LMFDB - Embedded newform 210.3.v.b.193.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(37,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("210.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.v (of order $12$, 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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.3
Character	$\chi$	$=$	210.193
Dual form			210.3.v.b.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 + 0.366025i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(2.17130 - 4.50394i) q^{5} -2.44949 q^{6} +(1.63812 + 6.80563i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})$	\(q+(1.36603 + 0.366025i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(2.17130 - 4.50394i) q^{5} -2.44949 q^{6} +(1.63812 + 6.80563i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +(4.61461 - 5.35774i) q^{10} +(9.66984 - 16.7487i) q^{11} +(-3.34607 - 0.896575i) q^{12} +(10.3969 + 10.3969i) q^{13} +(-0.253320 + 9.89625i) q^{14} +(-1.61360 + 8.50860i) q^{15} +(2.00000 + 3.46410i) q^{16} +(6.19178 + 23.1080i) q^{17} +(4.09808 - 1.09808i) q^{18} +(2.70091 - 1.55937i) q^{19} +(8.26474 - 5.62975i) q^{20} +(-5.79151 - 10.6517i) q^{21} +(19.3397 - 19.3397i) q^{22} +(9.18722 - 34.2872i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-15.5709 - 19.5588i) q^{25} +(10.3969 + 18.0080i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(-3.96832 + 13.4258i) q^{28} +36.5420i q^{29} +(-5.31858 + 11.0323i) q^{30} +(-1.49997 + 2.59803i) q^{31} +(1.46410 + 5.46410i) q^{32} +(-8.66974 + 32.3559i) q^{33} +33.8325i q^{34} +(34.2090 + 7.39909i) q^{35} +6.00000 q^{36} +(0.422582 + 0.113231i) q^{37} +(4.26029 - 1.14154i) q^{38} +(-22.0552 - 12.7336i) q^{39} +(13.3505 - 4.66527i) q^{40} -64.3827 q^{41} +(-4.01256 - 16.6703i) q^{42} +(-38.9059 - 38.9059i) q^{43} +(33.4973 - 19.3397i) q^{44} +(-1.11470 - 14.9585i) q^{45} +(25.1000 - 43.4744i) q^{46} +(10.7803 + 2.88858i) q^{47} +(-4.89898 - 4.89898i) q^{48} +(-43.6331 + 22.2969i) q^{49} +(-14.1112 - 32.4172i) q^{50} +(-20.7181 - 35.8848i) q^{51} +(7.61109 + 28.4050i) q^{52} +(29.6867 - 7.95451i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(-54.4388 - 79.9188i) q^{55} +(-10.3350 + 16.8875i) q^{56} +(-3.81967 + 3.81967i) q^{57} +(-13.3753 + 49.9173i) q^{58} +(-34.4561 - 19.8933i) q^{59} +(-11.3034 + 13.1237i) q^{60} +(-21.4176 - 37.0964i) q^{61} +(-2.99995 + 2.99995i) q^{62} +(14.4644 + 15.2244i) q^{63} +8.00000i q^{64} +(69.4021 - 24.2523i) q^{65} +(-23.6862 + 41.0257i) q^{66} +(-1.06830 - 3.98696i) q^{67} +(-12.3836 + 46.2161i) q^{68} +61.4821i q^{69} +(44.0221 + 22.6287i) q^{70} -81.1650 q^{71} +(8.19615 + 2.19615i) q^{72} +(-101.361 + 27.1596i) q^{73} +(0.535813 + 0.309352i) q^{74} +(34.8186 + 25.7423i) q^{75} +6.23750 q^{76} +(129.825 + 38.3730i) q^{77} +(-25.4672 - 25.4672i) q^{78} +(-25.8510 + 14.9251i) q^{79} +(19.9447 - 1.48626i) q^{80} +(4.50000 - 7.79423i) q^{81} +(-87.9485 - 23.5657i) q^{82} +(6.76277 + 6.76277i) q^{83} +(0.620506 - 24.2408i) q^{84} +(117.521 + 22.2871i) q^{85} +(-38.9059 - 67.3869i) q^{86} +(-16.3813 - 61.1360i) q^{87} +(52.8370 - 14.1576i) q^{88} +(101.345 - 58.5117i) q^{89} +(3.95249 - 20.8417i) q^{90} +(-53.7263 + 87.7891i) q^{91} +(50.1999 - 50.1999i) q^{92} +(1.34484 - 5.01901i) q^{93} +(13.6689 + 7.89175i) q^{94} +(-1.15882 - 15.5506i) q^{95} +(-4.89898 - 8.48528i) q^{96} +(-63.8427 + 63.8427i) q^{97} +(-67.7652 + 14.4872i) q^{98} -58.0191i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8}+O(q^{10}) $ 32 * q + 16 * q^2 - 8 * q^5 + 24 * q^7 + 64 * q^8	$ 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8} + 12 q^{10} + 16 q^{11} + 32 q^{13} + 48 q^{15} + 64 q^{16} - 56 q^{17} + 48 q^{18} + 16 q^{20} + 32 q^{22} - 28 q^{25} + 32 q^{26} + 72 q^{28} + 36 q^{30} + 112 q^{31} - 64 q^{32} + 12 q^{33} - 112 q^{35} + 192 q^{36} - 52 q^{37} - 8 q^{40} - 336 q^{41} - 312 q^{43} + 12 q^{45} - 212 q^{47} + 96 q^{50} - 144 q^{51} - 32 q^{52} - 96 q^{53} - 312 q^{55} + 96 q^{56} + 48 q^{57} - 96 q^{58} - 24 q^{60} + 216 q^{61} + 224 q^{62} + 36 q^{63} + 248 q^{65} - 24 q^{66} + 128 q^{67} + 112 q^{68} - 264 q^{70} - 848 q^{71} + 96 q^{72} + 84 q^{73} - 144 q^{75} - 324 q^{77} + 48 q^{78} + 32 q^{80} + 144 q^{81} - 168 q^{82} - 416 q^{83} + 536 q^{85} - 312 q^{86} - 72 q^{87} + 32 q^{88} - 24 q^{90} + 504 q^{91} + 168 q^{93} + 168 q^{95} + 488 q^{97} - 328 q^{98}+O(q^{100}) $ 32 * q + 16 * q^2 - 8 * q^5 + 24 * q^7 + 64 * q^8 + 12 * q^10 + 16 * q^11 + 32 * q^13 + 48 * q^15 + 64 * q^16 - 56 * q^17 + 48 * q^18 + 16 * q^20 + 32 * q^22 - 28 * q^25 + 32 * q^26 + 72 * q^28 + 36 * q^30 + 112 * q^31 - 64 * q^32 + 12 * q^33 - 112 * q^35 + 192 * q^36 - 52 * q^37 - 8 * q^40 - 336 * q^41 - 312 * q^43 + 12 * q^45 - 212 * q^47 + 96 * q^50 - 144 * q^51 - 32 * q^52 - 96 * q^53 - 312 * q^55 + 96 * q^56 + 48 * q^57 - 96 * q^58 - 24 * q^60 + 216 * q^61 + 224 * q^62 + 36 * q^63 + 248 * q^65 - 24 * q^66 + 128 * q^67 + 112 * q^68 - 264 * q^70 - 848 * q^71 + 96 * q^72 + 84 * q^73 - 144 * q^75 - 324 * q^77 + 48 * q^78 + 32 * q^80 + 144 * q^81 - 168 * q^82 - 416 * q^83 + 536 * q^85 - 312 * q^86 - 72 * q^87 + 32 * q^88 - 24 * q^90 + 504 * q^91 + 168 * q^93 + 168 * q^95 + 488 * q^97 - 328 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$3$	−1.67303	+	0.448288i	−0.557678	+	0.149429i
$3$	−1.67303	+	0.448288i	−0.557678	+	0.149429i
$4$	1.73205	+	1.00000i	0.433013	+	0.250000i
$5$	2.17130	−	4.50394i	0.434260	−	0.900787i
$5$	2.17130	−	4.50394i	0.434260	−	0.900787i
$6$	−2.44949			−0.408248
$7$	1.63812	+	6.80563i	0.234017	+	0.972233i
$7$	1.63812	+	6.80563i	0.234017	+	0.972233i
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	2.59808	−	1.50000i	0.288675	−	0.166667i
$10$	4.61461	−	5.35774i	0.461461	−	0.535774i
$11$	9.66984	−	16.7487i	0.879077	−	1.52261i	0.0267208	−	0.999643i	$-0.491493\pi$
$11$	9.66984	−	16.7487i	0.879077	−	1.52261i	0.852356	−	0.522962i	$-0.175173\pi$
$12$	−3.34607	−	0.896575i	−0.278839	−	0.0747146i
$13$	10.3969	+	10.3969i	0.799765	+	0.799765i	0.983058	−	0.183293i	$-0.0586759\pi$
$13$	10.3969	+	10.3969i	0.799765	+	0.799765i	−0.183293	+	0.983058i	$0.558676\pi$
$14$	−0.253320	+	9.89625i	−0.0180943	+	0.706875i
$15$	−1.61360	+	8.50860i	−0.107573	+	0.567240i
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	6.19178	+	23.1080i	0.364222	+	1.35930i	0.868472	+	0.495738i	$0.165102\pi$
$17$	6.19178	+	23.1080i	0.364222	+	1.35930i	−0.504250	+	0.863558i	$0.668231\pi$
$18$	4.09808	−	1.09808i	0.227671	−	0.0610042i
$19$	2.70091	−	1.55937i	0.142153	−	0.0820723i	−0.427236	−	0.904140i	$-0.640513\pi$
$19$	2.70091	−	1.55937i	0.142153	−	0.0820723i	0.569390	+	0.822068i	$0.307179\pi$
$20$	8.26474	−	5.62975i	0.413237	−	0.281487i
$21$	−5.79151	−	10.6517i	−0.275786	−	0.507223i
$22$	19.3397	−	19.3397i	0.879077	−	0.879077i
$23$	9.18722	−	34.2872i	0.399444	−	1.49075i	−0.414632	−	0.909989i	$-0.636090\pi$
$23$	9.18722	−	34.2872i	0.399444	−	1.49075i	0.814076	−	0.580758i	$-0.197244\pi$
$24$	−4.24264	−	2.44949i	−0.176777	−	0.102062i
$25$	−15.5709	−	19.5588i	−0.622836	−	0.782352i
$26$	10.3969	+	18.0080i	0.399882	+	0.692617i
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	−3.96832	+	13.4258i	−0.141726	+	0.479493i
$29$			36.5420i			1.26007i	0.776567	+	0.630034i	$0.216959\pi$
$29$			36.5420i			1.26007i	−0.776567	+	0.630034i	$0.783041\pi$
$30$	−5.31858	+	11.0323i	−0.177286	+	0.367745i
$31$	−1.49997	+	2.59803i	−0.0483862	+	0.0838074i	−0.889204	−	0.457511i	$-0.848741\pi$
$31$	−1.49997	+	2.59803i	−0.0483862	+	0.0838074i	0.840818	+	0.541318i	$0.182075\pi$
$32$	1.46410	+	5.46410i	0.0457532	+	0.170753i
$33$	−8.66974	+	32.3559i	−0.262720	+	0.980483i
$34$			33.8325i			0.995074i
$35$	34.2090	+	7.39909i	0.977399	+	0.211402i
$36$	6.00000			0.166667
$37$	0.422582	+	0.113231i	0.0114211	+	0.00306029i	0.264525	−	0.964379i	$-0.414785\pi$
$37$	0.422582	+	0.113231i	0.0114211	+	0.00306029i	−0.253104	+	0.967439i	$0.581451\pi$
$38$	4.26029	−	1.14154i	0.112113	−	0.0300406i
$39$	−22.0552	−	12.7336i	−0.565519	−	0.326503i
$40$	13.3505	−	4.66527i	0.333762	−	0.116632i
$41$	−64.3827			−1.57031			−0.785155	−	0.619299i	$-0.787417\pi$
$41$	−64.3827			−1.57031			−0.785155	+	0.619299i	$0.787417\pi$
$42$	−4.01256	−	16.6703i	−0.0955370	−	0.396912i
$43$	−38.9059	−	38.9059i	−0.904787	−	0.904787i	0.0910583	−	0.995846i	$-0.470975\pi$
$43$	−38.9059	−	38.9059i	−0.904787	−	0.904787i	−0.995846	+	0.0910583i	$0.970975\pi$
$44$	33.4973	−	19.3397i	0.761303	−	0.439538i
$45$	−1.11470	−	14.9585i	−0.0247711	−	0.332412i
$46$	25.1000	−	43.4744i	0.545651	−	0.945096i
$47$	10.7803	+	2.88858i	0.229369	+	0.0614592i	0.371673	−	0.928364i	$-0.378784\pi$
$47$	10.7803	+	2.88858i	0.229369	+	0.0614592i	−0.142304	+	0.989823i	$0.545451\pi$
$48$	−4.89898	−	4.89898i	−0.102062	−	0.102062i
$49$	−43.6331	+	22.2969i	−0.890472	+	0.455038i
$50$	−14.1112	−	32.4172i	−0.282224	−	0.648344i
$51$	−20.7181	−	35.8848i	−0.406237	−	0.703623i
$52$	7.61109	+	28.4050i	0.146367	+	0.546249i
$53$	29.6867	−	7.95451i	0.560125	−	0.150085i	0.0323615	−	0.999476i	$-0.489697\pi$
$53$	29.6867	−	7.95451i	0.560125	−	0.150085i	0.527764	+	0.849391i	$0.323031\pi$
$54$	−6.36396	+	3.67423i	−0.117851	+	0.0680414i
$55$	−54.4388	−	79.9188i	−0.989796	−	1.45307i
$56$	−10.3350	+	16.8875i	−0.184554	+	0.301562i
$57$	−3.81967	+	3.81967i	−0.0670118	+	0.0670118i
$58$	−13.3753	+	49.9173i	−0.230609	+	0.860643i
$59$	−34.4561	−	19.8933i	−0.584002	−	0.337174i	0.178720	−	0.983900i	$-0.442804\pi$
