LMFDB - Embedded newform 21.4.g.a.17.2

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			17.2
Root			$0.00299931 + 3.00000i$ of defining polynomial
Character	$\chi$	$=$	21.17
Dual form			21.4.g.a.5.2

$q$-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 $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

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

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	−0.840747	−	0.541429i	$-0.817884\pi$
$2$	−2.24076	+	1.29370i	−0.792229	+	0.457393i	0.0485179	+	0.998822i	$0.484550\pi$
$3$	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	0.960670	+	0.277694i	$0.0895701\pi$
$5$	8.05907	+	13.9587i	0.720825	+	1.24851i	−0.239845	+	0.970811i	$0.577097\pi$
$6$	−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	0.0139322	−	0.999903i	$-0.495565\pi$
$11$	−30.8296	−	17.7995i	−0.845043	−	0.487886i	−0.858975	+	0.512017i	$0.828898\pi$
$12$	−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	$-0.0251813\pi$
$14$	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	−0.744246	−	0.667905i	$-0.767191\pi$
$17$	14.4601	−	25.0457i	0.206300	−	0.357322i	0.950546	+	0.310584i	$0.100524\pi$
$18$	−60.4306	+	35.0509i	−0.791313	+	0.458977i
$19$	30.4580	−	17.5849i	0.367765	−	0.212329i	−0.304716	−	0.952443i	$-0.598562\pi$
$19$	30.4580	−	17.5849i	0.367765	−	0.212329i	0.672482	+	0.740114i	$0.265228\pi$
$20$	−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	−0.701549	−	0.712621i	$-0.747508\pi$
$23$	−48.0017	+	27.7138i	−0.435175	+	0.251249i	0.266374	+	0.963870i	$0.414175\pi$
$24$	−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	$0.0700169\pi$
$29$			68.1510i			0.436390i	−0.975905	+	0.218195i	$0.929983\pi$
$30$	−187.777	−	108.163i	−1.14277	−	0.658259i
$31$	−154.734	−	89.3356i	−0.896484	−	0.517585i	−0.0204262	−	0.999791i	$-0.506502\pi$
$31$	−154.734	−	89.3356i	−0.896484	−	0.517585i	−0.876058	+	0.482206i	$0.839836\pi$
$32$	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	0.999753	+	0.0222405i	$0.00707996\pi$
$37$	116.838	+	202.370i	0.519137	+	0.899172i	−0.480615	+	0.876931i	$0.659587\pi$
$38$	−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	0.969160	−	0.246434i	$-0.0792588\pi$
$47$	87.3726	+	151.334i	0.271162	+	0.469666i	−0.697998	+	0.716100i	$0.745925\pi$
$48$	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	0.773319	−	0.634017i	$-0.218595\pi$
$53$	235.715	+	136.090i	0.610905	+	0.352706i	−0.162415	+	0.986723i	$0.551928\pi$
$54$	−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	−0.807626	−	0.589695i	$-0.799248\pi$
$59$	48.4354	−	83.8926i	0.106877	−	0.185117i	0.914504	+	0.404578i	$0.132581\pi$
$60$	−109.323	+	0.109298i	−0.235227	+	0.000235173i
$61$	−333.882	+	192.767i	−0.700807	+	0.404611i	−0.807648	−	0.589665i	$-0.799260\pi$
$61$	−333.882	+	192.767i	−0.700807	+	0.404611i	0.106841	+	0.994276i	$0.465927\pi$
$62$	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	0.141708	−	0.989908i	$-0.454741\pi$
$67$	509.009	−	881.630i	0.928140	−	1.60759i	0.786432	−	0.617677i	$-0.211926\pi$
$68$	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	$0.0334038\pi$
$71$			125.333i			0.209497i	−0.994499	+	0.104749i	$0.966596\pi$
$72$	−1.29984	−	650.068i	−0.00212761	−	1.06405i
$73$	195.346	+	112.783i	0.313199	+	0.180825i	0.648357	−	0.761337i	$-0.275456\pi$
