LMFDB - Embedded newform 483.3.f.a.22.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,3,Mod(22,483)]

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([0, 0, 1]))

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

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

chi := DirichletCharacter("483.22");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	483.f (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:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			22.26
Character	$\chi$	$=$	483.22
Dual form			483.3.f.a.22.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.299460 q^{2} -1.73205 q^{3} -3.91032 q^{4} +2.23813i q^{5} -0.518680 q^{6} +2.64575i q^{7} -2.36883 q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+0.299460 q^{2} -1.73205 q^{3} -3.91032 q^{4} +2.23813i q^{5} -0.518680 q^{6} +2.64575i q^{7} -2.36883 q^{8} +3.00000 q^{9} +0.670230i q^{10} +17.7479i q^{11} +6.77288 q^{12} -2.29555 q^{13} +0.792297i q^{14} -3.87655i q^{15} +14.9319 q^{16} -25.6106i q^{17} +0.898380 q^{18} -5.56819i q^{19} -8.75181i q^{20} -4.58258i q^{21} +5.31478i q^{22} +(-20.7248 - 9.97418i) q^{23} +4.10293 q^{24} +19.9908 q^{25} -0.687427 q^{26} -5.19615 q^{27} -10.3457i q^{28} -32.8502 q^{29} -1.16087i q^{30} -53.8161 q^{31} +13.9468 q^{32} -30.7402i q^{33} -7.66934i q^{34} -5.92153 q^{35} -11.7310 q^{36} -11.4053i q^{37} -1.66745i q^{38} +3.97602 q^{39} -5.30174i q^{40} -20.9701 q^{41} -1.37230i q^{42} -52.8779i q^{43} -69.4000i q^{44} +6.71439i q^{45} +(-6.20624 - 2.98687i) q^{46} +72.5217 q^{47} -25.8629 q^{48} -7.00000 q^{49} +5.98644 q^{50} +44.3588i q^{51} +8.97636 q^{52} -72.9954i q^{53} -1.55604 q^{54} -39.7221 q^{55} -6.26732i q^{56} +9.64439i q^{57} -9.83732 q^{58} +42.7209 q^{59} +15.1586i q^{60} -98.2277i q^{61} -16.1158 q^{62} +7.93725i q^{63} -55.5512 q^{64} -5.13775i q^{65} -9.20547i q^{66} -7.20999i q^{67} +100.146i q^{68} +(35.8963 + 17.2758i) q^{69} -1.77326 q^{70} -113.813 q^{71} -7.10648 q^{72} +43.6776 q^{73} -3.41544i q^{74} -34.6250 q^{75} +21.7734i q^{76} -46.9565 q^{77} +1.19066 q^{78} +24.0288i q^{79} +33.4196i q^{80} +9.00000 q^{81} -6.27971 q^{82} +44.2213i q^{83} +17.9194i q^{84} +57.3198 q^{85} -15.8348i q^{86} +56.8982 q^{87} -42.0416i q^{88} +21.5910i q^{89} +2.01069i q^{90} -6.07347i q^{91} +(81.0405 + 39.0023i) q^{92} +93.2122 q^{93} +21.7174 q^{94} +12.4623 q^{95} -24.1566 q^{96} +59.2662i q^{97} -2.09622 q^{98} +53.2437i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9}+O(q^{10}) $ 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9	$ 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9} + 16 q^{13} + 324 q^{16} + 12 q^{18} - 4 q^{23} - 24 q^{24} - 176 q^{25} + 136 q^{26} - 128 q^{29} - 8 q^{31} - 252 q^{32} - 56 q^{35} + 348 q^{36} + 96 q^{39} - 24 q^{41} - 148 q^{46} - 408 q^{47} - 96 q^{48} - 336 q^{49} + 236 q^{50} - 32 q^{52} - 72 q^{54} - 24 q^{55} - 56 q^{58} + 136 q^{59} + 184 q^{62} + 716 q^{64} - 48 q^{69} - 112 q^{70} + 48 q^{71} - 12 q^{72} - 224 q^{73} - 48 q^{75} + 224 q^{77} - 96 q^{78} + 432 q^{81} + 640 q^{82} - 424 q^{85} + 312 q^{87} + 1060 q^{92} + 192 q^{93} + 216 q^{94} + 624 q^{95} + 48 q^{96} - 28 q^{98}+O(q^{100}) $ 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9 + 16 * q^13 + 324 * q^16 + 12 * q^18 - 4 * q^23 - 24 * q^24 - 176 * q^25 + 136 * q^26 - 128 * q^29 - 8 * q^31 - 252 * q^32 - 56 * q^35 + 348 * q^36 + 96 * q^39 - 24 * q^41 - 148 * q^46 - 408 * q^47 - 96 * q^48 - 336 * q^49 + 236 * q^50 - 32 * q^52 - 72 * q^54 - 24 * q^55 - 56 * q^58 + 136 * q^59 + 184 * q^62 + 716 * q^64 - 48 * q^69 - 112 * q^70 + 48 * q^71 - 12 * q^72 - 224 * q^73 - 48 * q^75 + 224 * q^77 - 96 * q^78 + 432 * q^81 + 640 * q^82 - 424 * q^85 + 312 * q^87 + 1060 * q^92 + 192 * q^93 + 216 * q^94 + 624 * q^95 + 48 * q^96 - 28 * q^98

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 $

$2$	0.299460			0.149730			0.0748650	−	0.997194i	$-0.476147\pi$
$2$	0.299460			0.149730			0.0748650	+	0.997194i	$0.476147\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−3.91032			−0.977581
$5$			2.23813i			0.447626i	0.974632	+	0.223813i	$0.0718505\pi$
$5$			2.23813i			0.447626i	−0.974632	+	0.223813i	$0.928150\pi$
$6$	−0.518680			−0.0864466
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	−2.36883			−0.296103
$9$	3.00000			0.333333
$10$			0.670230i			0.0670230i
$11$			17.7479i			1.61344i	0.590931	+	0.806722i	$0.298761\pi$
$11$			17.7479i			1.61344i	−0.590931	+	0.806722i	$0.701239\pi$
$12$	6.77288			0.564407
$13$	−2.29555			−0.176581			−0.0882906	−	0.996095i	$-0.528140\pi$
$13$	−2.29555			−0.176581			−0.0882906	+	0.996095i	$0.528140\pi$
$14$			0.792297i			0.0565926i
$15$		−	3.87655i		−	0.258437i
$16$	14.9319			0.933245
$17$		−	25.6106i		−	1.50650i	−0.657732	−	0.753252i	$-0.728484\pi$
$17$		−	25.6106i		−	1.50650i	0.657732	−	0.753252i	$-0.271516\pi$
$18$	0.898380			0.0499100
$19$		−	5.56819i		−	0.293063i	−0.989206	−	0.146531i	$-0.953189\pi$
$19$		−	5.56819i		−	0.293063i	0.989206	−	0.146531i	$-0.0468109\pi$
$20$		−	8.75181i		−	0.437591i
$21$		−	4.58258i		−	0.218218i
$22$			5.31478i			0.241581i
$23$	−20.7248	−	9.97418i	−0.901077	−	0.433660i
$23$	−20.7248	−	9.97418i	−0.901077	−	0.433660i
$24$	4.10293			0.170955
$25$	19.9908			0.799631
$26$	−0.687427			−0.0264395
$27$	−5.19615			−0.192450
$28$		−	10.3457i		−	0.369491i
$29$	−32.8502			−1.13277			−0.566383	−	0.824142i	$-0.691658\pi$
$29$	−32.8502			−1.13277			−0.566383	+	0.824142i	$0.691658\pi$
$30$		−	1.16087i		−	0.0386958i
$31$	−53.8161			−1.73600			−0.868002	−	0.496561i	$-0.834596\pi$
$31$	−53.8161			−1.73600			−0.868002	+	0.496561i	$0.834596\pi$
$32$	13.9468			0.435838
$33$		−	30.7402i		−	0.931522i
$34$		−	7.66934i		−	0.225569i
$35$	−5.92153			−0.169187
$36$	−11.7310			−0.325860
$37$		−	11.4053i		−	0.308253i	−0.988051	−	0.154126i	$-0.950744\pi$
$37$		−	11.4053i		−	0.308253i	0.988051	−	0.154126i	$-0.0492563\pi$
$38$		−	1.66745i		−	0.0438803i
$39$	3.97602			0.101949
$40$		−	5.30174i		−	0.132543i
$41$	−20.9701			−0.511466			−0.255733	−	0.966747i	$-0.582317\pi$
$41$	−20.9701			−0.511466			−0.255733	+	0.966747i	$0.582317\pi$
$42$		−	1.37230i		−	0.0326738i
$43$		−	52.8779i		−	1.22972i	−0.788637	−	0.614859i	$-0.789213\pi$
$43$		−	52.8779i		−	1.22972i	0.788637	−	0.614859i	$-0.210787\pi$
$44$		−	69.4000i		−	1.57727i
$45$			6.71439i			0.149209i
$46$	−6.20624	−	2.98687i	−0.134918	−	0.0649319i
$47$	72.5217			1.54302			0.771508	−	0.636220i	$-0.219503\pi$
$47$	72.5217			1.54302			0.771508	+	0.636220i	$0.219503\pi$
$48$	−25.8629			−0.538809
$49$	−7.00000			−0.142857
$50$	5.98644			0.119729
$51$			44.3588i			0.869781i
$52$	8.97636			0.172622
$53$		−	72.9954i		−	1.37727i	−0.725107	−	0.688636i	$-0.758210\pi$
