LMFDB - Embedded newform 147.4.g.d.68.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,4,Mod(68,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("147.68");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.g (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.67328077084$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 29x^{9} + 6x^{8} - 49x^{7} + 1564x^{6} - 441x^{5} + 486x^{4} - 21141x^{3} - 59049x + 531441 $ x^12 - x^11 - 29x^9 + 6x^8 - 49x^7 + 1564x^6 - 441x^5 + 486x^4 - 21141x^3 - 59049x + 531441
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.2
Root			$0.00299931 - 3.00000i$ of defining polynomial
Character	$\chi$	$=$	147.68
Dual form			147.4.g.d.80.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.24076 - 1.29370i) q^{2} +(-5.19615 - 0.00519496i) q^{3} +(-0.652660 - 1.13044i) q^{4} +(-8.05907 + 13.9587i) q^{5} +(11.6366 + 6.73392i) q^{6} +24.0767i q^{8} +(26.9999 + 0.0539876i) q^{9} +O(q^{10})$	\(q+(-2.24076 - 1.29370i) q^{2} +(-5.19615 - 0.00519496i) q^{3} +(-0.652660 - 1.13044i) q^{4} +(-8.05907 + 13.9587i) q^{5} +(11.6366 + 6.73392i) q^{6} +24.0767i q^{8} +(26.9999 + 0.0539876i) q^{9} +(36.1169 - 20.8521i) q^{10} +(-30.8296 + 17.7995i) q^{11} +(3.38545 + 5.87733i) q^{12} -7.40831i q^{13} +(41.9486 - 72.4897i) q^{15} +(25.9268 - 44.9065i) q^{16} +(-14.4601 - 25.0457i) q^{17} +(-60.4306 - 35.0509i) q^{18} +(-30.4580 - 17.5849i) q^{19} +21.0393 q^{20} +92.1090 q^{22} +(-48.0017 - 27.7138i) q^{23} +(0.125077 - 125.106i) q^{24} +(-67.3971 - 116.735i) q^{25} +(-9.58416 + 16.6003i) q^{26} +(-140.295 - 0.420792i) q^{27} -68.1510i q^{29} +(-187.777 + 108.163i) q^{30} +(154.734 - 89.3356i) q^{31} +(50.6165 - 29.2234i) q^{32} +(160.288 - 92.3286i) q^{33} +74.8285i q^{34} +(-17.5608 - 30.5571i) q^{36} +(116.838 - 202.370i) q^{37} +(45.4994 + 78.8072i) q^{38} +(-0.0384859 + 38.4947i) q^{39} +(-336.079 - 194.035i) q^{40} +370.068 q^{41} -187.068 q^{43} +(40.2425 + 23.2340i) q^{44} +(-218.348 + 376.449i) q^{45} +(71.7068 + 124.200i) q^{46} +(-87.3726 + 151.334i) q^{47} +(-134.953 + 233.206i) q^{48} +348.768i q^{50} +(75.0068 + 130.216i) q^{51} +(-8.37465 + 4.83511i) q^{52} +(235.715 - 136.090i) q^{53} +(313.824 + 182.444i) q^{54} -573.789i q^{55} +(158.173 + 91.5321i) q^{57} +(-88.1672 + 152.710i) q^{58} +(-48.4354 - 83.8926i) q^{59} +(-109.323 - 0.109298i) q^{60} +(333.882 + 192.767i) q^{61} -462.295 q^{62} -566.055 q^{64} +(103.411 + 59.7041i) q^{65} +(-478.612 - 0.478503i) q^{66} +(509.009 + 881.630i) q^{67} +(-18.8751 + 32.6926i) q^{68} +(249.280 + 144.254i) q^{69} -125.333i q^{71} +(-1.29984 + 650.068i) q^{72} +(-195.346 + 112.783i) q^{73} +(-523.613 + 302.308i) q^{74} +(349.599 + 606.924i) q^{75} +45.9079i q^{76} +(49.8870 - 86.2076i) q^{78} +(532.154 - 921.718i) q^{79} +(417.891 + 723.809i) q^{80} +(728.994 + 2.91533i) q^{81} +(-829.234 - 478.758i) q^{82} -601.040 q^{83} +466.140 q^{85} +(419.175 + 242.011i) q^{86} +(-0.354042 + 354.123i) q^{87} +(-428.552 - 742.274i) q^{88} +(752.606 - 1303.55i) q^{89} +(976.280 - 561.055i) q^{90} +72.3506i q^{92} +(-804.484 + 463.397i) q^{93} +(391.562 - 226.069i) q^{94} +(490.926 - 283.436i) q^{95} +(-263.163 + 151.586i) q^{96} +327.463i q^{97} +(-833.358 + 478.920i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} + 14 q^{4} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 + 14 * q^4 - 3 * q^9	$ 12 q + 3 q^{3} + 14 q^{4} - 3 q^{9} - 30 q^{10} + 192 q^{12} + 6 q^{15} + 134 q^{16} + 66 q^{18} - 300 q^{19} - 268 q^{22} - 414 q^{24} - 42 q^{25} - 822 q^{30} + 930 q^{31} + 855 q^{33} + 852 q^{36} + 764 q^{37} - 426 q^{39} - 2298 q^{40} - 1012 q^{43} - 2367 q^{45} + 608 q^{46} - 1341 q^{51} + 3000 q^{52} + 4158 q^{54} + 270 q^{57} + 2870 q^{58} - 918 q^{60} - 2358 q^{61} - 548 q^{64} - 2934 q^{66} + 792 q^{67} - 2712 q^{72} + 2904 q^{73} + 2418 q^{75} + 4296 q^{78} + 1674 q^{79} + 837 q^{81} - 5040 q^{82} + 348 q^{85} - 1638 q^{87} - 554 q^{88} - 1479 q^{93} + 1356 q^{94} + 4410 q^{96} - 3354 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 + 14 * q^4 - 3 * q^9 - 30 * q^10 + 192 * q^12 + 6 * q^15 + 134 * q^16 + 66 * q^18 - 300 * q^19 - 268 * q^22 - 414 * q^24 - 42 * q^25 - 822 * q^30 + 930 * q^31 + 855 * q^33 + 852 * q^36 + 764 * q^37 - 426 * q^39 - 2298 * q^40 - 1012 * q^43 - 2367 * q^45 + 608 * q^46 - 1341 * q^51 + 3000 * q^52 + 4158 * q^54 + 270 * q^57 + 2870 * q^58 - 918 * q^60 - 2358 * q^61 - 548 * q^64 - 2934 * q^66 + 792 * q^67 - 2712 * q^72 + 2904 * q^73 + 2418 * q^75 + 4296 * q^78 + 1674 * q^79 + 837 * q^81 - 5040 * q^82 + 348 * q^85 - 1638 * q^87 - 554 * q^88 - 1479 * q^93 + 1356 * q^94 + 4410 * q^96 - 3354 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−2.24076	−	1.29370i	−0.792229	−	0.457393i	0.0485179	−	0.998822i	$-0.484550\pi$
$2$	−2.24076	−	1.29370i	−0.792229	−	0.457393i	−0.840747	+	0.541429i	$0.817884\pi$
$3$	−5.19615	−	0.00519496i	−1.00000	−	0.000999771i
$3$	−5.19615	−	0.00519496i	−1.00000	−	0.000999771i
$4$	−0.652660	−	1.13044i	−0.0815825	−	0.141305i
$5$	−8.05907	+	13.9587i	−0.720825	+	1.24851i	0.239845	+	0.970811i	$0.422903\pi$
$5$	−8.05907	+	13.9587i	−0.720825	+	1.24851i	−0.960670	+	0.277694i	$0.910430\pi$
$6$	11.6366	+	6.73392i	0.791771	+	0.458185i
$7$		0			0
$7$		0			0
$8$			24.0767i			1.06405i
$9$	26.9999	+	0.0539876i	0.999998	+	0.00199954i
$10$	36.1169	−	20.8521i	1.14212	−	0.659401i
$11$	−30.8296	+	17.7995i	−0.845043	+	0.487886i	−0.858975	−	0.512017i	$-0.828898\pi$
$11$	−30.8296	+	17.7995i	−0.845043	+	0.487886i	0.0139322	+	0.999903i	$0.495565\pi$
$12$	3.38545	+	5.87733i	0.0814412	+	0.141386i
$13$		−	7.40831i		−	0.158054i	−0.996872	−	0.0790268i	$-0.974819\pi$
$13$		−	7.40831i		−	0.158054i	0.996872	−	0.0790268i	$-0.0251813\pi$
$14$		0			0
$15$	41.9486	−	72.4897i	0.722073	−	1.24778i
$16$	25.9268	−	44.9065i	0.405106	−	0.701664i
$17$	−14.4601	−	25.0457i	−0.206300	−	0.357322i	0.744246	−	0.667905i	$-0.232809\pi$
$17$	−14.4601	−	25.0457i	−0.206300	−	0.357322i	−0.950546	+	0.310584i	$0.899476\pi$
$18$	−60.4306	−	35.0509i	−0.791313	−	0.458977i
$19$	−30.4580	−	17.5849i	−0.367765	−	0.212329i	0.304716	−	0.952443i	$-0.401438\pi$
$19$	−30.4580	−	17.5849i	−0.367765	−	0.212329i	−0.672482	+	0.740114i	$0.734772\pi$
$20$	21.0393			0.235227
$21$		0			0
$22$	92.1090			0.892623
$23$	−48.0017	−	27.7138i	−0.435175	−	0.251249i	0.266374	−	0.963870i	$-0.414175\pi$
$23$	−48.0017	−	27.7138i	−0.435175	−	0.251249i	−0.701549	+	0.712621i	$0.747508\pi$
$24$	0.125077	−	125.106i	0.00106380	−	1.06405i
$25$	−67.3971	−	116.735i	−0.539177	−	0.933881i
$26$	−9.58416	+	16.6003i	−0.0722927	+	0.125215i
$27$	−140.295	−	0.420792i	−0.999996	−	0.00299931i
$28$		0			0
$29$		−	68.1510i		−	0.436390i	−0.975905	−	0.218195i	$-0.929983\pi$
$29$		−	68.1510i		−	0.436390i	0.975905	−	0.218195i	$-0.0700169\pi$
$30$	−187.777	+	108.163i	−1.14277	+	0.658259i
$31$	154.734	−	89.3356i	0.896484	−	0.517585i	0.0204262	−	0.999791i	$-0.493498\pi$
$31$	154.734	−	89.3356i	0.896484	−	0.517585i	0.876058	+	0.482206i	$0.160164\pi$
$32$	50.6165	−	29.2234i	0.279619	−	0.161438i
$33$	160.288	−	92.3286i	0.845530	−	0.487041i
$34$			74.8285i			0.377440i
$35$		0			0
$36$	−17.5608	−	30.5571i	−0.0812998	−	0.141468i
$37$	116.838	−	202.370i	0.519137	−	0.899172i	−0.480615	−	0.876931i	$-0.659587\pi$
$37$	116.838	−	202.370i	0.519137	−	0.899172i	0.999753	−	0.0222405i	$-0.00707996\pi$
$38$	45.4994	+	78.8072i	0.194236	+	0.336427i
$39$	−0.0384859	+	38.4947i	−0.000158017	+	0.158053i
$40$	−336.079	−	194.035i	−1.32847	−	0.766992i
$41$	370.068			1.40963			0.704816	−	0.709390i	$-0.251030\pi$
$41$	370.068			1.40963			0.704816	+	0.709390i	$0.251030\pi$
$42$		0			0
$43$	−187.068			−0.663432			−0.331716	−	0.943379i	$-0.607628\pi$
$43$	−187.068			−0.663432			−0.331716	+	0.943379i	$0.607628\pi$
$44$	40.2425	+	23.2340i	0.137881	+	0.0796059i
$45$	−218.348	+	376.449i	−0.723320	+	1.24706i
$46$	71.7068	+	124.200i	0.229839	+	0.398093i
$47$	−87.3726	+	151.334i	−0.271162	+	0.469666i	−0.969160	−	0.246434i	$-0.920741\pi$
$47$	−87.3726	+	151.334i	−0.271162	+	0.469666i	0.697998	+	0.716100i	$0.254075\pi$
$48$	−134.953	+	233.206i	−0.405807	+	0.701259i
$49$		0			0
$50$			348.768i			0.986464i
$51$	75.0068	+	130.216i	0.205942	+	0.357528i
$52$	−8.37465	+	4.83511i	−0.0223338	+	0.0128944i
$53$	235.715	−	136.090i	0.610905	−	0.352706i	−0.162415	−	0.986723i	$-0.551928\pi$
$53$	235.715	−	136.090i	0.610905	−	0.352706i	0.773319	+	0.634017i	$0.218595\pi$
$54$	313.824	+	182.444i	0.790853	+	0.459768i
$55$		−	573.789i		−	1.40672i
$56$		0			0
$57$	158.173	+	91.5321i	0.367553	+	0.212697i
