LMFDB - Embedded newform 42.5.h.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,5,Mod(11,42)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(42, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("42.11");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	42.h (of order $6$, 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:	$4.34153844952$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 20 x^{18} - 684 x^{17} - 3593 x^{16} - 62280 x^{15} + 1340206 x^{14} + 6921828 x^{13} + \cdots + 81\!\cdots\!09 $ x^20 - 20x^18 - 684x^17 - 3593x^16 - 62280x^15 + 1340206x^14 + 6921828x^13 + 37679467x^12 - 380890548x^11 - 2077817540x^10 - 73982451888x^9 + 507364948243x^8 + 687686868324x^7 + 27986581473280x^6 - 42677138798460x^5 - 1338007627265483x^4 - 14348052126267588x^3 + 52054868201143878x^2 - 406604690130980484x + 8145239244704821809
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.5
Root			$-7.38407 - 3.33167i$ of defining polynomial
Character	$\chi$	$=$	42.11
Dual form			42.5.h.a.23.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.44949 + 1.41421i) q^{2} +(8.60881 - 2.62456i) q^{3} +(4.00000 - 6.92820i) q^{4} +(3.82445 - 2.20805i) q^{5} +(-17.3755 + 18.6035i) q^{6} +(2.10732 - 48.9547i) q^{7} +22.6274i q^{8} +(67.2234 - 45.1887i) q^{9} +O(q^{10})$	\(q+(-2.44949 + 1.41421i) q^{2} +(8.60881 - 2.62456i) q^{3} +(4.00000 - 6.92820i) q^{4} +(3.82445 - 2.20805i) q^{5} +(-17.3755 + 18.6035i) q^{6} +(2.10732 - 48.9547i) q^{7} +22.6274i q^{8} +(67.2234 - 45.1887i) q^{9} +(-6.24530 + 10.8172i) q^{10} +(81.1907 + 46.8755i) q^{11} +(16.2518 - 70.1419i) q^{12} +275.630 q^{13} +(64.0705 + 122.894i) q^{14} +(27.1288 - 29.0462i) q^{15} +(-32.0000 - 55.4256i) q^{16} +(-296.745 - 171.326i) q^{17} +(-100.756 + 205.757i) q^{18} +(34.1435 + 59.1383i) q^{19} -35.3287i q^{20} +(-110.343 - 426.972i) q^{21} -265.168 q^{22} +(-675.025 + 389.726i) q^{23} +(59.3870 + 194.795i) q^{24} +(-302.749 + 524.377i) q^{25} +(-675.153 + 389.800i) q^{26} +(460.113 - 565.453i) q^{27} +(-330.739 - 210.419i) q^{28} -300.833i q^{29} +(-25.3743 + 109.514i) q^{30} +(-136.000 + 235.560i) q^{31} +(156.767 + 90.5097i) q^{32} +(821.983 + 190.452i) q^{33} +969.165 q^{34} +(-100.035 - 191.878i) q^{35} +(-44.1832 - 646.492i) q^{36} +(-19.9152 - 34.4941i) q^{37} +(-167.268 - 96.5725i) q^{38} +(2372.85 - 723.408i) q^{39} +(49.9624 + 86.5374i) q^{40} +1684.03i q^{41} +(874.114 + 889.816i) q^{42} -1320.00 q^{43} +(649.526 - 375.004i) q^{44} +(157.314 - 321.254i) q^{45} +(1102.31 - 1909.26i) q^{46} +(-742.107 + 428.456i) q^{47} +(-420.950 - 393.163i) q^{48} +(-2392.12 - 206.326i) q^{49} -1712.61i q^{50} +(-3004.28 - 696.087i) q^{51} +(1102.52 - 1909.62i) q^{52} +(3780.96 + 2182.94i) q^{53} +(-327.370 + 2035.77i) q^{54} +414.013 q^{55} +(1107.72 + 47.6832i) q^{56} +(449.148 + 419.499i) q^{57} +(425.442 + 736.886i) q^{58} +(-1574.24 - 908.890i) q^{59} +(-92.7224 - 304.139i) q^{60} +(2642.23 + 4576.47i) q^{61} -769.335i q^{62} +(-2070.54 - 3386.12i) q^{63} -512.000 q^{64} +(1054.13 - 608.604i) q^{65} +(-2282.78 + 695.949i) q^{66} +(2267.38 - 3927.22i) q^{67} +(-2373.96 + 1370.61i) q^{68} +(-4788.31 + 5126.73i) q^{69} +(516.390 + 328.532i) q^{70} -7785.12i q^{71} +(1022.50 + 1521.09i) q^{72} +(-4683.26 + 8111.64i) q^{73} +(97.5640 + 56.3286i) q^{74} +(-1230.05 + 5308.85i) q^{75} +546.297 q^{76} +(2465.87 - 3875.88i) q^{77} +(-4789.21 + 5127.69i) q^{78} +(1836.44 + 3180.81i) q^{79} +(-244.765 - 141.315i) q^{80} +(2476.96 - 6075.47i) q^{81} +(-2381.58 - 4125.03i) q^{82} -943.920i q^{83} +(-3399.52 - 943.411i) q^{84} -1513.18 q^{85} +(3233.32 - 1866.76i) q^{86} +(-789.554 - 2589.81i) q^{87} +(-1060.67 + 1837.14i) q^{88} +(-5151.07 + 2973.97i) q^{89} +(68.9843 + 1009.38i) q^{90} +(580.840 - 13493.4i) q^{91} +6235.62i q^{92} +(-552.562 + 2384.83i) q^{93} +(1211.86 - 2098.99i) q^{94} +(261.160 + 150.781i) q^{95} +(1587.13 + 367.735i) q^{96} +11112.5 q^{97} +(6151.26 - 2877.57i) q^{98} +(7576.16 - 517.777i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 80 q^{4} - 64 q^{6} + 130 q^{7} + 52 q^{9}+O(q^{10}) $ 20 * q + 80 * q^4 - 64 * q^6 + 130 * q^7 + 52 * q^9	$ 20 q + 80 q^{4} - 64 q^{6} + 130 q^{7} + 52 q^{9} + 32 q^{10} - 324 q^{13} + 964 q^{15} - 640 q^{16} + 576 q^{18} + 1030 q^{19} - 1442 q^{21} - 1280 q^{22} - 256 q^{24} + 22 q^{25} - 3780 q^{27} + 544 q^{28} - 128 q^{30} - 318 q^{31} + 842 q^{33} + 1024 q^{34} + 832 q^{36} + 2806 q^{37} + 5542 q^{39} - 256 q^{40} + 1632 q^{42} - 6644 q^{43} + 1526 q^{45} - 3008 q^{46} - 8350 q^{49} - 5266 q^{51} - 1296 q^{52} + 7040 q^{54} + 49696 q^{55} - 3840 q^{57} + 7904 q^{58} + 3856 q^{60} - 15960 q^{61} - 144 q^{63} - 10240 q^{64} + 896 q^{66} - 12490 q^{67} - 56932 q^{69} - 19904 q^{70} - 4608 q^{72} - 23746 q^{73} + 31738 q^{75} + 16480 q^{76} + 5888 q^{78} + 15474 q^{79} + 29788 q^{81} - 9984 q^{82} + 7168 q^{84} - 39368 q^{85} + 16084 q^{87} - 5120 q^{88} - 30208 q^{90} + 16074 q^{91} - 15176 q^{93} + 15360 q^{94} + 2048 q^{96} + 102512 q^{97} + 73276 q^{99}+O(q^{100}) $ 20 * q + 80 * q^4 - 64 * q^6 + 130 * q^7 + 52 * q^9 + 32 * q^10 - 324 * q^13 + 964 * q^15 - 640 * q^16 + 576 * q^18 + 1030 * q^19 - 1442 * q^21 - 1280 * q^22 - 256 * q^24 + 22 * q^25 - 3780 * q^27 + 544 * q^28 - 128 * q^30 - 318 * q^31 + 842 * q^33 + 1024 * q^34 + 832 * q^36 + 2806 * q^37 + 5542 * q^39 - 256 * q^40 + 1632 * q^42 - 6644 * q^43 + 1526 * q^45 - 3008 * q^46 - 8350 * q^49 - 5266 * q^51 - 1296 * q^52 + 7040 * q^54 + 49696 * q^55 - 3840 * q^57 + 7904 * q^58 + 3856 * q^60 - 15960 * q^61 - 144 * q^63 - 10240 * q^64 + 896 * q^66 - 12490 * q^67 - 56932 * q^69 - 19904 * q^70 - 4608 * q^72 - 23746 * q^73 + 31738 * q^75 + 16480 * q^76 + 5888 * q^78 + 15474 * q^79 + 29788 * q^81 - 9984 * q^82 + 7168 * q^84 - 39368 * q^85 + 16084 * q^87 - 5120 * q^88 - 30208 * q^90 + 16074 * q^91 - 15176 * q^93 + 15360 * q^94 + 2048 * q^96 + 102512 * q^97 + 73276 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.44949	+	1.41421i	−0.612372	+	0.353553i
$2$	−2.44949	+	1.41421i	−0.612372	+	0.353553i
$3$	8.60881	−	2.62456i	0.956535	−	0.291618i
$3$	8.60881	−	2.62456i	0.956535	−	0.291618i
$4$	4.00000	−	6.92820i	0.250000	−	0.433013i
$5$	3.82445	−	2.20805i	0.152978	−	0.0883219i	−0.421557	−	0.906802i	$-0.638516\pi$
$5$	3.82445	−	2.20805i	0.152978	−	0.0883219i	0.574535	+	0.818480i	$0.305183\pi$
$6$	−17.3755	+	18.6035i	−0.482653	+	0.516765i
$7$	2.10732	−	48.9547i	0.0430065	−	0.999075i
$7$	2.10732	−	48.9547i	0.0430065	−	0.999075i
$8$			22.6274i			0.353553i
$9$	67.2234	−	45.1887i	0.829918	−	0.557885i
$10$	−6.24530	+	10.8172i	−0.0624530	+	0.108172i
$11$	81.1907	+	46.8755i	0.670998	+	0.387401i	0.796455	−	0.604698i	$-0.206706\pi$
$11$	81.1907	+	46.8755i	0.670998	+	0.387401i	−0.125457	+	0.992099i	$0.540040\pi$
$12$	16.2518	−	70.1419i	0.112859	−	0.487096i
$13$	275.630			1.63095			0.815474	−	0.578794i	$-0.196477\pi$
$13$	275.630			1.63095			0.815474	+	0.578794i	$0.196477\pi$
$14$	64.0705	+	122.894i	0.326890	+	0.627011i
$15$	27.1288	−	29.0462i	0.120573	−	0.129094i
$16$	−32.0000	−	55.4256i	−0.125000	−	0.216506i
$17$	−296.745	−	171.326i	−1.02680	−	0.592823i	−0.110733	−	0.993850i	$-0.535320\pi$
$17$	−296.745	−	171.326i	−1.02680	−	0.592823i	−0.916066	+	0.401027i	$0.868653\pi$
$18$	−100.756	+	205.757i	−0.310977	+	0.635054i
$19$	34.1435	+	59.1383i	0.0945804	+	0.163818i	0.909433	−	0.415850i	$-0.136516\pi$
$19$	34.1435	+	59.1383i	0.0945804	+	0.163818i	−0.814853	+	0.579668i	$0.803182\pi$
$20$		−	35.3287i		−	0.0883219i
$21$	−110.343	−	426.972i	−0.250211	−	0.968191i
$22$	−265.168			−0.547867
$23$	−675.025	+	389.726i	−1.27604	+	0.736722i	−0.976118	−	0.217241i	$-0.930294\pi$
$23$	−675.025	+	389.726i	−1.27604	+	0.736722i	−0.299923	+	0.953964i	$0.596961\pi$
$24$	59.3870	+	194.795i	0.103102	+	0.338186i
$25$	−302.749	+	524.377i	−0.484398	+	0.839003i
$26$	−675.153	+	389.800i	−0.998747	+	0.576627i
$27$	460.113	−	565.453i	0.631156	−	0.775656i
$28$	−330.739	−	210.419i	−0.421860	−	0.268391i
$29$		−	300.833i		−	0.357708i	−0.983876	−	0.178854i	$-0.942761\pi$
$29$		−	300.833i		−	0.357708i	0.983876	−	0.178854i	$-0.0572390\pi$
$30$	−25.3743	+	109.514i	−0.0281936	+	0.121682i
$31$	−136.000	+	235.560i	−0.141520	+	0.245119i	−0.928069	−	0.372408i	$-0.878532\pi$
$31$	−136.000	+	235.560i	−0.141520	+	0.245119i	0.786549	+	0.617527i	$0.211866\pi$
$32$	156.767	+	90.5097i	0.153093	+	0.0883883i
$33$	821.983	+	190.452i	0.754806	+	0.174887i
$34$	969.165			0.838378
$35$	−100.035	−	191.878i	−0.0816611	−	0.156635i
$36$	−44.1832	−	646.492i	−0.0340919	−	0.498836i
$37$	−19.9152	−	34.4941i	−0.0145472	−	0.0251966i	0.858660	−	0.512545i	$-0.171297\pi$
$37$	−19.9152	−	34.4941i	−0.0145472	−	0.0251966i	−0.873207	+	0.487349i	$0.837964\pi$
$38$	−167.268	−	96.5725i	−0.115837	−	0.0668785i
$39$	2372.85	−	723.408i	1.56006	−	0.475613i
$40$	49.9624	+	86.5374i	0.0312265	+	0.0540859i
$41$			1684.03i			1.00181i	0.865504	+	0.500903i	$0.166999\pi$
$41$			1684.03i			1.00181i	−0.865504	+	0.500903i	$0.833001\pi$
$42$	874.114	+	889.816i	0.495530	+	0.504431i
$43$	−1320.00			−0.713898			−0.356949	−	0.934124i	$-0.616183\pi$
$43$	−1320.00			−0.713898			−0.356949	+	0.934124i	$0.616183\pi$
$44$	649.526	−	375.004i	0.335499	−	0.193700i
$45$	157.314	−	321.254i	0.0776857	−	0.158644i
$46$	1102.31	−	1909.26i	0.520941	−	0.902297i
$47$	−742.107	+	428.456i	−0.335947	+	0.193959i	−0.658478	−	0.752600i	$-0.728800\pi$
