LMFDB - Embedded newform 48.4.k.a.11.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,4,Mod(11,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

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

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

chi := DirichletCharacter("48.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	48.k (of order $4$, 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:	$2.83209168028$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.8
Character	$\chi$	$=$	48.11
Dual form			48.4.k.a.35.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13198 - 2.59203i) q^{2} +(-1.13522 + 5.07063i) q^{3} +(-5.43724 + 5.86826i) q^{4} +(11.2665 - 11.2665i) q^{5} +(14.4283 - 2.79732i) q^{6} +30.2121 q^{7} +(21.3655 + 7.45073i) q^{8} +(-24.4225 - 11.5126i) q^{9} +O(q^{10})$	\(q+(-1.13198 - 2.59203i) q^{2} +(-1.13522 + 5.07063i) q^{3} +(-5.43724 + 5.86826i) q^{4} +(11.2665 - 11.2665i) q^{5} +(14.4283 - 2.79732i) q^{6} +30.2121 q^{7} +(21.3655 + 7.45073i) q^{8} +(-24.4225 - 11.5126i) q^{9} +(-41.9567 - 16.4497i) q^{10} +(14.9799 + 14.9799i) q^{11} +(-23.5833 - 34.2320i) q^{12} +(10.4733 - 10.4733i) q^{13} +(-34.1995 - 78.3106i) q^{14} +(44.3383 + 69.9184i) q^{15} +(-4.87289 - 63.8142i) q^{16} +69.5806i q^{17} +(-2.19516 + 76.3360i) q^{18} +(-36.4354 - 36.4354i) q^{19} +(4.85610 + 127.374i) q^{20} +(-34.2975 + 153.194i) q^{21} +(21.8714 - 55.7853i) q^{22} +1.28579i q^{23} +(-62.0345 + 99.8785i) q^{24} -128.869i q^{25} +(-39.0027 - 15.2916i) q^{26} +(86.1012 - 110.768i) q^{27} +(-164.270 + 177.292i) q^{28} +(-119.373 - 119.373i) q^{29} +(131.040 - 194.073i) q^{30} +172.615i q^{31} +(-159.892 + 84.8672i) q^{32} +(-92.9630 + 58.9519i) q^{33} +(180.355 - 78.7640i) q^{34} +(340.385 - 340.385i) q^{35} +(200.350 - 80.7210i) q^{36} +(-235.193 - 235.193i) q^{37} +(-53.1974 + 135.686i) q^{38} +(41.2167 + 64.9958i) q^{39} +(324.659 - 156.772i) q^{40} +19.9510 q^{41} +(435.908 - 84.5128i) q^{42} +(-294.812 + 294.812i) q^{43} +(-169.355 + 6.45663i) q^{44} +(-404.864 + 145.450i) q^{45} +(3.33280 - 1.45549i) q^{46} +69.5052 q^{47} +(329.110 + 47.7348i) q^{48} +569.769 q^{49} +(-334.033 + 145.878i) q^{50} +(-352.818 - 78.9896i) q^{51} +(4.51421 + 118.406i) q^{52} +(122.813 - 122.813i) q^{53} +(-384.579 - 97.7893i) q^{54} +337.543 q^{55} +(645.497 + 225.102i) q^{56} +(226.113 - 143.388i) q^{57} +(-174.291 + 444.548i) q^{58} +(-63.2396 - 63.2396i) q^{59} +(-651.377 - 119.974i) q^{60} +(-352.521 + 352.521i) q^{61} +(447.423 - 195.397i) q^{62} +(-737.855 - 347.819i) q^{63} +(400.973 + 318.378i) q^{64} -235.996i q^{65} +(258.037 + 174.230i) q^{66} +(-228.455 - 228.455i) q^{67} +(-408.317 - 378.327i) q^{68} +(-6.51976 - 1.45966i) q^{69} +(-1267.60 - 496.979i) q^{70} +524.753i q^{71} +(-436.024 - 427.939i) q^{72} -578.802i q^{73} +(-343.393 + 875.860i) q^{74} +(653.449 + 146.296i) q^{75} +(411.920 - 15.7044i) q^{76} +(452.573 + 452.573i) q^{77} +(121.815 - 180.409i) q^{78} +745.229i q^{79} +(-773.865 - 664.064i) q^{80} +(463.920 + 562.334i) q^{81} +(-22.5842 - 51.7136i) q^{82} +(-286.237 + 286.237i) q^{83} +(-712.499 - 1034.22i) q^{84} +(783.932 + 783.932i) q^{85} +(1097.88 + 430.440i) q^{86} +(740.814 - 469.783i) q^{87} +(208.442 + 431.665i) q^{88} +203.128 q^{89} +(835.310 + 884.773i) q^{90} +(316.421 - 316.421i) q^{91} +(-7.54534 - 6.99114i) q^{92} +(-875.266 - 195.957i) q^{93} +(-78.6786 - 180.160i) q^{94} -821.001 q^{95} +(-248.816 - 907.098i) q^{96} -39.4244 q^{97} +(-644.968 - 1476.86i) q^{98} +(-193.389 - 538.304i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7}+O(q^{10}) $ 44 * q - 2 * q^3 - 4 * q^4 + 28 * q^6 - 8 * q^7	$ 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7} + 56 q^{10} - 80 q^{12} - 4 q^{13} - 112 q^{16} + 52 q^{18} + 20 q^{19} - 56 q^{21} - 40 q^{22} - 120 q^{24} - 134 q^{27} - 296 q^{28} - 332 q^{30} - 4 q^{33} + 520 q^{34} - 604 q^{36} - 4 q^{37} + 596 q^{39} + 632 q^{40} + 696 q^{42} - 436 q^{43} - 252 q^{45} + 664 q^{46} + 1200 q^{48} + 972 q^{49} - 648 q^{51} + 320 q^{52} + 1592 q^{54} + 280 q^{55} - 424 q^{58} + 800 q^{60} - 916 q^{61} - 2056 q^{64} - 668 q^{66} - 1636 q^{67} + 52 q^{69} - 5192 q^{70} - 3704 q^{72} + 1454 q^{75} - 568 q^{76} - 4932 q^{78} - 4 q^{81} + 768 q^{82} - 2096 q^{84} + 736 q^{85} + 1284 q^{87} + 8864 q^{88} + 2672 q^{90} + 424 q^{91} - 2084 q^{93} + 5616 q^{94} + 8008 q^{96} - 8 q^{97} + 1196 q^{99}+O(q^{100}) $ 44 * q - 2 * q^3 - 4 * q^4 + 28 * q^6 - 8 * q^7 + 56 * q^10 - 80 * q^12 - 4 * q^13 - 112 * q^16 + 52 * q^18 + 20 * q^19 - 56 * q^21 - 40 * q^22 - 120 * q^24 - 134 * q^27 - 296 * q^28 - 332 * q^30 - 4 * q^33 + 520 * q^34 - 604 * q^36 - 4 * q^37 + 596 * q^39 + 632 * q^40 + 696 * q^42 - 436 * q^43 - 252 * q^45 + 664 * q^46 + 1200 * q^48 + 972 * q^49 - 648 * q^51 + 320 * q^52 + 1592 * q^54 + 280 * q^55 - 424 * q^58 + 800 * q^60 - 916 * q^61 - 2056 * q^64 - 668 * q^66 - 1636 * q^67 + 52 * q^69 - 5192 * q^70 - 3704 * q^72 + 1454 * q^75 - 568 * q^76 - 4932 * q^78 - 4 * q^81 + 768 * q^82 - 2096 * q^84 + 736 * q^85 + 1284 * q^87 + 8864 * q^88 + 2672 * q^90 + 424 * q^91 - 2084 * q^93 + 5616 * q^94 + 8008 * q^96 - 8 * q^97 + 1196 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.13198	−	2.59203i	−0.400216	−	0.916421i
$2$	−1.13198	−	2.59203i	−0.400216	−	0.916421i
$3$	−1.13522	+	5.07063i	−0.218474	+	0.975843i
$3$	−1.13522	+	5.07063i	−0.218474	+	0.975843i
$4$	−5.43724	+	5.86826i	−0.679655	+	0.733532i
$5$	11.2665	−	11.2665i	1.00771	−	1.00771i	0.00773900	−	0.999970i	$-0.497537\pi$
$5$	11.2665	−	11.2665i	1.00771	−	1.00771i	0.999970	−	0.00773900i	$-0.00246343\pi$
$6$	14.4283	−	2.79732i	0.981719	−	0.190333i
$7$	30.2121			1.63130			0.815649	−	0.578547i	$-0.196380\pi$
$7$	30.2121			1.63130			0.815649	+	0.578547i	$0.196380\pi$
$8$	21.3655	+	7.45073i	0.944233	+	0.329279i
$9$	−24.4225	−	11.5126i	−0.904538	−	0.426393i
$10$	−41.9567	−	16.4497i	−1.32679	−	0.520185i
$11$	14.9799	+	14.9799i	0.410601	+	0.410601i	0.881948	−	0.471347i	$-0.156232\pi$
$11$	14.9799	+	14.9799i	0.410601	+	0.410601i	−0.471347	+	0.881948i	$0.656232\pi$
$12$	−23.5833	−	34.2320i	−0.567325	−	0.823494i
$13$	10.4733	−	10.4733i	0.223444	−	0.223444i	−0.586503	−	0.809947i	$-0.699496\pi$
$13$	10.4733	−	10.4733i	0.223444	−	0.223444i	0.809947	+	0.586503i	$0.199496\pi$
$14$	−34.1995	−	78.3106i	−0.652871	−	1.49496i
$15$	44.3383	+	69.9184i	0.763207	+	1.20352i
$16$	−4.87289	−	63.8142i	−0.0761390	−	0.997097i
$17$			69.5806i			0.992693i	0.868124	+	0.496347i	$0.165325\pi$
$17$			69.5806i			0.992693i	−0.868124	+	0.496347i	$0.834675\pi$
$18$	−2.19516	+	76.3360i	−0.0287446	+	0.999587i
$19$	−36.4354	−	36.4354i	−0.439940	−	0.439940i	0.452052	−	0.891992i	$-0.350692\pi$
$19$	−36.4354	−	36.4354i	−0.439940	−	0.439940i	−0.891992	+	0.452052i	$0.850692\pi$
$20$	4.85610	+	127.374i	0.0542928	+	1.42408i
$21$	−34.2975	+	153.194i	−0.356396	+	1.59189i
$22$	21.8714	−	55.7853i	0.211954	−	0.540612i
$23$			1.28579i			0.0116568i	0.999983	+	0.00582838i	$0.00185524\pi$
$23$			1.28579i			0.0116568i	−0.999983	+	0.00582838i	$0.998145\pi$
$24$	−62.0345	+	99.8785i	−0.527615	+	0.849484i
$25$		−	128.869i		−	1.03096i
$26$	−39.0027	−	15.2916i	−0.294195	−	0.115343i
$27$	86.1012	−	110.768i	0.613710	−	0.789531i
$28$	−164.270	+	177.292i	−1.10872	+	1.19661i
$29$	−119.373	−	119.373i	−0.764382	−	0.764382i	0.212729	−	0.977111i	$-0.431765\pi$
$29$	−119.373	−	119.373i	−0.764382	−	0.764382i	−0.977111	+	0.212729i	$0.931765\pi$
$30$	131.040	−	194.073i	0.797487	−	1.18109i
$31$			172.615i			1.00008i	0.866002	+	0.500041i	$0.166682\pi$
$31$			172.615i			1.00008i	−0.866002	+	0.500041i	$0.833318\pi$
$32$	−159.892	+	84.8672i	−0.883289	+	0.468829i
$33$	−92.9630	+	58.9519i	−0.490387	+	0.310976i
$34$	180.355	−	78.7640i	0.909725	−	0.397291i
$35$	340.385	−	340.385i	1.64387	−	1.64387i
$36$	200.350	−	80.7210i	0.927546	−	0.373708i
$37$	−235.193	−	235.193i	−1.04501	−	1.04501i	−0.998938	−	0.0460739i	$-0.985329\pi$
$37$	−235.193	−	235.193i	−1.04501	−	1.04501i	−0.0460739	−	0.998938i	$-0.514671\pi$
$38$	−53.1974	+	135.686i	−0.227099	+	0.579241i
$39$	41.2167	+	64.9958i	0.169230	+	0.266863i
$40$	324.659	−	156.772i	1.28333	−	0.619695i
$41$	19.9510			0.0759957			0.0379979	−	0.999278i	$-0.487902\pi$
$41$	19.9510			0.0759957			0.0379979	+	0.999278i	$0.487902\pi$
$42$	435.908	−	84.5128i	1.60148	−	0.310491i
$43$	−294.812	+	294.812i	−1.04554	+	1.04554i	−0.0466324	+	0.998912i	$0.514849\pi$
$43$	−294.812	+	294.812i	−1.04554	+	1.04554i	−0.998912	+	0.0466324i	$0.985151\pi$
$44$	−169.355	+	6.45663i	−0.580255	+	0.0221221i
$45$	−404.864	+	145.450i	−1.34119	+	0.481832i
$46$	3.33280	−	1.45549i	0.0106825	−	0.00466522i
$47$	69.5052			0.215710			0.107855	−	0.994167i	$-0.465602\pi$
$47$	69.5052			0.215710			0.107855	+	0.994167i	$0.465602\pi$
$48$	329.110	+	47.7348i	0.989644	+	0.143540i
$49$	569.769			1.66113
$50$	−334.033	+	145.878i	−0.944789	+	0.412604i
$51$	−352.818	−	78.9896i	−0.968713	−	0.216878i
$52$	4.51421	+	118.406i	0.0120386	+	0.315768i
$53$	122.813	−	122.813i	0.318295	−	0.318295i	−0.529817	−	0.848112i	$-0.677739\pi$
$53$	122.813	−	122.813i	0.318295	−	0.318295i	0.848112	+	0.529817i	$0.177739\pi$
$54$	−384.579	−	97.7893i	−0.969160	−	0.246434i
$55$	337.543			0.827532
$56$	645.497	+	225.102i	1.54033	+	0.537152i
$57$	226.113	−	143.388i	0.525427	−	0.333196i
