LMFDB - Embedded newform 16.4.e.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,4,Mod(5,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("16.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	16.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.944030560092$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - x^{8} + 6x^{7} + 14x^{6} - 80x^{5} + 56x^{4} + 96x^{3} - 64x^{2} - 512x + 1024 $ x^10 - 2x^9 - x^8 + 6x^7 + 14x^6 - 80x^5 + 56x^4 + 96x^3 - 64x^2 - 512x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.1
Root			$1.28199 + 1.53509i$ of defining polynomial
Character	$\chi$	$=$	16.13
Dual form			16.4.e.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.81708 + 0.253099i) q^{2} +(5.49618 + 5.49618i) q^{3} +(7.87188 - 1.42600i) q^{4} +(-4.66372 + 4.66372i) q^{5} +(-16.8743 - 14.0921i) q^{6} -24.8965i q^{7} +(-21.8148 + 6.00953i) q^{8} +33.4160i q^{9} +(11.9577 - 14.3185i) q^{10} +(22.3431 - 22.3431i) q^{11} +(51.1028 + 35.4277i) q^{12} +(-11.2714 - 11.2714i) q^{13} +(6.30129 + 70.1355i) q^{14} -51.2653 q^{15} +(59.9330 - 22.4506i) q^{16} -88.4846 q^{17} +(-8.45756 - 94.1356i) q^{18} +(37.8187 + 37.8187i) q^{19} +(-30.0618 + 43.3627i) q^{20} +(136.836 - 136.836i) q^{21} +(-57.2873 + 68.5974i) q^{22} +48.1224i q^{23} +(-152.928 - 86.8686i) q^{24} +81.4994i q^{25} +(34.6053 + 28.8997i) q^{26} +(-35.2635 + 35.2635i) q^{27} +(-35.5025 - 195.982i) q^{28} +(10.4432 + 10.4432i) q^{29} +(144.419 - 12.9752i) q^{30} -96.9578 q^{31} +(-163.154 + 78.4142i) q^{32} +245.604 q^{33} +(249.268 - 22.3954i) q^{34} +(116.110 + 116.110i) q^{35} +(47.6513 + 263.047i) q^{36} +(-163.279 + 163.279i) q^{37} +(-116.110 - 96.9665i) q^{38} -123.899i q^{39} +(73.7114 - 129.765i) q^{40} -360.519i q^{41} +(-350.844 + 420.110i) q^{42} +(-100.249 + 100.249i) q^{43} +(144.021 - 207.744i) q^{44} +(-155.843 - 155.843i) q^{45} +(-12.1797 - 135.565i) q^{46} +220.669 q^{47} +(452.796 + 206.010i) q^{48} -276.837 q^{49} +(-20.6274 - 229.590i) q^{50} +(-486.327 - 486.327i) q^{51} +(-104.800 - 72.6542i) q^{52} +(-175.752 + 175.752i) q^{53} +(90.4150 - 108.265i) q^{54} +208.404i q^{55} +(149.616 + 543.113i) q^{56} +415.717i q^{57} +(-32.0624 - 26.7761i) q^{58} +(405.008 - 405.008i) q^{59} +(-403.555 + 73.1044i) q^{60} +(664.576 + 664.576i) q^{61} +(273.138 - 24.5399i) q^{62} +831.942 q^{63} +(439.771 - 262.193i) q^{64} +105.133 q^{65} +(-691.885 + 62.1621i) q^{66} +(-107.377 - 107.377i) q^{67} +(-696.540 + 126.179i) q^{68} +(-264.489 + 264.489i) q^{69} +(-356.480 - 297.705i) q^{70} +215.050i q^{71} +(-200.814 - 728.964i) q^{72} -668.587i q^{73} +(418.644 - 501.296i) q^{74} +(-447.935 + 447.935i) q^{75} +(351.634 + 243.775i) q^{76} +(-556.266 - 556.266i) q^{77} +(31.3588 + 349.035i) q^{78} -822.956 q^{79} +(-174.808 + 384.215i) q^{80} +514.603 q^{81} +(91.2471 + 1015.61i) q^{82} +(326.873 + 326.873i) q^{83} +(882.027 - 1272.28i) q^{84} +(412.668 - 412.668i) q^{85} +(257.037 - 307.783i) q^{86} +114.795i q^{87} +(-353.139 + 621.682i) q^{88} -262.733i q^{89} +(478.466 + 399.578i) q^{90} +(-280.619 + 280.619i) q^{91} +(68.6226 + 378.814i) q^{92} +(-532.898 - 532.898i) q^{93} +(-621.643 + 55.8512i) q^{94} -352.752 q^{95} +(-1327.70 - 465.745i) q^{96} -150.801 q^{97} +(779.871 - 70.0671i) q^{98} +(746.618 + 746.618i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{5} - 32 q^{6} - 44 q^{8} - 68 q^{10} + 18 q^{11} + 100 q^{12} - 2 q^{13} + 188 q^{14} - 124 q^{15} + 280 q^{16} - 4 q^{17} + 174 q^{18} - 26 q^{19} - 196 q^{20}+ \cdots + 4958 q^{99}+O(q^{100}) $ 10 * q - 2 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^5 - 32 * q^6 - 44 * q^8 - 68 * q^10 + 18 * q^11 + 100 * q^12 - 2 * q^13 + 188 * q^14 - 124 * q^15 + 280 * q^16 - 4 * q^17 + 174 * q^18 - 26 * q^19 - 196 * q^20 + 52 * q^21 - 588 * q^22 - 848 * q^24 - 264 * q^26 + 184 * q^27 + 280 * q^28 - 202 * q^29 + 1236 * q^30 + 368 * q^31 + 968 * q^32 - 4 * q^33 + 436 * q^34 + 476 * q^35 - 596 * q^36 - 10 * q^37 - 1232 * q^38 - 1336 * q^40 - 680 * q^42 - 838 * q^43 + 868 * q^44 + 194 * q^45 + 1132 * q^46 - 944 * q^47 + 1768 * q^48 + 94 * q^49 + 726 * q^50 - 1500 * q^51 - 236 * q^52 - 378 * q^53 - 1376 * q^54 - 488 * q^56 + 8 * q^58 + 1706 * q^59 - 192 * q^60 + 910 * q^61 - 80 * q^62 + 2628 * q^63 + 512 * q^64 - 492 * q^65 - 428 * q^66 + 1942 * q^67 - 880 * q^68 + 580 * q^69 + 160 * q^70 + 1092 * q^72 - 452 * q^74 - 2954 * q^75 - 1228 * q^76 - 268 * q^77 - 772 * q^78 - 4416 * q^79 - 2648 * q^80 + 482 * q^81 - 704 * q^82 - 2562 * q^83 + 1960 * q^84 - 12 * q^85 + 3764 * q^86 + 1528 * q^88 + 1896 * q^90 + 3332 * q^91 + 632 * q^92 - 2192 * q^93 - 3248 * q^94 + 6900 * q^95 - 4432 * q^96 - 4 * q^97 + 314 * q^98 + 4958 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−2.81708	+	0.253099i	−0.995988	+	0.0894841i
$2$	−2.81708	+	0.253099i	−0.995988	+	0.0894841i
$3$	5.49618	+	5.49618i	1.05774	+	1.05774i	0.998228	+	0.0595129i	$0.0189548\pi$
$3$	5.49618	+	5.49618i	1.05774	+	1.05774i	0.0595129	+	0.998228i	$0.481045\pi$
$4$	7.87188	−	1.42600i	0.983985	−	0.178250i
$5$	−4.66372	+	4.66372i	−0.417136	+	0.417136i	−0.884215	−	0.467079i	$-0.845306\pi$
$5$	−4.66372	+	4.66372i	−0.417136	+	0.417136i	0.467079	+	0.884215i	$0.345306\pi$
$6$	−16.8743	−	14.0921i	−1.14815	−	0.958846i
$7$		−	24.8965i		−	1.34429i	−0.740422	−	0.672143i	$-0.765374\pi$
$7$		−	24.8965i		−	1.34429i	0.740422	−	0.672143i	$-0.234626\pi$
$8$	−21.8148	+	6.00953i	−0.964087	+	0.265586i
$9$			33.4160i			1.23763i
$10$	11.9577	−	14.3185i	0.378136	−	0.452790i
$11$	22.3431	−	22.3431i	0.612427	−	0.612427i	−0.331151	−	0.943578i	$-0.607437\pi$
$11$	22.3431	−	22.3431i	0.612427	−	0.612427i	0.943578	+	0.331151i	$0.107437\pi$
$12$	51.1028	+	35.4277i	1.22934	+	0.852259i
$13$	−11.2714	−	11.2714i	−0.240471	−	0.240471i	0.576574	−	0.817045i	$-0.304389\pi$
$13$	−11.2714	−	11.2714i	−0.240471	−	0.240471i	−0.817045	+	0.576574i	$0.804389\pi$
$14$	6.30129	+	70.1355i	0.120292	+	1.33889i
$15$	−51.2653			−0.882443
$16$	59.9330	−	22.4506i	0.936454	−	0.350791i
$17$	−88.4846			−1.26239			−0.631196	−	0.775623i	$-0.717436\pi$
$17$	−88.4846			−1.26239			−0.631196	+	0.775623i	$0.717436\pi$
$18$	−8.45756	−	94.1356i	−0.110748	−	1.23266i
$19$	37.8187	+	37.8187i	0.456643	+	0.456643i	0.897552	−	0.440909i	$-0.145344\pi$
$19$	37.8187	+	37.8187i	0.456643	+	0.456643i	−0.440909	+	0.897552i	$0.645344\pi$
$20$	−30.0618	+	43.3627i	−0.336101	+	0.484810i
$21$	136.836	−	136.836i	1.42191	−	1.42191i
$22$	−57.2873	+	68.5974i	−0.555168	+	0.664773i
$23$			48.1224i			0.436270i	0.975919	+	0.218135i	$0.0699973\pi$
$23$			48.1224i			0.436270i	−0.975919	+	0.218135i	$0.930003\pi$
$24$	−152.928	−	86.8686i	−1.30068	−	0.738833i
$25$			81.4994i			0.651995i
$26$	34.6053	+	28.8997i	0.261025	+	0.217988i
$27$	−35.2635	+	35.2635i	−0.251351	+	0.251351i
$28$	−35.5025	−	195.982i	−0.239619	−	1.32276i
$29$	10.4432	+	10.4432i	0.0668705	+	0.0668705i	0.739751	−	0.672881i	$-0.234943\pi$
$29$	10.4432	+	10.4432i	0.0668705	+	0.0668705i	−0.672881	+	0.739751i	$0.734943\pi$
$30$	144.419	−	12.9752i	0.878903	−	0.0789646i
$31$	−96.9578			−0.561746			−0.280873	−	0.959745i	$-0.590624\pi$
$31$	−96.9578			−0.561746			−0.280873	+	0.959745i	$0.590624\pi$
$32$	−163.154	+	78.4142i	−0.901307	+	0.433181i
$33$	245.604			1.29558
$34$	249.268	−	22.3954i	1.25733	−	0.112964i
$35$	116.110	+	116.110i	0.560750	+	0.560750i
$36$	47.6513	+	263.047i	0.220608	+	1.21781i
$37$	−163.279	+	163.279i	−0.725484	+	0.725484i	−0.969717	−	0.244233i	$-0.921464\pi$
$37$	−163.279	+	163.279i	−0.725484	+	0.725484i	0.244233	+	0.969717i	$0.421464\pi$
$38$	−116.110	−	96.9665i	−0.495673	−	0.413949i
$39$		−	123.899i		−	0.508713i
$40$	73.7114	−	129.765i	0.291370	−	0.512941i
$41$		−	360.519i		−	1.37326i	−0.727008	−	0.686629i	$-0.759090\pi$
$41$		−	360.519i		−	1.37326i	0.727008	−	0.686629i	$-0.240910\pi$
$42$	−350.844	+	420.110i	−1.28896	+	1.54344i
$43$	−100.249	+	100.249i	−0.355531	+	0.355531i	−0.862163	−	0.506632i	$-0.830890\pi$
$43$	−100.249	+	100.249i	−0.355531	+	0.355531i	0.506632	+	0.862163i	$0.330890\pi$
$44$	144.021	−	207.744i	0.493454	−	0.711785i
$45$	−155.843	−	155.843i	−0.516260	−	0.516260i
$46$	−12.1797	−	135.565i	−0.0390392	−	0.434520i
$47$	220.669			0.684849			0.342425	−	0.939545i	$-0.388752\pi$
$47$	220.669			0.684849			0.342425	+	0.939545i	$0.388752\pi$
$48$	452.796	+	206.010i	1.36157	+	0.619479i
$49$	−276.837			−0.807104
$50$	−20.6274	−	229.590i	−0.0583432	−	0.649379i
$51$	−486.327	−	486.327i	−1.33528	−	1.33528i
$52$	−104.800	−	72.6542i	−0.279484	−	0.193756i
$53$	−175.752	+	175.752i	−0.455498	+	0.455498i	−0.897174	−	0.441676i	$-0.854384\pi$
$53$	−175.752	+	175.752i	−0.455498	+	0.455498i	0.441676	+	0.897174i	$0.354384\pi$
$54$	90.4150	−	108.265i	0.227850	−	0.272834i
$55$			208.404i			0.510931i
$56$	149.616	+	543.113i	0.357024	+	1.29601i
$57$			415.717i			0.966019i
$58$	−32.0624	−	26.7761i	−0.0725861	−	0.0606184i
$59$	405.008	−	405.008i	0.893687	−	0.893687i	−0.101181	−	0.994868i	$-0.532262\pi$
