LMFDB - Embedded newform 196.4.f.d.19.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,4,Mod(19,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("196.19");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	196.f (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:	$11.5643743611$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} - 24 x^{17} + 28 x^{16} + 56 x^{15} - 192 x^{14} + 352 x^{13} - 448 x^{12} + \cdots + 1073741824 $ x^20 - 2x^18 - 24x^17 + 28x^16 + 56x^15 - 192x^14 + 352x^13 - 448x^12 + 5376x^11 - 41472x^10 + 43008x^9 - 28672x^8 + 180224x^7 - 786432x^6 + 1835008x^5 + 7340032x^4 - 50331648x^3 - 33554432*x^2 + 1073741824
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{24} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.9
Root			$-2.26510 - 1.69390i$ of defining polynomial
Character	$\chi$	$=$	196.19
Dual form			196.4.f.d.31.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.59951 + 1.11469i) q^{2} +(-1.67134 - 2.89484i) q^{3} +(5.51494 + 5.79529i) q^{4} +(15.9583 + 9.21354i) q^{5} +(-1.11782 - 9.38820i) q^{6} +(7.87623 + 21.2124i) q^{8} +(7.91327 - 13.7062i) q^{9} +(31.2137 + 41.7393i) q^{10} +(-35.6274 + 20.5695i) q^{11} +(7.55911 - 25.6508i) q^{12} +24.8455i q^{13} -61.5957i q^{15} +(-3.17079 + 63.9214i) q^{16} +(41.3826 - 23.8923i) q^{17} +(35.8487 - 26.8086i) q^{18} +(30.9150 - 53.5464i) q^{19} +(34.6141 + 143.295i) q^{20} +(-115.542 + 13.7572i) q^{22} +(64.3994 + 37.1810i) q^{23} +(48.2426 - 58.2535i) q^{24} +(107.279 + 185.812i) q^{25} +(-27.6950 + 64.5862i) q^{26} -143.155 q^{27} +28.8513 q^{29} +(68.6600 - 160.119i) q^{30} +(11.5660 + 20.0328i) q^{31} +(-79.4949 + 162.630i) q^{32} +(119.091 + 68.7571i) q^{33} +(134.207 - 15.9796i) q^{34} +(123.072 - 29.7291i) q^{36} +(51.8900 - 89.8761i) q^{37} +(140.052 - 104.734i) q^{38} +(71.9237 - 41.5252i) q^{39} +(-69.7496 + 411.082i) q^{40} +96.1780i q^{41} -195.747i q^{43} +(-315.689 - 93.0315i) q^{44} +(252.565 - 145.818i) q^{45} +(125.962 + 168.438i) q^{46} +(89.8186 - 155.570i) q^{47} +(190.342 - 97.6553i) q^{48} +(71.7499 + 602.603i) q^{50} +(-138.329 - 79.8641i) q^{51} +(-143.987 + 137.021i) q^{52} +(-218.681 - 378.767i) q^{53} +(-372.134 - 159.573i) q^{54} -758.071 q^{55} -206.678 q^{57} +(74.9993 + 32.1601i) q^{58} +(-286.640 - 496.475i) q^{59} +(356.965 - 339.697i) q^{60} +(-368.470 - 212.736i) q^{61} +(7.73553 + 64.9681i) q^{62} +(-387.930 + 334.147i) q^{64} +(-228.915 + 396.492i) q^{65} +(232.935 + 311.484i) q^{66} +(-728.093 + 420.365i) q^{67} +(366.686 + 108.060i) q^{68} -248.568i q^{69} -1179.04i q^{71} +(353.067 + 59.9061i) q^{72} +(-716.185 + 413.489i) q^{73} +(235.072 - 175.793i) q^{74} +(358.597 - 621.109i) q^{75} +(480.812 - 116.144i) q^{76} +(233.254 - 27.7728i) q^{78} +(282.007 + 162.817i) q^{79} +(-639.543 + 990.864i) q^{80} +(25.6023 + 44.3445i) q^{81} +(-107.208 + 250.016i) q^{82} +507.854 q^{83} +880.530 q^{85} +(218.197 - 508.848i) q^{86} +(-48.2202 - 83.5198i) q^{87} +(-716.937 - 593.731i) q^{88} +(176.826 + 102.090i) q^{89} +(819.088 - 97.5260i) q^{90} +(139.684 + 578.264i) q^{92} +(38.6612 - 66.9632i) q^{93} +(406.897 - 304.288i) q^{94} +(986.704 - 569.674i) q^{95} +(603.651 - 41.6847i) q^{96} -1116.33i q^{97} +651.087i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{4} + 6 q^{5} + 72 q^{8} - 56 q^{9} + 12 q^{10} + 168 q^{12} - 104 q^{16} + 6 q^{17} + 68 q^{18} - 184 q^{22} - 348 q^{24} - 36 q^{25} - 396 q^{26} - 352 q^{29} + 644 q^{30} - 40 q^{32} - 30 q^{33}+ \cdots + 11784 q^{96}+O(q^{100}) $ 20 * q + 4 * q^4 + 6 * q^5 + 72 * q^8 - 56 * q^9 + 12 * q^10 + 168 * q^12 - 104 * q^16 + 6 * q^17 + 68 * q^18 - 184 * q^22 - 348 * q^24 - 36 * q^25 - 396 * q^26 - 352 * q^29 + 644 * q^30 - 40 * q^32 - 30 * q^33 + 208 * q^36 + 258 * q^37 + 1620 * q^38 + 1548 * q^40 - 1248 * q^44 + 504 * q^45 + 232 * q^46 - 864 * q^50 - 2592 * q^52 + 570 * q^53 - 4572 * q^54 + 1452 * q^57 + 2244 * q^58 - 736 * q^60 - 294 * q^61 + 2560 * q^64 - 124 * q^65 + 4272 * q^66 + 6084 * q^68 - 4672 * q^72 - 966 * q^73 + 832 * q^74 - 4056 * q^78 - 7032 * q^80 - 1262 * q^81 - 7692 * q^82 - 2980 * q^85 + 5696 * q^86 - 1396 * q^88 + 3186 * q^89 + 3312 * q^92 - 306 * q^93 + 6780 * q^94 + 11784 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.59951	+	1.11469i	0.919067	+	0.394102i
$2$	2.59951	+	1.11469i	0.919067	+	0.394102i
$3$	−1.67134	−	2.89484i	−0.321649	−	0.557112i	0.659179	−	0.751986i	$-0.270904\pi$
$3$	−1.67134	−	2.89484i	−0.321649	−	0.557112i	−0.980828	+	0.194873i	$0.937570\pi$
$4$	5.51494	+	5.79529i	0.689368	+	0.724411i
$5$	15.9583	+	9.21354i	1.42736	+	0.824084i	0.996911	−	0.0785333i	$-0.0250237\pi$
$5$	15.9583	+	9.21354i	1.42736	+	0.824084i	0.430444	+	0.902617i	$0.358357\pi$
$6$	−1.11782	−	9.38820i	−0.0760581	−	0.638786i
$7$		0			0
$7$		0			0
$8$	7.87623	+	21.2124i	0.348084	+	0.937463i
$9$	7.91327	−	13.7062i	0.293084	−	0.507636i
$10$	31.2137	+	41.7393i	0.987062	+	1.31991i
$11$	−35.6274	+	20.5695i	−0.976551	+	0.563812i	−0.901227	−	0.433347i	$-0.857332\pi$
$11$	−35.6274	+	20.5695i	−0.976551	+	0.563812i	−0.0753237	+	0.997159i	$0.523999\pi$
$12$	7.55911	−	25.6508i	0.181844	−	0.617062i
$13$			24.8455i			0.530069i	0.964239	+	0.265035i	$0.0853834\pi$
$13$			24.8455i			0.530069i	−0.964239	+	0.265035i	$0.914617\pi$
$14$		0			0
$15$		−	61.5957i		−	1.06026i
$16$	−3.17079	+	63.9214i	−0.0495436	+	0.998772i
$17$	41.3826	−	23.8923i	0.590398	−	0.340866i	−0.174857	−	0.984594i	$-0.555946\pi$
$17$	41.3826	−	23.8923i	0.590398	−	0.340866i	0.765255	+	0.643728i	$0.222613\pi$
$18$	35.8487	−	26.8086i	0.469424	−	0.351047i
$19$	30.9150	−	53.5464i	0.373284	−	0.646547i	−0.616785	−	0.787132i	$-0.711565\pi$
$19$	30.9150	−	53.5464i	0.373284	−	0.646547i	0.990069	+	0.140585i	$0.0448984\pi$
$20$	34.6141	+	143.295i	0.386997	+	1.60209i
$21$		0			0
$22$	−115.542	+	13.7572i	−1.11971	+	0.133321i
$23$	64.3994	+	37.1810i	0.583835	+	0.337077i	0.762656	−	0.646804i	$-0.223895\pi$
$23$	64.3994	+	37.1810i	0.583835	+	0.337077i	−0.178821	+	0.983882i	$0.557228\pi$
$24$	48.2426	−	58.2535i	0.410312	−	0.495456i
$25$	107.279	+	185.812i	0.858229	+	1.48650i
$26$	−27.6950	+	64.5862i	−0.208901	+	0.487169i
$27$	−143.155			−1.02038
$28$		0			0
$29$	28.8513			0.184743			0.0923715	−	0.995725i	$-0.470555\pi$
$29$	28.8513			0.184743			0.0923715	+	0.995725i	$0.470555\pi$
$30$	68.6600	−	160.119i	0.417851	−	0.974453i
$31$	11.5660	+	20.0328i	0.0670099	+	0.116065i	0.897584	−	0.440844i	$-0.145321\pi$
$31$	11.5660	+	20.0328i	0.0670099	+	0.116065i	−0.830574	+	0.556908i	$0.811987\pi$
$32$	−79.4949	+	162.630i	−0.439151	+	0.898413i
$33$	119.091	+	68.7571i	0.628213	+	0.362699i
$34$	134.207	−	15.9796i	0.676951	−	0.0806023i
$35$		0			0
$36$	123.072	−	29.7291i	0.569780	−	0.137635i
$37$	51.8900	−	89.8761i	0.230558	−	0.399339i	−0.727414	−	0.686199i	$-0.759278\pi$
$37$	51.8900	−	89.8761i	0.230558	−	0.399339i	0.957973	+	0.286860i	$0.0926114\pi$
$38$	140.052	−	104.734i	0.597878	−	0.447108i
$39$	71.9237	−	41.5252i	0.295308	−	0.170496i
$40$	−69.7496	+	411.082i	−0.275710	+	1.62494i
$41$			96.1780i			0.366353i	0.983080	+	0.183177i	$0.0586380\pi$
$41$			96.1780i			0.366353i	−0.983080	+	0.183177i	$0.941362\pi$
$42$		0			0
$43$		−	195.747i		−	0.694213i	−0.937826	−	0.347107i	$-0.887164\pi$
$43$		−	195.747i		−	0.694213i	0.937826	−	0.347107i	$-0.112836\pi$
$44$	−315.689	−	93.0315i	−1.08163	−	0.318751i
$45$	252.565	−	145.818i	0.836670	−	0.483052i
$46$	125.962	+	168.438i	0.403741	+	0.539887i
$47$	89.8186	−	155.570i	0.278753	−	0.482815i	−0.692322	−	0.721589i	$-0.743412\pi$
$47$	89.8186	−	155.570i	0.278753	−	0.482815i	0.971075	+	0.238774i	$0.0767456\pi$
$48$	190.342	−	97.6553i	0.572364	−	0.293653i
$49$		0			0
$50$	71.7499	+	602.603i	0.202939	+	1.70442i
$51$	−138.329	−	79.8641i	−0.379802	−	0.219279i
$52$	−143.987	+	137.021i	−0.383988	+	0.365413i
$53$	−218.681	−	378.767i	−0.566758	−	0.981654i	−0.996884	−	0.0788851i	$-0.974864\pi$
$53$	−218.681	−	378.767i	−0.566758	−	0.981654i	0.430125	−	0.902769i	$-0.358469\pi$
$54$	−372.134	−	159.573i	−0.937796	−	0.402133i
$55$	−758.071			−1.85851
$56$		0			0
$57$	−206.678			−0.480266
$58$	74.9993	+	32.1601i	0.169791	+	0.0728075i
$59$	−286.640	−	496.475i	−0.632497	−	1.09552i	−0.987040	−	0.160477i	$-0.948697\pi$
$59$	−286.640	−	496.475i	−0.632497	−	1.09552i	0.354542	−	0.935040i	$-0.384637\pi$
$60$	356.965	−	339.697i	0.768067	−	0.730911i
$61$	−368.470	−	212.736i	−0.773405	−	0.446526i	0.0606829	−	0.998157i	$-0.480672\pi$
$61$	−368.470	−	212.736i	−0.773405	−	0.446526i	−0.834088	+	0.551632i	$0.814005\pi$
