LMFDB - Embedded newform 152.4.p.a.45.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,4,Mod(45,152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, 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("152.45");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	152.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:	$8.96829032087$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$58$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			45.9
Character	$\chi$	$=$	152.45
Dual form			152.4.p.a.125.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.55889 + 1.20502i) q^{2} +(-4.74696 + 2.74066i) q^{3} +(5.09583 - 6.16705i) q^{4} +(2.75286 - 1.58936i) q^{5} +(8.84438 - 12.7332i) q^{6} +6.39182 q^{7} +(-5.60823 + 21.9214i) q^{8} +(1.52239 - 2.63686i) q^{9} +(-5.12904 + 7.38426i) q^{10} +61.8197i q^{11} +(-7.28793 + 43.2406i) q^{12} +(-48.9939 - 28.2866i) q^{13} +(-16.3560 + 7.70229i) q^{14} +(-8.71179 + 15.0893i) q^{15} +(-12.0650 - 62.8525i) q^{16} +(-3.16069 - 5.47448i) q^{17} +(-0.718153 + 8.58197i) q^{18} +(50.2899 - 65.8022i) q^{19} +(4.22642 - 25.0761i) q^{20} +(-30.3417 + 17.5178i) q^{21} +(-74.4942 - 158.190i) q^{22} +(36.5338 - 63.2785i) q^{23} +(-33.4570 - 119.430i) q^{24} +(-57.4479 + 99.5026i) q^{25} +(159.456 + 13.3435i) q^{26} -131.306i q^{27} +(32.5716 - 39.4186i) q^{28} +(-226.243 - 130.622i) q^{29} +(4.10958 - 49.1097i) q^{30} -112.649 q^{31} +(106.612 + 146.294i) q^{32} +(-169.426 - 293.455i) q^{33} +(14.6847 + 10.1999i) q^{34} +(17.5957 - 10.1589i) q^{35} +(-8.50380 - 22.8257i) q^{36} -227.883i q^{37} +(-49.3930 + 228.981i) q^{38} +310.096 q^{39} +(19.4024 + 69.2600i) q^{40} +(-25.3562 - 43.9183i) q^{41} +(56.5316 - 81.3885i) q^{42} +(-407.779 + 235.431i) q^{43} +(381.245 + 315.023i) q^{44} -9.67854i q^{45} +(-17.2340 + 205.947i) q^{46} +(67.6767 - 117.219i) q^{47} +(229.529 + 265.292i) q^{48} -302.145 q^{49} +(27.0997 - 323.842i) q^{50} +(30.0073 + 17.3247i) q^{51} +(-424.110 + 158.004i) q^{52} +(-364.115 - 210.222i) q^{53} +(158.227 + 335.998i) q^{54} +(98.2539 + 170.181i) q^{55} +(-35.8468 + 140.118i) q^{56} +(-58.3826 + 450.187i) q^{57} +(736.334 + 61.6177i) q^{58} +(330.020 - 190.537i) q^{59} +(48.6624 + 130.618i) q^{60} +(291.562 + 168.333i) q^{61} +(288.255 - 135.744i) q^{62} +(9.73086 - 16.8543i) q^{63} +(-449.096 - 245.880i) q^{64} -179.831 q^{65} +(787.164 + 546.757i) q^{66} +(-469.568 - 271.105i) q^{67} +(-49.8677 - 8.40488i) q^{68} +400.507i q^{69} +(-32.7838 + 47.1988i) q^{70} +(513.735 + 889.815i) q^{71} +(49.2658 + 48.1611i) q^{72} +(-335.367 - 580.873i) q^{73} +(274.604 + 583.126i) q^{74} -629.779i q^{75} +(-149.537 - 645.457i) q^{76} +395.140i q^{77} +(-793.501 + 373.673i) q^{78} +(83.2056 + 144.116i) q^{79} +(-133.109 - 153.848i) q^{80} +(400.969 + 694.499i) q^{81} +(117.806 + 81.8271i) q^{82} -213.128i q^{83} +(-46.5831 + 276.386i) q^{84} +(-17.4018 - 10.0470i) q^{85} +(759.761 - 1093.83i) q^{86} +1431.96 q^{87} +(-1355.17 - 346.699i) q^{88} +(-315.321 + 546.152i) q^{89} +(11.6629 + 24.7663i) q^{90} +(-313.160 - 180.803i) q^{91} +(-204.071 - 547.763i) q^{92} +(534.738 - 308.731i) q^{93} +(-31.9249 + 381.504i) q^{94} +(33.8573 - 261.073i) q^{95} +(-907.023 - 402.265i) q^{96} +(-320.342 - 554.849i) q^{97} +(773.155 - 364.092i) q^{98} +(163.010 + 94.1139i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - q^{2} - 7 q^{4} - 11 q^{6} - 8 q^{7} - 46 q^{8} + 484 q^{9} - 44 q^{10} - 58 q^{12} + 24 q^{14} - 230 q^{15} - 67 q^{16} - 2 q^{17} + 196 q^{18} - 840 q^{20} + 137 q^{22} - 2 q^{23} + 77 q^{24}+ \cdots + 55 q^{98}+O(q^{100}) $ 116 * q - q^2 - 7 * q^4 - 11 * q^6 - 8 * q^7 - 46 * q^8 + 484 * q^9 - 44 * q^10 - 58 * q^12 + 24 * q^14 - 230 * q^15 - 67 * q^16 - 2 * q^17 + 196 * q^18 - 840 * q^20 + 137 * q^22 - 2 * q^23 + 77 * q^24 + 1248 * q^25 + 492 * q^26 - 96 * q^28 - 904 * q^30 + 208 * q^31 - 431 * q^32 - 180 * q^33 + 224 * q^34 - 84 * q^36 + 1552 * q^38 - 116 * q^39 - 58 * q^40 - 22 * q^41 - 568 * q^42 - 89 * q^44 - 1852 * q^46 + 202 * q^47 - 89 * q^48 + 5220 * q^49 - 942 * q^50 + 232 * q^52 - 231 * q^54 + 248 * q^55 - 2296 * q^56 - 398 * q^57 - 3620 * q^58 - 1378 * q^60 + 614 * q^62 - 796 * q^63 + 1550 * q^64 - 508 * q^65 - 797 * q^66 + 1860 * q^68 - 2968 * q^70 + 1986 * q^71 - 1596 * q^72 - 218 * q^73 + 2490 * q^74 - 4697 * q^76 + 1254 * q^78 + 1250 * q^79 + 3136 * q^80 - 3810 * q^81 - 169 * q^82 + 4136 * q^84 - 2360 * q^86 - 1404 * q^87 + 4434 * q^88 - 2 * q^89 + 1378 * q^90 - 1958 * q^92 - 4608 * q^94 + 438 * q^95 + 3410 * q^96 - 1586 * q^97 + 55 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−2.55889	+	1.20502i	−0.904704	+	0.426040i
$2$	−2.55889	+	1.20502i	−0.904704	+	0.426040i
$3$	−4.74696	+	2.74066i	−0.913552	+	0.527440i	−0.881572	−	0.472049i	$-0.843515\pi$
$3$	−4.74696	+	2.74066i	−0.913552	+	0.527440i	−0.0319798	+	0.999489i	$0.510181\pi$
$4$	5.09583	−	6.16705i	0.636979	−	0.770881i
$5$	2.75286	−	1.58936i	0.246223	−	0.142157i	−0.371811	−	0.928309i	$-0.621263\pi$
$5$	2.75286	−	1.58936i	0.246223	−	0.142157i	0.618034	+	0.786152i	$0.287930\pi$
$6$	8.84438	−	12.7332i	0.601784	−	0.866387i
$7$	6.39182			0.345126			0.172563	−	0.984999i	$-0.444795\pi$
$7$	6.39182			0.345126			0.172563	+	0.984999i	$0.444795\pi$
$8$	−5.60823	+	21.9214i	−0.247851	+	0.968798i
$9$	1.52239	−	2.63686i	0.0563850	−	0.0976616i
$10$	−5.12904	+	7.38426i	−0.162194	+	0.233511i
$11$			61.8197i			1.69448i	0.531206	+	0.847242i	$0.321739\pi$
$11$			61.8197i			1.69448i	−0.531206	+	0.847242i	$0.678261\pi$
$12$	−7.28793	+	43.2406i	−0.175320	+	1.04021i
$13$	−48.9939	−	28.2866i	−1.04527	−	0.603485i	−0.123946	−	0.992289i	$-0.539555\pi$
$13$	−48.9939	−	28.2866i	−1.04527	−	0.603485i	−0.921320	+	0.388804i	$0.872888\pi$
$14$	−16.3560	+	7.70229i	−0.312237	+	0.147037i
$15$	−8.71179	+	15.0893i	−0.149958	+	0.259735i
$16$	−12.0650	−	62.8525i	−0.188515	−	0.982070i
$17$	−3.16069	−	5.47448i	−0.0450929	−	0.0781033i	0.842598	−	0.538543i	$-0.181025\pi$
$17$	−3.16069	−	5.47448i	−0.0450929	−	0.0781033i	−0.887691	+	0.460440i	$0.847692\pi$
$18$	−0.718153	+	8.58197i	−0.00940391	+	0.112377i
$19$	50.2899	−	65.8022i	0.607226	−	0.794529i
$19$	50.2899	−	65.8022i	0.607226	−	0.794529i
$20$	4.22642	−	25.0761i	0.0472528	−	0.280360i
$21$	−30.3417	+	17.5178i	−0.315290	+	0.182033i
$22$	−74.4942	−	158.190i	−0.721919	−	1.53301i
$23$	36.5338	−	63.2785i	0.331210	−	0.573673i	−0.651539	−	0.758615i	$-0.725876\pi$
$23$	36.5338	−	63.2785i	0.331210	−	0.573673i	0.982749	+	0.184942i	$0.0592098\pi$
$24$	−33.4570	−	119.430i	−0.284558	−	1.01577i
$25$	−57.4479	+	99.5026i	−0.459583	+	0.796021i
$26$	159.456	+	13.3435i	1.20277	+	0.100649i
$27$		−	131.306i		−	0.935920i
$28$	32.5716	−	39.4186i	0.219838	−	0.266051i
$29$	−226.243	−	130.622i	−1.44870	−	0.836408i	−0.450297	−	0.892879i	$-0.648682\pi$
$29$	−226.243	−	130.622i	−1.44870	−	0.836408i	−0.998404	+	0.0564711i	$0.982015\pi$
$30$	4.10958	−	49.1097i	0.0250101	−	0.298872i
$31$	−112.649			−0.652654			−0.326327	−	0.945257i	$-0.605811\pi$
$31$	−112.649			−0.652654			−0.326327	+	0.945257i	$0.605811\pi$
$32$	106.612	+	146.294i	0.588952	+	0.808168i
$33$	−169.426	−	293.455i	−0.893738	−	1.54800i
$34$	14.6847	+	10.1999i	0.0740709	+	0.0514489i
$35$	17.5957	−	10.1589i	0.0849778	−	0.0490620i
$36$	−8.50380	−	22.8257i	−0.0393695	−	0.105675i
$37$		−	227.883i		−	1.01253i	−0.862378	−	0.506266i	$-0.831026\pi$
$37$		−	227.883i		−	1.01253i	0.862378	−	0.506266i	$-0.168974\pi$
$38$	−49.3930	+	228.981i	−0.210858	+	0.977517i
$39$	310.096			1.27321
$40$	19.4024	+	69.2600i	0.0766947	+	0.273774i
$41$	−25.3562	−	43.9183i	−0.0965848	−	0.167290i	0.813684	−	0.581307i	$-0.197459\pi$
$41$	−25.3562	−	43.9183i	−0.0965848	−	0.167290i	−0.910269	+	0.414017i	$0.864125\pi$
$42$	56.5316	−	81.3885i	0.207691	−	0.299012i
$43$	−407.779	+	235.431i	−1.44618	+	0.834953i	−0.998251	−	0.0591165i	$-0.981172\pi$
$43$	−407.779	+	235.431i	−1.44618	+	0.834953i	−0.447929	+	0.894069i	$0.647838\pi$
$44$	381.245	+	315.023i	1.30625	+	1.07935i
$45$		−	9.67854i		−	0.0320620i
$46$	−17.2340	+	205.947i	−0.0552394	+	0.660113i
$47$	67.6767	−	117.219i	0.210035	−	0.363792i	−0.741690	−	0.670743i	$-0.765975\pi$
$47$	67.6767	−	117.219i	0.210035	−	0.363792i	0.951725	+	0.306951i	$0.0993088\pi$
$48$	229.529	+	265.292i	0.690201	+	0.797742i
$49$	−302.145			−0.880888
$50$	27.0997	−	323.842i	0.0766494	−	0.915964i
$51$	30.0073	+	17.3247i	0.0823895	+	0.0475676i
$52$	−424.110	+	158.004i	−1.13103	+	0.421369i
$53$	−364.115	−	210.222i	−0.943680	−	0.544834i	−0.0525679	−	0.998617i	$-0.516741\pi$
$53$	−364.115	−	210.222i	−0.943680	−	0.544834i	−0.891112	+	0.453784i	$0.850074\pi$
$54$	158.227	+	335.998i	0.398740	+	0.846731i
$55$	98.2539	+	170.181i	0.240883	+	0.417221i
$56$	−35.8468	+	140.118i	−0.0855397	+	0.334357i
$57$	−58.3826	+	450.187i	−0.135666	+	1.04612i
$58$	736.334	+	61.6177i	1.66699	+	0.139496i
$59$	330.020	−	190.537i	0.728219	−	0.420437i	−0.0895512	−	0.995982i	$-0.528543\pi$
$59$	330.020	−	190.537i	0.728219	−	0.420437i	0.817770	+	0.575545i	$0.195210\pi$
$60$	48.6624	+	130.618i	0.104705	+	0.281046i
$61$	291.562	+	168.333i	0.611978	+	0.353326i	0.773739	−	0.633504i	$-0.218384\pi$