$53$		−	72.9954i		−	1.37727i	0.725107	−	0.688636i	$-0.241790\pi$
$54$	−1.55604			−0.0288155
$55$	−39.7221			−0.722219
$56$		−	6.26732i		−	0.111916i
$57$			9.64439i			0.169200i
$58$	−9.83732			−0.169609
$59$	42.7209			0.724083			0.362042	−	0.932162i	$-0.382080\pi$
$59$	42.7209			0.724083			0.362042	+	0.932162i	$0.382080\pi$
$60$			15.1586i			0.252643i
$61$		−	98.2277i		−	1.61029i	−0.593078	−	0.805145i	$-0.702087\pi$
$61$		−	98.2277i		−	1.61029i	0.593078	−	0.805145i	$-0.297913\pi$
$62$	−16.1158			−0.259932
$63$			7.93725i			0.125988i
$64$	−55.5512			−0.867987
$65$		−	5.13775i		−	0.0790423i
$66$		−	9.20547i		−	0.139477i
$67$		−	7.20999i		−	0.107612i	−0.998551	−	0.0538059i	$-0.982865\pi$
$67$		−	7.20999i		−	0.107612i	0.998551	−	0.0538059i	$-0.0171352\pi$
$68$			100.146i			1.47273i
$69$	35.8963	+	17.2758i	0.520237	+	0.250374i
$70$	−1.77326			−0.0253323
$71$	−113.813			−1.60300			−0.801500	−	0.597995i	$-0.795964\pi$
$71$	−113.813			−1.60300			−0.801500	+	0.597995i	$0.795964\pi$
$72$	−7.10648			−0.0987011
$73$	43.6776			0.598323			0.299161	−	0.954203i	$-0.403293\pi$
$73$	43.6776			0.598323			0.299161	+	0.954203i	$0.403293\pi$
$74$		−	3.41544i		−	0.0461547i
$75$	−34.6250			−0.461667
$76$			21.7734i			0.286493i
$77$	−46.9565			−0.609825
$78$	1.19066			0.0152648
$79$			24.0288i			0.304162i	0.988368	+	0.152081i	$0.0485975\pi$
$79$			24.0288i			0.304162i	−0.988368	+	0.152081i	$0.951403\pi$
$80$			33.4196i			0.417745i
$81$	9.00000			0.111111
$82$	−6.27971			−0.0765818
$83$			44.2213i			0.532786i	0.963864	+	0.266393i	$0.0858320\pi$
$83$			44.2213i			0.532786i	−0.963864	+	0.266393i	$0.914168\pi$
$84$			17.9194i			0.213326i
$85$	57.3198			0.674350
$86$		−	15.8348i		−	0.184126i
$87$	56.8982			0.654003
$88$		−	42.0416i		−	0.477746i
$89$			21.5910i			0.242595i	0.992616	+	0.121298i	$0.0387055\pi$
$89$			21.5910i			0.242595i	−0.992616	+	0.121298i	$0.961294\pi$
$90$			2.01069i			0.0223410i
$91$		−	6.07347i		−	0.0667414i
$92$	81.0405	+	39.0023i	0.880875	+	0.423938i
$93$	93.2122			1.00228
$94$	21.7174			0.231036
$95$	12.4623			0.131183
$96$	−24.1566			−0.251631
$97$			59.2662i			0.610992i	0.952193	+	0.305496i	$0.0988222\pi$
$97$			59.2662i			0.610992i	−0.952193	+	0.305496i	$0.901178\pi$
$98$	−2.09622			−0.0213900
$99$			53.2437i			0.537815i
$100$	−78.1704			−0.781704
$101$	29.2064			0.289173			0.144586	−	0.989492i	$-0.453815\pi$
$101$	29.2064			0.289173			0.144586	+	0.989492i	$0.453815\pi$
$102$			13.2837i			0.130232i
$103$		−	158.707i		−	1.54085i	−0.637533	−	0.770423i	$-0.720045\pi$
$103$		−	158.707i		−	1.54085i	0.637533	−	0.770423i	$-0.279955\pi$
$104$	5.43777			0.0522862
$105$	10.2564			0.0976800
$106$		−	21.8592i		−	0.206219i
$107$			120.885i			1.12976i	0.825172	+	0.564882i	$0.191078\pi$
$107$			120.885i			1.12976i	−0.825172	+	0.564882i	$0.808922\pi$
$108$	20.3186			0.188136
$109$		−	105.904i		−	0.971600i	−0.874070	−	0.485800i	$-0.838528\pi$
$109$		−	105.904i		−	0.971600i	0.874070	−	0.485800i	$-0.161472\pi$
$110$	−11.8952			−0.108138
$111$			19.7546i			0.177970i
$112$			39.5062i			0.352734i
$113$			133.536i			1.18173i	0.806769	+	0.590867i	$0.201214\pi$
$113$			133.536i			1.18173i	−0.806769	+	0.590867i	$0.798786\pi$
$114$			2.88811i			0.0253343i
$115$	22.3235	−	46.3847i	0.194117	−	0.403345i
$116$	128.455			1.10737
$117$	−6.88666			−0.0588604
$118$	12.7932			0.108417
$119$	67.7592			0.569405
$120$			9.18288i			0.0765240i
$121$	−193.987			−1.60320
$122$		−	29.4153i		−	0.241109i
$123$	36.3213			0.295295
$124$	210.438			1.69708
$125$			100.695i			0.805562i
$126$			2.37689i			0.0188642i
$127$	−52.8091			−0.415820			−0.207910	−	0.978148i	$-0.566666\pi$
$127$	−52.8091			−0.415820			−0.207910	+	0.978148i	$0.566666\pi$
$128$	−72.4226			−0.565802
$129$			91.5872i			0.709978i
$130$		−	1.53855i		−	0.0118350i
$131$	138.095			1.05416			0.527081	−	0.849815i	$-0.323287\pi$
$131$	138.095			1.05416			0.527081	+	0.849815i	$0.323287\pi$
$132$			120.204i			0.910639i
$133$	14.7321			0.110767
$134$		−	2.15910i		−	0.0161127i
$135$		−	11.6297i		−	0.0861457i
$136$			60.6670i			0.446081i
$137$			84.9718i			0.620232i	0.950699	+	0.310116i	$0.100368\pi$
$137$			84.9718i			0.620232i	−0.950699	+	0.310116i	$0.899632\pi$
$138$	10.7495	+	5.17341i	0.0778951	+	0.0374884i
$139$	−242.796			−1.74673			−0.873367	−	0.487063i	$-0.838068\pi$
$139$	−242.796			−1.74673			−0.873367	+	0.487063i	$0.838068\pi$
$140$	23.1551			0.165394
$141$	−125.611			−0.890860
$142$	−34.0824			−0.240017
$143$		−	40.7412i		−	0.284904i
$144$	44.7958			0.311082
$145$		−	73.5230i		−	0.507055i
$146$	13.0797			0.0895868
$147$	12.1244			0.0824786
$148$			44.5986i			0.301342i
$149$		−	32.4768i		−	0.217965i	−0.994044	−	0.108982i	$-0.965241\pi$
$149$		−	32.4768i		−	0.217965i	0.994044	−	0.108982i	$-0.0347592\pi$
$150$	−10.3688			−0.0691254
$151$	−105.977			−0.701832			−0.350916	−	0.936407i	$-0.614130\pi$
$151$	−105.977			−0.701832			−0.350916	+	0.936407i	$0.614130\pi$
$152$			13.1901i			0.0867768i
$153$		−	76.8317i		−	0.502168i
$154$	−14.0616			−0.0913090
$155$		−	120.447i		−	0.777080i
$156$	−15.5475			−0.0996636
$157$		−	235.156i		−	1.49781i	−0.662677	−	0.748906i	$-0.730580\pi$
$157$		−	235.156i		−	1.49781i	0.662677	−	0.748906i	$-0.269420\pi$
$158$			7.19567i			0.0455422i
$159$			126.432i			0.795168i
$160$			31.2148i			0.195092i
$161$	26.3892	−	54.8326i	0.163908	−	0.340575i
$162$	2.69514			0.0166367
$163$	76.8192			0.471284			0.235642	−	0.971840i	$-0.424281\pi$
$163$	76.8192			0.471284			0.235642	+	0.971840i	$0.424281\pi$
$164$	81.9999			0.500000
$165$	68.8006			0.416974
$166$			13.2425i			0.0797741i
$167$	152.168			0.911183			0.455592	−	0.890189i	$-0.349428\pi$
$167$	152.168			0.911183			0.455592	+	0.890189i	$0.349428\pi$
$168$			10.8553i			0.0646150i
$169$	−163.730			−0.968819
$170$	17.1650			0.100970
$171$		−	16.7046i		−	0.0976876i
$172$			206.770i			1.20215i
$173$	−182.069			−1.05242			−0.526211	−	0.850354i	$-0.676388\pi$
$173$	−182.069			−1.05242			−0.526211	+	0.850354i	$0.676388\pi$
$174$	17.0387			0.0979238
$175$			52.8906i			0.302232i
$176$			265.010i			1.50574i
$177$	−73.9948			−0.418050
$178$			6.46563i			0.0363238i
$179$	178.229			0.995694			0.497847	−	0.867265i	$-0.334124\pi$
$179$	178.229			0.995694			0.497847	+	0.867265i	$0.334124\pi$
$180$		−	26.2554i		−	0.145864i
$181$		−	316.640i		−	1.74939i	−0.484671	−	0.874697i	$-0.661060\pi$
$181$		−	316.640i		−	1.74939i	0.484671	−	0.874697i	$-0.338940\pi$
$182$		−	1.81876i		−	0.00999319i
$183$			170.135i			0.929701i
$184$	49.0933	+	23.6271i	0.266812	+	0.128408i
$185$	25.5266			0.137982
$186$	27.9133			0.150072
$187$	454.533			2.43066
$188$	−283.583			−1.50842
$189$		−	13.7477i		−	0.0727393i
$190$	3.73197			0.0196420
$191$			244.300i			1.27906i	0.768767	+	0.639529i	$0.220871\pi$
