LMFDB - Embedded newform 51.3.f.a.38.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,3,Mod(38,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.38"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	51.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.38964934824$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
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} + 62 x^{18} + 1545 x^{16} + 20120 x^{14} + 149608 x^{12} + 655792 x^{10} + 1690896 x^{8} + \cdots + 36864 $ x^20 + 62x^18 + 1545x^16 + 20120x^14 + 149608x^12 + 655792x^10 + 1690896x^8 + 2476352x^6 + 1880640x^4 + 593152*x^2 + 36864
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			38.1
Root			$-4.37647i$ of defining polynomial
Character	$\chi$	$=$	51.38
Dual form			51.3.f.a.47.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.37647 q^{2} +(-1.14794 + 2.77168i) q^{3} +7.40053 q^{4} +(-1.81992 - 1.81992i) q^{5} +(3.87599 - 9.35849i) q^{6} +(-8.06294 - 8.06294i) q^{7} -11.4818 q^{8} +(-6.36445 - 6.36347i) q^{9} +(6.14491 + 6.14491i) q^{10} +(5.55928 - 5.55928i) q^{11} +(-8.49539 + 20.5119i) q^{12} -3.00160 q^{13} +(27.2242 + 27.2242i) q^{14} +(7.13342 - 2.95508i) q^{15} +9.16568 q^{16} +(-11.3285 - 12.6754i) q^{17} +(21.4893 + 21.4861i) q^{18} +18.5232i q^{19} +(-13.4684 - 13.4684i) q^{20} +(31.6037 - 13.0921i) q^{21} +(-18.7707 + 18.7707i) q^{22} +(-29.6493 + 29.6493i) q^{23} +(13.1804 - 31.8238i) q^{24} -18.3758i q^{25} +10.1348 q^{26} +(24.9436 - 10.3353i) q^{27} +(-59.6700 - 59.6700i) q^{28} +(-19.6537 - 19.6537i) q^{29} +(-24.0858 + 9.97773i) q^{30} +(-9.81702 + 9.81702i) q^{31} +14.9794 q^{32} +(9.02681 + 21.7903i) q^{33} +(38.2501 + 42.7981i) q^{34} +29.3478i q^{35} +(-47.1003 - 47.0930i) q^{36} +(1.50230 - 1.50230i) q^{37} -62.5430i q^{38} +(3.44567 - 8.31948i) q^{39} +(20.8959 + 20.8959i) q^{40} +(26.4853 - 26.4853i) q^{41} +(-106.709 + 44.2050i) q^{42} -10.3809i q^{43} +(41.1416 - 41.1416i) q^{44} +(0.00177433 + 23.1638i) q^{45} +(100.110 - 100.110i) q^{46} +28.9824i q^{47} +(-10.5217 + 25.4043i) q^{48} +81.0219i q^{49} +62.0451i q^{50} +(48.1367 - 16.8482i) q^{51} -22.2134 q^{52} -7.41735 q^{53} +(-84.2211 + 34.8969i) q^{54} -20.2349 q^{55} +(92.5767 + 92.5767i) q^{56} +(-51.3404 - 21.2636i) q^{57} +(66.3601 + 66.3601i) q^{58} +22.7526 q^{59} +(52.7911 - 21.8691i) q^{60} +(-49.7010 - 49.7010i) q^{61} +(33.1468 - 33.1468i) q^{62} +(0.00786092 + 102.624i) q^{63} -87.2403 q^{64} +(5.46268 + 5.46268i) q^{65} +(-30.4787 - 73.5742i) q^{66} +18.0861 q^{67} +(-83.8365 - 93.8047i) q^{68} +(-48.1426 - 116.214i) q^{69} -99.0920i q^{70} +(-12.6033 - 12.6033i) q^{71} +(73.0751 + 73.0639i) q^{72} +(84.8754 - 84.8754i) q^{73} +(-5.07248 + 5.07248i) q^{74} +(50.9318 + 21.0943i) q^{75} +137.081i q^{76} -89.6482 q^{77} +(-11.6342 + 28.0904i) q^{78} +(-19.0745 - 19.0745i) q^{79} +(-16.6808 - 16.6808i) q^{80} +(0.0124090 + 81.0000i) q^{81} +(-89.4267 + 89.4267i) q^{82} +92.0738 q^{83} +(233.884 - 96.8884i) q^{84} +(-2.45136 + 43.6852i) q^{85} +35.0509i q^{86} +(77.0352 - 31.9125i) q^{87} +(-63.8303 + 63.8303i) q^{88} +12.6276i q^{89} +(-0.00599095 - 78.2119i) q^{90} +(24.2017 + 24.2017i) q^{91} +(-219.420 + 219.420i) q^{92} +(-15.9403 - 38.4790i) q^{93} -97.8583i q^{94} +(33.7108 - 33.7108i) q^{95} +(-17.1956 + 41.5183i) q^{96} +(-8.53997 + 8.53997i) q^{97} -273.568i q^{98} +(-70.7581 + 0.00541999i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{3} + 24 q^{4} - 2 q^{6} - 4 q^{7} - 16 q^{10} - 42 q^{12} - 12 q^{13} - 64 q^{16} - 4 q^{18} + 88 q^{21} - 40 q^{22} - 82 q^{24} + 54 q^{27} - 160 q^{28} + 48 q^{31} + 264 q^{33} + 152 q^{34}+ \cdots - 864 q^{99}+O(q^{100}) $ 20 * q - 6 * q^3 + 24 * q^4 - 2 * q^6 - 4 * q^7 - 16 * q^10 - 42 * q^12 - 12 * q^13 - 64 * q^16 - 4 * q^18 + 88 * q^21 - 40 * q^22 - 82 * q^24 + 54 * q^27 - 160 * q^28 + 48 * q^31 + 264 * q^33 + 152 * q^34 + 32 * q^37 + 56 * q^39 + 52 * q^40 + 64 * q^45 + 388 * q^46 - 230 * q^48 - 298 * q^51 + 64 * q^52 - 254 * q^54 - 204 * q^55 - 24 * q^57 + 396 * q^58 - 336 * q^61 - 400 * q^63 - 480 * q^64 - 408 * q^67 - 132 * q^69 + 276 * q^72 - 88 * q^73 - 358 * q^75 + 380 * q^78 - 172 * q^79 + 388 * q^81 + 372 * q^82 + 1320 * q^84 + 648 * q^85 - 156 * q^88 + 672 * q^90 - 124 * q^91 + 194 * q^96 + 688 * q^97 - 864 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−3.37647			−1.68823			−0.844117	−	0.536160i	$-0.819875\pi$
$2$	−3.37647			−1.68823			−0.844117	+	0.536160i	$0.819875\pi$
$3$	−1.14794	+	2.77168i	−0.382648	+	0.923894i
$3$	−1.14794	+	2.77168i	−0.382648	+	0.923894i
$4$	7.40053			1.85013
$5$	−1.81992	−	1.81992i	−0.363985	−	0.363985i	0.501293	−	0.865278i	$-0.332858\pi$
$5$	−1.81992	−	1.81992i	−0.363985	−	0.363985i	−0.865278	+	0.501293i	$0.832858\pi$
$6$	3.87599	−	9.35849i	0.645999	−	1.55975i
$7$	−8.06294	−	8.06294i	−1.15185	−	1.15185i	−0.986182	−	0.165666i	$-0.947023\pi$
$7$	−8.06294	−	8.06294i	−1.15185	−	1.15185i	−0.165666	−	0.986182i	$-0.552977\pi$
$8$	−11.4818			−1.43522
$9$	−6.36445	−	6.36347i	−0.707161	−	0.707053i
$10$	6.14491	+	6.14491i	0.614491	+	0.614491i
$11$	5.55928	−	5.55928i	0.505389	−	0.505389i	−0.407719	−	0.913108i	$-0.633676\pi$
$11$	5.55928	−	5.55928i	0.505389	−	0.505389i	0.913108	+	0.407719i	$0.133676\pi$
$12$	−8.49539	+	20.5119i	−0.707949	+	1.70933i
$13$	−3.00160			−0.230892			−0.115446	−	0.993314i	$-0.536830\pi$
$13$	−3.00160			−0.230892			−0.115446	+	0.993314i	$0.536830\pi$
$14$	27.2242	+	27.2242i	1.94459	+	1.94459i
$15$	7.13342	−	2.95508i	0.475561	−	0.197005i
$16$	9.16568			0.572855
$17$	−11.3285	−	12.6754i	−0.666380	−	0.745613i
$17$	−11.3285	−	12.6754i	−0.666380	−	0.745613i
$18$	21.4893	+	21.4861i	1.19385	+	1.19367i
$19$			18.5232i			0.974905i	0.873149	+	0.487453i	$0.162074\pi$
$19$			18.5232i			0.974905i	−0.873149	+	0.487453i	$0.837926\pi$
$20$	−13.4684	−	13.4684i	−0.673419	−	0.673419i
$21$	31.6037	−	13.0921i	1.50494	−	0.623433i
$22$	−18.7707	+	18.7707i	−0.853214	+	0.853214i
$23$	−29.6493	+	29.6493i	−1.28910	+	1.28910i	−0.353763	+	0.935335i	$0.615098\pi$
$23$	−29.6493	+	29.6493i	−1.28910	+	1.28910i	−0.935335	+	0.353763i	$0.884902\pi$
$24$	13.1804	−	31.8238i	0.549184	−	1.32599i
$25$		−	18.3758i		−	0.735030i
$26$	10.1348			0.389800
$27$	24.9436	−	10.3353i	0.923836	−	0.382790i
$28$	−59.6700	−	59.6700i	−2.13107	−	2.13107i
$29$	−19.6537	−	19.6537i	−0.677714	−	0.677714i	0.281769	−	0.959482i	$-0.409079\pi$
$29$	−19.6537	−	19.6537i	−0.677714	−	0.677714i	−0.959482	+	0.281769i	$0.909079\pi$
$30$	−24.0858	+	9.97773i	−0.802858	+	0.332591i
$31$	−9.81702	+	9.81702i	−0.316678	+	0.316678i	−0.847490	−	0.530812i	$-0.821887\pi$
$31$	−9.81702	+	9.81702i	−0.316678	+	0.316678i	0.530812	+	0.847490i	$0.321887\pi$
$32$	14.9794			0.468108
$33$	9.02681	+	21.7903i	0.273540	+	0.660312i
$34$	38.2501	+	42.7981i	1.12500	+	1.25877i
$35$			29.3478i			0.838510i
$36$	−47.1003	−	47.0930i	−1.30834	−	1.30814i
$37$	1.50230	−	1.50230i	0.0406028	−	0.0406028i	−0.686514	−	0.727117i	$-0.740860\pi$
$37$	1.50230	−	1.50230i	0.0406028	−	0.0406028i	0.727117	+	0.686514i	$0.240860\pi$
$38$		−	62.5430i		−	1.64587i
$39$	3.44567	−	8.31948i	0.0883505	−	0.213320i
$40$	20.8959	+	20.8959i	0.522398	+	0.522398i
$41$	26.4853	−	26.4853i	0.645983	−	0.645983i	−0.306037	−	0.952020i	$-0.599003\pi$
$41$	26.4853	−	26.4853i	0.645983	−	0.645983i	0.952020	+	0.306037i	$0.0990031\pi$
$42$	−106.709	+	44.2050i	−2.54069	+	1.05250i
$43$		−	10.3809i		−	0.241417i	−0.992688	−	0.120709i	$-0.961483\pi$
$43$		−	10.3809i		−	0.241417i	0.992688	−	0.120709i	$-0.0385167\pi$
$44$	41.1416	−	41.1416i	0.935036	−	0.935036i
$45$	0.00177433	+	23.1638i	3.94295e−5	+	0.514752i
$46$	100.110	−	100.110i	2.17630	−	2.17630i
$47$			28.9824i			0.616648i	0.951281	+	0.308324i	$0.0997681\pi$
$47$			28.9824i			0.616648i	−0.951281	+	0.308324i	$0.900232\pi$
$48$	−10.5217	+	25.4043i	−0.219202	+	0.529257i
$49$			81.0219i			1.65351i
$50$			62.0451i			1.24090i
$51$	48.1367	−	16.8482i	0.943856	−	0.330357i
$52$	−22.2134			−0.427181
$53$	−7.41735			−0.139950			−0.0699750	−	0.997549i	$-0.522292\pi$
$53$	−7.41735			−0.139950			−0.0699750	+	0.997549i	$0.522292\pi$
$54$	−84.2211	+	34.8969i	−1.55965	+	0.646238i
$55$	−20.2349			−0.367908
$56$	92.5767	+	92.5767i	1.65316	+	1.65316i
$57$	−51.3404	−	21.2636i	−0.900709	−	0.373046i
$58$	66.3601	+	66.3601i	1.14414	+	1.14414i
$59$	22.7526			0.385637			0.192819	−	0.981234i	$-0.438237\pi$
$59$	22.7526			0.385637			0.192819	+	0.981234i	$0.438237\pi$
$60$	52.7911	−	21.8691i	0.879851	−	0.364486i
$61$	−49.7010	−	49.7010i	−0.814771	−	0.814771i	0.170574	−	0.985345i	$-0.445438\pi$
