LMFDB - Embedded newform 70.3.h.a.19.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [70,3,Mod(19,70)] 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("70.19"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(70, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	70.h (of order $6$, 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:	$1.90736185052$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 42x^{14} + 1322x^{12} + 17616x^{10} + 175407x^{8} + 205392x^{6} + 203018x^{4} + 23226x^{2} + 2401 $ x^16 + 42x^14 + 1322x^12 + 17616x^10 + 175407x^8 + 205392x^6 + 203018x^4 + 23226*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.1
Root			$-2.51048 - 4.34828i$ of defining polynomial
Character	$\chi$	$=$	70.19
Dual form			70.3.h.a.59.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22474 - 0.707107i) q^{2} +(-2.51048 - 4.34828i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-4.93710 + 0.790609i) q^{5} +7.10072i q^{6} +(2.74755 + 6.43824i) q^{7} -2.82843i q^{8} +(-8.10505 + 14.0384i) q^{9} +(6.60573 + 2.52276i) q^{10} +(-4.76531 - 8.25377i) q^{11} +(5.02097 - 8.69657i) q^{12} -15.1849 q^{13} +(1.18747 - 9.82802i) q^{14} +(15.8323 + 19.4831i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-11.6790 - 20.2287i) q^{17} +(19.8532 - 11.4623i) q^{18} +(-9.15855 - 5.28769i) q^{19} +(-6.30647 - 7.76070i) q^{20} +(21.0976 - 28.1102i) q^{21} +13.4783i q^{22} +(18.2632 + 10.5443i) q^{23} +(-12.2988 + 7.10072i) q^{24} +(23.7499 - 7.80663i) q^{25} +(18.5976 + 10.7373i) q^{26} +36.2016 q^{27} +(-8.40380 + 11.1971i) q^{28} -37.0510 q^{29} +(-5.61389 - 35.0569i) q^{30} +(13.4505 - 7.76565i) q^{31} +(4.89898 - 2.82843i) q^{32} +(-23.9265 + 41.4419i) q^{33} +33.0333i q^{34} +(-18.6551 - 29.6140i) q^{35} -32.4202 q^{36} +(-16.9168 - 9.76693i) q^{37} +(7.47792 + 12.9521i) q^{38} +(38.1214 + 66.0282i) q^{39} +(2.23618 + 13.9642i) q^{40} -37.7426i q^{41} +(-45.7161 + 19.5096i) q^{42} -18.2540i q^{43} +(9.53063 - 16.5075i) q^{44} +(28.9166 - 75.7167i) q^{45} +(-14.9119 - 25.8281i) q^{46} +(0.155040 - 0.268537i) q^{47} +20.0839 q^{48} +(-33.9019 + 35.3788i) q^{49} +(-34.6077 - 7.23256i) q^{50} +(-58.6400 + 101.567i) q^{51} +(-15.1849 - 26.3010i) q^{52} +(8.87784 - 5.12562i) q^{53} +(-44.3378 - 25.5984i) q^{54} +(30.0523 + 36.9821i) q^{55} +(18.2101 - 7.77126i) q^{56} +53.0986i q^{57} +(45.3780 + 26.1990i) q^{58} +(-3.10758 + 1.79416i) q^{59} +(-17.9134 + 46.9054i) q^{60} +(96.8741 + 55.9303i) q^{61} -21.9646 q^{62} +(-112.651 - 13.6111i) q^{63} -8.00000 q^{64} +(74.9693 - 12.0053i) q^{65} +(58.6077 - 33.8371i) q^{66} +(11.0746 - 6.39394i) q^{67} +(23.3581 - 40.4573i) q^{68} -105.885i q^{69} +(1.90747 + 49.4607i) q^{70} -32.7865 q^{71} +(39.7065 + 22.9245i) q^{72} +(-30.1530 - 52.2266i) q^{73} +(13.8125 + 23.9240i) q^{74} +(-93.5691 - 83.6728i) q^{75} -21.1508i q^{76} +(40.0468 - 53.3579i) q^{77} -107.824i q^{78} +(45.6617 - 79.0884i) q^{79} +(7.13544 - 18.6838i) q^{80} +(-17.9382 - 31.0698i) q^{81} +(-26.6881 + 46.2251i) q^{82} +103.825 q^{83} +(69.7860 + 8.43189i) q^{84} +(73.6535 + 90.6374i) q^{85} +(-12.9075 + 22.3565i) q^{86} +(93.0158 + 161.108i) q^{87} +(-23.3452 + 13.4783i) q^{88} +(-52.3329 - 30.2144i) q^{89} +(-88.9552 + 72.2865i) q^{90} +(-41.7213 - 97.7639i) q^{91} +42.1771i q^{92} +(-67.5345 - 38.9911i) q^{93} +(-0.379769 + 0.219259i) q^{94} +(49.3972 + 18.8650i) q^{95} +(-24.5976 - 14.2014i) q^{96} -130.271 q^{97} +(66.5378 - 19.3578i) q^{98} +154.492 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4} - 6 q^{5} - 12 q^{9} + 24 q^{10} - 12 q^{11} + 32 q^{14} - 28 q^{15} - 32 q^{16} - 12 q^{19} - 8 q^{21} - 24 q^{24} - 42 q^{25} - 48 q^{26} - 136 q^{29} + 32 q^{30} + 84 q^{31} - 190 q^{35}+ \cdots + 176 q^{99}+O(q^{100}) $ 16 * q + 16 * q^4 - 6 * q^5 - 12 * q^9 + 24 * q^10 - 12 * q^11 + 32 * q^14 - 28 * q^15 - 32 * q^16 - 12 * q^19 - 8 * q^21 - 24 * q^24 - 42 * q^25 - 48 * q^26 - 136 * q^29 + 32 * q^30 + 84 * q^31 - 190 * q^35 - 48 * q^36 + 312 * q^39 + 48 * q^40 + 24 * q^44 + 384 * q^45 - 68 * q^46 + 296 * q^49 - 96 * q^50 - 76 * q^51 - 108 * q^54 + 56 * q^56 - 372 * q^59 - 28 * q^60 + 348 * q^61 - 128 * q^64 - 104 * q^65 + 480 * q^66 - 296 * q^70 - 384 * q^71 + 208 * q^74 - 150 * q^75 + 148 * q^79 + 24 * q^80 - 140 * q^81 + 256 * q^84 + 580 * q^85 - 188 * q^86 - 912 * q^89 - 616 * q^91 - 600 * q^94 - 310 * q^95 - 48 * q^96 + 176 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$3$	−2.51048	−	4.34828i	−0.836828	−	1.44943i	−0.892534	−	0.450981i	$-0.851074\pi$
$3$	−2.51048	−	4.34828i	−0.836828	−	1.44943i	0.0557061	−	0.998447i	$-0.482259\pi$
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	−4.93710	+	0.790609i	−0.987420	+	0.158122i
$5$	−4.93710	+	0.790609i	−0.987420	+	0.158122i
$6$			7.10072i			1.18345i
$7$	2.74755	+	6.43824i	0.392508	+	0.919749i
$7$	2.74755	+	6.43824i	0.392508	+	0.919749i
$8$		−	2.82843i		−	0.353553i
$9$	−8.10505	+	14.0384i	−0.900561	+	1.55982i
$10$	6.60573	+	2.52276i	0.660573	+	0.252276i
$11$	−4.76531	−	8.25377i	−0.433210	−	0.750342i	0.563937	−	0.825818i	$-0.309286\pi$
$11$	−4.76531	−	8.25377i	−0.433210	−	0.750342i	−0.997148	+	0.0754753i	$0.975953\pi$
$12$	5.02097	−	8.69657i	0.418414	−	0.724714i
$13$	−15.1849			−1.16807			−0.584034	−	0.811729i	$-0.698527\pi$
$13$	−15.1849			−1.16807			−0.584034	+	0.811729i	$0.698527\pi$
$14$	1.18747	−	9.82802i	0.0848193	−	0.702001i
$15$	15.8323	+	19.4831i	1.05549	+	1.29887i
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−11.6790	−	20.2287i	−0.687002	−	1.18992i	−0.972803	−	0.231633i	$-0.925593\pi$
$17$	−11.6790	−	20.2287i	−0.687002	−	1.18992i	0.285802	−	0.958289i	$-0.407740\pi$
$18$	19.8532	−	11.4623i	1.10296	−	0.636793i
$19$	−9.15855	−	5.28769i	−0.482029	−	0.278300i	0.239233	−	0.970962i	$-0.423104\pi$
$19$	−9.15855	−	5.28769i	−0.482029	−	0.278300i	−0.721262	+	0.692663i	$0.756437\pi$
$20$	−6.30647	−	7.76070i	−0.315324	−	0.388035i
$21$	21.0976	−	28.1102i	1.00465	−	1.33858i
$22$			13.4783i			0.612652i
$23$	18.2632	+	10.5443i	0.794053	+	0.458447i	0.841387	−	0.540432i	$-0.181739\pi$
$23$	18.2632	+	10.5443i	0.794053	+	0.458447i	−0.0473345	+	0.998879i	$0.515073\pi$
$24$	−12.2988	+	7.10072i	−0.512450	+	0.295863i
$25$	23.7499	−	7.80663i	0.949995	−	0.312265i
$26$	18.5976	+	10.7373i	0.715293	+	0.412974i
$27$	36.2016			1.34080
$28$	−8.40380	+	11.1971i	−0.300136	+	0.399898i
$29$	−37.0510			−1.27762			−0.638810	−	0.769365i	$-0.720573\pi$
$29$	−37.0510			−1.27762			−0.638810	+	0.769365i	$0.720573\pi$
$30$	−5.61389	−	35.0569i	−0.187130	−	1.16856i
$31$	13.4505	−	7.76565i	0.433887	−	0.250505i	−0.267114	−	0.963665i	$-0.586070\pi$
$31$	13.4505	−	7.76565i	0.433887	−	0.250505i	0.701001	+	0.713160i	$0.252737\pi$
$32$	4.89898	−	2.82843i	0.153093	−	0.0883883i
$33$	−23.9265	+	41.4419i	−0.725045	+	1.25581i
$34$			33.0333i			0.971567i
$35$	−18.6551	−	29.6140i	−0.533002	−	0.846114i
$36$	−32.4202			−0.900561
$37$	−16.9168	−	9.76693i	−0.457212	−	0.263971i	0.253660	−	0.967294i	$-0.418366\pi$
$37$	−16.9168	−	9.76693i	−0.457212	−	0.263971i	−0.710871	+	0.703322i	$0.751699\pi$
$38$	7.47792	+	12.9521i	0.196787	+	0.340846i
$39$	38.1214	+	66.0282i	0.977471	+	1.69303i
$40$	2.23618	+	13.9642i	0.0559045	+	0.349106i
$41$		−	37.7426i		−	0.920552i	−0.887776	−	0.460276i	$-0.847751\pi$
$41$		−	37.7426i		−	0.920552i	0.887776	−	0.460276i	$-0.152249\pi$
$42$	−45.7161	+	19.5096i	−1.08848	+	0.464515i
$43$		−	18.2540i		−	0.424512i	−0.977214	−	0.212256i	$-0.931919\pi$
$43$		−	18.2540i		−	0.424512i	0.977214	−	0.212256i	$-0.0680810\pi$
$44$	9.53063	−	16.5075i	0.216605	−	0.375171i
$45$	28.9166	−	75.7167i	0.642590	−	1.68259i
$46$	−14.9119	−	25.8281i	−0.324171	−	0.561480i
$47$	0.155040	−	0.268537i	0.00329872	−	0.00571355i	−0.864371	−	0.502854i	$-0.832283\pi$
$47$	0.155040	−	0.268537i	0.00329872	−	0.00571355i	0.867670	+	0.497141i	$0.165617\pi$
$48$	20.0839			0.418414
$49$	−33.9019	+	35.3788i	−0.691875	+	0.722017i
$50$	−34.6077	−	7.23256i	−0.692153	−	0.144651i
$51$	−58.6400	+	101.567i	−1.14980	+	1.99152i
$52$	−15.1849	−	26.3010i	−0.292017	−	0.505788i
$53$	8.87784	−	5.12562i	0.167506	−	0.0967099i	−0.413903	−	0.910321i	$-0.635835\pi$
$53$	8.87784	−	5.12562i	0.167506	−	0.0967099i	0.581410	+	0.813611i	$0.302501\pi$
$54$	−44.3378	−	25.5984i	−0.821070	−	0.474045i
$55$	30.0523	+	36.9821i	0.546406	+	0.672403i
$56$	18.2101	−	7.77126i	0.325180	−	0.138772i
$57$			53.0986i			0.931555i
$58$	45.3780	+	26.1990i	0.782379	+	0.451707i
$59$	−3.10758	+	1.79416i	−0.0526708	+	0.0304095i	−0.526104	−	0.850420i	$-0.676348\pi$
$59$	−3.10758	+	1.79416i	−0.0526708	+	0.0304095i	0.473433	+	0.880830i	$0.343014\pi$
$60$	−17.9134	+	46.9054i	−0.298557	+	0.781757i
$61$	96.8741	+	55.9303i	1.58810	+	0.916890i	0.993620	+	0.112779i	$0.0359753\pi$
$61$	96.8741	+	55.9303i	1.58810	+	0.916890i	0.594480	+	0.804111i	$0.297358\pi$
$62$	−21.9646			−0.354267
$63$	−112.651	−	13.6111i	−1.78812	−	0.216049i
$64$	−8.00000			−0.125000
$65$	74.9693	−	12.0053i	1.15337	−	0.184697i
$66$	58.6077	−	33.8371i	0.887995	−	0.512684i
