LMFDB - Embedded newform 483.3.b.a.323.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,3,Mod(323,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("483.323");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	483.b (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:	$13.1607967686$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.12
Character	$\chi$	$=$	483.323
Dual form			483.3.b.a.323.77

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.14953i q^{2} +(2.25271 + 1.98124i) q^{3} -5.91951 q^{4} +0.146549i q^{5} +(6.23996 - 7.09496i) q^{6} -2.64575 q^{7} +6.04554i q^{8} +(1.14940 + 8.92630i) q^{9} +O(q^{10})$	\(q-3.14953i q^{2} +(2.25271 + 1.98124i) q^{3} -5.91951 q^{4} +0.146549i q^{5} +(6.23996 - 7.09496i) q^{6} -2.64575 q^{7} +6.04554i q^{8} +(1.14940 + 8.92630i) q^{9} +0.461560 q^{10} -11.2512i q^{11} +(-13.3349 - 11.7279i) q^{12} +22.3962 q^{13} +8.33286i q^{14} +(-0.290349 + 0.330133i) q^{15} -4.63746 q^{16} -25.8454i q^{17} +(28.1136 - 3.62006i) q^{18} -2.10387 q^{19} -0.867499i q^{20} +(-5.96011 - 5.24186i) q^{21} -35.4358 q^{22} -4.79583i q^{23} +(-11.9776 + 13.6188i) q^{24} +24.9785 q^{25} -70.5374i q^{26} +(-15.0959 + 22.3856i) q^{27} +15.6615 q^{28} -33.3615i q^{29} +(1.03976 + 0.914460i) q^{30} +32.3985 q^{31} +38.7879i q^{32} +(22.2912 - 25.3456i) q^{33} -81.4008 q^{34} -0.387733i q^{35} +(-6.80388 - 52.8393i) q^{36} -47.8911 q^{37} +6.62620i q^{38} +(50.4521 + 44.3722i) q^{39} -0.885968 q^{40} -53.0373i q^{41} +(-16.5094 + 18.7715i) q^{42} +0.0643844 q^{43} +66.6013i q^{44} +(-1.30814 + 0.168444i) q^{45} -15.1046 q^{46} -49.7044i q^{47} +(-10.4468 - 9.18790i) q^{48} +7.00000 q^{49} -78.6705i q^{50} +(51.2059 - 58.2222i) q^{51} -132.574 q^{52} +16.5993i q^{53} +(70.5040 + 47.5448i) q^{54} +1.64885 q^{55} -15.9950i q^{56} +(-4.73942 - 4.16827i) q^{57} -105.073 q^{58} -11.9310i q^{59} +(1.71872 - 1.95422i) q^{60} -24.4629 q^{61} -102.040i q^{62} +(-3.04103 - 23.6168i) q^{63} +103.614 q^{64} +3.28214i q^{65} +(-79.8266 - 70.2067i) q^{66} +112.891 q^{67} +152.992i q^{68} +(9.50168 - 10.8036i) q^{69} -1.22117 q^{70} +108.944i q^{71} +(-53.9643 + 6.94874i) q^{72} +20.1369 q^{73} +150.834i q^{74} +(56.2694 + 49.4884i) q^{75} +12.4539 q^{76} +29.7678i q^{77} +(139.751 - 158.900i) q^{78} -76.7270 q^{79} -0.679616i q^{80} +(-78.3578 + 20.5198i) q^{81} -167.042 q^{82} +72.6961i q^{83} +(35.2809 + 31.0292i) q^{84} +3.78762 q^{85} -0.202780i q^{86} +(66.0970 - 75.1538i) q^{87} +68.0193 q^{88} +100.445i q^{89} +(0.530517 + 4.12003i) q^{90} -59.2548 q^{91} +28.3890i q^{92} +(72.9844 + 64.1891i) q^{93} -156.545 q^{94} -0.308321i q^{95} +(-76.8481 + 87.3780i) q^{96} -180.293 q^{97} -22.0467i q^{98} +(100.431 - 12.9321i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9}+O(q^{10}) $ 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9	$ 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9} - 16 q^{10} - 18 q^{12} + 64 q^{13} + 20 q^{15} + 272 q^{16} - 38 q^{18} - 48 q^{19} - 28 q^{21} + 208 q^{22} + 228 q^{24} - 568 q^{25} - 88 q^{27} - 8 q^{30} + 8 q^{31} - 160 q^{33} - 32 q^{34} - 138 q^{36} - 136 q^{37} + 76 q^{39} - 48 q^{40} - 140 q^{42} + 424 q^{43} + 172 q^{45} + 334 q^{48} + 616 q^{49} + 288 q^{51} - 140 q^{52} - 240 q^{55} - 252 q^{57} - 380 q^{58} - 364 q^{60} + 312 q^{61} - 252 q^{64} + 44 q^{66} - 224 q^{67} + 168 q^{70} - 592 q^{72} + 216 q^{73} - 284 q^{75} + 328 q^{76} + 470 q^{78} - 8 q^{79} + 380 q^{81} - 548 q^{82} + 224 q^{84} - 712 q^{85} + 56 q^{87} - 896 q^{88} + 1136 q^{90} + 168 q^{91} - 236 q^{93} - 252 q^{94} - 546 q^{96} + 480 q^{97} - 248 q^{99}+O(q^{100}) $ 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9 - 16 * q^10 - 18 * q^12 + 64 * q^13 + 20 * q^15 + 272 * q^16 - 38 * q^18 - 48 * q^19 - 28 * q^21 + 208 * q^22 + 228 * q^24 - 568 * q^25 - 88 * q^27 - 8 * q^30 + 8 * q^31 - 160 * q^33 - 32 * q^34 - 138 * q^36 - 136 * q^37 + 76 * q^39 - 48 * q^40 - 140 * q^42 + 424 * q^43 + 172 * q^45 + 334 * q^48 + 616 * q^49 + 288 * q^51 - 140 * q^52 - 240 * q^55 - 252 * q^57 - 380 * q^58 - 364 * q^60 + 312 * q^61 - 252 * q^64 + 44 * q^66 - 224 * q^67 + 168 * q^70 - 592 * q^72 + 216 * q^73 - 284 * q^75 + 328 * q^76 + 470 * q^78 - 8 * q^79 + 380 * q^81 - 548 * q^82 + 224 * q^84 - 712 * q^85 + 56 * q^87 - 896 * q^88 + 1136 * q^90 + 168 * q^91 - 236 * q^93 - 252 * q^94 - 546 * q^96 + 480 * q^97 - 248 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		−	3.14953i		−	1.57476i	−0.616466	−	0.787381i	$-0.711436\pi$
$2$		−	3.14953i		−	1.57476i	0.616466	−	0.787381i	$-0.288564\pi$
$3$	2.25271	+	1.98124i	0.750903	+	0.660412i
$3$	2.25271	+	1.98124i	0.750903	+	0.660412i
$4$	−5.91951			−1.47988
$5$			0.146549i			0.0293098i	0.999893	+	0.0146549i	$0.00466497\pi$
$5$			0.146549i			0.0293098i	−0.999893	+	0.0146549i	$0.995335\pi$
$6$	6.23996	−	7.09496i	1.03999	−	1.18249i
$7$	−2.64575			−0.377964
$7$	−2.64575			−0.377964
$8$			6.04554i			0.755692i
$9$	1.14940	+	8.92630i	0.127711	+	0.991811i
$10$	0.461560			0.0461560
$11$		−	11.2512i		−	1.02283i	−0.859333	−	0.511416i	$-0.829121\pi$
$11$		−	11.2512i		−	1.02283i	0.859333	−	0.511416i	$-0.170879\pi$
$12$	−13.3349	−	11.7279i	−1.11124	−	0.977329i
$13$	22.3962			1.72278			0.861392	−	0.507941i	$-0.169593\pi$
$13$	22.3962			1.72278			0.861392	+	0.507941i	$0.169593\pi$
$14$			8.33286i			0.595204i
$15$	−0.290349	+	0.330133i	−0.0193566	+	0.0220088i
$16$	−4.63746			−0.289841
$17$		−	25.8454i		−	1.52032i	−0.649737	−	0.760159i	$-0.725121\pi$
$17$		−	25.8454i		−	1.52032i	0.649737	−	0.760159i	$-0.274879\pi$
$18$	28.1136	−	3.62006i	1.56187	−	0.201115i
$19$	−2.10387			−0.110730			−0.0553651	−	0.998466i	$-0.517632\pi$
$19$	−2.10387			−0.110730			−0.0553651	+	0.998466i	$0.517632\pi$
$20$		−	0.867499i		−	0.0433749i
$21$	−5.96011	−	5.24186i	−0.283815	−	0.249612i
$22$	−35.4358			−1.61072
$23$		−	4.79583i		−	0.208514i
$23$		−	4.79583i		−	0.208514i
$24$	−11.9776	+	13.6188i	−0.499068	+	0.567452i
$25$	24.9785			0.999141
$26$		−	70.5374i		−	2.71298i
$27$	−15.0959	+	22.3856i	−0.559106	+	0.829096i
$28$	15.6615			0.559341
$29$		−	33.3615i		−	1.15040i	−0.818014	−	0.575198i	$-0.804925\pi$
$29$		−	33.3615i		−	1.15040i	0.818014	−	0.575198i	$-0.195075\pi$
$30$	1.03976	+	0.914460i	0.0346587	+	0.0304820i
$31$	32.3985			1.04511			0.522556	−	0.852605i	$-0.324978\pi$
$31$	32.3985			1.04511			0.522556	+	0.852605i	$0.324978\pi$
$32$			38.7879i			1.21212i
$33$	22.2912	−	25.3456i	0.675491	−	0.768048i
$34$	−81.4008			−2.39414
$35$		−	0.387733i		−	0.0110781i
$36$	−6.80388	−	52.8393i	−0.188997	−	1.46776i
$37$	−47.8911			−1.29435			−0.647176	−	0.762340i	$-0.724050\pi$
$37$	−47.8911			−1.29435			−0.647176	+	0.762340i	$0.724050\pi$
$38$			6.62620i			0.174374i
$39$	50.4521	+	44.3722i	1.29364	+	1.13775i
$40$	−0.885968			−0.0221492
$41$		−	53.0373i		−	1.29359i	−0.762663	−	0.646796i	$-0.776108\pi$
$41$		−	53.0373i		−	1.29359i	0.762663	−	0.646796i	$-0.223892\pi$
$42$	−16.5094	+	18.7715i	−0.393080	+	0.446941i
$43$	0.0643844			0.00149731			0.000748656	−	1.00000i	$-0.499762\pi$
$43$	0.0643844			0.00149731			0.000748656		1.00000i	$0.499762\pi$
$44$			66.6013i			1.51367i
$45$	−1.30814	+	0.168444i	−0.0290698	+	0.00374319i
$46$	−15.1046			−0.328361
$47$		−	49.7044i		−	1.05754i	−0.848765	−	0.528770i	$-0.822653\pi$
$47$		−	49.7044i		−	1.05754i	0.848765	−	0.528770i	$-0.177347\pi$
$48$	−10.4468	−	9.18790i	−0.217643	−	0.191415i
$49$	7.00000			0.142857
$50$		−	78.6705i		−	1.57341i
$51$	51.2059	−	58.2222i	1.00404	−	1.14161i
$52$	−132.574			−2.54951
$53$			16.5993i			0.313194i	0.987663	+	0.156597i	$0.0500524\pi$
