LMFDB - Embedded newform 45.5.i.a.41.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,5,Mod(11,45)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("45.11"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	45.i (of order $6$, 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:	$4.65164833877$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.3
Character	$\chi$	$=$	45.41
Dual form			45.5.i.a.11.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.11159 + 2.95118i) q^{2} +(1.28176 - 8.90826i) q^{3} +(9.41890 - 16.3140i) q^{4} +(-9.68246 - 5.59017i) q^{5} +(19.7380 + 49.3181i) q^{6} +(36.1606 + 62.6320i) q^{7} +16.7497i q^{8} +(-77.7142 - 22.8364i) q^{9} +65.9903 q^{10} +(-187.805 + 108.429i) q^{11} +(-133.257 - 104.817i) q^{12} +(-13.6629 + 23.6648i) q^{13} +(-369.676 - 213.433i) q^{14} +(-62.2092 + 79.0886i) q^{15} +(101.271 + 175.407i) q^{16} +339.847i q^{17} +(464.638 - 112.618i) q^{18} -301.434 q^{19} +(-182.396 + 105.307i) q^{20} +(604.291 - 241.849i) q^{21} +(639.988 - 1108.49i) q^{22} +(329.599 + 190.294i) q^{23} +(149.211 + 21.4691i) q^{24} +(62.5000 + 108.253i) q^{25} -161.286i q^{26} +(-303.044 + 663.028i) q^{27} +1362.37 q^{28} +(136.804 - 78.9837i) q^{29} +(84.5836 - 587.859i) q^{30} +(-201.104 + 348.322i) q^{31} +(-1267.40 - 731.735i) q^{32} +(725.196 + 1812.00i) q^{33} +(-1002.95 - 1737.16i) q^{34} -808.575i q^{35} +(-1104.54 + 1052.74i) q^{36} +291.824 q^{37} +(1540.80 - 889.584i) q^{38} +(193.300 + 152.045i) q^{39} +(93.6338 - 162.179i) q^{40} +(-2548.83 - 1471.56i) q^{41} +(-2375.15 + 3019.60i) q^{42} +(-1200.28 - 2078.95i) q^{43} +4085.14i q^{44} +(624.805 + 655.548i) q^{45} -2246.36 q^{46} +(2053.78 - 1185.75i) q^{47} +(1692.37 - 677.320i) q^{48} +(-1414.68 + 2450.29i) q^{49} +(-638.949 - 368.897i) q^{50} +(3027.44 + 435.601i) q^{51} +(257.379 + 445.793i) q^{52} +1566.51i q^{53} +(-407.677 - 4283.46i) q^{54} +2424.55 q^{55} +(-1049.07 + 605.680i) q^{56} +(-386.364 + 2685.25i) q^{57} +(-466.190 + 807.464i) q^{58} +(2631.23 + 1519.14i) q^{59} +(704.310 + 1759.81i) q^{60} +(-977.183 - 1692.53i) q^{61} -2373.97i q^{62} +(-1379.90 - 5693.17i) q^{63} +5397.25 q^{64} +(264.581 - 152.756i) q^{65} +(-9054.43 - 7122.00i) q^{66} +(-1896.89 + 3285.51i) q^{67} +(5544.27 + 3200.99i) q^{68} +(2117.65 - 2692.24i) q^{69} +(2386.25 + 4133.11i) q^{70} +1205.47i q^{71} +(382.504 - 1301.69i) q^{72} -6117.56 q^{73} +(-1491.68 + 861.223i) q^{74} +(1044.46 - 418.012i) q^{75} +(-2839.17 + 4917.59i) q^{76} +(-13582.3 - 7841.74i) q^{77} +(-1436.78 - 206.730i) q^{78} +(931.321 + 1613.09i) q^{79} -2264.49i q^{80} +(5517.99 + 3549.43i) q^{81} +17371.4 q^{82} +(721.466 - 416.539i) q^{83} +(1746.23 - 12136.4i) q^{84} +(1899.80 - 3290.55i) q^{85} +(12270.7 + 7084.49i) q^{86} +(-528.258 - 1319.92i) q^{87} +(-1816.16 - 3145.68i) q^{88} +9603.06i q^{89} +(-5128.39 - 1506.98i) q^{90} -1976.23 q^{91} +(6208.92 - 3584.72i) q^{92} +(2845.17 + 2237.95i) q^{93} +(-6998.73 + 12122.2i) q^{94} +(2918.62 + 1685.06i) q^{95} +(-8142.99 + 10352.4i) q^{96} +(-3468.03 - 6006.81i) q^{97} -16699.9i q^{98} +(17071.3 - 4137.70i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{3} + 128 q^{4} + 98 q^{6} - 26 q^{7} - 220 q^{9} - 738 q^{11} - 214 q^{12} + 10 q^{13} + 1998 q^{14} - 50 q^{15} - 1024 q^{16} - 2504 q^{18} + 508 q^{19} - 1620 q^{21} + 672 q^{22} + 1998 q^{23}+ \cdots + 53512 q^{99}+O(q^{100}) $ 32 * q - 8 * q^3 + 128 * q^4 + 98 * q^6 - 26 * q^7 - 220 * q^9 - 738 * q^11 - 214 * q^12 + 10 * q^13 + 1998 * q^14 - 50 * q^15 - 1024 * q^16 - 2504 * q^18 + 508 * q^19 - 1620 * q^21 + 672 * q^22 + 1998 * q^23 + 4164 * q^24 + 2000 * q^25 + 2158 * q^27 - 1664 * q^28 - 270 * q^29 + 2000 * q^30 - 1472 * q^31 - 6048 * q^32 - 1354 * q^33 - 594 * q^34 + 4498 * q^36 + 2068 * q^37 - 7164 * q^38 - 4616 * q^39 + 1650 * q^40 - 13428 * q^41 - 10230 * q^42 + 568 * q^43 - 100 * q^45 + 5724 * q^46 + 12528 * q^47 + 25844 * q^48 - 1674 * q^49 + 1454 * q^51 + 1534 * q^52 + 8456 * q^54 + 21294 * q^56 - 12512 * q^57 - 8190 * q^58 - 4374 * q^59 - 5050 * q^60 - 4478 * q^61 + 5604 * q^63 - 37216 * q^64 - 8550 * q^65 - 19472 * q^66 + 12838 * q^67 + 65736 * q^68 + 8706 * q^69 + 2400 * q^70 - 36372 * q^72 + 29236 * q^73 - 20628 * q^74 + 1000 * q^75 + 6190 * q^76 - 31806 * q^77 - 42430 * q^78 - 3512 * q^79 - 3088 * q^81 + 34692 * q^82 - 43074 * q^83 - 19350 * q^84 - 4350 * q^85 - 10746 * q^86 + 69622 * q^87 - 16128 * q^88 - 26750 * q^90 - 48904 * q^91 + 27036 * q^92 + 27030 * q^93 + 5118 * q^94 + 6300 * q^95 + 53566 * q^96 + 23266 * q^97 + 53512 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−5.11159	+	2.95118i	−1.27790	+	0.737794i	−0.976461	−	0.215692i	$-0.930799\pi$
$2$	−5.11159	+	2.95118i	−1.27790	+	0.737794i	−0.301436	+	0.953486i	$0.597466\pi$
$3$	1.28176	−	8.90826i	0.142417	−	0.989807i
$3$	1.28176	−	8.90826i	0.142417	−	0.989807i
$4$	9.41890	−	16.3140i	0.588681	−	1.01963i
$5$	−9.68246	−	5.59017i	−0.387298	−	0.223607i
$5$	−9.68246	−	5.59017i	−0.387298	−	0.223607i
$6$	19.7380	+	49.3181i	0.548279	+	1.36995i
$7$	36.1606	+	62.6320i	0.737971	+	1.27820i	0.953407	+	0.301686i	$0.0975494\pi$
$7$	36.1606	+	62.6320i	0.737971	+	1.27820i	−0.215436	+	0.976518i	$0.569117\pi$
$8$			16.7497i			0.261715i
$9$	−77.7142	−	22.8364i	−0.959435	−	0.281931i
$10$	65.9903			0.659903
$11$	−187.805	+	108.429i	−1.55211	+	0.896110i	−0.554138	+	0.832425i	$0.686952\pi$
$11$	−187.805	+	108.429i	−1.55211	+	0.896110i	−0.997970	+	0.0636853i	$0.979715\pi$
$12$	−133.257	−	104.817i	−0.925394	−	0.727893i
$13$	−13.6629	+	23.6648i	−0.0808455	+	0.140028i	−0.903613	−	0.428349i	$-0.859095\pi$
$13$	−13.6629	+	23.6648i	−0.0808455	+	0.140028i	0.822768	+	0.568378i	$0.192429\pi$
$14$	−369.676	−	213.433i	−1.88610	−	1.08894i
$15$	−62.2092	+	79.0886i	−0.276486	+	0.351505i
$16$	101.271	+	175.407i	0.395590	+	0.685182i
$17$			339.847i			1.17594i	0.808882	+	0.587970i	$0.200073\pi$
$17$			339.847i			1.17594i	−0.808882	+	0.587970i	$0.799927\pi$
$18$	464.638	−	112.618i	1.43407	−	0.347586i
$19$	−301.434			−0.834996			−0.417498	−	0.908678i	$-0.637093\pi$
$19$	−301.434			−0.834996			−0.417498	+	0.908678i	$0.637093\pi$
$20$	−182.396	+	105.307i	−0.455991	+	0.263266i
$21$	604.291	−	241.849i	1.37027	−	0.548410i
$22$	639.988	−	1108.49i	1.32229	−	2.29027i
$23$	329.599	+	190.294i	0.623060	+	0.359724i	0.778059	−	0.628191i	$-0.216204\pi$
$23$	329.599	+	190.294i	0.623060	+	0.359724i	−0.154999	+	0.987915i	$0.549538\pi$
$24$	149.211	+	21.4691i	0.259047	+	0.0372727i
$25$	62.5000	+	108.253i	0.100000	+	0.173205i
$26$		−	161.286i		−	0.238589i
$27$	−303.044	+	663.028i	−0.415698	+	0.909503i
$28$	1362.37			1.73772
$29$	136.804	−	78.9837i	0.162668	−	0.0939164i	−0.416456	−	0.909156i	$-0.636728\pi$
$29$	136.804	−	78.9837i	0.162668	−	0.0939164i	0.579124	+	0.815239i	$0.303395\pi$
$30$	84.5836	−	587.859i	0.0939817	−	0.653177i
$31$	−201.104	+	348.322i	−0.209265	+	0.362457i	−0.951483	−	0.307701i	$-0.900440\pi$
$31$	−201.104	+	348.322i	−0.209265	+	0.362457i	0.742218	+	0.670158i	$0.233774\pi$
$32$	−1267.40	−	731.735i	−1.23770	−	0.714585i
$33$	725.196	+	1812.00i	0.665929	+	1.66391i
$34$	−1002.95	−	1737.16i	−0.867603	−	1.50273i
$35$		−	808.575i		−	0.660062i
$36$	−1104.54	+	1052.74i	−0.852266	+	0.812297i
$37$	291.824			0.213165			0.106583	−	0.994304i	$-0.466009\pi$
$37$	291.824			0.213165			0.106583	+	0.994304i	$0.466009\pi$
$38$	1540.80	−	889.584i	1.06704	−	0.616055i
$39$	193.300	+	152.045i	0.127087	+	0.0999639i
$40$	93.6338	−	162.179i	0.0585212	−	0.101362i
$41$	−2548.83	−	1471.56i	−1.51626	−	0.875410i	−0.999818	−	0.0190855i	$-0.993925\pi$
$41$	−2548.83	−	1471.56i	−1.51626	−	0.875410i	−0.516437	−	0.856325i	$-0.672742\pi$
$42$	−2375.15	+	3019.60i	−1.34646	+	1.71179i
$43$	−1200.28	−	2078.95i	−0.649152	−	1.12436i	−0.983326	−	0.181853i	$-0.941790\pi$
$43$	−1200.28	−	2078.95i	−0.649152	−	1.12436i	0.334174	−	0.942512i	$-0.391543\pi$
$44$			4085.14i			2.11009i
$45$	624.805	+	655.548i	0.308546	+	0.323728i
$46$	−2246.36			−1.06161
$47$	2053.78	−	1185.75i	0.929734	−	0.536782i	0.0430067	−	0.999075i	$-0.486306\pi$
$47$	2053.78	−	1185.75i	0.929734	−	0.536782i	0.886728	+	0.462292i	$0.152973\pi$
$48$	1692.37	−	677.320i	0.734536	−	0.293976i
$49$	−1414.68	+	2450.29i	−0.589203	+	1.02053i
$50$	−638.949	−	368.897i	−0.255580	−	0.147559i
$51$	3027.44	+	435.601i	1.16395	+	0.167474i
$52$	257.379	+	445.793i	0.0951844	+	0.164864i
$53$			1566.51i			0.557676i	0.960338	+	0.278838i	$0.0899493\pi$
$53$			1566.51i			0.557676i	−0.960338	+	0.278838i	$0.910051\pi$
$54$	−407.677	−	4283.46i	−0.139807	−	1.46895i
$55$	2424.55			0.801505
$56$	−1049.07	+	605.680i	−0.334525	+	0.193138i
$57$	−386.364	+	2685.25i	−0.118918	+	0.826485i
$58$	−466.190	+	807.464i	−0.138582	+	0.240031i
$59$	2631.23	+	1519.14i	0.755884	+	0.436410i	0.827816	−	0.561000i	$-0.189583\pi$
$59$	2631.23	+	1519.14i	0.755884	+	0.436410i	−0.0719319	+	0.997410i	$0.522916\pi$
$60$	704.310	+	1759.81i	0.195642	+	0.488836i
$61$	−977.183	−	1692.53i	−0.262613	−	0.454859i	0.704323	−	0.709880i	$-0.251251\pi$