$191$			244.300i			1.27906i	−0.768767	+	0.639529i	$0.779129\pi$
$192$	96.2175			0.501133
$193$	−248.629			−1.28823			−0.644116	−	0.764928i	$-0.722775\pi$
$193$	−248.629			−1.28823			−0.644116	+	0.764928i	$0.722775\pi$
$194$			17.7479i			0.0914838i
$195$			8.89884i			0.0456351i
$196$	27.3723			0.139654
$197$	−32.1526			−0.163211			−0.0816056	−	0.996665i	$-0.526005\pi$
$197$	−32.1526			−0.163211			−0.0816056	+	0.996665i	$0.526005\pi$
$198$			15.9443i			0.0805270i
$199$			28.6501i			0.143970i	0.997406	+	0.0719852i	$0.0229334\pi$
$199$			28.6501i			0.143970i	−0.997406	+	0.0719852i	$0.977067\pi$
$200$	−47.3547			−0.236773
$201$			12.4881i			0.0621297i
$202$	8.74616			0.0432978
$203$		−	86.9135i		−	0.428145i
$204$		−	173.457i		−	0.850281i
$205$		−	46.9338i		−	0.228946i
$206$		−	47.5264i		−	0.230711i
$207$	−62.1743	−	29.9225i	−0.300359	−	0.144553i
$208$	−34.2771			−0.164794
$209$	98.8237			0.472840
$210$	3.07138			0.0146256
$211$	186.669			0.884687			0.442343	−	0.896846i	$-0.354147\pi$
$211$	186.669			0.884687			0.442343	+	0.896846i	$0.354147\pi$
$212$			285.436i			1.34639i
$213$	197.130			0.925493
$214$			36.2001i			0.169159i
$215$	118.348			0.550454
$216$	12.3088			0.0569851
$217$		−	142.384i		−	0.656148i
$218$		−	31.7141i		−	0.145478i
$219$	−75.6517			−0.345442
$220$	155.326			0.706028
$221$			58.7905i			0.266020i
$222$			5.91572i			0.0266474i
$223$	−242.763			−1.08862			−0.544311	−	0.838884i	$-0.683209\pi$
$223$	−242.763			−1.08862			−0.544311	+	0.838884i	$0.683209\pi$
$224$			36.8998i			0.164731i
$225$	59.9723			0.266544
$226$			39.9886i			0.176941i
$227$		−	95.4916i		−	0.420668i	−0.977630	−	0.210334i	$-0.932545\pi$
$227$		−	95.4916i		−	0.420668i	0.977630	−	0.210334i	$-0.0674551\pi$
$228$		−	37.7127i		−	0.165407i
$229$			128.624i			0.561677i	0.959755	+	0.280838i	$0.0906125\pi$
$229$			128.624i			0.561677i	−0.959755	+	0.280838i	$0.909387\pi$
$230$	6.68500	−	13.8904i	0.0290652	−	0.0603929i
$231$	81.3310			0.352082
$232$	77.8164			0.335416
$233$	−374.207			−1.60604			−0.803019	−	0.595953i	$-0.796774\pi$
$233$	−374.207			−1.60604			−0.803019	+	0.595953i	$0.796774\pi$
$234$	−2.06228			−0.00881316
$235$			162.313i			0.690694i
$236$	−167.053			−0.707850
$237$		−	41.6191i		−	0.175608i
$238$	20.2912			0.0852570
$239$	−212.635			−0.889688			−0.444844	−	0.895608i	$-0.646741\pi$
$239$	−212.635			−0.889688			−0.444844	+	0.895608i	$0.646741\pi$
$240$		−	57.8844i		−	0.241185i
$241$			221.950i			0.920956i	0.887671	+	0.460478i	$0.152322\pi$
$241$			221.950i			0.920956i	−0.887671	+	0.460478i	$0.847678\pi$
$242$	−58.0915			−0.240047
$243$	−15.5885			−0.0641500
$244$			384.102i			1.57419i
$245$		−	15.6669i		−	0.0639466i
$246$	10.8768			0.0442145
$247$			12.7821i			0.0517494i
$248$	127.481			0.514036
$249$		−	76.5935i		−	0.307604i
$250$			30.1542i			0.120617i
$251$		−	169.084i		−	0.673642i	−0.941569	−	0.336821i	$-0.890648\pi$
$251$		−	169.084i		−	0.673642i	0.941569	−	0.336821i	$-0.109352\pi$
$252$		−	31.0372i		−	0.123164i
$253$	177.021	−	367.821i	0.699686	−	1.45384i
$254$	−15.8142			−0.0622607
$255$	−99.2808			−0.389336
$256$	200.517			0.783270
$257$	−56.7589			−0.220852			−0.110426	−	0.993884i	$-0.535222\pi$
$257$	−56.7589			−0.220852			−0.110426	+	0.993884i	$0.535222\pi$
$258$			27.4267i			0.106305i
$259$	30.1757			0.116509
$260$			20.0903i			0.0772702i
$261$	−98.5506			−0.377589
$262$	41.3540			0.157840
$263$		−	51.9956i		−	0.197702i	−0.995102	−	0.0988509i	$-0.968483\pi$
$263$		−	51.9956i		−	0.197702i	0.995102	−	0.0988509i	$-0.0315167\pi$
$264$			72.8183i			0.275827i
$265$	163.373			0.616503
$266$	4.41166			0.0165852
$267$		−	37.3967i		−	0.140062i
$268$			28.1934i			0.105199i
$269$	−0.616990			−0.00229364			−0.00114682	−	0.999999i	$-0.500365\pi$
$269$	−0.616990			−0.00229364			−0.00114682	+	0.999999i	$0.500365\pi$
$270$		−	3.48262i		−	0.0128986i
$271$	225.807			0.833237			0.416619	−	0.909081i	$-0.363215\pi$
$271$	225.807			0.833237			0.416619	+	0.909081i	$0.363215\pi$
$272$		−	382.415i		−	1.40594i
$273$			10.5196i			0.0385332i
$274$			25.4457i			0.0928674i
$275$			354.794i			1.29016i
$276$	−140.366	−	67.5539i	−0.508574	−	0.244761i
$277$	−483.225			−1.74450			−0.872248	−	0.489064i	$-0.837338\pi$
$277$	−483.225			−1.74450			−0.872248	+	0.489064i	$0.837338\pi$
$278$	−72.7077			−0.261538
$279$	−161.448			−0.578668
$280$	14.0271			0.0500967
$281$		−	478.838i		−	1.70405i	−0.523501	−	0.852025i	$-0.675374\pi$
$281$		−	478.838i		−	1.70405i	0.523501	−	0.852025i	$-0.324626\pi$
$282$	−37.6156			−0.133388
$283$		−	242.939i		−	0.858440i	−0.903200	−	0.429220i	$-0.858788\pi$
$283$		−	242.939i		−	0.858440i	0.903200	−	0.429220i	$-0.141212\pi$
$284$	445.046			1.56706
$285$	−21.5854			−0.0757383
$286$		−	12.2004i		−	0.0426586i
$287$		−	55.4817i		−	0.193316i
$288$	41.8404			0.145279
$289$	−366.901			−1.26956
$290$		−	22.0172i		−	0.0759214i
$291$		−	102.652i		−	0.352756i
$292$	−170.793			−0.584909
$293$			191.192i			0.652532i	0.945278	+	0.326266i	$0.105790\pi$
$293$			191.192i			0.652532i	−0.945278	+	0.326266i	$0.894210\pi$
$294$	3.63076			0.0123495
$295$			95.6149i			0.324118i
$296$			27.0173i			0.0912746i
$297$		−	92.2207i		−	0.310507i
$298$		−	9.72549i		−	0.0326359i
$299$	47.5748	+	22.8963i	0.159113	+	0.0765762i
$300$	135.395			0.451317
$301$	139.902			0.464790
$302$	−31.7358			−0.105085
$303$	−50.5870			−0.166954
$304$		−	83.1439i		−	0.273500i
$305$	219.846			0.720808
$306$		−	23.0080i		−	0.0751896i
$307$	117.388			0.382372			0.191186	−	0.981554i	$-0.438767\pi$
$307$	117.388			0.382372			0.191186	+	0.981554i	$0.438767\pi$
$308$	183.615			0.596153
$309$			274.889i			0.889608i
$310$		−	36.0692i		−	0.116352i
$311$	299.729			0.963760			0.481880	−	0.876237i	$-0.339954\pi$
$311$	299.729			0.963760			0.481880	+	0.876237i	$0.339954\pi$
$312$	−9.41849			−0.0301875
$313$		−	207.793i		−	0.663877i	−0.943301	−	0.331938i	$-0.892297\pi$
$313$		−	207.793i		−	0.663877i	0.943301	−	0.331938i	$-0.107703\pi$
$314$		−	70.4199i		−	0.224267i
$315$	−17.7646			−0.0563956
$316$		−	93.9604i		−	0.297343i
$317$	−211.154			−0.666100			−0.333050	−	0.942909i	$-0.608078\pi$
$317$	−211.154			−0.666100			−0.333050	+	0.942909i	$0.608078\pi$
$318$			37.8612i			0.119061i
$319$		−	583.022i		−	1.82765i
$320$		−	124.331i		−	0.388534i
$321$		−	209.378i		−	0.652269i
$322$	7.90251	−	16.4202i	0.0245420	−	0.0509943i
$323$	−142.605			−0.441500
$324$	−35.1929			−0.108620
$325$	−45.8899			−0.141200
$326$	23.0043			0.0705653
$327$			183.432i			0.560954i
$328$	49.6745			0.151447
$329$			191.874i			0.583205i
$330$	20.6030			0.0624334
$331$	−508.921			−1.53752			−0.768762	−	0.639534i	$-0.779127\pi$
$331$	−508.921			−1.53752			−0.768762	+	0.639534i	$0.779127\pi$
$332$		−	172.919i		−	0.520842i
$333$		−	34.2160i		−	0.102751i
