LMFDB - Embedded newform 35.4.f.b.13.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [35,4,Mod(13,35)] 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("35.13"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(35, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	35.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.06506685020$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10654x^{12} + 22102125x^{8} + 5700572500x^{4} + 44626562500 $ x^16 + 10654x^12 + 22102125x^8 + 5700572500*x^4 + 44626562500
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.1
Root			$-4.94129 - 4.94129i$ of defining polynomial
Character	$\chi$	$=$	35.13
Dual form			35.4.f.b.27.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.57033 + 3.57033i) q^{2} +(-4.94129 + 4.94129i) q^{3} -17.4944i q^{4} +(3.01167 + 10.7671i) q^{5} -35.2840i q^{6} +(0.826888 - 18.5018i) q^{7} +(33.8983 + 33.8983i) q^{8} -21.8328i q^{9} +(-49.1946 - 27.6893i) q^{10} -30.6825 q^{11} +(86.4452 + 86.4452i) q^{12} +(-38.4644 + 38.4644i) q^{13} +(63.1052 + 69.0097i) q^{14} +(-68.0848 - 38.3217i) q^{15} -102.100 q^{16} +(-34.5683 - 34.5683i) q^{17} +(77.9500 + 77.9500i) q^{18} +22.1767 q^{19} +(188.364 - 52.6875i) q^{20} +(87.3369 + 95.5087i) q^{21} +(109.546 - 109.546i) q^{22} +(-3.20638 - 3.20638i) q^{23} -335.002 q^{24} +(-106.860 + 64.8538i) q^{25} -274.661i q^{26} +(-25.5329 - 25.5329i) q^{27} +(-323.679 - 14.4660i) q^{28} +179.259i q^{29} +(379.906 - 106.264i) q^{30} -37.6201i q^{31} +(93.3444 - 93.3444i) q^{32} +(151.611 - 151.611i) q^{33} +246.840 q^{34} +(201.700 - 46.8182i) q^{35} -381.952 q^{36} +(-135.426 + 135.426i) q^{37} +(-79.1782 + 79.1782i) q^{38} -380.128i q^{39} +(-262.895 + 467.076i) q^{40} +326.823i q^{41} +(-652.818 - 29.1760i) q^{42} +(193.381 + 193.381i) q^{43} +536.773i q^{44} +(235.075 - 65.7531i) q^{45} +22.8956 q^{46} +(-91.5534 - 91.5534i) q^{47} +(504.506 - 504.506i) q^{48} +(-341.633 - 30.5978i) q^{49} +(149.975 - 613.073i) q^{50} +341.624 q^{51} +(672.914 + 672.914i) q^{52} +(210.622 + 210.622i) q^{53} +182.321 q^{54} +(-92.4056 - 330.360i) q^{55} +(655.209 - 599.149i) q^{56} +(-109.582 + 109.582i) q^{57} +(-640.012 - 640.012i) q^{58} -230.155 q^{59} +(-670.417 + 1191.11i) q^{60} -37.1467i q^{61} +(134.316 + 134.316i) q^{62} +(-403.945 - 18.0532i) q^{63} -150.261i q^{64} +(-529.992 - 298.307i) q^{65} +1082.60i q^{66} +(325.340 - 325.340i) q^{67} +(-604.753 + 604.753i) q^{68} +31.6873 q^{69} +(-552.980 + 887.292i) q^{70} -474.107 q^{71} +(740.092 - 740.092i) q^{72} +(642.183 - 642.183i) q^{73} -967.032i q^{74} +(207.563 - 848.486i) q^{75} -387.970i q^{76} +(-25.3710 + 567.681i) q^{77} +(1357.18 + 1357.18i) q^{78} +636.110i q^{79} +(-307.492 - 1099.32i) q^{80} +841.815 q^{81} +(-1166.87 - 1166.87i) q^{82} +(-993.219 + 993.219i) q^{83} +(1670.87 - 1527.91i) q^{84} +(268.091 - 476.308i) q^{85} -1380.87 q^{86} +(-885.770 - 885.770i) q^{87} +(-1040.08 - 1040.08i) q^{88} +1205.77 q^{89} +(-604.534 + 1074.05i) q^{90} +(679.855 + 743.467i) q^{91} +(-56.0938 + 56.0938i) q^{92} +(185.892 + 185.892i) q^{93} +653.751 q^{94} +(66.7891 + 238.779i) q^{95} +922.484i q^{96} +(917.344 + 917.344i) q^{97} +(1328.98 - 1110.50i) q^{98} +669.883i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 32 q^{7} + 176 q^{8} - 152 q^{11} - 480 q^{15} - 504 q^{16} + 288 q^{18} + 328 q^{21} + 348 q^{22} - 72 q^{23} - 160 q^{25} - 528 q^{28} + 1780 q^{30} + 432 q^{32} + 160 q^{35} + 344 q^{36}+ \cdots + 3308 q^{98}+O(q^{100}) $ 16 * q + 4 * q^2 + 32 * q^7 + 176 * q^8 - 152 * q^11 - 480 * q^15 - 504 * q^16 + 288 * q^18 + 328 * q^21 + 348 * q^22 - 72 * q^23 - 160 * q^25 - 528 * q^28 + 1780 * q^30 + 432 * q^32 + 160 * q^35 + 344 * q^36 - 256 * q^37 - 1300 * q^42 - 312 * q^43 - 1856 * q^46 - 20 * q^50 + 696 * q^51 + 1768 * q^53 + 1304 * q^56 - 3920 * q^57 - 4764 * q^58 - 2000 * q^60 + 2544 * q^63 - 1000 * q^65 + 4504 * q^67 - 180 * q^70 + 6368 * q^71 + 7848 * q^72 - 3016 * q^77 + 5340 * q^78 - 3088 * q^81 - 2280 * q^85 - 9336 * q^86 - 2048 * q^88 + 1608 * q^91 - 6328 * q^92 - 3960 * q^93 + 1240 * q^95 + 3308 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−3.57033	+	3.57033i	−1.26230	+	1.26230i	−0.312325	+	0.949975i	$0.601108\pi$
$2$	−3.57033	+	3.57033i	−1.26230	+	1.26230i	−0.949975	+	0.312325i	$0.898892\pi$
$3$	−4.94129	+	4.94129i	−0.950952	+	0.950952i	−0.998852	−	0.0478999i	$-0.984747\pi$
$3$	−4.94129	+	4.94129i	−0.950952	+	0.950952i	0.0478999	+	0.998852i	$0.484747\pi$
$4$		−	17.4944i		−	2.18681i
$5$	3.01167	+	10.7671i	0.269372	+	0.963036i
$5$	3.01167	+	10.7671i	0.269372	+	0.963036i
$6$		−	35.2840i		−	2.40078i
$7$	0.826888	−	18.5018i	0.0446478	−	0.999003i
$7$	0.826888	−	18.5018i	0.0446478	−	0.999003i
$8$	33.8983	+	33.8983i	1.49811	+	1.49811i
$9$		−	21.8328i		−	0.808620i
$10$	−49.1946	−	27.6893i	−1.55567	−	0.875612i
$11$	−30.6825			−0.841010			−0.420505	−	0.907290i	$-0.638147\pi$
$11$	−30.6825			−0.841010			−0.420505	+	0.907290i	$0.638147\pi$
$12$	86.4452	+	86.4452i	2.07955	+	2.07955i
$13$	−38.4644	+	38.4644i	−0.820624	+	0.820624i	−0.986198	−	0.165573i	$-0.947053\pi$
$13$	−38.4644	+	38.4644i	−0.820624	+	0.820624i	0.165573	+	0.986198i	$0.447053\pi$
$14$	63.1052	+	69.0097i	1.20468	+	1.31740i
$15$	−68.0848	−	38.3217i	−1.17196	−	0.659641i
$16$	−102.100			−1.59531
$17$	−34.5683	−	34.5683i	−0.493179	−	0.493179i	0.416127	−	0.909306i	$-0.363387\pi$
$17$	−34.5683	−	34.5683i	−0.493179	−	0.493179i	−0.909306	+	0.416127i	$0.863387\pi$
$18$	77.9500	+	77.9500i	1.02072	+	1.02072i
$19$	22.1767			0.267773			0.133887	−	0.990997i	$-0.457254\pi$
$19$	22.1767			0.267773			0.133887	+	0.990997i	$0.457254\pi$
$20$	188.364	−	52.6875i	2.10597	−	0.589065i
$21$	87.3369	+	95.5087i	0.907546	+	0.992462i
$22$	109.546	−	109.546i	1.06161	−	1.06161i
$23$	−3.20638	−	3.20638i	−0.0290685	−	0.0290685i	0.692423	−	0.721492i	$-0.256543\pi$
$23$	−3.20638	−	3.20638i	−0.0290685	−	0.0290685i	−0.721492	+	0.692423i	$0.756543\pi$
$24$	−335.002			−2.84925
$25$	−106.860	+	64.8538i	−0.854877	+	0.518830i
$26$		−	274.661i		−	2.07175i
$27$	−25.5329	−	25.5329i	−0.181993	−	0.181993i
$28$	−323.679	−	14.4660i	−2.18463	−	0.0976360i
$29$			179.259i			1.14785i	0.818910	+	0.573923i	$0.194579\pi$
$29$			179.259i			1.14785i	−0.818910	+	0.573923i	$0.805421\pi$
$30$	379.906	−	106.264i	2.31203	−	0.646702i
$31$		−	37.6201i		−	0.217960i	−0.994044	−	0.108980i	$-0.965242\pi$
$31$		−	37.6201i		−	0.217960i	0.994044	−	0.108980i	$-0.0347585\pi$
$32$	93.3444	−	93.3444i	0.515660	−	0.515660i
$33$	151.611	−	151.611i	0.799761	−	0.799761i
$34$	246.840			1.24508
$35$	201.700	−	46.8182i	0.974103	−	0.226106i
$36$	−381.952			−1.76830
$37$	−135.426	+	135.426i	−0.601728	+	0.601728i	−0.940771	−	0.339043i	$-0.889897\pi$
$37$	−135.426	+	135.426i	−0.601728	+	0.601728i	0.339043	+	0.940771i	$0.389897\pi$
$38$	−79.1782	+	79.1782i	−0.338010	+	0.338010i
$39$		−	380.128i		−	1.56075i
$40$	−262.895	+	467.076i	−1.03918	+	1.84628i
$41$			326.823i			1.24491i	0.782656	+	0.622454i	$0.213864\pi$
$41$			326.823i			1.24491i	−0.782656	+	0.622454i	$0.786136\pi$
$42$	−652.818	−	29.1760i	−2.39838	−	0.107189i
$43$	193.381	+	193.381i	0.685823	+	0.685823i	0.961306	−	0.275483i	$-0.0888377\pi$
$43$	193.381	+	193.381i	0.685823	+	0.685823i	−0.275483	+	0.961306i	$0.588838\pi$
$44$			536.773i			1.83913i
$45$	235.075	−	65.7531i	0.778731	−	0.217820i
$46$	22.8956			0.0733864
$47$	−91.5534	−	91.5534i	−0.284137	−	0.284137i	0.550620	−	0.834756i	$-0.314392\pi$
$47$	−91.5534	−	91.5534i	−0.284137	−	0.284137i	−0.834756	+	0.550620i	$0.814392\pi$
$48$	504.506	−	504.506i	1.51707	−	1.51707i
$49$	−341.633	−	30.5978i	−0.996013	−	0.0892065i
$50$	149.975	−	613.073i	0.424192	−	1.73403i
$51$	341.624			0.937979
$52$	672.914	+	672.914i	1.79455	+	1.79455i
$53$	210.622	+	210.622i	0.545871	+	0.545871i	0.925244	−	0.379373i	$-0.123860\pi$
$53$	210.622	+	210.622i	0.545871	+	0.545871i	−0.379373	+	0.925244i	$0.623860\pi$
$54$	182.321			0.459459
$55$	−92.4056	−	330.360i	−0.226545	−	0.809923i
$56$	655.209	−	599.149i	1.56350	−	1.42972i
$57$	−109.582	+	109.582i	−0.254640	+	0.254640i
$58$	−640.012	−	640.012i	−1.44893	−	1.44893i
$59$	−230.155			−0.507858			−0.253929	−	0.967223i	$-0.581723\pi$
$59$	−230.155			−0.507858			−0.253929	+	0.967223i	$0.581723\pi$
$60$	−670.417	+	1191.11i	−1.44251	+	2.56285i
$61$		−	37.1467i		−	0.0779696i	−0.999240	−	0.0389848i	$-0.987588\pi$
$61$		−	37.1467i		−	0.0779696i	0.999240	−	0.0389848i	$-0.0124124\pi$
$62$	134.316	+	134.316i	0.275131	+	0.275131i
$63$	−403.945	−	18.0532i	−0.807814	−	0.0361031i
