Properties

Label 330.2.m.f.301.2
Level $330$
Weight $2$
Character 330.301
Analytic conductor $2.635$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [330,2,Mod(31,330)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(330, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("330.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 330.m (of order \(5\), degree \(4\), 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: \(2.63506326670\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.2769390625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} - 2x^{6} + 5x^{5} + 21x^{4} + 75x^{3} - 198x^{2} - 87x + 841 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 301.2
Root \(-1.07877 - 2.33544i\) of defining polynomial
Character \(\chi\) \(=\) 330.301
Dual form 330.2.m.f.91.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(0.809017 - 0.587785i) q^{6} +(1.57877 + 4.85894i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(0.809017 - 0.587785i) q^{6} +(1.57877 + 4.85894i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +1.00000 q^{10} +(1.45132 - 2.98223i) q^{11} +1.00000 q^{12} +(-1.07877 - 0.783769i) q^{13} +(-1.57877 + 4.85894i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.627445 + 0.455866i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(-0.0242693 + 0.0746932i) q^{19} +(0.809017 + 0.587785i) q^{20} +5.10899 q^{21} +(2.92705 - 1.55961i) q^{22} +6.64849 q^{23} +(0.809017 + 0.587785i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-0.412052 - 1.26816i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-4.13326 + 3.00299i) q^{28} +(-0.623850 - 1.92001i) q^{29} +(0.309017 - 0.951057i) q^{30} +(-6.86933 - 4.99086i) q^{31} -1.00000 q^{32} +(-2.38778 - 2.30185i) q^{33} -0.775565 q^{34} +(4.13326 + 3.00299i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-1.21539 - 3.74060i) q^{37} +(-0.0635378 + 0.0461629i) q^{38} +(-1.07877 + 0.783769i) q^{39} +(0.309017 + 0.951057i) q^{40} +(-3.67612 + 11.3139i) q^{41} +(4.13326 + 3.00299i) q^{42} -6.01163 q^{43} +(3.28475 + 0.458729i) q^{44} -1.00000 q^{45} +(5.37874 + 3.90788i) q^{46} +(2.03009 - 6.24796i) q^{47} +(0.309017 + 0.951057i) q^{48} +(-15.4537 + 11.2278i) q^{49} +(0.809017 - 0.587785i) q^{50} +(0.239663 + 0.737606i) q^{51} +(0.412052 - 1.26816i) q^{52} +(-8.36933 - 6.08067i) q^{53} -1.00000 q^{54} +(-0.578765 - 3.26574i) q^{55} -5.10899 q^{56} +(0.0635378 + 0.0461629i) q^{57} +(0.623850 - 1.92001i) q^{58} +(-1.64590 - 5.06555i) q^{59} +(0.809017 - 0.587785i) q^{60} +(3.03046 - 2.20175i) q^{61} +(-2.62385 - 8.07538i) q^{62} +(1.57877 - 4.85894i) q^{63} +(-0.809017 - 0.587785i) q^{64} -1.33343 q^{65} +(-0.578765 - 3.26574i) q^{66} +0.588036 q^{67} +(-0.627445 - 0.455866i) q^{68} +(2.05450 - 6.32309i) q^{69} +(1.57877 + 4.85894i) q^{70} +(1.87292 - 1.36076i) q^{71} +(0.809017 - 0.587785i) q^{72} +(3.38197 + 10.4086i) q^{73} +(1.21539 - 3.74060i) q^{74} +(-0.809017 - 0.587785i) q^{75} -0.0785371 q^{76} +(16.7818 + 2.34364i) q^{77} -1.33343 q^{78} +(-9.97251 - 7.24545i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-9.62422 + 6.99241i) q^{82} +(6.47214 - 4.70228i) q^{83} +(1.57877 + 4.85894i) q^{84} +(-0.239663 + 0.737606i) q^{85} +(-4.86351 - 3.53355i) q^{86} -2.01882 q^{87} +(2.38778 + 2.30185i) q^{88} -9.67821 q^{89} +(-0.809017 - 0.587785i) q^{90} +(2.10517 - 6.47904i) q^{91} +(2.05450 + 6.32309i) q^{92} +(-6.86933 + 4.99086i) q^{93} +(5.31483 - 3.86145i) q^{94} +(0.0242693 + 0.0746932i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(10.8846 + 7.90809i) q^{97} -19.1018 q^{98} +(-2.92705 + 1.55961i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} + 2 q^{8} - 2 q^{9} + 8 q^{10} + 10 q^{11} + 8 q^{12} + q^{13} - 3 q^{14} + 2 q^{15} - 2 q^{16} + 3 q^{17} + 2 q^{18} - 12 q^{19} + 2 q^{20} - 2 q^{21} + 10 q^{22} + 2 q^{24} - 2 q^{25} - q^{26} - 2 q^{27} - 2 q^{28} + 27 q^{29} - 2 q^{30} - 6 q^{31} - 8 q^{32} - 5 q^{33} + 22 q^{34} + 2 q^{35} - 2 q^{36} - 4 q^{37} - 13 q^{38} + q^{39} - 2 q^{40} - 23 q^{41} + 2 q^{42} - 2 q^{43} + 10 q^{44} - 8 q^{45} - 5 q^{46} + 5 q^{47} - 2 q^{48} - 53 q^{49} + 2 q^{50} + 8 q^{51} + q^{52} - 18 q^{53} - 8 q^{54} + 5 q^{55} + 2 q^{56} + 13 q^{57} - 27 q^{58} - 40 q^{59} + 2 q^{60} - 20 q^{61} + 11 q^{62} + 3 q^{63} - 2 q^{64} + 4 q^{65} + 5 q^{66} + 18 q^{67} + 3 q^{68} - 5 q^{69} + 3 q^{70} - 10 q^{71} + 2 q^{72} + 36 q^{73} + 4 q^{74} - 2 q^{75} - 2 q^{76} + 50 q^{77} + 4 q^{78} - 11 q^{79} + 2 q^{80} - 2 q^{81} - 12 q^{82} + 16 q^{83} + 3 q^{84} - 8 q^{85} - 13 q^{86} - 18 q^{87} + 5 q^{88} - 46 q^{89} - 2 q^{90} - 39 q^{91} - 5 q^{92} - 6 q^{93} + 15 q^{94} + 12 q^{95} + 2 q^{96} + 16 q^{97} - 62 q^{98} - 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/330\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(211\) \(221\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\) \(1\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 + 0.587785i 0.572061 + 0.415627i
\(3\) 0.309017 0.951057i 0.178411 0.549093i
\(4\) 0.309017 + 0.951057i 0.154508 + 0.475528i
\(5\) 0.809017 0.587785i 0.361803 0.262866i
\(6\) 0.809017 0.587785i 0.330280 0.239962i
\(7\) 1.57877 + 4.85894i 0.596717 + 1.83651i 0.545986 + 0.837795i \(0.316155\pi\)
0.0507316 + 0.998712i \(0.483845\pi\)
\(8\) −0.309017 + 0.951057i −0.109254 + 0.336249i
\(9\) −0.809017 0.587785i −0.269672 0.195928i
\(10\) 1.00000 0.316228
\(11\) 1.45132 2.98223i 0.437590 0.899175i
\(12\) 1.00000 0.288675
\(13\) −1.07877 0.783769i −0.299196 0.217378i 0.428051 0.903755i \(-0.359200\pi\)
−0.727247 + 0.686376i \(0.759200\pi\)
\(14\) −1.57877 + 4.85894i −0.421943 + 1.29861i
\(15\) −0.309017 0.951057i −0.0797878 0.245562i
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) −0.627445 + 0.455866i −0.152178 + 0.110564i −0.661269 0.750149i \(-0.729982\pi\)
0.509091 + 0.860713i \(0.329982\pi\)
\(18\) −0.309017 0.951057i −0.0728360 0.224166i
\(19\) −0.0242693 + 0.0746932i −0.00556776 + 0.0171358i −0.953802 0.300437i \(-0.902868\pi\)
0.948234 + 0.317572i \(0.102868\pi\)
\(20\) 0.809017 + 0.587785i 0.180902 + 0.131433i
\(21\) 5.10899 1.11487
\(22\) 2.92705 1.55961i 0.624049 0.332509i
\(23\) 6.64849 1.38631 0.693153 0.720791i \(-0.256221\pi\)
0.693153 + 0.720791i \(0.256221\pi\)
\(24\) 0.809017 + 0.587785i 0.165140 + 0.119981i
\(25\) 0.309017 0.951057i 0.0618034 0.190211i
\(26\) −0.412052 1.26816i −0.0808100 0.248708i
\(27\) −0.809017 + 0.587785i −0.155695 + 0.113119i
\(28\) −4.13326 + 3.00299i −0.781113 + 0.567512i
\(29\) −0.623850 1.92001i −0.115846 0.356538i 0.876276 0.481809i \(-0.160020\pi\)
−0.992123 + 0.125271i \(0.960020\pi\)
\(30\) 0.309017 0.951057i 0.0564185 0.173638i
\(31\) −6.86933 4.99086i −1.23377 0.896385i −0.236601 0.971607i \(-0.576033\pi\)
−0.997167 + 0.0752219i \(0.976033\pi\)
\(32\) −1.00000 −0.176777
\(33\) −2.38778 2.30185i −0.415660 0.400700i
\(34\) −0.775565 −0.133008
\(35\) 4.13326 + 3.00299i 0.698649 + 0.507598i
\(36\) 0.309017 0.951057i 0.0515028 0.158509i
\(37\) −1.21539 3.74060i −0.199809 0.614950i −0.999887 0.0150533i \(-0.995208\pi\)
0.800077 0.599897i \(-0.204792\pi\)
\(38\) −0.0635378 + 0.0461629i −0.0103072 + 0.00748862i
\(39\) −1.07877 + 0.783769i −0.172741 + 0.125503i
\(40\) 0.309017 + 0.951057i 0.0488599 + 0.150375i
\(41\) −3.67612 + 11.3139i −0.574114 + 1.76694i 0.0650614 + 0.997881i \(0.479276\pi\)
−0.639176 + 0.769061i \(0.720724\pi\)
\(42\) 4.13326 + 3.00299i 0.637776 + 0.463371i
\(43\) −6.01163 −0.916765 −0.458383 0.888755i \(-0.651571\pi\)
−0.458383 + 0.888755i \(0.651571\pi\)
\(44\) 3.28475 + 0.458729i 0.495194 + 0.0691560i
\(45\) −1.00000 −0.149071
\(46\) 5.37874 + 3.90788i 0.793052 + 0.576186i
\(47\) 2.03009 6.24796i 0.296118 0.911359i −0.686725 0.726917i \(-0.740952\pi\)
0.982843 0.184442i \(-0.0590476\pi\)
\(48\) 0.309017 + 0.951057i 0.0446028 + 0.137273i
