LMFDB - Embedded newform 279.3.v.a.244.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [279,3,Mod(46,279)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(279, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("279.46"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 279 = 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	279.v (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,3,0,-11,14,0,-1,19] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$7.60219937565$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 20 x^{18} - 33 x^{17} + 250 x^{16} - 510 x^{15} + 2908 x^{14} - 6447 x^{13} + \cdots + 731025 $ x^20 - 2x^19 + 20x^18 - 33x^17 + 250x^16 - 510x^15 + 2908x^14 - 6447x^13 + 39842x^12 - 79034x^11 + 199542x^10 - 173039x^9 + 688988x^8 - 636120x^7 + 3401146x^6 - 2156427x^5 + 7116556x^4 - 6139950x^3 + 6454710x^2 - 3116475*x + 731025
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			244.1
Root			$-2.86150 - 2.07900i$ of defining polynomial
Character	$\chi$	$=$	279.244
Dual form			279.3.v.a.271.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.09299 - 3.36389i) q^{2} +(-6.88507 + 5.00229i) q^{4} -8.82683 q^{5} +(2.08188 - 1.51257i) q^{7} +(12.9065 + 9.37714i) q^{8} +(9.64768 + 29.6925i) q^{10} +(6.28416 + 8.64940i) q^{11} +(-2.12141 - 0.689289i) q^{13} +(-7.36362 - 5.34998i) q^{14} +(6.91748 - 21.2898i) q^{16} +(0.840800 - 1.15726i) q^{17} +(-2.52727 - 7.77815i) q^{19} +(60.7733 - 44.1544i) q^{20} +(22.2271 - 30.5930i) q^{22} +(1.14986 - 1.58264i) q^{23} +52.9129 q^{25} +7.88959i q^{26} +(-6.76754 + 20.8283i) q^{28} +(26.7713 - 8.69853i) q^{29} +(-21.3083 + 22.5157i) q^{31} -15.3640 q^{32} +(-4.81190 - 1.56348i) q^{34} +(-18.3764 + 13.3512i) q^{35} +6.07061i q^{37} +(-23.4025 + 17.0029i) q^{38} +(-113.924 - 82.7704i) q^{40} +(20.7157 + 63.7563i) q^{41} +(55.9522 - 18.1800i) q^{43} +(-86.5337 - 28.1165i) q^{44} +(-6.58063 - 2.13818i) q^{46} +(11.9110 - 36.6584i) q^{47} +(-13.0955 + 40.3038i) q^{49} +(-57.8335 - 177.993i) q^{50} +(18.0541 - 5.86613i) q^{52} +(-45.0108 + 61.9521i) q^{53} +(-55.4692 - 76.3468i) q^{55} +41.0534 q^{56} +(-58.5218 - 80.5484i) q^{58} +(7.78185 - 23.9501i) q^{59} +87.4422i q^{61} +(99.0302 + 47.0692i) q^{62} +(-10.8771 - 33.4763i) q^{64} +(18.7253 + 6.08423i) q^{65} +31.7457 q^{67} +12.1738i q^{68} +(64.9974 + 47.2234i) q^{70} +(51.7571 + 37.6037i) q^{71} +(42.4801 + 58.4689i) q^{73} +(20.4209 - 6.63515i) q^{74} +(56.3090 + 40.9109i) q^{76} +(26.1657 + 8.50176i) q^{77} +(-54.8015 + 75.4277i) q^{79} +(-61.0594 + 187.921i) q^{80} +(191.827 - 139.371i) q^{82} +(-85.7251 + 27.8538i) q^{83} +(-7.42160 + 10.2150i) q^{85} +(-122.311 - 168.347i) q^{86} +170.561i q^{88} +(35.3705 + 48.6833i) q^{89} +(-5.45912 + 1.77378i) q^{91} +16.6485i q^{92} -136.334 q^{94} +(22.3078 + 68.6564i) q^{95} +(-10.3369 + 7.51019i) q^{97} +149.891 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 3 q^{2} - 11 q^{4} + 14 q^{5} - q^{7} + 19 q^{8} + 12 q^{10} + 10 q^{11} + 10 q^{13} - 103 q^{16} - 35 q^{17} + 47 q^{19} + 125 q^{20} + 150 q^{22} - 75 q^{23} + 82 q^{25} + 88 q^{28} - 5 q^{29}+ \cdots + 1000 q^{98}+O(q^{100}) $ 20 * q + 3 * q^2 - 11 * q^4 + 14 * q^5 - q^7 + 19 * q^8 + 12 * q^10 + 10 * q^11 + 10 * q^13 - 103 * q^16 - 35 * q^17 + 47 * q^19 + 125 * q^20 + 150 * q^22 - 75 * q^23 + 82 * q^25 + 88 * q^28 - 5 * q^29 + 73 * q^31 - 226 * q^32 - 265 * q^34 + 50 * q^35 - 8 * q^38 - 466 * q^40 + 98 * q^41 + 245 * q^43 - 380 * q^44 - 445 * q^46 + 187 * q^47 + 328 * q^49 + 44 * q^50 - 15 * q^52 - 25 * q^53 + 190 * q^55 - 64 * q^56 - 85 * q^58 + 173 * q^59 + 40 * q^62 - 469 * q^64 + 345 * q^65 + 76 * q^67 - 11 * q^70 + 467 * q^71 - 15 * q^73 - 45 * q^74 + 55 * q^76 + 320 * q^77 + 500 * q^79 - 1030 * q^80 + 178 * q^82 + 50 * q^83 + 20 * q^85 - 1125 * q^86 - 55 * q^89 + 300 * q^91 + 62 * q^94 + 559 * q^95 - 405 * q^97 + 1000 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/279\mathbb{Z}\right)^\times$.

$n$	$127$	$218$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−1.09299	−	3.36389i	−0.546497	−	1.68195i	−0.717403	−	0.696659i	$-0.754669\pi$
$2$	−1.09299	−	3.36389i	−0.546497	−	1.68195i	0.170905	−	0.985287i	$-0.445331\pi$
$3$		0			0
$3$		0			0
$4$	−6.88507	+	5.00229i	−1.72127	+	1.25057i
$5$	−8.82683			−1.76537			−0.882683	−	0.469969i	$-0.844265\pi$
$5$	−8.82683			−1.76537			−0.882683	+	0.469969i	$0.844265\pi$
$6$		0			0
$7$	2.08188	−	1.51257i	0.297411	−	0.216082i	−0.429065	−	0.903274i	$-0.641157\pi$
$7$	2.08188	−	1.51257i	0.297411	−	0.216082i	0.726476	+	0.687192i	$0.241157\pi$
$8$	12.9065	+	9.37714i	1.61332	+	1.17214i
$9$		0			0
$10$	9.64768	+	29.6925i	0.964768	+	2.96925i
$11$	6.28416	+	8.64940i	0.571287	+	0.786309i	0.992706	−	0.120557i	$-0.0384680\pi$
$11$	6.28416	+	8.64940i	0.571287	+	0.786309i	−0.421419	+	0.906866i	$0.638468\pi$
$12$		0			0
$13$	−2.12141	−	0.689289i	−0.163186	−	0.0530222i	0.226285	−	0.974061i	$-0.427342\pi$
$13$	−2.12141	−	0.689289i	−0.163186	−	0.0530222i	−0.389470	+	0.921039i	$0.627342\pi$
$14$	−7.36362	−	5.34998i	−0.525973	−	0.382142i
$15$		0			0
$16$	6.91748	−	21.2898i	0.432342	−	1.33061i
$17$	0.840800	−	1.15726i	0.0494588	−	0.0680743i	−0.783571	−	0.621302i	$-0.786604\pi$
$17$	0.840800	−	1.15726i	0.0494588	−	0.0680743i	0.833030	+	0.553228i	$0.186604\pi$
$18$		0			0
$19$	−2.52727	−	7.77815i	−0.133014	−	0.409376i	0.862262	−	0.506463i	$-0.169047\pi$
$19$	−2.52727	−	7.77815i	−0.133014	−	0.409376i	−0.995276	+	0.0970872i	$0.969047\pi$
$20$	60.7733	−	44.1544i	3.03866	−	2.20772i
$21$		0			0
$22$	22.2271	−	30.5930i	1.01032	−	1.39059i
$23$	1.14986	−	1.58264i	0.0499938	−	0.0688106i	−0.783288	−	0.621659i	$-0.786459\pi$
$23$	1.14986	−	1.58264i	0.0499938	−	0.0688106i	0.833282	+	0.552848i	$0.186459\pi$
$24$		0			0
$25$	52.9129			2.11652
$26$			7.88959i			0.303446i
$27$		0			0
$28$	−6.76754	+	20.8283i	−0.241698	+	0.743869i
$29$	26.7713	−	8.69853i	0.923149	−	0.299949i	0.191391	−	0.981514i	$-0.438700\pi$
$29$	26.7713	−	8.69853i	0.923149	−	0.299949i	0.731758	+	0.681565i	$0.238700\pi$
$30$		0			0
$31$	−21.3083	+	22.5157i	−0.687364	+	0.726313i
$31$	−21.3083	+	22.5157i	−0.687364	+	0.726313i
$32$	−15.3640			−0.480125
$33$		0			0
$34$	−4.81190	−	1.56348i	−0.141526	−	0.0459847i
$35$	−18.3764	+	13.3512i	−0.525040	+	0.381464i
$36$		0			0
$37$			6.07061i			0.164071i	0.996629	+	0.0820353i	$0.0261420\pi$
$37$			6.07061i			0.164071i	−0.996629	+	0.0820353i	$0.973858\pi$
$38$	−23.4025	+	17.0029i	−0.615857	+	0.447446i
$39$		0			0
$40$	−113.924	−	82.7704i	−2.84809	−	2.06926i
$41$	20.7157	+	63.7563i	0.505260	+	1.55503i	0.800333	+	0.599556i	$0.204656\pi$
$41$	20.7157	+	63.7563i	0.505260	+	1.55503i	−0.295072	+	0.955475i	$0.595344\pi$
$42$		0			0
$43$	55.9522	−	18.1800i	1.30121	−	0.422790i	0.425210	−	0.905095i	$-0.360200\pi$
$43$	55.9522	−	18.1800i	1.30121	−	0.422790i	0.876004	+	0.482304i	$0.160200\pi$
$44$	−86.5337	−	28.1165i	−1.96667	−	0.639011i
$45$		0			0
$46$	−6.58063	−	2.13818i	−0.143057	−	0.0464821i
$47$	11.9110	−	36.6584i	0.253426	−	0.779967i	−0.740709	−	0.671826i	$-0.765510\pi$
$47$	11.9110	−	36.6584i	0.253426	−	0.779967i	0.994136	−	0.108141i	$-0.0344897\pi$
$48$		0			0
$49$	−13.0955	+	40.3038i	−0.267255	+	0.822526i
$50$	−57.8335	−	177.993i	−1.15667	−	3.55987i
$51$		0			0
$52$	18.0541	−	5.86613i	0.347194	−	0.112810i
$53$	−45.0108	+	61.9521i	−0.849261	+	1.16891i	0.134764	+	0.990878i	$0.456972\pi$
$53$	−45.0108	+	61.9521i	−0.849261	+	1.16891i	−0.984025	+	0.178030i	$0.943028\pi$
$54$		0			0
$55$	−55.4692	−	76.3468i	−1.00853	−	1.38812i
$56$	41.0534			0.733097
