LMFDB - Embedded newform 63.3.t.a.52.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,3,Mod(40,63)]

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, 5]))

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

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

chi := DirichletCharacter("63.40");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	63.t (of order $6$, 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:	$1.71662566547$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			52.12
Character	$\chi$	$=$	63.52
Dual form			63.3.t.a.40.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.65681 q^{2} +(-2.49911 + 1.65965i) q^{3} +3.05866 q^{4} +(7.97090 + 4.60200i) q^{5} +(-6.63967 + 4.40939i) q^{6} +(-2.88812 - 6.37642i) q^{7} -2.50096 q^{8} +(3.49110 - 8.29531i) q^{9} +O(q^{10})$	\(q+2.65681 q^{2} +(-2.49911 + 1.65965i) q^{3} +3.05866 q^{4} +(7.97090 + 4.60200i) q^{5} +(-6.63967 + 4.40939i) q^{6} +(-2.88812 - 6.37642i) q^{7} -2.50096 q^{8} +(3.49110 - 8.29531i) q^{9} +(21.1772 + 12.2267i) q^{10} +(-3.52733 - 6.10952i) q^{11} +(-7.64393 + 5.07632i) q^{12} +(-4.15930 + 2.40137i) q^{13} +(-7.67319 - 16.9410i) q^{14} +(-27.5579 + 1.72803i) q^{15} -18.8792 q^{16} +(-2.74329 - 1.58384i) q^{17} +(9.27520 - 22.0391i) q^{18} +(1.70864 - 0.986484i) q^{19} +(24.3803 + 14.0760i) q^{20} +(17.8004 + 11.1421i) q^{21} +(-9.37147 - 16.2319i) q^{22} +(2.51399 - 4.35435i) q^{23} +(6.25018 - 4.15073i) q^{24} +(29.8569 + 51.7136i) q^{25} +(-11.0505 + 6.38000i) q^{26} +(5.04271 + 26.5249i) q^{27} +(-8.83378 - 19.5033i) q^{28} +(22.9425 - 39.7376i) q^{29} +(-73.2162 + 4.59105i) q^{30} +15.2726i q^{31} -40.1548 q^{32} +(18.9549 + 9.41421i) q^{33} +(-7.28840 - 4.20796i) q^{34} +(6.32341 - 64.1170i) q^{35} +(10.6781 - 25.3726i) q^{36} +(17.6998 + 30.6570i) q^{37} +(4.53954 - 2.62090i) q^{38} +(6.40909 - 12.9043i) q^{39} +(-19.9349 - 11.5094i) q^{40} +(-48.4509 + 27.9732i) q^{41} +(47.2923 + 29.6025i) q^{42} +(-3.45068 + 5.97676i) q^{43} +(-10.7889 - 18.6870i) q^{44} +(66.0023 - 50.0551i) q^{45} +(6.67920 - 11.5687i) q^{46} +51.3447i q^{47} +(47.1813 - 31.3330i) q^{48} +(-32.3175 + 36.8317i) q^{49} +(79.3241 + 137.393i) q^{50} +(9.48440 - 0.594723i) q^{51} +(-12.7219 + 7.34498i) q^{52} +(-10.3556 + 17.9365i) q^{53} +(13.3975 + 70.4718i) q^{54} -64.9312i q^{55} +(7.22307 + 15.9472i) q^{56} +(-2.63286 + 5.30108i) q^{57} +(60.9540 - 105.575i) q^{58} -49.3508i q^{59} +(-84.2903 + 5.28546i) q^{60} -2.30422i q^{61} +40.5764i q^{62} +(-62.9771 + 1.69713i) q^{63} -31.1668 q^{64} -44.2045 q^{65} +(50.3596 + 25.0118i) q^{66} +30.8279 q^{67} +(-8.39079 - 4.84442i) q^{68} +(0.943990 + 15.0544i) q^{69} +(16.8001 - 170.347i) q^{70} +81.2604 q^{71} +(-8.73110 + 20.7463i) q^{72} +(-61.7481 - 35.6503i) q^{73} +(47.0251 + 81.4499i) q^{74} +(-160.442 - 79.6859i) q^{75} +(5.22615 - 3.01732i) q^{76} +(-28.7695 + 40.1368i) q^{77} +(17.0278 - 34.2843i) q^{78} -29.0358 q^{79} +(-150.485 - 86.8823i) q^{80} +(-56.6245 - 57.9195i) q^{81} +(-128.725 + 74.3195i) q^{82} +(-55.9283 - 32.2902i) q^{83} +(54.4453 + 34.0799i) q^{84} +(-14.5776 - 25.2492i) q^{85} +(-9.16783 + 15.8791i) q^{86} +(8.61480 + 137.385i) q^{87} +(8.82172 + 15.2797i) q^{88} +(89.0979 - 51.4407i) q^{89} +(175.356 - 132.987i) q^{90} +(27.3247 + 19.5860i) q^{91} +(7.68944 - 13.3185i) q^{92} +(-25.3472 - 38.1679i) q^{93} +136.413i q^{94} +18.1592 q^{95} +(100.351 - 66.6430i) q^{96} +(48.7891 + 28.1684i) q^{97} +(-85.8617 + 97.8551i) q^{98} +(-62.9946 + 7.93140i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 3 q^{3} + 46 q^{4} - 3 q^{5} - 12 q^{6} - 16 q^{8} - 15 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 - 3 * q^3 + 46 * q^4 - 3 * q^5 - 12 * q^6 - 16 * q^8 - 15 * q^9	\( 28 q - 2 q^{2} - 3 q^{3} + 46 q^{4} - 3 q^{5} - 12 q^{6} - 16 q^{8} - 15 q^{9} - 6 q^{10} + 7 q^{11} - 30 q^{12} - 15 q^{13} + 10 q^{14} - 18 q^{15} + 54 q^{16} - 33 q^{17} - 42 q^{18} - 6 q^{19} - 108 q^{20} + 21 q^{21} - 10 q^{22} + 34 q^{23} - 78 q^{24} + 31 q^{25} + 54 q^{26} + 81 q^{27} - 16 q^{28} + 70 q^{29} - 27 q^{30} - 306 q^{32} - 3 q^{33} - 12 q^{34} + 18 q^{35} - 174 q^{36} + 9 q^{37} + 87 q^{38} + 129 q^{39} - 102 q^{40} + 234 q^{41} + 306 q^{42} + 30 q^{43} + 51 q^{44} + 273 q^{45} - 22 q^{46} - 147 q^{48} - 38 q^{49} + 241 q^{50} + 12 q^{51} - 219 q^{52} + 148 q^{53} + 171 q^{54} + 110 q^{56} + 189 q^{57} + 17 q^{58} + 33 q^{60} - 471 q^{63} - 48 q^{64} - 228 q^{65} + 258 q^{66} + 68 q^{67} - 18 q^{68} - 78 q^{69} - 225 q^{70} - 350 q^{71} + 162 q^{72} - 6 q^{73} + 359 q^{74} - 510 q^{75} - 72 q^{76} - 224 q^{77} - 375 q^{78} + 164 q^{79} - 609 q^{80} - 435 q^{81} - 18 q^{82} - 738 q^{83} - 21 q^{84} + 3 q^{85} + 17 q^{86} - 561 q^{87} + 25 q^{88} + 21 q^{89} + 543 q^{90} + 39 q^{91} + 288 q^{92} - 222 q^{93} - 1014 q^{95} + 231 q^{96} + 57 q^{97} + 811 q^{98} - 162 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 - 3 * q^3 + 46 * q^4 - 3 * q^5 - 12 * q^6 - 16 * q^8 - 15 * q^9 - 6 * q^10 + 7 * q^11 - 30 * q^12 - 15 * q^13 + 10 * q^14 - 18 * q^15 + 54 * q^16 - 33 * q^17 - 42 * q^18 - 6 * q^19 - 108 * q^20 + 21 * q^21 - 10 * q^22 + 34 * q^23 - 78 * q^24 + 31 * q^25 + 54 * q^26 + 81 * q^27 - 16 * q^28 + 70 * q^29 - 27 * q^30 - 306 * q^32 - 3 * q^33 - 12 * q^34 + 18 * q^35 - 174 * q^36 + 9 * q^37 + 87 * q^38 + 129 * q^39 - 102 * q^40 + 234 * q^41 + 306 * q^42 + 30 * q^43 + 51 * q^44 + 273 * q^45 - 22 * q^46 - 147 * q^48 - 38 * q^49 + 241 * q^50 + 12 * q^51 - 219 * q^52 + 148 * q^53 + 171 * q^54 + 110 * q^56 + 189 * q^57 + 17 * q^58 + 33 * q^60 - 471 * q^63 - 48 * q^64 - 228 * q^65 + 258 * q^66 + 68 * q^67 - 18 * q^68 - 78 * q^69 - 225 * q^70 - 350 * q^71 + 162 * q^72 - 6 * q^73 + 359 * q^74 - 510 * q^75 - 72 * q^76 - 224 * q^77 - 375 * q^78 + 164 * q^79 - 609 * q^80 - 435 * q^81 - 18 * q^82 - 738 * q^83 - 21 * q^84 + 3 * q^85 + 17 * q^86 - 561 * q^87 + 25 * q^88 + 21 * q^89 + 543 * q^90 + 39 * q^91 + 288 * q^92 - 222 * q^93 - 1014 * q^95 + 231 * q^96 + 57 * q^97 + 811 * q^98 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.65681			1.32841			0.664204	−	0.747552i	$-0.268771\pi$
$2$	2.65681			1.32841			0.664204	+	0.747552i	$0.268771\pi$
$3$	−2.49911	+	1.65965i	−0.833037	+	0.553218i
$3$	−2.49911	+	1.65965i	−0.833037	+	0.553218i
$4$	3.05866			0.764665
$5$	7.97090	+	4.60200i	1.59418	+	0.920400i	0.992579	+	0.121604i	$0.0388039\pi$
$5$	7.97090	+	4.60200i	1.59418	+	0.920400i	0.601602	+	0.798796i	$0.294529\pi$
$6$	−6.63967	+	4.40939i	−1.10661	+	0.734899i
$7$	−2.88812	−	6.37642i	−0.412588	−	0.910918i
$7$	−2.88812	−	6.37642i	−0.412588	−	0.910918i
$8$	−2.50096			−0.312620
$9$	3.49110	−	8.29531i	0.387900	−	0.921702i
$10$	21.1772	+	12.2267i	2.11772	+	1.22267i
$11$	−3.52733	−	6.10952i	−0.320667	−	0.555411i	0.659959	−	0.751301i	$-0.270574\pi$
$11$	−3.52733	−	6.10952i	−0.320667	−	0.555411i	−0.980626	+	0.195891i	$0.937240\pi$
$12$	−7.64393	+	5.07632i	−0.636994	+	0.423027i
$13$	−4.15930	+	2.40137i	−0.319946	+	0.184721i	−0.651368	−	0.758762i	$-0.725805\pi$
$13$	−4.15930	+	2.40137i	−0.319946	+	0.184721i	0.331423	+	0.943482i	$0.392471\pi$
$14$	−7.67319	−	16.9410i	−0.548085	−	1.21007i
$15$	−27.5579	+	1.72803i	−1.83719	+	0.115202i
$16$	−18.8792			−1.17995
$17$	−2.74329	−	1.58384i	−0.161370	−	0.0931669i	0.417140	−	0.908842i	$-0.363032\pi$
$17$	−2.74329	−	1.58384i	−0.161370	−	0.0931669i	−0.578510	+	0.815675i	$0.696366\pi$
$18$	9.27520	−	22.0391i	0.515289	−	1.22439i
$19$	1.70864	−	0.986484i	0.0899284	−	0.0519202i	−0.454361	−	0.890817i	$-0.650133\pi$
$19$	1.70864	−	0.986484i	0.0899284	−	0.0519202i	0.544290	+	0.838897i	$0.316799\pi$
$20$	24.3803	+	14.0760i	1.21901	+	0.703798i
$21$	17.8004	+	11.1421i	0.847637	+	0.530576i
$22$	−9.37147	−	16.2319i	−0.425976	−	0.737812i
$23$	2.51399	−	4.35435i	0.109304	−	0.189320i	−0.806185	−	0.591664i	$-0.798471\pi$
$23$	2.51399	−	4.35435i	0.109304	−	0.189320i	0.915488	+	0.402344i	$0.131805\pi$
$24$	6.25018	−	4.15073i	0.260424	−	0.172947i
$25$	29.8569	+	51.7136i	1.19427	+	2.06854i
$26$	−11.0505	+	6.38000i	−0.425018	+	0.245384i
$27$	5.04271	+	26.5249i	0.186767	+	0.982404i
$28$	−8.83378	−	19.5033i	−0.315492	−	0.696547i
$29$	22.9425	−	39.7376i	0.791121	−	1.37026i	−0.134152	−	0.990961i	$-0.542831\pi$
$29$	22.9425	−	39.7376i	0.791121	−	1.37026i	0.925273	−	0.379301i	$-0.123836\pi$
$30$	−73.2162	+	4.59105i	−2.44054	+	0.153035i
$31$			15.2726i			0.492664i	0.969185	+	0.246332i	$0.0792254\pi$
$31$			15.2726i			0.492664i	−0.969185	+	0.246332i	$0.920775\pi$
$32$	−40.1548			−1.25484
$33$	18.9549	+	9.41421i	0.574390	+	0.285279i
$34$	−7.28840	−	4.20796i	−0.214365	−	0.123764i
$35$	6.32341	−	64.1170i	0.180669	−	1.83191i
$36$	10.6781	−	25.3726i	0.296614	−	0.704793i
$37$	17.6998	+	30.6570i	0.478373	+	0.828567i	0.999693	−	0.0247946i	$-0.00789319\pi$
$37$	17.6998	+	30.6570i	0.478373	+	0.828567i	−0.521319	+	0.853362i	$0.674560\pi$
$38$	4.53954	−	2.62090i	0.119462	−	0.0689711i
$39$	6.40909	−	12.9043i	0.164336	−	0.330879i
$40$	−19.9349	−	11.5094i	−0.498373	−	0.287736i
$41$	−48.4509	+	27.9732i	−1.18173	+	0.682272i	−0.956414	−	0.292014i	$-0.905675\pi$
$41$	−48.4509	+	27.9732i	−1.18173	+	0.682272i	−0.225316	+	0.974286i	$0.572341\pi$
$42$	47.2923	+	29.6025i	1.12601	+	0.704821i
$43$	−3.45068	+	5.97676i	−0.0802485	+	0.138994i	−0.903357	−	0.428890i	$-0.858905\pi$
$43$	−3.45068	+	5.97676i	−0.0802485	+	0.138994i	0.823108	+	0.567885i	$0.192238\pi$
$44$	−10.7889	−	18.6870i	−0.245203	−	0.424703i
$45$	66.0023	−	50.0551i	1.46672	−	1.11234i