$61$	−49.7010	−	49.7010i	−0.814771	−	0.814771i	−0.985345	+	0.170574i	$0.945438\pi$
$62$	33.1468	−	33.1468i	0.534626	−	0.534626i
$63$	0.00786092	+	102.624i	0.000124777	+	1.62896i
$64$	−87.2403			−1.36313
$65$	5.46268	+	5.46268i	0.0840412	+	0.0840412i
$66$	−30.4787	−	73.5742i	−0.461799	−	1.11476i
$67$	18.0861			0.269941			0.134971	−	0.990850i	$-0.456906\pi$
$67$	18.0861			0.269941			0.134971	+	0.990850i	$0.456906\pi$
$68$	−83.8365	−	93.8047i	−1.23289	−	1.37948i
$69$	−48.1426	−	116.214i	−0.697719	−	1.68426i
$70$		−	99.0920i		−	1.41560i
$71$	−12.6033	−	12.6033i	−0.177511	−	0.177511i	0.612759	−	0.790270i	$-0.290060\pi$
$71$	−12.6033	−	12.6033i	−0.177511	−	0.177511i	−0.790270	+	0.612759i	$0.790060\pi$
$72$	73.0751	+	73.0639i	1.01493	+	1.01478i
$73$	84.8754	−	84.8754i	1.16268	−	1.16268i	0.178790	−	0.983887i	$-0.442782\pi$
$73$	84.8754	−	84.8754i	1.16268	−	1.16268i	0.983887	−	0.178790i	$-0.0572181\pi$
$74$	−5.07248	+	5.07248i	−0.0685470	+	0.0685470i
$75$	50.9318	+	21.0943i	0.679090	+	0.281258i
$76$			137.081i			1.80370i
$77$	−89.6482			−1.16426
$78$	−11.6342	+	28.0904i	−0.149156	+	0.360134i
$79$	−19.0745	−	19.0745i	−0.241450	−	0.241450i	0.576000	−	0.817450i	$-0.304613\pi$
$79$	−19.0745	−	19.0745i	−0.241450	−	0.241450i	−0.817450	+	0.576000i	$0.804613\pi$
$80$	−16.6808	−	16.6808i	−0.208510	−	0.208510i
$81$	0.0124090	+	81.0000i	0.000153198	+	1.00000i
$82$	−89.4267	+	89.4267i	−1.09057	+	1.09057i
$83$	92.0738			1.10932			0.554662	−	0.832076i	$-0.312848\pi$
$83$	92.0738			1.10932			0.554662	+	0.832076i	$0.312848\pi$
$84$	233.884	−	96.8884i	2.78433	−	1.15343i
$85$	−2.45136	+	43.6852i	−0.0288396	+	0.513943i
$86$			35.0509i			0.407569i
$87$	77.0352	−	31.9125i	0.885462	−	0.366810i
$88$	−63.8303	+	63.8303i	−0.725344	+	0.725344i
$89$			12.6276i			0.141883i	0.997480	+	0.0709417i	$0.0226004\pi$
$89$			12.6276i			0.141883i	−0.997480	+	0.0709417i	$0.977400\pi$
$90$	−0.00599095	−	78.2119i	−6.65661e−5	−	0.869021i
$91$	24.2017	+	24.2017i	0.265953	+	0.265953i
$92$	−219.420	+	219.420i	−2.38500	+	2.38500i
$93$	−15.9403	−	38.4790i	−0.171401	−	0.413753i
$94$		−	97.8583i		−	1.04105i
$95$	33.7108	−	33.7108i	0.354851	−	0.354851i
$96$	−17.1956	+	41.5183i	−0.179120	+	0.432482i
$97$	−8.53997	+	8.53997i	−0.0880409	+	0.0880409i	−0.749756	−	0.661715i	$-0.769829\pi$
$97$	−8.53997	+	8.53997i	−0.0880409	+	0.0880409i	0.661715	+	0.749756i	$0.269829\pi$
$98$		−	273.568i		−	2.79151i
$99$	−70.7581	+	0.00541999i	−0.714728	+	5.47474e-5i
$100$		−	135.990i		−	1.35990i
$101$			94.3793i			0.934448i	0.884139	+	0.467224i	$0.154746\pi$
$101$			94.3793i			0.934448i	−0.884139	+	0.467224i	$0.845254\pi$
$102$	−162.532	+	56.8874i	−1.59345	+	0.557720i
$103$	14.4497			0.140289			0.0701443	−	0.997537i	$-0.477654\pi$
$103$	14.4497			0.140289			0.0701443	+	0.997537i	$0.477654\pi$
$104$	34.4636			0.331381
$105$	−81.3429	−	33.6897i	−0.774694	−	0.320854i
$106$	25.0444			0.236268
$107$	−98.7663	−	98.7663i	−0.923050	−	0.923050i	0.0741939	−	0.997244i	$-0.476362\pi$
$107$	−98.7663	−	98.7663i	−0.923050	−	0.923050i	−0.997244	+	0.0741939i	$0.976362\pi$
$108$	184.595	−	76.4868i	1.70922	−	0.708211i
$109$	−19.9590	−	19.9590i	−0.183110	−	0.183110i	0.609600	−	0.792709i	$-0.291330\pi$
$109$	−19.9590	−	19.9590i	−0.183110	−	0.183110i	−0.792709	+	0.609600i	$0.791330\pi$
$110$	68.3225			0.621114
$111$	2.43935	+	5.88847i	0.0219761	+	0.0530493i
$112$	−73.9023	−	73.9023i	−0.659842	−	0.659842i
$113$	32.3133	−	32.3133i	0.285958	−	0.285958i	−0.549522	−	0.835480i	$-0.685190\pi$
$113$	32.3133	−	32.3133i	0.285958	−	0.285958i	0.835480	+	0.549522i	$0.185190\pi$
$114$	173.349	+	71.7958i	1.52061	+	0.629788i
$115$	107.919			0.938424
$116$	−145.448	−	145.448i	−1.25386	−	1.25386i
$117$	19.1035	+	19.1006i	0.163278	+	0.163253i
$118$	−76.8234			−0.651046
$119$	−10.8605	+	193.542i	−0.0912643	+	1.62640i
$120$	−81.9042	+	33.9295i	−0.682535	+	0.282746i
$121$			59.1888i			0.489164i
$122$	167.814	+	167.814i	1.37552	+	1.37552i
$123$	43.0052	+	103.812i	0.349636	+	0.844004i
$124$	−72.6511	+	72.6511i	−0.585896	+	0.585896i
$125$	−78.9405	+	78.9405i	−0.631524	+	0.631524i
$126$	−0.0265421	−	346.508i	−0.000210652	−	2.75006i
$127$			165.909i			1.30637i	0.757199	+	0.653185i	$0.226568\pi$
$127$			165.909i			1.30637i	−0.757199	+	0.653185i	$0.773432\pi$
$128$	234.646			1.83317
$129$	28.7727	+	11.9167i	0.223044	+	0.0923779i
$130$	−18.4446	−	18.4446i	−0.141881	−	0.141881i
$131$	−122.294	−	122.294i	−0.933546	−	0.933546i	0.0643798	−	0.997925i	$-0.479493\pi$
$131$	−122.294	−	122.294i	−0.933546	−	0.933546i	−0.997925	+	0.0643798i	$0.979493\pi$
$132$	66.8032	+	161.260i	0.506085	+	1.22166i
$133$	149.351	−	149.351i	1.12294	−	1.12294i
$134$	−61.0670			−0.455724
$135$	−64.2048	−	26.5859i	−0.475591	−	0.196932i
$136$	130.071	+	145.536i	0.956401	+	1.07012i
$137$		−	46.0773i		−	0.336331i	−0.985759	−	0.168165i	$-0.946216\pi$
$137$		−	46.0773i		−	0.336331i	0.985759	−	0.168165i	$-0.0537842\pi$
$138$	162.552	+	392.393i	1.17791	+	2.84343i
$139$	85.9526	−	85.9526i	0.618364	−	0.618364i	−0.326748	−	0.945112i	$-0.605953\pi$
$139$	85.9526	−	85.9526i	0.618364	−	0.618364i	0.945112	+	0.326748i	$0.105953\pi$
$140$			217.190i			1.55135i
$141$	−80.3301	−	33.2702i	−0.569717	−	0.235959i
$142$	42.5545	+	42.5545i	0.299679	+	0.299679i
$143$	−16.6867	+	16.6867i	−0.116690	+	0.116690i
$144$	−58.3345	−	58.3255i	−0.405100	−	0.405038i
$145$			71.5364i			0.493355i
$146$	−286.579	+	286.579i	−1.96287	+	1.96287i
$147$	−224.567	−	93.0086i	−1.52767	−	0.632712i
$148$	11.1178	−	11.1178i	0.0751205	−	0.0751205i
$149$		−	204.162i		−	1.37021i	−0.728444	−	0.685106i	$-0.759756\pi$
$149$		−	204.162i		−	1.37021i	0.728444	−	0.685106i	$-0.240244\pi$
$150$	−171.969	−	71.2243i	−1.14646	−	0.474829i
$151$		−	66.9943i		−	0.443671i	−0.975084	−	0.221835i	$-0.928795\pi$
$151$		−	66.9943i		−	0.443671i	0.975084	−	0.221835i	$-0.0712048\pi$
$152$		−	212.679i		−	1.39920i
$153$	−8.56030	+	152.760i	−0.0559497	+	0.998434i
$154$	302.694			1.96555
$155$	35.7324			0.230532
$156$	25.4998	−	61.5685i	0.163460	−	0.394670i
$157$	94.9528			0.604795			0.302397	−	0.953182i	$-0.402213\pi$
$157$	94.9528			0.604795			0.302397	+	0.953182i	$0.402213\pi$
$158$	64.4045	+	64.4045i	0.407623	+	0.407623i
$159$	8.51470	−	20.5585i	0.0535516	−	0.129299i
$160$	−27.2614	−	27.2614i	−0.170384	−	0.170384i
$161$	478.120			2.96969
$162$	−0.0418987	−	273.494i	−0.000258634	−	1.68823i
$163$	−165.935	−	165.935i	−1.01800	−	1.01800i	−0.999835	−	0.0181684i	$-0.994217\pi$
$163$	−165.935	−	165.935i	−1.01800	−	1.01800i	−0.0181684	−	0.999835i	$-0.505783\pi$
$164$	196.005	−	196.005i	1.19515	−	1.19515i
$165$	23.2286	−	56.0848i	0.140779	−	0.339908i
$166$	−310.884			−1.87280
$167$	35.4176	+	35.4176i	0.212082	+	0.212082i	0.805151	−	0.593070i	$-0.202084\pi$
$167$	35.4176	+	35.4176i	0.212082	+	0.212082i	−0.593070	+	0.805151i	$0.702084\pi$
$168$	−362.866	+	150.320i	−2.15992	+	0.894764i
$169$	−159.990			−0.946689
$170$	8.27695	−	147.502i	0.0486879	−	0.867656i
$171$	117.872	−	117.890i	0.689309	−	0.689415i
$172$		−	76.8245i		−	0.446654i
$173$	−101.804	−	101.804i	−0.588463	−	0.588463i	0.348752	−	0.937215i	$-0.386606\pi$
$173$	−101.804	−	101.804i	−0.588463	−	0.588463i	−0.937215	+	0.348752i	$0.886606\pi$
$174$	−260.107	+	107.751i	−1.49487	+	0.619261i
$175$	−148.163	+	148.163i	−0.846643	+	0.846643i
$176$	50.9545	−	50.9545i	0.289514	−	0.289514i
$177$	−26.1187	+	63.0630i	−0.147563	+	0.356288i
$178$		−	42.6367i		−	0.239532i
$179$	−148.271			−0.828330			−0.414165	−	0.910202i	$-0.635926\pi$
$179$	−148.271			−0.828330			−0.414165	+	0.910202i	$0.635926\pi$
$180$	0.0131309	+	171.425i	7.29497e−5	+	0.952359i
$181$	24.0702	+	24.0702i	0.132984	+	0.132984i	0.770466	−	0.637481i	$-0.220024\pi$
$181$	24.0702	+	24.0702i	0.132984	+	0.132984i	−0.637481	+	0.770466i	$0.720024\pi$
$182$	−81.7162	−	81.7162i	−0.448990	−	0.448990i
$183$	194.809	−	80.7014i	1.06453	−	0.440991i
$184$	340.426	−	340.426i	1.85014	−	1.85014i
$185$	−5.46815			−0.0295576
$186$	53.8218	+	129.923i	0.289364	+	0.698512i
$187$	−133.444	−	7.48813i	−0.713605	−	0.0400435i
$188$			214.485i			1.14088i
$189$	−284.451	−	117.785i	−1.50503	−	0.623203i
$190$	−113.823	+	113.823i	−0.599070	+	0.599070i
$191$		−	219.220i		−	1.14775i	−0.818943	−	0.573875i	$-0.805439\pi$
$191$		−	219.220i		−	1.14775i	0.818943	−	0.573875i	$-0.194561\pi$
$192$	100.147	−	241.802i	0.521599	−	1.25939i
$193$	−176.196	−	176.196i	−0.912935	−	0.912935i	0.0835674	−	0.996502i	$-0.473369\pi$
$193$	−176.196	−	176.196i	−0.912935	−	0.912935i	−0.996502	+	0.0835674i	$0.973369\pi$
$194$	28.8349	−	28.8349i	0.148634	−	0.148634i
$195$	−21.4117	+	8.86996i	−0.109803	+	0.0454870i
