LMFDB - Embedded newform 48.4.j.a.13.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [48,4,Mod(13,48)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(48, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("48.13"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	48.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.83209168028$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.11
Character	$\chi$	$=$	48.13
Dual form			48.4.j.a.37.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.59717 - 1.12013i) q^{2} +(2.12132 + 2.12132i) q^{3} +(5.49064 - 5.81833i) q^{4} +(0.706564 - 0.706564i) q^{5} +(7.88559 + 3.13329i) q^{6} +4.44122i q^{7} +(7.74288 - 21.2614i) q^{8} +9.00000i q^{9} +(1.04363 - 2.62651i) q^{10} +(-17.7126 + 17.7126i) q^{11} +(23.9899 - 0.695136i) q^{12} +(-17.7078 - 17.7078i) q^{13} +(4.97472 + 11.5346i) q^{14} +2.99770 q^{15} +(-3.70584 - 63.8926i) q^{16} -105.640 q^{17} +(10.0811 + 23.3746i) q^{18} +(40.2862 + 40.2862i) q^{19} +(-0.231534 - 7.99050i) q^{20} +(-9.42125 + 9.42125i) q^{21} +(-26.1624 + 65.8432i) q^{22} +42.9921i q^{23} +(61.5274 - 28.6771i) q^{24} +124.002i q^{25} +(-65.8252 - 26.1553i) q^{26} +(-19.0919 + 19.0919i) q^{27} +(25.8405 + 24.3851i) q^{28} +(-185.646 - 185.646i) q^{29} +(7.78554 - 3.35780i) q^{30} +291.485 q^{31} +(-81.1925 - 161.789i) q^{32} -75.1483 q^{33} +(-274.367 + 118.331i) q^{34} +(3.13800 + 3.13800i) q^{35} +(52.3649 + 49.4157i) q^{36} +(151.040 - 151.040i) q^{37} +(149.756 + 59.5047i) q^{38} -75.1278i q^{39} +(-9.55170 - 20.4934i) q^{40} -60.3918i q^{41} +(-13.9156 + 35.0216i) q^{42} +(120.532 - 120.532i) q^{43} +(5.80426 + 200.312i) q^{44} +(6.35907 + 6.35907i) q^{45} +(48.1565 + 111.658i) q^{46} +500.182 q^{47} +(127.675 - 143.398i) q^{48} +323.276 q^{49} +(138.897 + 322.054i) q^{50} +(-224.097 - 224.097i) q^{51} +(-200.257 + 5.80267i) q^{52} +(192.407 - 192.407i) q^{53} +(-28.1996 + 70.9703i) q^{54} +25.0302i q^{55} +(94.4266 + 34.3878i) q^{56} +170.920i q^{57} +(-690.102 - 274.208i) q^{58} +(-500.053 + 500.053i) q^{59} +(16.4593 - 17.4416i) q^{60} +(-166.418 - 166.418i) q^{61} +(757.037 - 326.500i) q^{62} -39.9710 q^{63} +(-392.096 - 329.249i) q^{64} -25.0234 q^{65} +(-195.173 + 84.1756i) q^{66} +(-575.426 - 575.426i) q^{67} +(-580.033 + 614.651i) q^{68} +(-91.2000 + 91.2000i) q^{69} +(11.6649 + 4.63498i) q^{70} +457.290i q^{71} +(191.353 + 69.6860i) q^{72} +1082.59i q^{73} +(223.094 - 561.462i) q^{74} +(-263.047 + 263.047i) q^{75} +(455.595 - 13.2014i) q^{76} +(-78.6657 - 78.6657i) q^{77} +(-84.1526 - 195.120i) q^{78} -544.309 q^{79} +(-47.7626 - 42.5258i) q^{80} -81.0000 q^{81} +(-67.6465 - 156.848i) q^{82} +(48.6931 + 48.6931i) q^{83} +(3.08725 + 106.545i) q^{84} +(-74.6417 + 74.6417i) q^{85} +(178.032 - 448.054i) q^{86} -787.630i q^{87} +(239.449 + 513.743i) q^{88} -43.6714i q^{89} +(23.6386 + 9.39266i) q^{90} +(78.6442 - 78.6442i) q^{91} +(250.142 + 236.054i) q^{92} +(618.332 + 618.332i) q^{93} +(1299.06 - 560.266i) q^{94} +56.9295 q^{95} +(170.972 - 515.442i) q^{96} +690.537 q^{97} +(839.603 - 362.109i) q^{98} +(-159.414 - 159.414i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{4} + 84 q^{8} + 72 q^{10} - 40 q^{11} - 24 q^{12} - 348 q^{14} + 120 q^{15} - 192 q^{16} - 36 q^{18} + 24 q^{19} + 80 q^{20} + 704 q^{22} + 228 q^{24} - 20 q^{26} - 344 q^{28} + 400 q^{29}+ \cdots - 360 q^{99}+O(q^{100}) $ 24 * q - 20 * q^4 + 84 * q^8 + 72 * q^10 - 40 * q^11 - 24 * q^12 - 348 * q^14 + 120 * q^15 - 192 * q^16 - 36 * q^18 + 24 * q^19 + 80 * q^20 + 704 * q^22 + 228 * q^24 - 20 * q^26 - 344 * q^28 + 400 * q^29 - 408 * q^30 - 744 * q^31 - 960 * q^32 - 704 * q^34 - 456 * q^35 + 108 * q^36 + 16 * q^37 + 1256 * q^38 + 1744 * q^40 + 660 * q^42 + 1240 * q^43 - 200 * q^44 - 1432 * q^46 - 528 * q^48 - 1176 * q^49 + 708 * q^50 + 744 * q^51 + 1008 * q^52 + 752 * q^53 + 108 * q^54 + 1344 * q^56 + 1936 * q^58 - 1376 * q^59 - 1224 * q^60 - 912 * q^61 - 996 * q^62 - 504 * q^63 - 56 * q^64 + 976 * q^65 - 1368 * q^66 - 2256 * q^67 - 1568 * q^68 - 528 * q^69 - 1760 * q^70 - 612 * q^72 - 2740 * q^74 + 1104 * q^75 - 1880 * q^76 + 1904 * q^77 + 1692 * q^78 + 5992 * q^79 + 712 * q^80 - 1944 * q^81 - 40 * q^82 + 2680 * q^83 + 1800 * q^84 - 240 * q^85 - 1712 * q^86 - 3936 * q^88 + 648 * q^90 - 3496 * q^91 + 5296 * q^92 + 5272 * q^94 - 7728 * q^95 + 2880 * q^96 + 6760 * q^98 - 360 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	2.59717	−	1.12013i	0.918240	−	0.396024i
$2$	2.59717	−	1.12013i	0.918240	−	0.396024i
$3$	2.12132	+	2.12132i	0.408248	+	0.408248i
$3$	2.12132	+	2.12132i	0.408248	+	0.408248i
$4$	5.49064	−	5.81833i	0.686329	−	0.727291i
$5$	0.706564	−	0.706564i	0.0631970	−	0.0631970i	−0.674802	−	0.737999i	$-0.735771\pi$
$5$	0.706564	−	0.706564i	0.0631970	−	0.0631970i	0.737999	+	0.674802i	$0.235771\pi$
$6$	7.88559	+	3.13329i	0.536546	+	0.213194i
$7$			4.44122i			0.239803i	0.992786	+	0.119902i	$0.0382579\pi$
$7$			4.44122i			0.239803i	−0.992786	+	0.119902i	$0.961742\pi$
$8$	7.74288	−	21.2614i	0.342190	−	0.939631i
$9$			9.00000i			0.333333i
$10$	1.04363	−	2.62651i	0.0330024	−	0.0830575i
$11$	−17.7126	+	17.7126i	−0.485506	+	0.485506i	−0.906885	−	0.421379i	$-0.861546\pi$
$11$	−17.7126	+	17.7126i	−0.485506	+	0.485506i	0.421379	+	0.906885i	$0.361546\pi$
$12$	23.9899	−	0.695136i	0.577108	−	0.0167224i
$13$	−17.7078	−	17.7078i	−0.377789	−	0.377789i	0.492515	−	0.870304i	$-0.336078\pi$
$13$	−17.7078	−	17.7078i	−0.377789	−	0.377789i	−0.870304	+	0.492515i	$0.836078\pi$
$14$	4.97472	+	11.5346i	0.0949679	+	0.220197i
$15$	2.99770			0.0516001
$16$	−3.70584	−	63.8926i	−0.0579037	−	0.998322i
$17$	−105.640			−1.50715			−0.753576	−	0.657361i	$-0.771673\pi$
$17$	−105.640			−1.50715			−0.753576	+	0.657361i	$0.771673\pi$
$18$	10.0811	+	23.3746i	0.132008	+	0.306080i
$19$	40.2862	+	40.2862i	0.486436	+	0.486436i	0.907180	−	0.420743i	$-0.138231\pi$
$19$	40.2862	+	40.2862i	0.486436	+	0.486436i	−0.420743	+	0.907180i	$0.638231\pi$
$20$	−0.231534	−	7.99050i	−0.00258863	−	0.0893365i
$21$	−9.42125	+	9.42125i	−0.0978993	+	0.0978993i
$22$	−26.1624	+	65.8432i	−0.253539	+	0.638083i
$23$			42.9921i			0.389759i	0.980827	+	0.194880i	$0.0624316\pi$
$23$			42.9921i			0.389759i	−0.980827	+	0.194880i	$0.937568\pi$
$24$	61.5274	−	28.6771i	0.523301	−	0.243904i
$25$			124.002i			0.992012i
$26$	−65.8252	−	26.1553i	−0.496515	−	0.197287i
$27$	−19.0919	+	19.0919i	−0.136083	+	0.136083i
$28$	25.8405	+	24.3851i	0.174407	+	0.164584i
$29$	−185.646	−	185.646i	−1.18875	−	1.18875i	−0.977415	−	0.211331i	$-0.932220\pi$
$29$	−185.646	−	185.646i	−1.18875	−	1.18875i	−0.211331	−	0.977415i	$-0.567780\pi$
$30$	7.78554	−	3.35780i	0.0473813	−	0.0204349i
$31$	291.485			1.68878			0.844390	−	0.535729i	$-0.179963\pi$
$31$	291.485			1.68878			0.844390	+	0.535729i	$0.179963\pi$
$32$	−81.1925	−	161.789i	−0.448529	−	0.893768i
$33$	−75.1483			−0.396414
$34$	−274.367	+	118.331i	−1.38393	+	0.596869i
$35$	3.13800	+	3.13800i	0.0151548	+	0.0151548i
$36$	52.3649	+	49.4157i	0.242430	+	0.228776i
$37$	151.040	−	151.040i	0.671104	−	0.671104i	−0.286867	−	0.957971i	$-0.592614\pi$
$37$	151.040	−	151.040i	0.671104	−	0.671104i	0.957971	+	0.286867i	$0.0926137\pi$
$38$	149.756	+	59.5047i	0.639306	+	0.254025i
$39$		−	75.1278i		−	0.308463i
$40$	−9.55170	−	20.4934i	−0.0377564	−	0.0810072i
$41$		−	60.3918i		−	0.230040i	−0.993363	−	0.115020i	$-0.963307\pi$
$41$		−	60.3918i		−	0.230040i	0.993363	−	0.115020i	$-0.0366931\pi$
$42$	−13.9156	+	35.0216i	−0.0511245	+	0.128666i
$43$	120.532	−	120.532i	0.427464	−	0.427464i	−0.460300	−	0.887764i	$-0.652258\pi$
$43$	120.532	−	120.532i	0.427464	−	0.427464i	0.887764	+	0.460300i	$0.152258\pi$
$44$	5.80426	+	200.312i	0.0198869	+	0.686320i
$45$	6.35907	+	6.35907i	0.0210657	+	0.0210657i
$46$	48.1565	+	111.658i	0.154354	+	0.357893i
$47$	500.182			1.55232			0.776159	−	0.630537i	$-0.217165\pi$
$47$	500.182			1.55232			0.776159	+	0.630537i	$0.217165\pi$
$48$	127.675	−	143.398i	0.383924	−	0.431202i
$49$	323.276			0.942494
$50$	138.897	+	322.054i	0.392861	+	0.910905i
$51$	−224.097	−	224.097i	−0.615292	−	0.615292i
$52$	−200.257	+	5.80267i	−0.534050	+	0.0154747i
$53$	192.407	−	192.407i	0.498663	−	0.498663i	−0.412359	−	0.911022i	$-0.635295\pi$
$53$	192.407	−	192.407i	0.498663	−	0.498663i	0.911022	+	0.412359i	$0.135295\pi$
$54$	−28.1996	+	70.9703i	−0.0710646	+	0.178849i
$55$			25.0302i			0.0613650i
$56$	94.4266	+	34.3878i	0.225327	+	0.0820584i
$57$			170.920i			0.397174i
$58$	−690.102	−	274.208i	−1.56233	−	0.620781i
$59$	−500.053	+	500.053i	−1.10341	+	1.10341i	−0.109417	+	0.993996i	$0.534898\pi$
$59$	−500.053	+	500.053i	−1.10341	+	1.10341i	−0.993996	+	0.109417i	$0.965102\pi$
$60$	16.4593	−	17.4416i	0.0354147	−	0.0375283i
$61$	−166.418	−	166.418i	−0.349306	−	0.349306i	0.510545	−	0.859851i	$-0.329444\pi$
$61$	−166.418	−	166.418i	−0.349306	−	0.349306i	−0.859851	+	0.510545i	$0.829444\pi$
$62$	757.037	−	326.500i	1.55071	−	0.668798i