$46$	6.67920	−	11.5687i	0.145200	−	0.251494i
$47$			51.3447i			1.09244i	0.837642	+	0.546220i	$0.183934\pi$
$47$			51.3447i			1.09244i	−0.837642	+	0.546220i	$0.816066\pi$
$48$	47.1813	−	31.3330i	0.982943	−	0.652771i
$49$	−32.3175	+	36.8317i	−0.659542	+	0.751668i
$50$	79.3241	+	137.393i	1.58648	+	2.74787i
$51$	9.48440	−	0.594723i	0.185969	−	0.0116612i
$52$	−12.7219	+	7.34498i	−0.244652	+	0.141250i
$53$	−10.3556	+	17.9365i	−0.195390	+	0.338425i	−0.947028	−	0.321151i	$-0.895930\pi$
$53$	−10.3556	+	17.9365i	−0.195390	+	0.338425i	0.751639	+	0.659575i	$0.229264\pi$
$54$	13.3975	+	70.4718i	0.248103	+	1.30503i
$55$		−	64.9312i		−	1.18057i
$56$	7.22307	+	15.9472i	0.128983	+	0.284771i
$57$	−2.63286	+	5.30108i	−0.0461905	+	0.0930014i
$58$	60.9540	−	105.575i	1.05093	−	1.82027i
$59$		−	49.3508i		−	0.836454i	−0.908342	−	0.418227i	$-0.862652\pi$
$59$		−	49.3508i		−	0.836454i	0.908342	−	0.418227i	$-0.137348\pi$
$60$	−84.2903	+	5.28546i	−1.40484	+	0.0880909i
$61$		−	2.30422i		−	0.0377741i	−0.999822	−	0.0188871i	$-0.993988\pi$
$61$		−	2.30422i		−	0.0377741i	0.999822	−	0.0188871i	$-0.00601229\pi$
$62$			40.5764i			0.654459i
$63$	−62.9771	+	1.69713i	−0.999637	+	0.0269386i
$64$	−31.1668			−0.486982
$65$	−44.2045			−0.680069
$66$	50.3596	+	25.0118i	0.763024	+	0.378967i
$67$	30.8279			0.460117			0.230059	−	0.973177i	$-0.426108\pi$
$67$	30.8279			0.460117			0.230059	+	0.973177i	$0.426108\pi$
$68$	−8.39079	−	4.84442i	−0.123394	−	0.0712415i
$69$	0.943990	+	15.0544i	0.0136810	+	0.218179i
$70$	16.8001	−	170.347i	0.240002	−	2.43353i
$71$	81.2604			1.14451			0.572256	−	0.820075i	$-0.306068\pi$
$71$	81.2604			1.14451			0.572256	+	0.820075i	$0.306068\pi$
$72$	−8.73110	+	20.7463i	−0.121265	+	0.288142i
$73$	−61.7481	−	35.6503i	−0.845864	−	0.488360i	0.0133893	−	0.999910i	$-0.495738\pi$
$73$	−61.7481	−	35.6503i	−0.845864	−	0.488360i	−0.859253	+	0.511551i	$0.829071\pi$
$74$	47.0251	+	81.4499i	0.635475	+	1.10067i
$75$	−160.442	−	79.6859i	−2.13923	−	1.06248i
$76$	5.22615	−	3.01732i	0.0687651	−	0.0397016i
$77$	−28.7695	+	40.1368i	−0.373630	+	0.521257i
$78$	17.0278	−	34.2843i	0.218305	−	0.439542i
$79$	−29.0358			−0.367542			−0.183771	−	0.982969i	$-0.558831\pi$
$79$	−29.0358			−0.367542			−0.183771	+	0.982969i	$0.558831\pi$
$80$	−150.485	−	86.8823i	−1.88106	−	1.08603i
$81$	−56.6245	−	57.9195i	−0.699067	−	0.715056i
$82$	−128.725	+	74.3195i	−1.56982	+	0.906335i
$83$	−55.9283	−	32.2902i	−0.673835	−	0.389039i	0.123693	−	0.992321i	$-0.460526\pi$
$83$	−55.9283	−	32.2902i	−0.673835	−	0.389039i	−0.797528	+	0.603282i	$0.793860\pi$
$84$	54.4453	+	34.0799i	0.648159	+	0.405713i
$85$	−14.5776	−	25.2492i	−0.171502	−	0.297050i
$86$	−9.16783	+	15.8791i	−0.106603	+	0.184641i
$87$	8.61480	+	137.385i	0.0990207	+	1.57914i
$88$	8.82172	+	15.2797i	0.100247	+	0.173633i
$89$	89.0979	−	51.4407i	1.00110	−	0.577985i	0.0925265	−	0.995710i	$-0.470506\pi$
$89$	89.0979	−	51.4407i	1.00110	−	0.577985i	0.908574	+	0.417725i	$0.137172\pi$
$90$	175.356	−	132.987i	1.94840	−	1.47763i
$91$	27.3247	+	19.5860i	0.300271	+	0.215231i
$92$	7.68944	−	13.3185i	0.0835808	−	0.144766i
$93$	−25.3472	−	38.1679i	−0.272551	−	0.410407i
$94$			136.413i			1.45121i
$95$	18.1592			0.191149
$96$	100.351	−	66.6430i	1.04532	−	0.694198i
$97$	48.7891	+	28.1684i	0.502981	+	0.290396i	0.729944	−	0.683507i	$-0.239546\pi$
$97$	48.7891	+	28.1684i	0.502981	+	0.290396i	−0.226963	+	0.973903i	$0.572880\pi$
$98$	−85.8617	+	97.8551i	−0.876140	+	0.998521i
$99$	−62.9946	+	7.93140i	−0.636310	+	0.0801151i
$100$	91.3220	+	158.174i	0.913220	+	1.58174i
$101$	96.9924	−	55.9986i	0.960321	−	0.554442i	0.0640493	−	0.997947i	$-0.479599\pi$
$101$	96.9924	−	55.9986i	0.960321	−	0.554442i	0.896272	+	0.443505i	$0.146265\pi$
$102$	25.1983	−	1.58007i	0.247042	−	0.0154909i
$103$	74.9527	+	43.2740i	0.727696	+	0.420136i	0.817579	−	0.575817i	$-0.195316\pi$
$103$	74.9527	+	43.2740i	0.727696	+	0.420136i	−0.0898825	+	0.995952i	$0.528649\pi$
$104$	10.4022	−	6.00573i	0.100022	−	0.0577474i
$105$	90.6091	+	170.730i	0.862944	+	1.62600i
$106$	−27.5130	+	47.6540i	−0.259557	+	0.449566i
$107$	−25.4526	−	44.0852i	−0.237875	−	0.412012i	0.722229	−	0.691654i	$-0.243118\pi$
$107$	−25.4526	−	44.0852i	−0.237875	−	0.412012i	−0.960104	+	0.279642i	$0.909784\pi$
$108$	15.4239	+	81.1307i	0.142814	+	0.751211i
$109$	21.9214	−	37.9690i	0.201114	−	0.348340i	−0.747774	−	0.663954i	$-0.768877\pi$
$109$	21.9214	−	37.9690i	0.201114	−	0.348340i	0.948888	+	0.315614i	$0.102211\pi$
$110$		−	172.510i		−	1.56827i
$111$	−95.1138	−	47.2396i	−0.856881	−	0.425582i
$112$	54.5255	+	120.382i	0.486835	+	1.07484i
$113$	−53.2988	−	92.3163i	−0.471671	−	0.816959i	0.527803	−	0.849367i	$-0.323016\pi$
$113$	−53.2988	−	92.3163i	−0.471671	−	0.816959i	−0.999475	+	0.0324080i	$0.989682\pi$
$114$	−6.99501	+	14.0840i	−0.0613597	+	0.123544i
$115$	40.0775	−	23.1387i	0.348500	−	0.201207i
$116$	70.1734	−	121.544i	0.604943	−	1.04779i
$117$	5.39961	+	42.8861i	0.0461505	+	0.366548i
$118$		−	131.116i		−	1.11115i
$119$	−2.17628	+	22.0667i	−0.0182881	+	0.185434i
$120$	68.9212	−	4.32173i	0.574343	−	0.0360144i
$121$	35.6159	−	61.6885i	0.294346	−	0.509822i
$122$		−	6.12189i		−	0.0501794i
$123$	74.6584	−	150.320i	0.606979	−	1.22211i
$124$			46.7137i			0.376723i
$125$			319.505i			2.55604i
$126$	−167.319	+	4.50896i	−1.32793	+	0.0357854i
$127$	−184.052			−1.44923			−0.724614	−	0.689155i	$-0.757982\pi$
$127$	−184.052			−1.44923			−0.724614	+	0.689155i	$0.757982\pi$
$128$	77.8146			0.607927
$129$	−1.29571	−	20.6635i	−0.0100443	−	0.160182i
$130$	−117.443			−0.903408
$131$	−6.29953	−	3.63703i	−0.0480880	−	0.0277636i	0.475763	−	0.879573i	$-0.342172\pi$
$131$	−6.29953	−	3.63703i	−0.0480880	−	0.0277636i	−0.523851	+	0.851810i	$0.675505\pi$
$132$	57.9766	+	28.7949i	0.439216	+	0.218143i
$133$	−11.2250	−	8.04593i	−0.0843984	−	0.0604957i
$134$	81.9039			0.611223
$135$	−81.8728	+	234.634i	−0.606465	+	1.73803i
$136$	6.86085	+	3.96111i	0.0504474	+	0.0291258i
$137$	23.6360	+	40.9388i	0.172526	+	0.298823i	0.939302	−	0.343091i	$-0.111474\pi$
$137$	23.6360	+	40.9388i	0.172526	+	0.298823i	−0.766777	+	0.641914i	$0.778141\pi$
$138$	2.50801	+	39.9966i	0.0181740	+	0.289831i
$139$	−219.353	+	126.643i	−1.57808	+	0.911103i	−0.582948	+	0.812509i	$0.698101\pi$
$139$	−219.353	+	126.643i	−1.57808	+	0.911103i	−0.995128	+	0.0985934i	$0.968566\pi$
$140$	19.3412	−	196.112i	0.138151	−	1.40080i
$141$	−85.2144	−	128.316i	−0.604358	−	0.910043i
$142$	215.894			1.52038
$143$	29.3424	+	16.9409i	0.205192	+	0.118468i
$144$	−65.9093	+	156.609i	−0.457703	+	1.08756i
$145$	365.745	−	211.163i	2.52238	−	1.45630i
$146$	−164.053	−	94.7161i	−1.12365	−	0.648741i
$147$	19.6372	−	145.682i	0.133586	−	0.991037i
$148$	54.1378	+	93.7693i	0.365796	+	0.633577i
$149$	128.422	−	222.433i	0.861892	−	1.49284i	−0.00820848	−	0.999966i	$-0.502613\pi$
$149$	128.422	−	222.433i	0.861892	−	1.49284i	0.870100	−	0.492874i	$-0.164054\pi$
$150$	−426.265	−	211.711i	−2.84177	−	1.41140i
$151$	59.1932	+	102.526i	0.392008	+	0.678978i	0.992714	−	0.120492i	$-0.0384471\pi$
$151$	59.1932	+	102.526i	0.392008	+	0.678978i	−0.600706	+	0.799470i	$0.705114\pi$
$152$	−4.27324	+	2.46716i	−0.0281134	+	0.0162313i
$153$	−22.7155	+	17.2271i	−0.148467	+	0.112595i
$154$	−76.4353	+	106.636i	−0.496333	+	0.692441i
$155$	−70.2845	+	121.736i	−0.453448	+	0.785396i
$156$	19.6032	−	39.4698i	0.125662	−	0.253012i
$157$		−	51.0244i		−	0.324996i	−0.986709	−	0.162498i	$-0.948045\pi$
$157$		−	51.0244i		−	0.324996i	0.986709	−	0.162498i	$-0.0519551\pi$
$158$	−77.1428			−0.488246
$159$	−3.88849	−	62.0121i	−0.0244559	−	0.390013i
$160$	−320.070	−	184.792i	−2.00044	−	1.15495i
$161$	−35.0259	−	3.45436i	−0.217552	−	0.0214556i
$162$	−150.441	−	153.881i	−0.928646	−	0.949885i
$163$	143.157	+	247.955i	0.878263	+	1.52120i	0.853246	+	0.521508i	$0.174630\pi$
$163$	143.157	+	247.955i	0.878263	+	1.52120i	0.0250163	+	0.999687i	$0.492036\pi$
$164$	−148.195	+	85.5604i	−0.903628	+	0.521710i
$165$	107.763	+	162.270i	0.653111	+	0.983455i
$166$	−148.591	−	85.7892i	−0.895128	−	0.516802i
$167$	162.132	−	93.6068i	0.970848	−	0.560519i	0.0713535	−	0.997451i	$-0.477268\pi$
$167$	162.132	−	93.6068i	0.970848	−	0.560519i	0.899495	+	0.436932i	$0.143935\pi$
$168$	−44.5181	−	27.8660i	−0.264988	−	0.165869i
$169$	−72.9668	+	126.382i	−0.431756	+	0.747824i
$170$	−38.7301	−	67.0825i	−0.227824	−	0.394603i
$171$	−2.21816	−	17.6176i	−0.0129717	−	0.103027i
$172$	−10.5545	+	18.2809i	−0.0613632	+	0.106284i
$173$			148.886i			0.860613i	0.902683	+	0.430306i	$0.141594\pi$
$173$			148.886i			0.860613i	−0.902683	+	0.430306i	$0.858406\pi$
$174$	22.8879	+	365.007i	0.131540	+	2.09774i
$175$	243.518	−	339.735i	1.39153	−	1.94134i
$176$	66.5933	+	115.343i	0.378371	+	0.655358i
$177$	81.9053	+	123.333i	0.462742	+	0.696797i
$178$	236.717	−	136.668i	1.32987	−	0.767800i
$179$	98.1713	−	170.038i	0.548443	−	0.949931i	−0.449938	−	0.893060i	$-0.648554\pi$
$179$	98.1713	−	170.038i	0.548443	−	0.949931i	0.998381	−	0.0568718i	$-0.0181126\pi$
$180$	201.879	−	153.102i	1.12155	−	0.850564i
$181$		−	80.6783i		−	0.445736i	−0.974849	−	0.222868i	$-0.928458\pi$
$181$		−	80.6783i		−	0.445736i	0.974849	−	0.222868i	$-0.0715419\pi$
$182$	72.5966	+	52.0363i	0.398883	+	0.285914i
$183$	3.82421	+	5.75850i	0.0208973	+	0.0314672i
$184$	−6.28738	+	10.8901i	−0.0341706	+	0.0591852i
$185$			325.818i			1.76118i
$186$	−67.3429	−	101.405i	−0.362058	−	0.545188i
$187$			22.3469i			0.119502i
$188$			157.046i			0.835351i
$189$	154.570	−	108.762i	0.817831	−	0.575458i
$190$	48.2456			0.253924
