LMFDB - Embedded newform 105.3.k.c.83.5

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			83.5
Root			$-0.817327 + 1.97320i$ of defining polynomial
Character	$\chi$	$=$	105.83
Dual form			105.3.k.c.62.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-2.99611 + 0.152778i) q^{3} -3.00000i q^{4} +(4.24762 + 2.63775i) q^{5} +(-2.22660 - 2.01054i) q^{6} +(4.33402 - 5.49694i) q^{7} +(4.94975 - 4.94975i) q^{8} +(8.95332 - 0.915476i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-2.99611 + 0.152778i) 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} +(0.458333 + 8.98832i) q^{12} +(14.6307 - 14.6307i) q^{13} +(6.95153 - 0.822309i) q^{14} +(-13.1293 - 7.25405i) q^{15} -5.00000 q^{16} +(4.86435 - 4.86435i) q^{17} +(6.97829 + 5.68361i) q^{18} -21.7515 q^{19} +(7.91326 - 12.7429i) q^{20} +(-12.1454 + 17.1316i) 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} +(-26.6852 + 4.11073i) q^{27} +(-16.4908 - 13.0020i) q^{28} -28.0452 q^{29} +(-4.15444 - 14.4132i) q^{30} +17.2472i q^{31} +(-23.3345 - 23.3345i) q^{32} +(-2.12408 - 41.6551i) 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} +(-20.7019 + 3.52576i) q^{42} +(33.1548 + 33.1548i) q^{43} +41.7092 q^{44} +(40.4451 + 19.7280i) q^{45} +2.50714 q^{46} +(-18.5656 + 18.5656i) q^{47} +(14.9805 - 0.763888i) 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} +(65.1697 - 3.32314i) q^{57} +(-19.8310 - 19.8310i) q^{58} +29.6668i q^{59} +(-21.7621 + 39.3879i) q^{60} +21.0717i q^{61} +(-12.1956 + 12.1956i) q^{62} +(33.7715 - 53.1835i) 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} +(39.7853 - 48.8480i) q^{72} +(57.3597 - 57.3597i) q^{73} -9.20249 q^{74} +(-36.6339 - 65.4443i) q^{75} +65.2544i q^{76} +(76.4243 + 60.2561i) q^{77} +(-61.9921 + 3.16110i) 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} +(51.3947 + 36.4361i) q^{84} +(33.4929 - 7.83095i) q^{85} +46.8879i q^{86} +(84.0264 - 4.28468i) q^{87} +(68.8167 + 68.8167i) q^{88} +174.294i q^{89} +(14.6492 + 42.5488i) q^{90} +(-17.0143 - 143.833i) q^{91} +(-5.31846 - 5.31846i) q^{92} +(-2.63499 - 51.6745i) 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	0.861430	−	0.507877i	$-0.169569\pi$
$2$	0.707107	+	0.707107i	0.353553	+	0.353553i	−0.507877	+	0.861430i	$0.669569\pi$
$3$	−2.99611	+	0.152778i	−0.998702	+	0.0509259i
$3$	−2.99611	+	0.152778i	−0.998702	+	0.0509259i
$4$		−	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	$0.217748\pi$
$11$			13.9031i			1.26392i	−0.775003	+	0.631958i	$0.782252\pi$
$12$	0.458333	+	8.98832i	0.0381944	+	0.749027i
$13$	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
$15$	−13.1293	−	7.25405i	−0.875287	−	0.483603i
$16$	−5.00000			−0.312500
$17$	4.86435	−	4.86435i	0.286138	−	0.286138i	−0.549413	−	0.835551i	$-0.685149\pi$
$17$	4.86435	−	4.86435i	0.286138	−	0.286138i	0.835551	+	0.549413i	$0.185149\pi$
$18$	6.97829	+	5.68361i	0.387683	+	0.315756i
$19$	−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
$21$	−12.1454	+	17.1316i	−0.578351	+	0.815788i
$22$	−9.83095	+	9.83095i	−0.446861	+	0.446861i
$23$	1.77282	−	1.77282i	0.0770791	−	0.0770791i	−0.667516	−	0.744595i	$-0.732643\pi$
$23$	1.77282	−	1.77282i	0.0770791	−	0.0770791i	0.744595	+	0.667516i	$0.232643\pi$
$24$	−14.0738	+	15.5862i	−0.586407	+	0.649424i
$25$	11.0845	+	22.4083i	0.443381	+	0.896333i
$26$	20.6909			0.795802
$27$	−26.6852	+	4.11073i	−0.988342	+	0.152249i
$28$	−16.4908	−	13.0020i	−0.588957	−	0.464359i
$29$	−28.0452			−0.967076			−0.483538	−	0.875323i	$-0.660648\pi$
$29$	−28.0452			−0.967076			−0.483538	+	0.875323i	$0.660648\pi$
$30$	−4.15444	−	14.4132i	−0.138481	−	0.480440i
$31$			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
$33$	−2.12408	−	41.6551i	−0.0643660	−	1.26228i
$34$	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	$-0.394352\pi$
$41$	26.7192			0.651687			0.325844	+	0.945424i	$0.394352\pi$
$42$	−20.7019	+	3.52576i	−0.492903	+	0.0839468i
$43$	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
$45$	40.4451	+	19.7280i	0.898779	+	0.438401i
$46$	2.50714			0.0545031
$47$	−18.5656	+	18.5656i	−0.395012	+	0.395012i	−0.876470	−	0.481457i	$-0.840108\pi$
$47$	−18.5656	+	18.5656i	−0.395012	+	0.395012i	0.481457	+	0.876470i	$0.340108\pi$
$48$	14.9805	−	0.763888i	0.312095	−	0.0159143i
$49$	−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	−0.996379	−	0.0850185i	$-0.972905\pi$
$53$	−48.3021	+	48.3021i	−0.911361	+	0.911361i	0.0850185	+	0.996379i	$0.472905\pi$
$54$	−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
$57$	65.1697	−	3.32314i	1.14333	−	0.0583006i
$58$	−19.8310	−	19.8310i	−0.341913	−	0.341913i
$59$			29.6668i			0.502826i	0.967880	+	0.251413i	$0.0808953\pi$
$59$			29.6668i			0.502826i	−0.967880	+	0.251413i	$0.919105\pi$
$60$	−21.7621	+	39.3879i	−0.362702	+	0.656465i
$61$			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
$63$	33.7715	−	53.1835i	0.536056	−	0.844183i
$64$		−	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	$0.0360200\pi$
$71$			16.0345i			0.225838i	−0.993604	+	0.112919i	$0.963980\pi$
$72$	39.7853	−	48.8480i	0.552573	−	0.678445i
$73$	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
$75$	−36.6339	−	65.4443i	−0.488452	−	0.872591i
$76$			65.2544i			0.858610i