$59$	405.008	−	405.008i	0.893687	−	0.893687i	0.994868	+	0.101181i	$0.0322622\pi$
$60$	−403.555	+	73.1044i	−0.868311	+	0.157296i
$61$	664.576	+	664.576i	1.39492	+	1.39492i	0.813860	+	0.581061i	$0.197362\pi$
$61$	664.576	+	664.576i	1.39492	+	1.39492i	0.581061	+	0.813860i	$0.302638\pi$
$62$	273.138	−	24.5399i	0.559493	−	0.0502674i
$63$	831.942			1.66373
$64$	439.771	−	262.193i	0.858928	−	0.512096i
$65$	105.133			0.200619
$66$	−691.885	+	62.1621i	−1.29038	+	0.115934i
$67$	−107.377	−	107.377i	−0.195794	−	0.195794i	0.602400	−	0.798194i	$-0.294211\pi$
$67$	−107.377	−	107.377i	−0.195794	−	0.195794i	−0.798194	+	0.602400i	$0.794211\pi$
$68$	−696.540	+	126.179i	−1.24218	+	0.225022i
$69$	−264.489	+	264.489i	−0.461461	+	0.461461i
$70$	−356.480	−	297.705i	−0.608679	−	0.508322i
$71$			215.050i			0.359461i	0.983716	+	0.179731i	$0.0575226\pi$
$71$			215.050i			0.359461i	−0.983716	+	0.179731i	$0.942477\pi$
$72$	−200.814	−	728.964i	−0.328697	−	1.19318i
$73$		−	668.587i		−	1.07195i	−0.844235	−	0.535974i	$-0.819945\pi$
$73$		−	668.587i		−	1.07195i	0.844235	−	0.535974i	$-0.180055\pi$
$74$	418.644	−	501.296i	0.657654	−	0.787492i
$75$	−447.935	+	447.935i	−0.689642	+	0.689642i
$76$	351.634	+	243.775i	0.530726	+	0.367933i
$77$	−556.266	−	556.266i	−0.823277	−	0.823277i
$78$	31.3588	+	349.035i	0.0455217	+	0.506672i
$79$	−822.956			−1.17202			−0.586012	−	0.810303i	$-0.699303\pi$
$79$	−822.956			−1.17202			−0.586012	+	0.810303i	$0.699303\pi$
$80$	−174.808	+	384.215i	−0.244301	+	0.536956i
$81$	514.603			0.705902
$82$	91.2471	+	1015.61i	0.122885	+	1.36775i
$83$	326.873	+	326.873i	0.432277	+	0.432277i	0.889402	−	0.457125i	$-0.151121\pi$
$83$	326.873	+	326.873i	0.432277	+	0.432277i	−0.457125	+	0.889402i	$0.651121\pi$
$84$	882.027	−	1272.28i	1.14568	−	1.65259i
$85$	412.668	−	412.668i	0.526589	−	0.526589i
$86$	257.037	−	307.783i	0.322290	−	0.385919i
$87$			114.795i			0.141463i
$88$	−353.139	+	621.682i	−0.427781	+	0.753086i
$89$		−	262.733i		−	0.312918i	−0.987684	−	0.156459i	$-0.949992\pi$
$89$		−	262.733i		−	0.312918i	0.987684	−	0.156459i	$-0.0500079\pi$
$90$	478.466	+	399.578i	0.560386	+	0.467992i
$91$	−280.619	+	280.619i	−0.323262	+	0.323262i
$92$	68.6226	+	378.814i	0.0777652	+	0.429283i
$93$	−532.898	−	532.898i	−0.594182	−	0.594182i
$94$	−621.643	+	55.8512i	−0.682102	+	0.0612831i
$95$	−352.752			−0.380964
$96$	−1327.70	−	465.745i	−1.41154	−	0.495155i
$97$	−150.801			−0.157850			−0.0789251	−	0.996881i	$-0.525149\pi$
$97$	−150.801			−0.157850			−0.0789251	+	0.996881i	$0.525149\pi$
$98$	779.871	−	70.0671i	0.803866	−	0.0722229i
$99$	746.618	+	746.618i	0.757958	+	0.757958i
$100$	116.218	+	641.553i	0.116218	+	0.641553i
$101$	487.985	−	487.985i	0.480755	−	0.480755i	−0.424617	−	0.905373i	$-0.639591\pi$
$101$	487.985	−	487.985i	0.480755	−	0.480755i	0.905373	+	0.424617i	$0.139591\pi$
$102$	1493.11	+	1246.93i	1.44941	+	1.21044i
$103$		−	1840.58i		−	1.76075i	−0.474275	−	0.880377i	$-0.657290\pi$
$103$		−	1840.58i		−	1.76075i	0.474275	−	0.880377i	$-0.342710\pi$
$104$	313.620	+	178.148i	0.295701	+	0.167970i
$105$			1276.33i			1.18626i
$106$	450.625	−	539.590i	0.412911	−	0.494431i
$107$	−79.4098	+	79.4098i	−0.0717461	+	0.0717461i	−0.742069	−	0.670323i	$-0.766155\pi$
$107$	−79.4098	+	79.4098i	−0.0717461	+	0.0717461i	0.670323	+	0.742069i	$0.266155\pi$
$108$	−227.304	+	327.876i	−0.202522	+	0.292129i
$109$	952.979	+	952.979i	0.837421	+	0.837421i	0.988519	−	0.151098i	$-0.0482809\pi$
$109$	952.979	+	952.979i	0.837421	+	0.837421i	−0.151098	+	0.988519i	$0.548281\pi$
$110$	−52.7469	−	587.091i	−0.0457202	−	0.508881i
$111$	−1794.82			−1.53475
$112$	−558.942	−	1492.12i	−0.471563	−	1.25886i
$113$	−720.469			−0.599788			−0.299894	−	0.953973i	$-0.596951\pi$
$113$	−720.469			−0.599788			−0.299894	+	0.953973i	$0.596951\pi$
$114$	−105.218	−	1171.11i	−0.0864433	−	0.962144i
$115$	−224.430	−	224.430i	−0.181984	−	0.181984i
$116$	97.0993	+	67.3153i	0.0777193	+	0.0538799i
$117$	376.646	−	376.646i	0.297615	−	0.297615i
$118$	−1038.43	+	1243.45i	−0.810131	+	0.970072i
$119$			2202.96i			1.69702i
$120$	1118.34	−	308.080i	0.850752	−	0.234365i
$121$			332.571i			0.249865i
$122$	−2040.37	−	1703.96i	−1.51415	−	1.26450i
$123$	1981.48	−	1981.48i	1.45255	−	1.45255i
$124$	−763.240	+	138.262i	−0.552750	+	0.100131i
$125$	−963.056	−	963.056i	−0.689107	−	0.689107i
$126$	−2343.65	+	210.564i	−1.65705	+	0.148877i
$127$	2622.35			1.83225			0.916124	−	0.400895i	$-0.131301\pi$
$127$	2622.35			1.83225			0.916124	+	0.400895i	$0.131301\pi$
$128$	−1172.51	+	849.925i	−0.809658	+	0.586902i
$129$	−1101.97			−0.752119
$130$	−296.169	+	26.6092i	−0.199814	+	0.0179522i
$131$	657.574	+	657.574i	0.438569	+	0.438569i	0.891530	−	0.452961i	$-0.149632\pi$
$131$	657.574	+	657.574i	0.438569	+	0.438569i	−0.452961	+	0.891530i	$0.649632\pi$
$132$	1933.36	−	350.231i	1.27483	−	0.230937i
$133$	941.555	−	941.555i	0.613858	−	0.613858i
$134$	329.666	+	275.312i	0.212529	+	0.177488i
$135$		−	328.919i		−	0.209695i
$136$	1930.27	−	531.751i	1.21706	−	0.335274i
$137$			2511.52i			1.56623i	0.621874	+	0.783117i	$0.286371\pi$
$137$			2511.52i			1.56623i	−0.621874	+	0.783117i	$0.713629\pi$
$138$	678.146	−	812.030i	0.418316	−	0.500903i
$139$	−1086.02	+	1086.02i	−0.662697	+	0.662697i	−0.956015	−	0.293318i	$-0.905241\pi$
$139$	−1086.02	+	1086.02i	−0.662697	+	0.662697i	0.293318	+	0.956015i	$0.405241\pi$
$140$	1079.58	+	748.434i	0.651723	+	0.451816i
$141$	1212.84	+	1212.84i	0.724393	+	0.724393i
$142$	−54.4290	−	605.813i	−0.0321661	−	0.358019i
$143$	−503.677			−0.294543
$144$	750.210	+	2002.72i	0.434149	+	1.15898i
$145$	−97.4080			−0.0557882
$146$	169.219	+	1883.46i	0.0959222	+	1.06765i
$147$	−1521.54	−	1521.54i	−0.853706	−	0.853706i
$148$	−1052.48	+	1518.15i	−0.584547	+	0.843183i
$149$	−2284.63	+	2284.63i	−1.25614	+	1.25614i	−0.303214	+	0.952922i	$0.598060\pi$
$149$	−2284.63	+	2284.63i	−1.25614	+	1.25614i	−0.952922	+	0.303214i	$0.901940\pi$
$150$	1148.50	−	1375.24i	0.625163	−	0.748587i
$151$		−	2814.39i		−	1.51677i	−0.651809	−	0.758383i	$-0.725990\pi$
$151$		−	2814.39i		−	1.51677i	0.651809	−	0.758383i	$-0.274010\pi$
$152$	−1052.28	−	597.735i	−0.561521	−	0.318965i
$153$		−	2956.80i		−	1.56237i
$154$	1707.84	+	1426.25i	0.893645	+	0.746304i
$155$	452.184	−	452.184i	0.234325	−	0.234325i
$156$	−176.681	−	975.322i	−0.0906781	−	0.500566i
$157$	−906.308	−	906.308i	−0.460709	−	0.460709i	0.438179	−	0.898888i	$-0.355624\pi$
$157$	−906.308	−	906.308i	−0.460709	−	0.460709i	−0.898888	+	0.438179i	$0.855624\pi$
$158$	2318.33	−	208.290i	1.16732	−	0.104877i
$159$	−1931.93			−0.963598
$160$	395.203	−	1126.61i	0.195272	−	0.556663i
$161$	1198.08			0.586472
$162$	−1449.68	+	130.246i	−0.703070	+	0.0631670i
$163$	1392.36	+	1392.36i	0.669067	+	0.669067i	0.957500	−	0.288433i	$-0.0931342\pi$
$163$	1392.36	+	1392.36i	0.669067	+	0.669067i	−0.288433	+	0.957500i	$0.593134\pi$
$164$	−514.101	−	2837.96i	−0.244784	−	1.35127i
$165$	−1145.43	+	1145.43i	−0.540433	+	0.540433i
$166$	−1003.56	−	838.097i	−0.469225	−	0.391861i
$167$		−	1221.66i		−	0.566075i	−0.959109	−	0.283038i	$-0.908658\pi$
$167$		−	1221.66i		−	0.566075i	0.959109	−	0.283038i	$-0.0913421\pi$
$168$	−2162.73	+	3807.36i	−0.993202	+	1.74848i
$169$		−	1942.91i		−	0.884347i
$170$	−1058.07	+	1266.96i	−0.477356	+	0.571598i
$171$	−1263.75	+	1263.75i	−0.565155	+	0.565155i
$172$	−646.193	+	932.104i	−0.286464	+	0.413211i
$173$	−563.418	−	563.418i	−0.247606	−	0.247606i	0.572381	−	0.819988i	$-0.306020\pi$
$173$	−563.418	−	563.418i	−0.247606	−	0.247606i	−0.819988	+	0.572381i	$0.806020\pi$
$174$	−29.0545	−	323.387i	−0.0126587	−	0.140896i
$175$	2029.05			0.876468
$176$	837.474	−	1840.71i	0.358676	−	0.788344i
$177$	4451.99			1.89058
$178$	66.4976	+	740.141i	0.0280012	+	0.311662i
$179$	−2202.23	−	2202.23i	−0.919565	−	0.919565i	0.0774329	−	0.996998i	$-0.475328\pi$
$179$	−2202.23	−	2202.23i	−0.919565	−	0.919565i	−0.996998	+	0.0774329i	$0.975328\pi$
$180$	−1449.01	−	1004.55i	−0.600016	−	0.415969i
$181$	121.294	−	121.294i	0.0498104	−	0.0498104i	−0.681763	−	0.731573i	$-0.738786\pi$
$181$	121.294	−	121.294i	0.0498104	−	0.0498104i	0.731573	+	0.681763i	$0.238786\pi$
$182$	719.502	−	861.551i	0.293039	−	0.350892i
$183$			7305.26i			2.95093i
$184$	−289.193	−	1049.78i	−0.115867	−	0.420602i
$185$		−	1522.98i		−	0.605251i
$186$	1636.09	+	1366.34i	0.644968	+	0.538628i
$187$	−1977.02	+	1977.02i	−0.773124	+	0.773124i
$188$	1737.08	−	314.675i	0.673882	−	0.122074i
$189$	877.939	+	877.939i	0.337887	+	0.337887i
$190$	993.731	−	89.2813i	0.379436	−	0.0340902i
$191$	3927.65			1.48793			0.743966	−	0.668218i	$-0.232942\pi$
$191$	3927.65			1.48793			0.743966	+	0.668218i	$0.232942\pi$
$192$	3858.12	+	976.000i	1.45019	+	0.366858i
$193$	−3249.02			−1.21176			−0.605880	−	0.795556i	$-0.707179\pi$
$193$	−3249.02			−1.21176			−0.605880	+	0.795556i	$0.707179\pi$
$194$	424.817	−	38.1675i	0.157217	−	0.0141251i
$195$	577.833	+	577.833i	0.212202	+	0.212202i
$196$	−2179.23	+	394.769i	−0.794178	+	0.143866i
$197$	2420.90	−	2420.90i	0.875545	−	0.875545i	−0.117525	−	0.993070i	$-0.537496\pi$