$58$	−174.291	+	444.548i	−0.394578	+	1.00641i
$59$	−63.2396	−	63.2396i	−0.139544	−	0.139544i	0.633884	−	0.773428i	$-0.281460\pi$
$59$	−63.2396	−	63.2396i	−0.139544	−	0.139544i	−0.773428	+	0.633884i	$0.781460\pi$
$60$	−651.377	−	119.974i	−1.40154	−	0.258143i
$61$	−352.521	+	352.521i	−0.739928	+	0.739928i	−0.972564	−	0.232636i	$-0.925265\pi$
$61$	−352.521	+	352.521i	−0.739928	+	0.739928i	0.232636	+	0.972564i	$0.425265\pi$
$62$	447.423	−	195.397i	0.916497	−	0.400249i
$63$	−737.855	−	347.819i	−1.47557	−	0.695574i
$64$	400.973	+	318.378i	0.783151	+	0.621831i
$65$		−	235.996i		−	0.450334i
$66$	258.037	+	174.230i	0.481246	+	0.324944i
$67$	−228.455	−	228.455i	−0.416570	−	0.416570i	0.467450	−	0.884020i	$-0.345173\pi$
$67$	−228.455	−	228.455i	−0.416570	−	0.416570i	−0.884020	+	0.467450i	$0.845173\pi$
$68$	−408.317	−	378.327i	−0.728172	−	0.674689i
$69$	−6.51976	−	1.45966i	−0.0113752	−	0.00254670i
$70$	−1267.60	−	496.979i	−2.16439	−	0.848576i
$71$			524.753i			0.877137i	0.898698	+	0.438568i	$0.144514\pi$
$71$			524.753i			0.877137i	−0.898698	+	0.438568i	$0.855486\pi$
$72$	−436.024	−	427.939i	−0.713693	−	0.700459i
$73$		−	578.802i		−	0.927994i	−0.885837	−	0.463997i	$-0.846415\pi$
$73$		−	578.802i		−	0.927994i	0.885837	−	0.463997i	$-0.153585\pi$
$74$	−343.393	+	875.860i	−0.539441	+	1.37590i
$75$	653.449	+	146.296i	1.00605	+	0.225237i
$76$	411.920	−	15.7044i	0.621717	−	0.0237028i
$77$	452.573	+	452.573i	0.669812	+	0.669812i
$78$	121.815	−	180.409i	0.176831	−	0.261888i
$79$			745.229i			1.06133i	0.847583	+	0.530664i	$0.178057\pi$
$79$			745.229i			1.06133i	−0.847583	+	0.530664i	$0.821943\pi$
$80$	−773.865	−	664.064i	−1.08151	−	0.928058i
$81$	463.920	+	562.334i	0.636379	+	0.771377i
$82$	−22.5842	−	51.7136i	−0.0304147	−	0.0696441i
$83$	−286.237	+	286.237i	−0.378537	+	0.378537i	−0.870574	−	0.492037i	$-0.836252\pi$
$83$	−286.237	+	286.237i	−0.378537	+	0.378537i	0.492037	+	0.870574i	$0.336252\pi$
$84$	−712.499	−	1034.22i	−0.925477	−	1.34336i
$85$	783.932	+	783.932i	1.00035	+	1.00035i
$86$	1097.88	+	430.440i	1.37660	+	0.539715i
$87$	740.814	−	469.783i	0.912914	−	0.578919i
$88$	208.442	+	431.665i	0.252501	+	0.522905i
$89$	203.128			0.241927			0.120964	−	0.992657i	$-0.461402\pi$
$89$	203.128			0.241927			0.120964	+	0.992657i	$0.461402\pi$
$90$	835.310	+	884.773i	0.978326	+	1.03626i
$91$	316.421	−	316.421i	0.364504	−	0.364504i
$92$	−7.54534	−	6.99114i	−0.00855061	−	0.00792258i
$93$	−875.266	−	195.957i	−0.975923	−	0.218492i
$94$	−78.6786	−	180.160i	−0.0863306	−	0.197681i
$95$	−821.001			−0.886662
$96$	−248.816	−	907.098i	−0.264528	−	0.964378i
$97$	−39.4244			−0.0412674			−0.0206337	−	0.999787i	$-0.506568\pi$
$97$	−39.4244			−0.0412674			−0.0206337	+	0.999787i	$0.506568\pi$
$98$	−644.968	−	1476.86i	−0.664812	−	1.52230i
$99$	−193.389	−	538.304i	−0.196327	−	0.546481i
$100$	756.239	+	700.693i	0.756239	+	0.700693i
$101$	477.063	−	477.063i	0.469996	−	0.469996i	−0.431917	−	0.901913i	$-0.642163\pi$
$101$	477.063	−	477.063i	0.469996	−	0.469996i	0.901913	+	0.431917i	$0.142163\pi$
$102$	194.639	+	1003.93i	0.188943	+	0.974546i
$103$	−1080.92			−1.03404			−0.517022	−	0.855972i	$-0.672960\pi$
$103$	−1080.92			−1.03404			−0.517022	+	0.855972i	$0.672960\pi$
$104$	301.802	−	145.734i	0.284559	−	0.137408i
$105$	1339.55	+	2112.38i	1.24502	+	1.96331i
$106$	−457.357	−	179.313i	−0.419079	−	0.164306i
$107$	−1267.21	−	1267.21i	−1.14491	−	1.14491i	−0.987539	−	0.157374i	$-0.949697\pi$
$107$	−1267.21	−	1267.21i	−1.14491	−	1.14491i	−0.157374	−	0.987539i	$-0.550303\pi$
$108$	181.864	+	1107.54i	0.162036	+	0.986785i
$109$	1252.27	−	1252.27i	1.10042	−	1.10042i	0.106058	−	0.994360i	$-0.466177\pi$
$109$	1252.27	−	1252.27i	1.10042	−	1.10042i	0.994360	−	0.106058i	$-0.0338230\pi$
$110$	−382.092	−	874.921i	−0.331191	−	0.758367i
$111$	1459.57	−	925.578i	1.24808	−	0.791459i
$112$	−147.220	−	1927.96i	−0.124205	−	1.62656i
$113$			644.877i			0.536858i	0.963299	+	0.268429i	$0.0865045\pi$
$113$			644.877i			0.536858i	−0.963299	+	0.268429i	$0.913496\pi$
$114$	−627.621	−	423.778i	−0.515632	−	0.348162i
$115$	14.4864	+	14.4864i	0.0117466	+	0.0117466i
$116$	1349.58	−	51.4523i	1.08021	−	0.0411830i
$117$	−376.360	+	135.210i	−0.297389	+	0.106839i
$118$	−92.3329	+	235.505i	−0.0720333	+	0.183729i
$119$			2102.18i			1.61938i
$120$	426.370	+	1824.20i	0.324351	+	1.38771i
$121$		−	882.206i		−	0.662814i
$122$	1312.79	+	514.697i	0.974217	+	0.381955i
$123$	−22.6489	+	101.164i	−0.0166031	+	0.0741599i
$124$	−1012.95	−	938.549i	−0.733593	−	0.679711i
$125$	−43.5945	−	43.5945i	−0.0311937	−	0.0311937i
$126$	−66.3202	+	2306.27i	−0.0468911	+	1.63062i
$127$			713.342i			0.498417i	0.968450	+	0.249208i	$0.0801704\pi$
$127$			713.342i			0.498417i	−0.968450	+	0.249208i	$0.919830\pi$
$128$	371.350	−	1399.73i	0.256430	−	0.966563i
$129$	−1160.20	−	1829.56i	−0.791863	−	1.24871i
$130$	−611.708	+	267.143i	−0.412695	+	0.180231i
$131$	342.230	−	342.230i	0.228250	−	0.228250i	−0.583711	−	0.811961i	$-0.698400\pi$
$131$	342.230	−	342.230i	0.228250	−	0.228250i	0.811961	+	0.583711i	$0.198400\pi$
$132$	159.517	−	866.066i	0.105183	−	0.571071i
$133$	−1100.79	−	1100.79i	−0.717673	−	0.717673i
$134$	−333.555	+	850.768i	−0.215036	+	0.548471i
$135$	−277.912	−	2218.03i	−0.177177	−	1.41406i
$136$	−518.426	+	1486.63i	−0.326873	+	0.937334i
$137$	−3148.95			−1.96374			−0.981872	−	0.189546i	$-0.939299\pi$
$137$	−3148.95			−1.96374			−0.981872	+	0.189546i	$0.939299\pi$
$138$	3.59676	+	18.5517i	0.00221867	+	0.0114437i
$139$	−308.310	+	308.310i	−0.188133	+	0.188133i	−0.794889	−	0.606755i	$-0.792471\pi$
$139$	−308.310	+	308.310i	−0.188133	+	0.188133i	0.606755	+	0.794889i	$0.292471\pi$
$140$	146.713	+	3848.22i	0.0885678	+	2.32310i
$141$	−78.9040	+	352.435i	−0.0471271	+	0.210499i
$142$	1360.17	−	594.010i	0.803826	−	0.351044i
$143$	313.778			0.183493
$144$	−615.659	+	1614.60i	−0.356284	+	0.934378i
$145$	−2689.85			−1.54055
$146$	−1500.27	+	655.192i	−0.850434	+	0.371398i
$147$	−646.816	+	2889.09i	−0.362915	+	1.62101i
$148$	2658.97	−	101.373i	1.47680	−	0.0563026i
$149$	397.287	−	397.287i	0.218437	−	0.218437i	−0.589403	−	0.807839i	$-0.700637\pi$
$149$	397.287	−	397.287i	0.218437	−	0.218437i	0.807839	+	0.589403i	$0.200637\pi$
$150$	−360.489	−	1859.36i	−0.196225	−	1.01211i
$151$	−1028.33			−0.554200			−0.277100	−	0.960841i	$-0.589373\pi$
$151$	−1028.33			−0.554200			−0.277100	+	0.960841i	$0.589373\pi$
$152$	−506.992	−	1049.93i	−0.270543	−	0.560268i
$153$	801.054	−	1699.34i	0.423277	−	0.897929i
$154$	660.779	−	1685.39i	0.345760	−	0.881899i
$155$	1944.77	+	1944.77i	1.00779	+	1.00779i
$156$	−605.517	−	111.528i	−0.310770	−	0.0572394i
$157$	154.961	−	154.961i	0.0787721	−	0.0787721i	−0.666623	−	0.745395i	$-0.732261\pi$
$157$	154.961	−	154.961i	0.0787721	−	0.0787721i	0.745395	+	0.666623i	$0.232261\pi$
$158$	1931.66	−	843.585i	0.972622	−	0.424760i
$159$	483.318	+	762.159i	0.241067	+	0.380145i
$160$	−845.273	+	2757.59i	−0.417655	+	1.36254i
$161$			38.8464i			0.0190157i
$162$	932.437	−	1839.05i	0.452217	−	0.891908i
$163$	1541.10	+	1541.10i	0.740540	+	0.740540i	0.972682	−	0.232142i	$-0.0745733\pi$
$163$	1541.10	+	1541.10i	0.740540	+	0.740540i	−0.232142	+	0.972682i	$0.574573\pi$
$164$	−108.478	+	117.078i	−0.0516509	+	0.0557453i
$165$	−383.187	+	1711.55i	−0.180794	+	0.807541i
$166$	1065.95	+	417.920i	0.498396	+	0.195403i
$167$		−	2839.46i		−	1.31571i	−0.753143	−	0.657856i	$-0.771463\pi$
$167$		−	2839.46i		−	1.31571i	0.753143	−	0.657856i	$-0.228537\pi$
$168$	−1874.19	+	3017.54i	−0.860697	+	1.38576i
$169$			1977.62i			0.900145i
$170$	1144.58	−	2919.37i	0.516384	−	1.31709i
$171$	470.378	+	1309.31i	0.210355	+	0.585529i
$172$	−127.070	−	3333.00i	−0.0563313	−	1.47755i
$173$	2220.59	+	2220.59i	0.975885	+	0.975885i	0.999716	−	0.0238309i	$-0.00758631\pi$
$173$	2220.59	+	2220.59i	0.975885	+	0.975885i	−0.0238309	+	0.999716i	$0.507586\pi$
$174$	−2056.28	−	1388.43i	−0.895896	−	0.604921i
$175$		−	3893.41i		−	1.68180i
$176$	882.935	−	1028.93i	0.378146	−	0.440671i
$177$	392.456	−	248.873i	0.166660	−	0.105686i
$178$	−229.937	−	526.514i	−0.0968230	−	0.221707i
$179$	1986.85	−	1986.85i	0.829630	−	0.829630i	−0.157835	−	0.987465i	$-0.550451\pi$
$179$	1986.85	−	1986.85i	0.829630	−	0.829630i	0.987465	+	0.157835i	$0.0504515\pi$
$180$	1347.80	−	3166.69i	0.558108	−	1.31129i
$181$	8.17608	+	8.17608i	0.00335759	+	0.00335759i	0.708784	−	0.705426i	$-0.249244\pi$
$181$	8.17608	+	8.17608i	0.00335759	+	0.00335759i	−0.705426	+	0.708784i	$0.749244\pi$
$182$	−1178.35	−	461.989i	−0.479920	−	0.188159i
$183$	−1387.31	−	2187.69i	−0.560399	−	0.883709i
$184$	−9.58007	+	27.4716i	−0.00383833	+	0.0110067i
$185$	−5299.61			−2.10614
$186$	482.859	+	2490.54i	0.190349	+	0.981801i
$187$	−1042.31	+	1042.31i	−0.407600	+	0.407600i
$188$	−377.916	+	407.875i	−0.146608	+	0.158230i
$189$	2601.29	−	3346.54i	1.00114	−	1.28796i
$190$	929.357	+	2128.06i	0.354856	+	0.812556i
$191$	3114.07			1.17972			0.589860	−	0.807506i	$-0.299183\pi$
$191$	3114.07			1.17972			0.589860	+	0.807506i	$0.299183\pi$
$192$	−2069.57	+	1671.76i	−0.777908	+	0.628378i
$193$	4424.82			1.65029			0.825144	−	0.564922i	$-0.191094\pi$
$193$	4424.82			1.65029			0.825144	+	0.564922i	$0.191094\pi$
$194$	44.6277	+	102.189i	0.0165159	+	0.0378183i
$195$	1196.65	+	267.908i	0.439455	+	0.0983862i