$77$	76.4243	+	60.2561i	0.992523	+	0.782547i
$78$	−61.9921	+	3.16110i	−0.794770	+	0.0405269i
$79$		−	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	0.320974	−	0.947088i	$-0.395990\pi$
$83$	−51.9675	−	51.9675i	−0.626114	−	0.626114i	−0.947088	+	0.320974i	$0.895990\pi$
$84$	51.3947	+	36.4361i	0.611841	+	0.433763i
$85$	33.4929	−	7.83095i	0.394034	−	0.0921288i
$86$			46.8879i			0.545208i
$87$	84.0264	−	4.28468i	0.965821	−	0.0492492i
$88$	68.8167	+	68.8167i	0.782008	+	0.782008i
$89$			174.294i			1.95836i	0.202987	+	0.979181i	$0.434935\pi$
$89$			174.294i			1.95836i	−0.202987	+	0.979181i	$0.565065\pi$
$90$	14.6492	+	42.5488i	0.162768	+	0.472765i
$91$	−17.0143	−	143.833i	−0.186970	−	1.58058i
$92$	−5.31846	−	5.31846i	−0.0578093	−	0.0578093i
$93$	−2.63499	−	51.6745i	−0.0283332	−	0.555640i
$94$	−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	$-0.689187\pi$
$101$	−113.114			−1.11994			−0.559968	+	0.828514i	$0.689187\pi$
$102$	−20.6109	+	1.05099i	−0.202068	+	0.0103038i
$103$	−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
$105$	−96.7777	+	40.7318i	−0.921692	+	0.387922i
$106$	−68.3095			−0.644429
$107$	−139.010	−	139.010i	−1.29916	−	1.29916i	−0.928945	−	0.370218i	$-0.879283\pi$
$107$	−139.010	−	139.010i	−1.29916	−	1.29916i	−0.370218	−	0.928945i	$-0.620717\pi$
$108$	12.3322	+	80.0557i	0.114187	+	0.741257i
$109$		−	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	−0.257361	−	0.966315i	$-0.582853\pi$
$113$	80.1118	−	80.1118i	0.708954	−	0.708954i	0.966315	+	0.257361i	$0.0828530\pi$
$114$	48.4318	+	43.7321i	0.424840	+	0.383615i
$115$	12.2065	−	2.85400i	0.106144	−	0.0248174i
$116$			84.1356i			0.725307i
$117$	117.599	−	144.387i	1.00512	−	1.23408i
$118$	−20.9776	+	20.9776i	−0.177776	+	0.177776i
$119$	−5.65685	−	47.8212i	−0.0475366	−	0.401859i
$120$	−100.892	+	29.0811i	−0.840771	+	0.242342i
$121$	−72.2952			−0.597481
$122$	−14.8999	+	14.8999i	−0.122131	+	0.122131i
$123$	−80.0535	+	4.08209i	−0.650842	+	0.0331877i
$124$	51.7417			0.417272
$125$	−12.0248	+	124.420i	−0.0961984	+	0.995362i
$126$	61.4865	−	13.7264i	0.487988	−	0.108939i
$127$	−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	$-0.598093\pi$
$131$	−79.4683			−0.606629			−0.303314	+	0.952891i	$0.598093\pi$
$132$	−124.965	+	6.37223i	−0.946706	+	0.0482745i
$133$	−94.2712	+	119.566i	−0.708806	+	0.898996i
$134$	−45.9316			−0.342773
$135$	−124.192	−	52.9282i	−0.919939	−	0.392061i
$136$		−	48.1546i		−	0.354078i
$137$	7.42967	+	7.42967i	0.0542312	+	0.0542312i	0.733702	−	0.679471i	$-0.237791\pi$
$137$	7.42967	+	7.42967i	0.0542312	+	0.0542312i	−0.679471	+	0.733702i	$0.737791\pi$
$138$	−7.51167	+	0.383035i	−0.0544324	+	0.00277562i
$139$	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
$147$	41.5328	+	141.011i	0.282536	+	0.959257i
$148$	19.5214	+	19.5214i	0.131902	+	0.131902i
$149$	24.7386			0.166031			0.0830155	−	0.996548i	$-0.473545\pi$
$149$	24.7386			0.166031			0.0830155	+	0.996548i	$0.473545\pi$
$150$	20.3720	−	72.1802i	0.135813	−	0.481201i
$151$	−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
$153$	39.0989	−	48.0053i	0.255548	−	0.313760i
$154$	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
$162$	67.6821	+	44.4987i	0.417791	+	0.274684i
$163$	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
$165$	100.854	−	182.538i	0.611233	−	1.10629i
$166$		−	73.4931i		−	0.442730i
$167$	138.252	−	138.252i	0.827855	−	0.827855i	−0.159365	−	0.987220i	$-0.550945\pi$
$167$	138.252	−	138.252i	0.827855	−	0.827855i	0.987220	+	0.159365i	$0.0509447\pi$
$168$	24.6804	+	144.913i	0.146907	+	0.862579i
$169$		−	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	0.624893	−	0.780711i	$-0.285143\pi$
$173$	−26.9566	−	26.9566i	−0.155818	−	0.155818i	−0.780711	+	0.624893i	$0.785143\pi$
$174$	62.4454	+	56.3859i	0.358882	+	0.324057i
$175$	171.218	+	36.1871i	0.978387	+	0.206784i
$176$		−	69.5153i		−	0.394973i
$177$	−4.53242	−	88.8848i	−0.0256069	−	0.502174i
$178$	−123.245	+	123.245i	−0.692386	+	0.692386i
$179$	187.393			1.04689			0.523445	−	0.852059i	$-0.324646\pi$
$179$	187.393			1.04689			0.523445	+	0.852059i	$0.324646\pi$
$180$	59.1841	−	121.335i	0.328801	−	0.674085i
$181$			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
$183$	−3.21928	−	63.1331i	−0.0175917	−	0.344990i
$184$		−	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
$189$	−93.0578	+	164.503i	−0.492369	+	0.870386i
$190$	−24.7607	−	105.901i	−0.130320	−	0.557375i
$191$		−	107.063i		−	0.560538i	−0.959922	−	0.280269i	$-0.909576\pi$
$191$		−	107.063i		−	0.560538i	0.959922	−	0.280269i	$-0.0904236\pi$
$192$	1.98611	+	38.9494i	0.0103443	+	0.202861i
$193$	−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
$195$	−298.222	+	85.9589i	−1.52934	+	0.440815i
$196$	−142.943	+	34.2979i	−0.729300	+	0.174989i
$197$	165.702	+	165.702i	0.841127	+	0.841127i	0.989006	−	0.147878i	$-0.0472444\pi$
$197$	165.702	+	165.702i	0.841127	+	0.841127i	−0.147878	+	0.989006i	$0.547244\pi$
$198$	−79.0196	+	97.0196i	−0.399089	+	0.489998i
$199$	−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
$207$	14.2496	−	17.4956i	0.0688388	−	0.0845197i
$208$	−73.1533	+	73.1533i	−0.351698	+	0.351698i
$209$		−	302.412i		−	1.44695i
$210$	−97.2339	−	39.6304i	−0.463019	−	0.188716i