$67$	11.0746	−	6.39394i	0.165293	−	0.0954319i	−0.415072	−	0.909789i	$-0.636243\pi$
$67$	11.0746	−	6.39394i	0.165293	−	0.0954319i	0.580364	+	0.814357i	$0.302910\pi$
$68$	23.3581	−	40.4573i	0.343501	−	0.594961i
$69$		−	105.885i		−	1.53456i
$70$	1.90747	+	49.4607i	0.0272495	+	0.706582i
$71$	−32.7865			−0.461781			−0.230891	−	0.972980i	$-0.574164\pi$
$71$	−32.7865			−0.461781			−0.230891	+	0.972980i	$0.574164\pi$
$72$	39.7065	+	22.9245i	0.551479	+	0.318396i
$73$	−30.1530	−	52.2266i	−0.413055	−	0.715433i	0.582167	−	0.813069i	$-0.302205\pi$
$73$	−30.1530	−	52.2266i	−0.413055	−	0.715433i	−0.995222	+	0.0976365i	$0.968872\pi$
$74$	13.8125	+	23.9240i	0.186656	+	0.323297i
$75$	−93.5691	−	83.6728i	−1.24759	−	1.11564i
$76$		−	21.1508i		−	0.278300i
$77$	40.0468	−	53.3579i	0.520088	−	0.692960i
$78$		−	107.824i		−	1.38235i
$79$	45.6617	−	79.0884i	0.577997	−	1.00112i	−0.417712	−	0.908579i	$-0.637168\pi$
$79$	45.6617	−	79.0884i	0.577997	−	1.00112i	0.995709	−	0.0925400i	$-0.0294986\pi$
$80$	7.13544	−	18.6838i	0.0891931	−	0.233548i
$81$	−17.9382	−	31.0698i	−0.221459	−	0.383578i
$82$	−26.6881	+	46.2251i	−0.325464	+	0.563720i
$83$	103.825			1.25091			0.625453	−	0.780262i	$-0.284914\pi$
$83$	103.825			1.25091			0.625453	+	0.780262i	$0.284914\pi$
$84$	69.7860	+	8.43189i	0.830785	+	0.100380i
$85$	73.6535	+	90.6374i	0.866512	+	1.06632i
$86$	−12.9075	+	22.3565i	−0.150088	+	0.259959i
$87$	93.0158	+	161.108i	1.06915	+	1.85182i
$88$	−23.3452	+	13.4783i	−0.265286	+	0.153163i
$89$	−52.3329	−	30.2144i	−0.588010	−	0.339488i	0.176300	−	0.984336i	$-0.443587\pi$
$89$	−52.3329	−	30.2144i	−0.588010	−	0.339488i	−0.764310	+	0.644849i	$0.776920\pi$
$90$	−88.9552	+	72.2865i	−0.988391	+	0.803183i
$91$	−41.7213	−	97.7639i	−0.458476	−	1.07433i
$92$			42.1771i			0.458447i
$93$	−67.5345	−	38.9911i	−0.726178	−	0.419259i
$94$	−0.379769	+	0.219259i	−0.00404009	+	0.00233255i
$95$	49.3972	+	18.8650i	0.519970	+	0.198579i
$96$	−24.5976	−	14.2014i	−0.256225	−	0.147932i
$97$	−130.271			−1.34300			−0.671501	−	0.741003i	$-0.734350\pi$
$97$	−130.271			−1.34300			−0.671501	+	0.741003i	$0.734350\pi$
$98$	66.5378	−	19.3578i	0.678957	−	0.197529i
$99$	154.492			1.56053
$100$	37.2714	+	33.3294i	0.372714	+	0.333294i
$101$	−124.520	+	71.8914i	−1.23287	+	0.711796i	−0.967627	−	0.252386i	$-0.918785\pi$
$101$	−124.520	+	71.8914i	−1.23287	+	0.711796i	−0.265241	+	0.964182i	$0.585451\pi$
$102$	143.638	−	82.9295i	1.40822	−	0.813034i
$103$	−26.8014	+	46.4213i	−0.260207	+	0.450692i	−0.966297	−	0.257430i	$-0.917124\pi$
$103$	−26.8014	+	46.4213i	−0.260207	+	0.450692i	0.706090	+	0.708123i	$0.250458\pi$
$104$			42.9493i			0.412974i
$105$	−81.9367	+	155.463i	−0.780350	+	1.48060i
$106$	−14.4975			−0.136768
$107$	−94.2108	−	54.3926i	−0.880475	−	0.508342i	−0.00965987	−	0.999953i	$-0.503075\pi$
$107$	−94.2108	−	54.3926i	−0.880475	−	0.508342i	−0.870815	+	0.491611i	$0.836408\pi$
$108$	36.2016	+	62.7031i	0.335200	+	0.580584i
$109$	30.6519	+	53.0907i	0.281210	+	0.487071i	0.971683	−	0.236288i	$-0.0759308\pi$
$109$	30.6519	+	53.0907i	0.281210	+	0.487071i	−0.690473	+	0.723358i	$0.742597\pi$
$110$	−10.6561	−	66.5439i	−0.0968737	−	0.604945i
$111$			98.0789i			0.883593i
$112$	−27.7978	−	3.35867i	−0.248195	−	0.0299881i
$113$			95.2204i			0.842658i	0.906908	+	0.421329i	$0.138436\pi$
$113$			95.2204i			0.842658i	−0.906908	+	0.421329i	$0.861564\pi$
$114$	37.5464	−	65.0323i	0.329354	−	0.570459i
$115$	−98.5037	−	37.6190i	−0.856554	−	0.327122i
$116$	−37.0510	−	64.1742i	−0.319405	−	0.553226i
$117$	123.074	−	213.171i	1.05192	−	1.82197i
$118$	5.07465			0.0430055
$119$	98.1483	−	130.772i	0.824775	−	1.09892i
$120$	55.1065	−	44.7805i	0.459221	−	0.373171i
$121$	15.0836	−	26.1255i	0.124658	−	0.215913i
$122$	−79.0974	−	137.001i	−0.648339	−	1.12296i
$123$	−164.116	+	94.7522i	−1.33427	+	0.770343i
$124$	26.9010	+	15.5313i	0.216944	+	0.125252i
$125$	−111.083	+	57.3190i	−0.888668	+	0.458552i
$126$	128.345	+	96.3267i	1.01861	+	0.764497i
$127$		−	116.435i		−	0.916812i	−0.888743	−	0.458406i	$-0.848420\pi$
$127$		−	116.435i		−	0.916812i	0.888743	−	0.458406i	$-0.151580\pi$
$128$	9.79796	+	5.65685i	0.0765466	+	0.0441942i
$129$	−79.3736	+	45.8263i	−0.615299	+	0.355243i
$130$	−100.307	−	38.3078i	−0.771594	−	0.294676i
$131$	142.914	+	82.5112i	1.09094	+	0.629857i	0.933828	−	0.357723i	$-0.116447\pi$
$131$	142.914	+	82.5112i	1.09094	+	0.629857i	0.157116	+	0.987580i	$0.449780\pi$
$132$	−95.7059			−0.725045
$133$	8.87981	−	73.4932i	0.0667655	−	0.552580i
$134$	−18.0848			−0.134961
$135$	−178.731	+	28.6214i	−1.32393	+	0.212010i
$136$	−57.2153	+	33.0333i	−0.420701	+	0.242892i
$137$	−184.822	+	106.707i	−1.34907	+	0.778884i	−0.988117	−	0.153702i	$-0.950880\pi$
$137$	−184.822	+	106.707i	−1.34907	+	0.778884i	−0.360949	+	0.932586i	$0.617547\pi$
$138$	−74.8719	+	129.682i	−0.542550	+	0.939724i
$139$		−	53.0872i		−	0.381922i	−0.981598	−	0.190961i	$-0.938840\pi$
$139$		−	53.0872i		−	0.381922i	0.981598	−	0.190961i	$-0.0611604\pi$
$140$	32.6378	−	61.9255i	0.233127	−	0.442325i
$141$	−1.55690			−0.0110418
$142$	40.1551	+	23.1835i	0.282782	+	0.163264i
$143$	72.3607	+	125.332i	0.506019	+	0.876451i
$144$	−32.4202	−	56.1534i	−0.225140	−	0.389954i
$145$	182.924	−	29.2928i	1.26155	−	0.202020i
$146$			85.2857i			0.584149i
$147$	238.947	+	58.5970i	1.62549	+	0.398619i
$148$		−	39.0677i		−	0.263971i
$149$	−0.00284218	+	0.00492280i	−1.90750e−5	+	3.30389e-5i	−0.866035	−	0.499983i	$-0.833339\pi$
$149$	−0.00284218	+	0.00492280i	−1.90750e−5	+	3.30389e-5i	0.866016	+	0.500017i	$0.166673\pi$
$150$	55.4327	+	168.641i	0.369551	+	1.12427i
$151$	−114.888	−	198.993i	−0.760851	−	1.31783i	−0.942412	−	0.334453i	$-0.891448\pi$
$151$	−114.888	−	198.993i	−0.760851	−	1.31783i	0.181562	−	0.983380i	$-0.441885\pi$
$152$	−14.9558	+	25.9043i	−0.0983937	+	0.170423i
$153$	378.636			2.47475
$154$	−86.7768	+	37.0325i	−0.563486	+	0.240471i
$155$	−60.2669	+	48.9739i	−0.388818	+	0.315961i
$156$	−76.2428	+	132.056i	−0.488736	+	0.846515i
$157$	−22.0591	−	38.2074i	−0.140504	−	0.243360i	0.787183	−	0.616720i	$-0.211539\pi$
$157$	−22.0591	−	38.2074i	−0.140504	−	0.243360i	−0.927686	+	0.373360i	$0.878206\pi$
$158$	−111.848	+	64.5754i	−0.707898	+	0.408705i
$159$	−44.5753	−	25.7356i	−0.280348	−	0.161859i
$160$	−21.9506	+	17.8374i	−0.137191	+	0.111484i
$161$	−17.7074	+	146.554i	−0.109984	+	0.910273i
$162$			50.7368i			0.313190i
$163$	26.4560	+	15.2744i	0.162307	+	0.0937079i	0.578953	−	0.815361i	$-0.303461\pi$
$163$	26.4560	+	15.2744i	0.162307	+	0.0937079i	−0.416646	+	0.909069i	$0.636795\pi$
$164$	65.3721	−	37.7426i	0.398611	−	0.230138i
$165$	85.3630	−	223.519i	0.517352	−	1.35466i
$166$	−127.159	−	73.4155i	−0.766021	−	0.442262i
$167$	102.148			0.611665			0.305833	−	0.952085i	$-0.401065\pi$
$167$	102.148			0.611665			0.305833	+	0.952085i	$0.401065\pi$
$168$	−79.5078	−	59.6730i	−0.473261	−	0.355197i
$169$	61.5807			0.364383
$170$	−26.1164	−	163.089i	−0.153626	−	0.959344i
$171$	148.461	−	85.7140i	0.868193	−	0.501251i
$172$	31.6169	−	18.2540i	0.183819	−	0.106128i
$173$	−136.689	+	236.753i	−0.790111	+	1.36851i	0.135787	+	0.990738i	$0.456644\pi$
$173$	−136.689	+	236.753i	−0.790111	+	1.36851i	−0.925898	+	0.377774i	$0.876689\pi$
$174$		−	263.088i		−	1.51200i
$175$	115.515	+	131.458i	0.660086	+	0.751190i
$176$	38.1225			0.216605
$177$	15.6030	+	9.00842i	0.0881528	+	0.0508950i
$178$	42.7296	+	74.0098i	0.240054	+	0.415786i
$179$	4.82428	+	8.35590i	0.0269513	+	0.0466810i	0.879186	−	0.476478i	$-0.158087\pi$
$179$	4.82428	+	8.35590i	0.0269513	+	0.0466810i	−0.852235	+	0.523159i	$0.824753\pi$
$180$	160.062	−	25.6317i	0.889231	−	0.142398i
$181$		−	221.537i		−	1.22396i	−0.790873	−	0.611980i	$-0.790373\pi$
$181$		−	221.537i		−	1.22396i	0.790873	−	0.611980i	$-0.209627\pi$
$182$	−18.0316	+	149.237i	−0.0990747	+	0.819985i
$183$		−	561.648i		−	3.06911i
$184$	29.8237	−	51.6562i	0.162085	−	0.280740i
$185$	91.2419	+	34.8457i	0.493199	+	0.188355i
$186$	55.1417	+	95.5082i	0.296461	+	0.513485i
$187$	−111.308	+	192.792i	−0.595232	+	1.03097i
$188$	0.620160			0.00329872
$189$	99.4660	+	233.075i	0.526275	+	1.23320i
$190$	−47.1593	−	58.0339i	−0.248207	−	0.305442i
$191$	104.905	−	181.701i	0.549241	−	0.951313i	−0.449086	−	0.893489i	$-0.648250\pi$
$191$	104.905	−	181.701i	0.549241	−	0.951313i	0.998327	−	0.0578244i	$-0.0184164\pi$
$192$	20.0839	+	34.7863i	0.104603	+	0.181178i
$193$	217.576	−	125.618i	1.12734	−	0.650868i	0.184073	−	0.982913i	$-0.441072\pi$
$193$	217.576	−	125.618i	1.12734	−	0.650868i	0.943264	+	0.332044i	$0.107738\pi$
$194$	159.549	+	92.1157i	0.822418	+	0.474823i
$195$	−240.412	−	295.848i	−1.23288	−	1.51717i
$196$	−95.1798	−	23.3409i	−0.485611	−	0.119086i
$197$		−	128.792i		−	0.653768i	−0.945065	−	0.326884i	$-0.894001\pi$
$197$		−	128.792i		−	0.653768i	0.945065	−	0.326884i	$-0.105999\pi$
$198$	−189.214	−	109.243i	−0.955625	−	0.551730i
$199$	−173.384	+	100.103i	−0.871275	+	0.503031i	−0.867772	−	0.496963i	$-0.834448\pi$
$199$	−173.384	+	100.103i	−0.871275	+	0.503031i	−0.00350309	+	0.999994i	$0.501115\pi$
$200$	−22.0805	−	67.1748i	−0.110402	−	0.335874i
