LMFDB - Embedded newform 196.3.c.h.99.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [196,3,Mod(99,196)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(196, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("196.99"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	196.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,2,0,4,-2,6,0,-4,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$5.34061318146$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.15582448.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 13x^{4} - 21x^{3} + 20x^{2} - 10x + 2 $ x^6 - 3x^5 + 13x^4 - 21x^3 + 20x^2 - 10*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.3
Root			$0.500000 + 0.759064i$ of defining polynomial
Character	$\chi$	$=$	196.99
Dual form			196.3.c.h.99.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.789608 - 1.83753i) q^{2} +2.15693i q^{3} +(-2.75304 - 2.90186i) q^{4} +6.50608 q^{5} +(3.96343 + 1.70313i) q^{6} +(-7.50608 + 2.76746i) q^{8} +4.34764 q^{9} +(5.13725 - 11.9551i) q^{10} -0.610527i q^{11} +(6.25911 - 5.93812i) q^{12} +10.6645 q^{13} +14.0332i q^{15} +(-0.841567 + 15.9779i) q^{16} +11.9814 q^{17} +(3.43293 - 7.98893i) q^{18} -12.2180i q^{19} +(-17.9115 - 18.8797i) q^{20} +(-1.12186 - 0.482077i) q^{22} -40.1286i q^{23} +(-5.96922 - 16.1901i) q^{24} +17.3290 q^{25} +(8.42078 - 19.5964i) q^{26} +28.7900i q^{27} -9.04293 q^{29} +(25.7864 + 11.0807i) q^{30} +34.9190i q^{31} +(28.6953 + 14.1626i) q^{32} +1.31687 q^{33} +(9.46059 - 22.0161i) q^{34} +(-11.9692 - 12.6162i) q^{36} -50.8165 q^{37} +(-22.4509 - 9.64740i) q^{38} +23.0026i q^{39} +(-48.8351 + 18.0053i) q^{40} -25.7382 q^{41} +19.8107i q^{43} +(-1.77166 + 1.68080i) q^{44} +28.2861 q^{45} +(-73.7375 - 31.6859i) q^{46} +47.0968i q^{47} +(-34.4631 - 1.81520i) q^{48} +(13.6831 - 31.8426i) q^{50} +25.8430i q^{51} +(-29.3598 - 30.9469i) q^{52} -26.8780 q^{53} +(52.9024 + 22.7328i) q^{54} -3.97214i q^{55} +26.3533 q^{57} +(-7.14037 + 16.6167i) q^{58} +46.0315i q^{59} +(40.7223 - 38.6338i) q^{60} -42.2070 q^{61} +(64.1648 + 27.5724i) q^{62} +(48.6823 - 41.5455i) q^{64} +69.3841 q^{65} +(1.03981 - 2.41978i) q^{66} +27.7812i q^{67} +(-32.9852 - 34.7683i) q^{68} +86.5547 q^{69} -57.1882i q^{71} +(-32.6337 + 12.0319i) q^{72} -56.3290 q^{73} +(-40.1251 + 93.3768i) q^{74} +37.3775i q^{75} +(-35.4548 + 33.6365i) q^{76} +(42.2680 + 18.1631i) q^{78} -18.3938i q^{79} +(-5.47530 + 103.953i) q^{80} -22.9692 q^{81} +(-20.3231 + 47.2948i) q^{82} +37.3775i q^{83} +77.9517 q^{85} +(36.4027 + 15.6427i) q^{86} -19.5050i q^{87} +(1.68961 + 4.58266i) q^{88} +24.7074 q^{89} +(22.3349 - 51.9766i) q^{90} +(-116.448 + 110.476i) q^{92} -75.3180 q^{93} +(86.5418 + 37.1880i) q^{94} -79.4910i q^{95} +(-30.5479 + 61.8938i) q^{96} -109.895 q^{97} -2.65435i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 4 q^{4} - 2 q^{5} + 6 q^{6} - 4 q^{8} - 4 q^{9} - 2 q^{10} - 24 q^{12} + 12 q^{13} - 16 q^{16} - 2 q^{17} - 56 q^{18} - 76 q^{20} + 22 q^{22} - 44 q^{24} + 56 q^{26} + 36 q^{29} + 74 q^{30}+ \cdots - 372 q^{97}+O(q^{100}) $ 6 * q + 2 * q^2 + 4 * q^4 - 2 * q^5 + 6 * q^6 - 4 * q^8 - 4 * q^9 - 2 * q^10 - 24 * q^12 + 12 * q^13 - 16 * q^16 - 2 * q^17 - 56 * q^18 - 76 * q^20 + 22 * q^22 - 44 * q^24 + 56 * q^26 + 36 * q^29 + 74 * q^30 + 112 * q^32 - 14 * q^33 + 158 * q^34 - 80 * q^36 - 86 * q^37 - 2 * q^38 - 148 * q^40 - 4 * q^41 - 64 * q^44 + 156 * q^45 - 162 * q^46 - 256 * q^48 + 104 * q^50 - 64 * q^52 + 74 * q^53 + 182 * q^54 - 110 * q^57 + 176 * q^58 + 232 * q^60 + 86 * q^61 + 266 * q^62 - 80 * q^64 + 140 * q^65 + 102 * q^66 - 68 * q^68 + 150 * q^69 - 152 * q^72 - 234 * q^73 - 290 * q^74 - 288 * q^76 + 32 * q^78 - 146 * q^81 + 272 * q^82 + 134 * q^85 + 16 * q^86 + 188 * q^88 + 6 * q^89 + 320 * q^90 - 224 * q^92 - 162 * q^93 + 102 * q^94 - 320 * q^96 - 372 * q^97

Character values

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

$n$	$99$	$101$
$\chi(n)$	$-1$	$1$

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 $

$2$	0.789608	−	1.83753i	0.394804	−	0.918765i
$2$	0.789608	−	1.83753i	0.394804	−	0.918765i
$3$			2.15693i			0.718977i	0.933149	+	0.359489i	$0.117049\pi$
$3$			2.15693i			0.718977i	−0.933149	+	0.359489i	$0.882951\pi$
$4$	−2.75304	−	2.90186i	−0.688259	−	0.725465i
$5$	6.50608			1.30122			0.650608	−	0.759414i	$-0.274514\pi$
$5$	6.50608			1.30122			0.650608	+	0.759414i	$0.274514\pi$
$6$	3.96343	+	1.70313i	0.660572	+	0.283855i
$7$		0			0
$7$		0			0
$8$	−7.50608	+	2.76746i	−0.938259	+	0.345932i
$9$	4.34764			0.483071
$10$	5.13725	−	11.9551i	0.513725	−	1.19551i
$11$		−	0.610527i		−	0.0555025i	−0.999615	−	0.0277512i	$-0.991165\pi$
$11$		−	0.610527i		−	0.0555025i	0.999615	−	0.0277512i	$-0.00883463\pi$
$12$	6.25911	−	5.93812i	0.521593	−	0.494843i
$13$	10.6645			0.820347			0.410173	−	0.912008i	$-0.365468\pi$
$13$	10.6645			0.820347			0.410173	+	0.912008i	$0.365468\pi$
$14$		0			0
$15$			14.0332i			0.935544i
$16$	−0.841567	+	15.9779i	−0.0525979	+	0.998616i
$17$	11.9814			0.704787			0.352393	−	0.935852i	$-0.385368\pi$
$17$	11.9814			0.704787			0.352393	+	0.935852i	$0.385368\pi$
$18$	3.43293	−	7.98893i	0.190719	−	0.443829i
$19$		−	12.2180i		−	0.643051i	−0.946901	−	0.321525i	$-0.895804\pi$
$19$		−	12.2180i		−	0.643051i	0.946901	−	0.321525i	$-0.104196\pi$
$20$	−17.9115	−	18.8797i	−0.895574	−	0.943986i
$21$		0			0
$22$	−1.12186	−	0.482077i	−0.0509937	−	0.0219126i
$23$		−	40.1286i		−	1.74472i	−0.488862	−	0.872361i	$-0.662588\pi$
$23$		−	40.1286i		−	1.74472i	0.488862	−	0.872361i	$-0.337412\pi$
$24$	−5.96922	−	16.1901i	−0.248718	−	0.674587i
$25$	17.3290			0.693161
$26$	8.42078	−	19.5964i	0.323876	−	0.753706i
$27$			28.7900i			1.06629i
$28$		0			0
$29$	−9.04293			−0.311825			−0.155913	−	0.987771i	$-0.549832\pi$
$29$	−9.04293			−0.311825			−0.155913	+	0.987771i	$0.549832\pi$
$30$	25.7864	+	11.0807i	0.859546	+	0.369357i
$31$			34.9190i			1.12642i	0.826314	+	0.563210i	$0.190434\pi$
$31$			34.9190i			1.12642i	−0.826314	+	0.563210i	$0.809566\pi$
$32$	28.6953	+	14.1626i	0.896728	+	0.442583i
$33$	1.31687			0.0399050
$34$	9.46059	−	22.0161i	0.278253	−	0.647534i
$35$		0			0
$36$	−11.9692	−	12.6162i	−0.332478	−	0.350451i
$37$	−50.8165			−1.37342			−0.686709	−	0.726932i	$-0.740945\pi$
$37$	−50.8165			−1.37342			−0.686709	+	0.726932i	$0.740945\pi$
$38$	−22.4509	−	9.64740i	−0.590813	−	0.253879i
$39$			23.0026i			0.589811i
$40$	−48.8351	+	18.0053i	−1.22088	+	0.450133i
$41$	−25.7382			−0.627761			−0.313881	−	0.949462i	$-0.601629\pi$
$41$	−25.7382			−0.627761			−0.313881	+	0.949462i	$0.601629\pi$
$42$		0			0
$43$			19.8107i			0.460713i	0.973106	+	0.230357i	$0.0739893\pi$
$43$			19.8107i			0.460713i	−0.973106	+	0.230357i	$0.926011\pi$
$44$	−1.77166	+	1.68080i	−0.0402651	+	0.0382001i
$45$	28.2861			0.628580
$46$	−73.7375	−	31.6859i	−1.60299	−	0.688823i
$47$			47.0968i			1.00206i	0.865430	+	0.501030i	$0.167045\pi$
$47$			47.0968i			1.00206i	−0.865430	+	0.501030i	$0.832955\pi$
$48$	−34.4631	−	1.81520i	−0.717982	−	0.0378167i
$49$		0			0
$50$	13.6831	−	31.8426i	0.273663	−	0.636852i
$51$			25.8430i			0.506726i
$52$	−29.3598	−	30.9469i	−0.564611	−	0.595133i
$53$	−26.8780			−0.507132			−0.253566	−	0.967318i	$-0.581604\pi$
$53$	−26.8780			−0.507132			−0.253566	+	0.967318i	$0.581604\pi$
$54$	52.9024	+	22.7328i	0.979675	+	0.420978i
$55$		−	3.97214i		−	0.0722207i
$56$		0			0
$57$	26.3533			0.462339
$58$	−7.14037	+	16.6167i	−0.123110	+	0.286494i
$59$			46.0315i			0.780194i	0.920774	+	0.390097i	$0.127559\pi$
$59$			46.0315i			0.780194i	−0.920774	+	0.390097i	$0.872441\pi$
