LMFDB - Embedded newform 56.4.p.a.53.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,4,Mod(37,56)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(56, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("56.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 56 = 2^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	56.p (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:	$3.30410696032$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			53.20
Character	$\chi$	$=$	56.53
Dual form			56.4.p.a.37.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.53540 + 1.25369i) q^{2} +(-7.07996 - 4.08762i) q^{3} +(4.85654 + 6.35720i) q^{4} +(17.0228 - 9.82813i) q^{5} +(-12.8260 - 19.2398i) q^{6} +(15.6931 - 9.83491i) q^{7} +(4.34335 + 22.2066i) q^{8} +(19.9172 + 34.4977i) q^{9} +(55.4811 - 3.57700i) q^{10} +(-29.7141 - 17.1555i) q^{11} +(-8.39831 - 64.8604i) q^{12} -3.09910i q^{13} +(52.1183 - 5.26121i) q^{14} -160.695 q^{15} +(-16.8280 + 61.7480i) q^{16} +(-14.8109 + 25.6532i) q^{17} +(7.24898 + 112.435i) q^{18} +(-40.0355 + 23.1145i) q^{19} +(145.151 + 60.4868i) q^{20} +(-151.308 + 5.48329i) q^{21} +(-53.8297 - 80.7482i) q^{22} +(49.7004 + 86.0836i) q^{23} +(60.0215 - 174.976i) q^{24} +(130.684 - 226.352i) q^{25} +(3.88530 - 7.85747i) q^{26} -104.925i q^{27} +(138.737 + 52.0007i) q^{28} +136.943i q^{29} +(-407.425 - 201.461i) q^{30} +(-0.290223 + 0.502681i) q^{31} +(-120.078 + 135.459i) q^{32} +(140.250 + 242.920i) q^{33} +(-69.7127 + 46.4730i) q^{34} +(170.483 - 321.652i) q^{35} +(-122.580 + 294.157i) q^{36} +(-128.221 + 74.0282i) q^{37} +(-130.484 + 8.41263i) q^{38} +(-12.6679 + 21.9415i) q^{39} +(292.186 + 335.333i) q^{40} -141.194 q^{41} +(-390.502 - 175.791i) q^{42} +259.780i q^{43} +(-35.2472 - 272.215i) q^{44} +(678.095 + 391.498i) q^{45} +(18.0887 + 280.565i) q^{46} +(-174.311 - 301.916i) q^{47} +(371.544 - 368.387i) q^{48} +(149.549 - 308.681i) q^{49} +(615.111 - 410.056i) q^{50} +(209.721 - 121.083i) q^{51} +(19.7016 - 15.0509i) q^{52} +(-184.884 - 106.743i) q^{53} +(131.543 - 266.027i) q^{54} -674.424 q^{55} +(286.561 + 305.775i) q^{56} +377.933 q^{57} +(-171.683 + 347.205i) q^{58} +(-100.398 - 57.9647i) q^{59} +(-780.420 - 1021.57i) q^{60} +(345.954 - 199.737i) q^{61} +(-1.36604 + 0.910650i) q^{62} +(651.846 + 345.492i) q^{63} +(-474.271 + 192.903i) q^{64} +(-30.4584 - 52.7554i) q^{65} +(51.0446 + 791.730i) q^{66} +(893.014 + 515.582i) q^{67} +(-235.012 + 30.4301i) q^{68} -812.625i q^{69} +(835.493 - 601.786i) q^{70} +476.543 q^{71} +(-679.570 + 592.131i) q^{72} +(-554.624 + 960.638i) q^{73} +(-417.899 + 26.9429i) q^{74} +(-1850.48 + 1068.37i) q^{75} +(-341.377 - 142.257i) q^{76} +(-635.030 + 23.0130i) q^{77} +(-59.6261 + 39.7490i) q^{78} +(-225.997 - 391.439i) q^{79} +(320.407 + 1216.51i) q^{80} +(108.872 - 188.573i) q^{81} +(-357.984 - 177.013i) q^{82} -770.316i q^{83} +(-769.693 - 935.267i) q^{84} +582.253i q^{85} +(-325.683 + 658.648i) q^{86} +(559.769 - 969.549i) q^{87} +(251.906 - 734.363i) q^{88} +(-615.389 - 1065.88i) q^{89} +(1228.43 + 1842.73i) q^{90} +(-30.4794 - 48.6346i) q^{91} +(-305.879 + 734.024i) q^{92} +(4.10953 - 2.37264i) q^{93} +(-63.4414 - 984.010i) q^{94} +(-454.344 + 786.948i) q^{95} +(1403.86 - 468.210i) q^{96} +706.293 q^{97} +(766.156 - 595.144i) q^{98} -1366.76i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{4} - 20 q^{6} - 4 q^{7} - 12 q^{8} + 160 q^{9} - 14 q^{10} - 110 q^{12} + 102 q^{14} - 116 q^{15} - 104 q^{16} - 2 q^{17} - 38 q^{18} + 256 q^{20} - 360 q^{22} + 162 q^{23} + 186 q^{24} + 348 q^{25}+ \cdots - 2670 q^{98}+O(q^{100}) $ 44 * q + 4 * q^4 - 20 * q^6 - 4 * q^7 - 12 * q^8 + 160 * q^9 - 14 * q^10 - 110 * q^12 + 102 * q^14 - 116 * q^15 - 104 * q^16 - 2 * q^17 - 38 * q^18 + 256 * q^20 - 360 * q^22 + 162 * q^23 + 186 * q^24 + 348 * q^25 - 302 * q^26 - 642 * q^28 - 396 * q^30 - 374 * q^31 - 140 * q^32 - 110 * q^33 - 148 * q^34 + 1440 * q^36 + 52 * q^38 + 52 * q^39 + 658 * q^40 - 8 * q^41 - 1710 * q^42 + 374 * q^44 - 486 * q^46 - 738 * q^47 + 936 * q^48 + 356 * q^49 + 2328 * q^50 + 96 * q^52 + 944 * q^54 - 2268 * q^55 + 1848 * q^56 - 452 * q^57 + 918 * q^58 + 410 * q^60 + 1416 * q^62 + 668 * q^63 - 2984 * q^64 + 248 * q^65 + 868 * q^66 - 64 * q^68 + 3422 * q^70 + 1248 * q^71 - 2172 * q^72 - 218 * q^73 - 176 * q^74 - 3028 * q^76 - 3716 * q^78 + 298 * q^79 - 2540 * q^80 - 1050 * q^81 - 146 * q^82 - 4844 * q^84 - 2412 * q^86 + 2140 * q^87 + 1626 * q^88 + 422 * q^89 - 4916 * q^90 + 1652 * q^92 - 2676 * q^94 - 2434 * q^95 - 400 * q^96 + 1672 * q^97 - 2670 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$29$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	2.53540	+	1.25369i	0.896400	+	0.443245i
$2$	2.53540	+	1.25369i	0.896400	+	0.443245i
$3$	−7.07996	−	4.08762i	−1.36254	−	0.786662i	−0.372578	−	0.928001i	$-0.621526\pi$
$3$	−7.07996	−	4.08762i	−1.36254	−	0.786662i	−0.989961	+	0.141338i	$0.954859\pi$
$4$	4.85654	+	6.35720i	0.607068	+	0.794650i
$5$	17.0228	−	9.82813i	1.52257	−	0.879055i	0.522923	−	0.852380i	$-0.324842\pi$
$5$	17.0228	−	9.82813i	1.52257	−	0.879055i	0.999644	−	0.0266746i	$-0.00849178\pi$
$6$	−12.8260	−	19.2398i	−0.872697	−	1.30910i
$7$	15.6931	−	9.83491i	0.847350	−	0.531035i
$7$	15.6931	−	9.83491i	0.847350	−	0.531035i
$8$	4.34335	+	22.2066i	0.191951	+	0.981405i
$9$	19.9172	+	34.4977i	0.737676	+	1.27769i
$10$	55.4811	−	3.57700i	1.75447	−	0.113115i
$11$	−29.7141	−	17.1555i	−0.814468	−	0.470233i	0.0340372	−	0.999421i	$-0.489164\pi$
$11$	−29.7141	−	17.1555i	−0.814468	−	0.470233i	−0.848505	+	0.529187i	$0.822497\pi$
$12$	−8.39831	−	64.8604i	−0.202032	−	1.56030i
$13$		−	3.09910i		−	0.0661182i	−0.999453	−	0.0330591i	$-0.989475\pi$
$13$		−	3.09910i		−	0.0661182i	0.999453	−	0.0330591i	$-0.0105249\pi$
$14$	52.1183	−	5.26121i	0.994943	−	0.100437i
$15$	−160.695			−2.76608
$16$	−16.8280	+	61.7480i	−0.262938	+	0.964813i
$17$	−14.8109	+	25.6532i	−0.211304	+	0.365989i	−0.952123	−	0.305716i	$-0.901104\pi$
$17$	−14.8109	+	25.6532i	−0.211304	+	0.365989i	0.740819	+	0.671705i	$0.234438\pi$
$18$	7.24898	+	112.435i	0.0949222	+	1.47229i
$19$	−40.0355	+	23.1145i	−0.483409	+	0.279096i	−0.721836	−	0.692064i	$-0.756702\pi$
$19$	−40.0355	+	23.1145i	−0.483409	+	0.279096i	0.238427	+	0.971160i	$0.423368\pi$
$20$	145.151	+	60.4868i	1.62284	+	0.676263i
$21$	−151.308	+	5.48329i	−1.57229	+	0.0569786i
$22$	−53.8297	−	80.7482i	−0.521661	−	0.782526i
$23$	49.7004	+	86.0836i	0.450576	+	0.780420i	0.998422	−	0.0561589i	$-0.0178854\pi$
$23$	49.7004	+	86.0836i	0.450576	+	0.780420i	−0.547846	+	0.836579i	$0.684552\pi$
$24$	60.0215	−	174.976i	0.510493	−	1.48820i
$25$	130.684	−	226.352i	1.04547	−	1.81081i
$26$	3.88530	−	7.85747i	0.0293065	−	0.0592683i
$27$		−	104.925i		−	0.747882i
$28$	138.737	+	52.0007i	0.936386	+	0.350972i
$29$			136.943i			0.876883i	0.898760	+	0.438442i	$0.144469\pi$
$29$			136.943i			0.876883i	−0.898760	+	0.438442i	$0.855531\pi$
$30$	−407.425	−	201.461i	−2.47951	−	1.22605i
$31$	−0.290223	+	0.502681i	−0.00168147	+	0.00291239i	−0.866865	−	0.498543i	$-0.833869\pi$
$31$	−0.290223	+	0.502681i	−0.00168147	+	0.00291239i	0.865183	+	0.501455i	$0.167202\pi$
$32$	−120.078	+	135.459i	−0.663346	+	0.748313i
$33$	140.250	+	242.920i	0.739830	+	1.28142i
$34$	−69.7127	+	46.4730i	−0.351636	+	0.234414i
$35$	170.483	−	321.652i	0.823337	−	1.55340i
$36$	−122.580	+	294.157i	−0.567499	+	1.36184i
$37$	−128.221	+	74.0282i	−0.569712	+	0.328923i	−0.757034	−	0.653375i	$-0.773352\pi$
$37$	−128.221	+	74.0282i	−0.569712	+	0.328923i	0.187322	+	0.982299i	$0.440019\pi$
$38$	−130.484	+	8.41263i	−0.557036	+	0.0359134i
$39$	−12.6679	+	21.9415i	−0.0520127	+	0.0900886i
$40$	292.186	+	335.333i	1.15497	+	1.32552i
$41$	−141.194			−0.537825			−0.268913	−	0.963165i	$-0.586664\pi$
$41$	−141.194			−0.537825			−0.268913	+	0.963165i	$0.586664\pi$
$42$	−390.502	−	175.791i	−1.43466	−	0.645835i
$43$			259.780i			0.921306i	0.887580	+	0.460653i	$0.152385\pi$
$43$			259.780i			0.921306i	−0.887580	+	0.460653i	$0.847615\pi$
$44$	−35.2472	−	272.215i	−0.120766	−	0.932680i
$45$	678.095	+	391.498i	2.24632	+	1.29691i
$46$	18.0887	+	280.565i	0.0579790	+	0.899285i
$47$	−174.311	−	301.916i	−0.540977	−	0.936999i	−0.998848	−	0.0479808i	$-0.984721\pi$
$47$	−174.311	−	301.916i	−0.540977	−	0.936999i	0.457872	−	0.889018i	$-0.348612\pi$
$48$	371.544	−	368.387i	1.11725	−	1.10775i
$49$	149.549	−	308.681i	0.436003	−	0.899945i
$50$	615.111	−	410.056i	1.73980	−	1.15981i
$51$	209.721	−	121.083i	0.575820	−	0.332450i
$52$	19.7016	−	15.0509i	0.0525408	−	0.0401382i
$53$	−184.884	−	106.743i	−0.479165	−	0.276646i	0.240904	−	0.970549i	$-0.422556\pi$
$53$	−184.884	−	106.743i	−0.479165	−	0.276646i	−0.720068	+	0.693903i	$0.755890\pi$
$54$	131.543	−	266.027i	0.331495	−	0.670402i
$55$	−674.424			−1.65344
$56$	286.561	+	305.775i	0.683810	+	0.729660i
$57$	377.933			0.878218
$58$	−171.683	+	347.205i	−0.388674	+	0.786039i
$59$	−100.398	−	57.9647i	−0.221537	−	0.127904i	0.385125	−	0.922864i	$-0.374158\pi$
$59$	−100.398	−	57.9647i	−0.221537	−	0.127904i	−0.606662	+	0.794960i	$0.707492\pi$
$60$	−780.420	−	1021.57i	−1.67920	−	2.19806i
$61$	345.954	−	199.737i	0.726146	−	0.419240i	−0.0908649	−	0.995863i	$-0.528963\pi$
