LMFDB - Embedded newform 201.4.e.b.37.2

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			37.2
Character	$\chi$	$=$	201.37
Dual form			201.4.e.b.163.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.52313 - 4.37020i) q^{2} -3.00000 q^{3} +(-8.73242 + 15.1250i) q^{4} +0.340792 q^{5} +(7.56940 + 13.1106i) q^{6} +(12.2513 - 21.2198i) q^{7} +47.7621 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+(-2.52313 - 4.37020i) q^{2} -3.00000 q^{3} +(-8.73242 + 15.1250i) q^{4} +0.340792 q^{5} +(7.56940 + 13.1106i) q^{6} +(12.2513 - 21.2198i) q^{7} +47.7621 q^{8} +9.00000 q^{9} +(-0.859864 - 1.48933i) q^{10} +(30.8399 - 53.4163i) q^{11} +(26.1973 - 45.3750i) q^{12} +(-17.8101 - 30.8480i) q^{13} -123.646 q^{14} -1.02238 q^{15} +(-50.6509 - 87.7300i) q^{16} +(66.3875 + 114.987i) q^{17} +(-22.7082 - 39.3318i) q^{18} +(-48.3880 - 83.8105i) q^{19} +(-2.97594 + 5.15448i) q^{20} +(-36.7538 + 63.6594i) q^{21} -311.253 q^{22} +(13.0492 + 22.6018i) q^{23} -143.286 q^{24} -124.884 q^{25} +(-89.8745 + 155.667i) q^{26} -27.0000 q^{27} +(213.966 + 370.601i) q^{28} +(94.5511 - 163.767i) q^{29} +(2.57959 + 4.46798i) q^{30} +(59.8561 - 103.674i) q^{31} +(-64.5498 + 111.804i) q^{32} +(-92.5197 + 160.249i) q^{33} +(335.009 - 580.253i) q^{34} +(4.17513 - 7.23154i) q^{35} +(-78.5918 + 136.125i) q^{36} +(-4.14163 - 7.17352i) q^{37} +(-244.179 + 422.930i) q^{38} +(53.4303 + 92.5439i) q^{39} +16.2769 q^{40} +(-218.339 + 378.174i) q^{41} +370.939 q^{42} -333.318 q^{43} +(538.614 + 932.907i) q^{44} +3.06713 q^{45} +(65.8496 - 114.055i) q^{46} +(106.274 - 184.072i) q^{47} +(151.953 + 263.190i) q^{48} +(-128.687 - 222.892i) q^{49} +(315.099 + 545.767i) q^{50} +(-199.163 - 344.960i) q^{51} +622.101 q^{52} -394.607 q^{53} +(68.1246 + 117.995i) q^{54} +(10.5100 - 18.2038i) q^{55} +(585.147 - 1013.50i) q^{56} +(145.164 + 251.431i) q^{57} -954.260 q^{58} -216.789 q^{59} +(8.92781 - 15.4634i) q^{60} +(316.175 + 547.631i) q^{61} -604.100 q^{62} +(110.261 - 190.978i) q^{63} -158.944 q^{64} +(-6.06954 - 10.5127i) q^{65} +933.759 q^{66} +(-117.250 - 535.738i) q^{67} -2318.90 q^{68} +(-39.1475 - 67.8055i) q^{69} -42.1377 q^{70} +(105.665 - 183.018i) q^{71} +429.859 q^{72} +(-498.365 - 863.193i) q^{73} +(-20.8998 + 36.1995i) q^{74} +374.652 q^{75} +1690.18 q^{76} +(-755.656 - 1308.83i) q^{77} +(269.624 - 467.002i) q^{78} +(-552.021 + 956.128i) q^{79} +(-17.2614 - 29.8977i) q^{80} +81.0000 q^{81} +2203.60 q^{82} +(-394.490 - 683.277i) q^{83} +(-641.899 - 1111.80i) q^{84} +(22.6243 + 39.1865i) q^{85} +(841.005 + 1456.66i) q^{86} +(-283.653 + 491.302i) q^{87} +(1472.98 - 2551.28i) q^{88} +334.823 q^{89} +(-7.73878 - 13.4040i) q^{90} -872.785 q^{91} -455.803 q^{92} +(-179.568 + 311.021i) q^{93} -1072.57 q^{94} +(-16.4902 - 28.5619i) q^{95} +(193.649 - 335.411i) q^{96} +(211.758 + 366.776i) q^{97} +(-649.389 + 1124.78i) q^{98} +(277.559 - 480.747i) 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 $

$2$	−2.52313	−	4.37020i	−0.892063	−	1.54510i	−0.837398	−	0.546593i	$-0.815924\pi$
$2$	−2.52313	−	4.37020i	−0.892063	−	1.54510i	−0.0546648	−	0.998505i	$-0.517409\pi$
$3$	−3.00000			−0.577350
$3$	−3.00000			−0.577350
$4$	−8.73242	+	15.1250i	−1.09155	+	1.89062i
$5$	0.340792			0.0304814			0.0152407	−	0.999884i	$-0.495149\pi$
$5$	0.340792			0.0304814			0.0152407	+	0.999884i	$0.495149\pi$
$6$	7.56940	+	13.1106i	0.515033	+	0.892063i
$7$	12.2513	−	21.2198i	0.661506	−	1.14576i	−0.318714	−	0.947851i	$-0.603251\pi$
$7$	12.2513	−	21.2198i	0.661506	−	1.14576i	0.980220	−	0.197911i	$-0.0634158\pi$
$8$	47.7621			2.11081
$9$	9.00000			0.333333
$10$	−0.859864	−	1.48933i	−0.0271913	−	0.0470967i
$11$	30.8399	−	53.4163i	0.845326	−	1.46415i	−0.0400127	−	0.999199i	$-0.512740\pi$
$11$	30.8399	−	53.4163i	0.845326	−	1.46415i	0.885338	−	0.464948i	$-0.153927\pi$
$12$	26.1973	−	45.3750i	0.630208	−	1.09155i
$13$	−17.8101	−	30.8480i	−0.379972	−	0.658130i	0.611086	−	0.791564i	$-0.290733\pi$
$13$	−17.8101	−	30.8480i	−0.379972	−	0.658130i	−0.991058	+	0.133434i	$0.957400\pi$
$14$	−123.646			−2.36042
$15$	−1.02238			−0.0175984
$16$	−50.6509	−	87.7300i	−0.791421	−	1.37078i
$17$	66.3875	+	114.987i	0.947138	+	1.64049i	0.751413	+	0.659832i	$0.229373\pi$
$17$	66.3875	+	114.987i	0.947138	+	1.64049i	0.195725	+	0.980659i	$0.437294\pi$
$18$	−22.7082	−	39.3318i	−0.297354	−	0.515033i
$19$	−48.3880	−	83.8105i	−0.584262	−	1.01197i	−0.994967	−	0.100203i	$-0.968051\pi$
$19$	−48.3880	−	83.8105i	−0.584262	−	1.01197i	0.410706	−	0.911768i	$-0.365282\pi$
$20$	−2.97594	+	5.15448i	−0.0332720	+	0.0576288i
$21$	−36.7538	+	63.6594i	−0.381921	+	0.661506i
$22$	−311.253			−3.01633
$23$	13.0492	+	22.6018i	0.118302	+	0.204905i	0.919095	−	0.394037i	$-0.128922\pi$
$23$	13.0492	+	22.6018i	0.118302	+	0.204905i	−0.800793	+	0.598941i	$0.795588\pi$
$24$	−143.286			−1.21868
$25$	−124.884			−0.999071
$26$	−89.8745	+	155.667i	−0.677917	+	1.17419i
$27$	−27.0000			−0.192450
$28$	213.966	+	370.601i	1.44414	+	2.50132i
$29$	94.5511	−	163.767i	0.605438	−	1.04865i	−0.386544	−	0.922271i	$-0.626331\pi$
$29$	94.5511	−	163.767i	0.605438	−	1.04865i	0.991982	−	0.126378i	$-0.0403353\pi$
$30$	2.57959	+	4.46798i	0.0156989	+	0.0271913i
$31$	59.8561	−	103.674i	0.346789	−	0.600657i	−0.638888	−	0.769300i	$-0.720605\pi$
$31$	59.8561	−	103.674i	0.346789	−	0.600657i	0.985677	+	0.168643i	$0.0539386\pi$
$32$	−64.5498	+	111.804i	−0.356591	+	0.617633i
$33$	−92.5197	+	160.249i	−0.488049	+	0.845326i
$34$	335.009	−	580.253i	1.68981	−	2.92684i
$35$	4.17513	−	7.23154i	0.0201636	−	0.0349244i
$36$	−78.5918	+	136.125i	−0.363851	+	0.630208i
$37$	−4.14163	−	7.17352i	−0.0184022	−	0.0318735i	0.856678	−	0.515852i	$-0.172525\pi$
$37$	−4.14163	−	7.17352i	−0.0184022	−	0.0318735i	−0.875080	+	0.483979i	$0.839191\pi$
$38$	−244.179	+	422.930i	−1.04240	+	1.80548i
$39$	53.4303	+	92.5439i	0.219377	+	0.379972i
$40$	16.2769			0.0643403
$41$	−218.339	+	378.174i	−0.831679	+	1.44051i	0.0650276	+	0.997883i	$0.479286\pi$
$41$	−218.339	+	378.174i	−0.831679	+	1.44051i	−0.896706	+	0.442626i	$0.854047\pi$
$42$	370.939			1.36279
$43$	−333.318			−1.18210			−0.591052	−	0.806634i	$-0.701287\pi$
$43$	−333.318			−1.18210			−0.591052	+	0.806634i	$0.701287\pi$
$44$	538.614	+	932.907i	1.84543	+	3.19639i
$45$	3.06713			0.0101605
$46$	65.8496	−	114.055i	0.211065	−	0.365576i
$47$	106.274	−	184.072i	0.329822	−	0.571269i	−0.652654	−	0.757656i	$-0.726345\pi$
$47$	106.274	−	184.072i	0.329822	−	0.571269i	0.982476	+	0.186387i	$0.0596779\pi$
$48$	151.953	+	263.190i	0.456927	+	0.791421i
$49$	−128.687	−	222.892i	−0.375181	−	0.649832i
$50$	315.099	+	545.767i	0.891234	+	1.54366i
$51$	−199.163	−	344.960i	−0.546830	−	0.947138i
$52$	622.101			1.65904
$53$	−394.607			−1.02271			−0.511353	−	0.859371i	$-0.670855\pi$
$53$	−394.607			−1.02271			−0.511353	+	0.859371i	$0.670855\pi$
$54$	68.1246	+	117.995i	0.171678	+	0.297354i
$55$	10.5100	−	18.2038i	0.0257667	−	0.0446292i
$56$	585.147	−	1013.50i	1.39631	−	2.41848i
$57$	145.164	+	251.431i	0.337324	+	0.584262i
$58$	−954.260			−2.16035
$59$	−216.789			−0.478365			−0.239183	−	0.970975i	$-0.576879\pi$
$59$	−216.789			−0.478365			−0.239183	+	0.970975i	$0.576879\pi$
$60$	8.92781	−	15.4634i	0.0192096	−	0.0332720i
$61$	316.175	+	547.631i	0.663640	+	1.14946i	0.979652	+	0.200704i	$0.0643228\pi$
$61$	316.175	+	547.631i	0.663640	+	1.14946i	−0.316012	+	0.948755i	$0.602344\pi$
$62$	−604.100			−1.23743
$63$	110.261	−	190.978i	0.220502	−	0.381921i
$64$	−158.944			−0.310437
$65$	−6.06954	−	10.5127i	−0.0115820	−	0.0200607i
$66$	933.759			1.74148
$67$	−117.250	−	535.738i	−0.213797	−	0.976878i
$67$	−117.250	−	535.738i	−0.213797	−	0.976878i
$68$	−2318.90			−4.13540
$69$	−39.1475	−	67.8055i	−0.0683015	−	0.118302i
$70$	−42.1377			−0.0719488
$71$	105.665	−	183.018i	0.176622	−	0.305919i	−0.764099	−	0.645099i	$-0.776816\pi$
$71$	105.665	−	183.018i	0.176622	−	0.305919i	0.940722	+	0.339180i	$0.110150\pi$
$72$	429.859			0.703603
$73$	−498.365	−	863.193i	−0.799030	−	1.38396i	−0.920248	−	0.391335i	$-0.872013\pi$
$73$	−498.365	−	863.193i	−0.799030	−	1.38396i	0.121218	−	0.992626i	$-0.461320\pi$
$74$	−20.8998	+	36.1995i	−0.0328318	+	0.0568663i
$75$	374.652			0.576814
$76$	1690.18			2.55101
$77$	−755.656	−	1308.83i	−1.11838	−	1.93708i