$191$	27.5621			0.144304			0.0721521	−	0.997394i	$-0.477013\pi$
$191$	27.5621			0.144304			0.0721521	+	0.997394i	$0.477013\pi$
$192$	77.8893	−	51.7262i	0.405674	−	0.269407i
$193$	−124.534			−0.645251			−0.322626	−	0.946527i	$-0.604565\pi$
$193$	−124.534			−0.645251			−0.322626	+	0.946527i	$0.604565\pi$
$194$	129.624	+	74.8382i	0.668163	+	0.385764i
$195$	110.472	−	73.3641i	0.566522	−	0.376226i
$196$	−98.8484	+	112.656i	−0.504329	+	0.574775i
$197$	−115.102			−0.584274			−0.292137	−	0.956376i	$-0.594366\pi$
$197$	−115.102			−0.584274			−0.292137	+	0.956376i	$0.594366\pi$
$198$	−167.365	+	21.0723i	−0.845278	+	0.106426i
$199$	−104.660	−	60.4253i	−0.525928	−	0.303645i	0.213429	−	0.976959i	$-0.431537\pi$
$199$	−104.660	−	60.4253i	−0.525928	−	0.303645i	−0.739357	+	0.673314i	$0.764870\pi$
$200$	−74.6708	−	129.334i	−0.373354	−	0.646668i
$201$	−77.0422	+	51.1636i	−0.383295	+	0.254545i
$202$	257.691	−	148.778i	1.27570	−	0.736524i
$203$	−319.644	−	31.5243i	−1.57460	−	0.155292i
$204$	29.0096	−	1.81906i	0.142204	−	0.00891694i
$205$	−514.930			−2.51185
$206$	199.135	+	114.971i	0.966677	+	0.558111i
$207$	−27.3442	−	36.0558i	−0.132097	−	0.174183i
$208$	78.5243	−	45.3360i	0.377521	−	0.217962i
$209$	−12.0539	−	6.95931i	−0.0576741	−	0.0332981i
$210$	240.732	+	453.598i	1.14634	+	2.15999i
$211$	60.1908	+	104.254i	0.285264	+	0.494092i	0.972673	−	0.232178i	$-0.0745853\pi$
$211$	60.1908	+	104.254i	0.285264	+	0.494092i	−0.687409	+	0.726271i	$0.741252\pi$
$212$	−31.6744	+	54.8617i	−0.149408	+	0.258782i
$213$	−203.079	+	134.864i	−0.953421	+	0.633165i
$214$	−67.6229	−	117.126i	−0.315995	−	0.547319i
$215$	−55.0101	+	31.7601i	−0.255861	+	0.147721i
$216$	−12.6116	−	66.3378i	−0.0583872	−	0.307119i
$217$	97.3845	−	44.1091i	0.448777	−	0.203268i
$218$	58.2411	−	100.877i	0.267161	−	0.462737i
$219$	213.482	−	13.3865i	0.974805	−	0.0611256i
$220$		−	198.602i		−	0.902739i
$221$	15.2135			0.0688395
$222$	−252.700	−	125.507i	−1.13829	−	0.565346i
$223$	203.615	+	117.557i	0.913072	+	0.527162i	0.881418	−	0.472336i	$-0.156589\pi$
$223$	203.615	+	117.557i	0.913072	+	0.527162i	0.0316538	+	0.999499i	$0.489923\pi$
$224$	115.972	+	256.044i	0.517731	+	1.14305i
$225$	533.214	−	67.1348i	2.36984	−	0.298377i
$226$	−141.605	−	245.267i	−0.626571	−	1.08525i
$227$	−130.976	+	75.6193i	−0.576989	+	0.333125i	−0.759936	−	0.649998i	$-0.774770\pi$
$227$	−130.976	+	75.6193i	−0.576989	+	0.333125i	0.182947	+	0.983123i	$0.441436\pi$
$228$	−8.05302	+	16.2142i	−0.0353203	+	0.0711150i
$229$	−358.522	−	206.993i	−1.56560	−	0.903899i	−0.996672	−	0.0815115i	$-0.974025\pi$
$229$	−358.522	−	206.993i	−1.56560	−	0.903899i	−0.568927	−	0.822388i	$-0.692641\pi$
$230$	106.478	−	61.4754i	0.462950	−	0.267284i
$231$	5.28504	−	148.054i	0.0228790	−	0.640925i
$232$	−57.3783	+	99.3822i	−0.247320	+	0.428372i
$233$	166.801	+	288.909i	0.715886	+	1.23995i	0.962617	+	0.270867i	$0.0873103\pi$
$233$	166.801	+	288.909i	0.715886	+	1.23995i	−0.246731	+	0.969084i	$0.579356\pi$
$234$	14.3458	+	113.940i	0.0613067	+	0.486925i
$235$	−236.288	+	409.264i	−1.00548	+	1.74155i
$236$		−	150.947i		−	0.639608i
$237$	72.5637	−	48.1894i	0.306176	−	0.203331i
$238$	−5.78197	+	58.6270i	−0.0242940	+	0.246332i
$239$	−104.819	−	181.552i	−0.438573	−	0.759631i	0.559007	−	0.829163i	$-0.311183\pi$
$239$	−104.819	−	181.552i	−0.438573	−	0.759631i	−0.997580	+	0.0695323i	$0.977849\pi$
$240$	520.272	−	32.6239i	2.16780	−	0.135933i
$241$	197.233	−	113.873i	0.818394	−	0.472500i	−0.0314682	−	0.999505i	$-0.510018\pi$
$241$	197.233	−	113.873i	0.818394	−	0.472500i	0.849862	+	0.527005i	$0.176685\pi$
$242$	94.6247	−	163.895i	0.391011	−	0.677251i
$243$	237.637	+	50.7702i	0.977930	+	0.208931i
$244$		−	7.04783i		−	0.0288846i
$245$	−427.100	+	144.857i	−1.74326	+	0.591252i
$246$	198.354	−	399.372i	0.806315	−	1.62346i
$247$	−4.73783	+	8.20615i	−0.0191815	+	0.0332233i
$248$		−	38.1962i		−	0.154017i
$249$	193.362	−	12.1248i	0.776553	−	0.0486941i
$250$			848.866i			3.39546i
$251$		−	422.578i		−	1.68358i	−0.539808	−	0.841788i	$-0.681503\pi$
$251$		−	422.578i		−	1.68358i	0.539808	−	0.841788i	$-0.318497\pi$
$252$	−192.626	+	5.19094i	−0.764388	+	0.0205990i
$253$	−35.4707			−0.140200
$254$	−488.992			−1.92516
$255$	78.3361	+	38.9067i	0.307200	+	0.152575i
$256$	331.406			1.29456
$257$	75.4797	+	43.5782i	0.293695	+	0.169565i	0.639607	−	0.768702i	$-0.279097\pi$
$257$	75.4797	+	43.5782i	0.293695	+	0.169565i	−0.345912	+	0.938267i	$0.612430\pi$
$258$	−3.44247	−	54.8991i	−0.0133429	−	0.212787i
$259$	144.363	−	201.403i	0.557385	−	0.777616i
$260$	−135.206			−0.520025
$261$	−249.541	−	329.043i	−0.956097	−	1.26070i
$262$	−16.7367	−	9.66292i	−0.0638804	−	0.0368814i
$263$	22.0938	+	38.2676i	0.0840069	+	0.145504i	0.904968	−	0.425481i	$-0.139895\pi$
$263$	22.0938	+	38.2676i	0.0840069	+	0.145504i	−0.820961	+	0.570985i	$0.806562\pi$
$264$	−47.4054	−	23.5446i	−0.179566	−	0.0891840i
$265$	−165.088	+	95.3134i	−0.622972	+	0.359673i
$266$	−29.8227	−	21.3765i	−0.112115	−	0.0803629i
$267$	−137.292	+	276.428i	−0.514201	+	1.03531i
$268$	94.2920			0.351836
$269$	−169.996	−	98.1474i	−0.631957	−	0.364860i	0.149553	−	0.988754i	$-0.452217\pi$
$269$	−169.996	−	98.1474i	−0.631957	−	0.364860i	−0.781509	+	0.623893i	$0.785550\pi$
$270$	−217.521	+	623.379i	−0.805632	+	2.30881i
$271$	−146.761	+	84.7324i	−0.541553	+	0.312666i	−0.745708	−	0.666273i	$-0.767889\pi$
$271$	−146.761	+	84.7324i	−0.541553	+	0.312666i	0.204155	+	0.978938i	$0.434555\pi$
$272$	51.7912	+	29.9016i	0.190409	+	0.109932i
$273$	−100.793	−	3.59800i	−0.369206	−	0.0131795i
$274$	62.7965	+	108.767i	0.229184	+	0.396959i
$275$	210.630	−	364.822i	0.765928	−	1.32663i
$276$	2.88735	+	46.0462i	0.0104614	+	0.166834i
$277$	−185.050	−	320.517i	−0.668052	−	1.15710i	−0.978448	−	0.206493i	$-0.933795\pi$
$277$	−185.050	−	320.517i	−0.668052	−	1.15710i	0.310396	−	0.950607i	$-0.399538\pi$
$278$	−582.779	+	336.468i	−2.09633	+	1.21032i
$279$	126.691	+	53.3181i	0.454089	+	0.191104i
$280$	−15.8146	+	160.354i	−0.0564807	+	0.572693i
$281$	61.5023	−	106.525i	0.218869	−	0.379093i	−0.735593	−	0.677424i	$-0.763096\pi$
$281$	61.5023	−	106.525i	0.218869	−	0.379093i	0.954463	+	0.298331i	$0.0964298\pi$
$282$	−226.399	−	340.912i	−0.802833	−	1.20891i
$283$			150.448i			0.531617i	0.964026	+	0.265809i	$0.0856389\pi$
$283$			150.448i			0.531617i	−0.964026	+	0.265809i	$0.914361\pi$
$284$	248.548			0.875169
$285$	−45.3818	+	30.1380i	−0.159234	+	0.105747i
$286$	77.9574	+	45.0087i	0.272578	+	0.157373i
$287$	318.301	+	228.154i	1.10906	+	0.794961i
$288$	−140.184	+	333.096i	−0.486751	+	1.15658i
$289$	−139.483	−	241.592i	−0.482640	−	0.835957i
$290$	971.717	−	561.021i	3.35075	−	1.93456i
$291$	−168.679	+	10.5771i	−0.579653	+	0.0363474i
$292$	−188.866	−	109.042i	−0.646803	−	0.373432i
$293$	−373.737	+	215.777i	−1.27555	+	0.736440i	−0.976027	−	0.217648i	$-0.930162\pi$
$293$	−373.737	+	215.777i	−1.27555	+	0.736440i	−0.299525	+	0.954088i	$0.596828\pi$
$294$	52.1723	−	387.051i	0.177457	−	1.31650i
$295$	227.113	−	393.370i	0.769873	−	1.33346i
$296$	−44.2666	−	76.6719i	−0.149549	−	0.259027i
$297$	144.267	−	124.371i	0.485748	−	0.418757i
$298$	341.193	−	590.964i	1.14494	−	1.98310i
$299$			24.1481i			0.0807627i
$300$	−490.738	−	243.732i	−1.63579	−	0.812441i
$301$	48.0763	+	4.74143i	0.159722	+	0.0157523i
$302$	157.265	+	272.392i	0.520746	+	0.901959i
$303$	−149.456	+	300.921i	−0.493256	+	0.993137i
$304$	−32.2578	+	18.6241i	−0.106111	+	0.0612633i
$305$	10.6040	−	18.3667i	0.0347673	−	0.0602187i
$306$	−60.3509	+	45.7692i	−0.197225	+	0.149572i
$307$			157.167i			0.511946i	0.966684	+	0.255973i	$0.0823958\pi$
$307$			157.167i			0.511946i	−0.966684	+	0.255973i	$0.917604\pi$
$308$	−87.9962	+	122.765i	−0.285702	+	0.398587i
$309$	−259.135	+	16.2492i	−0.838624	+	0.0525863i
$310$	−186.733	+	323.431i	−0.602364	+	1.04333i
$311$			331.813i			1.06692i	0.845825	+	0.533461i	$0.179109\pi$
$311$			331.813i			1.06692i	−0.845825	+	0.533461i	$0.820891\pi$
$312$	−16.0289	+	32.2731i	−0.0513747	+	0.103439i
$313$		−	408.491i		−	1.30508i	−0.757753	−	0.652541i	$-0.773703\pi$
$313$		−	408.491i		−	1.30508i	0.757753	−	0.652541i	$-0.226297\pi$
$314$		−	135.562i		−	0.431727i
$315$	−509.795	−	276.293i	−1.61840	−	0.877122i
$316$	−88.8108			−0.281047
$317$	38.7454			0.122225			0.0611126	−	0.998131i	$-0.480535\pi$
$317$	38.7454			0.122225			0.0611126	+	0.998131i	$0.480535\pi$
$318$	−10.3310	−	164.755i	−0.0324874	−	0.518096i
$319$	−323.704			−1.01474
$320$	−248.428	−	143.430i	−0.776337	−	0.448218i
$321$	136.775	+	67.9313i	0.426091	+	0.211624i
$322$	−93.0573	−	9.17758i	−0.288998	−	0.0285018i
$323$	−6.24972			−0.0193490
$324$	−173.195	−	177.156i	−0.534553	−	0.546778i
$325$	−248.367	−	143.395i	−0.764206	−	0.441215i
$326$	380.341	+	658.770i	1.16669	+	2.02077i
$327$	8.23139	+	131.271i	0.0251724	+	0.401439i
$328$	121.174	−	69.9598i	0.369433	−	0.213292i
$329$	327.395	−	148.290i	0.995123	−	0.450728i
$330$	286.307	+	431.122i	0.867597	+	1.30643i
$331$	285.046			0.861167			0.430583	−	0.902551i	$-0.358308\pi$
$331$	285.046			0.861167			0.430583	+	0.902551i	$0.358308\pi$
$332$	−171.066	−	98.7649i	−0.515259	−	0.297485i
$333$	316.101	−	39.7990i	0.949253	−	0.119517i
$334$	430.754	−	248.696i	1.28968	−	0.744598i
$335$	245.726	+	141.870i	0.733510	+	0.423492i
$336$	−336.058	−	210.354i	−1.00017	−	0.626055i
$337$	298.113	+	516.347i	0.884608	+	1.53219i	0.846163	+	0.532925i	$0.178907\pi$
$337$	298.113	+	516.347i	0.884608	+	1.53219i	0.0384451	+	0.999261i	$0.487760\pi$
$338$	−193.859	+	335.774i	−0.573548	+	0.993415i