$62$	7.73553	+	64.9681i	0.0158454	+	0.133080i
$63$		0			0
$64$	−387.930	+	334.147i	−0.757675	+	0.652631i
$65$	−228.915	+	396.492i	−0.436822	+	0.756597i
$66$	232.935	+	311.484i	0.434430	+	0.580924i
$67$	−728.093	+	420.365i	−1.32762	+	0.766504i	−0.984932	−	0.172944i	$-0.944672\pi$
$67$	−728.093	+	420.365i	−1.32762	+	0.766504i	−0.342692	+	0.939448i	$0.611339\pi$
$68$	366.686	+	108.060i	0.653929	+	0.192709i
$69$		−	248.568i		−	0.433682i
$70$		0			0
$71$		−	1179.04i		−	1.97079i	−0.170279	−	0.985396i	$-0.554467\pi$
$71$		−	1179.04i		−	1.97079i	0.170279	−	0.985396i	$-0.445533\pi$
$72$	353.067	+	59.9061i	0.577908	+	0.0980556i
$73$	−716.185	+	413.489i	−1.14826	+	0.662949i	−0.948463	−	0.316888i	$-0.897362\pi$
$73$	−716.185	+	413.489i	−1.14826	+	0.662949i	−0.199798	+	0.979837i	$0.564029\pi$
$74$	235.072	−	175.793i	0.369279	−	0.276156i
$75$	358.597	−	621.109i	0.552097	−	0.956260i
$76$	480.812	−	116.144i	0.725696	−	0.175297i
$77$		0			0
$78$	233.254	−	27.7728i	0.338601	−	0.0403160i
$79$	282.007	+	162.817i	0.401623	+	0.231877i	0.687184	−	0.726483i	$-0.258847\pi$
$79$	282.007	+	162.817i	0.401623	+	0.231877i	−0.285561	+	0.958361i	$0.592180\pi$
$80$	−639.543	+	990.864i	−0.893788	+	1.38477i
$81$	25.6023	+	44.3445i	0.0351198	+	0.0608292i
$82$	−107.208	+	250.016i	−0.144380	+	0.336703i
$83$	507.854			0.671617			0.335808	−	0.941930i	$-0.390991\pi$
$83$	507.854			0.671617			0.335808	+	0.941930i	$0.390991\pi$
$84$		0			0
$85$	880.530			1.12361
$86$	218.197	−	508.848i	0.273591	−	0.638029i
$87$	−48.2202	−	83.5198i	−0.0594224	−	0.102923i
$88$	−716.937	−	593.731i	−0.868474	−	0.719227i
$89$	176.826	+	102.090i	0.210601	+	0.121590i	0.601591	−	0.798805i	$-0.294534\pi$
$89$	176.826	+	102.090i	0.210601	+	0.121590i	−0.390990	+	0.920395i	$0.627867\pi$
$90$	819.088	−	97.5260i	0.959327	−	0.114224i
$91$		0			0
$92$	139.684	+	578.264i	0.158295	+	0.655307i
$93$	38.6612	−	66.9632i	0.0431074	−	0.0746641i
$94$	406.897	−	304.288i	0.446471	−	0.333882i
$95$	986.704	−	569.674i	1.06562	−	0.615235i
$96$	603.651	−	41.6847i	0.641770	−	0.0443170i
$97$		−	1116.33i		−	1.16852i	−0.811566	−	0.584261i	$-0.801385\pi$
$97$		−	1116.33i		−	1.16852i	0.811566	−	0.584261i	$-0.198615\pi$
$98$		0			0
$99$			651.087i			0.660977i
$100$	−485.199	+	1646.45i	−0.485199	+	1.64645i
$101$	3.43081	−	1.98078i	0.00337999	−	0.00195144i	−0.498309	−	0.866999i	$-0.666046\pi$
$101$	3.43081	−	1.98078i	0.00337999	−	0.00195144i	0.501689	+	0.865048i	$0.332712\pi$
$102$	−270.564	−	361.801i	−0.262645	−	0.351212i
$103$	179.406	−	310.741i	0.171626	−	0.297264i	−0.767363	−	0.641213i	$-0.778431\pi$
$103$	179.406	−	310.741i	0.171626	−	0.297264i	0.938988	+	0.343949i	$0.111765\pi$
$104$	−527.032	+	195.689i	−0.496920	+	0.184508i
$105$		0			0
$106$	−146.258	−	1228.37i	−0.134017	−	1.12557i
$107$	803.472	+	463.885i	0.725931	+	0.419116i	0.816932	−	0.576735i	$-0.195673\pi$
$107$	803.472	+	463.885i	0.725931	+	0.419116i	−0.0910010	+	0.995851i	$0.529007\pi$
$108$	−789.493	−	829.626i	−0.703416	−	0.739174i
$109$	−594.270	−	1029.31i	−0.522209	−	0.904492i	−0.999666	−	0.0258371i	$-0.991775\pi$
$109$	−594.270	−	1029.31i	−0.522209	−	0.904492i	0.477458	−	0.878655i	$-0.341558\pi$
$110$	−1970.62	−	845.012i	−1.70810	−	0.732443i
$111$	−346.903			−0.296635
$112$		0			0
$113$	−662.367			−0.551418			−0.275709	−	0.961241i	$-0.588913\pi$
$113$	−662.367			−0.551418			−0.275709	+	0.961241i	$0.588913\pi$
$114$	−537.262	−	230.381i	−0.441396	−	0.189273i
$115$	685.137	+	1186.69i	0.555560	+	0.962258i
$116$	159.113	+	167.201i	0.127356	+	0.133830i
$117$	340.537	+	196.609i	0.269082	+	0.155355i
$118$	−191.710	−	1610.11i	−0.149562	−	1.25612i
$119$		0			0
$120$	1306.59	−	485.142i	0.993958	−	0.369060i
$121$	180.707	−	312.993i	0.135768	−	0.235156i
$122$	−720.708	−	963.739i	−0.534835	−	0.715187i
$123$	278.420	−	160.746i	0.204100	−	0.117837i
$124$	−52.3105	+	177.508i	−0.0378840	+	0.128554i
$125$			1650.28i			1.18084i
$126$		0			0
$127$			1496.04i			1.04529i	0.852549	+	0.522647i	$0.175055\pi$
$127$			1496.04i			1.04529i	−0.852549	+	0.522647i	$0.824945\pi$
$128$	−1380.90	+	436.200i	−0.953558	+	0.301211i
$129$	−566.657	+	327.160i	−0.386755	+	0.223293i
$130$	−1037.03	+	775.518i	−0.699644	+	0.523211i
$131$	−984.794	+	1705.71i	−0.656808	+	1.13762i	0.324630	+	0.945841i	$0.394760\pi$
$131$	−984.794	+	1705.71i	−0.656808	+	1.13762i	−0.981437	+	0.191783i	$0.938573\pi$
$132$	258.311	+	1069.36i	0.170327	+	0.705118i
$133$		0			0
$134$	−2361.26	+	281.148i	−1.52225	+	0.181250i
$135$	−2284.52	−	1318.97i	−1.45644	−	0.840878i
$136$	832.751	+	689.643i	0.525058	+	0.434826i
$137$	896.791	+	1553.29i	0.559256	+	0.968660i	0.997559	+	0.0698322i	$0.0222464\pi$
$137$	896.791	+	1553.29i	0.559256	+	0.968660i	−0.438303	+	0.898827i	$0.644420\pi$
$138$	277.076	−	646.156i	0.170915	−	0.398583i
$139$	306.409			0.186973			0.0934867	−	0.995621i	$-0.470199\pi$
$139$	306.409			0.186973			0.0934867	+	0.995621i	$0.470199\pi$
$140$		0			0
$141$	−600.469			−0.358643
$142$	1314.26	−	3064.93i	0.776692	−	1.81129i
$143$	−511.059	−	885.180i	−0.298859	−	0.517639i
$144$	851.027	+	549.286i	0.492492	+	0.317874i
$145$	460.418	+	265.822i	0.263694	+	0.152244i
$146$	−2322.64	+	276.549i	−1.31660	+	0.156763i
$147$		0			0
$148$	807.028	−	194.944i	0.448225	−	0.108272i
$149$	714.928	−	1238.29i	0.393082	−	0.680838i	−0.599773	−	0.800171i	$-0.704742\pi$
$149$	714.928	−	1238.29i	0.393082	−	0.680838i	0.992854	+	0.119333i	$0.0380756\pi$
$150$	1624.52	−	1214.86i	0.884277	−	0.661285i
$151$	−1079.16	+	623.054i	−0.581595	+	0.335784i	−0.761767	−	0.647851i	$-0.775668\pi$
$151$	−1079.16	+	623.054i	−0.581595	+	0.335784i	0.180172	+	0.983635i	$0.442335\pi$
$152$	1379.34	+	234.037i	0.736048	+	0.124888i
$153$		−	756.264i		−	0.399610i
$154$		0			0
$155$			426.254i			0.220887i
$156$	637.306	+	187.810i	0.327085	+	0.0963899i
$157$	2201.64	−	1271.12i	1.11917	−	0.646154i	0.177982	−	0.984034i	$-0.443043\pi$
$157$	2201.64	−	1271.12i	1.11917	−	0.646154i	0.941189	+	0.337880i	$0.109710\pi$
$158$	551.591	+	737.594i	0.277736	+	0.371391i
$159$	−730.980	+	1266.10i	−0.364594	+	0.631496i
$160$	−2767.00	+	1862.87i	−1.36719	+	0.920457i
$161$		0			0
$162$	17.1233	+	143.813i	0.00830453	+	0.0697469i
$163$	637.434	+	368.022i	0.306305	+	0.176845i	0.645272	−	0.763953i	$-0.276744\pi$
$163$	637.434	+	368.022i	0.306305	+	0.176845i	−0.338967	+	0.940798i	$0.610078\pi$
$164$	−557.379	+	530.416i	−0.265390	+	0.252552i
$165$	1266.99	+	2194.49i	0.597789	+	1.03540i
$166$	1320.17	+	566.098i	0.617261	+	0.264685i
$167$	3110.82			1.44145			0.720726	−	0.693220i	$-0.243809\pi$
$167$	3110.82			1.44145			0.720726	+	0.693220i	$0.243809\pi$
$168$		0			0
$169$	1579.70			0.719027
$170$	2288.95	+	981.515i	1.03267	+	0.442816i
$171$	−489.278	−	847.454i	−0.218807	−	0.378985i
$172$	1134.41	−	1079.54i	0.502896	−	0.478569i
$173$	−2719.50	−	1570.10i	−1.19514	−	0.690015i	−0.235674	−	0.971832i	$-0.575730\pi$
$173$	−2719.50	−	1570.10i	−1.19514	−	0.690015i	−0.959468	+	0.281817i	$0.909063\pi$
$174$	−32.2506	−	270.861i	−0.0140512	−	0.118011i
$175$		0			0
$176$	−1201.86	−	2342.57i	−0.514738	−	1.00328i
$177$	−958.144	+	1659.55i	−0.406884	+	0.704744i
$178$	345.862	+	462.491i	0.145637	+	0.194748i
$179$	206.742	−	119.362i	0.0863274	−	0.0498411i	−0.456215	−	0.889870i	$-0.650795\pi$
$179$	206.742	−	119.362i	0.0863274	−	0.0498411i	0.542542	+	0.840028i	$0.317462\pi$
$180$	2237.94	+	659.506i	0.926701	+	0.273093i
$181$			1947.09i			0.799591i	0.916604	+	0.399796i	$0.130919\pi$
$181$			1947.09i			0.799591i	−0.916604	+	0.399796i	$0.869081\pi$
$182$		0			0
$183$			1422.21i			0.574498i
$184$	−281.473	+	1658.91i	−0.112774	+	0.664655i
$185$	1656.15	−	956.181i	0.658177	−	0.379999i
$186$	175.143	−	130.977i	0.0690438	−	0.0516327i
$187$	−982.903	+	1702.44i	−0.384369	+	0.665746i
$188$	1396.92	−	337.437i	0.541920	−	0.130905i
$189$		0			0
$190$	3199.96	−	381.008i	1.22184	−	0.145480i
$191$	−393.391	−	227.124i	−0.149030	−	0.0860427i	0.423631	−	0.905835i	$-0.360755\pi$
$191$	−393.391	−	227.124i	−0.149030	−	0.0860427i	−0.572661	+	0.819792i	$0.694089\pi$
$192$	1615.66	+	564.522i	0.607295	+	0.212192i
$193$	−1605.08	−	2780.08i	−0.598634	−	1.03686i	−0.993023	−	0.117921i	$-0.962377\pi$
$193$	−1605.08	−	2780.08i	−0.598634	−	1.03686i	0.394389	−	0.918944i	$-0.370956\pi$
$194$	1244.36	−	2901.93i	0.460516	−	1.07395i
$195$	1530.38			0.562013
$196$		0			0
$197$	−4173.52			−1.50940			−0.754698	−	0.656073i	$-0.772216\pi$
$197$	−4173.52			−1.50940			−0.754698	+	0.656073i	$0.772216\pi$
