LMFDB - Embedded newform 88.4.c.a.45.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [88,4,Mod(45,88)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(88, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("88.45");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$88 = 2^{3} \cdot 11$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	88.c (of order $2$ , degree $1$ , 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:	$5.19216808051$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			45.28
Character	$\chi$	$=$	88.45
Dual form			88.4.c.a.45.27

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.79633 + 0.424903i) q^{2} -0.294095i q^{3} +(7.63891 + 2.37634i) q^{4} +20.9824i q^{5} +(0.124962 - 0.822387i) q^{6} -24.0791 q^{7} +(20.3512 + 9.89082i) q^{8} +26.9135 q^{9} +(-8.91547 + 58.6736i) q^{10} -11.0000i q^{11} +(0.698870 - 2.24657i) q^{12} -41.3985i q^{13} +(-67.3332 - 10.2313i) q^{14} +6.17082 q^{15} +(52.7060 + 36.3053i) q^{16} +89.3793 q^{17} +(75.2590 + 11.4356i) q^{18} -57.7857i q^{19} +(-49.8612 + 160.283i) q^{20} +7.08157i q^{21} +(4.67393 - 30.7596i) q^{22} +14.4637 q^{23} +(2.90885 - 5.98520i) q^{24} -315.260 q^{25} +(17.5903 - 115.764i) q^{26} -15.8557i q^{27} +(-183.939 - 57.2202i) q^{28} -68.8866i q^{29} +(17.2556 + 2.62200i) q^{30} -39.7739 q^{31} +(131.957 + 123.917i) q^{32} -3.23505 q^{33} +(249.934 + 37.9776i) q^{34} -505.237i q^{35} +(205.590 + 63.9556i) q^{36} +118.669i q^{37} +(24.5533 - 161.588i) q^{38} -12.1751 q^{39} +(-207.533 + 427.016i) q^{40} +48.1005 q^{41} +(-3.00898 + 19.8024i) q^{42} -396.400i q^{43} +(26.1397 - 84.0281i) q^{44} +564.709i q^{45} +(40.4454 + 6.14569i) q^{46} -7.59761 q^{47} +(10.6772 - 15.5006i) q^{48} +236.805 q^{49} +(-881.570 - 133.955i) q^{50} -26.2861i q^{51} +(98.3768 - 316.240i) q^{52} -459.047i q^{53} +(6.73714 - 44.3378i) q^{54} +230.806 q^{55} +(-490.040 - 238.163i) q^{56} -16.9945 q^{57} +(29.2701 - 192.630i) q^{58} +718.914i q^{59} +(47.1383 + 14.6639i) q^{60} +618.281i q^{61} +(-111.221 - 16.9001i) q^{62} -648.054 q^{63} +(316.343 + 402.580i) q^{64} +868.638 q^{65} +(-9.04626 - 1.37458i) q^{66} -629.643i q^{67} +(682.761 + 212.396i) q^{68} -4.25372i q^{69} +(214.677 - 1412.81i) q^{70} -618.726 q^{71} +(547.722 + 266.197i) q^{72} -836.321 q^{73} +(-50.4227 + 331.837i) q^{74} +92.7164i q^{75} +(137.318 - 441.420i) q^{76} +264.871i q^{77} +(-34.0456 - 5.17324i) q^{78} +667.382 q^{79} +(-761.771 + 1105.90i) q^{80} +722.002 q^{81} +(134.505 + 20.4381i) q^{82} +833.371i q^{83} +(-16.8282 + 54.0955i) q^{84} +1875.39i q^{85} +(168.432 - 1108.46i) q^{86} -20.2592 q^{87} +(108.799 - 223.863i) q^{88} -277.793 q^{89} +(-239.947 + 1579.11i) q^{90} +996.840i q^{91} +(110.487 + 34.3707i) q^{92} +11.6973i q^{93} +(-21.2454 - 3.22825i) q^{94} +1212.48 q^{95} +(36.4433 - 38.8080i) q^{96} -131.322 q^{97} +(662.185 + 100.619i) q^{98} -296.049i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$30 q + 12 q^{4} - 42 q^{6} - 48 q^{8} - 270 q^{9} + 54 q^{10} + 188 q^{12} - 68 q^{14} - 120 q^{15} + 160 q^{16} + 52 q^{17} + 122 q^{18} - 308 q^{20} + 276 q^{23} + 464 q^{24} - 706 q^{25} - 172 q^{26}+ \cdots - 3032 q^{98}+O(q^{100})$ 30 * q + 12 * q^4 - 42 * q^6 - 48 * q^8 - 270 * q^9 + 54 * q^10 + 188 * q^12 - 68 * q^14 - 120 * q^15 + 160 * q^16 + 52 * q^17 + 122 * q^18 - 308 * q^20 + 276 * q^23 + 464 * q^24 - 706 * q^25 - 172 * q^26 - 76 * q^28 + 22 * q^30 - 900 * q^31 + 1020 * q^32 + 544 * q^34 + 208 * q^36 + 504 * q^38 + 600 * q^39 - 396 * q^40 + 236 * q^41 - 180 * q^42 + 308 * q^44 + 326 * q^46 - 1348 * q^47 - 2432 * q^48 + 2190 * q^49 - 90 * q^50 + 204 * q^52 + 846 * q^54 + 440 * q^55 - 1064 * q^56 - 336 * q^57 + 412 * q^58 + 1340 * q^60 + 530 * q^62 - 40 * q^63 + 912 * q^64 - 1744 * q^65 + 550 * q^66 - 1148 * q^68 - 4108 * q^70 + 1876 * q^71 - 1876 * q^72 + 1172 * q^73 - 2466 * q^74 - 2036 * q^76 - 2168 * q^78 + 2832 * q^79 + 3304 * q^80 + 3662 * q^81 + 1284 * q^82 - 2580 * q^84 + 5892 * q^86 - 5344 * q^87 - 396 * q^88 - 1068 * q^89 - 3404 * q^90 + 2780 * q^92 - 3328 * q^94 + 3864 * q^95 - 1844 * q^96 - 2492 * q^97 - 3032 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/88\mathbb{Z}\right)^\times$ .

$n$	$23$	$45$	$57$
$\chi(n)$	$1$	$-1$	$1$

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

)

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

$2$	2.79633	+	0.424903i	0.988652	+	0.150226i
$2$	2.79633	+	0.424903i	0.988652	+	0.150226i
$3$		−	0.294095i		−	0.0565987i	−0.999599	−	0.0282993i	$-0.990991\pi$
$3$		−	0.294095i		−	0.0565987i	0.999599	−	0.0282993i	$-0.00900916\pi$
$4$	7.63891	+	2.37634i	0.954864	+	0.297042i
$5$			20.9824i			1.87672i	0.345660	+	0.938360i	$0.387655\pi$
$5$			20.9824i			1.87672i	−0.345660	+	0.938360i	$0.612345\pi$
$6$	0.124962	−	0.822387i	0.00850259	−	0.0559564i
$7$	−24.0791			−1.30015			−0.650076	−	0.759869i	$-0.725263\pi$
$7$	−24.0791			−1.30015			−0.650076	+	0.759869i	$0.725263\pi$
$8$	20.3512	+	9.89082i	0.899405	+	0.437117i
$9$	26.9135			0.996797
$10$	−8.91547	+	58.6736i	−0.281932	+	1.85542i
$11$		−	11.0000i		−	0.301511i
$11$		−	11.0000i		−	0.301511i
$12$	0.698870	−	2.24657i	0.0168122	−	0.0540441i
$13$		−	41.3985i		−	0.883221i	−0.897207	−	0.441611i	$-0.854407\pi$
$13$		−	41.3985i		−	0.883221i	0.897207	−	0.441611i	$-0.145593\pi$
$14$	−67.3332	−	10.2313i	−1.28540	−	0.195317i
$15$	6.17082			0.106220
$16$	52.7060	+	36.3053i	0.823532	+	0.567270i
$17$	89.3793			1.27516			0.637579	−	0.770385i	$-0.279936\pi$
$17$	89.3793			1.27516			0.637579	+	0.770385i	$0.279936\pi$
$18$	75.2590	+	11.4356i	0.985485	+	0.149745i
$19$		−	57.7857i		−	0.697734i	−0.937172	−	0.348867i	$-0.886567\pi$
$19$		−	57.7857i		−	0.697734i	0.937172	−	0.348867i	$-0.113433\pi$
$20$	−49.8612	+	160.283i	−0.557465	+	1.79201i
$21$			7.08157i			0.0735869i
$22$	4.67393	−	30.7596i	0.0452948	−	0.298090i
$23$	14.4637			0.131126			0.0655630	−	0.997848i	$-0.479116\pi$
$23$	14.4637			0.131126			0.0655630	+	0.997848i	$0.479116\pi$
$24$	2.90885	−	5.98520i	0.0247402	−	0.0509051i
$25$	−315.260			−2.52208
$26$	17.5903	−	115.764i	0.132683	−	0.873198i
$27$		−	15.8557i		−	0.113016i
$28$	−183.939	−	57.2202i	−1.24147	−	0.386200i
$29$		−	68.8866i		−	0.441101i	−0.975376	−	0.220550i	$-0.929215\pi$
$29$		−	68.8866i		−	0.441101i	0.975376	−	0.220550i	$-0.0707853\pi$
$30$	17.2556	+	2.62200i	0.105014	+	0.0159570i
$31$	−39.7739			−0.230439			−0.115219	−	0.993340i	$-0.536757\pi$
$31$	−39.7739			−0.230439			−0.115219	+	0.993340i	$0.536757\pi$
$32$	131.957	+	123.917i	0.728967	+	0.684548i
$33$	−3.23505			−0.0170651
$34$	249.934	+	37.9776i	1.26069	+	0.191562i
$35$		−	505.237i		−	2.44002i
$36$	205.590	+	63.9556i	0.951806	+	0.296091i
$37$			118.669i			0.527270i	0.964622	+	0.263635i	$0.0849215\pi$
$37$			118.669i			0.527270i	−0.964622	+	0.263635i	$0.915079\pi$
$38$	24.5533	−	161.588i	0.104818	−	0.689816i
$39$	−12.1751			−0.0499892
$40$	−207.533	+	427.016i	−0.820346	+	1.68793i
$41$	48.1005			0.183220			0.0916102	−	0.995795i	$-0.470799\pi$
$41$	48.1005			0.183220			0.0916102	+	0.995795i	$0.470799\pi$
$42$	−3.00898	+	19.8024i	−0.0110547	+	0.0727518i
$43$		−	396.400i		−	1.40582i	−0.711277	−	0.702912i	$-0.751883\pi$
$43$		−	396.400i		−	1.40582i	0.711277	−	0.702912i	$-0.248117\pi$
$44$	26.1397	−	84.0281i	0.0895616	−	0.287902i
$45$			564.709i			1.87071i
$46$	40.4454	+	6.14569i	0.129638	+	0.0196985i
$47$	−7.59761			−0.0235793			−0.0117896	−	0.999930i	$-0.503753\pi$
$47$	−7.59761			−0.0235793			−0.0117896	+	0.999930i	$0.503753\pi$
$48$	10.6772	−	15.5006i	0.0321067	−	0.0466108i