$196$	−3097.97	+	3343.55i	−1.12900	+	1.21850i
$197$	−1951.27	+	1951.27i	−0.705697	+	0.705697i	−0.965627	−	0.259931i	$-0.916300\pi$
$197$	−1951.27	+	1951.27i	−0.705697	+	0.705697i	0.259931	+	0.965627i	$0.416300\pi$
$198$	−1176.39	+	1110.62i	−0.422233	+	0.398628i
$199$	2770.53			0.986922			0.493461	−	0.869768i	$-0.335731\pi$
$199$	2770.53			0.986922			0.493461	+	0.869768i	$0.335731\pi$
$200$	960.170	−	2753.37i	0.339472	−	0.973462i
$201$	1417.76	−	899.062i	0.497517	−	0.315497i
$202$	−1776.59	−	696.536i	−0.618814	−	0.242614i
$203$	−3606.52	−	3606.52i	−1.24694	−	1.24694i
$204$	2381.88	−	1640.94i	0.817477	−	0.563180i
$205$	224.779	−	224.779i	0.0765816	−	0.0765816i
$206$	1223.59	+	2801.79i	0.413841	+	0.947620i
$207$	14.8028	−	31.4022i	0.00497036	−	0.0105440i
$208$	−719.382	−	617.311i	−0.239808	−	0.205783i
$209$		−	1091.60i		−	0.361279i
$210$	3959.00	−	5863.34i	1.30094	−	1.92671i
$211$	3424.36	+	3424.36i	1.11726	+	1.11726i	0.992141	+	0.125124i	$0.0399328\pi$
$211$	3424.36	+	3424.36i	1.11726	+	1.11726i	0.125124	+	0.992141i	$0.460067\pi$
$212$	52.9348	+	1388.46i	0.0171489	+	0.449811i
$213$	−2660.83	−	595.712i	−0.855947	−	0.191632i
$214$	−1850.19	+	4719.10i	−0.591010	+	1.50743i
$215$			6643.02i			2.10721i
$216$	2664.90	−	1725.11i	0.839461	−	0.543420i
$217$			5215.06i			1.63143i
$218$	−4663.46	−	1828.37i	−1.44885	−	0.568042i
$219$	2934.89	+	657.070i	0.905577	+	0.202743i
$220$	−1835.30	+	1980.79i	−0.562436	+	0.607021i
$221$	728.740	+	728.740i	0.221812	+	0.221812i
$222$	−4051.33	−	2735.51i	−1.22481	−	0.827008i
$223$		−	1568.26i		−	0.470934i	−0.971882	−	0.235467i	$-0.924338\pi$
$223$		−	1568.26i		−	0.470934i	0.971882	−	0.235467i	$-0.0756619\pi$
$224$	−4830.68	+	2564.01i	−1.44091	+	0.764801i
$225$	−1483.62	+	3147.32i	−0.439592	+	0.932538i
$226$	1671.54	−	729.989i	0.491988	−	0.214859i
$227$	−2298.97	+	2298.97i	−0.672193	+	0.672193i	−0.958221	−	0.286028i	$-0.907665\pi$
$227$	−2298.97	+	2298.97i	−0.672193	+	0.672193i	0.286028	+	0.958221i	$0.407665\pi$
$228$	−387.991	+	2106.52i	−0.112699	+	0.611876i
$229$	−844.364	−	844.364i	−0.243656	−	0.243656i	0.574705	−	0.818361i	$-0.305117\pi$
$229$	−844.364	−	844.364i	−0.243656	−	0.243656i	−0.818361	+	0.574705i	$0.805117\pi$
$230$	21.1508	−	53.9475i	0.00606367	−	0.0154660i
$231$	−2808.60	+	1781.06i	−0.799968	+	0.507295i
$232$	−1661.06	−	3439.90i	−0.470060	−	0.973450i
$233$	7011.40			1.97138			0.985692	−	0.168558i	$-0.0539111\pi$
$233$	7011.40			1.97138			0.985692	+	0.168558i	$0.0539111\pi$
$234$	776.500	+	822.481i	0.216929	+	0.229775i
$235$	783.083	−	783.083i	0.217373	−	0.217373i
$236$	714.955	−	27.2575i	0.197202	−	0.00751828i
$237$	−3778.78	−	846.002i	−1.03569	−	0.231872i
$238$	5448.90	−	2379.62i	1.48403	−	0.648101i
$239$	−1850.30			−0.500779			−0.250389	−	0.968145i	$-0.580559\pi$
$239$	−1850.30			−0.500779			−0.250389	+	0.968145i	$0.580559\pi$
$240$	4245.73	−	3170.12i	1.14192	−	0.852627i
$241$	−5628.68			−1.50446			−0.752231	−	0.658900i	$-0.771022\pi$
$241$	−5628.68			−1.50446			−0.752231	+	0.658900i	$0.771022\pi$
$242$	−2286.70	+	998.640i	−0.607417	+	0.265269i
$243$	−3378.04	+	1713.99i	−0.891775	+	0.452480i
$244$	−151.943	−	3985.42i	−0.0398655	−	1.04566i
$245$	6419.32	−	6419.32i	1.67394	−	1.67394i
$246$	287.859	−	55.8094i	0.0746065	−	0.0144645i
$247$	−763.199			−0.196604
$248$	−1286.11	+	3688.01i	−0.329306	+	0.944311i
$249$	−1126.46	−	1776.34i	−0.286692	−	0.452093i
$250$	−63.6502	+	162.347i	−0.0161024	+	0.0410708i
$251$	−598.579	−	598.579i	−0.150526	−	0.150526i	0.627827	−	0.778353i	$-0.283944\pi$
$251$	−598.579	−	598.579i	−0.150526	−	0.150526i	−0.778353	+	0.627827i	$0.783944\pi$
$252$	6052.99	−	2438.75i	1.51310	−	0.609630i
$253$	−19.2610	+	19.2610i	−0.00478628	+	0.00478628i
$254$	1849.00	−	807.490i	0.456759	−	0.199474i
$255$	−4864.97	+	3085.09i	−1.19473	+	0.757631i
$256$	−4048.51	+	621.920i	−0.988406	+	0.151836i
$257$		−	6418.48i		−	1.55787i	−0.627102	−	0.778937i	$-0.715759\pi$
$257$		−	6418.48i		−	1.55787i	0.627102	−	0.778937i	$-0.284241\pi$
$258$	−3428.94	+	5078.31i	−0.827429	+	1.22543i
$259$	−7105.66	−	7105.66i	−1.70473	−	1.70473i
$260$	1384.88	+	1283.17i	0.330334	+	0.306071i
$261$	1541.10	+	4289.70i	0.365486	+	1.01734i
$262$	−1274.47	−	499.672i	−0.300522	−	0.117824i
$263$		−	3467.23i		−	0.812922i	−0.913668	−	0.406461i	$-0.866763\pi$
$263$		−	3467.23i		−	0.812922i	0.913668	−	0.406461i	$-0.133237\pi$
$264$	−2425.44	+	566.898i	−0.565437	+	0.132160i
$265$		−	2767.35i		−	0.641498i
$266$	−1607.20	+	4099.35i	−0.370466	+	0.944914i
$267$	−230.596	+	1029.99i	−0.0528548	+	0.236083i
$268$	2582.79	−	98.4686i	0.588691	−	0.0224437i
$269$	2049.90	+	2049.90i	0.464627	+	0.464627i	0.900169	−	0.435542i	$-0.143443\pi$
$269$	2049.90	+	2049.90i	0.464627	+	0.464627i	−0.435542	+	0.900169i	$0.643443\pi$
$270$	−5434.62	+	3231.13i	−1.22496	+	0.728297i
$271$			2445.74i			0.548223i	0.961698	+	0.274111i	$0.0883837\pi$
$271$			2445.74i			0.548223i	−0.961698	+	0.274111i	$0.911616\pi$
$272$	4440.23	−	339.059i	0.989812	−	0.0755826i
$273$	1245.24	+	1963.66i	0.276064	+	0.435334i
$274$	3564.55	+	8162.17i	0.785921	+	1.79962i
$275$	1930.45	−	1930.45i	0.423311	−	0.423311i
$276$	44.0151	−	30.3231i	0.00959928	−	0.00661318i
$277$	4784.71	+	4784.71i	1.03785	+	1.03785i	0.999255	+	0.0385995i	$0.0122896\pi$
$277$	4784.71	+	4784.71i	1.03785	+	1.03785i	0.0385995	+	0.999255i	$0.487710\pi$
$278$	1148.15	+	450.148i	0.247703	+	0.0971154i
$279$	1987.25	−	4215.69i	0.426428	−	0.904613i
$280$	9808.63	−	4736.40i	2.09349	−	1.01091i
$281$	−1716.06			−0.364312			−0.182156	−	0.983270i	$-0.558308\pi$
$281$	−1716.06			−0.364312			−0.182156	+	0.983270i	$0.558308\pi$
$282$	1002.84	−	194.428i	0.211767	−	0.0410569i
$283$	4822.50	−	4822.50i	1.01296	−	1.01296i	0.0130454	−	0.999915i	$-0.495847\pi$
$283$	4822.50	−	4822.50i	1.01296	−	1.01296i	0.999915	−	0.0130454i	$-0.00415259\pi$
$284$	−3079.38	−	2853.21i	−0.643408	−	0.596150i
$285$	932.020	−	4162.99i	0.193713	−	0.865243i
$286$	−355.191	−	813.322i	−0.0734367	−	0.168157i
$287$	602.761			0.123972
$288$	4882.02	−	231.895i	0.998874	−	0.0474463i
$289$	71.5338			0.0145601
$290$	3044.86	+	6972.17i	0.616552	+	1.41179i
$291$	44.7555	−	199.906i	0.00901586	−	0.0402705i
$292$	3396.56	+	3147.08i	0.680714	+	0.630716i
$293$	768.551	−	768.551i	0.153240	−	0.153240i	−0.626324	−	0.779563i	$-0.715441\pi$
$293$	768.551	−	768.551i	0.153240	−	0.153240i	0.779563	+	0.626324i	$0.215441\pi$
$294$	8220.78	−	1593.83i	1.63077	−	0.316170i
$295$	−1424.98			−0.281239
$296$	−3272.66	−	6777.38i	−0.642634	−	1.33083i
$297$	2949.08	−	369.509i	0.576172	−	0.0721923i
$298$	−1479.50	−	580.059i	−0.287602	−	0.112758i
$299$	13.4665	+	13.4665i	0.00260464	+	0.00260464i
$300$	−4411.46	+	3039.16i	−0.848985	+	0.584887i
$301$	−8906.88	+	8906.88i	−1.70560	+	1.70560i
$302$	1164.05	+	2665.46i	0.221799	+	0.507880i
$303$	1877.44	+	2960.59i	0.355960	+	0.561324i
$304$	−2147.55	+	2502.64i	−0.405166	+	0.472159i
$305$			7943.37i			1.49127i
$306$	−5311.51	−	152.740i	−0.992283	−	0.0285346i
$307$	−5562.98	−	5562.98i	−1.03419	−	1.03419i	−0.999395	−	0.0347941i	$-0.988922\pi$
$307$	−5562.98	−	5562.98i	−1.03419	−	1.03419i	−0.0347941	−	0.999395i	$-0.511078\pi$
$308$	−5116.57	+	195.068i	−0.946570	+	0.0360878i
$309$	1227.09	−	5480.96i	0.225912	−	1.00906i
$310$	2839.46	−	7242.35i	0.520228	−	1.32690i
$311$		−	907.726i		−	0.165506i	−0.996570	−	0.0827531i	$-0.973629\pi$
$311$		−	907.726i		−	0.165506i	0.996570	−	0.0827531i	$-0.0263713\pi$
$312$	396.352	+	1695.77i	0.0719199	+	0.307705i
$313$		−	1022.22i		−	0.184599i	−0.995731	−	0.0922993i	$-0.970578\pi$
$313$		−	1022.22i		−	0.184599i	0.995731	−	0.0922993i	$-0.0294217\pi$
$314$	−577.076	−	226.250i	−0.103714	−	0.0406626i
$315$	−12231.8	+	4394.35i	−2.18788	+	0.786011i
$316$	−4373.20	−	4051.99i	−0.778518	−	0.721336i
$317$	−4180.59	−	4180.59i	−0.740711	−	0.740711i	0.232004	−	0.972715i	$-0.425472\pi$
$317$	−4180.59	−	4180.59i	−0.740711	−	0.740711i	−0.972715	+	0.232004i	$0.925472\pi$
$318$	1428.43	−	2115.52i	0.251894	−	0.373059i
$319$		−	3576.40i		−	0.627712i
$320$	8104.59	−	930.567i	1.41581	−	0.162563i
$321$	7864.11	−	4986.98i	1.36739	−	0.867122i
$322$	100.691	−	43.9734i	0.0174264	−	0.00761037i
$323$	2535.20	−	2535.20i	0.436725	−	0.436725i
$324$	−5822.36	−	335.139i	−0.998347	−	0.0574655i
$325$	−1349.69	−	1349.69i	−0.230361	−	0.230361i
$326$	2250.08	−	5739.06i	0.382271	−	0.975023i
$327$	4928.18	+	7771.39i	0.833422	+	1.31425i
$328$	426.264	+	148.650i	0.0717577	+	0.0250238i
$329$	2099.90			0.351888
$330$	4870.16	−	944.215i	0.812404	−	0.157507i
$331$	1915.71	−	1915.71i	0.318117	−	0.318117i	−0.529926	−	0.848044i	$-0.677780\pi$
$331$	1915.71	−	1915.71i	0.318117	−	0.318117i	0.848044	+	0.529926i	$0.177780\pi$
$332$	−123.374	−	3236.05i	−0.0203946	−	0.534944i
$333$	3036.32	+	8451.68i	0.499668	+	1.39084i
$334$	−7359.97	+	3214.22i	−1.20575	+	0.526569i
$335$	−5147.78			−0.839563
$336$	9943.09	+	1442.17i	1.61441	+	0.234157i
$337$	3088.80			0.499281			0.249641	−	0.968339i	$-0.419687\pi$
$337$	3088.80			0.499281			0.249641	+	0.968339i	$0.419687\pi$
$338$	5126.05	−	2238.63i	0.824912	−	0.360252i
$339$	−3269.93	−	732.080i	−0.523889	−	0.117290i
$340$	−8862.74	+	337.890i	−1.41368	+	0.0538961i
$341$	−2585.75	+	2585.75i	−0.410635	+	0.410635i
$342$	2861.31	−	2701.35i	0.452404	−	0.427112i
$343$	6851.17			1.07851
$344$	−8495.38	+	4102.26i	−1.33151	+	0.642962i