$57$		0			0
$58$	−58.5218	−	80.5484i	−1.00900	−	1.38877i
$59$	7.78185	−	23.9501i	0.131896	−	0.405933i	−0.863199	−	0.504865i	$-0.831542\pi$
$59$	7.78185	−	23.9501i	0.131896	−	0.405933i	0.995094	+	0.0989313i	$0.0315424\pi$
$60$		0			0
$61$			87.4422i			1.43348i	0.697342	+	0.716739i	$0.254366\pi$
$61$			87.4422i			1.43348i	−0.697342	+	0.716739i	$0.745634\pi$
$62$	99.0302	+	47.0692i	1.59726	+	0.759181i
$63$		0			0
$64$	−10.8771	−	33.4763i	−0.169955	−	0.523068i
$65$	18.7253	+	6.08423i	0.288082	+	0.0936036i
$66$		0			0
$67$	31.7457			0.473816			0.236908	−	0.971532i	$-0.423866\pi$
$67$	31.7457			0.473816			0.236908	+	0.971532i	$0.423866\pi$
$68$			12.1738i			0.179026i
$69$		0			0
$70$	64.9974	+	47.2234i	0.928534	+	0.674620i
$71$	51.7571	+	37.6037i	0.728973	+	0.529630i	0.889238	−	0.457444i	$-0.151235\pi$
$71$	51.7571	+	37.6037i	0.728973	+	0.529630i	−0.160265	+	0.987074i	$0.551235\pi$
$72$		0			0
$73$	42.4801	+	58.4689i	0.581920	+	0.800944i	0.993904	−	0.110247i	$-0.0351642\pi$
$73$	42.4801	+	58.4689i	0.581920	+	0.800944i	−0.411985	+	0.911191i	$0.635164\pi$
$74$	20.4209	−	6.63515i	0.275958	−	0.0896642i
$75$		0			0
$76$	56.3090	+	40.9109i	0.740908	+	0.538301i
$77$	26.1657	+	8.50176i	0.339814	+	0.110412i
$78$		0			0
$79$	−54.8015	+	75.4277i	−0.693689	+	0.954781i	0.306307	+	0.951933i	$0.400907\pi$
$79$	−54.8015	+	75.4277i	−0.693689	+	0.954781i	−0.999996	+	0.00284853i	$0.999093\pi$
$80$	−61.0594	+	187.921i	−0.763242	+	2.34902i
$81$		0			0
$82$	191.827	−	139.371i	2.33936	−	1.69964i
$83$	−85.7251	+	27.8538i	−1.03283	+	0.335588i	−0.775909	−	0.630844i	$-0.782709\pi$
$83$	−85.7251	+	27.8538i	−1.03283	+	0.335588i	−0.256923	+	0.966432i	$0.582709\pi$
$84$		0			0
$85$	−7.42160	+	10.2150i	−0.0873130	+	0.120176i
$86$	−122.311	−	168.347i	−1.42222	−	1.95752i
$87$		0			0
$88$			170.561i			1.93819i
$89$	35.3705	+	48.6833i	0.397421	+	0.547003i	0.960094	−	0.279676i	$-0.0902271\pi$
$89$	35.3705	+	48.6833i	0.397421	+	0.547003i	−0.562673	+	0.826679i	$0.690227\pi$
$90$		0			0
$91$	−5.45912	+	1.77378i	−0.0599904	+	0.0194921i
$92$			16.6485i			0.180962i
$93$		0			0
$94$	−136.334			−1.45036
$95$	22.3078	+	68.6564i	0.234819	+	0.722699i
$96$		0			0
$97$	−10.3369	+	7.51019i	−0.106566	+	0.0774246i	−0.639792	−	0.768548i	$-0.720979\pi$
$97$	−10.3369	+	7.51019i	−0.106566	+	0.0774246i	0.533226	+	0.845973i	$0.320979\pi$
$98$	149.891			1.52950
$99$		0			0
$100$	−364.309	+	264.686i	−3.64309	+	2.64686i
$101$	−91.2036	−	66.2633i	−0.903005	−	0.656072i	0.0362307	−	0.999343i	$-0.488465\pi$
$101$	−91.2036	−	66.2633i	−0.903005	−	0.656072i	−0.939236	+	0.343272i	$0.888465\pi$
$102$		0			0
$103$	21.6220	+	66.5456i	0.209922	+	0.646074i	0.999475	+	0.0323918i	$0.0103124\pi$
$103$	21.6220	+	66.5456i	0.209922	+	0.646074i	−0.789553	+	0.613682i	$0.789688\pi$
$104$	−20.9165	−	28.7891i	−0.201120	−	0.276818i
$105$		0			0
$106$	257.597	+	83.6983i	2.43016	+	0.789606i
$107$	22.8705	+	16.6164i	0.213743	+	0.155294i	0.689506	−	0.724280i	$-0.257828\pi$
$107$	22.8705	+	16.6164i	0.213743	+	0.155294i	−0.475762	+	0.879574i	$0.657828\pi$
$108$		0			0
$109$	41.1765	−	126.728i	0.377766	−	1.16264i	−0.563828	−	0.825892i	$-0.690672\pi$
$109$	41.1765	−	126.728i	0.377766	−	1.16264i	0.941594	−	0.336751i	$-0.109328\pi$
$110$	−196.195	+	270.039i	−1.78359	+	2.45490i
$111$		0			0
$112$	−17.8011	−	54.7860i	−0.158938	−	0.489161i
$113$	96.5883	−	70.1755i	0.854764	−	0.621022i	−0.0716917	−	0.997427i	$-0.522840\pi$
$113$	96.5883	−	70.1755i	0.854764	−	0.621022i	0.926455	+	0.376405i	$0.122840\pi$
$114$		0			0
$115$	−10.1496	+	13.9697i	−0.0882573	+	0.121476i
$116$	−140.810	+	193.808i	−1.21388	+	1.67076i
$117$		0			0
$118$	−89.0710			−0.754839
$119$		−	3.68105i		−	0.0309332i
$120$		0			0
$121$	2.06956	−	6.36944i	0.0171038	−	0.0526400i
$122$	294.146	−	95.5738i	2.41103	−	0.783392i
$123$		0			0
$124$	34.0788	−	261.612i	0.274829	−	2.10978i
$125$	−246.382			−1.97106
$126$		0			0
$127$	63.5833	+	20.6595i	0.500656	+	0.162673i	0.548449	−	0.836184i	$-0.315219\pi$
$127$	63.5833	+	20.6595i	0.500656	+	0.162673i	−0.0477924	+	0.998857i	$0.515219\pi$
$128$	−150.441	+	109.302i	−1.17532	+	0.853921i
$129$		0			0
$130$		−	69.6401i		−	0.535693i
$131$	−172.109	+	125.044i	−1.31381	+	0.954536i	−0.313819	+	0.949483i	$0.601609\pi$
$131$	−172.109	+	125.044i	−1.31381	+	0.954536i	−0.999987	+	0.00505353i	$0.998391\pi$
$132$		0			0
$133$	−17.0265	−	12.3705i	−0.128019	−	0.0930111i
$134$	−34.6979	−	106.789i	−0.258939	−	0.796933i
$135$		0			0
$136$	21.7036	−	7.05193i	0.159585	−	0.0518525i
$137$	146.518	+	47.6066i	1.06948	+	0.347494i	0.790283	−	0.612741i	$-0.209933\pi$
$137$	146.518	+	47.6066i	1.06948	+	0.347494i	0.279192	+	0.960235i	$0.409933\pi$
$138$		0			0
$139$	105.217	+	34.1869i	0.756953	+	0.245949i	0.661971	−	0.749530i	$-0.269720\pi$
$139$	105.217	+	34.1869i	0.756953	+	0.245949i	0.0949829	+	0.995479i	$0.469720\pi$
$140$	59.7359	−	183.848i	0.426685	−	1.31320i
$141$		0			0
$142$	69.9247	−	215.206i	0.492427	−	1.51554i
$143$	−7.36936	−	22.6805i	−0.0515340	−	0.158605i
$144$		0			0
$145$	−236.306	+	76.7804i	−1.62970	+	0.529520i
$146$	150.252	−	206.805i	1.02913	−	1.41647i
$147$		0			0
$148$	−30.3670	−	41.7966i	−0.205182	−	0.282409i
$149$	−68.8403			−0.462015			−0.231008	−	0.972952i	$-0.574202\pi$
$149$	−68.8403			−0.462015			−0.231008	+	0.972952i	$0.574202\pi$
$150$		0			0
$151$	−21.7773	−	29.9739i	−0.144220	−	0.198502i	0.730796	−	0.682596i	$-0.239149\pi$
$151$	−21.7773	−	29.9739i	−0.144220	−	0.198502i	−0.875016	+	0.484094i	$0.839149\pi$
$152$	40.3184	−	124.087i	0.265253	−	0.816365i
$153$		0			0
$154$		−	97.3110i		−	0.631890i
$155$	188.085	−	198.742i	1.21345	−	1.28221i
$156$		0			0
$157$	−6.60304	−	20.3221i	−0.0420576	−	0.129440i	0.927823	−	0.373021i	$-0.121678\pi$
$157$	−6.60304	−	20.3221i	−0.0420576	−	0.129440i	−0.969881	+	0.243581i	$0.921678\pi$
$158$	313.628	+	101.904i	1.98499	+	0.644962i
$159$		0			0
$160$	135.615			0.847597
$161$		−	5.03412i		−	0.0312678i
$162$		0			0
$163$	−52.1576	−	37.8947i	−0.319985	−	0.232483i	0.416184	−	0.909280i	$-0.363367\pi$
$163$	−52.1576	−	37.8947i	−0.319985	−	0.232483i	−0.736169	+	0.676797i	$0.763367\pi$
$164$	−461.556	−	335.340i	−2.81437	−	2.04476i
$165$		0			0
$166$	187.394	+	257.926i	1.12888	+	1.55377i
$167$	62.8998	−	20.4374i	0.376646	−	0.122380i	−0.114575	−	0.993415i	$-0.536551\pi$
$167$	62.8998	−	20.4374i	0.376646	−	0.122380i	0.491221	+	0.871035i	$0.336551\pi$
$168$		0			0
$169$	−132.699	−	96.4112i	−0.785199	−	0.570480i
$170$	42.4738	+	13.8006i	0.249846	+	0.0811798i
$171$		0			0
$172$	−294.293	+	405.060i	−1.71101	+	2.35500i
$173$	26.0370	−	80.1335i	0.150503	−	0.463200i	−0.847175	−	0.531314i	$-0.821698\pi$
$173$	26.0370	−	80.1335i	0.150503	−	0.463200i	0.997678	+	0.0681146i	$0.0216984\pi$
$174$		0			0
$175$	110.158	−	80.0347i	0.629476	−	0.457341i
$176$	227.615	−	73.9565i	1.29326	−	0.420207i
$177$		0			0
$178$	125.106	−	172.193i	0.702841	−	0.967377i
$179$	−33.5421	−	46.1667i	−0.187386	−	0.257915i	0.704980	−	0.709227i	$-0.250956\pi$
$179$	−33.5421	−	46.1667i	−0.187386	−	0.257915i	−0.892366	+	0.451313i	$0.850956\pi$
$180$		0			0
$181$		−	133.782i		−	0.739127i	−0.929206	−	0.369563i	$-0.879507\pi$
$181$		−	133.782i		−	0.739127i	0.929206	−	0.369563i	$-0.120493\pi$
$182$	11.9336	+	16.4252i	0.0655692	+	0.0902482i
$183$		0			0
$184$	29.6813	−	9.64405i	0.161312	−	0.0524133i
$185$		−	53.5843i		−	0.289645i
$186$		0			0
$187$	15.2933			0.0817826
$188$	101.368	+	311.978i	0.539191	+	1.65946i
$189$		0			0
$190$	206.570	−	150.082i	1.08721	−	0.789906i
$191$	−144.839			−0.758319			−0.379159	−	0.925331i	$-0.623787\pi$