$63$	−39.9710			−0.0799344
$64$	−392.096	−	329.249i	−0.765812	−	0.643065i
$65$	−25.0234			−0.0477502
$66$	−195.173	+	84.1756i	−0.364003	+	0.156989i
$67$	−575.426	−	575.426i	−1.04925	−	1.04925i	−0.998723	−	0.0505233i	$-0.983911\pi$
$67$	−575.426	−	575.426i	−1.04925	−	1.04925i	−0.0505233	−	0.998723i	$-0.516089\pi$
$68$	−580.033	+	614.651i	−1.03440	+	1.09614i
$69$	−91.2000	+	91.2000i	−0.159119	+	0.159119i
$70$	11.6649	+	4.63498i	0.0199175	+	0.00791409i
$71$			457.290i			0.764371i	0.924086	+	0.382186i	$0.124828\pi$
$71$			457.290i			0.764371i	−0.924086	+	0.382186i	$0.875172\pi$
$72$	191.353	+	69.6860i	0.313210	+	0.114063i
$73$			1082.59i			1.73572i	0.496812	+	0.867858i	$0.334504\pi$
$73$			1082.59i			1.73572i	−0.496812	+	0.867858i	$0.665496\pi$
$74$	223.094	−	561.462i	0.350461	−	0.882008i
$75$	−263.047	+	263.047i	−0.404987	+	0.404987i
$76$	455.595	−	13.2014i	0.687636	−	0.0199251i
$77$	−78.6657	−	78.6657i	−0.116426	−	0.116426i
$78$	−84.1526	−	195.120i	−0.122159	−	0.283243i
$79$	−544.309			−0.775184			−0.387592	−	0.921831i	$-0.626693\pi$
$79$	−544.309			−0.775184			−0.387592	+	0.921831i	$0.626693\pi$
$80$	−47.7626	−	42.5258i	−0.0667503	−	0.0594316i
$81$	−81.0000			−0.111111
$82$	−67.6465	−	156.848i	−0.0911013	−	0.211232i
$83$	48.6931	+	48.6931i	0.0643947	+	0.0643947i	0.738571	−	0.674176i	$-0.235501\pi$
$83$	48.6931	+	48.6931i	0.0643947	+	0.0643947i	−0.674176	+	0.738571i	$0.735501\pi$
$84$	3.08725	+	106.545i	0.00401008	+	0.138392i
$85$	−74.6417	+	74.6417i	−0.0952474	+	0.0952474i
$86$	178.032	−	448.054i	0.223228	−	0.561801i
$87$		−	787.630i		−	0.970607i
$88$	239.449	+	513.743i	0.290061	+	0.622331i
$89$		−	43.6714i		−	0.0520131i	−0.999662	−	0.0260065i	$-0.991721\pi$
$89$		−	43.6714i		−	0.0520131i	0.999662	−	0.0260065i	$-0.00827907\pi$
$90$	23.6386	+	9.39266i	0.0276858	+	0.0110008i
$91$	78.6442	−	78.6442i	0.0905950	−	0.0905950i
$92$	250.142	+	236.054i	0.283468	+	0.267503i
$93$	618.332	+	618.332i	0.689442	+	0.689442i
$94$	1299.06	−	560.266i	1.42540	−	0.614756i
$95$	56.9295			0.0614826
$96$	170.972	−	515.442i	0.181768	−	0.547991i
$97$	690.537			0.722818			0.361409	−	0.932407i	$-0.382296\pi$
$97$	690.537			0.722818			0.361409	+	0.932407i	$0.382296\pi$
$98$	839.603	−	362.109i	0.865436	−	0.373251i
$99$	−159.414	−	159.414i	−0.161835	−	0.161835i
$100$	721.481	+	680.847i	0.721481	+	0.680847i
$101$	564.484	−	564.484i	0.556121	−	0.556121i	−0.372080	−	0.928201i	$-0.621355\pi$
$101$	564.484	−	564.484i	0.556121	−	0.556121i	0.928201	+	0.372080i	$0.121355\pi$
$102$	−833.037	−	331.003i	−0.808656	−	0.321315i
$103$			110.408i			0.105620i	0.998605	+	0.0528098i	$0.0168177\pi$
$103$			110.408i			0.105620i	−0.998605	+	0.0528098i	$0.983182\pi$
$104$	−513.602	+	239.383i	−0.484258	+	0.225706i
$105$			13.3134i			0.0123739i
$106$	284.195	−	715.235i	0.260410	−	0.655375i
$107$	−254.357	+	254.357i	−0.229810	+	0.229810i	−0.812613	−	0.582803i	$-0.801956\pi$
$107$	−254.357	+	254.357i	−0.229810	+	0.229810i	0.582803	+	0.812613i	$0.301956\pi$
$108$	6.25623	+	215.909i	0.00557413	+	0.192369i
$109$	−205.025	−	205.025i	−0.180164	−	0.180164i	0.611263	−	0.791427i	$-0.290662\pi$
$109$	−205.025	−	205.025i	−0.180164	−	0.180164i	−0.791427	+	0.611263i	$0.790662\pi$
$110$	28.0370	+	65.0078i	0.0243020	+	0.0563478i
$111$	640.809			0.547954
$112$	283.761	−	16.4584i	0.239401	−	0.0138855i
$113$	−729.046			−0.606928			−0.303464	−	0.952843i	$-0.598143\pi$
$113$	−729.046			−0.606928			−0.303464	+	0.952843i	$0.598143\pi$
$114$	191.452	+	443.909i	0.157290	+	0.364701i
$115$	30.3766	+	30.3766i	0.0246316	+	0.0246316i
$116$	−2099.46	+	60.8344i	−1.68043	+	0.0486926i
$117$	159.370	−	159.370i	0.125930	−	0.125930i
$118$	−738.603	+	1858.85i	−0.576220	+	1.45018i
$119$		−	469.172i		−	0.361420i
$120$	23.2108	−	63.7352i	0.0176571	−	0.0484850i
$121$			703.525i			0.528569i
$122$	−618.626	−	245.808i	−0.459080	−	0.182413i
$123$	128.110	−	128.110i	0.0939132	−	0.0939132i
$124$	1600.44	−	1695.95i	1.15906	−	1.22823i
$125$	175.935	+	175.935i	0.125889	+	0.125889i
$126$	−103.812	+	44.7725i	−0.0733990	+	0.0316560i
$127$	−2431.21			−1.69870			−0.849352	−	0.527827i	$-0.823007\pi$
$127$	−2431.21			−1.69870			−0.849352	+	0.527827i	$0.823007\pi$
$128$	−1387.14	−	415.922i	−0.957868	−	0.287208i
$129$	511.374			0.349023
$130$	−64.9900	+	28.0293i	−0.0438462	+	0.0189103i
$131$	898.181	+	898.181i	0.599042	+	0.599042i	0.940058	−	0.341016i	$-0.110771\pi$
$131$	898.181	+	898.181i	0.599042	+	0.599042i	−0.341016	+	0.940058i	$0.610771\pi$
$132$	−412.612	+	437.238i	−0.272070	+	0.288308i
$133$	−178.920	+	178.920i	−0.116649	+	0.116649i
$134$	−2139.03	−	849.933i	−1.37899	−	0.547933i
$135$			26.9793i			0.0172000i
$136$	−817.962	+	2246.07i	−0.515733	+	1.41617i
$137$		−	3061.79i		−	1.90939i	−0.297590	−	0.954694i	$-0.596183\pi$
$137$		−	3061.79i		−	1.90939i	0.297590	−	0.954694i	$-0.403817\pi$
$138$	−134.707	+	339.018i	−0.0830942	+	0.209124i
$139$	1811.69	−	1811.69i	1.10551	−	1.10551i	0.111776	−	0.993733i	$-0.464346\pi$
$139$	1811.69	−	1811.69i	1.10551	−	1.10551i	0.993733	−	0.111776i	$-0.0356538\pi$
$140$	35.4876	−	1.02829i	0.0214232	−	0.000620762i
$141$	1061.05	+	1061.05i	0.633731	+	0.633731i
$142$	512.222	+	1187.66i	0.302710	+	0.701876i
$143$	627.303			0.366837
$144$	575.034	−	33.3525i	0.332774	−	0.0193012i
$145$	−262.342			−0.150250
$146$	1212.63	+	2811.67i	0.687386	+	1.59380i
$147$	685.771	+	685.771i	0.384772	+	0.384772i
$148$	−49.4944	−	1708.11i	−0.0274893	−	0.948686i
$149$	−869.143	+	869.143i	−0.477872	+	0.477872i	−0.904451	−	0.426578i	$-0.859719\pi$
$149$	−869.143	+	869.143i	−0.477872	+	0.477872i	0.426578	+	0.904451i	$0.359719\pi$
$150$	−388.533	+	977.825i	−0.211491	+	0.532260i
$151$			1033.70i			0.557097i	0.960422	+	0.278549i	$0.0898534\pi$
$151$			1033.70i			0.557097i	−0.960422	+	0.278549i	$0.910147\pi$
$152$	1168.47	−	544.610i	0.623524	−	0.290617i
$153$		−	950.764i		−	0.502384i
$154$	−292.424	−	116.193i	−0.153014	−	0.0607994i
$155$	205.952	−	205.952i	0.106726	−	0.106726i
$156$	−437.118	−	412.499i	−0.224343	−	0.211708i
$157$	−2314.43	−	2314.43i	−1.17651	−	1.17651i	−0.980628	−	0.195879i	$-0.937244\pi$
$157$	−2314.43	−	2314.43i	−1.17651	−	1.17651i	−0.195879	−	0.980628i	$-0.562756\pi$
$158$	−1413.67	+	609.695i	−0.711805	+	0.306992i
$159$	816.314			0.407157
$160$	−171.682	−	56.9468i	−0.0848291	−	0.0281377i
$161$	−190.937			−0.0934656
$162$	−210.371	+	90.7302i	−0.102027	+	0.0440027i
$163$	737.872	+	737.872i	0.354568	+	0.354568i	0.861806	−	0.507238i	$-0.169333\pi$
$163$	737.872	+	737.872i	0.354568	+	0.354568i	−0.507238	+	0.861806i	$0.669333\pi$
$164$	−351.379	−	331.590i	−0.167306	−	0.157883i
$165$	−53.0971	+	53.0971i	−0.0250521	+	0.0250521i
$166$	181.007	+	71.9221i	0.0846317	+	0.0336279i
$167$		−	468.664i		−	0.217164i	−0.994088	−	0.108582i	$-0.965369\pi$
$167$		−	468.664i		−	0.217164i	0.994088	−	0.108582i	$-0.0346309\pi$
$168$	127.361	+	273.257i	0.0584890	+	0.125489i
$169$		−	1569.87i		−	0.714551i
$170$	−110.249	+	277.466i	−0.0497397	+	0.125180i
$171$	−362.576	+	362.576i	−0.162145	+	0.162145i
$172$	−39.4972	−	1363.09i	−0.0175095	−	0.604272i
$173$	1671.65	+	1671.65i	0.734643	+	0.734643i	0.971536	−	0.236893i	$-0.0761290\pi$
$173$	1671.65	+	1671.65i	0.734643	+	0.734643i	−0.236893	+	0.971536i	$0.576129\pi$
$174$	−882.244	−	2045.61i	−0.384384	−	0.891250i
$175$	−550.718			−0.237888
$176$	1197.35	+	1066.07i	0.512803	+	0.456578i
$177$	−2121.55			−0.900933
$178$	−48.9175	−	113.422i	−0.0205984	−	0.0477605i
$179$	1413.56	+	1413.56i	0.590247	+	0.590247i	0.937698	−	0.347451i	$-0.112953\pi$
$179$	1413.56	+	1413.56i	0.590247	+	0.590247i	−0.347451	+	0.937698i	$0.612953\pi$
$180$	71.9145	−	2.08381i	0.0297788	−	0.000862877i
$181$	−2515.65	+	2515.65i	−1.03308	+	1.03308i	−0.0336429	+	0.999434i	$0.510711\pi$
$181$	−2515.65	+	2515.65i	−1.03308	+	1.03308i	−0.999434	+	0.0336429i	$0.989289\pi$
$182$	116.161	−	292.344i	0.0473101	−	0.119066i
$183$		−	706.053i		−	0.285207i
$184$	914.072	+	332.883i	0.366230	+	0.133372i
$185$		−	213.439i		−	0.0848235i
$186$	2298.53	+	913.307i	0.906109	+	0.360037i
$187$	1871.17	−	1871.17i	0.731730	−	0.731730i
$188$	2746.31	−	2910.22i	1.06540	−	1.12899i
$189$	−84.7912	−	84.7912i	−0.0326331	−	0.0326331i
$190$	147.856	−	63.7683i	0.0564558	−	0.0243486i
$191$	18.1653			0.00688165			0.00344082	−	0.999994i	$-0.498905\pi$
$191$	18.1653			0.00688165			0.00344082	+	0.999994i	$0.498905\pi$
$192$	−133.317	−	1530.20i	−0.0501110	−	0.575171i
$193$	1318.14			0.491616			0.245808	−	0.969319i	$-0.420947\pi$
$193$	1318.14			0.491616			0.245808	+	0.969319i	$0.420947\pi$
$194$	1793.44	−	773.488i	0.663721	−	0.286254i
$195$	−53.0826	−	53.0826i	−0.0194940	−	0.0194940i
$196$	1774.99	−	1880.92i	0.646862	−	0.685467i
$197$	−1818.15	+	1818.15i	−0.657551	+	0.657551i	−0.954800	−	0.297249i	$-0.903931\pi$
$197$	−1818.15	+	1818.15i	−0.657551	+	0.657551i	0.297249	+	0.954800i	$0.403931\pi$
$198$	−592.589	−	235.462i	−0.212694	−	0.0845129i