$47$	−742.107	+	428.456i	−0.335947	+	0.193959i	0.322531	+	0.946559i	$0.395466\pi$
$48$	−420.950	−	393.163i	−0.182704	−	0.170644i
$49$	−2392.12	−	206.326i	−0.996301	−	0.0859334i
$50$		−	1712.61i		−	0.685043i
$51$	−3004.28	−	696.087i	−1.15505	−	0.267623i
$52$	1102.52	−	1909.62i	0.407737	−	0.706221i
$53$	3780.96	+	2182.94i	1.34602	+	0.777123i	0.987683	−	0.156470i	$-0.0500114\pi$
$53$	3780.96	+	2182.94i	1.34602	+	0.777123i	0.358335	+	0.933593i	$0.383345\pi$
$54$	−327.370	+	2035.77i	−0.112267	+	0.698138i
$55$	414.013			0.136864
$56$	1107.72	+	47.6832i	0.353226	+	0.0152051i
$57$	449.148	+	419.499i	0.138242	+	0.129116i
$58$	425.442	+	736.886i	0.126469	+	0.219051i
$59$	−1574.24	−	908.890i	−0.452239	−	0.261100i	0.256536	−	0.966535i	$-0.417419\pi$
$59$	−1574.24	−	908.890i	−0.452239	−	0.261100i	−0.708775	+	0.705434i	$0.750752\pi$
$60$	−92.7224	−	304.139i	−0.0257562	−	0.0844829i
$61$	2642.23	+	4576.47i	0.710085	+	1.22990i	0.964825	+	0.262894i	$0.0846768\pi$
$61$	2642.23	+	4576.47i	0.710085	+	1.22990i	−0.254740	+	0.967010i	$0.581990\pi$
$62$		−	769.335i		−	0.200139i
$63$	−2070.54	−	3386.12i	−0.521677	−	0.853143i
$64$	−512.000			−0.125000
$65$	1054.13	−	608.604i	0.249499	−	0.144048i
$66$	−2282.78	+	695.949i	−0.524054	+	0.159768i
$67$	2267.38	−	3927.22i	0.505097	−	0.874853i	−0.494886	−	0.868958i	$-0.664790\pi$
$67$	2267.38	−	3927.22i	0.505097	−	0.874853i	0.999983	−	0.00589539i	$-0.00187657\pi$
$68$	−2373.96	+	1370.61i	−0.513400	+	0.296412i
$69$	−4788.31	+	5126.73i	−1.00574	+	1.07682i
$70$	516.390	+	328.532i	0.105386	+	0.0670473i
$71$		−	7785.12i		−	1.54436i	−0.635403	−	0.772181i	$-0.719166\pi$
$71$		−	7785.12i		−	1.54436i	0.635403	−	0.772181i	$-0.280834\pi$
$72$	1022.50	+	1521.09i	0.197242	+	0.293420i
$73$	−4683.26	+	8111.64i	−0.878825	+	1.52217i	−0.0261924	+	0.999657i	$0.508338\pi$
$73$	−4683.26	+	8111.64i	−0.878825	+	1.52217i	−0.852632	+	0.522512i	$0.824995\pi$
$74$	97.5640	+	56.3286i	0.0178167	+	0.0102865i
$75$	−1230.05	+	5308.85i	−0.218676	+	0.943795i
$76$	546.297			0.0945804
$77$	2465.87	−	3875.88i	0.415900	−	0.653716i
$78$	−4789.21	+	5127.69i	−0.787182	+	0.842816i
$79$	1836.44	+	3180.81i	0.294254	+	0.509664i	0.974811	−	0.223032i	$-0.0715954\pi$
$79$	1836.44	+	3180.81i	0.294254	+	0.509664i	−0.680557	+	0.732695i	$0.738262\pi$
$80$	−244.765	−	141.315i	−0.0382445	−	0.0220805i
$81$	2476.96	−	6075.47i	0.377528	−	0.925998i
$82$	−2381.58	−	4125.03i	−0.354192	−	0.613478i
$83$		−	943.920i		−	0.137018i	−0.997650	−	0.0685092i	$-0.978176\pi$
$83$		−	943.920i		−	0.137018i	0.997650	−	0.0685092i	$-0.0218242\pi$
$84$	−3399.52	−	943.411i	−0.481792	−	0.133703i
$85$	−1513.18			−0.209437
$86$	3233.32	−	1866.76i	0.437172	−	0.252401i
$87$	−789.554	−	2589.81i	−0.104314	−	0.342160i
$88$	−1060.67	+	1837.14i	−0.136967	+	0.237234i
$89$	−5151.07	+	2973.97i	−0.650305	+	0.375454i	−0.788573	−	0.614941i	$-0.789180\pi$
$89$	−5151.07	+	2973.97i	−0.650305	+	0.375454i	0.138268	+	0.990395i	$0.455847\pi$
$90$	68.9843	+	1009.38i	0.00851657	+	0.124615i
$91$	580.840	−	13493.4i	0.0701413	−	1.62944i
$92$			6235.62i			0.736722i
$93$	−552.562	+	2384.83i	−0.0638874	+	0.275735i
$94$	1211.86	−	2098.99i	0.137150	−	0.237550i
$95$	261.160	+	150.781i	0.0289374	+	0.0167070i
$96$	1587.13	+	367.735i	0.172215	+	0.0399019i
$97$	11112.5			1.18105			0.590525	−	0.807019i	$-0.298921\pi$
$97$	11112.5			1.18105			0.590525	+	0.807019i	$0.298921\pi$
$98$	6151.26	−	2877.57i	0.640489	−	0.299622i
$99$	7576.16	−	517.777i	0.772998	−	0.0528290i
$100$	2421.99	+	4195.01i	0.242199	+	0.419501i
$101$	14892.1	+	8597.96i	1.45987	+	0.842854i	0.999004	−	0.0446174i	$-0.0142069\pi$
$101$	14892.1	+	8597.96i	1.45987	+	0.842854i	0.460862	+	0.887472i	$0.347540\pi$
$102$	8343.36	−	2543.63i	0.801938	−	0.244486i
$103$	−3929.81	−	6806.64i	−0.370423	−	0.641591i	0.619208	−	0.785227i	$-0.287454\pi$
$103$	−3929.81	−	6806.64i	−0.370423	−	0.641591i	−0.989631	+	0.143636i	$0.954121\pi$
$104$			6236.80i			0.576627i
$105$	−1364.78	−	1389.29i	−0.123789	−	0.126013i
$106$	−12348.6			−1.09902
$107$	3331.84	−	1923.64i	0.291015	−	0.168018i	−0.347384	−	0.937723i	$-0.612930\pi$
$107$	3331.84	−	1923.64i	0.291015	−	0.168018i	0.638400	+	0.769705i	$0.279597\pi$
$108$	−2077.12	−	5449.57i	−0.178080	−	0.467213i
$109$	−4585.52	+	7942.35i	−0.385954	+	0.668492i	−0.991901	−	0.127013i	$-0.959461\pi$
$109$	−4585.52	+	7942.35i	−0.385954	+	0.668492i	0.605947	+	0.795505i	$0.292794\pi$
$110$	−1014.12	+	585.503i	−0.0838116	+	0.0483887i
$111$	−261.978	−	244.685i	−0.0212627	−	0.0198592i
$112$	−2780.78	+	1449.75i	−0.221682	+	0.115573i
$113$		−	18454.5i		−	1.44526i	−0.691237	−	0.722628i	$-0.742934\pi$
$113$		−	18454.5i		−	1.44526i	0.691237	−	0.722628i	$-0.257066\pi$
$114$	−1693.44	−	392.368i	−0.130305	−	0.0301915i
$115$	−1721.07	+	2980.98i	−0.130137	+	0.225405i
$116$	−2084.23	−	1203.33i	−0.154892	−	0.0894271i
$117$	18528.8	−	12455.4i	1.35355	−	0.909882i
$118$	5141.46			0.369251
$119$	−9012.54	+	14166.0i	−0.636434	+	1.00035i
$120$	657.240	+	613.855i	0.0456416	+	0.0426288i
$121$	−2925.88	−	5067.77i	−0.199841	−	0.346135i
$122$	−12944.2	−	7473.34i	−0.869673	−	0.502106i
$123$	4419.85	+	14497.5i	0.292144	+	0.958262i
$124$	1088.00	+	1884.48i	0.0707599	+	0.122560i
$125$			5433.99i			0.347776i
$126$	9860.46	+	5366.09i	0.621092	+	0.338000i
$127$	8510.39			0.527645			0.263823	−	0.964571i	$-0.415017\pi$
$127$	8510.39			0.527645			0.263823	+	0.964571i	$0.415017\pi$
$128$	1254.14	−	724.077i	0.0765466	−	0.0441942i
$129$	−11363.6	+	3464.42i	−0.682869	+	0.208186i
$130$	−1721.39	+	2981.54i	−0.101858	+	0.176422i
$131$	−22442.9	+	12957.4i	−1.30779	+	0.755050i	−0.981726	−	0.190299i	$-0.939054\pi$
$131$	−22442.9	+	12957.4i	−1.30779	+	0.755050i	−0.326059	+	0.945349i	$0.605721\pi$
$132$	4607.43	−	4933.06i	0.264430	−	0.283119i
$133$	2967.05	−	1546.86i	0.167734	−	0.0874477i
$134$			12826.2i			0.714315i
$135$	511.131	−	3178.50i	0.0280456	−	0.174403i
$136$	3876.66	−	6714.57i	0.209595	−	0.363028i
$137$	−27083.3	−	15636.5i	−1.44298	−	0.833104i	−0.444931	−	0.895565i	$-0.646772\pi$
$137$	−27083.3	−	15636.5i	−1.44298	−	0.833104i	−0.998047	+	0.0624613i	$0.980105\pi$
$138$	4478.63	−	19329.6i	0.235173	−	1.01499i
$139$	−12472.3			−0.645531			−0.322766	−	0.946479i	$-0.604613\pi$
$139$	−12472.3			−0.645531			−0.322766	+	0.946479i	$0.604613\pi$
$140$	−1729.51	−	74.4489i	−0.0882401	−	0.00379841i
$141$	−5264.15	+	5636.20i	−0.264783	+	0.283497i
$142$	11009.8	+	19069.6i	0.546014	+	0.945724i
$143$	22378.6	+	12920.3i	1.09436	+	0.631830i
$144$	−4655.76	−	2279.86i	−0.224525	−	0.109947i
$145$	−664.252	−	1150.52i	−0.0315935	−	0.0547215i
$146$		−	26492.5i		−	1.24285i
$147$	−21134.8	+	4502.04i	−0.978056	+	0.208341i
$148$	−318.643			−0.0145472
$149$	−30309.8	+	17499.4i	−1.36525	+	0.788225i	−0.990316	−	0.138829i	$-0.955666\pi$
$149$	−30309.8	+	17499.4i	−1.36525	+	0.788225i	−0.374929	+	0.927053i	$0.622333\pi$
$150$	−4494.84	−	14743.5i	−0.199771	−	0.655267i
$151$	−8722.04	+	15107.0i	−0.382529	+	0.662560i	−0.991423	−	0.130692i	$-0.958280\pi$
$151$	−8722.04	+	15107.0i	−0.382529	+	0.662560i	0.608894	+	0.793252i	$0.291613\pi$
$152$	−1338.15	+	772.580i	−0.0579185	+	0.0334392i
$153$	−27690.2	+	1892.43i	−1.18289	+	0.0808420i
$154$	−558.793	+	12981.2i	−0.0235619	+	0.547360i
$155$			1201.18i			0.0499972i
$156$	4479.47	−	19333.2i	0.184068	−	0.794428i
$157$	6316.20	−	10940.0i	0.256246	−	0.443831i	−0.708987	−	0.705221i	$-0.750848\pi$
$157$	6316.20	−	10940.0i	0.256246	−	0.443831i	0.965233	+	0.261390i	$0.0841810\pi$
$158$	−8996.69	−	5194.24i	−0.360387	−	0.208069i
$159$	38278.9	+	8869.16i	1.51414	+	0.350823i
$160$	799.398			0.0312265
$161$	17656.4	+	33866.9i	0.681163	+	1.30654i
$162$	2524.73	+	18384.8i	0.0962022	+	0.700532i
$163$	−23748.5	−	41133.6i	−0.893842	−	1.54818i	−0.835232	−	0.549898i	$-0.814666\pi$
$163$	−23748.5	−	41133.6i	−0.893842	−	1.54818i	−0.0586101	−	0.998281i	$-0.518667\pi$
$164$	11667.3	+	6736.14i	0.433794	+	0.250451i
$165$	3564.16	−	1086.60i	0.130915	−	0.0399119i
$166$	1334.90	+	2312.12i	0.0484433	+	0.0839063i
$167$		−	32946.4i		−	1.18134i	−0.806912	−	0.590671i	$-0.798863\pi$
$167$		−	32946.4i		−	1.18134i	0.806912	−	0.590671i	$-0.201137\pi$
$168$	9661.28	−	2496.78i	0.342307	−	0.0884629i
$169$	47410.9			1.65999
$170$	3706.52	−	2139.96i	0.128253	−	0.0740471i
$171$	4967.63	+	2432.58i	0.169886	+	0.0831906i
$172$	−5279.99	+	9145.21i	−0.178475	+	0.309127i
$173$	28978.4	−	16730.7i	0.968240	−	0.559013i	0.0695405	−	0.997579i	$-0.477847\pi$
$173$	28978.4	−	16730.7i	0.968240	−	0.559013i	0.898699	+	0.438566i	$0.144513\pi$
$174$	5596.55	+	5227.12i	0.184851	+	0.172649i
$175$	25032.7	+	15926.0i	0.817394	+	0.520033i
$176$		−	6000.06i		−	0.193700i
$177$	−15937.8	−	3692.77i	−0.508724	−	0.117871i
$178$	8411.66	−	14569.4i	0.265486	−	0.459835i
$179$	9753.39	+	5631.12i	0.304403	+	0.175747i	0.644419	−	0.764672i	$-0.277099\pi$
$179$	9753.39	+	5631.12i	0.304403	+	0.175747i	−0.340016	+	0.940420i	$0.610432\pi$
$180$	−1596.46	−	2374.92i	−0.0492735	−	0.0732999i
$181$	4875.68			0.148826			0.0744129	−	0.997228i	$-0.476292\pi$
$181$	4875.68			0.148826			0.0744129	+	0.997228i	$0.476292\pi$
$182$	17659.8	+	33873.3i	0.533141	+	1.02262i
$183$	34757.7	+	32463.3i	1.03788	+	0.969372i
$184$	−8818.50	−	15274.1i	−0.260471	−	0.451148i
$185$	−152.329	−	87.9473i	−0.00445081	−	0.00256968i
$186$	−2019.17	−	6623.06i	−0.0583642	−	0.191440i
$187$	−16062.0	−	27820.1i	−0.459320	−	0.795566i
$188$			6855.29i			0.193959i