$61$	291.562	+	168.333i	0.611978	+	0.353326i	−0.161761	+	0.986830i	$0.551717\pi$
$62$	288.255	−	135.744i	0.590459	−	0.278057i
$63$	9.73086	−	16.8543i	0.0194599	−	0.0337055i
$64$	−449.096	−	245.880i	−0.877140	−	0.480235i
$65$	−179.831			−0.343158
$66$	787.164	+	546.757i	1.46808	+	1.01971i
$67$	−469.568	−	271.105i	−0.856223	−	0.494340i	0.00652287	−	0.999979i	$-0.497924\pi$
$67$	−469.568	−	271.105i	−0.856223	−	0.494340i	−0.862746	+	0.505638i	$0.831257\pi$
$68$	−49.8677	−	8.40488i	−0.0889316	−	0.0149888i
$69$			400.507i			0.698773i
$70$	−32.7838	+	47.1988i	−0.0559774	+	0.0805906i
$71$	513.735	+	889.815i	0.858720	+	1.48735i	0.873151	+	0.487450i	$0.162073\pi$
$71$	513.735	+	889.815i	0.858720	+	1.48735i	−0.0144309	+	0.999896i	$0.504594\pi$
$72$	49.2658	+	48.1611i	0.0806393	+	0.0788312i
$73$	−335.367	−	580.873i	−0.537696	−	0.931316i	−0.999028	−	0.0440884i	$-0.985962\pi$
$73$	−335.367	−	580.873i	−0.537696	−	0.931316i	0.461332	−	0.887228i	$-0.347372\pi$
$74$	274.604	+	583.126i	0.431379	+	0.916041i
$75$		−	629.779i		−	0.969609i
$76$	−149.537	−	645.457i	−0.225698	−	0.974197i
$77$			395.140i			0.584810i
$78$	−793.501	+	373.673i	−1.15188	+	0.542438i
$79$	83.2056	+	144.116i	0.118498	+	0.205245i	0.919173	−	0.393855i	$-0.128859\pi$
$79$	83.2056	+	144.116i	0.118498	+	0.205245i	−0.800674	+	0.599100i	$0.795525\pi$
$80$	−133.109	−	153.848i	−0.186025	−	0.215009i
$81$	400.969	+	694.499i	0.550026	+	0.952674i
$82$	117.806	+	81.8271i	0.158653	+	0.110199i
$83$		−	213.128i		−	0.281854i	−0.990020	−	0.140927i	$-0.954992\pi$
$83$		−	213.128i		−	0.281854i	0.990020	−	0.140927i	$-0.0450083\pi$
$84$	−46.5831	+	276.386i	−0.0605076	+	0.359002i
$85$	−17.4018	−	10.0470i	−0.0222058	−	0.0128205i
$86$	759.761	−	1093.83i	0.952642	−	1.37152i
$87$	1431.96			1.76462
$88$	−1355.17	−	346.699i	−1.64161	−	0.419980i
$89$	−315.321	+	546.152i	−0.375550	+	0.650471i	−0.990409	−	0.138165i	$-0.955879\pi$
$89$	−315.321	+	546.152i	−0.375550	+	0.650471i	0.614859	+	0.788637i	$0.289213\pi$
$90$	11.6629	+	24.7663i	0.0136597	+	0.0290067i
$91$	−313.160	−	180.803i	−0.360748	−	0.208278i
$92$	−204.071	−	547.763i	−0.231260	−	0.620741i
$93$	534.738	−	308.731i	0.596233	−	0.344235i
$94$	−31.9249	+	381.504i	−0.0350298	+	0.418607i
$95$	33.8573	−	261.073i	0.0365651	−	0.281953i
$96$	−907.023	−	402.265i	−0.964298	−	0.427667i
$97$	−320.342	−	554.849i	−0.335317	−	0.580787i	0.648228	−	0.761446i	$-0.275510\pi$
$97$	−320.342	−	554.849i	−0.335317	−	0.580787i	−0.983546	+	0.180659i	$0.942177\pi$
$98$	773.155	−	364.092i	0.796943	−	0.375294i
$99$	163.010	+	94.1139i	0.165486	+	0.0955435i
$100$	320.893	+	861.332i	0.320893	+	0.861332i
$101$	863.815	+	498.724i	0.851018	+	0.491336i	0.860994	−	0.508615i	$-0.169842\pi$
$101$	863.815	+	498.724i	0.851018	+	0.491336i	−0.00997612	+	0.999950i	$0.503176\pi$
$102$	−97.6621	−	8.17253i	−0.0948038	−	0.00793334i
$103$	−706.149			−0.675523			−0.337762	−	0.941232i	$-0.609670\pi$
$103$	−706.149			−0.675523			−0.337762	+	0.941232i	$0.609670\pi$
$104$	894.851	−	915.377i	0.843725	−	0.863077i
$105$	−55.6842	+	96.4478i	−0.0517545	+	0.0896414i
$106$	1185.05	+	99.1672i	1.08587	+	0.0908676i
$107$			1358.71i			1.22758i	0.789469	+	0.613791i	$0.210356\pi$
$107$			1358.71i			1.22758i	−0.789469	+	0.613791i	$0.789644\pi$
$108$	−809.771	−	669.113i	−0.721483	−	0.596162i
$109$	383.566	−	221.452i	0.337055	−	0.194599i	−0.321914	−	0.946769i	$-0.604326\pi$
$109$	383.566	−	221.452i	0.337055	−	0.194599i	0.658969	+	0.752170i	$0.270993\pi$
$110$	−456.493	−	317.075i	−0.395681	−	0.274836i
$111$	624.548	+	1081.75i	0.534049	+	0.925000i
$112$	−77.1171	−	401.742i	−0.0650615	−	0.338938i
$113$	−1241.51			−1.03355			−0.516776	−	0.856121i	$-0.672868\pi$
$113$	−1241.51			−1.03355			−0.516776	+	0.856121i	$0.672868\pi$
$114$	−393.092	−	1222.33i	−0.322951	−	1.00423i
$115$		−	232.262i		−	0.188335i
$116$	−1958.45	+	729.627i	−1.56756	+	0.584002i
$117$	−149.176	+	86.1268i	−0.117875	+	0.0680549i
$118$	−614.883	+	885.245i	−0.479699	+	0.690622i
$119$	−20.2025	−	34.9918i	−0.0155627	−	0.0269554i
$120$	−281.920	−	275.599i	−0.214464	−	0.209655i
$121$	−2490.67			−1.87128
$122$	−948.921	−	79.4073i	−0.704191	−	0.0589278i
$123$	240.730	+	138.985i	0.176470	+	0.101885i
$124$	−574.038	+	694.709i	−0.415727	+	0.503119i
$125$			762.562i			0.545645i
$126$	−4.59030	+	54.8543i	−0.00324553	+	0.0387842i
$127$	938.410	−	1625.37i	0.655673	−	1.13566i	−0.326052	−	0.945352i	$-0.605718\pi$
$127$	938.410	−	1625.37i	0.655673	−	1.13566i	0.981725	−	0.190307i	$-0.0609483\pi$
$128$	1445.48	+	88.0100i	0.998152	+	0.0607739i
$129$	1290.47	−	2235.17i	0.880774	−	1.52555i
$130$	460.167	−	216.701i	0.310456	−	0.146199i
$131$	−110.321	+	63.6936i	−0.0735783	+	0.0424804i	−0.536338	−	0.844003i	$-0.680193\pi$
$131$	−110.321	+	63.6936i	−0.0735783	+	0.0424804i	0.462760	+	0.886484i	$0.346859\pi$
$132$	−2673.12	−	450.538i	−1.76262	−	0.297078i
$133$	321.444	−	420.595i	0.209569	−	0.274212i
$134$	1528.26	+	127.888i	0.985237	+	0.0824463i
$135$	−208.693	−	361.467i	−0.133048	−	0.230445i
$136$	137.734	−	38.5846i	0.0868426	−	0.0243280i
$137$	933.960	−	1617.67i	0.582435	−	1.00881i	−0.412755	−	0.910842i	$-0.635433\pi$
$137$	933.960	−	1617.67i	0.582435	−	1.00881i	0.995190	−	0.0979652i	$-0.0312334\pi$
$138$	−482.621	−	1024.85i	−0.297706	−	0.632183i
$139$	1560.88	+	901.173i	0.952460	+	0.549903i	0.893844	−	0.448378i	$-0.147998\pi$
$139$	1560.88	+	901.173i	0.952460	+	0.549903i	0.0586157	+	0.998281i	$0.481331\pi$
$140$	27.0145	−	160.282i	0.0163082	−	0.0967593i
$141$			741.914i			0.443123i
$142$	−2386.84	−	1657.87i	−1.41056	−	0.979759i
$143$	1748.67	−	3028.79i	1.02260	−	1.77119i
$144$	−184.101	−	63.8726i	−0.106540	−	0.0369633i
$145$	−830.420			−0.475605
$146$	1558.13	+	1082.26i	0.883234	+	0.613485i
$147$	1434.27	−	828.075i	0.804737	−	0.464615i
$148$	−1405.36	−	1161.25i	−0.780541	−	0.644961i
$149$	−1.35824	+	0.784180i	−0.000746788	+	0.000431158i	−0.500373	−	0.865810i	$-0.666804\pi$
$149$	−1.35824	+	0.784180i	−0.000746788	+	0.000431158i	0.499627	+	0.866241i	$0.333471\pi$
$150$	758.899	+	1611.54i	0.413093	+	0.877209i
$151$	−2598.55			−1.40044			−0.700221	−	0.713926i	$-0.746915\pi$
$151$	−2598.55			−1.40044			−0.700221	+	0.713926i	$0.746915\pi$
$152$	1160.44	+	1471.46i	0.619237	+	0.785204i
$153$	−19.2473			−0.0101703
$154$	−476.153	−	1011.12i	−0.249153	−	0.529080i
$155$	−310.105	+	179.039i	−0.160698	+	0.0927793i
$156$	1580.20	−	1912.38i	0.811006	−	0.981491i
$157$	−2111.46	+	1219.05i	−1.07333	+	0.619689i	−0.929090	−	0.369854i	$-0.879408\pi$
$157$	−2111.46	+	1219.05i	−1.07333	+	0.619689i	−0.144242	+	0.989542i	$0.546074\pi$
$158$	−386.578	−	268.513i	−0.194649	−	0.135201i
$159$	2304.58			1.14947
$160$	526.001	+	233.282i	0.259900	+	0.115266i
$161$	233.518	−	404.464i	0.114309	−	0.197989i
$162$	−1862.92	−	1293.97i	−0.903489	−	0.627554i
$163$			966.960i			0.464651i	0.972638	+	0.232326i	$0.0746335\pi$
$163$			966.960i			0.464651i	−0.972638	+	0.232326i	$0.925366\pi$
$164$	−400.057	−	67.4271i	−0.190483	−	0.0321047i
$165$	−932.814	−	538.560i	−0.440118	−	0.254102i
$166$	256.825	+	545.372i	0.120081	+	0.254995i
$167$	−1541.94	+	2670.72i	−0.714485	+	1.23752i	0.248672	+	0.968588i	$0.420006\pi$
$167$	−1541.94	+	2670.72i	−0.714485	+	1.23752i	−0.963158	+	0.268937i	$0.913328\pi$
$168$	−213.851	−	763.375i	−0.0982081	−	0.350570i
$169$	501.767	+	869.086i	0.228387	+	0.395578i
$170$	56.6362	+	4.73942i	0.0255518	+	0.00213822i
$171$	−96.9504	−	232.784i	−0.0433566	−	0.104102i
$172$	−626.058	+	3714.51i	−0.277537	+	1.64668i
$173$	311.262	−	179.707i	0.136791	−	0.0789762i	−0.430043	−	0.902808i	$-0.641502\pi$
$173$	311.262	−	179.707i	0.136791	−	0.0789762i	0.566834	+	0.823832i	$0.308168\pi$
$174$	−3664.22	+	1725.54i	−1.59646	+	0.751799i
$175$	−367.196	+	636.002i	−0.158614	+	0.274727i
$176$	3885.52	−	745.853i	1.66410	−	0.319436i
$177$	−1044.39	+	1808.94i	−0.443511	+	0.768183i
$178$	148.745	−	1777.51i	0.0626344	−	0.748484i
$179$			3379.39i			1.41110i	0.708658	+	0.705552i	$0.249301\pi$
$179$			3379.39i			1.41110i	−0.708658	+	0.705552i	$0.750699\pi$
$180$	−59.6881	−	49.3202i	−0.0247160	−	0.0204229i
$181$	4023.87	+	2323.18i	1.65244	+	0.954039i	0.976064	+	0.217485i	$0.0697854\pi$
$181$	4023.87	+	2323.18i	1.65244	+	0.954039i	0.676380	+	0.736553i	$0.263548\pi$
$182$	1019.21	+	85.2895i	0.415105	+	0.0347367i
$183$	−1845.38			−0.745432
$184$	1182.26	+	1155.75i	0.473682	+	0.463061i
$185$	−362.188	−	627.328i	−0.143938	−	0.249308i
$186$	−996.306	+	1434.38i	−0.392757	+	0.565451i
$187$	338.430	−	195.393i	0.132345	−	0.0764093i
$188$	−378.029	−	1014.70i	−0.146652	−	0.393640i
$189$		−	839.284i		−	0.323010i
$190$	227.962	+	708.855i	0.0870427	+	0.270662i
$191$	1388.26			0.525923			0.262961	−	0.964806i	$-0.415301\pi$
$191$	1388.26			0.525923			0.262961	+	0.964806i	$0.415301\pi$
$192$	2805.71	−	63.6327i	1.05461	−	0.0239182i
$193$	1038.65	+	1798.99i	0.387376	+	0.670956i	0.992096	−	0.125483i	$-0.0400481\pi$
$193$	1038.65	+	1798.99i	0.387376	+	0.670956i	−0.604719	+	0.796439i	$0.706715\pi$
$194$	1488.33	+	1033.78i	0.550802	+	0.382582i
$195$	853.649	−	492.854i	0.313493	−	0.180995i
$196$	−1539.68	+	1863.34i	−0.561107	+	0.679060i
$197$		−	2552.51i		−	0.923140i	−0.887104	−	0.461570i	$-0.847286\pi$