$61$	345.954	−	199.737i	0.726146	−	0.419240i	0.817010	+	0.576623i	$0.195630\pi$
$62$	−1.36604	+	0.910650i	−0.00279817	+	0.00186537i
$63$	651.846	+	345.492i	1.30357	+	0.690920i
$64$	−474.271	+	192.903i	−0.926310	+	0.376763i
$65$	−30.4584	−	52.7554i	−0.0581215	−	0.100669i
$66$	51.0446	+	791.730i	0.0951994	+	1.47659i
$67$	893.014	+	515.582i	1.62834	+	0.940125i	0.984587	+	0.174895i	$0.0559586\pi$
$67$	893.014	+	515.582i	1.62834	+	0.940125i	0.643757	+	0.765230i	$0.277375\pi$
$68$	−235.012	+	30.4301i	−0.419109	+	0.0542675i
$69$		−	812.625i		−	1.41780i
$70$	835.493	−	601.786i	1.42658	−	1.02753i
$71$	476.543			0.796553			0.398276	−	0.917265i	$-0.369608\pi$
$71$	476.543			0.796553			0.398276	+	0.917265i	$0.369608\pi$
$72$	−679.570	+	592.131i	−1.11233	+	0.969212i
$73$	−554.624	+	960.638i	−0.889231	+	1.54019i	−0.0484453	+	0.998826i	$0.515427\pi$
$73$	−554.624	+	960.638i	−0.889231	+	1.54019i	−0.840786	+	0.541368i	$0.817907\pi$
$74$	−417.899	+	26.9429i	−0.656484	+	0.0423250i
$75$	−1850.48	+	1068.37i	−2.84900	+	1.64487i
$76$	−341.377	−	142.257i	−0.515246	−	0.214711i
$77$	−635.030	+	23.0130i	−0.939850	+	0.0340594i
$78$	−59.6261	+	39.7490i	−0.0865555	+	0.0577011i
$79$	−225.997	−	391.439i	−0.321857	−	0.557472i	0.659014	−	0.752130i	$-0.270974\pi$
$79$	−225.997	−	391.439i	−0.321857	−	0.557472i	−0.980871	+	0.194658i	$0.937640\pi$
$80$	320.407	+	1216.51i	0.447783	+	1.70013i
$81$	108.872	−	188.573i	0.149345	−	0.258673i
$82$	−357.984	−	177.013i	−0.482107	−	0.238388i
$83$		−	770.316i		−	1.01871i	−0.860556	−	0.509356i	$-0.829883\pi$
$83$		−	770.316i		−	1.01871i	0.860556	−	0.509356i	$-0.170117\pi$
$84$	−769.693	−	935.267i	−0.999766	−	1.21483i
$85$			582.253i			0.742991i
$86$	−325.683	+	658.648i	−0.408364	+	0.825859i
$87$	559.769	−	969.549i	0.689811	−	1.19479i
$88$	251.906	−	734.363i	0.305151	−	0.889584i
$89$	−615.389	−	1065.88i	−0.732934	−	1.26948i	−0.955624	−	0.294589i	$-0.904817\pi$
$89$	−615.389	−	1065.88i	−0.732934	−	1.26948i	0.222690	−	0.974889i	$-0.428516\pi$
$90$	1228.43	+	1842.73i	1.43875	+	2.15823i
$91$	−30.4794	−	48.6346i	−0.0351111	−	0.0560252i
$92$	−305.879	+	734.024i	−0.346631	+	0.831818i
$93$	4.10953	−	2.37264i	0.00458214	−	0.00264550i
$94$	−63.4414	−	984.010i	−0.0696115	−	1.07971i
$95$	−454.344	+	786.948i	−0.490682	+	0.849885i
$96$	1403.86	−	468.210i	1.49250	−	0.497776i
$97$	706.293			0.739311			0.369656	−	0.929169i	$-0.379476\pi$
$97$	706.293			0.739311			0.369656	+	0.929169i	$0.379476\pi$
$98$	766.156	−	595.144i	0.789729	−	0.613455i
$99$		−	1366.76i		−	1.38752i
$100$	2073.64	−	268.500i	2.07364	−	0.268500i
$101$	−760.005	−	438.789i	−0.748745	−	0.432288i	0.0764951	−	0.997070i	$-0.475627\pi$
$101$	−760.005	−	438.789i	−0.748745	−	0.432288i	−0.825240	+	0.564782i	$0.808960\pi$
$102$	683.527	−	44.0686i	0.663522	−	0.0427788i
$103$	808.543	+	1400.44i	0.773477	+	1.33970i	0.935646	+	0.352939i	$0.114818\pi$
$103$	808.543	+	1400.44i	0.773477	+	1.33970i	−0.162169	+	0.986763i	$0.551849\pi$
$104$	68.8207	−	13.4605i	0.0648887	−	0.0126914i
$105$	−2521.80	+	1580.42i	−2.34383	+	1.46888i
$106$	−334.933	−	502.422i	−0.306901	−	0.460373i
$107$	−544.209	+	314.199i	−0.491688	+	0.283876i	−0.725275	−	0.688460i	$-0.758287\pi$
$107$	−544.209	+	314.199i	−0.491688	+	0.283876i	0.233586	+	0.972336i	$0.424954\pi$
$108$	667.029	−	509.572i	0.594305	−	0.454015i
$109$	−398.630	−	230.149i	−0.350292	−	0.202241i	0.314522	−	0.949250i	$-0.398156\pi$
$109$	−398.630	−	230.149i	−0.350292	−	0.202241i	−0.664814	+	0.747009i	$0.731489\pi$
$110$	−1709.94	−	845.516i	−1.48215	−	0.732880i
$111$	1210.40			1.03501
$112$	343.202	+	1134.52i	0.289550	+	0.957163i
$113$	−1015.23			−0.845171			−0.422586	−	0.906323i	$-0.638877\pi$
$113$	−1015.23			−0.845171			−0.422586	+	0.906323i	$0.638877\pi$
$114$	958.212	+	473.809i	0.787235	+	0.389266i
$115$	1692.08	+	976.923i	1.37206	+	0.792161i
$116$	−870.572	+	665.068i	−0.696816	+	0.532328i
$117$	106.912	−	61.7256i	0.0844786	−	0.0487738i
$118$	−181.879	−	272.831i	−0.141893	−	0.212849i
$119$	19.8679	+	548.243i	0.0153049	+	0.422331i
$120$	−697.953	−	3568.49i	−0.530951	−	2.71464i
$121$	−76.8805	−	133.161i	−0.0577614	−	0.100046i
$122$	1127.54	−	72.6951i	0.836743	−	0.0539468i
$123$	999.650	+	577.148i	0.732808	+	0.423087i
$124$	−4.60512	+	0.596284i	−0.00333510	+	0.000431838i
$125$		−	2680.49i		−	1.91800i
$126$	1219.55	+	1693.17i	0.862273	+	1.19714i
$127$	112.340			0.0784925			0.0392463	−	0.999230i	$-0.487504\pi$
$127$	112.340			0.0784925			0.0392463	+	0.999230i	$0.487504\pi$
$128$	−1444.31	−	105.501i	−0.997343	−	0.0728517i
$129$	1061.88	−	1839.24i	0.724757	−	1.25532i
$130$	−11.0855	−	171.942i	−0.00747892	−	0.116002i
$131$	475.899	−	274.760i	0.317400	−	0.183251i	−0.332833	−	0.942986i	$-0.608004\pi$
$131$	475.899	−	274.760i	0.317400	−	0.183251i	0.650233	+	0.759735i	$0.274671\pi$
$132$	−863.162	+	2071.35i	−0.569156	+	1.36582i
$133$	−400.953	+	756.484i	−0.261406	+	0.493199i
$134$	1617.77	+	2426.77i	1.04294	+	1.56448i
$135$	−1031.22	−	1786.12i	−0.657429	−	1.13870i
$136$	−634.001	−	217.479i	−0.399744	−	0.137123i
$137$	927.547	−	1606.56i	0.578436	−	1.00188i	−0.417223	−	0.908804i	$-0.636997\pi$
$137$	927.547	−	1606.56i	0.578436	−	1.00188i	0.995659	−	0.0930760i	$-0.0296700\pi$
$138$	1018.78	−	2060.33i	0.628435	−	1.27092i
$139$		−	150.835i		−	0.0920405i	−0.998941	−	0.0460203i	$-0.985346\pi$
$139$		−	150.835i		−	0.0920405i	0.998941	−	0.0460203i	$-0.0146539\pi$
$140$	2872.76	−	478.325i	1.73423	−	0.288756i
$141$			2850.07i			1.70226i
$142$	1208.23	+	597.436i	0.714030	+	0.353068i
$143$	−53.1665	+	92.0871i	−0.0310910	+	0.0538511i
$144$	−2465.33	+	649.323i	−1.42670	+	0.375765i
$145$	1345.89	+	2331.15i	0.770828	+	1.33511i
$146$	−2610.53	+	1740.28i	−1.47979	+	0.986483i
$147$	−2320.57	+	1574.15i	−1.30202	+	0.883224i
$148$	−1093.32	−	455.603i	−0.607233	−	0.253043i
$149$	2697.57	−	1557.44i	1.48318	−	0.856312i	0.483359	−	0.875422i	$-0.339417\pi$
$149$	2697.57	−	1557.44i	1.48318	−	0.856312i	0.999817	+	0.0191102i	$0.00608335\pi$
$150$	−6031.12	+	388.840i	−3.28292	+	0.211658i
$151$	448.845	−	777.422i	0.241897	−	0.418978i	−0.719357	−	0.694640i	$-0.755564\pi$
$151$	448.845	−	777.422i	0.241897	−	0.418978i	0.961255	+	0.275662i	$0.0888970\pi$
$152$	−687.184	−	788.659i	−0.366697	−	0.420847i
$153$	−1179.97			−0.623495
$154$	−1638.91	−	737.782i	−0.857578	−	0.386053i
$155$			11.4094i			0.00591241i
$156$	−201.009	+	26.0272i	−0.103164	+	0.0133580i
$157$	−1805.49	−	1042.40i	−0.917794	−	0.529889i	−0.0348634	−	0.999392i	$-0.511100\pi$
$157$	−1805.49	−	1042.40i	−0.917794	−	0.529889i	−0.882931	+	0.469503i	$0.844433\pi$
$158$	−82.2529	−	1275.79i	−0.0414157	−	0.642380i
$159$	872.646	+	1511.47i	0.435254	+	0.753881i
$160$	−712.765	+	3486.04i	−0.352181	+	1.72247i
$161$	1626.58	+	862.122i	0.796226	+	0.422017i
$162$	512.447	−	341.616i	0.248528	−	0.165678i
$163$	470.091	−	271.407i	0.225892	−	0.130419i	−0.382784	−	0.923838i	$-0.625035\pi$
$163$	470.091	−	271.407i	0.225892	−	0.130419i	0.608675	+	0.793419i	$0.291701\pi$
$164$	−685.716	−	897.600i	−0.326496	−	0.427383i
$165$	4774.90	+	2756.79i	2.25288	+	1.30070i
$166$	965.735	−	1953.06i	0.451539	−	0.913175i
$167$	−2401.40			−1.11273			−0.556366	−	0.830938i	$-0.687805\pi$
$167$	−2401.40			−1.11273			−0.556366	+	0.830938i	$0.687805\pi$
$168$	−778.950	−	3336.23i	−0.357722	−	1.53212i
$169$	2187.40			0.995628
$170$	−729.963	+	1476.25i	−0.329327	+	0.666017i
$171$	−1594.79	−	920.754i	−0.713198	−	0.411765i
$172$	−1651.48	+	1261.63i	−0.732116	+	0.559295i
$173$	67.3790	−	38.9013i	0.0296111	−	0.0170960i	−0.485121	−	0.874447i	$-0.661225\pi$
$173$	67.3790	−	38.9013i	0.0296111	−	0.0170960i	0.514732	+	0.857351i	$0.327891\pi$
$174$	2634.75	−	1756.42i	1.14793	−	0.765253i
$175$	−175.305	−	4837.44i	−0.0757245	−	2.08958i
$176$	1559.35	−	1546.10i	0.667841	−	0.662167i
$177$	473.875	+	820.775i	0.201235	+	0.348549i
$178$	−223.974	−	3473.95i	−0.0943121	−	1.46283i
$179$	−648.975	−	374.686i	−0.270987	−	0.156454i	0.358349	−	0.933588i	$-0.383340\pi$
$179$	−648.975	−	374.686i	−0.270987	−	0.156454i	−0.629336	+	0.777133i	$0.716673\pi$
$180$	804.363	+	6212.12i	0.333076	+	2.57235i
$181$			3814.83i			1.56660i	0.621647	+	0.783298i	$0.286464\pi$
$181$			3814.83i			1.56660i	−0.621647	+	0.783298i	$0.713536\pi$
$182$	−16.3050	−	161.520i	−0.00664070	−	0.0657838i
$183$	−3265.79			−1.31920
$184$	−1695.76	+	1477.57i	−0.679420	+	0.592000i
$185$	−1455.12	+	2520.34i	−0.578283	+	1.00162i
$186$	13.3939	−	0.863534i	0.00528003	−	0.000340416i
$187$	880.185	−	508.175i	0.344201	−	0.198724i
$188$	1072.79	−	2574.40i	0.416177	−	0.998709i
$189$	−1031.93	−	1646.60i	−0.397152	−	0.633717i
$190$	−2138.53	+	1425.62i	−0.816555	+	0.544346i
$191$	499.858	+	865.779i	0.189364	+	0.327987i	0.945038	−	0.326960i	$-0.106024\pi$
$191$	499.858	+	865.779i	0.189364	+	0.327987i	−0.755675	+	0.654947i	$0.772691\pi$
$192$	4146.33	+	572.893i	1.55852	+	0.215339i
$193$	406.904	−	704.779i	0.151760	−	0.262855i	−0.780115	−	0.625636i	$-0.784839\pi$
$193$	406.904	−	704.779i	0.151760	−	0.262855i	0.931874	+	0.362781i	$0.118173\pi$
$194$	1790.74	+	885.470i	0.662719	+	0.327696i
$195$			498.009i			0.182888i
$196$	2688.64	−	548.411i	0.979825	−	0.199858i
$197$			12.8192i			0.00463618i	0.999997	+	0.00231809i	$0.000737872\pi$