$191$	−144.839			−0.758319			−0.379159	+	0.925331i	$0.623787\pi$
$192$		0			0
$193$	−20.2680	+	14.7256i	−0.105016	+	0.0762984i	−0.639054	−	0.769162i	$-0.720674\pi$
$193$	−20.2680	+	14.7256i	−0.105016	+	0.0762984i	0.534038	+	0.845460i	$0.320674\pi$
$194$	36.5616	+	26.5636i	0.188462	+	0.136926i
$195$		0			0
$196$	−111.448	−	343.002i	−0.568612	−	1.75001i
$197$	80.4506	+	110.731i	0.408379	+	0.562085i	0.962822	−	0.270136i	$-0.0870688\pi$
$197$	80.4506	+	110.731i	0.408379	+	0.562085i	−0.554443	+	0.832221i	$0.687069\pi$
$198$		0			0
$199$	48.4061	+	15.7281i	0.243247	+	0.0790357i	0.428103	−	0.903730i	$-0.359182\pi$
$199$	48.4061	+	15.7281i	0.243247	+	0.0790357i	−0.184856	+	0.982766i	$0.559182\pi$
$200$	682.922	+	496.172i	3.41461	+	2.48086i
$201$		0			0
$202$	−123.217	+	379.224i	−0.609987	+	1.87735i
$203$	42.5775	−	58.6029i	0.209741	−	0.288684i
$204$		0			0
$205$	−182.854	−	562.766i	−0.891969	−	2.74520i
$206$	200.220	−	145.468i	0.971940	−	0.706156i
$207$		0			0
$208$	−29.3496	+	40.3963i	−0.141104	+	0.194213i
$209$	51.3945	−	70.7385i	0.245907	−	0.338462i
$210$		0			0
$211$	−64.2302			−0.304409			−0.152204	−	0.988349i	$-0.548637\pi$
$211$	−64.2302			−0.304409			−0.152204	+	0.988349i	$0.548637\pi$
$212$		−	651.702i		−	3.07406i
$213$		0			0
$214$	30.8984	−	95.0957i	0.144385	−	0.444372i
$215$	−493.881	+	160.472i	−2.29712	+	0.746379i
$216$		0			0
$217$	−10.3046	+	79.1053i	−0.0474867	+	0.364541i
$218$	−471.305			−2.16195
$219$		0			0
$220$	763.818	+	248.179i	3.47190	+	1.12809i
$221$	−2.58137	+	1.87548i	−0.0116804	+	0.00848632i
$222$		0			0
$223$			239.452i			1.07377i	0.843654	+	0.536887i	$0.180400\pi$
$223$			239.452i			1.07377i	−0.843654	+	0.536887i	$0.819600\pi$
$224$	−31.9860	+	23.2392i	−0.142795	+	0.103746i
$225$		0			0
$226$	−341.633	−	248.211i	−1.51165	−	1.09828i
$227$	−73.4319	−	226.000i	−0.323489	−	0.995595i	−0.972118	−	0.234491i	$-0.924658\pi$
$227$	−73.4319	−	226.000i	−0.323489	−	0.995595i	0.648630	−	0.761104i	$-0.275342\pi$
$228$		0			0
$229$	−349.938	+	113.702i	−1.52811	+	0.496514i	−0.948067	−	0.318070i	$-0.896965\pi$
$229$	−349.938	+	113.702i	−1.52811	+	0.496514i	−0.580046	+	0.814584i	$0.696965\pi$
$230$	58.0861	+	18.8733i	0.252548	+	0.0820579i
$231$		0			0
$232$	427.092	+	138.771i	1.84091	+	0.598149i
$233$	−74.6446	+	229.733i	−0.320363	+	0.985977i	0.653127	+	0.757248i	$0.273457\pi$
$233$	−74.6446	+	229.733i	−0.320363	+	0.985977i	−0.973490	+	0.228728i	$0.926543\pi$
$234$		0			0
$235$	−105.137	+	323.578i	−0.447390	+	1.37693i
$236$	66.2267	+	203.825i	0.280622	+	0.863665i
$237$		0			0
$238$	−12.3827	+	4.02337i	−0.0520280	+	0.0169049i
$239$	−261.838	+	360.389i	−1.09556	+	1.50790i	−0.254408	+	0.967097i	$0.581881\pi$
$239$	−261.838	+	360.389i	−1.09556	+	1.50790i	−0.841148	+	0.540806i	$0.818119\pi$
$240$		0			0
$241$	−1.21971	−	1.67879i	−0.00506105	−	0.00696594i	0.806479	−	0.591263i	$-0.201370\pi$
$241$	−1.21971	−	1.67879i	−0.00506105	−	0.00696594i	−0.811540	+	0.584297i	$0.801370\pi$
$242$	−23.6881			−0.0978848
$243$		0			0
$244$	−437.411	−	602.045i	−1.79267	−	2.46740i
$245$	115.592	−	355.755i	0.471803	−	1.45206i
$246$		0			0
$247$			18.2427i			0.0738570i
$248$	−486.149	+	90.7887i	−1.96028	+	0.366083i
$249$		0			0
$250$	269.295	+	828.804i	1.07718	+	3.31522i
$251$	433.842	+	140.964i	1.72846	+	0.561609i	0.993225	−	0.116208i	$-0.0370738\pi$
$251$	433.842	+	140.964i	1.72846	+	0.561609i	0.735231	+	0.677817i	$0.237074\pi$
$252$		0			0
$253$	20.9148			0.0826672
$254$		−	236.468i		−	0.930977i
$255$		0			0
$256$	418.205	+	303.843i	1.63361	+	1.18689i
$257$	210.122	+	152.663i	0.817596	+	0.594018i	0.916023	−	0.401126i	$-0.131381\pi$
$257$	210.122	+	152.663i	0.817596	+	0.594018i	−0.0984272	+	0.995144i	$0.531381\pi$
$258$		0			0
$259$	9.18225	+	12.6383i	0.0354527	+	0.0487965i
$260$	−159.360	+	51.7793i	−0.612924	+	0.199151i
$261$		0			0
$262$	608.749	+	442.282i	2.32347	+	1.68810i
$263$	238.181	+	77.3895i	0.905629	+	0.294257i	0.724559	−	0.689213i	$-0.242044\pi$
$263$	238.181	+	77.3895i	0.905629	+	0.294257i	0.181071	+	0.983470i	$0.442044\pi$
$264$		0			0
$265$	397.303	−	546.841i	1.49926	−	2.06355i
$266$	−23.0031	+	70.7962i	−0.0864777	+	0.266151i
$267$		0			0
$268$	−218.571	+	158.801i	−0.815564	+	0.592542i
$269$	−105.828	+	34.3857i	−0.393413	+	0.127828i	−0.499042	−	0.866578i	$-0.666315\pi$
$269$	−105.828	+	34.3857i	−0.393413	+	0.127828i	0.105628	+	0.994406i	$0.466315\pi$
$270$		0			0
$271$	−23.5512	+	32.4155i	−0.0869049	+	0.119614i	−0.850256	−	0.526370i	$-0.823553\pi$
$271$	−23.5512	+	32.4155i	−0.0869049	+	0.119614i	0.763351	+	0.645984i	$0.223553\pi$
$272$	−18.8217	−	25.9058i	−0.0691973	−	0.0952420i
$273$		0			0
$274$		−	544.905i		−	1.98871i
$275$	332.513	+	457.665i	1.20914	+	1.66424i
$276$		0			0
$277$	−93.4930	+	30.3777i	−0.337520	+	0.109667i	−0.472873	−	0.881131i	$-0.656783\pi$
$277$	−93.4930	+	30.3777i	−0.337520	+	0.109667i	0.135353	+	0.990797i	$0.456783\pi$
$278$		−	391.303i		−	1.40757i
$279$		0			0
$280$	−362.372			−1.29418
$281$	−71.5798	−	220.300i	−0.254733	−	0.783986i	−0.993882	−	0.110445i	$-0.964772\pi$
$281$	−71.5798	−	220.300i	−0.254733	−	0.783986i	0.739150	−	0.673541i	$-0.235228\pi$
$282$		0			0
$283$	−56.8697	+	41.3182i	−0.200953	+	0.146001i	−0.683711	−	0.729753i	$-0.739635\pi$
$283$	−56.8697	+	41.3182i	−0.200953	+	0.146001i	0.482758	+	0.875754i	$0.339635\pi$
$284$	−544.456			−1.91710
$285$		0			0
$286$	−68.2402	+	49.5794i	−0.238602	+	0.173355i
$287$	139.564	+	101.399i	0.486284	+	0.353306i
$288$		0			0
$289$	88.6736	+	272.909i	0.306829	+	0.944323i
$290$	516.562	+	710.987i	1.78125	+	2.45168i
$291$		0			0
$292$	−584.957	−	190.064i	−2.00328	−	0.650904i
$293$	−349.682	−	254.059i	−1.19345	−	0.867095i	−0.199829	−	0.979831i	$-0.564039\pi$
$293$	−349.682	−	254.059i	−1.19345	−	0.867095i	−0.993625	+	0.112735i	$0.964039\pi$
$294$		0			0
$295$	−68.6890	+	211.403i	−0.232844	+	0.716621i
$296$	−56.9250	+	78.3505i	−0.192314	+	0.264698i
$297$		0			0
$298$	75.2421	+	231.571i	0.252490	+	0.777085i
$299$	−3.53022	+	2.56485i	−0.0118068	+	0.00857811i
$300$		0			0
$301$	88.9872	−	122.480i	0.295639	−	0.406911i
$302$	−77.0264	+	106.018i	−0.255054	+	0.351052i
$303$		0			0
$304$	−183.078			−0.602229
$305$		−	771.837i		−	2.53061i
$306$		0			0
$307$	41.1089	−	126.520i	0.133905	−	0.412117i	−0.861513	−	0.507735i	$-0.830483\pi$
$307$	41.1089	−	126.520i	0.133905	−	0.412117i	0.995418	+	0.0956180i	$0.0304827\pi$
$308$	−222.681	+	72.3534i	−0.722990	+	0.234914i
$309$		0			0
$310$	−874.123	−	415.472i	−2.81975	−	1.34023i
$311$	498.250			1.60209			0.801045	−	0.598604i	$-0.204278\pi$
$311$	498.250			1.60209			0.801045	+	0.598604i	$0.204278\pi$
$312$		0			0
$313$	573.864	+	186.460i	1.83343	+	0.595718i	0.999005	+	0.0445979i	$0.0142007\pi$
$313$	573.864	+	186.460i	1.83343	+	0.595718i	0.834426	+	0.551120i	$0.185799\pi$
$314$	−61.1442	+	44.4238i	−0.194727	+	0.141477i
$315$		0			0
$316$		−	793.458i		−	2.51094i
$317$	88.4313	−	64.2491i	0.278963	−	0.202678i	−0.439502	−	0.898242i	$-0.644845\pi$
$317$	88.4313	−	64.2491i	0.278963	−	0.202678i	0.718465	+	0.695563i	$0.244845\pi$
$318$		0			0
$319$	243.472	+	176.893i	0.763236	+	0.554523i
$320$	96.0105	+	295.490i	0.300033	+	0.923406i
$321$		0			0
$322$	−16.9342	+	5.50226i	−0.0525908	+	0.0170878i
$323$	−11.1263	−	3.61515i	−0.0344467	−	0.0111924i
$324$		0			0
$325$	−112.250	−	36.4723i	−0.345385	−	0.112222i
$326$	−70.4658	+	216.871i	−0.216153	+	0.665250i
$327$		0			0
$328$	−330.484	+	1017.13i	−1.00757	+	3.10099i
$329$	−30.6512	−	94.3348i	−0.0931648	−	0.286732i
$330$		0			0
