LMFDB - Embedded newform 63.4.f.c.22.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(22,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("63.22");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.f (of order $3$, 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:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 6 x^{16} - 23 x^{15} - 6 x^{14} + 255 x^{13} - 56 x^{12} - 81 x^{11} + \cdots + 387420489 $ x^18 - 3x^17 + 6x^16 - 23x^15 - 6x^14 + 255x^13 - 56x^12 - 81x^11 + 5832x^10 - 32373x^9 + 52488x^8 - 6561x^7 - 40824x^6 + 1673055x^5 - 354294x^4 - 12223143x^3 + 28697814x^2 - 129140163*x + 387420489
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.6
Root			$2.81021 + 1.05012i$ of defining polynomial
Character	$\chi$	$=$	63.22
Dual form			63.4.f.c.43.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32666 + 2.29785i) q^{2} +(5.12474 + 0.858536i) q^{3} +(0.479932 - 0.831266i) q^{4} +(-10.0300 + 17.3725i) q^{5} +(4.82601 + 12.9148i) q^{6} +(-3.50000 - 6.06218i) q^{7} +23.7734 q^{8} +(25.5258 + 8.79954i) q^{9} +O(q^{10})$	\(q+(1.32666 + 2.29785i) q^{2} +(5.12474 + 0.858536i) q^{3} +(0.479932 - 0.831266i) q^{4} +(-10.0300 + 17.3725i) q^{5} +(4.82601 + 12.9148i) q^{6} +(-3.50000 - 6.06218i) q^{7} +23.7734 q^{8} +(25.5258 + 8.79954i) q^{9} -53.2258 q^{10} +(-0.517107 - 0.895656i) q^{11} +(3.17319 - 3.84798i) q^{12} +(30.1411 - 52.2059i) q^{13} +(9.28664 - 16.0849i) q^{14} +(-66.3161 + 80.4183i) q^{15} +(27.6999 + 47.9776i) q^{16} -104.870 q^{17} +(13.6442 + 70.3285i) q^{18} -6.08988 q^{19} +(9.62744 + 16.6752i) q^{20} +(-12.7320 - 34.0719i) q^{21} +(1.37205 - 2.37647i) q^{22} +(105.565 - 182.844i) q^{23} +(121.833 + 20.4103i) q^{24} +(-138.702 - 240.240i) q^{25} +159.948 q^{26} +(123.258 + 67.0102i) q^{27} -6.71904 q^{28} +(24.6842 + 42.7544i) q^{29} +(-272.768 - 45.6963i) q^{30} +(-25.8062 + 44.6977i) q^{31} +(21.5969 - 37.4070i) q^{32} +(-1.88109 - 5.03396i) q^{33} +(-139.126 - 240.974i) q^{34} +140.420 q^{35} +(19.5654 - 16.9956i) q^{36} -198.547 q^{37} +(-8.07921 - 13.9936i) q^{38} +(199.286 - 241.664i) q^{39} +(-238.448 + 413.004i) q^{40} +(-45.3683 + 78.5802i) q^{41} +(61.4011 - 74.4581i) q^{42} +(86.4171 + 149.679i) q^{43} -0.992705 q^{44} +(-408.894 + 355.188i) q^{45} +560.198 q^{46} +(50.2236 + 86.9898i) q^{47} +(100.764 + 269.654i) q^{48} +(-24.5000 + 42.4352i) q^{49} +(368.023 - 637.434i) q^{50} +(-537.429 - 90.0343i) q^{51} +(-28.9313 - 50.1106i) q^{52} -151.257 q^{53} +(9.54323 + 372.129i) q^{54} +20.7464 q^{55} +(-83.2070 - 144.119i) q^{56} +(-31.2090 - 5.22838i) q^{57} +(-65.4953 + 113.441i) q^{58} +(-174.950 + 303.023i) q^{59} +(35.0218 + 93.7216i) q^{60} +(73.2503 + 126.873i) q^{61} -136.945 q^{62} +(-35.9960 - 185.541i) q^{63} +557.805 q^{64} +(604.632 + 1047.25i) q^{65} +(9.07170 - 11.0008i) q^{66} +(-133.490 + 231.211i) q^{67} +(-50.3302 + 87.1745i) q^{68} +(697.972 - 846.397i) q^{69} +(186.290 + 322.664i) q^{70} -808.387 q^{71} +(606.837 + 209.195i) q^{72} -107.711 q^{73} +(-263.405 - 456.232i) q^{74} +(-504.559 - 1350.25i) q^{75} +(-2.92272 + 5.06231i) q^{76} +(-3.61975 + 6.26959i) q^{77} +(819.693 + 137.321i) q^{78} +(-253.647 - 439.330i) q^{79} -1111.32 q^{80} +(574.136 + 449.231i) q^{81} -240.754 q^{82} +(590.857 + 1023.39i) q^{83} +(-34.4333 - 5.76854i) q^{84} +(1051.84 - 1821.85i) q^{85} +(-229.293 + 397.147i) q^{86} +(89.7941 + 240.297i) q^{87} +(-12.2934 - 21.2928i) q^{88} -931.512 q^{89} +(-1358.63 - 468.362i) q^{90} -421.976 q^{91} +(-101.328 - 175.506i) q^{92} +(-170.625 + 206.908i) q^{93} +(-133.259 + 230.812i) q^{94} +(61.0816 - 105.796i) q^{95} +(142.794 - 173.159i) q^{96} +(206.661 + 357.947i) q^{97} -130.013 q^{98} +(-5.31823 - 27.4127i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9}+O(q^{10}) $ 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9	\( 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9} + 111 q^{11} - 18 q^{13} + 42 q^{14} - 36 q^{15} - 144 q^{16} - 546 q^{17} - 45 q^{18} + 90 q^{19} + 402 q^{20} - 63 q^{21} + 162 q^{22} + 312 q^{23} - 36 q^{24} - 279 q^{25} + 102 q^{26} + 432 q^{27} + 504 q^{28} + 378 q^{29} - 864 q^{30} - 18 q^{31} + 891 q^{32} + 513 q^{33} + 324 q^{34} - 336 q^{35} + 414 q^{36} - 72 q^{37} + 147 q^{38} - 810 q^{39} - 405 q^{40} + 477 q^{41} + 315 q^{42} + 171 q^{43} - 1896 q^{44} - 720 q^{45} - 756 q^{46} + 654 q^{47} - 2709 q^{48} - 441 q^{49} + 429 q^{50} + 1341 q^{51} - 747 q^{52} - 1896 q^{53} - 108 q^{54} - 432 q^{55} + 525 q^{56} - 1143 q^{57} - 297 q^{58} + 957 q^{59} + 5400 q^{60} + 198 q^{61} - 600 q^{62} - 504 q^{63} + 4770 q^{64} + 2478 q^{65} - 2646 q^{66} + 333 q^{67} + 1443 q^{68} + 3366 q^{69} - 5652 q^{71} - 3681 q^{72} + 306 q^{73} + 2100 q^{74} - 4113 q^{75} + 144 q^{76} + 777 q^{77} + 6336 q^{78} - 1152 q^{79} - 8418 q^{80} - 1917 q^{81} - 6048 q^{82} + 1890 q^{83} + 1008 q^{84} + 648 q^{85} + 3837 q^{86} + 4212 q^{87} + 2268 q^{88} - 2604 q^{89} - 135 q^{90} + 252 q^{91} + 987 q^{92} + 378 q^{93} - 324 q^{94} + 3144 q^{95} + 5643 q^{96} + 1737 q^{97} - 588 q^{98} + 720 q^{99}+O(q^{100}) \) 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9 + 111 * q^11 - 18 * q^13 + 42 * q^14 - 36 * q^15 - 144 * q^16 - 546 * q^17 - 45 * q^18 + 90 * q^19 + 402 * q^20 - 63 * q^21 + 162 * q^22 + 312 * q^23 - 36 * q^24 - 279 * q^25 + 102 * q^26 + 432 * q^27 + 504 * q^28 + 378 * q^29 - 864 * q^30 - 18 * q^31 + 891 * q^32 + 513 * q^33 + 324 * q^34 - 336 * q^35 + 414 * q^36 - 72 * q^37 + 147 * q^38 - 810 * q^39 - 405 * q^40 + 477 * q^41 + 315 * q^42 + 171 * q^43 - 1896 * q^44 - 720 * q^45 - 756 * q^46 + 654 * q^47 - 2709 * q^48 - 441 * q^49 + 429 * q^50 + 1341 * q^51 - 747 * q^52 - 1896 * q^53 - 108 * q^54 - 432 * q^55 + 525 * q^56 - 1143 * q^57 - 297 * q^58 + 957 * q^59 + 5400 * q^60 + 198 * q^61 - 600 * q^62 - 504 * q^63 + 4770 * q^64 + 2478 * q^65 - 2646 * q^66 + 333 * q^67 + 1443 * q^68 + 3366 * q^69 - 5652 * q^71 - 3681 * q^72 + 306 * q^73 + 2100 * q^74 - 4113 * q^75 + 144 * q^76 + 777 * q^77 + 6336 * q^78 - 1152 * q^79 - 8418 * q^80 - 1917 * q^81 - 6048 * q^82 + 1890 * q^83 + 1008 * q^84 + 648 * q^85 + 3837 * q^86 + 4212 * q^87 + 2268 * q^88 - 2604 * q^89 - 135 * q^90 + 252 * q^91 + 987 * q^92 + 378 * q^93 - 324 * q^94 + 3144 * q^95 + 5643 * q^96 + 1737 * q^97 - 588 * q^98 + 720 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.32666	+	2.29785i	0.469046	+	0.812412i	0.999374	−	0.0353810i	$-0.0112645\pi$
$2$	1.32666	+	2.29785i	0.469046	+	0.812412i	−0.530328	+	0.847793i	$0.677931\pi$
$3$	5.12474	+	0.858536i	0.986256	+	0.165225i
$3$	5.12474	+	0.858536i	0.986256	+	0.165225i
$4$	0.479932	−	0.831266i	0.0599915	−	0.103908i
$5$	−10.0300	+	17.3725i	−0.897112	+	1.55384i	−0.0659427	+	0.997823i	$0.521005\pi$
$5$	−10.0300	+	17.3725i	−0.897112	+	1.55384i	−0.831169	+	0.556020i	$0.812328\pi$
$6$	4.82601	+	12.9148i	0.328368	+	0.878744i
$7$	−3.50000	−	6.06218i	−0.188982	−	0.327327i
$7$	−3.50000	−	6.06218i	−0.188982	−	0.327327i
$8$	23.7734			1.05065
$9$	25.5258	+	8.79954i	0.945401	+	0.325909i
$10$	−53.2258			−1.68315
$11$	−0.517107	−	0.895656i	−0.0141740	−	0.0245500i	0.858851	−	0.512225i	$-0.171179\pi$
$11$	−0.517107	−	0.895656i	−0.0141740	−	0.0245500i	−0.873025	+	0.487675i	$0.837845\pi$
$12$	3.17319	−	3.84798i	0.0763352	−	0.0925680i
$13$	30.1411	−	52.2059i	0.643049	−	1.11379i	−0.341699	−	0.939809i	$-0.611002\pi$
$13$	30.1411	−	52.2059i	0.643049	−	1.11379i	0.984748	−	0.173985i	$-0.0556643\pi$
$14$	9.28664	−	16.0849i	0.177283	−	0.307063i
$15$	−66.3161	+	80.4183i	−1.14152	+	1.38426i
$16$	27.6999	+	47.9776i	0.432811	+	0.749650i
$17$	−104.870			−1.49615			−0.748076	−	0.663613i	$-0.769022\pi$
$17$	−104.870			−1.49615			−0.748076	+	0.663613i	$0.769022\pi$
$18$	13.6442	+	70.3285i	0.178665	+	0.920921i
$19$	−6.08988			−0.0735323			−0.0367661	−	0.999324i	$-0.511706\pi$
$19$	−6.08988			−0.0735323			−0.0367661	+	0.999324i	$0.511706\pi$
$20$	9.62744	+	16.6752i	0.107638	+	0.186435i
$21$	−12.7320	−	34.0719i	−0.132302	−	0.354053i
$22$	1.37205	−	2.37647i	0.0132965	−	0.0230302i
$23$	105.565	−	182.844i	0.957038	−	1.65764i	0.227404	−	0.973801i	$-0.426976\pi$
$23$	105.565	−	182.844i	0.957038	−	1.65764i	0.729634	−	0.683838i	$-0.239690\pi$
$24$	121.833	+	20.4103i	1.03621	+	0.173594i
$25$	−138.702	−	240.240i	−1.10962	−	1.92192i
$26$	159.948			1.20648
$27$	123.258	+	67.0102i	0.878559	+	0.477634i
$28$	−6.71904			−0.0453493
$29$	24.6842	+	42.7544i	0.158060	+	0.273768i	0.934169	−	0.356830i	$-0.116143\pi$
$29$	24.6842	+	42.7544i	0.158060	+	0.273768i	−0.776109	+	0.630599i	$0.782809\pi$
$30$	−272.768	−	45.6963i	−1.66001	−	0.278099i
$31$	−25.8062	+	44.6977i	−0.149514	+	0.258966i	−0.931048	−	0.364897i	$-0.881104\pi$
$31$	−25.8062	+	44.6977i	−0.149514	+	0.258966i	0.781534	+	0.623863i	$0.214438\pi$
$32$	21.5969	−	37.4070i	0.119307	−	0.206646i
$33$	−1.88109	−	5.03396i	−0.00992288	−	0.0265545i
$34$	−139.126	−	240.974i	−0.701765	−	1.21549i
$35$	140.420			0.678153
$36$	19.5654	−	16.9956i	0.0905806	−	0.0786832i
$37$	−198.547			−0.882189			−0.441094	−	0.897461i	$-0.645410\pi$
$37$	−198.547			−0.882189			−0.441094	+	0.897461i	$0.645410\pi$
$38$	−8.07921	−	13.9936i	−0.0344900	−	0.0597385i
$39$	199.286	−	241.664i	0.818238	−	0.992238i
$40$	−238.448	+	413.004i	−0.942548	+	1.63254i
$41$	−45.3683	+	78.5802i	−0.172813	+	0.299321i	−0.939402	−	0.342817i	$-0.888619\pi$
