LMFDB - Embedded newform 26.4.e.a.23.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [26,4,Mod(17,26)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("26.17"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(26, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 4, names="a")

Level:	$N$	$=$	$26 = 2 \cdot 13$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	26.e (of order $6$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.53404966015$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} + 122x^{6} + 5305x^{4} + 97056x^{2} + 627264$ x^8 + 122x^6 + 5305x^4 + 97056*x^2 + 627264
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$2^{4}$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.3
Root			$-6.87513i$ of defining polynomial
Character	$\chi$	$=$	26.23
Dual form			26.4.e.a.17.3

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 - 1.00000i) q^{2} +(-3.93757 - 6.82006i) q^{3} +(2.00000 - 3.46410i) q^{4} +3.30629i q^{5} +(-13.6401 - 7.87513i) q^{6} +(27.1849 + 15.6952i) q^{7} -8.00000i q^{8} +(-17.5089 + 30.3262i) q^{9} +(3.30629 + 5.72666i) q^{10} +(13.5192 - 7.80533i) q^{11} -31.5005 q^{12} +(-45.2497 - 12.2255i) q^{13} +62.7808 q^{14} +(22.5491 - 13.0187i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-53.8638 + 93.2949i) q^{17} +70.0354i q^{18} +(52.6358 + 30.3893i) q^{19} +(11.4533 + 6.61258i) q^{20} -247.203i q^{21} +(15.6107 - 27.0385i) q^{22} +(-62.1540 - 107.654i) q^{23} +(-54.5605 + 31.5005i) q^{24} +114.068 q^{25} +(-90.6003 + 24.0746i) q^{26} +63.1404 q^{27} +(108.740 - 62.7808i) q^{28} +(-29.1001 - 50.4028i) q^{29} +(26.0375 - 45.0982i) q^{30} +200.934i q^{31} +(-27.7128 - 16.0000i) q^{32} +(-106.466 - 61.4680i) q^{33} +215.455i q^{34} +(-51.8928 + 89.8810i) q^{35} +(70.0354 + 121.305i) q^{36} +(-90.9447 + 52.5069i) q^{37} +121.557 q^{38} +(94.7953 + 356.745i) q^{39} +26.4503 q^{40} +(-191.461 + 110.540i) q^{41} +(-247.203 - 428.169i) q^{42} +(56.0339 - 97.0535i) q^{43} -62.4426i q^{44} +(-100.267 - 57.8893i) q^{45} +(-215.308 - 124.308i) q^{46} -512.102i q^{47} +(-63.0011 + 109.121i) q^{48} +(321.178 + 556.297i) q^{49} +(197.572 - 114.068i) q^{50} +848.370 q^{51} +(-132.850 + 132.299i) q^{52} -221.755 q^{53} +(109.362 - 63.1404i) q^{54} +(25.8067 + 44.6985i) q^{55} +(125.562 - 217.479i) q^{56} -478.639i q^{57} +(-100.806 - 58.2002i) q^{58} +(-482.310 - 278.462i) q^{59} -104.150i q^{60} +(229.105 - 396.821i) q^{61} +(200.934 + 348.028i) q^{62} +(-951.952 + 549.610i) q^{63} -64.0000 q^{64} +(40.4209 - 149.609i) q^{65} -245.872 q^{66} +(458.769 - 264.870i) q^{67} +(215.455 + 373.180i) q^{68} +(-489.471 + 847.789i) q^{69} +207.571i q^{70} +(58.5007 + 33.7754i) q^{71} +(242.610 + 140.071i) q^{72} +104.504i q^{73} +(-105.014 + 181.889i) q^{74} +(-449.152 - 777.954i) q^{75} +(210.543 - 121.557i) q^{76} +490.025 q^{77} +(520.935 + 523.105i) q^{78} +611.085 q^{79} +(45.8133 - 26.4503i) q^{80} +(224.119 + 388.186i) q^{81} +(-221.080 + 382.922i) q^{82} +491.565i q^{83} +(-856.338 - 494.407i) q^{84} +(-308.460 - 178.089i) q^{85} -224.136i q^{86} +(-229.167 + 396.929i) q^{87} +(-62.4426 - 108.154i) q^{88} +(326.626 - 188.578i) q^{89} -231.557 q^{90} +(-1038.23 - 1042.55i) q^{91} -497.232 q^{92} +(1370.38 - 791.191i) q^{93} +(-512.102 - 886.987i) q^{94} +(-100.476 + 174.029i) q^{95} +252.004i q^{96} +(-496.503 - 286.656i) q^{97} +(1112.59 + 642.357i) q^{98} +546.649i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q - 6 q^{3} + 16 q^{4} + 18 q^{7} - 22 q^{9} - 8 q^{10} - 18 q^{11} - 48 q^{12} - 130 q^{13} + 80 q^{14} - 192 q^{15} - 64 q^{16} + 112 q^{17} + 594 q^{19} + 72 q^{20} - 72 q^{22} - 230 q^{23} - 180 q^{25}+ \cdots + 4272 q^{98}+O(q^{100})$ 8 * q - 6 * q^3 + 16 * q^4 + 18 * q^7 - 22 * q^9 - 8 * q^10 - 18 * q^11 - 48 * q^12 - 130 * q^13 + 80 * q^14 - 192 * q^15 - 64 * q^16 + 112 * q^17 + 594 * q^19 + 72 * q^20 - 72 * q^22 - 230 * q^23 - 180 * q^25 - 184 * q^26 + 468 * q^27 + 72 * q^28 + 32 * q^29 + 328 * q^30 - 42 * q^33 - 128 * q^35 + 88 * q^36 - 768 * q^37 - 576 * q^38 - 230 * q^39 - 64 * q^40 - 564 * q^41 - 688 * q^42 - 114 * q^43 + 630 * q^45 + 576 * q^46 - 96 * q^48 - 110 * q^49 + 1968 * q^50 + 1300 * q^51 - 104 * q^52 + 36 * q^53 + 648 * q^54 + 1248 * q^55 + 160 * q^56 - 1848 * q^58 - 1110 * q^59 + 900 * q^61 + 1064 * q^62 - 1980 * q^63 - 512 * q^64 + 1870 * q^65 - 2400 * q^66 + 510 * q^67 - 448 * q^68 - 2402 * q^69 - 1470 * q^71 + 576 * q^72 - 680 * q^74 - 862 * q^75 + 2376 * q^76 + 2340 * q^77 + 1016 * q^78 + 784 * q^79 + 288 * q^80 + 1868 * q^81 + 704 * q^82 - 2136 * q^84 - 2898 * q^85 + 1598 * q^87 + 288 * q^88 - 4434 * q^89 - 2384 * q^90 - 886 * q^91 - 1840 * q^92 + 3108 * q^93 - 2568 * q^94 - 816 * q^95 + 1854 * q^97 + 4272 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$ .

$n$	$15$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$	−3.93757	−	6.82006i	−0.757785	−	1.31252i	−0.943978	−	0.330009i	$-0.892948\pi$
$3$	−3.93757	−	6.82006i	−0.757785	−	1.31252i	0.186193	−	0.982513i	$-0.440385\pi$
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$			3.30629i			0.295723i	0.989008	+	0.147862i	$0.0472390\pi$
$5$			3.30629i			0.295723i	−0.989008	+	0.147862i	$0.952761\pi$
$6$	−13.6401	−	7.87513i	−0.928093	−	0.535835i
$7$	27.1849	+	15.6952i	1.46785	+	0.847461i	0.999352	−	0.0360059i	$-0.0114635\pi$
$7$	27.1849	+	15.6952i	1.46785	+	0.847461i	0.468494	+	0.883467i	$0.344797\pi$
$8$		−	8.00000i		−	0.353553i
$9$	−17.5089	+	30.3262i	−0.648476	+	1.12319i
$10$	3.30629	+	5.72666i	0.104554	+	0.181093i
$11$	13.5192	−	7.80533i	0.370564	−	0.213945i	−0.303141	−	0.952946i	$-0.598035\pi$
$11$	13.5192	−	7.80533i	0.370564	−	0.213945i	0.673705	+	0.739001i	$0.264702\pi$
$12$	−31.5005			−0.757785
$13$	−45.2497	−	12.2255i	−0.965386	−	0.260826i
$13$	−45.2497	−	12.2255i	−0.965386	−	0.260826i
$14$	62.7808			1.19849
$15$	22.5491	−	13.0187i	0.388143	−	0.224095i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−53.8638	+	93.2949i	−0.768465	+	1.33102i	0.169930	+	0.985456i	$0.445646\pi$
$17$	−53.8638	+	93.2949i	−0.768465	+	1.33102i	−0.938395	+	0.345564i	$0.887688\pi$
$18$			70.0354i			0.917083i
$19$	52.6358	+	30.3893i	0.635551	+	0.366936i	0.782899	−	0.622149i	$-0.213740\pi$
$19$	52.6358	+	30.3893i	0.635551	+	0.366936i	−0.147347	+	0.989085i	$0.547074\pi$
$20$	11.4533	+	6.61258i	0.128052	+	0.0739308i
$21$		−	247.203i		−	2.56877i
$22$	15.6107	−	27.0385i	0.151282	−	0.262028i
$23$	−62.1540	−	107.654i	−0.563479	−	0.975974i	−0.997189	−	0.0749214i	$-0.976129\pi$
$23$	−62.1540	−	107.654i	−0.563479	−	0.975974i	0.433711	−	0.901052i	$-0.357204\pi$
$24$	−54.5605	+	31.5005i	−0.464047	+	0.267917i
$25$	114.068			0.912548
$26$	−90.6003	+	24.0746i	−0.683392	+	0.181593i
$27$	63.1404			0.450051
$28$	108.740	−	62.7808i	0.733923	−	0.423730i
$29$	−29.1001	−	50.4028i	−0.186336	−	0.322744i	0.757690	−	0.652615i	$-0.226328\pi$
$29$	−29.1001	−	50.4028i	−0.186336	−	0.322744i	−0.944026	+	0.329871i	$0.892995\pi$
$30$	26.0375	−	45.0982i	0.158459	−	0.274459i
$31$			200.934i			1.16416i	0.813133	+	0.582078i	$0.197760\pi$
$31$			200.934i			1.16416i	−0.813133	+	0.582078i	$0.802240\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$	−106.466	−	61.4680i	−0.561615	−	0.324249i
$34$			215.455i			1.08677i
$35$	−51.8928	+	89.8810i	−0.250614	+	0.434076i
$36$	70.0354	+	121.305i	0.324238	+	0.561597i
$37$	−90.9447	+	52.5069i	−0.404087	+	0.233300i	−0.688246	−	0.725478i	$-0.741619\pi$
$37$	−90.9447	+	52.5069i	−0.404087	+	0.233300i	0.284159	+	0.958777i	$0.408286\pi$
$38$	121.557			0.518926
$39$	94.7953	+	356.745i	0.389215	+	1.46474i
$40$	26.4503			0.104554
$41$	−191.461	+	110.540i	−0.729298	+	0.421060i	−0.818165	−	0.574983i	$-0.805009\pi$
$41$	−191.461	+	110.540i	−0.729298	+	0.421060i	0.0888675	+	0.996043i	$0.471675\pi$
$42$	−247.203	−	428.169i	−0.908198	−	1.57305i
$43$	56.0339	−	97.0535i	0.198723	−	0.344198i	−0.749392	−	0.662127i	$-0.769654\pi$
$43$	56.0339	−	97.0535i	0.198723	−	0.344198i	0.948115	+	0.317929i	$0.102987\pi$
$44$		−	62.4426i		−	0.213945i
$45$	−100.267	−	57.8893i	−0.332154	−	0.191769i
$46$	−215.308	−	124.308i	−0.690117	−	0.398440i
$47$		−	512.102i		−	1.58931i	−0.607058	−	0.794657i	$-0.707651\pi$
$47$		−	512.102i		−	1.58931i	0.607058	−	0.794657i	$-0.292349\pi$
$48$	−63.0011	+	109.121i	−0.189446	+	0.328130i
$49$	321.178	+	556.297i	0.936380	+	1.62186i
$50$	197.572	−	114.068i	0.558819	−	0.322634i
