LMFDB - Embedded newform 448.4.i.k.193.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,4,Mod(65,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("448.65");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	448.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$26.4328556826$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.11163123.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 14x^{4} + 49x^{2} + 27 $ x^6 + 14x^4 + 49x^2 + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.3
Root			$-0.821510i$ of defining polynomial
Character	$\chi$	$=$	448.193
Dual form			448.4.i.k.65.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.82512 - 6.62530i) q^{3} +(7.30445 + 12.6517i) q^{5} +(10.7631 - 15.0717i) q^{7} +(-15.7631 - 27.3025i) q^{9} +O(q^{10})$	\(q+(3.82512 - 6.62530i) q^{3} +(7.30445 + 12.6517i) q^{5} +(10.7631 - 15.0717i) q^{7} +(-15.7631 - 27.3025i) q^{9} +(8.67092 - 15.0185i) q^{11} -81.5103 q^{13} +111.762 q^{15} +(39.1645 - 67.8350i) q^{17} +(5.55479 + 9.62118i) q^{19} +(-58.6844 - 128.960i) q^{21} +(-66.8537 - 115.794i) q^{23} +(-44.2099 + 76.5737i) q^{25} -34.6265 q^{27} +93.8411 q^{29} +(157.715 - 273.171i) q^{31} +(-66.3346 - 114.895i) q^{33} +(269.300 + 26.0808i) q^{35} +(89.6830 + 155.335i) q^{37} +(-311.787 + 540.031i) q^{39} +265.555 q^{41} +6.73466 q^{43} +(230.281 - 398.859i) q^{45} +(86.0427 + 149.030i) q^{47} +(-111.312 - 324.436i) q^{49} +(-299.618 - 518.954i) q^{51} +(187.998 - 325.621i) q^{53} +253.345 q^{55} +84.9910 q^{57} +(-56.9033 + 98.5594i) q^{59} +(-179.764 - 311.360i) q^{61} +(-581.154 - 56.2828i) q^{63} +(-595.388 - 1031.24i) q^{65} +(-214.299 + 371.176i) q^{67} -1022.89 q^{69} -729.780 q^{71} +(-578.969 + 1002.80i) q^{73} +(338.216 + 585.807i) q^{75} +(-133.028 - 292.331i) q^{77} +(223.827 + 387.680i) q^{79} +(293.153 - 507.756i) q^{81} -10.3976 q^{83} +1144.30 q^{85} +(358.954 - 621.726i) q^{87} +(-383.026 - 663.420i) q^{89} +(-877.304 + 1228.50i) q^{91} +(-1206.56 - 2089.82i) q^{93} +(-81.1494 + 140.555i) q^{95} +532.824 q^{97} -546.722 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} + 13 q^{5} + 20 q^{7} - 50 q^{9}+O(q^{10}) $ 6 * q - q^3 + 13 * q^5 + 20 * q^7 - 50 * q^9	$ 6 q - q^{3} + 13 q^{5} + 20 q^{7} - 50 q^{9} + 11 q^{11} - 140 q^{13} + 82 q^{15} - 97 q^{17} + 81 q^{19} - 345 q^{21} + 191 q^{23} - 12 q^{25} + 230 q^{27} + 324 q^{29} + 597 q^{31} - 343 q^{33} + 815 q^{35} + 217 q^{37} - 806 q^{39} + 1396 q^{41} - 616 q^{43} + 1118 q^{45} + 139 q^{47} + 1030 q^{49} - 1475 q^{51} + 197 q^{53} - 294 q^{55} - 2294 q^{57} - 353 q^{59} + 449 q^{61} - 2094 q^{63} - 906 q^{65} + 519 q^{67} - 5114 q^{69} - 448 q^{71} - 1701 q^{73} + 1132 q^{75} - 1253 q^{77} + 1143 q^{79} - 251 q^{81} - 2760 q^{83} + 2050 q^{85} + 1458 q^{87} - 1749 q^{89} - 616 q^{91} - 601 q^{93} - 2167 q^{95} + 5204 q^{97} + 2188 q^{99}+O(q^{100}) $ 6 * q - q^3 + 13 * q^5 + 20 * q^7 - 50 * q^9 + 11 * q^11 - 140 * q^13 + 82 * q^15 - 97 * q^17 + 81 * q^19 - 345 * q^21 + 191 * q^23 - 12 * q^25 + 230 * q^27 + 324 * q^29 + 597 * q^31 - 343 * q^33 + 815 * q^35 + 217 * q^37 - 806 * q^39 + 1396 * q^41 - 616 * q^43 + 1118 * q^45 + 139 * q^47 + 1030 * q^49 - 1475 * q^51 + 197 * q^53 - 294 * q^55 - 2294 * q^57 - 353 * q^59 + 449 * q^61 - 2094 * q^63 - 906 * q^65 + 519 * q^67 - 5114 * q^69 - 448 * q^71 - 1701 * q^73 + 1132 * q^75 - 1253 * q^77 + 1143 * q^79 - 251 * q^81 - 2760 * q^83 + 2050 * q^85 + 1458 * q^87 - 1749 * q^89 - 616 * q^91 - 601 * q^93 - 2167 * q^95 + 5204 * q^97 + 2188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	3.82512	−	6.62530i	0.736145	−	1.27504i	−0.218074	−	0.975932i	$-0.569978\pi$
$3$	3.82512	−	6.62530i	0.736145	−	1.27504i	0.954219	−	0.299108i	$-0.0966891\pi$
$4$		0			0
$5$	7.30445	+	12.6517i	0.653329	+	1.13160i	0.982310	+	0.187263i	$0.0599617\pi$
$5$	7.30445	+	12.6517i	0.653329	+	1.13160i	−0.328980	+	0.944337i	$0.606705\pi$
$6$		0			0
$7$	10.7631	−	15.0717i	0.581153	−	0.813795i
$7$	10.7631	−	15.0717i	0.581153	−	0.813795i
$8$		0			0
$9$	−15.7631	−	27.3025i	−0.583818	−	1.01120i
$10$		0			0
$11$	8.67092	−	15.0185i	0.237671	−	0.411658i	−0.722375	−	0.691502i	$-0.756949\pi$
$11$	8.67092	−	15.0185i	0.237671	−	0.411658i	0.960046	+	0.279844i	$0.0902827\pi$
$12$		0			0
$13$	−81.5103			−1.73899			−0.869496	−	0.493940i	$-0.835556\pi$
$13$	−81.5103			−1.73899			−0.869496	+	0.493940i	$0.835556\pi$
$14$		0			0
$15$	111.762			1.92378
$16$		0			0
$17$	39.1645	−	67.8350i	0.558753	−	0.967788i	−0.438848	−	0.898561i	$-0.644613\pi$
$17$	39.1645	−	67.8350i	0.558753	−	0.967788i	0.997601	−	0.0692270i	$-0.0220533\pi$
$18$		0			0
$19$	5.55479	+	9.62118i	0.0670714	+	0.116171i	0.897611	−	0.440789i	$-0.145301\pi$
$19$	5.55479	+	9.62118i	0.0670714	+	0.116171i	−0.830540	+	0.556960i	$0.811968\pi$
$20$		0			0
$21$	−58.6844	−	128.960i	−0.609808	−	1.34006i
$22$		0			0
$23$	−66.8537	−	115.794i	−0.606085	−	1.04977i	−0.991879	−	0.127186i	$-0.959406\pi$
$23$	−66.8537	−	115.794i	−0.606085	−	1.04977i	0.385793	−	0.922585i	$-0.373928\pi$
$24$		0			0
$25$	−44.2099	+	76.5737i	−0.353679	+	0.612590i
$26$		0			0
$27$	−34.6265			−0.246810
$28$		0			0
$29$	93.8411			0.600892			0.300446	−	0.953799i	$-0.402865\pi$
$29$	93.8411			0.600892			0.300446	+	0.953799i	$0.402865\pi$
$30$		0			0
$31$	157.715	−	273.171i	0.913759	−	1.58268i	0.105050	−	0.994467i	$-0.466500\pi$
$31$	157.715	−	273.171i	0.913759	−	1.58268i	0.808709	−	0.588209i	$-0.200167\pi$
$32$		0			0
$33$	−66.3346	−	114.895i	−0.349920	−	0.606080i
$34$		0			0
$35$	269.300	+	26.0808i	1.30057	+	0.125956i
$36$		0			0
$37$	89.6830	+	155.335i	0.398481	+	0.690189i	0.993539	−	0.113494i	$-0.0362042\pi$
$37$	89.6830	+	155.335i	0.398481	+	0.690189i	−0.595058	+	0.803683i	$0.702871\pi$
$38$		0			0
$39$	−311.787	+	540.031i	−1.28015	+	2.21729i
$40$		0			0
$41$	265.555			1.01153			0.505765	−	0.862671i	$-0.331210\pi$
$41$	265.555			1.01153			0.505765	+	0.862671i	$0.331210\pi$
$42$		0			0
$43$	6.73466			0.0238843			0.0119422	−	0.999929i	$-0.496199\pi$
$43$	6.73466			0.0238843			0.0119422	+	0.999929i	$0.496199\pi$
$44$		0			0
$45$	230.281	−	398.859i	0.762852	−	1.32130i
$46$		0			0
$47$	86.0427	+	149.030i	0.267035	+	0.462517i	0.968095	−	0.250585i	$-0.0806229\pi$
$47$	86.0427	+	149.030i	0.267035	+	0.462517i	−0.701060	+	0.713102i	$0.747290\pi$
$48$		0			0
$49$	−111.312	−	324.436i	−0.324523	−	0.945878i
$50$		0			0
$51$	−299.618	−	518.954i	−0.822646	−	1.42486i
$52$		0			0
$53$	187.998	−	325.621i	0.487235	−	0.843916i	−0.512657	−	0.858593i	$-0.671339\pi$
$53$	187.998	−	325.621i	0.487235	−	0.843916i	0.999892	+	0.0146775i	$0.00467218\pi$
$54$		0			0
$55$	253.345			0.621110
$56$		0			0
$57$	84.9910			0.197497
$58$		0			0
$59$	−56.9033	+	98.5594i	−0.125562	+	0.217480i	−0.921953	−	0.387303i	$-0.873407\pi$