$73$	195.346	+	112.783i	0.313199	+	0.180825i	−0.335158	+	0.942162i	$0.608790\pi$
$74$	−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	0.943933	+	0.330138i	$0.107095\pi$
$79$	532.154	+	921.718i	0.757874	+	1.31268i	−0.186059	+	0.982539i	$0.559572\pi$
$80$	−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	−0.832112	−	0.554607i	$-0.812869\pi$
$89$	−752.606	−	1303.55i	−0.896360	−	1.55254i	−0.0642474	−	0.997934i	$-0.520465\pi$
$90$	−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	$0.0548244\pi$
$97$			327.463i			0.342771i	−0.985204	+	0.171386i	$0.945176\pi$
$98$	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	−0.459190	−	0.888338i	$-0.651860\pi$
$101$	547.845	−	948.895i	0.539729	−	0.934837i	0.998918	−	0.0464990i	$-0.0148064\pi$
$102$	0.388731	+	388.820i	0.000377354	+	0.377440i
$103$	179.848	−	103.835i	0.172048	−	0.0993318i	−0.411503	−	0.911408i	$-0.634996\pi$
$103$	179.848	−	103.835i	0.172048	−	0.0993318i	0.583551	+	0.812076i	$0.301663\pi$
$104$	−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	−0.995443	−	0.0953593i	$-0.969600\pi$
$107$	−1561.25	+	901.391i	−1.41058	+	0.814399i	−0.415138	+	0.909759i	$0.636267\pi$
$108$	−91.0895	+	158.870i	−0.0811583	+	0.141549i
$109$	−141.825	+	245.647i	−0.124627	+	0.215860i	−0.921587	−	0.388172i	$-0.873107\pi$
$109$	−141.825	+	245.647i	−0.124627	+	0.215860i	0.796960	+	0.604032i	$0.206440\pi$
$110$	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	$0.142126\pi$
$113$			1037.39i			0.863627i	−0.901963	+	0.431814i	$0.857874\pi$
$114$	−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	0.742026	−	0.670371i	$-0.233865\pi$
$131$	−314.185	−	544.184i	−0.209545	−	0.362943i	−0.951571	+	0.307428i	$0.900532\pi$
$132$	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	0.359186	−	0.933266i	$-0.383054\pi$
$137$	−432.079	−	249.461i	−0.269453	−	0.155569i	−0.628639	+	0.777697i	$0.716388\pi$
$138$	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	$-0.121055\pi$
$140$	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	0.167648	−	0.985847i	$-0.446383\pi$
$149$	2010.18	−	1160.58i	1.10524	−	0.638111i	0.937592	+	0.347736i	$0.113050\pi$
$150$	−1.81183	−	1812.25i	−0.000986238	−	0.986463i
$151$	−488.726	+	846.497i	−0.263390	+	0.456205i	−0.967141	−	0.254242i	$-0.918174\pi$
$151$	−488.726	+	846.497i	−0.263390	+	0.456205i	0.703750	+	0.710447i	$0.251507\pi$
$152$	−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	0.463018	−	0.886349i	$-0.346767\pi$
$157$	−143.752	−	82.9950i	−0.0730740	−	0.0421893i	−0.536092	+	0.844160i	$0.680100\pi$
$158$	−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	0.724455	−	0.689322i	$-0.242092\pi$
$163$	−488.511	−	846.127i	−0.234743	−	0.406587i	−0.959198	+	0.282735i	$0.908758\pi$
$164$	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	0.862616	+	0.505860i	$0.168825\pi$
$173$	1978.27	+	3426.47i	0.869395	+	1.50584i	0.00677983	+	0.999977i	$0.497842\pi$
$174$	−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	0.911770	−	0.410701i	$-0.134716\pi$
$179$	2423.54	+	1399.23i	1.01198	+	0.584266i	0.100208	+	0.994967i	$0.468049\pi$
$180$	−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	$0.899879\pi$
$182$	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	−0.961972	−	0.273148i	$-0.911935\pi$