$51$	848.370			2.32932
$52$	−132.850	+	132.299i	−0.354287	+	0.352818i
$53$	−221.755			−0.574724			−0.287362	−	0.957822i	$-0.592778\pi$
$53$	−221.755			−0.574724			−0.287362	+	0.957822i	$0.592778\pi$
$54$	109.362	−	63.1404i	0.275599	−	0.159117i
$55$	25.8067	+	44.6985i	0.0632686	+	0.109584i
$56$	125.562	−	217.479i	0.299623	−	0.518962i
$57$		−	478.639i		−	1.11223i
$58$	−100.806	−	58.2002i	−0.228214	−	0.131760i
$59$	−482.310	−	278.462i	−1.06426	−	0.614452i	−0.137654	−	0.990480i	$-0.543956\pi$
$59$	−482.310	−	278.462i	−1.06426	−	0.614452i	−0.926608	+	0.376028i	$0.877290\pi$
$60$		−	104.150i		−	0.224095i
$61$	229.105	−	396.821i	0.480882	−	0.832913i	−0.518877	−	0.854849i	$-0.673650\pi$
$61$	229.105	−	396.821i	0.480882	−	0.832913i	0.999759	+	0.0219361i	$0.00698304\pi$
$62$	200.934	+	348.028i	0.411591	+	0.712897i
$63$	−951.952	+	549.610i	−1.90372	+	1.09912i
$64$	−64.0000			−0.125000
$65$	40.4209	−	149.609i	0.0771323	−	0.285487i
$66$	−245.872			−0.458557
$67$	458.769	−	264.870i	0.836530	−	0.482971i	−0.0195533	−	0.999809i	$-0.506224\pi$
$67$	458.769	−	264.870i	0.836530	−	0.482971i	0.856083	+	0.516838i	$0.172891\pi$
$68$	215.455	+	373.180i	0.384232	+	0.665510i
$69$	−489.471	+	847.789i	−0.853991	+	1.47916i
$70$			207.571i			0.354422i
$71$	58.5007	+	33.7754i	0.0977854	+	0.0564564i	0.548095	−	0.836416i	$-0.315353\pi$
$71$	58.5007	+	33.7754i	0.0977854	+	0.0564564i	−0.450310	+	0.892872i	$0.648686\pi$
$72$	242.610	+	140.071i	0.397109	+	0.229271i
$73$			104.504i			0.167552i	0.996485	+	0.0837759i	$0.0266980\pi$
$73$			104.504i			0.167552i	−0.996485	+	0.0837759i	$0.973302\pi$
$74$	−105.014	+	181.889i	−0.164968	+	0.285732i
$75$	−449.152	−	777.954i	−0.691515	−	1.19774i
$76$	210.543	−	121.557i	0.317776	−	0.183468i
$77$	490.025			0.725240
$78$	520.935	+	523.105i	0.756209	+	0.759358i
$79$	611.085			0.870284			0.435142	−	0.900362i	$-0.356698\pi$
$79$	611.085			0.870284			0.435142	+	0.900362i	$0.356698\pi$
$80$	45.8133	−	26.4503i	0.0640260	−	0.0369654i
$81$	224.119	+	388.186i	0.307434	+	0.532491i
$82$	−221.080	+	382.922i	−0.297735	+	0.515691i
$83$			491.565i			0.650075i	0.945701	+	0.325038i	$0.105377\pi$
$83$			491.565i			0.650075i	−0.945701	+	0.325038i	$0.894623\pi$
$84$	−856.338	−	494.407i	−1.11231	−	0.642193i
$85$	−308.460	−	178.089i	−0.393614	−	0.227253i
$86$		−	224.136i		−	0.281037i
$87$	−229.167	+	396.929i	−0.282406	+	0.489141i
$88$	−62.4426	−	108.154i	−0.0756410	−	0.131014i
$89$	326.626	−	188.578i	0.389014	−	0.224598i	−0.292719	−	0.956199i	$-0.594560\pi$
$89$	326.626	−	188.578i	0.389014	−	0.224598i	0.681733	+	0.731601i	$0.261227\pi$
$90$	−231.557			−0.271203
$91$	−1038.23	−	1042.55i	−1.19600	−	1.20098i
$92$	−497.232			−0.563479
$93$	1370.38	−	791.191i	1.52798	−	0.882179i
$94$	−512.102	−	886.987i	−0.561908	−	0.973252i
$95$	−100.476	+	174.029i	−0.108511	+	0.187947i
$96$			252.004i			0.267917i
$97$	−496.503	−	286.656i	−0.519713	−	0.300057i	0.217104	−	0.976148i	$-0.430339\pi$
$97$	−496.503	−	286.656i	−0.519713	−	0.300057i	−0.736817	+	0.676092i	$0.763672\pi$
$98$	1112.59	+	642.357i	1.14683	+	0.662121i
$99$			546.649i			0.554953i
$100$	228.137	−	395.145i	0.228137	−	0.395145i
$101$	477.751	+	827.489i	0.470673	+	0.815230i	0.999437	−	0.0335385i	$-0.0106776\pi$
$101$	477.751	+	827.489i	0.470673	+	0.815230i	−0.528764	+	0.848769i	$0.677344\pi$
$102$	1469.42	−	848.370i	1.42641	−	0.823540i
$103$	−1478.96			−1.41481			−0.707407	−	0.706806i	$-0.750135\pi$
$103$	−1478.96			−1.41481			−0.707407	+	0.706806i	$0.750135\pi$
$104$	−97.8037	+	361.998i	−0.0922158	+	0.341315i
$105$	817.326			0.759646
$106$	−384.091	+	221.755i	−0.351945	+	0.203196i
$107$	−106.558	−	184.564i	−0.0962741	−	0.166752i	0.813866	−	0.581053i	$-0.197359\pi$
$107$	−106.558	−	184.564i	−0.0962741	−	0.166752i	−0.910140	+	0.414302i	$0.864026\pi$
$108$	126.281	−	218.725i	0.112513	−	0.194878i
$109$			84.4197i			0.0741829i	0.999312	+	0.0370915i	$0.0118093\pi$
$109$			84.4197i			0.0741829i	−0.999312	+	0.0370915i	$0.988191\pi$
$110$	89.3969	+	51.6133i	0.0774878	+	0.0447376i
$111$	716.201	+	413.499i	0.612422	+	0.353582i
$112$		−	502.246i		−	0.423730i
$113$	393.209	−	681.058i	0.327345	−	0.566979i	−0.654639	−	0.755942i	$-0.727179\pi$
$113$	393.209	−	681.058i	0.327345	−	0.566979i	0.981984	+	0.188963i	$0.0605127\pi$
$114$	−478.639	−	829.027i	−0.393234	−	0.681101i
$115$	355.935	−	205.499i	0.288618	−	0.166634i
$116$	−232.801			−0.186336
$117$	1163.02	−	1158.20i	0.918987	−	0.915176i
$118$	−1113.85			−0.868966
$119$	−2928.56	+	1690.81i	−2.25598	+	1.30249i
$120$	−104.150	−	180.393i	−0.0792294	−	0.137229i
$121$	−543.654	+	941.636i	−0.408455	+	0.707465i
$122$		−	916.418i		−	0.680070i
$123$	1507.78	+	870.518i	1.10530	+	0.638146i
$124$	696.056	+	401.868i	0.504094	+	0.291039i
$125$			790.429i			0.565585i
$126$	−1099.22	+	1903.90i	−0.777192	+	1.34614i
$127$	−366.227	−	634.324i	−0.255885	−	0.443206i	0.709250	−	0.704957i	$-0.249034\pi$
$127$	−366.227	−	634.324i	−0.255885	−	0.443206i	−0.965136	+	0.261750i	$0.915700\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$	−882.549			−0.602357
$130$	−79.5975	−	299.551i	−0.0537013	−	0.202095i
$131$	1862.41			1.24213			0.621066	−	0.783758i	$-0.286700\pi$
$131$	1862.41			1.24213			0.621066	+	0.783758i	$0.286700\pi$
$132$	−425.863	+	245.872i	−0.280808	+	0.162124i
$133$	953.932	+	1652.26i	0.621927	+	1.07721i
$134$	529.740	−	917.537i	0.341512	−	0.591516i
$135$			208.760i			0.133091i
$136$	746.359	+	430.911i	0.470587	+	0.271693i
$137$	−768.559	−	443.728i	−0.479288	−	0.276717i	0.240832	−	0.970567i	$-0.422580\pi$
$137$	−768.559	−	443.728i	−0.479288	−	0.276717i	−0.720120	+	0.693850i	$0.755913\pi$
$138$			1957.88i			1.20773i
$139$	726.060	−	1257.57i	0.443047	−	0.767381i	−0.554867	−	0.831939i	$-0.687231\pi$
$139$	726.060	−	1257.57i	0.443047	−	0.767381i	0.997914	+	0.0645588i	$0.0205640\pi$
$140$	207.571	+	359.524i	0.125307	+	0.217038i
$141$	−3492.57	+	2016.44i	−2.08601	+	1.20436i
$142$	135.102			0.0798414
$143$	−707.165	+	187.910i	−0.413539	+	0.109887i
$144$	560.283			0.324238
$145$	166.646	−	96.2133i	0.0954429	−	0.0551040i
$146$	104.504	+	181.007i	0.0592385	+	0.102604i
$147$	2529.32	−	4380.91i	1.41915	−	2.45804i
$148$			420.055i			0.233300i
$149$	1336.02	+	771.351i	0.734570	+	0.424104i	0.820092	−	0.572232i	$-0.193922\pi$
$149$	1336.02	+	771.351i	0.734570	+	0.424104i	−0.0855217	+	0.996336i	$0.527256\pi$
$150$	−1555.91	−	898.304i	−0.846929	−	0.488975i
$151$		−	1623.81i		−	0.875125i	−0.899188	−	0.437562i	$-0.855842\pi$
$151$		−	1623.81i		−	0.875125i	0.899188	−	0.437562i	$-0.144158\pi$
$152$	243.114	−	421.086i	0.129731	−	0.224701i
$153$	−1886.19	−	3266.97i	−0.996662	−	1.72627i
$154$	848.748	−	490.025i	0.444117	−	0.256411i
$155$	−664.346			−0.344268
$156$	1425.39	+	385.109i	0.731555	+	0.197650i
$157$	−2795.18			−1.42089			−0.710445	−	0.703753i	$-0.751506\pi$
$157$	−2795.18			−1.42089			−0.710445	+	0.703753i	$0.751506\pi$
$158$	1058.43	−	611.085i	0.532938	−	0.307692i
$159$	873.174	+	1512.38i	0.435517	+	0.754338i
$160$	52.9006	−	91.6265i	0.0261385	−	0.0452732i
$161$		−	3902.08i		−	1.91010i
$162$	776.372	+	448.239i	0.376528	+	0.217389i
$163$	250.884	+	144.848i	0.120557	+	0.0696036i	0.559066	−	0.829123i	$-0.311160\pi$
$163$	250.884	+	144.848i	0.120557	+	0.0696036i	−0.438509	+	0.898727i	$0.644493\pi$
$164$			884.321i			0.421060i
$165$	203.231	−	352.006i	0.0958879	−	0.166083i
$166$	491.565	+	851.415i	0.229836	+	0.398088i
$167$	2016.21	−	1164.06i	0.934246	−	0.539387i	0.0460940	−	0.998937i	$-0.485323\pi$
$167$	2016.21	−	1164.06i	0.934246	−	0.539387i	0.888152	+	0.459550i	$0.151989\pi$
$168$	−1977.63			−0.908198
$169$	1898.08	+	1106.40i	0.863940	+	0.503595i
$170$	−712.357			−0.321384
$171$	−1843.18	+	1064.16i	−0.824280	+	0.475898i
$172$	−224.136	−	388.214i	−0.0993615	−	0.172099i
$173$	531.941	−	921.349i	0.233773	−	0.404907i	−0.725142	−	0.688599i	$-0.758226\pi$
$173$	531.941	−	921.349i	0.233773	−	0.404907i	0.958915	+	0.283692i	$0.0915594\pi$
$174$			916.668i			0.399382i
$175$	3100.94	+	1790.33i	1.33948	+	0.773349i
$176$	−216.308	−	124.885i	−0.0926409	−	0.0534863i
$177$			4385.85i			1.86249i
$178$	377.155	−	653.252i	0.158814	−	0.275075i
$179$	1235.50	+	2139.95i	0.515898	+	0.893561i	0.999830	+	0.0184553i	$0.00587483\pi$
$179$	1235.50	+	2139.95i	0.515898	+	0.893561i	−0.483932	+	0.875106i	$0.660792\pi$
$180$	−401.069	+	231.557i	−0.166077	+	0.0958847i