$58$	−88.1672	+	152.710i	−0.199602	+	0.345721i
$59$	−48.4354	−	83.8926i	−0.106877	−	0.185117i	0.807626	−	0.589695i	$-0.200752\pi$
$59$	−48.4354	−	83.8926i	−0.106877	−	0.185117i	−0.914504	+	0.404578i	$0.867419\pi$
$60$	−109.323	−	0.109298i	−0.235227	−	0.000235173i
$61$	333.882	+	192.767i	0.700807	+	0.404611i	0.807648	−	0.589665i	$-0.200740\pi$
$61$	333.882	+	192.767i	0.700807	+	0.404611i	−0.106841	+	0.994276i	$0.534073\pi$
$62$	−462.295			−0.946960
$63$		0			0
$64$	−566.055			−1.10558
$65$	103.411	+	59.7041i	0.197331	+	0.113929i
$66$	−478.612	−	0.478503i	−0.892623	−	0.000892419i
$67$	509.009	+	881.630i	0.928140	+	1.60759i	0.786432	+	0.617677i	$0.211926\pi$
$67$	509.009	+	881.630i	0.928140	+	1.60759i	0.141708	+	0.989908i	$0.454741\pi$
$68$	−18.8751	+	32.6926i	−0.0336609	+	0.0583023i
$69$	249.280	+	144.254i	0.434924	+	0.251684i
$70$		0			0
$71$		−	125.333i		−	0.209497i	−0.994499	−	0.104749i	$-0.966596\pi$
$71$		−	125.333i		−	0.209497i	0.994499	−	0.104749i	$-0.0334038\pi$
$72$	−1.29984	+	650.068i	−0.00212761	+	1.06405i
$73$	−195.346	+	112.783i	−0.313199	+	0.180825i	−0.648357	−	0.761337i	$-0.724544\pi$
$73$	−195.346	+	112.783i	−0.313199	+	0.180825i	0.335158	+	0.942162i	$0.391210\pi$
$74$	−523.613	+	302.308i	−0.822551	+	0.474900i
$75$	349.599	+	606.924i	0.538243	+	0.934420i
$76$			45.9079i			0.0692894i
$77$		0			0
$78$	49.8870	−	86.2076i	0.0724178	−	0.125142i
$79$	532.154	−	921.718i	0.757874	−	1.31268i	−0.186059	−	0.982539i	$-0.559572\pi$
$79$	532.154	−	921.718i	0.757874	−	1.31268i	0.943933	−	0.330138i	$-0.107095\pi$
$80$	417.891	+	723.809i	0.584021	+	1.01155i
$81$	728.994	+	2.91533i	0.999992	+	0.00399908i
$82$	−829.234	−	478.758i	−1.11675	−	0.644756i
$83$	−601.040			−0.794852			−0.397426	−	0.917634i	$-0.630096\pi$
$83$	−601.040			−0.794852			−0.397426	+	0.917634i	$0.630096\pi$
$84$		0			0
$85$	466.140			0.594824
$86$	419.175	+	242.011i	0.525590	+	0.303450i
$87$	−0.354042	+	354.123i	−0.000436290	+	0.436390i
$88$	−428.552	−	742.274i	−0.519134	−	0.899166i
$89$	752.606	−	1303.55i	0.896360	−	1.55254i	0.0642474	−	0.997934i	$-0.479535\pi$
$89$	752.606	−	1303.55i	0.896360	−	1.55254i	0.832112	−	0.554607i	$-0.187131\pi$
$90$	976.280	−	561.055i	1.14343	−	0.657116i
$91$		0			0
$92$			72.3506i			0.0819900i
$93$	−804.484	+	463.397i	−0.897001	+	0.516689i
$94$	391.562	−	226.069i	0.429645	−	0.248055i
$95$	490.926	−	283.436i	0.530189	−	0.306105i
$96$	−263.163	+	151.586i	−0.279781	+	0.161159i
$97$			327.463i			0.342771i	0.985204	+	0.171386i	$0.0548244\pi$
$97$			327.463i			0.342771i	−0.985204	+	0.171386i	$0.945176\pi$
$98$		0			0
$99$	−833.358	+	478.920i	−0.846017	+	0.486195i
$100$	−87.9747	+	152.377i	−0.0879747	+	0.152377i
$101$	−547.845	−	948.895i	−0.539729	−	0.934837i	−0.998918	−	0.0464990i	$-0.985194\pi$
$101$	−547.845	−	948.895i	−0.539729	−	0.934837i	0.459190	−	0.888338i	$-0.348140\pi$
$102$	0.388731	−	388.820i	0.000377354	−	0.377440i
$103$	−179.848	−	103.835i	−0.172048	−	0.0993318i	0.411503	−	0.911408i	$-0.365004\pi$
$103$	−179.848	−	103.835i	−0.172048	−	0.0993318i	−0.583551	+	0.812076i	$0.698337\pi$
$104$	178.367			0.168177
$105$		0			0
$106$	−704.242			−0.645302
$107$	−1561.25	−	901.391i	−1.41058	−	0.814399i	−0.415138	−	0.909759i	$-0.636267\pi$
$107$	−1561.25	−	901.391i	−1.41058	−	0.814399i	−0.995443	+	0.0953593i	$0.969600\pi$
$108$	91.0895	+	158.870i	0.0811583	+	0.141549i
$109$	−141.825	−	245.647i	−0.124627	−	0.215860i	0.796960	−	0.604032i	$-0.206440\pi$
$109$	−141.825	−	245.647i	−0.124627	−	0.215860i	−0.921587	+	0.388172i	$0.873107\pi$
$110$	−742.313	+	1285.72i	−0.643425	+	1.11444i
$111$	−608.160	+	1050.94i	−0.520036	+	0.898652i
$112$		0			0
$113$		−	1037.39i		−	0.863627i	−0.901963	−	0.431814i	$-0.857874\pi$
$113$		−	1037.39i		−	0.863627i	0.901963	−	0.431814i	$-0.142126\pi$
$114$	−236.012	−	409.730i	−0.193900	−	0.336621i
$115$	773.697	−	446.694i	0.627371	−	0.362213i
$116$	−77.0406	+	44.4794i	−0.0616641	+	0.0356018i
$117$	0.399957	−	200.024i	0.000316035	−	0.158053i
$118$			250.644i			0.195540i
$119$		0			0
$120$	1745.31	+	1009.98i	1.32770	+	0.768320i
$121$	−31.8573	+	55.1785i	−0.0239349	+	0.0414564i
$122$	−498.767	−	863.890i	−0.370133	−	0.641090i
$123$	−1922.93	−	1.92249i	−1.40963	−	0.00140931i
$124$	−201.977	−	116.611i	−0.146275	−	0.0844518i
$125$	157.864			0.112958
$126$		0			0
$127$	1645.81			1.14994			0.574968	−	0.818176i	$-0.305015\pi$
$127$	1645.81			1.14994			0.574968	+	0.818176i	$0.305015\pi$
$128$	863.461	+	498.520i	0.596249	+	0.344245i
$129$	972.033	+	0.971811i	0.663432	+	0.000663281i
$130$	−154.479	−	267.565i	−0.104221	−	0.180516i
$131$	314.185	−	544.184i	0.209545	−	0.362943i	−0.742026	−	0.670371i	$-0.766135\pi$
$131$	314.185	−	544.184i	0.209545	−	0.362943i	0.951571	+	0.307428i	$0.0994683\pi$
$132$	−208.985	−	120.936i	−0.137802	−	0.0797437i
$133$		0			0
$134$		−	2634.03i		−	1.69810i
$135$	1136.52	−	1954.95i	0.724566	−	1.24634i
$136$	603.016	−	348.151i	0.380207	−	0.219513i
$137$	−432.079	+	249.461i	−0.269453	+	0.155569i	−0.628639	−	0.777697i	$-0.716388\pi$
$137$	−432.079	+	249.461i	−0.269453	+	0.155569i	0.359186	+	0.933266i	$0.383054\pi$
$138$	−371.954	−	645.734i	−0.229441	−	0.398322i
$139$		−	1216.65i		−	0.742410i	−0.928551	−	0.371205i	$-0.878945\pi$
$139$		−	1216.65i		−	0.742410i	0.928551	−	0.371205i	$-0.121055\pi$
$140$		0			0
$141$	454.788	−	785.900i	0.271631	−	0.469395i
$142$	−162.144	+	280.841i	−0.0958226	+	0.165970i
$143$	131.864	+	228.395i	0.0771121	+	0.133562i
$144$	702.446	−	1211.07i	0.406508	−	0.700853i
$145$	951.300	+	549.233i	0.544835	+	0.314561i
$146$	583.631			0.330833
$147$		0			0
$148$	−305.022			−0.169410
$149$	2010.18	+	1160.58i	1.10524	+	0.638111i	0.937592	−	0.347736i	$-0.113050\pi$
$149$	2010.18	+	1160.58i	1.10524	+	0.638111i	0.167648	+	0.985847i	$0.446383\pi$
$150$	1.81183	−	1812.25i	0.000986238	−	0.986463i
$151$	−488.726	−	846.497i	−0.263390	−	0.456205i	0.703750	−	0.710447i	$-0.251507\pi$
$151$	−488.726	−	846.497i	−0.263390	−	0.456205i	−0.967141	+	0.254242i	$0.918174\pi$
$152$	423.386	−	733.326i	0.225929	−	0.391320i
$153$	−389.070	−	677.012i	−0.205585	−	0.357733i
$154$		0			0
$155$			2879.85i			1.49235i
$156$	43.5411	−	25.0804i	0.0223466	−	0.0128721i
$157$	143.752	−	82.9950i	0.0730740	−	0.0421893i	−0.463018	−	0.886349i	$-0.653233\pi$
$157$	143.752	−	82.9950i	0.0730740	−	0.0421893i	0.536092	+	0.844160i	$0.319900\pi$
$158$	−2384.86	+	1376.90i	−1.20082	+	0.693293i
$159$	−1225.52	+	705.920i	−0.611257	+	0.352095i
$160$			942.055i			0.465475i
$161$		0			0
$162$	−1629.73	−	949.635i	−0.790393	−	0.460558i
$163$	−488.511	+	846.127i	−0.234743	+	0.406587i	−0.959198	−	0.282735i	$-0.908758\pi$
$163$	−488.511	+	846.127i	−0.234743	+	0.406587i	0.724455	+	0.689322i	$0.242092\pi$
$164$	−241.528	−	418.340i	−0.115001	−	0.199188i
$165$	−2.98081	+	2981.49i	−0.00140640	+	1.40672i
$166$	1346.79	+	777.568i	0.629704	+	0.363560i
$167$	1.00709			0.000466651			0.000233326	−	1.00000i	$-0.499926\pi$
$167$	1.00709			0.000466651			0.000233326		1.00000i	$0.499926\pi$
$168$		0			0
$169$	2142.12			0.975019
$170$	−1044.51	−	603.048i	−0.471236	−	0.272068i
$171$	−821.414	−	476.436i	−0.367340	−	0.213064i
$172$	122.092	+	211.469i	0.0541245	+	0.0937463i
$173$	−1978.27	+	3426.47i	−0.869395	+	1.50584i	−0.00677983	+	0.999977i	$0.502158\pi$
$173$	−1978.27	+	3426.47i	−0.869395	+	1.50584i	−0.862616	+	0.505860i	$0.831175\pi$
$174$	458.923	−	793.046i	0.199948	−	0.345521i
$175$		0			0
$176$			1845.93i			0.790582i
$177$	251.242	+	436.170i	0.106692	+	0.185224i
$178$	−3372.82	+	1947.30i	−1.42024	+	0.819978i
$179$	2423.54	−	1399.23i	1.01198	−	0.584266i	0.100208	−	0.994967i	$-0.468049\pi$
$179$	2423.54	−	1399.23i	1.01198	−	0.584266i	0.911770	+	0.410701i	$0.134716\pi$
$180$	568.060	+	1.13586i	0.235226	+	0.000470346i
$181$			1506.74i			0.618758i	0.950939	+	0.309379i	$0.100121\pi$
$181$			1506.74i			0.618758i	−0.950939	+	0.309379i	$0.899879\pi$
$182$		0			0
$183$	−1733.90	−	1003.38i	−0.700403	−	0.405312i
$184$	667.255	−	1155.72i	0.267341	−	0.463048i
$185$	1883.21	+	3261.82i	0.748414	+	1.29629i
$186$	2402.16	+	2.40161i	0.946960	+	0.000946744i
$187$	891.599	+	514.765i	0.348664	+	0.201301i
$188$	228.098			0.0884882
$189$		0			0
$190$	−1466.73			−0.560041
$191$	−3184.51	−	1838.58i	−1.20640	−	0.696518i	−0.244433	−	0.969666i	$-0.578602\pi$
$191$	−3184.51	−	1838.58i	−1.20640	−	0.696518i	−0.961972	+	0.273148i	$0.911935\pi$
$192$	2941.30	+	2.94063i	1.10557	+	0.00110532i
$193$	64.7335	+	112.122i	0.0241431	+	0.0418171i	0.877845	−	0.478946i	$-0.158981\pi$
$193$	64.7335	+	112.122i	0.0241431	+	0.0418171i	−0.853701	+	0.520763i	$0.825648\pi$