$60$	40.7223	−	38.6338i	0.678704	−	0.643897i
$61$	−42.2070			−0.691919			−0.345959	−	0.938250i	$-0.612446\pi$
$61$	−42.2070			−0.691919			−0.345959	+	0.938250i	$0.612446\pi$
$62$	64.1648	+	27.5724i	1.03492	+	0.444715i
$63$		0			0
$64$	48.6823	−	41.5455i	0.760661	−	0.649149i
$65$	69.3841			1.06745
$66$	1.03981	−	2.41978i	0.0157547	−	0.0366634i
$67$			27.7812i			0.414644i	0.978273	+	0.207322i	$0.0664748\pi$
$67$			27.7812i			0.414644i	−0.978273	+	0.207322i	$0.933525\pi$
$68$	−32.9852	−	34.7683i	−0.485076	−	0.511298i
$69$	86.5547			1.25442
$70$		0			0
$71$		−	57.1882i		−	0.805467i	−0.915317	−	0.402734i	$-0.868060\pi$
$71$		−	57.1882i		−	0.805467i	0.915317	−	0.402734i	$-0.131940\pi$
$72$	−32.6337	+	12.0319i	−0.453246	+	0.167110i
$73$	−56.3290			−0.771630			−0.385815	−	0.922576i	$-0.626080\pi$
$73$	−56.3290			−0.771630			−0.385815	+	0.922576i	$0.626080\pi$
$74$	−40.1251	+	93.3768i	−0.542231	+	1.26185i
$75$			37.3775i			0.498367i
$76$	−35.4548	+	33.6365i	−0.466510	+	0.442586i
$77$		0			0
$78$	42.2680	+	18.1631i	0.541898	+	0.232860i
$79$		−	18.3938i		−	0.232832i	−0.993201	−	0.116416i	$-0.962859\pi$
$79$		−	18.3938i		−	0.232832i	0.993201	−	0.116416i	$-0.0371406\pi$
$80$	−5.47530	+	103.953i	−0.0684412	+	1.29941i
$81$	−22.9692			−0.283571
$82$	−20.3231	+	47.2948i	−0.247843	+	0.576765i
$83$			37.3775i			0.450332i	0.974320	+	0.225166i	$0.0722924\pi$
$83$			37.3775i			0.450332i	−0.974320	+	0.225166i	$0.927708\pi$
$84$		0			0
$85$	77.9517			0.917079
$86$	36.4027	+	15.6427i	0.423287	+	0.181892i
$87$		−	19.5050i		−	0.224195i
$88$	1.68961	+	4.58266i	0.0192001	+	0.0520757i
$89$	24.7074			0.277612			0.138806	−	0.990320i	$-0.455674\pi$
$89$	24.7074			0.277612			0.138806	+	0.990320i	$0.455674\pi$
$90$	22.3349	−	51.9766i	0.248166	−	0.577517i
$91$		0			0
$92$	−116.448	+	110.476i	−1.26573	+	1.20082i
$93$	−75.3180			−0.809871
$94$	86.5418	+	37.1880i	0.920658	+	0.395617i
$95$		−	79.4910i		−	0.836747i
$96$	−30.5479	+	61.8938i	−0.318207	+	0.644727i
$97$	−109.895			−1.13294			−0.566468	−	0.824084i	$-0.691690\pi$
$97$	−109.895			−1.13294			−0.566468	+	0.824084i	$0.691690\pi$
$98$		0			0
$99$		−	2.65435i		−	0.0268117i
$100$	−47.7074	−	50.2864i	−0.477074	−	0.502864i
$101$	−43.1512			−0.427239			−0.213620	−	0.976917i	$-0.568525\pi$
$101$	−43.1512			−0.427239			−0.213620	+	0.976917i	$0.568525\pi$
$102$	47.4873	+	20.4059i	0.465562	+	0.200057i
$103$		−	150.616i		−	1.46229i	−0.682223	−	0.731144i	$-0.738987\pi$
$103$		−	150.616i		−	1.46229i	0.682223	−	0.731144i	$-0.261013\pi$
$104$	−80.0486	+	29.5136i	−0.769698	+	0.283785i
$105$		0			0
$106$	−21.2231	+	49.3892i	−0.200218	+	0.465936i
$107$			40.5909i			0.379354i	0.981847	+	0.189677i	$0.0607440\pi$
$107$			40.5909i			0.379354i	−0.981847	+	0.189677i	$0.939256\pi$
$108$	83.5444	−	79.2599i	0.773559	−	0.733888i
$109$	66.5304			0.610370			0.305185	−	0.952293i	$-0.401282\pi$
$109$	66.5304			0.610370			0.305185	+	0.952293i	$0.401282\pi$
$110$	−7.29892	−	3.13643i	−0.0663538	−	0.0285130i
$111$		−	109.608i		−	0.987457i
$112$		0			0
$113$	−143.395			−1.26899			−0.634493	−	0.772929i	$-0.718791\pi$
$113$	−143.395			−1.26899			−0.634493	+	0.772929i	$0.718791\pi$
$114$	20.8088	−	48.4250i	0.182533	−	0.424781i
$115$		−	261.080i		−	2.27026i
$116$	24.8955	+	26.2413i	0.214617	+	0.226218i
$117$	46.3655			0.396286
$118$	84.5842	+	36.3468i	0.716815	+	0.308024i
$119$		0			0
$120$	−38.8362	−	105.334i	−0.323635	−	0.877783i
$121$	120.627			0.996919
$122$	−33.3270	+	77.5567i	−0.273172	+	0.635711i
$123$		−	55.5156i		−	0.451346i
$124$	101.330	−	96.1334i	0.817178	−	0.775269i
$125$	−49.9080			−0.399264
$126$		0			0
$127$		−	83.0059i		−	0.653590i	−0.945095	−	0.326795i	$-0.894031\pi$
$127$		−	83.0059i		−	0.653590i	0.945095	−	0.326795i	$-0.105969\pi$
$128$	−37.9012	−	122.260i	−0.296103	−	0.955156i
$129$	−42.7303			−0.331243
$130$	54.7863	−	127.495i	0.421433	−	0.980734i
$131$			29.4874i			0.225095i	0.993646	+	0.112547i	$0.0359010\pi$
$131$			29.4874i			0.225095i	−0.993646	+	0.112547i	$0.964099\pi$
$132$	−3.62538	−	3.82136i	−0.0274650	−	0.0289497i
$133$		0			0
$134$	51.0487	+	21.9362i	0.380961	+	0.163703i
$135$			187.310i			1.38748i
$136$	−89.9331	+	33.1580i	−0.661273	+	0.243809i
$137$	−23.5171			−0.171658			−0.0858288	−	0.996310i	$-0.527354\pi$
$137$	−23.5171			−0.171658			−0.0858288	+	0.996310i	$0.527354\pi$
$138$	68.3443	−	159.047i	0.495248	−	1.15251i
$139$		−	256.175i		−	1.84299i	−0.388396	−	0.921493i	$-0.626971\pi$
$139$		−	256.175i		−	1.84299i	0.388396	−	0.921493i	$-0.373029\pi$
$140$		0			0
$141$	−101.585			−0.720459
$142$	−105.085	−	45.1563i	−0.740036	−	0.318002i
$143$		−	6.51097i		−	0.0455313i
$144$	−3.65883	+	69.4660i	−0.0254086	+	0.482403i
$145$	−58.8340			−0.405751
$146$	−44.4779	+	103.506i	−0.304643	+	0.708947i
$147$		0			0
$148$	139.900	+	147.462i	0.945268	+	0.996366i
$149$	89.5652			0.601109			0.300554	−	0.953765i	$-0.402828\pi$
$149$	89.5652			0.601109			0.300554	+	0.953765i	$0.402828\pi$
$150$	68.6823	+	29.5136i	0.457882	+	0.196757i
$151$			47.1444i			0.312215i	0.987740	+	0.156107i	$0.0498946\pi$
$151$			47.1444i			0.312215i	−0.987740	+	0.156107i	$0.950105\pi$
$152$	33.8127	+	91.7089i	0.222452	+	0.603348i
$153$	52.0907			0.340462
$154$		0			0
$155$			227.186i			1.46572i
$156$	66.7504	−	63.3271i	0.427887	−	0.405943i
$157$	287.794			1.83308			0.916540	−	0.399943i	$-0.130970\pi$
$157$	287.794			1.83308			0.916540	+	0.399943i	$0.130970\pi$
$158$	−33.7991	−	14.5239i	−0.213918	−	0.0919232i
$159$		−	57.9741i		−	0.364617i
$160$	186.694	+	92.1433i	1.16684	+	0.575895i
$161$		0			0
$162$	−18.1367	+	42.2067i	−0.111955	+	0.260535i
$163$		−	13.6185i		−	0.0835491i	−0.999127	−	0.0417746i	$-0.986699\pi$
$163$		−	13.6185i		−	0.0835491i	0.999127	−	0.0417746i	$-0.0133011\pi$
$164$	70.8583	+	74.6887i	0.432063	+	0.455419i
$165$	8.56763			0.0519250
$166$	68.6823	+	29.5136i	0.413749	+	0.177793i
$167$			241.587i			1.44663i	0.690519	+	0.723314i	$0.257382\pi$
$167$			241.587i			1.44663i	−0.690519	+	0.723314i	$0.742618\pi$
$168$		0			0
$169$	−55.2683			−0.327031
$170$	61.5513	−	143.239i	0.362067	−	0.842580i
$171$		−	53.1193i		−	0.310639i
$172$	57.4878	−	54.5395i	0.334231	−	0.317090i
$173$	114.755			0.663323			0.331662	−	0.943398i	$-0.392391\pi$
$173$	114.755			0.663323			0.331662	+	0.943398i	$0.392391\pi$
$174$	−35.8410	−	15.4013i	−0.205983	−	0.0885132i
$175$		0			0
$176$	9.75491	+	0.513800i	0.0554256	+	0.00291932i
$177$	−99.2867			−0.560942
$178$	19.5092	−	45.4007i	0.109602	−	0.255060i
$179$		−	26.8330i		−	0.149905i	−0.997187	−	0.0749526i	$-0.976119\pi$
$179$		−	26.8330i		−	0.149905i	0.997187	−	0.0749526i	$-0.0238806\pi$
$180$	−77.8727	−	82.0822i	−0.432626	−	0.456012i
$181$	46.5388			0.257120			0.128560	−	0.991702i	$-0.458964\pi$
$181$	46.5388			0.257120			0.128560	+	0.991702i	$0.458964\pi$
$182$		0			0
$183$		−	91.0377i		−	0.497474i
$184$	111.054	+	301.208i	0.603556	+	1.63700i
$185$	−330.616			−1.78711
$186$	−59.4717	+	138.399i	−0.319740	+	0.744081i
$187$		−	7.31495i		−	0.0391174i
$188$	136.668	−	129.659i	0.726959	−	0.689677i
$189$		0			0
$190$	−146.067	−	62.7667i	−0.768774	−	0.330351i
$191$		−	75.4221i		−	0.394880i	−0.980315	−	0.197440i	$-0.936737\pi$
$191$		−	75.4221i		−	0.394880i	0.980315	−	0.197440i	$-0.0632628\pi$
$192$	89.6109	+	105.005i	0.466723	+	0.546898i
$193$	−166.069			−0.860464			−0.430232	−	0.902718i	$-0.641568\pi$
$193$	−166.069			−0.860464			−0.430232	+	0.902718i	$0.641568\pi$
$194$	−86.7738	+	201.935i	−0.447288	+	1.04090i
$195$			149.657i			0.767471i
$196$		0			0