$189$	−26712.0	−	23716.3i	−0.747794	−	0.663930i
$190$	−852.946			−0.0236273
$191$	45157.0	−	26071.4i	1.23782	−	0.714657i	0.269173	−	0.963092i	$-0.413250\pi$
$191$	45157.0	−	26071.4i	1.23782	−	0.714657i	0.968649	+	0.248435i	$0.0799163\pi$
$192$	−4407.71	+	1343.78i	−0.119567	+	0.0364522i
$193$	6815.94	−	11805.6i	0.182983	−	0.316936i	−0.759912	−	0.650026i	$-0.774758\pi$
$193$	6815.94	−	11805.6i	0.182983	−	0.316936i	0.942895	+	0.333090i	$0.108091\pi$
$194$	−27220.0	+	15715.5i	−0.723243	+	0.417564i
$195$	7477.52	−	8005.99i	0.196647	−	0.210546i
$196$	−10997.9	+	15747.8i	−0.286285	+	0.409928i
$197$		−	17350.2i		−	0.447066i	−0.974696	−	0.223533i	$-0.928241\pi$
$197$		−	17350.2i		−	0.447066i	0.974696	−	0.223533i	$-0.0717590\pi$
$198$	−17825.5	+	11982.6i	−0.454685	+	0.305647i
$199$	−11445.4	+	19823.9i	−0.289017	+	0.500592i	−0.973575	−	0.228366i	$-0.926662\pi$
$199$	−11445.4	+	19823.9i	−0.289017	+	0.500592i	0.684558	+	0.728958i	$0.259995\pi$
$200$	−11865.3	−	6850.43i	−0.296632	−	0.171261i
$201$	9212.23	−	39759.6i	0.228020	−	0.984123i
$202$	−48637.4			−1.19198
$203$	−14727.2	−	633.950i	−0.357377	−	0.0153838i
$204$	−16839.7	+	18029.9i	−0.404646	+	0.433245i
$205$	3718.43	+	6440.50i	0.0884813	+	0.153254i
$206$	19252.1	+	11115.2i	0.453673	+	0.261928i
$207$	−27766.3	+	56702.2i	−0.648002	+	1.32330i
$208$	−8820.16	−	15277.0i	−0.203868	−	0.353110i
$209$			6401.98i			0.146562i
$210$	5307.76	+	1472.97i	0.120357	+	0.0334007i
$211$	−24669.6			−0.554112			−0.277056	−	0.960854i	$-0.589359\pi$
$211$	−24669.6			−0.554112			−0.277056	+	0.960854i	$0.589359\pi$
$212$	30247.7	−	17463.5i	0.673009	−	0.388562i
$213$	−20432.5	−	67020.7i	−0.450363	−	1.47724i
$214$	−5440.87	+	9423.86i	−0.118807	+	0.205779i
$215$	−5048.26	+	2914.62i	−0.109211	+	0.0630528i
$216$	12794.7	+	10411.2i	0.274236	+	0.223147i
$217$	11245.2	+	7154.26i	0.238806	+	0.151931i
$218$		−	25939.6i		−	0.545821i
$219$	−19027.8	+	82123.1i	−0.396735	+	1.71229i
$220$	1656.05	−	2868.37i	0.0342159	−	0.0592638i
$221$	−81791.9	−	47222.6i	−1.67466	−	0.966863i
$222$	987.749	+	228.860i	0.0200420	+	0.00464370i
$223$	−12458.1			−0.250519			−0.125260	−	0.992124i	$-0.539976\pi$
$223$	−12458.1			−0.250519			−0.125260	+	0.992124i	$0.539976\pi$
$224$	4761.23	−	7483.76i	0.0948906	−	0.149150i
$225$	3344.10	+	48931.2i	0.0660563	+	0.966542i
$226$	26098.6	+	45204.0i	0.510975	+	0.885035i
$227$	27164.4	+	15683.4i	0.527167	+	0.304360i	0.739862	−	0.672759i	$-0.234891\pi$
$227$	27164.4	+	15683.4i	0.527167	+	0.304360i	−0.212695	+	0.977119i	$0.568224\pi$
$228$	4702.97	−	1433.79i	0.0904695	−	0.0275813i
$229$	23877.4	+	41356.8i	0.455319	+	0.788635i	0.998706	−	0.0508467i	$-0.0161920\pi$
$229$	23877.4	+	41356.8i	0.455319	+	0.788635i	−0.543388	+	0.839482i	$0.682859\pi$
$230$		−	9735.82i		−	0.184042i
$231$	11055.7	−	39838.6i	0.207187	−	0.746586i
$232$	6807.06			0.126469
$233$	54468.3	−	31447.3i	1.00330	−	0.579257i	0.0940787	−	0.995565i	$-0.470009\pi$
$233$	54468.3	−	31447.3i	1.00330	−	0.579257i	0.909224	+	0.416308i	$0.136676\pi$
$234$	−27771.5	+	56712.9i	−0.507186	+	1.03574i
$235$	−1892.10	+	3277.21i	−0.0342616	+	0.0593429i
$236$	−12593.9	+	7271.12i	−0.226119	+	0.130550i
$237$	24157.8	+	22563.2i	0.430092	+	0.401701i
$238$	2042.34	−	47445.2i	0.0360557	−	0.837603i
$239$		−	52495.3i		−	0.919020i	−0.888173	−	0.459510i	$-0.848025\pi$
$239$		−	52495.3i		−	0.919020i	0.888173	−	0.459510i	$-0.151975\pi$
$240$	−2478.02	−	574.154i	−0.0430212	−	0.00996796i
$241$	−24728.3	+	42830.7i	−0.425755	+	0.737430i	−0.996491	−	0.0837042i	$-0.973325\pi$
$241$	−24728.3	+	42830.7i	−0.425755	+	0.737430i	0.570735	+	0.821134i	$0.306658\pi$
$242$	14333.8	+	8275.63i	0.244755	+	0.141309i
$243$	5378.24	−	58803.6i	0.0910809	−	0.995843i
$244$	42275.6			0.710085
$245$	−9604.11	+	4492.82i	−0.160002	+	0.0748492i
$246$	−31329.0	−	29261.0i	−0.517698	−	0.483524i
$247$	9410.99	+	16300.3i	0.154256	+	0.267179i
$248$	−5330.11	−	3077.34i	−0.0866628	−	0.0500348i
$249$	−2477.37	−	8126.03i	−0.0399570	−	0.131063i
$250$	−7684.83	−	13310.5i	−0.122957	−	0.212968i
$251$			36828.1i			0.584563i	0.956332	+	0.292282i	$0.0944144\pi$
$251$			36828.1i			0.584563i	−0.956332	+	0.292282i	$0.905586\pi$
$252$	−31741.9	+	800.607i	−0.499841	+	0.0126072i
$253$	−73074.4			−1.14163
$254$	−20846.1	+	12035.5i	−0.323115	+	0.186551i
$255$	−13026.7	+	3971.44i	−0.200334	+	0.0610756i
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	−41294.6	+	23841.5i	−0.625212	+	0.360966i	−0.778895	−	0.627154i	$-0.784220\pi$
$257$	−41294.6	+	23841.5i	−0.625212	+	0.360966i	0.153683	+	0.988120i	$0.450886\pi$
$258$	22935.6	−	24556.6i	0.344565	−	0.368918i
$259$	−1730.61	+	902.251i	−0.0257989	+	0.0134502i
$260$		−	9737.66i		−	0.144048i
$261$	−13594.2	−	20223.0i	−0.199560	−	0.296868i
$262$	36649.1	−	63478.1i	0.533901	−	0.924744i
$263$	96838.2	+	55909.6i	1.40002	+	0.808304i	0.994394	−	0.105734i	$-0.0337193\pi$
$263$	96838.2	+	55909.6i	1.40002	+	0.808304i	0.405629	+	0.914038i	$0.367053\pi$
$264$	−4309.44	+	18599.4i	−0.0618320	+	0.266864i
$265$	19280.1			0.274548
$266$	−5080.16	+	7985.06i	−0.0717983	+	0.112854i
$267$	−36539.2	+	39121.7i	−0.512551	+	0.548776i
$268$	−18139.0	−	31417.7i	−0.252548	−	0.437427i
$269$	32362.9	+	18684.8i	0.447243	+	0.258216i	0.706665	−	0.707548i	$-0.250199\pi$
$269$	32362.9	+	18684.8i	0.447243	+	0.258216i	−0.259422	+	0.965764i	$0.583532\pi$
$270$	3243.06	+	8508.54i	0.0444864	+	0.116715i
$271$	−9451.68	−	16370.8i	−0.128698	−	0.222911i	0.794475	−	0.607297i	$-0.207746\pi$
$271$	−9451.68	−	16370.8i	−0.128698	−	0.222911i	−0.923172	+	0.384387i	$0.874413\pi$
$272$			21929.7i			0.296412i
$273$	−30413.8	−	117686.i	−0.408081	−	1.57907i
$274$	88453.5			1.17819
$275$	−49160.8	+	28383.0i	−0.650061	+	0.375313i
$276$	16365.8	+	53681.3i	0.214841	+	0.704701i
$277$	47203.5	−	81758.9i	0.615198	−	1.06555i	−0.375152	−	0.926963i	$-0.622409\pi$
$277$	47203.5	−	81758.9i	0.615198	−	1.06555i	0.990350	−	0.138591i	$-0.0442572\pi$
$278$	30550.8	−	17638.5i	0.395306	−	0.228230i
$279$	1502.23	+	21980.8i	0.0192987	+	0.282381i
$280$	4341.70	−	2263.53i	0.0553788	−	0.0288716i
$281$			26913.5i			0.340845i	0.985371	+	0.170423i	$0.0545133\pi$
$281$			26913.5i			0.340845i	−0.985371	+	0.170423i	$0.945487\pi$
$282$	4923.70	−	21250.4i	0.0619146	−	0.267221i
$283$	15436.5	−	26736.7i	0.192741	−	0.333838i	−0.753416	−	0.657544i	$-0.771596\pi$
$283$	15436.5	−	26736.7i	0.192741	−	0.333838i	0.946158	+	0.323706i	$0.104929\pi$
$284$	−53936.9	−	31140.5i	−0.668728	−	0.386090i
$285$	2644.02	+	612.614i	0.0325517	+	0.00754219i
$286$	−73088.2			−0.893543
$287$	82441.4	+	3548.80i	1.00088	+	0.0430841i
$288$	14628.4	−	999.751i	0.176365	−	0.0120533i
$289$	16944.6	+	29348.9i	0.202878	+	0.351395i
$290$	3254.16	+	1878.79i	0.0386939	+	0.0223399i
$291$	95665.5	−	29165.5i	1.12972	−	0.344416i
$292$	37466.0	+	64893.1i	0.439412	+	0.761084i
$293$		−	10045.8i		−	0.117017i	−0.998287	−	0.0585085i	$-0.981366\pi$
$293$		−	10045.8i		−	0.117017i	0.998287	−	0.0585085i	$-0.0186345\pi$
$294$	45402.7	−	40916.8i	0.525275	−	0.473377i
$295$	−8027.48			−0.0922434
$296$	780.512	−	450.629i	0.00890833	−	0.00514323i
$297$	63862.8	−	24341.5i	0.723994	−	0.275953i
$298$	49495.7	−	85729.1i	0.557359	−	0.965374i
$299$	−186057.	+	107420.i	−2.08115	+	1.20156i
$300$	31860.6	+	29757.4i	0.354006	+	0.330638i
$301$	−2781.66	+	64620.1i	−0.0307023	+	0.713238i
$302$		−	49339.3i		−	0.540978i
$303$	150769.	+	34933.0i	1.64220	+	0.380496i
$304$	2185.19	−	3784.85i	0.0236451	−	0.0409545i
$305$	20210.1	+	11668.3i	0.217255	+	0.125432i
$306$	65150.6	−	43795.3i	0.695785	−	0.467719i
$307$	−64202.3			−0.681199			−0.340599	−	0.940209i	$-0.610630\pi$
$307$	−64202.3			−0.681199			−0.340599	+	0.940209i	$0.610630\pi$
$308$	−16989.4	−	32587.6i	−0.179092	−	0.343519i
$309$	−51695.5	−	48283.1i	−0.541422	−	0.505682i
$310$	−1698.73	−	2942.28i	−0.0176767	−	0.0306169i
$311$	−138302.	−	79848.8i	−1.42991	−	0.825559i	−0.432796	−	0.901492i	$-0.642473\pi$
$311$	−138302.	−	79848.8i	−1.42991	−	0.825559i	−0.997113	+	0.0759331i	$0.975806\pi$
$312$	16368.9	+	53691.4i	0.168155	+	0.551564i
$313$	62515.7	+	108280.i	0.638117	+	1.10525i	0.985846	+	0.167656i	$0.0536197\pi$
$313$	62515.7	+	108280.i	0.638117	+	1.10525i	−0.347729	+	0.937595i	$0.613047\pi$
$314$			35729.8i			0.362386i
$315$	−15395.4	−	8378.21i	−0.155156	−	0.0844365i
$316$	29383.1			0.294254
$317$	7016.68	−	4051.08i	0.0698253	−	0.0403137i	−0.464681	−	0.885478i	$-0.653831\pi$
$317$	7016.68	−	4051.08i	0.0698253	−	0.0403137i	0.534506	+	0.845165i	$0.320498\pi$
$318$	−106307.	+	32409.6i	−1.05125	+	0.320493i
$319$	14101.7	−	24424.8i	0.138576	−	0.240021i
$320$	−1958.12	+	1130.52i	−0.0191222	+	0.0110402i
$321$	23634.5	−	25304.8i	0.229369	−	0.245580i
$322$	−91144.3	−	57986.7i	−0.879058	−	0.559264i
$323$		−	23398.7i		−	0.224278i
$324$	−32184.3	−	41462.8i	−0.306587	−	0.394974i
$325$	−83446.7	+	144534.i	−0.790028	+	1.36837i
$326$	116343.	+	67170.8i	1.09473	+	0.632042i
$327$	−18630.7	+	80409.2i	−0.174234	+	0.751987i
$328$	−38105.4			−0.354192
$329$	19411.0	+	37232.5i	0.179332	+	0.343978i
$330$	−7193.69	+	7702.11i	−0.0660577	+	0.0707264i
$331$	−90814.8	−	157296.i	−0.828897	−	1.43569i	−0.898904	−	0.438146i	$-0.855635\pi$
$331$	−90814.8	−	157296.i	−0.828897	−	1.43569i	0.0700064	−	0.997547i	$-0.477698\pi$
$332$	−6539.67	−	3775.68i	−0.0593307	−	0.0342546i
$333$	−2897.51	−	1418.87i	−0.0261298	−	0.0127954i
$334$	46593.3	+	80702.0i	0.417667	+	0.723421i