$339$	286.413	+	142.251i	0.844875	+	0.419619i
$340$	−44.5881	−	77.2288i	−0.131141	−	0.227144i
$341$	93.3082	−	53.8715i	0.273631	−	0.157981i
$342$	−5.89324	−	46.8067i	−0.0172317	−	0.136862i
$343$	328.192	+	99.6959i	0.956827	+	0.290659i
$344$	8.63003	−	14.9476i	0.0250873	−	0.0434525i
$345$	−61.7557	+	124.341i	−0.179002	+	0.360409i
$346$			395.562i			1.14324i
$347$	−290.571			−0.837379			−0.418690	−	0.908129i	$-0.637510\pi$
$347$	−290.571			−0.837379			−0.418690	+	0.908129i	$0.637510\pi$
$348$	26.3498	+	420.215i	0.0757177	+	1.20751i
$349$	283.473	+	163.663i	0.812243	+	0.468949i	0.847734	−	0.530421i	$-0.177966\pi$
$349$	283.473	+	163.663i	0.812243	+	0.468949i	−0.0354909	+	0.999370i	$0.511299\pi$
$350$	646.981	−	902.612i	1.84852	−	2.57889i
$351$	−84.6703	−	98.2155i	−0.241226	−	0.279816i
$352$	141.639	+	245.326i	0.402384	+	0.696950i
$353$	−72.8629	+	42.0674i	−0.206411	+	0.119171i	−0.599642	−	0.800268i	$-0.704690\pi$
$353$	−72.8629	+	42.0674i	−0.206411	+	0.119171i	0.393232	+	0.919439i	$0.371357\pi$
$354$	217.607	+	327.673i	0.614709	+	0.925630i
$355$	647.719	+	373.961i	1.82456	+	1.05341i
$356$	272.520	−	157.340i	0.765507	−	0.441965i
$357$	−31.1843	−	58.7589i	−0.0873509	−	0.164591i
$358$	260.823	−	451.759i	0.728556	−	1.26190i
$359$	−106.191	−	183.928i	−0.295796	−	0.512334i	0.679374	−	0.733792i	$-0.262252\pi$
$359$	−106.191	−	183.928i	−0.295796	−	0.512334i	−0.975170	+	0.221459i	$0.928918\pi$
$360$	−165.069	+	125.186i	−0.458525	+	0.347738i
$361$	−178.554	+	309.264i	−0.494609	+	0.856687i
$362$		−	214.347i		−	0.592119i
$363$	13.3736	+	213.276i	0.0368418	+	0.587538i
$364$	83.5770	+	59.9069i	0.229607	+	0.164579i
$365$	−328.125	−	568.329i	−0.898973	−	1.55707i
$366$	10.1602	+	15.2993i	0.0277601	+	0.0418013i
$367$	−363.389	+	209.803i	−0.990162	+	0.571670i	−0.905323	−	0.424724i	$-0.860371\pi$
$367$	−363.389	+	209.803i	−0.990162	+	0.571670i	−0.0848392	+	0.996395i	$0.527038\pi$
$368$	−47.4622	+	82.2069i	−0.128973	+	0.223388i
$369$	62.8992	+	499.573i	0.170458	+	1.35386i
$370$			865.639i			2.33957i
$371$	144.279	+	14.2292i	0.388892	+	0.0383537i
$372$	−77.5286	−	116.743i	−0.208410	−	0.313824i
$373$	110.530	−	191.443i	0.296326	−	0.513252i	−0.678966	−	0.734169i	$-0.737572\pi$
$373$	110.530	−	191.443i	0.296326	−	0.513252i	0.975292	+	0.220918i	$0.0709052\pi$
$374$			59.3715i			0.158747i
$375$	−530.268	−	798.478i	−1.41405	−	2.12928i
$376$		−	128.411i		−	0.341519i
$377$			220.374i			0.584546i
$378$	410.664	−	288.959i	1.08641	−	0.764442i
$379$	317.062			0.836575			0.418287	−	0.908315i	$-0.362631\pi$
$379$	317.062			0.836575			0.418287	+	0.908315i	$0.362631\pi$
$380$	55.5428			0.146165
$381$	459.966	−	305.462i	1.20726	−	0.801739i
$382$	73.2274			0.191695
$383$	240.396	+	138.793i	0.627666	+	0.362383i	0.779847	−	0.625970i	$-0.215297\pi$
$383$	240.396	+	138.793i	0.627666	+	0.362383i	−0.152182	+	0.988353i	$0.548630\pi$
$384$	−194.467	+	129.145i	−0.506425	+	0.336316i
$385$	−414.029	+	187.529i	−1.07540	+	0.487088i
$386$	−330.862			−0.857156
$387$	37.5324	+	49.4900i	0.0969830	+	0.127881i
$388$	149.229	+	86.1576i	0.384612	+	0.222056i
$389$	36.2173	+	62.7303i	0.0931037	+	0.161260i	0.908816	−	0.417198i	$-0.136988\pi$
$389$	36.2173	+	62.7303i	0.0931037	+	0.161260i	−0.815712	+	0.578458i	$0.803655\pi$
$390$	293.503	−	194.915i	0.752572	−	0.499781i
$391$	−13.7932	+	7.96349i	−0.0352767	+	0.0203670i
$392$	80.8249	−	92.1147i	0.206186	−	0.234987i
$393$	21.7794	−	1.36569i	0.0554184	−	0.00347503i
$394$	−305.805			−0.776154
$395$	−231.442	−	133.623i	−0.585929	−	0.338286i
$396$	−192.679	+	24.2595i	−0.486564	+	0.0612613i
$397$	−590.904	+	341.158i	−1.48842	+	0.859341i	−0.999913	−	0.0132172i	$-0.995793\pi$
$397$	−590.904	+	341.158i	−1.48842	+	0.859341i	−0.488510	+	0.872558i	$0.662459\pi$
$398$	−278.061	−	160.539i	−0.698647	−	0.403364i
$399$	41.4059	+	1.47806i	0.103774	+	0.00370441i
$400$	−563.675	−	976.313i	−1.40919	−	2.44078i
$401$	−224.827	+	389.411i	−0.560665	+	0.971100i	0.436774	+	0.899571i	$0.356121\pi$
$401$	−224.827	+	389.411i	−0.560665	+	0.971100i	−0.997439	+	0.0715286i	$0.977212\pi$
$402$	−204.687	+	135.932i	−0.509171	+	0.338140i
$403$	−36.6752	−	63.5232i	−0.0910054	−	0.157626i
$404$	296.667	−	171.281i	0.734324	−	0.423962i
$405$	−184.802	−	722.257i	−0.456302	−	1.78335i
$406$	−849.236	−	83.7542i	−2.09171	−	0.206291i
$407$	124.866	−	216.275i	0.306797	−	0.531388i
$408$	−23.7201	+	1.48738i	−0.0581375	+	0.00364554i
$409$		−	148.908i		−	0.364079i	−0.983291	−	0.182040i	$-0.941730\pi$
$409$		−	148.908i		−	0.364079i	0.983291	−	0.182040i	$-0.0582699\pi$
$410$	−1368.07			−3.33676
$411$	−127.013	−	63.0829i	−0.309035	−	0.153486i
$412$	229.255	+	132.360i	0.556444	+	0.321263i
$413$	−314.682	+	142.531i	−0.761941	+	0.345111i
$414$	−72.6483	−	95.7935i	−0.175479	−	0.231385i
$415$	−297.199	−	514.765i	−0.716143	−	1.24040i
$416$	167.016	−	96.4265i	0.401480	−	0.231794i
$417$	338.002	−	680.545i	0.810557	−	1.63200i
$418$	−32.0249	−	18.4896i	−0.0766146	−	0.0442335i
$419$	399.171	−	230.461i	0.952675	−	0.550027i	0.0587641	−	0.998272i	$-0.481284\pi$
$419$	399.171	−	230.461i	0.952675	−	0.550027i	0.893911	+	0.448245i	$0.147951\pi$
$420$	277.143	+	522.205i	0.659863	+	1.24335i
$421$	−63.9001	+	110.678i	−0.151782	+	0.262894i	−0.931883	−	0.362760i	$-0.881834\pi$
$421$	−63.9001	+	110.678i	−0.151782	+	0.262894i	0.780101	+	0.625654i	$0.215168\pi$
$422$	159.916	+	276.982i	0.378947	+	0.656356i
$423$	425.920	+	179.249i	1.00690	+	0.423757i
$424$	25.8991	−	44.8585i	0.0610827	−	0.105798i
$425$		−	189.154i		−	0.445067i
$426$	−539.542	+	358.309i	−1.26653	+	0.841101i
$427$	−14.6927	+	6.65486i	−0.0344091	+	0.0155852i
$428$	−77.8510	−	134.842i	−0.181895	−	0.315051i
$429$	−101.446	+	6.36121i	−0.236471	+	0.0148280i
$430$	−146.152	+	84.3807i	−0.339888	+	0.196234i
$431$	−104.431	+	180.879i	−0.242298	+	0.419673i	−0.961369	−	0.275264i	$-0.911235\pi$
$431$	−104.431	+	180.879i	−0.242298	+	0.419673i	0.719070	+	0.694937i	$0.244568\pi$
$432$	−95.2025	−	500.770i	−0.220376	−	1.15919i
$433$		−	492.194i		−	1.13671i	−0.822784	−	0.568354i	$-0.807581\pi$
$433$		−	492.194i		−	1.13671i	0.822784	−	0.568354i	$-0.192419\pi$
$434$	258.733	−	117.190i	0.596158	−	0.270022i
$435$	−563.580	+	1134.73i	−1.29559	+	2.60857i
$436$	67.0502	−	116.134i	0.153785	−	0.266363i
$437$		−	9.92003i		−	0.0227003i
$438$	567.183	−	35.5654i	1.29494	−	0.0811996i
$439$			70.4474i			0.160472i	0.996776	+	0.0802362i	$0.0255675\pi$
$439$			70.4474i			0.160472i	−0.996776	+	0.0802362i	$0.974433\pi$
$440$			162.390i			0.369069i
$441$	192.707	+	396.667i	0.436977	+	0.899472i
$442$	40.4195			0.0914468
$443$	716.071			1.61641			0.808206	−	0.588900i	$-0.200439\pi$
$443$	716.071			1.61641			0.808206	+	0.588900i	$0.200439\pi$
$444$	−290.921	−	144.490i	−0.655227	−	0.325428i
$445$	946.921			2.12791
$446$	540.967	+	312.328i	1.21293	+	0.700286i
$447$	48.2218	+	769.021i	0.107879	+	1.72041i
$448$	90.0135	+	198.733i	0.200923	+	0.443600i
$449$	−130.350			−0.290313			−0.145156	−	0.989409i	$-0.546369\pi$
$449$	−130.350			−0.290313			−0.145156	+	0.989409i	$0.546369\pi$
$450$	1416.65	−	178.365i	3.14811	−	0.396366i
$451$	341.805	+	197.341i	0.757883	+	0.437564i
$452$	−163.023	−	282.364i	−0.360671	−	0.624700i
$453$	−318.088	−	157.983i	−0.702180	−	0.348748i
$454$	−347.980	+	200.906i	−0.766476	+	0.442525i
$455$	127.668	+	281.866i	0.280588	+	0.619486i
$456$	6.58467	−	13.2578i	0.0144401	−	0.0290741i
$457$	−211.530			−0.462866			−0.231433	−	0.972851i	$-0.574341\pi$
$457$	−211.530			−0.462866			−0.231433	+	0.972851i	$0.574341\pi$
$458$	−952.527	−	549.942i	−2.07975	−	1.20075i
$459$	28.1775	−	80.7523i	0.0613890	−	0.175931i
$460$	122.583	−	70.7736i	0.266486	−	0.153856i
$461$	−457.027	−	263.865i	−0.991381	−	0.572374i	−0.0856943	−	0.996321i	$-0.527311\pi$
$461$	−457.027	−	263.865i	−0.991381	−	0.572374i	−0.905687	+	0.423947i	$0.860644\pi$
$462$	14.0414	−	393.351i	0.0303926	−	0.851409i
$463$	−367.066	−	635.777i	−0.792800	−	1.37317i	−0.924227	−	0.381843i	$-0.875289\pi$
$463$	−367.066	−	635.777i	−0.792800	−	1.37317i	0.131428	−	0.991326i	$-0.458044\pi$
$464$	−433.137	+	750.216i	−0.933485	+	1.61684i
$465$	−26.3915	−	420.880i	−0.0567559	−	0.905119i
$466$	443.160	+	767.576i	0.950988	+	1.64716i
$467$	280.938	−	162.200i	0.601581	−	0.347323i	−0.168082	−	0.985773i	$-0.553757\pi$
$467$	280.938	−	162.200i	0.601581	−	0.347323i	0.769663	+	0.638450i	$0.220424\pi$
$468$	16.5156	+	131.174i	0.0352897	+	0.280286i
$469$	−89.0345	−	196.571i	−0.189839	−	0.419129i
$470$	−627.774	+	1087.34i	−1.33569	+	2.31348i
$471$	84.6828	+	127.516i	0.179794	+	0.270734i
$472$			123.424i			0.261492i
$473$	48.6868			0.102932
$474$	192.788	−	128.030i	0.406727	−	0.270106i
$475$	102.029	+	58.9066i	0.214798	+	0.124014i
$476$	−6.65650	+	67.4945i	−0.0139843	+	0.141795i
$477$	112.636	+	148.521i	0.236135	+	0.311366i
$478$	−278.485	−	482.349i	−0.582604	−	1.00910i
$479$	−364.187	+	210.264i	−0.760307	+	0.438964i	−0.829406	−	0.558646i	$-0.811321\pi$
$479$	−364.187	+	210.264i	−0.760307	+	0.438964i	0.0690988	+	0.997610i	$0.477988\pi$
$480$	1106.58	−	69.3886i	2.30538	−	0.144560i
$481$	−147.238	−	85.0077i	−0.306107	−	0.176731i
$482$	524.011	−	302.538i	1.08716	−	0.627672i
$483$	93.2666	−	49.4980i	0.193099	−	0.102480i
$484$	108.937	−	188.684i	0.225076	−	0.389843i
$485$	259.262	+	449.055i	0.534561	+	0.925887i
$486$	631.358	+	134.887i	1.29909	+	0.277545i
$487$	19.3349	−	33.4890i	0.0397020	−	0.0687658i	−0.845492	−	0.533989i	$-0.820692\pi$
$487$	19.3349	−	33.4890i	0.0397020	−	0.0687658i	0.885194	+	0.465223i	$0.154026\pi$