$49$	236.805			0.690394
$50$	−881.570	−	133.955i	−2.49346	−	0.378881i
$51$		−	26.2861i		−	0.0721722i
$52$	98.3768	−	316.240i	0.262354	−	0.843356i
$53$		−	459.047i		−	1.18972i	−0.803831	−	0.594858i	$-0.797208\pi$
$53$		−	459.047i		−	1.18972i	0.803831	−	0.594858i	$-0.202792\pi$
$54$	6.73714	−	44.3378i	0.0169779	−	0.111734i
$55$	230.806			0.565852
$56$	−490.040	−	238.163i	−1.16936	−	0.568318i
$57$	−16.9945			−0.0394908
$58$	29.2701	−	192.630i	0.0662648	−	0.436095i
$59$			718.914i			1.58635i	0.608993	+	0.793175i	$0.291574\pi$
$59$			718.914i			1.58635i	−0.608993	+	0.793175i	$0.708426\pi$
$60$	47.1383	+	14.6639i	0.101426	+	0.0315518i
$61$			618.281i			1.29775i	0.760895	+	0.648875i	$0.224760\pi$
$61$			618.281i			1.29775i	−0.760895	+	0.648875i	$0.775240\pi$
$62$	−111.221	−	16.9001i	−0.227824	−	0.0346179i
$63$	−648.054			−1.29599
$64$	316.343	+	402.580i	0.617858	+	0.786290i
$65$	868.638			1.65756
$66$	−9.04626	−	1.37458i	−0.0168715	−	0.00256363i
$67$		−	629.643i		−	1.14811i	−0.818818	−	0.574053i	$-0.805370\pi$
$67$		−	629.643i		−	1.14811i	0.818818	−	0.574053i	$-0.194630\pi$
$68$	682.761	+	212.396i	1.21760	+	0.378776i
$69$		−	4.25372i		−	0.00742156i
$70$	214.677	−	1412.81i	0.366554	−	2.41233i
$71$	−618.726			−1.03422			−0.517108	−	0.855920i	$-0.672991\pi$
$71$	−618.726			−1.03422			−0.517108	+	0.855920i	$0.672991\pi$
$72$	547.722	+	266.197i	0.896524	+	0.435716i
$73$	−836.321			−1.34088			−0.670438	−	0.741966i	$-0.733894\pi$
$73$	−836.321			−1.34088			−0.670438	+	0.741966i	$0.733894\pi$
$74$	−50.4227	+	331.837i	−0.0792097	+	0.521287i
$75$			92.7164i			0.142746i
$76$	137.318	−	441.420i	0.207256	−	0.666241i
$77$			264.871i			0.392010i
$78$	−34.0456	−	5.17324i	−0.0494219	−	0.00750967i
$79$	667.382			0.950460			0.475230	−	0.879862i	$-0.342365\pi$
$79$	667.382			0.950460			0.475230	+	0.879862i	$0.342365\pi$
$80$	−761.771	+	1105.90i	−1.06461	+	1.54554i
$81$	722.002			0.990400
$82$	134.505	+	20.4381i	0.181141	+	0.0275245i
$83$			833.371i			1.10210i	0.834472	+	0.551050i	$0.185773\pi$
$83$			833.371i			1.10210i	−0.834472	+	0.551050i	$0.814227\pi$
$84$	−16.8282	+	54.0955i	−0.0218584	+	0.0702655i
$85$			1875.39i			2.39311i
$86$	168.432	−	1108.46i	0.211191	−	1.38987i
$87$	−20.2592			−0.0249657
$88$	108.799	−	223.863i	0.131796	−	0.271181i
$89$	−277.793			−0.330854			−0.165427	−	0.986222i	$-0.552900\pi$
$89$	−277.793			−0.330854			−0.165427	+	0.986222i	$0.552900\pi$
$90$	−239.947	+	1579.11i	−0.281029	+	1.84948i
$91$			996.840i			1.14832i
$92$	110.487	+	34.3707i	0.125208	+	0.0389500i
$93$			11.6973i			0.0130425i
$94$	−21.2454	−	3.22825i	−0.0233117	−	0.00354222i
$95$	1212.48			1.30945
$96$	36.4433	−	38.8080i	0.0387445	−	0.0412586i
$97$	−131.322			−0.137461			−0.0687305	−	0.997635i	$-0.521895\pi$
$97$	−131.322			−0.137461			−0.0687305	+	0.997635i	$0.521895\pi$
$98$	662.185	+	100.619i	0.682560	+	0.103715i
$99$		−	296.049i		−	0.300545i
$100$	−2408.24	−	749.164i	−2.40824	−	0.749164i
$101$			507.954i			0.500429i	0.968190	+	0.250214i	$0.0805011\pi$
$101$			507.954i			0.500429i	−0.968190	+	0.250214i	$0.919499\pi$
$102$	11.1690	−	73.5045i	0.0108421	−	0.0713532i
$103$	1964.45			1.87925			0.939624	−	0.342208i	$-0.111175\pi$
$103$	1964.45			1.87925			0.939624	+	0.342208i	$0.111175\pi$
$104$	409.465	−	842.509i	0.386071	−	0.794373i
$105$	−148.588			−0.138102
$106$	195.050	−	1283.65i	0.178726	−	1.17621i
$107$		−	1735.61i		−	1.56811i	−0.620690	−	0.784056i	$-0.713148\pi$
$107$		−	1735.61i		−	1.56811i	0.620690	−	0.784056i	$-0.286852\pi$
$108$	37.6785	−	121.120i	0.0335705	−	0.107915i
$109$		−	1019.73i		−	0.896079i	−0.894014	−	0.448039i	$-0.852122\pi$
$109$		−	1019.73i		−	0.896079i	0.894014	−	0.448039i	$-0.147878\pi$
$110$	645.410	+	98.0702i	0.559431	+	0.0850057i
$111$	34.8999			0.0298428
$112$	−1269.12	−	874.200i	−1.07072	−	0.737537i
$113$	−613.445			−0.510691			−0.255346	−	0.966850i	$-0.582189\pi$
$113$	−613.445			−0.510691			−0.255346	+	0.966850i	$0.582189\pi$
$114$	−47.5222	−	7.22101i	−0.0390426	−	0.00593254i
$115$			303.483i			0.246087i
$116$	163.698	−	526.219i	0.131026	−	0.421191i
$117$		−	1114.18i		−	0.880392i
$118$	−305.469	+	2010.32i	−0.238311	+	1.56835i
$119$	−2152.18			−1.65790
$120$	125.584	+	61.0345i	0.0955347	+	0.0464305i
$121$	−121.000			−0.0909091
$122$	−262.710	+	1728.92i	−0.194956	+	1.28302i
$123$		−	14.1461i		−	0.0103700i
$124$	−303.830	−	94.5163i	−0.220038	−	0.0684501i
$125$		−	3992.10i		−	2.85651i
$126$	−1812.17	−	275.360i	−1.28128	−	0.194691i
$127$	−2315.99			−1.61820			−0.809099	−	0.587673i	$-0.800044\pi$
$127$	−2315.99			−1.61820			−0.809099	+	0.587673i	$0.800044\pi$
$128$	713.542	+	1260.16i	0.492725	+	0.870185i
$129$	−116.579			−0.0795677
$130$	2429.00	+	369.087i	1.63875	+	0.249008i
$131$		−	317.016i		−	0.211434i	−0.994396	−	0.105717i	$-0.966286\pi$
$131$		−	317.016i		−	0.211434i	0.994396	−	0.105717i	$-0.0337137\pi$
$132$	−24.7123	−	7.68757i	−0.0162949	−	0.00506907i
$133$			1391.43i			0.907160i
$134$	267.537	−	1760.69i	0.172475	−	1.13508i
$135$	332.690			0.212099
$136$	1818.98	+	884.035i	1.14688	+	0.557393i
$137$	−2018.87			−1.25901			−0.629504	−	0.776997i	$-0.716742\pi$
$137$	−2018.87			−1.25901			−0.629504	+	0.776997i	$0.716742\pi$
$138$	1.80742	−	11.8948i	0.00111491	−	0.00733733i
$139$			1900.84i			1.15991i	0.814650	+	0.579953i	$0.196929\pi$
$139$			1900.84i			1.15991i	−0.814650	+	0.579953i	$0.803071\pi$
$140$	1200.62	−	3859.47i	0.724789	−	2.32989i
$141$			2.23442i			0.00133455i
$142$	−1730.16	−	262.899i	−1.02248	−	0.155366i
$143$	−455.383			−0.266301
$144$	1418.50	+	977.103i	0.820894	+	0.565453i
$145$	1445.40			0.827823
$146$	−2338.63	−	355.355i	−1.32566	−	0.201434i
$147$		−	69.6433i		−	0.0390754i
$148$	−281.997	+	906.500i	−0.156622	+	0.503472i
$149$		−	2601.12i		−	1.43015i	−0.699048	−	0.715075i	$-0.746393\pi$
$149$		−	2601.12i		−	1.43015i	0.699048	−	0.715075i	$-0.253607\pi$
$150$	−39.3955	+	259.266i	−0.0214442	+	0.141126i
$151$	−158.879			−0.0856252			−0.0428126	−	0.999083i	$-0.513632\pi$
$151$	−158.879			−0.0856252			−0.0428126	+	0.999083i	$0.513632\pi$
$152$	571.548	−	1176.01i	0.304991	−	0.627545i
$153$	2405.51			1.27107
$154$	−112.544	+	740.665i	−0.0588901	+	0.387562i
$155$		−	834.551i		−	0.432469i
$156$	−93.0046	−	28.9322i	−0.0477329	−	0.0148489i
$157$		−	2710.22i		−	1.37770i	−0.724904	−	0.688850i	$-0.758116\pi$
$157$		−	2710.22i		−	1.37770i	0.724904	−	0.688850i	$-0.241884\pi$
$158$	1866.22	+	283.573i	0.939674	+	0.142784i
$159$	−135.004			−0.0673363
$160$	−2600.06	+	2768.77i	−1.28471	+	1.36807i
$161$	−348.274			−0.170484
$162$	2018.95	+	306.781i	0.979161	+	0.148784i
$163$			3777.71i			1.81530i	0.419731	+	0.907648i	$0.362124\pi$
$163$			3777.71i			1.81530i	−0.419731	+	0.907648i	$0.637876\pi$
$164$	367.436	+	114.303i	0.174951	+	0.0544242i
$165$		−	67.8790i		−	0.0320265i
$166$	−354.102	+	2330.38i	−0.165564	+	1.08959i
$167$	−2044.24			−0.947234			−0.473617	−	0.880731i	$-0.657052\pi$
$167$	−2044.24			−0.947234			−0.473617	+	0.880731i	$0.657052\pi$
$168$	−70.0425	+	144.118i	−0.0321661	+	0.0661844i
$169$	483.165			0.219920
$170$	−796.859	+	5244.21i	−0.359508	+	2.36596i
$171$		−	1555.21i		−	0.695499i
$172$	941.980	−	3028.06i	0.417589	−	1.34237i
$173$		−	690.514i		−	0.303461i	−0.988422	−	0.151731i	$-0.951515\pi$
$173$		−	690.514i		−	0.303461i	0.988422	−	0.151731i	$-0.0484846\pi$
$174$	−56.6515	−	8.60821i	−0.0246824	−	0.00375050i
$175$	7591.18			3.27908
$176$	399.358	−	579.766i	0.171038	−	0.248304i
$177$	211.429			0.0897854
$178$	−776.801	−	118.035i	−0.327100	−	0.0497029i
$179$			1154.26i			0.481974i	0.970528	+	0.240987i	$0.0774711\pi$
