LMFDB - Embedded newform 105.3.k.c.83.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(62,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("105.62");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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} + 433x^{8} + 16 $ x^16 + 433*x^8 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			83.2
Root			$-0.611750 - 0.253395i$ of defining polynomial
Character	$\chi$	$=$	105.83
Dual form			105.3.k.c.62.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.152778 + 2.99611i) q^{3} -3.00000i q^{4} +(-4.24762 - 2.63775i) q^{5} +(2.22660 - 2.01054i) q^{6} +(4.33402 - 5.49694i) q^{7} +(-4.94975 + 4.94975i) q^{8} +(-8.95332 - 0.915476i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.152778 + 2.99611i) q^{3} -3.00000i q^{4} +(-4.24762 - 2.63775i) q^{5} +(2.22660 - 2.01054i) q^{6} +(4.33402 - 5.49694i) q^{7} +(-4.94975 + 4.94975i) q^{8} +(-8.95332 - 0.915476i) q^{9} +(1.13835 + 4.86869i) q^{10} -13.9031i q^{11} +(8.98832 + 0.458333i) q^{12} +(14.6307 - 14.6307i) q^{13} +(-6.95153 + 0.822309i) q^{14} +(8.55193 - 12.3233i) q^{15} -5.00000 q^{16} +(-4.86435 + 4.86435i) q^{17} +(5.68361 + 6.97829i) q^{18} -21.7515 q^{19} +(-7.91326 + 12.7429i) q^{20} +(15.8073 + 13.8250i) q^{21} +(-9.83095 + 9.83095i) q^{22} +(-1.77282 + 1.77282i) q^{23} +(-14.0738 - 15.5862i) q^{24} +(11.0845 + 22.4083i) q^{25} -20.6909 q^{26} +(4.11073 - 26.6852i) q^{27} +(-16.4908 - 13.0020i) q^{28} +28.0452 q^{29} +(-14.7610 + 2.66678i) q^{30} +17.2472i q^{31} +(23.3345 + 23.3345i) q^{32} +(41.6551 + 2.12408i) q^{33} +6.87923 q^{34} +(-32.9088 + 11.9168i) q^{35} +(-2.74643 + 26.8600i) q^{36} +(-6.50714 + 6.50714i) q^{37} +(15.3806 + 15.3806i) q^{38} +(41.5998 + 46.0702i) q^{39} +(34.0808 - 7.96843i) q^{40} -26.7192 q^{41} +(-1.40169 - 20.9532i) q^{42} +(33.1548 + 33.1548i) q^{43} -41.7092 q^{44} +(35.6155 + 27.5052i) q^{45} +2.50714 q^{46} +(18.5656 - 18.5656i) q^{47} +(0.763888 - 14.9805i) q^{48} +(-11.4326 - 47.6476i) q^{49} +(8.00714 - 23.6830i) q^{50} +(-13.8310 - 15.3173i) q^{51} +(-43.8920 - 43.8920i) q^{52} +(48.3021 - 48.3021i) q^{53} +(-21.7760 + 15.9626i) q^{54} +(-36.6728 + 59.0549i) q^{55} +(5.75616 + 48.6607i) q^{56} +(3.32314 - 65.1697i) q^{57} +(-19.8310 - 19.8310i) q^{58} -29.6668i q^{59} +(-36.9700 - 25.6558i) q^{60} +21.0717i q^{61} +(12.1956 - 12.1956i) q^{62} +(-43.8361 + 45.2481i) q^{63} -13.0000i q^{64} +(-100.737 + 23.5534i) q^{65} +(-27.9526 - 30.9565i) q^{66} +(-32.4786 + 32.4786i) q^{67} +(14.5931 + 14.5931i) q^{68} +(-5.04071 - 5.58240i) q^{69} +(31.6965 + 14.8436i) q^{70} -16.0345i q^{71} +(48.8480 - 39.7853i) q^{72} +(57.3597 - 57.3597i) q^{73} +9.20249 q^{74} +(-68.8312 + 29.7869i) q^{75} +65.2544i q^{76} +(-76.4243 - 60.2561i) q^{77} +(3.16110 - 61.9921i) q^{78} -75.8024i q^{79} +(21.2381 + 13.1888i) q^{80} +(79.3238 + 16.3931i) q^{81} +(18.8933 + 18.8933i) q^{82} +(51.9675 + 51.9675i) q^{83} +(41.4750 - 47.4218i) q^{84} +(33.4929 - 7.83095i) q^{85} -46.8879i q^{86} +(-4.28468 + 84.0264i) q^{87} +(68.8167 + 68.8167i) q^{88} -174.294i q^{89} +(-5.73481 - 44.6331i) q^{90} +(-17.0143 - 143.833i) q^{91} +(5.31846 + 5.31846i) q^{92} +(-51.6745 - 2.63499i) q^{93} -26.2557 q^{94} +(92.3919 + 57.3750i) q^{95} +(-73.4777 + 66.3477i) q^{96} +(-16.6658 - 16.6658i) q^{97} +(-25.6079 + 41.7760i) q^{98} +(-12.7279 + 124.479i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{7}+O(q^{10}) $ 16 * q + 32 * q^7	$ 16 q + 32 q^{7} + 80 q^{15} - 80 q^{16} + 8 q^{18} - 64 q^{21} - 64 q^{22} + 224 q^{25} - 96 q^{28} - 128 q^{30} + 96 q^{36} - 384 q^{37} - 112 q^{42} + 64 q^{43} + 320 q^{46} - 128 q^{51} + 408 q^{57} - 224 q^{58} - 120 q^{60} - 72 q^{63} + 320 q^{67} + 128 q^{70} + 56 q^{72} - 424 q^{78} + 896 q^{81} + 256 q^{85} + 448 q^{88} - 832 q^{91} + 32 q^{93}+O(q^{100}) $ 16 * q + 32 * q^7 + 80 * q^15 - 80 * q^16 + 8 * q^18 - 64 * q^21 - 64 * q^22 + 224 * q^25 - 96 * q^28 - 128 * q^30 + 96 * q^36 - 384 * q^37 - 112 * q^42 + 64 * q^43 + 320 * q^46 - 128 * q^51 + 408 * q^57 - 224 * q^58 - 120 * q^60 - 72 * q^63 + 320 * q^67 + 128 * q^70 + 56 * q^72 - 424 * q^78 + 896 * q^81 + 256 * q^85 + 448 * q^88 - 832 * q^91 + 32 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.353553	−	0.353553i	0.507877	−	0.861430i	$-0.330431\pi$
$2$	−0.707107	−	0.707107i	−0.353553	−	0.353553i	−0.861430	+	0.507877i	$0.830431\pi$
$3$	−0.152778	+	2.99611i	−0.0509259	+	0.998702i
$3$	−0.152778	+	2.99611i	−0.0509259	+	0.998702i
$4$		−	3.00000i		−	0.750000i
$5$	−4.24762	−	2.63775i	−0.849524	−	0.527550i
$5$	−4.24762	−	2.63775i	−0.849524	−	0.527550i
$6$	2.22660	−	2.01054i	0.371100	−	0.335090i
$7$	4.33402	−	5.49694i	0.619145	−	0.785277i
$7$	4.33402	−	5.49694i	0.619145	−	0.785277i
$8$	−4.94975	+	4.94975i	−0.618718	+	0.618718i
$9$	−8.95332	−	0.915476i	−0.994813	−	0.101720i
$10$	1.13835	+	4.86869i	0.113835	+	0.486869i
$11$		−	13.9031i		−	1.26392i	−0.775003	−	0.631958i	$-0.782252\pi$
$11$		−	13.9031i		−	1.26392i	0.775003	−	0.631958i	$-0.217748\pi$
$12$	8.98832	+	0.458333i	0.749027	+	0.0381944i
$13$	14.6307	−	14.6307i	1.12543	−	1.12543i	0.134524	−	0.990910i	$-0.457049\pi$
$13$	14.6307	−	14.6307i	1.12543	−	1.12543i	0.990910	−	0.134524i	$-0.0429507\pi$
$14$	−6.95153	+	0.822309i	−0.496538	+	0.0587364i
$15$	8.55193	−	12.3233i	0.570129	−	0.821555i
$16$	−5.00000			−0.312500
$17$	−4.86435	+	4.86435i	−0.286138	+	0.286138i	−0.835551	−	0.549413i	$-0.814851\pi$
$17$	−4.86435	+	4.86435i	−0.286138	+	0.286138i	0.549413	+	0.835551i	$0.314851\pi$
$18$	5.68361	+	6.97829i	0.315756	+	0.387683i
$19$	−21.7515			−1.14481			−0.572407	−	0.819970i	$-0.693990\pi$
$19$	−21.7515			−1.14481			−0.572407	+	0.819970i	$0.693990\pi$
$20$	−7.91326	+	12.7429i	−0.395663	+	0.637143i
$21$	15.8073	+	13.8250i	0.752727	+	0.658333i
$22$	−9.83095	+	9.83095i	−0.446861	+	0.446861i
$23$	−1.77282	+	1.77282i	−0.0770791	+	0.0770791i	−0.744595	−	0.667516i	$-0.767357\pi$
$23$	−1.77282	+	1.77282i	−0.0770791	+	0.0770791i	0.667516	+	0.744595i	$0.267357\pi$
$24$	−14.0738	−	15.5862i	−0.586407	−	0.649424i
$25$	11.0845	+	22.4083i	0.443381	+	0.896333i
$26$	−20.6909			−0.795802
$27$	4.11073	−	26.6852i	0.152249	−	0.988342i
$28$	−16.4908	−	13.0020i	−0.588957	−	0.464359i
$29$	28.0452			0.967076			0.483538	−	0.875323i	$-0.339352\pi$
$29$	28.0452			0.967076			0.483538	+	0.875323i	$0.339352\pi$
$30$	−14.7610	+	2.66678i	−0.492035	+	0.0888928i
$31$			17.2472i			0.556362i	0.960529	+	0.278181i	$0.0897315\pi$
$31$			17.2472i			0.556362i	−0.960529	+	0.278181i	$0.910268\pi$
$32$	23.3345	+	23.3345i	0.729204	+	0.729204i
$33$	41.6551	+	2.12408i	1.26228	+	0.0643660i
$34$	6.87923			0.202330
$35$	−32.9088	+	11.9168i	−0.940251	+	0.340481i
$36$	−2.74643	+	26.8600i	−0.0762897	+	0.746110i
$37$	−6.50714	+	6.50714i	−0.175869	+	0.175869i	−0.789552	−	0.613683i	$-0.789687\pi$
$37$	−6.50714	+	6.50714i	−0.175869	+	0.175869i	0.613683	+	0.789552i	$0.289687\pi$
$38$	15.3806	+	15.3806i	0.404753	+	0.404753i
$39$	41.5998	+	46.0702i	1.06666	+	1.18129i
$40$	34.0808	−	7.96843i	0.852021	−	0.199211i
$41$	−26.7192			−0.651687			−0.325844	−	0.945424i	$-0.605648\pi$
$41$	−26.7192			−0.651687			−0.325844	+	0.945424i	$0.605648\pi$
$42$	−1.40169	−	20.9532i	−0.0333735	−	0.498885i
$43$	33.1548	+	33.1548i	0.771041	+	0.771041i	0.978289	−	0.207248i	$-0.0664506\pi$
$43$	33.1548	+	33.1548i	0.771041	+	0.771041i	−0.207248	+	0.978289i	$0.566451\pi$
$44$	−41.7092			−0.947936
$45$	35.6155	+	27.5052i	0.791455	+	0.611227i
$46$	2.50714			0.0545031
$47$	18.5656	−	18.5656i	0.395012	−	0.395012i	−0.481457	−	0.876470i	$-0.659892\pi$
$47$	18.5656	−	18.5656i	0.395012	−	0.395012i	0.876470	+	0.481457i	$0.159892\pi$
$48$	0.763888	−	14.9805i	0.0159143	−	0.312095i
$49$	−11.4326	−	47.6476i	−0.233319	−	0.972400i
$50$	8.00714	−	23.6830i	0.160143	−	0.473661i
$51$	−13.8310	−	15.3173i	−0.271195	−	0.300339i
$52$	−43.8920	−	43.8920i	−0.844076	−	0.844076i
$53$	48.3021	−	48.3021i	0.911361	−	0.911361i	−0.0850185	−	0.996379i	$-0.527095\pi$
$53$	48.3021	−	48.3021i	0.911361	−	0.911361i	0.996379	+	0.0850185i	$0.0270949\pi$
$54$	−21.7760	+	15.9626i	−0.403260	+	0.295603i
$55$	−36.6728	+	59.0549i	−0.666779	+	1.07373i
$56$	5.75616	+	48.6607i	0.102789	+	0.868942i
$57$	3.32314	−	65.1697i	0.0583006	−	1.14333i
$58$	−19.8310	−	19.8310i	−0.341913	−	0.341913i
$59$		−	29.6668i		−	0.502826i	−0.967880	−	0.251413i	$-0.919105\pi$
$59$		−	29.6668i		−	0.502826i	0.967880	−	0.251413i	$-0.0808953\pi$
$60$	−36.9700	−	25.6558i	−0.616167	−	0.427597i
$61$			21.0717i			0.345438i	0.984971	+	0.172719i	$0.0552552\pi$
$61$			21.0717i			0.345438i	−0.984971	+	0.172719i	$0.944745\pi$
$62$	12.1956	−	12.1956i	0.196704	−	0.196704i
$63$	−43.8361	+	45.2481i	−0.695812	+	0.718224i
$64$		−	13.0000i		−	0.203125i
$65$	−100.737	+	23.5534i	−1.54981	+	0.362360i
$66$	−27.9526	−	30.9565i	−0.423525	−	0.469038i
