LMFDB - Embedded newform 105.3.k.c.62.2

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			62.2
Root			$-0.611750 + 0.253395i$ of defining polynomial
Character	$\chi$	$=$	105.62
Dual form			105.3.k.c.83.2

$q$-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 $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

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

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	$-0.830431\pi$
$2$	−0.707107	+	0.707107i	−0.353553	+	0.353553i	0.507877	+	0.861430i	$0.330431\pi$
$3$	−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	$0.217748\pi$
$11$			13.9031i			1.26392i	−0.775003	+	0.631958i	$0.782252\pi$
$12$	8.98832	−	0.458333i	0.749027	−	0.0381944i
$13$	14.6307	+	14.6307i	1.12543	+	1.12543i	0.990910	+	0.134524i	$0.0429507\pi$
$13$	14.6307	+	14.6307i	1.12543	+	1.12543i	0.134524	+	0.990910i	$0.457049\pi$
$14$	−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	0.549413	−	0.835551i	$-0.314851\pi$
$17$	−4.86435	−	4.86435i	−0.286138	−	0.286138i	−0.835551	+	0.549413i	$0.814851\pi$
$18$	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	0.667516	−	0.744595i	$-0.267357\pi$
$23$	−1.77282	−	1.77282i	−0.0770791	−	0.0770791i	−0.744595	+	0.667516i	$0.767357\pi$
$24$	−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	$-0.910268\pi$
$31$		−	17.2472i		−	0.556362i	0.960529	−	0.278181i	$-0.0897315\pi$
$32$	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	0.613683	−	0.789552i	$-0.289687\pi$
$37$	−6.50714	−	6.50714i	−0.175869	−	0.175869i	−0.789552	+	0.613683i	$0.789687\pi$
$38$	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	−0.207248	−	0.978289i	$-0.566451\pi$
$43$	33.1548	−	33.1548i	0.771041	−	0.771041i	0.978289	+	0.207248i	$0.0664506\pi$
$44$	−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	0.876470	−	0.481457i	$-0.159892\pi$
$47$	18.5656	+	18.5656i	0.395012	+	0.395012i	−0.481457	+	0.876470i	$0.659892\pi$
$48$	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	0.996379	−	0.0850185i	$-0.0270949\pi$
$53$	48.3021	+	48.3021i	0.911361	+	0.911361i	−0.0850185	+	0.996379i	$0.527095\pi$
$54$	−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	$0.0808953\pi$
$59$			29.6668i			0.502826i	−0.967880	+	0.251413i	$0.919105\pi$
$60$	−36.9700	+	25.6558i	−0.616167	+	0.427597i
$61$		−	21.0717i		−	0.345438i	−0.984971	−	0.172719i	$-0.944745\pi$
$61$		−	21.0717i		−	0.345438i	0.984971	−	0.172719i	$-0.0552552\pi$
$62$	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	0.421892	−	0.906646i	$-0.361366\pi$
$67$	−32.4786	−	32.4786i	−0.484755	−	0.484755i	−0.906646	+	0.421892i	$0.861366\pi$
$68$	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	$0.963980\pi$
$72$	48.8480	+	39.7853i	0.678445	+	0.552573i
$73$	57.3597	+	57.3597i	0.785749	+	0.785749i	0.980794	−	0.195045i	$-0.0624853\pi$
$73$	57.3597	+	57.3597i	0.785749	+	0.785749i	−0.195045	+	0.980794i	$0.562485\pi$
$74$	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	$0.159277\pi$
$79$			75.8024i			0.959524i	−0.877399	+	0.479762i	$0.840723\pi$
$80$	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	$-0.604010\pi$
$83$	51.9675	−	51.9675i	0.626114	−	0.626114i	0.947088	+	0.320974i	$0.104010\pi$
$84$	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	$0.434935\pi$
$89$			174.294i			1.95836i	−0.202987	+	0.979181i	$0.565065\pi$
$90$	−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	−0.787775	−	0.615963i	$-0.788767\pi$
$97$	−16.6658	+	16.6658i	−0.171812	+	0.171812i	0.615963	+	0.787775i	$0.288767\pi$
$98$	−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	0.624173	−	0.781286i	$-0.285436\pi$
$103$	−16.1826	−	16.1826i	−0.157113	−	0.157113i	−0.781286	+	0.624173i	$0.785436\pi$