$41$	−45.3683	+	78.5802i	−0.172813	+	0.299321i	0.766589	+	0.642138i	$0.221952\pi$
$42$	61.4011	−	74.4581i	0.225581	−	0.273551i
$43$	86.4171	+	149.679i	0.306476	+	0.530833i	0.977589	−	0.210523i	$-0.0675166\pi$
$43$	86.4171	+	149.679i	0.306476	+	0.530833i	−0.671113	+	0.741355i	$0.734183\pi$
$44$	−0.992705			−0.00340127
$45$	−408.894	+	355.188i	−1.35454	+	1.17663i
$46$	560.198			1.79558
$47$	50.2236	+	86.9898i	0.155869	+	0.269974i	0.933375	−	0.358902i	$-0.116849\pi$
$47$	50.2236	+	86.9898i	0.155869	+	0.269974i	−0.777506	+	0.628876i	$0.783515\pi$
$48$	100.764	+	269.654i	0.303001	+	0.810858i
$49$	−24.5000	+	42.4352i	−0.0714286	+	0.123718i
$50$	368.023	−	637.434i	1.04093	−	1.80294i
$51$	−537.429	−	90.0343i	−1.47559	−	0.247202i
$52$	−28.9313	−	50.1106i	−0.0771549	−	0.133636i
$53$	−151.257			−0.392013			−0.196007	−	0.980603i	$-0.562797\pi$
$53$	−151.257			−0.392013			−0.196007	+	0.980603i	$0.562797\pi$
$54$	9.54323	+	372.129i	0.0240494	+	0.937784i
$55$	20.7464			0.0508626
$56$	−83.2070	−	144.119i	−0.198554	−	0.343905i
$57$	−31.2090	−	5.22838i	−0.0725217	−	0.0121494i
$58$	−65.4953	+	113.441i	−0.148275	+	0.256820i
$59$	−174.950	+	303.023i	−0.386044	+	0.668647i	−0.991913	−	0.126917i	$-0.959492\pi$
$59$	−174.950	+	303.023i	−0.386044	+	0.668647i	0.605870	+	0.795564i	$0.292825\pi$
$60$	35.0218	+	93.7216i	0.0753550	+	0.201657i
$61$	73.2503	+	126.873i	0.153750	+	0.266303i	0.932603	−	0.360904i	$-0.117532\pi$
$61$	73.2503	+	126.873i	0.153750	+	0.266303i	−0.778853	+	0.627206i	$0.784198\pi$
$62$	−136.945			−0.280516
$63$	−35.9960	−	185.541i	−0.0719853	−	0.371046i
$64$	557.805			1.08946
$65$	604.632	+	1047.25i	1.15377	+	1.99840i
$66$	9.07170	−	11.0008i	0.0169189	−	0.0205168i
$67$	−133.490	+	231.211i	−0.243408	+	0.421596i	−0.961683	−	0.274164i	$-0.911599\pi$
$67$	−133.490	+	231.211i	−0.243408	+	0.421596i	0.718275	+	0.695760i	$0.244932\pi$
$68$	−50.3302	+	87.1745i	−0.0897564	+	0.155463i
$69$	697.972	−	846.397i	1.21777	−	1.47673i
$70$	186.290	+	322.664i	0.318085	+	0.550939i
$71$	−808.387			−1.35124			−0.675619	−	0.737251i	$-0.736123\pi$
$71$	−808.387			−1.35124			−0.675619	+	0.737251i	$0.736123\pi$
$72$	606.837	+	209.195i	0.993283	+	0.342415i
$73$	−107.711			−0.172693			−0.0863465	−	0.996265i	$-0.527519\pi$
$73$	−107.711			−0.172693			−0.0863465	+	0.996265i	$0.527519\pi$
$74$	−263.405	−	456.232i	−0.413787	−	0.716701i
$75$	−504.559	−	1350.25i	−0.776819	−	2.07884i
$76$	−2.92272	+	5.06231i	−0.00441131	+	0.00764061i
$77$	−3.61975	+	6.26959i	−0.00535726	+	0.00927905i
$78$	819.693	+	137.321i	1.18990	+	0.199341i
$79$	−253.647	−	439.330i	−0.361235	−	0.625677i	0.626930	−	0.779076i	$-0.284311\pi$
$79$	−253.647	−	439.330i	−0.361235	−	0.625677i	−0.988164	+	0.153399i	$0.950978\pi$
$80$	−1111.32			−1.55312
$81$	574.136	+	449.231i	0.787567	+	0.616229i
$82$	−240.754			−0.324230
$83$	590.857	+	1023.39i	0.781386	+	1.35340i	0.931135	+	0.364676i	$0.118820\pi$
$83$	590.857	+	1023.39i	0.781386	+	1.35340i	−0.149749	+	0.988724i	$0.547846\pi$
$84$	−34.4333	−	5.76854i	−0.0447260	−	0.00749285i
$85$	1051.84	−	1821.85i	1.34222	−	2.32479i
$86$	−229.293	+	397.147i	−0.287503	+	0.497970i
$87$	89.7941	+	240.297i	0.110654	+	0.296121i
$88$	−12.2934	−	21.2928i	−0.0148919	−	0.0257934i
$89$	−931.512			−1.10944			−0.554720	−	0.832037i	$-0.687174\pi$
$89$	−931.512			−1.10944			−0.554720	+	0.832037i	$0.687174\pi$
$90$	−1358.63	−	468.362i	−1.59125	−	0.548553i
$91$	−421.976			−0.486100
$92$	−101.328	−	175.506i	−0.114828	−	0.198888i
$93$	−170.625	+	206.908i	−0.190247	+	0.230703i
$94$	−133.259	+	230.812i	−0.146220	+	0.253260i
$95$	61.0816	−	105.796i	0.0659667	−	0.114258i
$96$	142.794	−	173.159i	0.151811	−	0.184094i
$97$	206.661	+	357.947i	0.216322	+	0.374680i	0.953681	−	0.300821i	$-0.0972606\pi$
$97$	206.661	+	357.947i	0.216322	+	0.374680i	−0.737359	+	0.675501i	$0.763927\pi$
$98$	−130.013			−0.134013
$99$	−5.31823	−	27.4127i	−0.00539902	−	0.0278291i
$100$	−266.271			−0.266271
$101$	−668.861	−	1158.50i	−0.658952	−	1.14134i	−0.980887	−	0.194577i	$-0.937667\pi$
$101$	−668.861	−	1158.50i	−0.658952	−	1.14134i	0.321935	−	0.946762i	$-0.395667\pi$
$102$	−506.102	−	1354.37i	−0.491289	−	1.31474i
$103$	−7.65783	+	13.2637i	−0.00732571	+	0.0126885i	−0.869665	−	0.493642i	$-0.835665\pi$
$103$	−7.65783	+	13.2637i	−0.00732571	+	0.0126885i	0.862339	+	0.506331i	$0.168999\pi$
$104$	716.558	−	1241.11i	0.675618	−	1.17020i
$105$	719.616	+	120.556i	0.668832	+	0.112048i
$106$	−200.667	−	347.565i	−0.183872	−	0.318476i
$107$	−242.474			−0.219073			−0.109537	−	0.993983i	$-0.534937\pi$
$107$	−242.474			−0.219073			−0.109537	+	0.993983i	$0.534937\pi$
$108$	114.859	−	70.3002i	0.102336	−	0.0626356i
$109$	1616.06			1.42010			0.710050	−	0.704152i	$-0.248672\pi$
$109$	1616.06			1.42010			0.710050	+	0.704152i	$0.248672\pi$
$110$	27.5234	+	47.6720i	0.0238569	+	0.0413213i
$111$	−1017.50	−	170.460i	−0.870064	−	0.145760i
$112$	193.899	−	335.843i	0.163587	−	0.283341i
$113$	−499.796	+	865.672i	−0.416078	+	0.720668i	−0.995541	−	0.0943303i	$-0.969929\pi$
$113$	−499.796	+	865.672i	−0.416078	+	0.720668i	0.579463	+	0.814999i	$0.303262\pi$
$114$	−29.3898	−	78.6498i	−0.0241457	−	0.0646161i
$115$	2117.64	+	3667.86i	1.71714	+	2.97417i
$116$	47.3870			0.0379291
$117$	1228.77	−	1067.37i	0.970935	−	0.843407i
$118$	−928.400			−0.724289
$119$	367.043	+	635.738i	0.282746	+	0.489731i
$120$	−1576.56	+	1911.82i	−1.19933	+	1.45437i
$121$	664.965	−	1151.75i	0.499598	−	0.865329i
$122$	−194.357	+	336.636i	−0.144232	+	0.249816i
$123$	−299.965	+	363.753i	−0.219894	+	0.266654i
$124$	24.7704	+	42.9037i	0.0179391	+	0.0310715i
$125$	3057.24			2.18759
$126$	378.589	−	328.863i	0.267678	−	0.232519i
$127$	56.1563			0.0392367			0.0196184	−	0.999808i	$-0.493755\pi$
$127$	56.1563			0.0392367			0.0196184	+	0.999808i	$0.493755\pi$
$128$	567.244	+	982.496i	0.391701	+	0.678447i
$129$	314.360	+	841.257i	0.214557	+	0.574175i
$130$	−1604.28	+	2778.70i	−1.08235	+	1.87468i
$131$	657.968	−	1139.63i	0.438831	−	0.760078i	−0.558768	−	0.829324i	$-0.688726\pi$
$131$	657.968	−	1139.63i	0.438831	−	0.760078i	0.997600	+	0.0692456i	$0.0220592\pi$
$132$	−5.08735	−	0.852273i	−0.00335452	−	0.000561976i
$133$	21.3146	+	36.9179i	0.0138963	+	0.0240691i
$134$	−708.383			−0.456679
$135$	−2400.42	+	1469.19i	−1.53033	+	0.936652i
$136$	−2493.11			−1.57193
$137$	574.950	+	995.842i	0.358550	+	0.621026i	0.987719	−	0.156242i	$-0.0499381\pi$
$137$	574.950	+	995.842i	0.358550	+	0.621026i	−0.629169	+	0.777268i	$0.716605\pi$
$138$	2870.87	+	480.950i	1.77090	+	0.296675i
$139$	−78.8479	+	136.569i	−0.0481136	+	0.0833352i	−0.889079	−	0.457753i	$-0.848654\pi$
$139$	−78.8479	+	136.569i	−0.0481136	+	0.0833352i	0.840966	+	0.541089i	$0.181988\pi$
$140$	67.3921	−	116.727i	0.0406834	−	0.0704657i
$141$	182.699	+	488.918i	0.109121	+	0.292017i
$142$	−1072.46	−	1857.55i	−0.633793	−	1.09776i
$143$	−62.3448			−0.0364583
$144$	284.882	+	1468.41i	0.164862	+	0.849777i
$145$	−990.333			−0.567191
$146$	−142.896	−	247.503i	−0.0810010	−	0.140298i
$147$	−161.988	+	196.435i	−0.0908882	+	0.110216i
$148$	−95.2892	+	165.046i	−0.0529238	+	0.0916667i
$149$	513.911	−	890.119i	0.282558	−	0.489406i	−0.689456	−	0.724328i	$-0.742150\pi$
$149$	513.911	−	890.119i	0.282558	−	0.489406i	0.972014	+	0.234922i	$0.0754836\pi$
$150$	2433.28	−	2950.72i	1.32451	−	1.60617i
$151$	−848.072	−	1468.90i	−0.457054	−	0.791641i	0.541750	−	0.840540i	$-0.317762\pi$
$151$	−848.072	−	1468.90i	−0.457054	−	0.791641i	−0.998804	+	0.0488992i	$0.984429\pi$
$152$	−144.777			−0.0772565
$153$	−2676.88	−	922.804i	−1.41446	−	0.487609i
$154$	−19.2088			−0.0100512
$155$	−517.673	−	896.637i	−0.268261	−	0.464643i
$156$	−105.244	−	281.642i	−0.0540144	−	0.144547i
$157$	1751.67	−	3033.99i	0.890438	−	1.54228i	0.0510873	−	0.998694i	$-0.483731\pi$
$157$	1751.67	−	3033.99i	0.890438	−	1.54228i	0.839351	−	0.543590i	$-0.182935\pi$
$158$	673.008	−	1165.68i	0.338871	−	0.586942i
$159$	−775.150	−	129.859i	−0.386625	−	0.0647705i
$160$	433.235	+	750.386i	0.214064	+	0.370770i
$161$	−1477.91			−0.723453
$162$	−270.580	+	1915.26i	−0.131227	+	0.928868i
$163$	626.192			0.300903			0.150451	−	0.988617i	$-0.451927\pi$
$163$	626.192			0.300903			0.150451	+	0.988617i	$0.451927\pi$
$164$	43.5474	+	75.4263i	0.0207346	+	0.0359134i
$165$	106.320	+	17.8115i	0.0501635	+	0.00840378i
$166$	−1567.74	+	2715.40i	−0.733012	+	1.26961i
$167$	−545.075	+	944.097i	−0.252570	+	0.437464i	−0.964233	−	0.265058i	$-0.914609\pi$
$167$	−545.075	+	944.097i	−0.252570	+	0.437464i	0.711663	+	0.702521i	$0.247942\pi$
$168$	−302.683	−	810.007i	−0.139003	−	0.371984i
$169$	−718.474	−	1244.43i	−0.327025	−	0.566424i
$170$	5581.76			2.51825
$171$	−155.449	−	53.5881i	−0.0695175	−	0.0239648i
$172$	165.897			0.0735439
$173$	96.2476	+	166.706i	0.0422981	+	0.0732624i	0.886399	−	0.462921i	$-0.153199\pi$
$173$	96.2476	+	166.706i	0.0422981	+	0.0732624i	−0.844101	+	0.536184i	$0.819865\pi$
$174$	−433.040	+	525.126i	−0.188670	+	0.228792i
$175$	−970.917	+	1681.68i	−0.419397	+	0.726416i
$176$	28.6476	−	49.6191i	0.0122693	−	0.0212510i
$177$	−1156.73	+	1402.71i	−0.491215	+	0.595673i
$178$	−1235.80	−	2140.47i	−0.520378	−	0.901321i
$179$	−2781.44			−1.16142			−0.580710	−	0.814110i	$-0.697225\pi$
$179$	−2781.44			−1.16142			−0.580710	+	0.814110i	$0.697225\pi$
$180$	99.0142	+	510.366i	0.0410005	+	0.211336i
$181$	−1108.65			−0.455276			−0.227638	−	0.973746i	$-0.573100\pi$