$198$	−725.758	+	1692.51i	−0.260492	+	0.607482i
$199$	2639.30	+	4571.40i	0.940176	+	1.62843i	0.765134	+	0.643871i	$0.222673\pi$
$199$	2639.30	+	4571.40i	0.940176	+	1.62843i	0.175042	+	0.984561i	$0.443994\pi$
$200$	−3096.56	+	3739.13i	−1.09480	+	1.32198i
$201$	2433.78	+	1405.14i	0.854057	+	0.493090i
$202$	11.1264	−	1.32478i	0.00387550	−	0.000461443i
$203$		0			0
$204$	−300.039	−	1242.10i	−0.102975	−	0.426296i
$205$	−886.140	+	1534.84i	−0.301906	+	0.522916i
$206$	812.748	−	607.793i	0.274888	−	0.205568i
$207$	1019.22	−	588.446i	0.342225	−	0.197584i
$208$	−1588.16	−	78.7798i	−0.529418	−	0.0262615i
$209$			2543.62i			0.841848i
$210$		0			0
$211$			871.583i			0.284371i	0.989840	+	0.142185i	$0.0454130\pi$
$211$			871.583i			0.284371i	−0.989840	+	0.142185i	$0.954587\pi$
$212$	989.051	−	3356.20i	0.320416	−	1.08729i
$213$	−3413.13	+	1970.57i	−1.09795	+	0.633903i
$214$	1571.55	+	2101.49i	0.502004	+	0.671286i
$215$	1803.53	−	3123.80i	0.572090	−	0.990889i
$216$	−1127.52	−	3036.66i	−0.355177	−	0.956568i
$217$		0			0
$218$	−397.459	−	3338.12i	−0.123483	−	1.03709i
$219$	2393.97	+	1382.16i	0.738674	+	0.426474i
$220$	−4180.72	−	4393.24i	−1.28120	−	1.34633i
$221$	593.615	+	1028.17i	0.180683	+	0.312952i
$222$	−901.778	−	386.688i	−0.272628	−	0.116904i
$223$	1930.21			0.579624			0.289812	−	0.957084i	$-0.406407\pi$
$223$	1930.21			0.579624			0.289812	+	0.957084i	$0.406407\pi$
$224$		0			0
$225$	3395.70			1.00613
$226$	−1721.83	−	738.333i	−0.506790	−	0.217315i
$227$	988.231	+	1711.67i	0.288948	+	0.500473i	0.973559	−	0.228436i	$-0.0733612\pi$
$227$	988.231	+	1711.67i	0.288948	+	0.500473i	−0.684611	+	0.728909i	$0.740028\pi$
$228$	−1139.82	−	1197.76i	−0.331080	−	0.347910i
$229$	2237.66	+	1291.92i	0.645716	+	0.372804i	0.786813	−	0.617192i	$-0.211730\pi$
$229$	2237.66	+	1291.92i	0.645716	+	0.372804i	−0.141097	+	0.989996i	$0.545063\pi$
$230$	458.233	+	3848.54i	0.131369	+	1.10333i
$231$		0			0
$232$	227.239	+	612.004i	0.0643060	+	0.173190i
$233$	1724.22	−	2986.43i	0.484795	−	0.839690i	−0.515052	−	0.857159i	$-0.672227\pi$
$233$	1724.22	−	2986.43i	0.484795	−	0.839690i	0.999847	+	0.0174686i	$0.00556071\pi$
$234$	666.072	+	890.680i	0.186079	+	0.248827i
$235$	2866.71	−	1655.10i	0.795759	−	0.459432i
$236$	1296.41	−	4399.19i	0.357582	−	1.21340i
$237$		−	1088.49i		−	0.298333i
$238$		0			0
$239$			3647.94i			0.987304i	0.869659	+	0.493652i	$0.164338\pi$
$239$			3647.94i			0.987304i	−0.869659	+	0.493652i	$0.835662\pi$
$240$	3937.28	+	195.307i	1.05896	+	0.0525292i
$241$	2194.49	−	1266.99i	0.586553	−	0.338646i	−0.177180	−	0.984178i	$-0.556698\pi$
$241$	2194.49	−	1266.99i	0.586553	−	0.338646i	0.763733	+	0.645532i	$0.223364\pi$
$242$	818.639	−	612.198i	0.217455	−	0.162618i
$243$	−1847.01	+	3199.12i	−0.487597	+	0.844542i
$244$	−799.222	−	3308.62i	−0.209692	−	0.868084i
$245$		0			0
$246$	902.938	−	107.510i	0.234021	−	0.0278641i
$247$	1330.39	+	768.099i	0.342714	+	0.197866i
$248$	−333.848	+	403.125i	−0.0854813	+	0.103220i
$249$	−848.795	−	1470.16i	−0.216025	−	0.374166i
$250$	−1839.54	+	4289.92i	−0.465372	+	1.08527i
$251$	−5658.23			−1.42289			−0.711443	−	0.702744i	$-0.751958\pi$
$251$	−5658.23			−1.42289			−0.711443	+	0.702744i	$0.751958\pi$
$252$		0			0
$253$	−3059.18			−0.760193
$254$	−1667.62	+	3888.98i	−0.411952	+	0.960695i
$255$	−1471.66	−	2548.99i	−0.361408	−	0.625977i
$256$	−4075.89	−	405.362i	−0.995091	−	0.0989655i
$257$	−4328.82	−	2499.25i	−1.05068	−	0.606610i	−0.127840	−	0.991795i	$-0.540804\pi$
$257$	−4328.82	−	2499.25i	−1.05068	−	0.606610i	−0.922840	+	0.385185i	$0.874138\pi$
$258$	−1837.71	+	218.810i	−0.443454	+	0.0528006i
$259$		0			0
$260$	−3560.24	+	860.004i	−0.849218	+	0.205135i
$261$	228.308	−	395.441i	0.0541452	−	0.0937822i
$262$	−4461.32	+	3336.29i	−1.05199	+	0.786704i
$263$	−1646.99	+	950.892i	−0.386152	+	0.222945i	−0.680491	−	0.732756i	$-0.738234\pi$
$263$	−1646.99	+	950.892i	−0.386152	+	0.222945i	0.294340	+	0.955701i	$0.404900\pi$
$264$	−520.514	+	3067.74i	−0.121346	+	0.715176i
$265$		−	8059.32i		−	1.86823i
$266$		0			0
$267$		−	682.509i		−	0.156438i
$268$	−6451.53	−	1901.22i	−1.47048	−	0.433342i
$269$	−6976.20	+	4027.71i	−1.58121	+	0.912913i	−0.586530	+	0.809928i	$0.699506\pi$
$269$	−6976.20	+	4027.71i	−1.58121	+	0.912913i	−0.994683	+	0.102986i	$0.967160\pi$
$270$	−4468.39	−	5975.19i	−1.00718	−	1.34681i
$271$	2189.04	−	3791.53i	0.490682	−	0.849886i	−0.509261	−	0.860612i	$-0.670081\pi$
$271$	2189.04	−	3791.53i	0.490682	−	0.849886i	0.999942	+	0.0107264i	$0.00341438\pi$
$272$	1396.01	+	2720.99i	0.311197	+	0.606560i
$273$		0			0
$274$	599.791	+	5037.44i	0.132243	+	1.11067i
$275$	−7644.11	−	4413.33i	−1.67621	−	0.967759i
$276$	1440.52	−	1370.84i	0.314164	−	0.298967i
$277$	1602.26	+	2775.19i	0.347547	+	0.601968i	0.985813	−	0.167847i	$-0.0536815\pi$
$277$	1602.26	+	2775.19i	0.347547	+	0.601968i	−0.638266	+	0.769815i	$0.720348\pi$
$278$	796.515	+	341.551i	0.171841	+	0.0736865i
$279$	366.098			0.0785581
$280$		0			0
$281$	6258.33			1.32861			0.664307	−	0.747460i	$-0.268727\pi$
$281$	6258.33			1.32861			0.664307	+	0.747460i	$0.268727\pi$
$282$	−1560.93	−	669.335i	−0.329617	−	0.141342i
$283$	−3029.37	−	5247.02i	−0.636316	−	1.10213i	−0.986235	−	0.165351i	$-0.947124\pi$
$283$	−3029.37	−	5247.02i	−0.636316	−	1.10213i	0.349919	−	0.936780i	$-0.386209\pi$
$284$	6832.87	−	6502.33i	1.42766	−	1.35860i
$285$	−3298.23	−	1904.23i	−0.685510	−	0.395779i
$286$	−341.806	−	2870.71i	−0.0706692	−	0.593526i
$287$		0			0
$288$	1599.97	+	2376.51i	0.327359	+	0.486240i
$289$	−1314.82	+	2277.33i	−0.267620	+	0.463532i
$290$	900.554	+	1204.23i	0.182353	+	0.243844i
$291$	−3231.61	+	1865.77i	−0.650998	+	0.375854i
$292$	−6346.01	−	1870.13i	−1.27182	−	0.374798i
$293$			457.644i			0.0912486i	0.998959	+	0.0456243i	$0.0145277\pi$
$293$			457.644i			0.0912486i	−0.998959	+	0.0456243i	$0.985472\pi$
$294$		0			0
$295$		−	10563.9i		−	2.08492i
$296$	2315.18	+	392.825i	0.454619	+	0.0771367i
$297$	5100.24	−	2944.63i	0.996451	−	0.575301i
$298$	3238.77	−	2422.03i	0.629588	−	0.470821i
$299$	−923.780	+	1600.03i	−0.178674	+	0.309473i
$300$	5577.15	−	1347.20i	1.07332	−	0.259270i
$301$		0			0
$302$	−3499.80	+	416.710i	−0.666858	+	0.0794005i
$303$	−11.4681	−	6.62110i	−0.00217434	−	0.00125535i
$304$	3324.74	+	2145.92i	0.627259	+	0.404858i
$305$	−3920.10	−	6789.82i	−0.735949	−	1.27470i
$306$	842.997	−	1965.92i	0.157487	−	0.367268i
$307$	4195.62			0.779989			0.389995	−	0.920817i	$-0.372477\pi$
$307$	4195.62			0.779989			0.389995	+	0.920817i	$0.372477\pi$
$308$		0			0
$309$	−1199.39			−0.220813
$310$	−475.140	+	1108.05i	−0.0870520	+	0.203010i
$311$	−3254.20	−	5636.44i	−0.593341	−	1.02770i	−0.993779	−	0.111372i	$-0.964475\pi$
$311$	−3254.20	−	5636.44i	−0.593341	−	1.02770i	0.400438	−	0.916324i	$-0.368858\pi$
$312$	1447.34	+	1198.61i	0.262626	+	0.217494i
$313$	7481.59	+	4319.50i	1.35107	+	0.780040i	0.988399	−	0.151878i	$-0.0485320\pi$
$313$	7481.59	+	4319.50i	1.35107	+	0.780040i	0.362670	+	0.931918i	$0.381865\pi$
$314$	7140.09	−	850.146i	1.28324	−	0.152792i
$315$		0			0
$316$	611.682	+	2532.24i	0.108892	+	0.450789i
$317$	−463.165	+	802.226i	−0.0820629	+	0.142137i	−0.904136	−	0.427245i	$-0.859484\pi$
$317$	−463.165	+	802.226i	−0.0820629	+	0.142137i	0.822073	+	0.569382i	$0.192818\pi$
$318$	−3311.49	+	2476.42i	−0.583960	+	0.436700i
$319$	−1027.90	+	593.455i	−0.180411	+	0.104160i
$320$	−9269.39	+	1758.22i	−1.61930	+	0.307149i
$321$		−	3101.23i		−	0.539233i
$322$		0			0
$323$		−	2954.52i		−	0.508960i
$324$	−115.794	+	392.930i	−0.0198549	+	0.0673749i
$325$	−4616.59	+	2665.39i	−0.787946	+	0.454921i
$326$	1246.79	+	1667.22i	0.211820	+	0.283248i
$327$	−1986.45	+	3440.63i	−0.335936	+	0.581858i
$328$	−2040.16	+	757.520i	−0.343443	+	0.127522i
$329$		0			0
$330$	847.387	+	7116.92i	0.141355	+	1.18719i
$331$	8260.72	+	4769.33i	1.37175	+	0.791982i	0.991149	−	0.132756i	$-0.0423828\pi$
$331$	8260.72	+	4769.33i	1.37175	+	0.791982i	0.380604	+	0.924738i	$0.375716\pi$
$332$	2800.79	+	2943.16i	0.462991	+	0.486527i
$333$	−821.238	−	1422.43i	−0.135146	−	0.234080i
$334$	8086.62	+	3467.59i	1.32479	+	0.568078i
$335$	−15492.2			−2.52665
$336$		0			0
$337$	4736.32			0.765589			0.382795	−	0.923833i	$-0.374962\pi$
$337$	4736.32			0.765589			0.382795	+	0.923833i	$0.374962\pi$
$338$	4106.46	+	1760.87i	0.660834	+	0.283370i
$339$	1107.04	+	1917.45i	0.177363	+	0.307202i
$340$	4856.07	+	5102.92i	0.774581	+	0.813956i
$341$	−824.130	−	475.812i	−0.130877	−	0.0755620i
$342$	−327.238	−	2748.36i	−0.0517398	−	0.434545i
$343$		0			0
$344$	4152.26	−	1541.75i	0.650800	−	0.241644i