$104$		−	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	0.370218	−	0.928945i	$-0.379283\pi$
$107$	139.010	−	139.010i	1.29916	−	1.29916i	0.928945	−	0.370218i	$-0.120717\pi$
$108$	−80.0557	+	12.3322i	−0.741257	+	0.114187i
$109$			3.01429i			0.0276540i	0.999904	+	0.0138270i	$0.00440141\pi$
$109$			3.01429i			0.0276540i	−0.999904	+	0.0138270i	$0.995599\pi$
$110$	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	$-0.417147\pi$
$113$	−80.1118	−	80.1118i	−0.708954	−	0.708954i	−0.966315	+	0.257361i	$0.917147\pi$
$114$	−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	0.366330	−	0.930485i	$-0.380614\pi$
$127$	−71.6476	−	71.6476i	−0.564154	−	0.564154i	−0.930485	+	0.366330i	$0.880614\pi$
$128$	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	−0.733702	−	0.679471i	$-0.762209\pi$
$137$	−7.42967	+	7.42967i	−0.0542312	+	0.0542312i	0.679471	+	0.733702i	$0.262209\pi$
$138$	−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	−0.272042	−	0.962285i	$-0.587699\pi$
$157$	108.368	−	108.368i	0.690244	−	0.690244i	0.962285	+	0.272042i	$0.0876988\pi$
$158$	−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	−0.577837	−	0.816152i	$-0.696103\pi$
$163$	38.8452	−	38.8452i	0.238314	−	0.238314i	0.816152	+	0.577837i	$0.196103\pi$
$164$		−	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	0.159365	−	0.987220i	$-0.449055\pi$
$167$	−138.252	−	138.252i	−0.827855	−	0.827855i	−0.987220	+	0.159365i	$0.949055\pi$
$168$	−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	−0.624893	−	0.780711i	$-0.714857\pi$
$173$	26.9566	−	26.9566i	0.155818	−	0.155818i	0.780711	+	0.624893i	$0.214857\pi$
$174$	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	$-0.834773\pi$
$181$		−	179.581i		−	0.992158i	0.868277	−	0.496079i	$-0.165227\pi$
$182$	−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	$-0.909576\pi$
$191$		−	107.063i		−	0.560538i	0.959922	−	0.280269i	$-0.0904236\pi$
$192$	38.9494	−	1.98611i	0.202861	−	0.0103443i
$193$	−81.6333	+	81.6333i	−0.422971	+	0.422971i	−0.886225	−	0.463255i	$-0.846682\pi$
$193$	−81.6333	+	81.6333i	−0.422971	+	0.422971i	0.463255	+	0.886225i	$0.346682\pi$
$194$		−	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	−0.989006	−	0.147878i	$-0.952756\pi$
$197$	−165.702	+	165.702i	−0.841127	+	0.841127i	0.147878	+	0.989006i	$0.452756\pi$
$198$	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	0.979517	−	0.201362i	$-0.0645368\pi$
$223$	173.529	+	173.529i	0.778155	+	0.778155i	−0.201362	+	0.979517i	$0.564537\pi$
$224$	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	0.146140	−	0.989264i	$-0.453315\pi$
$227$	−191.389	−	191.389i	−0.843123	−	0.843123i	−0.989264	+	0.146140i	$0.953315\pi$
$228$	−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	0.873187	−	0.487385i	$-0.162049\pi$
$233$	89.8918	+	89.8918i	0.385802	+	0.385802i	−0.487385	+	0.873187i	$0.662049\pi$
$234$	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	$0.339021\pi$
$241$			421.664i			1.74964i	−0.484445	+	0.874822i	$0.660979\pi$
$242$	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	0.989206	−	0.146530i	$-0.0468104\pi$
$257$	216.568	+	216.568i	0.842676	+	0.842676i	−0.146530	+	0.989206i	$0.546810\pi$
$258$	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	0.226623	−	0.973982i	$-0.427231\pi$
$263$	−196.555	−	196.555i	−0.747359	−	0.747359i	−0.973982	+	0.226623i	$0.927231\pi$
$264$	−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	$0.225434\pi$
$269$			349.961i			1.30097i	−0.759519	+	0.650485i	$0.774566\pi$
$270$	134.602	+	10.3632i	0.498525	+	0.0383822i
$271$		−	137.978i		−	0.509143i	−0.967054	−	0.254572i	$-0.918066\pi$
$271$		−	137.978i		−	0.509143i	0.967054	−	0.254572i	$-0.0819344\pi$