$488$			5.76277i			0.0118089i
$489$	−769.284	−	382.076i	−1.57318	−	0.781341i
$490$	−1134.72	+	384.857i	−2.31576	+	0.785423i
$491$	435.683	+	754.625i	0.887338	+	1.53691i	0.843011	+	0.537897i	$0.180781\pi$
$491$	435.683	+	754.625i	0.887338	+	1.53691i	0.0443266	+	0.999017i	$0.485886\pi$
$492$	228.355	−	459.777i	0.464136	−	0.934507i
$493$	−125.876	+	72.6744i	−0.255326	+	0.147413i
$494$	−12.5875	+	21.8022i	−0.0254808	+	0.0441341i
$495$	−538.624	−	226.681i	−1.08813	−	0.457942i
$496$		−	288.335i		−	0.581320i
$497$	−234.690	−	518.151i	−0.472213	−	1.04256i
$498$	513.726	−	32.2134i	1.03158	−	0.0646856i
$499$	184.126	−	318.916i	0.368991	−	0.639111i	−0.620417	−	0.784272i	$-0.713037\pi$
$499$	184.126	−	318.916i	0.368991	−	0.639111i	0.989408	+	0.145161i	$0.0463700\pi$
$500$			977.258i			1.95452i
$501$	−249.830	+	503.016i	−0.498663	+	1.00402i
$502$		−	1122.71i		−	2.23648i
$503$		−	603.853i		−	1.20050i	−0.799811	−	0.600251i	$-0.795067\pi$
$503$		−	603.853i		−	1.20050i	0.799811	−	0.600251i	$-0.204933\pi$
$504$	157.503	−	4.24445i	0.312507	−	0.00842154i
$505$	1030.82			2.04123
$506$	−94.2390			−0.186243
$507$	−27.3987	−	436.943i	−0.0540408	−	0.861820i
$508$	−562.953			−1.10817
$509$	−197.693	−	114.138i	−0.388394	−	0.224240i	0.293070	−	0.956091i	$-0.405323\pi$
$509$	−197.693	−	114.138i	−0.388394	−	0.224240i	−0.681464	+	0.731851i	$0.738656\pi$
$510$	208.124	+	103.368i	0.408087	+	0.202682i
$511$	−48.9854	+	496.694i	−0.0958619	+	0.972004i
$512$	569.227			1.11177
$513$	34.7826	+	40.3470i	0.0678023	+	0.0786491i
$514$	200.535	+	115.779i	0.390147	+	0.225251i
$515$	398.294	+	689.865i	0.773386	+	1.33954i
$516$	−3.96315	−	63.2027i	−0.00768053	−	0.122486i
$517$	313.691	−	181.110i	0.606753	−	0.350309i
$518$	383.545	−	535.089i	0.740434	−	1.03299i
$519$	−247.099	−	372.082i	−0.476106	−	0.716922i
$520$	110.554			0.212603
$521$	409.376	+	236.354i	0.785751	+	0.453654i	0.838465	−	0.544956i	$-0.183454\pi$
$521$	409.376	+	236.354i	0.785751	+	0.453654i	−0.0527134	+	0.998610i	$0.516787\pi$
$522$	−662.985	−	874.207i	−1.27009	−	1.67473i
$523$	242.231	−	139.852i	0.463156	−	0.267403i	−0.250214	−	0.968190i	$-0.580501\pi$
$523$	242.231	−	139.852i	0.463156	−	0.267403i	0.713370	+	0.700787i	$0.247168\pi$
$524$	−19.2681	−	11.1245i	−0.0367712	−	0.0212299i
$525$	−44.7348	+	1253.19i	−0.0852092	+	2.38703i
$526$	58.6991	+	101.670i	0.111595	+	0.193289i
$527$	24.1893	−	41.8971i	0.0459000	−	0.0795011i
$528$	−357.854	−	177.733i	−0.677753	−	0.336616i
$529$	251.860	+	436.234i	0.476105	+	0.824639i
$530$	−438.607	+	253.230i	−0.827561	+	0.477792i
$531$	−409.380	−	172.289i	−0.770961	−	0.324460i
$532$	−34.3334	−	24.6098i	−0.0645366	−	0.0462590i
$533$	134.348	−	232.697i	0.252060	−	0.436580i
$534$	−364.759	+	734.417i	−0.683068	+	1.37531i
$535$		−	468.532i		−	0.875761i
$536$	−77.0993			−0.143842
$537$	36.8628	+	587.873i	0.0686459	+	1.09474i
$538$	−451.649	−	260.759i	−0.839496	−	0.484683i
$539$	339.019	+	67.5269i	0.628978	+	0.125282i
$540$	−250.421	+	717.666i	−0.463743	+	1.32901i
$541$	508.919	+	881.473i	0.940700	+	1.62934i	0.764139	+	0.645051i	$0.223164\pi$
$541$	508.919	+	881.473i	0.940700	+	1.62934i	0.176561	+	0.984290i	$0.443503\pi$
$542$	−389.916	+	225.118i	−0.719402	+	0.415347i
$543$	133.898	+	201.624i	0.246589	+	0.371315i
$544$	110.156	+	63.5986i	0.202493	+	0.116909i
$545$	349.467	−	201.765i	0.641224	−	0.370211i
$546$	−267.789	−	9.55921i	−0.490457	−	0.0175077i
$547$	−195.785	+	339.109i	−0.357924	+	0.619943i	−0.987614	−	0.156904i	$-0.949849\pi$
$547$	−195.785	+	339.109i	−0.357924	+	0.619943i	0.629690	+	0.776847i	$0.283182\pi$
$548$	72.2946	+	125.218i	0.131924	+	0.228500i
$549$	−19.1142	−	8.04426i	−0.0348165	−	0.0146526i
$550$	559.605	−	969.264i	1.01746	−	1.76230i
$551$		−	90.5297i		−	0.164301i
$552$	−2.36088	−	37.6504i	−0.00427696	−	0.0682072i
$553$	83.8589	+	185.145i	0.151644	+	0.334801i
$554$	−491.645	−	851.554i	−0.887445	−	1.53710i
$555$	−540.746	−	814.256i	−0.974317	−	1.46713i
$556$	−670.925	+	387.359i	−1.20670	+	0.696689i
$557$	249.913	−	432.862i	0.448677	−	0.777131i	−0.549623	−	0.835413i	$-0.685229\pi$
$557$	249.913	−	432.862i	0.448677	−	0.777131i	0.998300	+	0.0582814i	$0.0185621\pi$
$558$	336.594	+	141.656i	0.603216	+	0.253864i
$559$		−	33.1455i		−	0.0592942i
$560$	−119.381	+	1210.48i	−0.213180	+	2.16157i
$561$	−37.0881	−	55.8473i	−0.0661107	−	0.0995496i
$562$	163.400	−	283.018i	0.290748	−	0.503590i
$563$		−	323.183i		−	0.574038i	−0.957925	−	0.287019i	$-0.907336\pi$
$563$		−	323.183i		−	0.574038i	0.957925	−	0.287019i	$-0.0926643\pi$
$564$	−260.642	−	392.475i	−0.462131	−	0.695878i
$565$		−	981.126i		−	1.73651i
$566$			399.712i			0.706204i
$567$	−205.781	+	528.340i	−0.362930	+	0.931817i
$568$	−203.229			−0.357798
$569$	176.881			0.310863			0.155431	−	0.987847i	$-0.450323\pi$
$569$	176.881			0.310863			0.155431	+	0.987847i	$0.450323\pi$
$570$	−120.571	+	80.0710i	−0.211528	+	0.140475i
$571$	−557.593			−0.976519			−0.488260	−	0.872698i	$-0.662368\pi$
$571$	−557.593			−0.976519			−0.488260	+	0.872698i	$0.662368\pi$
$572$	89.7486	+	51.8164i	0.156903	+	0.0905881i
$573$	−68.8807	+	45.7436i	−0.120211	+	0.0798317i
$574$	845.666	+	606.162i	1.47329	+	1.05603i
$575$	300.239			0.522155
$576$	−108.807	+	258.539i	−0.188900	+	0.448852i
$577$	−640.283	−	369.668i	−1.10968	−	0.640672i	−0.170931	−	0.985283i	$-0.554677\pi$
$577$	−640.283	−	369.668i	−1.10968	−	0.640672i	−0.938745	+	0.344611i	$0.888011\pi$
$578$	−370.580	−	641.864i	−0.641142	−	1.11049i
$579$	311.223	−	206.683i	0.537518	−	0.356965i
$580$	1118.69	−	645.876i	1.92878	−	1.11358i
$581$	−44.3686	+	449.881i	−0.0763659	+	0.774321i
$582$	−448.149	+	28.1014i	−0.770016	+	0.0482842i
$583$	146.111			0.250620
$584$	154.430	+	89.1599i	0.264434	+	0.152671i
$585$	−154.322	+	366.690i	−0.263798	+	0.626820i
$586$	−992.949	+	573.280i	−1.69445	+	0.978293i
$587$	47.8551	+	27.6292i	0.0815249	+	0.0470684i	0.540208	−	0.841531i	$-0.318345\pi$
$587$	47.8551	+	27.6292i	0.0815249	+	0.0470684i	−0.458683	+	0.888600i	$0.651679\pi$
$588$	60.0634	−	445.593i	0.102149	−	0.757812i
$589$	15.0662	+	26.0954i	0.0255792	+	0.0443045i
$590$	603.396	−	1045.11i	1.02270	−	1.77138i
$591$	287.652	−	191.029i	0.486722	−	0.323231i
$592$	−334.159	−	578.780i	−0.564458	−	0.977670i
$593$	−663.928	+	383.319i	−1.11961	+	0.646406i	−0.941301	−	0.337569i	$-0.890395\pi$
$593$	−663.928	+	383.319i	−1.11961	+	0.646406i	−0.178307	+	0.983975i	$0.557062\pi$
$594$	383.291	−	330.430i	0.645271	−	0.556279i
$595$	−118.898	+	165.876i	−0.199828	+	0.278783i
$596$	392.799	−	680.348i	0.659059	−	1.14152i
$597$	361.841	−	22.6894i	0.606099	−	0.0380057i
$598$			64.1569i			0.107286i
$599$	−906.266			−1.51296			−0.756482	−	0.654014i	$-0.773084\pi$
$599$	−906.266			−1.51296			−0.756482	+	0.654014i	$0.773084\pi$
$600$	401.260	+	199.291i	0.668766	+	0.332152i
$601$	192.859	+	111.347i	0.320897	+	0.185270i	0.651793	−	0.758397i	$-0.274017\pi$
$601$	192.859	+	111.347i	0.320897	+	0.185270i	−0.330895	+	0.943668i	$0.607351\pi$
$602$	127.730	+	12.5971i	0.212176	+	0.0209254i
$603$	107.623	−	255.727i	0.178479	−	0.424091i
$604$	181.052	+	313.591i	0.299755	+	0.519191i
$605$	567.781	−	327.808i	0.938481	−	0.541832i
$606$	−397.078	+	799.490i	−0.655244	+	1.31929i
$607$	518.849	+	299.558i	0.854776	+	0.493505i	0.862259	−	0.506467i	$-0.169049\pi$
$607$	518.849	+	299.558i	0.854776	+	0.493505i	−0.00748365	+	0.999972i	$0.502382\pi$
$608$	−68.6100	+	39.6120i	−0.112845	+	0.0651514i
$609$	851.146	−	451.717i	1.39761	−	0.741735i
$610$	28.1729	−	48.7970i	0.0461851	−	0.0799950i
$611$	−123.298	−	213.558i	−0.201796	−	0.349522i
$612$	−69.4791	+	52.6918i	−0.113528	+	0.0860978i
$613$	−270.643	+	468.768i	−0.441506	+	0.764711i	−0.997801	−	0.0662736i	$-0.978889\pi$
$613$	−270.643	+	468.768i	−0.441506	+	0.764711i	0.556295	+	0.830985i	$0.312222\pi$
$614$			417.565i			0.680073i
$615$	1286.87	−	854.606i	2.09247	−	1.38960i
$616$	71.9515	−	100.381i	0.116804	−	0.162955i
$617$	331.635	+	574.409i	0.537497	+	0.930972i	0.999038	+	0.0438529i	$0.0139633\pi$
$617$	331.635	+	574.409i	0.537497	+	0.930972i	−0.461541	+	0.887119i	$0.652703\pi$
$618$	−688.473	+	43.1710i	−1.11403	+	0.0698560i
$619$	−847.625	+	489.377i	−1.36935	+	0.790592i	−0.990844	−	0.135008i	$-0.956894\pi$
$619$	−847.625	+	489.377i	−1.36935	+	0.790592i	−0.378502	+	0.925601i	$0.623561\pi$
$620$	−214.977	+	372.350i	−0.346736	+	0.600565i
$621$	128.176	+	44.7255i	0.206403	+	0.0720218i
$622$			881.565i			1.41731i
$623$	−585.333	−	419.559i	−0.939539	−	0.673450i
$624$	−120.999	+	243.623i	−0.193908	+	0.390421i
$625$	−723.942	+	1253.90i	−1.15831	+	2.00625i
$626$		−	1085.28i		−	1.73368i
$627$	41.6740	−	2.61319i	0.0664657	−	0.00416776i
$628$		−	156.066i		−	0.248513i
$629$		−	112.135i		−	0.178274i
$630$	−1354.43	−	734.060i	−2.14989	−	1.16517i
$631$	256.500			0.406498			0.203249	−	0.979127i	$-0.434850\pi$
$631$	256.500			0.406498			0.203249	+	0.979127i	$0.434850\pi$
$632$	72.6175			0.114901
$633$	−323.448	−	160.645i	−0.510977	−	0.253784i
$634$	102.939			0.162365
$635$	−1467.06	−	847.007i	−2.31033	−	1.33387i
$636$	−11.8936	−	189.674i	−0.0187006	−	0.298229i
$637$	45.9716	−	230.800i	0.0721689	−	0.362324i
$638$	−860.020			−1.34799
$639$	283.688	−	674.081i	0.443956	−	1.05490i
$640$	620.253	+	358.103i	0.969145	+	0.559536i
$641$	168.080	+	291.123i	0.262215	+	0.454170i	0.966830	−	0.255419i	$-0.0822136\pi$
$641$	168.080	+	291.123i	0.262215	+	0.454170i	−0.704615	+	0.709590i	$0.748880\pi$
$642$	363.386	+	180.481i	0.566022	+	0.281123i