$197$	279.737			1.41998			0.709991	−	0.704210i	$-0.248699\pi$
$197$	279.737			1.41998			0.709991	+	0.704210i	$0.248699\pi$
$198$	−4.87746	−	2.09590i	−0.0246336	−	0.0105854i
$199$			0.275346i			0.00138365i	1.00000		0.000691824i	$0.000220215\pi$
$199$			0.275346i			0.00138365i	−1.00000		0.000691824i	$0.999780\pi$
$200$	−130.073	+	47.9574i	−0.650365	+	0.239787i
$201$	−59.9221			−0.298120
$202$	−34.0725	+	79.2916i	−0.168676	+	0.392533i
$203$		0			0
$204$	74.9928	−	71.1468i	0.367612	−	0.348759i
$205$	−167.455			−0.816852
$206$	−276.761	−	118.927i	−1.34350	−	0.577317i
$207$		−	174.465i		−	0.842825i
$208$	−8.97490	+	170.396i	−0.0431486	+	0.819211i
$209$	−7.45940			−0.0356909
$210$		0			0
$211$		−	301.264i		−	1.42779i	−0.700252	−	0.713896i	$-0.746929\pi$
$211$		−	301.264i		−	1.42779i	0.700252	−	0.713896i	$-0.253071\pi$
$212$	73.9962	+	77.9962i	0.349039	+	0.367907i
$213$	123.351			0.579113
$214$	74.5869	+	32.0509i	0.348537	+	0.149770i
$215$			128.890i			0.599487i
$216$	−79.6751	−	216.100i	−0.368866	−	1.00046i
$217$		0			0
$218$	52.5329	−	122.252i	0.240977	−	0.560787i
$219$		−	121.498i		−	0.554785i
$220$	−11.5266	+	10.9354i	−0.0523935	+	0.0497065i
$221$	127.775			0.578170
$222$	−201.407	−	86.5471i	−0.907241	−	0.389852i
$223$		−	215.034i		−	0.964279i	−0.876094	−	0.482140i	$-0.839860\pi$
$223$		−	215.034i		−	0.964279i	0.876094	−	0.482140i	$-0.160140\pi$
$224$		0			0
$225$	75.3404			0.334846
$226$	−113.226	+	263.494i	−0.501001	+	1.16590i
$227$			421.401i			1.85639i	0.372094	+	0.928195i	$0.378640\pi$
$227$			421.401i			1.85639i	−0.372094	+	0.928195i	$0.621360\pi$
$228$	−72.5517	−	76.4736i	−0.318209	−	0.335411i
$229$	−45.5273			−0.198809			−0.0994046	−	0.995047i	$-0.531694\pi$
$229$	−45.5273			−0.198809			−0.0994046	+	0.995047i	$0.531694\pi$
$230$	−479.742	−	206.151i	−2.08583	−	0.896307i
$231$		0			0
$232$	67.8769	−	25.0259i	0.292573	−	0.107870i
$233$	151.446			0.649985			0.324992	−	0.945717i	$-0.394638\pi$
$233$	151.446			0.649985			0.324992	+	0.945717i	$0.394638\pi$
$234$	36.6106	−	85.1980i	0.156455	−	0.364094i
$235$			306.415i			1.30390i
$236$	133.577	−	126.726i	0.566003	−	0.536976i
$237$	39.6741			0.167401
$238$		0			0
$239$			200.986i			0.840944i	0.907306	+	0.420472i	$0.138135\pi$
$239$			200.986i			0.840944i	−0.907306	+	0.420472i	$0.861865\pi$
$240$	−224.220	−	11.8098i	−0.934249	−	0.0492077i
$241$	−248.637			−1.03169			−0.515844	−	0.856683i	$-0.672522\pi$
$241$	−248.637			−1.03169			−0.515844	+	0.856683i	$0.672522\pi$
$242$	95.2483	−	221.656i	0.393588	−	0.915935i
$243$			209.567i			0.862414i
$244$	116.198	+	122.479i	0.476220	+	0.501963i
$245$		0			0
$246$	−102.012	−	43.8356i	−0.414681	−	0.178193i
$247$		−	130.299i		−	0.527525i
$248$	−96.6370	−	262.105i	−0.389665	−	1.05687i
$249$	−80.6208			−0.323778
$250$	−39.4078	+	91.7075i	−0.157631	+	0.366830i
$251$			226.888i			0.903938i	0.892034	+	0.451969i	$0.149278\pi$
$251$			226.888i			0.903938i	−0.892034	+	0.451969i	$0.850722\pi$
$252$		0			0
$253$	−24.4996			−0.0968364
$254$	−152.526	−	65.5421i	−0.600495	−	0.258040i
$255$			168.137i			0.659359i
$256$	−254.584	−	26.8929i	−0.994467	−	0.105050i
$257$	−355.166			−1.38197			−0.690984	−	0.722870i	$-0.742823\pi$
$257$	−355.166			−1.38197			−0.690984	+	0.722870i	$0.742823\pi$
$258$	−33.7402	+	78.5182i	−0.130776	+	0.304334i
$259$		0			0
$260$	−191.017	−	201.343i	−0.734681	−	0.774396i
$261$	−39.3154			−0.150634
$262$	54.1840	+	23.2835i	0.206809	+	0.0888683i
$263$			390.604i			1.48519i	0.669743	+	0.742593i	$0.266404\pi$
$263$			390.604i			1.48519i	−0.669743	+	0.742593i	$0.733596\pi$
$264$	−9.88449	+	3.64437i	−0.0374413	+	0.0138044i
$265$	−174.870			−0.659888
$266$		0			0
$267$			53.2923i			0.199597i
$268$	80.6170	−	76.4826i	0.300810	−	0.285383i
$269$	374.742			1.39309			0.696546	−	0.717512i	$-0.254719\pi$
$269$	374.742			1.39309			0.696546	+	0.717512i	$0.254719\pi$
$270$	344.187	+	147.901i	1.27477	+	0.547782i
$271$			153.297i			0.565672i	0.959168	+	0.282836i	$0.0912752\pi$
$271$			153.297i			0.565672i	−0.959168	+	0.282836i	$0.908725\pi$
$272$	−10.0831	+	191.437i	−0.0370703	+	0.703811i
$273$		0			0
$274$	−18.5693	+	43.2134i	−0.0677712	+	0.157713i
$275$		−	10.5798i		−	0.0384721i
$276$	−238.288	−	251.169i	−0.863363	−	0.910034i
$277$	449.775			1.62374			0.811869	−	0.583840i	$-0.198451\pi$
$277$	449.775			1.62374			0.811869	+	0.583840i	$0.198451\pi$
$278$	−470.729	−	202.278i	−1.69327	−	0.727618i
$279$			151.815i			0.544141i
$280$		0			0
$281$	−3.27554			−0.0116567			−0.00582836	−	0.999983i	$-0.501855\pi$
$281$	−3.27554			−0.0116567			−0.00582836	+	0.999983i	$0.501855\pi$
$282$	−80.2121	+	186.665i	−0.284440	+	0.661932i
$283$			342.307i			1.20957i	0.796390	+	0.604783i	$0.206740\pi$
$283$			342.307i			1.20957i	−0.796390	+	0.604783i	$0.793260\pi$
$284$	−165.952	+	157.441i	−0.584338	+	0.554371i
$285$	171.457			0.601602
$286$	−11.9641	−	5.14112i	−0.0418326	−	0.0179759i
$287$		0			0
$288$	124.757	+	61.5741i	0.433183	+	0.213799i
$289$	−145.447			−0.503276
$290$	−46.4558	+	108.109i	−0.160192	+	0.372790i
$291$		−	237.035i		−	0.814555i
$292$	155.076	+	163.459i	0.531082	+	0.559791i
$293$	243.752			0.831919			0.415959	−	0.909383i	$-0.363446\pi$
$293$	243.752			0.831919			0.415959	+	0.909383i	$0.363446\pi$
$294$		0			0
$295$			299.484i			1.01520i
$296$	381.432	−	140.633i	1.28862	−	0.475110i
$297$	17.5771			0.0591820
$298$	70.7214	−	164.579i	0.237320	−	0.552278i
$299$		−	427.952i		−	1.43128i
$300$	108.464	−	102.902i	0.361548	−	0.343006i
$301$		0			0
$302$	86.6293	+	37.2256i	0.286852	+	0.123264i
$303$		−	93.0741i		−	0.307175i
$304$	195.217	+	10.2822i	0.642160	+	0.0338231i
$305$	−274.602			−0.900335
$306$	41.1313	−	95.7183i	0.134416	−	0.312805i
$307$		−	58.4520i		−	0.190397i	−0.995458	−	0.0951987i	$-0.969651\pi$
$307$		−	58.4520i		−	0.190397i	0.995458	−	0.0951987i	$-0.0303487\pi$
$308$		0			0
$309$	324.868			1.05135
$310$	417.461	+	179.388i	1.34665	+	0.578670i
$311$		−	124.387i		−	0.399957i	−0.979800	−	0.199978i	$-0.935913\pi$
$311$		−	124.387i		−	0.399957i	0.979800	−	0.199978i	$-0.0640872\pi$
$312$	−63.6588	−	172.659i	−0.204035	−	0.553396i
$313$	481.450			1.53818			0.769090	−	0.639140i	$-0.220710\pi$
$313$	481.450			1.53818			0.769090	+	0.639140i	$0.220710\pi$
$314$	227.244	−	528.830i	0.723708	−	1.68417i
$315$		0			0
$316$	−53.3761	+	50.6387i	−0.168912	+	0.160249i
$317$	−359.147			−1.13296			−0.566478	−	0.824077i	$-0.691694\pi$
$317$	−359.147			−1.13296			−0.566478	+	0.824077i	$0.691694\pi$
$318$	−106.529	−	45.7768i	−0.334997	−	0.143952i
$319$			5.52095i			0.0173071i
$320$	316.731	−	270.298i	0.989784	−	0.844682i
$321$	−87.5517			−0.272747
$322$		0			0
$323$		−	146.388i		−	0.453214i
$324$	63.2351	+	66.6534i	0.195170	+	0.205720i
$325$	184.805			0.568632
$326$	−25.0244	−	10.7533i	−0.0767620	−	0.0329855i
$327$			143.502i			0.438843i
$328$	193.193	−	71.2295i	0.589003	−	0.217163i
$329$		0			0
$330$	6.76507	−	15.7433i	0.0205002	−	0.0477069i
$331$		−	126.695i		−	0.382765i	−0.981516	−	0.191383i	$-0.938703\pi$
$331$		−	126.695i		−	0.382765i	0.981516	−	0.191383i	$-0.0612971\pi$
$332$	108.464	−	102.902i	0.326700	−	0.309945i
$333$	−220.932			−0.663459
$334$	443.923	+	190.759i	1.32911	+	0.571135i
$335$			180.746i			0.539541i
$336$		0			0
$337$	−551.430			−1.63629			−0.818146	−	0.575011i	$-0.804998\pi$
$337$	−551.430			−1.63629			−0.818146	+	0.575011i	$0.804998\pi$
$338$	−43.6403	+	101.557i	−0.129113	+	0.300465i
$339$		−	309.294i		−	0.912373i
$340$	−214.604	−	226.205i	−0.631188	−	0.665308i
$341$	21.3190			0.0625191
$342$	−97.6084	−	41.9435i	−0.285405	−	0.122642i