$199$			4114.56i			1.46570i	0.680392	+	0.732849i	$0.261810\pi$
$199$			4114.56i			1.46570i	−0.680392	+	0.732849i	$0.738190\pi$
$200$	2636.45	+	960.129i	0.932125	+	0.339457i
$201$		−	2441.33i		−	0.856706i
$202$	833.770	−	2098.36i	0.290415	−	0.730890i
$203$	824.495	−	824.495i	0.285065	−	0.285065i
$204$	−2534.31	+	73.4345i	−0.869789	+	0.0252032i
$205$	−42.6707	−	42.6707i	−0.0145378	−	0.0145378i
$206$	123.671	+	286.749i	0.0418279	+	0.0969841i
$207$	−386.929			−0.129920
$208$	−1065.77	+	1197.02i	−0.355280	+	0.399030i
$209$	−1427.15			−0.472335
$210$	14.9127	+	34.5773i	0.00490036	+	0.0113622i
$211$	1636.19	+	1636.19i	0.533840	+	0.533840i	0.921713	−	0.387873i	$-0.126790\pi$
$211$	1636.19	+	1636.19i	0.533840	+	0.533840i	−0.387873	+	0.921713i	$0.626790\pi$
$212$	−63.0499	−	2175.92i	−0.0204259	−	0.704920i
$213$	−970.059	+	970.059i	−0.312053	+	0.312053i
$214$	−375.698	+	945.522i	−0.120010	+	0.302031i
$215$		−	170.327i		−	0.0540289i
$216$	258.094	+	553.747i	0.0813013	+	0.174434i
$217$			1294.55i			0.404975i
$218$	−762.140	−	302.832i	−0.236783	−	0.0940843i
$219$	−2296.51	+	2296.51i	−0.708603	+	0.708603i
$220$	145.634	+	137.432i	0.0446302	+	0.0421166i
$221$	1870.66	+	1870.66i	0.569385	+	0.569385i
$222$	1664.29	−	717.787i	0.503153	−	0.217003i
$223$	−3121.80			−0.937450			−0.468725	−	0.883344i	$-0.655286\pi$
$223$	−3121.80			−0.937450			−0.468725	+	0.883344i	$0.655286\pi$
$224$	718.542	−	360.594i	0.214329	−	0.107559i
$225$	−1116.01			−0.330671
$226$	−1893.46	+	816.624i	−0.557306	+	0.240358i
$227$	−3405.69	−	3405.69i	−0.995787	−	0.995787i	0.00420438	−	0.999991i	$-0.498662\pi$
$227$	−3405.69	−	3405.69i	−0.995787	−	0.995787i	−0.999991	+	0.00420438i	$0.998662\pi$
$228$	994.468	+	938.459i	0.288861	+	0.272592i
$229$	2566.84	−	2566.84i	0.740706	−	0.740706i	−0.232008	−	0.972714i	$-0.574529\pi$
$229$	2566.84	−	2566.84i	0.740706	−	0.740706i	0.972714	+	0.232008i	$0.0745294\pi$
$230$	112.919	+	44.8678i	0.0323725	+	0.0128630i
$231$		−	333.750i		−	0.0950613i
$232$	−5384.53	+	2509.66i	−1.52376	+	0.710204i
$233$			1509.90i			0.424534i	0.977212	+	0.212267i	$0.0680847\pi$
$233$			1509.90i			0.424534i	−0.977212	+	0.212267i	$0.931915\pi$
$234$	235.397	−	592.427i	0.0657624	−	0.165505i
$235$	353.410	−	353.410i	0.0981018	−	0.0981018i
$236$	163.863	+	5655.08i	0.0451972	+	1.55981i
$237$	−1154.65	−	1154.65i	−0.316468	−	0.316468i
$238$	−525.532	−	1218.52i	−0.143131	−	0.331870i
$239$	−2608.05			−0.705860			−0.352930	−	0.935650i	$-0.614815\pi$
$239$	−2608.05			−0.705860			−0.352930	+	0.935650i	$0.614815\pi$
$240$	−11.1090	−	191.531i	−0.00298784	−	0.0515135i
$241$	2222.20			0.593962			0.296981	−	0.954883i	$-0.404020\pi$
$241$	2222.20			0.593962			0.296981	+	0.954883i	$0.404020\pi$
$242$	788.037	+	1827.18i	0.209326	+	0.485353i
$243$	−171.827	−	171.827i	−0.0453609	−	0.0453609i
$244$	−1882.02	+	54.5336i	−0.493786	+	0.0143080i
$245$	228.415	−	228.415i	0.0595628	−	0.0595628i
$246$	189.225	−	476.225i	0.0490430	−	0.123427i
$247$		−	1426.76i		−	0.367541i
$248$	2256.93	−	6197.38i	0.577884	−	1.58683i
$249$			206.587i			0.0525781i
$250$	654.005	+	259.865i	0.165452	+	0.0657413i
$251$	−2551.97	+	2551.97i	−0.641749	+	0.641749i	−0.950985	−	0.309236i	$-0.899927\pi$
$251$	−2551.97	+	2551.97i	−0.641749	+	0.641749i	0.309236	+	0.950985i	$0.399927\pi$
$252$	−219.466	+	232.564i	−0.0548613	+	0.0581356i
$253$	−761.503	−	761.503i	−0.189230	−	0.189230i
$254$	−6314.29	+	2723.27i	−1.55982	+	0.672728i
$255$	−316.678			−0.0777692
$256$	−4068.53	+	473.551i	−0.993294	+	0.115613i
$257$	2203.05			0.534718			0.267359	−	0.963597i	$-0.413849\pi$
$257$	2203.05			0.534718			0.267359	+	0.963597i	$0.413849\pi$
$258$	1328.13	−	572.803i	0.320487	−	0.138222i
$259$	670.802	+	670.802i	0.160933	+	0.160933i
$260$	−137.394	+	145.594i	−0.0327724	+	0.0347283i
$261$	1670.81	−	1670.81i	0.396248	−	0.396248i
$262$	3338.81	+	1326.66i	0.787299	+	0.312829i
$263$		−	7230.57i		−	1.69527i	−0.530581	−	0.847635i	$-0.678026\pi$
$263$		−	7230.57i		−	1.69527i	0.530581	−	0.847635i	$-0.321974\pi$
$264$	−581.865	+	1597.76i	−0.135649	+	0.372482i
$265$		−	271.896i		−	0.0630280i
$266$	−264.273	+	665.099i	−0.0609160	+	0.153308i
$267$	92.6411	−	92.6411i	0.0212342	−	0.0212342i
$268$	−6507.47	+	188.562i	−1.48324	+	0.0429785i
$269$	3750.63	+	3750.63i	0.850112	+	0.850112i	0.990147	−	0.140035i	$-0.0447215\pi$
$269$	3750.63	+	3750.63i	0.850112	+	0.850112i	−0.140035	+	0.990147i	$0.544721\pi$
$270$	30.2202	+	70.0699i	0.00681163	+	0.0157938i
$271$	2751.65			0.616792			0.308396	−	0.951258i	$-0.400208\pi$
$271$	2751.65			0.616792			0.308396	+	0.951258i	$0.400208\pi$
$272$	391.486	+	6749.65i	0.0872697	+	1.50462i
$273$	333.659			0.0739705
$274$	−3429.59	−	7952.00i	−0.756164	−	1.75328i
$275$	−2196.39	−	2196.39i	−0.481627	−	0.481627i
$276$	29.8853	+	1031.38i	0.00651771	+	0.224933i
$277$	3621.67	−	3621.67i	0.785578	−	0.785578i	−0.195188	−	0.980766i	$-0.562532\pi$
$277$	3621.67	−	3621.67i	0.785578	−	0.785578i	0.980766	+	0.195188i	$0.0625318\pi$
$278$	2675.96	−	6734.61i	0.577314	−	1.45293i
$279$			2623.36i			0.562927i
$280$	91.0156	−	42.4212i	0.0194258	−	0.00905411i
$281$			4989.59i			1.05927i	0.848227	+	0.529633i	$0.177670\pi$
$281$			4989.59i			1.05927i	−0.848227	+	0.529633i	$0.822330\pi$
$282$	3944.22	+	1567.22i	0.832891	+	0.330944i
$283$	2426.42	−	2426.42i	0.509667	−	0.509667i	−0.404757	−	0.914424i	$-0.632644\pi$
$283$	2426.42	−	2426.42i	0.509667	−	0.509667i	0.914424	+	0.404757i	$0.132644\pi$
$284$	2660.66	+	2510.81i	0.555920	+	0.524610i
$285$	120.766	+	120.766i	0.0251002	+	0.0251002i
$286$	1629.22	−	702.659i	0.336845	−	0.145276i
$287$	268.213			0.0551642
$288$	1456.10	−	730.732i	0.297923	−	0.149510i
$289$	6246.91			1.27151
$290$	−681.347	+	293.856i	−0.137966	+	0.0595027i
$291$	1464.85	+	1464.85i	0.295089	+	0.295089i
$292$	6298.85	+	5944.09i	1.26237	+	1.19127i
$293$	3379.84	−	3379.84i	0.673899	−	0.673899i	−0.284714	−	0.958613i	$-0.591899\pi$
$293$	3379.84	−	3379.84i	0.673899	−	0.673899i	0.958613	+	0.284714i	$0.0918985\pi$
$294$	2549.22	+	1012.92i	0.505692	+	0.200934i
$295$			706.639i			0.139465i
$296$	−2041.84	−	4380.81i	−0.400944	−	0.860235i
$297$		−	676.335i		−	0.132138i
$298$	−1283.77	+	3230.87i	−0.249552	+	0.628051i
$299$	761.294	−	761.294i	0.147247	−	0.147247i
$300$	86.1980	+	2974.79i	0.0165888	+	0.572498i
$301$	535.309	+	535.309i	0.102507	+	0.102507i
$302$	1157.88	+	2684.71i	0.220624	+	0.511549i
$303$	2394.90			0.454071
$304$	2424.70	−	2723.29i	0.457454	−	0.513787i
$305$	−235.170			−0.0441502
$306$	−1064.98	−	2469.30i	−0.198956	−	0.461309i
$307$	−2575.52	−	2575.52i	−0.478803	−	0.478803i	0.425946	−	0.904749i	$-0.359941\pi$
$307$	−2575.52	−	2575.52i	−0.478803	−	0.478803i	−0.904749	+	0.425946i	$0.859941\pi$
$308$	−889.627	+	25.7780i	−0.164582	+	0.00476895i
$309$	−234.211	+	234.211i	−0.0431190	+	0.0431190i
$310$	304.202	−	765.587i	0.0557339	−	0.140266i
$311$		−	2993.88i		−	0.545875i	−0.962032	−	0.272938i	$-0.912005\pi$
$311$		−	2993.88i		−	0.545875i	0.962032	−	0.272938i	$-0.0879953\pi$
$312$	−1597.32	−	581.706i	−0.289842	−	0.105553i
$313$			6133.96i			1.10771i	0.832614	+	0.553853i	$0.186843\pi$
$313$			6133.96i			1.10771i	−0.832614	+	0.553853i	$0.813157\pi$
$314$	−8603.43	−	3418.53i	−1.54624	−	0.614391i
$315$	−28.2420	+	28.2420i	−0.00505161	+	0.00505161i
$316$	−2988.60	+	3166.97i	−0.532032	+	0.563784i
$317$	−6740.75	−	6740.75i	−1.19432	−	1.19432i	−0.975843	−	0.218474i	$-0.929892\pi$
$317$	−6740.75	−	6740.75i	−1.19432	−	1.19432i	−0.218474	−	0.975843i	$-0.570108\pi$
$318$	2120.11	−	914.374i	0.373867	−	0.161244i
$319$	6576.56			1.15428
$320$	−509.676	+	44.4048i	−0.0890367	+	0.00775720i
$321$	−1079.15			−0.187639
$322$	−495.897	+	213.874i	−0.0858238	+	0.0370146i
$323$	−4255.85	−	4255.85i	−0.733133	−	0.733133i
$324$	−444.741	+	471.284i	−0.0762588	+	0.0808101i
$325$	2195.79	−	2195.79i	0.374771	−	0.374771i
$326$	2742.89	+	1089.87i	0.465996	+	0.185161i
$327$		−	869.848i		−	0.147103i
$328$	−1284.02	−	467.607i	−0.216152	−	0.0787173i
$329$			2221.42i			0.372251i
$330$	−78.4270	+	197.378i	−0.0130826	+	0.0329251i
$331$	−6485.75	+	6485.75i	−1.07701	+	1.07701i	−0.0802296	+	0.996776i	$0.525565\pi$
$331$	−6485.75	+	6485.75i	−1.07701	+	1.07701i	−0.996776	+	0.0802296i	$0.974435\pi$
$332$	550.668	−	15.9563i	0.0910297	−	0.00263769i
$333$	1359.36	+	1359.36i	0.223701	+	0.223701i
$334$	−524.963	−	1217.20i	−0.0860021	−	0.199408i
$335$	−813.150			−0.132618
$336$	636.862	+	567.035i	0.103404	+	0.0920663i
$337$	−9405.38			−1.52031			−0.760154	−	0.649743i	$-0.774877\pi$
$337$	−9405.38			−1.52031			−0.760154	+	0.649743i	$0.774877\pi$
$338$	−1758.45	−	4077.22i	−0.282980	−	0.656129i
$339$	−1546.54	−	1546.54i	−0.247777	−	0.247777i
$340$	24.4594	+	844.120i	0.00390146	+	0.134644i
$341$	−5162.96	+	5162.96i	−0.819912	+	0.819912i
$342$	−535.542	+	1347.80i	−0.0846749	+	0.213102i
$343$			2959.08i			0.465817i
$344$	−1629.42	−	3495.95i	−0.255384	−	0.547932i
$345$			128.877i			0.0201116i