$78$	269.624	−	467.002i	0.391396	−	0.677917i
$79$	−552.021	+	956.128i	−0.786167	+	1.36168i	0.142132	+	0.989848i	$0.454604\pi$
$79$	−552.021	+	956.128i	−0.786167	+	1.36168i	−0.928299	+	0.371834i	$0.878729\pi$
$80$	−17.2614	−	29.8977i	−0.0241236	−	0.0417833i
$81$	81.0000			0.111111
$82$	2203.60			2.96764
$83$	−394.490	−	683.277i	−0.521698	−	0.903607i	−0.999681	−	0.0252385i	$-0.991965\pi$
$83$	−394.490	−	683.277i	−0.521698	−	0.903607i	0.477984	−	0.878369i	$-0.341368\pi$
$84$	−641.899	−	1111.80i	−0.833773	−	1.44414i
$85$	22.6243	+	39.1865i	0.0288700	+	0.0500044i
$86$	841.005	+	1456.66i	1.05451	+	1.82647i
$87$	−283.653	+	491.302i	−0.349550	+	0.605438i
$88$	1472.98	−	2551.28i	1.78432	−	3.09053i
$89$	334.823			0.398777			0.199388	−	0.979921i	$-0.436104\pi$
$89$	334.823			0.398777			0.199388	+	0.979921i	$0.436104\pi$
$90$	−7.73878	−	13.4040i	−0.00906376	−	0.0156989i
$91$	−872.785			−1.00541
$92$	−455.803			−0.516530
$93$	−179.568	+	311.021i	−0.200219	+	0.346789i
$94$	−1072.57			−1.17689
$95$	−16.4902	−	28.5619i	−0.0178091	−	0.0308462i
$96$	193.649	−	335.411i	0.205878	−	0.356591i
$97$	211.758	+	366.776i	0.221657	+	0.383922i	0.955311	−	0.295601i	$-0.0955200\pi$
$97$	211.758	+	366.776i	0.221657	+	0.383922i	−0.733654	+	0.679523i	$0.762187\pi$
$98$	−649.389	+	1124.78i	−0.669370	+	1.15938i
$99$	277.559	−	480.747i	0.281775	−	0.488049i
$100$	1090.54	−	1888.87i	1.09054	−	1.88887i
$101$	800.838	−	1387.09i	0.788974	−	1.36654i	−0.137622	−	0.990485i	$-0.543946\pi$
$101$	800.838	−	1387.09i	0.788974	−	1.36654i	0.926596	−	0.376058i	$-0.122721\pi$
$102$	−1005.03	+	1740.76i	−0.975614	+	1.68981i
$103$	155.005	−	268.476i	0.148282	−	0.256832i	−0.782311	−	0.622889i	$-0.785959\pi$
$103$	155.005	−	268.476i	0.148282	−	0.256832i	0.930593	+	0.366056i	$0.119292\pi$
$104$	−850.648	−	1473.37i	−0.802047	−	1.38919i
$105$	−12.5254	+	21.6946i	−0.0116415	+	0.0201636i
$106$	995.646	+	1724.51i	0.912317	+	1.58018i
$107$	−358.855			−0.324223			−0.162111	−	0.986772i	$-0.551830\pi$
$107$	−358.855			−0.324223			−0.162111	+	0.986772i	$0.551830\pi$
$108$	235.775	−	408.375i	0.210069	−	0.363851i
$109$	358.129			0.314702			0.157351	−	0.987543i	$-0.449705\pi$
$109$	358.129			0.314702			0.157351	+	0.987543i	$0.449705\pi$
$110$	−106.072			−0.0919420
$111$	12.4249	+	21.5205i	0.0106245	+	0.0184022i
$112$	−2482.15			−2.09412
$113$	−626.102	+	1084.44i	−0.521228	+	0.902793i	0.478467	+	0.878105i	$0.341193\pi$
$113$	−626.102	+	1084.44i	−0.521228	+	0.902793i	−0.999695	+	0.0246879i	$0.992141\pi$
$114$	732.537	−	1268.79i	0.601828	−	1.04240i
$115$	4.44705	+	7.70252i	0.00360600	+	0.00624577i
$116$	1651.32	+	2860.17i	1.32173	+	2.28931i
$117$	−160.291	−	277.632i	−0.126657	−	0.219377i
$118$	546.988	+	947.412i	0.426732	+	0.739121i
$119$	3253.33			2.50615
$120$	−48.8308			−0.0371469
$121$	−1236.70	−	2142.03i	−0.929150	−	1.60934i
$122$	1595.50	−	2763.49i	1.18402	−	2.05078i
$123$	655.017	−	1134.52i	0.480170	−	0.831679i
$124$	1045.38	+	1810.65i	0.757077	+	1.31130i
$125$	−85.1584			−0.0609344
$126$	−1112.82			−0.786807
$127$	−160.088	+	277.281i	−0.111855	+	0.193738i	−0.916518	−	0.399993i	$-0.869012\pi$
$127$	−160.088	+	277.281i	−0.111855	+	0.193738i	0.804663	+	0.593731i	$0.202346\pi$
$128$	917.435	+	1589.04i	0.633520	+	1.09729i
$129$	999.953			0.682488
$130$	−30.6285	+	53.0501i	−0.0206638	+	0.0357908i
$131$	2273.28			1.51616			0.758082	−	0.652160i	$-0.226137\pi$
$131$	2273.28			1.51616			0.758082	+	0.652160i	$0.226137\pi$
$132$	−1615.84	−	2798.72i	−1.06546	−	1.84543i
$133$	−2371.26			−1.54597
$134$	−2045.44	+	1864.15i	−1.31865	+	1.20177i
$135$	−9.20138			−0.00586614
$136$	3170.81	+	5492.00i	1.99923	+	3.46276i
$137$	1389.44			0.866482			0.433241	−	0.901278i	$-0.357370\pi$
$137$	1389.44			0.866482			0.433241	+	0.901278i	$0.357370\pi$
$138$	−197.549	+	342.165i	−0.121859	+	0.211065i
$139$	108.458			0.0661817			0.0330908	−	0.999452i	$-0.489465\pi$
$139$	108.458			0.0661817			0.0330908	+	0.999452i	$0.489465\pi$
$140$	72.9180	+	126.298i	0.0440193	+	0.0762436i
$141$	−318.822	+	552.216i	−0.190423	+	0.329822i
$142$	−1066.43			−0.630233
$143$	−2197.05			−1.28480
$144$	−455.858	−	789.570i	−0.263807	−	0.456927i
$145$	32.2222	−	55.8106i	0.0184546	−	0.0319642i
$146$	−2514.88	+	4355.91i	−1.42557	+	2.46916i
$147$	386.061	+	668.677i	0.216611	+	0.375181i
$148$	144.666			0.0803477
$149$	−2182.20			−1.19982			−0.599908	−	0.800069i	$-0.704796\pi$
$149$	−2182.20			−1.19982			−0.599908	+	0.800069i	$0.704796\pi$
$150$	−945.296	−	1637.30i	−0.514554	−	0.891234i
$151$	686.566	+	1189.17i	0.370013	+	0.640881i	0.989567	−	0.144073i	$-0.0460200\pi$
$151$	686.566	+	1189.17i	0.370013	+	0.640881i	−0.619554	+	0.784954i	$0.712687\pi$
$152$	−2311.11	−	4002.97i	−1.23326	−	2.13608i
$153$	597.488	+	1034.88i	0.315713	+	0.546830i
$154$	−3813.24	+	6604.73i	−1.99532	+	3.45600i
$155$	20.3985	−	35.3312i	0.0105706	−	0.0183088i
$156$	−1866.30			−0.957845
$157$	−1066.47	−	1847.18i	−0.542124	−	0.938987i	−0.998782	−	0.0493444i	$-0.984287\pi$
$157$	−1066.47	−	1847.18i	−0.542124	−	0.938987i	0.456657	−	0.889643i	$-0.349047\pi$
$158$	5571.29			2.80524
$159$	1183.82			0.590459
$160$	−21.9981	+	38.1017i	−0.0108694	+	0.0188263i
$161$	639.475			0.313029
$162$	−204.374	−	353.986i	−0.0991181	−	0.171678i
$163$	308.482	−	534.306i	0.148234	−	0.256749i	−0.782341	−	0.622851i	$-0.785974\pi$
$163$	308.482	−	534.306i	0.148234	−	0.256749i	0.930575	+	0.366102i	$0.119308\pi$
$164$	−3813.26	−	6604.75i	−1.81564	−	3.14478i
$165$	−31.5300	+	54.6115i	−0.0148764	+	0.0257667i
$166$	−1990.70	+	3448.00i	−0.930775	+	1.61215i
$167$	−633.814	+	1097.80i	−0.293689	+	0.508684i	−0.974679	−	0.223609i	$-0.928216\pi$
$167$	−633.814	+	1097.80i	−0.293689	+	0.508684i	0.680990	+	0.732292i	$0.261550\pi$
$168$	−1755.44	+	3040.51i	−0.806161	+	1.39631i
$169$	464.101	−	803.847i	0.211243	−	0.365884i
$170$	114.169	−	197.746i	0.0515078	−	0.0892141i
$171$	−435.492	−	754.294i	−0.194754	−	0.337324i
$172$	2910.67	−	5041.43i	1.29033	−	2.23491i
$173$	444.125	+	769.246i	0.195180	+	0.338062i	0.946960	−	0.321353i	$-0.104138\pi$
$173$	444.125	+	769.246i	0.195180	+	0.338062i	−0.751779	+	0.659415i	$0.770804\pi$
$174$	2862.78			1.24728
$175$	−1529.99	+	2650.01i	−0.660892	+	1.14470i
$176$	−6248.28			−2.67603
$177$	650.368			0.276184
$178$	−844.802	−	1463.24i	−0.355734	−	0.616149i
$179$	3302.39			1.37895			0.689476	−	0.724308i	$-0.257841\pi$
$179$	3302.39			1.37895			0.689476	+	0.724308i	$0.257841\pi$
$180$	−26.7834	+	46.3903i	−0.0110907	+	0.0192096i
$181$	910.928	−	1577.77i	0.374082	−	0.647928i	−0.616108	−	0.787662i	$-0.711291\pi$
$181$	910.928	−	1577.77i	0.374082	−	0.647928i	0.990189	+	0.139734i	$0.0446247\pi$
$182$	2202.15	+	3814.24i	0.896893	+	1.55346i
$183$	−948.525	−	1642.89i	−0.383153	−	0.663640i
$184$	623.256	+	1079.51i	0.249712	+	0.432514i
$185$	−1.41143	−	2.44468i	−0.000560923	−	0.000971547i
$186$	1812.30			0.714431
$187$	8189.54			3.20256
$188$	1856.06	+	3214.79i	0.720037	+	1.24714i
$189$	−330.784	+	572.935i	−0.127307	+	0.220502i
$190$	−83.2142	+	144.131i	−0.0317736	+	0.0550336i
$191$	1137.92	+	1970.94i	0.431084	+	0.746660i	0.996967	−	0.0778261i	$-0.0247979\pi$
$191$	1137.92	+	1970.94i	0.431084	+	0.746660i	−0.565883	+	0.824486i	$0.691465\pi$
$192$	476.831			0.179231
$193$	−3200.87			−1.19380			−0.596901	−	0.802315i	$-0.703602\pi$
$193$	−3200.87			−1.19380			−0.596901	+	0.802315i	$0.703602\pi$
$194$	1068.59	−	1850.85i	0.395465	−	0.684965i
$195$	18.2086	+	31.5382i	0.00668690	+	0.0115820i
$196$	4495.00			1.63812
$197$	−278.803	+	482.902i	−0.100832	+	0.174646i	−0.912028	−	0.410129i	$-0.865484\pi$
$197$	−278.803	+	482.902i	−0.100832	+	0.174646i	0.811196	+	0.584775i	$0.198817\pi$
$198$	−2801.28			−1.00544
$199$	−1147.12	−	1986.86i	−0.408628	−	0.707764i	0.586109	−	0.810232i	$-0.300659\pi$
$199$	−1147.12	−	1986.86i	−0.408628	−	0.707764i	−0.994736	+	0.102469i	$0.967326\pi$
$200$	−5964.72			−2.10885
$201$	351.751	+	1607.21i	0.123436	+	0.564001i
$202$	−8082.49			−2.81526
$203$	−2316.74	−	4012.71i	−0.801002	−	1.38738i
$204$	6956.69			2.38758
$205$	−74.4082	+	128.879i	−0.0253507	+	0.0439087i
$206$	−1564.39			−0.529108
$207$	117.443	+	203.416i	0.0394339	+	0.0683015i
$208$	−1804.20	+	3124.96i	−0.601435	+	1.04172i
$209$	−5969.13			−1.97556
$210$	126.413			0.0415397