$334$	45.5681			0.136431
$335$	16.1369			0.0481698
$336$		−	68.4267i		−	0.203651i
$337$			646.068i			1.91712i	0.284896	+	0.958558i	$0.408041\pi$
$337$			646.068i			1.91712i	−0.284896	+	0.958558i	$0.591959\pi$
$338$	−49.0307			−0.145061
$339$		−	231.291i		−	0.682274i
$340$	−224.139			−0.659232
$341$		−	955.122i		−	2.80094i
$342$		−	5.00235i		−	0.0146268i
$343$		−	18.5203i		−	0.0539949i
$344$			125.258i			0.364123i
$345$	−38.6654	+	80.3407i	−0.112074	+	0.232872i
$346$	−54.5224			−0.157579
$347$	−412.479			−1.18870			−0.594350	−	0.804207i	$-0.702591\pi$
$347$	−412.479			−1.18870			−0.594350	+	0.804207i	$0.702591\pi$
$348$	−222.491			−0.639341
$349$	−411.715			−1.17970			−0.589850	−	0.807513i	$-0.700813\pi$
$349$	−411.715			−1.17970			−0.589850	+	0.807513i	$0.700813\pi$
$350$			15.8386i			0.0452532i
$351$	11.9281			0.0339831
$352$			247.526i			0.703200i
$353$	−119.691			−0.339067			−0.169533	−	0.985524i	$-0.554226\pi$
$353$	−119.691			−0.339067			−0.169533	+	0.985524i	$0.554226\pi$
$354$	−22.1585			−0.0625946
$355$		−	254.728i		−	0.717544i
$356$		−	84.4277i		−	0.237156i
$357$	−117.362			−0.328746
$358$	53.3725			0.149085
$359$		−	318.418i		−	0.886959i	−0.896284	−	0.443480i	$-0.853744\pi$
$359$		−	318.418i		−	0.886959i	0.896284	−	0.443480i	$-0.146256\pi$
$360$		−	15.9052i		−	0.0441812i
$361$	329.995			0.914114
$362$		−	94.8211i		−	0.261937i
$363$	335.996			0.925609
$364$			23.7492i			0.0652451i
$365$			97.7560i			0.267825i
$366$			50.9487i			0.139204i
$367$			509.344i			1.38786i	0.720043	+	0.693929i	$0.244122\pi$
$367$			509.344i			1.38786i	−0.720043	+	0.693929i	$0.755878\pi$
$368$	−309.461	−	148.934i	−0.840926	−	0.404711i
$369$	−62.9103			−0.170489
$370$	7.64421			0.0206600
$371$	193.128			0.520560
$372$	−364.490			−0.979812
$373$		−	246.136i		−	0.659882i	−0.944002	−	0.329941i	$-0.892971\pi$
$373$		−	246.136i		−	0.659882i	0.944002	−	0.329941i	$-0.107029\pi$
$374$	136.115			0.363943
$375$		−	174.409i		−	0.465091i
$376$	−171.791			−0.456892
$377$	75.4095			0.200025
$378$		−	4.11689i		−	0.0108913i
$379$			137.963i			0.364019i	0.983297	+	0.182010i	$0.0582602\pi$
$379$			137.963i			0.364019i	−0.983297	+	0.182010i	$0.941740\pi$
$380$	−48.7318			−0.128242
$381$	91.4681			0.240074
$382$			73.1581i			0.191513i
$383$			688.826i			1.79850i	0.437434	+	0.899251i	$0.355887\pi$
$383$			688.826i			1.79850i	−0.437434	+	0.899251i	$0.644113\pi$
$384$	125.440			0.326666
$385$		−	105.095i		−	0.272973i
$386$	−74.4544			−0.192887
$387$		−	158.634i		−	0.409906i
$388$		−	231.750i		−	0.597294i
$389$			404.932i			1.04096i	0.853875	+	0.520479i	$0.174247\pi$
$389$			404.932i			1.04096i	−0.853875	+	0.520479i	$0.825753\pi$
$390$			2.66485i			0.00683294i
$391$	−255.444	+	530.773i	−0.653311	+	1.35748i
$392$	16.5818			0.0423005
$393$	−239.188			−0.608620
$394$	−9.62842			−0.0244376
$395$	−53.7796			−0.136151
$396$		−	208.200i		−	0.525757i
$397$	785.576			1.97878			0.989391	−	0.145277i	$-0.0464073\pi$
$397$	785.576			1.97878			0.989391	+	0.145277i	$0.0464073\pi$
$398$			8.57956i			0.0215567i
$399$	−25.5167			−0.0639515
$400$	298.501			0.746252
$401$		−	659.729i		−	1.64521i	−0.568614	−	0.822605i	$-0.692520\pi$
$401$		−	659.729i		−	1.64521i	0.568614	−	0.822605i	$-0.307480\pi$
$402$			3.73968i			0.00930268i
$403$	123.538			0.306545
$404$	−114.207			−0.282690
$405$			20.1432i			0.0497362i
$406$		−	26.0271i		−	0.0641062i
$407$	202.421			0.497348
$408$		−	105.078i		−	0.257545i
$409$	−111.629			−0.272930			−0.136465	−	0.990645i	$-0.543574\pi$
$409$	−111.629			−0.272930			−0.136465	+	0.990645i	$0.543574\pi$
$410$		−	14.0548i		−	0.0342800i
$411$		−	147.175i		−	0.358091i
$412$			620.596i			1.50630i
$413$			113.029i			0.273678i
$414$	−18.6187	−	8.96060i	−0.0449727	−	0.0216440i
$415$	−98.9729			−0.238489
$416$	−32.0157			−0.0769608
$417$	420.535			1.00848
$418$	29.5937			0.0707984
$419$			343.072i			0.818787i	0.912358	+	0.409394i	$0.134260\pi$
$419$			343.072i			0.818787i	−0.912358	+	0.409394i	$0.865740\pi$
$420$	−40.1058			−0.0954901
$421$		−	786.898i		−	1.86912i	−0.355811	−	0.934558i	$-0.615795\pi$
$421$		−	786.898i		−	1.86912i	0.355811	−	0.934558i	$-0.384205\pi$
$422$	55.8999			0.132464
$423$	217.565			0.514338
$424$			172.913i			0.407815i
$425$		−	511.975i		−	1.20465i
$426$	59.0325			0.138574
$427$	259.886			0.608632
$428$		−	472.698i		−	1.10443i
$429$			70.5659i			0.164489i
$430$	35.4404			0.0824194
$431$		−	33.8925i		−	0.0786370i	−0.999227	−	0.0393185i	$-0.987481\pi$
$431$		−	33.8925i		−	0.0786370i	0.999227	−	0.0393185i	$-0.0125187\pi$
$432$	−77.5886			−0.179603
$433$		−	847.725i		−	1.95780i	−0.204351	−	0.978898i	$-0.565508\pi$
$433$		−	847.725i		−	1.95780i	0.204351	−	0.978898i	$-0.434492\pi$
$434$		−	42.6383i		−	0.0982450i
$435$			127.346i			0.292749i
$436$			414.120i			0.949818i
$437$	−55.5382	+	115.399i	−0.127090	+	0.264072i
$438$	−22.6547			−0.0517230
$439$	419.290			0.955103			0.477552	−	0.878604i	$-0.341524\pi$
$439$	419.290			0.955103			0.477552	+	0.878604i	$0.341524\pi$
$440$	94.0946			0.213851
$441$	−21.0000			−0.0476190
$442$			17.6054i			0.0398312i
$443$	−652.816			−1.47362			−0.736812	−	0.676097i	$-0.763670\pi$
$443$	−652.816			−1.47362			−0.736812	+	0.676097i	$0.763670\pi$
$444$		−	77.2470i		−	0.173980i
$445$	−48.3234			−0.108592
$446$	−72.6977			−0.162999
$447$			56.2514i			0.125842i
$448$		−	146.975i		−	0.328068i
$449$	175.921			0.391806			0.195903	−	0.980623i	$-0.437236\pi$
$449$	175.921			0.391806			0.195903	+	0.980623i	$0.437236\pi$
$450$	17.9593			0.0399096
$451$		−	372.175i		−	0.825222i
$452$		−	522.168i		−	1.15524i
$453$	183.557			0.405203
$454$		−	28.5959i		−	0.0629866i
$455$	13.5932			0.0298752
$456$		−	22.8459i		−	0.0501006i
$457$			466.627i			1.02107i	0.859858	+	0.510533i	$0.170552\pi$
$457$			466.627i			1.02107i	−0.859858	+	0.510533i	$0.829448\pi$
$458$			38.5177i			0.0840999i
$459$			133.076i			0.289927i
$460$	−87.2921	+	181.379i	−0.189766	+	0.394303i
$461$	−152.082			−0.329896			−0.164948	−	0.986302i	$-0.552746\pi$
$461$	−152.082			−0.329896			−0.164948	+	0.986302i	$0.552746\pi$
$462$	24.3554			0.0527173
$463$	−156.569			−0.338163			−0.169082	−	0.985602i	$-0.554080\pi$
$463$	−156.569			−0.338163			−0.169082	+	0.985602i	$0.554080\pi$
$464$	−490.517			−1.05715
$465$			208.621i			0.448647i
$466$	−112.060			−0.240472
$467$			699.315i			1.49746i	0.662874	+	0.748731i	$0.269336\pi$
$467$			699.315i			1.49746i	−0.662874	+	0.748731i	$0.730664\pi$
$468$	26.9291			0.0575408
$469$	19.0758			0.0406734
$470$			48.6063i			0.103418i
$471$			407.303i			0.864762i
$472$	−101.198			−0.214403
$473$	938.471			1.98408
$474$		−	12.4633i		−	0.0262938i
$475$		−	111.313i		−	0.234342i
$476$	−264.960			−0.556640
$477$		−	218.986i		−	0.459091i
$478$	−63.6758			−0.133213