$345$	−89.9004	+	57.0098i	−0.0140292	+	0.00889653i
$346$	3242.17	−	8269.49i	0.503757	−	1.28489i
$347$	2015.99	+	2015.99i	0.311884	+	0.311884i	0.845639	−	0.533755i	$-0.179220\pi$
$347$	2015.99	+	2015.99i	0.311884	+	0.311884i	−0.533755	+	0.845639i	$0.679220\pi$
$348$	−1271.18	+	6901.60i	−0.195811	+	1.06312i
$349$	2106.10	−	2106.10i	0.323029	−	0.323029i	−0.526899	−	0.849928i	$-0.676645\pi$
$349$	2106.10	−	2106.10i	0.323029	−	0.323029i	0.849928	+	0.526899i	$0.176645\pi$
$350$	−10091.8	+	4407.27i	−1.54123	+	0.673081i
$351$	−258.346	−	2061.87i	−0.0392862	−	0.313546i
$352$	−3666.47	−	1123.87i	−0.555180	−	0.170177i
$353$			6982.94i			1.05287i	0.850214	+	0.526437i	$0.176472\pi$
$353$			6982.94i			1.05287i	−0.850214	+	0.526437i	$0.823528\pi$
$354$	−1089.34	−	735.537i	−0.163553	−	0.110433i
$355$	5912.14	+	5912.14i	0.883898	+	0.883898i
$356$	−1104.45	+	1192.01i	−0.164427	+	0.177461i
$357$	−10659.3	−	2386.44i	−1.58026	−	0.353792i
$358$	−7399.04	−	2900.89i	−1.09232	−	0.428259i
$359$			8753.09i			1.28683i	0.765519	+	0.643413i	$0.222482\pi$
$359$			8753.09i			1.28683i	−0.765519	+	0.643413i	$0.777518\pi$
$360$	−9733.86	+	91.0899i	−1.42505	+	0.0133357i
$361$		−	4203.93i		−	0.612906i
$362$	11.9375	−	30.4478i	0.00173320	−	0.00442072i
$363$	4473.34	+	1001.50i	0.646803	+	0.144808i
$364$	136.384	+	3577.29i	0.0196386	+	0.515113i
$365$	−6521.08	−	6521.08i	−0.935148	−	0.935148i
$366$	−4100.15	+	6072.38i	−0.585569	+	0.867235i
$367$			8242.34i			1.17233i	0.810190	+	0.586167i	$0.199364\pi$
$367$			8242.34i			1.17233i	−0.810190	+	0.586167i	$0.800636\pi$
$368$	82.0517	−	6.26552i	0.0116229	−	0.000887534i
$369$	−487.254	−	229.688i	−0.0687410	−	0.0324040i
$370$	5999.06	+	13736.7i	0.842909	+	1.93011i
$371$	3710.43	−	3710.43i	0.519234	−	0.519234i
$372$	5908.95	−	4070.82i	0.823562	−	0.567372i
$373$	−298.350	−	298.350i	−0.0414154	−	0.0414154i	0.686096	−	0.727511i	$-0.259323\pi$
$373$	−298.350	−	298.350i	−0.0414154	−	0.0414154i	−0.727511	+	0.686096i	$0.759323\pi$
$374$	3881.57	+	1521.82i	0.536662	+	0.210405i
$375$	270.541	−	171.562i	0.0372552	−	0.0236251i
$376$	1485.02	+	517.864i	0.203681	+	0.0710288i
$377$	−2500.47			−0.341594
$378$	−11618.9	−	2954.42i	−1.58099	−	0.402007i
$379$	−1059.78	+	1059.78i	−0.143633	+	0.143633i	−0.775267	−	0.631634i	$-0.782385\pi$
$379$	−1059.78	+	1059.78i	−0.143633	+	0.143633i	0.631634	+	0.775267i	$0.282385\pi$
$380$	4463.98	−	4817.84i	0.602624	−	0.650395i
$381$	−3617.09	−	809.804i	−0.486376	−	0.108891i
$382$	−3525.07	−	8071.77i	−0.472142	−	1.08112i
$383$	−4404.31			−0.587597			−0.293799	−	0.955867i	$-0.594920\pi$
$383$	−4404.31			−0.587597			−0.293799	+	0.955867i	$0.594920\pi$
$384$	6675.96	+	3471.99i	0.887190	+	0.461404i
$385$	10197.9			1.34995
$386$	−5008.82	−	11469.3i	−0.660472	−	1.51236i
$387$	10594.1	−	3806.00i	1.39155	−	0.499923i
$388$	214.360	−	231.353i	0.0280476	−	0.0302710i
$389$	−9687.95	+	9687.95i	−1.26272	+	1.26272i	−0.312953	+	0.949769i	$0.601318\pi$
$389$	−9687.95	+	9687.95i	−1.26272	+	1.26272i	−0.949769	+	0.312953i	$0.898682\pi$
$390$	−660.156	−	3405.01i	−0.0857136	−	0.442101i
$391$	−89.4661			−0.0115716
$392$	12173.4	+	4245.19i	1.56850	+	0.546976i
$393$	1346.81	+	2123.83i	0.172869	+	0.272603i
$394$	7266.55	+	2848.95i	0.929146	+	0.364284i
$395$	8396.15	+	8396.15i	1.06951	+	1.06951i
$396$	4210.41	+	1792.03i	0.534296	+	0.227406i
$397$	73.0707	−	73.0707i	0.00923757	−	0.00923757i	−0.702473	−	0.711710i	$-0.747921\pi$
$397$	73.0707	−	73.0707i	0.00923757	−	0.00923757i	0.711710	+	0.702473i	$0.247921\pi$
$398$	−3136.19	−	7181.29i	−0.394982	−	0.904436i
$399$	6831.33	−	4332.05i	0.857129	−	0.543543i
$400$	−8223.70	+	627.967i	−1.02796	+	0.0784958i
$401$			340.273i			0.0423751i	0.999776	+	0.0211875i	$0.00674471\pi$
$401$			340.273i			0.0423751i	−0.999776	+	0.0211875i	$0.993255\pi$
$402$	−3935.27	−	2657.15i	−0.488242	−	0.329668i
$403$	1807.85	+	1807.85i	0.223463	+	0.223463i
$404$	205.624	+	5393.44i	0.0253222	+	0.664192i
$405$	11562.3	+	1108.78i	1.41861	+	0.136039i
$406$	−5265.69	+	13430.7i	−0.643675	+	1.64176i
$407$		−	7046.32i		−	0.858165i
$408$	−6949.61	−	4316.40i	−0.843277	−	0.523759i
$409$		−	10873.6i		−	1.31458i	−0.753636	−	0.657291i	$-0.771702\pi$
$409$		−	10873.6i		−	1.31458i	0.753636	−	0.657291i	$-0.228298\pi$
$410$	−837.078	−	328.188i	−0.100830	−	0.0395318i
$411$	3574.76	−	15967.2i	0.429027	−	1.91631i
$412$	5877.24	−	6343.14i	0.702793	−	0.758505i
$413$	−1910.60	−	1910.60i	−0.227638	−	0.227638i
$414$	−98.1520	−	2.82251i	−0.0116520	−	0.000335069i
$415$			6449.80i			0.762911i
$416$	−785.762	+	2563.44i	−0.0926086	+	0.302123i
$417$	−1213.32	−	1913.33i	−0.142486	−	0.224691i
$418$	−2829.45	+	1235.67i	−0.331083	+	0.144589i
$419$	−5701.01	+	5701.01i	−0.664708	+	0.664708i	−0.956486	−	0.291778i	$-0.905753\pi$
$419$	−5701.01	+	5701.01i	−0.664708	+	0.664708i	0.291778	+	0.956486i	$0.405753\pi$
$420$	−19679.5	−	3624.67i	−2.28633	−	0.421109i
$421$	−1062.79	−	1062.79i	−0.123034	−	0.123034i	0.642909	−	0.765943i	$-0.277727\pi$
$421$	−1062.79	−	1062.79i	−0.123034	−	0.123034i	−0.765943	+	0.642909i	$0.777727\pi$
$422$	4999.74	−	12752.4i	0.576738	−	1.47103i
$423$	−1697.49	−	800.186i	−0.195118	−	0.0919772i
$424$	3539.01	−	1708.92i	0.405353	−	0.195737i
$425$	8966.82			1.02342
$426$	1467.90	+	7571.28i	0.166948	+	0.861102i
$427$	−10650.4	+	10650.4i	−1.20704	+	1.20704i
$428$	14326.4	−	546.192i	1.61798	−	0.0616851i
$429$	−356.209	+	1591.05i	−0.0400884	+	0.179060i
$430$	17218.9	−	7519.77i	1.93109	−	0.843338i
$431$	2350.06			0.262641			0.131321	−	0.991340i	$-0.458078\pi$
$431$	2350.06			0.262641			0.131321	+	0.991340i	$0.458078\pi$
$432$	−7488.15	−	4954.72i	−0.833967	−	0.551815i
$433$	−8617.75			−0.956450			−0.478225	−	0.878237i	$-0.658720\pi$
$433$	−8617.75			−0.956450			−0.478225	+	0.878237i	$0.658720\pi$
$434$	13517.6	−	5903.34i	1.49508	−	0.652925i
$435$	3053.58	−	13639.2i	0.336570	−	1.50333i
$436$	539.753	+	14157.5i	0.0592878	+	1.55510i
$437$	46.8482	−	46.8482i	0.00512827	−	0.00512827i
$438$	−1619.09	−	8351.11i	−0.176628	−	0.911030i
$439$	−4948.07			−0.537947			−0.268973	−	0.963148i	$-0.586684\pi$
$439$	−4948.07			−0.537947			−0.268973	+	0.963148i	$0.586684\pi$
$440$	7211.79	+	2514.94i	0.781383	+	0.272489i
$441$	−13915.2	−	6559.52i	−1.50256	−	0.708295i
$442$	1064.00	−	2713.84i	0.114500	−	0.292045i
$443$	−6128.78	−	6128.78i	−0.657307	−	0.657307i	0.297435	−	0.954742i	$-0.403869\pi$
$443$	−6128.78	−	6128.78i	−0.657307	−	0.657307i	−0.954742	+	0.297435i	$0.903869\pi$
$444$	−2504.50	+	13597.7i	−0.267699	+	1.45342i
$445$	2288.55	−	2288.55i	0.243792	−	0.243792i
$446$	−4064.97	+	1775.24i	−0.431574	+	0.188475i
$447$	1563.49	+	2465.51i	0.165437	+	0.260882i
$448$	12114.2	+	9618.85i	1.27755	+	1.01439i
$449$		−	13057.1i		−	1.37239i	−0.727416	−	0.686197i	$-0.759279\pi$
$449$		−	13057.1i		−	1.37239i	0.727416	−	0.686197i	$-0.240721\pi$
$450$	9837.37	+	282.888i	1.03053	+	0.0296344i
$451$	298.864	+	298.864i	0.0312039	+	0.0312039i
$452$	−3784.31	−	3506.35i	−0.393803	−	0.364878i
$453$	1167.38	−	5214.27i	0.121078	−	0.540812i
$454$	8561.38	+	3356.60i	0.885034	+	0.346990i
$455$		−	7129.92i		−	0.734628i
$456$	5899.36	−	1378.86i	0.605840	−	0.141603i
$457$			16737.3i			1.71321i	0.515973	+	0.856605i	$0.327430\pi$
$457$			16737.3i			1.71321i	−0.515973	+	0.856605i	$0.672570\pi$
$458$	−1232.81	+	3144.42i	−0.125776	+	0.320806i
$459$	7707.32	+	5990.97i	0.783762	+	0.609226i
$460$	−163.776	+	6.24392i	−0.0166002	+	0.000632879i
$461$	11008.3	+	11008.3i	1.11216	+	1.11216i	0.992857	+	0.119306i	$0.0380671\pi$
$461$	11008.3	+	11008.3i	1.11216	+	1.11216i	0.119306	+	0.992857i	$0.461933\pi$
$462$	7795.84	+	5263.86i	0.785055	+	0.530080i
$463$			1019.62i			0.102345i	0.998690	+	0.0511723i	$0.0162958\pi$
$463$			1019.62i			0.102345i	−0.998690	+	0.0511723i	$0.983704\pi$
$464$	−7036.03	+	8199.41i	−0.703964	+	0.820363i
$465$	−12069.0	+	7653.46i	−1.20362	+	0.763270i
$466$	−7936.78	−	18173.8i	−0.788979	−	1.80662i
$467$	−9386.52	+	9386.52i	−0.930099	+	0.930099i	−0.997712	−	0.0676128i	$-0.978462\pi$
$467$	−9386.52	+	9386.52i	−0.930099	+	0.930099i	0.0676128	+	0.997712i	$0.478462\pi$
$468$	1252.91	−	2943.74i	0.123752	−	0.290758i
$469$	−6902.09	−	6902.09i	−0.679550	−	0.679550i
$470$	−2916.21	−	1143.34i	−0.286201	−	0.112209i
$471$	609.833	+	961.664i	0.0596595	+	0.0940788i
$472$	−879.968	−	1822.33i	−0.0858131	−	0.177711i
$473$	−8832.50			−0.858602
$474$	2084.64	+	10752.4i	0.202006	+	1.04193i
$475$	−4695.41	+	4695.41i	−0.453558	+	0.453558i
$476$	−12336.1	−	11430.0i	−1.18787	−	1.10062i
$477$	−4413.30	+	1585.51i	−0.423629	+	0.152191i
$478$	2094.51	+	4796.04i	0.200419	+	0.458924i
$479$	19141.8			1.82592			0.912958	−	0.408054i	$-0.133793\pi$
$479$	19141.8			1.82592			0.912958	+	0.408054i	$0.133793\pi$
$480$	−13023.1	−	7416.55i	−1.23838	−	0.705245i
$481$	−4926.49			−0.467004
$482$	6371.56	+	14589.7i	0.602109	+	1.37872i
$483$	−196.975	−	44.0993i	−0.0185563	−	0.00415443i
$484$	5177.01	+	4796.76i	0.486196	+	0.450485i
$485$	−444.176	+	444.176i	−0.0415856	+	0.0415856i
$486$	8266.59	+	6815.77i	0.771564	+	0.636151i
$487$	9857.78			0.917246			0.458623	−	0.888631i	$-0.348343\pi$
$487$	9857.78			0.917246			0.458623	+	0.888631i	$0.348343\pi$
$488$	−10158.3	+	4905.26i	−0.942307	+	0.455022i
$489$	−9563.82	+	6064.84i	−0.884440	+	0.560862i
$490$	−23905.6	−	9372.52i	−2.20397	−	0.864097i