$59$	−56.9033	+	98.5594i	−0.125562	+	0.217480i	0.796390	+	0.604783i	$0.206740\pi$
$60$		0			0
$61$	−179.764	−	311.360i	−0.377318	−	0.653533i	0.613353	−	0.789809i	$-0.289820\pi$
$61$	−179.764	−	311.360i	−0.377318	−	0.653533i	−0.990671	+	0.136275i	$0.956487\pi$
$62$		0			0
$63$	−581.154	−	56.2828i	−1.16220	−	0.112555i
$64$		0			0
$65$	−595.388	−	1031.24i	−1.13613	−	1.96784i
$66$		0			0
$67$	−214.299	+	371.176i	−0.390757	+	0.676812i	−0.992550	−	0.121841i	$-0.961120\pi$
$67$	−214.299	+	371.176i	−0.390757	+	0.676812i	0.601792	+	0.798653i	$0.294454\pi$
$68$		0			0
$69$	−1022.89			−1.78467
$70$		0			0
$71$	−729.780			−1.21984			−0.609922	−	0.792461i	$-0.708799\pi$
$71$	−729.780			−1.21984			−0.609922	+	0.792461i	$0.708799\pi$
$72$		0			0
$73$	−578.969	+	1002.80i	−0.928263	+	1.60780i	−0.142035	+	0.989862i	$0.545365\pi$
$73$	−578.969	+	1002.80i	−0.928263	+	1.60780i	−0.786228	+	0.617937i	$0.787969\pi$
$74$		0			0
$75$	338.216	+	585.807i	0.520718	+	0.901910i
$76$		0			0
$77$	−133.028	−	292.331i	−0.196882	−	0.432651i
$78$		0			0
$79$	223.827	+	387.680i	0.318766	+	0.552119i	0.980231	−	0.197857i	$-0.0633982\pi$
$79$	223.827	+	387.680i	0.318766	+	0.552119i	−0.661465	+	0.749976i	$0.730065\pi$
$80$		0			0
$81$	293.153	−	507.756i	0.402131	−	0.696511i
$82$		0			0
$83$	−10.3976			−0.0137505			−0.00687523	−	0.999976i	$-0.502188\pi$
$83$	−10.3976			−0.0137505			−0.00687523	+	0.999976i	$0.502188\pi$
$84$		0			0
$85$	1144.30			1.46020
$86$		0			0
$87$	358.954	−	621.726i	0.442343	−	0.766161i
$88$		0			0
$89$	−383.026	−	663.420i	−0.456187	−	0.790139i	0.542568	−	0.840012i	$-0.317452\pi$
$89$	−383.026	−	663.420i	−0.456187	−	0.790139i	−0.998756	+	0.0498722i	$0.984119\pi$
$90$		0			0
$91$	−877.304	+	1228.50i	−1.01062	+	1.41518i
$92$		0			0
$93$	−1206.56	−	2089.82i	−1.34532	−	2.33016i
$94$		0			0
$95$	−81.1494	+	140.555i	−0.0876395	+	0.151796i
$96$		0			0
$97$	532.824			0.557733			0.278866	−	0.960330i	$-0.410041\pi$
$97$	532.824			0.557733			0.278866	+	0.960330i	$0.410041\pi$
$98$		0			0
$99$	−546.722			−0.555026
$100$		0			0
$101$	−662.737	+	1147.89i	−0.652919	+	1.13089i	0.329493	+	0.944158i	$0.393122\pi$
$101$	−662.737	+	1147.89i	−0.652919	+	1.13089i	−0.982411	+	0.186730i	$0.940211\pi$
$102$		0			0
$103$	148.682	+	257.525i	0.142234	+	0.246356i	0.928338	−	0.371738i	$-0.121238\pi$
$103$	148.682	+	257.525i	0.142234	+	0.246356i	−0.786104	+	0.618095i	$0.787905\pi$
$104$		0			0
$105$	1202.90	−	1684.44i	1.11801	−	1.56556i
$106$		0			0
$107$	−413.876	−	716.854i	−0.373934	−	0.647672i	0.616233	−	0.787564i	$-0.288658\pi$
$107$	−413.876	−	716.854i	−0.373934	−	0.647672i	−0.990167	+	0.139892i	$0.955325\pi$
$108$		0			0
$109$	−44.7559	+	77.5195i	−0.0393288	+	0.0681194i	−0.885020	−	0.465553i	$-0.845855\pi$
$109$	−44.7559	+	77.5195i	−0.0393288	+	0.0681194i	0.845691	+	0.533673i	$0.179189\pi$
$110$		0			0
$111$	1372.19			1.17336
$112$		0			0
$113$	267.310			0.222535			0.111267	−	0.993790i	$-0.464509\pi$
$113$	267.310			0.222535			0.111267	+	0.993790i	$0.464509\pi$
$114$		0			0
$115$	976.659	−	1691.62i	0.791947	−	1.37169i
$116$		0			0
$117$	1284.86	+	2225.43i	1.01526	+	1.75847i
$118$		0			0
$119$	−600.856	−	1320.39i	−0.462860	−	1.01714i
$120$		0			0
$121$	515.130	+	892.232i	0.387025	+	0.670347i
$122$		0			0
$123$	1015.78	−	1759.38i	0.744633	−	1.28974i
$124$		0			0
$125$	534.397			0.382384
$126$		0			0
$127$	2133.98			1.49102			0.745511	−	0.666493i	$-0.232206\pi$
$127$	2133.98			1.49102			0.745511	+	0.666493i	$0.232206\pi$
$128$		0			0
$129$	25.7609	−	44.6192i	0.0175823	−	0.0304535i
$130$		0			0
$131$	719.638	+	1246.45i	0.479962	+	0.831319i	0.999736	−	0.0229852i	$-0.00731708\pi$
$131$	719.638	+	1246.45i	0.479962	+	0.831319i	−0.519774	+	0.854304i	$0.673984\pi$
$132$		0			0
$133$	204.794	+	19.8336i	0.133518	+	0.0129308i
$134$		0			0
$135$	−252.927	−	438.083i	−0.161248	−	0.279290i
$136$		0			0
$137$	−1140.84	+	1975.99i	−0.711448	+	1.23226i	0.252866	+	0.967501i	$0.418627\pi$
$137$	−1140.84	+	1975.99i	−0.711448	+	1.23226i	−0.964314	+	0.264762i	$0.914707\pi$
$138$		0			0
$139$	1494.99			0.912253			0.456127	−	0.889915i	$-0.349236\pi$
$139$	1494.99			0.912253			0.456127	+	0.889915i	$0.349236\pi$
$140$		0			0
$141$	1316.50			0.786304
$142$		0			0
$143$	−706.769	+	1224.16i	−0.413308	+	0.715870i
$144$		0			0
$145$	685.458	+	1187.25i	0.392580	+	0.679969i
$146$		0			0
$147$	−2575.27	−	503.534i	−1.44493	−	0.282523i
$148$		0			0
$149$	−640.498	−	1109.38i	−0.352159	−	0.609957i	0.634469	−	0.772949i	$-0.281219\pi$
$149$	−640.498	−	1109.38i	−0.352159	−	0.609957i	−0.986627	+	0.162992i	$0.947886\pi$
$150$		0			0
$151$	61.1915	−	105.987i	0.0329781	−	0.0571198i	−0.849065	−	0.528288i	$-0.822834\pi$
$151$	61.1915	−	105.987i	0.0329781	−	0.0571198i	0.882043	+	0.471168i	$0.156167\pi$
$152$		0			0
$153$	−2469.42			−1.30484
$154$		0			0
$155$	4608.09			2.38794
$156$		0			0
$157$	−459.726	+	796.269i	−0.233695	+	0.404772i	−0.958893	−	0.283769i	$-0.908415\pi$
$157$	−459.726	+	796.269i	−0.233695	+	0.404772i	0.725197	+	0.688541i	$0.241748\pi$
$158$		0			0
$159$	−1438.23	−	2491.08i	−0.717351	−	1.24249i
$160$		0			0
$161$	−2464.76	−	238.704i	−1.20653	−	0.116848i
$162$		0			0
$163$	141.844	+	245.681i	0.0681600	+	0.118057i	0.898091	−	0.439809i	$-0.144954\pi$
$163$	141.844	+	245.681i	0.0681600	+	0.118057i	−0.829931	+	0.557866i	$0.811620\pi$
$164$		0			0
$165$	969.075	−	1678.49i	0.457227	−	0.791940i
$166$		0			0
$167$	276.828			0.128273			0.0641365	−	0.997941i	$-0.479571\pi$
$167$	276.828			0.128273			0.0641365	+	0.997941i	$0.479571\pi$
$168$		0			0
$169$	4446.94			2.02409
$170$		0			0
$171$	175.121	−	303.319i	0.0783151	−	0.135646i
$172$		0			0
$173$	508.401	+	880.577i	0.223428	+	0.386989i	0.955847	−	0.293866i	$-0.0949419\pi$
$173$	508.401	+	880.577i	0.223428	+	0.386989i	−0.732419	+	0.680855i	$0.761609\pi$
$174$		0			0
$175$	678.260	+	1490.49i	0.292981	+	0.643830i
$176$		0			0
$177$	435.324	+	754.004i	0.184864	+	0.320194i
$178$		0			0
$179$	−1387.36	+	2402.99i	−0.579310	+	1.00339i	0.416249	+	0.909251i	$0.363345\pi$
$179$	−1387.36	+	2402.99i	−0.579310	+	1.00339i	−0.995559	+	0.0941434i	$0.969989\pi$
$180$		0			0
$181$	−3632.00			−1.49152			−0.745758	−	0.666217i	$-0.767912\pi$
$181$	−3632.00			−1.49152			−0.745758	+	0.666217i	$0.767912\pi$
$182$		0			0
$183$	−2750.47			−1.11104
$184$		0			0
$185$	−1310.17	+	2269.28i	−0.520679	+	0.901842i
$186$		0			0
$187$	−679.185	−	1176.38i	−0.265599	−	0.460030i
$188$		0			0
$189$	−372.688	+	521.879i	−0.143434	+	0.200853i
$190$		0			0
$191$	1116.00	+	1932.97i	0.422780	+	0.732277i	0.996210	−	0.0869777i	$-0.0277209\pi$
$191$	1116.00	+	1932.97i	0.422780	+	0.732277i	−0.573430	+	0.819255i	$0.694388\pi$
$192$		0			0
$193$	−1400.09	+	2425.02i	−0.522178	+	0.904440i	0.477489	+	0.878638i	$0.341547\pi$
