LMFDB - Embedded newform 201.4.e.b.37.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,4,Mod(37,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("201.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	201.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.8593839112$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.15
Character	$\chi$	$=$	201.37
Dual form			201.4.e.b.163.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.13007 + 3.68940i) q^{2} -3.00000 q^{3} +(-5.07443 + 8.78916i) q^{4} +13.6463 q^{5} +(-6.39022 - 11.0682i) q^{6} +(12.7106 - 22.0154i) q^{7} -9.15443 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+(2.13007 + 3.68940i) q^{2} -3.00000 q^{3} +(-5.07443 + 8.78916i) q^{4} +13.6463 q^{5} +(-6.39022 - 11.0682i) q^{6} +(12.7106 - 22.0154i) q^{7} -9.15443 q^{8} +9.00000 q^{9} +(29.0676 + 50.3465i) q^{10} +(19.8621 - 34.4022i) q^{11} +(15.2233 - 26.3675i) q^{12} +(20.1368 + 34.8779i) q^{13} +108.298 q^{14} -40.9388 q^{15} +(21.0958 + 36.5390i) q^{16} +(28.3842 + 49.1628i) q^{17} +(19.1707 + 33.2046i) q^{18} +(-37.6641 - 65.2361i) q^{19} +(-69.2470 + 119.939i) q^{20} +(-38.1318 + 66.0462i) q^{21} +169.231 q^{22} +(-94.6604 - 163.957i) q^{23} +27.4633 q^{24} +61.2209 q^{25} +(-85.7857 + 148.585i) q^{26} -27.0000 q^{27} +(128.998 + 223.431i) q^{28} +(-77.7374 + 134.645i) q^{29} +(-87.2027 - 151.040i) q^{30} +(-79.7351 + 138.105i) q^{31} +(-126.489 + 219.085i) q^{32} +(-59.5863 + 103.206i) q^{33} +(-120.921 + 209.441i) q^{34} +(173.452 - 300.428i) q^{35} +(-45.6698 + 79.1025i) q^{36} +(198.924 + 344.546i) q^{37} +(160.454 - 277.915i) q^{38} +(-60.4104 - 104.634i) q^{39} -124.924 q^{40} +(208.578 - 361.268i) q^{41} -324.894 q^{42} +188.240 q^{43} +(201.577 + 349.142i) q^{44} +122.816 q^{45} +(403.267 - 698.480i) q^{46} +(-273.259 + 473.298i) q^{47} +(-63.2874 - 109.617i) q^{48} +(-151.619 - 262.612i) q^{49} +(130.405 + 225.868i) q^{50} +(-85.1525 - 147.489i) q^{51} -408.731 q^{52} -224.301 q^{53} +(-57.5120 - 99.6137i) q^{54} +(271.044 - 469.461i) q^{55} +(-116.358 + 201.539i) q^{56} +(112.992 + 195.708i) q^{57} -662.346 q^{58} +40.8284 q^{59} +(207.741 - 359.818i) q^{60} +(-182.112 - 315.426i) q^{61} -679.366 q^{62} +(114.395 - 198.139i) q^{63} -740.190 q^{64} +(274.792 + 475.954i) q^{65} -507.693 q^{66} +(436.027 - 332.632i) q^{67} -576.134 q^{68} +(283.981 + 491.870i) q^{69} +1477.87 q^{70} +(-64.4330 + 111.601i) q^{71} -82.3899 q^{72} +(-489.368 - 847.609i) q^{73} +(-847.445 + 1467.82i) q^{74} -183.663 q^{75} +764.494 q^{76} +(-504.918 - 874.544i) q^{77} +(257.357 - 445.756i) q^{78} +(54.5072 - 94.4093i) q^{79} +(287.879 + 498.621i) q^{80} +81.0000 q^{81} +1777.15 q^{82} +(1.73691 + 3.00841i) q^{83} +(-386.994 - 670.294i) q^{84} +(387.338 + 670.890i) q^{85} +(400.964 + 694.491i) q^{86} +(233.212 - 403.936i) q^{87} +(-181.826 + 314.932i) q^{88} +901.441 q^{89} +(261.608 + 453.119i) q^{90} +1023.80 q^{91} +1921.39 q^{92} +(239.205 - 414.316i) q^{93} -2328.24 q^{94} +(-513.974 - 890.229i) q^{95} +(379.467 - 657.256i) q^{96} +(-616.042 - 1067.02i) q^{97} +(645.919 - 1118.76i) q^{98} +(178.759 - 309.619i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 2 q^{2} - 108 q^{3} - 90 q^{4} - 4 q^{5} - 6 q^{6} + 22 q^{7} + 48 q^{8} + 324 q^{9}+O(q^{10}) $ 36 * q + 2 * q^2 - 108 * q^3 - 90 * q^4 - 4 * q^5 - 6 * q^6 + 22 * q^7 + 48 * q^8 + 324 * q^9	\( 36 q + 2 q^{2} - 108 q^{3} - 90 q^{4} - 4 q^{5} - 6 q^{6} + 22 q^{7} + 48 q^{8} + 324 q^{9} + 14 q^{10} - 16 q^{11} + 270 q^{12} - 46 q^{13} + 14 q^{14} + 12 q^{15} - 346 q^{16} - 8 q^{17} + 18 q^{18} - 154 q^{19} - 180 q^{20} - 66 q^{21} + 214 q^{22} - 104 q^{23} - 144 q^{24} + 1032 q^{25} - 333 q^{26} - 972 q^{27} - 473 q^{28} + 76 q^{29} - 42 q^{30} + 498 q^{31} - 285 q^{32} + 48 q^{33} + 26 q^{34} - 392 q^{35} - 810 q^{36} - 124 q^{37} + 20 q^{38} + 138 q^{39} + 638 q^{40} - 508 q^{41} - 42 q^{42} - 1400 q^{43} - 333 q^{44} - 36 q^{45} - 1372 q^{46} + 18 q^{47} + 1038 q^{48} - 238 q^{49} - 337 q^{50} + 24 q^{51} + 3640 q^{52} + 724 q^{53} - 54 q^{54} - 178 q^{55} - 829 q^{56} + 462 q^{57} - 1472 q^{58} + 720 q^{59} + 540 q^{60} + 232 q^{61} - 3882 q^{62} + 198 q^{63} + 3628 q^{64} - 1428 q^{65} - 642 q^{66} - 1164 q^{67} + 1634 q^{68} + 312 q^{69} + 2550 q^{70} + 406 q^{71} + 432 q^{72} - 2120 q^{73} + 1375 q^{74} - 3096 q^{75} + 4190 q^{76} - 800 q^{77} + 999 q^{78} + 1306 q^{79} - 1927 q^{80} + 2916 q^{81} - 794 q^{82} - 1010 q^{83} + 1419 q^{84} + 472 q^{85} + 737 q^{86} - 228 q^{87} - 1838 q^{88} + 1904 q^{89} + 126 q^{90} + 7340 q^{91} + 7368 q^{92} - 1494 q^{93} - 9862 q^{94} + 1678 q^{95} + 855 q^{96} - 2358 q^{97} - 2610 q^{98} - 144 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 - 108 * q^3 - 90 * q^4 - 4 * q^5 - 6 * q^6 + 22 * q^7 + 48 * q^8 + 324 * q^9 + 14 * q^10 - 16 * q^11 + 270 * q^12 - 46 * q^13 + 14 * q^14 + 12 * q^15 - 346 * q^16 - 8 * q^17 + 18 * q^18 - 154 * q^19 - 180 * q^20 - 66 * q^21 + 214 * q^22 - 104 * q^23 - 144 * q^24 + 1032 * q^25 - 333 * q^26 - 972 * q^27 - 473 * q^28 + 76 * q^29 - 42 * q^30 + 498 * q^31 - 285 * q^32 + 48 * q^33 + 26 * q^34 - 392 * q^35 - 810 * q^36 - 124 * q^37 + 20 * q^38 + 138 * q^39 + 638 * q^40 - 508 * q^41 - 42 * q^42 - 1400 * q^43 - 333 * q^44 - 36 * q^45 - 1372 * q^46 + 18 * q^47 + 1038 * q^48 - 238 * q^49 - 337 * q^50 + 24 * q^51 + 3640 * q^52 + 724 * q^53 - 54 * q^54 - 178 * q^55 - 829 * q^56 + 462 * q^57 - 1472 * q^58 + 720 * q^59 + 540 * q^60 + 232 * q^61 - 3882 * q^62 + 198 * q^63 + 3628 * q^64 - 1428 * q^65 - 642 * q^66 - 1164 * q^67 + 1634 * q^68 + 312 * q^69 + 2550 * q^70 + 406 * q^71 + 432 * q^72 - 2120 * q^73 + 1375 * q^74 - 3096 * q^75 + 4190 * q^76 - 800 * q^77 + 999 * q^78 + 1306 * q^79 - 1927 * q^80 + 2916 * q^81 - 794 * q^82 - 1010 * q^83 + 1419 * q^84 + 472 * q^85 + 737 * q^86 - 228 * q^87 - 1838 * q^88 + 1904 * q^89 + 126 * q^90 + 7340 * q^91 + 7368 * q^92 - 1494 * q^93 - 9862 * q^94 + 1678 * q^95 + 855 * q^96 - 2358 * q^97 - 2610 * q^98 - 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	2.13007	+	3.68940i	0.753095	+	1.30440i	0.946316	+	0.323243i	$0.104773\pi$
$2$	2.13007	+	3.68940i	0.753095	+	1.30440i	−0.193221	+	0.981155i	$0.561894\pi$
$3$	−3.00000			−0.577350
$3$	−3.00000			−0.577350
$4$	−5.07443	+	8.78916i	−0.634303	+	1.09865i
$5$	13.6463			1.22056			0.610280	−	0.792186i	$-0.291057\pi$
$5$	13.6463			1.22056			0.610280	+	0.792186i	$0.291057\pi$
$6$	−6.39022	−	11.0682i	−0.434799	−	0.753095i
$7$	12.7106	−	22.0154i	0.686308	−	1.18872i	−0.286716	−	0.958016i	$-0.592563\pi$
$7$	12.7106	−	22.0154i	0.686308	−	1.18872i	0.973024	−	0.230705i	$-0.0741032\pi$
$8$	−9.15443			−0.404572
$9$	9.00000			0.333333
$10$	29.0676	+	50.3465i	0.919197	+	1.59210i
$11$	19.8621	−	34.4022i	0.544422	−	0.942967i	−0.454221	−	0.890889i	$-0.650082\pi$
$11$	19.8621	−	34.4022i	0.544422	−	0.942967i	0.998643	−	0.0520780i	$-0.0165845\pi$
$12$	15.2233	−	26.3675i	0.366215	−	0.634303i
$13$	20.1368	+	34.8779i	0.429611	+	0.744108i	0.996839	−	0.0794532i	$-0.0253174\pi$
$13$	20.1368	+	34.8779i	0.429611	+	0.744108i	−0.567228	+	0.823561i	$0.691984\pi$
$14$	108.298			2.06742
$15$	−40.9388			−0.704691
$16$	21.0958	+	36.5390i	0.329622	+	0.570922i
$17$	28.3842	+	49.1628i	0.404951	+	0.701397i	0.994316	−	0.106471i	$-0.0339551\pi$
$17$	28.3842	+	49.1628i	0.404951	+	0.701397i	−0.589364	+	0.807867i	$0.700622\pi$
$18$	19.1707	+	33.2046i	0.251032	+	0.434799i
$19$	−37.6641	−	65.2361i	−0.454775	−	0.787694i	0.543900	−	0.839150i	$-0.316947\pi$
$19$	−37.6641	−	65.2361i	−0.454775	−	0.787694i	−0.998675	+	0.0514564i	$0.983614\pi$
$20$	−69.2470	+	119.939i	−0.774205	+	1.34096i
$21$	−38.1318	+	66.0462i	−0.396240	+	0.686308i
$22$	169.231			1.64001
$23$	−94.6604	−	163.957i	−0.858177	−	1.48641i	−0.873666	−	0.486526i	$-0.838264\pi$
$23$	−94.6604	−	163.957i	−0.858177	−	1.48641i	0.0154895	−	0.999880i	$-0.495069\pi$
$24$	27.4633			0.233580
$25$	61.2209			0.489767
$26$	−85.7857	+	148.585i	−0.647075	+	1.12077i
$27$	−27.0000			−0.192450
$28$	128.998	+	223.431i	0.870655	+	1.50802i
$29$	−77.7374	+	134.645i	−0.497775	+	0.862172i	−0.999997	−	0.00256705i	$-0.999183\pi$
$29$	−77.7374	+	134.645i	−0.497775	+	0.862172i	0.502221	+	0.864739i	$0.332516\pi$
$30$	−87.2027	−	151.040i	−0.530699	−	0.919197i
$31$	−79.7351	+	138.105i	−0.461963	+	0.800143i	−0.999059	−	0.0433781i	$-0.986188\pi$
$31$	−79.7351	+	138.105i	−0.461963	+	0.800143i	0.537096	+	0.843521i	$0.319521\pi$
$32$	−126.489	+	219.085i	−0.698759	+	1.21029i
$33$	−59.5863	+	103.206i	−0.314322	+	0.544422i
$34$	−120.921	+	209.441i	−0.609934	+	1.05644i
$35$	173.452	−	300.428i	0.837680	−	1.45090i
$36$	−45.6698	+	79.1025i	−0.211434	+	0.366215i
$37$	198.924	+	344.546i	0.883861	+	1.53089i	0.847013	+	0.531572i	$0.178398\pi$
$37$	198.924	+	344.546i	0.883861	+	1.53089i	0.0368481	+	0.999321i	$0.488268\pi$
$38$	160.454	−	277.915i	0.684977	−	1.18642i
$39$	−60.4104	−	104.634i	−0.248036	−	0.429611i
$40$	−124.924			−0.493805
