LMFDB - Embedded newform 21.4.g.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,4,Mod(5,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, 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("21.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	21.g (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.23904011012$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.2
Root			$0.00299931 - 3.00000i$ of defining polynomial
Character	$\chi$	$=$	21.5
Dual form			21.4.g.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.24076 - 1.29370i) q^{2} +(5.19615 + 0.00519496i) q^{3} +(-0.652660 - 1.13044i) q^{4} +(8.05907 - 13.9587i) q^{5} +(-11.6366 - 6.73392i) q^{6} +(-5.67909 + 17.6280i) q^{7} +24.0767i q^{8} +(26.9999 + 0.0539876i) q^{9} +O(q^{10})$	\(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} +(-5.67909 + 17.6280i) q^{7} +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} +(35.5309 - 32.1532i) q^{14} +(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} +(-29.6010 + 91.5685i) q^{21} +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} +(23.6340 - 5.08525i) q^{28} -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} +(200.297 + 221.338i) q^{35} +(-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} +(184.791 - 166.888i) q^{42} -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} +(-278.496 - 200.222i) q^{49} +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} +(-424.424 - 136.733i) q^{56} +(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} +(-154.287 + 475.650i) q^{63} -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} +(-162.471 - 755.091i) q^{70} -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} +(-138.686 - 644.550i) q^{77} +(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} +(122.832 - 26.3009i) q^{84} +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} +(-130.594 - 42.0725i) q^{91} +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} +(365.014 + 808.942i) q^{98} +(-833.358 + 478.920i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} + 14 q^{4} - 56 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 + 14 * q^4 - 56 * q^7 - 3 * q^9	$ 12 q - 3 q^{3} + 14 q^{4} - 56 q^{7} - 3 q^{9} + 30 q^{10} - 192 q^{12} + 6 q^{15} + 134 q^{16} + 66 q^{18} + 300 q^{19} + 357 q^{21} - 268 q^{22} + 414 q^{24} - 42 q^{25} - 602 q^{28} - 822 q^{30} - 930 q^{31} - 855 q^{33} + 852 q^{36} + 764 q^{37} - 426 q^{39} + 2298 q^{40} + 966 q^{42} - 1012 q^{43} + 2367 q^{45} + 608 q^{46} - 336 q^{49} - 1341 q^{51} - 3000 q^{52} - 4158 q^{54} + 270 q^{57} + 2870 q^{58} - 918 q^{60} + 2358 q^{61} + 1071 q^{63} - 548 q^{64} + 2934 q^{66} + 792 q^{67} - 4242 q^{70} - 2712 q^{72} - 2904 q^{73} - 2418 q^{75} + 4296 q^{78} + 1674 q^{79} + 837 q^{81} + 5040 q^{82} + 3864 q^{84} + 348 q^{85} + 1638 q^{87} - 554 q^{88} - 1218 q^{91} - 1479 q^{93} - 1356 q^{94} - 4410 q^{96} - 3354 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 + 14 * q^4 - 56 * q^7 - 3 * q^9 + 30 * q^10 - 192 * q^12 + 6 * q^15 + 134 * q^16 + 66 * q^18 + 300 * q^19 + 357 * q^21 - 268 * q^22 + 414 * q^24 - 42 * q^25 - 602 * q^28 - 822 * q^30 - 930 * q^31 - 855 * q^33 + 852 * q^36 + 764 * q^37 - 426 * q^39 + 2298 * q^40 + 966 * q^42 - 1012 * q^43 + 2367 * q^45 + 608 * q^46 - 336 * q^49 - 1341 * q^51 - 3000 * q^52 - 4158 * q^54 + 270 * q^57 + 2870 * q^58 - 918 * q^60 + 2358 * q^61 + 1071 * q^63 - 548 * q^64 + 2934 * q^66 + 792 * q^67 - 4242 * q^70 - 2712 * q^72 - 2904 * q^73 - 2418 * q^75 + 4296 * q^78 + 1674 * q^79 + 837 * q^81 + 5040 * q^82 + 3864 * q^84 + 348 * q^85 + 1638 * q^87 - 554 * q^88 - 1218 * q^91 - 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 $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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	$-0.577097\pi$
$5$	8.05907	−	13.9587i	0.720825	−	1.24851i	0.960670	−	0.277694i	$-0.0895701\pi$
$6$	−11.6366	−	6.73392i	−0.791771	−	0.458185i
$7$	−5.67909	+	17.6280i	−0.306642	+	0.951825i
$7$	−5.67909	+	17.6280i	−0.306642	+	0.951825i
$8$			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	$0.0251813\pi$
$13$			7.40831i			0.158054i	−0.996872	+	0.0790268i	$0.974819\pi$
$14$	35.5309	−	32.1532i	0.678289	−	0.613807i
$15$	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	0.950546	−	0.310584i	$-0.100524\pi$
$17$	14.4601	+	25.0457i	0.206300	+	0.357322i	−0.744246	+	0.667905i	$0.767191\pi$
$18$	−60.4306	−	35.0509i	−0.791313	−	0.458977i
$19$	30.4580	+	17.5849i	0.367765	+	0.212329i	0.672482	−	0.740114i	$-0.265228\pi$
$19$	30.4580	+	17.5849i	0.367765	+	0.212329i	−0.304716	+	0.952443i	$0.598562\pi$
$20$	−21.0393			−0.235227
$21$	−29.6010	+	91.5685i	−0.307593	+	0.951518i
