LMFDB - Embedded newform 75.3.j.a.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,3,Mod(11,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 8]))

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

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

chi := DirichletCharacter("75.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	75.j (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.04360198270$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			41.1
Character	$\chi$	$=$	75.41
Dual form			75.3.j.a.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.26850 + 3.12232i) q^{2} +(0.549348 + 2.94927i) q^{3} +(-3.36674 - 10.3618i) q^{4} +(-3.89421 - 3.13610i) q^{5} +(-10.4548 - 4.97519i) q^{6} -5.08243 q^{7} +(25.3081 + 8.22311i) q^{8} +(-8.39643 + 3.24035i) q^{9} +O(q^{10})$	\(q+(-2.26850 + 3.12232i) q^{2} +(0.549348 + 2.94927i) q^{3} +(-3.36674 - 10.3618i) q^{4} +(-3.89421 - 3.13610i) q^{5} +(-10.4548 - 4.97519i) q^{6} -5.08243 q^{7} +(25.3081 + 8.22311i) q^{8} +(-8.39643 + 3.24035i) q^{9} +(18.6259 - 5.04472i) q^{10} +(-0.876573 + 1.20650i) q^{11} +(28.7101 - 15.6216i) q^{12} +(-6.15884 + 4.47466i) q^{13} +(11.5295 - 15.8690i) q^{14} +(7.10995 - 13.2079i) q^{15} +(-47.8298 + 34.7504i) q^{16} +(-9.55783 - 3.10553i) q^{17} +(8.92988 - 33.5671i) q^{18} +(0.414770 - 1.27653i) q^{19} +(-19.3847 + 50.9093i) q^{20} +(-2.79202 - 14.9895i) q^{21} +(-1.77857 - 5.47389i) q^{22} +(-11.3794 + 15.6624i) q^{23} +(-10.3492 + 79.1580i) q^{24} +(5.32971 + 24.4253i) q^{25} -29.3806i q^{26} +(-14.1693 - 22.9833i) q^{27} +(17.1112 + 52.6629i) q^{28} +(-23.4047 + 7.60466i) q^{29} +(25.1104 + 52.1617i) q^{30} +(10.6713 - 32.8429i) q^{31} -121.729i q^{32} +(-4.03984 - 1.92247i) q^{33} +(31.3784 - 22.7978i) q^{34} +(19.7921 + 15.9390i) q^{35} +(61.8443 + 76.0924i) q^{36} +(-39.9646 + 29.0360i) q^{37} +(3.04484 + 4.19086i) q^{38} +(-16.5803 - 15.7060i) q^{39} +(-72.7666 - 111.391i) q^{40} +(25.2193 + 34.7113i) q^{41} +(53.1357 + 25.2861i) q^{42} +33.8714 q^{43} +(15.4526 + 5.02087i) q^{44} +(42.8595 + 13.7135i) q^{45} +(-23.0889 - 71.0602i) q^{46} +(-16.9342 + 5.50226i) q^{47} +(-128.764 - 121.973i) q^{48} -23.1689 q^{49} +(-88.3540 - 38.7677i) q^{50} +(3.90848 - 29.8947i) q^{51} +(67.1005 + 48.7513i) q^{52} +(39.4840 - 12.8291i) q^{53} +(103.904 + 7.89666i) q^{54} +(7.19727 - 1.94934i) q^{55} +(-128.627 - 41.7934i) q^{56} +(3.99269 + 0.522012i) q^{57} +(29.3494 - 90.3283i) q^{58} +(39.6675 + 54.5977i) q^{59} +(-160.794 - 29.2041i) q^{60} +(34.9695 + 25.4068i) q^{61} +(78.3383 + 107.823i) q^{62} +(42.6743 - 16.4689i) q^{63} +(188.758 + 137.141i) q^{64} +(38.0168 + 1.88950i) q^{65} +(15.1669 - 8.25257i) q^{66} +(-20.7554 + 63.8784i) q^{67} +109.491i q^{68} +(-52.4439 - 24.9568i) q^{69} +(-94.6651 + 25.6395i) q^{70} +(-34.7343 + 11.2859i) q^{71} +(-239.144 + 12.9625i) q^{72} +(51.3438 + 37.3034i) q^{73} -190.650i q^{74} +(-69.1090 + 29.1368i) q^{75} -14.6235 q^{76} +(4.45513 - 6.13196i) q^{77} +(86.6515 - 16.1402i) q^{78} +(-38.2940 - 117.857i) q^{79} +(295.240 + 14.6740i) q^{80} +(60.0002 - 54.4148i) q^{81} -165.590 q^{82} +(-90.7253 - 29.4784i) q^{83} +(-145.917 + 79.3959i) q^{84} +(27.4809 + 42.0679i) q^{85} +(-76.8374 + 105.758i) q^{86} +(-35.2856 - 64.8494i) q^{87} +(-32.1056 + 23.3261i) q^{88} +(-62.7307 + 86.3414i) q^{89} +(-140.045 + 102.712i) q^{90} +(31.3019 - 22.7421i) q^{91} +(200.601 + 65.1792i) q^{92} +(102.725 + 13.4304i) q^{93} +(21.2355 - 65.3560i) q^{94} +(-5.61854 + 3.67032i) q^{95} +(359.012 - 66.8716i) q^{96} +(30.7650 + 94.6849i) q^{97} +(52.5586 - 72.3407i) q^{98} +(3.45061 - 12.9707i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - q^{3} + 26 q^{4} - 11 q^{6} - 8 q^{7} - 13 q^{9}+O(q^{10}) $ 72 * q - q^3 + 26 * q^4 - 11 * q^6 - 8 * q^7 - 13 * q^9	$ 72 q - q^{3} + 26 q^{4} - 11 q^{6} - 8 q^{7} - 13 q^{9} - 20 q^{10} + 31 q^{12} - 42 q^{13} + 45 q^{15} - 130 q^{16} + 30 q^{18} - 36 q^{19} - 60 q^{21} - 70 q^{22} - 72 q^{24} + 100 q^{25} - 154 q^{27} - 62 q^{28} + 15 q^{30} + 114 q^{31} - 10 q^{33} + 178 q^{34} + 271 q^{36} - 98 q^{37} - 155 q^{39} - 120 q^{40} - 475 q^{42} - 52 q^{43} + 35 q^{45} + 198 q^{46} - 326 q^{48} + 112 q^{49} + 44 q^{51} + 412 q^{52} + 304 q^{54} + 10 q^{55} + 622 q^{57} + 190 q^{58} + 360 q^{60} - 306 q^{61} + 293 q^{63} + 474 q^{64} + 320 q^{66} + 472 q^{67} + 269 q^{69} - 840 q^{70} + 175 q^{72} + 318 q^{73} - 310 q^{75} + 112 q^{76} + 815 q^{78} - 346 q^{79} - 373 q^{81} - 1620 q^{82} - 730 q^{84} - 530 q^{85} - 370 q^{87} - 810 q^{88} - 230 q^{90} - 550 q^{91} - 272 q^{93} - 612 q^{94} - 698 q^{96} + 182 q^{97} - 160 q^{99}+O(q^{100}) $ 72 * q - q^3 + 26 * q^4 - 11 * q^6 - 8 * q^7 - 13 * q^9 - 20 * q^10 + 31 * q^12 - 42 * q^13 + 45 * q^15 - 130 * q^16 + 30 * q^18 - 36 * q^19 - 60 * q^21 - 70 * q^22 - 72 * q^24 + 100 * q^25 - 154 * q^27 - 62 * q^28 + 15 * q^30 + 114 * q^31 - 10 * q^33 + 178 * q^34 + 271 * q^36 - 98 * q^37 - 155 * q^39 - 120 * q^40 - 475 * q^42 - 52 * q^43 + 35 * q^45 + 198 * q^46 - 326 * q^48 + 112 * q^49 + 44 * q^51 + 412 * q^52 + 304 * q^54 + 10 * q^55 + 622 * q^57 + 190 * q^58 + 360 * q^60 - 306 * q^61 + 293 * q^63 + 474 * q^64 + 320 * q^66 + 472 * q^67 + 269 * q^69 - 840 * q^70 + 175 * q^72 + 318 * q^73 - 310 * q^75 + 112 * q^76 + 815 * q^78 - 346 * q^79 - 373 * q^81 - 1620 * q^82 - 730 * q^84 - 530 * q^85 - 370 * q^87 - 810 * q^88 - 230 * q^90 - 550 * q^91 - 272 * q^93 - 612 * q^94 - 698 * q^96 + 182 * q^97 - 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−2.26850	+	3.12232i	−1.13425	+	1.56116i	−0.354517	+	0.935050i	$0.615355\pi$
$2$	−2.26850	+	3.12232i	−1.13425	+	1.56116i	−0.779733	+	0.626112i	$0.784645\pi$
$3$	0.549348	+	2.94927i	0.183116	+	0.983091i
$3$	0.549348	+	2.94927i	0.183116	+	0.983091i
$4$	−3.36674	−	10.3618i	−0.841684	−	2.59044i
$5$	−3.89421	−	3.13610i	−0.778842	−	0.627221i
$5$	−3.89421	−	3.13610i	−0.778842	−	0.627221i
$6$	−10.4548	−	4.97519i	−1.74246	−	0.829198i
$7$	−5.08243			−0.726062			−0.363031	−	0.931777i	$-0.618258\pi$
$7$	−5.08243			−0.726062			−0.363031	+	0.931777i	$0.618258\pi$
$8$	25.3081	+	8.22311i	3.16352	+	1.02789i
$9$	−8.39643	+	3.24035i	−0.932937	+	0.360039i
$10$	18.6259	−	5.04472i	1.86259	−	0.504472i
$11$	−0.876573	+	1.20650i	−0.0796885	+	0.109682i	−0.847000	−	0.531592i	$-0.821594\pi$
$11$	−0.876573	+	1.20650i	−0.0796885	+	0.109682i	0.767312	+	0.641274i	$0.221594\pi$
$12$	28.7101	−	15.6216i	2.39251	−	1.30180i
$13$	−6.15884	+	4.47466i	−0.473757	+	0.344204i	−0.798904	−	0.601459i	$-0.794586\pi$
$13$	−6.15884	+	4.47466i	−0.473757	+	0.344204i	0.325147	+	0.945664i	$0.394586\pi$
$14$	11.5295	−	15.8690i	0.823536	−	1.13350i
$15$	7.10995	−	13.2079i	0.473997	−	0.880527i
$16$	−47.8298	+	34.7504i	−2.98936	+	2.17190i
$17$	−9.55783	−	3.10553i	−0.562226	−	0.182678i	0.0140968	−	0.999901i	$-0.495513\pi$
$17$	−9.55783	−	3.10553i	−0.562226	−	0.182678i	−0.576322	+	0.817222i	$0.695513\pi$
$18$	8.92988	−	33.5671i	0.496105	−	1.86484i
$19$	0.414770	−	1.27653i	0.0218300	−	0.0671859i	−0.939548	−	0.342417i	$-0.888754\pi$
$19$	0.414770	−	1.27653i	0.0218300	−	0.0671859i	0.961378	+	0.275231i	$0.0887544\pi$
$20$	−19.3847	+	50.9093i	−0.969237	+	2.54546i
$21$	−2.79202	−	14.9895i	−0.132953	−	0.713785i
$22$	−1.77857	−	5.47389i	−0.0808443	−	0.248813i
$23$	−11.3794	+	15.6624i	−0.494756	+	0.680973i	−0.981256	−	0.192708i	$-0.938273\pi$
$23$	−11.3794	+	15.6624i	−0.494756	+	0.680973i	0.486501	+	0.873680i	$0.338273\pi$
$24$	−10.3492	+	79.1580i	−0.431219	+	3.29825i
$25$	5.32971	+	24.4253i	0.213189	+	0.977011i
$26$		−	29.3806i		−	1.13002i
$27$	−14.1693	−	22.9833i	−0.524787	−	0.851234i
$28$	17.1112	+	52.6629i	0.611115	+	1.88082i
$29$	−23.4047	+	7.60466i	−0.807060	+	0.262230i	−0.683352	−	0.730089i	$-0.739479\pi$
$29$	−23.4047	+	7.60466i	−0.807060	+	0.262230i	−0.123708	+	0.992319i	$0.539479\pi$
$30$	25.1104	+	52.1617i	0.837013	+	1.73872i
$31$	10.6713	−	32.8429i	0.344236	−	1.05945i	−0.617756	−	0.786370i	$-0.711958\pi$
$31$	10.6713	−	32.8429i	0.344236	−	1.05945i	0.961992	−	0.273079i	$-0.0880421\pi$
$32$		−	121.729i		−	3.80403i
$33$	−4.03984	−	1.92247i	−0.122419	−	0.0582566i
$34$	31.3784	−	22.7978i	0.922894	−	0.670522i
$35$	19.7921	+	15.9390i	0.565487	+	0.455401i
$36$	61.8443	+	76.0924i	1.71790	+	2.11368i
$37$	−39.9646	+	29.0360i	−1.08012	+	0.784755i	−0.977704	−	0.209986i	$-0.932658\pi$
$37$	−39.9646	+	29.0360i	−1.08012	+	0.784755i	−0.102419	+	0.994741i	$0.532658\pi$
$38$	3.04484	+	4.19086i	0.0801273	+	0.110286i
$39$	−16.5803	−	15.7060i	−0.425137	−	0.402717i
$40$	−72.7666	−	111.391i	−1.81917	−	2.78479i
$41$	25.2193	+	34.7113i	0.615104	+	0.846618i	0.996985	−	0.0775936i	$-0.0247237\pi$
$41$	25.2193	+	34.7113i	0.615104	+	0.846618i	−0.381881	+	0.924211i	$0.624724\pi$
$42$	53.1357	+	25.2861i	1.26514	+	0.602049i
$43$	33.8714			0.787708			0.393854	−	0.919173i	$-0.371142\pi$
$43$	33.8714			0.787708			0.393854	+	0.919173i	$0.371142\pi$
$44$	15.4526	+	5.02087i	0.351197	+	0.114111i
$45$	42.8595	+	13.7135i	0.952434	+	0.304744i
$46$	−23.0889	−	71.0602i	−0.501932	−	1.54479i
$47$	−16.9342	+	5.50226i	−0.360303	+	0.117069i	−0.483574	−	0.875304i	$-0.660662\pi$
$47$	−16.9342	+	5.50226i	−0.360303	+	0.117069i	0.123271	+	0.992373i	$0.460662\pi$
$48$	−128.764	−	121.973i	−2.68257	−	2.54111i
$49$	−23.1689			−0.472834
$50$	−88.3540	−	38.7677i	−1.76708	−	0.775353i
$51$	3.90848	−	29.8947i	0.0766369	−	0.586170i
$52$	67.1005	+	48.7513i	1.29039	+	0.937526i
$53$	39.4840	−	12.8291i	0.744982	−	0.242059i	0.0881614	−	0.996106i	$-0.471901\pi$
$53$	39.4840	−	12.8291i	0.744982	−	0.242059i	0.656821	+	0.754047i	$0.271901\pi$