$53$			16.5993i			0.313194i	−0.987663	+	0.156597i	$0.949948\pi$
$54$	70.5040	+	47.5448i	1.30563	+	0.880459i
$55$	1.64885			0.0299790
$56$		−	15.9950i		−	0.285625i
$57$	−4.73942	−	4.16827i	−0.0831476	−	0.0731276i
$58$	−105.073			−1.81160
$59$		−	11.9310i		−	0.202220i	−0.994875	−	0.101110i	$-0.967761\pi$
$59$		−	11.9310i		−	0.202220i	0.994875	−	0.101110i	$-0.0322394\pi$
$60$	1.71872	−	1.95422i	0.0286453	−	0.0325704i
$61$	−24.4629			−0.401031			−0.200515	−	0.979691i	$-0.564262\pi$
$61$	−24.4629			−0.401031			−0.200515	+	0.979691i	$0.564262\pi$
$62$		−	102.040i		−	1.64580i
$63$	−3.04103	−	23.6168i	−0.0482703	−	0.374869i
$64$	103.614			1.61897
$65$			3.28214i			0.0504945i
$66$	−79.8266	−	70.2067i	−1.20949	−	1.06374i
$67$	112.891			1.68494			0.842471	−	0.538741i	$-0.181100\pi$
$67$	112.891			1.68494			0.842471	+	0.538741i	$0.181100\pi$
$68$			152.992i			2.24988i
$69$	9.50168	−	10.8036i	0.137705	−	0.156574i
$70$	−1.22117			−0.0174453
$71$			108.944i			1.53443i	0.641392	+	0.767213i	$0.278357\pi$
$71$			108.944i			1.53443i	−0.641392	+	0.767213i	$0.721643\pi$
$72$	−53.9643	+	6.94874i	−0.749504	+	0.0965103i
$73$	20.1369			0.275847			0.137924	−	0.990443i	$-0.455957\pi$
$73$	20.1369			0.275847			0.137924	+	0.990443i	$0.455957\pi$
$74$			150.834i			2.03830i
$75$	56.2694	+	49.4884i	0.750258	+	0.659845i
$76$	12.4539			0.163867
$77$			29.7678i			0.386594i
$78$	139.751	−	158.900i	1.79168	−	2.03718i
$79$	−76.7270			−0.971228			−0.485614	−	0.874173i	$-0.661404\pi$
$79$	−76.7270			−0.971228			−0.485614	+	0.874173i	$0.661404\pi$
$80$		−	0.679616i		−	0.00849519i
$81$	−78.3578	+	20.5198i	−0.967380	+	0.253331i
$82$	−167.042			−2.03710
$83$			72.6961i			0.875857i	0.899010	+	0.437929i	$0.144288\pi$
$83$			72.6961i			0.875857i	−0.899010	+	0.437929i	$0.855712\pi$
$84$	35.2809	+	31.0292i	0.420011	+	0.369396i
$85$	3.78762			0.0445603
$86$		−	0.202780i		−	0.00235791i
$87$	66.0970	−	75.1538i	0.759736	−	0.863836i
$88$	68.0193			0.772947
$89$			100.445i			1.12859i	0.825573	+	0.564295i	$0.190852\pi$
$89$			100.445i			1.12859i	−0.825573	+	0.564295i	$0.809148\pi$
$90$	0.530517	+	4.12003i	0.00589464	+	0.0457781i
$91$	−59.2548			−0.651151
$92$			28.3890i			0.308576i
$93$	72.9844	+	64.1891i	0.784779	+	0.690205i
$94$	−156.545			−1.66537
$95$		−	0.308321i		−	0.00324548i
$96$	−76.8481	+	87.3780i	−0.800501	+	0.910187i
$97$	−180.293			−1.85869			−0.929343	−	0.369217i	$-0.879626\pi$
$97$	−180.293			−1.85869			−0.929343	+	0.369217i	$0.879626\pi$
$98$		−	22.0467i		−	0.224966i
$99$	100.431	−	12.9321i	1.01446	−	0.130627i
$100$	−147.861			−1.47861
$101$			174.539i			1.72811i	0.503399	+	0.864054i	$0.332082\pi$
$101$			174.539i			1.72811i	−0.503399	+	0.864054i	$0.667918\pi$
$102$	−183.372	−	161.274i	−1.79777	−	1.58112i
$103$	82.4544			0.800528			0.400264	−	0.916400i	$-0.368918\pi$
$103$	82.4544			0.800528			0.400264	+	0.916400i	$0.368918\pi$
$104$			135.397i			1.30189i
$105$	0.768190	−	0.873449i	0.00731610	−	0.00831856i
$106$	52.2799			0.493206
$107$			170.322i			1.59180i	0.605431	+	0.795898i	$0.293001\pi$
$107$			170.322i			1.59180i	−0.605431	+	0.795898i	$0.706999\pi$
$108$	89.3600	−	132.512i	0.827408	−	1.22696i
$109$	181.454			1.66472			0.832358	−	0.554238i	$-0.186990\pi$
$109$	181.454			1.66472			0.832358	+	0.554238i	$0.186990\pi$
$110$		−	5.19309i		−	0.0472099i
$111$	−107.885	−	94.8835i	−0.971934	−	0.854807i
$112$	12.2696			0.109550
$113$		−	65.3042i		−	0.577913i	−0.957342	−	0.288957i	$-0.906692\pi$
$113$		−	65.3042i		−	0.577913i	0.957342	−	0.288957i	$-0.0933083\pi$
$114$	−13.1281	+	14.9269i	−0.115159	+	0.130938i
$115$	0.702825			0.00611152
$116$			197.484i			1.70245i
$117$	25.7422	+	199.915i	0.220019	+	1.70868i
$118$	−37.5769			−0.318448
$119$			68.3805i			0.574626i
$120$	−1.99583	−	1.75531i	−0.0166319	−	0.0146276i
$121$	−5.58852			−0.0461861
$122$			77.0464i			0.631528i
$123$	105.079	−	119.478i	0.854304	−	0.971363i
$124$	−191.783			−1.54664
$125$			7.32431i			0.0585945i
$126$	−74.3816	+	9.57779i	−0.590330	+	0.0760142i
$127$	−50.6859			−0.399102			−0.199551	−	0.979887i	$-0.563948\pi$
$127$	−50.6859			−0.399102			−0.199551	+	0.979887i	$0.563948\pi$
$128$		−	171.182i		−	1.33736i
$129$	0.145039	+	0.127561i	0.00112434	+	0.000988843i
$130$	10.3372			0.0795168
$131$		−	104.727i		−	0.799440i	−0.916637	−	0.399720i	$-0.869107\pi$
$131$		−	104.727i		−	0.799440i	0.916637	−	0.399720i	$-0.130893\pi$
$132$	−131.953	+	150.033i	−0.999644	+	1.13662i
$133$	5.56633			0.0418521
$134$		−	355.553i		−	2.65338i
$135$	−3.28059	−	2.21228i	−0.0243007	−	0.0163873i
$136$	156.249			1.14889
$137$		−	57.8836i		−	0.422508i	−0.977431	−	0.211254i	$-0.932245\pi$
$137$		−	57.8836i		−	0.422508i	0.977431	−	0.211254i	$-0.0677547\pi$
$138$	−34.0263	−	29.9258i	−0.246567	−	0.216853i
$139$	142.173			1.02283			0.511414	−	0.859334i	$-0.329122\pi$
$139$	142.173			1.02283			0.511414	+	0.859334i	$0.329122\pi$
$140$			2.29519i			0.0163942i
$141$	98.4761	−	111.969i	0.698412	−	0.794110i
$142$	343.123			2.41636
$143$		−	251.983i		−	1.76212i
$144$	−5.33030	−	41.3954i	−0.0370159	−	0.287468i
$145$	4.88910			0.0337179
$146$		−	63.4216i		−	0.434394i
$147$	15.7690	+	13.8687i	0.107272	+	0.0943446i
$148$	283.492			1.91548
$149$		−	272.050i		−	1.82584i	−0.408142	−	0.912918i	$-0.633823\pi$
$149$		−	272.050i		−	1.82584i	0.408142	−	0.912918i	$-0.366177\pi$
$150$	155.865	−	177.222i	1.03910	−	1.18148i
$151$	126.137			0.835344			0.417672	−	0.908598i	$-0.362846\pi$
$151$	126.137			0.835344			0.417672	+	0.908598i	$0.362846\pi$
$152$		−	12.7190i		−	0.0836779i
$153$	230.704	−	29.7067i	1.50787	−	0.194162i
$154$	93.7543			0.608794
$155$			4.74797i			0.0306321i
$156$	−298.652	−	262.661i	−1.91443	−	1.68373i
$157$	13.6995			0.0872579			0.0436290	−	0.999048i	$-0.486108\pi$
$157$	13.6995			0.0872579			0.0436290	+	0.999048i	$0.486108\pi$
$158$			241.654i			1.52945i
$159$	−32.8871	+	37.3934i	−0.206837	+	0.235178i
$160$	−5.68434			−0.0355271
$161$			12.6886i			0.0788110i
$162$	64.6276	+	246.790i	0.398936	+	1.52339i
$163$	−294.768			−1.80839			−0.904197	−	0.427116i	$-0.859530\pi$
$163$	−294.768			−1.80839			−0.904197	+	0.427116i	$0.859530\pi$
$164$			313.955i			1.91436i
$165$	3.71437	+	3.26676i	0.0225114	+	0.0197985i
$166$	228.958			1.37927
$167$			167.742i			1.00444i	0.864739	+	0.502221i	$0.167484\pi$
$167$			167.742i			1.00444i	−0.864739	+	0.502221i	$0.832516\pi$
$168$	31.6899	−	36.0321i	0.188630	−	0.214477i
$169$	332.589			1.96798
$170$		−	11.9292i		−	0.0701718i
$171$	−2.41819	−	18.7798i	−0.0141415	−	0.109823i
$172$	−0.381124			−0.00221584
$173$			37.9144i			0.219159i	0.993978	+	0.109579i	$0.0349503\pi$
$173$			37.9144i			0.219159i	−0.993978	+	0.109579i	$0.965050\pi$
$174$	−236.699	−	208.174i	−1.36034	−	1.19640i
$175$	−66.0870			−0.377640
$176$			52.1768i			0.296459i
$177$	23.6381	−	26.8770i	0.133549	−	0.151848i
$178$	316.353			1.77726
$179$			45.3189i			0.253178i	0.991955	+	0.126589i	$0.0404029\pi$
$179$			45.3189i			0.253178i	−0.991955	+	0.126589i	$0.959597\pi$
$180$	7.74356	−	0.997103i	0.0430198	−	0.00553946i
$181$	−267.725			−1.47914			−0.739572	−	0.673077i	$-0.764972\pi$
$181$	−267.725			−1.47914			−0.739572	+	0.673077i	$0.764972\pi$
$182$			186.624i			1.02541i
$183$	−55.1077	−	48.4667i	−0.301135	−	0.264846i
$184$	28.9934			0.157573
$185$		−	7.01839i		−	0.0379373i
$186$	202.165	−	229.866i	1.08691	−	1.23584i
$187$	−290.791			−1.55503
$188$			294.225i			1.56503i
$189$	39.9399	−	59.2267i	0.211322	−	0.313369i
$190$	−0.971064			−0.00511086
$191$			182.884i			0.957506i	0.877950	+	0.478753i	$0.158911\pi$
$191$			182.884i			0.957506i	−0.877950	+	0.478753i	$0.841089\pi$