$196$			599.605i			3.05921i
$197$	49.8216	−	49.8216i	0.252902	−	0.252902i	−0.569258	−	0.822159i	$-0.692769\pi$
$197$	49.8216	−	49.8216i	0.252902	−	0.252902i	0.822159	+	0.569258i	$0.192769\pi$
$198$	238.912	−	0.0183004i	1.20663	−	9.24264e-5i
$199$	−179.790	+	179.790i	−0.903469	+	0.903469i	−0.995734	−	0.0922656i	$-0.970589\pi$
$199$	−179.790	+	179.790i	−0.903469	+	0.903469i	0.0922656	+	0.995734i	$0.470589\pi$
$200$			210.986i			1.05493i
$201$	−20.7618	+	50.1289i	−0.103293	+	0.249397i
$202$		−	318.668i		−	1.57757i
$203$			316.933i			1.56125i
$204$	356.237	−	124.686i	1.74626	−	0.611204i
$205$	−96.4024			−0.470256
$206$	−48.7890			−0.236840
$207$	377.373	−	0.0289064i	1.82306	−	0.000139644i
$208$	−27.5117			−0.132268
$209$	102.976	+	102.976i	0.492706	+	0.492706i
$210$	274.652	+	113.752i	1.30786	+	0.541677i
$211$	171.893	+	171.893i	0.814660	+	0.814660i	0.985328	−	0.170669i	$-0.0545928\pi$
$211$	171.893	+	171.893i	0.814660	+	0.814660i	−0.170669	+	0.985328i	$0.554593\pi$
$212$	−54.8923			−0.258926
$213$	49.4000	−	20.4644i	0.231925	−	0.0960769i
$214$	333.481	+	333.481i	1.55832	+	1.55832i
$215$	−18.8925	+	18.8925i	−0.0878722	+	0.0878722i
$216$	−286.396	+	118.668i	−1.32591	+	0.549387i
$217$	158.308			0.729530
$218$	67.3907	+	67.3907i	0.309132	+	0.309132i
$219$	137.815	+	332.680i	0.629294	+	1.51909i
$220$	−149.749			−0.680677
$221$	34.0035	+	38.0465i	0.153862	+	0.172156i
$222$	−8.23638	−	19.8822i	−0.0371008	−	0.0895596i
$223$		−	297.453i		−	1.33387i	−0.745117	−	0.666934i	$-0.767606\pi$
$223$		−	297.453i		−	1.33387i	0.745117	−	0.666934i	$-0.232394\pi$
$224$	−120.778	−	120.778i	−0.539189	−	0.539189i
$225$	−116.934	+	116.952i	−0.519705	+	0.519785i
$226$	−109.105	+	109.105i	−0.482764	+	0.482764i
$227$	14.9743	−	14.9743i	0.0659660	−	0.0659660i	−0.673354	−	0.739320i	$-0.735147\pi$
$227$	14.9743	−	14.9743i	0.0659660	−	0.0659660i	0.739320	+	0.673354i	$0.235147\pi$
$228$	−379.946	−	157.362i	−1.66643	−	0.690183i
$229$			2.04325i			0.00892250i	0.999990	+	0.00446125i	$0.00142007\pi$
$229$			2.04325i			0.00892250i	−0.999990	+	0.00446125i	$0.998580\pi$
$230$	−364.384			−1.58428
$231$	102.911	−	248.476i	0.445503	−	1.07566i
$232$	225.659	+	225.659i	0.972668	+	0.972668i
$233$	220.897	+	220.897i	0.948057	+	0.948057i	0.998716	−	0.0506589i	$-0.0161321\pi$
$233$	220.897	+	220.897i	0.948057	+	0.948057i	−0.0506589	+	0.998716i	$0.516132\pi$
$234$	−64.5024	−	64.4925i	−0.275651	−	0.275609i
$235$	52.7458	−	52.7458i	0.224450	−	0.224450i
$236$	168.381			0.713480
$237$	74.7650	−	30.9720i	0.315464	−	0.130684i
$238$	36.6700	−	653.487i	0.154075	−	2.74574i
$239$		−	15.3708i		−	0.0643129i	−0.999483	−	0.0321565i	$-0.989763\pi$
$239$		−	15.3708i		−	0.0643129i	0.999483	−	0.0321565i	$-0.0102375\pi$
$240$	65.3826	−	27.0853i	0.272428	−	0.112855i
$241$	−222.478	+	222.478i	−0.923147	+	0.923147i	−0.997251	−	0.0741038i	$-0.976390\pi$
$241$	−222.478	+	222.478i	−0.923147	+	0.923147i	0.0741038	+	0.997251i	$0.476390\pi$
$242$		−	199.849i		−	0.825823i
$243$	−224.521	−	92.9491i	−0.923953	−	0.382507i
$244$	−367.814	−	367.814i	−1.50743	−	1.50743i
$245$	147.454	−	147.454i	0.601851	−	0.601851i
$246$	−145.206	−	350.519i	−0.590267	−	1.42488i
$247$		−	55.5992i		−	0.225098i
$248$	112.717	−	112.717i	0.454503	−	0.454503i
$249$	−105.696	+	255.199i	−0.424480	+	1.02490i
$250$	266.540	−	266.540i	1.06616	−	1.06616i
$251$			143.527i			0.571822i	0.958256	+	0.285911i	$0.0922962\pi$
$251$			143.527i			0.571822i	−0.958256	+	0.285911i	$0.907704\pi$
$252$	0.0581750	+	759.475i	0.000230853	+	3.01379i
$253$			329.657i			1.30299i
$254$		−	560.186i		−	2.20546i
$255$	−118.267	−	56.9426i	−0.463794	−	0.223304i
$256$	−443.314			−1.73169
$257$	400.725			1.55924			0.779621	−	0.626252i	$-0.215412\pi$
$257$	400.725			1.55924			0.779621	+	0.626252i	$0.215412\pi$
$258$	−97.1500	−	40.2365i	−0.376550	−	0.155955i
$259$	−24.2260			−0.0935365
$260$	40.4267	+	40.4267i	0.155487	+	0.155487i
$261$	0.0191613	+	250.151i	7.34149e−5	+	0.958432i
$262$	412.923	+	412.923i	1.57604	+	1.57604i
$263$	−449.598			−1.70950			−0.854749	−	0.519041i	$-0.826289\pi$
$263$	−449.598			−1.70950			−0.854749	+	0.519041i	$0.826289\pi$
$264$	−103.644	−	250.191i	−0.392590	−	0.947693i
$265$	13.4990	+	13.4990i	0.0509396	+	0.0509396i
$266$	−504.280	+	504.280i	−1.89579	+	1.89579i
$267$	−34.9997	−	14.4958i	−0.131085	−	0.0542914i
$268$	133.846			0.499427
$269$	227.689	+	227.689i	0.846428	+	0.846428i	0.989685	−	0.143258i	$-0.0457577\pi$
$269$	227.689	+	227.689i	0.846428	+	0.846428i	−0.143258	+	0.989685i	$0.545758\pi$
$270$	216.786	+	89.7663i	0.802909	+	0.332468i
$271$	475.631			1.75510			0.877549	−	0.479488i	$-0.159177\pi$
$271$	475.631			1.75510			0.877549	+	0.479488i	$0.159177\pi$
$272$	−103.833	−	116.179i	−0.381739	−	0.427128i
$273$	−94.8617	+	39.2972i	−0.347479	+	0.143946i
$274$			155.578i			0.567805i
$275$	−102.156	−	102.156i	−0.371476	−	0.371476i
$276$	−356.281	−	860.045i	−1.29087	−	3.11610i
$277$	242.909	−	242.909i	0.876926	−	0.876926i	−0.116289	−	0.993215i	$-0.537100\pi$
$277$	242.909	−	242.909i	0.876926	−	0.876926i	0.993215	+	0.116289i	$0.0370999\pi$
$278$	−290.216	+	290.216i	−1.04394	+	1.04394i
$279$	124.950	−	0.00957105i	0.447850	−	3.43049e-5i
$280$		−	336.965i		−	1.20345i
$281$	−45.4334			−0.161685			−0.0808424	−	0.996727i	$-0.525761\pi$
$281$	−45.4334			−0.161685			−0.0808424	+	0.996727i	$0.525761\pi$
$282$	271.232	+	112.336i	0.961816	+	0.398354i
$283$	56.9618	+	56.9618i	0.201278	+	0.201278i	0.800548	−	0.599269i	$-0.204542\pi$
$283$	56.9618	+	56.9618i	0.201278	+	0.201278i	−0.599269	+	0.800548i	$0.704542\pi$
$284$	−93.2707	−	93.2707i	−0.328418	−	0.328418i
$285$	54.7375	+	132.134i	0.192061	+	0.463627i
$286$	56.3422	−	56.3422i	0.197001	−	0.197001i
$287$	−427.098			−1.48815
$288$	−95.3359	−	95.3213i	−0.331027	−	0.330977i
$289$	−32.3323	+	287.186i	−0.111876	+	0.993722i
$290$		−	241.540i		−	0.832898i
$291$	−13.8667	−	33.4735i	−0.0476518	−	0.115029i
$292$	628.123	−	628.123i	2.15110	−	2.15110i
$293$		−	227.538i		−	0.776581i	−0.921537	−	0.388290i	$-0.873066\pi$
$293$		−	227.538i		−	0.776581i	0.921537	−	0.388290i	$-0.126934\pi$
$294$	758.243	+	314.040i	2.57906	+	1.06816i
$295$	−41.4080	−	41.4080i	−0.140366	−	0.140366i
$296$	−17.2491	+	17.2491i	−0.0582740	+	0.0582740i
$297$	81.2113	−	196.125i	0.273439	−	0.660354i
$298$			689.345i			2.31324i
$299$	88.9952	−	88.9952i	0.297643	−	0.297643i
$300$	376.922	+	156.109i	1.25641	+	0.520364i
$301$	−83.7009	+	83.7009i	−0.278076	+	0.278076i
$302$			226.204i			0.749020i
$303$	−261.589	−	108.342i	−0.863331	−	0.357565i
$304$			169.778i			0.558479i
$305$			180.904i			0.593128i
$306$	28.9036	−	515.790i	0.0944561	−	1.68559i
$307$	−128.053			−0.417110			−0.208555	−	0.978011i	$-0.566876\pi$
$307$	−128.053			−0.417110			−0.208555	+	0.978011i	$0.566876\pi$
$308$	−663.444			−2.15404
$309$	−16.5875	+	40.0501i	−0.0536812	+	0.129612i
$310$	−120.649			−0.389191
$311$	−214.390	−	214.390i	−0.689357	−	0.689357i	0.272733	−	0.962090i	$-0.412072\pi$
$311$	−214.390	−	214.390i	−0.689357	−	0.689357i	−0.962090	+	0.272733i	$0.912072\pi$
$312$	−39.5623	+	95.5223i	−0.126802	+	0.306161i
$313$	−99.6696	−	99.6696i	−0.318433	−	0.318433i	0.529732	−	0.848165i	$-0.322293\pi$
$313$	−99.6696	−	99.6696i	−0.318433	−	0.318433i	−0.848165	+	0.529732i	$0.822293\pi$
$314$	−320.605			−1.02103
$315$	186.754	−	186.783i	0.592871	−	0.592962i
$316$	−141.161	−	141.161i	−0.446714	−	0.446714i
$317$	30.0511	−	30.0511i	0.0947985	−	0.0947985i	−0.658117	−	0.752916i	$-0.728647\pi$
$317$	30.0511	−	30.0511i	0.0947985	−	0.0947985i	0.752916	+	0.658117i	$0.228647\pi$
$318$	−28.7496	+	69.4152i	−0.0904075	+	0.218287i
$319$	−218.521			−0.685018
$320$	158.771	+	158.771i	0.496158	+	0.496158i
$321$	387.127	−	160.371i	1.20600	−	0.499597i
$322$	−1614.36			−5.01353
$323$	234.789	−	209.839i	0.726902	−	0.649657i
$324$	0.0918333	+	599.443i	0.000283436	+	1.85013i
$325$			55.1567i			0.169713i
$326$	560.272	+	560.272i	1.71863	+	1.71863i
$327$	78.2317	−	32.4081i	0.239241	−	0.0991074i
$328$	−304.098	+	304.098i	−0.927127	+	0.927127i
$329$	233.684	−	233.684i	0.710285	−	0.710285i
$330$	−78.4304	+	189.368i	−0.237668	+	0.573843i
$331$		−	476.109i		−	1.43840i	−0.694805	−	0.719198i	$-0.744509\pi$
$331$		−	476.109i		−	1.43840i	0.694805	−	0.719198i	$-0.255491\pi$
$332$	681.395			2.05239
$333$	−19.1212	+	0.00146466i	−0.0574210	+	4.39839e-6i
$334$	−119.586	−	119.586i	−0.358043	−	0.358043i
$335$	−32.9153	−	32.9153i	−0.0982546	−	0.0982546i
$336$	289.669	−	119.998i	0.862111	−	0.357137i
$337$	−46.5612	+	46.5612i	−0.138164	+	0.138164i	−0.772806	−	0.634642i	$-0.781147\pi$