$211$	713.020	+	1234.99i	0.232637	+	0.402939i	0.958583	−	0.284813i	$-0.0919314\pi$
$211$	713.020	+	1234.99i	0.232637	+	0.402939i	−0.725947	+	0.687751i	$0.758598\pi$
$212$	3445.87	−	5968.42i	1.11634	−	1.93355i
$213$	−316.996	+	549.054i	−0.101973	+	0.176622i
$214$	905.440	+	1568.27i	0.289227	+	0.500956i
$215$	−113.592			−0.0360321
$216$	−1289.58			−0.406225
$217$	−1466.63	−	2540.27i	−0.458806	−	0.794676i
$218$	−903.608	−	1565.10i	−0.280734	−	0.486246i
$219$	1495.09	+	2589.58i	0.461320	+	0.799030i
$220$	183.555	+	317.927i	0.0562513	+	0.0974302i
$221$	2364.74	−	4095.84i	0.719771	−	1.24668i
$222$	62.6994	−	108.598i	0.0189554	−	0.0328318i
$223$	−1667.84			−0.500837			−0.250418	−	0.968138i	$-0.580568\pi$
$223$	−1667.84			−0.500837			−0.250418	+	0.968138i	$0.580568\pi$
$224$	1581.63	+	2739.47i	0.471774	+	0.817136i
$225$	−1123.95			−0.333024
$226$	6318.96			1.85987
$227$	−2791.75	+	4835.45i	−0.816276	+	1.41383i	0.0921313	+	0.995747i	$0.470632\pi$
$227$	−2791.75	+	4835.45i	−0.816276	+	1.41383i	−0.908408	+	0.418085i	$0.862701\pi$
$228$	−5070.53			−1.47283
$229$	1834.93	+	3178.20i	0.529501	+	0.917123i	0.999408	+	0.0344068i	$0.0109542\pi$
$229$	1834.93	+	3178.20i	0.529501	+	0.917123i	−0.469907	+	0.882716i	$0.655712\pi$
$230$	22.4410	−	38.8690i	0.00643355	−	0.0111432i
$231$	2266.97	+	3926.50i	0.645695	+	1.11838i
$232$	4515.96	−	7821.87i	1.27796	−	2.21350i
$233$	3136.27	−	5432.18i	0.881820	−	1.52736i	0.0325039	−	0.999472i	$-0.489652\pi$
$233$	3136.27	−	5432.18i	0.881820	−	1.52736i	0.849316	−	0.527885i	$-0.177015\pi$
$234$	−808.871	+	1401.01i	−0.225972	+	0.391396i
$235$	36.2173	−	62.7302i	0.0100534	−	0.0174131i
$236$	1893.09	−	3278.93i	0.522161	−	0.904409i
$237$	1656.06	−	2868.39i	0.453894	−	0.786167i
$238$	−8208.58	−	14217.7i	−2.23564	−	3.87225i
$239$	2873.75	−	4977.49i	0.777773	−	1.34714i	−0.155450	−	0.987844i	$-0.549683\pi$
$239$	2873.75	−	4977.49i	0.777773	−	1.34714i	0.933223	−	0.359298i	$-0.116984\pi$
$240$	51.7843	+	89.6930i	0.0139278	+	0.0241236i
$241$	1944.24			0.519667			0.259833	−	0.965653i	$-0.416332\pi$
$241$	1944.24			0.519667			0.259833	+	0.965653i	$0.416332\pi$
$242$	−6240.72	+	10809.2i	−1.65772	+	2.87126i
$243$	−243.000			−0.0641500
$244$	−11043.9			−2.89759
$245$	−43.8555	−	75.9600i	−0.0114360	−	0.0198078i
$246$	−6610.79			−1.71337
$247$	−1723.59	+	2985.34i	−0.444006	+	0.769040i
$248$	2858.85	−	4951.68i	0.732006	−	1.26787i
$249$	1183.47	+	2049.83i	0.301202	+	0.521698i
$250$	214.866	+	372.159i	0.0543573	+	0.0941496i
$251$	50.5388	+	87.5358i	0.0127091	+	0.0220128i	0.872310	−	0.488953i	$-0.162621\pi$
$251$	50.5388	+	87.5358i	0.0127091	+	0.0220128i	−0.859601	+	0.510966i	$0.829288\pi$
$252$	1925.70	+	3335.41i	0.481379	+	0.833773i
$253$	1609.74			0.400014
$254$	1615.70			0.399125
$255$	−67.8730	−	117.560i	−0.0166681	−	0.0288700i
$256$	3993.85	−	6917.55i	0.975061	−	1.68885i
$257$	2.77382	−	4.80440i	0.000673253	−	0.00116611i	−0.865689	−	0.500583i	$-0.833119\pi$
$257$	2.77382	−	4.80440i	0.000673253	−	0.00116611i	0.866362	+	0.499417i	$0.166452\pi$
$258$	−2523.02	−	4369.99i	−0.608822	−	1.05451i
$259$	−202.961			−0.0486926
$260$	212.007			0.0505697
$261$	850.960	−	1473.91i	0.201813	−	0.349550i
$262$	−5735.79	−	9934.68i	−1.35251	−	2.34262i
$263$	1393.07			0.326618			0.163309	−	0.986575i	$-0.447783\pi$
$263$	1393.07			0.326618			0.163309	+	0.986575i	$0.447783\pi$
$264$	−4418.94	+	7653.83i	−1.03018	+	1.78432i
$265$	−134.479			−0.0311734
$266$	5983.00	+	10362.9i	1.37910	+	2.38868i
$267$	−1004.47			−0.230234
$268$	9126.91	+	2904.88i	2.08028	+	0.662104i
$269$	3577.82			0.810942			0.405471	−	0.914108i	$-0.367107\pi$
$269$	3577.82			0.810942			0.405471	+	0.914108i	$0.367107\pi$
$270$	23.2163	+	40.2119i	0.00523297	+	0.00906376i
$271$	1502.78			0.336854			0.168427	−	0.985714i	$-0.446131\pi$
$271$	1502.78			0.336854			0.168427	+	0.985714i	$0.446131\pi$
$272$	6725.18	−	11648.4i	1.49917	−	2.59664i
$273$	2618.35			0.580476
$274$	−3505.75	−	6072.13i	−0.772956	−	1.33880i
$275$	−3851.41	+	6670.83i	−0.844540	+	1.46279i
$276$	1367.41			0.298219
$277$	−845.028			−0.183295			−0.0916477	−	0.995791i	$-0.529213\pi$
$277$	−845.028			−0.183295			−0.0916477	+	0.995791i	$0.529213\pi$
$278$	−273.653	−	473.981i	−0.0590382	−	0.102257i
$279$	538.705	−	933.064i	0.115596	−	0.200219i
$280$	199.413	−	345.394i	0.0425615	−	0.0737187i
$281$	−2233.16	−	3867.95i	−0.474090	−	0.821147i	0.525470	−	0.850812i	$-0.323889\pi$
$281$	−2233.16	−	3867.95i	−0.474090	−	0.821147i	−0.999560	+	0.0296646i	$0.990556\pi$
$282$	3217.72			0.679477
$283$	−614.318			−0.129037			−0.0645184	−	0.997917i	$-0.520551\pi$
$283$	−614.318			−0.129037			−0.0645184	+	0.997917i	$0.520551\pi$
$284$	1845.43	+	3196.38i	0.385585	+	0.667853i
$285$	49.4707	+	85.6858i	0.0102821	+	0.0178091i
$286$	5543.44	+	9601.52i	1.14612	+	1.98514i
$287$	5349.86	+	9266.23i	1.10032	+	1.90581i
$288$	−580.948	+	1006.23i	−0.118864	+	0.205878i
$289$	−6358.11	+	11012.6i	−1.29414	+	2.24152i
$290$	−325.204			−0.0658505
$291$	−635.274	−	1100.33i	−0.127974	−	0.221657i
$292$	17407.7			3.48873
$293$	−1442.87			−0.287691			−0.143846	−	0.989600i	$-0.545947\pi$
$293$	−1442.87			−0.287691			−0.143846	+	0.989600i	$0.545947\pi$
$294$	1948.17	−	3374.33i	0.386461	−	0.669370i
$295$	−73.8800			−0.0145812
$296$	−197.813	−	342.622i	−0.0388434	−	0.0672788i
$297$	−832.677	+	1442.24i	−0.162683	+	0.281775i
$298$	5505.98	+	9536.64i	1.07031	+	1.85383i
$299$	464.814	−	805.081i	0.0899026	−	0.155716i
$300$	−3271.61	+	5666.60i	−0.629623	+	1.09054i
$301$	−4083.56	+	7072.94i	−0.781969	+	1.35441i
$302$	3464.60	−	6000.86i	0.660149	−	1.14341i
$303$	−2402.51	+	4161.28i	−0.455514	+	0.788974i
$304$	−4901.80	+	8490.16i	−0.924794	+	1.60179i
$305$	107.750	+	186.628i	0.0202287	+	0.0350371i
$306$	3015.08	−	5222.28i	0.563271	−	0.975614i
$307$	−1428.41	−	2474.08i	−0.265550	−	0.459946i	0.702158	−	0.712022i	$-0.252220\pi$
$307$	−1428.41	−	2474.08i	−0.265550	−	0.459946i	−0.967708	+	0.252076i	$0.918887\pi$
$308$	26394.8			4.88306
$309$	−465.014	+	805.428i	−0.0856107	+	0.148282i
$310$	−205.872			−0.0377186
$311$	6199.98			1.13045			0.565223	−	0.824938i	$-0.308790\pi$
$311$	6199.98			1.13045			0.565223	+	0.824938i	$0.308790\pi$
$312$	2551.94	+	4420.10i	0.463062	+	0.802047i
$313$	−8332.36			−1.50471			−0.752353	−	0.658761i	$-0.771081\pi$
$313$	−8332.36			−1.50471			−0.752353	+	0.658761i	$0.771081\pi$
$314$	−5381.69	+	9321.36i	−0.967218	+	1.67527i
$315$	37.5762	−	65.0839i	0.00672120	−	0.0116415i
$316$	−9640.96	−	16698.6i	−1.71629	−	2.97269i
$317$	2747.52	+	4758.84i	0.486801	+	0.843164i	0.999885	−	0.0151742i	$-0.00483027\pi$
$317$	2747.52	+	4758.84i	0.486801	+	0.843164i	−0.513084	+	0.858339i	$0.671497\pi$
$318$	−2986.94	−	5173.53i	−0.526727	−	0.912317i
$319$	−5831.89	−	10101.1i	−1.02358	−	1.77290i
$320$	−54.1667			−0.00946254
$321$	1076.57			0.187190
$322$	−1613.48	−	2794.63i	−0.279242	−	0.483661i
$323$	6424.72	−	11127.9i	1.10675	−	1.91695i
$324$	−707.326	+	1225.12i	−0.121284	+	0.210069i
$325$	2224.19	+	3852.41i	0.379618	+	0.657519i
$326$	−3113.36			−0.528936
$327$	−1074.39			−0.181694
$328$	−10428.3	+	18062.4i	−1.75551	+	3.04064i
$329$	−2603.98	−	4510.23i	−0.436359	−	0.755796i
$330$	318.217			0.0530827
$331$	1672.44	−	2896.75i	0.277720	−	0.481026i	−0.693097	−	0.720844i	$-0.743754\pi$
$331$	1672.44	−	2896.75i	0.277720	−	0.481026i	0.970818	+	0.239818i	$0.0770878\pi$
$332$	13779.4			2.27784
$333$	−37.2747	−	64.5616i	−0.00613405	−	0.0106245i
$334$	6396.80			1.04796
$335$	−39.9579	−	182.575i	−0.00651682	−	0.0297766i
$336$	7446.46			1.20904
$337$	−3649.21	−	6320.63i	−0.589868	−	1.02168i	−0.994249	−	0.107090i	$-0.965847\pi$
$337$	−3649.21	−	6320.63i	−0.589868	−	1.02168i	0.404382	−	0.914590i	$-0.367487\pi$
$338$	−4683.96			−0.753769
$339$	1878.31	−	3253.32i	0.300931	−	0.521228i
$340$	−790.261			−0.126053
$341$	−3691.91	−	6394.58i	−0.586300	−	1.01550i
$342$	−2197.61	+	3806.37i	−0.347465	+	0.601828i
$343$	2098.05			0.330275
$344$	−15920.0			−2.49519
$345$	−13.3412	−	23.1076i	−0.00208192	−	0.00360600i
$346$	2241.17	−	3881.82i	0.348226	−	0.603145i
$347$	−3925.64	+	6799.42i	−0.607319	+	1.05191i	0.384362	+	0.923183i	$0.374422\pi$
$347$	−3925.64	+	6799.42i	−0.607319	+	1.05191i	−0.991680	+	0.128724i	$0.958912\pi$
$348$	−4953.96	−	8580.51i	−0.763103	−	1.32173i