$192$	233.412	+	205.283i	1.21569	+	1.06918i
$193$	106.451			0.551561			0.275780	−	0.961221i	$-0.411064\pi$
$193$	106.451			0.551561			0.275780	+	0.961221i	$0.411064\pi$
$194$			567.836i			2.92699i
$195$	−6.50270	+	7.39371i	−0.0333472	+	0.0379165i
$196$	−41.4366			−0.211411
$197$		−	186.486i		−	0.946627i	−0.880894	−	0.473314i	$-0.843058\pi$
$197$		−	186.486i		−	0.946627i	0.880894	−	0.473314i	$-0.156942\pi$
$198$	−40.7299	−	316.311i	−0.205707	−	1.59753i
$199$	−226.846			−1.13993			−0.569964	−	0.821670i	$-0.693043\pi$
$199$	−226.846			−1.13993			−0.569964	+	0.821670i	$0.693043\pi$
$200$			151.009i			0.755043i
$201$	254.311	+	223.664i	1.26523	+	1.11276i
$202$	549.715			2.72136
$203$			88.2662i			0.434809i
$204$	−303.114	+	344.647i	−1.48585	+	1.68944i
$205$	7.77257			0.0379150
$206$		−	259.692i		−	1.26064i
$207$	42.8090	−	5.51233i	0.206807	−	0.0266296i
$208$	−103.861			−0.499334
$209$			23.6710i			0.113258i
$210$	−2.75095	−	2.41943i	−0.0130998	−	0.0115211i
$211$	23.5108			0.111426			0.0557128	−	0.998447i	$-0.482257\pi$
$211$	23.5108			0.111426			0.0557128	+	0.998447i	$0.482257\pi$
$212$		−	98.2596i		−	0.463489i
$213$	−215.845	+	245.420i	−1.01335	+	1.15221i
$214$	536.434			2.50670
$215$			0.00943547i			4.38859e-5i
$216$	−135.333	−	91.2626i	−0.626542	−	0.422512i
$217$	−85.7184			−0.395016
$218$		−	571.494i		−	2.62153i
$219$	45.3625	+	39.8959i	0.207135	+	0.182173i
$220$	−9.76036			−0.0443653
$221$		−	578.839i		−	2.61918i
$222$	−298.838	+	339.785i	−1.34612	+	1.53056i
$223$	267.315			1.19872			0.599361	−	0.800478i	$-0.295421\pi$
$223$	267.315			1.19872			0.599361	+	0.800478i	$0.295421\pi$
$224$		−	102.623i		−	0.458140i
$225$	28.7103	+	222.966i	0.127601	+	0.990959i
$226$	−205.677			−0.910076
$227$			222.347i			0.979502i	0.871862	+	0.489751i	$0.162912\pi$
$227$			222.347i			0.979502i	−0.871862	+	0.489751i	$0.837088\pi$
$228$	28.0550	+	24.6741i	0.123048	+	0.108220i
$229$	137.206			0.599155			0.299577	−	0.954072i	$-0.403154\pi$
$229$	137.206			0.599155			0.299577	+	0.954072i	$0.403154\pi$
$230$		−	2.21356i		−	0.00962420i
$231$	−58.9770	+	67.0581i	−0.255312	+	0.290295i
$232$	201.688			0.869346
$233$			277.770i			1.19215i	0.802930	+	0.596073i	$0.203273\pi$
$233$			277.770i			1.19215i	−0.802930	+	0.596073i	$0.796727\pi$
$234$	629.638	−	81.0757i	2.69076	−	0.346477i
$235$	7.28413			0.0309963
$236$			70.6255i			0.299261i
$237$	−172.844	−	152.014i	−0.729298	−	0.641411i
$238$	215.366			0.904900
$239$			244.897i			1.02467i	0.858785	+	0.512337i	$0.171220\pi$
$239$			244.897i			1.02467i	−0.858785	+	0.512337i	$0.828780\pi$
$240$	1.34648	−	1.53098i	0.00561033	−	0.00637907i
$241$	157.896			0.655169			0.327585	−	0.944822i	$-0.393765\pi$
$241$	157.896			0.655169			0.327585	+	0.944822i	$0.393765\pi$
$242$			17.6012i			0.0727322i
$243$	−217.172	−	109.020i	−0.893711	−	0.448643i
$244$	144.808			0.593476
$245$			1.02584i			0.00418712i
$246$	−376.298	−	330.950i	−1.52967	−	1.34533i
$247$	−47.1187			−0.190764
$248$			195.866i			0.789784i
$249$	−144.028	+	163.763i	−0.578427	+	0.657684i
$250$	23.0681			0.0922724
$251$			2.46917i			0.00983733i	0.999988	+	0.00491867i	$0.00156567\pi$
$251$			2.46917i			0.00983733i	−0.999988	+	0.00491867i	$0.998434\pi$
$252$	18.0014	+	139.800i	0.0714341	+	0.554761i
$253$	−53.9587			−0.213275
$254$			159.637i			0.628491i
$255$	8.53241	+	7.50418i	0.0334604	+	0.0294281i
$256$	−124.688			−0.487063
$257$		−	297.321i		−	1.15689i	−0.815720	−	0.578446i	$-0.803659\pi$
$257$		−	297.321i		−	1.15689i	0.815720	−	0.578446i	$-0.196341\pi$
$258$	0.401756	−	0.456805i	0.00155719	−	0.00177056i
$259$	126.708			0.489219
$260$		−	19.4287i		−	0.0747256i
$261$	297.795	−	38.3457i	1.14098	−	0.146918i
$262$	−329.839			−1.25893
$263$		−	236.614i		−	0.899674i	−0.893111	−	0.449837i	$-0.851482\pi$
$263$		−	236.614i		−	0.899674i	0.893111	−	0.449837i	$-0.148518\pi$
$264$	153.228	+	134.762i	0.580408	+	0.510463i
$265$	−2.43261			−0.00917966
$266$		−	17.5313i		−	0.0659071i
$267$	−199.004	+	226.272i	−0.745335	+	0.847462i
$268$	−668.260			−2.49351
$269$			83.1118i			0.308966i	0.987995	+	0.154483i	$0.0493712\pi$
$269$			83.1118i			0.308966i	−0.987995	+	0.154483i	$0.950629\pi$
$270$	−6.96765	+	10.3323i	−0.0258061	+	0.0382678i
$271$	416.045			1.53522			0.767610	−	0.640917i	$-0.221446\pi$
$271$	416.045			1.53522			0.767610	+	0.640917i	$0.221446\pi$
$272$			119.857i			0.440651i
$273$	−133.484	−	117.398i	−0.488951	−	0.430028i
$274$	−182.306			−0.665349
$275$		−	281.037i		−	1.02195i
$276$	−56.2453	+	63.9521i	−0.203787	+	0.231710i
$277$	−342.164			−1.23525			−0.617625	−	0.786473i	$-0.711905\pi$
$277$	−342.164			−1.23525			−0.617625	+	0.786473i	$0.711905\pi$
$278$		−	447.778i		−	1.61071i
$279$	37.2388	+	289.199i	0.133473	+	1.03655i
$280$	2.34405			0.00837161
$281$			120.521i			0.428899i	0.976735	+	0.214450i	$0.0687958\pi$
$281$			120.521i			0.428899i	−0.976735	+	0.214450i	$0.931204\pi$
$282$	−352.651	−	310.153i	−1.25053	−	1.09983i
$283$	−285.902			−1.01026			−0.505128	−	0.863045i	$-0.668555\pi$
$283$	−285.902			−1.01026			−0.505128	+	0.863045i	$0.668555\pi$
$284$		−	644.897i		−	2.27076i
$285$	0.610857	−	0.694557i	0.00214336	−	0.00243704i
$286$	−793.627			−2.77492
$287$			140.323i			0.488932i
$288$	−346.233	+	44.5829i	−1.20220	+	0.154802i
$289$	−378.985			−1.31137
$290$		−	15.3983i		−	0.0530977i
$291$	−406.147	−	357.202i	−1.39569	−	1.22750i
$292$	−119.200			−0.408220
$293$			96.8414i			0.330517i	0.986250	+	0.165258i	$0.0528458\pi$
$293$			96.8414i			0.330517i	−0.986250	+	0.165258i	$0.947154\pi$
$294$	43.6797	−	49.6648i	0.148570	−	0.168928i
$295$	1.74847			0.00592703
$296$		−	289.527i		−	0.978132i
$297$	251.864	+	169.846i	0.848027	+	0.571872i
$298$	−856.827			−2.87526
$299$		−	107.408i		−	0.359225i
$300$	−333.087	−	292.947i	−1.11029	−	0.976489i
$301$	−0.170345			−0.000565930
$302$		−	397.272i		−	1.31547i
$303$	−345.803	+	393.185i	−1.14126	+	1.29764i
$304$	9.75663			0.0320942
$305$		−	3.58501i		−	0.0117541i
$306$	−93.5620	−	726.608i	−0.305758	−	2.37454i
$307$	−24.6079			−0.0801560			−0.0400780	−	0.999197i	$-0.512761\pi$
$307$	−24.6079			−0.0801560			−0.0400780	+	0.999197i	$0.512761\pi$
$308$		−	176.211i		−	0.572112i
$309$	185.746	+	163.362i	0.601119	+	0.528678i
$310$	14.9539			0.0482382
$311$			241.085i			0.775191i	0.921829	+	0.387596i	$0.126694\pi$
$311$			241.085i			0.775191i	−0.921829	+	0.387596i	$0.873306\pi$
$312$	−268.254	+	305.010i	−0.859787	+	0.977597i
$313$	−298.277			−0.952961			−0.476481	−	0.879185i	$-0.658088\pi$
$313$	−298.277			−0.952961			−0.476481	+	0.879185i	$0.658088\pi$
$314$		−	43.1469i		−	0.137410i
$315$	3.46102	−	0.445660i	0.0109874	−	0.00141479i
$316$	454.186			1.43730
$317$			133.496i			0.421123i	0.977581	+	0.210561i	$0.0675292\pi$
$317$			133.496i			0.421123i	−0.977581	+	0.210561i	$0.932471\pi$
$318$	117.771	+	103.579i	0.370350	+	0.325720i
$319$	−375.355			−1.17666
$320$			15.1845i			0.0474516i
$321$	−337.448	+	383.686i	−1.05124	+	1.19528i
$322$	39.9630			0.124109
$323$			54.3755i			0.168345i
$324$	463.839	−	121.467i	1.43160	−	0.374898i
$325$	559.424			1.72130
$326$			928.380i			2.84779i
$327$	408.763	+	359.504i	1.25004	+	1.09940i
$328$	320.639			0.977558
$329$			131.505i			0.399712i
$330$	10.2887	−	11.6985i	0.0311780	−	0.0354500i
$331$	−191.268			−0.577850			−0.288925	−	0.957352i	$-0.593298\pi$
$331$	−191.268			−0.577850			−0.288925	+	0.957352i	$0.593298\pi$
$332$		−	430.325i		−	1.29616i
$333$	−55.0460	−	427.490i	−0.165303	−	1.28375i
$334$	528.307			1.58176
$335$			16.5441i			0.0493854i
$336$	27.6398	+	24.3089i	0.0822612	+	0.0723479i
$337$	281.898			0.836494			0.418247	−	0.908333i	$-0.362645\pi$