$59$	−34.4561	−	19.8933i	−0.584002	−	0.337174i	−0.762722	+	0.646726i	$0.776138\pi$
$60$	−11.3034	+	13.1237i	−0.188391	+	0.218729i
$61$	−21.4176	−	37.0964i	−0.351109	−	0.608138i	0.635335	−	0.772236i	$-0.280862\pi$
$61$	−21.4176	−	37.0964i	−0.351109	−	0.608138i	−0.986444	+	0.164098i	$0.947529\pi$
$62$	−2.99995	+	2.99995i	−0.0483862	+	0.0483862i
$63$	14.4644	+	15.2244i	0.229594	+	0.241657i
$64$			8.00000i			0.125000i
$65$	69.4021	−	24.2523i	1.06772	−	0.373112i
$66$	−23.6862	+	41.0257i	−0.358882	+	0.621601i
$67$	−1.06830	−	3.98696i	−0.0159448	−	0.0595068i	0.957495	−	0.288450i	$-0.0931398\pi$
$67$	−1.06830	−	3.98696i	−0.0159448	−	0.0595068i	−0.973440	+	0.228943i	$0.926473\pi$
$68$	−12.3836	+	46.2161i	−0.182111	+	0.679648i
$69$			61.4821i			0.891045i
$70$	44.0221	+	22.6287i	0.628887	+	0.323267i
$71$	−81.1650			−1.14317			−0.571585	−	0.820543i	$-0.693671\pi$
$71$	−81.1650			−1.14317			−0.571585	+	0.820543i	$0.693671\pi$
$72$	8.19615	+	2.19615i	0.113835	+	0.0305021i
$73$	−101.361	+	27.1596i	−1.38851	+	0.372049i	−0.874203	−	0.485560i	$-0.838616\pi$
$73$	−101.361	+	27.1596i	−1.38851	+	0.372049i	−0.514303	+	0.857609i	$0.671949\pi$
$74$	0.535813	+	0.309352i	0.00724071	+	0.00418043i
$75$	34.8186	+	25.7423i	0.464248	+	0.343231i
$76$	6.23750			0.0820723
$77$	129.825	+	38.3730i	1.68605	+	0.498351i
$78$	−25.4672	−	25.4672i	−0.326503	−	0.326503i
$79$	−25.8510	+	14.9251i	−0.327227	+	0.188925i	−0.654609	−	0.755967i	$-0.727167\pi$
$79$	−25.8510	+	14.9251i	−0.327227	+	0.188925i	0.327382	+	0.944892i	$0.393834\pi$
$80$	19.9447	−	1.48626i	0.249309	−	0.0185783i
$81$	4.50000	−	7.79423i	0.0555556	−	0.0962250i
$82$	−87.9485	−	23.5657i	−1.07254	−	0.287387i
$83$	6.76277	+	6.76277i	0.0814791	+	0.0814791i	0.746672	−	0.665193i	$-0.231651\pi$
$83$	6.76277	+	6.76277i	0.0814791	+	0.0814791i	−0.665193	+	0.746672i	$0.731651\pi$
$84$	0.620506	−	24.2408i	0.00738697	−	0.288581i
$85$	117.521	+	22.2871i	1.38260	+	0.262201i
$86$	−38.9059	−	67.3869i	−0.452394	−	0.783569i
$87$	−16.3813	−	61.1360i	−0.188291	−	0.702712i
$88$	52.8370	−	14.1576i	0.600420	−	0.160882i
$89$	101.345	−	58.5117i	1.13871	−	0.657435i	0.192600	−	0.981277i	$-0.438308\pi$
$89$	101.345	−	58.5117i	1.13871	−	0.657435i	0.946111	+	0.323842i	$0.104975\pi$
$90$	3.95249	−	20.8417i	0.0439166	−	0.231575i
$91$	−53.7263	+	87.7891i	−0.590399	+	0.964716i
$92$	50.1999	−	50.1999i	0.545651	−	0.545651i
$93$	1.34484	−	5.01901i	0.0144606	−	0.0539678i
$94$	13.6689	+	7.89175i	0.145414	+	0.0839548i
$95$	−1.15882	−	15.5506i	−0.0121981	−	0.163691i
$96$	−4.89898	−	8.48528i	−0.0510310	−	0.0883883i
$97$	−63.8427	+	63.8427i	−0.658172	+	0.658172i	−0.954947	−	0.296775i	$-0.904089\pi$
$97$	−63.8427	+	63.8427i	−0.658172	+	0.658172i	0.296775	+	0.954947i	$0.404089\pi$
$98$	−67.7652	+	14.4872i	−0.691481	+	0.147829i
$99$		−	58.0191i		−	0.586051i
$100$	−7.41077	−	49.4478i	−0.0741077	−	0.494478i
$101$	33.9899	−	58.8723i	0.336534	−	0.582894i	−0.647244	−	0.762283i	$-0.724079\pi$
$101$	33.9899	−	58.8723i	0.336534	−	0.582894i	0.983778	+	0.179389i	$0.0574119\pi$
$102$	−15.1667	−	56.6029i	−0.148693	−	0.554930i
$103$	−33.2868	+	124.228i	−0.323173	+	1.20610i	0.592963	+	0.805230i	$0.297958\pi$
$103$	−33.2868	+	124.228i	−0.323173	+	1.20610i	−0.916136	+	0.400868i	$0.868708\pi$
$104$			41.5878i			0.399882i
$105$	−60.5496	+	2.95655i	−0.576663	+	0.0281576i
$106$	43.4643			0.410040
$107$	50.0631	+	13.4144i	0.467880	+	0.125368i	0.485053	−	0.874485i	$-0.338800\pi$
$107$	50.0631	+	13.4144i	0.467880	+	0.125368i	−0.0171737	+	0.999853i	$0.505467\pi$
$108$	−10.0382	+	2.68973i	−0.0929463	+	0.0249049i
$109$	125.372	+	72.3837i	1.15020	+	0.664071i	0.948937	−	0.315465i	$-0.102161\pi$
$109$	125.372	+	72.3837i	1.15020	+	0.664071i	0.201268	+	0.979536i	$0.435494\pi$
$110$	−45.1124	−	129.097i	−0.410113	−	1.17361i
$111$	−0.757754			−0.00682661
$112$	−20.2991	+	19.2859i	−0.181242	+	0.172195i
$113$	131.253	+	131.253i	1.16153	+	1.16153i	0.984141	+	0.177388i	$0.0567647\pi$
$113$	131.253	+	131.253i	1.16153	+	1.16153i	0.177388	+	0.984141i	$0.443235\pi$
$114$	−6.61586	+	3.81967i	−0.0580339	+	0.0335059i
$115$	−134.479	−	115.826i	−1.16938	−	1.00719i
$116$	−36.5420	+	63.2926i	−0.315017	+	0.545626i
$117$	42.6075	+	11.4166i	0.364166	+	0.0975781i
$118$	−39.7865	−	39.7865i	−0.337174	−	0.337174i
$119$	−147.122	+	79.9926i	−1.23632	+	0.672207i
$120$	−20.2444	+	13.7900i	−0.168703	+	0.114917i
$121$	−126.512	−	219.125i	−1.04555	−	1.81095i
$122$	−15.6788	−	58.5140i	−0.128515	−	0.479623i
$123$	107.714	−	28.8620i	0.875727	−	0.234650i
$124$	−5.19606	+	2.99995i	−0.0419037	+	0.0241931i
$125$	−121.901	+	27.6623i	−0.975206	+	0.221298i
$126$	14.1862	+	26.0912i	0.112589	+	0.207073i
$127$	9.10167	−	9.10167i	0.0716667	−	0.0716667i	−0.670365	−	0.742032i	$-0.733862\pi$
$127$	9.10167	−	9.10167i	0.0716667	−	0.0716667i	0.742032	+	0.670365i	$0.233862\pi$
$128$	−2.92820	+	10.9282i	−0.0228766	+	0.0853766i
$129$	82.5318	+	47.6497i	0.639781	+	0.369378i
$130$	103.682	−	7.72630i	0.797553	−	0.0594331i
$131$	107.486	+	186.170i	0.820500	+	1.42115i	0.905310	+	0.424751i	$0.139638\pi$
$131$	107.486	+	186.170i	0.820500	+	1.42115i	−0.0848102	+	0.996397i	$0.527028\pi$
$132$	−47.3724	+	47.3724i	−0.358882	+	0.358882i
$133$	15.0369	+	15.8270i	0.113060	+	0.119000i
$134$		−	5.83731i		−	0.0435620i
$135$	8.57065	+	24.5264i	0.0634863	+	0.181677i
$136$	−33.8325	+	58.5996i	−0.248768	+	0.430880i
$137$	−33.5756	−	125.306i	−0.245077	−	0.914640i	−0.973345	−	0.229347i	$-0.926341\pi$
$137$	−33.5756	−	125.306i	−0.245077	−	0.914640i	0.728267	−	0.685293i	$-0.240326\pi$
$138$	−22.5040	+	83.9861i	−0.163073	+	0.608595i
$139$		−	68.0948i		−	0.489890i	−0.969537	−	0.244945i	$-0.921230\pi$
$139$		−	68.0948i		−	0.489890i	0.969537	−	0.244945i	$-0.0787700\pi$
$140$	51.8526	+	47.0246i	0.370376	+	0.335890i
$141$	−19.3308			−0.137098
$142$	−110.873	−	29.7085i	−0.780799	−	0.209214i
$143$	274.672	−	73.5980i	1.92078	−	0.514672i
$144$	10.3923	+	6.00000i	0.0721688	+	0.0416667i
$145$	164.583	+	79.3437i	1.13505	+	0.547198i
$146$	−148.403			−1.01646
$147$	63.0042	−	56.8636i	0.428600	−	0.386827i
$148$	0.618703	+	0.618703i	0.00418043	+	0.00418043i
$149$	−208.836	+	120.572i	−1.40159	+	0.809206i	−0.994556	−	0.104208i	$-0.966769\pi$
$149$	−208.836	+	120.572i	−1.40159	+	0.809206i	−0.407031	+	0.913414i	$0.633436\pi$
$150$	38.1408	+	47.9091i	0.254272	+	0.319394i
$151$	51.4548	−	89.1223i	0.340760	−	0.590214i	−0.643814	−	0.765182i	$-0.722649\pi$
$151$	51.4548	−	89.1223i	0.340760	−	0.590214i	0.984574	+	0.174968i	$0.0559823\pi$
$152$	8.52058	+	2.28308i	0.0560564	+	0.0150203i
$153$	50.7488	+	50.7488i	0.331691	+	0.331691i
$154$	163.299	+	99.9380i	1.06039	+	0.648948i
$155$	8.44447	+	12.3969i	0.0544804	+	0.0799800i
$156$	−25.4672	−	44.1105i	−0.163251	−	0.282760i
$157$	18.9599	+	70.7594i	0.120764	+	0.450697i	0.999653	−	0.0263285i	$-0.00838158\pi$
$157$	18.9599	+	70.7594i	0.120764	+	0.450697i	−0.878889	+	0.477026i	$0.841715\pi$
$158$	−40.7760	+	10.9259i	−0.258076	+	0.0691512i
$159$	−46.1008	+	26.6163i	−0.289942	+	0.167398i
$160$	27.7890	+	5.26999i	0.173681	+	0.0329374i
$161$	248.396	+	6.35833i	1.54283	+	0.0394927i
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	−17.3760	+	64.8481i	−0.106601	+	0.397841i	−0.998522	−	0.0543506i	$-0.982691\pi$
$163$	−17.3760	+	64.8481i	−0.106601	+	0.397841i	0.891921	+	0.452192i	$0.149358\pi$
$164$	−111.514	−	64.3827i	−0.679965	−	0.392578i
$165$	126.904	+	109.302i	0.769118	+	0.662439i
$166$	6.76277	+	11.7135i	0.0407396	+	0.0705630i
$167$	92.5655	−	92.5655i	0.554284	−	0.554284i	−0.373390	−	0.927674i	$-0.621805\pi$
$167$	92.5655	−	92.5655i	0.554284	−	0.554284i	0.927674	+	0.373390i	$0.121805\pi$
$168$	9.72036	−	32.8864i	0.0578593	−	0.195752i
$169$			47.1928i			0.279247i
$170$	152.379	+	73.4606i	0.896350	+	0.432121i
$171$	4.67812	−	8.10274i	0.0273574	−	0.0473845i
$172$	−28.4811	−	106.293i	−0.165588	−	0.617981i
$173$	45.5179	−	169.875i	0.263109	−	0.981936i	−0.700289	−	0.713860i	$-0.746945\pi$
$173$	45.5179	−	169.875i	0.263109	−	0.981936i	0.963398	−	0.268077i	$-0.0863880\pi$
$174$		−	89.5092i		−	0.514421i
$175$	107.603	−	138.009i	0.614874	−	0.788625i
$176$	77.3587			0.439538
$177$	66.5642	+	17.8358i	0.376069	+	0.100767i
$178$	159.857	−	42.8336i	0.898073	−	0.240638i
$179$	−220.202	−	127.134i	−1.23018	−	0.710243i	−0.263111	−	0.964766i	$-0.584748\pi$
$179$	−220.202	−	127.134i	−1.23018	−	0.710243i	−0.967067	+	0.254522i	$0.918082\pi$
$180$	13.0278	−	27.0236i	0.0723767	−	0.150131i
$181$	−114.712			−0.633771			−0.316885	−	0.948464i	$-0.602637\pi$
$181$	−114.712			−0.633771			−0.316885	+	0.948464i	$0.602637\pi$
$182$	−105.525	+	100.257i	−0.579805	+	0.550863i
$183$	52.4623	+	52.4623i	0.286679	+	0.286679i
$184$	86.9488	−	50.1999i	0.472548	−	0.272826i
$185$	1.42754	−	1.65743i	0.00771641	−	0.00895906i
$186$	3.67417	−	6.36385i	0.0197536	−	0.0342142i
$187$	446.902	+	119.747i	2.38985	+	0.640359i
$188$	15.7835	+	15.7835i	0.0839548	+	0.0839548i
$189$	−31.0243	−	18.9866i	−0.164150	−	0.100458i
$190$	4.10894	−	21.6667i	0.0216260	−	0.114035i
$191$	−159.306	−	275.926i	−0.834063	−	1.44464i	−0.894791	−	0.446485i	$-0.852675\pi$
$191$	−159.306	−	275.926i	−0.834063	−	1.44464i	0.0607278	−	0.998154i	$-0.480658\pi$
$192$	−3.58630	−	13.3843i	−0.0186787	−	0.0697097i
$193$	98.2599	−	26.3287i	0.509119	−	0.136418i	0.00489001	−	0.999988i	$-0.498443\pi$
$193$	98.2599	−	26.3287i	0.509119	−	0.136418i	0.504229	+	0.863570i	$0.331777\pi$
$194$	−110.579	+	63.8427i	−0.569994	+	0.329086i
$195$	−105.240	+	71.6869i	−0.539692	+	0.367625i
$196$	−97.8717	−	5.01384i	−0.499345	−	0.0255808i