$331$	140.683	−	45.7106i	0.425024	−	0.138099i	−0.0886918	−	0.996059i	$-0.528269\pi$
$331$	140.683	−	45.7106i	0.425024	−	0.138099i	0.513716	+	0.857961i	$0.328269\pi$
$332$	450.890	−	620.597i	1.35810	−	1.86927i
$333$		0			0
$334$	−137.498	−	189.250i	−0.411672	−	0.566618i
$335$	−280.214			−0.836459
$336$		0			0
$337$	30.8900	+	42.5164i	0.0916617	+	0.126161i	0.852385	−	0.522915i	$-0.175155\pi$
$337$	30.8900	+	42.5164i	0.0916617	+	0.126161i	−0.760723	+	0.649077i	$0.775155\pi$
$338$	−179.278	+	551.761i	−0.530408	+	1.63243i
$339$		0			0
$340$		−	107.456i		−	0.316046i
$341$	−328.652	−	42.8117i	−0.963789	−	0.125548i
$342$		0			0
$343$	72.6644	+	223.638i	0.211849	+	0.652006i
$344$	892.625	+	290.031i	2.59484	+	0.843114i
$345$		0			0
$346$	−298.019			−0.861326
$347$			541.910i			1.56170i	0.624718	+	0.780851i	$0.285214\pi$
$347$			541.910i			1.56170i	−0.624718	+	0.780851i	$0.714786\pi$
$348$		0			0
$349$	247.884	+	180.098i	0.710269	+	0.516041i	0.883261	−	0.468882i	$-0.155343\pi$
$349$	247.884	+	180.098i	0.710269	+	0.516041i	−0.172991	+	0.984923i	$0.555343\pi$
$350$	−389.630	−	283.083i	−1.11323	−	0.808809i
$351$		0			0
$352$	−96.5499	−	132.889i	−0.274289	−	0.377527i
$353$	−502.795	+	163.368i	−1.42435	+	0.462799i	−0.916981	−	0.398931i	$-0.869381\pi$
$353$	−502.795	+	163.368i	−1.42435	+	0.462799i	−0.507368	+	0.861730i	$0.669381\pi$
$354$		0			0
$355$	−456.851	−	331.922i	−1.28690	−	0.934991i
$356$	−487.056	−	158.254i	−1.36814	−	0.444534i
$357$		0			0
$358$	−118.639	+	163.292i	−0.331393	+	0.456123i
$359$	166.648	−	512.890i	0.464201	−	1.42866i	−0.395784	−	0.918344i	$-0.629527\pi$
$359$	166.648	−	512.890i	0.464201	−	1.42866i	0.859985	−	0.510320i	$-0.170473\pi$
$360$		0			0
$361$	237.943	−	172.875i	0.659121	−	0.478879i
$362$	−450.028	+	146.223i	−1.24317	+	0.403931i
$363$		0			0
$364$	28.7135	−	39.5207i	0.0788832	−	0.108573i
$365$	−374.965	−	516.095i	−1.02730	−	1.41396i
$366$		0			0
$367$		−	441.199i		−	1.20218i	−0.799182	−	0.601089i	$-0.794734\pi$
$367$		−	441.199i		−	1.20218i	0.799182	−	0.601089i	$-0.205266\pi$
$368$	−25.7401	−	35.4281i	−0.0699458	−	0.0962721i
$369$		0			0
$370$	−180.252	+	58.5673i	−0.487167	+	0.158290i
$371$			197.059i			0.531156i
$372$		0			0
$373$	81.3830			0.218185			0.109093	−	0.994032i	$-0.465206\pi$
$373$	81.3830			0.218185			0.109093	+	0.994032i	$0.465206\pi$
$374$	−16.7156	−	51.4452i	−0.0446940	−	0.137554i
$375$		0			0
$376$	497.481	−	361.441i	1.32309	−	0.961280i
$377$	−62.7888			−0.166549
$378$		0			0
$379$	−28.1638	+	20.4622i	−0.0743108	+	0.0539900i	−0.624320	−	0.781168i	$-0.714624\pi$
$379$	−28.1638	+	20.4622i	−0.0743108	+	0.0539900i	0.550010	+	0.835158i	$0.314624\pi$
$380$	−497.030	−	361.113i	−1.30797	−	0.950298i
$381$		0			0
$382$	158.308	+	487.223i	0.414419	+	1.27545i
$383$	106.036	+	145.946i	0.276857	+	0.381061i	0.924690	−	0.380722i	$-0.124324\pi$
$383$	106.036	+	145.946i	0.276857	+	0.381061i	−0.647833	+	0.761783i	$0.724324\pi$
$384$		0			0
$385$	−230.960	−	75.0435i	−0.599897	−	0.194918i
$386$	71.6882	+	52.0845i	0.185721	+	0.134934i
$387$		0			0
$388$	33.6020	−	103.416i	0.0866031	−	0.266537i
$389$	67.2257	−	92.5282i	0.172817	−	0.237862i	−0.713819	−	0.700330i	$-0.753036\pi$
$389$	67.2257	−	92.5282i	0.172817	−	0.237862i	0.886636	+	0.462468i	$0.153036\pi$
$390$		0			0
$391$	−0.864733	−	2.66137i	−0.00221159	−	0.00680658i
$392$	−546.951	+	397.383i	−1.39528	+	1.01373i
$393$		0			0
$394$	284.554	−	391.655i	0.722219	−	0.994049i
$395$	483.723	−	665.788i	1.22462	−	1.68554i
$396$		0			0
$397$	−410.101			−1.03300			−0.516500	−	0.856287i	$-0.672765\pi$
$397$	−410.101			−1.03300			−0.516500	+	0.856287i	$0.672765\pi$
$398$		−	180.024i		−	0.452321i
$399$		0			0
$400$	366.024	−	1126.51i	0.915059	−	2.81626i
$401$	652.806	−	212.109i	1.62794	−	0.528951i	0.654147	−	0.756368i	$-0.273028\pi$
$401$	652.806	−	212.109i	1.62794	−	0.528951i	0.973798	+	0.227416i	$0.0730278\pi$
$402$		0			0
$403$	60.7235	−	33.0775i	0.150679	−	0.0820782i
$404$	959.411			2.37478
$405$		0			0
$406$	−243.671	−	79.1734i	−0.600174	−	0.195008i
$407$	−52.5072	+	38.1487i	−0.129010	+	0.0937314i
$408$		0			0
$409$		−	613.235i		−	1.49935i	−0.661804	−	0.749677i	$-0.730209\pi$
$409$		−	613.235i		−	1.49935i	0.661804	−	0.749677i	$-0.269791\pi$
$410$	−1693.23	+	1230.20i	−4.12982	+	3.00049i
$411$		0			0
$412$	−481.750	−	350.012i	−1.16930	−	0.849543i
$413$	−20.0254	−	61.6318i	−0.0484876	−	0.149229i
$414$		0			0
$415$	756.681	−	245.860i	1.82333	−	0.592435i
$416$	32.5934	+	10.5902i	0.0783495	+	0.0254573i
$417$		0			0
$418$	−294.131	−	95.5688i	−0.703662	−	0.228634i
$419$	−95.8862	+	295.107i	−0.228845	+	0.704314i	0.769033	+	0.639209i	$0.220738\pi$
$419$	−95.8862	+	295.107i	−0.228845	+	0.704314i	−0.997878	+	0.0651046i	$0.979262\pi$
$420$		0			0
$421$	5.71156	−	17.5784i	0.0135666	−	0.0417538i	−0.944044	−	0.329819i	$-0.893012\pi$
$421$	5.71156	−	17.5784i	0.0135666	−	0.0417538i	0.957611	+	0.288066i	$0.0930121\pi$
$422$	70.2033	+	216.064i	0.166359	+	0.511999i
$423$		0			0
$424$	−1161.87	+	377.513i	−2.74025	+	0.890362i
$425$	44.4892	−	61.2341i	0.104680	−	0.144080i
$426$		0			0
$427$	132.263	+	182.044i	0.309749	+	0.426333i
$428$	−240.585			−0.562115
$429$		0			0
$430$	1079.62	+	1485.97i	2.51074	+	3.45574i
$431$	−25.9029	+	79.7209i	−0.0600995	+	0.184967i	−0.976599	−	0.215069i	$-0.931002\pi$
$431$	−25.9029	+	79.7209i	−0.0600995	+	0.184967i	0.916499	+	0.400036i	$0.131002\pi$
$432$		0			0
$433$			608.121i			1.40444i	0.711962	+	0.702218i	$0.247807\pi$
$433$			608.121i			1.40444i	−0.711962	+	0.702218i	$0.752193\pi$
$434$	277.365	−	51.7981i	0.639089	−	0.119350i
$435$		0			0
$436$	350.429	+	1078.51i	0.803735	+	2.47364i
$437$	−15.2160	−	4.94399i	−0.0348193	−	0.0113135i
$438$		0			0
$439$	433.644			0.987800			0.493900	−	0.869519i	$-0.335571\pi$
$439$	433.644			0.987800			0.493900	+	0.869519i	$0.335571\pi$
$440$		−	1505.51i		−	3.42162i
$441$		0			0
$442$	9.13033	+	6.63357i	0.0206569	+	0.0150081i
$443$	196.016	+	142.414i	0.442473	+	0.321476i	0.786617	−	0.617441i	$-0.211831\pi$
$443$	196.016	+	142.414i	0.442473	+	0.321476i	−0.344144	+	0.938917i	$0.611831\pi$
$444$		0			0
$445$	−312.209	−	429.719i	−0.701594	−	0.965661i
$446$	805.490	−	261.719i	1.80603	−	0.586815i
$447$		0			0
$448$	−73.2803	−	53.2413i	−0.163572	−	0.118842i
$449$	443.545	+	144.117i	0.987851	+	0.320972i	0.758001	−	0.652254i	$-0.226176\pi$
$449$	443.545	+	144.117i	0.987851	+	0.320972i	0.229850	+	0.973226i	$0.426176\pi$
$450$		0			0
$451$	−421.273	+	579.833i	−0.934087	+	1.28566i
$452$	−313.978	+	966.326i	−0.694642	+	2.13789i
$453$		0			0
$454$	−679.979	+	494.034i	−1.49775	+	1.08818i
$455$	48.1868	−	15.6568i	0.105905	−	0.0344106i
$456$		0			0
$457$	−199.560	+	274.671i	−0.436675	+	0.601031i	−0.969469	−	0.245214i	$-0.921142\pi$
$457$	−199.560	+	274.671i	−0.436675	+	0.601031i	0.532794	+	0.846245i	$0.321142\pi$
$458$	764.961	+	1052.88i	1.67022	+	2.29886i
$459$		0			0
$460$		−	146.954i		−	0.319465i
$461$	−248.643	−	342.228i	−0.539356	−	0.742359i	0.449164	−	0.893449i	$-0.351722\pi$
$461$	−248.643	−	342.228i	−0.539356	−	0.742359i	−0.988520	+	0.151090i	$0.951722\pi$
$462$		0			0
$463$	340.867	−	110.754i	0.736214	−	0.239210i	0.0831752	−	0.996535i	$-0.473494\pi$
$463$	340.867	−	110.754i	0.736214	−	0.239210i	0.653039	+	0.757325i	$0.273494\pi$
$464$		−	630.128i		−	1.35803i
$465$		0			0
$466$	854.382			1.83344
$467$	45.2667	+	139.317i	0.0969309	+	0.298323i	0.987752	−	0.156031i	$-0.0498701\pi$
$467$	45.2667	+	139.317i	0.0969309	+	0.298323i	−0.890821	+	0.454354i	$0.849870\pi$
$468$		0			0
$469$	66.0907	−	48.0177i	0.140918	−	0.102383i