$61$	−977.183	−	1692.53i	−0.262613	−	0.454859i	−0.966935	+	0.255021i	$0.917918\pi$
$62$		−	2373.97i		−	0.617578i
$63$	−1379.90	−	5693.17i	−0.347669	−	1.43441i
$64$	5397.25			1.31769
$65$	264.581	−	152.756i	0.0626226	−	0.0361552i
$66$	−9054.43	−	7122.00i	−2.07861	−	1.63499i
$67$	−1896.89	+	3285.51i	−0.422565	+	0.731903i	−0.996190	−	0.0872147i	$-0.972203\pi$
$67$	−1896.89	+	3285.51i	−0.422565	+	0.731903i	0.573625	+	0.819118i	$0.305537\pi$
$68$	5544.27	+	3200.99i	1.19902	+	0.692255i
$69$	2117.65	−	2692.24i	0.444792	−	0.565478i
$70$	2386.25	+	4133.11i	0.486990	+	0.843491i
$71$			1205.47i			0.239132i	0.992826	+	0.119566i	$0.0381503\pi$
$71$			1205.47i			0.239132i	−0.992826	+	0.119566i	$0.961850\pi$
$72$	382.504	−	1301.69i	0.0737855	−	0.251098i
$73$	−6117.56			−1.14797			−0.573987	−	0.818864i	$-0.694604\pi$
$73$	−6117.56			−1.14797			−0.573987	+	0.818864i	$0.694604\pi$
$74$	−1491.68	+	861.223i	−0.272404	+	0.157272i
$75$	1044.46	−	418.012i	0.185681	−	0.0743133i
$76$	−2839.17	+	4917.59i	−0.491547	+	0.851384i
$77$	−13582.3	−	7841.74i	−2.29082	−	1.32261i
$78$	−1436.78	−	206.730i	−0.236157	−	0.0339793i
$79$	931.321	+	1613.09i	0.149226	+	0.258467i	0.930942	−	0.365168i	$-0.118988\pi$
$79$	931.321	+	1613.09i	0.149226	+	0.258467i	−0.781715	+	0.623635i	$0.785655\pi$
$80$		−	2264.49i		−	0.353826i
$81$	5517.99	+	3549.43i	0.841029	+	0.540989i
$82$	17371.4			2.58349
$83$	721.466	−	416.539i	0.104727	−	0.0604643i	−0.446722	−	0.894673i	$-0.647409\pi$
$83$	721.466	−	416.539i	0.104727	−	0.0604643i	0.551449	+	0.834209i	$0.314075\pi$
$84$	1746.23	−	12136.4i	0.247482	−	1.72001i
$85$	1899.80	−	3290.55i	0.262948	−	0.455440i
$86$	12270.7	+	7084.49i	1.65910	+	0.957882i
$87$	−528.258	−	1319.92i	−0.0697923	−	0.174385i
$88$	−1816.16	−	3145.68i	−0.234525	−	0.406209i
$89$			9603.06i			1.21235i	0.795330	+	0.606177i	$0.207298\pi$
$89$			9603.06i			1.21235i	−0.795330	+	0.606177i	$0.792702\pi$
$90$	−5128.39	−	1506.98i	−0.633134	−	0.186047i
$91$	−1976.23			−0.238646
$92$	6208.92	−	3584.72i	0.733568	−	0.423525i
$93$	2845.17	+	2237.95i	0.328960	+	0.258752i
$94$	−6998.73	+	12122.2i	−0.792070	+	1.37191i
$95$	2918.62	+	1685.06i	0.323393	+	0.186711i
$96$	−8142.99	+	10352.4i	−0.883571	+	1.12331i
$97$	−3468.03	−	6006.81i	−0.368587	−	0.638411i	0.620758	−	0.784002i	$-0.286825\pi$
$97$	−3468.03	−	6006.81i	−0.368587	−	0.638411i	−0.989345	+	0.145591i	$0.953492\pi$
$98$		−	16699.9i		−	1.73884i
$99$	17071.3	−	4137.70i	1.74179	−	0.422171i
$100$	2354.73			0.235473
$101$	9040.99	−	5219.82i	0.886285	−	0.511697i	0.0135595	−	0.999908i	$-0.495684\pi$
$101$	9040.99	−	5219.82i	0.886285	−	0.511697i	0.872726	+	0.488211i	$0.162350\pi$
$102$	−16760.6	+	6707.91i	−1.61098	+	0.644744i
$103$	−3748.81	+	6493.13i	−0.353362	+	0.612040i	−0.986836	−	0.161723i	$-0.948295\pi$
$103$	−3748.81	+	6493.13i	−0.353362	+	0.612040i	0.633475	+	0.773763i	$0.281628\pi$
$104$	−396.379	−	228.850i	−0.0366475	−	0.0211584i
$105$	−7203.00	−	1036.40i	−0.653333	−	0.0940043i
$106$	−4623.06	−	8007.37i	−0.411450	−	0.712653i
$107$		−	1396.48i		−	0.121974i	−0.998139	−	0.0609870i	$-0.980575\pi$
$107$		−	1396.48i		−	0.121974i	0.998139	−	0.0609870i	$-0.0194248\pi$
$108$	7962.30	+	11188.9i	0.682639	+	0.959264i
$109$	−17017.9			−1.43236			−0.716180	−	0.697916i	$-0.754111\pi$
$109$	−17017.9			−1.43236			−0.716180	+	0.697916i	$0.754111\pi$
$110$	−12393.3	+	7155.29i	−1.02424	+	0.591346i
$111$	374.047	−	2599.64i	0.0303585	−	0.210993i
$112$	−7324.04	+	12685.6i	−0.583868	+	1.01129i
$113$	17895.2	+	10331.8i	1.40146	+	0.809133i	0.994543	−	0.104332i	$-0.0332705\pi$
$113$	17895.2	+	10331.8i	1.40146	+	0.809133i	0.406917	+	0.913465i	$0.366604\pi$
$114$	−5949.71	−	14866.1i	−0.457811	−	1.14390i
$115$	−2127.55	−	3685.03i	−0.160873	−	0.278641i
$116$		−	2975.76i		−	0.221147i
$117$	1602.22	−	1527.08i	0.117044	−	0.111555i
$118$	−17933.0			−1.28792
$119$	−21285.3	+	12289.1i	−1.50309	+	0.867811i
$120$	−1324.71	−	1041.99i	−0.0919940	−	0.0723603i
$121$	16193.3	−	28047.7i	1.10603	−	1.91569i
$122$	9989.91	+	5767.68i	0.671185	+	0.387509i
$123$	−16376.1	+	20819.4i	−1.08243	+	1.37613i
$124$	3788.35	+	6561.62i	0.246381	+	0.426744i
$125$		−	1397.54i		−	0.0894427i
$126$	23855.1	+	25028.8i	1.50259	+	1.57652i
$127$	18405.1			1.14112			0.570558	−	0.821257i	$-0.306727\pi$
$127$	18405.1			1.14112			0.570558	+	0.821257i	$0.306727\pi$
$128$	−7310.10	+	4220.49i	−0.446173	+	0.257598i
$129$	−20058.3	+	8027.72i	−1.20535	+	0.482406i
$130$	−901.618	+	1561.65i	−0.0533502	+	0.0924052i
$131$	−5531.53	−	3193.63i	−0.322332	−	0.186098i	0.330100	−	0.943946i	$-0.392918\pi$
$131$	−5531.53	−	3193.63i	−0.322332	−	0.186098i	−0.652431	+	0.757848i	$0.726251\pi$
$132$	36391.5	+	5236.16i	2.08858	+	0.300514i
$133$	−10900.0	−	18879.4i	−0.616203	−	1.06730i
$134$		−	22392.3i		−	1.24706i
$135$	6640.64	−	4725.67i	0.364370	−	0.259296i
$136$	−5692.34			−0.307761
$137$	−9299.23	+	5368.91i	−0.495457	+	0.286052i	−0.726835	−	0.686812i	$-0.759010\pi$
$137$	−9299.23	+	5368.91i	−0.495457	+	0.286052i	0.231379	+	0.972864i	$0.425676\pi$
$138$	−2879.29	+	20011.2i	−0.151192	+	1.05079i
$139$	11291.3	−	19557.1i	0.584405	−	1.01222i	−0.410544	−	0.911841i	$-0.634661\pi$
$139$	11291.3	−	19557.1i	0.584405	−	1.01222i	0.994949	−	0.100378i	$-0.0320054\pi$
$140$	−13191.1	−	7615.89i	−0.673016	−	0.388566i
$141$	−7930.54	−	19815.5i	−0.398900	−	0.996704i
$142$	−3557.54	−	6161.84i	−0.176430	−	0.305586i
$143$		−	5925.83i		−	0.289786i
$144$	−3864.53	−	15944.2i	−0.186368	−	0.768916i
$145$	−1766.13			−0.0840013
$146$	31270.4	−	18054.0i	1.46699	−	0.846969i
$147$	20014.6	+	15743.0i	0.926215	+	0.728538i
$148$	2748.66	−	4760.81i	0.125487	−	0.217349i
$149$	−26665.8	−	15395.5i	−1.20111	−	0.693459i	−0.240305	−	0.970697i	$-0.577247\pi$
$149$	−26665.8	−	15395.5i	−1.20111	−	0.693459i	−0.960801	+	0.277239i	$0.910581\pi$
$150$	−4105.21	+	5219.09i	−0.182454	+	0.231959i
$151$	15309.2	+	26516.4i	0.671429	+	1.16295i	0.977499	+	0.210940i	$0.0676524\pi$
$151$	15309.2	+	26516.4i	0.671429	+	1.16295i	−0.306070	+	0.952009i	$0.599014\pi$
$152$		−	5048.93i		−	0.218531i
$153$	7760.90	−	26410.9i	0.331535	−	1.12824i
$154$	92569.4			3.90325
$155$	3894.35	−	2248.41i	0.162096	−	0.0935861i
$156$	4301.14	−	1721.40i	0.176740	−	0.0707346i
$157$	5843.75	−	10121.7i	0.237079	−	0.410632i	−0.722796	−	0.691061i	$-0.757143\pi$
$157$	5843.75	−	10121.7i	0.237079	−	0.410632i	0.959875	+	0.280429i	$0.0904768\pi$
$158$	−9521.06	−	5496.99i	−0.381392	−	0.220197i
$159$	13954.9	+	2007.89i	0.551992	+	0.0794228i
$160$	8181.05	+	14170.0i	0.319572	+	0.553515i
$161$			27524.6i			1.06186i
$162$	−38680.7	−	1858.66i	−1.47389	−	0.0708222i
$163$	19003.8			0.715263			0.357631	−	0.933863i	$-0.383584\pi$
$163$	19003.8			0.715263			0.357631	+	0.933863i	$0.383584\pi$
$164$	−48014.3	+	27721.1i	−1.78518	+	1.03068i
$165$	3107.69	−	21598.6i	0.114148	−	0.793335i
$166$	−2458.56	+	4258.35i	−0.0892205	+	0.154534i
$167$	17505.7	+	10106.9i	0.627693	+	0.362399i	0.779858	−	0.625956i	$-0.215291\pi$
$167$	17505.7	+	10106.9i	0.627693	+	0.362399i	−0.152165	+	0.988355i	$0.548625\pi$
$168$	4050.91	+	10121.7i	0.143527	+	0.358621i
$169$	13907.2	+	24087.9i	0.486928	+	0.843384i
$170$			22426.6i			0.776008i
$171$	23425.7	+	6883.67i	0.801124	+	0.235412i
$172$	−45221.4			−1.52858
$173$	−11421.0	+	6593.90i	−0.381602	+	0.220318i	−0.678515	−	0.734587i	$-0.737376\pi$
$173$	−11421.0	+	6593.90i	−0.381602	+	0.220318i	0.296913	+	0.954904i	$0.404043\pi$
$174$	6595.56	+	5187.91i	0.217848	+	0.171354i
$175$	−4520.07	+	7829.00i	−0.147594	+	0.255641i
$176$	−38038.4	−	21961.5i	−1.22800	−	0.708984i
$177$	16905.5	−	21492.5i	0.539613	−	0.686027i
$178$	−28340.3	−	49086.9i	−0.894468	−	1.54926i
$179$			41686.8i			1.30105i	0.759487	+	0.650523i	$0.225450\pi$
$179$			41686.8i			1.30105i	−0.759487	+	0.650523i	$0.774550\pi$
$180$	16579.6	−	4018.53i	0.511716	−	0.124029i
$181$	−37621.8			−1.14837			−0.574185	−	0.818726i	$-0.694681\pi$
$181$	−37621.8			−1.14837			−0.574185	+	0.818726i	$0.694681\pi$
$182$	10101.7	−	5832.21i	0.304966	−	0.176072i
$183$	−16330.0	+	6535.59i	−0.487623	+	0.195156i
$184$	−3187.37	+	5520.69i	−0.0941449	+	0.163064i
$185$	−2825.57	−	1631.34i	−0.0825586	−	0.0476653i
$186$	−21147.9	−	3042.85i	−0.611283	−	0.0879539i
$187$	−36849.4	−	63825.0i	−1.05377	−	1.82519i
$188$		−	44673.9i		−	1.26398i
$189$	−52485.0	+	4995.24i	−1.46930	+	0.139841i
$190$	−19891.7			−0.551017
$191$	−27541.2	+	15900.9i	−0.754948	+	0.435869i	−0.827479	−	0.561497i	$-0.810226\pi$
$191$	−27541.2	+	15900.9i	−0.754948	+	0.435869i	0.0725312	+	0.997366i	$0.476892\pi$
$192$	6917.96	−	48080.1i	0.187662	−	1.30426i
$193$	−21377.1	+	37026.2i	−0.573897	+	0.994019i	0.422263	+	0.906473i	$0.361236\pi$
$193$	−21377.1	+	37026.2i	−0.573897	+	0.994019i	−0.996160	+	0.0875460i	$0.972098\pi$
$194$	35454.3	+	20469.6i	0.942033	+	0.543883i
$195$	−1021.66	−	2552.75i	−0.0268681	−	0.0671334i
$196$	26649.4	+	46158.1i	0.693706	+	1.20153i
$197$			47493.1i			1.22377i	0.790948	+	0.611883i	$0.209588\pi$