$343$		0			0
$344$	−54.8252	−	148.700i	−0.159376	−	0.432269i
$345$	563.131			1.63226
$346$	90.6114	−	210.866i	0.261883	−	0.609438i
$347$		−	411.284i		−	1.18526i	−0.805476	−	0.592628i	$-0.798090\pi$
$347$		−	411.284i		−	1.18526i	0.805476	−	0.592628i	$-0.201910\pi$
$348$	−56.6007	+	53.6980i	−0.162646	+	0.154304i
$349$	402.535			1.15340			0.576698	−	0.816957i	$-0.304341\pi$
$349$	402.535			1.15340			0.576698	+	0.816957i	$0.304341\pi$
$350$		0			0
$351$			307.031i			0.874732i
$352$	8.64668	−	17.5193i	0.0245644	−	0.0497706i
$353$	59.9189			0.169742			0.0848709	−	0.996392i	$-0.472952\pi$
$353$	59.9189			0.169742			0.0848709	+	0.996392i	$0.472952\pi$
$354$	−78.3976	+	182.442i	−0.221462	+	0.515374i
$355$		−	372.071i		−	1.04809i
$356$	−68.0205	−	71.6975i	−0.191069	−	0.201397i
$357$		0			0
$358$	−49.3065	−	21.1876i	−0.137728	−	0.0591832i
$359$		−	140.712i		−	0.391955i	−0.980608	−	0.195977i	$-0.937212\pi$
$359$		−	140.712i		−	0.391955i	0.980608	−	0.195977i	$-0.0627879\pi$
$360$	−212.318	+	78.2806i	−0.589771	+	0.217446i
$361$	211.721			0.586486
$362$	36.7474	−	85.5164i	0.101512	−	0.236233i
$363$			260.185i			0.716763i
$364$		0			0
$365$	−366.481			−1.00406
$366$	−167.285	−	71.8841i	−0.457062	−	0.196405i
$367$		−	333.378i		−	0.908387i	−0.890903	−	0.454193i	$-0.849928\pi$
$367$		−	333.378i		−	0.908387i	0.890903	−	0.454193i	$-0.150072\pi$
$368$	641.169	+	33.7709i	1.74231	+	0.0917688i
$369$	−111.901			−0.303254
$370$	−261.057	+	607.517i	−0.705559	+	1.64194i
$371$		0			0
$372$	207.353	+	218.562i	0.557401	+	0.587533i
$373$	−257.441			−0.690191			−0.345095	−	0.938568i	$-0.612153\pi$
$373$	−257.441			−0.690191			−0.345095	+	0.938568i	$0.612153\pi$
$374$	−13.4415	−	5.77595i	−0.0359397	−	0.0154437i
$375$		−	107.648i		−	0.287062i
$376$	−130.339	−	353.512i	−0.346645	−	0.940192i
$377$	−96.4384			−0.255805
$378$		0			0
$379$		−	122.957i		−	0.324426i	−0.986756	−	0.162213i	$-0.948137\pi$
$379$		−	122.957i		−	0.324426i	0.986756	−	0.162213i	$-0.0518631\pi$
$380$	−230.672	+	218.842i	−0.607030	+	0.575899i
$381$	179.038			0.469916
$382$	−138.590	−	59.5539i	−0.362802	−	0.155900i
$383$			348.730i			0.910522i	0.890358	+	0.455261i	$0.150454\pi$
$383$			348.730i			0.910522i	−0.890358	+	0.455261i	$0.849546\pi$
$384$	263.706	−	81.7503i	0.686736	−	0.212891i
$385$		0			0
$386$	−131.130	+	305.158i	−0.339715	+	0.790564i
$387$			86.1297i			0.222557i
$388$	302.544	+	318.899i	0.779753	+	0.821904i
$389$	−353.379			−0.908429			−0.454215	−	0.890892i	$-0.650080\pi$
$389$	−353.379			−0.908429			−0.454215	+	0.890892i	$0.650080\pi$
$390$	274.999	+	118.170i	0.705126	+	0.303001i
$391$		−	480.796i		−	1.22966i
$392$		0			0
$393$	−63.6023			−0.161838
$394$	220.882	−	514.025i	0.560615	−	1.30463i
$395$		−	119.671i		−	0.302965i
$396$	−7.70256	+	7.30754i	−0.0194509	+	0.0184534i
$397$	−182.332			−0.459274			−0.229637	−	0.973276i	$-0.573754\pi$
$397$	−182.332			−0.459274			−0.229637	+	0.973276i	$0.573754\pi$
$398$	0.505957	+	0.217416i	0.00127125	+	0.000546270i
$399$		0			0
$400$	−14.5835	+	276.880i	−0.0364588	+	0.692201i
$401$	345.868			0.862514			0.431257	−	0.902229i	$-0.358070\pi$
$401$	345.868			0.862514			0.431257	+	0.902229i	$0.358070\pi$
$402$	−47.3150	+	110.109i	−0.117699	+	0.273902i
$403$			372.394i			0.924055i
$404$	118.797	+	125.219i	0.294051	+	0.309947i
$405$	−149.439			−0.368986
$406$		0			0
$407$			31.0248i			0.0762281i
$408$	−71.5195	−	193.980i	−0.175293	−	0.475440i
$409$	−305.791			−0.747656			−0.373828	−	0.927498i	$-0.621955\pi$
$409$	−305.791			−0.747656			−0.373828	+	0.927498i	$0.621955\pi$
$410$	−132.224	+	307.703i	−0.322497	+	0.750496i
$411$		−	50.7248i		−	0.123418i
$412$	−437.065	+	414.650i	−1.06084	+	1.00643i
$413$		0			0
$414$	−320.584	−	137.759i	−0.774358	−	0.332751i
$415$			243.181i			0.585978i
$416$	306.021	+	151.038i	0.735628	+	0.363071i
$417$	552.552			1.32506
$418$	−5.89000	+	13.7069i	−0.0140909	+	0.0327916i
$419$		−	749.709i		−	1.78928i	−0.446786	−	0.894641i	$-0.647431\pi$
$419$		−	749.709i		−	1.78928i	0.446786	−	0.894641i	$-0.352569\pi$
$420$		0			0
$421$	356.196			0.846070			0.423035	−	0.906113i	$-0.360965\pi$
$421$	356.196			0.846070			0.423035	+	0.906113i	$0.360965\pi$
$422$	−553.582	−	237.881i	−1.31181	−	0.563698i
$423$			204.760i			0.484066i
$424$	201.748	−	74.3838i	0.475822	−	0.175434i
$425$	207.625			0.488530
$426$	97.3990	−	226.661i	0.228636	−	0.532069i
$427$		0			0
$428$	117.789	−	111.748i	0.275208	−	0.261094i
$429$	14.0437			0.0327360
$430$	236.839	+	101.772i	0.550788	+	0.236680i
$431$		−	189.284i		−	0.439174i	−0.975593	−	0.219587i	$-0.929529\pi$
$431$		−	189.284i		−	0.439174i	0.975593	−	0.219587i	$-0.0704710\pi$
$432$	−460.002	−	24.2287i	−1.06482	−	0.0560849i
$433$	−771.353			−1.78142			−0.890708	−	0.454575i	$-0.849791\pi$
$433$	−771.353			−1.78142			−0.890708	+	0.454575i	$0.849791\pi$
$434$		0			0
$435$		−	126.901i		−	0.291726i
$436$	−183.161	−	193.062i	−0.420093	−	0.442802i
$437$	−490.290			−1.12194
$438$	−223.256	−	95.9357i	−0.509717	−	0.219031i
$439$		−	803.234i		−	1.82969i	−0.403804	−	0.914845i	$-0.632312\pi$
$439$		−	803.234i		−	1.82969i	0.403804	−	0.914845i	$-0.367688\pi$
$440$	10.9927	+	29.8152i	0.0249835	+	0.0677617i
$441$		0			0
$442$	100.893	−	234.791i	0.228264	−	0.531202i
$443$			724.505i			1.63545i	0.575607	+	0.817726i	$0.304766\pi$
$443$			724.505i			1.63545i	−0.575607	+	0.817726i	$0.695234\pi$
$444$	−318.066	+	301.754i	−0.716365	+	0.679626i
$445$	160.748			0.361232
$446$	−395.132	−	169.793i	−0.885946	−	0.380701i
$447$			193.186i			0.432184i
$448$		0			0
$449$	675.025			1.50340			0.751698	−	0.659507i	$-0.229235\pi$
$449$	675.025			1.50340			0.751698	+	0.659507i	$0.229235\pi$
$450$	59.4894	−	138.440i	0.132199	−	0.307645i
$451$			15.7139i			0.0348423i
$452$	394.773	+	416.113i	0.873392	+	0.920605i
$453$	−101.687			−0.224475
$454$	774.337	+	332.741i	1.70559	+	0.732911i
$455$		0			0
$456$	−197.810	+	72.9317i	−0.433794	+	0.159938i
$457$	363.890			0.796258			0.398129	−	0.917330i	$-0.369660\pi$
$457$	363.890			0.796258			0.398129	+	0.917330i	$0.369660\pi$
$458$	−35.9488	+	83.6579i	−0.0784907	+	0.182659i
$459$			344.943i			0.751510i
$460$	−757.616	+	718.762i	−1.64699	+	1.56253i
$461$	233.360			0.506205			0.253102	−	0.967439i	$-0.418549\pi$
$461$	233.360			0.506205			0.253102	+	0.967439i	$0.418549\pi$
$462$		0			0
$463$		−	872.151i		−	1.88370i	−0.336040	−	0.941848i	$-0.609088\pi$
$463$		−	872.151i		−	1.88370i	0.336040	−	0.941848i	$-0.390912\pi$
$464$	7.61023	−	144.487i	0.0164014	−	0.311393i
$465$	−490.025			−1.05382
$466$	119.583	−	278.287i	0.256617	−	0.597183i
$467$			767.807i			1.64413i	0.569396	+	0.822063i	$0.307177\pi$
$467$			767.807i			1.64413i	−0.569396	+	0.822063i	$0.692823\pi$
$468$	−127.646	−	134.546i	−0.272748	−	0.287492i
$469$		0			0
$470$	563.048	+	241.948i	1.19797	+	0.514783i
$471$			620.751i			1.31794i
$472$	−127.390	−	345.516i	−0.269894	−	0.732025i
$473$	12.0950			0.0255707
$474$	31.3270	−	72.9023i	0.0660907	−	0.153802i
$475$		−	211.725i		−	0.445737i
$476$		0			0
$477$	−116.856			−0.244981
$478$	369.317	+	158.700i	0.772630	+	0.332008i
$479$		−	787.730i		−	1.64453i	−0.569105	−	0.822265i	$-0.692710\pi$
$479$		−	787.730i		−	1.64453i	0.569105	−	0.822265i	$-0.307290\pi$
$480$	−198.747	+	402.686i	−0.414056	+	0.838928i
$481$	−541.933			−1.12668
$482$	−196.326	+	456.878i	−0.407315	+	0.947879i
$483$		0			0
$484$	−332.091	−	350.043i	−0.686139	−	0.723230i
$485$	−714.983			−1.47419
$486$	385.085	+	165.476i	0.792356	+	0.340485i
$487$		−	36.7668i		−	0.0754965i	−0.999287	−	0.0377483i	$-0.987981\pi$