$67$	−32.4786	+	32.4786i	−0.484755	+	0.484755i	−0.906646	−	0.421892i	$-0.861366\pi$
$67$	−32.4786	+	32.4786i	−0.484755	+	0.484755i	0.421892	+	0.906646i	$0.361366\pi$
$68$	14.5931	+	14.5931i	0.214604	+	0.214604i
$69$	−5.04071	−	5.58240i	−0.0730537	−	0.0809044i
$70$	31.6965	+	14.8436i	0.452807	+	0.212051i
$71$		−	16.0345i		−	0.225838i	−0.993604	−	0.112919i	$-0.963980\pi$
$71$		−	16.0345i		−	0.225838i	0.993604	−	0.112919i	$-0.0360200\pi$
$72$	48.8480	−	39.7853i	0.678445	−	0.552573i
$73$	57.3597	−	57.3597i	0.785749	−	0.785749i	−0.195045	−	0.980794i	$-0.562485\pi$
$73$	57.3597	−	57.3597i	0.785749	−	0.785749i	0.980794	+	0.195045i	$0.0624853\pi$
$74$	9.20249			0.124358
$75$	−68.8312	+	29.7869i	−0.917750	+	0.397159i
$76$			65.2544i			0.858610i
$77$	−76.4243	−	60.2561i	−0.992523	−	0.782547i
$78$	3.16110	−	61.9921i	0.0405269	−	0.794770i
$79$		−	75.8024i		−	0.959524i	−0.877399	−	0.479762i	$-0.840723\pi$
$79$		−	75.8024i		−	0.959524i	0.877399	−	0.479762i	$-0.159277\pi$
$80$	21.2381	+	13.1888i	0.265476	+	0.164860i
$81$	79.3238	+	16.3931i	0.979306	+	0.202384i
$82$	18.8933	+	18.8933i	0.230406	+	0.230406i
$83$	51.9675	+	51.9675i	0.626114	+	0.626114i	0.947088	−	0.320974i	$-0.104010\pi$
$83$	51.9675	+	51.9675i	0.626114	+	0.626114i	−0.320974	+	0.947088i	$0.604010\pi$
$84$	41.4750	−	47.4218i	0.493749	−	0.564545i
$85$	33.4929	−	7.83095i	0.394034	−	0.0921288i
$86$		−	46.8879i		−	0.545208i
$87$	−4.28468	+	84.0264i	−0.0492492	+	0.965821i
$88$	68.8167	+	68.8167i	0.782008	+	0.782008i
$89$		−	174.294i		−	1.95836i	−0.202987	−	0.979181i	$-0.565065\pi$
$89$		−	174.294i		−	1.95836i	0.202987	−	0.979181i	$-0.434935\pi$
$90$	−5.73481	−	44.6331i	−0.0637201	−	0.495923i
$91$	−17.0143	−	143.833i	−0.186970	−	1.58058i
$92$	5.31846	+	5.31846i	0.0578093	+	0.0578093i
$93$	−51.6745	−	2.63499i	−0.555640	−	0.0283332i
$94$	−26.2557			−0.279316
$95$	92.3919	+	57.3750i	0.972547	+	0.603947i
$96$	−73.4777	+	66.3477i	−0.765393	+	0.691122i
$97$	−16.6658	−	16.6658i	−0.171812	−	0.171812i	0.615963	−	0.787775i	$-0.288767\pi$
$97$	−16.6658	−	16.6658i	−0.171812	−	0.171812i	−0.787775	+	0.615963i	$0.788767\pi$
$98$	−25.6079	+	41.7760i	−0.261305	+	0.426286i
$99$	−12.7279	+	124.479i	−0.128565	+	1.25736i
$100$	67.2250	−	33.2536i	0.672250	−	0.332536i
$101$	113.114			1.11994			0.559968	−	0.828514i	$-0.310813\pi$
$101$	113.114			1.11994			0.559968	+	0.828514i	$0.310813\pi$
$102$	−1.05099	+	20.6109i	−0.0103038	+	0.202068i
$103$	−16.1826	+	16.1826i	−0.157113	+	0.157113i	−0.781286	−	0.624173i	$-0.785436\pi$
$103$	−16.1826	+	16.1826i	−0.157113	+	0.157113i	0.624173	+	0.781286i	$0.285436\pi$
$104$			144.836i			1.39265i
$105$	−30.6764	−	100.419i	−0.292156	−	0.956371i
$106$	−68.3095			−0.644429
$107$	139.010	+	139.010i	1.29916	+	1.29916i	0.928945	+	0.370218i	$0.120717\pi$
$107$	139.010	+	139.010i	1.29916	+	1.29916i	0.370218	+	0.928945i	$0.379283\pi$
$108$	−80.0557	−	12.3322i	−0.741257	−	0.114187i
$109$		−	3.01429i		−	0.0276540i	−0.999904	−	0.0138270i	$-0.995599\pi$
$109$		−	3.01429i		−	0.0276540i	0.999904	−	0.0138270i	$-0.00440141\pi$
$110$	67.6897	−	15.8265i	0.615361	−	0.143877i
$111$	−18.5020	−	20.4902i	−0.166684	−	0.184597i
$112$	−21.6701	+	27.4847i	−0.193483	+	0.245399i
$113$	−80.1118	+	80.1118i	−0.708954	+	0.708954i	−0.966315	−	0.257361i	$-0.917147\pi$
$113$	−80.1118	+	80.1118i	−0.708954	+	0.708954i	0.257361	+	0.966315i	$0.417147\pi$
$114$	−48.4318	+	43.7321i	−0.424840	+	0.383615i
$115$	12.2065	−	2.85400i	0.106144	−	0.0248174i
$116$		−	84.1356i		−	0.725307i
$117$	−144.387	+	117.599i	−1.23408	+	1.00512i
$118$	−20.9776	+	20.9776i	−0.177776	+	0.177776i
$119$	5.65685	+	47.8212i	0.0475366	+	0.401859i
$120$	18.6675	+	103.327i	0.155562	+	0.861061i
$121$	−72.2952			−0.597481
$122$	14.8999	−	14.8999i	0.122131	−	0.122131i
$123$	4.08209	−	80.0535i	0.0331877	−	0.650842i
$124$	51.7417			0.417272
$125$	12.0248	−	124.420i	0.0961984	−	0.995362i
$126$	62.9921	−	0.998435i	0.499937	−	0.00792409i
$127$	−71.6476	+	71.6476i	−0.564154	+	0.564154i	−0.930485	−	0.366330i	$-0.880614\pi$
$127$	−71.6476	+	71.6476i	−0.564154	+	0.564154i	0.366330	+	0.930485i	$0.380614\pi$
$128$	84.1457	−	84.1457i	0.657388	−	0.657388i
$129$	−104.401	+	94.2699i	−0.809306	+	0.730775i
$130$	87.8869	+	54.5774i	0.676053	+	0.419826i
$131$	79.4683			0.606629			0.303314	−	0.952891i	$-0.401907\pi$
$131$	79.4683			0.606629			0.303314	+	0.952891i	$0.401907\pi$
$132$	6.37223	−	124.965i	0.0482745	−	0.946706i
$133$	−94.2712	+	119.566i	−0.708806	+	0.898996i
$134$	45.9316			0.342773
$135$	−87.8499	+	102.506i	−0.650740	+	0.759301i
$136$		−	48.1546i		−	0.354078i
$137$	−7.42967	−	7.42967i	−0.0542312	−	0.0542312i	0.679471	−	0.733702i	$-0.262209\pi$
$137$	−7.42967	−	7.42967i	−0.0542312	−	0.0542312i	−0.733702	+	0.679471i	$0.762209\pi$
$138$	−0.383035	+	7.51167i	−0.00277562	+	0.0544324i
$139$	179.589			1.29201			0.646003	−	0.763335i	$-0.276439\pi$
$139$	179.589			1.29201			0.646003	+	0.763335i	$0.276439\pi$
$140$	35.7505	+	98.7264i	0.255361	+	0.705189i
$141$	52.7881	+	58.4609i	0.374384	+	0.414616i
$142$	−11.3381	+	11.3381i	−0.0798457	+	0.0798457i
$143$	−203.411	−	203.411i	−1.42245	−	1.42245i
$144$	44.7666	+	4.57738i	0.310879	+	0.0317874i
$145$	−119.125	−	73.9763i	−0.821554	−	0.510181i
$146$	−81.1188			−0.555609
$147$	144.504	−	26.9739i	0.983021	−	0.183496i
$148$	19.5214	+	19.5214i	0.131902	+	0.131902i
$149$	−24.7386			−0.166031			−0.0830155	−	0.996548i	$-0.526455\pi$
$149$	−24.7386			−0.166031			−0.0830155	+	0.996548i	$0.526455\pi$
$150$	69.7336	+	27.6085i	0.464890	+	0.184057i
$151$	−163.324			−1.08161			−0.540807	−	0.841147i	$-0.681881\pi$
$151$	−163.324			−1.08161			−0.540807	+	0.841147i	$0.681881\pi$
$152$	107.664	−	107.664i	0.708317	−	0.708317i
$153$	48.0053	−	39.0989i	0.313760	−	0.255548i
$154$	11.4326	+	96.6476i	0.0742378	+	0.627582i
$155$	45.4939	−	73.2596i	0.293509	−	0.472643i
$156$	138.211	−	124.799i	0.885966	−	0.799995i
$157$	108.368	+	108.368i	0.690244	+	0.690244i	0.962285	−	0.272042i	$-0.0876988\pi$
$157$	108.368	+	108.368i	0.690244	+	0.690244i	−0.272042	+	0.962285i	$0.587699\pi$
$158$	−53.6004	+	53.6004i	−0.339243	+	0.339243i
$159$	137.339	+	152.098i	0.863766	+	0.956590i
$160$	−37.5655	−	160.667i	−0.234784	−	1.00417i
$161$	2.06165	+	17.4285i	0.0128053	+	0.108252i
$162$	−44.4987	−	67.6821i	−0.274684	−	0.417791i
$163$	38.8452	+	38.8452i	0.238314	+	0.238314i	0.816152	−	0.577837i	$-0.196103\pi$
$163$	38.8452	+	38.8452i	0.238314	+	0.238314i	−0.577837	+	0.816152i	$0.696103\pi$
$164$			80.1575i			0.488765i
$165$	−171.332	−	118.898i	−1.03838	−	0.720594i
$166$		−	73.4931i		−	0.442730i
$167$	−138.252	+	138.252i	−0.827855	+	0.827855i	−0.987220	−	0.159365i	$-0.949055\pi$
$167$	−138.252	+	138.252i	−0.827855	+	0.827855i	0.159365	+	0.987220i	$0.449055\pi$
$168$	−146.672	+	9.81182i	−0.873049	+	0.0584037i
$169$		−	259.112i		−	1.53321i
$170$	−29.2203	−	18.1457i	−0.171884	−	0.106739i
$171$	194.748	+	19.9129i	1.13888	+	0.116450i
$172$	99.4643	−	99.4643i	0.578281	−	0.578281i
$173$	26.9566	+	26.9566i	0.155818	+	0.155818i	0.780711	−	0.624893i	$-0.214857\pi$
$173$	26.9566	+	26.9566i	0.155818	+	0.155818i	−0.624893	+	0.780711i	$0.714857\pi$
$174$	62.4454	−	56.3859i	0.358882	−	0.324057i
$175$	171.218	+	36.1871i	0.978387	+	0.206784i
$176$			69.5153i			0.394973i
$177$	88.8848	+	4.53242i	0.502174	+	0.0256069i
$178$	−123.245	+	123.245i	−0.692386	+	0.692386i
$179$	−187.393			−1.04689			−0.523445	−	0.852059i	$-0.675354\pi$
$179$	−187.393			−1.04689			−0.523445	+	0.852059i	$0.675354\pi$
$180$	82.5157	−	106.846i	0.458420	−	0.593591i
$181$			179.581i			0.992158i	0.868277	+	0.496079i	$0.165227\pi$
$181$			179.581i			0.992158i	−0.868277	+	0.496079i	$0.834773\pi$
$182$	−89.6745	+	113.736i	−0.492717	+	0.624925i
$183$	−63.1331	−	3.21928i	−0.344990	−	0.0175917i
$184$		−	17.5500i		−	0.0953805i
$185$	44.8041	−	10.4756i	0.242184	−	0.0566250i
$186$	34.6762	+	38.4026i	0.186431	+	0.206466i
$187$	67.6294	+	67.6294i	0.361654	+	0.361654i
$188$	−55.6968	−	55.6968i	−0.296259	−	0.296259i
$189$	−128.871	−	138.251i	−0.681858	−	0.731485i
$190$	−24.7607	−	105.901i	−0.130320	−	0.557375i
$191$			107.063i			0.560538i	0.959922	+	0.280269i	$0.0904236\pi$
$191$			107.063i			0.560538i	−0.959922	+	0.280269i	$0.909576\pi$
$192$	38.9494	+	1.98611i	0.202861	+	0.0103443i
$193$	−81.6333	−	81.6333i	−0.422971	−	0.422971i	0.463255	−	0.886225i	$-0.346682\pi$
$193$	−81.6333	−	81.6333i	−0.422971	−	0.422971i	−0.886225	+	0.463255i	$0.846682\pi$
$194$			23.5689i			0.121489i
$195$	−55.1781	−	305.419i	−0.282964	−	1.56625i
$196$	−142.943	+	34.2979i	−0.729300	+	0.174989i
$197$	−165.702	−	165.702i	−0.841127	−	0.841127i	0.147878	−	0.989006i	$-0.452756\pi$
$197$	−165.702	−	165.702i	−0.841127	−	0.841127i	−0.989006	+	0.147878i	$0.952756\pi$
$198$	97.0196	−	79.0196i	0.489998	−	0.399089i
$199$	−220.037			−1.10571			−0.552857	−	0.833276i	$-0.686462\pi$
$199$	−220.037			−1.10571			−0.552857	+	0.833276i	$0.686462\pi$