$179$			1154.26i			0.481974i	−0.970528	+	0.240987i	$0.922529\pi$
$180$	−1341.94	+	4313.76i	−0.555679	+	1.78627i
$181$			1741.57i			0.715193i	0.933876	+	0.357597i	$0.116404\pi$
$181$			1741.57i			0.715193i	−0.933876	+	0.357597i	$0.883596\pi$
$182$	−423.561	+	2787.49i	−0.172508	+	1.13529i
$183$	181.834			0.0734510
$184$	294.354	+	143.058i	0.117935	+	0.0573174i
$185$	−2489.95			−0.989539
$186$	−4.97023	+	32.7096i	−0.00195933	+	0.0128945i
$187$		−	983.173i		−	0.384474i
$188$	−58.0375	−	18.0545i	−0.0225150	−	0.00700404i
$189$			381.792i			0.146938i
$190$	3390.49	+	515.186i	1.29459	+	0.196713i
$191$	−3503.98			−1.32743			−0.663714	−	0.747986i	$-0.731021\pi$
$191$	−3503.98			−1.32743			−0.663714	+	0.747986i	$0.731021\pi$
$192$	118.397	−	93.0351i	0.0445030	−	0.0349699i
$193$	−331.149			−0.123506			−0.0617529	−	0.998091i	$-0.519669\pi$
$193$	−331.149			−0.123506			−0.0617529	+	0.998091i	$0.519669\pi$
$194$	−367.219	−	55.7991i	−0.135901	−	0.0206502i
$195$		−	255.463i		−	0.0938156i
$196$	1808.94	+	562.729i	0.659233	+	0.205076i
$197$			547.680i			0.198074i	0.995084	+	0.0990370i	$0.0315762\pi$
$197$			547.680i			0.198074i	−0.995084	+	0.0990370i	$0.968424\pi$
$198$	125.792	−	827.849i	0.0451497	−	0.297135i
$199$	−646.747			−0.230385			−0.115193	−	0.993343i	$-0.536749\pi$
$199$	−646.747			−0.230385			−0.115193	+	0.993343i	$0.536749\pi$
$200$	−6415.92	−	3118.18i	−2.26837	−	1.10244i
$201$	−185.175			−0.0649813
$202$	−215.831	+	1420.41i	−0.0751774	+	0.494750i
$203$			1658.73i			0.573498i
$204$	62.4645	−	200.797i	0.0214382	−	0.0689147i
$205$			1009.26i			0.343853i
$206$	5493.24	+	834.699i	1.85792	+	0.282312i
$207$	389.270			0.130706
$208$	1502.98	−	2181.95i	0.501025	−	0.727361i
$209$	−635.642			−0.210375
$210$	−415.501	−	63.1355i	−0.136535	−	0.0207465i
$211$			1950.03i			0.636237i	0.948051	+	0.318118i	$0.103051\pi$
$211$			1950.03i			0.636237i	−0.948051	+	0.318118i	$0.896949\pi$
$212$	1090.85	−	3506.62i	0.353396	−	1.13602i
$213$			181.964i			0.0585352i
$214$	737.467	−	4853.34i	0.235571	−	1.55032i
$215$	8317.41			2.63834
$216$	156.826	−	322.683i	0.0494012	−	0.101647i
$217$	957.722			0.299606
$218$	433.287	−	2851.51i	0.134614	−	0.885910i
$219$			245.958i			0.0758918i
$220$	1763.11	+	548.473i	0.540312	+	0.168082i
$221$		−	3700.17i		−	1.12625i
$222$	97.5916	+	14.8291i	0.0295041	+	0.00448316i
$223$	−5202.12			−1.56215			−0.781075	−	0.624437i	$-0.785329\pi$
$223$	−5202.12			−1.56215			−0.781075	+	0.624437i	$0.785329\pi$
$224$	−3177.42	−	2983.80i	−0.947768	−	0.890017i
$225$	−8484.74			−2.51400
$226$	−1715.40	−	260.655i	−0.504896	−	0.0767190i
$227$			243.075i			0.0710724i	0.999368	+	0.0355362i	$0.0113139\pi$
$227$			243.075i			0.0710724i	−0.999368	+	0.0355362i	$0.988686\pi$
$228$	−129.819	−	40.3847i	−0.0377084	−	0.0117304i
$229$			3378.62i			0.974959i	0.873135	+	0.487479i	$0.162084\pi$
$229$			3378.62i			0.974959i	−0.873135	+	0.487479i	$0.837916\pi$
$230$	−128.951	+	848.640i	−0.0369686	+	0.243294i
$231$	77.8972			0.0221873
$232$	681.345	−	1401.93i	0.192813	−	0.396728i
$233$	5177.76			1.45582			0.727911	−	0.685672i	$-0.240491\pi$
$233$	5177.76			1.45582			0.727911	+	0.685672i	$0.240491\pi$
$234$	473.418	−	3115.61i	0.132258	−	0.870401i
$235$		−	159.416i		−	0.0442517i
$236$	−1708.38	+	5491.73i	−0.471213	+	1.51475i
$237$		−	196.274i		−	0.0537948i
$238$	−6018.20	−	914.467i	−1.63908	−	0.249059i
$239$	−1925.53			−0.521139			−0.260569	−	0.965455i	$-0.583910\pi$
$239$	−1925.53			−0.521139			−0.260569	+	0.965455i	$0.583910\pi$
$240$	325.239	+	224.033i	0.0874754	+	0.0602554i
$241$	−1213.30			−0.324297			−0.162148	−	0.986766i	$-0.551842\pi$
$241$	−1213.30			−0.324297			−0.162148	+	0.986766i	$0.551842\pi$
$242$	−338.356	−	51.4133i	−0.0898774	−	0.0136569i
$243$		−	640.442i		−	0.169071i
$244$	−1469.25	+	4723.00i	−0.385487	+	1.23918i
$245$			4968.73i			1.29568i
$246$	6.01074	−	39.5573i	0.00155785	−	0.0102524i
$247$	−2392.24			−0.616253
$248$	−809.447	−	393.397i	−0.207258	−	0.100729i
$249$	245.090			0.0623774
$250$	1696.26	−	11163.2i	0.429122	−	2.82410i
$251$		−	2947.18i		−	0.741133i	−0.928806	−	0.370566i	$-0.879164\pi$
$251$		−	2947.18i		−	0.741133i	0.928806	−	0.370566i	$-0.120836\pi$
$252$	−4950.43	−	1540.00i	−1.23749	−	0.384963i
$253$		−	159.101i		−	0.0395360i
$254$	−6476.28	−	984.072i	−1.59983	−	0.243095i
$255$	551.544			0.135447
$256$	1459.85	+	3827.02i	0.356409	+	0.934330i
$257$	4031.78			0.978581			0.489290	−	0.872121i	$-0.337256\pi$
$257$	4031.78			0.978581			0.489290	+	0.872121i	$0.337256\pi$
$258$	−325.994	−	49.5349i	−0.0786648	−	0.0119531i
$259$		−	2857.44i		−	0.685531i
$260$	6635.45	+	2064.18i	1.58274	+	0.492365i
$261$		−	1853.98i		−	0.439688i
$262$	134.701	−	886.480i	0.0317628	−	0.209034i
$263$	1930.57			0.452640			0.226320	−	0.974053i	$-0.427330\pi$
$263$	1930.57			0.452640			0.226320	+	0.974053i	$0.427330\pi$
$264$	−65.8372	−	31.9973i	−0.0153485	−	0.00745946i
$265$	9631.89			2.23276
$266$	−591.223	+	3890.89i	−0.136279	+	0.896865i
$267$			81.6977i			0.0187259i
$268$	1496.25	−	4809.79i	0.341036	−	1.09629i
$269$			1148.26i			0.260264i	0.991497	+	0.130132i	$0.0415401\pi$
$269$			1148.26i			0.260264i	−0.991497	+	0.130132i	$0.958460\pi$
$270$	930.312	+	141.361i	0.209692	+	0.0318628i
$271$	3157.23			0.707706			0.353853	−	0.935301i	$-0.384871\pi$
$271$	3157.23			0.707706			0.353853	+	0.935301i	$0.384871\pi$
$272$	4710.83	+	3244.94i	1.05013	+	0.723359i
$273$	293.166			0.0649935
$274$	−5645.44	−	857.826i	−1.24472	−	0.189136i
$275$			3467.86i			0.760435i
$276$	10.1083	−	32.4938i	0.00220452	−	0.00708658i
$277$			1237.80i			0.268492i	0.990948	+	0.134246i	$0.0428612\pi$
$277$			1237.80i			0.268492i	−0.990948	+	0.134246i	$0.957139\pi$
$278$	−807.671	+	5315.36i	−0.174248	+	1.14674i
$279$	−1070.46			−0.229701
$280$	4997.21	−	10282.2i	1.06657	−	2.19457i
$281$	2882.75			0.611994			0.305997	−	0.952032i	$-0.401010\pi$
$281$	2882.75			0.611994			0.305997	+	0.952032i	$0.401010\pi$
$282$	−0.949413	+	6.24818i	−0.000200485	+	0.00131941i
$283$			5858.26i			1.23052i	0.788324	+	0.615261i	$0.210949\pi$
$283$			5858.26i			1.23052i	−0.788324	+	0.615261i	$0.789051\pi$
$284$	−4726.40	−	1470.30i	−0.987535	−	0.307206i
$285$		−	356.585i		−	0.0741132i
$286$	−1273.40	−	193.494i	−0.263279	−	0.0400054i
$287$	−1158.22			−0.238214
$288$	3551.43	+	3335.03i	0.726632	+	0.682356i
$289$	3075.67			0.626026
$290$	4041.83	+	614.157i	0.818428	+	0.124360i
$291$			38.6211i			0.00778011i
$292$	−6388.58	−	1987.38i	−1.28035	−	0.398297i
$293$			2845.16i			0.567290i	0.958929	+	0.283645i	$0.0915437\pi$
$293$			2845.16i			0.567290i	−0.958929	+	0.283645i	$0.908456\pi$
$294$	29.5917	−	194.746i	0.00587014	−	0.0386320i
$295$	−15084.5			−2.97714
$296$	−1173.73	+	2415.05i	−0.230479	+	0.474229i
$297$	−174.413			−0.0340756
$298$	1105.23	−	7273.60i	0.214846	−	1.41392i
$299$		−	598.777i		−	0.115813i
$300$	−220.326	+	708.253i	−0.0424017	+	0.136303i
$301$			9544.97i			1.82778i
$302$	−444.279	−	67.5083i	−0.0846535	−	0.0128631i
$303$	149.387			0.0283236
$304$	2097.93	−	3045.65i	0.395803	−	0.574606i
$305$	−12973.0			−2.43552
$306$	6726.60	+	1022.11i	1.25665	+	0.190948i
$307$		−	9739.49i		−	1.81063i	−0.424745	−	0.905313i	$-0.639636\pi$
$307$		−	9739.49i		−	1.81063i	0.424745	−	0.905313i	$-0.360364\pi$
$308$	−629.422	+	2023.32i	−0.116444	+	0.374317i
$309$		−	577.734i		−	0.106363i
$310$	354.603	−	2333.68i	0.0649681	−	0.427562i
$311$	5094.39			0.928862			0.464431	−	0.885609i	$-0.346259\pi$
$311$	5094.39			0.928862			0.464431	+	0.885609i	$0.346259\pi$
$312$	−247.778	−	120.422i	−0.0449605	−	0.0218511i