$197$		−	2552.51i		−	0.923140i	0.887104	−	0.461570i	$-0.152714\pi$
$198$	−530.534	−	44.3960i	−0.190421	−	0.0159348i
$199$	−44.5813	+	77.2171i	−0.0158808	+	0.0275064i	−0.873857	−	0.486184i	$-0.838389\pi$
$199$	−44.5813	+	77.2171i	−0.0158808	+	0.0275064i	0.857976	+	0.513690i	$0.171722\pi$
$200$	−1859.06	−	1817.37i	−0.657275	−	0.642538i
$201$	2972.03			1.04294
$202$	−2811.38	−	235.261i	−0.979248	−	0.0819451i
$203$	−1446.11	−	834.909i	−0.499984	−	0.288666i
$204$	259.755	−	96.7726i	0.0891493	−	0.0332129i
$205$	−139.604	−	80.6005i	−0.0475628	−	0.0274604i
$206$	1806.96	−	850.926i	0.611149	−	0.287800i
$207$	−111.238	−	192.670i	−0.0373505	−	0.0646930i
$208$	−1186.78	+	3420.67i	−0.395616	+	1.14029i
$209$	4067.87	+	3108.90i	1.34632	+	1.02893i
$210$	26.2677	−	313.900i	0.00863163	−	0.103148i
$211$	143.613	−	82.9147i	0.0468564	−	0.0270525i	−0.476389	−	0.879235i	$-0.658055\pi$
$211$	143.613	−	82.9147i	0.0468564	−	0.0270525i	0.523245	+	0.852182i	$0.324721\pi$
$212$	−3151.92	+	1174.26i	−1.02111	+	0.380417i
$213$	−4877.35	−	2815.94i	−1.56897	−	0.905846i
$214$	−1637.28	−	3476.78i	−0.522999	−	1.11060i
$215$	−748.372	+	1296.22i	−0.237389	+	0.411169i
$216$	2878.41	+	736.394i	0.906718	+	0.231969i
$217$	−720.029			−0.225248
$218$	−714.648	+	1028.88i	−0.222028	+	0.319653i
$219$	3183.95	+	1838.25i	0.982426	+	0.567204i
$220$	1550.20	+	261.276i	0.475065	+	0.0800692i
$221$			357.621i			0.108852i
$222$	−2901.68	−	2015.48i	−0.877244	−	0.609325i
$223$	1649.50	+	2857.01i	0.495330	+	0.857937i	0.999986	−	0.00538423i	$-0.00171386\pi$
$223$	1649.50	+	2857.01i	0.495330	+	0.857937i	−0.504656	+	0.863321i	$0.668381\pi$
$224$	681.443	+	935.084i	0.203262	+	0.278919i
$225$	174.917	+	302.964i	0.0518271	+	0.0897672i
$226$	3176.88	−	1496.05i	0.935058	−	0.440335i
$227$		−	2190.15i		−	0.640377i	−0.947354	−	0.320188i	$-0.896254\pi$
$227$		−	2190.15i		−	0.640377i	0.947354	−	0.320188i	$-0.103746\pi$
$228$	2478.82	+	2654.13i	0.720017	+	0.770938i
$229$		−	5275.55i		−	1.52235i	−0.648547	−	0.761175i	$-0.724623\pi$
$229$		−	5275.55i		−	1.52235i	0.648547	−	0.761175i	$-0.275377\pi$
$230$	279.881	+	594.333i	0.0802384	+	0.170388i
$231$	−1082.94	−	1875.71i	−0.308452	−	0.534254i
$232$	4132.23	−	4227.01i	1.16937	−	1.19619i
$233$	351.609	+	609.005i	0.0988612	+	0.171233i	0.911214	−	0.411934i	$-0.135147\pi$
$233$	351.609	+	609.005i	0.0988612	+	0.171233i	−0.812352	+	0.583167i	$0.801813\pi$
$234$	277.940	−	400.150i	0.0776475	−	0.111789i
$235$		−	430.251i		−	0.119432i
$236$	506.675	−	3006.19i	0.139753	−	0.829180i
$237$	−789.947	−	456.076i	−0.216509	−	0.125001i
$238$	93.8621	+	65.1957i	0.0255638	+	0.0177563i
$239$	−3283.69			−0.888721			−0.444361	−	0.895848i	$-0.646569\pi$
$239$	−3283.69			−0.888721			−0.444361	+	0.895848i	$0.646569\pi$
$240$	1053.51	+	365.506i	0.283348	+	0.0983055i
$241$	−463.112	+	802.133i	−0.123783	+	0.214398i	−0.921256	−	0.388956i	$-0.872836\pi$
$241$	−463.112	+	802.133i	−0.123783	+	0.214398i	0.797474	+	0.603354i	$0.206169\pi$
$242$	6373.35	−	3001.32i	1.69295	−	0.797240i
$243$	−736.480	−	425.207i	−0.194425	−	0.112251i
$244$	2523.87	−	940.278i	0.662190	−	0.246701i
$245$	−831.761	+	480.217i	−0.216895	+	0.125224i
$246$	−783.482	−	65.5631i	−0.203061	−	0.0169925i
$247$	−4325.22	+	1801.37i	−1.11420	+	0.464043i
$248$	631.759	−	2469.41i	0.161761	−	0.632290i
$249$	584.112	+	1011.71i	0.148661	+	0.257488i
$250$	−918.906	−	1951.31i	−0.232467	−	0.493648i
$251$	−5566.76	−	3213.97i	−1.39988	−	0.808223i	−0.405504	−	0.914093i	$-0.632904\pi$
$251$	−5566.76	−	3213.97i	−1.39988	−	0.808223i	−0.994380	+	0.105870i	$0.966237\pi$
$252$	−54.3547	−	145.898i	−0.0135874	−	0.0364710i
$253$	3911.85	+	2258.51i	0.972080	+	0.561231i
$254$	−442.673	+	5289.96i	−0.109353	+	1.30678i
$255$	110.141			0.0270482
$256$	−3804.87	+	1516.63i	−0.928924	+	0.370271i
$257$	621.051	−	1075.69i	0.150740	−	0.261089i	−0.780760	−	0.624831i	$-0.785168\pi$
$257$	621.051	−	1075.69i	0.150740	−	0.261089i	0.931500	+	0.363742i	$0.118501\pi$
$258$	−608.750	+	7274.59i	−0.146896	+	1.75541i
$259$		−	1456.58i		−	0.349450i
$260$	−916.388	+	1109.03i	−0.218584	+	0.264534i
$261$	−688.863	+	397.715i	−0.163370	+	0.0943217i
$262$	205.546	−	295.924i	0.0484682	−	0.0697795i
$263$	1023.95	+	1773.53i	0.240074	+	0.415820i	0.960735	−	0.277467i	$-0.0894950\pi$
$263$	1023.95	+	1773.53i	0.240074	+	0.415820i	−0.720661	+	0.693287i	$0.756162\pi$
$264$	7383.13	−	2068.30i	1.72121	−	0.482179i
$265$	−1336.47			−0.309808
$266$	−315.711	+	1463.60i	−0.0727725	+	0.337366i
$267$		−	3456.74i		−	0.792319i
$268$	−4064.76	+	1514.34i	−0.926474	+	0.345161i
$269$	−1938.16	+	1119.00i	−0.439300	+	0.253630i	−0.703301	−	0.710893i	$-0.748291\pi$
$269$	−1938.16	+	1119.00i	−0.439300	+	0.253630i	0.264001	+	0.964522i	$0.414958\pi$
$270$	969.598	+	673.473i	0.218548	+	0.151801i
$271$	−3298.44	−	5713.07i	−0.739359	−	1.28061i	−0.952784	−	0.303648i	$-0.901795\pi$
$271$	−3298.44	−	5713.07i	−0.739359	−	1.28061i	0.213426	−	0.976959i	$-0.431538\pi$
$272$	−305.951	+	264.707i	−0.0682022	+	0.0590081i
$273$	1982.07			0.439416
$274$	−440.574	+	5264.88i	−0.0971388	+	1.16081i
$275$	−6151.22	−	3551.41i	−1.34885	−	0.778756i
$276$	2469.95	+	2040.92i	0.538671	+	0.445104i
$277$		−	1603.05i		−	0.347718i	−0.984771	−	0.173859i	$-0.944376\pi$
$277$		−	1603.05i		−	0.347718i	0.984771	−	0.173859i	$-0.0556237\pi$
$278$	−5080.05	−	425.107i	−1.09598	−	0.0917131i
$279$	−171.495	+	297.039i	−0.0367999	+	0.0637392i
$280$	124.017	+	442.697i	0.0264693	+	0.0944864i
$281$	857.822	−	1485.79i	0.182112	−	0.315427i	−0.760488	−	0.649352i	$-0.775040\pi$
$281$	857.822	−	1485.79i	0.182112	−	0.315427i	0.942599	+	0.333926i	$0.108373\pi$
$282$	−894.024	−	1898.48i	−0.188789	−	0.400896i
$283$	395.275	−	228.212i	0.0830271	−	0.0479357i	−0.457912	−	0.888998i	$-0.651402\pi$
$283$	395.275	−	228.212i	0.0830271	−	0.0479357i	0.540939	+	0.841062i	$0.318069\pi$
$284$	8105.44	+	1366.12i	1.69355	+	0.285438i
$285$	554.792	+	1332.09i	0.115309	+	0.276864i
$286$	−824.894	+	9857.52i	−0.170549	+	2.03807i
$287$	−162.072	−	280.717i	−0.0333339	−	0.0577360i
$288$	548.062	−	58.4035i	0.112135	−	0.0119495i
$289$	2436.52	−	4220.18i	0.495933	−	0.858982i
$290$	2124.95	−	1000.68i	0.430281	−	0.202627i
$291$	3041.30	+	1755.89i	0.612660	+	0.353719i
$292$	−5291.25	−	891.806i	−1.06043	−	0.178729i
$293$			8541.68i			1.70311i	0.524268	+	0.851553i	$0.324339\pi$
$293$			8541.68i			1.70311i	−0.524268	+	0.851553i	$0.675661\pi$
$294$	−2672.28	+	3847.28i	−0.530104	+	0.763190i
$295$	605.665	−	1049.04i	0.119536	−	0.207043i
$296$	4995.50	+	1278.02i	0.980938	+	0.250957i
$297$	8117.29			1.58590
$298$	2.53063	−	3.64334i	0.000491931	−	0.000708232i
$299$	−3579.87	+	2066.84i	−0.692405	+	0.399760i
$300$	−3883.88	−	3209.25i	−0.747453	−	0.617620i
$301$	−2606.45	+	1504.83i	−0.499114	+	0.288163i
$302$	6649.39	−	3131.31i	1.26699	−	0.596645i
$303$	−5467.32			−1.03660
$304$	−4742.58	−	2366.94i	−0.894755	−	0.446557i
$305$	1070.17			0.200911
$306$	49.2516	−	23.1934i	0.00920107	−	0.00433294i
$307$	−7852.60	+	4533.70i	−1.45984	+	0.842840i	−0.999003	−	0.0446434i	$-0.985785\pi$
$307$	−7852.60	+	4533.70i	−1.45984	+	0.842840i	−0.460839	+	0.887484i	$0.652451\pi$
$308$	2436.85	+	2013.57i	0.450819	+	0.372512i
$309$	3352.06	−	1935.31i	0.617126	−	0.356298i
$310$	577.778	−	831.826i	0.105857	−	0.152402i
$311$	−8924.69			−1.62724			−0.813622	−	0.581395i	$-0.802507\pi$
$311$	−8924.69			−1.62724			−0.813622	+	0.581395i	$0.802507\pi$
$312$	−1739.09	+	6797.73i	−0.315566	+	1.23348i
$313$	−2712.33	+	4697.89i	−0.489808	+	0.848373i	−0.999931	−	0.0117286i	$-0.996267\pi$
$313$	−2712.33	+	4697.89i	−0.489808	+	0.848373i	0.510123	+	0.860102i	$0.329600\pi$
$314$	3934.01	−	5663.79i	0.707036	−	1.01792i
$315$		−	61.8635i		−	0.0110654i
$316$	1312.77	+	221.260i	0.233700	+	0.0393887i
$317$	−4881.35	−	2818.25i	−0.864870	−	0.499333i	0.000770037	−	1.00000i	$-0.499755\pi$
$317$	−4881.35	−	2818.25i	−0.864870	−	0.499333i	−0.865640	+	0.500667i	$0.833088\pi$
$318$	−5897.17	+	2777.08i	−1.03993	+	0.489720i
$319$	8074.99	−	13986.3i	1.41728	−	2.45480i
$320$	−1627.09	+	36.9019i	−0.284241	+	0.00644649i
$321$	−3723.75	−	6449.73i	−0.647475	−	1.12146i
$322$	−110.156	+	1316.37i	−0.0190645	+	0.227822i
$323$	−519.183	−	67.3303i	−0.0894369	−	0.0115986i
$324$	6326.28	+	1066.25i	1.08475	+	0.182828i
$325$	5629.19	−	3250.01i	0.960773	−	0.554702i
$326$	−1165.21	−	2474.34i	−0.197960	−	0.420372i
$327$	−1213.85	+	2102.44i	−0.205278	+	0.355552i
$328$	1104.95	−	309.540i	0.186009	−	0.0521082i
$329$	432.577	−	749.245i	0.0724885	−	0.125554i
$330$	3035.94	+	254.053i	0.506434	+	0.0423793i
$331$			3650.02i			0.606112i	0.952973	+	0.303056i	$0.0980069\pi$
$331$			3650.02i			0.606112i	−0.952973	+	0.303056i	$0.901993\pi$
$332$	−1314.37	−	1086.07i	−0.217276	−	0.179535i
$333$	−600.895	−	346.927i	−0.0988855	−	0.0570915i
$334$	727.375	−	8692.16i	0.119162	−	1.42399i
$335$	−1723.54			−0.281096
$336$	1467.11	+	1695.70i	0.238206	+	0.275321i
$337$	134.374	+	232.742i	0.0217205	+	0.0376210i	0.876681	−	0.481072i	$-0.159752\pi$
$337$	134.374	+	232.742i	0.0217205	+	0.0376210i	−0.854961	+	0.518693i	$0.826419\pi$
$338$	−2331.24	−	1619.25i	−0.375155	−	0.260579i
$339$	5893.39	−	3402.55i	0.944203	−	0.545136i