$272$	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	0.904966	−	0.425484i	$-0.139896\pi$
$277$	132.817	+	132.817i	0.479483	+	0.479483i	−0.425484	+	0.904966i	$0.639896\pi$
$278$	−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	$0.918634\pi$
$282$	4.01128	+	78.6649i	0.0142244	+	0.278954i
$283$	−120.235	−	120.235i	−0.424858	−	0.424858i	0.462014	−	0.886873i	$-0.347127\pi$
$283$	−120.235	−	120.235i	−0.424858	−	0.424858i	−0.886873	+	0.462014i	$0.847127\pi$
$284$	−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	0.354747	−	0.934962i	$-0.384567\pi$
$293$	377.885	−	377.885i	1.28971	−	1.28971i	0.934962	−	0.354747i	$-0.115433\pi$
$294$	−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	−0.844264	−	0.535928i	$-0.819962\pi$
$307$	−94.6590	+	94.6590i	−0.308335	+	0.308335i	0.535928	+	0.844264i	$0.319962\pi$
$308$	−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	0.968989	−	0.247104i	$-0.0794790\pi$
$313$	225.950	+	225.950i	0.721885	+	0.721885i	−0.247104	+	0.968989i	$0.579479\pi$
$314$			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	−0.538848	−	0.842403i	$-0.681140\pi$
$317$	96.2271	−	96.2271i	0.303556	−	0.303556i	0.842403	+	0.538848i	$0.181140\pi$
$318$	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	0.850739	−	0.525588i	$-0.176155\pi$
$337$	109.576	+	109.576i	0.325152	+	0.325152i	−0.525588	+	0.850739i	$0.676155\pi$
$338$	−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	−0.978814	−	0.204752i	$-0.934361\pi$
$347$	−268.600	+	268.600i	−0.774062	+	0.774062i	0.204752	+	0.978814i	$0.434361\pi$
$348$	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	−0.279509	−	0.960143i	$-0.590172\pi$
$353$	240.264	−	240.264i	0.680635	−	0.680635i	0.960143	+	0.279509i	$0.0901715\pi$
$354$	−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	−0.555904	−	0.831247i	$-0.687628\pi$
$367$	101.051	−	101.051i	0.275343	−	0.275343i	0.831247	+	0.555904i	$0.187628\pi$
$368$	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	−0.999955	−	0.00943464i	$-0.996997\pi$
$373$	−369.464	+	369.464i	−0.990521	+	0.990521i	0.00943464	+	0.999955i	$0.496997\pi$
$374$			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	$-0.888013\pi$
$379$		−	261.209i		−	0.689207i	0.938748	−	0.344604i	$-0.111987\pi$
$380$	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	$-0.652200\pi$
$383$	163.813	−	163.813i	0.427710	−	0.427710i	0.887847	+	0.460138i	$0.152200\pi$
$384$	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	−0.977391	−	0.211440i	$-0.932185\pi$
$397$	−304.082	+	304.082i	−0.765950	+	0.765950i	0.211440	+	0.977391i	$0.432185\pi$
$398$	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	$-0.740996\pi$
$401$		−	582.912i		−	1.45365i	0.686825	−	0.726823i	$-0.259004\pi$
$402$	−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	$-0.865384\pi$
$419$		−	343.927i		−	0.820828i	0.911899	−	0.410414i	$-0.134616\pi$
$420$	−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	$-0.828164\pi$
$431$		−	443.066i		−	1.02800i	0.857791	−	0.513998i	$-0.171836\pi$
$432$	−20.5537	−	133.426i	−0.0475779	−	0.308857i
$433$	487.352	+	487.352i	1.12553	+	1.12553i	0.990896	+	0.134629i	$0.0429843\pi$
$433$	487.352	+	487.352i	1.12553	+	1.12553i	0.134629	+	0.990896i	$0.457016\pi$
$434$	−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	0.462315	−	0.886716i	$-0.347019\pi$
$443$	−188.010	−	188.010i	−0.424401	−	0.424401i	−0.886716	+	0.462315i	$0.847019\pi$
$444$	−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	0.630927	−	0.775842i	$-0.282675\pi$
$457$	−66.2262	−	66.2262i	−0.144915	−	0.144915i	−0.775842	+	0.630927i	$0.782675\pi$
$458$	−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	−0.659161	−	0.752002i	$-0.729088\pi$