$491$	−2235.97	−	2235.97i	−0.205515	−	0.205515i	0.596843	−	0.802358i	$-0.296422\pi$
$491$	−2235.97	−	2235.97i	−0.205515	−	0.205515i	−0.802358	+	0.596843i	$0.796422\pi$
$492$	−470.510	−	682.963i	−0.0431143	−	0.0625820i
$493$	8306.08	−	8306.08i	0.758797	−	0.758797i
$494$	863.926	+	1978.23i	0.0786840	+	0.180172i
$495$	−8243.65	−	3885.99i	−0.748534	−	0.352853i
$496$	11015.3	−	841.134i	0.997180	−	0.0761453i
$497$			15853.9i			1.43087i
$498$	−3329.21	+	4930.60i	−0.299569	+	0.443666i
$499$	−1879.08	−	1879.08i	−0.168576	−	0.168576i	0.617777	−	0.786353i	$-0.288033\pi$
$499$	−1879.08	−	1879.08i	−0.168576	−	0.168576i	−0.786353	+	0.617777i	$0.788033\pi$
$500$	492.858	−	18.7901i	0.0440826	−	0.00168064i
$501$	14397.8	+	3223.42i	1.28393	+	0.287449i
$502$	−873.954	+	2229.11i	−0.0777021	+	0.198188i
$503$		−	18597.9i		−	1.64859i	−0.566161	−	0.824295i	$-0.691572\pi$
$503$		−	18597.9i		−	1.64859i	0.566161	−	0.824295i	$-0.308428\pi$
$504$	−13173.2	−	12928.9i	−1.16425	−	1.14266i
$505$		−	10749.7i		−	0.947238i
$506$	71.7281	+	28.1220i	0.00630179	+	0.00247070i
$507$	−10027.8	−	2245.04i	−0.878400	−	0.196658i
$508$	−4186.08	−	3878.61i	−0.365605	−	0.338751i
$509$	−12280.3	−	12280.3i	−1.06938	−	1.06938i	−0.997407	−	0.0719701i	$-0.977071\pi$
$509$	−12280.3	−	12280.3i	−1.06938	−	1.06938i	−0.0719701	−	0.997407i	$-0.522929\pi$
$510$	13503.7	+	9117.88i	1.17246	+	0.791660i
$511$		−	17486.8i		−	1.51384i
$512$	6194.87	+	9789.86i	0.534721	+	0.845029i
$513$	−7173.01	+	898.753i	−0.617341	+	0.0773507i
$514$	−16636.9	+	7265.59i	−1.42767	+	0.623486i
$515$	−12178.3	+	12178.3i	−1.04202	+	1.04202i
$516$	17044.6	+	3139.37i	1.45416	+	0.267836i
$517$	1041.18	+	1041.18i	0.0885707	+	0.0885707i
$518$	−10374.6	+	26461.5i	−0.879989	+	2.24451i
$519$	−13780.6	+	8738.91i	−1.16552	+	0.739105i
$520$	1758.34	−	5042.18i	0.148285	−	0.425220i
$521$	9893.24			0.831921			0.415961	−	0.909383i	$-0.363445\pi$
$521$	9893.24			0.831921			0.415961	+	0.909383i	$0.363445\pi$
$522$	9374.53	−	8850.44i	0.786038	−	0.742094i
$523$	7608.31	−	7608.31i	0.636115	−	0.636115i	−0.313480	−	0.949595i	$-0.601495\pi$
$523$	7608.31	−	7608.31i	0.636115	−	0.636115i	0.949595	+	0.313480i	$0.101495\pi$
$524$	147.508	+	3869.07i	0.0122975	+	0.322560i
$525$	19742.0	+	4419.89i	1.64117	+	0.367429i
$526$	−8987.16	+	3924.84i	−0.744979	+	0.325344i
$527$	−12010.7			−0.992775
$528$	4214.97	+	5645.09i	0.347411	+	0.465286i
$529$	12165.3			0.999864
$530$	−7173.05	+	3132.59i	−0.587882	+	0.256738i
$531$	816.419	+	2272.52i	0.0667223	+	0.185723i
$532$	12445.0	−	474.462i	1.01421	−	0.0386664i
$533$	208.953	−	208.953i	0.0169808	−	0.0169808i
$534$	2930.78	−	568.214i	0.237505	−	0.0460468i
$535$	−28554.1			−2.30748
$536$	−3178.91	−	6583.22i	−0.256171	−	0.530507i
$537$	7819.04	+	12330.1i	0.628336	+	0.990841i
$538$	2992.95	−	7633.85i	0.239843	−	0.611745i
$539$	8535.08	+	8535.08i	0.682063	+	0.682063i
$540$	14527.1	+	10429.1i	1.15768	+	0.831107i
$541$	9518.30	−	9518.30i	0.756421	−	0.756421i	−0.219248	−	0.975669i	$-0.570361\pi$
$541$	9518.30	−	9518.30i	0.756421	−	0.756421i	0.975669	+	0.219248i	$0.0703605\pi$
$542$	6339.44	−	2768.54i	0.502403	−	0.219407i
$543$	−50.7396	+	32.1762i	−0.00401002	+	0.00254293i
$544$	−5905.11	−	11125.4i	−0.465404	−	0.876835i
$545$		−	28217.4i		−	2.21780i
$546$	3680.27	−	5450.53i	0.288464	−	0.427218i
$547$	3126.99	+	3126.99i	0.244425	+	0.244425i	0.818678	−	0.574253i	$-0.194707\pi$
$547$	3126.99	+	3126.99i	0.244425	+	0.244425i	−0.574253	+	0.818678i	$0.694707\pi$
$548$	17121.6	−	18478.8i	1.33467	−	1.44047i
$549$	12667.9	−	4551.02i	0.984794	−	0.353794i
$550$	−7189.01	−	2818.55i	−0.557346	−	0.218515i
$551$			8698.83i			0.672564i
$552$	−128.423	−	79.7634i	−0.00990224	−	0.00615028i
$553$			22514.9i			1.73134i
$554$	6985.92	−	17818.3i	0.535746	−	1.36648i
$555$	6016.25	−	26872.4i	0.460136	−	2.05526i
$556$	−132.888	−	3485.60i	−0.0101361	−	0.265867i
$557$	8497.54	+	8497.54i	0.646414	+	0.646414i	0.952124	−	0.305711i	$-0.0988940\pi$
$557$	8497.54	+	8497.54i	0.646414	+	0.646414i	−0.305711	+	0.952124i	$0.598894\pi$
$558$	−13176.7	−	378.917i	−0.999669	−	0.0287470i
$559$			6175.32i			0.467242i
$560$	−23380.1	−	20062.8i	−1.76427	−	1.51394i
$561$	−4101.91	−	6468.42i	−0.308704	−	0.486804i
$562$	1942.55	+	4448.08i	0.145803	+	0.333863i
$563$	3772.00	−	3772.00i	0.282364	−	0.282364i	−0.551687	−	0.834051i	$-0.686016\pi$
$563$	3772.00	−	3772.00i	0.282364	−	0.282364i	0.834051	+	0.551687i	$0.186016\pi$
$564$	−1639.16	−	2379.30i	−0.122378	−	0.177636i
$565$	7265.53	+	7265.53i	0.540997	+	0.540997i
$566$	−17959.0	−	7041.08i	−1.33370	−	0.522895i
$567$	14016.0	+	16989.3i	1.03812	+	1.25835i
$568$	−3909.79	+	11211.6i	−0.288822	+	0.828221i
$569$	21830.1			1.60838			0.804189	−	0.594374i	$-0.202600\pi$
$569$	21830.1			1.60838			0.804189	+	0.594374i	$0.202600\pi$
$570$	−11845.6	+	2296.60i	−0.870453	+	0.168761i
$571$	−189.972	+	189.972i	−0.0139231	+	0.0139231i	−0.714034	−	0.700111i	$-0.753134\pi$
$571$	−189.972	+	189.972i	−0.0139231	+	0.0139231i	0.700111	+	0.714034i	$0.253134\pi$
$572$	−1706.09	+	1841.33i	−0.124712	+	0.134598i
$573$	−3535.17	+	15790.3i	−0.257738	+	1.15122i
$574$	−682.315	−	1562.38i	−0.0496154	−	0.113610i
$575$	165.699			0.0120176
$576$	−6127.43	−	12391.8i	−0.443246	−	0.896400i
$577$	−20253.3			−1.46127			−0.730637	−	0.682766i	$-0.760777\pi$
$577$	−20253.3			−1.46127			−0.730637	+	0.682766i	$0.760777\pi$
$578$	−80.9749	−	185.418i	−0.00582718	−	0.0133432i
$579$	−5023.17	+	22436.6i	−0.360545	+	1.61042i
$580$	14625.3	−	15784.7i	1.04704	−	1.13004i
$581$	−8647.81	+	8647.81i	−0.617507	+	0.617507i
$582$	−568.826	+	110.283i	−0.0405130	+	0.00785457i
$583$	3679.45			0.261384
$584$	4312.49	−	12366.4i	0.305569	−	0.876243i
$585$	−2716.93	+	5763.62i	−0.192019	+	0.407344i
$586$	−2862.09	−	1122.12i	−0.201761	−	0.0791031i
$587$	19.1015	+	19.1015i	0.00134311	+	0.00134311i	0.707778	−	0.706435i	$-0.249698\pi$
$587$	19.1015	+	19.1015i	0.00134311	+	0.00134311i	−0.706435	+	0.707778i	$0.749698\pi$
$588$	−13437.0	−	19504.3i	−0.942404	−	1.36793i
$589$	6289.29	−	6289.29i	0.439976	−	0.439976i
$590$	1613.05	+	3693.59i	0.112556	+	0.257734i
$591$	−7679.04	−	12109.3i	−0.534473	−	0.842825i
$592$	−13862.6	+	16154.7i	−0.962412	+	1.12154i
$593$			2075.52i			0.143729i	0.997414	+	0.0718646i	$0.0228950\pi$
$593$			2075.52i			0.143729i	−0.997414	+	0.0718646i	$0.977105\pi$
$594$	−4296.08	−	7225.83i	−0.296752	−	0.499123i
$595$	23684.2	+	23684.2i	1.63186	+	1.63186i
$596$	171.239	+	4491.53i	0.0117688	+	0.308692i
$597$	−3145.17	+	14048.3i	−0.215617	+	0.963081i
$598$	19.6617	−	50.1493i	0.00134453	−	0.00342936i
$599$		−	2373.75i		−	0.161918i	−0.996717	−	0.0809589i	$-0.974202\pi$
$599$		−	2373.75i		−	0.161918i	0.996717	−	0.0809589i	$-0.0257982\pi$
$600$	12871.3	+	7994.35i	0.875780	+	0.543947i
$601$		−	18198.0i		−	1.23512i	−0.786522	−	0.617562i	$-0.788120\pi$
$601$		−	18198.0i		−	1.23512i	0.786522	−	0.617562i	$-0.211880\pi$
$602$	33169.3	+	13004.5i	2.24565	+	0.880437i
$603$	2949.34	+	8209.55i	0.199181	+	0.554426i
$604$	5591.26	−	6034.49i	0.376664	−	0.406523i
$605$	−9939.40	−	9939.40i	−0.667924	−	0.667924i
$606$	5548.70	−	8217.70i	0.371948	−	0.550860i
$607$		−	6359.38i		−	0.425238i	−0.977135	−	0.212619i	$-0.931801\pi$
$607$		−	6359.38i		−	0.425238i	0.977135	−	0.212619i	$-0.0681993\pi$
$608$	8917.91	+	2733.57i	0.594850	+	0.182337i
$609$	22381.5	−	14193.1i	1.48924	−	0.944390i
$610$	20589.4	−	8991.74i	1.36663	−	0.596828i
$611$	727.950	−	727.950i	0.0481992	−	0.0481992i
$612$	5616.62	+	13940.5i	0.370978	+	0.920769i
$613$	−14688.4	−	14688.4i	−0.967796	−	0.967796i	0.0317012	−	0.999497i	$-0.489908\pi$
$613$	−14688.4	−	14688.4i	−0.967796	−	0.967796i	−0.999497	+	0.0317012i	$0.989908\pi$
$614$	−8122.22	+	20716.6i	−0.533854	+	1.36165i
$615$	884.595	+	1394.94i	0.0580005	+	0.0914627i
$616$	6297.48	+	13041.5i	0.411904	+	0.853013i
$617$	8344.93			0.544496			0.272248	−	0.962227i	$-0.412233\pi$
$617$	8344.93			0.544496			0.272248	+	0.962227i	$0.412233\pi$
$618$	−15595.9	+	3023.69i	−1.01514	+	0.196813i
$619$	−7771.63	+	7771.63i	−0.504634	+	0.504634i	−0.912874	−	0.408241i	$-0.866142\pi$
$619$	−7771.63	+	7771.63i	−0.504634	+	0.504634i	0.408241	+	0.912874i	$0.366142\pi$
$620$	−21986.6	+	838.235i	−1.42420	+	0.0542973i
$621$	142.425	+	110.708i	0.00920338	+	0.00715388i
$622$	−2352.85	+	1027.53i	−0.151673	+	0.0662382i
$623$	6136.91			0.394655
$624$	3946.81	−	2946.93i	0.253204	−	0.189057i
$625$	15126.4			0.968087
$626$	−2649.63	+	1157.14i	−0.169170	+	0.0738793i
$627$	5535.08	+	1239.21i	0.352551	+	0.0789300i
$628$	66.7912	+	1751.91i	0.00424404	+	0.111320i
$629$	16364.9	−	16364.9i	1.03738	−	1.03738i
$630$	25236.4	+	26730.8i	1.59594	+	1.69045i
$631$	2424.40			0.152954			0.0764768	−	0.997071i	$-0.475633\pi$
$631$	2424.40			0.152954			0.0764768	+	0.997071i	$0.475633\pi$
$632$	−5552.50	+	15922.2i	−0.349472	+	1.00214i
$633$	−21251.1	+	13476.3i	−1.33437	+	0.846182i
$634$	−6103.87	+	15568.6i	−0.382359	+	0.975247i
$635$	8036.89	+	8036.89i	0.502259	+	0.502259i
$636$	−7100.46	−	1307.80i	−0.442691	−	0.0815373i
$637$	5967.37	−	5967.37i	0.371171	−	0.371171i
$638$	−9270.14	+	4048.42i	−0.575248	+	0.251220i
$639$	6041.27	−	12815.8i	0.374005	−	0.793404i
$640$	−11586.3	−	19954.0i	−0.715607	−	1.23242i
$641$			17744.2i			1.09338i	0.837337	+	0.546688i	$0.184111\pi$