\(49\) −15.4537 + 11.2278i −2.20767 + 1.60397i
\(50\) 0.809017 0.587785i 0.114412 0.0831254i
\(51\) 0.239663 + 0.737606i 0.0335595 + 0.103286i
\(52\) 0.412052 1.26816i 0.0571413 0.175863i
\(53\) −8.36933 6.08067i −1.14962 0.835245i −0.161186 0.986924i \(-0.551532\pi\)
−0.988430 + 0.151679i \(0.951532\pi\)
\(54\) −1.00000 −0.136083
\(55\) −0.578765 3.26574i −0.0780407 0.440352i
\(56\) −5.10899 −0.682718
\(57\) 0.0635378 + 0.0461629i 0.00841579 + 0.00611443i
\(58\) 0.623850 1.92001i 0.0819156 0.252110i
\(59\) −1.64590 5.06555i −0.214278 0.659479i −0.999204 0.0398899i \(-0.987299\pi\)
0.784926 0.619589i \(-0.212701\pi\)
\(60\) 0.809017 0.587785i 0.104444 0.0758827i
\(61\) 3.03046 2.20175i 0.388010 0.281906i −0.376630 0.926364i \(-0.622917\pi\)
0.764640 + 0.644458i \(0.222917\pi\)
\(62\) −2.62385 8.07538i −0.333229 1.02557i
\(63\) 1.57877 4.85894i 0.198906 0.612169i
\(64\) −0.809017 0.587785i −0.101127 0.0734732i
\(65\) −1.33343 −0.165391
\(66\) −0.578765 3.26574i −0.0712411 0.401984i
\(67\) 0.588036 0.0718400 0.0359200 0.999355i \(-0.488564\pi\)
0.0359200 + 0.999355i \(0.488564\pi\)
\(68\) −0.627445 0.455866i −0.0760889 0.0552818i
\(69\) 2.05450 6.32309i 0.247332 0.761210i
\(70\) 1.57877 + 4.85894i 0.188699 + 0.580754i
\(71\) 1.87292 1.36076i 0.222275 0.161492i −0.471075 0.882093i \(-0.656134\pi\)
0.693350 + 0.720601i \(0.256134\pi\)
\(72\) 0.809017 0.587785i 0.0953436 0.0692712i
\(73\) 3.38197 + 10.4086i 0.395829 + 1.21824i 0.928314 + 0.371797i \(0.121258\pi\)
−0.532485 + 0.846440i \(0.678742\pi\)
\(74\) 1.21539 3.74060i 0.141287 0.434836i
\(75\) −0.809017 0.587785i −0.0934172 0.0678716i
\(76\) −0.0785371 −0.00900882
\(77\) 16.7818 + 2.34364i 1.91246 + 0.267083i
\(78\) −1.33343 −0.150981
\(79\) −9.97251 7.24545i −1.12199 0.815177i −0.137484 0.990504i \(-0.543902\pi\)
−0.984510 + 0.175327i \(0.943902\pi\)
\(80\) −0.309017 + 0.951057i −0.0345492 + 0.106331i
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) −9.62422 + 6.99241i −1.06282 + 0.772182i
\(83\) 6.47214 4.70228i 0.710409 0.516143i −0.172896 0.984940i \(-0.555313\pi\)
0.883306 + 0.468798i \(0.155313\pi\)
\(84\) 1.57877 + 4.85894i 0.172257 + 0.530154i
\(85\) −0.239663 + 0.737606i −0.0259951 + 0.0800046i
\(86\) −4.86351 3.53355i −0.524446 0.381032i
\(87\) −2.01882 −0.216440
\(88\) 2.38778 + 2.30185i 0.254538 + 0.245378i
\(89\) −9.67821 −1.02589 −0.512944 0.858422i \(-0.671445\pi\)
−0.512944 + 0.858422i \(0.671445\pi\)
\(90\) −0.809017 0.587785i −0.0852779 0.0619580i
\(91\) 2.10517 6.47904i 0.220682 0.679188i
\(92\) 2.05450 + 6.32309i 0.214196 + 0.659228i
\(93\) −6.86933 + 4.99086i −0.712316 + 0.517528i
\(94\) 5.31483 3.86145i 0.548183 0.398278i
\(95\) 0.0242693 + 0.0746932i 0.00248998 + 0.00766336i
\(96\) −0.309017 + 0.951057i −0.0315389 + 0.0970668i
\(97\) 10.8846 + 7.90809i 1.10516 + 0.802945i 0.981895 0.189429i \(-0.0606635\pi\)
0.123265 + 0.992374i \(0.460664\pi\)
\(98\) −19.1018 −1.92957
\(99\) −2.92705 + 1.55961i −0.294180 + 0.156746i
\(100\) 1.00000 0.100000
\(101\) 8.60862 + 6.25453i 0.856590 + 0.622349i 0.926955 0.375172i \(-0.122416\pi\)
−0.0703651 + 0.997521i \(0.522416\pi\)
\(102\) −0.239663 + 0.737606i −0.0237301 + 0.0730339i
\(103\) 5.16326 + 15.8909i 0.508751 + 1.56577i 0.794372 + 0.607432i \(0.207800\pi\)
−0.285620 + 0.958343i \(0.592200\pi\)
\(104\) 1.07877 0.783769i 0.105782 0.0768549i
\(105\) 4.13326 3.00299i 0.403365 0.293062i
\(106\) −3.19680 9.83874i −0.310501 0.955623i
\(107\) 5.42360 16.6921i 0.524319 1.61369i −0.241340 0.970441i \(-0.577587\pi\)
0.765659 0.643247i \(-0.222413\pi\)
\(108\) −0.809017 0.587785i −0.0778477 0.0565597i
\(109\) −8.94427 −0.856706 −0.428353 0.903612i \(-0.640906\pi\)
−0.428353 + 0.903612i \(0.640906\pi\)
\(110\) 1.45132 2.98223i 0.138378 0.284344i
\(111\) −3.93310 −0.373313
\(112\) −4.13326 3.00299i −0.390557 0.283756i
\(113\) −1.76975 + 5.44673i −0.166484 + 0.512385i −0.999143 0.0414017i \(-0.986818\pi\)
0.832659 + 0.553787i \(0.186818\pi\)
\(114\) 0.0242693 + 0.0746932i 0.00227303 + 0.00699566i
\(115\) 5.37874 3.90788i 0.501570 0.364412i
\(116\) 1.63326 1.18663i 0.151645 0.110176i
\(117\) 0.412052 + 1.26816i 0.0380942 + 0.117242i
\(118\) 1.64590 5.06555i 0.151517 0.466322i
\(119\) −3.20561 2.32901i −0.293858 0.213500i
\(120\) 1.00000 0.0912871
\(121\) −6.78734 8.65633i −0.617031 0.786939i
\(122\) 3.74585 0.339133
\(123\) 9.62422 + 6.99241i 0.867787 + 0.630484i
\(124\) 2.62385 8.07538i 0.235629 0.725191i
\(125\) −0.309017 0.951057i −0.0276393 0.0850651i
\(126\) 4.13326 3.00299i 0.368220 0.267528i
\(127\) 5.63303 4.09264i 0.499851 0.363163i −0.309109 0.951027i \(-0.600031\pi\)
0.808960 + 0.587864i \(0.200031\pi\)
\(128\) −0.309017 0.951057i −0.0273135 0.0840623i
\(129\) −1.85770 + 5.71740i −0.163561 + 0.503389i
\(130\) −1.07877 0.783769i −0.0946140 0.0687411i
\(131\) −2.19916 −0.192142 −0.0960709 0.995374i \(-0.530628\pi\)
−0.0960709 + 0.995374i \(0.530628\pi\)
\(132\) 1.45132 2.98223i 0.126321 0.259569i
\(133\) −0.401245 −0.0347924
\(134\) 0.475731 + 0.345639i 0.0410969 + 0.0298586i
\(135\) −0.309017 + 0.951057i −0.0265959 + 0.0818539i
\(136\) −0.239663 0.737606i −0.0205509 0.0632492i
\(137\) 1.76034 1.27896i 0.150396 0.109269i −0.510043 0.860149i \(-0.670370\pi\)
0.660438 + 0.750880i \(0.270370\pi\)
\(138\) 5.37874 3.90788i 0.457869 0.332661i
\(139\) 3.18517 + 9.80293i 0.270162 + 0.831474i 0.990459 + 0.137808i \(0.0440057\pi\)
−0.720297 + 0.693666i \(0.755994\pi\)
\(140\) −1.57877 + 4.85894i −0.133430 + 0.410655i
\(141\) −5.31483 3.86145i −0.447590 0.325193i
\(142\) 2.31506 0.194276
\(143\) −3.90301 + 2.07962i −0.326386 + 0.173907i
\(144\) 1.00000 0.0833333
\(145\) −1.63326 1.18663i −0.135635 0.0985446i
\(146\) −3.38197 + 10.4086i −0.279893 + 0.861424i
\(147\) 5.90278 + 18.1669i 0.486853 + 1.49838i
\(148\) 3.18194 2.31182i 0.261554 0.190030i
\(149\) 12.3356 8.96237i 1.01058 0.734226i 0.0462460 0.998930i \(-0.485274\pi\)
0.964330 + 0.264704i \(0.0852742\pi\)
\(150\) −0.309017 0.951057i −0.0252311 0.0776534i
\(151\) 2.03000 6.24769i 0.165199 0.508430i −0.833852 0.551988i \(-0.813869\pi\)
0.999051 + 0.0435581i \(0.0138694\pi\)
\(152\) −0.0635378 0.0461629i −0.00515360 0.00374431i
\(153\) 0.775565 0.0627007
\(154\) 12.1992 + 11.7601i 0.983037 + 0.947657i
\(155\) −8.49096 −0.682010
\(156\) −1.07877 0.783769i −0.0863704 0.0627517i
\(157\) −2.87638 + 8.85258i −0.229560 + 0.706513i 0.768237 + 0.640166i \(0.221134\pi\)
−0.997797 + 0.0663469i \(0.978866\pi\)
\(158\) −3.80916 11.7234i −0.303040 0.932662i
\(159\) −8.36933 + 6.08067i −0.663731 + 0.482229i
\(160\) −0.809017 + 0.587785i −0.0639584 + 0.0464685i
\(161\) 10.4964 + 32.3046i 0.827233 + 2.54596i
\(162\) −0.309017 + 0.951057i −0.0242787 + 0.0747221i
\(163\) 15.1300 + 10.9926i 1.18508 + 0.861008i 0.992735 0.120320i \(-0.0383921\pi\)
0.192341 + 0.981328i \(0.438392\pi\)
\(164\) −11.8962 −0.928936
\(165\) −3.28475 0.458729i −0.255717 0.0357120i
\(166\) 8.00000 0.620920
\(167\) 1.92123 + 1.39586i 0.148670 + 0.108015i 0.659634 0.751587i \(-0.270711\pi\)
−0.510964 + 0.859602i \(0.670711\pi\)
\(168\) −1.57877 + 4.85894i −0.121804 + 0.374875i
\(169\) −3.46778 10.6727i −0.266752 0.820979i
\(170\) −0.627445 + 0.455866i −0.0481228 + 0.0349633i
\(171\) 0.0635378 0.0461629i 0.00485886 0.00353017i
\(172\) −1.85770 5.71740i −0.141648 0.435948i
\(173\) 0.900560 2.77164i 0.0684683 0.210724i −0.910968 0.412477i \(-0.864664\pi\)
0.979436 + 0.201753i \(0.0646638\pi\)
\(174\) −1.63326 1.18663i −0.123817 0.0899585i
\(175\) 5.10899 0.386204
\(176\) 0.578765 + 3.26574i 0.0436261 + 0.246164i
\(177\) −5.32624 −0.400345
\(178\) −7.82983 5.68871i −0.586871 0.426387i
\(179\) 0.482779 1.48584i 0.0360846 0.111057i −0.931392 0.364018i \(-0.881405\pi\)
0.967476 + 0.252961i \(0.0814045\pi\)