$487$		−	36.7668i		−	0.0754965i	0.999287	−	0.0377483i	$-0.0120185\pi$
$488$	316.809	−	116.806i	0.649199	−	0.239357i
$489$	29.3742			0.0600699
$490$		0			0
$491$		−	413.002i		−	0.841145i	−0.907259	−	0.420573i	$-0.861829\pi$
$491$		−	413.002i		−	0.841145i	0.907259	−	0.420573i	$-0.138171\pi$
$492$	−161.098	+	152.836i	−0.327436	+	0.310643i
$493$	−108.347			−0.219770
$494$	−239.428	−	102.885i	−0.484671	−	0.208269i
$495$		−	17.2694i		−	0.0348877i
$496$	−557.931	−	29.3867i	−1.12486	−	0.0592474i
$497$		0			0
$498$	−63.6588	+	148.143i	−0.127829	+	0.297476i
$499$		−	676.459i		−	1.35563i	−0.735233	−	0.677814i	$-0.762927\pi$
$499$		−	676.459i		−	1.35563i	0.735233	−	0.677814i	$-0.237073\pi$
$500$	137.399	+	144.826i	0.274797	+	0.289652i
$501$	−521.087			−1.04009
$502$	416.914	+	179.153i	0.830507	+	0.356878i
$503$			88.3032i			0.175553i	0.996140	+	0.0877765i	$0.0279761\pi$
$503$			88.3032i			0.175553i	−0.996140	+	0.0877765i	$0.972024\pi$
$504$		0			0
$505$	−280.745			−0.555930
$506$	−19.3451	+	45.0188i	−0.0382314	+	0.0889699i
$507$		−	119.210i		−	0.235128i
$508$	−240.871	+	228.518i	−0.474156	+	0.449839i
$509$	260.268			0.511332			0.255666	−	0.966765i	$-0.417705\pi$
$509$	260.268			0.511332			0.255666	+	0.966765i	$0.417705\pi$
$510$	308.956	+	132.762i	0.605796	+	0.260318i
$511$		0			0
$512$	−250.438	+	446.570i	−0.489136	+	0.872207i
$513$	351.755			0.685682
$514$	−280.442	+	652.628i	−0.545607	+	1.26970i
$515$		−	979.917i		−	1.90275i
$516$	117.638	+	123.997i	0.227981	+	0.240305i
$517$	28.7539			0.0556168
$518$		0			0
$519$			247.519i			0.476914i
$520$	−520.802	+	192.018i	−1.00154	+	0.369265i
$521$	592.291			1.13683			0.568417	−	0.822740i	$-0.307556\pi$
$521$	592.291			1.13683			0.568417	+	0.822740i	$0.307556\pi$
$522$	−31.0438	+	72.2433i	−0.0594708	+	0.138397i
$523$			482.245i			0.922075i	0.887381	+	0.461038i	$0.152523\pi$
$523$			482.245i			0.922075i	−0.887381	+	0.461038i	$0.847477\pi$
$524$	85.5682	−	81.1799i	0.163298	−	0.154923i
$525$		0			0
$526$	717.746	+	308.424i	1.36454	+	0.586357i
$527$			418.378i			0.793886i
$528$	−1.10823	+	21.0407i	−0.00209892	+	0.0398498i
$529$	−1081.30			−2.04405
$530$	−138.079	+	321.330i	−0.260527	+	0.606283i
$531$			200.128i			0.376889i
$532$		0			0
$533$	−274.485			−0.514982
$534$	97.9262	+	42.0800i	0.183382	+	0.0788015i
$535$			264.087i			0.493621i
$536$	−76.8832	−	208.527i	−0.143439	−	0.389044i
$537$	57.8770			0.107778
$538$	295.899	−	688.600i	0.549999	−	1.27993i
$539$		0			0
$540$	543.546	−	515.671i	1.00657	−	0.954946i
$541$	381.660			0.705472			0.352736	−	0.935723i	$-0.385251\pi$
$541$	381.660			0.705472			0.352736	+	0.935723i	$0.385251\pi$
$542$	281.688	+	121.045i	0.519720	+	0.223330i
$543$			100.381i			0.184864i
$544$	343.809	+	169.688i	0.632002	+	0.311926i
$545$	432.852			0.794223
$546$		0			0
$547$			826.228i			1.51047i	0.655453	+	0.755236i	$0.272478\pi$
$547$			826.228i			1.51047i	−0.655453	+	0.755236i	$0.727522\pi$
$548$	64.7435	+	68.2433i	0.118145	+	0.124532i
$549$	−183.501			−0.334246
$550$	−19.4408	−	8.35393i	−0.0353469	−	0.0151890i
$551$			110.486i			0.200519i
$552$	−649.686	+	239.537i	−1.17697	+	0.433943i
$553$		0			0
$554$	355.146	−	826.476i	0.641058	−	1.49183i
$555$		−	713.116i		−	1.28489i
$556$	−743.384	+	705.259i	−1.33702	+	1.26845i
$557$	358.892			0.644330			0.322165	−	0.946683i	$-0.395589\pi$
$557$	358.892			0.644330			0.322165	+	0.946683i	$0.395589\pi$
$558$	278.966	+	119.875i	0.499938	+	0.214829i
$559$			211.271i			0.377945i
$560$		0			0
$561$	15.7779			0.0281245
$562$	−2.58639	+	6.01890i	−0.00460212	+	0.0107098i
$563$		−	92.7643i		−	0.164768i	−0.996601	−	0.0823839i	$-0.973747\pi$
$563$		−	92.7643i		−	0.164768i	0.996601	−	0.0823839i	$-0.0262534\pi$
$564$	279.666	+	294.784i	0.495862	+	0.522667i
$565$	−932.942			−1.65122
$566$	629.000	+	270.289i	1.11131	+	0.477542i
$567$		0			0
$568$	158.266	+	429.259i	0.278637	+	0.755737i
$569$	−377.886			−0.664124			−0.332062	−	0.943258i	$-0.607744\pi$
$569$	−377.886			−0.664124			−0.332062	+	0.943258i	$0.607744\pi$
$570$	135.384	−	315.057i	0.237515	−	0.552731i
$571$			792.937i			1.38868i	0.719646	+	0.694341i	$0.244304\pi$
$571$			792.937i			1.38868i	−0.719646	+	0.694341i	$0.755696\pi$
$572$	−18.8939	+	17.9250i	−0.0330313	+	0.0313373i
$573$	162.680			0.283910
$574$		0			0
$575$		−	695.389i		−	1.20937i
$576$	211.653	−	180.625i	0.367454	−	0.313585i
$577$	−404.295			−0.700684			−0.350342	−	0.936622i	$-0.613935\pi$
$577$	−404.295			−0.700684			−0.350342	+	0.936622i	$0.613935\pi$
$578$	−114.846	+	267.263i	−0.198695	+	0.462392i
$579$		−	358.201i		−	0.618654i
$580$	161.972	+	170.728i	0.279262	+	0.294358i
$581$		0			0
$582$	−435.560	−	187.165i	−0.748385	−	0.321590i
$583$			16.4098i			0.0281471i
$584$	422.810	−	155.888i	0.723989	−	0.266932i
$585$	301.657			0.515653
$586$	192.469	−	447.902i	0.328445	−	0.764338i
$587$			252.412i			0.430003i	0.976614	+	0.215002i	$0.0689756\pi$
$587$			252.412i			0.430003i	−0.976614	+	0.215002i	$0.931024\pi$
$588$		0			0
$589$	426.639			0.724345
$590$	550.311	+	236.475i	0.932731	+	0.400805i
$591$			603.373i			1.02094i
$592$	42.7655	−	811.938i	0.0722390	−	1.37152i
$593$	442.666			0.746486			0.373243	−	0.927734i	$-0.378246\pi$
$593$	442.666			0.746486			0.373243	+	0.927734i	$0.378246\pi$
$594$	13.8790	−	32.2984i	0.0233653	−	0.0543744i
$595$		0			0
$596$	−246.576	−	259.906i	−0.413719	−	0.436083i
$597$	−0.593903			−0.000994812
$598$	−786.375	−	337.914i	−1.31501	−	0.565074i
$599$		−	232.189i		−	0.387628i	−0.981038	−	0.193814i	$-0.937914\pi$
$599$		−	232.189i		−	0.387628i	0.981038	−	0.193814i	$-0.0620858\pi$
$600$	−103.441	−	280.558i	−0.172401	−	0.467597i
$601$	−127.875			−0.212770			−0.106385	−	0.994325i	$-0.533928\pi$
$601$	−127.875			−0.212770			−0.106385	+	0.994325i	$0.533928\pi$
$602$		0			0
$603$			120.783i			0.200303i
$604$	136.806	−	129.790i	0.226501	−	0.214885i
$605$	784.810			1.29721
$606$	−171.027	−	73.4921i	−0.282222	−	0.121274i
$607$		−	191.867i		−	0.316090i	−0.987432	−	0.158045i	$-0.949481\pi$
$607$		−	191.867i		−	0.316090i	0.987432	−	0.158045i	$-0.0505192\pi$
$608$	173.039	−	350.598i	0.284603	−	0.576641i
$609$		0			0
$610$	−216.828	+	504.590i	−0.355456	+	0.827197i
$611$			502.264i			0.822037i
$612$	−143.408	−	151.160i	−0.234326	−	0.246993i
$613$	326.870			0.533229			0.266615	−	0.963803i	$-0.414095\pi$
$613$	326.870			0.533229			0.266615	+	0.963803i	$0.414095\pi$
$614$	−107.407	−	46.1542i	−0.174931	−	0.0751697i
$615$		−	361.189i		−	0.587299i
$616$		0			0
$617$	−557.014			−0.902778			−0.451389	−	0.892327i	$-0.649071\pi$
$617$	−557.014			−0.902778			−0.451389	+	0.892327i	$0.649071\pi$
$618$	256.518	−	596.954i	0.415078	−	0.965946i
$619$		−	468.023i		−	0.756095i	−0.925786	−	0.378048i	$-0.876596\pi$
$619$		−	468.023i		−	0.756095i	0.925786	−	0.378048i	$-0.123404\pi$
$620$	659.261	−	625.451i	1.06332	−	1.00879i
$621$	1155.30			1.86039
$622$	−228.564	−	98.2166i	−0.367466	−	0.157905i
$623$		0			0
$624$	−367.533	−	19.3583i	−0.588994	−	0.0310228i
$625$	−757.931			−1.21269
$626$	380.157	−	884.680i	0.607280	−	1.41323i
$627$		−	16.0894i		−	0.0256610i
$628$	−792.307	−	835.136i	−1.26163	−	1.32984i
$629$	−608.851			−0.967967
$630$		0			0
$631$			557.865i			0.884096i	0.896991	+	0.442048i	$0.145748\pi$
$631$			557.865i			0.884096i	−0.896991	+	0.442048i	$0.854252\pi$
$632$	50.9040	+	138.065i	0.0805443	+	0.218457i
$633$	649.806			1.02655
$634$	−283.585	+	659.943i	−0.447296	+	1.04092i
$635$		−	540.042i		−	0.850461i
$636$	−168.233	+	159.605i	−0.264517	+	0.250951i
$637$		0			0