$340$	−150.637	+	56.1204i	−0.0240278	+	0.00895164i
$341$		−	6963.89i		−	1.10591i
$342$	528.596	+	478.842i	0.0835767	+	0.0757100i
$343$	−4123.65			−0.649143
$344$	−2874.07	−	10259.4i	−0.450463	−	1.60800i
$345$	636.551	+	1102.54i	0.0993355	+	0.172054i
$346$	−579.934	+	834.929i	−0.0901082	+	0.129729i
$347$	−5735.95	+	3311.65i	−0.887383	+	0.512331i	−0.873085	−	0.487567i	$-0.837884\pi$
$347$	−5735.95	+	3311.65i	−0.887383	+	0.512331i	−0.0142971	+	0.999898i	$0.504551\pi$
$348$	7297.01	−	8830.94i	1.12402	−	1.36031i
$349$			5975.97i			0.916580i	0.888803	+	0.458290i	$0.151538\pi$
$349$			5975.97i			0.916580i	−0.888803	+	0.458290i	$0.848462\pi$
$350$	173.216	−	2069.94i	0.0264537	−	0.316123i
$351$	−3714.20	+	6433.19i	−0.564814	+	0.978286i
$352$	−9043.85	+	6590.70i	−1.36943	+	0.997971i
$353$	1584.14			0.238854			0.119427	−	0.992843i	$-0.461894\pi$
$353$	1584.14			0.238854			0.119427	+	0.992843i	$0.461894\pi$
$354$	492.668	−	5887.40i	0.0739689	−	0.883932i
$355$	2828.48	+	1633.02i	0.422873	+	0.244146i
$356$	1761.32	+	4727.70i	0.262219	+	0.703841i
$357$	191.801	+	110.736i	0.0284347	+	0.0164168i
$358$	−4072.25	−	8647.49i	−0.601187	−	1.27663i
$359$	3969.58	+	6875.51i	0.583583	+	1.01080i	0.995050	+	0.0993707i	$0.0316830\pi$
$359$	3969.58	+	6875.51i	0.583583	+	1.01080i	−0.411468	+	0.911424i	$0.634984\pi$
$360$	212.167	+	54.2795i	0.0310617	+	0.00794661i
$361$	−1800.86	−	6618.37i	−0.262554	−	0.964917i
$362$	−13096.1	−	1095.91i	−1.90143	−	0.159115i
$363$	11823.1	−	6826.08i	1.70951	−	0.986986i
$364$	−2710.83	+	1009.93i	−0.390347	+	0.145425i
$365$	−1846.44	−	1066.04i	−0.264786	−	0.152874i
$366$	4722.11	−	2223.72i	0.674396	−	0.317584i
$367$	2360.44	−	4088.40i	0.335733	−	0.581506i	−0.647893	−	0.761732i	$-0.724349\pi$
$367$	2360.44	−	4088.40i	0.335733	−	0.581506i	0.983625	+	0.180226i	$0.0576828\pi$
$368$	−4417.99	−	1532.79i	−0.625825	−	0.217126i
$369$	−154.409			−0.0217837
$370$	1682.74	+	1168.82i	0.236437	+	0.164227i
$371$	−2327.36	−	1343.70i	−0.325688	−	0.188036i
$372$	820.975	−	4870.99i	0.114424	−	0.678896i
$373$		−	5353.86i		−	0.743197i	−0.928394	−	0.371598i	$-0.878810\pi$
$373$		−	5353.86i		−	0.743197i	0.928394	−	0.371598i	$-0.121190\pi$
$374$	−630.553	+	907.805i	−0.0871794	+	0.125512i
$375$	−2089.92	−	3619.85i	−0.287795	−	0.498475i
$376$	2190.07	+	2140.96i	0.300383	+	0.293648i
$377$	7389.69	+	12799.3i	1.00952	+	1.74854i
$378$	1011.36	+	2147.63i	0.137615	+	0.292229i
$379$		−	11268.1i		−	1.52719i	−0.645698	−	0.763593i	$-0.723434\pi$
$379$		−	11268.1i		−	1.52719i	0.645698	−	0.763593i	$-0.276566\pi$
$380$	−1437.52	−	1539.18i	−0.194061	−	0.207785i
$381$			10287.4i			1.38331i
$382$	−3552.41	+	1672.89i	−0.475804	+	0.224064i
$383$	1046.07	+	1811.85i	0.139561	+	0.241727i	0.927331	−	0.374243i	$-0.122098\pi$
$383$	1046.07	+	1811.85i	0.139561	+	0.241727i	−0.787770	+	0.615970i	$0.788764\pi$
$384$	−7102.82	+	3543.78i	−0.943918	+	0.470945i
$385$	628.021	+	1087.76i	0.0831348	+	0.143994i
$386$	−4825.62	−	3351.83i	−0.636315	−	0.441978i
$387$			1433.68i			0.188315i
$388$	−5054.19	−	851.851i	−0.661308	−	0.111459i
$389$	−4810.82	−	2777.53i	−0.627039	−	0.362021i	0.152565	−	0.988293i	$-0.451247\pi$
$389$	−4810.82	−	2777.53i	−0.627039	−	0.362021i	−0.779605	+	0.626272i	$0.784580\pi$
$390$	−1590.49	+	2289.83i	−0.206507	+	0.297308i
$391$	−461.889			−0.0597410
$392$	1694.50	−	6623.43i	0.218329	−	0.853403i
$393$	349.125	−	604.702i	0.0448117	−	0.0776162i
$394$	3075.83	+	6531.58i	0.393295	+	0.835169i
$395$	458.106	+	264.488i	0.0583540	+	0.0336907i
$396$	1411.08	−	525.702i	0.179064	−	0.0667109i
$397$	12606.1	−	7278.16i	1.59366	−	0.920102i	0.600992	−	0.799255i	$-0.294773\pi$
$397$	12606.1	−	7278.16i	1.59366	−	0.920102i	0.992671	−	0.120846i	$-0.0385608\pi$
$398$	21.0302	−	251.312i	0.00264861	−	0.0316511i
$399$	−373.171	+	2877.51i	−0.0468218	+	0.361042i
$400$	6947.09	+	2410.24i	0.868387	+	0.301281i
$401$	−2718.61	−	4708.78i	−0.338556	−	0.586397i	0.645605	−	0.763671i	$-0.276605\pi$
$401$	−2718.61	−	4708.78i	−0.338556	−	0.586397i	−0.984161	+	0.177275i	$0.943272\pi$
$402$	−7605.09	+	3581.37i	−0.943551	+	0.444334i
$403$	5519.09	+	3186.45i	0.682197	+	0.393867i
$404$	7477.51	−	2785.78i	0.920842	−	0.343063i
$405$	2207.62	+	1274.57i	0.270858	+	0.156380i
$406$	4706.51	+	393.849i	0.575321	+	0.0481438i
$407$	14087.6			1.71572
$408$	−548.070	+	560.641i	−0.0665037	+	0.0680291i
$409$	−2336.00	+	4046.08i	−0.282415	+	0.489158i	−0.971979	−	0.235067i	$-0.924469\pi$
$409$	−2336.00	+	4046.08i	−0.282415	+	0.489158i	0.689564	+	0.724225i	$0.257802\pi$
$410$	454.357	+	38.0214i	0.0547295	+	0.00457986i
$411$			10238.7i			1.22880i
$412$	−3598.42	+	4354.85i	−0.430294	+	0.520748i
$413$	2109.43	−	1217.88i	0.251327	−	0.145104i
$414$	516.817	+	358.976i	0.0613531	+	0.0426152i
$415$	−338.738	−	586.712i	−0.0400675	−	0.0693989i
$416$	−1085.16	−	10183.2i	−0.127895	−	1.20017i
$417$	−9879.23			−1.16016
$418$	−14155.5	−	3053.46i	−1.65639	−	0.357296i
$419$			10426.9i			1.21572i	0.794045	+	0.607859i	$0.207972\pi$
$419$			10426.9i			1.21572i	−0.794045	+	0.607859i	$0.792028\pi$
$420$	311.041	+	834.889i	0.0361363	+	0.0969962i
$421$	−3703.90	+	2138.44i	−0.428781	+	0.247557i	−0.698827	−	0.715291i	$-0.746294\pi$
$421$	−3703.90	+	2138.44i	−0.428781	+	0.247557i	0.270046	+	0.962847i	$0.412961\pi$
$422$	−267.574	+	385.226i	−0.0308657	+	0.0444372i
$423$	−206.061	−	356.908i	−0.0236857	−	0.0410248i
$424$	6650.40	−	6802.94i	0.761726	−	0.779198i
$425$	726.299			0.0828958
$426$	15873.9	+	1328.35i	1.80538	+	0.151077i
$427$	1863.61	+	1075.96i	0.211209	+	0.121942i
$428$	8379.22	+	6923.75i	0.946319	+	0.781944i
$429$			19170.0i			2.15743i
$430$	353.027	−	4218.69i	0.0395918	−	0.473123i
$431$	−3000.72	+	5197.39i	−0.335358	+	0.580858i	−0.983554	−	0.180617i	$-0.942191\pi$
$431$	−3000.72	+	5197.39i	−0.335358	+	0.580858i	0.648195	+	0.761474i	$0.275524\pi$
$432$	−8252.91	+	1584.20i	−0.919140	+	0.176435i
$433$	−6833.50	+	11836.0i	−0.758423	+	1.31363i	0.185231	+	0.982695i	$0.440697\pi$
$433$	−6833.50	+	11836.0i	−0.758423	+	1.31363i	−0.943654	+	0.330932i	$0.892637\pi$
$434$	1842.47	−	867.652i	0.203782	−	0.0959646i
$435$	3941.97	−	2275.90i	0.434490	−	0.250853i
$436$	588.883	−	3493.95i	0.0646844	−	0.383784i
$437$	−2326.58	−	5586.27i	−0.254681	−	0.611505i
$438$	−10362.5	−	867.152i	−1.13046	−	0.0945985i
$439$	8156.07	+	14126.7i	0.886715	+	1.53584i	0.843735	+	0.536760i	$0.180352\pi$
$439$	8156.07	+	14126.7i	0.886715	+	1.53584i	0.0429802	+	0.999076i	$0.486315\pi$
$440$	−4281.63	+	1199.45i	−0.463906	+	0.129958i
$441$	−459.983	+	796.714i	−0.0496689	+	0.0860290i
$442$	−430.942	−	915.113i	−0.0463752	−	0.0984785i
$443$	13879.7	+	8013.44i	1.48859	+	0.859436i	0.999915	−	0.0130319i	$-0.00414829\pi$
$443$	13879.7	+	8013.44i	1.48859	+	0.859436i	0.488672	+	0.872468i	$0.337482\pi$
$444$	9853.78	+	1660.79i	1.05324	+	0.177517i
$445$			2004.64i			0.213548i
$446$	−7663.66	−	5323.10i	−0.813643	−	0.565148i
$447$	4.29834	−	7.44494i	0.000454820	−	0.000787771i
$448$	−2870.54	−	1571.62i	−0.302723	−	0.165741i
$449$	13840.3			1.45471			0.727355	−	0.686261i	$-0.240749\pi$
$449$	13840.3			1.45471			0.727355	+	0.686261i	$0.240749\pi$
$450$	−812.672	−	564.474i	−0.0851327	−	0.0591323i
$451$	2715.01	−	1567.51i	0.283470	−	0.163661i
$452$	−6326.52	+	7656.44i	−0.658350	+	0.796745i
$453$	12335.2	−	7121.72i	1.27938	−	0.738648i
$454$	2639.19	+	5604.36i	0.272826	+	0.579352i
$455$	−1149.45			−0.118433
$456$	−9541.31	−	3804.58i	−0.979853	−	0.390715i
$457$	5522.47			0.565274			0.282637	−	0.959227i	$-0.408791\pi$
$457$	5522.47			0.565274			0.282637	+	0.959227i	$0.408791\pi$
$458$	6357.16	+	13499.5i	0.648582	+	1.37728i
$459$	−718.831	+	415.018i	−0.0730984	+	0.0422034i
$460$	−1432.37	−	1183.57i	−0.145184	−	0.119966i
$461$	−14990.7	+	8654.86i	−1.51450	+	0.874397i	−0.514644	+	0.857404i	$0.672076\pi$
$461$	−14990.7	+	8654.86i	−1.51450	+	0.874397i	−0.999856	+	0.0169930i	$0.994591\pi$
$462$	5031.41	+	3494.77i	0.506672	+	0.351929i
$463$	8476.57			0.850842			0.425421	−	0.904996i	$-0.360126\pi$
$463$	8476.57			0.850842			0.425421	+	0.904996i	$0.360126\pi$
$464$	−5480.27	+	15795.9i	−0.548309	+	1.58040i
$465$	981.370	−	1699.78i	0.0978709	−	0.169517i
$466$	−1633.59	−	1134.68i	−0.162392	−	0.112796i
$467$			5033.78i			0.498792i	0.968402	+	0.249396i	$0.0802320\pi$
$467$			5033.78i			0.498792i	−0.968402	+	0.249396i	$0.919768\pi$
$468$	−229.028	+	1358.86i	−0.0226214	+	0.134217i
$469$	−3001.39	−	1732.86i	−0.295504	−	0.170610i
$470$	518.463	+	1100.96i	0.0508828	+	0.108050i
$471$	6682.02	−	11573.6i	0.653697	−	1.13224i
$472$	2326.01	+	8303.07i	0.226829	+	0.809703i
$473$	−14554.3	−	25208.8i	−1.41481	−	2.45053i
$474$	2570.97	+	215.143i	0.249132	+	0.0208478i
$475$	3658.44	+	8784.17i	0.353391	+	0.848516i
$476$	−318.745	−	53.7225i	−0.0306926	−	0.00517303i
$477$	−1108.65	+	640.081i	−0.106419	+	0.0614409i
$478$	8402.61	−	3956.93i	0.804030	−	0.378631i
$479$	−751.425	+	1301.51i	−0.0716774	+	0.124149i	−0.899637	−	0.436640i	$-0.856169\pi$
$479$	−751.425	+	1301.51i	−0.0716774	+	0.124149i	0.827959	+	0.560788i	$0.189502\pi$
$480$	−3136.25	+	334.210i	−0.298228	+	0.0317803i
$481$	−6446.03	+	11164.8i	−0.611047	+	1.05836i