$197$	2420.90	−	2420.90i	0.875545	−	0.875545i	0.993070	+	0.117525i	$0.0374961\pi$
$198$	−2292.25	−	1914.31i	−0.822743	−	0.687093i
$199$			1371.30i			0.488488i	0.969714	+	0.244244i	$0.0785397\pi$
$199$			1371.30i			0.488488i	−0.969714	+	0.244244i	$0.921460\pi$
$200$	−489.773	−	1777.89i	−0.173161	−	0.628580i
$201$		−	1180.33i		−	0.414198i
$202$	−1251.18	+	1498.20i	−0.435807	+	0.521847i
$203$	259.998	−	259.998i	0.0898931	−	0.0898931i
$204$	−4521.82	−	3134.81i	−1.55191	−	1.07588i
$205$	1681.36	+	1681.36i	0.572836	+	0.572836i
$206$	465.849	+	5185.06i	0.157559	+	1.75369i
$207$	−1608.06			−0.539941
$208$	−928.580	−	422.480i	−0.309546	−	0.140835i
$209$	1689.98			0.559321
$210$	−323.038	−	3595.52i	−0.106151	−	1.18150i
$211$	−1620.50	−	1620.50i	−0.528719	−	0.528719i	0.391471	−	0.920190i	$-0.371966\pi$
$211$	−1620.50	−	1620.50i	−0.528719	−	0.528719i	−0.920190	+	0.391471i	$0.871966\pi$
$212$	−1132.88	+	1634.12i	−0.367011	+	0.529396i
$213$	−1181.95	+	1181.95i	−0.380217	+	0.380217i
$214$	203.605	−	243.802i	0.0650382	−	0.0778784i
$215$		−	935.068i		−	0.296610i
$216$	557.350	−	981.184i	0.175569	−	0.309079i
$217$			2413.91i			0.755148i
$218$	−2925.82	−	2443.42i	−0.908997	−	0.759125i
$219$	3674.67	−	3674.67i	1.13384	−	1.13384i
$220$	297.185	+	1640.53i	0.0910736	+	0.502749i
$221$	997.347	+	997.347i	0.303569	+	0.303569i
$222$	5056.15	−	454.268i	1.52859	−	0.137335i
$223$	−419.617			−0.126007			−0.0630036	−	0.998013i	$-0.520068\pi$
$223$	−419.617			−0.126007			−0.0630036	+	0.998013i	$0.520068\pi$
$224$	1952.24	+	4061.97i	0.582320	+	1.21161i
$225$	−2723.38			−0.806929
$226$	2029.62	−	182.350i	0.597381	−	0.0536714i
$227$	−2133.64	−	2133.64i	−0.623853	−	0.623853i	0.322661	−	0.946515i	$-0.395423\pi$
$227$	−2133.64	−	2133.64i	−0.623853	−	0.623853i	−0.946515	+	0.322661i	$0.895423\pi$
$228$	592.813	+	3272.48i	0.172193	+	0.950548i
$229$	−1574.42	+	1574.42i	−0.454325	+	0.454325i	−0.896787	−	0.442462i	$-0.854105\pi$
$229$	−1574.42	+	1574.42i	−0.454325	+	0.454325i	0.442462	+	0.896787i	$0.354105\pi$
$230$	689.039	+	575.433i	0.197539	+	0.164969i
$231$		−	6114.67i		−	1.74163i
$232$	−290.574	−	165.057i	−0.0822289	−	0.0467091i
$233$			1194.86i			0.335957i	0.985791	+	0.167978i	$0.0537239\pi$
$233$			1194.86i			0.335957i	−0.985791	+	0.167978i	$0.946276\pi$
$234$	−965.712	+	1156.37i	−0.269789	+	0.323052i
$235$	−1029.14	+	1029.14i	−0.285675	+	0.285675i
$236$	2610.63	−	3765.71i	0.720075	−	1.03867i
$237$	−4523.12	−	4523.12i	−1.23970	−	1.23970i
$238$	−557.567	−	6205.91i	−0.151856	−	1.69021i
$239$	−4241.03			−1.14782			−0.573911	−	0.818917i	$-0.694575\pi$
$239$	−4241.03			−1.14782			−0.573911	+	0.818917i	$0.694575\pi$
$240$	−3072.49	+	1150.94i	−0.826367	+	0.309553i
$241$	−5571.19			−1.48910			−0.744548	−	0.667569i	$-0.767335\pi$
$241$	−5571.19			−1.48910			−0.744548	+	0.667569i	$0.767335\pi$
$242$	−84.1734	−	936.878i	−0.0223590	−	0.248863i
$243$	3780.46	+	3780.46i	0.998012	+	0.998012i
$244$	6179.15	+	4283.77i	1.62123	+	1.12394i
$245$	1291.09	−	1291.09i	0.336672	−	0.336672i
$246$	−5080.47	+	6083.49i	−1.31674	+	1.57670i
$247$		−	852.541i		−	0.219619i
$248$	2115.12	−	582.671i	0.541572	−	0.149192i
$249$			3593.11i			0.914474i
$250$	2956.75	+	2469.26i	0.748006	+	0.624678i
$251$	−482.728	+	482.728i	−0.121393	+	0.121393i	−0.765193	−	0.643801i	$-0.777357\pi$
$251$	−482.728	+	482.728i	−0.121393	+	0.121393i	0.643801	+	0.765193i	$0.277357\pi$
$252$	6548.95	−	1186.35i	1.63708	−	0.296560i
$253$	1075.20	+	1075.20i	0.267184	+	0.267184i
$254$	−7387.36	+	663.713i	−1.82490	+	0.163957i
$255$	4536.19			1.11399
$256$	3087.94	−	2691.07i	0.753891	−	0.656999i
$257$	8093.12			1.96434			0.982169	−	0.188002i	$-0.0602013\pi$
$257$	8093.12			1.96434			0.982169	+	0.188002i	$0.0602013\pi$
$258$	3104.35	−	278.909i	0.749102	−	0.0673027i
$259$	4065.08	+	4065.08i	0.975257	+	0.975257i
$260$	827.598	−	149.921i	0.197406	−	0.0357603i
$261$	−348.969	+	348.969i	−0.0827610	+	0.0827610i
$262$	−2018.87	−	1686.01i	−0.476054	−	0.397564i
$263$		−	410.300i		−	0.0961984i	−0.998843	−	0.0480992i	$-0.984684\pi$
$263$		−	410.300i		−	0.0961984i	0.998843	−	0.0480992i	$-0.0153164\pi$
$264$	−5357.79	+	1475.96i	−1.24905	+	0.344088i
$265$		−	1639.32i		−	0.380009i
$266$	−2414.13	+	2890.74i	−0.556465	+	0.666326i
$267$	1444.03	−	1444.03i	0.330986	−	0.330986i
$268$	−998.378	−	692.139i	−0.227558	−	0.157758i
$269$	−4.77962	−	4.77962i	−0.00108334	−	0.00108334i	0.706565	−	0.707648i	$-0.250244\pi$
$269$	−4.77962	−	4.77962i	−0.00108334	−	0.00108334i	−0.707648	+	0.706565i	$0.750244\pi$
$270$	83.2490	+	926.590i	0.0187643	+	0.208854i
$271$	−2833.98			−0.635247			−0.317623	−	0.948217i	$-0.602885\pi$
$271$	−2833.98			−0.635247			−0.317623	+	0.948217i	$0.602885\pi$
$272$	−5303.15	+	1986.54i	−1.18217	+	0.442836i
$273$	−3084.67			−0.683855
$274$	−635.665	−	7075.17i	−0.140153	−	1.55995i
$275$	1820.95	+	1820.95i	0.399300	+	0.399300i
$276$	−1704.87	+	2459.19i	−0.371815	+	0.536326i
$277$	1525.80	−	1525.80i	0.330962	−	0.330962i	−0.521989	−	0.852952i	$-0.674810\pi$
$277$	1525.80	−	1525.80i	0.330962	−	0.330962i	0.852952	+	0.521989i	$0.174810\pi$
$278$	2784.53	−	3334.27i	0.600738	−	0.719339i
$279$		−	3239.94i		−	0.695234i
$280$	−3230.70	−	1835.16i	−0.689539	−	0.391684i
$281$			4750.23i			1.00845i	0.863572	+	0.504226i	$0.168222\pi$
$281$			4750.23i			1.00845i	−0.863572	+	0.504226i	$0.831778\pi$
$282$	−3723.63	−	3109.69i	−0.786308	−	0.656665i
$283$	644.104	−	644.104i	0.135293	−	0.135293i	−0.636217	−	0.771510i	$-0.719502\pi$
$283$	644.104	−	644.104i	0.135293	−	0.135293i	0.771510	+	0.636217i	$0.219502\pi$
$284$	306.662	+	1692.85i	0.0640740	+	0.353705i
$285$	−1938.79	−	1938.79i	−0.402961	−	0.402961i
$286$	1418.90	−	127.480i	0.293361	−	0.0263569i
$287$	−8975.67			−1.84605
$288$	−2620.29	−	5451.95i	−0.536118	−	1.11548i
$289$	2916.53			0.593635
$290$	274.406	−	24.6539i	0.0555644	−	0.00499216i
$291$	−828.827	−	828.827i	−0.166965	−	0.166965i
$292$	−953.405	−	5263.03i	−0.191075	−	1.05478i
$293$	−1433.16	+	1433.16i	−0.285755	+	0.285755i	−0.835399	−	0.549644i	$-0.814763\pi$
$293$	−1433.16	+	1433.16i	−0.285755	+	0.285755i	0.549644	+	0.835399i	$0.314763\pi$
$294$	4671.41	+	3901.21i	0.926675	+	0.773888i
$295$			3777.69i			0.745578i
$296$	2580.67	−	4543.13i	0.506751	−	0.892108i
$297$			1575.79i			0.307868i
$298$	5857.75	−	7014.23i	1.13869	−	1.36350i
$299$	542.407	−	542.407i	0.104910	−	0.104910i
$300$	−2887.34	+	4164.85i	−0.555668	+	0.801526i
$301$	2495.85	+	2495.85i	0.477935	+	0.477935i
$302$	712.319	+	7928.36i	0.135726	+	1.51068i
$303$	5364.10			1.01703
$304$	3115.65	+	1417.54i	0.587811	+	0.267439i
$305$	−6198.79			−1.16374
$306$	748.364	+	8329.55i	0.139808	+	1.55611i
$307$	−231.211	−	231.211i	−0.0429834	−	0.0429834i	0.685288	−	0.728272i	$-0.259676\pi$
$307$	−231.211	−	231.211i	−0.0429834	−	0.0429834i	−0.728272	+	0.685288i	$0.759676\pi$
$308$	−5172.09	−	3585.62i	−0.956842	−	0.663343i
$309$	10116.2	−	10116.2i	1.86242	−	1.86242i
$310$	−1159.39	+	1388.29i	−0.212416	+	0.254353i
$311$			871.410i			0.158885i	0.996839	+	0.0794423i	$0.0253140\pi$
$311$			871.410i			0.158885i	−0.996839	+	0.0794423i	$0.974686\pi$
$312$	744.577	+	2702.84i	0.135107	+	0.490443i
$313$		−	3515.02i		−	0.634762i	−0.948298	−	0.317381i	$-0.897197\pi$
$313$		−	3515.02i		−	0.634762i	0.948298	−	0.317381i	$-0.102803\pi$
$314$	2782.53	+	2323.76i	0.500087	+	0.417634i
$315$	−3879.95	+	3879.95i	−0.694001	+	0.694001i
$316$	−6478.22	+	1173.54i	−1.15325	+	0.208913i
$317$	4723.77	+	4723.77i	0.836951	+	0.836951i	0.988456	−	0.151506i	$-0.0484121\pi$
$317$	4723.77	+	4723.77i	0.836951	+	0.836951i	−0.151506	+	0.988456i	$0.548412\pi$
$318$	5442.40	−	488.970i	0.959732	−	0.0862266i
$319$	466.665			0.0819067
$320$	−828.174	+	3273.77i	−0.144676	+	0.571904i
$321$	−872.901			−0.151778
$322$	−3375.09	+	303.233i	−0.584119	+	0.0524799i
$323$	−3346.38	−	3346.38i	−0.576462	−	0.576462i
$324$	4050.89	−	733.824i	0.694597	−	0.125827i
$325$	918.613	−	918.613i	0.156786	−	0.156786i
$326$	−4274.79	−	3569.98i	−0.726254	−	0.606512i
$327$			10475.5i			1.77155i
$328$	2166.55	+	7864.65i	0.364718	+	1.32394i
$329$		−	5493.90i		−	0.920633i
$330$	2936.85	−	3516.67i	0.489904	−	0.586625i
$331$	−1820.26	+	1820.26i	−0.302268	+	0.302268i	−0.841901	−	0.539633i	$-0.818563\pi$
$331$	−1820.26	+	1820.26i	−0.302268	+	0.302268i	0.539633	+	0.841901i	$0.318563\pi$
$332$	3039.23	+	2106.99i	0.502408	+	0.348301i
$333$	−5456.13	−	5456.13i	−0.897880	−	0.897880i
$334$	309.200	+	3441.50i	0.0506547	+	0.563804i
$335$	1001.55			0.163345
$336$	5128.93	−	11273.0i	0.832757	−	1.83034i
$337$	74.0970			0.0119772			0.00598861	−	0.999982i	$-0.498094\pi$
$337$	74.0970			0.0119772			0.00598861	+	0.999982i	$0.498094\pi$
$338$	491.749	+	5473.33i	0.0791350	+	0.880799i
$339$	−3959.83	−	3959.83i	−0.634420	−	0.634420i
$340$	2660.01	−	3836.94i	0.424292	−	0.612021i
$341$	−2166.34	+	2166.34i	−0.344029	+	0.344029i
$342$	3240.23	−	3879.94i	0.512315	−	0.613460i
$343$		−	1647.24i		−	0.259307i