$54$	103.904	+	7.89666i	1.92415	+	0.146234i
$55$	7.19727	−	1.94934i	0.130859	−	0.0354425i
$56$	−128.627	−	41.7934i	−2.29691	−	0.746311i
$57$	3.99269	+	0.522012i	0.0700473	+	0.00915810i
$58$	29.3494	−	90.3283i	0.506025	−	1.55738i
$59$	39.6675	+	54.5977i	0.672331	+	0.925384i	0.999810	−	0.0194743i	$-0.00619926\pi$
$59$	39.6675	+	54.5977i	0.672331	+	0.925384i	−0.327480	+	0.944858i	$0.606199\pi$
$60$	−160.794	−	29.2041i	−2.67991	−	0.486734i
$61$	34.9695	+	25.4068i	0.573270	+	0.416505i	0.836291	−	0.548285i	$-0.184719\pi$
$61$	34.9695	+	25.4068i	0.573270	+	0.416505i	−0.263022	+	0.964790i	$0.584719\pi$
$62$	78.3383	+	107.823i	1.26352	+	1.73909i
$63$	42.6743	−	16.4689i	0.677370	−	0.261411i
$64$	188.758	+	137.141i	2.94935	+	2.14283i
$65$	38.0168	+	1.88950i	0.584873	+	0.0290693i
$66$	15.1669	−	8.25257i	0.229802	−	0.125039i
$67$	−20.7554	+	63.8784i	−0.309782	+	0.953410i	0.668068	+	0.744100i	$0.267122\pi$
$67$	−20.7554	+	63.8784i	−0.309782	+	0.953410i	−0.977849	+	0.209309i	$0.932878\pi$
$68$			109.491i			1.61017i
$69$	−52.4439	−	24.9568i	−0.760056	−	0.361693i
$70$	−94.6651	+	25.6395i	−1.35236	+	0.366278i
$71$	−34.7343	+	11.2859i	−0.489216	+	0.158956i	−0.543229	−	0.839584i	$-0.682799\pi$
$71$	−34.7343	+	11.2859i	−0.489216	+	0.158956i	0.0540135	+	0.998540i	$0.482799\pi$
$72$	−239.144	+	12.9625i	−3.32144	+	0.180035i
$73$	51.3438	+	37.3034i	0.703339	+	0.511006i	0.881018	−	0.473083i	$-0.156859\pi$
$73$	51.3438	+	37.3034i	0.703339	+	0.511006i	−0.177679	+	0.984089i	$0.556859\pi$
$74$		−	190.650i		−	2.57636i
$75$	−69.1090	+	29.1368i	−0.921453	+	0.388490i
$76$	−14.6235			−0.192415
$77$	4.45513	−	6.13196i	0.0578588	−	0.0796358i
$78$	86.6515	−	16.1402i	1.11092	−	0.206925i
$79$	−38.2940	−	117.857i	−0.484734	−	1.49186i	−0.832366	−	0.554226i	$-0.813014\pi$
$79$	−38.2940	−	117.857i	−0.484734	−	1.49186i	0.347633	−	0.937631i	$-0.386986\pi$
$80$	295.240	+	14.6740i	3.69050	+	0.183425i
$81$	60.0002	−	54.4148i	0.740743	−	0.671788i
$82$	−165.590			−2.01939
$83$	−90.7253	−	29.4784i	−1.09308	−	0.355162i	−0.293641	−	0.955916i	$-0.594867\pi$
$83$	−90.7253	−	29.4784i	−1.09308	−	0.355162i	−0.799434	+	0.600754i	$0.794867\pi$
$84$	−145.917	+	79.3959i	−1.73711	+	0.945190i
$85$	27.4809	+	42.0679i	0.323305	+	0.494917i
$86$	−76.8374	+	105.758i	−0.893458	+	1.22974i
$87$	−35.2856	−	64.8494i	−0.405581	−	0.745395i
$88$	−32.1056	+	23.3261i	−0.364837	+	0.265069i
$89$	−62.7307	+	86.3414i	−0.704839	+	0.970128i	0.295053	+	0.955481i	$0.404663\pi$
$89$	−62.7307	+	86.3414i	−0.704839	+	0.970128i	−0.999893	+	0.0146473i	$0.995337\pi$
$90$	−140.045	+	102.712i	−1.55605	+	1.14125i
$91$	31.3019	−	22.7421i	0.343977	−	0.249914i
$92$	200.601	+	65.1792i	2.18045	+	0.708470i
$93$	102.725	+	13.4304i	1.10457	+	0.144413i
$94$	21.2355	−	65.3560i	0.225909	−	0.695277i
$95$	−5.61854	+	3.67032i	−0.0591425	+	0.0386349i
$96$	359.012	−	66.8716i	3.73971	−	0.696579i
$97$	30.7650	+	94.6849i	0.317165	+	0.976133i	0.974854	+	0.222844i	$0.0715340\pi$
$97$	30.7650	+	94.6849i	0.317165	+	0.976133i	−0.657689	+	0.753289i	$0.728466\pi$
$98$	52.5586	−	72.3407i	0.536312	−	0.738170i
$99$	3.45061	−	12.9707i	0.0348546	−	0.131017i
$100$	235.145	−	137.459i	2.35145	−	1.37459i
$101$		−	172.115i		−	1.70411i	−0.523449	−	0.852057i	$-0.675355\pi$
$101$		−	172.115i		−	1.70411i	0.523449	−	0.852057i	$-0.324645\pi$
$102$	84.4745	+	80.0196i	0.828181	+	0.784506i
$103$	−8.29268	−	25.5222i	−0.0805114	−	0.247789i	0.902696	−	0.430278i	$-0.141584\pi$
$103$	−8.29268	−	25.5222i	−0.0805114	−	0.247789i	−0.983208	+	0.182489i	$0.941584\pi$
$104$	−192.664	+	62.6004i	−1.85254	+	0.601927i
$105$	−36.1359	+	67.1283i	−0.344151	+	0.639317i
$106$	−49.5128	+	152.385i	−0.467102	+	1.43759i
$107$		−	128.403i		−	1.20003i	−0.799989	−	0.600015i	$-0.795161\pi$
$107$		−	128.403i		−	1.20003i	0.799989	−	0.600015i	$-0.204839\pi$
$108$	−190.443	+	224.197i	−1.76336	+	2.07590i
$109$	51.6182	−	37.5028i	0.473561	−	0.344062i	−0.325266	−	0.945622i	$-0.605454\pi$
$109$	51.6182	−	37.5028i	0.473561	−	0.344062i	0.798828	+	0.601560i	$0.205454\pi$
$110$	−10.2405	+	26.8943i	−0.0930959	+	0.244493i
$111$	−107.589	−	101.916i	−0.969274	−	0.918159i
$112$	243.092	−	176.616i	2.17046	−	1.57693i
$113$	−70.2784	−	96.7299i	−0.621932	−	0.856016i	0.375559	−	0.926798i	$-0.377451\pi$
$113$	−70.2784	−	96.7299i	−0.621932	−	0.856016i	−0.997492	+	0.0707819i	$0.977451\pi$
$114$	−10.6873	+	11.2823i	−0.0937484	+	0.0989675i
$115$	93.4325	−	25.3056i	0.812456	−	0.220049i
$116$	157.595	+	216.911i	1.35858	+	1.86992i
$117$	37.2128	−	57.5280i	0.318058	−	0.491692i
$118$	−260.457			−2.20726
$119$	48.5771	+	15.7836i	0.408211	+	0.132636i
$120$	288.550	−	275.801i	2.40458	−	2.29834i
$121$	36.7038	+	112.963i	0.303337	+	0.933576i
$122$	−158.656	+	51.5506i	−1.30046	+	0.422546i
$123$	−88.5191	+	93.4471i	−0.719667	+	0.759732i
$124$	−376.238			−3.03418
$125$	55.8452	−	111.832i	0.446761	−	0.894653i
$126$	−45.3855	+	170.603i	−0.360203	+	1.35399i
$127$	−112.968	−	82.0758i	−0.889509	−	0.646266i	0.0462411	−	0.998930i	$-0.485276\pi$
$127$	−112.968	−	82.0758i	−0.889509	−	0.646266i	−0.935750	+	0.352664i	$0.885276\pi$
$128$	−393.311	+	127.795i	−3.07275	+	0.998396i
$129$	18.6072	+	99.8962i	0.144242	+	0.774389i
$130$	−92.1407	+	114.414i	−0.708775	+	0.880110i
$131$	60.1938	+	19.5582i	0.459495	+	0.149299i	0.529612	−	0.848240i	$-0.322337\pi$
$131$	60.1938	+	19.5582i	0.459495	+	0.149299i	−0.0701175	+	0.997539i	$0.522337\pi$
$132$	−6.31904	+	48.3323i	−0.0478715	+	0.366154i
$133$	−2.10804	+	6.48789i	−0.0158499	+	0.0487811i
$134$	−152.366	−	209.713i	−1.13706	−	1.56502i
$135$	−16.9000	+	133.938i	−0.125185	+	0.992133i
$136$	−216.354	−	157.190i	−1.59084	−	1.15581i
$137$	13.9573	+	19.2105i	0.101878	+	0.140223i	0.856912	−	0.515462i	$-0.172380\pi$
$137$	13.9573	+	19.2105i	0.101878	+	0.140223i	−0.755034	+	0.655685i	$0.772380\pi$
$138$	196.892	−	107.132i	1.42675	−	0.776320i
$139$	−33.6767	−	24.4675i	−0.242278	−	0.176026i	0.460019	−	0.887909i	$-0.347842\pi$
$139$	−33.6767	−	24.4675i	−0.242278	−	0.176026i	−0.702298	+	0.711883i	$0.747842\pi$
$140$	98.5217	−	258.743i	0.703726	−	1.84816i
$141$	−25.5305	−	46.9210i	−0.181067	−	0.332773i
$142$	43.5567	−	134.054i	0.306737	−	0.944041i
$143$		−	11.3530i		−	0.0793916i
$144$	288.996	−	446.765i	2.00692	−	3.10253i
$145$	114.992	+	43.7855i	0.793047	+	0.301969i
$146$	−232.947	+	75.6890i	−1.59553	+	0.518418i
$147$	−12.7278	−	68.3313i	−0.0865834	−	0.464839i
$148$	435.414	+	316.346i	2.94198	+	2.13748i
$149$			78.8939i			0.529489i	0.964319	+	0.264745i	$0.0852877\pi$
$149$			78.8939i			0.529489i	−0.964319	+	0.264745i	$0.914712\pi$
$150$	65.7994	−	281.877i	0.438662	−	1.87918i
$151$	13.5286			0.0895931			0.0447966	−	0.998996i	$-0.485736\pi$
$151$	13.5286			0.0895931			0.0447966	+	0.998996i	$0.485736\pi$
$152$	20.9941	−	28.8959i	0.138119	−	0.190105i
$153$	90.3147	−	4.89539i	0.590292	−	0.0319960i
$154$	9.03949	+	27.8207i	0.0586980	+	0.180654i
$155$	−144.555	+	94.4308i	−0.932614	+	0.609231i
$156$	−106.920	+	224.679i	−0.685382	+	1.44025i
$157$	83.8758			0.534241			0.267121	−	0.963663i	$-0.413928\pi$
$157$	83.8758			0.534241			0.267121	+	0.963663i	$0.413928\pi$
$158$	454.856	+	147.792i	2.87884	+	0.935391i
$159$	59.5271	+	109.402i	0.374384	+	0.688060i
$160$	−381.755	+	474.038i	−2.38597	+	2.96274i
$161$	57.8349	−	79.6030i	0.359223	−	0.494428i
$162$	33.7901	+	310.780i	0.208581	+	1.91840i
$163$	−107.354	+	77.9976i	−0.658616	+	0.478513i	−0.866195	−	0.499705i	$-0.833442\pi$
$163$	−107.354	+	77.9976i	−0.658616	+	0.478513i	0.207579	+	0.978218i	$0.433442\pi$
$164$	274.764	−	378.180i	1.67539	−	2.30597i
$165$	9.70293	+	20.1559i	0.0588056	+	0.122157i
$166$	297.851	−	216.402i	1.79429	−	1.30362i
$167$	4.69984	+	1.52707i	0.0281427	+	0.00914413i	0.323055	−	0.946380i	$-0.395290\pi$
$167$	4.69984	+	1.52707i	0.0281427	+	0.00914413i	−0.294912	+	0.955524i	$0.595290\pi$
$168$	52.5994	−	402.315i	0.313091	−	2.39473i
$169$	−34.3152	+	105.611i	−0.203048	+	0.624918i
$170$	−193.690	−	9.62676i	−1.13935	−	0.0566280i
$171$	0.653822	+	12.0623i	0.00382352	+	0.0705399i
$172$	−114.036	−	350.968i	−0.663002	−	2.04051i
$173$	−139.909	+	192.568i	−0.808722	+	1.11311i	0.182797	+	0.983151i	$0.441485\pi$
$173$	−139.909	+	192.568i	−0.808722	+	1.11311i	−0.991519	+	0.129960i	$0.958515\pi$
$174$	282.526	+	36.9379i	1.62371	+	0.212287i
$175$	−27.0879	−	124.140i	−0.154788	−	0.709371i
$176$		−	88.1679i		−	0.500954i
$177$	−139.232	+	146.983i	−0.786623	+	0.830415i
$178$	−127.281	−	391.731i	−0.715062	−	2.20074i
$179$	308.274	−	100.164i	1.72220	−	0.559577i	0.729913	−	0.683540i	$-0.239561\pi$
$179$	308.274	−	100.164i	1.72220	−	0.559577i	0.992287	+	0.123964i	$0.0395606\pi$
$180$	−2.20121	−	490.270i	−0.0122289	−	2.72372i
$181$	11.3373	−	34.8925i	0.0626368	−	0.192776i	−0.914841	−	0.403814i	$-0.867684\pi$
$181$	11.3373	−	34.8925i	0.0626368	−	0.192776i	0.977478	+	0.211038i	$0.0676843\pi$
$182$			149.325i			0.820468i
$183$	−55.7212	+	117.092i	−0.304487	+	0.639845i
$184$	−416.784	+	302.812i	−2.26513	+	1.64572i
$185$	246.690	+	12.2609i	1.33346	+	0.0662754i
$186$	−274.966	+	290.274i	−1.47831	+	1.56061i
$187$	12.1250	−	8.80930i	0.0648394	−	0.0471086i
$188$	114.026	+	156.944i	0.606522	+	0.834806i
$189$	72.0143	+	116.811i	0.381028	+	0.618048i
$190$	1.28574	−	25.8690i	0.00676703	−	0.136153i
$191$	47.6293	+	65.5562i	0.249368	+	0.343226i	0.915290	−	0.402796i	$-0.131961\pi$
$191$	47.6293	+	65.5562i	0.249368	+	0.343226i	−0.665922	+	0.746022i	$0.731961\pi$
$192$	−300.772	+	632.038i	−1.56652	+	3.29186i
$193$	−351.090			−1.81912			−0.909561	−	0.415571i	$-0.863582\pi$
$193$	−351.090			−1.81912			−0.909561	+	0.415571i	$0.863582\pi$