$345$	2290.19	−	3966.73i	0.357391	−	0.619019i
$346$	−5319.20	−	7112.89i	−0.826479	−	1.10518i
$347$	−1694.40	+	978.260i	−0.262133	+	0.151342i	−0.625307	−	0.780379i	$-0.715026\pi$
$347$	−1694.40	+	978.260i	−0.262133	+	0.151342i	0.363174	+	0.931721i	$0.381693\pi$
$348$	218.090	−	740.057i	0.0335944	−	0.113998i
$349$			9739.50i			1.49382i	0.664924	+	0.746911i	$0.268464\pi$
$349$			9739.50i			1.49382i	−0.664924	+	0.746911i	$0.731536\pi$
$350$		0			0
$351$		−	3556.76i		−	0.540871i
$352$	−513.022	−	7429.25i	−0.0776823	−	1.12494i
$353$	2590.09	−	1495.39i	0.390528	−	0.225471i	−0.291861	−	0.956461i	$-0.594274\pi$
$353$	2590.09	−	1495.39i	0.390528	−	0.225471i	0.682389	+	0.730989i	$0.260941\pi$
$354$	−4340.59	+	3246.00i	−0.651695	+	0.487353i
$355$	10863.1	−	18815.5i	1.62410	−	2.81302i
$356$	383.540	+	1587.78i	0.0571000	+	0.236382i
$357$		0			0
$358$	670.480	−	79.8318i	0.0989831	−	0.0117856i
$359$	1144.24	+	660.628i	0.168219	+	0.0971215i	0.581746	−	0.813371i	$-0.302370\pi$
$359$	1144.24	+	660.628i	0.168219	+	0.0971215i	−0.413527	+	0.910492i	$0.635703\pi$
$360$	5082.41	+	4209.00i	0.744074	+	0.616205i
$361$	1518.02	+	2629.29i	0.221318	+	0.383334i
$362$	−2170.40	+	5061.49i	−0.315120	+	0.734878i
$363$	−1208.09			−0.174678
$364$		0			0
$365$	−15238.8			−2.18530
$366$	−1585.32	+	3697.07i	−0.226411	+	0.528002i
$367$	3367.76	+	5833.14i	0.479008	+	0.829666i	0.999710	−	0.0240726i	$-0.00766327\pi$
$367$	3367.76	+	5833.14i	0.479008	+	0.829666i	−0.520703	+	0.853738i	$0.674330\pi$
$368$	−2580.86	+	3998.61i	−0.365589	+	0.566418i
$369$	1318.23	+	761.082i	0.185974	+	0.107372i
$370$	5371.04	−	639.511i	0.754667	−	0.0898557i
$371$		0			0
$372$	601.286	−	145.245i	0.0838044	−	0.0202436i
$373$	−104.742	+	181.419i	−0.0145398	+	0.0251837i	−0.873204	−	0.487355i	$-0.837962\pi$
$373$	−104.742	+	181.419i	−0.0145398	+	0.0251837i	0.858664	+	0.512539i	$0.171295\pi$
$374$	−4452.76	+	3329.88i	−0.615632	+	0.460385i
$375$	4777.29	−	2758.17i	0.657862	−	0.379817i
$376$	4007.45	+	679.957i	0.549650	+	0.0932610i
$377$			716.824i			0.0979265i
$378$		0			0
$379$		−	1205.99i		−	0.163450i	−0.996655	−	0.0817250i	$-0.973957\pi$
$379$		−	1205.99i		−	0.163450i	0.996655	−	0.0817250i	$-0.0260429\pi$
$380$	8743.04	+	2576.52i	1.18029	+	0.347822i
$381$	4330.81	−	2500.39i	0.582346	−	0.336218i
$382$	−769.453	−	1028.92i	−0.103059	−	0.137812i
$383$	−1590.45	+	2754.73i	−0.212188	+	0.367520i	−0.952399	−	0.304854i	$-0.901392\pi$
$383$	−1590.45	+	2754.73i	−0.212188	+	0.367520i	0.740211	+	0.672375i	$0.234726\pi$
$384$	3570.68	+	3268.44i	0.474519	+	0.434354i
$385$		0			0
$386$	−1073.51	−	9016.03i	−0.141555	−	1.18887i
$387$	−2682.95	−	1549.00i	−0.352408	−	0.203463i
$388$	6469.48	−	6156.52i	0.846490	−	0.805541i
$389$	4006.02	+	6938.63i	0.522142	+	0.904377i	0.999668	+	0.0257595i	$0.00820040\pi$
$389$	4006.02	+	6938.63i	0.522142	+	0.904377i	−0.477526	+	0.878618i	$0.658466\pi$
$390$	3978.23	+	1705.89i	0.516527	+	0.221490i
$391$	3553.36			0.459593
$392$		0			0
$393$	6583.69			0.845046
$394$	−10849.1	−	4652.17i	−1.38724	−	0.594855i
$395$	3000.24	+	5196.56i	0.382173	+	0.661943i
$396$	−3773.24	+	3590.71i	−0.478819	+	0.455656i
$397$	−10496.5	−	6060.15i	−1.32696	−	0.766121i	−0.342132	−	0.939652i	$-0.611149\pi$
$397$	−10496.5	−	6060.15i	−1.32696	−	0.766121i	−0.984828	+	0.173531i	$0.944482\pi$
$398$	1765.21	+	14825.4i	0.222317	+	1.86716i
$399$		0			0
$400$	−12217.5	+	6268.23i	−1.52719	+	0.783529i
$401$	−5497.13	+	9521.31i	−0.684573	+	1.18571i	0.288998	+	0.957330i	$0.406678\pi$
$401$	−5497.13	+	9521.31i	−0.684573	+	1.18571i	−0.973571	+	0.228385i	$0.926655\pi$
$402$	4760.35	+	6365.59i	0.590608	+	0.789768i
$403$	−497.726	+	287.362i	−0.0615223	+	0.0355199i
$404$	30.3999	+	8.95866i	0.00374370	+	0.00110324i
$405$			943.552i			0.115767i
$406$		0			0
$407$			4269.40i			0.519966i
$408$	604.598	−	3563.31i	0.0733629	−	0.432377i
$409$	1739.78	−	1004.46i	0.210333	−	0.121436i	−0.391133	−	0.920334i	$-0.627917\pi$
$409$	1739.78	−	1004.46i	0.210333	−	0.121436i	0.601466	+	0.798898i	$0.294583\pi$
$410$	−4014.40	+	3002.07i	−0.483554	+	0.361613i
$411$	2997.68	−	5192.14i	0.359768	−	0.623137i
$412$	2790.25	−	674.007i	0.333655	−	0.0805969i
$413$		0			0
$414$	3305.41	−	393.564i	0.392396	−	0.0467213i
$415$	8104.49	+	4679.13i	0.958636	+	0.553469i
$416$	−4040.63	−	1975.09i	−0.476221	−	0.232781i
$417$	−512.113	−	887.006i	−0.0601398	−	0.104165i
$418$	−2835.35	+	6612.18i	−0.331773	+	0.773714i
$419$	−6662.83			−0.776850			−0.388425	−	0.921480i	$-0.626981\pi$
$419$	−6662.83			−0.776850			−0.388425	+	0.921480i	$0.626981\pi$
$420$		0			0
$421$	5859.67			0.678344			0.339172	−	0.940724i	$-0.389853\pi$
$421$	5859.67			0.678344			0.339172	+	0.940724i	$0.389853\pi$
$422$	−971.543	+	2265.69i	−0.112071	+	0.261356i
$423$	−1421.52	−	2462.14i	−0.163396	−	0.283010i
$424$	6312.17	−	7622.01i	0.722986	−	0.873013i
$425$	8878.94	+	5126.26i	1.01339	+	0.585083i
$426$	−11069.1	+	1317.95i	−1.25891	+	0.149895i
$427$		0			0
$428$	1742.76	+	7214.65i	0.196821	+	0.814798i
$429$	−1708.30	+	2958.87i	−0.192256	+	0.332996i
$430$	8170.35	−	6109.99i	0.916300	−	0.685232i
$431$	−3178.02	+	1834.83i	−0.355174	+	0.205060i	−0.666962	−	0.745092i	$-0.732406\pi$
$431$	−3178.02	+	1834.83i	−0.355174	+	0.205060i	0.311788	+	0.950152i	$0.399072\pi$
$432$	453.915	−	9150.68i	0.0505532	−	1.01913i
$433$		−	8282.34i		−	0.919224i	−0.888120	−	0.459612i	$-0.847989\pi$
$433$		−	8282.34i		−	0.919224i	0.888120	−	0.459612i	$-0.152011\pi$
$434$		0			0
$435$		−	1777.11i		−	0.195876i
$436$	2687.76	−	9120.53i	0.295230	−	1.00182i
$437$	3981.82	−	2298.90i	0.435872	−	0.251651i
$438$	4682.49	+	6261.47i	0.510817	+	0.683070i
$439$	−4840.93	+	8384.73i	−0.526298	+	0.911575i	0.473233	+	0.880938i	$0.343087\pi$
$439$	−4840.93	+	8384.73i	−0.526298	+	0.911575i	−0.999531	+	0.0306374i	$0.990246\pi$
$440$	−5970.74	−	16080.5i	−0.646918	−	1.74229i
$441$		0			0
$442$	397.021	+	3334.44i	0.0427248	+	0.358831i
$443$	−7154.34	−	4130.56i	−0.767298	−	0.443000i	0.0646117	−	0.997910i	$-0.479419\pi$
$443$	−7154.34	−	4130.56i	−0.767298	−	0.443000i	−0.831910	+	0.554911i	$0.812752\pi$
$444$	−1913.15	−	2010.40i	−0.204491	−	0.214886i
$445$	1881.23	+	3258.38i	0.200402	+	0.347106i
$446$	5017.60	+	2151.58i	0.532713	+	0.228431i
$447$	−4779.54			−0.505737
$448$		0			0
$449$	−73.1562			−0.00768921			−0.00384461	−	0.999993i	$-0.501224\pi$
$449$	−73.1562			−0.00768921			−0.00384461	+	0.999993i	$0.501224\pi$
$450$	8827.16	+	3785.14i	0.924703	+	0.396518i
$451$	−1978.33	−	3426.57i	−0.206554	−	0.357762i
$452$	−3652.92	−	3838.61i	−0.380130	−	0.399454i
$453$	3607.28	+	2082.67i	0.374139	+	0.216009i
$454$	660.948	+	5551.07i	0.0683256	+	0.573843i
$455$		0			0
$456$	−1627.84	−	4384.13i	−0.167173	−	0.450231i
$457$	6586.17	−	11407.6i	0.674153	−	1.16767i	−0.302563	−	0.953129i	$-0.597842\pi$
$457$	6586.17	−	11407.6i	0.674153	−	1.16767i	0.976716	−	0.214538i	$-0.0688245\pi$
$458$	4376.75	+	5852.65i	0.446533	+	0.597110i
$459$	−5924.14	+	3420.30i	−0.602429	+	0.347813i
$460$	−3098.74	+	10515.1i	−0.314085	+	1.06580i
$461$			12655.0i			1.27853i	0.768985	+	0.639267i	$0.220762\pi$
$461$			12655.0i			1.27853i	−0.768985	+	0.639267i	$0.779238\pi$
$462$		0			0
$463$			852.596i			0.0855799i	0.999084	+	0.0427899i	$0.0136246\pi$
$463$			852.596i			0.0855799i	−0.999084	+	0.0427899i	$0.986375\pi$
$464$	−91.4813	+	1844.21i	−0.00915283	+	0.184516i
$465$	1233.94	−	712.414i	0.123059	−	0.0710482i
$466$	7811.07	−	5841.31i	0.776483	−	0.580673i
$467$	−5462.60	+	9461.49i	−0.541282	+	0.937528i	0.457549	+	0.889185i	$0.348728\pi$
$467$	−5462.60	+	9461.49i	−0.541282	+	0.937528i	−0.998831	+	0.0483436i	$0.984606\pi$
$468$	738.635	+	3057.80i	0.0729560	+	0.302023i
$469$		0			0
$470$	9296.96	−	1106.96i	0.912419	−	0.108639i
$471$	−7359.36	−	4248.93i	−0.719961	−	0.415669i
$472$	8273.77	−	9990.67i	0.806846	−	0.974275i
$473$	4026.42	+	6973.96i	0.391406	+	0.677935i
$474$	1213.32	−	2829.54i	0.117573	−	0.274188i
$475$	13266.1			1.28145
$476$		0			0
$477$	−6921.93			−0.664431
$478$	−4066.32	+	9482.88i	−0.389098	+	0.907399i
$479$	−5330.56	−	9232.81i	−0.508475	−	0.880705i	−0.999952	−	0.00981425i	$-0.996876\pi$
$479$	−5330.56	−	9232.81i	−0.508475	−	0.880705i	0.491477	−	0.870891i	$-0.336457\pi$
$480$	10017.3	+	4896.55i	0.952554	+	0.465616i
$481$	2233.01	+	1289.23i	0.211677	+	0.122212i
$482$	7116.89	−	847.384i	0.672542	−	0.0800774i
$483$		0			0
$484$	2810.47	−	678.892i	0.263944	−	0.0637577i
$485$	10285.4	−	17814.8i	0.962960	−	1.66789i
$486$	−8367.36	+	6257.32i	−0.780969	+	0.584028i