$201$	−55.6053	−	32.1037i	−0.276643	−	0.159720i
$202$	203.340			1.00663
$203$	−101.800	−	238.543i	−0.501476	−	1.17509i
$204$	−234.560			−1.14980
$205$	29.8397	+	186.339i	0.145559	+	0.908971i
$206$	65.6497	−	37.9028i	0.318688	−	0.183994i
$207$	−296.048	+	170.924i	−1.43019	+	0.825718i
$208$	30.3698	−	52.6020i	0.146008	−	0.252894i
$209$			100.790i			0.482249i
$210$	210.281	−	132.464i	1.00134	−	0.630783i
$211$	167.518			0.793924			0.396962	−	0.917835i	$-0.370064\pi$
$211$	167.518			0.793924			0.396962	+	0.917835i	$0.370064\pi$
$212$	17.7557	+	10.2512i	0.0837532	+	0.0483549i
$213$	82.3099	+	142.565i	0.386431	+	0.669319i
$214$	76.9228	+	133.234i	0.359452	+	0.622590i
$215$	14.4318	+	90.1218i	0.0671246	+	0.419171i
$216$		−	102.394i		−	0.474045i
$217$	86.9531	+	65.2610i	0.400706	+	0.300742i
$218$		−	86.6967i		−	0.397691i
$219$	−151.397	+	262.228i	−0.691312	+	1.19739i
$220$	−34.0026	+	89.0343i	−0.154557	+	0.404701i
$221$	177.345	+	307.170i	0.802465	+	1.38991i
$222$	69.3522	−	120.122i	0.312397	−	0.541088i
$223$	−66.6389			−0.298829			−0.149415	−	0.988775i	$-0.547739\pi$
$223$	−66.6389			−0.298829			−0.149415	+	0.988775i	$0.547739\pi$
$224$	31.6703	+	23.7695i	0.141385	+	0.106114i
$225$	−82.9016	+	396.682i	−0.368452	+	1.76303i
$226$	67.3310	−	116.621i	0.297925	−	0.516021i
$227$	25.9245	+	44.9026i	0.114205	+	0.197809i	0.917462	−	0.397824i	$-0.130235\pi$
$227$	25.9245	+	44.9026i	0.114205	+	0.197809i	−0.803257	+	0.595633i	$0.796901\pi$
$228$	−91.9695	+	53.0986i	−0.403375	+	0.232889i
$229$	63.0828	+	36.4209i	0.275471	+	0.159043i	0.631371	−	0.775481i	$-0.282492\pi$
$229$	63.0828	+	36.4209i	0.275471	+	0.159043i	−0.355900	+	0.934524i	$0.615826\pi$
$230$	94.0412	+	115.726i	0.408875	+	0.503158i
$231$	−332.552	−	40.1806i	−1.43962	−	0.173942i
$232$			104.796i			0.451707i
$233$	119.380	+	68.9243i	0.512362	+	0.295813i	0.733804	−	0.679361i	$-0.237743\pi$
$233$	119.380	+	68.9243i	0.512362	+	0.295813i	−0.221442	+	0.975174i	$0.571076\pi$
$234$	−301.469	+	174.053i	−1.28833	+	0.743817i
$235$	−0.553139	+	1.44837i	−0.00235378	+	0.00616327i
$236$	−6.21515	−	3.58832i	−0.0263354	−	0.0152048i
$237$	−458.532			−1.93473
$238$	−212.676	+	90.7607i	−0.893597	+	0.381348i
$239$	−350.640			−1.46711			−0.733557	−	0.679628i	$-0.762141\pi$
$239$	−350.640			−1.46711			−0.733557	+	0.679628i	$0.762141\pi$
$240$	−99.1560	+	15.8785i	−0.413150	+	0.0661604i
$241$	−264.464	+	152.688i	−1.09736	+	0.633561i	−0.935526	−	0.353257i	$-0.885074\pi$
$241$	−264.464	+	152.688i	−1.09736	+	0.633561i	−0.161833	+	0.986818i	$0.551741\pi$
$242$	−36.9470	+	21.3314i	−0.152674	+	0.0881462i
$243$	72.8405	−	126.163i	0.299755	−	0.519191i
$244$			223.721i			0.916890i
$245$	139.406	−	201.472i	0.569004	−	0.822334i
$246$	268.000			1.08943
$247$	139.072	+	80.2930i	0.563043	+	0.325073i
$248$	−21.9646	−	38.0438i	−0.0885669	−	0.153402i
$249$	−260.652	−	451.462i	−1.04679	−	1.81310i
$250$	176.580	+	8.34674i	0.706318	+	0.0333870i
$251$			419.508i			1.67135i	0.549228	+	0.835673i	$0.314922\pi$
$251$			419.508i			1.67135i	−0.549228	+	0.835673i	$0.685078\pi$
$252$	−89.0763	−	208.729i	−0.353477	−	0.828290i
$253$		−	200.987i		−	0.794415i
$254$	−82.3321	+	142.603i	−0.324142	+	0.561431i
$255$	209.211	−	547.810i	0.820436	−	2.14827i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	3.64460	−	6.31263i	0.0141813	−	0.0245628i	−0.858848	−	0.512231i	$-0.828819\pi$
$257$	3.64460	−	6.31263i	0.0141813	−	0.0245628i	0.873029	+	0.487668i	$0.162152\pi$
$258$	129.616			0.502389
$259$	16.4020	−	135.750i	0.0633280	−	0.524130i
$260$	95.7631	+	117.845i	0.368319	+	0.453251i
$261$	300.300	−	520.135i	1.15057	−	1.99285i
$262$	−116.689	−	202.110i	−0.445376	−	0.771414i
$263$	−118.435	+	68.3785i	−0.450323	+	0.259994i	−0.707967	−	0.706246i	$-0.750387\pi$
$263$	−118.435	+	68.3785i	−0.450323	+	0.259994i	0.257643	+	0.966240i	$0.417054\pi$
$264$	117.215	+	67.6743i	0.443997	+	0.256342i
$265$	−39.7784	+	32.3246i	−0.150107	+	0.121980i
$266$	−62.8430	+	83.7314i	−0.236252	+	0.314780i
$267$			303.411i			1.13637i
$268$	22.1493	+	12.7879i	0.0826465	+	0.0477160i
$269$	216.274	−	124.866i	0.803993	−	0.464186i	−0.0408722	−	0.999164i	$-0.513014\pi$
$269$	216.274	−	124.866i	0.803993	−	0.464186i	0.844866	+	0.534979i	$0.179680\pi$
$270$	239.138	+	91.3281i	0.885697	+	0.338252i
$271$	−388.441	−	224.266i	−1.43336	−	0.827551i	−0.435985	−	0.899954i	$-0.643600\pi$
$271$	−388.441	−	224.266i	−1.43336	−	0.827551i	−0.997375	+	0.0724033i	$0.976933\pi$
$272$	93.4322			0.343501
$273$	−320.365	+	426.851i	−1.17350	+	1.56356i
$274$	301.813			1.10151
$275$	−177.610	−	158.825i	−0.645853	−	0.577545i
$276$	183.398	−	105.885i	0.664485	−	0.383641i
$277$	424.679	−	245.188i	1.53314	−	0.885157i	0.533922	−	0.845534i	$-0.320718\pi$
$277$	424.679	−	245.188i	1.53314	−	0.885157i	0.999215	−	0.0396228i	$-0.0126156\pi$
$278$	−37.5383	+	65.0183i	−0.135030	+	0.233879i
$279$			251.764i			0.902380i
$280$	−83.7610	+	52.7645i	−0.299146	+	0.188445i
$281$	−54.0733			−0.192432			−0.0962158	−	0.995360i	$-0.530674\pi$
$281$	−54.0733			−0.192432			−0.0962158	+	0.995360i	$0.530674\pi$
$282$	1.90680	+	1.10089i	0.00676172	+	0.00390388i
$283$	81.2503	+	140.730i	0.287104	+	0.497278i	0.973117	−	0.230311i	$-0.0739743\pi$
$283$	81.2503	+	140.730i	0.287104	+	0.497278i	−0.686014	+	0.727589i	$0.740641\pi$
$284$	−32.7865	−	56.7878i	−0.115445	−	0.199957i
$285$	−41.9803	−	262.153i	−0.147299	−	0.919836i
$286$		−	204.667i		−	0.715619i
$287$	242.996	−	103.700i	0.846676	−	0.361324i
$288$			91.6981i			0.318396i
$289$	−128.299	+	222.221i	−0.443942	+	0.768931i
$290$	−244.749	−	93.4707i	−0.843961	−	0.322313i
$291$	327.044	+	566.456i	1.12386	+	1.94659i
$292$	60.3061	−	104.453i	0.206528	−	0.357716i
$293$	298.153			1.01759			0.508794	−	0.860888i	$-0.330091\pi$
$293$	298.153			1.01759			0.508794	+	0.860888i	$0.330091\pi$
$294$	−251.215	−	240.728i	−0.854473	−	0.818802i
$295$	13.9239	−	11.3148i	0.0471998	−	0.0383553i
$296$	−27.6251	+	47.8480i	−0.0933279	+	0.161649i
$297$	−172.512	−	298.800i	−0.580849	−	1.00606i
$298$	0.00696189	−	0.00401945i	2.33620e−5	−	1.34881e-5i
$299$	−277.325	−	160.114i	−0.927508	−	0.535497i
$300$	51.3564	−	245.739i	0.171188	−	0.819131i
$301$	117.524	−	50.1539i	0.390444	−	0.166624i
$302$			324.954i			1.07601i
$303$	625.209	+	360.964i	2.06339	+	1.19130i
$304$	36.6342	−	21.1508i	0.120507	−	0.0695749i
$305$	−522.496	−	199.544i	−1.71310	−	0.654242i
$306$	−463.733	−	267.736i	−1.51547	−	0.874955i
$307$	−197.369			−0.642895			−0.321447	−	0.946927i	$-0.604169\pi$
$307$	−197.369			−0.642895			−0.321447	+	0.946927i	$0.604169\pi$
$308$	132.465	+	16.0051i	0.430082	+	0.0519647i
$309$	269.137			0.870995
$310$	108.441	−	17.3654i	0.349811	−	0.0560174i
$311$	277.559	−	160.249i	0.892474	−	0.515270i	0.0177229	−	0.999843i	$-0.494358\pi$
$311$	277.559	−	160.249i	0.892474	−	0.515270i	0.874751	+	0.484573i	$0.161025\pi$
$312$	186.756	−	107.824i	0.598577	−	0.345588i
$313$	−108.403	+	187.760i	−0.346337	+	0.599873i	−0.985596	−	0.169119i	$-0.945908\pi$
$313$	−108.403	+	187.760i	−0.346337	+	0.599873i	0.639259	+	0.768992i	$0.279241\pi$
$314$			62.3925i			0.198702i
$315$	566.932	−	21.8639i	1.79978	−	0.0694092i
$316$	182.647			0.577997
$317$	−339.651	−	196.098i	−1.07145	−	0.618605i	−0.142876	−	0.989741i	$-0.545635\pi$
$317$	−339.651	−	196.098i	−1.07145	−	0.618605i	−0.928579	+	0.371136i	$0.878968\pi$
$318$	36.3956	+	63.0390i	0.114452	+	0.198236i
$319$	176.560	+	305.810i	0.553478	+	0.958652i
$320$	39.4968	−	6.32487i	0.123427	−	0.0197652i
$321$			546.207i			1.70158i
$322$	125.316	−	166.970i	0.389181	−	0.518541i
$323$			247.020i			0.764769i
$324$	35.8763	−	62.1396i	0.110729	−	0.191789i
$325$	−360.639	+	118.543i	−1.10966	+	0.364747i
$326$	−21.6013	−	37.4145i	−0.0662615	−	0.114768i
$327$	153.902	−	266.567i	0.470649	−	0.815188i
$328$	−106.752			−0.325464
$329$	2.15489	+	0.260364i	0.00654981	+	0.000791380i
$330$	−262.600	+	213.393i	−0.795757	+	0.646646i
$331$	171.860	−	297.670i	0.519214	−	0.899304i	−0.480537	−	0.876974i	$-0.659558\pi$
$331$	171.860	−	297.670i	0.519214	−	0.899304i	0.999751	−	0.0223298i	$-0.00710839\pi$
$332$	103.825	+	179.831i	0.312727	+	0.541659i
$333$	274.223	−	158.323i	0.823494	−	0.475444i
$334$	−125.105	−	72.2296i	−0.374567	−	0.216256i
$335$	−49.6214	+	40.3232i	−0.148124	+	0.120368i
$336$	55.1815	+	129.305i	0.164231	+	0.384836i
$337$			86.0226i			0.255260i	0.991822	+	0.127630i	$0.0407370\pi$
$337$			86.0226i			0.255260i	−0.991822	+	0.127630i	$0.959263\pi$
$338$	−75.4206	−	43.5441i	−0.223138	−	0.128829i
$339$	414.045	−	239.049i	1.22137	−	0.705159i
$340$	−83.3351	+	218.209i	−0.245103	+	0.641791i
$341$	−128.192	−	74.0115i	−0.375929	−	0.217043i
$342$	−242.436			−0.708876
$343$	−320.925	−	121.063i	−0.935641	−	0.352954i
$344$	−51.6301			−0.150088
$345$	83.7136	+	522.764i	0.242648	+	1.51526i
$346$	334.819	−	193.308i	0.967685	−	0.558693i
$347$	531.356	−	306.778i	1.53129	−	0.884088i	0.531982	−	0.846756i	$-0.321447\pi$
$347$	531.356	−	306.778i	1.53129	−	0.884088i	0.999303	−	0.0373324i	$-0.0118860\pi$
$348$	−186.032	+	322.216i	−0.534574	+	0.925909i