$479$			356.147i			0.743523i	0.928328	+	0.371761i	$0.121246\pi$
$479$			356.147i			0.743523i	−0.928328	+	0.371761i	$0.878754\pi$
$480$		−	54.0656i		−	0.112637i
$481$			26.1816i			0.0544316i
$482$			66.4653i			0.137895i
$483$	−45.7074	+	94.9728i	−0.0946324	+	0.196631i
$484$	758.554			1.56726
$485$	−132.645			−0.273496
$486$	−4.66812			−0.00960518
$487$	194.007			0.398372			0.199186	−	0.979962i	$-0.436170\pi$
$487$	194.007			0.398372			0.199186	+	0.979962i	$0.436170\pi$
$488$			232.684i			0.476812i
$489$	−133.055			−0.272096
$490$		−	4.69161i		−	0.00957472i
$491$	−438.471			−0.893017			−0.446508	−	0.894779i	$-0.647333\pi$
$491$	−438.471			−0.893017			−0.446508	+	0.894779i	$0.647333\pi$
$492$	−142.028			−0.288675
$493$			841.313i			1.70652i
$494$			3.82773i			0.00774843i
$495$	−119.166			−0.240740
$496$	−803.578			−1.62012
$497$		−	301.121i		−	0.605877i
$498$		−	22.9367i		−	0.0460576i
$499$	−78.4964			−0.157307			−0.0786537	−	0.996902i	$-0.525062\pi$
$499$	−78.4964			−0.157307			−0.0786537	+	0.996902i	$0.525062\pi$
$500$		−	393.751i		−	0.787502i
$501$	−263.562			−0.526072
$502$		−	50.6340i		−	0.100864i
$503$		−	123.657i		−	0.245839i	−0.992417	−	0.122919i	$-0.960774\pi$
$503$		−	123.657i		−	0.245839i	0.992417	−	0.122919i	$-0.0392256\pi$
$504$		−	18.8020i		−	0.0373055i
$505$			65.3678i			0.129441i
$506$	53.0106	−	110.148i	0.104764	−	0.217683i
$507$	283.589			0.559348
$508$	206.501			0.406498
$509$	162.390			0.319037			0.159519	−	0.987195i	$-0.449006\pi$
$509$	162.390			0.319037			0.159519	+	0.987195i	$0.449006\pi$
$510$	−29.7306			−0.0582953
$511$			115.560i			0.226145i
$512$	349.737			0.683081
$513$			28.9332i			0.0564000i
$514$	−16.9970			−0.0330682
$515$	355.207			0.689723
$516$		−	358.136i		−	0.694061i
$517$			1287.11i			2.48957i
$518$	9.03642			0.0174448
$519$	315.353			0.607616
$520$			12.1704i			0.0234047i
$521$			372.783i			0.715514i	0.933815	+	0.357757i	$0.116458\pi$
$521$			372.783i			0.715514i	−0.933815	+	0.357757i	$0.883542\pi$
$522$	−29.5120			−0.0565363
$523$			4.17483i			0.00798246i	0.999992	+	0.00399123i	$0.00127045\pi$
$523$			4.17483i			0.00798246i	−0.999992	+	0.00399123i	$0.998730\pi$
$524$	−539.997			−1.03053
$525$		−	91.6092i		−	0.174494i
$526$		−	15.5706i		−	0.0296019i
$527$			1378.26i			2.61530i
$528$		−	459.011i		−	0.869339i
$529$	330.032	+	413.425i	0.623878	+	0.781522i
$530$	48.9237			0.0923089
$531$	128.163			0.241361
$532$	−57.6071			−0.108284
$533$	48.1380			0.0903153
$534$		−	11.1988i		−	0.0209715i
$535$	−270.556			−0.505711
$536$			17.0792i			0.0318642i
$537$	−308.702			−0.574864
$538$	−0.184764			−0.000343427
$539$		−	124.235i		−	0.230492i
$540$			45.4757i			0.0842143i
$541$	533.262			0.985697			0.492849	−	0.870115i	$-0.335956\pi$
$541$	533.262			0.985697			0.492849	+	0.870115i	$0.335956\pi$
$542$	67.6202			0.124761
$543$			548.437i			1.01001i
$544$		−	357.186i		−	0.656592i
$545$	237.028			0.434913
$546$			3.15019i			0.00576957i
$547$	−12.0226			−0.0219792			−0.0109896	−	0.999940i	$-0.503498\pi$
$547$	−12.0226			−0.0219792			−0.0109896	+	0.999940i	$0.503498\pi$
$548$		−	332.267i		−	0.606327i
$549$		−	294.683i		−	0.536763i
$550$			106.247i			0.193176i
$551$			182.916i			0.331972i
$552$	−85.0322	−	40.9233i	−0.154044	−	0.0741364i
$553$	−63.5743			−0.114963
$554$	−144.707			−0.261203
$555$	−44.2134			−0.0796639
$556$	949.411			1.70757
$557$		−	840.063i		−	1.50819i	−0.656764	−	0.754096i	$-0.728075\pi$
$557$		−	840.063i		−	1.50819i	0.656764	−	0.754096i	$-0.271925\pi$
$558$	−48.3473			−0.0866439
$559$			121.384i			0.217145i
$560$	−88.4199			−0.157893
$561$	−787.275			−1.40334
$562$		−	143.393i		−	0.255147i
$563$			166.070i			0.294973i	0.989064	+	0.147486i	$0.0471182\pi$
$563$			166.070i			0.294973i	−0.989064	+	0.147486i	$0.952882\pi$
$564$	491.181			0.870888
$565$	−298.871			−0.528974
$566$		−	72.7504i		−	0.128534i
$567$			23.8118i			0.0419961i
$568$	269.603			0.474653
$569$		−	107.590i		−	0.189086i	−0.995521	−	0.0945428i	$-0.969861\pi$
$569$		−	107.590i		−	0.189086i	0.995521	−	0.0945428i	$-0.0301389\pi$
$570$	−6.46396			−0.0113403
$571$			620.345i			1.08642i	0.839597	+	0.543210i	$0.182791\pi$
$571$			620.345i			1.08642i	−0.839597	+	0.543210i	$0.817209\pi$
$572$			159.311i			0.278517i
$573$		−	423.140i		−	0.738465i
$574$		−	16.6145i		−	0.0289452i
$575$	−414.304	−	199.392i	−0.720529	−	0.346768i
$576$	−166.654			−0.289329
$577$	−439.039			−0.760900			−0.380450	−	0.924802i	$-0.624231\pi$
$577$	−439.039			−0.760900			−0.380450	+	0.924802i	$0.624231\pi$
$578$	−109.872			−0.190090
$579$	430.638			0.743761
$580$			287.499i			0.495688i
$581$	−116.998			−0.201374
$582$		−	30.7402i		−	0.0528182i
$583$	1295.51			2.22215
$584$	−103.464			−0.177165
$585$		−	15.4132i		−	0.0263474i
$586$			57.2543i			0.0977035i
$587$	−295.927			−0.504134			−0.252067	−	0.967710i	$-0.581110\pi$
$587$	−295.927			−0.504134			−0.252067	+	0.967710i	$0.581110\pi$
$588$	−47.4102			−0.0806295
$589$			299.659i			0.508758i
$590$			28.6328i			0.0485302i
$591$	55.6899			0.0942300
$592$		−	170.304i		−	0.287675i
$593$	981.889			1.65580			0.827900	−	0.560876i	$-0.189535\pi$
$593$	981.889			1.65580			0.827900	+	0.560876i	$0.189535\pi$
$594$		−	27.6164i		−	0.0464923i
$595$			151.654i			0.254881i
$596$			126.995i			0.213078i
$597$		−	49.6234i		−	0.0831213i
$598$	14.2468	+	6.85652i	0.0238240	+	0.0114657i
$599$	491.151			0.819952			0.409976	−	0.912096i	$-0.365537\pi$
$599$	491.151			0.819952			0.409976	+	0.912096i	$0.365537\pi$
$600$	82.0207			0.136701
$601$	−1122.37			−1.86751			−0.933753	−	0.357918i	$-0.883487\pi$
$601$	−1122.37			−1.86751			−0.933753	+	0.357918i	$0.883487\pi$
$602$	41.8950			0.0695930
$603$		−	21.6300i		−	0.0358706i
$604$	414.403			0.686098
$605$		−	434.169i		−	0.717635i
$606$	−15.1488			−0.0249980
$607$	237.456			0.391196			0.195598	−	0.980684i	$-0.437335\pi$
$607$	237.456			0.391196			0.195598	+	0.980684i	$0.437335\pi$
$608$		−	77.6586i		−	0.127728i
$609$			150.539i			0.247190i
$610$	65.8352			0.107927
$611$	−166.478			−0.272467
$612$			300.437i			0.490910i
$613$			687.849i			1.12210i	0.827781	+	0.561051i	$0.189603\pi$
$613$			687.849i			1.12210i	−0.827781	+	0.561051i	$0.810397\pi$
$614$	35.1531			0.0572525
$615$			81.2918i			0.132182i
$616$	111.232			0.180571
$617$			792.532i			1.28449i	0.766499	+	0.642246i	$0.221997\pi$
$617$			792.532i			1.28449i	−0.766499	+	0.642246i	$0.778003\pi$
$618$			82.3182i			0.133201i
$619$			152.411i			0.246222i	0.992393	+	0.123111i	$0.0392871\pi$
$619$			152.411i			0.246222i	−0.992393	+	0.123111i	$0.960713\pi$
$620$			470.988i			0.759659i
$621$	107.689	+	51.8274i	0.173412	+	0.0834579i
$622$	89.7569			0.144304
$623$	−57.1243			−0.0916924
$624$	59.3696			0.0951436
$625$	274.400			0.439041