$194$	423.640	−	733.766i	0.156781	−	0.271553i
$195$	−537.026	−	310.769i	−0.197217	−	0.114126i
$196$		0			0
$197$			3044.81i			1.10119i	0.834774	+	0.550593i	$0.185598\pi$
$197$			3044.81i			1.10119i	−0.834774	+	0.550593i	$0.814402\pi$
$198$	2486.94	+	4.97275i	0.892621	+	0.00178484i
$199$	−3458.29	+	1996.64i	−1.23192	+	0.711248i	−0.967429	−	0.253141i	$-0.918536\pi$
$199$	−3458.29	+	1996.64i	−1.23192	+	0.711248i	−0.264488	+	0.964389i	$0.585203\pi$
$200$	2810.59	−	1622.70i	0.993695	−	0.573710i
$201$	−2640.31	−	4583.73i	−0.926532	−	1.60851i
$202$			2835.00i			0.987473i
$203$		0			0
$204$	98.2476	−	169.778i	0.0337191	−	0.0582687i
$205$	−2982.40	+	5165.67i	−1.01610	+	1.75993i
$206$	268.664	+	465.339i	0.0908674	+	0.157387i
$207$	−1294.55	−	750.862i	−0.434672	−	0.252118i
$208$	−332.682	−	192.074i	−0.110901	−	0.0640285i
$209$	1252.01			0.414370
$210$		0			0
$211$	−4383.67			−1.43026			−0.715129	−	0.698992i	$-0.753632\pi$
$211$	−4383.67			−1.43026			−0.715129	+	0.698992i	$0.753632\pi$
$212$	−307.683	−	177.641i	−0.0996783	−	0.0575493i
$213$	−0.651100	+	651.249i	−0.000209449	+	0.209497i
$214$	2332.27	+	4039.60i	0.745002	+	1.29038i
$215$	1507.59	−	2611.23i	0.478219	−	0.828299i
$216$	10.1313	−	3377.85i	0.00319141	−	1.06404i
$217$		0			0
$218$			733.916i			0.228014i
$219$	1015.63	−	585.022i	0.313379	−	0.180512i
$220$	−648.634	+	374.489i	−0.198777	+	0.114764i
$221$	−185.546	+	107.125i	−0.0564759	+	0.0326064i
$222$	2722.34	−	1568.12i	0.823025	−	0.474077i
$223$		−	4851.53i		−	1.45687i	−0.685114	−	0.728436i	$-0.740247\pi$
$223$		−	4851.53i		−	1.45687i	0.685114	−	0.728436i	$-0.259753\pi$
$224$		0			0
$225$	−1813.42	−	3155.48i	−0.537308	−	0.934958i
$226$	−1342.08	+	2324.55i	−0.395017	+	0.684190i
$227$	−1184.05	−	2050.83i	−0.346203	−	0.599642i	0.639368	−	0.768901i	$-0.279196\pi$
$227$	−1184.05	−	2050.83i	−0.346203	−	0.599642i	−0.985572	+	0.169259i	$0.945863\pi$
$228$	0.238490	−	238.544i	6.92736e−5	−	0.0692894i
$229$	3737.27	+	2157.72i	1.07845	+	0.622646i	0.930479	−	0.366345i	$-0.119391\pi$
$229$	3737.27	+	2157.72i	1.07845	+	0.622646i	0.147975	+	0.988991i	$0.452724\pi$
$230$	−2311.56			−0.662695
$231$		0			0
$232$	1640.85			0.464340
$233$	4826.98	+	2786.86i	1.35719	+	0.783576i	0.989245	−	0.146270i	$-0.0467267\pi$
$233$	4826.98	+	2786.86i	1.35719	+	0.783576i	0.367949	+	0.929846i	$0.380060\pi$
$234$	−259.668	+	447.689i	−0.0725429	+	0.125070i
$235$	−1408.28	−	2439.22i	−0.390920	−	0.677094i
$236$	−63.2237	+	109.507i	−0.0174386	+	0.0302046i
$237$	−2769.94	+	4786.62i	−0.759186	+	1.31192i
$238$		0			0
$239$		−	4683.70i		−	1.26763i	−0.773485	−	0.633814i	$-0.781488\pi$
$239$		−	4683.70i		−	1.26763i	0.773485	−	0.633814i	$-0.218512\pi$
$240$	−2167.67	−	3763.19i	−0.583009	−	1.01214i
$241$	1896.77	−	1095.10i	0.506977	−	0.292703i	−0.224613	−	0.974448i	$-0.572112\pi$
$241$	1896.77	−	1095.10i	0.506977	−	0.292703i	0.731590	+	0.681745i	$0.238778\pi$
$242$	142.769	−	82.4279i	0.0379238	−	0.0218953i
$243$	−3787.95	−	18.9356i	−0.999988	−	0.00499884i
$244$		−	503.245i		−	0.132037i
$245$		0			0
$246$	4306.34	+	2492.01i	1.11611	+	0.645872i
$247$	−130.275	+	225.642i	−0.0335594	+	0.0581266i
$248$	2150.90	+	3725.47i	0.550736	+	0.953902i
$249$	3123.09	+	3.12238i	0.794851	+	0.000794670i
$250$	−353.735	−	204.229i	−0.0894887	−	0.0516663i
$251$	2240.70			0.563473			0.281736	−	0.959492i	$-0.409090\pi$
$251$	2240.70			0.563473			0.281736	+	0.959492i	$0.409090\pi$
$252$		0			0
$253$	1973.16			0.490323
$254$	−3687.86	−	2129.19i	−0.911012	−	0.525973i
$255$	−2422.13	−	2.42158i	−0.594823	−	0.000594688i
$256$	974.345	+	1687.61i	0.237877	+	0.412015i
$257$	−555.785	+	962.648i	−0.134898	+	0.233651i	−0.925559	−	0.378604i	$-0.876404\pi$
$257$	−555.785	+	962.648i	−0.134898	+	0.233651i	0.790660	+	0.612255i	$0.209737\pi$
$258$	−2176.84	−	1259.70i	−0.525287	−	0.303975i
$259$		0			0
$260$		−	155.866i		−	0.0371784i
$261$	3.67931	−	1840.07i	0.000872580	−	0.436389i
$262$	−1408.03	+	812.924i	−0.332016	+	0.191689i
$263$	−1782.86	+	1029.34i	−0.418007	+	0.241337i	−0.694224	−	0.719759i	$-0.744252\pi$
$263$	−1782.86	+	1029.34i	−0.418007	+	0.241337i	0.276217	+	0.961095i	$0.410919\pi$
$264$	2222.96	+	3859.19i	0.518235	+	0.899685i
$265$			4387.04i			1.01696i
$266$		0			0
$267$	−3917.42	+	6769.54i	−0.897912	+	1.55164i
$268$	664.420	−	1150.81i	0.151440	−	0.262302i
$269$	−2414.62	−	4182.24i	−0.547294	−	0.947940i	−0.998459	−	0.0554999i	$-0.982325\pi$
$269$	−2414.62	−	4182.24i	−0.547294	−	0.947940i	0.451165	−	0.892441i	$-0.351009\pi$
$270$	−5075.81	+	2910.26i	−1.14409	+	0.655973i
$271$	191.772	+	110.720i	0.0429865	+	0.0248183i	0.521339	−	0.853350i	$-0.325433\pi$
$271$	191.772	+	110.720i	0.0429865	+	0.0248183i	−0.478353	+	0.878168i	$0.658766\pi$
$272$	−1499.62			−0.334293
$273$		0			0
$274$	1290.91			0.284624
$275$	4155.65	+	2399.27i	0.911255	+	0.526113i
$276$	0.375859	−	375.945i	8.19712e−5	−	0.0819899i
$277$	−1233.58	−	2136.62i	−0.267576	−	0.463455i	0.700660	−	0.713496i	$-0.252889\pi$
$277$	−1233.58	−	2136.62i	−0.267576	−	0.463455i	−0.968235	+	0.250041i	$0.919556\pi$
$278$	−1573.99	+	2726.22i	−0.339573	+	0.588158i
$279$	4182.63	−	2403.70i	0.897517	−	0.515792i
$280$		0			0
$281$		−	4174.76i		−	0.886282i	−0.896452	−	0.443141i	$-0.853864\pi$
$281$		−	4174.76i		−	0.886282i	0.896452	−	0.443141i	$-0.146136\pi$
$282$	−2035.79	+	1172.65i	−0.429892	+	0.247626i
$283$	5628.39	−	3249.55i	1.18224	−	0.682565i	0.225706	−	0.974195i	$-0.427531\pi$
$283$	5628.39	−	3249.55i	1.18224	−	0.682565i	0.956531	+	0.291630i	$0.0941977\pi$
$284$	−141.681	+	81.7998i	−0.0296030	+	0.0170913i
$285$	−2552.40	+	1470.23i	−0.530494	+	0.305574i
$286$		−	682.372i		−	0.141082i
$287$		0			0
$288$	1368.22	−	786.299i	0.279942	−	0.160879i
$289$	2038.31	−	3530.46i	0.414881	−	0.718595i
$290$	−1421.09	−	2461.40i	−0.287756	−	0.498408i
$291$	1.70116	−	1701.55i	0.000342693	−	0.342771i
$292$	254.989	+	147.218i	0.0511030	+	0.0295043i
$293$	5637.32			1.12401			0.562007	−	0.827133i	$-0.310030\pi$
$293$	5637.32			1.12401			0.562007	+	0.827133i	$0.310030\pi$
$294$		0			0
$295$	1561.38			0.308159
$296$	4872.38	+	2813.07i	0.956762	+	0.552387i
$297$	4332.74	−	2484.21i	0.846503	−	0.485349i
$298$	−3002.90	−	5201.17i	−0.583735	−	1.01106i
$299$	−205.312	+	355.611i	−0.0397108	+	0.0687810i
$300$	457.922	−	791.315i	0.0881270	−	0.152289i
$301$		0			0
$302$			2529.06i			0.481892i
$303$	2841.75	+	4933.45i	0.538794	+	0.935376i
$304$	−1579.36	+	911.841i	−0.297968	+	0.172032i
$305$	−5381.56	+	3107.05i	−1.01032	+	0.583308i
$306$	−4.03981	+	2020.36i	−0.000754708	+	0.377440i
$307$		−	3442.95i		−	0.640064i	−0.947407	−	0.320032i	$-0.896306\pi$
$307$		−	3442.95i		−	0.640064i	0.947407	−	0.320032i	$-0.103694\pi$
$308$		0			0
$309$	933.976	+	540.477i	0.171948	+	0.0995037i
$310$	3725.67	−	6453.05i	0.682593	−	1.18228i
$311$	−75.7324	−	131.172i	−0.0138083	−	0.0239167i	0.859039	−	0.511911i	$-0.171062\pi$
$311$	−75.7324	−	131.172i	−0.0138083	−	0.0239167i	−0.872847	+	0.487994i	$0.837729\pi$
$312$	−926.824	−	0.926612i	−0.168177	−	0.000168138i
$313$	−8335.31	−	4812.40i	−1.50524	−	0.869050i	−0.999982	−	0.00608123i	$-0.998064\pi$
$313$	−8335.31	−	4812.40i	−1.50524	−	0.869050i	−0.505257	−	0.862969i	$-0.668602\pi$
$314$	−429.484			−0.0771885
$315$		0			0
$316$	−1389.26			−0.247317
$317$	−7866.93	−	4541.98i	−1.39385	−	0.804741i	−0.400112	−	0.916466i	$-0.631029\pi$
$317$	−7866.93	−	4541.98i	−1.39385	−	0.804741i	−0.993739	+	0.111726i	$0.964362\pi$
$318$	3659.34	+	3.65851i	0.645301	+	0.000645154i
$319$	1213.05	+	2101.07i	0.212909	+	0.368768i
$320$	4561.87	−	7901.39i	0.796926	−	1.38032i
$321$	8107.83	+	4691.87i	1.40977	+	0.815809i
$322$		0			0
$323$			1017.12i			0.175214i
$324$	−472.490	−	825.987i	−0.0810167	−	0.141630i
$325$	−864.811	+	499.299i	−0.147603	+	0.0852188i
$326$	2189.27	−	1263.98i	0.371941	−	0.214740i
$327$	735.666	+	1277.16i	0.124411	+	0.215985i
$328$			8910.00i			1.49992i
$329$		0			0
$330$	3863.85	−	6676.95i	0.644539	−	1.11380i
$331$	702.788	−	1217.26i	0.116703	−	0.202136i	−0.801756	−	0.597651i	$-0.796101\pi$
$331$	702.788	−	1217.26i	0.116703	−	0.202136i	0.918459	+	0.395516i	$0.129434\pi$
$332$	392.275	+	679.440i	0.0648460	+	0.112317i
$333$	3165.55	−	5457.66i	0.520934	−	0.898132i
$334$	−2.25664	−	1.30287i	−0.000369695	−	0.000213443i
$335$	−16408.6			−2.67611
$336$		0			0
$337$	7983.35			1.29045			0.645223	−	0.763994i	$-0.276764\pi$
$337$	7983.35			1.29045			0.645223	+	0.763994i	$0.276764\pi$
$338$	−4799.97	−	2771.27i	−0.772438	−	0.445967i
$339$	−5.38923	+	5390.46i	−0.000863430	+	0.863627i
$340$	−304.231	−	526.944i	−0.0485272	−	0.0840516i