$197$	−217.833	+	217.833i	−1.10575	+	1.10575i	−0.112047	+	0.993703i	$0.535741\pi$
$197$	−217.833	+	217.833i	−1.10575	+	1.10575i	−0.993703	+	0.112047i	$0.964259\pi$
$198$	21.2364	−	79.2555i	0.107255	−	0.400280i
$199$	19.8344	+	11.4514i	0.0996704	+	0.0575447i	0.549007	−	0.835818i	$-0.315006\pi$
$199$	19.8344	+	11.4514i	0.0996704	+	0.0575447i	−0.449336	+	0.893363i	$0.648339\pi$
$200$	7.97583	−	70.2594i	0.0398791	−	0.351297i
$201$	3.57461	+	6.19140i	0.0177841	+	0.0308030i
$202$	67.9799	−	67.9799i	0.336534	−	0.336534i
$203$	−248.691	+	59.8601i	−1.22508	+	0.294878i
$204$		−	82.8724i		−	0.406237i
$205$	−139.794	+	289.976i	−0.681924	+	1.41452i
$206$	−90.9413	+	157.515i	−0.441463	+	0.764636i
$207$	−27.5617	−	102.862i	−0.133148	−	0.496916i
$208$	−15.2222	+	56.8099i	−0.0731836	+	0.273125i
$209$		−	60.3156i		−	0.288591i
$210$	−83.7945	−	18.1240i	−0.399022	−	0.0863047i
$211$	184.175			0.872868			0.436434	−	0.899736i	$-0.356241\pi$
$211$	184.175			0.872868			0.436434	+	0.899736i	$0.356241\pi$
$212$	59.3733	+	15.9090i	0.280063	+	0.0750426i
$213$	135.792	−	36.3853i	0.637520	−	0.170823i
$214$	63.4775	+	36.6487i	0.296624	+	0.171256i
$215$	−259.706	+	90.7532i	−1.20793	+	0.422108i
$216$	−14.6969			−0.0680414
$217$	−20.1384	−	5.95238i	−0.0928035	−	0.0274303i
$218$	144.767	+	144.767i	0.664071	+	0.664071i
$219$	157.405	−	90.8777i	0.718744	−	0.414967i
$220$	−14.3719	−	192.862i	−0.0653270	−	0.876646i
$221$	−175.877	+	304.628i	−0.795825	+	1.37841i
$222$	−1.03511	−	0.277357i	−0.00466266	−	0.00124936i
$223$	−150.693	−	150.693i	−0.675752	−	0.675752i	0.283284	−	0.959036i	$-0.408576\pi$
$223$	−150.693	−	150.693i	−0.675752	−	0.675752i	−0.959036	+	0.283284i	$0.908576\pi$
$224$	−34.7883	+	18.9150i	−0.155305	+	0.0844419i
$225$	−69.7926	−	27.4589i	−0.310189	−	0.122040i
$226$	131.253	+	227.336i	0.580764	+	1.00591i
$227$	24.8120	+	92.5998i	0.109304	+	0.407928i	0.998798	−	0.0490189i	$-0.0156095\pi$
$227$	24.8120	+	92.5998i	0.109304	+	0.407928i	−0.889494	+	0.456947i	$0.848943\pi$
$228$	−10.4355	+	2.79619i	−0.0457699	+	0.0122640i
$229$	−6.22985	+	3.59681i	−0.0272046	+	0.0157066i	−0.513541	−	0.858065i	$-0.671666\pi$
$229$	−6.22985	+	3.59681i	−0.0272046	+	0.0157066i	0.486336	+	0.873772i	$0.338333\pi$
$230$	−141.306	−	207.445i	−0.614376	−	0.901933i
$231$	−234.404	−	6.00019i	−1.01474	−	0.0259749i
$232$	−73.0840	+	73.0840i	−0.315017	+	0.315017i
$233$	27.2353	−	101.644i	0.116890	−	0.436239i	−0.882532	−	0.470253i	$-0.844163\pi$
$233$	27.2353	−	101.644i	0.116890	−	0.436239i	0.999421	+	0.0340145i	$0.0108292\pi$
$234$	54.0241	+	31.1908i	0.230872	+	0.133294i
$235$	36.4173	−	42.2820i	0.154967	−	0.179923i
$236$	−39.7865	−	68.9123i	−0.168587	−	0.292001i
$237$	36.5588	−	36.5588i	0.154256	−	0.154256i
$238$	−230.251	+	55.4217i	−0.967443	+	0.232864i
$239$		−	101.044i		−	0.422779i	−0.977402	−	0.211389i	$-0.932201\pi$
$239$		−	101.044i		−	0.422779i	0.977402	−	0.211389i	$-0.0677988\pi$
$240$	−32.7019	+	11.4275i	−0.136258	+	0.0476147i
$241$	85.2132	−	147.594i	0.353582	−	0.612422i	−0.633292	−	0.773913i	$-0.718297\pi$
$241$	85.2132	−	147.594i	0.353582	−	0.612422i	0.986874	+	0.161491i	$0.0516302\pi$
$242$	−92.6130	−	345.636i	−0.382698	−	1.42825i
$243$	−4.03459	+	15.0573i	−0.0166032	+	0.0619642i
$244$		−	85.6705i		−	0.351109i
$245$	5.68294	+	244.934i	0.0231957	+	0.999731i
$246$	157.705			0.641077
$247$	44.2940	+	11.8685i	0.179328	+	0.0480508i
$248$	−8.19601	+	2.19611i	−0.0330484	+	0.00885530i
$249$	−14.3460	−	8.28267i	−0.0576145	−	0.0332637i
$250$	−176.645	−	6.83143i	−0.706579	−	0.0273257i
$251$	−135.214			−0.538703			−0.269351	−	0.963042i	$-0.586809\pi$
$251$	−135.214			−0.538703			−0.269351	+	0.963042i	$0.586809\pi$
$252$	9.82871	+	40.8338i	0.0390028	+	0.162039i
$253$	−485.425	−	485.425i	−1.91868	−	1.91868i
$254$	15.7646	−	9.10167i	0.0620652	−	0.0358334i
$255$	−206.608	+	15.3963i	−0.810228	+	0.0603776i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−206.149	−	55.2375i	−0.802137	−	0.214932i	−0.165615	−	0.986191i	$-0.552961\pi$
$257$	−206.149	−	55.2375i	−0.802137	−	0.214932i	−0.636522	+	0.771259i	$0.719628\pi$
$258$	95.2995	+	95.2995i	0.369378	+	0.369378i
$259$	−0.0783651	+	3.06142i	−0.000302568	+	0.0118202i
$260$	144.460	+	27.3959i	0.555616	+	0.105369i
$261$	54.8130	+	94.9389i	0.210011	+	0.363751i
$262$	78.6849	+	293.656i	0.300324	+	1.12082i
$263$	−225.061	+	60.3049i	−0.855745	+	0.229296i	−0.659914	−	0.751342i	$-0.729407\pi$
$263$	−225.061	+	60.3049i	−0.855745	+	0.229296i	−0.195831	+	0.980638i	$0.562740\pi$
$264$	−82.0513	+	47.3724i	−0.310801	+	0.179441i
$265$	28.6320	−	150.978i	0.108045	−	0.569730i
$266$	14.7478	+	27.1240i	0.0554427	+	0.101970i
$267$	−143.324	+	143.324i	−0.536793	+	0.536793i
$268$	2.13660	−	7.97391i	0.00797240	−	0.0297534i
$269$	−146.659	−	84.6734i	−0.545199	−	0.314771i	0.201984	−	0.979389i	$-0.435261\pi$
$269$	−146.659	−	84.6734i	−0.545199	−	0.314771i	−0.747184	+	0.664618i	$0.768594\pi$
$270$	2.73044	+	36.6408i	0.0101127	+	0.135706i
$271$	48.7012	+	84.3530i	0.179709	+	0.311266i	0.941781	−	0.336227i	$-0.109151\pi$
$271$	48.7012	+	84.3530i	0.179709	+	0.311266i	−0.762072	+	0.647493i	$0.775818\pi$
$272$	−67.6650	+	67.6650i	−0.248768	+	0.248768i
$273$	50.5310	−	170.959i	0.185095	−	0.626223i
$274$		−	183.460i		−	0.669563i
$275$	−478.152	+	71.6610i	−1.73873	+	0.260586i
$276$	−61.4821	+	106.490i	−0.222761	+	0.385834i
$277$	20.0063	+	74.6644i	0.0722248	+	0.269547i	0.992590	−	0.121514i	$-0.0387749\pi$
$277$	20.0063	+	74.6644i	0.0722248	+	0.269547i	−0.920365	+	0.391061i	$0.872108\pi$
$278$	24.9244	−	93.0192i	0.0896562	−	0.334601i
$279$			8.99984i			0.0322575i
$280$	53.6198	+	83.2161i	0.191499	+	0.297200i
$281$	426.425			1.51753			0.758763	−	0.651367i	$-0.225804\pi$
$281$	426.425			1.51753			0.758763	+	0.651367i	$0.225804\pi$
$282$	−26.4063	−	7.07555i	−0.0936394	−	0.0250906i
$283$	68.4841	−	18.3503i	0.241993	−	0.0648419i	−0.135784	−	0.990739i	$-0.543355\pi$
$283$	68.4841	−	18.3503i	0.241993	−	0.0648419i	0.377777	+	0.925897i	$0.376689\pi$
$284$	−140.582	−	81.1650i	−0.495007	−	0.285792i
$285$	8.90990	+	25.4972i	0.0312628	+	0.0894639i
$286$	402.147			1.40611
$287$	−105.467	−	438.165i	−0.367479	−	1.52671i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$	−245.362	+	141.660i	−0.849002	+	0.490172i
$290$	195.783	+	168.627i	0.675112	+	0.581472i
$291$	78.1910	−	135.431i	0.268698	−	0.465398i
$292$	−202.722	−	54.3192i	−0.694253	−	0.186025i
$293$	−27.6890	−	27.6890i	−0.0945016	−	0.0945016i	0.658275	−	0.752777i	$-0.271286\pi$
$293$	−27.6890	−	27.6890i	−0.0945016	−	0.0945016i	−0.752777	+	0.658275i	$0.771286\pi$
$294$	106.879	−	54.6159i	0.363534	−	0.185768i
$295$	−164.413	+	111.994i	−0.557331	+	0.379641i
$296$	0.618703	+	1.07163i	0.00209021	+	0.00362036i
$297$	26.0092	+	97.0678i	0.0875732	+	0.326828i
$298$	−329.408	+	88.2646i	−1.10540	+	0.296190i
$299$	452.001	−	260.963i	1.51171	−	0.872785i
$300$	34.5653	+	79.4055i	0.115218	+	0.264685i
$301$	201.046	−	328.511i	0.667928	−	1.09140i
$302$	102.910	−	102.910i	0.340760	−	0.340760i
$303$	−30.4745	+	113.733i	−0.100576	+	0.375355i
$304$	10.8037	+	6.23750i	0.0355384	+	0.0205181i
$305$	−213.584	+	15.9161i	−0.700276	+	0.0521840i
$306$	50.7488	+	87.8994i	0.165846	+	0.287253i
$307$	−292.629	+	292.629i	−0.953190	+	0.953190i	−0.998952	−	0.0457623i	$-0.985428\pi$
$307$	−292.629	+	292.629i	−0.953190	+	0.953190i	0.0457623	+	0.998952i	$0.485428\pi$
$308$	186.491	+	196.290i	0.605491	+	0.637304i
$309$		−	222.760i		−	0.720905i
$310$	6.99778	+	20.0254i	0.0225735	+	0.0645979i
$311$	82.6523	−	143.158i	0.265763	−	0.460315i	−0.702000	−	0.712177i	$-0.747709\pi$
$311$	82.6523	−	143.158i	0.265763	−	0.460315i	0.967763	+	0.251862i	$0.0810428\pi$
$312$	−18.6433	−	69.5777i	−0.0597541	−	0.223005i
$313$	−30.0301	+	112.074i	−0.0959429	+	0.358064i	−0.997161	−	0.0753026i	$-0.976008\pi$
$313$	−30.0301	+	112.074i	−0.0959429	+	0.358064i	0.901218	+	0.433366i	$0.142674\pi$
$314$			103.599i			0.329933i
$315$	99.9761	−	32.0901i	0.317385	−	0.101873i
$316$	−59.7002			−0.188925
$317$	567.946	+	152.181i	1.79163	+	0.480065i	0.992621	−	0.121257i	$-0.0386926\pi$
$317$	567.946	+	152.181i	1.79163	+	0.480065i	0.799007	+	0.601322i	$0.205359\pi$
$318$	−72.7171	+	19.4845i	−0.228670	+	0.0612720i
$319$	612.029	+	353.355i	1.91859	+	1.10770i
$320$	36.0315	+	17.3704i	0.112598	+	0.0542825i
$321$	−89.7707			−0.279660
$322$	336.987	+	99.6047i	1.04654	+	0.309331i
$323$	52.7575	+	52.7575i	0.163336	+	0.163336i
$324$	15.5885	−	9.00000i	0.0481125	−	0.0277778i
$325$	41.4621	−	365.242i	0.127576	−	1.12382i
$326$	−47.4721	+	82.2241i	−0.145620	+	0.252221i
$327$	−242.201	−	64.8975i	−0.740675	−	0.198463i
$328$	−128.765	−	128.765i	−0.392578	−	0.392578i
$329$	−1.99914	+	78.0988i	−0.00607642	+	0.237382i
$330$	133.347	+	195.760i	0.404082	+	0.593213i
$331$	−78.4975	−	135.962i	−0.237152	−	0.410760i	0.722744	−	0.691116i	$-0.242881\pi$
$331$	−78.4975	−	135.962i	−0.237152	−	0.410760i	−0.959896	+	0.280356i	$0.909547\pi$
$332$	4.95069	+	18.4762i	0.0149117	+	0.0556513i
$333$	1.26775	−	0.339692i	0.00380705	−	0.00102010i
$334$	160.328	−	92.5655i	0.480024	−	0.277142i
$335$	−20.2766	−	3.84532i	−0.0605272	−	0.0114786i
$336$	25.3155	−	41.3657i	0.0753438	−	0.123112i
$337$	−208.968	+	208.968i	−0.620082	+	0.620082i	−0.945552	−	0.325470i	$-0.894477\pi$
$337$	−208.968	+	208.968i	−0.620082	+	0.620082i	0.325470	+	0.945552i	$0.394477\pi$
$338$	−17.2738	+	64.4666i	−0.0511058	+	0.190729i
$339$	−278.429	−	160.751i	−0.821325	−	0.474192i