$181$	−2196.50			−0.902014			−0.451007	−	0.892520i	$-0.648935\pi$
$181$	−2196.50			−0.902014			−0.451007	+	0.892520i	$0.648935\pi$
$182$	−2840.81	−	767.524i	−1.15701	−	0.312597i
$183$	−3608.46			−1.45762
$184$	−861.231	+	497.232i	−0.345059	+	0.199220i
$185$	−173.603	−	300.689i	−0.0689921	−	0.119498i
$186$	1582.38	−	2740.77i	0.623795	−	1.08044i
$187$			1681.70i			0.657637i
$188$	−1773.97	−	1024.20i	−0.688193	−	0.397329i
$189$	1716.47	+	991.002i	0.660606	+	0.381401i
$190$			401.903i			0.153458i
$191$	−1025.60	+	1776.39i	−0.388534	+	0.672960i	−0.992253	−	0.124237i	$-0.960352\pi$
$191$	−1025.60	+	1776.39i	−0.388534	+	0.672960i	0.603719	+	0.797197i	$0.293685\pi$
$192$	252.004	+	436.484i	0.0947231	+	0.164065i
$193$	3250.32	−	1876.57i	1.21224	−	0.699889i	0.248996	−	0.968505i	$-0.419899\pi$
$193$	3250.32	−	1876.57i	1.21224	−	0.699889i	0.963247	+	0.268616i	$0.0865661\pi$
$194$	−1146.62			−0.424344
$195$	−1179.50	+	313.421i	−0.433158	+	0.115100i
$196$	2569.43			0.936380
$197$	−646.501	+	373.258i	−0.233814	+	0.134992i	−0.612330	−	0.790602i	$-0.709768\pi$
$197$	−646.501	+	373.258i	−0.233814	+	0.134992i	0.378516	+	0.925595i	$0.376434\pi$
$198$	546.649	+	946.825i	0.196205	+	0.339838i
$199$	−1328.65	+	2301.28i	−0.473293	+	0.819767i	−0.999533	−	0.0305691i	$-0.990268\pi$
$199$	−1328.65	+	2301.28i	−0.473293	+	0.819767i	0.526240	+	0.850336i	$0.323601\pi$
$200$		−	912.548i		−	0.322634i
$201$	−3612.86	−	2085.89i	−1.26782	−	0.731976i
$202$	1654.98	+	955.502i	0.576455	+	0.332816i
$203$		−	1826.93i		−	0.631651i
$204$	1696.74	−	2938.84i	0.582331	−	1.00863i
$205$	−365.477	−	633.026i	−0.124517	−	0.215670i
$206$	−2561.63	+	1478.96i	−0.866394	+	0.500213i
$207$	4352.98			1.46161
$208$	192.597	+	724.802i	0.0642028	+	0.241615i
$209$	948.794			0.314016
$210$	1415.65	−	817.326i	0.465186	−	0.268575i
$211$	753.671	+	1305.40i	0.245900	+	0.425911i	0.962384	−	0.271692i	$-0.0875832\pi$
$211$	753.671	+	1305.40i	0.245900	+	0.425911i	−0.716484	+	0.697603i	$0.754250\pi$
$212$	−443.510	+	768.181i	−0.143681	+	0.248863i
$213$		−	531.972i		−	0.171127i
$214$	−369.127	−	213.116i	−0.117911	−	0.0680761i
$215$	320.887	+	185.264i	0.101787	+	0.0587670i
$216$		−	505.124i		−	0.159117i
$217$	−3153.70	+	5462.37i	−0.986576	+	1.70880i
$218$	84.4197	+	146.219i	0.0262276	+	0.0454276i
$219$	712.725	−	411.492i	0.219916	−	0.126968i
$220$	206.453			0.0632686
$221$	3577.90	−	3563.06i	1.08903	−	1.08451i
$222$	1654.00			0.500040
$223$	1713.91	−	989.529i	0.514673	−	0.297147i	−0.220079	−	0.975482i	$-0.570632\pi$
$223$	1713.91	−	989.529i	0.514673	−	0.297147i	0.734753	+	0.678335i	$0.237298\pi$
$224$	−502.246	−	869.916i	−0.149811	−	0.259481i
$225$	−1997.21	+	3459.27i	−0.591765	+	1.02497i
$226$		−	1572.84i		−	0.462936i
$227$	−1828.00	−	1055.39i	−0.534486	−	0.308586i	0.208355	−	0.978053i	$-0.433189\pi$
$227$	−1828.00	−	1055.39i	−0.534486	−	0.308586i	−0.742841	+	0.669467i	$0.766522\pi$
$228$	−1658.05	−	957.278i	−0.481611	−	0.278058i
$229$		−	5326.76i		−	1.53713i	−0.639774	−	0.768563i	$-0.720972\pi$
$229$		−	5326.76i		−	1.53713i	0.639774	−	0.768563i	$-0.279028\pi$
$230$	410.998	−	711.870i	0.117828	−	0.204084i
$231$	−1929.50	−	3342.00i	−0.549576	−	0.951894i
$232$	−403.223	+	232.801i	−0.114107	+	0.0658798i
$233$	148.949			0.0418797			0.0209398	−	0.999781i	$-0.493334\pi$
$233$	148.949			0.0418797			0.0209398	+	0.999781i	$0.493334\pi$
$234$	856.216	−	3169.08i	0.239199	−	0.885339i
$235$	1693.16			0.469997
$236$	−1929.24	+	1113.85i	−0.532131	+	0.307226i
$237$	−2406.19	−	4167.64i	−0.659488	−	1.14227i
$238$	−3381.61	+	5857.13i	−0.920998	+	1.59522i
$239$			3081.18i			0.833912i	0.908927	+	0.416956i	$0.136903\pi$
$239$			3081.18i			0.833912i	−0.908927	+	0.416956i	$0.863097\pi$
$240$	−360.785	−	208.300i	−0.0970358	−	0.0560237i
$241$	2225.94	+	1285.15i	0.594960	+	0.343500i	0.767056	−	0.641580i	$-0.221721\pi$
$241$	2225.94	+	1285.15i	0.594960	+	0.343500i	−0.172096	+	0.985080i	$0.555054\pi$
$242$			2174.61i			0.577643i
$243$	2617.36	−	4533.41i	0.690963	−	1.19678i
$244$	−916.418	−	1587.28i	−0.240441	−	0.416456i
$245$	−1839.28	+	1061.91i	−0.479621	+	0.276909i
$246$	3482.07			0.902475
$247$	−2010.23	−	2018.60i	−0.517846	−	0.520003i
$248$	1607.47			0.411591
$249$	3352.50	−	1935.57i	0.853238	−	0.492617i
$250$	790.429	+	1369.06i	0.199965	+	0.346349i
$251$	−1021.88	+	1769.95i	−0.256974	+	0.445093i	−0.965430	−	0.260663i	$-0.916059\pi$
$251$	−1021.88	+	1769.95i	−0.256974	+	0.445093i	0.708456	+	0.705755i	$0.249392\pi$
$252$			4396.88i			1.09912i
$253$	−1680.55	−	970.265i	−0.417609	−	0.241107i
$254$	−1268.65	−	732.455i	−0.313394	−	0.180938i
$255$			2804.95i			0.688836i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	3859.47	+	6684.79i	0.936758	+	1.62251i	0.771468	+	0.636268i	$0.219523\pi$
$257$	3859.47	+	6684.79i	0.936758	+	1.62251i	0.165290	+	0.986245i	$0.447144\pi$
$258$	−1528.62	+	882.549i	−0.368867	+	0.212965i
$259$	−3296.43			−0.790849
$260$	−437.418	−	439.239i	−0.104336	−	0.104771i
$261$	2038.04			0.483338
$262$	3225.78	−	1862.41i	0.760647	−	0.439160i
$263$	−742.261	−	1285.63i	−0.174030	−	0.301428i	0.765795	−	0.643084i	$-0.222345\pi$
$263$	−742.261	−	1285.63i	−0.174030	−	0.301428i	−0.939825	+	0.341656i	$0.889012\pi$
$264$	−491.744	+	851.726i	−0.114639	+	0.198561i
$265$		−	733.185i		−	0.169959i
$266$	3304.52	+	1907.86i	0.761702	+	0.439769i
$267$	−2572.22	−	1485.07i	−0.589578	−	0.340393i
$268$		−	2118.96i		−	0.482971i
$269$	1133.27	−	1962.88i	0.256865	−	0.444904i	−0.708535	−	0.705675i	$-0.750644\pi$
$269$	1133.27	−	1962.88i	0.256865	−	0.444904i	0.965400	+	0.260772i	$0.0839770\pi$
$270$	208.760	+	361.584i	0.0470547	+	0.0815011i
$271$	4561.73	−	2633.72i	1.02253	−	0.590357i	0.107693	−	0.994184i	$-0.465654\pi$
$271$	4561.73	−	2633.72i	1.02253	−	0.590357i	0.914835	+	0.403827i	$0.132320\pi$
$272$	1723.64			0.384232
$273$	−3022.18	+	11185.9i	−0.670002	+	2.47986i
$274$	−1774.91			−0.391337
$275$	1542.12	−	890.342i	0.338157	−	0.195235i
$276$	1957.88	+	3391.15i	0.426996	+	0.739578i
$277$	−2407.72	+	4170.29i	−0.522260	+	0.904580i	0.477405	+	0.878683i	$0.341577\pi$
$277$	−2407.72	+	4170.29i	−0.522260	+	0.904580i	−0.999665	+	0.0258968i	$0.991756\pi$
$278$		−	2904.24i		−	0.626564i
$279$	−6093.57	−	3518.12i	−1.30757	−	0.754927i
$280$	719.048	+	415.143i	0.153469	+	0.0886054i
$281$		−	1983.72i		−	0.421134i	−0.977579	−	0.210567i	$-0.932469\pi$
$281$		−	1983.72i		−	0.421134i	0.977579	−	0.210567i	$-0.0675310\pi$
$282$	−4032.87	+	6985.14i	−0.851610	+	1.47503i
$283$	−413.551	−	716.291i	−0.0868658	−	0.150456i	0.819319	−	0.573338i	$-0.194352\pi$
$283$	−413.551	−	716.291i	−0.0868658	−	0.150456i	−0.906185	+	0.422882i	$0.861018\pi$
$284$	234.003	−	135.102i	0.0488927	−	0.0282282i
$285$	1582.52			0.328913
$286$	−1036.94	+	1032.64i	−0.214389	+	0.213500i
$287$	−6939.80			−1.42733
$288$	970.439	−	560.283i	0.198554	−	0.114635i
$289$	−3346.13	−	5795.66i	−0.681076	−	1.17966i
$290$	192.427	−	333.292i	0.0389644	−	0.0674883i
$291$			4514.91i			0.909514i
$292$	362.013	+	209.008i	0.0725521	+	0.0418880i
$293$	−1027.62	−	593.298i	−0.204895	−	0.118296i	0.394041	−	0.919093i	$-0.371077\pi$
$293$	−1027.62	−	593.298i	−0.204895	−	0.118296i	−0.598937	+	0.800796i	$0.704410\pi$
$294$		−	10117.3i		−	2.00698i
$295$	920.676	−	1594.66i	0.181708	−	0.314727i
$296$	420.055	+	727.557i	0.0824839	+	0.142866i
$297$	853.610	−	492.832i	0.166773	−	0.0962863i
$298$	3085.40			0.599774
$299$	1496.33	+	5631.17i	0.289415	+	1.08916i
$300$	−3593.22			−0.691515
$301$	3046.55	−	1758.93i	0.583389	−	0.336820i
$302$	−1623.81	−	2812.52i	−0.309403	−	0.535902i
$303$	3762.35	−	6516.59i	0.713339	−	1.23554i
$304$		−	972.457i		−	0.183468i
$305$	1312.00	+	757.485i	0.246312	+	0.142208i
$306$	−6533.95	−	3772.38i	−1.22066	−	0.704746i
$307$			6191.17i			1.15097i	0.817811	+	0.575486i	$0.195187\pi$
$307$			6191.17i			1.15097i	−0.817811	+	0.575486i	$0.804813\pi$
$308$	980.050	−	1697.50i	0.181310	−	0.314038i
$309$	5823.49	+	10086.6i	1.07213	+	1.85698i
$310$	−1150.68	+	664.346i	−0.210820	+	0.121717i
$311$	10609.3			1.93440			0.967198	−	0.254024i	$-0.0817541\pi$
$311$	10609.3			1.93440			0.967198	+	0.254024i	$0.0817541\pi$
$312$	2853.96	−	758.363i	0.517864	−	0.137608i
$313$	9833.23			1.77574			0.887871	−	0.460093i	$-0.152184\pi$
$313$	9833.23			1.77574			0.887871	+	0.460093i	$0.152184\pi$
$314$	−4841.39	+	2795.18i	−0.870114	+	0.502360i
$315$	−1817.17	−	3147.43i	−0.325034	−	0.562976i