$194$	−365.427	−	118.734i	−1.88365	−	0.612033i
$195$	15.3118	+	113.160i	0.0785219	+	0.580307i
$196$	78.0035	+	240.070i	0.397977	+	1.22485i
$197$	3.23347	−	1.05062i	0.0164136	−	0.00533309i	−0.300799	−	0.953688i	$-0.597253\pi$
$197$	3.23347	−	1.05062i	0.0164136	−	0.00533309i	0.317212	+	0.948355i	$0.397253\pi$
$198$	32.6710	+	40.1980i	0.165005	+	0.203020i
$199$	105.020			0.527738			0.263869	−	0.964559i	$-0.415001\pi$
$199$	105.020			0.527738			0.263869	+	0.964559i	$0.415001\pi$
$200$	−65.9667	+	661.985i	−0.329833	+	3.30993i
$201$	−199.797	−	26.1218i	−0.994015	−	0.129959i
$202$	537.400	+	390.444i	2.66040	+	1.93289i
$203$	118.953	−	38.6502i	0.585975	−	0.190395i
$204$	−322.920	+	60.1489i	−1.58294	+	0.294847i
$205$	10.6493	−	214.263i	0.0519477	−	1.04519i
$206$	98.5006	+	32.0048i	0.478158	+	0.155363i
$207$	44.7946	−	168.381i	0.216399	−	0.813436i
$208$	139.080	−	428.044i	0.668653	−	2.05790i
$209$	1.17656	+	1.61939i	0.00562947	+	0.00774830i
$210$	−127.622	−	265.108i	−0.607723	−	1.26242i
$211$	87.8815	+	63.8497i	0.416500	+	0.302605i	0.776228	−	0.630452i	$-0.217131\pi$
$211$	87.8815	+	63.8497i	0.416500	+	0.302605i	−0.359728	+	0.933057i	$0.617131\pi$
$212$	−265.865	−	365.932i	−1.25408	−	1.72609i
$213$	−52.3663	−	96.2412i	−0.245851	−	0.451836i
$214$	400.916	+	291.283i	1.87344	+	1.36113i
$215$	−131.902	−	106.224i	−0.613500	−	0.494067i
$216$	−169.603	−	698.180i	−0.785199	−	3.23231i
$217$	−54.2362	+	166.922i	−0.249937	+	0.769226i
$218$			246.244i			1.12956i
$219$	−81.8125	+	171.919i	−0.373573	+	0.785020i
$220$	−44.4299	−	68.0134i	−0.201954	−	0.309152i
$221$	72.7613	−	23.6416i	0.329237	−	0.106975i
$222$	562.280	−	104.733i	2.53279	−	0.471772i
$223$	−298.481	−	216.859i	−1.33848	−	0.972464i	−0.999498	−	0.0316710i	$-0.989917\pi$
$223$	−298.481	−	216.859i	−1.33848	−	0.972464i	−0.338983	−	0.940793i	$-0.610083\pi$
$224$			618.680i			2.76196i
$225$	−123.897	−	187.815i	−0.550654	−	0.834734i
$226$	461.448			2.04181
$227$	119.922	−	165.059i	0.528291	−	0.727131i	−0.458577	−	0.888654i	$-0.651641\pi$
$227$	119.922	−	165.059i	0.528291	−	0.727131i	0.986869	+	0.161524i	$0.0516408\pi$
$228$	−8.03340	−	43.1288i	−0.0352342	−	0.189161i
$229$	−1.53357	−	4.71984i	−0.00669681	−	0.0206106i	0.947652	−	0.319304i	$-0.103449\pi$
$229$	−1.53357	−	4.71984i	−0.00669681	−	0.0206106i	−0.954349	+	0.298694i	$0.903449\pi$
$230$	−132.939	+	349.132i	−0.577997	+	1.51797i
$231$	20.5322	+	9.77081i	0.0888841	+	0.0422979i
$232$	−654.864			−2.82269
$233$	−179.767	−	58.4098i	−0.771532	−	0.250686i	−0.103311	−	0.994649i	$-0.532944\pi$
$233$	−179.767	−	58.4098i	−0.771532	−	0.250686i	−0.668221	+	0.743963i	$0.732944\pi$
$234$	95.2036	+	246.693i	0.406853	+	1.05424i
$235$	83.2011	+	31.6805i	0.354047	+	0.134811i
$236$	432.177	−	594.841i	1.83126	−	2.52051i
$237$	326.555	−	177.684i	1.37787	−	0.749720i
$238$	−159.479	+	115.868i	−0.670079	+	0.486841i
$239$	−204.363	+	281.281i	−0.855075	+	1.17691i	0.127647	+	0.991820i	$0.459257\pi$
$239$	−204.363	+	281.281i	−0.855075	+	1.17691i	−0.982722	+	0.185089i	$0.940743\pi$
$240$	118.912	+	878.805i	0.495466	+	3.66169i
$241$	−214.858	+	156.104i	−0.891528	+	0.647733i	−0.936276	−	0.351265i	$-0.885752\pi$
$241$	−214.858	+	156.104i	−0.891528	+	0.647733i	0.0447480	+	0.998998i	$0.485752\pi$
$242$	−435.968	−	141.655i	−1.80152	−	0.585350i
$243$	193.445	+	147.064i	0.796071	+	0.605203i
$244$	145.526	−	447.883i	0.596418	−	1.83559i
$245$	90.2244	+	72.6600i	0.368263	+	0.296571i
$246$	−90.9664	−	488.370i	−0.369782	−	1.98524i
$247$	3.15754	+	9.71790i	0.0127836	+	0.0393437i
$248$	540.142	−	743.442i	2.17799	−	2.99775i
$249$	37.1002	−	283.768i	0.148997	−	1.13963i
$250$	222.490	+	428.057i	0.889959	+	1.71223i
$251$			125.477i			0.499907i	0.968258	+	0.249953i	$0.0804153\pi$
$251$			125.477i			0.499907i	−0.968258	+	0.249953i	$0.919585\pi$
$252$	−314.320	−	386.734i	−1.24730	−	1.53466i
$253$	−8.92179	−	27.4584i	−0.0352640	−	0.108531i
$254$	512.534	−	166.532i	2.01785	−	0.655639i
$255$	−108.973	+	104.159i	−0.427346	+	0.408466i
$256$	204.814	−	630.353i	0.800055	−	2.46232i
$257$			325.161i			1.26522i	0.774471	+	0.632609i	$0.218016\pi$
$257$			325.161i			1.26522i	−0.774471	+	0.632609i	$0.781984\pi$
$258$	−354.119	−	168.517i	−1.37255	−	0.653166i
$259$	203.117	−	147.573i	0.784236	−	0.569781i
$260$	−108.414	−	400.282i	−0.416977	−	1.53955i
$261$	171.875	−	139.692i	0.658523	−	0.535217i
$262$	−197.617	+	143.577i	−0.754262	+	0.548003i
$263$	−268.384	−	369.399i	−1.02047	−	1.40456i	−0.911872	−	0.410474i	$-0.865363\pi$
$263$	−268.384	−	369.399i	−1.02047	−	1.40456i	−0.108600	−	0.994086i	$-0.534637\pi$
$264$	−86.4322	−	81.8742i	−0.327395	−	0.310129i
$265$	−193.993	−	73.8667i	−0.732048	−	0.278742i
$266$	−15.4752	−	21.2998i	−0.0581774	−	0.0800743i
$267$	−289.105	−	137.579i	−1.08279	−	0.515276i
$268$	731.770			2.73049
$269$	−323.885	−	105.236i	−1.20403	−	0.391214i	−0.362789	−	0.931871i	$-0.618175\pi$
$269$	−323.885	−	105.236i	−1.20403	−	0.391214i	−0.841243	+	0.540658i	$0.818175\pi$
$270$	−379.860	−	356.606i	−1.40689	−	1.32076i
$271$	105.369	+	324.293i	0.388816	+	1.19665i	0.933674	+	0.358125i	$0.116584\pi$
$271$	105.369	+	324.293i	0.388816	+	1.19665i	−0.544858	+	0.838529i	$0.683416\pi$
$272$	565.068	−	183.602i	2.07745	−	0.675006i
$273$	84.2684	+	79.8245i	0.308676	+	0.292397i
$274$	−91.6435			−0.334465
$275$	−34.1410	−	14.9803i	−0.124149	−	0.0544736i
$276$	−82.0317	+	627.433i	−0.297216	+	2.27331i
$277$	−94.8393	−	68.9048i	−0.342380	−	0.248754i	0.403285	−	0.915074i	$-0.367868\pi$
$277$	−94.8393	−	68.9048i	−0.342380	−	0.248754i	−0.745665	+	0.666321i	$0.767868\pi$
$278$	152.791	−	49.6449i	0.549609	−	0.178579i
$279$	16.8217	+	310.342i	0.0602928	+	1.11234i
$280$	369.832	+	566.140i	1.32083	+	2.02193i
$281$	−166.722	−	54.1712i	−0.593316	−	0.192780i	−0.00305911	−	0.999995i	$-0.500974\pi$
$281$	−166.722	−	54.1712i	−0.593316	−	0.192780i	−0.590257	+	0.807215i	$0.700974\pi$
$282$	204.418	+	26.7260i	0.724888	+	0.0947731i
$283$	50.6167	−	155.782i	0.178858	−	0.550467i	−0.820931	−	0.571027i	$-0.806545\pi$
$283$	50.6167	−	155.782i	0.178858	−	0.550467i	0.999789	+	0.0205604i	$0.00654504\pi$
$284$	233.883	+	321.912i	0.823531	+	1.13349i
$285$	−13.9113	−	14.5543i	−0.0488116	−	0.0510678i
$286$	35.4477	+	25.7543i	0.123943	+	0.0900499i
$287$	−128.175	−	176.418i	−0.446603	−	0.614697i
$288$	394.445	+	1022.09i	1.36960	+	3.54892i
$289$	−152.098	−	110.506i	−0.526291	−	0.382373i
$290$	−397.572	+	259.714i	−1.37094	+	0.895566i
$291$	−262.351	+	142.749i	−0.901550	+	0.490547i
$292$	213.668	−	657.602i	0.731740	−	2.25206i
$293$			545.939i			1.86327i	0.363393	+	0.931636i	$0.381618\pi$
$293$			545.939i			1.86327i	−0.363393	+	0.931636i	$0.618382\pi$
$294$	242.225	+	115.269i	0.823896	+	0.392073i
$295$	16.7503	−	337.016i	0.0567807	−	1.14243i
$296$	−1250.19	+	406.213i	−4.22363	+	1.37234i
$297$	40.1497	+	3.05136i	0.135184	+	0.0102739i
$298$	−246.332	−	178.971i	−0.826618	−	0.600573i
$299$		−	147.381i		−	0.492912i
$300$	534.580	+	617.994i	1.78193	+	2.05998i
$301$	−172.149			−0.571925
$302$	−30.6895	+	42.2405i	−0.101621	+	0.139869i
$303$	507.616	−	94.5512i	1.67530	−	0.312050i
$304$	24.5216	+	75.4697i	0.0806631	+	0.248255i
$305$	−56.5000	−	208.607i	−0.185246	−	0.683958i
$306$	−189.594	+	293.097i	−0.619588	+	0.957833i
$307$	407.377			1.32696			0.663481	−	0.748193i	$-0.269078\pi$
$307$	407.377			1.32696			0.663481	+	0.748193i	$0.269078\pi$
$308$	−78.5371	−	25.5182i	−0.254990	−	0.0828514i
$309$	70.7165	−	38.4780i	0.228856	−	0.124524i
$310$	33.0797	−	665.564i	0.106709	−	2.14698i
$311$	−278.431	+	383.228i	−0.895278	+	1.23224i	0.0766724	+	0.997056i	$0.475570\pi$
$311$	−278.431	+	383.228i	−0.895278	+	1.23224i	−0.971950	+	0.235188i	$0.924430\pi$
$312$	−290.465	−	533.830i	−0.930979	−	1.71099i
$313$	−201.003	+	146.037i	−0.642182	+	0.466572i	−0.860599	−	0.509283i	$-0.829911\pi$
$313$	−201.003	+	146.037i	−0.642182	+	0.466572i	0.218417	+	0.975855i	$0.429911\pi$
$314$	−190.272	+	261.887i	−0.605963	+	0.834036i
$315$	−217.831	−	69.6978i	−0.691526	−	0.221263i
$316$	−1092.28	+	793.585i	−3.45657	+	2.51135i
$317$	298.078	+	96.8515i	0.940310	+	0.305525i	0.738772	−	0.673955i	$-0.235406\pi$
$317$	298.078	+	96.8515i	0.940310	+	0.305525i	0.201538	+	0.979481i	$0.435406\pi$
$318$	−476.624	−	62.3147i	−1.49882	−	0.195958i
$319$	11.3409	−	34.9038i	0.0355516	−	0.109416i
$320$	−304.976	−	1126.02i	−0.953050	−	3.51881i
$321$	378.696	−	70.5380i	1.17974	−	0.219745i
$322$	117.348	+	361.159i	0.364433	+	1.12161i
$323$	−7.92861	+	10.9128i	−0.0245468	+	0.0337857i
$324$	−765.838	−	438.507i	−2.36370	−	1.35342i
$325$	−142.120	−	126.583i	−0.437291	−	0.389485i
$326$		−	512.133i		−	1.57096i
$327$	138.962	+	131.634i	0.424961	+	0.402551i
$328$	352.817	+	1085.86i	1.07566	+	3.31055i
$329$	86.0671	−	27.9649i	0.261602	−	0.0849997i
$330$	−84.9442	−	15.4279i	−0.257407	−	0.0467511i
$331$	47.4817	−	146.134i	0.143449	−	0.441492i	−0.853359	−	0.521324i	$-0.825438\pi$
$331$	47.4817	−	146.134i	0.143449	−	0.441492i	0.996808	+	0.0798322i	$0.0254384\pi$
$332$			1039.32i			3.13048i
$333$	241.473	−	373.298i	0.725144	−	1.12101i
$334$	−15.4296	+	11.2103i	−0.0461964	+	0.0335636i
$335$	281.155	−	183.665i	0.839269	−	0.548254i
$336$	654.432	+	619.920i	1.94772	+	1.84500i
$337$	92.3243	−	67.0775i	0.273959	−	0.199043i	−0.442319	−	0.896858i	$-0.645844\pi$
$337$	92.3243	−	67.0775i	0.273959	−	0.199043i	0.716278	+	0.697815i	$0.245844\pi$
$338$	−251.908	−	346.722i	−0.745291	−	1.02580i
$339$	246.676	−	260.408i	0.727657	−	0.768167i
$340$	343.376	−	426.382i	1.00993	−	1.25407i
$341$	30.2708	+	41.6642i	0.0887707	+	0.122182i
$342$	−39.1456	−	25.3219i	−0.114461	−	0.0740407i