$626$		−	62.2258i		−	0.0994023i
$627$	−171.168			−0.272995
$628$			919.537i			1.46423i
$629$	−292.097			−0.464384
$630$	−5.31979			−0.00844411
$631$		−	111.205i		−	0.176236i	−0.996110	−	0.0881181i	$-0.971915\pi$
$631$		−	111.205i		−	0.176236i	0.996110	−	0.0881181i	$-0.0280853\pi$
$632$		−	56.9201i		−	0.0900634i
$633$	−323.320			−0.510774
$634$	−63.2321			−0.0997352
$635$		−	118.194i		−	0.186132i
$636$		−	494.389i		−	0.777341i
$637$	16.0689			0.0252259
$638$		−	174.592i		−	0.273655i
$639$	−341.439			−0.534333
$640$		−	162.091i		−	0.253268i
$641$		−	576.346i		−	0.899135i	−0.893246	−	0.449568i	$-0.851578\pi$
$641$		−	576.346i		−	0.899135i	0.893246	−	0.449568i	$-0.148422\pi$
$642$		−	62.7004i		−	0.0976642i
$643$			201.552i			0.313456i	0.987642	+	0.156728i	$0.0500947\pi$
$643$			201.552i			0.313456i	−0.987642	+	0.156728i	$0.949905\pi$
$644$	−103.190	+	214.413i	−0.160233	+	0.332940i
$645$	−204.984			−0.317805
$646$	−42.7044			−0.0661058
$647$	438.725			0.678091			0.339046	−	0.940770i	$-0.389896\pi$
$647$	438.725			0.678091			0.339046	+	0.940770i	$0.389896\pi$
$648$	−21.3194			−0.0329004
$649$			758.206i			1.16827i
$650$	−13.7422			−0.0211418
$651$			246.616i			0.378827i
$652$	−300.388			−0.460718
$653$	502.740			0.769893			0.384946	−	0.922939i	$-0.374220\pi$
$653$	502.740			0.769893			0.384946	+	0.922939i	$0.374220\pi$
$654$			54.9305i			0.0839916i
$655$			309.075i			0.471870i
$656$	−313.124			−0.477323
$657$	131.033			0.199441
$658$			57.4587i			0.0873233i
$659$			856.448i			1.29962i	0.760097	+	0.649809i	$0.225151\pi$
$659$			856.448i			1.29962i	−0.760097	+	0.649809i	$0.774849\pi$
$660$	−269.033			−0.407625
$661$		−	167.376i		−	0.253216i	−0.991953	−	0.126608i	$-0.959591\pi$
$661$		−	167.376i		−	0.253216i	0.991953	−	0.126608i	$-0.0404091\pi$
$662$	−152.401			−0.230214
$663$		−	101.828i		−	0.153587i
$664$		−	104.752i		−	0.157760i
$665$			32.9723i			0.0495823i
$666$		−	10.2463i		−	0.0153849i
$667$	680.813	+	327.654i	1.02071	+	0.491235i
$668$	−595.025			−0.890755
$669$	420.477			0.628516
$670$	4.83236			0.00721247
$671$	1743.33			2.59811
$672$		−	63.9123i		−	0.0951076i
$673$	−319.026			−0.474036			−0.237018	−	0.971505i	$-0.576170\pi$
$673$	−319.026			−0.474036			−0.237018	+	0.971505i	$0.576170\pi$
$674$			193.472i			0.287050i
$675$	−103.875			−0.153889
$676$	640.239			0.947099
$677$		−	808.515i		−	1.19426i	−0.802144	−	0.597131i	$-0.796307\pi$
$677$		−	808.515i		−	1.19426i	0.802144	−	0.597131i	$-0.203693\pi$
$678$		−	69.2624i		−	0.102157i
$679$	−156.804			−0.230933
$680$	−135.781			−0.199677
$681$			165.396i			0.242873i
$682$		−	286.021i		−	0.419385i
$683$	−376.090			−0.550644			−0.275322	−	0.961352i	$-0.588784\pi$
$683$	−376.090			−0.550644			−0.275322	+	0.961352i	$0.588784\pi$
$684$			65.3203i			0.0954975i
$685$	−190.178			−0.277632
$686$		−	5.54608i		−	0.00808466i
$687$		−	222.783i		−	0.324284i
$688$		−	789.569i		−	1.14763i
$689$			167.565i			0.243200i
$690$	−11.5788	+	24.0588i	−0.0167808	+	0.0348678i
$691$	7.98529			0.0115561			0.00577807	−	0.999983i	$-0.498161\pi$
$691$	7.98529			0.0115561			0.00577807	+	0.999983i	$0.498161\pi$
$692$	711.949			1.02883
$693$	−140.869			−0.203275
$694$	−123.521			−0.177984
$695$		−	543.409i		−	0.781883i
$696$	−134.782			−0.193652
$697$			537.057i			0.770526i
$698$	−123.292			−0.176637
$699$	648.146			0.927247
$700$		−	206.819i		−	0.295456i
$701$			973.059i			1.38810i	0.719926	+	0.694050i	$0.244175\pi$
$701$			973.059i			1.38810i	−0.719926	+	0.694050i	$0.755825\pi$
$702$	3.57197			0.00508828
$703$	−63.5072			−0.0903374
$704$		−	985.916i		−	1.40045i
$705$		−	281.134i		−	0.398772i
$706$	−35.8425			−0.0507684
$707$			77.2729i			0.109297i
$708$	289.344			0.408677
$709$		−	872.985i		−	1.23129i	−0.788023	−	0.615645i	$-0.788895\pi$
$709$		−	872.985i		−	1.23129i	0.788023	−	0.615645i	$-0.211105\pi$
$710$		−	76.2809i		−	0.107438i
$711$			72.0864i			0.101387i
$712$		−	51.1452i		−	0.0718332i
$713$	1115.33	+	536.771i	1.56427	+	0.752835i
$714$	−35.1453			−0.0492232
$715$	91.1842			0.127530
$716$	−696.934			−0.973372
$717$	368.295			0.513662
$718$		−	95.3535i		−	0.132804i
$719$	−403.760			−0.561558			−0.280779	−	0.959772i	$-0.590593\pi$
$719$	−403.760			−0.561558			−0.280779	+	0.959772i	$0.590593\pi$
$720$			100.259i			0.139248i
$721$	419.900			0.582385
$722$	98.8204			0.136870
$723$		−	384.429i		−	0.531714i
$724$			1238.17i			1.71017i
$725$	−656.701			−0.905795
$726$	100.617			0.138591
$727$			631.483i			0.868615i	0.900765	+	0.434308i	$0.143007\pi$
$727$			631.483i			0.868615i	−0.900765	+	0.434308i	$0.856993\pi$
$728$			14.3870i			0.0197623i
$729$	27.0000			0.0370370
$730$			29.2740i			0.0401014i
$731$	−1354.23			−1.85258
$732$		−	665.284i		−	0.908858i
$733$		−	1425.23i		−	1.94437i	−0.234205	−	0.972187i	$-0.575249\pi$
$733$		−	1425.23i		−	1.94437i	0.234205	−	0.972187i	$-0.424751\pi$
$734$			152.528i			0.207804i
$735$			27.1359i			0.0369196i
$736$	−289.044	−	139.108i	−0.392723	−	0.189005i
$737$	127.962			0.173626
$738$	−18.8391			−0.0255273
$739$	−732.694			−0.991467			−0.495734	−	0.868475i	$-0.665101\pi$
$739$	−732.694			−0.991467			−0.495734	+	0.868475i	$0.665101\pi$
$740$	−99.8174			−0.134888
$741$		−	22.1392i		−	0.0298775i
$742$	57.8340			0.0779434
$743$			257.702i			0.346840i	0.984848	+	0.173420i	$0.0554819\pi$
$743$			257.702i			0.346840i	−0.984848	+	0.173420i	$0.944518\pi$
$744$	−220.804			−0.296779
$745$	72.6872			0.0975667
$746$		−	73.7079i		−	0.0988042i
$747$			132.664i			0.177595i
$748$	−1777.37			−2.37617
$749$	−319.831			−0.427010
$750$		−	52.2286i		−	0.0696381i
$751$		−	685.728i		−	0.913087i	−0.889701	−	0.456543i	$-0.849087\pi$
$751$		−	685.728i		−	0.913087i	0.889701	−	0.456543i	$-0.150913\pi$
$752$	1082.89			1.44001
$753$			292.863i			0.388928i
$754$	22.5821			0.0299498
$755$		−	237.190i		−	0.314158i
$756$			53.7581i			0.0711085i
$757$			1062.28i			1.40328i	0.712532	+	0.701639i	$0.247548\pi$
$757$			1062.28i			1.40328i	−0.712532	+	0.701639i	$0.752452\pi$
$758$			41.3145i			0.0545046i
$759$	−306.609	+	637.084i	−0.403964	+	0.839373i
$760$	−29.5211			−0.0388436
$761$	−204.509			−0.268737			−0.134369	−	0.990931i	$-0.542901\pi$
$761$	−204.509			−0.268737			−0.134369	+	0.990931i	$0.542901\pi$
$762$	27.3910			0.0359462
$763$	280.197			0.367230
$764$		−	955.293i		−	1.25038i
$765$	171.959			0.224783
$766$			206.276i			0.269290i
$767$	−98.0682			−0.127859
$768$	−347.306			−0.452221
$769$		−	1204.50i		−	1.56633i	−0.621816	−	0.783163i	$-0.713605\pi$
$769$		−	1204.50i		−	1.56633i	0.621816	−	0.783163i	$-0.286395\pi$
$770$		−	31.4717i		−	0.0408723i
$771$	98.3094			0.127509
$772$	972.219			1.25935
$773$		−	1319.49i		−	1.70697i	−0.521116	−	0.853486i	$-0.674484\pi$
$773$		−	1319.49i		−	1.70697i	0.521116	−	0.853486i	$-0.325516\pi$