$341$	−3180.25	+	5508.36i	−0.505045	+	0.874764i
$342$	1224.23	+	2130.25i	0.193563	+	0.336815i
$343$		0			0
$344$		−	4503.97i		−	0.705924i
$345$	−4022.57	+	2317.07i	−0.627732	+	0.361585i
$346$	8865.68	−	5118.60i	1.37752	−	0.795312i
$347$	−2268.41	+	1309.67i	−0.350935	+	0.202612i	−0.665097	−	0.746757i	$-0.731610\pi$
$347$	−2268.41	+	1309.67i	−0.350935	+	0.202612i	0.314162	+	0.949369i	$0.398276\pi$
$348$	400.545	−	230.721i	0.0616997	−	0.0355401i
$349$		−	6032.33i		−	0.925224i	−0.886561	−	0.462612i	$-0.846912\pi$
$349$		−	6032.33i		−	0.925224i	0.886561	−	0.462612i	$-0.153088\pi$
$350$		0			0
$351$	−3.11736	+	1039.35i	−0.000474052	+	0.158053i
$352$	−1040.32	+	1801.89i	−0.157527	+	0.272845i
$353$	−2658.15	−	4604.06i	−0.400791	−	0.694190i	0.593031	−	0.805180i	$-0.297931\pi$
$353$	−2658.15	−	4604.06i	−0.400791	−	0.694190i	−0.993822	+	0.110990i	$0.964598\pi$
$354$	1.30209	−	1302.39i	0.000195495	−	0.195540i
$355$	1749.49	+	1010.07i	0.261558	+	0.151011i
$356$	−1964.78			−0.292509
$357$		0			0
$358$	−7240.77			−1.06896
$359$	−1612.51	−	930.982i	−0.237061	−	0.136867i	0.376764	−	0.926309i	$-0.377037\pi$
$359$	−1612.51	−	930.982i	−0.237061	−	0.136867i	−0.613825	+	0.789442i	$0.710370\pi$
$360$	−9063.64	−	5257.09i	−1.32693	−	0.769647i
$361$	−2811.04	−	4868.87i	−0.409832	−	0.709851i
$362$	1949.28	−	3376.25i	0.283016	−	0.490198i
$363$	165.822	−	286.550i	0.0239763	−	0.0414325i
$364$		0			0
$365$		−	3635.70i		−	0.521373i
$366$	2587.18	+	4491.49i	0.369492	+	0.641459i
$367$	1675.89	−	967.574i	0.238367	−	0.137621i	−0.376059	−	0.926596i	$-0.622721\pi$
$367$	1675.89	−	967.574i	0.238367	−	0.137621i	0.614426	+	0.788975i	$0.289388\pi$
$368$	−2489.06	+	1437.06i	−0.352585	+	0.203565i
$369$	9991.81	+	19.9791i	1.40963	+	0.00281862i
$370$		−	9745.28i		−	1.36928i
$371$		0			0
$372$	1048.90	+	606.980i	0.146190	+	0.0845980i
$373$	−3871.04	+	6704.83i	−0.537359	+	0.930732i	0.461687	+	0.887043i	$0.347244\pi$
$373$	−3871.04	+	6704.83i	−0.537359	+	0.930732i	−0.999045	+	0.0436892i	$0.986089\pi$
$374$	−1331.91	−	2306.93i	−0.184148	−	0.318953i
$375$	−820.284	−	0.820097i	−0.112958	−	0.000112932i
$376$	−3643.61	−	2103.64i	−0.499747	−	0.288529i
$377$	−504.884			−0.0689730
$378$		0			0
$379$	−3722.15			−0.504470			−0.252235	−	0.967666i	$-0.581166\pi$
$379$	−3722.15			−0.504470			−0.252235	+	0.967666i	$0.581166\pi$
$380$	−640.815	−	369.975i	−0.0865082	−	0.0499455i
$381$	−8551.86	−	8.54991i	−1.14994	−	0.00114967i
$382$	4757.15	+	8239.63i	0.637165	+	1.10360i
$383$	3546.73	−	6143.12i	0.473184	−	0.819578i	−0.526345	−	0.850271i	$-0.676438\pi$
$383$	3546.73	−	6143.12i	0.473184	−	0.819578i	0.999529	+	0.0306926i	$0.00977131\pi$
$384$	−4484.08	−	2594.87i	−0.595905	−	0.344841i
$385$		0			0
$386$		−	334.984i		−	0.0441716i
$387$	−5050.82	−	10.0994i	−0.663431	−	0.00132656i
$388$	370.177	−	213.722i	0.0484353	−	0.0279641i
$389$	6173.12	−	3564.05i	0.804601	−	0.464537i	−0.0404765	−	0.999180i	$-0.512888\pi$
$389$	6173.12	−	3564.05i	0.804601	−	0.464537i	0.845077	+	0.534644i	$0.179554\pi$
$390$	801.305	+	1391.11i	0.104040	+	0.180620i
$391$			1602.98i			0.207330i
$392$		0			0
$393$	−1635.38	+	2826.03i	−0.209908	+	0.362733i
$394$	3939.08	−	6822.69i	0.503675	−	0.872391i
$395$	8577.33	+	14856.4i	1.09259	+	1.89242i
$396$	1085.29	+	629.489i	0.137722	+	0.0798814i
$397$	−7738.99	−	4468.11i	−0.978360	−	0.564857i	−0.0765855	−	0.997063i	$-0.524402\pi$
$397$	−7738.99	−	4468.11i	−0.978360	−	0.564857i	−0.901775	+	0.432206i	$0.857735\pi$
$398$	10332.3			1.30128
$399$		0			0
$400$	−6989.56			−0.873695
$401$	7719.60	+	4456.91i	0.961343	+	0.555032i	0.896586	−	0.442869i	$-0.146039\pi$
$401$	7719.60	+	4456.91i	0.961343	+	0.555032i	0.0647568	+	0.997901i	$0.479373\pi$
$402$	−13.6837	+	13686.8i	−0.00169771	+	1.69810i
$403$	−661.826	−	1146.32i	−0.0818062	−	0.141692i
$404$	−715.112	+	1238.61i	−0.0880648	+	0.152533i
$405$	−5915.71	+	10152.3i	−0.725812	+	1.24561i
$406$		0			0
$407$			8318.63i			1.01312i
$408$	−3135.17	+	1805.91i	−0.380427	+	0.219133i
$409$	2680.13	−	1547.37i	0.324019	−	0.187073i	−0.329163	−	0.944273i	$-0.606767\pi$
$409$	2680.13	−	1547.37i	0.324019	−	0.187073i	0.653183	+	0.757200i	$0.273433\pi$
$410$	13365.7	−	7716.69i	1.60996	−	0.929513i
$411$	2246.44	−	1293.99i	0.269608	−	0.155299i
$412$			271.076i			0.0324149i
$413$		0			0
$414$	1929.38	+	3357.26i	0.229043	+	0.398552i
$415$	4843.82	−	8389.74i	0.572949	−	0.992377i
$416$	−216.496	−	374.983i	−0.0255159	−	0.0441948i
$417$	−6.32046	+	6321.90i	−0.000742240	+	0.742409i
$418$	−2805.45	−	1619.73i	−0.328276	−	0.189530i
$419$	7234.25			0.843476			0.421738	−	0.906718i	$-0.361420\pi$
$419$	7234.25			0.843476			0.421738	+	0.906718i	$0.361420\pi$
$420$		0			0
$421$	406.124			0.0470148			0.0235074	−	0.999724i	$-0.492517\pi$
$421$	406.124			0.0470148			0.0235074	+	0.999724i	$0.492517\pi$
$422$	9822.77	+	5671.18i	1.13309	+	0.654191i
$423$	−2367.23	+	4081.29i	−0.272101	+	0.469123i
$424$	3276.60	+	5675.23i	0.375296	+	0.650032i
$425$	−1949.14	+	3376.01i	−0.222464	+	0.385319i
$426$	843.982	−	1458.45i	0.0959885	−	0.165874i
$427$		0			0
$428$			2353.21i			0.265763i
$429$	−683.999	−	1187.46i	−0.0769785	−	0.133639i
$430$	−6756.31	+	3900.76i	−0.757717	+	0.437468i
$431$	−10590.4	+	6114.37i	−1.18358	+	0.683338i	−0.956839	−	0.290618i	$-0.906139\pi$
$431$	−10590.4	+	6114.37i	−1.18358	+	0.683338i	−0.226737	+	0.973956i	$0.572806\pi$
$432$	−3656.31	+	6289.27i	−0.407209	+	0.700446i
$433$		−	3252.79i		−	0.361014i	−0.983574	−	0.180507i	$-0.942226\pi$
$433$		−	3252.79i		−	0.361014i	0.983574	−	0.180507i	$-0.0577738\pi$
$434$		0			0
$435$	−4940.24	−	2858.84i	−0.544521	−	0.315105i
$436$	−185.126	+	320.648i	−0.0203348	+	0.0352208i
$437$	974.689	+	1688.21i	0.106695	+	0.184801i
$438$	−3032.63	−	3.03194i	−0.330833	−	0.000330758i
$439$	13036.8	+	7526.81i	1.41734	+	0.818303i	0.996065	−	0.0886287i	$-0.0282485\pi$
$439$	13036.8	+	7526.81i	1.41734	+	0.818303i	0.421278	+	0.906932i	$0.361582\pi$
$440$	13814.9			1.49682
$441$		0			0
$442$	554.353			0.0596558
$443$	−204.373	−	117.995i	−0.0219189	−	0.0126549i	0.489001	−	0.872283i	$-0.337362\pi$
$443$	−204.373	−	117.995i	−0.0219189	−	0.0126549i	−0.510919	+	0.859629i	$0.670695\pi$
$444$	1584.94	+	1.58458i	0.169410	+	0.000169371i
$445$	12130.6	+	21010.8i	1.29224	+	2.23822i
$446$	−6276.44	+	10871.1i	−0.666364	+	1.15418i
$447$	−10439.2	−	6040.99i	−1.10460	−	0.639215i
$448$		0			0
$449$			5874.66i			0.617466i	0.951149	+	0.308733i	$0.0999049\pi$
$449$			5874.66i			0.617466i	−0.951149	+	0.308733i	$0.900095\pi$
$450$	−18.8291	+	9416.70i	−0.00197248	+	0.986462i
$451$	−11409.0	+	6587.02i	−1.19120	+	0.687739i
$452$	−1172.71	+	677.066i	−0.122035	+	0.0704568i
$453$	2535.09	+	4401.07i	0.262934	+	0.456468i
$454$			6127.24i			0.633405i
$455$		0			0
$456$	−2203.79	+	3808.27i	−0.226320	+	0.391094i
$457$	−153.883	+	266.533i	−0.0157513	+	0.0272821i	−0.873794	−	0.486297i	$-0.838347\pi$
$457$	−153.883	+	266.533i	−0.0157513	+	0.0272821i	0.858042	+	0.513579i	$0.171681\pi$
$458$	−5582.89	−	9669.85i	−0.569588	−	0.986556i
$459$	2018.15	+	3519.88i	0.205227	+	0.357939i
$460$	−1009.92	−	583.079i	−0.102365	−	0.0591004i
$461$	−4752.26			−0.480119			−0.240060	−	0.970758i	$-0.577167\pi$
$461$	−4752.26			−0.480119			−0.240060	+	0.970758i	$0.577167\pi$
$462$		0			0
$463$	−9529.43			−0.956523			−0.478261	−	0.878218i	$-0.658733\pi$
$463$	−9529.43			−0.956523			−0.478261	+	0.878218i	$0.658733\pi$
$464$	−3060.42	−	1766.94i	−0.306199	−	0.176784i
$465$	14.9607	−	14964.1i	0.00149201	−	1.49235i
$466$	−7210.74	−	12489.4i	−0.716805	−	1.24154i
$467$	−3269.28	+	5662.56i	−0.323949	+	0.561097i	−0.981299	−	0.192489i	$-0.938344\pi$
$467$	−3269.28	+	5662.56i	−0.323949	+	0.561097i	0.657350	+	0.753586i	$0.271677\pi$
$468$	−226.376	+	130.096i	−0.0223595	+	0.0128497i
$469$		0			0
$470$			7287.61i			0.715218i
$471$	−747.386	+	430.508i	−0.0731162	+	0.0421162i
$472$	2019.85	−	1166.16i	0.196973	−	0.113723i
$473$	5767.23	−	3329.71i	0.560629	−	0.323679i
$474$	12399.3	−	7142.19i	1.20151	−	0.692092i
$475$			4740.69i			0.457932i
$476$		0			0
$477$	6371.64	−	3661.70i	0.611609	−	0.351484i
$478$	−6059.32	+	10495.0i	−0.579805	+	1.00425i
$479$	3671.28	+	6358.85i	0.350199	+	0.606562i	0.986284	−	0.165057i	$-0.0527807\pi$
$479$	3671.28	+	6358.85i	0.350199	+	0.606562i	−0.636085	+	0.771619i	$0.719447\pi$
$480$	4.89394	−	4895.06i	0.000465368	−	0.465475i
$481$	−1499.22	−	865.574i	−0.142117	−	0.0820515i
$482$	−5666.94			−0.535523
$483$		0			0
$484$	83.1680			0.00781066
$485$	−4570.96	−	2639.05i	−0.427952	−	0.247078i
$486$	8463.39	+	4942.91i	0.789932	+	0.461348i