$313$	−4157.21			−0.750734			−0.375367	−	0.926876i	$-0.622483\pi$
$313$	−4157.21			−0.750734			−0.375367	+	0.926876i	$0.622483\pi$
$314$	1151.58	−	7578.66i	0.206966	−	1.36207i
$315$		−	13597.7i		−	2.43220i
$316$	5098.07	+	1585.93i	0.907560	+	0.282327i
$317$		−	4754.68i		−	0.842427i	−0.906962	−	0.421213i	$-0.861604\pi$
$317$		−	4754.68i		−	0.842427i	0.906962	−	0.421213i	$-0.138396\pi$
$318$	−377.514	−	57.3634i	−0.0665722	−	0.0101157i
$319$	−757.753			−0.132997
$320$	−8447.09	+	6637.63i	−1.47565	+	1.15955i
$321$	−510.435			−0.0887530
$322$	−973.890	−	147.983i	−0.168549	−	0.0256111i
$323$		−	5164.84i		−	0.889720i
$324$	5515.31	+	1715.72i	0.945698	+	0.294191i
$325$			13051.3i			2.22755i
$326$	−1605.16	+	10563.7i	−0.272705	+	1.79470i
$327$	−299.898			−0.0507169
$328$	978.903	+	475.754i	0.164789	+	0.0800887i
$329$	182.944			0.0306566
$330$	28.8420	−	189.812i	0.00481121	−	0.0316630i
$331$			7411.11i			1.23067i	0.788266	+	0.615335i	$0.210979\pi$
$331$			7411.11i			1.23067i	−0.788266	+	0.615335i	$0.789021\pi$
$332$	−1980.37	+	6366.05i	−0.327370	+	1.05236i
$333$			3193.79i			0.525581i
$334$	−5716.37	−	868.604i	−0.936484	−	0.142299i
$335$	13211.4			2.15467
$336$	−257.098	+	373.241i	−0.0417436	+	0.0606011i
$337$	−3581.05			−0.578849			−0.289424	−	0.957201i	$-0.593464\pi$
$337$	−3581.05			−0.578849			−0.289424	+	0.957201i	$0.593464\pi$
$338$	1351.09	+	205.298i	0.217425	+	0.0330377i
$339$			180.411i			0.0289044i
$340$	−4456.56	+	14325.9i	−0.710856	+	2.28510i
$341$			437.513i			0.0694799i
$342$	660.816	−	4348.89i	0.104482	−	0.687606i
$343$	2557.08			0.402534
$344$	3920.72	−	8067.21i	0.614509	−	1.26440i
$345$	89.2531			0.0139282
$346$	293.402	−	1930.90i	0.0455878	−	0.300018i
$347$			3415.51i			0.528399i	0.964468	+	0.264199i	$0.0851077\pi$
$347$			3415.51i			0.528399i	−0.964468	+	0.264199i	$0.914892\pi$
$348$	−154.759	−	48.1428i	−0.0238389	−	0.00741588i
$349$		−	3024.26i		−	0.463853i	−0.972733	−	0.231926i	$-0.925497\pi$
$349$		−	3024.26i		−	0.463853i	0.972733	−	0.231926i	$-0.0745029\pi$
$350$	21227.4	+	3225.52i	3.24187	+	0.492603i
$351$	−656.403			−0.0998182
$352$	1363.08	−	1451.53i	0.206399	−	0.219792i
$353$	4871.57			0.734525			0.367263	−	0.930117i	$-0.380295\pi$
$353$	4871.57			0.734525			0.367263	+	0.930117i	$0.380295\pi$
$354$	591.226	+	89.8370i	0.0887664	+	0.0134881i
$355$		−	12982.3i		−	1.94093i
$356$	−2122.04	−	660.131i	−0.315921	−	0.0982777i
$357$			632.946i			0.0938348i
$358$	−490.448	+	3227.69i	−0.0724050	+	0.476504i
$359$	5863.07			0.861952			0.430976	−	0.902363i	$-0.358169\pi$
$359$	5863.07			0.861952			0.430976	+	0.902363i	$0.358169\pi$
$360$	−5585.44	+	11492.5i	−0.817718	+	1.68252i
$361$	3519.82			0.513168
$362$	−739.999	+	4870.01i	−0.107441	+	0.707077i
$363$			35.5855i			0.00514533i
$364$	−2368.83	+	7614.78i	−0.341100	+	1.09649i
$365$		−	17548.0i		−	2.51645i
$366$	508.467	+	77.2617i	0.0726174	+	0.0110342i
$367$	1436.68			0.204343			0.102172	−	0.994767i	$-0.467421\pi$
$367$	1436.68			0.204343			0.102172	+	0.994767i	$0.467421\pi$
$368$	762.326	+	525.110i	0.107986	+	0.0743839i
$369$	1294.55			0.182634
$370$	−6962.72	−	1057.99i	−0.978309	−	0.148654i
$371$			11053.5i			1.54681i
$372$	−27.7968	+	89.3549i	−0.00387419	+	0.0124539i
$373$		−	3863.47i		−	0.536307i	−0.963376	−	0.268154i	$-0.913586\pi$
$373$		−	3863.47i		−	0.536307i	0.963376	−	0.268154i	$-0.0864135\pi$
$374$	417.753	−	2749.27i	0.0577580	−	0.380111i
$375$	−1174.06			−0.161675
$376$	−154.620	−	75.1466i	−0.0212073	−	0.0103069i
$377$	−2851.80			−0.389590
$378$	−162.225	+	1067.62i	−0.0220739	+	0.145271i
$379$		−	5646.05i		−	0.765220i	−0.923910	−	0.382610i	$-0.875025\pi$
$379$		−	5646.05i		−	0.765220i	0.923910	−	0.382610i	$-0.124975\pi$
$380$	9262.03	+	2881.26i	1.25035	+	0.388962i
$381$			681.123i			0.0915878i
$382$	−9798.27	−	1488.85i	−1.31236	−	0.199414i
$383$	−12358.9			−1.64885			−0.824425	−	0.565971i	$-0.808501\pi$
$383$	−12358.9			−1.64885			−0.824425	+	0.565971i	$0.808501\pi$
$384$	370.608	−	209.849i	0.0492513	−	0.0278876i
$385$	−5557.61			−0.735694
$386$	−926.001	−	140.706i	−0.122104	−	0.0185538i
$387$		−	10668.5i		−	1.40132i
$388$	−1003.16	−	312.065i	−0.131257	−	0.0408317i
$389$			9716.27i			1.26641i	0.773983	+	0.633206i	$0.218261\pi$
$389$			9716.27i			1.26641i	−0.773983	+	0.633206i	$0.781739\pi$
$390$	108.547	−	714.357i	0.0140935	−	0.0927510i
$391$	1292.76			0.167206
$392$	4819.27	+	2342.20i	0.620944	+	0.301783i
$393$	−93.2329			−0.0119669
$394$	−232.711	+	1531.49i	−0.0297558	+	0.195826i
$395$			14003.3i			1.78375i
$396$	703.512	−	2261.49i	0.0892747	−	0.286980i
$397$		−	9737.82i		−	1.23105i	−0.788117	−	0.615525i	$-0.788944\pi$
$397$		−	9737.82i		−	1.23105i	0.788117	−	0.615525i	$-0.211056\pi$
$398$	−1808.52	−	274.805i	−0.227771	−	0.0346099i
$399$	409.213			0.0513440
$400$	−16616.1	−	11445.6i	−2.07701	−	1.43070i
$401$	9826.63			1.22374			0.611868	−	0.790960i	$-0.290418\pi$
$401$	9826.63			1.22374			0.611868	+	0.790960i	$0.290418\pi$
$402$	−517.811	−	78.6815i	−0.0642439	−	0.00976188i
$403$			1646.58i			0.203529i
$404$	−1207.07	+	3880.22i	−0.148648	+	0.477841i
$405$			15149.3i			1.85870i
$406$	−704.800	+	4638.36i	−0.0861543	+	0.566990i
$407$	1305.35			0.158978
$408$	259.991	−	534.953i	0.0315477	−	0.0649120i
$409$	4221.42			0.510357			0.255178	−	0.966894i	$-0.417866\pi$
$409$	4221.42			0.510357			0.255178	+	0.966894i	$0.417866\pi$
$410$	−428.839	+	2822.23i	−0.0516557	+	0.339951i
$411$			593.741i			0.0712582i
$412$	15006.2	+	4668.19i	1.79443	+	0.558216i
$413$		−	17310.8i		−	2.06250i
$414$	1088.53	+	165.402i	0.129223	+	0.0196354i
$415$	−17486.1			−2.06833
$416$	5129.96	−	5462.83i	0.604608	−	0.643839i
$417$	559.027			0.0656491
$418$	−1777.47	−	270.086i	−0.207987	−	0.0316037i
$419$			6367.84i			0.742456i	0.928542	+	0.371228i	$0.121063\pi$
$419$			6367.84i			0.742456i	−0.928542	+	0.371228i	$0.878937\pi$
$420$	−1135.05	−	353.095i	−0.131869	−	0.0410221i
$421$		−	5873.22i		−	0.679912i	−0.940441	−	0.339956i	$-0.889588\pi$
$421$		−	5873.22i		−	0.679912i	0.940441	−	0.339956i	$-0.110412\pi$
$422$	−828.576	+	5452.94i	−0.0955792	+	0.629016i
$423$	−204.478			−0.0235037
$424$	4540.35	−	9342.16i	0.520045	−	1.07004i
$425$	−28177.7			−3.21605
$426$	−77.3173	+	508.833i	−0.00879351	+	0.0578709i
$427$		−	14887.7i		−	1.68727i
$428$	4124.40	−	13258.2i	0.465795	−	1.49733i
$429$			133.926i			0.0150723i
$430$	23258.2	+	3534.09i	2.60840	+	0.396347i
$431$	−1384.88			−0.154774			−0.0773868	−	0.997001i	$-0.524658\pi$
$431$	−1384.88			−0.154774			−0.0773868	+	0.997001i	$0.524658\pi$
$432$	575.646	−	835.692i	0.0641106	−	0.0930723i
$433$	13591.6			1.50847			0.754237	−	0.656602i	$-0.228007\pi$
$433$	13591.6			1.50847			0.754237	+	0.656602i	$0.228007\pi$
$434$	2678.11	+	406.939i	0.296206	+	0.0450085i
$435$		−	425.087i		−	0.0468537i
$436$	2423.23	−	7789.64i	0.266173	−	0.855634i
$437$		−	835.797i		−	0.0914910i
$438$	−104.508	+	687.780i	−0.0114009	+	0.0750306i
$439$	4897.14			0.532409			0.266205	−	0.963917i	$-0.414230\pi$
$439$	4897.14			0.532409			0.266205	+	0.963917i	$0.414230\pi$
$440$	4697.18	+	2282.86i	0.508930	+	0.247344i
$441$	6373.26			0.688183
$442$	1572.21	−	10346.9i	0.169191	−	1.11347i
$443$			686.581i			0.0736353i	0.999322	+	0.0368177i	$0.0117221\pi$
$443$			686.581i			0.0736353i	−0.999322	+	0.0368177i	$0.988278\pi$
$444$	266.597	+	82.9339i	0.0284958	+	0.00886457i
$445$		−	5828.76i		−	0.620921i
$446$	−14546.8	−	2210.40i	−1.54442	−	0.234676i
$447$	−764.978			−0.0809446
$448$	−7617.28	−	9693.79i	−0.803309	−	1.02230i
$449$	6070.36			0.638035			0.319018	−	0.947749i	$-0.396647\pi$