$337$	−46.5612	+	46.5612i	−0.138164	+	0.138164i	0.634642	+	0.772806i	$0.281147\pi$
$338$	540.202			1.59823
$339$	52.4683	+	126.656i	0.154774	+	0.373616i
$340$	−18.1414	+	323.293i	−0.0533570	+	0.950863i
$341$			109.151i			0.320091i
$342$	−397.990	+	398.051i	−1.16371	+	1.16389i
$343$	258.190	−	258.190i	0.752742	−	0.752742i
$344$			119.192i			0.346487i
$345$	−123.885	+	299.116i	−0.359086	+	0.867004i
$346$	343.738	+	343.738i	0.993463	+	0.993463i
$347$	111.677	−	111.677i	0.321837	−	0.321837i	−0.527635	−	0.849471i	$-0.676921\pi$
$347$	111.677	−	111.677i	0.321837	−	0.321837i	0.849471	+	0.527635i	$0.176921\pi$
$348$	570.101	−	236.169i	1.63822	−	0.678647i
$349$		−	411.484i		−	1.17904i	−0.807755	−	0.589518i	$-0.799318\pi$
$349$		−	411.484i		−	1.17904i	0.807755	−	0.589518i	$-0.200682\pi$
$350$	500.266	−	500.266i	1.42933	−	1.42933i
$351$	−74.8706	+	31.0225i	−0.213306	+	0.0883832i
$352$	83.2749	−	83.2749i	0.236576	−	0.236576i
$353$			297.073i			0.841567i	0.907161	+	0.420783i	$0.138245\pi$
$353$			297.073i			0.841567i	−0.907161	+	0.420783i	$0.861755\pi$
$354$	88.1890	−	212.930i	0.249121	−	0.601497i
$355$			45.8739i			0.129222i
$356$			93.4510i			0.262503i
$357$	−523.969	−	252.277i	−1.46770	−	0.706658i
$358$	500.632			1.39841
$359$	−653.255			−1.81965			−0.909826	−	0.414990i	$-0.863785\pi$
$359$	−653.255			−1.81965			−0.909826	+	0.414990i	$0.863785\pi$
$360$	−0.0203724	−	265.962i	−5.65899e−5	−	0.738782i
$361$	17.8911			0.0495598
$362$	−81.2722	−	81.2722i	−0.224509	−	0.224509i
$363$	−164.053	−	67.9455i	−0.451936	−	0.187178i
$364$	179.105	+	179.105i	0.492048	+	0.492048i
$365$	−308.933			−0.846393
$366$	−657.767	+	272.486i	−1.79718	+	0.744496i
$367$	156.207	+	156.207i	0.425631	+	0.425631i	0.887137	−	0.461506i	$-0.152691\pi$
$367$	156.207	+	156.207i	0.425631	+	0.425631i	−0.461506	+	0.887137i	$0.652691\pi$
$368$	−271.755	+	271.755i	−0.738466	+	0.738466i
$369$	−337.103	+	0.0258217i	−0.913558	+	6.99775e-5i
$370$	18.4630			0.0499001
$371$	59.8056	+	59.8056i	0.161201	+	0.161201i
$372$	−117.966	−	284.765i	−0.317114	−	0.765498i
$373$	−96.0702			−0.257561			−0.128780	−	0.991673i	$-0.541106\pi$
$373$	−96.0702			−0.257561			−0.128780	+	0.991673i	$0.541106\pi$
$374$	450.570	+	25.2834i	1.20473	+	0.0676027i
$375$	−128.179	−	309.417i	−0.341810	−	0.825113i
$376$		−	332.770i		−	0.885025i
$377$	58.9925	+	58.9925i	0.156479	+	0.156479i
$378$	960.440	+	397.698i	2.54085	+	1.05211i
$379$	−285.142	+	285.142i	−0.752353	+	0.752353i	−0.974918	−	0.222565i	$-0.928557\pi$
$379$	−285.142	+	285.142i	−0.752353	+	0.752353i	0.222565	+	0.974918i	$0.428557\pi$
$380$	249.478	−	249.478i	0.656520	−	0.656520i
$381$	−459.847	−	190.454i	−1.20695	−	0.499880i
$382$			740.190i			1.93767i
$383$	186.717			0.487511			0.243755	−	0.969837i	$-0.421621\pi$
$383$	186.717			0.487511			0.243755	+	0.969837i	$0.421621\pi$
$384$	−269.361	+	650.365i	−0.701460	+	1.69366i
$385$	163.153	+	163.153i	0.423774	+	0.423774i
$386$	594.921	+	594.921i	1.54125	+	1.54125i
$387$	−66.0589	+	66.0690i	−0.170695	+	0.170721i
$388$	−63.2002	+	63.2002i	−0.162887	+	0.162887i
$389$	−418.620			−1.07614			−0.538072	−	0.842899i	$-0.680847\pi$
$389$	−418.620			−1.07614			−0.538072	+	0.842899i	$0.680847\pi$
$390$	72.2958	−	29.9491i	0.185374	−	0.0767927i
$391$	711.697	+	39.9364i	1.82020	+	0.102139i
$392$		−	930.274i		−	2.37315i
$393$	479.349	−	198.574i	1.21972	−	0.505278i
$394$	−168.221	+	168.221i	−0.426957	+	0.426957i
$395$			69.4283i			0.175768i
$396$	−523.647	+	0.0401108i	−1.32234	+	0.000101290i
$397$	−265.965	−	265.965i	−0.669936	−	0.669936i	0.287765	−	0.957701i	$-0.407088\pi$
$397$	−265.965	−	265.965i	−0.669936	−	0.669936i	−0.957701	+	0.287765i	$0.907088\pi$
$398$	607.056	−	607.056i	1.52527	−	1.52527i
$399$	242.508	+	585.402i	0.607788	+	1.46717i
$400$		−	168.426i		−	0.421066i
$401$	−411.502	+	411.502i	−1.02619	+	1.02619i	−0.0265424	+	0.999648i	$0.508450\pi$
$401$	−411.502	+	411.502i	−1.02619	+	1.02619i	−0.999648	+	0.0265424i	$0.991550\pi$
$402$	70.1016	−	169.258i	0.174382	−	0.421041i
$403$	29.4668	−	29.4668i	0.0731185	−	0.0731185i
$404$			698.456i			1.72885i
$405$	147.391	−	147.436i	0.363929	−	0.364040i
$406$		−	1070.11i		−	2.63575i
$407$		−	16.7034i		−	0.0410404i
$408$	−552.694	+	193.447i	−1.35464	+	0.474135i
$409$	183.553			0.448785			0.224392	−	0.974499i	$-0.427960\pi$
$409$	183.553			0.448785			0.224392	+	0.974499i	$0.427960\pi$
$410$	325.499			0.793901
$411$	127.712	+	52.8942i	0.310734	+	0.128696i
$412$	106.936			0.259552
$413$	−183.453	−	183.453i	−0.444196	−	0.444196i
$414$	−1274.19	+	0.0976015i	−3.07775	+	0.000235752i
$415$	−167.567	−	167.567i	−0.403777	−	0.403777i
$416$	−44.9623			−0.108082
$417$	139.565	+	336.902i	0.334687	+	0.807919i
$418$	−347.694	−	347.694i	−0.831803	−	0.831803i
$419$	278.304	−	278.304i	0.664211	−	0.664211i	−0.292159	−	0.956370i	$-0.594374\pi$
$419$	278.304	−	278.304i	0.664211	−	0.664211i	0.956370	+	0.292159i	$0.0943736\pi$
$420$	−601.980	−	249.321i	−1.43329	−	0.593622i
$421$	432.375			1.02702			0.513509	−	0.858084i	$-0.328345\pi$
$421$	432.375			1.02702			0.513509	+	0.858084i	$0.328345\pi$
$422$	−580.392	−	580.392i	−1.37534	−	1.37534i
$423$	184.429	−	184.457i	0.436002	−	0.436069i
$424$	85.1642			0.200859
$425$	−232.920	+	208.169i	−0.548048	+	0.489809i
$426$	−166.798	+	69.0973i	−0.391544	+	0.162200i
$427$			801.472i			1.87698i
$428$	−730.923	−	730.923i	−1.70776	−	1.70776i
$429$	−27.0949	−	65.4057i	−0.0631582	−	0.152461i
$430$	63.7900	−	63.7900i	0.148349	−	0.148349i
$431$	233.712	−	233.712i	0.542255	−	0.542255i	−0.381934	−	0.924189i	$-0.624742\pi$
$431$	233.712	−	233.712i	0.542255	−	0.542255i	0.924189	+	0.381934i	$0.124742\pi$
$432$	228.625	−	94.7302i	0.529224	−	0.219283i
$433$		−	420.607i		−	0.971380i	−0.874131	−	0.485690i	$-0.838568\pi$
$433$		−	420.607i		−	0.971380i	0.874131	−	0.485690i	$-0.161432\pi$
$434$	−534.522			−1.23162
$435$	−198.276	−	82.1198i	−0.455808	−	0.188781i
$436$	−147.707	−	147.707i	−0.338777	−	0.338777i
$437$	−549.199	−	549.199i	−1.25675	−	1.25675i
$438$	−465.329	−	1123.28i	−1.06240	−	2.56457i
$439$	309.319	−	309.319i	0.704600	−	0.704600i	−0.260794	−	0.965394i	$-0.583984\pi$
$439$	309.319	−	309.319i	0.704600	−	0.704600i	0.965394	+	0.260794i	$0.0839845\pi$
$440$	232.332			0.528028
$441$	515.581	−	515.660i	1.16912	−	1.16930i
$442$	−114.812	−	128.463i	−0.259755	−	0.290640i
$443$			719.460i			1.62406i	0.583613	+	0.812032i	$0.301638\pi$
$443$			719.460i			1.62406i	−0.583613	+	0.812032i	$0.698362\pi$
$444$	18.0525	+	43.5778i	0.0406587	+	0.0981481i
$445$	22.9813	−	22.9813i	0.0516434	−	0.0516434i
$446$			1004.34i			2.25188i
$447$	565.871	+	234.366i	1.26593	+	0.524309i
$448$	703.413	+	703.413i	1.57012	+	1.57012i
$449$	−74.6267	+	74.6267i	−0.166206	+	0.166206i	−0.785310	−	0.619103i	$-0.787496\pi$
$449$	−74.6267	+	74.6267i	−0.166206	+	0.166206i	0.619103	+	0.785310i	$0.287496\pi$
$450$	394.823	−	394.883i	0.877384	−	0.877518i
$451$		−	294.478i		−	0.652945i
$452$	239.135	−	239.135i	0.529060	−	0.529060i
$453$	185.687	+	76.9057i	0.409905	+	0.169770i
$454$	−50.5602	+	50.5602i	−0.111366	+	0.111366i
$455$		−	88.0905i		−	0.193605i
$456$	589.478	+	244.144i	1.29272	+	0.535402i
$457$			743.882i			1.62775i	0.581039	+	0.813876i	$0.302646\pi$
$457$			743.882i			1.62775i	−0.581039	+	0.813876i	$0.697354\pi$
$458$		−	6.89898i		−	0.0150633i
$459$	−413.576	−	199.087i	−0.901038	−	0.433740i
$460$	798.655			1.73621
$461$	744.275			1.61448			0.807239	−	0.590224i	$-0.200961\pi$
$461$	744.275			1.61448			0.807239	+	0.590224i	$0.200961\pi$
$462$	−347.476	+	838.972i	−0.752113	+	1.81596i
$463$	−256.153			−0.553247			−0.276624	−	0.960978i	$-0.589215\pi$
$463$	−256.153			−0.553247			−0.276624	+	0.960978i	$0.589215\pi$
$464$	−180.139	−	180.139i	−0.388231	−	0.388231i
$465$	−41.0188	+	99.0390i	−0.0882125	+	0.212987i
$466$	−745.852	−	745.852i	−1.60054	−	1.60054i
$467$	178.129			0.381432			0.190716	−	0.981645i	$-0.438919\pi$
$467$	178.129			0.381432			0.190716	+	0.981645i	$0.438919\pi$
$468$	141.376	+	141.354i	0.302086	+	0.302039i
$469$	−145.827	−	145.827i	−0.310932	−	0.310932i
$470$	−178.095	+	178.095i	−0.378925	+	0.378925i
$471$	−109.000	+	263.179i	−0.231424	+	0.558766i
$472$	−261.240			−0.553474
$473$	−57.7106	−	57.7106i	−0.122010	−	0.122010i
$474$	−252.442	+	104.576i	−0.532577	+	0.220625i
$475$	340.378			0.716585
$476$	−80.3731	+	1432.31i	−0.168851	+	3.00905i
$477$	47.2073	+	47.2001i	0.0989671	+	0.0989520i
$478$			51.8989i			0.108575i
$479$	231.301	+	231.301i	0.482882	+	0.482882i	0.906051	−	0.423169i	$-0.139082\pi$
$479$	231.301	+	231.301i	0.482882	+	0.482882i	−0.423169	+	0.906051i	$0.639082\pi$