\(180\) −0.309017 0.951057i −0.0230328 0.0708876i
\(181\) −14.9443 + 10.8576i −1.11080 + 0.807043i −0.982789 0.184730i \(-0.940859\pi\)
−0.128010 + 0.991773i \(0.540859\pi\)
\(182\) 5.51140 4.00427i 0.408532 0.296816i
\(183\) −1.15753 3.56251i −0.0855671 0.263349i
\(184\) −2.05450 + 6.32309i −0.151459 + 0.466144i
\(185\) −3.18194 2.31182i −0.233941 0.169968i
\(186\) −8.49096 −0.622587
\(187\) 0.448870 + 2.53279i 0.0328246 + 0.185216i
\(188\) 6.56950 0.479130
\(189\) −4.13326 3.00299i −0.300651 0.218435i
\(190\) −0.0242693 + 0.0746932i −0.00176068 + 0.00541881i
\(191\) 6.40523 + 19.7133i 0.463466 + 1.42640i 0.860901 + 0.508772i \(0.169900\pi\)
−0.397435 + 0.917630i \(0.630100\pi\)
\(192\) −0.809017 + 0.587785i −0.0583858 + 0.0424197i
\(193\) −1.10899 + 0.805730i −0.0798270 + 0.0579977i −0.626983 0.779033i \(-0.715710\pi\)
0.547156 + 0.837031i \(0.315710\pi\)
\(194\) 4.15753 + 12.7956i 0.298493 + 0.918668i
\(195\) −0.412052 + 1.26816i −0.0295076 + 0.0908152i
\(196\) −15.4537 11.2278i −1.10383 0.801983i
\(197\) −5.01135 −0.357044 −0.178522 0.983936i \(-0.557132\pi\)
−0.178522 + 0.983936i \(0.557132\pi\)
\(198\) −3.28475 0.458729i −0.233437 0.0326005i
\(199\) 23.3086 1.65230 0.826152 0.563448i \(-0.190525\pi\)
0.826152 + 0.563448i \(0.190525\pi\)
\(200\) 0.809017 + 0.587785i 0.0572061 + 0.0415627i
\(201\) 0.181713 0.559255i 0.0128170 0.0394468i
\(202\) 3.28820 + 10.1200i 0.231357 + 0.712044i
\(203\) 8.34432 6.06250i 0.585657 0.425504i
\(204\) −0.627445 + 0.455866i −0.0439300 + 0.0319170i
\(205\) 3.67612 + 11.3139i 0.256752 + 0.790200i
\(206\) −5.16326 + 15.8909i −0.359741 + 1.10717i
\(207\) −5.37874 3.90788i −0.373848 0.271617i
\(208\) 1.33343 0.0924566
\(209\) 0.187529 + 0.180780i 0.0129717 + 0.0125048i
\(210\) 5.10899 0.352554
\(211\) 16.2484 + 11.8052i 1.11859 + 0.812702i 0.983995 0.178199i \(-0.0570269\pi\)
0.134594 + 0.990901i \(0.457027\pi\)
\(212\) 3.19680 9.83874i 0.219557 0.675727i
\(213\) −0.715393 2.20175i −0.0490180 0.150862i
\(214\) 14.1992 10.3163i 0.970635 0.705207i
\(215\) −4.86351 + 3.53355i −0.331689 + 0.240986i
\(216\) −0.309017 0.951057i −0.0210259 0.0647112i
\(217\) 13.4052 41.2571i 0.910006 2.80071i
\(218\) −7.23607 5.25731i −0.490088 0.356070i
\(219\) 10.9443 0.739545
\(220\) 2.92705 1.55961i 0.197342 0.105149i
\(221\) 1.03416 0.0695651
\(222\) −3.18194 2.31182i −0.213558 0.155159i
\(223\) 2.81483 8.66317i 0.188495 0.580129i −0.811496 0.584358i \(-0.801346\pi\)
0.999991 + 0.00422962i \(0.00134633\pi\)
\(224\) −1.57877 4.85894i −0.105486 0.324652i
\(225\) −0.809017 + 0.587785i −0.0539345 + 0.0391857i
\(226\) −4.63326 + 3.36626i −0.308200 + 0.223920i
\(227\) 6.39360 + 19.6775i 0.424358 + 1.30604i 0.903608 + 0.428361i \(0.140909\pi\)
−0.479250 + 0.877679i \(0.659091\pi\)
\(228\) −0.0242693 + 0.0746932i −0.00160727 + 0.00494668i
\(229\) −8.88456 6.45501i −0.587108 0.426559i 0.254172 0.967159i \(-0.418197\pi\)
−0.841280 + 0.540600i \(0.818197\pi\)
\(230\) 6.64849 0.438388
\(231\) 7.41478 15.2362i 0.487857 1.00247i
\(232\) 2.01882 0.132542
\(233\) 2.39719 + 1.74166i 0.157045 + 0.114100i 0.663533 0.748147i \(-0.269056\pi\)
−0.506487 + 0.862247i \(0.669056\pi\)
\(234\) −0.412052 + 1.26816i −0.0269367 + 0.0829025i
\(235\) −2.03009 6.24796i −0.132428 0.407572i
\(236\) 4.30902 3.13068i 0.280493 0.203790i
\(237\) −9.97251 + 7.24545i −0.647784 + 0.470643i
\(238\) −1.22444 3.76842i −0.0793683 0.244271i
\(239\) 2.64821 8.15034i 0.171298 0.527202i −0.828147 0.560511i \(-0.810605\pi\)
0.999445 + 0.0333094i \(0.0106047\pi\)
\(240\) 0.809017 + 0.587785i 0.0522218 + 0.0379414i
\(241\) 7.97000 0.513393 0.256696 0.966492i \(-0.417366\pi\)
0.256696 + 0.966492i \(0.417366\pi\)
\(242\) −0.403010 10.9926i −0.0259065 0.706632i
\(243\) 1.00000 0.0641500
\(244\) 3.03046 + 2.20175i 0.194005 + 0.140953i
\(245\) −5.90278 + 18.1669i −0.377115 + 1.16064i
\(246\) 3.67612 + 11.3139i 0.234381 + 0.721351i
\(247\) 0.0847231 0.0615549i 0.00539080 0.00391665i
\(248\) 6.86933 4.99086i 0.436203 0.316920i
\(249\) −2.47214 7.60845i −0.156665 0.482166i
\(250\) 0.309017 0.951057i 0.0195440 0.0601501i
\(251\) −16.3904 11.9083i −1.03455 0.751645i −0.0653367 0.997863i \(-0.520812\pi\)
−0.969215 + 0.246218i \(0.920812\pi\)
\(252\) 5.10899 0.321836
\(253\) 9.64909 19.8273i 0.606633 1.24653i
\(254\) 6.96281 0.436886
\(255\) 0.627445 + 0.455866i 0.0392921 + 0.0285474i
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) −6.16916 18.9867i −0.384822 1.18436i −0.936609 0.350375i \(-0.886054\pi\)
0.551788 0.833985i \(-0.313946\pi\)
\(258\) −4.86351 + 3.53355i −0.302789 + 0.219989i
\(259\) 16.2565 11.8110i 1.01013 0.733903i
\(260\) −0.412052 1.26816i −0.0255544 0.0786482i
\(261\) −0.623850 + 1.92001i −0.0386154 + 0.118846i
\(262\) −1.77916 1.29264i −0.109917 0.0798593i
\(263\) −0.696114 −0.0429242 −0.0214621 0.999770i \(-0.506832\pi\)
−0.0214621 + 0.999770i \(0.506832\pi\)
\(264\) 2.92705 1.55961i 0.180148 0.0959871i
\(265\) −10.3451 −0.635492
\(266\) −0.324614 0.235846i −0.0199034 0.0144606i
\(267\) −2.99073 + 9.20452i −0.183030 + 0.563307i
\(268\) 0.181713 + 0.559255i 0.0110999 + 0.0341619i
\(269\) −4.79079 + 3.48071i −0.292100 + 0.212223i −0.724178 0.689613i \(-0.757781\pi\)
0.432078 + 0.901836i \(0.357781\pi\)
\(270\) −0.809017 + 0.587785i −0.0492352 + 0.0357715i
\(271\) −4.29983 13.2335i −0.261196 0.803880i −0.992545 0.121876i \(-0.961109\pi\)
0.731349 0.682003i \(-0.238891\pi\)
\(272\) 0.239663 0.737606i 0.0145317 0.0447239i
\(273\) −5.51140 4.00427i −0.333565 0.242349i
\(274\) 2.17590 0.131451
\(275\) −2.38778 2.30185i −0.143989 0.138807i
\(276\) 6.64849 0.400192
\(277\) 8.17313 + 5.93813i 0.491076 + 0.356787i 0.805598 0.592463i \(-0.201844\pi\)
−0.314522 + 0.949250i \(0.601844\pi\)
\(278\) −3.18517 + 9.80293i −0.191034 + 0.587941i
\(279\) 2.62385 + 8.07538i 0.157086 + 0.483460i
\(280\) −4.13326 + 3.00299i −0.247010 + 0.179463i
\(281\) −23.3871 + 16.9918i −1.39516 + 1.01364i −0.399883 + 0.916566i \(0.630949\pi\)
−0.995277 + 0.0970773i \(0.969051\pi\)
\(282\) −2.03009 6.24796i −0.120890 0.372061i
\(283\) −4.05464 + 12.4789i −0.241023 + 0.741793i 0.755242 + 0.655446i \(0.227519\pi\)
−0.996265 + 0.0863469i \(0.972481\pi\)
\(284\) 1.87292 + 1.36076i 0.111138 + 0.0807462i
\(285\) 0.0785371 0.00465213
\(286\) −4.37997 0.611682i −0.258993 0.0361695i
\(287\) −60.7775 −3.58759
\(288\) 0.809017 + 0.587785i 0.0476718 + 0.0346356i
\(289\) −5.06741 + 15.5959i −0.298083 + 0.917406i
\(290\) −0.623850 1.92001i −0.0366338 0.112747i
\(291\) 10.8846 7.90809i 0.638064 0.463581i
\(292\) −8.85410 + 6.43288i −0.518147 + 0.376456i
\(293\) 7.00236 + 21.5511i 0.409082 + 1.25903i 0.917438 + 0.397879i \(0.130254\pi\)
−0.508356 + 0.861147i \(0.669746\pi\)
\(294\) −5.90278 + 18.1669i −0.344257 + 1.05951i
\(295\) −4.30902 3.13068i −0.250881 0.182275i
\(296\) 3.93310 0.228607
\(297\) 0.578765 + 3.26574i 0.0335834 + 0.189497i
\(298\) 15.2477 0.883276
\(299\) −7.17216 5.21088i −0.414777 0.301353i
\(300\) 0.309017 0.951057i 0.0178411 0.0549093i
\(301\) −9.49096 29.2102i −0.547050 1.68365i
\(302\) 5.31461 3.86129i 0.305821 0.222192i
\(303\) 8.60862 6.25453i 0.494552 0.359313i
\(304\) −0.0242693 0.0746932i −0.00139194 0.00428395i
\(305\) 1.15753 3.56251i 0.0662800 0.203989i
\(306\) 0.627445 + 0.455866i 0.0358687 + 0.0260601i
\(307\) −29.3158 −1.67314 −0.836571 0.547859i \(-0.815443\pi\)
−0.836571 + 0.547859i \(0.815443\pi\)
\(308\) 2.95691 + 16.6846i 0.168485 + 0.950694i
\(309\) 16.7087 0.950522
\(310\) −6.86933 4.99086i −0.390152 0.283462i
\(311\) 3.50950 10.8011i 0.199005 0.612476i −0.800901 0.598797i \(-0.795646\pi\)
0.999906 0.0136789i \(-0.00435427\pi\)
\(312\) −0.412052 1.26816i −0.0233278 0.0717957i
\(313\) 2.56995 1.86718i 0.145262 0.105539i −0.512781 0.858520i \(-0.671385\pi\)
0.658043 + 0.752980i \(0.271385\pi\)