$197$			12.8192i			0.00463618i	−0.999997	+	0.00231809i	$0.999262\pi$
$198$	1713.49	−	3465.28i	0.615011	−	1.24377i
$199$	75.7989	−	131.288i	0.0270012	−	0.0467675i	−0.852209	−	0.523201i	$-0.824738\pi$
$199$	75.7989	−	131.288i	0.0270012	−	0.0467675i	0.879210	+	0.476434i	$0.158071\pi$
$200$	5594.12	+	1918.93i	1.97782	+	0.678445i
$201$	−4215.00	−	7300.60i	−1.47912	−	2.56191i
$202$	−1376.81	−	2065.31i	−0.479566	−	0.719381i
$203$	1346.82	+	2149.06i	0.465656	+	0.743027i
$204$	1788.26	+	745.197i	0.613743	+	0.255756i
$205$	−2403.52	+	1387.68i	−0.818875	+	0.472778i
$206$	294.273	+	4564.34i	0.0995291	+	1.54375i
$207$	−1979.79	+	3429.09i	−0.664758	+	1.15139i
$208$	191.363	+	52.1517i	0.0637916	+	0.0173850i
$209$	1586.16			0.524961
$210$	−8375.13	+	845.447i	−2.75209	+	0.277816i
$211$		−	4630.42i		−	1.51077i	−0.655284	−	0.755383i	$-0.727451\pi$
$211$		−	4630.42i		−	1.51077i	0.655284	−	0.755383i	$-0.272549\pi$
$212$	−219.311	−	1693.74i	−0.0710487	−	0.548711i
$213$	−3373.91	−	1947.93i	−1.08533	−	0.626618i
$214$	−1773.70	+	114.354i	−0.566577	+	0.0365285i
$215$	2553.16	+	4422.19i	0.809878	+	1.40275i
$216$	2330.03	−	455.726i	0.733975	−	0.143557i
$217$	0.389316	+	10.7430i	0.000121790	+	0.00336073i
$218$	−722.152	−	1083.28i	−0.224359	−	0.336554i
$219$	7853.44	−	4534.19i	2.42322	−	1.39905i
$220$	−3275.37	−	4287.45i	−1.00375	−	1.31391i
$221$	79.5019	+	45.9004i	0.0241985	+	0.0139710i
$222$	3068.84	+	1517.46i	0.927781	+	0.458762i
$223$	−3007.58			−0.903151			−0.451575	−	0.892233i	$-0.649138\pi$
$223$	−3007.58			−0.903151			−0.451575	+	0.892233i	$0.649138\pi$
$224$	−552.179	+	3306.74i	−0.164705	+	0.986343i
$225$	10411.5			3.08488
$226$	−2574.01	−	1272.77i	−0.757612	−	0.374618i
$227$	1846.41	+	1066.03i	0.539870	+	0.311694i	0.745026	−	0.667035i	$-0.232437\pi$
$227$	1846.41	+	1066.03i	0.539870	+	0.311694i	−0.205156	+	0.978729i	$0.565770\pi$
$228$	1835.45	+	2402.60i	0.533138	+	0.697876i
$229$	−1627.50	+	939.637i	−0.469643	+	0.271148i	−0.716090	−	0.698008i	$-0.754070\pi$
$229$	−1627.50	+	939.637i	−0.469643	+	0.271148i	0.246447	+	0.969156i	$0.420737\pi$
$230$	3065.35	+	4598.23i	0.878797	+	1.31825i
$231$	4590.06	+	2432.83i	1.30738	+	0.692937i
$232$	−3041.04	+	594.791i	−0.860577	+	0.168319i
$233$	1664.34	+	2882.72i	0.467959	+	0.810528i	0.999330	−	0.0366112i	$-0.0116563\pi$
$233$	1664.34	+	2882.72i	0.467959	+	0.810528i	−0.531371	+	0.847139i	$0.678323\pi$
$234$	348.449	−	22.4653i	0.0973454	−	0.00627608i
$235$	−5934.54	−	3426.31i	−1.64735	−	0.951096i
$236$	−119.093	−	919.757i	−0.0328486	−	0.253691i
$237$			3695.16i			1.01277i
$238$	−636.952	+	1414.93i	−0.173477	+	0.385361i
$239$	−5724.47			−1.54931			−0.774655	−	0.632384i	$-0.782077\pi$
$239$	−5724.47			−1.54931			−0.774655	+	0.632384i	$0.782077\pi$
$240$	2704.17	−	9922.57i	0.727306	−	2.66875i
$241$	−921.960	+	1596.88i	−0.246426	+	0.426822i	−0.962532	−	0.271170i	$-0.912590\pi$
$241$	−921.960	+	1596.88i	−0.246426	+	0.426822i	0.716106	+	0.697992i	$0.245923\pi$
$242$	−27.9810	−	434.001i	−0.00743260	−	0.115284i
$243$	−3995.05	+	2306.54i	−1.05466	+	0.608909i
$244$	2949.91	+	1229.27i	0.773969	+	0.322524i
$245$	−488.015	−	6724.41i	−0.127258	−	1.75350i
$246$	1810.95	+	2716.55i	0.469358	+	0.704069i
$247$	71.6342	+	124.074i	0.0184533	+	0.0319621i
$248$	−12.4234	−	4.26156i	−0.00318099	−	0.00109117i
$249$	−3148.76	+	5453.81i	−0.801383	+	1.38804i
$250$	3360.50	−	6796.13i	0.850146	−	1.71930i
$251$		−	6537.91i		−	1.64410i	−0.569415	−	0.822050i	$-0.692830\pi$
$251$		−	6537.91i		−	1.64410i	0.569415	−	0.822050i	$-0.307170\pi$
$252$	969.351	+	5821.81i	0.242315	+	1.45532i
$253$		−	3410.53i		−	0.847503i
$254$	284.827	+	140.839i	0.0703608	+	0.0347914i
$255$	2380.03	−	4122.33i	0.584483	−	1.01235i
$256$	−3529.64	−	2078.19i	−0.861727	−	0.507372i
$257$	−3492.66	−	6049.46i	−0.847727	−	1.46831i	−0.883231	−	0.468937i	$-0.844637\pi$
$257$	−3492.66	−	6049.46i	−0.847727	−	1.46831i	0.0355040	−	0.999370i	$-0.488696\pi$
$258$	4998.13	−	3331.94i	1.20608	−	0.804020i
$259$	−1284.12	+	2422.77i	−0.308075	+	0.581251i
$260$	187.455	−	449.839i	0.0447132	−	0.107299i
$261$	−4724.20	+	2727.52i	−1.12039	+	0.646856i
$262$	1551.06	−	100.000i	0.365743	−	0.0235803i
$263$	3530.99	−	6115.85i	0.827870	−	1.43391i	−0.0718353	−	0.997417i	$-0.522886\pi$
$263$	3530.99	−	6115.85i	0.827870	−	1.43391i	0.899706	−	0.436497i	$-0.143781\pi$
$264$	−4785.28	+	4169.57i	−1.11558	+	0.972042i
$265$	−4196.32			−0.972747
$266$	−1964.97	+	1415.32i	−0.452933	+	0.326237i
$267$			10061.9i			2.30629i
$268$	1059.30	+	8181.02i	0.241445	+	1.86468i
$269$	4770.05	+	2753.99i	1.08117	+	0.624214i	0.931212	−	0.364478i	$-0.118753\pi$
$269$	4770.05	+	2753.99i	1.08117	+	0.624214i	0.149959	+	0.988692i	$0.452086\pi$
$270$	−375.316	−	5821.35i	−0.0845963	−	1.31213i
$271$	−1142.36	−	1978.63i	−0.256065	−	0.443517i	0.709120	−	0.705088i	$-0.249093\pi$
$271$	−1142.36	−	1978.63i	−0.256065	−	0.443517i	−0.965184	+	0.261571i	$0.915759\pi$
$272$	−1334.80	−	1346.24i	−0.297551	−	0.300101i
$273$	16.9933	+	468.919i	0.00376732	+	0.103957i
$274$	4365.83	−	2910.42i	0.962588	−	0.641697i
$275$	−7766.33	+	4483.90i	−1.70301	+	0.983233i
$276$	5166.02	−	3946.54i	1.12666	−	0.860703i
$277$	1467.21	+	847.095i	0.318253	+	0.183744i	0.650614	−	0.759409i	$-0.274512\pi$
$277$	1467.21	+	847.095i	0.318253	+	0.183744i	−0.332360	+	0.943152i	$0.607845\pi$
$278$	189.099	−	382.427i	0.0407965	−	0.0825052i
$279$	−23.1218			−0.00496152
$280$	7883.28	+	2388.80i	1.68256	+	0.509850i
$281$	−7993.95			−1.69708			−0.848539	−	0.529133i	$-0.822517\pi$
$281$	−7993.95			−1.69708			−0.848539	+	0.529133i	$0.822517\pi$
$282$	−3573.10	+	7226.08i	−0.754520	+	1.52591i
$283$	565.457	+	326.467i	0.118774	+	0.0685740i	0.558210	−	0.829700i	$-0.311488\pi$
$283$	565.457	+	326.467i	0.118774	+	0.0685740i	−0.439436	+	0.898274i	$0.644822\pi$
$284$	2314.35	+	3029.48i	0.483561	+	0.632981i
$285$	6433.48	−	3714.37i	1.33715	−	0.772002i
$286$	−250.247	+	166.824i	−0.0517392	+	0.0344913i
$287$	−2215.78	+	1388.63i	−0.455726	+	0.285604i
$288$	−7064.65	−	1444.46i	−1.44545	−	0.295540i
$289$	2017.78	+	3494.89i	0.410701	+	0.711355i
$290$	489.843	+	7597.73i	0.0991883	+	1.53846i
$291$	−5000.53	−	2887.06i	−1.00734	−	0.581589i
$292$	−8800.52	+	1139.52i	−1.76374	+	0.228374i
$293$			4866.56i			0.970332i	0.874422	+	0.485166i	$0.161241\pi$
$293$			4866.56i			0.970332i	−0.874422	+	0.485166i	$0.838759\pi$
$294$	−7857.08	+	1081.84i	−1.55862	+	0.214607i
$295$	−2278.74			−0.449740
$296$	−2200.83	−	2525.82i	−0.432164	−	0.495981i
$297$	−1800.04	+	3117.75i	−0.351679	+	0.609126i
$298$	8791.96	−	566.838i	1.70908	−	0.110188i
$299$	266.782	−	154.027i	0.0516000	−	0.0297912i
$300$	−15778.8	−	6575.26i	−3.03663	−	1.26541i
$301$	2554.92	+	4076.77i	0.489246	+	0.780668i
$302$	2112.65	−	1408.37i	0.402547	−	0.268353i
$303$	3587.20	+	6213.22i	0.680130	+	1.17802i
$304$	−753.556	−	2861.08i	−0.142169	−	0.539784i
$305$	3926.08	−	6800.16i	0.737070	−	1.27664i
$306$	−2991.70	−	1479.31i	−0.558901	−	0.276361i
$307$			8098.28i			1.50552i	0.658297	+	0.752758i	$0.271277\pi$
$307$			8098.28i			1.50552i	−0.658297	+	0.752758i	$0.728723\pi$
$308$	−3230.35	−	3925.25i	−0.597617	−	0.726175i
$309$		−	13220.1i		−	2.43386i
$310$	−14.3038	+	28.9274i	−0.00262065	+	0.00529989i
$311$	221.066	−	382.897i	0.0403071	−	0.0698139i	−0.845168	−	0.534501i	$-0.820500\pi$
$311$	221.066	−	382.897i	0.0403071	−	0.0698139i	0.885475	+	0.464687i	$0.153833\pi$
$312$	−542.269	−	186.013i	−0.0983972	−	0.0337529i
$313$	2747.89	+	4759.48i	0.496230	+	0.859495i	0.999991	−	0.00434826i	$-0.00138410\pi$
$313$	2747.89	+	4759.48i	0.496230	+	0.859495i	−0.503761	+	0.863843i	$0.668051\pi$
$314$	−3270.80	−	4906.42i	−0.587841	−	0.881800i
$315$	14491.8	−	525.171i	2.59213	−	0.0939366i
$316$	1390.89	−	3337.75i	0.247607	−	0.594187i
$317$	2494.51	−	1440.21i	0.441974	−	0.255174i	−0.262461	−	0.964943i	$-0.584534\pi$
$317$	2494.51	−	1440.21i	0.441974	−	0.255174i	0.704435	+	0.709769i	$0.251201\pi$
$318$	317.604	+	4926.20i	0.0560073	+	0.868704i
$319$	2349.31	−	4069.13i	0.412340	−	0.714193i
$320$	−6177.55	+	7944.94i	−1.07917	+	1.38792i
$321$	5137.30			0.893260
$322$	3043.20	+	4225.05i	0.526680	+	0.731220i
$323$		−	1369.38i		−	0.235897i
$324$	1727.54	−	223.687i	0.296217	−	0.0383550i
$325$	−701.487	−	405.004i	−0.119728	−	0.0691248i
$326$	1532.13	−	98.7799i	0.260297	−	0.0167819i
$327$	1881.52	+	3258.89i	0.318191	+	0.551123i
$328$	−613.256	−	3135.45i	−0.103236	−	0.527824i
$329$	−5704.81	−	3023.67i	−0.955976	−	0.506688i
$330$	8650.14	+	12975.8i	1.44295	+	2.16453i
$331$	3370.95	−	1946.22i	0.559771	−	0.323184i	−0.193283	−	0.981143i	$-0.561913\pi$
$331$	3370.95	−	1946.22i	0.559771	−	0.323184i	0.753053	+	0.657959i	$0.228580\pi$
$332$	4897.05	−	3741.07i	0.809520	−	0.618428i
$333$	−5107.60	−	2948.88i	−0.840526	−	0.485278i
$334$	−6088.52	−	3010.61i	−0.997453	−	0.493213i
$335$	20268.8			3.30568
$336$	2207.63	−	9435.25i	0.358442	−	1.53195i
$337$	7323.86			1.18385			0.591923	−	0.805994i	$-0.298369\pi$
$337$	7323.86			1.18385			0.591923	+	0.805994i	$0.298369\pi$
$338$	5545.93	+	2742.31i	0.892482	+	0.441307i
$339$	7187.76	+	4149.85i	1.15158	+	0.664865i
$340$	−3701.50	+	2827.74i	−0.590418	+	0.451046i
$341$	17.2474	−	9.95781i	0.00273901	−	0.00158137i