$41$	208.578	−	361.268i	0.794499	−	1.37611i	−0.128658	−	0.991689i	$-0.541067\pi$
$41$	208.578	−	361.268i	0.794499	−	1.37611i	0.923157	−	0.384424i	$-0.125600\pi$
$42$	−324.894			−1.19363
$43$	188.240			0.667588			0.333794	−	0.942646i	$-0.391671\pi$
$43$	188.240			0.667588			0.333794	+	0.942646i	$0.391671\pi$
$44$	201.577	+	349.142i	0.690658	+	1.19625i
$45$	122.816			0.406853
$46$	403.267	−	698.480i	1.29258	−	2.23881i
$47$	−273.259	+	473.298i	−0.848061	+	1.46888i	0.0348756	+	0.999392i	$0.488897\pi$
$47$	−273.259	+	473.298i	−0.848061	+	1.46888i	−0.882936	+	0.469493i	$0.844437\pi$
$48$	−63.2874	−	109.617i	−0.190307	−	0.329622i
$49$	−151.619	−	262.612i	−0.442038	−	0.765632i
$50$	130.405	+	225.868i	0.368841	+	0.638851i
$51$	−85.1525	−	147.489i	−0.233799	−	0.404951i
$52$	−408.731			−1.09001
$53$	−224.301			−0.581324			−0.290662	−	0.956826i	$-0.593875\pi$
$53$	−224.301			−0.581324			−0.290662	+	0.956826i	$0.593875\pi$
$54$	−57.5120	−	99.6137i	−0.144933	−	0.251032i
$55$	271.044	−	469.461i	0.664500	−	1.15095i
$56$	−116.358	+	201.539i	−0.277661	+	0.480924i
$57$	112.992	+	195.708i	0.262565	+	0.454775i
$58$	−662.346			−1.49949
$59$	40.8284			0.0900917			0.0450459	−	0.998985i	$-0.485657\pi$
$59$	40.8284			0.0900917			0.0450459	+	0.998985i	$0.485657\pi$
$60$	207.741	−	359.818i	0.446988	−	0.774205i
$61$	−182.112	−	315.426i	−0.382246	−	0.662069i	0.609137	−	0.793065i	$-0.291516\pi$
$61$	−182.112	−	315.426i	−0.382246	−	0.662069i	−0.991383	+	0.130996i	$0.958183\pi$
$62$	−679.366			−1.39161
$63$	114.395	−	198.139i	0.228769	−	0.396240i
$64$	−740.190			−1.44568
$65$	274.792	+	475.954i	0.524366	+	0.908228i
$66$	−507.693			−0.946858
$67$	436.027	−	332.632i	0.795061	−	0.606529i
$67$	436.027	−	332.632i	0.795061	−	0.606529i
$68$	−576.134			−1.02745
$69$	283.981	+	491.870i	0.495469	+	0.858177i
$70$	1477.87			2.52341
$71$	−64.4330	+	111.601i	−0.107701	+	0.186544i	−0.914839	−	0.403820i	$-0.867682\pi$
$71$	−64.4330	+	111.601i	−0.107701	+	0.186544i	0.807137	+	0.590364i	$0.201016\pi$
$72$	−82.3899			−0.134857
$73$	−489.368	−	847.609i	−0.784605	−	1.35898i	−0.929235	−	0.369489i	$-0.879533\pi$
$73$	−489.368	−	847.609i	−0.784605	−	1.35898i	0.144630	−	0.989486i	$-0.453801\pi$
$74$	−847.445	+	1467.82i	−1.33126	+	2.30581i
$75$	−183.663			−0.282767
$76$	764.494			1.15386
$77$	−504.918	−	874.544i	−0.747283	−	1.29433i
$78$	257.357	−	445.756i	0.373589	−	0.647075i
$79$	54.5072	−	94.4093i	0.0776271	−	0.134454i	−0.824599	−	0.565718i	$-0.808599\pi$
$79$	54.5072	−	94.4093i	0.0776271	−	0.134454i	0.902226	+	0.431264i	$0.141932\pi$
$80$	287.879	+	498.621i	0.402323	+	0.696845i
$81$	81.0000			0.111111
$82$	1777.15			2.39333
$83$	1.73691	+	3.00841i	0.00229699	+	0.00397851i	0.867172	−	0.498009i	$-0.165936\pi$
$83$	1.73691	+	3.00841i	0.00229699	+	0.00397851i	−0.864875	+	0.501988i	$0.832602\pi$
$84$	−386.994	−	670.294i	−0.502673	−	0.870655i
$85$	387.338	+	670.890i	0.494268	+	0.856097i
$86$	400.964	+	694.491i	0.502757	+	0.870801i
$87$	233.212	−	403.936i	0.287391	−	0.497775i
$88$	−181.826	+	314.932i	−0.220258	+	0.381499i
$89$	901.441			1.07362			0.536812	−	0.843702i	$-0.319628\pi$
$89$	901.441			1.07362			0.536812	+	0.843702i	$0.319628\pi$
$90$	261.608	+	453.119i	0.306399	+	0.530699i
$91$	1023.80			1.17938
$92$	1921.39			2.17738
$93$	239.205	−	414.316i	0.266714	−	0.461963i
$94$	−2328.24			−2.55468
$95$	−513.974	−	890.229i	−0.555080	−	0.961427i
$96$	379.467	−	657.256i	0.403429	−	0.698759i
$97$	−616.042	−	1067.02i	−0.644841	−	1.11690i	−0.984338	−	0.176291i	$-0.943590\pi$
$97$	−616.042	−	1067.02i	−0.644841	−	1.11690i	0.339497	−	0.940607i	$-0.389743\pi$
$98$	645.919	−	1118.76i	0.665793	−	1.15319i
$99$	178.759	−	309.619i	0.181474	−	0.314322i
$100$	−310.661	+	538.080i	−0.310661	+	0.538080i
$101$	−649.144	+	1124.35i	−0.639527	+	1.10769i	0.346010	+	0.938231i	$0.387536\pi$
$101$	−649.144	+	1124.35i	−0.639527	+	1.10769i	−0.985537	+	0.169462i	$0.945797\pi$
$102$	362.762	−	628.323i	0.352145	−	0.609934i
$103$	−1021.96	+	1770.09i	−0.977642	+	1.69333i	−0.306719	+	0.951800i	$0.599231\pi$
$103$	−1021.96	+	1770.09i	−0.977642	+	1.69333i	−0.670924	+	0.741526i	$0.734102\pi$
$104$	−184.341	−	319.288i	−0.173809	−	0.301045i
$105$	−520.357	+	901.285i	−0.483635	+	0.837680i
$106$	−477.778	−	827.536i	−0.437792	−	0.758278i
$107$	−163.880			−0.148065			−0.0740324	−	0.997256i	$-0.523587\pi$
$107$	−163.880			−0.148065			−0.0740324	+	0.997256i	$0.523587\pi$
$108$	137.010	−	237.307i	0.122072	−	0.211434i
$109$	182.890			0.160713			0.0803565	−	0.996766i	$-0.474394\pi$
$109$	182.890			0.160713			0.0803565	+	0.996766i	$0.474394\pi$
$110$	2309.37			2.00173
$111$	−596.771	−	1033.64i	−0.510298	−	0.883861i
$112$	1072.56			0.904889
$113$	−532.975	+	923.139i	−0.443699	+	0.768510i	−0.997961	−	0.0638329i	$-0.979668\pi$
$113$	−532.975	+	923.139i	−0.443699	+	0.768510i	0.554261	+	0.832343i	$0.313001\pi$
$114$	−481.363	+	833.746i	−0.395472	+	0.684977i
$115$	−1291.76	−	2237.40i	−1.04746	−	1.81425i
$116$	−788.946	−	1366.49i	−0.631481	−	1.09376i
$117$	181.231	+	313.902i	0.143204	+	0.248036i
$118$	86.9676	+	150.632i	0.0678476	+	0.117515i
$119$	1443.12			1.11169
$120$	374.772			0.285098
$121$	−123.505	−	213.918i	−0.0927915	−	0.160720i
$122$	775.822	−	1343.76i	0.575735	−	0.997201i
$123$	−625.735	+	1083.80i	−0.458704	+	0.794499i
$124$	−809.220	−	1401.61i	−0.586049	−	1.01507i
$125$	−870.348			−0.622770
$126$	974.683			0.689140
$127$	−17.5095	+	30.3273i	−0.0122340	+	0.0211899i	−0.872078	−	0.489368i	$-0.837228\pi$
$127$	−17.5095	+	30.3273i	−0.0122340	+	0.0211899i	0.859844	+	0.510558i	$0.170561\pi$
$128$	−564.748	−	978.172i	−0.389978	−	0.675461i
$129$	−564.719			−0.385432
$130$	−1170.66	+	2027.63i	−0.789794	+	1.36796i
$131$	621.459			0.414482			0.207241	−	0.978290i	$-0.433552\pi$
$131$	621.459			0.414482			0.207241	+	0.978290i	$0.433552\pi$
$132$	−604.732	−	1047.43i	−0.398751	−	0.690658i
$133$	−1914.93			−1.24846
$134$	2155.98	+	900.144i	1.38991	+	0.580303i
$135$	−368.449			−0.234897
$136$	−259.841	−	450.058i	−0.163832	−	0.283766i
$137$	−2396.90			−1.49475			−0.747377	−	0.664401i	$-0.768687\pi$
$137$	−2396.90			−1.49475			−0.747377	+	0.664401i	$0.768687\pi$
$138$	−1209.80	+	2095.44i	−0.746270	+	1.29258i
$139$	−1023.03			−0.624261			−0.312130	−	0.950039i	$-0.601043\pi$
$139$	−1023.03			−0.624261			−0.312130	+	0.950039i	$0.601043\pi$
$140$	1760.34	+	3049.00i	1.06269	+	1.84063i
$141$	819.776	−	1419.89i	0.489628	−	0.848061i
$142$	−548.988			−0.324437
$143$	1599.84			0.935559
$144$	189.862	+	328.851i	0.109874	+	0.190307i
$145$	−1060.83	+	1837.41i	−0.607565	+	1.05233i
$146$	2084.78	−	3610.94i	1.18176	−	2.04687i
$147$	454.857	+	787.835i	0.255211	+	0.442038i
$148$	−4037.70			−2.24254
$149$	−2934.53			−1.61346			−0.806732	−	0.590917i	$-0.798766\pi$
$149$	−2934.53			−1.61346			−0.806732	+	0.590917i	$0.798766\pi$
$150$	−391.215	−	677.604i	−0.212950	−	0.368841i
$151$	−677.395	−	1173.28i	−0.365070	−	0.632320i	0.623717	−	0.781650i	$-0.285622\pi$
$151$	−677.395	−	1173.28i	−0.365070	−	0.632320i	−0.988787	+	0.149330i	$0.952288\pi$
$152$	344.793	+	597.199i	0.183989	+	0.318679i
$153$	255.458	+	442.466i	0.134984	+	0.233799i
$154$	2151.03	−	3725.69i	1.12555	−	1.94951i
$155$	−1088.09	+	1884.62i	−0.563853	+	0.976623i
$156$	1226.19			0.629320
$157$	926.161	+	1604.16i	0.470801	+	0.815451i	0.999442	−	0.0333943i	$-0.0106317\pi$
$157$	926.161	+	1604.16i	0.470801	+	0.815451i	−0.528641	+	0.848845i	$0.677298\pi$
$158$	464.418			0.233842
$159$	672.904			0.335627
$160$	−1726.10	+	2989.70i	−0.852878	+	1.47723i
$161$	−4812.77			−2.35589
$162$	172.536	+	298.841i	0.0836772	+	0.144933i
$163$	891.440	−	1544.02i	0.428362	−	0.741944i	−0.568366	−	0.822776i	$-0.692424\pi$
$163$	891.440	−	1544.02i	0.428362	−	0.741944i	0.996728	+	0.0808316i	$0.0257576\pi$
$164$	2116.83	+	3666.46i	1.00791	+	1.74575i
$165$	−813.131	+	1408.38i	−0.383649	+	0.664500i
$166$	−7.39948	+	12.8163i	−0.00345971	+	0.00599239i
$167$	173.324	−	300.205i	0.0803125	−	0.139105i	−0.823072	−	0.567937i	$-0.807742\pi$
$167$	173.324	−	300.205i	0.0803125	−	0.139105i	0.903384	+	0.428832i	$0.141075\pi$
$168$	349.075	−	604.616i	0.160308	−	0.277661i
$169$	287.519	−	497.998i	0.130869	−	0.226672i
$170$	−1650.12	+	2858.09i	−0.744461	+	1.28944i
$171$	−338.976	−	587.125i	−0.151592	−	0.262565i
$172$	−955.209	+	1654.47i	−0.423453	+	0.733443i
$173$	1.87094	+	3.24056i	0.000822225	+	0.00142414i	0.866436	−	0.499288i	$-0.166405\pi$
$173$	1.87094	+	3.24056i	0.000822225	+	0.00142414i	−0.865614	+	0.500712i	$0.833072\pi$
$174$	1987.04			0.865730
$175$	778.154	−	1347.80i	0.336131	−	0.582196i
$176$	1676.03			0.717814
$177$	−122.485			−0.0520145
$178$	1920.14	+	3325.77i	0.808541	+	1.40043i
$179$	−537.156			−0.224296			−0.112148	−	0.993692i	$-0.535773\pi$
$179$	−537.156			−0.224296			−0.112148	+	0.993692i	$0.535773\pi$
$180$	−623.223	+	1079.45i	−0.258068	+	0.446988i
$181$	740.730	−	1282.98i	0.304188	−	0.526869i	−0.672892	−	0.739740i	$-0.734948\pi$