$22$	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
$28$	23.6340	−	5.08525i	0.159514	−	0.0343222i
$29$		−	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	−0.876058	−	0.482206i	$-0.839836\pi$
$31$	−154.734	+	89.3356i	−0.896484	+	0.517585i	−0.0204262	+	0.999791i	$0.506502\pi$
$32$	50.6165	−	29.2234i	0.279619	−	0.161438i
$33$	−160.288	+	92.3286i	−0.845530	+	0.487041i
$34$		−	74.8285i		−	0.377440i
$35$	200.297	+	221.338i	0.967323	+	1.06894i
$36$	−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	$-0.748970\pi$
$41$	−370.068			−1.40963			−0.704816	+	0.709390i	$0.748970\pi$
$42$	184.791	−	166.888i	0.678902	−	0.613129i
$43$	−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	−0.697998	−	0.716100i	$-0.745925\pi$
$47$	87.3726	−	151.334i	0.271162	−	0.469666i	0.969160	+	0.246434i	$0.0792588\pi$
$48$	134.953	−	233.206i	0.405807	−	0.701259i
$49$	−278.496	−	200.222i	−0.811942	−	0.583739i
$50$			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
$56$	−424.424	−	136.733i	−1.01279	−	0.326282i
$57$	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	0.914504	−	0.404578i	$-0.132581\pi$
$59$	48.4354	+	83.8926i	0.106877	+	0.185117i	−0.807626	+	0.589695i	$0.799248\pi$
$60$	−109.323	−	0.109298i	−0.235227	−	0.000235173i
$61$	−333.882	−	192.767i	−0.700807	−	0.404611i	0.106841	−	0.994276i	$-0.465927\pi$
$61$	−333.882	−	192.767i	−0.700807	−	0.404611i	−0.807648	+	0.589665i	$0.799260\pi$
$62$	462.295			0.946960
$63$	−154.287	+	475.650i	−0.308544	+	0.951210i
$64$	−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
$70$	−162.471	−	755.091i	−0.277414	−	1.28929i
$71$		−	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	−0.335158	−	0.942162i	$-0.608790\pi$
$73$	195.346	−	112.783i	0.313199	−	0.180825i	0.648357	+	0.761337i	$0.275456\pi$
$74$	−523.613	+	302.308i	−0.822551	+	0.474900i
$75$	−349.599	−	606.924i	−0.538243	−	0.934420i
$76$		−	45.9079i		−	0.0692894i
$77$	−138.686	−	644.550i	−0.205256	−	0.953939i
$78$	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	$-0.369904\pi$
$83$	601.040			0.794852			0.397426	+	0.917634i	$0.369904\pi$
$84$	122.832	−	26.3009i	0.159548	−	0.0341627i
$85$	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	$0.520465\pi$
$89$	−752.606	+	1303.55i	−0.896360	+	1.55254i	−0.832112	+	0.554607i	$0.812869\pi$
$90$	−976.280	+	561.055i	−1.14343	+	0.657116i
$91$	−130.594	−	42.0725i	−0.150439	−	0.0484658i
$92$			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	$-0.945176\pi$
$97$		−	327.463i		−	0.342771i	0.985204	−	0.171386i	$-0.0548244\pi$
$98$	365.014	+	808.942i	0.376245	+	0.833831i
$99$	−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	$0.0148064\pi$
$101$	547.845	+	948.895i	0.539729	+	0.934837i	−0.459190	+	0.888338i	$0.651860\pi$
$102$	0.388731	−	388.820i	0.000377354	−	0.377440i
$103$	179.848	+	103.835i	0.172048	+	0.0993318i	0.583551	−	0.812076i	$-0.301663\pi$
$103$	179.848	+	103.835i	0.172048	+	0.0993318i	−0.411503	+	0.911408i	$0.634996\pi$
$104$	−178.367			−0.168177
$105$	1039.62	+	1151.15i	0.966254	+	1.06991i
$106$	−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
$112$	644.374	+	712.067i	0.543639	+	0.600750i
$113$		−	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
$119$	−523.626	+	112.667i	−0.403368	+	0.0867915i
$120$	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
$126$	961.070	−	866.216i	0.679515	−	0.612450i
$127$	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	−0.951571	−	0.307428i	$-0.900532\pi$
$131$	−314.185	+	544.184i	−0.209545	+	0.362943i	0.742026	+	0.670371i	$0.233865\pi$
$132$	208.985	+	120.936i	0.137802	+	0.0797437i
$133$	−482.961	+	437.048i	−0.314873	+	0.284939i
$134$		−	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	$0.121055\pi$
$139$			1216.65i			0.742410i	−0.928551	+	0.371205i	$0.878945\pi$
$140$	119.484	−	370.882i	0.0721303	−	0.223895i
$141$	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
$147$	−1446.07	−	1041.83i	−0.811358	−	0.584550i
$148$	−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
$154$	−523.095	+	1623.70i	−0.273716	+	0.849621i
$155$			2879.85i			1.49235i
$156$	43.5411	−	25.0804i	0.0223466	−	0.0128721i
$157$	−143.752	+	82.9950i	−0.0730740	+	0.0421893i	−0.536092	−	0.844160i	$-0.680100\pi$
$157$	−143.752	+	82.9950i	−0.0730740	+	0.0421893i	0.463018	+	0.886349i	$0.346767\pi$
$158$	−2384.86	+	1376.90i	−1.20082	+	0.693293i
$159$	1225.52	−	705.920i	0.611257	−	0.352095i
$160$		−	942.055i		−	0.465475i
$161$	761.145	−	688.786i	0.372588	−	0.337168i
$162$	−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	$-0.500074\pi$
$167$	−1.00709			−0.000466651			−0.000233326		1.00000i	$0.500074\pi$
$168$	−2204.66	−	712.692i	−1.01246	−	0.327294i