$181$	−1108.65			−0.455276			−0.227638	+	0.973746i	$0.573100\pi$
$182$	−559.819	−	969.636i	−0.228003	−	0.394913i
$183$	266.463	+	713.080i	0.107637	+	0.288046i
$184$	2509.65	−	4346.84i	1.00551	−	1.74159i
$185$	1991.43	−	3449.26i	0.791422	−	1.37078i
$186$	−701.805	−	117.572i	−0.276660	−	0.0463483i
$187$	54.2288	+	93.9270i	0.0212064	+	0.0367306i
$188$	96.4155			0.0374033
$189$	−25.1769	−	981.750i	−0.00968970	−	0.377840i
$190$	324.139			0.123766
$191$	725.149	+	1255.99i	0.274712	+	0.475814i	0.970062	−	0.242856i	$-0.0780843\pi$
$191$	725.149	+	1255.99i	0.274712	+	0.475814i	−0.695351	+	0.718671i	$0.744751\pi$
$192$	2858.61	+	478.896i	1.07449	+	0.180007i
$193$	−697.490	+	1208.09i	−0.260137	+	0.450570i	−0.966278	−	0.257501i	$-0.917101\pi$
$193$	−697.490	+	1208.09i	−0.260137	+	0.450570i	0.706141	+	0.708071i	$0.250434\pi$
$194$	−548.338	+	949.749i	−0.202930	+	0.351485i
$195$	2199.47	+	5885.99i	0.807731	+	2.16156i
$196$	23.5166	+	40.7320i	0.00857021	+	0.0148440i
$197$	2438.24			0.881815			0.440907	−	0.897553i	$-0.354657\pi$
$197$	2438.24			0.881815			0.440907	+	0.897553i	$0.354657\pi$
$198$	55.9346	−	48.5879i	0.0200763	−	0.0174393i
$199$	1023.49			0.364588			0.182294	−	0.983244i	$-0.441648\pi$
$199$	1023.49			0.364588			0.182294	+	0.983244i	$0.441648\pi$
$200$	−3297.43	−	5711.32i	−1.16582	−	2.01926i
$201$	−882.602	+	1070.29i	−0.309721	+	0.375584i
$202$	1774.71	−	3073.88i	0.618158	−	1.07068i
$203$	172.790	−	299.281i	0.0597412	−	0.103475i
$204$	−332.771	+	403.536i	−0.114209	+	0.138496i
$205$	−910.090	−	1576.32i	−0.310066	−	0.537049i
$206$	−40.6374			−0.0137444
$207$	4303.59	−	3738.33i	1.44502	−	1.25523i
$208$	3339.62			1.11327
$209$	3.14912	+	5.45444i	0.00104225	+	0.00180522i
$210$	677.670	+	1813.51i	0.222684	+	0.595923i
$211$	−2277.74	+	3945.16i	−0.743156	+	1.28718i	0.207896	+	0.978151i	$0.433339\pi$
$211$	−2277.74	+	3945.16i	−0.743156	+	1.28718i	−0.951051	+	0.309033i	$0.899995\pi$
$212$	−72.5929	+	125.735i	−0.0235174	+	0.0407334i
$213$	−4142.77	−	694.029i	−1.33267	−	0.223259i
$214$	−321.681	−	557.168i	−0.102755	−	0.177978i
$215$	−3467.06			−1.09977
$216$	2930.28	+	1593.06i	0.923056	+	0.501825i
$217$	361.287			0.113022
$218$	2143.97	+	3713.47i	0.666092	+	1.15371i
$219$	−551.989	−	92.4736i	−0.170320	−	0.0285333i
$220$	9.95684	−	17.2458i	0.00305132	−	0.00528504i
$221$	−3160.88	+	5474.81i	−0.962100	+	1.66641i
$222$	−958.192	−	2564.21i	−0.289683	−	0.775218i
$223$	−2856.26	−	4947.19i	−0.857711	−	1.48560i	−0.874107	−	0.485733i	$-0.838553\pi$
$223$	−2856.26	−	4947.19i	−0.857711	−	1.48560i	0.0163960	−	0.999866i	$-0.494781\pi$
$224$	−302.357			−0.0901879
$225$	−1426.50	−	7352.83i	−0.422665	−	2.17862i
$226$	−2652.24			−0.780639
$227$	−1594.88	−	2762.41i	−0.466325	−	0.807699i	0.532935	−	0.846156i	$-0.321089\pi$
$227$	−1594.88	−	2762.41i	−0.466325	−	0.807699i	−0.999260	+	0.0384572i	$0.987756\pi$
$228$	−19.3244	+	23.4337i	−0.00561310	+	0.00680674i
$229$	134.440	−	232.857i	0.0387949	−	0.0671948i	−0.845976	−	0.533221i	$-0.820981\pi$
$229$	134.440	−	232.857i	0.0387949	−	0.0671948i	0.884771	+	0.466026i	$0.154315\pi$
$230$	−5618.79	+	9732.03i	−1.61084	+	2.79005i
$231$	−23.9329	+	29.0223i	−0.00681676	+	0.00826636i
$232$	586.829	+	1016.42i	0.166066	+	0.287634i
$233$	3469.32			0.975462			0.487731	−	0.872994i	$-0.337825\pi$
$233$	3469.32			0.975462			0.487731	+	0.872994i	$0.337825\pi$
$234$	4082.82	+	1407.47i	1.14061	+	0.393202i
$235$	−2014.97			−0.559329
$236$	167.928	+	290.860i	0.0463186	+	0.0802263i
$237$	−922.694	−	2469.21i	−0.252892	−	0.676762i
$238$	−973.885	+	1686.82i	−0.265242	+	0.459413i
$239$	−186.327	+	322.727i	−0.0504287	+	0.0873451i	−0.890138	−	0.455691i	$-0.849392\pi$
$239$	−186.327	+	322.727i	−0.0504287	+	0.0873451i	0.839709	+	0.543036i	$0.182725\pi$
$240$	−5695.22	−	954.109i	−1.53177	−	0.256614i
$241$	3672.65	+	6361.22i	0.981644	+	1.70026i	0.655994	+	0.754766i	$0.272250\pi$
$241$	3672.65	+	6361.22i	0.981644	+	1.70026i	0.325650	+	0.945490i	$0.394417\pi$
$242$	3528.74			0.937338
$243$	2556.62	+	2795.11i	0.674926	+	0.737886i
$244$	140.621			0.0368947
$245$	−491.471	−	851.252i	−0.128159	−	0.221978i
$246$	−1233.80	−	206.696i	−0.319773	−	0.0535709i
$247$	−183.556	+	317.928i	−0.0472849	+	0.0818998i
$248$	−613.502	+	1062.62i	−0.157086	+	0.272082i
$249$	2149.37	+	5751.90i	0.547030	+	1.46390i
$250$	4055.93	+	7025.08i	1.02608	+	1.77722i
$251$	−1201.36			−0.302109			−0.151054	−	0.988525i	$-0.548267\pi$
$251$	−1201.36			−0.302109			−0.151054	+	0.988525i	$0.548267\pi$
$252$	−171.509	−	59.1245i	−0.0428733	−	0.0147797i
$253$	−218.354			−0.0542601
$254$	74.5005	+	129.039i	0.0184038	+	0.0318764i
$255$	6954.54	−	8433.43i	1.70788	−	2.07107i
$256$	726.138	−	1257.71i	0.177280	−	0.307058i
$257$	3026.80	−	5242.58i	0.734657	−	1.27246i	−0.220217	−	0.975451i	$-0.570677\pi$
$257$	3026.80	−	5242.58i	0.734657	−	1.27246i	0.954874	−	0.297012i	$-0.0959901\pi$
$258$	−1516.03	+	1838.42i	−0.365829	+	0.443623i
$259$	694.916	+	1203.63i	0.166718	+	0.288764i
$260$	1160.73			0.276866
$261$	253.867	+	1308.55i	0.0602068	+	0.310334i
$262$	3491.61			0.823329
$263$	1532.86	+	2655.00i	0.359393	+	0.622488i	0.987860	−	0.155349i	$-0.0496503\pi$
$263$	1532.86	+	2655.00i	0.359393	+	0.622488i	−0.628466	+	0.777837i	$0.716317\pi$
$264$	−44.7199	−	119.674i	−0.0104254	−	0.0278994i
$265$	1517.11	−	2627.71i	0.351680	−	0.609127i
$266$	−56.5545	+	97.9553i	−0.0130360	+	0.0225790i
$267$	−4773.75	−	799.737i	−1.09419	−	0.183307i
$268$	128.132	+	221.931i	0.0292048	+	0.0505843i
$269$	−823.888			−0.186741			−0.0933706	−	0.995631i	$-0.529764\pi$
$269$	−823.888			−0.186741			−0.0933706	+	0.995631i	$0.529764\pi$
$270$	−6560.53	−	3566.67i	−1.47874	−	0.803928i
$271$	568.916			0.127525			0.0637624	−	0.997965i	$-0.479690\pi$
$271$	568.916			0.127525			0.0637624	+	0.997965i	$0.479690\pi$
$272$	−2904.87	−	5031.39i	−0.647551	−	1.12159i
$273$	−2162.51	−	362.281i	−0.479419	−	0.0803160i
$274$	−1525.53	+	2642.29i	−0.336353	+	0.582580i
$275$	−143.448	+	248.459i	−0.0314554	+	0.0544824i
$276$	−368.602	−	986.414i	−0.0803886	−	0.215127i
$277$	3237.37	+	5607.30i	0.702220	+	1.21628i	0.967685	+	0.252161i	$0.0811411\pi$
$277$	3237.37	+	5607.30i	0.702220	+	1.21628i	−0.265465	+	0.964120i	$0.585526\pi$
$278$	−418.418			−0.0902700
$279$	−1052.04	+	913.863i	−0.225750	+	0.196099i
$280$	3338.27			0.712499
$281$	1986.61	+	3440.91i	0.421748	+	0.730489i	0.996111	−	0.0881123i	$-0.0280834\pi$
$281$	1986.61	+	3440.91i	0.421748	+	0.730489i	−0.574363	+	0.818601i	$0.694750\pi$
$282$	−881.080	+	1068.44i	−0.186055	+	0.225620i
$283$	−3012.65	+	5218.06i	−0.632803	+	1.09605i	0.354173	+	0.935180i	$0.384762\pi$
$283$	−3012.65	+	5218.06i	−0.632803	+	1.09605i	−0.986976	+	0.160867i	$0.948571\pi$
$284$	−387.970	+	671.984i	−0.0810627	+	0.140405i
$285$	403.857	−	489.738i	0.0839383	−	0.101788i
$286$	−82.7105	−	143.259i	−0.0171006	−	0.0296191i
$287$	635.157			0.130635
$288$	880.444	−	764.802i	0.180141	−	0.156480i
$289$	6084.62			1.23847
$290$	−1313.84	−	2275.63i	−0.266039	−	0.460793i
$291$	751.771	+	2011.81i	0.151442	+	0.405273i
$292$	−51.6938	+	89.5363i	−0.0103601	+	0.0179442i
$293$	2583.72	−	4475.14i	0.515162	−	0.892287i	−0.484683	−	0.874690i	$-0.661065\pi$
$293$	2583.72	−	4475.14i	0.515162	−	0.892287i	0.999845	−	0.0175975i	$-0.00560173\pi$
$294$	−666.282	−	111.621i	−0.132171	−	0.0221424i
$295$	−3509.51	−	6078.64i	−0.692649	−	1.19970i
$296$	−4720.15			−0.926869
$297$	−3.71977	−	145.049i	−0.000726743	−	0.0283386i
$298$	2727.14			0.530132
$299$	−6363.71	−	11022.3i	−1.23085	−	2.13189i
$300$	−1364.57	−	228.603i	−0.262611	−	0.0439947i
$301$	604.920	−	1047.75i	0.115837	−	0.200636i
$302$	2250.21	−	3897.48i	0.428759	−	0.742632i
$303$	−2433.12	−	6511.26i	−0.461318	−	1.23453i
$304$	−168.689	−	292.178i	−0.0318256	−	0.0551235i
$305$	−2938.81			−0.551723
$306$	−1430.86	−	7375.31i	−0.267309	−	1.37784i
$307$	8320.41			1.54681			0.773406	−	0.633911i	$-0.218552\pi$
$307$	8320.41			1.54681			0.773406	+	0.633911i	$0.218552\pi$
$308$	3.47447	+	6.01795i	0.000642780	+	0.00111333i
$309$	−50.6317	+	61.3987i	−0.00932148	+	0.0113037i
$310$	1373.56	−	2379.07i	0.251654	−	0.435878i
$311$	−4800.83	+	8315.28i	−0.875338	+	1.51613i	−0.0189357	+	0.999821i	$0.506028\pi$
$311$	−4800.83	+	8315.28i	−0.875338	+	1.51613i	−0.856402	+	0.516309i	$0.827306\pi$
$312$	4737.71	−	5745.19i	0.859680	−	1.04249i
$313$	−3260.03	−	5646.54i	−0.588715	−	1.01968i	−0.994401	−	0.105672i	$-0.966301\pi$
$313$	−3260.03	−	5646.54i	−0.588715	−	1.01968i	0.405686	−	0.914013i	$-0.367033\pi$
$314$	9295.52			1.67063
$315$	3584.34	+	1235.63i	0.641126	+	0.221016i
$316$	−486.933			−0.0866839
$317$	4113.08	+	7124.06i	0.728749	+	1.26223i	0.957412	+	0.288725i	$0.0932312\pi$
$317$	4113.08	+	7124.06i	0.728749	+	1.26223i	−0.228663	+	0.973506i	$0.573435\pi$
$318$	−729.966	−	1953.46i	−0.128725	−	0.344479i
$319$	25.5288	−	44.2172i	0.00448069	−	0.00776078i
$320$	−5594.80	+	9690.47i	−0.977371	+	1.69286i
$321$	−1242.61	−	208.172i	−0.216062	−	0.0361964i
$322$	−1960.69	−	3396.02i	−0.339333	−	0.587741i
$323$	638.642			0.110016
$324$	648.977	−	261.660i	0.111279	−	0.0448662i
$325$	−16722.6			−2.85416
$326$	830.746	+	1438.89i	0.141137	+	0.244457i
$327$	8281.90	+	1387.45i	1.40058	+	0.234636i
$328$	−1078.56	+	1868.12i	−0.181566	+	0.314481i
$329$	351.565	−	608.928i	0.0589131	−	0.102040i
$330$	100.122	+	267.936i	0.0167017	+	0.0446952i
$331$	2.74700	+	4.75795i	0.000456160	+	0.000790092i	0.866253	−	0.499605i	$-0.166521\pi$