$181$	740.730	−	1282.98i	0.304188	−	0.526869i	0.977080	+	0.212872i	$0.0682816\pi$
$182$	2180.78	+	3777.21i	0.888186	+	1.53838i
$183$	546.335	+	946.279i	0.220690	+	0.382246i
$184$	866.562	+	1500.93i	0.347195	+	0.601359i
$185$	2714.57	+	4701.77i	1.07881	+	1.86855i
$186$	2038.10			0.803445
$187$	2255.08			0.881859
$188$	−2773.26	−	4803.43i	−1.07586	−	1.86344i
$189$	−343.186	+	594.416i	−0.132080	+	0.228769i
$190$	2189.61	−	3792.51i	0.836056	−	1.44809i
$191$	−1423.80	−	2466.10i	−0.539387	−	0.934245i	−0.998937	−	0.0460933i	$-0.985323\pi$
$191$	−1423.80	−	2466.10i	−0.539387	−	0.934245i	0.459551	−	0.888152i	$-0.348010\pi$
$192$	2220.57			0.834666
$193$	1879.13			0.700845			0.350422	−	0.936592i	$-0.386038\pi$
$193$	1879.13			0.700845			0.350422	+	0.936592i	$0.386038\pi$
$194$	2624.43	−	4545.65i	0.971253	−	1.68226i
$195$	−824.377	−	1427.86i	−0.302743	−	0.524366i
$196$	3077.52			1.12154
$197$	267.240	−	462.873i	0.0966501	−	0.167403i	−0.813646	−	0.581361i	$-0.802521\pi$
$197$	267.240	−	462.873i	0.0966501	−	0.167403i	0.910296	+	0.413958i	$0.135854\pi$
$198$	1523.08			0.546669
$199$	1153.33	+	1997.62i	0.410840	+	0.711595i	0.994982	−	0.100056i	$-0.0319023\pi$
$199$	1153.33	+	1997.62i	0.410840	+	0.711595i	−0.584142	+	0.811651i	$0.698569\pi$
$200$	−560.442			−0.198146
$201$	−1308.08	+	997.895i	−0.459029	+	0.350180i
$202$	−5530.89			−1.92650
$203$	1976.18	+	3422.84i	0.683254	+	1.18343i
$204$	1728.40			0.593197
$205$	2846.32	−	4929.97i	0.969734	−	1.67963i
$206$	−8707.44			−2.94503
$207$	−851.944	−	1475.61i	−0.286059	−	0.495469i
$208$	−849.604	+	1471.56i	−0.283218	+	0.490549i
$209$	−2992.35			−0.990359
$210$	−4433.60			−1.45689
$211$	−1899.21	−	3289.53i	−0.619654	−	1.07327i	−0.989549	−	0.144198i	$-0.953940\pi$
$211$	−1899.21	−	3289.53i	−0.619654	−	1.07327i	0.369895	−	0.929074i	$-0.379394\pi$
$212$	1138.20	−	1971.42i	0.368735	−	0.638669i
$213$	193.299	−	334.804i	0.0621813	−	0.107701i
$214$	−349.077	−	604.620i	−0.111507	−	0.193135i
$215$	2568.77			0.814831
$216$	247.170			0.0778600
$217$	2026.96	+	3510.80i	0.634098	+	1.09829i
$218$	389.570	+	674.755i	0.121032	+	0.209634i
$219$	1468.10	+	2542.83i	0.452992	+	0.784605i
$220$	2750.78	+	4764.49i	0.842989	+	1.46010i
$221$	−1143.13	+	1979.96i	−0.347943	+	0.602655i
$222$	2542.33	−	4403.45i	0.768605	−	1.33126i
$223$	2251.76			0.676183			0.338091	−	0.941113i	$-0.390219\pi$
$223$	2251.76			0.676183			0.338091	+	0.941113i	$0.390219\pi$
$224$	3215.50	+	5569.41i	0.959128	+	1.66126i
$225$	550.988			0.163256
$226$	−4541.10			−1.33659
$227$	850.944	−	1473.88i	0.248807	−	0.430946i	−0.714388	−	0.699750i	$-0.753295\pi$
$227$	850.944	−	1473.88i	0.248807	−	0.430946i	0.963195	+	0.268803i	$0.0866282\pi$
$228$	−2293.48			−0.666182
$229$	2143.52	+	3712.68i	0.618549	+	1.07136i	0.989751	+	0.142805i	$0.0456123\pi$
$229$	2143.52	+	3712.68i	0.618549	+	1.07136i	−0.371202	+	0.928552i	$0.621054\pi$
$230$	5503.10	−	9531.65i	1.57767	−	2.73260i
$231$	1514.76	+	2623.63i	0.431444	+	0.747283i
$232$	711.642	−	1232.60i	0.201386	−	0.348811i
$233$	−130.194	+	225.503i	−0.0366065	+	0.0634043i	−0.883748	−	0.467963i	$-0.844988\pi$
$233$	−130.194	+	225.503i	−0.0366065	+	0.0634043i	0.847142	+	0.531367i	$0.178321\pi$
$234$	−772.071	+	1337.27i	−0.215692	+	0.373589i
$235$	−3728.96	+	6458.75i	−1.03511	+	1.79286i
$236$	−207.181	+	358.848i	−0.0571455	+	0.0989789i
$237$	−163.522	+	283.228i	−0.0448180	+	0.0776271i
$238$	3073.95	+	5324.24i	0.837205	+	1.45008i
$239$	−319.058	+	552.624i	−0.0863520	+	0.149566i	−0.905967	−	0.423349i	$-0.860854\pi$
$239$	−319.058	+	552.624i	−0.0863520	+	0.149566i	0.819615	+	0.572915i	$0.194188\pi$
$240$	−863.638	−	1495.86i	−0.232282	−	0.402323i
$241$	5216.56			1.39431			0.697153	−	0.716922i	$-0.254450\pi$
$241$	5216.56			1.39431			0.697153	+	0.716922i	$0.254450\pi$
$242$	526.152	−	911.321i	0.139762	−	0.242074i
$243$	−243.000			−0.0641500
$244$	3696.45			0.969839
$245$	−2069.03	−	3583.67i	−0.539534	−	0.934500i
$246$	−5331.45			−1.38179
$247$	1516.87	−	2627.29i	0.390753	−	0.676803i
$248$	729.929	−	1264.27i	0.186897	−	0.323716i
$249$	−5.21072	−	9.02524i	−0.00132617	−	0.00229699i
$250$	−1853.90	−	3211.06i	−0.469005	−	0.812340i
$251$	2240.99	+	3881.50i	0.563545	+	0.976088i	0.997183	+	0.0750013i	$0.0238961\pi$
$251$	2240.99	+	3881.50i	0.563545	+	0.976088i	−0.433639	+	0.901087i	$0.642771\pi$
$252$	1160.98	+	2010.88i	0.290218	+	0.502673i
$253$	−7520.62			−1.86884
$254$	−149.186			−0.0368534
$255$	−1162.02	−	2012.67i	−0.285366	−	0.494268i
$256$	−554.852	+	961.031i	−0.135462	+	0.234627i
$257$	1879.20	−	3254.86i	0.456113	−	0.790010i	−0.542639	−	0.839966i	$-0.682575\pi$
$257$	1879.20	−	3254.86i	0.456113	−	0.790010i	0.998751	+	0.0499557i	$0.0159080\pi$
$258$	−1202.89	−	2083.47i	−0.290267	−	0.502757i
$259$	10113.8			2.42640
$260$	−5577.65			−1.33043
$261$	−699.637	+	1211.81i	−0.165925	+	0.287391i
$262$	1323.75	+	2292.81i	0.312144	+	0.540649i
$263$	−4764.67			−1.11712			−0.558560	−	0.829464i	$-0.688646\pi$
$263$	−4764.67			−1.11712			−0.558560	+	0.829464i	$0.688646\pi$
$264$	545.478	−	944.796i	0.127166	−	0.220258i
$265$	−3060.88			−0.709540
$266$	−4078.95	−	7064.94i	−0.940211	−	1.62849i
$267$	−2704.32			−0.619857
$268$	710.971	+	5520.22i	0.162050	+	1.25821i
$269$	−8177.61			−1.85352			−0.926762	−	0.375649i	$-0.877420\pi$
$269$	−8177.61			−1.85352			−0.926762	+	0.375649i	$0.877420\pi$
$270$	−784.824	−	1359.36i	−0.176900	−	0.306399i
$271$	−2062.25			−0.462261			−0.231131	−	0.972923i	$-0.574242\pi$
$271$	−2062.25			−0.462261			−0.231131	+	0.972923i	$0.574242\pi$
$272$	−1197.57	+	2074.26i	−0.266962	+	0.462391i
$273$	−3071.41			−0.680916
$274$	−5105.58	−	8843.12i	−1.12569	−	1.94975i
$275$	1215.97	−	2106.13i	0.266640	−	0.461834i
$276$	−5764.17			−1.25711
$277$	2124.31			0.460784			0.230392	−	0.973098i	$-0.425999\pi$
$277$	2124.31			0.460784			0.230392	+	0.973098i	$0.425999\pi$
$278$	−2179.13	−	3774.36i	−0.470127	−	0.814285i
$279$	−717.616	+	1242.95i	−0.153988	+	0.266714i
$280$	−1587.86	+	2750.25i	−0.338902	+	0.586996i
$281$	−4311.23	−	7467.26i	−0.915253	−	1.58527i	−0.806530	−	0.591193i	$-0.798657\pi$
$281$	−4311.23	−	7467.26i	−0.915253	−	1.58527i	−0.108723	−	0.994072i	$-0.534676\pi$
$282$	6984.73			1.47495
$283$	564.739			0.118623			0.0593114	−	0.998240i	$-0.481110\pi$
$283$	564.739			0.118623			0.0593114	+	0.998240i	$0.481110\pi$
$284$	−653.921	−	1132.62i	−0.136631	−	0.236651i
$285$	1541.92	+	2670.69i	0.320476	+	0.555080i
$286$	3407.77	+	5902.43i	0.704565	+	1.22034i
$287$	−5302.31	−	9183.88i	−1.09054	−	1.88887i
$288$	−1138.40	+	1971.77i	−0.232920	+	0.403429i
$289$	845.177	−	1463.89i	0.172029	−	0.297962i
$290$	−9038.56			−1.83021
$291$	1848.13	+	3201.05i	0.372299	+	0.644841i
$292$	9933.04			1.99071
$293$	8681.51			1.73099			0.865493	−	0.500921i	$-0.167005\pi$
$293$	8681.51			1.73099			0.865493	+	0.500921i	$0.167005\pi$
$294$	−1937.76	+	3356.29i	−0.384396	+	0.665793i
$295$	557.156			0.109962
$296$	−1821.03	−	3154.12i	−0.357586	−	0.619357i
$297$	−536.277	+	928.858i	−0.104774	+	0.181474i
$298$	−6250.77	−	10826.7i	−1.21509	−	2.10460i
$299$	3812.31	−	6603.12i	0.737364	−	1.27715i
$300$	931.983	−	1614.24i	0.179360	−	0.310661i
$301$	2392.64	−	4144.18i	0.458171	−	0.793576i
$302$	2885.80	−	4998.35i	0.549865	−	0.952394i
$303$	1947.43	−	3373.05i	0.369231	−	0.639527i
$304$	1589.11	−	2752.41i	0.299808	−	0.519282i
$305$	−2485.14	−	4304.40i	−0.466554	−	0.808095i
$306$	−1088.29	+	1884.97i	−0.203311	+	0.352145i
$307$	−862.622	−	1494.10i	−0.160366	−	0.277762i	0.774634	−	0.632410i	$-0.217934\pi$
$307$	−862.622	−	1494.10i	−0.160366	−	0.277762i	−0.935000	+	0.354648i	$0.884601\pi$
$308$	10248.7			1.89602
$309$	3065.89	−	5310.28i	0.564442	−	0.977642i
$310$	−9270.82			−1.69854
$311$	−8255.64			−1.50526			−0.752628	−	0.658446i	$-0.771214\pi$
$311$	−8255.64			−1.50526			−0.752628	+	0.658446i	$0.771214\pi$
$312$	553.022	+	957.863i	0.100348	+	0.173809i
$313$	1768.63			0.319389			0.159695	−	0.987166i	$-0.448949\pi$
$313$	1768.63			0.319389			0.159695	+	0.987166i	$0.448949\pi$
$314$	−3945.58	+	6833.95i	−0.709115	+	1.22822i
$315$	1561.07	−	2703.86i	0.279227	−	0.483635i
$316$	553.186	+	958.146i	0.0984783	+	0.170569i
$317$	1670.60	+	2893.56i	0.295994	+	0.512677i	0.975216	−	0.221256i	$-0.0710157\pi$
$317$	1670.60	+	2893.56i	0.295994	+	0.512677i	−0.679221	+	0.733933i	$0.737682\pi$
$318$	1433.33	+	2482.61i	0.252759	+	0.437792i
$319$	3088.06	+	5348.67i	0.542000	+	0.938771i
$320$	−10100.8			−1.76454
$321$	491.641			0.0854852
$322$	−10251.5	−	17756.2i	−1.77421	−	3.07303i
$323$	2138.13	−	3703.34i	0.368324	−	0.637955i
$324$	−411.029	+	711.922i	−0.0704781	+	0.122072i
$325$	1232.79	+	2135.26i	0.210409	+	0.364439i
$326$	7595.33			1.29039
$327$	−548.671			−0.0927877
$328$	−1909.42	+	3307.20i	−0.321432	+	0.556737i
$329$	6946.56	+	12031.8i	1.16406	+	2.01621i
$330$	−6928.11			−1.15570
$331$	−1766.08	+	3058.94i	−0.293271	+	0.507960i	−0.974581	−	0.224035i	$-0.928077\pi$
$331$	−1766.08	+	3058.94i	−0.293271	+	0.507960i	0.681310	+	0.731995i	$0.261410\pi$