$200$	−165.781	−	56.0500i	−0.828906	−	0.280250i
$201$	−92.3473	−	102.271i	−0.459439	−	0.508812i
$202$	−79.9833	−	79.9833i	−0.395957	−	0.395957i
$203$	121.548	−	154.163i	0.598760	−	0.759422i
$204$	−45.9518	+	41.4929i	−0.225254	+	0.203396i
$205$	113.493	+	70.4786i	0.553624	+	0.343798i
$206$	22.8856			0.111095
$207$	17.4956	−	14.2496i	0.0845197	−	0.0688388i
$208$	−73.1533	+	73.1533i	−0.351698	+	0.351698i
$209$			302.412i			1.44695i
$210$	−49.3154	+	92.6984i	−0.234835	+	0.441421i
$211$	276.590			1.31086			0.655428	−	0.755258i	$-0.272488\pi$
$211$	276.590			1.31086			0.655428	+	0.755258i	$0.272488\pi$
$212$	−144.906	−	144.906i	−0.683521	−	0.683521i
$213$	48.0411	+	2.44971i	0.225545	+	0.0115010i
$214$		−	196.590i		−	0.918647i
$215$	−53.3747	−	228.283i	−0.248255	−	1.06178i
$216$	111.738	+	152.432i	0.517306	+	0.705705i
$217$	94.8069	+	74.7497i	0.436898	+	0.344469i
$218$	−2.13142	+	2.13142i	−0.00977717	+	0.00977717i
$219$	163.092	+	180.619i	0.744715	+	0.824744i
$220$	177.165	+	110.019i	0.805294	+	0.500084i
$221$			142.337i			0.644060i
$222$	−1.40593	+	27.5717i	−0.00633304	+	0.124197i
$223$	173.529	−	173.529i	0.778155	−	0.778155i	−0.201362	−	0.979517i	$-0.564537\pi$
$223$	173.529	−	173.529i	0.778155	−	0.778155i	0.979517	+	0.201362i	$0.0645368\pi$
$224$	229.401	−	27.1362i	1.02411	−	0.121144i
$225$	−78.7290	−	210.777i	−0.349907	−	0.936785i
$226$	113.295			0.501306
$227$	−191.389	+	191.389i	−0.843123	+	0.843123i	−0.989264	−	0.146140i	$-0.953315\pi$
$227$	−191.389	+	191.389i	−0.843123	+	0.843123i	0.146140	+	0.989264i	$0.453315\pi$
$228$	−195.509	−	9.96941i	−0.857496	−	0.0437255i
$229$	123.490			0.539259			0.269630	−	0.962964i	$-0.413099\pi$
$229$	123.490			0.539259			0.269630	+	0.962964i	$0.413099\pi$
$230$	−10.6494	−	6.61323i	−0.0463017	−	0.0287532i
$231$	192.210	−	219.770i	0.832076	−	0.951383i
$232$	−138.817	+	138.817i	−0.598348	+	0.598348i
$233$	89.8918	−	89.8918i	0.385802	−	0.385802i	−0.487385	−	0.873187i	$-0.662049\pi$
$233$	89.8918	−	89.8918i	0.385802	−	0.385802i	0.873187	+	0.487385i	$0.162049\pi$
$234$	185.252	+	18.9420i	0.791675	+	0.0809487i
$235$	−127.831	+	29.8881i	−0.543961	+	0.127183i
$236$	−89.0003			−0.377120
$237$	227.112	+	11.5809i	0.958279	+	0.0488646i
$238$	29.8147	−	37.8147i	0.125272	−	0.158885i
$239$	49.2786			0.206187			0.103093	−	0.994672i	$-0.467126\pi$
$239$	49.2786			0.206187			0.103093	+	0.994672i	$0.467126\pi$
$240$	−42.7597	+	61.6167i	−0.178165	+	0.256736i
$241$		−	421.664i		−	1.74964i	−0.484445	−	0.874822i	$-0.660979\pi$
$241$		−	421.664i		−	1.74964i	0.484445	−	0.874822i	$-0.339021\pi$
$242$	51.1204	+	51.1204i	0.211242	+	0.211242i
$243$	−61.2344	+	235.158i	−0.251993	+	0.967729i
$244$	63.2151			0.259078
$245$	−77.1212	+	232.545i	−0.314780	+	0.949165i
$246$	−59.4929	+	53.7199i	−0.241841	+	0.218374i
$247$	−318.238	+	318.238i	−1.28841	+	1.28841i
$248$	−85.3694	−	85.3694i	−0.344231	−	0.344231i
$249$	−163.640	+	147.761i	−0.657187	+	0.593417i
$250$	−96.4812	+	79.4756i	−0.385925	+	0.317902i
$251$	−345.514			−1.37655			−0.688274	−	0.725450i	$-0.741631\pi$
$251$	−345.514			−1.37655			−0.688274	+	0.725450i	$0.741631\pi$
$252$	135.744	+	131.508i	0.538668	+	0.521859i
$253$	24.6476	+	24.6476i	0.0974214	+	0.0974214i
$254$	101.325			0.398917
$255$	18.3454	+	101.545i	0.0719428	+	0.398214i
$256$	−171.000			−0.667969
$257$	216.568	−	216.568i	0.842676	−	0.842676i	−0.146530	−	0.989206i	$-0.546810\pi$
$257$	216.568	−	216.568i	0.842676	−	0.842676i	0.989206	+	0.146530i	$0.0468104\pi$
$258$	140.481	+	7.16342i	0.544501	+	0.0277652i
$259$	7.56729	+	63.9714i	0.0292173	+	0.246994i
$260$	70.6602	+	302.212i	0.271770	+	1.16236i
$261$	−251.098	−	25.6747i	−0.962060	−	0.0983705i
$262$	−56.1926	−	56.1926i	−0.214476	−	0.214476i
$263$	−196.555	+	196.555i	−0.747359	+	0.747359i	−0.973982	−	0.226623i	$-0.927231\pi$
$263$	−196.555	+	196.555i	−0.747359	+	0.747359i	0.226623	+	0.973982i	$0.427231\pi$
$264$	−216.696	+	195.668i	−0.820817	+	0.741168i
$265$	−332.578	+	77.7599i	−1.25501	+	0.293434i
$266$	151.206	−	17.8864i	0.568444	−	0.0672422i
$267$	522.204	+	26.6283i	1.95582	+	0.0997313i
$268$	97.4357	+	97.4357i	0.363566	+	0.363566i
$269$		−	349.961i		−	1.30097i	−0.759519	−	0.650485i	$-0.774566\pi$
$269$		−	349.961i		−	1.30097i	0.759519	−	0.650485i	$-0.225434\pi$
$270$	134.602	−	10.3632i	0.498525	−	0.0383822i
$271$			137.978i			0.509143i	0.967054	+	0.254572i	$0.0819344\pi$
$271$			137.978i			0.509143i	−0.967054	+	0.254572i	$0.918066\pi$
$272$	24.3218	−	24.3218i	0.0894182	−	0.0894182i
$273$	433.539	−	29.0021i	1.58806	−	0.106235i
$274$			10.5071i			0.0383472i
$275$	311.545	−	154.109i	1.13289	−	0.560396i
$276$	−16.7472	+	15.1221i	−0.0606783	+	0.0547903i
$277$	132.817	−	132.817i	0.479483	−	0.479483i	−0.425484	−	0.904966i	$-0.639896\pi$
$277$	132.817	−	132.817i	0.479483	−	0.479483i	0.904966	+	0.425484i	$0.139896\pi$
$278$	−126.989	−	126.989i	−0.456793	−	0.456793i
$279$	15.7894	−	154.420i	0.0565929	−	0.553476i
$280$	103.905	−	221.876i	0.371089	−	0.792413i
$281$		−	142.098i		−	0.505687i	−0.967507	−	0.252844i	$-0.918634\pi$
$281$		−	142.098i		−	0.505687i	0.967507	−	0.252844i	$-0.0813658\pi$
$282$	4.01128	−	78.6649i	0.0142244	−	0.278954i
$283$	−120.235	+	120.235i	−0.424858	+	0.424858i	−0.886873	−	0.462014i	$-0.847127\pi$
$283$	−120.235	+	120.235i	−0.424858	+	0.424858i	0.462014	+	0.886873i	$0.347127\pi$
$284$	−48.1035			−0.169378
$285$	−186.017	+	268.050i	−0.652691	+	0.940528i
$286$			287.666i			1.00583i
$287$	−115.801	+	146.874i	−0.403489	+	0.511755i
$288$	−187.559	−	230.284i	−0.651247	−	0.799596i
$289$			241.676i			0.836250i
$290$	31.9252	+	136.543i	0.110087	+	0.470840i
$291$	52.4786	−	47.3863i	0.180339	−	0.162839i
$292$	−172.079	−	172.079i	−0.589312	−	0.589312i
$293$	377.885	+	377.885i	1.28971	+	1.28971i	0.934962	+	0.354747i	$0.115433\pi$
$293$	377.885	+	377.885i	1.28971	+	1.28971i	0.354747	+	0.934962i	$0.384567\pi$
$294$	−121.253	−	83.1064i	−0.412426	−	0.282675i
$295$	−78.2536	+	126.013i	−0.265266	+	0.427163i
$296$		−	64.4174i		−	0.217626i
$297$	−371.007	−	57.1518i	−1.24918	−	0.192430i
$298$	17.4929	+	17.4929i	0.0587009	+	0.0587009i
$299$			51.8750i			0.173495i
$300$	89.3608	+	206.494i	0.297869	+	0.688312i
$301$	325.943	−	38.5564i	1.08287	−	0.128094i
$302$	115.487	+	115.487i	0.382409	+	0.382409i
$303$	−17.2812	+	338.900i	−0.0570337	+	1.11848i
$304$	108.757			0.357754
$305$	55.5820	−	89.5046i	0.182236	−	0.293458i
$306$	−61.5919	−	6.29777i	−0.201281	−	0.0205809i
$307$	−94.6590	−	94.6590i	−0.308335	−	0.308335i	0.535928	−	0.844264i	$-0.319962\pi$
$307$	−94.6590	−	94.6590i	−0.308335	−	0.308335i	−0.844264	+	0.535928i	$0.819962\pi$
$308$	−180.768	+	229.273i	−0.586910	+	0.744392i
$309$	−46.0125	−	50.9571i	−0.148908	−	0.164910i
$310$	−83.9714	+	19.6333i	−0.270876	+	0.0633333i
$311$	221.432			0.712001			0.356000	−	0.934486i	$-0.384140\pi$
$311$	221.432			0.712001			0.356000	+	0.934486i	$0.384140\pi$
$312$	−433.944	−	22.1277i	−1.39085	−	0.0709221i
$313$	225.950	−	225.950i	0.721885	−	0.721885i	−0.247104	−	0.968989i	$-0.579479\pi$
$313$	225.950	−	225.950i	0.721885	−	0.721885i	0.968989	+	0.247104i	$0.0794790\pi$
$314$		−	153.256i		−	0.488076i
$315$	305.553	−	76.5679i	0.970008	−	0.243073i
$316$	−227.407			−0.719643
$317$	96.2271	+	96.2271i	0.303556	+	0.303556i	0.842403	−	0.538848i	$-0.181140\pi$
$317$	96.2271	+	96.2271i	0.303556	+	0.303556i	−0.538848	+	0.842403i	$0.681140\pi$
$318$	10.4362	−	204.663i	0.0328181	−	0.643593i
$319$		−	389.914i		−	1.22230i
$320$	−34.2908	+	55.2190i	−0.107159	+	0.172559i
$321$	−437.728	+	395.253i	−1.36364	+	1.23132i
$322$	10.8660	−	13.7816i	0.0337453	−	0.0428000i
$323$	105.807	−	105.807i	0.327575	−	0.327575i
$324$	49.1793	−	237.971i	0.151788	−	0.734480i
$325$	490.022	+	165.675i	1.50776	+	0.509768i
$326$		−	54.9355i		−	0.168514i
$327$	9.03113	+	0.460516i	0.0276181	+	0.00140830i
$328$	132.253	−	132.253i	0.403211	−	0.403211i
$329$	−21.5903	−	182.517i	−0.0656240	−	0.554764i
$330$	37.0765	+	205.224i	0.112353	+	0.621890i
$331$	175.014			0.528744			0.264372	−	0.964421i	$-0.414835\pi$
$331$	175.014			0.528744			0.264372	+	0.964421i	$0.414835\pi$
$332$	155.902	−	155.902i	0.469586	−	0.469586i
$333$	64.2177	−	52.3034i	0.192846	−	0.157067i
$334$	195.517			0.585382
$335$	223.627	−	52.2861i	0.667543	−	0.156078i
$336$	−79.0364	−	69.1249i	−0.235227	−	0.205729i
$337$	109.576	−	109.576i	0.325152	−	0.325152i	−0.525588	−	0.850739i	$-0.676155\pi$
$337$	109.576	−	109.576i	0.325152	−	0.325152i	0.850739	+	0.525588i	$0.176155\pi$
$338$	−183.220	+	183.220i	−0.542070	+	0.542070i
$339$	−227.784	−	252.263i	−0.671930	−	0.744138i
$340$	−23.4929	−	100.479i	−0.0690966	−	0.295525i
$341$	239.789			0.703194
$342$	−123.627	−	151.788i	−0.361482	−	0.443825i
$343$	−311.465	−	143.661i	−0.908061	−	0.418837i
$344$	−328.215			−0.954114
$345$	6.68601	+	37.0081i	0.0193797	+	0.107270i