$169$	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	$-0.497842\pi$
$173$	1978.27	−	3426.47i	0.869395	−	1.50584i	0.862616	−	0.505860i	$-0.168825\pi$
$174$	−458.923	+	793.046i	−0.199948	+	0.345521i
$175$	2440.57	−	525.130i	1.05423	−	0.226835i
$176$			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	$-0.899879\pi$
$181$		−	1506.74i		−	0.618758i	0.950939	−	0.309379i	$-0.100121\pi$
$182$	238.201	+	263.224i	0.0970144	+	0.107206i
$183$	−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
$189$	−804.168	+	2470.75i	−0.309495	+	0.950901i
$190$	−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
$196$	−44.5763	+	445.500i	−0.0162450	+	0.162354i
$197$			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	0.264488	−	0.964389i	$-0.414797\pi$
$199$	3458.29	−	1996.64i	1.23192	−	0.711248i	0.967429	+	0.253141i	$0.0814637\pi$
$200$	2810.59	−	1622.70i	0.993695	−	0.573710i
$201$	2640.31	+	4583.73i	0.926532	+	1.60851i
$202$		−	2835.00i		−	0.987473i
$203$	1201.37	+	387.035i	0.415367	+	0.133815i
$204$	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
$210$	−840.300	−	3924.41i	−0.276125	−	1.28957i
$211$	−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
$217$	−696.065	−	3235.00i	−0.217751	−	1.01201i
$218$			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	$0.259753\pi$
$223$			4851.53i			1.45687i	−0.685114	+	0.728436i	$0.740247\pi$
$224$	227.697	+	1058.23i	0.0679180	+	0.315652i
$225$	−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	0.985572	−	0.169259i	$-0.0541374\pi$
$227$	1184.05	+	2050.83i	0.346203	+	0.599642i	−0.639368	+	0.768901i	$0.720804\pi$
$228$	0.238490	−	238.544i	6.92736e−5	−	0.0692894i
$229$	−3737.27	−	2157.72i	−1.07845	−	0.622646i	−0.147975	−	0.988991i	$-0.547276\pi$
$229$	−3737.27	−	2157.72i	−1.07845	−	0.622646i	−0.930479	+	0.366345i	$0.880609\pi$
$230$	2311.56			0.662695
$231$	−717.285	−	3349.90i	−0.204303	−	0.954144i
$232$	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
$238$	1319.08	+	424.957i	0.359257	+	0.115739i
$239$		−	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	−0.731590	−	0.681745i	$-0.761222\pi$
$241$	−1896.77	+	1095.10i	−0.506977	+	0.292703i	0.224613	+	0.974448i	$0.427888\pi$
$242$	142.769	−	82.4279i	0.0379238	−	0.0218953i
$243$	3787.95	+	18.9356i	0.999988	+	0.00499884i
$244$			503.245i			0.132037i
$245$	−5039.26	+	2273.84i	−1.31407	+	0.592940i
$246$	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	$-0.590910\pi$
$251$	−2240.70			−0.563473			−0.281736	+	0.959492i	$0.590910\pi$
$252$	638.390	−	136.026i	0.159583	−	0.0340032i
$253$	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	−0.790660	−	0.612255i	$-0.790263\pi$
$257$	555.785	−	962.648i	0.134898	−	0.233651i	0.925559	+	0.378604i	$0.123596\pi$
$258$	2176.84	+	1259.70i	0.525287	+	0.303975i
$259$	2903.85	+	3208.90i	0.696665	+	0.769851i
$260$		−	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
$266$	1647.61	−	354.512i	0.379780	−	0.0817162i
$267$	−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	$0.0176752\pi$
$269$	2414.62	+	4182.24i	0.547294	+	0.947940i	−0.451165	+	0.892441i	$0.648991\pi$
$270$	−5075.81	+	2910.26i	−1.14409	+	0.655973i
$271$	−191.772	−	110.720i	−0.0429865	−	0.0248183i	0.478353	−	0.878168i	$-0.341234\pi$
$271$	−191.772	−	110.720i	−0.0429865	−	0.0248183i	−0.521339	+	0.853350i	$0.674567\pi$
$272$	1499.62			0.334293
$273$	−678.368	−	219.293i	−0.150391	−	0.0486162i
$274$	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
$280$	−5329.09	+	4822.47i	−1.13741	+	1.02928i
$281$		−	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	−0.956531	−	0.291630i	$-0.905802\pi$
$283$	−5628.39	+	3249.55i	−1.18224	+	0.682565i	−0.225706	+	0.974195i	$0.572469\pi$
$284$	−141.681	+	81.7998i	−0.0296030	+	0.0170913i
$285$	2552.40	−	1470.23i	0.530494	−	0.305574i
$286$			682.372i			0.141082i
$287$	2101.65	−	6523.57i	0.432252	−	1.34172i
$288$	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	$-0.689970\pi$
$293$	−5637.32			−1.12401			−0.562007	+	0.827133i	$0.689970\pi$
$294$	1892.47	+	4205.28i	0.375411	+	0.834207i
$295$	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
$301$	1062.38	−	3297.64i	0.203436	−	0.631472i
$302$			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	$0.103694\pi$
$307$			3442.95i			0.640064i	−0.947407	+	0.320032i	$0.896306\pi$
$308$	−638.111	+	577.448i	−0.118051	+	0.106828i
$309$	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	0.872847	−	0.487994i	$-0.162271\pi$
$311$	75.7324	+	131.172i	0.0138083	+	0.0239167i	−0.859039	+	0.511911i	$0.828938\pi$
$312$	−926.824	−	0.926612i	−0.168177	−	0.000168138i
$313$	8335.31	+	4812.40i	1.50524	+	0.869050i	0.999982	+	0.00608123i	$0.00193573\pi$