\(314\) −7.53046 + 5.47120i −0.424968 + 0.308757i
\(315\) −1.57877 4.85894i −0.0889534 0.273770i
\(316\) 3.80916 11.7234i 0.214282 0.659492i
\(317\) −3.82747 2.78082i −0.214972 0.156186i 0.475088 0.879938i \(-0.342416\pi\)
−0.690060 + 0.723752i \(0.742416\pi\)
\(318\) −10.3451 −0.580122
\(319\) −6.63132 0.926093i −0.371283 0.0518512i
\(320\) −1.00000 −0.0559017
\(321\) −14.1992 10.3163i −0.792520 0.575799i
\(322\) −10.4964 + 32.3046i −0.584942 + 1.80027i
\(323\) −0.0188224 0.0579294i −0.00104731 0.00322328i
\(324\) −0.809017 + 0.587785i −0.0449454 + 0.0326547i
\(325\) −1.07877 + 0.783769i −0.0598391 + 0.0434757i
\(326\) 5.77916 + 17.7864i 0.320078 + 0.985099i
\(327\) −2.76393 + 8.50651i −0.152846 + 0.470411i
\(328\) −9.62422 6.99241i −0.531409 0.386091i
\(329\) 33.5635 1.85042
\(330\) −2.38778 2.30185i −0.131443 0.126712i
\(331\) 30.0424 1.65128 0.825639 0.564199i \(-0.190815\pi\)
0.825639 + 0.564199i \(0.190815\pi\)
\(332\) 6.47214 + 4.70228i 0.355205 + 0.258071i
\(333\) −1.21539 + 3.74060i −0.0666032 + 0.204983i
\(334\) 0.733846 + 2.25855i 0.0401543 + 0.123582i
\(335\) 0.475731 0.345639i 0.0259919 0.0188843i
\(336\) −4.13326 + 3.00299i −0.225488 + 0.163827i
\(337\) −7.83574 24.1159i −0.426840 1.31368i −0.901222 0.433359i \(-0.857328\pi\)
0.474382 0.880319i \(-0.342672\pi\)
\(338\) 3.46778 10.6727i 0.188622 0.580520i
\(339\) 4.63326 + 3.36626i 0.251644 + 0.182830i
\(340\) −0.775565 −0.0420609
\(341\) −24.8535 + 13.2426i −1.34589 + 0.717125i
\(342\) 0.0785371 0.00424680
\(343\) −50.0199 36.3416i −2.70082 1.96226i
\(344\) 1.85770 5.71740i 0.100160 0.308262i
\(345\) −2.05450 6.32309i −0.110610 0.340424i
\(346\) 2.35770 1.71297i 0.126751 0.0920897i
\(347\) 2.56995 1.86718i 0.137962 0.100235i −0.516664 0.856189i \(-0.672826\pi\)
0.654626 + 0.755953i \(0.272826\pi\)
\(348\) −0.623850 1.92001i −0.0334419 0.102924i
\(349\) −2.15034 + 6.61807i −0.115105 + 0.354257i −0.991969 0.126482i \(-0.959632\pi\)
0.876864 + 0.480739i \(0.159632\pi\)
\(350\) 4.13326 + 3.00299i 0.220932 + 0.160517i
\(351\) 1.33343 0.0711731
\(352\) −1.45132 + 2.98223i −0.0773556 + 0.158953i
\(353\) 8.01163 0.426416 0.213208 0.977007i \(-0.431609\pi\)
0.213208 + 0.977007i \(0.431609\pi\)
\(354\) −4.30902 3.13068i −0.229022 0.166394i
\(355\) 0.715393 2.20175i 0.0379691 0.116857i
\(356\) −2.99073 9.20452i −0.158508 0.487839i
\(357\) −3.20561 + 2.32901i −0.169659 + 0.123264i
\(358\) 1.26393 0.918300i 0.0668009 0.0485337i
\(359\) −0.0557281 0.171513i −0.00294122 0.00905213i 0.949575 0.313540i \(-0.101515\pi\)
−0.952516 + 0.304487i \(0.901515\pi\)
\(360\) 0.309017 0.951057i 0.0162866 0.0501251i
\(361\) 15.3663 + 11.1643i 0.808754 + 0.587594i
\(362\) −18.4721 −0.970874
\(363\) −10.3301 + 3.78019i −0.542188 + 0.198409i
\(364\) 6.81247 0.357070
\(365\) 8.85410 + 6.43288i 0.463445 + 0.336712i
\(366\) 1.15753 3.56251i 0.0605051 0.186216i
\(367\) 9.53950 + 29.3596i 0.497958 + 1.53256i 0.812296 + 0.583245i \(0.198217\pi\)
−0.314338 + 0.949311i \(0.601783\pi\)
\(368\) −5.37874 + 3.90788i −0.280386 + 0.203713i
\(369\) 9.62422 6.99241i 0.501017 0.364010i
\(370\) −1.21539 3.74060i −0.0631853 0.194464i
\(371\) 16.3324 50.2660i 0.847937 2.60968i
\(372\) −6.86933 4.99086i −0.356158 0.258764i
\(373\) 16.1018 0.833720 0.416860 0.908971i \(-0.363131\pi\)
0.416860 + 0.908971i \(0.363131\pi\)
\(374\) −1.12559 + 2.31291i −0.0582030 + 0.119598i
\(375\) −1.00000 −0.0516398
\(376\) 5.31483 + 3.86145i 0.274092 + 0.199139i
\(377\) −0.831859 + 2.56020i −0.0428429 + 0.131857i
\(378\) −1.57877 4.85894i −0.0812029 0.249917i
\(379\) −26.3324 + 19.1316i −1.35261 + 0.982726i −0.353729 + 0.935348i \(0.615086\pi\)
−0.998877 + 0.0473775i \(0.984914\pi\)
\(380\) −0.0635378 + 0.0461629i −0.00325942 + 0.00236811i
\(381\) −2.15163 6.62203i −0.110231 0.339257i
\(382\) −6.40523 + 19.7133i −0.327720 + 1.00862i
\(383\) −1.70561 1.23920i −0.0871527 0.0633202i 0.543356 0.839503i \(-0.317154\pi\)
−0.630508 + 0.776182i \(0.717154\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 14.9543 7.96802i 0.762141 0.406088i
\(386\) −1.37079 −0.0697714
\(387\) 4.86351 + 3.53355i 0.247226 + 0.179620i
\(388\) −4.15753 + 12.7956i −0.211067 + 0.649596i
\(389\) −3.89460 11.9864i −0.197464 0.607732i −0.999939 0.0110463i \(-0.996484\pi\)
0.802475 0.596686i \(-0.203516\pi\)
\(390\) −1.07877 + 0.783769i −0.0546254 + 0.0396877i
\(391\) −4.17156 + 3.03082i −0.210965 + 0.153275i
\(392\) −5.90278 18.1669i −0.298135 0.917567i
\(393\) −0.679579 + 2.09153i −0.0342802 + 0.105504i
\(394\) −4.05427 2.94560i −0.204251 0.148397i
\(395\) −12.3267 −0.620223
\(396\) −2.38778 2.30185i −0.119991 0.115672i
\(397\) −30.6341 −1.53748 −0.768741 0.639560i \(-0.779116\pi\)
−0.768741 + 0.639560i \(0.779116\pi\)
\(398\) 18.8571 + 13.7005i 0.945219 + 0.686742i
\(399\) −0.123992 + 0.381607i −0.00620734 + 0.0191042i
\(400\) 0.309017 + 0.951057i 0.0154508 + 0.0475528i
\(401\) 16.1537 11.7364i 0.806678 0.586086i −0.106188 0.994346i \(-0.533864\pi\)
0.912865 + 0.408260i \(0.133864\pi\)
\(402\) 0.475731 0.345639i 0.0237273 0.0172389i
\(403\) 3.49871 + 10.7679i 0.174283 + 0.536389i
\(404\) −3.28820 + 10.1200i −0.163594 + 0.503491i
\(405\) 0.809017 + 0.587785i 0.0402004 + 0.0292073i
\(406\) 10.3141 0.511883
\(407\) −12.9192 1.80423i −0.640382 0.0894322i
\(408\) −0.775565 −0.0383962
\(409\) 5.77608 + 4.19656i 0.285609 + 0.207507i 0.721360 0.692560i \(-0.243517\pi\)
−0.435751 + 0.900067i \(0.643517\pi\)
\(410\) −3.67612 + 11.3139i −0.181551 + 0.558756i
\(411\) −0.672389 2.06940i −0.0331665 0.102076i
\(412\) −13.5176 + 9.82110i −0.665964 + 0.483851i
\(413\) 22.0147 15.9946i 1.08327 0.787045i
\(414\) −2.05450 6.32309i −0.100973 0.310763i
\(415\) 2.47214 7.60845i 0.121352 0.373484i
\(416\) 1.07877 + 0.783769i 0.0528908 + 0.0384274i
\(417\) 10.3074 0.504756
\(418\) 0.0454545 + 0.256481i 0.00222325 + 0.0125449i
\(419\) −22.3691 −1.09280 −0.546400 0.837524i \(-0.684002\pi\)
−0.546400 + 0.837524i \(0.684002\pi\)
\(420\) 4.13326 + 3.00299i 0.201683 + 0.146531i
\(421\) −1.87292 + 5.76427i −0.0912807 + 0.280933i −0.986267 0.165161i \(-0.947186\pi\)
0.894986 + 0.446095i \(0.147186\pi\)
\(422\) 6.20635 + 19.1012i 0.302120 + 0.929831i
\(423\) −5.31483 + 3.86145i −0.258416 + 0.187750i
\(424\) 8.36933 6.08067i 0.406451 0.295304i
\(425\) 0.239663 + 0.737606i 0.0116254 + 0.0357791i
\(426\) 0.715393 2.20175i 0.0346609 0.106675i
\(427\) 15.4826 + 11.2487i 0.749254 + 0.544365i
\(428\) 17.5511 0.848366
\(429\) 0.771742 + 4.35462i 0.0372600 + 0.210243i
\(430\) −6.01163 −0.289907
\(431\) −30.0649 21.8434i −1.44818 1.05216i −0.986253 0.165240i \(-0.947160\pi\)
−0.461922 0.886921i \(-0.652840\pi\)
\(432\) 0.309017 0.951057i 0.0148676 0.0457577i
\(433\) 9.47259 + 29.1536i 0.455224 + 1.40103i 0.870872 + 0.491509i \(0.163555\pi\)
−0.415649 + 0.909525i \(0.636445\pi\)
\(434\) 35.0954 25.4983i 1.68463 1.22396i
\(435\) −1.63326 + 1.18663i −0.0783089 + 0.0568947i
\(436\) −2.76393 8.50651i −0.132368 0.407388i
\(437\) −0.161354 + 0.496597i −0.00771861 + 0.0237554i
\(438\) 8.85410 + 6.43288i 0.423065 + 0.307375i
\(439\) 7.06017 0.336964 0.168482 0.985705i \(-0.446114\pi\)
0.168482 + 0.985705i \(0.446114\pi\)
\(440\) 3.28475 + 0.458729i 0.156594 + 0.0218691i
\(441\) 19.1018 0.909610
\(442\) 0.836653 + 0.607864i 0.0397955 + 0.0289131i
\(443\) 4.50932 13.8783i 0.214244 0.659377i −0.784962 0.619544i \(-0.787318\pi\)
0.999206 0.0398326i \(-0.0126825\pi\)
\(444\) −1.21539 3.74060i −0.0576800 0.177521i
\(445\) −7.82983 + 5.68871i −0.371170 + 0.269671i
\(446\) 7.36933 5.35413i 0.348948 0.253525i
\(447\) −4.71180 14.5014i −0.222860 0.685894i
\(448\) 1.57877 4.85894i 0.0745897 0.229563i
\(449\) −10.3301 7.50523i −0.487506 0.354194i 0.316719 0.948520i \(-0.397419\pi\)
−0.804224 + 0.594326i \(0.797419\pi\)
\(450\) −1.00000 −0.0471405