$349$		−	202.068i		−	0.578990i	−0.957180	−	0.289495i	$-0.906513\pi$
$349$		−	202.068i		−	0.578990i	0.957180	−	0.289495i	$-0.0934874\pi$
$350$	−48.5215	−	242.684i	−0.138633	−	0.693384i
$351$	−549.718			−1.56615
$352$	−46.6903	−	26.9567i	−0.132643	−	0.0765815i
$353$	−255.952	−	443.323i	−0.725078	−	1.25587i	−0.958942	−	0.283602i	$-0.908470\pi$
$353$	−255.952	−	443.323i	−0.725078	−	1.25587i	0.233864	−	0.972269i	$-0.424863\pi$
$354$	−12.7398	−	22.0660i	−0.0359882	−	0.0623334i
$355$	161.870	−	25.9213i	0.455972	−	0.0730177i
$356$		−	120.858i		−	0.339488i
$357$	−815.032	−	98.4762i	−2.28300	−	0.275844i
$358$		−	13.6451i		−	0.0381149i
$359$	79.2023	−	137.182i	0.220619	−	0.382124i	−0.734377	−	0.678742i	$-0.762525\pi$
$359$	79.2023	−	137.182i	0.220619	−	0.382124i	0.954996	+	0.296618i	$0.0958588\pi$
$360$	−214.159	−	81.7884i	−0.594886	−	0.227190i
$361$	−124.581	−	215.780i	−0.345099	−	0.597729i
$362$	−156.650	+	271.326i	−0.432736	+	0.749520i
$363$	−151.468			−0.417268
$364$	127.611	−	170.027i	0.350579	−	0.467108i
$365$	190.159	+	234.009i	0.520985	+	0.641119i
$366$	−397.145	+	687.876i	−1.08510	+	1.87944i
$367$	163.167	+	282.613i	0.444596	+	0.770062i	0.998024	−	0.0628347i	$-0.0200141\pi$
$367$	163.167	+	282.613i	0.444596	+	0.770062i	−0.553428	+	0.832897i	$0.686681\pi$
$368$	−73.0529	+	42.1771i	−0.198513	+	0.114612i
$369$	529.844	+	305.906i	1.43589	+	0.829013i
$370$	−87.1084	−	107.195i	−0.235428	−	0.289716i
$371$	57.3923	+	43.0747i	0.154696	+	0.116104i
$372$		−	155.964i		−	0.419259i
$373$	−252.630	−	145.856i	−0.677292	−	0.391035i	0.121542	−	0.992586i	$-0.461216\pi$
$373$	−252.630	−	145.856i	−0.677292	−	0.391035i	−0.798834	+	0.601551i	$0.794549\pi$
$374$	272.649	−	157.414i	0.729008	−	0.420893i
$375$	528.112	+	339.124i	1.40830	+	0.904331i
$376$	−0.759537	−	0.438519i	−0.00202005	−	0.00116627i
$377$	562.615			1.49235
$378$	42.9883	−	355.790i	0.113726	−	0.941244i
$379$	−677.228			−1.78688			−0.893441	−	0.449181i	$-0.851716\pi$
$379$	−677.228			−1.78688			−0.893441	+	0.449181i	$0.851716\pi$
$380$	16.7220	+	104.423i	0.0440052	+	0.274798i
$381$	−506.293	+	292.309i	−1.32885	+	0.767214i
$382$	−256.964	+	148.358i	−0.672680	+	0.388372i
$383$	124.602	−	215.817i	0.325332	−	0.563491i	−0.656248	−	0.754545i	$-0.727857\pi$
$383$	124.602	−	215.817i	0.325332	−	0.563491i	0.981579	+	0.191055i	$0.0611908\pi$
$384$		−	56.8057i		−	0.147932i
$385$	−155.530	+	295.095i	−0.403973	+	0.766479i
$386$	−355.300			−0.920467
$387$	256.256	+	147.950i	0.662160	+	0.382298i
$388$	−130.271	−	225.636i	−0.335751	−	0.581537i
$389$	14.3803	+	24.9074i	0.0369673	+	0.0640293i	0.883917	−	0.467644i	$-0.154897\pi$
$389$	14.3803	+	24.9074i	0.0369673	+	0.0640293i	−0.846950	+	0.531673i	$0.821564\pi$
$390$	85.2463	+	532.335i	0.218580	+	1.36496i
$391$		−	492.587i		−	1.25981i
$392$	100.066	+	95.8890i	0.255272	+	0.244615i
$393$		−	828.572i		−	2.10833i
$394$	−91.0699	+	157.738i	−0.231142	+	0.400349i
$395$	−162.908	+	426.568i	−0.412426	+	1.07992i
$396$	154.492	+	267.589i	0.390132	+	0.675729i
$397$	−126.465	+	219.043i	−0.318550	+	0.551746i	−0.980186	−	0.198080i	$-0.936529\pi$
$397$	−126.465	+	219.043i	−0.318550	+	0.551746i	0.661635	+	0.749826i	$0.269863\pi$
$398$	283.134			0.711393
$399$	−341.862	+	145.891i	−0.856796	+	0.365643i
$400$	−20.4568	+	97.8852i	−0.0511420	+	0.244713i
$401$	103.441	−	179.165i	0.257958	−	0.446796i	−0.707737	−	0.706476i	$-0.750284\pi$
$401$	103.441	−	179.165i	0.257958	−	0.446796i	0.965695	+	0.259680i	$0.0836171\pi$
$402$	45.4016	+	78.6378i	0.112939	+	0.195616i
$403$	−204.244	+	117.921i	−0.506810	+	0.292607i
$404$	−249.039	−	143.783i	−0.616434	−	0.355898i
$405$	113.126	+	139.213i	0.279325	+	0.343735i
$406$	−43.9969	+	364.138i	−0.108367	+	0.896891i
$407$			186.170i			0.457420i
$408$	287.276	+	165.859i	0.704108	+	0.406517i
$409$	577.695	−	333.532i	1.41246	−	0.815483i	0.416838	−	0.908981i	$-0.363138\pi$
$409$	577.695	−	333.532i	1.41246	−	0.815483i	0.995619	+	0.0934983i	$0.0298050\pi$
$410$	95.2156	−	249.318i	0.232233	−	0.608092i
$411$	927.985	+	535.773i	2.25787	+	1.30358i
$412$	−107.205			−0.260207
$413$	−20.0895	−	15.0778i	−0.0486428	−	0.0365079i
$414$	483.445			1.16774
$415$	−512.595	+	82.0852i	−1.23517	+	0.197796i
$416$	−74.3904	+	42.9493i	−0.178823	+	0.103244i
$417$	−230.838	+	133.274i	−0.553569	+	0.319603i
$418$	71.2693	−	123.442i	0.170501	−	0.295316i
$419$			82.9914i			0.198070i	0.995084	+	0.0990350i	$0.0315756\pi$
$419$			82.9914i			0.198070i	−0.995084	+	0.0990350i	$0.968424\pi$
$420$	−351.207	+	13.5444i	−0.836206	+	0.0322485i
$421$	155.483			0.369319			0.184659	−	0.982803i	$-0.440882\pi$
$421$	155.483			0.369319			0.184659	+	0.982803i	$0.440882\pi$
$422$	−205.167	−	118.453i	−0.486177	−	0.280695i
$423$	2.51321	+	4.35301i	0.00594140	+	0.0102908i
$424$	−14.4975	−	25.1103i	−0.0341921	−	0.0592225i
$425$	−435.293	−	389.254i	−1.02422	−	0.915893i
$426$		−	232.807i		−	0.546496i
$427$	−93.9257	+	777.370i	−0.219967	+	1.82054i
$428$		−	217.571i		−	0.508342i
$429$	363.321	−	629.290i	0.846901	−	1.46688i
$430$	46.0505	−	120.581i	0.107094	−	0.280421i
$431$	17.6114	+	30.5039i	0.0408618	+	0.0707748i	0.885733	−	0.464195i	$-0.153656\pi$
$431$	17.6114	+	30.5039i	0.0408618	+	0.0707748i	−0.844871	+	0.534970i	$0.820323\pi$
$432$	−72.4033	+	125.406i	−0.167600	+	0.290292i
$433$	98.0262			0.226388			0.113194	−	0.993573i	$-0.463892\pi$
$433$	98.0262			0.226388			0.113194	+	0.993573i	$0.463892\pi$
$434$	−60.3489	−	141.413i	−0.139053	−	0.325837i
$435$	−586.602	−	721.867i	−1.34851	−	1.65947i
$436$	−61.3038	+	106.181i	−0.140605	+	0.243535i
$437$	−111.510	−	193.141i	−0.255171	−	0.441969i
$438$	370.846	−	214.108i	0.846681	−	0.488832i
$439$	356.391	+	205.763i	0.811826	+	0.468708i	0.847589	−	0.530653i	$-0.178053\pi$
$439$	356.391	+	205.763i	0.811826	+	0.468708i	−0.0357638	+	0.999360i	$0.511386\pi$
$440$	104.601	−	85.0008i	0.237730	−	0.193184i
$441$	−221.884	−	762.674i	−0.503139	−	1.72942i
$442$		−	501.606i		−	1.13486i
$443$	−656.457	−	379.006i	−1.48184	−	0.855543i	−0.482057	−	0.876140i	$-0.660110\pi$
$443$	−656.457	−	379.006i	−1.48184	−	0.855543i	−0.999788	+	0.0205969i	$0.993443\pi$
$444$	−169.878	+	98.0789i	−0.382607	+	0.220898i
$445$	282.260	+	107.797i	0.634293	+	0.242239i
$446$	81.6157	+	47.1208i	0.182995	+	0.105652i
$447$	0.0285410			6.38500e−5
$448$	−21.9804	−	51.5059i	−0.0490635	−	0.114969i
$449$	−49.9480			−0.111243			−0.0556213	−	0.998452i	$-0.517714\pi$
$449$	−49.9480			−0.111243			−0.0556213	+	0.998452i	$0.517714\pi$
$450$	382.030	−	427.214i	0.848956	−	0.949365i
$451$	−311.519	+	179.855i	−0.690729	+	0.398792i
$452$	−164.926	+	95.2204i	−0.364882	+	0.210665i
$453$	−576.851	+	999.135i	−1.27340	+	2.20560i
$454$		−	73.3256i		−	0.161510i
$455$	283.275	+	449.685i	0.622583	+	0.988318i
$456$	150.186			0.329354
$457$	350.458	+	202.337i	0.766866	+	0.442750i	0.831755	−	0.555142i	$-0.187336\pi$
$457$	350.458	+	202.337i	0.766866	+	0.442750i	−0.0648896	+	0.997892i	$0.520670\pi$
$458$	−51.5069	−	89.2126i	−0.112461	−	0.194787i
$459$	−422.800	−	732.311i	−0.921133	−	1.59545i
$460$	−33.3456	−	208.232i	−0.0724904	−	0.452679i
$461$		−	41.4395i		−	0.0898904i	−0.998989	−	0.0449452i	$-0.985689\pi$
$461$		−	41.4395i		−	0.0898904i	0.998989	−	0.0449452i	$-0.0143113\pi$
$462$	378.879	+	284.361i	0.820085	+	0.615500i
$463$			668.770i			1.44443i	0.691670	+	0.722213i	$0.256875\pi$
$463$			668.770i			1.44443i	−0.691670	+	0.722213i	$0.743125\pi$
$464$	74.1019	−	128.348i	0.159702	−	0.276613i
$465$	364.251	+	139.109i	0.783336	+	0.299160i
$466$	−97.4737	−	168.829i	−0.209171	−	0.362295i
$467$	248.677	−	430.721i	0.532498	−	0.922314i	−0.466782	−	0.884373i	$-0.654587\pi$
$467$	248.677	−	430.721i	0.532498	−	0.922314i	0.999280	−	0.0379417i	$-0.0120801\pi$
$468$	492.297			1.05192
$469$	71.5939	+	53.7334i	0.152652	+	0.114570i
$470$	1.70161	−	1.38275i	0.00362044	−	0.00294203i
$471$	−110.758	+	191.838i	−0.235155	+	0.407300i
$472$	5.07465	+	8.78956i	0.0107514	+	0.0186219i
$473$	−150.664	+	86.9860i	−0.318529	+	0.183903i
$474$	561.585	+	324.231i	1.18478	+	0.684032i
$475$	−258.793	−	54.0846i	−0.544828	−	0.113862i
$476$	324.652	+	39.2260i	0.682041	+	0.0824076i
$477$			166.174i			0.348372i
$478$	429.445	+	247.940i	0.898420	+	0.518703i
$479$	383.598	−	221.470i	0.800830	−	0.462360i	−0.0429311	−	0.999078i	$-0.513670\pi$
$479$	383.598	−	221.470i	0.800830	−	0.462360i	0.843761	+	0.536718i	$0.180336\pi$
$480$	132.669	+	50.6668i	0.276393	+	0.105556i
$481$	256.880	+	148.310i	0.534054	+	0.308336i
$482$	431.867			0.895990
$483$	681.712	−	290.924i	1.41141	−	0.602328i
$484$	60.3343			0.124658
$485$	643.162	−	102.994i	1.32611	−	0.212358i
$486$	−178.422	+	103.012i	−0.367124	+	0.211959i
$487$	−97.2891	+	56.1699i	−0.199772	+	0.115339i	−0.596549	−	0.802576i	$-0.703462\pi$
$487$	−97.2891	+	56.1699i	−0.199772	+	0.115339i	0.396777	+	0.917915i	$0.370129\pi$
$488$	158.195	−	274.001i	0.324170	−	0.561478i
$489$		−	153.384i		−	0.313670i
$490$	−313.199	+	148.177i	−0.639182	+	0.302402i
$491$	−677.177			−1.37918			−0.689590	−	0.724200i	$-0.742209\pi$
$491$	−677.177			−1.37918			−0.689590	+	0.724200i	$0.742209\pi$