$487$	−3508.78	−	6077.39i	−0.326485	−	0.565489i	0.655327	−	0.755345i	$-0.272531\pi$
$487$	−3508.78	−	6077.39i	−0.326485	−	0.565489i	−0.981812	+	0.189857i	$0.939198\pi$
$488$	−4641.19	+	8038.77i	−0.430526	+	0.745693i
$489$	2542.77	−	4394.06i	0.235150	−	0.406352i
$490$		0			0
$491$			224.222i			0.0206089i	0.999947	+	0.0103045i	$0.00328007\pi$
$491$			224.222i			0.0206089i	−0.999947	+	0.0103045i	$0.996720\pi$
$492$	1252.84	+	2175.01i	0.114802	+	0.199303i
$493$	−1706.89	+	985.471i	−0.155932	+	0.0900272i
$494$	583.829	−	337.074i	0.0531735	−	0.0306997i
$495$	30.9775	−	15492.3i	0.00281280	−	1.40672i
$496$		−	9264.74i		−	0.838708i
$497$		0			0
$498$	−6994.07	−	4047.36i	−0.629341	−	0.364189i
$499$	10396.1	−	18006.6i	0.932651	−	1.61540i	0.153881	−	0.988089i	$-0.450823\pi$
$499$	10396.1	−	18006.6i	0.932651	−	1.61540i	0.778770	−	0.627309i	$-0.215844\pi$
$500$	−103.031	−	178.456i	−0.00921540	−	0.0159615i
$501$	−5.23298	−	0.00523178i	−0.000466651	−	4.66545e-7i
$502$	−5020.87	−	2898.80i	−0.446399	−	0.257729i
$503$	−7341.52			−0.650780			−0.325390	−	0.945580i	$-0.605496\pi$
$503$	−7341.52			−0.650780			−0.325390	+	0.945580i	$0.605496\pi$
$504$		0			0
$505$	17660.5			1.55620
$506$	−4421.38	−	2552.69i	−0.388448	−	0.224270i
$507$	−11130.8	−	11.1282i	−0.975019	−	0.000974796i
$508$	−1074.15	−	1860.49i	−0.0938146	−	0.162492i
$509$	9956.11	−	17244.5i	0.866988	−	1.50167i	0.00192778	−	0.999998i	$-0.499386\pi$
$509$	9956.11	−	17244.5i	0.866988	−	1.50167i	0.865060	−	0.501669i	$-0.167280\pi$
$510$	5424.29	+	3138.95i	0.470964	+	0.272539i
$511$		0			0
$512$		−	13018.4i		−	1.12370i
$513$	4265.72	+	2479.90i	0.367127	+	0.213431i
$514$	2490.76	−	1438.04i	0.213741	−	0.123403i
$515$	2898.81	−	1673.63i	0.248032	−	0.143202i
$516$	−633.308	−	1099.46i	−0.0540307	−	0.0938004i
$517$		−	6220.75i		−	0.529184i
$518$		0			0
$519$	10297.2	−	17794.2i	0.870900	−	1.50497i
$520$	−1437.47	+	2489.78i	−0.121226	+	0.209969i
$521$	3745.90	+	6488.08i	0.314992	+	0.545582i	0.979436	−	0.201756i	$-0.0646649\pi$
$521$	3745.90	+	6488.08i	0.314992	+	0.545582i	−0.664444	+	0.747338i	$0.731332\pi$
$522$	−2388.75	+	4118.40i	−0.200293	+	0.345321i
$523$	−249.515	−	144.058i	−0.0208614	−	0.0120444i	0.489533	−	0.871985i	$-0.337167\pi$
$523$	−249.515	−	144.058i	−0.0208614	−	0.0120444i	−0.510394	+	0.859940i	$0.670501\pi$
$524$	−820.223			−0.0683809
$525$		0			0
$526$	5326.62			0.441543
$527$	−4474.94	−	2583.61i	−0.369889	−	0.213555i
$528$	9.58956	−	9591.75i	0.000790401	−	0.790582i
$529$	−4547.39	−	7876.32i	−0.373748	−	0.647351i
$530$	5675.53	−	9830.30i	0.465149	−	0.805662i
$531$	−1303.23	−	2267.71i	−0.106507	−	0.185330i
$532$		0			0
$533$		−	2741.58i		−	0.222797i
$534$	17535.8	−	10100.9i	1.42106	−	0.818558i
$535$	25164.5	−	14528.7i	2.03356	−	1.17408i
$536$	−21226.7	+	12255.2i	−1.71055	+	0.987586i
$537$	−12600.4	+	7258.03i	−1.01256	+	0.583254i
$538$			12495.2i			1.00131i
$539$		0			0
$540$	−2951.72	−	8.85317i	−0.235226	−	0.000705518i
$541$	−7400.87	+	12818.7i	−0.588149	+	1.01870i	0.406326	+	0.913728i	$0.366810\pi$
$541$	−7400.87	+	12818.7i	−0.588149	+	1.01870i	−0.994475	+	0.104975i	$0.966524\pi$
$542$	−286.478	−	496.194i	−0.0227034	−	0.0393235i
$543$	7.82747	−	7829.25i	0.000618616	−	0.618758i
$544$	−1463.84	−	845.149i	−0.115371	−	0.0666093i
$545$	4571.90			0.359337
$546$		0			0
$547$	−4036.80			−0.315541			−0.157771	−	0.987476i	$-0.550431\pi$
$547$	−4036.80			−0.315541			−0.157771	+	0.987476i	$0.550431\pi$
$548$	564.001	+	325.626i	0.0439652	+	0.0253833i
$549$	9004.40	+	5222.73i	0.699997	+	0.406012i
$550$	−6207.88	−	10752.4i	−0.481282	−	0.833604i
$551$	−1198.43	+	2075.74i	−0.0926585	+	0.160489i
$552$	−3473.16	+	6001.82i	−0.267803	+	0.462780i
$553$		0			0
$554$			6383.53i			0.489549i
$555$	−9768.51	−	16958.7i	−0.747117	−	1.29704i
$556$	−1375.35	+	794.059i	−0.104906	+	0.0605676i
$557$	14891.1	−	8597.36i	1.13277	−	0.654007i	0.188142	−	0.982142i	$-0.439754\pi$
$557$	14891.1	−	8597.36i	1.13277	−	0.654007i	0.944631	+	0.328135i	$0.106420\pi$
$558$	−12481.9	−	24.9582i	−0.946959	−	0.00189349i
$559$			1385.86i			0.104858i
$560$		0			0
$561$	−4630.21	−	2679.43i	−0.348463	−	0.201650i
$562$	−5400.90	+	9354.64i	−0.405380	+	0.702138i
$563$	−9453.63	−	16374.2i	−0.707678	−	1.22573i	−0.965716	−	0.259600i	$-0.916409\pi$
$563$	−9453.63	−	16374.2i	−0.707678	−	1.22573i	0.258038	−	0.966135i	$-0.416924\pi$
$564$	−1185.23	−	1.18496i	−0.0884882	−	8.84680e-5i
$565$	14480.7	+	8360.43i	1.07824	+	0.622524i
$566$	−16815.8			−1.24880
$567$		0			0
$568$	3017.60			0.222915
$569$	−6255.57	−	3611.66i	−0.460891	−	0.266096i	0.251528	−	0.967850i	$-0.419067\pi$
$569$	−6255.57	−	3611.66i	−0.460891	−	0.266096i	−0.712419	+	0.701754i	$0.752400\pi$
$570$	7621.35	+	7.61961i	0.560041	+	0.000559913i
$571$	4965.17	+	8599.93i	0.363898	+	0.630290i	0.988599	−	0.150574i	$-0.0481122\pi$
$571$	4965.17	+	8599.93i	0.363898	+	0.630290i	−0.624700	+	0.780865i	$0.714779\pi$
$572$	172.125	−	298.129i	0.0125820	−	0.0217926i
$573$	16537.7	+	9570.08i	1.20571	+	0.697724i
$574$		0			0
$575$			7471.31i			0.541870i
$576$	−15283.4	−	30.5599i	−1.10557	−	0.00221064i
$577$	−7254.16	+	4188.19i	−0.523388	+	0.302178i	−0.738320	−	0.674451i	$-0.764380\pi$
$577$	−7254.16	+	4188.19i	−0.523388	+	0.302178i	0.214932	+	0.976629i	$0.431047\pi$
$578$	−9134.73	+	5273.94i	−0.657361	+	0.379528i
$579$	−335.782	−	582.937i	−0.0241013	−	0.0418412i
$580$		−	1433.85i		−	0.102651i
$581$		0			0
$582$	−2205.11	+	3810.56i	−0.157053	+	0.271397i
$583$	−4844.67	+	8391.21i	−0.344161	+	0.596104i
$584$	−2715.44	−	4703.27i	−0.192407	−	0.333258i
$585$	2788.85	+	1617.59i	0.197102	+	0.114323i
$586$	−12631.9	−	7293.03i	−0.890476	−	0.514116i
$587$	21277.2			1.49609			0.748043	−	0.663650i	$-0.230994\pi$
$587$	21277.2			1.49609			0.748043	+	0.663650i	$0.230994\pi$
$588$		0			0
$589$	−6283.84			−0.439594
$590$	−3498.67	−	2019.96i	−0.244132	−	0.140950i
$591$	15.8177	−	15821.3i	0.00110093	−	1.10118i
$592$	−6058.48	−	10493.6i	−0.420611	−	0.728520i
$593$	1424.49	−	2467.29i	0.0986454	−	0.170859i	−0.812479	−	0.582991i	$-0.801882\pi$
$593$	1424.49	−	2467.29i	0.0986454	−	0.170859i	0.911124	+	0.412132i	$0.135216\pi$
$594$	−12922.5	−	38.7587i	−0.892619	−	0.00267725i
$595$		0			0
$596$		−	3029.86i		−	0.208235i
$597$	17980.2	−	10356.9i	1.23263	−	0.710016i
$598$	920.111	−	531.227i	0.0629200	−	0.0363269i
$599$	3844.40	−	2219.57i	0.262234	−	0.151401i	−0.363119	−	0.931743i	$-0.618288\pi$
$599$	3844.40	−	2219.57i	0.262234	−	0.151401i	0.625353	+	0.780342i	$0.284955\pi$
$600$	−14612.7	+	8417.17i	−0.994268	+	0.572716i
$601$			7868.29i			0.534033i	0.963692	+	0.267017i	$0.0860379\pi$
$601$			7868.29i			0.534033i	−0.963692	+	0.267017i	$0.913962\pi$
$602$		0			0
$603$	13695.6	+	23831.4i	0.924924	+	1.60944i
$604$	−637.943	+	1104.95i	−0.0429761	+	0.0744367i
$605$	−513.480	−	889.374i	−0.0345057	−	0.0597656i
$606$	14.7277	−	14731.1i	0.000987247	−	0.987473i
$607$	15144.9	+	8743.92i	1.01271	+	0.584686i	0.911983	−	0.410228i	$-0.134551\pi$
$607$	15144.9	+	8743.92i	1.01271	+	0.584686i	0.100724	+	0.994914i	$0.467884\pi$
$608$	−2055.57			−0.137112
$609$		0			0
$610$	16078.4			1.06720
$611$	1121.13	+	647.284i	0.0742324	+	0.0428581i
$612$	−511.391	+	881.679i	−0.0337774	+	0.0582349i
$613$	−6422.07	−	11123.3i	−0.423140	−	0.732900i	0.573105	−	0.819482i	$-0.305739\pi$
$613$	−6422.07	−	11123.3i	−0.423140	−	0.732900i	−0.996245	+	0.0865820i	$0.972406\pi$
$614$	−4454.16	+	7714.83i	−0.292761	+	0.507077i
$615$	15523.8	−	26826.1i	1.01786	−	1.75892i
$616$		0			0
$617$		−	23625.5i		−	1.54153i	−0.637117	−	0.770767i	$-0.719873\pi$
$617$		−	23625.5i		−	1.54153i	0.637117	−	0.770767i	$-0.280127\pi$
$618$	−1393.60	−	2419.37i	−0.0907100	−	0.157478i
$619$	−16529.1	+	9543.05i	−1.07328	+	0.619657i	−0.929075	−	0.369891i	$-0.879395\pi$
$619$	−16529.1	+	9543.05i	−1.07328	+	0.619657i	−0.144202	+	0.989548i	$0.546062\pi$
$620$	3255.49	−	1879.56i	0.210877	−	0.121750i
$621$	6722.75	+	3908.32i	0.434420	+	0.252553i
$622$			391.901i			0.0252633i
$623$		0			0
$624$	1727.67	+	999.772i	0.110836	+	0.0641393i
$625$	7152.40	−	12388.3i	0.457754	−	0.792853i
$626$	12451.6	+	21566.9i	0.794996	+	1.37697i
$627$	−6505.63	−	6.50415i	−0.414370	−	0.000414275i
$628$	−187.642	−	108.335i	−0.0119231	−	0.00688382i
$629$	−6757.98			−0.428391
$630$		0			0
$631$	32.3893			0.00204342			0.00102171	−	0.999999i	$-0.499675\pi$
$631$	32.3893			0.00204342			0.00102171	+	0.999999i	$0.499675\pi$
$632$	22191.9	+	12812.5i	1.39675	+	0.806414i
$633$	22778.2	+	22.7730i	1.43026	+	0.00142993i
$634$	11751.9	+	20355.0i	0.736166	+	1.27508i
$635$	−13263.7	+	22973.4i	−0.828902	+	1.43570i