$211$	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
$213$	−2.44971	−	48.0411i	−0.0115010	−	0.225545i
$214$		−	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
$222$	27.5717	−	1.40593i	0.124197	−	0.00633304i
$223$	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
$225$	119.758	+	190.481i	0.532256	+	0.846584i
$226$	113.295			0.501306
$227$	191.389	−	191.389i	0.843123	−	0.843123i	−0.146140	−	0.989264i	$-0.546685\pi$
$227$	191.389	−	191.389i	0.843123	−	0.843123i	0.989264	+	0.146140i	$0.0466851\pi$
$228$	−9.96941	−	195.509i	−0.0437255	−	0.857496i
$229$	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
$231$	−238.181	−	168.858i	−1.03109	−	0.730986i
$232$	−138.817	+	138.817i	−0.598348	+	0.598348i
$233$	−89.8918	+	89.8918i	−0.385802	+	0.385802i	−0.873187	−	0.487385i	$-0.837951\pi$
$233$	−89.8918	+	89.8918i	−0.385802	+	0.385802i	0.487385	+	0.873187i	$0.337951\pi$
$234$	185.252	−	18.9420i	0.791675	−	0.0809487i
$235$	−127.831	+	29.8881i	−0.543961	+	0.127183i
$236$	89.0003			0.377120
$237$	11.5809	+	227.112i	0.0488646	+	0.958279i
$238$	29.8147	−	37.8147i	0.125272	−	0.158885i
$239$	−49.2786			−0.206187			−0.103093	−	0.994672i	$-0.532874\pi$
$239$	−49.2786			−0.206187			−0.103093	+	0.994672i	$0.532874\pi$
$240$	65.6465	+	36.2702i	0.273527	+	0.151126i
$241$		−	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
$243$	−235.158	+	61.2344i	−0.967729	+	0.251993i
$244$	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	$-0.258369\pi$
$251$	345.514			1.37655			0.688274	+	0.725450i	$0.258369\pi$
$252$	−159.551	−	101.315i	−0.633137	−	0.402042i
$253$	24.6476	+	24.6476i	0.0974214	+	0.0974214i
$254$	−101.325			−0.398917
$255$	−99.1518	+	28.5793i	−0.388831	+	0.112076i
$256$	−171.000			−0.667969
$257$	−216.568	+	216.568i	−0.842676	+	0.842676i	−0.989206	−	0.146530i	$-0.953190\pi$
$257$	−216.568	+	216.568i	−0.842676	+	0.842676i	0.146530	+	0.989206i	$0.453190\pi$
$258$	−7.16342	−	140.481i	−0.0277652	−	0.544501i
$259$	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	−0.226623	−	0.973982i	$-0.572769\pi$
$263$	196.555	−	196.555i	0.747359	−	0.747359i	0.973982	+	0.226623i	$0.0727686\pi$
$264$	−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
$267$	−26.6283	−	522.204i	−0.0997313	−	1.95582i
$268$	97.4357	+	97.4357i	0.363566	+	0.363566i
$269$			349.961i			1.30097i	0.759519	+	0.650485i	$0.225434\pi$
$269$			349.961i			1.30097i	−0.759519	+	0.650485i	$0.774566\pi$
$270$	−50.3909	−	125.243i	−0.186633	−	0.463862i
$271$			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
$273$	72.9511	+	428.340i	0.267220	+	1.56901i
$274$			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	$0.0813658\pi$
$281$			142.098i			0.505687i	−0.967507	+	0.252844i	$0.918634\pi$
$282$	78.6649	−	4.01128i	0.278954	−	0.0142244i
$283$	−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
$285$	285.582	+	157.786i	1.00204	+	0.553636i
$286$			287.666i			1.00583i
$287$	115.801	−	146.874i	0.403489	−	0.511755i
$288$	−230.284	−	187.559i	−0.799596	−	0.651247i
$289$			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	$-0.884567\pi$
$293$	−377.885	−	377.885i	−1.28971	−	1.28971i	−0.354747	−	0.934962i	$-0.615433\pi$
$294$	−70.3415	+	129.078i	−0.239257	+	0.439040i
$295$	−78.2536	+	126.013i	−0.265266	+	0.427163i
$296$			64.4174i			0.217626i
$297$	−57.1518	−	371.007i	−0.192430	−	1.24918i
$298$	17.4929	+	17.4929i	0.0587009	+	0.0587009i
$299$		−	51.8750i		−	0.173495i
$300$	−196.333	+	109.902i	−0.654443	+	0.366339i
$301$	325.943	−	38.5564i	1.08287	−	0.128094i
$302$	−115.487	−	115.487i	−0.382409	−	0.382409i
$303$	338.900	−	17.2812i	1.11848	−	0.0570337i
$304$	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	$-0.615860\pi$
$311$	−221.432			−0.712001			−0.356000	+	0.934486i	$0.615860\pi$
$312$	22.1277	+	433.944i	0.0709221	+	1.39085i
$313$	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
$315$	283.733	−	136.822i	0.900741	−	0.434357i
$316$	−227.407			−0.719643
$317$	−96.2271	−	96.2271i	−0.303556	−	0.303556i	0.538848	−	0.842403i	$-0.318860\pi$
$317$	−96.2271	−	96.2271i	−0.303556	−	0.303556i	−0.842403	+	0.538848i	$0.818860\pi$
$318$	204.663	−	10.4362i	0.643593	−	0.0328181i
$319$		−	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
$327$	0.460516	+	9.03113i	0.00140830	+	0.0276181i
$328$	132.253	−	132.253i	0.403211	−	0.403211i
$329$	21.5903	+	182.517i	0.0656240	+	0.554764i
$330$	200.388	−	57.7594i	0.607236	−	0.175029i
$331$	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
$333$	−52.3034	+	64.2177i	−0.157067	+	0.192846i
$334$	195.517			0.585382
$335$	−223.627	+	52.2861i	−0.667543	+	0.156078i
$336$	60.7268	−	85.6578i	0.180735	−	0.254934i
$337$	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
$342$	−151.788	−	123.627i	−0.443825	−	0.361482i
$343$	−311.465	−	143.661i	−0.908061	−	0.418837i
$344$	328.215			0.954114
$345$	−36.1360	+	10.4158i	−0.104742	+	0.0301906i
$346$		−	38.1223i		−	0.110180i
$347$	268.600	+	268.600i	0.774062	+	0.774062i	0.978814	−	0.204752i	$-0.0656387\pi$
$347$	268.600	+	268.600i	0.774062	+	0.774062i	−0.204752	+	0.978814i	$0.565639\pi$
$348$	−12.8540	−	252.079i	−0.0369369	−	0.724366i
$349$	−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	0.279509	−	0.960143i	$-0.409828\pi$