$449$	6070.36			0.638035			0.319018	+	0.947749i	$0.396647\pi$
$450$	−23726.1	−	3605.19i	−2.48547	−	0.377668i
$451$		−	529.106i		−	0.0552430i
$452$	−4686.06	−	1457.75i	−0.487641	−	0.151697i
$453$			46.7257i			0.00484628i
$454$	−103.283	+	679.717i	−0.0106769	+	0.0702659i
$455$	−20916.1			−2.15508
$456$	−345.858	−	168.090i	−0.0355182	−	0.0172621i
$457$	−4876.54			−0.499157			−0.249578	−	0.968355i	$-0.580292\pi$
$457$	−4876.54			−0.499157			−0.249578	+	0.968355i	$0.580292\pi$
$458$	−1435.59	+	9447.74i	−0.146464	+	0.963894i
$459$		−	1417.17i		−	0.144113i
$460$	−721.179	+	2318.28i	−0.0730982	+	0.234979i
$461$		−	565.844i		−	0.0571670i	−0.999591	−	0.0285835i	$-0.990900\pi$
$461$		−	565.844i		−	0.0571670i	0.999591	−	0.0285835i	$-0.00909965\pi$
$462$	217.826	+	33.0988i	0.0219355	+	0.00333310i
$463$	11097.2			1.11389			0.556943	−	0.830551i	$-0.311974\pi$
$463$	11097.2			1.11389			0.556943	+	0.830551i	$0.311974\pi$
$464$	2500.95	−	3630.74i	0.250223	−	0.363261i
$465$	−245.438			−0.0244772
$466$	14478.7	+	2200.05i	1.43930	+	0.218702i
$467$		−	4474.06i		−	0.443330i	−0.975123	−	0.221665i	$-0.928851\pi$
$467$		−	4474.06i		−	0.443330i	0.975123	−	0.221665i	$-0.0711491\pi$
$468$	2647.67	−	8511.12i	0.261514	−	0.840655i
$469$			15161.3i			1.49271i
$470$	67.7363	−	445.779i	0.00664775	−	0.0437495i
$471$	−797.062			−0.0779760
$472$	−7110.66	+	14630.8i	−0.693420	+	1.42677i
$473$	−4360.40			−0.423872
$474$	83.3974	−	548.847i	0.00808137	−	0.0531843i
$475$			18217.5i			1.75974i
$476$	−16440.3	−	5114.30i	−1.58307	−	0.492466i
$477$		−	12354.6i		−	1.18590i
$478$	−5384.41	−	818.163i	−0.515225	−	0.0782885i
$479$	7635.56			0.728345			0.364173	−	0.931331i	$-0.381352\pi$
$479$	7635.56			0.728345			0.364173	+	0.931331i	$0.381352\pi$
$480$	814.284	+	764.666i	0.0774308	+	0.0727126i
$481$	4912.70			0.465696
$482$	−3392.78	−	515.535i	−0.320616	−	0.0487178i
$483$			102.426i			0.00964915i
$484$	−924.309	−	287.537i	−0.0868058	−	0.0270038i
$485$		−	2755.44i		−	0.257976i
$486$	272.126	−	1790.89i	0.0253989	−	0.167153i
$487$	7647.64			0.711597			0.355798	−	0.934563i	$-0.384209\pi$
$487$	7647.64			0.711597			0.355798	+	0.934563i	$0.384209\pi$
$488$	−6115.31	+	12582.8i	−0.567269	+	1.16720i
$489$	1111.01			0.102743
$490$	−2111.23	+	13894.2i	−0.194644	+	1.28097i
$491$			11674.8i			1.07307i	0.843879	+	0.536533i	$0.180266\pi$
$491$			11674.8i			1.07307i	−0.843879	+	0.536533i	$0.819734\pi$
$492$	33.6160	−	108.061i	0.00308034	−	0.00990198i
$493$		−	6157.04i		−	0.562473i
$494$	−6689.49	−	1016.47i	−0.609260	−	0.0925772i
$495$	6211.80			0.564040
$496$	−2096.33	−	1444.00i	−0.189774	−	0.130721i
$497$	14898.4			1.34464
$498$	685.354	+	104.140i	0.0616695	+	0.00937071i
$499$			2477.03i			0.222219i	0.993808	+	0.111109i	$0.0354404\pi$
$499$			2477.03i			0.222219i	−0.993808	+	0.111109i	$0.964560\pi$
$500$	9486.58	−	30495.3i	0.848505	−	2.72758i
$501$			601.201i			0.0536122i
$502$	1252.27	−	8241.28i	0.111337	−	0.732722i
$503$	1457.36			0.129186			0.0645931	−	0.997912i	$-0.479425\pi$
$503$	1457.36			0.129186			0.0645931	+	0.997912i	$0.479425\pi$
$504$	−13188.7	−	6409.79i	−1.16562	−	0.566498i
$505$	−10658.1			−0.939164
$506$	67.6026	−	444.899i	0.00593933	−	0.0390873i
$507$		−	142.097i		−	0.0124472i
$508$	−17691.7	−	5503.58i	−1.54516	−	0.480673i
$509$			8700.46i			0.757645i	0.925469	+	0.378822i	$0.123671\pi$
$509$			8700.46i			0.757645i	−0.925469	+	0.378822i	$0.876329\pi$
$510$	1542.30	+	234.353i	0.133910	+	0.0203477i
$511$	20137.9			1.74334
$512$	2456.12	+	11321.9i	0.212004	+	0.977269i
$513$	−916.233			−0.0788551
$514$	11274.2	+	1713.11i	0.967476	+	0.147008i
$515$			41218.7i			3.52682i
$516$	−890.540	−	277.032i	−0.0759764	−	0.0236350i
$517$			83.5737i			0.00710941i
$518$	1214.13	−	7990.34i	0.102985	−	0.677752i
$519$	−203.077			−0.0171755
$520$	17677.8	+	8591.55i	1.49082	+	0.724547i
$521$	−13256.1			−1.11470			−0.557350	−	0.830278i	$-0.688182\pi$
$521$	−13256.1			−1.11470			−0.557350	+	0.830278i	$0.688182\pi$
$522$	787.762	−	5184.34i	0.0660525	−	0.434698i
$523$		−	4800.16i		−	0.401332i	−0.979660	−	0.200666i	$-0.935689\pi$
$523$		−	4800.16i		−	0.401332i	0.979660	−	0.200666i	$-0.0643106\pi$
$524$	753.337	−	2421.66i	0.0628047	−	0.201890i
$525$		−	2232.53i		−	0.185592i
$526$	5398.52	+	820.307i	0.447503	+	0.0679983i
$527$	−3554.97			−0.293846
$528$	−170.507	−	117.449i	−0.0140537	−	0.00968055i
$529$	−11957.8			−0.982806
$530$	26933.9	+	4092.62i	2.20743	+	0.335419i
$531$			19348.5i			1.58127i
$532$	−3306.51	+	10629.0i	−0.269465	+	0.866214i
$533$		−	1991.29i		−	0.161824i
$534$	−34.7136	+	228.454i	−0.00281312	+	0.0185134i
$535$	36417.2			2.94291
$536$	6227.69	−	12814.0i	0.501857	−	1.03261i
$537$	339.462			0.0272791
$538$	−487.901	+	3210.93i	−0.0390984	+	0.257310i
$539$		−	2604.86i		−	0.208162i
$540$	2541.39	+	790.585i	0.202526	+	0.0630025i
$541$			16580.1i			1.31763i	0.752307	+	0.658813i	$0.228941\pi$
$541$			16580.1i			1.31763i	−0.752307	+	0.658813i	$0.771059\pi$
$542$	8828.67	+	1341.52i	0.699675	+	0.106316i
$543$	512.188			0.0404790
$544$	11794.2	+	11075.6i	0.929548	+	0.872907i
$545$	21396.4			1.68169
$546$	819.789	+	124.567i	0.0642559	+	0.00976371i
$547$			9661.33i			0.755190i	0.925971	+	0.377595i	$0.123249\pi$
$547$			9661.33i			0.755190i	−0.925971	+	0.377595i	$0.876751\pi$
$548$	−15422.0	−	4797.53i	−1.20218	−	0.373978i
$549$			16640.1i			1.29359i
$550$	−1473.50	+	9697.27i	−0.114237	+	0.751805i
$551$	−3980.66			−0.307771
$552$	42.0728	−	86.5683i	0.00324409	−	0.00667498i
$553$	−16070.0			−1.23574
$554$	−525.945	+	3461.29i	−0.0403344	+	0.265445i
$555$			732.282i			0.0560066i
$556$	−4517.03	+	14520.3i	−0.344541	+	1.10755i
$557$		−	14289.4i		−	1.08701i	−0.839407	−	0.543504i	$-0.817097\pi$
$557$		−	14289.4i		−	1.08701i	0.839407	−	0.543504i	$-0.182903\pi$
$558$	−2993.35	−	454.840i	−0.227094	−	0.0345070i
$559$	−16410.4			−1.24165
$560$	18342.8	−	26629.1i	1.38415	−	2.00943i
$561$	−289.147			−0.0217607
$562$	8061.11	+	1224.89i	0.605049	+	0.0919374i
$563$			5293.03i			0.396225i	0.980179	+	0.198113i	$0.0634811\pi$
$563$			5293.03i			0.396225i	−0.980179	+	0.198113i	$0.936519\pi$
$564$	−5.30974	+	17.0686i	−0.000396419	+	0.00127432i
$565$		−	12871.5i		−	0.958424i
$566$	−2489.19	+	16381.6i	−0.184856	+	1.21656i
$567$	−17385.2			−1.28767
$568$	−12591.8	−	6119.71i	−0.930178	−	0.452073i
$569$	12441.8			0.916675			0.458337	−	0.888778i	$-0.348445\pi$
$569$	12441.8			0.916675			0.458337	+	0.888778i	$0.348445\pi$
$570$	151.514	−	997.128i	0.0111337	−	0.0732721i
$571$			3647.01i			0.267290i	0.991029	+	0.133645i	$0.0426682\pi$
$571$			3647.01i			0.267290i	−0.991029	+	0.133645i	$0.957332\pi$
$572$	−3478.64	−	1082.15i	−0.254282	−	0.0791027i
$573$			1030.50i			0.0751307i
$574$	−3238.76	−	492.131i	−0.235511	−	0.0357860i
$575$	−4559.83			−0.330710
$576$	8513.91	+	10834.8i	0.615879	+	0.783771i
$577$	−25905.8			−1.86910			−0.934552	−	0.355826i	$-0.884199\pi$
$577$	−25905.8			−1.86910			−0.934552	+	0.355826i	$0.884199\pi$
$578$	8600.58	+	1306.86i	0.618922	+	0.0940454i
$579$			97.3894i			0.00699027i
$580$	11041.3	+	3434.77i	0.790458	+	0.245898i
$581$		−	20066.9i		−	1.43290i
$582$	−16.4102	+	107.997i	−0.00116877	+	0.00769182i
$583$	−5049.52			−0.358713
$584$	−17020.1	−	8271.90i	−1.20599	−	0.586119i
$585$	23378.1			1.65225
$586$	−1208.92	+	7956.00i	−0.0852217	+	0.560852i
$587$			6636.23i			0.466621i	0.972402	+	0.233310i	$0.0749558\pi$
$587$			6636.23i			0.466621i	−0.972402	+	0.233310i	$0.925044\pi$
$588$	165.496	−	531.999i	0.0116070	−	0.0373117i
$589$			2298.36i			0.160785i