$197$			47493.1i			1.22377i	−0.790948	+	0.611883i	$0.790412\pi$
$198$	−75050.2	+	71530.5i	−1.91435	+	1.82457i
$199$	41458.3			1.04690			0.523450	−	0.852057i	$-0.324645\pi$
$199$	41458.3			1.04690			0.523450	+	0.852057i	$0.324645\pi$
$200$	−1813.21	+	1046.86i	−0.0453303	+	0.0261715i
$201$	26836.9	+	21109.2i	0.664262	+	0.522493i
$202$	−30809.2	+	53363.2i	−0.755054	+	1.30779i
$203$	9893.81	+	5712.19i	0.240088	+	0.138615i
$204$	35621.6	−	45286.9i	0.855960	−	1.08821i
$205$	16452.6	+	28496.7i	0.391495	+	0.678090i
$206$		−	44253.7i		−	1.04283i
$207$	−21268.9	−	22315.4i	−0.496368	−	0.520792i
$208$	−5534.61			−0.127927
$209$	56610.8	−	32684.2i	1.29600	−	0.748248i
$210$	39877.4	−	15959.7i	0.904249	−	0.361898i
$211$	32912.0	−	57005.2i	0.739246	−	1.28041i	−0.213589	−	0.976924i	$-0.568515\pi$
$211$	32912.0	−	57005.2i	0.739246	−	1.28041i	0.952835	−	0.303488i	$-0.0981512\pi$
$212$	25556.1	+	14754.8i	0.568621	+	0.328294i
$213$	10738.6	+	1545.11i	0.236695	+	0.0340566i
$214$	4121.26	+	7138.24i	0.0899918	+	0.155870i
$215$			26839.1i			0.580619i
$216$	−11105.5	−	5075.90i	−0.238030	−	0.108794i
$217$	−29088.1			−0.617726
$218$	86988.3	−	50222.7i	1.83041	−	1.05679i
$219$	−7841.22	+	54496.8i	−0.163492	+	1.13627i
$220$	22836.6	−	39554.2i	0.471831	−	0.817236i
$221$	−8042.41	−	4643.29i	−0.164665	−	0.0950695i
$222$	5760.03	+	14392.2i	0.116874	+	0.292025i
$223$	41210.8	+	71379.2i	0.828708	+	1.43536i	0.899053	+	0.437841i	$0.144257\pi$
$223$	41210.8	+	71379.2i	0.828708	+	1.43536i	−0.0703450	+	0.997523i	$0.522410\pi$
$224$		−	105840.i		−	2.10937i
$225$	−2385.02	−	9840.09i	−0.0471115	−	0.194372i
$226$	−121964.			−2.38790
$227$	80238.6	−	46325.8i	1.55715	−	0.899023i	0.559627	−	0.828745i	$-0.310945\pi$
$227$	80238.6	−	46325.8i	1.55715	−	0.899023i	0.997527	−	0.0702785i	$-0.0223888\pi$
$228$	40168.1	+	31595.2i	0.772700	+	0.607788i
$229$	−24969.1	+	43247.8i	−0.476138	+	0.824695i	−0.999626	−	0.0273379i	$-0.991297\pi$
$229$	−24969.1	+	43247.8i	−0.476138	+	0.824695i	0.523488	+	0.852033i	$0.324630\pi$
$230$	21750.3	+	12557.6i	0.411159	+	0.237383i
$231$	−87265.4	+	110943.i	−1.63538	+	2.07911i
$232$	1322.95	+	2291.43i	0.0245793	+	0.0425726i
$233$		−	2917.13i		−	0.0537333i	−0.999639	−	0.0268666i	$-0.991447\pi$
$233$		−	2917.13i		−	0.0537333i	0.999639	−	0.0268666i	$-0.00855295\pi$
$234$	−3683.21	+	12534.2i	−0.0672658	+	0.228911i
$235$	−26514.2			−0.480113
$236$	49566.6	−	28617.3i	0.889950	−	0.513813i
$237$	15563.6	−	6228.85i	0.277085	−	0.110895i
$238$	72534.4	−	125633.i	1.28053	−	2.21795i
$239$	−69610.5	−	40189.7i	−1.21865	−	0.703588i	−0.254021	−	0.967199i	$-0.581753\pi$
$239$	−69610.5	−	40189.7i	−1.21865	−	0.703588i	−0.964629	+	0.263611i	$0.915087\pi$
$240$	−20172.7	−	2902.52i	−0.350220	−	0.0503910i
$241$	−2582.58	−	4473.16i	−0.0444651	−	0.0770159i	0.842936	−	0.538013i	$-0.180825\pi$
$241$	−2582.58	−	4473.16i	−0.0444651	−	0.0770159i	−0.887401	+	0.460998i	$0.847492\pi$
$242$			191158.i			3.26408i
$243$	38692.0	−	44606.2i	0.655252	−	0.755410i
$244$	−36816.0			−0.618381
$245$	27395.1	−	15816.6i	0.456395	−	0.263500i
$246$	22265.9	−	154749.i	0.367934	−	2.55716i
$247$	4118.45	−	7133.37i	0.0675056	−	0.116923i
$248$	−5834.29	−	3368.43i	−0.0948604	−	0.0547677i
$249$	−2785.89	−	6960.91i	−0.0449330	−	0.112271i
$250$	4124.40	+	7143.66i	0.0659903	+	0.114299i
$251$			3095.71i			0.0491375i	0.999698	+	0.0245688i	$0.00782126\pi$
$251$			3095.71i			0.0491375i	−0.999698	+	0.0245688i	$0.992179\pi$
$252$	−105876.	−	31111.7i	−1.66723	−	0.489918i
$253$	−82533.7			−1.28941
$254$	−94079.1	+	54316.6i	−1.45823	+	0.841909i
$255$	−26878.0	−	21141.6i	−0.413349	−	0.325131i
$256$	−18267.2	+	31639.7i	−0.278735	+	0.482784i
$257$	−47832.5	−	27616.1i	−0.724197	−	0.418115i	0.0920984	−	0.995750i	$-0.470643\pi$
$257$	−47832.5	−	27616.1i	−0.724197	−	0.418115i	−0.816296	+	0.577634i	$0.803976\pi$
$258$	78838.6	−	100230.i	1.18440	−	1.50577i
$259$	10552.5	+	18277.5i	0.157310	+	0.272469i
$260$		−	5755.16i		−	0.0851355i
$261$	−12435.3	+	3014.04i	−0.182547	+	0.0442454i
$262$	37699.9			0.549209
$263$	86109.8	−	49715.5i	1.24492	−	0.718754i	0.274827	−	0.961494i	$-0.411379\pi$
$263$	86109.8	−	49715.5i	1.24492	−	0.718754i	0.970091	+	0.242740i	$0.0780461\pi$
$264$	−30350.5	+	12146.8i	−0.435469	+	0.174283i
$265$	8757.07	−	15167.7i	0.124700	−	0.215987i
$266$	111433.	+	64335.8i	1.57489	+	0.909262i
$267$	85546.5	+	12308.8i	1.20000	+	0.172660i
$268$	35733.3	+	61891.9i	0.497512	+	0.861716i
$269$		−	24838.3i		−	0.343256i	−0.985162	−	0.171628i	$-0.945097\pi$
$269$		−	24838.3i		−	0.343256i	0.985162	−	0.171628i	$-0.0549027\pi$
$270$	−19998.0	+	43753.4i	−0.274320	+	0.600184i
$271$	14233.2			0.193804			0.0969021	−	0.995294i	$-0.469107\pi$
$271$	14233.2			0.193804			0.0969021	+	0.995294i	$0.469107\pi$
$272$	−59611.4	+	34416.6i	−0.805733	+	0.465190i
$273$	−2533.05	+	17604.8i	−0.0339874	+	0.236214i
$274$	31689.2	−	54887.4i	0.422095	−	0.731091i
$275$	−23475.6	−	13553.7i	−0.310422	−	0.179222i
$276$	−23975.3	−	59905.4i	−0.314735	−	0.786407i
$277$	34677.1	+	60062.5i	0.451942	+	0.782787i	0.998507	−	0.0546300i	$-0.0173979\pi$
$277$	34677.1	+	60062.5i	0.451942	+	0.782787i	−0.546564	+	0.837417i	$0.684065\pi$
$278$			133290.i			1.72468i
$279$	23583.0	−	22477.0i	0.302964	−	0.288756i
$280$	13543.4			0.172748
$281$	−106581.	+	61534.7i	−1.34980	+	0.779306i	−0.988220	−	0.153037i	$-0.951095\pi$
$281$	−106581.	+	61534.7i	−1.34980	+	0.779306i	−0.361576	+	0.932343i	$0.617761\pi$
$282$	99016.7	+	77884.2i	1.24512	+	0.979379i
$283$	−37949.9	+	65731.2i	−0.473847	+	0.820727i	−0.999552	−	0.0299403i	$-0.990468\pi$
$283$	−37949.9	+	65731.2i	−0.473847	+	0.820727i	0.525705	+	0.850667i	$0.323802\pi$
$284$	19666.0	+	11354.2i	0.243825	+	0.140773i
$285$	18752.0	−	23840.0i	0.230864	−	0.293505i
$286$	17488.2	+	30290.4i	0.213802	+	0.370316i
$287$		−	212851.i		−	2.58411i
$288$	81785.0	+	85809.2i	0.986026	+	1.03454i
$289$	−31974.9			−0.382837
$290$	9027.72	−	5212.16i	0.107345	−	0.0619757i
$291$	−57955.4	+	23194.9i	−0.684397	+	0.273909i
$292$	−57620.7	+	99801.9i	−0.675791	+	1.17051i
$293$	54022.7	+	31190.0i	0.629276	+	0.363313i	0.780472	−	0.625191i	$-0.214979\pi$
$293$	54022.7	+	31190.0i	0.629276	+	0.363313i	−0.151196	+	0.988504i	$0.548312\pi$
$294$	−148767.	−	21405.1i	−1.72112	−	0.247642i
$295$	−16984.5	−	29418.1i	−0.195168	−	0.338042i
$296$			4887.97i			0.0557885i
$297$	−14978.5	−	157379.i	−0.169807	−	1.78416i
$298$	181739.			2.04652
$299$	−9006.54	+	5199.93i	−0.100743	+	0.0581641i
$300$	3018.19	−	20976.5i	0.0335354	−	0.233072i
$301$	86805.8	−	150352.i	0.958111	−	1.65950i
$302$	−156509.	−	90360.6i	−1.71603	−	0.990753i
$303$	−34911.2	−	87230.1i	−0.380259	−	0.950125i
$304$	−30526.5	−	52873.4i	−0.330316	−	0.572124i
$305$			21850.5i			0.234888i
$306$	38272.8	+	157906.i	0.408741	+	1.68638i
$307$	53124.3			0.563659			0.281830	−	0.959464i	$-0.409059\pi$
$307$	53124.3			0.563659			0.281830	+	0.959464i	$0.409059\pi$
$308$	−255860.	+	147721.i	−2.69713	+	1.55719i
$309$	53037.5	+	41718.0i	0.555477	+	0.436925i
$310$	−13270.9	+	22985.9i	−0.138095	+	0.239187i
$311$	−18850.6	−	10883.4i	−0.194897	−	0.112524i	0.399376	−	0.916787i	$-0.369227\pi$
$311$	−18850.6	−	10883.4i	−0.194897	−	0.112524i	−0.594273	+	0.804263i	$0.702560\pi$
$312$	−2546.71	+	3237.72i	−0.0261620	+	0.0332606i
$313$	17918.4	+	31035.5i	0.182898	+	0.316789i	0.942866	−	0.333171i	$-0.108119\pi$
$313$	17918.4	+	31035.5i	0.182898	+	0.316789i	−0.759968	+	0.649960i	$0.774785\pi$
$314$			68983.8i			0.699661i
$315$	−18465.0	+	62837.8i	−0.186092	+	0.633286i
$316$	35088.1			0.351387
$317$	−2844.75	+	1642.42i	−0.0283091	+	0.0163443i	−0.514088	−	0.857738i	$-0.671869\pi$
$317$	−2844.75	+	1642.42i	−0.0283091	+	0.0163443i	0.485779	+	0.874082i	$0.338536\pi$
$318$	−77257.4	+	30919.9i	−0.763986	+	0.305762i
$319$	−17128.3	+	29667.1i	−0.168319	+	0.291537i
$320$	−52258.7	−	30171.6i	−0.510339	−	0.294644i
$321$	−12440.2	−	1789.95i	−0.120731	−	0.0173712i
$322$	−81229.9	−	140694.i	−0.783437	−	1.35695i
$323$		−	102441.i		−	0.981906i
$324$	109879.	−	56588.9i	1.04671	−	0.539065i
$325$	−3415.72			−0.0323382
$326$	−97139.7	+	56083.7i	−0.914033	+	0.527717i
$327$	−21812.8	+	151600.i	−0.203993	+	1.41776i
$328$	24648.3	−	42692.1i	0.229108	−	0.396826i
$329$	148532.	+	85755.0i	1.37223	+	0.792260i
$330$	47855.9	+	119574.i	0.439449	+	1.09802i
$331$	39840.4	+	69005.5i	0.363636	+	0.629837i	0.988556	−	0.150852i	$-0.0482017\pi$
$331$	39840.4	+	69005.5i	0.363636	+	0.629837i	−0.624920	+	0.780689i	$0.714868\pi$
$332$		−	15693.3i		−	0.142377i
$333$	−22678.8	−	6664.21i	−0.204518	−	0.0600980i
$334$	−119309.			−1.06950
$335$	36733.2	−	21207.9i	0.327317	−	0.188977i
$336$	103619.	+	81504.3i	0.917827	+	0.721941i
$337$	7825.27	−	13553.8i	0.0689033	−	0.119344i	−0.829516	−	0.558484i	$-0.811383\pi$
$337$	7825.27	−	13553.8i	0.0689033	−	0.119344i	0.898419	+	0.439140i	$0.144717\pi$
$338$	−142175.	−	82085.0i	−1.24449	−	0.718506i
$339$	114976.	−	146173.i	1.00048	−	1.27194i
$340$	−35788.1	−	61986.8i	−0.309586	−	0.536218i
$341$		−	87222.1i		−	0.750098i