$487$	46.9282	−	27.0940i	0.00436657	−	0.00252104i	−0.497815	−	0.867283i	$-0.665864\pi$
$487$	46.9282	−	27.0940i	0.00436657	−	0.00252104i	0.502182	+	0.864762i	$0.332531\pi$
$488$	1610.48	−	9491.68i	0.149392	−	0.880467i
$489$		−	2460.36i		−	0.227528i
$490$		0			0
$491$		−	5628.07i		−	0.517294i	−0.965972	−	0.258647i	$-0.916723\pi$
$491$		−	5628.07i		−	0.517294i	0.965972	−	0.258647i	$-0.0832766\pi$
$492$	2467.04	+	727.020i	0.226062	+	0.0666191i
$493$	1193.94	−	689.322i	0.109072	−	0.0629727i
$494$	2602.17	+	3479.65i	0.236998	+	0.316917i
$495$	−5998.81	+	10390.3i	−0.544700	+	0.943449i
$496$	−1317.20	+	675.793i	−0.119242	+	0.0611774i
$497$		0			0
$498$	−567.690	−	4767.83i	−0.0510819	−	0.429019i
$499$	−536.728	−	309.880i	−0.0481508	−	0.0277999i	0.475731	−	0.879591i	$-0.342183\pi$
$499$	−536.728	−	309.880i	−0.0481508	−	0.0277999i	−0.523882	+	0.851791i	$0.675517\pi$
$500$	−9563.84	+	9101.19i	−0.855416	+	0.814035i
$501$	−5199.23	−	9005.33i	−0.463641	−	0.803050i
$502$	−14708.7	−	6307.16i	−1.30773	−	0.560762i
$503$	18680.1			1.65587			0.827935	−	0.560823i	$-0.189515\pi$
$503$	18680.1			1.65587			0.827935	+	0.560823i	$0.189515\pi$
$504$		0			0
$505$	73.0000			0.00643259
$506$	−7952.37	−	3410.02i	−0.698668	−	0.299593i
$507$	−2640.21	−	4572.98i	−0.231274	−	0.400579i
$508$	−8670.00	+	8250.59i	−0.757223	+	0.720592i
$509$	−3084.16	−	1780.64i	−0.268572	−	0.155060i	0.359667	−	0.933081i	$-0.382890\pi$
$509$	−3084.16	−	1780.64i	−0.268572	−	0.155060i	−0.628238	+	0.778021i	$0.716224\pi$
$510$	−984.275	−	8266.58i	−0.0854596	−	0.717746i
$511$		0			0
$512$	−10143.5	−	5597.09i	−0.875553	−	0.483123i
$513$	−4425.65	+	7665.44i	−0.380891	+	0.659722i
$514$	−8466.96	−	11322.1i	−0.726579	−	0.971590i
$515$	5726.05	−	3305.93i	0.489941	−	0.282868i
$516$	−5021.07	−	1479.68i	−0.428372	−	0.126239i
$517$			7390.09i			0.628657i
$518$		0			0
$519$			10496.7i			0.887771i
$520$	−10213.5	−	1732.96i	−0.861333	−	0.146145i
$521$	−10004.0	+	5775.82i	−0.841235	+	0.485687i	−0.857684	−	0.514177i	$-0.828097\pi$
$521$	−10004.0	+	5775.82i	−0.841235	+	0.485687i	0.0164486	+	0.999865i	$0.494764\pi$
$522$	1034.28	−	773.462i	0.0867228	−	0.0648534i
$523$	2135.62	−	3699.00i	0.178554	−	0.309265i	−0.762831	−	0.646598i	$-0.776191\pi$
$523$	2135.62	−	3699.00i	0.178554	−	0.309265i	0.941386	+	0.337332i	$0.109525\pi$
$524$	−15316.2	+	3699.74i	−1.27689	+	0.308443i
$525$		0			0
$526$	−5341.33	+	635.974i	−0.442762	+	0.0527182i
$527$	957.260	+	552.674i	0.0791250	+	0.0456829i
$528$	−4772.66	+	7394.43i	−0.393377	+	0.609472i
$529$	−3318.65	−	5748.06i	−0.272758	−	0.472431i
$530$	8983.62	−	20950.3i	0.736271	−	1.71702i
$531$	−9073.03			−0.741499
$532$		0			0
$533$	−2389.59			−0.194192
$534$	760.785	−	1774.19i	0.0616524	−	0.143777i
$535$	8548.04	+	14805.6i	0.690774	+	1.19646i
$536$	−14651.6	−	12133.7i	−1.18069	−	0.977791i
$537$	−691.070	−	398.990i	−0.0555342	−	0.0320627i
$538$	−22624.4	+	2693.81i	−1.81302	+	0.215870i
$539$		0			0
$540$	−4955.18	−	20513.5i	−0.394884	−	1.63474i
$541$	−4878.48	+	8449.78i	−0.387694	+	0.671505i	−0.992139	−	0.125142i	$-0.960061\pi$
$541$	−4878.48	+	8449.78i	−0.387694	+	0.671505i	0.604445	+	0.796647i	$0.293395\pi$
$542$	9916.82	−	7416.04i	0.785911	−	0.587724i
$543$	5636.51	−	3254.24i	0.445462	−	0.257188i
$544$	595.896	+	8629.38i	0.0469647	+	0.680113i
$545$		−	21901.3i		−	1.72138i
$546$		0			0
$547$			19891.0i			1.55480i	0.629005	+	0.777401i	$0.283463\pi$
$547$			19891.0i			1.55480i	−0.629005	+	0.777401i	$0.716537\pi$
$548$	−4056.00	+	13763.5i	−0.316175	+	1.07289i
$549$	−5831.60	+	3366.87i	−0.453345	+	0.261739i
$550$	−14951.5	−	19993.3i	−1.15915	−	1.55003i
$551$	891.938	−	1544.88i	0.0689616	−	0.119445i
$552$	5272.72	−	1957.78i	0.406561	−	0.150958i
$553$		0			0
$554$	1071.62	+	9000.17i	0.0821819	+	0.690218i
$555$	−5535.98	−	3196.20i	−0.423404	−	0.244453i
$556$	1689.83	+	1775.73i	0.128893	+	0.135446i
$557$	−3043.39	−	5271.30i	−0.231513	−	0.400992i	0.726741	−	0.686912i	$-0.241034\pi$
$557$	−3043.39	−	5271.30i	−0.231513	−	0.400992i	−0.958253	+	0.285920i	$0.907701\pi$
$558$	951.677	+	408.085i	0.0722002	+	0.0309599i
$559$	4863.44			0.367981
$560$		0			0
$561$	6571.05			0.494527
$562$	16268.6	+	6976.08i	1.22108	+	0.523609i
$563$	4067.94	+	7045.87i	0.304517	+	0.527439i	0.977154	−	0.212534i	$-0.0681716\pi$
$563$	4067.94	+	7045.87i	0.304517	+	0.527439i	−0.672637	+	0.739973i	$0.734838\pi$
$564$	−3311.55	−	3479.89i	−0.247237	−	0.259805i
$565$	−10570.3	−	6102.75i	−0.787070	−	0.454415i
$566$	−2026.10	−	17016.5i	−0.150465	−	1.26371i
$567$		0			0
$568$	25010.2	−	9286.39i	1.84755	−	0.686000i
$569$	−11495.9	+	19911.5i	−0.846985	+	1.46702i	0.0369008	+	0.999319i	$0.488251\pi$
$569$	−11495.9	+	19911.5i	−0.846985	+	1.46702i	−0.883886	+	0.467702i	$0.845082\pi$
$570$	−6451.17	−	8626.58i	−0.474052	−	0.633908i
$571$	16493.6	−	9522.59i	1.20882	−	0.697912i	0.246318	−	0.969189i	$-0.420779\pi$
$571$	16493.6	−	9522.59i	1.20882	−	0.697912i	0.962501	+	0.271277i	$0.0874459\pi$
$572$	2311.41	−	7843.45i	0.168960	−	0.573341i
$573$			1518.41i			0.110702i
$574$		0			0
$575$			15954.9i			1.15716i
$576$	1510.09	+	7961.23i	0.109237	+	0.575899i
$577$	−13902.1	+	8026.36i	−1.00303	+	0.579102i	−0.909144	−	0.416481i	$-0.863263\pi$
$577$	−13902.1	+	8026.36i	−1.00303	+	0.579102i	−0.0938892	+	0.995583i	$0.529930\pi$
$578$	−5956.40	+	4454.35i	−0.428640	+	0.320547i
$579$	−5365.27	+	9292.92i	−0.385100	+	0.667013i
$580$	998.660	+	4134.25i	0.0714950	+	0.295975i
$581$		0			0
$582$	−10480.4	+	1247.86i	−0.746435	+	0.0888755i
$583$	15582.1	+	8996.32i	1.10694	+	0.639090i
$584$	−14411.9	−	11935.2i	−1.02118	−	0.845691i
$585$	3622.93	+	6275.10i	0.256051	+	0.443493i
$586$	−510.130	+	1189.65i	−0.0359612	+	0.0838635i
$587$	21155.6			1.48754			0.743770	−	0.668436i	$-0.233036\pi$
$587$	21155.6			1.48754			0.743770	+	0.668436i	$0.233036\pi$
$588$		0			0
$589$	1430.25			0.100055
$590$	11775.4	−	27460.9i	0.821672	−	1.91618i
$591$	6975.36	+	12081.7i	0.485495	+	0.840903i
$592$	5580.47	+	3601.86i	0.387426	+	0.250060i
$593$	1240.18	+	716.018i	0.0858821	+	0.0495840i	0.542326	−	0.840168i	$-0.317544\pi$
$593$	1240.18	+	716.018i	0.0858821	+	0.0495840i	−0.456444	+	0.889752i	$0.650877\pi$
$594$	16540.5	−	1969.42i	1.14253	−	0.136038i
$595$		0			0
$596$	11119.0	−	2685.89i	0.764184	−	0.184595i
$597$	8822.32	−	15280.7i	0.604813	−	1.04757i
$598$	−4184.92	+	3129.59i	−0.286177	+	0.214010i
$599$	−4611.09	+	2662.21i	−0.314531	+	0.181595i	−0.648952	−	0.760829i	$-0.724793\pi$
$599$	−4611.09	+	2662.21i	−0.314531	+	0.181595i	0.334421	+	0.942424i	$0.391459\pi$
$600$	15999.6	+	2714.70i	1.08863	+	0.184712i
$601$		−	8711.39i		−	0.591256i	−0.955303	−	0.295628i	$-0.904471\pi$
$601$		−	8711.39i		−	0.591256i	0.955303	−	0.295628i	$-0.0955289\pi$
$602$		0			0
$603$			13305.8i			0.898599i
$604$	−9562.29	−	2817.94i	−0.644179	−	0.189835i
$605$	5767.55	−	3329.90i	0.387577	−	0.223768i
$606$	−22.4310	−	29.9950i	−0.00150363	−	0.00201067i
$607$	12379.6	−	21442.1i	0.827796	−	1.43378i	−0.0719681	−	0.997407i	$-0.522928\pi$
$607$	12379.6	−	21442.1i	0.827796	−	1.43378i	0.899764	−	0.436377i	$-0.143739\pi$
$608$	6250.67	+	9284.38i	0.416938	+	0.619295i
$609$		0			0
$610$	−2621.84	−	22019.9i	−0.174025	−	1.46157i
$611$	3865.22	+	2231.59i	0.255925	+	0.147758i
$612$	4382.77	−	4170.75i	0.289482	−	0.275478i
$613$	−3167.74	−	5486.69i	−0.208717	−	0.361509i	0.742593	−	0.669743i	$-0.233596\pi$
$613$	−3167.74	−	5486.69i	−0.208717	−	0.361509i	−0.951311	+	0.308233i	$0.900262\pi$
$614$	10906.6	+	4676.81i	0.716862	+	0.307395i
$615$	5924.15			0.388431
$616$		0			0
$617$	12720.7			0.830013			0.415006	−	0.909819i	$-0.363779\pi$
$617$	12720.7			0.830013			0.415006	+	0.909819i	$0.363779\pi$
$618$	−3117.84	−	1336.95i	−0.202942	−	0.0870226i
$619$	11135.8	+	19287.7i	0.723077	+	1.25241i	0.959761	+	0.280820i	$0.0906063\pi$
$619$	11135.8	+	19287.7i	0.723077	+	1.25241i	−0.236683	+	0.971587i	$0.576060\pi$
$620$	−2470.26	+	2350.77i	−0.160013	+	0.152273i
$621$	−9219.10	−	5322.65i	−0.595733	−	0.343946i
$622$	−2176.47	−	18279.4i	−0.140303	−	1.17836i
$623$		0			0
$624$	2426.29	+	4729.13i	0.155656	+	0.303392i
$625$	−1795.08	+	3109.16i	−0.114885	+	0.198987i
$626$	14633.6	+	19568.2i	0.934308	+	1.24937i
$627$	7363.39	−	4251.25i	0.469004	−	0.270779i
$628$	19508.4	+	5749.00i	1.23960	+	0.365303i
$629$		−	4959.08i		−	0.314358i
$630$		0			0
$631$		−	7895.30i		−	0.498110i	−0.968489	−	0.249055i	$-0.919880\pi$
$631$		−	7895.30i		−	0.498110i	0.968489	−	0.249055i	$-0.0801199\pi$
$632$	−1232.58	+	7264.42i	−0.0775780	+	0.457220i