$342$	−2889.11	−	4333.85i	−0.456798	−	0.685228i
$343$	−688.963	−	6314.98i	−0.108456	−	0.994101i
$344$	−5768.85	+	1128.32i	−0.904174	+	0.176845i
$345$	−7986.58	−	13833.2i	−1.24633	−	2.15870i
$346$	219.603	−	14.1583i	0.0341212	−	0.00219987i
$347$	1255.10	+	724.632i	0.194171	+	0.112105i	0.593934	−	0.804514i	$-0.297574\pi$
$347$	1255.10	+	724.632i	0.194171	+	0.112105i	−0.399763	+	0.916619i	$0.630908\pi$
$348$	8882.16	−	1150.09i	1.36820	−	0.177159i
$349$		−	6471.81i		−	0.992630i	−0.868142	−	0.496315i	$-0.834686\pi$
$349$		−	6471.81i		−	0.992630i	0.868142	−	0.496315i	$-0.165314\pi$
$350$	5620.16	−	12484.6i	0.858315	−	1.90666i
$351$	−325.173			−0.0494486
$352$	5891.89	−	1965.05i	0.892156	−	0.297549i
$353$	−2516.41	+	4358.55i	−0.379419	+	0.657173i	−0.990978	−	0.134026i	$-0.957209\pi$
$353$	−2516.41	+	4358.55i	−0.379419	+	0.657173i	0.611559	+	0.791199i	$0.290543\pi$
$354$	172.469	+	2675.09i	0.0258944	+	0.401636i
$355$	8112.11	−	4683.53i	1.21281	−	0.700213i
$356$	3787.38	−	9088.66i	0.563851	−	1.35309i
$357$	2100.34	−	3962.75i	0.311378	−	0.587482i
$358$	−1175.68	−	1763.59i	−0.173565	−	0.260360i
$359$	−5022.83	−	8699.80i	−0.738426	−	1.27899i	−0.953204	−	0.302329i	$-0.902236\pi$
$359$	−5022.83	−	8699.80i	−0.738426	−	1.27899i	0.214777	−	0.976663i	$-0.431097\pi$
$360$	−5748.66	+	16758.6i	−0.841614	+	2.45349i
$361$	−2360.94	+	4089.27i	−0.344211	+	0.596190i
$362$	−4782.60	+	9672.12i	−0.694386	+	1.40430i
$363$			1257.03i			0.181755i
$364$	161.156	−	429.960i	0.0232056	−	0.0619121i
$365$			21803.7i			3.12673i
$366$	−8280.09	−	4094.27i	−1.18253	−	0.584730i
$367$	−2105.38	+	3646.63i	−0.299455	+	0.518672i	−0.976011	−	0.217719i	$-0.930138\pi$
$367$	−2105.38	+	3646.63i	−0.299455	+	0.518672i	0.676556	+	0.736391i	$0.263472\pi$
$368$	−6151.85	+	1620.28i	−0.871433	+	0.229519i
$369$	−2812.20	−	4870.87i	−0.396741	−	0.687175i
$370$	−6849.03	+	4565.81i	−0.962335	+	0.641528i
$371$	−3951.21	+	143.189i	−0.552929	+	0.0200377i
$372$	35.0415	+	14.6023i	0.00488391	+	0.00203520i
$373$	−10289.1	+	5940.41i	−1.42828	+	0.824619i	−0.996985	−	0.0775918i	$-0.975277\pi$
$373$	−10289.1	+	5940.41i	−1.42828	+	0.824619i	−0.431296	+	0.902210i	$0.641944\pi$
$374$	2868.72	−	184.953i	0.396625	−	0.0255713i
$375$	−10956.8	+	18977.8i	−1.50882	+	2.61336i
$376$	5947.45	−	5182.20i	0.815734	−	0.710775i
$377$	424.399			0.0579779
$378$	−552.032	−	5468.51i	−0.0751150	−	0.744100i
$379$		−	6238.70i		−	0.845543i	−0.906236	−	0.422771i	$-0.861057\pi$
$379$		−	6238.70i		−	0.845543i	0.906236	−	0.422771i	$-0.138943\pi$
$380$	−7209.33	+	933.484i	−0.973239	+	0.126018i
$381$	−795.362	−	459.203i	−0.106949	−	0.0617471i
$382$	181.926	+	2821.77i	0.0243668	+	0.377943i
$383$	3360.68	+	5820.87i	0.448363	+	0.776587i	0.998280	−	0.0586324i	$-0.0186740\pi$
$383$	3360.68	+	5820.87i	0.448363	+	0.776587i	−0.549917	+	0.835219i	$0.685341\pi$
$384$	9794.39	+	6650.71i	1.30161	+	0.883835i
$385$	−10583.8	+	6632.90i	−1.40104	+	0.878037i
$386$	1915.24	−	1276.77i	0.252547	−	0.168357i
$387$	−8961.82	+	5174.11i	−1.17714	+	0.679625i
$388$	3430.14	+	4490.05i	0.448812	+	0.587494i
$389$	−351.685	−	203.046i	−0.0458385	−	0.0264648i	0.476906	−	0.878954i	$-0.341758\pi$
$389$	−351.685	−	203.046i	−0.0458385	−	0.0264648i	−0.522744	+	0.852490i	$0.675092\pi$
$390$	−624.347	+	1262.65i	−0.0810642	+	0.163941i
$391$	−2944.43			−0.380834
$392$	7504.32	+	1980.27i	0.966902	+	0.255150i
$393$	−4492.46			−0.576627
$394$	−16.0712	+	32.5017i	−0.00205496	+	0.00415587i
$395$	−7694.23	−	4442.26i	−0.980097	−	0.565860i
$396$	8688.75	−	6637.71i	1.10259	−	0.842317i
$397$	11599.8	−	6697.13i	1.46644	−	0.846648i	0.467143	−	0.884182i	$-0.345283\pi$
$397$	11599.8	−	6697.13i	1.46644	−	0.846648i	0.999295	+	0.0375335i	$0.0119501\pi$
$398$	356.774	−	237.839i	0.0449334	−	0.0299542i
$399$	5930.95	−	3716.94i	0.744158	−	0.466365i
$400$	11777.6	+	11878.5i	1.47220	+	1.48482i
$401$	2639.24	+	4571.30i	0.328672	+	0.569277i	0.982249	−	0.187584i	$-0.0600656\pi$
$401$	2639.24	+	4571.30i	0.328672	+	0.569277i	−0.653577	+	0.756860i	$0.726732\pi$
$402$	−1534.07	−	23794.3i	−0.190330	−	2.95211i
$403$	1.55786	+	0.899430i	0.000192562	+	0.000111176i
$404$	−901.524	−	6962.50i	−0.111021	−	0.857419i
$405$		−	4280.05i		−	0.525130i
$406$	720.484	+	7137.22i	0.0880715	+	0.872449i
$407$	5079.95			0.618683
$408$	3599.73	+	4131.30i	0.436797	+	0.501298i
$409$	3940.94	−	6825.91i	0.476447	−	0.825231i	−0.523189	−	0.852217i	$-0.675258\pi$
$409$	3940.94	−	6825.91i	0.476447	−	0.825231i	0.999636	+	0.0269860i	$0.00859097\pi$
$410$	−7833.61	+	505.051i	−0.943596	+	0.0608359i
$411$	−13134.0	+	7582.92i	−1.57628	+	0.910067i
$412$	−4976.14	+	11941.4i	−0.595041	+	1.42793i
$413$	−2145.63	+	77.7560i	−0.255641	+	0.00926422i
$414$	−9318.57	+	6212.10i	−1.10624	+	0.737460i
$415$	−7570.76	−	13112.9i	−0.895504	−	1.55106i
$416$	419.801	+	372.135i	0.0494771	+	0.0438592i
$417$	−616.555	+	1067.90i	−0.0724048	+	0.125409i
$418$	4021.55	+	1988.55i	0.470576	+	0.232686i
$419$			3028.37i			0.353092i	0.984292	+	0.176546i	$0.0564924\pi$
$419$			3028.37i			0.353092i	−0.984292	+	0.176546i	$0.943508\pi$
$420$	−22294.3	−	8356.24i	−2.59012	−	0.970816i
$421$			10492.4i			1.21465i	0.794452	+	0.607327i	$0.207758\pi$
$421$			10492.4i			1.21465i	−0.794452	+	0.607327i	$0.792242\pi$
$422$	5805.10	−	11740.0i	0.669639	−	1.35425i
$423$	6943.60	−	12026.7i	0.798131	−	1.38240i
$424$	1567.38	−	4569.27i	0.179525	−	0.523357i
$425$	3871.10	+	6704.94i	0.441826	+	0.765264i
$426$	−6112.13	−	9168.60i	−0.695149	−	1.04277i
$427$	3464.71	−	6536.92i	0.392668	−	0.740852i
$428$	−4640.40	−	1933.72i	−0.524071	−	0.218388i
$429$	752.834	−	434.649i	0.0847253	−	0.0489162i
$430$	929.233	+	14412.9i	0.104213	+	1.61640i
$431$	−6466.81	+	11200.8i	−0.722727	+	1.25180i	0.237176	+	0.971467i	$0.423778\pi$
$431$	−6466.81	+	11200.8i	−0.722727	+	1.25180i	−0.959903	+	0.280333i	$0.909555\pi$
$432$	6478.91	+	1765.68i	0.721566	+	0.196646i
$433$	15739.7			1.74689			0.873444	−	0.486925i	$-0.161881\pi$
$433$	15739.7			1.74689			0.873444	+	0.486925i	$0.161881\pi$
$434$	−12.4812	+	27.7258i	−0.00138046	+	0.00306655i
$435$		−	22005.9i		−	2.42553i
$436$	−472.858	−	3651.90i	−0.0519399	−	0.401133i
$437$	−3979.56	−	2297.60i	−0.435625	−	0.251508i
$438$	25596.1	−	1650.24i	2.79230	−	0.180026i
$439$	−2252.15	−	3900.84i	−0.244850	−	0.424093i	0.717239	−	0.696827i	$-0.245405\pi$
$439$	−2252.15	−	3900.84i	−0.244850	−	0.424093i	−0.962090	+	0.272734i	$0.912072\pi$
$440$	−2929.26	−	14976.7i	−0.317380	−	1.62270i
$441$	13627.4	−	988.990i	1.47148	−	0.106791i
$442$	144.025	+	216.047i	0.0154990	+	0.0232495i
$443$	−13011.1	+	7511.96i	−1.39543	+	0.805653i	−0.993910	−	0.110197i	$-0.964852\pi$
$443$	−13011.1	+	7511.96i	−1.39543	+	0.805653i	−0.401521	+	0.915850i	$0.631518\pi$
$444$	5878.34	+	7694.74i	0.628319	+	0.822468i
$445$	−20951.3	−	12096.2i	−2.23188	−	1.28858i
$446$	−7625.44	−	3770.57i	−0.809585	−	0.400317i
$447$	−25464.9			−2.69451
$448$	−5545.61	+	7691.66i	−0.584834	+	0.811153i
$449$	−1550.44			−0.162962			−0.0814809	−	0.996675i	$-0.525965\pi$
$449$	−1550.44			−0.162962			−0.0814809	+	0.996675i	$0.525965\pi$
$450$	26397.3	+	13052.7i	2.76529	+	1.36736i
$451$	4195.46	+	2422.25i	0.438041	+	0.252903i
$452$	−4930.48	−	6453.99i	−0.513076	−	0.671616i
$453$	−6355.61	+	3669.41i	−0.659189	+	0.380583i
$454$	3344.93	+	5017.62i	0.345783	+	0.518698i
$455$	−996.832	−	528.343i	−0.102708	−	0.0544376i
$456$	1641.50	+	8392.62i	0.168575	+	0.861887i
$457$	6335.06	+	10972.7i	0.648450	+	1.12315i	0.983493	+	0.180946i	$0.0579159\pi$
$457$	6335.06	+	10972.7i	0.648450	+	1.12315i	−0.335043	+	0.942203i	$0.608751\pi$
$458$	−5304.38	+	341.985i	−0.541173	+	0.0348907i
$459$	2691.66	+	1554.03i	0.273717	+	0.158030i
$460$	2007.16	+	15501.4i	0.203444	+	1.57121i
$461$			4811.69i			0.486123i	0.970011	+	0.243062i	$0.0781518\pi$
$461$			4811.69i			0.486123i	−0.970011	+	0.243062i	$0.921848\pi$
$462$	8587.64	+	11922.7i	0.864791	+	1.20064i
$463$	5222.12			0.524174			0.262087	−	0.965044i	$-0.415589\pi$
$463$	5222.12			0.524174			0.262087	+	0.965044i	$0.415589\pi$
$464$	−8455.94	−	2304.47i	−0.846028	−	0.230566i
$465$	46.6372	−	80.7781i	0.00465107	−	0.00805590i
$466$	605.744	+	9395.41i	0.0602157	+	0.933978i
$467$	10536.9	−	6083.50i	1.04409	−	0.602807i	0.123103	−	0.992394i	$-0.460716\pi$
$467$	10536.9	−	6083.50i	1.04409	−	0.602807i	0.920990	+	0.389587i	$0.127382\pi$
$468$	911.623	+	379.887i	0.0900423	+	0.0375220i
$469$	19084.9	−	691.621i	1.87902	−	0.0680940i
$470$	−10750.9	−	16127.1i	−1.05511	−	1.58274i
$471$	8521.86	+	14760.3i	0.833687	+	1.44399i
$472$	851.138	−	2481.26i	0.0830017	−	0.241969i
$473$	4456.65	−	7719.15i	0.433229	−	0.750374i
$474$	−4632.58	+	9368.73i	−0.448906	+	0.907848i
$475$			12082.8i			1.16715i
$476$	−3388.80	+	2788.87i	−0.326314	+	0.268545i
$477$		−	8504.07i		−	0.816299i
$478$	−14513.8	−	7176.69i	−1.38880	−	0.686724i
$479$	−6773.05	+	11731.3i	−0.646072	+	1.11903i	0.337981	+	0.941153i	$0.390256\pi$
$479$	−6773.05	+	11731.3i	−0.646072	+	1.11903i	−0.984053	+	0.177877i	$0.943077\pi$
$480$	19296.0	−	21767.5i	1.83487	−	2.06989i
$481$	229.421	+	397.369i	0.0217478	+	0.0376683i
$482$	−4339.53	+	2892.89i	−0.410083	+	0.273377i
$483$	−7992.09	−	12752.6i	−0.752904	−	1.20138i
$484$	473.157	−	1135.45i	0.0444363	−	0.106635i