$492$	−328.231	−	189.504i	−0.667137	−	0.385171i
$493$	432.719	+	749.492i	0.877727	+	1.52027i
$494$	−113.551	−	196.677i	−0.229861	−	0.398131i
$495$	−762.744	+	122.143i	−1.54090	+	0.246754i
$496$			62.1252i			0.125252i
$497$	−90.0826	−	211.087i	−0.181253	−	0.424723i
$498$			737.234i			1.48039i
$499$	−461.215	+	798.848i	−0.924279	+	1.60090i	−0.131562	+	0.991308i	$0.541999\pi$
$499$	−461.215	+	798.848i	−0.924279	+	1.60090i	−0.792717	+	0.609590i	$0.791334\pi$
$500$	−210.363	−	135.083i	−0.420726	−	0.270166i
$501$	−256.441	−	444.169i	−0.511858	−	0.886564i
$502$	296.637	−	513.790i	0.590910	−	1.02349i
$503$	−136.712			−0.271793			−0.135896	−	0.990723i	$-0.543391\pi$
$503$	−136.712			−0.271793			−0.135896	+	0.990723i	$0.543391\pi$
$504$	−38.4980	+	318.626i	−0.0763849	+	0.632195i
$505$	557.927	−	453.381i	1.10481	−	0.897785i
$506$	−142.119	+	246.158i	−0.280868	+	0.486478i
$507$	−154.597	−	267.770i	−0.304925	−	0.528146i
$508$	201.672	−	116.435i	0.396991	−	0.229203i
$509$	−619.262	−	357.531i	−1.21662	−	0.702418i	−0.252430	−	0.967615i	$-0.581230\pi$
$509$	−619.262	−	357.531i	−1.21662	−	0.702418i	−0.964194	+	0.265197i	$0.914563\pi$
$510$	−643.590	+	522.993i	−1.26194	+	1.02548i
$511$	253.400	−	337.628i	0.495891	−	0.660720i
$512$			22.6274i			0.0441942i
$513$	−331.554	−	191.423i	−0.646305	−	0.373144i
$514$	−8.92741	+	5.15424i	−0.0173685	+	0.0100277i
$515$	95.6198	−	250.376i	0.185670	−	0.486167i
$516$	−158.747	−	91.6527i	−0.307649	−	0.177622i
$517$	−2.95525			−0.00571616
$518$	−116.078	+	154.661i	−0.224088	+	0.298573i
$519$	1372.62			2.64475
$520$	−33.9561	−	212.045i	−0.0653003	−	0.407779i
$521$	14.6765	−	8.47346i	0.0281698	−	0.0162638i	−0.485849	−	0.874043i	$-0.661490\pi$
$521$	14.6765	−	8.47346i	0.0281698	−	0.0162638i	0.514019	+	0.857779i	$0.328156\pi$
$522$	−735.581	+	424.688i	−1.40916	+	0.813579i
$523$	351.622	−	609.027i	0.672317	−	1.16449i	−0.304928	−	0.952375i	$-0.598632\pi$
$523$	351.622	−	609.027i	0.672317	−	1.16449i	0.977245	−	0.212113i	$-0.0680343\pi$
$524$			330.045i			0.629857i
$525$	281.619	−	832.316i	0.536418	−	1.58536i
$526$	193.404			0.367687
$527$	−314.178	−	181.391i	−0.596162	−	0.344195i
$528$	−95.7059	−	165.767i	−0.181261	−	0.313954i
$529$	−42.1366	−	72.9828i	−0.0796533	−	0.137964i
$530$	71.5753	−	11.4618i	0.135048	−	0.0216261i
$531$		−	58.1670i		−	0.109542i
$532$	136.174	−	58.1129i	0.255966	−	0.109235i
$533$			573.117i			1.07527i
$534$	214.544	−	371.601i	0.401768	−	0.695882i
$535$	508.131	+	194.058i	0.949778	+	0.362725i
$536$	−18.0848	−	31.3238i	−0.0337403	−	0.0584399i
$537$	24.2225	−	41.9547i	0.0451071	−	0.0781279i
$538$	−353.174			−0.656458
$539$	453.562	+	111.227i	0.841488	+	0.206358i
$540$	−228.305	−	280.950i	−0.422786	−	0.520278i
$541$	−473.725	+	820.515i	−0.875647	+	1.51666i	−0.0195742	+	0.999808i	$0.506231\pi$
$541$	−473.725	+	820.515i	−0.875647	+	1.51666i	−0.856072	+	0.516856i	$0.827102\pi$
$542$	317.160	+	549.338i	0.585167	+	1.01354i
$543$	−963.305	+	556.165i	−1.77404	+	1.02424i
$544$	−114.431	−	66.0666i	−0.210350	−	0.121446i
$545$	−193.306	−	237.880i	−0.354689	−	0.436478i
$546$	694.194	−	296.251i	1.27142	−	0.542585i
$547$		−	451.960i		−	0.826252i	−0.910674	−	0.413126i	$-0.864437\pi$
$547$		−	451.960i		−	0.826252i	0.910674	−	0.413126i	$-0.135563\pi$
$548$	−369.644	−	213.414i	−0.674533	−	0.389442i
$549$	−1570.34	+	906.635i	−2.86036	+	1.65143i
$550$	105.220	+	320.109i	0.191310	+	0.582016i
$551$	339.333	+	195.914i	0.615850	+	0.355561i
$552$	−299.488			−0.542550
$553$	634.648	+	76.6814i	1.14765	+	0.138664i
$554$	−693.498			−1.25180
$555$	−77.5421	−	484.225i	−0.139715	−	0.872478i
$556$	91.9497	−	53.0872i	0.165377	−	0.0954806i
$557$	331.417	−	191.344i	0.595004	−	0.343526i	−0.172069	−	0.985085i	$-0.555045\pi$
$557$	331.417	−	191.344i	0.595004	−	0.343526i	0.767074	+	0.641559i	$0.221712\pi$
$558$	178.024	−	308.347i	0.319039	−	0.552592i
$559$			277.185i			0.495858i
$560$	139.896	−	5.39513i	0.249814	−	0.00963417i
$561$	1117.75			1.99243
$562$	66.2260	+	38.2356i	0.117840	+	0.0680349i
$563$	22.9940	+	39.8268i	0.0408419	+	0.0707402i	0.885724	−	0.464213i	$-0.153663\pi$
$563$	22.9940	+	39.8268i	0.0408419	+	0.0707402i	−0.844882	+	0.534953i	$0.820329\pi$
$564$	−1.55690	−	2.69663i	−0.00276046	−	0.00478126i
$565$	−75.2821	−	470.112i	−0.133243	−	0.832057i
$566$		−	229.811i		−	0.406026i
$567$	150.749	−	200.856i	0.265871	−	0.354244i
$568$			92.7341i			0.163264i
$569$	15.4807	−	26.8133i	0.0272068	−	0.0471236i	−0.852101	−	0.523377i	$-0.824672\pi$
$569$	15.4807	−	26.8133i	0.0272068	−	0.0471236i	0.879308	+	0.476253i	$0.158005\pi$
$570$	−133.955	+	350.755i	−0.235009	+	0.615360i
$571$	−200.579	−	347.414i	−0.351277	−	0.608430i	0.635196	−	0.772351i	$-0.280919\pi$
$571$	−200.579	−	347.414i	−0.351277	−	0.608430i	−0.986474	+	0.163921i	$0.947586\pi$
$572$	−144.721	+	250.665i	−0.253010	+	0.438225i
$573$	−1053.45			−1.83848
$574$	−370.935	−	44.8182i	−0.646228	−	0.0780805i
$575$	516.064	+	107.851i	0.897503	+	0.187567i
$576$	64.8404	−	112.307i	0.112570	−	0.194977i
$577$	−388.494	−	672.891i	−0.673300	−	1.16619i	−0.976963	−	0.213410i	$-0.931543\pi$
$577$	−388.494	−	672.891i	−0.673300	−	1.16619i	0.303663	−	0.952780i	$-0.401790\pi$
$578$	314.268	−	181.443i	0.543716	−	0.313915i
$579$	−1092.44	−	630.722i	−1.88677	−	1.08933i
$580$	233.661	+	287.541i	0.402864	+	0.495761i
$581$	285.266	+	668.452i	0.490991	+	1.15052i
$582$		−	925.019i		−	1.58938i
$583$	−84.6114	−	48.8504i	−0.145131	−	0.0837914i
$584$	−147.719	+	85.2857i	−0.252944	+	0.146037i
$585$	−439.095	+	1149.75i	−0.750589	+	1.96538i
$586$	−365.162	−	210.826i	−0.623143	−	0.359772i
$587$	−123.033			−0.209596			−0.104798	−	0.994494i	$-0.533420\pi$
$587$	−123.033			−0.209596			−0.104798	+	0.994494i	$0.533420\pi$
$588$	137.454	+	472.466i	0.233766	+	0.803514i
$589$	−164.249			−0.278862
$590$	−25.0541	+	4.01207i	−0.0424645	+	0.00680011i
$591$	−560.025	+	323.331i	−0.947589	+	0.547091i
$592$	67.6673	−	39.0677i	0.114303	−	0.0659928i
$593$	211.024	−	365.504i	0.355858	−	0.616364i	−0.631407	−	0.775452i	$-0.717522\pi$
$593$	211.024	−	365.504i	0.355858	−	0.616364i	0.987264	+	0.159088i	$0.0508554\pi$
$594$			487.938i			0.821445i
$595$	−381.178	+	723.230i	−0.640636	+	1.21551i
$596$	−0.0113687			−1.90750e−5
$597$	870.553	+	502.614i	1.45821	+	0.841900i
$598$	226.435	+	392.196i	0.378653	+	0.655847i
$599$	414.355	+	717.684i	0.691745	+	1.19814i	0.971266	+	0.237998i	$0.0764911\pi$
$599$	414.355	+	717.684i	0.691745	+	1.19814i	−0.279521	+	0.960140i	$0.590176\pi$
$600$	−236.662	+	264.653i	−0.394437	+	0.441089i
$601$			675.102i			1.12330i	0.827376	+	0.561649i	$0.189833\pi$
$601$			675.102i			1.12330i	−0.827376	+	0.561649i	$0.810167\pi$
$602$	−179.401	−	21.6761i	−0.298008	−	0.0360068i
$603$			207.293i			0.343769i
$604$	229.777	−	397.985i	0.380425	−	0.658916i
$605$	−53.8140	+	140.909i	−0.0889487	+	0.232908i
$606$	−510.481	−	884.178i	−0.842377	−	1.45904i
$607$	−491.492	+	851.289i	−0.809707	+	1.40245i	0.103360	+	0.994644i	$0.467041\pi$
$607$	−491.492	+	851.289i	−0.809707	+	1.40245i	−0.913067	+	0.407809i	$0.866293\pi$
$608$	−59.8234			−0.0983937
$609$	−781.687	+	1041.51i	−1.28356	+	1.71020i
$610$	498.825	+	613.851i	0.817747	+	1.00631i
$611$	−2.35426	+	4.07770i	−0.00385313	+	0.00667382i
$612$	378.636	+	655.817i	0.618687	+	1.07160i
$613$	418.163	−	241.427i	0.682159	−	0.393844i	−0.118509	−	0.992953i	$-0.537812\pi$
$613$	418.163	−	241.427i	0.682159	−	0.393844i	0.800668	+	0.599108i	$0.204478\pi$
$614$	241.726	+	139.561i	0.393691	+	0.227298i
$615$	735.343	−	597.552i	1.19568	−	0.971630i
$616$	−150.919	−	113.269i	−0.244998	−	0.183879i
$617$			550.193i			0.891722i	0.895102	+	0.445861i	$0.147103\pi$
$617$			550.193i			0.891722i	−0.895102	+	0.445861i	$0.852897\pi$
$618$	−329.625	−	190.309i	−0.533373	−	0.307943i
$619$	535.910	−	309.408i	0.865767	−	0.499851i	−0.000172089	−	1.00000i	$-0.500055\pi$
$619$	535.910	−	309.408i	0.865767	−	0.499851i	0.865939	+	0.500149i	$0.166721\pi$
$620$	−145.092	−	55.4114i	−0.234020	−	0.0893732i
$621$	661.158	+	381.720i	1.06467	+	0.614686i
$622$	−453.252			−0.728702
$623$	50.7401	−	419.947i	0.0814448	−	0.674073i
$624$	−304.971			−0.488736
$625$	503.113	−	370.813i	0.804981	−	0.593301i
$626$	265.533	−	153.306i	0.424174	−	0.244897i
$627$	438.264	−	253.032i	0.698985	−	0.403559i
$628$	44.1182	−	76.4149i	0.0702518	−	0.121680i
$629$			456.273i			0.725395i
$630$	−709.807	−	374.104i	−1.12668	−	0.593815i
$631$	−167.847			−0.266001			−0.133000	−	0.991116i	$-0.542461\pi$
$631$	−167.847			−0.266001			−0.133000	+	0.991116i	$0.542461\pi$
$632$	−223.696	−	129.151i	−0.353949	−	0.204353i
$633$	−420.551	−	728.416i	−0.664378	−	1.15074i
$634$	277.324	+	480.339i	0.437420	+	0.757633i
$635$	92.0547	+	574.852i	0.144968	+	0.905279i
$636$		−	102.942i		−	0.161859i
$637$	514.796	−	537.224i	0.808157	−	0.843365i
$638$		−	499.386i		−	0.782736i
$639$	265.736	−	460.268i	0.415862	−	0.720294i
$640$	−52.8458	−	20.1821i	−0.0825716	−	0.0315345i
$641$	−529.087	−	916.406i	−0.825409	−	1.42965i	−0.901606	−	0.432558i	$-0.857611\pi$