$633$	2523.10	−	1456.71i	0.158427	−	0.0914676i
$634$	−2098.23	+	1569.11i	−0.131438	+	0.0982924i
$635$	−13783.8	+	23874.3i	−0.861410	+	1.49201i
$636$	−11368.7	+	2746.20i	−0.708803	+	0.171217i
$637$		0			0
$638$	−3333.54	+	396.914i	−0.206859	+	0.0246301i
$639$	−16160.1	−	9330.05i	−1.00045	−	0.577607i
$640$	−26055.8	−	5761.95i	−1.60929	−	0.355876i
$641$	−4213.92	−	7298.73i	−0.259657	−	0.449739i	0.706493	−	0.707720i	$-0.250276\pi$
$641$	−4213.92	−	7298.73i	−0.259657	−	0.449739i	−0.966150	+	0.257981i	$0.916943\pi$
$642$	3456.90	−	8061.69i	0.212513	−	0.495591i
$643$	−12838.8			−0.787424			−0.393712	−	0.919234i	$-0.628809\pi$
$643$	−12838.8			−0.787424			−0.393712	+	0.919234i	$0.628809\pi$
$644$		0			0
$645$	−12057.2			−0.736049
$646$	3293.37	−	7680.32i	0.200582	−	0.467768i
$647$	−11376.3	−	19704.4i	−0.691267	−	1.19731i	−0.971423	−	0.237355i	$-0.923719\pi$
$647$	−11376.3	−	19704.4i	−0.691267	−	1.19731i	0.280156	−	0.959955i	$-0.409614\pi$
$648$	−739.003	+	892.354i	−0.0448006	+	0.0540972i
$649$	20424.5	+	11792.1i	1.23533	+	0.713219i
$650$	−14972.0	+	1782.66i	−0.903460	+	0.107572i
$651$		0			0
$652$	1382.61	+	5723.74i	0.0830480	+	0.343802i
$653$	−430.103	+	744.961i	−0.0257753	+	0.0446441i	−0.878625	−	0.477512i	$-0.841539\pi$
$653$	−430.103	+	744.961i	−0.0257753	+	0.0446441i	0.852850	+	0.522156i	$0.174872\pi$
$654$	−8999.04	+	6729.70i	−0.538058	+	0.402373i
$655$	−31431.3	+	18146.9i	−1.87500	+	1.08253i
$656$	−6147.83	−	304.960i	−0.365903	−	0.0181504i
$657$			13088.2i			0.777199i
$658$		0			0
$659$		−	19262.8i		−	1.13865i	−0.822111	−	0.569327i	$-0.807204\pi$
$659$		−	19262.8i		−	1.13865i	0.822111	−	0.569327i	$-0.192796\pi$
$660$	−5730.34	+	19445.1i	−0.337959	+	1.14682i
$661$	−3499.64	+	2020.52i	−0.205931	+	0.118894i	−0.599419	−	0.800436i	$-0.704602\pi$
$661$	−3499.64	+	2020.52i	−0.205931	+	0.118894i	0.393488	+	0.919330i	$0.371268\pi$
$662$	16157.5	+	21606.1i	0.948611	+	1.26849i
$663$	1984.26	−	3436.84i	0.116233	−	0.201321i
$664$	3999.98	+	10772.8i	0.233779	+	0.629616i
$665$		0			0
$666$	−549.259	−	4613.04i	−0.0319570	−	0.268396i
$667$	1858.00	+	1072.72i	0.107859	+	0.0622727i
$668$	17156.0	+	18028.1i	0.993691	+	1.04420i
$669$	−3226.03	−	5587.64i	−0.186435	−	0.322916i
$670$	−40272.2	−	17269.0i	−2.32216	−	0.995758i
$671$	17503.5			1.00703
$672$		0			0
$673$	−30094.8			−1.72373			−0.861863	−	0.507141i	$-0.830702\pi$
$673$	−30094.8			−1.72373			−0.861863	+	0.507141i	$0.830702\pi$
$674$	12312.1	+	5279.51i	0.703628	+	0.301720i
$675$	−15357.5	−	26599.9i	−0.875718	−	1.51679i
$676$	8711.97	+	9154.83i	0.495674	+	0.520871i
$677$	−16898.8	−	9756.55i	−0.959343	−	0.553877i	−0.0633724	−	0.997990i	$-0.520186\pi$
$677$	−16898.8	−	9756.55i	−0.959343	−	0.553877i	−0.895971	+	0.444113i	$0.853519\pi$
$678$	740.408	+	6218.43i	0.0419398	+	0.352238i
$679$		0			0
$680$	6935.26	+	18678.1i	0.391110	+	1.05334i
$681$	3303.34	−	5721.55i	0.185880	−	0.321953i
$682$	−1611.96	−	2155.53i	−0.0905058	−	0.121025i
$683$	19594.6	−	11312.9i	1.09775	−	0.633788i	0.162123	−	0.986771i	$-0.448166\pi$
$683$	19594.6	−	11312.9i	1.09775	−	0.633788i	0.935630	+	0.352982i	$0.114832\pi$
$684$	2212.90	−	7509.17i	0.123702	−	0.419766i
$685$			33050.5i			1.84350i
$686$		0			0
$687$		−	8636.90i		−	0.479648i
$688$	12512.4	+	620.673i	0.693361	+	0.0343938i
$689$	9410.66	−	5433.24i	0.520345	−	0.300421i
$690$	10375.0	−	7758.71i	0.572422	−	0.428071i
$691$	−102.478	+	177.498i	−0.00564177	+	0.00977182i	−0.868833	−	0.495106i	$-0.835129\pi$
$691$	−102.478	+	177.498i	−0.00564177	+	0.00977182i	0.863191	+	0.504878i	$0.168463\pi$
$692$	−5898.67	−	24419.3i	−0.324037	−	1.34145i
$693$		0			0
$694$	−5495.06	+	654.279i	−0.300562	+	0.0357869i
$695$	4889.78	+	2823.11i	0.266877	+	0.154082i
$696$	1391.86	−	1680.69i	0.0758022	−	0.0915320i
$697$	2297.91	+	3980.10i	0.124877	+	0.216294i
$698$	−10856.5	+	25318.0i	−0.588717	+	1.37292i
$699$	−11527.0			−0.623736
$700$		0			0
$701$	9946.71			0.535923			0.267962	−	0.963430i	$-0.413650\pi$
$701$	9946.71			0.535923			0.267962	+	0.963430i	$0.413650\pi$
$702$	3964.67	−	9245.84i	0.213158	−	0.497097i
$703$	−3208.36	−	5557.04i	−0.172127	−	0.298133i
$704$	6947.69	−	19884.3i	0.371947	−	1.06451i
$705$	−9582.47	−	5532.44i	−0.511910	−	0.295552i
$706$	8399.85	−	1000.14i	0.447780	−	0.0533157i
$707$		0			0
$708$	−14901.7	+	3599.62i	−0.791018	+	0.191076i
$709$	−14432.4	+	24997.6i	−0.764484	+	1.32412i	0.176035	+	0.984384i	$0.443673\pi$
$709$	−14432.4	+	24997.6i	−0.764484	+	1.32412i	−0.940519	+	0.339741i	$0.889661\pi$
$710$	49212.2	−	36802.1i	2.60127	−	1.94529i
$711$	4463.19	−	2576.82i	0.235419	−	0.135919i
$712$	−772.858	+	4554.98i	−0.0406799	+	0.239754i
$713$			1720.14i			0.0903501i
$714$		0			0
$715$		−	18834.6i		−	0.985141i
$716$	1831.91	+	539.852i	0.0956168	+	0.0281777i
$717$	10560.2	−	6096.94i	0.550039	−	0.317565i
$718$	2238.08	+	2992.78i	0.116329	+	0.155557i
$719$	−3063.07	+	5305.39i	−0.158878	+	0.275185i	−0.934464	−	0.356057i	$-0.884121\pi$
$719$	−3063.07	+	5305.39i	−0.158878	+	0.275185i	0.775586	+	0.631241i	$0.217454\pi$
$720$	8520.09	+	16606.7i	0.441007	+	0.859574i
$721$		0			0
$722$	1015.28	+	8527.00i	0.0523336	+	0.439532i
$723$	−7335.45	−	4235.12i	−0.377328	−	0.217851i
$724$	−11283.9	+	10738.1i	−0.579233	+	0.551213i
$725$	3095.12	+	5360.91i	0.158552	+	0.274620i
$726$	−3140.44	−	1346.64i	−0.160541	−	0.0688409i
$727$	−20742.9			−1.05820			−0.529101	−	0.848559i	$-0.677471\pi$
$727$	−20742.9			−1.05820			−0.529101	+	0.848559i	$0.677471\pi$
$728$		0			0
$729$	13730.5			0.697579
$730$	−39613.5	−	16986.5i	−2.00844	−	0.861231i
$731$	−4676.85	−	8100.54i	−0.236634	−	0.409862i
$732$	−8242.15	+	7843.43i	−0.416173	+	0.396040i
$733$	15694.9	+	9061.44i	0.790864	+	0.456606i	0.840267	−	0.542173i	$-0.182398\pi$
$733$	15694.9	+	9061.44i	0.790864	+	0.456606i	−0.0494026	+	0.998779i	$0.515732\pi$
$734$	2252.42	+	18917.3i	0.113268	+	0.951296i
$735$		0			0
$736$	−11166.2	+	7517.58i	−0.559227	+	0.376497i
$737$	17293.4	−	29953.0i	0.864328	−	1.49706i
$738$	2578.40	+	3447.86i	0.128607	+	0.171975i
$739$	−32754.4	+	18910.8i	−1.63043	+	0.941332i	−0.646476	+	0.762934i	$0.723758\pi$
$739$	−32754.4	+	18910.8i	−1.63043	+	0.941332i	−0.983958	+	0.178398i	$0.942909\pi$
$740$	14674.9	+	4324.61i	0.729002	+	0.214832i
$741$		−	5135.01i		−	0.254574i
$742$		0			0
$743$			4974.35i			0.245614i	0.992431	+	0.122807i	$0.0391896\pi$
$743$			4974.35i			0.245614i	−0.992431	+	0.122807i	$0.960810\pi$
$744$	1724.95	+	292.679i	0.0849999	+	0.0144222i
$745$	22818.1	−	13174.0i	1.12213	−	0.647865i
$746$	−474.504	+	354.846i	−0.0232880	+	0.0174153i
$747$	4018.78	−	6960.73i	0.196840	−	0.340937i
$748$	−15286.8	+	3692.64i	−0.747246	+	0.180503i
$749$		0			0
$750$	15493.1	−	1844.72i	0.754306	−	0.0898127i
$751$	−19034.7	−	10989.7i	−0.924884	−	0.533982i	−0.0396939	−	0.999212i	$-0.512638\pi$
$751$	−19034.7	−	10989.7i	−0.924884	−	0.533982i	−0.885190	+	0.465230i	$0.845972\pi$
$752$	9659.49	+	6234.61i	0.468411	+	0.302331i
$753$	9456.81	+	16379.7i	0.457670	+	0.792707i
$754$	−799.035	+	1863.39i	−0.0385930	+	0.0900011i
$755$	−22962.1			−1.10686
$756$		0			0
$757$	−10241.5			−0.491722			−0.245861	−	0.969305i	$-0.579071\pi$
$757$	−10241.5			−0.491722			−0.245861	+	0.969305i	$0.579071\pi$
$758$	1344.30	−	3134.99i	0.0644159	−	0.150221i
$759$	5112.91	+	8855.83i	0.244515	+	0.423513i
$760$	19855.6	+	16443.4i	0.947684	+	0.784824i
$761$	18578.2	+	10726.2i	0.884968	+	0.510937i	0.872293	−	0.488983i	$-0.162632\pi$
$761$	18578.2	+	10726.2i	0.884968	+	0.510937i	0.0126751	+	0.999920i	$0.495965\pi$
$762$	14045.1	−	1672.31i	0.667719	−	0.0795031i
$763$		0			0
$764$	−853.278	−	3532.39i	−0.0404064	−	0.167274i
$765$	6967.86	−	12068.7i	0.329312	−	0.570385i
$766$	−7205.05	+	5388.12i	−0.339855	+	0.254152i
$767$	12335.2	−	7121.71i	0.580700	−	0.335267i
$768$	5638.73	+	12476.6i	0.264935	+	0.586210i
$769$		−	26466.5i		−	1.24110i	−0.784166	−	0.620551i	$-0.786909\pi$
$769$		−	26466.5i		−	1.24110i	0.784166	−	0.620551i	$-0.213091\pi$
$770$		0			0
$771$			16708.3i			0.780462i
$772$	7259.46	−	24633.9i	0.338437	−	1.14844i
$773$	−9692.09	+	5595.73i	−0.450971	+	0.260368i	−0.708240	−	0.705972i	$-0.750511\pi$
$773$	−9692.09	+	5595.73i	−0.450971	+	0.260368i	0.257269	+	0.966340i	$0.417177\pi$
$774$	−5247.71	−	7017.29i	−0.243701	−	0.325880i
$775$	−2481.56	+	4298.19i	−0.115020	+	0.199220i
$776$	23680.1	−	8792.51i	1.09545	−	0.406743i
$777$		0			0
$778$	2679.30	+	22502.5i	0.123467	+	1.03696i
$779$	5149.99	+	2973.35i	0.236864	+	0.136754i
$780$	8439.94	+	8868.97i	0.387434	+	0.407128i