$193$	−1400.09	+	2425.02i	−0.522178	+	0.904440i	−0.999667	+	0.0258017i	$0.991786\pi$
$194$		0			0
$195$	−9109.72			−3.34544
$196$		0			0
$197$	3201.39			1.15781			0.578907	−	0.815394i	$-0.303480\pi$
$197$	3201.39			1.15781			0.578907	+	0.815394i	$0.303480\pi$
$198$		0			0
$199$	−352.360	+	610.305i	−0.125518	+	0.217404i	−0.921935	−	0.387344i	$-0.873393\pi$
$199$	−352.360	+	610.305i	−0.125518	+	0.217404i	0.796417	+	0.604748i	$0.206726\pi$
$200$		0			0
$201$	1639.44	+	2839.59i	0.575308	+	0.996463i
$202$		0			0
$203$	1010.02	−	1414.34i	0.349210	−	0.489003i
$204$		0			0
$205$	1939.73	+	3359.72i	0.660863	+	1.14465i
$206$		0			0
$207$	−2107.64	+	3650.55i	−0.707688	+	1.22575i
$208$		0			0
$209$	192.661			0.0637637
$210$		0			0
$211$	216.098			0.0705063			0.0352531	−	0.999378i	$-0.488776\pi$
$211$	216.098			0.0705063			0.0352531	+	0.999378i	$0.488776\pi$
$212$		0			0
$213$	−2791.50	+	4835.02i	−0.897982	+	1.55535i
$214$		0			0
$215$	49.1929	+	85.2047i	0.0156043	+	0.0270275i
$216$		0			0
$217$	−2419.64	−	5317.20i	−0.756940	−	1.66339i
$218$		0			0
$219$	4429.25	+	7671.69i	1.36667	+	2.36715i
$220$		0			0
$221$	−3192.32	+	5529.25i	−0.971667	+	1.68298i
$222$		0			0
$223$	−1251.23			−0.375734			−0.187867	−	0.982194i	$-0.560157\pi$
$223$	−1251.23			−0.375734			−0.187867	+	0.982194i	$0.560157\pi$
$224$		0			0
$225$	2787.54			0.825937
$226$		0			0
$227$	754.686	−	1307.15i	0.220662	−	0.382198i	−0.734347	−	0.678774i	$-0.762512\pi$
$227$	754.686	−	1307.15i	0.220662	−	0.382198i	0.955009	+	0.296576i	$0.0958449\pi$
$228$		0			0
$229$	−196.151	−	339.743i	−0.0566026	−	0.0980386i	0.836336	−	0.548218i	$-0.184693\pi$
$229$	−196.151	−	339.743i	−0.0566026	−	0.0980386i	−0.892938	+	0.450179i	$0.851360\pi$
$230$		0			0
$231$	−2445.63	−	236.850i	−0.696582	−	0.0674615i
$232$		0			0
$233$	−250.774	−	434.353i	−0.0705096	−	0.122126i	0.828615	−	0.559819i	$-0.189129\pi$
$233$	−250.774	−	434.353i	−0.0705096	−	0.122126i	−0.899125	+	0.437692i	$0.855796\pi$
$234$		0			0
$235$	−1256.99	+	2177.17i	−0.348923	+	0.604353i
$236$		0			0
$237$	3424.66			0.938632
$238$		0			0
$239$	4654.95			1.25985			0.629924	−	0.776656i	$-0.283086\pi$
$239$	4654.95			1.25985			0.629924	+	0.776656i	$0.283086\pi$
$240$		0			0
$241$	367.984	−	637.367i	0.0983565	−	0.170359i	−0.812648	−	0.582755i	$-0.801975\pi$
$241$	367.984	−	637.367i	0.0983565	−	0.170359i	0.911005	+	0.412396i	$0.135308\pi$
$242$		0			0
$243$	−2710.15	−	4694.12i	−0.715458	−	1.23921i
$244$		0			0
$245$	3291.59	−	3778.10i	0.858334	−	0.985200i
$246$		0			0
$247$	−452.773	−	784.226i	−0.116637	−	0.202021i
$248$		0			0
$249$	−39.7722	+	68.8874i	−0.0101223	+	0.0175324i
$250$		0			0
$251$	−1277.98			−0.321376			−0.160688	−	0.987005i	$-0.551371\pi$
$251$	−1277.98			−0.321376			−0.160688	+	0.987005i	$0.551371\pi$
$252$		0			0
$253$	−2318.73			−0.576195
$254$		0			0
$255$	4377.09	−	7581.34i	1.07492	−	1.86181i
$256$		0			0
$257$	1080.99	+	1872.33i	0.262374	+	0.454446i	0.966872	−	0.255260i	$-0.0821611\pi$
$257$	1080.99	+	1872.33i	0.262374	+	0.454446i	−0.704498	+	0.709706i	$0.748828\pi$
$258$		0			0
$259$	3306.43	+	320.217i	0.793250	+	0.0768236i
$260$		0			0
$261$	−1479.23	−	2562.10i	−0.350812	−	0.607624i
$262$		0			0
$263$	2325.39	−	4027.69i	0.545207	−	0.944326i	−0.453387	−	0.891314i	$-0.649784\pi$
$263$	2325.39	−	4027.69i	0.545207	−	0.944326i	0.998594	−	0.0530124i	$-0.0168823\pi$
$264$		0			0
$265$	5492.87			1.27330
$266$		0			0
$267$	−5860.48			−1.34328
$268$		0			0
$269$	−880.019	+	1524.24i	−0.199464	+	0.345481i	−0.948355	−	0.317212i	$-0.897253\pi$
$269$	−880.019	+	1524.24i	−0.199464	+	0.345481i	0.748891	+	0.662693i	$0.230587\pi$
$270$		0			0
$271$	2861.56	+	4956.37i	0.641430	+	1.11099i	0.985114	+	0.171904i	$0.0549919\pi$
$271$	2861.56	+	4956.37i	0.641430	+	1.11099i	−0.343684	+	0.939085i	$0.611675\pi$
$272$		0			0
$273$	4783.38	+	10511.6i	1.06045	+	2.33036i
$274$		0			0
$275$	766.680	+	1327.93i	0.168118	+	0.291189i
$276$		0			0
$277$	830.005	−	1437.61i	0.180037	−	0.311833i	−0.761856	−	0.647746i	$-0.775712\pi$
$277$	830.005	−	1437.61i	0.180037	−	0.311833i	0.941893	+	0.335914i	$0.109045\pi$
$278$		0			0
$279$	−9944.33			−2.13388
$280$		0			0
$281$	−5340.36			−1.13373			−0.566867	−	0.823809i	$-0.691845\pi$
$281$	−5340.36			−1.13373			−0.566867	+	0.823809i	$0.691845\pi$
$282$		0			0
$283$	2318.56	−	4015.87i	0.487012	−	0.843529i	−0.512877	−	0.858462i	$-0.671420\pi$
$283$	2318.56	−	4015.87i	0.487012	−	0.843529i	0.999888	+	0.0149331i	$0.00475353\pi$
$284$		0			0
$285$	620.812	+	1075.28i	0.129031	+	0.223488i
$286$		0			0
$287$	2858.20	−	4002.36i	0.587853	−	0.823178i
$288$		0			0
$289$	−611.223	−	1058.67i	−0.124409	−	0.215483i
$290$		0			0
$291$	2038.12	−	3530.12i	0.410572	−	0.711132i
$292$		0			0
$293$	−510.530			−0.101793			−0.0508967	−	0.998704i	$-0.516208\pi$
$293$	−510.530			−0.101793			−0.0508967	+	0.998704i	$0.516208\pi$
$294$		0			0
$295$	−1662.59			−0.328134
$296$		0			0
$297$	−300.243	+	520.036i	−0.0586595	+	0.101601i
$298$		0			0
$299$	5449.27	+	9438.41i	1.05398	+	1.82554i
$300$		0			0
$301$	72.4858	−	101.503i	0.0138804	−	0.0194369i
$302$		0			0
$303$	5070.10	+	8781.67i	0.961285	+	1.66500i
$304$		0			0
$305$	2626.15	−	4548.62i	0.493025	−	0.853945i
$306$		0			0
$307$	4901.40			0.911198			0.455599	−	0.890185i	$-0.349425\pi$
$307$	4901.40			0.911198			0.455599	+	0.890185i	$0.349425\pi$
$308$		0			0
$309$	2274.91			0.418819
$310$		0			0
$311$	179.701	−	311.252i	0.0327650	−	0.0567507i	−0.849178	−	0.528107i	$-0.822902\pi$
$311$	179.701	−	311.252i	0.0327650	−	0.0567507i	0.881943	+	0.471356i	$0.156235\pi$
$312$		0			0
$313$	−1933.49	−	3348.91i	−0.349161	−	0.604765i	0.636939	−	0.770914i	$-0.280200\pi$
$313$	−1933.49	−	3348.91i	−0.349161	−	0.604765i	−0.986101	+	0.166149i	$0.946867\pi$
$314$		0			0
$315$	−3532.94	−	7763.69i	−0.631932	−	1.38868i
$316$		0			0
$317$	2564.84	+	4442.43i	0.454435	+	0.787104i	0.998655	−	0.0518382i	$-0.0165080\pi$
$317$	2564.84	+	4442.43i	0.454435	+	0.787104i	−0.544221	+	0.838942i	$0.683175\pi$
$318$		0			0
$319$	813.689	−	1409.35i	0.142814	−	0.247362i
$320$		0			0
$321$	−6332.50			−1.10108
$322$		0			0
$323$	870.204			0.149905
$324$		0			0
$325$	3603.56	−	6241.55i	0.615045	−	1.06529i
$326$		0			0
$327$	342.393	+	593.043i	0.0579033	+	0.100292i
$328$		0			0
$329$	3172.23	+	307.219i	0.531582	+	0.0514819i
$330$		0			0
$331$	2033.53	+	3522.18i	0.337682	+	0.584883i	0.983996	−	0.178189i	$-0.0570237\pi$
$331$	2033.53	+	3522.18i	0.337682	+	0.584883i	−0.646314	+	0.763072i	$0.723690\pi$
$332$		0			0
$333$	2827.36	−	4897.14i	0.465281	−	0.805890i
$334$		0			0
$335$	−6261.33			−1.02117
$336$		0			0
$337$	−7574.84			−1.22441			−0.612207	−	0.790697i	$-0.709718\pi$
$337$	−7574.84			−1.22441			−0.612207	+	0.790697i	$0.709718\pi$
$338$		0			0