$342$	−140057.	+	33946.8i	−1.19744	+	0.290233i
$343$	−30979.0			−0.263318
$344$	34821.9	−	20104.4i	0.294263	−	0.169893i
$345$	−35554.2	+	14229.5i	−0.298712	+	0.119550i
$346$	38919.5	−	67410.6i	0.325099	−	0.563087i
$347$	−71593.4	−	41334.5i	−0.594585	−	0.343284i	0.172323	−	0.985040i	$-0.444873\pi$
$347$	−71593.4	−	41334.5i	−0.594585	−	0.343284i	−0.766908	+	0.641757i	$0.778206\pi$
$348$	−26508.8	−	3814.20i	−0.218893	−	0.0314952i
$349$	−73967.8	−	128116.i	−0.607284	−	1.05185i	−0.991686	−	0.128681i	$-0.958926\pi$
$349$	−73967.8	−	128116.i	−0.607284	−	1.05185i	0.384402	−	0.923166i	$-0.374408\pi$
$350$		−	53358.2i		−	0.435577i
$351$	−11550.0	−	16230.3i	−0.0937490	−	0.131739i
$352$	317366.			2.56139
$353$	52881.8	−	30531.3i	0.424382	−	0.245017i	−0.272569	−	0.962136i	$-0.587873\pi$
$353$	52881.8	−	30531.3i	0.424382	−	0.245017i	0.696950	+	0.717119i	$0.254540\pi$
$354$	−22985.8	+	159752.i	−0.183423	+	1.27480i
$355$	6738.76	−	11671.9i	0.0534716	−	0.0926155i
$356$	156664.	+	90450.3i	1.23615	+	0.713690i
$357$	82191.6	+	205366.i	0.644898	+	1.61136i
$358$	−123025.	−	213086.i	−0.959904	−	1.66260i
$359$		−	77227.2i		−	0.599213i	−0.954063	−	0.299607i	$-0.903145\pi$
$359$		−	77227.2i		−	0.599213i	0.954063	−	0.299607i	$-0.0968554\pi$
$360$	−10980.3	+	10465.3i	−0.0847242	+	0.0807509i
$361$	−39458.8			−0.302782
$362$	192307.	−	111028.i	1.46750	−	0.847261i
$363$	−229100.	−	180205.i	−1.73865	−	1.36758i
$364$	−18613.9	+	32240.3i	−0.140487	+	0.243330i
$365$	59233.0	+	34198.2i	0.444609	+	0.256695i
$366$	64184.6	−	81600.0i	0.479147	−	0.609155i
$367$	45050.6	+	78029.9i	0.334479	+	0.579334i	0.983385	−	0.181535i	$-0.0581065\pi$
$367$	45050.6	+	78029.9i	0.334479	+	0.579334i	−0.648906	+	0.760869i	$0.724773\pi$
$368$			77085.0i			0.569212i
$369$	164475.	+	172568.i	1.20794	+	1.26738i
$370$	19257.5			0.140669
$371$	−98113.8	+	56646.0i	−0.712824	+	0.411549i
$372$	63308.3	−	25337.2i	0.457483	−	0.183094i
$373$	−68803.0	+	119170.i	−0.494527	+	0.856545i	−0.999980	−	0.00630866i	$-0.997992\pi$
$373$	−68803.0	+	119170.i	−0.494527	+	0.856545i	0.505454	+	0.862854i	$0.331325\pi$
$374$	376718.	+	217498.i	2.69323	+	1.55494i
$375$	−12449.7	−	1791.31i	−0.0885310	−	0.0127382i
$376$	19861.0	+	34400.3i	0.140484	+	0.243325i
$377$			4316.58i			0.0303708i
$378$	253540.	−	180426.i	1.77444	−	1.26275i
$379$	−120747.			−0.840618			−0.420309	−	0.907381i	$-0.638078\pi$
$379$	−120747.			−0.840618			−0.420309	+	0.907381i	$0.638078\pi$
$380$	54980.4	−	31742.9i	0.380750	−	0.219826i
$381$	23590.8	−	163957.i	0.162515	−	1.12948i
$382$	93853.0	−	162558.i	0.643164	−	1.11399i
$383$	−27743.0	−	16017.4i	−0.189128	−	0.109193i	0.402446	−	0.915444i	$-0.368160\pi$
$383$	−27743.0	−	16017.4i	−0.189128	−	0.109193i	−0.591574	+	0.806250i	$0.701493\pi$
$384$	28227.4	+	70529.9i	0.191430	+	0.478311i
$385$	87673.3	+	151855.i	0.591488	+	1.02449i
$386$		−	252351.i		−	1.69367i
$387$	45803.2	+	188974.i	0.305825	+	1.26177i
$388$	−130660.			−0.867921
$389$	48954.6	−	28263.9i	0.323515	−	0.186781i	−0.329443	−	0.944175i	$-0.606861\pi$
$389$	48954.6	−	28263.9i	0.323515	−	0.186781i	0.652958	+	0.757394i	$0.273528\pi$
$390$	12755.9	+	10033.5i	0.0838653	+	0.0659665i
$391$	−64670.8	+	112013.i	−0.423014	+	0.732682i
$392$	−41041.7	−	23695.5i	−0.267088	−	0.154203i
$393$	−35539.8	+	45182.9i	−0.230107	+	0.292542i
$394$	−140161.	−	242765.i	−0.902888	−	1.56385i
$395$		−	20825.0i		−	0.133472i
$396$	93290.1	−	317473.i	0.594902	−	2.02450i
$397$	−12413.9			−0.0787637			−0.0393819	−	0.999224i	$-0.512539\pi$
$397$	−12413.9			−0.0787637			−0.0393819	+	0.999224i	$0.512539\pi$
$398$	−211918.	+	122351.i	−1.33783	+	0.772396i
$399$	−182154.	+	72901.4i	−1.14417	+	0.457921i
$400$	−12658.9	+	21925.8i	−0.0791180	+	0.137036i
$401$	56538.8	+	32642.7i	0.351607	+	0.203000i	0.665393	−	0.746493i	$-0.268264\pi$
$401$	56538.8	+	32642.7i	0.351607	+	0.203000i	−0.313786	+	0.949494i	$0.601597\pi$
$402$	−199476.	−	28701.4i	−1.23435	−	0.177604i
$403$	−5495.31	−	9518.15i	−0.0338362	−	0.0586061i
$404$		−	196660.i		−	1.20491i
$405$	−33585.8	−	65213.7i	−0.204760	−	0.397584i
$406$	−67430.8			−0.409078
$407$	−54805.9	+	31642.2i	−0.330856	+	0.191020i
$408$	−7296.20	+	50708.9i	−0.0438305	+	0.304624i
$409$	44708.7	−	77437.7i	0.267267	−	0.462920i	−0.700888	−	0.713271i	$-0.747213\pi$
$409$	44708.7	−	77437.7i	0.267267	−	0.462920i	0.968155	+	0.250351i	$0.0805461\pi$
$410$	−168198.	−	97109.1i	−1.00058	−	0.577686i
$411$	35908.3	+	89721.6i	0.212575	+	0.531145i
$412$	70619.4	+	122316.i	0.416035	+	0.720593i
$413$			219732.i			1.28823i
$414$	174574.	+	51299.0i	1.01854	+	0.299301i
$415$	−9314.09			−0.0540809
$416$	34632.7	−	19995.2i	0.200125	−	0.115542i
$417$	−159747.	−	125653.i	−0.918672	−	0.722606i
$418$	−192914.	+	334137.i	−1.10411	+	1.91237i
$419$	9707.06	+	5604.38i	0.0552917	+	0.0319227i	0.527391	−	0.849623i	$-0.323170\pi$
$419$	9707.06	+	5604.38i	0.0552917	+	0.0319227i	−0.472099	+	0.881545i	$0.656504\pi$
$420$	−84752.2	+	107748.i	−0.480454	+	0.610817i
$421$	7817.74	+	13540.7i	0.0441079	+	0.0763972i	0.887237	−	0.461315i	$-0.152622\pi$
$421$	7817.74	+	13540.7i	0.0441079	+	0.0763972i	−0.843129	+	0.537712i	$0.819289\pi$
$422$			388516.i			2.18165i
$423$	−186686.	+	45248.7i	−1.04335	+	0.252886i
$424$	−26238.7			−0.145952
$425$	−36789.5	+	21240.4i	−0.203679	+	0.117594i
$426$	−59451.2	+	23793.5i	−0.327598	+	0.131111i
$427$	70671.0	−	122406.i	0.387602	−	0.671346i
$428$	−22782.2	−	13153.3i	−0.124368	−	0.0718038i
$429$	−52788.8	−	7595.47i	−0.286832	−	0.0412705i
$430$	−79207.1	−	137191.i	−0.428378	−	0.741972i
$431$			186459.i			1.00375i	0.864939	+	0.501877i	$0.167357\pi$
$431$			186459.i			1.00375i	−0.864939	+	0.501877i	$0.832643\pi$
$432$	−146989.	+	13989.6i	−0.787620	+	0.0749616i
$433$	47098.6			0.251207			0.125604	−	0.992080i	$-0.459913\pi$
$433$	47098.6			0.251207			0.125604	+	0.992080i	$0.459913\pi$
$434$	148686.	−	85844.2i	0.789391	−	0.455755i
$435$	−2263.75	+	15733.1i	−0.0119633	+	0.0831451i
$436$	−160290.	+	277630.i	−0.843203	+	1.46047i
$437$	−99352.1	−	57361.0i	−0.520253	−	0.300368i
$438$	−120749.	−	301706.i	−0.629411	−	1.57266i
$439$	153533.	+	265927.i	0.796658	+	1.37985i	0.921781	+	0.387712i	$0.126734\pi$
$439$	153533.	+	265927.i	0.796658	+	1.37985i	−0.125122	+	0.992141i	$0.539932\pi$
$440$			40610.6i			0.209766i
$441$	165896.	−	158116.i	0.853021	−	0.813017i
$442$	54812.7			0.280567
$443$	−165463.	+	95530.4i	−0.843130	+	0.486781i	−0.858327	−	0.513103i	$-0.828496\pi$
$443$	−165463.	+	95530.4i	−0.843130	+	0.486781i	0.0151967	+	0.999885i	$0.495163\pi$
$444$	−38887.5	−	30588.0i	−0.197262	−	0.155162i
$445$	53682.7	−	92981.2i	0.271091	−	0.469543i
$446$	−421305.	−	243241.i	−2.11801	−	1.22283i
$447$	−171326.	+	217812.i	−0.857449	+	1.09010i
$448$	195168.	+	338041.i	0.972416	+	1.68427i
$449$		−	37138.3i		−	0.184217i	−0.995749	−	0.0921084i	$-0.970639\pi$
$449$		−	37138.3i		−	0.184217i	0.995749	−	0.0921084i	$-0.0293606\pi$
$450$	41231.1	+	43259.9i	0.203610	+	0.213629i
$451$	638243.			3.13786
$452$	337107.	−	194629.i	1.65003	−	0.952643i
$453$	255838.	−	102391.i	1.24672	−	0.498960i
$454$	−273431.	+	473597.i	−1.32659	+	2.29772i
$455$	19134.8	+	11047.5i	0.0924274	+	0.0533630i
$456$	−44977.2	−	6471.50i	−0.216303	−	0.0311226i
$457$	15762.6	+	27301.7i	0.0754738	+	0.130724i	0.901292	−	0.433212i	$-0.142620\pi$
$457$	15762.6	+	27301.7i	0.0754738	+	0.130724i	−0.825818	+	0.563936i	$0.809286\pi$
$458$		−	294754.i		−	1.40517i
$459$	−225328.	−	102988.i	−1.06952	−	0.488836i
$460$	−80156.8			−0.378813
$461$	107440.	−	62030.3i	0.505549	−	0.291879i	−0.225453	−	0.974254i	$-0.572386\pi$
$461$	107440.	−	62030.3i	0.505549	−	0.291879i	0.731002	+	0.682375i	$0.239053\pi$
$462$	118651.	−	824633.i	0.555890	−	3.86346i
$463$	156173.	−	270499.i	0.728523	−	1.26184i	−0.228984	−	0.973430i	$-0.573540\pi$
$463$	156173.	−	270499.i	0.728523	−	1.26184i	0.957507	−	0.288409i	$-0.0931263\pi$
$464$	27708.5	+	15997.5i	0.128700	+	0.0743047i
$465$	−15037.8	−	37573.8i	−0.0695469	−	0.173772i
$466$	8608.96	+	14911.2i	0.0396441	+	0.0686656i
$467$			103567.i			0.474883i	0.971402	+	0.237442i	$0.0763089\pi$
$467$			103567.i			0.474883i	−0.971402	+	0.237442i	$0.923691\pi$
$468$	−9821.65	−	40522.1i	−0.0448428	−	0.185012i
$469$	−274371.			−1.24736
$470$	135530.	−	78248.2i	0.613535	−	0.354224i
$471$	−82676.2	−	65031.2i	−0.372682	−	0.293143i
$472$	−25445.2	+	44072.4i	−0.114215	+	0.197826i
$473$	450838.	+	260292.i	2.01511	+	1.16342i
$474$	−61172.3	+	77770.3i	−0.272269	+	0.346144i
$475$	−18839.6	−	32631.1i	−0.0834996	−	0.144626i
$476$			462998.i			2.04346i
$477$	35773.6	−	121740.i	0.157226	−	0.535054i
$478$	474427.			2.07641
$479$	−127905.	+	73845.8i	−0.557462	+	0.321851i	−0.752126	−	0.659019i	$-0.770972\pi$
$479$	−127905.	+	73845.8i	−0.557462	+	0.321851i	0.194664	+	0.980870i	$0.437638\pi$
$480$	136716.	−	54716.4i	0.593386	−	0.237485i
$481$	−3987.15	+	6905.95i	−0.0172335	+	0.0298492i
$482$	26402.2	+	15243.3i	0.113644	+	0.0656123i
$483$	245196.	+	35279.8i	1.05104	+	0.151228i
$484$	−305047.	−	528357.i	−1.30219	−	2.25547i