$340$	181.266	+	156.124i	0.533135	+	0.459188i
$341$	29.0090	+	50.2451i	0.0850704	+	0.147346i
$342$	9.35624	−	9.35624i	0.0273574	−	0.0273574i
$343$	−223.220	−	260.426i	−0.650788	−	0.759259i
$344$		−	155.623i		−	0.452394i
$345$	276.911	+	133.496i	0.802642	+	0.386945i
$346$	124.357	−	215.393i	0.359414	−	0.622523i
$347$	69.5374	+	259.517i	0.200396	+	0.747888i	0.990804	+	0.135307i	$0.0432021\pi$
$347$	69.5374	+	259.517i	0.200396	+	0.747888i	−0.790408	+	0.612581i	$0.790131\pi$
$348$	32.7627	−	122.272i	0.0941456	−	0.351356i
$349$			260.737i			0.747097i	0.927611	+	0.373549i	$0.121859\pi$
$349$			260.737i			0.747097i	−0.927611	+	0.373549i	$0.878141\pi$
$350$	197.503	−	149.139i	0.564295	−	0.426111i
$351$	−76.4016			−0.217668
$352$	105.674	+	28.3153i	0.300210	+	0.0804411i
$353$	240.936	−	64.5587i	0.682539	−	0.182886i	0.0991424	−	0.995073i	$-0.468390\pi$
$353$	240.936	−	64.5587i	0.682539	−	0.182886i	0.583396	+	0.812188i	$0.301723\pi$
$354$	84.4000	+	48.7284i	0.238418	+	0.137651i
$355$	−176.234	+	365.562i	−0.496433	+	1.02975i
$356$	234.047			0.657435
$357$	210.280	−	199.783i	0.589019	−	0.559617i
$358$	−254.267	−	254.267i	−0.710243	−	0.710243i
$359$	508.866	−	293.794i	1.41746	−	0.818368i	0.421380	−	0.906884i	$-0.361546\pi$
$359$	508.866	−	293.794i	1.41746	−	0.818368i	0.996075	+	0.0885160i	$0.0282124\pi$
$360$	27.6877	−	32.1464i	0.0769101	−	0.0892957i
$361$	−175.637	+	304.212i	−0.486528	+	0.842692i
$362$	−156.700	−	41.9877i	−0.432873	−	0.115988i
$363$	309.889	+	309.889i	0.853689	+	0.853689i
$364$	−180.846	+	98.3290i	−0.496829	+	0.270135i
$365$	−97.7601	+	515.495i	−0.267836	+	1.41231i
$366$	52.4623	+	90.8673i	0.143339	+	0.248271i
$367$	−17.8386	−	66.5746i	−0.0486066	−	0.181402i	0.937355	−	0.348377i	$-0.113267\pi$
$367$	−17.8386	−	66.5746i	−0.0486066	−	0.181402i	−0.985961	+	0.166974i	$0.946600\pi$
$368$	137.149	−	36.7489i	0.372687	−	0.0998611i
$369$	−167.271	+	96.5741i	−0.453310	+	0.261718i
$370$	2.55671	−	1.74157i	0.00691003	−	0.00470695i
$371$	102.766	+	189.006i	0.276997	+	0.509450i
$372$	7.34834	−	7.34834i	0.0197536	−	0.0197536i
$373$	81.1209	−	302.747i	0.217482	−	0.811655i	−0.767796	−	0.640695i	$-0.778646\pi$
$373$	81.1209	−	302.747i	0.217482	−	0.811655i	0.985278	−	0.170960i	$-0.0546869\pi$
$374$	566.649	+	327.155i	1.51510	+	0.874746i
$375$	191.543	−	100.926i	0.510782	−	0.269137i
$376$	15.7835	+	27.3378i	0.0419774	+	0.0727070i
$377$	−379.925	+	379.925i	−1.00776	+	1.00776i
$378$	−35.4304	−	37.2919i	−0.0937312	−	0.0986559i
$379$			400.395i			1.05645i	0.849104	+	0.528226i	$0.177142\pi$
$379$			400.395i			1.05645i	−0.849104	+	0.528226i	$0.822858\pi$
$380$	13.5435	−	28.0933i	0.0356408	−	0.0739297i
$381$	−11.1472	+	19.3076i	−0.0292578	+	0.0506760i
$382$	−116.620	−	435.232i	−0.305288	−	1.13935i
$383$	155.366	−	579.836i	0.405657	−	1.51393i	−0.397185	−	0.917739i	$-0.630013\pi$
$383$	155.366	−	579.836i	0.405657	−	1.51393i	0.802842	−	0.596192i	$-0.203320\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	454.720	−	501.406i	1.18109	−	1.30235i
$386$	143.863			0.372701
$387$	−159.439	−	42.7216i	−0.411987	−	0.110392i
$388$	−174.421	+	46.7361i	−0.449540	+	0.120454i
$389$	113.750	+	65.6735i	0.292416	+	0.168826i	0.639031	−	0.769181i	$-0.279336\pi$
$389$	113.750	+	65.6735i	0.292416	+	0.168826i	−0.346615	+	0.938008i	$0.612669\pi$
$390$	−170.000	+	59.4057i	−0.435897	+	0.152322i
$391$	849.194			2.17185
$392$	−131.860	−	42.6726i	−0.336377	−	0.108859i
$393$	−263.285	−	263.285i	−0.669936	−	0.669936i
$394$	−377.297	+	217.833i	−0.957608	+	0.552875i
$395$	11.0913	+	148.838i	0.0280792	+	0.376805i
$396$	58.0191	−	100.492i	0.146513	−	0.253768i
$397$	−657.925	−	176.291i	−1.65724	−	0.444057i	−0.695615	−	0.718415i	$-0.744868\pi$
$397$	−657.925	−	176.291i	−1.65724	−	0.444057i	−0.961628	+	0.274358i	$0.911535\pi$
$398$	22.9028	+	22.9028i	0.0575447	+	0.0575447i
$399$	−32.2523	−	19.7382i	−0.0808329	−	0.0494691i
$400$	36.6119	−	93.0568i	0.0915298	−	0.232642i
$401$	−17.6363	−	30.5469i	−0.0439807	−	0.0761769i	0.843197	−	0.537605i	$-0.180671\pi$
$401$	−17.6363	−	30.5469i	−0.0439807	−	0.0761769i	−0.887178	+	0.461428i	$0.847337\pi$
$402$	2.61679	+	9.76601i	0.00650944	+	0.0242935i
$403$	−42.6067	+	11.4164i	−0.105724	+	0.0283286i
$404$	117.745	−	67.9799i	0.291447	−	0.168267i
$405$	−25.3339	−	37.1913i	−0.0625527	−	0.0918305i
$406$	−361.629	−	9.25683i	−0.890711	−	0.0228001i
$407$	5.98276	−	5.98276i	0.0146997	−	0.0146997i
$408$	30.3334	−	113.206i	0.0743466	−	0.277465i
$409$	−114.297	−	65.9892i	−0.279454	−	0.161343i	0.353722	−	0.935350i	$-0.384916\pi$
$409$	−114.297	−	65.9892i	−0.279454	−	0.161343i	−0.633176	+	0.774008i	$0.718249\pi$
$410$	−297.101	+	344.946i	−0.724637	+	0.841332i
$411$	112.346	+	194.589i	0.273348	+	0.473453i
$412$	−181.883	+	181.883i	−0.441463	+	0.441463i
$413$	78.9429	−	267.083i	0.191145	−	0.646691i
$414$		−	150.600i		−	0.363767i
$415$	45.1431	−	15.7751i	0.108779	−	0.0380122i
$416$	−41.5878	+	72.0321i	−0.0999706	+	0.173154i
$417$	30.5261	+	113.925i	0.0732040	+	0.273201i
$418$	22.0770	−	82.3926i	0.0528159	−	0.197112i
$419$		−	578.241i		−	1.38005i	−0.723786	−	0.690024i	$-0.757600\pi$
$419$		−	578.241i		−	1.38005i	0.723786	−	0.690024i	$-0.242400\pi$
$420$	−107.832	−	55.4287i	−0.256742	−	0.131973i
$421$	494.086			1.17360			0.586801	−	0.809732i	$-0.300387\pi$
$421$	494.086			1.17360			0.586801	+	0.809732i	$0.300387\pi$
$422$	251.588	+	67.4128i	0.596180	+	0.159746i
$423$	32.3410	−	8.66575i	0.0764563	−	0.0204864i
$424$	75.2823	+	43.4643i	0.177553	+	0.102510i
$425$	355.554	−	480.917i	0.836598	−	1.13157i
$426$	198.813			0.466697
$427$	217.380	−	206.529i	0.509086	−	0.483674i
$428$	73.2975	+	73.2975i	0.171256	+	0.171256i
$429$	−426.541	+	246.264i	−0.994269	+	0.574042i
$430$	−387.983	+	28.9122i	−0.902286	+	0.0672377i
$431$	−34.7168	+	60.1313i	−0.0805494	+	0.139516i	−0.903486	−	0.428617i	$-0.859001\pi$
$431$	−34.7168	+	60.1313i	−0.0805494	+	0.139516i	0.822937	+	0.568133i	$0.192334\pi$
$432$	−20.0764	−	5.37945i	−0.0464731	−	0.0124524i
$433$	473.011	+	473.011i	1.09240	+	1.09240i	0.995271	+	0.0971324i	$0.0309670\pi$
$433$	473.011	+	473.011i	1.09240	+	1.09240i	0.0971324	+	0.995271i	$0.469033\pi$
$434$	−25.3308	−	15.5023i	−0.0583659	−	0.0357195i
$435$	−310.921	−	58.9641i	−0.714762	−	0.135550i
$436$	144.767	+	250.745i	0.332036	+	0.575102i
$437$	−28.6526	−	106.933i	−0.0655667	−	0.244698i
$438$	248.283	−	66.5271i	0.566855	−	0.151888i
$439$	304.676	−	175.905i	0.694024	−	0.400695i	−0.111094	−	0.993810i	$-0.535435\pi$
$439$	304.676	−	175.905i	0.694024	−	0.400695i	0.805118	+	0.593115i	$0.202102\pi$
$440$	50.9600	−	268.715i	0.115818	−	0.610716i
$441$	−79.9169	+	123.379i	−0.181218	+	0.279770i
$442$	−351.755	+	351.755i	−0.795825	+	0.795825i
$443$	−60.7333	+	226.660i	−0.137095	+	0.511647i	0.862885	+	0.505400i	$0.168655\pi$
$443$	−60.7333	+	226.660i	−0.137095	+	0.511647i	−0.999980	+	0.00624700i	$0.998012\pi$
$444$	−1.31247	−	0.757754i	−0.00295601	−	0.00170665i
$445$	−43.4819	−	583.499i	−0.0977122	−	1.31123i
$446$	−150.693	−	261.007i	−0.337876	−	0.585218i
$447$	295.339	−	295.339i	0.660714	−	0.660714i
$448$	−54.4450	+	13.1050i	−0.121529	+	0.0292521i
$449$		−	40.1949i		−	0.0895210i	−0.998998	−	0.0447605i	$-0.985748\pi$
$449$		−	40.1949i		−	0.0895210i	0.998998	−	0.0447605i	$-0.0142525\pi$
$450$	−85.2878	−	63.0555i	−0.189528	−	0.140123i
$451$	−622.571	+	1078.32i	−1.38042	+	2.39096i
$452$	96.0837	+	358.589i	0.212575	+	0.793339i
$453$	−46.1331	+	172.171i	−0.101839	+	0.380068i
$454$			135.575i			0.298624i
$455$	278.741	+	432.597i	0.612617	+	0.950762i
$456$	−15.2787			−0.0335059
$457$	229.905	+	61.6028i	0.503074	+	0.134798i	0.501426	−	0.865200i	$-0.332809\pi$
$457$	229.905	+	61.6028i	0.503074	+	0.134798i	0.00164767	+	0.999999i	$0.499476\pi$
$458$	−9.82666	+	2.63305i	−0.0214556	+	0.00574901i
$459$	−107.654	−	62.1543i	−0.234541	−	0.135412i
$460$	−117.098	−	335.096i	−0.254561	−	0.728470i
$461$	782.863			1.69818			0.849092	−	0.528245i	$-0.177150\pi$
$461$	782.863			1.69818			0.849092	+	0.528245i	$0.177150\pi$
$462$	−318.006	−	93.9944i	−0.688325	−	0.203451i
$463$	504.302	+	504.302i	1.08921	+	1.08921i	0.995610	+	0.0935957i	$0.0298361\pi$
$463$	504.302	+	504.302i	1.08921	+	1.08921i	0.0935957	+	0.995610i	$0.470164\pi$
$464$	−126.585	+	73.0840i	−0.272813	+	0.157509i
$465$	−19.6852	−	16.9549i	−0.0423339	−	0.0364621i
$466$	74.4083	−	128.879i	0.159674	−	0.276564i
$467$	−208.514	−	55.8712i	−0.446497	−	0.119639i	0.0285628	−	0.999592i	$-0.490907\pi$
$467$	−208.514	−	55.8712i	−0.446497	−	0.119639i	−0.475060	+	0.879953i	$0.657574\pi$
$468$	62.3817	+	62.3817i	0.133294	+	0.133294i
$469$	25.3837	−	13.8016i	0.0541231	−	0.0294277i
$470$	65.2233	−	44.4286i	0.138773	−	0.0945289i
$471$	−63.4412	−	109.883i	−0.134695	−	0.233298i
$472$	−29.1258	−	108.699i	−0.0617071	−	0.230294i
$473$	−1027.83	+	275.407i	−2.17301	+	0.582257i
$474$	63.3216	−	36.5588i	0.133590	−	0.0771282i
$475$	−72.5552	−	28.5458i	−0.152748	−	0.0600965i
$476$	−334.815	−	8.57046i	−0.703393	−	0.0180052i
$477$	65.1964	−	65.1964i	0.136680	−	0.136680i
$478$	36.9847	−	138.029i	0.0773739	−	0.288763i
$479$	−144.556	−	83.4594i	−0.301787	−	0.174237i	0.341458	−	0.939897i	$-0.389079\pi$
$479$	−144.556	−	83.4594i	−0.301787	−	0.174237i	−0.643245	+	0.765660i	$0.722413\pi$
$480$	−48.8543	+	3.64059i	−0.101780	+	0.00758456i
$481$	3.21631	+	5.57081i	0.00668672	+	0.0115817i
$482$	170.426	−	170.426i	0.353582	−	0.353582i
$483$	−418.424	+	100.715i	−0.866303	+	0.208520i
$484$		−	506.047i		−	1.04555i
$485$	148.922	+	426.165i	0.307055	+	0.878691i