$337$	281.898			0.836494			0.418247	+	0.908333i	$0.362645\pi$
$338$		−	1047.50i		−	3.09911i
$339$	129.383	−	147.111i	0.381661	−	0.433957i
$340$	−22.4209			−0.0659437
$341$		−	364.521i		−	1.06898i
$342$	−59.1475	+	7.61616i	−0.172946	+	0.0222695i
$343$	−18.5203			−0.0539949
$344$			0.389238i			0.00113151i
$345$	1.58326	+	1.39246i	0.00458916	+	0.00403612i
$346$	119.412			0.345123
$347$			441.843i			1.27332i	0.771144	+	0.636661i	$0.219685\pi$
$347$			441.843i			1.27332i	−0.771144	+	0.636661i	$0.780315\pi$
$348$	−391.262	+	444.873i	−1.12432	+	1.27837i
$349$	−406.807			−1.16564			−0.582818	−	0.812603i	$-0.698050\pi$
$349$	−406.807			−1.16564			−0.582818	+	0.812603i	$0.698050\pi$
$350$			208.143i			0.594693i
$351$	−338.090	+	501.352i	−0.963218	+	1.42835i
$352$	436.409			1.23980
$353$		−	86.5668i		−	0.245232i	−0.992454	−	0.122616i	$-0.960872\pi$
$353$		−	86.5668i		−	0.245232i	0.992454	−	0.122616i	$-0.0391283\pi$
$354$	−84.6499	−	74.4488i	−0.239124	−	0.210307i
$355$	−15.9657			−0.0449738
$356$		−	594.582i		−	1.67017i
$357$	−135.478	+	154.041i	−0.379490	+	0.431489i
$358$	142.733			0.398695
$359$		−	202.961i		−	0.565351i	−0.959216	−	0.282676i	$-0.908778\pi$
$359$		−	202.961i		−	0.565351i	0.959216	−	0.282676i	$-0.0912220\pi$
$360$	−1.01833	−	7.90842i	−0.00282870	−	0.0219678i
$361$	−356.574			−0.987739
$362$			843.207i			2.32930i
$363$	−12.5893	−	11.0722i	−0.0346813	−	0.0305019i
$364$	350.759			0.963624
$365$			2.95104i			0.00808504i
$366$	−152.647	+	173.563i	−0.417069	+	0.474216i
$367$	−357.936			−0.975303			−0.487652	−	0.873038i	$-0.662146\pi$
$367$	−357.936			−0.975303			−0.487652	+	0.873038i	$0.662146\pi$
$368$			22.2405i			0.0604361i
$369$	473.427	−	60.9611i	1.28300	−	0.165206i
$370$	−22.1046			−0.0597422
$371$		−	43.9176i		−	0.118376i
$372$	−432.032	−	379.968i	−1.16138	−	1.02142i
$373$	484.082			1.29781			0.648903	−	0.760871i	$-0.275228\pi$
$373$	484.082			1.29781			0.648903	+	0.760871i	$0.275228\pi$
$374$			915.853i			2.44880i
$375$	−14.5112	+	16.4995i	−0.0386965	+	0.0439988i
$376$	300.490			0.799175
$377$		−	747.170i		−	1.98188i
$378$	−186.536	−	125.792i	−0.493482	−	0.332782i
$379$	−325.350			−0.858444			−0.429222	−	0.903199i	$-0.641212\pi$
$379$	−325.350			−0.858444			−0.429222	+	0.903199i	$0.641212\pi$
$380$			1.82511i			0.00480291i
$381$	−114.181	−	100.421i	−0.299687	−	0.263572i
$382$	575.996			1.50784
$383$			62.7678i			0.163885i	0.996637	+	0.0819423i	$0.0261123\pi$
$383$			62.7678i			0.163885i	−0.996637	+	0.0819423i	$0.973888\pi$
$384$	339.153	−	385.624i	0.883210	−	1.00423i
$385$	−4.36244			−0.0113310
$386$		−	335.271i		−	0.868577i
$387$	0.0740034	+	0.574714i	0.000191223	+	0.00148505i
$388$	1067.24			2.75063
$389$			53.9891i			0.138789i	0.997589	+	0.0693947i	$0.0221068\pi$
$389$			53.9891i			0.138789i	−0.997589	+	0.0693947i	$0.977893\pi$
$390$	23.2867	+	20.4804i	0.0597095	+	0.0525139i
$391$	−123.950			−0.317008
$392$			42.3188i			0.107956i
$393$	207.488	−	235.919i	0.527960	−	0.600302i
$394$	−587.341			−1.49071
$395$		−	11.2443i		−	0.0284665i
$396$	−594.503	+	76.5516i	−1.50127	+	0.193312i
$397$	−79.5613			−0.200406			−0.100203	−	0.994967i	$-0.531949\pi$
$397$	−79.5613			−0.200406			−0.100203	+	0.994967i	$0.531949\pi$
$398$			714.456i			1.79511i
$399$	12.5393	+	11.0282i	0.0314269	+	0.0276396i
$400$	−115.837			−0.289592
$401$			142.485i			0.355325i	0.984092	+	0.177662i	$0.0568535\pi$
$401$			142.485i			0.355325i	−0.984092	+	0.177662i	$0.943147\pi$
$402$	704.436	−	800.959i	1.75233	−	1.99243i
$403$	725.603			1.80050
$404$		−	1033.18i		−	2.55739i
$405$	−3.00716	−	11.4833i	−0.00742508	−	0.0283537i
$406$	277.997			0.684721
$407$			538.830i			1.32391i
$408$	351.984	+	309.567i	0.862707	+	0.758743i
$409$	−344.613			−0.842574			−0.421287	−	0.906927i	$-0.638422\pi$
$409$	−344.613			−0.842574			−0.421287	+	0.906927i	$0.638422\pi$
$410$		−	24.4799i		−	0.0597071i
$411$	114.681	−	130.395i	0.279029	−	0.317262i
$412$	−488.089			−1.18468
$413$			31.5664i			0.0764320i
$414$	−17.3612	−	134.828i	−0.0419353	−	0.325672i
$415$	−10.6536			−0.0256712
$416$			868.702i			2.08823i
$417$	320.275	+	281.679i	0.768045	+	0.675488i
$418$	74.5524			0.178355
$419$		−	803.725i		−	1.91820i	−0.283069	−	0.959100i	$-0.591352\pi$
$419$		−	803.725i		−	1.91820i	0.283069	−	0.959100i	$-0.408648\pi$
$420$	−4.54731	+	5.17039i	−0.0108269	+	0.0123104i
$421$	−91.5720			−0.217511			−0.108755	−	0.994069i	$-0.534686\pi$
$421$	−91.5720			−0.217511			−0.108755	+	0.994069i	$0.534686\pi$
$422$		−	74.0479i		−	0.175469i
$423$	443.676	−	57.1302i	1.04888	−	0.135060i
$424$	−100.352			−0.236678
$425$		−	645.580i		−	1.51901i
$426$	772.956	+	679.808i	1.81445	+	1.59579i
$427$	64.7227			0.151575
$428$		−	1008.22i		−	2.35566i
$429$	499.238	−	567.645i	1.16373	−	1.32318i
$430$	0.0297173			6.91099e−5
$431$			370.284i			0.859129i	0.903036	+	0.429564i	$0.141333\pi$
$431$			370.284i			0.859129i	−0.903036	+	0.429564i	$0.858667\pi$
$432$	70.0064	−	103.812i	0.162052	−	0.240306i
$433$	503.237			1.16221			0.581105	−	0.813829i	$-0.302621\pi$
$433$	503.237			1.16221			0.581105	+	0.813829i	$0.302621\pi$
$434$			269.972i			0.622056i
$435$	11.0137	+	9.68646i	0.0253189	+	0.0222677i
$436$	−1074.12			−2.46358
$437$			10.0898i			0.0230888i
$438$	125.653	−	142.870i	0.286879	−	0.326188i
$439$	625.445			1.42470			0.712352	−	0.701823i	$-0.247630\pi$
$439$	625.445			1.42470			0.712352	+	0.701823i	$0.247630\pi$
$440$			9.96817i			0.0226549i
$441$	8.04580	+	62.4841i	0.0182444	+	0.141687i
$442$	−1823.07			−4.12459
$443$		−	136.946i		−	0.309134i	−0.987982	−	0.154567i	$-0.950602\pi$
$443$		−	136.946i		−	0.309134i	0.987982	−	0.154567i	$-0.0493982\pi$
$444$	638.624	+	561.664i	1.43834	+	1.26501i
$445$	−14.7201			−0.0330788
$446$		−	841.916i		−	1.88770i
$447$	538.995	−	612.849i	1.20581	−	1.37103i
$448$	−274.136			−0.611911
$449$			756.023i			1.68379i	0.539638	+	0.841897i	$0.318561\pi$
$449$			756.023i			1.68379i	−0.539638	+	0.841897i	$0.681439\pi$
$450$	702.237	−	90.4239i	1.56053	−	0.200942i
$451$	−596.731			−1.32313
$452$			386.569i			0.855240i
$453$	284.150	+	249.907i	0.627263	+	0.551672i
$454$	700.287			1.54248
$455$		−	8.68373i		−	0.0190851i
$456$	25.1994	−	28.6523i	0.0552619	−	0.0628340i
$457$	−90.4852			−0.197998			−0.0989991	−	0.995088i	$-0.531564\pi$
$457$	−90.4852			−0.197998			−0.0989991	+	0.995088i	$0.531564\pi$
$458$		−	432.135i		−	0.943527i
$459$	578.565	+	390.159i	1.26049	+	0.850019i
$460$	−4.16038			−0.00904430
$461$			99.8376i			0.216567i	0.994120	+	0.108284i	$0.0345355\pi$
$461$			99.8376i			0.216567i	−0.994120	+	0.108284i	$0.965465\pi$
$462$	211.201	+	185.750i	0.457146	+	0.402055i
$463$	758.258			1.63771			0.818853	−	0.574003i	$-0.194610\pi$
$463$	758.258			1.63771			0.818853	+	0.574003i	$0.194610\pi$
$464$			154.713i			0.333432i
$465$	−9.40686	+	10.6958i	−0.0202298	+	0.0230017i
$466$	874.844			1.87735
$467$		−	286.822i		−	0.614179i	−0.951681	−	0.307090i	$-0.900645\pi$
$467$		−	286.822i		−	0.614179i	0.951681	−	0.307090i	$-0.0993551\pi$
$468$	−152.381	−	1183.40i	−0.325601	−	2.52863i
$469$	−298.682			−0.636848
$470$		−	22.9416i		−	0.0488118i
$471$	30.8610	+	27.1419i	0.0655222	+	0.0576262i
$472$	72.1292			0.152816
$473$		−	0.724399i		−	0.00153150i
$474$	−478.773	+	544.376i	−1.01007	+	1.14847i
$475$	−52.5516			−0.110635
$476$		−	404.779i		−	0.850376i
$477$	−148.170	+	19.0792i	−0.310629	+	0.0399984i
$478$	771.309			1.61362
$479$			364.583i			0.761134i	0.924753	+	0.380567i	$0.124271\pi$
$479$			364.583i			0.761134i	−0.924753	+	0.380567i	$0.875729\pi$
$480$	−12.8052	−	11.2620i	−0.0266774	−	0.0234626i
$481$	−1072.58			−2.22989