$590$	−42181.3	−	6409.46i	−2.94335	−	0.447243i
$591$	161.070			0.0112107
$592$	−4308.30	+	6254.55i	−0.299105	+	0.434224i
$593$	−14304.1			−0.990555			−0.495278	−	0.868735i	$-0.664934\pi$
$593$	−14304.1			−0.990555			−0.495278	+	0.868735i	$0.664934\pi$
$594$	−487.716	−	74.1086i	−0.0336889	−	0.00511904i
$595$		−	45157.8i		−	3.11141i
$596$	6181.15	−	19869.8i	0.424815	−	1.36560i
$597$			190.205i			0.0130395i
$598$	254.422	−	1674.38i	0.0173982	−	0.114499i
$599$	3855.70			0.263005			0.131502	−	0.991316i	$-0.458020\pi$
$599$	3855.70			0.263005			0.131502	+	0.991316i	$0.458020\pi$
$600$	−917.042	+	1886.89i	−0.0623968	+	0.128387i
$601$	−7823.33			−0.530982			−0.265491	−	0.964113i	$-0.585534\pi$
$601$	−7823.33			−0.530982			−0.265491	+	0.964113i	$0.585534\pi$
$602$	−4055.69	+	26690.9i	−0.274581	+	1.80704i
$603$		−	16945.9i		−	1.14443i
$604$	−1213.67	−	377.551i	−0.0817605	−	0.0254343i
$605$		−	2538.87i		−	0.170611i
$606$	417.735	+	63.4749i	0.0280022	+	0.00425494i
$607$	−16948.6			−1.13331			−0.566657	−	0.823954i	$-0.691763\pi$
$607$	−16948.6			−1.13331			−0.566657	+	0.823954i	$0.691763\pi$
$608$	7160.60	−	7625.23i	0.477632	−	0.508625i
$609$	487.825			0.0324592
$610$	−36276.8	−	5512.27i	−2.40788	−	0.365878i
$611$			314.529i			0.0208257i
$612$	18375.5	+	5716.31i	1.21370	+	0.377562i
$613$			19092.4i			1.25797i	0.777418	+	0.628984i	$0.216529\pi$
$613$			19092.4i			1.25797i	−0.777418	+	0.628984i	$0.783471\pi$
$614$	4138.34	−	27234.8i	0.272003	−	1.79008i
$615$	296.819			0.0194617
$616$	−2619.79	+	5390.44i	−0.171354	+	0.352576i
$617$	13315.1			0.868796			0.434398	−	0.900721i	$-0.356961\pi$
$617$	13315.1			0.868796			0.434398	+	0.900721i	$0.356961\pi$
$618$	245.481	−	1615.54i	0.0159785	−	0.105156i
$619$			52.8039i			0.00342871i	0.999999	+	0.00171435i	$0.000545696\pi$
$619$			52.8039i			0.00342871i	−0.999999	+	0.00171435i	$0.999454\pi$
$620$	1983.18	−	6375.06i	0.128462	−	0.412950i
$621$		−	229.333i		−	0.0148193i
$622$	14245.6	+	2164.62i	0.918321	+	0.139539i
$623$	6689.02			0.430161
$624$	−641.701	−	442.021i	−0.0411677	−	0.0283574i
$625$	44356.2			2.83880
$626$	−11624.9	−	1766.41i	−0.742214	−	0.112780i
$627$			186.939i			0.0119069i
$628$	6440.39	−	20703.1i	0.409235	−	1.31552i
$629$			10606.5i			0.672353i
$630$	5777.71	−	38023.7i	0.365380	−	2.40460i
$631$	−20052.2			−1.26508			−0.632539	−	0.774528i	$-0.717987\pi$
$631$	−20052.2			−1.26508			−0.632539	+	0.774528i	$0.717987\pi$
$632$	13582.0	+	6600.96i	0.854848	+	0.415462i
$633$	573.496			0.0360101
$634$	2020.28	−	13295.6i	0.126554	−	0.832867i
$635$		−	48595.0i		−	3.03690i
$636$	−1031.28	−	320.814i	−0.0642971	−	0.0200017i
$637$		−	9803.38i		−	0.609771i
$638$	−2118.93	−	321.972i	−0.131488	−	0.0199796i
$639$	−16652.1			−1.03090
$640$	−26441.2	+	14971.8i	−1.63309	+	0.924707i
$641$	26498.8			1.63283			0.816413	−	0.577469i	$-0.195959\pi$
$641$	26498.8			1.63283			0.816413	+	0.577469i	$0.195959\pi$
$642$	−1427.35	−	216.886i	−0.0877458	−	0.0133330i
$643$			16432.4i			1.00782i	0.863756	+	0.503911i	$0.168106\pi$
$643$			16432.4i			1.00782i	−0.863756	+	0.503911i	$0.831894\pi$
$644$	−2660.44	−	827.618i	−0.162789	−	0.0506409i
$645$		−	2446.11i		−	0.149326i
$646$	2194.56	−	14442.6i	0.133659	−	0.879623i
$647$	15880.0			0.964927			0.482464	−	0.875916i	$-0.339742\pi$
$647$	15880.0			0.964927			0.482464	+	0.875916i	$0.339742\pi$
$648$	14693.6	+	7141.19i	0.890771	+	0.432920i
$649$	7908.06			0.478303
$650$	−5545.53	+	36495.7i	−0.334636	+	2.20227i
$651$		−	281.662i		−	0.0169573i
$652$	−8977.12	+	28857.6i	−0.539220	+	1.73336i
$653$		−	16903.4i		−	1.01299i	−0.862243	−	0.506494i	$-0.830941\pi$
$653$		−	16903.4i		−	1.01299i	0.862243	−	0.506494i	$-0.169059\pi$
$654$	−838.615	−	127.428i	−0.0501413	−	0.00761899i
$655$	6651.74			0.396802
$656$	2535.19	+	1746.30i	0.150888	+	0.103935i
$657$	−22508.3			−1.33658
$658$	511.571	+	77.7334i	0.0303087	+	0.00460542i
$659$		−	23531.6i		−	1.39099i	−0.718533	−	0.695493i	$-0.755186\pi$
$659$		−	23531.6i		−	1.39099i	0.718533	−	0.695493i	$-0.244814\pi$
$660$	161.303	−	518.522i	0.00951322	−	0.0305810i
$661$			16612.9i			0.977562i	0.872406	+	0.488781i	$0.162558\pi$
$661$			16612.9i			0.977562i	−0.872406	+	0.488781i	$0.837442\pi$
$662$	−3149.00	+	20723.9i	−0.184878	+	1.21670i
$663$	−1088.20			−0.0637440
$664$	−8242.72	+	16960.1i	−0.481746	+	0.991234i
$665$	−29195.5			−1.70248
$666$	−1357.05	+	8930.89i	−0.0789559	+	0.519617i
$667$		−	996.358i		−	0.0578398i
$668$	−15615.8	−	4857.80i	−0.904480	−	0.281368i
$669$			1529.92i			0.0884157i
$670$	36943.4	+	5613.57i	2.13022	+	0.323688i
$671$	6801.09			0.391287
$672$	−877.523	+	934.463i	−0.0503738	+	0.0536424i
$673$	−23808.6			−1.36368			−0.681838	−	0.731503i	$-0.738819\pi$
$673$	−23808.6			−1.36368			−0.681838	+	0.731503i	$0.738819\pi$
$674$	−10013.8	−	1521.60i	−0.572280	−	0.0869581i
$675$			4998.67i			0.285035i
$676$	3690.85	+	1148.16i	0.209994	+	0.0653256i
$677$		−	29287.8i		−	1.66266i	−0.555779	−	0.831330i	$-0.687580\pi$
$677$		−	29287.8i		−	1.66266i	0.555779	−	0.831330i	$-0.312420\pi$
$678$	−76.6574	+	504.490i	−0.00434220	+	0.0285764i
$679$	3162.12			0.178720
$680$	−18549.2	+	38166.5i	−1.04607	+	2.15238i
$681$	71.4872			0.00402261
$682$	−185.901	+	1223.43i	−0.0104377	+	0.0686915i
$683$			23898.6i			1.33888i	0.742866	+	0.669440i	$0.233466\pi$
$683$			23898.6i			1.33888i	−0.742866	+	0.669440i	$0.766534\pi$
$684$	3695.72	−	11880.2i	0.206592	−	0.664107i
$685$		−	42360.7i		−	2.36280i
$686$	7150.43	+	1086.51i	0.397966	+	0.0604711i
$687$	993.637			0.0551814
$688$	14391.4	−	20892.7i	0.797482	−	1.15774i
$689$	−19003.8			−1.05078
$690$	249.581	+	37.9239i	0.0137701	+	0.00209237i
$691$			7611.37i			0.419031i	0.977805	+	0.209515i	$0.0671886\pi$
$691$			7611.37i			0.419031i	−0.977805	+	0.209515i	$0.932811\pi$
$692$	1640.89	−	5274.78i	0.0901408	−	0.289764i
$693$			7128.60i			0.390755i
$694$	−1451.26	+	9550.90i	−0.0793792	+	0.522402i
$695$	−39884.0			−2.17682
$696$	−412.300	−	200.380i	−0.0224543	−	0.0109129i
$697$	4299.19			0.233635
$698$	1285.02	−	8456.81i	0.0696827	−	0.458589i
$699$		−	1522.76i		−	0.0823976i
$700$	57988.4	+	18039.2i	3.13108	+	0.974026i
$701$			12574.5i			0.677509i	0.940875	+	0.338754i	$0.110006\pi$
$701$			12574.5i			0.677509i	−0.940875	+	0.338754i	$0.889994\pi$
$702$	−1835.52	−	278.908i	−0.0986854	−	0.0149953i
$703$	6857.34			0.367894
$704$	4428.38	−	3479.78i	0.237075	−	0.186291i
$705$	−46.8834			−0.00250459
$706$	13622.5	+	2069.94i	0.726190	+	0.110345i
$707$		−	12231.1i		−	0.650633i
$708$	1615.09	+	502.428i	0.0857328	+	0.0266700i
$709$			22118.8i			1.17164i	0.810443	+	0.585818i	$0.199227\pi$
$709$			22118.8i			1.17164i	−0.810443	+	0.585818i	$0.800773\pi$
$710$	5516.24	−	36302.9i	0.291578	−	1.91891i
$711$	17961.6			0.947415
$712$	−5653.43	−	2747.60i	−0.297572	−	0.144622i
$713$	−575.279			−0.0302165
$714$	−268.941	+	1769.92i	−0.0140964	+	0.0927700i
$715$		−	9555.02i		−	0.499773i
$716$	−2742.91	+	8817.28i	−0.143167	+	0.460219i
$717$			566.289i			0.0294958i
$718$	16395.1	+	2491.24i	0.852170	+	0.129488i
$719$	20757.1			1.07665			0.538323	−	0.842738i	$-0.319058\pi$
$719$	20757.1			1.07665			0.538323	+	0.842738i	$0.319058\pi$
$720$	−20501.9	+	29763.6i	−1.06120	+	1.54059i
$721$	−47302.2			−2.44331
$722$	9842.57	+	1495.58i	0.507344	+	0.0770911i
$723$			356.826i			0.0183548i
$724$	−4138.56	+	13303.7i	−0.212443	+	0.682912i
$725$			21717.2i			1.11249i
$726$	−15.1204	+	99.5089i	−0.000772963	+	0.00508694i
$727$	−8960.47			−0.457119			−0.228560	−	0.973530i	$-0.573402\pi$
$727$	−8960.47			−0.457119			−0.228560	+	0.973530i	$0.573402\pi$