$335$		−	20025.9i		−	0.178444i
$336$	−20134.2	+	19778.9i	−0.178343	+	0.175196i
$337$	−111912.			−0.985406			−0.492703	−	0.870197i	$-0.663991\pi$
$337$	−111912.			−0.985406			−0.492703	+	0.870197i	$0.663991\pi$
$338$	−116133.	+	67049.2i	−1.01653	+	0.586895i
$339$	−48434.9	−	158871.i	−0.421462	−	1.38244i
$340$	−6052.73	+	10483.6i	−0.0523592	+	0.0906888i
$341$	−22084.0	+	12750.2i	−0.189919	+	0.109650i
$342$	−15608.3	+	1066.72i	−0.133446	+	0.00912007i
$343$	−15141.6	+	116671.i	−0.128701	+	0.991683i
$344$		−	29868.1i		−	0.252401i
$345$	−6992.59	+	30179.7i	−0.0587489	+	0.253558i
$346$	−47321.6	+	81963.4i	−0.395282	+	0.684649i
$347$	−82395.1	−	47570.8i	−0.684294	−	0.395077i	0.117177	−	0.993111i	$-0.462615\pi$
$347$	−82395.1	−	47570.8i	−0.684294	−	0.395077i	−0.801471	+	0.598034i	$0.795949\pi$
$348$	−21101.0	−	4889.06i	−0.174238	−	0.0403708i
$349$	127908.			1.05014			0.525071	−	0.851059i	$-0.324039\pi$
$349$	127908.			1.05014			0.525071	+	0.851059i	$0.324039\pi$
$350$	−83840.1	−	3609.01i	−0.684409	−	0.0294613i
$351$	126821.	−	155856.i	1.02938	−	1.26505i
$352$	8485.37	+	14697.1i	0.0684834	+	0.118617i
$353$	14455.2	+	8345.71i	0.116004	+	0.0669752i	0.556880	−	0.830593i	$-0.311999\pi$
$353$	14455.2	+	8345.71i	0.116004	+	0.0669752i	−0.440875	+	0.897568i	$0.645332\pi$
$354$	44261.9	−	13494.1i	0.353202	−	0.107680i
$355$	−17189.9	−	29773.8i	−0.136401	−	0.236253i
$356$			47583.5i			0.375454i
$357$	−40407.7	+	145607.i	−0.317050	+	1.14247i
$358$	−31854.4			−0.248544
$359$	−13912.2	+	8032.20i	−0.107946	+	0.0623226i	−0.553001	−	0.833181i	$-0.686517\pi$
$359$	−13912.2	+	8032.20i	−0.107946	+	0.0623226i	0.445055	+	0.895503i	$0.353184\pi$
$360$	7269.15	+	3559.60i	0.0560891	+	0.0274660i
$361$	62828.9	−	108823.i	0.482109	−	0.835037i
$362$	−11942.9	+	6895.25i	−0.0911368	+	0.0526178i
$363$	−38489.0	−	35948.3i	−0.292095	−	0.272813i
$364$	−91161.5	−	57997.7i	−0.688032	−	0.437732i
$365$			41363.4i			0.310478i
$366$	−131049.	−	30363.8i	−0.978296	−	0.226670i
$367$	73521.1	−	127342.i	0.545858	−	0.945454i	−0.452694	−	0.891666i	$-0.649537\pi$
$367$	73521.1	−	127342.i	0.545858	−	0.945454i	0.998552	−	0.0537882i	$-0.0171296\pi$
$368$	43201.6	+	24942.5i	0.319010	+	0.184181i
$369$	76099.4	+	113206.i	0.558893	+	0.831416i
$370$	497.505			0.00363408
$371$	114833.	−	180496.i	0.834292	−	1.31135i
$372$	14312.4	+	13367.6i	0.103425	+	0.0965978i
$373$	35935.5	+	62242.2i	0.258289	+	0.447370i	0.965784	−	0.259349i	$-0.0835079\pi$
$373$	35935.5	+	62242.2i	0.258289	+	0.447370i	−0.707494	+	0.706719i	$0.750175\pi$
$374$	78687.2	+	45430.1i	0.562550	+	0.324788i
$375$	14261.8	+	46780.2i	0.101418	+	0.332660i
$376$	−9694.84	−	16792.0i	−0.0685749	−	0.118775i
$377$		−	82918.5i		−	0.583403i
$378$	98970.5	+	20316.3i	0.692663	+	0.142188i
$379$	9546.39			0.0664601			0.0332300	−	0.999448i	$-0.489421\pi$
$379$	9546.39			0.0664601			0.0332300	+	0.999448i	$0.489421\pi$
$380$	2089.28	−	1206.25i	0.0144687	−	0.00835352i
$381$	73264.4	−	22336.0i	0.504711	−	0.153871i
$382$	−73741.0	+	127723.i	−0.505339	+	0.875272i
$383$	99019.3	−	57168.8i	0.675029	−	0.389728i	−0.122951	−	0.992413i	$-0.539236\pi$
$383$	99019.3	−	57168.8i	0.675029	−	0.389728i	0.797979	+	0.602685i	$0.205902\pi$
$384$	8896.26	−	9525.01i	0.0603316	−	0.0645956i
$385$	872.457	−	20267.9i	0.00588603	−	0.136737i
$386$			38556.8i			0.258777i
$387$	−88734.7	+	59649.0i	−0.592477	+	0.398273i
$388$	44450.0	−	76989.7i	0.295263	−	0.511410i
$389$	144832.	+	83618.9i	0.957119	+	0.552593i	0.895285	−	0.445494i	$-0.146972\pi$
$389$	144832.	+	83618.9i	0.957119	+	0.552593i	0.0618338	+	0.998086i	$0.480305\pi$
$390$	−6993.91	+	30185.4i	−0.0459823	+	0.198458i
$391$	267081.			1.74698
$392$	4668.63	−	54127.5i	0.0303821	−	0.352246i
$393$	−159199.	+	170451.i	−1.03076	+	1.10361i
$394$	24536.9	+	42499.1i	0.158062	+	0.273771i
$395$	14046.8	+	8109.90i	0.0900289	+	0.0519782i
$396$	26717.4	−	54560.3i	0.170374	−	0.347925i
$397$	−79558.6	−	137799.i	−0.504784	−	0.874312i	−0.999985	−	0.00553339i	$-0.998239\pi$
$397$	−79558.6	−	137799.i	−0.504784	−	0.874312i	0.495200	−	0.868779i	$-0.335095\pi$
$398$		−	64744.7i		−	0.408732i
$399$	21482.9	−	21103.8i	0.134942	−	0.132561i
$400$	38751.9			0.242199
$401$	65373.1	−	37743.2i	0.406547	−	0.234720i	−0.282758	−	0.959191i	$-0.591249\pi$
$401$	65373.1	−	37743.2i	0.406547	−	0.234720i	0.689305	+	0.724471i	$0.257916\pi$
$402$	33663.2	+	110419.i	0.208307	+	0.683267i
$403$	−37485.8	+	64927.3i	−0.230811	+	0.399777i
$404$	119137.	−	68783.7i	0.729933	−	0.421427i
$405$	−3941.92	−	28704.6i	−0.0240325	−	0.175001i
$406$	36970.6	−	19274.5i	0.224287	−	0.116931i
$407$		−	3734.13i		−	0.0225424i
$408$	15750.6	−	67979.1i	0.0946189	−	0.408371i
$409$	23849.1	−	41307.8i	0.142569	−	0.246937i	−0.785894	−	0.618361i	$-0.787797\pi$
$409$	23849.1	−	41307.8i	0.142569	−	0.246937i	0.928463	+	0.371424i	$0.121130\pi$
$410$	−18216.5	−	10517.3i	−0.108367	−	0.0625657i
$411$	−274194.	−	63530.3i	−1.62321	−	0.376095i
$412$	−62877.0			−0.370423
$413$	−47811.8	+	75151.2i	−0.280308	+	0.440591i
$414$	−12175.9	−	178159.i	−0.0710396	−	1.03946i
$415$	−2084.22	−	3609.97i	−0.0121017	−	0.0209608i
$416$	43209.8	+	24947.2i	0.249687	+	0.144157i
$417$	−107372.	+	32734.3i	−0.617473	+	0.188248i
$418$	−9053.77	−	15681.6i	−0.0518175	−	0.0897506i
$419$			99252.9i			0.565347i	0.959216	+	0.282674i	$0.0912213\pi$
$419$			99252.9i			0.565347i	−0.959216	+	0.282674i	$0.908779\pi$
$420$	−15084.4	+	3898.28i	−0.0855125	+	0.0220991i
$421$	−117021.			−0.660238			−0.330119	−	0.943939i	$-0.607089\pi$
$421$	−117021.			−0.660238			−0.330119	+	0.943939i	$0.607089\pi$
$422$	60428.0	−	34888.1i	0.339323	−	0.195908i
$423$	−30525.6	+	62337.1i	−0.170601	+	0.348390i
$424$	−49394.3	+	85553.4i	−0.274755	+	0.475889i
$425$	179679.	−	103737.i	0.994760	−	0.574325i
$426$	144831.	+	135271.i	0.798072	+	0.745391i
$427$	229608.	−	119705.i	1.25930	−	0.656534i
$428$		−	30778.2i		−	0.168018i
$429$	226563.	+	52494.4i	1.23105	+	0.285232i
$430$	8243.78	−	14278.6i	0.0445851	−	0.0772236i
$431$	−3223.44	−	1861.06i	−0.0173526	−	0.0100186i	0.491299	−	0.870991i	$-0.336522\pi$
$431$	−3223.44	−	1861.06i	−0.0173526	−	0.0100186i	−0.508651	+	0.860973i	$0.669856\pi$
$432$	−46064.2	−	7407.55i	−0.246829	−	0.0396924i
$433$	25829.7			0.137767			0.0688833	−	0.997625i	$-0.478056\pi$
$433$	25829.7			0.137767			0.0688833	+	0.997625i	$0.478056\pi$
$434$	−37662.5	−	1621.23i	−0.199954	−	0.00860729i
$435$	−8738.03	−	8161.23i	−0.0461780	−	0.0431298i
$436$	36684.2	+	63538.8i	0.192977	+	0.334246i
$437$	−46095.5	−	26613.3i	−0.241377	−	0.139359i
$438$	−69531.2	−	228069.i	−0.362436	−	1.18883i
$439$	−90389.7	−	156559.i	−0.469018	−	0.812363i	0.530355	−	0.847776i	$-0.322059\pi$
$439$	−90389.7	−	156559.i	−0.469018	−	0.812363i	−0.999373	+	0.0354126i	$0.988725\pi$
$440$			9368.04i			0.0483887i
$441$	−170130.	+	94226.8i	−0.874789	+	0.484504i
$442$	267131.			1.36735
$443$	−116103.	+	67032.1i	−0.591611	+	0.341567i	−0.765734	−	0.643157i	$-0.777624\pi$
$443$	−116103.	+	67032.1i	−0.591611	+	0.341567i	0.174123	+	0.984724i	$0.444291\pi$
$444$	−2743.14	+	836.297i	−0.0139149	+	0.00424224i
$445$	−13133.3	+	22747.6i	−0.0663216	+	0.114872i
$446$	30515.9	−	17618.4i	0.153411	−	0.0885720i
$447$	−215003.	+	230199.i	−1.07604	+	1.15209i
$448$	−1078.95	+	25064.8i	−0.00537581	+	0.124884i
$449$			204185.i			1.01282i	0.862294	+	0.506408i	$0.169027\pi$
$449$			204185.i			1.01282i	−0.862294	+	0.506408i	$0.830973\pi$
$450$	−77390.5	−	115127.i	−0.382175	−	0.568529i
$451$	−78939.9	+	136728.i	−0.388100	+	0.672209i
$452$	−127856.	−	73817.9i	−0.625814	−	0.361314i
$453$	−35437.1	+	152945.i	−0.172688	+	0.745314i
$454$	−88718.4			−0.430430
$455$	−27572.6	−	52887.3i	−0.133185	−	0.255463i
$456$	−9492.18	+	10163.0i	−0.0456495	+	0.0488759i
$457$	37834.8	+	65531.9i	0.181159	+	0.313776i	0.942275	−	0.334839i	$-0.108682\pi$
$457$	37834.8	+	65531.9i	0.181159	+	0.313776i	−0.761117	+	0.648615i	$0.775349\pi$
$458$	−116975.	−	67535.4i	−0.557649	−	0.321959i
$459$	−233413.	+	88966.2i	−1.10790	+	0.422279i
$460$	13768.5	+	23847.8i	0.0650687	+	0.112702i
$461$		−	195391.i		−	0.919397i	−0.888075	−	0.459698i	$-0.847957\pi$
$461$		−	195391.i		−	0.919397i	0.888075	−	0.459698i	$-0.152043\pi$
$462$	29259.4	+	113219.i	0.137082	+	0.530440i
$463$	−127530.			−0.594910			−0.297455	−	0.954736i	$-0.596138\pi$
$463$	−127530.			−0.594910			−0.297455	+	0.954736i	$0.596138\pi$
$464$	−16673.8	+	9626.64i	−0.0774461	+	0.0447135i
$465$	3152.57	+	10340.7i	0.0145801	+	0.0478240i
$466$	−88946.3	+	154060.i	−0.409596	+	0.709442i
$467$	203472.	−	117475.i	0.932979	−	0.538656i	0.0452266	−	0.998977i	$-0.485599\pi$
$467$	203472.	−	117475.i	0.932979	−	0.538656i	0.887753	+	0.460321i	$0.152266\pi$
$468$	−12178.2	−	178193.i	−0.0556022	−	0.813576i
$469$	−187478.	−	119275.i	−0.852322	−	0.542254i
$470$		−	10703.3i		−	0.0484533i
$471$	25662.4	−	110758.i	0.115679	−	0.499265i
$472$	20565.8	−	35621.1i	0.0923129	−	0.159891i
$473$	−107172.	−	61875.5i	−0.479024	−	0.276565i
$474$	−91083.4	−	21103.9i	−0.405399	−	0.0939304i
$475$	−41347.7			−0.183258
$476$	62094.9	+	119105.i	0.274058	+	0.525672i
$477$	352813.	−	24112.3i	1.55063	−	0.105975i
$478$	74239.6	+	128587.i	0.324923	+	0.562782i
$479$	−108684.	−	62748.7i	−0.473690	−	0.273485i	0.244093	−	0.969752i	$-0.421510\pi$
$479$	−108684.	−	62748.7i	−0.473690	−	0.273485i	−0.717783	+	0.696267i	$0.754843\pi$
$480$	6881.87	−	2098.07i	0.0298692	−	0.00910620i
$481$	−5489.22	−	9507.61i	−0.0237258	−	0.0410943i