$641$	−529.087	−	916.406i	−0.825409	−	1.42965i	0.0761967	−	0.997093i	$-0.475722\pi$
$642$	386.227	−	668.964i	0.601599	−	1.04200i
$643$	−68.2597			−0.106158			−0.0530791	−	0.998590i	$-0.516904\pi$
$643$	−68.2597			−0.106158			−0.0530791	+	0.998590i	$0.516904\pi$
$644$	−271.546	+	115.884i	−0.421656	+	0.179944i
$645$	355.644	−	289.003i	0.551387	−	0.448066i
$646$	174.670	−	302.537i	0.270387	−	0.468323i
$647$	26.7770	+	46.3792i	0.0413865	+	0.0716835i	0.885977	−	0.463730i	$-0.153489\pi$
$647$	26.7770	+	46.3792i	0.0413865	+	0.0716835i	−0.844590	+	0.535413i	$0.820156\pi$
$648$	−87.8786	+	50.7368i	−0.135615	+	0.0782975i
$649$	29.6172	+	17.0995i	0.0456351	+	0.0263474i
$650$	525.513	+	109.826i	0.808482	+	0.168963i
$651$	65.4791	−	541.934i	0.100582	−	0.832463i
$652$			61.0976i			0.0937079i
$653$	39.7204	+	22.9326i	0.0608276	+	0.0351188i	0.530105	−	0.847932i	$-0.322152\pi$
$653$	39.7204	+	22.9326i	0.0608276	+	0.0351188i	−0.469278	+	0.883051i	$0.655486\pi$
$654$	−376.982	+	217.651i	−0.576425	+	0.332799i
$655$	−770.813	−	294.377i	−1.17681	−	0.449431i
$656$	130.744	+	75.4852i	0.199305	+	0.115069i
$657$	977.567			1.48793
$658$	−2.45508	−	1.84261i	−0.00373113	−	0.00280033i
$659$	997.845			1.51418			0.757090	−	0.653310i	$-0.226620\pi$
$659$	997.845			1.51418			0.757090	+	0.653310i	$0.226620\pi$
$660$	472.509	−	75.6660i	0.715923	−	0.114645i
$661$	229.919	−	132.744i	0.347836	−	0.200823i	−0.315896	−	0.948794i	$-0.602305\pi$
$661$	229.919	−	132.744i	0.347836	−	0.200823i	0.663732	+	0.747971i	$0.268972\pi$
$662$	−420.969	+	243.046i	−0.635904	+	0.367139i
$663$	890.441	−	1542.29i	1.34305	−	2.32623i
$664$		−	293.662i		−	0.442262i
$665$	14.2639	+	369.863i	0.0214495	+	0.556186i
$666$	−447.805			−0.672380
$667$	−676.670	−	390.676i	−1.01450	−	0.585720i
$668$	102.148	+	176.926i	0.152916	+	0.264859i
$669$	167.296	+	289.765i	0.250069	+	0.433131i
$670$	89.2864	−	14.2980i	0.133263	−	0.0213403i
$671$		−	1066.10i		−	1.58882i
$672$	23.8490	−	197.385i	0.0354895	−	0.293727i
$673$		−	859.611i		−	1.27728i	−0.769505	−	0.638641i	$-0.779497\pi$
$673$		−	859.611i		−	1.27728i	0.769505	−	0.638641i	$-0.220503\pi$
$674$	60.8271	−	105.356i	0.0902480	−	0.156314i
$675$	859.784	−	282.613i	1.27375	−	0.418686i
$676$	61.5807	+	106.661i	0.0910956	+	0.157782i
$677$	35.7345	−	61.8940i	0.0527836	−	0.0914239i	−0.838426	−	0.545015i	$-0.816524\pi$
$677$	35.7345	−	61.8940i	0.0527836	−	0.0914239i	0.891210	+	0.453591i	$0.149857\pi$
$678$	−676.133			−0.997246
$679$	−357.927	−	838.718i	−0.527139	−	1.23522i
$680$	256.361	−	208.323i	0.377002	−	0.306358i
$681$	130.166	−	225.454i	0.191140	−	0.331064i
$682$	104.668	+	181.291i	0.153472	+	0.265822i
$683$	−832.644	+	480.727i	−1.21910	+	0.703847i	−0.964725	−	0.263259i	$-0.915202\pi$
$683$	−832.644	+	480.727i	−1.21910	+	0.703847i	−0.254373	+	0.967106i	$0.581869\pi$
$684$	296.922	+	171.428i	0.434096	+	0.250626i
$685$	828.121	−	672.945i	1.20894	−	0.982402i
$686$	307.446	+	375.200i	0.448173	+	0.546938i
$687$		−	365.736i		−	0.532367i
$688$	63.2337	+	36.5080i	0.0919095	+	0.0530639i
$689$	−134.809	+	77.8320i	−0.195659	+	0.112964i
$690$	267.122	−	699.447i	0.387134	−	1.01369i
$691$	433.591	+	250.334i	0.627483	+	0.362277i	0.779777	−	0.626058i	$-0.215333\pi$
$691$	433.591	+	250.334i	0.627483	+	0.362277i	−0.152294	+	0.988335i	$0.548666\pi$
$692$	−546.757			−0.790111
$693$	424.476	+	994.659i	0.612520	+	1.43529i
$694$	−867.701			−1.25029
$695$	41.9712	+	262.097i	0.0603903	+	0.377117i
$696$	455.683	−	263.088i	0.654716	−	0.378001i
$697$	−763.483	+	440.797i	−1.09538	+	0.632420i
$698$	−142.883	+	247.481i	−0.204704	+	0.354558i
$699$		−	692.133i		−	0.990176i
$700$	−112.177	+	331.536i	−0.160253	+	0.473623i
$701$	−913.148			−1.30264			−0.651318	−	0.758805i	$-0.725784\pi$
$701$	−913.148			−1.30264			−0.651318	+	0.758805i	$0.725784\pi$
$702$	673.264	+	388.709i	0.959065	+	0.553717i
$703$	103.289	+	178.902i	0.146926	+	0.254484i
$704$	38.1225	+	66.0301i	0.0541513	+	0.0937928i
$705$	7.68657	−	1.23090i	0.0109029	−	0.00174596i
$706$			723.943i			1.02541i
$707$	−804.979	−	604.161i	−1.13858	−	0.854542i
$708$			36.0337i			0.0508950i
$709$	−573.474	+	993.286i	−0.808849	+	1.40097i	0.104812	+	0.994492i	$0.466576\pi$
$709$	−573.474	+	993.286i	−0.808849	+	1.40097i	−0.913661	+	0.406476i	$0.866757\pi$
$710$	−216.579	−	82.7124i	−0.305040	−	0.116496i
$711$	740.181	+	1282.03i	1.04104	+	1.80314i
$712$	−85.4592	+	148.020i	−0.120027	+	0.207893i
$713$	327.533			0.459373
$714$	928.573	+	696.923i	1.30052	+	0.976083i
$715$	−456.341	−	561.570i	−0.638239	−	0.785412i
$716$	−9.64856	+	16.7118i	−0.0134756	+	0.0233405i
$717$	880.277	+	1524.68i	1.22772	+	2.12648i
$718$	−194.005	+	112.009i	−0.270202	+	0.156001i
$719$	−84.0179	−	48.5077i	−0.116854	−	0.0674656i	0.440434	−	0.897785i	$-0.354825\pi$
$719$	−84.0179	−	48.5077i	−0.116854	−	0.0674656i	−0.557288	+	0.830319i	$0.688158\pi$
$720$	204.457	+	251.603i	0.283968	+	0.349449i
$721$	−372.510	−	45.0085i	−0.516657	−	0.0624251i
$722$			352.367i			0.488043i
$723$	1327.86	+	766.642i	1.83660	+	1.06036i
$724$	383.713	−	221.537i	0.529991	−	0.305990i
$725$	−879.956	+	289.243i	−1.21373	+	0.398956i
$726$	185.510	+	107.104i	0.255523	+	0.147526i
$727$	175.776			0.241782			0.120891	−	0.992666i	$-0.461425\pi$
$727$	175.776			0.241782			0.120891	+	0.992666i	$0.461425\pi$
$728$	−276.518	+	118.006i	−0.379833	+	0.162096i
$729$	−1054.35			−1.44629
$730$	−67.4277	−	421.064i	−0.0923667	−	0.576800i
$731$	−369.254	+	213.189i	−0.505136	+	0.291640i
$732$	972.803	−	561.648i	1.32897	−	0.767279i
$733$	−346.840	+	600.745i	−0.473179	+	0.819570i	−0.999529	−	0.0306981i	$-0.990227\pi$
$733$	−346.840	+	600.745i	−0.473179	+	0.819570i	0.526350	+	0.850268i	$0.323560\pi$
$734$		−	461.505i		−	0.628753i
$735$	−1226.03	−	100.385i	−1.66807	−	0.136579i
$736$	119.295			0.162085
$737$	−105.548	−	60.9383i	−0.143213	−	0.0826842i
$738$	−432.616	−	749.313i	−0.586201	−	1.01533i
$739$	−10.2585	−	17.7682i	−0.0138816	−	0.0240436i	0.859001	−	0.511974i	$-0.171085\pi$
$739$	−10.2585	−	17.7682i	−0.0138816	−	0.0240436i	−0.872883	+	0.487930i	$0.837752\pi$
$740$	30.8873	+	192.881i	0.0417396	+	0.260650i
$741$		−	806.296i		−	1.08812i
$742$	−39.8325	−	93.3381i	−0.0536827	−	0.125793i
$743$			896.676i			1.20683i	0.797427	+	0.603416i	$0.206194\pi$
$743$			896.676i			1.20683i	−0.797427	+	0.603416i	$0.793806\pi$
$744$	−110.283	+	191.016i	−0.148230	+	0.256743i
$745$	0.0101401	−	0.0265514i	1.36109e−5	−	3.56394e-5i
$746$	206.272	+	357.273i	0.276503	+	0.478918i
$747$	−841.509	+	1457.54i	−1.12652	+	1.95119i
$748$	−445.234			−0.595232
$749$	91.3435	−	755.999i	0.121954	−	1.00934i
$750$	−407.006	−	788.772i	−0.542674	−	1.05170i
$751$	298.227	−	516.545i	0.397107	−	0.687809i	−0.596261	−	0.802791i	$-0.703348\pi$
$751$	298.227	−	516.545i	0.397107	−	0.687809i	0.993368	+	0.114982i	$0.0366809\pi$
$752$	0.620160	+	1.07415i	0.000824680	+	0.00142839i
$753$	1824.14	−	1053.17i	2.42249	−	1.39863i
$754$	−689.059	−	397.829i	−0.913872	−	0.527624i
$755$	724.541	+	891.615i	0.959657	+	1.18095i
$756$	−304.231	+	405.355i	−0.402423	+	0.536184i
$757$		−	118.056i		−	0.155952i	−0.996955	−	0.0779761i	$-0.975154\pi$
$757$		−	118.056i		−	0.155952i	0.996955	−	0.0779761i	$-0.0248458\pi$
$758$	829.432	+	478.873i	1.09424	+	0.631758i
$759$	−873.949	+	504.575i	−1.15145	+	0.664789i
$760$	53.3583	−	139.716i	0.0702083	−	0.183837i
$761$	695.093	+	401.312i	0.913395	+	0.527349i	0.881522	−	0.472143i	$-0.156520\pi$
$761$	695.093	+	401.312i	0.913395	+	0.527349i	0.0318728	+	0.999492i	$0.489853\pi$
$762$	826.773			1.08500
$763$	−257.593	+	343.214i	−0.337605	+	0.449822i
$764$	419.620			0.549241
$765$	−1869.36	+	299.353i	−2.44361	+	0.391312i
$766$	−305.211	+	176.214i	−0.398448	+	0.230044i
$767$	47.1882	−	27.2441i	0.0615231	−	0.0355204i
$768$	−40.1677	+	69.5725i	−0.0523017	+	0.0905892i
$769$		−	1022.31i		−	1.32940i	−0.747109	−	0.664701i	$-0.768559\pi$
$769$		−	1022.31i		−	1.32940i	0.747109	−	0.664701i	$-0.231441\pi$
$770$	399.147	−	251.440i	0.518373	−	0.326545i
$771$	−36.5988			−0.0474693
$772$	435.152	+	251.235i	0.563669	+	0.325434i
$773$	−343.943	−	595.726i	−0.444945	−	0.770668i	0.553103	−	0.833113i	$-0.313444\pi$
$773$	−343.943	−	595.726i	−0.444945	−	0.770668i	−0.998048	+	0.0624449i	$0.980110\pi$
$774$	−209.232	−	362.401i	−0.270326	−	0.468218i
$775$	258.824	−	289.436i	0.333967	−	0.373466i
$776$			368.463i			0.474823i
$777$	−631.455	+	269.477i	−0.812684	+	0.346817i
$778$		−	40.6736i		−	0.0522797i
$779$	−199.571	+	345.668i	−0.256189	+	0.443733i
$780$	272.013	−	712.253i	0.348735	−	0.913145i
$781$	156.238	+	270.612i	0.200048	+	0.346494i
$782$	−348.312	+	603.294i	−0.445412	+	0.771476i
$783$	−1341.31			−1.71303
$784$	−54.7521	−	188.197i	−0.0698369	−	0.240048i
$785$	139.115	+	171.194i	0.177217	+	0.218081i
$786$	−585.889	+	1014.79i	−0.745406	+	1.29108i
$787$	−612.772	−	1061.35i	−0.778618	−	1.34861i	−0.932739	−	0.360553i	$-0.882588\pi$
$787$	−612.772	−	1061.35i	−0.778618	−	1.34861i	0.154121	−	0.988052i	$-0.450745\pi$
$788$	223.075	−	128.792i	0.283090	−	0.163442i
$789$	594.658	+	343.326i	0.753686	+	0.435141i
