863$	9951.19	−	5745.32i	0.392517	−	0.226620i	−0.290733	−	0.956804i	$-0.593899\pi$
$863$	9951.19	−	5745.32i	0.392517	−	0.226620i	0.683250	+	0.730184i	$0.260566\pi$
$864$		0			0
$865$	−31886.1	+	55228.3i	−1.25336	+	2.17089i
$866$		0			0
$867$	−10609.7	−	18334.2i	−0.415599	−	0.718180i
$868$		0			0
$869$		−	37888.3i		−	1.47902i
$870$		0			0
$871$	6531.39	+	3770.90i	0.254085	+	0.146696i
$872$		0			0
$873$	17.6790	+	8841.48i	0.000685386	+	0.342771i
$874$		0			0
$875$	−896.522	−	2782.83i	−0.0346377	−	0.107516i
$876$		0			0
$877$	14714.7	+	25486.6i	0.566568	+	0.981324i	0.996902	+	0.0786543i	$0.0250623\pi$
$877$	14714.7	+	25486.6i	0.566568	+	0.981324i	−0.430334	+	0.902670i	$0.641604\pi$
$878$		0			0
$879$	29292.4	−	29.2857i	1.12401	−	0.00112376i
$880$		0			0
$881$	−22330.5			−0.853956			−0.426978	−	0.904262i	$-0.640422\pi$
$881$	−22330.5			−0.853956			−0.426978	+	0.904262i	$0.640422\pi$
$882$		0			0
$883$	−15519.2			−0.591463			−0.295732	−	0.955271i	$-0.595563\pi$
$883$	−15519.2			−0.591463			−0.295732	+	0.955271i	$0.595563\pi$
$884$		0			0
$885$	8113.15	−	8.11130i	0.308159	−	0.000308089i
$886$		0			0
$887$	−19107.9	−	33095.9i	−0.723316	−	1.25282i	−0.959663	−	0.281152i	$-0.909284\pi$
$887$	−19107.9	−	33095.9i	−0.723316	−	1.25282i	0.236347	−	0.971669i	$-0.424050\pi$
$888$		0			0
$889$	−9346.69	−	29012.4i	−0.352618	−	1.09454i
$890$		0			0
$891$	22526.5	+	12885.8i	0.846987	+	0.484503i
$892$		0			0
$893$	5322.39	+	3072.88i	0.199448	+	0.115151i
$894$		0			0
$895$		−	45106.0i		−	1.68461i
$896$		0			0
$897$	1068.68	+	1846.74i	0.0397795	+	0.0687413i
$898$		0			0
$899$	−6088.31	+	10545.3i	−0.225869	+	0.391217i
$900$		0			0
$901$	6816.94	−	3935.76i	0.252059	−	0.145526i
$902$		0			0
$903$	−5537.39	−	17129.5i	−0.204067	−	0.631268i
$904$		0			0
$905$	−21032.2	+	12142.9i	−0.772522	+	0.446016i
$906$		0			0
$907$	−4432.30	+	7676.97i	−0.162262	+	0.281047i	−0.935680	−	0.352850i	$-0.885212\pi$
$907$	−4432.30	+	7676.97i	−0.162262	+	0.281047i	0.773417	+	0.633897i	$0.218546\pi$
$908$		0			0
$909$	14740.5	−	25649.7i	0.537858	−	0.935915i
$910$		0			0
$911$		−	15145.0i		−	0.550798i	−0.961330	−	0.275399i	$-0.911190\pi$
$911$		−	15145.0i		−	0.550798i	0.961330	−	0.275399i	$-0.0888100\pi$
$912$		0			0
$913$	−18529.8	−	10698.2i	−0.671684	−	0.387797i
$914$		0			0
$915$	27979.5	+	16116.7i	1.01090	+	0.582297i
$916$		0			0
$917$	−7808.61	+	8628.93i	−0.281203	+	0.310744i
$918$		0			0
$919$	−2244.07	−	3886.84i	−0.0805495	−	0.139516i	0.822937	−	0.568133i	$-0.192334\pi$