$316$	1222.17	−	2116.86i	0.217571	−	0.376844i
$317$		−	4674.74i		−	0.828263i	−0.910217	−	0.414131i	$-0.864085\pi$
$317$		−	4674.74i		−	0.828263i	0.910217	−	0.414131i	$-0.135915\pi$
$318$	3024.77	+	1746.35i	0.533398	+	0.307957i
$319$	−786.822	−	454.272i	−0.138099	−	0.0797314i
$320$		−	211.602i		−	0.0369654i
$321$	−839.157	+	1453.46i	−0.145910	+	0.252724i
$322$	−3902.08	−	6758.60i	−0.675324	−	1.16970i
$323$	−5670.33	+	3273.77i	−0.976798	+	0.563954i
$324$	1792.95			0.307434
$325$	−5161.57	−	1394.54i	−0.880961	−	0.238016i
$326$	579.393			0.0984344
$327$	575.748	−	332.408i	0.0973667	−	0.0562147i
$328$	884.321	+	1531.69i	0.148867	+	0.257846i
$329$	8037.54	−	13921.4i	1.34688	−	2.33287i
$330$		−	812.924i		−	0.135606i
$331$	−9018.24	−	5206.68i	−1.49755	−	0.864608i	−0.497549	−	0.867436i	$-0.665767\pi$
$331$	−9018.24	−	5206.68i	−1.49755	−	0.864608i	−0.999996	+	0.00282772i	$0.999100\pi$
$332$	1702.83	+	983.130i	0.281491	+	0.162519i
$333$		−	3677.34i		−	0.605157i
$334$	2328.12	−	4032.42i	0.381404	−	0.660612i
$335$	875.737	+	1516.82i	0.142826	+	0.247381i
$336$	−3425.35	+	1977.63i	−0.556156	+	0.321097i
$337$	−4873.47			−0.787759			−0.393879	−	0.919162i	$-0.628867\pi$
$337$	−4873.47			−0.787759			−0.393879	+	0.919162i	$0.628867\pi$
$338$	4393.96	+	18.2620i	0.707101	+	0.00293882i
$339$	−6193.15			−0.992229
$340$	−1233.84	+	712.357i	−0.196807	+	0.113626i
$341$	1568.36	+	2716.47i	0.249065	+	0.431394i
$342$	−2128.33	+	3686.37i	−0.336511	+	0.582854i
$343$			9396.92i			1.47926i
$344$	−776.428	−	448.271i	−0.121692	−	0.0702592i
$345$	−2803.03	−	1618.33i	−0.437421	−	0.252545i
$346$		−	2127.77i		−	0.330605i
$347$	−6060.84	+	10497.7i	−0.937645	+	1.62405i	−0.167798	+	0.985821i	$0.553666\pi$
$347$	−6060.84	+	10497.7i	−0.937645	+	1.62405i	−0.769847	+	0.638228i	$0.779668\pi$
$348$	916.668	+	1587.72i	0.141203	+	0.244570i
$349$	−7683.52	+	4436.08i	−1.17848	+	0.680396i	−0.955663	−	0.294464i	$-0.904859\pi$
$349$	−7683.52	+	4436.08i	−1.17848	+	0.680396i	−0.222818	+	0.974860i	$0.571526\pi$
$350$	7161.31			1.09368
$351$	−2857.09	−	771.921i	−0.434473	−	0.117385i
$352$	−499.541			−0.0756410
$353$	−3933.22	+	2270.84i	−0.593043	+	0.342393i	−0.766300	−	0.642483i	$-0.777904\pi$
$353$	−3933.22	+	2270.84i	−0.593043	+	0.342393i	0.173257	+	0.984877i	$0.444571\pi$
$354$	4385.85	+	7596.52i	0.658490	+	1.14054i
$355$	−111.671	+	193.420i	−0.0166955	+	0.0289174i
$356$		−	1508.62i		−	0.224598i
$357$	23062.8	+	13315.3i	3.41909	+	1.97401i
$358$	4279.90	+	2471.00i	0.631843	+	0.364795i
$359$		−	1398.34i		−	0.205576i	−0.994703	−	0.102788i	$-0.967224\pi$
$359$		−	1398.34i		−	0.205576i	0.994703	−	0.102788i	$-0.0327763\pi$
$360$	−463.114	+	802.138i	−0.0678007	+	0.117434i
$361$	−1582.48	−	2740.94i	−0.230716	−	0.399612i
$362$	−3804.45	+	2196.50i	−0.552368	+	0.318910i
$363$	8562.69			1.23808
$364$	−5687.96	+	1511.42i	−0.819038	+	0.217637i
$365$	−345.521			−0.0495490
$366$	−6250.03	+	3608.46i	−0.892607	+	0.515347i
$367$	−2019.26	−	3497.46i	−0.287205	−	0.497454i	0.685936	−	0.727662i	$-0.259393\pi$
$367$	−2019.26	−	3497.46i	−0.287205	−	0.497454i	−0.973142	+	0.230207i	$0.926060\pi$
$368$	−994.464	+	1722.46i	−0.140870	+	0.243993i
$369$		−	7741.72i		−	1.09219i
$370$	−601.378	−	347.206i	−0.0844978	−	0.0487848i
$371$	−6028.38	−	3480.49i	−0.843606	−	0.487056i
$372$		−	6329.53i		−	0.882179i
$373$	−315.134	+	545.828i	−0.0437454	+	0.0757692i	−0.887069	−	0.461637i	$-0.847262\pi$
$373$	−315.134	+	545.828i	−0.0437454	+	0.0757692i	0.843324	+	0.537406i	$0.180596\pi$
$374$	1681.70	+	2912.79i	0.232510	+	0.402719i
$375$	5390.78	−	3112.37i	0.742343	−	0.428592i
$376$	−4096.82			−0.561908
$377$	700.573	+	2636.48i	0.0957065	+	0.360174i
$378$	3964.01			0.539382
$379$	4259.91	−	2459.46i	0.577353	−	0.333335i	−0.182728	−	0.983164i	$-0.558493\pi$
$379$	4259.91	−	2459.46i	0.577353	−	0.333335i	0.760081	+	0.649828i	$0.225159\pi$
$380$	401.903	+	696.116i	0.0542557	+	0.0939737i
$381$	−2884.09	+	4995.39i	−0.387812	+	0.671710i
$382$			4102.41i			0.549470i
$383$	−8681.96	−	5012.53i	−1.15830	−	0.668742i	−0.207401	−	0.978256i	$-0.566500\pi$
$383$	−8681.96	−	5012.53i	−1.15830	−	0.668742i	−0.950895	+	0.309514i	$0.899834\pi$
$384$	872.968	+	504.008i	0.116012	+	0.0669794i
$385$			1620.16i			0.214471i
$386$	3753.14	−	6500.63i	0.494896	−	0.857185i
$387$	1962.18	+	3398.59i	0.257734	+	0.446409i
$388$	−1986.01	+	1146.62i	−0.259857	+	0.150028i
$389$	−13329.5			−1.73735			−0.868676	−	0.495380i	$-0.835029\pi$
$389$	−13329.5			−1.73735			−0.868676	+	0.495380i	$0.835029\pi$
$390$	−1729.53	+	1722.36i	−0.224560	+	0.223629i
$391$	13391.4			1.73205
$392$	4450.38	−	2569.43i	0.573413	−	0.331060i
$393$	−7333.35	−	12701.7i	−0.941269	−	1.63033i
$394$	−746.515	+	1293.00i	−0.0954540	+	0.165331i
$395$			2020.42i			0.257363i
$396$	1893.65	+	1093.30i	0.240302	+	0.138738i
$397$	401.196	+	231.631i	0.0507191	+	0.0292827i	0.525145	−	0.851013i	$-0.324011\pi$
$397$	401.196	+	231.631i	0.0507191	+	0.0292827i	−0.474426	+	0.880295i	$0.657344\pi$
$398$			5314.59i			0.669337i
$399$	7512.34	−	13011.7i	0.942574	−	1.63259i
$400$	−912.548	−	1580.58i	−0.114068	−	0.197572i
$401$	12170.0	−	7026.32i	1.51556	−	0.875007i	0.515723	−	0.856755i	$-0.327523\pi$
$401$	12170.0	−	7026.32i	1.51556	−	0.875007i	0.999833	−	0.0182521i	$-0.00581015\pi$
$402$	−8343.55			−1.03517
$403$	2456.51	−	9092.21i	0.303642	−	1.12386i
$404$	3822.01			0.470673
$405$	−1283.45	+	741.003i	−0.157470	+	0.0909154i
$406$	−1826.93	−	3164.33i	−0.223322	−	0.386805i
$407$	−819.668	+	1419.71i	−0.0998266	+	0.172905i
$408$		−	6786.96i		−	0.823540i
$409$	−3844.75	−	2219.77i	−0.464819	−	0.268363i	0.249250	−	0.968439i	$-0.419816\pi$
$409$	−3844.75	−	2219.77i	−0.464819	−	0.268363i	−0.714068	+	0.700076i	$0.753149\pi$
$410$	−1266.05	−	730.955i	−0.152502	−	0.0880471i
$411$			6988.83i			0.838768i
$412$	−2957.91	+	5123.26i	−0.353704	+	0.612633i
$413$	−8741.03	−	15139.9i	−1.04145	−	1.80384i
$414$	7539.58	−	4352.98i	0.895049	−	0.516757i
$415$	−1625.25			−0.192242
$416$	1058.39	+	1062.80i	0.124740	+	0.125259i
$417$	−11435.6			−1.34294
$418$	1643.36	−	948.794i	0.192295	−	0.111022i
$419$	6839.51	+	11846.4i	0.797451	+	1.38123i	0.921271	+	0.388921i	$0.127152\pi$
$419$	6839.51	+	11846.4i	0.797451	+	1.38123i	−0.123820	+	0.992305i	$0.539514\pi$
$420$	1634.65	−	2831.30i	0.189911	−	0.328936i
$421$			11133.2i			1.28884i	0.764673	+	0.644419i	$0.222901\pi$
$421$			11133.2i			1.28884i	−0.764673	+	0.644419i	$0.777099\pi$
$422$	2610.79	+	1507.34i	0.301165	+	0.173877i
$423$	15530.1	+	8966.32i	1.78511	+	1.03063i
$424$			1774.04i			0.203196i
$425$	−6144.17	+	10642.0i	−0.701261	+	1.21462i
$426$	−531.972	−	921.402i	−0.0605026	−	0.104794i
$427$	12456.4	−	7191.68i	1.41172	−	0.815058i
$428$	−852.463			−0.0962741
$429$	4066.07	+	4083.00i	0.457603	+	0.459509i
$430$	741.057			0.0831091
$431$	−1259.28	+	727.043i	−0.140736	+	0.0812539i	−0.568715	−	0.822535i	$-0.692559\pi$
$431$	−1259.28	+	727.043i	−0.140736	+	0.0812539i	0.427979	+	0.903789i	$0.359226\pi$
$432$	−505.124	−	874.900i	−0.0562564	−	0.0974390i
$433$	−3844.28	+	6658.49i	−0.426662	+	0.738999i	−0.996574	−	0.0827060i	$-0.973644\pi$
$433$	−3844.28	+	6658.49i	−0.426662	+	0.738999i	0.569912	+	0.821705i	$0.306977\pi$
$434$			12614.8i			1.39523i
$435$	−1312.36	−	757.692i	−0.144650	−	0.0835139i
$436$	292.438	+	168.839i	0.0321222	+	0.0185457i
$437$		−	7555.26i		−	0.827042i
$438$	822.984	−	1425.45i	0.0897801	−	0.155504i
$439$	−4320.81	−	7483.86i	−0.469751	−	0.813633i	0.529651	−	0.848216i	$-0.322323\pi$
$439$	−4320.81	−	7483.86i	−0.469751	−	0.813633i	−0.999402	+	0.0345828i	$0.988990\pi$
$440$	357.588	−	206.453i	0.0387439	−	0.0223688i
$441$	−22493.9			−2.42888
$442$	2634.04	−	9749.30i	0.283458	−	1.04916i
$443$	−13563.6			−1.45469			−0.727346	−	0.686271i	$-0.759246\pi$
$443$	−13563.6			−1.45469			−0.727346	+	0.686271i	$0.759246\pi$
$444$	2864.80	−	1654.00i	0.306211	−	0.176791i
$445$	623.492	+	1079.92i	0.0664187	+	0.115041i
$446$	1979.06	−	3427.83i	0.210115	−	0.363929i
$447$		−	12149.0i		−	1.28552i
$448$	−1739.83	−	1004.49i	−0.183481	−	0.105933i
$449$	16278.9	+	9398.65i	1.71103	+	0.987862i	0.933181	+	0.359406i	$0.117021\pi$
$449$	16278.9	+	9398.65i	1.71103	+	0.987862i	0.777845	+	0.628456i	$0.216313\pi$
$450$			7988.83i			0.836882i
$451$	−1725.60	+	2988.84i	−0.180168	+	0.312059i
$452$	−1572.84	−	2724.23i	−0.163673	−	0.283489i
$453$	−11074.5	+	6393.86i	−1.14862	+	0.663156i
$454$	−4221.58			−0.436406