$641$			17744.2i			1.09338i	−0.837337	+	0.546688i	$0.815889\pi$
$642$	−21828.4	−	14738.8i	−1.34190	−	0.906068i
$643$	−18580.6	−	18580.6i	−1.13958	−	1.13958i	−0.988526	−	0.151052i	$-0.951734\pi$
$643$	−18580.6	−	18580.6i	−1.13958	−	1.13958i	−0.151052	−	0.988526i	$-0.548266\pi$
$644$	−227.960	−	211.217i	−0.0139486	−	0.0129241i
$645$	−33684.3	−	7541.31i	−2.05630	−	0.460370i
$646$	−9441.10	−	3701.51i	−0.575008	−	0.225440i
$647$		−	32732.6i		−	1.98895i	−0.104958	−	0.994477i	$-0.533471\pi$
$647$		−	32732.6i		−	1.98895i	0.104958	−	0.994477i	$-0.466529\pi$
$648$	5722.11	+	15471.1i	0.346892	+	0.937905i
$649$		−	1894.64i		−	0.114594i
$650$	−1970.61	+	5026.26i	−0.118914	+	0.303302i
$651$	−26443.6	−	5920.26i	−1.59202	−	0.356426i
$652$	−17422.9	+	664.244i	−1.04652	+	0.0398985i
$653$	10271.0	+	10271.0i	0.615522	+	0.615522i	0.944380	−	0.328858i	$-0.106664\pi$
$653$	10271.0	+	10271.0i	0.615522	+	0.615522i	−0.328858	+	0.944380i	$0.606664\pi$
$654$	14565.1	−	21571.1i	0.870856	−	1.28975i
$655$		−	7711.48i		−	0.460019i
$656$	−97.2192	−	1273.16i	−0.00578624	−	0.0757751i
$657$	−6663.51	+	14135.8i	−0.395690	+	0.839406i
$658$	−2377.04	−	5442.99i	−0.140831	−	0.322477i
$659$	2233.64	−	2233.64i	0.132034	−	0.132034i	−0.638001	−	0.770035i	$-0.720239\pi$
$659$	2233.64	−	2233.64i	0.132034	−	0.132034i	0.770035	+	0.638001i	$0.220239\pi$
$660$	−7960.36	−	11554.8i	−0.469480	−	0.681467i
$661$	15832.2	+	15832.2i	0.931622	+	0.931622i	0.997807	−	0.0661854i	$-0.0210829\pi$
$661$	15832.2	+	15832.2i	0.931622	+	0.931622i	−0.0661854	+	0.997807i	$0.521083\pi$
$662$	−7134.12	−	2797.03i	−0.418845	−	0.164214i
$663$	−4522.45	+	2867.89i	−0.264913	+	0.167993i
$664$	−8248.28	+	3982.94i	−0.482072	+	0.232783i
$665$	−24804.1			−1.44641
$666$	18469.9	−	17437.4i	1.07462	−	1.01454i
$667$	153.489	−	153.489i	0.00891023	−	0.00891023i
$668$	16662.7	+	15438.8i	0.965118	+	0.894230i
$669$	7952.05	+	1780.32i	0.459557	+	0.102887i
$670$	5827.20	+	13343.2i	0.336006	+	0.769393i
$671$	−10561.4			−0.607630
$672$	−7517.25	−	27405.3i	−0.431524	−	1.57319i
$673$	7290.78			0.417591			0.208796	−	0.977959i	$-0.433046\pi$
$673$	7290.78			0.417591			0.208796	+	0.977959i	$0.433046\pi$
$674$	−3496.47	−	8006.27i	−0.199820	−	0.457552i
$675$	−14274.6	−	11095.8i	−0.813971	−	0.632708i
$676$	−11605.2	−	10752.8i	−0.660286	−	0.611788i
$677$	6254.52	−	6254.52i	0.355067	−	0.355067i	−0.506924	−	0.861991i	$-0.669217\pi$
$677$	6254.52	−	6254.52i	0.355067	−	0.355067i	0.861991	+	0.506924i	$0.169217\pi$
$678$	1803.93	+	9304.46i	0.102182	+	0.527044i
$679$	−1191.09			−0.0673195
$680$	10908.3	+	22590.0i	0.615167	+	1.27395i
$681$	−9047.37	−	14267.1i	−0.509098	−	0.802812i
$682$	9629.37	+	3775.33i	0.540656	+	0.211972i
$683$	11670.1	+	11670.1i	0.653798	+	0.653798i	0.953905	−	0.300108i	$-0.0970226\pi$
$683$	11670.1	+	11670.1i	0.653798	+	0.653798i	−0.300108	+	0.953905i	$0.597023\pi$
$684$	−10240.9	−	4358.73i	−0.572473	−	0.243655i
$685$	−35477.7	+	35477.7i	−1.97888	+	1.97888i
$686$	−7755.39	−	17758.4i	−0.431636	−	0.988367i
$687$	5240.00	−	3322.91i	0.291002	−	0.184537i
$688$	20249.8	+	17376.6i	1.12212	+	0.962903i
$689$		−	2572.52i		−	0.142242i
$690$	249.537	+	168.490i	0.0137677	+	0.00929612i
$691$	−2970.42	−	2970.42i	−0.163531	−	0.163531i	0.620598	−	0.784129i	$-0.286890\pi$
$691$	−2970.42	−	2970.42i	−0.163531	−	0.163531i	−0.784129	+	0.620598i	$0.786890\pi$
$692$	−25104.8	+	957.117i	−1.37911	+	0.0525782i
$693$	−5842.69	−	16263.3i	−0.320268	−	0.891474i
$694$	2943.44	−	7507.56i	0.160996	−	0.410638i
$695$			6947.17i			0.379167i
$696$	19328.1	−	4517.56i	1.05263	−	0.246031i
$697$			1388.20i			0.0754405i
$698$	−7843.14	−	3075.01i	−0.425311	−	0.166749i
$699$	−7959.52	+	35552.2i	−0.430696	+	1.92376i
$700$	22847.5	+	21169.4i	1.23365	+	1.14304i
$701$	2674.46	+	2674.46i	0.144099	+	0.144099i	0.775476	−	0.631377i	$-0.217510\pi$
$701$	2674.46	+	2674.46i	0.144099	+	0.144099i	−0.631377	+	0.775476i	$0.717510\pi$
$702$	−5052.00	+	3003.64i	−0.271617	+	0.161489i
$703$			17138.7i			0.919484i
$704$	1237.27	+	10775.8i	0.0662379	+	0.576887i
$705$	3081.75	+	4859.69i	0.164632	+	0.259612i
$706$	18100.0	−	7904.56i	0.964876	−	0.421377i
$707$	14413.1	−	14413.1i	0.766704	−	0.766704i
$708$	−673.421	+	3656.21i	−0.0357468	+	0.194080i
$709$	14743.1	+	14743.1i	0.780942	+	0.780942i	0.979990	−	0.199048i	$-0.0637849\pi$
$709$	14743.1	+	14743.1i	0.780942	+	0.780942i	−0.199048	+	0.979990i	$0.563785\pi$
$710$	8632.02	−	22016.9i	0.456273	−	1.16377i
$711$	8579.53	−	18200.4i	0.452542	−	0.960011i
$712$	4339.94	+	1513.45i	0.228436	+	0.0796614i
$713$	−221.947			−0.0116577
$714$	5880.46	+	30330.8i	0.308222	+	1.58978i
$715$	3535.19	−	3535.19i	0.184907	−	0.184907i
$716$	856.370	+	22462.3i	0.0446984	+	1.17242i
$717$	2100.51	−	9382.19i	0.109407	−	0.488681i
$718$	22688.3	−	9908.34i	1.17927	−	0.515008i
$719$	2860.53			0.148372			0.0741861	−	0.997244i	$-0.476364\pi$
$719$	2860.53			0.148372			0.0741861	+	0.997244i	$0.476364\pi$
$720$	11254.6	+	25127.3i	0.582550	+	1.30061i
$721$	−32656.9			−1.68684
$722$	−10896.7	+	4758.76i	−0.561680	+	0.245295i
$723$	6389.82	−	28540.9i	0.328686	−	1.46812i
$724$	−92.4347	+	3.52405i	−0.00474490	+	0.000180898i
$725$	−15383.6	+	15383.6i	−0.788044	+	0.788044i
$726$	−2467.81	−	12728.7i	−0.126156	−	0.650698i
$727$	−4158.25			−0.212133			−0.106067	−	0.994359i	$-0.533826\pi$
$727$	−4158.25			−0.212133			−0.106067	+	0.994359i	$0.533826\pi$
$728$	9118.06	−	4402.94i	0.464200	−	0.224153i
$729$	−4856.18	−	19074.5i	−0.246720	−	0.969087i
$730$	−9521.10	+	24284.6i	−0.482728	+	1.23125i
$731$	−20513.2	−	20513.2i	−1.03790	−	1.03790i
$732$	20381.1	+	3753.90i	1.02911	+	0.189546i
$733$	5464.41	−	5464.41i	0.275351	−	0.275351i	−0.555899	−	0.831250i	$-0.687626\pi$
$733$	5464.41	−	5464.41i	0.275351	−	0.275351i	0.831250	+	0.555899i	$0.187626\pi$
$734$	21364.4	−	9330.18i	1.07435	−	0.469187i
$735$	25262.6	+	39837.4i	1.26779	+	1.99922i
$736$	−109.121	−	205.588i	−0.00546503	−	0.0102963i
$737$		−	6844.45i		−	0.342088i
$738$	−43.7956	+	1522.98i	−0.00218447	+	0.0759643i
$739$	12274.6	+	12274.6i	0.611002	+	0.611002i	0.943207	−	0.332205i	$-0.107793\pi$
$739$	12274.6	+	12274.6i	0.611002	+	0.611002i	−0.332205	+	0.943207i	$0.607793\pi$
$740$	28815.2	−	31099.5i	1.43145	−	1.54492i
$741$	866.402	−	3869.90i	0.0429528	−	0.191854i
$742$	−13817.7	−	5417.41i	−0.683643	−	0.268032i
$743$			17013.3i			0.840052i	0.907512	+	0.420026i	$0.137979\pi$
$743$			17013.3i			0.840052i	−0.907512	+	0.420026i	$0.862021\pi$
$744$	−17240.5	−	10708.1i	−0.849554	−	0.527658i
$745$		−	8952.10i		−	0.440241i
$746$	−435.605	+	1111.06i	−0.0213789	+	0.0545291i
$747$	10286.0	−	3695.30i	0.503807	−	0.180996i
$748$	−449.256	−	11783.8i	−0.0219605	−	0.576016i
$749$	−38285.0	−	38285.0i	−1.86770	−	1.86770i
$750$	−750.942	−	507.046i	−0.0365607	−	0.0246863i
$751$			28248.5i			1.37257i	0.727332	+	0.686286i	$0.240760\pi$
$751$			28248.5i			1.37257i	−0.727332	+	0.686286i	$0.759240\pi$
$752$	−338.692	−	4435.42i	−0.0164239	−	0.215084i
$753$	3714.69	−	2355.65i	0.179775	−	0.114003i
$754$	2830.49	+	6481.29i	0.136711	+	0.313044i
$755$	−11585.7	+	11585.7i	−0.558472	+	0.558472i
$756$	5494.48	+	33461.0i	0.264329	+	1.60974i
$757$	−16064.6	−	16064.6i	−0.771306	−	0.771306i	0.207029	−	0.978335i	$-0.433621\pi$
$757$	−16064.6	−	16064.6i	−0.771306	−	0.771306i	−0.978335	+	0.207029i	$0.933621\pi$
$758$	3946.62	+	1547.33i	0.189113	+	0.0741443i
$759$	−75.7997	−	119.531i	−0.00362498	−	0.00571633i
$760$	−17541.1	−	6117.05i	−0.837215	−	0.291959i
$761$	23115.8			1.10111			0.550557	−	0.834798i	$-0.314415\pi$
$761$	23115.8			1.10111			0.550557	+	0.834798i	$0.314415\pi$
$762$	1995.45	+	10292.3i	0.0948654	+	0.489305i
$763$	37833.6	−	37833.6i	1.79511	−	1.79511i
$764$	−16932.0	+	18274.2i	−0.801802	+	0.865362i
$765$	−10120.5	−	28170.7i	−0.478311	−	1.33139i
$766$	4985.60	+	11416.1i	0.235166	+	0.538487i
$767$	−1324.66			−0.0623606
$768$	1442.44	−	21234.5i	0.0677730	−	0.997701i
$769$	−6409.50			−0.300562			−0.150281	−	0.988643i	$-0.548018\pi$
$769$	−6409.50			−0.300562			−0.150281	+	0.988643i	$0.548018\pi$
$770$	−11543.8	−	26433.2i	−0.540272	−	1.23712i
$771$	32545.7	+	7286.41i	1.52024	+	0.340355i
$772$	−24058.8	+	25966.0i	−1.12163	+	1.21054i
$773$	−15617.9	+	15617.9i	−0.726699	+	0.726699i	−0.969961	−	0.243262i	$-0.921782\pi$
$773$	−15617.9	+	15617.9i	−0.726699	+	0.726699i	0.243262	+	0.969961i	$0.421782\pi$
$774$	−21857.6	−	23151.9i	−1.01506	−	1.07517i
$775$	22244.8			1.03104
$776$	−842.324	−	293.740i	−0.0389661	−	0.0135885i
$777$	44096.7	−	27963.6i	2.03598	−	1.29111i
$778$	36078.0	+	14144.9i	1.66255	+	0.651823i
$779$	−726.923	−	726.923i	−0.0334335	−	0.0334335i
$780$	−8078.61	+	5565.55i	−0.370847	+	0.255486i
$781$	−7860.74	+	7860.74i	−0.360153	+	0.360153i
$782$	101.274	+	231.899i	0.00463113	+	0.0106045i
$783$	−23501.0	+	2944.59i	−1.07261	+	0.134395i
$784$	−2776.42	−	36359.4i	−0.126477	−	1.65631i
$785$		−	3491.74i		−	0.158759i
$786$	3980.46	−	5895.11i	0.180634	−	0.267521i
$787$	−24107.2	−	24107.2i	−1.09190	−	1.09190i	−0.995325	−	0.0965795i	$-0.969210\pi$
$787$	−24107.2	−	24107.2i	−1.09190	−	1.09190i	−0.0965795	−	0.995325i	$-0.530790\pi$
$788$	−841.036	−	22060.1i	−0.0380212	−	0.997281i
$789$	17581.0	+	3936.08i	0.793284	+	0.177602i
$790$	12258.8	−	31267.3i	0.552086	−	1.40815i
$791$			19483.1i			0.875776i
$792$	−121.112	−	12942.1i	−0.00543376	−	0.580651i