$191$	−3184.51	+	1838.58i	−1.20640	+	0.696518i	−0.244433	+	0.969666i	$0.578602\pi$
$192$	−2941.30	+	2.94063i	−1.10557	+	0.00110532i
$193$	64.7335	−	112.122i	0.0241431	−	0.0418171i	−0.853701	−	0.520763i	$-0.825648\pi$
$193$	64.7335	−	112.122i	0.0241431	−	0.0418171i	0.877845	+	0.478946i	$0.158981\pi$
$194$	−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	$-0.814402\pi$
$197$		−	3044.81i		−	1.10119i	0.834774	−	0.550593i	$-0.185598\pi$
$198$	2486.94	−	4.97275i	0.892621	−	0.00178484i
$199$	3458.29	+	1996.64i	1.23192	+	0.711248i	0.967429	−	0.253141i	$-0.0814637\pi$
$199$	3458.29	+	1996.64i	1.23192	+	0.711248i	0.264488	+	0.964389i	$0.414797\pi$
$200$	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	$-0.740247\pi$
$223$		−	4851.53i		−	1.45687i	0.685114	−	0.728436i	$-0.259753\pi$
$224$	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	−0.639368	−	0.768901i	$-0.720804\pi$
$227$	1184.05	−	2050.83i	0.346203	−	0.599642i	0.985572	+	0.169259i	$0.0541374\pi$
$228$	0.238490	+	238.544i	6.92736e−5	+	0.0692894i
$229$	−3737.27	+	2157.72i	−1.07845	+	0.622646i	−0.930479	−	0.366345i	$-0.880609\pi$
$229$	−3737.27	+	2157.72i	−1.07845	+	0.622646i	−0.147975	+	0.988991i	$0.547276\pi$
$230$	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	0.367949	−	0.929846i	$-0.380060\pi$
$233$	4826.98	−	2786.86i	1.35719	−	0.783576i	0.989245	+	0.146270i	$0.0467267\pi$
$234$	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	$0.218512\pi$
$239$			4683.70i			1.26763i	−0.773485	+	0.633814i	$0.781488\pi$
$240$	−2167.67	+	3763.19i	−0.583009	+	1.01214i
$241$	−1896.77	−	1095.10i	−0.506977	−	0.292703i	0.224613	−	0.974448i	$-0.427888\pi$
$241$	−1896.77	−	1095.10i	−0.506977	−	0.292703i	−0.731590	+	0.681745i	$0.761222\pi$
$242$	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	0.925559	−	0.378604i	$-0.123596\pi$
$257$	555.785	+	962.648i	0.134898	+	0.233651i	−0.790660	+	0.612255i	$0.790263\pi$
$258$	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	0.276217	−	0.961095i	$-0.410919\pi$
$263$	−1782.86	−	1029.34i	−0.418007	−	0.241337i	−0.694224	+	0.719759i	$0.744252\pi$
$264$	−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	−0.451165	−	0.892441i	$-0.648991\pi$
$269$	2414.62	−	4182.24i	0.547294	−	0.947940i	0.998459	−	0.0554999i	$-0.0176752\pi$
$270$	−5075.81	−	2910.26i	−1.14409	−	0.655973i
$271$	−191.772	+	110.720i	−0.0429865	+	0.0248183i	−0.521339	−	0.853350i	$-0.674567\pi$
$271$	−191.772	+	110.720i	−0.0429865	+	0.0248183i	0.478353	+	0.878168i	$0.341234\pi$
$272$	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	−0.968235	−	0.250041i	$-0.919556\pi$
$277$	−1233.58	+	2136.62i	−0.267576	+	0.463455i	0.700660	+	0.713496i	$0.252889\pi$
$278$	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	$0.146136\pi$
$281$			4174.76i			0.886282i	−0.896452	+	0.443141i	$0.853864\pi$
$282$	−2035.79	−	1172.65i	−0.429892	−	0.247626i
$283$	−5628.39	−	3249.55i	−1.18224	−	0.682565i	−0.225706	−	0.974195i	$-0.572469\pi$
$283$	−5628.39	−	3249.55i	−1.18224	−	0.682565i	−0.956531	+	0.291630i	$0.905802\pi$
$284$	−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	$-0.896306\pi$
$307$		−	3442.95i		−	0.640064i	0.947407	−	0.320032i	$-0.103694\pi$
$308$	−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	−0.859039	−	0.511911i	$-0.828938\pi$