$344$	1584.46	−	2789.36i	0.248339	−	0.437187i
$345$		−	2467.01i		−	0.384984i
$346$	1729.80	+	1444.59i	0.268770	+	0.224456i
$347$	2102.73	−	2102.73i	0.325305	−	0.325305i	−0.525493	−	0.850798i	$-0.676119\pi$
$347$	2102.73	−	2102.73i	0.325305	−	0.325305i	0.850798	+	0.525493i	$0.176119\pi$
$348$	163.698	+	903.652i	0.0252159	+	0.139198i
$349$	−6612.85	−	6612.85i	−1.01426	−	1.01426i	−0.999897	−	0.0143661i	$-0.995427\pi$
$349$	−6612.85	−	6612.85i	−1.01426	−	1.01426i	−0.0143661	−	0.999897i	$-0.504573\pi$
$350$	−5716.00	+	513.551i	−0.872951	+	0.0784299i
$351$	794.940			0.120885
$352$	−1893.35	+	5397.38i	−0.286693	+	0.817277i
$353$	2216.90			0.334259			0.167130	−	0.985935i	$-0.446550\pi$
$353$	2216.90			0.334259			0.167130	+	0.985935i	$0.446550\pi$
$354$	−12541.6	+	1126.80i	−1.88299	+	0.169177i
$355$	−1002.93	−	1002.93i	−0.149944	−	0.149944i
$356$	−374.658	−	2068.21i	−0.0557776	−	0.307906i
$357$	−12107.9	+	12107.9i	−1.79500	+	1.79500i
$358$	6761.23	+	5646.46i	0.998162	+	0.833589i
$359$		−	2082.23i		−	0.306117i	−0.988217	−	0.153059i	$-0.951088\pi$
$359$		−	2082.23i		−	0.306117i	0.988217	−	0.153059i	$-0.0489123\pi$
$360$	4336.23	+	2463.14i	0.634831	+	0.360608i
$361$		−	3998.49i		−	0.582955i
$362$	−310.995	+	372.393i	−0.0451533	+	0.0540678i
$363$	−1827.87	+	1827.87i	−0.264293	+	0.264293i
$364$	−1808.84	+	2609.16i	−0.260464	+	0.375707i
$365$	3118.10	+	3118.10i	0.447148	+	0.447148i
$366$	−1848.95	−	20579.5i	−0.264061	−	2.93909i
$367$	4509.22			0.641360			0.320680	−	0.947188i	$-0.396089\pi$
$367$	4509.22			0.641360			0.320680	+	0.947188i	$0.396089\pi$
$368$	1080.38	+	2884.12i	0.153040	+	0.408547i
$369$	12047.1			1.69959
$370$	385.464	+	4290.34i	0.0541603	+	0.602823i
$371$	4375.61	+	4375.61i	0.612320	+	0.612320i
$372$	−4954.82	−	3434.99i	−0.690579	−	0.478753i
$373$	−8661.56	+	8661.56i	−1.20236	+	1.20236i	−0.228908	+	0.973448i	$0.573515\pi$
$373$	−8661.56	+	8661.56i	−1.20236	+	1.20236i	−0.973448	+	0.228908i	$0.926485\pi$
$374$	5069.05	−	6069.81i	0.700840	−	0.839205i
$375$		−	10586.3i		−	1.45779i
$376$	−4813.86	+	1326.12i	−0.660254	+	0.181886i
$377$		−	235.418i		−	0.0321609i
$378$	−2695.43	−	2251.02i	−0.366767	−	0.306296i
$379$	3522.46	−	3522.46i	0.477405	−	0.477405i	−0.426896	−	0.904301i	$-0.640393\pi$
$379$	3522.46	−	3522.46i	0.477405	−	0.477405i	0.904301	+	0.426896i	$0.140393\pi$
$380$	−2776.82	+	503.025i	−0.374863	+	0.0679069i
$381$	14412.9	+	14412.9i	1.93804	+	1.93804i
$382$	−11064.5	+	994.086i	−1.48196	+	0.133146i
$383$	3044.88			0.406229			0.203115	−	0.979155i	$-0.434894\pi$
$383$	3044.88			0.406229			0.203115	+	0.979155i	$0.434894\pi$
$384$	−11115.7	−	1772.98i	−1.47720	−	0.235618i
$385$	5188.54			0.686837
$386$	9152.75	−	822.325i	1.20690	−	0.108433i
$387$	−3349.92	−	3349.92i	−0.440016	−	0.440016i
$388$	−1187.08	+	215.042i	−0.155322	+	0.0281368i
$389$	1932.73	−	1932.73i	0.251911	−	0.251911i	−0.569843	−	0.821754i	$-0.692996\pi$
$389$	1932.73	−	1932.73i	0.251911	−	0.251911i	0.821754	+	0.569843i	$0.192996\pi$
$390$	−1774.05	−	1481.55i	−0.230340	−	0.192362i
$391$		−	4258.09i		−	0.550744i
$392$	6039.14	−	1663.66i	0.778119	−	0.214356i
$393$			7228.29i			0.927784i
$394$	−6207.15	+	7432.61i	−0.793685	+	0.950379i
$395$	3838.04	−	3838.04i	0.488893	−	0.488893i
$396$	6941.96	+	4812.61i	0.880926	+	0.610714i
$397$	−672.457	−	672.457i	−0.0850117	−	0.0850117i	0.663322	−	0.748334i	$-0.269146\pi$
$397$	−672.457	−	672.457i	−0.0850117	−	0.0850117i	−0.748334	+	0.663322i	$0.769146\pi$
$398$	−347.075	−	3863.07i	−0.0437119	−	0.486528i
$399$	10349.9			1.29861
$400$	1829.71	+	4884.51i	0.228714	+	0.610563i
$401$	−7606.74			−0.947288			−0.473644	−	0.880716i	$-0.657062\pi$
$401$	−7606.74			−0.947288			−0.473644	+	0.880716i	$0.657062\pi$
$402$	298.740	+	3325.07i	0.0370641	+	0.412536i
$403$	1092.85	+	1092.85i	0.135084	+	0.135084i
$404$	3145.49	−	4537.23i	0.387361	−	0.558751i
$405$	−2399.96	+	2399.96i	−0.294457	+	0.294457i
$406$	−666.631	+	798.241i	−0.0814885	+	0.0975765i
$407$			7296.32i			0.888612i
$408$	13531.7	+	7686.54i	1.64196	+	0.932697i
$409$			4981.58i			0.602257i	0.953584	+	0.301129i	$0.0973634\pi$
$409$			4981.58i			0.602257i	−0.953584	+	0.301129i	$0.902637\pi$
$410$	−5162.08	−	4310.98i	−0.621797	−	0.519278i
$411$	−13803.8	+	13803.8i	−1.65667	+	1.65667i
$412$	−2624.67	−	14488.8i	−0.313855	−	1.73256i
$413$	−10083.3	−	10083.3i	−1.20137	−	1.20137i
$414$	4530.03	−	406.998i	0.537775	−	0.0483161i
$415$	−3048.89			−0.360637
$416$	2722.81	+	955.136i	0.320906	+	0.112571i
$417$	−11937.9			−1.40192
$418$	−4760.80	+	427.732i	−0.557077	+	0.0500503i
$419$	−3433.38	−	3433.38i	−0.400314	−	0.400314i	0.478030	−	0.878344i	$-0.341351\pi$
$419$	−3433.38	−	3433.38i	−0.400314	−	0.400314i	−0.878344	+	0.478030i	$0.841351\pi$
$420$	1820.05	+	10047.1i	0.211450	+	1.16726i
$421$	7973.72	−	7973.72i	0.923077	−	0.923077i	−0.0741686	−	0.997246i	$-0.523630\pi$
$421$	7973.72	−	7973.72i	0.923077	−	0.923077i	0.997246	+	0.0741686i	$0.0236303\pi$
$422$	4975.22	+	4154.93i	0.573910	+	0.479286i
$423$			7373.88i			0.847590i
$424$	2777.81	−	4890.18i	0.318166	−	0.560114i
$425$		−	7211.44i		−	0.823074i
$426$	3030.51	−	3628.81i	0.344668	−	0.412715i
$427$	16545.6	−	16545.6i	1.87517	−	1.87517i
$428$	−511.866	+	738.343i	−0.0578084	+	0.0833859i
$429$	−2768.30	−	2768.30i	−0.311550	−	0.311550i
$430$	236.665	+	2634.16i	0.0265418	+	0.295420i
$431$	4800.16			0.536463			0.268232	−	0.963354i	$-0.413561\pi$
$431$	4800.16			0.536463			0.268232	+	0.963354i	$0.413561\pi$
$432$	−1321.76	+	2905.14i	−0.147207	+	0.323550i
$433$	6242.32			0.692810			0.346405	−	0.938085i	$-0.387402\pi$
$433$	6242.32			0.692810			0.346405	+	0.938085i	$0.387402\pi$
$434$	−610.959	−	6800.18i	−0.0675737	−	0.752118i
$435$	−535.372	−	535.372i	−0.0590095	−	0.0590095i
$436$	8860.69	+	6142.79i	0.973280	+	0.674739i
$437$	−1819.93	+	1819.93i	−0.199220	+	0.199220i
$438$	−9421.79	+	11281.9i	−1.02783	+	1.23075i
$439$			4929.27i			0.535903i	0.963432	+	0.267951i	$0.0863466\pi$
$439$			4929.27i			0.535903i	−0.963432	+	0.267951i	$0.913653\pi$
$440$	−1252.41	−	4546.30i	−0.135696	−	0.492582i
$441$		−	9250.77i		−	0.998896i
$442$	−3062.03	−	2557.18i	−0.329516	−	0.275187i
$443$	−7670.67	+	7670.67i	−0.822674	+	0.822674i	−0.986491	−	0.163817i	$-0.947619\pi$
$443$	−7670.67	+	7670.67i	−0.822674	+	0.822674i	0.163817	+	0.986491i	$0.447619\pi$
$444$	−14128.6	+	2559.42i	−1.51017	+	0.273569i
$445$	1225.32	+	1225.32i	0.130529	+	0.130529i
$446$	1182.09	−	106.205i	0.125502	−	0.0112756i
$447$	−25113.5			−2.65733
$448$	−6527.70	−	10948.8i	−0.688404	−	1.15464i
$449$	−11515.2			−1.21032			−0.605162	−	0.796102i	$-0.706892\pi$
$449$	−11515.2			−1.21032			−0.605162	+	0.796102i	$0.706892\pi$
$450$	7671.99	−	689.286i	0.803691	−	0.0722073i
$451$	−8055.12	−	8055.12i	−0.841021	−	0.841021i
$452$	−5671.44	+	1027.39i	−0.590182	+	0.106912i
$453$	15468.4	−	15468.4i	1.60434	−	1.60434i
$454$	6550.66	+	5470.61i	0.677176	+	0.565526i
$455$		−	2617.46i		−	0.269689i
$456$	−2498.26	−	9068.79i	−0.256561	−	0.931326i
$457$			4829.89i			0.494383i	0.968967	+	0.247191i	$0.0795076\pi$
$457$			4829.89i			0.494383i	−0.968967	+	0.247191i	$0.920492\pi$
$458$	4036.78	−	4833.74i	0.411848	−	0.493157i
$459$	3120.28	−	3120.28i	0.317303	−	0.317303i
$460$	−2086.72	−	1446.65i	−0.211508	−	0.146631i
$461$	8265.79	+	8265.79i	0.835090	+	0.835090i	0.988208	−	0.153118i	$-0.0489315\pi$
$461$	8265.79	+	8265.79i	0.835090	+	0.835090i	−0.153118	+	0.988208i	$0.548931\pi$
$462$	1547.62	+	17225.5i	0.155848	+	1.73464i
$463$	−5043.86			−0.506281			−0.253141	−	0.967430i	$-0.581464\pi$
$463$	−5043.86			−0.506281			−0.253141	+	0.967430i	$0.581464\pi$
$464$	860.346	+	391.435i	0.0860788	+	0.0391636i
$465$	4970.57			0.495709
$466$	−302.418	−	3366.02i	−0.0300628	−	0.334609i
$467$	12438.8	+	12438.8i	1.23255	+	1.23255i	0.962982	+	0.269564i	$0.0868796\pi$
$467$	12438.8	+	12438.8i	1.23255	+	1.23255i	0.269564	+	0.962982i	$0.413120\pi$
$468$	2427.81	−	3502.01i	0.239798	−	0.345898i
$469$	−2673.31	+	2673.31i	−0.263203	+	0.263203i
$470$	2638.70	−	3159.64i	0.258966	−	0.310093i
$471$		−	9962.47i		−	0.974621i
$472$	−6401.26	+	11269.1i	−0.624241	+	1.09894i
$473$			4479.75i			0.435474i
$474$	13886.8	+	11597.2i	1.34566	+	1.12379i
$475$	−3082.20	+	3082.20i	−0.297729	+	0.297729i
$476$	3141.42	+	17341.4i	0.302493	+	1.66984i
$477$	−5872.93	−	5872.93i	−0.563738	−	0.563738i
$478$	11947.3	−	1073.40i	1.14322	−	0.102712i
$479$	13059.7			1.24575			0.622875	−	0.782321i	$-0.285964\pi$
$479$	13059.7			1.24575			0.622875	+	0.782321i	$0.285964\pi$
$480$	8364.14	−	4019.93i	0.795352	−	0.382258i
$481$	3680.77			0.348916
$482$	15694.5	−	1410.06i	1.48312	−	0.133250i
$483$	6584.87	+	6584.87i	0.620335	+	0.620335i
$484$	474.246	+	2617.96i	0.0445385	+	0.245864i
$485$	703.292	−	703.292i	0.0658450	−	0.0658450i
$486$	−11606.7	−	9693.04i	−1.08331	−	0.904702i
$487$			15549.3i			1.44683i	0.690414	+	0.723414i	$0.257428\pi$
$487$			15549.3i			1.44683i	−0.690414	+	0.723414i	$0.742572\pi$
$488$	−18491.4	−	10503.8i	−1.71530	−	0.974354i