$485$	12023.1	−	6941.54i	1.12565	−	0.649895i
$486$	−13020.8	+	839.478i	−1.21530	+	0.0783529i
$487$	3537.94	−	6127.89i	0.329198	−	0.570187i	−0.653155	−	0.757224i	$-0.726555\pi$
$487$	3537.94	−	6127.89i	0.329198	−	0.570187i	0.982353	+	0.187037i	$0.0598884\pi$
$488$	5938.08	+	6814.95i	0.550829	+	0.632169i
$489$	−4437.63			−0.410382
$490$	7192.99	−	17660.9i	0.663155	−	1.62824i
$491$			6617.13i			0.608202i	0.952640	+	0.304101i	$0.0983560\pi$
$491$			6617.13i			0.608202i	−0.952640	+	0.304101i	$0.901644\pi$
$492$	1185.79	+	9157.92i	0.108658	+	0.839168i
$493$	−3513.02	−	2028.24i	−0.320930	−	0.185289i
$494$	26.0716	+	404.384i	0.00237453	+	0.0368302i
$495$	−13432.7	−	23266.1i	−1.21970	−	2.11259i
$496$	−26.1557	−	26.3798i	−0.00236779	−	0.00238808i
$497$	7478.45	−	4686.76i	0.674959	−	0.422998i
$498$	−14820.7	+	9880.05i	−1.33360	+	0.889027i
$499$	11245.8	−	6492.78i	1.00888	−	0.582478i	0.0980181	−	0.995185i	$-0.468750\pi$
$499$	11245.8	−	6492.78i	1.00888	−	0.582478i	0.910864	+	0.412706i	$0.135416\pi$
$500$	17040.4	−	13017.9i	1.52414	−	1.16436i
$501$	17001.8	+	9816.02i	1.51614	+	0.875344i
$502$	8196.49	−	16576.2i	0.728739	−	1.47377i
$503$	−1755.69			−0.155631			−0.0778154	−	0.996968i	$-0.524794\pi$
$503$	−1755.69			−0.155631			−0.0778154	+	0.996968i	$0.524794\pi$
$504$	−4841.03	+	15975.9i	−0.427850	+	1.41195i
$505$	−17249.9			−1.52002
$506$	4275.74	−	8647.07i	0.375651	−	0.759702i
$507$	−15486.7	−	8941.24i	−1.35658	−	0.783223i
$508$	545.583	+	714.167i	0.0476503	+	0.0623741i
$509$	4198.62	−	2424.08i	0.365620	−	0.211091i	−0.305923	−	0.952056i	$-0.598965\pi$
$509$	4198.62	−	2424.08i	0.365620	−	0.211091i	0.671543	+	0.740965i	$0.265632\pi$
$510$	11202.4	−	7467.96i	0.972652	−	0.648406i
$511$	743.994	+	20530.1i	0.0644078	+	1.77730i
$512$	−6343.65	−	9694.12i	−0.547563	−	0.836765i
$513$	2425.29	+	4200.72i	0.208731	+	0.361533i
$514$	−1271.17	−	19716.5i	−0.109083	−	1.69194i
$515$	27527.4	+	15892.9i	2.35534	+	1.35986i
$516$	16849.5	−	2181.72i	1.43751	−	0.186133i
$517$			11961.6i			1.01754i
$518$	−6293.17	+	4532.82i	−0.533795	+	0.384480i
$519$	−636.054			−0.0537951
$520$	1039.23	−	905.514i	0.0876409	−	0.0763642i
$521$	6337.65	−	10977.1i	0.532932	−	0.923066i	−0.466328	−	0.884612i	$-0.654423\pi$
$521$	6337.65	−	10977.1i	0.532932	−	0.923066i	0.999260	−	0.0384538i	$-0.0122432\pi$
$522$	−15397.2	+	992.695i	−1.29103	+	0.0832357i
$523$	−2491.10	+	1438.24i	−0.208276	+	0.120248i	−0.600510	−	0.799617i	$-0.705036\pi$
$523$	−2491.10	+	1438.24i	−0.208276	+	0.120248i	0.392234	+	0.919865i	$0.371702\pi$
$524$	4057.93	+	1691.00i	0.338304	+	0.140976i
$525$	−18532.4	+	34965.4i	−1.54061	+	2.90670i
$526$	16619.8	−	11079.4i	1.37768	−	0.918411i
$527$	−8.59692	−	14.8903i	−0.000710603	−	0.00123080i
$528$	−17360.0	+	4572.29i	−1.43086	+	0.376863i
$529$	1143.25	−	1980.16i	0.0939628	−	0.162748i
$530$	−10639.4	−	5260.87i	−0.871971	−	0.431165i
$531$		−	4617.99i		−	0.377408i
$532$	−6756.37	+	1124.96i	−0.550612	+	0.0916788i
$533$			437.575i			0.0355600i
$534$	−12614.5	+	25511.0i	−1.02225	+	2.06736i
$535$	−6175.98	+	10697.1i	−0.499086	+	0.864442i
$536$	−7570.67	+	22070.2i	−0.610081	+	1.77852i
$537$	3063.15	+	5305.53i	0.246154	+	0.426351i
$538$	8641.36	+	12962.6i	0.692482	+	1.03877i
$539$	−9739.28	+	6606.61i	−0.778294	+	0.527954i
$540$	6346.57	−	15230.0i	0.505765	−	1.21369i
$541$	14454.9	−	8345.57i	1.14874	−	0.663224i	0.200158	−	0.979764i	$-0.435855\pi$
$541$	14454.9	−	8345.57i	1.14874	−	0.663224i	0.948579	+	0.316540i	$0.102521\pi$
$542$	−415.768	−	6448.78i	−0.0329497	−	0.511068i
$543$	15593.6	−	27008.8i	1.23238	−	2.13455i
$544$	−1696.49	−	5086.67i	−0.133707	−	0.400899i
$545$	−9047.73			−0.711123
$546$	−544.793	+	1210.20i	−0.0427014	+	0.0948570i
$547$		−	13392.5i		−	1.04684i	−0.852074	−	0.523422i	$-0.824655\pi$
$547$		−	13392.5i		−	1.04684i	0.852074	−	0.523422i	$-0.175345\pi$
$548$	14717.9	−	1905.71i	1.14729	−	0.148555i
$549$	13780.9	+	7956.41i	1.07132	+	0.618527i
$550$	−25312.2	+	1631.94i	−1.96239	+	0.126520i
$551$	−3165.36	−	5482.57i	−0.244735	−	0.423893i
$552$	18045.7	−	3529.52i	1.39144	−	0.272149i
$553$	−7396.38	−	3920.24i	−0.568763	−	0.301457i
$554$	2657.98	+	3987.15i	0.203839	+	0.305772i
$555$	20604.4	−	11895.9i	1.57587	−	0.909828i
$556$	958.887	−	732.535i	0.0731400	−	0.0558748i
$557$	−17896.2	−	10332.4i	−1.36138	−	0.785992i	−0.371571	−	0.928405i	$-0.621181\pi$
$557$	−17896.2	−	10332.4i	−1.36138	−	0.785992i	−0.989807	+	0.142413i	$0.954514\pi$
$558$	−58.6230	−	28.9874i	−0.00444751	−	0.00219917i
$559$	805.086			0.0609150
$560$	16992.5	+	15939.7i	1.28226	+	1.20282i
$561$	−8308.90			−0.625316
$562$	−20267.9	−	10021.9i	−1.52126	−	0.752221i
$563$	10428.6	+	6020.95i	0.780662	+	0.450715i	0.836665	−	0.547715i	$-0.184502\pi$
$563$	10428.6	+	6020.95i	0.780662	+	0.450715i	−0.0560031	+	0.998431i	$0.517836\pi$
$564$	−18118.5	+	13841.5i	−1.35270	+	1.03339i
$565$	−17282.0	+	9977.77i	−1.28683	+	0.742952i
$566$	1024.37	+	1536.63i	0.0760736	+	0.114116i
$567$	−146.046	−	4030.05i	−0.0108172	−	0.298494i
$568$	2069.79	+	10582.4i	0.152899	+	0.781741i
$569$	3066.49	+	5311.31i	0.225929	+	0.391321i	0.956598	−	0.291411i	$-0.0941248\pi$
$569$	3066.49	+	5311.31i	0.225929	+	0.391321i	−0.730669	+	0.682732i	$0.760792\pi$
$570$	20968.1	−	1351.86i	1.54080	−	0.0993392i
$571$	−9727.66	−	5616.27i	−0.712942	−	0.411617i	0.0992074	−	0.995067i	$-0.468369\pi$
$571$	−9727.66	−	5616.27i	−0.712942	−	0.411617i	−0.812149	+	0.583450i	$0.801703\pi$
$572$	−843.622	+	109.235i	−0.0616671	+	0.00798483i
$573$		−	8172.91i		−	0.595861i
$574$	−7358.81	+	742.852i	−0.535106	+	0.0540175i
$575$	25980.2			1.88426
$576$	−16100.9	−	12519.1i	−1.16470	−	0.905609i
$577$	3029.04	−	5246.45i	0.218545	−	0.378531i	−0.735818	−	0.677179i	$-0.763202\pi$
$577$	3029.04	−	5246.45i	0.218545	−	0.378531i	0.954363	+	0.298648i	$0.0965356\pi$
$578$	734.379	+	11390.6i	0.0528480	+	0.819701i
$579$	−5761.74	+	3326.54i	−0.413557	+	0.238767i
$580$	−8283.22	+	19877.4i	−0.593004	+	1.42304i
$581$	−7575.99	−	12088.7i	−0.540973	−	0.863206i
$582$	−9058.89	−	13588.9i	−0.645195	−	0.967835i
$583$	3662.44	+	6343.53i	0.260176	+	0.450638i
$584$	−23741.5	−	8143.96i	−1.68224	−	0.577054i
$585$	1213.29	−	2101.49i	0.0857496	−	0.148523i
$586$	−6101.14	+	12338.7i	−0.430095	+	0.869806i
$587$		−	6644.32i		−	0.467190i	−0.972334	−	0.233595i	$-0.924951\pi$
$587$		−	6644.32i		−	0.467190i	0.972334	−	0.233595i	$-0.0750489\pi$
$588$	−21277.2	−	7107.40i	−1.49227	−	0.498477i
$589$		−	26.8334i		−	0.00187717i
$590$	−5777.52	−	2856.82i	−0.403147	−	0.199345i
$591$	52.3998	−	90.7592i	0.00364711	−	0.00631698i
$592$	−2413.40	−	9163.12i	−0.167551	−	0.636152i
$593$	2137.96	+	3703.05i	0.148053	+	0.256435i	0.930508	−	0.366272i	$-0.119366\pi$
$593$	2137.96	+	3703.05i	0.148053	+	0.256435i	−0.782455	+	0.622707i	$0.786033\pi$
$594$	−8472.50	+	5648.08i	−0.585237	+	0.390141i
$595$	5726.41	+	9137.38i	0.394555	+	0.629573i
$596$	23001.8	+	9585.20i	1.58086	+	0.658767i
$597$	−1073.31	+	619.674i	−0.0735805	+	0.0424817i
$598$	869.500	−	56.0587i	0.0594590	−	0.00383346i
$599$	−3875.72	+	6712.95i	−0.264370	+	0.457903i	−0.967398	−	0.253259i	$-0.918497\pi$
$599$	−3875.72	+	6712.95i	−0.264370	+	0.457903i	0.703028	+	0.711162i	$0.251831\pi$
$600$	−31762.3	−	36452.6i	−2.16115	−	2.48029i
$601$	3307.77			0.224504			0.112252	−	0.993680i	$-0.464194\pi$
$601$	3307.77			0.224504			0.112252	+	0.993680i	$0.464194\pi$
$602$	1366.76	+	13539.3i	0.0925331	+	0.916647i
$603$			41075.9i			2.77403i
$604$	7122.07	−	922.185i	0.479789	−	0.0621245i
$605$	−2617.44	−	1511.18i	−0.175891	−	0.101551i
$606$	1305.58	+	20250.2i	0.0875174	+	1.35744i
$607$	9431.37	+	16335.6i	0.630655	+	1.09233i	0.987418	+	0.158131i	$0.0505469\pi$
$607$	9431.37	+	16335.6i	0.630655	+	1.09233i	−0.356764	+	0.934195i	$0.616120\pi$
$608$	1676.33	−	8198.72i	0.111816	−	0.546878i
$609$	−750.896	−	20720.5i	−0.0499636	−	1.37872i
$610$	18479.5	−	12319.1i	1.22658	−	0.817681i
$611$	−935.668	+	540.208i	−0.0619527	+	0.0357684i
$612$	−5730.56	−	7501.30i	−0.378504	−	0.495461i
$613$	9142.16	+	5278.23i	0.602363	+	0.347774i	0.769971	−	0.638079i	$-0.220271\pi$
$613$	9142.16	+	5278.23i	0.602363	+	0.347774i	−0.167608	+	0.985854i	$0.553604\pi$
$614$	−10152.7	+	20532.4i	−0.667313	+	1.34955i
$615$	22689.1			1.48767
$616$	−3269.20	−	14001.9i	−0.213831	−	0.915835i
$617$	29924.7			1.95255			0.976274	−	0.216541i	$-0.0694775\pi$
$617$	29924.7			1.95255			0.976274	+	0.216541i	$0.0694775\pi$
$618$	16573.8	−	33518.2i	1.07880	−	2.18171i
$619$	−2646.83	−	1528.15i	−0.171866	−	0.0992270i	0.411599	−	0.911365i	$-0.364970\pi$
$619$	−2646.83	−	1528.15i	−0.171866	−	0.0992270i	−0.583466	+	0.812138i	$0.698304\pi$
$620$	−72.5318	+	55.4102i	−0.00469830	+	0.00358924i
$621$	9032.31	−	5214.81i	0.583662	−	0.336978i
$622$	1040.52	−	693.652i	0.0670759	−	0.0447153i
$623$	−20140.3	−	10674.8i	−1.29519	−	0.686478i
$624$	−1141.67	−	1151.45i	−0.0732425	−	0.0738702i
$625$	−10008.7	−	17335.6i	−0.640557	−	1.10948i
$626$	1000.11	+	15512.2i	0.0638536	+	0.990403i
$627$	−11229.9	−	6483.61i	−0.715280	−	0.412967i
$628$	−2141.69	−	16540.3i	−0.136087	−	1.05100i
$629$		−	4385.70i		−	0.278011i
$630$	37400.9	+	16836.6i	2.36522	+	1.06474i
$631$	−27891.8			−1.75968			−0.879838	−	0.475274i	$-0.842349\pi$