$470$	1203.39			2.56041
$471$		0			0
$472$	325.020	−	236.141i	0.688601	−	0.500298i
$473$	508.858	+	369.707i	1.07581	+	0.781622i
$474$		0			0
$475$	−133.725	−	411.564i	−0.281527	−	0.866451i
$476$	18.4137	+	25.3443i	0.0386843	+	0.0532443i
$477$		0			0
$478$	1498.50	+	486.891i	3.13493	+	1.01860i
$479$	50.3660	+	36.5931i	0.105148	+	0.0763947i	0.639117	−	0.769110i	$-0.279300\pi$
$479$	50.3660	+	36.5931i	0.105148	+	0.0763947i	−0.533969	+	0.845504i	$0.679300\pi$
$480$		0			0
$481$	4.18441	−	12.8783i	0.00869939	−	0.0267740i
$482$	−4.31413	+	5.93789i	−0.00895048	+	0.0123193i
$483$		0			0
$484$	17.6128	+	54.2065i	0.0363900	+	0.111997i
$485$	91.2419	−	66.2912i	0.188128	−	0.136683i
$486$		0			0
$487$	−568.690	+	782.734i	−1.16774	+	1.60726i	−0.490654	+	0.871355i	$0.663242\pi$
$487$	−568.690	+	782.734i	−1.16774	+	1.60726i	−0.677087	+	0.735903i	$0.736758\pi$
$488$	−819.957	+	1128.57i	−1.68024	+	2.31265i
$489$		0			0
$490$	−1323.06			−2.70012
$491$			487.811i			0.993505i	0.867892	+	0.496752i	$0.165474\pi$
$491$			487.811i			0.993505i	−0.867892	+	0.496752i	$0.834526\pi$
$492$		0			0
$493$	12.4429	−	38.2952i	0.0252391	−	0.0776778i
$494$	61.3664	−	19.9392i	0.124223	−	0.0403627i
$495$		0			0
$496$	331.955	+	609.401i	0.669265	+	1.22863i
$497$	164.630			0.331248
$498$		0			0
$499$	272.058	+	88.3971i	0.545207	+	0.177149i	0.568654	−	0.822577i	$-0.307464\pi$
$499$	272.058	+	88.3971i	0.545207	+	0.177149i	−0.0234472	+	0.999725i	$0.507464\pi$
$500$	1696.36	−	1232.48i	3.39272	−	2.46495i
$501$		0			0
$502$		−	1613.47i		−	3.21409i
$503$	245.336	−	178.247i	0.487746	−	0.354368i	−0.316571	−	0.948569i	$-0.602531\pi$
$503$	245.336	−	178.247i	0.487746	−	0.354368i	0.804317	+	0.594201i	$0.202531\pi$
$504$		0			0
$505$	805.038	+	584.894i	1.59413	+	1.15821i
$506$	−22.8598	−	70.3551i	−0.0451774	−	0.139042i
$507$		0			0
$508$	−541.120	+	175.821i	−1.06520	+	0.346104i
$509$	−273.051	−	88.7196i	−0.536446	−	0.174302i	0.0282502	−	0.999601i	$-0.491006\pi$
$509$	−273.051	−	88.7196i	−0.536446	−	0.174302i	−0.564696	+	0.825299i	$0.691006\pi$
$510$		0			0
$511$	176.877	+	57.4708i	0.346139	+	0.112467i
$512$	335.147	−	1031.48i	0.654585	−	2.01460i
$513$		0			0
$514$	283.878	−	873.687i	0.552292	−	1.69978i
$515$	−190.854	−	587.387i	−0.370589	−	1.14056i
$516$		0			0
$517$	391.924	−	127.344i	0.758074	−	0.246313i
$518$	32.4777	−	44.7017i	0.0626982	−	0.0862967i
$519$		0			0
$520$	184.626	+	254.116i	0.355051	+	0.488685i
$521$	−285.592			−0.548161			−0.274081	−	0.961707i	$-0.588374\pi$
$521$	−285.592			−0.548161			−0.274081	+	0.961707i	$0.588374\pi$
$522$		0			0
$523$	−140.119	−	192.857i	−0.267914	−	0.368752i	0.653770	−	0.756693i	$-0.273186\pi$
$523$	−140.119	−	192.857i	−0.267914	−	0.368752i	−0.921684	+	0.387941i	$0.873186\pi$
$524$	559.471	−	1721.88i	1.06769	−	3.28602i
$525$		0			0
$526$		−	885.800i		−	1.68403i
$527$	8.14056	+	43.5905i	0.0154470	+	0.0827144i
$528$		0			0
$529$	162.287	+	499.469i	0.306781	+	0.944176i
$530$	−2273.76	−	738.790i	−4.29012	−	1.39394i
$531$		0			0
$532$	179.109			0.336672
$533$		−	149.532i		−	0.280549i
$534$		0			0
$535$	−201.874	−	146.670i	−0.377335	−	0.274150i
$536$	409.727	+	297.684i	0.764415	+	0.555380i
$537$		0			0
$538$	231.339	+	318.411i	0.429999	+	0.591843i
$539$	−430.898	+	140.007i	−0.799439	+	0.259753i
$540$		0			0
$541$	−503.228	−	365.617i	−0.930182	−	0.675817i	0.0158556	−	0.999874i	$-0.494953\pi$
$541$	−503.228	−	365.617i	−0.930182	−	0.675817i	−0.946037	+	0.324058i	$0.894953\pi$
$542$	134.784	+	43.7938i	0.248678	+	0.0808004i
$543$		0			0
$544$	−12.9181	+	17.7802i	−0.0237464	+	0.0326842i
$545$	−363.458	+	1118.61i	−0.666895	+	2.05249i
$546$		0			0
$547$	220.311	−	160.066i	0.402763	−	0.292625i	−0.367902	−	0.929864i	$-0.619924\pi$
$547$	220.311	−	160.066i	0.402763	−	0.292625i	0.770666	+	0.637240i	$0.219924\pi$
$548$	−1246.93	+	405.152i	−2.27542	+	0.739328i
$549$		0			0
$550$	1176.10	−	1618.76i	2.13836	−	2.94321i
$551$	−135.317	−	186.248i	−0.245584	−	0.338018i
$552$		0			0
$553$			239.923i			0.433857i
$554$	204.375	+	281.298i	0.368907	+	0.507757i
$555$		0			0
$556$	−895.436	+	290.945i	−1.61050	+	0.523282i
$557$		−	495.225i		−	0.889093i	−0.895756	−	0.444547i	$-0.853365\pi$
$557$		−	495.225i		−	0.889093i	0.895756	−	0.444547i	$-0.146635\pi$
$558$		0			0
$559$	−131.229			−0.234757
$560$	157.127	+	483.587i	0.280584	+	0.863548i
$561$		0			0
$562$	−662.829	+	481.574i	−1.17941	+	0.856893i
$563$	408.055			0.724786			0.362393	−	0.932025i	$-0.381960\pi$
$563$	408.055			0.724786			0.362393	+	0.932025i	$0.381960\pi$
$564$		0			0
$565$	−852.568	+	619.427i	−1.50897	+	1.09633i
$566$	201.148	+	146.143i	0.355386	+	0.258203i
$567$		0			0
$568$	315.389	+	970.667i	0.555262	+	1.70892i
$569$	−428.278	−	589.474i	−0.752685	−	1.03598i	−0.997787	−	0.0664854i	$-0.978821\pi$
$569$	−428.278	−	589.474i	−0.752685	−	1.03598i	0.245102	−	0.969497i	$-0.421179\pi$
$570$		0			0
$571$	−70.3591	−	22.8611i	−0.123221	−	0.0400369i	0.246757	−	0.969077i	$-0.420635\pi$
$571$	−70.3591	−	22.8611i	−0.123221	−	0.0400369i	−0.369978	+	0.929040i	$0.620635\pi$
$572$	164.193	+	119.293i	0.287051	+	0.208555i
$573$		0			0
$574$	188.553	−	580.305i	0.328489	−	1.01098i
$575$	60.8423	−	83.7422i	0.105813	−	0.145639i
$576$		0			0
$577$	−205.039	−	631.046i	−0.355354	−	1.09367i	−0.955804	−	0.294005i	$-0.905012\pi$
$577$	−205.039	−	631.046i	−0.355354	−	1.09367i	0.600450	−	0.799663i	$-0.294988\pi$
$578$	821.118	−	596.577i	1.42062	−	1.03214i
$579$		0			0
$580$	1242.90	−	1710.71i	2.14294	−	2.94950i
$581$	−136.338	+	187.654i	−0.234662	+	0.322984i
$582$		0			0
$583$	−818.704			−1.40429
$584$			1152.97i			1.97427i
$585$		0			0
$586$	−472.426	+	1453.98i	−0.806188	+	2.48119i
$587$	−547.895	+	178.022i	−0.933381	+	0.303274i	−0.735944	−	0.677042i	$-0.763262\pi$
$587$	−547.895	+	178.022i	−0.933381	+	0.303274i	−0.197436	+	0.980316i	$0.563262\pi$
$588$		0			0
$589$	228.982	+	108.836i	0.388764	+	0.184780i
$590$	786.214			1.33257
$591$		0			0
$592$	129.242	+	41.9933i	0.218315	+	0.0709347i
$593$	−190.989	+	138.761i	−0.322072	+	0.233999i	−0.737059	−	0.675828i	$-0.763786\pi$
$593$	−190.989	+	138.761i	−0.322072	+	0.233999i	0.414987	+	0.909827i	$0.363786\pi$
$594$		0			0
$595$			32.4920i			0.0546085i
$596$	473.970	−	344.359i	0.795251	−	0.577784i
$597$		0			0
$598$	12.4864	+	9.07191i	0.0208803	+	0.0151704i
$599$	234.612	+	722.060i	0.391672	+	1.20544i	0.931523	+	0.363682i	$0.118481\pi$
$599$	234.612	+	722.060i	0.391672	+	1.20544i	−0.539851	+	0.841761i	$0.681519\pi$
$600$		0			0
$601$	−529.221	+	171.954i	−0.880567	+	0.286114i	−0.714193	−	0.699949i	$-0.753206\pi$
$601$	−529.221	+	171.954i	−0.880567	+	0.286114i	−0.166374	+	0.986063i	$0.553206\pi$
$602$	−509.273	−	165.473i	−0.845969	−	0.274872i
$603$		0			0
$604$	299.876	+	97.4357i	0.496484	+	0.161317i
$605$	−18.2676	+	56.2220i	−0.0301944	+	0.0929289i
$606$		0			0
$607$	−61.5468	+	189.421i	−0.101395	+	0.312062i	−0.988867	−	0.148799i	$-0.952459\pi$
$607$	−61.5468	+	189.421i	−0.101395	+	0.312062i	0.887472	+	0.460861i	$0.152459\pi$
$608$	38.8290	+	119.504i	0.0638636	+	0.196552i
$609$		0			0
$610$	−2596.38	+	843.614i	−4.25635	+	1.38297i
$611$	−50.5365	+	69.5575i	−0.0827111	+	0.113842i
$612$		0			0
$613$	−558.852	−	769.194i	−0.911668	−	1.25480i	−0.966594	−	0.256312i	$-0.917492\pi$
$613$	−558.852	−	769.194i	−0.911668	−	1.25480i	0.0549264	−	0.998490i	$-0.482508\pi$
$614$	−470.532			−0.766338
$615$		0			0
$616$	257.986	+	355.088i	0.418809	+	0.576441i
$617$	76.8309	−	236.461i	0.124523	−	0.383244i	−0.869291	−	0.494301i	$-0.835424\pi$