\(451\) 28.4055 + 27.3832i 1.33756 + 1.28942i
\(452\) −5.72703 −0.269377
\(453\) −5.31461 3.86129i −0.249702 0.181419i
\(454\) −6.39360 + 19.6775i −0.300066 + 0.923510i
\(455\) −2.10517 6.47904i −0.0986919 0.303742i
\(456\) −0.0635378 + 0.0461629i −0.00297543 + 0.00216178i
\(457\) 14.0305 10.1937i 0.656317 0.476842i −0.209100 0.977894i \(-0.567053\pi\)
0.865417 + 0.501052i \(0.167053\pi\)
\(458\) −3.39360 10.4444i −0.158572 0.488036i
\(459\) 0.239663 0.737606i 0.0111865 0.0344285i
\(460\) 5.37874 + 3.90788i 0.250785 + 0.182206i
\(461\) −2.99355 −0.139424 −0.0697118 0.997567i \(-0.522208\pi\)
−0.0697118 + 0.997567i \(0.522208\pi\)
\(462\) 14.9543 7.96802i 0.695736 0.370706i
\(463\) −16.2589 −0.755614 −0.377807 0.925884i \(-0.623322\pi\)
−0.377807 + 0.925884i \(0.623322\pi\)
\(464\) 1.63326 + 1.18663i 0.0758223 + 0.0550881i
\(465\) −2.62385 + 8.07538i −0.121678 + 0.374487i
\(466\) 0.915646 + 2.81807i 0.0424165 + 0.130545i
\(467\) 15.0240 10.9156i 0.695228 0.505113i −0.183147 0.983086i \(-0.558628\pi\)
0.878375 + 0.477973i \(0.158628\pi\)
\(468\) −1.07877 + 0.783769i −0.0498660 + 0.0362297i
\(469\) 0.928370 + 2.85723i 0.0428682 + 0.131935i
\(470\) 2.03009 6.24796i 0.0936409 0.288197i
\(471\) 7.53046 + 5.47120i 0.346985 + 0.252099i
\(472\) 5.32624 0.245160
\(473\) −8.72480 + 17.9280i −0.401167 + 0.824332i
\(474\) −12.3267 −0.566184
\(475\) 0.0635378 + 0.0461629i 0.00291531 + 0.00211810i
\(476\) 1.22444 3.76842i 0.0561219 0.172725i
\(477\) 3.19680 + 9.83874i 0.146371 + 0.450485i
\(478\) 6.93310 5.03719i 0.317112 0.230396i
\(479\) 24.7198 17.9600i 1.12948 0.820614i 0.143859 0.989598i \(-0.454049\pi\)
0.985619 + 0.168984i \(0.0540487\pi\)
\(480\) 0.309017 + 0.951057i 0.0141046 + 0.0434096i
\(481\) −1.62064 + 4.98781i −0.0738948 + 0.227425i
\(482\) 6.44787 + 4.68465i 0.293692 + 0.213380i
\(483\) 33.9671 1.54556
\(484\) 6.13525 9.13010i 0.278875 0.415004i
\(485\) 13.4541 0.610917
\(486\) 0.809017 + 0.587785i 0.0366978 + 0.0266625i
\(487\) −0.157074 + 0.483424i −0.00711771 + 0.0219061i −0.954552 0.298043i \(-0.903666\pi\)
0.947435 + 0.319950i \(0.103666\pi\)
\(488\) 1.15753 + 3.56251i 0.0523990 + 0.161267i
\(489\) 15.1300 10.9926i 0.684204 0.497103i
\(490\) −15.4537 + 11.2278i −0.698126 + 0.507218i
\(491\) 12.1735 + 37.4662i 0.549383 + 1.69083i 0.710333 + 0.703865i \(0.248544\pi\)
−0.160950 + 0.986963i \(0.551456\pi\)
\(492\) −3.67612 + 11.3139i −0.165733 + 0.510072i
\(493\) 1.26670 + 0.920312i 0.0570493 + 0.0414488i
\(494\) 0.104723 0.00471173
\(495\) −1.45132 + 2.98223i −0.0652320 + 0.134041i
\(496\) 8.49096 0.381255
\(497\) 9.56876 + 6.95211i 0.429217 + 0.311845i
\(498\) 2.47214 7.60845i 0.110779 0.340943i
\(499\) 6.63175 + 20.4104i 0.296878 + 0.913696i 0.982584 + 0.185818i \(0.0594934\pi\)
−0.685706 + 0.727878i \(0.740507\pi\)
\(500\) 0.809017 0.587785i 0.0361803 0.0262866i
\(501\) 1.92123 1.39586i 0.0858344 0.0623624i
\(502\) −6.26057 19.2680i −0.279423 0.859975i
\(503\) −7.27779 + 22.3987i −0.324500 + 0.998710i 0.647165 + 0.762350i \(0.275954\pi\)
−0.971666 + 0.236360i \(0.924046\pi\)
\(504\) 4.13326 + 3.00299i 0.184110 + 0.133764i
\(505\) 10.6408 0.473511
\(506\) 19.4605 10.3690i 0.865123 0.460959i
\(507\) −11.2220 −0.498385
\(508\) 5.63303 + 4.09264i 0.249925 + 0.181581i
\(509\) 11.9645 36.8228i 0.530316 1.63214i −0.223243 0.974763i \(-0.571664\pi\)
0.753558 0.657381i \(-0.228336\pi\)
\(510\) 0.239663 + 0.737606i 0.0106124 + 0.0326617i
\(511\) −45.2355 + 32.8655i −2.00110 + 1.45389i
\(512\) 0.809017 0.587785i 0.0357538 0.0259767i
\(513\) −0.0242693 0.0746932i −0.00107152 0.00329778i
\(514\) 6.16916 18.9867i 0.272110 0.837469i
\(515\) 13.5176 + 9.82110i 0.595656 + 0.432770i
\(516\) −6.01163 −0.264647
\(517\) −15.6865 15.1220i −0.689893 0.665063i
\(518\) 20.0942 0.882887
\(519\) −2.35770 1.71297i −0.103491 0.0751909i
\(520\) 0.412052 1.26816i 0.0180697 0.0556127i
\(521\) 0.784660 + 2.41494i 0.0343766 + 0.105800i 0.966772 0.255638i \(-0.0822857\pi\)
−0.932396 + 0.361439i \(0.882286\pi\)
\(522\) −1.63326 + 1.18663i −0.0714859 + 0.0519376i
\(523\) −30.1927 + 21.9363i −1.32024 + 0.959207i −0.320306 + 0.947314i \(0.603786\pi\)
−0.999929 + 0.0118928i \(0.996214\pi\)
\(524\) −0.679579 2.09153i −0.0296875 0.0913688i
\(525\) 1.57877 4.85894i 0.0689030 0.212062i
\(526\) −0.563168 0.409166i −0.0245553 0.0178405i
\(527\) 6.58529 0.286860
\(528\) 3.28475 + 0.458729i 0.142950 + 0.0199636i
\(529\) 21.2024 0.921844
\(530\) −8.36933 6.08067i −0.363540 0.264128i
\(531\) −1.64590 + 5.06555i −0.0714259 + 0.219826i
\(532\) −0.123992 0.381607i −0.00537572 0.0165448i
\(533\) 12.8332 9.32386i 0.555868 0.403861i
\(534\) −7.82983 + 5.68871i −0.338830 + 0.246174i
\(535\) −5.42360 16.6921i −0.234483 0.721663i
\(536\) −0.181713 + 0.559255i −0.00784880 + 0.0241561i
\(537\) −1.26393 0.918300i −0.0545427 0.0396276i
\(538\) −5.92175 −0.255305
\(539\) 11.0555 + 62.3814i 0.476193 + 2.68696i
\(540\) −1.00000 −0.0430331
\(541\) 7.47140 + 5.42829i 0.321220 + 0.233380i 0.736696 0.676224i \(-0.236385\pi\)
−0.415476 + 0.909604i \(0.636385\pi\)
\(542\) 4.29983 13.2335i 0.184694 0.568429i
\(543\) 5.70820 + 17.5680i 0.244962 + 0.753917i
\(544\) 0.627445 0.455866i 0.0269015 0.0195451i
\(545\) −7.23607 + 5.25731i −0.309959 + 0.225198i
\(546\) −2.10517 6.47904i −0.0900929 0.277278i
\(547\) −7.84155 + 24.1338i −0.335281 + 1.03189i 0.631303 + 0.775536i \(0.282520\pi\)
−0.966584 + 0.256351i \(0.917480\pi\)
\(548\) 1.76034 + 1.27896i 0.0751979 + 0.0546345i
\(549\) −3.74585 −0.159869
\(550\) −0.578765 3.26574i −0.0246786 0.139251i
\(551\) 0.158552 0.00675456
\(552\) 5.37874 + 3.90788i 0.228934 + 0.166331i
\(553\) 19.4610 59.8947i 0.827564 2.54698i
\(554\) 3.12186 + 9.60809i 0.132635 + 0.408209i
\(555\) −3.18194 + 2.31182i −0.135066 + 0.0981311i
\(556\) −8.33887 + 6.05855i −0.353647 + 0.256940i
\(557\) −3.27888 10.0913i −0.138930 0.427584i 0.857250 0.514900i \(-0.172171\pi\)
−0.996181 + 0.0873160i \(0.972171\pi\)
\(558\) −2.62385 + 8.07538i −0.111076 + 0.341858i
\(559\) 6.48514 + 4.71173i 0.274292 + 0.199285i
\(560\) −5.10899 −0.215894
\(561\) 2.54754 + 0.355774i 0.107557 + 0.0150208i
\(562\) −28.9081 −1.21941
\(563\) 3.75748 + 2.72997i 0.158359 + 0.115055i 0.664143 0.747606i \(-0.268797\pi\)
−0.505784 + 0.862660i \(0.668797\pi\)
\(564\) 2.03009 6.24796i 0.0854820 0.263087i
\(565\) 1.76975 + 5.44673i 0.0744539 + 0.229145i
\(566\) −10.6152 + 7.71238i −0.446189 + 0.324175i
\(567\) −4.13326 + 3.00299i −0.173581 + 0.126114i
\(568\) 0.715393 + 2.20175i 0.0300172 + 0.0923836i
\(569\) −10.8497 + 33.3920i −0.454844 + 1.39987i 0.416473 + 0.909148i \(0.363266\pi\)
−0.871318 + 0.490719i \(0.836734\pi\)
\(570\) 0.0635378 + 0.0461629i 0.00266131 + 0.00193355i
\(571\) 17.7758 0.743896 0.371948 0.928254i \(-0.378690\pi\)
0.371948 + 0.928254i \(0.378690\pi\)
\(572\) −3.18393 3.06934i −0.133127 0.128336i
\(573\) 20.7278 0.865915
\(574\) −49.1701 35.7241i −2.05232 1.49110i
\(575\) 2.05450 6.32309i 0.0856784 0.263691i
\(576\) 0.309017 + 0.951057i 0.0128757 + 0.0396274i
\(577\) −2.94029 + 2.13624i −0.122406 + 0.0889329i −0.647304 0.762232i \(-0.724103\pi\)
0.524898 + 0.851165i \(0.324103\pi\)
\(578\) −13.2667 + 9.63880i −0.551820 + 0.400921i
\(579\) 0.423597 + 1.30370i 0.0176041 + 0.0541799i
\(580\) 0.623850 1.92001i 0.0259040 0.0797243i
\(581\) 33.0661 + 24.0239i 1.37181 + 0.996680i
\(582\) 13.4541 0.557688
\(583\) −30.2805 + 16.1342i −1.25409 + 0.668211i
\(584\) −10.9443 −0.452877
\(585\) 1.07877 + 0.783769i 0.0446015 + 0.0324049i
\(586\) −7.00236 + 21.5511i −0.289265 + 0.890266i
\(587\) 2.28461 + 7.03130i 0.0942958 + 0.290213i 0.987070 0.160293i \(-0.0512438\pi\)
−0.892774 + 0.450505i \(0.851244\pi\)
\(588\) −15.4537 + 11.2278i −0.637299 + 0.463025i
\(589\) 0.539497 0.391967i 0.0222296 0.0161507i
\(590\) −1.64590 5.06555i −0.0677605 0.208546i