$489$			15305.3i			1.41540i
$490$	−3310.33	+	3963.88i	−0.305195	+	0.365448i
$491$	−8628.34	+	8628.34i	−0.793058	+	0.793058i	−0.981990	−	0.188932i	$-0.939497\pi$
$491$	−8628.34	+	8628.34i	−0.793058	+	0.793058i	0.188932	+	0.981990i	$0.439497\pi$
$492$	12772.4	−	18423.5i	1.17037	−	1.68821i
$493$	−924.059	−	924.059i	−0.0844169	−	0.0844169i
$494$	215.777	+	2401.68i	0.0196524	+	0.218738i
$495$	−6964.03			−0.632344
$496$	−5810.98	+	2176.76i	−0.526049	+	0.197056i
$497$	5354.00			0.483219
$498$	−909.413	−	10122.1i	−0.0818309	−	0.910806i
$499$	1732.42	+	1732.42i	0.155418	+	0.155418i	0.780533	−	0.625115i	$-0.214948\pi$
$499$	1732.42	+	1732.42i	0.155418	+	0.155418i	−0.625115	+	0.780533i	$0.714948\pi$
$500$	−8954.38	−	6207.74i	−0.800904	−	0.555237i
$501$	6714.44	−	6714.44i	0.598761	−	0.598761i
$502$	1237.71	−	1482.06i	0.110043	−	0.131768i
$503$		−	16579.6i		−	1.46968i	−0.678241	−	0.734839i	$-0.737258\pi$
$503$		−	16579.6i		−	1.46968i	0.678241	−	0.734839i	$-0.262742\pi$
$504$	−18148.7	+	4999.58i	−1.60398	+	0.441863i
$505$			4551.65i			0.401081i
$506$	−3301.07	−	2756.80i	−0.290021	−	0.242203i
$507$	10678.6	−	10678.6i	0.935410	−	0.935410i
$508$	20642.8	−	3739.47i	1.80291	−	0.326599i
$509$	−7830.92	−	7830.92i	−0.681924	−	0.681924i	0.278509	−	0.960434i	$-0.410160\pi$
$509$	−7830.92	−	7830.92i	−0.681924	−	0.681924i	−0.960434	+	0.278509i	$0.910160\pi$
$510$	−12778.8	+	1148.11i	−1.10952	+	0.0996844i
$511$	−16645.5			−1.44100
$512$	−8017.86	+	8362.51i	−0.692076	+	0.721825i
$513$	−2667.24			−0.229555
$514$	−22799.0	+	2048.36i	−1.95646	+	0.175777i
$515$	8583.95	+	8583.95i	0.734474	+	0.734474i
$516$	−8674.61	+	1571.42i	−0.740074	+	0.134065i
$517$	4930.44	−	4930.44i	0.419420	−	0.419420i
$518$	−12480.5	−	10422.8i	−1.05861	−	0.884075i
$519$		−	6193.30i		−	0.523807i
$520$	−2293.47	+	631.803i	−0.193414	+	0.0532815i
$521$		−	3400.02i		−	0.285907i	−0.989729	−	0.142953i	$-0.954340\pi$
$521$		−	3400.02i		−	0.285907i	0.989729	−	0.142953i	$-0.0456599\pi$
$522$	894.749	−	1071.40i	0.0750232	−	0.0898348i
$523$	−2019.50	+	2019.50i	−0.168847	+	0.168847i	−0.786472	−	0.617626i	$-0.788095\pi$
$523$	−2019.50	+	2019.50i	−0.168847	+	0.168847i	0.617626	+	0.786472i	$0.288095\pi$
$524$	6114.05	+	4238.64i	0.509720	+	0.353370i
$525$	11152.0	+	11152.0i	0.927075	+	0.927075i
$526$	103.847	+	1155.85i	0.00860822	+	0.0958124i
$527$	8579.28			0.709144
$528$	14719.8	−	5513.95i	1.21325	−	0.454477i
$529$	9851.23			0.809668
$530$	414.910	+	4618.09i	0.0340048	+	0.378485i
$531$	13533.7	+	13533.7i	1.10605	+	1.10605i
$532$	6069.15	−	8754.47i	0.494607	−	0.713448i
$533$	−4063.56	+	4063.56i	−0.330229	+	0.330229i
$534$	−3702.47	+	4433.43i	−0.300040	+	0.359276i
$535$		−	740.691i		−	0.0598558i
$536$	2987.69	+	1697.12i	0.240762	+	0.136762i
$537$		−	24207.7i		−	1.94532i
$538$	14.6743	+	12.2548i	0.00117594	+	0.000982052i
$539$	−6185.39	+	6185.39i	−0.494293	+	0.494293i
$540$	−469.038	−	2589.21i	−0.0373781	−	0.206337i
$541$	−13432.6	−	13432.6i	−1.06749	−	1.06749i	−0.997551	−	0.0699388i	$-0.977720\pi$
$541$	−13432.6	−	13432.6i	−1.06749	−	1.06749i	−0.0699388	−	0.997551i	$-0.522280\pi$
$542$	7983.54	−	717.278i	0.632699	−	0.0568445i
$543$	1333.30			0.105373
$544$	14436.6	−	6938.45i	1.13780	−	0.546845i
$545$	−8888.86			−0.698637
$546$	8689.75	−	780.726i	0.681112	−	0.0611941i
$547$	−5376.46	−	5376.46i	−0.420257	−	0.420257i	0.465035	−	0.885292i	$-0.346042\pi$
$547$	−5376.46	−	5376.46i	−0.420257	−	0.420257i	−0.885292	+	0.465035i	$0.846042\pi$
$548$	3581.44	+	19770.4i	0.279181	+	1.54115i
$549$	−22207.5	+	22207.5i	−1.72640	+	1.72640i
$550$	−5590.64	−	4668.88i	−0.433429	−	0.361967i
$551$			789.894i			0.0610719i
$552$	4180.33	−	7359.24i	0.322331	−	0.567446i
$553$			20488.7i			1.57553i
$554$	−3912.13	+	4684.49i	−0.300019	+	0.359251i
$555$	8370.55	−	8370.55i	0.640198	−	0.640198i
$556$	−7000.34	+	10097.7i	−0.533958	+	0.770210i
$557$	−2076.28	−	2076.28i	−0.157944	−	0.157944i	0.623711	−	0.781655i	$-0.285624\pi$
$557$	−2076.28	−	2076.28i	−0.157944	−	0.157944i	−0.781655	+	0.623711i	$0.785624\pi$
$558$	820.027	+	9127.18i	0.0622124	+	0.692445i
$559$	2259.90			0.170990
$560$	9565.61	+	4352.10i	0.721823	+	0.328410i
$561$	−21732.1			−1.63553
$562$	−1202.28	−	13381.8i	−0.0902405	−	1.00441i
$563$	−16643.1	−	16643.1i	−1.24587	−	1.24587i	−0.957528	−	0.288339i	$-0.906897\pi$
$563$	−16643.1	−	16643.1i	−1.24587	−	1.24587i	−0.288339	−	0.957528i	$-0.593103\pi$
$564$	11276.8	+	7817.81i	0.841915	+	0.583669i
$565$	3360.07	−	3360.07i	0.250193	−	0.250193i
$566$	−1651.47	+	1977.51i	−0.122644	+	0.146857i
$567$		−	12811.8i		−	0.948934i
$568$	−1292.35	−	4691.28i	−0.0954679	−	0.346552i
$569$			5659.60i			0.416982i	0.978024	+	0.208491i	$0.0668551\pi$
$569$			5659.60i			0.416982i	−0.978024	+	0.208491i	$0.933145\pi$
$570$	5952.43	+	4971.02i	0.437403	+	0.365286i
$571$	4872.67	−	4872.67i	0.357119	−	0.357119i	−0.505631	−	0.862750i	$-0.668740\pi$
$571$	4872.67	−	4872.67i	0.357119	−	0.357119i	0.862750	+	0.505631i	$0.168740\pi$
$572$	−3964.89	+	718.244i	−0.289825	+	0.0525023i
$573$	21587.1	+	21587.1i	1.57385	+	1.57385i
$574$	25285.2	−	2271.73i	1.83865	−	0.165192i
$575$	−3921.95			−0.284446
$576$	8761.45	+	14695.4i	0.633786	+	1.06303i
$577$	10652.2			0.768556			0.384278	−	0.923217i	$-0.374450\pi$
$577$	10652.2			0.768556			0.384278	+	0.923217i	$0.374450\pi$
$578$	−8216.10	+	738.171i	−0.591254	+	0.0531209i
$579$	−17857.2	−	17857.2i	−1.28173	−	1.28173i
$580$	−766.784	+	138.904i	−0.0548948	+	0.00994426i
$581$	8138.01	−	8138.01i	0.581104	−	0.581104i
$582$	2544.65	+	2125.10i	0.181235	+	0.151354i
$583$			7853.69i			0.557919i
$584$	4017.89	+	14585.1i	0.284694	+	1.03345i
$585$			3513.14i			0.248291i
$586$	3674.61	−	4400.07i	0.259039	−	0.310180i
$587$	9903.95	−	9903.95i	0.696388	−	0.696388i	−0.267242	−	0.963630i	$-0.586112\pi$
$587$	9903.95	−	9903.95i	0.696388	−	0.696388i	0.963630	+	0.267242i	$0.0861122\pi$
$588$	−14147.1	−	9807.69i	−0.992208	−	0.687861i
$589$	−3666.82	−	3666.82i	−0.256517	−	0.256517i
$590$	−956.129	−	10642.0i	−0.0667173	−	0.742587i
$591$	26611.5			1.85220
$592$	−6120.09	+	13451.5i	−0.424889	+	0.933875i
$593$	−3528.04			−0.244316			−0.122158	−	0.992511i	$-0.538981\pi$
$593$	−3528.04			−0.244316			−0.122158	+	0.992511i	$0.538981\pi$
$594$	−398.832	−	4439.14i	−0.0275493	−	0.306633i
$595$	−10274.0	−	10274.0i	−0.707887	−	0.707887i
$596$	−14726.5	+	21242.2i	−1.01211	+	1.45993i
$597$	−7536.93	+	7536.93i	−0.516693	+	0.516693i
$598$	−1390.72	+	1665.29i	−0.0951018	+	0.113877i
$599$			19024.9i			1.29772i	0.760907	+	0.648861i	$0.224754\pi$
$599$			19024.9i			1.29772i	−0.760907	+	0.648861i	$0.775246\pi$
$600$	7079.74	−	12463.5i	0.481715	−	0.848034i
$601$			1065.92i			0.0723460i	0.999346	+	0.0361730i	$0.0115167\pi$
$601$			1065.92i			0.0723460i	−0.999346	+	0.0361730i	$0.988483\pi$
$602$	−7662.72	−	6399.32i	−0.518786	−	0.433250i
$603$	3588.11	−	3588.11i	0.242320	−	0.242320i
$604$	−4013.32	−	22154.5i	−0.270364	−	1.49248i
$605$	−1551.02	−	1551.02i	−0.104228	−	0.104228i
$606$	−15111.1	+	1357.65i	−1.01295	+	0.0910079i
$607$	12909.7			0.863242			0.431621	−	0.902055i	$-0.357942\pi$
$607$	12909.7			0.863242			0.431621	+	0.902055i	$0.357942\pi$
$608$	−9135.80	−	3204.75i	−0.609384	−	0.213766i
$609$	2858.00			0.190167
$610$	17462.5	−	1568.91i	1.15908	−	0.104137i
$611$	−2487.25	−	2487.25i	−0.164687	−	0.164687i
$612$	−4216.40	−	23275.6i	−0.278494	−	1.53735i
$613$	−8763.41	+	8763.41i	−0.577408	+	0.577408i	−0.934188	−	0.356781i	$-0.883874\pi$
$613$	−8763.41	+	8763.41i	−0.577408	+	0.577408i	0.356781	+	0.934188i	$0.383874\pi$
$614$	709.859	+	592.820i	0.0466573	+	0.0389646i
$615$			18482.1i			1.21182i
$616$	15477.7	+	8791.93i	1.01236	+	0.575060i
$617$		−	18921.2i		−	1.23459i	−0.786733	−	0.617293i	$-0.788229\pi$
$617$		−	18921.2i		−	1.23459i	0.786733	−	0.617293i	$-0.211771\pi$
$618$	−25937.6	+	31058.4i	−1.68829	+	2.02161i
$619$	−15116.6	+	15116.6i	−0.981565	+	0.981565i	−0.999833	−	0.0182677i	$-0.994185\pi$
$619$	−15116.6	+	15116.6i	−0.981565	+	0.981565i	0.0182677	+	0.999833i	$0.494185\pi$
$620$	2914.73	−	4204.36i	0.188804	−	0.272340i
$621$	−1696.97	−	1696.97i	−0.109657	−	0.109657i
$622$	−220.553	−	2454.83i	−0.0142176	−	0.158247i
$623$	−6541.15			−0.420651
$624$	−2781.62	−	7425.67i	−0.178452	−	0.476386i
$625$	−1204.57			−0.0770926
$626$	889.648	+	9902.09i	0.0568011	+	0.632216i
$627$	9288.42	+	9288.42i	0.591617	+	0.591617i
$628$	−8426.75	−	5841.95i	−0.535452	−	0.371209i
$629$	14447.7	−	14447.7i	0.915845	−	0.915845i
$630$	9948.11	−	11912.1i	0.629115	−	0.753319i
$631$		−	9602.80i		−	0.605834i	−0.953017	−	0.302917i	$-0.902039\pi$
$631$		−	9602.80i		−	0.605834i	0.953017	−	0.302917i	$-0.0979605\pi$
$632$	17952.6	−	4945.58i	1.12993	−	0.311273i
$633$		−	17813.1i		−	1.11849i
$634$	−14502.8	−	12111.7i	−0.908487	−	0.758699i
$635$	−12229.9	+	12229.9i	−0.764297	+	0.764297i
$636$	−15207.9	+	2754.93i	−0.948166	+	0.171761i
$637$	3120.34	+	3120.34i	0.194085	+	0.194085i
$638$	−1314.63	+	118.113i	−0.0815781	+	0.00732935i
$639$	−7186.12			−0.444880