$919$	−2244.07	−	3886.84i	−0.0805495	−	0.139516i	−0.903486	+	0.428617i	$0.859001\pi$
$920$		0			0
$921$	−17.8860	−	17890.1i	−0.000639917	−	0.640063i
$922$		0			0
$923$	−928.506			−0.0331118
$924$		0			0
$925$	−31498.2			−1.11963
$926$		0			0
$927$	−4850.27	+	2813.25i	−0.171849	+	0.0996756i
$928$		0			0
$929$	−8911.93	−	15435.9i	−0.314737	−	0.545141i	0.664644	−	0.747160i	$-0.268583\pi$
$929$	−8911.93	−	15435.9i	−0.314737	−	0.545141i	−0.979382	+	0.202019i	$0.935250\pi$
$930$		0			0
$931$	4961.53	−	10995.7i	0.174659	−	0.387078i
$932$		0			0
$933$	392.835	−	681.984i	0.0137844	−	0.0239305i
$934$		0			0
$935$	14370.9	+	8297.05i	0.502652	+	0.290206i
$936$		0			0
$937$		−	51270.5i		−	1.78755i	−0.448516	−	0.893775i	$-0.648047\pi$
$937$		−	51270.5i		−	1.78755i	0.448516	−	0.893775i	$-0.351953\pi$
$938$		0			0
$939$	−43286.5	+	25049.2i	−1.50437	+	0.870554i
$940$		0			0
$941$	−5422.48	+	9392.01i	−0.187851	+	0.325367i	−0.944533	−	0.328415i	$-0.893486\pi$
$941$	−5422.48	+	9392.01i	−0.187851	+	0.325367i	0.756683	+	0.653782i	$0.226819\pi$
$942$		0			0
$943$	−17763.9	+	10256.0i	−0.613437	+	0.354168i
$944$		0			0
$945$	28007.6	−	31137.0i	0.964113	−	1.07184i
$946$		0			0
$947$	−36916.8	+	21313.9i	−1.26677	+	0.731372i	−0.974376	−	0.224926i	$-0.927786\pi$
$947$	−36916.8	+	21313.9i	−1.26677	+	0.731372i	−0.292397	+	0.956297i	$0.594453\pi$
$948$		0			0
$949$	835.531	−	1447.18i	0.0285801	−	0.0495021i
$950$		0			0
$951$	40854.2	−	23641.7i	1.39305	−	0.806134i
$952$		0			0
$953$		−	33229.0i		−	1.12948i	−0.825269	−	0.564739i	$-0.808977\pi$
$953$		−	33229.0i		−	1.12948i	0.825269	−	0.564739i	$-0.191023\pi$
$954$		0			0
$955$	51328.4	+	29634.5i	1.73921	+	1.00413i
$956$		0			0
$957$	6292.28	−	10923.8i	0.212540	−	0.368981i
$958$		0			0
$959$	1943.69	−	9033.42i	0.0654486	−	0.304175i
$960$		0			0
$961$	1066.19	+	1846.70i	0.0357891	+	0.0619885i
$962$		0			0
$963$	42105.1	−	24421.8i	1.40895	−	0.817218i
$964$		0			0
$965$	2086.77			0.0696118
$966$		0			0
$967$	16853.4			0.560464			0.280232	−	0.959932i	$-0.409589\pi$
$967$	16853.4			0.560464			0.280232	+	0.959932i	$0.409589\pi$
$968$		0			0
$969$	−5.28390	−	5285.11i	−0.000175174	−	0.175214i
$970$		0			0
$971$	−634.824	−	1099.55i	−0.0209809	−	0.0363400i	0.855344	−	0.518060i	$-0.173346\pi$
$971$	−634.824	−	1099.55i	−0.0209809	−	0.0363400i	−0.876325	+	0.481720i	$0.840012\pi$
$972$		0			0
$973$	−21447.2	+	6909.46i	−0.706644	+	0.227654i
$974$		0			0