$631$	−27891.8			−1.75968			−0.879838	+	0.475274i	$0.842349\pi$
$632$	7710.96	−	6718.80i	0.485325	−	0.422879i
$633$	−18927.4	+	32783.2i	−1.18846	+	2.05848i
$634$	8130.16	−	524.170i	0.509290	−	0.0328351i
$635$	1912.34	−	1104.09i	0.119510	−	0.0689992i
$636$	−5370.66	+	12888.1i	−0.334844	+	0.803531i
$637$	−956.635	−	463.467i	−0.0595027	−	0.0288277i
$638$	11057.9	−	7371.59i	0.686184	−	0.457436i
$639$	9491.42	+	16439.6i	0.587598	+	1.01775i
$640$	−25623.0	+	12398.9i	−1.58256	+	0.765797i
$641$	−3917.07	+	6784.57i	−0.241365	+	0.418057i	−0.961103	−	0.276189i	$-0.910928\pi$
$641$	−3917.07	+	6784.57i	−0.241365	+	0.418057i	0.719738	+	0.694245i	$0.244262\pi$
$642$	13025.1	+	6440.57i	0.800718	+	0.395933i
$643$			5261.50i			0.322695i	0.986898	+	0.161348i	$0.0515841\pi$
$643$			5261.50i			0.322695i	−0.986898	+	0.161348i	$0.948416\pi$
$644$	2418.86	+	14527.4i	0.148007	+	0.888914i
$645$		−	41745.3i		−	2.54840i
$646$	1716.78	−	3471.94i	0.104560	−	0.211458i
$647$	3563.73	−	6172.57i	0.216545	−	0.375067i	−0.737204	−	0.675670i	$-0.763854\pi$
$647$	3563.73	−	6172.57i	0.216545	−	0.375067i	0.953749	+	0.300603i	$0.0971878\pi$
$648$	4660.44	+	1598.66i	0.282530	+	0.0969153i
$649$	1988.82	+	3444.74i	0.120290	+	0.208348i
$650$	−1270.80	−	1906.29i	−0.0766847	−	0.115032i
$651$	41.1567	−	77.6511i	0.00247782	−	0.00467494i
$652$	4008.40	+	1670.36i	0.240769	+	0.100332i
$653$	5945.31	−	3432.52i	0.356291	−	0.205705i	−0.311162	−	0.950357i	$-0.600718\pi$
$653$	5945.31	−	3432.52i	0.356291	−	0.205705i	0.667452	+	0.744652i	$0.267385\pi$
$654$	684.789	+	10621.4i	0.0409440	+	0.635063i
$655$	5400.76	−	9354.38i	0.322176	−	0.558024i
$656$	2376.02	−	8718.46i	0.141415	−	0.518901i
$657$	−44186.4			−2.62386
$658$	−10673.3	−	14818.3i	−0.632351	−	0.877927i
$659$			19567.2i			1.15665i	0.815807	+	0.578324i	$0.196293\pi$
$659$			19567.2i			1.15665i	−0.815807	+	0.578324i	$0.803707\pi$
$660$	5664.03	+	43743.4i	0.334048	+	2.57987i
$661$	−6568.19	−	3792.15i	−0.386495	−	0.223143i	0.294146	−	0.955761i	$-0.404965\pi$
$661$	−6568.19	−	3792.15i	−0.386495	−	0.223143i	−0.680640	+	0.732618i	$0.738298\pi$
$662$	10986.7	−	708.336i	0.645028	−	0.0415865i
$663$	−375.247	−	649.947i	−0.0219810	−	0.0380722i
$664$	17106.1	−	3345.75i	0.999769	−	0.195543i
$665$	609.475	+	16818.1i	0.0355405	+	0.980719i
$666$	−9252.87	−	13879.9i	−0.538351	−	0.807562i
$667$	−11788.5	+	6806.10i	−0.684338	+	0.395103i
$668$	−11662.5	−	15266.2i	−0.675503	−	0.884232i
$669$	21293.6	+	12293.8i	1.23058	+	0.710475i
$670$	51389.7	+	25410.8i	2.96322	+	1.46523i
$671$	−13706.3			−0.788563
$672$	17426.1	−	21154.5i	1.00034	−	1.21436i
$673$	−31020.7			−1.77676			−0.888379	−	0.459110i	$-0.848168\pi$
$673$	−31020.7			−1.77676			−0.888379	+	0.459110i	$0.848168\pi$
$674$	18569.0	+	9181.83i	1.06120	+	0.524734i
$675$	−23749.9	−	13712.0i	−1.35427	−	0.781891i
$676$	10623.2	+	13905.7i	0.604414	+	0.791176i
$677$	−19466.4	+	11238.9i	−1.10510	+	0.638032i	−0.937557	−	0.347832i	$-0.886918\pi$
$677$	−19466.4	+	11238.9i	−1.10510	+	0.638032i	−0.167547	+	0.985864i	$0.553585\pi$
$678$	13021.2	+	19532.7i	0.737578	+	1.10642i
$679$	11084.0	−	6946.33i	0.626455	−	0.392601i
$680$	−12929.9	+	2528.93i	−0.729175	+	0.142618i
$681$	−8715.01	−	15094.8i	−0.490396	−	0.849391i
$682$	56.2132	−	3.62419i	0.00315618	−	0.000203486i
$683$	7487.89	+	4323.14i	0.419497	+	0.242196i	0.694862	−	0.719143i	$-0.255465\pi$
$683$	7487.89	+	4323.14i	0.419497	+	0.242196i	−0.275365	+	0.961340i	$0.588799\pi$
$684$	−1891.76	−	14610.1i	−0.105750	−	0.816712i
$685$		−	36464.2i		−	2.03391i
$686$	6170.20	−	16874.8i	0.343410	−	0.939186i
$687$	15363.5			0.853209
$688$	−16040.9	−	4371.59i	−0.888887	−	0.242246i
$689$	−330.806	+	572.973i	−0.0182913	+	0.0316815i
$690$	−2906.75	−	45085.3i	−0.160374	−	2.48749i
$691$	−2663.91	+	1538.01i	−0.146657	+	0.0846724i	−0.571533	−	0.820579i	$-0.693651\pi$
$691$	−2663.91	+	1538.01i	−0.146657	+	0.0846724i	0.424876	+	0.905252i	$0.360318\pi$
$692$	574.532	+	239.416i	0.0315613	+	0.0131521i
$693$	−13441.9	−	21448.7i	−0.736821	−	1.17571i
$694$	2273.72	+	3410.74i	0.124365	+	0.186556i
$695$	−1482.42	−	2567.63i	−0.0809087	−	0.140138i
$696$	23961.7	+	8219.51i	1.30498	+	0.447643i
$697$	2091.21	−	3622.09i	0.113645	−	0.196838i
$698$	8113.62	−	16408.6i	0.439979	−	0.889794i
$699$		−	27212.7i		−	1.47250i
$700$	29901.2	−	24607.7i	1.61451	−	1.32869i
$701$			1052.30i			0.0566972i	0.999598	+	0.0283486i	$0.00902485\pi$
$701$			1052.30i			0.0566972i	−0.999598	+	0.0283486i	$0.990975\pi$
$702$	−824.445	−	407.665i	−0.0443257	−	0.0219178i
$703$	3422.25	−	5927.51i	0.183603	−	0.318009i
$704$	17401.9	+	2404.40i	0.931616	+	0.128720i
$705$	28010.9	+	48516.2i	1.49638	+	2.59181i
$706$	−11844.4	+	7895.89i	−0.631400	+	0.420915i
$707$	−16242.3	+	588.608i	−0.864009	+	0.0313110i
$708$	−2916.44	+	6998.65i	−0.154812	+	0.371505i
$709$	−14804.1	+	8547.16i	−0.784175	+	0.452744i	−0.837908	−	0.545812i	$-0.816221\pi$
$709$	−14804.1	+	8547.16i	−0.784175	+	0.452744i	0.0537327	+	0.998555i	$0.482888\pi$
$710$	26439.1	−	1704.59i	1.39753	−	0.0901017i
$711$	9002.49	−	15592.8i	0.474852	−	0.822468i
$712$	20996.9	−	18295.2i	1.10518	−	0.962982i
$713$	−57.6967			−0.00303052
$714$	10293.3	−	7414.00i	0.539518	−	0.388602i
$715$			2090.11i			0.109323i
$716$	−769.820	−	5945.34i	−0.0401809	−	0.310318i
$717$	40529.0	+	23399.5i	2.11100	+	1.21878i
$718$	−1828.09	−	28354.6i	−0.0950188	−	1.47379i
$719$	−11239.8	−	19467.9i	−0.582995	−	1.00978i	−0.995122	−	0.0986507i	$-0.968547\pi$
$719$	−11239.8	−	19467.9i	−0.582995	−	1.00978i	0.412127	−	0.911126i	$-0.364786\pi$
$720$	−35585.3	+	35282.9i	−1.84192	+	1.82627i
$721$	26461.8	+	14025.3i	1.36683	+	0.724452i
$722$	−11112.6	+	7408.07i	−0.572809	+	0.381856i
$723$	13054.9	−	7537.24i	0.671530	−	0.387708i
$724$	−24251.6	+	18526.9i	−1.24490	+	0.951030i
$725$	30997.2	+	17896.2i	1.58787	+	0.916759i
$726$	−1575.92	+	3187.08i	−0.0805620	+	0.162925i
$727$	26355.5			1.34453			0.672265	−	0.740311i	$-0.265322\pi$
$727$	26355.5			1.34453			0.672265	+	0.740311i	$0.265322\pi$
$728$	947.629	−	888.083i	0.0482438	−	0.0452123i
$729$	31834.0			1.61733
$730$	−27335.0	+	55281.1i	−1.38591	+	2.80280i
$731$	−6664.20	−	3847.58i	−0.337188	−	0.194676i
$732$	−15860.4	−	20761.3i	−0.800845	−	1.04830i
$733$	−19348.2	+	11170.7i	−0.974954	+	0.562890i	−0.900743	−	0.434353i	$-0.856977\pi$
$733$	−19348.2	+	11170.7i	−0.974954	+	0.562890i	−0.0742108	+	0.997243i	$0.523644\pi$
$734$	−9909.72	+	6606.19i	−0.498330	+	0.332205i
$735$	−24031.7	+	49603.4i	−1.20602	+	2.48932i
$736$	−17628.7	−	3604.42i	−0.882886	−	0.180517i
$737$	−17690.1	−	30640.1i	−0.884156	−	1.53140i
$738$	−1023.51	−	15875.2i	−0.0510516	−	0.791837i
$739$	−7009.10	−	4046.71i	−0.348896	−	0.201435i	0.315303	−	0.948991i	$-0.397894\pi$
$739$	−7009.10	−	4046.71i	−0.348896	−	0.201435i	−0.664199	+	0.747556i	$0.731227\pi$
$740$	−23089.1	+	2989.65i	−1.14699	+	0.148516i
$741$		−	1171.25i		−	0.0580662i
$742$	−10197.4	−	4590.53i	−0.504527	−	0.227121i
$743$	17583.7			0.868214			0.434107	−	0.900861i	$-0.357064\pi$
$743$	17583.7			0.868214			0.434107	+	0.900861i	$0.357064\pi$
$744$	70.5376	+	80.9538i	0.00347585	+	0.00398912i
$745$	30613.5	−	53024.1i	1.50549	−	2.60759i
$746$	−33534.4	+	2162.04i	−1.64582	+	0.106110i
$747$	26574.1	−	15342.6i	1.30160	−	0.751480i
$748$	7505.23	+	3127.54i	0.366869	+	0.152880i
$749$	−5450.22	+	10283.0i	−0.265883	+	0.501647i
$750$	−51572.2	+	34379.9i	−2.51087	+	1.67384i
$751$	1665.58	+	2884.86i	0.0809291	+	0.140173i	0.903649	−	0.428273i	$-0.140878\pi$
$751$	1665.58	+	2884.86i	0.0809291	+	0.140173i	−0.822720	+	0.568447i	$0.807545\pi$
$752$	21576.0	−	5682.73i	1.04627	−	0.275569i
$753$	−26724.5	+	46288.1i	−1.29335	+	2.24015i
$754$	1076.02	+	532.064i	0.0519714	+	0.0256984i
$755$		−	17645.2i		−	0.850564i
$756$	5456.17	−	14557.0i	0.262486	−	0.700306i
$757$		−	20862.2i		−	1.00165i	−0.865548	−	0.500826i	$-0.833030\pi$
$757$		−	20862.2i		−	1.00165i	0.865548	−	0.500826i	$-0.166970\pi$
$758$	7821.38	−	15817.6i	0.374783	−	0.757945i
$759$	−13940.9	+	24146.4i	−0.666699	+	1.15476i
$760$	−19448.8	−	6671.48i	−0.928268	−	0.318421i
$761$	−15284.5	−	26473.6i	−0.728074	−	1.26106i	−0.957696	−	0.287782i	$-0.907082\pi$
$761$	−15284.5	−	26473.6i	−0.728074	−	1.26106i	0.229622	−	0.973280i	$-0.426251\pi$
$762$	−1440.87	−	2161.40i	−0.0685002	−	0.102755i
$763$	−8519.24	+	308.730i	−0.404217	+	0.0146485i
$764$	−3076.35	+	7382.39i	−0.145679	+	0.349588i
$765$	−20086.4	+	11596.9i	−0.949313	+	0.548086i
$766$	1223.14	+	18971.5i	0.0576942	+	0.894867i
$767$	−179.638	+	311.143i	−0.00845680	+	0.0146476i
$768$	16494.8	+	29141.3i	0.775007	+	1.36920i
$769$	−20444.9			−0.958729			−0.479365	−	0.877616i	$-0.659133\pi$
$769$	−20444.9			−0.958729			−0.479365	+	0.877616i	$0.659133\pi$
$770$	−35149.9	+	3548.29i	−1.64508	+	0.166067i
$771$			57106.6i			2.66750i
$772$	6456.57	−	836.015i	0.301007	−	0.0389752i
$773$	−30330.4	−	17511.3i	−1.41127	−	0.814796i	−0.415760	−	0.909474i	$-0.636484\pi$
$773$	−30330.4	−	17511.3i	−1.41127	−	0.814796i	−0.995508	+	0.0946782i	$0.969818\pi$
$774$	−29208.5	+	1883.14i	−1.35643	+	0.0874524i
$775$	75.8551	+	131.385i	0.00351587	+	0.00608966i
$776$	3067.68	+	15684.4i	0.141912	+	0.725564i
$777$	18994.9	−	11904.1i	0.877013	−	0.549625i