$353$	−240.264	−	240.264i	−0.680635	−	0.680635i	−0.960143	+	0.279509i	$0.909828\pi$
$354$	59.6461	−	66.0559i	0.168492	−	0.186599i
$355$	−42.2950	+	68.1084i	−0.119141	+	0.191855i
$356$	522.883			1.46877
$357$	24.2545	+	142.413i	0.0679399	+	0.398916i
$358$	132.507	+	132.507i	0.370132	+	0.370132i
$359$	161.739			0.450526			0.225263	−	0.974298i	$-0.427676\pi$
$359$	161.739			0.450526			0.225263	+	0.974298i	$0.427676\pi$
$360$	297.842	−	102.544i	0.827338	−	0.284845i
$361$	112.126			0.310599
$362$	−126.983	+	126.983i	−0.350781	+	0.350781i
$363$	216.604	−	11.0451i	0.596706	−	0.0304272i
$364$	−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
$372$	−155.024	+	7.90497i	−0.416730	+	0.0212499i
$373$	−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
$375$	17.0190	−	374.614i	0.0453839	−	0.998970i
$376$			183.790i			0.488803i
$377$	−410.320	+	410.320i	−1.08838	+	1.08838i
$378$	−182.123	+	50.5194i	−0.481807	+	0.133649i
$379$			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	0.460138	−	0.887847i	$-0.347800\pi$
$383$	−163.813	−	163.813i	−0.427710	−	0.427710i	−0.887847	+	0.460138i	$0.847800\pi$
$384$	239.254	−	264.965i	0.623057	−	0.690013i
$385$	165.680	+	457.533i	0.430339	+	1.18840i
$386$		−	115.447i		−	0.299085i
$387$	327.197	+	266.493i	0.845472	+	0.688612i
$388$	−49.9973	+	49.9973i	−0.128859	+	0.128859i
$389$	−401.000			−1.03085			−0.515425	−	0.856935i	$-0.672366\pi$
$389$	−401.000			−1.03085			−0.515425	+	0.856935i	$0.672366\pi$
$390$	−271.657	−	150.093i	−0.696556	−	0.384853i
$391$		−	17.2472i		−	0.0441105i
$392$	−292.432	−	179.255i	−0.746001	−	0.457283i
$393$	238.096	−	12.1410i	0.605841	−	0.0308931i
$394$			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
$399$	264.180	−	372.636i	0.662104	−	0.933926i
$400$	−55.4226	−	112.042i	−0.138557	−	0.280104i
$401$		−	582.912i		−	1.45365i	−0.686825	−	0.726823i	$-0.740996\pi$
$401$		−	582.912i		−	1.45365i	0.686825	−	0.726823i	$-0.259004\pi$
$402$	137.616	−	7.01732i	0.342329	−	0.0174560i
$403$	252.338	+	252.338i	0.626149	+	0.626149i
$404$			339.341i			0.839952i
$405$	380.178	+	139.605i	0.938712	+	0.344704i
$406$	−194.957	+	23.0618i	−0.480190	+	0.0568025i
$407$	−90.4693	−	90.4693i	−0.222283	−	0.222283i
$408$	7.35694	+	144.276i	0.0180317	+	0.353619i
$409$	−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
$417$	−538.068	+	27.4372i	−1.29033	+	0.0657965i
$418$	213.838	−	213.838i	0.511573	−	0.511573i
$419$		−	343.927i		−	0.820828i	−0.911899	−	0.410414i	$-0.865384\pi$
$419$		−	343.927i		−	0.820828i	0.911899	−	0.410414i	$-0.134616\pi$
$420$	122.195	+	290.333i	0.290942	+	0.691269i
$421$	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
$423$	−149.227	+	183.220i	−0.352783	+	0.433144i
$424$			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	$-0.828164\pi$
$431$		−	443.066i		−	1.02800i	0.857791	−	0.513998i	$-0.171836\pi$
$432$	133.426	−	20.5537i	0.308857	−	0.0475779i
$433$	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
$435$	368.214	+	203.441i	0.846469	+	0.467681i
$436$	−9.04287			−0.0207405
$437$	−38.5614	+	38.5614i	−0.0882412	+	0.0882412i
$438$	−243.041	+	12.3931i	−0.554888	+	0.0282948i
$439$	−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
$441$	−145.980	−	416.138i	−0.331021	−	0.943624i
$442$	100.648	−	100.648i	0.227710	−	0.227710i
$443$	188.010	−	188.010i	0.424401	−	0.424401i	−0.462315	−	0.886716i	$-0.652981\pi$
$443$	188.010	−	188.010i	0.424401	−	0.424401i	0.886716	+	0.462315i	$0.152981\pi$
$444$	−61.4707	−	55.5059i	−0.138448	−	0.125013i
$445$	−459.745	+	740.336i	−1.03314	+	1.66368i
$446$	245.406			0.550239
$447$	−74.1196	+	3.77951i	−0.165816	+	0.00845528i
$448$	−71.4602	−	56.3422i	−0.159509	−	0.125764i
$449$	−397.613			−0.885552			−0.442776	−	0.896632i	$-0.646006\pi$
$449$	−397.613			−0.885552			−0.442776	+	0.896632i	$0.646006\pi$
$450$	−50.0092	+	219.372i	−0.111132	+	0.487493i
$451$			371.478i			0.823677i
$452$	−240.335	−	240.335i	−0.531716	−	0.531716i
$453$	489.336	−	24.9522i	1.08021	−	0.0550821i
$454$	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	$-0.566614\pi$
$461$	−191.545			−0.415499			−0.207750	+	0.978182i	$0.566614\pi$
$462$	−49.0189	−	287.820i	−0.106102	−	0.622987i
$463$	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
$465$	125.112	−	226.444i	0.269058	−	0.486977i
$466$	−127.126			−0.272803
$467$	252.836	−	252.836i	0.541405	−	0.541405i	−0.382536	−	0.923941i	$-0.624949\pi$
$467$	252.836	−	252.836i	0.541405	−	0.541405i	0.923941	+	0.382536i	$0.124949\pi$
$468$	−433.161	−	352.797i	−0.925557	−	0.753839i
$469$	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
$477$	−388.245	+	476.684i	−0.813930	+	0.999337i
$478$	−34.8452	−	34.8452i	−0.0728980	−	0.0728980i
$479$		−	91.5191i		−	0.191063i	−0.995426	−	0.0955314i	$-0.969545\pi$
$479$		−	91.5191i		−	0.191063i	0.995426	−	0.0955314i	$-0.0304550\pi$
$480$	137.096	+	475.636i	0.285618	+	0.990908i
$481$			190.408i			0.395858i
$482$	298.161	−	298.161i	0.618592	−	0.618592i
$483$	8.83960	+	51.9027i	0.0183015	+	0.107459i
$484$			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	$0.176913\pi$
$491$			518.117i			1.05523i	−0.849484	+	0.527614i	$0.823087\pi$
$492$	12.2463	+	240.161i	0.0248908	+	0.488131i
$493$	−136.422	+	136.422i	−0.276717	+	0.276717i