$482$	218.462	−	2610.63i	0.0206445	−	0.246703i
$483$			2559.97i			0.241165i
$484$	−12692.0	+	15360.1i	−1.19197	+	1.44253i
$485$	−1763.71	−	1018.28i	−0.165126	−	0.0953354i
$486$	2396.96	+	200.581i	0.223720	+	0.0187213i
$487$	9650.47			0.897956			0.448978	−	0.893543i	$-0.351788\pi$
$487$	9650.47			0.897956			0.448978	+	0.893543i	$0.351788\pi$
$488$	−5325.25	+	5447.39i	−0.493981	+	0.505311i
$489$	−2650.11	−	4590.12i	−0.245075	−	0.424483i
$490$	1549.71	−	2231.12i	0.142875	−	0.205697i
$491$	−10592.0	+	6115.29i	−0.973544	+	0.562076i	−0.900315	−	0.435239i	$-0.856664\pi$
$491$	−10592.0	+	6115.29i	−0.973544	+	0.562076i	−0.0732292	+	0.997315i	$0.523330\pi$
$492$	2083.85	−	776.346i	0.190949	−	0.0711390i
$493$			1651.42i			0.150864i
$494$	8897.06	−	9821.51i	0.810319	−	0.894515i
$495$	598.324			0.0543287
$496$	1359.10	+	7080.24i	0.123035	+	0.640952i
$497$	3283.70	+	5687.53i	0.296366	+	0.513321i
$498$	−2713.81	−	1884.99i	−0.244195	−	0.169615i
$499$	13405.5	−	7739.69i	1.20263	−	0.694341i	0.241494	−	0.970402i	$-0.422363\pi$
$499$	13405.5	−	7739.69i	1.20263	−	0.694341i	0.961140	+	0.276061i	$0.0890292\pi$
$500$	4702.76	+	3885.89i	0.420628	+	0.347565i
$501$		−	16903.7i		−	1.50739i
$502$	18117.6	+	1516.11i	1.61082	+	0.134796i
$503$	7682.63	−	13306.7i	0.681017	−	1.17956i	−0.293653	−	0.955912i	$-0.594871\pi$
$503$	7682.63	−	13306.7i	0.681017	−	1.17956i	0.974671	−	0.223645i	$-0.0717955\pi$
$504$	314.898	+	307.837i	0.0278307	+	0.0272067i
$505$	3170.61			0.279387
$506$	−12731.6	−	1065.40i	−1.11855	−	0.0936023i
$507$	−4763.73	−	2750.34i	−0.417287	−	0.240921i
$508$	−5241.78	−	14069.9i	−0.457808	−	1.22884i
$509$	5526.47	+	3190.71i	0.481251	+	0.277850i	0.720938	−	0.693000i	$-0.243711\pi$
$509$	5526.47	+	3190.71i	0.481251	+	0.277850i	−0.239687	+	0.970850i	$0.577045\pi$
$510$	−281.839	+	132.723i	−0.0244707	+	0.0115236i
$511$	−2143.61	−	3712.83i	−0.185572	−	0.321421i
$512$	7908.68	−	8465.85i	0.682651	−	0.730744i
$513$	−8640.22	−	6603.36i	−0.743616	−	0.568315i
$514$	−292.966	+	3500.96i	−0.0251404	+	0.300429i
$515$	−1943.93	+	1122.33i	−0.166329	+	0.0960303i
$516$	−7208.34	−	19348.4i	−0.614979	−	1.65071i
$517$	7246.46	+	4183.75i	0.616439	+	0.355901i
$518$	1755.22	+	3727.24i	0.148880	+	0.316149i
$519$	−985.032	+	1706.12i	−0.0833104	+	0.144298i
$520$	1008.53	−	3942.14i	0.0850521	−	0.332451i
$521$	−18913.6			−1.59044			−0.795220	−	0.606321i	$-0.792645\pi$
$521$	−18913.6			−1.59044			−0.795220	+	0.606321i	$0.792645\pi$
$522$	1283.47	−	1847.81i	0.107617	−	0.154935i
$523$	−4850.23	−	2800.28i	−0.405517	−	0.234126i	0.283345	−	0.959018i	$-0.408556\pi$
$523$	−4850.23	−	2800.28i	−0.405517	−	0.234126i	−0.688862	+	0.724893i	$0.741889\pi$
$524$	−169.374	+	1004.92i	−0.0141205	+	0.0837792i
$525$		−	4025.43i		−	0.334637i
$526$	−4757.33	−	3304.39i	−0.394352	−	0.273913i
$527$	356.047	+	616.692i	0.0294301	+	0.0509744i
$528$	−16400.3	+	14189.4i	−1.35176	+	1.16954i
$529$	3414.06	+	5913.32i	0.280600	+	0.486013i
$530$	3419.89	−	1610.48i	0.280284	−	0.131991i
$531$		−	1160.29i		−	0.0948254i
$532$	−955.810	−	4125.64i	−0.0778940	−	0.336220i
$533$			2868.97i			0.233150i
$534$	4165.46	+	8845.43i	0.337560	+	0.716815i
$535$	2159.48	+	3740.33i	0.174509	+	0.302259i
$536$	8576.46	−	8773.18i	0.691132	−	0.706984i
$537$	−9261.75	−	16041.8i	−0.744272	−	1.28912i
$538$	3611.12	−	5198.92i	0.289380	−	0.416620i
$539$		−	18678.5i		−	1.49265i
$540$	−3292.65	−	554.954i	−0.262394	−	0.0442249i
$541$	322.475	+	186.181i	0.0256272	+	0.0147959i	0.512759	−	0.858533i	$-0.328623\pi$
$541$	322.475	+	186.181i	0.0256272	+	0.0147959i	−0.487132	+	0.873329i	$0.661957\pi$
$542$	15324.7	+	10644.4i	1.21449	+	0.843574i
$543$	−25468.2			−2.01279
$544$	463.916	−	1046.03i	0.0365630	−	0.0824417i
$545$	703.934	−	1219.25i	0.0553270	−	0.0958292i
$546$	−5071.91	+	2388.45i	−0.397542	+	0.187209i
$547$	−17836.0	−	10297.6i	−1.39417	−	0.804924i	−0.400395	−	0.916343i	$-0.631127\pi$
$547$	−17836.0	−	10297.6i	−1.39417	−	0.804924i	−0.993774	+	0.111419i	$0.964460\pi$
$548$	−5216.92	−	14003.1i	−0.406672	−	1.09158i
$549$	887.744	−	512.539i	0.0690128	−	0.0398445i
$550$	20019.8	+	1675.29i	1.55209	+	0.129881i
$551$	−19972.9	+	8318.36i	−1.54424	+	0.643147i
$552$	−8779.67	−	2246.13i	−0.676970	−	0.173192i
$553$	531.835	+	921.165i	0.0408968	+	0.0708353i
$554$	1931.71	+	4102.03i	0.148142	+	0.314582i
$555$	3438.58	+	1985.27i	0.262990	+	0.151837i
$556$	13511.6	−	5033.78i	1.03061	−	0.383957i
$557$	11170.9	+	6449.52i	0.849777	+	0.490619i	0.860576	−	0.509323i	$-0.170104\pi$
$557$	11170.9	+	6449.52i	0.849777	+	0.490619i	−0.0107985	+	0.999942i	$0.503437\pi$
$558$	80.8989	−	966.746i	0.00613750	−	0.0733434i
$559$	26638.3			2.01552
$560$	−850.805	−	983.370i	−0.0642019	−	0.0742053i
$561$	−1071.01	+	1855.04i	−0.0806026	+	0.139608i
$562$	−404.657	+	4835.67i	−0.0303727	+	0.362955i
$563$		−	7425.42i		−	0.555851i	−0.960603	−	0.277926i	$-0.910353\pi$
$563$		−	7425.42i		−	0.555851i	0.960603	−	0.277926i	$-0.0896469\pi$
$564$	4575.42	+	3780.67i	0.341596	+	0.282260i
$565$	−3417.69	+	1973.21i	−0.254484	+	0.146926i
$566$	−736.465	+	1060.29i	−0.0546924	+	0.0787406i
$567$	2562.92	+	4439.11i	0.189828	+	0.328792i
$568$	−22387.1	+	6271.50i	−1.65377	+	0.463286i
$569$	1865.19			0.137421			0.0687106	−	0.997637i	$-0.478111\pi$
$569$	1865.19			0.137421			0.0687106	+	0.997637i	$0.478111\pi$
$570$	−3024.86	−	2740.14i	−0.222276	−	0.201354i
$571$		−	10029.2i		−	0.735044i	−0.930015	−	0.367522i	$-0.880206\pi$
$571$		−	10029.2i		−	0.735044i	0.930015	−	0.367522i	$-0.119794\pi$
$572$	−9767.74	−	26218.3i	−0.714003	−	1.91651i
$573$	−6590.03	+	3804.75i	−0.480458	+	0.277392i
$574$	752.996	+	523.024i	0.0547552	+	0.0380324i
$575$	4197.58	+	7270.43i	0.304437	+	0.527300i
$576$	−1332.05	+	809.877i	−0.0963581	+	0.0585848i
$577$	−17785.1			−1.28320			−0.641599	−	0.767040i	$-0.721729\pi$
$577$	−17785.1			−1.28320			−0.641599	+	0.767040i	$0.721729\pi$
$578$	−1149.37	+	13735.0i	−0.0827120	+	0.988412i
$579$	−9860.85	−	5693.16i	−0.707777	−	0.408635i
$580$	−4231.68	+	5121.24i	−0.302950	+	0.366635i
$581$		−	1362.28i		−	0.0972750i
$582$	−9898.24	−	828.301i	−0.704975	−	0.0589935i
$583$	12995.8	−	22509.5i	0.923213	−	1.59905i
$584$	14614.4	−	4094.05i	1.03553	−	0.290091i
$585$	−273.773	+	474.189i	−0.0193490	+	0.0335134i
$586$	−10292.9	−	21857.2i	−0.725592	−	1.54081i
$587$	−6144.71	+	3547.65i	−0.432060	+	0.249450i	−0.700224	−	0.713923i	$-0.746916\pi$
$587$	−6144.71	+	3547.65i	−0.432060	+	0.249450i	0.268164	+	0.963373i	$0.413583\pi$
$588$	2202.01	−	13064.9i	0.154438	−	0.916307i
$589$	−5665.08	+	7412.52i	−0.396308	+	0.518553i
$590$	−285.708	+	3414.22i	−0.0199363	+	0.238240i
$591$	6995.54	+	12116.6i	0.486901	+	0.843336i
$592$	−14323.0	+	2749.40i	−0.994377	+	0.190878i
$593$	1904.63	−	3298.91i	0.131895	−	0.228448i	−0.792512	−	0.609856i	$-0.791227\pi$
$593$	1904.63	−	3298.91i	0.131895	−	0.228448i	0.924407	+	0.381408i	$0.124561\pi$
$594$	−20771.3	+	9781.54i	−1.43477	+	0.675659i
$595$	−111.229	−	64.2183i	−0.00766380	−	0.00442470i
$596$	−2.08529	+	12.3724i	−0.000143317	+	0.000850323i
$597$		−	488.728i		−	0.0335047i
$598$	6669.90	−	9602.64i	0.456108	−	0.656658i
$599$	6335.15	−	10972.8i	0.432132	−	0.748474i	−0.564925	−	0.825142i	$-0.691095\pi$
$599$	6335.15	−	10972.8i	0.432132	−	0.748474i	0.997057	+	0.0766680i	$0.0244281\pi$
$600$	13805.6	+	3531.95i	0.939355	+	0.240319i
$601$	4805.35			0.326147			0.163073	−	0.986614i	$-0.447859\pi$
$601$	4805.35			0.326147			0.163073	+	0.986614i	$0.447859\pi$
$602$	4856.25	−	6991.54i	0.328781	−	0.473345i
$603$	−1429.74	+	825.459i	−0.0965562	+	0.0557467i
$604$	−13241.8	+	16025.4i	−0.892052	+	1.07957i
$605$	−6856.46	+	3958.58i	−0.460752	+	0.266015i
$606$	13990.3	−	6588.26i	0.937816	−	0.441633i
$607$	9703.21			0.648832			0.324416	−	0.945915i	$-0.394832\pi$
$607$	9703.21			0.648832			0.324416	+	0.945915i	$0.394832\pi$
$608$	14988.0	+	341.821i	0.999740	+	0.0228004i
$609$	9152.80			0.609015
$610$	−2738.45	+	1289.58i	−0.181765	+	0.0855961i
$611$	−6631.48	+	3828.69i	−0.439085	+	0.253506i
$612$	−98.0808	+	118.699i	−0.00647824	+	0.00784006i
$613$	13966.3	−	8063.43i	0.920216	−	0.531287i	0.0365118	−	0.999333i	$-0.488375\pi$
$613$	13966.3	−	8063.43i	0.920216	−	0.531287i	0.883704	+	0.468046i	$0.155042\pi$
$614$	14630.7	−	21063.8i	0.961641	−	1.38447i
$615$	883.593			0.0579348
$616$	−8662.02	−	2216.04i	−0.566563	−	0.144946i
$617$	−4323.51	+	7488.54i	−0.282104	+	0.488618i	−0.971903	−	0.235383i	$-0.924366\pi$
$617$	−4323.51	+	7488.54i	−0.282104	+	0.488618i	0.689799	+	0.724001i	$0.257699\pi$
$618$	−6245.45	+	8991.56i	−0.406519	+	0.585264i
$619$		−	3788.37i		−	0.245989i	−0.992407	−	0.122995i	$-0.960750\pi$
$619$		−	3788.37i		−	0.245989i	0.992407	−	0.122995i	$-0.0392498\pi$
$620$	−476.100	+	2824.79i	−0.0308397	+	0.182978i
$621$	−8308.84	−	4797.11i	−0.536912	−	0.309986i
$622$	22837.3	−	10754.5i	1.47217	−	0.693271i
$623$	−2015.47	+	3490.90i	−0.129612	+	0.224494i
$624$	−3741.30	−	19490.3i	−0.240019	−	1.25038i
$625$	−5968.99	−	10338.6i	−0.382016	−	0.661670i
$626$	1279.48	−	15289.8i	0.0816904	−	0.976205i
$627$	−27830.4	−	3609.19i	−1.77263	−	0.229884i
$628$	−3241.70	+	19233.6i	−0.205984	+	1.22214i
$629$	−1247.54	+	720.266i	−0.0790820	+	0.0456580i