$346$		−	38.1223i		−	0.110180i
$347$	−268.600	−	268.600i	−0.774062	−	0.774062i	0.204752	−	0.978814i	$-0.434361\pi$
$347$	−268.600	−	268.600i	−0.774062	−	0.774062i	−0.978814	+	0.204752i	$0.934361\pi$
$348$	252.079	+	12.8540i	0.724366	+	0.0369369i
$349$	−304.193			−0.871613			−0.435807	−	0.900040i	$-0.643537\pi$
$349$	−304.193			−0.871613			−0.435807	+	0.900040i	$0.643537\pi$
$350$	−95.4810	−	146.657i	−0.272803	−	0.419021i
$351$	−330.280	−	450.565i	−0.940968	−	1.28366i
$352$	324.421	−	324.421i	0.921652	−	0.921652i
$353$	240.264	+	240.264i	0.680635	+	0.680635i	0.960143	−	0.279509i	$-0.0901715\pi$
$353$	240.264	+	240.264i	0.680635	+	0.680635i	−0.279509	+	0.960143i	$0.590172\pi$
$354$	−59.6461	−	66.0559i	−0.168492	−	0.186599i
$355$	−42.2950	+	68.1084i	−0.119141	+	0.191855i
$356$	−522.883			−1.46877
$357$	−144.142	+	9.64254i	−0.403758	+	0.0270099i
$358$	132.507	+	132.507i	0.370132	+	0.370132i
$359$	−161.739			−0.450526			−0.225263	−	0.974298i	$-0.572324\pi$
$359$	−161.739			−0.450526			−0.225263	+	0.974298i	$0.572324\pi$
$360$	−312.432	+	40.1437i	−0.867865	+	0.111510i
$361$	112.126			0.310599
$362$	126.983	−	126.983i	0.350781	−	0.350781i
$363$	11.0451	−	216.604i	0.0304272	−	0.596706i
$364$	−431.500	+	51.0429i	−1.18544	+	0.140228i
$365$	−394.943	+	92.3414i	−1.08203	+	0.252990i
$366$	42.3655	+	46.9182i	0.115753	+	0.128192i
$367$	101.051	+	101.051i	0.275343	+	0.275343i	0.831247	−	0.555904i	$-0.187628\pi$
$367$	101.051	+	101.051i	0.275343	+	0.275343i	−0.555904	+	0.831247i	$0.687628\pi$
$368$	8.86409	−	8.86409i	0.0240872	−	0.0240872i
$369$	239.225	+	24.4608i	0.648307	+	0.0662893i
$370$	−39.0887	−	24.2739i	−0.105645	−	0.0656051i
$371$	−56.1715	−	474.856i	−0.151406	−	1.27993i
$372$	−7.90497	+	155.024i	−0.0212499	+	0.416730i
$373$	−369.464	−	369.464i	−0.990521	−	0.990521i	0.00943464	−	0.999955i	$-0.496997\pi$
$373$	−369.464	−	369.464i	−0.990521	−	0.990521i	−0.999955	+	0.00943464i	$0.996997\pi$
$374$		−	95.6424i		−	0.255728i
$375$	370.939	+	55.0362i	0.989172	+	0.146763i
$376$			183.790i			0.488803i
$377$	410.320	−	410.320i	1.08838	−	1.08838i
$378$	−6.63236	+	188.884i	−0.0175459	+	0.499692i
$379$			261.209i			0.689207i	0.938748	+	0.344604i	$0.111987\pi$
$379$			261.209i			0.689207i	−0.938748	+	0.344604i	$0.888013\pi$
$380$	172.125	−	277.176i	0.452960	−	0.729410i
$381$	−203.718	−	225.610i	−0.534692	−	0.592152i
$382$	75.7048	−	75.7048i	0.198180	−	0.198180i
$383$	163.813	+	163.813i	0.427710	+	0.427710i	0.887847	−	0.460138i	$-0.152200\pi$
$383$	163.813	+	163.813i	0.427710	+	0.427710i	−0.460138	+	0.887847i	$0.652200\pi$
$384$	239.254	+	264.965i	0.623057	+	0.690013i
$385$	165.680	+	457.533i	0.430339	+	1.18840i
$386$			115.447i			0.299085i
$387$	−266.493	−	327.197i	−0.688612	−	0.845472i
$388$	−49.9973	+	49.9973i	−0.128859	+	0.128859i
$389$	401.000			1.03085			0.515425	−	0.856935i	$-0.327634\pi$
$389$	401.000			1.03085			0.515425	+	0.856935i	$0.327634\pi$
$390$	−176.947	+	254.980i	−0.453710	+	0.653796i
$391$		−	17.2472i		−	0.0441105i
$392$	292.432	+	179.255i	0.746001	+	0.457283i
$393$	−12.1410	+	238.096i	−0.0308931	+	0.605841i
$394$			234.338i			0.594767i
$395$	−199.948	+	321.980i	−0.506197	+	0.815138i
$396$	373.436	+	38.1838i	0.943019	+	0.0964237i
$397$	−304.082	−	304.082i	−0.765950	−	0.765950i	0.211440	−	0.977391i	$-0.432185\pi$
$397$	−304.082	−	304.082i	−0.765950	−	0.765950i	−0.977391	+	0.211440i	$0.932185\pi$
$398$	155.590	+	155.590i	0.390929	+	0.390929i
$399$	−343.831	−	300.714i	−0.861733	−	0.753668i
$400$	−55.4226	−	112.042i	−0.138557	−	0.280104i
$401$			582.912i			1.45365i	0.686825	+	0.726823i	$0.259004\pi$
$401$			582.912i			1.45365i	−0.686825	+	0.726823i	$0.740996\pi$
$402$	−7.01732	+	137.616i	−0.0174560	+	0.342329i
$403$	252.338	+	252.338i	0.626149	+	0.626149i
$404$		−	339.341i		−	0.839952i
$405$	−293.696	−	278.868i	−0.725176	−	0.688563i
$406$	−194.957	+	23.0618i	−0.480190	+	0.0568025i
$407$	90.4693	+	90.4693i	0.222283	+	0.222283i
$408$	144.276	+	7.35694i	0.353619	+	0.0180317i
$409$	−344.830			−0.843104			−0.421552	−	0.906804i	$-0.638515\pi$
$409$	−344.830			−0.843104			−0.421552	+	0.906804i	$0.638515\pi$
$410$	−30.4157	−	130.087i	−0.0741846	−	0.317286i
$411$	23.3952	−	21.1250i	0.0569226	−	0.0513991i
$412$	48.5478	+	48.5478i	0.117834	+	0.117834i
$413$	−163.076	−	128.576i	−0.394858	−	0.311323i
$414$	−22.4473	−	2.29523i	−0.0542204	−	0.00554403i
$415$	−83.6607	−	357.815i	−0.201592	−	0.862206i
$416$	682.799			1.64134
$417$	−27.4372	+	538.068i	−0.0657965	+	1.29033i
$418$	213.838	−	213.838i	0.511573	−	0.511573i
$419$			343.927i			0.820828i	0.911899	+	0.410414i	$0.134616\pi$
$419$			343.927i			0.820828i	−0.911899	+	0.410414i	$0.865384\pi$
$420$	−301.257	+	92.0291i	−0.717278	+	0.219117i
$421$	14.6762			0.0348603			0.0174302	−	0.999848i	$-0.494452\pi$
$421$	14.6762			0.0348603			0.0174302	+	0.999848i	$0.494452\pi$
$422$	−195.579	−	195.579i	−0.463457	−	0.463457i
$423$	−183.220	+	149.227i	−0.433144	+	0.352783i
$424$			478.167i			1.12775i
$425$	−162.921	−	55.0830i	−0.383343	−	0.129607i
$426$	−32.2379	−	35.7024i	−0.0756759	−	0.0838084i
$427$	115.830	+	91.3251i	0.271264	+	0.213876i
$428$	417.031	−	417.031i	0.974372	−	0.974372i
$429$	640.518	−	578.364i	1.49305	−	1.34817i
$430$	−123.679	+	199.162i	−0.287625	+	0.463167i
$431$			443.066i			1.02800i	0.857791	+	0.513998i	$0.171836\pi$
$431$			443.066i			1.02800i	−0.857791	+	0.513998i	$0.828164\pi$
$432$	−20.5537	+	133.426i	−0.0475779	+	0.308857i
$433$	487.352	−	487.352i	1.12553	−	1.12553i	0.134629	−	0.990896i	$-0.457016\pi$
$433$	487.352	−	487.352i	1.12553	−	1.12553i	0.990896	−	0.134629i	$-0.0429843\pi$
$434$	−14.1825	−	119.895i	−0.0326787	−	0.276255i
$435$	239.841	−	345.610i	0.551358	−	0.794506i
$436$	−9.04287			−0.0207405
$437$	38.5614	−	38.5614i	0.0882412	−	0.0882412i
$438$	12.3931	−	243.041i	0.0282948	−	0.554888i
$439$	−151.065			−0.344111			−0.172056	−	0.985087i	$-0.555041\pi$
$439$	−151.065			−0.344111			−0.172056	+	0.985087i	$0.555041\pi$
$440$	−110.786	−	473.828i	−0.251785	−	1.07688i
$441$	58.7396	+	437.071i	0.133196	+	0.991090i
$442$	100.648	−	100.648i	0.227710	−	0.227710i
$443$	−188.010	+	188.010i	−0.424401	+	0.424401i	−0.886716	−	0.462315i	$-0.847019\pi$
$443$	−188.010	+	188.010i	−0.424401	+	0.424401i	0.462315	+	0.886716i	$0.347019\pi$
$444$	−61.4707	+	55.5059i	−0.138448	+	0.125013i
$445$	−459.745	+	740.336i	−1.03314	+	1.66368i
$446$	−245.406			−0.550239
$447$	3.77951	−	74.1196i	0.00845528	−	0.165816i
$448$	−71.4602	−	56.3422i	−0.159509	−	0.125764i
$449$	397.613			0.885552			0.442776	−	0.896632i	$-0.353994\pi$
$449$	397.613			0.885552			0.442776	+	0.896632i	$0.353994\pi$
$450$	−93.3717	+	204.711i	−0.207493	+	0.454914i
$451$			371.478i			0.823677i
$452$	240.335	+	240.335i	0.531716	+	0.531716i
$453$	24.9522	−	489.336i	0.0550821	−	1.08021i
$454$	270.665			0.596178
$455$	−307.126	+	655.828i	−0.675003	+	1.44138i
$456$	306.125	+	339.022i	0.671327	+	0.743470i
$457$	−66.2262	+	66.2262i	−0.144915	+	0.144915i	−0.775842	−	0.630927i	$-0.782675\pi$
$457$	−66.2262	+	66.2262i	−0.144915	+	0.144915i	0.630927	+	0.775842i	$0.282675\pi$
$458$	−87.3209	−	87.3209i	−0.190657	−	0.190657i
$459$	109.810	+	149.802i	0.239238	+	0.326367i
$460$	−8.56200	−	36.6195i	−0.0186130	−	0.0796077i
$461$	191.545			0.415499			0.207750	−	0.978182i	$-0.433386\pi$
$461$	191.545			0.415499			0.207750	+	0.978182i	$0.433386\pi$
$462$	−291.313	+	19.4878i	−0.630548	+	0.0421813i
$463$	42.9857	+	42.9857i	0.0928417	+	0.0928417i	0.752002	−	0.659161i	$-0.229088\pi$
$463$	42.9857	+	42.9857i	0.0928417	+	0.0928417i	−0.659161	+	0.752002i	$0.729088\pi$
$464$	−140.226			−0.302211
$465$	212.543	+	147.497i	0.457082	+	0.317198i
$466$	−127.126			−0.272803
$467$	−252.836	+	252.836i	−0.541405	+	0.541405i	−0.923941	−	0.382536i	$-0.875051\pi$
$467$	−252.836	+	252.836i	−0.541405	+	0.541405i	0.382536	+	0.923941i	$0.375051\pi$
$468$	352.797	+	433.161i	0.753839	+	0.925557i
$469$	37.7700	+	319.295i	0.0805331	+	0.680800i
$470$	111.524	+	69.2561i	0.237286	+	0.147353i
$471$	−341.239	+	308.127i	−0.724500	+	0.654197i
$472$	146.843	+	146.843i	0.311108	+	0.311108i
$473$	460.953	−	460.953i	0.974530	−	0.974530i
$474$	−152.404	−	168.781i	−0.321526	−	0.356079i
$475$	−241.105	−	487.414i	−0.507589	−	1.02613i
$476$	143.464	−	16.9706i	0.301394	−	0.0356524i
$477$	−476.684	+	388.245i	−0.999337	+	0.813930i
$478$	−34.8452	−	34.8452i	−0.0728980	−	0.0728980i
$479$			91.5191i			0.191063i	0.995426	+	0.0955314i	$0.0304550\pi$
$479$			91.5191i			0.191063i	−0.995426	+	0.0955314i	$0.969545\pi$
$480$	487.114	−	88.0038i	1.01482	−	0.183341i
$481$			190.408i			0.395858i
$482$	−298.161	+	298.161i	−0.618592	+	0.618592i
$483$	−52.5326	+	3.51424i	−0.108763	+	0.00727585i
$484$			216.886i			0.448111i
$485$	26.8296	+	114.750i	0.0553189	+	0.236598i
$486$	209.581	−	122.983i	0.431237	−	0.253051i