$793$			7384.12i			0.330666i
$794$	−272.116	−	106.687i	−0.0121625	−	0.00476848i
$795$	14032.2	+	3141.56i	0.626001	+	0.140151i
$796$	−15064.0	+	16258.2i	−0.670766	+	0.723939i
$797$	10177.6	+	10177.6i	0.452335	+	0.452335i	0.896129	−	0.443794i	$-0.146368\pi$
$797$	10177.6	+	10177.6i	0.452335	+	0.452335i	−0.443794	+	0.896129i	$0.646368\pi$
$798$	−18961.7	−	12803.2i	−0.841150	−	0.567956i
$799$			4836.22i			0.214134i
$800$	10936.8	+	20605.2i	0.483342	+	0.910631i
$801$	−4960.90	−	2338.53i	−0.218832	−	0.103156i
$802$	881.997	−	385.182i	0.0388334	−	0.0169592i
$803$	8670.38	−	8670.38i	0.381035	−	0.381035i
$804$	−2432.75	+	13208.2i	−0.106712	+	0.579374i
$805$	437.664	+	437.664i	0.0191623	+	0.0191623i
$806$	2639.55	−	6732.46i	0.115353	−	0.294219i
$807$	−12721.4	+	8067.18i	−0.554912	+	0.351894i
$808$	13747.2	−	6638.25i	0.598545	−	0.289026i
$809$	−15986.6			−0.694759			−0.347380	−	0.937725i	$-0.612928\pi$
$809$	−15986.6			−0.694759			−0.347380	+	0.937725i	$0.612928\pi$
$810$	−10214.3	−	31225.0i	−0.443081	−	1.35449i
$811$	−13233.6	+	13233.6i	−0.572990	+	0.572990i	−0.932963	−	0.359973i	$-0.882786\pi$
$811$	−13233.6	+	13233.6i	−0.572990	+	0.572990i	0.359973	+	0.932963i	$0.382786\pi$
$812$	40773.5	−	1554.48i	1.76215	−	0.0671818i
$813$	−12401.5	−	2776.47i	−0.534979	−	0.119772i
$814$	−18264.3	+	7976.30i	−0.786440	+	0.343451i
$815$	34725.6			1.49250
$816$	−3321.42	+	22899.7i	−0.142491	+	0.982413i
$817$	21483.2			0.919953
$818$	−28184.7	+	12308.7i	−1.20471	+	0.526117i
$819$	−11370.6	+	4084.97i	−0.485130	+	0.174286i
$820$	96.8841	+	2541.23i	0.00412602	+	0.108224i
$821$	6092.12	−	6092.12i	0.258972	−	0.258972i	−0.565664	−	0.824636i	$-0.691380\pi$
$821$	6092.12	−	6092.12i	0.258972	−	0.258972i	0.824636	+	0.565664i	$0.191380\pi$
$822$	−45433.9	+	8808.62i	−1.92785	+	0.373766i
$823$	28908.7			1.22442			0.612208	−	0.790697i	$-0.290281\pi$
$823$	28908.7			1.22442			0.612208	+	0.790697i	$0.290281\pi$
$824$	−23094.5	−	8053.67i	−0.976379	−	0.340489i
$825$	7597.10	+	11980.1i	0.320602	+	0.505567i
$826$	−2789.57	+	7115.09i	−0.117508	+	0.299716i
$827$	−8950.54	−	8950.54i	−0.376349	−	0.376349i	0.493434	−	0.869783i	$-0.335741\pi$
$827$	−8950.54	−	8950.54i	−0.376349	−	0.376349i	−0.869783	+	0.493434i	$0.835741\pi$
$828$	103.790	+	257.608i	0.00435623	+	0.0108122i
$829$	−5252.07	+	5252.07i	−0.220038	+	0.220038i	−0.808515	−	0.588476i	$-0.799728\pi$
$829$	−5252.07	+	5252.07i	−0.220038	+	0.220038i	0.588476	+	0.808515i	$0.299728\pi$
$830$	16718.1	−	7301.05i	0.699148	−	0.305329i
$831$	−29693.2	+	18829.8i	−1.23953	+	0.786038i
$832$	7533.99	−	865.051i	0.313935	−	0.0360460i
$833$			39644.9i			1.64900i
$834$	−3585.94	+	5310.82i	−0.148886	+	0.220502i
$835$	−31990.9	−	31990.9i	−1.32586	−	1.32586i
$836$	6405.77	+	5935.27i	0.265010	+	0.245545i
$837$	19120.2	+	14862.3i	0.789597	+	0.613761i
$838$	21230.6	+	8323.76i	0.875179	+	0.343126i
$839$			26507.2i			1.09074i	0.838195	+	0.545370i	$0.183611\pi$
$839$			26507.2i			1.09074i	−0.838195	+	0.545370i	$0.816389\pi$
$840$	12881.5	+	55112.8i	0.529113	+	2.26378i
$841$			4111.02i			0.168560i
$842$	−1551.73	+	3957.84i	−0.0635107	+	0.161991i
$843$	1948.11	−	8701.50i	0.0795926	−	0.355511i
$844$	−38714.1	+	1475.97i	−1.57890	+	0.0601954i
$845$	22280.9	+	22280.9i	0.907085	+	0.907085i
$846$	−152.575	+	5305.75i	−0.00620051	+	0.215621i
$847$		−	26653.3i		−	1.08125i
$848$	−8435.66	−	7238.75i	−0.341606	−	0.293137i
$849$	18978.5	+	29927.7i	0.767184	+	1.20980i
$850$	−10150.3	−	23242.3i	−0.409590	−	0.937886i
$851$	302.408	−	302.408i	0.0121815	−	0.0121815i
$852$	17963.3	−	12375.4i	0.722317	−	0.497622i
$853$	−11291.0	−	11291.0i	−0.453222	−	0.453222i	0.443201	−	0.896422i	$-0.353843\pi$
$853$	−11291.0	−	11291.0i	−0.453222	−	0.453222i	−0.896422	+	0.443201i	$0.853843\pi$
$854$	39662.1	+	15550.1i	1.58924	+	0.623082i
$855$	20050.9	+	9451.85i	0.802020	+	0.378066i
$856$	−17633.0	−	36516.2i	−0.704069	−	1.45806i
$857$	−37764.6			−1.50527			−0.752634	−	0.658439i	$-0.771217\pi$
$857$	−37764.6			−1.50527			−0.752634	+	0.658439i	$0.771217\pi$
$858$	4527.28	−	877.738i	0.180138	−	0.0349248i
$859$	−10557.9	+	10557.9i	−0.419359	+	0.419359i	−0.884983	−	0.465624i	$-0.845830\pi$
$859$	−10557.9	+	10557.9i	−0.419359	+	0.419359i	0.465624	+	0.884983i	$0.345830\pi$
$860$	−38982.9	−	36119.7i	−1.54571	−	1.43217i
$861$	−684.269	+	3056.38i	−0.0270846	+	0.120977i
$862$	−2660.22	−	6091.43i	−0.105113	−	0.240690i
$863$	−42832.2			−1.68949			−0.844743	−	0.535173i	$-0.820247\pi$
$863$	−42832.2			−1.68949			−0.844743	+	0.535173i	$0.820247\pi$
$864$	−4366.33	+	25018.1i	−0.171928	+	0.985110i
$865$	50036.6			1.96682
$866$	9755.13	+	22337.5i	0.382786	+	0.876511i
$867$	−81.2069	+	362.721i	−0.00318100	+	0.0142084i
$868$	−30603.3	−	28355.5i	−1.19671	−	1.10881i
$869$	−11163.5	+	11163.5i	−0.435782	+	0.435782i
$870$	−38809.9	+	7524.36i	−1.51239	+	0.293218i
$871$	−4785.36			−0.186160
$872$	36085.7	−	17425.1i	1.40140	−	0.676707i
$873$	962.844	+	453.877i	0.0373280	+	0.0175961i
$874$	−174.463	−	68.4007i	−0.00675207	−	0.00264724i
$875$	−1317.08	−	1317.08i	−0.0508863	−	0.0508863i
$876$	−19813.5	+	13650.0i	−0.764198	+	0.526475i
$877$	2791.16	−	2791.16i	0.107469	−	0.107469i	−0.651327	−	0.758797i	$-0.725788\pi$
$877$	2791.16	−	2791.16i	0.107469	−	0.107469i	0.758797	+	0.651327i	$0.225788\pi$
$878$	5601.12	+	12825.5i	0.215295	+	0.492986i
$879$	3024.56	+	4769.51i	0.116059	+	0.183017i
$880$	−1644.81	−	21540.0i	−0.0630074	−	0.825130i
$881$			8537.89i			0.326503i	0.986585	+	0.163251i	$0.0521981\pi$
$881$			8537.89i			0.326503i	−0.986585	+	0.163251i	$0.947802\pi$
$882$	−1250.73	+	43493.9i	−0.0477487	+	1.66045i
$883$	28914.0	+	28914.0i	1.10196	+	1.10196i	0.994174	+	0.107791i	$0.0343779\pi$
$883$	28914.0	+	28914.0i	1.10196	+	1.10196i	0.107791	+	0.994174i	$0.465622\pi$
$884$	−8238.77	+	314.101i	−0.313461	+	0.0119507i
$885$	1617.67	−	7225.55i	0.0614435	−	0.274445i
$886$	−8948.32	+	22823.6i	−0.339305	+	0.865435i
$887$		−	3233.15i		−	0.122389i	−0.998126	−	0.0611943i	$-0.980509\pi$
$887$		−	3233.15i		−	0.122389i	0.998126	−	0.0611943i	$-0.0194909\pi$
$888$	38080.8	−	8900.62i	1.43908	−	0.336357i
$889$			21551.5i			0.813066i
$890$	−8522.57	−	3341.39i	−0.320986	−	0.125847i
$891$	−1474.22	+	15373.2i	−0.0554302	+	0.578025i
$892$	9202.94	+	8526.99i	0.345445	+	0.320072i
$893$	−2532.45	−	2532.45i	−0.0948994	−	0.0948994i
$894$	4620.83	−	6843.51i	0.172868	−	0.256019i
$895$		−	44769.7i		−	1.67205i
$896$	11219.3	−	42288.8i	0.418314	−	1.57675i
$897$	−83.5710	+	52.9960i	−0.00311076	+	0.00197267i
$898$	−33844.5	+	14780.4i	−1.25769	+	0.549254i
$899$	20605.6	−	20605.6i	0.764445	−	0.764445i
$900$	−10402.5	−	25819.0i	−0.385276	−	0.956259i
$901$	8545.40	+	8545.40i	0.315970	+	0.315970i
$902$	436.356	−	1112.97i	0.0161076	−	0.0410842i
$903$	−35052.2	−	55274.8i	−1.29176	−	2.03702i
$904$	−4804.80	+	13778.2i	−0.176776	+	0.506919i
$905$	184.232			0.00676694
$906$	−14837.0	+	2876.56i	−0.544069	+	0.105483i
$907$	−24455.2	+	24455.2i	−0.895284	+	0.895284i	−0.995014	−	0.0997307i	$-0.968202\pi$
$907$	−24455.2	+	24455.2i	−0.895284	+	0.895284i	0.0997307	+	0.995014i	$0.468202\pi$
$908$	−990.901	−	25991.0i	−0.0362161	−	0.949935i
$909$	−17143.3	+	6158.86i	−0.625532	+	0.224727i
$910$	−18481.0	+	8070.94i	−0.673229	+	0.294010i
$911$	26302.8			0.956589			0.478294	−	0.878200i	$-0.341255\pi$
$911$	26302.8			0.956589			0.478294	+	0.878200i	$0.341255\pi$
$912$	−10252.0	−	13730.5i	−0.372235	−	0.498533i
$913$	−8575.60			−0.310855
$914$	43383.5	−	18946.3i	1.57002	−	0.685653i
$915$	−40277.9	−	9017.50i	−1.45524	−	0.325803i
$916$	9545.95	−	363.938i	0.344331	−	0.0131276i
$917$	10339.5	−	10339.5i	0.372344	−	0.372344i
$918$	6804.24	−	26759.3i	0.244633	−	0.962078i
$919$	14271.1			0.512252			0.256126	−	0.966643i	$-0.417554\pi$
$919$	14271.1			0.512252			0.256126	+	0.966643i	$0.417554\pi$
$920$	201.576	+	417.444i	0.00722364	+	0.0149595i
$921$	34523.0	−	21892.6i	1.23515	−	0.783262i
$922$	16072.7	−	40995.0i	0.574105	−	1.46432i
$923$	5495.90	+	5495.90i	0.195991	+	0.195991i
$924$	4819.33	−	26165.7i	0.171585	−	0.931587i
$925$	−30309.1	+	30309.1i	−1.07736	+	1.07736i
$926$	2642.87	−	1154.19i	0.0937908	−	0.0409599i
$927$	26398.9	+	12444.2i	0.935333	+	0.440909i
$928$	29217.8	+	8956.01i	1.03354	+	0.316805i
$929$		−	14189.2i		−	0.501113i	−0.968102	−	0.250556i	$-0.919386\pi$
$929$		−	14189.2i		−	0.501113i	0.968102	−	0.250556i	$-0.0806135\pi$
$930$	33499.8	+	22619.5i	1.18119	+	0.797553i
$931$	−20759.8	−	20759.8i	−0.730799	−	0.730799i
$932$	−38122.7	+	41144.7i	−1.33986	+	1.44607i
$933$	4602.74	+	1030.47i	0.161508	+	0.0361588i
$934$	34955.5	+	13704.8i	1.22460	+	0.480122i
$935$			23486.4i			0.821485i
$936$	−9048.55	+	84.6767i	−0.315984	+	0.00295699i
$937$		−	37715.2i		−	1.31494i	−0.753479	−	0.657472i	$-0.771626\pi$
$937$		−	37715.2i		−	1.31494i	0.753479	−	0.657472i	$-0.228374\pi$
$938$	−10077.4	+	25703.5i	−0.350787	+	0.894721i
$939$	5183.30	+	1160.45i	0.180139	+	0.0403300i
$940$	337.524	+	8853.14i	0.0117115	+	0.307189i
$941$	20871.8	+	20871.8i	0.723062	+	0.723062i	0.969228	−	0.246166i	$-0.0791709\pi$
$941$	20871.8	+	20871.8i	0.723062	+	0.723062i	−0.246166	+	0.969228i	$0.579171\pi$
$942$	1802.34	−	2669.29i	0.0623391	−	0.0923251i
$943$			25.6528i			0.000885865i
$944$	−3727.43	+	4343.75i	−0.128514	+	0.149764i
$945$	−8396.29	−	67011.4i	−0.289028	−	2.30675i