$346$	6214.03	+	2469.11i	0.965515	+	0.383642i
$347$	−1557.96	+	1557.96i	−0.241025	+	0.241025i	−0.817274	−	0.576249i	$-0.804516\pi$
$347$	−1557.96	+	1557.96i	−0.241025	+	0.241025i	0.576249	+	0.817274i	$0.304516\pi$
$348$	−4582.69	−	4324.59i	−0.705913	−	0.666156i
$349$	−3041.63	−	3041.63i	−0.466518	−	0.466518i	0.434266	−	0.900784i	$-0.357008\pi$
$349$	−3041.63	−	3041.63i	−0.466518	−	0.466518i	−0.900784	+	0.434266i	$0.857008\pi$
$350$	−1430.31	+	616.873i	−0.218438	+	0.0942094i
$351$	676.150			0.102821
$352$	4303.85	+	1427.58i	0.651693	+	0.216166i
$353$	1629.66			0.245717			0.122859	−	0.992424i	$-0.460794\pi$
$353$	1629.66			0.245717			0.122859	+	0.992424i	$0.460794\pi$
$354$	−5510.03	+	2376.40i	−0.827273	+	0.356791i
$355$	323.104	+	323.104i	0.0483059	+	0.0483059i
$356$	−254.095	−	239.784i	−0.0378286	−	0.0356981i
$357$	995.265	−	995.265i	0.147549	−	0.147549i
$358$	5254.62	+	2087.89i	0.775740	+	0.308236i
$359$			9276.15i			1.36372i	0.731482	+	0.681861i	$0.238829\pi$
$359$			9276.15i			1.36372i	−0.731482	+	0.681861i	$0.761171\pi$
$360$	184.440	−	85.9653i	0.0270024	−	0.0125855i
$361$		−	3613.04i		−	0.526759i
$362$	−3715.74	+	9351.43i	−0.539489	+	1.35774i
$363$	−1492.40	+	1492.40i	−0.215787	+	0.215787i
$364$	−25.7709	−	889.384i	−0.00371089	−	0.128067i
$365$	764.917	+	764.917i	0.109692	+	0.109692i
$366$	−790.868	−	1833.74i	−0.112949	−	0.261889i
$367$	1016.63			0.144599			0.0722994	−	0.997383i	$-0.476966\pi$
$367$	1016.63			0.144599			0.0722994	+	0.997383i	$0.476966\pi$
$368$	2746.88	−	159.322i	0.389105	−	0.0225685i
$369$	543.527			0.0766798
$370$	−239.078	−	554.338i	−0.0335922	−	0.0778883i
$371$	854.522	+	854.522i	0.119581	+	0.119581i
$372$	6992.70	−	202.622i	0.974609	−	0.0282404i
$373$	−8897.07	+	8897.07i	−1.23505	+	1.23505i	−0.273047	+	0.962001i	$0.588031\pi$
$373$	−8897.07	+	8897.07i	−1.23505	+	1.23505i	−0.962001	+	0.273047i	$0.911969\pi$
$374$	2763.81	−	6955.71i	0.382121	−	0.961687i
$375$			746.431i			0.102788i
$376$	3872.85	−	10634.6i	0.531188	−	1.45861i
$377$			6574.76i			0.898190i
$378$	−315.195	−	125.241i	−0.0428885	−	0.0170415i
$379$	−5154.79	+	5154.79i	−0.698638	+	0.698638i	−0.964117	−	0.265478i	$-0.914470\pi$
$379$	−5154.79	+	5154.79i	−0.698638	+	0.698638i	0.265478	+	0.964117i	$0.414470\pi$
$380$	312.579	−	331.235i	0.0421973	−	0.0447157i
$381$	−5157.39	−	5157.39i	−0.693493	−	0.693493i
$382$	47.1785	−	20.3474i	0.00631901	−	0.00272530i
$383$	10573.7			1.41068			0.705340	−	0.708870i	$-0.250795\pi$
$383$	10573.7			1.41068			0.705340	+	0.708870i	$0.250795\pi$
$384$	−2060.27	−	3824.87i	−0.273796	−	0.508300i
$385$	−111.165			−0.0147155
$386$	3423.44	−	1476.48i	0.451422	−	0.194692i
$387$	1084.79	+	1084.79i	0.142488	+	0.142488i
$388$	3791.48	−	4017.77i	0.496091	−	0.525699i
$389$	7789.01	−	7789.01i	1.01522	−	1.01522i	0.0153326	−	0.999882i	$-0.495119\pi$
$389$	7789.01	−	7789.01i	1.01522	−	1.01522i	0.999882	−	0.0153326i	$-0.00488071\pi$
$390$	−197.324	−	78.4055i	−0.0256202	−	0.0101800i
$391$		−	4541.70i		−	0.587426i
$392$	2503.09	−	6873.30i	0.322512	−	0.885597i
$393$			3810.66i			0.489115i
$394$	−2685.49	+	6758.60i	−0.343384	+	0.864196i
$395$	−384.589	+	384.589i	−0.0489893	+	0.0489893i
$396$	−1802.80	+	52.2383i	−0.228773	+	0.00662898i
$397$	−1219.69	−	1219.69i	−0.154193	−	0.154193i	0.625795	−	0.779988i	$-0.284775\pi$
$397$	−1219.69	−	1219.69i	−0.154193	−	0.154193i	−0.779988	+	0.625795i	$0.784775\pi$
$398$	4608.83	+	10686.2i	0.580452	+	1.34586i
$399$	−759.093			−0.0952435
$400$	7922.78	−	459.530i	0.990348	−	0.0574412i
$401$	−5714.97			−0.711701			−0.355850	−	0.934543i	$-0.615809\pi$
$401$	−5714.97			−0.711701			−0.355850	+	0.934543i	$0.615809\pi$
$402$	−2734.59	−	6340.55i	−0.339276	−	0.786662i
$403$	−5161.55	−	5161.55i	−0.638003	−	0.638003i
$404$	−184.976	−	6383.73i	−0.0227794	−	0.786144i
$405$	−57.2316	+	57.2316i	−0.00702189	+	0.00702189i
$406$	1217.82	−	3064.90i	0.148865	−	0.374651i
$407$			5350.64i			0.651649i
$408$	−6499.78	+	3029.47i	−0.788694	+	0.367600i
$409$			1504.54i			0.181894i	0.995856	+	0.0909469i	$0.0289894\pi$
$409$			1504.54i			0.181894i	−0.995856	+	0.0909469i	$0.971011\pi$
$410$	−158.620	−	63.0267i	−0.0191065	−	0.00759187i
$411$	6495.03	−	6495.03i	0.779504	−	0.779504i
$412$	642.389	+	606.210i	0.0768161	+	0.0724898i
$413$	−2220.85	−	2220.85i	−0.264602	−	0.264602i
$414$	−1004.92	+	433.409i	−0.119298	+	0.0514514i
$415$	68.8095			0.00813910
$416$	−1427.19	+	4302.67i	−0.168206	+	0.507105i
$417$	7686.36			0.902644
$418$	−3706.56	+	1598.59i	−0.433717	+	0.187056i
$419$	9630.38	+	9630.38i	1.12285	+	1.12285i	0.991311	+	0.131541i	$0.0419927\pi$
$419$	9630.38	+	9630.38i	1.12285	+	1.12285i	0.131541	+	0.991311i	$0.458007\pi$
$420$	77.4618	+	73.0991i	0.00899940	+	0.00849255i
$421$	2831.19	−	2831.19i	0.327752	−	0.327752i	−0.523979	−	0.851731i	$-0.675553\pi$
$421$	2831.19	−	2831.19i	0.327752	−	0.327752i	0.851731	+	0.523979i	$0.175553\pi$
$422$	6082.22	+	2416.74i	0.701607	+	0.278779i
$423$			4501.63i			0.517440i
$424$	−2601.06	−	5580.63i	−0.297921	−	0.639197i
$425$		−	13099.6i		−	1.49511i
$426$	−1432.82	+	3606.00i	−0.162959	+	0.410120i
$427$	739.100	−	739.100i	0.0837647	−	0.0837647i
$428$	83.3504	+	2876.52i	0.00941330	+	0.324864i
$429$	1330.71	+	1330.71i	0.149761	+	0.149761i
$430$	−190.788	−	442.369i	−0.0213967	−	0.0496115i
$431$	5555.36			0.620864			0.310432	−	0.950596i	$-0.399526\pi$
$431$	5555.36			0.620864			0.310432	+	0.950596i	$0.399526\pi$
$432$	1290.58	+	1149.08i	0.143734	+	0.127975i
$433$	−14582.8			−1.61848			−0.809241	−	0.587476i	$-0.800122\pi$
$433$	−14582.8			−1.61848			−0.809241	+	0.587476i	$0.800122\pi$
$434$	1450.06	+	3362.17i	0.160380	+	0.371864i
$435$	−556.510	−	556.510i	−0.0613394	−	0.0613394i
$436$	−2318.62	+	67.1847i	−0.254683	+	0.00737974i
$437$	−1731.99	+	1731.99i	−0.189593	+	0.189593i
$438$	−3392.06	+	8536.84i	−0.370044	+	0.931292i
$439$		−	4862.86i		−	0.528682i	−0.964429	−	0.264341i	$-0.914846\pi$
$439$		−	4862.86i		−	0.528682i	0.964429	−	0.264341i	$-0.0851545\pi$
$440$	532.178	+	193.806i	0.0576604	+	0.0209985i
$441$			2909.48i			0.314165i
$442$	6953.80	+	2763.05i	0.748323	+	0.297342i
$443$	9325.47	−	9325.47i	1.00015	−	1.00015i	0.000149687	−	1.00000i	$-0.499952\pi$
$443$	9325.47	−	9325.47i	1.00015	−	1.00015i	1.00000		0.000149687i	$-4.76467e-5\pi$
$444$	3518.45	−	3728.44i	0.376077	−	0.398522i
$445$	−30.8566	−	30.8566i	−0.00328707	−	0.00328707i
$446$	−8107.87	+	3496.81i	−0.860804	+	0.371253i
$447$	−3687.46			−0.390181
$448$	1462.27	−	1741.38i	0.154209	−	0.183644i
$449$	11461.1			1.20464			0.602318	−	0.798256i	$-0.294244\pi$
$449$	11461.1			1.20464			0.602318	+	0.798256i	$0.294244\pi$
$450$	−2898.48	+	1250.08i	−0.303635	+	0.130954i
$451$	1069.70	+	1069.70i	0.111685	+	0.111685i
$452$	−4002.93	+	4241.83i	−0.416553	+	0.441413i
$453$	−2192.82	+	2192.82i	−0.227434	+	0.227434i
$454$	−12660.0	−	5030.37i	−1.30873	−	0.520015i
$455$		−	111.134i		−	0.0114507i
$456$	3634.00	+	1323.41i	0.373197	+	0.135909i
$457$		−	13856.7i		−	1.41835i	−0.705031	−	0.709177i	$-0.749067\pi$
$457$		−	13856.7i		−	1.41835i	0.705031	−	0.709177i	$-0.250933\pi$
$458$	3791.35	−	9541.73i	0.386808	−	0.973484i
$459$	2016.88	−	2016.88i	0.205097	−	0.205097i
$460$	343.528	−	9.95413i	0.0348197	−	0.00100894i
$461$	−3166.73	−	3166.73i	−0.319934	−	0.319934i	0.528808	−	0.848741i	$-0.322639\pi$
$461$	−3166.73	−	3166.73i	−0.319934	−	0.319934i	−0.848741	+	0.528808i	$0.822639\pi$
$462$	−373.842	−	866.808i	−0.0376466	−	0.0872891i
$463$	1566.96			0.157285			0.0786426	−	0.996903i	$-0.474941\pi$
$463$	1566.96			0.157285			0.0786426	+	0.996903i	$0.474941\pi$
$464$	−11173.4	+	12549.4i	−1.11792	+	1.25558i
$465$	873.782			0.0871412
$466$	1691.27	+	3921.46i	0.168126	+	0.389825i
$467$	5309.28	+	5309.28i	0.526090	+	0.526090i	0.919404	−	0.393314i	$-0.128671\pi$
$467$	5309.28	+	5309.28i	0.526090	+	0.526090i	−0.393314	+	0.919404i	$0.628671\pi$
$468$	−52.2240	−	1802.31i	−0.00515824	−	0.178017i
$469$	2555.59	−	2555.59i	0.251613	−	0.251613i
$470$	522.004	−	1313.73i	0.0512303	−	0.128932i
$471$		−	9819.30i		−	0.960614i
$472$	6759.98	+	14503.7i	0.659224	+	1.41438i
$473$			4269.88i			0.415072i
$474$	−4292.19	−	1705.48i	−0.415922	−	0.165264i
$475$	−4995.55	+	4995.55i	−0.482551	+	0.482551i
$476$	−2729.80	−	2576.05i	−0.262857	−	0.248053i
$477$	1731.66	+	1731.66i	0.166221	+	0.166221i
$478$	−6773.55	+	2921.34i	−0.648149	+	0.279538i
$479$	−4034.12			−0.384809			−0.192405	−	0.981316i	$-0.561629\pi$
$479$	−4034.12			−0.384809			−0.192405	+	0.981316i	$0.561629\pi$
$480$	−243.390	−	484.995i	−0.0231442	−	0.0461185i
$481$	−5349.17			−0.507071
$482$	5771.45	−	2489.15i	0.545399	−	0.235223i
$483$	−405.039	−	405.039i	−0.0381572	−	0.0381572i
$484$	4093.34	+	3862.80i	0.384423	+	0.362772i
$485$	487.908	−	487.908i	0.0456799	−	0.0456799i
$486$	−638.732	−	253.797i	−0.0596162	−	0.0236882i
$487$		−	16499.3i		−	1.53522i	−0.640915	−	0.767612i	$-0.721445\pi$