\(591\) −1.54859 + 4.76608i −0.0637006 + 0.196050i
\(592\) 3.18194 + 2.31182i 0.130777 + 0.0950150i
\(593\) −35.9315 −1.47553 −0.737766 0.675057i \(-0.764119\pi\)
−0.737766 + 0.675057i \(0.764119\pi\)
\(594\) −1.45132 + 2.98223i −0.0595484 + 0.122362i
\(595\) −3.96236 −0.162441
\(596\) 12.3356 + 8.96237i 0.505288 + 0.367113i
\(597\) 7.20276 22.1678i 0.294789 0.907268i
\(598\) −2.73952 8.43138i −0.112027 0.344785i
\(599\) 16.6297 12.0822i 0.679470 0.493664i −0.193712 0.981058i \(-0.562053\pi\)
0.873182 + 0.487395i \(0.162053\pi\)
\(600\) 0.809017 0.587785i 0.0330280 0.0239962i
\(601\) −1.58259 4.87071i −0.0645551 0.198680i 0.913577 0.406667i \(-0.133309\pi\)
−0.978132 + 0.207986i \(0.933309\pi\)
\(602\) 9.49096 29.2102i 0.386823 1.19052i
\(603\) −0.475731 0.345639i −0.0193733 0.0140755i
\(604\) 6.56921 0.267297
\(605\) −10.5791 3.01362i −0.430103 0.122521i
\(606\) 10.6408 0.432255
\(607\) 30.2529 + 21.9800i 1.22793 + 0.892141i 0.996733 0.0807668i \(-0.0257369\pi\)
0.231194 + 0.972908i \(0.425737\pi\)
\(608\) 0.0242693 0.0746932i 0.000984249 0.00302921i
\(609\) −3.18725 9.80934i −0.129154 0.397494i
\(610\) 3.03046 2.20175i 0.122700 0.0891464i
\(611\) −7.08694 + 5.14897i −0.286707 + 0.208305i
\(612\) 0.239663 + 0.737606i 0.00968779 + 0.0298160i
\(613\) −2.59477 + 7.98588i −0.104802 + 0.322546i −0.989684 0.143268i \(-0.954239\pi\)
0.884882 + 0.465815i \(0.154239\pi\)
\(614\) −23.7170 17.2314i −0.957139 0.695403i
\(615\) 11.8962 0.479701
\(616\) −7.41478 + 15.2362i −0.298750 + 0.613883i
\(617\) −25.9029 −1.04281 −0.521406 0.853309i \(-0.674592\pi\)
−0.521406 + 0.853309i \(0.674592\pi\)
\(618\) 13.5176 + 9.82110i 0.543757 + 0.395063i
\(619\) 7.76994 23.9134i 0.312300 0.961162i −0.664551 0.747243i \(-0.731377\pi\)
0.976851 0.213919i \(-0.0686228\pi\)
\(620\) −2.62385 8.07538i −0.105376 0.324315i
\(621\) −5.37874 + 3.90788i −0.215841 + 0.156818i
\(622\) 9.18799 6.67546i 0.368405 0.267662i
\(623\) −15.2796 47.0258i −0.612165 1.88405i
\(624\) 0.412052 1.26816i 0.0164953 0.0507672i
\(625\) −0.809017 0.587785i −0.0323607 0.0235114i
\(626\) 3.17664 0.126964
\(627\) 0.229882 0.122487i 0.00918060 0.00489166i
\(628\) −9.30815 −0.371436
\(629\) 2.46780 + 1.79296i 0.0983977 + 0.0714901i
\(630\) 1.57877 4.85894i 0.0628995 0.193585i
\(631\) −12.9922 39.9858i −0.517210 1.59181i −0.779224 0.626746i \(-0.784387\pi\)
0.262014 0.965064i \(-0.415613\pi\)
\(632\) 9.97251 7.24545i 0.396685 0.288209i
\(633\) 16.2484 11.8052i 0.645818 0.469214i
\(634\) −1.46196 4.49946i −0.0580620 0.178696i
\(635\) 2.15163 6.62203i 0.0853847 0.262787i
\(636\) −8.36933 6.08067i −0.331866 0.241114i
\(637\) 25.4709 1.00919
\(638\) −4.82051 4.64702i −0.190846 0.183977i
\(639\) −2.31506 −0.0915824
\(640\) −0.809017 0.587785i −0.0319792 0.0232343i
\(641\) −0.653762 + 2.01207i −0.0258220 + 0.0794720i −0.963137 0.269011i \(-0.913303\pi\)
0.937315 + 0.348483i \(0.113303\pi\)
\(642\) −5.42360 16.6921i −0.214052 0.658785i
\(643\) 31.9422 23.2073i 1.25968 0.915208i 0.260934 0.965357i \(-0.415970\pi\)
0.998742 + 0.0501487i \(0.0159695\pi\)
\(644\) −27.4799 + 19.9653i −1.08286 + 0.786745i
\(645\) 1.85770 + 5.71740i 0.0731467 + 0.225123i
\(646\) 0.0188224 0.0579294i 0.000740558 0.00227920i
\(647\) 13.0619 + 9.49005i 0.513518 + 0.373092i 0.814156 0.580646i \(-0.197200\pi\)
−0.300639 + 0.953738i \(0.597200\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −17.4953 2.44330i −0.686752 0.0959080i
\(650\) −1.33343 −0.0523013
\(651\) −35.0954 25.4983i −1.37550 0.999356i
\(652\) −5.77916 + 17.7864i −0.226329 + 0.696570i
\(653\) −0.399046 1.22814i −0.0156159 0.0480607i 0.942945 0.332949i \(-0.108044\pi\)
−0.958561 + 0.284888i \(0.908044\pi\)
\(654\) −7.23607 + 5.25731i −0.282953 + 0.205577i
\(655\) −1.77916 + 1.29264i −0.0695175 + 0.0505074i
\(656\) −3.67612 11.3139i −0.143529 0.441736i
\(657\) 3.38197 10.4086i 0.131943 0.406079i
\(658\) 27.1534 + 19.7281i 1.05855 + 0.769083i
\(659\) −23.7015 −0.923278 −0.461639 0.887068i \(-0.652738\pi\)
−0.461639 + 0.887068i \(0.652738\pi\)
\(660\) −0.578765 3.26574i −0.0225284 0.127119i
\(661\) −17.0796 −0.664318 −0.332159 0.943223i \(-0.607777\pi\)
−0.332159 + 0.943223i \(0.607777\pi\)
\(662\) 24.3048 + 17.6585i 0.944632 + 0.686316i
\(663\) 0.319573 0.983544i 0.0124112 0.0381977i
\(664\) 2.47214 + 7.60845i 0.0959375 + 0.295265i
\(665\) −0.324614 + 0.235846i −0.0125880 + 0.00914572i
\(666\) −3.18194 + 2.31182i −0.123298 + 0.0895810i
\(667\) −4.14766 12.7652i −0.160598 0.494270i
\(668\) −0.733846 + 2.25855i −0.0283934 + 0.0873858i
\(669\) −7.36933 5.35413i −0.284915 0.207003i
\(670\) 0.588036 0.0227178
\(671\) −2.16797 12.2330i −0.0836935 0.472248i
\(672\) −5.10899 −0.197084
\(673\) 6.88530 + 5.00246i 0.265409 + 0.192831i 0.712528 0.701644i \(-0.247550\pi\)
−0.447119 + 0.894474i \(0.647550\pi\)
\(674\) 7.83574 24.1159i 0.301821 0.928910i
\(675\) 0.309017 + 0.951057i 0.0118941 + 0.0366062i
\(676\) 9.07877 6.59611i 0.349183 0.253697i
\(677\) −18.3748 + 13.3501i −0.706200 + 0.513084i −0.881946 0.471351i \(-0.843766\pi\)
0.175746 + 0.984436i \(0.443766\pi\)
\(678\) 1.76975 + 5.44673i 0.0679668 + 0.209180i
\(679\) −21.2408 + 65.3724i −0.815147 + 2.50876i
\(680\) −0.627445 0.455866i −0.0240614 0.0174816i
\(681\) 20.6901 0.792847
\(682\) −27.8907 3.89505i −1.06799 0.149149i
\(683\) −11.0419 −0.422507 −0.211254 0.977431i \(-0.567755\pi\)
−0.211254 + 0.977431i \(0.567755\pi\)
\(684\) 0.0635378 + 0.0461629i 0.00242943 + 0.00176508i
\(685\) 0.672389 2.06940i 0.0256907 0.0790677i
\(686\) −19.1059 58.8019i −0.729467 2.24507i
\(687\) −8.88456 + 6.45501i −0.338967 + 0.246274i
\(688\) 4.86351 3.53355i 0.185420 0.134715i
\(689\) 4.26270 + 13.1192i 0.162396 + 0.499803i
\(690\) 2.05450 6.32309i 0.0782133 0.240716i
\(691\) −7.68513 5.58357i −0.292356 0.212409i 0.431933 0.901906i \(-0.357832\pi\)
−0.724289 + 0.689497i \(0.757832\pi\)
\(692\) 2.91427 0.110784
\(693\) −12.1992 11.7601i −0.463408 0.446730i
\(694\) 3.17664 0.120583
\(695\) 8.33887 + 6.05855i 0.316312 + 0.229814i
\(696\) 0.623850 1.92001i 0.0236470 0.0727780i
\(697\) −2.85107 8.77470i −0.107992 0.332366i
\(698\) −5.62967 + 4.09019i −0.213086 + 0.154816i
\(699\) 2.39719 1.74166i 0.0906702 0.0658758i
\(700\) 1.57877 + 4.85894i 0.0596717 + 0.183651i
\(701\) 7.97028 24.5300i 0.301033 0.926486i −0.680094 0.733125i \(-0.738061\pi\)
0.981128 0.193361i \(-0.0619389\pi\)
\(702\) 1.07877 + 0.783769i 0.0407154 + 0.0295815i
\(703\) 0.308894 0.0116501
\(704\) −2.92705 + 1.55961i −0.110317 + 0.0587799i
\(705\) −6.56950 −0.247422
\(706\) 6.48155 + 4.70912i 0.243936 + 0.177230i
\(707\) −16.7994 + 51.7032i −0.631806 + 1.94450i
\(708\) −1.64590 5.06555i −0.0618566 0.190375i
\(709\) 11.1583 8.10696i 0.419058 0.304463i −0.358201 0.933645i \(-0.616610\pi\)
0.777259 + 0.629181i \(0.216610\pi\)
\(710\) 1.87292 1.36076i 0.0702896 0.0510684i
\(711\) 3.80916 + 11.7234i 0.142855 + 0.439661i
\(712\) 2.99073 9.20452i 0.112082 0.344954i
\(713\) −45.6707 33.1817i −1.71038 1.24266i
\(714\) −3.96236 −0.148287
\(715\) −1.93523 + 3.97658i −0.0723735 + 0.148716i
\(716\) 1.56231 0.0583861
\(717\) −6.93310 5.03719i −0.258921 0.188117i
\(718\) 0.0557281 0.171513i 0.00207975 0.00640082i
\(719\) −5.99601 18.4538i −0.223614 0.688212i −0.998429 0.0560248i \(-0.982157\pi\)
0.774816 0.632187i \(-0.217843\pi\)
\(720\) 0.809017 0.587785i 0.0301503 0.0219055i
\(721\) −69.0613 + 50.1759i −2.57198 + 1.86865i
\(722\) 5.86942 + 18.0642i 0.218437 + 0.672280i
\(723\) 2.46287 7.57992i 0.0915950 0.281900i
\(724\) −14.9443 10.8576i −0.555399 0.403521i
\(725\) −2.01882 −0.0749772
\(726\) −10.5791 3.01362i −0.392629 0.111846i
\(727\) −1.37752 −0.0510895 −0.0255447 0.999674i \(-0.508132\pi\)
−0.0255447 + 0.999674i \(0.508132\pi\)