$485$			77547.6i			0.329674i
$486$	−66136.7	+	342196.i	−0.280008	+	1.44878i
$487$	−325253.			−1.37140			−0.685699	−	0.727885i	$-0.740504\pi$
$487$	−325253.			−1.37140			−0.685699	+	0.727885i	$0.740504\pi$
$488$	28349.4	−	16367.5i	0.119043	−	0.0687296i
$489$	24358.3	−	169291.i	0.101866	−	0.707972i
$490$	−93355.0	+	161696.i	−0.388817	+	0.673451i
$491$	−74368.9	−	42936.9i	−0.308481	−	0.178102i	0.337765	−	0.941230i	$-0.390329\pi$
$491$	−74368.9	−	42936.9i	−0.308481	−	0.178102i	−0.646247	+	0.763129i	$0.723662\pi$
$492$	185404.	+	463255.i	0.765929	+	1.91377i
$493$	26842.4	+	46492.3i	0.110440	+	0.191288i
$494$			48617.1i			0.199221i
$495$	−188422.	−	55368.2i	−0.768992	−	0.225969i
$496$	−81463.8			−0.331132
$497$	−75500.7	+	43590.3i	−0.305660	+	0.176473i
$498$	34783.2	+	27359.7i	0.140253	+	0.110319i
$499$	157701.	−	273146.i	0.633335	−	1.09697i	−0.353530	−	0.935423i	$-0.615019\pi$
$499$	157701.	−	273146.i	0.633335	−	1.09697i	0.986865	−	0.161546i	$-0.0516480\pi$
$500$	−22799.5	−	13163.3i	−0.0911981	−	0.0526533i
$501$	112473.	−	142991.i	0.448099	−	0.569683i
$502$	−9136.00	−	15824.0i	−0.0362534	−	0.0627927i
$503$		−	181943.i		−	0.719116i	−0.933123	−	0.359558i	$-0.882927\pi$
$503$		−	181943.i		−	0.719116i	0.933123	−	0.359558i	$-0.117073\pi$
$504$	95359.1	−	23113.0i	0.375406	−	0.0909901i
$505$	−116719.			−0.457676
$506$	421879.	−	243572.i	1.64773	−	0.951318i
$507$	232407.	−	93013.7i	0.904134	−	0.361852i
$508$	173355.	−	300260.i	0.671753	−	1.16351i
$509$	57532.4	+	33216.4i	0.222063	+	0.128208i	0.606905	−	0.794774i	$-0.292411\pi$
$509$	57532.4	+	33216.4i	0.222063	+	0.128208i	−0.384842	+	0.922983i	$0.625744\pi$
$510$	199782.	+	28745.5i	0.768097	+	0.110517i
$511$	−221215.	−	383155.i	−0.847172	−	1.46735i
$512$		−	350695.i		−	1.33779i
$513$	91347.5	−	199859.i	0.347106	−	0.759431i
$514$	326000.			1.23393
$515$	72595.4	−	41913.0i	0.273713	−	0.158028i
$516$	−57962.8	+	402844.i	−0.217696	+	1.51299i
$517$	−257141.	+	445381.i	−0.962032	+	1.66629i
$518$	−107880.	−	62284.7i	−0.402052	−	0.232125i
$519$	44101.2	+	110193.i	0.163725	+	0.409089i
$520$	2558.62	+	4431.65i	0.00946234	+	0.0163893i
$521$			360429.i			1.32784i	0.747805	+	0.663918i	$0.231108\pi$
$521$			360429.i			1.32784i	−0.747805	+	0.663918i	$0.768892\pi$
$522$	54669.2	−	52105.3i	0.200633	−	0.191223i
$523$	−47180.3			−0.172488			−0.0862438	−	0.996274i	$-0.527486\pi$
$523$	−47180.3			−0.172488			−0.0862438	+	0.996274i	$0.527486\pi$
$524$	−104202.	+	60161.0i	−0.379501	+	0.219105i
$525$	63949.1	+	50300.9i	0.232015	+	0.182497i
$526$	−293439.	+	508250.i	−1.06059	+	1.83699i
$527$	−118376.	−	68344.4i	−0.426229	−	0.246083i
$528$	−244395.	+	310707.i	−0.876645	+	1.11451i
$529$	−67497.0	−	116908.i	−0.241198	−	0.417766i
$530$			103375.i			0.368012i
$531$	−169792.	−	178147.i	−0.602184	−	0.631814i
$532$	−410665.			−1.45099
$533$	69648.6	−	40211.6i	0.245165	−	0.141546i
$534$	−473604.	+	189546.i	−1.66086	+	0.664708i
$535$	−7806.56	+	13521.4i	−0.0272742	+	0.0472403i
$536$	−55031.5	−	31772.4i	−0.191550	−	0.110591i
$537$	371357.	+	53432.3i	1.28778	+	0.185292i
$538$	73302.3	+	126963.i	0.253252	+	0.438646i
$539$		−	613570.i		−	2.11196i
$540$	−14547.1	−	152846.i	−0.0498872	−	0.524164i
$541$	293419.			1.00252			0.501261	−	0.865296i	$-0.332870\pi$
$541$	293419.			1.00252			0.501261	+	0.865296i	$0.332870\pi$
$542$	−72754.2	+	42004.6i	−0.247662	+	0.142988i
$543$	−48221.9	+	335144.i	−0.163548	+	1.13666i
$544$	248678.	−	430723.i	0.840310	−	1.45546i
$545$	164775.	+	95132.7i	0.554750	+	0.320285i
$546$	−39006.9	−	97463.9i	−0.130845	−	0.326933i
$547$	−7308.40	−	12658.5i	−0.0244257	−	0.0423066i	0.853554	−	0.521004i	$-0.174442\pi$
$547$	−7308.40	−	12658.5i	−0.0244257	−	0.0423066i	−0.877980	+	0.478698i	$0.841109\pi$
$548$			202277.i			0.673574i
$549$	37289.6	+	153849.i	0.123721	+	0.510446i
$550$	159997.			0.528916
$551$	−41237.2	+	23808.3i	−0.135827	+	0.0784198i
$552$	45094.3	+	35470.1i	0.147994	+	0.116408i
$553$	−67354.2	+	116661.i	−0.220249	+	0.381483i
$554$	−354510.	−	204677.i	−1.15507	−	0.666881i
$555$	−18154.1	+	23079.9i	−0.0589372	+	0.0749287i
$556$	−212703.	−	368413.i	−0.688057	−	1.19175i
$557$			404572.i			1.30403i	0.758208	+	0.652013i	$0.226075\pi$
$557$			404572.i			1.30403i	−0.758208	+	0.652013i	$0.773925\pi$
$558$	−54213.0	+	184491.i	−0.174115	+	0.592526i
$559$	65597.3			0.209924
$560$	141829.	−	81885.2i	0.452262	−	0.261114i
$561$	−615801.	+	246456.i	−1.95666	+	0.783093i
$562$	363200.	−	629081.i	1.14993	−	1.99175i
$563$	−230397.	−	133020.i	−0.726875	−	0.419662i	0.0904025	−	0.995905i	$-0.471185\pi$
$563$	−230397.	−	133020.i	−0.726875	−	0.419662i	−0.817278	+	0.576244i	$0.804518\pi$
$564$	−397967.	−	57261.1i	−1.25109	−	0.180012i
$565$	−115513.	−	200075.i	−0.361855	−	0.626752i
$566$		−	447988.i		−	1.39841i
$567$	−22774.0	+	473952.i	−0.0708392	+	1.47424i
$568$	−20191.2			−0.0625844
$569$	−211791.	+	122277.i	−0.654158	+	0.377678i	−0.790047	−	0.613046i	$-0.789944\pi$
$569$	−211791.	+	122277.i	−0.654158	+	0.377678i	0.135890	+	0.990724i	$0.456611\pi$
$570$	−25496.3	+	177200.i	−0.0784744	+	0.545400i
$571$	253912.	−	439789.i	0.778774	−	1.34888i	−0.153875	−	0.988090i	$-0.549175\pi$
$571$	253912.	−	439789.i	0.778774	−	1.34888i	0.932649	−	0.360785i	$-0.117491\pi$
$572$	−96674.1	−	55814.8i	−0.295473	−	0.170591i
$573$	106349.	+	265726.i	0.323909	+	0.809328i
$574$	628160.	+	1.08801e6i	1.90654	+	3.30223i
$575$			47573.5i			0.143890i
$576$	−419443.	−	123254.i	−1.26424	−	0.371498i
$577$	−558857.			−1.67861			−0.839304	−	0.543662i	$-0.817037\pi$
$577$	−558857.			−1.67861			−0.839304	+	0.543662i	$0.817037\pi$
$578$	163443.	−	94363.7i	0.489227	−	0.282455i
$579$	302439.	+	237891.i	0.902154	+	0.709613i
$580$	−16635.0	+	28812.6i	−0.0494500	+	0.0856500i
$581$	52177.3	+	30124.6i	0.154571	+	0.0892419i
$582$	227792.	−	289600.i	0.672501	−	0.854972i
$583$	−169856.	−	294199.i	−0.499739	−	0.865574i
$584$		−	102467.i		−	0.300442i
$585$	−24050.1	+	5829.20i	−0.0702756	+	0.0170333i
$586$	−368189.			−1.07220
$587$	51861.3	−	29942.1i	0.150511	−	0.0868973i	−0.422853	−	0.906198i	$-0.638971\pi$
$587$	51861.3	−	29942.1i	0.150511	−	0.0868973i	0.573364	+	0.819301i	$0.305638\pi$
$588$	445347.	−	178236.i	1.28808	−	0.515515i
$589$	60619.4	−	104996.i	0.174735	−	0.302651i
$590$	173636.	+	100249.i	0.498811	+	0.287988i
$591$	423081.	+	60874.6i	1.21129	+	0.174286i
$592$	29553.3	+	51187.8i	0.0843261	+	0.146057i
$593$		−	607115.i		−	1.72648i	−0.504795	−	0.863239i	$-0.668432\pi$
$593$		−	607115.i		−	1.72648i	0.504795	−	0.863239i	$-0.331568\pi$
$594$	541017.	+	760252.i	1.53334	+	2.15469i
$595$	274792.			0.776193
$596$	−502324.	+	290017.i	−1.41414	+	0.816453i
$597$	53139.4	−	369321.i	0.149097	−	1.03623i
$598$	30691.8	−	53159.8i	0.0858263	−	0.148655i
$599$	−237381.	−	137052.i	−0.661596	−	0.381973i	0.131289	−	0.991344i	$-0.458089\pi$
$599$	−237381.	−	137052.i	−0.661596	−	0.381973i	−0.792885	+	0.609371i	$0.791422\pi$
$600$	7001.59	+	17494.4i	0.0194489	+	0.0485955i
$601$	−238264.	−	412685.i	−0.659643	−	1.14254i	−0.980708	−	0.195478i	$-0.937374\pi$
$601$	−238264.	−	412685.i	−0.659643	−	1.14254i	0.321065	−	0.947057i	$-0.395959\pi$
$602$			1.02472e6i			2.82756i
$603$	222445.	−	212013.i	0.611770	−	0.583079i
$604$	576785.			1.58103
$605$	−313583.	+	181047.i	−0.856724	+	0.494630i
$606$	435883.	+	342855.i	1.18693	+	0.933610i
$607$	−335428.	+	580978.i	−0.910378	+	1.57682i	−0.0968473	+	0.995299i	$0.530876\pi$
$607$	−335428.	+	580978.i	−0.910378	+	1.57682i	−0.813531	+	0.581522i	$0.802457\pi$
$608$	382038.	+	220570.i	1.03347	+	0.596676i
$609$	63567.1	−	80815.0i	0.171395	−	0.217900i
$610$	−64484.6	−	111691.i	−0.173299	−	0.300163i
$611$			64803.2i			0.173586i
$612$	−357769.	−	375373.i	−0.955213	−	1.00221i
$613$	374906.			0.997702			0.498851	−	0.866688i	$-0.333755\pi$
$613$	374906.			0.997702			0.498851	+	0.866688i	$0.333755\pi$
$614$	−271550.	+	156779.i	−0.720299	+	0.415865i
$615$	274945.	−	110038.i	0.726934	−	0.290933i
$616$	131347.	−	227500.i	0.346145	−	0.599542i
$617$	62481.0	+	36073.4i	0.164126	+	0.0947583i	0.579813	−	0.814749i	$-0.303126\pi$
$617$	62481.0	+	36073.4i	0.164126	+	0.0947583i	−0.415687	+	0.909508i	$0.636459\pi$
$618$	−394223.	−	56722.4i	−1.03220	−	0.148518i
$619$	325797.	+	564297.i	0.850287	+	1.47274i	0.880949	+	0.473211i	$0.156905\pi$
$619$	325797.	+	564297.i	0.850287	+	1.47274i	−0.0306617	+	0.999530i	$0.509761\pi$
$620$		−	84710.1i		−	0.220370i
$621$	−226053.	+	160866.i	−0.586174	+	0.417138i
$622$	128475.			0.332077
$623$	−601459.	+	347252.i	−1.54964	+	0.894683i
$624$	−7094.03	+	49303.8i	−0.0182190	+	0.126623i
$625$	−7812.50	+	13531.6i	−0.0200000	+	0.0346410i
$626$	−183183.	−	105761.i	−0.467450	−	0.269883i
$627$	−218598.	−	546197.i	−0.556048	−	1.38936i
$628$	−110083.	−	190670.i	−0.279128	−	0.483463i
$629$			99175.3i			0.250670i
$630$	−91060.1	−	375694.i	−0.229428	−	0.946572i
$631$	−113922.			−0.286120			−0.143060	−	0.989714i	$-0.545694\pi$
$631$	−113922.			−0.286120			−0.143060	+	0.989714i	$0.545694\pi$