$487$	252.690	−	252.690i	0.518872	−	0.518872i	−0.398358	−	0.917230i	$-0.630420\pi$
$487$	252.690	−	252.690i	0.518872	−	0.518872i	0.917230	+	0.398358i	$0.130420\pi$
$488$	−104.300	−	104.300i	−0.213729	−	0.213729i
$489$	−122.319	+	110.450i	−0.250141	+	0.225869i
$490$	218.967	−	109.901i	0.446872	−	0.224289i
$491$		−	518.117i		−	1.05523i	−0.849484	−	0.527614i	$-0.823087\pi$
$491$		−	518.117i		−	1.05523i	0.849484	−	0.527614i	$-0.176913\pi$
$492$	−240.161	−	12.2463i	−0.488131	−	0.0248908i
$493$	−136.422	+	136.422i	−0.276717	+	0.276717i
$494$	450.057			0.911046
$495$	382.407	−	495.164i	0.772539	−	1.00033i
$496$		−	86.2361i		−	0.173863i
$497$	−88.1406	−	69.4937i	−0.177345	−	0.139826i
$498$	220.193	+	11.2281i	0.442155	+	0.0225464i
$499$		−	217.267i		−	0.435404i	−0.976015	−	0.217702i	$-0.930144\pi$
$499$		−	217.267i		−	0.435404i	0.976015	−	0.217702i	$-0.0698561\pi$
$500$	−373.261	−	36.0744i	−0.746522	−	0.0721488i
$501$	−393.095	−	435.339i	−0.784621	−	0.868940i
$502$	244.315	+	244.315i	0.486684	+	0.486684i
$503$	12.7399	+	12.7399i	0.0253279	+	0.0253279i	0.719657	−	0.694329i	$-0.244299\pi$
$503$	12.7399	+	12.7399i	0.0253279	+	0.0253279i	−0.694329	+	0.719657i	$0.744299\pi$
$504$	−6.98904	−	440.945i	−0.0138671	−	0.874890i
$505$	−480.463	−	298.365i	−0.951412	−	0.590823i
$506$		−	34.8570i		−	0.0688873i
$507$	776.327	+	39.5865i	1.53122	+	0.0780798i
$508$	214.943	+	214.943i	0.423116	+	0.423116i
$509$			611.593i			1.20156i	0.799415	+	0.600779i	$0.205143\pi$
$509$			611.593i			1.20156i	−0.799415	+	0.600779i	$0.794857\pi$
$510$	58.8307	−	84.7750i	0.115354	−	0.166226i
$511$	−66.7048	−	563.900i	−0.130538	−	1.10352i
$512$	−215.668	−	215.668i	−0.421226	−	0.421226i
$513$	−89.4144	+	580.443i	−0.174297	+	1.13147i
$514$	−306.273			−0.595862
$515$	111.423	−	26.0518i	0.216356	−	0.0505860i
$516$	282.810	+	313.202i	0.548081	+	0.606980i
$517$	−258.119	−	258.119i	−0.499262	−	0.499262i
$518$	39.8837	−	50.5855i	0.0769956	−	0.0976554i
$519$	−84.8831	+	76.6464i	−0.163551	+	0.147681i
$520$	382.042	−	615.208i	0.734695	−	1.18309i
$521$	−692.510			−1.32919			−0.664597	−	0.747202i	$-0.731397\pi$
$521$	−692.510			−1.32919			−0.664597	+	0.747202i	$0.731397\pi$
$522$	159.398	+	195.708i	0.305360	+	0.374919i
$523$	−583.903	+	583.903i	−1.11645	+	1.11645i	−0.124191	+	0.992258i	$0.539634\pi$
$523$	−583.903	+	583.903i	−1.11645	+	1.11645i	−0.992258	+	0.124191i	$0.960366\pi$
$524$		−	238.405i		−	0.454971i
$525$	−134.579	+	507.458i	−0.256340	+	0.966587i
$526$	277.971			0.528463
$527$	−83.8965	−	83.8965i	−0.159196	−	0.159196i
$528$	−208.275	−	10.6204i	−0.394461	−	0.0201144i
$529$			522.714i			0.988118i
$530$	290.153	+	180.184i	0.547458	+	0.339969i
$531$	−27.1592	+	265.616i	−0.0511473	+	0.500218i
$532$	358.699	+	282.814i	0.674247	+	0.531604i
$533$	−390.919	+	390.919i	−0.733431	+	0.733431i
$534$	−350.425	−	388.083i	−0.656227	−	0.726748i
$535$	−223.788	−	957.138i	−0.418296	−	1.78904i
$536$		−	321.521i		−	0.599853i
$537$	28.6295	−	561.451i	0.0533138	−	1.04553i
$538$	−247.460	+	247.460i	−0.459963	+	0.459963i
$539$	−662.448	+	158.948i	−1.22903	+	0.294895i
$540$	307.517	+	263.550i	0.569476	+	0.488055i
$541$	314.562			0.581445			0.290723	−	0.956807i	$-0.406104\pi$
$541$	314.562			0.581445			0.290723	+	0.956807i	$0.406104\pi$
$542$	97.5650	−	97.5650i	0.180009	−	0.180009i
$543$	−538.043	−	27.4359i	−0.990871	−	0.0505265i
$544$	−227.015			−0.417306
$545$	−7.95095	+	12.8035i	−0.0145889	+	0.0234927i
$546$	−327.066	−	286.051i	−0.599022	−	0.523903i
$547$	223.888	−	223.888i	0.409302	−	0.409302i	−0.472193	−	0.881495i	$-0.656538\pi$
$547$	223.888	−	223.888i	0.409302	−	0.409302i	0.881495	+	0.472193i	$0.156538\pi$
$548$	−22.2890	+	22.2890i	−0.0406734	+	0.0406734i
$549$	19.2906	−	188.662i	0.0351378	−	0.343646i
$550$	−329.267	−	111.324i	−0.598667	−	0.202407i
$551$	−610.024			−1.10712
$552$	52.5817	+	2.68125i	0.0952567	+	0.00485733i
$553$	−416.681	−	328.529i	−0.753492	−	0.594084i
$554$	−187.831			−0.339045
$555$	24.5411	+	135.838i	0.0442181	+	0.244754i
$556$		−	538.767i		−	0.969005i
$557$	245.854	+	245.854i	0.441390	+	0.441390i	0.892479	−	0.451089i	$-0.148964\pi$
$557$	245.854	+	245.854i	0.441390	+	0.441390i	−0.451089	+	0.892479i	$0.648964\pi$
$558$	−120.356	+	98.0265i	−0.215692	+	0.175675i
$559$	970.151			1.73551
$560$	164.544	−	59.5841i	0.293829	−	0.106400i
$561$	−212.957	+	192.293i	−0.379603	+	0.342768i
$562$	−100.479	+	100.479i	−0.178787	+	0.178787i
$563$	−406.434	−	406.434i	−0.721907	−	0.721907i	0.247086	−	0.968993i	$-0.420527\pi$
$563$	−406.434	−	406.434i	−0.721907	−	0.721907i	−0.968993	+	0.247086i	$0.920527\pi$
$564$	175.383	−	158.364i	0.310962	−	0.280788i
$565$	551.600	−	128.969i	0.976283	−	0.228264i
$566$	170.038			0.300420
$567$	433.902	−	364.990i	0.765260	−	0.643721i
$568$	79.3667	+	79.3667i	0.139730	+	0.139730i
$569$	−690.156			−1.21293			−0.606464	−	0.795111i	$-0.707413\pi$
$569$	−690.156			−1.21293			−0.606464	+	0.795111i	$0.707413\pi$
$570$	321.074	−	58.0064i	0.563288	−	0.101766i
$571$	612.476			1.07264			0.536319	−	0.844015i	$-0.319814\pi$
$571$	612.476			1.07264			0.536319	+	0.844015i	$0.319814\pi$
$572$	−610.233	+	610.233i	−1.06684	+	1.06684i
$573$	−320.771	−	16.3568i	−0.559810	−	0.0285459i
$574$	185.739	−	21.9714i	0.323587	−	0.0382777i
$575$	−59.3768	−	20.0751i	−0.103264	−	0.0349131i
$576$	−11.9012	+	116.393i	−0.0206618	+	0.202071i
$577$	254.442	+	254.442i	0.440973	+	0.440973i	0.892339	−	0.451366i	$-0.149063\pi$
$577$	254.442	+	254.442i	0.440973	+	0.440973i	−0.451366	+	0.892339i	$0.649063\pi$
$578$	170.891	−	170.891i	0.295659	−	0.295659i
$579$	257.054	−	232.110i	0.443962	−	0.400882i
$580$	−221.929	+	357.376i	−0.382636	+	0.616165i
$581$	510.890	−	60.4341i	0.879329	−	0.104017i
$582$	−70.6151	−	3.60081i	−0.121332	−	0.00618695i
$583$	−671.548	−	671.548i	−1.15188	−	1.15188i
$584$			567.832i			0.972315i
$585$	923.497	−	118.658i	1.57863	−	0.202835i
$586$		−	534.410i		−	0.911962i
$587$	195.495	−	195.495i	0.333040	−	0.333040i	−0.520700	−	0.853740i	$-0.674329\pi$
$587$	195.495	−	195.495i	0.333040	−	0.333040i	0.853740	+	0.520700i	$0.174329\pi$
$588$	−80.9216	−	433.512i	−0.137622	−	0.737265i
$589$		−	375.152i		−	0.636931i
$590$	144.438	−	33.7711i	0.244811	−	0.0572391i
$591$	521.777	−	471.146i	0.882871	−	0.797201i
$592$	32.5357	−	32.5357i	0.0549590	−	0.0549590i
$593$	181.904	+	181.904i	0.306751	+	0.306751i	0.843648	−	0.536897i	$-0.180403\pi$
$593$	181.904	+	181.904i	0.306751	+	0.306751i	−0.536897	+	0.843648i	$0.680403\pi$
$594$	221.929	+	302.754i	0.373618	+	0.509686i
$595$	102.112	−	218.048i	0.171617	−	0.366466i
$596$			74.2159i			0.124523i
$597$	33.6167	−	659.255i	0.0563094	−	1.10428i
$598$	36.6812	−	36.6812i	0.0613397	−	0.0613397i
$599$	−376.201			−0.628048			−0.314024	−	0.949415i	$-0.601677\pi$
$599$	−376.201			−0.628048			−0.314024	+	0.949415i	$0.601677\pi$
$600$	193.259	−	488.135i	0.322099	−	0.813558i
$601$			1122.87i			1.86834i	0.356832	+	0.934169i	$0.383857\pi$
$601$			1122.87i			1.86834i	−0.356832	+	0.934169i	$0.616143\pi$
$602$	−257.740	−	203.213i	−0.428139	−	0.337563i
$603$	320.524	−	261.058i	0.531549	−	0.432931i
$604$			489.971i			0.811211i
$605$	307.083	+	190.697i	0.507574	+	0.315202i
$606$	251.858	−	227.419i	0.415608	−	0.375279i
$607$	127.880	+	127.880i	0.210675	+	0.210675i	0.804554	−	0.593879i	$-0.202404\pi$
$607$	127.880	+	127.880i	0.210675	+	0.210675i	−0.593879	+	0.804554i	$0.702404\pi$
$608$	−507.560	−	507.560i	−0.834803	−	0.834803i
$609$	443.318	+	387.724i	0.727944	+	0.636658i
$610$	−102.592	+	23.9869i	−0.168183	+	0.0393228i
$611$		−	543.253i		−	0.889122i
$612$	−117.297	−	144.016i	−0.191661	−	0.235320i
$613$	668.817	+	668.817i	1.09105	+	1.09105i	0.995416	+	0.0956388i	$0.0304894\pi$
$613$	668.817	+	668.817i	1.09105	+	1.09105i	0.0956388	+	0.995416i	$0.469511\pi$
$614$			133.868i			0.218026i
$615$	−228.501	+	329.269i	−0.371546	+	0.535397i
$616$	676.533	−	80.0283i	1.09827	−	0.129916i
$617$	416.614	+	416.614i	0.675225	+	0.675225i	0.958916	−	0.283691i	$-0.0915589\pi$
$617$	416.614	+	416.614i	0.675225	+	0.675225i	−0.283691	+	0.958916i	$0.591559\pi$
$618$	−3.49641	+	68.5679i	−0.00565763	+	0.110951i
$619$	1140.08			1.84180			0.920902	−	0.389794i	$-0.127454\pi$
$619$	1140.08			1.84180			0.920902	+	0.389794i	$0.127454\pi$
$620$	−219.779	−	136.482i	−0.354482	−	0.220132i
$621$	40.0205	+	54.5957i	0.0644453	+	0.0879157i
$622$	−156.576	−	156.576i	−0.251730	−	0.251730i
$623$	−958.085	−	755.394i	−1.53786	−	1.21251i
$624$	−207.999	−	230.351i	−0.333331	−	0.369153i
$625$	−379.267	+	496.771i	−0.606827	+	0.794834i
$626$	−319.542			−0.510450
$627$	−906.059	−	46.2018i	−1.44507	−	0.0736870i
$628$	325.105	−	325.105i	0.517683	−	0.517683i
$629$		−	63.3061i		−	0.100646i
$630$	−270.200	−	161.917i	−0.428889	−	0.257010i
$631$	−76.8167			−0.121738			−0.0608690	−	0.998146i	$-0.519387\pi$
$631$	−76.8167			−0.121738			−0.0608690	+	0.998146i	$0.519387\pi$