$487$		−	16499.3i		−	1.53522i	0.640915	−	0.767612i	$-0.278555\pi$
$488$	−4826.84	+	2249.73i	−0.447748	+	0.208689i
$489$			3130.53i			0.289504i
$490$	337.380	−	849.086i	0.0311046	−	0.0782812i
$491$	1060.25	−	1060.25i	0.0974506	−	0.0974506i	−0.656701	−	0.754151i	$-0.728049\pi$
$491$	1060.25	−	1060.25i	0.0974506	−	0.0974506i	0.754151	+	0.656701i	$0.228049\pi$
$492$	−41.9806	−	1448.80i	−0.00384681	−	0.132758i
$493$	19611.7	+	19611.7i	1.79162	+	1.79162i
$494$	−1598.15	−	3705.54i	−0.145555	−	0.337490i
$495$	−225.272			−0.0204550
$496$	−1080.20	−	18623.7i	−0.0977867	−	1.68595i
$497$	−2030.93			−0.183299
$498$	231.404	+	536.543i	0.0208222	+	0.0482793i
$499$	4275.19	+	4275.19i	0.383534	+	0.383534i	0.872374	−	0.488839i	$-0.162580\pi$
$499$	4275.19	+	4275.19i	0.383534	+	0.383534i	−0.488839	+	0.872374i	$0.662580\pi$
$500$	1989.65	−	57.6523i	0.177959	−	0.00515658i
$501$	994.187	−	994.187i	0.0886567	−	0.0886567i
$502$	−3769.39	+	9486.45i	−0.335132	+	0.843428i
$503$			13976.3i			1.23891i	0.785031	+	0.619456i	$0.212647\pi$
$503$			13976.3i			1.23891i	−0.785031	+	0.619456i	$0.787353\pi$
$504$	−309.491	+	849.839i	−0.0273528	+	0.0751088i
$505$		−	797.687i		−	0.0702903i
$506$	−2830.74	−	1124.78i	−0.248699	−	0.0988191i
$507$	3330.19	−	3330.19i	0.291714	−	0.291714i
$508$	−13348.9	+	14145.6i	−1.16587	+	1.23545i
$509$	−9315.16	−	9315.16i	−0.811174	−	0.811174i	0.173636	−	0.984810i	$-0.444448\pi$
$509$	−9315.16	−	9315.16i	−0.811174	−	0.811174i	−0.984810	+	0.173636i	$0.944448\pi$
$510$	−822.468	+	354.719i	−0.0714108	+	0.0307985i
$511$	−4808.01			−0.416230
$512$	−10036.3	+	5787.17i	−0.866297	+	0.499529i
$513$	−1538.28			−0.132391
$514$	5721.71	−	2467.69i	0.490999	−	0.211761i
$515$	78.0102	+	78.0102i	0.00667484	+	0.00667484i
$516$	2807.77	−	2975.34i	0.239545	−	0.253841i
$517$	−8859.53	+	8859.53i	−0.753659	+	0.753659i
$518$	2493.57	+	990.808i	0.211508	+	0.0840417i
$519$			7092.21i			0.599834i
$520$	−193.753	+	532.032i	−0.0163397	+	0.0448676i
$521$		−	10404.0i		−	0.874870i	−0.899250	−	0.437435i	$-0.855887\pi$
$521$		−	10404.0i		−	0.874870i	0.899250	−	0.437435i	$-0.144113\pi$
$522$	2467.88	−	6210.92i	0.206927	−	0.520775i
$523$	2520.38	−	2520.38i	0.210724	−	0.210724i	−0.593851	−	0.804575i	$-0.702393\pi$
$523$	2520.38	−	2520.38i	0.210724	−	0.210724i	0.804575	+	0.593851i	$0.202393\pi$
$524$	10157.5	−	294.325i	0.846817	−	0.0245375i
$525$	−1168.25	−	1168.25i	−0.0971173	−	0.0971173i
$526$	−8099.14	−	18779.0i	−0.671368	−	1.55666i
$527$	−30792.6			−2.54525
$528$	278.488	+	4801.42i	0.0229538	+	0.395748i
$529$	10318.7			0.848088
$530$	−304.557	−	706.160i	−0.0249606	−	0.0578748i
$531$	−4500.48	−	4500.48i	−0.367804	−	0.367804i
$532$	58.6303	+	2023.40i	0.00477810	+	0.164897i
$533$	−1069.41	+	1069.41i	−0.0869064	+	0.0869064i
$534$	136.835	−	344.375i	0.0110889	−	0.0279074i
$535$			359.439i			0.0290465i
$536$	−16689.8	+	7778.92i	−1.34495	+	0.626862i
$537$			5997.21i			0.481935i
$538$	13942.2	+	5539.87i	1.11727	+	0.443942i
$539$	−5726.06	+	5726.06i	−0.457586	+	0.457586i
$540$	156.974	+	148.133i	0.0125094	+	0.0118049i
$541$	13635.3	+	13635.3i	1.08360	+	1.08360i	0.996171	+	0.0874292i	$0.0278651\pi$
$541$	13635.3	+	13635.3i	1.08360	+	1.08360i	0.0874292	+	0.996171i	$0.472135\pi$
$542$	7146.51	−	3082.19i	0.566363	−	0.244265i
$543$	−10673.0			−0.843504
$544$	8577.21	+	17091.5i	0.676002	+	1.34704i
$545$	−289.726			−0.0227716
$546$	866.571	−	373.740i	0.0679227	−	0.0292941i
$547$	−1729.49	−	1729.49i	−0.135188	−	0.135188i	0.636275	−	0.771463i	$-0.280474\pi$
$547$	−1729.49	−	1729.49i	−0.135188	−	0.135188i	−0.771463	+	0.636275i	$0.780474\pi$
$548$	−17814.5	−	16811.2i	−1.38868	−	1.31047i
$549$	1497.76	−	1497.76i	0.116435	−	0.116435i
$550$	−8164.66	−	3244.18i	−0.632986	−	0.251513i
$551$		−	14958.0i		−	1.15650i
$552$	1232.89	+	2645.19i	0.0950639	+	0.203962i
$553$		−	2417.39i		−	0.185892i
$554$	5349.38	−	13462.8i	0.410241	−	1.03246i
$555$	452.772	−	452.772i	0.0346290	−	0.0346290i
$556$	−593.674	−	20488.4i	−0.0452831	−	1.56277i
$557$	3758.29	+	3758.29i	0.285896	+	0.285896i	0.835455	−	0.549559i	$-0.185204\pi$
$557$	3758.29	+	3758.29i	0.285896	+	0.285896i	−0.549559	+	0.835455i	$0.685204\pi$
$558$	2938.50	+	6813.33i	0.222933	+	0.516902i
$559$	−4268.71			−0.322982
$560$	188.866	−	212.124i	0.0142519	−	0.0160069i
$561$	7938.71			0.597455
$562$	5588.97	+	12958.8i	0.419495	+	0.972661i
$563$	1676.08	+	1676.08i	0.125468	+	0.125468i	0.767052	−	0.641585i	$-0.221723\pi$
$563$	1676.08	+	1676.08i	0.125468	+	0.125468i	−0.641585	+	0.767052i	$0.721723\pi$
$564$	11999.3	−	347.694i	0.895856	−	0.0259585i
$565$	−515.118	+	515.118i	−0.0383560	+	0.0383560i
$566$	3583.94	−	9019.74i	0.266156	−	0.669837i
$567$		−	359.739i		−	0.0266448i
$568$	9722.63	+	3540.74i	0.718226	+	0.261560i
$569$		−	11314.4i		−	0.833611i	−0.908996	−	0.416805i	$-0.863150\pi$
$569$		−	11314.4i		−	0.833611i	0.908996	−	0.416805i	$-0.136850\pi$
$570$	448.923	+	178.377i	0.0329883	+	0.0131077i
$571$	4555.47	−	4555.47i	0.333871	−	0.333871i	−0.520184	−	0.854055i	$-0.674136\pi$
$571$	4555.47	−	4555.47i	0.333871	−	0.333871i	0.854055	+	0.520184i	$0.174136\pi$
$572$	3444.29	−	3649.85i	0.251771	−	0.266797i
$573$	38.5344	+	38.5344i	0.00280942	+	0.00280942i
$574$	696.597	−	300.433i	0.0506540	−	0.0218464i
$575$	−5331.08			−0.386646
$576$	2963.24	−	3528.86i	0.214355	−	0.255271i
$577$	15216.2			1.09785			0.548925	−	0.835872i	$-0.315037\pi$
$577$	15216.2			1.09785			0.548925	+	0.835872i	$0.315037\pi$
$578$	16224.3	−	6997.32i	1.16755	−	0.503547i
$579$	2796.20	+	2796.20i	0.200701	+	0.200701i
$580$	−1440.42	+	1526.39i	−0.103121	+	0.109276i
$581$	−216.257	+	216.257i	−0.0154421	+	0.0154421i
$582$	5445.29	+	2163.65i	0.387825	+	0.154100i
$583$			6816.07i			0.484207i
$584$	23017.3	+	8382.35i	1.63093	+	0.593945i
$585$		−	225.210i		−	0.0159167i
$586$	4992.19	−	12563.9i	0.351921	−	0.885681i
$587$	3111.52	−	3111.52i	0.218784	−	0.218784i	−0.589202	−	0.807986i	$-0.700558\pi$
$587$	3111.52	−	3111.52i	0.218784	−	0.218784i	0.807986	+	0.589202i	$0.200558\pi$
$588$	7755.36	−	224.721i	0.543921	−	0.0157607i
$589$	11742.8	+	11742.8i	0.821484	+	0.821484i
$590$	791.524	+	1835.26i	0.0552314	+	0.128062i
$591$	−7713.74			−0.536888
$592$	−10210.1	−	9090.62i	−0.708837	−	0.631118i
$593$	−7275.10			−0.503799			−0.251899	−	0.967753i	$-0.581055\pi$
$593$	−7275.10			−0.503799			−0.251899	+	0.967753i	$0.581055\pi$
$594$	−757.581	−	1756.56i	−0.0523298	−	0.121334i
$595$	−331.500	−	331.500i	−0.0228406	−	0.0228406i
$596$	284.810	+	9829.11i	0.0195743	+	0.675530i
$597$	−8728.31	+	8728.31i	−0.598368	+	0.598368i
$598$	1124.47	−	2829.96i	0.0768946	−	0.193521i
$599$			18975.0i			1.29432i	0.762355	+	0.647159i	$0.224043\pi$
$599$			18975.0i			1.29432i	−0.762355	+	0.647159i	$0.775957\pi$
$600$	3556.01	+	7629.49i	0.241956	+	0.519121i
$601$		−	2493.99i		−	0.169271i	−0.996412	−	0.0846357i	$-0.973027\pi$
$601$		−	2493.99i		−	0.169271i	0.996412	−	0.0846357i	$-0.0269726\pi$
$602$	1989.90	+	790.677i	0.134722	+	0.0535309i
$603$	5178.84	−	5178.84i	0.349749	−	0.349749i
$604$	6014.43	+	5675.70i	0.405172	+	0.382352i
$605$	497.085	+	497.085i	0.0334039	+	0.0334039i
$606$	6219.98	−	2682.59i	0.416946	−	0.179823i
$607$	13075.7			0.874341			0.437171	−	0.899379i	$-0.355981\pi$
$607$	13075.7			0.874341			0.437171	+	0.899379i	$0.355981\pi$
$608$	3246.94	−	9788.82i	0.216580	−	0.652942i
$609$	3498.04			0.232755
$610$	−610.778	+	263.420i	−0.0405404	+	0.0174845i
$611$	−8857.11	−	8857.11i	−0.586449	−	0.586449i
$612$	−5531.86	−	5220.30i	−0.365379	−	0.344801i
$613$	10449.8	−	10449.8i	0.688523	−	0.688523i	−0.273382	−	0.961906i	$-0.588142\pi$
$613$	10449.8	−	10449.8i	0.688523	−	0.688523i	0.961906	+	0.273382i	$0.0881423\pi$
$614$	−9573.97	−	3804.17i	−0.629274	−	0.250038i
$615$		−	181.036i		−	0.0118701i
$616$	−2281.64	+	1063.44i	−0.149237	+	0.0695575i
$617$			6927.08i			0.451983i	0.974129	+	0.225992i	$0.0725622\pi$
$617$			6927.08i			0.451983i	−0.974129	+	0.225992i	$0.927438\pi$
$618$	−345.940	+	870.631i	−0.0225174	+	0.0566698i
$619$	−16635.4	+	16635.4i	−1.08018	+	1.08018i	−0.0836922	+	0.996492i	$0.526671\pi$
$619$	−16635.4	+	16635.4i	−1.08018	+	1.08018i	−0.996492	+	0.0836922i	$0.973329\pi$
$620$	−67.4886	−	2329.11i	−0.00437163	−	0.150870i
$621$	−820.800	−	820.800i	−0.0530395	−	0.0530395i
$622$	−3353.52	−	7775.62i	−0.216180	−	0.501245i
$623$	193.954			0.0124729
$624$	−4800.11	+	278.411i	−0.307946	+	0.0178612i
$625$	−15251.6			−0.976101
$626$	6870.81	+	15931.0i	0.438679	+	1.01714i
$627$	−3027.44	−	3027.44i	−0.192830	−	0.192830i
$628$	−26173.8	+	758.417i	−1.66313	+	0.0481913i
$629$	−15955.9	+	15955.9i	−1.01146	+	1.01146i
$630$	−41.7149	+	104.984i	−0.00263803	+	0.00663915i
$631$		−	22231.3i		−	1.40256i	−0.712888	−	0.701278i	$-0.752613\pi$
$631$		−	22231.3i		−	1.40256i	0.712888	−	0.701278i	$-0.247387\pi$
$632$	−4214.52	+	11572.8i	−0.265260	+	0.728387i
$633$			6941.78i			0.435878i
$634$	−25057.4	−	9956.42i	−1.56965	−	0.623691i
$635$	−1717.81	+	1717.81i	−0.107353	+	0.107353i