$313$	8335.31	+	4812.40i	1.50524	+	0.869050i	0.505257	+	0.862969i	$0.331398\pi$
$314$	429.484			0.0771885
$315$	5396.05	+	5986.94i	0.965184	+	1.07087i
$316$	−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
$322$	−2596.63	+	558.709i	−0.449393	+	0.0966946i
$323$			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
$329$	2171.52	+	2399.65i	0.363890	+	0.402118i
$330$	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
$336$	3344.56	+	3703.35i	0.543038	+	0.601293i
$337$	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
$343$	5111.13	−	3772.26i	0.804592	−	0.593828i
$344$		−	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	$0.153088\pi$
$349$			6032.33i			0.925224i	−0.886561	+	0.462612i	$0.846912\pi$
$350$	−6148.09	−	1980.68i	−0.938941	−	0.302491i
$351$	−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	0.993822	−	0.110990i	$-0.0354020\pi$
$353$	2658.15	+	4604.06i	0.400791	+	0.694190i	−0.593031	+	0.805180i	$0.702069\pi$
$354$	1.30209	−	1302.39i	0.000195495	−	0.195540i
$355$	−1749.49	−	1010.07i	−0.261558	−	0.151011i
$356$	1964.78			0.292509
$357$	−2721.43	+	582.715i	−0.403454	+	0.0863881i
$358$	−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
$364$	37.6731	+	175.088i	0.00542475	+	0.0252118i
$365$		−	3635.70i		−	0.521373i
$366$	2587.18	+	4491.49i	0.369492	+	0.641459i
$367$	−1675.89	+	967.574i	−0.238367	+	0.137621i	−0.614426	−	0.788975i	$-0.710612\pi$
$367$	−1675.89	+	967.574i	−0.238367	+	0.137621i	0.376059	+	0.926596i	$0.377279\pi$
$368$	−2489.06	+	1437.06i	−0.352585	+	0.203565i
$369$	−9991.81	−	19.9791i	−1.40963	−	0.00281862i
$370$			9745.28i			1.36928i
$371$	1060.36	+	4928.06i	0.148385	+	0.689629i
$372$	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
$378$	4998.36	−	4495.99i	0.680127	−	0.611770i
$379$	−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	−0.999529	−	0.0306926i	$-0.990229\pi$
$383$	−3546.73	+	6143.12i	−0.473184	+	0.819578i	0.526345	+	0.850271i	$0.323562\pi$
$384$	4484.08	+	2594.87i	0.595905	+	0.344841i
$385$	−10114.8	−	3258.60i	−1.33895	−	0.431359i
$386$		−	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
$392$	4820.69	−	6705.25i	0.621126	−	0.863945i
$393$	−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	0.901775	−	0.432206i	$-0.142265\pi$
$397$	7738.99	+	4468.11i	0.978360	+	0.564857i	0.0765855	+	0.997063i	$0.475598\pi$
$398$	−10332.3			−1.30128
$399$	−2511.81	+	2268.46i	−0.315157	+	0.284624i
$400$	−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
$406$	−2191.27	−	2421.47i	−0.267859	−	0.295999i
$407$			8318.63i			1.01312i
$408$	−3135.17	+	1805.91i	−0.380427	+	0.219133i
$409$	−2680.13	+	1547.37i	−0.324019	+	0.187073i	−0.653183	−	0.757200i	$-0.726567\pi$
$409$	−2680.13	+	1547.37i	−0.324019	+	0.187073i	0.329163	+	0.944273i	$0.393233\pi$
$410$	13365.7	−	7716.69i	1.60996	−	0.929513i
$411$	−2246.44	+	1293.99i	−0.269608	+	0.155299i
$412$		−	271.076i		−	0.0324149i
$413$	−1753.93	+	377.389i	−0.208972	+	0.0449639i
$414$	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	$-0.638580\pi$
$419$	−7234.25			−0.843476			−0.421738	+	0.906718i	$0.638580\pi$
$420$	622.784	−	1926.54i	0.0723542	−	0.223822i
$421$	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
$427$	5294.25	−	4790.95i	0.600016	−	0.542975i
$428$			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	$0.0577738\pi$
$433$			3252.79i			0.361014i	−0.983574	+	0.180507i	$0.942226\pi$
$434$	−2625.41	+	8149.36i	−0.290378	+	0.901341i
$435$	−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	−0.421278	−	0.906932i	$-0.638418\pi$
$439$	−13036.8	−	7526.81i	−1.41734	−	0.818303i	−0.996065	+	0.0886287i	$0.971752\pi$
$440$	−13814.9			−1.49682
$441$	−7508.57	−	5421.03i	−0.810773	−	0.585361i
$442$	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
$448$	3214.67	−	9978.44i	0.339016	−	1.05231i
$449$			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
$455$	−1639.74	+	1483.86i	−0.168950	+	0.152889i
$456$	−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	$-0.422833\pi$
$461$	4752.26			0.480119			0.240060	+	0.970758i	$0.422833\pi$
$462$	−2726.52	+	8434.28i	−0.274565	+	0.849347i
$463$	−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	−0.657350	−	0.753586i	$-0.728323\pi$
$467$	3269.28	−	5662.56i	0.323949	−	0.561097i	0.981299	+	0.192489i	$0.0616559\pi$
$468$	226.376	−	130.096i	0.0223595	−	0.0128497i
$469$	−18432.1	+	3965.99i	−1.81475	+	0.390474i
$470$			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
$476$	469.113	+	518.395i	0.0451718	+	0.0499172i
$477$	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	0.636085	−	0.771619i	$-0.280553\pi$
$479$	−3671.28	−	6358.85i	−0.350199	−	0.606562i	−0.986284	+	0.165057i	$0.947219\pi$
$480$	4.89394	−	4895.06i	0.000465368	−	0.465475i