$636$	1597.85	+	924.648i	0.0996207	+	0.0576489i
$637$		0			0
$638$		−	6277.32i		−	0.389532i
$639$	6.76643	−	3383.98i	0.000418898	−	0.209497i
$640$	−13917.4	+	8035.20i	−0.859583	+	0.496280i
$641$	−18742.7	+	10821.1i	−1.15490	+	0.666784i	−0.950078	−	0.312014i	$-0.898996\pi$
$641$	−18742.7	+	10821.1i	−1.15490	+	0.666784i	−0.204827	+	0.978798i	$0.565663\pi$
$642$	−12097.8	−	21002.5i	−0.743711	−	1.29112i
$643$			19867.3i			1.21849i	0.792982	+	0.609246i	$0.208528\pi$
$643$			19867.3i			1.21849i	−0.792982	+	0.609246i	$0.791472\pi$
$644$		0			0
$645$	−7847.24	+	13560.5i	−0.479046	+	0.827820i
$646$	1315.85	−	2279.12i	0.0801417	−	0.138809i
$647$	−11212.2	−	19420.1i	−0.681294	−	1.18004i	−0.974586	−	0.224012i	$-0.928084\pi$
$647$	−11212.2	−	19420.1i	−0.681294	−	1.18004i	0.293293	−	0.956023i	$-0.405249\pi$
$648$	−70.1913	+	17551.7i	−0.00425521	+	1.06404i
$649$	2986.49	+	1724.25i	0.180632	+	0.104288i
$650$	2583.78			0.155914
$651$		0			0
$652$	1275.33			0.0766038
$653$	17358.5	+	10021.9i	1.04026	+	0.600594i	0.919907	−	0.392137i	$-0.128264\pi$
$653$	17358.5	+	10021.9i	1.04026	+	0.600594i	0.120353	+	0.992731i	$0.461597\pi$
$654$	3.81267	−	3813.54i	0.000227962	−	0.228014i
$655$	5064.07	+	8771.22i	0.302091	+	0.523237i
$656$	9594.67	−	16618.5i	0.571050	−	0.989088i
$657$	−5280.41	+	3034.59i	−0.313559	+	0.180199i
$658$		0			0
$659$		−	13217.9i		−	0.781327i	−0.920533	−	0.390664i	$-0.872246\pi$
$659$		−	13217.9i		−	0.781327i	0.920533	−	0.390664i	$-0.127754\pi$
$660$	3372.34	−	1942.53i	0.198891	−	0.114565i
$661$	−8470.90	+	4890.68i	−0.498457	+	0.287784i	−0.728076	−	0.685496i	$-0.759585\pi$
$661$	−8470.90	+	4890.68i	−0.498457	+	0.287784i	0.229619	+	0.973281i	$0.426252\pi$
$662$	−3149.56	+	1818.40i	−0.184911	+	0.106758i
$663$	964.682	−	555.674i	0.0565085	−	0.0325499i
$664$		−	14471.0i		−	0.845761i
$665$		0			0
$666$	−14153.8	+	8134.03i	−0.823499	+	0.473254i
$667$	−1888.72	+	3271.36i	−0.109642	+	0.189906i
$668$	−0.657286	−	1.13845i	−3.80706e−5	−	6.59402e-5i
$669$	−25.2035	+	25209.3i	−0.00145654	+	1.45687i
$670$	36767.7	+	21227.8i	2.12009	+	1.22403i
$671$	−13724.6			−0.789617
$672$		0			0
$673$	−4670.73			−0.267524			−0.133762	−	0.991014i	$-0.542706\pi$
$673$	−4670.73			−0.267524			−0.133762	+	0.991014i	$0.542706\pi$
$674$	−17888.8	−	10328.1i	−1.02233	−	0.590242i
$675$	9406.39	+	16405.8i	0.536373	+	0.935494i
$676$	−1398.07	−	2421.53i	−0.0795445	−	0.137775i
$677$	13521.0	−	23419.1i	0.767584	−	1.32949i	−0.171286	−	0.985221i	$-0.554792\pi$
$677$	13521.0	−	23419.1i	0.767584	−	1.32949i	0.938870	−	0.344273i	$-0.111875\pi$
$678$	6985.73	−	12071.8i	0.395701	−	0.683795i
$679$		0			0
$680$			11223.1i			0.632921i
$681$	6141.85	+	10662.6i	0.345604	+	0.599988i
$682$	14252.4	−	8228.61i	0.800222	−	0.462009i
$683$	11596.9	−	6695.45i	0.649694	−	0.375101i	−0.138645	−	0.990342i	$-0.544275\pi$
$683$	11596.9	−	6695.45i	0.649694	−	0.375101i	0.788339	+	0.615241i	$0.210941\pi$
$684$	−2.47846	+	1239.51i	−0.000138547	+	0.0692893i
$685$		−	8041.69i		−	0.448551i
$686$		0			0
$687$	−19408.2	−	11231.2i	−1.07783	−	0.623724i
$688$	−4850.07	+	8400.57i	−0.268761	+	0.465507i
$689$	−1008.20	−	1746.25i	−0.0557464	−	0.0965557i
$690$	12011.2	+	12.0085i	0.662694	+	0.000662543i
$691$	−26837.3	−	15494.6i	−1.47748	−	0.853025i	−0.477807	−	0.878465i	$-0.658568\pi$
$691$	−26837.3	−	15494.6i	−1.47748	−	0.853025i	−0.999676	+	0.0254396i	$0.991901\pi$
$692$	5164.56			0.283710
$693$		0			0
$694$	6777.28			0.370694
$695$	16982.9	+	9805.07i	0.926903	+	0.535147i
$696$	−8526.09	−	8.52414i	−0.464340	−	0.000464234i
$697$	−5351.23	−	9268.60i	−0.290807	−	0.503692i
$698$	−7804.05	+	13517.0i	−0.423191	+	0.732989i
$699$	−25067.3	−	14506.0i	−1.35641	−	0.784933i
$700$		0			0
$701$		−	2892.67i		−	0.155855i	−0.996959	−	0.0779277i	$-0.975170\pi$
$701$		−	2892.67i		−	0.155855i	0.996959	−	0.0779277i	$-0.0248303\pi$
$702$	1351.60	−	2324.91i	0.0726679	−	0.124997i
$703$	−7117.31	+	4109.18i	−0.381841	+	0.220456i
$704$	17451.2	−	10075.5i	0.934259	−	0.539395i
$705$	7304.98	+	12681.9i	0.390243	+	0.677485i
$706$			13755.5i			0.733277i
$707$		0			0
$708$	329.089	−	568.685i	0.0174688	−	0.0301871i
$709$	−7965.19	+	13796.1i	−0.421917	+	0.730781i	−0.996127	−	0.0879267i	$-0.971976\pi$
$709$	−7965.19	+	13796.1i	−0.421917	+	0.730781i	0.574210	+	0.818708i	$0.305309\pi$
$710$	−2613.46	−	4526.64i	−0.138143	−	0.239270i
$711$	14417.9	−	24857.6i	0.760497	−	1.31116i
$712$	31385.2	+	18120.2i	1.65198	+	0.953770i
$713$	−9903.30			−0.520171
$714$		0			0
$715$	−4250.81			−0.222337
$716$	−3163.50	−	1826.45i	−0.165119	−	0.0953317i
$717$	−24.3316	+	24337.2i	−0.00126734	+	1.26763i
$718$	2408.83	+	4172.22i	0.125204	+	0.216860i
$719$	5938.87	−	10286.4i	0.308042	−	0.533545i	−0.669892	−	0.742459i	$-0.733659\pi$
$719$	5938.87	−	10286.4i	0.308042	−	0.533545i	0.977934	+	0.208914i	$0.0669928\pi$
$720$	11244.0	+	19565.4i	0.581997	+	1.01272i
$721$		0			0
$722$			14546.6i			0.749819i
$723$	−9861.57	+	5680.44i	−0.507270	+	0.292196i
$724$	1703.28	−	983.389i	0.0874336	−	0.0504798i
$725$	−7955.61	+	4593.18i	−0.407537	+	0.235291i
$726$	−742.279	+	427.566i	−0.0379457	+	0.0218574i
$727$		−	16795.8i		−	0.856839i	−0.903580	−	0.428419i	$-0.859071\pi$
$727$		−	16795.8i		−	0.856839i	0.903580	−	0.428419i	$-0.140929\pi$
$728$		0			0
$729$	19682.6	+	118.070i	0.999982	+	0.00599859i
$730$	−4703.52	+	8146.74i	−0.238473	+	0.413047i
$731$	2705.03	+	4685.24i	0.136866	+	0.237059i
$732$	−2.61434	+	2614.94i	−0.000132007	+	0.132037i
$733$	−22048.4	−	12729.7i	−1.11102	−	0.641447i	−0.171926	−	0.985110i	$-0.554999\pi$
$733$	−22048.4	−	12729.7i	−1.11102	−	0.641447i	−0.939093	+	0.343663i	$0.888332\pi$
$734$	−5007.02			−0.251788
$735$		0			0
$736$	−3239.57			−0.162245
$737$	−31385.1	−	18120.2i	−1.56864	−	0.905653i
$738$	−22363.4	−	12971.2i	−1.11546	−	0.646988i
$739$	9319.48	+	16141.8i	0.463901	+	0.803499i	0.999151	−	0.0411940i	$-0.0131162\pi$
$739$	9319.48	+	16141.8i	0.463901	+	0.803499i	−0.535251	+	0.844693i	$0.679783\pi$
$740$	2458.19	−	4257.72i	0.122115	−	0.211509i
$741$	678.099	−	1171.79i	0.0336175	−	0.0580930i
$742$		0			0
$743$			14043.3i			0.693401i	0.937976	+	0.346700i	$0.112698\pi$
$743$			14043.3i			0.693401i	−0.937976	+	0.346700i	$0.887302\pi$
$744$	−11157.1	−	19369.3i	−0.549782	−	0.954452i
$745$	−32400.4	+	18706.4i	−1.59337	+	0.919932i
$746$	17348.1	−	10016.0i	0.851422	−	0.491569i
$747$	−16228.0	−	32.4487i	−0.794850	−	0.00158934i
$748$		−	1343.87i		−	0.0656907i
$749$		0			0
$750$	1837.00	+	1063.04i	0.0894370	+	0.0517557i
$751$	−8115.13	+	14055.8i	−0.394308	+	0.682961i	−0.993013	−	0.118009i	$-0.962349\pi$
$751$	−8115.13	+	14055.8i	−0.394308	+	0.682961i	0.598705	+	0.800970i	$0.295682\pi$
$752$	4530.58	+	7847.20i	0.219699	+	0.380529i
$753$	−11643.0	−	11.6404i	−0.563473	−	0.000563344i
$754$	1131.32	+	653.170i	0.0546424	+	0.0315478i
$755$	15754.7			0.759433
$756$		0			0
$757$	−33345.7			−1.60102			−0.800508	−	0.599322i	$-0.795437\pi$
$757$	−33345.7			−1.60102			−0.800508	+	0.599322i	$0.795437\pi$
$758$	8340.45	+	4815.36i	0.399655	+	0.230741i
$759$	−10252.8	−	10.2505i	−0.490322	−	0.000490211i
$760$	6824.19	+	11819.9i	0.325710	+	0.564146i
$761$	−5394.02	+	9342.71i	−0.256942	+	0.445037i	−0.965421	−	0.260695i	$-0.916048\pi$
$761$	−5394.02	+	9342.71i	−0.256942	+	0.445037i	0.708479	+	0.705732i	$0.249382\pi$
$762$	19151.6	+	11082.7i	0.910486	+	0.526884i
$763$		0			0
$764$			4799.87i			0.227295i
$765$	12585.8	+	25.1658i	0.594822	+	0.00118937i
$766$	−15894.7	+	9176.84i	−0.749740	+	0.432862i
$767$	−621.503	+	358.825i	−0.0292584	+	0.0168923i
$768$	−5054.08	−	8774.16i	−0.237465	−	0.412253i
$769$			35799.6i			1.67876i	0.543543	+	0.839381i	$0.317082\pi$
$769$			35799.6i			1.67876i	−0.543543	+	0.839381i	$0.682918\pi$
$770$		0			0
$771$	2892.94	−	4999.17i	0.135132	−	0.233516i
$772$	84.4979	−	146.355i	0.00393931	−	0.00682308i
$773$	18306.3	+	31707.5i	0.851788	+	1.47534i	0.879593	+	0.475727i	$0.157815\pi$
$773$	18306.3	+	31707.5i	0.851788	+	1.47534i	−0.0278053	+	0.999613i	$0.508852\pi$
$774$	11304.6	+	6556.90i	0.524982	+	0.304500i
$775$	−20857.2	−	12041.9i	−0.966727	−	0.558140i
$776$	−7884.22			−0.364725
$777$		0			0
$778$	−18443.3			−0.849904
$779$	−11271.5	−	6507.62i	−0.518414	−	0.299306i
$780$	−0.809717	+	809.902i	−3.71699e−5	+	0.0371784i
$781$	2230.86	+	3863.97i	0.102211	+	0.177034i
$782$	2073.78	−	3591.89i	0.0948314	−	0.164253i
$783$	−28.6773	+	9561.27i	−0.00130887	+	0.436388i
$784$		0			0
$785$			2675.45i			0.121644i
$786$	7320.53	−	4216.76i	0.332207	−	0.191357i
$787$	34874.9	−	20135.0i	1.57961	−	0.911990i	0.584701	−	0.811249i	$-0.301212\pi$