$482$		−	139884.i		−	0.602109i
$483$	240887.	+	245214.i	1.03257	+	1.05112i
$484$	−46814.0			−0.199841
$485$	42499.2	−	24536.9i	0.180675	−	0.104313i
$486$	69986.9	+	151645.i	0.296308	+	0.642029i
$487$	−141748.	+	245515.i	−0.597667	+	1.03519i	0.395497	+	0.918467i	$0.370572\pi$
$487$	−141748.	+	245515.i	−0.597667	+	1.03519i	−0.993165	+	0.116723i	$0.962761\pi$
$488$	−103554.	+	59786.8i	−0.434836	+	0.251053i
$489$	−312404.	−	291782.i	−1.30647	−	1.22023i
$490$	17171.4	−	24587.4i	0.0715175	−	0.102405i
$491$			356870.i			1.48029i	0.672448	+	0.740145i	$0.265243\pi$
$491$			356870.i			1.48029i	−0.672448	+	0.740145i	$0.734757\pi$
$492$	118121.	+	27368.5i	0.487976	+	0.113063i
$493$	−51540.4	+	89270.6i	−0.212058	+	0.367295i
$494$	−46104.2	−	26618.3i	−0.188924	−	0.109075i
$495$	27831.3	−	18708.7i	0.113586	−	0.0763543i
$496$	17408.1			0.0707599
$497$	−381118.	−	16405.7i	−1.54293	−	0.0664176i
$498$	17560.2	+	16401.1i	0.0708063	+	0.0661324i
$499$	−40233.4	−	69686.3i	−0.161579	−	0.279864i	0.773856	−	0.633362i	$-0.218325\pi$
$499$	−40233.4	−	69686.3i	−0.161579	−	0.279864i	−0.935435	+	0.353498i	$0.884992\pi$
$500$	37647.8	+	21736.0i	0.150591	+	0.0869439i
$501$	−86470.0	−	283630.i	−0.344500	−	1.12999i
$502$	−52082.7	−	90209.9i	−0.206674	−	0.357970i
$503$			338596.i			1.33828i	0.743137	+	0.669139i	$0.233337\pi$
$503$			338596.i			1.33828i	−0.743137	+	0.669139i	$0.766663\pi$
$504$	76619.2	−	46850.9i	0.301632	−	0.184441i
$505$	75938.7			0.297770
$506$	178995.	−	103343.i	0.699101	−	0.403626i
$507$	408152.	−	124433.i	1.58784	−	0.484082i
$508$	34041.6	−	58961.7i	0.131911	−	0.228477i
$509$	299034.	−	172647.i	1.15421	−	0.666383i	0.204300	−	0.978908i	$-0.434508\pi$
$509$	299034.	−	172647.i	1.15421	−	0.666383i	0.949910	+	0.312525i	$0.101175\pi$
$510$	26292.3	−	28150.5i	0.101085	−	0.108230i
$511$	387233.	+	246361.i	1.48297	+	0.943475i
$512$		−	11585.2i		−	0.0441942i
$513$	49149.8	+	7903.74i	0.186761	+	0.0300330i
$514$	67433.9	−	116799.i	0.255242	−	0.442092i
$515$	−30058.8	−	17354.4i	−0.113333	−	0.0654328i
$516$	−21452.3	+	92587.1i	−0.0805702	+	0.347737i
$517$	−80336.2			−0.300559
$518$	2963.15	−	4657.51i	0.0110432	−	0.0173578i
$519$	205559.	−	220087.i	0.763137	−	0.817072i
$520$	13771.1	+	23852.3i	0.0509288	+	0.0882112i
$521$	−162213.	−	93653.7i	−0.597599	−	0.345024i	0.170497	−	0.985358i	$-0.445463\pi$
$521$	−162213.	−	93653.7i	−0.597599	−	0.345024i	−0.768097	+	0.640334i	$0.778796\pi$
$522$	61898.6	+	30310.8i	0.227164	+	0.111239i
$523$	−56538.7	−	97927.9i	−0.206701	−	0.358016i	0.743972	−	0.668210i	$-0.232939\pi$
$523$	−56538.7	−	97927.9i	−0.206701	−	0.358016i	−0.950673	+	0.310194i	$0.899606\pi$
$524$			207319.i			0.755050i
$525$	257301.	+	71404.2i	0.933517	+	0.259063i
$526$	−316272.			−1.14311
$527$	80714.9	−	46600.8i	0.290625	−	0.167792i
$528$	−15747.5	−	51653.4i	−0.0564865	−	0.185281i
$529$	163852.	−	283801.i	0.585520	−	1.01415i
$530$	−47226.5	+	27266.2i	−0.168126	+	0.0970674i
$531$	−146897.	+	10039.4i	−0.520985	+	0.0356057i
$532$	1151.22	−	26743.8i	0.00406757	−	0.0944929i
$533$			464171.i			1.63389i
$534$	34176.1	−	147502.i	0.119850	−	0.517269i
$535$	8494.96	−	14713.7i	0.0296793	−	0.0514061i
$536$	88862.8	+	51304.9i	0.309307	+	0.178579i
$537$	98744.3	+	22878.9i	0.342424	+	0.0793390i
$538$	−105697.			−0.365172
$539$	−184546.	−	128883.i	−0.635225	−	0.443629i
$540$	−19976.7	−	16255.2i	−0.0685074	−	0.0557449i
$541$	−236536.	−	409693.i	−0.808171	−	1.39979i	−0.914130	−	0.405422i	$-0.867125\pi$
$541$	−236536.	−	409693.i	−0.808171	−	1.39979i	0.105959	−	0.994371i	$-0.466209\pi$
$542$	46303.6	+	26733.4i	0.157622	+	0.0910029i
$543$	41973.8	−	12796.5i	0.142357	−	0.0434002i
$544$	−31013.3	−	53716.6i	−0.104797	−	0.181514i
$545$			40500.2i			0.136353i
$546$	240932.	+	245260.i	0.808183	+	0.822700i
$547$	542161.			1.81198			0.905991	−	0.423296i	$-0.139127\pi$
$547$	542161.			1.81198			0.905991	+	0.423296i	$0.139127\pi$
$548$	−216666.	+	125092.i	−0.721489	+	0.416552i
$549$	384424.	+	188247.i	1.27546	+	0.624573i
$550$	80279.3	−	139048.i	0.265386	−	0.459662i
$551$	17790.7	−	10271.5i	0.0585991	−	0.0338322i
$552$	−116005.	−	108347.i	−0.380712	−	0.355581i
$553$	159585.	−	83199.4i	0.521847	−	0.272063i
$554$			267023.i			0.870021i
$555$	−1542.20	−	357.325i	−0.00500672	−	0.00116005i
$556$	−49889.2	+	86410.7i	−0.161383	+	0.279523i
$557$	−254172.	−	146746.i	−0.819253	−	0.472996i	0.0309061	−	0.999522i	$-0.490161\pi$
$557$	−254172.	−	146746.i	−0.819253	−	0.472996i	−0.850159	+	0.526527i	$0.823494\pi$
$558$	−34765.3	−	51717.3i	−0.111655	−	0.166099i
$559$	−363831.			−1.16433
$560$	−7433.82	+	11684.6i	−0.0237048	+	0.0372595i
$561$	−211290.	−	197343.i	−0.671357	−	0.627040i
$562$	−38061.4	−	65924.3i	−0.120507	−	0.208724i
$563$	191717.	+	110688.i	0.604845	+	0.349208i	0.770945	−	0.636901i	$-0.219784\pi$
$563$	191717.	+	110688.i	0.604845	+	0.349208i	−0.166100	+	0.986109i	$0.553117\pi$
$564$	17992.1	+	59015.9i	0.0565619	+	0.185529i
$565$	−40748.3	−	70578.2i	−0.127648	−	0.221092i
$566$			87321.8i			0.272577i
$567$	−292203.	−	134062.i	−0.908905	−	0.417002i
$568$	176157.			0.546014
$569$	−178283.	+	102932.i	−0.550663	+	0.317926i	−0.749390	−	0.662129i	$-0.769653\pi$
$569$	−178283.	+	102932.i	−0.550663	+	0.317926i	0.198726	+	0.980055i	$0.436320\pi$
$570$	−7342.86	+	2238.61i	−0.0226004	+	0.00689015i
$571$	−243717.	+	422130.i	−0.747504	+	1.29471i	0.201512	+	0.979486i	$0.435415\pi$
$571$	−243717.	+	422130.i	−0.747504	+	1.29471i	−0.949016	+	0.315229i	$0.897919\pi$
$572$	179029.	−	103362.i	0.547181	−	0.315915i
$573$	320322.	−	342961.i	0.975613	−	1.04456i
$574$	−206958.	+	107897.i	−0.628143	+	0.327480i
$575$		−	471957.i		−	1.42747i
$576$	−34418.4	+	23136.6i	−0.103740	+	0.0697357i
$577$	−32498.0	+	56288.2i	−0.0976125	+	0.169070i	−0.910696	−	0.413077i	$-0.864454\pi$
$577$	−32498.0	+	56288.2i	−0.0976125	+	0.169070i	0.813083	+	0.582147i	$0.197787\pi$
$578$	−83011.2	−	47926.6i	−0.248474	−	0.143457i
$579$	27692.8	−	119521.i	0.0826055	−	0.356522i
$580$	−10628.0			−0.0315935
$581$	−46209.3	−	1989.14i	−0.136892	−	0.00589268i
$582$	−193085.	+	206732.i	−0.570038	+	0.610326i
$583$	204653.	+	354469.i	0.602116	+	1.04290i
$584$	−183545.	−	105970.i	−0.538168	−	0.310711i
$585$	43360.3	−	88547.3i	0.126701	−	0.258740i
$586$	14206.9	+	24607.1i	0.0413718	+	0.0716580i
$587$		−	246446.i		−	0.715230i	−0.933869	−	0.357615i	$-0.883590\pi$
$587$		−	246446.i		−	0.715230i	0.933869	−	0.357615i	$-0.116410\pi$
$588$	−53348.2	+	164434.i	−0.154300	+	0.475596i
$589$	−18574.2			−0.0535400
$590$	19663.2	−	11352.6i	0.0564873	−	0.0326130i
$591$	−45536.6	−	149365.i	−0.130372	−	0.427634i
$592$	−1274.57	+	2207.62i	−0.00363681	+	0.00629914i
$593$	−34342.1	+	19827.4i	−0.0976601	+	0.0563841i	−0.548035	−	0.836456i	$-0.684624\pi$
$593$	−34342.1	+	19827.4i	−0.0976601	+	0.0563841i	0.450375	+	0.892840i	$0.351290\pi$
$594$	−122007.	+	149940.i	−0.345790	+	0.424956i
$595$	−3188.76	+	74077.3i	−0.00900715	+	0.209243i
$596$			279990.i			0.788225i
$597$	−46501.8	+	200700.i	−0.130473	+	0.563116i
$598$	303830.	−	526250.i	0.849628	−	1.47160i
$599$	613383.	+	354137.i	1.70953	+	0.987000i	0.935126	+	0.354315i	$0.115286\pi$
$599$	613383.	+	354137.i	1.70953	+	0.987000i	0.774409	+	0.632686i	$0.218048\pi$
$600$	−120125.	−	27832.9i	−0.333682	−	0.0773136i
$601$	671747.			1.85976			0.929879	−	0.367865i	$-0.119911\pi$
$601$	671747.			1.85976			0.929879	+	0.367865i	$0.119911\pi$
$602$	−84572.9	−	162220.i	−0.233366	−	0.447622i
$603$	−25045.0	−	366461.i	−0.0688789	−	1.00784i
$604$	69776.3	+	120856.i	0.191264	+	0.331280i
$605$	−22379.7	−	12920.9i	−0.0611427	−	0.0353007i
$606$	−418710.	+	127652.i	−1.14017	+	0.347602i
$607$	207208.	+	358895.i	0.562379	+	0.974068i	0.997288	+	0.0735943i	$0.0234470\pi$
$607$	207208.	+	358895.i	0.562379	+	0.974068i	−0.434910	+	0.900474i	$0.643220\pi$
$608$			12361.3i			0.0334392i
$609$	−128447.	+	33194.8i	−0.346330	+	0.0895025i
$610$	−66006.0			−0.177388
$611$	−204547.	+	118095.i	−0.547912	+	0.316337i
$612$	−97649.7	+	199413.i	−0.260716	+	0.532415i
$613$	−47119.4	+	81613.3i	−0.125395	+	0.217190i	−0.921887	−	0.387458i	$-0.873353\pi$
$613$	−47119.4	+	81613.3i	−0.125395	+	0.217190i	0.796492	+	0.604648i	$0.206686\pi$
$614$	157263.	−	90795.7i	0.417147	−	0.240840i
$615$	48914.7	+	45685.9i	0.129327	+	0.120790i
$616$	87701.2	+	55796.2i	0.231124	+	0.147043i
$617$		−	270952.i		−	0.711741i	−0.934535	−	0.355871i	$-0.884184\pi$
$617$		−	270952.i		−	0.711741i	0.934535	−	0.355871i	$-0.115816\pi$
$618$	194910.	+	45160.4i	0.510337	+	0.118244i
$619$	−191197.	+	331163.i	−0.499000	+	0.864293i	−0.999999	−	0.00115485i	$-0.999632\pi$
$619$	−191197.	+	331163.i	−0.499000	+	0.864293i	0.501000	+	0.865447i	$0.332966\pi$
$620$	8322.03	+	4804.73i	0.0216494	+	0.0124993i
$621$	−90216.1	+	561013.i	−0.233938	+	1.45476i
$622$	451693.			1.16752
$623$	134735.	+	258436.i	0.347139	+	0.665851i
$624$	−116026.	−	108368.i	−0.297981	−	0.278311i
$625$	−177220.	−	306953.i	−0.453682	−	0.785801i
$626$	−306263.	−	176821.i	−0.781530	−	0.451217i
$627$	16802.4	+	55113.4i	0.0427401	+	0.140192i
$628$	−50529.6	−	87519.9i	−0.128123	−	0.221915i
$629$			13647.9i			0.0344958i
$630$	49559.4	−	1250.01i	0.124866	−	0.00314943i
$631$	−243213.			−0.610841			−0.305420	−	0.952218i	$-0.598797\pi$
$631$	−243213.			−0.610841			−0.305420	+	0.952218i	$0.598797\pi$
$632$	−71973.5	+	41553.9i	−0.180193	+	0.104035i
$633$	−212376.	+	64747.0i	−0.530028	+	0.161589i