$486$	−11.0227	+	19.0919i	−0.0226805	+	0.0392837i
$487$	181.869	+	678.744i	0.373447	+	1.39372i	0.855600	+	0.517637i	$0.173188\pi$
$487$	181.869	+	678.744i	0.373447	+	1.39372i	−0.482153	+	0.876087i	$0.660145\pi$
$488$	31.3576	−	117.028i	0.0642573	−	0.239812i
$489$		−	116.283i		−	0.237797i
$490$	−81.8890	+	336.666i	−0.167121	+	0.687074i
$491$	71.9764			0.146591			0.0732957	−	0.997310i	$-0.476648\pi$
$491$	71.9764			0.146591			0.0732957	+	0.997310i	$0.476648\pi$
$492$	215.429	+	57.7240i	0.437864	+	0.117325i
$493$	−844.414	+	226.260i	−1.71281	+	0.458945i
$494$	56.1625	+	32.4254i	0.113689	+	0.0656385i
$495$	−261.314	−	125.977i	−0.527907	−	0.254499i
$496$	−11.9998			−0.0241931
$497$	−132.958	−	552.379i	−0.267521	−	1.11143i
$498$	−16.5653	−	16.5653i	−0.0332637	−	0.0332637i
$499$	−33.5121	+	19.3482i	−0.0671586	+	0.0387740i	−0.533203	−	0.845987i	$-0.679012\pi$
$499$	−33.5121	+	19.3482i	−0.0671586	+	0.0387740i	0.466045	+	0.884761i	$0.345679\pi$
$500$	−238.801	−	73.9883i	−0.477601	−	0.147977i
$501$	−113.369	+	196.361i	−0.226286	+	0.391938i
$502$	−184.706	−	49.4919i	−0.367941	−	0.0985894i
$503$	152.122	+	152.122i	0.302429	+	0.302429i	0.841963	−	0.539535i	$-0.181400\pi$
$503$	152.122	+	152.122i	0.302429	+	0.302429i	−0.539535	+	0.841963i	$0.681400\pi$
$504$	−1.51992	+	59.3775i	−0.00301572	+	0.117813i
$505$	−191.355	−	280.918i	−0.378920	−	0.556273i
$506$	−485.425	−	840.781i	−0.959338	−	1.66162i
$507$	−21.1560	−	78.9551i	−0.0417277	−	0.155730i
$508$	24.8662	−	6.66289i	0.0489493	−	0.0131159i
$509$	500.986	−	289.245i	0.984256	−	0.568260i	0.0807035	−	0.996738i	$-0.474283\pi$
$509$	500.986	−	289.245i	0.984256	−	0.568260i	0.903552	+	0.428478i	$0.140950\pi$
$510$	−287.867	−	54.5921i	−0.564446	−	0.107043i
$511$	−350.879	−	645.334i	−0.686652	−	1.26288i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−4.19429	+	15.6533i	−0.00817600	+	0.0305133i
$514$	−261.387	−	150.912i	−0.508534	−	0.293602i
$515$	487.240	+	419.659i	0.946097	+	0.814871i
$516$	95.2995	+	165.064i	0.184689	+	0.319891i
$517$	152.624	−	152.624i	0.295211	−	0.295211i
$518$	−1.22761	+	4.15330i	−0.00236990	+	0.00801795i
$519$			304.612i			0.586920i
$520$	187.309	+	90.2996i	0.360209	+	0.173653i
$521$	−158.312	+	274.205i	−0.303862	+	0.526305i	−0.977007	−	0.213205i	$-0.931610\pi$
$521$	−158.312	+	274.205i	−0.303862	+	0.526305i	0.673145	+	0.739511i	$0.264943\pi$
$522$	40.1259	+	149.752i	0.0768695	+	0.286881i
$523$	−169.840	+	633.850i	−0.324741	+	1.21195i	0.589831	+	0.807527i	$0.299194\pi$
$523$	−169.840	+	633.850i	−0.324741	+	1.21195i	−0.914572	+	0.404423i	$0.867472\pi$
$524$			429.942i			0.820500i
$525$	−118.155	+	279.131i	−0.225058	+	0.531679i
$526$	−329.512			−0.626449
$527$	−69.3229	−	18.5750i	−0.131542	−	0.0352467i
$528$	−129.424	+	34.6790i	−0.245121	+	0.0656799i
$529$	−633.078	−	365.508i	−1.19674	−	0.690941i
$530$	94.3740	−	195.760i	0.178064	−	0.369359i
$531$	−119.360			−0.224783
$532$	10.2178	+	42.4501i	0.0192063	+	0.0797934i
$533$	−669.384	−	669.384i	−1.25588	−	1.25588i
$534$	−248.244	+	143.324i	−0.464877	+	0.268397i
$535$	169.120	−	196.354i	0.316111	−	0.367018i
$536$	5.83731	−	10.1105i	0.0108905	−	0.0188629i
$537$	425.397	+	113.985i	0.792173	+	0.212262i
$538$	−169.347	−	169.347i	−0.314771	−	0.314771i
$539$	−48.4831	+	946.404i	−0.0899501	+	1.75585i
$540$	−9.68159	+	51.0516i	−0.0179289	+	0.0945400i
$541$	−279.416	−	483.962i	−0.516480	−	0.894570i	−0.999817	−	0.0191352i	$-0.993909\pi$
$541$	−279.416	−	483.962i	−0.516480	−	0.894570i	0.483337	−	0.875434i	$-0.339425\pi$
$542$	35.6518	+	133.054i	0.0657782	+	0.245488i
$543$	191.918	−	51.4242i	0.353440	−	0.0947039i
$544$	−117.199	+	67.6650i	−0.215440	+	0.124384i
$545$	598.233	−	407.502i	1.09768	−	0.747710i
$546$	131.602	−	215.039i	0.241029	−	0.393844i
$547$	374.501	−	374.501i	0.684646	−	0.684646i	−0.276398	−	0.961043i	$-0.589141\pi$
$547$	374.501	−	374.501i	0.684646	−	0.684646i	0.961043	+	0.276398i	$0.0891407\pi$
$548$	67.1511	−	250.611i	0.122539	−	0.457320i
$549$	−111.289	−	64.2529i	−0.202713	−	0.117036i
$550$	−679.398	−	77.1250i	−1.23527	−	0.140227i
$551$	56.9826	+	98.6968i	0.103417	+	0.179123i
$552$	−122.964	+	122.964i	−0.222761	+	0.222761i
$553$	−143.921	−	151.483i	−0.260255	−	0.273929i
$554$			109.316i			0.197322i
$555$	−1.64531	+	3.41287i	−0.00296453	+	0.00614932i
$556$	68.0948	−	117.944i	0.122473	−	0.212129i
$557$	−62.7273	−	234.101i	−0.112616	−	0.420290i	0.886481	−	0.462765i	$-0.153142\pi$
$557$	−62.7273	−	234.101i	−0.112616	−	0.420290i	−0.999098	+	0.0424747i	$0.986476\pi$
$558$	−3.29417	+	12.2940i	−0.00590353	+	0.0220323i
$559$		−	809.004i		−	1.44723i
$560$	42.7868	+	133.302i	0.0764049	+	0.238038i
$561$	−801.363			−1.42845
$562$	582.507	+	156.082i	1.03649	+	0.277727i
$563$	940.702	−	252.060i	1.67087	−	0.447709i	0.705528	−	0.708682i	$-0.250710\pi$
$563$	940.702	−	252.060i	1.67087	−	0.447709i	0.965346	+	0.260973i	$0.0840433\pi$
$564$	−33.4819	−	19.3308i	−0.0593650	−	0.0342744i
$565$	876.144	−	306.165i	1.55070	−	0.541885i
$566$	100.268			0.177151
$567$	60.4162	+	17.8574i	0.106554	+	0.0314946i
$568$	−162.330	−	162.330i	−0.285792	−	0.285792i
$569$	258.001	−	148.957i	0.453429	−	0.261788i	−0.255848	−	0.966717i	$-0.582355\pi$
$569$	258.001	−	148.957i	0.453429	−	0.261788i	0.709277	+	0.704929i	$0.249021\pi$
$570$	2.83852	+	38.0911i	0.00497986	+	0.0668265i
$571$	−185.885	+	321.962i	−0.325543	+	0.563857i	−0.981622	−	0.190835i	$-0.938880\pi$
$571$	−185.885	+	321.962i	−0.325543	+	0.563857i	0.656079	+	0.754692i	$0.272214\pi$
$572$	549.343	+	147.196i	0.960390	+	0.257336i
$573$	390.219	+	390.219i	0.681010	+	0.681010i
$574$	16.3095	−	637.148i	0.0284137	−	1.11001i
$575$	−813.670	+	354.191i	−1.41508	+	0.615984i
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	68.6631	+	256.254i	0.119000	+	0.444115i	0.999555	−	0.0298294i	$-0.00949642\pi$
$577$	68.6631	+	256.254i	0.119000	+	0.444115i	−0.880555	+	0.473944i	$0.842830\pi$
$578$	−387.021	+	103.702i	−0.669587	+	0.179415i
$579$	−152.589	+	88.0975i	−0.263539	+	0.152155i
$580$	205.722	+	302.010i	0.354693	+	0.520707i
$581$	−34.9467	+	57.1031i	−0.0601492	+	0.0982842i
$582$	156.382	−	156.382i	0.268698	−	0.268698i
$583$	153.838	−	574.130i	0.263873	−	0.984786i
$584$	−257.041	−	148.403i	−0.440139	−	0.254114i
$585$	143.933	−	167.112i	0.246040	−	0.285662i
$586$	−27.6890	−	47.9587i	−0.0472508	−	0.0818408i
$587$	−348.454	+	348.454i	−0.593618	+	0.593618i	−0.938607	−	0.344989i	$-0.887883\pi$
$587$	−348.454	+	348.454i	−0.593618	+	0.593618i	0.344989	+	0.938607i	$0.387883\pi$
$588$	165.990	−	35.4863i	0.282296	−	0.0603509i
$589$			9.35608i			0.0158847i
$590$	−265.585	+	92.8075i	−0.450143	+	0.157301i
$591$	266.790	−	462.093i	0.451421	−	0.781883i
$592$	0.452922	+	1.69033i	0.000765071	+	0.00285529i
$593$	103.985	−	388.078i	0.175354	−	0.654432i	−0.821136	−	0.570732i	$-0.806660\pi$
$593$	103.985	−	388.078i	0.175354	−	0.654432i	0.996491	−	0.0837000i	$-0.0266738\pi$
$594$			142.117i			0.239254i
$595$	40.8361	+	836.315i	0.0686320	+	1.40557i
$596$	−482.287			−0.809206
$597$	−38.3171	−	10.2670i	−0.0641828	−	0.0171977i
$598$	712.964	−	191.038i	1.19225	−	0.319462i
$599$	−471.995	−	272.507i	−0.787972	−	0.454936i	0.0512762	−	0.998685i	$-0.483671\pi$
$599$	−471.995	−	272.507i	−0.787972	−	0.454936i	−0.839248	+	0.543749i	$0.817004\pi$
$600$	18.1526	+	121.122i	0.0302544	+	0.201870i
$601$	628.276			1.04539			0.522693	−	0.852521i	$-0.324928\pi$
$601$	628.276			1.04539			0.522693	+	0.852521i	$0.324928\pi$
$602$	394.878	−	375.167i	0.655943	−	0.623200i
$603$	−8.75596	−	8.75596i	−0.0145207	−	0.0145207i
$604$	178.245	−	102.910i	0.295107	−	0.170380i
$605$	−1261.62	+	94.0149i	−2.08532	+	0.155397i
$606$	−83.2580	+	144.207i	−0.137389	+	0.237966i
$607$	−550.219	−	147.431i	−0.906457	−	0.242884i	−0.224670	−	0.974435i	$-0.572130\pi$
$607$	−550.219	−	147.431i	−0.906457	−	0.242884i	−0.681787	+	0.731551i	$0.738797\pi$
$608$	12.4750	+	12.4750i	0.0205181	+	0.0205181i
$609$	389.234	−	211.633i	0.639136	−	0.347509i
$610$	−297.587	−	56.4354i	−0.487847	−	0.0925170i
$611$	82.0501	+	142.115i	0.134288	+	0.232594i
$612$	37.1507	+	138.648i	0.0607037	+	0.226549i
$613$	136.360	−	36.5375i	0.222447	−	0.0596044i	−0.145874	−	0.989303i	$-0.546599\pi$
$613$	136.360	−	36.5375i	0.222447	−	0.0596044i	0.368321	+	0.929699i	$0.379933\pi$
$614$	−506.849	+	292.629i	−0.825487	+	0.476595i
$615$	103.888	−	547.807i	0.168923	−	0.890743i
$616$	182.905	+	336.397i	0.296923	+	0.546099i
$617$	21.2335	−	21.2335i	0.0344141	−	0.0344141i	−0.689690	−	0.724104i	$-0.742253\pi$
$617$	21.2335	−	21.2335i	0.0344141	−	0.0344141i	0.724104	+	0.689690i	$0.242253\pi$
$618$	81.5357	−	304.296i	0.131935	−	0.492388i
$619$	768.980	+	443.971i	1.24229	+	0.717239i	0.969561	−	0.244851i	$-0.0787390\pi$
$619$	768.980	+	443.971i	1.24229	+	0.717239i	0.272733	+	0.962090i	$0.412072\pi$
$620$	2.22936	+	29.9165i	0.00359574	+	0.0482524i
$621$	92.2231	+	159.735i	0.148507	+	0.257222i
$622$	165.305	−	165.305i	0.265763	−	0.265763i
$623$	564.225	+	593.869i	0.905657	+	0.953241i
$624$		−	101.869i		−	0.163251i
$625$	−140.094	+	609.097i	−0.224151	+	0.974554i
$626$	−82.0438	+	142.104i	−0.131060	+	0.227003i
$627$	27.0387	+	100.910i	0.0431240	+	0.160941i
$628$	−37.9199	+	141.519i	−0.0603820	+	0.225349i
$629$			10.4661i			0.0166393i
$630$	148.316	−	7.24204i	0.235422	−	0.0114953i
$631$	−205.514			−0.325695			−0.162847	−	0.986651i	$-0.552068\pi$
$631$	−205.514			−0.325695			−0.162847	+	0.986651i	$0.552068\pi$
$632$	−81.5520	−	21.8518i	−0.129038	−	0.0345756i