$636$	4482.08	−	4749.58i	0.279444	−	0.296121i
$637$	−5724.50	−	5724.50i	−0.356064	−	0.356064i
$638$	17080.5	−	7366.58i	1.05991	−	0.457125i
$639$	−4115.61			−0.254790
$640$	−1273.98	+	686.228i	−0.0786850	+	0.0423837i
$641$	8447.90			0.520549			0.260274	−	0.965535i	$-0.416187\pi$
$641$	8447.90			0.520549			0.260274	+	0.965535i	$0.416187\pi$
$642$	−2802.73	+	1208.78i	−0.172297	+	0.0743095i
$643$	5326.38	+	5326.38i	0.326675	+	0.326675i	0.851321	−	0.524646i	$-0.175802\pi$
$643$	5326.38	+	5326.38i	0.326675	+	0.326675i	−0.524646	+	0.851321i	$0.675802\pi$
$644$	−1048.37	+	1110.93i	−0.0641482	+	0.0679767i
$645$	361.318	−	361.318i	0.0220572	−	0.0220572i
$646$	−15820.3	−	6286.11i	−0.963531	−	0.382854i
$647$			7105.36i			0.431747i	0.976421	+	0.215874i	$0.0692599\pi$
$647$			7105.36i			0.431747i	−0.976421	+	0.215874i	$0.930740\pi$
$648$	−627.174	+	1722.17i	−0.0380211	+	0.104403i
$649$		−	17714.5i		−	1.07143i
$650$	3243.29	−	8162.42i	0.195711	−	0.492549i
$651$	−2746.15	+	2746.15i	−0.165330	+	0.165330i
$652$	8344.57	−	241.794i	0.501225	−	0.0145236i
$653$	1518.80	+	1518.80i	0.0910189	+	0.0910189i	0.751150	−	0.660131i	$-0.229499\pi$
$653$	1518.80	+	1518.80i	0.0910189	+	0.0910189i	−0.660131	+	0.751150i	$0.729499\pi$
$654$	−974.339	−	2259.15i	−0.0582564	−	0.135076i
$655$	1269.24			0.0757152
$656$	−3858.59	+	223.802i	−0.229654	+	0.0133201i
$657$	−9743.29			−0.578572
$658$	2488.27	+	5769.40i	0.147420	+	0.341816i
$659$	5425.29	+	5425.29i	0.320697	+	0.320697i	0.849035	−	0.528337i	$-0.177184\pi$
$659$	5425.29	+	5425.29i	0.320697	+	0.320697i	−0.528337	+	0.849035i	$0.677184\pi$
$660$	17.3994	+	600.473i	0.00102617	+	0.0354142i
$661$	−18128.4	+	18128.4i	−1.06674	+	1.06674i	−0.0691300	+	0.997608i	$0.522022\pi$
$661$	−18128.4	+	18128.4i	−1.06674	+	1.06674i	−0.997608	+	0.0691300i	$0.977978\pi$
$662$	−9579.77	+	24109.5i	−0.562429	+	1.41547i
$663$			7936.53i			0.464901i
$664$	1412.31	−	658.259i	0.0825425	−	0.0384720i
$665$			252.837i			0.0147437i
$666$	5053.15	+	2007.84i	0.294003	+	0.116820i
$667$	7981.31	−	7981.31i	0.463325	−	0.463325i
$668$	−2726.84	−	2573.26i	−0.157941	−	0.149046i
$669$	−6622.34	−	6622.34i	−0.382712	−	0.382712i
$670$	−2111.89	+	910.831i	−0.121775	+	0.0525201i
$671$	5895.41			0.339180
$672$	2289.19	+	759.323i	0.131410	+	0.0435885i
$673$	1072.11			0.0614071			0.0307036	−	0.999529i	$-0.490225\pi$
$673$	1072.11			0.0614071			0.0307036	+	0.999529i	$0.490225\pi$
$674$	−24427.4	+	10535.2i	−1.39601	+	0.602079i
$675$	−2367.42	−	2367.42i	−0.134996	−	0.134996i
$676$	−9134.01	−	8619.58i	−0.519686	−	0.490417i
$677$	4806.53	−	4806.53i	0.272865	−	0.272865i	−0.557387	−	0.830253i	$-0.688196\pi$
$677$	4806.53	−	4806.53i	0.272865	−	0.272865i	0.830253	+	0.557387i	$0.188196\pi$
$678$	−5748.96	−	2284.32i	−0.325645	−	0.129393i
$679$			3066.82i			0.173334i
$680$	1009.05	+	2164.93i	0.0569046	+	0.122090i
$681$		−	14449.1i		−	0.813057i
$682$	−7625.95	+	19192.3i	−0.428171	+	1.07758i
$683$	21855.0	−	21855.0i	1.22439	−	1.22439i	0.258334	−	0.966056i	$-0.416826\pi$
$683$	21855.0	−	21855.0i	1.22439	−	1.22439i	0.966056	−	0.258334i	$-0.0831737\pi$
$684$	118.813	+	4100.36i	0.00664169	+	0.229212i
$685$	−2163.35	−	2163.35i	−0.120667	−	0.120667i
$686$	3314.54	+	7685.24i	0.184475	+	0.427731i
$687$	10890.2			0.604784
$688$	−8147.78	−	7254.43i	−0.451499	−	0.401995i
$689$	−6814.21			−0.376779
$690$	144.359	+	334.716i	0.00796469	+	0.0184673i
$691$	−585.815	−	585.815i	−0.0322510	−	0.0322510i	0.690797	−	0.723048i	$-0.257260\pi$
$691$	−585.815	−	585.815i	−0.0322510	−	0.0322510i	−0.723048	+	0.690797i	$0.757260\pi$
$692$	18904.6	−	547.784i	1.03851	−	0.0300919i
$693$	707.991	−	707.991i	0.0388086	−	0.0388086i
$694$	−2301.18	+	5791.40i	−0.125867	+	0.316770i
$695$		−	2560.15i		−	0.139730i
$696$	−16746.1	−	6098.53i	−0.912012	−	0.332132i
$697$			6379.82i			0.346704i
$698$	−11306.7	−	4492.64i	−0.613128	−	0.243623i
$699$	−3202.97	+	3202.97i	−0.173315	+	0.173315i
$700$	−3023.79	+	3204.26i	−0.163269	+	0.173014i
$701$	−7273.96	−	7273.96i	−0.391917	−	0.391917i	0.483453	−	0.875370i	$-0.339382\pi$
$701$	−7273.96	−	7273.96i	−0.391917	−	0.391917i	−0.875370	+	0.483453i	$0.839382\pi$
$702$	1756.08	−	757.373i	0.0944145	−	0.0407197i
$703$	12169.7			0.652899
$704$	12776.9	−	1113.17i	0.684017	−	0.0595941i
$705$	1499.39			0.0800998
$706$	4232.52	−	1825.43i	0.225627	−	0.0973100i
$707$	2507.00	+	2507.00i	0.133360	+	0.133360i
$708$	−11648.6	+	12343.8i	−0.618337	+	0.655240i
$709$	17600.7	−	17600.7i	0.932309	−	0.932309i	−0.0655405	−	0.997850i	$-0.520877\pi$
$709$	17600.7	−	17600.7i	0.932309	−	0.932309i	0.997850	+	0.0655405i	$0.0208772\pi$
$710$	1201.08	+	477.241i	0.0634868	+	0.0252261i
$711$		−	4898.78i		−	0.258395i
$712$	−928.516	−	338.143i	−0.0488731	−	0.0177984i
$713$			12531.5i			0.658218i
$714$	1470.06	−	3699.70i	0.0770524	−	0.193918i
$715$	443.230	−	443.230i	0.0231830	−	0.0231830i
$716$	15985.9	−	463.209i	0.834385	−	0.0241773i
$717$	−5532.50	−	5532.50i	−0.288166	−	0.288166i
$718$	10390.5	+	24091.8i	0.540067	+	1.25222i
$719$	14431.8			0.748562			0.374281	−	0.927315i	$-0.377890\pi$
$719$	14431.8			0.748562			0.374281	+	0.927315i	$0.377890\pi$
$720$	382.732	−	429.863i	0.0198105	−	0.0222501i
$721$	−490.346			−0.0253279
$722$	−4047.06	−	9383.70i	−0.208609	−	0.483691i
$723$	4714.01	+	4714.01i	0.242484	+	0.242484i
$724$	824.355	+	28449.4i	0.0423162	+	1.46038i
$725$	23020.4	−	23020.4i	1.17925	−	1.17925i
$726$	−2204.35	+	5547.71i	−0.112688	+	0.283602i
$727$			5802.18i			0.295998i	0.988987	+	0.147999i	$0.0472833\pi$
$727$			5802.18i			0.295998i	−0.988987	+	0.147999i	$0.952717\pi$
$728$	−1063.15	−	2281.02i	−0.0541251	−	0.116127i
$729$		−	729.000i		−	0.0370370i
$730$	2843.43	+	1129.82i	0.144164	+	0.0572829i
$731$	−12733.1	+	12733.1i	−0.644253	+	0.644253i
$732$	−4108.04	−	3876.68i	−0.207429	−	0.195746i
$733$	−16743.4	−	16743.4i	−0.843699	−	0.843699i	0.145639	−	0.989338i	$-0.453476\pi$
$733$	−16743.4	−	16743.4i	−0.843699	−	0.843699i	−0.989338	+	0.145639i	$0.953476\pi$
$734$	2640.37	−	1138.76i	0.132776	−	0.0572647i
$735$	969.082			0.0486328
$736$	6955.66	−	3490.63i	0.348355	−	0.174819i
$737$	20384.6			1.01883
$738$	1411.63	−	608.818i	0.0704105	−	0.0303671i
$739$	5259.84	+	5259.84i	0.261822	+	0.261822i	0.825794	−	0.563972i	$-0.190727\pi$
$739$	5259.84	+	5259.84i	0.261822	+	0.261822i	−0.563972	+	0.825794i	$0.690727\pi$
$740$	−1241.86	−	1171.92i	−0.0616913	−	0.0582168i
$741$	3026.61	−	3026.61i	0.150048	−	0.150048i
$742$	3176.51	+	1262.17i	0.157161	+	0.0624471i
$743$		−	29413.6i		−	1.45233i	−0.687522	−	0.726163i	$-0.741302\pi$
$743$		−	29413.6i		−	1.45233i	0.687522	−	0.726163i	$-0.258698\pi$
$744$	17934.3	−	8358.95i	0.883741	−	0.411900i
$745$			1228.21i			0.0604002i
$746$	−13141.4	+	33073.1i	−0.644961	+	1.62318i
$747$	−438.238	+	438.238i	−0.0214649	+	0.0214649i
$748$	−613.165	−	21161.0i	−0.0299726	−	1.03439i
$749$	−1129.66	−	1129.66i	−0.0551091	−	0.0551091i
$750$	836.096	+	1938.61i	0.0407066	+	0.0943841i
$751$	37261.5			1.81051			0.905254	−	0.424870i	$-0.139680\pi$
$751$	37261.5			1.81051			0.905254	+	0.424870i	$0.139680\pi$
$752$	−1853.59	−	31957.9i	−0.0898850	−	1.54971i
$753$	−10827.1			−0.523986
$754$	7364.56	+	17075.8i	0.355705	+	0.824754i
$755$	730.378	+	730.378i	0.0352069	+	0.0352069i
$756$	−958.901	+	27.7853i	−0.0461308	+	0.00133669i
$757$	4651.56	−	4651.56i	0.223334	−	0.223334i	−0.586567	−	0.809901i	$-0.699521\pi$
$757$	4651.56	−	4651.56i	0.223334	−	0.223334i	0.809901	+	0.586567i	$0.199521\pi$
$758$	−7613.88	+	19161.9i	−0.364840	+	0.918196i
$759$		−	3230.78i		−	0.154506i
$760$	440.799	−	1210.40i	0.0210388	−	0.0577709i
$761$			25144.7i			1.19776i	0.800839	+	0.598879i	$0.204387\pi$
$761$			25144.7i			1.19776i	−0.800839	+	0.598879i	$0.795613\pi$
$762$	−19171.6	−	7617.71i	−0.911433	−	0.362153i
$763$	910.561	−	910.561i	0.0432038	−	0.0432038i
$764$	99.7390	−	105.692i	0.00472308	−	0.00500496i
$765$	−671.775	−	671.775i	−0.0317491	−	0.0317491i
$766$	27461.7	−	11843.9i	1.29534	−	0.558663i
$767$	17709.7			0.833715
$768$	−9635.22	−	7626.11i	−0.452710	−	0.358312i
$769$	−29241.9			−1.37125			−0.685625	−	0.727955i	$-0.740471\pi$
$769$	−29241.9			−1.37125			−0.685625	+	0.727955i	$0.740471\pi$
$770$	−288.714	+	124.518i	−0.0135124	+	0.00582770i
$771$	4673.38	+	4673.38i	0.218298	+	0.218298i
$772$	7237.44	−	7669.38i	0.337411	−	0.357548i
$773$	−6698.95	+	6698.95i	−0.311700	+	0.311700i	−0.845568	−	0.533868i	$-0.820738\pi$
$773$	−6698.95	+	6698.95i	−0.311700	+	0.311700i	0.533868	+	0.845568i	$0.320738\pi$
$774$	4032.48	+	1602.28i	0.187267	+	0.0744095i
$775$			36144.5i			1.67529i
$776$	5346.74	−	14681.8i	0.247341	−	0.679182i
$777$			2845.97i			0.131401i
$778$	11504.8	−	28954.1i	0.530161	−	1.33426i
$779$	2432.96	−	2432.96i	0.111900	−	0.111900i
$780$	−600.309	+	17.3946i	−0.0275570	+	0.000798498i
$781$	−8099.81	−	8099.81i	−0.371106	−	0.371106i
$782$	−5087.28	−	11795.6i	−0.232635	−	0.539399i
$783$	7088.67			0.323536