$781$	24252.2	+	42006.1i	1.11116	+	1.92458i
$782$	9237.00	+	3960.88i	0.422397	+	0.181126i
$783$	−4130.21			−0.188508
$784$		0			0
$785$	46845.9			2.12994
$786$	17114.4	+	7338.75i	0.776654	+	0.333034i
$787$	15026.0	+	26025.7i	0.680582	+	1.17880i	0.974804	+	0.223065i	$0.0716062\pi$
$787$	15026.0	+	26025.7i	0.680582	+	1.17880i	−0.294222	+	0.955737i	$0.595061\pi$
$788$	−23016.7	−	24186.8i	−1.04053	−	1.09342i
$789$	5505.36	+	3178.52i	0.248411	+	0.143420i
$790$	2006.61	+	16852.9i	0.0903698	+	0.758985i
$791$		0			0
$792$	−13811.1	+	5128.11i	−0.619641	+	0.230075i
$793$	5285.53	−	9154.81i	0.236689	−	0.409958i
$794$	−20530.6	−	27453.7i	−0.917636	−	1.22707i
$795$	−23330.4	+	13469.8i	−1.04081	+	0.600913i
$796$	−11937.0	+	40506.5i	−0.531528	+	1.80366i
$797$		−	26567.8i		−	1.18078i	−0.807119	−	0.590389i	$-0.798974\pi$
$797$		−	26567.8i		−	1.18078i	0.807119	−	0.590389i	$-0.201026\pi$
$798$		0			0
$799$		−	8583.89i		−	0.380070i
$800$	−38746.7	+	2675.63i	−1.71238	+	0.118247i
$801$	2798.54	−	1615.74i	0.123447	−	0.0712724i
$802$	−24903.2	+	18623.2i	−1.09646	+	0.819960i
$803$	17010.5	−	29463.1i	0.747557	−	1.29481i
$804$	5278.94	+	21853.7i	0.231560	+	0.958609i
$805$		0			0
$806$	−1614.16	+	192.193i	−0.0705415	+	0.00839914i
$807$	23319.1	+	13463.3i	1.01719	+	0.587275i
$808$	69.0390	+	57.1746i	0.00300592	+	0.00248935i
$809$	980.413	+	1698.13i	0.0426075	+	0.0737984i	0.886543	−	0.462647i	$-0.153100\pi$
$809$	980.413	+	1698.13i	0.0426075	+	0.0737984i	−0.843935	+	0.536445i	$0.819767\pi$
$810$	−1051.77	+	2452.78i	−0.0456238	+	0.106397i
$811$	2633.82			0.114040			0.0570198	−	0.998373i	$-0.481840\pi$
$811$	2633.82			0.114040			0.0570198	+	0.998373i	$0.481840\pi$
$812$		0			0
$813$	−14634.5			−0.631309
$814$	−4759.04	+	11098.4i	−0.204919	+	0.477884i
$815$	6781.58	+	11746.0i	0.291470	+	0.504841i
$816$	5543.63	−	8588.93i	0.237826	−	0.368471i
$817$	−10481.6	−	6051.53i	−0.448841	−	0.259139i
$818$	5642.23	−	671.801i	0.241169	−	0.0287151i
$819$		0			0
$820$	−13781.8	+	3329.11i	−0.586931	+	0.141778i
$821$	−5333.16	+	9237.30i	−0.226710	+	0.392672i	−0.956831	−	0.290645i	$-0.906130\pi$
$821$	−5333.16	+	9237.30i	−0.226710	+	0.392672i	0.730121	+	0.683317i	$0.239463\pi$
$822$	13580.1	−	10155.6i	0.576230	−	0.430919i
$823$	32943.1	−	19019.7i	1.39529	−	0.805571i	0.401395	−	0.915905i	$-0.368525\pi$
$823$	32943.1	−	19019.7i	1.39529	−	0.805571i	0.993895	+	0.110334i	$0.0351922\pi$
$824$	8004.60	+	1358.17i	0.338414	+	0.0574199i
$825$			29504.6i			1.24512i
$826$		0			0
$827$		−	22277.0i		−	0.936697i	−0.883544	−	0.468349i	$-0.844849\pi$
$827$		−	22277.0i		−	0.936697i	0.883544	−	0.468349i	$-0.155151\pi$
$828$	9031.15	+	2661.42i	0.379051	+	0.111704i
$829$	−18752.2	+	10826.6i	−0.785633	+	0.453585i	−0.838423	−	0.545020i	$-0.816522\pi$
$829$	−18752.2	+	10826.6i	−0.785633	+	0.453585i	0.0527901	+	0.998606i	$0.483189\pi$
$830$	15852.0	+	21197.4i	0.662928	+	0.886475i
$831$	5355.83	−	9276.57i	0.223576	−	0.387245i
$832$	−8302.05	−	9638.31i	−0.345940	−	0.401620i
$833$		0			0
$834$	−342.511	−	2876.63i	−0.0142208	−	0.119436i
$835$	49643.4	+	28661.7i	2.05746	+	1.18788i
$836$	−14741.0	+	14027.9i	−0.609844	+	0.580343i
$837$	−1655.73	−	2867.80i	−0.0683755	−	0.118430i
$838$	−17320.1	−	7426.97i	−0.713977	−	0.306158i
$839$	−47337.4			−1.94788			−0.973939	−	0.226811i	$-0.927170\pi$
$839$	−47337.4			−1.94788			−0.973939	+	0.226811i	$0.927170\pi$
$840$		0			0
$841$	−23556.6			−0.965870
$842$	15232.3	+	6531.70i	0.623443	+	0.267336i
$843$	−10459.8	−	18116.9i	−0.427347	−	0.740187i
$844$	−5051.08	+	4806.73i	−0.206002	+	0.196036i
$845$	25209.4	+	14554.6i	1.02631	+	0.592538i
$846$	−950.737	−	7984.92i	−0.0386371	−	0.324500i
$847$		0			0
$848$	24904.7	−	12777.4i	1.00853	−	0.517428i
$849$	−10126.2	+	17539.1i	−0.409341	+	0.708999i
$850$	17366.8	+	23223.0i	0.700794	+	0.937110i
$851$	6683.37	−	3858.64i	0.269216	−	0.155432i
$852$	−30243.3	−	8912.49i	−1.21610	−	0.358377i
$853$			16562.9i			0.664833i	0.943133	+	0.332417i	$0.107864\pi$
$853$			16562.9i			0.664833i	−0.943133	+	0.332417i	$0.892136\pi$
$854$		0			0
$855$		−	18031.9i		−	0.721261i
$856$	−3511.76	+	20697.2i	−0.140222	+	0.826421i
$857$	28076.8	−	16210.2i	1.11912	−	0.646124i	0.177944	−	0.984041i	$-0.443056\pi$
$857$	28076.8	−	16210.2i	1.11912	−	0.646124i	0.941176	+	0.337917i	$0.109722\pi$
$858$	−7738.97	+	5787.39i	−0.307930	+	0.230278i
$859$	16065.2	−	27825.8i	0.638112	−	1.10524i	−0.347735	−	0.937593i	$-0.613049\pi$
$859$	16065.2	−	27825.8i	0.638112	−	1.10524i	0.985847	−	0.167649i	$-0.0536177\pi$
$860$	28049.7	−	6775.61i	1.11219	−	0.268659i
$861$		0			0
$862$	−10306.6	+	1227.17i	−0.407243	+	0.0484891i
$863$	−33292.7	−	19221.5i	−1.31320	−	0.758179i	−0.330579	−	0.943778i	$-0.607244\pi$
$863$	−33292.7	−	19221.5i	−1.31320	−	0.758179i	−0.982625	+	0.185600i	$0.940577\pi$
$864$	11380.1	−	23281.3i	0.448101	−	0.916721i
$865$	−28932.4	−	50112.4i	−1.13726	−	1.96979i
$866$	9232.22	−	21530.1i	0.362267	−	0.844828i
$867$	8790.02			0.344319
$868$		0			0
$869$	−13396.2			−0.522941
$870$	1980.93	−	4619.63i	0.0771951	−	0.180023i
$871$	−10444.2	−	18089.8i	−0.406300	−	0.703732i
$872$	17153.4	−	20712.9i	0.666156	−	0.804390i
$873$	−15300.7	−	8833.85i	−0.593184	−	0.342475i
$874$	12913.4	−	1537.55i	0.499772	−	0.0595062i
$875$		0			0
$876$	5192.60	+	21496.3i	0.200276	+	0.829101i
$877$	10742.3	−	18606.2i	0.413616	−	0.716404i	−0.581666	−	0.813428i	$-0.697599\pi$
$877$	10742.3	−	18606.2i	0.413616	−	0.716404i	0.995282	+	0.0970237i	$0.0309323\pi$
$878$	−21930.4	+	16400.1i	−0.842956	+	0.630383i
$879$	1324.81	−	764.877i	0.0508357	−	0.0293500i
$880$	2403.68	−	48456.9i	0.0920774	−	1.85623i
$881$			17193.8i			0.657517i	0.944414	+	0.328759i	$0.106630\pi$
$881$			17193.8i			0.657517i	−0.944414	+	0.328759i	$0.893370\pi$
$882$		0			0
$883$		−	16514.2i		−	0.629384i	−0.949194	−	0.314692i	$-0.898099\pi$
$883$		−	16514.2i		−	0.629384i	0.949194	−	0.314692i	$-0.101901\pi$
$884$	−2684.80	+	9110.48i	−0.102149	+	0.346627i
$885$	−30580.7	+	17655.8i	−1.16154	+	0.670614i
$886$	−13993.5	−	18712.3i	−0.530612	−	0.709540i
$887$	10239.6	−	17735.5i	0.387612	−	0.671364i	−0.604516	−	0.796593i	$-0.706633\pi$
$887$	10239.6	−	17735.5i	0.387612	−	0.671364i	0.992128	+	0.125229i	$0.0399667\pi$
$888$	−2732.29	−	7358.63i	−0.103254	−	0.278085i
$889$		0			0
$890$	1258.20	+	10567.2i	0.0473876	+	0.397992i
$891$	−1824.29	−	1053.25i	−0.0685925	−	0.0396019i
$892$	10645.0	+	11186.1i	0.399574	+	0.419886i
$893$	−5553.49	−	9618.93i	−0.208108	−	0.360454i
$894$	−12424.5	−	5327.70i	−0.464806	−	0.199312i
$895$	4399.00			0.164293
$896$		0			0
$897$	6175.79			0.229882
$898$	−190.171	−	81.5463i	−0.00706690	−	0.00303033i
$899$	333.693	+	577.973i	0.0123796	+	0.0214421i
$900$	18727.1	+	19679.0i	0.693595	+	0.728854i
$901$	−18099.2	−	10449.6i	−0.669226	−	0.386378i
$902$	−1323.14	−	11112.6i	−0.0488424	−	0.410211i
$903$		0			0
$904$	−5216.96	−	14050.4i	−0.191940	−	0.516935i
$905$	−17939.6	+	31072.3i	−0.658930	+	1.14130i
$906$	7055.66	+	9434.91i	0.258729	+	0.345976i
$907$	−26983.7	+	15579.0i	−0.987848	+	0.570334i	−0.904630	−	0.426197i	$-0.859853\pi$
$907$	−26983.7	+	15579.0i	−0.987848	+	0.570334i	−0.0832177	+	0.996531i	$0.526520\pi$
$908$	−4469.57	+	15166.8i	−0.163357	+	0.554327i
$909$		−	62.6978i		−	0.00228774i
$910$		0			0
$911$			412.348i			0.0149964i	0.999972	+	0.00749818i	$0.00238677\pi$
$911$			412.348i			0.0149964i	−0.999972	+	0.00749818i	$0.997613\pi$
$912$	655.331	−	13211.1i	0.0237941	−	0.479676i
$913$	−18093.5	+	10446.3i	−0.655868	+	0.378666i
$914$	29836.7	−	22312.6i	1.07977	−	0.807480i
$915$	−13103.6	+	22696.2i	−0.473435	+	0.820013i
$916$	4853.56	+	20092.7i	0.175072	+	0.724763i
$917$		0			0
$918$	−19212.4	+	2287.56i	−0.690746	+	0.0822448i
$919$	8444.08	+	4875.19i	0.303095	+	0.174992i	0.643832	−	0.765166i	$-0.277343\pi$
$919$	8444.08	+	4875.19i	0.303095	+	0.174992i	−0.340737	+	0.940159i	$0.610677\pi$
$920$	−19776.3	+	23880.1i	−0.708700	+	0.855763i
$921$	−7012.30	−	12145.7i	−0.250883	−	0.434542i
$922$	−14106.4	+	32897.0i	−0.503872	+	1.17506i
$923$	29293.8			1.04466
$924$		0			0
$925$	22266.7			0.791487
$926$	−950.378	+	2216.33i	−0.0337272	+	0.0786536i
$927$	−2839.38	−	4917.95i	−0.100601	−	0.174247i
$928$	−2293.53	+	4692.09i	−0.0811301	+	0.165976i
$929$	19036.4	+	10990.7i	0.672297	+	0.388151i	0.796946	−	0.604050i	$-0.206447\pi$
$929$	19036.4	+	10990.7i	0.672297	+	0.388151i	−0.124650	+	0.992201i	$0.539781\pi$
$930$	4001.75	−	476.475i	0.141100	−	0.0168003i
$931$		0			0
$932$	26816.2	−	6477.67i	0.942484	−	0.227664i