$64$		−	150.261i		−	0.293478i
$65$	−529.992	−	298.307i	−1.01134	−	0.569238i
$66$			1082.60i			2.01908i
$67$	325.340	−	325.340i	0.593232	−	0.593232i	−0.345271	−	0.938503i	$-0.612213\pi$
$67$	325.340	−	325.340i	0.593232	−	0.593232i	0.938503	+	0.345271i	$0.112213\pi$
$68$	−604.753	+	604.753i	−1.07849	+	1.07849i
$69$	31.6873			0.0552855
$70$	−552.980	+	887.292i	−0.944196	+	1.51502i
$71$	−474.107			−0.792481			−0.396240	−	0.918147i	$-0.629685\pi$
$71$	−474.107			−0.792481			−0.396240	+	0.918147i	$0.629685\pi$
$72$	740.092	−	740.092i	1.21140	−	1.21140i
$73$	642.183	−	642.183i	1.02961	−	1.02961i	0.0300668	−	0.999548i	$-0.490428\pi$
$73$	642.183	−	642.183i	1.02961	−	1.02961i	0.999548	−	0.0300668i	$-0.00957200\pi$
$74$		−	967.032i		−	1.51912i
$75$	207.563	−	848.486i	0.319565	−	1.30633i
$76$		−	387.970i		−	0.585568i
$77$	−25.3710	+	567.681i	−0.0375492	+	0.840172i
$78$	1357.18	+	1357.18i	1.97013	+	1.97013i
$79$			636.110i			0.905923i	0.891530	+	0.452962i	$0.149633\pi$
$79$			636.110i			0.905923i	−0.891530	+	0.452962i	$0.850367\pi$
$80$	−307.492	−	1099.32i	−0.429733	−	1.53634i
$81$	841.815			1.15475
$82$	−1166.87	−	1166.87i	−1.57145	−	1.57145i
$83$	−993.219	+	993.219i	−1.31349	+	1.31349i	−0.394670	+	0.918823i	$0.629141\pi$
$83$	−993.219	+	993.219i	−1.31349	+	1.31349i	−0.918823	+	0.394670i	$0.870859\pi$
$84$	1670.87	−	1527.91i	2.17032	−	1.98463i
$85$	268.091	−	476.308i	0.342100	−	0.607798i
$86$	−1380.87			−1.73143
$87$	−885.770	−	885.770i	−1.09155	−	1.09155i
$88$	−1040.08	−	1040.08i	−1.25992	−	1.25992i
$89$	1205.77			1.43608			0.718041	−	0.696001i	$-0.245039\pi$
$89$	1205.77			1.43608			0.718041	+	0.696001i	$0.245039\pi$
$90$	−604.534	+	1074.05i	−0.708038	+	1.25795i
$91$	679.855	+	743.467i	0.783167	+	0.856445i
$92$	−56.0938	+	56.0938i	−0.0635672	+	0.0635672i
$93$	185.892	+	185.892i	0.207270	+	0.207270i
$94$	653.751			0.717332
$95$	66.7891	+	238.779i	0.0721307	+	0.257875i
$96$			922.484i			0.980736i
$97$	917.344	+	917.344i	0.960229	+	0.960229i	0.999239	−	0.0390103i	$-0.0124205\pi$
$97$	917.344	+	917.344i	0.960229	+	0.960229i	−0.0390103	+	0.999239i	$0.512421\pi$
$98$	1328.98	−	1110.50i	1.36987	−	1.14466i
$99$			669.883i			0.680058i
$100$	1134.58	+	1869.45i	1.13458	+	1.86945i
$101$		−	295.537i		−	0.291159i	−0.989347	−	0.145580i	$-0.953495\pi$
$101$		−	295.537i		−	0.291159i	0.989347	−	0.145580i	$-0.0465047\pi$
$102$	−1219.71	+	1219.71i	−1.18401	+	1.18401i
$103$	59.7442	−	59.7442i	0.0571531	−	0.0571531i	−0.677953	−	0.735106i	$-0.737133\pi$
$103$	59.7442	−	59.7442i	0.0571531	−	0.0571531i	0.735106	+	0.677953i	$0.237133\pi$
$104$	−2607.76			−2.45876
$105$	−765.319	+	1228.00i	−0.711309	+	1.14134i
$106$	−1503.98			−1.37811
$107$	697.268	−	697.268i	0.629976	−	0.629976i	−0.318086	−	0.948062i	$-0.603040\pi$
$107$	697.268	−	697.268i	0.629976	−	0.629976i	0.948062	+	0.318086i	$0.103040\pi$
$108$	−446.684	+	446.684i	−0.397983	+	0.397983i
$109$			869.901i			0.764417i	0.924076	+	0.382208i	$0.124836\pi$
$109$			869.901i			0.764417i	−0.924076	+	0.382208i	$0.875164\pi$
$110$	1509.41	+	849.576i	1.30833	+	0.736399i
$111$		−	1338.36i		−	1.14443i
$112$	−84.4254	+	1889.03i	−0.0712272	+	1.59372i
$113$	−787.832	−	787.832i	−0.655867	−	0.655867i	0.298532	−	0.954400i	$-0.403503\pi$
$113$	−787.832	−	787.832i	−0.655867	−	0.655867i	−0.954400	+	0.298532i	$0.903503\pi$
$114$		−	782.485i		−	0.642864i
$115$	24.8667	−	44.1798i	0.0201638	−	0.0358243i
$116$	3136.03			2.51011
$117$	839.785	+	839.785i	0.663574	+	0.663574i
$118$	821.728	−	821.728i	0.641070	−	0.641070i
$119$	−668.159	+	610.991i	−0.514706	+	0.470668i
$120$	−1008.92	−	3607.00i	−0.767510	−	2.74393i
$121$	−389.586			−0.292702
$122$	132.626	+	132.626i	0.0984210	+	0.0984210i
$123$	−1614.93	−	1614.93i	−1.18385	−	1.18385i
$124$	−658.142			−0.476636
$125$	−1020.11	−	955.247i	−0.729933	−	0.683519i
$126$	1506.67	−	1377.76i	1.06528	−	0.974131i
$127$	691.381	−	691.381i	0.483072	−	0.483072i	−0.423039	−	0.906111i	$-0.639037\pi$
$127$	691.381	−	691.381i	0.483072	−	0.483072i	0.906111	+	0.423039i	$0.139037\pi$
$128$	1283.24	+	1283.24i	0.886117	+	0.886117i
$129$	−1911.11			−1.30437
$130$	2957.30	−	827.190i	1.99517	−	0.558072i
$131$			1847.22i			1.23200i	0.787746	+	0.616000i	$0.211248\pi$
$131$			1847.22i			1.23200i	−0.787746	+	0.616000i	$0.788752\pi$
$132$	−2652.35	−	2652.35i	−1.74892	−	1.74892i
$133$	18.3377	−	410.309i	0.0119555	−	0.267506i
$134$			2323.14i			1.49767i
$135$	198.018	−	351.811i	0.126242	−	0.224290i
$136$		−	2343.61i		−	1.47767i
$137$	−1532.08	+	1532.08i	−0.955432	+	0.955432i	−0.999048	−	0.0436159i	$-0.986112\pi$
$137$	−1532.08	+	1532.08i	−0.955432	+	0.955432i	0.0436159	+	0.999048i	$0.486112\pi$
$138$	−113.134	+	113.134i	−0.0697870	+	0.0697870i
$139$	160.189			0.0977488			0.0488744	−	0.998805i	$-0.484437\pi$
$139$	160.189			0.0977488			0.0488744	+	0.998805i	$0.484437\pi$
$140$	−819.058	−	3528.64i	−0.494450	−	2.13017i
$141$	904.784			0.540401
$142$	1692.72	−	1692.72i	1.00035	−	1.00035i
$143$	1180.18	−	1180.18i	0.690154	−	0.690154i
$144$			2229.13i			1.29000i
$145$	−1930.09	+	539.869i	−1.10542	+	0.309198i
$146$			4585.61i			2.59937i
$147$	1839.30	−	1536.91i	1.03199	−	0.862330i
$148$	2369.21	+	2369.21i	1.31586	+	1.31586i
$149$		−	398.652i		−	0.219187i	−0.993976	−	0.109594i	$-0.965045\pi$
$149$		−	398.652i		−	0.219187i	0.993976	−	0.109594i	$-0.0349549\pi$
$150$	2288.30	+	3770.44i	1.24560	+	2.05237i
$151$	−3472.49			−1.87144			−0.935718	−	0.352748i	$-0.885247\pi$
$151$	−3472.49			−1.87144			−0.935718	+	0.352748i	$0.885247\pi$
$152$	751.753	+	751.753i	0.401153	+	0.401153i
$153$	−754.721	+	754.721i	−0.398795	+	0.398795i
$154$	−1936.22	−	2117.39i	−1.01315	−	1.10795i
$155$	405.058	−	113.299i	0.209903	−	0.0587124i
$156$	−6650.13			−3.41306
$157$	515.983	+	515.983i	0.262292	+	0.262292i	0.825985	−	0.563692i	$-0.190620\pi$
$157$	515.983	+	515.983i	0.262292	+	0.262292i	−0.563692	+	0.825985i	$0.690620\pi$
$158$	−2271.12	−	2271.12i	−1.14355	−	1.14355i
$159$	−2081.49			−1.03819
$160$	1286.17	+	723.923i	0.635504	+	0.357695i
$161$	−61.9750	+	56.6724i	−0.0303374	+	0.0277417i
$162$	−3005.55	+	3005.55i	−1.45765	+	1.45765i
$163$	−70.5300	−	70.5300i	−0.0338916	−	0.0338916i	0.689958	−	0.723850i	$-0.257629\pi$
$163$	−70.5300	−	70.5300i	−0.0338916	−	0.0338916i	−0.723850	+	0.689958i	$0.757629\pi$
$164$	5717.59			2.72237
$165$	2089.01	+	1175.80i	0.985632	+	0.554765i
$166$		−	7092.23i		−	3.31605i
$167$	1207.85	+	1207.85i	0.559676	+	0.559676i	0.929215	−	0.369539i	$-0.120484\pi$
$167$	1207.85	+	1207.85i	0.559676	+	0.559676i	−0.369539	+	0.929215i	$0.620484\pi$
$168$	−277.010	+	6198.15i	−0.127213	+	2.84641i
$169$		−	762.027i		−	0.346849i
$170$	743.401	+	2657.74i	0.335390	+	1.19906i
$171$		−	484.179i		−	0.216527i
$172$	3383.10	−	3383.10i	1.49976	−	1.49976i
$173$	800.716	−	800.716i	0.351892	−	0.351892i	−0.508921	−	0.860813i	$-0.669956\pi$
$173$	800.716	−	800.716i	0.351892	−	0.351892i	0.860813	+	0.508921i	$0.169956\pi$
$174$	6324.97			2.75572
$175$	1111.55	+	2030.72i	0.480145	+	0.877189i
$176$	3132.68			1.34168
$177$	1137.26	−	1137.26i	0.482949	−	0.482949i
$178$	−4304.99	+	4304.99i	−1.81277	+	1.81277i
$179$		−	1435.34i		−	0.599343i	−0.954042	−	0.299672i	$-0.903123\pi$
$179$		−	1435.34i		−	0.599343i	0.954042	−	0.299672i	$-0.0968771\pi$
$180$	−1150.31	−	4112.50i	−0.476330	−	1.70293i
$181$		−	3536.87i		−	1.45245i	−0.687458	−	0.726224i	$-0.741273\pi$
$181$		−	3536.87i		−	1.45245i	0.687458	−	0.726224i	$-0.258727\pi$
$182$	−5081.72	−	227.114i	−2.06968	−	0.0924990i
$183$	183.553	+	183.553i	0.0741453	+	0.0741453i
$184$		−	217.381i		−	0.0870954i
$185$	−1866.00	−	1050.28i	−0.741575	−	0.417397i
$186$	−1327.39			−0.523273
$187$	1060.64	+	1060.64i	0.414769	+	0.414769i
$188$	−1601.68	+	1601.68i	−0.621352	+	0.621352i
$189$	−493.517	+	451.291i	−0.189937	+	0.173686i
$190$	−1090.98	−	614.058i	−0.416567	−	0.234466i
$191$	1402.92			0.531474			0.265737	−	0.964046i	$-0.414385\pi$
$191$	1402.92			0.531474			0.265737	+	0.964046i	$0.414385\pi$
$192$	742.482	+	742.482i	0.279084	+	0.279084i
$193$	3290.28	+	3290.28i	1.22715	+	1.22715i	0.965038	+	0.262110i	$0.0844184\pi$
$193$	3290.28	+	3290.28i	1.22715	+	1.22715i	0.262110	+	0.965038i	$0.415582\pi$
$194$	−6550.43			−2.42419
$195$	4092.87	−	1144.82i	1.50306	−	0.420422i
$196$	−535.292	+	5976.67i	−0.195077	+	2.17809i
$197$	1207.31	−	1207.31i	0.436636	−	0.436636i	−0.454242	−	0.890878i	$-0.650090\pi$
$197$	1207.31	−	1207.31i	0.436636	−	0.436636i	0.890878	+	0.454242i	$0.150090\pi$
$198$	−2391.70	−	2391.70i	−0.858438	−	0.858438i
$199$	1348.10			0.480221			0.240111	−	0.970746i	$-0.422816\pi$