$494$	−450.057			−0.911046
$495$	−274.280	+	562.311i	−0.554102	+	1.13598i
$496$		−	86.2361i		−	0.173863i
$497$	88.1406	+	69.4937i	0.177345	+	0.139826i
$498$	11.2281	+	220.193i	0.0225464	+	0.442155i
$499$		−	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	0.694329	−	0.719657i	$-0.255701\pi$
$503$	−12.7399	−	12.7399i	−0.0253279	−	0.0253279i	−0.719657	+	0.694329i	$0.755701\pi$
$504$	−96.0845	−	430.405i	−0.190644	−	0.853979i
$505$	−480.463	−	298.365i	−0.951412	−	0.590823i
$506$			34.8570i			0.0688873i
$507$	39.5865	+	776.327i	0.0780798	+	1.53122i
$508$	214.943	+	214.943i	0.423116	+	0.423116i
$509$		−	611.593i		−	1.20156i	−0.799415	−	0.600779i	$-0.794857\pi$
$509$		−	611.593i		−	1.20156i	0.799415	−	0.600779i	$-0.205143\pi$
$510$	−90.3195	−	49.9023i	−0.177097	−	0.0978476i
$511$	−66.7048	−	563.900i	−0.130538	−	1.10352i
$512$	215.668	+	215.668i	0.421226	+	0.421226i
$513$	580.443	−	89.4144i	1.13147	−	0.174297i
$514$	−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	$-0.268603\pi$
$521$	692.510			1.32919			0.664597	+	0.747202i	$0.268603\pi$
$522$	−195.708	−	159.398i	−0.374919	−	0.305360i
$523$	−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
$525$	−518.515	−	82.2623i	−0.987648	−	0.156690i
$526$	277.971			0.528463
$527$	83.8965	+	83.8965i	0.159196	+	0.159196i
$528$	10.6204	+	208.275i	0.0201144	+	0.394461i
$529$			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
$537$	−561.451	+	28.6295i	−1.04553	+	0.0533138i
$538$	−247.460	+	247.460i	−0.459963	+	0.459963i
$539$	662.448	−	158.948i	1.22903	−	0.294895i
$540$	−158.785	+	372.575i	−0.294046	+	0.689954i
$541$	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
$543$	−27.4359	−	538.043i	−0.0505265	−	0.990871i
$544$	−227.015			−0.417306
$545$	7.95095	−	12.8035i	0.0145889	−	0.0234927i
$546$	−251.298	+	354.467i	−0.460253	+	0.649206i
$547$	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
$552$	2.68125	+	52.5817i	0.00485733	+	0.0952567i
$553$	−416.681	−	328.529i	−0.753492	−	0.594084i
$554$	187.831			0.339045
$555$	132.637	−	38.2312i	0.238986	−	0.0688850i
$556$		−	538.767i		−	0.969005i
$557$	−245.854	−	245.854i	−0.441390	−	0.441390i	0.451089	−	0.892479i	$-0.351036\pi$
$557$	−245.854	−	245.854i	−0.441390	−	0.441390i	−0.892479	+	0.451089i	$0.851036\pi$
$558$	−98.0265	+	120.356i	−0.175675	+	0.215692i
$559$	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	0.968993	−	0.247086i	$-0.0794732\pi$
$563$	406.434	+	406.434i	0.721907	+	0.721907i	−0.247086	+	0.968993i	$0.579473\pi$
$564$	−175.383	−	158.364i	−0.310962	−	0.280788i
$565$	551.600	−	128.969i	0.976283	−	0.228264i
$566$	−170.038			−0.300420
$567$	253.679	−	507.086i	0.447405	−	0.894331i
$568$	79.3667	+	79.3667i	0.139730	+	0.139730i
$569$	690.156			1.21293			0.606464	−	0.795111i	$-0.292587\pi$
$569$	690.156			1.21293			0.606464	+	0.795111i	$0.292587\pi$
$570$	90.3651	+	313.508i	0.158535	+	0.550015i
$571$	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
$573$	16.3568	+	320.771i	0.0285459	+	0.559810i
$574$	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
$582$	3.60081	+	70.6151i	0.00618695	+	0.121332i
$583$	−671.548	−	671.548i	−1.15188	−	1.15188i
$584$		−	567.832i		−	0.972315i
$585$	880.372	−	303.104i	1.50491	−	0.518126i
$586$		−	534.410i		−	0.911962i
$587$	−195.495	+	195.495i	−0.333040	+	0.333040i	−0.853740	−	0.520700i	$-0.825671\pi$
$587$	−195.495	+	195.495i	−0.333040	+	0.333040i	0.520700	+	0.853740i	$0.325671\pi$
$588$	423.032	−	124.599i	0.719442	−	0.211902i
$589$		−	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	0.536897	−	0.843648i	$-0.319597\pi$
$593$	−181.904	−	181.904i	−0.306751	−	0.306751i	−0.843648	+	0.536897i	$0.819597\pi$
$594$	221.929	−	302.754i	0.373618	−	0.509686i
$595$	102.112	−	218.048i	0.171617	−	0.366466i
$596$		−	74.2159i		−	0.124523i
$597$	659.255	−	33.6167i	1.10428	−	0.0563094i
$598$	36.6812	−	36.6812i	0.0613397	−	0.0613397i
$599$	376.201			0.628048			0.314024	−	0.949415i	$-0.398323\pi$
$599$	376.201			0.628048			0.314024	+	0.949415i	$0.398323\pi$
$600$	−505.261	−	142.604i	−0.842102	−	0.237674i
$601$			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
$603$	−261.058	+	320.524i	−0.432931	+	0.531549i
$604$			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
$609$	340.619	−	480.458i	0.559309	−	0.788929i
$610$	−102.592	+	23.9869i	−0.168183	+	0.0393228i
$611$			543.253i			0.889122i
$612$	−144.016	−	117.297i	−0.235320	−	0.191661i
$613$	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
$615$	−350.804	−	193.822i	−0.570414	−	0.315158i
$616$	676.533	−	80.0283i	1.09827	−	0.129916i
$617$	−416.614	−	416.614i	−0.675225	−	0.675225i	0.283691	−	0.958916i	$-0.408441\pi$
$617$	−416.614	−	416.614i	−0.675225	−	0.675225i	−0.958916	+	0.283691i	$0.908441\pi$
$618$	68.5679	−	3.49641i	0.110951	−	0.00565763i
$619$	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
$627$	46.2018	+	906.059i	0.0736870	+	1.44507i
$628$	325.105	−	325.105i	0.517683	−	0.517683i
$629$			63.3061i			0.100646i
$630$	297.378	+	103.882i	0.472028	+	0.164892i
$631$	−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
$633$	−828.695	+	42.2568i	−1.30915	+	0.0667564i
$634$		−	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	$0.0466304\pi$