$784$	−1198.01	−	20654.9i	−0.0545739	−	0.940913i
$785$	−3270.58			−0.148703
$786$	4268.42	+	9896.95i	0.193702	+	0.449125i
$787$	−4317.53	−	4317.53i	−0.195557	−	0.195557i	0.602535	−	0.798092i	$-0.294157\pi$
$787$	−4317.53	−	4317.53i	−0.195557	−	0.195557i	−0.798092	+	0.602535i	$0.794157\pi$
$788$	595.789	+	20561.4i	0.0269342	+	0.929528i
$789$	15338.3	−	15338.3i	0.692091	−	0.692091i
$790$	−568.057	+	1429.63i	−0.0255830	+	0.0643849i
$791$		−	3237.85i		−	0.145543i
$792$	−4623.68	+	2155.04i	−0.207444	+	0.0966869i
$793$			5893.80i			0.263928i
$794$	−4533.97	−	1801.55i	−0.202651	−	0.0805221i
$795$	576.778	−	576.778i	0.0257311	−	0.0257311i
$796$	23939.9	+	22591.6i	1.06599	+	1.00595i
$797$	12492.2	+	12492.2i	0.555201	+	0.555201i	0.927937	−	0.372736i	$-0.121580\pi$
$797$	12492.2	+	12492.2i	0.555201	+	0.555201i	−0.372736	+	0.927937i	$0.621580\pi$
$798$	−1971.50	+	850.280i	−0.0874564	+	0.0377188i
$799$	−52839.4			−2.33958
$800$	20062.1	−	10068.0i	0.886629	−	0.444947i
$801$	393.043			0.0173377
$802$	−14842.8	+	6401.48i	−0.653512	+	0.281851i
$803$	−19175.5	−	19175.5i	−0.842700	−	0.842700i
$804$	−14204.4	−	13404.4i	−0.623074	−	0.587983i
$805$	−134.909	+	134.909i	−0.00590674	+	0.00590674i
$806$	−19187.0	−	7623.86i	−0.838504	−	0.333175i
$807$			15912.6i			0.694113i
$808$	−7630.99	−	16372.5i	−0.332249	−	0.712848i
$809$		−	4276.80i		−	0.185864i	−0.995672	−	0.0929321i	$-0.970376\pi$
$809$		−	4276.80i		−	0.185864i	0.995672	−	0.0929321i	$-0.0296239\pi$
$810$	−84.5340	+	212.747i	−0.00366694	+	0.00922861i
$811$	−15331.3	+	15331.3i	−0.663817	+	0.663817i	−0.956277	−	0.292461i	$-0.905526\pi$
$811$	−15331.3	+	15331.3i	−0.663817	+	0.663817i	0.292461	+	0.956277i	$0.405526\pi$
$812$	−270.179	−	9324.18i	−0.0116766	−	0.402974i
$813$	5837.13	+	5837.13i	0.251804	+	0.251804i
$814$	5993.39	+	13896.5i	0.258069	+	0.598370i
$815$	1042.71			0.0448152
$816$	−13487.7	+	15148.6i	−0.578632	+	0.649887i
$817$	9711.55			0.415868
$818$	1685.27	+	3907.55i	0.0720344	+	0.167022i
$819$	707.797	+	707.797i	0.0301983	+	0.0301983i
$820$	−482.561	+	13.9828i	−0.0205509	+	0.000595487i
$821$	−12527.1	+	12527.1i	−0.532521	+	0.532521i	−0.921322	−	0.388801i	$-0.872890\pi$
$821$	−12527.1	+	12527.1i	−0.532521	+	0.532521i	0.388801	+	0.921322i	$0.372890\pi$
$822$	9593.48	−	24144.0i	0.407069	−	1.02447i
$823$		−	15241.1i		−	0.645532i	−0.946479	−	0.322766i	$-0.895387\pi$
$823$		−	15241.1i		−	0.645532i	0.946479	−	0.322766i	$-0.104613\pi$
$824$	2347.43	+	854.876i	0.0992434	+	0.0361420i
$825$		−	9318.51i		−	0.393247i
$826$	−8255.55	−	3280.30i	−0.347757	−	0.138179i
$827$	−25529.5	+	25529.5i	−1.07345	+	1.07345i	−0.0763756	+	0.997079i	$0.524335\pi$
$827$	−25529.5	+	25529.5i	−1.07345	+	1.07345i	−0.997079	+	0.0763756i	$0.975665\pi$
$828$	−2124.48	+	2251.28i	−0.0891678	+	0.0944895i
$829$	−23542.4	−	23542.4i	−0.986322	−	0.986322i	0.0135854	−	0.999908i	$-0.495676\pi$
$829$	−23542.4	−	23542.4i	−0.986322	−	0.986322i	−0.999908	+	0.0135854i	$0.995676\pi$
$830$	178.710	−	77.0754i	0.00747365	−	0.00322328i
$831$	15365.4			0.641421
$832$	1112.87	+	12773.4i	0.0463723	+	0.532258i
$833$	−34151.0			−1.42048
$834$	19962.8	−	8609.69i	0.828844	−	0.357469i
$835$	−331.141	−	331.141i	−0.0137241	−	0.0137241i
$836$	−7835.96	+	8303.62i	−0.324177	+	0.343525i
$837$	−5564.99	+	5564.99i	−0.229814	+	0.229814i
$838$	35799.0	+	14224.5i	1.47572	+	0.586371i
$839$		−	3385.26i		−	0.139299i	−0.997572	−	0.0696497i	$-0.977812\pi$
$839$		−	3385.26i		−	0.139299i	0.997572	−	0.0696497i	$-0.0221882\pi$
$840$	283.062	+	103.084i	0.0116269	+	0.00423422i
$841$			44540.0i			1.82623i
$842$	4181.81	−	10524.4i	0.171157	−	0.430753i
$843$	−10584.5	+	10584.5i	−0.432444	+	0.432444i
$844$	18503.6	−	536.165i	0.754647	−	0.0218668i
$845$	−1109.21	−	1109.21i	−0.0451575	−	0.0451575i
$846$	5042.40	+	11691.5i	0.204919	+	0.475134i
$847$	−3124.51			−0.126753
$848$	−13006.4	−	11580.4i	−0.526701	−	0.468952i
$849$	10294.4			0.416141
$850$	−14673.2	−	34021.9i	−0.592101	−	1.37287i
$851$	6493.53	+	6493.53i	0.261569	+	0.261569i
$852$	317.879	+	10970.4i	0.0127821	+	0.441125i
$853$	4371.94	−	4371.94i	0.175489	−	0.175489i	−0.613897	−	0.789386i	$-0.710399\pi$
$853$	4371.94	−	4371.94i	0.175489	−	0.175489i	0.789386	+	0.613897i	$0.210399\pi$
$854$	1091.69	−	2747.46i	0.0437432	−	0.110089i
$855$			512.366i			0.0204942i
$856$	3438.54	+	7377.45i	0.137298	+	0.294575i
$857$			32205.4i			1.28368i	0.766838	+	0.641840i	$0.221829\pi$
$857$			32205.4i			1.28368i	−0.766838	+	0.641840i	$0.778171\pi$
$858$	4946.65	+	1965.53i	0.196825	+	0.0782074i
$859$	2875.17	−	2875.17i	0.114202	−	0.114202i	−0.647696	−	0.761898i	$-0.724268\pi$
$859$	2875.17	−	2875.17i	0.114202	−	0.114202i	0.761898	+	0.647696i	$0.224268\pi$
$860$	−991.018	−	935.203i	−0.0392947	−	0.0370816i
$861$	568.966	+	568.966i	0.0225207	+	0.0225207i
$862$	14428.2	−	6222.70i	0.570102	−	0.245877i
$863$	18181.9			0.717173			0.358586	−	0.933497i	$-0.383259\pi$
$863$	18181.9			0.717173			0.358586	+	0.933497i	$0.383259\pi$
$864$	4638.98	+	1538.74i	0.182664	+	0.0605893i
$865$	2362.26			0.0928544
$866$	−37874.0	+	16334.5i	−1.48616	+	0.640959i
$867$	13251.7	+	13251.7i	0.519090	+	0.519090i
$868$	7532.10	+	7107.89i	0.294535	+	0.277946i
$869$	9641.15	−	9641.15i	0.376356	−	0.376356i
$870$	−2068.72	−	821.993i	−0.0806162	−	0.0320324i
$871$			20379.0i			0.792787i
$872$	−5946.61	+	2771.64i	−0.230938	+	0.107637i
$873$			6214.83i			0.240939i
$874$	−2558.23	+	6438.32i	−0.0990085	+	0.249176i
$875$	−781.368	+	781.368i	−0.0301886	+	0.0301886i
$876$	752.546	+	25971.2i	0.0290253	+	1.00170i
$877$	−26665.8	−	26665.8i	−1.02673	−	1.02673i	−0.999633	−	0.0270950i	$-0.991374\pi$
$877$	−26665.8	−	26665.8i	−1.02673	−	1.02673i	−0.0270950	−	0.999633i	$-0.508626\pi$
$878$	−5447.01	−	12629.7i	−0.209371	−	0.485457i
$879$	14339.4			0.550236
$880$	1599.25	−	92.7579i	0.0612620	−	0.00355326i
$881$	26033.2			0.995552			0.497776	−	0.867305i	$-0.334150\pi$
$881$	26033.2			0.995552			0.497776	+	0.867305i	$0.334150\pi$
$882$	3258.98	+	7556.43i	0.124417	+	0.288479i
$883$	−27917.9	−	27917.9i	−1.06400	−	1.06400i	−0.997807	−	0.0661953i	$-0.978914\pi$
$883$	−27917.9	−	27917.9i	−1.06400	−	1.06400i	−0.0661953	−	0.997807i	$-0.521086\pi$
$884$	21155.2	−	612.997i	0.804894	−	0.0233228i
$885$	−1499.01	+	1499.01i	−0.0569362	+	0.0569362i
$886$	13774.2	−	34665.6i	0.522294	−	1.31446i
$887$		−	28947.2i		−	1.09577i	−0.836553	−	0.547887i	$-0.815433\pi$
$887$		−	28947.2i		−	1.09577i	0.836553	−	0.547887i	$-0.184567\pi$
$888$	4961.71	−	13624.5i	0.187505	−	0.514874i
$889$		−	10797.6i		−	0.407355i
$890$	−114.703	−	45.5768i	−0.00432008	−	0.00171656i
$891$	1434.72	−	1434.72i	0.0539451	−	0.0539451i
$892$	−17140.7	+	18163.7i	−0.643400	+	0.681799i
$893$	20150.4	+	20150.4i	0.755104	+	0.755104i
$894$	−9576.99	+	4130.42i	−0.358280	+	0.154521i
$895$	1997.54			0.0746036
$896$	1847.20	−	6160.60i	0.0688734	−	0.229700i
$897$	3229.90			0.120227
$898$	29766.4	−	12837.9i	1.10615	−	0.477065i
$899$	−54113.0	−	54113.0i	−2.00753	−	2.00753i
$900$	−6127.63	+	6493.33i	−0.226949	+	0.240494i
$901$	−20326.0	+	20326.0i	−0.751561	+	0.751561i
$902$	3976.39	+	1580.00i	0.146784	+	0.0583239i
$903$			2271.12i			0.0836968i
$904$	−5644.92	+	15500.6i	−0.207685	+	0.570288i
$905$			3554.94i			0.130575i
$906$	−3238.90	+	8151.37i	−0.118770	+	0.298909i
$907$	3191.29	−	3191.29i	0.116830	−	0.116830i	−0.646275	−	0.763105i	$-0.723674\pi$
$907$	3191.29	−	3191.29i	0.116830	−	0.116830i	0.763105	+	0.646275i	$0.223674\pi$
$908$	−38514.8	+	1116.01i	−1.40766	+	0.0407887i
$909$	5080.35	+	5080.35i	0.185374	+	0.185374i
$910$	−124.484	−	288.635i	−0.00453474	−	0.0105145i
$911$	−40016.6			−1.45534			−0.727668	−	0.685930i	$-0.759396\pi$
$911$	−40016.6			−1.45534			−0.727668	+	0.685930i	$0.759396\pi$
$912$	10920.5	−	633.402i	0.396507	−	0.0229978i
$913$	−1724.97			−0.0625280
$914$	−15521.2	−	35988.2i	−0.561702	−	1.30239i
$915$	−498.871	−	498.871i	−0.0180242	−	0.0180242i
$916$	−841.130	−	29028.3i	−0.0303403	−	1.04708i
$917$	−3989.02	+	3989.02i	−0.143652	+	0.143652i
$918$	2979.02	−	7497.33i	0.107105	−	0.269552i
$919$			15342.1i			0.550694i	0.961345	+	0.275347i	$0.0887928\pi$
$919$			15342.1i			0.550694i	−0.961345	+	0.275347i	$0.911207\pi$
$920$	881.053	−	410.647i	0.0315733	−	0.0147159i
$921$		−	10927.0i		−	0.390941i
$922$	−11771.7	−	4677.42i	−0.420477	−	0.167074i
$923$	8097.60	−	8097.60i	0.288771	−	0.288771i
$924$	−1941.87	−	1832.50i	−0.0691372	−	0.0652434i
$925$	18729.2	+	18729.2i	0.665743	+	0.665743i
$926$	4069.68	−	1755.20i	0.144426	−	0.0622887i
$927$	−993.671			−0.0352065
$928$	−14962.5	+	45108.6i	−0.529275	+	1.59565i
$929$	−104.186			−0.00367946			−0.00183973	−	0.999998i	$-0.500586\pi$
$929$	−104.186			−0.00367946			−0.00183973	+	0.999998i	$0.500586\pi$
$930$	2269.37	−	978.746i	0.0800166	−	0.0345101i
$931$	13023.5	+	13023.5i	0.458464	+	0.458464i
$932$	8785.06	+	8290.29i	0.308760	+	0.291371i
$933$	6350.97	−	6350.97i	0.222853	−	0.222853i