$455$	3446.97	−	3432.68i	0.355157	−	0.353684i
$456$	−3829.11			−0.393234
$457$	6257.55	−	3612.80i	0.640516	−	0.369802i	−0.144297	−	0.989534i	$-0.546092\pi$
$457$	6257.55	−	3612.80i	0.640516	−	0.369802i	0.784813	+	0.619732i	$0.212759\pi$
$458$	−5326.76	−	9226.21i	−0.543456	−	0.941294i
$459$	−3400.99	+	5890.68i	−0.345849	+	0.599027i
$460$		−	1643.99i		−	0.166634i
$461$	1987.84	+	1147.68i	0.200831	+	0.115950i	0.597043	−	0.802209i	$-0.296342\pi$
$461$	1987.84	+	1147.68i	0.200831	+	0.115950i	−0.396212	+	0.918159i	$0.629676\pi$
$462$	−6684.00	−	3859.01i	−0.673091	−	0.388609i
$463$			9457.75i			0.949328i	0.880167	+	0.474664i	$0.157430\pi$
$463$			9457.75i			0.949328i	−0.880167	+	0.474664i	$0.842570\pi$
$464$	−465.601	+	806.445i	−0.0465841	+	0.0806859i
$465$	2615.91	+	4530.88i	0.260881	+	0.451859i
$466$	257.987	−	148.949i	0.0256460	−	0.0148067i
$467$	13310.9			1.31896			0.659481	−	0.751721i	$-0.270776\pi$
$467$	13310.9			1.31896			0.659481	+	0.751721i	$0.270776\pi$
$468$	−1686.07	−	6345.23i	−0.166536	−	0.626727i
$469$	16628.8			1.63720
$470$	2932.63	−	1693.16i	0.287813	−	0.166169i
$471$	11006.2	+	19063.3i	1.07673	+	1.86495i
$472$	−2227.70	+	3858.48i	−0.217242	+	0.376273i
$473$		−	1749.45i		−	0.170063i
$474$	−8335.27	−	4812.37i	−0.807704	−	0.466328i
$475$	6004.08	+	3466.46i	0.579971	+	0.334846i
$476$			13526.5i			1.30249i
$477$	3882.67	−	6724.99i	0.372695	−	0.645526i
$478$	3081.18	+	5336.76i	0.294833	+	0.510665i
$479$	−6901.57	+	3984.62i	−0.658332	+	0.380088i	−0.791641	−	0.610987i	$-0.790773\pi$
$479$	−6901.57	+	3984.62i	−0.658332	+	0.380088i	0.133309	+	0.991074i	$0.457440\pi$
$480$	−833.198			−0.0792294
$481$	4757.14	−	1264.08i	0.450950	−	0.119828i
$482$	5140.59			0.485783
$483$	−26612.4	+	15364.7i	−2.50705	+	1.44745i
$484$	2174.61	+	3766.54i	0.204228	+	0.353732i
$485$	947.767	−	1641.58i	0.0887338	−	0.153691i
$486$		−	10469.5i		−	0.977169i
$487$	−1225.83	−	707.734i	−0.114061	−	0.0658532i	0.441884	−	0.897072i	$-0.354310\pi$
$487$	−1225.83	−	707.734i	−0.114061	−	0.0658532i	−0.555945	+	0.831219i	$0.687644\pi$
$488$	−3174.57	−	1832.84i	−0.294479	−	0.170018i
$489$		−	2281.40i		−	0.210978i
$490$	−2123.82	+	3678.56i	−0.195805	+	0.339143i
$491$	−1600.46	−	2772.07i	−0.147103	−	0.254790i	0.783053	−	0.621956i	$-0.213662\pi$
$491$	−1600.46	−	2772.07i	−0.147103	−	0.254790i	−0.930156	+	0.367166i	$0.880328\pi$
$492$	6031.13	−	3482.07i	0.552651	−	0.319073i
$493$	6269.77			0.572771
$494$	−5500.43	−	1486.09i	−0.500963	−	0.135349i
$495$	−1807.38			−0.164113
$496$	2784.22	−	1607.47i	0.252047	−	0.145519i
$497$	1060.22	+	1836.36i	0.0956892	+	0.165739i
$498$	3871.14	−	6705.01i	0.348333	−	0.603330i
$499$		−	1480.51i		−	0.132819i	−0.997792	−	0.0664097i	$-0.978846\pi$
$499$		−	1480.51i		−	0.132819i	0.997792	−	0.0664097i	$-0.0211544\pi$
$500$	2738.13	+	1580.86i	0.244905	+	0.141396i
$501$	−15877.9	−	9167.12i	−1.41591	−	0.817479i
$502$			4087.52i			0.363417i
$503$	10129.6	−	17545.1i	0.897929	−	1.55526i	0.0677919	−	0.997699i	$-0.478405\pi$
$503$	10129.6	−	17545.1i	0.897929	−	1.55526i	0.830137	−	0.557559i	$-0.188262\pi$
$504$	4396.88	+	7615.61i	0.388596	+	0.673068i
$505$	−2735.92	+	1579.58i	−0.241083	+	0.139189i
$506$	−3881.06			−0.340977
$507$	71.9077	−	17301.5i	0.00629889	−	1.51556i
$508$	−2929.82			−0.255885
$509$	−6122.14	+	3534.62i	−0.533122	+	0.307798i	−0.742287	−	0.670082i	$-0.766259\pi$
$509$	−6122.14	+	3534.62i	−0.533122	+	0.307798i	0.209165	+	0.977880i	$0.432925\pi$
$510$	2804.95	+	4858.32i	0.243540	+	0.421824i
$511$	−1640.21	+	2840.93i	−0.141994	+	0.245940i
$512$			512.000i			0.0441942i
$513$	3323.45	+	1918.79i	0.286031	+	0.165140i
$514$	13369.6	+	7718.93i	1.14729	+	0.662388i
$515$		−	4889.86i		−	0.418394i
$516$	−1765.10	+	3057.24i	−0.150589	+	0.260828i
$517$	−3997.13	−	6923.23i	−0.340026	−	0.588942i
$518$	−5709.58	+	3296.43i	−0.484294	+	0.279607i
$519$	−8378.22			−0.708599
$520$	−1196.87	−	323.367i	−0.100935	−	0.0272704i
$521$	−13874.4			−1.16670			−0.583348	−	0.812223i	$-0.698257\pi$
$521$	−13874.4			−1.16670			−0.583348	+	0.812223i	$0.698257\pi$
$522$	3529.98	−	2038.04i	0.295983	−	0.170886i
$523$	8176.89	+	14162.8i	0.683653	+	1.18412i	0.973858	+	0.227158i	$0.0729432\pi$
$523$	8176.89	+	14162.8i	0.683653	+	1.18412i	−0.290205	+	0.956965i	$0.593723\pi$
$524$	3724.82	−	6451.57i	0.310533	−	0.537859i
$525$		−	28198.1i		−	2.34413i
$526$	−2571.27	−	1484.52i	−0.213142	−	0.123057i
$527$	−18746.1	−	10823.1i	−1.54951	−	0.894613i
$528$			1966.98i			0.162124i
$529$	−1642.74	+	2845.31i	−0.135016	+	0.233855i
$530$	−733.185	−	1269.91i	−0.0600897	−	0.104078i
$531$	16889.4	−	9751.10i	1.38030	−	0.796915i
$532$	7631.45			0.621927
$533$	10015.0	−	2661.21i	0.813877	−	0.216266i
$534$	−5940.29			−0.481389
$535$	610.220	−	352.311i	0.0493124	−	0.0284705i
$536$	−2118.96	−	3670.15i	−0.170756	−	0.295758i
$537$	9729.73	−	16852.4i	0.781879	−	1.35425i
$538$		−	4533.08i		−	0.363262i
$539$	8684.17	+	5013.81i	0.693977	+	0.400668i
$540$	723.167	+	417.521i	0.0576300	+	0.0332727i
$541$		−	2609.54i		−	0.207381i	−0.994610	−	0.103690i	$-0.966935\pi$
$541$		−	2609.54i		−	0.207381i	0.994610	−	0.103690i	$-0.0330651\pi$
$542$	5267.43	−	9123.46i	0.417446	−	0.723037i
$543$	8648.86	+	14980.3i	0.683533	+	1.18391i
$544$	2985.44	−	1723.64i	0.235293	−	0.135847i
$545$	−279.116			−0.0219376
$546$	5951.32	+	22396.7i	0.466471	+	1.75548i
$547$	−22168.6			−1.73284			−0.866419	−	0.499318i	$-0.833584\pi$
$547$	−22168.6			−1.73284			−0.866419	+	0.499318i	$0.833584\pi$
$548$	−3074.24	+	1774.91i	−0.239644	+	0.138358i
$549$	8022.71	+	13895.7i	0.623681	+	1.08025i
$550$	1780.68	−	3084.24i	0.138052	−	0.239113i
$551$		−	3537.32i		−	0.273494i
$552$	6782.31	+	3915.77i	0.522961	+	0.301931i
$553$	16612.3	+	9591.09i	1.27744	+	0.737531i
$554$			9630.88i			0.738587i
$555$	−1367.15	+	2367.97i	−0.104562	+	0.181107i
$556$	−2904.24	−	5030.29i	−0.221524	−	0.383690i
$557$	−18090.3	+	10444.4i	−1.37614	+	0.794514i	−0.991692	−	0.128634i	$-0.958941\pi$
$557$	−18090.3	+	10444.4i	−1.37614	+	0.794514i	−0.384446	+	0.923147i	$0.625608\pi$
$558$	−14072.5			−1.06763
$559$	−3722.04	+	3706.61i	−0.281620	+	0.280452i
$560$	1660.57			0.125307
$561$	11469.3	−	6621.81i	0.863163	−	0.498347i
$562$	−1983.72	−	3435.90i	−0.148893	−	0.257891i
$563$	6340.33	−	10981.8i	0.474623	−	0.822071i	−0.524955	−	0.851130i	$-0.675918\pi$
$563$	6340.33	−	10981.8i	0.474623	−	0.822071i	0.999578	+	0.0290588i	$0.00925100\pi$
$564$			16131.5i			1.20436i
$565$	2251.77	+	1300.06i	0.167669	+	0.0968036i
$566$	−1432.58	−	827.101i	−0.106388	−	0.0614234i
$567$			14070.4i			1.04215i
$568$	270.203	−	468.006i	0.0199604	−	0.0345723i
$569$	−316.343	−	547.922i	−0.0233072	−	0.0403692i	0.854137	−	0.520049i	$-0.174086\pi$
$569$	−316.343	−	547.922i	−0.0233072	−	0.0403692i	−0.877444	+	0.479680i	$0.840753\pi$
$570$	2741.00	−	1582.52i	0.201418	−	0.116288i
$571$	−8050.66			−0.590034			−0.295017	−	0.955492i	$-0.595325\pi$
$571$	−8050.66			−0.590034			−0.295017	+	0.955492i	$0.595325\pi$
$572$	−763.391	+	2825.51i	−0.0558024	+	0.206540i
$573$	16153.5			1.17770
$574$	−12020.1	+	6939.80i	−0.874057	+	0.504637i
$575$	−7089.81	−	12279.9i	−0.514201	−	0.890622i
$576$	1120.57	−	1940.88i	0.0810595	−	0.140399i
$577$			14173.9i			1.02265i	0.859389	+	0.511323i	$0.170844\pi$
$577$			14173.9i			1.02265i	−0.859389	+	0.511323i	$0.829156\pi$
$578$	−11591.3	−	6692.26i	−0.834145	−	0.481594i
$579$	−25596.7	−	14778.2i	−1.83724	−	1.06073i
$580$		−	769.706i		−	0.0551040i
$581$	−7715.21	+	13363.1i	−0.550913	+	0.954210i
$582$	4514.91	+	7820.05i	0.321562	+	0.556961i
$583$	−2997.96	+	1730.87i	−0.212972	+	0.122959i
$584$	836.033			0.0592385
$585$	3829.34	+	3845.29i	0.270639	+	0.271766i
$586$	−2373.19			−0.167296
$587$	11411.7	−	6588.56i	0.802406	−	0.463269i	−0.0419057	−	0.999122i	$-0.513343\pi$
$587$	11411.7	−	6588.56i	0.802406	−	0.463269i	0.844312	+	0.535852i	$0.180010\pi$
$588$	−10117.3	−	17523.7i	−0.709575	−	1.22902i
$589$	−6106.24	+	10576.3i	−0.427170	+	0.739881i
$590$		−	3682.70i		−	0.256974i
$591$	5091.28	+	2939.45i	0.354361	+	0.204590i
$592$	1455.11	+	840.111i	0.101022	+	0.0583249i
$593$			20637.4i			1.42913i	0.699568	+	0.714566i	$0.253376\pi$
$593$			20637.4i			1.42913i	−0.699568	+	0.714566i	$0.746624\pi$
$594$	985.664	−	1707.22i	0.0680847	−	0.117926i
$595$	−5590.30	−	9682.68i	−0.385176	−	0.667145i
$596$	5344.08	−	3085.40i	0.367285	−	0.212052i
$597$	20926.5			1.43462