$482$		−	497.297i		−	1.03174i
$483$	−25.1391	+	28.5837i	−0.0520478	+	0.0591795i
$484$	33.0813			0.0683498
$485$		−	26.4217i		−	0.0544778i
$486$	−343.362	+	683.988i	−0.706506	+	1.40738i
$487$	696.634			1.43046			0.715230	−	0.698890i	$-0.246322\pi$
$487$	696.634			1.43046			0.715230	+	0.698890i	$0.246322\pi$
$488$		−	147.891i		−	0.303056i
$489$	−664.027	−	584.006i	−1.35793	−	1.19429i
$490$	3.23092			0.00659372
$491$		−	184.728i		−	0.376228i	−0.982147	−	0.188114i	$-0.939763\pi$
$491$		−	184.728i		−	0.376228i	0.982147	−	0.188114i	$-0.0602374\pi$
$492$	−622.019	+	707.249i	−1.26427	+	1.43750i
$493$	−862.241			−1.74897
$494$			148.402i			0.300408i
$495$	1.89519	+	14.7181i	0.00382866	+	0.0297336i
$496$	−150.247			−0.302917
$497$		−	288.240i		−	0.579959i
$498$	515.777	+	453.621i	1.03570	+	0.910885i
$499$	−100.728			−0.201859			−0.100930	−	0.994894i	$-0.532182\pi$
$499$	−100.728			−0.201859			−0.100930	+	0.994894i	$0.532182\pi$
$500$		−	43.3563i		−	0.0867126i
$501$	−332.337	+	377.874i	−0.663346	+	0.754239i
$502$	7.77671			0.0154915
$503$			353.851i			0.703482i	0.936097	+	0.351741i	$0.114410\pi$
$503$			353.851i			0.703482i	−0.936097	+	0.351741i	$0.885590\pi$
$504$	142.776	−	18.3846i	0.283286	−	0.0364775i
$505$	−25.5785			−0.0506505
$506$			169.944i			0.335858i
$507$	749.227	+	658.938i	1.47777	+	1.29968i
$508$	300.036			0.590622
$509$			735.468i			1.44493i	0.691409	+	0.722464i	$0.256990\pi$
$509$			735.468i			1.44493i	−0.691409	+	0.722464i	$0.743010\pi$
$510$	23.6346	−	26.8730i	0.0463423	−	0.0526922i
$511$	−53.2771			−0.104261
$512$		−	292.021i		−	0.570354i
$513$	31.7598	−	47.0965i	0.0619099	−	0.0918060i
$514$	−936.421			−1.82183
$515$			12.0836i			0.0234633i
$516$	−0.858561	−	0.755097i	−0.00166388	−	0.00146337i
$517$	−559.232			−1.08169
$518$		−	399.069i		−	0.770404i
$519$	−75.1175	+	85.4102i	−0.144735	+	0.164567i
$520$	−19.8423			−0.0381583
$521$			386.213i			0.741291i	0.928774	+	0.370645i	$0.120863\pi$
$521$			386.213i			0.741291i	−0.928774	+	0.370645i	$0.879137\pi$
$522$	−120.771	−	937.912i	−0.231362	−	1.79677i
$523$	59.0380			0.112883			0.0564417	−	0.998406i	$-0.482025\pi$
$523$	59.0380			0.112883			0.0564417	+	0.998406i	$0.482025\pi$
$524$			619.930i			1.18307i
$525$	−148.875	−	130.934i	−0.283571	−	0.249398i
$526$	−745.222			−1.41677
$527$		−	837.352i		−	1.58890i
$528$	−103.375	+	117.539i	−0.195785	+	0.222612i
$529$	−23.0000			−0.0434783
$530$			7.66157i			0.0144558i
$531$	106.500	−	13.7135i	0.200564	−	0.0258257i
$532$	−32.9499			−0.0619359
$533$		−	1187.83i		−	2.22858i
$534$	712.650	+	626.769i	1.33455	+	1.17373i
$535$	−24.9606			−0.0466553
$536$			682.488i			1.27330i
$537$	−89.7874	+	102.090i	−0.167202	+	0.190112i
$538$	261.763			0.486548
$539$		−	78.7581i		−	0.146119i
$540$	19.4195	+	13.0956i	0.0359620	+	0.0242512i
$541$	171.035			0.316146			0.158073	−	0.987427i	$-0.449472\pi$
$541$	171.035			0.316146			0.158073	+	0.987427i	$0.449472\pi$
$542$		−	1310.34i		−	2.41761i
$543$	−603.107	−	530.427i	−1.11069	−	0.976845i
$544$	1002.49			1.84281
$545$			26.5919i			0.0487926i
$546$	−369.747	+	420.410i	−0.677192	+	0.769982i
$547$	133.487			0.244035			0.122017	−	0.992528i	$-0.461064\pi$
$547$	133.487			0.244035			0.122017	+	0.992528i	$0.461064\pi$
$548$			342.642i			0.625260i
$549$	−28.1176	−	218.363i	−0.0512161	−	0.397747i
$550$	−885.134			−1.60933
$551$			70.1884i			0.127384i
$552$	65.3137	+	57.4428i	0.118322	+	0.104063i
$553$	203.001			0.367090
$554$			1077.65i			1.94523i
$555$	13.9051	−	15.8104i	0.0250542	−	0.0284872i
$556$	−841.595			−1.51366
$557$		−	351.517i		−	0.631090i	−0.948911	−	0.315545i	$-0.897813\pi$
$557$		−	351.517i		−	0.631090i	0.948911	−	0.315545i	$-0.102187\pi$
$558$	910.839	−	117.285i	1.63233	−	0.210188i
$559$	1.44196			0.00257954
$560$			1.79809i			0.00321088i
$561$	−655.067	−	576.125i	−1.16768	−	1.02696i
$562$	379.583			0.675414
$563$			237.562i			0.421958i	0.977491	+	0.210979i	$0.0676652\pi$
$563$			237.562i			0.421958i	−0.977491	+	0.210979i	$0.932335\pi$
$564$	−582.930	+	662.804i	−1.03356	+	1.17518i
$565$	9.57027			0.0169385
$566$			900.456i			1.59091i
$567$	207.315	−	54.2903i	0.365635	−	0.0957500i
$568$	−658.627			−1.15955
$569$		−	1079.92i		−	1.89792i	−0.315393	−	0.948961i	$-0.602136\pi$
$569$		−	1079.92i		−	1.89792i	0.315393	−	0.948961i	$-0.397864\pi$
$570$	−2.18753	−	1.92391i	−0.00383776	−	0.00337528i
$571$	571.514			1.00090			0.500451	−	0.865765i	$-0.333168\pi$
$571$	571.514			1.00090			0.500451	+	0.865765i	$0.333168\pi$
$572$			1491.62i			2.60772i
$573$	−362.336	+	411.984i	−0.632348	+	0.718994i
$574$	441.952			0.769952
$575$		−	119.793i		−	0.208335i
$576$	119.094	+	924.888i	0.206760	+	1.60571i
$577$	−791.321			−1.37144			−0.685720	−	0.727865i	$-0.740513\pi$
$577$	−791.321			−1.37144			−0.685720	+	0.727865i	$0.740513\pi$
$578$			1193.62i			2.06509i
$579$	239.804	+	210.905i	0.414169	+	0.364257i
$580$	−28.9411			−0.0498984
$581$		−	192.336i		−	0.331043i
$582$	−1125.02	+	1279.17i	−1.93302	+	2.19789i
$583$	186.761			0.320345
$584$			121.738i			0.208456i
$585$	−29.2974	+	3.77250i	−0.0500810	+	0.00644871i
$586$	305.004			0.520485
$587$			121.477i			0.206945i	0.994632	+	0.103472i	$0.0329953\pi$
$587$			121.477i			0.206945i	−0.994632	+	0.103472i	$0.967005\pi$
$588$	−93.3445	−	82.0956i	−0.158749	−	0.139618i
$589$	−68.1623			−0.115726
$590$		−	5.50686i		−	0.00933367i
$591$	369.472	−	420.098i	0.625164	−	0.710826i
$592$	222.093			0.375157
$593$		−	775.005i		−	1.30692i	−0.756960	−	0.653461i	$-0.773316\pi$
$593$		−	775.005i		−	1.30692i	0.756960	−	0.653461i	$-0.226684\pi$
$594$	534.934	−	793.252i	0.900562	−	1.33544i
$595$	−10.0211			−0.0168422
$596$			1610.40i			2.70201i
$597$	−511.017	−	449.435i	−0.855975	−	0.752822i
$598$	−338.285			−0.565695
$599$		−	317.946i		−	0.530794i	−0.964139	−	0.265397i	$-0.914497\pi$
$599$		−	317.946i		−	0.530794i	0.964139	−	0.265397i	$-0.0855031\pi$
$600$	−299.184	+	340.179i	−0.498640	+	0.566964i
$601$	−173.248			−0.288266			−0.144133	−	0.989558i	$-0.546039\pi$
$601$	−173.248			−0.288266			−0.144133	+	0.989558i	$0.546039\pi$
$602$			0.536506i			0.000891206i
$603$	129.757	+	1007.70i	0.215186	+	1.67115i
$604$	−746.669			−1.23621
$605$		−	0.818993i		−	0.00135371i
$606$	1238.35	+	1089.11i	2.04348	+	1.79722i
$607$	−55.7247			−0.0918034			−0.0459017	−	0.998946i	$-0.514616\pi$
$607$	−55.7247			−0.0918034			−0.0459017	+	0.998946i	$0.514616\pi$
$608$		−	81.6049i		−	0.134219i
$609$	−174.876	+	198.838i	−0.287153	+	0.326499i
$610$	−11.2911			−0.0185100
$611$		−	1113.19i		−	1.82191i
$612$	−1365.65	+	175.849i	−2.23146	+	0.287335i
$613$	994.900			1.62300			0.811501	−	0.584351i	$-0.198651\pi$
$613$	994.900			1.62300			0.811501	+	0.584351i	$0.198651\pi$
$614$			77.5032i			0.126227i
$615$	17.5093	+	15.3993i	0.0284705	+	0.0250395i
$616$	−179.962			−0.292146
$617$		−	173.507i		−	0.281211i	−0.990066	−	0.140605i	$-0.955095\pi$
$617$		−	173.507i		−	0.281211i	0.990066	−	0.140605i	$-0.0449049\pi$
$618$	514.511	−	585.011i	0.832543	−	0.946619i
$619$	−633.006			−1.02263			−0.511313	−	0.859394i	$-0.670841\pi$
$619$	−633.006			−1.02263			−0.511313	+	0.859394i	$0.670841\pi$
$620$		−	28.1057i		−	0.0453317i
$621$	107.358	+	72.3972i	0.172879	+	0.116582i
$622$	759.302			1.22074
$623$		−	265.751i		−	0.426567i
$624$	−233.970	−	205.774i	−0.374951	−	0.329766i
$625$	623.390			0.997424
$626$			939.430i			1.50069i
$627$	−46.8979	+	53.3239i	−0.0747972	+	0.0850461i
$628$	−81.0942			−0.129131
$629$			1237.76i			1.96783i
$630$	−1.40362	−	10.9006i	−0.00222796	−	0.0173025i
$631$	−305.976			−0.484907			−0.242454	−	0.970163i	$-0.577952\pi$