$349$	1448.81			0.222215			0.111108	−	0.993808i	$-0.464560\pi$
$349$	1448.81			0.222215			0.111108	+	0.993808i	$0.464560\pi$
$350$	15441.4			2.35823
$351$	480.872	+	832.895i	0.0731256	+	0.126657i
$352$	3981.42	+	6896.02i	0.602870	+	1.04420i
$353$	704.209	+	1219.73i	0.106179	+	0.183908i	0.914219	−	0.405220i	$-0.132805\pi$
$353$	704.209	+	1219.73i	0.106179	+	0.183908i	−0.808040	+	0.589127i	$0.799472\pi$
$354$	−1640.96	−	2842.23i	−0.246374	−	0.426732i
$355$	36.0099	−	62.3710i	0.00538369	−	0.00932482i
$356$	−2923.81	+	5064.19i	−0.435286	+	0.753937i
$357$	−9759.98			−1.44693
$358$	−8332.38	−	14432.1i	−1.23011	−	2.13062i
$359$	−6449.36			−0.948146			−0.474073	−	0.880486i	$-0.657217\pi$
$359$	−6449.36			−0.948146			−0.474073	+	0.880486i	$0.657217\pi$
$360$	146.493			0.0214468
$361$	−1253.30	+	2170.78i	−0.182723	+	0.316486i
$362$	−9193.58			−1.33482
$363$	3710.10	+	6426.08i	0.536445	+	0.929150i
$364$	7621.52	−	13200.9i	1.09746	−	1.90086i
$365$	−169.839	−	294.169i	−0.0243555	−	0.0421850i
$366$	−4786.51	+	8290.48i	−0.683593	+	1.18402i
$367$	6337.42	−	10976.7i	0.901391	−	1.56126i	0.0757018	−	0.997130i	$-0.475880\pi$
$367$	6337.42	−	10976.7i	0.901391	−	1.56126i	0.825689	−	0.564125i	$-0.190786\pi$
$368$	1321.91	−	2289.61i	0.187253	−	0.324332i
$369$	−1965.05	+	3403.57i	−0.277226	+	0.480170i
$370$	−7.12248	+	12.3365i	−0.00100076	+	0.00173336i
$371$	−4834.43	+	8373.48i	−0.676526	+	1.17178i
$372$	−3136.13	−	5431.94i	−0.437099	−	0.757077i
$373$	−6443.45	+	11160.4i	−0.894448	+	1.54923i	−0.0599612	+	0.998201i	$0.519098\pi$
$373$	−6443.45	+	11160.4i	−0.894448	+	1.54923i	−0.834487	+	0.551028i	$0.814236\pi$
$374$	−20663.3	−	35789.9i	−2.85688	−	4.94827i
$375$	255.475			0.0351805
$376$	5075.87	−	8791.66i	0.696191	−	1.20584i
$377$	−6735.85			−0.920196
$378$	3338.45			0.454263
$379$	2837.43	+	4914.58i	0.384563	+	0.666082i	0.991708	−	0.128509i	$-0.0410190\pi$
$379$	2837.43	+	4914.58i	0.384563	+	0.666082i	−0.607146	+	0.794590i	$0.707686\pi$
$380$	575.999			0.0777582
$381$	480.265	−	831.843i	0.0645793	−	0.111855i
$382$	5742.26	−	9945.88i	0.769108	−	1.33213i
$383$	−2828.24	−	4898.65i	−0.377327	−	0.653549i	0.613346	−	0.789815i	$-0.289823\pi$
$383$	−2828.24	−	4898.65i	−0.377327	−	0.653549i	−0.990672	+	0.136265i	$0.956490\pi$
$384$	−2752.30	−	4767.13i	−0.365763	−	0.633520i
$385$	−257.521	−	446.040i	−0.0340896	−	0.0590450i
$386$	8076.23	+	13988.4i	1.06495	+	1.84454i
$387$	−2999.86			−0.394034
$388$	−7396.64			−0.967803
$389$	−2903.70	−	5029.35i	−0.378466	−	0.655523i	0.612373	−	0.790569i	$-0.290215\pi$
$389$	−2903.70	−	5029.35i	−0.378466	−	0.655523i	−0.990839	+	0.135046i	$0.956882\pi$
$390$	91.8855	−	159.150i	0.0119303	−	0.0206638i
$391$	−1732.60	+	3000.96i	−0.224096	+	0.388146i
$392$	−6146.37	−	10645.8i	−0.791935	−	1.37167i
$393$	−6819.84			−0.875357
$394$	2813.83			0.359794
$395$	−188.124	+	325.841i	−0.0239634	+	0.0415059i
$396$	4847.53	+	8396.16i	0.615145	+	1.06546i
$397$	12476.6			1.57728			0.788641	−	0.614854i	$-0.210785\pi$
$397$	12476.6			1.57728			0.788641	+	0.614854i	$0.210785\pi$
$398$	−5788.66	+	10026.2i	−0.729043	+	1.26274i
$399$	7113.77			0.892566
$400$	6325.49	+	10956.1i	0.790686	+	1.36951i
$401$	−2382.79			−0.296735			−0.148368	−	0.988932i	$-0.547402\pi$
$401$	−2382.79			−0.296735			−0.148368	+	0.988932i	$0.547402\pi$
$402$	6136.33	−	5592.44i	0.761324	−	0.693845i
$403$	−4264.17			−0.527080
$404$	13986.5	+	24225.3i	1.72241	+	2.98331i
$405$	27.6041			0.00338682
$406$	−11690.9	+	20249.2i	−1.42909	+	2.47525i
$407$	−510.910			−0.0622233
$408$	−9512.43	−	16476.0i	−1.15425	−	1.99923i
$409$	−2409.82	+	4173.94i	−0.291340	+	0.504616i	−0.974127	−	0.226002i	$-0.927435\pi$
$409$	−2409.82	+	4173.94i	−0.291340	+	0.504616i	0.682787	+	0.730618i	$0.260768\pi$
$410$	750.967			0.0904577
$411$	−4168.32			−0.500263
$412$	2707.13	+	4688.89i	0.323715	+	0.560692i
$413$	−2655.94	+	4600.23i	−0.316442	+	0.548093i
$414$	592.647	−	1026.49i	0.0703551	−	0.121859i
$415$	−134.439	−	232.855i	−0.0159021	−	0.0275432i
$416$	4598.55			0.541977
$417$	−325.373			−0.0382100
$418$	15060.9	+	26086.3i	1.76233	+	3.05244i
$419$	−3122.05	−	5407.54i	−0.364014	−	0.630491i	0.624603	−	0.780942i	$-0.285261\pi$
$419$	−3122.05	−	5407.54i	−0.364014	−	0.630491i	−0.988617	+	0.150451i	$0.951927\pi$
$420$	−218.754	−	378.893i	−0.0254145	−	0.0440193i
$421$	749.928	+	1298.91i	0.0868154	+	0.150369i	0.906163	−	0.422928i	$-0.138998\pi$
$421$	749.928	+	1298.91i	0.0868154	+	0.150369i	−0.819348	+	0.573297i	$0.805664\pi$
$422$	3598.09	−	6232.08i	0.415053	−	0.718893i
$423$	956.465	−	1656.65i	0.109941	−	0.190423i
$424$	−18847.3			−2.15873
$425$	−8290.73	−	14360.0i	−0.946258	−	1.63897i
$426$	3199.30			0.363865
$427$	15494.2			1.75601
$428$	3133.67	−	5427.68i	0.353906	−	0.612984i
$429$	6591.14			0.741779
$430$	286.608	+	496.419i	0.0321429	+	0.0556732i
$431$	6129.41	−	10616.5i	0.685020	−	1.18649i	−0.288411	−	0.957507i	$-0.593127\pi$
$431$	6129.41	−	10616.5i	0.685020	−	1.18649i	0.973431	−	0.228982i	$-0.0735397\pi$
$432$	1367.58	+	2368.71i	0.152309	+	0.263807i
$433$	5398.34	−	9350.20i	0.599140	−	1.03774i	−0.393808	−	0.919193i	$-0.628843\pi$
$433$	5398.34	−	9350.20i	0.599140	−	1.03774i	0.992948	−	0.118548i	$-0.0378240\pi$
$434$	−7400.99	+	12818.9i	−0.818568	+	1.41780i
$435$	−96.6667	+	167.432i	−0.0106547	+	0.0184546i
$436$	−3127.34	+	5416.70i	−0.343514	+	0.594984i
$437$	1262.85	−	2187.31i	0.138238	−	0.239436i
$438$	7544.65	−	13067.7i	0.823053	−	1.42557i
$439$	−2123.87	−	3678.64i	−0.230903	−	0.399936i	0.727171	−	0.686457i	$-0.240835\pi$
$439$	−2123.87	−	3678.64i	−0.230903	−	0.399936i	−0.958074	+	0.286520i	$0.907501\pi$
$440$	501.980	−	869.454i	0.0543885	−	0.0942036i
$441$	−1158.18	−	2006.03i	−0.125060	−	0.216611i
$442$	−23866.2			−2.56832
$443$	4272.58	−	7400.32i	0.458231	−	0.793679i	−0.540637	−	0.841256i	$-0.681817\pi$
$443$	4272.58	−	7400.32i	0.458231	−	0.793679i	0.998868	+	0.0475770i	$0.0151499\pi$
$444$	−433.998			−0.0463888
$445$	114.105			0.0121553
$446$	4208.18	+	7288.78i	0.446778	+	0.773842i
$447$	6546.60			0.692714
$448$	−1947.26	+	3372.76i	−0.205356	+	0.355687i
$449$	−4646.78	+	8048.46i	−0.488408	+	0.845947i	−0.999911	−	0.0133344i	$-0.995755\pi$
$449$	−4646.78	+	8048.46i	−0.488408	+	0.845947i	0.511503	+	0.859281i	$0.329089\pi$
$450$	2835.89	+	4911.90i	0.297078	+	0.514554i
$451$	13467.1	+	23325.7i	1.40608	+	2.43540i
$452$	−10934.8	−	18939.6i	−1.13790	−	1.97089i
$453$	−2059.70	−	3567.50i	−0.213627	−	0.370013i
$454$	28175.8			2.91268
$455$	−297.438			−0.0306464
$456$	6933.34	+	12008.9i	0.712025	+	1.23326i
$457$	1237.48	−	2143.38i	0.126667	−	0.219394i	−0.795716	−	0.605670i	$-0.792905\pi$
$457$	1237.48	−	2143.38i	0.126667	−	0.219394i	0.922383	+	0.386276i	$0.126239\pi$
$458$	9259.56	−	16038.0i	0.944697	−	1.63626i
$459$	−1792.46	−	3104.64i	−0.182277	−	0.315713i
$460$	−155.334			−0.0157445
$461$	14227.9			1.43743			0.718717	−	0.695302i	$-0.244730\pi$
$461$	14227.9			1.43743			0.718717	+	0.695302i	$0.244730\pi$
$462$	11439.7	−	19814.2i	1.15200	−	1.99532i
$463$	5686.46	+	9849.23i	0.570782	+	0.988624i	0.996486	+	0.0837610i	$0.0266932\pi$
$463$	5686.46	+	9849.23i	0.570782	+	0.988624i	−0.425704	+	0.904863i	$0.639973\pi$
$464$	−19156.4			−1.91662
$465$	−61.1954	+	105.994i	−0.00610294	+	0.0105706i
$466$	−31652.9			−3.14655
$467$	−474.388	−	821.664i	−0.0470065	−	0.0814177i	0.841565	−	0.540156i	$-0.181635\pi$
$467$	−474.388	−	821.664i	−0.0470065	−	0.0814177i	−0.888571	+	0.458738i	$0.848301\pi$
$468$	5598.91			0.553012
$469$	−12804.7	−	4075.44i	−1.26070	−	0.401250i
$470$	−365.525			−0.0358732
$471$	3199.41	+	5541.54i	0.312996	+	0.542124i
$472$	−10354.3			−1.00974
$473$	−10279.5	+	17804.6i	−0.999262	+	1.73077i
$474$	−16713.9			−1.61961
$475$	6042.88	+	10466.6i	0.583719	+	1.01103i
$476$	−28409.4	+	49206.5i	−2.73559	+	4.73819i
$477$	−3551.46			−0.340902
$478$	−29003.5			−2.77529
$479$	−8845.36	−	15320.6i	−0.843747	−	1.46141i	−0.886705	−	0.462335i	$-0.847012\pi$
$479$	−8845.36	−	15320.6i	−0.843747	−	1.46141i	0.0429586	−	0.999077i	$-0.486322\pi$
$480$	65.9942	−	114.305i	0.00627543	−	0.0108694i
$481$	−147.526	+	255.522i	−0.0139846	+	0.0242220i
$482$	−4905.59	−	8496.73i	−0.463575	−	0.802936i
$483$	−1918.43			−0.180728
$484$	43197.5			4.05687