$199$	1348.10			0.480221			0.240111	+	0.970746i	$0.422816\pi$
$200$	−5820.79	−	1423.93i	−2.05796	−	0.503434i
$201$			3215.20i			1.12827i
$202$	1055.16	+	1055.16i	0.367530	+	0.367530i
$203$	3316.61	+	148.227i	1.14670	+	0.0512487i
$204$		−	5976.52i		−	2.05118i
$205$	−3518.93	+	984.285i	−1.19889	+	0.335344i
$206$			426.612i			0.144289i
$207$	−70.0040	+	70.0040i	−0.0235054	+	0.0235054i
$208$	3927.22	−	3927.22i	1.30915	−	1.30915i
$209$	−680.437			−0.225200
$210$	−1651.93	−	7116.81i	−0.542830	−	2.33860i
$211$	−1242.22			−0.405298			−0.202649	−	0.979251i	$-0.564955\pi$
$211$	−1242.22			−0.405298			−0.202649	+	0.979251i	$0.564955\pi$
$212$	3684.71	−	3684.71i	1.19371	−	1.19371i
$213$	2342.70	−	2342.70i	0.753611	−	0.753611i
$214$			4978.95i			1.59044i
$215$	−1499.75	+	2664.55i	−0.475731	+	0.845214i
$216$		−	1731.04i		−	0.545289i
$217$	−696.038	−	31.1076i	−0.217743	−	0.00973143i
$218$	−3105.83	−	3105.83i	−0.964924	−	0.964924i
$219$			6346.43i			1.95823i
$220$	−5779.47	+	1616.58i	−1.77115	+	0.495410i
$221$	2659.30			0.809429
$222$	4778.39	+	4778.39i	1.44461	+	1.44461i
$223$	803.061	−	803.061i	0.241152	−	0.241152i	−0.576174	−	0.817327i	$-0.695455\pi$
$223$	803.061	−	803.061i	0.241152	−	0.241152i	0.817327	+	0.576174i	$0.195455\pi$
$224$	−1649.85	−	1804.22i	−0.492123	−	0.538169i
$225$	1415.94	+	2333.04i	0.419537	+	0.691271i
$226$	5625.63			1.65580
$227$	−3190.90	−	3190.90i	−0.932986	−	0.932986i	0.0649056	−	0.997891i	$-0.479325\pi$
$227$	−3190.90	−	3190.90i	−0.932986	−	0.932986i	−0.997891	+	0.0649056i	$0.979325\pi$
$228$	1917.07	+	1917.07i	0.556847	+	0.556847i
$229$	4312.63			1.24448			0.622242	−	0.782825i	$-0.286222\pi$
$229$	4312.63			1.24448			0.622242	+	0.782825i	$0.286222\pi$
$230$	68.9541	+	246.519i	0.0197683	+	0.0706737i
$231$	−2679.71	−	2930.44i	−0.763256	−	0.834671i
$232$	−6076.56	+	6076.56i	−1.71959	+	1.71959i
$233$	−4511.59	−	4511.59i	−1.26852	−	1.26852i	−0.946855	−	0.321661i	$-0.895759\pi$
$233$	−4511.59	−	4511.59i	−1.26852	−	1.26852i	−0.321661	−	0.946855i	$-0.604241\pi$
$234$	−5996.61			−1.67526
$235$	710.033	−	1261.49i	0.197095	−	0.350173i
$236$			4026.43i			1.11059i
$237$	−3143.21	−	3143.21i	−0.861490	−	0.861490i
$238$	204.109	−	4566.98i	0.0555900	−	1.24384i
$239$		−	1219.08i		−	0.329941i	−0.986298	−	0.164971i	$-0.947247\pi$
$239$		−	1219.08i		−	0.329941i	0.986298	−	0.164971i	$-0.0527529\pi$
$240$	6951.47	+	3912.65i	1.86965	+	1.05233i
$241$			2266.52i			0.605807i	0.953021	+	0.302904i	$0.0979560\pi$
$241$			2266.52i			0.605807i	−0.953021	+	0.302904i	$0.902044\pi$
$242$	1390.95	−	1390.95i	0.369477	−	0.369477i
$243$	−3470.27	+	3470.27i	−0.916123	+	0.916123i
$244$	−649.860			−0.170504
$245$	−699.436	−	3770.53i	−0.182389	−	0.983226i
$246$	11531.6			2.98874
$247$	−853.016	+	853.016i	−0.219741	+	0.219741i
$248$	1275.25	−	1275.25i	0.326527	−	0.326527i
$249$		−	9815.57i		−	2.49814i
$250$	7052.67	−	231.587i	1.78420	−	0.0585875i
$251$		−	2913.88i		−	0.732758i	−0.930466	−	0.366379i	$-0.880597\pi$
$251$		−	2913.88i		−	0.732758i	0.930466	−	0.366379i	$-0.119403\pi$
$252$	−315.832	+	7066.79i	−0.0789505	+	1.76653i
$253$	98.3796	+	98.3796i	0.0244469	+	0.0244469i
$254$			4936.91i			1.21956i
$255$	1028.86	+	3678.29i	0.252666	+	0.903308i
$256$	−7961.05			−1.94362
$257$	−2533.26	−	2533.26i	−0.614866	−	0.614866i	0.329344	−	0.944210i	$-0.393172\pi$
$257$	−2533.26	−	2533.26i	−0.614866	−	0.614866i	−0.944210	+	0.329344i	$0.893172\pi$
$258$	6823.28	−	6823.28i	1.64651	−	1.64651i
$259$	2393.65	+	2617.61i	0.574262	+	0.627994i
$260$	−5218.72	+	9271.91i	−1.24481	+	2.21161i
$261$	3913.71			0.928171
$262$	−6595.16	−	6595.16i	−1.55515	−	1.55515i
$263$	4347.32	+	4347.32i	1.01927	+	1.01927i	0.999811	+	0.0194552i	$0.00619316\pi$
$263$	4347.32	+	4347.32i	1.01927	+	1.01927i	0.0194552	+	0.999811i	$0.493807\pi$
$264$	10278.7			2.39625
$265$	−1633.46	+	2902.11i	−0.378651	+	0.672736i
$266$	1399.47	+	1530.41i	0.322582	+	0.352765i
$267$	−5958.06	+	5958.06i	−1.36565	+	1.36565i
$268$	−5691.64	−	5691.64i	−1.29728	−	1.29728i
$269$	−719.233			−0.163020			−0.0815100	−	0.996673i	$-0.525974\pi$
$269$	−719.233			−0.163020			−0.0815100	+	0.996673i	$0.525974\pi$
$270$	549.093	+	1963.07i	0.123766	+	0.442476i
$271$			5060.37i			1.13430i	0.823614	+	0.567151i	$0.191954\pi$
$271$			5060.37i			1.13430i	−0.823614	+	0.567151i	$0.808046\pi$
$272$	3529.43	+	3529.43i	0.786775	+	0.786775i
$273$	−7033.05	−	314.324i	−1.55919	−	0.0696840i
$274$		−	10940.0i		−	2.41209i
$275$	3278.72	−	1989.87i	0.718961	−	0.436342i
$276$		−	554.352i		−	0.120899i
$277$	365.718	−	365.718i	0.0793281	−	0.0793281i	−0.666329	−	0.745658i	$-0.732136\pi$
$277$	365.718	−	365.718i	0.0793281	−	0.0793281i	0.745658	+	0.666329i	$0.232136\pi$
$278$	−571.928	+	571.928i	−0.123388	+	0.123388i
$279$	−821.349			−0.176247
$280$	8424.35	+	5250.24i	1.79804	+	1.12058i
$281$	914.357			0.194114			0.0970569	−	0.995279i	$-0.469057\pi$
$281$	914.357			0.194114			0.0970569	+	0.995279i	$0.469057\pi$
$282$	−3230.37	+	3230.37i	−0.682149	+	0.682149i
$283$	−6608.81	+	6608.81i	−1.38817	+	1.38817i	−0.559019	+	0.829155i	$0.688822\pi$
$283$	−6608.81	+	6608.81i	−1.38817	+	1.38817i	−0.829155	+	0.559019i	$0.811178\pi$
$284$			8294.24i			1.73300i
$285$	−1509.90	−	849.850i	−0.313820	−	0.176634i
$286$			8427.28i			1.74236i
$287$	6046.82	+	270.246i	1.24367	+	0.0555824i
$288$	−2037.97	−	2037.97i	−0.416973	−	0.416973i
$289$		−	2523.07i		−	0.513549i
$290$	4963.55	−	8818.56i	1.00507	−	1.78567i
$291$	−9065.73			−1.82626
$292$	−11234.6	−	11234.6i	−2.25157	−	2.25157i
$293$	1637.54	−	1637.54i	0.326505	−	0.326505i	−0.524751	−	0.851256i	$-0.675841\pi$
$293$	1637.54	−	1637.54i	0.326505	−	0.326505i	0.851256	+	0.524751i	$0.175841\pi$
$294$	−1079.62	+	12054.2i	−0.214165	+	2.39120i
$295$	−693.151	−	2478.10i	−0.136803	−	0.489086i
$296$	−9181.43			−1.80290
$297$	783.412	+	783.412i	0.153058	+	0.153058i
$298$	1423.32	+	1423.32i	0.276680	+	0.276680i
$299$	246.663			0.0477087
$300$	−14843.8	−	3631.20i	−2.85669	−	0.698826i
$301$	3737.81	−	3418.00i	0.715760	−	0.654519i
$302$	12397.9	−	12397.9i	2.36232	−	2.36232i
$303$	1460.34	+	1460.34i	0.276878	+	0.276878i
$304$	−2264.25			−0.427182
$305$	399.961	−	111.874i	0.0750875	−	0.0210028i
$306$		−	5389.20i		−	1.00680i
$307$	2309.09	+	2309.09i	0.429273	+	0.429273i	0.888380	−	0.459108i	$-0.151831\pi$
$307$	2309.09	+	2309.09i	0.429273	+	0.429273i	−0.459108	+	0.888380i	$0.651831\pi$
$308$	9931.26	+	443.851i	1.83729	+	0.0821129i
$309$			590.427i			0.108700i
$310$	−1041.67	+	1850.70i	−0.190849	+	0.339074i
$311$		−	4040.25i		−	0.736661i	−0.929695	−	0.368331i	$-0.879929\pi$
$311$		−	4040.25i		−	0.736661i	0.929695	−	0.368331i	$-0.120071\pi$
$312$	12885.7	−	12885.7i	2.33817	−	2.33817i
$313$	2531.50	−	2531.50i	0.457153	−	0.457153i	−0.440566	−	0.897720i	$-0.645222\pi$
$313$	2531.50	−	2531.50i	0.457153	−	0.457153i	0.897720	+	0.440566i	$0.145222\pi$
$314$	−3684.45			−0.662184
$315$	−1022.17	−	4403.68i	−0.182834	−	0.787679i
$316$	11128.4			1.98108
$317$	−2394.74	+	2394.74i	−0.424297	+	0.424297i	−0.886680	−	0.462383i	$-0.846994\pi$
$317$	−2394.74	+	2394.74i	−0.424297	+	0.424297i	0.462383	+	0.886680i	$0.346994\pi$
$318$	7431.60	−	7431.60i	1.31051	−	1.31051i
$319$		−	5500.10i		−	0.965350i
$320$	1617.87	−	452.536i	0.282630	−	0.0790548i
$321$			6890.81i			1.19815i
$322$	18.9321	−	423.610i	0.00327654	−	0.0733132i
$323$	−766.612	−	766.612i	−0.132060	−	0.132060i
$324$		−	14727.1i		−	2.52522i
$325$	1615.73	−	6604.86i	0.275768	−	1.12730i
$326$	503.630			0.0855629
$327$	−4298.44	−	4298.44i	−0.726924	−	0.726924i
$328$	−11078.7	+	11078.7i	−1.86500	+	1.86500i
$329$	−1769.61	+	1618.20i	−0.296540	+	0.271167i
$330$	−11656.5	+	3260.44i	−1.94444	+	0.543883i
$331$	1609.07			0.267198			0.133599	−	0.991036i	$-0.457347\pi$
$331$	1609.07			0.267198			0.133599	+	0.991036i	$0.457347\pi$
$332$	17375.8	+	17375.8i	2.87235	+	2.87235i
$333$	2956.73	+	2956.73i	0.486570	+	0.486570i
$334$	−8624.80			−1.41296
$335$	4482.77	+	2523.14i	0.731104	+	0.411504i
$336$	−8917.10	−	9751.44i	−1.44782	−	1.58329i
$337$	−7839.49	+	7839.49i	−1.26719	+	1.26719i	−0.319663	+	0.947531i	$0.603570\pi$
$337$	−7839.49	+	7839.49i	−1.26719	+	1.26719i	−0.947531	+	0.319663i	$0.896430\pi$
$338$	2720.69	+	2720.69i	0.437828	+	0.437828i
$339$	7785.82			1.24740
$340$	−8332.74	−	4690.10i	−1.32914	−	0.748107i
$341$			1154.28i			0.183307i
$342$	1728.68	+	1728.68i	0.273322	+	0.273322i
$343$	−848.606	+	6295.51i	−0.133587	+	0.991037i
$344$			13110.6i			2.05487i
$345$	95.4317	+	341.179i	0.0148924	+	0.0532420i
$346$			5717.63i			0.888387i