$631$	−305.976			−0.484907			−0.242454	+	0.970163i	$0.577952\pi$
$632$		−	463.856i		−	0.733950i
$633$	52.9630	+	46.5805i	0.0836699	+	0.0735869i
$634$	420.449			0.663169
$635$		−	7.42798i		−	0.0116976i
$636$	194.676	−	221.350i	0.306094	−	0.348035i
$637$	156.773			0.246112
$638$			1182.19i			1.85296i
$639$	−972.470	+	125.221i	−1.52186	+	0.195963i
$640$	25.0866			0.0391979
$641$		−	280.932i		−	0.438271i	−0.975694	−	0.219136i	$-0.929676\pi$
$641$		−	280.932i		−	0.438271i	0.975694	−	0.219136i	$-0.0703237\pi$
$642$	1208.43	+	1062.80i	1.88229	+	1.65546i
$643$	355.988			0.553636			0.276818	−	0.960922i	$-0.410720\pi$
$643$	355.988			0.553636			0.276818	+	0.960922i	$0.410720\pi$
$644$		−	75.1101i		−	0.116631i
$645$	−0.0186939	+	0.0212554i	−2.89828e−5	+	3.29541e-5i
$646$	171.257			0.265104
$647$		−	348.688i		−	0.538931i	−0.963010	−	0.269465i	$-0.913153\pi$
$647$		−	348.688i		−	0.538931i	0.963010	−	0.269465i	$-0.0868470\pi$
$648$	−124.053	−	473.715i	−0.191440	−	0.731041i
$649$	−134.237			−0.206837
$650$		−	1761.92i		−	2.71064i
$651$	−193.099	−	169.828i	−0.296618	−	0.260873i
$652$	1744.88			2.67620
$653$			517.040i			0.791791i	0.918295	+	0.395896i	$0.129566\pi$
$653$			517.040i			0.791791i	−0.918295	+	0.395896i	$0.870434\pi$
$654$	1132.27	−	1287.41i	1.73129	−	1.96852i
$655$	15.3476			0.0234314
$656$			245.958i			0.374936i
$657$	23.1453	+	179.748i	0.0352288	+	0.273589i
$658$	414.180			0.629452
$659$			355.938i			0.540118i	0.962844	+	0.270059i	$0.0870432\pi$
$659$			355.938i			0.540118i	−0.962844	+	0.270059i	$0.912957\pi$
$660$	−21.9873	−	19.3376i	−0.0333140	−	0.0292994i
$661$	641.859			0.971043			0.485522	−	0.874225i	$-0.338630\pi$
$661$	641.859			0.971043			0.485522	+	0.874225i	$0.338630\pi$
$662$			602.405i			0.909977i
$663$	1146.82	−	1303.96i	1.72974	−	1.96675i
$664$	−439.487			−0.661878
$665$			0.815740i			0.00122668i
$666$	−1346.39	+	173.369i	−2.02161	+	0.260313i
$667$	−159.996			−0.239874
$668$		−	992.950i		−	1.48645i
$669$	602.184	+	529.615i	0.900125	+	0.791651i
$670$	52.1061			0.0777702
$671$			275.235i			0.410187i
$672$	203.321	−	231.180i	0.302561	−	0.344018i
$673$	−883.223			−1.31237			−0.656183	−	0.754602i	$-0.727830\pi$
$673$	−883.223			−1.31237			−0.656183	+	0.754602i	$0.727830\pi$
$674$		−	887.846i		−	1.31728i
$675$	−377.072	+	559.159i	−0.558625	+	0.828384i
$676$	−1968.77			−2.91238
$677$		−	326.813i		−	0.482736i	−0.970434	−	0.241368i	$-0.922404\pi$
$677$		−	326.813i		−	0.482736i	0.970434	−	0.241368i	$-0.0775962\pi$
$678$	−463.331	−	407.495i	−0.683379	−	0.601025i
$679$	477.009			0.702517
$680$			22.8982i			0.0336738i
$681$	−440.522	+	500.883i	−0.646875	+	0.735511i
$682$	−1148.07			−1.68338
$683$			134.084i			0.196316i	0.995171	+	0.0981581i	$0.0312951\pi$
$683$			134.084i			0.196316i	−0.995171	+	0.0981581i	$0.968705\pi$
$684$	14.3145	+	111.167i	0.0209276	+	0.162525i
$685$	8.48279			0.0123836
$686$			58.3300i			0.0850292i
$687$	309.086	+	271.838i	0.449907	+	0.395689i
$688$	−0.298580			−0.000433982
$689$			371.761i			0.539566i
$690$	4.38560	−	4.98652i	0.00635594	−	0.00722684i
$691$	−429.261			−0.621216			−0.310608	−	0.950538i	$-0.600533\pi$
$691$	−429.261			−0.621216			−0.310608	+	0.950538i	$0.600533\pi$
$692$		−	224.435i		−	0.324328i
$693$	−265.716	+	34.2151i	−0.383429	+	0.0493724i
$694$	1391.60			2.00518
$695$			20.8353i			0.0299789i
$696$	454.345	+	399.592i	0.652794	+	0.574127i
$697$	−1370.77			−1.96667
$698$			1281.25i			1.83560i
$699$	−550.329	+	625.736i	−0.787308	+	0.895187i
$700$	391.202			0.558860
$701$		−	118.130i		−	0.168517i	−0.996444	−	0.0842583i	$-0.973148\pi$
$701$		−	118.130i		−	0.168517i	0.996444	−	0.0842583i	$-0.0268521\pi$
$702$	1579.02	+	1064.82i	2.24932	+	1.51684i
$703$	100.757			0.143324
$704$		−	1165.77i		−	1.65593i
$705$	16.4090	+	14.4316i	0.0232752	+	0.0204703i
$706$	−272.644			−0.386182
$707$		−	461.786i		−	0.653163i
$708$	−139.926	+	159.099i	−0.197635	+	0.224716i
$709$	569.951			0.803880			0.401940	−	0.915666i	$-0.368336\pi$
$709$	569.951			0.803880			0.401940	+	0.915666i	$0.368336\pi$
$710$			50.2844i			0.0708230i
$711$	−88.1901	−	684.889i	−0.124037	−	0.963275i
$712$	−607.241			−0.852867
$713$		−	155.378i		−	0.217921i
$714$	485.157	+	426.691i	0.679492	+	0.597607i
$715$	36.9279			0.0516474
$716$		−	268.265i		−	0.374672i
$717$	−485.199	+	551.682i	−0.676707	+	0.769431i
$718$	−639.231			−0.890294
$719$		−	270.250i		−	0.375869i	−0.982182	−	0.187934i	$-0.939821\pi$
$719$		−	270.250i		−	0.375869i	0.982182	−	0.187934i	$-0.0601792\pi$
$720$	6.06645	−	0.781150i	0.00842563	−	0.00108493i
$721$	−218.154			−0.302571
$722$			1123.04i			1.55545i
$723$	355.693	+	312.829i	0.491969	+	0.432682i
$724$	1584.80			2.18895
$725$		−	833.321i		−	1.14941i
$726$	−34.8721	+	39.6504i	−0.0480332	+	0.0546148i
$727$	1096.43			1.50816			0.754081	−	0.656782i	$-0.228083\pi$
$727$	1096.43			1.50816			0.754081	+	0.656782i	$0.228083\pi$
$728$		−	358.227i		−	0.492070i
$729$	−273.230	−	675.860i	−0.374801	−	0.927105i
$730$	9.29438			0.0127320
$731$		−	1.66404i		−	0.00227639i
$732$	326.211	+	286.899i	0.445643	+	0.391939i
$733$	1363.53			1.86020			0.930099	−	0.367308i	$-0.119721\pi$
$733$	1363.53			1.86020			0.930099	+	0.367308i	$0.119721\pi$
$734$			1127.33i			1.53587i
$735$	−2.03244	+	2.31093i	−0.00276522	+	0.00314412i
$736$	186.020			0.252745
$737$		−	1270.16i		−	1.72341i
$738$	−191.998	−	1491.07i	−0.260160	−	2.02042i
$739$	838.424			1.13454			0.567269	−	0.823533i	$-0.308000\pi$
$739$	838.424			1.13454			0.567269	+	0.823533i	$0.308000\pi$
$740$			41.5454i			0.0561425i
$741$	−106.145	−	93.3534i	−0.143245	−	0.125983i
$742$	−138.320			−0.186414
$743$			1166.86i			1.57046i	0.619201	+	0.785232i	$0.287457\pi$
$743$			1166.86i			1.57046i	−0.619201	+	0.785232i	$0.712543\pi$
$744$	−388.058	+	441.230i	−0.521583	+	0.593051i
$745$	39.8686			0.0535150
$746$		−	1524.63i		−	2.04374i
$747$	−648.908	+	83.5570i	−0.868685	+	0.111857i
$748$	1721.34			2.30125
$749$		−	450.630i		−	0.601642i
$750$	51.9657	+	45.7034i	0.0692876	+	0.0609378i
$751$	209.614			0.279114			0.139557	−	0.990214i	$-0.455432\pi$
$751$	209.614			0.279114			0.139557	+	0.990214i	$0.455432\pi$
$752$			230.502i			0.306519i
$753$	−4.89201	+	5.56232i	−0.00649669	+	0.00738688i
$754$	−2353.23			−3.12100
$755$			18.4853i			0.0244838i
$756$	−236.424	+	350.593i	−0.312731	+	0.463747i
$757$	332.253			0.438908			0.219454	−	0.975623i	$-0.429572\pi$
$757$	332.253			0.438908			0.219454	+	0.975623i	$0.429572\pi$
$758$			1024.70i			1.35185i
$759$	−121.553	−	106.905i	−0.160149	−	0.140850i
$760$	1.86397			0.00245259
$761$			669.663i			0.879977i	0.898003	+	0.439989i	$0.145018\pi$
$761$			669.663i			0.879977i	−0.898003	+	0.439989i	$0.854982\pi$
$762$	−316.278	+	359.615i	−0.415063	+	0.471936i
$763$	−480.082			−0.629204
$764$		−	1082.58i		−	1.41699i
$765$	4.35349	+	33.8095i	0.00569084	+	0.0441954i
$766$	197.689			0.258079
$767$		−	267.208i		−	0.348381i
$768$	−280.886	−	247.037i	−0.365737	−	0.321662i
$769$	−546.405			−0.710540			−0.355270	−	0.934764i	$-0.615611\pi$
$769$	−546.405			−0.710540			−0.355270	+	0.934764i	$0.615611\pi$
$770$			13.7396i			0.0178437i
$771$	589.064	−	669.779i	0.764026	−	0.868714i
$772$	−630.139			−0.816242
$773$		−	793.858i		−	1.02698i	−0.858095	−	0.513491i	$-0.828352\pi$
$773$		−	793.858i		−	1.02698i	0.858095	−	0.513491i	$-0.171648\pi$
$774$	1.81008	−	0.233076i	0.00233860	−	0.000301131i
$775$	809.267			1.04421
$776$		−	1089.97i		−	1.40459i
$777$	285.436	+	251.038i	0.367356	+	0.323087i
$778$	170.040			0.218560
$779$			111.584i			0.143240i
$780$	38.4928	−	43.7671i	0.0493497	−	0.0561117i
$781$	1225.75			1.56946
$782$			390.384i			0.499213i