$946$	9998.23	+	22894.1i	0.343626	+	0.786841i
$947$	−35217.3	+	35217.3i	−1.20846	+	1.20846i	−0.236931	+	0.971526i	$0.576142\pi$
$947$	−35217.3	+	35217.3i	−1.20846	+	1.20846i	−0.971526	+	0.236931i	$0.923858\pi$
$948$	25510.7	−	17574.9i	0.873996	−	0.602118i
$949$	−6061.97	−	6061.97i	−0.207355	−	0.207355i
$950$	17485.7	+	6855.52i	0.597171	+	0.234129i
$951$	25944.1	−	16452.3i	0.884644	−	0.560991i
$952$	−15662.7	+	44914.1i	−0.533227	+	1.52907i
$953$	8998.22			0.305856			0.152928	−	0.988237i	$-0.451130\pi$
$953$	8998.22			0.305856			0.152928	+	0.988237i	$0.451130\pi$
$954$	9105.45	+	9644.63i	0.309014	+	0.327313i
$955$	35084.8	−	35084.8i	1.18881	−	1.18881i
$956$	10060.5	−	10858.0i	0.340357	−	0.367337i
$957$	18134.6	+	4060.02i	0.612548	+	0.137139i
$958$	−21668.2	−	49616.2i	−0.730760	−	1.67331i
$959$	−95136.3			−3.20345
$960$	−4481.97	+	42151.8i	−0.150682	+	1.41713i
$961$	−4.92611			−0.000165356
$962$	5576.70	+	12769.6i	0.186902	+	0.427972i
$963$	16359.6	+	45537.3i	0.547435	+	1.52380i
$964$	30604.5	−	33030.6i	1.02251	−	1.10357i
$965$	49852.4	−	49852.4i	1.66301	−	1.66301i
$966$	108.666	+	560.486i	0.00361932	+	0.0186681i
$967$	27956.6			0.929702			0.464851	−	0.885389i	$-0.346108\pi$
$967$	27956.6			0.929702			0.464851	+	0.885389i	$0.346108\pi$
$968$	6573.07	−	18848.8i	0.218251	−	0.625851i
$969$	9977.03	+	15733.1i	0.330762	+	0.521588i
$970$	1654.12	+	648.519i	0.0547531	+	0.0214667i
$971$	−10274.5	−	10274.5i	−0.339571	−	0.339571i	0.516635	−	0.856206i	$-0.327184\pi$
$971$	−10274.5	−	10274.5i	−0.339571	−	0.339571i	−0.856206	+	0.516635i	$0.827184\pi$
$972$	8309.05	−	29142.6i	0.274190	−	0.961675i
$973$	−9314.69	+	9314.69i	−0.306901	+	0.306901i
$974$	−11158.8	−	25551.7i	−0.367096	−	0.840583i
$975$	8375.97	−	5311.57i	0.275124	−	0.174468i
$976$	24213.6	+	20778.0i	0.794118	+	0.681443i
$977$		−	50724.0i		−	1.66101i	−0.557013	−	0.830504i	$-0.688053\pi$
$977$		−	50724.0i		−	1.66101i	0.557013	−	0.830504i	$-0.311947\pi$
$978$	26546.3	+	17924.4i	0.867953	+	0.586053i
$979$	3042.83	+	3042.83i	0.0993354	+	0.0993354i
$980$	2766.86	+	72573.6i	0.0901877	+	2.36559i
$981$	−45000.4	+	16166.7i	−1.46458	+	0.526160i
$982$	−3264.63	+	8326.78i	−0.106088	+	0.270589i
$983$		−	8090.00i		−	0.262493i	−0.991350	−	0.131247i	$-0.958102\pi$
$983$		−	8090.00i		−	0.262493i	0.991350	−	0.131247i	$-0.0418980\pi$
$984$	−1237.65	+	1992.68i	−0.0400965	+	0.0645572i
$985$			43968.1i			1.42227i
$986$	−30931.9	−	12127.3i	−0.999060	−	0.391695i
$987$	−2383.85	+	10647.8i	−0.0768783	+	0.343387i
$988$	4149.69	−	4478.65i	0.133623	−	0.144215i
$989$	−379.066	−	379.066i	−0.0121877	−	0.0121877i
$990$	−740.959	+	25766.7i	−0.0237871	+	0.827190i
$991$		−	35268.5i		−	1.13052i	−0.824914	−	0.565258i	$-0.808777\pi$
$991$		−	35268.5i		−	1.13052i	0.824914	−	0.565258i	$-0.191223\pi$
$992$	−14649.3	−	27599.8i	−0.468868	−	0.883362i
$993$	7539.08	+	11888.6i	0.240932	+	0.379933i
$994$	41093.7	−	17946.3i	1.31128	−	0.572657i
$995$	31214.2	−	31214.2i	0.994531	−	0.994531i
$996$	16548.9	+	3048.06i	0.526477	+	0.0969694i
$997$	17738.4	+	17738.4i	0.563473	+	0.563473i	0.930292	−	0.366820i	$-0.119553\pi$
$997$	17738.4	+	17738.4i	0.563473	+	0.563473i	−0.366820	+	0.930292i	$0.619553\pi$
$998$	−2743.55	+	6997.73i	−0.0870197	+	0.221953i
$999$	−46302.2	+	5801.51i	−1.46640	+	0.183735i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.4.k.a.11.8	✓	44
3.2	odd	2	inner	48.4.k.a.11.15	yes	44
4.3	odd	2		192.4.k.a.143.13		44
8.3	odd	2		384.4.k.a.287.10		44
8.5	even	2		384.4.k.b.287.13		44
12.11	even	2		192.4.k.a.143.2		44
16.3	odd	4	inner	48.4.k.a.35.15	yes	44
16.5	even	4		384.4.k.a.95.21		44
16.11	odd	4		384.4.k.b.95.2		44
16.13	even	4		192.4.k.a.47.2		44
24.5	odd	2		384.4.k.b.287.2		44
24.11	even	2		384.4.k.a.287.21		44
48.5	odd	4		384.4.k.a.95.10		44
48.11	even	4		384.4.k.b.95.13		44
48.29	odd	4		192.4.k.a.47.13		44
48.35	even	4	inner	48.4.k.a.35.8	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.k.a.11.8	✓	44	1.1	even	1	trivial
48.4.k.a.11.15	yes	44	3.2	odd	2	inner
48.4.k.a.35.8	yes	44	48.35	even	4	inner
48.4.k.a.35.15	yes	44	16.3	odd	4	inner
192.4.k.a.47.2		44	16.13	even	4
192.4.k.a.47.13		44	48.29	odd	4
192.4.k.a.143.2		44	12.11	even	2
192.4.k.a.143.13		44	4.3	odd	2
384.4.k.a.95.10		44	48.5	odd	4
384.4.k.a.95.21		44	16.5	even	4
384.4.k.a.287.10		44	8.3	odd	2
384.4.k.a.287.21		44	24.11	even	2
384.4.k.b.95.2		44	16.11	odd	4
384.4.k.b.95.13		44	48.11	even	4
384.4.k.b.287.2		44	24.5	odd	2
384.4.k.b.287.13		44	8.5	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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	48.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13198 - 2.59203i) q^{2} +(-1.13522 + 5.07063i) q^{3} +(-5.43724 + 5.86826i) q^{4} +(11.2665 - 11.2665i) q^{5} +(14.4283 - 2.79732i) q^{6} +30.2121 q^{7} +(21.3655 + 7.45073i) q^{8} +(-24.4225 - 11.5126i) q^{9} +O(q^{10})\)	\(q+(-1.13198 - 2.59203i) q^{2} +(-1.13522 + 5.07063i) q^{3} +(-5.43724 + 5.86826i) q^{4} +(11.2665 - 11.2665i) q^{5} +(14.4283 - 2.79732i) q^{6} +30.2121 q^{7} +(21.3655 + 7.45073i) q^{8} +(-24.4225 - 11.5126i) q^{9} +(-41.9567 - 16.4497i) q^{10} +(14.9799 + 14.9799i) q^{11} +(-23.5833 - 34.2320i) q^{12} +(10.4733 - 10.4733i) q^{13} +(-34.1995 - 78.3106i) q^{14} +(44.3383 + 69.9184i) q^{15} +(-4.87289 - 63.8142i) q^{16} +69.5806i q^{17} +(-2.19516 + 76.3360i) q^{18} +(-36.4354 - 36.4354i) q^{19} +(4.85610 + 127.374i) q^{20} +(-34.2975 + 153.194i) q^{21} +(21.8714 - 55.7853i) q^{22} +1.28579i q^{23} +(-62.0345 + 99.8785i) q^{24} -128.869i q^{25} +(-39.0027 - 15.2916i) q^{26} +(86.1012 - 110.768i) q^{27} +(-164.270 + 177.292i) q^{28} +(-119.373 - 119.373i) q^{29} +(131.040 - 194.073i) q^{30} +172.615i q^{31} +(-159.892 + 84.8672i) q^{32} +(-92.9630 + 58.9519i) q^{33} +(180.355 - 78.7640i) q^{34} +(340.385 - 340.385i) q^{35} +(200.350 - 80.7210i) q^{36} +(-235.193 - 235.193i) q^{37} +(-53.1974 + 135.686i) q^{38} +(41.2167 + 64.9958i) q^{39} +(324.659 - 156.772i) q^{40} +19.9510 q^{41} +(435.908 - 84.5128i) q^{42} +(-294.812 + 294.812i) q^{43} +(-169.355 + 6.45663i) q^{44} +(-404.864 + 145.450i) q^{45} +(3.33280 - 1.45549i) q^{46} +69.5052 q^{47} +(329.110 + 47.7348i) q^{48} +569.769 q^{49} +(-334.033 + 145.878i) q^{50} +(-352.818 - 78.9896i) q^{51} +(4.51421 + 118.406i) q^{52} +(122.813 - 122.813i) q^{53} +(-384.579 - 97.7893i) q^{54} +337.543 q^{55} +(645.497 + 225.102i) q^{56} +(226.113 - 143.388i) q^{57} +(-174.291 + 444.548i) q^{58} +(-63.2396 - 63.2396i) q^{59} +(-651.377 - 119.974i) q^{60} +(-352.521 + 352.521i) q^{61} +(447.423 - 195.397i) q^{62} +(-737.855 - 347.819i) q^{63} +(400.973 + 318.378i) q^{64} -235.996i q^{65} +(258.037 + 174.230i) q^{66} +(-228.455 - 228.455i) q^{67} +(-408.317 - 378.327i) q^{68} +(-6.51976 - 1.45966i) q^{69} +(-1267.60 - 496.979i) q^{70} +524.753i q^{71} +(-436.024 - 427.939i) q^{72} -578.802i q^{73} +(-343.393 + 875.860i) q^{74} +(653.449 + 146.296i) q^{75} +(411.920 - 15.7044i) q^{76} +(452.573 + 452.573i) q^{77} +(121.815 - 180.409i) q^{78} +745.229i q^{79} +(-773.865 - 664.064i) q^{80} +(463.920 + 562.334i) q^{81} +(-22.5842 - 51.7136i) q^{82} +(-286.237 + 286.237i) q^{83} +(-712.499 - 1034.22i) q^{84} +(783.932 + 783.932i) q^{85} +(1097.88 + 430.440i) q^{86} +(740.814 - 469.783i) q^{87} +(208.442 + 431.665i) q^{88} +203.128 q^{89} +(835.310 + 884.773i) q^{90} +(316.421 - 316.421i) q^{91} +(-7.54534 - 6.99114i) q^{92} +(-875.266 - 195.957i) q^{93} +(-78.6786 - 180.160i) q^{94} -821.001 q^{95} +(-248.816 - 907.098i) q^{96} -39.4244 q^{97} +(-644.968 - 1476.86i) q^{98} +(-193.389 - 538.304i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7}+O(q^{10}) \) 44 * q - 2 * q^3 - 4 * q^4 + 28 * q^6 - 8 * q^7	\( 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7} + 56 q^{10} - 80 q^{12} - 4 q^{13} - 112 q^{16} + 52 q^{18} + 20 q^{19} - 56 q^{21} - 40 q^{22} - 120 q^{24} - 134 q^{27} - 296 q^{28} - 332 q^{30} - 4 q^{33} + 520 q^{34} - 604 q^{36} - 4 q^{37} + 596 q^{39} + 632 q^{40} + 696 q^{42} - 436 q^{43} - 252 q^{45} + 664 q^{46} + 1200 q^{48} + 972 q^{49} - 648 q^{51} + 320 q^{52} + 1592 q^{54} + 280 q^{55} - 424 q^{58} + 800 q^{60} - 916 q^{61} - 2056 q^{64} - 668 q^{66} - 1636 q^{67} + 52 q^{69} - 5192 q^{70} - 3704 q^{72} + 1454 q^{75} - 568 q^{76} - 4932 q^{78} - 4 q^{81} + 768 q^{82} - 2096 q^{84} + 736 q^{85} + 1284 q^{87} + 8864 q^{88} + 2672 q^{90} + 424 q^{91} - 2084 q^{93} + 5616 q^{94} + 8008 q^{96} - 8 q^{97} + 1196 q^{99}+O(q^{100}) \) 44 * q - 2 * q^3 - 4 * q^4 + 28 * q^6 - 8 * q^7 + 56 * q^10 - 80 * q^12 - 4 * q^13 - 112 * q^16 + 52 * q^18 + 20 * q^19 - 56 * q^21 - 40 * q^22 - 120 * q^24 - 134 * q^27 - 296 * q^28 - 332 * q^30 - 4 * q^33 + 520 * q^34 - 604 * q^36 - 4 * q^37 + 596 * q^39 + 632 * q^40 + 696 * q^42 - 436 * q^43 - 252 * q^45 + 664 * q^46 + 1200 * q^48 + 972 * q^49 - 648 * q^51 + 320 * q^52 + 1592 * q^54 + 280 * q^55 - 424 * q^58 + 800 * q^60 - 916 * q^61 - 2056 * q^64 - 668 * q^66 - 1636 * q^67 + 52 * q^69 - 5192 * q^70 - 3704 * q^72 + 1454 * q^75 - 568 * q^76 - 4932 * q^78 - 4 * q^81 + 768 * q^82 - 2096 * q^84 + 736 * q^85 + 1284 * q^87 + 8864 * q^88 + 2672 * q^90 + 424 * q^91 - 2084 * q^93 + 5616 * q^94 + 8008 * q^96 - 8 * q^97 + 1196 * q^99

Introduction

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