$634$	−11458.2	+	19846.2i	−0.0285061	+	0.0493740i
$635$	32547.6	−	18791.3i	0.0807181	−	0.0466026i
$636$	214563.	−	229727.i	0.530445	−	0.567934i
$637$	−659340.	−	56869.7i	−1.62491	−	0.140153i
$638$			79771.1i			0.195977i
$639$	−351800.	−	523342.i	−0.861577	−	1.28169i
$640$	3197.59	−	5538.39i	0.00780662	−	0.0135215i
$641$	−185454.	−	107072.i	−0.451358	−	0.260591i	0.257046	−	0.966399i	$-0.417251\pi$
$641$	−185454.	−	107072.i	−0.451358	−	0.260591i	−0.708403	+	0.705808i	$0.750584\pi$
$642$	−22105.9	+	95408.1i	−0.0536338	+	0.231481i
$643$	−124078.			−0.300104			−0.150052	−	0.988678i	$-0.547944\pi$
$643$	−124078.			−0.300104			−0.150052	+	0.988678i	$0.547944\pi$
$644$	305263.	+	13140.4i	0.736041	+	0.0316839i
$645$	−35810.0	+	38340.9i	−0.0860765	+	0.0921600i
$646$	33090.7	+	57314.8i	0.0792942	+	0.137342i
$647$	−584674.	−	337562.i	−1.39671	−	0.806389i	−0.402661	−	0.915349i	$-0.631915\pi$
$647$	−584674.	−	337562.i	−1.39671	−	0.806389i	−0.994046	+	0.108960i	$0.965248\pi$
$648$	137472.	+	56047.2i	0.327390	+	0.133476i
$649$	−85209.3	−	147587.i	−0.202301	−	0.350395i
$650$		−	472046.i		−	1.11727i
$651$	115584.	+	32076.1i	0.272732	+	0.0756867i
$652$	−379976.			−0.893842
$653$	−183626.	+	106017.i	−0.430634	+	0.248626i	−0.699617	−	0.714519i	$-0.746646\pi$
$653$	−183626.	+	106017.i	−0.430634	+	0.248626i	0.268983	+	0.963145i	$0.413312\pi$
$654$	−68080.1	−	223309.i	−0.159171	−	0.522097i
$655$	−57221.2	+	99110.0i	−0.133375	+	0.231012i
$656$	93338.7	−	53889.1i	0.216897	−	0.125226i
$657$	51730.3	+	756922.i	0.119843	+	1.75356i
$658$	−100202.	−	63749.2i	−0.231432	−	0.147239i
$659$		−	406793.i		−	0.936704i	−0.883542	−	0.468352i	$-0.844848\pi$
$659$		−	406793.i		−	0.936704i	0.883542	−	0.468352i	$-0.155152\pi$
$660$	6728.44	−	29039.6i	0.0154464	−	0.0666658i
$661$	−119012.	+	206135.i	−0.272388	+	0.471791i	−0.969473	−	0.245198i	$-0.921147\pi$
$661$	−119012.	+	206135.i	−0.272388	+	0.471791i	0.697085	+	0.716989i	$0.254480\pi$
$662$	444900.	+	256863.i	1.01519	+	0.586119i
$663$	−828069.	−	191862.i	−1.88382	−	0.436479i
$664$	21358.5			0.0484433
$665$	7931.78	−	12467.3i	0.0179361	−	0.0281922i
$666$	9104.00	−	622.194i	0.0205250	−	0.00140274i
$667$	117242.	+	203070.i	0.263532	+	0.456450i
$668$	−228260.	−	131786.i	−0.511536	−	0.295335i
$669$	−107249.	+	32697.0i	−0.239631	+	0.0730559i
$670$	28320.9	+	49053.3i	0.0630896	+	0.109274i
$671$			495423.i			1.10035i
$672$	21347.0	−	76922.4i	0.0472713	−	0.170339i
$673$	−10442.3			−0.0230550			−0.0115275	−	0.999934i	$-0.503669\pi$
$673$	−10442.3			−0.0230550			−0.0115275	+	0.999934i	$0.503669\pi$
$674$	274126.	−	158267.i	0.603436	−	0.348394i
$675$	157212.	+	412463.i	0.345046	+	0.905268i
$676$	189644.	−	328473.i	0.414997	−	0.718796i
$677$	259688.	−	149931.i	0.566598	−	0.327125i	−0.189192	−	0.981940i	$-0.560587\pi$
$677$	259688.	−	149931.i	0.566598	−	0.327125i	0.755789	+	0.654815i	$0.227253\pi$
$678$	343318.	+	320656.i	0.746857	+	0.697557i
$679$	23417.6	−	544009.i	0.0507929	−	1.17996i
$680$		−	34239.4i		−	0.0740471i
$681$	275015.	+	63720.5i	0.593010	+	0.137400i
$682$	36062.9	−	62462.9i	0.0775340	−	0.134293i
$683$	538988.	+	311185.i	1.15541	+	0.667079i	0.950201	−	0.311638i	$-0.100878\pi$
$683$	538988.	+	311185.i	1.15541	+	0.667079i	0.205214	+	0.978717i	$0.434211\pi$
$684$	36723.9	−	24686.4i	0.0784940	−	0.0527650i
$685$	−138105.			−0.294325
$686$	−127908.	−	307197.i	−0.271800	−	0.652782i
$687$	314099.	+	293366.i	0.665508	+	0.621578i
$688$	42239.9	+	73161.7i	0.0892373	+	0.154564i
$689$	1.04215e6	+	601684.i	2.19528	+	1.26745i
$690$	−25552.3	−	83813.9i	−0.0536700	−	0.176043i
$691$	228061.	+	395013.i	0.477633	+	0.827285i	0.999671	−	0.0256370i	$-0.00816141\pi$
$691$	228061.	+	395013.i	0.477633	+	0.827285i	−0.522038	+	0.852922i	$0.674828\pi$
$692$		−	267691.i		−	0.559013i
$693$	−9382.21	−	371979.i	−0.0195361	−	0.774555i
$694$	269101.			0.558723
$695$	−47699.7	+	27539.4i	−0.0987521	+	0.0570145i
$696$	58600.8	−	17865.6i	0.120972	−	0.0368806i
$697$	288519.	−	499729.i	0.593893	−	1.02865i
$698$	−313310.	+	180890.i	−0.643078	+	0.371281i
$699$	386372.	−	413679.i	0.790772	−	0.846660i
$700$	210469.	−	109728.i	0.429529	−	0.223934i
$701$		−	126449.i		−	0.257323i	−0.991689	−	0.128661i	$-0.958932\pi$
$701$		−	126449.i		−	0.257323i	0.991689	−	0.128661i	$-0.0410680\pi$
$702$	−90233.1	+	561119.i	−0.183101	+	1.13863i
$703$	1359.95	−	2355.50i	0.00275177	−	0.00476620i
$704$	−41569.6	−	24000.2i	−0.0838747	−	0.0484251i
$705$	−7687.49	+	33178.8i	−0.0154670	+	0.0667549i
$706$	−47210.5			−0.0947172
$707$	452292.	−	710919.i	0.904858	−	1.42227i
$708$	−89335.5	+	95649.3i	−0.178220	+	0.190816i
$709$	−145281.	−	251633.i	−0.289011	−	0.500583i	0.684563	−	0.728954i	$-0.259993\pi$
$709$	−145281.	−	251633.i	−0.289011	−	0.500583i	−0.973574	+	0.228372i	$0.926660\pi$
$710$	84213.1	+	48620.4i	0.167056	+	0.0964500i
$711$	267189.	+	130838.i	0.528541	+	0.258819i
$712$	−67293.3	−	116555.i	−0.132743	−	0.229918i
$713$		−	212012.i		−	0.417043i
$714$	−106941.	−	413807.i	−0.209771	−	0.811711i
$715$	114114.			0.223218
$716$	78027.1	−	45049.0i	0.152202	−	0.0878737i
$717$	−137777.	−	451922.i	−0.268003	−	0.879074i
$718$	22718.5	−	39349.6i	0.0440688	−	0.0763293i
$719$	−379770.	+	219260.i	−0.734620	+	0.424133i	−0.820110	−	0.572206i	$-0.806088\pi$
$719$	−379770.	+	219260.i	−0.734620	+	0.424133i	0.0854903	+	0.996339i	$0.472754\pi$
$720$	−22839.7	+	1560.94i	−0.0440582	+	0.00301106i
$721$	−341498.	+	178039.i	−0.656928	+	0.342487i
$722$			355414.i			0.681805i
$723$	−100470.	+	433622.i	−0.192202	+	0.829535i
$724$	19502.7	−	33779.7i	0.0372064	−	0.0644434i
$725$	157750.	+	91076.8i	0.300118	+	0.173273i
$726$	145117.	+	33623.4i	0.275325	+	0.0637923i
$727$	−199481.			−0.377426			−0.188713	−	0.982032i	$-0.560432\pi$
$727$	−199481.			−0.377426			−0.188713	+	0.982032i	$0.560432\pi$
$728$	305320.	+	13142.9i	0.576093	+	0.0247987i
$729$	−108033.	−	520344.i	−0.203284	−	0.979120i
$730$	−58496.7	−	101319.i	−0.109770	−	0.190128i
$731$	391703.	+	226150.i	0.733031	+	0.423215i
$732$	363943.	−	110955.i	0.679221	−	0.207073i
$733$	422865.	+	732424.i	0.787035	+	1.36318i	0.927776	+	0.373138i	$0.121718\pi$
$733$	422865.	+	732424.i	0.787035	+	1.36318i	−0.140741	+	0.990046i	$0.544949\pi$
$734$			415898.i			0.771960i
$735$	−70888.3	+	63884.5i	−0.131220	+	0.118255i
$736$	−141096.			−0.260471
$737$	368180.	−	212569.i	0.677838	−	0.391350i
$738$	−346503.	−	169677.i	−0.636200	−	0.311538i
$739$	264373.	−	457907.i	0.484092	−	0.838472i	−0.515741	−	0.856745i	$-0.672483\pi$
$739$	264373.	−	457907.i	0.484092	−	0.838472i	0.999833	+	0.0182724i	$0.00581662\pi$
$740$	−1218.63	+	703.578i	−0.00222541	+	0.00128484i
$741$	123799.	+	115627.i	0.225465	+	0.210582i
$742$	−26022.4	+	604520.i	−0.0472649	+	1.09800i
$743$			19273.6i			0.0349128i	0.999848	+	0.0174564i	$0.00555682\pi$
$743$			19273.6i			0.0349128i	−0.999848	+	0.0174564i	$0.994443\pi$
$744$	−53962.6	−	12503.0i	−0.0974870	−	0.0225876i
$745$	−77278.9	+	133851.i	−0.139235	+	0.241162i
$746$	−176048.	−	101641.i	−0.316339	−	0.182638i
$747$	−42654.5	−	63453.5i	−0.0764406	−	0.113714i
$748$	−256991.			−0.459320
$749$	−87149.7	−	167163.i	−0.155347	−	0.297972i
$750$	−101092.	−	94418.4i	−0.179718	−	0.167855i
$751$	−350906.	−	607786.i	−0.622172	−	1.07763i	−0.989080	−	0.147376i	$-0.952917\pi$
$751$	−350906.	−	607786.i	−0.622172	−	1.07763i	0.366909	−	0.930257i	$-0.380416\pi$
$752$	47494.8	+	27421.2i	0.0839867	+	0.0484898i
$753$	96657.5	+	317046.i	0.170469	+	0.559155i
$754$	117264.	+	203108.i	0.206264	+	0.357260i
$755$			77034.7i			0.135143i
$756$	−271159.	+	90200.8i	−0.474439	+	0.157822i
$757$	−340302.			−0.593845			−0.296923	−	0.954902i	$-0.595960\pi$
$757$	−340302.			−0.593845			−0.296923	+	0.954902i	$0.595960\pi$
$758$	−23383.8	+	13500.6i	−0.0406983	+	0.0234972i
$759$	−629084.	+	191788.i	−1.09201	+	0.332919i
$760$	−3411.79	+	5909.39i	−0.00590683	+	0.0102309i
$761$	−128409.	+	74137.2i	−0.221732	+	0.128017i	−0.606752	−	0.794891i	$-0.707528\pi$
$761$	−128409.	+	74137.2i	−0.221732	+	0.128017i	0.385020	+	0.922908i	$0.374194\pi$
$762$	−147872.	+	158323.i	−0.254670	+	0.272669i
$763$	379152.	+	241220.i	0.651275	+	0.414346i
$764$		−	417142.i		−	0.714657i
$765$	−101721.	+	68378.7i	−0.173815	+	0.116842i
$766$	−161698.	+	280069.i	−0.275579	+	0.477318i
$767$	−433909.	−	250517.i	−0.737578	−	0.425841i
$768$	−8320.90	+	35912.6i	−0.0141074	+	0.0608870i
$769$	−626381.			−1.05922			−0.529610	−	0.848241i	$-0.677662\pi$
$769$	−626381.			−1.05922			−0.529610	+	0.848241i	$0.677662\pi$
$770$	26526.0	+	50879.8i	0.0447394	+	0.0858151i
$771$	−292924.	+	313627.i	−0.492773	+	0.527600i
$772$	−54527.5	−	94444.4i	−0.0914916	−	0.158468i
$773$	−870041.	−	502318.i	−1.45607	−	0.840660i	−0.457251	−	0.889338i	$-0.651166\pi$
$773$	−870041.	−	502318.i	−1.45607	−	0.840660i	−0.998815	+	0.0486783i	$0.984499\pi$
$774$	132998.	−	271599.i	0.222006	−	0.453364i
$775$	−82348.0	−	142631.i	−0.137104	−	0.237471i
$776$			251447.i			0.417564i
$777$	−12530.5	+	12309.4i	−0.0207552	+	0.0203890i
$778$	−473020.			−0.781484
$779$	−99591.0	+	57498.9i	−0.164114	+	0.0947512i
$780$	−25557.1	−	83829.7i	−0.0420071	−	0.137787i
$781$	364931.	−	632080.i	0.598287	−	1.03626i
$782$	−654211.	+	377709.i	−1.06980	+	0.617652i
$783$	−170107.	−	138417.i	−0.277458	−	0.225770i
$784$	65112.0	+	139187.i	0.105932	+	0.226447i
$785$		−	55785.9i		−	0.0905284i
$786$	148903.	−	642659.i	0.241023	−	1.04024i