$790$	501.150	−	407.243i	0.634367	−	0.515498i
$791$	−613.052	+	261.623i	−0.775034	+	0.330750i
$792$		−	436.970i		−	0.551730i
$793$	−1471.02	−	849.295i	−1.85501	−	1.07099i
$794$	309.774	−	178.848i	0.390143	−	0.225249i
$795$	240.420	+	91.8174i	0.302414	+	0.115494i
$796$	−346.767	−	200.206i	−0.435637	−	0.251515i
$797$	−691.172			−0.867217			−0.433608	−	0.901101i	$-0.642760\pi$
$797$	−691.172			−0.867217			−0.433608	+	0.901101i	$0.642760\pi$
$798$	521.854	+	63.0530i	0.653953	+	0.0790138i
$799$	−7.24286			−0.00906491
$800$	94.2697	−	105.419i	0.117837	−	0.131774i
$801$	848.321	−	489.778i	1.05908	−	0.611458i
$802$	−253.378	+	146.288i	−0.315932	+	0.182404i
$803$	−287.377	+	497.752i	−0.357880	+	0.619866i
$804$		−	128.415i		−	0.159720i
$805$	−28.4439	−	737.551i	−0.0353340	−	0.916212i
$806$	333.530			0.413808
$807$	−1085.91	−	626.948i	−1.34561	−	0.776887i
$808$	203.340	+	352.195i	0.251658	+	0.435884i
$809$	511.628	+	886.165i	0.632420	+	1.09538i	0.987056	+	0.160379i	$0.0512716\pi$
$809$	511.628	+	886.165i	0.632420	+	1.09538i	−0.354636	+	0.935005i	$0.615395\pi$
$810$	−40.1130	−	250.492i	−0.0495222	−	0.309250i
$811$			346.588i			0.427359i	0.976904	+	0.213679i	$0.0685448\pi$
$811$			346.588i			0.427359i	−0.976904	+	0.213679i	$0.931455\pi$
$812$	311.369	−	414.865i	0.383460	−	0.510918i
$813$			2252.07i			2.77007i
$814$	131.642	−	228.011i	0.161722	−	0.280112i
$815$	−142.692	−	54.4948i	−0.175082	−	0.0668648i
$816$	−234.560	−	406.270i	−0.287451	−	0.497880i
$817$	−96.5215	+	167.180i	−0.118141	+	0.204627i
$818$	−943.372			−1.15327
$819$	1710.60	+	206.683i	2.08864	+	0.252360i
$820$	−292.909	+	238.023i	−0.357206	+	0.290272i
$821$	302.304	−	523.605i	0.368214	−	0.637765i	−0.621072	−	0.783753i	$-0.713303\pi$
$821$	302.304	−	523.605i	0.368214	−	0.637765i	0.989286	+	0.145988i	$0.0466360\pi$
$822$	−757.697	−	1312.37i	−0.921772	−	1.59656i
$823$	1002.77	−	578.951i	1.21844	−	0.703464i	0.253853	−	0.967243i	$-0.418302\pi$
$823$	1002.77	−	578.951i	1.21844	−	0.703464i	0.964583	+	0.263779i	$0.0849689\pi$
$824$	131.299	+	75.8057i	0.159344	+	0.0919972i
$825$	−244.729	+	1171.02i	−0.296642	+	1.41942i
$826$	13.9429	+	32.6718i	0.0168800	+	0.0395543i
$827$		−	248.293i		−	0.300234i	−0.988668	−	0.150117i	$-0.952035\pi$
$827$		−	248.293i		−	0.300234i	0.988668	−	0.150117i	$-0.0479650\pi$
$828$	−592.097	−	341.847i	−0.715093	−	0.412859i
$829$	808.027	−	466.515i	0.974701	−	0.562744i	0.0740349	−	0.997256i	$-0.476412\pi$
$829$	808.027	−	466.515i	0.974701	−	0.562744i	0.900666	+	0.434512i	$0.143079\pi$
$830$	685.842	+	261.926i	0.826315	+	0.315574i
$831$	−2132.30	−	1231.08i	−2.56594	−	1.48145i
$832$	121.479			0.146008
$833$	1111.61	+	272.600i	1.33446	+	0.327250i
$834$	376.957			0.451987
$835$	−504.315	+	80.7592i	−0.603970	+	0.0967176i
$836$	−174.573	+	100.790i	−0.208820	+	0.120562i
$837$	486.930	−	281.129i	0.581757	−	0.335877i
$838$	58.6838	−	101.643i	0.0700283	−	0.121293i
$839$			1426.14i			1.69981i	0.526934	+	0.849906i	$0.323341\pi$
$839$			1426.14i			1.69981i	−0.526934	+	0.849906i	$0.676659\pi$
$840$	439.716	+	231.752i	0.523471	+	0.275895i
$841$	531.775			0.632312
$842$	−190.427	−	109.943i	−0.226161	−	0.130574i
$843$	135.750	+	235.126i	0.161032	+	0.278916i
$844$	167.518	+	290.150i	0.198481	+	0.343779i
$845$	−304.030	+	48.6862i	−0.359798	+	0.0576169i
$846$		−	7.10843i		−	0.00840240i
$847$	209.645	+	25.3304i	0.247515	+	0.0299060i
$848$			41.0050i			0.0483549i
$849$	407.955	−	706.599i	0.480512	−	0.832272i
$850$	257.879	+	784.536i	0.303387	+	0.922984i
$851$	−205.970	−	356.751i	−0.242033	−	0.419214i
$852$	−164.620	+	285.130i	−0.193216	+	0.334659i
$853$	350.268			0.410631			0.205315	−	0.978696i	$-0.434178\pi$
$853$	350.268			0.410631			0.205315	+	0.978696i	$0.434178\pi$
$854$	664.719	−	885.665i	0.778359	−	1.03708i
$855$	−665.200	+	540.553i	−0.778012	+	0.632226i
$856$	−153.846	+	266.468i	−0.179726	+	0.311295i
$857$	−15.1063	−	26.1649i	−0.0176269	−	0.0305308i	0.857077	−	0.515188i	$-0.172278\pi$
$857$	−15.1063	−	26.1649i	−0.0176269	−	0.0305308i	−0.874704	+	0.484657i	$0.838944\pi$
$858$	−889.950	+	513.813i	−1.03724	+	0.598850i
$859$	370.864	+	214.119i	0.431740	+	0.249265i	0.700087	−	0.714057i	$-0.253144\pi$
$859$	370.864	+	214.119i	0.431740	+	0.249265i	−0.268348	+	0.963322i	$0.586478\pi$
$860$	−141.664	+	115.118i	−0.164725	+	0.133859i
$861$	−1060.95	−	796.279i	−1.23223	−	0.924830i
$862$		−	49.8127i		−	0.0577874i
$863$	1021.22	+	589.602i	1.18334	+	0.683200i	0.956784	−	0.290798i	$-0.0939209\pi$
$863$	1021.22	+	589.602i	1.18334	+	0.683200i	0.226553	+	0.973999i	$0.427254\pi$
$864$	177.351	−	102.394i	0.205267	−	0.118511i
$865$	487.669	−	1276.94i	0.563779	−	1.47623i
$866$	−120.057	−	69.3150i	−0.138634	−	0.0800404i
$867$	1288.37			1.48601
$868$	−26.0823	+	215.868i	−0.0300487	+	0.248696i
$869$	−870.370			−1.00158
$870$	208.000	+	1298.89i	0.239081	+	1.49298i
$871$	−168.167	+	97.0912i	−0.193073	+	0.111471i
$872$	150.163	−	86.6967i	0.172205	−	0.0994229i
$873$	1055.85	−	1828.79i	1.20946	−	2.09484i
$874$			315.397i			0.360866i
$875$	−674.241	−	557.695i	−0.770561	−	0.637366i
$876$	−605.590			−0.691312
$877$	1423.08	+	821.617i	1.62267	+	0.936850i	0.986202	+	0.165548i	$0.0529393\pi$
$877$	1423.08	+	821.617i	1.62267	+	0.936850i	0.636470	+	0.771302i	$0.280394\pi$
$878$	−290.992	−	504.014i	−0.331426	−	0.574047i
$879$	−748.509	−	1296.45i	−0.851546	−	1.47492i
$880$	−188.215	+	30.1400i	−0.213880	+	0.0342500i
$881$			571.268i			0.648431i	0.945983	+	0.324216i	$0.105100\pi$
$881$			571.268i			0.648431i	−0.945983	+	0.324216i	$0.894900\pi$
$882$	−267.540	+	1090.98i	−0.303334	+	1.23694i
$883$			13.3627i			0.0151333i	0.999971	+	0.00756666i	$0.00240856\pi$
$883$			13.3627i			0.0151333i	−0.999971	+	0.00756666i	$0.997591\pi$
$884$	−354.689	+	614.340i	−0.401232	+	0.694955i
$885$	−84.1559	−	32.1395i	−0.0950914	−	0.0363159i
$886$	535.995	+	928.370i	0.604960	+	1.04782i
$887$	662.731	−	1147.88i	0.747160	−	1.29412i	−0.202018	−	0.979382i	$-0.564750\pi$
$887$	662.731	−	1147.88i	0.747160	−	1.29412i	0.949179	−	0.314738i	$-0.101917\pi$
$888$	277.409			0.312397
$889$	749.638	−	319.912i	0.843237	−	0.359856i
$890$	−269.473	−	331.611i	−0.302779	−	0.372597i
$891$	−170.962	+	296.115i	−0.191876	+	0.332340i
$892$	−66.6389	−	115.422i	−0.0747073	−	0.129397i
$893$	−2.83988	+	1.63961i	−0.00318016	+	0.00183607i
$894$	−0.0349554	−	0.0201815i	−3.91000e−5	−	2.25744e-5i
$895$	−30.4242	−	37.4398i	−0.0339935	−	0.0418321i
$896$	−9.49976	+	78.6241i	−0.0106024	+	0.0877502i
$897$			1607.85i			1.79247i
$898$	61.1735	+	35.3185i	0.0681219	+	0.0393302i
$899$	−498.354	+	287.725i	−0.554343	+	0.320050i
$900$	−769.975	+	253.092i	−0.855528	+	0.281214i
$901$	−207.369	−	119.725i	−0.230154	−	0.132880i
$902$	508.708			0.563978
$903$	−513.124	−	385.116i	−0.568244	−	0.426485i
$904$	269.324			0.297925
$905$	175.149	+	1093.75i	0.193535	+	1.20856i
$906$	1412.99	−	815.791i	1.55959	−	0.900431i
$907$	−417.494	+	241.041i	−0.460303	+	0.265756i	−0.712171	−	0.702006i	$-0.752288\pi$
$907$	−417.494	+	241.041i	−0.460303	+	0.265756i	0.251869	+	0.967761i	$0.418955\pi$
$908$	−51.8490	+	89.8052i	−0.0571025	+	0.0989044i
$909$		−	2330.73i		−	2.56406i
$910$	−28.9647	−	751.055i	−0.0318293	−	0.825335i
$911$	1582.96			1.73761			0.868806	−	0.495153i	$-0.164888\pi$
$911$	1582.96			1.73761			0.868806	+	0.495153i	$0.164888\pi$
$912$	−183.939	−	106.197i	−0.201688	−	0.116444i
$913$	−494.760	−	856.949i	−0.541906	−	0.938608i
$914$	−286.148	−	495.622i	−0.313072	−	0.542256i
$915$	444.044	+	2772.91i	0.485294	+	3.03050i
$916$			145.684i			0.159043i
$917$	−138.564	+	1146.82i	−0.151106	+	1.25062i
$918$			1195.86i			1.30268i
$919$	669.468	−	1159.55i	0.728474	−	1.26175i	−0.229054	−	0.973414i	$-0.573563\pi$
$919$	669.468	−	1159.55i	0.728474	−	1.26175i	0.957528	−	0.288340i	$-0.0931034\pi$
$920$	−106.403	+	278.611i	−0.115655	+	0.302838i
$921$	495.491	+	858.215i	0.537992	+	0.931830i
$922$	−29.3021	+	50.7528i	−0.0317811	+	0.0550464i
$923$	497.859			0.539392
$924$	−262.957	−	616.178i	−0.284586	−	0.666859i
$925$	−478.019	−	99.9000i	−0.516778	−	0.108000i
$926$	472.892	−	819.072i	0.510682	−	0.884527i
$927$	−434.453	−	752.494i	−0.468665	−	0.811752i
$928$	−181.512	+	104.796i	−0.195595	+	0.112927i
$929$	641.135	+	370.159i	0.690135	+	0.398449i	0.803662	−	0.595085i	$-0.202882\pi$
$929$	641.135	+	370.159i	0.690135	+	0.398449i	−0.113528	+	0.993535i	$0.536215\pi$
$930$	−347.750	−	427.938i	−0.373924	−	0.460148i
$931$	497.564	−	144.756i	0.534441	−	0.155485i
$932$			275.697i			0.295813i
$933$	−1393.62	−	804.604i	−1.49369	−	0.862384i
$934$	−609.131	+	351.682i	−0.652175	+	0.376533i
$935$	397.118	−	1039.83i	0.424725	−	1.11212i
$936$	−602.938	−	348.106i	−0.644164	−	0.371909i
$937$	−272.107			−0.290402			−0.145201	−	0.989402i	$-0.546383\pi$
$937$	−272.107			−0.290402			−0.145201	+	0.989402i	$0.546383\pi$
$938$	−49.6890	−	116.434i	−0.0529733	−	0.124130i
$939$	1088.58			1.15930
$940$	−3.06179	+	0.490304i	−0.00325722	+	0.000521600i
$941$	203.843	−	117.689i	0.216623	−	0.125068i	−0.387762	−	0.921759i	$-0.626752\pi$