$343$	366.793			1.06937
$344$	857.223	+	278.529i	2.49193	+	0.809677i
$345$	125.960	+	261.656i	0.365102	+	0.758424i
$346$	−283.876	−	873.681i	−0.820452	−	2.52509i
$347$	71.7570	−	23.3153i	0.206793	−	0.0671910i	−0.203789	−	0.979015i	$-0.565326\pi$
$347$	71.7570	−	23.3153i	0.206793	−	0.0671910i	0.410582	+	0.911824i	$0.365326\pi$
$348$	−553.156	+	583.951i	−1.58953	+	1.67802i
$349$	54.5204			0.156219			0.0781094	−	0.996945i	$-0.475112\pi$
$349$	54.5204			0.156219			0.0781094	+	0.996945i	$0.475112\pi$
$350$	449.054	+	197.034i	1.28301	+	0.562954i
$351$	190.108	+	78.1479i	0.541620	+	0.222644i
$352$	146.866	+	106.704i	0.417233	+	0.303138i
$353$	139.829	−	45.4331i	0.396115	−	0.128706i	−0.104184	−	0.994558i	$-0.533223\pi$
$353$	139.829	−	45.4331i	0.396115	−	0.128706i	0.500300	+	0.865852i	$0.333223\pi$
$354$	−143.082	−	768.160i	−0.404185	−	2.16994i
$355$	170.656	+	64.9809i	0.480722	+	0.183045i
$356$	1105.85	+	359.311i	3.10631	+	1.00930i
$357$	−19.8646	+	151.938i	−0.0556431	+	0.425596i
$358$	−386.574	+	1189.75i	−1.07982	+	3.32333i
$359$	195.730	+	269.399i	0.545209	+	0.750416i	0.989352	−	0.145540i	$-0.0464919\pi$
$359$	195.730	+	269.399i	0.545209	+	0.750416i	−0.444143	+	0.895956i	$0.646492\pi$
$360$	971.928	+	699.501i	2.69980	+	1.94306i
$361$	290.598	+	211.132i	0.804980	+	0.584852i
$362$	83.2271	+	114.552i	0.229909	+	0.316443i
$363$	−312.995	+	170.305i	−0.862244	+	0.469161i
$364$	−341.034	−	247.775i	−0.936906	−	0.680702i
$365$	−82.9559	−	306.287i	−0.227277	−	0.839142i
$366$	−239.194	−	439.602i	−0.653536	−	1.20110i
$367$	−53.3254	+	164.119i	−0.145301	+	0.447190i	−0.997050	−	0.0767607i	$-0.975542\pi$
$367$	−53.3254	+	164.119i	−0.145301	+	0.447190i	0.851749	+	0.523950i	$0.175542\pi$
$368$		−	1144.57i		−	3.11023i
$369$	−324.229	−	209.732i	−0.878669	−	0.568380i
$370$	−597.899	+	742.432i	−1.61594	+	2.00657i
$371$	−200.675	+	65.2033i	−0.540903	+	0.175750i
$372$	−206.685	−	1109.63i	−0.555606	−	2.98287i
$373$	3.03329	+	2.20381i	0.00813214	+	0.00590834i	0.591844	−	0.806053i	$-0.298400\pi$
$373$	3.03329	+	2.20381i	0.00813214	+	0.00590834i	−0.583712	+	0.811961i	$0.698400\pi$
$374$			57.8420i			0.154658i
$375$	360.501	+	103.268i	0.961335	+	0.275382i
$376$	−473.820			−1.26016
$377$	110.118	−	151.564i	0.292089	−	0.402026i
$378$	−528.086	−	40.1342i	−1.39705	−	0.106175i
$379$	−67.1607	−	206.699i	−0.177205	−	0.545381i	0.822522	−	0.568733i	$-0.192566\pi$
$379$	−67.1607	−	206.699i	−0.177205	−	0.545381i	−0.999727	+	0.0233520i	$0.992566\pi$
$380$	56.9471	+	45.8609i	0.149861	+	0.120687i
$381$	180.005	−	378.261i	0.472455	−	0.992810i
$382$	−312.735			−0.818677
$383$	504.528	+	163.931i	1.31731	+	0.428019i	0.881569	−	0.472056i	$-0.156488\pi$
$383$	504.528	+	163.931i	1.31731	+	0.428019i	0.435737	+	0.900074i	$0.356488\pi$
$384$	−592.966	−	1089.78i	−1.54418	−	2.83797i
$385$	−36.5796	+	9.90737i	−0.0950120	+	0.0257334i
$386$	796.449	−	1096.22i	2.06334	−	2.83994i
$387$	−284.399	+	109.755i	−0.734882	+	0.283606i
$388$	877.524	−	637.558i	2.26166	−	1.64319i
$389$	−229.507	+	315.890i	−0.589993	+	0.812056i	−0.994746	−	0.102370i	$-0.967357\pi$
$389$	−229.507	+	315.890i	−0.589993	+	0.812056i	0.404753	+	0.914426i	$0.367357\pi$
$390$	−388.056	−	208.895i	−0.995016	−	0.535628i
$391$	157.402	−	114.359i	0.402563	−	0.292479i
$392$	−586.361	−	190.520i	−1.49582	−	0.486021i
$393$	−24.6150	+	188.272i	−0.0626337	+	0.479064i
$394$	−4.05476	+	12.4793i	−0.0102913	+	0.0316733i
$395$	−220.486	+	579.052i	−0.558193	+	1.46596i
$396$	−146.017	+	7.91464i	−0.368729	+	0.0199865i
$397$	−46.3685	−	142.708i	−0.116797	−	0.359465i	0.875520	−	0.483181i	$-0.160519\pi$
$397$	−46.3685	−	142.708i	−0.116797	−	0.359465i	−0.992318	+	0.123716i	$0.960519\pi$
$398$	−238.237	+	327.906i	−0.598586	+	0.823883i
$399$	−20.2926	−	2.65309i	−0.0508587	−	0.00664935i
$400$	−1103.71	−	983.046i	−2.75927	−	2.45762i
$401$			760.398i			1.89625i	0.317892	+	0.948127i	$0.397025\pi$
$401$			760.398i			1.89625i	−0.317892	+	0.948127i	$0.602975\pi$
$402$	534.800	−	564.573i	1.33035	−	1.40441i
$403$	81.2379	+	250.025i	0.201583	+	0.620409i
$404$	−1783.42	+	579.468i	−4.41440	+	1.43433i
$405$	−404.304	+	23.7358i	−0.998281	+	0.0586069i
$406$	−149.167	+	459.088i	−0.367405	+	1.13076i
$407$		−	73.6694i		−	0.181006i
$408$	344.744	−	724.439i	0.844960	−	1.77559i
$409$	−337.035	+	244.870i	−0.824046	+	0.598704i	−0.917869	−	0.396885i	$-0.870091\pi$
$409$	−337.035	+	244.870i	−0.824046	+	0.598704i	0.0938227	+	0.995589i	$0.470091\pi$
$410$	644.841	+	519.307i	1.57278	+	1.26660i
$411$	−48.9897	+	51.7171i	−0.119196	+	0.125832i
$412$	−236.536	+	171.853i	−0.574116	+	0.417120i
$413$	−201.608	−	277.489i	−0.488154	−	0.671886i
$414$	424.124	+	521.836i	1.02445	+	1.26047i
$415$	260.856	+	399.319i	0.628568	+	0.962214i
$416$	544.696	+	749.709i	1.30936	+	1.80219i
$417$	53.6613	−	112.763i	0.128684	−	0.270415i
$418$	−7.72529			−0.0184816
$419$	525.113	+	170.619i	1.25325	+	0.407206i	0.859085	−	0.511833i	$-0.171033\pi$
$419$	525.113	+	170.619i	1.25325	+	0.407206i	0.394167	+	0.919039i	$0.371033\pi$
$420$	817.226	+	148.428i	1.94578	+	0.353399i
$421$	−132.141	−	406.689i	−0.313875	−	0.966006i	−0.976215	−	0.216804i	$-0.930437\pi$
$421$	−132.141	−	406.689i	−0.313875	−	0.966006i	0.662341	−	0.749203i	$-0.269563\pi$
$422$	−398.718	+	129.551i	−0.944831	+	0.306994i
$423$	124.358	−	101.072i	0.293990	−	0.238942i
$424$	1104.76			2.60557
$425$	24.9129	−	250.004i	0.0586186	−	0.588246i
$426$	419.289	+	54.8185i	0.984247	+	0.128682i
$427$	−177.730	−	129.128i	−0.416229	−	0.302408i
$428$	−1330.48	+	432.300i	−3.10860	+	1.01005i
$429$	33.4831	−	6.23674i	0.0780492	−	0.0145379i
$430$	630.887	−	170.872i	1.46718	−	0.397377i
$431$	−500.521	−	162.629i	−1.16130	−	0.377330i	−0.335912	−	0.941893i	$-0.609045\pi$
$431$	−500.521	−	162.629i	−1.16130	−	0.377330i	−0.825390	+	0.564563i	$0.809045\pi$
$432$	1476.39	+	606.900i	3.41757	+	1.40486i
$433$	96.8430	−	298.052i	0.223656	−	0.688342i	−0.774769	−	0.632244i	$-0.782134\pi$
$433$	96.8430	−	298.052i	0.223656	−	0.688342i	0.998425	−	0.0560981i	$-0.0178660\pi$
$434$	−398.149	−	548.006i	−0.917395	−	1.26269i
$435$	−65.9650	+	363.196i	−0.151644	+	0.834933i
$436$	−562.380	−	408.593i	−1.28986	−	0.937139i
$437$	15.2737	+	21.0224i	0.0349512	+	0.0481062i
$438$	−351.196	−	645.444i	−0.801818	−	1.47362i
$439$	224.740	+	163.283i	0.511937	+	0.371944i	0.813558	−	0.581484i	$-0.197528\pi$
$439$	224.740	+	163.283i	0.511937	+	0.371944i	−0.301621	+	0.953428i	$0.597528\pi$
$440$	198.179	+	9.84986i	0.450407	+	0.0223860i
$441$	194.536	−	75.0753i	0.441124	−	0.170239i
$442$	−91.2424	+	280.815i	−0.206431	+	0.635329i
$443$		−	155.952i		−	0.352037i	−0.984387	−	0.176019i	$-0.943678\pi$
$443$		−	155.952i		−	0.352037i	0.984387	−	0.176019i	$-0.0563219\pi$
$444$	−693.799	+	1457.94i	−1.56261	+	3.28364i
$445$	515.062	−	139.501i	1.15744	−	0.313486i
$446$	1354.21	−	440.009i	3.03634	−	0.986568i
$447$	−232.680	+	43.3402i	−0.520536	+	0.0969579i
$448$	−959.351	−	697.010i	−2.14141	−	1.55583i
$449$		−	719.532i		−	1.60252i	−0.598315	−	0.801261i	$-0.704163\pi$
$449$		−	719.532i		−	1.60252i	0.598315	−	0.801261i	$-0.295837\pi$
$450$	867.480	+	39.2118i	1.92773	+	0.0871373i
$451$	−63.9857			−0.141875
$452$	−765.682	+	1053.87i	−1.69399	+	2.33157i
$453$	7.43188	+	39.8994i	0.0164059	+	0.0880782i
$454$	243.323	+	748.871i	0.535954	+	1.64950i
$455$	−193.218	−	9.60327i	−0.424654	−	0.0211061i
$456$	96.7551	+	46.0435i	0.212182	+	0.100973i
$457$	−709.855			−1.55329			−0.776646	−	0.629937i	$-0.783081\pi$
$457$	−709.855			−1.55329			−0.776646	+	0.629937i	$0.783081\pi$
$458$	18.2158	+	5.91866i	0.0397724	+	0.0129228i
$459$	64.0520	+	263.674i	0.139547	+	0.574452i
$460$	−576.773	−	882.927i	−1.25386	−	1.91941i
$461$	83.4519	−	114.862i	0.181024	−	0.249158i	−0.708856	−	0.705353i	$-0.750788\pi$
$461$	83.4519	−	114.862i	0.181024	−	0.249158i	0.889879	+	0.456196i	$0.150788\pi$
$462$	−77.0850	+	41.9432i	−0.166851	+	0.0907861i
$463$	78.3487	−	56.9237i	0.169220	−	0.122945i	−0.499952	−	0.866053i	$-0.666649\pi$
$463$	78.3487	−	56.9237i	0.169220	−	0.122945i	0.669172	+	0.743108i	$0.266649\pi$
$464$	855.179	−	1177.05i	1.84306	−	2.53675i
$465$	−357.913	−	374.457i	−0.769706	−	0.805284i
$466$	590.176	−	428.788i	1.26647	−	0.920145i
$467$	311.511	+	101.216i	0.667047	+	0.216737i	0.622915	−	0.782289i	$-0.285948\pi$
$467$	311.511	+	101.216i	0.667047	+	0.216737i	0.0441312	+	0.999026i	$0.485948\pi$
$468$	−721.376	−	191.908i	−1.54140	−	0.410060i
$469$	105.488	−	324.658i	0.224921	−	0.692234i
$470$	−287.658	+	187.913i	−0.612039	+	0.399816i
$471$	46.0770	+	247.373i	0.0978280	+	0.525208i
$472$	554.948	+	1707.96i	1.17574	+	3.61855i
$473$	−29.6908	+	40.8659i	−0.0627713	+	0.0863972i
$474$	−186.004	+	1422.69i	−0.392414	+	3.00145i
$475$	33.3902	+	3.32733i	0.0702952	+	0.00700491i
$476$		−	556.483i		−	1.16908i
$477$	−289.954	+	235.661i	−0.607870	+	0.494049i
$478$	−414.654	−	1276.17i	−0.867477	−	2.66982i
$479$	386.308	−	125.519i	0.806488	−	0.262044i	0.123379	−	0.992360i	$-0.460627\pi$
$479$	386.308	−	125.519i	0.806488	−	0.262044i	0.683110	+	0.730316i	$0.260627\pi$
$480$	−1607.79	−	865.488i	−3.34955	−	1.80310i
$481$	116.209	−	357.655i	0.241599	−	0.743566i
$482$		−	1024.98i		−	2.12651i
$483$	266.542	+	126.841i	0.551848	+	0.262612i
$484$	1046.92	−	760.631i	2.16306	−	1.57155i
$485$	177.136	−	465.205i	0.365230	−	0.959185i
$486$	−898.013	+	270.383i	−1.84776	+	0.556343i
$487$	−293.180	+	213.008i	−0.602013	+	0.437388i	−0.846593	−	0.532241i	$-0.821350\pi$
$487$	−293.180	+	213.008i	−0.602013	+	0.437388i	0.244580	+	0.969629i	$0.421350\pi$
$488$	676.089	+	930.556i	1.38543	+	1.90688i
$489$	−289.011	−	273.770i	−0.591025	−	0.559857i