$640$	1504.44	−	9432.08i	0.0929194	−	0.582556i
$641$	4450.84			0.274256			0.137128	−	0.990553i	$-0.456213\pi$
$641$	4450.84			0.274256			0.137128	+	0.990553i	$0.456213\pi$
$642$	2459.03	−	220.931i	0.151169	−	0.0135817i
$643$	6491.27	+	6491.27i	0.398119	+	0.398119i	0.877569	−	0.479450i	$-0.159164\pi$
$643$	6491.27	+	6491.27i	0.398119	+	0.398119i	−0.479450	+	0.877569i	$0.659164\pi$
$644$	9431.15	−	1708.46i	0.577080	−	0.104539i
$645$	5139.30	−	5139.30i	0.313736	−	0.313736i
$646$	10274.0	+	8580.05i	0.625734	+	0.522566i
$647$		−	5546.17i		−	0.337005i	−0.985701	−	0.168503i	$-0.946107\pi$
$647$		−	5546.17i		−	0.337005i	0.985701	−	0.168503i	$-0.0538932\pi$
$648$	−11226.0	+	3092.52i	−0.680551	+	0.187478i
$649$		−	18098.3i		−	1.09464i
$650$	−2355.31	+	2820.31i	−0.142127	+	0.170187i
$651$	−13267.3	+	13267.3i	−0.798750	+	0.798750i
$652$	12946.0	+	8974.98i	0.777613	+	0.539091i
$653$	6327.58	+	6327.58i	0.379200	+	0.379200i	0.870813	−	0.491614i	$-0.163593\pi$
$653$	6327.58	+	6327.58i	0.379200	+	0.379200i	−0.491614	+	0.870813i	$0.663593\pi$
$654$	−2651.34	−	29510.3i	−0.158525	−	1.76444i
$655$	−6133.49			−0.365886
$656$	−8093.88	−	21607.0i	−0.481727	−	1.28599i
$657$	22341.5			1.32667
$658$	1390.50	+	15476.7i	0.0823820	+	0.916940i
$659$	15135.2	+	15135.2i	0.894663	+	0.894663i	0.994958	−	0.100294i	$-0.0319785\pi$
$659$	15135.2	+	15135.2i	0.894663	+	0.894663i	−0.100294	+	0.994958i	$0.531978\pi$
$660$	−7383.28	+	10650.0i	−0.435445	+	0.628110i
$661$	−23460.1	+	23460.1i	−1.38047	+	1.38047i	−0.536694	+	0.843777i	$0.680327\pi$
$661$	−23460.1	+	23460.1i	−1.38047	+	1.38047i	−0.843777	+	0.536694i	$0.819673\pi$
$662$	4667.12	−	5588.53i	0.274007	−	0.328103i
$663$			10963.2i			0.642195i
$664$	−9095.03	−	5166.32i	−0.531560	−	0.301946i
$665$			8782.30i			0.512125i
$666$	16751.3	+	13989.4i	0.974624	+	0.813932i
$667$	−502.550	+	502.550i	−0.0291736	+	0.0291736i
$668$	−1742.08	−	9616.73i	−0.100903	−	0.557009i
$669$	−2306.29	−	2306.29i	−0.133283	−	0.133283i
$670$	−2821.45	+	253.492i	−0.162690	+	0.0146168i
$671$	29697.4			1.70858
$672$	−11595.4	+	33055.2i	−0.665630	+	1.89752i
$673$	30638.5			1.75487			0.877436	−	0.479694i	$-0.159252\pi$
$673$	30638.5			1.75487			0.877436	+	0.479694i	$0.159252\pi$
$674$	−208.737	+	18.7539i	−0.0119292	+	0.00107177i
$675$	−2873.96	−	2873.96i	−0.163879	−	0.163879i
$676$	−2770.59	−	15294.4i	−0.157635	−	0.870184i
$677$	−12468.9	+	12468.9i	−0.707855	+	0.707855i	−0.966084	−	0.258229i	$-0.916861\pi$
$677$	−12468.9	+	12468.9i	−0.707855	+	0.707855i	0.258229	+	0.966084i	$0.416861\pi$
$678$	12157.4	+	10152.9i	0.688645	+	0.575104i
$679$			3754.41i			0.212196i
$680$	−6522.33	+	11482.2i	−0.367823	+	0.647533i
$681$		−	23453.8i		−	1.31975i
$682$	5554.45	−	6651.05i	0.311864	−	0.373434i
$683$	13838.5	−	13838.5i	0.775280	−	0.775280i	−0.203744	−	0.979024i	$-0.565311\pi$
$683$	13838.5	−	13838.5i	0.775280	−	0.775280i	0.979024	+	0.203744i	$0.0653111\pi$
$684$	−8145.99	+	11750.2i	−0.455365	+	0.656843i
$685$	−11713.1	−	11713.1i	−0.653333	−	0.653333i
$686$	416.914	+	4640.40i	0.0232039	+	0.258267i
$687$	−17306.6			−0.961116
$688$	−3757.58	+	8258.89i	−0.208221	+	0.457656i
$689$	3961.95			0.219068
$690$	624.398	+	6949.77i	0.0344499	+	0.383439i
$691$	−106.012	−	106.012i	−0.00583628	−	0.00583628i	0.704183	−	0.710019i	$-0.251314\pi$
$691$	−106.012	−	106.012i	−0.00583628	−	0.00583628i	−0.710019	+	0.704183i	$0.751314\pi$
$692$	−5238.60	−	3631.73i	−0.287777	−	0.199505i
$693$	18588.2	−	18588.2i	1.01891	−	1.01891i
$694$	−5391.37	+	6455.77i	−0.294890	+	0.353109i
$695$		−	10129.8i		−	0.552870i
$696$	−689.863	−	2504.23i	−0.0375707	−	0.136383i
$697$			31900.4i			1.73359i
$698$	20302.6	+	16955.2i	1.10095	+	0.919434i
$699$	−6567.17	+	6567.17i	−0.355355	+	0.355355i
$700$	15972.4	−	2893.43i	0.862431	−	0.156231i
$701$	7839.35	+	7839.35i	0.422380	+	0.422380i	0.886022	−	0.463643i	$-0.153458\pi$
$701$	7839.35	+	7839.35i	0.422380	+	0.422380i	−0.463643	+	0.886022i	$0.653458\pi$
$702$	−2239.41	+	201.199i	−0.120400	+	0.0108173i
$703$	−12350.0			−0.662574
$704$	3967.64	−	15684.1i	0.212409	−	0.839653i
$705$	−11312.7			−0.604341
$706$	−6245.17	+	561.095i	−0.332918	+	0.0299109i
$707$	−12149.1	−	12149.1i	−0.646273	−	0.646273i
$708$	35045.5	−	6348.55i	1.86030	−	0.336996i
$709$	2728.30	−	2728.30i	0.144518	−	0.144518i	−0.631146	−	0.775664i	$-0.717415\pi$
$709$	2728.30	−	2728.30i	0.144518	−	0.144518i	0.775664	+	0.631146i	$0.217415\pi$
$710$	3079.19	+	2571.50i	0.162760	+	0.135925i
$711$		−	27499.9i		−	1.45053i
$712$	1578.90	+	5731.48i	0.0831066	+	0.301680i
$713$		−	4665.84i		−	0.245073i
$714$	31044.3	−	37173.3i	1.62718	−	1.94843i
$715$	2349.01	−	2349.01i	0.122864	−	0.122864i
$716$	−20476.0	−	14195.3i	−1.06875	−	0.740925i
$717$	−23309.5	−	23309.5i	−1.21410	−	1.21410i
$718$	527.011	+	5865.82i	0.0273926	+	0.304889i
$719$	−32717.8			−1.69704			−0.848519	−	0.529166i	$-0.822505\pi$
$719$	−32717.8			−1.69704			−0.848519	+	0.529166i	$0.822505\pi$
$720$	−12838.9	−	5841.37i	−0.664553	−	0.302354i
$721$	−45824.0			−2.36696
$722$	1012.01	+	11264.1i	0.0521652	+	0.580616i
$723$	−30620.3	−	30620.3i	−1.57508	−	1.57508i
$724$	781.844	−	1127.77i	0.0401340	−	0.0578914i
$725$	−851.111	+	851.111i	−0.0435993	+	0.0435993i
$726$	4686.62	−	5611.88i	0.239582	−	0.286882i
$727$			25847.2i			1.31859i	0.751883	+	0.659297i	$0.229146\pi$
$727$			25847.2i			1.31859i	−0.751883	+	0.659297i	$0.770854\pi$
$728$	4435.26	−	7808.03i	0.225799	−	0.397507i
$729$			27662.0i			1.40537i
$730$	−9573.13	−	7994.75i	−0.485366	−	0.405341i
$731$	8870.50	−	8870.50i	0.448820	−	0.448820i
$732$	10417.3	+	57506.1i	0.526004	+	2.90367i
$733$	10131.9	+	10131.9i	0.510547	+	0.510547i	0.914694	−	0.404147i	$-0.132432\pi$
$733$	10131.9	+	10131.9i	0.510547	+	0.510547i	−0.404147	+	0.914694i	$0.632432\pi$
$734$	−12702.8	+	1141.28i	−0.638787	+	0.0573915i
$735$	14192.1			0.712223
$736$	−3773.48	−	7851.36i	−0.188984	−	0.393213i
$737$	−4798.27			−0.239819
$738$	−33937.7	+	3049.11i	−1.69277	+	0.152086i
$739$	19163.7	+	19163.7i	0.953921	+	0.953921i	0.998984	−	0.0450633i	$-0.0143490\pi$
$739$	19163.7	+	19163.7i	0.953921	+	0.953921i	−0.0450633	+	0.998984i	$0.514349\pi$
$740$	−2171.76	−	11988.7i	−0.107886	−	0.595558i
$741$	4685.72	−	4685.72i	0.232300	−	0.232300i
$742$	−13433.9	−	11219.0i	−0.664656	−	0.555070i
$743$		−	23322.1i		−	1.15155i	−0.817607	−	0.575777i	$-0.804699\pi$
$743$		−	23322.1i		−	1.15155i	0.817607	−	0.575777i	$-0.195301\pi$
$744$	14827.5	+	8422.59i	0.730650	+	0.415037i
$745$		−	21309.8i		−	1.04796i
$746$	22208.1	−	26592.5i	1.08994	−	1.30512i
$747$	−10922.8	+	10922.8i	−0.534999	+	0.534999i
$748$	−12743.6	+	18382.1i	−0.622933	+	0.898552i
$749$	1977.03	+	1977.03i	0.0964473	+	0.0964473i
$750$	2679.37	+	29822.3i	0.130449	+	1.45194i
$751$	25994.0			1.26303			0.631515	−	0.775364i	$-0.282434\pi$
$751$	25994.0			1.26303			0.631515	+	0.775364i	$0.282434\pi$
$752$	13225.4	−	4954.16i	0.641330	−	0.240239i
$753$	−5306.32			−0.256804
$754$	59.5842	+	663.192i	0.00287789	+	0.0320319i
$755$	13125.5	+	13125.5i	0.632698	+	0.632698i
$756$	8162.97	+	5659.09i	0.392704	+	0.272247i
$757$	22145.0	−	22145.0i	1.06324	−	1.06324i	0.0653808	−	0.997860i	$-0.479174\pi$
$757$	22145.0	−	22145.0i	1.06324	−	1.06324i	0.997860	−	0.0653808i	$-0.0208262\pi$
$758$	−9031.52	+	10814.6i	−0.432770	+	0.518210i
$759$			11819.0i			0.565222i
$760$	7695.22	−	2119.87i	0.367283	−	0.101179i
$761$			16497.5i			0.785853i	0.919570	+	0.392926i	$0.128537\pi$
$761$			16497.5i			0.785853i	−0.919570	+	0.392926i	$0.871463\pi$
$762$	−44250.1	−	36954.4i	−2.10369	−	1.75684i
$763$	23725.9	−	23725.9i	1.12573	−	1.12573i
$764$	30918.0	−	5600.84i	1.46410	−	0.265224i
$765$	13789.7	+	13789.7i	0.651723	+	0.651723i
$766$	−8577.66	+	770.656i	−0.404600	+	0.0363511i
$767$	−9130.02			−0.429812
$768$	31762.5	+	2181.27i	1.49236	+	0.102487i
$769$	−24867.3			−1.16611			−0.583055	−	0.812433i	$-0.698143\pi$
$769$	−24867.3			−1.16611			−0.583055	+	0.812433i	$0.698143\pi$
$770$	−14616.5	+	1313.21i	−0.684082	+	0.0614610i
$771$	44481.2	+	44481.2i	2.07776	+	2.07776i
$772$	−25575.9	+	4633.11i	−1.19235	+	0.215996i
$773$	1881.72	−	1881.72i	0.0875559	−	0.0875559i	−0.661972	−	0.749528i	$-0.730280\pi$
$773$	1881.72	−	1881.72i	0.0875559	−	0.0875559i	0.749528	+	0.661972i	$0.230280\pi$
$774$	10284.9	+	8589.14i	0.477625	+	0.398876i
$775$		−	7902.00i		−	0.366256i
$776$	3289.68	−	906.240i	0.152181	−	0.0419228i
$777$			44684.8i			2.06314i
$778$	−4955.49	+	5933.84i	−0.228359	+	0.273443i
$779$	13634.4	−	13634.4i	0.627089	−	0.627089i
$780$	5372.62	+	3724.64i	0.246629	+	0.170979i
$781$	4804.89	+	4804.89i	0.220144	+	0.220144i
$782$	1077.72	+	11995.4i	0.0492828	+	0.548535i
$783$	−736.525			−0.0336159
$784$	−16591.7	+	6215.16i	−0.755815	+	0.283125i
$785$	8453.54			0.384356
$786$	−1829.47	−	20362.7i	−0.0830219	−	0.924062i
$787$	−7790.94	−	7790.94i	−0.352881	−	0.352881i	0.508300	−	0.861180i	$-0.330274\pi$
$787$	−7790.94	−	7790.94i	−0.352881	−	0.352881i	−0.861180	+	0.508300i	$0.830274\pi$
$788$	15604.9	−	22509.3i	0.705457	−	1.01759i