$311$	75.7324	−	131.172i	0.0138083	−	0.0239167i	0.872847	+	0.487994i	$0.162271\pi$
$312$	−926.824	+	0.926612i	−0.168177	+	0.000168138i
$313$	8335.31	−	4812.40i	1.50524	−	0.869050i	0.505257	−	0.862969i	$-0.331398\pi$
$313$	8335.31	−	4812.40i	1.50524	−	0.869050i	0.999982	−	0.00608123i	$-0.00193573\pi$
$314$	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	−0.993739	−	0.111726i	$-0.964362\pi$
$317$	−7866.93	+	4541.98i	−1.39385	+	0.804741i	−0.400112	+	0.916466i	$0.631029\pi$
$318$	−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	0.918459	−	0.395516i	$-0.129434\pi$
$331$	702.788	+	1217.26i	0.116703	+	0.202136i	−0.801756	+	0.597651i	$0.796101\pi$
$332$	−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	0.314162	−	0.949369i	$-0.398276\pi$
$347$	−2268.41	−	1309.67i	−0.350935	−	0.202612i	−0.665097	+	0.746757i	$0.731610\pi$
$348$	−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	$-0.153088\pi$
$350$	−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	−0.593031	−	0.805180i	$-0.702069\pi$
$353$	2658.15	−	4604.06i	0.400791	−	0.694190i	0.993822	+	0.110990i	$0.0354020\pi$
$354$	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	−0.613825	−	0.789442i	$-0.710370\pi$
$359$	−1612.51	+	930.982i	−0.237061	+	0.136867i	0.376764	+	0.926309i	$0.377037\pi$
$360$	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	0.376059	−	0.926596i	$-0.377279\pi$
$367$	−1675.89	−	967.574i	−0.238367	−	0.137621i	−0.614426	+	0.788975i	$0.710612\pi$
$368$	−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	−0.999045	−	0.0436892i	$-0.986089\pi$
$373$	−3871.04	−	6704.83i	−0.537359	−	0.930732i	0.461687	−	0.887043i	$-0.347244\pi$
$374$	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	0.526345	−	0.850271i	$-0.323562\pi$
$383$	−3546.73	−	6143.12i	−0.473184	−	0.819578i	−0.999529	+	0.0306926i	$0.990229\pi$
$384$	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	0.845077	−	0.534644i	$-0.179554\pi$
$389$	6173.12	+	3564.05i	0.804601	+	0.464537i	−0.0404765	+	0.999180i	$0.512888\pi$
$390$	−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	0.0765855	−	0.997063i	$-0.475598\pi$
$397$	7738.99	−	4468.11i	0.978360	−	0.564857i	0.901775	+	0.432206i	$0.142265\pi$
$398$	−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	0.0647568	−	0.997901i	$-0.479373\pi$
$401$	7719.60	−	4456.91i	0.961343	−	0.555032i	0.896586	+	0.442869i	$0.146039\pi$
$402$	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	0.329163	−	0.944273i	$-0.393233\pi$
$409$	−2680.13	−	1547.37i	−0.324019	−	0.187073i	−0.653183	+	0.757200i	$0.726567\pi$
$410$	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	−0.226737	−	0.973956i	$-0.572806\pi$
$431$	−10590.4	−	6114.37i	−1.18358	−	0.683338i	−0.956839	+	0.290618i	$0.906139\pi$
$432$	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	$-0.0577738\pi$
$434$	−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	−0.996065	−	0.0886287i	$-0.971752\pi$
$439$	−13036.8	+	7526.81i	−1.41734	+	0.818303i	−0.421278	+	0.906932i	$0.638418\pi$
$440$	−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	−0.510919	−	0.859629i	$-0.670695\pi$
$443$	−204.373	+	117.995i	−0.0219189	+	0.0126549i	0.489001	+	0.872283i	$0.337362\pi$
$444$	−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	$-0.900095\pi$