$339$	1022.49	−	1771.01i	0.163818	−	0.283741i
$340$		0			0
$341$	−2735.07	−	4737.29i	−0.434348	−	0.752312i
$342$		0			0
$343$	−6087.86	−	1814.28i	−0.958348	−	0.285604i
$344$		0			0
$345$	−7471.68	−	12941.3i	−1.16598	−	2.01953i
$346$		0			0
$347$	3667.86	−	6352.93i	0.567439	−	0.982833i	−0.429380	−	0.903124i	$-0.641268\pi$
$347$	3667.86	−	6352.93i	0.567439	−	0.982833i	0.996818	−	0.0797085i	$-0.0253989\pi$
$348$		0			0
$349$	6304.89			0.967029			0.483515	−	0.875336i	$-0.339360\pi$
$349$	6304.89			0.967029			0.483515	+	0.875336i	$0.339360\pi$
$350$		0			0
$351$	2822.41			0.429200
$352$		0			0
$353$	−2371.38	+	4107.35i	−0.357552	+	0.619298i	−0.987551	−	0.157298i	$-0.949722\pi$
$353$	−2371.38	+	4107.35i	−0.357552	+	0.619298i	0.629999	+	0.776596i	$0.283055\pi$
$354$		0			0
$355$	−5330.64	−	9232.94i	−0.796961	−	1.38038i
$356$		0			0
$357$	−11046.3	−	1069.80i	−1.63763	−	0.158599i
$358$		0			0
$359$	5031.56	+	8714.91i	0.739708	+	1.28121i	0.952627	+	0.304143i	$0.0983699\pi$
$359$	5031.56	+	8714.91i	0.739708	+	1.28121i	−0.212918	+	0.977070i	$0.568297\pi$
$360$		0			0
$361$	3367.79	−	5833.18i	0.491003	−	0.850442i
$362$		0			0
$363$	7881.74			1.13963
$364$		0			0
$365$	−16916.2			−2.42585
$366$		0			0
$367$	6227.84	−	10786.9i	0.885805	−	1.53426i	0.0410164	−	0.999158i	$-0.486940\pi$
$367$	6227.84	−	10786.9i	0.885805	−	1.53426i	0.844788	−	0.535100i	$-0.179726\pi$
$368$		0			0
$369$	−4185.97	−	7250.31i	−0.590550	−	1.02286i
$370$		0			0
$371$	−2884.23	−	6338.14i	−0.403616	−	0.886953i
$372$		0			0
$373$	−3192.66	−	5529.86i	−0.443190	−	0.767628i	0.554734	−	0.832028i	$-0.312820\pi$
$373$	−3192.66	−	5529.86i	−0.443190	−	0.767628i	−0.997924	+	0.0644000i	$0.979487\pi$
$374$		0			0
$375$	2044.13	−	3540.55i	0.281490	−	0.487555i
$376$		0			0
$377$	−7649.02			−1.04495
$378$		0			0
$379$	−109.028			−0.0147767			−0.00738835	−	0.999973i	$-0.502352\pi$
$379$	−109.028			−0.0147767			−0.00738835	+	0.999973i	$0.502352\pi$
$380$		0			0
$381$	8162.72	−	14138.2i	1.09761	−	1.90111i
$382$		0			0
$383$	2803.66	+	4856.08i	0.374048	+	0.647870i	0.990184	−	0.139770i	$-0.0446363\pi$
$383$	2803.66	+	4856.08i	0.374048	+	0.647870i	−0.616136	+	0.787640i	$0.711303\pi$
$384$		0			0
$385$	2726.78	−	3818.34i	0.360959	−	0.505456i
$386$		0			0
$387$	−106.159	−	183.873i	−0.0139441	−	0.0241519i
$388$		0			0
$389$	−7256.92	+	12569.4i	−0.945862	+	1.63828i	−0.191847	+	0.981425i	$0.561448\pi$
$389$	−7256.92	+	12569.4i	−0.945862	+	1.63828i	−0.754015	+	0.656857i	$0.771886\pi$
$390$		0			0
$391$	−10473.2			−1.35461
$392$		0			0
$393$	11010.8			1.41329
$394$		0			0
$395$	−3269.87	+	5663.58i	−0.416519	+	0.721431i
$396$		0			0
$397$	−5406.37	−	9364.11i	−0.683471	−	1.18381i	−0.973915	−	0.226914i	$-0.927136\pi$
$397$	−5406.37	−	9364.11i	−0.683471	−	1.18381i	0.290444	−	0.956892i	$-0.406197\pi$
$398$		0			0
$399$	914.767	−	1280.96i	0.114776	−	0.160722i
$400$		0			0
$401$	7869.19	+	13629.8i	0.979972	+	1.69736i	0.662442	+	0.749113i	$0.269520\pi$
$401$	7869.19	+	13629.8i	0.979972	+	1.69736i	0.317529	+	0.948248i	$0.397147\pi$
$402$		0			0
$403$	−12855.4	+	22266.3i	−1.58902	+	2.75226i
$404$		0			0
$405$	8565.29			1.05090
$406$		0			0
$407$	3110.53			0.378829
$408$		0			0
$409$	3047.10	−	5277.73i	0.368385	−	0.638061i	−0.620929	−	0.783867i	$-0.713244\pi$
$409$	3047.10	−	5277.73i	0.368385	−	0.638061i	0.989313	+	0.145806i	$0.0465776\pi$
$410$		0			0
$411$	8727.68	+	15116.8i	1.04746	+	1.81425i
$412$		0			0
$413$	873.001	+	1918.43i	0.104014	+	0.228571i
$414$		0			0
$415$	−75.9489	−	131.547i	−0.00898358	−	0.0155600i
$416$		0			0
$417$	5718.51	−	9904.75i	0.671551	−	1.16316i
$418$		0			0
$419$	−15324.8			−1.78679			−0.893395	−	0.449272i	$-0.851683\pi$
$419$	−15324.8			−1.78679			−0.893395	+	0.449272i	$0.851683\pi$
$420$		0			0
$421$	12916.8			1.49531			0.747655	−	0.664087i	$-0.231180\pi$
$421$	12916.8			1.49531			0.747655	+	0.664087i	$0.231180\pi$
$422$		0			0
$423$	2712.60	−	4698.36i	0.311799	−	0.540052i
$424$		0			0
$425$	3462.92	+	5997.95i	0.395238	+	0.684572i
$426$		0			0
$427$	−6627.53	−	641.854i	−0.751121	−	0.0727435i
$428$		0			0
$429$	5406.96	+	9365.12i	0.608509	+	1.05397i
$430$		0			0
$431$	−3143.58	+	5444.83i	−0.351324	+	0.608511i	−0.986482	−	0.163871i	$-0.947602\pi$
$431$	−3143.58	+	5444.83i	−0.351324	+	0.608511i	0.635158	+	0.772383i	$0.280935\pi$
$432$		0			0
$433$	5218.91			0.579226			0.289613	−	0.957144i	$-0.406473\pi$
$433$	5218.91			0.579226			0.289613	+	0.957144i	$0.406473\pi$
$434$		0			0
$435$	10487.8			1.15598
$436$		0			0
$437$	742.717	−	1286.42i	0.0813020	−	0.140819i
$438$		0			0
$439$	1505.66	+	2607.89i	0.163693	+	0.283525i	0.936191	−	0.351493i	$-0.114326\pi$
$439$	1505.66	+	2607.89i	0.163693	+	0.283525i	−0.772497	+	0.635018i	$0.780993\pi$
$440$		0			0
$441$	−7103.30	+	8153.20i	−0.767012	+	0.880380i
$442$		0			0
$443$	−1100.87	−	1906.77i	−0.118068	−	0.204500i	0.800934	−	0.598753i	$-0.204337\pi$
$443$	−1100.87	−	1906.77i	−0.118068	−	0.204500i	−0.919002	+	0.394253i	$0.871003\pi$
$444$		0			0
$445$	5595.58	−	9691.83i	0.596081	−	1.03244i
$446$		0			0
$447$	−9799.94			−1.03696
$448$		0			0
$449$	−10317.0			−1.08439			−0.542193	−	0.840254i	$-0.682406\pi$
$449$	−10317.0			−1.08439			−0.542193	+	0.840254i	$0.682406\pi$
$450$		0			0
$451$	2302.61	−	3988.23i	0.240411	−	0.416405i
$452$		0			0
$453$	−468.130	−	810.825i	−0.0485534	−	0.0840969i
$454$		0			0
$455$	−21950.8	−	2125.86i	−2.26169	−	0.219037i
$456$		0			0
$457$	2639.72	+	4572.13i	0.270199	+	0.467998i	0.968913	−	0.247403i	$-0.0795772\pi$
$457$	2639.72	+	4572.13i	0.270199	+	0.467998i	−0.698714	+	0.715401i	$0.746244\pi$
$458$		0			0
$459$	−1356.13	+	2348.89i	−0.137906	+	0.238860i
$460$		0			0
$461$	−15855.0			−1.60182			−0.800912	−	0.598782i	$-0.795652\pi$
$461$	−15855.0			−1.60182			−0.800912	+	0.598782i	$0.795652\pi$
$462$		0			0
$463$	8167.07			0.819775			0.409888	−	0.912136i	$-0.365568\pi$
$463$	8167.07			0.819775			0.409888	+	0.912136i	$0.365568\pi$
$464$		0			0
$465$	17626.5	−	30530.0i	1.75787	−	3.04472i
$466$		0			0
$467$	−8136.15	−	14092.2i	−0.806202	−	1.39638i	−0.915477	−	0.402371i	$-0.868186\pi$
$467$	−8136.15	−	14092.2i	−0.806202	−	1.39638i	0.109275	−	0.994012i	$-0.465147\pi$
$468$		0			0
$469$	3287.73	+	7224.85i	0.323696	+	0.711327i
$470$		0			0
$471$	3517.02	+	6091.65i	0.344067	+	0.595942i
$472$		0			0
$473$	58.3957	−	101.144i	0.00567661	−	0.00983217i
$474$		0			0
$475$	−982.306			−0.0948870
$476$		0			0
$477$	−11853.7			−1.13783
$478$		0			0
$479$	−4191.69	+	7260.22i	−0.399840	+	0.692543i	−0.993706	−	0.112021i	$-0.964268\pi$
$479$	−4191.69	+	7260.22i	−0.399840	+	0.692543i	0.593866	+	0.804564i	$0.297601\pi$
$480$		0			0
$481$	−7310.09	−	12661.4i	−0.692955	−	1.20023i
$482$		0			0
$483$	−11009.5	+	15416.7i	−1.03716	+	1.45235i
$484$		0			0