$632$	375.203	+	375.203i	0.593675	+	0.593675i
$633$	−42.2568	+	828.695i	−0.0667564	+	1.30915i
$634$		−	136.086i		−	0.214646i
$635$	493.320	−	115.343i	0.776883	−	0.181643i
$636$	456.293	−	412.017i	0.717443	−	0.647825i
$637$	−864.382	−	529.849i	−1.35696	−	0.831788i
$638$	−275.711	+	275.711i	−0.432149	+	0.432149i
$639$	−14.6792	+	143.562i	−0.0229721	+	0.224666i
$640$	−579.374	+	135.463i	−0.905272	+	0.211661i
$641$		−	187.134i		−	0.291941i	−0.989289	−	0.145970i	$-0.953370\pi$
$641$		−	187.134i		−	0.291941i	0.989289	−	0.145970i	$-0.0466304\pi$
$642$	589.006	+	30.0346i	0.917455	+	0.0467829i
$643$	−767.988	+	767.988i	−1.19438	+	1.19438i	−0.218559	+	0.975824i	$0.570136\pi$
$643$	−767.988	+	767.988i	−1.19438	+	1.19438i	−0.975824	+	0.218559i	$0.929864\pi$
$644$	52.2855	−	6.18494i	0.0811886	−	0.00960395i
$645$	692.114	−	125.040i	1.07305	−	0.193860i
$646$	−149.633			−0.231631
$647$	−573.588	+	573.588i	−0.886535	+	0.886535i	−0.994188	−	0.107654i	$-0.965666\pi$
$647$	−573.588	+	573.588i	−0.886535	+	0.886535i	0.107654	+	0.994188i	$0.465666\pi$
$648$	−473.774	+	311.491i	−0.731133	+	0.480696i
$649$	−412.459			−0.635530
$650$	−229.348	−	463.648i	−0.352844	−	0.713304i
$651$	−238.443	+	272.632i	−0.366271	+	0.418789i
$652$	116.536	−	116.536i	0.178736	−	0.178736i
$653$	142.398	−	142.398i	0.218067	−	0.218067i	−0.589616	−	0.807683i	$-0.700721\pi$
$653$	142.398	−	142.398i	0.218067	−	0.218067i	0.807683	+	0.589616i	$0.200721\pi$
$654$	−6.06034	−	6.71161i	−0.00926658	−	0.0102624i
$655$	−337.551	−	209.618i	−0.515345	−	0.320027i
$656$	133.596			0.203652
$657$	−566.071	+	461.048i	−0.861600	+	0.701747i
$658$	−113.793	+	144.326i	−0.172937	+	0.219340i
$659$	960.106			1.45691			0.728457	−	0.685092i	$-0.240238\pi$
$659$	960.106			1.45691			0.728457	+	0.685092i	$0.240238\pi$
$660$	−356.694	+	513.996i	−0.540446	+	0.778782i
$661$			94.8355i			0.143473i	0.997424	+	0.0717364i	$0.0228540\pi$
$661$			94.8355i			0.143473i	−0.997424	+	0.0717364i	$0.977146\pi$
$662$	−123.754	−	123.754i	−0.186939	−	0.186939i
$663$	−426.458	−	21.7459i	−0.643224	−	0.0327993i
$664$	−514.452			−0.774777
$665$	715.815	−	259.208i	1.07641	−	0.389787i
$666$	−82.3928	−	8.42466i	−0.123713	−	0.0126496i
$667$	−49.7191	+	49.7191i	−0.0745413	+	0.0745413i
$668$	414.755	+	414.755i	0.620891	+	0.620891i
$669$	493.399	+	546.421i	0.737517	+	0.816773i
$670$	−195.100	−	121.156i	−0.291194	−	0.180830i
$671$	292.961			0.436604
$672$	46.2557	+	691.455i	0.0688329	+	1.02895i
$673$	−442.857	−	442.857i	−0.658034	−	0.658034i	0.296880	−	0.954915i	$-0.404054\pi$
$673$	−442.857	−	442.857i	−0.658034	−	0.658034i	−0.954915	+	0.296880i	$0.904054\pi$
$674$	−154.964			−0.229917
$675$	643.537	−	203.679i	0.953388	−	0.301746i
$676$	−777.336			−1.14990
$677$	−447.410	+	447.410i	−0.660872	+	0.660872i	−0.955586	−	0.294714i	$-0.904776\pi$
$677$	−447.410	+	447.410i	−0.660872	+	0.660872i	0.294714	+	0.955586i	$0.404776\pi$
$678$	−17.3090	+	339.445i	−0.0255295	+	0.500656i
$679$	−163.840	+	19.3810i	−0.241296	+	0.0285434i
$680$	−127.020	+	204.542i	−0.186794	+	0.300798i
$681$	−544.182	−	602.662i	−0.799093	−	0.884966i
$682$	−169.557	−	169.557i	−0.248617	−	0.248617i
$683$	199.643	−	199.643i	0.292303	−	0.292303i	−0.545686	−	0.837990i	$-0.683731\pi$
$683$	199.643	−	199.643i	0.292303	−	0.292303i	0.837990	+	0.545686i	$0.183731\pi$
$684$	59.7388	−	584.243i	0.0873375	−	0.854157i
$685$	11.9608	+	51.1561i	0.0174610	+	0.0746804i
$686$	118.655	+	321.823i	0.172967	+	0.469129i
$687$	−18.8666	+	369.991i	−0.0274622	+	0.538560i
$688$	−165.774	−	165.774i	−0.240950	−	0.240950i
$689$		−	1413.38i		−	2.05135i
$690$	21.4409	−	30.8964i	0.0310738	−	0.0447773i
$691$		−	207.196i		−	0.299849i	−0.988697	−	0.149925i	$-0.952097\pi$
$691$		−	207.196i		−	0.299849i	0.988697	−	0.149925i	$-0.0479031\pi$
$692$	80.8697	−	80.8697i	0.116864	−	0.116864i
$693$	629.088	+	609.457i	0.907775	+	0.879447i
$694$			379.857i			0.547345i
$695$	−762.825	−	473.711i	−1.09759	−	0.681599i
$696$	−394.702	−	437.118i	−0.567100	−	0.628043i
$697$	129.971	−	129.971i	0.186473	−	0.186473i
$698$	215.097	+	215.097i	0.308162	+	0.308162i
$699$	255.592	+	283.059i	0.365654	+	0.404948i
$700$	108.561	−	513.653i	0.155088	−	0.733790i
$701$			8.12497i			0.0115905i	0.999983	+	0.00579527i	$0.00184470\pi$
$701$			8.12497i			0.0115905i	−0.999983	+	0.00579527i	$0.998155\pi$
$702$	−85.0546	+	552.141i	−0.121160	+	0.786525i
$703$	141.540	−	141.540i	0.201337	−	0.201337i
$704$	−180.740			−0.256733
$705$	−70.0183	−	387.561i	−0.0993167	−	0.549733i
$706$		−	339.785i		−	0.481281i
$707$	490.236	−	621.778i	0.693403	−	0.879459i
$708$	13.5972	−	266.654i	0.0192052	−	0.376631i
$709$			854.167i			1.20475i	0.798214	+	0.602374i	$0.205778\pi$
$709$			854.167i			1.20475i	−0.798214	+	0.602374i	$0.794222\pi$
$710$	78.0670	−	18.2528i	0.109954	−	0.0257082i
$711$	−69.3953	+	678.683i	−0.0976023	+	0.954547i
$712$	862.713	+	862.713i	1.21168	+	1.21168i
$713$	−30.5762	−	30.5762i	−0.0428839	−	0.0428839i
$714$	108.742	+	95.1052i	0.152300	+	0.133201i
$715$	327.464	+	1400.56i	0.457992	+	1.95882i
$716$			562.180i			0.785168i
$717$	−7.52867	+	147.644i	−0.0105002	+	0.205919i
$718$	114.367	+	114.367i	0.159285	+	0.159285i
$719$			1236.22i			1.71936i	0.510837	+	0.859678i	$0.329336\pi$
$719$			1236.22i			1.71936i	−0.510837	+	0.859678i	$0.670664\pi$
$720$	−178.077	−	137.526i	−0.247330	−	0.191009i
$721$	18.8191	+	159.090i	0.0261014	+	0.220652i
$722$	−79.2852	−	79.2852i	−0.109813	−	0.109813i
$723$	1263.35	+	64.4208i	1.74737	+	0.0891021i
$724$	538.742			0.744118
$725$	310.868	+	628.446i	0.428783	+	0.866822i
$726$	−160.972	+	145.352i	−0.221725	+	0.200210i
$727$	635.035	+	635.035i	0.873501	+	0.873501i	0.992852	−	0.119351i	$-0.0380815\pi$
$727$	635.035	+	635.035i	0.873501	+	0.873501i	−0.119351	+	0.992852i	$0.538081\pi$
$728$	796.155	+	627.722i	1.09362	+	0.862255i
$729$	−695.204	−	219.392i	−0.953640	−	0.300949i
$730$	344.562	+	213.971i	0.472003	+	0.293112i
$731$	−322.553			−0.441249
$732$	−9.65785	+	189.399i	−0.0131938	+	0.258742i
$733$	174.851	−	174.851i	0.238542	−	0.238542i	−0.577704	−	0.816246i	$-0.696051\pi$
$733$	174.851	−	174.851i	0.238542	−	0.238542i	0.816246	+	0.577704i	$0.196051\pi$
$734$		−	142.908i		−	0.194697i
$735$	−684.948	−	266.591i	−0.931902	−	0.362709i
$736$	−82.7358			−0.112413
$737$	451.552	+	451.552i	0.612689	+	0.612689i
$738$	−151.861	−	186.454i	−0.205774	−	0.252648i
$739$		−	1448.98i		−	1.96073i	−0.197187	−	0.980366i	$-0.563181\pi$
$739$		−	1448.98i		−	1.96073i	0.197187	−	0.980366i	$-0.436819\pi$
$740$	−31.4269	−	134.412i	−0.0424688	−	0.181638i
$741$	−904.856	−	1002.10i	−1.22113	−	1.35236i
$742$	−296.055	+	375.493i	−0.398995	+	0.506055i
$743$	30.8955	−	30.8955i	0.0415822	−	0.0415822i	−0.686010	−	0.727592i	$-0.740639\pi$
$743$	30.8955	−	30.8955i	0.0415822	−	0.0415822i	0.727592	+	0.686010i	$0.240639\pi$
$744$	268.818	−	242.733i	0.361315	−	0.326254i
$745$	105.080	+	65.2544i	0.141047	+	0.0875898i
$746$			522.501i			0.700404i
$747$	−417.706	−	512.856i	−0.559179	−	0.686555i
$748$	202.888	−	202.888i	0.271241	−	0.271241i
$749$	1366.61	−	161.658i	1.82457	−	0.215832i
$750$	−223.377	−	301.210i	−0.297836	−	0.401614i
$751$	1095.21			1.45833			0.729167	−	0.684335i	$-0.239908\pi$
$751$	1095.21			1.45833			0.729167	+	0.684335i	$0.239908\pi$
$752$	−92.8279	+	92.8279i	−0.123441	+	0.123441i
$753$	52.7867	−	1035.20i	0.0701019	−	1.37476i
$754$	−580.279			−0.769601
$755$	693.737	+	430.808i	0.918857	+	0.570606i
$756$	−414.752	+	386.613i	−0.548614	+	0.511393i
$757$	209.069	−	209.069i	0.276181	−	0.276181i	−0.555401	−	0.831582i	$-0.687435\pi$
$757$	209.069	−	209.069i	0.276181	−	0.276181i	0.831582	+	0.555401i	$0.187435\pi$
$758$	184.703	−	184.703i	0.243672	−	0.243672i
$759$	−77.6125	+	70.0813i	−0.102256	+	0.0923337i
$760$	−741.308	+	173.325i	−0.975406	+	0.228059i
$761$	710.902			0.934168			0.467084	−	0.884213i	$-0.345305\pi$
$761$	710.902			0.934168			0.467084	+	0.884213i	$0.345305\pi$
$762$	−15.4802	+	303.581i	−0.0203152	+	0.398400i
$763$	−16.5694	−	13.0640i	−0.0217161	−	0.0171219i
$764$	321.188			0.420403
$765$	−307.041	+	39.4511i	−0.401361	+	0.0515701i
$766$		−	231.666i		−	0.302436i
$767$	−434.044	−	434.044i	−0.565898	−	0.565898i
$768$	26.1250	−	512.334i	0.0340169	−	0.667102i
$769$	248.259			0.322833			0.161417	−	0.986886i	$-0.448394\pi$
$769$	248.259			0.322833			0.161417	+	0.986886i	$0.448394\pi$
$770$	206.371	−	440.679i	0.268014	−	0.572310i
$771$	615.774	+	681.947i	0.798669	+	0.884497i
$772$	−244.900	+	244.900i	−0.317228	+	0.317228i
$773$	307.323	+	307.323i	0.397572	+	0.397572i	0.877376	−	0.479804i	$-0.159292\pi$
$773$	307.323	+	307.323i	0.397572	+	0.397572i	−0.479804	+	0.877376i	$0.659292\pi$
$774$	−42.9248	+	419.802i	−0.0554583	+	0.542380i
$775$	−386.481	+	191.177i	−0.498686	+	0.246680i
$776$	164.983			0.212606
$777$	−192.821	+	12.8990i	−0.248161	+	0.0166011i
$778$	−283.550	−	283.550i	−0.364460	−	0.364460i