$787$	34874.9	−	20135.0i	1.57961	−	0.911990i	0.994913	−	0.100742i	$-0.0321216\pi$
$788$	3441.97	−	1987.22i	0.155603	−	0.0898374i
$789$	9269.36	−	5339.32i	0.418248	−	0.240919i
$790$		−	44386.1i		−	1.99897i
$791$		0			0
$792$	−11530.8	−	20064.5i	−0.517335	−	0.900203i
$793$	1428.08	−	2473.51i	0.0639503	−	0.110765i
$794$	11560.8	+	20023.9i	0.516723	+	0.894991i
$795$	22.7905	−	22795.7i	0.00101672	−	1.01696i
$796$	4514.17	+	2606.26i	0.201006	+	0.116051i
$797$	11444.6			0.508645			0.254323	−	0.967119i	$-0.418148\pi$
$797$	11444.6			0.508645			0.254323	+	0.967119i	$0.418148\pi$
$798$		0			0
$799$	5053.68			0.223762
$800$	−6822.81	−	3939.15i	−0.301528	−	0.174087i
$801$	20390.7	−	35155.2i	0.899462	−	1.55075i
$802$	−11531.9	−	19973.8i	−0.507736	−	0.879424i
$803$	4014.95	−	6954.10i	0.176444	−	0.305610i
$804$	−3458.40	+	5976.32i	−0.151702	+	0.262150i
$805$		0			0
$806$			3424.83i			0.149670i
$807$	12525.0	+	21744.1i	0.546346	+	0.948487i
$808$	22846.2	−	13190.3i	0.994712	−	0.574297i
$809$	−2702.86	+	1560.50i	−0.117463	+	0.0678172i	−0.557580	−	0.830123i	$-0.688270\pi$
$809$	−2702.86	+	1560.50i	−0.117463	+	0.0678172i	0.440117	+	0.897940i	$0.354937\pi$
$810$	26389.8	−	15095.8i	1.14474	−	0.654828i
$811$			3571.23i			0.154628i	0.997007	+	0.0773138i	$0.0246343\pi$
$811$			3571.23i			0.154628i	−0.997007	+	0.0773138i	$0.975366\pi$
$812$		0			0
$813$	−995.903	−	576.313i	−0.0429617	−	0.0248612i
$814$	10761.8	−	18640.1i	0.463394	−	0.802622i
$815$	−7873.89	−	13638.0i	−0.338418	−	0.586157i
$816$	7792.24	+	7.79046i	0.334293	+	0.000334217i
$817$	5697.71	+	3289.58i	0.243987	+	0.140866i
$818$	−8007.37			−0.342263
$819$		0			0
$820$	7785.98			0.331583
$821$	24420.3	+	14099.1i	1.03809	+	0.599344i	0.919293	−	0.393574i	$-0.128762\pi$
$821$	24420.3	+	14099.1i	1.03809	+	0.599344i	0.118801	+	0.992918i	$0.462095\pi$
$822$	−6707.78	−	6.70625i	−0.284624	−	0.000284559i
$823$	5700.86	+	9874.18i	0.241457	+	0.418217i	0.961130	−	0.276097i	$-0.0890412\pi$
$823$	5700.86	+	9874.18i	0.241457	+	0.418217i	−0.719672	+	0.694314i	$0.755708\pi$
$824$	2500.00	−	4330.13i	0.105694	−	0.183067i
$825$	−21580.9	−	12488.5i	−0.910729	−	0.527024i
$826$		0			0
$827$			18948.2i			0.796726i	0.917228	+	0.398363i	$0.130422\pi$
$827$			18948.2i			0.796726i	−0.917228	+	0.398363i	$0.869578\pi$
$828$	−3.90604	+	1953.46i	−0.000163942	+	0.0819898i
$829$	−663.246	+	382.925i	−0.0277871	+	0.0160429i	−0.513829	−	0.857893i	$-0.671773\pi$
$829$	−663.246	+	382.925i	−0.0277871	+	0.0160429i	0.486042	+	0.873935i	$0.338440\pi$
$830$	−21707.7	+	12532.9i	−0.907813	+	0.524126i
$831$	6398.75	+	11108.6i	0.267112	+	0.463722i
$832$			4193.51i			0.174740i
$833$		0			0
$834$	8192.83	−	14157.7i	0.340161	−	0.587819i
$835$	−8.11618	+	14.0576i	−0.000336374	+	0.000582617i
$836$	−817.136	−	1415.32i	−0.0338053	−	0.0585525i
$837$	−21746.0	+	12468.3i	−0.898032	+	0.514894i
$838$	−16210.2	−	9358.98i	−0.668225	−	0.385800i
$839$	5355.68			0.220380			0.110190	−	0.993911i	$-0.464854\pi$
$839$	5355.68			0.220380			0.110190	+	0.993911i	$0.464854\pi$
$840$		0			0
$841$	19744.4			0.809564
$842$	−910.026	−	525.404i	−0.0372465	−	0.0215043i
$843$	−21.6877	+	21692.7i	−0.000886080	+	0.886282i
$844$	2861.05	+	4955.48i	0.116684	+	0.202103i
$845$	−17263.5	+	29901.2i	−0.702818	+	1.21732i
$846$	10584.4	−	6082.70i	0.430140	−	0.247196i
$847$		0			0
$848$		−	14113.5i		−	0.571533i
$849$	−29262.9	+	16855.9i	−1.18292	+	0.681383i
$850$	8735.11	−	5043.22i	0.352485	−	0.203507i
$851$	−11216.8	+	6476.05i	−0.451832	+	0.260865i
$852$	736.623	−	424.308i	0.0296201	−	0.0170617i
$853$		−	8591.74i		−	0.344872i	−0.985021	−	0.172436i	$-0.944836\pi$
$853$		−	8591.74i		−	0.344872i	0.985021	−	0.172436i	$-0.0551638\pi$
$854$		0			0
$855$	13270.3	−	7626.26i	0.530800	−	0.305044i
$856$	21702.5	−	37589.8i	0.866560	−	1.50093i
$857$	−20273.3	−	35114.5i	−0.808080	−	1.39964i	−0.914192	−	0.405281i	$-0.867174\pi$
$857$	−20273.3	−	35114.5i	−0.808080	−	1.39964i	0.106112	−	0.994354i	$-0.466160\pi$
$858$	−3.54490	+	3545.71i	−0.000141050	+	0.141082i
$859$	8352.92	+	4822.56i	0.331779	+	0.191553i	0.656631	−	0.754212i	$-0.271981\pi$
$859$	8352.92	+	4822.56i	0.331779	+	0.191553i	−0.324852	+	0.945765i	$0.605314\pi$
$860$	−3935.78			−0.156057
$861$		0			0
$862$	31640.7			1.25022
$863$	−9951.19	−	5745.32i	−0.392517	−	0.226620i	0.290733	−	0.956804i	$-0.406101\pi$
$863$	−9951.19	−	5745.32i	−0.392517	−	0.226620i	−0.683250	+	0.730184i	$0.739434\pi$
$864$	−7113.56	+	4078.62i	−0.280102	+	0.160599i
$865$	−31886.1	−	55228.3i	−1.25336	−	2.17089i
$866$	−4208.14	+	7288.72i	−0.165125	+	0.286006i
$867$	−10609.7	+	18334.2i	−0.415599	+	0.718180i
$868$		0			0
$869$			37888.3i			1.47902i
$870$	7371.41	+	12797.2i	0.287258	+	0.498696i
$871$	6531.39	−	3770.90i	0.254085	−	0.146696i
$872$	5914.37	−	3414.66i	0.229686	−	0.132609i
$873$	−17.6790	+	8841.48i	−0.000685386	+	0.342771i
$874$		−	5043.84i		−	0.195206i
$875$		0			0
$876$	−1324.19	−	766.290i	−0.0510735	−	0.0295554i
$877$	14714.7	−	25486.6i	0.566568	−	0.981324i	−0.430334	−	0.902670i	$-0.641604\pi$
$877$	14714.7	−	25486.6i	0.566568	−	0.981324i	0.996902	−	0.0786543i	$-0.0250623\pi$
$878$	−19474.9	−	33731.6i	−0.748573	−	1.29657i
$879$	−29292.4	−	29.2857i	−1.12401	−	0.00112376i
$880$	−25766.8	−	14876.5i	−0.987046	−	0.569871i
$881$	22330.5			0.853956			0.426978	−	0.904262i	$-0.359578\pi$
$881$	22330.5			0.853956			0.426978	+	0.904262i	$0.359578\pi$
$882$		0			0
$883$	15519.2			0.591463			0.295732	−	0.955271i	$-0.404437\pi$
$883$	15519.2			0.591463			0.295732	+	0.955271i	$0.404437\pi$
$884$	242.197	+	139.832i	0.00921489	+	0.00532022i
$885$	−8113.15	−	8.11130i	−0.308159	−	0.000308089i
$886$	305.301	+	528.797i	0.0115765	+	0.0200511i
$887$	−19107.9	+	33095.9i	−0.723316	+	1.25282i	0.236347	+	0.971669i	$0.424050\pi$
$887$	−19107.9	+	33095.9i	−0.723316	+	1.25282i	−0.959663	+	0.281152i	$0.909284\pi$
$888$	−25303.0	−	14642.5i	−0.956209	−	0.553343i
$889$		0			0
$890$		−	62773.6i		−	2.36424i
$891$	−22526.5	+	12885.8i	−0.846987	+	0.484503i
$892$	−5484.36	+	3166.40i	−0.205863	+	0.118855i
$893$	5322.39	−	3072.88i	0.199448	−	0.115151i
$894$	15576.5	+	27041.6i	0.582724	+	1.01164i
$895$			45106.0i			1.68461i
$896$		0			0
$897$	1068.68	−	1846.74i	0.0397795	−	0.0687413i
$898$	7600.07	−	13163.7i	0.282425	−	0.489174i
$899$	−6088.31	−	10545.3i	−0.225869	−	0.391217i
$900$	−2383.54	+	4109.41i	−0.0882792	+	0.152201i
$901$	−6816.94	−	3935.76i	−0.252059	−	0.145526i
$902$	34086.6			1.25827
$903$		0			0
$904$	24977.0			0.918941
$905$	−21032.2	−	12142.9i	−0.772522	−	0.446016i
$906$	13.1384	−	13141.4i	0.000481782	−	0.481892i
$907$	4432.30	+	7676.97i	0.162262	+	0.281047i	0.935680	−	0.352850i	$-0.114788\pi$
$907$	4432.30	+	7676.97i	0.162262	+	0.281047i	−0.773417	+	0.633897i	$0.781454\pi$
$908$	−1545.56	+	2677.00i	−0.0564883	+	0.0978405i
$909$	−14740.5	−	25649.7i	−0.537858	−	0.935915i
$910$		0			0
$911$		−	15145.0i		−	0.550798i	−0.961330	−	0.275399i	$-0.911190\pi$
$911$		−	15145.0i		−	0.550798i	0.961330	−	0.275399i	$-0.0888100\pi$
$912$	8211.30	−	4729.86i	0.298140	−	0.171734i
$913$	18529.8	−	10698.2i	0.671684	−	0.387797i
$914$	689.630	−	398.158i	0.0249573	−	0.0144091i
$915$	27979.5	−	16116.7i	1.01090	−	0.582297i
$916$		−	5633.02i		−	0.203188i
$917$		0			0
$918$	31.4872	−	10498.1i	0.00113206	−	0.377439i
$919$	2244.07	−	3886.84i	0.0805495	−	0.139516i	−0.822937	−	0.568133i	$-0.807666\pi$
$919$	2244.07	−	3886.84i	0.0805495	−	0.139516i	0.903486	+	0.428617i	$0.140999\pi$
$920$	10754.9	+	18628.0i	0.385412	+	0.667552i
$921$	−17.8860	+	17890.1i	−0.000639917	+	0.640063i
$922$	10648.7	+	6148.02i	0.380364	+	0.219603i
$923$	−928.506			−0.0331118
$924$		0			0
$925$	−31498.2			−1.11963
$926$	21353.2	+	12328.3i	0.757785	+	0.437507i
$927$	−4850.27	−	2813.25i	−0.171849	−	0.0996756i
$928$	−1991.61	−	3449.56i	−0.0704501	−	0.122023i
$929$	8911.93	−	15435.9i	0.314737	−	0.545141i	−0.664644	−	0.747160i	$-0.731417\pi$
$929$	8911.93	−	15435.9i	0.314737	−	0.545141i	0.979382	+	0.202019i	$0.0647503\pi$
$930$	−19392.6	+	33511.6i	−0.683774	+	1.18160i
$931$		0			0
$932$		−	7275.49i		−	0.255704i
$933$	392.835	+	681.984i	0.0137844	+	0.0239305i
$934$	14651.4	−	8458.97i	0.513284	−	0.296345i
$935$	−14370.9	+	8297.05i	−0.502652	+	0.290206i
$936$	4815.91	+	9.62963i	0.168176	+	0.000336276i
$937$		−	51270.5i		−	1.78755i	−0.448516	−	0.893775i	$-0.648047\pi$
$937$		−	51270.5i		−	1.78755i	0.448516	−	0.893775i	$-0.351953\pi$
$938$		0			0
$939$	43286.5	+	25049.2i	1.50437	+	0.870554i
$940$	−1838.26	+	3183.96i	−0.0637845	+	0.110478i
$941$	5422.48	+	9392.01i	0.187851	+	0.325367i	0.944533	−	0.328415i	$-0.106514\pi$