$485$	3891.98	+	6741.11i	0.364383	+	0.631130i
$486$		0			0
$487$	−188.547	+	326.573i	−0.0175439	+	0.0303870i	−0.874664	−	0.484730i	$-0.838918\pi$
$487$	−188.547	+	326.573i	−0.0175439	+	0.0303870i	0.857120	+	0.515117i	$0.172251\pi$
$488$		0			0
$489$	2170.28			0.200703
$490$		0			0
$491$	−1658.74			−0.152460			−0.0762299	−	0.997090i	$-0.524288\pi$
$491$	−1658.74			−0.152460			−0.0762299	+	0.997090i	$0.524288\pi$
$492$		0			0
$493$	3675.25	−	6365.71i	0.335750	−	0.581536i
$494$		0			0
$495$	−3993.50	−	6916.95i	−0.362615	−	0.628068i
$496$		0			0
$497$	−7854.69	+	10999.0i	−0.708916	+	0.992703i
$498$		0			0
$499$	8027.34	+	13903.8i	0.720146	+	1.24733i	0.960941	+	0.276754i	$0.0892587\pi$
$499$	8027.34	+	13903.8i	0.720146	+	1.24733i	−0.240795	+	0.970576i	$0.577408\pi$
$500$		0			0
$501$	1058.90	−	1834.07i	0.0944275	−	0.163553i
$502$		0			0
$503$	20948.9			1.85699			0.928494	−	0.371348i	$-0.121104\pi$
$503$	20948.9			1.85699			0.928494	+	0.371348i	$0.121104\pi$
$504$		0			0
$505$	−19363.7			−1.70628
$506$		0			0
$507$	17010.1	−	29462.3i	1.49003	−	2.58080i
$508$		0			0
$509$	−1404.04	−	2431.86i	−0.122265	−	0.211769i	0.798396	−	0.602133i	$-0.205682\pi$
$509$	−1404.04	−	2431.86i	−0.122265	−	0.211769i	−0.920661	+	0.390364i	$0.872349\pi$
$510$		0			0
$511$	8882.45	+	19519.3i	0.768955	+	1.68979i
$512$		0			0
$513$	−192.343	−	333.148i	−0.0165539	−	0.0286722i
$514$		0			0
$515$	−2172.08	+	3762.15i	−0.185851	+	0.321904i
$516$		0			0
$517$	2984.28			0.253865
$518$		0			0
$519$	7778.79			0.657902
$520$		0			0
$521$	−1208.04	+	2092.39i	−0.101584	+	0.175949i	−0.912337	−	0.409439i	$-0.865724\pi$
$521$	−1208.04	+	2092.39i	−0.101584	+	0.175949i	0.810753	+	0.585388i	$0.199058\pi$
$522$		0			0
$523$	−9433.08	−	16338.6i	−0.788680	−	1.36603i	−0.926776	−	0.375615i	$-0.877431\pi$
$523$	−9433.08	−	16338.6i	−0.788680	−	1.36603i	0.138096	−	0.990419i	$-0.455902\pi$
$524$		0			0
$525$	12469.4	+	1207.61i	1.03659	+	0.100390i
$526$		0			0
$527$	−12353.7	−	21397.2i	−1.02113	−	1.76865i
$528$		0			0
$529$	−2855.34	+	4945.60i	−0.234679	+	0.406476i
$530$		0			0
$531$	3587.89			0.293223
$532$		0			0
$533$	−21645.5			−1.75904
$534$		0			0
$535$	6046.27	−	10472.4i	0.488604	−	0.846287i
$536$		0			0
$537$	10613.7	+	18383.4i	0.852912	+	1.47729i
$538$		0			0
$539$	−5837.70	−	1141.43i	−0.466508	−	0.0912149i
$540$		0			0
$541$	−4399.31	−	7619.82i	−0.349614	−	0.605549i	0.636567	−	0.771221i	$-0.280354\pi$
$541$	−4399.31	−	7619.82i	−0.349614	−	0.605549i	−0.986181	+	0.165673i	$0.947020\pi$
$542$		0			0
$543$	−13892.8	+	24063.1i	−1.09797	+	1.90174i
$544$		0			0
$545$	−1307.67			−0.102779
$546$		0			0
$547$	19572.3			1.52989			0.764947	−	0.644094i	$-0.222765\pi$
$547$	19572.3			1.52989			0.764947	+	0.644094i	$0.222765\pi$
$548$		0			0
$549$	−5667.26	+	9815.99i	−0.440570	+	0.763090i
$550$		0			0
$551$	521.268	+	902.863i	0.0403027	+	0.0698063i
$552$		0			0
$553$	8252.07	+	799.184i	0.634563	+	0.0614553i
$554$		0			0
$555$	10023.1	+	17360.5i	0.766590	+	1.32777i
$556$		0			0
$557$	1311.22	−	2271.11i	0.0997457	−	0.172765i	−0.811834	−	0.583889i	$-0.801530\pi$
$557$	1311.22	−	2271.11i	0.0997457	−	0.172765i	0.911579	+	0.411124i	$0.134864\pi$
$558$		0			0
$559$	−548.944			−0.0415347
$560$		0			0
$561$	−10391.9			−0.782076
$562$		0			0
$563$	10895.0	−	18870.8i	0.815579	−	1.41262i	−0.0933323	−	0.995635i	$-0.529752\pi$
$563$	10895.0	−	18870.8i	0.815579	−	1.41262i	0.908911	−	0.416989i	$-0.136915\pi$
$564$		0			0
$565$	1952.55	+	3381.92i	0.145389	+	0.251821i
$566$		0			0
$567$	−4497.51	−	9883.34i	−0.333117	−	0.732031i
$568$		0			0
$569$	3136.28	+	5432.19i	0.231071	+	0.400227i	0.958124	−	0.286355i	$-0.0924436\pi$
$569$	3136.28	+	5432.19i	0.231071	+	0.400227i	−0.727052	+	0.686582i	$0.759110\pi$
$570$		0			0
$571$	6636.08	−	11494.0i	0.486359	−	0.842399i	−0.513518	−	0.858079i	$-0.671658\pi$
$571$	6636.08	−	11494.0i	0.486359	−	0.842399i	0.999877	+	0.0156801i	$0.00499133\pi$
$572$		0			0
$573$	17075.4			1.24491
$574$		0			0
$575$	11822.4			0.857438
$576$		0			0
$577$	−7427.50	+	12864.8i	−0.535894	+	0.928196i	0.463225	+	0.886240i	$0.346692\pi$
$577$	−7427.50	+	12864.8i	−0.535894	+	0.928196i	−0.999119	+	0.0419552i	$0.986641\pi$
$578$		0			0
$579$	10711.0	+	18552.0i	0.768798	+	1.33160i
$580$		0			0
$581$	−111.911	+	156.710i	−0.00799111	+	0.0111900i
$582$		0			0
$583$	−3260.22	−	5646.87i	−0.231603	−	0.401148i
$584$		0			0
$585$	−18770.3	+	32511.1i	−1.32659	+	2.29773i
$586$		0			0
$587$	−17006.2			−1.19578			−0.597889	−	0.801579i	$-0.703994\pi$
$587$	−17006.2			−1.19578			−0.597889	+	0.801579i	$0.703994\pi$
$588$		0			0
$589$	3504.31			0.245148
$590$		0			0
$591$	12245.7	−	21210.1i	0.852318	−	1.47626i
$592$		0			0
$593$	−10477.6	−	18147.7i	−0.725568	−	1.25672i	−0.958740	−	0.284286i	$-0.908244\pi$
$593$	−10477.6	−	18147.7i	−0.725568	−	1.25672i	0.233171	−	0.972436i	$-0.425090\pi$
$594$		0			0
$595$	12316.2	−	17246.5i	0.848598	−	1.18830i
$596$		0			0
$597$	2695.64	+	4668.98i	0.184799	+	0.320081i
$598$		0			0
$599$	4679.20	−	8104.60i	0.319177	−	0.552830i	−0.661140	−	0.750263i	$-0.729927\pi$
$599$	4679.20	−	8104.60i	0.319177	−	0.552830i	0.980316	+	0.197433i	$0.0632604\pi$
$600$		0			0
$601$	14036.8			0.952700			0.476350	−	0.879256i	$-0.341960\pi$
$601$	14036.8			0.952700			0.476350	+	0.879256i	$0.341960\pi$
$602$		0			0
$603$	13512.0			0.912525
$604$		0			0
$605$	−7525.48	+	13034.5i	−0.505710	+	0.875915i
$606$		0			0
$607$	−13364.2	−	23147.5i	−0.893635	−	1.54782i	−0.835484	−	0.549514i	$-0.814813\pi$
$607$	−13364.2	−	23147.5i	−0.893635	−	1.54782i	−0.0581511	−	0.998308i	$-0.518521\pi$
$608$		0			0
$609$	−5507.01	−	12101.7i	−0.366429	−	0.805233i
$610$		0			0
$611$	−7013.37	−	12147.5i	−0.464371	−	0.804314i
$612$		0			0
$613$	8026.90	−	13903.0i	0.528880	−	0.916047i	−0.470553	−	0.882372i	$-0.655945\pi$
$613$	8026.90	−	13903.0i	0.528880	−	0.916047i	0.999433	−	0.0336753i	$-0.0107212\pi$
$614$		0			0
$615$	29678.9			1.94596
$616$		0			0
$617$	26329.9			1.71799			0.858996	−	0.511982i	$-0.171088\pi$
$617$	26329.9			1.71799			0.858996	+	0.511982i	$0.171088\pi$
$618$		0			0
$619$	−7082.79	+	12267.7i	−0.459905	+	0.796579i	−0.998955	−	0.0456946i	$-0.985450\pi$
$619$	−7082.79	+	12267.7i	−0.459905	+	0.796579i	0.539050	+	0.842273i	$0.318783\pi$
$620$		0			0
$621$	2314.91	+	4009.54i	0.149588	+	0.259094i
$622$		0			0
$623$	−14121.4	−	1367.61i	−0.908126	−	0.0879488i
$624$		0			0
$625$	9429.71	+	16332.7i	0.603501	+	1.04530i
$626$		0			0
$627$	736.950	−	1276.43i	0.0469393	−	0.0813013i
$628$		0			0
$629$	14049.6			0.890609
$630$		0			0
$631$	−21047.8			−1.32789			−0.663945	−	0.747781i	$-0.731119\pi$
$631$	−21047.8			−1.32789			−0.663945	+	0.747781i	$0.731119\pi$
$632$		0			0
$633$	826.602	−	1431.72i	0.0519028	−	0.0898983i
$634$		0			0
$635$	15587.5	+	26998.4i	0.974128	+	1.68724i