$449$		−	5874.66i		−	0.617466i	0.951149	−	0.308733i	$-0.0999049\pi$
$450$	−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	0.858042	−	0.513579i	$-0.171681\pi$
$457$	−153.883	−	266.533i	−0.0157513	−	0.0272821i	−0.873794	+	0.486297i	$0.838347\pi$
$458$	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	0.981299	−	0.192489i	$-0.0616559\pi$
$467$	3269.28	+	5662.56i	0.323949	+	0.561097i	−0.657350	+	0.753586i	$0.728323\pi$
$468$	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	−0.986284	−	0.165057i	$-0.947219\pi$
$479$	−3671.28	+	6358.85i	−0.350199	+	0.606562i	0.636085	+	0.771619i	$0.280553\pi$
$480$	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	−0.981812	−	0.189857i	$-0.939198\pi$
$487$	−3508.78	+	6077.39i	−0.326485	+	0.565489i	0.655327	+	0.755345i	$0.272531\pi$
$488$	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	$-0.996720\pi$
$491$		−	224.222i		−	0.0206089i	0.999947	−	0.0103045i	$-0.00328007\pi$
$492$	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	0.778770	+	0.627309i	$0.215844\pi$
$499$	10396.1	+	18006.6i	0.932651	+	1.61540i	0.153881	+	0.988089i	$0.450823\pi$
$500$	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	−0.865060	−	0.501669i	$-0.832720\pi$
$509$	−9956.11	−	17244.5i	−0.866988	−	1.50167i	−0.00192778	−	0.999998i	$-0.500614\pi$
$510$	−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	−0.979436	−	0.201756i	$-0.935335\pi$
$521$	−3745.90	+	6488.08i	−0.314992	+	0.545582i	0.664444	+	0.747338i	$0.268668\pi$
$522$	−2388.75	−	4118.40i	−0.200293	−	0.345321i
$523$	249.515	−	144.058i	0.0208614	−	0.0120444i	−0.489533	−	0.871985i	$-0.662833\pi$
$523$	249.515	−	144.058i	0.0208614	−	0.0120444i	0.510394	+	0.859940i	$0.329499\pi$
$524$	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	−0.994475	−	0.104975i	$-0.966524\pi$
$541$	−7400.87	−	12818.7i	−0.588149	−	1.01870i	0.406326	−	0.913728i	$-0.366810\pi$
$542$	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	0.944631	−	0.328135i	$-0.106420\pi$
$557$	14891.1	+	8597.36i	1.13277	+	0.654007i	0.188142	+	0.982142i	$0.439754\pi$
$558$	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	−0.258038	−	0.966135i	$-0.583076\pi$
$563$	9453.63	−	16374.2i	0.707678	−	1.22573i	0.965716	−	0.259600i	$-0.0835907\pi$
$564$	−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	−0.712419	−	0.701754i	$-0.752400\pi$
$569$	−6255.57	+	3611.66i	−0.460891	+	0.266096i	0.251528	+	0.967850i	$0.419067\pi$
$570$	−7621.35	+	7.61961i	−0.560041	+	0.000559913i
$571$	4965.17	−	8599.93i	0.363898	−	0.630290i	−0.624700	−	0.780865i	$-0.714779\pi$
$571$	4965.17	−	8599.93i	0.363898	−	0.630290i	0.988599	+	0.150574i	$0.0481122\pi$
$572$	−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	0.738320	−	0.674451i	$-0.235620\pi$
$577$	7254.16	+	4188.19i	0.523388	+	0.302178i	−0.214932	+	0.976629i	$0.568953\pi$
$578$	−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	0.812479	−	0.582991i	$-0.198118\pi$
$593$	−1424.49	−	2467.29i	−0.0986454	−	0.170859i	−0.911124	+	0.412132i	$0.864784\pi$
$594$	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	0.625353	−	0.780342i	$-0.284955\pi$
$599$	3844.40	+	2219.57i	0.262234	+	0.151401i	−0.363119	+	0.931743i	$0.618288\pi$
$600$	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	$0.913962\pi$