$783$	746.817	+	503.620i	0.953789	+	0.643193i
$784$	−32.4622			−0.0414059
$785$			2.00765i			0.00255751i
$786$	−743.031	−	653.489i	−0.945333	−	0.831411i
$787$	−256.390			−0.325781			−0.162891	−	0.986644i	$-0.552082\pi$
$787$	−256.390			−0.325781			−0.162891	+	0.986644i	$0.552082\pi$
$788$			1103.90i			1.40089i
$789$	468.789	−	533.023i	0.594155	−	0.675568i
$790$	−35.4141			−0.0448280
$791$			172.779i			0.218431i
$792$	78.1814	+	607.161i	0.0987139	+	0.766617i
$793$	−547.875			−0.690889
$794$			250.580i			0.315592i
$795$	−5.47997	−	4.81958i	−0.00689304	−	0.00606236i
$796$	1342.81			1.68695
$797$		−	1192.58i		−	1.49634i	−0.663508	−	0.748169i	$-0.730933\pi$
$797$		−	1192.58i		−	1.49634i	0.663508	−	0.748169i	$-0.269067\pi$
$798$	34.7336	−	39.4929i	0.0435258	−	0.0494898i
$799$	−1284.63			−1.60780
$800$			968.866i			1.21108i
$801$	−896.598	+	115.451i	−1.11935	+	0.144134i
$802$	448.761			0.559552
$803$		−	226.563i		−	0.282146i
$804$	−1505.40	−	1323.98i	−1.87238	−	1.64674i
$805$	−1.85950			−0.00230994
$806$		−	2285.30i		−	2.83537i
$807$	−164.664	+	187.227i	−0.204045	+	0.232003i
$808$	−1055.18			−1.30592
$809$		−	439.523i		−	0.543292i	−0.962397	−	0.271646i	$-0.912432\pi$
$809$		−	439.523i		−	0.543292i	0.962397	−	0.271646i	$-0.0875679\pi$
$810$	−36.1668	+	9.47112i	−0.0446504	+	0.0116927i
$811$	−929.655			−1.14631			−0.573154	−	0.819448i	$-0.694280\pi$
$811$	−929.655			−1.14631			−0.573154	+	0.819448i	$0.694280\pi$
$812$		−	522.493i		−	0.643464i
$813$	937.227	+	824.283i	1.15280	+	1.01388i
$814$	1697.06			2.08484
$815$		−	43.1980i		−	0.0530037i
$816$	−237.465	+	270.003i	−0.291011	+	0.330886i
$817$	−0.135457			−0.000165798
$818$			1085.37i			1.32685i
$819$	−68.1074	−	528.926i	−0.0831593	−	0.645819i
$820$	−46.0098			−0.0561095
$821$		−	733.453i		−	0.893365i	−0.894692	−	0.446683i	$-0.852605\pi$
$821$		−	733.453i		−	0.893365i	0.894692	−	0.446683i	$-0.147395\pi$
$822$	−410.682	−	361.191i	−0.499613	−	0.439405i
$823$	1032.96			1.25512			0.627560	−	0.778568i	$-0.284054\pi$
$823$	1032.96			1.25512			0.627560	+	0.778568i	$0.284054\pi$
$824$			498.481i			0.604953i
$825$	556.801	−	633.095i	0.674911	−	0.767388i
$826$	99.4192			0.120362
$827$		−	513.587i		−	0.621024i	−0.950569	−	0.310512i	$-0.899500\pi$
$827$		−	513.587i		−	0.621024i	0.950569	−	0.310512i	$-0.100500\pi$
$828$	−253.408	+	32.6303i	−0.306049	+	0.0394086i
$829$	−841.458			−1.01503			−0.507514	−	0.861644i	$-0.669435\pi$
$829$	−841.458			−1.01503			−0.507514	+	0.861644i	$0.669435\pi$
$830$			33.5536i			0.0404261i
$831$	−770.797	−	677.909i	−0.927553	−	0.815774i
$832$	2320.55			2.78913
$833$		−	180.918i		−	0.217188i
$834$	887.154	−	1008.71i	1.06373	−	1.20949i
$835$	−24.5824			−0.0294400
$836$		−	140.121i		−	0.167609i
$837$	−489.083	+	725.260i	−0.584329	+	0.866499i
$838$	−2531.35			−3.02071
$839$			991.939i			1.18229i	0.806566	+	0.591143i	$0.201323\pi$
$839$			991.939i			1.18229i	−0.806566	+	0.591143i	$0.798677\pi$
$840$	5.28047	+	4.64412i	0.00628627	+	0.00552872i
$841$	−271.989			−0.323412
$842$			288.408i			0.342527i
$843$	−238.780	+	271.498i	−0.283250	+	0.322062i
$844$	−139.172			−0.164896
$845$			48.7407i			0.0576813i
$846$	−179.933	−	1397.37i	−0.212687	−	1.65174i
$847$	14.7858			0.0174567
$848$		−	76.9785i		−	0.0907765i
$849$	−644.055	−	566.440i	−0.758604	−	0.667185i
$850$	−2033.27			−2.39208
$851$			229.677i			0.269891i
$852$	1277.69	−	1452.76i	1.49964	−	1.70512i
$853$	840.658			0.985531			0.492766	−	0.870162i	$-0.335986\pi$
$853$	840.658			0.985531			0.492766	+	0.870162i	$0.335986\pi$
$854$		−	203.846i		−	0.238695i
$855$	2.75216	−	0.354384i	0.00321891	−	0.000414484i
$856$	−1029.69			−1.20291
$857$		−	1170.83i		−	1.36620i	−0.730324	−	0.683101i	$-0.760631\pi$
$857$		−	1170.83i		−	1.36620i	0.730324	−	0.683101i	$-0.239369\pi$
$858$	−1787.81	−	1572.36i	−2.08370	−	1.83259i
$859$	−1137.30			−1.32398			−0.661990	−	0.749513i	$-0.730288\pi$
$859$	−1137.30			−1.32398			−0.661990	+	0.749513i	$0.730288\pi$
$860$		−	0.0558534i		−	6.49458e-5i
$861$	−278.014	+	316.108i	−0.322897	+	0.367141i
$862$	1166.22			1.35292
$863$			668.523i			0.774650i	0.921943	+	0.387325i	$0.126601\pi$
$863$			668.523i			0.774650i	−0.921943	+	0.387325i	$0.873399\pi$
$864$	−868.291	−	585.537i	−1.00497	−	0.677705i
$865$	−5.55633			−0.00642350
$866$		−	1584.96i		−	1.83020i
$867$	−853.743	−	750.859i	−0.984710	−	0.866043i
$868$	507.411			0.584574
$869$			863.268i			0.993404i
$870$	30.5078	−	34.6880i	0.0350664	−	0.0398712i
$871$	2528.33			2.90279
$872$			1096.99i			1.25801i
$873$	−207.228	−	1609.35i	−0.237375	−	1.84347i
$874$	31.7781			0.0363594
$875$		−	19.3783i		−	0.0221466i
$876$	−268.524	−	236.164i	−0.306534	−	0.269594i
$877$	−885.732			−1.00996			−0.504978	−	0.863132i	$-0.668499\pi$
$877$	−885.732			−1.00996			−0.504978	+	0.863132i	$0.668499\pi$
$878$		−	1969.85i		−	2.24357i
$879$	−191.866	+	218.156i	−0.218277	+	0.248186i
$880$	−7.64646			−0.00868916
$881$			655.693i			0.744260i	0.928181	+	0.372130i	$0.121372\pi$
$881$			655.693i			0.744260i	−0.928181	+	0.372130i	$0.878628\pi$
$882$	196.795	−	25.3405i	0.223124	−	0.0287307i
$883$	851.322			0.964124			0.482062	−	0.876137i	$-0.339888\pi$
$883$	851.322			0.964124			0.482062	+	0.876137i	$0.339888\pi$
$884$			3426.44i			3.87606i
$885$	3.93880	+	3.46414i	0.00445063	+	0.00391428i
$886$	−431.316			−0.486812
$887$			374.284i			0.421966i	0.977490	+	0.210983i	$0.0676665\pi$
$887$			374.284i			0.421966i	−0.977490	+	0.210983i	$0.932334\pi$
$888$	573.622	−	652.221i	0.645971	−	0.734483i
$889$	134.102			0.150846
$890$			46.3612i			0.0520912i
$891$	230.871	+	881.615i	0.259115	+	0.989467i
$892$	−1582.37			−1.77396
$893$			104.572i			0.117102i
$894$	−1930.18	−	1697.58i	−2.15904	−	1.89886i
$895$	−6.64144			−0.00742061
$896$			452.906i			0.505475i
$897$	212.801	−	241.960i	0.237237	−	0.269743i
$898$	2381.11			2.65158
$899$		−	1080.86i		−	1.20229i
$900$	−169.951	−	1319.85i	−0.188834	−	1.46650i
$901$	429.015			0.476155
$902$			1879.42i			2.08361i
$903$	−0.383738	−	0.337494i	−0.000424959	−	0.000373747i
$904$	394.799			0.436724
$905$		−	39.2349i		−	0.0433535i
$906$	787.089	−	894.938i	0.868752	−	0.987790i
$907$	424.138			0.467627			0.233814	−	0.972281i	$-0.424879\pi$
$907$	424.138			0.467627			0.233814	+	0.972281i	$0.424879\pi$
$908$		−	1316.18i		−	1.44954i
$909$	−1557.99	+	200.615i	−1.71396	+	0.220699i
$910$	−27.3496			−0.0300545
$911$			212.514i			0.233276i	0.993175	+	0.116638i	$0.0372117\pi$
$911$			212.514i			0.233276i	−0.993175	+	0.116638i	$0.962788\pi$
$912$	21.9788	+	19.3302i	0.0240996	+	0.0211954i
$913$	817.916			0.895855
$914$			284.985i			0.311800i
$915$	7.10276	−	8.07599i	0.00776258	−	0.00882622i
$916$	−812.195			−0.886675
$917$			277.081i			0.302160i
$918$	1228.81	−	1822.20i	1.33858	−	1.98497i
$919$	−501.467			−0.545666			−0.272833	−	0.962061i	$-0.587961\pi$
$919$	−501.467			−0.545666			−0.272833	+	0.962061i	$0.587961\pi$
$920$			4.24896i			0.00461843i
$921$	−55.4344	−	48.7541i	−0.0601894	−	0.0529360i
$922$	314.441			0.341042
$923$			2439.94i			2.64349i
$924$	349.115	−	396.951i	0.377830	−	0.429601i
$925$	−1196.25			−1.29324
$926$		−	2388.15i		−	2.57900i
$927$	94.7731	+	736.013i	0.102236	+	0.793973i
$928$	1294.02			1.39442
$929$		−	1344.46i		−	1.44721i	−0.690214	−	0.723605i	$-0.742484\pi$
$929$		−	1344.46i		−	1.44721i	0.690214	−	0.723605i	$-0.257516\pi$
$930$	33.6867	+	29.6271i	0.0362223	+	0.0318571i
$931$	−14.7271			−0.0158186
$932$		−	1644.26i		−	1.76423i
$933$	−477.646	+	543.093i	−0.511946	+	0.582094i
$934$	−903.352			−0.967186
$935$		−	42.6151i		−	0.0455777i
$936$	−1208.59	+	155.625i	−1.29123	+	0.166266i