$633$	−308.131	+	82.5634i	−0.486779	+	0.130432i
$634$	720.127	+	415.765i	1.13585	+	0.655781i
$635$	−21.2309	−	60.7558i	−0.0334345	−	0.0956785i
$636$	−106.465			−0.167398
$637$	−685.470	−	221.832i	−1.07609	−	0.348245i
$638$	706.711	+	706.711i	1.10770	+	1.10770i
$639$	−210.873	+	121.747i	−0.330004	+	0.190528i
$640$	42.8619	+	36.9169i	0.0669718	+	0.0576826i
$641$	−351.377	+	608.603i	−0.548170	+	0.949458i	0.450230	+	0.892913i	$0.351342\pi$
$641$	−351.377	+	608.603i	−0.548170	+	0.949458i	−0.998400	+	0.0565458i	$0.981991\pi$
$642$	−122.629	−	32.8584i	−0.191011	−	0.0511813i
$643$	839.690	+	839.690i	1.30589	+	1.30589i	0.924351	+	0.381542i	$0.124607\pi$
$643$	839.690	+	839.690i	1.30589	+	1.30589i	0.381542	+	0.924351i	$0.375393\pi$
$644$	423.875	+	259.408i	0.658192	+	0.402808i
$645$	393.813	−	268.256i	0.610563	−	0.415901i
$646$	52.7575	+	91.3787i	0.0816680	+	0.141453i
$647$	−165.502	−	617.660i	−0.255798	−	0.954653i	−0.967645	−	0.252317i	$-0.918807\pi$
$647$	−165.502	−	617.660i	−0.255798	−	0.954653i	0.711846	−	0.702336i	$-0.247859\pi$
$648$	24.5885	−	6.58846i	0.0379452	−	0.0101674i
$649$	−666.371	+	384.729i	−1.02677	+	0.592804i
$650$	190.326	−	483.753i	0.292809	−	0.744235i
$651$	36.3605	+	0.930742i	0.0558533	+	0.00142971i
$652$	−94.9443	+	94.9443i	−0.145620	+	0.145620i
$653$	−113.984	+	425.395i	−0.174555	+	0.651447i	0.822072	+	0.569383i	$0.192818\pi$
$653$	−113.984	+	425.395i	−0.174555	+	0.651447i	−0.996627	+	0.0820642i	$0.973849\pi$
$654$	−307.098	−	177.303i	−0.469569	−	0.271106i
$655$	1071.88	−	79.8760i	1.63646	−	0.121948i
$656$	−128.765	−	223.028i	−0.196289	−	0.339982i
$657$	−222.604	+	222.604i	−0.338819	+	0.338819i
$658$	−31.3170	+	105.953i	−0.0475942	+	0.161023i
$659$		−	455.444i		−	0.691114i	−0.938398	−	0.345557i	$-0.887690\pi$
$659$		−	455.444i		−	0.691114i	0.938398	−	0.345557i	$-0.112310\pi$
$660$	110.502	+	316.222i	0.167428	+	0.479124i
$661$	179.361	−	310.663i	0.271348	−	0.469989i	−0.697859	−	0.716235i	$-0.745864\pi$
$661$	179.361	−	310.663i	0.271348	−	0.469989i	0.969207	+	0.246246i	$0.0791972\pi$
$662$	−57.4641	−	214.459i	−0.0868038	−	0.323956i
$663$	157.687	−	588.497i	0.237839	−	0.887627i
$664$			27.0511i			0.0407396i
$665$	103.933	−	33.3603i	0.156291	−	0.0501658i
$666$	1.85611			0.00278695
$667$	1252.92	+	335.719i	1.87844	+	0.503327i
$668$	252.894	−	67.7626i	0.378583	−	0.101441i
$669$	319.667	+	184.560i	0.477828	+	0.275874i
$670$	−26.2909	−	12.6746i	−0.0392401	−	0.0189172i
$671$	−828.420			−1.23461
$672$	49.7226	−	47.2405i	0.0739919	−	0.0702984i
$673$	412.089	+	412.089i	0.612316	+	0.612316i	0.943549	−	0.331233i	$-0.107464\pi$
$673$	412.089	+	412.089i	0.612316	+	0.612316i	−0.331233	+	0.943549i	$0.607464\pi$
$674$	−361.943	+	208.968i	−0.537007	+	0.310041i
$675$	129.075	+	14.6525i	0.191222	+	0.0217075i
$676$	−47.1928	+	81.7403i	−0.0698118	+	0.120918i
$677$	−619.729	−	166.056i	−0.915404	−	0.245282i	−0.229784	−	0.973242i	$-0.573802\pi$
$677$	−619.729	−	166.056i	−0.915404	−	0.245282i	−0.685620	+	0.727960i	$0.740469\pi$
$678$	−321.502	−	321.502i	−0.474192	−	0.474192i
$679$	−539.071	−	329.908i	−0.793919	−	0.485873i
$680$	190.468	+	279.617i	0.280101	+	0.411201i
$681$	−83.0227	−	143.799i	−0.121913	−	0.211159i
$682$	21.2361	+	79.2541i	0.0311379	+	0.116208i
$683$	−661.567	+	177.266i	−0.968620	+	0.259541i	−0.708245	−	0.705967i	$-0.750513\pi$
$683$	−661.567	+	177.266i	−0.968620	+	0.259541i	−0.260375	+	0.965508i	$0.583846\pi$
$684$	16.2055	−	9.35624i	0.0236922	−	0.0136787i
$685$	−637.272	−	120.854i	−0.930324	−	0.176430i
$686$	−209.602	−	437.453i	−0.305543	−	0.637686i
$687$	8.81034	−	8.81034i	0.0128244	−	0.0128244i
$688$	56.9621	−	212.586i	0.0827938	−	0.308991i
$689$	391.353	+	225.948i	0.568001	+	0.327936i
$690$	329.405	+	283.716i	0.477399	+	0.411182i
$691$	−205.847	−	356.537i	−0.297897	−	0.515972i	0.677758	−	0.735285i	$-0.262952\pi$
$691$	−205.847	−	356.537i	−0.297897	−	0.515972i	−0.975655	+	0.219313i	$0.929618\pi$
$692$	248.714	−	248.714i	0.359414	−	0.359414i
$693$	394.856	−	95.0421i	0.569778	−	0.137146i
$694$			379.960i			0.547492i
$695$	−306.695	−	147.854i	−0.441287	−	0.212740i
$696$	89.5092	−	155.035i	0.128605	−	0.222751i
$697$	−398.644	−	1487.76i	−0.571942	−	2.13452i
$698$	−95.4364	+	356.173i	−0.136728	+	0.510277i
$699$			182.262i			0.260747i
$700$	324.383	−	131.436i	0.463405	−	0.187766i
$701$	612.759			0.874122			0.437061	−	0.899432i	$-0.356019\pi$
$701$	612.759			0.874122			0.437061	+	0.899432i	$0.356019\pi$
$702$	−104.367	−	27.9649i	−0.148670	−	0.0398361i
$703$	1.31793	−	0.353138i	0.00187472	−	0.000502329i
$704$	133.989	+	77.3587i	0.190326	+	0.109885i
$705$	−41.9729	+	87.0646i	−0.0595361	+	0.123496i
$706$	352.755			0.499653
$707$	456.343	+	134.883i	0.645463	+	0.190782i
$708$	97.4567	+	97.4567i	0.137651	+	0.137651i
$709$	−494.328	+	285.400i	−0.697218	+	0.402539i	−0.806311	−	0.591492i	$-0.798539\pi$
$709$	−494.328	+	285.400i	−0.697218	+	0.402539i	0.109092	+	0.994032i	$0.465206\pi$
$710$	−374.545	+	434.861i	−0.527528	+	0.612480i
$711$	−44.7752	+	77.5529i	−0.0629749	+	0.109076i
$712$	319.714	+	85.6671i	0.449037	+	0.120319i
$713$	75.2985	+	75.2985i	0.105608	+	0.105608i
$714$	360.373	−	195.941i	0.504725	−	0.274427i
$715$	264.914	−	1396.91i	0.370509	−	1.95372i
$716$	−254.267	−	440.404i	−0.355122	−	0.615089i
$717$	45.2969	+	169.050i	0.0631755	+	0.235774i
$718$	802.661	−	215.072i	1.11791	−	0.299544i
$719$	−650.053	+	375.309i	−0.904108	+	0.521987i	−0.878531	−	0.477686i	$-0.841476\pi$
$719$	−650.053	+	375.309i	−0.904108	+	0.521987i	−0.0255771	+	0.999673i	$0.508142\pi$
$720$	49.5885	−	33.7785i	0.0688728	−	0.0469146i
$721$	−899.978	−	23.0373i	−1.24824	−	0.0319518i
$722$	−351.273	+	351.273i	−0.486528	+	0.486528i
$723$	−76.4001	+	285.129i	−0.105671	+	0.394369i
$724$	−198.688	−	114.712i	−0.274431	−	0.158443i
$725$	714.718	−	568.992i	0.985818	−	0.784816i
$726$	309.889	+	536.744i	0.426845	+	0.739316i
$727$	−578.879	+	578.879i	−0.796257	+	0.796257i	−0.982503	−	0.186246i	$-0.940368\pi$
$727$	−578.879	+	578.879i	−0.796257	+	0.796257i	0.186246	+	0.982503i	$0.440368\pi$
$728$	−283.031	+	68.1257i	−0.388779	+	0.0935793i
$729$		−	27.0000i		−	0.0370370i
$730$	−322.227	+	668.396i	−0.441407	+	0.915612i
$731$	658.141	−	1139.93i	0.900330	−	1.55942i
$732$	38.4050	+	143.330i	0.0524659	+	0.195805i
$733$	218.521	−	815.530i	0.298118	−	1.11259i	−0.640591	−	0.767882i	$-0.721311\pi$
$733$	218.521	−	815.530i	0.298118	−	1.11259i	0.938709	−	0.344710i	$-0.112023\pi$
$734$		−	97.4720i		−	0.132796i
$735$	−119.309	−	407.235i	−0.162325	−	0.554061i
$736$	200.800			0.272826
$737$	−77.1065	−	20.6606i	−0.104622	−	0.0280334i
$738$	−263.845	+	70.6972i	−0.357514	+	0.0957956i
$739$	465.097	+	268.524i	0.629360	+	0.363361i	0.780504	−	0.625151i	$-0.214962\pi$
$739$	465.097	+	268.524i	0.629360	+	0.363361i	−0.151144	+	0.988512i	$0.548296\pi$
$740$	4.12999	−	1.44321i	0.00558107	−	0.00195028i
$741$	−79.4258			−0.107187
$742$	71.1997	+	295.802i	0.0959564	+	0.398655i
$743$	705.189	+	705.189i	0.949110	+	0.949110i	0.998766	−	0.0496559i	$-0.0158125\pi$
$743$	705.189	+	705.189i	0.949110	+	0.949110i	−0.0496559	+	0.998766i	$0.515812\pi$
$744$	12.7277	−	7.34834i	0.0171071	−	0.00987680i
$745$	89.6007	+	1202.38i	0.120269	+	1.61394i
$746$	221.626	−	383.868i	0.297086	−	0.514569i
$747$	27.7143	+	7.42604i	0.0371009	+	0.00994115i
$748$	654.310	+	654.310i	0.874746	+	0.874746i
$749$	−9.28387	+	362.685i	−0.0123950	+	0.484226i
$750$	298.595	−	67.7584i	0.398126	−	0.0903446i
$751$	−298.749	−	517.448i	−0.397802	−	0.689012i	0.595653	−	0.803242i	$-0.296893\pi$
$751$	−298.749	−	517.448i	−0.397802	−	0.689012i	−0.993454	+	0.114230i	$0.963560\pi$
$752$	11.5543	+	43.1213i	0.0153648	+	0.0573422i
$753$	226.218	−	60.6149i	0.300422	−	0.0804979i
$754$	−658.049	+	379.925i	−0.872745	+	0.503879i
$755$	−289.677	−	425.260i	−0.383678	−	0.563259i
$756$	−34.7490	−	63.9101i	−0.0459643	−	0.0845372i
$757$	578.181	−	578.181i	0.763779	−	0.763779i	−0.213224	−	0.977003i	$-0.568397\pi$
$757$	578.181	−	578.181i	0.763779	−	0.763779i	0.977003	+	0.213224i	$0.0683965\pi$
$758$	−146.555	+	546.950i	−0.193344	+	0.721570i
$759$	1029.74	+	594.522i	1.35671	+	0.783297i
$760$	28.7836	−	33.4189i	0.0378732	−	0.0439722i
$761$	−686.531	−	1189.11i	−0.902144	−	1.56256i	−0.824706	−	0.565561i	$-0.808660\pi$
$761$	−686.531	−	1189.11i	−0.902144	−	1.56256i	−0.0774372	−	0.996997i	$-0.524674\pi$
$762$	−22.2945	+	22.2945i	−0.0292578	+	0.0292578i
$763$	−287.242	+	971.810i	−0.376464	+	1.27367i
$764$		−	637.224i		−	0.834063i
$765$	338.760	−	118.378i	0.442824	−	0.154743i
$766$	424.469	−	735.202i	0.554137	−	0.959794i
$767$	−151.409	−	565.068i	−0.197405	−	0.736724i
$768$	7.17260	−	26.7685i	0.00933933	−	0.0348548i
$769$			481.250i			0.625812i	0.949784	+	0.312906i	$0.101303\pi$
$769$			481.250i			0.625812i	−0.949784	+	0.312906i	$0.898697\pi$
$770$	804.687	−	518.495i	1.04505	−	0.673370i
$771$	369.657			0.479451
$772$	196.520	+	52.6573i	0.254559	+	0.0682090i
$773$	69.8393	−	18.7134i	0.0903484	−	0.0242088i	−0.213362	−	0.976973i	$-0.568441\pi$
$773$	69.8393	−	18.7134i	0.0903484	−	0.0242088i	0.303710	+	0.952765i	$0.401775\pi$
$774$	−202.161	−	116.718i	−0.261190	−	0.150798i
$775$	74.1703	−	11.1160i	0.0957036	−	0.0143432i
$776$	−255.371			−0.329086
$777$	−1.24129	−	5.15699i	−0.00159754	−	0.00663705i
$778$	131.347	+	131.347i	0.168826	+	0.168826i
$779$	−173.892	+	100.397i	−0.223225	+	0.128879i
$780$	−253.968	+	18.9255i	−0.325600	+	0.0242635i
$781$	−784.853	+	1359.40i	−1.00493	+	1.74060i
$782$	1160.02	+	310.827i	1.48340	+	0.397477i