$774$		−	47.5044i		−	0.0613752i
$775$	−1075.83			−1.38816
$776$		−	140.391i		−	0.180917i
$777$	−52.2659			−0.0672662
$778$			121.261i			0.155863i
$779$			116.766i			0.149892i
$780$		−	34.7974i		−	0.0446120i
$781$		−	2019.94i		−	2.58635i
$782$	−76.4954	+	158.945i	−0.0978202	+	0.203255i
$783$	170.695			0.218001
$784$	−104.523			−0.133321
$785$	526.310			0.670459
$786$	−71.6271			−0.0911287
$787$		−	1351.01i		−	1.71666i	−0.513098	−	0.858330i	$-0.671502\pi$
$787$		−	1351.01i		−	1.71666i	0.513098	−	0.858330i	$-0.328498\pi$
$788$	125.727			0.159552
$789$			90.0590i			0.114143i
$790$	−16.1048			−0.0203859
$791$	−353.303			−0.446653
$792$		−	126.125i		−	0.159249i
$793$			225.487i			0.284347i
$794$	235.249			0.296283
$795$	−282.971			−0.355938
$796$		−	112.031i		−	0.140743i
$797$		−	284.911i		−	0.357480i	−0.983896	−	0.178740i	$-0.942798\pi$
$797$		−	284.911i		−	0.357480i	0.983896	−	0.178740i	$-0.0572020\pi$
$798$	−7.64122			−0.00957546
$799$		−	1857.32i		−	2.32456i
$800$	278.808			0.348510
$801$			64.7729i			0.0808651i
$802$		−	197.562i		−	0.246337i
$803$			775.184i			0.965360i
$804$		−	48.8324i		−	0.0607368i
$805$	122.722	+	59.0624i	0.152450	+	0.0733695i
$806$	36.9946			0.0458991
$807$	1.06866			0.00132424
$808$	−69.1849			−0.0856249
$809$	−1363.76			−1.68574			−0.842870	−	0.538118i	$-0.819136\pi$
$809$	−1363.76			−1.68574			−0.842870	+	0.538118i	$0.819136\pi$
$810$			6.03207i			0.00744700i
$811$	−1133.87			−1.39811			−0.699055	−	0.715068i	$-0.746396\pi$
$811$	−1133.87			−1.39811			−0.699055	+	0.715068i	$0.746396\pi$
$812$			339.860i			0.418547i
$813$	−391.110			−0.481070
$814$	60.6169			0.0744679
$815$			171.931i			0.210959i
$816$			662.363i			0.811719i
$817$	−294.434			−0.360385
$818$	−33.4283			−0.0408659
$819$		−	18.2204i		−	0.0222471i
$820$			183.526i			0.223813i
$821$	−496.142			−0.604314			−0.302157	−	0.953258i	$-0.597707\pi$
$821$	−496.142			−0.604314			−0.302157	+	0.953258i	$0.597707\pi$
$822$		−	44.0732i		−	0.0536170i
$823$	−915.395			−1.11227			−0.556133	−	0.831093i	$-0.687716\pi$
$823$	−915.395			−1.11227			−0.556133	+	0.831093i	$0.687716\pi$
$824$			375.949i			0.456249i
$825$		−	614.521i		−	0.744874i
$826$			33.8476i			0.0409778i
$827$			610.884i			0.738675i	0.929295	+	0.369337i	$0.120415\pi$
$827$			610.884i			0.738675i	−0.929295	+	0.369337i	$0.879585\pi$
$828$	243.122	+	117.007i	0.293625	+	0.141313i
$829$	677.701			0.817493			0.408746	−	0.912648i	$-0.365966\pi$
$829$	677.701			0.817493			0.408746	+	0.912648i	$0.365966\pi$
$830$	−29.6384			−0.0357090
$831$	836.971			1.00718
$832$	127.521			0.153270
$833$			179.274i			0.215215i
$834$	125.933			0.150999
$835$			340.571i			0.407869i
$836$	−386.432			−0.462240
$837$	279.637			0.334094
$838$			102.736i			0.122597i
$839$		−	556.507i		−	0.663298i	−0.943403	−	0.331649i	$-0.892395\pi$
$839$		−	556.507i		−	0.663298i	0.943403	−	0.331649i	$-0.107605\pi$
$840$	−24.2956			−0.0289234
$841$	238.137			0.283159
$842$		−	235.644i		−	0.279863i
$843$			829.372i			0.983834i
$844$	−729.936			−0.864853
$845$		−	366.450i		−	0.433669i
$846$	65.1521			0.0770119
$847$		−	513.242i		−	0.605953i
$848$		−	1089.96i		−	1.28533i
$849$			420.782i			0.495621i
$850$		−	153.316i		−	0.180372i
$851$	−113.759	+	236.373i	−0.133677	+	0.277759i
$852$	−770.842			−0.904744
$853$	247.618			0.290291			0.145145	−	0.989410i	$-0.453635\pi$
$853$	247.618			0.290291			0.145145	+	0.989410i	$0.453635\pi$
$854$	77.8255			0.0911305
$855$	37.3870			0.0437275
$856$		−	286.355i		−	0.334526i
$857$	−820.438			−0.957337			−0.478668	−	0.877996i	$-0.658880\pi$
$857$	−820.438			−0.957337			−0.478668	+	0.877996i	$0.658880\pi$
$858$			21.1317i			0.0246290i
$859$	1109.91			1.29210			0.646048	−	0.763297i	$-0.276421\pi$
$859$	1109.91			1.29210			0.646048	+	0.763297i	$0.276421\pi$
$860$	−462.777			−0.538113
$861$			96.0971i			0.111611i
$862$		−	10.1495i		−	0.0117743i
$863$	1032.56			1.19648			0.598239	−	0.801318i	$-0.295868\pi$
$863$	1032.56			1.19648			0.598239	+	0.801318i	$0.295868\pi$
$864$	−72.4698			−0.0838771
$865$		−	407.494i		−	0.471091i
$866$		−	253.860i		−	0.293141i
$867$	635.492			0.732978
$868$			556.768i			0.641437i
$869$	−426.461			−0.490749
$870$			38.1349i			0.0438332i
$871$			16.5509i			0.0190022i
$872$			250.869i			0.287694i
$873$			177.799i			0.203664i
$874$	−16.6315	+	34.5575i	−0.0190291	+	0.0395395i
$875$	−266.414			−0.304474
$876$	295.823			0.337697
$877$	625.292			0.712990			0.356495	−	0.934297i	$-0.383972\pi$
$877$	625.292			0.712990			0.356495	+	0.934297i	$0.383972\pi$
$878$	125.561			0.143008
$879$		−	331.154i		−	0.376739i
$880$	−593.127			−0.674008
$881$			408.171i			0.463304i	0.972799	+	0.231652i	$0.0744131\pi$
$881$			408.171i			0.463304i	−0.972799	+	0.231652i	$0.925587\pi$
$882$	−6.28866			−0.00713000
$883$	−657.599			−0.744733			−0.372366	−	0.928086i	$-0.621453\pi$
$883$	−657.599			−0.744733			−0.372366	+	0.928086i	$0.621453\pi$
$884$		−	229.890i		−	0.260056i
$885$		−	165.610i		−	0.187130i
$886$	−195.492			−0.220646
$887$	179.854			0.202767			0.101383	−	0.994847i	$-0.467673\pi$
$887$	179.854			0.202767			0.101383	+	0.994847i	$0.467673\pi$
$888$		−	46.7953i		−	0.0526974i
$889$		−	139.720i		−	0.157165i
$890$	−14.4709			−0.0162595
$891$			159.731i			0.179272i
$892$	949.280			1.06422
$893$		−	403.815i		−	0.452200i
$894$			16.8450i			0.0188423i
$895$			398.900i			0.445699i
$896$		−	191.612i		−	0.213853i
$897$	−82.4020	−	39.6575i	−0.0918640	−	0.0442113i
$898$	52.6812			0.0586651
$899$	1767.87			1.96649
$900$	−234.511			−0.260568
$901$	−1869.45			−2.07487
$902$		−	111.452i		−	0.123560i
$903$	−242.317			−0.268347
$904$		−	316.323i		−	0.349915i
$905$	708.682			0.783074
$906$	54.9680			0.0606710
$907$		−	54.2424i		−	0.0598041i	−0.999553	−	0.0299021i	$-0.990480\pi$
$907$		−	54.2424i		−	0.0598041i	0.999553	−	0.0299021i	$-0.00951954\pi$
$908$			373.403i			0.411237i
$909$	87.6193			0.0963909
$910$	4.07062			0.00447321
$911$		−	1273.20i		−	1.39758i	−0.715326	−	0.698791i	$-0.753722\pi$
$911$		−	1273.20i		−	1.39758i	0.715326	−	0.698791i	$-0.246278\pi$
$912$			144.009i			0.157905i
$913$	−784.834			−0.859621
$914$			139.736i			0.152884i
$915$	−380.785			−0.416159
$916$		−	502.962i		−	0.549085i
$917$			365.365i			0.398435i
$918$			39.8511i			0.0434107i
$919$		−	1646.87i		−	1.79203i	−0.444026	−	0.896014i	$-0.646450\pi$
$919$		−	1646.87i		−	1.79203i	0.444026	−	0.896014i	$-0.353550\pi$
$920$	−52.8805	+	109.877i	−0.0574788	+	0.119432i
$921$	−203.322			−0.220763
$922$	−45.5425			−0.0493953
$923$	261.264			0.283060
$924$	−318.031			−0.344189
$925$		−	228.002i		−	0.246488i
$926$	−46.8863			−0.0506331
$927$		−	476.121i		−	0.513615i
$928$	−458.156			−0.493702
$929$	630.405			0.678585			0.339292	−	0.940681i	$-0.389812\pi$