$934$	19736.2	+	7842.07i	0.691422	+	0.274733i
$935$		−	2644.20i		−	0.0924863i
$936$	−2154.45	−	4622.42i	−0.0752355	−	0.161419i
$937$			3137.81i			0.109400i	0.998503	+	0.0547001i	$0.0174203\pi$
$937$			3137.81i			0.109400i	−0.998503	+	0.0547001i	$0.982580\pi$
$938$	3774.74	−	9499.91i	0.131396	−	0.330686i
$939$	−13012.1	+	13012.1i	−0.452219	+	0.452219i
$940$	−115.809	−	3996.70i	−0.00401838	−	0.138679i
$941$	7984.14	+	7984.14i	0.276595	+	0.276595i	0.831748	−	0.555153i	$-0.187340\pi$
$941$	7984.14	+	7984.14i	0.276595	+	0.276595i	−0.555153	+	0.831748i	$0.687340\pi$
$942$	−10998.8	−	25502.4i	−0.380427	−	0.882074i
$943$	2596.37			0.0896601
$944$	33802.8	+	30096.6i	1.16545	+	1.03767i
$945$	−119.821			−0.00412462
$946$	4782.80	+	11089.6i	0.164379	+	0.381136i
$947$	20247.7	+	20247.7i	0.694787	+	0.694787i	0.963281	−	0.268495i	$-0.0865261\pi$
$947$	20247.7	+	20247.7i	0.694787	+	0.694787i	−0.268495	+	0.963281i	$0.586526\pi$
$948$	−13057.9	+	378.369i	−0.447365	+	0.0129629i
$949$	19170.2	−	19170.2i	0.655734	−	0.655734i
$950$	−7378.68	+	18570.0i	−0.251996	+	0.634199i
$951$		−	28598.6i		−	0.975155i
$952$	−9975.27	−	3632.75i	−0.339601	−	0.123674i
$953$		−	34966.0i		−	1.18852i	−0.804272	−	0.594261i	$-0.797445\pi$
$953$		−	34966.0i		−	1.18852i	0.804272	−	0.594261i	$-0.202555\pi$
$954$	6437.11	+	2557.75i	0.218458	+	0.0868032i
$955$	12.8349	−	12.8349i	0.000434899	−	0.000434899i
$956$	−14319.8	+	15174.5i	−0.484452	+	0.513365i
$957$	13951.0	+	13951.0i	0.471235	+	0.471235i
$958$	−10477.3	+	4518.72i	−0.353347	+	0.152394i
$959$	13598.1			0.457877
$960$	−1175.38	−	986.989i	−0.0395160	−	0.0331822i
$961$	55172.3			1.85198
$962$	−13892.7	+	5991.75i	−0.465613	+	0.200813i
$963$	−2289.21	−	2289.21i	−0.0766032	−	0.0766032i
$964$	12201.3	−	12929.5i	0.407653	−	0.431983i
$965$	931.351	−	931.351i	0.0310686	−	0.0310686i
$966$	−1505.65	−	598.262i	−0.0501486	−	0.0199263i
$967$		−	15161.3i		−	0.504194i	−0.967702	−	0.252097i	$-0.918880\pi$
$967$		−	15161.3i		−	0.504194i	0.967702	−	0.252097i	$-0.0811201\pi$
$968$	14957.9	+	5447.31i	0.496659	+	0.180871i
$969$		−	18056.1i		−	0.598601i
$970$	720.664	−	1813.70i	0.0238548	−	0.0600355i
$971$	13515.9	−	13515.9i	0.446701	−	0.446701i	−0.447555	−	0.894256i	$-0.647705\pi$
$971$	13515.9	−	13515.9i	0.446701	−	0.446701i	0.894256	+	0.447555i	$0.147705\pi$
$972$	−1943.18	+	56.3060i	−0.0641231	+	0.00185804i
$973$	8046.12	+	8046.12i	0.265105	+	0.265105i
$974$	−18481.3	−	42851.5i	−0.607986	−	1.40970i
$975$	9315.96			0.305999
$976$	−10016.2	+	11249.6i	−0.328494	+	0.368946i
$977$	22582.6			0.739490			0.369745	−	0.929133i	$-0.379445\pi$
$977$	22582.6			0.739490			0.369745	+	0.929133i	$0.379445\pi$
$978$	3506.58	+	8130.52i	0.114650	+	0.265834i
$979$	773.536	+	773.536i	0.0252526	+	0.0252526i
$980$	−74.8493	−	2583.13i	−0.00243977	−	0.0841992i
$981$	1845.23	−	1845.23i	0.0600546	−	0.0600546i
$982$	1566.04	−	3941.25i	0.0508902	−	0.128076i
$983$			39898.2i			1.29456i	0.762252	+	0.647281i	$0.224094\pi$
$983$			39898.2i			1.29456i	−0.762252	+	0.647281i	$0.775906\pi$
$984$	−1731.86	−	3715.75i	−0.0561076	−	0.120380i
$985$			2569.27i			0.0831105i
$986$	72902.7	+	28967.5i	2.35466	+	0.935612i
$987$	−4712.33	+	4712.33i	−0.151971	+	0.151971i
$988$	−8301.35	−	7833.82i	−0.267309	−	0.252254i
$989$	5181.92	+	5181.92i	0.166608	+	0.166608i
$990$	−585.070	+	252.333i	−0.0187826	+	0.00810067i
$991$	−36767.4			−1.17856			−0.589281	−	0.807928i	$-0.700589\pi$
$991$	−36767.4			−1.17856			−0.589281	+	0.807928i	$0.700589\pi$
$992$	−23666.4	−	47159.1i	−0.757468	−	1.50938i
$993$	−27516.7			−0.879372
$994$	−5274.67	+	2274.89i	−0.168312	+	0.0725907i
$995$	2907.20	+	2907.20i	0.0926276	+	0.0926276i
$996$	1201.99	+	1134.30i	0.0382396	+	0.0360859i
$997$	6130.71	−	6130.71i	0.194746	−	0.194746i	−0.602997	−	0.797743i	$-0.706027\pi$
$997$	6130.71	−	6130.71i	0.194746	−	0.194746i	0.797743	+	0.602997i	$0.206027\pi$
$998$	15892.2	+	6314.66i	0.504066	+	0.200288i
$999$			5767.28i			0.182651i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.4.j.a.13.11	✓	24
3.2	odd	2		144.4.k.b.109.2		24
4.3	odd	2		192.4.j.a.145.4		24
8.3	odd	2		384.4.j.a.289.10		24
8.5	even	2		384.4.j.b.289.3		24
12.11	even	2		576.4.k.b.145.6		24
16.3	odd	4		384.4.j.a.97.10		24
16.5	even	4	inner	48.4.j.a.37.11	yes	24
16.11	odd	4		192.4.j.a.49.4		24
16.13	even	4		384.4.j.b.97.3		24
48.5	odd	4		144.4.k.b.37.2		24
48.11	even	4		576.4.k.b.433.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.11	✓	24	1.1	even	1	trivial
48.4.j.a.37.11	yes	24	16.5	even	4	inner
144.4.k.b.37.2		24	48.5	odd	4
144.4.k.b.109.2		24	3.2	odd	2
192.4.j.a.49.4		24	16.11	odd	4
192.4.j.a.145.4		24	4.3	odd	2
384.4.j.a.97.10		24	16.3	odd	4
384.4.j.a.289.10		24	8.3	odd	2
384.4.j.b.97.3		24	16.13	even	4
384.4.j.b.289.3		24	8.5	even	2
576.4.k.b.145.6		24	12.11	even	2
576.4.k.b.433.6		24	48.11	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	48.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.59717 - 1.12013i) q^{2} +(2.12132 + 2.12132i) q^{3} +(5.49064 - 5.81833i) q^{4} +(0.706564 - 0.706564i) q^{5} +(7.88559 + 3.13329i) q^{6} +4.44122i q^{7} +(7.74288 - 21.2614i) q^{8} +9.00000i q^{9} +(1.04363 - 2.62651i) q^{10} +(-17.7126 + 17.7126i) q^{11} +(23.9899 - 0.695136i) q^{12} +(-17.7078 - 17.7078i) q^{13} +(4.97472 + 11.5346i) q^{14} +2.99770 q^{15} +(-3.70584 - 63.8926i) q^{16} -105.640 q^{17} +(10.0811 + 23.3746i) q^{18} +(40.2862 + 40.2862i) q^{19} +(-0.231534 - 7.99050i) q^{20} +(-9.42125 + 9.42125i) q^{21} +(-26.1624 + 65.8432i) q^{22} +42.9921i q^{23} +(61.5274 - 28.6771i) q^{24} +124.002i q^{25} +(-65.8252 - 26.1553i) q^{26} +(-19.0919 + 19.0919i) q^{27} +(25.8405 + 24.3851i) q^{28} +(-185.646 - 185.646i) q^{29} +(7.78554 - 3.35780i) q^{30} +291.485 q^{31} +(-81.1925 - 161.789i) q^{32} -75.1483 q^{33} +(-274.367 + 118.331i) q^{34} +(3.13800 + 3.13800i) q^{35} +(52.3649 + 49.4157i) q^{36} +(151.040 - 151.040i) q^{37} +(149.756 + 59.5047i) q^{38} -75.1278i q^{39} +(-9.55170 - 20.4934i) q^{40} -60.3918i q^{41} +(-13.9156 + 35.0216i) q^{42} +(120.532 - 120.532i) q^{43} +(5.80426 + 200.312i) q^{44} +(6.35907 + 6.35907i) q^{45} +(48.1565 + 111.658i) q^{46} +500.182 q^{47} +(127.675 - 143.398i) q^{48} +323.276 q^{49} +(138.897 + 322.054i) q^{50} +(-224.097 - 224.097i) q^{51} +(-200.257 + 5.80267i) q^{52} +(192.407 - 192.407i) q^{53} +(-28.1996 + 70.9703i) q^{54} +25.0302i q^{55} +(94.4266 + 34.3878i) q^{56} +170.920i q^{57} +(-690.102 - 274.208i) q^{58} +(-500.053 + 500.053i) q^{59} +(16.4593 - 17.4416i) q^{60} +(-166.418 - 166.418i) q^{61} +(757.037 - 326.500i) q^{62} -39.9710 q^{63} +(-392.096 - 329.249i) q^{64} -25.0234 q^{65} +(-195.173 + 84.1756i) q^{66} +(-575.426 - 575.426i) q^{67} +(-580.033 + 614.651i) q^{68} +(-91.2000 + 91.2000i) q^{69} +(11.6649 + 4.63498i) q^{70} +457.290i q^{71} +(191.353 + 69.6860i) q^{72} +1082.59i q^{73} +(223.094 - 561.462i) q^{74} +(-263.047 + 263.047i) q^{75} +(455.595 - 13.2014i) q^{76} +(-78.6657 - 78.6657i) q^{77} +(-84.1526 - 195.120i) q^{78} -544.309 q^{79} +(-47.7626 - 42.5258i) q^{80} -81.0000 q^{81} +(-67.6465 - 156.848i) q^{82} +(48.6931 + 48.6931i) q^{83} +(3.08725 + 106.545i) q^{84} +(-74.6417 + 74.6417i) q^{85} +(178.032 - 448.054i) q^{86} -787.630i q^{87} +(239.449 + 513.743i) q^{88} -43.6714i q^{89} +(23.6386 + 9.39266i) q^{90} +(78.6442 - 78.6442i) q^{91} +(250.142 + 236.054i) q^{92} +(618.332 + 618.332i) q^{93} +(1299.06 - 560.266i) q^{94} +56.9295 q^{95} +(170.972 - 515.442i) q^{96} +690.537 q^{97} +(839.603 - 362.109i) q^{98} +(-159.414 - 159.414i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{4} + 84 q^{8} + 72 q^{10} - 40 q^{11} - 24 q^{12} - 348 q^{14} + 120 q^{15} - 192 q^{16} - 36 q^{18} + 24 q^{19} + 80 q^{20} + 704 q^{22} + 228 q^{24} - 20 q^{26} - 344 q^{28} + 400 q^{29}+ \cdots - 360 q^{99}+O(q^{100}) \) 24 * q - 20 * q^4 + 84 * q^8 + 72 * q^10 - 40 * q^11 - 24 * q^12 - 348 * q^14 + 120 * q^15 - 192 * q^16 - 36 * q^18 + 24 * q^19 + 80 * q^20 + 704 * q^22 + 228 * q^24 - 20 * q^26 - 344 * q^28 + 400 * q^29 - 408 * q^30 - 744 * q^31 - 960 * q^32 - 704 * q^34 - 456 * q^35 + 108 * q^36 + 16 * q^37 + 1256 * q^38 + 1744 * q^40 + 660 * q^42 + 1240 * q^43 - 200 * q^44 - 1432 * q^46 - 528 * q^48 - 1176 * q^49 + 708 * q^50 + 744 * q^51 + 1008 * q^52 + 752 * q^53 + 108 * q^54 + 1344 * q^56 + 1936 * q^58 - 1376 * q^59 - 1224 * q^60 - 912 * q^61 - 996 * q^62 - 504 * q^63 - 56 * q^64 + 976 * q^65 - 1368 * q^66 - 2256 * q^67 - 1568 * q^68 - 528 * q^69 - 1760 * q^70 - 612 * q^72 - 2740 * q^74 + 1104 * q^75 - 1880 * q^76 + 1904 * q^77 + 1692 * q^78 + 5992 * q^79 + 712 * q^80 - 1944 * q^81 - 40 * q^82 + 2680 * q^83 + 1800 * q^84 - 240 * q^85 - 1712 * q^86 - 3936 * q^88 + 648 * q^90 - 3496 * q^91 + 5296 * q^92 + 5272 * q^94 - 7728 * q^95 + 2880 * q^96 + 6760 * q^98 - 360 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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