$617$	76.8309	−	236.461i	0.124523	−	0.383244i	0.993814	+	0.111058i	$0.0354239\pi$
$618$		0			0
$619$			45.3246i			0.0732223i	0.999330	+	0.0366112i	$0.0116563\pi$
$619$			45.3246i			0.0732223i	−0.999330	+	0.0366112i	$0.988344\pi$
$620$	−300.808	+	2309.21i	−0.485174	+	3.72453i
$621$		0			0
$622$	−544.585	−	1676.06i	−0.875538	−	2.69463i
$623$	147.274	+	47.8523i	0.236395	+	0.0768094i
$624$		0			0
$625$	851.953			1.36312
$626$		−	2134.22i		−	3.40929i
$627$		0			0
$628$	147.119	+	106.888i	0.234266	+	0.170205i
$629$	7.02529	+	5.10417i	0.0111690	+	0.00811474i
$630$		0			0
$631$	−578.834	−	796.697i	−0.917328	−	1.26259i	−0.964602	−	0.263712i	$-0.915053\pi$
$631$	−578.834	−	796.697i	−0.917328	−	1.26259i	0.0472736	−	0.998882i	$-0.484947\pi$
$632$	−1414.59	+	459.629i	−2.23828	+	0.727261i
$633$		0			0
$634$	−312.782	−	227.249i	−0.493347	−	0.358437i
$635$	−561.239	−	182.358i	−0.883841	−	0.287177i
$636$		0			0
$637$	55.5619	−	76.4744i	0.0872243	−	0.120054i
$638$	328.935	−	1012.36i	0.515572	−	1.58677i
$639$		0			0
$640$	1327.92	−	964.789i	2.07487	−	1.50748i
$641$	−231.242	+	75.1352i	−0.360753	+	0.117216i	−0.483785	−	0.875187i	$-0.660738\pi$
$641$	−231.242	+	75.1352i	−0.360753	+	0.117216i	0.123032	+	0.992403i	$0.460738\pi$
$642$		0			0
$643$	−351.097	+	483.243i	−0.546029	+	0.751544i	−0.989467	−	0.144761i	$-0.953759\pi$
$643$	−351.097	+	483.243i	−0.546029	+	0.751544i	0.443438	+	0.896305i	$0.353759\pi$
$644$	25.1821	+	34.6602i	0.0391027	+	0.0538202i
$645$		0			0
$646$			41.3790i			0.0640541i
$647$	−499.498	−	687.500i	−0.772022	−	1.06260i	−0.996118	−	0.0880296i	$-0.971943\pi$
$647$	−499.498	−	687.500i	−0.772022	−	1.06260i	0.224096	−	0.974567i	$-0.428057\pi$
$648$		0			0
$649$	256.056	−	83.1977i	0.394539	−	0.128194i
$650$			417.461i			0.642248i
$651$		0			0
$652$	548.669			0.841517
$653$	−215.935	−	664.580i	−0.330682	−	1.01773i	−0.968810	−	0.247804i	$-0.920291\pi$
$653$	−215.935	−	664.580i	−0.330682	−	1.01773i	0.638129	−	0.769930i	$-0.279709\pi$
$654$		0			0
$655$	1519.17	−	1103.74i	2.31935	−	1.68511i
$656$	1500.66			2.28759
$657$		0			0
$658$	−283.830	+	206.215i	−0.431353	+	0.313396i
$659$	280.419	+	203.736i	0.425522	+	0.309160i	0.779856	−	0.625959i	$-0.215292\pi$
$659$	280.419	+	203.736i	0.425522	+	0.309160i	−0.354334	+	0.935119i	$0.615292\pi$
$660$		0			0
$661$	136.527	+	420.188i	0.206547	+	0.635685i	0.999646	+	0.0265933i	$0.00846592\pi$
$661$	136.527	+	420.188i	0.206547	+	0.635685i	−0.793100	+	0.609092i	$0.791534\pi$
$662$	−307.531	−	423.281i	−0.464549	−	0.639397i
$663$		0			0
$664$	−1367.60	−	444.361i	−2.05964	−	0.669218i
$665$	150.290	+	109.192i	0.226000	+	0.164199i
$666$		0			0
$667$	17.0165	−	52.3715i	0.0255121	−	0.0785180i
$668$	−330.836	+	455.356i	−0.495263	+	0.681671i
$669$		0			0
$670$	306.272	+	942.609i	0.457123	+	1.40688i
$671$	−756.322	+	549.500i	−1.12716	+	0.818927i
$672$		0			0
$673$	−10.1557	+	13.9782i	−0.0150903	+	0.0207700i	−0.816495	−	0.577352i	$-0.804086\pi$
$673$	−10.1557	+	13.9782i	−0.0150903	+	0.0207700i	0.801405	+	0.598122i	$0.204086\pi$
$674$	109.258	−	150.381i	0.162104	−	0.223117i
$675$		0			0
$676$	1395.92			2.06496
$677$			879.412i			1.29898i	0.760369	+	0.649492i	$0.225018\pi$
$677$			879.412i			1.29898i	−0.760369	+	0.649492i	$0.774982\pi$
$678$		0			0
$679$	−10.1604	+	31.2706i	−0.0149638	+	0.0460539i
$680$	−191.574	+	62.2462i	−0.281727	+	0.0915386i
$681$		0			0
$682$	215.201	+	1152.34i	0.315544	+	1.68965i
$683$	1008.40			1.47643			0.738214	−	0.674566i	$-0.235669\pi$
$683$	1008.40			1.47643			0.738214	+	0.674566i	$0.235669\pi$
$684$		0			0
$685$	−1293.29	−	420.216i	−1.88802	−	0.613454i
$686$	672.872	−	488.870i	0.980863	−	0.712639i
$687$		0			0
$688$		−	1316.97i		−	1.91420i
$689$	138.189	−	100.400i	0.200565	−	0.145719i
$690$		0			0
$691$	−1092.52	−	793.762i	−1.58107	−	1.14871i	−0.915456	−	0.402418i	$-0.868170\pi$
$691$	−1092.52	−	793.762i	−1.58107	−	1.14871i	−0.665614	−	0.746297i	$-0.731830\pi$
$692$	221.585	+	681.969i	0.320210	+	0.985504i
$693$		0			0
$694$	1822.93	−	592.305i	2.62670	−	0.853466i
$695$	−928.728	−	301.762i	−1.33630	−	0.434190i
$696$		0			0
$697$	91.2005	+	29.6328i	0.130847	+	0.0425148i
$698$	334.895	−	1030.70i	0.479793	−	1.47665i
$699$		0			0
$700$	−358.090	+	1102.09i	−0.511557	+	1.57441i
$701$	290.266	+	893.346i	0.414074	+	1.27439i	0.913077	+	0.407787i	$0.133700\pi$
$701$	290.266	+	893.346i	0.414074	+	1.27439i	−0.499003	+	0.866600i	$0.666300\pi$
$702$		0			0
$703$	47.2181	−	15.3421i	0.0671666	−	0.0218238i
$704$	221.197	−	304.451i	0.314200	−	0.432459i
$705$		0			0
$706$	1099.10	+	1512.79i	1.55681	+	2.14276i
$707$	−290.103			−0.410329
$708$		0			0
$709$	86.1836	+	118.622i	0.121557	+	0.167308i	0.865459	−	0.500980i	$-0.167027\pi$
$709$	86.1836	+	118.622i	0.121557	+	0.167308i	−0.743902	+	0.668289i	$0.767027\pi$
$710$	−617.213	+	1899.59i	−0.869314	+	2.67547i
$711$		0			0
$712$			960.006i			1.34832i
$713$	11.1328	+	59.6133i	0.0156141	+	0.0836091i
$714$		0			0
$715$	65.0480	+	200.197i	0.0909763	+	0.279996i
$716$	461.879	+	150.074i	0.645082	+	0.209600i
$717$		0			0
$718$	−1907.45			−2.65662
$719$		−	327.196i		−	0.455071i	−0.973770	−	0.227536i	$-0.926933\pi$
$719$		−	327.196i		−	0.455071i	0.973770	−	0.227536i	$-0.0730668\pi$
$720$		0			0
$721$	145.670	+	105.835i	0.202038	+	0.146789i
$722$	−841.605	−	611.462i	−1.16566	−	0.846900i
$723$		0			0
$724$	669.216	+	921.097i	0.924332	+	1.27223i
$725$	1416.55	−	460.265i	1.95386	−	0.634848i
$726$		0			0
$727$	468.043	+	340.053i	0.643800	+	0.467748i	0.861154	−	0.508345i	$-0.169742\pi$
$727$	468.043	+	340.053i	0.643800	+	0.467748i	−0.217354	+	0.976093i	$0.569742\pi$
$728$	−87.0913	−	28.2977i	−0.119631	−	0.0388704i
$729$		0			0
$730$	−1326.25	+	1825.43i	−1.81678	+	2.50059i
$731$	26.0056	−	80.0371i	0.0355754	−	0.109490i
$732$		0			0
$733$	−333.818	+	242.533i	−0.455414	+	0.330877i	−0.791730	−	0.610872i	$-0.790819\pi$
$733$	−333.818	+	242.533i	−0.455414	+	0.330877i	0.336316	+	0.941749i	$0.390819\pi$
$734$	−1484.15	+	482.229i	−2.02200	+	0.656987i
$735$		0			0
$736$	−17.6664	+	24.3157i	−0.0240033	+	0.0330377i
$737$	199.495	+	274.581i	0.270685	+	0.372566i
$738$		0			0
$739$		−	484.270i		−	0.655305i	−0.944798	−	0.327653i	$-0.893742\pi$
$739$		−	484.270i		−	0.655305i	0.944798	−	0.327653i	$-0.106258\pi$
$740$	268.044	+	368.931i	0.362222	+	0.498556i
$741$		0			0
$742$	662.885	−	215.384i	0.893376	−	0.290276i
$743$			1194.64i			1.60786i	0.594724	+	0.803930i	$0.297261\pi$
$743$			1194.64i			1.60786i	−0.594724	+	0.803930i	$0.702739\pi$
$744$		0			0
$745$	607.641			0.815626
$746$	−88.9512	−	273.764i	−0.119238	−	0.366975i
$747$		0			0
$748$	−105.296	+	76.5018i	−0.140770	+	0.102275i
$749$	72.7472			0.0971258
$750$		0			0
$751$	211.035	−	153.326i	0.281005	−	0.204162i	−0.438350	−	0.898804i	$-0.644437\pi$
$751$	211.035	−	153.326i	0.281005	−	0.204162i	0.719356	+	0.694642i	$0.244437\pi$
$752$	−698.056	−	507.168i	−0.928267	−	0.674425i
$753$		0			0
$754$	68.6279	+	211.215i	0.0910184	+	0.280126i
$755$	192.224	+	264.574i	0.254602	+	0.350429i
$756$		0			0
$757$	636.366	+	206.768i	0.840641	+	0.273141i	0.697521	−	0.716564i	$-0.254286\pi$
$757$	636.366	+	206.768i	0.840641	+	0.273141i	0.143120	+	0.989705i	$0.454286\pi$
$758$	99.6155	+	72.3749i	0.131419	+	0.0954814i
$759$		0			0
$760$	−355.884	+	1095.30i	−0.468268	+	1.44118i
$761$	305.231	−	420.114i	0.401091	−	0.552055i	−0.559926	−	0.828543i	$-0.689170\pi$
$761$	305.231	−	420.114i	0.401091	−	0.552055i	0.961017	+	0.276488i	$0.0891705\pi$
$762$		0			0
$763$	−105.961	−	326.115i	−0.138874	−	0.427412i
$764$	997.225	−	724.527i	1.30527	−	0.948333i
$765$		0			0