$636$		0			0
$637$	9073.04	+	26444.9i	0.564344	+	1.64487i
$638$		0			0
$639$	11503.6	+	19924.8i	0.712168	+	1.23351i
$640$		0			0
$641$	−501.953	+	869.409i	−0.0309297	+	0.0535719i	−0.881076	−	0.472975i	$-0.843180\pi$
$641$	−501.953	+	869.409i	−0.0309297	+	0.0535719i	0.850146	+	0.526547i	$0.176513\pi$
$642$		0			0
$643$	−9759.07			−0.598538			−0.299269	−	0.954169i	$-0.596743\pi$
$643$	−9759.07			−0.598538			−0.299269	+	0.954169i	$0.596743\pi$
$644$		0			0
$645$	752.676			0.0459482
$646$		0			0
$647$	−1106.50	+	1916.51i	−0.0672346	+	0.116454i	−0.897683	−	0.440642i	$-0.854751\pi$
$647$	−1106.50	+	1916.51i	−0.0672346	+	0.116454i	0.830448	+	0.557096i	$0.188084\pi$
$648$		0			0
$649$	986.808	+	1709.20i	0.0596850	+	0.103378i
$650$		0			0
$651$	−44483.5	−	4308.08i	−2.67810	−	0.259365i
$652$		0			0
$653$	263.941	+	457.160i	0.0158175	+	0.0273967i	0.873826	−	0.486239i	$-0.161632\pi$
$653$	263.941	+	457.160i	0.0158175	+	0.0273967i	−0.858008	+	0.513636i	$0.828298\pi$
$654$		0			0
$655$	−10513.1	+	18209.2i	−0.627147	+	1.08625i
$656$		0			0
$657$	36505.4			2.16775
$658$		0			0
$659$	−9476.80			−0.560188			−0.280094	−	0.959973i	$-0.590366\pi$
$659$	−9476.80			−0.560188			−0.280094	+	0.959973i	$0.590366\pi$
$660$		0			0
$661$	−16438.8	+	28472.8i	−0.967313	+	1.67543i	−0.264044	+	0.964511i	$0.585056\pi$
$661$	−16438.8	+	28472.8i	−0.967313	+	1.67543i	−0.703269	+	0.710924i	$0.748277\pi$
$662$		0			0
$663$	24422.0	+	42300.1i	1.43057	+	2.47783i
$664$		0			0
$665$	1244.98	+	2735.86i	0.0725989	+	0.159537i
$666$		0			0
$667$	−6273.63	−	10866.2i	−0.364192	−	0.630799i
$668$		0			0
$669$	−4786.11	+	8289.79i	−0.276595	+	0.479076i
$670$		0			0
$671$	−6234.86			−0.358710
$672$		0			0
$673$	17749.9			1.01665			0.508327	−	0.861164i	$-0.330264\pi$
$673$	17749.9			1.01665			0.508327	+	0.861164i	$0.330264\pi$
$674$		0			0
$675$	1530.83	−	2651.48i	0.0872914	−	0.151193i
$676$		0			0
$677$	5222.65	+	9045.90i	0.296489	+	0.513534i	0.975330	−	0.220751i	$-0.0708510\pi$
$677$	5222.65	+	9045.90i	0.296489	+	0.513534i	−0.678841	+	0.734285i	$0.737518\pi$
$678$		0			0
$679$	5734.83	−	8030.55i	0.324128	−	0.453880i
$680$		0			0
$681$	−5773.53	−	10000.0i	−0.324878	−	0.562705i
$682$		0			0
$683$	−1684.40	+	2917.47i	−0.0943659	+	0.163447i	−0.909344	−	0.416046i	$-0.863416\pi$
$683$	−1684.40	+	2917.47i	−0.0943659	+	0.163447i	0.814978	+	0.579492i	$0.196749\pi$
$684$		0			0
$685$	−33332.7			−1.85924
$686$		0			0
$687$	−3001.20			−0.166671
$688$		0			0
$689$	−15323.7	+	26541.5i	−0.847298	+	1.46756i
$690$		0			0
$691$	4363.51	+	7557.82i	0.240225	+	0.416083i	0.960778	−	0.277317i	$-0.0894453\pi$
$691$	4363.51	+	7557.82i	0.240225	+	0.416083i	−0.720553	+	0.693400i	$0.756112\pi$
$692$		0			0
$693$	−5884.42	+	8240.02i	−0.322555	+	0.451678i
$694$		0			0
$695$	10920.1	+	18914.1i	0.596002	+	1.03231i
$696$		0			0
$697$	10400.3	−	18013.9i	0.565195	−	0.978947i
$698$		0			0
$699$	−3836.96			−0.207621
$700$		0			0
$701$	227.187			0.0122407			0.00612036	−	0.999981i	$-0.498052\pi$
$701$	227.187			0.0122407			0.00612036	+	0.999981i	$0.498052\pi$
$702$		0			0
$703$	−996.341	+	1725.71i	−0.0534533	+	0.0925839i
$704$		0			0
$705$	9616.27	+	16655.9i	0.513716	+	0.889782i
$706$		0			0
$707$	10167.6	+	22343.5i	0.540866	+	1.18856i
$708$		0			0
$709$	9220.42	+	15970.2i	0.488406	+	0.845945i	0.999911	−	0.0133357i	$-0.00424502\pi$
$709$	9220.42	+	15970.2i	0.488406	+	0.845945i	−0.511505	+	0.859281i	$0.670912\pi$
$710$		0			0
$711$	7056.42	−	12222.1i	0.372203	−	0.644675i
$712$		0			0
$713$	−42175.4			−2.21526
$714$		0			0
$715$	−20650.2			−1.08010
$716$		0			0
$717$	17805.8	−	30840.5i	0.927431	−	1.60636i
$718$		0			0
$719$	−10301.1	−	17841.9i	−0.534304	−	0.925441i	−0.999197	−	0.0400744i	$-0.987241\pi$
$719$	−10301.1	−	17841.9i	−0.534304	−	0.925441i	0.464893	−	0.885367i	$-0.346093\pi$
$720$		0			0
$721$	5481.62	+	530.876i	0.283143	+	0.0274214i
$722$		0			0
$723$	−2815.17	−	4876.01i	−0.144809	−	0.250817i
$724$		0			0
$725$	−4148.70	+	7185.76i	−0.212523	+	0.368100i
$726$		0			0
$727$	−32847.4			−1.67571			−0.837856	−	0.545892i	$-0.816191\pi$
$727$	−32847.4			−1.67571			−0.837856	+	0.545892i	$0.816191\pi$
$728$		0			0
$729$	−25636.3			−1.30246
$730$		0			0
$731$	263.760	−	456.845i	0.0133454	−	0.0231150i
$732$		0			0
$733$	14889.3	+	25789.0i	0.750270	+	1.29951i	0.947691	+	0.319188i	$0.103410\pi$
$733$	14889.3	+	25789.0i	0.750270	+	1.29951i	−0.197421	+	0.980319i	$0.563257\pi$
$734$		0			0
$735$	−12440.3	−	36259.5i	−0.624312	−	1.81966i
$736$		0			0
$737$	3716.33	+	6436.87i	0.185743	+	0.321717i
$738$		0			0
$739$	−15178.0	+	26289.1i	−0.755523	+	1.30860i	0.189591	+	0.981863i	$0.439284\pi$
$739$	−15178.0	+	26289.1i	−0.755523	+	1.30860i	−0.945114	+	0.326741i	$0.894049\pi$
$740$		0			0
$741$	−6927.65			−0.343446
$742$		0			0
$743$	−16361.0			−0.807843			−0.403921	−	0.914794i	$-0.632353\pi$
$743$	−16361.0			−0.807843			−0.403921	+	0.914794i	$0.632353\pi$
$744$		0			0
$745$	9356.97	−	16206.8i	0.460152	−	0.797006i
$746$		0			0
$747$	163.899	+	283.881i	0.00802777	+	0.0139045i
$748$		0			0
$749$	−15258.8	−	1477.76i	−0.744385	−	0.0720911i
$750$		0			0
$751$	−2025.68	−	3508.58i	−0.0984261	−	0.170479i	0.812607	−	0.582812i	$-0.198047\pi$
$751$	−2025.68	−	3508.58i	−0.0984261	−	0.170479i	−0.911033	+	0.412333i	$0.864714\pi$
$752$		0			0
$753$	−4888.42	+	8466.99i	−0.236579	+	0.409767i
$754$		0			0
$755$	1787.88			0.0861823
$756$		0			0
$757$	34778.4			1.66981			0.834903	−	0.550397i	$-0.185524\pi$
$757$	34778.4			1.66981			0.834903	+	0.550397i	$0.185524\pi$
$758$		0			0
$759$	−8869.43	+	15362.3i	−0.424163	+	0.734672i
$760$		0			0
$761$	−6269.11	−	10858.4i	−0.298627	−	0.517237i	0.677195	−	0.735804i	$-0.263195\pi$
$761$	−6269.11	−	10858.4i	−0.298627	−	0.517237i	−0.975822	+	0.218566i	$0.929862\pi$
$762$		0			0
$763$	686.637	+	1508.90i	0.0325792	+	0.0715933i
$764$		0			0
$765$	−18037.7	−	31242.3i	−0.852491	−	1.47656i
$766$		0			0
$767$	4638.21	−	8033.61i	0.218352	−	0.378197i
$768$		0			0
$769$	7227.06			0.338900			0.169450	−	0.985539i	$-0.445801\pi$
$769$	7227.06			0.338900			0.169450	+	0.985539i	$0.445801\pi$
$770$		0			0
$771$	16539.7			0.772582
$772$		0			0
$773$	15447.2	−	26755.3i	0.718752	−	1.24492i	−0.242742	−	0.970091i	$-0.578047\pi$
$773$	15447.2	−	26755.3i	0.718752	−	1.24492i	0.961494	−	0.274825i	$-0.0886198\pi$
$774$		0			0
$775$	13945.1	+	24153.7i	0.646354	+	1.11952i
$776$		0			0
$777$	14769.0	−	20681.3i	0.681900	−	0.954873i
$778$		0			0
$779$	1475.10	+	2554.95i	0.0678448	+	0.117511i
$780$		0			0
$781$	−6327.86	+	10960.2i	−0.289922	+	0.502159i
$782$		0			0
$783$	−3249.39			−0.148306
$784$		0			0
$785$	−13432.2			−0.610720
$786$		0			0
$787$	9223.17	−	15975.0i	0.417751	−	0.723567i	−0.577961	−	0.816064i	$-0.696152\pi$