$332$	−35.2552			−0.00582796
$333$	1790.31	+	3100.91i	0.294620	+	0.510298i
$334$	1476.77			0.241932
$335$	5950.14	−	4539.19i	0.970420	−	0.740305i
$336$	−3217.69			−0.522438
$337$	3690.72	+	6392.51i	0.596577	+	1.03330i	0.993322	+	0.115372i	$0.0368062\pi$
$337$	3690.72	+	6392.51i	0.596577	+	1.03330i	−0.396746	+	0.917929i	$0.629861\pi$
$338$	2449.75			0.394227
$339$	1598.92	−	2769.42i	0.256170	−	0.443699i
$340$	−7862.08			−1.25406
$341$	3167.41	+	5486.12i	0.503006	+	0.871232i
$342$	1444.09	−	2501.24i	0.228326	−	0.395472i
$343$	1010.80			0.159120
$344$	−1723.23			−0.270088
$345$	3875.29	+	6712.20i	0.604749	+	1.04746i
$346$	−7.97048	+	13.8053i	−0.00123843	+	0.00214502i
$347$	−3300.31	+	5716.30i	−0.510575	+	0.884343i	0.489350	+	0.872088i	$0.337234\pi$
$347$	−3300.31	+	5716.30i	−0.510575	+	0.884343i	−0.999925	+	0.0122548i	$0.996099\pi$
$348$	2366.84	+	4099.48i	0.364586	+	0.631481i
$349$	5249.85			0.805209			0.402604	−	0.915374i	$-0.368105\pi$
$349$	5249.85			0.805209			0.402604	+	0.915374i	$0.368105\pi$
$350$	6630.10			1.01255
$351$	−543.693	−	941.705i	−0.0826786	−	0.143204i
$352$	5024.67	+	8702.98i	0.760840	+	1.31781i
$353$	3869.08	+	6701.44i	0.583371	+	1.01043i	0.995076	+	0.0991118i	$0.0316001\pi$
$353$	3869.08	+	6701.44i	0.583371	+	1.01043i	−0.411705	+	0.911317i	$0.635067\pi$
$354$	−260.903	−	451.897i	−0.0391718	−	0.0678476i
$355$	−879.270	+	1522.94i	−0.131456	+	0.227688i
$356$	−4574.30	+	7922.91i	−0.681003	+	1.17953i
$357$	−4329.36			−0.641832
$358$	−1144.18	−	1981.78i	−0.168916	−	0.292571i
$359$	−7762.37			−1.14118			−0.570588	−	0.821237i	$-0.693285\pi$
$359$	−7762.37			−1.14118			−0.570588	+	0.821237i	$0.693285\pi$
$360$	−1124.31			−0.164602
$361$	592.338	−	1025.96i	0.0863592	−	0.149579i
$362$	6311.23			0.916329
$363$	370.516	+	641.753i	0.0535732	+	0.0927915i
$364$	−5195.21	+	8998.37i	−0.748086	+	1.29572i
$365$	−6678.05	−	11566.7i	−0.957657	−	1.65871i
$366$	−2327.47	+	4031.29i	−0.332400	+	0.575735i
$367$	−1153.94	+	1998.68i	−0.164128	+	0.284279i	−0.936345	−	0.351080i	$-0.885814\pi$
$367$	−1153.94	+	1998.68i	−0.164128	+	0.284279i	0.772217	+	0.635359i	$0.219148\pi$
$368$	3993.88	−	6917.60i	0.565748	−	0.979904i
$369$	1877.20	−	3251.41i	0.264833	−	0.458704i
$370$	−11564.5	+	20030.2i	−1.62489	+	2.81439i
$371$	−2851.01	+	4938.09i	−0.398967	+	0.691031i
$372$	2427.66	+	4204.83i	0.338356	+	0.586049i
$373$	4029.33	−	6979.01i	0.559333	−	0.968792i	−0.438220	−	0.898868i	$-0.644391\pi$
$373$	4029.33	−	6979.01i	0.559333	−	0.968792i	0.997552	−	0.0699246i	$-0.0222759\pi$
$374$	4803.48	+	8319.87i	0.664123	+	1.15029i
$375$	2611.04			0.359556
$376$	2501.53	−	4332.77i	0.343102	−	0.594270i
$377$	−6261.53			−0.855399
$378$	−2924.05			−0.397875
$379$	2429.12	+	4207.35i	0.329222	+	0.570230i	0.982358	−	0.187011i	$-0.0598801\pi$
$379$	2429.12	+	4207.35i	0.329222	+	0.570230i	−0.653135	+	0.757241i	$0.726547\pi$
$380$	10432.5			1.40836
$381$	52.5284	−	90.9819i	0.00706329	−	0.0122340i
$382$	6065.61	−	10506.0i	0.812418	−	1.40715i
$383$	−2406.96	−	4168.98i	−0.321123	−	0.556201i	0.659597	−	0.751619i	$-0.270727\pi$
$383$	−2406.96	−	4168.98i	−0.321123	−	0.556201i	−0.980720	+	0.195418i	$0.937394\pi$
$384$	1694.24	+	2934.52i	0.225154	+	0.389978i
$385$	−6890.26	−	11934.3i	−0.912104	−	1.57981i
$386$	4002.69	+	6932.87i	0.527802	+	0.914181i
$387$	1694.16			0.222529
$388$	12504.2			1.63610
$389$	−2417.74	−	4187.65i	−0.315127	−	0.545815i	0.664338	−	0.747433i	$-0.268714\pi$
$389$	−2417.74	−	4187.65i	−0.315127	−	0.545815i	−0.979464	+	0.201617i	$0.935380\pi$
$390$	3511.97	−	6082.90i	0.455988	−	0.789794i
$391$	5373.72	−	9307.55i	0.695040	−	1.20384i
$392$	1387.98	+	2404.06i	0.178836	+	0.309754i
$393$	−1864.38			−0.239301
$394$	2276.96			0.291147
$395$	743.821	−	1288.34i	0.0947486	−	0.164109i
$396$	1814.20	+	3142.28i	0.230219	+	0.398751i
$397$	13206.8			1.66960			0.834802	−	0.550551i	$-0.185582\pi$
$397$	13206.8			1.66960			0.834802	+	0.550551i	$0.185582\pi$
$398$	−4913.34	+	8510.15i	−0.618802	+	1.07180i
$399$	5744.80			0.720801
$400$	1291.50	+	2236.95i	0.161438	+	0.279619i
$401$	3273.43			0.407649			0.203824	−	0.979007i	$-0.434663\pi$
$401$	3273.43			0.407649			0.203824	+	0.979007i	$0.434663\pi$
$402$	−6467.94	−	2700.43i	−0.802466	−	0.335038i
$403$	−6422.44			−0.793857
$404$	−6588.06	−	11410.9i	−0.811308	−	1.40523i
$405$	1105.35			0.135618
$406$	−8418.82	+	14581.8i	−1.02911	+	1.78247i
$407$	15804.2			1.92478
$408$	779.523	+	1350.17i	0.0945886	+	0.163832i
$409$	−6990.62	+	12108.1i	−0.845144	+	1.46383i	0.0403525	+	0.999186i	$0.487152\pi$
$409$	−6990.62	+	12108.1i	−0.845144	+	1.46383i	−0.885496	+	0.464646i	$0.846181\pi$
$410$	24251.5			2.92121
$411$	7190.71			0.862996
$412$	−10371.8	−	17964.4i	−1.24024	−	2.14817i
$413$	518.954	−	898.855i	0.0618307	−	0.107094i
$414$	3629.41	−	6286.32i	0.430859	−	0.746270i
$415$	23.7023	+	41.0536i	0.00280362	+	0.00485601i
$416$	−10188.3			−1.20078
$417$	3069.09			0.360417
$418$	−6373.92	−	11040.0i	−0.745834	−	1.29182i
$419$	5269.27	+	9126.64i	0.614369	+	1.06412i	0.990495	+	0.137550i	$0.0439228\pi$
$419$	5269.27	+	9126.64i	0.614369	+	1.06412i	−0.376126	+	0.926569i	$0.622744\pi$
$420$	−5281.03	−	9147.01i	−0.613543	−	1.06269i
$421$	−6437.05	−	11149.3i	−0.745185	−	1.29070i	−0.950108	−	0.311920i	$-0.899028\pi$
$421$	−6437.05	−	11149.3i	−0.745185	−	1.29070i	0.204924	−	0.978778i	$-0.434305\pi$
$422$	8090.91	−	14013.9i	0.933316	−	1.61655i
$423$	−2459.33	+	4259.68i	−0.282687	+	0.489628i
$424$	2053.35			0.235187
$425$	1737.70	+	3009.79i	0.198332	+	0.343521i
$426$	1646.96			0.187314
$427$	−9258.99			−1.04935
$428$	831.599	−	1440.37i	0.0939179	−	0.162671i
$429$	−4799.51			−0.540145
$430$	5471.67	+	9477.21i	0.613645	+	1.06286i
$431$	−2202.60	+	3815.01i	−0.246161	+	0.426363i	−0.962457	−	0.271433i	$-0.912503\pi$
$431$	−2202.60	+	3815.01i	−0.246161	+	0.426363i	0.716296	+	0.697796i	$0.245836\pi$
$432$	−569.587	−	986.553i	−0.0634358	−	0.109874i
$433$	−4785.03	+	8287.91i	−0.531071	+	0.919842i	0.468271	+	0.883585i	$0.344877\pi$
$433$	−4785.03	+	8287.91i	−0.531071	+	0.919842i	−0.999342	+	0.0362576i	$0.988456\pi$
$434$	−8635.16	+	14956.5i	−0.955071	+	1.65423i
$435$	3182.48	−	5512.22i	0.350778	−	0.607565i
$436$	−928.063	+	1607.45i	−0.101941	+	0.176567i
$437$	−7130.59	+	12350.5i	−0.780555	+	1.35196i
$438$	−6254.33	+	10832.8i	−0.682291	+	1.18176i
$439$	3731.89	+	6463.83i	0.405726	+	0.702737i	0.994406	−	0.105629i	$-0.0336856\pi$
$439$	3731.89	+	6463.83i	0.405726	+	0.702737i	−0.588680	+	0.808366i	$0.700352\pi$
$440$	−2481.25	+	4297.65i	−0.268838	+	0.465642i
$441$	−1364.57	−	2363.51i	−0.147346	−	0.255211i
$442$	−9739.83			−1.04814
$443$	7536.22	−	13053.1i	0.808254	−	1.39994i	−0.105818	−	0.994386i	$-0.533746\pi$
$443$	7536.22	−	13053.1i	0.808254	−	1.39994i	0.914072	−	0.405552i	$-0.132921\pi$
$444$	12113.1			1.29473
$445$	12301.3			1.31042
$446$	4796.40	+	8307.62i	0.509229	+	0.882011i
$447$	8803.60			0.931534
$448$	−9408.26	+	16295.6i	−0.992185	+	1.71851i
$449$	−5954.98	+	10314.3i	−0.625909	+	1.08411i	0.362456	+	0.932001i	$0.381938\pi$
$449$	−5954.98	+	10314.3i	−0.625909	+	1.08411i	−0.988364	+	0.152104i	$0.951395\pi$
$450$	1173.64	+	2032.81i	0.122947	+	0.212950i
$451$	−8285.60	−	14351.1i	−0.865086	−	1.49837i
$452$	−5409.08	−	9368.80i	−0.562880	−	0.974937i
$453$	2032.18	+	3519.85i	0.210773	+	0.365070i
$454$	7250.30			0.749501
$455$	13971.1			1.43951
$456$	−1034.38	−	1791.60i	−0.106226	−	0.183989i
$457$	2474.53	−	4286.00i	0.253290	−	0.438711i	−0.711140	−	0.703051i	$-0.751821\pi$
$457$	2474.53	−	4286.00i	0.253290	−	0.438711i	0.964430	+	0.264340i	$0.0851541\pi$
$458$	−9131.70	+	15816.6i	−0.931651	+	1.61367i
$459$	−766.373	−	1327.40i	−0.0779329	−	0.134984i
$460$	26219.8			2.65762
$461$	90.2841			0.00912136			0.00456068	−	0.999990i	$-0.498548\pi$
$461$	90.2841			0.00912136			0.00456068	+	0.999990i	$0.498548\pi$
$462$	−6453.08	+	11177.1i	−0.649837	+	1.12555i
$463$	−5089.04	−	8814.48i	−0.510816	−	0.884760i	−0.999921	−	0.0125348i	$-0.996010\pi$
$463$	−5089.04	−	8814.48i	−0.510816	−	0.884760i	0.489105	−	0.872225i	$-0.337323\pi$
$464$	−6559.74			−0.656311
$465$	3264.26	−	5653.87i	0.325541	−	0.563853i
$466$	−1109.29			−0.110273
$467$	−1078.57	−	1868.13i	−0.106874	−	0.185111i	0.807628	−	0.589692i	$-0.200751\pi$
$467$	−1078.57	−	1868.13i	−0.106874	−	0.185111i	−0.914502	+	0.404581i	$0.867417\pi$
$468$	−3678.58			−0.363338
$469$	−1780.86	−	13827.3i	−0.175336	−	1.36137i
$470$	−31771.9			−3.11814
$471$	−2778.48	−	4812.48i	−0.271817	−	0.470801i
$472$	−373.761			−0.0364486
$473$	3738.83	−	6475.85i	0.363450	−	0.629514i
$474$	−1393.25			−0.135009
$475$	−2305.83	−	3993.81i	−0.222734	−	0.385786i
$476$	−7323.01	+	12683.8i	−0.705146	+	1.22135i
$477$	−2018.71			−0.193775
$478$	−2718.47			−0.260125
$479$	5591.90	+	9685.45i	0.533403	+	0.923882i	0.999239	+	0.0390104i	$0.0124206\pi$
$479$	5591.90	+	9685.45i	0.533403	+	0.923882i	−0.465835	+	0.884871i	$0.654246\pi$
$480$	5178.31	−	8969.10i	0.492409	−	0.852878i