$638$	10.1449	+	4.35939i	0.0159011	+	0.00683290i
$639$		−	248.634i		−	0.389098i
$640$	−246.588	−	795.433i	−0.385294	−	1.24286i
$641$	723.554			1.12879			0.564395	−	0.825505i	$-0.309110\pi$
$641$	723.554			1.12879			0.564395	+	0.825505i	$0.309110\pi$
$642$	−69.1316	+	160.879i	−0.107682	+	0.250590i
$643$		−	145.293i		−	0.225961i	−0.993597	−	0.112980i	$-0.963960\pi$
$643$		−	145.293i		−	0.225961i	0.993597	−	0.112980i	$-0.0360397\pi$
$644$		0			0
$645$	−278.006			−0.431018
$646$	−268.992	−	115.589i	−0.416397	−	0.178931i
$647$			340.305i			0.525973i	0.964799	+	0.262987i	$0.0847075\pi$
$647$			340.305i			0.525973i	−0.964799	+	0.262987i	$0.915292\pi$
$648$	172.409	−	63.5664i	0.266063	−	0.0980963i
$649$	28.1035			0.0433027
$650$	145.924	−	339.586i	0.224498	−	0.522439i
$651$		0			0
$652$	−39.5190	+	37.4923i	−0.0606119	+	0.0575035i
$653$	813.859			1.24634			0.623169	−	0.782087i	$-0.285845\pi$
$653$	813.859			1.24634			0.623169	+	0.782087i	$0.285845\pi$
$654$	263.688	+	113.310i	0.403193	+	0.173257i
$655$			191.847i			0.292896i
$656$	21.6604	−	411.241i	0.0330190	−	0.626892i
$657$	−244.898			−0.372753
$658$		0			0
$659$			939.024i			1.42492i	0.701711	+	0.712462i	$0.252420\pi$
$659$			939.024i			1.42492i	−0.701711	+	0.712462i	$0.747580\pi$
$660$	−23.5870	−	24.8620i	−0.0357379	−	0.0376698i
$661$	208.296			0.315122			0.157561	−	0.987509i	$-0.449637\pi$
$661$	208.296			0.315122			0.157561	+	0.987509i	$0.449637\pi$
$662$	−232.806	−	100.040i	−0.351671	−	0.151117i
$663$			275.603i			0.415691i
$664$	−103.441	−	280.558i	−0.155784	−	0.422528i
$665$		0			0
$666$	−174.450	+	405.969i	−0.261936	+	0.609563i
$667$			362.880i			0.544048i
$668$	701.051	−	665.098i	1.04948	−	0.995656i
$669$	463.814			0.693295
$670$	332.127	+	142.719i	0.495712	+	0.213013i
$671$			25.7685i			0.0384032i
$672$		0			0
$673$	634.671			0.943048			0.471524	−	0.881853i	$-0.343704\pi$
$673$	634.671			0.943048			0.471524	+	0.881853i	$0.343704\pi$
$674$	−435.414	+	1013.27i	−0.646015	+	1.50337i
$675$			498.902i			0.739114i
$676$	152.156	+	160.381i	0.225082	+	0.237250i
$677$	−290.116			−0.428531			−0.214266	−	0.976775i	$-0.568736\pi$
$677$	−290.116			−0.428531			−0.214266	+	0.976775i	$0.568736\pi$
$678$	−568.338	−	244.221i	−0.838256	−	0.360208i
$679$		0			0
$680$	−585.112	+	215.728i	−0.860458	+	0.317247i
$681$	−908.933			−1.33470
$682$	16.8337	−	39.1743i	0.0246828	−	0.0574404i
$683$			712.629i			1.04338i	0.853135	+	0.521691i	$0.174698\pi$
$683$			712.629i			1.04338i	−0.853135	+	0.521691i	$0.825302\pi$
$684$	−154.145	+	146.240i	−0.225358	+	0.213800i
$685$	−153.004			−0.223364
$686$		0			0
$687$		−	98.1994i		−	0.142939i
$688$	−316.532	−	16.6720i	−0.460076	−	0.0242326i
$689$	−286.641			−0.416024
$690$	444.653	−	1034.77i	0.644425	−	1.49967i
$691$			404.171i			0.584907i	0.956280	+	0.292454i	$0.0944717\pi$
$691$			404.171i			0.584907i	−0.956280	+	0.292454i	$0.905528\pi$
$692$	−315.925	−	333.003i	−0.456538	−	0.481218i
$693$		0			0
$694$	−755.746	−	324.753i	−1.08897	−	0.467944i
$695$		−	1666.69i		−	2.39812i
$696$	53.9793	+	146.406i	0.0775564	+	0.210353i
$697$	−308.379			−0.442438
$698$	317.845	−	739.671i	0.455365	−	1.05970i
$699$			326.660i			0.467324i
$700$		0			0
$701$	−111.341			−0.158831			−0.0794156	−	0.996842i	$-0.525305\pi$
$701$	−111.341			−0.158831			−0.0794156	+	0.996842i	$0.525305\pi$
$702$	564.178	+	242.434i	0.803673	+	0.345348i
$703$			620.874i			0.883177i
$704$	−25.3647	−	29.7219i	−0.0360294	−	0.0422186i
$705$	−660.917			−0.937472
$706$	47.3124	−	110.103i	0.0670148	−	0.155953i
$707$		0			0
$708$	273.340	+	288.116i	0.386074	+	0.406944i
$709$	772.746			1.08991			0.544955	−	0.838466i	$-0.316547\pi$
$709$	772.746			1.08991			0.544955	+	0.838466i	$0.316547\pi$
$710$	−683.691	−	293.790i	−0.962945	−	0.413789i
$711$		−	79.9695i		−	0.112475i
$712$	−185.456	+	68.3768i	−0.260472	+	0.0960349i
$713$	1401.25			1.96529
$714$		0			0
$715$		−	42.3609i		−	0.0592460i
$716$	−77.8657	+	73.8724i	−0.108751	+	0.103174i
$717$	−433.512			−0.604620
$718$	−258.562	−	111.107i	−0.360115	−	0.154745i
$719$		−	927.896i		−	1.29054i	−0.763956	−	0.645269i	$-0.776745\pi$
$719$		−	927.896i		−	1.29054i	0.763956	−	0.645269i	$-0.223255\pi$
$720$	−23.8046	+	451.951i	−0.0330620	+	0.627710i
$721$		0			0
$722$	167.177	−	389.045i	0.231547	−	0.538843i
$723$		−	536.293i		−	0.741760i
$724$	−128.123	−	135.049i	−0.176965	−	0.186532i
$725$	−156.705			−0.216145
$726$	478.098	+	205.444i	0.658537	+	0.282981i
$727$			811.924i			1.11681i	0.829567	+	0.558407i	$0.188587\pi$
$727$			811.924i			1.11681i	−0.829567	+	0.558407i	$0.811413\pi$
$728$		0			0
$729$	−658.744			−0.903627
$730$	−289.376	+	673.420i	−0.396406	+	0.922493i
$731$			237.359i			0.324705i
$732$	−264.179	+	250.630i	−0.360900	+	0.342391i
$733$	990.793			1.35170			0.675848	−	0.737041i	$-0.263778\pi$
$733$	990.793			1.35170			0.675848	+	0.737041i	$0.263778\pi$
$734$	−612.592	−	263.238i	−0.834594	−	0.358635i
$735$		0			0
$736$	568.327	−	1151.50i	0.772184	−	1.56454i
$737$	16.9611			0.0230138
$738$	−88.3576	+	205.621i	−0.119726	+	0.278619i
$739$		−	1142.78i		−	1.54638i	−0.634173	−	0.773191i	$-0.718659\pi$
$739$		−	1142.78i		−	1.54638i	0.634173	−	0.773191i	$-0.281341\pi$
$740$	910.198	+	959.400i	1.23000	+	1.29649i
$741$	281.045			0.379278
$742$		0			0
$743$			143.488i			0.193120i	0.995327	+	0.0965601i	$0.0307840\pi$
$743$			143.488i			0.193120i	−0.995327	+	0.0965601i	$0.969216\pi$
$744$	565.343	−	208.439i	0.759869	−	0.280161i
$745$	582.718			0.782172
$746$	−203.278	+	473.056i	−0.272490	+	0.634123i
$747$			162.504i			0.217542i
$748$	−21.2270	+	20.1383i	−0.0283783	+	0.0269229i
$749$		0			0
$750$	−197.807	−	84.9999i	−0.263742	−	0.113333i
$751$		−	1388.41i		−	1.84874i	−0.381492	−	0.924372i	$-0.624590\pi$
$751$		−	1388.41i		−	1.84874i	0.381492	−	0.924372i	$-0.375410\pi$
$752$	−752.506	−	39.6351i	−1.00067	−	0.0527063i
$753$	−489.383			−0.649911
$754$	−76.1485	+	177.208i	−0.100993	+	0.235024i
$755$			306.725i			0.406258i
$756$		0			0
$757$	206.398			0.272652			0.136326	−	0.990664i	$-0.456470\pi$
$757$	206.398			0.272652			0.136326	+	0.990664i	$0.456470\pi$
$758$	−225.938	−	97.0882i	−0.298071	−	0.128085i
$759$		−	52.8440i		−	0.0696232i
$760$	219.988	+	596.665i	0.289458	+	0.785086i
$761$	569.735			0.748666			0.374333	−	0.927294i	$-0.377872\pi$
$761$	569.735			0.748666			0.374333	+	0.927294i	$0.377872\pi$
$762$	141.370	−	328.988i	0.185525	−	0.431743i
$763$		0			0
$764$	−218.864	+	207.640i	−0.286472	+	0.271780i
$765$	338.906			0.443015
$766$	640.802	+	275.360i	0.836556	+	0.359478i
$767$			490.903i			0.640030i
$768$	58.0061	−	549.119i	0.0755288	−	0.714999i
$769$	945.548			1.22958			0.614791	−	0.788690i	$-0.289240\pi$
$769$	945.548			1.22958			0.614791	+	0.788690i	$0.289240\pi$
$770$		0			0
$771$		−	766.069i		−	0.993604i
$772$	457.196	+	481.910i	0.592222	+	0.624236i
$773$	−132.943			−0.171984			−0.0859918	−	0.996296i	$-0.527406\pi$
$773$	−132.943			−0.171984			−0.0859918	+	0.996296i	$0.527406\pi$
$774$	158.266	+	68.0087i	0.204478	+	0.0878666i
$775$			605.112i			0.780790i
$776$	824.878	−	304.129i	1.06299	−	0.391919i
$777$		0			0
$778$	−279.031	+	649.345i	−0.358652	+	0.834633i
$779$			314.468i			0.403682i
$780$	434.283	−	412.011i	0.556773	−	0.528219i
$781$	−34.9149			−0.0447054
$782$	−883.477	−	379.640i	−1.12977	−	0.485474i
$783$		−	260.346i		−	0.332497i
$784$		0			0
$785$	1872.41			2.38523
$786$	−50.2209	+	116.871i	−0.0638943	+	0.148691i
$787$			233.948i			0.297266i	0.988892	+	0.148633i	$0.0474873\pi$
$787$			233.948i			0.297266i	−0.988892	+	0.148633i	$0.952513\pi$