$347$	−8391.62	+	8391.62i	−1.29823	+	1.29823i	−0.368668	+	0.929561i	$0.620186\pi$
$347$	−8391.62	+	8391.62i	−1.29823	+	1.29823i	−0.929561	+	0.368668i	$0.879814\pi$
$348$	−15496.1	+	15496.1i	−2.38700	+	2.38700i
$349$	−504.762			−0.0774192			−0.0387096	−	0.999251i	$-0.512325\pi$
$349$	−504.762			−0.0774192			−0.0387096	+	0.999251i	$0.512325\pi$
$350$	−11218.9	−	3281.74i	−1.71336	−	0.501190i
$351$	1964.22			0.298696
$352$	−2864.04	+	2864.04i	−0.433675	+	0.433675i
$353$	−2910.85	+	2910.85i	−0.438892	+	0.438892i	−0.891639	−	0.452747i	$-0.850444\pi$
$353$	−2910.85	+	2910.85i	−0.438892	+	0.438892i	0.452747	+	0.891639i	$0.350444\pi$
$354$			8120.80i			1.21925i
$355$	−1427.85	−	5104.74i	−0.213472	−	0.763188i
$356$		−	21094.3i		−	3.14043i
$357$	282.485	−	6320.66i	0.0418787	−	0.937044i
$358$	5124.64	+	5124.64i	0.756552	+	0.756552i
$359$			122.174i			0.0179612i	0.999960	+	0.00898060i	$0.00285865\pi$
$359$			122.174i			0.0179612i	−0.999960	+	0.00898060i	$0.997141\pi$
$360$	10197.5	+	5739.71i	1.49294	+	0.840304i
$361$	−6367.19			−0.928297
$362$	12627.8	+	12627.8i	1.83343	+	1.83343i
$363$	1925.06	−	1925.06i	0.278345	−	0.278345i
$364$	13006.5	−	11893.7i	1.87288	−	1.71263i
$365$	8848.48	+	4980.39i	1.26891	+	0.714207i
$366$	−1310.68			−0.187187
$367$	7525.98	+	7525.98i	1.07044	+	1.07044i	0.997323	+	0.0731207i	$0.0232958\pi$
$367$	7525.98	+	7525.98i	1.07044	+	1.07044i	0.0731207	+	0.997323i	$0.476704\pi$
$368$	327.371	+	327.371i	0.0463734	+	0.0463734i
$369$	7135.45			1.00666
$370$	10412.1	−	2912.38i	1.46297	−	0.409210i
$371$	4071.04	−	3722.72i	0.569698	−	0.520955i
$372$	3252.07	−	3252.07i	0.453258	−	0.453258i
$373$	3824.72	+	3824.72i	0.530929	+	0.530929i	0.920849	−	0.389920i	$-0.127497\pi$
$373$	3824.72	+	3824.72i	0.530929	+	0.530929i	−0.389920	+	0.920849i	$0.627497\pi$
$374$	−7573.66			−1.04713
$375$	9760.83	−	320.515i	1.34413	−	0.0441368i
$376$		−	6207.00i		−	0.851334i
$377$	−6895.09	−	6895.09i	−0.941950	−	0.941950i
$378$	150.759	−	3373.27i	0.0205138	−	0.459001i
$379$		−	6001.43i		−	0.813385i	−0.913565	−	0.406692i	$-0.866682\pi$
$379$		−	6001.43i		−	0.813385i	0.913565	−	0.406692i	$-0.133318\pi$
$380$	4177.30	−	1168.44i	0.563923	−	0.157736i
$381$			6832.64i			0.918757i
$382$	−5008.87	+	5008.87i	−0.670880	+	0.670880i
$383$	5683.84	−	5683.84i	0.758305	−	0.758305i	−0.217709	−	0.976014i	$-0.569858\pi$
$383$	5683.84	−	5683.84i	0.758305	−	0.758305i	0.976014	+	0.217709i	$0.0698584\pi$
$384$	−12681.7			−1.68531
$385$	−6188.67	+	1436.50i	−0.819230	+	0.190158i
$386$	−23494.7			−3.09806
$387$	4222.05	−	4222.05i	0.554571	−	0.554571i
$388$	16048.4	−	16048.4i	2.09983	−	2.09983i
$389$		−	5540.42i		−	0.722134i	−0.932540	−	0.361067i	$-0.882413\pi$
$389$		−	5540.42i		−	0.722134i	0.932540	−	0.361067i	$-0.117587\pi$
$390$	−10525.5	+	18700.3i	−1.36661	+	2.42801i
$391$			221.678i			0.0286719i
$392$	−10543.5	−	12618.0i	−1.35849	−	1.62577i
$393$	−9127.64	−	9127.64i	−1.17157	−	1.17157i
$394$			8620.98i			1.10233i
$395$	−6849.04	+	1915.75i	−0.872437	+	0.244031i
$396$	11719.2			1.48716
$397$	−3568.08	−	3568.08i	−0.451076	−	0.451076i	0.444636	−	0.895711i	$-0.353333\pi$
$397$	−3568.08	−	3568.08i	−0.451076	−	0.451076i	−0.895711	+	0.444636i	$0.853333\pi$
$398$	−4813.14	+	4813.14i	−0.606184	+	0.606184i
$399$	1936.85	+	2118.07i	0.243017	+	0.265755i
$400$	10910.4	−	6621.58i	1.36380	−	0.827697i
$401$	−304.302			−0.0378956			−0.0189478	−	0.999820i	$-0.506032\pi$
$401$	−304.302			−0.0378956			−0.0189478	+	0.999820i	$0.506032\pi$
$402$	−11479.3	−	11479.3i	−1.42422	−	1.42422i
$403$	1447.03	+	1447.03i	0.178863	+	0.178863i
$404$	−5170.26			−0.636708
$405$	2535.27	+	9063.89i	0.311058	+	1.11207i
$406$	−12370.6	+	11312.1i	−1.51217	+	1.38279i
$407$	4155.21	−	4155.21i	0.506060	−	0.506060i
$408$	11580.5	+	11580.5i	1.40519	+	1.40519i
$409$	11817.3			1.42867			0.714334	−	0.699805i	$-0.246730\pi$
$409$	11817.3			1.42867			0.714334	+	0.699805i	$0.246730\pi$
$410$	9049.51	−	16077.9i	1.09006	−	1.93667i
$411$		−	15140.9i		−	1.81714i
$412$	−1045.19	−	1045.19i	−0.124983	−	0.124983i
$413$	−190.312	+	4258.28i	−0.0226747	+	0.507352i
$414$		−	499.874i		−	0.0593417i
$415$	−13685.3	−	7702.81i	−1.61876	−	0.911123i
$416$			7180.88i			0.846326i
$417$	−791.543	+	791.543i	−0.0929545	+	0.0929545i
$418$	2429.38	−	2429.38i	0.284270	−	0.284270i
$419$	−6280.26			−0.732246			−0.366123	−	0.930567i	$-0.619315\pi$
$419$	−6280.26			−0.732246			−0.366123	+	0.930567i	$0.619315\pi$
$420$	21483.2	+	13388.8i	2.49589	+	1.55549i
$421$	5592.95			0.647467			0.323734	−	0.946148i	$-0.395062\pi$
$421$	5592.95			0.647467			0.323734	+	0.946148i	$0.395062\pi$
$422$	4435.13	−	4435.13i	0.511608	−	0.511608i
$423$	−1998.86	+	1998.86i	−0.229759	+	0.229759i
$424$			14279.4i			1.63554i
$425$	5935.84	+	1452.07i	0.677484	+	0.165731i
$426$			16728.4i			1.90257i
$427$	−687.280	−	30.7161i	−0.0778918	−	0.00348117i
$428$	−12198.3	−	12198.3i	−1.37764	−	1.37764i
$429$			11663.3i			1.31261i
$430$	−4158.73	−	14867.9i	−0.466399	−	1.66743i
$431$	3211.63			0.358930			0.179465	−	0.983764i	$-0.442563\pi$
$431$	3211.63			0.358930			0.179465	+	0.983764i	$0.442563\pi$
$432$	2606.91	+	2606.91i	0.290336	+	0.290336i
$433$	−8998.00	+	8998.00i	−0.998652	+	0.998652i	−0.999999	−	0.00134740i	$-0.999571\pi$
$433$	−8998.00	+	8998.00i	−0.998652	+	0.998652i	0.00134740	+	0.999999i	$0.499571\pi$
$434$	2596.15	−	2374.02i	0.287141	−	0.262573i
$435$	6869.50	−	12204.8i	0.757166	−	1.34523i
$436$	15218.4			1.67163
$437$	−71.1070	−	71.1070i	−0.00778377	−	0.00778377i
$438$	−22658.8	−	22658.8i	−2.47187	−	2.47187i
$439$	−15391.3			−1.67332			−0.836658	−	0.547725i	$-0.815494\pi$
$439$	−15391.3			−1.67332			−0.836658	+	0.547725i	$0.815494\pi$
$440$	8066.26	−	14331.0i	0.873963	−	1.55274i
$441$	−668.035	+	7458.78i	−0.0721342	+	0.805397i
$442$	−9494.57	+	9494.57i	−1.02174	+	1.02174i
$443$	−5980.38	−	5980.38i	−0.641391	−	0.641391i	0.309506	−	0.950897i	$-0.399836\pi$
$443$	−5980.38	−	5980.38i	−0.641391	−	0.641391i	−0.950897	+	0.309506i	$0.899836\pi$
$444$	−23413.9			−2.50265
$445$	3631.38	+	12982.6i	0.386841	+	1.38300i
$446$			5734.38i			0.608813i
$447$	1969.86	+	1969.86i	0.208436	+	0.208436i
$448$	−2780.09	−	124.249i	−0.293185	−	0.0131031i
$449$			9630.65i			1.01225i	0.862461	+	0.506123i	$0.168922\pi$
$449$			9630.65i			1.01225i	−0.862461	+	0.506123i	$0.831078\pi$
$450$	−13385.1	−	3274.36i	−1.40217	−	0.343011i
$451$		−	10027.7i		−	1.04698i
$452$	−13782.7	+	13782.7i	−1.43425	+	1.43425i
$453$	17158.6	−	17158.6i	1.77965	−	1.77965i
$454$	22785.1			2.35542
$455$	−5957.46	+	9559.13i	−0.613824	+	0.984921i
$456$	−7429.26			−0.762954
$457$	10749.0	−	10749.0i	1.10025	−	1.10025i	0.105873	−	0.994380i	$-0.466236\pi$
$457$	10749.0	−	10749.0i	1.10025	−	1.10025i	0.994380	−	0.105873i	$-0.0337637\pi$
$458$	−15397.5	+	15397.5i	−1.57091	+	1.57091i
$459$			1765.26i			0.179510i
$460$	−772.902	−	435.030i	−0.0783407	−	0.0440943i
$461$			7419.80i			0.749620i	0.927102	+	0.374810i	$0.122292\pi$
$461$			7419.80i			0.749620i	−0.927102	+	0.374810i	$0.877708\pi$
$462$	20030.1	+	895.191i	2.01706	+	0.0901473i
$463$	7829.44	+	7829.44i	0.785886	+	0.785886i	0.980817	−	0.194931i	$-0.0624483\pi$
$463$	7829.44	+	7829.44i	0.785886	+	0.785886i	−0.194931	+	0.980817i	$0.562448\pi$
$464$		−	18302.3i		−	1.83117i
$465$	−1441.66	+	2561.35i	−0.143775	+	0.255441i
$466$	32215.7			3.20250
$467$	2236.87	+	2236.87i	0.221649	+	0.221649i	0.809193	−	0.587543i	$-0.199905\pi$
$467$	2236.87	+	2236.87i	0.221649	+	0.221649i	−0.587543	+	0.809193i	$0.699905\pi$
$468$	14691.6	−	14691.6i	1.45111	−	1.45111i
$469$	−5750.35	−	6288.39i	−0.566154	−	0.619127i
$470$	1968.88	+	7038.98i	0.193229	+	0.690817i
$471$	−5099.24			−0.498855
$472$	−7801.85	−	7801.85i	−0.760825	−	0.760825i
$473$	−5933.42	−	5933.42i	−0.576784	−	0.576784i
$474$	22444.5			2.17492
$475$	−2369.80	+	1438.25i	−0.228913	+	0.138929i
$476$	10689.0	+	11689.1i	1.02926	+	1.12556i
$477$	4598.46	−	4598.46i	0.441402	−	0.441402i
$478$	4352.52	+	4352.52i	0.416485	+	0.416485i
$479$	−16127.0			−1.53833			−0.769167	−	0.639047i	$-0.779329\pi$
$479$	−16127.0			−1.53833			−0.769167	+	0.639047i	$0.779329\pi$
$480$	−9932.45	+	2778.22i	−0.944484	+	0.264183i
$481$		−	10418.2i		−	0.987586i
$482$	−8092.22	−	8092.22i	−0.764711	−	0.764711i
$483$	26.2018	−	586.272i	0.00246838	−	0.0552304i
$484$			6815.59i			0.640081i
$485$	−7114.37	+	12639.8i	−0.666076	+	1.18339i
$486$		−	24780.0i		−	2.31284i
$487$	7934.50	−	7934.50i	0.738288	−	0.738288i	−0.233958	−	0.972247i	$-0.575168\pi$
$487$	7934.50	−	7934.50i	0.738288	−	0.738288i	0.972247	+	0.233958i	$0.0751679\pi$