$632$	−27018.9	+	15599.4i	−0.0676447	+	0.0390547i
$633$	−465632.	−	366255.i	−1.16208	−	0.914063i
$634$	9694.14	−	16790.7i	0.0241174	−	0.0417726i
$635$	−178206.	−	102887.i	−0.441952	−	0.255161i
$636$	164197.	−	208748.i	0.405929	−	0.516070i
$637$	−38657.1	−	66956.1i	−0.0952688	−	0.165010i
$638$		−	202194.i		−	0.496739i
$639$	27528.5	−	93681.8i	0.0674189	−	0.229432i
$640$	94373.0			0.230403
$641$	−142661.	+	82365.3i	−0.347207	+	0.200460i	−0.663455	−	0.748217i	$-0.730910\pi$
$641$	−142661.	+	82365.3i	−0.347207	+	0.200460i	0.316247	+	0.948677i	$0.397577\pi$
$642$	68871.7	−	27563.8i	0.167098	−	0.0668758i
$643$	14038.6	−	24315.6i	0.0339549	−	0.0588117i	−0.848549	−	0.529118i	$-0.822523\pi$
$643$	14038.6	−	24315.6i	0.0339549	−	0.0588117i	0.882503	+	0.470306i	$0.155856\pi$
$644$	449036.	+	259251.i	1.08270	+	0.625099i
$645$	239090.	+	34401.2i	0.574701	+	0.0826903i
$646$	302322.	+	523638.i	0.724445	+	1.25478i
$647$		−	119765.i		−	0.286103i	−0.989715	−	0.143051i	$-0.954309\pi$
$647$		−	119765.i		−	0.286103i	0.989715	−	0.143051i	$-0.0456914\pi$
$648$	−59452.0	+	92424.9i	−0.141585	+	0.220110i
$649$	−658879.			−1.56429
$650$	17459.8	−	10080.4i	0.0413249	−	0.0238589i
$651$	−37283.9	+	259124.i	−0.0879749	+	0.611429i
$652$	178995.	−	310029.i	0.421062	−	0.729301i
$653$	−206814.	−	119404.i	−0.485013	−	0.280022i	0.237490	−	0.971390i	$-0.423675\pi$
$653$	−206814.	−	119404.i	−0.485013	−	0.280022i	−0.722503	+	0.691368i	$0.757009\pi$
$654$	−335899.	−	839288.i	−0.785332	−	1.96225i
$655$	35705.9	+	61844.4i	0.0832257	+	0.144151i
$656$		−	596107.i		−	1.38521i
$657$	475421.	+	139703.i	1.10141	+	0.323650i
$658$	−1.01231e6			−2.33810
$659$	293403.	−	169396.i	0.675607	−	0.390062i	−0.122591	−	0.992457i	$-0.539120\pi$
$659$	293403.	−	169396.i	0.675607	−	0.390062i	0.798198	+	0.602395i	$0.205787\pi$
$660$	−323088.	−	254133.i	−0.741708	−	0.583410i
$661$	−100873.	+	174717.i	−0.230873	+	0.399883i	−0.958065	−	0.286550i	$-0.907491\pi$
$661$	−100873.	+	174717.i	−0.230873	+	0.399883i	0.727193	+	0.686434i	$0.240825\pi$
$662$	−407295.	−	235152.i	−0.929380	−	0.536578i
$663$	−51672.0	+	65692.3i	−0.117552	+	0.149447i
$664$	6976.91	+	12084.4i	0.0158244	+	0.0274086i
$665$			243732.i			0.551149i
$666$	135592.	−	32864.6i	0.305693	−	0.0740934i
$667$	60120.4			0.135136
$668$	329769.	−	190393.i	0.739022	−	0.426675i
$669$	688687.	−	275626.i	1.53875	−	0.615840i
$670$	−125177.	+	216812.i	−0.278852	+	0.482986i
$671$	367040.	+	211910.i	0.815207	+	0.470660i
$672$	−942850.	−	135661.i	−2.08787	−	0.300412i
$673$	118260.	+	204833.i	0.261101	+	0.452240i	0.966535	−	0.256536i	$-0.0825811\pi$
$673$	118260.	+	204833.i	0.261101	+	0.452240i	−0.705434	+	0.708776i	$0.749248\pi$
$674$			92375.1i			0.203346i
$675$	−90715.1	+	8633.78i	−0.199100	+	0.0189493i
$676$	523960.			1.14658
$677$	604763.	−	349160.i	1.31949	−	0.761810i	0.335847	−	0.941917i	$-0.390977\pi$
$677$	604763.	−	349160.i	1.31949	−	0.761810i	0.983647	+	0.180106i	$0.0576441\pi$
$678$	−156328.	+	1.08649e6i	−0.340078	+	2.36356i
$679$	250812.	−	434420.i	0.544013	−	0.942258i
$680$	55115.9	+	31821.2i	0.119195	+	0.0688174i
$681$	−309836.	−	774165.i	−0.668093	−	1.66932i
$682$	257408.	+	445844.i	0.553418	+	0.958548i
$683$		−	517576.i		−	1.10951i	−0.832012	−	0.554757i	$-0.812811\pi$
$683$		−	517576.i		−	1.10951i	0.832012	−	0.554757i	$-0.187189\pi$
$684$	332944.	−	317330.i	0.711639	−	0.678265i
$685$	120053.			0.255853
$686$	158352.	−	91424.7i	0.336493	−	0.194274i
$687$	353259.	+	277865.i	0.748478	+	0.588735i
$688$	243108.	−	421075.i	0.513596	−	0.889574i
$689$	−37071.2	−	21403.1i	−0.0780905	−	0.0450856i
$690$	139745.	−	177662.i	0.293519	−	0.373161i
$691$	361558.	+	626237.i	0.757220	+	1.31154i	0.944263	+	0.329192i	$0.106776\pi$
$691$	361558.	+	626237.i	0.757220	+	1.31154i	−0.187043	+	0.982352i	$0.559890\pi$
$692$			248429.i			0.518788i
$693$	876459.	+	919585.i	1.82501	+	1.91481i
$694$	487941.			1.01309
$695$	−218655.	+	126240.i	−0.452678	+	0.261354i
$696$	22108.3	−	8848.18i	0.0456391	−	0.0182657i
$697$	500107.	−	866210.i	1.02943	−	1.78303i
$698$	756187.	+	436584.i	1.55209	+	0.896102i
$699$	−25986.5	−	3739.05i	−0.0531856	−	0.00765255i
$700$	85148.3	+	147481.i	0.173772	+	0.300982i
$701$		−	60491.0i		−	0.123099i	−0.998104	−	0.0615495i	$-0.980396\pi$
$701$		−	60491.0i		−	0.123099i	0.998104	−	0.0615495i	$-0.0196042\pi$
$702$	106937.	+	48876.8i	0.216998	+	0.0991810i
$703$	−87965.4			−0.177992
$704$	−1.01363e6	+	585220.i	−2.04520	+	1.18079i
$705$	−33984.8	+	236196.i	−0.0683764	+	0.475219i
$706$	−180207.	+	312127.i	−0.361544	+	0.626213i
$707$	653855.	+	377504.i	1.30811	+	0.755235i
$708$	−191398.	−	478233.i	−0.381831	−	0.954054i
$709$	−173953.	−	301296.i	−0.346051	−	0.599378i	0.639493	−	0.768797i	$-0.279144\pi$
$709$	−173953.	−	301296.i	−0.346051	−	0.599378i	−0.985544	+	0.169419i	$0.945811\pi$
$710$			79549.1i			0.157804i
$711$	−35539.5	−	146628.i	−0.0703027	−	0.290054i
$712$	−160849.			−0.317291
$713$	−132567.	+	76537.6i	−0.260769	+	0.150555i
$714$	−1.02620e6	−	807187.i	−2.01297	−	1.58335i
$715$	−33126.4	+	57376.6i	−0.0647980	+	0.112234i
$716$	680079.	+	392644.i	1.32658	+	0.765901i
$717$	−447244.	+	568595.i	−0.869973	+	1.10603i
$718$	227911.	+	394754.i	0.442096	+	0.765733i
$719$		−	49842.0i		−	0.0964134i	−0.998837	−	0.0482067i	$-0.984649\pi$
$719$		−	49842.0i		−	0.0964134i	0.998837	−	0.0482067i	$-0.0153506\pi$
$720$	−51712.9	+	175983.i	−0.0997547	+	0.339473i
$721$	−542237.			−1.04308
$722$	201697.	−	116450.i	0.386924	−	0.223391i
$723$	−43158.3	+	17272.8i	−0.0825635	+	0.0330435i
$724$	−354356.	+	613762.i	−0.676024	+	1.17091i
$725$	17100.5	+	9872.96i	0.0325336	+	0.0187833i
$726$	1.70288e6	+	245018.i	3.23081	+	0.464862i
$727$	−103653.	−	179532.i	−0.196115	−	0.339682i	0.751150	−	0.660131i	$-0.229499\pi$
$727$	−103653.	−	179532.i	−0.196115	−	0.339682i	−0.947266	+	0.320450i	$0.896166\pi$
$728$		−	33101.3i		−	0.0624573i
$729$	−347770.	−	401853.i	−0.654391	−	0.756157i
$730$	−403700.			−0.757553
$731$	706525.	−	407912.i	1.32219	−	0.763365i
$732$	−47189.1	+	327966.i	−0.0880683	+	0.612078i
$733$	−229832.	+	398080.i	−0.427762	+	0.740905i	−0.996674	−	0.0814934i	$-0.974031\pi$
$733$	−229832.	+	398080.i	−0.427762	+	0.740905i	0.568912	+	0.822398i	$0.307364\pi$
$734$	−460560.	−	265905.i	−0.854859	−	0.493553i
$735$	−105784.	−	264316.i	−0.195815	−	0.489270i
$736$	−278490.	−	482358.i	−0.514107	−	0.890459i
$737$		−	822715.i		−	1.51466i
$738$	−1.35000e6	−	396701.i	−2.47869	−	0.728367i
$739$	−435511.			−0.797463			−0.398731	−	0.917068i	$-0.630549\pi$
$739$	−435511.			−0.797463			−0.398731	+	0.917068i	$0.630549\pi$
$740$	−53227.5	+	30730.9i	−0.0972015	+	0.0561193i
$741$	−58267.0	−	45831.5i	−0.106117	−	0.0834694i
$742$	334345.	−	579102.i	0.607277	−	1.05183i
$743$	−279726.	−	161500.i	−0.506704	−	0.292546i	0.224774	−	0.974411i	$-0.427836\pi$
$743$	−279726.	−	161500.i	−0.506704	−	0.292546i	−0.731478	+	0.681865i	$0.761169\pi$
$744$	−37485.0	+	47655.9i	−0.0677192	+	0.0860936i
$745$	172127.	+	298132.i	0.310124	+	0.537151i
$746$		−	812199.i		−	1.45944i
$747$	−65580.4	+	15895.2i	−0.117526	+	0.0284856i
$748$	−1.38832e6			−2.48135
$749$	87464.4	−	50497.6i	0.155908	−	0.0900133i
$750$	68924.1	−	27584.8i	0.122532	−	0.0490396i
$751$	−504633.	+	874051.i	−0.894738	+	1.54973i	−0.0606105	+	0.998161i	$0.519305\pi$
$751$	−504633.	+	874051.i	−0.894738	+	1.54973i	−0.834128	+	0.551571i	$0.814029\pi$
$752$	415977.	+	240165.i	0.735587	+	0.424691i
$753$	27577.4	+	3967.95i	0.0486366	+	0.00699804i
$754$	−12739.0	−	22064.6i	−0.0224074	−	0.0388108i
$755$		−	342325.i		−	0.600544i
$756$	−412858.	+	903290.i	−0.722366	+	1.58046i
$757$	−658657.			−1.14939			−0.574695	−	0.818368i	$-0.694879\pi$
$757$	−658657.			−1.14939			−0.574695	+	0.818368i	$0.694879\pi$
$758$	617210.	−	356346.i	1.07422	−	0.620203i
$759$	−105788.	+	735232.i	−0.183634	+	1.27627i
$760$	−28224.4	+	48886.1i	−0.0488649	+	0.0846365i
$761$	100035.	+	57755.3i	0.172736	+	0.0997293i	0.583875	−	0.811843i	$-0.301536\pi$
$761$	100035.	+	57755.3i	0.172736	+	0.0997293i	−0.411139	+	0.911573i	$0.634869\pi$
$762$	363280.	+	907702.i	0.625650	+	1.56327i
$763$	−615376.	−	1.06586e6i	−1.05704	−	1.83085i
$764$			599078.i			1.02635i
$765$	−222786.	+	212338.i	−0.380685	+	0.362831i
$766$	189081.			0.322249
$767$	−71900.4	+	41511.7i	−0.122220	+	0.0705635i
$768$	258441.	+	203283.i	0.438166	+	0.344651i
$769$	69634.2	−	120610.i	0.117752	−	0.203953i	−0.801124	−	0.598498i	$-0.795764\pi$
$769$	69634.2	−	120610.i	0.117752	−	0.203953i	0.918877	+	0.394545i	$0.129098\pi$
$770$	−896300.	−	517479.i	−1.51172	−	0.872793i
$771$	−307321.	+	390707.i	−0.516992	+	0.657268i
$772$	402698.	+	697493.i	0.675685	+	1.17032i
$773$			1.15082e6i			1.92597i	0.269558	+	0.962984i	$0.413122\pi$
$773$			1.15082e6i			1.92597i	−0.269558	+	0.962984i	$0.586878\pi$
$774$	−791823.	−	830785.i	−1.32174	−	1.38678i
$775$	−50275.9			−0.0837060
$776$	100612.	−	58088.6i	0.167082	−	0.0964646i
$777$	176346.	−	70577.2i	0.292095	−	0.116902i
$778$	−166824.	+	288947.i	−0.275613	+	0.477375i