$481$	1499.22	+	865.574i	0.142117	+	0.0820515i
$482$	5666.94			0.535523
$483$	3958.60	−	3575.08i	0.372925	−	0.336795i
$484$	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
$490$	14233.5	+	1424.19i	1.31225	+	0.131302i
$491$			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
$497$	2209.38	+	711.777i	0.199405	+	0.0642406i
$498$	−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	$-0.394504\pi$
$503$	7341.52			0.650780			0.325390	+	0.945580i	$0.394504\pi$
$504$	−11452.1	−	3714.71i	−1.01213	−	0.328306i
$505$	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	$0.500614\pi$
$509$	−9956.11	+	17244.5i	−0.866988	+	1.50167i	−0.865060	+	0.501669i	$0.832720\pi$
$510$	−5424.29	−	3138.95i	−0.470964	−	0.272539i
$511$	878.757	+	4084.07i	0.0760742	+	0.353559i
$512$		−	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
$518$	−2355.46	−	10947.1i	−0.199793	−	0.928548i
$519$	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	0.664444	−	0.747338i	$-0.268668\pi$
$521$	−3745.90	−	6488.08i	−0.314992	−	0.545582i	−0.979436	+	0.201756i	$0.935335\pi$
$522$	−2388.75	+	4118.40i	−0.200293	+	0.345321i
$523$	249.515	+	144.058i	0.0208614	+	0.0120444i	0.510394	−	0.859940i	$-0.329499\pi$
$523$	249.515	+	144.058i	0.0208614	+	0.0120444i	−0.489533	+	0.871985i	$0.662833\pi$
$524$	820.223			0.0683809
$525$	12684.3	−	2715.97i	1.05445	−	0.225781i
$526$	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
$532$	809.266	+	260.715i	0.0659514	+	0.0212470i
$533$		−	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
$539$	12149.8	+	1215.69i	0.970923	+	0.0971496i
$540$	−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
$546$	1236.36	+	1368.99i	0.0969072	+	0.107303i
$547$	−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
$553$	13225.9	+	14615.4i	1.01704	+	1.12388i
$554$			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
$560$	15132.6	−	3256.03i	1.14191	−	0.245701i
$561$	−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	$0.0835907\pi$
$563$	9453.63	+	16374.2i	0.707678	+	1.22573i	−0.258038	+	0.966135i	$0.583076\pi$
$564$	−1185.23	−	1.18496i	−0.0884882	−	8.84680e-5i
$565$	−14480.7	−	8360.43i	−1.07824	−	0.622524i
$566$	16815.8			1.24880
$567$	−4191.41	+	12834.2i	−0.310446	+	0.950591i
$568$	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
$574$	−13148.9	+	11898.9i	−0.956138	+	0.865242i
$575$			7471.31i			0.541870i
$576$	−15283.4	−	30.5599i	−1.10557	−	0.00221064i
$577$	7254.16	−	4188.19i	0.523388	−	0.302178i	−0.214932	−	0.976629i	$-0.568953\pi$
$577$	7254.16	−	4188.19i	0.523388	−	0.302178i	0.738320	+	0.674451i	$0.235620\pi$
$578$	−9134.73	+	5273.94i	−0.657361	+	0.379528i
$579$	335.782	+	582.937i	0.0241013	+	0.0418412i
$580$			1433.85i			0.102651i
$581$	−3413.36	+	10595.2i	−0.243735	+	0.756560i
$582$	−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	$-0.769006\pi$
$587$	−21277.2			−1.49609			−0.748043	+	0.663650i	$0.769006\pi$
$588$	−233.939	+	2314.65i	−0.0164073	+	0.162338i
$589$	−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	−0.911124	−	0.412132i	$-0.864784\pi$
$593$	−1424.49	+	2467.29i	−0.0986454	+	0.170859i	0.812479	+	0.582991i	$0.198118\pi$
$594$	12922.5	+	38.7587i	0.892619	+	0.00267725i
$595$	−2647.25	+	8217.14i	−0.182398	+	0.566168i
$596$		−	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	$-0.913962\pi$
$601$		−	7868.29i		−	0.534033i	0.963692	−	0.267017i	$-0.0860379\pi$
$602$	−6646.70	+	6014.83i	−0.449999	+	0.407220i
$603$	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	−0.100724	−	0.994914i	$-0.532116\pi$
$607$	−15144.9	−	8743.92i	−1.01271	−	0.584686i	−0.911983	+	0.410228i	$0.865449\pi$
$608$	2055.57			0.137112
$609$	6240.48	+	2017.33i	0.415233	+	0.134231i
$610$	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
$616$	15518.6	−	3339.10i	1.01504	−	0.218403i
$617$		−	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	0.144202	−	0.989548i	$-0.453938\pi$
$619$	16529.1	−	9543.05i	1.07328	−	0.619657i	0.929075	+	0.369891i	$0.120605\pi$
$620$	3255.49	−	1879.56i	0.210877	−	0.121750i
$621$	−6722.75	−	3908.32i	−0.434420	−	0.252553i
$622$		−	391.901i		−	0.0252633i
$623$	−18704.9	−	20669.9i	−1.20289	−	1.32925i
$624$	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
$630$	−4345.94	−	20396.2i	−0.274835	−	1.28985i
$631$	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
$637$	1483.31	−	2063.19i	0.0922620	−	0.128330i
$638$		−	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	$-0.791472\pi$
$643$		−	19867.3i		−	1.21849i	0.792982	−	0.609246i	$-0.208528\pi$
$644$	−1275.40	−	410.886i	−0.0780401	−	0.0251416i
$645$	−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	$0.0719156\pi$