$787$	9223.17	−	15975.0i	0.417751	−	0.723567i	0.995713	+	0.0924973i	$0.0294850\pi$
$788$		0			0
$789$	−17789.8	−	30812.8i	−0.802703	−	1.39032i
$790$		0			0
$791$	2877.09	−	4028.82i	0.129327	−	0.181098i
$792$		0			0
$793$	14652.6	+	25379.0i	0.656152	+	1.13649i
$794$		0			0
$795$	21010.9	−	36391.9i	0.937333	−	1.62351i
$796$		0			0
$797$	−22292.7			−0.990773			−0.495387	−	0.868673i	$-0.664974\pi$
$797$	−22292.7			−0.990773			−0.495387	+	0.868673i	$0.664974\pi$
$798$		0			0
$799$	13479.3			0.596825
$800$		0			0
$801$	−12075.3	+	20915.1i	−0.532661	+	0.922596i
$802$		0			0
$803$	10040.4	+	17390.5i	0.441242	+	0.764254i
$804$		0			0
$805$	−14983.7	−	32927.0i	−0.656034	−	1.44164i
$806$		0			0
$807$	6732.35	+	11660.8i	0.293668	+	0.508648i
$808$		0			0
$809$	2563.12	−	4439.45i	0.111390	−	0.192933i	−0.804941	−	0.593355i	$-0.797803\pi$
$809$	2563.12	−	4439.45i	0.111390	−	0.192933i	0.916331	+	0.400422i	$0.131136\pi$
$810$		0			0
$811$	−16954.8			−0.734109			−0.367054	−	0.930200i	$-0.619634\pi$
$811$	−16954.8			−0.734109			−0.367054	+	0.930200i	$0.619634\pi$
$812$		0			0
$813$	43783.3			1.88874
$814$		0			0
$815$	−2072.18	+	3589.13i	−0.0890619	+	0.154260i
$816$		0			0
$817$	37.4096	+	64.7954i	0.00160196	+	0.00277467i
$818$		0			0
$819$	47370.1	+	4587.63i	2.02106	+	0.195732i
$820$		0			0
$821$	−8297.24	−	14371.2i	−0.352711	−	0.610913i	0.634012	−	0.773323i	$-0.281407\pi$
$821$	−8297.24	−	14371.2i	−0.352711	−	0.610913i	−0.986723	+	0.162410i	$0.948073\pi$
$822$		0			0
$823$	−8486.45	+	14699.0i	−0.359440	+	0.622568i	−0.987867	−	0.155300i	$-0.950366\pi$
$823$	−8486.45	+	14699.0i	−0.359440	+	0.622568i	0.628428	+	0.777868i	$0.283699\pi$
$824$		0			0
$825$	11730.6			0.495038
$826$		0			0
$827$	−34042.7			−1.43142			−0.715709	−	0.698399i	$-0.753896\pi$
$827$	−34042.7			−1.43142			−0.715709	+	0.698399i	$0.753896\pi$
$828$		0			0
$829$	−23.6086	+	40.8913i	−0.000989096	+	0.00171316i	−0.866520	−	0.499143i	$-0.833648\pi$
$829$	−23.6086	+	40.8913i	−0.000989096	+	0.00171316i	0.865530	+	0.500856i	$0.166982\pi$
$830$		0			0
$831$	−6349.74	−	10998.1i	−0.265066	−	0.459108i
$832$		0			0
$833$	−26367.6	−	5155.57i	−1.09674	−	0.214442i
$834$		0			0
$835$	2022.07	+	3502.34i	0.0838045	+	0.145154i
$836$		0			0
$837$	−5461.13	+	9458.95i	−0.225525	+	0.390620i
$838$		0			0
$839$	−5261.84			−0.216519			−0.108259	−	0.994123i	$-0.534528\pi$
$839$	−5261.84			−0.216519			−0.108259	+	0.994123i	$0.534528\pi$
$840$		0			0
$841$	−15582.8			−0.638929
$842$		0			0
$843$	−20427.5	+	35381.5i	−0.834593	+	1.44556i
$844$		0			0
$845$	32482.4	+	56261.2i	1.32240	+	2.29046i
$846$		0			0
$847$	18991.8	+	1839.29i	0.770446	+	0.0746150i
$848$		0			0
$849$	−17737.6	−	30722.4i	−0.717022	−	1.24192i
$850$		0			0
$851$	11991.3	−	20769.5i	0.483027	−	0.836627i
$852$		0			0
$853$	−26959.2			−1.08214			−0.541069	−	0.840978i	$-0.681980\pi$
$853$	−26959.2			−1.08214			−0.541069	+	0.840978i	$0.681980\pi$
$854$		0			0
$855$	5116.66			0.204662
$856$		0			0
$857$	−7808.61	+	13524.9i	−0.311245	+	0.539092i	−0.978632	−	0.205619i	$-0.934079\pi$
$857$	−7808.61	+	13524.9i	−0.311245	+	0.539092i	0.667387	+	0.744711i	$0.267413\pi$
$858$		0			0
$859$	−24140.5	−	41812.6i	−0.958863	−	1.66080i	−0.725269	−	0.688465i	$-0.758285\pi$
$859$	−24140.5	−	41812.6i	−0.958863	−	1.66080i	−0.233594	−	0.972334i	$-0.575049\pi$
$860$		0			0
$861$	−15583.9	−	34245.9i	−0.616840	−	1.35551i
$862$		0			0
$863$	17663.6	+	30594.3i	0.696728	+	1.20677i	0.969595	+	0.244716i	$0.0786948\pi$
$863$	17663.6	+	30594.3i	0.696728	+	1.20677i	−0.272867	+	0.962052i	$0.587972\pi$
$864$		0			0
$865$	−7427.18	+	12864.3i	−0.291944	+	0.505662i
$866$		0			0
$867$	−9352.01			−0.366333
$868$		0			0
$869$	7763.15			0.303046
$870$		0			0
$871$	17467.6	−	30254.7i	0.679524	−	1.17697i
$872$		0			0
$873$	−8398.95	−	14547.4i	−0.325615	−	0.563981i
$874$		0			0
$875$	5751.77	−	8054.27i	0.222223	−	0.311182i
$876$		0			0
$877$	1536.20	+	2660.77i	0.0591490	+	0.102449i	0.894084	−	0.447900i	$-0.147828\pi$
$877$	1536.20	+	2660.77i	0.0591490	+	0.102449i	−0.834935	+	0.550349i	$0.814495\pi$
$878$		0			0
$879$	−1952.84	+	3382.41i	−0.0749347	+	0.129791i
$880$		0			0
$881$	−23851.6			−0.912124			−0.456062	−	0.889948i	$-0.650740\pi$
$881$	−23851.6			−0.912124			−0.456062	+	0.889948i	$0.650740\pi$
$882$		0			0
$883$	42506.1			1.61998			0.809991	−	0.586443i	$-0.199472\pi$
$883$	42506.1			1.61998			0.809991	+	0.586443i	$0.199472\pi$
$884$		0			0
$885$	−6359.60	+	11015.2i	−0.241554	+	0.418385i
$886$		0			0
$887$	−13808.2	−	23916.5i	−0.522698	−	0.905340i	−0.999651	−	0.0264111i	$-0.991592\pi$
$887$	−13808.2	−	23916.5i	−0.522698	−	0.905340i	0.476953	−	0.878929i	$-0.341741\pi$
$888$		0			0
$889$	22968.2	−	32162.6i	0.866511	−	1.21339i
$890$		0			0
$891$	−5083.81	−	8805.42i	−0.191149	−	0.331081i
$892$		0			0
$893$	−955.899	+	1655.67i	−0.0358208	+	0.0620434i
$894$		0			0
$895$	−40535.7			−1.51392
$896$		0			0
$897$	83376.5			3.10352
$898$		0			0
$899$	14800.2	−	25634.7i	0.549070	−	0.951017i
$900$		0			0
$901$	−14725.7	−	25505.6i	−0.544488	−	0.943081i
$902$		0			0
$903$	−395.219	−	868.500i	−0.0145649	−	0.0320065i
$904$		0			0
$905$	−26529.7	−	45950.8i	−0.974451	−	1.68780i
$906$		0			0
$907$	−2979.93	+	5161.39i	−0.109093	+	0.188954i	−0.915403	−	0.402539i	$-0.868128\pi$
$907$	−2979.93	+	5161.39i	−0.109093	+	0.188954i	0.806310	+	0.591493i	$0.201461\pi$
$908$		0			0
$909$	41787.1			1.52474
$910$		0			0
$911$	−10070.8			−0.366257			−0.183128	−	0.983089i	$-0.558622\pi$
$911$	−10070.8			−0.366257			−0.183128	+	0.983089i	$0.558622\pi$
$912$		0			0
$913$	−90.1570	+	156.156i	−0.00326808	+	0.00566049i
$914$		0			0
$915$	−20090.7	−	34798.0i	−0.725876	−	1.25725i
$916$		0			0
$917$	26531.6	+	2569.50i	0.955454	+	0.0925324i
$918$		0			0
$919$	16035.4	+	27774.1i	0.575580	+	0.996934i	0.995978	+	0.0895941i	$0.0285570\pi$
$919$	16035.4	+	27774.1i	0.575580	+	0.996934i	−0.420398	+	0.907340i	$0.638110\pi$
$920$		0			0
$921$	18748.5	−	32473.3i	0.670774	−	1.16181i
$922$		0			0
$923$	59484.6			2.12130
$924$		0			0
$925$	−15859.5			−0.563737
$926$		0			0
$927$	4687.38	−	8118.78i	0.166077	−	0.287655i
$928$		0			0
$929$	11040.8	+	19123.3i	0.389922	+	0.675365i	0.992439	−	0.122741i	$-0.0391686\pi$
$929$	11040.8	+	19123.3i	0.389922	+	0.675365i	−0.602517	+	0.798106i	$0.705835\pi$
$930$		0			0
$931$	2503.15	−	2873.12i	0.0881174	−	0.101142i
$932$		0			0
$933$	−1374.76	−	2381.15i	−0.0482396	−	0.0835534i
$934$		0			0
$935$	9922.14	−	17185.6i	0.347047	−	0.601103i
$936$		0			0
$937$	−31573.1			−1.10080			−0.550399	−	0.834902i	$-0.685524\pi$
$937$	−31573.1			−1.10080			−0.550399	+	0.834902i	$0.685524\pi$
$938$		0			0
$939$	−29583.4			−1.02813
$940$		0			0
$941$	−16258.1	+	28159.9i	−0.563230	+	0.975543i	0.433982	+	0.900922i	$0.357108\pi$