$779$	768301.	+	443579.i	1.26607	+	0.730964i
$780$	−51268.5	−	7376.72i	−0.0842677	−	0.0121248i
$781$	−130708.	−	226393.i	−0.214289	−	0.371159i
$782$		−	763420.i		−	1.24839i
$783$	10910.8	+	114640.i	0.0177965	+	0.186988i
$784$	−573063.			−0.932331
$785$	−113164.	+	65335.1i	−0.183640	+	0.106025i
$786$	48322.1	−	335841.i	0.0782169	−	0.543611i
$787$	−396524.	+	686800.i	−0.640206	+	1.10887i	0.345180	+	0.938536i	$0.387818\pi$
$787$	−396524.	+	686800.i	−0.640206	+	1.10887i	−0.985386	+	0.170333i	$0.945516\pi$
$788$	774804.	+	447333.i	1.24778	+	0.720408i
$789$	−332507.	−	830811.i	−0.534129	−	1.33459i
$790$	61458.2	+	106449.i	0.0984749	+	0.170564i
$791$			1.49442e6i			2.38847i
$792$	69305.3	+	285939.i	0.110488	+	0.455851i
$793$	53404.5			0.0849242
$794$	63454.6	−	36635.5i	0.100652	−	0.0581114i
$795$	−123893.	−	97451.6i	−0.196026	−	0.154189i
$796$	390491.	−	676351.i	0.616290	−	1.06745i
$797$	−1.01991e6	−	588844.i	−1.60563	−	0.927008i	−0.990333	−	0.138710i	$-0.955705\pi$
$797$	−1.01991e6	−	588844.i	−1.60563	−	0.927008i	−0.615293	−	0.788299i	$-0.710962\pi$
$798$	715950.	−	910210.i	1.12429	−	1.42934i
$799$	402974.	+	697972.i	0.631224	+	1.09331i
$800$		−	182934.i		−	0.285834i
$801$	219300.	−	746294.i	0.341801	−	1.16317i
$802$	−385337.			−0.599090
$803$	1.14891e6	−	663323.i	1.78178	−	1.02871i
$804$	597150.	−	238991.i	0.923786	−	0.369717i
$805$	153867.	−	266505.i	0.237440	−	0.411258i
$806$	56179.5	+	32435.3i	0.0864785	+	0.0499284i
$807$	−221266.	−	31836.7i	−0.339757	−	0.0488856i
$808$	87430.6	+	151434.i	0.133919	+	0.231954i
$809$			663952.i			1.01447i	0.861807	+	0.507236i	$0.169333\pi$
$809$			663952.i			1.01447i	−0.861807	+	0.507236i	$0.830667\pi$
$810$	364134.	+	234228.i	0.554998	+	0.357001i
$811$	1.04793e6			1.59328			0.796640	−	0.604454i	$-0.206609\pi$
$811$	1.04793e6			1.59328			0.796640	+	0.604454i	$0.206609\pi$
$812$	186378.	−	107605.i	0.282671	−	0.163200i
$813$	18243.5	−	126793.i	0.0276011	−	0.191829i
$814$	186764.	−	323484.i	0.281867	−	0.488207i
$815$	−184004.	−	106235.i	−0.277020	−	0.159938i
$816$	230185.	+	575147.i	0.345698	+	0.863771i
$817$	361805.	+	626665.i	0.542039	+	0.938840i
$818$			527773.i			0.788752i
$819$	153581.	+	45130.1i	0.228966	+	0.0672819i
$820$	619862.			0.921864
$821$	−881534.	+	508954.i	−1.30783	+	0.755079i	−0.981734	−	0.190256i	$-0.939068\pi$
$821$	−881534.	+	508954.i	−1.30783	+	0.755079i	−0.326100	+	0.945335i	$0.605735\pi$
$822$	−448333.	−	352648.i	−0.663525	−	0.521913i
$823$	226891.	−	392987.i	0.334979	−	0.580201i	−0.648502	−	0.761213i	$-0.724604\pi$
$823$	226891.	−	392987.i	0.334979	−	0.580201i	0.983481	+	0.181012i	$0.0579374\pi$
$824$	−108758.	−	62791.6i	−0.160180	−	0.0924799i
$825$	−150830.	+	191755.i	−0.221605	+	0.281733i
$826$	−648470.	−	1.12318e6i	−0.950450	−	1.64623i
$827$		−	52527.2i		−	0.0768022i	−0.999262	−	0.0384011i	$-0.987774\pi$
$827$		−	52527.2i		−	0.0768022i	0.999262	−	0.0384011i	$-0.0122265\pi$
$828$	−564383.	+	136794.i	−0.823215	+	0.199529i
$829$	1.21231e6			1.76403			0.882015	−	0.471222i	$-0.156187\pi$
$829$	1.21231e6			1.76403			0.882015	+	0.471222i	$0.156187\pi$
$830$	47609.8	−	27487.5i	0.0691099	−	0.0399006i
$831$	579500.	−	231927.i	0.839172	−	0.335853i
$832$	−73742.0	+	127725.i	−0.106529	+	0.184514i
$833$	−832724.	−	480774.i	−1.20008	−	0.692868i
$834$	1.18739e6	+	170846.i	1.70710	+	0.245625i
$835$	−112999.	−	195720.i	−0.162070	−	0.280713i
$836$		−	1.23140e6i		−	1.76192i
$837$	−170004.	−	238894.i	−0.242665	−	0.341000i
$838$	−66158.0			−0.0942095
$839$	−323211.	+	186606.i	−0.459158	+	0.265095i	−0.711690	−	0.702494i	$-0.752070\pi$
$839$	−323211.	+	186606.i	−0.459158	+	0.265095i	0.252532	+	0.967588i	$0.418737\pi$
$840$	17359.4	−	120648.i	0.0246023	−	0.170987i
$841$	−341164.	+	590913.i	−0.482359	+	0.835471i
$842$	−79922.1	−	46143.1i	−0.112731	−	0.0650852i
$843$	411556.	+	1.02833e6i	0.579127	+	1.44702i
$844$	−619989.	−	1.07385e6i	−0.870361	−	1.50751i
$845$		−	310973.i		−	0.435522i
$846$	820728.	−	782238.i	1.14672	−	1.09294i
$847$	2.34224e6			3.26486
$848$	−274776.	+	158642.i	−0.382110	+	0.220611i
$849$	536908.	+	422319.i	0.744877	+	0.585902i
$850$	125369.	−	217145.i	0.173521	−	0.300546i
$851$	96184.7	+	55532.2i	0.132815	+	0.0766807i
$852$	126353.	−	160636.i	0.174063	−	0.221292i
$853$	−190966.	−	330763.i	−0.262457	−	0.454588i	0.704437	−	0.709766i	$-0.251199\pi$
$853$	−190966.	−	330763.i	−0.262457	−	0.454588i	−0.966894	+	0.255178i	$0.917866\pi$
$854$			834251.i			1.14388i
$855$	−188337.	−	197604.i	−0.257634	−	0.270311i
$856$	23390.7			0.0319224
$857$	765820.	−	442146.i	1.04271	−	0.602011i	0.122113	−	0.992516i	$-0.461033\pi$
$857$	765820.	−	442146.i	1.04271	−	0.602011i	0.920601	+	0.390505i	$0.127700\pi$
$858$	292250.	−	116964.i	0.396991	−	0.158883i
$859$	−589517.	+	1.02107e6i	−0.798933	+	1.38379i	0.121379	+	0.992606i	$0.461268\pi$
$859$	−589517.	+	1.02107e6i	−0.798933	+	1.38379i	−0.920312	+	0.391186i	$0.872065\pi$
$860$	437854.	+	252795.i	0.592015	+	0.341800i
$861$	−1.89613e6	−	272823.i	−2.55777	−	0.368022i
$862$	−550272.	−	953099.i	−0.740565	−	1.28270i
$863$			1.09614e6i			1.47179i	0.677097	+	0.735894i	$0.263238\pi$
$863$			1.09614e6i			1.47179i	−0.677097	+	0.735894i	$0.736762\pi$
$864$	869239.	−	618575.i	1.16443	−	0.828638i
$865$	147444.			0.197058
$866$	−240749.	+	138996.i	−0.321017	+	0.185339i
$867$	−40984.1	+	284841.i	−0.0545227	+	0.378935i
$868$	−273978.	+	474544.i	−0.363644	+	0.629850i
$869$	−349814.	−	201965.i	−0.463230	−	0.267446i
$870$	−34859.9	−	87102.0i	−0.0460562	−	0.115077i
$871$	−51834.0	−	89779.2i	−0.0683249	−	0.118342i
$872$		−	285045.i		−	0.374869i
$873$	132341.	+	546012.i	0.173647	+	0.716430i
$874$	677130.			0.886439
$875$	87530.9	−	50536.0i	0.114326	−	0.0660062i
$876$	815206.	+	641222.i	1.06233	+	0.835603i
$877$	599705.	−	1.03872e6i	0.779719	−	1.35051i	−0.152384	−	0.988321i	$-0.548695\pi$
$877$	599705.	−	1.03872e6i	0.779719	−	1.35051i	0.932104	−	0.362192i	$-0.117972\pi$
$878$	−1.56959e6	−	906205.i	−2.03610	−	1.17554i
$879$	347093.	−	441270.i	0.449229	−	0.571120i
$880$	245537.	+	425282.i	0.317067	+	0.549177i
$881$		−	658543.i		−	0.848462i	−0.905554	−	0.424231i	$-0.860544\pi$
$881$		−	658543.i		−	0.848462i	0.905554	−	0.424231i	$-0.139456\pi$
$882$	−381365.	+	1.29782e6i	−0.490235	+	1.66831i
$883$	851604.			1.09224			0.546118	−	0.837708i	$-0.316105\pi$
$883$	851604.			1.09224			0.546118	+	0.837708i	$0.316105\pi$
$884$	−151501.	+	87469.4i	−0.193871	+	0.111931i
$885$	−283834.	+	113596.i	−0.362391	+	0.145036i
$886$	563854.	−	976624.i	0.718289	−	1.24411i
$887$	−916591.	−	529194.i	−1.16501	−	0.672617i	−0.212508	−	0.977159i	$-0.568163\pi$
$887$	−916591.	−	529194.i	−1.16501	−	0.672617i	−0.952499	+	0.304543i	$0.901496\pi$
$888$	43543.3	+	6265.18i	0.0552198	+	0.00794525i
$889$	665538.	+	1.15274e6i	0.842110	+	1.45858i
$890$			633709.i			0.800037i
$891$	−1.42117e6	−	68289.0i	−1.79015	−	0.0860192i
$892$	1.55264e6			1.95138
$893$	−619079.	+	357425.i	−0.776324	+	0.448211i
$894$	232945.	−	1.61898e6i	0.291460	−	2.02566i
$895$	233036.	−	403631.i	0.290923	−	0.503893i
$896$	−528675.	−	305231.i	−0.658526	−	0.380200i
$897$	34778.1	+	86897.6i	0.0432236	+	0.108000i
$898$	109602.	+	189836.i	0.135914	+	0.235410i
$899$			63535.6i			0.0786136i
$900$	−182996.	−	53773.6i	−0.225921	−	0.0663871i
$901$	−532374.			−0.655794
$902$	−3.26244e6	+	1.88357e6i	−4.00986	+	2.31509i
$903$	−1.22811e6	−	966004.i	−1.50613	−	1.18469i
$904$	−173055.	+	299740.i	−0.211762	+	0.366782i
$905$	364271.	+	210312.i	0.444762	+	0.256783i
$906$	−1.00556e6	+	1.27840e6i	−1.22505	+	1.55744i
$907$	225404.	+	390411.i	0.273997	+	0.474577i	0.969882	−	0.243576i	$-0.0783207\pi$
$907$	225404.	+	390411.i	0.273997	+	0.474577i	−0.695884	+	0.718154i	$0.744987\pi$
$908$		−	1.74535e6i		−	2.11695i
$909$	−821816.	+	199190.i	−0.994596	+	0.241068i
$910$	−130412.			−0.157484
$911$	1.39879e6	−	807592.i	1.68545	−	0.973095i	0.727522	−	0.686085i	$-0.240672\pi$
$911$	1.39879e6	−	807592.i	1.68545	−	0.973095i	0.957928	−	0.287010i	$-0.0926613\pi$
$912$	−510138.	+	204167.i	−0.613335	+	0.245469i
$913$	−90330.0	+	156456.i	−0.108365	+	0.187694i
$914$	−161144.	−	93036.6i	−0.192895	−	0.111368i
$915$	194650.	+	28007.0i	0.232494	+	0.0334522i
$916$	470364.	+	814694.i	0.560587	+	0.970965i
$917$		−	461935.i		−	0.549341i
$918$	1.45572e6	−	138548.i	1.72740	−	0.164405i
$919$	−1.49446e6			−1.76951			−0.884754	−	0.466058i	$-0.845674\pi$
$919$	−1.49446e6			−1.76951			−0.884754	+	0.466058i	$0.845674\pi$
$920$	61723.2	−	35635.9i	0.0729244	−	0.0421029i
$921$	68092.4	−	473245.i	0.0802749	−	0.557914i
$922$	−366125.	+	634147.i	−0.430693	+	0.745982i
$923$	−28527.1	−	16470.1i	−0.0334853	−	0.0193327i
$924$	987987.	+	2.46861e6i	1.15720	+	2.89141i
$925$	18239.0	+	31590.8i	0.0213165	+	0.0369213i
$926$			1.84358e6i			2.15000i
$927$	439616.	−	418999.i	0.511581	−	0.487589i
$928$	−231181.			−0.268445
$929$	693031.	−	400121.i	0.803010	−	0.463618i	−0.0415126	−	0.999138i	$-0.513218\pi$
$929$	693031.	−	400121.i	0.803010	−	0.463618i	0.844523	+	0.535520i	$0.179884\pi$