$488$	1259.21	−	1259.21i	0.116807	−	0.116807i
$489$	697.019			0.0644587
$490$	15959.2	+	10964.8i	1.47136	+	1.01090i
$491$	−4160.37			−0.382393			−0.191196	−	0.981552i	$-0.561237\pi$
$491$	−4160.37			−0.382393			−0.191196	+	0.981552i	$0.561237\pi$
$492$	−28252.3	+	28252.3i	−2.58885	+	2.58885i
$493$	6196.67	−	6196.67i	0.566093	−	0.566093i
$494$		−	6091.09i		−	0.554759i
$495$	−7212.68	+	2017.47i	−0.654921	+	0.183189i
$496$			3841.01i			0.347715i
$497$	−392.033	+	8771.83i	−0.0353825	+	0.791691i
$498$	35044.8	+	35044.8i	3.15340	+	3.15340i
$499$			5858.81i			0.525603i	0.964850	+	0.262802i	$0.0846465\pi$
$499$			5858.81i			0.525603i	−0.964850	+	0.262802i	$0.915353\pi$
$500$	−16711.5	+	17846.3i	−1.49472	+	1.59622i
$501$	−11936.6			−1.06445
$502$	10403.5	+	10403.5i	0.924961	+	0.924961i
$503$	13951.3	−	13951.3i	1.23669	−	1.23669i	0.275347	−	0.961345i	$-0.411207\pi$
$503$	13951.3	−	13951.3i	1.23669	−	1.23669i	0.961345	−	0.275347i	$-0.0887929\pi$
$504$	−13081.1	−	14305.0i	−1.15610	−	1.26428i
$505$	3182.07	−	890.062i	0.280397	−	0.0784302i
$506$	−702.494			−0.0617187
$507$	3765.40	+	3765.40i	0.329837	+	0.329837i
$508$	−12095.3	−	12095.3i	−1.05639	−	1.05639i
$509$	18246.3			1.58891			0.794454	−	0.607324i	$-0.207757\pi$
$509$	18246.3			1.58891			0.794454	+	0.607324i	$0.207757\pi$
$510$	−16806.1	−	9459.33i	−1.45919	−	0.821306i
$511$	−11350.5	−	12412.6i	−0.982618	−	1.07456i
$512$	18157.7	−	18157.7i	1.56731	−	1.56731i
$513$	−566.236	−	566.236i	−0.0487328	−	0.0487328i
$514$	18089.1			1.55229
$515$	823.200	+	463.340i	0.0704360	+	0.0396451i
$516$			33433.8i			2.85240i
$517$	2809.08	+	2809.08i	0.238962	+	0.238962i
$518$	−17891.8	−	799.627i	−1.51761	−	0.0678255i
$519$			7913.14i			0.669265i
$520$	−7853.71	−	28077.9i	−0.662323	−	2.36788i
$521$			14936.8i			1.25603i	0.778200	+	0.628016i	$0.216133\pi$
$521$			14936.8i			1.25603i	−0.778200	+	0.628016i	$0.783867\pi$
$522$	−13973.2	+	13973.2i	−1.17163	+	1.17163i
$523$	−15191.9	+	15191.9i	−1.27017	+	1.27017i	−0.324165	+	0.946001i	$0.605083\pi$
$523$	−15191.9	+	15191.9i	−1.27017	+	1.27017i	−0.946001	+	0.324165i	$0.894917\pi$
$524$	32316.0			2.69415
$525$	−15526.9	−	4541.90i	−1.29076	−	0.377571i
$526$	−31042.7			−2.57324
$527$	−1300.46	+	1300.46i	−0.107493	+	0.107493i
$528$	−15479.5	+	15479.5i	−1.27587	+	1.27587i
$529$		−	12146.4i		−	0.998310i
$530$	−4529.49	−	16193.4i	−0.371223	−	1.32717i
$531$			5024.92i			0.410664i
$532$	−7178.14	−	320.808i	−0.584984	−	0.0261443i
$533$	−12571.1	−	12571.1i	−1.02160	−	1.02160i
$534$		−	42544.4i		−	3.44771i
$535$	9607.47	+	5407.59i	0.776388	+	0.436992i
$536$	22056.9			1.77745
$537$	7092.44	+	7092.44i	0.569947	+	0.569947i
$538$	2567.89	−	2567.89i	0.205780	−	0.205780i
$539$	10482.1	+	938.817i	0.837657	+	0.0750236i
$540$	−6154.74	−	3464.21i	−0.490478	−	0.276066i
$541$	8027.88			0.637977			0.318988	−	0.947759i	$-0.396657\pi$
$541$	8027.88			0.637977			0.318988	+	0.947759i	$0.396657\pi$
$542$	−18067.2	−	18067.2i	−1.43183	−	1.43183i
$543$	17476.7	+	17476.7i	1.38121	+	1.38121i
$544$	−6453.51			−0.508625
$545$	−9366.29	+	2619.86i	−0.736161	+	0.205913i
$546$	26232.5	−	23988.0i	2.05613	−	1.88021i
$547$	5287.54	−	5287.54i	0.413307	−	0.413307i	−0.469582	−	0.882889i	$-0.655595\pi$
$547$	5287.54	−	5287.54i	0.413307	−	0.413307i	0.882889	+	0.469582i	$0.155595\pi$
$548$	26802.9	+	26802.9i	2.08935	+	2.08935i
$549$	−811.014			−0.0630478
$550$	−4601.59	+	18810.6i	−0.356750	+	1.45834i
$551$			3975.37i			0.307362i
$552$	1074.14	+	1074.14i	0.0828236	+	0.0828236i
$553$	11769.2	+	525.992i	0.905020	+	0.0404475i
$554$			2611.47i			0.200272i
$555$	14410.2	−	4030.71i	1.10213	−	0.308278i
$556$		−	2802.43i		−	0.213758i
$557$	−4891.64	+	4891.64i	−0.372111	+	0.372111i	−0.868245	−	0.496135i	$-0.834752\pi$
$557$	−4891.64	+	4891.64i	−0.372111	+	0.372111i	0.496135	+	0.868245i	$0.334752\pi$
$558$	2932.48	−	2932.48i	0.222477	−	0.222477i
$559$	−14876.6			−1.12561
$560$	−20593.6	+	4780.14i	−1.55400	+	0.360710i
$561$	−10481.9			−0.788850
$562$	−3264.55	+	3264.55i	−0.245030	+	0.245030i
$563$	−1138.04	+	1138.04i	−0.0851916	+	0.0851916i	−0.748418	−	0.663227i	$-0.769186\pi$
$563$	−1138.04	+	1138.04i	−0.0851916	+	0.0851916i	0.663227	+	0.748418i	$0.269186\pi$
$564$		−	15828.7i		−	1.18175i
$565$	6109.95	−	10855.3i	0.454952	−	0.808297i
$566$		−	47191.2i		−	3.50459i
$567$	696.087	−	15575.1i	0.0515572	−	1.15360i
$568$	−16071.4	−	16071.4i	−1.18722	−	1.18722i
$569$		−	7200.63i		−	0.530521i	−0.964177	−	0.265260i	$-0.914542\pi$
$569$		−	7200.63i		−	0.530521i	0.964177	−	0.265260i	$-0.0854579\pi$
$570$	8425.07	−	2356.59i	0.619101	−	0.173170i
$571$	2089.22			0.153119			0.0765597	−	0.997065i	$-0.475606\pi$
$571$	2089.22			0.153119			0.0765597	+	0.997065i	$0.475606\pi$
$572$	−20646.7	−	20646.7i	−1.50923	−	1.50923i
$573$	−6932.22	+	6932.22i	−0.505406	+	0.505406i
$574$	−22554.0	+	20624.2i	−1.64004	+	1.49972i
$575$	550.578	+	134.687i	0.0399316	+	0.00976838i
$576$	−3280.61			−0.237312
$577$	7943.75	+	7943.75i	0.573141	+	0.573141i	0.933005	−	0.359864i	$-0.117177\pi$
$577$	7943.75	+	7943.75i	0.573141	+	0.573141i	−0.359864	+	0.933005i	$0.617177\pi$
$578$	9008.17	+	9008.17i	0.648253	+	0.648253i
$579$	−32516.5			−2.33392
$580$	9444.70	+	33765.9i	0.676155	+	2.41733i
$581$	17555.0	+	19197.6i	1.25354	+	1.37083i
$582$	32367.6	−	32367.6i	2.30529	−	2.30529i
$583$	−6462.40	−	6462.40i	−0.459083	−	0.459083i
$584$	43537.8			3.08494
$585$	−6512.87	+	11571.2i	−0.460297	+	0.817794i
$586$			11693.1i			0.824295i
$587$	18688.9	+	18688.9i	1.31410	+	1.31410i	0.918368	+	0.395727i	$0.129507\pi$
$587$	18688.9	+	18688.9i	1.31410	+	1.31410i	0.395727	+	0.918368i	$0.370493\pi$
$588$	−26887.5	−	32177.5i	−1.88575	−	2.25677i
$589$		−	834.290i		−	0.0583639i
$590$	11322.4	+	6372.83i	0.790059	+	0.444687i
$591$			11931.4i			0.830440i
$592$	13827.0	−	13827.0i	0.959945	−	0.959945i
$593$	−5453.19	+	5453.19i	−0.377632	+	0.377632i	−0.870247	−	0.492615i	$-0.836041\pi$
$593$	−5453.19	+	5453.19i	−0.377632	+	0.377632i	0.492615	+	0.870247i	$0.336041\pi$
$594$	−5594.07			−0.386410
$595$	−8590.86	−	5354.01i	−0.591918	−	0.368896i
$596$	−6974.20			−0.479320
$597$	−6661.34	+	6661.34i	−0.456668	+	0.456668i
$598$	−880.667	+	880.667i	−0.0602227	+	0.0602227i
$599$		−	13401.4i		−	0.914136i	−0.889432	−	0.457068i	$-0.848900\pi$
$599$		−	13401.4i		−	0.914136i	0.889432	−	0.457068i	$-0.151100\pi$
$600$	35798.3	−	21726.2i	2.43576	−	1.47828i
$601$		−	15689.8i		−	1.06489i	−0.846464	−	0.532446i	$-0.821273\pi$
$601$		−	15689.8i		−	1.06489i	0.846464	−	0.532446i	$-0.178727\pi$
$602$	−1141.82	+	25548.6i	−0.0773045	+	1.72970i
$603$	−7103.06	−	7103.06i	−0.479700	−	0.479700i
$604$			60749.2i			4.09247i
$605$	−1173.30	−	4194.70i	−0.0788457	−	0.281882i
$606$	−10427.8			−0.699008
$607$	−9429.70	−	9429.70i	−0.630543	−	0.630543i	0.317661	−	0.948204i	$-0.397103\pi$
$607$	−9429.70	−	9429.70i	−0.630543	−	0.630543i	−0.948204	+	0.317661i	$0.897103\pi$
$608$	2070.08	−	2070.08i	0.138080	−	0.138080i
$609$	−17120.8	+	15655.9i	−1.13919	+	1.04172i
$610$	−1028.56	+	1827.42i	−0.0682711	+	0.121295i
$611$	7043.10			0.466339
$612$	13203.4	+	13203.4i	0.872086	+	0.872086i
$613$	−13138.6	−	13138.6i	−0.865681	−	0.865681i	0.126310	−	0.991991i	$-0.459687\pi$
$613$	−13138.6	−	13138.6i	−0.865681	−	0.865681i	−0.991991	+	0.126310i	$0.959687\pi$
$614$	−16488.4			−1.08374
$615$	12524.4	−	22251.7i	0.821193	−	1.45898i
$616$	−20103.4	+	18383.4i	−1.31492	+	1.20241i
$617$	−10622.2	+	10622.2i	−0.693088	+	0.693088i	−0.962910	−	0.269822i	$-0.913035\pi$
$617$	−10622.2	+	10622.2i	−0.693088	+	0.693088i	0.269822	+	0.962910i	$0.413035\pi$
$618$	−2108.02	−	2108.02i	−0.137212	−	0.137212i
$619$	1244.71			0.0808224			0.0404112	−	0.999183i	$-0.487133\pi$
$619$	1244.71			0.0808224			0.0404112	+	0.999183i	$0.487133\pi$
$620$	−1982.11	−	7086.26i	−0.128393	−	0.459018i
$621$			163.736i			0.0105805i
$622$	14425.0	+	14425.0i	0.929888	+	0.929888i
$623$	997.036	−	22308.9i	0.0641178	−	1.43465i
$624$			38811.1i			2.48989i
$625$	7212.97	−	13860.5i	0.461630	−	0.887072i
$626$			18076.6i			1.15413i
$627$	3362.24	−	3362.24i	0.214155	−	0.214155i
$628$	9026.83	−	9026.83i	0.573582	−	0.573582i
$629$	9362.91			0.593519
$630$	19372.0	+	12073.1i	1.22508	+	0.763497i
$631$	−7532.27			−0.475206			−0.237603	−	0.971362i	$-0.576362\pi$
$631$	−7532.27			−0.475206			−0.237603	+	0.971362i	$0.576362\pi$
$632$	−21563.0	+	21563.0i	−1.35717	+	1.35717i
$633$	6138.17	−	6138.17i	0.385419	−	0.385419i
$634$		−	17100.0i		−	1.07118i
$635$	9526.37	+	5361.94i	0.595342	+	0.335090i
$636$			36414.5i			2.27033i