$331$	2.74700	+	4.75795i	0.000456160	+	0.000790092i	−0.865797	+	0.500395i	$0.833188\pi$
$332$	1134.28			0.187506
$333$	−5068.09	−	1747.13i	−0.834022	−	0.287513i
$334$	−2892.52			−0.473867
$335$	−2677.81	−	4638.10i	−0.436729	−	0.756437i
$336$	1282.02	−	1554.64i	0.208154	−	0.252418i
$337$	−4849.78	+	8400.06i	−0.783930	+	1.35781i	0.145707	+	0.989328i	$0.453454\pi$
$337$	−4849.78	+	8400.06i	−0.783930	+	1.35781i	−0.929636	+	0.368478i	$0.879879\pi$
$338$	1906.34	−	3301.89i	0.306780	−	0.531358i
$339$	−3304.53	+	4007.25i	−0.529432	+	0.642017i
$340$	−1009.63	−	1748.72i	−0.161043	−	0.278935i
$341$	53.3783			0.00847683
$342$	−83.0913	−	428.292i	−0.0131376	−	0.0677175i
$343$	343.000			0.0539949
$344$	2054.43	+	3558.38i	0.321999	+	0.557718i
$345$	7703.36	+	20614.9i	1.20213	+	3.21701i
$346$	−255.376	+	442.324i	−0.0396795	+	0.0687269i
$347$	555.376	−	961.939i	0.0859197	−	0.148817i	−0.819863	−	0.572560i	$-0.805950\pi$
$347$	555.376	−	961.939i	0.0859197	−	0.148817i	0.905783	+	0.423742i	$0.139284\pi$
$348$	242.846	+	40.6834i	0.0374078	+	0.00626684i
$349$	−1984.74	−	3437.68i	−0.304415	−	0.527262i	0.672716	−	0.739901i	$-0.265128\pi$
$349$	−1984.74	−	3437.68i	−0.304415	−	0.527262i	−0.977131	+	0.212639i	$0.931794\pi$
$350$	−5152.32			−0.786865
$351$	7213.48	−	4415.06i	1.09694	−	0.671392i
$352$	−44.6718			−0.00676424
$353$	2307.06	+	3995.95i	0.347854	+	0.602501i	0.985868	−	0.167524i	$-0.0535771\pi$
$353$	2307.06	+	3995.95i	0.347854	+	0.602501i	−0.638014	+	0.770025i	$0.720244\pi$
$354$	−4757.80	−	797.065i	−0.714335	−	0.119671i
$355$	8108.13	−	14043.7i	1.21221	−	2.09961i
$356$	−447.062	+	774.334i	−0.0665569	+	0.115280i
$357$	1335.20	+	3573.11i	0.197944	+	0.529717i
$358$	−3690.03	−	6391.32i	−0.544760	−	0.943552i
$359$	−8896.15			−1.30786			−0.653928	−	0.756556i	$-0.726880\pi$
$359$	−8896.15			−1.30786			−0.653928	+	0.756556i	$0.726880\pi$
$360$	−9720.82	+	8444.04i	−1.42315	+	1.23622i
$361$	−6821.91			−0.994593
$362$	−1470.80	−	2547.50i	−0.213546	−	0.369872i
$363$	4396.59	−	5331.54i	0.635706	−	0.770890i
$364$	−202.519	+	350.774i	−0.0291618	+	0.0505098i
$365$	1080.34	−	1871.20i	0.154925	−	0.268338i
$366$	−1285.04	+	1558.31i	−0.183525	+	0.222552i
$367$	2974.51	+	5152.01i	0.423074	+	0.732786i	0.996238	−	0.0866543i	$-0.0276176\pi$
$367$	2974.51	+	5152.01i	0.423074	+	0.732786i	−0.573164	+	0.819441i	$0.694284\pi$
$368$	11696.6			1.65686
$369$	−1849.53	+	1606.61i	−0.260929	+	0.226657i
$370$	10567.8			1.48485
$371$	529.398	+	916.945i	0.0740835	+	0.128316i
$372$	90.1076	+	241.136i	0.0125588	+	0.0336084i
$373$	3849.57	−	6667.64i	0.534378	−	0.925570i	−0.464815	−	0.885408i	$-0.653879\pi$
$373$	3849.57	−	6667.64i	0.534378	−	0.925570i	0.999193	−	0.0401620i	$-0.0127874\pi$
$374$	−143.887	+	249.219i	−0.0198936	+	0.0344567i
$375$	15667.6	+	2624.75i	2.15752	+	0.361445i
$376$	1193.99	+	2068.05i	0.163764	+	0.283647i
$377$	2976.04			0.406562
$378$	2222.51	−	1360.30i	0.302417	−	0.185097i
$379$	10982.7			1.48850			0.744250	−	0.667901i	$-0.232807\pi$
$379$	10982.7			1.48850			0.744250	+	0.667901i	$0.232807\pi$
$380$	−58.6299	−	101.550i	−0.00791487	−	0.0137090i
$381$	287.786	+	48.2122i	0.0386975	+	0.00648290i
$382$	−1924.06	+	3332.56i	−0.257705	+	0.446358i
$383$	−309.074	+	535.332i	−0.0412349	+	0.0714209i	−0.885906	−	0.463864i	$-0.846463\pi$
$383$	−309.074	+	535.332i	−0.0412349	+	0.0714209i	0.844671	+	0.535285i	$0.179796\pi$
$384$	2063.47	+	5522.03i	0.274221	+	0.733841i
$385$	−72.6123	−	125.768i	−0.00961212	−	0.0166487i
$386$	−3701.33			−0.488065
$387$	888.764	+	4581.11i	0.116740	+	0.601733i
$388$	396.732			0.0519098
$389$	−4860.07	−	8417.89i	−0.633458	−	1.09718i	−0.986840	−	0.161702i	$-0.948302\pi$
$389$	−4860.07	−	8417.89i	−0.633458	−	1.09718i	0.353381	−	0.935479i	$-0.385032\pi$
$390$	−10607.2	+	12862.8i	−1.37722	+	1.67008i
$391$	−11070.6	+	19174.8i	−1.43187	+	2.48008i
$392$	−582.449	+	1008.83i	−0.0750462	+	0.129984i
$393$	4350.33	−	5275.43i	0.558384	−	0.677126i
$394$	3234.72	+	5602.71i	0.413612	+	0.716397i
$395$	10176.3			1.29627
$396$	−25.3396	−	8.73535i	−0.00321556	−	0.00110850i
$397$	−12054.2			−1.52389			−0.761943	−	0.647644i	$-0.775754\pi$
$397$	−12054.2			−1.52389			−0.761943	+	0.647644i	$0.775754\pi$
$398$	1357.82	+	2351.82i	0.171009	+	0.296196i
$399$	77.5362	+	207.494i	0.00972848	+	0.0260343i
$400$	7684.08	−	13309.2i	0.960510	−	1.66365i
$401$	3240.01	−	5611.87i	0.403488	−	0.698861i	−0.590657	−	0.806923i	$-0.701131\pi$
$401$	3240.01	−	5611.87i	0.403488	−	0.698861i	0.994144	+	0.108062i	$0.0344645\pi$
$402$	−3630.28	−	608.172i	−0.450402	−	0.0754549i
$403$	1555.66	+	2694.48i	0.192290	+	0.333056i
$404$	−1284.03			−0.158126
$405$	−13562.9	+	5468.38i	−1.66406	+	0.670929i
$406$	916.935			0.112085
$407$	102.670	+	177.830i	0.0125041	+	0.0216578i
$408$	−12776.5	−	2140.42i	−1.55032	−	0.259722i
$409$	3615.77	−	6262.70i	0.437135	−	0.757141i	−0.560332	−	0.828268i	$-0.689326\pi$
$409$	3615.77	−	6262.70i	0.437135	−	0.757141i	0.997467	+	0.0711276i	$0.0226598\pi$
$410$	2414.76	−	4182.50i	0.290870	−	0.503802i
$411$	2091.50	+	5597.04i	0.251012	+	0.671732i
$412$	7.35047	+	12.7314i	0.000878960	+	0.00152240i
$413$	2449.30			0.291822
$414$	14299.5	+	4929.48i	1.69754	+	0.585195i
$415$	−23705.2			−2.80396
$416$	−1301.91	−	2254.98i	−0.153441	−	0.265768i
$417$	−521.323	+	632.184i	−0.0612214	+	0.0742402i
$418$	−8.35564	+	14.4724i	−0.000977722	+	0.00169346i
$419$	6230.52	−	10791.6i	0.726446	−	1.25824i	−0.231930	−	0.972732i	$-0.574504\pi$
$419$	6230.52	−	10791.6i	0.726446	−	1.25824i	0.958376	−	0.285509i	$-0.0921625\pi$
$420$	445.581	−	540.334i	0.0517669	−	0.0627752i
$421$	3284.01	+	5688.07i	0.380173	+	0.658479i	0.991087	−	0.133218i	$-0.0425312\pi$
$421$	3284.01	+	5688.07i	0.380173	+	0.658479i	−0.610914	+	0.791697i	$0.709198\pi$
$422$	−12087.2			−1.39430
$423$	516.528	+	2662.43i	0.0593723	+	0.306033i
$424$	−3595.89			−0.411868
$425$	14545.7	+	25193.8i	1.66016	+	2.87548i
$426$	−3901.28	−	10440.2i	−0.443704	−	1.18739i
$427$	512.752	−	888.113i	0.0581120	−	0.100653i
$428$	−116.371	+	201.560i	−0.0131425	+	0.0227635i
$429$	−319.500	−	53.5252i	−0.0359572	−	0.00602383i
$430$	−4599.62	−	7966.77i	−0.515845	−	0.893470i
$431$	7217.88			0.806667			0.403333	−	0.915053i	$-0.367852\pi$
$431$	7217.88			0.806667			0.403333	+	0.915053i	$0.367852\pi$
$432$	199.257	+	7769.82i	0.0221915	+	0.865337i
$433$	−7181.20			−0.797013			−0.398506	−	0.917166i	$-0.630471\pi$
$433$	−7181.20			−0.797013			−0.398506	+	0.917166i	$0.630471\pi$
$434$	479.306	+	830.182i	0.0530125	+	0.0918203i
$435$	−5075.20	−	850.237i	−0.559396	−	0.0937143i
$436$	775.600	−	1343.38i	0.0851938	−	0.147560i
$437$	−642.879	+	1113.50i	−0.0703732	+	0.121890i
$438$	−519.813	−	1391.07i	−0.0567070	−	0.151753i
$439$	5578.89	+	9662.92i	0.606528	+	1.05054i	0.991808	+	0.127738i	$0.0407716\pi$
$439$	5578.89	+	9662.92i	0.606528	+	1.05054i	−0.385280	+	0.922800i	$0.625895\pi$
$440$	493.213			0.0534386
$441$	−998.794	+	867.606i	−0.107849	+	0.0936839i
$442$	−16773.7			−1.80508
$443$	1011.86	+	1752.59i	0.108521	+	0.187964i	0.915171	−	0.403065i	$-0.132055\pi$
$443$	1011.86	+	1752.59i	0.108521	+	0.187964i	−0.806650	+	0.591029i	$0.798722\pi$
$444$	−630.029	+	764.006i	−0.0673421	+	0.0816625i
$445$	9343.08	−	16182.7i	0.995291	−	1.72389i
$446$	7578.60	−	13126.5i	0.804612	−	1.39363i
$447$	3397.86	−	4120.42i	0.359537	−	0.435993i
$448$	−1952.32	−	3381.52i	−0.205889	−	0.356611i
$449$	−4539.58			−0.477141			−0.238570	−	0.971125i	$-0.576679\pi$
$449$	−4539.58			−0.477141			−0.238570	+	0.971125i	$0.576679\pi$
$450$	15003.2	−	13032.6i	1.57168	−	1.36525i
$451$	93.8412			0.00979780
$452$	479.735	+	830.926i	0.0499223	+	0.0864679i
$453$	−3085.04	−	8255.85i	−0.319973	−	0.856277i
$454$	4231.73	−	7329.58i	0.437456	−	0.757696i
$455$	4232.42	−	7330.77i	0.436086	−	0.755323i
$456$	−741.945	−	124.297i	−0.0761947	−	0.0127647i
$457$	−876.248	−	1517.71i	−0.0896918	−	0.155351i	0.817689	−	0.575660i	$-0.195255\pi$
$457$	−876.248	−	1517.71i	−0.0896918	−	0.155351i	−0.907381	+	0.420309i	$0.861922\pi$
$458$	713.425			0.0727864
$459$	−12926.1	−	7027.32i	−1.31446	−	0.714613i
$460$	4065.29			0.412055
$461$	−4638.06	−	8033.35i	−0.468581	−	0.811606i	0.530774	−	0.847513i	$-0.321901\pi$
$461$	−4638.06	−	8033.35i	−0.468581	−	0.811606i	−0.999355	+	0.0359074i	$0.988568\pi$
$462$	−98.4398	−	16.4914i	−0.00991306	−	0.00166071i
$463$	71.7468	−	124.269i	0.00720164	−	0.0124736i	−0.862402	−	0.506224i	$-0.831041\pi$
$463$	71.7468	−	124.269i	0.00720164	−	0.0124736i	0.869604	+	0.493750i	$0.164374\pi$
$464$	−1367.50	+	2368.58i	−0.136820	+	0.236980i
$465$	−1883.14	−	5039.47i	−0.187804	−	0.502580i
$466$	4602.62	+	7971.96i	0.457537	+	0.792477i
$467$	−13059.9			−1.29409			−0.647044	−	0.762453i	$-0.723995\pi$
$467$	−13059.9			−1.29409			−0.647044	+	0.762453i	$0.723995\pi$
$468$	−297.547	−	1533.70i	−0.0293891	−	0.151485i
$469$	1868.86			0.183999
$470$	−2673.19	−	4630.10i	−0.262351	−	0.454405i
$471$	11581.7	−	14044.5i	1.13302	−	1.37396i
$472$	−4159.17	+	7203.89i	−0.405596	+	0.702513i
$473$	89.3739	−	154.800i	0.00868798	−	0.0150480i
$474$	4449.77	−	5396.02i	0.431192	−	0.522885i
$475$	844.680	+	1463.03i	0.0815928	+	0.141323i
$476$	704.623			0.0678494
$477$	−3860.95	−	1330.99i	−0.370610	−	0.127761i
$478$	−988.770			−0.0946136
$479$	−503.457	−	872.013i	−0.0480241	−	0.0831801i	0.841014	−	0.541013i	$-0.181959\pi$