$937$	−1059.15			−1.13036			−0.565181	−	0.824967i	$-0.691194\pi$
$937$	−1059.15			−1.13036			−0.565181	+	0.824967i	$0.691194\pi$
$938$			940.706i			1.00288i
$939$	−671.931	−	590.957i	−0.715582	−	0.629347i
$940$	−43.1185			−0.0458707
$941$			1095.67i			1.16436i	0.813059	+	0.582182i	$0.197801\pi$
$941$			1095.67i			1.16436i	−0.813059	+	0.582182i	$0.802199\pi$
$942$	85.4842	−	97.1974i	0.0907476	−	0.103182i
$943$	−254.358			−0.269733
$944$			55.3294i			0.0586117i
$945$	8.67963	+	5.85316i	0.00918479	+	0.00619382i
$946$	−2.28151			−0.00241175
$947$			733.055i			0.774081i	0.922063	+	0.387041i	$0.126503\pi$
$947$			733.055i			0.774081i	−0.922063	+	0.387041i	$0.873497\pi$
$948$	1023.15	+	899.851i	1.07927	+	0.949210i
$949$	450.989			0.475226
$950$			165.513i			0.174224i
$951$	−264.487	+	300.728i	−0.278115	+	0.316223i
$952$	−413.397			−0.434241
$953$		−	439.051i		−	0.460704i	−0.973107	−	0.230352i	$-0.926012\pi$
$953$		−	439.051i		−	0.460704i	0.973107	−	0.230352i	$-0.0739877\pi$
$954$	60.0905	+	466.666i	0.0629879	+	0.489168i
$955$	−26.8014			−0.0280643
$956$		−	1449.67i		−	1.51639i
$957$	−845.567	−	743.668i	−0.883560	−	0.777083i
$958$	1148.26			1.19861
$959$			153.146i			0.159693i
$960$	−30.0841	+	34.2063i	−0.0313376	+	0.0356315i
$961$	88.6626			0.0922607
$962$			3378.11i			3.51155i
$963$	−1520.35	+	195.768i	−1.57876	+	0.203290i
$964$	−934.665			−0.969570
$965$			15.6003i			0.0161661i
$966$	90.0250	+	79.1762i	0.0931936	+	0.0819629i
$967$	507.667			0.524991			0.262496	−	0.964933i	$-0.415454\pi$
$967$	507.667			0.524991			0.262496	+	0.964933i	$0.415454\pi$
$968$		−	33.7856i		−	0.0349025i
$969$	−107.731	+	122.492i	−0.111177	+	0.126411i
$970$	−83.2159			−0.0857895
$971$			1090.56i			1.12313i	0.827432	+	0.561566i	$0.189801\pi$
$971$			1090.56i			1.12313i	−0.827432	+	0.561566i	$0.810199\pi$
$972$	1285.55	+	645.346i	1.32258	+	0.663936i
$973$	−376.155			−0.386593
$974$		−	2194.07i		−	2.25263i
$975$	1260.22	+	1108.35i	1.29253	+	1.13677i
$976$	113.446			0.116235
$977$		−	967.015i		−	0.989780i	−0.868956	−	0.494890i	$-0.835208\pi$
$977$		−	967.015i		−	0.989780i	0.868956	−	0.494890i	$-0.164792\pi$
$978$	−1839.34	+	2091.37i	−1.88072	+	2.13841i
$979$	1130.12			1.15436
$980$		−	6.07249i		−	0.00619642i
$981$	208.563	+	1619.71i	0.212603	+	1.65108i
$982$	−581.805			−0.592469
$983$			1093.04i			1.11195i	0.831200	+	0.555974i	$0.187655\pi$
$983$			1093.04i			1.11195i	−0.831200	+	0.555974i	$0.812345\pi$
$984$	722.306	+	635.262i	0.734051	+	0.645591i
$985$	27.3293			0.0277455
$986$			2715.65i			2.75421i
$987$	−260.543	+	296.243i	−0.263975	+	0.300145i
$988$	278.920			0.282307
$989$		−	0.308777i		−	0.000312211i
$990$	46.3551	−	5.96893i	0.0468233	−	0.00602923i
$991$	−63.7423			−0.0643212			−0.0321606	−	0.999483i	$-0.510239\pi$
$991$	−63.7423			−0.0643212			−0.0321606	+	0.999483i	$0.510239\pi$
$992$			1256.67i			1.26681i
$993$	−430.872	−	378.948i	−0.433910	−	0.381619i
$994$	−907.818			−0.913298
$995$		−	33.2440i		−	0.0334111i
$996$	852.577	−	969.398i	0.856001	−	0.973291i
$997$	894.769			0.897461			0.448731	−	0.893667i	$-0.351876\pi$
$997$	894.769			0.897461			0.448731	+	0.893667i	$0.351876\pi$
$998$			317.245i			0.317880i
$999$	722.957	−	1072.07i	0.723680	−	1.07314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.b.a.323.12	✓	88
3.2	odd	2	inner	483.3.b.a.323.77	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.b.a.323.12	✓	88	1.1	even	1	trivial
483.3.b.a.323.77	yes	88	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	483.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.14953i q^{2} +(2.25271 + 1.98124i) q^{3} -5.91951 q^{4} +0.146549i q^{5} +(6.23996 - 7.09496i) q^{6} -2.64575 q^{7} +6.04554i q^{8} +(1.14940 + 8.92630i) q^{9} +O(q^{10})\)	\(q-3.14953i q^{2} +(2.25271 + 1.98124i) q^{3} -5.91951 q^{4} +0.146549i q^{5} +(6.23996 - 7.09496i) q^{6} -2.64575 q^{7} +6.04554i q^{8} +(1.14940 + 8.92630i) q^{9} +0.461560 q^{10} -11.2512i q^{11} +(-13.3349 - 11.7279i) q^{12} +22.3962 q^{13} +8.33286i q^{14} +(-0.290349 + 0.330133i) q^{15} -4.63746 q^{16} -25.8454i q^{17} +(28.1136 - 3.62006i) q^{18} -2.10387 q^{19} -0.867499i q^{20} +(-5.96011 - 5.24186i) q^{21} -35.4358 q^{22} -4.79583i q^{23} +(-11.9776 + 13.6188i) q^{24} +24.9785 q^{25} -70.5374i q^{26} +(-15.0959 + 22.3856i) q^{27} +15.6615 q^{28} -33.3615i q^{29} +(1.03976 + 0.914460i) q^{30} +32.3985 q^{31} +38.7879i q^{32} +(22.2912 - 25.3456i) q^{33} -81.4008 q^{34} -0.387733i q^{35} +(-6.80388 - 52.8393i) q^{36} -47.8911 q^{37} +6.62620i q^{38} +(50.4521 + 44.3722i) q^{39} -0.885968 q^{40} -53.0373i q^{41} +(-16.5094 + 18.7715i) q^{42} +0.0643844 q^{43} +66.6013i q^{44} +(-1.30814 + 0.168444i) q^{45} -15.1046 q^{46} -49.7044i q^{47} +(-10.4468 - 9.18790i) q^{48} +7.00000 q^{49} -78.6705i q^{50} +(51.2059 - 58.2222i) q^{51} -132.574 q^{52} +16.5993i q^{53} +(70.5040 + 47.5448i) q^{54} +1.64885 q^{55} -15.9950i q^{56} +(-4.73942 - 4.16827i) q^{57} -105.073 q^{58} -11.9310i q^{59} +(1.71872 - 1.95422i) q^{60} -24.4629 q^{61} -102.040i q^{62} +(-3.04103 - 23.6168i) q^{63} +103.614 q^{64} +3.28214i q^{65} +(-79.8266 - 70.2067i) q^{66} +112.891 q^{67} +152.992i q^{68} +(9.50168 - 10.8036i) q^{69} -1.22117 q^{70} +108.944i q^{71} +(-53.9643 + 6.94874i) q^{72} +20.1369 q^{73} +150.834i q^{74} +(56.2694 + 49.4884i) q^{75} +12.4539 q^{76} +29.7678i q^{77} +(139.751 - 158.900i) q^{78} -76.7270 q^{79} -0.679616i q^{80} +(-78.3578 + 20.5198i) q^{81} -167.042 q^{82} +72.6961i q^{83} +(35.2809 + 31.0292i) q^{84} +3.78762 q^{85} -0.202780i q^{86} +(66.0970 - 75.1538i) q^{87} +68.0193 q^{88} +100.445i q^{89} +(0.530517 + 4.12003i) q^{90} -59.2548 q^{91} +28.3890i q^{92} +(72.9844 + 64.1891i) q^{93} -156.545 q^{94} -0.308321i q^{95} +(-76.8481 + 87.3780i) q^{96} -180.293 q^{97} -22.0467i q^{98} +(100.431 - 12.9321i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9}+O(q^{10}) \) 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9	\( 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9} - 16 q^{10} - 18 q^{12} + 64 q^{13} + 20 q^{15} + 272 q^{16} - 38 q^{18} - 48 q^{19} - 28 q^{21} + 208 q^{22} + 228 q^{24} - 568 q^{25} - 88 q^{27} - 8 q^{30} + 8 q^{31} - 160 q^{33} - 32 q^{34} - 138 q^{36} - 136 q^{37} + 76 q^{39} - 48 q^{40} - 140 q^{42} + 424 q^{43} + 172 q^{45} + 334 q^{48} + 616 q^{49} + 288 q^{51} - 140 q^{52} - 240 q^{55} - 252 q^{57} - 380 q^{58} - 364 q^{60} + 312 q^{61} - 252 q^{64} + 44 q^{66} - 224 q^{67} + 168 q^{70} - 592 q^{72} + 216 q^{73} - 284 q^{75} + 328 q^{76} + 470 q^{78} - 8 q^{79} + 380 q^{81} - 548 q^{82} + 224 q^{84} - 712 q^{85} + 56 q^{87} - 896 q^{88} + 1136 q^{90} + 168 q^{91} - 236 q^{93} - 252 q^{94} - 546 q^{96} + 480 q^{97} - 248 q^{99}+O(q^{100}) \) 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9 - 16 * q^10 - 18 * q^12 + 64 * q^13 + 20 * q^15 + 272 * q^16 - 38 * q^18 - 48 * q^19 - 28 * q^21 + 208 * q^22 + 228 * q^24 - 568 * q^25 - 88 * q^27 - 8 * q^30 + 8 * q^31 - 160 * q^33 - 32 * q^34 - 138 * q^36 - 136 * q^37 + 76 * q^39 - 48 * q^40 - 140 * q^42 + 424 * q^43 + 172 * q^45 + 334 * q^48 + 616 * q^49 + 288 * q^51 - 140 * q^52 - 240 * q^55 - 252 * q^57 - 380 * q^58 - 364 * q^60 + 312 * q^61 - 252 * q^64 + 44 * q^66 - 224 * q^67 + 168 * q^70 - 592 * q^72 + 216 * q^73 - 284 * q^75 + 328 * q^76 + 470 * q^78 - 8 * q^79 + 380 * q^81 - 548 * q^82 + 224 * q^84 - 712 * q^85 + 56 * q^87 - 896 * q^88 + 1136 * q^90 + 168 * q^91 - 236 * q^93 - 252 * q^94 - 546 * q^96 + 480 * q^97 - 248 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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