$480$	106.855	−	44.2654i	0.222614	−	0.0922197i
$481$	−4.50931	+	4.50931i	−0.00937487	+	0.00937487i
$482$	751.191	−	751.191i	1.55849	−	1.55849i
$483$	−548.855	+	1325.20i	−1.13635	+	2.74368i
$484$			438.029i			0.905018i
$485$	31.0842			0.0640911
$486$	758.086	+	313.839i	1.55985	+	0.645760i
$487$	133.787	+	133.787i	0.274718	+	0.274718i	0.830996	−	0.556278i	$-0.187771\pi$
$487$	133.787	+	133.787i	0.274718	+	0.274718i	−0.556278	+	0.830996i	$0.687771\pi$
$488$	570.655	+	570.655i	1.16937	+	1.16937i
$489$	650.401	−	269.434i	1.33006	−	0.550990i
$490$	−497.872	+	497.872i	−1.01607	+	1.01607i
$491$	−263.750			−0.537168			−0.268584	−	0.963256i	$-0.586556\pi$
$491$	−263.750			−0.537168			−0.268584	+	0.963256i	$0.586556\pi$
$492$	318.261	+	768.267i	0.646872	+	1.56152i
$493$	−26.4727	+	471.765i	−0.0536973	+	0.956927i
$494$			187.729i			0.380018i
$495$	128.784	+	128.764i	0.260170	+	0.260130i
$496$	−89.9796	+	89.9796i	−0.181410	+	0.181410i
$497$			203.238i			0.408930i
$498$	356.878	−	861.672i	0.716622	−	1.73027i
$499$	132.044	+	132.044i	0.264618	+	0.264618i	0.826927	−	0.562309i	$-0.190087\pi$
$499$	132.044	+	132.044i	0.264618	+	0.264618i	−0.562309	+	0.826927i	$0.690087\pi$
$500$	−584.202	+	584.202i	−1.16840	+	1.16840i
$501$	−138.824	+	57.5090i	−0.277094	+	0.114788i
$502$		−	484.615i		−	0.965369i
$503$	−447.931	+	447.931i	−0.890518	+	0.890518i	−0.994572	−	0.104054i	$-0.966819\pi$
$503$	−447.931	+	447.931i	−0.890518	+	0.890518i	0.104054	+	0.994572i	$0.466819\pi$
$504$	−0.0902572	−	1178.31i	−0.000179082	−	2.33791i
$505$	171.763	−	171.763i	0.340125	−	0.340125i
$506$		−	1113.08i		−	2.19975i
$507$	183.660	−	443.443i	0.362249	−	0.874640i
$508$			1227.81i			2.41696i
$509$		−	682.119i		−	1.34011i	−0.742309	−	0.670057i	$-0.766269\pi$
$509$		−	682.119i		−	1.34011i	0.742309	−	0.670057i	$-0.233731\pi$
$510$	399.326	+	192.265i	0.782992	+	0.376990i
$511$	−1368.69			−2.67845
$512$	558.249			1.09033
$513$	191.443	+	462.035i	0.373184	+	0.900652i
$514$	−1353.04			−2.63236
$515$	−26.2974	−	26.2974i	−0.0510629	−	0.0510629i
$516$	212.933	+	88.1902i	0.412661	+	0.170911i
$517$	161.122	+	161.122i	0.311647	+	0.311647i
$518$	81.7981			0.157911
$519$	399.034	−	165.303i	0.768852	−	0.318503i
$520$	−62.7212	−	62.7212i	−0.120618	−	0.120618i
$521$	457.174	−	457.174i	0.877493	−	0.877493i	−0.115782	−	0.993275i	$-0.536937\pi$
$521$	457.174	−	457.174i	0.877493	−	0.877493i	0.993275	+	0.115782i	$0.0369372\pi$
$522$	−0.0646974	−	844.626i	−0.000123941	−	1.61806i
$523$	−982.417			−1.87843			−0.939214	−	0.343334i	$-0.888444\pi$
$523$	−982.417			−1.87843			−0.939214	+	0.343334i	$0.888444\pi$
$524$	−905.043	−	905.043i	−1.72718	−	1.72718i
$525$	−240.577	−	580.742i	−0.458242	−	1.10618i
$526$	1518.05			2.88603
$527$	235.646	+	13.2231i	0.447147	+	0.0250913i
$528$	82.7368	+	199.723i	0.156699	+	0.378263i
$529$		−	1229.16i		−	2.32355i
$530$	−45.5789	−	45.5789i	−0.0859980	−	0.0859980i
$531$	−144.808	−	144.786i	−0.272708	−	0.272666i
$532$	1105.28	−	1105.28i	2.07759	−	2.07759i
$533$	−79.4982	+	79.4982i	−0.149152	+	0.149152i
$534$	118.175	+	48.9446i	0.221302	+	0.0916565i
$535$			359.494i			0.671952i
$536$	−207.660			−0.387425
$537$	170.207	−	410.960i	0.316959	−	0.765289i
$538$	−768.785	−	768.785i	−1.42897	−	1.42897i
$539$	450.423	+	450.423i	0.835665	+	0.835665i
$540$	−475.150	−	196.749i	−0.879907	−	0.364351i
$541$	−302.196	+	302.196i	−0.558588	+	0.558588i	−0.928905	−	0.370317i	$-0.879249\pi$
$541$	−302.196	+	302.196i	−0.558588	+	0.558588i	0.370317	+	0.928905i	$0.379249\pi$
$542$	−1605.95			−2.96301
$543$	−94.3461	+	39.0837i	−0.173750	+	0.0719773i
$544$	−169.694	−	189.871i	−0.311937	−	0.349027i
$545$			72.6475i			0.133298i
$546$	320.297	−	132.686i	0.586625	−	0.243014i
$547$	−496.002	+	496.002i	−0.906768	+	0.906768i	−0.996010	−	0.0892419i	$-0.971556\pi$
$547$	−496.002	+	496.002i	−0.906768	+	0.906768i	0.0892419	+	0.996010i	$0.471556\pi$
$548$		−	340.996i		−	0.622256i
$549$	0.0484558	+	632.590i	8.82619e−5	+	1.15226i
$550$	344.926	+	344.926i	0.627139	+	0.627139i
$551$	364.049	−	364.049i	0.660707	−	0.660707i
$552$	552.762	+	1334.34i	1.00138	+	2.41729i
$553$			307.593i			0.556227i
$554$	−820.173	+	820.173i	−1.48046	+	1.48046i
$555$	6.27714	−	15.1560i	0.0113102	−	0.0273081i
$556$	636.094	−	636.094i	1.14405	−	1.14405i
$557$			535.144i			0.960762i	0.877060	+	0.480381i	$0.159502\pi$
$557$			535.144i			0.960762i	−0.877060	+	0.480381i	$0.840498\pi$
$558$	−421.890	+	0.0323163i	−0.756076	+	5.79146e-5i
$559$			31.1594i			0.0557414i
$560$			268.993i			0.480344i
$561$	173.941	−	361.269i	0.310056	−	0.643973i
$562$	153.404			0.272962
$563$	42.5493			0.0755760			0.0377880	−	0.999286i	$-0.487969\pi$
$563$	42.5493			0.0755760			0.0377880	+	0.999286i	$0.487969\pi$
$564$	−594.485	−	246.217i	−1.05405	−	0.436555i
$565$	−117.615			−0.208169
$566$	−192.330	−	192.330i	−0.339805	−	0.339805i
$567$	652.998	−	653.198i	1.15167	−	1.15202i
$568$	144.708	+	144.708i	0.254767	+	0.254767i
$569$	−270.203			−0.474873			−0.237436	−	0.971403i	$-0.576307\pi$
$569$	−270.203			−0.474873			−0.237436	+	0.971403i	$0.576307\pi$
$570$	−184.819	−	446.145i	−0.324245	−	0.782711i
$571$	−632.245	−	632.245i	−1.10726	−	1.10726i	−0.993509	−	0.113750i	$-0.963714\pi$
$571$	−632.245	−	632.245i	−1.10726	−	1.10726i	−0.113750	−	0.993509i	$-0.536286\pi$
$572$	−123.491	+	123.491i	−0.215893	+	0.215893i
$573$	607.609	+	251.653i	1.06040	+	0.439185i
$574$	1442.08			2.51234
$575$	544.828	+	544.828i	0.947526	+	0.947526i
$576$	555.236	+	555.151i	0.963952	+	0.963804i
$577$	−300.072			−0.520056			−0.260028	−	0.965601i	$-0.583732\pi$
$577$	−300.072			−0.520056			−0.260028	+	0.965601i	$0.583732\pi$
$578$	109.169	−	969.673i	0.188873	−	1.67763i
$579$	690.624	−	286.097i	1.19279	−	0.494122i
$580$			529.407i			0.912771i
$581$	−742.385	−	742.385i	−1.27777	−	1.27777i
$582$	46.8203	+	113.022i	0.0804473	+	0.194196i
$583$	−41.2351	+	41.2351i	−0.0707292	+	0.0707292i
$584$	−974.519	+	974.519i	−1.66870	+	1.66870i
$585$	−0.00532581	−	69.5286i	−9.10396e−6	−	0.118852i
$586$			768.275i			1.31105i
$587$	415.532			0.707891			0.353946	−	0.935266i	$-0.384840\pi$
$587$	415.532			0.707891			0.353946	+	0.935266i	$0.384840\pi$
$588$	−1661.91	−	688.313i	−2.82638	−	1.17060i
$589$	−181.843	−	181.843i	−0.308731	−	0.308731i
$590$	139.813	+	139.813i	0.236971	+	0.236971i
$591$	80.8973	+	195.282i	0.136882	+	0.330427i
$592$	13.7696	−	13.7696i	0.0232595	−	0.0232595i
$593$	−1066.87			−1.79910			−0.899549	−	0.436819i	$-0.856105\pi$
$593$	−1066.87			−1.79910			−0.899549	+	0.436819i	$0.856105\pi$
$594$	−274.207	+	662.210i	−0.461628	+	1.11483i
$595$	371.996	−	332.466i	0.625204	−	0.558766i
$596$		−	1510.90i		−	2.53507i
$597$	−291.932	−	704.711i	−0.488999	−	1.18042i
$598$	−300.489	+	300.489i	−0.502490	+	0.502490i
$599$			902.903i			1.50735i	0.657247	+	0.753676i	$0.271721\pi$
$599$			902.903i			1.50735i	−0.657247	+	0.753676i	$0.728279\pi$
$600$	−584.786	−	242.200i	−0.974644	−	0.403667i
$601$	181.754	+	181.754i	0.302419	+	0.302419i	0.841960	−	0.539540i	$-0.181402\pi$
$601$	181.754	+	181.754i	0.302419	+	0.302419i	−0.539540	+	0.841960i	$0.681402\pi$
$602$	282.613	−	282.613i	0.469457	−	0.469457i
$603$	−115.108	−	115.090i	−0.190892	−	0.190863i
$604$		−	495.793i		−	0.820849i
$605$	107.719	−	107.719i	0.178048	−	0.178048i
$606$	883.248	+	365.814i	1.45750	+	0.603653i
$607$	107.393	−	107.393i	0.176924	−	0.176924i	−0.613090	−	0.790013i	$-0.710074\pi$
$607$	107.393	−	107.393i	0.176924	−	0.176924i	0.790013	+	0.613090i	$0.210074\pi$
$608$			277.467i			0.456361i
$609$	−878.438	−	363.821i	−1.44243	−	0.597408i
$610$		−	610.816i		−	1.00134i
$611$		−	86.9937i		−	0.142379i
$612$	−63.3507	+	1130.51i	−0.103514	+	1.84723i
$613$	879.570			1.43486			0.717431	−	0.696630i	$-0.245318\pi$
$613$	879.570			1.43486			0.717431	+	0.696630i	$0.245318\pi$
$614$	432.366			0.704179
$615$	110.665	−	267.197i	0.179942	−	0.434466i
$616$	1029.32			1.67097
$617$	190.283	+	190.283i	0.308400	+	0.308400i	0.844288	−	0.535889i	$-0.180023\pi$
$617$	190.283	+	190.283i	0.308400	+	0.308400i	−0.535889	+	0.844288i	$0.680023\pi$
$618$	56.0071	−	135.228i	0.0906264	−	0.218815i
$619$	283.669	+	283.669i	0.458270	+	0.458270i	0.898087	−	0.439817i	$-0.144957\pi$
$619$	283.669	+	283.669i	0.458270	+	0.458270i	−0.439817	+	0.898087i	$0.644957\pi$
$620$	264.439			0.426514
$621$	−433.124	+	1045.99i	−0.697461	+	1.68437i
$622$	723.880	+	723.880i	1.16379	+	1.16379i
$623$	101.816	−	101.816i	0.163428	−	0.163428i
$624$	31.5819	−	76.2537i	0.0506120	−	0.122201i
$625$	−172.063			−0.275300
$626$	336.531	+	336.531i	0.537590	+	0.537590i