$479$	−503.457	−	872.013i	−0.0480241	−	0.0831801i	−0.889038	+	0.457833i	$0.848626\pi$
$480$	1575.98	+	4217.48i	0.149861	+	0.401043i
$481$	−5984.44	+	10365.4i	−0.567291	+	0.982577i
$482$	−9744.73	+	16878.4i	−0.920872	+	1.59500i
$483$	−7573.91	−	1268.84i	−0.713509	−	0.119533i
$484$	−638.276	−	1105.53i	−0.0599432	−	0.103825i
$485$	−8291.24			−0.776259
$486$	−3030.96	+	9582.88i	−0.282896	+	0.894420i
$487$	10739.7			0.999306			0.499653	−	0.866226i	$-0.333461\pi$
$487$	10739.7			0.999306			0.499653	+	0.866226i	$0.333461\pi$
$488$	1741.41	+	3016.21i	0.161537	+	0.279790i
$489$	3209.07	+	537.608i	0.296767	+	0.0497168i
$490$	1304.03	−	2258.65i	0.120225	−	0.208235i
$491$	8337.78	−	14441.5i	0.766352	−	1.32736i	−0.173177	−	0.984891i	$-0.555403\pi$
$491$	8337.78	−	14441.5i	0.766352	−	1.32736i	0.939529	−	0.342470i	$-0.111263\pi$
$492$	158.413	+	423.927i	0.0145158	+	0.0388457i
$493$	−2588.62	−	4483.63i	−0.236482	−	0.409599i
$494$	−974.066			−0.0887152
$495$	529.569	+	182.559i	0.0480855	+	0.0165766i
$496$	−2859.32			−0.258845
$497$	2829.35	+	4900.58i	0.255360	+	0.442296i
$498$	−10365.5	+	12569.7i	−0.932710	+	1.13105i
$499$	−8797.13	+	15237.1i	−0.789206	+	1.36694i	0.137249	+	0.990537i	$0.456174\pi$
$499$	−8797.13	+	15237.1i	−0.789206	+	1.36694i	−0.926454	+	0.376408i	$0.877159\pi$
$500$	1467.27	−	2541.38i	0.131236	−	0.227308i
$501$	−3603.90	+	4370.28i	−0.321378	+	0.389720i
$502$	−1593.80	−	2760.55i	−0.141703	−	0.245437i
$503$	8838.85			0.783509			0.391754	−	0.920070i	$-0.371868\pi$
$503$	8838.85			0.783509			0.391754	+	0.920070i	$0.371868\pi$
$504$	−855.749	−	4410.94i	−0.0756312	−	0.389839i
$505$	26834.8			2.36462
$506$	−289.682	−	501.745i	−0.0254505	−	0.0440816i
$507$	−2613.60	−	6994.23i	−0.228943	−	0.612671i
$508$	26.9512	−	46.6808i	0.00235387	−	0.00407702i
$509$	3395.99	−	5882.03i	0.295726	−	0.512213i	−0.679427	−	0.733743i	$-0.737772\pi$
$509$	3395.99	−	5882.03i	0.295726	−	0.512213i	0.975154	+	0.221530i	$0.0711050\pi$
$510$	28605.1	+	4792.14i	2.48363	+	0.416078i
$511$	376.988	+	652.962i	0.0326359	+	0.0565271i
$512$	12929.3			1.11601
$513$	−750.629	−	408.084i	−0.0646025	−	0.0351215i
$514$	16062.2			1.37835
$515$	−153.616	−	266.071i	−0.0131440	−	0.0227660i
$516$	850.179	+	142.429i	0.0725331	+	0.0121513i
$517$	51.9420	−	89.9661i	0.00441858	−	0.00765320i
$518$	−1843.84	+	3193.62i	−0.156397	+	0.270887i
$519$	350.121	+	936.955i	0.0296119	+	0.0792442i
$520$	14374.2	+	24896.8i	1.21221	+	2.09961i
$521$	−18833.0			−1.58367			−0.791834	−	0.610737i	$-0.790873\pi$
$521$	−18833.0			−1.58367			−0.791834	+	0.610737i	$0.790873\pi$
$522$	−2670.05	+	2319.35i	−0.223879	+	0.194474i
$523$	−1128.96			−0.0943902			−0.0471951	−	0.998886i	$-0.515028\pi$
$523$	−1128.96			−0.0943902			−0.0471951	+	0.998886i	$0.515028\pi$
$524$	−631.559	−	1093.89i	−0.0526523	−	0.0911964i
$525$	−6419.47	+	7784.58i	−0.533655	+	0.647137i
$526$	−4067.19	+	7044.58i	−0.337144	+	0.583951i
$527$	2706.29	−	4687.42i	0.223696	−	0.387452i
$528$	189.411	−	229.690i	0.0156119	−	0.0189318i
$529$	−16204.5	−	28067.1i	−1.33184	−	2.30682i
$530$	8050.75			0.659816
$531$	−7132.21	+	6195.42i	−0.582884	+	0.506325i
$532$	40.9181			0.00333464
$533$	2734.90	+	4736.99i	0.222255	+	0.384957i
$534$	−4495.49	−	12030.3i	−0.364305	−	0.974913i
$535$	2432.01	−	4212.37i	0.196533	−	0.340405i
$536$	−3173.51	+	5496.68i	−0.255736	+	0.442948i
$537$	−14254.1	−	2387.96i	−1.14546	−	0.191896i
$538$	−1093.02	−	1893.17i	−0.0875902	−	0.151711i
$539$	50.6765			0.00404971
$540$	69.2541	+	2700.50i	0.00551893	+	0.215205i
$541$	20082.5			1.59596			0.797980	−	0.602683i	$-0.205902\pi$
$541$	20082.5			1.59596			0.797980	+	0.602683i	$0.205902\pi$
$542$	754.760	+	1307.28i	0.0598150	+	0.103603i
$543$	−5681.52	−	951.813i	−0.449019	−	0.0752232i
$544$	−2264.86	+	3922.85i	−0.178502	+	0.309175i
$545$	−16209.1	+	28075.1i	−1.27399	+	2.20661i
$546$	−2036.46	−	5449.75i	−0.159620	−	0.427157i
$547$	10289.0	+	17821.1i	0.804253	+	1.39301i	0.916794	+	0.399360i	$0.130768\pi$
$547$	10289.0	+	17821.1i	0.804253	+	1.39301i	−0.112541	+	0.993647i	$0.535899\pi$
$548$	1103.75			0.0860396
$549$	753.349	+	3883.12i	0.0585649	+	0.301871i
$550$	−761.229			−0.0590162
$551$	−150.324	−	260.369i	−0.0116225	−	0.0201308i
$552$	16593.2	−	20121.8i	1.27944	−	1.55152i
$553$	−1775.53	+	3075.31i	−0.136534	+	0.236484i
$554$	−8589.81	+	14878.0i	−0.658747	+	1.14098i
$555$	13166.9	−	15966.8i	1.00703	−	1.22118i
$556$	75.6832	+	131.087i	0.00577281	+	0.00999880i
$557$	−18750.9			−1.42639			−0.713196	−	0.700965i	$-0.752753\pi$
$557$	−18750.9			−1.42639			−0.713196	+	0.700965i	$0.752753\pi$
$558$	−3495.62	−	1205.05i	−0.265200	−	0.0914226i
$559$	10418.8			0.788318
$560$	3889.62	+	6737.02i	0.293512	+	0.508377i
$561$	197.269	+	527.909i	0.0148461	+	0.0397296i
$562$	−5271.12	+	9129.85i	−0.395638	+	0.685266i
$563$	1727.71	−	2992.49i	0.129333	−	0.224011i	−0.794085	−	0.607806i	$-0.792050\pi$
$563$	1727.71	−	2992.49i	0.129333	−	0.224011i	0.923418	+	0.383795i	$0.125383\pi$
$564$	494.104	+	82.7762i	0.0368892	+	0.00617998i
$565$	−10025.9	−	17365.4i	−0.746537	−	1.29304i
$566$	−15987.1			−1.18725
$567$	713.843	−	5052.82i	0.0528723	−	0.374248i
$568$	−19218.1			−1.41967
$569$	−4696.49	−	8134.56i	−0.346023	−	0.599329i	0.639516	−	0.768778i	$-0.279135\pi$
$569$	−4696.49	−	8134.56i	−0.346023	−	0.599329i	−0.985539	+	0.169448i	$0.945801\pi$
$570$	1661.12	+	278.285i	0.122065	+	0.0204492i
$571$	−3586.52	+	6212.03i	−0.262857	+	0.455281i	−0.967000	−	0.254777i	$-0.917998\pi$
$571$	−3586.52	+	6212.03i	−0.262857	+	0.455281i	0.704143	+	0.710058i	$0.251331\pi$
$572$	−29.9212	+	51.8251i	−0.00218718	+	0.00378831i
$573$	2637.88	+	7059.21i	0.192319	+	0.514664i
$574$	842.639	+	1459.49i	0.0612736	+	0.106129i
$575$	−58568.6			−4.24779
$576$	14238.4	+	4908.43i	1.02998	+	0.355066i
$577$	14769.7			1.06563			0.532815	−	0.846232i	$-0.321134\pi$
$577$	14769.7			1.06563			0.532815	+	0.846232i	$0.321134\pi$
$578$	8072.23	+	13981.5i	0.580901	+	1.00615i
$579$	−4611.64	+	5592.31i	−0.331007	+	0.401396i
$580$	−475.292	+	823.230i	−0.0340266	+	0.0589358i
$581$	4136.00	−	7163.76i	0.295336	−	0.511537i
$582$	−3625.48	+	4396.45i	−0.258215	+	0.313125i
$583$	78.2159	+	135.474i	0.00555639	+	0.00962394i
$584$	−2560.65			−0.181439
$585$	6218.38	+	32052.5i	0.439485	+	2.26531i
$586$	13710.9			0.966540
$587$	−4494.86	−	7785.33i	−0.316053	−	0.547419i	0.663608	−	0.748080i	$-0.269024\pi$
$587$	−4494.86	−	7785.33i	−0.316053	−	0.547419i	−0.979661	+	0.200661i	$0.935691\pi$
$588$	85.5467	+	228.931i	0.00599981	+	0.0160560i
$589$	157.157	−	272.203i	0.0109941	−	0.0190423i
$590$	9311.86	−	16128.6i	0.649768	−	1.12543i
$591$	12495.3	+	2093.32i	0.869695	+	0.145698i
$592$	−5499.74	−	9525.83i	−0.381821	−	0.661333i
$593$	24601.6			1.70365			0.851826	−	0.523826i	$-0.175496\pi$
$593$	24601.6			1.70365			0.851826	+	0.523826i	$0.175496\pi$
$594$	328.365	−	200.978i	0.0226818	−	0.0138825i
$595$	−14725.8			−1.01462
$596$	−493.284	−	854.393i	−0.0339022	−	0.0587203i
$597$	5245.10	+	878.701i	0.359577	+	0.0602392i
$598$	16885.0	−	29245.7i	1.15465	−	1.99991i
$599$	−10648.7	+	18444.1i	−0.726366	+	1.25810i	0.232043	+	0.972706i	$0.425459\pi$
$599$	−10648.7	+	18444.1i	−0.726366	+	1.25810i	−0.958409	+	0.285398i	$0.907874\pi$
$600$	−11995.1	−	32100.0i	−0.816163	−	2.18413i
$601$	−682.854	−	1182.74i	−0.0463464	−	0.0802743i	0.841922	−	0.539600i	$-0.181424\pi$
$601$	−682.854	−	1182.74i	−0.0463464	−	0.0802743i	−0.888268	+	0.459326i	$0.848091\pi$
$602$	3210.10			0.217332
$603$	−5441.98	+	4727.20i	−0.367520	+	0.319248i
$604$	−1628.07			−0.109677
$605$	13339.2	+	23104.2i	0.896391	+	1.55259i
$606$	11733.9	−	14229.2i	0.786566	−	0.953830i
$607$	4818.30	−	8345.53i	0.322189	−	0.558047i	−0.658751	−	0.752361i	$-0.728915\pi$
$607$	4818.30	−	8345.53i	0.322189	−	0.558047i	0.980939	+	0.194314i	$0.0622481\pi$
$608$	−131.523	+	227.804i	−0.00877295	+	0.0151952i
$609$	1142.44	−	1385.39i	0.0760167	−	0.0921818i
$610$	−3898.81	−	6752.93i	−0.258784	−	0.448227i
$611$	6055.18			0.400927
$612$	−2051.82	+	1782.32i	−0.135522	+	0.117722i
$613$	16732.6			1.10248			0.551241	−	0.834346i	$-0.314154\pi$
$613$	16732.6			1.10248			0.551241	+	0.834346i	$0.314154\pi$
$614$	11038.4	+	19119.0i	0.725526	+	1.25665i
$615$	−3310.64	−	8859.58i	−0.217070	−	0.580899i
$616$	−86.0539	+	149.050i	−0.00562859	+	0.00974900i
$617$	−133.434	+	231.115i	−0.00870641	+	0.0150799i	−0.870346	−	0.492441i	$-0.836105\pi$
$617$	−133.434	+	231.115i	−0.00870641	+	0.0150799i	0.861639	+	0.507521i	$0.169438\pi$
$618$	−208.256	−	34.8887i	−0.0135555	−	0.00227092i
$619$	−7248.38	−	12554.6i	−0.470657	−	0.815203i	0.528779	−	0.848759i	$-0.322650\pi$
$619$	−7248.38	−	12554.6i	−0.470657	−	0.815203i	−0.999437	+	0.0335568i	$0.989317\pi$
$620$	−993.791			−0.0643736
$621$	25264.2	−	15463.2i	1.63256	−	0.999219i
$622$	−25476.3			−1.64230
$623$	3260.29	+	5646.99i	0.209664	+	0.363149i
$624$	17114.7	+	2867.18i	1.09797	+	0.183941i
$625$	−13326.4	+	23082.0i	−0.852890	+	1.47725i
$626$	8649.93	−	14982.1i	0.552269	−	0.956558i
$627$	11.4556	+	30.6562i	0.000729652	+	0.00195262i
$628$	−1681.37	−	2912.21i	−0.106837	−	0.185048i
$629$	20821.6			1.31989
$630$	1915.92	+	9875.54i	0.121162	+	0.624525i
$631$	17862.8			1.12695			0.563475	−	0.826133i	$-0.309464\pi$
$631$	17862.8			1.12695			0.563475	+	0.826133i	$0.309464\pi$
$632$	−6030.06	−	10444.4i	−0.379530	−	0.657365i
$633$	−15059.9	+	18262.4i	−0.945617	+	1.14670i