$728$	−9859.57	+	20286.9i	−0.501951	+	1.03281i
$729$	19305.7			0.980831
$730$	7456.19	−	49069.9i	0.378036	−	2.48789i
$731$		−	35430.0i		−	1.79265i
$732$	1389.01	+	432.098i	0.0701357	+	0.0218180i
$733$		−	167.235i		−	0.00842697i	−0.999991	−	0.00421348i	$-0.998659\pi$
$733$		−	167.235i		−	0.00842697i	0.999991	−	0.00421348i	$-0.00134120\pi$
$734$	4017.42	+	610.449i	0.202024	+	0.0306976i
$735$	1461.28			0.0733336
$736$	1908.59	+	1792.30i	0.0955866	+	0.0897621i
$737$	−6926.08			−0.346167
$738$	3620.00	+	550.060i	0.180561	+	0.0274363i
$739$		−	37258.2i		−	1.85462i	−0.374294	−	0.927310i	$-0.622115\pi$
$739$		−	37258.2i		−	1.85462i	0.374294	−	0.927310i	$-0.377885\pi$
$740$	−19020.5	−	5916.96i	−0.944875	−	0.293935i
$741$			703.546i			0.0348791i
$742$	−4696.65	+	30909.1i	−0.232371	+	1.52926i
$743$	10834.0			0.534941			0.267471	−	0.963566i	$-0.413812\pi$
$743$	10834.0			0.534941			0.267471	+	0.963566i	$0.413812\pi$
$744$	−115.696	+	238.055i	−0.00570111	+	0.0117305i
$745$	54577.7			2.68399
$746$	1641.60	−	10803.5i	0.0805673	−	0.530221i
$747$			22428.9i			1.09857i
$748$	2336.35	−	7510.37i	0.114205	−	0.367121i
$749$			41792.1i			2.03878i
$750$	−3283.05	−	498.861i	−0.159840	−	0.0242878i
$751$	−11856.1			−0.576080			−0.288040	−	0.957618i	$-0.593004\pi$
$751$	−11856.1			−0.576080			−0.288040	+	0.957618i	$0.593004\pi$
$752$	−400.440	−	275.833i	−0.0194183	−	0.0133758i
$753$	−866.752			−0.0419471
$754$	−7974.58	−	1211.74i	−0.385168	−	0.0585265i
$755$		−	3333.66i		−	0.160695i
$756$	−907.267	+	2916.48i	−0.0436468	+	0.140306i
$757$		−	22519.4i		−	1.08122i	−0.841274	−	0.540608i	$-0.818194\pi$
$757$		−	22519.4i		−	1.08122i	0.841274	−	0.540608i	$-0.181806\pi$
$758$	2399.03	−	15788.2i	0.114956	−	0.756536i
$759$	−46.7909			−0.00223768
$760$	24675.4	+	11992.4i	1.17773	+	0.572383i
$761$	−12771.5			−0.608367			−0.304183	−	0.952613i	$-0.598384\pi$
$761$	−12771.5			−0.608367			−0.304183	+	0.952613i	$0.598384\pi$
$762$	−289.411	+	1904.64i	−0.0137589	+	0.0905485i
$763$			24554.3i			1.16504i
$764$	−26766.6	−	8326.63i	−1.26751	−	0.394302i
$765$			50473.3i			2.38545i
$766$	−34559.5	−	5251.33i	−1.63014	−	0.247700i
$767$	29762.0			1.40110
$768$	1125.51	−	429.336i	0.0528818	−	0.0201723i
$769$	−17307.6			−0.811610			−0.405805	−	0.913960i	$-0.633009\pi$
$769$	−17307.6			−0.811610			−0.405805	+	0.913960i	$0.633009\pi$
$770$	−15540.9	−	2361.45i	−0.727345	−	0.110520i
$771$		−	1185.73i		−	0.0553864i
$772$	−2529.62	−	786.922i	−0.117931	−	0.0366864i
$773$			15532.5i			0.722724i	0.932426	+	0.361362i	$0.117688\pi$
$773$			15532.5i			0.722724i	−0.932426	+	0.361362i	$0.882312\pi$
$774$	4533.08	−	29832.7i	0.210515	−	1.38542i
$775$	12539.1			0.581185
$776$	−2672.56	−	1298.88i	−0.123633	−	0.0600865i
$777$	−840.360			−0.0388002
$778$	−4128.47	+	27169.9i	−0.190248	+	1.25204i
$779$		−	2779.52i		−	0.127839i
$780$	607.065	−	1951.46i	0.0278672	−	0.0895812i
$781$			6805.99i			0.311828i
$782$	3614.98	+	549.297i	0.165309	+	0.0251187i
$783$	−1092.25			−0.0498515
$784$	12481.1	+	8597.28i	0.568562	+	0.391640i
$785$	56866.8			2.58556
$786$	−260.710	−	39.6149i	−0.0118311	−	0.00179773i
$787$		−	16787.5i		−	0.760368i	−0.924911	−	0.380184i	$-0.875861\pi$
$787$		−	16787.5i		−	0.760368i	0.924911	−	0.380184i	$-0.124139\pi$
$788$	−1301.47	+	4183.68i	−0.0588363	+	0.189134i
$789$		−	567.773i		−	0.0256188i
$790$	−5950.03	+	39157.7i	−0.267965	+	1.76350i
$791$	14771.2			0.663976
$792$	2928.16	−	6024.95i	0.131373	−	0.270312i
$793$	25595.9			1.14620
$794$	4137.63	−	27230.1i	0.184936	−	1.21708i
$795$		−	2832.69i		−	0.126371i
$796$	−4940.45	−	1536.89i	−0.219987	−	0.0684342i
$797$			14217.3i			0.631874i	0.948780	+	0.315937i	$0.102319\pi$
$797$			14217.3i			0.631874i	−0.948780	+	0.315937i	$0.897681\pi$
$798$	1144.29	+	173.876i	0.0507614	+	0.00771321i
$799$	−679.069			−0.0300673
$800$	−41600.8	−	39065.9i	−1.83851	−	1.72648i
$801$	−7476.39			−0.329794
$802$	27478.5	+	4175.36i	1.20985	+	0.183837i
$803$			9199.53i			0.404289i
$804$	−1414.54	−	440.039i	−0.0620484	−	0.0193022i
$805$		−	7307.62i		−	0.319950i
$806$	−699.637	+	4604.38i	−0.0305753	+	0.201219i
$807$	337.699			0.0147306
$808$	−5024.08	+	10337.5i	−0.218746	+	0.450088i
$809$	−21274.5			−0.924565			−0.462282	−	0.886733i	$-0.652969\pi$
$809$	−21274.5			−0.924565			−0.462282	+	0.886733i	$0.652969\pi$
$810$	−6436.99	+	42362.4i	−0.279225	+	1.83761i
$811$		−	22733.7i		−	0.984327i	−0.870503	−	0.492163i	$-0.836206\pi$
$811$		−	22733.7i		−	0.984327i	0.870503	−	0.492163i	$-0.163794\pi$
$812$	−3941.71	+	12670.9i	−0.170353	+	0.547613i
$813$		−	928.528i		−	0.0400552i
$814$	3650.20	+	554.649i	0.157174	+	0.0238826i
$815$	−79265.4			−3.40680
$816$	954.323	−	1385.43i	0.0409411	−	0.0594361i
$817$	−22906.2			−0.980890
$818$	11804.5	+	1793.70i	0.504565	+	0.0766688i
$819$			26828.5i			1.14464i
$820$	−2398.35	+	7709.67i	−0.102139	+	0.328333i
$821$		−	30432.9i		−	1.29368i	−0.762624	−	0.646842i	$-0.776089\pi$
$821$		−	30432.9i		−	1.29368i	0.762624	−	0.646842i	$-0.223911\pi$
$822$	−252.283	+	1660.30i	−0.0107048	+	0.0704495i
$823$	−12281.5			−0.520179			−0.260090	−	0.965584i	$-0.583752\pi$
$823$	−12281.5			−0.520179			−0.260090	+	0.965584i	$0.583752\pi$
$824$	39978.8	+	19430.0i	1.69021	+	0.821451i
$825$	1019.88			0.0430396
$826$	7355.43	−	48406.8i	0.309840	−	2.03909i
$827$			5926.97i			0.249215i	0.992206	+	0.124608i	$0.0397672\pi$
$827$			5926.97i			0.249215i	−0.992206	+	0.124608i	$0.960233\pi$
$828$	2973.60	+	925.037i	0.124806	+	0.0388252i
$829$			18559.1i			0.777543i	0.921334	+	0.388772i	$0.127101\pi$
$829$			18559.1i			0.777543i	−0.921334	+	0.388772i	$0.872899\pi$
$830$	−48896.9	−	7429.89i	−2.04486	−	0.310717i
$831$	364.031			0.0151963
$832$	16666.2	−	13096.1i	0.694468	−	0.545705i
$833$	21165.5			0.880361
$834$	1563.22	+	237.532i	0.0649041	+	0.00986220i
$835$		−	42893.0i		−	1.77769i
$836$	−4855.62	−	1510.50i	−0.200879	−	0.0624902i
$837$			630.644i			0.0260433i
$838$	−2705.71	+	17806.6i	−0.111536	+	0.734031i
$839$	−1796.20			−0.0739116			−0.0369558	−	0.999317i	$-0.511766\pi$
$839$	−1796.20			−0.0739116			−0.0369558	+	0.999317i	$0.511766\pi$
$840$	−3023.94	−	1469.66i	−0.124210	−	0.0603667i
$841$	19643.6			0.805430
$842$	2495.55	−	16423.4i	0.102140	−	0.672196i
$843$		−	847.803i		−	0.0346381i
$844$	−4633.94	+	14896.1i	−0.188989	+	0.607520i
$845$			10137.9i			0.412729i
$846$	−571.789	−	86.8835i	−0.0232370	−	0.00353087i
$847$	2913.58			0.118196
$848$	16665.8	−	24194.5i	0.674890	−	0.979769i
$849$	1722.89			0.0696459
$850$	−78794.1	−	11972.8i	−3.17955	−	0.483134i
$851$			1716.39i			0.0691388i
$852$	−432.409	+	1390.01i	−0.0173874	+	0.0558932i
$853$			27068.5i			1.08653i	0.839562	+	0.543264i	$0.182812\pi$
$853$			27068.5i			1.08653i	−0.839562	+	0.543264i	$0.817188\pi$
$854$	6325.82	−	41630.9i	0.253472	−	1.66813i
$855$	32632.1			1.30526
$856$	17166.6	−	35321.8i	0.685448	−	1.41037i
$857$	−7725.26			−0.307923			−0.153961	−	0.988077i	$-0.549203\pi$
$857$	−7725.26			−0.307923			−0.153961	+	0.988077i	$0.549203\pi$
$858$	−56.9056	+	374.502i	−0.00226425	+	0.0149013i
$859$			16537.8i			0.656884i	0.944524	+	0.328442i	$0.106524\pi$
$859$			16537.8i			0.656884i	−0.944524	+	0.328442i	$0.893476\pi$
$860$	63536.0	+	19765.0i	2.51925	+	0.783697i
$861$			340.627i			0.0134826i
$862$	−3872.59	−	588.441i	−0.153017	−	0.0232510i
$863$	28677.1			1.13115			0.565573	−	0.824698i	$-0.308655\pi$
$863$	28677.1			1.13115			0.565573	+	0.824698i	$0.308655\pi$
$864$	1964.78	−	2092.28i	0.0773650	−	0.0823850i
$865$	14488.6			0.569512
$866$	38006.5	+	5775.10i	1.49136	+	0.226612i
$867$		−	904.540i		−	0.0354323i