$627$	−403.626	+	167.205i	−0.643742	+	0.266675i
$628$	702.701			1.11895
$629$	−36.0611	−	2.02354i	−0.0573308	−	0.00321708i
$630$	−630.569	+	630.666i	−1.00090	+	1.00106i
$631$			547.479i			0.867637i	0.901000	+	0.433818i	$0.142834\pi$
$631$			547.479i			0.867637i	−0.901000	+	0.433818i	$0.857166\pi$
$632$	219.009	+	219.009i	0.346533	+	0.346533i
$633$	−673.757	+	279.110i	−1.06439	+	0.440931i
$634$	−101.467	+	101.467i	−0.160042	+	0.160042i
$635$	301.942	−	301.942i	0.475498	−	0.475498i
$636$	63.0132	−	152.144i	0.0990774	−	0.239220i
$637$		−	243.195i		−	0.381782i
$638$	737.828			1.15647
$639$	0.0122875	+	160.413i	1.92292e−5	+	0.251038i
$640$	−427.038	−	427.038i	−0.667247	−	0.667247i
$641$	66.0342	+	66.0342i	0.103017	+	0.103017i	0.756737	−	0.653719i	$-0.226792\pi$
$641$	66.0342	+	66.0342i	0.103017	+	0.103017i	−0.653719	+	0.756737i	$0.726792\pi$
$642$	−1307.12	+	541.486i	−2.03602	+	0.843437i
$643$	346.384	−	346.384i	0.538700	−	0.538700i	−0.384447	−	0.923147i	$-0.625608\pi$
$643$	346.384	−	346.384i	0.538700	−	0.538700i	0.923147	+	0.384447i	$0.125608\pi$
$644$	3538.34			5.49432
$645$	−30.6765	−	74.0517i	−0.0475605	−	0.114809i
$646$	−792.758	+	708.515i	−1.22718	+	1.09677i
$647$		−	467.269i		−	0.722209i	−0.932525	−	0.361104i	$-0.882400\pi$
$647$		−	467.269i		−	0.722209i	0.932525	−	0.361104i	$-0.117600\pi$
$648$	−0.142477	−	930.023i	−0.000219873	−	1.43522i
$649$	126.488	−	126.488i	0.194897	−	0.194897i
$650$		−	186.235i		−	0.286515i
$651$	−181.729	+	438.779i	−0.279153	+	0.674008i
$652$	−1228.00	−	1228.00i	−1.88344	−	1.88344i
$653$	205.842	−	205.842i	0.315225	−	0.315225i	−0.531705	−	0.846930i	$-0.678448\pi$
$653$	205.842	−	205.842i	0.315225	−	0.315225i	0.846930	+	0.531705i	$0.178448\pi$
$654$	−264.147	+	109.425i	−0.403894	+	0.167316i
$655$			445.133i			0.679593i
$656$	242.756	−	242.756i	0.370054	−	0.370054i
$657$	−1080.29	+	0.0827489i	−1.64427	+	0.000125950i
$658$	−789.025	+	789.025i	−1.19913	+	1.19913i
$659$		−	1130.65i		−	1.71570i	−0.513898	−	0.857851i	$-0.671799\pi$
$659$		−	1130.65i		−	1.71570i	0.513898	−	0.857851i	$-0.328201\pi$
$660$	171.904	−	415.057i	0.260460	−	0.628874i
$661$		−	1249.51i		−	1.89034i	−0.326586	−	0.945168i	$-0.605898\pi$
$661$		−	1249.51i		−	1.89034i	0.326586	−	0.945168i	$-0.394102\pi$
$662$			1607.57i			2.42835i
$663$	−144.487	+	50.5716i	−0.217929	+	0.0762769i
$664$	−1057.17			−1.59212
$665$	−543.616			−0.817468
$666$	64.5621	−	0.00494539i	0.0969401	−	7.42551e-6i
$667$	1165.44			1.74728
$668$	262.109	+	262.109i	0.392379	+	0.392379i
$669$	824.444	+	341.459i	1.23235	+	0.510402i
$670$	111.137	+	111.137i	0.165877	+	0.165877i
$671$	−552.603			−0.823552
$672$	473.406	−	196.112i	0.704473	−	0.291834i
$673$	375.660	+	375.660i	0.558187	+	0.558187i	0.928791	−	0.370604i	$-0.120849\pi$
$673$	375.660	+	375.660i	0.558187	+	0.558187i	−0.370604	+	0.928791i	$0.620849\pi$
$674$	157.212	−	157.212i	0.233253	−	0.233253i
$675$	−189.919	−	458.357i	−0.281362	−	0.679047i
$676$	−1184.01			−1.75150
$677$	149.866	+	149.866i	0.221368	+	0.221368i	0.809074	−	0.587706i	$-0.199969\pi$
$677$	149.866	+	149.866i	0.221368	+	0.221368i	−0.587706	+	0.809074i	$0.699969\pi$
$678$	−177.157	−	427.649i	−0.261294	−	0.630751i
$679$	137.714			0.202819
$680$	28.1460	−	501.583i	0.0413911	−	0.737622i
$681$	24.3143	+	58.6936i	0.0357038	+	0.0861874i
$682$		−	368.545i		−	0.540388i
$683$	782.854	+	782.854i	1.14620	+	1.14620i	0.987294	+	0.158905i	$0.0507965\pi$
$683$	782.854	+	782.854i	1.14620	+	1.14620i	0.158905	+	0.987294i	$0.449204\pi$
$684$	872.314	−	872.448i	1.27531	−	1.27551i
$685$	−83.8571	+	83.8571i	−0.122419	+	0.122419i
$686$	−871.771	+	871.771i	−1.27080	+	1.27080i
$687$	−5.66325	−	2.34554i	−0.00824345	−	0.00341418i
$688$		−	95.1484i		−	0.138297i
$689$	22.2639			0.0323134
$690$	418.292	−	1009.96i	0.606221	−	1.46371i
$691$	450.324	+	450.324i	0.651699	+	0.651699i	0.953402	−	0.301703i	$-0.0975551\pi$
$691$	450.324	+	450.324i	0.651699	+	0.651699i	−0.301703	+	0.953402i	$0.597555\pi$
$692$	−753.404	−	753.404i	−1.08873	−	1.08873i
$693$	570.561	+	570.474i	0.823321	+	0.823195i
$694$	−377.075	+	377.075i	−0.543335	+	0.543335i
$695$	−312.854			−0.450150
$696$	−884.499	+	366.411i	−1.27083	+	0.526453i
$697$	−635.750	−	35.6746i	−0.912123	−	0.0511831i
$698$			1389.36i			1.99049i
$699$	−865.835	+	358.679i	−1.23868	+	0.513132i
$700$	−1096.48	+	1096.48i	−1.56640	+	1.56640i
$701$		−	647.604i		−	0.923829i	−0.886924	−	0.461914i	$-0.847163\pi$
$701$		−	647.604i		−	0.923829i	0.886924	−	0.461914i	$-0.152837\pi$
$702$	252.798	−	104.746i	0.360111	−	0.149211i
$703$	27.8275	+	27.8275i	0.0395839	+	0.0395839i
$704$	−484.993	+	484.993i	−0.688911	+	0.688911i
$705$	85.6454	+	206.744i	0.121483	+	0.293254i
$706$		−	1003.06i		−	1.42076i
$707$	760.974	−	760.974i	1.07634	−	1.07634i
$708$	−193.292	+	466.699i	−0.273012	+	0.659180i
$709$	−15.4814	+	15.4814i	−0.0218355	+	0.0218355i	−0.717940	−	0.696105i	$-0.754915\pi$
$709$	−15.4814	+	15.4814i	−0.0218355	+	0.0218355i	0.696105	+	0.717940i	$0.254915\pi$
$710$		−	154.892i		−	0.218157i
$711$	0.0185966	+	242.779i	2.61556e−5	+	0.341461i
$712$		−	144.987i		−	0.203634i
$713$		−	582.135i		−	0.816458i
$714$	1769.16	+	851.804i	2.47782	+	1.19300i
$715$	60.7371			0.0849470
$716$	−1097.28			−1.53252
$717$	42.6029	+	17.6448i	0.0594183	+	0.0246092i
$718$	2205.69			3.07200
$719$	731.607	+	731.607i	1.01753	+	1.01753i	0.999844	+	0.0176899i	$0.00563118\pi$
$719$	731.607	+	731.607i	1.01753	+	1.01753i	0.0176899	+	0.999844i	$0.494369\pi$
$720$	0.0162629	+	212.312i	2.25873e−5	+	0.294878i
$721$	−116.507	−	116.507i	−0.161591	−	0.161591i
$722$	−60.4086			−0.0836685
$723$	−361.247	−	872.032i	−0.499650	−	1.20613i
$724$	178.132	+	178.132i	0.246039	+	0.246039i
$725$	−361.152	+	361.152i	−0.498140	+	0.498140i
$726$	553.918	+	229.416i	0.762973	+	0.316000i
$727$	−354.772			−0.487995			−0.243997	−	0.969776i	$-0.578459\pi$
$727$	−354.772			−0.487995			−0.243997	+	0.969776i	$0.578459\pi$
$728$	−277.878	−	277.878i	−0.381701	−	0.381701i
$729$	515.362	−	515.599i	0.706944	−	0.707269i
$730$	1043.10			1.42891
$731$	−131.583	+	117.600i	−0.180004	+	0.160876i
$732$	1441.69	−	597.233i	1.96952	−	0.815892i
$733$			585.834i			0.799227i	0.916684	+	0.399614i	$0.130856\pi$
$733$			585.834i			0.799227i	−0.916684	+	0.399614i	$0.869144\pi$
$734$	−527.427	−	527.427i	−0.718565	−	0.718565i
$735$	239.426	+	577.963i	0.325750	+	0.786344i
$736$	−444.129	+	444.129i	−0.603437	+	0.603437i
$737$	100.546	−	100.546i	0.136425	−	0.136425i
$738$	1138.22	−	0.0871861i	1.54230	−	0.000118138i
$739$		−	722.220i		−	0.977293i	−0.872482	−	0.488647i	$-0.837491\pi$
$739$		−	722.220i		−	0.977293i	0.872482	−	0.488647i	$-0.162509\pi$
$740$	−40.4672			−0.0546854
$741$	154.103	+	63.8248i	0.207967	+	0.0861333i
$742$	−201.932	−	201.932i	−0.272145	−	0.272145i
$743$	−932.973	−	932.973i	−1.25568	−	1.25568i	−0.953134	−	0.302549i	$-0.902162\pi$
$743$	−932.973	−	932.973i	−1.25568	−	1.25568i	−0.302549	−	0.953134i	$-0.597838\pi$
$744$	183.022	+	441.807i	0.245998	+	0.593827i
$745$	−371.558	+	371.558i	−0.498736	+	0.498736i
$746$	324.378			0.434823
$747$	−585.999	−	585.909i	−0.784470	−	0.784350i
$748$	−987.557	−	55.4161i	−1.32026	−	0.0740857i
$749$			1592.69i			2.12643i
$750$	432.791	+	1044.74i	0.577055	+	1.39298i
$751$	565.689	−	565.689i	0.753248	−	0.753248i	−0.221836	−	0.975084i	$-0.571205\pi$
$751$	565.689	−	565.689i	0.753248	−	0.753248i	0.975084	+	0.221836i	$0.0712050\pi$
$752$			265.644i			0.353250i
$753$	−397.812	−	164.761i	−0.528303	−	0.218807i
$754$	−199.186	−	199.186i	−0.264173	−	0.264173i
$755$	−121.924	+	121.924i	−0.161489	+	0.161489i
$756$	−2105.09	−	871.673i	−2.78451	−	1.15301i
$757$			521.038i			0.688294i	0.938916	+	0.344147i	$0.111832\pi$
$757$			521.038i			0.688294i	−0.938916	+	0.344147i	$0.888168\pi$
$758$	962.771	−	962.771i	1.27015	−	1.27015i
$759$	−913.704	−	378.428i	−1.20383	−	0.498587i
$760$	−387.059	+	387.059i	−0.509289	+	0.509289i
$761$		−	203.340i		−	0.267201i	−0.991035	−	0.133600i	$-0.957346\pi$
$761$		−	203.340i		−	0.267201i	0.991035	−	0.133600i	$-0.0426539\pi$
$762$	1552.66	+	643.062i	2.03761	+	0.843914i
$763$			321.856i			0.421829i
$764$		−	1622.35i		−	2.12349i
$765$	293.591	−	262.433i	0.383779	−	0.343050i
$766$	−630.442			−0.823032
$767$	−68.2942			−0.0890407
$768$	508.899	−	1228.72i	0.662629	−	1.59990i
$769$	502.038			0.652845			0.326423	−	0.945224i	$-0.394157\pi$
$769$	502.038			0.652845			0.326423	+	0.945224i	$0.394157\pi$
$770$	−550.880	−	550.880i	−0.715429	−	0.715429i
$771$	−460.010	+	1110.68i	−0.596641	+	1.44057i
$772$	−1303.95	−	1303.95i	−1.68905	−	1.68905i