$490$	−431.542	+	116.881i	−0.880698	+	0.238532i
$491$	−449.536	−	618.733i	−0.915552	−	1.26015i	−0.965235	−	0.261384i	$-0.915821\pi$
$491$	−449.536	−	618.733i	−0.915552	−	1.26015i	0.0496832	−	0.998765i	$-0.484179\pi$
$492$	1266.30	+	602.601i	2.57377	+	1.22480i
$493$	247.315			0.501653
$494$	−37.5053	−	12.1862i	−0.0759217	−	0.0246684i
$495$	−54.1148	+	39.6892i	−0.109323	+	0.0801801i
$496$	630.897	+	1941.70i	1.27197	+	3.91472i
$497$	176.535	−	57.3597i	0.355201	−	0.115412i
$498$	801.852	+	759.566i	1.61014	+	1.52523i
$499$	−378.718			−0.758954			−0.379477	−	0.925201i	$-0.623896\pi$
$499$	−378.718			−0.758954			−0.379477	+	0.925201i	$0.623896\pi$
$500$	−1346.79	−	202.146i	−2.69358	−	0.404292i
$501$	−1.92190	+	14.7000i	−0.00383613	+	0.0293413i
$502$	−391.779	−	284.644i	−0.780435	−	0.567019i
$503$	664.638	−	215.954i	1.32135	−	0.429332i	0.438391	−	0.898785i	$-0.355549\pi$
$503$	664.638	−	215.954i	1.32135	−	0.429332i	0.882958	+	0.469452i	$0.155549\pi$
$504$	1215.43	−	65.8810i	2.41157	−	0.130716i
$505$	−539.772	+	670.253i	−1.06886	+	1.32723i
$506$	105.973	+	34.4328i	0.209433	+	0.0680490i
$507$	−330.327	−	43.1875i	−0.651533	−	0.0851825i
$508$	−470.117	+	1446.87i	−0.925426	+	2.84817i
$509$	−208.895	−	287.519i	−0.410402	−	0.564870i	0.552915	−	0.833238i	$-0.313516\pi$
$509$	−208.895	−	287.519i	−0.410402	−	0.564870i	−0.963316	+	0.268368i	$0.913516\pi$
$510$	−78.0113	−	576.534i	−0.152963	−	1.13046i
$511$	−260.951	−	189.592i	−0.510668	−	0.371022i
$512$	531.225	+	731.168i	1.03755	+	1.42806i
$513$	−35.2159	+	8.55471i	−0.0686470	+	0.0166758i
$514$	−1015.26	−	737.628i	−1.97521	−	1.43507i
$515$	−47.7470	+	125.396i	−0.0927125	+	0.243487i
$516$	972.454	−	529.127i	1.88460	−	1.02544i
$517$	8.20561	−	25.2543i	0.0158716	−	0.0488477i
$518$			968.968i			1.87059i
$519$	−644.795	−	306.843i	−1.24238	−	0.591219i
$520$	946.596	+	360.436i	1.82038	+	0.693146i
$521$	−198.005	+	64.3358i	−0.380048	+	0.123485i	−0.492810	−	0.870137i	$-0.664030\pi$
$521$	−198.005	+	64.3358i	−0.380048	+	0.123485i	0.112762	+	0.993622i	$0.464030\pi$
$522$	46.2649	+	853.538i	0.0886301	+	1.63513i
$523$	−25.6560	−	18.6402i	−0.0490554	−	0.0356408i	0.562987	−	0.826466i	$-0.309652\pi$
$523$	−25.6560	−	18.6402i	−0.0490554	−	0.0356408i	−0.612043	+	0.790825i	$0.709652\pi$
$524$		−	689.561i		−	1.31596i
$525$	351.242	−	148.086i	0.669032	−	0.282068i
$526$	1762.21			3.35022
$527$	−203.989	+	280.767i	−0.387076	+	0.532765i
$528$	260.031	−	48.4348i	0.492484	−	0.0917326i
$529$	47.6504	+	146.653i	0.0900763	+	0.277226i
$530$	670.708	−	438.141i	1.26549	−	0.826681i
$531$	−509.981	−	329.889i	−0.960417	−	0.621260i
$532$	74.3231			0.139705
$533$	−310.643	−	100.934i	−0.582819	−	0.189369i
$534$	1085.40	−	590.583i	2.03258	−	1.10596i
$535$	−402.686	+	500.029i	−0.752684	+	0.934633i
$536$	−1050.56	+	1445.97i	−1.96000	+	2.69771i
$537$	464.761	+	854.159i	0.865477	+	1.59061i
$538$	1063.31	−	772.543i	1.97642	−	1.43595i
$539$	20.3092	−	27.9532i	0.0376794	−	0.0518613i
$540$	1444.73	−	275.820i	2.67543	−	0.510779i
$541$	301.502	−	219.054i	0.557305	−	0.404906i	−0.273167	−	0.961967i	$-0.588071\pi$
$541$	301.502	−	219.054i	0.557305	−	0.404906i	0.830472	+	0.557061i	$0.188071\pi$
$542$	−1251.58	−	406.662i	−2.30918	−	0.750299i
$543$	109.136	+	14.2686i	0.200986	+	0.0262773i
$544$	−378.033	+	1163.47i	−0.694914	+	2.13873i
$545$	−318.625	−	15.8362i	−0.584632	−	0.0290573i
$546$	−440.401	+	82.0314i	−0.806595	+	0.150241i
$547$	31.0880	+	95.6790i	0.0568336	+	0.174916i	0.975444	−	0.220250i	$-0.0706872\pi$
$547$	31.0880	+	95.6790i	0.0568336	+	0.174916i	−0.918610	+	0.395166i	$0.870687\pi$
$548$	152.064	−	209.299i	0.277490	−	0.381932i
$549$	−375.946	−	100.013i	−0.684783	−	0.182173i
$550$	124.222	−	72.6164i	0.225858	−	0.132030i
$551$			33.0311i			0.0599475i
$552$	−1122.03	−	1062.86i	−2.03267	−	1.92548i
$553$	194.627	+	598.999i	0.351947	+	1.08318i
$554$	430.286	−	139.808i	0.776689	−	0.252362i
$555$	99.3577	+	734.292i	0.179023	+	1.32305i
$556$	−140.146	+	431.325i	−0.252061	+	0.775765i
$557$			54.7026i			0.0982093i	0.998794	+	0.0491046i	$0.0156368\pi$
$557$			54.7026i			0.0982093i	−0.998794	+	0.0491046i	$0.984363\pi$
$558$	−1007.15	−	651.489i	−1.80493	−	1.16754i
$559$	−208.609	+	151.563i	−0.373182	+	0.271133i
$560$	−1500.54	−	74.5795i	−2.67953	−	0.133178i
$561$	32.6419	+	30.9205i	0.0581851	+	0.0551167i
$562$	547.349	−	397.672i	0.973930	−	0.707602i
$563$	−343.760	−	473.145i	−0.610586	−	0.840400i	0.386040	−	0.922482i	$-0.373843\pi$
$563$	−343.760	−	473.145i	−0.610586	−	0.840400i	−0.996626	+	0.0820827i	$0.973843\pi$
$564$	−400.230	+	422.511i	−0.709627	+	0.749133i
$565$	−29.6763	+	597.086i	−0.0525244	+	1.05679i
$566$	371.578	+	511.433i	0.656498	+	0.903593i
$567$	−304.947	+	276.560i	−0.537826	+	0.487760i
$568$	−971.866			−1.71103
$569$	−336.914	−	109.470i	−0.592117	−	0.192390i	−0.00239531	−	0.999997i	$-0.500762\pi$
$569$	−336.914	−	109.470i	−0.592117	−	0.192390i	−0.589721	+	0.807607i	$0.700762\pi$
$570$	77.0011	−	10.4191i	0.135090	−	0.0182791i
$571$	53.0268	+	163.200i	0.0928665	+	0.285814i	0.986692	−	0.162602i	$-0.0519886\pi$
$571$	53.0268	+	163.200i	0.0928665	+	0.285814i	−0.893825	+	0.448415i	$0.851989\pi$
$572$	−117.637	+	38.2226i	−0.205659	+	0.0668227i
$573$	−167.178	+	176.485i	−0.291759	+	0.308002i
$574$	841.599			1.46620
$575$	−443.207	−	194.469i	−0.770794	−	0.338206i
$576$	−2029.28	−	539.851i	−3.52306	−	0.937242i
$577$	456.181	+	331.435i	0.790609	+	0.574411i	0.908144	−	0.418658i	$-0.137499\pi$
$577$	456.181	+	331.435i	0.790609	+	0.574411i	−0.117535	+	0.993069i	$0.537499\pi$
$578$	690.069	−	224.217i	1.19389	−	0.387919i
$579$	−192.871	−	1035.46i	−0.333110	−	1.78836i
$580$	66.5474	−	1338.93i	0.114737	−	2.30850i
$581$	461.105	+	149.822i	0.793641	+	0.257869i
$582$	149.434	−	1142.97i	0.256759	−	1.96387i
$583$	−19.1323	+	58.8832i	−0.0328170	+	0.101000i
$584$	992.665	+	1366.29i	1.69977	+	2.33953i
$585$	−325.328	+	107.323i	−0.556116	+	0.183458i
$586$	−1704.60	−	1238.46i	−2.90887	−	2.11342i
$587$	125.132	+	172.229i	0.213172	+	0.293406i	0.902191	−	0.431338i	$-0.141958\pi$
$587$	125.132	+	172.229i	0.213172	+	0.293406i	−0.689019	+	0.724743i	$0.741958\pi$
$588$	−665.181	+	361.936i	−1.13126	+	0.615537i
$589$	−37.4989	−	27.2445i	−0.0636653	−	0.0462556i
$590$	1014.27	+	816.821i	1.71911	+	1.38444i
$591$	4.87486	+	8.95924i	0.00824850	+	0.0151595i
$592$	902.486	−	2777.57i	1.52447	−	4.69184i
$593$			426.291i			0.718872i	0.933170	+	0.359436i	$0.117031\pi$
$593$			426.291i			0.718872i	−0.933170	+	0.359436i	$0.882969\pi$
$594$	−100.607	+	118.438i	−0.169372	+	0.199391i
$595$	−139.670	−	213.807i	−0.234740	−	0.359340i
$596$	817.479	−	265.615i	1.37161	−	0.445663i
$597$	57.6924	+	309.732i	0.0966371	+	0.518814i
$598$	460.170	+	334.333i	0.769516	+	0.559086i
$599$			467.375i			0.780259i	0.920760	+	0.390130i	$0.127570\pi$
$599$			467.375i			0.780259i	−0.920760	+	0.390130i	$0.872430\pi$
$600$	−1988.61	+	169.106i	−3.31436	+	0.281844i
$601$	−838.959			−1.39594			−0.697969	−	0.716128i	$-0.745913\pi$
$601$	−838.959			−1.39594			−0.697969	+	0.716128i	$0.745913\pi$
$602$	390.521	−	537.506i	0.648706	−	0.892867i
$603$	−32.7177	−	603.606i	−0.0542582	−	1.00100i
$604$	−45.5471	−	140.180i	−0.0754091	−	0.232085i
$605$	211.330	−	555.007i	0.349306	−	0.917367i
$606$	−856.307	+	1799.43i	−1.41305	+	2.96936i
$607$	514.792			0.848092			0.424046	−	0.905641i	$-0.360609\pi$
$607$	514.792			0.848092			0.424046	+	0.905641i	$0.360609\pi$
$608$	−155.391	−	50.4896i	−0.255577	−	0.0830421i
$609$	179.336	+	329.593i	0.294477	+	0.541203i
$610$	779.509	+	296.814i	1.27788	+	0.486581i
$611$	79.6744	−	109.662i	0.130400	−	0.179480i
$612$	−354.791	−	919.338i	−0.579724	−	1.50219i
$613$	260.783	−	189.470i	0.425422	−	0.309087i	−0.354394	−	0.935096i	$-0.615313\pi$
$613$	260.783	−	189.470i	0.425422	−	0.309087i	0.779816	+	0.626009i	$0.215313\pi$
$614$	−924.135	+	1271.96i	−1.50511	+	2.07160i
$615$	637.771	−	86.2974i	1.03703	−	0.140321i
$616$	163.175	−	118.553i	0.264894	−	0.192457i
$617$	828.270	+	269.121i	1.34241	+	0.436177i	0.890134	−	0.455699i	$-0.150611\pi$
$617$	828.270	+	269.121i	1.34241	+	0.436177i	0.452280	+	0.891876i	$0.350611\pi$
$618$	−40.2798	+	308.087i	−0.0651777	+	0.498523i
$619$	−111.908	+	344.417i	−0.180788	+	0.556408i	−0.999850	−	0.0172962i	$-0.994494\pi$
$619$	−111.908	+	344.417i	−0.180788	+	0.556408i	0.819062	+	0.573704i	$0.194494\pi$
$620$	1465.15	+	1179.92i	2.36314	+	1.90310i
$621$	521.210	+	39.6117i	0.839308	+	0.0637869i
$622$	−564.939	−	1738.70i	−0.908263	−	2.79535i
$623$	318.825	−	438.824i	0.511757	−	0.704373i
$624$	1338.82	+	175.040i	2.14555	+	0.280512i
$625$	−568.188	+	260.359i	−0.909101	+	0.416575i
$626$		−	958.881i		−	1.53176i
$627$	−4.12970	+	4.35960i	−0.00658644	+	0.00695312i
$628$	−282.388	−	869.101i	−0.449662	−	1.38392i
$629$	472.147	−	153.410i	0.750631	−	0.243895i
$630$	711.768	−	522.028i	1.12979	−	0.828617i
$631$	111.846	−	344.227i	0.177252	−	0.545526i	−0.822477	−	0.568798i	$-0.807408\pi$
$631$	111.846	−	344.227i	0.177252	−	0.545526i	0.999729	+	0.0232723i	$0.00740846\pi$
$632$		−	3297.63i		−	5.21777i
$633$	−140.033	+	294.262i	−0.221221	+	0.464869i
$634$	−978.592	+	710.989i	−1.54352	+	1.12143i
$635$	182.521	+	673.898i	0.287435	+	1.06126i
$636$	933.180	−	985.132i	1.46726	−	1.54895i
$637$	142.693	−	103.673i	0.224008	−	0.162752i
$638$	83.2541	+	114.589i	0.130492	+	0.179607i
$639$	255.074	−	207.313i	0.399177	−	0.324433i
$640$	1932.41	+	735.806i	3.01940	+	1.14970i
$641$	404.858	+	557.240i	0.631605	+	0.869329i	0.998133	−	0.0610778i	$-0.0194538\pi$
$641$	404.858	+	557.240i	0.631605	+	0.869329i	−0.366529	+	0.930407i	$0.619454\pi$