$641$			187.134i			0.291941i	−0.989289	+	0.145970i	$0.953370\pi$
$642$	30.0346	+	589.006i	0.0467829	+	0.917455i
$643$	−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
$645$	−194.793	−	675.805i	−0.302004	−	1.04776i
$646$	−149.633			−0.231631
$647$	573.588	−	573.588i	0.886535	−	0.886535i	−0.107654	−	0.994188i	$-0.534334\pi$
$647$	573.588	−	573.588i	0.886535	−	0.886535i	0.994188	+	0.107654i	$0.0343337\pi$
$648$	311.491	−	473.774i	0.480696	−	0.731133i
$649$	−412.459			−0.635530
$650$	229.348	+	463.648i	0.352844	+	0.713304i
$651$	−295.472	−	209.474i	−0.453874	−	0.321772i
$652$	116.536	−	116.536i	0.178736	−	0.178736i
$653$	−142.398	+	142.398i	−0.218067	+	0.218067i	−0.807683	−	0.589616i	$-0.799279\pi$
$653$	−142.398	+	142.398i	−0.218067	+	0.218067i	0.589616	+	0.807683i	$0.299279\pi$
$654$	−6.06034	+	6.71161i	−0.00926658	+	0.0102624i
$655$	−337.551	−	209.618i	−0.515345	−	0.320027i
$656$	−133.596			−0.203652
$657$	461.048	−	566.071i	0.701747	−	0.861600i
$658$	−113.793	+	144.326i	−0.172937	+	0.219340i
$659$	−960.106			−1.45691			−0.728457	−	0.685092i	$-0.759762\pi$
$659$	−960.106			−1.45691			−0.728457	+	0.685092i	$0.759762\pi$
$660$	−547.613	−	302.561i	−0.829717	−	0.458425i
$661$			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
$663$	21.7459	+	426.458i	0.0327993	+	0.643224i
$664$	−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
$672$	683.163	−	116.350i	1.01661	−	0.173140i
$673$	−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
$675$	−387.908	−	552.406i	−0.574678	−	0.818379i
$676$	−777.336			−1.14990
$677$	447.410	−	447.410i	0.660872	−	0.660872i	−0.294714	−	0.955586i	$-0.595224\pi$
$677$	447.410	−	447.410i	0.660872	−	0.660872i	0.955586	+	0.294714i	$0.0952243\pi$
$678$	−339.445	+	17.3090i	−0.500656	+	0.0255295i
$679$	−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	−0.837990	−	0.545686i	$-0.816269\pi$
$683$	−199.643	+	199.643i	−0.292303	+	0.292303i	0.545686	+	0.837990i	$0.316269\pi$
$684$	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
$687$	−369.991	+	18.8666i	−0.538560	+	0.0274622i
$688$	−165.774	−	165.774i	−0.240950	−	0.240950i
$689$			1413.38i			2.05135i
$690$	−32.9171	−	18.1869i	−0.0477059	−	0.0263579i
$691$		−	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
$693$	739.414	+	469.527i	1.06698	+	0.677529i
$694$			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	$-0.998155\pi$
$701$		−	8.12497i		−	0.0115905i	0.999983	−	0.00579527i	$-0.00184470\pi$
$702$	−552.141	+	85.0546i	−0.786525	+	0.121160i
$703$	141.540	−	141.540i	0.201337	−	0.201337i
$704$	180.740			0.256733
$705$	378.429	−	109.078i	0.536779	−	0.154720i
$706$		−	339.785i		−	0.481281i
$707$	−490.236	+	621.778i	−0.693403	+	0.879459i
$708$	−266.654	+	13.5972i	−0.376631	+	0.0192052i
$709$			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
$714$	−83.5508	+	117.852i	−0.117018	+	0.165059i
$715$	327.464	+	1400.56i	0.457992	+	1.95882i
$716$		−	562.180i		−	0.785168i
$717$	147.644	−	7.52867i	0.205919	−	0.0105002i
$718$	114.367	+	114.367i	0.159285	+	0.159285i
$719$		−	1236.22i		−	1.71936i	−0.510837	−	0.859678i	$-0.670664\pi$
$719$		−	1236.22i		−	1.71936i	0.510837	−	0.859678i	$-0.329336\pi$
$720$	−202.225	−	98.6402i	−0.280869	−	0.137000i
$721$	18.8191	+	159.090i	0.0261014	+	0.220652i
$722$	79.2852	+	79.2852i	0.109813	+	0.109813i
$723$	64.4208	+	1263.35i	0.0891021	+	1.74737i
$724$	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
$732$	−189.399	+	9.65785i	−0.258742	+	0.0131938i
$733$	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
$735$	−195.536	+	708.513i	−0.266035	+	0.963963i
$736$	−82.7358			−0.112413
$737$	−451.552	−	451.552i	−0.612689	−	0.612689i
$738$	186.454	+	151.861i	0.252648	+	0.205774i
$739$		−	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	−0.727592	−	0.686010i	$-0.759361\pi$
$743$	−30.8955	+	30.8955i	−0.0415822	+	0.0415822i	0.686010	+	0.727592i	$0.259361\pi$
$744$	−268.818	−	242.733i	−0.361315	−	0.326254i
$745$	105.080	+	65.2544i	0.141047	+	0.0875898i
$746$		−	522.501i		−	0.700404i
$747$	−512.856	−	417.706i	−0.686555	−	0.559179i
$748$	202.888	−	202.888i	0.271241	−	0.271241i
$749$	−1366.61	+	161.658i	−1.82457	+	0.215832i
$750$	276.926	−	252.858i	0.369235	−	0.337143i
$751$	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
$753$	−1035.20	+	52.7867i	−1.37476	+	0.0701019i
$754$	−580.279			−0.769601
$755$	−693.737	−	430.808i	−0.918857	−	0.570606i
$756$	493.509	+	279.173i	0.652790	+	0.369277i
$757$	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	$-0.654695\pi$
$761$	−710.902			−0.934168			−0.467084	+	0.884213i	$0.654695\pi$
$762$	303.581	−	15.4802i	0.398400	−	0.0203152i
$763$	−16.5694	−	13.0640i	−0.0217161	−	0.0171219i
$764$	−321.188			−0.420403
$765$	292.703	−	100.775i	0.382618	−	0.131732i
$766$		−	231.666i		−	0.302436i
$767$	434.044	+	434.044i	0.565898	+	0.565898i
$768$	512.334	−	26.1250i	0.667102	−	0.0340169i
$769$	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	0.479804	−	0.877376i	$-0.340708\pi$
$773$	−307.323	−	307.323i	−0.397572	−	0.397572i	−0.877376	+	0.479804i	$0.840708\pi$
$774$	42.9248	+	419.802i	0.0554583	+	0.542380i
$775$	−386.481	+	191.177i	−0.498686	+	0.246680i
$776$	−164.983			−0.212606
$777$	−32.4458	−	190.509i	−0.0417578	−	0.245186i