$933$	−10877.7	+	18840.8i	−0.381695	+	0.661115i
$934$	−24746.7	+	18506.2i	−0.866956	+	0.648331i
$935$	−31371.0	+	18112.0i	−1.09726	+	0.633505i
$936$	−1488.40	+	8772.13i	−0.0519762	+	0.306331i
$937$		−	19723.5i		−	0.687662i	−0.939032	−	0.343831i	$-0.888275\pi$
$937$		−	19723.5i		−	0.687662i	0.939032	−	0.343831i	$-0.111725\pi$
$938$		0			0
$939$		−	28877.4i		−	1.00360i
$940$	25401.5	+	7485.65i	0.881389	+	0.259739i
$941$	9773.15	−	5642.53i	0.338571	−	0.195474i	−0.321069	−	0.947056i	$-0.604042\pi$
$941$	9773.15	−	5642.53i	0.338571	−	0.195474i	0.659640	+	0.751582i	$0.270709\pi$
$942$	−14394.5	−	19248.5i	−0.497876	−	0.665766i
$943$	−3575.99	+	6193.80i	−0.123489	+	0.213890i
$944$	32644.2	−	16748.2i	1.12551	−	0.577445i
$945$		0			0
$946$	2692.94	+	22617.1i	0.0925530	+	0.777321i
$947$	−26386.0	−	15234.0i	−0.905417	−	0.522743i	−0.0264635	−	0.999650i	$-0.508425\pi$
$947$	−26386.0	−	15234.0i	−0.905417	−	0.522743i	−0.878954	+	0.476907i	$0.841758\pi$
$948$	6308.10	−	6002.94i	0.216115	−	0.205661i
$949$	−10273.3	−	17794.0i	−0.351409	−	0.608658i
$950$	34485.4	+	14787.5i	1.17774	+	0.505022i
$951$	3096.42			0.105582
$952$		0			0
$953$	11791.2			0.400791			0.200395	−	0.979715i	$-0.435777\pi$
$953$	11791.2			0.400791			0.200395	+	0.979715i	$0.435777\pi$
$954$	−17993.7	−	7715.79i	−0.610657	−	0.261853i
$955$	−4185.24	−	7249.05i	−0.141813	−	0.245627i
$956$	−21140.9	+	20118.2i	−0.715215	+	0.680616i
$957$	3435.92	+	1983.73i	0.116058	+	0.0670061i
$958$	−3565.18	−	29942.7i	−0.120236	−	1.00982i
$959$		0			0
$960$	20582.0	+	23894.8i	0.691961	+	0.803335i
$961$	14628.0	−	25336.4i	0.491019	−	0.850470i
$962$	4367.66	+	5840.49i	0.146382	+	0.195743i
$963$	12716.2	−	7341.69i	0.425517	−	0.245672i
$964$	19445.0	+	5730.32i	0.649670	+	0.191454i
$965$		−	59154.0i		−	1.97330i
$966$		0			0
$967$		−	40914.1i		−	1.36061i	−0.732929	−	0.680305i	$-0.761847\pi$
$967$		−	40914.1i		−	1.36061i	0.732929	−	0.680305i	$-0.238153\pi$
$968$	8062.61	+	1368.01i	0.267709	+	0.0454230i
$969$	−8552.87	+	4938.00i	−0.283548	+	0.163706i
$970$	46595.0	−	34844.9i	1.54234	−	1.15340i
$971$	−9276.00	+	16066.5i	−0.306572	+	0.530997i	−0.977610	−	0.210425i	$-0.932515\pi$
$971$	−9276.00	+	16066.5i	−0.306572	+	0.530997i	0.671038	+	0.741423i	$0.265849\pi$
$972$	−28726.0	+	6939.00i	−0.947930	+	0.228980i
$973$		0			0
$974$	152.192	−	18.1210i	0.00500671	−	0.000596133i
$975$	15431.8	+	8909.53i	0.506884	+	0.292650i
$976$	14766.7	−	22878.6i	0.484294	−	0.750333i
$977$	1455.74	+	2521.42i	0.0476697	+	0.0825664i	0.888876	−	0.458148i	$-0.151487\pi$
$977$	1455.74	+	2521.42i	0.0476697	+	0.0825664i	−0.841206	+	0.540715i	$0.818154\pi$
$978$	2742.53	−	6395.74i	0.0896692	−	0.209114i
$979$	−8399.78			−0.274217
$980$		0			0
$981$	−18810.5			−0.612204
$982$	6273.54	−	14630.3i	0.203866	−	0.475428i
$983$	−18251.1	−	31611.8i	−0.592186	−	1.02570i	−0.993937	−	0.109947i	$-0.964932\pi$
$983$	−18251.1	−	31611.8i	−0.592186	−	1.02570i	0.401752	−	0.915749i	$-0.368402\pi$
$984$	5602.70	+	4639.88i	0.181512	+	0.150319i
$985$	−66602.3	−	38452.9i	−2.15444	−	1.24387i
$986$	3872.05	−	461.032i	0.125062	−	0.0148907i
$987$		0			0
$988$	2885.65	+	11946.0i	0.0929198	+	0.384669i
$989$	7278.08	−	12606.0i	0.234004	−	0.405306i
$990$	−27175.9	+	20322.8i	−0.872431	+	0.652425i
$991$	31879.7	−	18405.7i	1.02189	−	0.589987i	0.107238	−	0.994233i	$-0.465799\pi$
$991$	31879.7	−	18405.7i	1.02189	−	0.589987i	0.914650	+	0.404246i	$0.132466\pi$
$992$	−4177.38	+	288.466i	−0.133701	+	0.00923266i
$993$		−	31884.6i		−	1.01896i
$994$		0			0
$995$			97269.2i			3.09914i
$996$	3838.92	−	13026.8i	0.122129	−	0.414429i
$997$	10060.1	−	5808.18i	0.319564	−	0.184500i	−0.331634	−	0.943408i	$-0.607600\pi$
$997$	10060.1	−	5808.18i	0.319564	−	0.184500i	0.651198	+	0.758908i	$0.274267\pi$
$998$	−1049.81	−	1403.82i	−0.0332978	−	0.0445262i
$999$	−7428.32	+	12866.2i	−0.235257	+	0.407477i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.4.f.d.19.9		20
4.3	odd	2	inner	196.4.f.d.19.2		20
7.2	even	3		196.4.d.b.195.10		20
7.3	odd	6	inner	196.4.f.d.31.2		20
7.4	even	3		28.4.f.a.3.2	✓	20
7.5	odd	6		196.4.d.b.195.9		20
7.6	odd	2		28.4.f.a.19.9	yes	20
28.3	even	6	inner	196.4.f.d.31.9		20
28.11	odd	6		28.4.f.a.3.9	yes	20
28.19	even	6		196.4.d.b.195.12		20
28.23	odd	6		196.4.d.b.195.11		20
28.27	even	2		28.4.f.a.19.2	yes	20
56.11	odd	6		448.4.p.h.255.4		20
56.13	odd	2		448.4.p.h.383.4		20
56.27	even	2		448.4.p.h.383.7		20
56.53	even	6		448.4.p.h.255.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.4.f.a.3.2	✓	20	7.4	even	3
28.4.f.a.3.9	yes	20	28.11	odd	6
28.4.f.a.19.2	yes	20	28.27	even	2
28.4.f.a.19.9	yes	20	7.6	odd	2
196.4.d.b.195.9		20	7.5	odd	6
196.4.d.b.195.10		20	7.2	even	3
196.4.d.b.195.11		20	28.23	odd	6
196.4.d.b.195.12		20	28.19	even	6
196.4.f.d.19.2		20	4.3	odd	2	inner
196.4.f.d.19.9		20	1.1	even	1	trivial
196.4.f.d.31.2		20	7.3	odd	6	inner
196.4.f.d.31.9		20	28.3	even	6	inner
448.4.p.h.255.4		20	56.11	odd	6
448.4.p.h.255.7		20	56.53	even	6
448.4.p.h.383.4		20	56.13	odd	2
448.4.p.h.383.7		20	56.27	even	2

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	196.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.59951 + 1.11469i) q^{2} +(-1.67134 - 2.89484i) q^{3} +(5.51494 + 5.79529i) q^{4} +(15.9583 + 9.21354i) q^{5} +(-1.11782 - 9.38820i) q^{6} +(7.87623 + 21.2124i) q^{8} +(7.91327 - 13.7062i) q^{9} +(31.2137 + 41.7393i) q^{10} +(-35.6274 + 20.5695i) q^{11} +(7.55911 - 25.6508i) q^{12} +24.8455i q^{13} -61.5957i q^{15} +(-3.17079 + 63.9214i) q^{16} +(41.3826 - 23.8923i) q^{17} +(35.8487 - 26.8086i) q^{18} +(30.9150 - 53.5464i) q^{19} +(34.6141 + 143.295i) q^{20} +(-115.542 + 13.7572i) q^{22} +(64.3994 + 37.1810i) q^{23} +(48.2426 - 58.2535i) q^{24} +(107.279 + 185.812i) q^{25} +(-27.6950 + 64.5862i) q^{26} -143.155 q^{27} +28.8513 q^{29} +(68.6600 - 160.119i) q^{30} +(11.5660 + 20.0328i) q^{31} +(-79.4949 + 162.630i) q^{32} +(119.091 + 68.7571i) q^{33} +(134.207 - 15.9796i) q^{34} +(123.072 - 29.7291i) q^{36} +(51.8900 - 89.8761i) q^{37} +(140.052 - 104.734i) q^{38} +(71.9237 - 41.5252i) q^{39} +(-69.7496 + 411.082i) q^{40} +96.1780i q^{41} -195.747i q^{43} +(-315.689 - 93.0315i) q^{44} +(252.565 - 145.818i) q^{45} +(125.962 + 168.438i) q^{46} +(89.8186 - 155.570i) q^{47} +(190.342 - 97.6553i) q^{48} +(71.7499 + 602.603i) q^{50} +(-138.329 - 79.8641i) q^{51} +(-143.987 + 137.021i) q^{52} +(-218.681 - 378.767i) q^{53} +(-372.134 - 159.573i) q^{54} -758.071 q^{55} -206.678 q^{57} +(74.9993 + 32.1601i) q^{58} +(-286.640 - 496.475i) q^{59} +(356.965 - 339.697i) q^{60} +(-368.470 - 212.736i) q^{61} +(7.73553 + 64.9681i) q^{62} +(-387.930 + 334.147i) q^{64} +(-228.915 + 396.492i) q^{65} +(232.935 + 311.484i) q^{66} +(-728.093 + 420.365i) q^{67} +(366.686 + 108.060i) q^{68} -248.568i q^{69} -1179.04i q^{71} +(353.067 + 59.9061i) q^{72} +(-716.185 + 413.489i) q^{73} +(235.072 - 175.793i) q^{74} +(358.597 - 621.109i) q^{75} +(480.812 - 116.144i) q^{76} +(233.254 - 27.7728i) q^{78} +(282.007 + 162.817i) q^{79} +(-639.543 + 990.864i) q^{80} +(25.6023 + 44.3445i) q^{81} +(-107.208 + 250.016i) q^{82} +507.854 q^{83} +880.530 q^{85} +(218.197 - 508.848i) q^{86} +(-48.2202 - 83.5198i) q^{87} +(-716.937 - 593.731i) q^{88} +(176.826 + 102.090i) q^{89} +(819.088 - 97.5260i) q^{90} +(139.684 + 578.264i) q^{92} +(38.6612 - 66.9632i) q^{93} +(406.897 - 304.288i) q^{94} +(986.704 - 569.674i) q^{95} +(603.651 - 41.6847i) q^{96} -1116.33i q^{97} +651.087i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{4} + 6 q^{5} + 72 q^{8} - 56 q^{9} + 12 q^{10} + 168 q^{12} - 104 q^{16} + 6 q^{17} + 68 q^{18} - 184 q^{22} - 348 q^{24} - 36 q^{25} - 396 q^{26} - 352 q^{29} + 644 q^{30} - 40 q^{32} - 30 q^{33}+ \cdots + 11784 q^{96}+O(q^{100}) \) 20 * q + 4 * q^4 + 6 * q^5 + 72 * q^8 - 56 * q^9 + 12 * q^10 + 168 * q^12 - 104 * q^16 + 6 * q^17 + 68 * q^18 - 184 * q^22 - 348 * q^24 - 36 * q^25 - 396 * q^26 - 352 * q^29 + 644 * q^30 - 40 * q^32 - 30 * q^33 + 208 * q^36 + 258 * q^37 + 1620 * q^38 + 1548 * q^40 - 1248 * q^44 + 504 * q^45 + 232 * q^46 - 864 * q^50 - 2592 * q^52 + 570 * q^53 - 4572 * q^54 + 1452 * q^57 + 2244 * q^58 - 736 * q^60 - 294 * q^61 + 2560 * q^64 - 124 * q^65 + 4272 * q^66 + 6084 * q^68 - 4672 * q^72 - 966 * q^73 + 832 * q^74 - 4056 * q^78 - 7032 * q^80 - 1262 * q^81 - 7692 * q^82 - 2980 * q^85 + 5696 * q^86 - 1396 * q^88 + 3186 * q^89 + 3312 * q^92 - 306 * q^93 + 6780 * q^94 + 11784 * q^96

Introduction

L-functions

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