$647$	11212.2	+	19420.1i	0.681294	+	1.18004i	−0.293293	+	0.956023i	$0.594751\pi$
$648$	−70.1913	+	17551.7i	−0.00425521	+	1.06404i
$649$	−2986.49	−	1724.25i	−0.180632	−	0.104288i
$650$	−2583.78			−0.155914
$651$	−3600.05	−	16813.2i	−0.216739	−	1.01223i
$652$	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
$658$	−1761.43	−	8186.34i	−0.104358	−	0.485011i
$659$		−	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	−0.229619	−	0.973281i	$-0.573748\pi$
$661$	8470.90	−	4890.68i	0.498457	−	0.287784i	0.728076	+	0.685496i	$0.240415\pi$
$662$	−3149.56	+	1818.40i	−0.184911	+	0.106758i
$663$	−964.682	+	555.674i	−0.0565085	+	0.0325499i
$664$			14471.0i			0.845761i
$665$	2208.41	+	10263.7i	0.128780	+	0.598511i
$666$	−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
$672$	1177.65	+	5499.92i	0.0676024	+	0.315720i
$673$	−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	$0.445208\pi$
$677$	−13521.0	+	23419.1i	−0.767584	+	1.32949i	−0.938870	+	0.344273i	$0.888125\pi$
$678$	−6985.73	+	12071.8i	−0.395701	+	0.683795i
$679$	5772.53	+	1859.69i	0.326258	+	0.105108i
$680$			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
$686$	−16333.0	+	1840.44i	−0.909034	+	0.102432i
$687$	−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	0.999676	−	0.0254396i	$-0.00809856\pi$
$691$	26837.3	+	15494.6i	1.47748	+	0.853025i	0.477807	+	0.878465i	$0.341432\pi$
$692$	−5164.56			−0.283710
$693$	−3709.72	−	17410.3i	−0.203348	−	0.954348i
$694$	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
$700$	−2186.49	−	2416.18i	−0.118059	−	0.130462i
$701$		−	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
$707$	−19838.4	+	4268.57i	−1.05530	+	0.227067i
$708$	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
$714$	6851.93	+	2214.99i	0.359141	+	0.116098i
$715$	−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	−0.977934	−	0.208914i	$-0.933007\pi$
$719$	−5938.87	+	10286.4i	−0.308042	+	0.533545i	0.669892	+	0.742459i	$0.266341\pi$
$720$	−11244.0	−	19565.4i	−0.581997	−	1.01272i
$721$	−2851.78	+	2580.67i	−0.147303	+	0.133300i
$722$			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	$0.140929\pi$
$727$			16795.8i			0.856839i	−0.903580	+	0.428419i	$0.859071\pi$
$728$	1012.96	−	3144.27i	0.0515700	−	0.160075i
$729$	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	0.939093	−	0.343663i	$-0.111668\pi$
$733$	22048.4	+	12729.7i	1.11102	+	0.641447i	0.171926	+	0.985110i	$0.445001\pi$
$734$	5007.02			0.251788
$735$	−26196.6	+	11789.0i	−1.31466	+	0.591626i
$736$	−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
$742$	3999.45	−	12414.4i	0.197877	−	0.614214i
$743$			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
$749$	24756.3	−	22402.8i	1.20771	−	1.09290i
$750$	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
$756$	3317.88	−	703.493i	0.159616	−	0.0338436i
$757$	−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	−0.708479	−	0.705732i	$-0.750618\pi$
$761$	5394.02	−	9342.71i	0.256942	−	0.445037i	0.965421	+	0.260695i	$0.0839517\pi$
$762$	−19151.6	−	11082.7i	−0.910486	−	0.526884i
$763$	5135.72	−	1105.04i	0.243677	−	0.0524313i
$764$			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	$-0.682918\pi$
$769$		−	35799.6i		−	1.67876i	0.543543	−	0.839381i	$-0.317082\pi$
$770$	18449.1	+	20387.3i	0.863455	+	0.954163i
$771$	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	$-0.842185\pi$
$773$	−18306.3	−	31707.5i	−0.851788	−	1.47534i	0.0278053	−	0.999613i	$-0.491148\pi$
$774$	11304.6	+	6556.90i	0.524982	+	0.304500i
$775$	20857.2	+	12041.9i	0.966727	+	0.558140i
$776$	7884.22			0.364725
$777$	15072.2	+	16689.0i	0.695895	+	0.770548i
$778$	−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
$784$	−16211.8	+	7315.16i	−0.738511	+	0.333234i
$785$			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	$0.698788\pi$
$787$	−34874.9	+	20135.0i	−1.57961	+	0.911990i	−0.994913	+	0.100742i	$0.967878\pi$
$788$	3441.97	−	1987.22i	0.155603	−	0.0898374i
$789$	−9269.36	+	5339.32i	−0.418248	+	0.240919i
$790$			44386.1i			1.99897i
$791$	18287.2	+	5891.45i	0.822022	+	0.264824i
$792$	−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	$-0.581852\pi$
$797$	−11444.6			−0.508645			−0.254323	+	0.967119i	$0.581852\pi$
$798$	8563.08	−	1833.54i	0.379862	−	0.0813365i
$799$	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
$805$	−3480.45	−	16175.6i	−0.152385	−	0.708216i
$806$			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	$-0.975366\pi$
$811$		−	3571.23i		−	0.154628i	0.997007	−	0.0773138i	$-0.0246343\pi$
$812$	−346.565	−	1610.68i	−0.0149779	−	0.0696104i
$813$	−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
$819$	−3523.76	−	1143.00i	−0.150342	−	0.0487666i