$930$	187754.	+	147683.i	0.217082	+	0.170751i
$931$	426431.	−	738600.i	0.491982	−	0.852138i
$932$	−47590.0	−	27476.1i	−0.0547879	−	0.0316318i
$933$	−121114.	+	153976.i	−0.139133	+	0.176885i
$934$	−305644.	−	529391.i	−0.350366	−	0.606852i
$935$			823977.i			0.942523i
$936$	25578.2	+	26836.8i	0.0291956	+	0.0306322i
$937$	−1.34081e6			−1.52717			−0.763587	−	0.645705i	$-0.776564\pi$
$937$	−1.34081e6			−1.52717			−0.763587	+	0.645705i	$0.776564\pi$
$938$	1.40247e6	−	809718.i	1.59400	−	0.920297i
$939$	299439.	−	119841.i	0.339608	−	0.135918i
$940$	−249735.	+	432554.i	−0.282633	+	0.489535i
$941$	−45424.0	−	26225.5i	−0.0512986	−	0.0296173i	0.474131	−	0.880454i	$-0.342762\pi$
$941$	−45424.0	−	26225.5i	−0.0512986	−	0.0296173i	−0.525430	+	0.850837i	$0.676096\pi$
$942$	614526.	+	88420.4i	0.692529	+	0.0996439i
$943$	−560060.	−	970052.i	−0.629812	−	1.09087i
$944$			615381.i			0.690557i
$945$	536108.	+	245034.i	0.600328	+	0.274386i
$946$	−3.07267e6			−3.43347
$947$	−80995.2	+	46762.6i	−0.0903149	+	0.0521433i	−0.544477	−	0.838776i	$-0.683272\pi$
$947$	−80995.2	+	46762.6i	−0.0903149	+	0.0521433i	0.454162	+	0.890919i	$0.349939\pi$
$948$	44974.4	−	312574.i	0.0500436	−	0.347805i
$949$	83583.5	−	144771.i	0.0928085	−	0.160749i
$950$	192601.	+	111198.i	0.213408	+	0.123211i
$951$	10984.8	+	27447.0i	0.0121460	+	0.0303483i
$952$	−205839.	−	356523.i	−0.227119	−	0.393381i
$953$			323193.i			0.355857i	0.984043	+	0.177929i	$0.0569397\pi$
$953$			323193.i			0.355857i	−0.984043	+	0.177929i	$0.943060\pi$
$954$	176417.	+	727861.i	0.193841	+	0.799745i
$955$	355556.			0.389853
$956$	−1.31131e6	+	757085.i	−1.43479	+	0.828378i
$957$	242328.	+	190609.i	0.264593	+	0.208123i
$958$	435864.	−	754939.i	0.474920	−	0.822585i
$959$	−672531.	−	388286.i	−0.731266	−	0.422196i
$960$	−335759.	+	426861.i	−0.364322	+	0.463174i
$961$	380875.	+	659695.i	0.412416	+	0.714326i
$962$		−	47067.2i		−	0.0508590i
$963$	−31890.7	+	108526.i	−0.0343883	+	0.117026i
$964$	−97300.3			−0.104703
$965$	413966.	−	239003.i	0.444539	−	0.256655i
$966$	−1.35746e6	+	543281.i	−1.45470	+	0.582197i
$967$	−516034.	+	893798.i	−0.551856	+	0.955842i	0.446285	+	0.894891i	$0.352747\pi$
$967$	−516034.	+	893798.i	−0.551856	+	0.955842i	−0.998141	+	0.0609514i	$0.980587\pi$
$968$	469791.	+	271234.i	0.501365	+	0.289463i
$969$	−912574.	−	131305.i	−0.971897	−	0.139841i
$970$	−228857.	−	396392.i	−0.243232	−	0.421290i
$971$			625840.i			0.663781i	0.943318	+	0.331890i	$0.107686\pi$
$971$			625840.i			0.663781i	−0.943318	+	0.331890i	$0.892314\pi$
$972$	−363271.	−	1.05136e6i	−0.384501	−	1.11281i
$973$	1.63320e6			1.72510
$974$	1.66256e6	−	959880.i	1.75251	−	1.01181i
$975$	−4378.12	+	30428.1i	−0.00460552	+	0.0320085i
$976$	197921.	−	342808.i	0.207774	−	0.359875i
$977$	952685.	+	550033.i	0.998068	+	0.576235i	0.907676	−	0.419671i	$-0.137855\pi$
$977$	952685.	+	550033.i	0.998068	+	0.576235i	0.0903922	+	0.995906i	$0.471188\pi$
$978$	375098.	+	937232.i	0.392164	+	0.979872i
$979$	−1.04125e6	−	1.80350e6i	−1.08640	−	1.88170i
$980$		−	595899.i		−	0.620469i
$981$	1.32253e6	+	388627.i	1.37425	+	0.403827i
$982$	506858.			0.525610
$983$	46616.3	−	26914.0i	0.0482426	−	0.0278529i	−0.475685	−	0.879616i	$-0.657800\pi$
$983$	46616.3	−	26914.0i	0.0482426	−	0.0278529i	0.523927	+	0.851763i	$0.324466\pi$
$984$	−348720.	−	274295.i	−0.360152	−	0.283287i
$985$	265495.	−	459850.i	0.273642	−	0.473963i
$986$	−274414.	−	158433.i	−0.282262	−	0.162964i
$987$	954310.	−	1.21324e6i	0.979614	−	1.24542i
$988$	−77582.6	−	134377.i	−0.0794786	−	0.137661i
$989$		−	913626.i		−	0.934062i
$990$	1.12654e6	−	273048.i	1.14941	−	0.278592i
$991$	134455.			0.136908			0.0684541	−	0.997654i	$-0.478193\pi$
$991$	134455.			0.136908			0.0684541	+	0.997654i	$0.478193\pi$
$992$	509759.	−	294309.i	0.518014	−	0.299075i
$993$	665785.	−	266460.i	0.675205	−	0.270230i
$994$	257286.	−	445632.i	0.260401	−	0.451028i
$995$	−401418.	−	231759.i	−0.405462	−	0.234094i
$996$	−139800.	−	20115.1i	−0.140926	−	0.0202769i
$997$	−571318.	−	989552.i	−0.574761	−	0.995516i	−0.996068	−	0.0885973i	$-0.971762\pi$
$997$	−571318.	−	989552.i	−0.574761	−	0.995516i	0.421306	−	0.906918i	$-0.361572\pi$
$998$			1.86162e6i			1.86909i
$999$	−88435.3	+	193487.i	−0.0886124	+	0.193875i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.i.a.41.3	yes	32
3.2	odd	2		135.5.i.a.71.14		32
9.2	odd	6	inner	45.5.i.a.11.3	✓	32
9.4	even	3		405.5.c.b.161.6		32
9.5	odd	6		405.5.c.b.161.27		32
9.7	even	3		135.5.i.a.116.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.i.a.11.3	✓	32	9.2	odd	6	inner
45.5.i.a.41.3	yes	32	1.1	even	1	trivial
135.5.i.a.71.14		32	3.2	odd	2
135.5.i.a.116.14		32	9.7	even	3
405.5.c.b.161.6		32	9.4	even	3
405.5.c.b.161.27		32	9.5	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	45.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.11159 + 2.95118i) q^{2} +(1.28176 - 8.90826i) q^{3} +(9.41890 - 16.3140i) q^{4} +(-9.68246 - 5.59017i) q^{5} +(19.7380 + 49.3181i) q^{6} +(36.1606 + 62.6320i) q^{7} +16.7497i q^{8} +(-77.7142 - 22.8364i) q^{9} +65.9903 q^{10} +(-187.805 + 108.429i) q^{11} +(-133.257 - 104.817i) q^{12} +(-13.6629 + 23.6648i) q^{13} +(-369.676 - 213.433i) q^{14} +(-62.2092 + 79.0886i) q^{15} +(101.271 + 175.407i) q^{16} +339.847i q^{17} +(464.638 - 112.618i) q^{18} -301.434 q^{19} +(-182.396 + 105.307i) q^{20} +(604.291 - 241.849i) q^{21} +(639.988 - 1108.49i) q^{22} +(329.599 + 190.294i) q^{23} +(149.211 + 21.4691i) q^{24} +(62.5000 + 108.253i) q^{25} -161.286i q^{26} +(-303.044 + 663.028i) q^{27} +1362.37 q^{28} +(136.804 - 78.9837i) q^{29} +(84.5836 - 587.859i) q^{30} +(-201.104 + 348.322i) q^{31} +(-1267.40 - 731.735i) q^{32} +(725.196 + 1812.00i) q^{33} +(-1002.95 - 1737.16i) q^{34} -808.575i q^{35} +(-1104.54 + 1052.74i) q^{36} +291.824 q^{37} +(1540.80 - 889.584i) q^{38} +(193.300 + 152.045i) q^{39} +(93.6338 - 162.179i) q^{40} +(-2548.83 - 1471.56i) q^{41} +(-2375.15 + 3019.60i) q^{42} +(-1200.28 - 2078.95i) q^{43} +4085.14i q^{44} +(624.805 + 655.548i) q^{45} -2246.36 q^{46} +(2053.78 - 1185.75i) q^{47} +(1692.37 - 677.320i) q^{48} +(-1414.68 + 2450.29i) q^{49} +(-638.949 - 368.897i) q^{50} +(3027.44 + 435.601i) q^{51} +(257.379 + 445.793i) q^{52} +1566.51i q^{53} +(-407.677 - 4283.46i) q^{54} +2424.55 q^{55} +(-1049.07 + 605.680i) q^{56} +(-386.364 + 2685.25i) q^{57} +(-466.190 + 807.464i) q^{58} +(2631.23 + 1519.14i) q^{59} +(704.310 + 1759.81i) q^{60} +(-977.183 - 1692.53i) q^{61} -2373.97i q^{62} +(-1379.90 - 5693.17i) q^{63} +5397.25 q^{64} +(264.581 - 152.756i) q^{65} +(-9054.43 - 7122.00i) q^{66} +(-1896.89 + 3285.51i) q^{67} +(5544.27 + 3200.99i) q^{68} +(2117.65 - 2692.24i) q^{69} +(2386.25 + 4133.11i) q^{70} +1205.47i q^{71} +(382.504 - 1301.69i) q^{72} -6117.56 q^{73} +(-1491.68 + 861.223i) q^{74} +(1044.46 - 418.012i) q^{75} +(-2839.17 + 4917.59i) q^{76} +(-13582.3 - 7841.74i) q^{77} +(-1436.78 - 206.730i) q^{78} +(931.321 + 1613.09i) q^{79} -2264.49i q^{80} +(5517.99 + 3549.43i) q^{81} +17371.4 q^{82} +(721.466 - 416.539i) q^{83} +(1746.23 - 12136.4i) q^{84} +(1899.80 - 3290.55i) q^{85} +(12270.7 + 7084.49i) q^{86} +(-528.258 - 1319.92i) q^{87} +(-1816.16 - 3145.68i) q^{88} +9603.06i q^{89} +(-5128.39 - 1506.98i) q^{90} -1976.23 q^{91} +(6208.92 - 3584.72i) q^{92} +(2845.17 + 2237.95i) q^{93} +(-6998.73 + 12122.2i) q^{94} +(2918.62 + 1685.06i) q^{95} +(-8142.99 + 10352.4i) q^{96} +(-3468.03 - 6006.81i) q^{97} -16699.9i q^{98} +(17071.3 - 4137.70i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{3} + 128 q^{4} + 98 q^{6} - 26 q^{7} - 220 q^{9} - 738 q^{11} - 214 q^{12} + 10 q^{13} + 1998 q^{14} - 50 q^{15} - 1024 q^{16} - 2504 q^{18} + 508 q^{19} - 1620 q^{21} + 672 q^{22} + 1998 q^{23}+ \cdots + 53512 q^{99}+O(q^{100}) \) 32 * q - 8 * q^3 + 128 * q^4 + 98 * q^6 - 26 * q^7 - 220 * q^9 - 738 * q^11 - 214 * q^12 + 10 * q^13 + 1998 * q^14 - 50 * q^15 - 1024 * q^16 - 2504 * q^18 + 508 * q^19 - 1620 * q^21 + 672 * q^22 + 1998 * q^23 + 4164 * q^24 + 2000 * q^25 + 2158 * q^27 - 1664 * q^28 - 270 * q^29 + 2000 * q^30 - 1472 * q^31 - 6048 * q^32 - 1354 * q^33 - 594 * q^34 + 4498 * q^36 + 2068 * q^37 - 7164 * q^38 - 4616 * q^39 + 1650 * q^40 - 13428 * q^41 - 10230 * q^42 + 568 * q^43 - 100 * q^45 + 5724 * q^46 + 12528 * q^47 + 25844 * q^48 - 1674 * q^49 + 1454 * q^51 + 1534 * q^52 + 8456 * q^54 + 21294 * q^56 - 12512 * q^57 - 8190 * q^58 - 4374 * q^59 - 5050 * q^60 - 4478 * q^61 + 5604 * q^63 - 37216 * q^64 - 8550 * q^65 - 19472 * q^66 + 12838 * q^67 + 65736 * q^68 + 8706 * q^69 + 2400 * q^70 - 36372 * q^72 + 29236 * q^73 - 20628 * q^74 + 1000 * q^75 + 6190 * q^76 - 31806 * q^77 - 42430 * q^78 - 3512 * q^79 - 3088 * q^81 + 34692 * q^82 - 43074 * q^83 - 19350 * q^84 - 4350 * q^85 - 10746 * q^86 + 69622 * q^87 - 16128 * q^88 - 26750 * q^90 - 48904 * q^91 + 27036 * q^92 + 27030 * q^93 + 5118 * q^94 + 6300 * q^95 + 53566 * q^96 + 23266 * q^97 + 53512 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more