$643$	−754.603	+	435.671i	−1.17357	+	0.677559i	−0.954518	−	0.298155i	$-0.903629\pi$
$643$	−754.603	+	435.671i	−1.17357	+	0.677559i	−0.219049	+	0.975714i	$0.570296\pi$
$644$	−107.132	−	10.5657i	−0.166355	−	0.0164064i
$645$	84.7656	−	170.670i	0.131419	−	0.264604i
$646$	−16.6043			−0.0257033
$647$	−707.666	−	408.571i	−1.09376	−	0.631485i	−0.159189	−	0.987248i	$-0.550888\pi$
$647$	−707.666	−	408.571i	−1.09376	−	0.631485i	−0.934576	+	0.355763i	$0.884221\pi$
$648$	141.616	+	144.854i	0.218543	+	0.223541i
$649$	−301.510	+	174.077i	−0.464576	+	0.268223i
$650$	−659.865	−	380.973i	−1.01518	−	0.586113i
$651$	−170.169	+	271.858i	−0.261396	+	0.417601i
$652$	437.868	+	758.410i	0.671577	+	1.16321i
$653$	180.418	−	312.493i	0.276291	−	0.478550i	−0.694169	−	0.719812i	$-0.744228\pi$
$653$	180.418	−	312.493i	0.276291	−	0.478550i	0.970460	+	0.241262i	$0.0775613\pi$
$654$	21.8693	+	348.762i	0.0334392	+	0.533275i
$655$	−33.4753	−	57.9809i	−0.0511073	−	0.0885204i
$656$	914.716	−	528.112i	1.39438	−	0.805048i
$657$	−511.299	+	387.761i	−0.778232	+	0.590199i
$658$	869.829	−	393.978i	1.32193	−	0.598750i
$659$	515.473	−	892.826i	0.782205	−	1.35482i	−0.148449	−	0.988920i	$-0.547428\pi$
$659$	515.473	−	892.826i	0.782205	−	1.35482i	0.930654	−	0.365899i	$-0.119239\pi$
$660$	329.611	+	496.329i	0.499411	+	0.752014i
$661$		−	332.364i		−	0.502820i	−0.967881	−	0.251410i	$-0.919106\pi$
$661$		−	332.364i		−	0.502820i	0.967881	−	0.251410i	$-0.0808942\pi$
$662$	757.315			1.14398
$663$	−38.0203	+	25.2492i	−0.0573458	+	0.0380832i
$664$	139.875	+	80.7566i	0.210654	+	0.121621i
$665$	−52.4459	−	115.791i	−0.0788660	−	0.174121i
$666$	839.822	−	105.739i	1.26099	−	0.158767i
$667$	−115.354	−	199.800i	−0.172945	−	0.299550i
$668$	495.906	−	286.311i	0.742374	−	0.428610i
$669$	−703.961	+	44.1422i	−1.05226	+	0.0659823i
$670$	652.848	+	376.922i	0.974400	+	0.562570i
$671$	−14.0777	+	8.12775i	−0.0209801	+	0.0121129i
$672$	−714.770	−	447.409i	−1.06365	−	0.665787i
$673$	−241.240	+	417.840i	−0.358455	+	0.620862i	−0.987703	−	0.156343i	$-0.950030\pi$
$673$	−241.240	+	417.840i	−0.358455	+	0.620862i	0.629248	+	0.777204i	$0.283363\pi$
$674$	792.030	+	1371.84i	1.17512	+	2.03537i
$675$	−1221.14	+	1052.73i	−1.80909	+	1.55960i
$676$	−223.181	+	386.561i	−0.330149	+	0.571835i
$677$		−	622.267i		−	0.919154i	−0.888138	−	0.459577i	$-0.848001\pi$
$677$		−	622.267i		−	0.919154i	0.888138	−	0.459577i	$-0.151999\pi$
$678$	760.946	+	377.934i	1.12234	+	0.557425i
$679$	38.7049	−	392.454i	0.0570029	−	0.577988i
$680$	36.4581	+	63.1473i	0.0536149	+	0.0928637i
$681$	201.823	−	406.356i	0.296362	−	0.596705i
$682$	247.903	−	143.127i	0.363494	−	0.209863i
$683$	235.625	−	408.115i	0.344986	−	0.597533i	−0.640366	−	0.768070i	$-0.721217\pi$
$683$	235.625	−	408.115i	0.344986	−	0.597533i	0.985351	+	0.170538i	$0.0545505\pi$
$684$	−6.78461	−	53.8863i	−0.00991901	−	0.0787812i
$685$			435.092i			0.635171i
$686$	871.944	+	264.874i	1.27106	+	0.386113i
$687$	1239.52	−	77.7248i	1.80426	−	0.113137i
$688$	65.1463	−	112.837i	0.0946894	−	0.164007i
$689$		−	99.4710i		−	0.144370i
$690$	−164.073	+	330.351i	−0.237788	+	0.478770i
$691$			519.523i			0.751843i	0.926652	+	0.375921i	$0.122674\pi$
$691$			519.523i			0.751843i	−0.926652	+	0.375921i	$0.877326\pi$
$692$			455.392i			0.658081i
$693$	232.510	+	378.774i	0.335512	+	0.546571i
$694$	−771.992			−1.11238
$695$	−2331.25			−3.35432
$696$	−21.5453	−	343.595i	−0.0309559	−	0.493671i
$697$	177.220			0.254261
$698$	753.135	+	434.823i	1.07899	+	0.622955i
$699$	−896.343	−	445.182i	−1.28232	−	0.636883i
$700$	744.838	−	1039.13i	1.06405	−	1.48448i
$701$	−985.712			−1.40615			−0.703076	−	0.711115i	$-0.748191\pi$
$701$	−985.712			−1.40615			−0.703076	+	0.711115i	$0.748191\pi$
$702$	−224.953	−	260.940i	−0.320446	−	0.371710i
$703$	60.4852	+	34.9212i	0.0860387	+	0.0496745i
$704$	109.936	+	190.414i	0.156159	+	0.270475i
$705$	−88.7251	−	1414.95i	−0.125851	−	2.00702i
$706$	−193.583	+	111.765i	−0.274197	+	0.158308i
$707$	−637.196	−	456.734i	−0.901268	−	0.646017i
$708$	250.520	+	377.234i	0.353842	+	0.532817i
$709$	590.228			0.832479			0.416240	−	0.909255i	$-0.363348\pi$
$709$	590.228			0.832479			0.416240	+	0.909255i	$0.363348\pi$
$710$	1720.87	+	993.544i	2.42376	+	1.39936i
$711$	−101.367	+	240.861i	−0.142570	+	0.338764i
$712$	−222.830	+	128.651i	−0.312964	+	0.180690i
$713$	66.5023	+	38.3951i	0.0932711	+	0.0538501i
$714$	−82.8508	−	156.111i	−0.116038	−	0.218643i
$715$	155.924	+	270.068i	0.218075	+	0.377717i
$716$	300.273	−	520.088i	0.419376	−	0.726380i
$717$	563.267	+	279.755i	0.785589	+	0.390174i
$718$	−282.129	−	488.662i	−0.392938	−	0.680588i
$719$	320.943	−	185.297i	0.446375	−	0.257715i	−0.259923	−	0.965629i	$-0.583697\pi$
$719$	320.943	−	185.297i	0.446375	−	0.257715i	0.706298	+	0.707915i	$0.250364\pi$
$720$	−1246.07	+	945.002i	−1.73066	+	1.31250i
$721$	59.4608	−	602.911i	0.0824699	−	0.836214i
$722$	−474.384	+	821.657i	−0.657042	+	1.13803i
$723$	−303.918	+	611.918i	−0.420357	+	0.846360i
$724$		−	246.768i		−	0.340839i
$725$	2739.97			3.77926
$726$	35.5311	+	566.635i	0.0489409	+	0.780489i
$727$	−98.4688	−	56.8510i	−0.135445	−	0.0781995i	0.430746	−	0.902473i	$-0.358250\pi$
$727$	−98.4688	−	56.8510i	−0.135445	−	0.0781995i	−0.566192	+	0.824274i	$0.691584\pi$
$728$	−68.3380	−	48.9838i	−0.0938709	−	0.0672854i
$729$	−678.142	+	267.515i	−0.930236	+	0.366962i
$730$	−871.768	−	1509.95i	−1.19420	−	2.06842i
$731$	18.9324	−	10.9306i	0.0258994	−	0.0149530i
$732$	11.6970	+	17.6133i	0.0159795	+	0.0240619i
$733$	526.757	+	304.124i	0.718632	+	0.414903i	0.814249	−	0.580516i	$-0.197149\pi$
$733$	526.757	+	304.124i	0.718632	+	0.414903i	−0.0956168	+	0.995418i	$0.530482\pi$
$734$	−965.458	+	557.407i	−1.31534	+	0.759411i
$735$	826.957	−	1070.85i	1.12511	−	1.45694i
$736$	−100.949	+	174.848i	−0.137158	+	0.237565i
$737$	−108.740	−	188.343i	−0.147544	−	0.255554i
$738$	167.111	+	1327.27i	0.226438	+	1.79847i
$739$	605.973	−	1049.58i	0.819990	−	1.42026i	−0.0856983	−	0.996321i	$-0.527312\pi$
$739$	605.973	−	1049.58i	0.819990	−	1.42026i	0.905689	−	0.423944i	$-0.139355\pi$
$740$			996.568i			1.34671i
$741$	−1.77903	−	28.3712i	−0.00240085	−	0.0382878i
$742$	383.323	+	37.8044i	0.516607	+	0.0509493i
$743$	82.8636	+	143.524i	0.111526	+	0.193168i	0.916386	−	0.400297i	$-0.131093\pi$
$743$	82.8636	+	143.524i	0.111526	+	0.193168i	−0.804860	+	0.593465i	$0.797760\pi$
$744$	63.3924	+	95.4564i	0.0852048	+	0.128302i
$745$	2047.28	−	1182.00i	2.74802	−	1.58657i
$746$	293.657	−	508.628i	0.393642	−	0.681807i
$747$	−463.109	+	351.215i	−0.619958	+	0.470167i
$748$			68.3515i			0.0913791i
$749$	−207.596	+	289.620i	−0.277164	+	0.386676i
$750$	−1408.82	−	2121.41i	−1.87843	−	2.82854i
$751$	−676.588	+	1171.89i	−0.900916	+	1.56043i	−0.0746094	+	0.997213i	$0.523771\pi$
$751$	−676.588	+	1171.89i	−0.900916	+	1.56043i	−0.826307	+	0.563220i	$0.809562\pi$
$752$		−	969.349i		−	1.28903i
$753$	701.333	+	1056.07i	0.931385	+	1.40248i
$754$			585.493i			0.776515i
$755$			1089.63i			1.44322i
$756$	472.778	−	332.665i	0.625367	−	0.440033i
$757$	128.108			0.169231			0.0846155	−	0.996414i	$-0.473034\pi$
$757$	128.108			0.169231			0.0846155	+	0.996414i	$0.473034\pi$
$758$	842.374			1.11131
$759$	88.6451	−	58.8690i	0.116792	−	0.0775613i
$760$	−45.4154			−0.0597572
$761$	697.444	+	402.669i	0.916483	+	0.529132i	0.882511	−	0.470291i	$-0.155851\pi$
$761$	697.444	+	402.669i	0.916483	+	0.529132i	0.0339717	+	0.999423i	$0.489184\pi$
$762$	1222.04	−	811.557i	1.60373	−	1.06504i
$763$	−305.418	−	30.1212i	−0.400286	−	0.0394774i
$764$	84.3032			0.110344
$765$	−260.342	+	32.7786i	−0.340317	+	0.0428479i
$766$	638.687	+	368.746i	0.833795	+	0.481392i
$767$	118.510	+	205.265i	0.154511	+	0.267620i
$768$	−828.221	+	550.020i	−1.07841	+	0.716172i
$769$	−501.209	+	289.373i	−0.651767	+	0.376298i	−0.789133	−	0.614222i	$-0.789470\pi$
$769$	−501.209	+	289.373i	−0.651767	+	0.376298i	0.137366	+	0.990520i	$0.456136\pi$
$770$	−1100.00	+	498.229i	−1.42857	+	0.647051i
$771$	−260.957	+	16.3634i	−0.338465	+	0.0212236i
$772$	−380.906			−0.493401
$773$	685.032	+	395.504i	0.886200	+	0.511648i	0.872698	−	0.488261i	$-0.162369\pi$
$773$	685.032	+	395.504i	0.886200	+	0.511648i	0.0135021	+	0.999909i	$0.495702\pi$
$774$	99.7167	+	131.486i	0.128833	+	0.169878i
$775$	−789.801	+	455.992i	−1.01910	+	0.588376i
$776$	−122.020	−	70.4481i	−0.157242	−	0.0907836i
$777$	−26.5198	+	742.919i	−0.0341310	+	0.956138i
$778$	96.2228	+	166.663i	0.123680	+	0.214219i
$779$	−55.1901	+	95.5921i	−0.0708474	+	0.122711i
$780$	337.896	−	224.396i	0.433200	−	0.287687i
$781$	−286.633	−	496.462i	−0.367007	−	0.635675i
$782$	−36.6459	+	21.1575i	−0.0468618	+	0.0270557i
$783$	1169.73	+	408.163i	1.49391	+	0.521281i
$784$	610.131	−	695.355i	0.778228	−	0.886932i
$785$	234.814	−	406.710i	0.299126	−	0.518102i
$786$	57.8639	−	3.62838i	0.0736182	−	0.00461626i
$787$		−	989.401i		−	1.25718i	−0.777737	−	0.628590i	$-0.783632\pi$
$787$		−	989.401i		−	1.25718i	0.777737	−	0.628590i	$-0.216368\pi$
$788$	−352.058			−0.446774
$789$	−118.726	−	58.9668i	−0.150476	−	0.0747362i
$790$	−614.898	−	355.011i	−0.778352	−	0.449382i
$791$	−434.714	+	606.476i	−0.549576	+	0.766721i
$792$	157.547	−	19.8361i	0.198923	−	0.0250456i
$793$	5.53329	+	9.58394i	0.00697766	+	0.0120857i
$794$	−1569.92	+	906.395i	−1.97723	+	1.14155i
$795$	254.385	−	512.187i	0.319981	−	0.644260i
$796$	−320.119	−	184.821i	−0.402159	−	0.232187i
$797$	104.384	−	60.2662i	0.130971	−	0.0756163i	−0.433083	−	0.901354i	$-0.642574\pi$
$797$	104.384	−	60.2662i	0.130971	−	0.0756163i	0.564054	+	0.825738i	$0.309241\pi$