$634$	−10913.3	+	18902.4i	−0.683634	+	1.18409i
$635$	−563.248	+	975.575i	−0.0351997	+	0.0609677i
$636$	−479.967	+	582.033i	−0.0299244	+	0.0362879i
$637$	1476.91	+	2558.09i	0.0918642	+	0.159113i
$638$	135.472			0.00840659
$639$	−20634.7	−	7113.43i	−1.27746	−	0.440380i
$640$	−22757.9			−1.40560
$641$	−6693.97	−	11594.3i	−0.412474	−	0.714426i	0.582685	−	0.812698i	$-0.302002\pi$
$641$	−6693.97	−	11594.3i	−0.412474	−	0.714426i	−0.995160	+	0.0982714i	$0.968669\pi$
$642$	−1170.18	−	3131.51i	−0.0719367	−	0.192509i
$643$	2236.84	−	3874.33i	0.137189	−	0.237618i	−0.789243	−	0.614082i	$-0.789527\pi$
$643$	2236.84	−	3874.33i	0.137189	−	0.237618i	0.926432	+	0.376463i	$0.122860\pi$
$644$	−709.297	+	1228.54i	−0.0434010	+	0.0751727i
$645$	−17767.8	−	2976.60i	−1.08466	−	0.181711i
$646$	847.263	+	1467.50i	0.0516024	+	0.0893779i
$647$	27545.8			1.67378			0.836890	−	0.547372i	$-0.184372\pi$
$647$	27545.8			1.67378			0.836890	+	0.547372i	$0.184372\pi$
$648$	13649.2	+	10679.8i	0.827455	+	0.647440i
$649$	361.872			0.0218871
$650$	−22185.2	−	38425.9i	−1.33873	−	2.31875i
$651$	1851.50	+	310.178i	0.111469	+	0.0186741i
$652$	300.529	−	520.532i	0.0180516	−	0.0312663i
$653$	−1564.46	+	2709.72i	−0.0937551	+	0.162389i	−0.909088	−	0.416603i	$-0.863220\pi$
$653$	−1564.46	+	2709.72i	−0.0937551	+	0.162389i	0.815333	+	0.578992i	$0.196554\pi$
$654$	7799.14	+	20871.2i	0.466316	+	1.24790i
$655$	13198.9	+	22861.1i	0.787362	+	1.36375i
$656$	−5026.79			−0.299182
$657$	−2749.41	−	947.805i	−0.163264	−	0.0562822i
$658$	1865.63			0.110532
$659$	−7388.04	−	12796.5i	−0.436718	−	0.756418i	0.560716	−	0.828008i	$-0.310526\pi$
$659$	−7388.04	−	12796.5i	−0.436718	−	0.756418i	−0.997434	+	0.0715903i	$0.977193\pi$
$660$	65.8323	−	79.8316i	0.00388260	−	0.00470825i
$661$	12912.1	−	22364.5i	0.759794	−	1.31600i	−0.183161	−	0.983083i	$-0.558633\pi$
$661$	12912.1	−	22364.5i	0.759794	−	1.31600i	0.942955	−	0.332919i	$-0.108034\pi$
$662$	−7.28869	+	12.6244i	−0.000427920	+	0.000741180i
$663$	−20899.0	+	25343.2i	−1.22421	+	1.48454i
$664$	14046.7	+	24329.6i	0.820961	+	1.42195i
$665$	−855.142			−0.0498661
$666$	−2709.01	−	13963.5i	−0.157616	−	0.812426i
$667$	10423.2			0.605079
$668$	523.197	+	906.204i	0.0303040	+	0.0524882i
$669$	−10390.3	−	27805.3i	−0.600464	−	1.60690i
$670$	7105.09	−	12306.4i	0.409692	−	0.709607i
$671$	75.7566	−	131.214i	0.00435850	−	0.00754914i
$672$	−1549.50	−	259.585i	−0.0889483	−	0.0149013i
$673$	5050.69	+	8748.04i	0.289286	+	0.501058i	0.973640	−	0.228092i	$-0.0732487\pi$
$673$	5050.69	+	8748.04i	0.289286	+	0.501058i	−0.684353	+	0.729151i	$0.739915\pi$
$674$	−25736.1			−1.47080
$675$	−997.743	−	38906.0i	−0.0568936	−	2.21851i
$676$	−1379.27			−0.0784748
$677$	−64.6433	−	111.965i	−0.00366978	−	0.00635625i	0.864185	−	0.503175i	$-0.167835\pi$
$677$	−64.6433	−	111.965i	−0.00366978	−	0.00635625i	−0.867854	+	0.496819i	$0.834501\pi$
$678$	−13592.0	−	2277.04i	−0.769910	−	0.128981i
$679$	1446.62	−	2505.63i	0.0817620	−	0.141616i
$680$	25005.9	−	43311.5i	1.41020	−	2.44253i
$681$	−5801.70	−	15525.9i	−0.326464	−	0.873647i
$682$	70.8151	+	122.655i	0.00397602	+	0.00688668i
$683$	22889.1			1.28232			0.641162	−	0.767406i	$-0.278453\pi$
$683$	22889.1			1.28232			0.641162	+	0.767406i	$0.278453\pi$
$684$	−119.151	+	103.501i	−0.00666060	+	0.00578576i
$685$	−23067.0			−1.28664
$686$	455.045	+	788.162i	0.0253261	+	0.0438661i
$687$	888.884	−	1077.91i	0.0493640	−	0.0598613i
$688$	−4787.49	+	8292.17i	−0.265292	+	0.459500i
$689$	−4559.04	+	7896.50i	−0.252084	+	0.436622i
$690$	−37150.1	+	45050.2i	−2.04968	+	2.48555i
$691$	−14839.9	−	25703.5i	−0.816987	−	1.41506i	−0.907892	−	0.419204i	$-0.862309\pi$
$691$	−14839.9	−	25703.5i	−0.816987	−	1.41506i	0.0909051	−	0.995860i	$-0.471024\pi$
$692$	184.769			0.0101501
$693$	−147.567	+	128.184i	−0.00808888	+	0.00702644i
$694$	2947.19			0.161201
$695$	−1581.69	−	2739.57i	−0.0863265	−	0.149522i
$696$	2134.71	+	5712.69i	0.116259	+	0.311119i
$697$	4757.75	−	8240.67i	0.258555	−	0.447830i
$698$	5266.17	−	9121.27i	0.285569	−	0.494621i
$699$	17779.3	+	2978.53i	0.962055	+	0.161171i
$700$	931.947	+	1614.18i	0.0503204	+	0.0871575i
$701$	3469.60			0.186940			0.0934700	−	0.995622i	$-0.470204\pi$
$701$	3469.60			0.186940			0.0934700	+	0.995622i	$0.470204\pi$
$702$	19715.0	+	10718.2i	1.05996	+	0.576255i
$703$	1209.13			0.0648694
$704$	−288.445	−	499.602i	−0.0154420	−	0.0267464i
$705$	−10326.2	−	1729.93i	−0.551641	−	0.0924153i
$706$	−6121.39	+	10602.6i	−0.326319	+	0.565202i
$707$	−4682.03	+	8109.51i	−0.249061	+	0.431386i
$708$	610.874	+	1634.75i	0.0324266	+	0.0867766i
$709$	−10210.5	−	17685.2i	−0.540853	−	0.936785i	−0.998855	−	0.0478338i	$-0.984768\pi$
$709$	−10210.5	−	17685.2i	−0.540853	−	0.936785i	0.458002	−	0.888951i	$-0.348565\pi$
$710$	43027.0			2.27433
$711$	−2608.65	−	13446.2i	−0.137598	−	0.709245i
$712$	−22145.2			−1.16563
$713$	5448.48	+	9437.04i	0.286181	+	0.495680i
$714$	−6439.10	+	7808.39i	−0.337503	+	0.409274i
$715$	625.319	−	1083.08i	0.0327071	−	0.0566504i
$716$	−1334.90	+	2312.11i	−0.0696753	+	0.120681i
$717$	−1231.95	+	1493.92i	−0.0641673	+	0.0778125i
$718$	−11802.2	−	20442.0i	−0.613445	−	1.06252i
$719$	23453.7			1.21652			0.608259	−	0.793739i	$-0.291868\pi$
$719$	23453.7			1.21652			0.608259	+	0.793739i	$0.291868\pi$
$720$	−28367.4	−	9779.11i	−1.46832	−	0.506175i
$721$	107.210			0.00553771
$722$	−9050.38	−	15675.7i	−0.466510	−	0.808019i
$723$	13360.0	+	35752.6i	0.687226	+	1.83908i
$724$	−532.074	+	921.580i	−0.0273127	+	0.0473070i
$725$	6847.53	−	11860.3i	0.350773	−	0.607557i
$726$	18083.9	+	3029.55i	0.924455	+	0.154872i
$727$	10397.4	+	18008.8i	0.530423	+	0.918720i	0.999370	+	0.0354935i	$0.0113003\pi$
$727$	10397.4	+	18008.8i	0.530423	+	0.918720i	−0.468947	+	0.883226i	$0.655366\pi$
$728$	−10031.8			−0.510719
$729$	10702.3	+	16519.1i	0.543732	+	0.839259i
$730$	5732.99			0.290668
$731$	−9062.52	−	15696.7i	−0.458535	−	0.794207i
$732$	720.643	+	120.728i	0.0363876	+	0.00609594i
$733$	−11526.8	+	19964.9i	−0.580833	+	1.00603i	0.414548	+	0.910028i	$0.363940\pi$
$733$	−11526.8	+	19964.9i	−0.580833	+	1.00603i	−0.995381	+	0.0960050i	$0.969394\pi$
$734$	−7892.35	+	13670.0i	−0.396883	+	0.687421i
$735$	−1787.83	−	4784.39i	−0.0897211	−	0.240102i
$736$	−4559.77	−	7897.76i	−0.228363	−	0.395537i
$737$	276.114			0.0138003
$738$	−6145.44	−	2118.52i	−0.306527	−	0.105669i
$739$	−23162.2			−1.15296			−0.576478	−	0.817112i	$-0.695573\pi$
$739$	−23162.2			−1.15296			−0.576478	+	0.817112i	$0.695573\pi$
$740$	−1911.50	−	3310.82i	−0.0949571	−	0.164471i
$741$	−1213.63	+	1471.71i	−0.0601669	+	0.0729615i
$742$	−1404.67	+	2432.95i	−0.0694972	+	0.120373i
$743$	−16033.4	+	27770.6i	−0.791666	+	1.37121i	0.133268	+	0.991080i	$0.457453\pi$
$743$	−16033.4	+	27770.6i	−0.791666	+	1.37121i	−0.924935	+	0.380126i	$0.875881\pi$
$744$	−4056.33	+	4918.92i	−0.199882	+	0.242388i
$745$	10309.1	+	17855.8i	0.506973	+	0.878103i
$746$	20428.3			1.00259
$747$	6076.72	+	31322.3i	0.297638	+	1.53417i
$748$	104.104			0.00508882
$749$	848.658	+	1469.92i	0.0414009	+	0.0717085i
$750$	14754.3	+	39483.8i	0.718334	+	1.92233i
$751$	2375.55	−	4114.58i	0.115426	−	0.199924i	−0.802524	−	0.596620i	$-0.796510\pi$
$751$	2375.55	−	4114.58i	0.115426	−	0.199924i	0.917950	+	0.396696i	$0.129843\pi$
$752$	−2782.37	+	4819.21i	−0.134924	+	0.233695i
$753$	−6156.67	−	1031.41i	−0.297957	−	0.0499161i
$754$	3948.21	+	6838.49i	0.190696	+	0.330296i
$755$	34024.7			1.64011
$756$	−828.179	−	450.244i	−0.0398420	−	0.0216603i
$757$	−40462.6			−1.94272			−0.971359	−	0.237618i	$-0.923633\pi$
$757$	−40462.6			−1.94272			−0.971359	+	0.237618i	$0.923633\pi$
$758$	14570.3	+	25236.5i	0.698175	+	1.20927i
$759$	−1119.01	−	187.465i	−0.0535144	−	0.00896515i
$760$	1452.12	−	2515.14i	0.0693077	−	0.120044i
$761$	−2405.16	+	4165.86i	−0.114569	+	0.198439i	−0.917607	−	0.397488i	$-0.869882\pi$
$761$	−2405.16	+	4165.86i	−0.114569	+	0.198439i	0.803038	+	0.595927i	$0.203215\pi$
$762$	271.011	+	725.250i	0.0128841	+	0.0344790i
$763$	−5656.22	−	9796.87i	−0.268374	−	0.464837i
$764$	1392.09			0.0659214
$765$	42880.6	−	37248.4i	2.02660	−	1.76042i
$766$	−1640.15			−0.0773642
$767$	10546.4	+	18266.9i	0.496490	+	0.859946i
$768$	4801.05	−	5822.01i	0.225577	−	0.273546i
$769$	−7975.55	+	13814.1i	−0.374000	+	0.647786i	−0.990177	−	0.139821i	$-0.955347\pi$
$769$	−7975.55	+	13814.1i	−0.374000	+	0.647786i	0.616177	+	0.787608i	$0.288681\pi$
$770$	192.664	−	333.704i	0.00901706	−	0.0156180i
$771$	20012.5	−	24268.2i	0.934803	−	1.13359i
$772$	669.495	+	1159.60i	0.0312120	+	0.0540607i
$773$	−11689.6			−0.543913			−0.271956	−	0.962310i	$-0.587671\pi$
$773$	−11689.6			−0.543913			−0.271956	+	0.962310i	$0.587671\pi$
$774$	−9347.60	+	8119.83i	−0.434099	+	0.377082i
$775$	14317.5			0.663614
$776$	4913.03	+	8509.63i	0.227278	+	0.393657i
$777$	2527.90	+	6764.89i	0.116715	+	0.312341i
$778$	12895.3	−	22335.4i	0.594242	−	1.02926i
$779$	276.288	−	478.544i	0.0127074	−	0.0220098i
$780$	5948.42	+	996.526i	0.273061	+	0.0457453i
$781$	418.023	+	724.037i	0.0191524	+	0.0331729i
$782$	−58747.7			−2.68646
$783$	177.564	+	6923.93i	0.00810423	+	0.316017i
$784$	−2714.59			−0.123660
$785$	35138.6	+	60861.9i	1.59765	+	2.76720i
$786$	17893.6	+	2997.67i	0.812013	+	0.136035i
$787$	−8383.99	+	14521.5i	−0.379742	+	0.657732i	−0.991025	−	0.133680i	$-0.957321\pi$
$787$	−8383.99	+	14521.5i	−0.379742	+	0.657732i	0.611283	+	0.791412i	$0.290654\pi$