$787$	344567.	−	596807.i	0.556319	−	0.963573i	−0.441481	−	0.897271i	$-0.645547\pi$
$787$	344567.	−	596807.i	0.556319	−	0.963573i	0.997800	−	0.0663019i	$-0.0211200\pi$
$788$	−120206.	−	69400.7i	−0.193585	−	0.111767i
$789$	980400.	+	227157.i	1.57489	+	0.364899i
$790$	−45876.5			−0.0735083
$791$	−903432.	−	38889.4i	−1.44392	−	0.0621554i
$792$	11716.0	+	171429.i	0.0186779	+	0.273296i
$793$	728277.	+	1.26141e6i	1.15811	+	2.00591i
$794$	389756.	+	225026.i	0.618232	+	0.356936i
$795$	165979.	−	50601.9i	0.262615	−	0.0800631i
$796$	91562.9	+	158592.i	0.144509	+	0.250296i
$797$			142213.i			0.223884i	0.993715	+	0.111942i	$0.0357071\pi$
$797$			142213.i			0.223884i	−0.993715	+	0.111942i	$0.964293\pi$
$798$	−22776.9	+	82075.1i	−0.0357675	+	0.128886i
$799$	293622.			0.459934
$800$	−94922.3	+	54803.4i	−0.148316	+	0.0856304i
$801$	−211882.	+	432690.i	−0.330240	+	0.674392i
$802$	−106754.	+	184903.i	−0.165972	+	0.287472i
$803$	−760474.	+	439060.i	−1.17938	+	0.680914i
$804$	−238613.	−	222862.i	−0.369133	−	0.344766i
$805$	142306.	+	90536.1i	0.219599	+	0.139711i
$806$		−	212052.i		−	0.326416i
$807$	327646.	+	75915.1i	0.503104	+	0.116568i
$808$	−194550.	+	336970.i	−0.297994	+	0.516141i
$809$	−160237.	−	92512.9i	−0.244831	−	0.141353i	0.372564	−	0.928006i	$-0.378479\pi$
$809$	−160237.	−	92512.9i	−0.244831	−	0.141353i	−0.617395	+	0.786653i	$0.711812\pi$
$810$	50250.1	+	64736.9i	0.0765891	+	0.0986692i
$811$	476049.			0.723786			0.361893	−	0.932220i	$-0.382131\pi$
$811$	476049.			0.723786			0.361893	+	0.932220i	$0.382131\pi$
$812$	−63300.8	+	99497.0i	−0.0960057	+	0.150903i
$813$	−124334.	−	116127.i	−0.188108	−	0.175691i
$814$	5280.86	+	9146.72i	0.00796996	+	0.0138044i
$815$	−181650.	−	104875.i	−0.273476	−	0.157892i
$816$	57555.9	+	188789.i	0.0864389	+	0.283528i
$817$	−45069.4	−	78062.5i	−0.0675208	−	0.116949i
$818$			134911.i			0.201623i
$819$	−570702.	−	933318.i	−0.850828	−	1.39143i
$820$	59494.8			0.0884813
$821$	−328402.	+	189603.i	−0.487213	+	0.281293i	−0.723418	−	0.690411i	$-0.757430\pi$
$821$	−328402.	+	189603.i	−0.487213	+	0.281293i	0.236204	+	0.971703i	$0.424097\pi$
$822$	761480.	−	232152.i	1.12698	−	0.343580i
$823$	207062.	−	358641.i	0.305703	−	0.529493i	−0.671714	−	0.740810i	$-0.734442\pi$
$823$	207062.	−	358641.i	0.305703	−	0.529493i	0.977418	+	0.211317i	$0.0677752\pi$
$824$	154017.	−	88921.6i	0.226837	−	0.130964i
$825$	−348723.	+	373370.i	−0.512358	+	0.548569i
$826$	10834.7	−	251698.i	0.0158802	−	0.368910i
$827$		−	329049.i		−	0.481116i	−0.970635	−	0.240558i	$-0.922670\pi$
$827$		−	329049.i		−	0.481116i	0.970635	−	0.240558i	$-0.0773304\pi$
$828$	281780.	+	419179.i	0.411007	+	0.611419i
$829$	4218.55	−	7306.74i	0.00613838	−	0.0106320i	−0.862940	−	0.505307i	$-0.831379\pi$
$829$	4218.55	−	7306.74i	0.00613838	−	0.0106320i	0.869078	+	0.494675i	$0.164713\pi$
$830$	10210.5	+	5895.06i	0.0148215	+	0.00855721i
$831$	191785.	−	827736.i	0.277724	−	1.19864i
$832$	−141123.			−0.203868
$833$	674500.	+	471058.i	0.972058	+	0.678867i
$834$	216713.	−	232029.i	0.311568	−	0.333588i
$835$	−72747.3	−	126002.i	−0.104338	−	0.180719i
$836$	44354.2	+	25607.9i	0.0634633	+	0.0366405i
$837$	70622.4	+	185286.i	0.100807	+	0.264479i
$838$	−140365.	−	243119.i	−0.199880	−	0.346203i
$839$		−	36805.9i		−	0.0522869i	−0.999658	−	0.0261435i	$-0.991677\pi$
$839$		−	36805.9i		−	0.0522869i	0.999658	−	0.0261435i	$-0.00832267\pi$
$840$	31436.1	−	30881.4i	0.0445523	−	0.0437661i
$841$	616781.			0.872045
$842$	286642.	−	165493.i	0.404312	−	0.233430i
$843$	70636.1	+	231693.i	0.0993966	+	0.326030i
$844$	−98678.6	+	170916.i	−0.138528	+	0.239938i
$845$	181321.	−	104686.i	0.253942	−	0.146613i
$846$	−13385.9	−	195864.i	−0.0187028	−	0.273661i
$847$	−254257.	+	132556.i	−0.354410	+	0.184770i
$848$		−	279416.i		−	0.388562i
$849$	62717.4	−	270685.i	0.0870107	−	0.375534i
$850$	−293414.	+	508208.i	−0.406109	+	0.703402i
$851$	26886.5	+	15522.9i	0.0371257	+	0.0214346i
$852$	−546063.	−	126522.i	−0.752253	−	0.174296i
$853$	−786098.			−1.08039			−0.540193	−	0.841541i	$-0.681649\pi$
$853$	−786098.			−1.08039			−0.540193	+	0.841541i	$0.681649\pi$
$854$	−393133.	+	617931.i	−0.539043	+	0.847275i
$855$	24369.7	−	1665.50i	0.0333363	−	0.00227830i
$856$	43526.9	+	75390.8i	0.0594033	+	0.102890i
$857$	415384.	+	239822.i	0.565572	+	0.326533i	0.755379	−	0.655288i	$-0.227453\pi$
$857$	415384.	+	239822.i	0.565572	+	0.326533i	−0.189807	+	0.981821i	$0.560786\pi$
$858$	−629203.	+	191824.i	−0.854705	+	0.260573i
$859$	205109.	+	355259.i	0.277970	+	0.481458i	0.970880	−	0.239566i	$-0.0770050\pi$
$859$	205109.	+	355259.i	0.277970	+	0.481458i	−0.692910	+	0.721024i	$0.743672\pi$
$860$			46633.9i			0.0630528i
$861$	719036.	−	185821.i	0.969939	−	0.250663i
$862$	10527.7			0.0141684
$863$	436577.	−	252058.i	0.586192	−	0.338438i	−0.177398	−	0.984139i	$-0.556768\pi$
$863$	436577.	−	252058.i	0.586192	−	0.338438i	0.763590	+	0.645701i	$0.223435\pi$
$864$	123310.	−	46999.9i	0.165185	−	0.0629607i
$865$	73884.4	−	127972.i	0.0987462	−	0.171033i
$866$	−63269.7	+	36528.7i	−0.0843645	+	0.0487079i
$867$	222901.	+	208187.i	0.296533	+	0.276959i
$868$	94546.8	−	49291.7i	0.125489	−	0.0654235i
$869$			344336.i			0.455977i
$870$	32945.4	+	7633.41i	0.0435268	+	0.0100851i
$871$	624958.	−	1.08246e6i	0.823786	−	1.42684i
$872$	−179715.	−	103758.i	−0.236348	−	0.136455i
$873$	747020.	−	502160.i	0.980175	−	0.658891i
$874$	150547.			0.197083
$875$	266019.	+	11451.2i	0.347454	+	0.0149566i
$876$	492854.	+	460321.i	0.642259	+	0.599863i
$877$	50382.3	+	87264.6i	0.0655056	+	0.113459i	0.896918	−	0.442197i	$-0.145801\pi$
$877$	50382.3	+	87264.6i	0.0655056	+	0.113459i	−0.831413	+	0.555656i	$0.812467\pi$
$878$	442817.	+	255661.i	0.574428	+	0.331646i
$879$	−26365.8	−	86482.4i	−0.0341243	−	0.111931i
$880$	−13248.4	−	22946.9i	−0.0171080	−	0.0296319i
$881$			663851.i			0.855300i	0.903944	+	0.427650i	$0.140658\pi$
$881$			663851.i			0.855300i	−0.903944	+	0.427650i	$0.859342\pi$
$882$	283474.	−	471408.i	0.364399	−	0.605982i
$883$	−111648.			−0.143196			−0.0715978	−	0.997434i	$-0.522810\pi$
$883$	−111648.			−0.143196			−0.0715978	+	0.997434i	$0.522810\pi$
$884$	−654335.	+	377780.i	−0.837328	+	0.483431i
$885$	−69107.1	+	21068.6i	−0.0882341	+	0.0268998i
$886$	189596.	−	328389.i	0.241524	−	0.418332i
$887$	−325519.	+	187939.i	−0.413742	+	0.238874i	−0.692396	−	0.721518i	$-0.743445\pi$
$887$	−325519.	+	187939.i	−0.413742	+	0.238874i	0.278654	+	0.960391i	$0.410112\pi$
$888$	5536.58	−	5927.88i	0.00702127	−	0.00751750i
$889$	17934.1	−	416623.i	0.0226922	−	0.527157i
$890$		−	74293.3i		−	0.0937929i
$891$	485897.	−	377163.i	0.612053	−	0.475088i
$892$	−49832.3	+	86312.1i	−0.0626299	+	0.108478i
$893$	−50676.3	−	29258.0i	−0.0635480	−	0.0366895i
$894$	201098.	−	867930.i	0.251613	−	1.08595i
$895$	49735.1			0.0620893
$896$	−32804.1	−	62921.8i	−0.0408613	−	0.0783764i
$897$	−1.31980e6	+	1.41308e6i	−1.64030	+	1.75623i
$898$	−288761.	−	500149.i	−0.358085	−	0.620221i
$899$	70864.1	+	40913.4i	0.0876812	+	0.0506228i
$900$	352382.	+	172556.i	0.435039	+	0.213032i
$901$	−747988.	−	1.29555e6i	−0.921393	−	1.59590i
$902$		−	446552.i		−	0.548856i
$903$	145653.	+	563603.i	0.178625	+	0.691190i
$904$	417577.			0.510975
$905$	18646.8	−	10765.7i	0.0227671	−	0.0131446i
$906$	−129494.	−	424753.i	−0.157759	−	0.517464i
$907$	−647684.	+	1.12182e6i	−0.787315	+	1.36367i	0.140291	+	0.990110i	$0.455196\pi$
$907$	−647684.	+	1.12182e6i	−0.787315	+	1.36367i	−0.927606	+	0.373560i	$0.878137\pi$
$908$	217315.	−	125467.i	0.263583	−	0.152180i
$909$	1.38963e6	−	94971.2i	1.68179	−	0.114938i
$910$	142333.	+	90553.2i	0.171879	+	0.109351i
$911$			612762.i			0.738338i	0.929362	+	0.369169i	$0.120358\pi$
$911$			612762.i			0.738338i	−0.929362	+	0.369169i	$0.879642\pi$
$912$	8878.28	−	38318.3i	0.0106743	−	0.0460698i
$913$	44246.7	−	76637.5i	0.0530810	−	0.0919390i
$914$	−185352.	−	107013.i	−0.221873	−	0.128099i
$915$	204609.	+	47407.7i	0.244390	+	0.0566248i
$916$	382038.			0.455319
$917$	587032.	+	1.12599e6i	0.698108	+	1.33905i
$918$	445925.	−	548018.i	0.529148	−	0.650293i
$919$	−316934.	−	548945.i	−0.375264	−	0.649977i	0.615102	−	0.788447i	$-0.289115\pi$
$919$	−316934.	−	548945.i	−0.375264	−	0.649977i	−0.990367	+	0.138470i	$0.955781\pi$
$920$	−67451.8	−	38943.3i	−0.0796925	−	0.0460105i
$921$	−552705.	+	168503.i	−0.651590	+	0.198650i
$922$	276325.	+	478609.i	0.325056	+	0.563013i
$923$		−	2.14581e6i		−	2.51877i
$924$	−231787.	−	235951.i	−0.271484	−	0.276361i
$925$	24117.2			0.0281867
$926$	312384.	−	180355.i	0.364307	−	0.210333i
$927$	−571759.	−	279982.i	−0.665355	−	0.325815i
$928$	27228.3	−	47160.7i	0.0316172	−	0.0547627i
$929$	−400398.	+	231170.i	−0.463938	+	0.267855i	−0.713699	−	0.700453i	$-0.752981\pi$
$929$	−400398.	+	231170.i	−0.463938	+	0.267855i	0.249760	+	0.968308i	$0.419648\pi$
$930$	−22346.2	−	20871.1i	−0.0258368	−	0.0241313i
$931$	−69473.6	−	148511.i	−0.0801531	−	0.171340i
$932$		−	503156.i		−	0.579257i
$933$	−1.40019e6	−	324421.i	−1.60851	−	0.372688i
$934$	−332269.	+	575507.i	−0.380887	+	0.659716i
$935$	−122856.	−	70931.1i	−0.140532	−	0.0811360i
$936$	281833.	+	419258.i	0.321692	+	0.478553i
$937$	765416.			0.871802			0.435901	−	0.899995i	$-0.356430\pi$
$937$	765416.			0.871802			0.435901	+	0.899995i	$0.356430\pi$
$938$	627904.	+	27029.0i	0.713654	+	0.0307202i
$939$	822374.	+	768089.i	0.932692	+	0.871125i
$940$	15136.8	+	26217.7i	0.0171308	+	0.0296715i