$975$	−4496.28	−	2589.94i	−0.147688	−	0.0850712i
$976$		0			0
$977$	49580.5	+	28625.3i	1.62356	+	0.937364i	0.985957	+	0.167001i	$0.0534082\pi$
$977$	49580.5	+	28625.3i	1.62356	+	0.937364i	0.637605	+	0.770363i	$0.279925\pi$
$978$		0			0
$979$		−	53583.9i		−	1.74929i
$980$		0			0
$981$	−3816.00	+	6640.13i	−0.124195	+	0.216109i
$982$		0			0
$983$	30733.8	−	53232.4i	0.997207	−	1.72721i	0.433924	−	0.900950i	$-0.357129\pi$
$983$	30733.8	−	53232.4i	0.997207	−	1.72721i	0.563283	−	0.826264i	$-0.309538\pi$
$984$		0			0
$985$	42501.6	−	24538.3i	1.37484	−	0.793762i
$986$		0			0
$987$	−11271.1	+	12480.2i	−0.363488	+	0.402482i
$988$		0			0
$989$	8979.57	−	5184.36i	0.288710	−	0.166687i
$990$		0			0
$991$	−25996.6	+	45027.4i	−0.833308	+	1.44333i	0.0620930	+	0.998070i	$0.480222\pi$
$991$	−25996.6	+	45027.4i	−0.833308	+	1.44333i	−0.895401	+	0.445261i	$0.853111\pi$
$992$		0			0
$993$	3658.12	+	6321.44i	0.116905	+	0.202019i
$994$		0			0
$995$		−	64364.3i		−	2.05074i
$996$		0			0
$997$	29417.3	+	16984.1i	0.934460	+	0.539510i	0.888219	−	0.459420i	$-0.151943\pi$
$997$	29417.3	+	16984.1i	0.934460	+	0.539510i	0.0462403	+	0.998930i	$0.485276\pi$
$998$		0			0
$999$	−16477.0	−	28342.4i	−0.521832	−	0.897611i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bc.d.17.1		12
3.2	odd	2	inner	336.4.bc.d.17.2		12
4.3	odd	2		21.4.g.a.17.2	yes	12
7.5	odd	6	inner	336.4.bc.d.257.2		12
12.11	even	2		21.4.g.a.17.5	yes	12
21.5	even	6	inner	336.4.bc.d.257.1		12
28.3	even	6		147.4.c.a.146.4		12
28.11	odd	6		147.4.c.a.146.3		12
28.19	even	6		21.4.g.a.5.5	yes	12
28.23	odd	6		147.4.g.d.68.5		12
28.27	even	2		147.4.g.d.80.2		12
84.11	even	6		147.4.c.a.146.10		12
84.23	even	6		147.4.g.d.68.2		12
84.47	odd	6		21.4.g.a.5.2	✓	12
84.59	odd	6		147.4.c.a.146.9		12
84.83	odd	2		147.4.g.d.80.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.g.a.5.2	✓	12	84.47	odd	6
21.4.g.a.5.5	yes	12	28.19	even	6
21.4.g.a.17.2	yes	12	4.3	odd	2
21.4.g.a.17.5	yes	12	12.11	even	2
147.4.c.a.146.3		12	28.11	odd	6
147.4.c.a.146.4		12	28.3	even	6
147.4.c.a.146.9		12	84.59	odd	6
147.4.c.a.146.10		12	84.11	even	6
147.4.g.d.68.2		12	84.23	even	6
147.4.g.d.68.5		12	28.23	odd	6
147.4.g.d.80.2		12	28.27	even	2
147.4.g.d.80.5		12	84.83	odd	2
336.4.bc.d.17.1		12	1.1	even	1	trivial
336.4.bc.d.17.2		12	3.2	odd	2	inner
336.4.bc.d.257.1		12	21.5	even	6	inner