$598$	8222.90	+	8257.14i	0.562306	+	0.564648i
$599$	286.244			0.0195252			0.00976262	−	0.999952i	$-0.496892\pi$
$599$	286.244			0.0195252			0.00976262	+	0.999952i	$0.496892\pi$
$600$	−6223.63	+	3593.22i	−0.423465	+	0.244487i
$601$	−10160.8	−	17599.1i	−0.689633	−	1.19448i	−0.971957	−	0.235160i	$-0.924439\pi$
$601$	−10160.8	−	17599.1i	−0.689633	−	1.19448i	0.282324	−	0.959319i	$-0.408895\pi$
$602$	3517.85	−	6093.10i	0.238168	−	0.412518i
$603$			18550.3i			1.25278i
$604$	−5625.04	−	3247.62i	−0.378940	−	0.218781i
$605$	−3113.32	−	1797.48i	−0.209214	−	0.120790i
$606$		−	15049.4i		−	1.00881i
$607$	−2454.43	+	4251.19i	−0.164122	+	0.284268i	−0.936343	−	0.351086i	$-0.885812\pi$
$607$	−2454.43	+	4251.19i	−0.164122	+	0.284268i	0.772221	+	0.635354i	$0.219146\pi$
$608$	−972.457	−	1684.35i	−0.0648657	−	0.112351i
$609$	−12459.8	+	7193.64i	−0.829055	+	0.478655i
$610$	3029.94			0.201113
$611$	−6260.69	+	23172.5i	−0.414534	+	1.53430i
$612$	−15089.5			−0.996662
$613$	−7008.38	+	4046.29i	−0.461771	+	0.266604i	−0.712789	−	0.701379i	$-0.752568\pi$
$613$	−7008.38	+	4046.29i	−0.461771	+	0.266604i	0.251018	+	0.967983i	$0.419235\pi$
$614$	6191.17	+	10723.4i	0.406930	+	0.704824i
$615$	−2878.18	+	4985.16i	−0.188715	+	0.326863i
$616$		−	3920.20i		−	0.256411i
$617$	19404.8	+	11203.4i	1.26614	+	0.731006i	0.974255	−	0.225448i	$-0.0723847\pi$
$617$	19404.8	+	11203.4i	1.26614	+	0.731006i	0.291884	+	0.956454i	$0.405718\pi$
$618$	20173.2	+	11647.0i	1.31308	+	0.758107i
$619$		−	29226.6i		−	1.89777i	−0.315627	−	0.948883i	$-0.602215\pi$
$619$		−	29226.6i		−	1.89777i	0.315627	−	0.948883i	$-0.397785\pi$
$620$	−1328.69	+	2301.36i	−0.0860670	+	0.149072i
$621$	−3924.43	−	6797.32i	−0.253594	−	0.439238i
$622$	18375.8	−	10609.3i	1.18457	−	0.683912i
$623$	11839.0			0.761351
$624$	4184.84	−	4167.48i	0.268474	−	0.267360i
$625$	11645.2			0.745291
$626$	17031.7	−	9833.23i	1.08742	−	0.627819i
$627$	−3735.94	−	6470.83i	−0.237957	−	0.412153i
$628$	−5590.36	+	9682.79i	−0.355222	+	0.615263i
$629$		−	11312.9i		−	0.717130i
$630$	−6294.85	−	3634.34i	−0.398084	−	0.229834i
$631$	5473.32	+	3160.03i	0.345308	+	0.199364i	0.662617	−	0.748958i	$-0.269446\pi$
$631$	5473.32	+	3160.03i	0.345308	+	0.199364i	−0.317309	+	0.948322i	$0.602779\pi$
$632$		−	4888.68i		−	0.307692i
$633$	5935.26	−	10280.2i	0.372678	−	0.645498i
$634$	−4674.74	−	8096.88i	−0.292835	−	0.507205i
$635$	2097.26	−	1210.85i	0.131066	−	0.0756712i
$636$	6985.40			0.435517
$637$	−7732.24	−	29098.9i	−0.480946	−	1.80995i
$638$	−1817.09			−0.112757
$639$	−2048.56	+	1182.74i	−0.126823	+	0.0732212i
$640$	−211.602	−	366.506i	−0.0130692	−	0.0226366i
$641$	−4201.52	+	7277.24i	−0.258892	+	0.448415i	−0.965945	−	0.258746i	$-0.916691\pi$
$641$	−4201.52	+	7277.24i	−0.258892	+	0.448415i	0.707053	+	0.707160i	$0.250024\pi$
$642$			3356.63i			0.206348i
$643$	−271.587	−	156.801i	−0.0166568	−	0.00961684i	0.491648	−	0.870794i	$-0.336395\pi$
$643$	−271.587	−	156.801i	−0.0166568	−	0.00961684i	−0.508305	+	0.861177i	$0.669728\pi$
$644$	−13517.2	−	7804.15i	−0.827099	−	0.477526i
$645$		−	2917.96i		−	0.178131i
$646$	−6547.54	+	11340.7i	−0.398776	+	0.690700i
$647$	−4037.44	−	6993.04i	−0.245329	−	0.424923i	0.716895	−	0.697181i	$-0.245563\pi$
$647$	−4037.44	−	6993.04i	−0.245329	−	0.424923i	−0.962224	+	0.272259i	$0.912229\pi$
$648$	3105.49	−	1792.95i	0.188264	−	0.108694i
$649$	−8693.95			−0.525836
$650$	−10334.6	+	2746.15i	−0.623627	+	0.165712i
$651$	49671.6			2.99045
$652$	1003.54	−	579.393i	0.0602785	−	0.0348018i
$653$	9083.36	+	15732.8i	0.544348	+	0.942839i	0.998648	+	0.0519898i	$0.0165563\pi$
$653$	9083.36	+	15732.8i	0.544348	+	0.942839i	−0.454299	+	0.890849i	$0.650110\pi$
$654$	664.816	−	1151.50i	0.0397498	−	0.0688487i
$655$			6157.66i			0.367327i
$656$	3063.38	+	1768.64i	0.182324	+	0.105265i
$657$	−3169.22	−	1829.75i	−0.188193	−	0.108653i
$658$		−	32150.2i		−	1.90478i
$659$	9822.68	−	17013.4i	0.580633	−	1.00569i	−0.414771	−	0.909926i	$-0.636138\pi$
$659$	9822.68	−	17013.4i	0.580633	−	1.00569i	0.995404	−	0.0957607i	$-0.0305284\pi$
$660$	−812.924	−	1408.03i	−0.0479440	−	0.0830414i
$661$	−9515.27	+	5493.64i	−0.559911	+	0.323265i	−0.753110	−	0.657895i	$-0.771447\pi$
$661$	−9515.27	+	5493.64i	−0.559911	+	0.323265i	0.193199	+	0.981160i	$0.438114\pi$
$662$	−20826.7			−1.22274
$663$	−38388.5	−	10371.7i	−2.24870	−	0.607548i
$664$	3932.52			0.229836
$665$	−5462.84	+	3153.97i	−0.318556	+	0.183918i
$666$	−3677.34	−	6369.35i	−0.213955	−	0.370581i
$667$	−3617.37	+	6265.48i	−0.209993	+	0.363718i
$668$		−	9312.48i		−	0.539387i
$669$	−13497.3	−	7792.67i	−0.780023	−	0.450347i
$670$	3033.64	+	1751.47i	0.174925	+	0.100993i
$671$		−	7152.95i		−	0.411530i
$672$	−3955.26	+	6850.70i	−0.227050	+	0.393261i
$673$	17128.5	+	29667.5i	0.981065	+	1.69925i	0.658264	+	0.752787i	$0.271291\pi$
$673$	17128.5	+	29667.5i	0.981065	+	1.69925i	0.322801	+	0.946467i	$0.395376\pi$
$674$	−8441.09	+	4873.47i	−0.482402	+	0.278515i
$675$	7202.33			0.410693
$676$	7628.83	−	4362.33i	0.434048	−	0.248198i
$677$	25142.1			1.42731			0.713656	−	0.700497i	$-0.247038\pi$
$677$	25142.1			1.42731			0.713656	+	0.700497i	$0.247038\pi$
$678$	−10726.8	+	6193.15i	−0.607614	+	0.350806i
$679$	−8998.24	−	15585.4i	−0.508573	−	0.880874i
$680$	−1424.71	+	2467.68i	−0.0803461	+	0.139163i
$681$			16622.7i			0.935367i
$682$	5432.95	+	3136.71i	0.305041	+	0.176116i
$683$	8664.54	+	5002.48i	0.485416	+	0.280255i	0.722671	−	0.691192i	$-0.242914\pi$
$683$	8664.54	+	5002.48i	0.485416	+	0.280255i	−0.237255	+	0.971448i	$0.576248\pi$
$684$			8513.30i			0.475898i
$685$	1467.09	−	2541.08i	0.0818317	−	0.141737i
$686$	9396.92	+	16275.9i	0.522997	+	0.905858i
$687$	−36328.8	+	20974.5i	−2.01751	+	1.16481i
$688$	−1793.08			−0.0993615
$689$	10034.3	+	2711.06i	0.554831	+	0.149903i
$690$	−6473.33			−0.357153
$691$	6354.19	−	3668.59i	0.349819	−	0.201968i	−0.314787	−	0.949162i	$-0.601933\pi$
$691$	6354.19	−	3668.59i	0.349819	−	0.201968i	0.664605	+	0.747195i	$0.268600\pi$
$692$	−2127.77	−	3685.40i	−0.116887	−	0.202453i
$693$	−8579.77	+	14860.6i	−0.470301	+	0.814585i
$694$			24243.4i			1.32603i
$695$	4157.90	+	2400.56i	0.226932	+	0.131019i
$696$	3175.43	+	1833.34i	0.172937	+	0.0998454i
$697$		−	23816.5i		−	1.29428i
$698$	−8872.17	+	15367.0i	−0.481113	+	0.833311i
$699$	−586.496	−	1015.84i	−0.0317358	−	0.0549680i
$700$	12403.7	−	7161.31i	0.669739	−	0.386674i
$701$	7785.35			0.419470			0.209735	−	0.977758i	$-0.432740\pi$
$701$	7785.35			0.419470			0.209735	+	0.977758i	$0.432740\pi$
$702$	−5720.54	+	1520.08i	−0.307561	+	0.0817261i
$703$	−6382.59			−0.342424
$704$	−865.231	+	499.541i	−0.0463205	+	0.0267431i
$705$	−6666.92	−	11547.4i	−0.356157	−	0.616882i
$706$	−4541.69	+	7866.44i	−0.242109	+	0.419345i
$707$			29993.6i			1.59551i
$708$	15193.0	+	8771.70i	0.806482	+	0.465622i
$709$	517.039	+	298.513i	0.0273876	+	0.0158122i	0.513631	−	0.858011i	$-0.328300\pi$
$709$	517.039	+	298.513i	0.0273876	+	0.0158122i	−0.486244	+	0.873823i	$0.661633\pi$
$710$			446.685i			0.0236110i
$711$	−10699.4	+	18531.9i	−0.564358	+	0.977497i
$712$	−1508.62	−	2613.01i	−0.0794072	−	0.137537i
$713$	21631.3	−	12488.9i	1.13618	−	0.655977i
$714$	53261.3			2.79167
$715$	−621.285	−	2338.09i	−0.0324962	−	0.122293i
$716$	9884.01			0.515898
$717$	21013.9	−	12132.4i	1.09453	−	0.631926i
$718$	−1398.34	−	2422.00i	−0.0726820	−	0.125889i
$719$	−6006.81	+	10404.1i	−0.311566	+	0.539648i	−0.978702	−	0.205288i	$-0.934187\pi$
$719$	−6006.81	+	10404.1i	−0.311566	+	0.539648i	0.667135	+	0.744936i	$0.267520\pi$
$720$			1852.46i			0.0958847i
$721$	−40205.3	−	23212.5i	−2.07673	−	1.19900i
$722$	−5481.88	−	3164.97i	−0.282569	−	0.163141i
$723$		−	20241.4i		−	1.04120i
$724$	−4393.00	+	7608.90i	−0.225503	+	0.390583i
$725$	−3319.40	−	5749.37i	−0.170041	−	0.294519i
$726$	14831.0	−	8562.69i	0.758169	−	0.437729i
$727$	−1137.34			−0.0580216			−0.0290108	−	0.999579i	$-0.509236\pi$
$727$	−1137.34			−0.0580216			−0.0290108	+	0.999579i	$0.509236\pi$
$728$	−8340.41	+	8305.82i	−0.424610	+	0.422849i
$729$	−29121.7			−1.47954
$730$	−598.460	+	345.521i	−0.0303424	+	0.0175182i
$731$	6036.40	+	10455.4i	0.305423	+	0.529009i
$732$	−7216.91	+	12500.1i	−0.364405	+	0.631169i
$733$		−	24930.1i		−	1.25623i	−0.778122	−	0.628113i	$-0.783828\pi$
$733$		−	24930.1i		−	1.25623i	0.778122	−	0.628113i	$-0.216172\pi$
$734$	−6994.91	−	4038.51i	−0.351753	−	0.203085i
$735$	14484.6	+	8362.67i	0.726899	+	0.419676i