$788$	1170.19	−	2026.83i	0.0529013	−	0.0916278i
$789$	5576.11	+	14922.2i	0.251603	+	0.673313i
$790$	13500.6	+	23383.7i	0.608011	+	1.05311i
$791$	6997.14			0.314525
$792$	−126.433	−	651.694i	−0.00567246	−	0.0292385i
$793$	8831.39			0.395475
$794$	−15991.9	−	27698.7i	−0.714773	−	1.23802i
$795$	10030.7	−	12163.8i	0.447489	−	0.542649i
$796$	491.204	−	850.790i	0.0218722	−	0.0378837i
$797$	17129.0	−	29668.4i	0.761282	−	1.31858i	−0.180908	−	0.983500i	$-0.557903\pi$
$797$	17129.0	−	29668.4i	0.761282	−	1.31858i	0.942190	−	0.335079i	$-0.108763\pi$
$798$	−373.925	+	453.441i	−0.0165875	+	0.0201148i
$799$	−5266.92	−	9122.57i	−0.233204	−	0.403922i
$800$	−11982.2			−0.529543
$801$	−23777.6	−	8196.88i	−1.04886	−	0.361576i
$802$	17193.6			0.757017
$803$	55.6980	+	96.4718i	0.00244775	+	0.00423962i
$804$	466.106	+	1247.34i	0.0204456	+	0.0547144i
$805$	14823.5	−	25675.0i	0.649018	−	1.12413i
$806$	−4127.66	+	7149.32i	−0.180385	+	0.312437i
$807$	−4222.21	−	707.338i	−0.184175	−	0.0308544i
$808$	−15901.1	−	27541.6i	−0.692327	−	1.19914i
$809$	4334.51			0.188372			0.0941861	−	0.995555i	$-0.469975\pi$
$809$	4334.51			0.188372			0.0941861	+	0.995555i	$0.469975\pi$
$810$	−30558.9	−	23910.7i	−1.32559	−	1.03720i
$811$	−6398.52			−0.277044			−0.138522	−	0.990359i	$-0.544235\pi$
$811$	−6398.52			−0.277044			−0.138522	+	0.990359i	$0.544235\pi$
$812$	−165.854	−	287.268i	−0.00716792	−	0.0124152i
$813$	2915.54	+	488.435i	0.125772	+	0.0210703i
$814$	−272.418	+	471.841i	−0.0117300	+	0.0203170i
$815$	−6280.72	+	10878.5i	−0.269943	+	0.467556i
$816$	−10567.1	−	28278.5i	−0.453335	−	1.21317i
$817$	−526.270	−	911.526i	−0.0225359	−	0.0390333i
$818$	19187.6			0.820146
$819$	−10771.3	−	3713.19i	−0.459559	−	0.158424i
$820$	−1747.12			−0.0744051
$821$	−11482.0	−	19887.4i	−0.488093	−	0.845401i	0.511814	−	0.859097i	$-0.328974\pi$
$821$	−11482.0	−	19887.4i	−0.488093	−	0.845401i	−0.999906	+	0.0136952i	$0.995641\pi$
$822$	−10086.4	+	12231.3i	−0.427987	+	0.518999i
$823$	8918.01	−	15446.4i	0.377718	−	0.654227i	−0.613012	−	0.790074i	$-0.710042\pi$
$823$	8918.01	−	15446.4i	0.377718	−	0.654227i	0.990730	+	0.135847i	$0.0433754\pi$
$824$	−182.053	+	315.325i	−0.00769674	+	0.0133311i
$825$	−948.445	+	1150.13i	−0.0400250	+	0.0485364i
$826$	3249.40	+	5628.13i	0.136878	+	0.237079i
$827$	−20518.6			−0.862757			−0.431378	−	0.902171i	$-0.641973\pi$
$827$	−20518.6			−0.862757			−0.431378	+	0.902171i	$0.641973\pi$
$828$	−1042.12	−	5371.57i	−0.0437393	−	0.225453i
$829$	29982.8			1.25615			0.628073	−	0.778155i	$-0.283844\pi$
$829$	29982.8			1.25615			0.628073	+	0.778155i	$0.283844\pi$
$830$	−31448.8	−	54471.0i	−1.31519	−	2.27797i
$831$	11776.6	+	31515.3i	0.491608	+	1.31559i
$832$	16812.9	−	29120.8i	0.700579	−	1.21344i
$833$	2569.30	−	4450.16i	0.106868	−	0.185101i
$834$	−2144.28	−	359.227i	−0.0890293	−	0.0149149i
$835$	−10934.2	−	18938.6i	−0.453167	−	0.784907i
$836$	6.04545			0.000250103
$837$	−6176.03	+	3780.09i	−0.255048	+	0.156104i
$838$	33063.2			1.36295
$839$	−8874.61	−	15371.3i	−0.365179	−	0.632509i	0.623625	−	0.781723i	$-0.285659\pi$
$839$	−8874.61	−	15371.3i	−0.365179	−	0.632509i	−0.988805	+	0.149214i	$0.952326\pi$
$840$	17107.8	+	2866.03i	0.702707	+	0.117723i
$841$	10975.9	−	19010.8i	0.450034	−	0.779482i
$842$	−8713.54	+	15092.3i	−0.356637	+	0.617714i
$843$	7226.70	+	19339.3i	0.295256	+	0.790132i
$844$	2186.32	+	3786.81i	0.0891660	+	0.154440i
$845$	28825.2			1.17351
$846$	−5432.60	+	4719.05i	−0.220776	+	0.191778i
$847$	−9309.51			−0.377661
$848$	−4189.79	−	7256.93i	−0.169667	−	0.293873i
$849$	−19918.9	+	24154.7i	−0.805200	+	0.976427i
$850$	−38594.4	+	66847.4i	−1.55738	+	2.69747i
$851$	−20959.7	+	36303.3i	−0.844288	+	1.46235i
$852$	−2565.17	+	3110.66i	−0.103147	+	0.125081i
$853$	−7935.96	−	13745.5i	−0.318549	−	0.551742i	0.661637	−	0.749824i	$-0.269862\pi$
$853$	−7935.96	−	13745.5i	−0.318549	−	0.551742i	−0.980185	+	0.198082i	$0.936529\pi$
$854$	2721.00			0.109029
$855$	2490.12	−	2163.05i	0.0996026	−	0.0865202i
$856$	−5764.43			−0.230169
$857$	−24641.4	−	42680.1i	−0.982186	−	1.70120i	−0.653827	−	0.756644i	$-0.726838\pi$
$857$	−24641.4	−	42680.1i	−0.982186	−	1.70120i	−0.328359	−	0.944553i	$-0.606496\pi$
$858$	−300.877	−	805.173i	−0.0119717	−	0.0320375i
$859$	−2762.84	+	4785.37i	−0.109740	+	0.190075i	−0.915665	−	0.401942i	$-0.868335\pi$
$859$	−2762.84	+	4785.37i	−0.109740	+	0.190075i	0.805925	+	0.592018i	$0.201669\pi$
$860$	−1663.95	+	2882.05i	−0.0659771	+	0.114276i
$861$	3255.01	+	545.305i	0.128839	+	0.0215841i
$862$	9575.70	+	16585.6i	0.378364	+	0.655345i
$863$	−42645.7			−1.68213			−0.841065	−	0.540935i	$-0.818071\pi$
$863$	−42645.7			−1.68213			−0.841065	+	0.540935i	$0.818071\pi$
$864$	5168.65	−	3163.51i	0.203520	−	0.124566i
$865$	−3861.46			−0.151784
$866$	−9527.03	−	16501.3i	−0.373836	−	0.647503i
$867$	31182.0	+	5223.86i	1.22145	+	0.204627i
$868$	173.393	−	300.326i	0.00678035	−	0.0117439i
$869$	−262.326	+	454.361i	−0.0102403	+	0.0177367i
$870$	−4779.36	−	12790.0i	−0.186248	−	0.498416i
$871$	8047.05	+	13937.9i	0.313047	+	0.542213i
$872$	38419.4			1.49202
$873$	2125.42	+	10955.4i	0.0823992	+	0.424724i
$874$	−3411.54			−0.132033
$875$	−10700.4	−	18533.6i	−0.413415	−	0.716055i
$876$	−341.787	+	414.469i	−0.0131826	+	0.0159859i
$877$	7011.81	−	12144.8i	0.269979	−	0.467618i	−0.698877	−	0.715242i	$-0.746316\pi$
$877$	7011.81	−	12144.8i	0.269979	−	0.467618i	0.968856	+	0.247624i	$0.0796498\pi$
$878$	−14802.6	+	25638.9i	−0.568979	+	0.985501i
$879$	17083.0	−	20715.7i	0.655510	−	0.794906i
$880$	574.672	+	995.361i	0.0220139	+	0.0381291i
$881$	−28450.0			−1.08797			−0.543987	−	0.839094i	$-0.683086\pi$
$881$	−28450.0			−1.08797			−0.543987	+	0.839094i	$0.683086\pi$
$882$	−3318.69	−	1144.05i	−0.126696	−	0.0436761i
$883$	−15592.0			−0.594237			−0.297118	−	0.954841i	$-0.596026\pi$
$883$	−15592.0			−0.594237			−0.297118	+	0.954841i	$0.596026\pi$
$884$	3034.02	+	5255.07i	0.115436	+	0.199940i
$885$	−12766.6	−	34164.5i	−0.484908	−	1.29766i
$886$	−2684.79	+	4650.19i	−0.101803	+	0.176328i
$887$	−18487.3	+	32021.0i	−0.699824	+	1.21213i	0.268704	+	0.963223i	$0.413405\pi$
$887$	−18487.3	+	32021.0i	−0.699824	+	1.21213i	−0.968527	+	0.248907i	$0.919929\pi$
$888$	−24189.5	−	4052.42i	−0.914130	−	0.153142i
$889$	−196.547	−	340.429i	−0.00741504	−	0.0128432i
$890$	49580.5			1.86735
$891$	105.467	−	746.529i	0.00396551	−	0.0280692i
$892$	−5483.24			−0.205821
$893$	−305.855	−	529.757i	−0.0114614	−	0.0198518i
$894$	13975.9	+	2341.35i	0.522846	+	0.0875912i
$895$	27897.9	−	48320.5i	1.04192	−	1.80467i
$896$	3970.71	−	6877.47i	0.148049	−	0.256429i
$897$	−23149.3	−	61949.7i	−0.861687	−	2.30595i
$898$	−6022.50	−	10431.3i	−0.223801	−	0.387635i
$899$	−2548.03			−0.0945289
$900$	−6796.78	−	2343.06i	−0.251733	−	0.0867800i
$901$	15862.2			0.586512
$902$	124.496	+	215.633i	0.00459562	+	0.00795985i
$903$	3999.59	−	4850.11i	0.147395	−	0.178739i
$904$	−11881.9	+	20580.0i	−0.437151	+	0.757168i
$905$	11119.7	−	19260.0i	0.408434	−	0.707428i
$906$	14877.9	−	18041.7i	0.545567	−	0.661583i
$907$	16554.8	+	28673.7i	0.606056	+	1.04972i	0.991884	+	0.127149i	$0.0405825\pi$
$907$	16554.8	+	28673.7i	0.606056	+	1.04972i	−0.385828	+	0.922571i	$0.626084\pi$
$908$	−3061.73			−0.111902
$909$	−6878.96	−	35457.4i	−0.251002	−	1.29378i
$910$	22460.0			0.818177
$911$	−10620.6	−	18395.4i	−0.386253	−	0.669010i	0.605689	−	0.795701i	$-0.292897\pi$
$911$	−10620.6	−	18395.4i	−0.386253	−	0.669010i	−0.991942	+	0.126692i	$0.959564\pi$
$912$	−613.641	−	1642.16i	−0.0222803	−	0.0596242i
$913$	611.073	−	1058.41i	0.0221507	−	0.0383661i
$914$	2324.97	−	4026.97i	0.0841392	−	0.145733i
$915$	−15060.6	−	2523.07i	−0.544140	−	0.0911587i
$916$	−129.044	−	223.511i	−0.00465473	−	0.00806222i
$917$	−9211.55			−0.331725
$918$	−1000.79	−	39025.0i	−0.0359816	−	1.40307i
$919$	−33447.0			−1.20056			−0.600279	−	0.799790i	$-0.704944\pi$
$919$	−33447.0			−1.20056			−0.600279	+	0.799790i	$0.704944\pi$
$920$	50343.6	+	87197.7i	1.80411	+	3.12481i
$921$	42639.9	+	7143.37i	1.52555	+	0.255572i
$922$	12306.3	−	21315.1i	0.439572	−	0.761361i
$923$	−24365.7	+	42202.6i	−0.868912	+	1.50500i
$924$	12.6391	+	33.8234i	0.000449995	+	0.00120423i
$925$	27539.0	+	47698.9i	0.978893	+	1.69549i
$926$	380.735			0.0135116
$927$	−312.187	+	271.183i	−0.0110610	+	0.00960821i
$928$	2132.42			0.0754310
$929$	7815.35	+	13536.6i	0.276010	+	0.478063i	0.970389	−	0.241546i	$-0.0776544\pi$
$929$	7815.35	+	13536.6i	0.276010	+	0.478063i	−0.694380	+	0.719609i	$0.744321\pi$
$930$	9081.63	−	11012.9i	0.320213	−	0.388307i
$931$	149.202	−	258.425i	0.00525231	−	0.00909726i
$932$	1665.04	−	2883.93i	0.0585194	−	0.101359i
$933$	−31742.0	+	38491.9i	−1.11381	+	1.35066i
$934$	−17326.1	−	30009.6i	−0.606987	−	1.05133i
$935$	−2175.66			−0.0760982
$936$	29212.0	−	25375.1i	1.02011	−	0.886123i
$937$	13243.6			0.461738			0.230869	−	0.972985i	$-0.425843\pi$
$937$	13243.6			0.461738			0.230869	+	0.972985i	$0.425843\pi$
$938$	2479.34	+	4294.34i	0.0863042	+	0.149483i
$939$	−11859.0	−	31735.9i	−0.412146	−	1.10294i
$940$	−967.049	+	1674.98i	−0.0335550	+	0.0581189i
$941$	−10744.2	+	18609.5i	−0.372212	+	0.644689i	−0.989905	−	0.141729i	$-0.954734\pi$
$941$	−10744.2	+	18609.5i	−0.372212	+	0.644689i	0.617694	+	0.786419i	$0.288067\pi$
$942$	47637.1	+	7980.54i	1.64766	+	0.276030i
$943$	9578.64	+	16590.7i	0.330778	+	0.572924i
$944$	−19384.4			−0.668335