$463$	42.9857	−	42.9857i	0.0928417	−	0.0928417i	0.752002	+	0.659161i	$0.229088\pi$
$464$	−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	0.382536	−	0.923941i	$-0.375051\pi$
$467$	−252.836	−	252.836i	−0.541405	−	0.541405i	−0.923941	+	0.382536i	$0.875051\pi$
$468$	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	$-0.969545\pi$
$479$		−	91.5191i		−	0.191063i	0.995426	−	0.0955314i	$-0.0304550\pi$
$480$	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	0.917230	−	0.398358i	$-0.130420\pi$
$487$	252.690	+	252.690i	0.518872	+	0.518872i	−0.398358	+	0.917230i	$0.630420\pi$
$488$	−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	$0.823087\pi$
$492$	−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	$0.0698561\pi$
$499$			217.267i			0.435404i	−0.976015	+	0.217702i	$0.930144\pi$
$500$	−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	$-0.744299\pi$
$503$	12.7399	−	12.7399i	0.0253279	−	0.0253279i	0.719657	+	0.694329i	$0.244299\pi$
$504$	−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	$-0.794857\pi$
$509$		−	611.593i		−	1.20156i	0.799415	−	0.600779i	$-0.205143\pi$
$510$	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	−0.992258	−	0.124191i	$-0.960366\pi$
$523$	−583.903	−	583.903i	−1.11645	−	1.11645i	−0.124191	−	0.992258i	$-0.539634\pi$
$524$			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	0.881495	−	0.472193i	$-0.156538\pi$
$547$	223.888	+	223.888i	0.409302	+	0.409302i	−0.472193	+	0.881495i	$0.656538\pi$
$548$	−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	−0.451089	−	0.892479i	$-0.648964\pi$
$557$	245.854	−	245.854i	0.441390	−	0.441390i	0.892479	+	0.451089i	$0.148964\pi$
$558$	−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	−0.968993	−	0.247086i	$-0.920527\pi$
$563$	−406.434	+	406.434i	−0.721907	+	0.721907i	0.247086	+	0.968993i	$0.420527\pi$
$564$	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	−0.451366	−	0.892339i	$-0.649063\pi$
$577$	254.442	−	254.442i	0.440973	−	0.440973i	0.892339	+	0.451366i	$0.149063\pi$
$578$	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	0.853740	−	0.520700i	$-0.174329\pi$
$587$	195.495	+	195.495i	0.333040	+	0.333040i	−0.520700	+	0.853740i	$0.674329\pi$
$588$	−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	−0.536897	−	0.843648i	$-0.680403\pi$
$593$	181.904	−	181.904i	0.306751	−	0.306751i	0.843648	+	0.536897i	$0.180403\pi$
$594$	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	$-0.616143\pi$
$601$		−	1122.87i		−	1.86834i	0.356832	−	0.934169i	$-0.383857\pi$
$602$	−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	−0.593879	−	0.804554i	$-0.702404\pi$
$607$	127.880	−	127.880i	0.210675	−	0.210675i	0.804554	+	0.593879i	$0.202404\pi$
$608$	−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	0.0956388	−	0.995416i	$-0.469511\pi$
$613$	668.817	−	668.817i	1.09105	−	1.09105i	0.995416	−	0.0956388i	$-0.0304894\pi$
$614$		−	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	−0.283691	−	0.958916i	$-0.591559\pi$
$617$	416.614	−	416.614i	0.675225	−	0.675225i	0.958916	+	0.283691i	$0.0915589\pi$
$618$	−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	$0.0466304\pi$
$641$			187.134i			0.291941i	−0.989289	+	0.145970i	$0.953370\pi$
$642$	589.006	−	30.0346i	0.917455	−	0.0467829i
$643$	−767.988	−	767.988i	−1.19438	−	1.19438i	−0.975824	−	0.218559i	$-0.929864\pi$
$643$	−767.988	−	767.988i	−1.19438	−	1.19438i	−0.218559	−	0.975824i	$-0.570136\pi$
$644$	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	0.107654	−	0.994188i	$-0.465666\pi$
$647$	−573.588	−	573.588i	−0.886535	−	0.886535i	−0.994188	+	0.107654i	$0.965666\pi$
$648$	−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	0.807683	−	0.589616i	$-0.200721\pi$