$481$	−8011.37	+	13876.1i	−0.759433	+	1.31538i
$482$	11111.6	+	19245.9i	1.05004	+	1.81873i
$483$	14438.3			1.36018
$484$	2506.88			0.235432
$485$	−8406.68	−	14560.8i	−0.787068	−	1.36324i
$486$	−517.608	−	896.523i	−0.0483110	−	0.0836772i
$487$	2391.02	+	4141.36i	0.222479	+	0.385345i	0.955560	−	0.294796i	$-0.0952517\pi$
$487$	2391.02	+	4141.36i	0.222479	+	0.385345i	−0.733081	+	0.680141i	$0.761918\pi$
$488$	1667.13	+	2887.55i	0.154646	+	0.267855i
$489$	−2674.32	+	4632.06i	−0.247315	+	0.428362i
$490$	8814.39	−	15267.0i	0.812640	−	1.40753i
$491$	−383.082			−0.0352103			−0.0176052	−	0.999845i	$-0.505604\pi$
$491$	−383.082			−0.0352103			−0.0176052	+	0.999845i	$0.505604\pi$
$492$	−6350.49	−	10999.4i	−0.581915	−	1.00791i
$493$	−8826.05			−0.806299
$494$	12924.1			1.17709
$495$	2439.39	−	4225.15i	0.221500	−	0.383649i
$496$	−6728.30			−0.609092
$497$	1637.96	+	2837.04i	0.147832	+	0.256053i
$498$	22.1984	−	38.4488i	0.00199746	−	0.00345971i
$499$	3735.73	+	6470.48i	0.335139	+	0.580478i	0.983512	−	0.180846i	$-0.0578834\pi$
$499$	3735.73	+	6470.48i	0.335139	+	0.580478i	−0.648373	+	0.761323i	$0.724550\pi$
$500$	4416.51	−	7649.63i	0.395025	−	0.684203i
$501$	−519.971	+	900.616i	−0.0463684	+	0.0803125i
$502$	−9546.93	+	16535.8i	−0.848805	+	1.47017i
$503$	10380.8	−	17980.2i	0.920197	−	1.59383i	0.121088	−	0.992642i	$-0.461362\pi$
$503$	10380.8	−	17980.2i	0.920197	−	1.59383i	0.799109	−	0.601186i	$-0.205305\pi$
$504$	−1047.22	+	1813.85i	−0.0925538	+	0.160308i
$505$	−8858.39	+	15343.2i	−0.780581	+	1.35201i
$506$	−16019.5	−	27746.5i	−1.40742	−	2.43772i
$507$	−862.558	+	1493.99i	−0.0755573	+	0.130869i
$508$	−177.701	−	307.787i	−0.0155201	−	0.0268816i
$509$	19464.6			1.69499			0.847497	−	0.530800i	$-0.178108\pi$
$509$	19464.6			1.69499			0.847497	+	0.530800i	$0.178108\pi$
$510$	4950.36	−	8574.27i	0.429815	−	0.744461i
$511$	−24880.6			−2.15392
$512$	−13763.5			−1.18802
$513$	1016.93	+	1761.37i	0.0875215	+	0.151592i
$514$	16011.3			1.37398
$515$	−13946.0	+	24155.2i	−1.19327	+	2.06681i
$516$	2865.63	−	4963.41i	0.244481	−	0.423453i
$517$	10855.0	+	18801.4i	0.923407	+	1.59939i
$518$	21543.1	+	37313.7i	1.82731	+	3.16500i
$519$	−5.61282	−	9.72169i	−0.000474712	−	0.000822225i
$520$	−2515.57	−	4357.09i	−0.212144	−	0.367444i
$521$	−12719.4			−1.06957			−0.534786	−	0.844988i	$-0.679608\pi$
$521$	−12719.4			−1.06957			−0.534786	+	0.844988i	$0.679608\pi$
$522$	−5961.11			−0.499829
$523$	2520.14	+	4365.00i	0.210703	+	0.364949i	0.951935	−	0.306301i	$-0.0990913\pi$
$523$	2520.14	+	4365.00i	0.210703	+	0.364949i	−0.741232	+	0.671249i	$0.765758\pi$
$524$	−3153.55	+	5462.10i	−0.262907	+	0.455368i
$525$	−2334.46	+	4043.41i	−0.194065	+	0.336131i
$526$	−10149.1	−	17578.8i	−0.841297	−	1.45717i
$527$	−9052.86			−0.748290
$528$	−5028.08			−0.414430
$529$	−11837.7	+	20503.5i	−0.972935	+	1.68517i
$530$	−6519.89	−	11292.8i	−0.534351	−	0.925523i
$531$	367.456			0.0300306
$532$	9717.18	−	16830.6i	0.791904	−	1.37162i
$533$	16800.4			1.36530
$534$	−5760.41	−	9977.32i	−0.466811	−	0.808541i
$535$	−2236.36			−0.180722
$536$	−3991.57	+	3045.05i	−0.321660	+	0.245385i
$537$	1611.47			0.129497
$538$	−17418.9	−	30170.5i	−1.39588	−	2.41773i
$539$	−12045.9			−0.962621
$540$	1869.67	−	3238.36i	0.148996	−	0.258068i
$541$	−17337.1			−1.37778			−0.688890	−	0.724865i	$-0.741902\pi$
$541$	−17337.1			−1.37778			−0.688890	+	0.724865i	$0.741902\pi$
$542$	−4392.75	−	7608.46i	−0.348127	−	0.602973i
$543$	−2222.19	+	3848.94i	−0.175623	+	0.304188i
$544$	−14361.1			−1.13185
$545$	2495.77			0.196160
$546$	−6542.33	−	11331.6i	−0.512794	−	0.888186i
$547$	9356.97	−	16206.7i	0.731399	−	1.26682i	−0.224887	−	0.974385i	$-0.572201\pi$
$547$	9356.97	−	16206.7i	0.731399	−	1.26682i	0.956285	−	0.292435i	$-0.0944655\pi$
$548$	12162.9	−	21066.8i	0.948127	−	1.64220i
$549$	−1639.00	−	2838.84i	−0.127415	−	0.220690i
$550$	10360.5			0.803221
$551$	11711.6			0.905503
$552$	−2599.69	−	4502.79i	−0.200453	−	0.347195i
$553$	−1385.64	−	2400.00i	−0.106552	−	0.184554i
$554$	4524.93	+	7837.41i	0.347014	+	0.601046i
$555$	−8143.71	−	14105.3i	−0.622849	−	1.07881i
$556$	5191.29	−	8991.57i	0.395971	−	0.685841i
$557$	−4830.29	+	8366.31i	−0.367444	+	0.636431i	−0.989165	−	0.146807i	$-0.953100\pi$
$557$	−4830.29	+	8366.31i	−0.367444	+	0.636431i	0.621721	+	0.783238i	$0.286434\pi$
$558$	−6114.30			−0.463869
$559$	3790.54	+	6565.41i	0.286803	+	0.496758i
$560$	14636.5			1.10447
$561$	−6765.23			−0.509141
$562$	18366.5	−	31811.6i	1.37854	−	2.38771i
$563$	−9337.71			−0.699001			−0.349501	−	0.936936i	$-0.613649\pi$
$563$	−9337.71			−0.699001			−0.349501	+	0.936936i	$0.613649\pi$
$564$	8319.78	+	14410.3i	0.621145	+	1.07586i
$565$	−7273.12	+	12597.4i	−0.541562	+	0.938013i
$566$	1202.93	+	2083.54i	0.0893341	+	0.154731i
$567$	1029.56	−	1783.25i	0.0762565	−	0.132080i
$568$	589.847	−	1021.65i	0.0435729	−	0.0754706i
$569$	3691.88	−	6394.53i	0.272007	−	0.471129i	−0.697369	−	0.716712i	$-0.745646\pi$
$569$	3691.88	−	6394.53i	0.272007	−	0.471129i	0.969376	+	0.245583i	$0.0789794\pi$
$570$	−6568.82	+	11377.5i	−0.482697	+	0.836056i
$571$	1985.60	−	3439.17i	0.145525	−	0.252057i	−0.784043	−	0.620706i	$-0.786846\pi$
$571$	1985.60	−	3439.17i	0.145525	−	0.252057i	0.929569	+	0.368649i	$0.120179\pi$
$572$	−8118.25	+	14061.2i	−0.593428	+	1.02785i
$573$	4271.41	+	7398.30i	0.311415	+	0.539387i
$574$	22588.6	−	39124.7i	1.64256	−	2.84500i
$575$	−5795.20	−	10037.6i	−0.420307	−	0.727993i
$576$	−6661.71			−0.481895
$577$	−2513.98	+	4354.34i	−0.181384	+	0.314166i	−0.942352	−	0.334623i	$-0.891391\pi$
$577$	−2513.98	+	4354.34i	−0.181384	+	0.314166i	0.760968	+	0.648789i	$0.224724\pi$
$578$	7201.15			0.518215
$579$	−5637.40			−0.404633
$580$	−10766.2	−	18647.6i	−0.770760	−	1.33500i
$581$	88.3086			0.00630578
$582$	−7873.29	+	13636.9i	−0.560753	+	0.971253i
$583$	−4455.09	+	7716.45i	−0.316486	+	0.548169i
$584$	4479.88	+	7759.38i	0.317429	+	0.549804i
$585$	2473.13	+	4283.59i	0.174789	+	0.302743i
$586$	18492.2	+	32029.5i	1.30360	+	2.25790i
$587$	−6419.22	−	11118.4i	−0.451362	−	0.781782i	0.547109	−	0.837061i	$-0.315728\pi$
$587$	−6419.22	−	11118.4i	−0.451362	−	0.781782i	−0.998471	+	0.0552795i	$0.982395\pi$
$588$	−9232.55			−0.647524
$589$	12012.6			0.840357
$590$	1186.78	+	2055.57i	0.0828121	+	0.143435i
$591$	−801.720	+	1388.62i	−0.0558010	+	0.0966501i
$592$	−8392.91	+	14537.0i	−0.582680	+	1.00923i
$593$	7371.36	+	12767.6i	0.510465	+	0.884151i	0.999926	+	0.0121260i	$0.00385992\pi$
$593$	7371.36	+	12767.6i	0.510465	+	0.884151i	−0.489462	+	0.872025i	$0.662807\pi$
$594$	−4569.23			−0.315619
$595$	19693.2			1.35688
$596$	14891.1	−	25792.1i	1.02343	−	1.77263i
$597$	−3459.98	−	5992.85i	−0.237198	−	0.410840i
$598$	32482.0			2.22122
$599$	−3244.79	+	5620.14i	−0.221333	+	0.383360i	−0.955213	−	0.295919i	$-0.904374\pi$
$599$	−3244.79	+	5620.14i	−0.221333	+	0.383360i	0.733880	+	0.679279i	$0.237707\pi$
$600$	1681.33			0.114400
$601$	3802.60	+	6586.29i	0.258089	+	0.447022i	0.965730	−	0.259549i	$-0.0835740\pi$
$601$	3802.60	+	6586.29i	0.258089	+	0.447022i	−0.707641	+	0.706572i	$0.750241\pi$
$602$	20386.0			1.38019
$603$	3924.24	−	2993.69i	0.265020	−	0.202176i
$604$	13749.6			0.926261
$605$	−1685.39	−	2919.18i	−0.113258	−	0.196168i
$606$	16592.7			1.11226
$607$	6215.06	−	10764.8i	0.415587	−	0.719819i	−0.579903	−	0.814686i	$-0.696909\pi$
$607$	6215.06	−	10764.8i	0.415587	−	0.719819i	0.995490	+	0.0948674i	$0.0302427\pi$
$608$	19056.3			1.27111
$609$	−5928.54	−	10268.5i	−0.394477	−	0.683254i
$610$	10587.1	−	18337.4i	0.702719	−	1.21714i
$611$	−22010.2			−1.45734
$612$	−5185.20			−0.342483
$613$	−12101.7	−	20960.8i	−0.797365	−	1.38108i	−0.921327	−	0.388789i	$-0.872894\pi$
$613$	−12101.7	−	20960.8i	−0.797365	−	1.38108i	0.123962	−	0.992287i	$-0.460440\pi$
$614$	3674.89	−	6365.10i	0.241542	−	0.418363i
$615$	−8538.95	+	14789.9i	−0.559876	+	0.969734i
$616$	4622.24	+	8005.95i	0.302330	+	0.523651i
$617$	−2177.65			−0.142089			−0.0710443	−	0.997473i	$-0.522633\pi$
$617$	−2177.65			−0.142089			−0.0710443	+	0.997473i	$0.522633\pi$
$618$	26122.3			1.70031
$619$	2211.39	+	3830.24i	0.143592	+	0.248708i	0.928847	−	0.370465i	$-0.120802\pi$
$619$	2211.39	+	3830.24i	0.143592	+	0.248708i	−0.785255	+	0.619172i	$0.787468\pi$
$620$	−11042.8	−	19126.8i	−0.715308	−	1.23895i
$621$	2555.83	+	4426.83i	0.165156	+	0.286059i
$622$	−17585.1	−	30458.3i	−1.13360	−	1.96345i
$623$	11457.9	−	19845.6i	0.736837	−	1.27624i
$624$	2548.81	−	4414.67i	0.163516	−	0.283218i
$625$	−19529.6			−1.24990
$626$	3767.31	+	6525.17i	0.240530	+	0.416611i
$627$	8977.04			0.571784
$628$	−18799.0			−1.19452
$629$	−11292.6	+	19559.3i	−0.715842	+	1.23987i
$630$	13300.8			0.841137
$631$	14958.9	+	25909.5i	0.943744	+	1.63461i	0.758246	+	0.651969i	$0.226057\pi$
$631$	14958.9	+	25909.5i	0.943744	+	1.63461i	0.185499	+	0.982645i	$0.440610\pi$
$632$	−498.982	+	864.263i	−0.0314058	+	0.0543964i
$633$	5697.63	+	9868.58i	0.357757	+	0.619654i
$634$	−7117.00	+	12327.0i	−0.445823	+	0.772189i