$630$	74.5470	+	158.302i	0.00471432	+	0.0100109i
$631$	−4423.47	+	7661.68i	−0.279074	+	0.483370i	−0.971155	−	0.238450i	$-0.923361\pi$
$631$	−4423.47	+	7661.68i	−0.279074	+	0.483370i	0.692081	+	0.721820i	$0.256694\pi$
$632$	−3625.87	+	1015.75i	−0.228211	+	0.0639307i
$633$	−454.482	+	787.185i	−0.0285372	+	0.0494278i
$634$	15886.9	+	1329.44i	0.995188	+	0.0832790i
$635$		−	5965.90i		−	0.372834i
$636$	11743.8	−	14212.5i	0.732187	−	0.886103i
$637$	14803.2	+	8546.66i	0.920763	+	0.531603i
$638$	−3809.18	+	45519.9i	−0.236375	+	2.82469i
$639$	3128.43			0.193676
$640$	4119.07	−	2055.11i	0.254407	−	0.126930i
$641$	−9320.92	−	16144.3i	−0.574344	−	0.994792i	−0.996113	−	0.0880891i	$-0.971924\pi$
$641$	−9320.92	−	16144.3i	−0.574344	−	0.994792i	0.421769	−	0.906703i	$-0.361409\pi$
$642$	17300.7	+	12016.9i	1.06356	+	0.738739i
$643$	13897.4	−	8023.65i	0.852346	−	0.492102i	−0.00909547	−	0.999959i	$-0.502895\pi$
$643$	13897.4	−	8023.65i	0.852346	−	0.492102i	0.861442	+	0.507856i	$0.169562\pi$
$644$	−1304.38	−	3501.20i	−0.0798136	−	0.214234i
$645$		−	8204.12i		−	0.500832i
$646$	1409.67	−	453.337i	0.0858554	−	0.0276104i
$647$	−7100.80			−0.431470			−0.215735	−	0.976452i	$-0.569215\pi$
$647$	−7100.80			−0.431470			−0.215735	+	0.976452i	$0.569215\pi$
$648$	−17473.1	+	4894.90i	−1.05927	+	0.296743i
$649$	11778.9	+	20401.7i	0.712425	+	1.23396i
$650$	−10488.1	+	15099.7i	−0.632889	+	0.911169i
$651$	3417.94	−	1973.35i	0.205775	−	0.118804i
$652$	5963.29	+	4927.47i	0.358191	+	0.295973i
$653$			23545.3i			1.41103i	0.708696	+	0.705514i	$0.249284\pi$
$653$			23545.3i			1.41103i	−0.708696	+	0.705514i	$0.750716\pi$
$654$	572.603	−	6842.64i	0.0342363	−	0.409126i
$655$	−202.464	+	350.679i	−0.0120778	+	0.0209193i
$656$	−2454.45	+	2123.57i	−0.146083	+	0.126390i
$657$	−2042.24			−0.121272
$658$	−204.058	+	2438.50i	−0.0120897	+	0.144472i
$659$	3758.22	+	2169.81i	0.222154	+	0.128261i	0.606947	−	0.794742i	$-0.292394\pi$
$659$	3758.22	+	2169.81i	0.222154	+	0.128261i	−0.384793	+	0.923003i	$0.625727\pi$
$660$	−8074.79	+	3008.29i	−0.476228	+	0.177421i
$661$	−18725.6	−	10811.2i	−1.10188	−	0.636169i	−0.165164	−	0.986266i	$-0.552815\pi$
$661$	−18725.6	−	10811.2i	−1.10188	−	0.636169i	−0.936713	+	0.350097i	$0.886149\pi$
$662$	−4398.36	−	9339.99i	−0.258228	−	0.548352i
$663$	−980.116	−	1697.61i	−0.0574126	−	0.0994416i
$664$	4672.07	+	1195.27i	0.273060	+	0.0698578i
$665$	216.409	−	1668.73i	0.0126195	−	0.0973091i
$666$	1955.68	+	163.655i	0.113785	+	0.00952175i
$667$	−16531.1	+	9544.22i	−0.959649	+	0.554054i
$668$	8612.99	+	23118.8i	0.498872	+	1.33906i
$669$	−15660.2	−	9041.41i	−0.905019	−	0.522513i
$670$	4410.35	−	2076.91i	0.254308	−	0.119758i
$671$	−10406.3	+	18024.3i	−0.598705	+	1.03699i
$672$	−5797.52	−	2571.20i	−0.332804	−	0.147599i
$673$	−17333.9			−0.992827			−0.496413	−	0.868086i	$-0.665350\pi$
$673$	−17333.9			−0.992827			−0.496413	+	0.868086i	$0.665350\pi$
$674$	−624.308	−	433.638i	−0.0356787	−	0.0247821i
$675$	13065.3	+	7543.25i	0.745012	+	0.430133i
$676$	7916.62	+	1334.29i	0.450422	+	0.0759157i
$677$		−	14293.2i		−	0.811421i	−0.914002	−	0.405711i	$-0.867024\pi$
$677$		−	14293.2i		−	0.811421i	0.914002	−	0.405711i	$-0.132976\pi$
$678$	−10980.4	+	15808.4i	−0.621974	+	0.895455i
$679$	−2047.57	−	3546.49i	−0.115727	−	0.200444i
$680$	317.837	−	325.127i	0.0179243	−	0.0183354i
$681$	6002.46	+	10396.6i	0.337760	+	0.585018i
$682$	8391.66	+	17819.8i	0.471163	+	1.00052i
$683$			18942.7i			1.06123i	0.847613	+	0.530615i	$0.178039\pi$
$683$			18942.7i			1.06123i	−0.847613	+	0.530615i	$0.821961\pi$
$684$	−1929.64	−	588.332i	−0.107868	−	0.0328881i
$685$		−	5937.61i		−	0.331189i
$686$	10552.0	−	4969.09i	0.587282	−	0.276561i
$687$	14458.5	+	25042.8i	0.802947	+	1.39075i
$688$	19717.3	+	22789.5i	1.09261	+	1.26285i
$689$	11892.9	+	20599.2i	0.657598	+	1.13899i
$690$	−2957.45	−	2054.21i	−0.163171	−	0.113337i
$691$		−	2165.53i		−	0.119220i	−0.998222	−	0.0596098i	$-0.981014\pi$
$691$		−	2165.53i		−	0.119220i	0.998222	−	0.0596098i	$-0.0189856\pi$
$692$	477.876	−	2835.33i	0.0262516	−	0.155756i
$693$	1041.93	+	601.559i	0.0571135	+	0.0329745i
$694$	10687.0	−	15386.1i	0.584545	−	0.841568i
$695$	5729.16			0.312690
$696$	−8030.74	+	31390.5i	−0.437363	+	1.70956i
$697$	−160.286	+	277.624i	−0.00871058	+	0.0150872i
$698$	−7201.19	−	15291.9i	−0.390500	−	0.829234i
$699$	−3338.14	−	1927.28i	−0.180630	−	0.104287i
$700$	2051.09	+	5505.48i	0.110748	+	0.297268i
$701$	−10719.2	+	6188.71i	−0.577542	+	0.333444i	−0.760156	−	0.649741i	$-0.774877\pi$
$701$	−10719.2	+	6188.71i	−0.577542	+	0.333444i	0.182614	+	0.983185i	$0.441544\pi$
$702$	1752.09	−	20937.5i	0.0941998	−	1.12569i
$703$	−14995.2	−	11460.2i	−0.804486	−	0.614835i
$704$	15200.3	−	27762.9i	0.813751	−	1.48630i
$705$	1179.17	+	2042.38i	0.0629931	+	0.109107i
$706$	−4053.65	+	1908.93i	−0.216092	+	0.101761i
$707$	5521.35	+	3187.75i	0.293708	+	0.169572i
$708$	5833.78	+	15658.9i	0.309671	+	0.831211i
$709$	−30096.3	−	17376.1i	−1.59421	−	0.920415i	−0.992574	−	0.121641i	$-0.961184\pi$
$709$	−30096.3	−	17376.1i	−1.59421	−	0.920415i	−0.601632	−	0.798774i	$-0.705482\pi$
$710$	−9205.59	−	770.339i	−0.486591	−	0.0407188i
$711$	506.687			0.0267261
$712$	−10204.0	−	9975.22i	−0.537095	−	0.525052i
$713$	−4115.48	+	7128.23i	−0.216166	+	0.374410i
$714$	−624.238	−	52.2373i	−0.0327192	−	0.00273800i
$715$		−	11117.1i		−	0.581476i
$716$	20840.9	+	17220.8i	1.08779	+	0.898844i
$717$	15587.5	−	8999.47i	0.811893	−	0.468747i
$718$	−18442.9	−	12810.2i	−0.958609	−	0.665841i
$719$	986.626	+	1708.89i	0.0511752	+	0.0886380i	0.890478	−	0.455026i	$-0.150370\pi$
$719$	986.626	+	1708.89i	0.0511752	+	0.0886380i	−0.839303	+	0.543664i	$0.817037\pi$
$720$	−608.321	+	116.771i	−0.0314872	+	0.00604419i
$721$	−4513.57			−0.233140
$722$	12583.5	+	14765.6i	0.648627	+	0.761106i
$723$		−	5076.92i		−	0.261152i
$724$	34832.2	−	12976.9i	1.78802	−	0.666135i
$725$	25994.4	−	15007.9i	1.33160	−	0.768797i
$726$	−22028.4	+	31714.3i	−1.12611	+	1.62125i
$727$	−11470.7	−	19867.9i	−0.585180	−	1.01356i	−0.994853	−	0.101329i	$-0.967691\pi$
$727$	−11470.7	−	19867.9i	−0.585180	−	1.01356i	0.409673	−	0.912232i	$-0.365643\pi$
$728$	5719.73	−	5850.92i	0.291191	−	0.297870i
$729$	−16991.0			−0.863230
$730$	6009.43	+	502.879i	0.304684	+	0.0254964i
$731$	2577.73	+	1488.25i	0.130425	+	0.0753009i
$732$	−9403.73	+	11380.5i	−0.474825	+	0.574640i
$733$			25024.7i			1.26100i	0.776191	+	0.630498i	$0.217149\pi$
$733$			25024.7i			1.26100i	−0.776191	+	0.630498i	$0.782851\pi$
$734$	−1113.48	+	13306.1i	−0.0559936	+	0.669126i
$735$	2632.22	−	4559.14i	0.132097	−	0.228798i
$736$	13152.2	−	1401.55i	0.658691	−	0.0701925i
$737$	16759.7	−	29028.6i	0.837652	−	1.45086i
$738$	395.115	−	186.066i	0.0197078	−	0.00928075i
$739$	10350.8	−	5976.04i	0.515237	−	0.297473i	−0.219746	−	0.975557i	$-0.570523\pi$
$739$	10350.8	−	5976.04i	0.515237	−	0.297473i	0.734984	+	0.678085i	$0.237190\pi$
$740$	−5714.41	−	963.127i	−0.283873	−	0.0478449i
$741$	15594.7	−	20405.0i	0.773124	−	1.01160i
$742$	7574.64	+	633.858i	0.374762	+	0.0313607i
$743$	777.408	+	1346.51i	0.0383854	+	0.0664854i	0.884580	−	0.466389i	$-0.154445\pi$
$743$	777.408	+	1346.51i	0.0383854	+	0.0664854i	−0.846194	+	0.532874i	$0.821112\pi$
$744$	3768.88	+	13453.6i	0.185718	+	0.662949i
$745$	−2.49269	+	4.31747i	−0.000122584	+	0.000212322i
$746$	6451.53	+	13699.9i	0.316632	+	0.672373i
$747$	−561.991	−	324.465i	−0.0275263	−	0.0158923i
$748$	519.587	−	3082.80i	0.0253984	−	0.150693i
$749$			8684.61i			0.423670i
$750$	9709.89	+	6744.39i	0.472740	+	0.328360i
$751$	15585.9	−	26995.6i	0.757307	−	1.31169i	−0.186912	−	0.982377i	$-0.559848\pi$
$751$	15585.9	−	26995.6i	0.757307	−	1.31169i	0.944219	−	0.329317i	$-0.106819\pi$
$752$	−8184.05	−	2839.40i	−0.396864	−	0.137689i
$753$	35233.6			1.70516
$754$	−34332.9	−	23847.3i	−1.65826	−	1.15181i
$755$	−7153.43	+	4130.03i	−0.344821	+	0.199082i
$756$	−5175.90	−	4276.85i	−0.249002	−	0.205751i
$757$	17756.7	−	10251.9i	0.852549	−	0.492219i	−0.00896105	−	0.999960i	$-0.502852\pi$
$757$	17756.7	−	10251.9i	0.852549	−	0.492219i	0.861510	+	0.507740i	$0.169519\pi$
$758$	13578.3	+	28833.8i	0.650643	+	1.38165i
$759$	−24759.2			−1.18406
$760$	5533.20	+	2206.35i	0.264093	+	0.105306i
$761$	30533.3			1.45444			0.727222	−	0.686403i	$-0.240811\pi$
$761$	30533.3			1.45444			0.727222	+	0.686403i	$0.240811\pi$
$762$	−12396.6	−	26324.4i	−0.589347	−	1.25149i
$763$	2451.68	−	1415.48i	0.116326	−	0.0671609i
$764$	7074.36	−	8561.49i	0.335002	−	0.405424i
$765$	−52.9849	+	30.5909i	−0.00250415	+	0.00144577i
$766$	−4860.11	−	3375.79i	−0.229247	−	0.159232i
$767$	−21558.6			−1.01491
$768$	13905.0	−	17627.2i	0.653325	−	0.828213i
$769$	8105.11	−	14038.5i	0.380075	−	0.658309i	−0.610997	−	0.791633i	$-0.709231\pi$
$769$	8105.11	−	14038.5i	0.380075	−	0.658309i	0.991073	+	0.133323i	$0.0425648\pi$
$770$	−2917.82	−	2026.69i	−0.136560	−	0.0948529i
$771$			6808.35i			0.318024i
$772$	16387.3	+	2761.97i	0.763978	+	0.128764i
$773$	−21339.9	−	12320.6i	−0.992942	−	0.573275i	−0.0867894	−	0.996227i	$-0.527661\pi$
$773$	−21339.9	−	12320.6i	−0.992942	−	0.573275i	−0.906152	+	0.422951i	$0.860994\pi$
$774$	−1727.62	−	3668.62i	−0.0802298	−	0.170369i