$789$	2255.08	−	2255.08i	0.101753	−	0.101753i
$790$	−9840.66	+	11783.5i	−0.443184	+	0.530680i
$791$			17937.2i			0.806286i
$792$	−20774.1	−	11800.5i	−0.932041	−	0.529435i
$793$		−	14981.4i		−	0.670877i
$794$	2064.56	+	1724.17i	0.0922778	+	0.0770634i
$795$	9009.98	−	9009.98i	0.401951	−	0.401951i
$796$	1955.48	+	10794.7i	0.0870730	+	0.480665i
$797$	−4209.84	−	4209.84i	−0.187102	−	0.187102i	0.607340	−	0.794442i	$-0.292237\pi$
$797$	−4209.84	−	4209.84i	−0.187102	−	0.187102i	−0.794442	+	0.607340i	$0.792237\pi$
$798$	−29156.5	+	2619.55i	−1.29340	+	0.116205i
$799$	−19525.8			−0.864549
$800$	−6390.71	−	13296.9i	−0.282432	−	0.587648i
$801$	8779.50			0.387276
$802$	21428.8	−	1925.26i	0.943488	−	0.0847672i
$803$	−14938.3	−	14938.3i	−0.656490	−	0.656490i
$804$	−1683.15	−	9291.39i	−0.0738308	−	0.407565i
$805$	−5587.51	+	5587.51i	−0.244639	+	0.244639i
$806$	−3355.25	−	2802.05i	−0.146630	−	0.122454i
$807$		−	52.5393i		−	0.00229178i
$808$	−7712.73	+	13577.8i	−0.335808	+	0.591172i
$809$			27554.3i			1.19747i	0.800946	+	0.598737i	$0.204330\pi$
$809$			27554.3i			1.19747i	−0.800946	+	0.598737i	$0.795670\pi$
$810$	6153.46	−	7368.32i	0.266927	−	0.319625i
$811$	3406.54	−	3406.54i	0.147497	−	0.147497i	−0.629502	−	0.776999i	$-0.716741\pi$
$811$	3406.54	−	3406.54i	0.147497	−	0.147497i	0.776999	+	0.629502i	$0.216741\pi$
$812$	1675.92	−	2417.43i	0.0724300	−	0.104477i
$813$	−15576.1	−	15576.1i	−0.671926	−	0.671926i
$814$	−1846.69	−	20554.3i	−0.0795166	−	0.885047i
$815$	−12987.1			−0.558184
$816$	−40065.4	−	18228.7i	−1.71884	−	0.782026i
$817$	−7582.59			−0.324701
$818$	−1260.83	−	14033.5i	−0.0538924	−	0.599841i
$819$	−9377.16	−	9377.16i	−0.400079	−	0.400079i
$820$	15633.1	+	10837.8i	0.665770	+	0.461554i
$821$	−9839.14	+	9839.14i	−0.418256	+	0.418256i	−0.884602	−	0.466346i	$-0.845570\pi$
$821$	−9839.14	+	9839.14i	−0.418256	+	0.418256i	0.466346	+	0.884602i	$0.345570\pi$
$822$	35392.7	−	42380.1i	1.50178	−	1.79827i
$823$		−	36653.5i		−	1.55244i	−0.630461	−	0.776221i	$-0.717134\pi$
$823$		−	36653.5i		−	1.55244i	0.630461	−	0.776221i	$-0.282866\pi$
$824$	11061.0	+	40151.9i	0.467632	+	1.69752i
$825$			20016.5i			0.844711i
$826$	30957.5	+	25853.3i	1.30405	+	1.08905i
$827$	−22223.2	+	22223.2i	−0.934431	+	0.934431i	−0.997979	−	0.0635475i	$-0.979759\pi$
$827$	−22223.2	+	22223.2i	−0.934431	+	0.934431i	0.0635475	+	0.997979i	$0.479759\pi$
$828$	−12658.4	+	2293.09i	−0.531294	+	0.0962446i
$829$	14715.5	+	14715.5i	0.616516	+	0.616516i	0.944636	−	0.328120i	$-0.106415\pi$
$829$	14715.5	+	14715.5i	0.616516	+	0.616516i	−0.328120	+	0.944636i	$0.606415\pi$
$830$	8588.98	−	771.672i	0.359190	−	0.0322713i
$831$	16772.2			0.700145
$832$	−7912.13	−	2001.55i	−0.329692	−	0.0834031i
$833$	24495.8			1.01888
$834$	33630.0	−	3021.47i	1.39630	−	0.125450i
$835$	5697.46	+	5697.46i	0.236130	+	0.236130i
$836$	13303.3	−	2409.91i	0.550364	−	0.0996991i
$837$	3419.07	−	3419.07i	0.141195	−	0.141195i
$838$	10541.1	+	8803.12i	0.434530	+	0.362886i
$839$		−	11010.0i		−	0.453050i	−0.974005	−	0.226525i	$-0.927263\pi$
$839$		−	11010.0i		−	0.453050i	0.974005	−	0.226525i	$-0.0727365\pi$
$840$	−7670.13	−	27842.8i	−0.315053	−	1.14365i
$841$		−	24170.9i		−	0.991057i
$842$	−20444.5	+	24480.8i	−0.836773	+	1.00197i
$843$	−26108.1	+	26108.1i	−1.06668	+	1.06668i
$844$	−15067.2	−	10445.5i	−0.614496	−	0.426007i
$845$	9061.20	+	9061.20i	0.368893	+	0.368893i
$846$	−1866.32	−	20772.8i	−0.0758458	−	0.844190i
$847$	8279.85			0.335890
$848$	−6587.61	+	14479.1i	−0.266768	+	0.586338i
$849$	7080.22			0.286210
$850$	1825.21	+	20315.2i	0.0736520	+	0.819772i
$851$	−7857.37	−	7857.37i	−0.316507	−	0.316507i
$852$	−7618.74	+	10989.7i	−0.306354	+	0.441901i
$853$	12809.9	−	12809.9i	0.514190	−	0.514190i	−0.401617	−	0.915808i	$-0.631552\pi$
$853$	12809.9	−	12809.9i	0.514190	−	0.514190i	0.915808	+	0.401617i	$0.131552\pi$
$854$	−42422.7	+	50798.0i	−1.69985	+	2.03545i
$855$		−	11787.6i		−	0.471493i
$856$	1255.09	−	2209.52i	0.0501147	−	0.0882243i
$857$		−	38510.8i		−	1.53501i	−0.641043	−	0.767505i	$-0.721498\pi$
$857$		−	38510.8i		−	1.53501i	0.641043	−	0.767505i	$-0.278502\pi$
$858$	8499.18	+	7097.87i	0.338178	+	0.282421i
$859$	23234.6	−	23234.6i	0.922882	−	0.922882i	−0.0743503	−	0.997232i	$-0.523688\pi$
$859$	23234.6	−	23234.6i	0.922882	−	0.922882i	0.997232	+	0.0743503i	$0.0236883\pi$
$860$	−1333.41	−	7360.74i	−0.0528707	−	0.291860i
$861$	−49331.9	−	49331.9i	−1.95264	−	1.95264i
$862$	−13522.4	+	1214.92i	−0.534311	+	0.0480049i
$863$	−22079.5			−0.870911			−0.435456	−	0.900210i	$-0.643413\pi$
$863$	−22079.5			−0.870911			−0.435456	+	0.900210i	$0.643413\pi$
$864$	2988.22	−	8518.55i	0.117664	−	0.335425i
$865$	5255.26			0.206571
$866$	−17585.1	+	1579.93i	−0.690031	+	0.0619955i
$867$	16029.8	+	16029.8i	0.627912	+	0.627912i
$868$	3442.24	+	19002.0i	0.134605	+	0.743054i
$869$	−18387.4	+	18387.4i	−0.717779	+	0.717779i
$870$	1643.69	+	1372.68i	0.0640531	+	0.0534923i
$871$			2420.58i			0.0941656i
$872$	−26516.0	−	15062.1i	−1.02975	−	0.584939i
$873$		−	5039.15i		−	0.195360i
$874$	4666.26	−	5587.51i	0.180593	−	0.216247i
$875$	−23976.7	+	23976.7i	−0.926356	+	0.926356i
$876$	23686.5	−	34166.7i	0.913576	−	1.31779i
$877$	4082.13	+	4082.13i	0.157176	+	0.157176i	0.781314	−	0.624138i	$-0.214550\pi$
$877$	4082.13	+	4082.13i	0.157176	+	0.157176i	−0.624138	+	0.781314i	$0.714550\pi$
$878$	−1247.59	−	13886.2i	−0.0479547	−	0.533753i
$879$	−15753.9			−0.604510
$880$	4678.80	+	12490.3i	0.179230	+	0.478463i
$881$	7132.59			0.272762			0.136381	−	0.990656i	$-0.456453\pi$
$881$	7132.59			0.272762			0.136381	+	0.990656i	$0.456453\pi$
$882$	2341.36	+	26060.2i	0.0893853	+	0.994889i
$883$	19170.0	+	19170.0i	0.730601	+	0.730601i	0.970739	−	0.240138i	$-0.0771926\pi$
$883$	19170.0	+	19170.0i	0.730601	+	0.730601i	−0.240138	+	0.970739i	$0.577193\pi$
$884$	9273.21	+	6428.78i	0.352819	+	0.244596i
$885$	−20762.9	+	20762.9i	−0.788628	+	0.788628i
$886$	19667.4	−	23550.3i	0.745757	−	0.892989i
$887$			45045.7i			1.70517i	0.522589	+	0.852585i	$0.324966\pi$
$887$			45045.7i			1.70517i	−0.522589	+	0.852585i	$0.675034\pi$
$888$	39153.7	−	10786.0i	1.47963	−	0.407607i
$889$		−	65287.3i		−	2.46306i
$890$	−3761.94	−	3141.69i	−0.141686	−	0.118325i
$891$	11497.8	−	11497.8i	0.432314	−	0.432314i
$892$	−3303.17	+	598.374i	−0.123989	+	0.0224608i
$893$	8345.43	+	8345.43i	0.312731	+	0.312731i
$894$	70746.8	−	6356.21i	2.64667	−	0.237789i
$895$	20541.1			0.767167
$896$	21160.2	+	29191.4i	0.788964	+	1.08841i
$897$	5962.34			0.221936
$898$	32439.2	−	2914.49i	1.20547	−	0.108305i
$899$	−1012.55	−	1012.55i	−0.0375643	−	0.0375643i
$900$	−21438.2	+	3883.55i	−0.794006	+	0.143835i
$901$	15551.4	−	15551.4i	0.575017	−	0.575017i
$902$	24730.6	+	20653.2i	0.912905	+	0.762389i
$903$			27435.3i			1.01106i
$904$	15716.9	−	4329.68i	0.578247	−	0.159295i
$905$			1131.36i			0.0415554i
$906$	−39660.6	+	47490.7i	−1.45435	+	1.74147i
$907$	−33658.2	+	33658.2i	−1.23220	+	1.23220i	−0.269079	+	0.963118i	$0.586719\pi$
$907$	−33658.2	+	33658.2i	−1.23220	+	1.23220i	−0.963118	+	0.269079i	$0.913281\pi$
$908$	−19838.3	−	13753.2i	−0.725065	−	0.502661i
$909$	16306.5	+	16306.5i	0.594997	+	0.594997i
$910$	662.476	+	7373.59i	0.0241328	+	0.268607i
$911$	−42503.8			−1.54579			−0.772895	−	0.634534i	$-0.781192\pi$
$911$	−42503.8			−1.54579			−0.772895	+	0.634534i	$0.781192\pi$
$912$	9333.11	+	24915.2i	0.338871	+	0.904632i
$913$	14606.7			0.529477
$914$	−1222.44	−	13606.2i	−0.0442394	−	0.492399i
$915$	−34069.7	−	34069.7i	−1.23094	−	1.23094i
$916$	−10148.5	+	14638.7i	−0.366066	+	0.528033i
$917$	16371.3	−	16371.3i	0.589562	−	0.589562i
$918$	−8000.34	+	9579.82i	−0.287637	+	0.344424i
$919$			8819.41i			0.316568i	0.987394	+	0.158284i	$0.0505961\pi$
$919$			8819.41i			0.316568i	−0.987394	+	0.158284i	$0.949404\pi$
$920$	6244.60	+	3547.17i	0.223781	+	0.127116i
$921$		−	2541.55i		−	0.0909305i
$922$	−25377.5	−	21193.3i	−0.906467	−	0.757012i
$923$	2423.92	−	2423.92i	0.0864402	−	0.0864402i
$924$	−8719.53	−	48134.0i	−0.310445	−	1.71374i
$925$	−13307.1	−	13307.1i	−0.473012	−	0.473012i
$926$	14209.0	−	1276.60i	0.504250	−	0.0453041i
$927$	61504.8			2.17916
$928$	−2522.73	−	884.950i	−0.0892380	−	0.0313038i
$929$	−14155.6			−0.499925			−0.249963	−	0.968256i	$-0.580418\pi$
$929$	−14155.6			−0.499925			−0.249963	+	0.968256i	$0.580418\pi$
$930$	−14002.5	+	1258.05i	−0.493721	+	0.0443581i
$931$	−10469.6	−	10469.6i	−0.368558	−	0.368558i
$932$	1703.87	+	9405.80i	0.0598844	+	0.330577i
$933$	−4789.43	+	4789.43i	−0.168059	+	0.168059i
$934$	−38189.4	−	31892.9i	−1.33790	−	1.11731i
$935$		−	18440.6i		−	0.644996i
$936$	−5952.99	+	10479.9i	−0.207884	+	0.365969i
$937$			38518.7i			1.34296i	0.741023	+	0.671479i	$0.234341\pi$
$937$			38518.7i			1.34296i	−0.741023	+	0.671479i	$0.765659\pi$
$938$	6854.32	−	8207.55i	0.238594	−	0.285699i
$939$	19319.2	−	19319.2i	0.671414	−	0.671414i
$940$	−6633.71	+	9568.82i	−0.230179	+	0.332022i
$941$	27998.2	+	27998.2i	0.969942	+	0.969942i	0.999561	−	0.0296196i	$-0.00942960\pi$