$788$	−770.125	−	811.756i	−0.977317	−	1.03015i
$789$	−842.506			−1.06781
$790$	−219.899	−	94.4933i	−0.278354	−	0.119612i
$791$		0			0
$792$	7.34582	+	19.9238i	0.00927502	+	0.0251563i
$793$	−450.117			−0.567613
$794$	−143.971	+	335.040i	−0.181323	+	0.421965i
$795$		−	377.184i		−	0.474445i
$796$	0.799016	−	0.758038i	0.00100379	−	0.000952309i
$797$	−1208.00			−1.51569			−0.757843	−	0.652437i	$-0.773747\pi$
$797$	−1208.00			−1.51569			−0.757843	+	0.652437i	$0.773747\pi$
$798$		0			0
$799$			564.285i			0.706239i
$800$	497.261	+	245.425i	0.621576	+	0.306781i
$801$	107.419			0.134106
$802$	273.100	−	635.543i	0.340524	−	0.792448i
$803$			34.3904i			0.0428274i
$804$	164.968	+	173.885i	0.205184	+	0.216275i
$805$		0			0
$806$	684.286	+	294.046i	0.848990	+	0.364821i
$807$			808.293i			1.00160i
$808$	323.896	−	119.419i	0.400861	−	0.147796i
$809$	69.4856			0.0858907			0.0429453	−	0.999077i	$-0.486326\pi$
$809$	69.4856			0.0858907			0.0429453	+	0.999077i	$0.486326\pi$
$810$	−117.999	+	274.600i	−0.145677	+	0.339012i
$811$			1095.24i			1.35048i	0.737599	+	0.675239i	$0.235959\pi$
$811$			1095.24i			1.35048i	−0.737599	+	0.675239i	$0.764041\pi$
$812$		0			0
$813$	−330.651			−0.406705
$814$	57.0091	+	24.4975i	0.0700357	+	0.0300952i
$815$		−	88.6030i		−	0.108715i
$816$	−412.916	−	21.7486i	−0.506024	−	0.0266527i
$817$	242.046			0.296262
$818$	−241.455	+	561.901i	−0.295178	+	0.686920i
$819$		0			0
$820$	461.009	+	485.930i	0.562206	+	0.592598i
$821$	−756.021			−0.920854			−0.460427	−	0.887698i	$-0.652304\pi$
$821$	−756.021			−0.920854			−0.460427	+	0.887698i	$0.652304\pi$
$822$	−93.2084	−	40.0527i	−0.113392	−	0.0487259i
$823$		−	320.066i		−	0.388902i	−0.980912	−	0.194451i	$-0.937707\pi$
$823$		−	320.066i		−	0.388902i	0.980912	−	0.194451i	$-0.0622925\pi$
$824$	416.823	+	1130.53i	0.505853	+	1.37200i
$825$	22.8200			0.0276606
$826$		0			0
$827$		−	104.960i		−	0.126917i	−0.997984	−	0.0634585i	$-0.979787\pi$
$827$		−	104.960i		−	0.126917i	0.997984	−	0.0634585i	$-0.0202131\pi$
$828$	−506.272	+	480.308i	−0.611440	+	0.580082i
$829$	−817.667			−0.986329			−0.493164	−	0.869936i	$-0.664160\pi$
$829$	−817.667			−0.986329			−0.493164	+	0.869936i	$0.664160\pi$
$830$	446.852	+	192.018i	0.538376	+	0.231347i
$831$			970.135i			1.16743i
$832$	519.173	−	443.063i	0.624006	−	0.532527i
$833$		0			0
$834$	436.300	−	1015.33i	0.523141	−	1.21742i
$835$			1571.78i			1.88237i
$836$	20.5360	+	21.6461i	0.0245646	+	0.0258925i
$837$	−1005.32			−1.20110
$838$	−1377.61	−	591.976i	−1.64393	−	0.706416i
$839$		−	1029.02i		−	1.22648i	−0.789896	−	0.613240i	$-0.789866\pi$
$839$		−	1029.02i		−	1.22648i	0.789896	−	0.613240i	$-0.210134\pi$
$840$		0			0
$841$	−759.225			−0.902765
$842$	281.255	−	654.520i	0.334032	−	0.777340i
$843$		−	7.06511i		−	0.00838092i
$844$	−874.225	+	829.391i	−1.03581	+	0.982691i
$845$	−359.579			−0.425538
$846$	376.253	+	161.680i	0.444744	+	0.191111i
$847$		0			0
$848$	22.6197	−	429.453i	0.0266741	−	0.506430i
$849$	−738.334			−0.869651
$850$	163.943	−	381.518i	0.192874	−	0.448845i
$851$			2039.19i			2.39623i
$852$	−339.590	−	357.947i	−0.398580	−	0.420126i
$853$	−583.808			−0.684417			−0.342209	−	0.939624i	$-0.611175\pi$
$853$	−583.808			−0.684417			−0.342209	+	0.939624i	$0.611175\pi$
$854$		0			0
$855$		−	345.598i		−	0.404209i
$856$	−112.334	−	304.678i	−0.131231	−	0.355932i
$857$	1098.14			1.28138			0.640691	−	0.767799i	$-0.278648\pi$
$857$	1098.14			1.28138			0.640691	+	0.767799i	$0.278648\pi$
$858$	11.0890	−	25.8058i	0.0129243	−	0.0300767i
$859$		−	299.173i		−	0.348281i	−0.984721	−	0.174141i	$-0.944285\pi$
$859$		−	299.173i		−	0.348281i	0.984721	−	0.174141i	$-0.0557147\pi$
$860$	374.020	−	354.838i	0.434907	−	0.412603i
$861$		0			0
$862$	−347.815	−	149.460i	−0.403498	−	0.173388i
$863$			941.506i			1.09097i	0.838121	+	0.545485i	$0.183654\pi$
$863$			941.506i			1.09097i	−0.838121	+	0.545485i	$0.816346\pi$
$864$	−407.742	+	826.136i	−0.471924	+	0.956176i
$865$	746.604			0.863126
$866$	−609.067	+	1417.39i	−0.703311	+	1.63670i
$867$		−	313.719i		−	0.361844i
$868$		0			0
$869$	−11.2299			−0.0129228
$870$	−233.184	−	100.202i	−0.268028	−	0.115175i
$871$			296.272i			0.340152i
$872$	−499.382	+	184.120i	−0.572686	+	0.211147i
$873$	−477.783			−0.547289
$874$	−387.137	+	900.922i	−0.442948	+	1.03080i
$875$		0			0
$876$	−352.570	+	334.488i	−0.402477	+	0.381836i
$877$	983.390			1.12131			0.560655	−	0.828049i	$-0.310549\pi$
$877$	983.390			1.12131			0.560655	+	0.828049i	$0.310549\pi$
$878$	−1475.97	−	634.240i	−1.68106	−	0.722369i
$879$			525.757i			0.598131i
$880$	63.4662	+	3.34282i	0.0721207	+	0.00379866i
$881$	155.250			0.176220			0.0881102	−	0.996111i	$-0.471917\pi$
$881$	155.250			0.176220			0.0881102	+	0.996111i	$0.471917\pi$
$882$		0			0
$883$		−	612.809i		−	0.694008i	−0.937864	−	0.347004i	$-0.887199\pi$
$883$		−	612.809i		−	0.694008i	0.937864	−	0.347004i	$-0.112801\pi$
$884$	−351.771	−	370.786i	−0.397931	−	0.419442i
$885$	−645.967			−0.729906
$886$	1331.30	+	572.075i	1.50260	+	0.645683i
$887$			142.947i			0.161158i	0.996748	+	0.0805791i	$0.0256770\pi$
$887$			142.947i			0.161158i	−0.996748	+	0.0805791i	$0.974323\pi$
$888$	303.335	+	822.724i	0.341593	+	0.926490i
$889$		0			0
$890$	126.928	−	295.380i	0.142616	−	0.331888i
$891$			14.0233i			0.0157389i
$892$	−623.999	+	591.997i	−0.699551	+	0.663674i
$893$	575.427			0.644375
$894$	354.985	+	152.541i	0.397075	+	0.170628i
$895$		−	174.578i		−	0.195059i
$896$		0			0
$897$	923.063			1.02906
$898$	533.005	−	1240.38i	0.593547	−	1.38127i
$899$		−	315.770i		−	0.351246i
$900$	−207.415	−	218.627i	−0.230461	−	0.242919i
$901$	−322.036			−0.357420
$902$	28.8747	+	12.4078i	0.0320119	+	0.0137559i
$903$		0			0
$904$	1076.34	−	396.841i	1.19064	−	0.438984i
$905$	302.785			0.334569
$906$	−80.2931	+	186.854i	−0.0886238	+	0.206240i
$907$		−	1350.76i		−	1.48926i	−0.667475	−	0.744632i	$-0.732625\pi$
$907$		−	1350.76i		−	1.48926i	0.667475	−	0.744632i	$-0.267375\pi$
$908$	1222.85	−	1160.13i	1.34675	−	1.27768i
$909$	−187.606			−0.206387
$910$		0			0
$911$		−	215.218i		−	0.236244i	−0.992999	−	0.118122i	$-0.962313\pi$
$911$		−	215.218i		−	0.236244i	0.992999	−	0.118122i	$-0.0376874\pi$
$912$	−22.1781	+	421.069i	−0.0243181	+	0.461699i
$913$	22.8200			0.0249945
$914$	287.330	−	668.658i	0.314366	−	0.731574i
$915$		−	592.298i		−	0.647321i
$916$	125.338	+	132.114i	0.136832	+	0.144229i
$917$		0			0
$918$	633.844	+	272.370i	0.690462	+	0.296699i
$919$			8.84031i			0.00961949i	0.999988	+	0.00480975i	$0.00153100\pi$
$919$			8.84031i			0.00961949i	−0.999988	+	0.00480975i	$0.998469\pi$
$920$	722.528	+	1959.68i	0.785356	+	2.13009i
$921$	126.077			0.136891
$922$	184.263	−	428.807i	0.199852	−	0.465083i
$923$		−	609.884i		−	0.660763i
$924$		0			0
$925$	−880.599			−0.951999
$926$	−1602.60	−	688.658i	−1.73067	−	0.743691i
$927$		−	654.823i		−	0.706389i
$928$	−259.489	−	128.072i	−0.279622	−	0.138008i
$929$	−1424.55			−1.53342			−0.766710	−	0.641993i	$-0.778108\pi$
$929$	−1424.55			−1.53342			−0.766710	+	0.641993i	$0.778108\pi$
$930$	−386.927	+	900.435i	−0.416051	+	0.968210i
$931$		0			0
$932$	−416.938	−	439.476i	−0.447358	−	0.471541i
$933$	268.293			0.287560
$934$	1410.87	+	606.267i	1.51057	+	0.649108i
$935$		−	47.5916i		−	0.0509002i
$936$	−348.023	+	128.315i	−0.371819	+	0.137088i
$937$	−616.709			−0.658174			−0.329087	−	0.944300i	$-0.606741\pi$
$937$	−616.709			−0.658174			−0.329087	+	0.944300i	$0.606741\pi$
$938$		0			0
$939$			1038.46i			1.10592i
$940$	889.174	−	843.573i	0.945930	−	0.897418i