$941$	203.843	−	117.689i	0.216623	−	0.125068i	0.604386	+	0.796692i	$0.293419\pi$
$942$	271.300	−	156.635i	0.288005	−	0.166279i
$943$	397.968	−	689.302i	0.422024	−	0.730967i
$944$		−	14.3533i		−	0.0152048i
$945$	−675.344	−	1072.07i	−0.714650	−	1.13447i
$946$	246.034			0.260078
$947$	526.514	+	303.983i	0.555981	+	0.320996i	0.751531	−	0.659698i	$-0.229316\pi$
$947$	526.514	+	303.983i	0.555981	+	0.320996i	−0.195550	+	0.980694i	$0.562649\pi$
$948$	−458.532	−	794.201i	−0.483683	−	0.837764i
$949$	457.870	+	793.055i	0.482477	+	0.835674i
$950$	278.712	+	249.234i	0.293381	+	0.262352i
$951$			1969.20i			2.07066i
$952$	−369.878	−	277.605i	−0.388528	−	0.291602i
$953$		−	188.561i		−	0.197860i	−0.995094	−	0.0989302i	$-0.968458\pi$
$953$		−	188.561i		−	0.197860i	0.995094	−	0.0989302i	$-0.0315421\pi$
$954$	117.503	−	203.520i	0.123168	−	0.213334i
$955$	−374.272	+	980.013i	−0.391908	+	1.02619i
$956$	−350.640	−	607.327i	−0.366779	−	0.635279i
$957$	886.499	−	1535.46i	0.926331	−	1.60445i
$958$	−626.412			−0.653875
$959$	−1194.81	−	896.745i	−1.24590	−	0.935084i
$960$	−126.658	−	155.865i	−0.131936	−	0.162359i
$961$	−359.889	+	623.347i	−0.374495	+	0.648644i
$962$	−209.742	−	363.283i	−0.218027	−	0.377633i
$963$	1527.17	−	881.710i	1.58584	−	0.915586i
$964$	−528.927	−	305.376i	−0.548680	−	0.316780i
$965$	−974.880	+	792.204i	−1.01024	+	0.820937i
$966$	−1040.64	−	125.735i	−1.07727	−	0.130161i
$967$		−	1088.32i		−	1.12546i	−0.826640	−	0.562732i	$-0.809750\pi$
$967$		−	1088.32i		−	1.12546i	0.826640	−	0.562732i	$-0.190250\pi$
$968$	−73.8941	−	42.6628i	−0.0763369	−	0.0440731i
$969$	1074.11	−	620.140i	1.10848	−	0.639980i
$970$	−860.537	−	328.643i	−0.887151	−	0.338807i
$971$	−164.230	−	94.8183i	−0.169135	−	0.0976501i	0.413043	−	0.910712i	$-0.364466\pi$
$971$	−164.230	−	94.8183i	−0.169135	−	0.0976501i	−0.582178	+	0.813061i	$0.697799\pi$
$972$	291.362			0.299755
$973$	341.788	−	145.860i	0.351272	−	0.149907i
$974$	158.872			0.163113
$975$	1420.84	+	1270.56i	1.45727	+	1.30314i
$976$	−387.496	+	223.721i	−0.397025	+	0.229222i
$977$	−687.092	+	396.693i	−0.703267	+	0.406032i	−0.808563	−	0.588409i	$-0.799754\pi$
$977$	−687.092	+	396.693i	−0.703267	+	0.406032i	0.105296	+	0.994441i	$0.466421\pi$
$978$	−108.459	+	187.857i	−0.110899	+	0.192083i
$979$			575.924i			0.588278i
$980$	488.366	+	39.9865i	0.498332	+	0.0408025i
$981$	−993.741			−1.01299
$982$	829.369	+	478.837i	0.844572	+	0.487614i
$983$	−26.9121	−	46.6132i	−0.0273775	−	0.0474193i	0.852012	−	0.523522i	$-0.175382\pi$
$983$	−26.9121	−	46.6132i	−0.0273775	−	0.0474193i	−0.879390	+	0.476103i	$0.842049\pi$
$984$	268.000	+	464.189i	0.272357	+	0.471737i
$985$	101.824	+	635.860i	0.103375	+	0.645543i
$986$		−	1223.92i		−	1.24129i
$987$	−4.27767	−	10.0237i	−0.00433401	−	0.0101557i
$988$			321.172i			0.325073i
$989$	192.475	−	333.377i	0.194616	−	0.337085i
$990$	1020.54	+	389.747i	1.03084	+	0.393684i
$991$	718.340	+	1244.20i	0.724864	+	1.25550i	0.959030	+	0.283304i	$0.0914306\pi$
$991$	718.340	+	1244.20i	0.724864	+	1.25550i	−0.234166	+	0.972197i	$0.575236\pi$
$992$	43.9292	−	76.0875i	0.0442834	−	0.0767012i
$993$	−1725.80			−1.73797
$994$	−38.9329	+	322.226i	−0.0391680	+	0.324171i
$995$	776.870	−	631.298i	0.780774	−	0.634470i
$996$	521.303	−	902.923i	0.523397	−	0.906550i
$997$	110.002	+	190.529i	0.110333	+	0.191102i	0.915905	−	0.401396i	$-0.131475\pi$
$997$	110.002	+	190.529i	0.110333	+	0.191102i	−0.805572	+	0.592499i	$0.798142\pi$
$998$	1129.74	−	652.257i	1.13201	−	0.653564i
$999$	−612.417	−	353.579i	−0.613030	−	0.353933i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.3.h.a.19.1	✓	16
3.2	odd	2		630.3.bc.a.19.8		16
4.3	odd	2		560.3.br.b.369.8		16
5.2	odd	4		350.3.k.e.201.5		16
5.3	odd	4		350.3.k.e.201.4		16
5.4	even	2	inner	70.3.h.a.19.8	yes	16
7.2	even	3		490.3.d.a.489.16		16
7.3	odd	6	inner	70.3.h.a.59.8	yes	16
7.4	even	3		490.3.h.b.129.5		16
7.5	odd	6		490.3.d.a.489.9		16
7.6	odd	2		490.3.h.b.19.4		16
15.14	odd	2		630.3.bc.a.19.3		16
20.19	odd	2		560.3.br.b.369.1		16
21.17	even	6		630.3.bc.a.199.3		16
28.3	even	6		560.3.br.b.129.1		16
35.3	even	12		350.3.k.e.101.4		16
35.4	even	6		490.3.h.b.129.4		16
35.9	even	6		490.3.d.a.489.1		16
35.17	even	12		350.3.k.e.101.5		16
35.19	odd	6		490.3.d.a.489.8		16
35.24	odd	6	inner	70.3.h.a.59.1	yes	16
35.34	odd	2		490.3.h.b.19.5		16
105.59	even	6		630.3.bc.a.199.8		16
140.59	even	6		560.3.br.b.129.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.h.a.19.1	✓	16	1.1	even	1	trivial
70.3.h.a.19.8	yes	16	5.4	even	2	inner
70.3.h.a.59.1	yes	16	35.24	odd	6	inner
70.3.h.a.59.8	yes	16	7.3	odd	6	inner
350.3.k.e.101.4		16	35.3	even	12
350.3.k.e.101.5		16	35.17	even	12
350.3.k.e.201.4		16	5.3	odd	4
350.3.k.e.201.5		16	5.2	odd	4
490.3.d.a.489.1		16	35.9	even	6
490.3.d.a.489.8		16	35.19	odd	6
490.3.d.a.489.9		16	7.5	odd	6
490.3.d.a.489.16		16	7.2	even	3
490.3.h.b.19.4		16	7.6	odd	2
490.3.h.b.19.5		16	35.34	odd	2
490.3.h.b.129.4		16	35.4	even	6
490.3.h.b.129.5		16	7.4	even	3
560.3.br.b.129.1		16	28.3	even	6
560.3.br.b.129.8		16	140.59	even	6
560.3.br.b.369.1		16	20.19	odd	2
560.3.br.b.369.8		16	4.3	odd	2
630.3.bc.a.19.3		16	15.14	odd	2
630.3.bc.a.19.8		16	3.2	odd	2
630.3.bc.a.199.3		16	21.17	even	6
630.3.bc.a.199.8		16	105.59	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:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	70.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(-2.51048 - 4.34828i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-4.93710 + 0.790609i) q^{5} +7.10072i q^{6} +(2.74755 + 6.43824i) q^{7} -2.82843i q^{8} +(-8.10505 + 14.0384i) q^{9} +(6.60573 + 2.52276i) q^{10} +(-4.76531 - 8.25377i) q^{11} +(5.02097 - 8.69657i) q^{12} -15.1849 q^{13} +(1.18747 - 9.82802i) q^{14} +(15.8323 + 19.4831i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-11.6790 - 20.2287i) q^{17} +(19.8532 - 11.4623i) q^{18} +(-9.15855 - 5.28769i) q^{19} +(-6.30647 - 7.76070i) q^{20} +(21.0976 - 28.1102i) q^{21} +13.4783i q^{22} +(18.2632 + 10.5443i) q^{23} +(-12.2988 + 7.10072i) q^{24} +(23.7499 - 7.80663i) q^{25} +(18.5976 + 10.7373i) q^{26} +36.2016 q^{27} +(-8.40380 + 11.1971i) q^{28} -37.0510 q^{29} +(-5.61389 - 35.0569i) q^{30} +(13.4505 - 7.76565i) q^{31} +(4.89898 - 2.82843i) q^{32} +(-23.9265 + 41.4419i) q^{33} +33.0333i q^{34} +(-18.6551 - 29.6140i) q^{35} -32.4202 q^{36} +(-16.9168 - 9.76693i) q^{37} +(7.47792 + 12.9521i) q^{38} +(38.1214 + 66.0282i) q^{39} +(2.23618 + 13.9642i) q^{40} -37.7426i q^{41} +(-45.7161 + 19.5096i) q^{42} -18.2540i q^{43} +(9.53063 - 16.5075i) q^{44} +(28.9166 - 75.7167i) q^{45} +(-14.9119 - 25.8281i) q^{46} +(0.155040 - 0.268537i) q^{47} +20.0839 q^{48} +(-33.9019 + 35.3788i) q^{49} +(-34.6077 - 7.23256i) q^{50} +(-58.6400 + 101.567i) q^{51} +(-15.1849 - 26.3010i) q^{52} +(8.87784 - 5.12562i) q^{53} +(-44.3378 - 25.5984i) q^{54} +(30.0523 + 36.9821i) q^{55} +(18.2101 - 7.77126i) q^{56} +53.0986i q^{57} +(45.3780 + 26.1990i) q^{58} +(-3.10758 + 1.79416i) q^{59} +(-17.9134 + 46.9054i) q^{60} +(96.8741 + 55.9303i) q^{61} -21.9646 q^{62} +(-112.651 - 13.6111i) q^{63} -8.00000 q^{64} +(74.9693 - 12.0053i) q^{65} +(58.6077 - 33.8371i) q^{66} +(11.0746 - 6.39394i) q^{67} +(23.3581 - 40.4573i) q^{68} -105.885i q^{69} +(1.90747 + 49.4607i) q^{70} -32.7865 q^{71} +(39.7065 + 22.9245i) q^{72} +(-30.1530 - 52.2266i) q^{73} +(13.8125 + 23.9240i) q^{74} +(-93.5691 - 83.6728i) q^{75} -21.1508i q^{76} +(40.0468 - 53.3579i) q^{77} -107.824i q^{78} +(45.6617 - 79.0884i) q^{79} +(7.13544 - 18.6838i) q^{80} +(-17.9382 - 31.0698i) q^{81} +(-26.6881 + 46.2251i) q^{82} +103.825 q^{83} +(69.7860 + 8.43189i) q^{84} +(73.6535 + 90.6374i) q^{85} +(-12.9075 + 22.3565i) q^{86} +(93.0158 + 161.108i) q^{87} +(-23.3452 + 13.4783i) q^{88} +(-52.3329 - 30.2144i) q^{89} +(-88.9552 + 72.2865i) q^{90} +(-41.7213 - 97.7639i) q^{91} +42.1771i q^{92} +(-67.5345 - 38.9911i) q^{93} +(-0.379769 + 0.219259i) q^{94} +(49.3972 + 18.8650i) q^{95} +(-24.5976 - 14.2014i) q^{96} -130.271 q^{97} +(66.5378 - 19.3578i) q^{98} +154.492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} - 6 q^{5} - 12 q^{9} + 24 q^{10} - 12 q^{11} + 32 q^{14} - 28 q^{15} - 32 q^{16} - 12 q^{19} - 8 q^{21} - 24 q^{24} - 42 q^{25} - 48 q^{26} - 136 q^{29} + 32 q^{30} + 84 q^{31} - 190 q^{35}+ \cdots + 176 q^{99}+O(q^{100}) \) 16 * q + 16 * q^4 - 6 * q^5 - 12 * q^9 + 24 * q^10 - 12 * q^11 + 32 * q^14 - 28 * q^15 - 32 * q^16 - 12 * q^19 - 8 * q^21 - 24 * q^24 - 42 * q^25 - 48 * q^26 - 136 * q^29 + 32 * q^30 + 84 * q^31 - 190 * q^35 - 48 * q^36 + 312 * q^39 + 48 * q^40 + 24 * q^44 + 384 * q^45 - 68 * q^46 + 296 * q^49 - 96 * q^50 - 76 * q^51 - 108 * q^54 + 56 * q^56 - 372 * q^59 - 28 * q^60 + 348 * q^61 - 128 * q^64 - 104 * q^65 + 480 * q^66 - 296 * q^70 - 384 * q^71 + 208 * q^74 - 150 * q^75 + 148 * q^79 + 24 * q^80 - 140 * q^81 + 256 * q^84 + 580 * q^85 - 188 * q^86 - 912 * q^89 - 616 * q^91 - 600 * q^94 - 310 * q^95 - 48 * q^96 + 176 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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