$941$	5422.48	+	9392.01i	0.187851	+	0.325367i	−0.756683	+	0.653782i	$0.773181\pi$
$942$	2231.66	+	2.23115i	0.0771884	+	7.71708e-5i
$943$	−17763.9	−	10256.0i	−0.613437	−	0.354168i
$944$	−5023.10			−0.173186
$945$		0			0
$946$	−17230.6			−0.592195
$947$	36916.8	+	21313.9i	1.26677	+	0.731372i	0.974376	−	0.224926i	$-0.0722139\pi$
$947$	36916.8	+	21313.9i	1.26677	+	0.731372i	0.292397	+	0.956297i	$0.405547\pi$
$948$	7218.82	+	7.21717i	0.247317	+	0.000247260i
$949$	835.531	+	1447.18i	0.0285801	+	0.0495021i
$950$	6133.05	−	10622.8i	0.209455	−	0.362787i
$951$	40854.2	+	23641.7i	1.39305	+	0.806134i
$952$		0			0
$953$			33229.0i			1.12948i	0.825269	+	0.564739i	$0.191023\pi$
$953$			33229.0i			1.12948i	−0.825269	+	0.564739i	$0.808977\pi$
$954$	−19014.5	−	38.0203i	−0.645300	−	0.00129031i
$955$	51328.4	−	29634.5i	1.73921	−	1.00413i
$956$	−5294.64	+	3056.86i	−0.179122	+	0.103416i
$957$	−6292.28	−	10923.8i	−0.212540	−	0.368981i
$958$		−	18998.2i		−	0.640715i
$959$		0			0
$960$	−23745.2	+	41033.1i	−0.798306	+	1.37952i
$961$	1066.19	−	1846.70i	0.0357891	−	0.0619885i
$962$	2239.59	+	3879.09i	0.0750596	+	0.130007i
$963$	−42105.1	−	24421.8i	−1.40895	−	0.817218i
$964$	−2475.89	−	1429.45i	−0.0827209	−	0.0477589i
$965$	−2086.77			−0.0696118
$966$		0			0
$967$	−16853.4			−0.560464			−0.280232	−	0.959932i	$-0.590411\pi$
$967$	−16853.4			−0.560464			−0.280232	+	0.959932i	$0.590411\pi$
$968$	−1328.51	−	767.018i	−0.0441116	−	0.0254679i
$969$	5.28390	−	5285.11i	0.000175174	−	0.175214i
$970$	6828.29	+	11826.9i	0.226024	+	0.391485i
$971$	−634.824	+	1099.55i	−0.0209809	+	0.0363400i	−0.876325	−	0.481720i	$-0.840012\pi$
$971$	−634.824	+	1099.55i	−0.0209809	+	0.0363400i	0.855344	+	0.518060i	$0.173346\pi$
$972$	2450.84	+	4294.41i	0.0808751	+	0.141711i
$973$		0			0
$974$			18157.3i			0.597328i
$975$	4496.28	−	2589.94i	0.147688	−	0.0850712i
$976$	17313.0	−	9995.66i	0.567803	−	0.327821i
$977$	49580.5	−	28625.3i	1.62356	−	0.937364i	0.637605	−	0.770363i	$-0.279925\pi$
$977$	49580.5	−	28625.3i	1.62356	−	0.937364i	0.985957	−	0.167001i	$-0.0534082\pi$
$978$	−11382.4	+	6556.45i	−0.372155	+	0.214368i
$979$			53583.9i			1.74929i
$980$		0			0
$981$	−3816.00	−	6640.13i	−0.124195	−	0.216109i
$982$	290.077	−	502.428i	0.00942640	−	0.0163270i
$983$	30733.8	+	53232.4i	0.997207	+	1.72721i	0.563283	+	0.826264i	$0.309538\pi$
$983$	30733.8	+	53232.4i	0.997207	+	1.72721i	0.433924	+	0.900950i	$0.357129\pi$
$984$	46.2871	−	46297.7i	0.00149957	−	1.49992i
$985$	−42501.6	−	24538.3i	−1.37484	−	0.793762i
$986$	5099.63			0.164711
$987$		0			0
$988$	340.100			0.0109514
$989$	8979.57	+	5184.36i	0.288710	+	0.166687i
$990$	−20111.8	+	34674.4i	−0.645652	+	1.11316i
$991$	25996.6	+	45027.4i	0.833308	+	1.44333i	0.895401	+	0.445261i	$0.146889\pi$
$991$	25996.6	+	45027.4i	0.833308	+	1.44333i	−0.0620930	+	0.998070i	$0.519778\pi$
$992$	5221.39	−	9043.71i	0.167116	−	0.289454i
$993$	−3658.12	+	6321.44i	−0.116905	+	0.202019i
$994$		0			0
$995$		−	64364.3i		−	2.05074i
$996$	−2034.79	−	3532.51i	−0.0647337	−	0.112381i
$997$	−29417.3	+	16984.1i	−0.934460	+	0.539510i	−0.888219	−	0.459420i	$-0.848057\pi$
$997$	−29417.3	+	16984.1i	−0.934460	+	0.539510i	−0.0462403	+	0.998930i	$0.514724\pi$
$998$	−46590.3	+	26898.9i	−1.47775	+	0.853177i
$999$	−16477.0	+	28342.4i	−0.521832	+	0.897611i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.g.d.68.2		12
3.2	odd	2	inner	147.4.g.d.68.5		12
7.2	even	3		147.4.c.a.146.10		12
7.3	odd	6	inner	147.4.g.d.80.5		12
7.4	even	3		21.4.g.a.17.5	yes	12
7.5	odd	6		147.4.c.a.146.9		12
7.6	odd	2		21.4.g.a.5.2	✓	12
21.2	odd	6		147.4.c.a.146.3		12
21.5	even	6		147.4.c.a.146.4		12
21.11	odd	6		21.4.g.a.17.2	yes	12
21.17	even	6	inner	147.4.g.d.80.2		12
21.20	even	2		21.4.g.a.5.5	yes	12
28.11	odd	6		336.4.bc.d.17.2		12
28.27	even	2		336.4.bc.d.257.1		12
84.11	even	6		336.4.bc.d.17.1		12
84.83	odd	2		336.4.bc.d.257.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.g.a.5.2	✓	12	7.6	odd	2
21.4.g.a.5.5	yes	12	21.20	even	2
21.4.g.a.17.2	yes	12	21.11	odd	6
21.4.g.a.17.5	yes	12	7.4	even	3
147.4.c.a.146.3		12	21.2	odd	6
147.4.c.a.146.4		12	21.5	even	6
147.4.c.a.146.9		12	7.5	odd	6
147.4.c.a.146.10		12	7.2	even	3
147.4.g.d.68.2		12	1.1	even	1	trivial
147.4.g.d.68.5		12	3.2	odd	2	inner
147.4.g.d.80.2		12	21.17	even	6	inner
147.4.g.d.80.5		12	7.3	odd	6	inner
336.4.bc.d.17.1		12	84.11	even	6
336.4.bc.d.17.2		12	28.11	odd	6
336.4.bc.d.257.1		12	28.27	even	2
336.4.bc.d.257.2		12	84.83	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.g (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.24076 - 1.29370i) q^{2} +(-5.19615 - 0.00519496i) q^{3} +(-0.652660 - 1.13044i) q^{4} +(-8.05907 + 13.9587i) q^{5} +(11.6366 + 6.73392i) q^{6} +24.0767i q^{8} +(26.9999 + 0.0539876i) q^{9} +O(q^{10})\)	\(q+(-2.24076 - 1.29370i) q^{2} +(-5.19615 - 0.00519496i) q^{3} +(-0.652660 - 1.13044i) q^{4} +(-8.05907 + 13.9587i) q^{5} +(11.6366 + 6.73392i) q^{6} +24.0767i q^{8} +(26.9999 + 0.0539876i) q^{9} +(36.1169 - 20.8521i) q^{10} +(-30.8296 + 17.7995i) q^{11} +(3.38545 + 5.87733i) q^{12} -7.40831i q^{13} +(41.9486 - 72.4897i) q^{15} +(25.9268 - 44.9065i) q^{16} +(-14.4601 - 25.0457i) q^{17} +(-60.4306 - 35.0509i) q^{18} +(-30.4580 - 17.5849i) q^{19} +21.0393 q^{20} +92.1090 q^{22} +(-48.0017 - 27.7138i) q^{23} +(0.125077 - 125.106i) q^{24} +(-67.3971 - 116.735i) q^{25} +(-9.58416 + 16.6003i) q^{26} +(-140.295 - 0.420792i) q^{27} -68.1510i q^{29} +(-187.777 + 108.163i) q^{30} +(154.734 - 89.3356i) q^{31} +(50.6165 - 29.2234i) q^{32} +(160.288 - 92.3286i) q^{33} +74.8285i q^{34} +(-17.5608 - 30.5571i) q^{36} +(116.838 - 202.370i) q^{37} +(45.4994 + 78.8072i) q^{38} +(-0.0384859 + 38.4947i) q^{39} +(-336.079 - 194.035i) q^{40} +370.068 q^{41} -187.068 q^{43} +(40.2425 + 23.2340i) q^{44} +(-218.348 + 376.449i) q^{45} +(71.7068 + 124.200i) q^{46} +(-87.3726 + 151.334i) q^{47} +(-134.953 + 233.206i) q^{48} +348.768i q^{50} +(75.0068 + 130.216i) q^{51} +(-8.37465 + 4.83511i) q^{52} +(235.715 - 136.090i) q^{53} +(313.824 + 182.444i) q^{54} -573.789i q^{55} +(158.173 + 91.5321i) q^{57} +(-88.1672 + 152.710i) q^{58} +(-48.4354 - 83.8926i) q^{59} +(-109.323 - 0.109298i) q^{60} +(333.882 + 192.767i) q^{61} -462.295 q^{62} -566.055 q^{64} +(103.411 + 59.7041i) q^{65} +(-478.612 - 0.478503i) q^{66} +(509.009 + 881.630i) q^{67} +(-18.8751 + 32.6926i) q^{68} +(249.280 + 144.254i) q^{69} -125.333i q^{71} +(-1.29984 + 650.068i) q^{72} +(-195.346 + 112.783i) q^{73} +(-523.613 + 302.308i) q^{74} +(349.599 + 606.924i) q^{75} +45.9079i q^{76} +(49.8870 - 86.2076i) q^{78} +(532.154 - 921.718i) q^{79} +(417.891 + 723.809i) q^{80} +(728.994 + 2.91533i) q^{81} +(-829.234 - 478.758i) q^{82} -601.040 q^{83} +466.140 q^{85} +(419.175 + 242.011i) q^{86} +(-0.354042 + 354.123i) q^{87} +(-428.552 - 742.274i) q^{88} +(752.606 - 1303.55i) q^{89} +(976.280 - 561.055i) q^{90} +72.3506i q^{92} +(-804.484 + 463.397i) q^{93} +(391.562 - 226.069i) q^{94} +(490.926 - 283.436i) q^{95} +(-263.163 + 151.586i) q^{96} +327.463i q^{97} +(-833.358 + 478.920i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} + 14 q^{4} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 + 14 * q^4 - 3 * q^9	\( 12 q + 3 q^{3} + 14 q^{4} - 3 q^{9} - 30 q^{10} + 192 q^{12} + 6 q^{15} + 134 q^{16} + 66 q^{18} - 300 q^{19} - 268 q^{22} - 414 q^{24} - 42 q^{25} - 822 q^{30} + 930 q^{31} + 855 q^{33} + 852 q^{36} + 764 q^{37} - 426 q^{39} - 2298 q^{40} - 1012 q^{43} - 2367 q^{45} + 608 q^{46} - 1341 q^{51} + 3000 q^{52} + 4158 q^{54} + 270 q^{57} + 2870 q^{58} - 918 q^{60} - 2358 q^{61} - 548 q^{64} - 2934 q^{66} + 792 q^{67} - 2712 q^{72} + 2904 q^{73} + 2418 q^{75} + 4296 q^{78} + 1674 q^{79} + 837 q^{81} - 5040 q^{82} + 348 q^{85} - 1638 q^{87} - 554 q^{88} - 1479 q^{93} + 1356 q^{94} + 4410 q^{96} - 3354 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 + 14 * q^4 - 3 * q^9 - 30 * q^10 + 192 * q^12 + 6 * q^15 + 134 * q^16 + 66 * q^18 - 300 * q^19 - 268 * q^22 - 414 * q^24 - 42 * q^25 - 822 * q^30 + 930 * q^31 + 855 * q^33 + 852 * q^36 + 764 * q^37 - 426 * q^39 - 2298 * q^40 - 1012 * q^43 - 2367 * q^45 + 608 * q^46 - 1341 * q^51 + 3000 * q^52 + 4158 * q^54 + 270 * q^57 + 2870 * q^58 - 918 * q^60 - 2358 * q^61 - 548 * q^64 - 2934 * q^66 + 792 * q^67 - 2712 * q^72 + 2904 * q^73 + 2418 * q^75 + 4296 * q^78 + 1674 * q^79 + 837 * q^81 - 5040 * q^82 + 348 * q^85 - 1638 * q^87 - 554 * q^88 - 1479 * q^93 + 1356 * q^94 + 4410 * q^96 - 3354 * q^99

Introduction

L-functions

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