$485$	72.1654	+	124.994i	0.00675642	+	0.0117025i
$486$	613.122	+	1061.96i	0.0572259	+	0.0991181i
$487$	4963.65	+	8597.29i	0.461857	+	0.799959i	0.999054	−	0.0434976i	$-0.0138501\pi$
$487$	4963.65	+	8597.29i	0.461857	+	0.799959i	−0.537197	+	0.843457i	$0.680517\pi$
$488$	15101.2	+	26156.0i	1.40082	+	2.42629i
$489$	−925.445	+	1602.92i	−0.0855829	+	0.148234i
$490$	−221.307	+	383.314i	−0.0204033	+	0.0353396i
$491$	−7526.62			−0.691795			−0.345898	−	0.938272i	$-0.612426\pi$
$491$	−7526.62			−0.691795			−0.345898	+	0.938272i	$0.612426\pi$
$492$	11439.8	+	19814.3i	1.04826	+	1.81564i
$493$	25108.1			2.29373
$494$	17395.4			1.58432
$495$	94.5899	−	163.835i	0.00858889	−	0.0148764i
$496$	−12127.1			−1.09783
$497$	−2589.07	−	4484.40i	−0.233673	−	0.404734i
$498$	5972.11	−	10344.0i	0.537383	−	0.930775i
$499$	10133.0	+	17550.9i	0.909050	+	1.57452i	0.815387	+	0.578916i	$0.196524\pi$
$499$	10133.0	+	17550.9i	0.909050	+	1.57452i	0.0936625	+	0.995604i	$0.470143\pi$
$500$	743.639	−	1288.02i	0.0665131	−	0.115204i
$501$	1901.44	−	3293.40i	0.169561	−	0.293689i
$502$	255.033	−	441.729i	0.0226746	−	0.0392736i
$503$	−10189.8	+	17649.3i	−0.903263	+	1.56450i	−0.0800301	+	0.996792i	$0.525502\pi$
$503$	−10189.8	+	17649.3i	−0.903263	+	1.56450i	−0.823233	+	0.567704i	$0.807832\pi$
$504$	5266.32	−	9121.53i	0.465437	−	0.806161i
$505$	272.919	−	472.710i	0.0240490	−	0.0416541i
$506$	−4061.59	−	7034.88i	−0.356838	−	0.618061i
$507$	−1392.30	+	2411.54i	−0.121961	+	0.211243i
$508$	−2795.91	−	4842.67i	−0.244190	−	0.422950i
$509$	16774.8			1.46077			0.730385	−	0.683036i	$-0.239341\pi$
$509$	16774.8			1.46077			0.730385	+	0.683036i	$0.239341\pi$
$510$	−342.506	+	593.237i	−0.0297380	+	0.0515078i
$511$	−24422.4			−2.11425
$512$	−25629.1			−2.21222
$513$	1306.48	+	2262.88i	0.112441	+	0.194754i
$514$	−27.9949			−0.00240234
$515$	52.8243	−	91.4944i	0.00451984	−	0.00782859i
$516$	−8732.01	+	15124.3i	−0.744971	+	1.29033i
$517$	−6554.96	−	11353.5i	−0.557614	−	0.965816i
$518$	512.098	+	886.979i	0.0434368	+	0.0752348i
$519$	−1332.37	−	2307.74i	−0.112687	−	0.195180i
$520$	−289.894	−	502.111i	−0.0244475	−	0.0423443i
$521$	16668.7			1.40166			0.700832	−	0.713326i	$-0.252812\pi$
$521$	16668.7			1.40166			0.700832	+	0.713326i	$0.252812\pi$
$522$	−8588.34			−0.720118
$523$	−7343.11	−	12718.6i	−0.613942	−	1.06338i	−0.990569	−	0.137014i	$-0.956249\pi$
$523$	−7343.11	−	12718.6i	−0.613942	−	1.06338i	0.376627	−	0.926365i	$-0.377084\pi$
$524$	−19851.2	+	34383.3i	−1.65497	+	2.86650i
$525$	4589.96	−	7950.04i	0.381566	−	0.660892i
$526$	−3514.91	−	6088.00i	−0.291363	−	0.504656i
$527$	15894.8			1.31383
$528$	18744.8			1.54501
$529$	5742.94	−	9947.06i	0.472009	−	0.817544i
$530$	339.308	+	587.699i	0.0278087	+	0.0481660i
$531$	−1951.10			−0.159455
$532$	20706.8	−	35865.2i	1.68751	−	2.92285i
$533$	15554.5			1.26406
$534$	2534.41	+	4389.72i	0.205383	+	0.355734i
$535$	−122.295			−0.00988275
$536$	−5600.12	−	25588.0i	−0.451284	−	2.06200i
$537$	−9907.18			−0.796139
$538$	−9027.32	−	15635.8i	−0.723411	−	1.25299i
$539$	−15874.8			−1.26860
$540$	80.3503	−	139.171i	0.00640320	−	0.0110907i
$541$	7429.54			0.590427			0.295213	−	0.955431i	$-0.404609\pi$
$541$	7429.54			0.590427			0.295213	+	0.955431i	$0.404609\pi$
$542$	−3791.71	−	6567.44i	−0.300495	−	0.520472i
$543$	−2732.78	+	4733.32i	−0.215976	+	0.374082i
$544$	−17141.2			−1.35096
$545$	122.048			0.00959256
$546$	−6606.46	−	11442.7i	−0.517821	−	0.896893i
$547$	4773.37	−	8267.72i	0.373116	−	0.646256i	−0.616927	−	0.787020i	$-0.711623\pi$
$547$	4773.37	−	8267.72i	0.373116	−	0.646256i	0.990043	+	0.140764i	$0.0449560\pi$
$548$	−12133.2	+	21015.3i	−0.945810	+	1.63819i
$549$	2845.58	+	4928.68i	0.221213	+	0.383153i
$550$	38870.5			3.01353
$551$	−18300.6			−1.41494
$552$	−1869.77	−	3238.53i	−0.144171	−	0.249712i
$553$	13525.9	+	23427.6i	1.04011	+	1.80152i
$554$	2132.12	+	3692.94i	0.163511	+	0.283209i
$555$	4.23430	+	7.33403i	0.000323849	+	0.000560923i
$556$	−947.097	+	1640.42i	−0.0722408	+	0.125125i
$557$	−7294.10	+	12633.8i	−0.554867	+	0.961058i	0.443047	+	0.896499i	$0.353898\pi$
$557$	−7294.10	+	12633.8i	−0.554867	+	0.961058i	−0.997914	+	0.0645595i	$0.979436\pi$
$558$	−5436.90			−0.412477
$559$	5936.42	+	10282.2i	0.449166	+	0.777978i
$560$	−845.898			−0.0638316
$561$	−24568.6			−1.84900
$562$	−11269.1	+	19518.7i	−0.845836	+	1.46503i
$563$	21219.0			1.58841			0.794205	−	0.607650i	$-0.207887\pi$
$563$	21219.0			1.58841			0.794205	+	0.607650i	$0.207887\pi$
$564$	−5568.17	−	9644.36i	−0.415713	−	0.720037i
$565$	−213.371	+	369.569i	−0.0158877	+	0.0275184i
$566$	1550.01	+	2684.69i	0.115109	+	0.199374i
$567$	992.353	−	1718.80i	0.0735007	−	0.127307i
$568$	5046.81	−	8741.33i	0.372816	−	0.645736i
$569$	−2216.64	+	3839.34i	−0.163315	+	0.282871i	−0.936056	−	0.351852i	$-0.885552\pi$
$569$	−2216.64	+	3839.34i	−0.163315	+	0.282871i	0.772740	+	0.634722i	$0.218885\pi$
$570$	249.643	−	432.394i	0.0183445	−	0.0317736i
$571$	12815.2	−	22196.6i	0.939231	−	1.62680i	0.172322	−	0.985041i	$-0.444873\pi$
$571$	12815.2	−	22196.6i	0.939231	−	1.62680i	0.766910	−	0.641755i	$-0.221793\pi$
$572$	19185.5	−	33230.3i	1.40242	−	2.42907i
$573$	−3413.76	−	5912.81i	−0.248887	−	0.431084i
$574$	26996.8	−	46759.9i	1.96311	−	3.40021i
$575$	−1629.63	−	2822.60i	−0.118192	−	0.204714i
$576$	−1430.49			−0.103479
$577$	4379.30	−	7585.16i	0.315966	−	0.547269i	−0.663676	−	0.748020i	$-0.731005\pi$
$577$	4379.30	−	7585.16i	0.315966	−	0.547269i	0.979642	+	0.200750i	$0.0643380\pi$
$578$	64169.5			4.61782
$579$	9602.62			0.689242
$580$	562.756	+	974.723i	0.0402882	+	0.0697813i
$581$	−19332.0			−1.38043
$582$	−3205.77	+	5552.55i	−0.228322	+	0.395465i
$583$	−12169.6	+	21078.4i	−0.864519	+	1.49739i
$584$	−23803.0	−	41227.9i	−1.68660	−	2.92127i
$585$	−54.6258	−	94.6147i	−0.00386068	−	0.00668690i
$586$	3640.56	+	6305.64i	0.256639	+	0.444511i
$587$	4201.22	+	7276.72i	0.295405	+	0.511657i	0.975079	−	0.221858i	$-0.0712121\pi$
$587$	4201.22	+	7276.72i	0.295405	+	0.511657i	−0.679674	+	0.733514i	$0.737879\pi$
$588$	−13485.0			−0.945768
$589$	−11585.3			−0.810463
$590$	186.409	+	322.870i	0.0130074	+	0.0225294i
$591$	836.410	−	1448.70i	0.0582154	−	0.100832i
$592$	−419.555	+	726.691i	−0.0291277	+	0.0504507i
$593$	2427.02	+	4203.72i	0.168071	+	0.291107i	0.937741	−	0.347334i	$-0.112913\pi$
$593$	2427.02	+	4203.72i	0.168071	+	0.291107i	−0.769671	+	0.638441i	$0.779580\pi$
$594$	8403.83			0.580494
$595$	1108.71			0.0763909
$596$	19055.9	−	33005.7i	1.30966	−	2.26840i
$597$	3441.35	+	5960.59i	0.235921	+	0.408628i
$598$	−4691.15			−0.320795
$599$	2572.08	−	4454.98i	0.175447	−	0.303882i	−0.764869	−	0.644186i	$-0.777196\pi$
$599$	2572.08	−	4454.98i	0.175447	−	0.303882i	0.940316	+	0.340303i	$0.110530\pi$
$600$	17894.2			1.21754
$601$	−1960.53	−	3395.74i	−0.133065	−	0.230475i	0.791792	−	0.610791i	$-0.209148\pi$
$601$	−1960.53	−	3395.74i	−0.133065	−	0.230475i	−0.924856	+	0.380316i	$0.875815\pi$
$602$	41213.5			2.79026
$603$	−1055.25	−	4821.64i	−0.0712657	−	0.325626i
$604$	−23981.5			−1.61555
$605$	−421.457	−	729.985i	−0.0283218	−	0.0490547i
$606$	24247.5			1.62539
$607$	7931.92	−	13738.5i	0.530390	−	0.918663i	−0.468981	−	0.883208i	$-0.655379\pi$
$607$	7931.92	−	13738.5i	0.530390	−	0.918663i	0.999371	−	0.0354545i	$-0.0112879\pi$
$608$	12493.7			0.833369
$609$	6950.22	+	12038.1i	0.462458	+	0.801002i
$610$	543.735	−	941.777i	0.0360905	−	0.0625105i
$611$	−7570.99			−0.501292
$612$	−20870.1			−1.37847
$613$	−9552.30	−	16545.1i	−0.629386	−	1.09013i	−0.987675	−	0.156518i	$-0.949973\pi$
$613$	−9552.30	−	16545.1i	−0.629386	−	1.09013i	0.358289	−	0.933611i	$-0.383360\pi$
$614$	−7208.16	+	12484.9i	−0.473775	+	0.820602i
$615$	223.225	−	386.636i	0.0146362	−	0.0253507i
$616$	−36091.7	−	62512.7i	−2.36068	−	4.08881i
$617$	5713.17			0.372777			0.186389	−	0.982476i	$-0.440322\pi$
$617$	5713.17			0.372777			0.186389	+	0.982476i	$0.440322\pi$
$618$	4693.17			0.305481
$619$	−568.525	−	984.713i	−0.0369159	−	0.0639402i	0.846977	−	0.531629i	$-0.178420\pi$
$619$	−568.525	−	984.713i	−0.0369159	−	0.0639402i	−0.883893	+	0.467689i	$0.845087\pi$
$620$	356.256	+	617.053i	0.0230767	+	0.0399701i
$621$	−352.328	−	610.249i	−0.0227672	−	0.0394339i
$622$	−15643.4	−	27095.1i	−1.00843	−	1.74665i
$623$	4102.00	−	7104.87i	0.263793	−	0.456903i