$778$	−637.109	−	955.706i	−0.0293592	−	0.0440408i
$779$	5652.78	−	3263.63i	0.259989	−	0.150105i
$780$	−3165.94	+	2418.60i	−0.145332	+	0.111025i
$781$	−14160.1	−	8175.31i	−0.648767	−	0.374566i
$782$	−7465.31	−	3691.39i	−0.341380	−	0.168803i
$783$	14368.7			0.655805
$784$	16543.8	+	14428.8i	0.753637	+	0.657291i
$785$	−40979.3			−1.86320
$786$	−11390.2	−	5632.13i	−0.516889	−	0.255587i
$787$	5306.74	+	3063.85i	0.240362	+	0.138773i	0.615343	−	0.788259i	$-0.289018\pi$
$787$	5306.74	+	3063.85i	0.240362	+	0.138773i	−0.374981	+	0.927032i	$0.622351\pi$
$788$	−81.4940	+	62.2568i	−0.00368414	+	0.00281447i
$789$	−49998.5	+	28866.6i	−2.25601	+	1.30251i
$790$	−13938.8	−	20909.1i	−0.627745	−	0.941660i
$791$	−15932.1	+	9984.66i	−0.716156	+	0.448816i
$792$	30351.1	−	5936.31i	1.36172	−	0.266335i
$793$	−619.004	−	1072.15i	−0.0277194	−	0.0480114i
$794$	37806.2	−	2437.45i	1.68979	−	0.108945i
$795$	29709.8	+	17153.0i	1.32541	+	0.765223i
$796$	1202.74	−	155.735i	0.0535554	−	0.00693450i
$797$			23892.7i			1.06189i	0.847407	+	0.530944i	$0.178162\pi$
$797$			23892.7i			1.06189i	−0.847407	+	0.530944i	$0.821838\pi$
$798$	19697.2	−	1988.38i	0.873777	−	0.0882055i
$799$	10326.8			0.457242
$800$	14969.0	+	44882.3i	0.661544	+	1.98354i
$801$	24513.7	−	42459.0i	1.08133	−	1.87293i
$802$	960.565	+	14898.9i	0.0422927	+	0.655982i
$803$	32960.4	−	19029.7i	1.44850	−	0.836292i
$804$	25941.1	−	62251.3i	1.13790	−	2.73064i
$805$	36162.0	−	1310.48i	1.58328	−	0.0573769i
$806$	2.82220	+	4.23348i	0.000123335	+	0.000185010i
$807$	−22514.5	−	38996.3i	−0.982092	−	1.70103i
$808$	6443.06	−	18783.0i	0.280527	−	0.817800i
$809$	−12610.4	+	21841.8i	−0.548030	+	0.949216i	0.450379	+	0.892837i	$0.351289\pi$
$809$	−12610.4	+	21841.8i	−0.548030	+	0.949216i	−0.998409	+	0.0563787i	$0.982045\pi$
$810$	5365.84	−	10851.7i	0.232761	−	0.470726i
$811$			1732.97i			0.0750345i	0.999296	+	0.0375172i	$0.0119449\pi$
$811$			1732.97i			0.0750345i	−0.999296	+	0.0375172i	$0.988055\pi$
$812$	−7121.12	+	18999.0i	−0.307762	+	0.821101i
$813$			18678.1i			0.805746i
$814$	12879.7	+	6368.67i	0.554588	+	0.274228i
$815$	5334.84	−	9240.22i	0.229290	−	0.397142i
$816$	3947.41	+	14987.4i	0.169347	+	0.642972i
$817$	−6004.69	−	10400.4i	−0.257133	−	0.445367i
$818$	18549.4	−	12365.7i	0.792867	−	0.528554i
$819$	1070.72	−	2020.14i	0.0456823	−	0.0861896i
$820$	−20494.5	−	8540.38i	−0.872805	−	0.363711i
$821$	5968.24	−	3445.76i	0.253706	−	0.146477i	−0.367754	−	0.929923i	$-0.619873\pi$
$821$	5968.24	−	3445.76i	0.253706	−	0.146477i	0.621460	+	0.783446i	$0.286540\pi$
$822$	−42806.6	+	2759.84i	−1.81636	+	0.117105i
$823$	−12426.4	+	21523.1i	−0.526314	+	0.911602i	0.473216	+	0.880946i	$0.343093\pi$
$823$	−12426.4	+	21523.1i	−0.526314	+	0.911602i	−0.999530	+	0.0306558i	$0.990240\pi$
$824$	−27587.2	+	24037.6i	−1.16632	+	1.01625i
$825$	73313.8			3.09389
$826$	−5537.53	−	2492.81i	−0.233263	−	0.105007i
$827$		−	40056.0i		−	1.68426i	−0.539274	−	0.842130i	$-0.681301\pi$
$827$		−	40056.0i		−	1.68426i	0.539274	−	0.842130i	$-0.318699\pi$
$828$	−31414.4	+	4067.62i	−1.31851	+	0.170724i
$829$	17833.4	+	10296.1i	0.747143	+	0.431363i	0.824661	−	0.565628i	$-0.191366\pi$
$829$	17833.4	+	10296.1i	0.747143	+	0.431363i	−0.0775180	+	0.996991i	$0.524700\pi$
$830$	−2755.42	−	42738.0i	−0.115231	−	1.78730i
$831$	−6925.20	−	11994.8i	−0.289089	−	0.500716i
$832$	597.825	+	1469.81i	0.0249109	+	0.0612459i
$833$	5703.71	+	8408.25i	0.237241	+	0.349734i
$834$	−2902.03	+	1934.60i	−0.120491	+	0.0803235i
$835$	−40878.6	+	23601.3i	−1.69421	+	0.978151i
$836$	7703.25	+	10083.5i	0.318687	+	0.417161i
$837$	52.7437	+	30.4516i	0.00217812	+	0.00125754i
$838$	−3796.62	+	7678.13i	−0.156506	+	0.316511i
$839$	−28341.7			−1.16622			−0.583112	−	0.812392i	$-0.698165\pi$
$839$	−28341.7			−1.16622			−0.583112	+	0.812392i	$0.698165\pi$
$840$	−46048.8	−	49136.4i	−1.89147	−	2.01830i
$841$	5635.70			0.231075
$842$	−13154.2	+	26602.5i	−0.538389	+	1.08882i
$843$	56596.8	+	32676.2i	2.31233	+	1.33503i
$844$	29436.5	−	22487.8i	1.20053	−	0.917137i
$845$	37235.6	−	21498.0i	1.51591	−	0.875212i
$846$	32682.5	−	21787.4i	1.32819	−	0.885419i
$847$	−2516.12	−	1333.60i	−0.102072	−	0.0541003i
$848$	9702.37	−	9619.93i	0.392902	−	0.389563i
$849$	−2668.94	−	4622.74i	−0.107889	−	0.186869i
$850$	1408.91	+	21852.9i	0.0568530	+	0.881820i
$851$	−12745.2	−	7358.46i	−0.513397	−	0.296410i
$852$	−4002.16	−	30908.8i	−0.160929	−	1.24286i
$853$			15664.3i			0.628763i	0.949297	+	0.314382i	$0.101797\pi$
$853$			15664.3i			0.628763i	−0.949297	+	0.314382i	$0.898203\pi$
$854$	16979.7	−	12230.1i	0.680367	−	0.490052i
$855$	−36197.1			−1.44786
$856$	−9341.00	−	10720.4i	−0.372978	−	0.428055i
$857$	−12500.5	+	21651.5i	−0.498260	+	0.863011i	−0.999998	−	0.00200842i	$-0.999361\pi$
$857$	−12500.5	+	21651.5i	−0.498260	+	0.863011i	0.501738	+	0.865019i	$0.332694\pi$
$858$	2453.65	−	158.193i	0.0976297	−	0.00629441i
$859$	2767.80	−	1597.99i	0.109937	−	0.0634724i	−0.444023	−	0.896015i	$-0.646449\pi$
$859$	2767.80	−	1597.99i	0.109937	−	0.0634724i	0.553960	+	0.832543i	$0.313116\pi$
$860$	−15713.3	+	37707.5i	−0.623045	+	1.49513i
$861$	21363.8	−	774.208i	0.845619	−	0.0306445i
$862$	−30438.3	+	20291.3i	−1.20271	+	0.801769i
$863$	1905.67	+	3300.72i	0.0751677	+	0.130194i	0.901159	−	0.433488i	$-0.142717\pi$
$863$	1905.67	+	3300.72i	0.0751677	+	0.130194i	−0.825991	+	0.563683i	$0.809384\pi$
$864$	14213.0	+	12599.2i	0.559650	+	0.496105i
$865$	764.653	−	1324.42i	0.0300566	−	0.0520596i
$866$	39906.5	+	19732.7i	1.56591	+	0.774299i
$867$		−	32991.6i		−	1.29233i
$868$	−66.4044	+	54.6486i	−0.00259667	+	0.00213697i
$869$			15508.4i			0.605391i
$870$	27588.6	−	55793.9i	1.07510	−	2.17424i
$871$	1597.84	−	2767.54i	0.0621593	−	0.107663i
$872$	3379.45	−	9851.85i	0.131241	−	0.382598i
$873$	14067.4	+	24365.5i	0.545372	+	0.944612i
$874$	−7209.31	−	10814.5i	−0.279014	−	0.418540i
$875$	−26362.4	−	42065.3i	−1.01853	−	1.62522i
$876$	66965.3	+	27905.4i	2.58282	+	1.07630i
$877$	29051.2	−	16772.7i	1.11858	−	0.645810i	0.177538	−	0.984114i	$-0.443187\pi$
$877$	29051.2	−	16772.7i	1.11858	−	0.645810i	0.941037	+	0.338304i	$0.109853\pi$
$878$	−819.681	−	12713.7i	−0.0315067	−	0.488686i
$879$	19892.6	−	34455.0i	0.763324	−	1.32212i
$880$	11349.2	−	41644.4i	0.434753	−	1.59526i
$881$	27593.4			1.05522			0.527608	−	0.849488i	$-0.323089\pi$
$881$	27593.4			1.05522			0.527608	+	0.849488i	$0.323089\pi$
$882$	35790.8	+	14577.0i	1.36637	+	0.556499i
$883$			6231.84i			0.237506i	0.992924	+	0.118753i	$0.0378897\pi$
$883$			6231.84i			0.237506i	−0.992924	+	0.118753i	$0.962110\pi$
$884$	94.3059	+	728.327i	0.00358807	+	0.0277107i
$885$	16133.4	+	9314.61i	0.612788	+	0.353793i
$886$	−42406.0	+	2734.02i	−1.60797	+	0.103669i
$887$	15706.2	+	27203.9i	0.594546	+	1.02978i	0.993611	+	0.112862i	$0.0360017\pi$
$887$	15706.2	+	27203.9i	0.594546	+	1.02978i	−0.399064	+	0.916923i	$0.630665\pi$
$888$	5257.18	+	26878.9i	0.198671	+	1.01576i
$889$	1762.96	−	1104.85i	0.0665106	−	0.0416823i
$890$	−37955.1	−	56935.2i	−1.42950	−	2.14435i
$891$	−6470.10	+	3735.52i	−0.243273	+	0.140454i
$892$	−14606.4	−	19119.8i	−0.548274	−	0.717689i
$893$	13957.3	+	8058.23i	0.523026	+	0.301969i
$894$	−64563.8	−	31925.0i	−2.41536	−	1.19433i
$895$	−14729.8			−0.550128
$896$	−23703.3	+	12549.0i	−0.883785	+	0.467894i
$897$	−2518.41			−0.0937426
$898$	−3930.99	−	1943.77i	−0.146079	−	0.0722320i
$899$	−68.8385	−	39.7439i	−0.00255383	−	0.00147445i
$900$	50563.8	+	66187.9i	1.87273	+	2.45140i
$901$	5476.58	−	3161.91i	0.202499	−	0.116913i
$902$	7600.45	+	11401.2i	0.280562	+	0.420862i
$903$	−1424.45	−	39306.9i	−0.0524947	−	1.44856i
$904$	−4409.48	−	22544.8i	−0.162231	−	0.829455i
$905$	37492.6	+	64939.1i	1.37712	+	2.38525i
$906$	−20714.3	+	1335.50i	−0.759589	+	0.0489725i
$907$	−19169.5	−	11067.5i	−0.701778	−	0.405172i	0.106231	−	0.994341i	$-0.466122\pi$
$907$	−19169.5	−	11067.5i	−0.701778	−	0.405172i	−0.808009	+	0.589170i	$0.799455\pi$
$908$	2190.23	+	16915.2i	0.0800499	+	0.618228i
$909$		−	34957.9i		−	1.27555i
$910$	−1865.00	−	2589.28i	−0.0679385	−	0.0943228i
$911$	9718.26			0.353436			0.176718	−	0.984262i	$-0.443452\pi$
$911$	9718.26			0.353436			0.176718	+	0.984262i	$0.443452\pi$
$912$	−6359.86	+	23336.6i	−0.230917	+	0.847316i
$913$	−13215.1	+	22889.3i	−0.479033	+	0.829709i
$914$	2305.68	+	35762.3i	0.0834409	+	1.29421i
$915$	−55592.9	+	32096.6i	−2.00857	+	1.15965i
$916$	−13877.5	−	5782.95i	−0.500573	−	0.208596i
$917$	4766.10	−	8992.27i	0.171636	−	0.323829i
$918$	4876.18	+	7314.60i	0.175314	+	0.262982i
$919$	4150.94	+	7189.64i	0.148996	+	0.258068i	0.930857	−	0.365385i	$-0.119063\pi$
$919$	4150.94	+	7189.64i	0.148996	+	0.258068i	−0.781861	+	0.623453i	$0.785729\pi$
$920$	−14344.9	+	41818.6i	−0.514062	+	1.49861i
$921$	33102.7	−	57335.5i	1.18433	−	2.05133i
$922$	−6032.35	+	12199.6i	−0.215472	+	0.435761i
$923$		−	1476.86i		−	0.0526666i
$924$	6825.82	+	40995.1i	0.243023	+	1.45957i
$925$			38697.3i			1.37552i
$926$	13240.2	+	6546.90i	0.469870	+	0.232337i
$927$	−32207.9	+	55785.7i	−1.14115	+	1.97653i
$928$	−18550.1	−	16443.9i	−0.656183	−	0.581677i
$929$	−8647.88	−	14978.6i	−0.305412	−	0.528989i	0.671941	−	0.740605i	$-0.265461\pi$
$929$	−8647.88	−	14978.6i	−0.305412	−	0.528989i	−0.977353	+	0.211615i	$0.932128\pi$