$775$	6471.42	−	11208.8i	0.299949	−	0.519526i
$776$	13959.6	−	3910.63i	0.645774	−	0.180906i
$777$	3991.99	+	6914.34i	0.184314	+	0.319241i
$778$	15657.3	+	1310.23i	0.721521	+	0.0603781i
$779$	−4165.08	−	540.149i	−0.191565	−	0.0248432i
$780$	1310.59	−	7776.00i	0.0601626	−	0.356956i
$781$	−55008.1	+	31758.9i	−2.52029	+	1.45509i
$782$	1181.92	−	556.587i	0.0540479	−	0.0254521i
$783$	−17151.4	+	29707.1i	−0.782811	+	1.35587i
$784$	3645.37	+	18990.5i	0.166061	+	0.865094i
$785$	−3875.04	+	6711.76i	−0.176186	+	0.305163i
$786$	−164.691	+	1968.07i	−0.00747372	+	0.0893113i
$787$			16195.9i			0.733570i	0.930306	+	0.366785i	$0.119542\pi$
$787$			16195.9i			0.733570i	−0.930306	+	0.366785i	$0.880458\pi$
$788$	−15741.4	−	13007.1i	−0.711631	−	0.588021i
$789$	−9721.29	−	5612.59i	−0.438640	−	0.253249i
$790$	−1490.96	−	124.766i	−0.0671467	−	0.00561895i
$791$	−7935.49			−0.356705
$792$	−2977.31	+	3045.60i	−0.133578	+	0.136642i
$793$	−9523.17	−	16494.6i	−0.426453	−	0.738639i
$794$	−23487.4	+	33814.7i	−1.04979	+	1.51138i
$795$	6344.19	−	3662.82i	0.283025	−	0.163405i
$796$	249.023	+	668.421i	0.0110884	+	0.0297633i
$797$			13372.3i			0.594319i	0.954828	+	0.297160i	$0.0960393\pi$
$797$			13372.3i			0.594319i	−0.954828	+	0.297160i	$0.903961\pi$
$798$	−2512.57	−	7812.92i	−0.111459	−	0.346585i
$799$	−855.620			−0.0378844
$800$	−20681.3	+	2203.87i	−0.913991	+	0.0973982i
$801$	960.085	+	1662.92i	0.0423507	+	0.0733536i
$802$	12630.8	+	8773.24i	0.556122	+	0.386277i
$803$	35909.4	−	20732.3i	1.57810	−	0.911117i
$804$	15145.0	−	18328.6i	0.664330	−	0.803982i
$805$		−	1484.58i		−	0.0649993i
$806$	−17962.5	−	1503.13i	−0.784989	−	0.0656892i
$807$	6133.57	−	10623.7i	0.267549	−	0.463408i
$808$	−15777.2	+	16139.1i	−0.686931	+	0.702687i
$809$	−31075.8			−1.35052			−0.675259	−	0.737581i	$-0.735968\pi$
$809$	−31075.8			−1.35052			−0.675259	+	0.737581i	$0.735968\pi$
$810$	−7184.95	−	601.249i	−0.311671	−	0.0260811i
$811$	38107.1	+	22001.2i	1.64997	+	0.952608i	0.977083	+	0.212860i	$0.0682778\pi$
$811$	38107.1	+	22001.2i	1.64997	+	0.952608i	0.672884	+	0.739748i	$0.265055\pi$
$812$	−12518.0	+	4663.64i	−0.541006	+	0.201554i
$813$	31315.1	+	18079.8i	1.35089	+	0.779934i
$814$	−36048.7	+	16975.9i	−1.55222	+	0.730966i
$815$	1536.85	+	2661.90i	0.0660534	+	0.114408i
$816$	726.865	−	2095.06i	0.0311830	−	0.0898795i
$817$	−5015.26	+	38672.6i	−0.214763	+	1.65604i
$818$	1101.95	−	13168.4i	0.0471014	−	0.562864i
$819$	−953.505	+	550.507i	−0.0406815	+	0.0234875i
$820$	−1208.47	+	450.219i	−0.0514652	+	0.0191736i
$821$	12045.0	+	6954.20i	0.512027	+	0.295619i	0.733666	−	0.679510i	$-0.237807\pi$
$821$	12045.0	+	6954.20i	0.512027	+	0.295619i	−0.221640	+	0.975129i	$0.571141\pi$
$822$	−12337.8	−	26199.6i	−0.523517	−	1.11170i
$823$	−3643.46	+	6310.66i	−0.154317	+	0.267285i	−0.932810	−	0.360368i	$-0.882651\pi$
$823$	−3643.46	+	6310.66i	−0.154317	+	0.267285i	0.778493	+	0.627653i	$0.215984\pi$
$824$	3960.24	−	15479.8i	0.167429	−	0.654446i
$825$	38932.8			1.64299
$826$	−3930.22	+	5658.32i	−0.165557	+	0.238351i
$827$	−3443.56	−	1988.14i	−0.144794	−	0.0835967i	0.425853	−	0.904792i	$-0.359974\pi$
$827$	−3443.56	−	1988.14i	−0.144794	−	0.0835967i	−0.570647	+	0.821196i	$0.693307\pi$
$828$	−1755.05	−	295.803i	−0.0736622	−	0.0124153i
$829$		−	36952.6i		−	1.54815i	−0.633094	−	0.774075i	$-0.718215\pi$
$829$		−	36952.6i		−	1.54815i	0.633094	−	0.774075i	$-0.281785\pi$
$830$	1573.80	+	1093.14i	0.0658160	+	0.0457151i
$831$	4393.41	+	7609.61i	0.183400	+	0.317659i
$832$	15047.8	+	24750.0i	0.627030	+	1.03131i
$833$	954.986	+	1654.08i	0.0397218	+	0.0688002i
$834$	25279.8	−	11904.7i	1.04960	−	0.494276i
$835$			9802.82i			0.406276i
$836$	39901.9	−	9244.30i	1.65076	−	0.382441i
$837$			14791.4i			0.610832i
$838$	−12564.6	−	26681.2i	−0.517945	−	1.09987i
$839$	10745.5	+	18611.8i	0.442166	+	0.765854i	0.997850	−	0.0655394i	$-0.0208768\pi$
$839$	10745.5	+	18611.8i	0.442166	+	0.765854i	−0.555684	+	0.831394i	$0.687543\pi$
$840$	−1801.98	−	1761.58i	−0.0740170	−	0.0723573i
$841$	21929.5	+	37983.0i	0.899156	+	1.55738i
$842$	6900.98	−	9935.33i	0.282451	−	0.406644i
$843$			9403.99i			0.384212i
$844$	220.486	−	1308.18i	0.00899224	−	0.0533526i
$845$	2762.58	+	1594.98i	0.112468	+	0.0649337i
$846$	957.371	+	664.980i	0.0389067	+	0.0270242i
$847$	−15919.9			−0.645826
$848$	−8819.93	+	25421.9i	−0.357167	+	1.02947i
$849$	−1250.90	+	2166.63i	−0.0505664	+	0.0875836i
$850$	−1858.52	+	875.208i	−0.0749961	+	0.0353169i
$851$	−14420.1	−	8325.43i	−0.580862	−	0.335361i
$852$	−42220.2	+	15729.3i	−1.69770	+	0.632485i
$853$	27559.1	−	15911.3i	1.10622	−	0.638677i	0.168372	−	0.985723i	$-0.446149\pi$
$853$	27559.1	−	15911.3i	1.10622	−	0.638677i	0.937848	+	0.347047i	$0.112816\pi$
$854$	−6065.33	−	507.557i	−0.243034	−	0.0203375i
$855$	−636.869	−	486.733i	−0.0254742	−	0.0194689i
$856$	−29784.8	−	7619.94i	−1.18928	−	0.304257i
$857$	−11832.5	−	20494.5i	−0.471633	−	0.816893i	0.527840	−	0.849344i	$-0.323002\pi$
$857$	−11832.5	−	20494.5i	−0.471633	−	0.816893i	−0.999473	+	0.0324509i	$0.989669\pi$
$858$	−23100.3	−	49054.0i	−0.919152	−	1.95184i
$859$	25238.7	+	14571.5i	1.00248	+	0.578783i	0.908982	−	0.416836i	$-0.136861\pi$
$859$	25238.7	+	14571.5i	1.00248	+	0.578783i	0.0935000	+	0.995619i	$0.470194\pi$
$860$	4180.26	+	11220.6i	0.165751	+	0.444904i
$861$	1538.70	+	888.369i	0.0609045	+	0.0351632i
$862$	1415.52	−	16915.5i	0.0559312	−	0.668380i
$863$	−49067.9			−1.93545			−0.967724	−	0.252014i	$-0.918907\pi$
$863$	−49067.9			−1.93545			−0.967724	+	0.252014i	$0.918907\pi$
$864$	19209.3	−	13998.8i	0.756381	−	0.551212i
$865$	571.240	−	989.417i	0.0224540	−	0.0388915i
$866$	3223.54	−	38521.5i	0.126490	−	1.51156i
$867$			26710.7i			1.04630i
$868$	−3669.14	+	4440.45i	−0.143478	+	0.173639i
$869$	−8909.22	+	5143.74i	−0.347785	+	0.200793i
$870$	−7344.55	+	10573.9i	−0.286211	+	0.412058i
$871$	15337.3	+	26565.0i	0.596654	+	1.03343i
$872$	2703.41	+	9650.25i	0.104987	+	0.374769i
$873$	−1950.75			−0.0756275
$874$	12685.1	+	11491.1i	0.490937	+	0.444727i
$875$			4874.16i			0.188316i
$876$	27561.5	−	10268.1i	1.06303	−	0.396036i
$877$	6393.42	−	3691.24i	0.246169	−	0.142126i	−0.371840	−	0.928297i	$-0.621273\pi$
$877$	6393.42	−	3691.24i	0.246169	−	0.142126i	0.618009	+	0.786171i	$0.287940\pi$
$878$	−37893.5	−	26320.5i	−1.45654	−	1.01170i
$879$	−23409.8	−	40547.0i	−0.898286	−	1.55588i
$880$	9510.85	−	8228.73i	0.364330	−	0.315216i
$881$	22901.8			0.875802			0.437901	−	0.899023i	$-0.355722\pi$
$881$	22901.8			0.875802			0.437901	+	0.899023i	$0.355722\pi$
$882$	216.986	−	2593.00i	0.00828379	−	0.0989917i
$883$	−4238.68	−	2447.20i	−0.161543	−	0.0932671i	0.417049	−	0.908884i	$-0.363064\pi$
$883$	−4238.68	−	2447.20i	−0.161543	−	0.0932671i	−0.578592	+	0.815617i	$0.696398\pi$
$884$	2205.47	+	1822.38i	0.0839116	+	0.0693362i
$885$			6639.68i			0.252192i
$886$	−45173.0	−	3780.15i	−1.71288	−	0.143337i
$887$	20720.0	−	35888.1i	0.784341	−	1.35852i	−0.145052	−	0.989424i	$-0.546335\pi$
$887$	20720.0	−	35888.1i	0.784341	−	1.35852i	0.929392	−	0.369094i	$-0.120332\pi$
$888$	−27216.0	+	7624.27i	−1.02850	+	0.288123i
$889$	5998.15	−	10389.1i	0.226289	−	0.391945i
$890$	−2415.64	−	5129.64i	−0.0909801	−	0.193198i
$891$	−42933.7	+	24787.8i	−1.61429	+	0.932011i
$892$	26024.9	+	4386.33i	0.976882	+	0.164647i
$893$	−4309.84	−	10348.2i	−0.161504	−	0.387783i
$894$	−2.02764	+	24.2304i	−7.58550e−5	+	0.000906471i
$895$	5371.08	+	9302.98i	0.200598	+	0.347446i
$896$	9239.23	+	562.544i	0.344488	+	0.0209746i
$897$	11329.0	−	19622.4i	0.421699	−	0.730404i
$898$	−35415.8	+	16677.9i	−1.31608	+	0.619765i
$899$	25486.0	+	14714.3i	0.945500	+	0.545885i
$900$	2759.74	+	465.137i	0.102213	+	0.0172273i
$901$			2657.78i			0.0982726i
$902$	−5058.53	+	7282.75i	−0.186730	+	0.268835i
$903$	8248.47	−	14286.8i	0.303978	−	0.526505i
$904$	6962.66	−	27215.6i	0.256167	−	1.00130i
$905$	14769.5			0.542493
$906$	−22982.5	+	33087.9i	−0.842763	+	1.21332i
$907$	−12042.1	+	6952.48i	−0.440849	+	0.254524i	−0.703958	−	0.710242i	$-0.748585\pi$
$907$	−12042.1	+	6952.48i	−0.440849	+	0.254524i	0.263109	+	0.964766i	$0.415252\pi$
$908$	−13506.8	−	11160.7i	−0.493654	−	0.407907i
$909$	2630.13	−	1518.51i	0.0959693	−	0.0554079i
$910$	2941.30	−	1385.11i	0.107146	−	0.0504571i
$911$	−47260.7			−1.71879			−0.859395	−	0.511313i	$-0.829159\pi$
$911$	−47260.7			−1.71879			−0.859395	+	0.511313i	$0.829159\pi$
$912$	28999.8	−	1762.01i	1.05294	−	0.0639758i
$913$	13175.5			0.477597
$914$	−14131.4	+	6654.71i	−0.511406	+	0.240829i
$915$	−5080.05	+	2932.97i	−0.183543	+	0.105968i
$916$	−32534.6	−	26883.3i	−1.17355	−	0.969705i
$917$	−705.149	+	407.118i	−0.0253937	+	0.0146611i
$918$	1339.30	−	1928.19i	0.0481521	−	0.0693245i
$919$	22188.4			0.796438			0.398219	−	0.917290i	$-0.369628\pi$
$919$	22188.4			0.796438			0.398219	+	0.917290i	$0.369628\pi$
$920$	5091.51	+	1302.58i	0.182459	+	0.0466791i
$921$	24850.6	−	43042.6i	0.889095	−	1.53996i
$922$	27930.1	−	40210.9i	0.997646	−	1.43631i
$923$		−	58127.3i		−	2.07290i
$924$	−17086.1	−	2879.75i	−0.608324	−	0.102529i
$925$	22674.9	+	13091.4i	0.805996	+	0.465342i
$926$	−21690.6	+	10214.5i	−0.769760	+	0.362493i
$927$	−1075.04	+	1862.02i	−0.0380894	+	0.0659727i
$928$	−5011.03	−	47023.8i	−0.177258	−	1.66340i