$736$			3977.86i			0.199220i
$737$	4134.80	−	7161.68i	0.206658	−	0.357943i
$738$	−7741.72	−	13409.1i	−0.386147	−	0.668827i
$739$	−9626.47	+	5557.84i	−0.479182	+	0.276656i	−0.720075	−	0.693896i	$-0.755893\pi$
$739$	−9626.47	+	5557.84i	−0.479182	+	0.276656i	0.240894	+	0.970552i	$0.422560\pi$
$740$	−1388.82			−0.0689921
$741$	−5851.59	+	21658.3i	−0.290099	+	1.07373i
$742$	−13921.9			−0.688802
$743$	10675.7	−	6163.62i	0.527125	−	0.304336i	−0.212720	−	0.977113i	$-0.568232\pi$
$743$	10675.7	−	6163.62i	0.527125	−	0.304336i	0.739845	+	0.672777i	$0.234899\pi$
$744$	−6329.53	−	10963.1i	−0.311898	−	0.540222i
$745$	−2550.31	+	4417.26i	−0.125418	+	0.217230i
$746$			1260.54i			0.0618653i
$747$	−14907.3	−	8606.73i	−0.730160	−	0.421558i
$748$	5825.58	+	3363.40i	0.284765	+	0.164409i
$749$		−	6689.78i		−	0.326354i
$750$	6224.73	−	10781.6i	0.303060	−	0.524916i
$751$	−6902.03	−	11954.7i	−0.335364	−	0.580868i	0.648190	−	0.761478i	$-0.275526\pi$
$751$	−6902.03	−	11954.7i	−0.335364	−	0.580868i	−0.983555	+	0.180610i	$0.942193\pi$
$752$	−7095.90	+	4096.82i	−0.344097	+	0.198664i
$753$	16094.9			0.778925
$754$	3849.90	+	3865.94i	0.185949	+	0.186723i
$755$	5368.78			0.258795
$756$	6865.86	−	3964.01i	0.330303	−	0.190700i
$757$	−450.515	−	780.315i	−0.0216304	−	0.0374650i	0.855008	−	0.518616i	$-0.173552\pi$
$757$	−450.515	−	780.315i	−0.0216304	−	0.0374650i	−0.876638	+	0.481151i	$0.840219\pi$
$758$	4918.92	−	8519.82i	0.235704	−	0.408250i
$759$			15281.9i			0.730829i
$760$	1392.23	+	803.806i	0.0664494	+	0.0383646i
$761$	−25742.3	−	14862.3i	−1.22623	−	0.707962i	−0.259987	−	0.965612i	$-0.583718\pi$
$761$	−25742.3	−	14862.3i	−1.22623	−	0.707962i	−0.966238	+	0.257650i	$0.917052\pi$
$762$			11536.4i			0.548449i
$763$	−1324.98	+	2294.94i	−0.0628671	+	0.108889i
$764$	4102.41	+	7105.58i	0.194267	+	0.336480i
$765$	10801.6	−	6236.28i	0.510498	−	0.294736i
$766$	−20050.1			−0.945745
$767$	18420.1	+	18496.8i	0.867159	+	0.870770i
$768$	2016.03			0.0947231
$769$	22531.8	−	13008.7i	1.05659	−	0.610021i	0.132101	−	0.991236i	$-0.457828\pi$
$769$	22531.8	−	13008.7i	1.05659	−	0.610021i	0.924486	+	0.381215i	$0.124494\pi$
$770$	1620.16	+	2806.20i	0.0758268	+	0.131336i
$771$	30393.8	−	52643.6i	1.41972	−	2.45903i
$772$		−	15012.6i		−	0.699889i
$773$	−3392.26	−	1958.52i	−0.157841	−	0.0911296i	0.418999	−	0.907987i	$-0.362381\pi$
$773$	−3392.26	−	1958.52i	−0.157841	−	0.0911296i	−0.576840	+	0.816857i	$0.695714\pi$
$774$	6797.18	+	3924.36i	0.315659	+	0.182246i
$775$			22920.2i			1.06235i
$776$	−2293.25	+	3972.02i	−0.106086	+	0.183746i
$777$	12979.9	+	22481.8i	0.599294	+	1.03801i
$778$	−23087.3	+	13329.5i	−1.06391	+	0.614247i
$779$	−13436.9			−0.618008
$780$	−1273.28	+	4712.75i	−0.0584497	+	0.216338i
$781$	1054.51			0.0483143
$782$	23194.6	−	13391.4i	1.06066	−	0.612374i
$783$	−1837.39	−	3182.46i	−0.0838609	−	0.145251i
$784$	5138.85	−	8900.76i	0.234095	−	0.405464i
$785$		−	9241.67i		−	0.420190i
$786$	−25403.5	−	14666.7i	−1.15281	−	0.665578i
$787$	−1556.50	−	898.643i	−0.0704995	−	0.0407029i	0.464336	−	0.885659i	$-0.346293\pi$
$787$	−1556.50	−	898.643i	−0.0704995	−	0.0407029i	−0.534835	+	0.844956i	$0.679626\pi$
$788$			2986.06i			0.134992i
$789$	−5845.40	+	10124.5i	−0.263754	+	0.456835i
$790$	2020.42	+	3499.47i	0.0909916	+	0.157602i
$791$	21378.7	−	12343.0i	0.960984	−	0.554825i
$792$	4373.20			0.196205
$793$	−15218.2	+	15155.1i	−0.681482	+	0.678656i
$794$	926.524			0.0414120
$795$	−5000.37	+	2886.97i	−0.223075	+	0.128793i
$796$	5314.59	+	9205.13i	0.236646	+	0.409883i
$797$	−17645.3	+	30562.5i	−0.784226	+	1.35832i	0.145234	+	0.989397i	$0.453607\pi$
$797$	−17645.3	+	30562.5i	−0.784226	+	1.35832i	−0.929460	+	0.368923i	$0.879727\pi$
$798$		−	30049.3i		−	1.33300i
$799$	47776.5	+	27583.8i	2.11541	+	1.22133i
$800$	−3161.16	−	1825.10i	−0.139705	−	0.0806586i
$801$			13207.1i			0.582584i
$802$	14052.6	−	24339.9i	0.618724	−	1.07166i
$803$	815.690	+	1412.82i	0.0358469	+	0.0620887i
$804$	−14451.5	+	8343.55i	−0.633910	+	0.365988i
$805$	12901.4			0.564862
$806$	−4837.41	−	18204.7i	−0.211402	−	0.795574i
$807$	−17849.3			−0.778594
$808$	6619.92	−	3822.01i	0.288227	−	0.166408i
$809$	−9348.92	−	16192.8i	−0.406292	−	0.703719i	0.588178	−	0.808731i	$-0.299845\pi$
$809$	−9348.92	−	16192.8i	−0.406292	−	0.703719i	−0.994471	+	0.105012i	$0.966512\pi$
$810$	−1482.01	+	2566.91i	−0.0642869	+	0.111348i
$811$		−	22245.0i		−	0.963165i	−0.876401	−	0.481582i	$-0.840062\pi$
$811$		−	22245.0i		−	0.963165i	0.876401	−	0.481582i	$-0.159938\pi$
$812$	−6328.66	−	3653.85i	−0.273513	−	0.157913i
$813$	−35924.2	−	20740.9i	−1.54971	−	0.894728i
$814$			3278.67i			0.141176i
$815$	−478.910	+	829.496i	−0.0205834	+	0.0356515i
$816$	−6786.96	−	11755.4i	−0.291166	−	0.504313i
$817$	5898.78	−	3405.66i	0.252597	−	0.145837i
$818$	−8879.08			−0.379523
$819$	49794.8	−	13231.6i	2.12451	−	0.564531i
$820$	−2923.82			−0.124517
$821$	−34027.2	+	19645.6i	−1.44648	+	0.835123i	−0.998269	−	0.0588066i	$-0.981270\pi$
$821$	−34027.2	+	19645.6i	−1.44648	+	0.835123i	−0.448207	+	0.893930i	$0.647937\pi$
$822$	6988.83	+	12105.0i	0.296549	+	0.513638i
$823$	15.7571	−	27.2921i	0.000667386	−	0.00115595i	−0.865692	−	0.500578i	$-0.833121\pi$
$823$	15.7571	−	27.2921i	0.000667386	−	0.00115595i	0.866359	+	0.499422i	$0.166454\pi$
$824$			11831.7i			0.500213i
$825$	−12144.4	−	7011.56i	−0.512501	−	0.295892i
$826$	−30279.8	−	17482.1i	−1.27551	−	0.736415i
$827$		−	30870.8i		−	1.29805i	−0.760769	−	0.649023i	$-0.775178\pi$
$827$		−	30870.8i		−	1.29805i	0.760769	−	0.649023i	$-0.224822\pi$
$828$	8705.96	−	15079.2i	0.365402	−	0.632895i
$829$	19332.5	+	33484.9i	0.809946	+	1.40287i	0.912901	+	0.408181i	$0.133837\pi$
$829$	19332.5	+	33484.9i	0.809946	+	1.40287i	−0.102955	+	0.994686i	$0.532830\pi$
$830$	−2815.02	+	1625.25i	−0.117724	+	0.0679680i
$831$	37922.2			1.58304
$832$	2895.98	+	782.430i	0.120673	+	0.0326032i
$833$	−69199.6			−2.87830
$834$	−19807.1	+	11435.6i	−0.822378	+	0.474800i
$835$	3848.72	+	6666.17i	0.159509	+	0.276278i
$836$	1897.59	−	3286.72i	0.0785041	−	0.135973i
$837$			12687.1i			0.523930i
$838$	23692.8	+	13679.0i	0.976674	+	0.563883i
$839$	8566.99	+	4946.15i	0.352521	+	0.203528i	0.665795	−	0.746135i	$-0.268092\pi$
$839$	8566.99	+	4946.15i	0.352521	+	0.203528i	−0.313274	+	0.949663i	$0.601426\pi$
$840$		−	6538.61i		−	0.268575i
$841$	10500.9	−	18188.0i	0.430558	−	0.745748i
$842$	11133.2	+	19283.3i	0.455673	+	0.789248i
$843$	−13529.1	+	7811.02i	−0.552748	+	0.319129i
$844$	6029.37			0.245900
$845$	−3658.07	+	6275.58i	−0.148925	+	0.255487i
$846$	35865.3			1.45753
$847$	−29558.3	+	17065.5i	−1.19910	+	0.692299i
$848$	1774.04	+	3072.73i	0.0718405	+	0.124431i
$849$	−3256.77	+	5640.88i	−0.131651	+	0.228027i
$850$			24576.7i			0.991733i
$851$	11305.1	+	6527.03i	0.455388	+	0.262919i
$852$	−1842.80	−	1063.94i	−0.0741003	−	0.0427818i
$853$			35366.0i			1.41959i	0.704409	+	0.709794i	$0.251212\pi$
$853$			35366.0i			1.41959i	−0.704409	+	0.709794i	$0.748788\pi$
$854$	14383.4	−	24912.7i	0.576333	−	0.998238i
$855$	−3518.43	−	6094.10i	−0.140734	−	0.243759i
$856$	−1476.51	+	852.463i	−0.0589556	+	0.0340381i
$857$	−760.177			−0.0303001			−0.0151500	−	0.999885i	$-0.504823\pi$
$857$	−760.177			−0.0303001			−0.0151500	+	0.999885i	$0.504823\pi$
$858$	11125.6	+	3005.90i	0.442684	+	0.119603i
$859$	27332.4			1.08565			0.542823	−	0.839847i	$-0.317355\pi$
$859$	27332.4			1.08565			0.542823	+	0.839847i	$0.317355\pi$
$860$	1283.55	−	741.057i	0.0508937	−	0.0293835i
$861$	27325.9	+	47329.9i	1.08161	+	1.87340i
$862$	−1454.09	+	2518.55i	−0.0574552	+	0.0995153i
$863$		−	35583.9i		−	1.40358i	−0.712384	−	0.701790i	$-0.752385\pi$
$863$		−	35583.9i		−	1.40358i	0.712384	−	0.701790i	$-0.247615\pi$
$864$	−1749.80	−	1010.25i	−0.0688997	−	0.0397793i
$865$	3046.25	+	1758.75i	0.119740	+	0.0691322i
$866$			15377.1i			0.603391i
$867$	−26351.2	+	45641.6i	−1.03222	+	1.78786i
$868$	12614.8	+	21849.5i	0.493288	+	0.854400i
$869$	8261.39	−	4769.72i	0.322496	−	0.186193i
$870$	−3030.77			−0.118107
$871$	−23997.3	+	6376.64i	−0.933545	+	0.248065i
$872$	675.358			0.0262276
$873$	17386.4	−	10038.0i	0.674043	−	0.389159i
$874$	−7555.26	−	13086.1i	−0.292403	−	0.506458i
$875$	−12405.9	+	21487.7i	−0.479311	+	0.830191i
$876$		−	3291.94i		−	0.126968i
$877$	−2983.50	−	1722.52i	−0.114875	−	0.0663232i	0.441462	−	0.897280i	$-0.354460\pi$
$877$	−2983.50	−	1722.52i	−0.114875	−	0.0663232i	−0.556337	+	0.830957i	$0.687793\pi$