$930$	219.515	−	146.336i	0.00773996	−	0.00515974i
$931$	1147.75	+	15814.9i	0.0404038	+	0.556728i
$932$	−10243.1	+	24580.6i	−0.360004	+	0.863909i
$933$	−3130.28	+	1807.27i	−0.109840	+	0.0634161i
$934$	34342.2	−	2214.12i	1.20312	−	0.0775677i
$935$	9988.82	−	17301.1i	0.349379	−	0.605142i
$936$	1835.07	+	2106.06i	0.0640825	+	0.0735455i
$937$	−43100.4			−1.50270			−0.751350	−	0.659904i	$-0.770597\pi$
$937$	−43100.4			−1.50270			−0.751350	+	0.659904i	$0.770597\pi$
$938$	49255.0	+	22172.9i	1.71453	+	0.771825i
$939$		−	44929.3i		−	1.56146i
$940$	−7039.60	−	54367.0i	−0.244262	−	1.88644i
$941$	−39293.0	−	22685.8i	−1.36123	−	0.785904i	−0.371439	−	0.928457i	$-0.621135\pi$
$941$	−39293.0	−	22685.8i	−1.36123	−	0.785904i	−0.989787	+	0.142553i	$0.954469\pi$
$942$	3101.57	+	48107.0i	0.107277	+	1.66392i
$943$	−7017.41	−	12154.5i	−0.242331	−	0.419730i
$944$	5268.70	−	5223.93i	0.181654	−	0.180111i
$945$	−33749.3	−	17887.9i	−1.16176	−	0.615759i
$946$	20976.8	−	13983.9i	0.720946	−	0.480609i
$947$	3279.36	−	1893.34i	0.112529	−	0.0649687i	−0.442679	−	0.896680i	$-0.645972\pi$
$947$	3279.36	−	1893.34i	0.112529	−	0.0649687i	0.555208	+	0.831711i	$0.312639\pi$
$948$	−23490.9	+	17945.7i	−0.804799	+	0.614820i
$949$	2977.11	+	1718.84i	0.101835	+	0.0587943i
$950$	−15148.0	+	30634.8i	−0.517334	+	1.04623i
$951$	−23548.1			−0.802942
$952$	−12088.3	+	2822.41i	−0.411540	+	0.0960871i
$953$	7167.42			0.243626			0.121813	−	0.992553i	$-0.461129\pi$
$953$	7167.42			0.243626			0.121813	+	0.992553i	$0.461129\pi$
$954$	10661.4	−	21561.3i	0.361821	−	0.731731i
$955$	17018.0	+	9825.34i	0.576638	+	0.332922i
$956$	−27801.1	−	36391.6i	−0.940536	−	1.23116i
$957$	−33266.1	+	19206.2i	−1.12366	+	0.648744i
$958$	−31879.7	+	21252.2i	−1.07514	+	0.716730i
$959$	−1244.25	−	34334.3i	−0.0418966	−	1.15611i
$960$	76212.7	−	30998.4i	2.56224	−	1.04216i
$961$	14895.3	+	25799.5i	0.499994	+	0.866016i
$962$	83.4989	+	1295.11i	0.00279845	+	0.0434055i
$963$	−21678.3	−	12516.0i	−0.725413	−	0.418817i
$964$	−14629.2	+	1894.24i	−0.488772	+	0.0632876i
$965$		−	15996.4i		−	0.533620i
$966$	−4275.39	−	42352.6i	−0.142400	−	1.41064i
$967$	41487.5			1.37968			0.689838	−	0.723963i	$-0.257682\pi$
$967$	41487.5			1.37968			0.689838	+	0.723963i	$0.257682\pi$
$968$	2623.14	−	2285.62i	0.0870980	−	0.0758912i
$969$	−5597.52	+	9695.19i	−0.185571	+	0.321418i
$970$	39185.9	−	2526.41i	1.29710	−	0.0836269i
$971$	24879.2	−	14364.0i	0.822258	−	0.474731i	−0.0289362	−	0.999581i	$-0.509212\pi$
$971$	24879.2	−	14364.0i	0.822258	−	0.474731i	0.851195	+	0.524850i	$0.175879\pi$
$972$	−34065.3	−	14195.5i	−1.12412	−	0.468438i
$973$	−1483.45	−	2367.07i	−0.0488768	−	0.0779905i
$974$	16652.6	−	11101.2i	0.547826	−	0.365201i
$975$	3311.00	+	5734.82i	0.108756	+	0.188371i
$976$	6511.62	+	24723.1i	0.213557	+	0.810829i
$977$	21126.3	−	36591.9i	0.691803	−	1.19824i	−0.279444	−	0.960162i	$-0.590150\pi$
$977$	21126.3	−	36591.9i	0.691803	−	1.19824i	0.971247	−	0.238075i	$-0.0765165\pi$
$978$	−11251.2	−	5563.40i	−0.367866	−	0.181900i
$979$			42229.1i			1.37860i
$980$	40378.4	−	35759.8i	1.31616	−	1.16562i
$981$		−	18335.7i		−	0.596753i
$982$	−8295.81	+	16777.1i	−0.269582	+	0.545192i
$983$	−2241.94	+	3883.16i	−0.0727435	+	0.125995i	−0.900103	−	0.435678i	$-0.856509\pi$
$983$	−2241.94	+	3883.16i	−0.0727435	+	0.125995i	0.827359	+	0.561673i	$0.189842\pi$
$984$	−8474.69	+	24705.6i	−0.274556	+	0.800393i
$985$	125.988	+	218.218i	0.00407545	+	0.00705889i
$986$	−6364.14	−	9546.64i	−0.205553	−	0.308344i
$987$	28030.2	+	44726.5i	0.903963	+	1.44241i
$988$	−440.869	+	1057.96i	−0.0141963	+	0.0340671i
$989$	−22362.8	+	12911.2i	−0.719006	+	0.415118i
$990$	−4888.89	−	75829.2i	−0.156948	−	2.43435i
$991$	−10162.7	+	17602.3i	−0.325761	+	0.564235i	−0.981666	−	0.190609i	$-0.938954\pi$
$991$	−10162.7	+	17602.3i	−0.325761	+	0.564235i	0.655905	+	0.754844i	$0.272287\pi$
$992$	−33.2432	−	99.6745i	−0.00106398	−	0.00319019i
$993$	−31821.6			−1.01695
$994$	24836.6	−	2507.19i	0.792525	−	0.0800033i
$995$		−	2979.85i		−	0.0949422i
$996$	−49963.0	+	6469.36i	−1.58950	+	0.205813i
$997$	14049.1	+	8111.27i	0.446279	+	0.257659i	0.706258	−	0.707955i	$-0.250382\pi$
$997$	14049.1	+	8111.27i	0.446279	+	0.257659i	−0.259978	+	0.965614i	$0.583715\pi$
$998$	36652.6	−	2363.08i	1.16254	−	0.0749519i
$999$	7767.41	+	13453.5i	0.245996	+	0.426077i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.4.p.a.53.20	yes	44
4.3	odd	2		224.4.t.a.81.21		44
7.2	even	3	inner	56.4.p.a.37.11	✓	44
8.3	odd	2		224.4.t.a.81.2		44
8.5	even	2	inner	56.4.p.a.53.11	yes	44
28.23	odd	6		224.4.t.a.177.2		44
56.37	even	6	inner	56.4.p.a.37.20	yes	44
56.51	odd	6		224.4.t.a.177.21		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.4.p.a.37.11	✓	44	7.2	even	3	inner
56.4.p.a.37.20	yes	44	56.37	even	6	inner
56.4.p.a.53.11	yes	44	8.5	even	2	inner
56.4.p.a.53.20	yes	44	1.1	even	1	trivial
224.4.t.a.81.2		44	8.3	odd	2
224.4.t.a.81.21		44	4.3	odd	2
224.4.t.a.177.2		44	28.23	odd	6
224.4.t.a.177.21		44	56.51	odd	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:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	56.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.53540 + 1.25369i) q^{2} +(-7.07996 - 4.08762i) q^{3} +(4.85654 + 6.35720i) q^{4} +(17.0228 - 9.82813i) q^{5} +(-12.8260 - 19.2398i) q^{6} +(15.6931 - 9.83491i) q^{7} +(4.34335 + 22.2066i) q^{8} +(19.9172 + 34.4977i) q^{9} +(55.4811 - 3.57700i) q^{10} +(-29.7141 - 17.1555i) q^{11} +(-8.39831 - 64.8604i) q^{12} -3.09910i q^{13} +(52.1183 - 5.26121i) q^{14} -160.695 q^{15} +(-16.8280 + 61.7480i) q^{16} +(-14.8109 + 25.6532i) q^{17} +(7.24898 + 112.435i) q^{18} +(-40.0355 + 23.1145i) q^{19} +(145.151 + 60.4868i) q^{20} +(-151.308 + 5.48329i) q^{21} +(-53.8297 - 80.7482i) q^{22} +(49.7004 + 86.0836i) q^{23} +(60.0215 - 174.976i) q^{24} +(130.684 - 226.352i) q^{25} +(3.88530 - 7.85747i) q^{26} -104.925i q^{27} +(138.737 + 52.0007i) q^{28} +136.943i q^{29} +(-407.425 - 201.461i) q^{30} +(-0.290223 + 0.502681i) q^{31} +(-120.078 + 135.459i) q^{32} +(140.250 + 242.920i) q^{33} +(-69.7127 + 46.4730i) q^{34} +(170.483 - 321.652i) q^{35} +(-122.580 + 294.157i) q^{36} +(-128.221 + 74.0282i) q^{37} +(-130.484 + 8.41263i) q^{38} +(-12.6679 + 21.9415i) q^{39} +(292.186 + 335.333i) q^{40} -141.194 q^{41} +(-390.502 - 175.791i) q^{42} +259.780i q^{43} +(-35.2472 - 272.215i) q^{44} +(678.095 + 391.498i) q^{45} +(18.0887 + 280.565i) q^{46} +(-174.311 - 301.916i) q^{47} +(371.544 - 368.387i) q^{48} +(149.549 - 308.681i) q^{49} +(615.111 - 410.056i) q^{50} +(209.721 - 121.083i) q^{51} +(19.7016 - 15.0509i) q^{52} +(-184.884 - 106.743i) q^{53} +(131.543 - 266.027i) q^{54} -674.424 q^{55} +(286.561 + 305.775i) q^{56} +377.933 q^{57} +(-171.683 + 347.205i) q^{58} +(-100.398 - 57.9647i) q^{59} +(-780.420 - 1021.57i) q^{60} +(345.954 - 199.737i) q^{61} +(-1.36604 + 0.910650i) q^{62} +(651.846 + 345.492i) q^{63} +(-474.271 + 192.903i) q^{64} +(-30.4584 - 52.7554i) q^{65} +(51.0446 + 791.730i) q^{66} +(893.014 + 515.582i) q^{67} +(-235.012 + 30.4301i) q^{68} -812.625i q^{69} +(835.493 - 601.786i) q^{70} +476.543 q^{71} +(-679.570 + 592.131i) q^{72} +(-554.624 + 960.638i) q^{73} +(-417.899 + 26.9429i) q^{74} +(-1850.48 + 1068.37i) q^{75} +(-341.377 - 142.257i) q^{76} +(-635.030 + 23.0130i) q^{77} +(-59.6261 + 39.7490i) q^{78} +(-225.997 - 391.439i) q^{79} +(320.407 + 1216.51i) q^{80} +(108.872 - 188.573i) q^{81} +(-357.984 - 177.013i) q^{82} -770.316i q^{83} +(-769.693 - 935.267i) q^{84} +582.253i q^{85} +(-325.683 + 658.648i) q^{86} +(559.769 - 969.549i) q^{87} +(251.906 - 734.363i) q^{88} +(-615.389 - 1065.88i) q^{89} +(1228.43 + 1842.73i) q^{90} +(-30.4794 - 48.6346i) q^{91} +(-305.879 + 734.024i) q^{92} +(4.10953 - 2.37264i) q^{93} +(-63.4414 - 984.010i) q^{94} +(-454.344 + 786.948i) q^{95} +(1403.86 - 468.210i) q^{96} +706.293 q^{97} +(766.156 - 595.144i) q^{98} -1366.76i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{4} - 20 q^{6} - 4 q^{7} - 12 q^{8} + 160 q^{9} - 14 q^{10} - 110 q^{12} + 102 q^{14} - 116 q^{15} - 104 q^{16} - 2 q^{17} - 38 q^{18} + 256 q^{20} - 360 q^{22} + 162 q^{23} + 186 q^{24} + 348 q^{25}+ \cdots - 2670 q^{98}+O(q^{100}) \) 44 * q + 4 * q^4 - 20 * q^6 - 4 * q^7 - 12 * q^8 + 160 * q^9 - 14 * q^10 - 110 * q^12 + 102 * q^14 - 116 * q^15 - 104 * q^16 - 2 * q^17 - 38 * q^18 + 256 * q^20 - 360 * q^22 + 162 * q^23 + 186 * q^24 + 348 * q^25 - 302 * q^26 - 642 * q^28 - 396 * q^30 - 374 * q^31 - 140 * q^32 - 110 * q^33 - 148 * q^34 + 1440 * q^36 + 52 * q^38 + 52 * q^39 + 658 * q^40 - 8 * q^41 - 1710 * q^42 + 374 * q^44 - 486 * q^46 - 738 * q^47 + 936 * q^48 + 356 * q^49 + 2328 * q^50 + 96 * q^52 + 944 * q^54 - 2268 * q^55 + 1848 * q^56 - 452 * q^57 + 918 * q^58 + 410 * q^60 + 1416 * q^62 + 668 * q^63 - 2984 * q^64 + 248 * q^65 + 868 * q^66 - 64 * q^68 + 3422 * q^70 + 1248 * q^71 - 2172 * q^72 - 218 * q^73 - 176 * q^74 - 3028 * q^76 - 3716 * q^78 + 298 * q^79 - 2540 * q^80 - 1050 * q^81 - 146 * q^82 - 4844 * q^84 - 2412 * q^86 + 2140 * q^87 + 1626 * q^88 + 422 * q^89 - 4916 * q^90 + 1652 * q^92 - 2676 * q^94 - 2434 * q^95 - 400 * q^96 + 1672 * q^97 - 2670 * q^98

Introduction

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