$941$	−935.337			−0.993981			−0.496991	−	0.867756i	$-0.665562\pi$
$941$	−935.337			−0.993981			−0.496991	+	0.867756i	$0.665562\pi$
$942$	1140.65	+	490.150i	1.21088	+	0.520330i
$943$			1032.84i			1.09527i
$944$	−735.484	−	38.7386i	−0.779114	−	0.0410366i
$945$		0			0
$946$	9.55028	−	22.2248i	0.0100954	−	0.0234935i
$947$		−	1140.94i		−	1.20479i	−0.798198	−	0.602395i	$-0.794213\pi$
$947$		−	1140.94i		−	1.20479i	0.798198	−	0.602395i	$-0.205787\pi$
$948$	−109.224	−	115.129i	−0.115215	−	0.121444i
$949$	−600.721			−0.633004
$950$	−389.052	−	167.180i	−0.409528	−	0.175979i
$951$		−	774.656i		−	0.814570i
$952$		0			0
$953$	−1265.64			−1.32806			−0.664030	−	0.747706i	$-0.731155\pi$
$953$	−1265.64			−1.32806			−0.664030	+	0.747706i	$0.731155\pi$
$954$	−92.2705	+	214.727i	−0.0967196	+	0.225080i
$955$		−	490.702i		−	0.513824i
$956$	583.232	−	553.321i	0.610075	−	0.578788i
$957$	−11.9083			−0.0124434
$958$	−1447.48	−	621.998i	−1.51094	−	0.649267i
$959$		0			0
$960$	583.015	+	683.167i	0.607307	+	0.711633i
$961$	−258.339			−0.268823
$962$	−427.914	+	995.818i	−0.444818	+	1.03515i
$963$			176.475i			0.183255i
$964$	684.506	+	721.509i	0.710069	+	0.748453i
$965$	−1080.46			−1.11965
$966$		0			0
$967$		−	1527.55i		−	1.57968i	−0.613313	−	0.789840i	$-0.710164\pi$
$967$		−	1527.55i		−	1.57968i	0.613313	−	0.789840i	$-0.289836\pi$
$968$	−905.437	+	333.831i	−0.935369	+	0.344867i
$969$	315.749			0.325850
$970$	−564.557	+	1313.80i	−0.582017	+	1.35444i
$971$			180.481i			0.185871i	0.995672	+	0.0929356i	$0.0296251\pi$
$971$			180.481i			0.185871i	−0.995672	+	0.0929356i	$0.970375\pi$
$972$	608.133	−	576.945i	0.625651	−	0.593565i
$973$		0			0
$974$	−67.5601	−	29.0314i	−0.0693636	−	0.0298063i
$975$			398.613i			0.408834i
$976$	35.5201	−	674.378i	0.0363935	−	0.690961i
$977$	−893.776			−0.914817			−0.457408	−	0.889257i	$-0.651222\pi$
$977$	−893.776			−0.914817			−0.457408	+	0.889257i	$0.651222\pi$
$978$	23.1941	−	53.9760i	0.0237159	−	0.0551902i
$979$		−	15.0846i		−	0.0154081i
$980$		0			0
$981$	289.250			0.294852
$982$	−758.904	−	326.110i	−0.772815	−	0.332088i
$983$		−	647.994i		−	0.659201i	−0.944121	−	0.329600i	$-0.893086\pi$
$983$		−	647.994i		−	0.659201i	0.944121	−	0.329600i	$-0.106914\pi$
$984$	153.637	+	416.704i	0.156135	+	0.423480i
$985$	1819.99			1.84770
$986$	−85.5514	+	199.090i	−0.0867662	+	0.201917i
$987$		0			0
$988$	−378.108	+	358.717i	−0.382700	+	0.363074i
$989$	794.975			0.803817
$990$	−31.7331	−	13.6361i	−0.0320536	−	0.0137738i
$991$		−	1348.08i		−	1.36032i	−0.733062	−	0.680162i	$-0.761909\pi$
$991$		−	1348.08i		−	1.36032i	0.733062	−	0.680162i	$-0.238091\pi$
$992$	−494.546	+	1002.01i	−0.498534	+	1.01009i
$993$	273.273			0.275199
$994$		0			0
$995$			1.79142i			0.00180042i
$996$	221.952	+	233.950i	0.222843	+	0.234890i
$997$	−513.572			−0.515117			−0.257559	−	0.966263i	$-0.582918\pi$
$997$	−513.572			−0.515117			−0.257559	+	0.966263i	$0.582918\pi$
$998$	−1243.01	−	534.137i	−1.24550	−	0.535208i
$999$		−	1463.00i		−	1.46447i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.3.c.h.99.3		6
4.3	odd	2	inner	196.3.c.h.99.4		6
7.2	even	3		196.3.g.i.67.1		12
7.3	odd	6		28.3.g.a.23.5	yes	12
7.4	even	3		196.3.g.i.79.5		12
7.5	odd	6		28.3.g.a.11.1	✓	12
7.6	odd	2		196.3.c.i.99.3		6
21.5	even	6		252.3.y.c.235.6		12
21.17	even	6		252.3.y.c.163.2		12
28.3	even	6		28.3.g.a.23.1	yes	12
28.11	odd	6		196.3.g.i.79.1		12
28.19	even	6		28.3.g.a.11.5	yes	12
28.23	odd	6		196.3.g.i.67.5		12
28.27	even	2		196.3.c.i.99.4		6
56.3	even	6		448.3.r.h.191.2		12
56.5	odd	6		448.3.r.h.319.2		12
56.19	even	6		448.3.r.h.319.5		12
56.45	odd	6		448.3.r.h.191.5		12
84.47	odd	6		252.3.y.c.235.2		12
84.59	odd	6		252.3.y.c.163.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.3.g.a.11.1	✓	12	7.5	odd	6
28.3.g.a.11.5	yes	12	28.19	even	6
28.3.g.a.23.1	yes	12	28.3	even	6
28.3.g.a.23.5	yes	12	7.3	odd	6
196.3.c.h.99.3		6	1.1	even	1	trivial
196.3.c.h.99.4		6	4.3	odd	2	inner
196.3.c.i.99.3		6	7.6	odd	2
196.3.c.i.99.4		6	28.27	even	2
196.3.g.i.67.1		12	7.2	even	3
196.3.g.i.67.5		12	28.23	odd	6
196.3.g.i.79.1		12	28.11	odd	6
196.3.g.i.79.5		12	7.4	even	3
252.3.y.c.163.2		12	21.17	even	6
252.3.y.c.163.6		12	84.59	odd	6
252.3.y.c.235.2		12	84.47	odd	6
252.3.y.c.235.6		12	21.5	even	6
448.3.r.h.191.2		12	56.3	even	6
448.3.r.h.191.5		12	56.45	odd	6
448.3.r.h.319.2		12	56.5	odd	6
448.3.r.h.319.5		12	56.19	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	196.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.789608 - 1.83753i) q^{2} +2.15693i q^{3} +(-2.75304 - 2.90186i) q^{4} +6.50608 q^{5} +(3.96343 + 1.70313i) q^{6} +(-7.50608 + 2.76746i) q^{8} +4.34764 q^{9} +(5.13725 - 11.9551i) q^{10} -0.610527i q^{11} +(6.25911 - 5.93812i) q^{12} +10.6645 q^{13} +14.0332i q^{15} +(-0.841567 + 15.9779i) q^{16} +11.9814 q^{17} +(3.43293 - 7.98893i) q^{18} -12.2180i q^{19} +(-17.9115 - 18.8797i) q^{20} +(-1.12186 - 0.482077i) q^{22} -40.1286i q^{23} +(-5.96922 - 16.1901i) q^{24} +17.3290 q^{25} +(8.42078 - 19.5964i) q^{26} +28.7900i q^{27} -9.04293 q^{29} +(25.7864 + 11.0807i) q^{30} +34.9190i q^{31} +(28.6953 + 14.1626i) q^{32} +1.31687 q^{33} +(9.46059 - 22.0161i) q^{34} +(-11.9692 - 12.6162i) q^{36} -50.8165 q^{37} +(-22.4509 - 9.64740i) q^{38} +23.0026i q^{39} +(-48.8351 + 18.0053i) q^{40} -25.7382 q^{41} +19.8107i q^{43} +(-1.77166 + 1.68080i) q^{44} +28.2861 q^{45} +(-73.7375 - 31.6859i) q^{46} +47.0968i q^{47} +(-34.4631 - 1.81520i) q^{48} +(13.6831 - 31.8426i) q^{50} +25.8430i q^{51} +(-29.3598 - 30.9469i) q^{52} -26.8780 q^{53} +(52.9024 + 22.7328i) q^{54} -3.97214i q^{55} +26.3533 q^{57} +(-7.14037 + 16.6167i) q^{58} +46.0315i q^{59} +(40.7223 - 38.6338i) q^{60} -42.2070 q^{61} +(64.1648 + 27.5724i) q^{62} +(48.6823 - 41.5455i) q^{64} +69.3841 q^{65} +(1.03981 - 2.41978i) q^{66} +27.7812i q^{67} +(-32.9852 - 34.7683i) q^{68} +86.5547 q^{69} -57.1882i q^{71} +(-32.6337 + 12.0319i) q^{72} -56.3290 q^{73} +(-40.1251 + 93.3768i) q^{74} +37.3775i q^{75} +(-35.4548 + 33.6365i) q^{76} +(42.2680 + 18.1631i) q^{78} -18.3938i q^{79} +(-5.47530 + 103.953i) q^{80} -22.9692 q^{81} +(-20.3231 + 47.2948i) q^{82} +37.3775i q^{83} +77.9517 q^{85} +(36.4027 + 15.6427i) q^{86} -19.5050i q^{87} +(1.68961 + 4.58266i) q^{88} +24.7074 q^{89} +(22.3349 - 51.9766i) q^{90} +(-116.448 + 110.476i) q^{92} -75.3180 q^{93} +(86.5418 + 37.1880i) q^{94} -79.4910i q^{95} +(-30.5479 + 61.8938i) q^{96} -109.895 q^{97} -2.65435i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 4 q^{4} - 2 q^{5} + 6 q^{6} - 4 q^{8} - 4 q^{9} - 2 q^{10} - 24 q^{12} + 12 q^{13} - 16 q^{16} - 2 q^{17} - 56 q^{18} - 76 q^{20} + 22 q^{22} - 44 q^{24} + 56 q^{26} + 36 q^{29} + 74 q^{30}+ \cdots - 372 q^{97}+O(q^{100}) \) 6 * q + 2 * q^2 + 4 * q^4 - 2 * q^5 + 6 * q^6 - 4 * q^8 - 4 * q^9 - 2 * q^10 - 24 * q^12 + 12 * q^13 - 16 * q^16 - 2 * q^17 - 56 * q^18 - 76 * q^20 + 22 * q^22 - 44 * q^24 + 56 * q^26 + 36 * q^29 + 74 * q^30 + 112 * q^32 - 14 * q^33 + 158 * q^34 - 80 * q^36 - 86 * q^37 - 2 * q^38 - 148 * q^40 - 4 * q^41 - 64 * q^44 + 156 * q^45 - 162 * q^46 - 256 * q^48 + 104 * q^50 - 64 * q^52 + 74 * q^53 + 182 * q^54 - 110 * q^57 + 176 * q^58 + 232 * q^60 + 86 * q^61 + 266 * q^62 - 80 * q^64 + 140 * q^65 + 102 * q^66 - 68 * q^68 + 150 * q^69 - 152 * q^72 - 234 * q^73 - 290 * q^74 - 288 * q^76 + 32 * q^78 - 146 * q^81 + 272 * q^82 + 134 * q^85 + 16 * q^86 + 188 * q^88 + 6 * q^89 + 320 * q^90 - 224 * q^92 - 162 * q^93 + 102 * q^94 - 320 * q^96 - 372 * q^97

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