$798$	110.008	+	3.92693i	0.137854	+	0.00492096i
$799$	81.3216	−	140.853i	0.101779	−	0.176287i
$800$	−1198.90	−	2076.55i	−1.49862	−	2.59568i
$801$	−115.667	−	918.680i	−0.144404	−	1.14692i
$802$	−597.323	+	1034.59i	−0.744791	+	1.29002i
$803$			503.001i			0.626403i
$804$	−235.646	+	156.492i	−0.293092	+	0.194642i
$805$	−263.291	−	188.724i	−0.327070	−	0.234439i
$806$	−97.4391	−	168.769i	−0.120892	−	0.209391i
$807$	587.730	−	36.8539i	0.728290	−	0.0456677i
$808$	−242.574	+	140.050i	−0.300216	+	0.173330i
$809$	−94.3098	+	163.349i	−0.116576	+	0.201915i	−0.918409	−	0.395633i	$-0.870525\pi$
$809$	−94.3098	+	163.349i	−0.116576	+	0.201915i	0.801833	+	0.597548i	$0.203858\pi$
$810$	−490.985	−	1918.90i	−0.606155	−	2.36901i
$811$		−	1191.68i		−	1.46940i	−0.678394	−	0.734699i	$-0.737324\pi$
$811$		−	1191.68i		−	1.46940i	0.678394	−	0.734699i	$-0.262676\pi$
$812$	−977.684	−	96.4221i	−1.20404	−	0.118746i
$813$	226.145	−	455.327i	0.278161	−	0.560058i
$814$	331.747	−	574.602i	0.407551	−	0.705899i
$815$			2635.23i			3.23341i
$816$	−179.058	+	11.2279i	−0.219434	+	0.0137597i
$817$			13.6162i			0.0166661i
$818$		−	395.622i		−	0.483645i
$819$	257.865	−	158.290i	0.314854	−	0.193273i
$820$	−1575.00			−1.92073
$821$	−677.226			−0.824879			−0.412440	−	0.910985i	$-0.635323\pi$
$821$	−677.226			−0.824879			−0.412440	+	0.910985i	$0.635323\pi$
$822$	−337.450	−	167.600i	−0.410524	−	0.203892i
$823$	−1610.79			−1.95722			−0.978608	−	0.205732i	$-0.934043\pi$
$823$	−1610.79			−1.95722			−0.978608	+	0.205732i	$0.934043\pi$
$824$	−187.454	−	108.227i	−0.227493	−	0.131343i
$825$	79.0906	+	1261.30i	0.0958674	+	1.52885i
$826$	−836.051	+	378.678i	−1.01217	+	0.458448i
$827$	−626.312			−0.757331			−0.378665	−	0.925534i	$-0.623617\pi$
$827$	−626.312			−0.757331			−0.378665	+	0.925534i	$0.623617\pi$
$828$	−83.6365	−	110.282i	−0.101010	−	0.133191i
$829$	−469.693	−	271.178i	−0.566578	−	0.327114i	0.189203	−	0.981938i	$-0.439409\pi$
$829$	−469.693	−	271.178i	−0.566578	−	0.327114i	−0.755782	+	0.654824i	$0.772743\pi$
$830$	−789.604	−	1367.63i	−0.951330	−	1.64775i
$831$	994.408	+	493.887i	1.19664	+	0.594329i
$832$	129.632	−	74.8431i	0.155808	−	0.0899557i
$833$	146.992	−	49.8543i	0.176461	−	0.0598491i
$834$	898.009	−	1808.08i	1.07675	−	2.16796i
$835$	1723.11			2.06361
$836$	−36.8687	−	21.2862i	−0.0441014	−	0.0254619i
$837$	−405.104	+	77.0153i	−0.483996	+	0.0920135i
$838$	1060.52	−	612.293i	1.26554	−	0.730660i
$839$	1281.98	+	740.153i	1.52799	+	0.882185i	0.999446	+	0.0332790i	$0.0105950\pi$
$839$	1281.98	+	740.153i	1.52799	+	0.882185i	0.528543	+	0.848906i	$0.322738\pi$
$840$	−226.610	−	426.989i	−0.269774	−	0.508320i
$841$	−632.218	−	1095.03i	−0.751746	−	1.30206i
$842$	−169.771	+	294.051i	−0.201628	+	0.349230i
$843$	23.0938	+	368.291i	0.0273948	+	0.436881i
$844$	184.103	+	318.876i	0.218132	+	0.377815i
$845$	−1163.22	+	671.587i	−1.37660	+	0.794778i
$846$	1131.59	+	476.232i	1.33758	+	0.562922i
$847$	−496.215	−	48.9381i	−0.585850	−	0.0577782i
$848$	195.507	−	338.627i	0.230550	−	0.399325i
$849$	−249.691	−	375.985i	−0.294100	−	0.442857i
$850$		−	502.546i		−	0.591230i
$851$	177.988			0.209152
$852$	−621.149	+	412.504i	−0.729048	+	0.484159i
$853$	−744.542	−	429.861i	−0.872851	−	0.503941i	−0.00455615	−	0.999990i	$-0.501450\pi$
$853$	−744.542	−	429.861i	−0.872851	−	0.503941i	−0.868294	+	0.496049i	$0.834784\pi$
$854$	−39.0357	+	17.6807i	−0.0457093	+	0.0207034i
$855$	63.3955	−	150.636i	0.0741468	−	0.176183i
$856$	63.6560	+	110.255i	0.0743645	+	0.128803i
$857$	383.456	−	221.388i	0.447440	−	0.258330i	−0.259308	−	0.965795i	$-0.583495\pi$
$857$	383.456	−	221.388i	0.447440	−	0.258330i	0.706748	+	0.707465i	$0.250161\pi$
$858$	−269.523	+	16.9006i	−0.314129	+	0.0196976i
$859$	433.921	+	250.524i	0.505146	+	0.291646i	0.730836	−	0.682553i	$-0.239130\pi$
$859$	433.921	+	250.524i	0.505146	+	0.291646i	−0.225690	+	0.974199i	$0.572464\pi$
$860$	−168.257	+	97.1434i	−0.195648	+	0.112957i
$861$	−1174.12	−	41.9125i	−1.36368	−	0.0486788i
$862$	−277.453	+	480.562i	−0.321871	+	0.557497i
$863$	−182.251	−	315.667i	−0.211183	−	0.365779i	0.740902	−	0.671613i	$-0.234398\pi$
$863$	−182.251	−	315.667i	−0.211183	−	0.365779i	−0.952085	+	0.305834i	$0.901065\pi$
$864$	−202.489	−	1065.10i	−0.234362	−	1.23276i
$865$	−685.174	+	1186.76i	−0.792108	+	1.37197i
$866$		−	1307.67i		−	1.51001i
$867$	749.541	+	372.270i	0.864523	+	0.429378i
$868$	297.866	−	134.915i	0.343164	−	0.155432i
$869$	102.419	+	177.395i	0.117859	+	0.204137i
$870$	−1497.33	+	3014.77i	−1.72106	+	3.46525i
$871$	−128.222	+	74.0291i	−0.147213	+	0.0849932i
$872$	−54.8246	+	94.9590i	−0.0628723	+	0.108898i
$873$	403.993	−	306.382i	0.462764	−	0.350953i
$874$		−	26.3557i		−	0.0301552i
$875$	2037.30	−	922.769i	2.32834	−	1.05459i
$876$	652.970	−	40.9448i	0.745400	−	0.0467406i
$877$	391.240	−	677.647i	0.446111	−	0.772688i	−0.552017	−	0.833833i	$-0.686142\pi$
$877$	391.240	−	677.647i	0.446111	−	0.772688i	0.998129	+	0.0611449i	$0.0194752\pi$
$878$			187.166i			0.213173i
$879$	575.894	−	1159.52i	0.655170	−	1.31914i
$880$			1225.85i			1.39301i
$881$		−	337.263i		−	0.382818i	−0.981510	−	0.191409i	$-0.938694\pi$
$881$		−	337.263i		−	0.382818i	0.981510	−	0.191409i	$-0.0613058\pi$
$882$	511.987	+	1053.87i	0.580484	+	1.19487i
$883$	556.002			0.629674			0.314837	−	0.949146i	$-0.398050\pi$
$883$	556.002			0.629674			0.314837	+	0.949146i	$0.398050\pi$
$884$	46.5330			0.0526392
$885$	85.2796	+	1360.00i	0.0963612	+	1.53673i
$886$	1902.47			2.14725
$887$	−626.057	−	361.454i	−0.705814	−	0.407502i	0.103695	−	0.994609i	$-0.466933\pi$
$887$	−626.057	−	361.454i	−0.705814	−	0.407502i	−0.809509	+	0.587107i	$0.800267\pi$
$888$	237.876	+	118.144i	0.267878	+	0.133045i
$889$	531.564	+	1173.59i	0.597934	+	1.32013i
$890$	2515.79			2.82673
$891$	−154.127	+	550.250i	−0.172982	+	0.617564i
$892$	622.790	+	359.568i	0.698195	+	0.403103i
$893$	50.6507	+	87.7296i	0.0567197	+	0.0982414i
$894$	128.116	+	2043.15i	0.143307	+	2.28540i
$895$	1565.03	−	903.569i	1.74863	−	1.00957i
$896$	−224.738	−	496.179i	−0.250823	−	0.553771i
$897$	−40.0774	−	60.3486i	−0.0446794	−	0.0672783i
$898$	−346.317			−0.385653
$899$	606.896	+	350.392i	0.675079	+	0.389757i
$900$	1630.92	−	205.342i	1.81213	−	0.228158i
$901$	56.8170	−	32.8033i	0.0630599	−	0.0364077i
$902$	908.113	+	524.299i	1.00678	+	0.581263i
$903$	−128.017	+	67.9407i	−0.141769	+	0.0752389i
$904$	133.298	+	230.879i	0.147454	+	0.255398i
$905$	371.282	−	643.079i	0.410256	−	0.710584i
$906$	−845.100	−	419.731i	−0.932781	−	0.463279i
$907$	−563.871	−	976.653i	−0.621688	−	1.07679i	−0.989171	−	0.146765i	$-0.953114\pi$
$907$	−563.871	−	976.653i	−0.621688	−	1.07679i	0.367484	−	0.930030i	$-0.380219\pi$
$908$	−400.613	+	231.294i	−0.441203	+	0.254729i
$909$	−125.916	−	1000.08i	−0.138521	−	1.10020i
$910$	339.189	+	748.866i	0.372736	+	0.822930i
$911$	−890.109	+	1541.71i	−0.977068	+	1.69233i	−0.304136	+	0.952629i	$0.598368\pi$
$911$	−890.109	+	1541.71i	−0.977068	+	1.69233i	−0.672933	+	0.739703i	$0.734966\pi$
$912$	49.7063	−	100.080i	0.0545025	−	0.109737i
$913$			455.594i			0.499007i
$914$	−561.995			−0.614875
$915$	3.98176	+	63.4995i	0.00435165	+	0.0693983i
$916$	−1096.60	−	633.121i	−1.19716	−	0.691181i
$917$	−4.99748	+	50.6726i	−0.00544982	+	0.0552591i
$918$	74.8625	−	214.544i	0.0815496	−	0.233708i
$919$	−350.534	−	607.142i	−0.381429	−	0.660655i	0.609837	−	0.792527i	$-0.291235\pi$
$919$	−350.534	−	607.142i	−0.381429	−	0.660655i	−0.991267	+	0.131871i	$0.957901\pi$
$920$	−100.232	+	57.8691i	−0.108948	+	0.0629012i
$921$	−260.844	−	392.779i	−0.283218	−	0.426470i
$922$	−1214.24	−	701.039i	−1.31696	−	0.760346i
$923$	−337.986	+	195.136i	−0.366182	+	0.211415i
$924$	16.1651	−	452.846i	0.0174947	−	0.490093i
$925$	−1056.92	+	1830.64i	−1.14262	+	1.97907i
$926$	−975.227	−	1689.14i	−1.05316	−	1.82413i
$927$	620.638	−	470.683i	0.669513	−	0.507748i
$928$	−921.252	+	1595.65i	−0.992728	+	1.71946i
$929$			981.172i			1.05616i	0.849195	+	0.528080i	$0.177088\pi$
$929$			981.172i			1.05616i	−0.849195	+	0.528080i	$0.822912\pi$
$930$	−70.1173	−	1118.20i	−0.0753949	−	1.20237i
$931$	−18.8851	+	94.8129i	−0.0202848	+	0.101840i
$932$	510.189	+	883.674i	0.547413	+	0.948148i
$933$	−550.695	−	829.237i	−0.590241	−	0.888785i
$934$	746.401	−	430.935i	0.799145	−	0.461386i
$935$	−102.840	+	178.125i	−0.109990	+	0.190508i
$936$	−13.5042	−	107.256i	−0.0144276	−	0.114590i
$937$		−	949.998i		−	1.01387i	−0.861984	−	0.506936i	$-0.830778\pi$
$937$		−	949.998i		−	1.01387i	0.861984	−	0.506936i	$-0.169222\pi$
$938$	−236.548	−	522.254i	−0.252184	−	0.556774i
$939$	677.953	+	1020.86i	0.721995	+	1.08718i
$940$	−722.726	+	1251.80i	−0.768858	+	1.33170i
$941$		−	380.205i		−	0.404043i	−0.979381	−	0.202022i	$-0.935249\pi$
$941$		−	380.205i		−	0.404043i	0.979381	−	0.202022i	$-0.0647512\pi$
$942$	224.986	+	338.785i	0.238839	+	0.359644i
$943$			281.297i			0.298300i
$944$			931.705i			0.986976i
$945$	1732.58	−	155.596i	1.83342	−	0.164651i
$946$	129.352			0.136736
$947$	326.068			0.344317			0.172159	−	0.985069i	$-0.444926\pi$
$947$	326.068			0.344317			0.172159	+	0.985069i	$0.444926\pi$
$948$	221.948	−	147.395i	0.234122	−	0.155480i
$949$	342.438			0.360841
$950$	271.073	+	156.504i	0.285340	+	0.164741i
$951$	−96.8290	+	64.3039i	−0.101818	+	0.0676172i
$952$	5.44279	−	55.1879i	0.00571722	−	0.0579704i
$953$	1009.14			1.05891			0.529455	−	0.848338i	$-0.322397\pi$
$953$	1009.14			1.05891			0.529455	+	0.848338i	$0.322397\pi$
$954$	299.254	+	394.594i	0.313683	+	0.413620i
$955$	219.695	+	126.841i	0.230047	+	0.132818i