$602$	−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	−0.911983	−	0.410228i	$-0.865449\pi$
$607$	−15144.9	+	8743.92i	−1.01271	+	0.584686i	−0.100724	+	0.994914i	$0.532116\pi$
$608$	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	−0.996245	−	0.0865820i	$-0.972406\pi$
$613$	−6422.07	+	11123.3i	−0.423140	+	0.732900i	0.573105	+	0.819482i	$0.305739\pi$
$614$	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	$0.280127\pi$
$617$			23625.5i			1.54153i	−0.637117	+	0.770767i	$0.719873\pi$
$618$	−1393.60	+	2419.37i	−0.0907100	+	0.157478i
$619$	16529.1	+	9543.05i	1.07328	+	0.619657i	0.929075	−	0.369891i	$-0.120605\pi$
$619$	16529.1	+	9543.05i	1.07328	+	0.619657i	0.144202	+	0.989548i	$0.453938\pi$
$620$	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	−0.204827	−	0.978798i	$-0.565663\pi$
$641$	−18742.7	−	10821.1i	−1.15490	−	0.666784i	−0.950078	+	0.312014i	$0.898996\pi$
$642$	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	$0.791472\pi$
$644$	−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	−0.293293	−	0.956023i	$-0.594751\pi$
$647$	11212.2	−	19420.1i	0.681294	−	1.18004i	0.974586	−	0.224012i	$-0.0719156\pi$
$648$	−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	0.120353	−	0.992731i	$-0.461597\pi$
$653$	17358.5	−	10021.9i	1.04026	−	0.600594i	0.919907	+	0.392137i	$0.128264\pi$
$654$	−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	$0.127754\pi$
$659$			13217.9i			0.781327i	−0.920533	+	0.390664i	$0.872246\pi$
$660$	3372.34	+	1942.53i	0.198891	+	0.114565i
$661$	8470.90	+	4890.68i	0.498457	+	0.287784i	0.728076	−	0.685496i	$-0.240415\pi$
$661$	8470.90	+	4890.68i	0.498457	+	0.287784i	−0.229619	+	0.973281i	$0.573748\pi$
$662$	−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	−0.938870	−	0.344273i	$-0.888125\pi$
$677$	−13521.0	−	23419.1i	−0.767584	−	1.32949i	0.171286	−	0.985221i	$-0.445208\pi$
$678$	−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	0.788339	−	0.615241i	$-0.210941\pi$
$683$	11596.9	+	6695.45i	0.649694	+	0.375101i	−0.138645	+	0.990342i	$0.544275\pi$
$684$	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	0.477807	−	0.878465i	$-0.341432\pi$
$691$	26837.3	−	15494.6i	1.47748	−	0.853025i	0.999676	+	0.0254396i	$0.00809856\pi$
$692$	−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	$0.0248303\pi$
$701$			2892.67i			0.155855i	−0.996959	+	0.0779277i	$0.975170\pi$
$702$	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	0.574210	−	0.818708i	$-0.305309\pi$
$709$	−7965.19	−	13796.1i	−0.421917	−	0.730781i	−0.996127	+	0.0879267i	$0.971976\pi$
$710$	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	0.669892	−	0.742459i	$-0.266341\pi$
$719$	−5938.87	−	10286.4i	−0.308042	−	0.533545i	−0.977934	+	0.208914i	$0.933007\pi$
$720$	−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	$-0.859071\pi$
$727$		−	16795.8i		−	0.856839i	0.903580	−	0.428419i	$-0.140929\pi$
$728$	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	0.171926	−	0.985110i	$-0.445001\pi$
$733$	22048.4	−	12729.7i	1.11102	−	0.641447i	0.939093	+	0.343663i	$0.111668\pi$
$734$	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	−0.535251	−	0.844693i	$-0.679783\pi$
$739$	9319.48	−	16141.8i	0.463901	−	0.803499i	0.999151	+	0.0411940i	$0.0131162\pi$
$740$	−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	$-0.887302\pi$