$783$	−134.264	−	134.264i	−0.171474	−	0.171474i
$784$	−164.505	−	106.556i	−0.209828	−	0.135913i
$785$	359.864	+	68.2457i	0.458425	+	0.0869373i
$786$	−263.285	−	456.022i	−0.334968	−	0.580181i
$787$	243.402	+	908.388i	0.309278	+	1.15424i	0.929200	+	0.369578i	$0.120498\pi$
$787$	243.402	+	908.388i	0.309278	+	1.15424i	−0.619922	+	0.784664i	$0.712836\pi$
$788$	−595.130	+	159.465i	−0.755241	+	0.202366i
$789$	349.500	−	201.784i	0.442966	−	0.255747i
$790$	−39.3275	+	207.376i	−0.0497816	+	0.262501i
$791$	−678.250	+	1108.27i	−0.857459	+	1.40109i
$792$	116.038	−	116.038i	0.146513	−	0.146513i
$793$	163.011	−	608.367i	0.205563	−	0.767172i
$794$	−834.216	−	481.635i	−1.05065	−	0.606593i
$795$	19.7794	+	265.427i	0.0248798	+	0.333871i
$796$	22.9028	+	39.6688i	0.0287724	+	0.0498352i
$797$	−56.0999	+	56.0999i	−0.0703888	+	0.0703888i	−0.741425	−	0.671036i	$-0.765850\pi$
$797$	−56.0999	+	56.0999i	−0.0703888	+	0.0703888i	0.671036	+	0.741425i	$0.265850\pi$
$798$	−36.8328	−	38.7680i	−0.0461564	−	0.0485815i
$799$			266.998i			0.334165i
$800$	84.0740	−	113.717i	0.105092	−	0.142146i
$801$	175.535	−	304.036i	0.219145	−	0.379570i
$802$	−12.9107	−	48.1832i	−0.0160981	−	0.0600788i
$803$	−525.258	+	1960.29i	−0.654119	+	2.44121i
$804$			14.2984i			0.0177841i
$805$	567.979	−	1104.95i	0.705564	−	1.37261i
$806$	−62.3805			−0.0773952
$807$	283.323	+	75.9161i	0.351081	+	0.0940720i
$808$	185.724	−	49.7647i	0.229857	−	0.0615900i
$809$	549.005	+	316.968i	0.678622	+	0.391802i	0.799336	−	0.600885i	$-0.205185\pi$
$809$	549.005	+	316.968i	0.678622	+	0.391802i	−0.120714	+	0.992687i	$0.538518\pi$
$810$	−20.9937	−	60.0771i	−0.0259182	−	0.0741693i
$811$	−1582.07			−1.95076			−0.975382	−	0.220520i	$-0.929225\pi$
$811$	−1582.07			−1.95076			−0.975382	+	0.220520i	$0.929225\pi$
$812$	−490.606	−	145.010i	−0.604195	−	0.178584i
$813$	−119.293	−	119.293i	−0.146732	−	0.146732i
$814$	10.3624	−	5.98276i	0.0127303	−	0.00734983i
$815$	254.343	+	219.065i	0.312078	+	0.268792i
$816$	82.8724	−	143.539i	0.101559	−	0.175906i
$817$	−165.750	−	44.4126i	−0.202877	−	0.0543606i
$818$	−131.978	−	131.978i	−0.161343	−	0.161343i
$819$	−7.90127	+	308.672i	−0.00964746	+	0.376889i
$820$	−532.107	+	362.458i	−0.648911	+	0.442023i
$821$	167.547	+	290.200i	0.204077	+	0.353471i	0.949838	−	0.312742i	$-0.101248\pi$
$821$	167.547	+	290.200i	0.204077	+	0.353471i	−0.745762	+	0.666213i	$0.767914\pi$
$822$	82.2430	+	306.935i	0.100052	+	0.373400i
$823$	−572.797	+	153.481i	−0.695987	+	0.186489i	−0.589432	−	0.807818i	$-0.700649\pi$
$823$	−572.797	+	153.481i	−0.695987	+	0.186489i	−0.106555	+	0.994307i	$0.533982\pi$
$824$	−315.030	+	181.883i	−0.382318	+	0.220731i
$825$	767.839	−	334.241i	0.930714	−	0.405140i
$826$	205.597	−	335.947i	0.248907	−	0.406716i
$827$	−255.866	+	255.866i	−0.309390	+	0.309390i	−0.844673	−	0.535283i	$-0.820205\pi$
$827$	−255.866	+	255.866i	−0.309390	+	0.309390i	0.535283	+	0.844673i	$0.320205\pi$
$828$	55.1233	−	205.723i	0.0665741	−	0.248458i
$829$	336.274	+	194.148i	0.405638	+	0.234195i	0.688914	−	0.724843i	$-0.258088\pi$
$829$	336.274	+	194.148i	0.405638	+	0.234195i	−0.283276	+	0.959039i	$0.591421\pi$
$830$	67.4407	−	5.02563i	0.0812539	−	0.00605498i
$831$	−66.9423	−	115.947i	−0.0805563	−	0.139528i
$832$	−83.1755	+	83.1755i	−0.0999706	+	0.0999706i
$833$	−785.403	−	870.219i	−0.942861	−	1.04468i
$834$			166.797i			0.199997i
$835$	−215.922	−	617.897i	−0.258589	−	0.739996i
$836$	60.3156	−	104.470i	0.0721478	−	0.124964i
$837$	−4.03452	−	15.0570i	−0.00482021	−	0.0179893i
$838$	211.651	−	789.891i	0.252566	−	0.942591i
$839$		−	402.486i		−	0.479721i	−0.970807	−	0.239861i	$-0.922898\pi$
$839$		−	402.486i		−	0.479721i	0.970807	−	0.239861i	$-0.0771017\pi$
$840$	−127.012	−	115.186i	−0.151205	−	0.137126i
$841$	−494.318			−0.587774
$842$	674.934	+	180.848i	0.801584	+	0.214784i
$843$	−713.423	+	191.161i	−0.846290	+	0.226763i
$844$	319.001	+	184.175i	0.377963	+	0.218217i
$845$	212.553	+	102.470i	0.251543	+	0.121266i
$846$	47.3505			0.0559699
$847$	1284.04	−	1219.94i	1.51599	−	1.44031i
$848$	86.9285	+	86.9285i	0.102510	+	0.102510i
$849$	−106.350	+	61.4012i	−0.125265	+	0.0723218i
$850$	661.724	−	526.802i	0.778498	−	0.619768i
$851$	7.76471	−	13.4489i	0.00912422	−	0.0158036i
$852$	271.583	+	72.7705i	0.318760	+	0.0854114i
$853$	−814.676	−	814.676i	−0.955072	−	0.955072i	0.0439612	−	0.999033i	$-0.486002\pi$
$853$	−814.676	−	814.676i	−0.955072	−	0.955072i	−0.999033	+	0.0439612i	$0.986002\pi$
$854$	372.541	−	202.557i	0.436231	−	0.237186i
$855$	−26.3366	−	38.6635i	−0.0308031	−	0.0452204i
$856$	73.2975	+	126.955i	0.0856279	+	0.148312i
$857$	−133.226	−	497.208i	−0.155457	−	0.580173i	−0.999066	−	0.0432147i	$-0.986240\pi$
$857$	−133.226	−	497.208i	−0.155457	−	0.580173i	0.843609	−	0.536958i	$-0.180427\pi$
$858$	−672.805	+	180.278i	−0.784155	+	0.210114i
$859$	437.684	−	252.697i	0.509527	−	0.294176i	−0.223112	−	0.974793i	$-0.571622\pi$
$859$	437.684	−	252.697i	0.509527	−	0.294176i	0.732639	+	0.680617i	$0.238288\pi$
$860$	−540.577	−	102.517i	−0.628578	−	0.119206i
$861$	372.873	+	685.785i	0.433070	+	0.796498i
$862$	−69.4336	+	69.4336i	−0.0805494	+	0.0805494i
$863$	214.292	−	799.747i	0.248310	−	0.926706i	−0.723381	−	0.690449i	$-0.757413\pi$
$863$	214.292	−	799.747i	0.248310	−	0.926706i	0.971691	−	0.236256i	$-0.0759205\pi$
$864$	−25.4558	−	14.6969i	−0.0294628	−	0.0170103i
$865$	−666.273	−	573.859i	−0.770258	−	0.663421i
$866$	473.011	+	819.279i	0.546202	+	0.946049i
$867$	346.994	−	346.994i	0.400223	−	0.400223i
$868$	−28.9283	−	30.4482i	−0.0333275	−	0.0350785i
$869$			577.292i			0.664317i
$870$	−403.144	−	194.352i	−0.463384	−	0.223393i
$871$	30.3451	−	52.5592i	0.0348393	−	0.0603435i
$872$	105.977	+	395.512i	0.121533	+	0.453569i
$873$	−70.1041	+	261.632i	−0.0803025	+	0.299693i
$874$		−	156.561i		−	0.179131i
$875$	−387.947	−	784.297i	−0.443368	−	0.896340i
$876$	363.511			0.414967
$877$	−188.443	−	50.4932i	−0.214872	−	0.0575749i	0.149777	−	0.988720i	$-0.452144\pi$
$877$	−188.443	−	50.4932i	−0.214872	−	0.0575749i	−0.364649	+	0.931145i	$0.618811\pi$
$878$	480.582	−	128.771i	0.547359	−	0.146664i
$879$	58.7372	+	33.9119i	0.0668227	+	0.0385801i
$880$	167.969	−	348.419i	0.190874	−	0.395931i
$881$	750.867			0.852290			0.426145	−	0.904655i	$-0.359871\pi$
$881$	750.867			0.852290			0.426145	+	0.904655i	$0.359871\pi$
$882$	−154.328	+	139.287i	−0.174975	+	0.157921i
$883$	368.540	+	368.540i	0.417373	+	0.417373i	0.884297	−	0.466924i	$-0.154638\pi$
$883$	368.540	+	368.540i	0.417373	+	0.417373i	−0.466924	+	0.884297i	$0.654638\pi$
$884$	−609.257	+	351.755i	−0.689205	+	0.397912i
$885$	224.862	−	261.074i	0.254082	−	0.294999i
$886$	−165.926	+	287.393i	−0.187276	+	0.324371i
$887$	−559.206	−	149.839i	−0.630447	−	0.168928i	−0.0705744	−	0.997507i	$-0.522483\pi$
$887$	−559.206	−	149.839i	−0.630447	−	0.168928i	−0.559872	+	0.828579i	$0.689150\pi$
$888$	−1.51551	−	1.51551i	−0.00170665	−	0.00170665i
$889$	76.8522	+	47.0330i	0.0864479	+	0.0529055i
$890$	154.178	−	812.990i	0.173234	−	0.913472i
$891$	−87.0286	−	150.738i	−0.0976752	−	0.169178i
$892$	−110.315	−	411.700i	−0.123671	−	0.461547i
$893$	33.6211	−	9.00876i	0.0376497	−	0.0100882i
$894$	511.543	−	295.339i	0.572195	−	0.330357i
$895$	−1050.73	+	715.730i	−1.17400	+	0.799698i
$896$	−79.1700	−	2.02656i	−0.0883594	−	0.00226179i
$897$	−639.226	+	639.226i	−0.712626	+	0.712626i
$898$	14.7124	−	54.9073i	0.0163835	−	0.0611440i
$899$	−94.9372	−	54.8120i	−0.105603	−	0.0609700i
$900$	−93.4254	−	117.353i	−0.103806	−	0.130392i
$901$	367.626	+	636.747i	0.408020	+	0.706712i
$902$	−1245.14	+	1245.14i	−1.38042	+	1.38042i
$903$	−189.090	+	639.737i	−0.209401	+	0.708457i
$904$			525.011i			0.580764i
$905$	−249.075	+	516.658i	−0.275221	+	0.570893i
$906$	−126.038	+	218.304i	−0.139115	+	0.240954i
$907$	−408.774	−	1525.57i	−0.450688	−	1.68199i	−0.700464	−	0.713687i	$-0.747024\pi$
$907$	−408.774	−	1525.57i	−0.450688	−	1.68199i	0.249776	−	0.968304i	$-0.419643\pi$
$908$	−49.6241	+	185.200i	−0.0546520	+	0.203964i
$909$		−	203.940i		−	0.224356i
$910$	222.426	+	692.964i	0.244424	+	0.761499i
$911$	81.9889			0.0899988			0.0449994	−	0.998987i	$-0.485671\pi$
$911$	81.9889			0.0899988			0.0449994	+	0.998987i	$0.485671\pi$
$912$	−20.8711	−	5.59239i	−0.0228849	−	0.00613200i
$913$	178.662	−	47.8724i	0.195687	−	0.0524342i
$914$	291.508	+	168.302i	0.318936	+	0.184138i
$915$	350.198	−	122.375i	0.382730	−	0.133744i
$916$	−14.3872			−0.0157066
$917$	−1090.93	+	1036.48i	−1.18968	+	1.13029i
$918$	−124.309	−	124.309i	−0.135412	−	0.135412i
$919$	104.595	−	60.3880i	0.113814	−	0.0657106i	−0.442012	−	0.897009i	$-0.645735\pi$
$919$	104.595	−	60.3880i	0.113814	−	0.0657106i	0.555826	+	0.831298i	$0.312402\pi$
$920$	−37.3052	−	500.611i	−0.0405491	−	0.544142i
$921$	358.396	−	620.761i	0.389138	−	0.674007i
$922$	1069.41	+	286.548i	1.15988	+	0.310789i
$923$	−843.868	−	843.868i	−0.914266	−	0.914266i
$924$	−400.000	−	244.797i	−0.432901	−	0.264932i
$925$	−4.36533	−	10.0283i	−0.00471927	−	0.0108414i
$926$	504.302	+	873.477i	0.544603	+	0.943280i
$927$	99.8605	+	372.684i	0.107724	+	0.402033i
$928$	−199.669	+	53.5012i	−0.215161	+	0.0576522i
$929$	829.040	−	478.647i	0.892401	−	0.515228i	0.0176737	−	0.999844i	$-0.494374\pi$
$929$	829.040	−	478.647i	0.892401	−	0.515228i	0.874727	+	0.484616i	$0.161041\pi$
$930$	−20.6846	−	30.3661i	−0.0222415	−	0.0326517i
$931$	−83.0802	+	128.262i	−0.0892376	+	0.137768i
$932$	148.817	−	148.817i	0.159674	−	0.159674i
$933$	−74.1040	+	276.560i	−0.0794255	+	0.296420i