$779$	581.181			0.746061
$780$	−916.256	+	165.534i	−1.17469	+	0.212223i
$781$	−222.929			−0.285440
$782$	−12.1956	+	12.1956i	−0.0155954	+	0.0155954i
$783$	115.286	−	748.393i	0.147237	−	0.955802i
$784$	57.1631	+	238.238i	0.0729121	+	0.303875i
$785$	−174.458	−	746.156i	−0.222240	−	0.950517i
$786$	176.944	−	159.774i	0.225120	−	0.203275i
$787$	−196.357	−	196.357i	−0.249501	−	0.249501i	0.571265	−	0.820766i	$-0.306453\pi$
$787$	−196.357	−	196.357i	−0.249501	−	0.249501i	−0.820766	+	0.571265i	$0.806453\pi$
$788$	−497.106	+	497.106i	−0.630845	+	0.630845i
$789$	−558.872	−	618.931i	−0.708330	−	0.784449i
$790$	369.058	−	86.2894i	0.467163	−	0.109227i
$791$	93.1637	+	787.576i	0.117780	+	0.995671i
$792$	−553.137	−	679.137i	−0.698406	−	0.857497i
$793$	308.293	+	308.293i	0.388768	+	0.388768i
$794$			430.037i			0.541609i
$795$	−182.167	−	1008.32i	−0.229140	−	1.26833i
$796$			660.111i			0.829285i
$797$	941.657	−	941.657i	1.18150	−	1.18150i	0.202147	−	0.979355i	$-0.435208\pi$
$797$	941.657	−	941.657i	1.18150	−	1.18150i	0.979355	−	0.202147i	$-0.0647918\pi$
$798$	30.4888	+	455.762i	0.0382065	+	0.571130i
$799$			180.619i			0.226056i
$800$	−264.236	+	781.540i	−0.330295	+	0.976925i
$801$	−159.562	+	1560.51i	−0.199204	+	1.94821i
$802$	412.181	−	412.181i	0.513941	−	0.513941i
$803$	−797.475	−	797.475i	−0.993120	−	0.993120i
$804$	−306.814	+	277.042i	−0.381609	+	0.344579i
$805$	37.2150	−	79.4677i	0.0462298	−	0.0987177i
$806$		−	356.860i		−	0.442754i
$807$	1048.52	+	53.4662i	1.29928	+	0.0662530i
$808$	−559.883	+	559.883i	−0.692925	+	0.692925i
$809$	−1461.04			−1.80598			−0.902990	−	0.429662i	$-0.858633\pi$
$809$	−1461.04			−1.80598			−0.902990	+	0.429662i	$0.858633\pi$
$810$	10.4851	+	404.864i	0.0129446	+	0.499832i
$811$		−	1284.35i		−	1.58367i	−0.610738	−	0.791833i	$-0.709127\pi$
$811$		−	1284.35i		−	1.58367i	0.610738	−	0.791833i	$-0.290873\pi$
$812$	−462.488	−	364.645i	−0.569567	−	0.449070i
$813$	−413.396	−	21.0799i	−0.508482	−	0.0259285i
$814$		−	127.943i		−	0.157178i
$815$	−62.5356	−	267.464i	−0.0767308	−	0.328177i
$816$	69.1548	+	76.5864i	0.0847485	+	0.0938559i
$817$	−721.165	−	721.165i	−0.882698	−	0.882698i
$818$	243.831	+	243.831i	0.298082	+	0.298082i
$819$	20.6585	+	1303.36i	0.0252240	+	1.59141i
$820$	211.436	−	340.479i	0.257848	−	0.415218i
$821$		−	782.279i		−	0.952837i	−0.879219	−	0.476418i	$-0.841935\pi$
$821$		−	782.279i		−	0.952837i	0.879219	−	0.476418i	$-0.158065\pi$
$822$	−31.4805	−	1.60526i	−0.0382975	−	0.00195287i
$823$	−361.067	−	361.067i	−0.438720	−	0.438720i	0.452861	−	0.891581i	$-0.350403\pi$
$823$	−361.067	−	361.067i	−0.438720	−	0.438720i	−0.891581	+	0.452861i	$0.850403\pi$
$824$		−	160.200i		−	0.194417i
$825$	414.130	+	956.965i	0.501975	+	1.15996i
$826$	24.3953	+	206.229i	0.0295342	+	0.249672i
$827$	−711.346	−	711.346i	−0.860152	−	0.860152i	0.131203	−	0.991356i	$-0.458116\pi$
$827$	−711.346	−	711.346i	−0.860152	−	0.860152i	−0.991356	+	0.131203i	$0.958116\pi$
$828$	−42.7489	−	52.4867i	−0.0516291	−	0.0633898i
$829$	−1369.60			−1.65211			−0.826054	−	0.563591i	$-0.809419\pi$
$829$	−1369.60			−1.65211			−0.826054	+	0.563591i	$0.809419\pi$
$830$	−193.857	+	312.171i	−0.233562	+	0.376109i
$831$	377.642	+	418.224i	0.454442	+	0.503278i
$832$	−190.198	−	190.198i	−0.228604	−	0.228604i
$833$	287.387	+	176.162i	0.345002	+	0.211480i
$834$	399.872	−	361.070i	0.479463	−	0.432938i
$835$	951.914	−	222.567i	1.14002	−	0.266547i
$836$	907.236			1.08521
$837$	460.246	+	70.8987i	0.549876	+	0.0847057i
$838$	243.193	−	243.193i	0.290206	−	0.290206i
$839$		−	915.483i		−	1.09116i	−0.838059	−	0.545580i	$-0.816310\pi$
$839$		−	915.483i		−	1.09116i	0.838059	−	0.545580i	$-0.183690\pi$
$840$	648.889	+	345.208i	0.772486	+	0.410962i
$841$	−54.4667			−0.0647642
$842$	−10.3776	−	10.3776i	−0.0123250	−	0.0123250i
$843$	425.741	+	21.7094i	0.505031	+	0.0257526i
$844$		−	829.771i		−	0.983141i
$845$	−683.473	+	1100.61i	−0.808844	+	1.30250i
$846$	235.076	+	24.0365i	0.277867	+	0.0284119i
$847$	−313.329	+	397.402i	−0.369928	+	0.469188i
$848$	−241.511	+	241.511i	−0.284800	+	0.284800i
$849$	−341.868	−	378.606i	−0.402671	−	0.445943i
$850$	76.2530	+	154.152i	0.0897094	+	0.181355i
$851$		−	23.0720i		−	0.0271116i
$852$	7.34913	−	144.123i	0.00862574	−	0.169159i
$853$	286.958	−	286.958i	0.336411	−	0.336411i	−0.518604	−	0.855015i	$-0.673548\pi$
$853$	286.958	−	286.958i	0.336411	−	0.336411i	0.855015	+	0.518604i	$0.173548\pi$
$854$	−17.3275	−	146.481i	−0.0202898	−	0.171523i
$855$	−774.689	−	598.279i	−0.906069	−	0.699742i
$856$	−1376.13			−1.60763
$857$	605.241	−	605.241i	0.706232	−	0.706232i	−0.259509	−	0.965741i	$-0.583561\pi$
$857$	605.241	−	605.241i	0.706232	−	0.706232i	0.965741	+	0.259509i	$0.0835606\pi$
$858$	−861.880	−	43.9490i	−1.00452	−	0.0512226i
$859$	1440.15			1.67654			0.838272	−	0.545253i	$-0.183566\pi$
$859$	1440.15			1.67654			0.838272	+	0.545253i	$0.183566\pi$
$860$	−684.848	+	160.124i	−0.796335	+	0.186191i
$861$	−422.357	−	369.392i	−0.490543	−	0.429027i
$862$	313.295	−	313.295i	0.363452	−	0.363452i
$863$	761.642	−	761.642i	0.882551	−	0.882551i	−0.111242	−	0.993793i	$-0.535483\pi$
$863$	761.642	−	761.642i	0.882551	−	0.882551i	0.993793	+	0.111242i	$0.0354830\pi$
$864$	718.609	−	526.765i	0.831724	−	0.609682i
$865$	−43.3965	−	185.606i	−0.0501693	−	0.214573i
$866$	−689.220			−0.795866
$867$	−724.088	−	36.9227i	−0.835165	−	0.0425867i
$868$	224.249	−	284.421i	0.258352	−	0.327674i
$869$	−1053.89			−1.21276
$870$	−413.976	+	74.7905i	−0.475835	+	0.0859661i
$871$			950.365i			1.09112i
$872$	14.9200	+	14.9200i	0.0171101	+	0.0171101i
$873$	133.957	+	164.471i	0.153444	+	0.188397i
$874$	−54.5341			−0.0623959
$875$	−631.815	−	605.339i	−0.722074	−	0.691816i
$876$	541.857	−	489.277i	0.618558	−	0.558536i
$877$	−21.5786	+	21.5786i	−0.0246050	+	0.0246050i	−0.719302	−	0.694697i	$-0.755538\pi$
$877$	−21.5786	+	21.5786i	−0.0246050	+	0.0246050i	0.694697	+	0.719302i	$0.255538\pi$
$878$	106.819	+	106.819i	0.121662	+	0.121662i
$879$	−1189.92	+	1074.45i	−1.35372	+	1.22236i
$880$	183.364	−	295.275i	0.208368	−	0.335539i
$881$	269.114			0.305465			0.152732	−	0.988268i	$-0.451193\pi$
$881$	269.114			0.305465			0.152732	+	0.988268i	$0.451193\pi$
$882$	267.520	−	350.591i	0.303311	−	0.397495i
$883$	659.321	+	659.321i	0.746683	+	0.746683i	0.973855	−	0.227171i	$-0.0729478\pi$
$883$	659.321	+	659.321i	0.746683	+	0.746683i	−0.227171	+	0.973855i	$0.572948\pi$
$884$	427.012			0.483045
$885$	−365.593	−	253.708i	−0.413100	−	0.286676i
$886$	265.886			0.300097
$887$	366.008	−	366.008i	0.412636	−	0.412636i	−0.470020	−	0.882656i	$-0.655753\pi$
$887$	366.008	−	366.008i	0.412636	−	0.412636i	0.882656	+	0.470020i	$0.155753\pi$
$888$	193.002	+	9.84154i	0.217344	+	0.0110828i
$889$	83.3205	+	704.364i	0.0937239	+	0.792311i
$890$	848.585	−	198.407i	0.953467	−	0.222930i
$891$	227.914	−	1102.84i	0.255796	−	1.23776i
$892$	−520.586	−	520.586i	−0.583616	−	0.583616i
$893$	−403.829	+	403.829i	−0.452216	+	0.452216i
$894$	−55.0830	+	49.7380i	−0.0616141	+	0.0556353i
$895$	795.976	+	494.297i	0.889358	+	0.552288i
$896$	−97.8548	−	827.232i	−0.109213	−	0.923250i
$897$	−155.423	−	7.92533i	−0.173270	−	0.00883538i
$898$	−281.155	−	281.155i	−0.313090	−	0.313090i
$899$			483.702i			0.538044i
$900$	−632.330	+	236.187i	−0.702588	+	0.262430i
$901$			469.917i			0.521550i
$902$	262.675	−	262.675i	0.291214	−	0.291214i
$903$	65.7222	+	982.450i	0.0727821	+	1.08798i
$904$		−	793.067i		−	0.877286i
$905$	473.689	−	762.790i	0.523413	−	0.842862i
$906$	−363.656	+	328.369i	−0.401387	+	0.362438i
$907$	65.0405	−	65.0405i	0.0717094	−	0.0717094i	−0.670342	−	0.742052i	$-0.733853\pi$
$907$	65.0405	−	65.0405i	0.0717094	−	0.0717094i	0.742052	+	0.670342i	$0.233853\pi$
$908$	574.167	+	574.167i	0.632343	+	0.632343i
$909$	−1012.74	−	103.553i	−1.11413	−	0.113919i
$910$	680.912	−	246.569i	0.748254	−	0.270955i
$911$			1604.19i			1.76091i	0.474126	+	0.880457i	$0.342764\pi$
$911$			1604.19i			1.76091i	−0.474126	+	0.880457i	$0.657236\pi$
$912$	−16.6157	+	325.849i	−0.0182189	+	0.357290i
$913$	722.507	−	722.507i	0.791355	−	0.791355i
$914$	93.6580			0.102470
$915$	259.674	+	180.204i	0.283796	+	0.196944i
$916$		−	370.471i		−	0.404445i
$917$	344.417	−	436.832i	0.375591	−	0.476371i
$918$	28.2787	−	183.574i	0.0308046	−	0.199972i
$919$		−	18.0596i		−	0.0196513i	−0.999952	−	0.00982566i	$-0.996872\pi$
$919$		−	18.0596i		−	0.0196513i	0.999952	−	0.00982566i	$-0.00312766\pi$
$920$	−46.2926	+	74.5457i	−0.0503180	+	0.0810280i
$921$	298.070	−	269.147i	0.323638	−	0.292233i
$922$	−135.443	−	135.443i	−0.146901	−	0.146901i
$923$	−234.595	−	234.595i	−0.254166	−	0.254166i
$924$	−659.309	−	576.629i	−0.713537	−	0.624057i
$925$	−217.943	−	73.6857i	−0.235614	−	0.0796602i
$926$		−	60.7910i		−	0.0656490i
$927$	159.703	−	130.073i	0.172279	−	0.140316i
$928$	654.421	+	654.421i	0.705195	+	0.705195i