$743$		−	14043.3i		−	0.693401i	0.937976	−	0.346700i	$-0.112698\pi$
$744$	−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	0.598705	−	0.800970i	$-0.295682\pi$
$751$	−8115.13	−	14055.8i	−0.394308	−	0.682961i	−0.993013	+	0.118009i	$0.962349\pi$
$752$	−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	0.965421	−	0.260695i	$-0.0839517\pi$
$761$	5394.02	+	9342.71i	0.256942	+	0.445037i	−0.708479	+	0.705732i	$0.750618\pi$
$762$	−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	$0.317082\pi$
$769$			35799.6i			1.67876i	−0.543543	+	0.839381i	$0.682918\pi$
$770$	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	0.0278053	+	0.999613i	$0.491148\pi$
$773$	−18306.3	+	31707.5i	−0.851788	+	1.47534i	−0.879593	+	0.475727i	$0.842185\pi$
$774$	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	−0.994913	−	0.100742i	$-0.967878\pi$
$787$	−34874.9	−	20135.0i	−1.57961	−	0.911990i	−0.584701	−	0.811249i	$-0.698788\pi$
$788$	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	0.440117	−	0.897940i	$-0.354937\pi$
$809$	−2702.86	−	1560.50i	−0.117463	−	0.0678172i	−0.557580	+	0.830123i	$0.688270\pi$
$810$	−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	$0.975366\pi$
$812$	−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	0.118801	−	0.992918i	$-0.462095\pi$
$821$	24420.3	−	14099.1i	1.03809	−	0.599344i	0.919293	+	0.393574i	$0.128762\pi$
$822$	6707.78	−	6.70625i	0.284624	−	0.000284559i
$823$	5700.86	−	9874.18i	0.241457	−	0.418217i	−0.719672	−	0.694314i	$-0.755708\pi$
$823$	5700.86	−	9874.18i	0.241457	−	0.418217i	0.961130	+	0.276097i	$0.0890412\pi$
$824$	−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	$-0.869578\pi$
$827$		−	18948.2i		−	0.796726i	0.917228	−	0.398363i	$-0.130422\pi$
$828$	−3.90604	−	1953.46i	−0.000163942	−	0.0819898i
$829$	663.246	+	382.925i	0.0277871	+	0.0160429i	0.513829	−	0.857893i	$-0.328227\pi$
$829$	663.246	+	382.925i	0.0277871	+	0.0160429i	−0.486042	+	0.873935i	$0.661560\pi$
$830$	−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	$-0.944836\pi$
$853$		−	8591.74i		−	0.344872i	0.985021	−	0.172436i	$-0.0551638\pi$
$854$	−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	−0.106112	−	0.994354i	$-0.533840\pi$
$857$	20273.3	−	35114.5i	0.808080	−	1.39964i	0.914192	−	0.405281i	$-0.132826\pi$
$858$	−3.54490	−	3545.71i	−0.000141050	−	0.141082i
$859$	−8352.92	+	4822.56i	−0.331779	+	0.191553i	−0.656631	−	0.754212i	$-0.728019\pi$
$859$	−8352.92	+	4822.56i	−0.331779	+	0.191553i	0.324852	+	0.945765i	$0.394686\pi$
$860$	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	−0.683250	−	0.730184i	$-0.739434\pi$
$863$	−9951.19	+	5745.32i	−0.392517	+	0.226620i	0.290733	+	0.956804i	$0.406101\pi$
$864$	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	0.996902	+	0.0786543i	$0.0250623\pi$
$877$	14714.7	+	25486.6i	0.566568	+	0.981324i	−0.430334	+	0.902670i	$0.641604\pi$
$878$	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	0.959663	+	0.281152i	$0.0907165\pi$
$887$	19107.9	+	33095.9i	0.723316	+	1.25282i	−0.236347	+	0.971669i	$0.575950\pi$
$888$	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	−0.773417	−	0.633897i	$-0.781454\pi$
$907$	4432.30	−	7676.97i	0.162262	−	0.281047i	0.935680	+	0.352850i	$0.114788\pi$
$908$	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	$0.0888100\pi$