$929$	−15325.1	−	26543.9i	−0.541228	−	0.937435i	−0.998834	−	0.0482796i	$-0.984626\pi$
$929$	−15325.1	−	26543.9i	−0.541228	−	0.937435i	0.457606	−	0.889155i	$-0.348707\pi$
$930$	−462.938	+	5532.13i	−0.0163229	+	0.195060i
$931$	−15194.8	+	19881.8i	−0.534898	+	0.699892i
$932$	5547.50	+	934.996i	0.194973	+	0.0328614i
$933$	42365.1	−	24459.5i	1.48657	−	0.858273i
$934$	−6065.83	−	12880.9i	−0.212505	−	0.451259i
$935$	621.100	−	1075.78i	0.0217242	−	0.0376274i
$936$	−1051.41	−	3753.17i	−0.0367161	−	0.131064i
$937$	−25506.0	+	44177.7i	−0.889268	+	1.54026i	−0.0485257	+	0.998822i	$0.515452\pi$
$937$	−25506.0	+	44177.7i	−0.889268	+	1.54026i	−0.840742	+	0.541435i	$0.817881\pi$
$938$	9768.37	+	817.434i	0.340031	+	0.0284543i
$939$		−	29734.3i		−	1.03338i
$940$	−2653.38	−	2192.49i	−0.0920677	−	0.0760756i
$941$	−9061.27	−	5231.53i	−0.313910	−	0.181236i	0.334765	−	0.942302i	$-0.391343\pi$
$941$	−9061.27	−	5231.53i	−0.313910	−	0.181236i	−0.648675	+	0.761066i	$0.724676\pi$
$942$	−3152.08	+	37667.5i	−0.109024	+	1.30284i
$943$	−3705.44			−0.127959
$944$	−15957.4	−	18443.7i	−0.550180	−	0.635903i
$945$	−1333.93	−	2310.43i	−0.0459181	−	0.0795325i
$946$	67620.0	+	46968.2i	2.32401	+	1.61424i
$947$	−3818.37	+	2204.54i	−0.131025	+	0.0756471i	−0.564080	−	0.825720i	$-0.690769\pi$
$947$	−3818.37	+	2204.54i	−0.131025	+	0.0756471i	0.433055	+	0.901368i	$0.357436\pi$
$948$	−6838.08	+	2547.55i	−0.234273	+	0.0872792i
$949$			37945.6i			1.29796i
$950$	−19946.7	−	18069.2i	−0.681217	−	0.617097i
$951$	30895.4			1.05347
$952$	880.370	−	246.626i	0.0299716	−	0.00839621i
$953$	19342.4	+	33502.1i	0.657464	+	1.13876i	0.981270	+	0.192637i	$0.0617041\pi$
$953$	19342.4	+	33502.1i	0.657464	+	1.13876i	−0.323806	+	0.946123i	$0.604963\pi$
$954$	2065.61	−	2973.85i	0.0701012	−	0.100924i
$955$	3821.69	−	2206.45i	0.129494	−	0.0747635i
$956$	−16733.1	+	20250.7i	−0.566097	+	0.685098i
$957$			88523.1i			2.99012i
$958$	354.467	−	4235.89i	0.0119544	−	0.142855i
$959$	5969.70	−	10339.8i	0.201013	−	0.348165i
$960$	7622.58	−	4634.46i	0.256269	−	0.155809i
$961$	−17101.3			−0.574043
$962$	3040.76	−	36337.2i	0.101911	−	1.21784i
$963$	3582.73	+	2068.49i	0.119888	+	0.0692171i
$964$	2586.85	+	6943.57i	0.0864284	+	0.231989i
$965$	5718.51	+	3301.58i	0.190762	+	0.110136i
$966$	−3084.82	−	6550.67i	−0.102746	−	0.218183i
$967$	−18421.0	−	31906.1i	−0.612595	−	1.06105i	−0.990801	−	0.135325i	$-0.956792\pi$
$967$	−18421.0	−	31906.1i	−0.612595	−	1.06105i	0.378206	−	0.925721i	$-0.376541\pi$
$968$	13968.3	−	54599.0i	0.463798	−	1.81289i
$969$	2649.07	−	1103.29i	0.0878229	−	0.0365766i
$970$	5740.19	+	480.349i	0.190007	+	0.0159001i
$971$	26691.1	−	15410.1i	0.882140	−	0.509304i	0.0107765	−	0.999942i	$-0.496570\pi$
$971$	26691.1	−	15410.1i	0.882140	−	0.509304i	0.871363	+	0.490638i	$0.163236\pi$
$972$	−6375.25	+	2375.12i	−0.210377	+	0.0783767i
$973$	9976.84	+	5760.13i	0.328718	+	0.189786i
$974$	−24694.5	+	11629.0i	−0.812384	+	0.382565i
$975$	−17814.3	+	30855.3i	−0.585144	+	1.01350i
$976$	7062.48	−	20356.3i	0.231624	−	0.667613i
$977$	13392.6			0.438555			0.219278	−	0.975662i	$-0.429630\pi$
$977$	13392.6			0.438555			0.219278	+	0.975662i	$0.429630\pi$
$978$	12312.5	+	8552.16i	0.402568	+	0.279620i
$979$	−33762.9	−	19493.0i	−1.10221	−	0.636364i
$980$	−1276.99	+	7576.62i	−0.0416245	+	0.246965i
$981$		−	1348.55i		−	0.0438897i
$982$	19734.7	−	28412.0i	0.641302	−	0.923281i
$983$	2753.68	+	4769.51i	0.0893476	+	0.154754i	0.907236	−	0.420623i	$-0.138188\pi$
$983$	2753.68	+	4769.51i	0.0893476	+	0.154754i	−0.817888	+	0.575378i	$0.804855\pi$
$984$	−4396.82	+	4497.67i	−0.142445	+	0.145712i
$985$	−4056.86	−	7026.68i	−0.131231	−	0.227298i
$986$	−1990.00	−	4225.80i	−0.0642743	−	0.136488i
$987$			4742.18i			0.152933i
$988$	−10931.4	+	35853.3i	−0.351999	+	1.15450i
$989$			34404.9i			1.10618i
$990$	−1531.05	+	720.995i	−0.0491514	+	0.0231462i
$991$	−13422.3	−	23248.1i	−0.430245	−	0.745206i	0.566649	−	0.823959i	$-0.308239\pi$
$991$	−13422.3	−	23248.1i	−0.430245	−	0.745206i	−0.996894	+	0.0787530i	$0.974906\pi$
$992$	−12009.7	−	16479.8i	−0.384382	−	0.527454i
$993$	−10003.4	−	17326.5i	−0.319687	−	0.553715i
$994$	−15256.2	−	10596.8i	−0.486819	−	0.338140i
$995$			283.424i			0.00903028i
$996$	9215.81	+	1553.27i	0.293187	+	0.0494148i
$997$	−2888.90	−	1667.91i	−0.0917676	−	0.0529821i	0.453414	−	0.891300i	$-0.350206\pi$
$997$	−2888.90	−	1667.91i	−0.0917676	−	0.0529821i	−0.545182	+	0.838318i	$0.683539\pi$
$998$	−24976.8	+	35959.0i	−0.792211	+	1.14054i
$999$	−29922.3			−0.947649

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.4.p.a.45.9	✓	116
8.5	even	2	inner	152.4.p.a.45.48	yes	116
19.11	even	3	inner	152.4.p.a.125.48	yes	116
152.125	even	6	inner	152.4.p.a.125.9	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.4.p.a.45.9	✓	116	1.1	even	1	trivial
152.4.p.a.45.48	yes	116	8.5	even	2	inner
152.4.p.a.125.9	yes	116	152.125	even	6	inner
152.4.p.a.125.48	yes	116	19.11	even	3	inner

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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	152.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.55889 + 1.20502i) q^{2} +(-4.74696 + 2.74066i) q^{3} +(5.09583 - 6.16705i) q^{4} +(2.75286 - 1.58936i) q^{5} +(8.84438 - 12.7332i) q^{6} +6.39182 q^{7} +(-5.60823 + 21.9214i) q^{8} +(1.52239 - 2.63686i) q^{9} +(-5.12904 + 7.38426i) q^{10} +61.8197i q^{11} +(-7.28793 + 43.2406i) q^{12} +(-48.9939 - 28.2866i) q^{13} +(-16.3560 + 7.70229i) q^{14} +(-8.71179 + 15.0893i) q^{15} +(-12.0650 - 62.8525i) q^{16} +(-3.16069 - 5.47448i) q^{17} +(-0.718153 + 8.58197i) q^{18} +(50.2899 - 65.8022i) q^{19} +(4.22642 - 25.0761i) q^{20} +(-30.3417 + 17.5178i) q^{21} +(-74.4942 - 158.190i) q^{22} +(36.5338 - 63.2785i) q^{23} +(-33.4570 - 119.430i) q^{24} +(-57.4479 + 99.5026i) q^{25} +(159.456 + 13.3435i) q^{26} -131.306i q^{27} +(32.5716 - 39.4186i) q^{28} +(-226.243 - 130.622i) q^{29} +(4.10958 - 49.1097i) q^{30} -112.649 q^{31} +(106.612 + 146.294i) q^{32} +(-169.426 - 293.455i) q^{33} +(14.6847 + 10.1999i) q^{34} +(17.5957 - 10.1589i) q^{35} +(-8.50380 - 22.8257i) q^{36} -227.883i q^{37} +(-49.3930 + 228.981i) q^{38} +310.096 q^{39} +(19.4024 + 69.2600i) q^{40} +(-25.3562 - 43.9183i) q^{41} +(56.5316 - 81.3885i) q^{42} +(-407.779 + 235.431i) q^{43} +(381.245 + 315.023i) q^{44} -9.67854i q^{45} +(-17.2340 + 205.947i) q^{46} +(67.6767 - 117.219i) q^{47} +(229.529 + 265.292i) q^{48} -302.145 q^{49} +(27.0997 - 323.842i) q^{50} +(30.0073 + 17.3247i) q^{51} +(-424.110 + 158.004i) q^{52} +(-364.115 - 210.222i) q^{53} +(158.227 + 335.998i) q^{54} +(98.2539 + 170.181i) q^{55} +(-35.8468 + 140.118i) q^{56} +(-58.3826 + 450.187i) q^{57} +(736.334 + 61.6177i) q^{58} +(330.020 - 190.537i) q^{59} +(48.6624 + 130.618i) q^{60} +(291.562 + 168.333i) q^{61} +(288.255 - 135.744i) q^{62} +(9.73086 - 16.8543i) q^{63} +(-449.096 - 245.880i) q^{64} -179.831 q^{65} +(787.164 + 546.757i) q^{66} +(-469.568 - 271.105i) q^{67} +(-49.8677 - 8.40488i) q^{68} +400.507i q^{69} +(-32.7838 + 47.1988i) q^{70} +(513.735 + 889.815i) q^{71} +(49.2658 + 48.1611i) q^{72} +(-335.367 - 580.873i) q^{73} +(274.604 + 583.126i) q^{74} -629.779i q^{75} +(-149.537 - 645.457i) q^{76} +395.140i q^{77} +(-793.501 + 373.673i) q^{78} +(83.2056 + 144.116i) q^{79} +(-133.109 - 153.848i) q^{80} +(400.969 + 694.499i) q^{81} +(117.806 + 81.8271i) q^{82} -213.128i q^{83} +(-46.5831 + 276.386i) q^{84} +(-17.4018 - 10.0470i) q^{85} +(759.761 - 1093.83i) q^{86} +1431.96 q^{87} +(-1355.17 - 346.699i) q^{88} +(-315.321 + 546.152i) q^{89} +(11.6629 + 24.7663i) q^{90} +(-313.160 - 180.803i) q^{91} +(-204.071 - 547.763i) q^{92} +(534.738 - 308.731i) q^{93} +(-31.9249 + 381.504i) q^{94} +(33.8573 - 261.073i) q^{95} +(-907.023 - 402.265i) q^{96} +(-320.342 - 554.849i) q^{97} +(773.155 - 364.092i) q^{98} +(163.010 + 94.1139i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - q^{2} - 7 q^{4} - 11 q^{6} - 8 q^{7} - 46 q^{8} + 484 q^{9} - 44 q^{10} - 58 q^{12} + 24 q^{14} - 230 q^{15} - 67 q^{16} - 2 q^{17} + 196 q^{18} - 840 q^{20} + 137 q^{22} - 2 q^{23} + 77 q^{24}+ \cdots + 55 q^{98}+O(q^{100}) \) 116 * q - q^2 - 7 * q^4 - 11 * q^6 - 8 * q^7 - 46 * q^8 + 484 * q^9 - 44 * q^10 - 58 * q^12 + 24 * q^14 - 230 * q^15 - 67 * q^16 - 2 * q^17 + 196 * q^18 - 840 * q^20 + 137 * q^22 - 2 * q^23 + 77 * q^24 + 1248 * q^25 + 492 * q^26 - 96 * q^28 - 904 * q^30 + 208 * q^31 - 431 * q^32 - 180 * q^33 + 224 * q^34 - 84 * q^36 + 1552 * q^38 - 116 * q^39 - 58 * q^40 - 22 * q^41 - 568 * q^42 - 89 * q^44 - 1852 * q^46 + 202 * q^47 - 89 * q^48 + 5220 * q^49 - 942 * q^50 + 232 * q^52 - 231 * q^54 + 248 * q^55 - 2296 * q^56 - 398 * q^57 - 3620 * q^58 - 1378 * q^60 + 614 * q^62 - 796 * q^63 + 1550 * q^64 - 508 * q^65 - 797 * q^66 + 1860 * q^68 - 2968 * q^70 + 1986 * q^71 - 1596 * q^72 - 218 * q^73 + 2490 * q^74 - 4697 * q^76 + 1254 * q^78 + 1250 * q^79 + 3136 * q^80 - 3810 * q^81 - 169 * q^82 + 4136 * q^84 - 2360 * q^86 - 1404 * q^87 + 4434 * q^88 - 2 * q^89 + 1378 * q^90 - 1958 * q^92 - 4608 * q^94 + 438 * q^95 + 3410 * q^96 - 1586 * q^97 + 55 * q^98

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