$941$	−16258.1	+	28159.9i	−0.563230	+	0.975543i	−0.997212	+	0.0746214i	$0.976225\pi$
$942$		0			0
$943$	−17753.3	−	30749.7i	−0.613074	−	1.06187i
$944$		0			0
$945$	−9324.92	−	903.087i	−0.320994	−	0.0310872i
$946$		0			0
$947$	18909.1	+	32751.6i	0.648854	+	1.12385i	0.983397	+	0.181467i	$0.0580846\pi$
$947$	18909.1	+	32751.6i	0.648854	+	1.12385i	−0.334543	+	0.942380i	$0.608582\pi$
$948$		0			0
$949$	47192.0	−	81738.9i	1.61424	−	2.79595i
$950$		0			0
$951$	39243.3			1.33812
$952$		0			0
$953$	25258.5			0.858554			0.429277	−	0.903173i	$-0.358768\pi$
$953$	25258.5			0.858554			0.429277	+	0.903173i	$0.358768\pi$
$954$		0			0
$955$	−16303.5	+	28238.6i	−0.552430	+	0.956836i
$956$		0			0
$957$	−6224.91	−	10781.9i	−0.210264	−	0.364188i
$958$		0			0
$959$	17502.5	+	38462.1i	0.589350	+	1.29511i
$960$		0			0
$961$	−34852.8	−	60366.8i	−1.16991	−	2.02634i
$962$		0			0
$963$	−13047.9	+	22599.7i	−0.436619	+	0.756246i
$964$		0			0
$965$	−40907.4			−1.36462
$966$		0			0
$967$	57660.1			1.91750			0.958751	−	0.284246i	$-0.0917433\pi$
$967$	57660.1			1.91750			0.958751	+	0.284246i	$0.0917433\pi$
$968$		0			0
$969$	3328.63	−	5765.36i	0.110352	−	0.191135i
$970$		0			0
$971$	17268.3	+	29909.6i	0.570717	+	0.988511i	0.996492	+	0.0836822i	$0.0266680\pi$
$971$	17268.3	+	29909.6i	0.570717	+	0.988511i	−0.425775	+	0.904829i	$0.639999\pi$
$972$		0			0
$973$	16090.7	−	22532.0i	0.530158	−	0.742387i
$974$		0			0
$975$	−27568.1	−	47749.4i	−0.905524	−	1.56841i
$976$		0			0
$977$	−2976.64	+	5155.69i	−0.0974731	+	0.168828i	−0.910638	−	0.413205i	$-0.864409\pi$
$977$	−2976.64	+	5155.69i	−0.0974731	+	0.168828i	0.813165	+	0.582033i	$0.197743\pi$
$978$		0			0
$979$	−13284.7			−0.433690
$980$		0			0
$981$	2821.97			0.0918434
$982$		0			0
$983$	12717.2	−	22026.9i	0.412632	−	0.714699i	−0.582545	−	0.812798i	$-0.697943\pi$
$983$	12717.2	−	22026.9i	0.412632	−	0.714699i	0.995177	+	0.0980995i	$0.0312763\pi$
$984$		0			0
$985$	23384.3	+	40502.9i	0.756434	+	1.31018i
$986$		0			0
$987$	14169.6	−	19841.8i	0.456963	−	0.639890i
$988$		0			0
$989$	−450.237	−	779.833i	−0.0144759	−	0.0250731i
$990$		0			0
$991$	321.536	−	556.917i	0.0103067	−	0.0178517i	−0.860826	−	0.508899i	$-0.830053\pi$
$991$	321.536	−	556.917i	0.0103067	−	0.0178517i	0.871133	+	0.491048i	$0.163386\pi$
$992$		0			0
$993$	31114.0			0.994332
$994$		0			0
$995$	−10295.2			−0.328019
$996$		0			0
$997$	4627.06	−	8014.30i	0.146981	−	0.254579i	−0.783129	−	0.621859i	$-0.786378\pi$
$997$	4627.06	−	8014.30i	0.146981	−	0.254579i	0.930110	+	0.367280i	$0.119711\pi$
$998$		0			0
$999$	−3105.40	−	5378.72i	−0.0983490	−	0.170345i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.4.i.k.193.3		6
4.3	odd	2		448.4.i.l.193.1		6
7.2	even	3	inner	448.4.i.k.65.3		6
8.3	odd	2		56.4.i.a.25.3	yes	6
8.5	even	2		112.4.i.f.81.1		6
24.11	even	2		504.4.s.i.361.3		6
28.23	odd	6		448.4.i.l.65.1		6
56.3	even	6		392.4.a.j.1.3		3
56.11	odd	6		392.4.a.k.1.1		3
56.19	even	6		392.4.i.n.177.1		6
56.27	even	2		392.4.i.n.361.1		6
56.37	even	6		112.4.i.f.65.1		6
56.45	odd	6		784.4.a.bd.1.1		3
56.51	odd	6		56.4.i.a.9.3	✓	6
56.53	even	6		784.4.a.bc.1.3		3
168.107	even	6		504.4.s.i.289.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.4.i.a.9.3	✓	6	56.51	odd	6
56.4.i.a.25.3	yes	6	8.3	odd	2
112.4.i.f.65.1		6	56.37	even	6
112.4.i.f.81.1		6	8.5	even	2
392.4.a.j.1.3		3	56.3	even	6
392.4.a.k.1.1		3	56.11	odd	6
392.4.i.n.177.1		6	56.19	even	6
392.4.i.n.361.1		6	56.27	even	2
448.4.i.k.65.3		6	7.2	even	3	inner
448.4.i.k.193.3		6	1.1	even	1	trivial
448.4.i.l.65.1		6	28.23	odd	6
448.4.i.l.193.1		6	4.3	odd	2
504.4.s.i.289.3		6	168.107	even	6
504.4.s.i.361.3		6	24.11	even	2
784.4.a.bc.1.3		3	56.53	even	6
784.4.a.bd.1.1		3	56.45	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	448.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.82512 - 6.62530i) q^{3} +(7.30445 + 12.6517i) q^{5} +(10.7631 - 15.0717i) q^{7} +(-15.7631 - 27.3025i) q^{9} +O(q^{10})\)	\(q+(3.82512 - 6.62530i) q^{3} +(7.30445 + 12.6517i) q^{5} +(10.7631 - 15.0717i) q^{7} +(-15.7631 - 27.3025i) q^{9} +(8.67092 - 15.0185i) q^{11} -81.5103 q^{13} +111.762 q^{15} +(39.1645 - 67.8350i) q^{17} +(5.55479 + 9.62118i) q^{19} +(-58.6844 - 128.960i) q^{21} +(-66.8537 - 115.794i) q^{23} +(-44.2099 + 76.5737i) q^{25} -34.6265 q^{27} +93.8411 q^{29} +(157.715 - 273.171i) q^{31} +(-66.3346 - 114.895i) q^{33} +(269.300 + 26.0808i) q^{35} +(89.6830 + 155.335i) q^{37} +(-311.787 + 540.031i) q^{39} +265.555 q^{41} +6.73466 q^{43} +(230.281 - 398.859i) q^{45} +(86.0427 + 149.030i) q^{47} +(-111.312 - 324.436i) q^{49} +(-299.618 - 518.954i) q^{51} +(187.998 - 325.621i) q^{53} +253.345 q^{55} +84.9910 q^{57} +(-56.9033 + 98.5594i) q^{59} +(-179.764 - 311.360i) q^{61} +(-581.154 - 56.2828i) q^{63} +(-595.388 - 1031.24i) q^{65} +(-214.299 + 371.176i) q^{67} -1022.89 q^{69} -729.780 q^{71} +(-578.969 + 1002.80i) q^{73} +(338.216 + 585.807i) q^{75} +(-133.028 - 292.331i) q^{77} +(223.827 + 387.680i) q^{79} +(293.153 - 507.756i) q^{81} -10.3976 q^{83} +1144.30 q^{85} +(358.954 - 621.726i) q^{87} +(-383.026 - 663.420i) q^{89} +(-877.304 + 1228.50i) q^{91} +(-1206.56 - 2089.82i) q^{93} +(-81.1494 + 140.555i) q^{95} +532.824 q^{97} -546.722 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} + 13 q^{5} + 20 q^{7} - 50 q^{9}+O(q^{10}) \) 6 * q - q^3 + 13 * q^5 + 20 * q^7 - 50 * q^9	\( 6 q - q^{3} + 13 q^{5} + 20 q^{7} - 50 q^{9} + 11 q^{11} - 140 q^{13} + 82 q^{15} - 97 q^{17} + 81 q^{19} - 345 q^{21} + 191 q^{23} - 12 q^{25} + 230 q^{27} + 324 q^{29} + 597 q^{31} - 343 q^{33} + 815 q^{35} + 217 q^{37} - 806 q^{39} + 1396 q^{41} - 616 q^{43} + 1118 q^{45} + 139 q^{47} + 1030 q^{49} - 1475 q^{51} + 197 q^{53} - 294 q^{55} - 2294 q^{57} - 353 q^{59} + 449 q^{61} - 2094 q^{63} - 906 q^{65} + 519 q^{67} - 5114 q^{69} - 448 q^{71} - 1701 q^{73} + 1132 q^{75} - 1253 q^{77} + 1143 q^{79} - 251 q^{81} - 2760 q^{83} + 2050 q^{85} + 1458 q^{87} - 1749 q^{89} - 616 q^{91} - 601 q^{93} - 2167 q^{95} + 5204 q^{97} + 2188 q^{99}+O(q^{100}) \) 6 * q - q^3 + 13 * q^5 + 20 * q^7 - 50 * q^9 + 11 * q^11 - 140 * q^13 + 82 * q^15 - 97 * q^17 + 81 * q^19 - 345 * q^21 + 191 * q^23 - 12 * q^25 + 230 * q^27 + 324 * q^29 + 597 * q^31 - 343 * q^33 + 815 * q^35 + 217 * q^37 - 806 * q^39 + 1396 * q^41 - 616 * q^43 + 1118 * q^45 + 139 * q^47 + 1030 * q^49 - 1475 * q^51 + 197 * q^53 - 294 * q^55 - 2294 * q^57 - 353 * q^59 + 449 * q^61 - 2094 * q^63 - 906 * q^65 + 519 * q^67 - 5114 * q^69 - 448 * q^71 - 1701 * q^73 + 1132 * q^75 - 1253 * q^77 + 1143 * q^79 - 251 * q^81 - 2760 * q^83 + 2050 * q^85 + 1458 * q^87 - 1749 * q^89 - 616 * q^91 - 601 * q^93 - 2167 * q^95 + 5204 * q^97 + 2188 * q^99

Introduction

L-functions

Modular forms

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