$778$	−283.550	−	283.550i	−0.364460	−	0.364460i
$779$	−581.181			−0.746061
$780$	257.877	+	894.665i	0.330611	+	1.14701i
$781$	−222.929			−0.285440
$782$	12.1956	−	12.1956i	0.0155954	−	0.0155954i
$783$	748.393	−	115.286i	0.955802	−	0.147237i
$784$	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
$792$	679.137	+	553.137i	0.857497	+	0.698406i
$793$	308.293	+	308.293i	0.388768	+	0.388768i
$794$		−	430.037i		−	0.541609i
$795$	984.560	−	283.788i	1.23844	−	0.356966i
$796$			660.111i			0.829285i
$797$	−941.657	+	941.657i	−1.18150	+	1.18150i	−0.202147	+	0.979355i	$0.564792\pi$
$797$	−941.657	+	941.657i	−1.18150	+	1.18150i	−0.979355	+	0.202147i	$0.935208\pi$
$798$	450.297	−	76.6905i	0.564282	−	0.0961034i
$799$			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
$807$	−53.4662	−	1048.52i	−0.0662530	−	1.29928i
$808$	−559.883	+	559.883i	−0.692925	+	0.692925i
$809$	1461.04			1.80598			0.902990	−	0.429662i	$-0.141367\pi$
$809$	1461.04			1.80598			0.902990	+	0.429662i	$0.141367\pi$
$810$	170.111	+	367.542i	0.210014	+	0.453756i
$811$		−	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
$813$	−21.0799	−	413.396i	−0.0259285	−	0.508482i
$814$		−	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
$819$	−284.010	−	1272.21i	−0.346777	−	1.55337i
$820$	211.436	−	340.479i	0.257848	−	0.415218i
$821$			782.279i			0.952837i	0.879219	+	0.476418i	$0.158065\pi$
$821$			782.279i			0.952837i	−0.879219	+	0.476418i	$0.841935\pi$
$822$	−1.60526	−	31.4805i	−0.00195287	−	0.0382975i
$823$	−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
$825$	909.876	−	509.324i	1.10288	−	0.617362i
$826$	24.3953	+	206.229i	0.0295342	+	0.249672i
$827$	711.346	+	711.346i	0.860152	+	0.860152i	0.991356	−	0.131203i	$-0.0418840\pi$
$827$	711.346	+	711.346i	0.860152	+	0.860152i	−0.131203	+	0.991356i	$0.541884\pi$
$828$	−52.4867	−	42.7489i	−0.0633898	−	0.0516291i
$829$	−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
$837$	−70.8987	−	460.246i	−0.0847057	−	0.549876i
$838$	243.193	−	243.193i	0.290206	−	0.290206i
$839$			915.483i			1.09116i	0.838059	+	0.545580i	$0.183690\pi$
$839$			915.483i			1.09116i	−0.838059	+	0.545580i	$0.816310\pi$
$840$	−277.413	+	680.637i	−0.330253	+	0.810282i
$841$	−54.4667			−0.0647642
$842$	10.3776	+	10.3776i	0.0123250	+	0.0123250i
$843$	−21.7094	−	425.741i	−0.0257526	−	0.505031i
$844$		−	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
$852$	−144.123	+	7.34913i	−0.169159	+	0.00862574i
$853$	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
$855$	−879.740	−	429.114i	−1.02894	−	0.501888i
$856$	−1376.13			−1.60763
$857$	−605.241	+	605.241i	−0.706232	+	0.706232i	−0.965741	−	0.259509i	$-0.916439\pi$
$857$	−605.241	+	605.241i	−0.706232	+	0.706232i	0.259509	+	0.965741i	$0.416439\pi$
$858$	−43.9490	−	861.880i	−0.0512226	−	1.00452i
$859$	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
$861$	−324.514	+	457.741i	−0.376904	+	0.531639i
$862$	313.295	−	313.295i	0.363452	−	0.363452i
$863$	−761.642	+	761.642i	−0.882551	+	0.882551i	−0.993793	−	0.111242i	$-0.964517\pi$
$863$	−761.642	+	761.642i	−0.882551	+	0.882551i	0.111242	+	0.993793i	$0.464517\pi$
$864$	718.609	+	526.765i	0.831724	+	0.609682i
$865$	−43.3965	−	185.606i	−0.0501693	−	0.214573i
$866$	689.220			0.795866
$867$	−36.9227	−	724.088i	−0.0425867	−	0.835165i
$868$	224.249	−	284.421i	0.258352	−	0.327674i
$869$	1053.89			1.21276
$870$	116.512	+	404.221i	0.133922	+	0.464622i
$871$			950.365i			1.09112i
$872$	−14.9200	−	14.9200i	−0.0171101	−	0.0171101i
$873$	−164.471	−	133.957i	−0.188397	−	0.153444i
$874$	−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	$-0.548807\pi$
$881$	−269.114			−0.305465			−0.152732	+	0.988268i	$0.548807\pi$
$882$	191.030	−	397.478i	0.216588	−	0.450655i
$883$	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
$885$	215.204	−	389.504i	0.243169	−	0.440118i
$886$	265.886			0.300097
$887$	−366.008	+	366.008i	−0.412636	+	0.412636i	−0.882656	−	0.470020i	$-0.844247\pi$
$887$	−366.008	+	366.008i	−0.412636	+	0.412636i	0.470020	+	0.882656i	$0.344247\pi$
$888$	−9.84154	−	193.002i	−0.0110828	−	0.217344i
$889$	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
$897$	7.92533	+	155.423i	0.00883538	+	0.173270i
$898$	−281.155	−	281.155i	−0.313090	−	0.313090i
$899$		−	483.702i		−	0.538044i
$900$	571.444	−	359.273i	0.634938	−	0.399192i
$901$			469.917i			0.521550i
$902$	−262.675	+	262.675i	−0.291214	+	0.291214i
$903$	−970.669	+	165.316i	−1.07494	+	0.183074i
$904$		−	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	$-0.657236\pi$
$911$		−	1604.19i		−	1.76091i	0.474126	−	0.880457i	$-0.342764\pi$
$912$	−325.849	+	16.6157i	−0.357290	+	0.0182189i
$913$	722.507	−	722.507i	0.791355	−	0.791355i
$914$	−93.6580			−0.102470
$915$	152.855	−	276.657i	0.167055	−	0.302357i
$916$		−	370.471i		−	0.404445i
$917$	−344.417	+	436.832i	−0.375591	+	0.476371i
$918$	−183.574	+	28.2787i	−0.199972	+	0.0308046i
$919$		−	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
$924$	−506.574	+	714.543i	−0.548240	+	0.773315i
$925$	−217.943	−	73.6857i	−0.235614	−	0.0796602i
$926$			60.7910i			0.0656490i
$927$	−130.073	+	159.703i	−0.140316	+	0.172279i
$928$	654.421	+	654.421i	0.705195	+	0.705195i