$653$	142.398	+	142.398i	0.218067	+	0.218067i	−0.589616	+	0.807683i	$0.700721\pi$
$654$	−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	$-0.977146\pi$
$661$		−	94.8355i		−	0.143473i	0.997424	−	0.0717364i	$-0.0228540\pi$
$662$	−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	−0.954915	−	0.296880i	$-0.904054\pi$
$673$	−442.857	+	442.857i	−0.658034	+	0.658034i	0.296880	+	0.954915i	$0.404054\pi$
$674$	−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	0.294714	−	0.955586i	$-0.404776\pi$
$677$	−447.410	−	447.410i	−0.660872	−	0.660872i	−0.955586	+	0.294714i	$0.904776\pi$
$678$	−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	0.837990	−	0.545686i	$-0.183731\pi$
$683$	199.643	+	199.643i	0.292303	+	0.292303i	−0.545686	+	0.837990i	$0.683731\pi$
$684$	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	$0.0479031\pi$
$691$			207.196i			0.299849i	−0.988697	+	0.149925i	$0.952097\pi$
$692$	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	$-0.998155\pi$
$701$		−	8.12497i		−	0.0115905i	0.999983	−	0.00579527i	$-0.00184470\pi$
$702$	−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	$-0.794222\pi$
$709$		−	854.167i		−	1.20475i	0.798214	−	0.602374i	$-0.205778\pi$
$710$	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	$-0.670664\pi$
$719$		−	1236.22i		−	1.71936i	0.510837	−	0.859678i	$-0.329336\pi$
$720$	−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	−0.119351	−	0.992852i	$-0.538081\pi$
$727$	635.035	−	635.035i	0.873501	−	0.873501i	0.992852	+	0.119351i	$0.0380815\pi$
$728$	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	0.816246	−	0.577704i	$-0.196051\pi$
$733$	174.851	+	174.851i	0.238542	+	0.238542i	−0.577704	+	0.816246i	$0.696051\pi$
$734$			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	$0.436819\pi$
$739$			1448.98i			1.96073i	−0.197187	+	0.980366i	$0.563181\pi$
$740$	−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	$-0.240639\pi$
$743$	30.8955	+	30.8955i	0.0415822	+	0.0415822i	−0.686010	+	0.727592i	$0.740639\pi$
$744$	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	0.831582	−	0.555401i	$-0.187435\pi$
$757$	209.069	+	209.069i	0.276181	+	0.276181i	−0.555401	+	0.831582i	$0.687435\pi$
$758$	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	−0.479804	−	0.877376i	$-0.659292\pi$
$773$	307.323	−	307.323i	0.397572	−	0.397572i	0.877376	+	0.479804i	$0.159292\pi$
$774$	−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	−0.820766	−	0.571265i	$-0.806453\pi$
$787$	−196.357	+	196.357i	−0.249501	+	0.249501i	0.571265	+	0.820766i	$0.306453\pi$
$788$	−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	0.979355	+	0.202147i	$0.0647918\pi$
$797$	941.657	+	941.657i	1.18150	+	1.18150i	0.202147	+	0.979355i	$0.435208\pi$
$798$	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	$0.290873\pi$
$811$			1284.35i			1.58367i	−0.610738	+	0.791833i	$0.709127\pi$
$812$	−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	$0.158065\pi$
$821$			782.279i			0.952837i	−0.879219	+	0.476418i	$0.841935\pi$
$822$	−31.4805	+	1.60526i	−0.0382975	+	0.00195287i
$823$	−361.067	+	361.067i	−0.438720	+	0.438720i	−0.891581	−	0.452861i	$-0.850403\pi$
$823$	−361.067	+	361.067i	−0.438720	+	0.438720i	0.452861	+	0.891581i	$0.350403\pi$
$824$			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	−0.991356	−	0.131203i	$-0.958116\pi$
$827$	−711.346	+	711.346i	−0.860152	+	0.860152i	0.131203	+	0.991356i	$0.458116\pi$
$828$	−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	$0.183690\pi$
$839$			915.483i			1.09116i	−0.838059	+	0.545580i	$0.816310\pi$
$840$	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	0.855015	−	0.518604i	$-0.173548\pi$