$624$	5412.59	−	9374.88i	0.347239	−	0.601435i
$625$	15581.5			0.997214
$626$	21023.7	+	36414.1i	1.34229	+	2.32492i
$627$	17907.4			1.14059
$628$	37251.4			2.36703
$629$	549.905	−	952.464i	0.0348588	−	0.0603772i
$630$	−379.239			−0.0239829
$631$	415.182	+	719.116i	0.0261936	+	0.0453686i	0.878825	−	0.477144i	$-0.158328\pi$
$631$	415.182	+	719.116i	0.0261936	+	0.0453686i	−0.852631	+	0.522513i	$0.824995\pi$
$632$	−26365.7	+	45666.7i	−1.65945	+	2.87425i
$633$	−2139.06	−	3704.96i	−0.134313	−	0.232637i
$634$	13864.7	−	24014.4i	0.868515	−	1.50431i
$635$	−54.5568	+	94.4951i	−0.00340948	+	0.00590539i
$636$	−10337.6	+	17905.3i	−0.644517	+	1.11634i
$637$	−4583.85	+	7939.47i	−0.285116	+	0.493835i
$638$	−29429.3	+	50973.0i	−1.82620	+	3.16308i
$639$	950.989	−	1647.16i	0.0588741	−	0.101973i
$640$	312.654	+	541.533i	0.0193105	+	0.0334468i
$641$	−2236.69	+	3874.06i	−0.137822	+	0.238715i	−0.926672	−	0.375871i	$-0.877344\pi$
$641$	−2236.69	+	3874.06i	−0.137822	+	0.238715i	0.788850	+	0.614586i	$0.210677\pi$
$642$	−2716.32	−	4704.81i	−0.166985	−	0.289227i
$643$	13707.6			0.840705			0.420352	−	0.907361i	$-0.361906\pi$
$643$	13707.6			0.840705			0.420352	+	0.907361i	$0.361906\pi$
$644$	−5584.17	+	9672.06i	−0.341688	+	0.591821i
$645$	340.776			0.0208032
$646$	−64841.7			−3.94917
$647$	6096.09	+	10558.7i	0.370420	+	0.641587i	0.989630	−	0.143639i	$-0.0458803\pi$
$647$	6096.09	+	10558.7i	0.370420	+	0.641587i	−0.619210	+	0.785225i	$0.712547\pi$
$648$	3868.73			0.234534
$649$	−6685.76	+	11580.1i	−0.404374	+	0.700397i
$650$	11223.9	−	19440.3i	0.677287	−	1.17310i
$651$	4399.88	+	7620.81i	0.264892	+	0.458806i
$652$	5387.58	+	9331.56i	0.323610	+	0.560510i
$653$	−15086.1	−	26129.9i	−0.904082	−	1.56592i	−0.822145	−	0.569279i	$-0.807223\pi$
$653$	−15086.1	−	26129.9i	−0.904082	−	1.56592i	−0.0819373	−	0.996637i	$-0.526111\pi$
$654$	2710.83	+	4695.29i	0.162082	+	0.280734i
$655$	774.716			0.0462147
$656$	44236.3			2.63283
$657$	−4485.28	−	7768.74i	−0.266343	−	0.461320i
$658$	−13140.4	+	22759.8i	−0.778519	+	1.34843i
$659$	10893.4	−	18867.9i	0.643924	−	1.11531i	−0.340624	−	0.940199i	$-0.610638\pi$
$659$	10893.4	−	18867.9i	0.643924	−	1.11531i	0.984549	−	0.175110i	$-0.0560282\pi$
$660$	−550.666	−	953.781i	−0.0324767	−	0.0562513i
$661$	8483.39			0.499191			0.249596	−	0.968350i	$-0.419702\pi$
$661$	8483.39			0.499191			0.249596	+	0.968350i	$0.419702\pi$
$662$	−16879.1			−0.990977
$663$	−7094.21	+	12287.5i	−0.415560	+	0.719771i
$664$	−18841.7	−	32634.8i	−1.10120	−	1.90734i
$665$	−808.105			−0.0471233
$666$	−188.098	+	325.795i	−0.0109439	+	0.0189554i
$667$	4935.25			0.286497
$668$	−11069.5	−	19172.9i	−0.641153	−	1.11051i
$669$	5003.51			0.289158
$670$	−697.071	+	635.286i	−0.0401943	+	0.0366317i
$671$	39003.2			2.24397
$672$	−4744.90	−	8218.41i	−0.272379	−	0.471774i
$673$	−5739.39			−0.328733			−0.164366	−	0.986399i	$-0.552558\pi$
$673$	−5739.39			−0.328733			−0.164366	+	0.986399i	$0.552558\pi$
$674$	−18414.9	+	31895.6i	−1.05240	+	1.82281i
$675$	3371.86			0.192271
$676$	8105.46	+	14039.1i	0.461166	+	0.798763i
$677$	10175.0	−	17623.6i	0.577630	−	1.00049i	−0.418120	−	0.908392i	$-0.637311\pi$
$677$	10175.0	−	17623.6i	0.577630	−	1.00049i	0.995750	−	0.0920935i	$-0.0293559\pi$
$678$	−18956.9			−1.07380
$679$	10377.2			0.586511
$680$	1080.59	+	1871.63i	0.0609391	+	0.105550i
$681$	8375.24	−	14506.3i	0.471277	−	0.816276i
$682$	−18630.4	+	32268.8i	−1.04603	+	1.81178i
$683$	−10461.6	−	18120.1i	−0.586095	−	1.01515i	−0.994738	−	0.102452i	$-0.967331\pi$
$683$	−10461.6	−	18120.1i	−0.586095	−	1.01515i	0.408643	−	0.912694i	$-0.366002\pi$
$684$	15211.6			0.850336
$685$	473.510			0.0264115
$686$	−5293.67	−	9168.91i	−0.294626	−	0.510307i
$687$	−5504.80	−	9534.59i	−0.305708	−	0.529501i
$688$	16882.8	+	29241.9i	0.935541	+	1.62041i
$689$	7027.98	+	12172.8i	0.388599	+	0.673073i
$690$	−67.3231	+	116.607i	−0.00371441	+	0.00643355i
$691$	−896.312	+	1552.46i	−0.0493449	+	0.0854678i	−0.889643	−	0.456657i	$-0.849047\pi$
$691$	−896.312	+	1552.46i	−0.0493449	+	0.0854678i	0.840298	+	0.542125i	$0.182380\pi$
$692$	−15513.1			−0.852198
$693$	−6800.90	−	11779.5i	−0.372792	−	0.645695i
$694$	39619.7			2.16707
$695$	36.9615			0.00201731
$696$	−13547.9	+	23465.6i	−0.737832	+	1.27796i
$697$	−57980.0			−3.15086
$698$	−3655.55	−	6331.60i	−0.198230	−	0.343345i
$699$	−9408.82	+	16296.5i	−0.509119	+	0.881820i
$700$	−26720.9	−	46282.0i	−1.44280	−	2.49900i
$701$	−3317.35	+	5745.83i	−0.178737	+	0.309582i	−0.941448	−	0.337158i	$-0.890534\pi$
$701$	−3317.35	+	5745.83i	−0.178737	+	0.309582i	0.762711	+	0.646739i	$0.223868\pi$
$702$	2426.61	−	4203.02i	0.130465	−	0.225972i
$703$	−400.811	+	694.224i	−0.0215033	+	0.0372449i
$704$	−4901.81	+	8490.18i	−0.262420	+	0.454525i
$705$	−108.652	+	188.191i	−0.00580435	+	0.0100534i
$706$	3553.63	−	6155.06i	0.189437	−	0.328115i
$707$	−19622.6	−	33987.3i	−1.04382	−	1.80795i
$708$	−5679.28	+	9836.80i	−0.301470	+	0.522161i
$709$	−13098.6	−	22687.5i	−0.693836	−	1.20176i	−0.970571	−	0.240813i	$-0.922586\pi$
$709$	−13098.6	−	22687.5i	−0.693836	−	1.20176i	0.276735	−	0.960946i	$-0.410747\pi$
$710$	−363.432			−0.0192104
$711$	−4968.19	+	8605.16i	−0.262056	+	0.453894i
$712$	15991.8			0.841741
$713$	3124.29			0.164103
$714$	24625.7	+	42653.0i	1.29075	+	2.23564i
$715$	−748.735			−0.0391624
$716$	−28837.9	+	49948.7i	−1.50520	+	2.60708i
$717$	−8621.26	+	14932.5i	−0.449047	+	0.777773i
$718$	16272.6	+	28185.0i	0.845806	+	1.46498i
$719$	−1300.30	−	2252.19i	−0.0674452	−	0.116819i	0.830331	−	0.557271i	$-0.188151\pi$
$719$	−1300.30	−	2252.19i	−0.0674452	−	0.116819i	−0.897776	+	0.440452i	$0.854818\pi$
$720$	−155.353	−	269.079i	−0.00804120	−	0.0139278i
$721$	−3798.01	−	6578.34i	−0.196179	−	0.339792i
$722$	12649.0			0.652002
$723$	−5832.73			−0.300030
$724$	15909.2	+	27555.6i	0.816659	+	1.41450i
$725$	−11807.9	+	20451.9i	−0.604875	+	1.04767i
$726$	18722.2	−	32427.7i	0.957086	−	1.65772i
$727$	−3202.00	−	5546.02i	−0.163350	−	0.282931i	0.772718	−	0.634749i	$-0.218897\pi$
$727$	−3202.00	−	5546.02i	−0.163350	−	0.282931i	−0.936068	+	0.351819i	$0.885563\pi$
$728$	−41686.0			−2.12224
$729$	729.000			0.0370370
$730$	−857.052	+	1484.46i	−0.0434533	+	0.0752633i
$731$	−22128.1	−	38327.0i	−1.11961	−	1.93923i
$732$	33131.7			1.67293
$733$	18206.7	−	31534.9i	0.917434	−	1.58904i	0.114135	−	0.993465i	$-0.463590\pi$
$733$	18206.7	−	31534.9i	0.917434	−	1.58904i	0.803299	−	0.595576i	$-0.203076\pi$
$734$	−63960.7			−3.21639
$735$	131.566	+	227.880i	0.00660259	+	0.0114360i
$736$	−3369.28			−0.168741
$737$	−32233.1	−	10259.0i	−1.61102	−	0.512750i
$738$	19832.4			0.989213
$739$	17932.8	+	31060.6i	0.892652	+	1.54612i	0.836684	+	0.547686i	$0.184491\pi$
$739$	17932.8	+	31060.6i	0.892652	+	1.54612i	0.0559683	+	0.998433i	$0.482175\pi$
$740$	49.3010			0.00244911
$741$	5170.77	−	8956.03i	0.256347	−	0.444006i
$742$	48791.7			2.41401
$743$	8894.74	+	15406.1i	0.439188	+	0.760695i	0.997627	−	0.0688500i	$-0.0219330\pi$
$743$	8894.74	+	15406.1i	0.439188	+	0.760695i	−0.558439	+	0.829545i	$0.688600\pi$
$744$	−8576.56	+	14855.0i	−0.422624	+	0.732006i
$745$	−743.676			−0.0365720
$746$	65030.7			3.19161
$747$	−3550.41	−	6149.49i	−0.173899	−	0.301202i
$748$	−71514.5	+	123867.i	−3.49576	+	6.05484i
$749$	−4396.43	+	7614.84i	−0.214475	+	0.371482i
$750$	−644.598	−	1116.48i	−0.0313832	−	0.0543573i
$751$	9828.54			0.477561			0.238781	−	0.971074i	$-0.423252\pi$
$751$	9828.54			0.477561			0.238781	+	0.971074i	$0.423252\pi$
$752$	−21531.5			−1.04411
$753$	−151.617	−	262.607i	−0.00733760	−	0.0127091i
$754$	16995.5	+	29437.0i	0.820873	+	1.42179i
$755$	233.976	+	405.258i	0.0112785	+	0.0195349i
$756$	−5777.09	−	10006.2i	−0.277924	−	0.481379i
$757$	583.782	−	1011.14i	0.0280290	−	0.0485476i	−0.851671	−	0.524077i	$-0.824410\pi$
$757$	583.782	−	1011.14i	0.0280290	−	0.0485476i	0.879700	+	0.475530i	$0.157744\pi$
$758$	14318.5	−	24800.3i	0.686108	−	1.18837i
$759$	−4829.22			−0.230948
$760$	−787.609	−	1364.18i	−0.0375916	−	0.0651105i
$761$	12608.6			0.600604			0.300302	−	0.953844i	$-0.402913\pi$
$761$	12608.6			0.600604			0.300302	+	0.953844i	$0.402913\pi$
$762$	−4847.09			−0.230435
$763$	4387.54	−	7599.44i	0.208178	−	0.360574i
$764$	−39747.2			−1.88220
$765$	203.619	+	352.679i	0.00962335	+	0.0166681i