$635$	−238.939	+	413.855i	−0.0149323	+	0.0258635i
$636$	−3414.60	+	5914.26i	−0.212890	+	0.368735i
$637$	6106.24	−	10576.3i	0.379808	−	0.657848i
$638$	−13155.6	+	22786.1i	−0.816355	+	1.41397i
$639$	−579.897	+	1004.41i	−0.0359004	+	0.0621813i
$640$	−7706.71	−	13348.4i	−0.475991	−	0.824441i
$641$	14738.8	−	25528.4i	0.908188	−	1.57303i	0.0916094	−	0.995795i	$-0.470799\pi$
$641$	14738.8	−	25528.4i	0.908188	−	1.57303i	0.816579	−	0.577234i	$-0.195868\pi$
$642$	1047.23	+	1813.86i	0.0643785	+	0.111507i
$643$	29190.4			1.79029			0.895146	−	0.445773i	$-0.147071\pi$
$643$	29190.4			1.79029			0.895146	+	0.445773i	$0.147071\pi$
$644$	24422.0	−	42300.2i	1.49435	−	2.58829i
$645$	−7706.31			−0.470443
$646$	18217.5			1.10953
$647$	3704.91	+	6417.08i	0.225123	+	0.389925i	0.956356	−	0.292203i	$-0.0943881\pi$
$647$	3704.91	+	6417.08i	0.225123	+	0.389925i	−0.731233	+	0.682128i	$0.761055\pi$
$648$	−741.509			−0.0449525
$649$	810.938	−	1404.59i	0.0490479	−	0.0849535i
$650$	−5251.88	+	9096.52i	−0.316916	+	0.548915i
$651$	−6080.89	−	10532.4i	−0.366096	−	0.634098i
$652$	9047.09	+	15670.0i	0.543422	+	0.941235i
$653$	−10892.9	−	18867.0i	−0.652787	−	1.13066i	−0.982444	−	0.186560i	$-0.940266\pi$
$653$	−10892.9	−	18867.0i	−0.652787	−	1.13066i	0.329656	−	0.944101i	$-0.393067\pi$
$654$	−1168.71	−	2024.26i	−0.0698779	−	0.121032i
$655$	8480.60			0.505900
$656$	17600.5			1.04754
$657$	−4404.31	−	7628.48i	−0.261535	−	0.452992i
$658$	−29593.4	+	51257.2i	−1.75330	+	3.03680i
$659$	−14330.3	+	24820.8i	−0.847085	+	1.46719i	0.0367129	+	0.999326i	$0.488311\pi$
$659$	−14330.3	+	24820.8i	−0.847085	+	1.46719i	−0.883798	+	0.467869i	$0.845022\pi$
$660$	−8252.35	−	14293.5i	−0.486700	−	0.842989i
$661$	−25488.6			−1.49984			−0.749919	−	0.661530i	$-0.769907\pi$
$661$	−25488.6			−1.49984			−0.749919	+	0.661530i	$0.769907\pi$
$662$	−15047.5			−0.883443
$663$	3429.40	−	5939.89i	0.200885	−	0.347943i
$664$	−15.9004	−	27.5403i	−0.000929300	−	0.00160959i
$665$	−26131.7			−1.52382
$666$	−7627.00	+	13210.4i	−0.443754	+	0.768605i
$667$	29434.6			1.70872
$668$	1759.04	+	3046.74i	0.101885	+	0.176470i
$669$	−6755.27			−0.390394
$670$	29421.1	+	12283.6i	1.69647	+	0.708295i
$671$	−14468.5			−0.832413
$672$	−9646.51	−	16708.2i	−0.553753	−	0.959128i
$673$	2469.49			0.141444			0.0707220	−	0.997496i	$-0.477470\pi$
$673$	2469.49			0.141444			0.0707220	+	0.997496i	$0.477470\pi$
$674$	−15723.0	+	27233.1i	−0.898557	+	1.55635i
$675$	−1652.96			−0.0942557
$676$	2917.99	+	5054.11i	0.166021	+	0.287557i
$677$	7403.46	−	12823.2i	0.420292	−	0.727968i	−0.575676	−	0.817678i	$-0.695261\pi$
$677$	7403.46	−	12823.2i	0.420292	−	0.727968i	0.995968	+	0.0897105i	$0.0285942\pi$
$678$	13623.3			0.771681
$679$	−31321.1			−1.77024
$680$	−3545.86	−	6141.61i	−0.199967	−	0.346353i
$681$	−2552.83	+	4421.64i	−0.143649	+	0.248807i
$682$	−13493.6	+	23371.7i	−0.757622	+	1.31224i
$683$	−4190.80	−	7258.67i	−0.234782	−	0.406655i	0.724427	−	0.689352i	$-0.242104\pi$
$683$	−4190.80	−	7258.67i	−0.234782	−	0.406655i	−0.959209	+	0.282696i	$0.908771\pi$
$684$	6880.45			0.384620
$685$	−32708.8			−1.82444
$686$	2153.08	+	3729.24i	0.119832	+	0.207556i
$687$	−6430.55	−	11138.0i	−0.357119	−	0.618549i
$688$	3971.07	+	6878.09i	0.220052	+	0.381141i
$689$	−4516.71	−	7823.17i	−0.249743	−	0.432567i
$690$	−16509.3	+	28594.9i	−0.910867	+	1.57767i
$691$	9368.10	−	16226.0i	0.515745	−	0.893296i	−0.484088	−	0.875019i	$-0.660849\pi$
$691$	9368.10	−	16226.0i	0.515745	−	0.893296i	0.999833	−	0.0182766i	$-0.00581795\pi$
$692$	−37.9758			−0.00208616
$693$	−4544.27	−	7870.90i	−0.249094	−	0.431444i
$694$	−28119.6			−1.53805
$695$	−13960.5			−0.761948
$696$	−2134.93	+	3697.80i	−0.116270	+	0.201386i
$697$	23681.3			1.28693
$698$	11182.6	+	19368.8i	0.606398	+	1.05031i
$699$	390.583	−	676.509i	0.0211348	−	0.0366065i
$700$	7897.37	+	13678.7i	0.426418	+	0.738578i
$701$	−5777.66	+	10007.2i	−0.311297	+	0.539182i	−0.978643	−	0.205565i	$-0.934097\pi$
$701$	−5777.66	+	10007.2i	−0.311297	+	0.539182i	0.667346	+	0.744747i	$0.267430\pi$
$702$	2316.21	−	4011.80i	0.124530	−	0.215692i
$703$	14984.6	−	25954.0i	0.803916	−	1.39242i
$704$	−14701.7	+	25464.1i	−0.787063	+	1.36323i
$705$	11186.9	−	19376.3i	0.597621	−	1.03511i
$706$	−16482.8	+	28549.1i	−0.878668	+	1.52190i
$707$	16502.0	+	28582.3i	0.877825	+	1.52044i
$708$	621.543	−	1076.54i	0.0329930	−	0.0571455i
$709$	7047.25	+	12206.2i	0.373293	+	0.646563i	0.990070	−	0.140575i	$-0.0448952\pi$
$709$	7047.25	+	12206.2i	0.373293	+	0.646563i	−0.616777	+	0.787138i	$0.711562\pi$
$710$	−7491.64			−0.395995
$711$	490.565	−	849.684i	0.0258757	−	0.0448180i
$712$	−8252.18			−0.434359
$713$	30191.0			1.58578
$714$	−9221.86	−	15972.7i	−0.483360	−	0.837205i
$715$	21831.8			1.14191
$716$	2725.76	−	4721.15i	0.142271	−	0.246421i
$717$	957.173	−	1657.87i	0.0498553	−	0.0863520i
$718$	−16534.4	−	28638.4i	−0.859414	−	1.48855i
$719$	−6444.84	−	11162.8i	−0.334287	−	0.579001i	0.649061	−	0.760736i	$-0.275162\pi$
$719$	−6444.84	−	11162.8i	−0.334287	−	0.579001i	−0.983348	+	0.181735i	$0.941829\pi$
$720$	2590.91	+	4487.59i	0.134108	+	0.232282i
$721$	25979.6	+	44998.0i	1.34193	+	2.32429i
$722$	5046.89			0.260147
$723$	−15649.7			−0.805003
$724$	7517.56	+	13020.8i	0.385895	+	0.668389i
$725$	−4759.16	+	8243.10i	−0.243794	+	0.422263i
$726$	−1578.45	+	2733.96i	−0.0806914	+	0.139762i
$727$	−4596.31	−	7961.04i	−0.234481	−	0.406133i	0.724641	−	0.689127i	$-0.242006\pi$
$727$	−4596.31	−	7961.04i	−0.234481	−	0.406133i	−0.959122	+	0.282994i	$0.908672\pi$
$728$	−9372.33			−0.477145
$729$	729.000			0.0370370
$730$	28449.5	−	49275.9i	1.44241	−	2.49833i
$731$	5343.03	+	9254.40i	0.270341	+	0.468244i
$732$	−11089.3			−0.559937
$733$	−11838.8	+	20505.4i	−0.596557	+	1.03327i	0.396768	+	0.917919i	$0.370132\pi$
$733$	−11838.8	+	20505.4i	−0.596557	+	1.03327i	−0.993325	+	0.115348i	$0.963202\pi$
$734$	−9831.90			−0.494417
$735$	6207.10	+	10751.0i	0.311500	+	0.539534i
$736$	47894.0			2.39864
$737$	−2782.85	−	21607.0i	−0.139088	−	1.07992i
$738$	15994.3			0.797777
$739$	−10163.7	−	17604.0i	−0.505922	−	0.876282i	−0.999977	−	0.00685137i	$-0.997819\pi$
$739$	−10163.7	−	17604.0i	−0.505922	−	0.876282i	0.494055	−	0.869431i	$-0.335514\pi$
$740$	−55099.5			−2.73716
$741$	−4550.60	+	7881.87i	−0.225601	+	0.390753i
$742$	−24291.4			−1.20184
$743$	−8208.88	−	14218.2i	−0.405322	−	0.702039i	0.589037	−	0.808106i	$-0.299507\pi$
$743$	−8208.88	−	14218.2i	−0.405322	−	0.702039i	−0.994359	+	0.106067i	$0.966174\pi$
$744$	−2189.79	+	3792.82i	−0.107905	+	0.186897i
$745$	−40045.4			−1.96933
$746$	34331.1			1.68492
$747$	15.6322	+	27.0757i	0.000765664	+	0.00132617i
$748$	−11443.2	+	19820.2i	−0.559366	+	0.968850i
$749$	−2083.02	+	3607.90i	−0.101618	+	0.176008i
$750$	5561.71	+	9633.17i	0.270780	+	0.469005i
$751$	17987.3			0.873990			0.436995	−	0.899464i	$-0.356043\pi$
$751$	17987.3			0.873990			0.436995	+	0.899464i	$0.356043\pi$
$752$	−23058.4			−1.11816
$753$	−6722.96	−	11644.5i	−0.325363	−	0.563545i
$754$	−13337.5	−	23101.3i	−0.644196	−	1.11578i
$755$	−9243.91	−	16010.9i	−0.445590	−	0.771785i
$756$	−3482.95	−	6032.64i	−0.167558	−	0.290218i
$757$	−12847.9	+	22253.2i	−0.616862	+	1.06844i	0.373193	+	0.927754i	$0.378263\pi$
$757$	−12847.9	+	22253.2i	−0.616862	+	1.06844i	−0.990055	+	0.140682i	$0.955071\pi$
$758$	−10348.4	+	17923.9i	−0.495871	+	0.858874i
$759$	22561.9			1.07898
$760$	4705.14	+	8149.54i	0.224570	+	0.388967i
$761$	−29534.6			−1.40687			−0.703435	−	0.710759i	$-0.748352\pi$
$761$	−29534.6			−1.40687			−0.703435	+	0.710759i	$0.748352\pi$
$762$	447.558			0.0212773
$763$	2324.65	−	4026.41i	0.110299	−	0.191043i
$764$	28900.0			1.36854
$765$	3486.05	+	6038.01i	0.164756	+	0.285366i
$766$	10254.0	−	17760.5i	0.483672	−	0.837744i
$767$	822.154	+	1424.01i	0.0387044	+	0.0670379i
$768$	1664.56	−	2883.09i	0.0782089	−	0.135462i
$769$	15980.2	−	27678.5i	0.749363	−	1.29794i	−0.198765	−	0.980047i	$-0.563693\pi$
$769$	15980.2	−	27678.5i	0.749363	−	1.29794i	0.948128	−	0.317888i	$-0.102974\pi$
$770$	29353.5	−	50841.8i	1.37380	−	2.37949i
$771$	−5637.59	+	9764.59i	−0.263337	+	0.456113i
$772$	−9535.53	+	16516.0i	−0.444548	+	0.769980i
$773$	5153.26	−	8925.70i	0.239780	−	0.415311i	−0.720871	−	0.693069i	$-0.756258\pi$
$773$	5153.26	−	8925.70i	0.239780	−	0.415311i	0.960651	+	0.277758i	$0.0895914\pi$
$774$	3608.68	+	6250.42i	0.167586	+	0.290267i
$775$	−4881.45	+	8454.92i	−0.226254	+	0.391884i
$776$	5639.51	+	9767.92i	0.260885	+	0.451866i
$777$	−30341.3			−1.40089
$778$	10299.9	−	17840.0i	0.474640	−	0.822101i
$779$	−31423.6			−1.44527
$780$	16733.0			0.768123
$781$	2559.55	+	4433.27i	0.117270	+	0.203117i
$782$	45785.7			2.09372
$783$	2098.91	−	3635.42i	0.0957969	−	0.165925i
$784$	6397.05	−	11080.0i	0.291411	−	0.504738i
$785$	12638.7	+	21890.8i	0.574641	+	0.995307i
$786$	−3971.26	−	6878.42i	−0.180216	−	0.312144i
$787$	−10274.0	−	17795.0i	−0.465345	−	0.806002i	0.533872	−	0.845566i	$-0.320737\pi$
$787$	−10274.0	−	17795.0i	−0.465345	−	0.806002i	−0.999217	+	0.0395636i	$0.987403\pi$