$868$	7315.96	+	2275.87i	0.286083	+	0.0889955i
$869$		−	7341.20i		−	0.286574i
$870$	180.621	−	1188.68i	0.00703864	−	0.0463220i
$871$	−26066.3			−1.01403
$872$	10086.0	−	20752.8i	0.391691	−	0.805938i
$873$	−3534.33			−0.137021
$874$	355.133	−	2337.16i	0.0137443	−	0.0904527i
$875$			96126.3i			3.71390i
$876$	−584.479	+	1878.85i	−0.0225431	+	0.0724664i
$877$		−	17806.7i		−	0.685620i	−0.939405	−	0.342810i	$-0.888621\pi$
$877$		−	17806.7i		−	0.685620i	0.939405	−	0.342810i	$-0.111379\pi$
$878$	13694.0	+	2080.81i	0.526367	+	0.0799817i
$879$	836.748			0.0321079
$880$	12164.9	+	8379.48i	0.465997	+	0.320991i
$881$	−27163.6			−1.03878			−0.519389	−	0.854538i	$-0.673840\pi$
$881$	−27163.6			−1.03878			−0.519389	+	0.854538i	$0.673840\pi$
$882$	17821.7	+	2708.02i	0.680373	+	0.103383i
$883$			40228.7i			1.53319i	0.642133	+	0.766593i	$0.278050\pi$
$883$			40228.7i			1.53319i	−0.642133	+	0.766593i	$0.721950\pi$
$884$	8792.86	−	28265.3i	0.334543	−	1.07541i
$885$			4436.29i			0.168502i
$886$	−291.730	+	1919.91i	−0.0110619	+	0.0727997i
$887$	−32740.5			−1.23937			−0.619683	−	0.784852i	$-0.712739\pi$
$887$	−32740.5			−1.23937			−0.619683	+	0.784852i	$0.712739\pi$
$888$	710.255	+	345.189i	0.0268408	+	0.0130448i
$889$	55767.1			2.10390
$890$	2476.66	−	16299.1i	0.0932784	−	0.613874i
$891$		−	7942.02i		−	0.298617i
$892$	−39738.5	−	12362.0i	−1.49164	−	0.464025i
$893$			439.033i			0.0164520i
$894$	−2139.13	−	325.042i	−0.0800260	−	0.0121600i
$895$	−24219.1			−0.904530
$896$	−17181.5	−	30343.6i	−0.640617	−	1.13137i
$897$	−176.098			−0.00655488
$898$	16974.7	+	2579.31i	0.630795	+	0.0958495i
$899$			2739.89i			0.101647i
$900$	−64814.2	−	20162.6i	−2.40053	−	0.746764i
$901$		−	41029.3i		−	1.51707i
$902$	224.819	−	1479.55i	0.00829894	−	0.0546161i
$903$	2807.13			0.103450
$904$	−12484.4	−	6067.48i	−0.459318	−	0.223232i
$905$	−36542.3			−1.34222
$906$	−19.8539	+	130.660i	−0.000728036	+	0.00479128i
$907$		−	2766.05i		−	0.101263i	−0.998717	−	0.0506314i	$-0.983877\pi$
$907$		−	2766.05i		−	0.101263i	0.998717	−	0.0506314i	$-0.0161234\pi$
$908$	−577.628	+	1856.83i	−0.0211115	+	0.0678645i
$909$			13670.8i			0.498826i
$910$	−58488.2	−	8887.30i	−2.13062	−	0.323749i
$911$	3663.71			0.133243			0.0666213	−	0.997778i	$-0.478778\pi$
$911$	3663.71			0.133243			0.0666213	+	0.997778i	$0.478778\pi$
$912$	−895.712	−	616.990i	−0.0325219	−	0.0224020i
$913$	9167.08			0.332296
$914$	−13636.4	−	2072.06i	−0.493492	−	0.0749863i
$915$			3815.30i			0.137847i
$916$	−8028.74	+	25809.0i	−0.289604	+	0.930953i
$917$			7633.47i			0.274896i
$918$	602.161	−	3962.88i	0.0216495	−	0.142478i
$919$	−21780.1			−0.781783			−0.390891	−	0.920437i	$-0.627833\pi$
$919$	−21780.1			−0.781783			−0.390891	+	0.920437i	$0.627833\pi$
$920$	−3001.70	+	6176.25i	−0.107569	+	0.221332i
$921$	−2864.34			−0.102479
$922$	240.429	−	1582.29i	0.00858797	−	0.0565183i
$923$			25614.3i			0.913441i
$924$	595.050	+	185.110i	0.0211858	+	0.00659056i
$925$		−	37411.4i		−	1.32982i
$926$	31031.3	+	4715.22i	1.10124	+	0.167335i
$927$	52870.1			1.87323
$928$	8536.19	−	9090.08i	0.301955	−	0.321548i
$929$	−29634.4			−1.04658			−0.523291	−	0.852154i	$-0.675296\pi$
$929$	−29634.4			−1.04658			−0.523291	+	0.852154i	$0.675296\pi$
$930$	−686.324	−	104.287i	−0.0241994	−	0.00367711i
$931$		−	13683.9i		−	0.481711i
$932$	39552.5	+	12304.1i	1.39011	+	0.432441i
$933$		−	1498.24i		−	0.0525724i
$934$	1901.04	−	12511.0i	0.0665996	−	0.438299i
$935$	20629.3			0.721551
$936$	11020.1	−	22674.9i	0.384834	−	0.791829i
$937$	3138.47			0.109423			0.0547115	−	0.998502i	$-0.482576\pi$
$937$	3138.47			0.109423			0.0547115	+	0.998502i	$0.482576\pi$
$938$	−6442.07	+	42395.9i	−0.224244	+	1.47577i
$939$			1222.62i			0.0424905i
$940$	378.826	−	1217.76i	0.0131446	−	0.0422543i
$941$		−	29234.7i		−	1.01278i	−0.862305	−	0.506389i	$-0.830980\pi$
$941$		−	29234.7i		−	1.01278i	0.862305	−	0.506389i	$-0.169020\pi$
$942$	−2228.85	−	338.674i	−0.0770911	−	0.0117140i
$943$	695.713			0.0240250
$944$	−26100.4	+	37891.1i	−0.899889	+	1.30641i
$945$	−8010.90			−0.275761
$946$	−12193.1	−	1852.75i	−0.419061	−	0.0636765i
$947$			25674.7i			0.881009i	0.897750	+	0.440505i	$0.145200\pi$
$947$			25674.7i			0.881009i	−0.897750	+	0.440505i	$0.854800\pi$
$948$	466.413	−	1499.32i	0.0159793	−	0.0513667i
$949$			34622.4i			1.18429i
$950$	−7740.67	+	50942.1i	−0.264358	+	1.73977i
$951$	−1398.33			−0.0476802
$952$	−43799.4	−	21286.8i	−1.49112	−	0.724695i
$953$	−17003.6			−0.577963			−0.288982	−	0.957335i	$-0.593317\pi$
$953$	−17003.6			−0.577963			−0.288982	+	0.957335i	$0.593317\pi$
$954$	5249.49	−	34547.4i	0.178154	−	1.17245i
$955$		−	73521.7i		−	2.49121i
$956$	−14709.0	−	4575.71i	−0.497617	−	0.154800i
$957$			222.852i			0.00752745i
$958$	21351.5	+	3244.37i	0.720080	+	0.109416i
$959$	48612.8			1.63690
$960$	1952.10	+	2484.25i	0.0656288	+	0.0835196i
$961$	−28209.0			−0.946898
$962$	13737.5	+	2087.42i	0.460411	+	0.0699597i
$963$		−	46711.4i		−	1.56309i
$964$	−9268.29	−	2883.21i	−0.309659	−	0.0963298i
$965$		−	6948.29i		−	0.231786i
$966$	−43.5211	+	286.417i	−0.00144955	+	0.00953965i
$967$	699.172			0.0232512			0.0116256	−	0.999932i	$-0.496299\pi$
$967$	699.172			0.0232512			0.0116256	+	0.999932i	$0.496299\pi$
$968$	−2462.50	−	1196.79i	−0.0817641	−	0.0397379i
$969$	−1518.96			−0.0503570
$970$	1170.80	−	7705.13i	0.0387546	−	0.255048i
$971$		−	30872.8i		−	1.02035i	−0.860072	−	0.510173i	$-0.829582\pi$
$971$		−	30872.8i		−	1.02035i	0.860072	−	0.510173i	$-0.170418\pi$
$972$	1521.91	−	4892.28i	0.0502213	−	0.161440i
$973$		−	45770.5i		−	1.50805i
$974$	21385.3	+	3249.51i	0.703521	+	0.106900i
$975$	3838.32			0.126077
$976$	−22446.9	+	32587.2i	−0.736175	+	1.06874i
$977$	34768.0			1.13851			0.569257	−	0.822160i	$-0.307231\pi$
$977$	34768.0			1.13851			0.569257	+	0.822160i	$0.307231\pi$
$978$	3106.74	+	472.071i	0.101577	+	0.0154347i
$979$			3055.73i			0.0997563i
$980$	−11807.4	+	37955.7i	−0.384871	+	1.23720i
$981$		−	27444.6i		−	0.893208i
$982$	−4960.65	+	32646.5i	−0.161202	+	1.06089i
$983$	47608.7			1.54474			0.772371	−	0.635172i	$-0.219071\pi$
$983$	47608.7			1.54474			0.772371	+	0.635172i	$0.219071\pi$
$984$	139.917	−	287.891i	0.00453292	−	0.00932686i
$985$	−11491.6			−0.371729
$986$	2616.15	−	17217.1i	0.0844980	−	0.556090i
$987$		−	53.8030i		−	0.00173512i
$988$	−18274.1	−	5684.77i	−0.588438	−	0.183053i
$989$		−	5733.42i		−	0.184340i
$990$	17370.2	+	2639.41i	0.557639	+	0.0847334i
$991$	6689.08			0.214415			0.107208	−	0.994237i	$-0.465809\pi$
$991$	6689.08			0.214415			0.107208	+	0.994237i	$0.465809\pi$
$992$	−5248.45	−	4928.64i	−0.167982	−	0.157747i
$993$	2179.57			0.0696543
$994$	41660.8	+	6330.38i	1.32938	+	0.201999i
$995$		−	13570.3i		−	0.432369i
$996$	1872.23	+	582.418i	0.0595620	+	0.0185287i
$997$			36400.3i			1.15628i	0.815938	+	0.578139i	$0.196221\pi$
$997$			36400.3i			1.15628i	−0.815938	+	0.578139i	$0.803779\pi$
$998$	−1052.50	+	6926.59i	−0.0333830	+	0.219697i
$999$	1881.58			0.0595900

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	88.4.c.a.45.28	yes	30
4.3	odd	2		352.4.c.a.177.16		30
8.3	odd	2		352.4.c.a.177.15		30
8.5	even	2	inner	88.4.c.a.45.27	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.4.c.a.45.27	✓	30	8.5	even	2	inner
88.4.c.a.45.28	yes	30	1.1	even	1	trivial
352.4.c.a.177.15		30	8.3	odd	2
352.4.c.a.177.16		30	4.3	odd	2

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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	88.4.c.a.45.28

Level	$88$
Weight	$4$
Character	88.45
Analytic conductor	$5.192$
Analytic rank	$0$
Dimension	$30$
Inner twists	$2$