$929$			891.704i			0.959854i	0.877308	+	0.479927i	$0.159337\pi$
$929$			891.704i			0.959854i	−0.877308	+	0.479927i	$0.840663\pi$
$930$	248.588	−	71.6525i	0.267299	−	0.0770457i
$931$	248.676	+	1036.41i	0.267107	+	1.11322i
$932$	269.675	+	269.675i	0.289351	+	0.289351i
$933$	663.435	−	33.8299i	0.711077	−	0.0362592i
$934$	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	$-0.243837\pi$
$941$	1356.29			1.44133			0.720665	+	0.693284i	$0.243837\pi$
$942$	−23.4141	−	459.171i	−0.0248557	−	0.487443i
$943$	47.3683	−	47.3683i	0.0502314	−	0.0502314i
$944$		−	148.334i		−	0.157133i
$945$	−829.192	+	453.283i	−0.877452	+	0.479664i
$946$	−651.886			−0.689097
$947$	−757.557	−	757.557i	−0.799955	−	0.799955i	0.183133	−	0.983088i	$-0.441376\pi$
$947$	−757.557	−	757.557i	−0.799955	−	0.799955i	−0.983088	+	0.183133i	$0.941376\pi$
$948$	681.336	−	34.7427i	0.718709	−	0.0366484i
$949$		−	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	$-0.452781\pi$
$953$	1083.39	−	1083.39i	1.13682	−	1.13682i	0.989017	−	0.147800i	$-0.0472192\pi$
$954$	−611.597	+	62.5357i	−0.641087	+	0.0655511i
$955$	282.405	−	454.762i	0.295712	−	0.476190i
$956$			147.836i			0.154640i
$957$	59.5702	+	1168.22i	0.0622468	+	1.22072i
$958$	64.7138	−	64.7138i	0.0675509	−	0.0675509i
$959$	73.0408	−	8.64012i	0.0761635	−	0.00900951i
$960$	−94.3026	+	170.681i	−0.0982319	+	0.177793i
$961$	663.533			0.690461
$962$	−134.638	+	134.638i	−0.139957	+	0.139957i
$963$	−1371.87	−	1117.34i	−1.42457	−	1.16027i
$964$	−1264.99			−1.31223
$965$	−131.419	−	562.076i	−0.136185	−	0.582462i
$966$	−30.4502	+	42.9513i	−0.0315219	+	0.0444630i
$967$	−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	$-0.560454\pi$
$971$	−366.616			−0.377565			−0.188783	+	0.982019i	$0.560454\pi$
$972$	183.703	+	705.474i	0.188995	+	0.725797i
$973$	778.341	−	987.189i	0.799939	−	1.01458i
$974$	357.358			0.366898
$975$	−1493.47	−	421.515i	−1.53176	−	0.432323i
$976$		−	105.359i		−	0.107949i
$977$	−576.937	−	576.937i	−0.590519	−	0.590519i	0.347253	−	0.937772i	$-0.387115\pi$
$977$	−576.937	−	576.937i	−0.590519	−	0.590519i	−0.937772	+	0.347253i	$0.887115\pi$
$978$	−8.39291	−	164.593i	−0.00858170	−	0.168295i
$979$	−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	0.318765	−	0.947834i	$-0.396732\pi$
$983$	−618.375	−	618.375i	−0.629069	−	0.629069i	−0.947834	+	0.318765i	$0.896732\pi$
$984$	−376.039	+	416.450i	−0.382154	+	0.423222i
$985$	266.758	+	1140.92i	0.270820	+	1.15829i
$986$	−192.929			−0.195669
$987$	−92.5714	−	543.543i	−0.0937907	−	0.550702i
$988$	954.714	+	954.714i	0.966310	+	0.966310i
$989$	117.555			0.118862
$990$	−591.559	+	203.668i	−0.597534	+	0.205725i
$991$	−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
$993$	−524.362	+	26.7383i	−0.528058	+	0.0269267i
$994$	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.83.5	yes	16
3.2	odd	2	inner	105.3.k.c.83.2	yes	16
5.2	odd	4	inner	105.3.k.c.62.3	yes	16
7.6	odd	2	inner	105.3.k.c.83.8	yes	16
15.2	even	4	inner	105.3.k.c.62.8	yes	16
21.20	even	2	inner	105.3.k.c.83.3	yes	16
35.27	even	4	inner	105.3.k.c.62.2	✓	16
105.62	odd	4	inner	105.3.k.c.62.5	yes	16

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

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-2.99611 + 0.152778i) q^{3} -3.00000i q^{4} +(4.24762 + 2.63775i) q^{5} +(-2.22660 - 2.01054i) q^{6} +(4.33402 - 5.49694i) q^{7} +(4.94975 - 4.94975i) q^{8} +(8.95332 - 0.915476i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-2.99611 + 0.152778i) 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} +(0.458333 + 8.98832i) q^{12} +(14.6307 - 14.6307i) q^{13} +(6.95153 - 0.822309i) q^{14} +(-13.1293 - 7.25405i) q^{15} -5.00000 q^{16} +(4.86435 - 4.86435i) q^{17} +(6.97829 + 5.68361i) q^{18} -21.7515 q^{19} +(7.91326 - 12.7429i) q^{20} +(-12.1454 + 17.1316i) 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} +(-26.6852 + 4.11073i) q^{27} +(-16.4908 - 13.0020i) q^{28} -28.0452 q^{29} +(-4.15444 - 14.4132i) q^{30} +17.2472i q^{31} +(-23.3345 - 23.3345i) q^{32} +(-2.12408 - 41.6551i) 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} +(-20.7019 + 3.52576i) q^{42} +(33.1548 + 33.1548i) q^{43} +41.7092 q^{44} +(40.4451 + 19.7280i) q^{45} +2.50714 q^{46} +(-18.5656 + 18.5656i) q^{47} +(14.9805 - 0.763888i) 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} +(65.1697 - 3.32314i) q^{57} +(-19.8310 - 19.8310i) q^{58} +29.6668i q^{59} +(-21.7621 + 39.3879i) q^{60} +21.0717i q^{61} +(-12.1956 + 12.1956i) q^{62} +(33.7715 - 53.1835i) 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} +(39.7853 - 48.8480i) q^{72} +(57.3597 - 57.3597i) q^{73} -9.20249 q^{74} +(-36.6339 - 65.4443i) q^{75} +65.2544i q^{76} +(76.4243 + 60.2561i) q^{77} +(-61.9921 + 3.16110i) 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} +(51.3947 + 36.4361i) q^{84} +(33.4929 - 7.83095i) q^{85} +46.8879i q^{86} +(84.0264 - 4.28468i) q^{87} +(68.8167 + 68.8167i) q^{88} +174.294i q^{89} +(14.6492 + 42.5488i) q^{90} +(-17.0143 - 143.833i) q^{91} +(-5.31846 - 5.31846i) q^{92} +(-2.63499 - 51.6745i) 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

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Representations

Groups

Database

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