$853$	286.958	+	286.958i	0.336411	+	0.336411i	−0.518604	+	0.855015i	$0.673548\pi$
$854$	−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	0.965741	−	0.259509i	$-0.0835606\pi$
$857$	605.241	+	605.241i	0.706232	+	0.706232i	−0.259509	+	0.965741i	$0.583561\pi$
$858$	−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	0.993793	−	0.111242i	$-0.0354830\pi$
$863$	761.642	+	761.642i	0.882551	+	0.882551i	−0.111242	+	0.993793i	$0.535483\pi$
$864$	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	0.694697	−	0.719302i	$-0.255538\pi$
$877$	−21.5786	−	21.5786i	−0.0246050	−	0.0246050i	−0.719302	+	0.694697i	$0.755538\pi$
$878$	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	−0.227171	−	0.973855i	$-0.572948\pi$
$883$	659.321	−	659.321i	0.746683	−	0.746683i	0.973855	+	0.227171i	$0.0729478\pi$
$884$	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	0.882656	−	0.470020i	$-0.155753\pi$
$887$	366.008	+	366.008i	0.412636	+	0.412636i	−0.470020	+	0.882656i	$0.655753\pi$
$888$	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	0.742052	−	0.670342i	$-0.233853\pi$
$907$	65.0405	+	65.0405i	0.0717094	+	0.0717094i	−0.670342	+	0.742052i	$0.733853\pi$
$908$	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	$-0.342764\pi$
$912$	−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	$0.00312766\pi$
$919$			18.0596i			0.0196513i	−0.999952	+	0.00982566i	$0.996872\pi$
$920$	−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	$0.159337\pi$
$929$			891.704i			0.959854i	−0.877308	+	0.479927i	$0.840663\pi$
$930$	−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	−0.398652	−	0.917102i	$-0.630522\pi$
$937$	485.788	−	485.788i	0.518450	−	0.518450i	0.917102	+	0.398652i	$0.130522\pi$
$938$	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	−0.183133	−	0.983088i	$-0.558624\pi$
$947$	757.557	−	757.557i	0.799955	−	0.799955i	0.983088	+	0.183133i	$0.0586240\pi$
$948$	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	−0.989017	−	0.147800i	$-0.952781\pi$
$953$	−1083.39	−	1083.39i	−1.13682	−	1.13682i	−0.147800	−	0.989017i	$-0.547219\pi$
$954$	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	−0.999884	−	0.0151989i	$-0.995162\pi$
$967$	−981.586	−	981.586i	−1.01508	−	1.01508i	−0.0151989	−	0.999884i	$-0.504838\pi$
$968$	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	−0.347253	−	0.937772i	$-0.612885\pi$
$977$	576.937	−	576.937i	0.590519	−	0.590519i	0.937772	+	0.347253i	$0.112885\pi$
$978$	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	−0.318765	−	0.947834i	$-0.603268\pi$
$983$	618.375	−	618.375i	0.629069	−	0.629069i	0.947834	+	0.318765i	$0.103268\pi$
$984$	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	−0.748986	−	0.662585i	$-0.769459\pi$
$997$	−86.1420	+	86.1420i	−0.0864012	+	0.0864012i	0.662585	+	0.748986i	$0.269459\pi$
$998$	−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.62.2	✓	16
3.2	odd	2	inner	105.3.k.c.62.5	yes	16
5.3	odd	4	inner	105.3.k.c.83.8	yes	16
7.6	odd	2	inner	105.3.k.c.62.3	yes	16
15.8	even	4	inner	105.3.k.c.83.3	yes	16
21.20	even	2	inner	105.3.k.c.62.8	yes	16
35.13	even	4	inner	105.3.k.c.83.5	yes	16
105.83	odd	4	inner	105.3.k.c.83.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.k.c.62.2	✓	16	1.1	even	1	trivial
105.3.k.c.62.3	yes	16	7.6	odd	2	inner
105.3.k.c.62.5	yes	16	3.2	odd	2	inner
105.3.k.c.62.8	yes	16	21.20	even	2	inner
105.3.k.c.83.2	yes	16	105.83	odd	4	inner
105.3.k.c.83.3	yes	16	15.8	even	4	inner
105.3.k.c.83.5	yes	16	35.13	even	4	inner
105.3.k.c.83.8	yes	16	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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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