$911$			15145.0i			0.550798i	−0.961330	+	0.275399i	$0.911190\pi$
$912$	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	0.903486	−	0.428617i	$-0.140999\pi$
$919$	2244.07	+	3886.84i	0.0805495	+	0.139516i	−0.822937	+	0.568133i	$0.807666\pi$
$920$	−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	0.664644	−	0.747160i	$-0.268583\pi$
$929$	−8911.93	−	15435.9i	−0.314737	−	0.545141i	−0.979382	+	0.202019i	$0.935250\pi$
$930$	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	$-0.648047\pi$
$937$		−	51270.5i		−	1.78755i	0.448516	−	0.893775i	$-0.351953\pi$
$938$	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	−0.944533	−	0.328415i	$-0.893486\pi$
$941$	−5422.48	+	9392.01i	−0.187851	+	0.325367i	0.756683	+	0.653782i	$0.226819\pi$
$942$	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	0.292397	−	0.956297i	$-0.405547\pi$
$947$	36916.8	−	21313.9i	1.26677	−	0.731372i	0.974376	+	0.224926i	$0.0722139\pi$
$948$	−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	$-0.808977\pi$
$953$		−	33229.0i		−	1.12948i	0.825269	−	0.564739i	$-0.191023\pi$
$954$	−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	0.876325	−	0.481720i	$-0.159988\pi$
$971$	634.824	+	1099.55i	0.0209809	+	0.0363400i	−0.855344	+	0.518060i	$0.826654\pi$
$972$	−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	0.985957	+	0.167001i	$0.0534082\pi$
$977$	49580.5	+	28625.3i	1.62356	+	0.937364i	0.637605	+	0.770363i	$0.279925\pi$
$978$	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	−0.433924	+	0.900950i	$0.642871\pi$
$983$	−30733.8	+	53232.4i	−0.997207	+	1.72721i	−0.563283	+	0.826264i	$0.690462\pi$
$984$	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	−0.0620930	−	0.998070i	$-0.519778\pi$
$991$	25996.6	−	45027.4i	0.833308	−	1.44333i	0.895401	−	0.445261i	$-0.146889\pi$
$992$	−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	0.888219	−	0.459420i	$-0.151943\pi$
$997$	29417.3	+	16984.1i	0.934460	+	0.539510i	0.0462403	+	0.998930i	$0.485276\pi$
$998$	−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.17.2	yes	12
3.2	odd	2	inner	21.4.g.a.17.5	yes	12
4.3	odd	2		336.4.bc.d.17.1		12
7.2	even	3		147.4.g.d.68.5		12
7.3	odd	6		147.4.c.a.146.4		12
7.4	even	3		147.4.c.a.146.3		12
7.5	odd	6	inner	21.4.g.a.5.5	yes	12
7.6	odd	2		147.4.g.d.80.2		12
12.11	even	2		336.4.bc.d.17.2		12
21.2	odd	6		147.4.g.d.68.2		12
21.5	even	6	inner	21.4.g.a.5.2	✓	12
21.11	odd	6		147.4.c.a.146.10		12
21.17	even	6		147.4.c.a.146.9		12
21.20	even	2		147.4.g.d.80.5		12
28.19	even	6		336.4.bc.d.257.2		12
84.47	odd	6		336.4.bc.d.257.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.g.a.5.2	✓	12	21.5	even	6	inner
21.4.g.a.5.5	yes	12	7.5	odd	6	inner
21.4.g.a.17.2	yes	12	1.1	even	1	trivial
21.4.g.a.17.5	yes	12	3.2	odd	2	inner
147.4.c.a.146.3		12	7.4	even	3
147.4.c.a.146.4		12	7.3	odd	6
147.4.c.a.146.9		12	21.17	even	6
147.4.c.a.146.10		12	21.11	odd	6
147.4.g.d.68.2		12	21.2	odd	6
147.4.g.d.68.5		12	7.2	even	3
147.4.g.d.80.2		12	7.6	odd	2
147.4.g.d.80.5		12	21.20	even	2
336.4.bc.d.17.1		12	4.3	odd	2
336.4.bc.d.17.2		12	12.11	even	2
336.4.bc.d.257.1		12	84.47	odd	6
336.4.bc.d.257.2		12	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
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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