$637$	14317.6	−	11963.8i	0.890558	−	0.744148i
$638$	19637.1	+	19637.1i	1.21856	+	1.21856i
$639$			10351.1i			0.640816i
$640$	−9952.00	+	17681.4i	−0.614668	+	1.09206i
$641$	−6109.53			−0.376462			−0.188231	−	0.982125i	$-0.560275\pi$
$641$	−6109.53			−0.376462			−0.188231	+	0.982125i	$0.560275\pi$
$642$	−24602.4	−	24602.4i	−1.51243	−	1.51243i
$643$	−1890.33	+	1890.33i	−0.115937	+	0.115937i	−0.762695	−	0.646758i	$-0.776124\pi$
$643$	−1890.33	+	1890.33i	−0.115937	+	0.115937i	0.646758	+	0.762695i	$0.276124\pi$
$644$	991.452	+	1084.22i	0.0606657	+	0.0663419i
$645$	−5755.64	−	20577.0i	−0.351361	−	1.25616i
$646$	5474.11			0.333399
$647$	−18918.1	−	18918.1i	−1.14953	−	1.14953i	−0.986644	−	0.162889i	$-0.947919\pi$
$647$	−18918.1	−	18918.1i	−1.14953	−	1.14953i	−0.162889	−	0.986644i	$-0.552081\pi$
$648$	28536.1	+	28536.1i	1.72994	+	1.72994i
$649$	7061.72			0.427114
$650$	17812.8	+	29350.2i	1.07489	+	1.77109i
$651$	3593.04	−	3285.62i	0.216317	−	0.197809i
$652$	−1233.88	+	1233.88i	−0.0741144	+	0.0741144i
$653$	−3650.44	−	3650.44i	−0.218764	−	0.218764i	0.589214	−	0.807977i	$-0.299438\pi$
$653$	−3650.44	−	3650.44i	−0.218764	−	0.218764i	−0.807977	+	0.589214i	$0.799438\pi$
$654$	30693.6			1.83519
$655$	−19889.1	+	5563.21i	−1.18646	+	0.331867i
$656$		−	33368.7i		−	1.98602i
$657$	−14020.6	−	14020.6i	−0.832567	−	0.832567i
$658$	540.579	−	12095.6i	0.0320273	−	0.716617i
$659$			30832.1i			1.82253i	0.411817	+	0.911267i	$0.364894\pi$
$659$			30832.1i			1.82253i	−0.411817	+	0.911267i	$0.635106\pi$
$660$	20570.0	−	36546.1i	1.21316	−	2.15539i
$661$		−	4032.29i		−	0.237274i	−0.992938	−	0.118637i	$-0.962148\pi$
$661$		−	4032.29i		−	0.237274i	0.992938	−	0.118637i	$-0.0378524\pi$
$662$	−5744.90	+	5744.90i	−0.337284	+	0.337284i
$663$	−13140.4	+	13140.4i	−0.769729	+	0.769729i
$664$	−67336.8			−3.93550
$665$	4473.06	−	1038.27i	0.260839	−	0.0605452i
$666$	−21113.0			−1.22839
$667$	574.771	−	574.771i	0.0333661	−	0.0333661i
$668$	21130.6	−	21130.6i	1.22390	−	1.22390i
$669$			7936.32i			0.458649i
$670$	−25013.4	+	6996.53i	−1.44232	+	0.403432i
$671$			1139.75i			0.0655732i
$672$	17067.6	+	762.791i	0.979758	+	0.0437877i
$673$	17723.3	+	17723.3i	1.01513	+	1.01513i	0.999884	+	0.0152461i	$0.00485316\pi$
$673$	17723.3	+	17723.3i	1.01513	+	1.01513i	0.0152461	+	0.999884i	$0.495147\pi$
$674$		−	55979.1i		−	3.19916i
$675$	4384.34	+	1072.53i	0.250005	+	0.0611581i
$676$	−13331.2			−0.758491
$677$	9377.64	+	9377.64i	0.532366	+	0.532366i	0.921276	−	0.388910i	$-0.127148\pi$
$677$	9377.64	+	9377.64i	0.532366	+	0.532366i	−0.388910	+	0.921276i	$0.627148\pi$
$678$	−27797.9	+	27797.9i	−1.57459	+	1.57459i
$679$	17731.0	−	16214.0i	1.00214	−	0.916399i
$680$	25233.8	−	7058.19i	1.42305	−	0.398043i
$681$	31534.4			1.77445
$682$	−4121.14	−	4121.14i	−0.231388	−	0.231388i
$683$	11971.7	+	11971.7i	0.670693	+	0.670693i	0.957876	−	0.287183i	$-0.0927187\pi$
$683$	11971.7	+	11971.7i	0.670693	+	0.670693i	−0.287183	+	0.957876i	$0.592719\pi$
$684$	−8470.45			−0.473502
$685$	−21110.1	−	11881.9i	−1.17748	−	0.662749i
$686$	−19447.2	−	25506.8i	−1.08236	−	1.41961i
$687$	−21310.0	+	21310.0i	−1.18344	+	1.18344i
$688$	−19744.3	−	19744.3i	−1.09410	−	1.09410i
$689$	−16202.9			−0.895910
$690$	−1558.84	−	877.399i	−0.0860060	−	0.0484087i
$691$			4704.44i			0.258995i	0.991580	+	0.129497i	$0.0413364\pi$
$691$			4704.44i			0.258995i	−0.991580	+	0.129497i	$0.958664\pi$
$692$	−14008.1	−	14008.1i	−0.769519	−	0.769519i
$693$	12394.0	+	553.918i	0.679380	+	0.0303631i
$694$		−	59921.6i		−	3.27751i
$695$	482.438	+	1724.77i	0.0263308	+	0.0941357i
$696$		−	60052.1i		−	3.27050i
$697$	11297.7	−	11297.7i	0.613962	−	0.613962i
$698$	1802.16	−	1802.16i	0.0977263	−	0.0977263i
$699$	44586.2			2.41260
$700$	35526.4	−	19446.0i	1.91824	−	1.04998i
$701$	29583.6			1.59395			0.796974	−	0.604014i	$-0.206433\pi$
$701$	29583.6			1.59395			0.796974	+	0.604014i	$0.206433\pi$
$702$	−7012.89	+	7012.89i	−0.377044	+	0.377044i
$703$	−3003.31	+	3003.31i	−0.161127	+	0.161127i
$704$			4610.37i			0.246818i
$705$	2724.91	+	9741.87i	0.145569	+	0.520426i
$706$		−	20785.4i		−	1.10803i
$707$	−5467.97	−	244.376i	−0.290869	−	0.0129996i
$708$	−19895.8	−	19895.8i	−1.05612	−	1.05612i
$709$			29637.0i			1.56988i	0.619574	+	0.784938i	$0.287305\pi$
$709$			29637.0i			1.56988i	−0.619574	+	0.784938i	$0.712695\pi$
$710$	23323.5	+	13127.7i	1.23284	+	0.693906i
$711$	13888.0			0.732548
$712$	40873.5	+	40873.5i	2.15140	+	2.15140i
$713$	−120.624	+	120.624i	−0.00633577	+	0.00633577i
$714$	21558.2	+	23575.4i	1.12997	+	1.23569i
$715$	16261.5	+	9152.80i	0.850551	+	0.478735i
$716$	−25110.5			−1.31065
$717$	6023.85	+	6023.85i	0.313758	+	0.313758i
$718$	−436.199	−	436.199i	−0.0226724	−	0.0226724i
$719$	19761.2			1.02499			0.512496	−	0.858690i	$-0.328721\pi$
$719$	19761.2			1.02499			0.512496	+	0.858690i	$0.328721\pi$
$720$	−24001.2	+	6713.40i	−1.24232	+	0.347491i
$721$	−1055.97	−	1154.78i	−0.0545444	−	0.0596479i
$722$	22732.9	−	22732.9i	1.17179	−	1.17179i
$723$	−11199.5	−	11199.5i	−0.576094	−	0.576094i
$724$	−61875.5			−3.17622
$725$	−11625.6	−	19155.5i	−0.595537	−	0.981267i
$726$			13746.2i			0.702711i
$727$	−2991.47	−	2991.47i	−0.152610	−	0.152610i	0.626673	−	0.779283i	$-0.284416\pi$
$727$	−2991.47	−	2991.47i	−0.152610	−	0.152610i	−0.779283	+	0.626673i	$0.784416\pi$
$728$	−2156.32	+	48248.2i	−0.109778	+	2.45631i
$729$		−	11566.2i		−	0.587624i
$730$	−49373.6	+	13810.3i	−2.50328	+	0.700197i
$731$		−	13369.7i		−	0.676467i
$732$	3211.15	−	3211.15i	0.162141	−	0.162141i
$733$	−14061.2	+	14061.2i	−0.708542	+	0.708542i	−0.966229	−	0.257687i	$-0.917040\pi$
$733$	−14061.2	+	14061.2i	−0.708542	+	0.708542i	0.257687	+	0.966229i	$0.417040\pi$
$734$	−53740.4			−2.70244
$735$	22087.4	+	15175.2i	1.10844	+	0.761558i
$736$	−598.595			−0.0299789
$737$	−9982.22	+	9982.22i	−0.498914	+	0.498914i
$738$	−25475.9	+	25475.9i	−1.27071	+	1.27071i
$739$		−	3186.25i		−	0.158604i	−0.996851	−	0.0793018i	$-0.974731\pi$
$739$		−	3186.25i		−	0.158604i	0.996851	−	0.0793018i	$-0.0252691\pi$
$740$	−18374.2	+	32644.7i	−0.912767	+	1.62168i
$741$		−	8430.00i		−	0.417927i
$742$	−1243.62	+	27826.3i	−0.0615294	+	1.37673i
$743$	−8149.04	−	8149.04i	−0.402368	−	0.402368i	0.476699	−	0.879067i	$-0.341833\pi$
$743$	−8149.04	−	8149.04i	−0.402368	−	0.402368i	−0.879067	+	0.476699i	$0.841833\pi$
$744$			12602.8i			0.621024i
$745$	4292.32	−	1200.61i	0.211085	−	0.0590429i
$746$	−27311.0			−1.34038
$747$	21684.7	+	21684.7i	1.06212	+	1.06212i
$748$	18555.3	−	18555.3i	0.907018	−	0.907018i
$749$	−12324.1	−	13477.3i	−0.601221	−	0.657475i
$750$	−33705.0	+	35993.7i	−1.64098	+	1.75240i
$751$	−33944.9			−1.64936			−0.824679	−	0.565601i	$-0.808644\pi$
$751$	−33944.9			−1.64936			−0.824679	+	0.565601i	$0.808644\pi$
$752$	9347.61	+	9347.61i	0.453287	+	0.453287i
$753$	14398.3	+	14398.3i	0.696818	+	0.696818i
$754$	49235.4			2.37805
$755$	−10458.0	−	37388.5i	−0.504113	−	1.80226i
$756$	7895.09	+	8633.81i	0.379817	+	0.415355i
$757$	−1632.37	+	1632.37i	−0.0783743	+	0.0783743i	−0.745207	−	0.666833i	$-0.767649\pi$
$757$	−1632.37	+	1632.37i	−0.0783743	+	0.0783743i	0.666833	+	0.745207i	$0.267649\pi$
$758$	21427.1	+	21427.1i	1.02674	+	1.02674i
$759$	−972.244			−0.0464957
$760$	−5830.14	+	10358.2i	−0.278265	+	0.494384i
$761$			8358.98i			0.398177i	0.979981	+	0.199089i	$0.0637982\pi$
$761$			8358.98i			0.398177i	−0.979981	+	0.199089i	$0.936202\pi$
$762$	−24394.7	−	24394.7i	−1.15975	−	1.15975i
$763$	16094.7	+	719.311i	0.763654	+	0.0341295i
$764$		−	24543.3i		−	1.16223i
$765$	−10399.1	−	5853.16i	−0.491478	−	0.276629i
$766$			40586.3i			1.91442i
$767$	8852.78	−	8852.78i	0.416761	−	0.416761i
$768$	39337.9	−	39337.9i	1.84829	−	1.84829i
$769$	26741.8			1.25401			0.627006	−	0.779014i	$-0.284280\pi$
$769$	26741.8			1.25401			0.627006	+	0.779014i	$0.284280\pi$
$770$	16966.8	−	27224.3i	0.794079	−	1.27415i
$771$	25035.2			1.16942
$772$	57561.6	−	57561.6i	2.68353	−	2.68353i
$773$	842.330	−	842.330i	0.0391934	−	0.0391934i	−0.687238	−	0.726432i	$-0.741177\pi$
$773$	842.330	−	842.330i	0.0391934	−	0.0391934i	0.726432	+	0.687238i	$0.241177\pi$
$774$			30148.2i			1.40007i
$775$	2439.80	+	4020.07i	0.113084	+	0.186329i
$776$			62192.7i			2.87705i
$777$	−24762.1	−	1106.68i	−1.14329	−	0.0510962i
$778$	19781.1	+	19781.1i	0.911551	+	0.911551i
$779$			7247.88i			0.333353i
$780$	−20028.0	−	71602.4i	−0.919382	−	3.28690i
$781$	14546.8			0.666485
$782$	−791.462	−	791.462i	−0.0361926	−	0.0361926i
$783$	4576.99	−	4576.99i	0.208900	−	0.208900i
$784$	34880.7	+	3124.04i	1.58895	+	0.142312i
$785$	−4001.65	+	7109.59i	−0.181943	+	0.323251i