$766$	−14272.0	+	24719.9i	−0.673199	+	1.16601i
$767$	3861.03	+	6687.51i	0.181765	+	0.314826i
$768$	−11981.5	+	20752.6i	−0.562952	+	0.975061i
$769$	−1199.95	+	2078.38i	−0.0562697	+	0.0974619i	−0.892788	−	0.450477i	$-0.851254\pi$
$769$	−1199.95	+	2078.38i	−0.0562697	+	0.0974619i	0.836518	+	0.547939i	$0.184587\pi$
$770$	−1299.52	+	2250.84i	−0.0608202	+	0.105344i
$771$	−8.32146	+	14.4132i	−0.000388703	+	0.000673253i
$772$	27951.4	−	48413.2i	1.30310	−	2.25703i
$773$	−13679.5	+	23693.5i	−0.636503	+	1.10245i	0.349692	+	0.936865i	$0.386286\pi$
$773$	−13679.5	+	23693.5i	−0.636503	+	1.10245i	−0.986195	+	0.165590i	$0.947047\pi$
$774$	7569.05	+	13110.0i	0.351504	+	0.608822i
$775$	−7475.06	+	12947.2i	−0.346467	+	0.600099i
$776$	10114.0	+	17518.0i	0.467876	+	0.810386i
$777$	608.883			0.0281127
$778$	−14652.9	+	25379.5i	−0.675232	+	1.16954i
$779$	42260.0			1.94367
$780$	−636.021			−0.0291964
$781$	−6517.42	−	11288.5i	−0.298607	−	0.517202i
$782$	17486.4			0.799631
$783$	−2552.88	+	4421.72i	−0.116517	+	0.201813i
$784$	−13036.2	+	22579.4i	−0.593852	+	1.02858i
$785$	−363.444	−	629.504i	−0.0165247	−	0.0286216i
$786$	17207.4	+	29804.0i	0.780874	+	1.35251i
$787$	7262.79	+	12579.5i	0.328959	+	0.569773i	0.982306	−	0.187285i	$-0.0599689\pi$
$787$	7262.79	+	12579.5i	0.328959	+	0.569773i	−0.653347	+	0.757059i	$0.726636\pi$
$788$	−4869.26	−	8433.80i	−0.220127	−	0.381271i
$789$	−4179.21			−0.188573
$790$	1898.65			0.0855076
$791$	15341.1	+	26571.6i	0.689591	+	1.19441i
$792$	13256.8	−	22961.5i	0.594773	−	1.03018i
$793$	11262.2	−	19506.7i	0.504329	−	0.873523i
$794$	−31480.1	−	54525.1i	−1.40704	−	2.43706i
$795$	403.436			0.0179980
$796$	40068.4			1.78415
$797$	−974.356	+	1687.63i	−0.0433042	+	0.0750051i	−0.886865	−	0.462028i	$-0.847122\pi$
$797$	−974.356	+	1687.63i	−0.0433042	+	0.0750051i	0.843561	+	0.537034i	$0.180455\pi$
$798$	−17949.0	−	31088.6i	−0.796225	−	1.37910i
$799$	28221.1			1.24955
$800$	8061.23	−	13962.5i	0.356259	−	0.617059i
$801$	3013.40			0.132926
$802$	6012.10	+	10413.3i	0.264707	+	0.458485i
$803$	−61478.1			−2.70176
$804$	−27380.7	−	8714.64i	−1.20105	−	0.382266i
$805$	217.928			0.00954156
$806$	10759.1	+	18635.3i	0.470189	+	0.814391i
$807$	−10733.5			−0.468198
$808$	38249.7	−	66250.5i	1.66537	−	2.88451i
$809$	19569.6			0.850471			0.425235	−	0.905083i	$-0.360191\pi$
$809$	19569.6			0.850471			0.425235	+	0.905083i	$0.360191\pi$
$810$	−69.6490	−	120.636i	−0.00302125	−	0.00523297i
$811$	13267.3	−	22979.6i	0.574447	−	0.994971i	−0.421655	−	0.906757i	$-0.638551\pi$
$811$	13267.3	−	22979.6i	0.574447	−	0.994971i	0.996101	−	0.0882147i	$-0.0281162\pi$
$812$	80923.0			3.49734
$813$	−4508.34			−0.194482
$814$	1289.09	+	2232.78i	0.0555071	+	0.0961411i
$815$	105.128	−	182.087i	0.00451837	−	0.00782605i
$816$	−20175.5	+	34945.1i	−0.865546	+	1.49917i
$817$	16128.6	+	27935.5i	0.690658	+	1.19625i
$818$	24321.2			1.03958
$819$	−7855.06			−0.335138
$820$	−1299.53	−	2250.85i	−0.0553432	−	0.0958573i
$821$	−175.579	−	304.112i	−0.00746377	−	0.0129276i	0.862269	−	0.506450i	$-0.169042\pi$
$821$	−175.579	−	304.112i	−0.00746377	−	0.0129276i	−0.869733	+	0.493522i	$0.835709\pi$
$822$	10517.2	+	18216.4i	0.446266	+	0.772956i
$823$	−5094.23	−	8823.47i	−0.215764	−	0.373714i	0.737745	−	0.675080i	$-0.235891\pi$
$823$	−5094.23	−	8823.47i	−0.215764	−	0.373714i	−0.953509	+	0.301366i	$0.902557\pi$
$824$	7403.35	−	12823.0i	0.312995	−	0.542123i
$825$	11554.2	−	20012.5i	0.487595	−	0.844540i
$826$	26805.2			1.12914
$827$	5336.02	+	9242.26i	0.224367	+	0.388615i	0.956129	−	0.292945i	$-0.0946352\pi$
$827$	5336.02	+	9242.26i	0.224367	+	0.388615i	−0.731762	+	0.681560i	$0.761302\pi$
$828$	−4102.23			−0.172177
$829$	−38266.5			−1.60320			−0.801599	−	0.597862i	$-0.796017\pi$
$829$	−38266.5			−1.60320			−0.801599	+	0.597862i	$0.796017\pi$
$830$	−678.416	+	1175.05i	−0.0283713	+	0.0491405i
$831$	2535.08			0.105826
$832$	2830.80	+	4903.09i	0.117957	+	0.204308i
$833$	17086.4	−	29594.6i	0.710696	−	1.23096i
$834$	820.960	+	1421.94i	0.0340857	+	0.0590382i
$835$	−215.999	+	374.121i	−0.00895203	+	0.0155054i
$836$	52124.9	−	90283.0i	2.15643	−	3.73505i
$837$	−1616.11	+	2799.19i	−0.0667396	+	0.115596i
$838$	−15754.7	+	27287.9i	−0.649447	+	1.12488i
$839$	−20811.5	+	36046.6i	−0.856368	+	1.48327i	0.0190018	+	0.999819i	$0.493951\pi$
$839$	−20811.5	+	36046.6i	−0.856368	+	1.48327i	−0.875370	+	0.483454i	$0.839382\pi$
$840$	−598.240	+	1036.18i	−0.0245729	+	0.0425615i
$841$	−5685.31	−	9847.25i	−0.233110	−	0.403758i
$842$	3784.34	−	6554.67i	0.154890	−	0.268277i
$843$	6699.48	+	11603.8i	0.273716	+	0.474090i
$844$	−24905.6			−1.01574
$845$	158.162	−	273.945i	0.00643898	−	0.0111526i
$846$	−9653.16			−0.392296
$847$	−60604.5			−2.45855
$848$	19987.2	+	34618.8i	0.809390	+	1.40191i
$849$	1842.95			0.0744994
$850$	−41837.3	+	72464.3i	−1.68824	+	2.92412i
$851$	108.090	−	187.217i	0.00435401	−	0.00754137i
$852$	−5536.29	−	9589.14i	−0.222618	−	0.385585i
$853$	7684.14	+	13309.3i	0.308441	+	0.534235i	0.978021	−	0.208504i	$-0.0668596\pi$
$853$	7684.14	+	13309.3i	0.308441	+	0.534235i	−0.669581	+	0.742739i	$0.733526\pi$
$854$	−39093.9	−	67712.6i	−1.56647	−	2.71321i
$855$	−148.412	−	257.057i	−0.00593636	−	0.0102821i
$856$	−17139.7			−0.684372
$857$	−10714.8			−0.427084			−0.213542	−	0.976934i	$-0.568500\pi$
$857$	−10714.8			−0.427084			−0.213542	+	0.976934i	$0.568500\pi$
$858$	−16630.3	−	28804.6i	−0.661713	−	1.14612i
$859$	−2390.48	+	4140.43i	−0.0949500	+	0.164458i	−0.909588	−	0.415512i	$-0.863602\pi$
$859$	−2390.48	+	4140.43i	−0.0949500	+	0.164458i	0.814638	+	0.579970i	$0.196936\pi$
$860$	991.932	−	1718.08i	0.0393309	−	0.0681232i
$861$	−16049.6	−	27798.7i	−0.635271	−	1.10032i
$862$	−61861.3			−2.44432
$863$	−2080.67			−0.0820704			−0.0410352	−	0.999158i	$-0.513066\pi$
$863$	−2080.67			−0.0820704			−0.0410352	+	0.999158i	$0.513066\pi$
$864$	1742.84	−	3018.70i	0.0686259	−	0.118864i
$865$	151.354	+	262.153i	0.00594936	+	0.0103046i
$866$	−54482.9			−2.13788
$867$	19074.3	−	33037.7i	0.747172	−	1.29414i
$868$	51228.7			2.00325
$869$	34048.5	+	58973.8i	1.32913	+	2.30213i
$870$	975.613			0.0380188
$871$	−14438.2	+	13158.5i	−0.561676	+	0.511892i
$872$	17105.0			0.664276
$873$	1905.82	+	3300.98i	0.0738858	+	0.127974i
$874$	−12745.3			−0.493269
$875$	−1043.30	+	1807.05i	−0.0403085	+	0.0698163i
$876$	−52223.2			−2.01422
$877$	−20190.1	−	34970.2i	−0.777389	−	1.34648i	−0.933442	−	0.358729i	$-0.883210\pi$
$877$	−20190.1	−	34970.2i	−0.777389	−	1.34648i	0.156052	−	0.987749i	$-0.450123\pi$
$878$	−10717.6	+	18563.4i	−0.411961	+	0.713537i
$879$	4328.62			0.166099
$880$	−2129.36			−0.0815691
$881$	−14595.1	−	25279.5i	−0.558142	−	0.966730i	−0.997652	−	0.0684922i	$-0.978181\pi$
$881$	−14595.1	−	25279.5i	−0.558142	−	0.966730i	0.439510	−	0.898238i	$-0.355152\pi$
$882$	−5844.50	+	10123.0i	−0.223123	+	0.386461i
$883$	24982.3	−	43270.7i	0.952121	−	1.64912i	0.211296	−	0.977422i	$-0.432231\pi$
$883$	24982.3	−	43270.7i	0.952121	−	1.64912i	0.740824	−	0.671699i	$-0.234435\pi$
$884$	41299.7	+	71533.2i	1.57134	+	2.72163i
$885$	221.640			0.00841847
$886$	−43121.2			−1.63508
$887$	−16626.6	−	28798.2i	−0.629389	−	1.09013i	−0.987674	−	0.156522i	$-0.949972\pi$
$887$	−16626.6	−	28798.2i	−0.629389	−	1.09013i	0.358285	−	0.933612i	$-0.383362\pi$
$888$	593.439	+	1027.87i	0.0224263	+	0.0388434i
$889$	3922.57	+	6794.08i	0.147985	+	0.256317i
$890$	−287.902	−	498.661i	−0.0108432	−	0.0187811i
$891$	2498.03	−	4326.72i	0.0939251	−	0.162683i
$892$	14564.3	−	25226.0i	0.546690	−	0.946894i
$893$	−20569.5			−0.770810
$894$	−16517.9	−	28609.9i	−0.617945	−	1.07031i
$895$	1125.43			0.0420323
$896$	44958.9			1.67631
$897$	−1394.44	+	2415.24i	−0.0519053	+	0.0899026i
$898$	46897.8			1.74276
$899$	−11318.9	−	19604.9i	−0.419919	−	0.727320i
$900$	9814.84	−	16999.8i	0.363513	−	0.629623i
$901$	−26197.0	−	45374.5i	−0.968643	−	1.67774i
$902$	67958.7	−	117708.i	2.50862	−	4.34506i
$903$	12250.7	−	21218.8i	0.451470	−	0.781969i
$904$	−29904.0	+	51795.2i	−1.10021	+	1.90562i
$905$	310.437	−	537.693i	0.0114025	−	0.0197497i
$906$	−10393.8	+	18002.6i	−0.381137	+	0.660149i
$907$	−10085.7	+	17468.9i	−0.369228	+	0.639521i	−0.989445	−	0.144909i	$-0.953711\pi$
$907$	−10085.7	+	17468.9i	−0.369228	+	0.639521i	0.620217	+	0.784430i	$0.287044\pi$