$956$	−320.606	−	555.306i	−0.335362	−	0.580864i
$957$	808.971	−	537.236i	0.845319	−	0.561375i
$958$	−967.578	+	558.631i	−1.01000	+	0.583122i
$959$	192.779	−	268.949i	0.201021	−	0.280448i
$960$	858.892	−	53.8572i	0.894679	−	0.0561013i
$961$	727.748			0.757282
$962$	−391.183	−	225.850i	−0.406635	−	0.234771i
$963$	−454.559	+	57.2316i	−0.472023	+	0.0594305i
$964$	603.269	−	348.298i	0.625798	−	0.361304i
$965$	−992.644	−	573.103i	−1.02865	−	0.593890i
$966$	247.792	−	131.507i	0.256513	−	0.136136i
$967$	277.066	+	479.892i	0.286521	+	0.496269i	0.972977	−	0.230902i	$-0.0741678\pi$
$967$	277.066	+	479.892i	0.286521	+	0.496269i	−0.686456	+	0.727172i	$0.740834\pi$
$968$	−89.0739	+	154.280i	−0.0920184	+	0.159381i
$969$	15.6187	−	10.3724i	0.0161184	−	0.0107042i
$970$	688.811	+	1193.06i	0.710115	+	1.22995i
$971$	1334.71	−	770.592i	1.37457	−	0.793607i	0.383069	−	0.923720i	$-0.374867\pi$
$971$	1334.71	−	770.592i	1.37457	−	0.793607i	0.991499	+	0.130113i	$0.0415340\pi$
$972$	726.851	+	155.289i	0.747790	+	0.159762i
$973$	1441.05	+	1032.92i	1.48104	+	1.06159i
$974$	51.3691	−	88.9739i	0.0527404	−	0.0913490i
$975$	858.682	−	53.8440i	0.880699	−	0.0552246i
$976$			43.5019i			0.0445716i
$977$	−1625.38			−1.66365			−0.831824	−	0.555039i	$-0.812703\pi$
$977$	−1625.38			−1.66365			−0.831824	+	0.555039i	$0.812703\pi$
$978$	−2043.84	−	1015.10i	−2.08982	−	1.03794i
$979$	−628.556	−	362.897i	−0.642039	−	0.370681i
$980$	−1306.35	+	443.068i	−1.33301	+	0.452110i
$981$	−238.435	−	314.399i	−0.243053	−	0.320488i
$982$	1157.53	+	2004.90i	1.17875	+	2.04165i
$983$	30.5458	−	17.6356i	0.0310740	−	0.0179406i	−0.484383	−	0.874856i	$-0.660956\pi$
$983$	30.5458	−	17.6356i	0.0310740	−	0.0179406i	0.515457	+	0.856916i	$0.327622\pi$
$984$	−186.718	+	375.944i	−0.189754	+	0.382057i
$985$	−917.466	−	529.699i	−0.931438	−	0.537766i
$986$	−334.429	+	193.082i	−0.339177	+	0.195824i
$987$	−572.088	+	913.955i	−0.579623	+	0.925993i
$988$	−14.4914	+	25.0998i	−0.0146674	+	0.0254047i
$989$	17.3499	+	30.0510i	0.0175429	+	0.0303852i
$990$	−1431.03	−	602.250i	−1.44548	−	0.608333i
$991$	567.488	−	982.918i	0.572642	−	0.991845i	−0.423652	−	0.905825i	$-0.639252\pi$
$991$	567.488	−	982.918i	0.572642	−	0.991845i	0.996293	−	0.0860197i	$-0.0274148\pi$
$992$		−	613.268i		−	0.618213i
$993$	−712.362	+	473.078i	−0.717384	+	0.476413i
$994$	−623.527	−	1376.63i	−0.627291	−	1.38494i
$995$	−556.155	−	963.288i	−0.558950	−	0.968129i
$996$	591.428	−	37.0857i	0.593803	−	0.0372347i
$997$	−44.4032	+	25.6362i	−0.0445368	+	0.0257133i	−0.522103	−	0.852882i	$-0.674852\pi$
$997$	−44.4032	+	25.6362i	−0.0445368	+	0.0257133i	0.477566	+	0.878596i	$0.341519\pi$
$998$	489.190	−	847.301i	0.490170	−	0.848999i
$999$	−723.919	+	624.081i	−0.724643	+	0.624705i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.3.t.a.52.12	yes	28
3.2	odd	2		189.3.t.a.73.3		28
7.2	even	3		441.3.k.b.313.3		28
7.3	odd	6		441.3.l.a.97.3		28
7.4	even	3		441.3.l.b.97.3		28
7.5	odd	6		63.3.k.a.61.3	yes	28
7.6	odd	2		441.3.t.a.178.12		28
9.4	even	3		63.3.k.a.31.3	✓	28
9.5	odd	6		189.3.k.a.10.12		28
21.5	even	6		189.3.k.a.19.12		28
63.4	even	3		441.3.l.a.391.3		28
63.5	even	6		189.3.t.a.145.3		28
63.13	odd	6		441.3.k.b.31.3		28
63.31	odd	6		441.3.l.b.391.3		28
63.40	odd	6	inner	63.3.t.a.40.12	yes	28
63.58	even	3		441.3.t.a.166.12		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.k.a.31.3	✓	28	9.4	even	3
63.3.k.a.61.3	yes	28	7.5	odd	6
63.3.t.a.40.12	yes	28	63.40	odd	6	inner
63.3.t.a.52.12	yes	28	1.1	even	1	trivial
189.3.k.a.10.12		28	9.5	odd	6
189.3.k.a.19.12		28	21.5	even	6
189.3.t.a.73.3		28	3.2	odd	2
189.3.t.a.145.3		28	63.5	even	6
441.3.k.b.31.3		28	63.13	odd	6
441.3.k.b.313.3		28	7.2	even	3
441.3.l.a.97.3		28	7.3	odd	6
441.3.l.a.391.3		28	63.4	even	3
441.3.l.b.97.3		28	7.4	even	3
441.3.l.b.391.3		28	63.31	odd	6
441.3.t.a.166.12		28	63.58	even	3
441.3.t.a.178.12		28	7.6	odd	2

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	63.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.65681 q^{2} +(-2.49911 + 1.65965i) q^{3} +3.05866 q^{4} +(7.97090 + 4.60200i) q^{5} +(-6.63967 + 4.40939i) q^{6} +(-2.88812 - 6.37642i) q^{7} -2.50096 q^{8} +(3.49110 - 8.29531i) q^{9} +O(q^{10})\)	\(q+2.65681 q^{2} +(-2.49911 + 1.65965i) q^{3} +3.05866 q^{4} +(7.97090 + 4.60200i) q^{5} +(-6.63967 + 4.40939i) q^{6} +(-2.88812 - 6.37642i) q^{7} -2.50096 q^{8} +(3.49110 - 8.29531i) q^{9} +(21.1772 + 12.2267i) q^{10} +(-3.52733 - 6.10952i) q^{11} +(-7.64393 + 5.07632i) q^{12} +(-4.15930 + 2.40137i) q^{13} +(-7.67319 - 16.9410i) q^{14} +(-27.5579 + 1.72803i) q^{15} -18.8792 q^{16} +(-2.74329 - 1.58384i) q^{17} +(9.27520 - 22.0391i) q^{18} +(1.70864 - 0.986484i) q^{19} +(24.3803 + 14.0760i) q^{20} +(17.8004 + 11.1421i) q^{21} +(-9.37147 - 16.2319i) q^{22} +(2.51399 - 4.35435i) q^{23} +(6.25018 - 4.15073i) q^{24} +(29.8569 + 51.7136i) q^{25} +(-11.0505 + 6.38000i) q^{26} +(5.04271 + 26.5249i) q^{27} +(-8.83378 - 19.5033i) q^{28} +(22.9425 - 39.7376i) q^{29} +(-73.2162 + 4.59105i) q^{30} +15.2726i q^{31} -40.1548 q^{32} +(18.9549 + 9.41421i) q^{33} +(-7.28840 - 4.20796i) q^{34} +(6.32341 - 64.1170i) q^{35} +(10.6781 - 25.3726i) q^{36} +(17.6998 + 30.6570i) q^{37} +(4.53954 - 2.62090i) q^{38} +(6.40909 - 12.9043i) q^{39} +(-19.9349 - 11.5094i) q^{40} +(-48.4509 + 27.9732i) q^{41} +(47.2923 + 29.6025i) q^{42} +(-3.45068 + 5.97676i) q^{43} +(-10.7889 - 18.6870i) q^{44} +(66.0023 - 50.0551i) q^{45} +(6.67920 - 11.5687i) q^{46} +51.3447i q^{47} +(47.1813 - 31.3330i) q^{48} +(-32.3175 + 36.8317i) q^{49} +(79.3241 + 137.393i) q^{50} +(9.48440 - 0.594723i) q^{51} +(-12.7219 + 7.34498i) q^{52} +(-10.3556 + 17.9365i) q^{53} +(13.3975 + 70.4718i) q^{54} -64.9312i q^{55} +(7.22307 + 15.9472i) q^{56} +(-2.63286 + 5.30108i) q^{57} +(60.9540 - 105.575i) q^{58} -49.3508i q^{59} +(-84.2903 + 5.28546i) q^{60} -2.30422i q^{61} +40.5764i q^{62} +(-62.9771 + 1.69713i) q^{63} -31.1668 q^{64} -44.2045 q^{65} +(50.3596 + 25.0118i) q^{66} +30.8279 q^{67} +(-8.39079 - 4.84442i) q^{68} +(0.943990 + 15.0544i) q^{69} +(16.8001 - 170.347i) q^{70} +81.2604 q^{71} +(-8.73110 + 20.7463i) q^{72} +(-61.7481 - 35.6503i) q^{73} +(47.0251 + 81.4499i) q^{74} +(-160.442 - 79.6859i) q^{75} +(5.22615 - 3.01732i) q^{76} +(-28.7695 + 40.1368i) q^{77} +(17.0278 - 34.2843i) q^{78} -29.0358 q^{79} +(-150.485 - 86.8823i) q^{80} +(-56.6245 - 57.9195i) q^{81} +(-128.725 + 74.3195i) q^{82} +(-55.9283 - 32.2902i) q^{83} +(54.4453 + 34.0799i) q^{84} +(-14.5776 - 25.2492i) q^{85} +(-9.16783 + 15.8791i) q^{86} +(8.61480 + 137.385i) q^{87} +(8.82172 + 15.2797i) q^{88} +(89.0979 - 51.4407i) q^{89} +(175.356 - 132.987i) q^{90} +(27.3247 + 19.5860i) q^{91} +(7.68944 - 13.3185i) q^{92} +(-25.3472 - 38.1679i) q^{93} +136.413i q^{94} +18.1592 q^{95} +(100.351 - 66.6430i) q^{96} +(48.7891 + 28.1684i) q^{97} +(-85.8617 + 97.8551i) q^{98} +(-62.9946 + 7.93140i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 3 q^{3} + 46 q^{4} - 3 q^{5} - 12 q^{6} - 16 q^{8} - 15 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 - 3 * q^3 + 46 * q^4 - 3 * q^5 - 12 * q^6 - 16 * q^8 - 15 * q^9	\( 28 q - 2 q^{2} - 3 q^{3} + 46 q^{4} - 3 q^{5} - 12 q^{6} - 16 q^{8} - 15 q^{9} - 6 q^{10} + 7 q^{11} - 30 q^{12} - 15 q^{13} + 10 q^{14} - 18 q^{15} + 54 q^{16} - 33 q^{17} - 42 q^{18} - 6 q^{19} - 108 q^{20} + 21 q^{21} - 10 q^{22} + 34 q^{23} - 78 q^{24} + 31 q^{25} + 54 q^{26} + 81 q^{27} - 16 q^{28} + 70 q^{29} - 27 q^{30} - 306 q^{32} - 3 q^{33} - 12 q^{34} + 18 q^{35} - 174 q^{36} + 9 q^{37} + 87 q^{38} + 129 q^{39} - 102 q^{40} + 234 q^{41} + 306 q^{42} + 30 q^{43} + 51 q^{44} + 273 q^{45} - 22 q^{46} - 147 q^{48} - 38 q^{49} + 241 q^{50} + 12 q^{51} - 219 q^{52} + 148 q^{53} + 171 q^{54} + 110 q^{56} + 189 q^{57} + 17 q^{58} + 33 q^{60} - 471 q^{63} - 48 q^{64} - 228 q^{65} + 258 q^{66} + 68 q^{67} - 18 q^{68} - 78 q^{69} - 225 q^{70} - 350 q^{71} + 162 q^{72} - 6 q^{73} + 359 q^{74} - 510 q^{75} - 72 q^{76} - 224 q^{77} - 375 q^{78} + 164 q^{79} - 609 q^{80} - 435 q^{81} - 18 q^{82} - 738 q^{83} - 21 q^{84} + 3 q^{85} + 17 q^{86} - 561 q^{87} + 25 q^{88} + 21 q^{89} + 543 q^{90} + 39 q^{91} + 288 q^{92} - 222 q^{93} - 1014 q^{95} + 231 q^{96} + 57 q^{97} + 811 q^{98} - 162 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 - 3 * q^3 + 46 * q^4 - 3 * q^5 - 12 * q^6 - 16 * q^8 - 15 * q^9 - 6 * q^10 + 7 * q^11 - 30 * q^12 - 15 * q^13 + 10 * q^14 - 18 * q^15 + 54 * q^16 - 33 * q^17 - 42 * q^18 - 6 * q^19 - 108 * q^20 + 21 * q^21 - 10 * q^22 + 34 * q^23 - 78 * q^24 + 31 * q^25 + 54 * q^26 + 81 * q^27 - 16 * q^28 + 70 * q^29 - 27 * q^30 - 306 * q^32 - 3 * q^33 - 12 * q^34 + 18 * q^35 - 174 * q^36 + 9 * q^37 + 87 * q^38 + 129 * q^39 - 102 * q^40 + 234 * q^41 + 306 * q^42 + 30 * q^43 + 51 * q^44 + 273 * q^45 - 22 * q^46 - 147 * q^48 - 38 * q^49 + 241 * q^50 + 12 * q^51 - 219 * q^52 + 148 * q^53 + 171 * q^54 + 110 * q^56 + 189 * q^57 + 17 * q^58 + 33 * q^60 - 471 * q^63 - 48 * q^64 - 228 * q^65 + 258 * q^66 + 68 * q^67 - 18 * q^68 - 78 * q^69 - 225 * q^70 - 350 * q^71 + 162 * q^72 - 6 * q^73 + 359 * q^74 - 510 * q^75 - 72 * q^76 - 224 * q^77 - 375 * q^78 + 164 * q^79 - 609 * q^80 - 435 * q^81 - 18 * q^82 - 738 * q^83 - 21 * q^84 + 3 * q^85 + 17 * q^86 - 561 * q^87 + 25 * q^88 + 21 * q^89 + 543 * q^90 + 39 * q^91 + 288 * q^92 - 222 * q^93 - 1014 * q^95 + 231 * q^96 + 57 * q^97 + 811 * q^98 - 162 * q^99

Introduction

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