336.4.bc.d.257.2		12	7.5	odd	6	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.bc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-5.19615 + 0.00519496i) q^{3} +(8.05907 + 13.9587i) q^{5} +(5.67909 + 17.6280i) q^{7} +(26.9999 - 0.0539876i) q^{9} +O(q^{10})\)	\(q+(-5.19615 + 0.00519496i) q^{3} +(8.05907 + 13.9587i) q^{5} +(5.67909 + 17.6280i) q^{7} +(26.9999 - 0.0539876i) q^{9} +(30.8296 + 17.7995i) q^{11} -7.40831i q^{13} +(-41.9486 - 72.4897i) q^{15} +(14.4601 - 25.0457i) q^{17} +(-30.4580 + 17.5849i) q^{19} +(-29.6010 - 91.5685i) q^{21} +(48.0017 - 27.7138i) q^{23} +(-67.3971 + 116.735i) q^{25} +(-140.295 + 0.420792i) q^{27} +68.1510i q^{29} +(154.734 + 89.3356i) q^{31} +(-160.288 - 92.3286i) q^{33} +(-200.297 + 221.338i) q^{35} +(116.838 + 202.370i) q^{37} +(0.0384859 + 38.4947i) q^{39} -370.068 q^{41} +187.068 q^{43} +(218.348 + 376.449i) q^{45} +(-87.3726 - 151.334i) q^{47} +(-278.496 + 200.222i) q^{49} +(-75.0068 + 130.216i) q^{51} +(235.715 + 136.090i) q^{53} +573.789i q^{55} +(158.173 - 91.5321i) q^{57} +(-48.4354 + 83.8926i) q^{59} +(-333.882 + 192.767i) q^{61} +(154.287 + 475.650i) q^{63} +(103.411 - 59.7041i) q^{65} +(-509.009 + 881.630i) q^{67} +(-249.280 + 144.254i) q^{69} -125.333i q^{71} +(195.346 + 112.783i) q^{73} +(349.599 - 606.924i) q^{75} +(-138.686 + 644.550i) q^{77} +(-532.154 - 921.718i) q^{79} +(728.994 - 2.91533i) q^{81} -601.040 q^{83} +466.140 q^{85} +(-0.354042 - 354.123i) q^{87} +(-752.606 - 1303.55i) q^{89} +(130.594 - 42.0725i) q^{91} +(-804.484 - 463.397i) q^{93} +(-490.926 - 283.436i) q^{95} +327.463i q^{97} +(833.358 + 478.920i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 + 56 * q^7 - 3 * q^9	\( 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9} - 6 q^{15} - 300 q^{19} + 357 q^{21} - 42 q^{25} + 930 q^{31} - 855 q^{33} + 764 q^{37} + 426 q^{39} + 1012 q^{43} + 2367 q^{45} - 336 q^{49} + 1341 q^{51} + 270 q^{57} + 2358 q^{61} - 1071 q^{63} - 792 q^{67} - 2904 q^{73} + 2418 q^{75} - 1674 q^{79} + 837 q^{81} + 348 q^{85} - 1638 q^{87} + 1218 q^{91} - 1479 q^{93} + 3354 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 + 56 * q^7 - 3 * q^9 - 6 * q^15 - 300 * q^19 + 357 * q^21 - 42 * q^25 + 930 * q^31 - 855 * q^33 + 764 * q^37 + 426 * q^39 + 1012 * q^43 + 2367 * q^45 - 336 * q^49 + 1341 * q^51 + 270 * q^57 + 2358 * q^61 - 1071 * q^63 - 792 * q^67 - 2904 * q^73 + 2418 * q^75 - 1674 * q^79 + 837 * q^81 + 348 * q^85 - 1638 * q^87 + 1218 * q^91 - 1479 * q^93 + 3354 * q^99

Introduction

L-functions

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