$766$	375.051	−	516.213i	0.489622	−	0.673907i
$767$	−33.0170	+	45.4440i	−0.0430470	+	0.0592491i
$768$		0			0
$769$	559.218			0.727202			0.363601	−	0.931555i	$-0.381547\pi$
$769$	559.218			0.727202			0.363601	+	0.931555i	$0.381547\pi$
$770$			858.948i			1.11552i
$771$		0			0
$772$	65.8851	−	202.773i	0.0853434	−	0.262660i
$773$	−1128.97	+	366.823i	−1.46050	+	0.474545i	−0.928222	−	0.372026i	$-0.878663\pi$
$773$	−1128.97	+	366.823i	−1.46050	+	0.474545i	−0.532276	+	0.846571i	$0.678663\pi$
$774$		0			0
$775$	−1127.48	+	1191.37i	−1.45482	+	1.53725i
$776$	−203.837			−0.262677
$777$		0			0
$778$	−384.732	−	125.007i	−0.494515	−	0.160678i
$779$	443.551	−	322.259i	0.569386	−	0.413683i
$780$		0			0
$781$			683.976i			0.875769i
$782$	−8.00743	+	5.81774i	−0.0102397	+	0.00743956i
$783$		0			0
$784$	767.472	+	557.601i	0.978918	+	0.711226i
$785$	58.2839	+	179.379i	0.0742470	+	0.228509i
$786$		0			0
$787$	60.0244	−	19.5031i	0.0762699	−	0.0247816i	−0.270634	−	0.962682i	$-0.587233\pi$
$787$	60.0244	−	19.5031i	0.0762699	−	0.0247816i	0.346903	+	0.937901i	$0.387233\pi$
$788$	−1107.82	−	359.951i	−1.40586	−	0.456791i
$789$		0			0
$790$	−2768.34	−	899.490i	−3.50423	−	1.13859i
$791$	94.9395	−	292.194i	0.120025	−	0.369398i
$792$		0			0
$793$	60.2729	−	185.501i	0.0760062	−	0.233923i
$794$	448.238	+	1379.54i	0.564532	+	1.73745i
$795$		0			0
$796$	−411.956	+	133.853i	−0.517533	+	0.168157i
$797$	464.198	−	638.914i	0.582432	−	0.801649i	−0.411527	−	0.911397i	$-0.635005\pi$
$797$	464.198	−	638.914i	0.582432	−	0.801649i	0.993959	+	0.109749i	$0.0350045\pi$
$798$		0			0
$799$	−32.4086	−	44.6066i	−0.0405615	−	0.0558281i
$800$	−812.954			−1.01619
$801$		0			0
$802$	−1427.03	−	1964.13i	−1.77933	−	2.44904i
$803$	−238.769	+	734.855i	−0.297346	+	0.915137i
$804$		0			0
$805$			44.4353i			0.0551991i
$806$	−177.640	−	168.114i	−0.220397	−	0.208578i
$807$		0			0
$808$	−555.761	−	1710.46i	−0.687823	−	2.11690i
$809$	−557.372	−	181.101i	−0.688965	−	0.223858i	−0.0564487	−	0.998405i	$-0.517978\pi$
$809$	−557.372	−	181.101i	−0.688965	−	0.223858i	−0.632516	+	0.774547i	$0.717978\pi$
$810$		0			0
$811$	−1257.33			−1.55034			−0.775170	−	0.631753i	$-0.782336\pi$
$811$	−1257.33			−1.55034			−0.775170	+	0.631753i	$0.782336\pi$
$812$			616.470i			0.759199i
$813$		0			0
$814$	185.718	+	134.932i	0.228155	+	0.165764i
$815$	460.386	+	334.490i	0.564891	+	0.410418i
$816$		0			0
$817$	−282.813	−	389.259i	−0.346160	−	0.476449i
$818$	−2062.86	+	670.263i	−2.52183	+	0.819393i
$819$		0			0
$820$	4074.08	+	2959.99i	4.96839	+	3.60975i
$821$	−697.843	−	226.743i	−0.849992	−	0.276179i	−0.148549	−	0.988905i	$-0.547460\pi$
$821$	−697.843	−	226.743i	−0.849992	−	0.276179i	−0.701443	+	0.712726i	$0.747460\pi$
$822$		0			0
$823$	843.839	−	1161.44i	1.02532	−	1.41123i	0.116915	−	0.993142i	$-0.462700\pi$
$823$	843.839	−	1161.44i	1.02532	−	1.41123i	0.908406	−	0.418090i	$-0.137300\pi$
$824$	−344.943	+	1061.63i	−0.418620	+	1.28838i
$825$		0			0
$826$	−185.435	+	134.726i	−0.224498	+	0.163107i
$827$	654.954	−	212.807i	0.791964	−	0.257325i	0.115024	−	0.993363i	$-0.463306\pi$
$827$	654.954	−	212.807i	0.791964	−	0.257325i	0.676940	+	0.736038i	$0.263306\pi$
$828$		0			0
$829$	−207.064	+	284.999i	−0.249776	+	0.343787i	−0.915433	−	0.402471i	$-0.868151\pi$
$829$	−207.064	+	284.999i	−0.249776	+	0.343787i	0.665657	+	0.746258i	$0.268151\pi$
$830$	−1654.10	−	2276.67i	−1.99289	−	2.74297i
$831$		0			0
$832$			78.5146i			0.0943685i
$833$	35.6314	+	49.0424i	0.0427747	+	0.0588744i
$834$		0			0
$835$	−555.206	+	180.397i	−0.664917	+	0.216045i
$836$			744.130i			0.890107i
$837$		0			0
$838$	1097.51			1.30968
$839$	82.9070	+	255.162i	0.0988165	+	0.304126i	0.988229	−	0.152979i	$-0.0488866\pi$
$839$	82.9070	+	255.162i	0.0988165	+	0.304126i	−0.889413	+	0.457104i	$0.848887\pi$
$840$		0			0
$841$	−39.3439	+	28.5850i	−0.0467823	+	0.0339893i
$842$	−65.3744			−0.0776418
$843$		0			0
$844$	442.229	−	321.298i	0.523968	−	0.380685i
$845$	1171.31	+	851.005i	1.38616	+	1.00711i
$846$		0			0
$847$	−5.32568	−	16.3908i	−0.00628770	−	0.0193516i
$848$	1007.59	+	1386.82i	1.18819	+	1.63541i
$849$		0			0
$850$	−254.611	−	82.7283i	−0.299543	−	0.0973274i
$851$	9.60761	+	6.98034i	0.0112898	+	0.00820252i
$852$		0			0
$853$	271.541	−	835.717i	0.318336	−	0.979739i	−0.656023	−	0.754741i	$-0.727763\pi$
$853$	271.541	−	835.717i	0.318336	−	0.979739i	0.974359	−	0.224998i	$-0.0722375\pi$
$854$	467.814	−	643.891i	0.547792	−	0.753970i
$855$		0			0
$856$	139.365	+	428.920i	0.162809	+	0.501075i
$857$	−236.019	+	171.478i	−0.275401	+	0.200090i	−0.716909	−	0.697167i	$-0.754444\pi$
$857$	−236.019	+	171.478i	−0.275401	+	0.200090i	0.441508	+	0.897257i	$0.354444\pi$
$858$		0			0
$859$	−665.151	+	915.502i	−0.774332	+	1.06578i	0.221552	+	0.975148i	$0.428888\pi$
$859$	−665.151	+	915.502i	−0.774332	+	1.06578i	−0.995885	+	0.0906286i	$0.971112\pi$
$860$	2597.67	−	3575.39i	3.02055	−	4.15743i
$861$		0			0
$862$	296.484			0.343949
$863$		−	1140.02i		−	1.32100i	−0.750826	−	0.660500i	$-0.770344\pi$
$863$		−	1140.02i		−	1.32100i	0.750826	−	0.660500i	$-0.229656\pi$
$864$		0			0
$865$	−229.824	+	707.325i	−0.265692	+	0.817717i
$866$	2045.65	−	664.673i	2.36219	−	0.767521i
$867$		0			0
$868$	−324.760	−	596.192i	−0.374148	−	0.686857i
$869$	−996.786			−1.14705
$870$		0			0
$871$	−67.3457	−	21.8819i	−0.0773200	−	0.0251228i
$872$	1719.79	−	1249.50i	1.97224	−	1.43292i
$873$		0			0
$874$			56.5888i			0.0647470i
$875$	−512.938	+	372.672i	−0.586215	+	0.425910i
$876$		0			0
$877$	909.106	+	660.504i	1.03661	+	0.753140i	0.969621	−	0.244613i	$-0.0786611\pi$
$877$	909.106	+	660.504i	1.03661	+	0.753140i	0.0669880	+	0.997754i	$0.478661\pi$
$878$	−473.971	−	1458.73i	−0.539830	−	1.66143i
$879$		0			0
$880$	−2009.11	+	652.801i	−2.28309	+	0.741819i
$881$	−555.443	−	180.474i	−0.630469	−	0.204852i	−0.0236860	−	0.999719i	$-0.507540\pi$
$881$	−555.443	−	180.474i	−0.630469	−	0.204852i	−0.606783	+	0.794868i	$0.707540\pi$
$882$		0			0
$883$	1387.15	+	450.713i	1.57095	+	0.510434i	0.959706	−	0.281005i	$-0.0906677\pi$
$883$	1387.15	+	450.713i	1.57095	+	0.510434i	0.611248	+	0.791439i	$0.290668\pi$
$884$	8.39123	−	25.8256i	0.00949235	−	0.0292144i
$885$		0			0
$886$	264.820	−	815.033i	0.298894	−	0.919902i
$887$	80.5351	+	247.862i	0.0907949	+	0.279438i	0.986135	−	0.165945i	$-0.0530675\pi$
$887$	80.5351	+	247.862i	0.0907949	+	0.279438i	−0.895340	+	0.445383i	$0.853067\pi$
$888$		0			0
$889$	163.622	−	53.1640i	0.184052	−	0.0598020i
$890$	−1104.29	+	1519.92i	−1.24077	+	1.70777i
$891$		0			0
$892$	−1197.81	−	1648.64i	−1.34283	−	1.84825i
$893$	−315.237			−0.353009
$894$		0			0
$895$	296.070	+	407.506i	0.330805	+	0.455314i
$896$	−147.873	+	455.107i	−0.165037	+	0.507932i
$897$		0			0
$898$		−	1649.56i		−	1.83692i
$899$	−374.598	+	788.126i	−0.416683	+	0.876670i
$900$		0			0
$901$	33.8497	+	104.179i	0.0375690	+	0.115626i
$902$	2410.94	+	783.363i	2.67289	+	0.868473i
$903$		0			0
$904$	1904.66			2.10693
$905$			1180.87i			1.30483i
$906$		0			0
$907$	1245.31	+	904.769i	1.37300	+	0.997540i	0.997496	+	0.0707175i	$0.0225289\pi$
$907$	1245.31	+	904.769i	1.37300	+	0.997540i	0.375500	+	0.926823i	$0.377471\pi$
$908$	1636.10	+	1188.70i	1.80187	+	1.30914i
$909$		0			0
$910$	−105.336	−	144.982i	−0.115754	−	0.159321i
$911$	971.241	−	315.575i	1.06613	−	0.346406i	0.277149	−	0.960827i	$-0.410611\pi$
$911$	971.241	−	315.575i	1.06613	−	0.346406i	0.788978	+	0.614422i	$0.210611\pi$
$912$		0			0
$913$	−779.628	−	566.433i	−0.853919	−	0.620409i
$914$	1142.08	+	371.085i	1.24954	+	0.406001i
$915$		0			0
$916$	1840.58	−	2533.34i	2.00936	−	2.76565i