$941$	27998.2	+	27998.2i	0.969942	+	0.969942i	−0.0296196	+	0.999561i	$0.509430\pi$
$942$	2521.49	+	28065.1i	0.0872130	+	0.970711i
$943$	17349.0			0.599112
$944$	15180.7	−	33366.0i	0.523399	−	1.15039i
$945$	−8188.93			−0.281890
$946$	−1133.82	−	12619.8i	−0.0389680	−	0.433727i
$947$	−32839.5	−	32839.5i	−1.12687	−	1.12687i	−0.990684	−	0.136181i	$-0.956517\pi$
$947$	−32839.5	−	32839.5i	−1.12687	−	1.12687i	−0.136181	−	0.990684i	$-0.543483\pi$
$948$	−42055.4	−	29155.5i	−1.44082	−	0.998867i
$949$	−7535.92	+	7535.92i	−0.257773	+	0.257773i
$950$	7902.71	−	9462.92i	0.269892	−	0.323176i
$951$			51925.4i			1.77055i
$952$	−13238.7	−	48057.1i	−0.450704	−	1.63607i
$953$			20600.1i			0.700211i	0.936710	+	0.350106i	$0.113854\pi$
$953$			20600.1i			0.700211i	−0.936710	+	0.350106i	$0.886146\pi$
$954$	18031.0	+	15058.1i	0.611922	+	0.511031i
$955$	−18317.5	+	18317.5i	−0.620670	+	0.620670i
$956$	−33384.9	+	6047.72i	−1.12944	+	0.204600i
$957$	2564.88	+	2564.88i	0.0866360	+	0.0866360i
$958$	−36790.3	+	3305.41i	−1.24075	+	0.111475i
$959$	62528.2			2.10547
$960$	−22545.0	+	13441.4i	−0.757955	+	0.451896i
$961$	−20390.2			−0.684441
$962$	−10369.0	+	931.599i	−0.347516	+	0.0312224i
$963$	−2653.56	−	2653.56i	−0.0887951	−	0.0887951i
$964$	−43855.8	+	7944.53i	−1.46525	+	0.265432i
$965$	15152.5	−	15152.5i	0.505469	−	0.505469i
$966$	−20216.7	−	16883.5i	−0.673356	−	0.562336i
$967$		−	38210.9i		−	1.27071i	−0.772219	−	0.635356i	$-0.780853\pi$
$967$		−	38210.9i		−	1.27071i	0.772219	−	0.635356i	$-0.219147\pi$
$968$	−1998.59	−	7254.96i	−0.0663607	−	0.240892i
$969$		−	36784.6i		−	1.21950i
$970$	−1803.23	+	2159.23i	−0.0596888	+	0.0714730i
$971$	37224.9	−	37224.9i	1.23028	−	1.23028i	0.266427	−	0.963855i	$-0.414157\pi$
$971$	37224.9	−	37224.9i	1.23028	−	1.23028i	0.963855	−	0.266427i	$-0.0858430\pi$
$972$	35150.3	+	24368.4i	1.15992	+	0.804133i
$973$	27038.1	+	27038.1i	0.890854	+	0.890854i
$974$	−3935.51	−	43803.6i	−0.129468	−	1.44102i
$975$	10097.7			0.331678
$976$	54750.2	+	24909.9i	1.79560	+	0.816953i
$977$	7985.95			0.261508			0.130754	−	0.991415i	$-0.458260\pi$
$977$	7985.95			0.261508			0.130754	+	0.991415i	$0.458260\pi$
$978$	−3873.76	−	43116.3i	−0.126656	−	1.40972i
$979$	−5870.28	−	5870.28i	−0.191639	−	0.191639i
$980$	8322.21	−	12004.4i	0.271269	−	0.391292i
$981$	−31844.8	+	31844.8i	−1.03642	+	1.03642i
$982$	22122.9	−	26490.5i	0.718910	−	0.860842i
$983$			10703.1i			0.347279i	0.984809	+	0.173639i	$0.0555527\pi$
$983$			10703.1i			0.347279i	−0.984809	+	0.173639i	$0.944447\pi$
$984$	−31317.8	+	55133.3i	−1.01461	+	1.78616i
$985$			22580.9i			0.730442i
$986$	2837.03	+	2369.27i	0.0916322	+	0.0765243i
$987$	30195.4	−	30195.4i	0.973791	−	0.973791i
$988$	−1215.72	−	6711.10i	−0.0391471	−	0.216102i
$989$	−4824.23	−	4824.23i	−0.155108	−	0.155108i
$990$	19618.2	−	1762.59i	0.629807	−	0.0565847i
$991$	−23945.4			−0.767558			−0.383779	−	0.923425i	$-0.625377\pi$
$991$	−23945.4			−0.767558			−0.383779	+	0.923425i	$0.625377\pi$
$992$	15819.0	−	7602.87i	0.506306	−	0.243338i
$993$	−20009.0			−0.639442
$994$	−15082.6	+	1355.09i	−0.481280	+	0.0432404i
$995$	−6395.37	−	6395.37i	−0.203766	−	0.203766i
$996$	5123.78	+	28284.5i	0.163005	+	0.899829i
$997$	−14292.5	+	14292.5i	−0.454010	+	0.454010i	−0.896683	−	0.442673i	$-0.854030\pi$
$997$	−14292.5	+	14292.5i	−0.454010	+	0.454010i	0.442673	+	0.896683i	$0.354030\pi$
$998$	−5318.83	−	4441.88i	−0.168702	−	0.140887i
$999$		−	11515.6i		−	0.364702i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.4.e.a.13.1	yes	10
3.2	odd	2		144.4.k.a.109.5		10
4.3	odd	2		64.4.e.a.17.1		10
8.3	odd	2		128.4.e.a.33.5		10
8.5	even	2		128.4.e.b.33.1		10
12.11	even	2		576.4.k.a.145.4		10
16.3	odd	4		128.4.e.a.97.5		10
16.5	even	4	inner	16.4.e.a.5.1	✓	10
16.11	odd	4		64.4.e.a.49.1		10
16.13	even	4		128.4.e.b.97.1		10
32.3	odd	8		1024.4.b.k.513.2		10
32.5	even	8		1024.4.a.n.1.2		10
32.11	odd	8		1024.4.a.m.1.2		10
32.13	even	8		1024.4.b.j.513.2		10
32.19	odd	8		1024.4.b.k.513.9		10
32.21	even	8		1024.4.a.n.1.9		10
32.27	odd	8		1024.4.a.m.1.9		10
32.29	even	8		1024.4.b.j.513.9		10
48.5	odd	4		144.4.k.a.37.5		10
48.11	even	4		576.4.k.a.433.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.4.e.a.5.1	✓	10	16.5	even	4	inner
16.4.e.a.13.1	yes	10	1.1	even	1	trivial
64.4.e.a.17.1		10	4.3	odd	2
64.4.e.a.49.1		10	16.11	odd	4
128.4.e.a.33.5		10	8.3	odd	2
128.4.e.a.97.5		10	16.3	odd	4
128.4.e.b.33.1		10	8.5	even	2
128.4.e.b.97.1		10	16.13	even	4
144.4.k.a.37.5		10	48.5	odd	4
144.4.k.a.109.5		10	3.2	odd	2
576.4.k.a.145.4		10	12.11	even	2
576.4.k.a.433.4		10	48.11	even	4
1024.4.a.m.1.2		10	32.11	odd	8
1024.4.a.m.1.9		10	32.27	odd	8
1024.4.a.n.1.2		10	32.5	even	8
1024.4.a.n.1.9		10	32.21	even	8
1024.4.b.j.513.2		10	32.13	even	8
1024.4.b.j.513.9		10	32.29	even	8
1024.4.b.k.513.2		10	32.3	odd	8
1024.4.b.k.513.9		10	32.19	odd	8

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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.81708 + 0.253099i) q^{2} +(5.49618 + 5.49618i) q^{3} +(7.87188 - 1.42600i) q^{4} +(-4.66372 + 4.66372i) q^{5} +(-16.8743 - 14.0921i) q^{6} -24.8965i q^{7} +(-21.8148 + 6.00953i) q^{8} +33.4160i q^{9} +(11.9577 - 14.3185i) q^{10} +(22.3431 - 22.3431i) q^{11} +(51.1028 + 35.4277i) q^{12} +(-11.2714 - 11.2714i) q^{13} +(6.30129 + 70.1355i) q^{14} -51.2653 q^{15} +(59.9330 - 22.4506i) q^{16} -88.4846 q^{17} +(-8.45756 - 94.1356i) q^{18} +(37.8187 + 37.8187i) q^{19} +(-30.0618 + 43.3627i) q^{20} +(136.836 - 136.836i) q^{21} +(-57.2873 + 68.5974i) q^{22} +48.1224i q^{23} +(-152.928 - 86.8686i) q^{24} +81.4994i q^{25} +(34.6053 + 28.8997i) q^{26} +(-35.2635 + 35.2635i) q^{27} +(-35.5025 - 195.982i) q^{28} +(10.4432 + 10.4432i) q^{29} +(144.419 - 12.9752i) q^{30} -96.9578 q^{31} +(-163.154 + 78.4142i) q^{32} +245.604 q^{33} +(249.268 - 22.3954i) q^{34} +(116.110 + 116.110i) q^{35} +(47.6513 + 263.047i) q^{36} +(-163.279 + 163.279i) q^{37} +(-116.110 - 96.9665i) q^{38} -123.899i q^{39} +(73.7114 - 129.765i) q^{40} -360.519i q^{41} +(-350.844 + 420.110i) q^{42} +(-100.249 + 100.249i) q^{43} +(144.021 - 207.744i) q^{44} +(-155.843 - 155.843i) q^{45} +(-12.1797 - 135.565i) q^{46} +220.669 q^{47} +(452.796 + 206.010i) q^{48} -276.837 q^{49} +(-20.6274 - 229.590i) q^{50} +(-486.327 - 486.327i) q^{51} +(-104.800 - 72.6542i) q^{52} +(-175.752 + 175.752i) q^{53} +(90.4150 - 108.265i) q^{54} +208.404i q^{55} +(149.616 + 543.113i) q^{56} +415.717i q^{57} +(-32.0624 - 26.7761i) q^{58} +(405.008 - 405.008i) q^{59} +(-403.555 + 73.1044i) q^{60} +(664.576 + 664.576i) q^{61} +(273.138 - 24.5399i) q^{62} +831.942 q^{63} +(439.771 - 262.193i) q^{64} +105.133 q^{65} +(-691.885 + 62.1621i) q^{66} +(-107.377 - 107.377i) q^{67} +(-696.540 + 126.179i) q^{68} +(-264.489 + 264.489i) q^{69} +(-356.480 - 297.705i) q^{70} +215.050i q^{71} +(-200.814 - 728.964i) q^{72} -668.587i q^{73} +(418.644 - 501.296i) q^{74} +(-447.935 + 447.935i) q^{75} +(351.634 + 243.775i) q^{76} +(-556.266 - 556.266i) q^{77} +(31.3588 + 349.035i) q^{78} -822.956 q^{79} +(-174.808 + 384.215i) q^{80} +514.603 q^{81} +(91.2471 + 1015.61i) q^{82} +(326.873 + 326.873i) q^{83} +(882.027 - 1272.28i) q^{84} +(412.668 - 412.668i) q^{85} +(257.037 - 307.783i) q^{86} +114.795i q^{87} +(-353.139 + 621.682i) q^{88} -262.733i q^{89} +(478.466 + 399.578i) q^{90} +(-280.619 + 280.619i) q^{91} +(68.6226 + 378.814i) q^{92} +(-532.898 - 532.898i) q^{93} +(-621.643 + 55.8512i) q^{94} -352.752 q^{95} +(-1327.70 - 465.745i) q^{96} -150.801 q^{97} +(779.871 - 70.0671i) q^{98} +(746.618 + 746.618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{5} - 32 q^{6} - 44 q^{8} - 68 q^{10} + 18 q^{11} + 100 q^{12} - 2 q^{13} + 188 q^{14} - 124 q^{15} + 280 q^{16} - 4 q^{17} + 174 q^{18} - 26 q^{19} - 196 q^{20}+ \cdots + 4958 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^5 - 32 * q^6 - 44 * q^8 - 68 * q^10 + 18 * q^11 + 100 * q^12 - 2 * q^13 + 188 * q^14 - 124 * q^15 + 280 * q^16 - 4 * q^17 + 174 * q^18 - 26 * q^19 - 196 * q^20 + 52 * q^21 - 588 * q^22 - 848 * q^24 - 264 * q^26 + 184 * q^27 + 280 * q^28 - 202 * q^29 + 1236 * q^30 + 368 * q^31 + 968 * q^32 - 4 * q^33 + 436 * q^34 + 476 * q^35 - 596 * q^36 - 10 * q^37 - 1232 * q^38 - 1336 * q^40 - 680 * q^42 - 838 * q^43 + 868 * q^44 + 194 * q^45 + 1132 * q^46 - 944 * q^47 + 1768 * q^48 + 94 * q^49 + 726 * q^50 - 1500 * q^51 - 236 * q^52 - 378 * q^53 - 1376 * q^54 - 488 * q^56 + 8 * q^58 + 1706 * q^59 - 192 * q^60 + 910 * q^61 - 80 * q^62 + 2628 * q^63 + 512 * q^64 - 492 * q^65 - 428 * q^66 + 1942 * q^67 - 880 * q^68 + 580 * q^69 + 160 * q^70 + 1092 * q^72 - 452 * q^74 - 2954 * q^75 - 1228 * q^76 - 268 * q^77 - 772 * q^78 - 4416 * q^79 - 2648 * q^80 + 482 * q^81 - 704 * q^82 - 2562 * q^83 + 1960 * q^84 - 12 * q^85 + 3764 * q^86 + 1528 * q^88 + 1896 * q^90 + 3332 * q^91 + 632 * q^92 - 2192 * q^93 - 3248 * q^94 + 6900 * q^95 - 4432 * q^96 - 4 * q^97 + 314 * q^98 + 4958 * q^99

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