$642$	−638.830	+	1342.43i	−0.995063	+	2.09101i
$643$	863.516			1.34295			0.671475	−	0.741028i	$-0.265661\pi$
$643$	863.516			1.34295			0.671475	+	0.741028i	$0.265661\pi$
$644$	−1019.54	−	331.269i	−1.58314	−	0.514393i
$645$	240.824	−	447.371i	0.373371	−	0.693598i
$646$	−16.0872	−	49.5114i	−0.0249028	−	0.0766430i
$647$	−181.464	+	58.9611i	−0.280469	+	0.0911300i	−0.445874	−	0.895096i	$-0.647107\pi$
$647$	−181.464	+	58.9611i	−0.280469	+	0.0911300i	0.165404	+	0.986226i	$0.447107\pi$
$648$	1965.95	−	883.749i	3.03388	−	1.36381i
$649$	−100.644			−0.155075
$650$	717.630	−	156.590i	1.10405	−	0.240908i
$651$	−522.093	−	68.2593i	−0.801986	−	0.104853i
$652$	1169.63	+	849.783i	1.79390	+	1.30335i
$653$	−240.889	+	78.2696i	−0.368896	+	0.119862i	−0.487598	−	0.873068i	$-0.662127\pi$
$653$	−240.889	+	78.2696i	−0.368896	+	0.119862i	0.118702	+	0.992930i	$0.462127\pi$
$654$	−726.240	+	135.273i	−1.11046	+	0.206840i
$655$	−173.071	−	264.938i	−0.264230	−	0.404485i
$656$	−2412.46	−	783.857i	−3.67754	−	1.19490i
$657$	−551.981	−	146.844i	−0.840154	−	0.223507i
$658$	−107.928	+	332.168i	−0.164024	+	0.504814i
$659$	−173.441	−	238.721i	−0.263188	−	0.362247i	0.656888	−	0.753989i	$-0.271873\pi$
$659$	−173.441	−	238.721i	−0.263188	−	0.362247i	−0.920075	+	0.391742i	$0.871873\pi$
$660$	176.183	−	168.399i	0.266944	−	0.255150i
$661$	476.519	+	346.211i	0.720906	+	0.523769i	0.886673	−	0.462396i	$-0.153010\pi$
$661$	476.519	+	346.211i	0.720906	+	0.523769i	−0.165768	+	0.986165i	$0.553010\pi$
$662$	348.564	+	479.758i	0.526532	+	0.724709i
$663$	109.697	+	201.606i	0.165455	+	0.304081i
$664$	−2053.68	−	1492.09i	−3.09290	−	2.24712i
$665$	28.5558	−	18.6541i	0.0429411	−	0.0280513i
$666$	617.774	+	1600.78i	0.927589	+	2.40358i
$667$	147.224	−	453.110i	0.220726	−	0.679325i
$668$		−	53.8398i		−	0.0805985i
$669$	475.608	−	999.434i	0.710923	−	1.49392i
$670$	−64.3391	+	1294.50i	−0.0960284	+	1.93209i
$671$	−61.3066	+	19.9197i	−0.0913660	+	0.0296866i
$672$	−1824.66	+	339.870i	−2.71526	+	0.505759i
$673$	364.799	+	265.042i	0.542049	+	0.393822i	0.824846	−	0.565358i	$-0.191262\pi$
$673$	364.799	+	265.042i	0.542049	+	0.393822i	−0.282796	+	0.959180i	$0.591262\pi$
$674$			440.432i			0.653459i
$675$	485.856	−	468.582i	0.719786	−	0.694196i
$676$	1209.85			1.78971
$677$	248.737	−	342.357i	0.367410	−	0.505697i	−0.584784	−	0.811189i	$-0.698821\pi$
$677$	248.737	−	342.357i	0.367410	−	0.505697i	0.952195	+	0.305492i	$0.0988209\pi$
$678$	253.496	+	1360.94i	0.373887	+	2.00728i
$679$	−156.361	−	481.230i	−0.230281	−	0.708733i
$680$	349.562	+	1290.64i	0.514062	+	1.89800i
$681$	552.682	+	263.009i	0.811574	+	0.386209i
$682$	−198.758			−0.291434
$683$	−672.119	−	218.385i	−0.984068	−	0.319743i	−0.227586	−	0.973758i	$-0.573083\pi$
$683$	−672.119	−	218.385i	−0.984068	−	0.319743i	−0.756482	+	0.654015i	$0.773083\pi$
$684$	122.785	−	47.3854i	0.179511	−	0.0692769i
$685$	5.89370	−	118.581i	0.00860395	−	0.173111i
$686$	−832.071	+	1145.25i	−1.21293	+	1.66946i
$687$	13.0776	−	7.11575i	0.0190359	−	0.0103577i
$688$	−1620.06	+	1177.05i	−2.35474	+	1.71082i
$689$	−185.770	+	255.690i	−0.269622	+	0.371103i
$690$	−1102.72	−	200.279i	−1.59814	−	0.290260i
$691$	96.3935	−	70.0340i	0.139499	−	0.101352i	−0.515847	−	0.856680i	$-0.672523\pi$
$691$	96.3935	−	70.0340i	0.139499	−	0.101352i	0.655346	+	0.755329i	$0.272523\pi$
$692$	2466.38	+	801.375i	3.56413	+	1.15806i
$693$	−17.5375	+	65.9227i	−0.0253066	+	0.0951266i
$694$	−89.9830	+	276.939i	−0.129658	+	0.399048i
$695$	54.4113	+	200.895i	0.0782896	+	0.289058i
$696$	−359.748	−	1931.37i	−0.516879	−	2.77496i
$697$	−133.244	−	410.084i	−0.191169	−	0.588356i
$698$	−123.680	+	170.230i	−0.177191	+	0.243883i
$699$	73.5120	−	562.269i	0.105167	−	0.804391i
$700$	−1195.11	+	698.625i	−1.70730	+	0.998035i
$701$		−	69.7599i		−	0.0995149i	−0.998761	−	0.0497574i	$-0.984155\pi$
$701$		−	69.7599i		−	0.0995149i	0.998761	−	0.0497574i	$-0.0158448\pi$
$702$	−675.264	+	416.302i	−0.961915	+	0.593022i
$703$	20.4892	+	63.0593i	0.0291454	+	0.0897002i
$704$	−330.921	+	107.523i	−0.470058	+	0.152731i
$705$	−47.7282	+	262.786i	−0.0676996	+	0.372747i
$706$	−175.345	+	539.655i	−0.248364	+	0.764384i
$707$			874.765i			1.23729i
$708$	1991.76	+	947.835i	2.81323	+	1.33875i
$709$	122.494	−	88.9974i	0.172771	−	0.125525i	−0.498039	−	0.867154i	$-0.665947\pi$
$709$	122.494	−	88.9974i	0.172771	−	0.125525i	0.670810	+	0.741629i	$0.265947\pi$
$710$	−590.025	+	385.435i	−0.831022	+	0.542866i
$711$	703.430	+	865.490i	0.989353	+	1.21729i
$712$	−2297.59	+	1669.30i	−3.22696	+	2.34452i
$713$	392.965	+	540.870i	0.551143	+	0.758584i
$714$	−429.336	−	406.695i	−0.601311	−	0.569600i
$715$	−35.6042	+	44.2109i	−0.0497961	+	0.0618335i
$716$	−2075.75	−	2857.03i	−2.89910	−	3.99026i
$717$	−941.842	−	448.201i	−1.31359	−	0.625106i
$718$	−1285.17			−1.78992
$719$	801.053	+	260.278i	1.11412	+	0.362000i	0.807521	−	0.589839i	$-0.200809\pi$
$719$	801.053	+	260.278i	1.11412	+	0.362000i	0.306600	+	0.951839i	$0.400809\pi$
$720$	−2526.51	+	833.473i	−3.50904	+	1.15760i
$721$	42.1470	+	129.715i	0.0584563	+	0.179910i
$722$	−1318.44	+	428.388i	−1.82610	+	0.593335i
$723$	−578.424	−	547.921i	−0.800034	−	0.757843i
$724$	−399.717			−0.552095
$725$	−310.486	−	531.136i	−0.428257	−	0.732602i
$726$	178.280	−	1363.61i	0.245565	−	1.87825i
$727$	−205.512	−	149.313i	−0.282685	−	0.205383i	0.437403	−	0.899266i	$-0.355898\pi$
$727$	−205.512	−	149.313i	−0.282685	−	0.205383i	−0.720088	+	0.693883i	$0.755898\pi$
$728$	979.203	−	318.162i	1.34506	−	0.437036i
$729$	−327.465	+	651.312i	−0.449197	+	0.893433i
$730$	1144.51	+	435.796i	1.56782	+	0.596981i
$731$	−323.738	−	105.189i	−0.442870	−	0.143897i
$732$	1400.87	+	183.153i	1.91376	+	0.250208i
$733$	230.230	−	708.575i	0.314093	−	0.966678i	−0.662033	−	0.749474i	$-0.730306\pi$
$733$	230.230	−	708.575i	0.314093	−	0.966678i	0.976126	−	0.217204i	$-0.0696937\pi$
$734$	−391.463	−	538.802i	−0.533328	−	0.734063i
$735$	−164.730	+	306.012i	−0.224122	+	0.416343i
$736$	1906.57	+	1385.20i	2.59044	+	1.88207i
$737$	−58.8757	−	81.0355i	−0.0798857	−	0.109953i
$738$	1390.36	−	536.570i	1.88396	−	0.727059i
$739$	988.689	+	718.324i	1.33787	+	0.972022i	0.999519	+	0.0310036i	$0.00987032\pi$
$739$	988.689	+	718.324i	1.33787	+	0.972022i	0.338355	+	0.941019i	$0.390130\pi$
$740$	−703.496	−	2597.42i	−0.950670	−	3.51003i
$741$	−26.9262	+	14.6510i	−0.0363376	+	0.0197719i
$742$	251.646	−	774.486i	0.339145	−	1.04378i
$743$		−	1200.30i		−	1.61548i	−0.589540	−	0.807739i	$-0.700691\pi$
$743$		−	1200.30i		−	1.61548i	0.589540	−	0.807739i	$-0.299309\pi$
$744$	2489.34	+	1184.62i	3.34589	+	1.59223i
$745$	247.419	−	307.229i	0.332107	−	0.412388i
$746$	−13.7620	+	4.47155i	−0.0184478	+	0.00599404i
$747$	857.289	−	46.4683i	1.14764	−	0.0622065i
$748$	−132.101	−	95.9773i	−0.176606	−	0.128312i
$749$			652.601i			0.871296i
$750$	−1140.23	+	891.335i	−1.52031	+	1.18845i
$751$	−938.466			−1.24962			−0.624811	−	0.780776i	$-0.714824\pi$
$751$	−938.466			−1.24962			−0.624811	+	0.780776i	$0.714824\pi$
$752$	618.755	−	851.643i	0.822812	−	1.13250i
$753$	−370.065	+	68.9303i	−0.491454	+	0.0915409i
$754$	223.430	+	687.646i	0.296326	+	0.911997i
$755$	−52.6830	−	42.4270i	−0.0697789	−	0.0561947i
$756$	967.915	−	1139.47i	1.28031	−	1.50723i
$757$	693.435			0.916030			0.458015	−	0.888944i	$-0.348561\pi$
$757$	693.435			0.916030			0.458015	+	0.888944i	$0.348561\pi$
$758$	797.736	+	259.200i	1.05242	+	0.341953i
$759$	76.0813	−	41.3970i	0.100239	−	0.0545415i
$760$	−172.376	+	46.6870i	−0.226811	+	0.0614303i
$761$	−257.519	+	354.444i	−0.338395	+	0.465761i	−0.943972	−	0.330026i	$-0.892942\pi$
$761$	−257.519	+	354.444i	−0.338395	+	0.465761i	0.605577	+	0.795787i	$0.292942\pi$
$762$	772.709	+	1420.12i	1.01405	+	1.86367i
$763$	−262.346	+	190.606i	−0.343835	+	0.249811i
$764$	518.921	−	714.234i	0.679216	−	0.934861i
$765$	−367.057	−	264.173i	−0.479813	−	0.345324i
$766$	−1656.37	+	1203.42i	−2.16236	+	1.57105i
$767$	−488.611	−	158.759i	−0.637042	−	0.206988i
$768$	1971.60	+	257.770i	2.56718	+	0.335638i
$769$	−179.693	+	553.037i	−0.233670	+	0.719164i	0.763625	+	0.645661i	$0.223418\pi$
$769$	−179.693	+	553.037i	−0.233670	+	0.719164i	−0.997295	+	0.0735031i	$0.976582\pi$
$770$	52.0469	−	136.688i	0.0675934	−	0.177517i
$771$	−958.989	+	178.626i	−1.24382	+	0.231681i
$772$	1182.03	+	3637.91i	1.53113	+	4.71232i
$773$	−876.055	+	1205.79i	−1.13332	+	1.55988i	−0.351712	+	0.936108i	$0.614400\pi$
$773$	−876.055	+	1205.79i	−1.13332	+	1.55988i	−0.781607	+	0.623771i	$0.785600\pi$
$774$	302.468	−	1136.97i	0.390786	−	1.46895i
$775$	859.073	+	85.6064i	1.10848	+	0.110460i
$776$			2649.28i			3.41402i
$777$	546.816	+	517.979i	0.703753	+	0.666640i
$778$	−465.672	−	1433.19i	−0.598551	−	1.84215i
$779$	54.7703	−	17.7960i	0.0703085	−	0.0228446i
$780$	1120.98	−	539.636i	1.43716	−	0.691841i
$781$	16.8308	−	51.7998i	0.0215503	−	0.0663250i
$782$			750.885i			0.960211i
$783$	506.408	+	430.166i	0.646753	+	0.549382i
$784$	1108.16	−	805.127i	1.41347	−	1.02695i
$785$	−326.630	−	263.043i	−0.416089	−	0.335087i
$786$	−532.008	−	503.952i	−0.676855	−	0.641160i
$787$	593.494	−	431.198i	0.754121	−	0.547901i	−0.142980	−	0.989726i	$-0.545669\pi$
$787$	593.494	−	431.198i	0.754121	−	0.547901i	0.897102	+	0.441824i	$0.145669\pi$
$788$	−21.7725	−	29.9673i	−0.0276301	−	0.0380295i
$789$	942.023	−	994.467i	1.19395	−	1.26041i
$790$	−1307.82	−	2002.01i	−1.65546	−	2.53419i
$791$	357.185	+	491.623i	0.451561	+	0.621521i
$792$	193.988	−	299.890i	0.244934	−	0.378649i
$793$	−329.058			−0.414953
$794$	550.766	+	178.955i	0.693660	+	0.225384i
$795$	111.284	−	612.716i	0.139980	−	0.770712i