$820$	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
$826$	4418.37	+	1423.43i	0.186120	+	0.0599607i
$827$			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	−0.486042	−	0.873935i	$-0.661560\pi$
$829$	663.246	−	382.925i	0.0277871	−	0.0160429i	0.513829	+	0.857893i	$0.328227\pi$
$830$	−21707.7	+	12532.9i	−0.907813	+	0.524126i
$831$	−6398.75	−	11108.6i	−0.267112	−	0.463722i
$832$		−	4193.51i		−	0.174740i
$833$	987.617	−	9870.36i	0.0410791	−	0.410549i
$834$	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	$-0.535146\pi$
$839$	−5355.68			−0.220380			−0.110190	+	0.993911i	$0.535146\pi$
$840$	−27715.8	+	25030.6i	−1.13844	+	1.02814i
$841$	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
$847$	−791.768	−	874.946i	−0.0321198	−	0.0354941i
$848$		−	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	$0.0551638\pi$
$853$			8591.74i			0.344872i	−0.985021	+	0.172436i	$0.944836\pi$
$854$	−18061.2	+	3886.18i	−0.723703	+	0.155717i
$855$	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	$0.132826\pi$
$857$	20273.3	+	35114.5i	0.808080	+	1.39964i	−0.106112	+	0.994354i	$0.533840\pi$
$858$	−3.54490	+	3545.71i	−0.000141050	+	0.141082i
$859$	−8352.92	−	4822.56i	−0.331779	−	0.191553i	0.324852	−	0.945765i	$-0.394686\pi$
$859$	−8352.92	−	4822.56i	−0.331779	−	0.191553i	−0.656631	+	0.754212i	$0.728019\pi$
$860$	3935.78			0.156057
$861$	10954.4	−	33886.6i	0.433593	−	1.34129i
$862$	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
$868$	−3202.68	+	2898.21i	−0.125237	+	0.113332i
$869$			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
$875$	896.522	−	2782.83i	0.0346377	−	0.107516i
$876$	−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	$-0.640422\pi$
$881$	−22330.5			−0.853956			−0.426978	+	0.904262i	$0.640422\pi$
$882$	9811.70	+	21861.1i	0.374577	+	0.834582i
$883$	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	$-0.575950\pi$
$887$	19107.9	−	33095.9i	0.723316	−	1.25282i	0.959663	−	0.281152i	$-0.0907165\pi$
$888$	25303.0	+	14642.5i	0.956209	+	0.553343i
$889$	−9346.69	+	29012.4i	−0.352618	+	1.09454i
$890$		−	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
$896$	−13691.6	+	12390.0i	−0.510496	+	0.461965i
$897$	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
$903$	5537.39	−	17129.5i	0.204067	−	0.631268i
$904$	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
$910$	5593.95	−	1203.63i	0.203778	−	0.0438462i
$911$		−	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
$917$	−7808.61	−	8628.93i	−0.281203	−	0.310744i
$918$	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
$924$	−3318.72	+	2997.19i	−0.118158	+	0.106710i
$925$	−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	−0.979382	−	0.202019i	$-0.935250\pi$
$929$	−8911.93	+	15435.9i	−0.314737	+	0.545141i	0.664644	+	0.747160i	$0.268583\pi$
$930$	19392.6	−	33511.6i	0.683774	−	1.18160i
$931$	−4961.53	−	10995.7i	−0.174659	−	0.387078i
$932$		−	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	$0.351953\pi$
$937$			51270.5i			1.78755i	−0.448516	+	0.893775i	$0.648047\pi$
$938$	46432.8	+	14958.9i	1.61629	+	0.520709i
$939$	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	0.756683	−	0.653782i	$-0.226819\pi$
$941$	−5422.48	−	9392.01i	−0.187851	−	0.325367i	−0.944533	+	0.328415i	$0.893486\pi$
$942$	2231.66	+	2.23115i	0.0771884	+	7.71708e-5i
$943$	17763.9	+	10256.0i	0.613437	+	0.354168i
$944$	5023.10			0.173186
$945$	28007.6	+	31137.0i	0.964113	+	1.07184i
$946$	−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
$952$	−2712.65	−	12607.2i	−0.0923503	−	0.429203i
$953$			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
$959$	−1943.69	−	9033.42i	−0.0654486	−	0.304175i
$960$	−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
$966$	−13495.4	+	2889.65i	−0.449489	+	0.0962452i
$967$	−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	−0.855344	−	0.518060i	$-0.826654\pi$
$971$	634.824	−	1099.55i	0.0209809	−	0.0363400i	0.876325	+	0.481720i	$0.159988\pi$
$972$	−2450.84	−	4294.41i	−0.0808751	−	0.141711i
$973$	−21447.2	−	6909.46i	−0.706644	−	0.227654i
$974$			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
$980$	5859.36	+	4212.54i	0.190990	+	0.137311i
$981$	−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	$-0.690462\pi$
$983$	−30733.8	−	53232.4i	−0.997207	−	1.72721i	−0.433924	−	0.900950i	$-0.642871\pi$
$984$	46.2871	−	46297.7i	0.00149957	−	1.49992i
$985$	42501.6	+	24538.3i	1.37484	+	0.793762i
$986$	−5099.63			−0.164711
$987$	11271.1	+	12480.2i	0.363488	+	0.402482i
$988$	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
$994$	−4029.85	−	4453.20i	−0.128591	−	0.142100i
$995$		−	64364.3i		−	2.05074i
$996$	−2034.79	−	3532.51i	−0.0647337	−	0.112381i