$929$		−	891.704i		−	0.959854i	−0.877308	−	0.479927i	$-0.840663\pi$
$929$		−	891.704i		−	0.959854i	0.877308	−	0.479927i	$-0.159337\pi$
$930$	−45.9946	−	254.587i	−0.0494566	−	0.273749i
$931$	248.676	+	1036.41i	0.267107	+	1.11322i
$932$	−269.675	−	269.675i	−0.289351	−	0.289351i
$933$	−33.8299	+	663.435i	−0.0362592	+	0.711077i
$934$	357.564			0.382831
$935$	−108.874	−	465.653i	−0.116443	−	0.498025i
$936$	132.594	−	1296.76i	0.141660	−	1.38543i
$937$	485.788	+	485.788i	0.518450	+	0.518450i	0.917102	−	0.398652i	$-0.130522\pi$
$937$	485.788	+	485.788i	0.518450	+	0.518450i	−0.398652	+	0.917102i	$0.630522\pi$
$938$	199.068	−	252.483i	0.212226	−	0.269172i
$939$	642.450	+	711.490i	0.684186	+	0.757711i
$940$	89.6643	+	383.493i	0.0953876	+	0.407971i
$941$	−1356.29			−1.44133			−0.720665	−	0.693284i	$-0.756163\pi$
$941$	−1356.29			−1.44133			−0.720665	+	0.693284i	$0.756163\pi$
$942$	459.171	+	23.4141i	0.487443	+	0.0248557i
$943$	47.3683	−	47.3683i	0.0502314	−	0.0502314i
$944$			148.334i			0.157133i
$945$	182.724	+	927.166i	0.193359	+	0.981128i
$946$	−651.886			−0.689097
$947$	757.557	+	757.557i	0.799955	+	0.799955i	0.983088	−	0.183133i	$-0.0586240\pi$
$947$	757.557	+	757.557i	0.799955	+	0.799955i	−0.183133	+	0.983088i	$0.558624\pi$
$948$	34.7427	−	681.336i	0.0366484	−	0.718709i
$949$		−	1678.42i		−	1.76862i
$950$	−174.167	+	515.140i	−0.183334	+	0.542253i
$951$	−303.008	+	273.606i	−0.318621	+	0.287703i
$952$	−264.703	−	208.703i	−0.278049	−	0.219226i
$953$	−1083.39	+	1083.39i	−1.13682	+	1.13682i	−0.147800	+	0.989017i	$0.547219\pi$
$953$	−1083.39	+	1083.39i	−1.13682	+	1.13682i	−0.989017	+	0.147800i	$0.952781\pi$
$954$	611.597	+	62.5357i	0.641087	+	0.0655511i
$955$	282.405	−	454.762i	0.295712	−	0.476190i
$956$		−	147.836i		−	0.154640i
$957$	1168.22	+	59.5702i	1.22072	+	0.0622468i
$958$	64.7138	−	64.7138i	0.0675509	−	0.0675509i
$959$	−73.0408	+	8.64012i	−0.0761635	+	0.00900951i
$960$	−160.203	−	111.175i	−0.166878	−	0.115807i
$961$	663.533			0.690461
$962$	134.638	−	134.638i	0.139957	−	0.139957i
$963$	−1117.34	−	1371.87i	−1.16027	−	1.42457i
$964$	−1264.99			−1.31223
$965$	131.419	+	562.076i	0.136185	+	0.582462i
$966$	39.6311	+	34.6612i	0.0410260	+	0.0358812i
$967$	−981.586	+	981.586i	−1.01508	+	1.01508i	−0.0151989	+	0.999884i	$0.504838\pi$
$967$	−981.586	+	981.586i	−1.01508	+	1.01508i	−0.999884	+	0.0151989i	$0.995162\pi$
$968$	357.843	−	357.843i	0.369673	−	0.369673i
$969$	300.843	+	333.173i	0.310468	+	0.343832i
$970$	62.1690	−	100.112i	0.0640918	−	0.103208i
$971$	366.616			0.377565			0.188783	−	0.982019i	$-0.439546\pi$
$971$	366.616			0.377565			0.188783	+	0.982019i	$0.439546\pi$
$972$	705.474	+	183.703i	0.725797	+	0.188995i
$973$	778.341	−	987.189i	0.799939	−	1.01458i
$974$	−357.358			−0.366898
$975$	−571.244	+	1442.85i	−0.585891	+	1.47984i
$976$		−	105.359i		−	0.107949i
$977$	576.937	+	576.937i	0.590519	+	0.590519i	0.937772	−	0.347253i	$-0.112885\pi$
$977$	576.937	+	576.937i	0.590519	+	0.590519i	−0.347253	+	0.937772i	$0.612885\pi$
$978$	164.593	+	8.39291i	0.168295	+	0.00858170i
$979$	−2423.23			−2.47520
$980$	697.636	+	231.364i	0.711873	+	0.236085i
$981$	−2.75951	+	26.9879i	−0.00281295	+	0.0275106i
$982$	−366.364	+	366.364i	−0.373080	+	0.373080i
$983$	618.375	+	618.375i	0.629069	+	0.629069i	0.947834	−	0.318765i	$-0.103268\pi$
$983$	618.375	+	618.375i	0.629069	+	0.629069i	−0.318765	+	0.947834i	$0.603268\pi$
$984$	376.039	+	416.450i	0.382154	+	0.423222i
$985$	266.758	+	1140.92i	0.270820	+	1.15829i
$986$	192.929			0.195669
$987$	550.140	−	36.8023i	0.557386	−	0.0372870i
$988$	954.714	+	954.714i	0.966310	+	0.966310i
$989$	−117.555			−0.118862
$990$	−620.537	+	79.7315i	−0.626805	+	0.0805369i
$991$	−1797.04			−1.81336			−0.906680	−	0.421818i	$-0.861392\pi$
$991$	−1797.04			−1.81336			−0.906680	+	0.421818i	$0.861392\pi$
$992$	−402.456	+	402.456i	−0.405701	+	0.405701i
$993$	−26.7383	+	524.362i	−0.0269267	+	0.528058i
$994$	13.1853	+	111.464i	0.0132649	+	0.112137i
$995$	934.634	+	580.403i	0.939330	+	0.583320i
$996$	443.282	+	490.919i	0.445062	+	0.492891i
$997$	−86.1420	−	86.1420i	−0.0864012	−	0.0864012i	0.662585	−	0.748986i	$-0.269459\pi$
$997$	−86.1420	−	86.1420i	−0.0864012	−	0.0864012i	−0.748986	+	0.662585i	$0.769459\pi$
$998$	−153.631	+	153.631i	−0.153939	+	0.153939i
$999$	146.896	+	200.394i	0.147043	+	0.200594i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.k.c.83.2	yes	16
3.2	odd	2	inner	105.3.k.c.83.5	yes	16
5.2	odd	4	inner	105.3.k.c.62.8	yes	16
7.6	odd	2	inner	105.3.k.c.83.3	yes	16
15.2	even	4	inner	105.3.k.c.62.3	yes	16
21.20	even	2	inner	105.3.k.c.83.8	yes	16
35.27	even	4	inner	105.3.k.c.62.5	yes	16
105.62	odd	4	inner	105.3.k.c.62.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.k.c.62.2	✓	16	105.62	odd	4	inner
105.3.k.c.62.3	yes	16	15.2	even	4	inner
105.3.k.c.62.5	yes	16	35.27	even	4	inner
105.3.k.c.62.8	yes	16	5.2	odd	4	inner
105.3.k.c.83.2	yes	16	1.1	even	1	trivial
105.3.k.c.83.3	yes	16	7.6	odd	2	inner
105.3.k.c.83.5	yes	16	3.2	odd	2	inner
105.3.k.c.83.8	yes	16	21.20	even	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.152778 + 2.99611i) q^{3} -3.00000i q^{4} +(-4.24762 - 2.63775i) q^{5} +(2.22660 - 2.01054i) q^{6} +(4.33402 - 5.49694i) q^{7} +(-4.94975 + 4.94975i) q^{8} +(-8.95332 - 0.915476i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.152778 + 2.99611i) q^{3} -3.00000i q^{4} +(-4.24762 - 2.63775i) q^{5} +(2.22660 - 2.01054i) q^{6} +(4.33402 - 5.49694i) q^{7} +(-4.94975 + 4.94975i) q^{8} +(-8.95332 - 0.915476i) q^{9} +(1.13835 + 4.86869i) q^{10} -13.9031i q^{11} +(8.98832 + 0.458333i) q^{12} +(14.6307 - 14.6307i) q^{13} +(-6.95153 + 0.822309i) q^{14} +(8.55193 - 12.3233i) q^{15} -5.00000 q^{16} +(-4.86435 + 4.86435i) q^{17} +(5.68361 + 6.97829i) q^{18} -21.7515 q^{19} +(-7.91326 + 12.7429i) q^{20} +(15.8073 + 13.8250i) q^{21} +(-9.83095 + 9.83095i) q^{22} +(-1.77282 + 1.77282i) q^{23} +(-14.0738 - 15.5862i) q^{24} +(11.0845 + 22.4083i) q^{25} -20.6909 q^{26} +(4.11073 - 26.6852i) q^{27} +(-16.4908 - 13.0020i) q^{28} +28.0452 q^{29} +(-14.7610 + 2.66678i) q^{30} +17.2472i q^{31} +(23.3345 + 23.3345i) q^{32} +(41.6551 + 2.12408i) q^{33} +6.87923 q^{34} +(-32.9088 + 11.9168i) q^{35} +(-2.74643 + 26.8600i) q^{36} +(-6.50714 + 6.50714i) q^{37} +(15.3806 + 15.3806i) q^{38} +(41.5998 + 46.0702i) q^{39} +(34.0808 - 7.96843i) q^{40} -26.7192 q^{41} +(-1.40169 - 20.9532i) q^{42} +(33.1548 + 33.1548i) q^{43} -41.7092 q^{44} +(35.6155 + 27.5052i) q^{45} +2.50714 q^{46} +(18.5656 - 18.5656i) q^{47} +(0.763888 - 14.9805i) q^{48} +(-11.4326 - 47.6476i) q^{49} +(8.00714 - 23.6830i) q^{50} +(-13.8310 - 15.3173i) q^{51} +(-43.8920 - 43.8920i) q^{52} +(48.3021 - 48.3021i) q^{53} +(-21.7760 + 15.9626i) q^{54} +(-36.6728 + 59.0549i) q^{55} +(5.75616 + 48.6607i) q^{56} +(3.32314 - 65.1697i) q^{57} +(-19.8310 - 19.8310i) q^{58} -29.6668i q^{59} +(-36.9700 - 25.6558i) q^{60} +21.0717i q^{61} +(12.1956 - 12.1956i) q^{62} +(-43.8361 + 45.2481i) q^{63} -13.0000i q^{64} +(-100.737 + 23.5534i) q^{65} +(-27.9526 - 30.9565i) q^{66} +(-32.4786 + 32.4786i) q^{67} +(14.5931 + 14.5931i) q^{68} +(-5.04071 - 5.58240i) q^{69} +(31.6965 + 14.8436i) q^{70} -16.0345i q^{71} +(48.8480 - 39.7853i) q^{72} +(57.3597 - 57.3597i) q^{73} +9.20249 q^{74} +(-68.8312 + 29.7869i) q^{75} +65.2544i q^{76} +(-76.4243 - 60.2561i) q^{77} +(3.16110 - 61.9921i) q^{78} -75.8024i q^{79} +(21.2381 + 13.1888i) q^{80} +(79.3238 + 16.3931i) q^{81} +(18.8933 + 18.8933i) q^{82} +(51.9675 + 51.9675i) q^{83} +(41.4750 - 47.4218i) q^{84} +(33.4929 - 7.83095i) q^{85} -46.8879i q^{86} +(-4.28468 + 84.0264i) q^{87} +(68.8167 + 68.8167i) q^{88} -174.294i q^{89} +(-5.73481 - 44.6331i) q^{90} +(-17.0143 - 143.833i) q^{91} +(5.31846 + 5.31846i) q^{92} +(-51.6745 - 2.63499i) q^{93} -26.2557 q^{94} +(92.3919 + 57.3750i) q^{95} +(-73.4777 + 66.3477i) q^{96} +(-16.6658 - 16.6658i) q^{97} +(-25.6079 + 41.7760i) q^{98} +(-12.7279 + 124.479i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{7}+O(q^{10}) \) 16 * q + 32 * q^7	\( 16 q + 32 q^{7} + 80 q^{15} - 80 q^{16} + 8 q^{18} - 64 q^{21} - 64 q^{22} + 224 q^{25} - 96 q^{28} - 128 q^{30} + 96 q^{36} - 384 q^{37} - 112 q^{42} + 64 q^{43} + 320 q^{46} - 128 q^{51} + 408 q^{57} - 224 q^{58} - 120 q^{60} - 72 q^{63} + 320 q^{67} + 128 q^{70} + 56 q^{72} - 424 q^{78} + 896 q^{81} + 256 q^{85} + 448 q^{88} - 832 q^{91} + 32 q^{93}+O(q^{100}) \) 16 * q + 32 * q^7 + 80 * q^15 - 80 * q^16 + 8 * q^18 - 64 * q^21 - 64 * q^22 + 224 * q^25 - 96 * q^28 - 128 * q^30 + 96 * q^36 - 384 * q^37 - 112 * q^42 + 64 * q^43 + 320 * q^46 - 128 * q^51 + 408 * q^57 - 224 * q^58 - 120 * q^60 - 72 * q^63 + 320 * q^67 + 128 * q^70 + 56 * q^72 - 424 * q^78 + 896 * q^81 + 256 * q^85 + 448 * q^88 - 832 * q^91 + 32 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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