$796$	−353.574	−	1088.19i	−0.444188	−	1.36707i
$797$	−606.020	+	196.908i	−0.760376	+	0.247061i	−0.663440	−	0.748230i	$-0.730904\pi$
$797$	−606.020	+	196.908i	−0.760376	+	0.247061i	−0.0969359	+	0.995291i	$0.530904\pi$
$798$	54.3176	−	57.3415i	0.0680671	−	0.0718565i
$799$	178.942			0.223957
$800$	2973.27	−	648.781i	3.71658	−	0.810976i
$801$	246.938	−	928.229i	0.308287	−	1.15884i
$802$	−2374.21	−	1724.96i	−2.96036	−	2.15083i
$803$	−90.0132	+	29.2471i	−0.112096	+	0.0364222i
$804$	401.996	+	2158.19i	0.499995	+	2.68432i
$805$	−474.864	+	128.614i	−0.589894	+	0.159769i
$806$	−964.946	−	313.530i	−1.19720	−	0.388995i
$807$	132.446	−	1013.04i	0.164121	−	1.25531i
$808$	1415.32	−	4355.92i	1.75164	−	5.39099i
$809$	−828.507	−	1140.34i	−1.02411	−	1.40957i	−0.909280	−	0.416185i	$-0.863367\pi$
$809$	−828.507	−	1140.34i	−1.02411	−	1.40957i	−0.114832	−	0.993385i	$-0.536633\pi$
$810$	843.053	−	1316.21i	1.04081	−	1.62495i
$811$	374.160	+	271.843i	0.461356	+	0.335195i	0.794063	−	0.607835i	$-0.207962\pi$
$811$	374.160	+	271.843i	0.461356	+	0.335195i	−0.332707	+	0.943030i	$0.607962\pi$
$812$	−800.967	−	1102.44i	−0.986413	−	1.35768i
$813$	−898.545	+	488.912i	−1.10522	+	0.601368i
$814$	230.020	+	167.119i	0.282579	+	0.205306i
$815$	662.669	+	32.9359i	0.813091	+	0.0404121i
$816$	851.910	+	1565.68i	1.04401	+	1.91872i
$817$	14.0489	−	43.2380i	0.0171957	−	0.0529229i
$818$		−	1607.82i		−	1.96555i
$819$	−189.132	+	292.382i	−0.230930	+	0.356999i
$820$	−2256.00	+	611.023i	−2.75122	+	0.745150i
$821$	27.4906	−	8.93222i	0.0334842	−	0.0108797i	−0.292227	−	0.956349i	$-0.594396\pi$
$821$	27.4906	−	8.93222i	0.0334842	−	0.0108797i	0.325711	+	0.945469i	$0.394396\pi$
$822$	−50.3442	−	270.282i	−0.0612459	−	0.328810i
$823$	−998.433	−	725.404i	−1.21316	−	0.881414i	−0.217648	−	0.976027i	$-0.569839\pi$
$823$	−998.433	−	725.404i	−1.21316	−	0.881414i	−0.995514	+	0.0946132i	$0.969839\pi$
$824$		−	714.112i		−	0.866641i
$825$	25.4256	−	108.920i	0.0308189	−	0.132025i
$826$	1323.76			1.60261
$827$	277.913	−	382.514i	0.336049	−	0.462532i	−0.607233	−	0.794524i	$-0.707721\pi$
$827$	277.913	−	382.514i	0.336049	−	0.462532i	0.943282	+	0.331992i	$0.107721\pi$
$828$	−1895.54	+	102.745i	−2.28930	+	0.124088i
$829$	462.426	+	1423.20i	0.557812	+	1.71677i	0.688400	+	0.725331i	$0.258313\pi$
$829$	462.426	+	1423.20i	0.557812	+	1.71677i	−0.130588	+	0.991437i	$0.541687\pi$
$830$	−1838.55	−	91.3795i	−2.21513	−	0.110096i
$831$	151.119	−	317.560i	0.181852	−	0.382142i
$832$	−1776.19			−2.13484
$833$	221.444	+	71.9516i	0.265839	+	0.0863765i
$834$	230.352	+	423.351i	0.276201	+	0.507615i
$835$	−13.5131	−	20.6859i	−0.0161834	−	0.0247735i
$836$	12.8186	−	17.6433i	0.0153332	−	0.0211044i
$837$	−906.043	+	220.098i	−1.08249	+	0.262960i
$838$	−1723.95	+	1252.52i	−2.05722	+	1.49466i
$839$	−600.238	+	826.156i	−0.715421	+	0.984692i	0.284243	+	0.958752i	$0.408258\pi$
$839$	−600.238	+	826.156i	−0.715421	+	0.984692i	−0.999664	+	0.0259396i	$0.991742\pi$
$840$	−1466.53	+	1401.74i	−1.74587	+	1.66874i
$841$	−190.433	+	138.357i	−0.226436	+	0.164515i
$842$	1569.58	+	509.986i	1.86410	+	0.605684i
$843$	68.1775	−	521.467i	0.0808749	−	0.618585i
$844$	365.720	−	1125.57i	0.433318	−	1.33362i
$845$	464.838	−	303.656i	0.550104	−	0.359356i
$846$	33.4745	+	617.568i	0.0395679	+	0.729986i
$847$	−186.545	−	574.125i	−0.220242	−	0.677834i
$848$	−1442.70	+	1985.70i	−1.70129	+	2.34163i
$849$	487.250	+	63.7039i	0.573911	+	0.0750341i
$850$	724.079	+	644.921i	0.851858	+	0.758731i
$851$		−	956.351i		−	1.12380i
$852$	−820.924	+	866.626i	−0.963525	+	1.01717i
$853$	427.033	+	1314.27i	0.500624	+	1.54076i	0.808004	+	0.589177i	$0.200548\pi$
$853$	427.033	+	1314.27i	0.500624	+	1.54076i	−0.307380	+	0.951587i	$0.599452\pi$
$854$	806.361	−	262.002i	0.944216	−	0.306794i
$855$	35.2825	−	49.0236i	0.0412661	−	0.0573376i
$856$	1055.87	−	3249.65i	1.23350	−	3.79632i
$857$			198.985i			0.232187i	0.993238	+	0.116094i	$0.0370373\pi$
$857$			198.985i			0.232187i	−0.993238	+	0.116094i	$0.962963\pi$
$858$	−56.4833	+	118.693i	−0.0658314	+	0.138337i
$859$	437.303	−	317.719i	0.509084	−	0.369871i	−0.303392	−	0.952866i	$-0.598119\pi$
$859$	437.303	−	317.719i	0.509084	−	0.369871i	0.812476	+	0.582995i	$0.198119\pi$
$860$	−656.590	+	1724.37i	−0.763476	+	2.00508i
$861$	449.892	−	474.939i	0.522523	−	0.551613i
$862$	1643.21	−	1193.86i	1.90628	−	1.38499i
$863$	547.320	+	753.322i	0.634206	+	0.872910i	0.998290	−	0.0584560i	$-0.0186177\pi$
$863$	547.320	+	753.322i	0.634206	+	0.872910i	−0.364084	+	0.931366i	$0.618618\pi$
$864$	−2797.74	+	1724.81i	−3.23812	+	1.99631i
$865$	1148.75	−	311.131i	1.32803	−	0.359689i
$866$	710.927	+	978.506i	0.820931	+	1.12992i
$867$	242.357	−	509.285i	0.279535	−	0.587410i
$868$	1912.20			2.20300
$869$	175.762	+	57.1084i	0.202257	+	0.0657174i
$870$	−984.374	−	1029.87i	−1.13146	−	1.18376i
$871$	−158.005	−	486.290i	−0.181407	−	0.558312i
$872$	1614.75	−	524.664i	1.85178	−	0.601679i
$873$	−565.129	−	695.326i	−0.647341	−	0.796479i
$874$	−100.287			−0.114745
$875$	−283.829	+	568.377i	−0.324376	+	0.649574i
$876$	2056.83	+	268.913i	2.34798	+	0.306978i
$877$	295.223	+	214.492i	0.336628	+	0.244575i	0.743238	−	0.669027i	$-0.233289\pi$
$877$	295.223	+	214.492i	0.336628	+	0.244575i	−0.406609	+	0.913602i	$0.633289\pi$
$878$	−1019.65	+	331.303i	−1.16133	+	0.377339i
$879$	−1610.12	+	299.910i	−1.83177	+	0.341195i
$880$	−276.504	+	343.344i	−0.314209	+	0.390164i
$881$	541.047	+	175.797i	0.614128	+	0.199542i	0.599531	−	0.800351i	$-0.295354\pi$
$881$	541.047	+	175.797i	0.614128	+	0.199542i	0.0145965	+	0.999893i	$0.495354\pi$
$882$	−206.895	+	777.712i	−0.234575	+	0.881760i
$883$	−95.0213	+	292.445i	−0.107612	+	0.331195i	−0.990335	−	0.138699i	$-0.955708\pi$
$883$	−95.0213	+	292.445i	−0.107612	+	0.331195i	0.882723	+	0.469894i	$0.155708\pi$
$884$	−489.936	−	674.340i	−0.554227	−	0.762828i
$885$	1003.15	−	135.738i	1.13351	−	0.153376i
$886$	486.934	+	353.778i	0.549587	+	0.399298i
$887$	−795.524	−	1094.94i	−0.896870	−	1.23444i	−0.971456	−	0.237221i	$-0.923764\pi$
$887$	−795.524	−	1094.94i	−0.896870	−	1.23444i	0.0745859	−	0.997215i	$-0.476236\pi$
$888$	−1884.82	−	3464.01i	−2.12255	−	3.90092i
$889$	574.150	+	417.145i	0.645838	+	0.469229i
$890$	−732.850	+	1924.65i	−0.823427	+	2.16253i
$891$	13.0569	+	120.089i	0.0146542	+	0.134780i
$892$	−1242.13	+	3822.90i	−1.39253	+	4.28576i
$893$			23.8993i			0.0267629i
$894$	392.512	−	824.819i	0.439052	−	0.922616i
$895$	−1514.61	−	576.718i	−1.69230	−	0.644378i
$896$	1998.98	−	649.508i	2.23100	−	0.724897i
$897$	434.666	−	80.9633i	0.484578	−	0.0902601i
$898$	2246.61	+	1632.26i	2.50180	+	1.81766i
$899$			849.831i			0.945308i
$900$	−1528.96	+	1916.12i	−1.69885	+	2.12902i
$901$	−417.223			−0.463067
$902$	145.152	−	199.784i	0.160922	−	0.221490i
$903$	−94.5699	−	507.716i	−0.104729	−	0.562254i
$904$	−983.194	−	3025.96i	−1.08760	−	3.34730i
$905$	−153.576	+	100.324i	−0.169697	+	0.110855i
$906$	−141.438	−	67.3071i	−0.156113	−	0.0742904i
$907$	−1108.39			−1.22204			−0.611019	−	0.791616i	$-0.709240\pi$
$907$	−1108.39			−1.22204			−0.611019	+	0.791616i	$0.709240\pi$
$908$	−2114.04	−	686.894i	−2.32824	−	0.756492i
$909$	557.715	+	1445.16i	0.613548	+	1.58983i
$910$	468.299	−	581.503i	0.514614	−	0.639014i
$911$	287.231	−	395.339i	0.315292	−	0.433962i	−0.621731	−	0.783231i	$-0.713570\pi$
$911$	287.231	−	395.339i	0.315292	−	0.433962i	0.937022	+	0.349269i	$0.113570\pi$
$912$	−209.110	+	113.780i	−0.229287	+	0.124759i
$913$	115.093	−	83.6200i	0.126060	−	0.0915882i
$914$	1610.31	−	2216.40i	1.76182	−	2.42494i
$915$	584.201	−	281.232i	0.638472	−	0.307357i
$916$	−43.7427	+	31.7809i	−0.0477540	+	0.0346953i
$917$	−305.931	−	99.4031i	−0.333622	−	0.108400i
$918$	−968.576	−	398.153i	−1.05509	−	0.433717i
$919$	−387.397	+	1192.29i	−0.421542	+	1.29737i	0.484724	+	0.874667i	$0.338920\pi$
$919$	−387.397	+	1192.29i	−0.421542	+	1.29737i	−0.906267	+	0.422707i	$0.861080\pi$
$920$	2572.69	+	127.868i	2.79641	+	0.138986i
$921$	223.792	+	1201.47i	0.242988	+	1.30452i
$922$	169.325	+	521.127i	0.183649	+	0.565214i
$923$	163.423	−	224.932i	0.177056	−	0.243697i
$924$	32.1161	−	245.646i	0.0347577	−	0.265850i
$925$	−922.211	−	821.392i	−0.996985	−	0.887991i
$926$			373.761i			0.403630i
$927$	152.330	+	187.425i	0.164326	+	0.202184i
$928$	925.708	+	2849.04i	0.997530	+	3.07008i
$929$	−285.520	+	92.7710i	−0.307341	+	0.0998611i	−0.458627	−	0.888629i	$-0.651659\pi$
$929$	−285.520	+	92.7710i	−0.307341	+	0.0998611i	0.151286	+	0.988490i	$0.451659\pi$
$930$	1981.10	−	268.065i	2.13022	−	0.288242i
$931$	−9.60976	+	29.5758i	−0.0103220	+	0.0317678i
$932$			2059.35i			2.20960i
$933$	−1283.20	−	610.645i	−1.37535	−	0.654496i
$934$	−1022.69	+	743.029i	−1.09496	+	0.795534i
$935$	−74.8440	−	3.71988i	−0.0800471	−	0.00397849i
$936$	1414.85	−	1149.92i	1.51159	−	1.22855i
$937$	811.451	−	589.554i	0.866010	−	0.629193i	−0.0635037	−	0.997982i	$-0.520227\pi$
$937$	811.451	−	589.554i	0.866010	−	0.629193i	0.929513	+	0.368789i	$0.120227\pi$
$938$	774.388	+	1065.85i	0.825573	+	1.13630i
$939$	−541.124	−	512.587i	−0.576277	−	0.545887i
$940$	48.1496	−	968.769i	0.0512230	−	1.03061i
$941$	−186.866	−	257.199i	−0.198582	−	0.273325i	0.698100	−	0.716001i	$-0.254029\pi$
$941$	−186.866	−	257.199i	−0.198582	−	0.273325i	−0.896682	+	0.442676i	$0.854029\pi$
$942$	−876.903	−	417.298i	−0.930895	−	0.442992i
$943$	−830.641			−0.880850
$944$	−3794.58	−	1232.93i	−4.01968	−	1.30607i
$945$	85.8932	−	680.731i	0.0908922	−	0.720350i
$946$	−60.2429	−	185.409i	−0.0636817	−	0.195992i
$947$	−1008.71	+	327.749i	−1.06516	+	0.346092i	−0.788602	−	0.614904i	$-0.789195\pi$
$947$	−1008.71	+	327.749i	−1.06516	+	0.346092i	−0.276560	+	0.960997i	$0.589195\pi$