$997$	29417.3	−	16984.1i	0.934460	−	0.539510i	0.0462403	−	0.998930i	$-0.485276\pi$
$997$	29417.3	−	16984.1i	0.934460	−	0.539510i	0.888219	+	0.459420i	$0.151943\pi$
$998$	−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	21.4.g.a.5.2	✓	12
3.2	odd	2	inner	21.4.g.a.5.5	yes	12
4.3	odd	2		336.4.bc.d.257.1		12
7.2	even	3		147.4.c.a.146.9		12
7.3	odd	6	inner	21.4.g.a.17.5	yes	12
7.4	even	3		147.4.g.d.80.5		12
7.5	odd	6		147.4.c.a.146.10		12
7.6	odd	2		147.4.g.d.68.2		12
12.11	even	2		336.4.bc.d.257.2		12
21.2	odd	6		147.4.c.a.146.4		12
21.5	even	6		147.4.c.a.146.3		12
21.11	odd	6		147.4.g.d.80.2		12
21.17	even	6	inner	21.4.g.a.17.2	yes	12
21.20	even	2		147.4.g.d.68.5		12
28.3	even	6		336.4.bc.d.17.2		12
84.59	odd	6		336.4.bc.d.17.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.g.a.5.2	✓	12	1.1	even	1	trivial
21.4.g.a.5.5	yes	12	3.2	odd	2	inner
21.4.g.a.17.2	yes	12	21.17	even	6	inner
21.4.g.a.17.5	yes	12	7.3	odd	6	inner
147.4.c.a.146.3		12	21.5	even	6
147.4.c.a.146.4		12	21.2	odd	6
147.4.c.a.146.9		12	7.2	even	3
147.4.c.a.146.10		12	7.5	odd	6
147.4.g.d.68.2		12	7.6	odd	2
147.4.g.d.68.5		12	21.20	even	2
147.4.g.d.80.2		12	21.11	odd	6
147.4.g.d.80.5		12	7.4	even	3
336.4.bc.d.17.1		12	84.59	odd	6
336.4.bc.d.17.2		12	28.3	even	6
336.4.bc.d.257.1		12	4.3	odd	2
336.4.bc.d.257.2		12	12.11	even	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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	21.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.24076 - 1.29370i) q^{2} +(5.19615 + 0.00519496i) q^{3} +(-0.652660 - 1.13044i) q^{4} +(8.05907 - 13.9587i) q^{5} +(-11.6366 - 6.73392i) q^{6} +(-5.67909 + 17.6280i) q^{7} +24.0767i q^{8} +(26.9999 + 0.0539876i) q^{9} +O(q^{10})\)	\(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} +(-5.67909 + 17.6280i) q^{7} +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} +(35.5309 - 32.1532i) q^{14} +(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} +(-29.6010 + 91.5685i) q^{21} +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} +(23.6340 - 5.08525i) q^{28} -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} +(200.297 + 221.338i) q^{35} +(-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} +(184.791 - 166.888i) q^{42} -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} +(-278.496 - 200.222i) q^{49} +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} +(-424.424 - 136.733i) q^{56} +(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} +(-154.287 + 475.650i) q^{63} -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} +(-162.471 - 755.091i) q^{70} -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} +(-138.686 - 644.550i) q^{77} +(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} +(122.832 - 26.3009i) q^{84} +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} +(-130.594 - 42.0725i) q^{91} +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} +(365.014 + 808.942i) q^{98} +(-833.358 + 478.920i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} + 14 q^{4} - 56 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 + 14 * q^4 - 56 * q^7 - 3 * q^9	\( 12 q - 3 q^{3} + 14 q^{4} - 56 q^{7} - 3 q^{9} + 30 q^{10} - 192 q^{12} + 6 q^{15} + 134 q^{16} + 66 q^{18} + 300 q^{19} + 357 q^{21} - 268 q^{22} + 414 q^{24} - 42 q^{25} - 602 q^{28} - 822 q^{30} - 930 q^{31} - 855 q^{33} + 852 q^{36} + 764 q^{37} - 426 q^{39} + 2298 q^{40} + 966 q^{42} - 1012 q^{43} + 2367 q^{45} + 608 q^{46} - 336 q^{49} - 1341 q^{51} - 3000 q^{52} - 4158 q^{54} + 270 q^{57} + 2870 q^{58} - 918 q^{60} + 2358 q^{61} + 1071 q^{63} - 548 q^{64} + 2934 q^{66} + 792 q^{67} - 4242 q^{70} - 2712 q^{72} - 2904 q^{73} - 2418 q^{75} + 4296 q^{78} + 1674 q^{79} + 837 q^{81} + 5040 q^{82} + 3864 q^{84} + 348 q^{85} + 1638 q^{87} - 554 q^{88} - 1218 q^{91} - 1479 q^{93} - 1356 q^{94} - 4410 q^{96} - 3354 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 + 14 * q^4 - 56 * q^7 - 3 * q^9 + 30 * q^10 - 192 * q^12 + 6 * q^15 + 134 * q^16 + 66 * q^18 + 300 * q^19 + 357 * q^21 - 268 * q^22 + 414 * q^24 - 42 * q^25 - 602 * q^28 - 822 * q^30 - 930 * q^31 - 855 * q^33 + 852 * q^36 + 764 * q^37 - 426 * q^39 + 2298 * q^40 + 966 * q^42 - 1012 * q^43 + 2367 * q^45 + 608 * q^46 - 336 * q^49 - 1341 * q^51 - 3000 * q^52 - 4158 * q^54 + 270 * q^57 + 2870 * q^58 - 918 * q^60 + 2358 * q^61 + 1071 * q^63 - 548 * q^64 + 2934 * q^66 + 792 * q^67 - 4242 * q^70 - 2712 * q^72 - 2904 * q^73 - 2418 * q^75 + 4296 * q^78 + 1674 * q^79 + 837 * q^81 + 5040 * q^82 + 3864 * q^84 + 348 * q^85 + 1638 * q^87 - 554 * q^88 - 1218 * q^91 - 1479 * q^93 - 1356 * q^94 - 4410 * q^96 - 3354 * q^99

Introduction

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