$934$	−264.385	−	152.643i	−0.283068	−	0.163429i
$935$	1509.69	−	1752.81i	1.61464	−	1.87466i
$936$	62.3817	+	108.048i	0.0666471	+	0.115436i
$937$	−772.608	+	772.608i	−0.824555	+	0.824555i	−0.986758	−	0.162202i	$-0.948140\pi$
$937$	−772.608	+	772.608i	−0.824555	+	0.824555i	0.162202	+	0.986758i	$0.448140\pi$
$938$	39.7265	−	9.56220i	0.0423524	−	0.0101942i
$939$		−	200.966i		−	0.214021i
$940$	105.359	−	36.8172i	0.112084	−	0.0391672i
$941$	182.831	−	316.673i	0.194295	−	0.336528i	−0.752374	−	0.658736i	$-0.771092\pi$
$941$	182.831	−	316.673i	0.194295	−	0.336528i	0.946669	+	0.322208i	$0.104425\pi$
$942$	−46.4422	−	173.325i	−0.0493017	−	0.183996i
$943$	−591.499	+	2207.50i	−0.627252	+	2.34094i
$944$		−	159.146i		−	0.168587i
$945$	−152.878	+	98.5058i	−0.161775	+	0.104239i
$946$	−1504.85			−1.59075
$947$	1400.05	+	375.143i	1.47841	+	0.396138i	0.905805	−	0.423695i	$-0.139267\pi$
$947$	1400.05	+	375.143i	1.47841	+	0.396138i	0.572602	+	0.819833i	$0.305934\pi$
$948$	99.8804	−	26.7629i	0.105359	−	0.0282309i
$949$	−1336.22	−	771.467i	−1.40803	−	0.812926i
$950$	−88.6637	−	65.5514i	−0.0933302	−	0.0690014i
$951$	−1018.41			−1.07089
$952$	−454.229	−	134.258i	−0.477131	−	0.141028i
$953$	−1067.49	−	1067.49i	−1.12014	−	1.12014i	−0.991720	−	0.128420i	$-0.959009\pi$
$953$	−1067.49	−	1067.49i	−1.12014	−	1.12014i	−0.128420	−	0.991720i	$-0.540991\pi$
$954$	112.923	−	65.1964i	0.118368	−	0.0683401i
$955$	−1588.66	+	118.385i	−1.66351	+	0.123964i
$956$	101.044	−	175.014i	0.105695	−	0.183069i
$957$	−1182.35	−	316.810i	−1.23548	−	0.331045i
$958$	−166.919	−	166.919i	−0.174237	−	0.174237i
$959$	797.783	−	433.769i	0.831891	−	0.452313i
$960$	−68.0688	−	12.9088i	−0.0709050	−	0.0134467i
$961$	476.000	+	824.456i	0.495318	+	0.857915i
$962$	2.35450	+	8.78713i	0.00244751	+	0.00913423i
$963$	150.189	−	40.2431i	0.155960	−	0.0417893i
$964$	295.187	−	170.426i	0.306211	−	0.176791i
$965$	94.7693	−	499.724i	0.0982065	−	0.517849i
$966$	−608.442	−	15.5747i	−0.629857	−	0.0161228i
$967$	418.223	−	418.223i	0.432495	−	0.432495i	−0.456981	−	0.889476i	$-0.651069\pi$
$967$	418.223	−	418.223i	0.432495	−	0.432495i	0.889476	+	0.456981i	$0.151069\pi$
$968$	185.226	−	691.273i	0.191349	−	0.714125i
$969$	−111.916	−	64.6145i	−0.115496	−	0.0666816i
$970$	47.4435	+	636.661i	0.0489109	+	0.656352i
$971$	442.281	+	766.053i	0.455490	+	0.788933i	0.998716	−	0.0506541i	$-0.0161306\pi$
$971$	442.281	+	766.053i	0.455490	+	0.788933i	−0.543226	+	0.839587i	$0.682797\pi$
$972$	−22.0454	+	22.0454i	−0.0226805	+	0.0226805i
$973$	463.428	−	111.547i	0.476287	−	0.114643i
$974$			993.750i			1.02028i
$975$	94.3658	+	629.648i	0.0967855	+	0.645793i
$976$	85.6705	−	148.386i	0.0877772	−	0.152034i
$977$	137.716	+	513.965i	0.140958	+	0.526064i	0.999902	+	0.0139939i	$0.00445455\pi$
$977$	137.716	+	513.965i	0.140958	+	0.526064i	−0.858944	+	0.512070i	$0.828879\pi$
$978$	42.5624	−	158.845i	0.0435198	−	0.162418i
$979$		−	2263.20i		−	2.31174i
$980$	−235.091	+	429.921i	−0.239889	+	0.438695i
$981$	434.302			0.442714
$982$	98.3216	+	26.3452i	0.100124	+	0.0268281i
$983$	−617.227	+	165.385i	−0.627901	+	0.168246i	−0.558717	−	0.829358i	$-0.688706\pi$
$983$	−617.227	+	165.385i	−0.627901	+	0.168246i	−0.0691839	+	0.997604i	$0.522040\pi$
$984$	273.153	+	157.705i	0.277594	+	0.160269i
$985$	508.124	+	1454.09i	0.515862	+	1.47623i
$986$	−1236.31			−1.25386
$987$	−31.6661	−	131.558i	−0.0320832	−	0.133291i
$988$	64.8509	+	64.8509i	0.0656385	+	0.0656385i
$989$	−1691.41	+	976.535i	−1.71022	+	0.987397i
$990$	−310.851	−	267.735i	−0.313991	−	0.270440i
$991$	239.387	−	414.630i	0.241561	−	0.418395i	−0.719598	−	0.694391i	$-0.755674\pi$
$991$	239.387	−	414.630i	0.241561	−	0.418395i	0.961159	+	0.275995i	$0.0890074\pi$
$992$	−16.3920	−	4.39223i	−0.0165242	−	0.00442765i
$993$	192.279	+	192.279i	0.193634	+	0.193634i
$994$	20.5607	−	803.229i	0.0206849	−	0.808078i
$995$	94.6428	−	64.4685i	0.0951184	−	0.0647924i
$996$	−16.5653	−	28.6920i	−0.0166319	−	0.0288072i
$997$	70.8513	+	264.421i	0.0710645	+	0.265216i	0.992312	−	0.123760i	$-0.0394954\pi$
$997$	70.8513	+	264.421i	0.0710645	+	0.265216i	−0.921248	+	0.388977i	$0.872829\pi$
$998$	−52.8604	+	14.1639i	−0.0529663	+	0.0141923i
$999$	−1.96870	+	1.13663i	−0.00197067	+	0.00113777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.v.b.193.3	yes	32
5.2	odd	4	inner	210.3.v.b.67.5	yes	32
7.2	even	3	inner	210.3.v.b.163.5	yes	32
35.2	odd	12	inner	210.3.v.b.37.3	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.v.b.37.3	✓	32	35.2	odd	12	inner
210.3.v.b.67.5	yes	32	5.2	odd	4	inner
210.3.v.b.163.5	yes	32	7.2	even	3	inner
210.3.v.b.193.3	yes	32	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 + 0.366025i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(2.17130 - 4.50394i) q^{5} -2.44949 q^{6} +(1.63812 + 6.80563i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\)	\(q+(1.36603 + 0.366025i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(2.17130 - 4.50394i) q^{5} -2.44949 q^{6} +(1.63812 + 6.80563i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +(4.61461 - 5.35774i) q^{10} +(9.66984 - 16.7487i) q^{11} +(-3.34607 - 0.896575i) q^{12} +(10.3969 + 10.3969i) q^{13} +(-0.253320 + 9.89625i) q^{14} +(-1.61360 + 8.50860i) q^{15} +(2.00000 + 3.46410i) q^{16} +(6.19178 + 23.1080i) q^{17} +(4.09808 - 1.09808i) q^{18} +(2.70091 - 1.55937i) q^{19} +(8.26474 - 5.62975i) q^{20} +(-5.79151 - 10.6517i) q^{21} +(19.3397 - 19.3397i) q^{22} +(9.18722 - 34.2872i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-15.5709 - 19.5588i) q^{25} +(10.3969 + 18.0080i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(-3.96832 + 13.4258i) q^{28} +36.5420i q^{29} +(-5.31858 + 11.0323i) q^{30} +(-1.49997 + 2.59803i) q^{31} +(1.46410 + 5.46410i) q^{32} +(-8.66974 + 32.3559i) q^{33} +33.8325i q^{34} +(34.2090 + 7.39909i) q^{35} +6.00000 q^{36} +(0.422582 + 0.113231i) q^{37} +(4.26029 - 1.14154i) q^{38} +(-22.0552 - 12.7336i) q^{39} +(13.3505 - 4.66527i) q^{40} -64.3827 q^{41} +(-4.01256 - 16.6703i) q^{42} +(-38.9059 - 38.9059i) q^{43} +(33.4973 - 19.3397i) q^{44} +(-1.11470 - 14.9585i) q^{45} +(25.1000 - 43.4744i) q^{46} +(10.7803 + 2.88858i) q^{47} +(-4.89898 - 4.89898i) q^{48} +(-43.6331 + 22.2969i) q^{49} +(-14.1112 - 32.4172i) q^{50} +(-20.7181 - 35.8848i) q^{51} +(7.61109 + 28.4050i) q^{52} +(29.6867 - 7.95451i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(-54.4388 - 79.9188i) q^{55} +(-10.3350 + 16.8875i) q^{56} +(-3.81967 + 3.81967i) q^{57} +(-13.3753 + 49.9173i) q^{58} +(-34.4561 - 19.8933i) q^{59} +(-11.3034 + 13.1237i) q^{60} +(-21.4176 - 37.0964i) q^{61} +(-2.99995 + 2.99995i) q^{62} +(14.4644 + 15.2244i) q^{63} +8.00000i q^{64} +(69.4021 - 24.2523i) q^{65} +(-23.6862 + 41.0257i) q^{66} +(-1.06830 - 3.98696i) q^{67} +(-12.3836 + 46.2161i) q^{68} +61.4821i q^{69} +(44.0221 + 22.6287i) q^{70} -81.1650 q^{71} +(8.19615 + 2.19615i) q^{72} +(-101.361 + 27.1596i) q^{73} +(0.535813 + 0.309352i) q^{74} +(34.8186 + 25.7423i) q^{75} +6.23750 q^{76} +(129.825 + 38.3730i) q^{77} +(-25.4672 - 25.4672i) q^{78} +(-25.8510 + 14.9251i) q^{79} +(19.9447 - 1.48626i) q^{80} +(4.50000 - 7.79423i) q^{81} +(-87.9485 - 23.5657i) q^{82} +(6.76277 + 6.76277i) q^{83} +(0.620506 - 24.2408i) q^{84} +(117.521 + 22.2871i) q^{85} +(-38.9059 - 67.3869i) q^{86} +(-16.3813 - 61.1360i) q^{87} +(52.8370 - 14.1576i) q^{88} +(101.345 - 58.5117i) q^{89} +(3.95249 - 20.8417i) q^{90} +(-53.7263 + 87.7891i) q^{91} +(50.1999 - 50.1999i) q^{92} +(1.34484 - 5.01901i) q^{93} +(13.6689 + 7.89175i) q^{94} +(-1.15882 - 15.5506i) q^{95} +(-4.89898 - 8.48528i) q^{96} +(-63.8427 + 63.8427i) q^{97} +(-67.7652 + 14.4872i) q^{98} -58.0191i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8}+O(q^{10}) \) 32 * q + 16 * q^2 - 8 * q^5 + 24 * q^7 + 64 * q^8	\( 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8} + 12 q^{10} + 16 q^{11} + 32 q^{13} + 48 q^{15} + 64 q^{16} - 56 q^{17} + 48 q^{18} + 16 q^{20} + 32 q^{22} - 28 q^{25} + 32 q^{26} + 72 q^{28} + 36 q^{30} + 112 q^{31} - 64 q^{32} + 12 q^{33} - 112 q^{35} + 192 q^{36} - 52 q^{37} - 8 q^{40} - 336 q^{41} - 312 q^{43} + 12 q^{45} - 212 q^{47} + 96 q^{50} - 144 q^{51} - 32 q^{52} - 96 q^{53} - 312 q^{55} + 96 q^{56} + 48 q^{57} - 96 q^{58} - 24 q^{60} + 216 q^{61} + 224 q^{62} + 36 q^{63} + 248 q^{65} - 24 q^{66} + 128 q^{67} + 112 q^{68} - 264 q^{70} - 848 q^{71} + 96 q^{72} + 84 q^{73} - 144 q^{75} - 324 q^{77} + 48 q^{78} + 32 q^{80} + 144 q^{81} - 168 q^{82} - 416 q^{83} + 536 q^{85} - 312 q^{86} - 72 q^{87} + 32 q^{88} - 24 q^{90} + 504 q^{91} + 168 q^{93} + 168 q^{95} + 488 q^{97} - 328 q^{98}+O(q^{100}) \) 32 * q + 16 * q^2 - 8 * q^5 + 24 * q^7 + 64 * q^8 + 12 * q^10 + 16 * q^11 + 32 * q^13 + 48 * q^15 + 64 * q^16 - 56 * q^17 + 48 * q^18 + 16 * q^20 + 32 * q^22 - 28 * q^25 + 32 * q^26 + 72 * q^28 + 36 * q^30 + 112 * q^31 - 64 * q^32 + 12 * q^33 - 112 * q^35 + 192 * q^36 - 52 * q^37 - 8 * q^40 - 336 * q^41 - 312 * q^43 + 12 * q^45 - 212 * q^47 + 96 * q^50 - 144 * q^51 - 32 * q^52 - 96 * q^53 - 312 * q^55 + 96 * q^56 + 48 * q^57 - 96 * q^58 - 24 * q^60 + 216 * q^61 + 224 * q^62 + 36 * q^63 + 248 * q^65 - 24 * q^66 + 128 * q^67 + 112 * q^68 - 264 * q^70 - 848 * q^71 + 96 * q^72 + 84 * q^73 - 144 * q^75 - 324 * q^77 + 48 * q^78 + 32 * q^80 + 144 * q^81 - 168 * q^82 - 416 * q^83 + 536 * q^85 - 312 * q^86 - 72 * q^87 + 32 * q^88 - 24 * q^90 + 504 * q^91 + 168 * q^93 + 168 * q^95 + 488 * q^97 - 328 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more