$773$	−164.983			−0.213432			−0.106716	−	0.994290i	$-0.534034\pi$
$773$	−164.983			−0.213432			−0.106716	+	0.994290i	$0.534034\pi$
$774$	223.046	−	223.080i	0.288173	−	0.288217i
$775$	180.395	+	180.395i	0.232768	+	0.232768i
$776$	98.0538	−	98.0538i	0.126358	−	0.126358i
$777$	27.8100	−	67.1467i	0.0357916	−	0.0864178i
$778$	1413.46			1.81678
$779$	490.592	+	490.592i	0.629772	+	0.629772i
$780$	−158.458	+	65.6424i	−0.203151	+	0.0841569i
$781$	−140.130			−0.179424
$782$	−2403.02	−	134.844i	−3.07292	−	0.172435i
$783$	−693.360	−	287.106i	−0.885518	−	0.366674i
$784$			742.620i			0.947220i
$785$	−172.807	−	172.807i	−0.220136	−	0.220136i
$786$	−1618.50	+	670.479i	−2.05917	+	0.853027i
$787$	362.354	−	362.354i	0.460424	−	0.460424i	−0.438370	−	0.898794i	$-0.644444\pi$
$787$	362.354	−	362.354i	0.460424	−	0.460424i	0.898794	+	0.438370i	$0.144444\pi$
$788$	368.706	−	368.706i	0.467901	−	0.467901i
$789$	516.114	−	1246.14i	0.654136	−	1.57940i
$790$		−	234.422i		−	0.296737i
$791$	−521.080			−0.658760
$792$	812.427	−	0.0622311i	1.02579	−	7.85746e-5i
$793$	149.183	+	149.183i	0.188124	+	0.188124i
$794$	898.021	+	898.021i	1.13101	+	1.13101i
$795$	−52.9110	+	21.9188i	−0.0665548	+	0.0275709i
$796$	−1330.54	+	1330.54i	−1.67154	+	1.67154i
$797$	774.302			0.971521			0.485760	−	0.874092i	$-0.338543\pi$
$797$	774.302			0.971521			0.485760	+	0.874092i	$0.338543\pi$
$798$	−818.819	−	1976.59i	−1.02609	−	2.47693i
$799$	367.365	−	328.326i	0.459780	−	0.410922i
$800$		−	275.259i		−	0.344073i
$801$	80.3555	−	80.3678i	0.100319	−	0.100334i
$802$	1389.42	−	1389.42i	1.73245	−	1.73245i
$803$		−	943.692i		−	1.17521i
$804$	−153.648	+	370.980i	−0.191105	+	0.461418i
$805$	−870.142	−	870.142i	−1.08092	−	1.08092i
$806$	−99.4935	+	99.4935i	−0.123441	+	0.123441i
$807$	−892.456	+	369.708i	−1.10589	+	0.458126i
$808$		−	1083.64i		−	1.34114i
$809$	−188.208	+	188.208i	−0.232643	+	0.232643i	−0.813795	−	0.581152i	$-0.802602\pi$
$809$	−188.208	+	188.208i	−0.232643	+	0.232643i	0.581152	+	0.813795i	$0.302602\pi$
$810$	−497.661	+	497.814i	−0.614397	+	0.614585i
$811$	−743.378	+	743.378i	−0.916619	+	0.916619i	−0.996782	−	0.0801630i	$-0.974456\pi$
$811$	−743.378	+	743.378i	−0.916619	+	0.916619i	0.0801630	+	0.996782i	$0.474456\pi$
$812$			2345.47i			2.88851i
$813$	−545.998	+	1318.30i	−0.671585	+	1.62152i
$814$			56.3986i			0.0692858i
$815$			603.976i			0.741075i
$816$	441.205	−	154.425i	0.540692	−	0.189247i
$817$	192.288			0.235359
$818$	−619.761			−0.757654
$819$	−0.0235953	−	308.037i	−2.88099e−5	−	0.376114i
$820$	−713.428			−0.870035
$821$	796.926	+	796.926i	0.970678	+	0.970678i	0.999582	−	0.0289045i	$-0.00920187\pi$
$821$	796.926	+	796.926i	0.970678	+	0.970678i	−0.0289045	+	0.999582i	$0.509202\pi$
$822$	−431.214	−	178.595i	−0.524591	−	0.217269i
$823$	−1085.50	−	1085.50i	−1.31895	−	1.31895i	−0.914605	−	0.404348i	$-0.867498\pi$
$823$	−1085.50	−	1085.50i	−1.31895	−	1.31895i	−0.404348	−	0.914605i	$-0.632502\pi$
$824$	−165.908			−0.201345
$825$	400.413	−	165.875i	0.485349	−	0.201060i
$826$	619.422	+	619.422i	0.749906	+	0.749906i
$827$	922.606	−	922.606i	1.11561	−	1.11561i	0.123228	−	0.992378i	$-0.460675\pi$
$827$	922.606	−	922.606i	1.11561	−	1.11561i	0.992378	−	0.123228i	$-0.0393246\pi$
$828$	2792.76	−	0.213923i	3.37290	−	0.000258361i
$829$	862.319			1.04019			0.520096	−	0.854108i	$-0.325896\pi$
$829$	862.319			1.04019			0.520096	+	0.854108i	$0.325896\pi$
$830$	565.785	+	565.785i	0.681669	+	0.681669i
$831$	394.420	+	952.111i	0.474633	+	1.14574i
$832$	261.860			0.314736
$833$	1026.99	−	917.853i	1.23288	−	1.10186i
$834$	−471.235	−	1137.54i	−0.565030	−	1.36395i
$835$		−	128.915i		−	0.154389i
$836$	762.074	+	762.074i	0.911571	+	0.911571i
$837$	−143.409	+	346.333i	−0.171337	+	0.413779i
$838$	−939.685	+	939.685i	−1.12134	+	1.12134i
$839$	−327.969	+	327.969i	−0.390904	+	0.390904i	−0.875010	−	0.484105i	$-0.839145\pi$
$839$	−327.969	+	327.969i	−0.390904	+	0.390904i	0.484105	+	0.875010i	$0.339145\pi$
$840$	933.960	+	386.817i	1.11186	+	0.460496i
$841$		−	68.4643i		−	0.0814082i
$842$	−1459.90			−1.73385
$843$	52.1551	−	125.927i	0.0618684	−	0.149380i
$844$	1272.10	+	1272.10i	1.50723	+	1.50723i
$845$	291.170	+	291.170i	0.344580	+	0.344580i
$846$	−622.718	+	622.814i	−0.736074	+	0.736187i
$847$	477.236	−	477.236i	0.563443	−	0.563443i
$848$	−67.9850			−0.0801710
$849$	−223.269	+	92.4911i	−0.262979	+	0.108941i
$850$	786.448	−	702.875i	0.925233	−	0.826912i
$851$			89.0844i			0.104682i
$852$	365.586	−	151.447i	0.429092	−	0.177755i
$853$	−1128.63	+	1128.63i	−1.32313	+	1.32313i	−0.411895	+	0.911231i	$0.635133\pi$
$853$	−1128.63	+	1128.63i	−1.32313	+	1.32313i	−0.911231	+	0.411895i	$0.864867\pi$
$854$		−	2706.14i		−	3.16879i
$855$	−429.068	+	0.0328662i	−0.501834	+	3.84400e-5i
$856$	1134.01	+	1134.01i	1.32478	+	1.32478i
$857$	−1100.11	+	1100.11i	−1.28368	+	1.28368i	−0.345116	+	0.938560i	$0.612160\pi$
$857$	−1100.11	+	1100.11i	−1.28368	+	1.28368i	−0.938560	+	0.345116i	$0.887840\pi$
$858$	91.4850	+	220.840i	0.106626	+	0.257390i
$859$		−	617.021i		−	0.718302i	−0.933279	−	0.359151i	$-0.883066\pi$
$859$		−	617.021i		−	0.718302i	0.933279	−	0.359151i	$-0.116934\pi$
$860$	−139.815	+	139.815i	−0.162575	+	0.162575i
$861$	490.285	−	1183.78i	0.569437	−	1.37489i
$862$	−789.121	+	789.121i	−0.915453	+	0.915453i
$863$		−	451.967i		−	0.523717i	−0.965106	−	0.261858i	$-0.915665\pi$
$863$		−	451.967i		−	0.523717i	0.965106	−	0.261858i	$-0.0843353\pi$
$864$	373.641	−	154.817i	0.432455	−	0.179187i
$865$			370.551i			0.428383i
$866$			1420.17i			1.63992i
$867$	−758.872	−	419.288i	−0.875285	−	0.483608i
$868$	1171.56			1.34973
$869$	−212.081			−0.244052
$870$	669.473	+	277.275i	0.769510	+	0.318707i
$871$	−54.2872			−0.0623274
$872$	229.164	+	229.164i	0.262803	+	0.262803i
$873$	108.696	−	0.00832600i	0.124509	−	9.53723e-6i
$874$	1854.35	+	1854.35i	2.12168	+	2.12168i
$875$	1272.99			1.45484
$876$	1019.91	+	2462.01i	1.16428	+	2.81051i
$877$	330.904	+	330.904i	0.377314	+	0.377314i	0.870132	−	0.492818i	$-0.164033\pi$
$877$	330.904	+	330.904i	0.377314	+	0.377314i	−0.492818	+	0.870132i	$0.664033\pi$
$878$	−1044.41	+	1044.41i	−1.18953	+	1.18953i
$879$	630.664	+	261.201i	0.717478	+	0.297157i
$880$	−185.467			−0.210758
$881$	−774.708	−	774.708i	−0.879351	−	0.879351i	0.114117	−	0.993467i	$-0.463596\pi$
$881$	−774.708	−	774.708i	−0.879351	−	0.879351i	−0.993467	+	0.114117i	$0.963596\pi$
$882$	−1740.84	+	1741.11i	−1.97374	+	1.97404i
$883$	491.496			0.556621			0.278310	−	0.960491i	$-0.410226\pi$
$883$	491.496			0.556621			0.278310	+	0.960491i	$0.410226\pi$
$884$	251.644	+	281.564i	0.284665	+	0.318512i
$885$	162.304	−	67.2357i	0.183394	−	0.0759726i
$886$		−	2429.23i		−	2.74180i
$887$	−179.018	−	179.018i	−0.201825	−	0.201825i	0.598957	−	0.800781i	$-0.295582\pi$
$887$	−179.018	−	179.018i	−0.201825	−	0.201825i	−0.800781	+	0.598957i	$0.795582\pi$
$888$	−28.0080	−	67.6100i	−0.0315406	−	0.0761374i
$889$	1337.71	−	1337.71i	1.50474	−	1.50474i
$890$	−77.5956	+	77.5956i	−0.0871860	+	0.0871860i
$891$	450.371	+	450.233i	0.505466	+	0.505312i
$892$		−	2201.31i		−	2.46783i
$893$	−536.848			−0.601173
$894$	−1910.64	−	791.329i	−2.13719	−	0.885156i
$895$	269.842	+	269.842i	0.301499	+	0.301499i
$896$	−1891.94	−	1891.94i	−2.11154	−	2.11154i
$897$	144.505	+	348.828i	0.161098	+	0.388883i
$898$	251.974	−	251.974i	0.280595	−	0.280595i
$899$	385.881			0.429234
$900$	−865.371	+	865.503i	−0.961523	+	0.961670i
$901$	84.0271	+	94.0179i	0.0932598	+	0.104348i
$902$			994.296i			1.10232i
$903$	−135.908	−	328.076i	−0.150508	−	0.363318i
$904$	−371.013	+	371.013i	−0.410413	+	0.410413i
$905$		−	87.6118i		−	0.0968086i
$906$	−626.966	−	259.670i	−0.692015	−	0.286611i
$907$	1138.68	+	1138.68i	1.25544	+	1.25544i	0.953248	+	0.302191i	$0.0977179\pi$
$907$	1138.68	+	1138.68i	1.25544	+	1.25544i	0.302191	+	0.953248i	$0.402282\pi$
$908$	110.818	−	110.818i	0.122046	−	0.122046i
$909$	600.580	−	600.672i	0.660704	−	0.660805i
$910$			297.435i			0.326851i
$911$	−64.7092	+	64.7092i	−0.0710310	+	0.0710310i	−0.741730	−	0.670699i	$-0.765994\pi$
$911$	−64.7092	+	64.7092i	−0.0710310	+	0.0710310i	0.670699	+	0.741730i	$0.265994\pi$
$912$	−470.570	−	194.895i	−0.515976	−	0.213701i
$913$	511.864	−	511.864i	0.560640	−	0.560640i
$914$		−	2511.69i		−	2.74802i
$915$	−501.408	−	207.668i	−0.547987	−	0.226959i
$916$			15.1211i			0.0165078i
$917$			1972.11i			2.15061i
$918$	1396.43	+	672.210i	1.52116	+	0.732255i
$919$	−1647.87			−1.79311			−0.896557	−	0.442929i	$-0.853940\pi$
$919$	−1647.87			−1.79311			−0.896557	+	0.442929i	$0.853940\pi$
$920$	−1239.10			−1.34684
$921$	146.997	−	354.922i	0.159606	−	0.385365i