$948$	−2940.54	−	2785.47i	−3.10183	−	2.93826i
$949$	−483.138			−0.509102
$950$	−86.1348	+	96.7071i	−0.0906682	+	0.101797i
$951$	−121.893	+	932.320i	−0.128174	+	0.980357i
$952$	1099.60	+	798.909i	1.15505	+	0.839190i
$953$	−186.960	+	60.7470i	−0.196181	+	0.0637430i	−0.405459	−	0.914113i	$-0.632888\pi$
$953$	−186.960	+	60.7470i	−0.196181	+	0.0637430i	0.209279	+	0.977856i	$0.432888\pi$
$954$	−78.0495	−	1439.93i	−0.0818128	−	1.50936i
$955$	20.1123	−	404.660i	0.0210600	−	0.423728i
$956$	3602.60	+	1170.56i	3.76841	+	1.22443i
$957$	109.171	+	14.2732i	0.114076	+	0.0149145i
$958$	−484.429	+	1490.92i	−0.505667	+	1.55628i
$959$	−70.9369	−	97.6363i	−0.0739696	−	0.101810i
$960$	3153.41	−	1518.03i	3.28480	−	1.58129i
$961$	−187.315	−	136.093i	−0.194917	−	0.141616i
$962$	853.095	+	1174.18i	0.886793	+	1.22057i
$963$	416.072	+	1078.13i	0.432058	+	1.11955i
$964$	2340.88	+	1700.75i	2.42830	+	1.76426i
$965$	1367.22	+	1101.06i	1.41681	+	1.14099i
$966$	−1000.69	+	544.492i	−1.03591	+	0.563656i
$967$	352.065	−	1083.54i	0.364079	−	1.12052i	−0.586476	−	0.809967i	$-0.699485\pi$
$967$	352.065	−	1083.54i	0.364079	−	1.12052i	0.950556	−	0.310555i	$-0.100515\pi$
$968$			3160.69i			3.26518i
$969$	−36.5404	−	17.3887i	−0.0377094	−	0.0179450i
$970$	1050.69	+	1608.39i	1.08318	+	1.65814i
$971$	261.082	−	84.8306i	0.268879	−	0.0873642i	−0.171474	−	0.985189i	$-0.554853\pi$
$971$	261.082	−	84.8306i	0.268879	−	0.0873642i	0.440354	+	0.897824i	$0.354853\pi$
$972$	872.566	−	2499.56i	0.897702	−	2.57156i
$973$	171.160	+	124.355i	0.175909	+	0.127805i
$974$		−	1398.61i		−	1.43595i
$975$	295.254	−	488.687i	0.302824	−	0.501218i
$976$	−2555.48			−2.61832
$977$	681.753	−	938.352i	0.697802	−	0.960443i	−0.302172	−	0.953253i	$-0.597712\pi$
$977$	681.753	−	938.352i	0.697802	−	0.960443i	0.999974	−	0.00718909i	$-0.00228838\pi$
$978$	1510.42	−	281.339i	1.54440	−	0.287668i
$979$	−49.1828	−	151.369i	−0.0502378	−	0.154616i
$980$	449.123	−	1179.51i	0.458288	−	1.20358i
$981$	−311.886	+	482.151i	−0.317927	+	0.491489i
$982$	2951.66			3.00576
$983$	−161.590	−	52.5039i	−0.164385	−	0.0534119i	0.225668	−	0.974204i	$-0.427543\pi$
$983$	−161.590	−	52.5039i	−0.164385	−	0.0534119i	−0.390053	+	0.920792i	$0.627543\pi$
$984$	−3008.68	+	1637.07i	−3.05760	+	1.66369i
$985$	−15.8867	−	6.04917i	−0.0161286	−	0.00614129i
$986$	−561.034	+	772.197i	−0.569000	+	0.783162i
$987$	129.757	+	238.473i	0.131466	+	0.241614i
$988$	90.0639	−	65.4353i	0.0911578	−	0.0662300i
$989$	−385.436	+	530.507i	−0.389723	+	0.536408i
$990$	−1.16285	−	258.999i	−0.00117460	−	0.261615i
$991$	−703.528	+	511.143i	−0.709917	+	0.515785i	−0.883147	−	0.469096i	$-0.844580\pi$
$991$	−703.528	+	511.143i	−0.709917	+	0.515785i	0.173230	+	0.984881i	$0.444580\pi$
$992$	−3997.94	−	1299.01i	−4.03018	−	1.30948i
$993$	457.072	+	59.7584i	0.460294	+	0.0601796i
$994$	−221.374	+	681.319i	−0.222710	+	0.685432i
$995$	−408.969	−	329.353i	−0.411024	−	0.331008i
$996$	−3065.24	+	570.947i	−3.07755	+	0.573240i
$997$	−185.152	−	569.838i	−0.185709	−	0.571553i	0.814251	−	0.580513i	$-0.197148\pi$
$997$	−185.152	−	569.838i	−0.185709	−	0.571553i	−0.999960	+	0.00896011i	$0.997148\pi$
$998$	859.122	−	1182.48i	0.860844	−	1.18485i
$999$	1233.61	+	507.100i	1.23484	+	0.507608i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.j.a.41.1	yes	72
3.2	odd	2	inner	75.3.j.a.41.18	yes	72
5.2	odd	4		375.3.h.b.299.2		144
5.3	odd	4		375.3.h.b.299.35		144
5.4	even	2		375.3.j.a.326.18		72
15.2	even	4		375.3.h.b.299.36		144
15.8	even	4		375.3.h.b.299.1		144
15.14	odd	2		375.3.j.a.326.1		72
25.2	odd	20		375.3.h.b.74.1		144
25.11	even	5	inner	75.3.j.a.11.18	yes	72
25.14	even	10		375.3.j.a.176.1		72
25.23	odd	20		375.3.h.b.74.36		144
75.2	even	20		375.3.h.b.74.35		144
75.11	odd	10	inner	75.3.j.a.11.1	✓	72
75.14	odd	10		375.3.j.a.176.18		72
75.23	even	20		375.3.h.b.74.2		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.j.a.11.1	✓	72	75.11	odd	10	inner
75.3.j.a.11.18	yes	72	25.11	even	5	inner
75.3.j.a.41.1	yes	72	1.1	even	1	trivial
75.3.j.a.41.18	yes	72	3.2	odd	2	inner
375.3.h.b.74.1		144	25.2	odd	20
375.3.h.b.74.2		144	75.23	even	20
375.3.h.b.74.35		144	75.2	even	20
375.3.h.b.74.36		144	25.23	odd	20
375.3.h.b.299.1		144	15.8	even	4
375.3.h.b.299.2		144	5.2	odd	4
375.3.h.b.299.35		144	5.3	odd	4
375.3.h.b.299.36		144	15.2	even	4
375.3.j.a.176.1		72	25.14	even	10
375.3.j.a.176.18		72	75.14	odd	10
375.3.j.a.326.1		72	15.14	odd	2
375.3.j.a.326.18		72	5.4	even	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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	75.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.26850 + 3.12232i) q^{2} +(0.549348 + 2.94927i) q^{3} +(-3.36674 - 10.3618i) q^{4} +(-3.89421 - 3.13610i) q^{5} +(-10.4548 - 4.97519i) q^{6} -5.08243 q^{7} +(25.3081 + 8.22311i) q^{8} +(-8.39643 + 3.24035i) q^{9} +O(q^{10})\)	\(q+(-2.26850 + 3.12232i) q^{2} +(0.549348 + 2.94927i) q^{3} +(-3.36674 - 10.3618i) q^{4} +(-3.89421 - 3.13610i) q^{5} +(-10.4548 - 4.97519i) q^{6} -5.08243 q^{7} +(25.3081 + 8.22311i) q^{8} +(-8.39643 + 3.24035i) q^{9} +(18.6259 - 5.04472i) q^{10} +(-0.876573 + 1.20650i) q^{11} +(28.7101 - 15.6216i) q^{12} +(-6.15884 + 4.47466i) q^{13} +(11.5295 - 15.8690i) q^{14} +(7.10995 - 13.2079i) q^{15} +(-47.8298 + 34.7504i) q^{16} +(-9.55783 - 3.10553i) q^{17} +(8.92988 - 33.5671i) q^{18} +(0.414770 - 1.27653i) q^{19} +(-19.3847 + 50.9093i) q^{20} +(-2.79202 - 14.9895i) q^{21} +(-1.77857 - 5.47389i) q^{22} +(-11.3794 + 15.6624i) q^{23} +(-10.3492 + 79.1580i) q^{24} +(5.32971 + 24.4253i) q^{25} -29.3806i q^{26} +(-14.1693 - 22.9833i) q^{27} +(17.1112 + 52.6629i) q^{28} +(-23.4047 + 7.60466i) q^{29} +(25.1104 + 52.1617i) q^{30} +(10.6713 - 32.8429i) q^{31} -121.729i q^{32} +(-4.03984 - 1.92247i) q^{33} +(31.3784 - 22.7978i) q^{34} +(19.7921 + 15.9390i) q^{35} +(61.8443 + 76.0924i) q^{36} +(-39.9646 + 29.0360i) q^{37} +(3.04484 + 4.19086i) q^{38} +(-16.5803 - 15.7060i) q^{39} +(-72.7666 - 111.391i) q^{40} +(25.2193 + 34.7113i) q^{41} +(53.1357 + 25.2861i) q^{42} +33.8714 q^{43} +(15.4526 + 5.02087i) q^{44} +(42.8595 + 13.7135i) q^{45} +(-23.0889 - 71.0602i) q^{46} +(-16.9342 + 5.50226i) q^{47} +(-128.764 - 121.973i) q^{48} -23.1689 q^{49} +(-88.3540 - 38.7677i) q^{50} +(3.90848 - 29.8947i) q^{51} +(67.1005 + 48.7513i) q^{52} +(39.4840 - 12.8291i) q^{53} +(103.904 + 7.89666i) q^{54} +(7.19727 - 1.94934i) q^{55} +(-128.627 - 41.7934i) q^{56} +(3.99269 + 0.522012i) q^{57} +(29.3494 - 90.3283i) q^{58} +(39.6675 + 54.5977i) q^{59} +(-160.794 - 29.2041i) q^{60} +(34.9695 + 25.4068i) q^{61} +(78.3383 + 107.823i) q^{62} +(42.6743 - 16.4689i) q^{63} +(188.758 + 137.141i) q^{64} +(38.0168 + 1.88950i) q^{65} +(15.1669 - 8.25257i) q^{66} +(-20.7554 + 63.8784i) q^{67} +109.491i q^{68} +(-52.4439 - 24.9568i) q^{69} +(-94.6651 + 25.6395i) q^{70} +(-34.7343 + 11.2859i) q^{71} +(-239.144 + 12.9625i) q^{72} +(51.3438 + 37.3034i) q^{73} -190.650i q^{74} +(-69.1090 + 29.1368i) q^{75} -14.6235 q^{76} +(4.45513 - 6.13196i) q^{77} +(86.6515 - 16.1402i) q^{78} +(-38.2940 - 117.857i) q^{79} +(295.240 + 14.6740i) q^{80} +(60.0002 - 54.4148i) q^{81} -165.590 q^{82} +(-90.7253 - 29.4784i) q^{83} +(-145.917 + 79.3959i) q^{84} +(27.4809 + 42.0679i) q^{85} +(-76.8374 + 105.758i) q^{86} +(-35.2856 - 64.8494i) q^{87} +(-32.1056 + 23.3261i) q^{88} +(-62.7307 + 86.3414i) q^{89} +(-140.045 + 102.712i) q^{90} +(31.3019 - 22.7421i) q^{91} +(200.601 + 65.1792i) q^{92} +(102.725 + 13.4304i) q^{93} +(21.2355 - 65.3560i) q^{94} +(-5.61854 + 3.67032i) q^{95} +(359.012 - 66.8716i) q^{96} +(30.7650 + 94.6849i) q^{97} +(52.5586 - 72.3407i) q^{98} +(3.45061 - 12.9707i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - q^{3} + 26 q^{4} - 11 q^{6} - 8 q^{7} - 13 q^{9}+O(q^{10}) \) 72 * q - q^3 + 26 * q^4 - 11 * q^6 - 8 * q^7 - 13 * q^9	\( 72 q - q^{3} + 26 q^{4} - 11 q^{6} - 8 q^{7} - 13 q^{9} - 20 q^{10} + 31 q^{12} - 42 q^{13} + 45 q^{15} - 130 q^{16} + 30 q^{18} - 36 q^{19} - 60 q^{21} - 70 q^{22} - 72 q^{24} + 100 q^{25} - 154 q^{27} - 62 q^{28} + 15 q^{30} + 114 q^{31} - 10 q^{33} + 178 q^{34} + 271 q^{36} - 98 q^{37} - 155 q^{39} - 120 q^{40} - 475 q^{42} - 52 q^{43} + 35 q^{45} + 198 q^{46} - 326 q^{48} + 112 q^{49} + 44 q^{51} + 412 q^{52} + 304 q^{54} + 10 q^{55} + 622 q^{57} + 190 q^{58} + 360 q^{60} - 306 q^{61} + 293 q^{63} + 474 q^{64} + 320 q^{66} + 472 q^{67} + 269 q^{69} - 840 q^{70} + 175 q^{72} + 318 q^{73} - 310 q^{75} + 112 q^{76} + 815 q^{78} - 346 q^{79} - 373 q^{81} - 1620 q^{82} - 730 q^{84} - 530 q^{85} - 370 q^{87} - 810 q^{88} - 230 q^{90} - 550 q^{91} - 272 q^{93} - 612 q^{94} - 698 q^{96} + 182 q^{97} - 160 q^{99}+O(q^{100}) \) 72 * q - q^3 + 26 * q^4 - 11 * q^6 - 8 * q^7 - 13 * q^9 - 20 * q^10 + 31 * q^12 - 42 * q^13 + 45 * q^15 - 130 * q^16 + 30 * q^18 - 36 * q^19 - 60 * q^21 - 70 * q^22 - 72 * q^24 + 100 * q^25 - 154 * q^27 - 62 * q^28 + 15 * q^30 + 114 * q^31 - 10 * q^33 + 178 * q^34 + 271 * q^36 - 98 * q^37 - 155 * q^39 - 120 * q^40 - 475 * q^42 - 52 * q^43 + 35 * q^45 + 198 * q^46 - 326 * q^48 + 112 * q^49 + 44 * q^51 + 412 * q^52 + 304 * q^54 + 10 * q^55 + 622 * q^57 + 190 * q^58 + 360 * q^60 - 306 * q^61 + 293 * q^63 + 474 * q^64 + 320 * q^66 + 472 * q^67 + 269 * q^69 - 840 * q^70 + 175 * q^72 + 318 * q^73 - 310 * q^75 + 112 * q^76 + 815 * q^78 - 346 * q^79 - 373 * q^81 - 1620 * q^82 - 730 * q^84 - 530 * q^85 - 370 * q^87 - 810 * q^88 - 230 * q^90 - 550 * q^91 - 272 * q^93 - 612 * q^94 - 698 * q^96 + 182 * q^97 - 160 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more