$908$	−48757.4	−	84450.3i	−1.78202	−	3.08654i
$909$	7207.54	−	12483.8i	0.262991	−	0.455514i
$910$	750.476	+	1299.86i	0.0273385	+	0.0473517i
$911$	−15836.8			−0.575958			−0.287979	−	0.957637i	$-0.592983\pi$
$911$	−15836.8			−0.575958			−0.287979	+	0.957637i	$0.592983\pi$
$912$	14705.4	−	25470.5i	0.533930	−	0.924794i
$913$	−48664.2			−1.76402
$914$	−12489.3			−0.451980
$915$	−323.250	−	559.885i	−0.0116790	−	0.0202287i
$916$	−64093.6			−2.31191
$917$	27850.6	−	48238.6i	1.00295	−	1.73716i
$918$	−9045.25	+	15666.8i	−0.325205	+	0.563271i
$919$	6100.13	+	10565.7i	0.218961	+	0.379251i	0.954490	−	0.298241i	$-0.0964000\pi$
$919$	6100.13	+	10565.7i	0.218961	+	0.379251i	−0.735530	+	0.677492i	$0.763067\pi$
$920$	212.401	+	367.889i	0.00761157	+	0.0131836i
$921$	4285.24	+	7422.25i	0.153315	+	0.265550i
$922$	−35898.8	−	62178.6i	−1.28228	−	2.22098i
$923$	−7527.64			−0.268446
$924$	−79184.4			−2.81924
$925$	517.223	+	895.856i	0.0183851	+	0.0318439i
$926$	28695.4	−	49701.9i	1.01835	−	1.76383i
$927$	1395.04	−	2416.28i	0.0494274	−	0.0856107i
$928$	12206.5	+	21142.3i	0.431787	+	0.747877i
$929$	41262.9			1.45726			0.728629	−	0.684909i	$-0.240158\pi$
$929$	41262.9			1.45726			0.728629	+	0.684909i	$0.240158\pi$
$930$	617.617			0.0217768
$931$	−12453.8	+	21570.6i	−0.438407	+	0.759344i
$932$	54774.5	+	94872.2i	1.92511	+	3.33438i
$933$	−18599.9			−0.652663
$934$	−2393.89	+	4146.34i	−0.0838656	+	0.145259i
$935$	2790.93			0.0976184
$936$	−7655.83	−	13260.3i	−0.267349	−	0.463062i
$937$	−10573.9			−0.368661			−0.184330	−	0.982864i	$-0.559012\pi$
$937$	−10573.9			−0.368661			−0.184330	+	0.982864i	$0.559012\pi$
$938$	14497.6	+	66242.1i	0.504651	+	2.30584i
$939$	24997.1			0.868742
$940$	632.529	+	1095.57i	0.0219477	+	0.0380145i
$941$	−36696.8			−1.27129			−0.635644	−	0.771982i	$-0.719265\pi$
$941$	−36696.8			−1.27129			−0.635644	+	0.771982i	$0.719265\pi$
$942$	16145.1	−	27964.1i	0.558424	−	0.967218i
$943$	−11396.6			−0.393556
$944$	10980.6	+	19018.9i	0.378588	+	0.655734i
$945$	−112.729	+	195.252i	−0.00388049	+	0.00672120i
$946$	103746.			3.56562
$947$	−35902.7			−1.23197			−0.615987	−	0.787756i	$-0.711243\pi$
$947$	−35902.7			−1.23197			−0.615987	+	0.787756i	$0.711243\pi$
$948$	28922.9	+	50095.9i	0.990898	+	1.71629i
$949$	−17751.8	+	30747.1i	−0.607217	+	1.05173i
$950$	30494.0	−	52817.2i	1.04143	−	1.80381i
$951$	−8242.55	−	14276.5i	−0.281055	−	0.486801i
$952$	155386.			5.29000
$953$	55691.5			1.89300			0.946498	−	0.322709i	$-0.104593\pi$
$953$	55691.5			1.89300			0.946498	+	0.322709i	$0.104593\pi$
$954$	8960.81	+	15520.6i	0.304106	+	0.526727i
$955$	387.794	+	671.679i	0.0131400	+	0.0227592i
$956$	50189.7	+	86931.0i	1.69796	+	2.94095i
$957$	17495.7	+	30303.4i	0.590966	+	1.02358i
$958$	−44636.1	+	77311.9i	−1.50535	+	2.60734i
$959$	17022.4	−	29483.7i	0.573183	−	0.992782i
$960$	162.500			0.00546320
$961$	7730.00	+	13388.8i	0.259474	+	0.449423i
$962$	1488.91			0.0499006
$963$	−3229.70			−0.108074
$964$	−16977.9	+	29406.7i	−0.567244	+	0.982495i
$965$	−1090.83			−0.0363887
$966$	4840.45	+	8383.90i	0.161220	+	0.279242i
$967$	−29347.9	+	50832.0i	−0.975970	+	1.69043i	−0.299276	+	0.954167i	$0.596745\pi$
$967$	−29347.9	+	50832.0i	−0.975970	+	1.69043i	−0.676695	+	0.736264i	$0.736588\pi$
$968$	−59067.4	−	102308.i	−1.96126	−	3.39700i
$969$	−19274.2	+	33383.8i	−0.638984	+	1.10675i
$970$	364.166	−	630.755i	0.0120543	−	0.0208787i
$971$	−16936.7	+	29335.2i	−0.559757	+	0.969528i	0.437759	+	0.899092i	$0.355772\pi$
$971$	−16936.7	+	29335.2i	−0.559757	+	0.969528i	−0.997516	+	0.0704355i	$0.977561\pi$
$972$	2121.98	−	3675.37i	0.0700231	−	0.121284i
$973$	1328.74	−	2301.45i	0.0437796	−	0.0758285i
$974$	25047.9	−	43384.2i	0.824011	−	1.42723i
$975$	−6672.58	−	11557.2i	−0.219173	−	0.379618i
$976$	32029.1	−	55476.1i	1.05044	−	1.81941i
$977$	22921.6	+	39701.4i	0.750590	+	1.30006i	0.947537	+	0.319646i	$0.103564\pi$
$977$	22921.6	+	39701.4i	0.750590	+	1.30006i	−0.196947	+	0.980414i	$0.563103\pi$
$978$	9340.09			0.305381
$979$	10325.9	−	17885.0i	0.337096	−	0.583867i
$980$	1531.86			0.0499321
$981$	3223.16			0.104901
$982$	18990.7	+	32892.8i	0.617125	+	1.06889i
$983$	4257.07			0.138128			0.0690638	−	0.997612i	$-0.477999\pi$
$983$	4257.07			0.138128			0.0690638	+	0.997612i	$0.477999\pi$
$984$	31285.0	−	54187.2i	1.01355	−	1.75551i
$985$	−95.0139	+	164.569i	−0.00307350	+	0.00532346i
$986$	−63351.0	−	109727.i	−2.04615	−	3.54404i
$987$	7811.94	+	13530.7i	0.251932	+	0.436359i
$988$	−30102.2	−	52138.6i	−0.969311	−	1.67890i
$989$	−4349.52	−	7533.58i	−0.139845	−	0.242218i
$990$	−954.652			−0.0306473
$991$	34397.2			1.10259			0.551293	−	0.834311i	$-0.314135\pi$
$991$	34397.2			1.10259			0.551293	+	0.834311i	$0.314135\pi$
$992$	7727.39	+	13384.2i	0.247324	+	0.428377i
$993$	−5017.31	+	8690.24i	−0.160342	+	0.277720i
$994$	−13065.2	+	22629.5i	−0.416903	+	0.722097i
$995$	−390.928	−	677.107i	−0.0124555	−	0.0215736i
$996$	−41338.2			−1.31511
$997$	32893.9			1.04489			0.522447	−	0.852672i	$-0.325019\pi$
$997$	32893.9			1.04489			0.522447	+	0.852672i	$0.325019\pi$
$998$	51133.9	−	88566.5i	1.62186	−	2.80914i
$999$	111.824	+	193.685i	0.00354150	+	0.00613405i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.e.b.37.2	✓	36
67.29	even	3	inner	201.4.e.b.163.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.e.b.37.2	✓	36	1.1	even	1	trivial
201.4.e.b.163.2	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)

\(f(q)\)	\(=\)	\(q+(-2.52313 - 4.37020i) q^{2} -3.00000 q^{3} +(-8.73242 + 15.1250i) q^{4} +0.340792 q^{5} +(7.56940 + 13.1106i) q^{6} +(12.2513 - 21.2198i) q^{7} +47.7621 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+(-2.52313 - 4.37020i) q^{2} -3.00000 q^{3} +(-8.73242 + 15.1250i) q^{4} +0.340792 q^{5} +(7.56940 + 13.1106i) q^{6} +(12.2513 - 21.2198i) q^{7} +47.7621 q^{8} +9.00000 q^{9} +(-0.859864 - 1.48933i) q^{10} +(30.8399 - 53.4163i) q^{11} +(26.1973 - 45.3750i) q^{12} +(-17.8101 - 30.8480i) q^{13} -123.646 q^{14} -1.02238 q^{15} +(-50.6509 - 87.7300i) q^{16} +(66.3875 + 114.987i) q^{17} +(-22.7082 - 39.3318i) q^{18} +(-48.3880 - 83.8105i) q^{19} +(-2.97594 + 5.15448i) q^{20} +(-36.7538 + 63.6594i) q^{21} -311.253 q^{22} +(13.0492 + 22.6018i) q^{23} -143.286 q^{24} -124.884 q^{25} +(-89.8745 + 155.667i) q^{26} -27.0000 q^{27} +(213.966 + 370.601i) q^{28} +(94.5511 - 163.767i) q^{29} +(2.57959 + 4.46798i) q^{30} +(59.8561 - 103.674i) q^{31} +(-64.5498 + 111.804i) q^{32} +(-92.5197 + 160.249i) q^{33} +(335.009 - 580.253i) q^{34} +(4.17513 - 7.23154i) q^{35} +(-78.5918 + 136.125i) q^{36} +(-4.14163 - 7.17352i) q^{37} +(-244.179 + 422.930i) q^{38} +(53.4303 + 92.5439i) q^{39} +16.2769 q^{40} +(-218.339 + 378.174i) q^{41} +370.939 q^{42} -333.318 q^{43} +(538.614 + 932.907i) q^{44} +3.06713 q^{45} +(65.8496 - 114.055i) q^{46} +(106.274 - 184.072i) q^{47} +(151.953 + 263.190i) q^{48} +(-128.687 - 222.892i) q^{49} +(315.099 + 545.767i) q^{50} +(-199.163 - 344.960i) q^{51} +622.101 q^{52} -394.607 q^{53} +(68.1246 + 117.995i) q^{54} +(10.5100 - 18.2038i) q^{55} +(585.147 - 1013.50i) q^{56} +(145.164 + 251.431i) q^{57} -954.260 q^{58} -216.789 q^{59} +(8.92781 - 15.4634i) q^{60} +(316.175 + 547.631i) q^{61} -604.100 q^{62} +(110.261 - 190.978i) q^{63} -158.944 q^{64} +(-6.06954 - 10.5127i) q^{65} +933.759 q^{66} +(-117.250 - 535.738i) q^{67} -2318.90 q^{68} +(-39.1475 - 67.8055i) q^{69} -42.1377 q^{70} +(105.665 - 183.018i) q^{71} +429.859 q^{72} +(-498.365 - 863.193i) q^{73} +(-20.8998 + 36.1995i) q^{74} +374.652 q^{75} +1690.18 q^{76} +(-755.656 - 1308.83i) q^{77} +(269.624 - 467.002i) q^{78} +(-552.021 + 956.128i) q^{79} +(-17.2614 - 29.8977i) q^{80} +81.0000 q^{81} +2203.60 q^{82} +(-394.490 - 683.277i) q^{83} +(-641.899 - 1111.80i) q^{84} +(22.6243 + 39.1865i) q^{85} +(841.005 + 1456.66i) q^{86} +(-283.653 + 491.302i) q^{87} +(1472.98 - 2551.28i) q^{88} +334.823 q^{89} +(-7.73878 - 13.4040i) q^{90} -872.785 q^{91} -455.803 q^{92} +(-179.568 + 311.021i) q^{93} -1072.57 q^{94} +(-16.4902 - 28.5619i) q^{95} +(193.649 - 335.411i) q^{96} +(211.758 + 366.776i) q^{97} +(-649.389 + 1124.78i) q^{98} +(277.559 - 480.747i) 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

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