$945$	17308.0	+	9409.58i	0.595797	+	0.323909i
$946$	474.276			0.0163003
$947$	6426.83	+	11131.6i	0.220532	+	0.381973i	0.954970	−	0.296703i	$-0.0958873\pi$
$947$	6426.83	+	11131.6i	0.220532	+	0.381973i	−0.734438	+	0.678676i	$0.762554\pi$
$948$	−2495.40	−	418.050i	−0.0854925	−	0.0143224i
$949$	−3246.52	+	5623.14i	−0.111050	+	0.192344i
$950$	−2241.21	+	3881.89i	−0.0765416	+	0.132574i
$951$	14962.2	+	40040.1i	0.510180	+	1.36529i
$952$	8725.88	+	15113.7i	0.297067	+	0.514534i
$953$	27206.4			0.924767			0.462384	−	0.886680i	$-0.346994\pi$
$953$	27206.4			0.924767			0.462384	+	0.886680i	$0.346994\pi$
$954$	−2063.77	−	10637.7i	−0.0700389	−	0.361013i
$955$	−29093.0			−0.985788
$956$	178.848	+	309.774i	0.00605059	+	0.0104799i
$957$	168.790	−	204.684i	0.00570138	−	0.00691379i
$958$	1335.83	−	2313.73i	0.0450510	−	0.0780306i
$959$	4024.65	−	6970.90i	0.135519	−	0.234726i
$960$	−36991.5	+	44857.8i	−1.24364	+	1.50810i
$961$	13563.6	+	23492.8i	0.455291	+	0.788587i
$962$	−31757.3			−1.06434
$963$	−6189.34	−	2133.66i	−0.207112	−	0.0713979i
$964$	7050.48			0.235561
$965$	−13991.7	−	24234.3i	−0.466744	−	0.808423i
$966$	−7132.43	−	19087.0i	−0.237559	−	0.635730i
$967$	−15806.0	+	27376.9i	−0.525634	+	0.910424i	0.473920	+	0.880568i	$0.342838\pi$
$967$	−15806.0	+	27376.9i	−0.525634	+	0.910424i	−0.999554	+	0.0298567i	$0.990495\pi$
$968$	15808.5	−	27381.1i	0.524901	−	0.909156i
$969$	3272.87	+	548.298i	0.108503	+	0.0181774i
$970$	−10999.7	−	19052.0i	−0.364101	−	0.630642i
$971$	−31420.7			−1.03845			−0.519227	−	0.854636i	$-0.673780\pi$
$971$	−31420.7			−1.03845			−0.519227	+	0.854636i	$0.673780\pi$
$972$	3550.48	−	783.767i	0.117162	−	0.0258635i
$973$	1103.87			0.0363705
$974$	14248.0	+	24678.2i	0.468721	+	0.811848i
$975$	−85698.8	−	14356.9i	−2.81493	−	0.471579i
$976$	−4058.05	+	7028.75i	−0.133089	+	0.230517i
$977$	22104.4	−	38285.9i	0.723830	−	1.25371i	−0.235624	−	0.971844i	$-0.575713\pi$
$977$	22104.4	−	38285.9i	0.723830	−	1.25371i	0.959454	−	0.281866i	$-0.0909533\pi$
$978$	3022.01	+	8087.18i	0.0988070	+	0.264417i
$979$	481.692	+	834.315i	0.0157252	+	0.0272368i
$980$	−943.489			−0.0307537
$981$	41251.4	+	14220.6i	1.34256	+	0.462823i
$982$	44245.7			1.43782
$983$	−5308.74	−	9195.02i	−0.172251	−	0.298347i	0.766956	−	0.641700i	$-0.221771\pi$
$983$	−5308.74	−	9195.02i	−0.172251	−	0.298347i	−0.939206	+	0.343353i	$0.888437\pi$
$984$	−7131.19	+	8647.65i	−0.231031	+	0.280160i
$985$	−24455.6	+	42358.3i	−0.791086	+	1.37020i
$986$	6868.46	−	11896.5i	0.221842	−	0.384242i
$987$	2324.46	−	2818.77i	0.0749630	−	0.0909041i
$988$	176.188	+	305.167i	0.00567338	+	0.00982658i
$989$	36490.6			1.17324
$990$	283.067	+	1459.06i	0.00908734	+	0.0468404i
$991$	−23631.8			−0.757506			−0.378753	−	0.925498i	$-0.623647\pi$
$991$	−23631.8			−0.757506			−0.378753	+	0.925498i	$0.623647\pi$
$992$	1114.67	+	1930.67i	0.0356762	+	0.0617931i
$993$	9.99280	+	26.7416i	0.000319347	+	0.000854602i
$994$	−7507.20	+	13002.8i	−0.239551	+	0.414915i
$995$	−10265.6	+	17780.5i	−0.327077	+	0.566513i
$996$	5812.91	+	973.824i	0.184929	+	0.0309807i
$997$	1699.95	+	2944.40i	0.0540000	+	0.0935307i	0.891762	−	0.452505i	$-0.149470\pi$
$997$	1699.95	+	2944.40i	0.0540000	+	0.0935307i	−0.837762	+	0.546036i	$0.816136\pi$
$998$	−46683.3			−1.48070
$999$	−24472.6	−	13304.7i	−0.775055	−	0.421363i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.f.c.22.6	✓	18
3.2	odd	2		189.4.f.c.64.4		18
9.2	odd	6		189.4.f.c.127.4		18
9.4	even	3		567.4.a.j.1.4		9
9.5	odd	6		567.4.a.k.1.6		9
9.7	even	3	inner	63.4.f.c.43.6	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.f.c.22.6	✓	18	1.1	even	1	trivial
63.4.f.c.43.6	yes	18	9.7	even	3	inner
189.4.f.c.64.4		18	3.2	odd	2
189.4.f.c.127.4		18	9.2	odd	6
567.4.a.j.1.4		9	9.4	even	3
567.4.a.k.1.6		9	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.32666 + 2.29785i) q^{2} +(5.12474 + 0.858536i) q^{3} +(0.479932 - 0.831266i) q^{4} +(-10.0300 + 17.3725i) q^{5} +(4.82601 + 12.9148i) q^{6} +(-3.50000 - 6.06218i) q^{7} +23.7734 q^{8} +(25.5258 + 8.79954i) q^{9} +O(q^{10})\)	\(q+(1.32666 + 2.29785i) q^{2} +(5.12474 + 0.858536i) q^{3} +(0.479932 - 0.831266i) q^{4} +(-10.0300 + 17.3725i) q^{5} +(4.82601 + 12.9148i) q^{6} +(-3.50000 - 6.06218i) q^{7} +23.7734 q^{8} +(25.5258 + 8.79954i) q^{9} -53.2258 q^{10} +(-0.517107 - 0.895656i) q^{11} +(3.17319 - 3.84798i) q^{12} +(30.1411 - 52.2059i) q^{13} +(9.28664 - 16.0849i) q^{14} +(-66.3161 + 80.4183i) q^{15} +(27.6999 + 47.9776i) q^{16} -104.870 q^{17} +(13.6442 + 70.3285i) q^{18} -6.08988 q^{19} +(9.62744 + 16.6752i) q^{20} +(-12.7320 - 34.0719i) q^{21} +(1.37205 - 2.37647i) q^{22} +(105.565 - 182.844i) q^{23} +(121.833 + 20.4103i) q^{24} +(-138.702 - 240.240i) q^{25} +159.948 q^{26} +(123.258 + 67.0102i) q^{27} -6.71904 q^{28} +(24.6842 + 42.7544i) q^{29} +(-272.768 - 45.6963i) q^{30} +(-25.8062 + 44.6977i) q^{31} +(21.5969 - 37.4070i) q^{32} +(-1.88109 - 5.03396i) q^{33} +(-139.126 - 240.974i) q^{34} +140.420 q^{35} +(19.5654 - 16.9956i) q^{36} -198.547 q^{37} +(-8.07921 - 13.9936i) q^{38} +(199.286 - 241.664i) q^{39} +(-238.448 + 413.004i) q^{40} +(-45.3683 + 78.5802i) q^{41} +(61.4011 - 74.4581i) q^{42} +(86.4171 + 149.679i) q^{43} -0.992705 q^{44} +(-408.894 + 355.188i) q^{45} +560.198 q^{46} +(50.2236 + 86.9898i) q^{47} +(100.764 + 269.654i) q^{48} +(-24.5000 + 42.4352i) q^{49} +(368.023 - 637.434i) q^{50} +(-537.429 - 90.0343i) q^{51} +(-28.9313 - 50.1106i) q^{52} -151.257 q^{53} +(9.54323 + 372.129i) q^{54} +20.7464 q^{55} +(-83.2070 - 144.119i) q^{56} +(-31.2090 - 5.22838i) q^{57} +(-65.4953 + 113.441i) q^{58} +(-174.950 + 303.023i) q^{59} +(35.0218 + 93.7216i) q^{60} +(73.2503 + 126.873i) q^{61} -136.945 q^{62} +(-35.9960 - 185.541i) q^{63} +557.805 q^{64} +(604.632 + 1047.25i) q^{65} +(9.07170 - 11.0008i) q^{66} +(-133.490 + 231.211i) q^{67} +(-50.3302 + 87.1745i) q^{68} +(697.972 - 846.397i) q^{69} +(186.290 + 322.664i) q^{70} -808.387 q^{71} +(606.837 + 209.195i) q^{72} -107.711 q^{73} +(-263.405 - 456.232i) q^{74} +(-504.559 - 1350.25i) q^{75} +(-2.92272 + 5.06231i) q^{76} +(-3.61975 + 6.26959i) q^{77} +(819.693 + 137.321i) q^{78} +(-253.647 - 439.330i) q^{79} -1111.32 q^{80} +(574.136 + 449.231i) q^{81} -240.754 q^{82} +(590.857 + 1023.39i) q^{83} +(-34.4333 - 5.76854i) q^{84} +(1051.84 - 1821.85i) q^{85} +(-229.293 + 397.147i) q^{86} +(89.7941 + 240.297i) q^{87} +(-12.2934 - 21.2928i) q^{88} -931.512 q^{89} +(-1358.63 - 468.362i) q^{90} -421.976 q^{91} +(-101.328 - 175.506i) q^{92} +(-170.625 + 206.908i) q^{93} +(-133.259 + 230.812i) q^{94} +(61.0816 - 105.796i) q^{95} +(142.794 - 173.159i) q^{96} +(206.661 + 357.947i) q^{97} -130.013 q^{98} +(-5.31823 - 27.4127i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9}+O(q^{10}) \) 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9	\( 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9} + 111 q^{11} - 18 q^{13} + 42 q^{14} - 36 q^{15} - 144 q^{16} - 546 q^{17} - 45 q^{18} + 90 q^{19} + 402 q^{20} - 63 q^{21} + 162 q^{22} + 312 q^{23} - 36 q^{24} - 279 q^{25} + 102 q^{26} + 432 q^{27} + 504 q^{28} + 378 q^{29} - 864 q^{30} - 18 q^{31} + 891 q^{32} + 513 q^{33} + 324 q^{34} - 336 q^{35} + 414 q^{36} - 72 q^{37} + 147 q^{38} - 810 q^{39} - 405 q^{40} + 477 q^{41} + 315 q^{42} + 171 q^{43} - 1896 q^{44} - 720 q^{45} - 756 q^{46} + 654 q^{47} - 2709 q^{48} - 441 q^{49} + 429 q^{50} + 1341 q^{51} - 747 q^{52} - 1896 q^{53} - 108 q^{54} - 432 q^{55} + 525 q^{56} - 1143 q^{57} - 297 q^{58} + 957 q^{59} + 5400 q^{60} + 198 q^{61} - 600 q^{62} - 504 q^{63} + 4770 q^{64} + 2478 q^{65} - 2646 q^{66} + 333 q^{67} + 1443 q^{68} + 3366 q^{69} - 5652 q^{71} - 3681 q^{72} + 306 q^{73} + 2100 q^{74} - 4113 q^{75} + 144 q^{76} + 777 q^{77} + 6336 q^{78} - 1152 q^{79} - 8418 q^{80} - 1917 q^{81} - 6048 q^{82} + 1890 q^{83} + 1008 q^{84} + 648 q^{85} + 3837 q^{86} + 4212 q^{87} + 2268 q^{88} - 2604 q^{89} - 135 q^{90} + 252 q^{91} + 987 q^{92} + 378 q^{93} - 324 q^{94} + 3144 q^{95} + 5643 q^{96} + 1737 q^{97} - 588 q^{98} + 720 q^{99}+O(q^{100}) \) 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9 + 111 * q^11 - 18 * q^13 + 42 * q^14 - 36 * q^15 - 144 * q^16 - 546 * q^17 - 45 * q^18 + 90 * q^19 + 402 * q^20 - 63 * q^21 + 162 * q^22 + 312 * q^23 - 36 * q^24 - 279 * q^25 + 102 * q^26 + 432 * q^27 + 504 * q^28 + 378 * q^29 - 864 * q^30 - 18 * q^31 + 891 * q^32 + 513 * q^33 + 324 * q^34 - 336 * q^35 + 414 * q^36 - 72 * q^37 + 147 * q^38 - 810 * q^39 - 405 * q^40 + 477 * q^41 + 315 * q^42 + 171 * q^43 - 1896 * q^44 - 720 * q^45 - 756 * q^46 + 654 * q^47 - 2709 * q^48 - 441 * q^49 + 429 * q^50 + 1341 * q^51 - 747 * q^52 - 1896 * q^53 - 108 * q^54 - 432 * q^55 + 525 * q^56 - 1143 * q^57 - 297 * q^58 + 957 * q^59 + 5400 * q^60 + 198 * q^61 - 600 * q^62 - 504 * q^63 + 4770 * q^64 + 2478 * q^65 - 2646 * q^66 + 333 * q^67 + 1443 * q^68 + 3366 * q^69 - 5652 * q^71 - 3681 * q^72 + 306 * q^73 + 2100 * q^74 - 4113 * q^75 + 144 * q^76 + 777 * q^77 + 6336 * q^78 - 1152 * q^79 - 8418 * q^80 - 1917 * q^81 - 6048 * q^82 + 1890 * q^83 + 1008 * q^84 + 648 * q^85 + 3837 * q^86 + 4212 * q^87 + 2268 * q^88 - 2604 * q^89 - 135 * q^90 + 252 * q^91 + 987 * q^92 + 378 * q^93 - 324 * q^94 + 3144 * q^95 + 5643 * q^96 + 1737 * q^97 - 588 * q^98 + 720 * q^99

Introduction

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