$941$	147480.	+	85147.9i	0.166554	+	0.0961600i	0.580960	−	0.813932i	$-0.302677\pi$
$941$	147480.	+	85147.9i	0.166554	+	0.0961600i	−0.414406	+	0.910092i	$0.636011\pi$
$942$	93775.1	+	307591.i	0.105678	+	0.346635i
$943$	−656312.	−	1.13677e6i	−0.738052	−	1.27834i
$944$			116338.i			0.130550i
$945$	−154525.	−	31720.4i	−0.173036	−	0.0355201i
$946$	350021.			0.391122
$947$	209021.	−	120679.i	0.233072	−	0.134564i	−0.378916	−	0.925431i	$-0.623703\pi$
$947$	209021.	−	120679.i	0.233072	−	0.134564i	0.611989	+	0.790867i	$0.290370\pi$
$948$	252953.	−	77117.6i	0.281465	−	0.0858098i
$949$	−1.29085e6	+	2.23581e6i	−1.43332	+	2.48258i
$950$	101281.	−	58474.5i	0.112222	−	0.0647917i
$951$	49773.0	−	53290.7i	0.0550342	−	0.0589237i
$952$	−320540.	−	203930.i	−0.353679	−	0.225013i
$953$			86986.9i			0.0957785i	0.998853	+	0.0478893i	$0.0152495\pi$
$953$			86986.9i			0.0957785i	−0.998853	+	0.0478893i	$0.984751\pi$
$954$	−830113.	+	558016.i	−0.912095	+	0.613126i
$955$	115134.	−	199417.i	0.126240	−	0.218653i
$956$	−363698.	−	209981.i	−0.397947	−	0.229755i
$957$	57294.3	−	247279.i	0.0625586	−	0.270000i
$958$	354961.			0.386767
$959$	−822554.	+	1.29290e6i	−0.894390	+	1.40581i
$960$	−13890.0	+	14871.6i	−0.0150716	+	0.0161368i
$961$	424768.	+	735720.i	0.459944	+	0.796647i
$962$	26891.6	+	15525.9i	0.0290580	+	0.0167767i
$963$	137051.	−	279875.i	0.147784	−	0.301794i
$964$	197826.	+	342645.i	0.212878	+	0.368715i
$965$		−	60199.6i		−	0.0646456i
$966$	−936834.	−	259983.i	−1.00394	−	0.278606i
$967$	−1.14713e6			−1.22676			−0.613381	−	0.789787i	$-0.710191\pi$
$967$	−1.14713e6			−1.22676			−0.613381	+	0.789787i	$0.710191\pi$
$968$	114671.	−	66205.1i	0.122377	−	0.0706546i
$969$	−61411.3	−	201435.i	−0.0654034	−	0.214530i
$970$	−69400.9	+	120206.i	−0.0737601	+	0.127756i
$971$	765864.	−	442172.i	0.812294	−	0.468978i	−0.0354576	−	0.999371i	$-0.511289\pi$
$971$	765864.	−	442172.i	0.812294	−	0.468978i	0.847752	+	0.530393i	$0.177956\pi$
$972$	−385890.	−	272476.i	−0.408443	−	0.288400i
$973$	−26283.1	+	610578.i	−0.0277620	+	0.644934i
$974$		−	801849.i		−	0.845229i
$975$	−339039.	+	1.46328e6i	−0.356649	+	1.53928i
$976$	169102.	−	292894.i	0.177521	−	0.307476i
$977$	−1.52599e6	−	881031.i	−1.59868	−	0.923000i	−0.991741	−	0.128254i	$-0.959063\pi$
$977$	−1.52599e6	−	881031.i	−1.59868	−	0.923000i	−0.606942	−	0.794746i	$-0.707604\pi$
$978$	1.17787e6	+	272911.i	1.23146	+	0.285328i
$979$	−557625.			−0.581805
$980$	−7289.24	+	84510.5i	−0.00758980	+	0.0879951i
$981$	50650.7	+	741125.i	0.0526317	+	0.770112i
$982$	−504690.	−	874148.i	−0.523361	−	0.906488i
$983$	469915.	+	271305.i	0.486308	+	0.280770i	0.723042	−	0.690804i	$-0.242743\pi$
$983$	469915.	+	271305.i	0.486308	+	0.280770i	−0.236733	+	0.971575i	$0.576077\pi$
$984$	−328042.	+	100010.i	−0.338797	+	0.103289i
$985$	−38310.0	−	66354.9i	−0.0394857	−	0.0683912i
$986$		−	291557.i		−	0.299895i
$987$	264825.	+	269582.i	0.271847	+	0.276730i
$988$	150576.			0.154256
$989$	891032.	−	514438.i	0.910963	−	0.525945i
$990$	−41714.5	+	85186.3i	−0.0425614	+	0.0869159i
$991$	−629303.	+	1.08999e6i	−0.640785	+	1.10987i	0.344472	+	0.938796i	$0.388058\pi$
$991$	−629303.	+	1.08999e6i	−0.640785	+	1.10987i	−0.985258	+	0.171077i	$0.945275\pi$
$992$	−42640.9	+	24618.7i	−0.0433314	+	0.0250174i
$993$	−1.19464e6	−	1.11578e6i	−1.21154	−	1.13157i
$994$	956746.	−	498797.i	0.968331	−	0.504837i
$995$			101088.i			0.102106i
$996$	−66208.3	−	15340.4i	−0.0667411	−	0.0154638i
$997$	−72973.5	+	126394.i	−0.0734133	+	0.127156i	−0.900395	−	0.435073i	$-0.856723\pi$
$997$	−72973.5	+	126394.i	−0.0734133	+	0.127156i	0.826982	+	0.562229i	$0.190056\pi$
$998$	197103.	+	113797.i	0.197893	+	0.114254i
$999$	−28668.0	−	4610.08i	−0.0287254	−	0.00461931i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.5.h.a.11.5	✓	20
3.2	odd	2	inner	42.5.h.a.11.8	yes	20
7.2	even	3	inner	42.5.h.a.23.8	yes	20
7.3	odd	6		294.5.b.f.197.4		10
7.4	even	3		294.5.b.e.197.2		10
21.2	odd	6	inner	42.5.h.a.23.5	yes	20
21.11	odd	6		294.5.b.e.197.7		10
21.17	even	6		294.5.b.f.197.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.5.h.a.11.5	✓	20	1.1	even	1	trivial
42.5.h.a.11.8	yes	20	3.2	odd	2	inner
42.5.h.a.23.5	yes	20	21.2	odd	6	inner
42.5.h.a.23.8	yes	20	7.2	even	3	inner
294.5.b.e.197.2		10	7.4	even	3
294.5.b.e.197.7		10	21.11	odd	6
294.5.b.f.197.4		10	7.3	odd	6
294.5.b.f.197.9		10	21.17	even	6

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:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	42.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.44949 + 1.41421i) q^{2} +(8.60881 - 2.62456i) q^{3} +(4.00000 - 6.92820i) q^{4} +(3.82445 - 2.20805i) q^{5} +(-17.3755 + 18.6035i) q^{6} +(2.10732 - 48.9547i) q^{7} +22.6274i q^{8} +(67.2234 - 45.1887i) q^{9} +O(q^{10})\)	\(q+(-2.44949 + 1.41421i) q^{2} +(8.60881 - 2.62456i) q^{3} +(4.00000 - 6.92820i) q^{4} +(3.82445 - 2.20805i) q^{5} +(-17.3755 + 18.6035i) q^{6} +(2.10732 - 48.9547i) q^{7} +22.6274i q^{8} +(67.2234 - 45.1887i) q^{9} +(-6.24530 + 10.8172i) q^{10} +(81.1907 + 46.8755i) q^{11} +(16.2518 - 70.1419i) q^{12} +275.630 q^{13} +(64.0705 + 122.894i) q^{14} +(27.1288 - 29.0462i) q^{15} +(-32.0000 - 55.4256i) q^{16} +(-296.745 - 171.326i) q^{17} +(-100.756 + 205.757i) q^{18} +(34.1435 + 59.1383i) q^{19} -35.3287i q^{20} +(-110.343 - 426.972i) q^{21} -265.168 q^{22} +(-675.025 + 389.726i) q^{23} +(59.3870 + 194.795i) q^{24} +(-302.749 + 524.377i) q^{25} +(-675.153 + 389.800i) q^{26} +(460.113 - 565.453i) q^{27} +(-330.739 - 210.419i) q^{28} -300.833i q^{29} +(-25.3743 + 109.514i) q^{30} +(-136.000 + 235.560i) q^{31} +(156.767 + 90.5097i) q^{32} +(821.983 + 190.452i) q^{33} +969.165 q^{34} +(-100.035 - 191.878i) q^{35} +(-44.1832 - 646.492i) q^{36} +(-19.9152 - 34.4941i) q^{37} +(-167.268 - 96.5725i) q^{38} +(2372.85 - 723.408i) q^{39} +(49.9624 + 86.5374i) q^{40} +1684.03i q^{41} +(874.114 + 889.816i) q^{42} -1320.00 q^{43} +(649.526 - 375.004i) q^{44} +(157.314 - 321.254i) q^{45} +(1102.31 - 1909.26i) q^{46} +(-742.107 + 428.456i) q^{47} +(-420.950 - 393.163i) q^{48} +(-2392.12 - 206.326i) q^{49} -1712.61i q^{50} +(-3004.28 - 696.087i) q^{51} +(1102.52 - 1909.62i) q^{52} +(3780.96 + 2182.94i) q^{53} +(-327.370 + 2035.77i) q^{54} +414.013 q^{55} +(1107.72 + 47.6832i) q^{56} +(449.148 + 419.499i) q^{57} +(425.442 + 736.886i) q^{58} +(-1574.24 - 908.890i) q^{59} +(-92.7224 - 304.139i) q^{60} +(2642.23 + 4576.47i) q^{61} -769.335i q^{62} +(-2070.54 - 3386.12i) q^{63} -512.000 q^{64} +(1054.13 - 608.604i) q^{65} +(-2282.78 + 695.949i) q^{66} +(2267.38 - 3927.22i) q^{67} +(-2373.96 + 1370.61i) q^{68} +(-4788.31 + 5126.73i) q^{69} +(516.390 + 328.532i) q^{70} -7785.12i q^{71} +(1022.50 + 1521.09i) q^{72} +(-4683.26 + 8111.64i) q^{73} +(97.5640 + 56.3286i) q^{74} +(-1230.05 + 5308.85i) q^{75} +546.297 q^{76} +(2465.87 - 3875.88i) q^{77} +(-4789.21 + 5127.69i) q^{78} +(1836.44 + 3180.81i) q^{79} +(-244.765 - 141.315i) q^{80} +(2476.96 - 6075.47i) q^{81} +(-2381.58 - 4125.03i) q^{82} -943.920i q^{83} +(-3399.52 - 943.411i) q^{84} -1513.18 q^{85} +(3233.32 - 1866.76i) q^{86} +(-789.554 - 2589.81i) q^{87} +(-1060.67 + 1837.14i) q^{88} +(-5151.07 + 2973.97i) q^{89} +(68.9843 + 1009.38i) q^{90} +(580.840 - 13493.4i) q^{91} +6235.62i q^{92} +(-552.562 + 2384.83i) q^{93} +(1211.86 - 2098.99i) q^{94} +(261.160 + 150.781i) q^{95} +(1587.13 + 367.735i) q^{96} +11112.5 q^{97} +(6151.26 - 2877.57i) q^{98} +(7576.16 - 517.777i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 80 q^{4} - 64 q^{6} + 130 q^{7} + 52 q^{9}+O(q^{10}) \) 20 * q + 80 * q^4 - 64 * q^6 + 130 * q^7 + 52 * q^9	\( 20 q + 80 q^{4} - 64 q^{6} + 130 q^{7} + 52 q^{9} + 32 q^{10} - 324 q^{13} + 964 q^{15} - 640 q^{16} + 576 q^{18} + 1030 q^{19} - 1442 q^{21} - 1280 q^{22} - 256 q^{24} + 22 q^{25} - 3780 q^{27} + 544 q^{28} - 128 q^{30} - 318 q^{31} + 842 q^{33} + 1024 q^{34} + 832 q^{36} + 2806 q^{37} + 5542 q^{39} - 256 q^{40} + 1632 q^{42} - 6644 q^{43} + 1526 q^{45} - 3008 q^{46} - 8350 q^{49} - 5266 q^{51} - 1296 q^{52} + 7040 q^{54} + 49696 q^{55} - 3840 q^{57} + 7904 q^{58} + 3856 q^{60} - 15960 q^{61} - 144 q^{63} - 10240 q^{64} + 896 q^{66} - 12490 q^{67} - 56932 q^{69} - 19904 q^{70} - 4608 q^{72} - 23746 q^{73} + 31738 q^{75} + 16480 q^{76} + 5888 q^{78} + 15474 q^{79} + 29788 q^{81} - 9984 q^{82} + 7168 q^{84} - 39368 q^{85} + 16084 q^{87} - 5120 q^{88} - 30208 q^{90} + 16074 q^{91} - 15176 q^{93} + 15360 q^{94} + 2048 q^{96} + 102512 q^{97} + 73276 q^{99}+O(q^{100}) \) 20 * q + 80 * q^4 - 64 * q^6 + 130 * q^7 + 52 * q^9 + 32 * q^10 - 324 * q^13 + 964 * q^15 - 640 * q^16 + 576 * q^18 + 1030 * q^19 - 1442 * q^21 - 1280 * q^22 - 256 * q^24 + 22 * q^25 - 3780 * q^27 + 544 * q^28 - 128 * q^30 - 318 * q^31 + 842 * q^33 + 1024 * q^34 + 832 * q^36 + 2806 * q^37 + 5542 * q^39 - 256 * q^40 + 1632 * q^42 - 6644 * q^43 + 1526 * q^45 - 3008 * q^46 - 8350 * q^49 - 5266 * q^51 - 1296 * q^52 + 7040 * q^54 + 49696 * q^55 - 3840 * q^57 + 7904 * q^58 + 3856 * q^60 - 15960 * q^61 - 144 * q^63 - 10240 * q^64 + 896 * q^66 - 12490 * q^67 - 56932 * q^69 - 19904 * q^70 - 4608 * q^72 - 23746 * q^73 + 31738 * q^75 + 16480 * q^76 + 5888 * q^78 + 15474 * q^79 + 29788 * q^81 - 9984 * q^82 + 7168 * q^84 - 39368 * q^85 + 16084 * q^87 - 5120 * q^88 - 30208 * q^90 + 16074 * q^91 - 15176 * q^93 + 15360 * q^94 + 2048 * q^96 + 102512 * q^97 + 73276 * q^99

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