\(728\) 5.51140 + 4.00427i 0.204266 + 0.148408i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) 3.38197 + 10.4086i 0.125172 + 0.385240i
\(731\) 3.77197 2.74050i 0.139511 0.101361i
\(732\) 3.03046 2.20175i 0.112009 0.0813792i
\(733\) 6.76062 + 20.8070i 0.249709 + 0.768526i 0.994826 + 0.101592i \(0.0323936\pi\)
−0.745117 + 0.666934i \(0.767606\pi\)
\(734\) −9.53950 + 29.3596i −0.352109 + 1.08368i
\(735\) 15.4537 + 11.2278i 0.570018 + 0.414142i
\(736\) −6.64849 −0.245067
\(737\) 0.853428 1.75365i 0.0314364 0.0645967i
\(738\) 11.8962 0.437905
\(739\) −0.425058 0.308822i −0.0156360 0.0113602i 0.579940 0.814659i \(-0.303076\pi\)
−0.595576 + 0.803299i \(0.703076\pi\)
\(740\) 1.21539 3.74060i 0.0446788 0.137507i
\(741\) −0.0323613 0.0995979i −0.00118882 0.00365882i
\(742\) 42.7588 31.0661i 1.56973 1.14047i
\(743\) −38.7413 + 28.1472i −1.42128 + 1.03262i −0.429720 + 0.902962i \(0.641388\pi\)
−0.991559 + 0.129657i \(0.958612\pi\)
\(744\) −2.62385 8.07538i −0.0961950 0.296058i
\(745\) 4.71180 14.5014i 0.172627 0.531291i
\(746\) 13.0266 + 9.46440i 0.476939 + 0.346516i
\(747\) −8.00000 −0.292705
\(748\) −2.27012 + 1.20958i −0.0830037 + 0.0442265i
\(749\) 89.6686 3.27642
\(750\) −0.809017 0.587785i −0.0295411 0.0214629i
\(751\) 11.1723 34.3848i 0.407683 1.25472i −0.510951 0.859610i \(-0.670707\pi\)
0.918634 0.395110i \(-0.129293\pi\)
\(752\) 2.03009 + 6.24796i 0.0740296 + 0.227840i
\(753\) −16.3904 + 11.9083i −0.597298 + 0.433963i
\(754\) −2.17784 + 1.58229i −0.0793121 + 0.0576236i
\(755\) −2.03000 6.24769i −0.0738792 0.227377i
\(756\) 1.57877 4.85894i 0.0574191 0.176718i
\(757\) 35.2824 + 25.6341i 1.28236 + 0.931689i 0.999622 0.0275084i \(-0.00875730\pi\)
0.282738 + 0.959197i \(0.408757\pi\)
\(758\) −32.5487 −1.18222
\(759\) −15.8751 15.3038i −0.576231 0.555493i
\(760\) −0.0785371 −0.00284884
\(761\) 0.891747 + 0.647892i 0.0323258 + 0.0234861i 0.603831 0.797112i \(-0.293640\pi\)
−0.571505 + 0.820599i \(0.693640\pi\)
\(762\) 2.15163 6.62203i 0.0779452 0.239891i
\(763\) −14.1209 43.4597i −0.511211 1.57335i
\(764\) −16.7691 + 12.1835i −0.606685 + 0.440783i
\(765\) 0.627445 0.455866i 0.0226853 0.0164819i
\(766\) −0.651486 2.00507i −0.0235391 0.0724461i
\(767\) −2.19469 + 6.75455i −0.0792455 + 0.243893i
\(768\) −0.809017 0.587785i −0.0291929 0.0212099i
\(769\) −26.9983 −0.973583 −0.486791 0.873518i \(-0.661833\pi\)
−0.486791 + 0.873518i \(0.661833\pi\)
\(770\) 16.7818 + 2.34364i 0.604772 + 0.0844591i
\(771\) −19.9638 −0.718980
\(772\) −1.10899 0.805730i −0.0399135 0.0289989i
\(773\) −7.26427 + 22.3571i −0.261278 + 0.804130i 0.731250 + 0.682109i \(0.238937\pi\)
−0.992528 + 0.122020i \(0.961063\pi\)
\(774\) 1.85770 + 5.71740i 0.0667735 + 0.205508i
\(775\) −6.86933 + 4.99086i −0.246754 + 0.179277i
\(776\) −10.8846 + 7.90809i −0.390733 + 0.283884i
\(777\) −6.20944 19.1107i −0.222762 0.685592i
\(778\) 3.89460 11.9864i 0.139628 0.429732i
\(779\) −0.755858 0.549163i −0.0270814 0.0196758i
\(780\) −1.33343 −0.0477444
\(781\) −1.33988 7.56038i −0.0479446 0.270532i
\(782\) −5.15633 −0.184390
\(783\) 1.63326 + 1.18663i 0.0583680 + 0.0424068i
\(784\) 5.90278 18.1669i 0.210814 0.648818i
\(785\) 2.87638 + 8.85258i 0.102662 + 0.315962i
\(786\) −1.77916 + 1.29264i −0.0634605 + 0.0461068i
\(787\) 26.1826 19.0227i 0.933308 0.678088i −0.0134929 0.999909i \(-0.504295\pi\)
0.946800 + 0.321821i \(0.104295\pi\)
\(788\) −1.54859 4.76608i −0.0551663 0.169784i
\(789\) −0.215111 + 0.662044i −0.00765816 + 0.0235694i
\(790\) −9.97251 7.24545i −0.354806 0.257782i
\(791\) −29.2593 −1.04034
\(792\) −0.578765 3.26574i −0.0205655 0.116043i
\(793\) −4.99482 −0.177371
\(794\) −24.7835 18.0063i −0.879534 0.639019i
\(795\) −3.19680 + 9.83874i −0.113379 + 0.348944i
\(796\) 7.20276 + 22.1678i 0.255295 + 0.785717i
\(797\) 32.6868 23.7483i 1.15782 0.841209i 0.168323 0.985732i \(-0.446165\pi\)
0.989501 + 0.144523i \(0.0461649\pi\)
\(798\) −0.324614 + 0.235846i −0.0114912 + 0.00834886i
\(799\) 1.57446 + 4.84570i 0.0557005 + 0.171429i
\(800\) −0.309017 + 0.951057i −0.0109254 + 0.0336249i
\(801\) 7.82983 + 5.68871i 0.276654 + 0.201001i
\(802\) 19.9671 0.705062
\(803\) 35.9492 + 5.02046i 1.26862 + 0.177168i
\(804\) 0.588036 0.0207384
\(805\) 27.4799 + 19.9653i 0.968541 + 0.703686i
\(806\) −3.49871 + 10.7679i −0.123237 + 0.379284i
\(807\) 1.82992 + 5.63191i 0.0644162 + 0.198253i
\(808\) −8.60862 + 6.25453i −0.302850 + 0.220034i
\(809\) −9.89956 + 7.19245i −0.348050 + 0.252873i −0.748050 0.663642i \(-0.769010\pi\)
0.400001 + 0.916515i \(0.369010\pi\)
\(810\) 0.309017 + 0.951057i 0.0108578 + 0.0334167i
\(811\) −4.68730 + 14.4260i −0.164593 + 0.506566i −0.999006 0.0445737i \(-0.985807\pi\)
0.834413 + 0.551140i \(0.185807\pi\)
\(812\) 8.34432 + 6.06250i 0.292828 + 0.212752i
\(813\) −13.9146 −0.488005
\(814\) −9.39138 9.05338i −0.329168 0.317321i
\(815\) 18.7018 0.655094
\(816\) −0.627445 0.455866i −0.0219650 0.0159585i
\(817\) 0.145898 0.449028i 0.00510433 0.0157095i
\(818\) 2.20626 + 6.79018i 0.0771402 + 0.237413i
\(819\) −5.51140 + 4.00427i −0.192584 + 0.139921i
\(820\) −9.62422 + 6.99241i −0.336092 + 0.244185i
\(821\) −4.47242 13.7647i −0.156088 0.480391i 0.842181 0.539195i \(-0.181271\pi\)
−0.998270 + 0.0588039i \(0.981271\pi\)
\(822\) 0.672389 2.06940i 0.0234523 0.0721786i
\(823\) −2.86910 2.08452i −0.100011 0.0726619i 0.536656 0.843801i \(-0.319687\pi\)
−0.636667 + 0.771139i \(0.719687\pi\)
\(824\) −16.7087 −0.582074
\(825\) −2.92705 + 1.55961i −0.101907 + 0.0542985i
\(826\) 27.2117 0.946816
\(827\) 30.1130 + 21.8784i 1.04713 + 0.760785i 0.971665 0.236363i \(-0.0759555\pi\)
0.0754661 + 0.997148i \(0.475956\pi\)
\(828\) 2.05450 6.32309i 0.0713987 0.219743i
\(829\) −12.6297 38.8701i −0.438646 1.35001i −0.889303 0.457318i \(-0.848810\pi\)
0.450657 0.892697i \(-0.351190\pi\)
\(830\) 6.47214 4.70228i 0.224651 0.163219i
\(831\) 8.17313 5.93813i 0.283523 0.205991i
\(832\) 0.412052 + 1.26816i 0.0142853 + 0.0439657i
\(833\) 4.57799 14.0896i 0.158618 0.488176i
\(834\) 8.33887 + 6.05855i 0.288752 + 0.209790i
\(835\) 2.37478 0.0821825
\(836\) −0.113982 + 0.234215i −0.00394216 + 0.00810050i
\(837\) 8.49096 0.293490
\(838\) −18.0970 13.1482i −0.625149 0.454197i
\(839\) −5.07209 + 15.6103i −0.175108 + 0.538927i −0.999638 0.0268909i \(-0.991439\pi\)
0.824530 + 0.565818i \(0.191439\pi\)
\(840\) 1.57877 + 4.85894i 0.0544726 + 0.167649i
\(841\) 20.1642 14.6502i 0.695318 0.505178i
\(842\) −4.90338 + 3.56251i −0.168982 + 0.122772i
\(843\) 8.93310 + 27.4932i 0.307672 + 0.946918i
\(844\) −6.20635 + 19.1012i −0.213631 + 0.657490i
\(845\) −9.07877 6.59611i −0.312319 0.226913i
\(846\) −6.56950 −0.225864
\(847\) 31.3450 46.6456i 1.07703 1.60276i
\(848\) 10.3451 0.355251
\(849\) 10.6152 + 7.71238i 0.364312 + 0.264688i
\(850\) −0.239663 + 0.737606i −0.00822036 + 0.0252997i
\(851\) −8.08053 24.8693i −0.276997 0.852509i
\(852\) 1.87292 1.36076i 0.0641653 0.0466188i
\(853\) −14.7144 + 10.6906i −0.503811 + 0.366040i −0.810471 0.585779i \(-0.800789\pi\)
0.306660 + 0.951819i \(0.400789\pi\)
\(854\) 5.91382 + 18.2009i 0.202367 + 0.622820i
\(855\) 0.0242693 0.0746932i 0.000829992 0.00255445i
\(856\) 14.1992 + 10.3163i 0.485317 + 0.352604i
\(857\) 48.5679 1.65905 0.829525 0.558470i \(-0.188611\pi\)
0.829525 + 0.558470i \(0.188611\pi\)
\(858\) −1.93523 + 3.97658i −0.0660677 + 0.135758i
\(859\) −29.1564 −0.994805 −0.497402 0.867520i \(-0.665713\pi\)
−0.497402 + 0.867520i \(0.665713\pi\)
\(860\) −4.86351 3.53355i −0.165844 0.120493i
\(861\) −18.7813 + 57.8029i −0.640065 + 1.96992i
\(862\) −11.4838 35.3434i −0.391139 1.20380i
\(863\) 24.0405 17.4664i 0.818348 0.594564i −0.0978910 0.995197i \(-0.531210\pi\)
0.916239 + 0.400633i \(0.131210\pi\)
\(864\) 0.809017 0.587785i 0.0275233 0.0199969i
\(865\) −0.900560 2.77164i −0.0306200 0.0942385i
\(866\) −9.47259 + 29.1536i −0.321892 + 0.990681i