$786$	65177.3			2.95776
$787$	−5939.92	−	5939.92i	−0.269041	−	0.269041i	0.559673	−	0.828714i	$-0.310927\pi$
$787$	−5939.92	−	5939.92i	−0.269041	−	0.269041i	−0.828714	+	0.559673i	$0.810927\pi$
$788$	−21121.2	−	21121.2i	−0.954838	−	0.954838i
$789$	−42962.7			−1.93855
$790$	17613.4	−	31293.2i	0.793238	−	1.40932i
$791$	−15227.8	+	13924.9i	−0.684496	+	0.625930i
$792$	−22707.9	+	22707.9i	−1.01880	+	1.01880i
$793$	1428.83	+	1428.83i	0.0639837	+	0.0639837i
$794$	25478.4			1.13879
$795$	−6268.77	−	22411.5i	−0.279661	−	0.999819i
$796$		−	23584.2i		−	1.05015i
$797$	−11178.2	−	11178.2i	−0.496803	−	0.496803i	0.413639	−	0.910441i	$-0.364258\pi$
$797$	−11178.2	−	11178.2i	−0.496803	−	0.496803i	−0.910441	+	0.413639i	$0.864258\pi$
$798$	−14477.4	−	647.028i	−0.642222	−	0.0287024i
$799$			6329.69i			0.280261i
$800$	−3921.01	+	16028.5i	−0.173286	+	0.708366i
$801$		−	26325.3i		−	1.16125i
$802$	1086.46	−	1086.46i	0.0478356	−	0.0478356i
$803$	−19703.8	+	19703.8i	−0.865917	+	0.865917i
$804$	56248.1			2.46731
$805$	−796.844	−	496.611i	−0.0348883	−	0.0217431i
$806$	−10332.8			−0.451559
$807$	3553.94	−	3553.94i	0.155024	−	0.155024i
$808$	10018.2	−	10018.2i	0.436187	−	0.436187i
$809$		−	8276.48i		−	0.359685i	−0.983695	−	0.179843i	$-0.942441\pi$
$809$		−	8276.48i		−	0.359685i	0.983695	−	0.179843i	$-0.0575589\pi$
$810$	−41412.8	−	23309.3i	−1.79642	−	1.01112i
$811$			38978.8i			1.68771i	0.536572	+	0.843854i	$0.319719\pi$
$811$			38978.8i			1.68771i	−0.536572	+	0.843854i	$0.680281\pi$
$812$	2593.15	−	58022.2i	0.112071	−	2.50761i
$813$	−25004.8	−	25004.8i	−1.07867	−	1.07867i
$814$			29670.9i			1.27760i
$815$	546.988	−	971.815i	0.0235094	−	0.0417683i
$816$	−34879.8			−1.49637
$817$	4288.57	+	4288.57i	0.183645	+	0.183645i
$818$	−42191.4	+	42191.4i	−1.80341	+	1.80341i
$819$	16231.9	−	14843.1i	0.692539	−	0.633285i
$820$	17219.5	+	61561.7i	0.733331	+	2.62174i
$821$	−23105.0			−0.982180			−0.491090	−	0.871109i	$-0.663401\pi$
$821$	−23105.0			−0.982180			−0.491090	+	0.871109i	$0.663401\pi$
$822$	54057.9	+	54057.9i	2.29378	+	2.29378i
$823$	3288.90	+	3288.90i	0.139300	+	0.139300i	0.773318	−	0.634018i	$-0.218596\pi$
$823$	3288.90	+	3288.90i	0.139300	+	0.139300i	−0.634018	+	0.773318i	$0.718596\pi$
$824$	4050.45			0.171243
$825$	−6368.56	+	26033.7i	−0.268757	+	1.09864i
$826$	−14524.0	−	15882.9i	−0.611808	−	0.669053i
$827$	786.261	−	786.261i	0.0330604	−	0.0330604i	−0.690383	−	0.723444i	$-0.742558\pi$
$827$	786.261	−	786.261i	0.0330604	−	0.0330604i	0.723444	+	0.690383i	$0.242558\pi$
$828$	1224.68	+	1224.68i	0.0514017	+	0.0514017i
$829$	−24870.0			−1.04194			−0.520971	−	0.853575i	$-0.674430\pi$
$829$	−24870.0			−1.04194			−0.520971	+	0.853575i	$0.674430\pi$
$830$	76362.5	−	21359.5i	3.19347	−	0.893251i
$831$			3614.24i			0.150874i
$832$	5779.70	+	5779.70i	0.240835	+	0.240835i
$833$	10751.9	+	12867.4i	0.447218	+	0.535207i
$834$		−	5652.13i		−	0.234673i
$835$	−9367.32	+	16642.6i	−0.388227	+	0.689749i
$836$			11903.9i			0.492469i
$837$	−960.549	+	960.549i	−0.0396672	+	0.0396672i
$838$	22422.6	−	22422.6i	0.924314	−	0.924314i
$839$	−22765.1			−0.936755			−0.468378	−	0.883528i	$-0.655161\pi$
$839$	−22765.1			−0.936755			−0.468378	+	0.883528i	$0.655161\pi$
$840$	−67570.1	+	15684.2i	−2.77547	+	0.644234i
$841$	−7744.68			−0.317548
$842$	−19968.7	+	19968.7i	−0.817299	+	0.817299i
$843$	−4518.11	+	4518.11i	−0.184593	+	0.184593i
$844$			21731.9i			0.886309i
$845$	8204.80	−	2294.98i	0.334028	−	0.0934315i
$846$		−	14273.2i		−	0.580049i
$847$	−322.144	+	7208.03i	−0.0130685	+	0.292410i
$848$	−21504.5	−	21504.5i	−0.870835	−	0.870835i
$849$		−	65312.2i		−	2.64017i
$850$	−26377.2	+	16008.5i	−1.06439	+	0.645985i
$851$	868.455			0.0349827
$852$	−40984.3	−	40984.3i	−1.64800	−	1.64800i
$853$	−11703.5	+	11703.5i	−0.469777	+	0.469777i	−0.901842	−	0.432065i	$-0.857785\pi$
$853$	−11703.5	+	11703.5i	−0.469777	+	0.469777i	0.432065	+	0.901842i	$0.357785\pi$
$854$	2563.48	−	2344.15i	0.102717	−	0.0939286i
$855$	5213.19	−	1458.19i	0.208523	−	0.0583263i
$856$	47272.3			1.88754
$857$	−25881.3	−	25881.3i	−1.03161	−	1.03161i	−0.999484	−	0.0321229i	$-0.989773\pi$
$857$	−25881.3	−	25881.3i	−1.03161	−	1.03161i	−0.0321229	−	0.999484i	$-0.510227\pi$
$858$	−41641.7	−	41641.7i	−1.65690	−	1.65690i
$859$	−11267.9			−0.447563			−0.223782	−	0.974639i	$-0.571840\pi$
$859$	−11267.9			−0.447563			−0.223782	+	0.974639i	$0.571840\pi$
$860$	46614.9	+	26237.3i	1.84832	+	1.04033i
$861$	−31214.5	+	28543.7i	−1.23552	+	1.12981i
$862$	−11466.6	+	11466.6i	−0.453077	+	0.453077i
$863$	21760.8	+	21760.8i	0.858338	+	0.858338i	0.991142	−	0.132804i	$-0.0423980\pi$
$863$	21760.8	+	21760.8i	0.858338	+	0.858338i	−0.132804	+	0.991142i	$0.542398\pi$
$864$	−4766.71			−0.187693
$865$	11032.9	+	6209.87i	0.433674	+	0.244095i
$866$		−	64251.6i		−	2.52120i
$867$	12467.2	+	12467.2i	0.488361	+	0.488361i
$868$	−544.210	+	12176.8i	−0.0212807	+	0.476161i
$869$		−	19517.4i		−	0.761891i
$870$	19048.7	+	68101.4i	0.742314	+	2.65386i
$871$			25028.0i			0.973642i
$872$	−29488.1	+	29488.1i	−1.14518	+	1.14518i
$873$	20028.1	−	20028.1i	0.776460	−	0.776460i
$874$	507.750			0.0196509
$875$	−18517.3	+	18084.0i	−0.715427	+	0.698687i
$876$	111027.			4.28227
$877$	−10089.3	+	10089.3i	−0.388473	+	0.388473i	−0.874143	−	0.485669i	$-0.838576\pi$
$877$	−10089.3	+	10089.3i	−0.388473	+	0.388473i	0.485669	+	0.874143i	$0.338576\pi$
$878$	54951.9	−	54951.9i	2.11223	−	2.11223i
$879$			16183.1i			0.620982i
$880$	9434.62	+	33729.8i	0.361410	+	1.29208i
$881$		−	12811.2i		−	0.489920i	−0.969533	−	0.244960i	$-0.921225\pi$
$881$		−	12811.2i		−	0.489920i	0.969533	−	0.244960i	$-0.0787748\pi$
$882$	−24245.2	−	29015.4i	−0.925598	−	1.10771i
$883$	−30984.3	−	30984.3i	−1.18086	−	1.18086i	−0.979521	−	0.201344i	$-0.935469\pi$
$883$	−30984.3	−	30984.3i	−1.18086	−	1.18086i	−0.201344	−	0.979521i	$-0.564531\pi$
$884$		−	46523.0i		−	1.77006i
$885$	15670.1	+	8819.93i	0.595190	+	0.335004i
$886$	42703.8			1.61926
$887$	−15820.5	−	15820.5i	−0.598871	−	0.598871i	0.341141	−	0.940012i	$-0.389187\pi$
$887$	−15820.5	−	15820.5i	−0.598871	−	0.598871i	−0.940012	+	0.341141i	$0.889187\pi$
$888$	45368.1	−	45368.1i	1.71448	−	1.71448i
$889$	−12220.1	−	13363.5i	−0.461022	−	0.504159i
$890$	−59317.3	−	33386.9i	−2.23407	−	1.25745i
$891$	−25829.0			−0.971160
$892$	−14049.1	−	14049.1i	−0.527353	−	0.527353i
$893$	−2030.36	−	2030.36i	−0.0760843	−	0.0760843i
$894$	−14066.1			−0.526219
$895$	15454.4	−	4322.78i	0.577189	−	0.161446i
$896$	24803.2	−	22681.1i	0.924797	−	0.845671i
$897$	−1218.83	+	1218.83i	−0.0453687	+	0.0453687i
$898$	−34384.6	−	34384.6i	−1.27776	−	1.27776i
$899$	6743.72			0.250184
$900$	40815.2	−	24771.0i	1.51168	−	0.917445i
$901$		−	14561.7i		−	0.538424i
$902$	35802.3	+	35802.3i	1.32160	+	1.32160i
$903$	−1580.27	+	35358.9i	−0.0582372	+	1.30307i
$904$		−	53412.3i		−	1.96512i
$905$	38081.7	−	10651.9i	1.39876	−	0.391249i
$906$			122523.i			4.49290i
$907$	−24731.1	+	24731.1i	−0.905384	+	0.905384i	−0.995895	−	0.0905113i	$-0.971150\pi$
$907$	−24731.1	+	24731.1i	−0.905384	+	0.905384i	0.0905113	+	0.995895i	$0.471150\pi$
$908$	−55823.1	+	55823.1i	−2.04026	+	2.04026i
$909$	−6452.39			−0.235437
$910$	−12859.1	−	55399.3i	−0.468435	−	2.01810i
$911$	24805.3			0.902127			0.451063	−	0.892492i	$-0.351045\pi$
$911$	24805.3			0.902127			0.451063	+	0.892492i	$0.351045\pi$
$912$	11188.3	−	11188.3i	0.406230	−	0.406230i
$913$	30474.4	−	30474.4i	1.10466	−	1.10466i
$914$			76754.6i			2.77770i
$915$	−1423.52	+	2529.12i	−0.0514319	+	0.0913773i
$916$		−	75447.1i		−	2.72144i
$917$	34176.8	+	1527.44i	1.23077	+	0.0550061i
$918$	−6302.54	−	6302.54i	−0.226596	−	0.226596i
$919$		−	33228.1i		−	1.19270i	−0.802724	−	0.596351i	$-0.796617\pi$
$919$		−	33228.1i		−	1.19270i	0.802724	−	0.596351i	$-0.203383\pi$
$920$	2340.56	−	654.681i	0.0838760	−	0.0234611i
$921$	−22819.8			−0.816435
$922$	−26491.1	−	26491.1i	−0.946245	−	0.946245i
$923$	18236.3	−	18236.3i	0.650329	−	0.650329i
$924$	−51266.5	+	46880.1i	−1.82526	+	1.66909i
$925$	5688.70	−	23254.5i	0.202209	−	0.826599i
$926$	−55907.3			−1.98405
$927$	−1304.38	−	1304.38i	−0.0462152	−	0.0462152i
$928$	16732.8	+	16732.8i	0.591898	+	0.591898i
$929$	41777.1			1.47542			0.737708	−	0.675120i	$-0.235908\pi$
$929$	41777.1			1.47542			0.737708	+	0.675120i	$0.235908\pi$
$930$	−3997.66	−	14292.1i	−0.140955	−	0.503931i
$931$	−7576.29	−	678.560i	−0.266706	−	0.0238871i
$932$	−78927.8	+	78927.8i	−2.77400	+	2.77400i
$933$	19964.1	+	19964.1i	0.700530	+	0.700530i
$934$	−15972.7			−0.559576
$935$	−8225.69	+	14614.3i	−0.287710	+	0.511164i