$788$	2712.18	+	4697.63i	0.122611	+	0.212368i
$789$	14294.0			0.644969
$790$	6337.57			0.285419
$791$	13548.9	+	23467.3i	0.609029	+	1.05487i
$792$	−1636.44	+	2834.39i	−0.0734194	+	0.127166i
$793$	7334.28	−	12703.4i	0.328434	−	0.568864i
$794$	28131.6	+	48725.3i	1.25737	+	2.17783i
$795$	9182.63			0.409653
$796$	−23409.9			−1.04239
$797$	−9151.05	+	15850.1i	−0.406709	+	0.704440i	−0.994519	−	0.104559i	$-0.966657\pi$
$797$	−9151.05	+	15850.1i	−0.406709	+	0.704440i	0.587810	+	0.808999i	$0.299990\pi$
$798$	12236.8	+	21194.8i	0.542831	+	0.940211i
$799$	−31024.9			−1.37369
$800$	−7743.76	+	13412.6i	−0.342229	+	0.592759i
$801$	8112.97			0.357875
$802$	6972.64	+	12077.0i	0.306998	+	0.531736i
$803$	−38879.5			−1.70863
$804$	−2132.91	−	16560.7i	−0.0935597	−	0.726430i
$805$	−65676.3			−2.87551
$806$	−13680.3	−	23694.9i	−0.597849	−	1.03551i
$807$	24532.8			1.07013
$808$	5942.54	−	10292.8i	0.258735	−	0.448142i
$809$	28427.3			1.23542			0.617708	−	0.786408i	$-0.288061\pi$
$809$	28427.3			1.23542			0.617708	+	0.786408i	$0.288061\pi$
$810$	2354.47	+	4078.07i	0.102133	+	0.176900i
$811$	8621.78	−	14933.4i	0.373306	−	0.646586i	−0.616766	−	0.787147i	$-0.711557\pi$
$811$	8621.78	−	14933.4i	0.373306	−	0.646586i	0.990072	+	0.140561i	$0.0448907\pi$
$812$	−40111.9			−1.73356
$813$	6186.75			0.266887
$814$	33664.0	+	58307.8i	1.44954	+	2.51067i
$815$	12164.8	−	21070.1i	0.522841	−	0.905588i
$816$	3592.72	−	6222.78i	0.154130	−	0.266962i
$817$	−7089.87	−	12280.0i	−0.303602	−	0.525855i
$818$	−59562.1			−2.54589
$819$	9214.23			0.393127
$820$	28886.9	+	50033.5i	1.23021	+	2.13079i
$821$	1982.41	+	3433.63i	0.0842711	+	0.145962i	0.905080	−	0.425241i	$-0.139811\pi$
$821$	1982.41	+	3433.63i	0.0842711	+	0.145962i	−0.820809	+	0.571202i	$0.806477\pi$
$822$	15316.7	+	26529.4i	0.649918	+	1.12569i
$823$	20747.2	+	35935.2i	0.878737	+	1.52202i	0.852727	+	0.522356i	$0.174947\pi$
$823$	20747.2	+	35935.2i	0.878737	+	1.52202i	0.0260099	+	0.999662i	$0.491720\pi$
$824$	9355.50	−	16204.2i	0.395527	−	0.685073i
$825$	−3647.92	+	6318.39i	−0.153945	+	0.266640i
$826$	4421.64			0.186257
$827$	4932.64	+	8543.58i	0.207406	+	0.359237i	0.950897	−	0.309509i	$-0.100165\pi$
$827$	4932.64	+	8543.58i	0.207406	+	0.359237i	−0.743491	+	0.668746i	$0.766831\pi$
$828$	17292.5			0.725792
$829$	26216.0			1.09833			0.549167	−	0.835712i	$-0.314945\pi$
$829$	26216.0			1.09833			0.549167	+	0.835712i	$0.314945\pi$
$830$	−100.975	+	174.894i	−0.00422278	+	0.00731407i
$831$	−6372.92			−0.266034
$832$	−14905.1	−	25816.3i	−0.621081	−	1.07574i
$833$	8607.16	−	14908.0i	0.358008	−	0.620088i
$834$	6537.38	+	11323.1i	0.271428	+	0.470127i
$835$	2365.22	−	4096.68i	0.0980262	−	0.169786i
$836$	15184.4	−	26300.2i	0.628188	−	1.08805i
$837$	2152.85	−	3728.84i	0.0889048	−	0.153988i
$838$	−22447.9	+	38880.8i	−0.925356	+	1.60276i
$839$	−8897.73	+	15411.3i	−0.366131	+	0.634157i	−0.988957	−	0.148203i	$-0.952651\pi$
$839$	−8897.73	+	15411.3i	−0.366131	+	0.634157i	0.622826	+	0.782360i	$0.285984\pi$
$840$	4763.57	−	8250.75i	0.195665	−	0.338902i
$841$	108.279	+	187.544i	0.00443966	+	0.00768971i
$842$	27422.8	−	47497.7i	1.12239	−	1.94404i
$843$	12933.7	+	22401.8i	0.528422	+	0.915253i
$844$	38549.6			1.57219
$845$	3923.57	−	6795.82i	0.159734	−	0.276667i
$846$	−20954.2			−0.851560
$847$	−6279.32			−0.254734
$848$	−4731.82	−	8195.75i	−0.191617	−	0.331890i
$849$	−1694.22			−0.0684869
$850$	−7402.88	+	12822.2i	−0.298725	+	0.517408i
$851$	37660.4	−	65229.8i	1.51702	−	2.62755i
$852$	1961.76	+	3397.87i	0.0788837	+	0.136631i
$853$	−2964.71	−	5135.03i	−0.119003	−	0.206120i	0.800370	−	0.599507i	$-0.204637\pi$
$853$	−2964.71	−	5135.03i	−0.119003	−	0.206120i	−0.919373	+	0.393387i	$0.871303\pi$
$854$	−19722.3	−	34160.1i	−0.790263	−	1.36877i
$855$	−4625.77	−	8012.06i	−0.185027	−	0.320476i
$856$	1500.23			0.0599029
$857$	34146.8			1.36106			0.680532	−	0.732719i	$-0.261749\pi$
$857$	34146.8			1.36106			0.680532	+	0.732719i	$0.261749\pi$
$858$	−10223.3	−	17707.3i	−0.406781	−	0.704565i
$859$	−10410.8	+	18032.0i	−0.413518	+	0.716235i	−0.995272	−	0.0971307i	$-0.969034\pi$
$859$	−10410.8	+	18032.0i	−0.413518	+	0.716235i	0.581753	+	0.813365i	$0.302367\pi$
$860$	−13035.0	+	22577.4i	−0.516850	+	0.895211i
$861$	15906.9	+	27551.6i	0.629625	+	1.09054i
$862$	−18766.8			−0.741530
$863$	38141.4			1.50446			0.752229	−	0.658902i	$-0.228979\pi$
$863$	38141.4			1.50446			0.752229	+	0.658902i	$0.228979\pi$
$864$	3415.20	−	5915.30i	0.134476	−	0.232920i
$865$	25.5314	+	44.2216i	0.00100358	+	0.00173824i
$866$	−40769.9			−1.59979
$867$	−2535.53	+	4391.67i	−0.0993208	+	0.172029i
$868$	−41142.7			−1.60884
$869$	−2165.26	−	3750.33i	−0.0845239	−	0.146400i
$870$	27115.7			1.05667
$871$	20381.7	+	8509.57i	0.792890	+	0.331040i
$872$	−1674.26			−0.0650200
$873$	−5544.38	−	9603.15i	−0.214947	−	0.372299i
$874$	−60754.7			−2.35133
$875$	−11062.6	+	19161.1i	−0.427412	+	0.740300i
$876$	−29799.1			−1.14934
$877$	−23902.7	−	41400.7i	−0.920339	−	1.59407i	−0.798891	−	0.601476i	$-0.794580\pi$
$877$	−23902.7	−	41400.7i	−0.920339	−	1.59407i	−0.121448	−	0.992598i	$-0.538754\pi$
$878$	−15898.4	+	27536.9i	−0.611099	+	1.05846i
$879$	−26044.5			−0.999385
$880$	22871.5			0.876136
$881$	2689.77	+	4658.82i	0.102861	+	0.178161i	0.912862	−	0.408267i	$-0.133867\pi$
$881$	2689.77	+	4658.82i	0.102861	+	0.178161i	−0.810001	+	0.586428i	$0.800534\pi$
$882$	5813.27	−	10068.9i	0.221931	−	0.384396i
$883$	5692.75	−	9860.13i	0.216961	−	0.375787i	−0.736917	−	0.675984i	$-0.763719\pi$
$883$	5692.75	−	9860.13i	0.216961	−	0.375787i	0.953877	+	0.300197i	$0.0970523\pi$
$884$	−11601.5	−	20094.4i	−0.441403	−	0.764532i
$885$	−1671.47			−0.0634868
$886$	64210.8			2.43477
$887$	15726.8	+	27239.6i	0.595327	+	1.03114i	0.993501	+	0.113826i	$0.0363106\pi$
$887$	15726.8	+	27239.6i	0.595327	+	1.03114i	−0.398174	+	0.917310i	$0.630356\pi$
$888$	5463.10	+	9462.37i	0.206452	+	0.357586i
$889$	445.112	+	770.957i	0.0167926	+	0.0290856i
$890$	26202.7	+	45384.4i	0.986873	+	1.70931i
$891$	1608.83	−	2786.57i	0.0604914	−	0.104774i
$892$	−11426.4	+	19791.0i	−0.428905	+	0.742885i
$893$	41168.1			1.54271
$894$	18752.3	+	32480.0i	0.701534	+	1.21509i
$895$	−7330.17			−0.273766
$896$	−28713.1			−1.07058
$897$	−11436.9	+	19809.4i	−0.425717	+	0.737364i
$898$	−50738.2			−1.88547
$899$	−12396.8	−	21471.9i	−0.459907	−	0.796583i
$900$	−2795.95	+	4842.72i	−0.103554	+	0.179360i
$901$	−6366.61	−	11027.3i	−0.235408	−	0.407738i
$902$	35297.9	−	61137.7i	1.30298	−	2.25683i
$903$	−7177.92	+	12432.5i	−0.264525	+	0.458171i
$904$	4879.08	−	8450.81i	0.179509	−	0.310918i
$905$	10108.2	−	17507.9i	0.371280	−	0.643075i
$906$	−8657.40	+	14995.1i	−0.317465	+	0.549865i
$907$	9313.15	−	16130.8i	0.340946	−	0.590536i	−0.643663	−	0.765309i	$-0.722586\pi$
$907$	9313.15	−	16130.8i	0.340946	−	0.590536i	0.984609	+	0.174774i	$0.0559193\pi$
$908$	8636.11	+	14958.2i	0.315638	+	0.546701i
$909$	−5842.29	+	10119.1i	−0.213176	+	0.369231i
$910$	29759.5	+	51544.9i	1.08408	+	1.87769i
$911$	41702.8			1.51666			0.758330	−	0.651871i	$-0.226016\pi$
$911$	41702.8			1.51666			0.758330	+	0.651871i	$0.226016\pi$
$912$	−4767.32	+	8257.24i	−0.173094	+	0.299808i
$913$	137.994			0.00500214
$914$	21083.7			0.763005
$915$	7455.43	+	12913.2i	0.269365	+	0.466554i
$916$	−43508.5			−1.56939
$917$	7899.12	−	13681.7i	0.284462	−	0.492703i
$918$	3264.86	−	5654.91i	0.117382	−	0.203311i
$919$	−11538.1	−	19984.6i	−0.414154	−	0.717335i	0.581185	−	0.813771i	$-0.302589\pi$
$919$	−11538.1	−	19984.6i	−0.414154	−	0.717335i	−0.995339	+	0.0964357i	$0.969256\pi$
$920$	11825.3	+	20482.1i	0.423772	+	0.733995i
$921$	2587.86	+	4482.31i	0.0925874	+	0.160366i
$922$	192.312	+	333.094i	0.00686925	+	0.0118979i
$923$	−5189.89			−0.185078
$924$	−30746.1			−1.09467
$925$	12178.3	+	21093.4i	0.432886	+	0.749781i
$926$	21680.1	−	37551.0i	0.769386	−	1.33262i
$927$	−9197.68	+	15930.9i	−0.325881	+	0.564442i
$928$	−19665.9	−	34062.3i	−0.695650	−	1.20490i
$929$	30993.3			1.09457			0.547286	−	0.836945i	$-0.315661\pi$
$929$	30993.3			1.09457			0.547286	+	0.836945i	$0.315661\pi$
$930$	27812.5			0.980653
$931$	−11421.2	+	19782.0i	−0.402056	+	0.696381i
$932$	−1321.32	−	2288.60i	−0.0464392	−	0.0804351i
$933$	24766.9			0.869060
$934$	4594.85	−	7958.52i	0.160972	−	0.278812i
$935$	30773.4			1.07636
$936$	−1659.07	−	2873.59i	−0.0579362	−	0.100348i
$937$	23324.7			0.813218			0.406609	−	0.913602i	$-0.366711\pi$
$937$	23324.7			0.813218			0.406609	+	0.913602i	$0.366711\pi$
$938$	47220.8	−	36023.4i	1.64373	−	1.25395i
$939$	−5305.89			−0.184399
$940$	−37844.7	−	65548.9i	−1.31315	−	2.27444i
$941$	−56908.0			−1.97147			−0.985733	−	0.168319i	$-0.946166\pi$
$941$	−56908.0			−1.97147			−0.985733	+	0.168319i	$0.946166\pi$
$942$	11836.8	−	20501.9i	0.409408	−	0.709115i
$943$	−78976.5			−2.72728
$944$	861.309	+	1491.83i	0.0296962	+	0.0514353i
$945$	−4683.22	+	8111.57i	−0.161212	+	0.279227i
$946$	31856.0			1.09485
$947$	−20805.7			−0.713933			−0.356966	−	0.934117i	$-0.616189\pi$