\(867\) 13.2667 + 9.63880i 0.450560 + 0.327351i
\(868\) 43.3802 1.47242
\(869\) −36.0809 + 19.2248i −1.22396 + 0.652156i
\(870\) −2.01882 −0.0684445
\(871\) −0.634352 0.460884i −0.0214942 0.0156165i
\(872\) 2.76393 8.50651i 0.0935985 0.288067i
\(873\) −4.15753 12.7956i −0.140711 0.433064i
\(874\) −0.422430 + 0.306914i −0.0142889 + 0.0103815i
\(875\) 4.13326 3.00299i 0.139730 0.101520i
\(876\) 3.38197 + 10.4086i 0.114266 + 0.351675i
\(877\) 8.25674 25.4116i 0.278810 0.858090i −0.709376 0.704831i \(-0.751023\pi\)
0.988186 0.153259i \(-0.0489770\pi\)
\(878\) 5.71180 + 4.14986i 0.192764 + 0.140051i
\(879\) 22.6601 0.764307
\(880\) 2.38778 + 2.30185i 0.0804921 + 0.0775952i
\(881\) 2.72012 0.0916431 0.0458216 0.998950i \(-0.485409\pi\)
0.0458216 + 0.998950i \(0.485409\pi\)
\(882\) 15.4537 + 11.2278i 0.520353 + 0.378058i
\(883\) 10.7306 33.0255i 0.361114 1.11140i −0.591265 0.806478i \(-0.701371\pi\)
0.952379 0.304917i \(-0.0986289\pi\)
\(884\) 0.319573 + 0.983544i 0.0107484 + 0.0330802i
\(885\) −4.30902 + 3.13068i −0.144846 + 0.105237i
\(886\) 11.8056 8.57724i 0.396616 0.288158i
\(887\) −11.5157 35.4418i −0.386661 1.19002i −0.935268 0.353939i \(-0.884842\pi\)
0.548608 0.836080i \(-0.315158\pi\)
\(888\) 1.21539 3.74060i 0.0407859 0.125526i
\(889\) 28.7791 + 20.9093i 0.965221 + 0.701274i
\(890\) −9.67821 −0.324414
\(891\) 3.28475 + 0.458729i 0.110043 + 0.0153680i
\(892\) 9.10899 0.304992
\(893\) 0.417411 + 0.303267i 0.0139681 + 0.0101484i
\(894\) 4.71180 14.5014i 0.157586 0.485000i
\(895\) −0.482779 1.48584i −0.0161375 0.0496662i
\(896\) 4.13326 3.00299i 0.138083 0.100323i
\(897\) −7.17216 + 5.21088i −0.239471 + 0.173986i
\(898\) −3.94573 12.1437i −0.131671 0.405241i
\(899\) −5.29709 + 16.3028i −0.176668 + 0.543728i
\(900\) −0.809017 0.587785i −0.0269672 0.0195928i
\(901\) 8.02327 0.267294
\(902\) 6.88510 + 38.8498i 0.229249 + 1.29356i
\(903\) −30.7134 −1.02208
\(904\) −4.63326 3.36626i −0.154100 0.111960i
\(905\) −5.70820 + 17.5680i −0.189747 + 0.583982i
\(906\) −2.03000 6.24769i −0.0674422 0.207566i
\(907\) 32.1937 23.3901i 1.06898 0.776656i 0.0932477 0.995643i \(-0.470275\pi\)
0.975728 + 0.218987i \(0.0702752\pi\)
\(908\) −16.7387 + 12.1613i −0.555492 + 0.403589i
\(909\) −3.28820 10.1200i −0.109063 0.335661i
\(910\) 2.10517 6.47904i 0.0697857 0.214778i
\(911\) 10.3743 + 7.53738i 0.343717 + 0.249725i 0.746228 0.665690i \(-0.231863\pi\)
−0.402512 + 0.915415i \(0.631863\pi\)
\(912\) −0.0785371 −0.00260062
\(913\) −4.63012 26.1259i −0.153235 0.864641i
\(914\) 17.3426 0.573642
\(915\) −3.03046 2.20175i −0.100184 0.0727878i
\(916\) 3.39360 10.4444i 0.112128 0.345093i
\(917\) −3.47196 10.6856i −0.114654 0.352870i
\(918\) 0.627445 0.455866i 0.0207088 0.0150458i
\(919\) 30.0258 21.8150i 0.990459 0.719610i 0.0304373 0.999537i \(-0.490310\pi\)
0.960022 + 0.279926i \(0.0903100\pi\)
\(920\) 2.05450 + 6.32309i 0.0677347 + 0.208466i
\(921\) −9.05908 + 27.8810i −0.298507 + 0.918710i
\(922\) −2.42183 1.75956i −0.0797588 0.0579482i
\(923\) −3.08697 −0.101609
\(924\) 16.7818 + 2.34364i 0.552079 + 0.0771002i
\(925\) −3.93310 −0.129319
\(926\) −13.1537 9.55673i −0.432258 0.314054i
\(927\) 5.16326 15.8909i 0.169584 0.521925i
\(928\) 0.623850 + 1.92001i 0.0204789 + 0.0630276i
\(929\) −8.06590 + 5.86022i −0.264634 + 0.192268i −0.712187 0.701989i \(-0.752295\pi\)
0.447554 + 0.894257i \(0.352295\pi\)
\(930\) −6.86933 + 4.99086i −0.225254 + 0.163657i
\(931\) −0.463587 1.42677i −0.0151935 0.0467606i
\(932\) −0.915646 + 2.81807i −0.0299930 + 0.0923090i
\(933\) −9.18799 6.67546i −0.300801 0.218545i
\(934\) 18.5707 0.607652
\(935\) 1.85188 + 1.78523i 0.0605630 + 0.0583833i
\(936\) −1.33343 −0.0435844
\(937\) −9.68938 7.03975i −0.316538 0.229979i 0.418159 0.908374i \(-0.362676\pi\)
−0.734697 + 0.678395i \(0.762676\pi\)
\(938\) −0.928370 + 2.85723i −0.0303124 + 0.0932919i
\(939\) −0.981634 3.02116i −0.0320344 0.0985918i
\(940\) 5.31483 3.86145i 0.173351 0.125947i
\(941\) −4.45765 + 3.23867i −0.145315 + 0.105578i −0.658068 0.752959i \(-0.728626\pi\)
0.512752 + 0.858537i \(0.328626\pi\)
\(942\) 2.87638 + 8.85258i 0.0937175 + 0.288433i
\(943\) −24.4407 + 75.2207i −0.795898 + 2.44952i
\(944\) 4.30902 + 3.13068i 0.140247 + 0.101895i
\(945\) −5.10899 −0.166196
\(946\) −17.5964 + 9.37578i −0.572107 + 0.304833i
\(947\) −27.3946 −0.890206 −0.445103 0.895479i \(-0.646833\pi\)
−0.445103 + 0.895479i \(0.646833\pi\)
\(948\) −9.97251 7.24545i −0.323892 0.235321i
\(949\) 4.50961 13.8791i 0.146388 0.450536i
\(950\) 0.0242693 + 0.0746932i 0.000787400 + 0.00242337i
\(951\) −3.82747 + 2.78082i −0.124114 + 0.0901743i
\(952\) 3.20561 2.32901i 0.103895 0.0754838i
\(953\) 2.46900 + 7.59879i 0.0799787 + 0.246149i 0.983049 0.183344i \(-0.0586922\pi\)
−0.903070 + 0.429493i \(0.858692\pi\)
\(954\) −3.19680 + 9.83874i −0.103500 + 0.318541i
\(955\) 16.7691 + 12.1835i 0.542636 + 0.394248i
\(956\) 8.56978 0.277166
\(957\) −2.92996 + 6.02058i −0.0947121 + 0.194618i
\(958\) 30.5554 0.987200
\(959\) 8.99355 + 6.53420i 0.290417 + 0.211000i
\(960\) −0.309017 + 0.951057i −0.00997348 + 0.0306952i
\(961\) 12.6995 + 39.0850i 0.409661 + 1.26081i
\(962\) −4.24289 + 3.08264i −0.136796 + 0.0993883i
\(963\) −14.1992 + 10.3163i −0.457562 + 0.332438i
\(964\) 2.46287 + 7.57992i 0.0793236 + 0.244133i
\(965\) −0.423597 + 1.30370i −0.0136361 + 0.0419675i
\(966\) 27.4799 + 19.9653i 0.884153 + 0.642375i
\(967\) −19.0966 −0.614106 −0.307053 0.951692i \(-0.599343\pi\)
−0.307053 + 0.951692i \(0.599343\pi\)
\(968\) 10.3301 3.78019i 0.332021 0.121500i
\(969\) −0.0609106 −0.00195673
\(970\) 10.8846 + 7.90809i 0.349482 + 0.253914i
\(971\) 0.0462836 0.142446i 0.00148531 0.00457131i −0.950311 0.311302i \(-0.899235\pi\)
0.951796 + 0.306730i \(0.0992350\pi\)
\(972\) 0.309017 + 0.951057i 0.00991172 + 0.0305052i
\(973\) −42.6032 + 30.9531i −1.36580 + 0.992310i
\(974\) −0.411225 + 0.298773i −0.0131765 + 0.00957330i
\(975\) 0.412052 + 1.26816i 0.0131962 + 0.0406138i
\(976\) −1.15753 + 3.56251i −0.0370517 + 0.114033i
\(977\) 15.4833 + 11.2493i 0.495355 + 0.359897i 0.807240 0.590223i \(-0.200960\pi\)
−0.311885 + 0.950120i \(0.600960\pi\)
\(978\) 18.7018 0.598016
\(979\) −14.0462 + 28.8626i −0.448918 + 0.922452i
\(980\) −19.1018 −0.610185
\(981\) 7.23607 + 5.25731i 0.231030 + 0.167853i
\(982\) −12.1735 + 37.4662i −0.388473 + 1.19560i
\(983\) 2.65314 + 8.16553i 0.0846221 + 0.260440i 0.984410 0.175887i \(-0.0562792\pi\)
−0.899788 + 0.436327i \(0.856279\pi\)
\(984\) −9.62422 + 6.99241i −0.306809 + 0.222910i
\(985\) −4.05427 + 2.94560i −0.129180 + 0.0938546i
\(986\) 0.483837 + 1.48910i 0.0154085 + 0.0474225i
\(987\) 10.3717 31.9208i 0.330135 1.01605i
\(988\) 0.0847231 + 0.0615549i 0.00269540 + 0.00195832i
\(989\) −39.9683 −1.27092
\(990\) −2.92705 + 1.55961i −0.0930278 + 0.0495675i
\(991\) −11.3086 −0.359230 −0.179615 0.983737i \(-0.557485\pi\)
−0.179615 + 0.983737i \(0.557485\pi\)
\(992\) 6.86933 + 4.99086i 0.218101 + 0.158460i
\(993\) 9.28360 28.5720i 0.294606 0.906705i
\(994\) 3.65494 + 11.2487i 0.115928 + 0.356789i
\(995\) 18.8571 13.7005i 0.597809 0.434334i
\(996\) 6.47214 4.70228i 0.205077 0.148998i
\(997\) −11.4436 35.2196i −0.362421 1.11542i −0.951580 0.307400i \(-0.900541\pi\)
0.589159 0.808017i \(-0.299459\pi\)
\(998\) −6.63175 + 20.4104i −0.209924 + 0.646081i
\(999\) 3.18194 + 2.31182i 0.100672 + 0.0731426i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 330.2.m.f.301.2 yes 8
3.2 odd 2 990.2.n.i.631.2 8
11.3 even 5 inner 330.2.m.f.91.2 8
11.5 even 5 3630.2.a.bq.1.4 4
11.6 odd 10 3630.2.a.bs.1.1 4
33.14 odd 10 990.2.n.i.91.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
330.2.m.f.91.2 8 11.3 even 5 inner
330.2.m.f.301.2 yes 8 1.1 even 1 trivial
990.2.n.i.91.2 8 33.14 odd 10
990.2.n.i.631.2 8 3.2 odd 2
3630.2.a.bq.1.4 4 11.5 even 5
3630.2.a.bs.1.1 4 11.6 odd 10