$936$			56934.5i			1.98821i
$937$	−12969.5	−	12969.5i	−0.452183	−	0.452183i	0.443896	−	0.896078i	$-0.353596\pi$
$937$	−12969.5	−	12969.5i	−0.452183	−	0.452183i	−0.896078	+	0.443896i	$0.853596\pi$
$938$	42982.2	+	1920.97i	1.49618	+	0.0668678i
$939$			25017.8i			0.869462i
$940$	−22069.1	−	12421.6i	−0.765760	−	0.431010i
$941$		−	6982.50i		−	0.241895i	−0.992659	−	0.120947i	$-0.961407\pi$
$941$		−	6982.50i		−	0.241895i	0.992659	−	0.120947i	$-0.0385932\pi$
$942$	18206.0	−	18206.0i	0.629705	−	0.629705i
$943$	1047.92	−	1047.92i	0.0361876	−	0.0361876i
$944$	23498.8			0.810193
$945$	−6345.40	−	3954.59i	−0.218429	−	0.136130i
$946$	42368.5			1.45615
$947$	12625.2	−	12625.2i	0.433226	−	0.433226i	−0.456498	−	0.889724i	$-0.650897\pi$
$947$	12625.2	−	12625.2i	0.433226	−	0.433226i	0.889724	+	0.456498i	$0.150897\pi$
$948$	−54988.6	+	54988.6i	−1.88391	+	1.88391i
$949$			49402.5i			1.68985i
$950$	3325.95	−	13596.0i	0.113587	−	0.464327i
$951$		−	23666.2i		−	0.806972i
$952$	−43361.0	−	1937.90i	−1.47619	−	0.0659746i
$953$	77.2788	+	77.2788i	0.00262676	+	0.00262676i	0.708419	−	0.705792i	$-0.249409\pi$
$953$	77.2788	+	77.2788i	0.00262676	+	0.00262676i	−0.705792	+	0.708419i	$0.749409\pi$
$954$			32836.0i			1.11436i
$955$	4225.13	+	15105.3i	0.143164	+	0.511829i
$956$	−21327.2			−0.721517
$957$	27177.6	+	27177.6i	0.918001	+	0.918001i
$958$	57578.7	−	57578.7i	1.94184	−	1.94184i
$959$	27079.3	+	29613.0i	0.911822	+	0.997138i
$960$	−5758.25	+	10230.5i	−0.193590	+	0.343945i
$961$	28375.7			0.952493
$962$	37196.3	+	37196.3i	1.24663	+	1.24663i
$963$	−15223.3	−	15223.3i	−0.509411	−	0.509411i
$964$	39651.5			1.32478
$965$	−25517.4	+	45335.9i	−0.851228	+	1.51235i
$966$	1999.63	+	2186.73i	0.0666015	+	0.0728332i
$967$	9581.76	−	9581.76i	0.318644	−	0.318644i	−0.529602	−	0.848246i	$-0.677659\pi$
$967$	9581.76	−	9581.76i	0.318644	−	0.318644i	0.848246	+	0.529602i	$0.177659\pi$
$968$	−13206.3	−	13206.3i	−0.438498	−	0.438498i
$969$	7576.11			0.251166
$970$	−19727.8	−	70529.0i	−0.653011	−	2.33459i
$971$			8228.52i			0.271952i	0.990712	+	0.135976i	$0.0434171\pi$
$971$			8228.52i			0.271952i	−0.990712	+	0.135976i	$0.956583\pi$
$972$	60710.4	+	60710.4i	2.00338	+	2.00338i
$973$	132.459	−	2963.79i	0.00436427	−	0.0976514i
$974$			56657.5i			1.86388i
$975$	24652.8	+	40620.4i	0.809764	+	1.33425i
$976$			3792.68i			0.124386i
$977$	37618.1	−	37618.1i	1.23184	−	1.23184i	0.268587	−	0.963256i	$-0.413443\pi$
$977$	37618.1	−	37618.1i	1.23184	−	1.23184i	0.963256	−	0.268587i	$-0.0865566\pi$
$978$	−2488.58	+	2488.58i	−0.0813662	+	0.0813662i
$979$	−36996.0			−1.20776
$980$	−65963.4	+	12236.3i	−2.15013	+	0.398850i
$981$	18992.3			0.618123
$982$	14853.9	−	14853.9i	0.482695	−	0.482695i
$983$	6732.17	−	6732.17i	0.218436	−	0.218436i	−0.589403	−	0.807839i	$-0.700637\pi$
$983$	6732.17	−	6732.17i	0.218436	−	0.218436i	0.807839	+	0.589403i	$0.200637\pi$
$984$		−	109487.i		−	3.54706i
$985$	16635.2	+	9363.18i	0.538114	+	0.302879i
$986$			44248.2i			1.42916i
$987$	748.155	−	16740.1i	0.0241277	−	0.539862i
$988$	14923.0	+	14923.0i	0.480532	+	0.480532i
$989$		−	1240.11i		−	0.0398717i
$990$	18548.6	−	32954.6i	0.595467	−	1.05795i
$991$	−26503.0			−0.849543			−0.424771	−	0.905301i	$-0.639646\pi$
$991$	−26503.0			−0.849543			−0.424771	+	0.905301i	$0.639646\pi$
$992$	−3511.62	−	3511.62i	−0.112393	−	0.112393i
$993$	−7950.88	+	7950.88i	−0.254092	+	0.254092i
$994$	−29918.6	−	32718.0i	−0.954688	−	1.04401i
$995$	4060.03	+	14515.1i	0.129358	+	0.462471i
$996$	−171718.			−5.46294
$997$	20316.7	+	20316.7i	0.645372	+	0.645372i	0.951871	−	0.306499i	$-0.0991576\pi$
$997$	20316.7	+	20316.7i	0.645372	+	0.645372i	−0.306499	+	0.951871i	$0.599158\pi$
$998$	−20917.8	−	20917.8i	−0.663470	−	0.663470i
$999$	6915.65			0.219020

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.4.f.b.13.1	✓	16
5.2	odd	4	inner	35.4.f.b.27.2	yes	16
5.3	odd	4		175.4.f.g.132.7		16
5.4	even	2		175.4.f.g.118.8		16
7.2	even	3		245.4.l.b.178.7		32
7.3	odd	6		245.4.l.b.68.1		32
7.4	even	3		245.4.l.b.68.2		32
7.5	odd	6		245.4.l.b.178.8		32
7.6	odd	2	inner	35.4.f.b.13.2	yes	16
35.2	odd	12		245.4.l.b.227.1		32
35.12	even	12		245.4.l.b.227.2		32
35.13	even	4		175.4.f.g.132.8		16
35.17	even	12		245.4.l.b.117.7		32
35.27	even	4	inner	35.4.f.b.27.1	yes	16
35.32	odd	12		245.4.l.b.117.8		32
35.34	odd	2		175.4.f.g.118.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.f.b.13.1	✓	16	1.1	even	1	trivial
35.4.f.b.13.2	yes	16	7.6	odd	2	inner
35.4.f.b.27.1	yes	16	35.27	even	4	inner
35.4.f.b.27.2	yes	16	5.2	odd	4	inner
175.4.f.g.118.7		16	35.34	odd	2
175.4.f.g.118.8		16	5.4	even	2
175.4.f.g.132.7		16	5.3	odd	4
175.4.f.g.132.8		16	35.13	even	4
245.4.l.b.68.1		32	7.3	odd	6
245.4.l.b.68.2		32	7.4	even	3
245.4.l.b.117.7		32	35.17	even	12
245.4.l.b.117.8		32	35.32	odd	12
245.4.l.b.178.7		32	7.2	even	3
245.4.l.b.178.8		32	7.5	odd	6
245.4.l.b.227.1		32	35.2	odd	12
245.4.l.b.227.2		32	35.12	even	12

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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	35.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.57033 + 3.57033i) q^{2} +(-4.94129 + 4.94129i) q^{3} -17.4944i q^{4} +(3.01167 + 10.7671i) q^{5} -35.2840i q^{6} +(0.826888 - 18.5018i) q^{7} +(33.8983 + 33.8983i) q^{8} -21.8328i q^{9} +(-49.1946 - 27.6893i) q^{10} -30.6825 q^{11} +(86.4452 + 86.4452i) q^{12} +(-38.4644 + 38.4644i) q^{13} +(63.1052 + 69.0097i) q^{14} +(-68.0848 - 38.3217i) q^{15} -102.100 q^{16} +(-34.5683 - 34.5683i) q^{17} +(77.9500 + 77.9500i) q^{18} +22.1767 q^{19} +(188.364 - 52.6875i) q^{20} +(87.3369 + 95.5087i) q^{21} +(109.546 - 109.546i) q^{22} +(-3.20638 - 3.20638i) q^{23} -335.002 q^{24} +(-106.860 + 64.8538i) q^{25} -274.661i q^{26} +(-25.5329 - 25.5329i) q^{27} +(-323.679 - 14.4660i) q^{28} +179.259i q^{29} +(379.906 - 106.264i) q^{30} -37.6201i q^{31} +(93.3444 - 93.3444i) q^{32} +(151.611 - 151.611i) q^{33} +246.840 q^{34} +(201.700 - 46.8182i) q^{35} -381.952 q^{36} +(-135.426 + 135.426i) q^{37} +(-79.1782 + 79.1782i) q^{38} -380.128i q^{39} +(-262.895 + 467.076i) q^{40} +326.823i q^{41} +(-652.818 - 29.1760i) q^{42} +(193.381 + 193.381i) q^{43} +536.773i q^{44} +(235.075 - 65.7531i) q^{45} +22.8956 q^{46} +(-91.5534 - 91.5534i) q^{47} +(504.506 - 504.506i) q^{48} +(-341.633 - 30.5978i) q^{49} +(149.975 - 613.073i) q^{50} +341.624 q^{51} +(672.914 + 672.914i) q^{52} +(210.622 + 210.622i) q^{53} +182.321 q^{54} +(-92.4056 - 330.360i) q^{55} +(655.209 - 599.149i) q^{56} +(-109.582 + 109.582i) q^{57} +(-640.012 - 640.012i) q^{58} -230.155 q^{59} +(-670.417 + 1191.11i) q^{60} -37.1467i q^{61} +(134.316 + 134.316i) q^{62} +(-403.945 - 18.0532i) q^{63} -150.261i q^{64} +(-529.992 - 298.307i) q^{65} +1082.60i q^{66} +(325.340 - 325.340i) q^{67} +(-604.753 + 604.753i) q^{68} +31.6873 q^{69} +(-552.980 + 887.292i) q^{70} -474.107 q^{71} +(740.092 - 740.092i) q^{72} +(642.183 - 642.183i) q^{73} -967.032i q^{74} +(207.563 - 848.486i) q^{75} -387.970i q^{76} +(-25.3710 + 567.681i) q^{77} +(1357.18 + 1357.18i) q^{78} +636.110i q^{79} +(-307.492 - 1099.32i) q^{80} +841.815 q^{81} +(-1166.87 - 1166.87i) q^{82} +(-993.219 + 993.219i) q^{83} +(1670.87 - 1527.91i) q^{84} +(268.091 - 476.308i) q^{85} -1380.87 q^{86} +(-885.770 - 885.770i) q^{87} +(-1040.08 - 1040.08i) q^{88} +1205.77 q^{89} +(-604.534 + 1074.05i) q^{90} +(679.855 + 743.467i) q^{91} +(-56.0938 + 56.0938i) q^{92} +(185.892 + 185.892i) q^{93} +653.751 q^{94} +(66.7891 + 238.779i) q^{95} +922.484i q^{96} +(917.344 + 917.344i) q^{97} +(1328.98 - 1110.50i) q^{98} +669.883i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 32 q^{7} + 176 q^{8} - 152 q^{11} - 480 q^{15} - 504 q^{16} + 288 q^{18} + 328 q^{21} + 348 q^{22} - 72 q^{23} - 160 q^{25} - 528 q^{28} + 1780 q^{30} + 432 q^{32} + 160 q^{35} + 344 q^{36}+ \cdots + 3308 q^{98}+O(q^{100}) \) 16 * q + 4 * q^2 + 32 * q^7 + 176 * q^8 - 152 * q^11 - 480 * q^15 - 504 * q^16 + 288 * q^18 + 328 * q^21 + 348 * q^22 - 72 * q^23 - 160 * q^25 - 528 * q^28 + 1780 * q^30 + 432 * q^32 + 160 * q^35 + 344 * q^36 - 256 * q^37 - 1300 * q^42 - 312 * q^43 - 1856 * q^46 - 20 * q^50 + 696 * q^51 + 1768 * q^53 + 1304 * q^56 - 3920 * q^57 - 4764 * q^58 - 2000 * q^60 + 2544 * q^63 - 1000 * q^65 + 4504 * q^67 - 180 * q^70 + 6368 * q^71 + 7848 * q^72 - 3016 * q^77 + 5340 * q^78 - 3088 * q^81 - 2280 * q^85 - 9336 * q^86 - 2048 * q^88 + 1608 * q^91 - 6328 * q^92 - 3960 * q^93 + 1240 * q^95 + 3308 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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