$929$	630.405			0.678585			0.339292	+	0.940681i	$0.389812\pi$
$930$			62.4737i			0.0671760i
$931$			38.9774i			0.0418661i
$932$	1463.27			1.57003
$933$	−519.146			−0.556427
$934$			209.417i			0.224215i
$935$			1017.30i			1.08803i
$936$	16.3133			0.0174287
$937$		−	385.538i		−	0.411460i	−0.978609	−	0.205730i	$-0.934043\pi$
$937$		−	385.538i		−	0.411460i	0.978609	−	0.205730i	$-0.0659568\pi$
$938$	5.71245			0.00609003
$939$			359.909i			0.383289i
$940$		−	634.696i		−	0.675209i
$941$			1491.55i			1.58507i	0.609826	+	0.792535i	$0.291239\pi$
$941$			1491.55i			1.58507i	−0.609826	+	0.792535i	$0.708761\pi$
$942$			121.971i			0.129481i
$943$	434.601	+	209.160i	0.460870	+	0.221802i
$944$	637.905			0.675747
$945$	30.7692			0.0325600
$946$	281.034			0.297077
$947$	437.003			0.461461			0.230730	−	0.973018i	$-0.425888\pi$
$947$	437.003			0.461461			0.230730	+	0.973018i	$0.425888\pi$
$948$			162.744i			0.171671i
$949$	−100.264			−0.105652
$950$		−	33.3336i		−	0.0350880i
$951$	365.729			0.384573
$952$	−160.510			−0.168603
$953$			1100.00i			1.15425i	0.816656	+	0.577124i	$0.195825\pi$
$953$			1100.00i			1.15425i	−0.816656	+	0.577124i	$0.804175\pi$
$954$		−	65.5776i		−	0.0687396i
$955$	−546.775			−0.572540
$956$	831.473			0.869742
$957$			1009.82i			1.05520i
$958$			106.652i			0.111328i
$959$	−224.814			−0.234426
$960$			215.347i			0.224320i
$961$	1935.17			2.01371
$962$			7.84034i			0.00815004i
$963$			362.654i			0.376588i
$964$		−	867.898i		−	0.900309i
$965$		−	556.463i		−	0.576646i
$966$	−13.6875	+	28.4405i	−0.0141693	+	0.0294416i
$967$	1353.43			1.39961			0.699807	−	0.714332i	$-0.253270\pi$
$967$	1353.43			1.39961			0.699807	+	0.714332i	$0.253270\pi$
$968$	459.522			0.474713
$969$	246.998			0.254900
$970$	−39.7220			−0.0409505
$971$		−	578.234i		−	0.595504i	−0.954643	−	0.297752i	$-0.903763\pi$
$971$		−	578.234i		−	0.595504i	0.954643	−	0.297752i	$-0.0962369\pi$
$972$	60.9559			0.0627118
$973$		−	642.378i		−	0.660203i
$974$	58.0974			0.0596483
$975$	79.4837			0.0815217
$976$		−	1466.73i		−	1.50280i
$977$			1117.15i			1.14345i	0.820446	+	0.571725i	$0.193725\pi$
$977$			1117.15i			1.14345i	−0.820446	+	0.571725i	$0.806275\pi$
$978$	−39.8446			−0.0407409
$979$	−383.194			−0.391414
$980$			61.2627i			0.0625129i
$981$		−	317.713i		−	0.323867i
$982$	−131.305			−0.133711
$983$			179.686i			0.182793i	0.995815	+	0.0913966i	$0.0291331\pi$
$983$			179.686i			0.182793i	−0.995815	+	0.0913966i	$0.970867\pi$
$984$	−86.0388			−0.0874378
$985$		−	71.9617i		−	0.0730576i
$986$			251.940i			0.255517i
$987$		−	332.336i		−	0.336714i
$988$		−	49.9821i		−	0.0505892i
$989$	−527.413	+	1095.88i	−0.533280	+	1.10807i
$990$	−35.6855			−0.0360460
$991$	−1275.15			−1.28673			−0.643367	−	0.765558i	$-0.722463\pi$
$991$	−1275.15			−1.28673			−0.643367	+	0.765558i	$0.722463\pi$
$992$	−750.563			−0.756616
$993$	881.477			0.887690
$994$		−	90.1737i		−	0.0907180i
$995$	−64.1226			−0.0644448
$996$			299.505i			0.300708i
$997$	−965.297			−0.968201			−0.484101	−	0.875012i	$-0.660853\pi$
$997$	−965.297			−0.968201			−0.484101	+	0.875012i	$0.660853\pi$
$998$	−23.5065			−0.0235536
$999$			59.2639i			0.0593232i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.f.a.22.26	yes	48
23.22	odd	2	inner	483.3.f.a.22.25	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.f.a.22.25	✓	48	23.22	odd	2	inner
483.3.f.a.22.26	yes	48	1.1	even	1	trivial

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.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.299460 q^{2} -1.73205 q^{3} -3.91032 q^{4} +2.23813i q^{5} -0.518680 q^{6} +2.64575i q^{7} -2.36883 q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+0.299460 q^{2} -1.73205 q^{3} -3.91032 q^{4} +2.23813i q^{5} -0.518680 q^{6} +2.64575i q^{7} -2.36883 q^{8} +3.00000 q^{9} +0.670230i q^{10} +17.7479i q^{11} +6.77288 q^{12} -2.29555 q^{13} +0.792297i q^{14} -3.87655i q^{15} +14.9319 q^{16} -25.6106i q^{17} +0.898380 q^{18} -5.56819i q^{19} -8.75181i q^{20} -4.58258i q^{21} +5.31478i q^{22} +(-20.7248 - 9.97418i) q^{23} +4.10293 q^{24} +19.9908 q^{25} -0.687427 q^{26} -5.19615 q^{27} -10.3457i q^{28} -32.8502 q^{29} -1.16087i q^{30} -53.8161 q^{31} +13.9468 q^{32} -30.7402i q^{33} -7.66934i q^{34} -5.92153 q^{35} -11.7310 q^{36} -11.4053i q^{37} -1.66745i q^{38} +3.97602 q^{39} -5.30174i q^{40} -20.9701 q^{41} -1.37230i q^{42} -52.8779i q^{43} -69.4000i q^{44} +6.71439i q^{45} +(-6.20624 - 2.98687i) q^{46} +72.5217 q^{47} -25.8629 q^{48} -7.00000 q^{49} +5.98644 q^{50} +44.3588i q^{51} +8.97636 q^{52} -72.9954i q^{53} -1.55604 q^{54} -39.7221 q^{55} -6.26732i q^{56} +9.64439i q^{57} -9.83732 q^{58} +42.7209 q^{59} +15.1586i q^{60} -98.2277i q^{61} -16.1158 q^{62} +7.93725i q^{63} -55.5512 q^{64} -5.13775i q^{65} -9.20547i q^{66} -7.20999i q^{67} +100.146i q^{68} +(35.8963 + 17.2758i) q^{69} -1.77326 q^{70} -113.813 q^{71} -7.10648 q^{72} +43.6776 q^{73} -3.41544i q^{74} -34.6250 q^{75} +21.7734i q^{76} -46.9565 q^{77} +1.19066 q^{78} +24.0288i q^{79} +33.4196i q^{80} +9.00000 q^{81} -6.27971 q^{82} +44.2213i q^{83} +17.9194i q^{84} +57.3198 q^{85} -15.8348i q^{86} +56.8982 q^{87} -42.0416i q^{88} +21.5910i q^{89} +2.01069i q^{90} -6.07347i q^{91} +(81.0405 + 39.0023i) q^{92} +93.2122 q^{93} +21.7174 q^{94} +12.4623 q^{95} -24.1566 q^{96} +59.2662i q^{97} -2.09622 q^{98} +53.2437i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9}+O(q^{10}) \) 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9} + 16 q^{13} + 324 q^{16} + 12 q^{18} - 4 q^{23} - 24 q^{24} - 176 q^{25} + 136 q^{26} - 128 q^{29} - 8 q^{31} - 252 q^{32} - 56 q^{35} + 348 q^{36} + 96 q^{39} - 24 q^{41} - 148 q^{46} - 408 q^{47} - 96 q^{48} - 336 q^{49} + 236 q^{50} - 32 q^{52} - 72 q^{54} - 24 q^{55} - 56 q^{58} + 136 q^{59} + 184 q^{62} + 716 q^{64} - 48 q^{69} - 112 q^{70} + 48 q^{71} - 12 q^{72} - 224 q^{73} - 48 q^{75} + 224 q^{77} - 96 q^{78} + 432 q^{81} + 640 q^{82} - 424 q^{85} + 312 q^{87} + 1060 q^{92} + 192 q^{93} + 216 q^{94} + 624 q^{95} + 48 q^{96} - 28 q^{98}+O(q^{100}) \) 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9 + 16 * q^13 + 324 * q^16 + 12 * q^18 - 4 * q^23 - 24 * q^24 - 176 * q^25 + 136 * q^26 - 128 * q^29 - 8 * q^31 - 252 * q^32 - 56 * q^35 + 348 * q^36 + 96 * q^39 - 24 * q^41 - 148 * q^46 - 408 * q^47 - 96 * q^48 - 336 * q^49 + 236 * q^50 - 32 * q^52 - 72 * q^54 - 24 * q^55 - 56 * q^58 + 136 * q^59 + 184 * q^62 + 716 * q^64 - 48 * q^69 - 112 * q^70 + 48 * q^71 - 12 * q^72 - 224 * q^73 - 48 * q^75 + 224 * q^77 - 96 * q^78 + 432 * q^81 + 640 * q^82 - 424 * q^85 + 312 * q^87 + 1060 * q^92 + 192 * q^93 + 216 * q^94 + 624 * q^95 + 48 * q^96 - 28 * q^98

Introduction

L-functions

Modular forms

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