$922$	−2513.02			−2.72562
$923$	37.8299	+	37.8299i	0.0409858	+	0.0409858i
$924$	761.597	−	1838.86i	0.824239	−	1.99010i
$925$	−27.6060	−	27.6060i	−0.0298443	−	0.0298443i
$926$	864.893			0.934010
$927$	−91.9646	−	91.9505i	−0.0992067	−	0.0991915i
$928$	−294.402	−	294.402i	−0.317243	−	0.317243i
$929$	8.12768	−	8.12768i	0.00874885	−	0.00874885i	−0.702719	−	0.711468i	$-0.748031\pi$
$929$	8.12768	−	8.12768i	0.00874885	−	0.00874885i	0.711468	+	0.702719i	$0.248031\pi$
$930$	138.499	−	334.402i	0.148923	−	0.359572i
$931$	−1500.78			−1.61201
$932$	1634.76	+	1634.76i	1.75403	+	1.75403i
$933$	840.329	−	348.113i	0.900674	−	0.373112i
$934$	−601.445			−0.643946
$935$	229.230	+	256.486i	0.245166	+	0.274317i
$936$	−219.342	−	219.308i	−0.234340	−	0.234304i
$937$			697.727i			0.744640i	0.928105	+	0.372320i	$0.121438\pi$
$937$			697.727i			0.744640i	−0.928105	+	0.372320i	$0.878562\pi$
$938$	492.380	+	492.380i	0.524925	+	0.524925i
$939$	390.668	−	161.837i	0.416047	−	0.172351i
$940$	390.347	−	390.347i	0.415263	−	0.415263i
$941$	−138.918	+	138.918i	−0.147628	+	0.147628i	−0.777057	−	0.629430i	$-0.783289\pi$
$941$	−138.918	+	138.918i	−0.147628	+	0.147628i	0.629430	+	0.777057i	$0.283289\pi$
$942$	368.037	−	888.615i	0.390697	−	0.943328i
$943$			1570.54i			1.66547i
$944$	208.543			0.220914
$945$	303.319	+	732.040i	0.320973	+	0.774645i
$946$	194.858	+	194.858i	0.205981	+	0.205981i
$947$	−460.270	−	460.270i	−0.486029	−	0.486029i	0.421021	−	0.907051i	$-0.361672\pi$
$947$	−460.270	−	460.270i	−0.486029	−	0.486029i	−0.907051	+	0.421021i	$0.861672\pi$
$948$	553.300	−	229.209i	0.583650	−	0.241782i
$949$	−254.762	+	254.762i	−0.268453	+	0.268453i
$950$	−1149.27			−1.20976
$951$	48.7952	+	117.789i	0.0513093	+	0.123858i
$952$	124.697	−	2222.20i	0.130984	−	2.33424i
$953$		−	1670.57i		−	1.75296i	−0.481441	−	0.876478i	$-0.659887\pi$
$953$		−	1670.57i		−	1.75296i	0.481441	−	0.876478i	$-0.340113\pi$
$954$	−159.394	−	159.370i	−0.167080	−	0.167054i
$955$	−398.964	+	398.964i	−0.417764	+	0.417764i
$956$		−	113.752i		−	0.118987i
$957$	250.850	−	605.670i	0.262121	−	0.632884i
$958$	−780.978	−	780.978i	−0.815218	−	0.815218i
$959$	−371.518	+	371.518i	−0.387402	+	0.387402i
$960$	−622.322	+	257.802i	−0.648252	+	0.268544i
$961$			768.252i			0.799430i
$962$	15.2255	−	15.2255i	0.0158270	−	0.0158270i
$963$	0.0962918	+	1257.09i	9.99915e−5	+	1.30539i
$964$	−1646.46	+	1646.46i	−1.70794	+	1.70794i
$965$			641.328i			0.664588i
$966$	1853.19	−	4474.48i	1.91842	−	4.63197i
$967$		−	741.765i		−	0.767079i	−0.923524	−	0.383540i	$-0.874705\pi$
$967$		−	741.765i		−	0.767079i	0.923524	−	0.383540i	$-0.125295\pi$
$968$		−	679.592i		−	0.702058i
$969$	312.083	+	891.645i	0.322067	+	0.920170i
$970$	−104.955			−0.108201
$971$	618.276			0.636742			0.318371	−	0.947966i	$-0.396864\pi$
$971$	618.276			0.636742			0.318371	+	0.947966i	$0.396864\pi$
$972$	−1661.57	−	687.872i	−1.70943	−	0.707687i
$973$	−1386.06			−1.42452
$974$	−451.729	−	451.729i	−0.463787	−	0.463787i
$975$	−152.877	−	63.3168i	−0.156797	−	0.0649403i
$976$	−455.543	−	455.543i	−0.466745	−	0.466745i
$977$	207.836			0.212729			0.106364	−	0.994327i	$-0.466079\pi$
$977$	207.836			0.212729			0.106364	+	0.994327i	$0.466079\pi$
$978$	−2196.06	+	909.736i	−2.24546	+	0.930200i
$979$	70.2004	+	70.2004i	0.0717063	+	0.0717063i
$980$	1091.23	−	1091.23i	1.11350	−	1.11350i
$981$	0.0194589	+	254.036i	1.98358e−5	+	0.258956i
$982$	890.542			0.906866
$983$	−383.143	−	383.143i	−0.389769	−	0.389769i	0.484836	−	0.874605i	$-0.338879\pi$
$983$	−383.143	−	383.143i	−0.389769	−	0.389769i	−0.874605	+	0.484836i	$0.838879\pi$
$984$	−493.775	−	1191.95i	−0.501804	−	1.21133i
$985$	−181.343			−0.184105
$986$	89.3843	−	1592.90i	0.0906535	−	1.61552i
$987$	379.441	+	915.953i	0.384439	+	0.928017i
$988$		−	411.463i		−	0.416461i
$989$	307.787	+	307.787i	0.311211	+	0.311211i
$990$	−434.835	−	434.769i	−0.439227	−	0.439160i
$991$	853.883	−	853.883i	0.861638	−	0.861638i	−0.129890	−	0.991528i	$-0.541463\pi$
$991$	853.883	−	853.883i	0.861638	−	0.861638i	0.991528	+	0.129890i	$0.0414626\pi$
$992$	−147.053	+	147.053i	−0.148239	+	0.148239i
$993$	1319.62	+	546.547i	1.32893	+	0.550400i
$994$		−	686.228i		−	0.690370i
$995$	654.409			0.657698
$996$	−782.203	+	1888.61i	−0.785344	+	1.89619i
$997$	508.838	+	508.838i	0.510369	+	0.510369i	0.914639	−	0.404271i	$-0.132475\pi$
$997$	508.838	+	508.838i	0.510369	+	0.510369i	−0.404271	+	0.914639i	$0.632475\pi$
$998$	−445.843	−	445.843i	−0.446737	−	0.446737i
$999$	21.9460	−	52.9996i	0.0219680	−	0.0530526i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.3.f.a.38.1	✓	20
3.2	odd	2	inner	51.3.f.a.38.10	yes	20
17.13	even	4	inner	51.3.f.a.47.10	yes	20
51.47	odd	4	inner	51.3.f.a.47.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.3.f.a.38.1	✓	20	1.1	even	1	trivial
51.3.f.a.38.10	yes	20	3.2	odd	2	inner
51.3.f.a.47.1	yes	20	51.47	odd	4	inner
51.3.f.a.47.10	yes	20	17.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	51.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-3.37647 q^{2} +(-1.14794 + 2.77168i) q^{3} +7.40053 q^{4} +(-1.81992 - 1.81992i) q^{5} +(3.87599 - 9.35849i) q^{6} +(-8.06294 - 8.06294i) q^{7} -11.4818 q^{8} +(-6.36445 - 6.36347i) q^{9} +(6.14491 + 6.14491i) q^{10} +(5.55928 - 5.55928i) q^{11} +(-8.49539 + 20.5119i) q^{12} -3.00160 q^{13} +(27.2242 + 27.2242i) q^{14} +(7.13342 - 2.95508i) q^{15} +9.16568 q^{16} +(-11.3285 - 12.6754i) q^{17} +(21.4893 + 21.4861i) q^{18} +18.5232i q^{19} +(-13.4684 - 13.4684i) q^{20} +(31.6037 - 13.0921i) q^{21} +(-18.7707 + 18.7707i) q^{22} +(-29.6493 + 29.6493i) q^{23} +(13.1804 - 31.8238i) q^{24} -18.3758i q^{25} +10.1348 q^{26} +(24.9436 - 10.3353i) q^{27} +(-59.6700 - 59.6700i) q^{28} +(-19.6537 - 19.6537i) q^{29} +(-24.0858 + 9.97773i) q^{30} +(-9.81702 + 9.81702i) q^{31} +14.9794 q^{32} +(9.02681 + 21.7903i) q^{33} +(38.2501 + 42.7981i) q^{34} +29.3478i q^{35} +(-47.1003 - 47.0930i) q^{36} +(1.50230 - 1.50230i) q^{37} -62.5430i q^{38} +(3.44567 - 8.31948i) q^{39} +(20.8959 + 20.8959i) q^{40} +(26.4853 - 26.4853i) q^{41} +(-106.709 + 44.2050i) q^{42} -10.3809i q^{43} +(41.1416 - 41.1416i) q^{44} +(0.00177433 + 23.1638i) q^{45} +(100.110 - 100.110i) q^{46} +28.9824i q^{47} +(-10.5217 + 25.4043i) q^{48} +81.0219i q^{49} +62.0451i q^{50} +(48.1367 - 16.8482i) q^{51} -22.2134 q^{52} -7.41735 q^{53} +(-84.2211 + 34.8969i) q^{54} -20.2349 q^{55} +(92.5767 + 92.5767i) q^{56} +(-51.3404 - 21.2636i) q^{57} +(66.3601 + 66.3601i) q^{58} +22.7526 q^{59} +(52.7911 - 21.8691i) q^{60} +(-49.7010 - 49.7010i) q^{61} +(33.1468 - 33.1468i) q^{62} +(0.00786092 + 102.624i) q^{63} -87.2403 q^{64} +(5.46268 + 5.46268i) q^{65} +(-30.4787 - 73.5742i) q^{66} +18.0861 q^{67} +(-83.8365 - 93.8047i) q^{68} +(-48.1426 - 116.214i) q^{69} -99.0920i q^{70} +(-12.6033 - 12.6033i) q^{71} +(73.0751 + 73.0639i) q^{72} +(84.8754 - 84.8754i) q^{73} +(-5.07248 + 5.07248i) q^{74} +(50.9318 + 21.0943i) q^{75} +137.081i q^{76} -89.6482 q^{77} +(-11.6342 + 28.0904i) q^{78} +(-19.0745 - 19.0745i) q^{79} +(-16.6808 - 16.6808i) q^{80} +(0.0124090 + 81.0000i) q^{81} +(-89.4267 + 89.4267i) q^{82} +92.0738 q^{83} +(233.884 - 96.8884i) q^{84} +(-2.45136 + 43.6852i) q^{85} +35.0509i q^{86} +(77.0352 - 31.9125i) q^{87} +(-63.8303 + 63.8303i) q^{88} +12.6276i q^{89} +(-0.00599095 - 78.2119i) q^{90} +(24.2017 + 24.2017i) q^{91} +(-219.420 + 219.420i) q^{92} +(-15.9403 - 38.4790i) q^{93} -97.8583i q^{94} +(33.7108 - 33.7108i) q^{95} +(-17.1956 + 41.5183i) q^{96} +(-8.53997 + 8.53997i) q^{97} -273.568i q^{98} +(-70.7581 + 0.00541999i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3} + 24 q^{4} - 2 q^{6} - 4 q^{7} - 16 q^{10} - 42 q^{12} - 12 q^{13} - 64 q^{16} - 4 q^{18} + 88 q^{21} - 40 q^{22} - 82 q^{24} + 54 q^{27} - 160 q^{28} + 48 q^{31} + 264 q^{33} + 152 q^{34}+ \cdots - 864 q^{99}+O(q^{100}) \) 20 * q - 6 * q^3 + 24 * q^4 - 2 * q^6 - 4 * q^7 - 16 * q^10 - 42 * q^12 - 12 * q^13 - 64 * q^16 - 4 * q^18 + 88 * q^21 - 40 * q^22 - 82 * q^24 + 54 * q^27 - 160 * q^28 + 48 * q^31 + 264 * q^33 + 152 * q^34 + 32 * q^37 + 56 * q^39 + 52 * q^40 + 64 * q^45 + 388 * q^46 - 230 * q^48 - 298 * q^51 + 64 * q^52 - 254 * q^54 - 204 * q^55 - 24 * q^57 + 396 * q^58 - 336 * q^61 - 400 * q^63 - 480 * q^64 - 408 * q^67 - 132 * q^69 + 276 * q^72 - 88 * q^73 - 358 * q^75 + 380 * q^78 - 172 * q^79 + 388 * q^81 + 372 * q^82 + 1320 * q^84 + 648 * q^85 - 156 * q^88 + 672 * q^90 - 124 * q^91 + 194 * q^96 + 688 * q^97 - 864 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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