$917$	−169.171	+	520.654i	−0.184483	+	0.567780i
$918$		0			0
$919$	−1098.42	+	798.050i	−1.19524	+	0.868390i	−0.993808	−	0.111113i	$-0.964558\pi$
$919$	−1098.42	+	798.050i	−1.19524	+	0.868390i	−0.201428	+	0.979503i	$0.564558\pi$
$920$	−261.992	+	85.1264i	−0.284774	+	0.0925287i
$921$		0			0
$922$	−879.452	+	1210.46i	−0.953852	+	1.31286i
$923$	−83.8783	−	115.449i	−0.0908757	−	0.125080i
$924$		0			0
$925$			321.214i			0.347258i
$926$	−745.132	−	1025.59i	−0.804678	−	1.10754i
$927$		0			0
$928$	−411.315	+	133.644i	−0.443227	+	0.144013i
$929$		−	1535.49i		−	1.65285i	−0.563049	−	0.826423i	$-0.690372\pi$
$929$		−	1535.49i		−	1.65285i	0.563049	−	0.826423i	$-0.309628\pi$
$930$		0			0
$931$	346.585			0.372271
$932$	−635.256	−	1955.12i	−0.681606	−	2.09777i
$933$		0			0
$934$	419.170	−	304.545i	0.448790	−	0.326065i
$935$	−134.992			−0.144376
$936$		0			0
$937$	−82.5709	+	59.9913i	−0.0881226	+	0.0640249i	−0.630974	−	0.775804i	$-0.717345\pi$
$937$	−82.5709	+	59.9913i	−0.0881226	+	0.0640249i	0.542852	+	0.839829i	$0.317345\pi$
$938$	−233.763	−	169.839i	−0.249214	−	0.181065i
$939$		0			0
$940$	−894.757	−	2753.78i	−0.951869	−	2.92955i
$941$	−746.278	−	1027.16i	−0.793069	−	1.09157i	−0.993719	−	0.111903i	$-0.964305\pi$
$941$	−746.278	−	1027.16i	−0.793069	−	1.09157i	0.200650	−	0.979663i	$-0.435695\pi$
$942$		0			0
$943$	124.723	+	40.5251i	0.132262	+	0.0429747i
$944$	−456.061	−	331.348i	−0.483116	−	0.351004i
$945$		0			0
$946$	687.476	−	2115.83i	0.726719	−	2.23661i
$947$	582.450	−	801.674i	0.615048	−	0.846541i	−0.381933	−	0.924190i	$-0.624741\pi$
$947$	582.450	−	801.674i	0.615048	−	0.846541i	0.996981	+	0.0776491i	$0.0247414\pi$
$948$		0			0
$949$	−49.8159	−	153.318i	−0.0524931	−	0.161557i
$950$	−1238.30	+	899.675i	−1.30347	+	0.947027i
$951$		0			0
$952$	34.5178	−	47.5096i	0.0362581	−	0.0499051i
$953$	−314.054	+	432.258i	−0.329542	+	0.453576i	−0.941351	−	0.337430i	$-0.890442\pi$
$953$	−314.054	+	432.258i	−0.329542	+	0.453576i	0.611808	+	0.791006i	$0.290442\pi$
$954$		0			0
$955$	1278.47			1.33871
$956$		−	3791.09i		−	3.96557i
$957$		0			0
$958$	68.0453	−	209.422i	0.0710285	−	0.218603i
$959$	377.042	−	122.508i	0.393161	−	0.127746i
$960$		0			0
$961$	−52.9136	−	959.542i	−0.0550610	−	0.998483i
$962$	−47.8947			−0.0497866
$963$		0			0
$964$	16.7956	+	5.45722i	0.0174228	+	0.00566102i
$965$	178.903	−	129.980i	0.185391	−	0.134695i
$966$		0			0
$967$			396.208i			0.409729i	0.978790	+	0.204865i	$0.0656754\pi$
$967$			396.208i			0.409729i	−0.978790	+	0.204865i	$0.934325\pi$
$968$	86.4379	−	62.8008i	0.0892954	−	0.0648769i
$969$		0			0
$970$	−322.723	−	234.472i	−0.332704	−	0.241724i
$971$	−200.452	−	616.927i	−0.206439	−	0.635353i	−0.999651	−	0.0264079i	$-0.991593\pi$
$971$	−200.452	−	616.927i	−0.206439	−	0.635353i	0.793213	−	0.608945i	$-0.208407\pi$
$972$		0			0
$973$	270.758	−	87.9747i	0.278272	−	0.0904160i
$974$	3254.61	+	1057.49i	3.34149	+	1.08572i
$975$		0			0
$976$	1861.63	+	604.879i	1.90740	+	0.619753i
$977$	413.927	−	1273.94i	0.423671	−	1.30393i	−0.480590	−	0.876946i	$-0.659577\pi$
$977$	413.927	−	1273.94i	0.423671	−	1.30393i	0.904261	−	0.426980i	$-0.140423\pi$
$978$		0			0
$979$	−198.808	+	611.867i	−0.203072	+	0.624992i
$980$	983.732	+	3027.62i	1.00381	+	3.08940i
$981$		0			0
$982$	1640.94	−	533.175i	1.67102	−	0.542948i
$983$	−842.335	+	1159.37i	−0.856902	+	1.17943i	0.125397	+	0.992107i	$0.459980\pi$
$983$	−842.335	+	1159.37i	−0.856902	+	1.17943i	−0.982299	+	0.187318i	$0.940020\pi$
$984$		0			0
$985$	−710.124	−	977.401i	−0.720938	−	0.992286i
$986$	−142.421			−0.144443
$987$		0			0
$988$	−91.2552	−	125.602i	−0.0923636	−	0.127128i
$989$	35.5647	−	109.457i	0.0359602	−	0.110674i
$990$		0			0
$991$		−	1165.24i		−	1.17582i	−0.808926	−	0.587910i	$-0.799951\pi$
$991$		−	1165.24i		−	1.17582i	0.808926	−	0.587910i	$-0.200049\pi$
$992$	327.381	−	345.931i	0.330021	−	0.348721i
$993$		0			0
$994$	−179.940	−	553.799i	−0.181026	−	0.557142i
$995$	−427.273	−	138.829i	−0.429420	−	0.139527i
$996$		0			0
$997$	−24.6995			−0.0247738			−0.0123869	−	0.999923i	$-0.503943\pi$
$997$	−24.6995			−0.0247738			−0.0123869	+	0.999923i	$0.503943\pi$
$998$		−	1011.79i		−	1.01382i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	279.3.v.a.244.1		20
3.2	odd	2		31.3.f.a.27.5	yes	20
31.23	odd	10	inner	279.3.v.a.271.1		20
93.23	even	10		31.3.f.a.23.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.3.f.a.23.5	✓	20	93.23	even	10
31.3.f.a.27.5	yes	20	3.2	odd	2
279.3.v.a.244.1		20	1.1	even	1	trivial
279.3.v.a.271.1		20	31.23	odd	10	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 279 = 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	279.v (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09299 - 3.36389i) q^{2} +(-6.88507 + 5.00229i) q^{4} -8.82683 q^{5} +(2.08188 - 1.51257i) q^{7} +(12.9065 + 9.37714i) q^{8} +(9.64768 + 29.6925i) q^{10} +(6.28416 + 8.64940i) q^{11} +(-2.12141 - 0.689289i) q^{13} +(-7.36362 - 5.34998i) q^{14} +(6.91748 - 21.2898i) q^{16} +(0.840800 - 1.15726i) q^{17} +(-2.52727 - 7.77815i) q^{19} +(60.7733 - 44.1544i) q^{20} +(22.2271 - 30.5930i) q^{22} +(1.14986 - 1.58264i) q^{23} +52.9129 q^{25} +7.88959i q^{26} +(-6.76754 + 20.8283i) q^{28} +(26.7713 - 8.69853i) q^{29} +(-21.3083 + 22.5157i) q^{31} -15.3640 q^{32} +(-4.81190 - 1.56348i) q^{34} +(-18.3764 + 13.3512i) q^{35} +6.07061i q^{37} +(-23.4025 + 17.0029i) q^{38} +(-113.924 - 82.7704i) q^{40} +(20.7157 + 63.7563i) q^{41} +(55.9522 - 18.1800i) q^{43} +(-86.5337 - 28.1165i) q^{44} +(-6.58063 - 2.13818i) q^{46} +(11.9110 - 36.6584i) q^{47} +(-13.0955 + 40.3038i) q^{49} +(-57.8335 - 177.993i) q^{50} +(18.0541 - 5.86613i) q^{52} +(-45.0108 + 61.9521i) q^{53} +(-55.4692 - 76.3468i) q^{55} +41.0534 q^{56} +(-58.5218 - 80.5484i) q^{58} +(7.78185 - 23.9501i) q^{59} +87.4422i q^{61} +(99.0302 + 47.0692i) q^{62} +(-10.8771 - 33.4763i) q^{64} +(18.7253 + 6.08423i) q^{65} +31.7457 q^{67} +12.1738i q^{68} +(64.9974 + 47.2234i) q^{70} +(51.7571 + 37.6037i) q^{71} +(42.4801 + 58.4689i) q^{73} +(20.4209 - 6.63515i) q^{74} +(56.3090 + 40.9109i) q^{76} +(26.1657 + 8.50176i) q^{77} +(-54.8015 + 75.4277i) q^{79} +(-61.0594 + 187.921i) q^{80} +(191.827 - 139.371i) q^{82} +(-85.7251 + 27.8538i) q^{83} +(-7.42160 + 10.2150i) q^{85} +(-122.311 - 168.347i) q^{86} +170.561i q^{88} +(35.3705 + 48.6833i) q^{89} +(-5.45912 + 1.77378i) q^{91} +16.6485i q^{92} -136.334 q^{94} +(22.3078 + 68.6564i) q^{95} +(-10.3369 + 7.51019i) q^{97} +149.891 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 3 q^{2} - 11 q^{4} + 14 q^{5} - q^{7} + 19 q^{8} + 12 q^{10} + 10 q^{11} + 10 q^{13} - 103 q^{16} - 35 q^{17} + 47 q^{19} + 125 q^{20} + 150 q^{22} - 75 q^{23} + 82 q^{25} + 88 q^{28} - 5 q^{29}+ \cdots + 1000 q^{98}+O(q^{100}) \) 20 * q + 3 * q^2 - 11 * q^4 + 14 * q^5 - q^7 + 19 * q^8 + 12 * q^10 + 10 * q^11 + 10 * q^13 - 103 * q^16 - 35 * q^17 + 47 * q^19 + 125 * q^20 + 150 * q^22 - 75 * q^23 + 82 * q^25 + 88 * q^28 - 5 * q^29 + 73 * q^31 - 226 * q^32 - 265 * q^34 + 50 * q^35 - 8 * q^38 - 466 * q^40 + 98 * q^41 + 245 * q^43 - 380 * q^44 - 445 * q^46 + 187 * q^47 + 328 * q^49 + 44 * q^50 - 15 * q^52 - 25 * q^53 + 190 * q^55 - 64 * q^56 - 85 * q^58 + 173 * q^59 + 40 * q^62 - 469 * q^64 + 345 * q^65 + 76 * q^67 - 11 * q^70 + 467 * q^71 - 15 * q^73 - 45 * q^74 + 55 * q^76 + 320 * q^77 + 500 * q^79 - 1030 * q^80 + 178 * q^82 + 50 * q^83 + 20 * q^85 - 1125 * q^86 - 55 * q^89 + 300 * q^91 + 62 * q^94 + 559 * q^95 - 405 * q^97 + 1000 * q^98

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