$878$	−14967.7	−	8641.61i	−0.575325	−	0.332164i
$879$			9344.60i			0.358573i
$880$	412.907	−	715.175i	0.0158171	−	0.0273961i
$881$	−10148.1	−	17577.0i	−0.388079	−	0.672173i	0.604112	−	0.796899i	$-0.293528\pi$
$881$	−10148.1	−	17577.0i	−0.388079	−	0.672173i	−0.992191	+	0.124727i	$0.960195\pi$
$882$	−38960.5	+	22493.9i	−1.48738	+	0.858739i
$883$	−2952.08			−0.112509			−0.0562545	−	0.998416i	$-0.517916\pi$
$883$	−2952.08			−0.112509			−0.0562545	+	0.998416i	$0.517916\pi$
$884$	−5187.00	−	19520.3i	−0.197350	−	0.742692i
$885$	−14500.9			−0.550782
$886$	−23492.9	+	13563.6i	−0.890813	+	0.514311i
$887$	−12377.2	−	21438.0i	−0.468531	−	0.811520i	0.530822	−	0.847483i	$-0.321883\pi$
$887$	−12377.2	−	21438.0i	−0.468531	−	0.811520i	−0.999353	+	0.0359637i	$0.988550\pi$
$888$	3307.99	−	5729.61i	0.125010	−	0.216524i
$889$		−	22992.0i		−	0.867411i
$890$	2159.84	+	1246.98i	0.0813460	+	0.0469651i
$891$	6059.84	+	3498.65i	0.227848	+	0.131548i
$892$		−	7916.23i		−	0.297147i
$893$	15562.4	−	26954.9i	0.583176	−	1.01009i
$894$	−12149.0	−	21042.7i	−0.454500	−	0.787216i
$895$	−7075.29	+	4084.92i	−0.264247	+	0.152563i
$896$	−4017.97			−0.149811
$897$	32513.0	−	32378.2i	1.21023	−	1.20521i
$898$	37594.6			1.39705
$899$	10127.6	−	5847.20i	0.375724	−	0.216924i
$900$	7988.83	+	13837.1i	0.295883	+	0.512484i
$901$	11944.6	−	20688.6i	0.441655	−	0.764969i
$902$			6902.42i			0.254795i
$903$	−23992.0	−	13851.8i	−0.884167	−	0.510474i
$904$	−5448.47	−	3145.67i	−0.200457	−	0.115734i
$905$		−	7262.26i		−	0.266747i
$906$	−12787.7	+	22149.0i	−0.468922	+	0.812197i
$907$	12103.5	+	20963.9i	0.443099	+	0.767469i	0.997918	−	0.0645018i	$-0.0205458\pi$
$907$	12103.5	+	20963.9i	0.443099	+	0.767469i	−0.554819	+	0.831971i	$0.687212\pi$
$908$	−7311.99	+	4221.58i	−0.267243	+	0.154293i
$909$	−33459.5			−1.22088
$910$	2537.66	−	9392.55i	0.0924423	−	0.342154i
$911$	−21027.3			−0.764725			−0.382363	−	0.924012i	$-0.624889\pi$
$911$	−21027.3			−0.764725			−0.382363	+	0.924012i	$0.624889\pi$
$912$	−6632.22	+	3829.11i	−0.240806	+	0.139029i
$913$	3836.83	+	6645.58i	0.139080	+	0.240894i
$914$	7225.60	−	12515.1i	0.261490	−	0.452913i
$915$		−	11930.6i		−	0.431053i
$916$	−18452.4	−	10653.5i	−0.665595	−	0.384282i
$917$	50629.3	+	29230.9i	1.82326	+	1.05266i
$918$			13603.9i			0.489104i
$919$	3949.78	−	6841.22i	0.141775	−	0.245561i	−0.786390	−	0.617730i	$-0.788052\pi$
$919$	3949.78	−	6841.22i	0.141775	−	0.245561i	0.928165	+	0.372169i	$0.121386\pi$
$920$	−1643.99	−	2847.48i	−0.0589139	−	0.102042i
$921$	42224.2	−	24378.1i	1.51068	−	0.872190i
$922$	4590.72			0.163977
$923$	−2234.22	−	2243.53i	−0.0796753	−	0.0800072i
$924$	−15436.0			−0.549576
$925$	−10373.9	+	5989.38i	−0.368748	+	0.212897i
$926$	9457.75	+	16381.3i	0.335638	+	0.581342i
$927$	25894.8	−	44851.2i	0.917473	−	1.58911i
$928$			1862.41i			0.0658798i
$929$	4706.55	+	2717.33i	0.166218	+	0.0959662i	0.580801	−	0.814045i	$-0.302739\pi$
$929$	4706.55	+	2717.33i	0.166218	+	0.0959662i	−0.414583	+	0.910011i	$0.636073\pi$
$930$	9061.76	+	5231.81i	0.319513	+	0.184471i
$931$			39041.5i			1.37437i
$932$	297.898	−	515.974i	0.0104699	−	0.0181344i
$933$	−41774.7	−	72356.0i	−1.46586	−	2.53894i
$934$	23055.2	−	13310.9i	0.807696	−	0.466323i
$935$	−5560.19			−0.194479
$936$	−9265.59	−	9304.18i	−0.323563	−	0.324911i
$937$	8130.03			0.283454			0.141727	−	0.989906i	$-0.454734\pi$
$937$	8130.03			0.283454			0.141727	+	0.989906i	$0.454734\pi$
$938$	28801.8	−	16628.8i	1.00257	−	0.578836i
$939$	−38719.0	−	67063.3i	−1.34563	−	2.33070i
$940$	3386.31	−	5865.27i	0.117499	−	0.203515i
$941$		−	5409.95i		−	0.187417i	−0.995600	−	0.0937084i	$-0.970128\pi$
$941$		−	5409.95i		−	0.187417i	0.995600	−	0.0937084i	$-0.0298721\pi$
$942$	38126.6	+	22012.4i	1.31872	+	0.761362i
$943$	23800.2	+	13741.0i	0.821887	+	0.474517i
$944$			8910.79i			0.307226i
$945$	−3276.54	+	5675.13i	−0.112789	+	0.195357i
$946$	−1749.45	−	3030.14i	−0.0601264	−	0.104142i
$947$	32164.9	−	18570.4i	1.10372	−	0.637231i	0.166522	−	0.986038i	$-0.446746\pi$
$947$	32164.9	−	18570.4i	1.10372	−	0.637231i	0.937195	+	0.348807i	$0.113413\pi$
$948$	−19249.5			−0.659488
$949$	1277.61	−	4728.79i	0.0437018	−	0.161752i
$950$	13865.8			0.473544
$951$	−31882.0	+	18407.1i	−1.08711	+	0.627645i
$952$	13526.5	+	23428.5i	0.460499	+	0.797608i
$953$	−1770.71	+	3066.97i	−0.0601879	+	0.104249i	−0.894549	−	0.446969i	$-0.852503\pi$
$953$	−1770.71	+	3066.97i	−0.0601879	+	0.104249i	0.834361	+	0.551218i	$0.185837\pi$
$954$		−	15530.7i		−	0.527070i
$955$	−5873.27	−	3390.93i	−0.199010	−	0.114899i
$956$	10673.5	+	6162.36i	0.361095	+	0.208478i
$957$			7154.90i			0.241677i
$958$	−7969.25	+	13803.1i	−0.268763	+	0.465511i
$959$	−13928.8	−	24125.4i	−0.469014	−	0.812356i
$960$	−1443.14	+	833.198i	−0.0485179	+	0.0280118i
$961$	−10583.5			−0.355258
$962$	6975.53	−	6946.60i	0.233784	−	0.232814i
$963$	7462.82			0.249726
$964$	8903.76	−	5140.59i	0.297480	−	0.171750i
$965$	6204.48	+	10746.5i	0.206974	+	0.358489i
$966$	−30729.4	+	53224.8i	−1.02350	+	1.77275i
$967$			48102.4i			1.59966i	0.600229	+	0.799828i	$0.295076\pi$
$967$			48102.4i			1.59966i	−0.600229	+	0.799828i	$0.704924\pi$
$968$	7533.09	+	4349.23i	0.250127	+	0.144411i
$969$	44654.6	+	25781.4i	1.48041	+	0.854712i
$970$		−	3791.07i		−	0.125488i
$971$	−17539.6	+	30379.5i	−0.579683	+	1.00404i	0.415833	+	0.909441i	$0.363490\pi$
$971$	−17539.6	+	30379.5i	−0.579683	+	1.00404i	−0.995515	+	0.0945990i	$0.969843\pi$
$972$	−10469.5	−	18133.6i	−0.345482	−	0.598392i
$973$	39475.7	−	22791.3i	1.30065	−	0.750931i
$974$	−2830.94			−0.0931305
$975$	10813.2	+	40693.3i	0.355178	+	1.33665i
$976$	−7331.35			−0.240441
$977$	−36950.2	+	21333.2i	−1.20997	+	0.698577i	−0.962753	−	0.270383i	$-0.912850\pi$
$977$	−36950.2	+	21333.2i	−1.20997	+	0.698577i	−0.247217	+	0.968960i	$0.579516\pi$
$978$	−2281.40	−	3951.50i	−0.0745921	−	0.129197i
$979$	2943.82	−	5098.85i	0.0961031	−	0.166455i
$980$			8495.26i			0.276909i
$981$	−2560.13	−	1478.09i	−0.0833218	−	0.0481059i
$982$	−5544.15	−	3200.91i	−0.180164	−	0.104018i
$983$		−	32297.0i		−	1.04793i	−0.851740	−	0.523964i	$-0.824453\pi$
$983$		−	32297.0i		−	1.04793i	0.851740	−	0.523964i	$-0.175547\pi$
$984$	6964.15	−	12062.3i	0.225619	−	0.390783i
$985$	−1234.10	−	2137.52i	−0.0399204	−	0.0691442i
$986$	10859.6	−	6269.77i	0.350749	−	0.202505i
$987$	−126593.			−4.08259
$988$	−11013.1	+	2926.44i	−0.354629	+	0.0942332i
$989$	−13930.9			−0.447905
$990$	−3130.47	+	1807.38i	−0.100498	+	0.0580225i
$991$	5674.60	+	9828.69i	0.181897	+	0.315054i	0.942526	−	0.334132i	$-0.108443\pi$
$991$	5674.60	+	9828.69i	0.181897	+	0.315054i	−0.760630	+	0.649186i	$0.775110\pi$
$992$	3214.94	−	5568.45i	0.102898	−	0.178224i
$993$			82006.7i			2.62075i
$994$	3672.72	+	2120.45i	0.117195	+	0.0676625i
$995$	−7608.70	−	4392.89i	−0.242424	−	0.139964i
$996$		−	15484.6i		−	0.492617i
$997$	15268.2	−	26445.3i	0.485003	−	0.840050i	−0.514848	−	0.857281i	$-0.672152\pi$
$997$	15268.2	−	26445.3i	0.485003	−	0.840050i	0.999852	+	0.0172310i	$0.00548508\pi$
$998$	−1480.51	−	2564.32i	−0.0469588	−	0.0813349i
$999$	−5742.29	+	3315.31i	−0.181860	+	0.104997i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.4.e.a.23.3	yes	8
3.2	odd	2		234.4.l.b.127.1		8
4.3	odd	2		208.4.w.d.49.4		8
13.2	odd	12		338.4.a.m.1.4		4
13.3	even	3		338.4.b.g.337.8		8
13.4	even	6	inner	26.4.e.a.17.3	✓	8
13.5	odd	4		338.4.c.m.315.1		8
13.6	odd	12		338.4.c.m.191.1		8
13.7	odd	12		338.4.c.n.191.1		8
13.8	odd	4		338.4.c.n.315.1		8
13.9	even	3		338.4.e.e.147.1		8
13.10	even	6		338.4.b.g.337.4		8
13.11	odd	12		338.4.a.l.1.4		4
13.12	even	2		338.4.e.e.23.1		8
39.17	odd	6		234.4.l.b.199.2		8
52.43	odd	6		208.4.w.d.17.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.4.e.a.17.3	✓	8	13.4	even	6	inner
26.4.e.a.23.3	yes	8	1.1	even	1	trivial
208.4.w.d.17.4		8	52.43	odd	6
208.4.w.d.49.4		8	4.3	odd	2
234.4.l.b.127.1		8	3.2	odd	2
234.4.l.b.199.2		8	39.17	odd	6
338.4.a.l.1.4		4	13.11	odd	12
338.4.a.m.1.4		4	13.2	odd	12
338.4.b.g.337.4		8	13.10	even	6
338.4.b.g.337.8		8	13.3	even	3
338.4.c.m.191.1		8	13.6	odd	12
338.4.c.m.315.1		8	13.5	odd	4
338.4.c.n.191.1		8	13.7	odd	12
338.4.c.n.315.1		8	13.8	odd	4
338.4.e.e.23.1		8	13.12	even	2
338.4.e.e.147.1		8	13.9	even	3

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	26.4.e.a.23.3

Level	$26$
Weight	$4$
Character	26.23
Analytic conductor	$1.534$
Analytic rank	$0$
Dimension	$8$
Inner twists	$2$