$947$	−20805.7			−0.713933			−0.356966	+	0.934117i	$0.616189\pi$
$948$	−1659.56	−	2874.44i	−0.0568565	−	0.0984783i
$949$	19708.6	−	34136.3i	0.674149	−	1.16766i
$950$	9823.16	−	17014.2i	0.335479	−	0.581067i
$951$	−5011.80	−	8680.69i	−0.170892	−	0.295994i
$952$	−13210.9			−0.449757
$953$	35533.3			1.20780			0.603902	−	0.797059i	$-0.293612\pi$
$953$	35533.3			1.20780			0.603902	+	0.797059i	$0.293612\pi$
$954$	−4300.00	−	7447.83i	−0.145931	−	0.252759i
$955$	−19429.6	−	33653.1i	−0.658354	−	1.14030i
$956$	−3238.07	−	5608.50i	−0.109547	−	0.189740i
$957$	−9264.17	−	16046.0i	−0.312924	−	0.542000i
$958$	−23822.3	+	41261.4i	−0.803407	+	1.39154i
$959$	−30466.1	+	52768.8i	−1.02586	+	1.77684i
$960$	30302.5			1.01876
$961$	2180.13	+	3776.09i	0.0731808	+	0.126753i
$962$	−68259.3			−2.28770
$963$	−1474.92			−0.0493549
$964$	−26471.0	+	45849.2i	−0.884413	+	1.53185i
$965$	25643.2			0.855423
$966$	30754.6	+	53268.6i	1.02434	+	1.77421i
$967$	23727.9	−	41097.9i	0.789077	−	1.36672i	−0.137455	−	0.990508i	$-0.543892\pi$
$967$	23727.9	−	41097.9i	0.789077	−	1.36672i	0.926533	−	0.376214i	$-0.122774\pi$
$968$	1130.62	+	1958.30i	0.0375409	+	0.0650227i
$969$	−6414.38	+	11110.0i	−0.212652	+	0.368324i
$970$	35813.7	−	62031.2i	1.18547	−	2.05330i
$971$	3464.04	−	5999.89i	0.114486	−	0.198296i	−0.803088	−	0.595860i	$-0.796811\pi$
$971$	3464.04	−	5999.89i	0.114486	−	0.198296i	0.917574	+	0.397564i	$0.130144\pi$
$972$	1233.09	−	2135.77i	0.0406906	−	0.0704781i
$973$	−13003.3	+	22522.4i	−0.428435	+	0.742071i
$974$	−10186.1	+	17642.8i	−0.335096	+	0.580403i
$975$	−3698.38	−	6405.78i	−0.121480	−	0.210409i
$976$	7683.58	−	13308.3i	0.251993	−	0.436465i
$977$	4160.06	+	7205.44i	0.136225	+	0.235949i	0.926065	−	0.377364i	$-0.123170\pi$
$977$	4160.06	+	7205.44i	0.136225	+	0.235949i	−0.789839	+	0.613314i	$0.789836\pi$
$978$	−22786.0			−0.745006
$979$	17904.5	−	31011.5i	0.584505	−	1.01239i
$980$	41996.6			1.36891
$981$	1646.01			0.0535710
$982$	−815.993	−	1413.34i	−0.0265167	−	0.0459283i
$983$	21197.7			0.687795			0.343898	−	0.939007i	$-0.388253\pi$
$983$	21197.7			0.687795			0.343898	+	0.939007i	$0.388253\pi$
$984$	5728.25	−	9921.61i	0.185579	−	0.321432i
$985$	3646.83	−	6316.50i	0.117967	−	0.204325i
$986$	−18800.1	−	32562.8i	−0.607220	−	1.05174i
$987$	−20839.7	−	36095.4i	−0.672072	−	1.16406i
$988$	15394.5	+	26664.0i	0.495711	+	0.858597i
$989$	−17818.9	−	30863.2i	−0.572909	−	0.992307i
$990$	20784.3			0.667242
$991$	−34492.2			−1.10563			−0.552816	−	0.833303i	$-0.686447\pi$
$991$	−34492.2			−1.10563			−0.552816	+	0.833303i	$0.686447\pi$
$992$	−20171.2	−	34937.6i	−0.645602	−	1.11821i
$993$	5298.24	−	9176.83i	0.169320	−	0.293271i
$994$	−6977.97	+	12086.2i	−0.222664	+	0.385665i
$995$	15738.6	+	27260.1i	0.501454	+	0.868544i
$996$	105.766			0.00336477
$997$	7669.07			0.243613			0.121806	−	0.992554i	$-0.461131\pi$
$997$	7669.07			0.243613			0.121806	+	0.992554i	$0.461131\pi$
$998$	−15914.8	+	27565.2i	−0.504783	+	0.874309i
$999$	−5370.94	−	9302.74i	−0.170099	−	0.294620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.e.b.37.15	✓	36
67.29	even	3	inner	201.4.e.b.163.15	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.e.b.37.15	✓	36	1.1	even	1	trivial
201.4.e.b.163.15	yes	36	67.29	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.13007 + 3.68940i) q^{2} -3.00000 q^{3} +(-5.07443 + 8.78916i) q^{4} +13.6463 q^{5} +(-6.39022 - 11.0682i) q^{6} +(12.7106 - 22.0154i) q^{7} -9.15443 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+(2.13007 + 3.68940i) q^{2} -3.00000 q^{3} +(-5.07443 + 8.78916i) q^{4} +13.6463 q^{5} +(-6.39022 - 11.0682i) q^{6} +(12.7106 - 22.0154i) q^{7} -9.15443 q^{8} +9.00000 q^{9} +(29.0676 + 50.3465i) q^{10} +(19.8621 - 34.4022i) q^{11} +(15.2233 - 26.3675i) q^{12} +(20.1368 + 34.8779i) q^{13} +108.298 q^{14} -40.9388 q^{15} +(21.0958 + 36.5390i) q^{16} +(28.3842 + 49.1628i) q^{17} +(19.1707 + 33.2046i) q^{18} +(-37.6641 - 65.2361i) q^{19} +(-69.2470 + 119.939i) q^{20} +(-38.1318 + 66.0462i) q^{21} +169.231 q^{22} +(-94.6604 - 163.957i) q^{23} +27.4633 q^{24} +61.2209 q^{25} +(-85.7857 + 148.585i) q^{26} -27.0000 q^{27} +(128.998 + 223.431i) q^{28} +(-77.7374 + 134.645i) q^{29} +(-87.2027 - 151.040i) q^{30} +(-79.7351 + 138.105i) q^{31} +(-126.489 + 219.085i) q^{32} +(-59.5863 + 103.206i) q^{33} +(-120.921 + 209.441i) q^{34} +(173.452 - 300.428i) q^{35} +(-45.6698 + 79.1025i) q^{36} +(198.924 + 344.546i) q^{37} +(160.454 - 277.915i) q^{38} +(-60.4104 - 104.634i) q^{39} -124.924 q^{40} +(208.578 - 361.268i) q^{41} -324.894 q^{42} +188.240 q^{43} +(201.577 + 349.142i) q^{44} +122.816 q^{45} +(403.267 - 698.480i) q^{46} +(-273.259 + 473.298i) q^{47} +(-63.2874 - 109.617i) q^{48} +(-151.619 - 262.612i) q^{49} +(130.405 + 225.868i) q^{50} +(-85.1525 - 147.489i) q^{51} -408.731 q^{52} -224.301 q^{53} +(-57.5120 - 99.6137i) q^{54} +(271.044 - 469.461i) q^{55} +(-116.358 + 201.539i) q^{56} +(112.992 + 195.708i) q^{57} -662.346 q^{58} +40.8284 q^{59} +(207.741 - 359.818i) q^{60} +(-182.112 - 315.426i) q^{61} -679.366 q^{62} +(114.395 - 198.139i) q^{63} -740.190 q^{64} +(274.792 + 475.954i) q^{65} -507.693 q^{66} +(436.027 - 332.632i) q^{67} -576.134 q^{68} +(283.981 + 491.870i) q^{69} +1477.87 q^{70} +(-64.4330 + 111.601i) q^{71} -82.3899 q^{72} +(-489.368 - 847.609i) q^{73} +(-847.445 + 1467.82i) q^{74} -183.663 q^{75} +764.494 q^{76} +(-504.918 - 874.544i) q^{77} +(257.357 - 445.756i) q^{78} +(54.5072 - 94.4093i) q^{79} +(287.879 + 498.621i) q^{80} +81.0000 q^{81} +1777.15 q^{82} +(1.73691 + 3.00841i) q^{83} +(-386.994 - 670.294i) q^{84} +(387.338 + 670.890i) q^{85} +(400.964 + 694.491i) q^{86} +(233.212 - 403.936i) q^{87} +(-181.826 + 314.932i) q^{88} +901.441 q^{89} +(261.608 + 453.119i) q^{90} +1023.80 q^{91} +1921.39 q^{92} +(239.205 - 414.316i) q^{93} -2328.24 q^{94} +(-513.974 - 890.229i) q^{95} +(379.467 - 657.256i) q^{96} +(-616.042 - 1067.02i) q^{97} +(645.919 - 1118.76i) q^{98} +(178.759 - 309.619i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} - 108 q^{3} - 90 q^{4} - 4 q^{5} - 6 q^{6} + 22 q^{7} + 48 q^{8} + 324 q^{9}+O(q^{10}) \) 36 * q + 2 * q^2 - 108 * q^3 - 90 * q^4 - 4 * q^5 - 6 * q^6 + 22 * q^7 + 48 * q^8 + 324 * q^9	\( 36 q + 2 q^{2} - 108 q^{3} - 90 q^{4} - 4 q^{5} - 6 q^{6} + 22 q^{7} + 48 q^{8} + 324 q^{9} + 14 q^{10} - 16 q^{11} + 270 q^{12} - 46 q^{13} + 14 q^{14} + 12 q^{15} - 346 q^{16} - 8 q^{17} + 18 q^{18} - 154 q^{19} - 180 q^{20} - 66 q^{21} + 214 q^{22} - 104 q^{23} - 144 q^{24} + 1032 q^{25} - 333 q^{26} - 972 q^{27} - 473 q^{28} + 76 q^{29} - 42 q^{30} + 498 q^{31} - 285 q^{32} + 48 q^{33} + 26 q^{34} - 392 q^{35} - 810 q^{36} - 124 q^{37} + 20 q^{38} + 138 q^{39} + 638 q^{40} - 508 q^{41} - 42 q^{42} - 1400 q^{43} - 333 q^{44} - 36 q^{45} - 1372 q^{46} + 18 q^{47} + 1038 q^{48} - 238 q^{49} - 337 q^{50} + 24 q^{51} + 3640 q^{52} + 724 q^{53} - 54 q^{54} - 178 q^{55} - 829 q^{56} + 462 q^{57} - 1472 q^{58} + 720 q^{59} + 540 q^{60} + 232 q^{61} - 3882 q^{62} + 198 q^{63} + 3628 q^{64} - 1428 q^{65} - 642 q^{66} - 1164 q^{67} + 1634 q^{68} + 312 q^{69} + 2550 q^{70} + 406 q^{71} + 432 q^{72} - 2120 q^{73} + 1375 q^{74} - 3096 q^{75} + 4190 q^{76} - 800 q^{77} + 999 q^{78} + 1306 q^{79} - 1927 q^{80} + 2916 q^{81} - 794 q^{82} - 1010 q^{83} + 1419 q^{84} + 472 q^{85} + 737 q^{86} - 228 q^{87} - 1838 q^{88} + 1904 q^{89} + 126 q^{90} + 7340 q^{91} + 7368 q^{92} - 1494 q^{93} - 9862 q^{94} + 1678 q^{95} + 855 q^{96} - 2358 q^{97} - 2610 q^{98} - 144 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 - 108 * q^3 - 90 * q^4 - 4 * q^5 - 6 * q^6 + 22 * q^7 + 48 * q^8 + 324 * q^9 + 14 * q^10 - 16 * q^11 + 270 * q^12 - 46 * q^13 + 14 * q^14 + 12 * q^15 - 346 * q^16 - 8 * q^17 + 18 * q^18 - 154 * q^19 - 180 * q^20 - 66 * q^21 + 214 * q^22 - 104 * q^23 - 144 * q^24 + 1032 * q^25 - 333 * q^26 - 972 * q^27 - 473 * q^28 + 76 * q^29 - 42 * q^30 + 498 * q^31 - 285 * q^32 + 48 * q^33 + 26 * q^34 - 392 * q^35 - 810 * q^36 - 124 * q^37 + 20 * q^38 + 138 * q^39 + 638 * q^40 - 508 * q^41 - 42 * q^42 - 1400 * q^43 - 333 * q^44 - 36 * q^45 - 1372 * q^46 + 18 * q^47 + 1038 * q^48 - 238 * q^49 - 337 * q^50 + 24 * q^51 + 3640 * q^52 + 724 * q^53 - 54 * q^54 - 178 * q^55 - 829 * q^56 + 462 * q^57 - 1472 * q^58 + 720 * q^59 + 540 * q^60 + 232 * q^61 - 3882 * q^62 + 198 * q^63 + 3628 * q^64 - 1428 * q^65 - 642 * q^66 - 1164 * q^67 + 1634 * q^68 + 312 * q^69 + 2550 * q^70 + 406 * q^71 + 432 * q^72 - 2120 * q^73 + 1375 * q^74 - 3096 * q^75 + 4190 * q^76 - 800 * q^77 + 999 * q^78 + 1306 * q^79 - 1927 * q^80 + 2916 * q^81 - 794 * q^82 - 1010 * q^83 + 1419 * q^84 + 472 * q^85 + 737 * q^86 - 228 * q^87 - 1838 * q^88 + 1904 * q^89 + 126 * q^90 + 7340 * q^91 + 7368 * q^92 - 1494 * q^93 - 9862 * q^94 + 1678 * q^95 + 855 * q^96 - 2358 * q^97 - 2610 * q^98 - 144 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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