Properties

Label 35.3.l.a.23.6
Level $35$
Weight $3$
Character 35.23
Analytic conductor $0.954$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [35,3,Mod(2,35)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(35, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("35.2");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 35.l (of order \(12\), 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: \(0.953680925261\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 23.6
Character \(\chi\) \(=\) 35.23
Dual form 35.3.l.a.32.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.949975 + 3.54535i) q^{2} +(0.379154 - 1.41502i) q^{3} +(-8.20298 + 4.73599i) q^{4} +(4.02777 - 2.96261i) q^{5} +5.37694 q^{6} +(-5.83212 - 3.87123i) q^{7} +(-14.2019 - 14.2019i) q^{8} +(5.93570 + 3.42698i) q^{9} +O(q^{10})\) \(q+(0.949975 + 3.54535i) q^{2} +(0.379154 - 1.41502i) q^{3} +(-8.20298 + 4.73599i) q^{4} +(4.02777 - 2.96261i) q^{5} +5.37694 q^{6} +(-5.83212 - 3.87123i) q^{7} +(-14.2019 - 14.2019i) q^{8} +(5.93570 + 3.42698i) q^{9} +(14.3298 + 11.4655i) q^{10} +(-0.586967 - 1.01666i) q^{11} +(3.59134 + 13.4031i) q^{12} +(2.48387 + 2.48387i) q^{13} +(8.18451 - 24.3545i) q^{14} +(-2.66501 - 6.82267i) q^{15} +(17.9153 - 31.0302i) q^{16} +(-15.6797 - 4.20137i) q^{17} +(-6.51109 + 24.2997i) q^{18} +(-2.54557 - 1.46969i) q^{19} +(-19.0089 + 43.3777i) q^{20} +(-7.68914 + 6.78478i) q^{21} +(3.04681 - 3.04681i) q^{22} +(-28.4572 + 7.62508i) q^{23} +(-25.4807 + 14.7113i) q^{24} +(7.44591 - 23.8654i) q^{25} +(-6.44658 + 11.1658i) q^{26} +(16.4226 - 16.4226i) q^{27} +(66.1749 + 4.13475i) q^{28} +11.3707i q^{29} +(21.6571 - 15.9298i) q^{30} +(15.6227 + 27.0593i) q^{31} +(49.4315 + 13.2451i) q^{32} +(-1.66114 + 0.445102i) q^{33} -59.5814i q^{34} +(-34.9594 + 1.68584i) q^{35} -64.9206 q^{36} +(9.91842 + 37.0160i) q^{37} +(2.79233 - 10.4211i) q^{38} +(4.45650 - 2.57296i) q^{39} +(-99.2765 - 15.1274i) q^{40} +59.3486 q^{41} +(-31.3589 - 20.8154i) q^{42} +(18.7104 + 18.7104i) q^{43} +(9.62976 + 5.55975i) q^{44} +(34.0604 - 3.78206i) q^{45} +(-54.0672 - 93.6472i) q^{46} +(-17.7878 - 66.3850i) q^{47} +(-37.1157 - 37.1157i) q^{48} +(19.0272 + 45.1549i) q^{49} +(91.6848 + 3.72685i) q^{50} +(-11.8901 + 20.5942i) q^{51} +(-32.1387 - 8.61155i) q^{52} +(1.94504 - 7.25898i) q^{53} +(73.8250 + 42.6229i) q^{54} +(-5.37613 - 2.35591i) q^{55} +(27.8483 + 137.806i) q^{56} +(-3.04480 + 3.04480i) q^{57} +(-40.3131 + 10.8019i) q^{58} +(-5.15171 + 2.97434i) q^{59} +(54.1731 + 43.3448i) q^{60} +(0.00821757 - 0.0142333i) q^{61} +(-81.0937 + 81.0937i) q^{62} +(-21.3511 - 42.9650i) q^{63} +44.5126i q^{64} +(17.3632 + 2.64573i) q^{65} +(-3.15609 - 5.46650i) q^{66} +(40.5504 + 10.8655i) q^{67} +(148.518 - 39.7953i) q^{68} +43.1586i q^{69} +(-39.1874 - 122.342i) q^{70} -15.7230 q^{71} +(-35.6286 - 132.968i) q^{72} +(-9.59964 + 35.8263i) q^{73} +(-121.813 + 70.3286i) q^{74} +(-30.9469 - 19.5848i) q^{75} +27.8417 q^{76} +(-0.512451 + 8.20155i) q^{77} +(13.3556 + 13.3556i) q^{78} +(-60.3579 - 34.8477i) q^{79} +(-19.7715 - 178.059i) q^{80} +(13.8312 + 23.9563i) q^{81} +(56.3797 + 210.412i) q^{82} +(-63.1958 - 63.1958i) q^{83} +(30.9412 - 92.0711i) q^{84} +(-75.6014 + 29.5307i) q^{85} +(-48.5606 + 84.1094i) q^{86} +(16.0898 + 4.31124i) q^{87} +(-6.10240 + 22.7745i) q^{88} +(-52.1411 - 30.1037i) q^{89} +(45.7653 + 117.163i) q^{90} +(-4.87059 - 24.1018i) q^{91} +(197.321 - 197.321i) q^{92} +(44.2129 - 11.8468i) q^{93} +(218.460 - 126.128i) q^{94} +(-14.6071 + 1.62197i) q^{95} +(37.4843 - 64.9247i) q^{96} +(51.7791 - 51.7791i) q^{97} +(-142.015 + 110.354i) q^{98} -8.04610i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 6 q^{7} - 36 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 6 q^{7} - 36 q^{8} + 14 q^{10} - 24 q^{11} - 46 q^{12} - 8 q^{13} + 52 q^{15} + 20 q^{16} - 48 q^{17} - 4 q^{18} - 72 q^{20} + 56 q^{21} + 104 q^{22} - 86 q^{23} - 16 q^{25} + 140 q^{26} + 76 q^{27} + 186 q^{28} + 64 q^{30} + 120 q^{31} + 130 q^{32} + 116 q^{33} - 240 q^{35} - 496 q^{36} + 44 q^{37} + 16 q^{38} - 158 q^{40} + 16 q^{41} - 370 q^{42} - 196 q^{43} - 104 q^{45} - 148 q^{46} - 208 q^{47} - 52 q^{48} + 580 q^{50} - 160 q^{51} - 288 q^{52} - 72 q^{53} + 208 q^{55} + 420 q^{56} + 656 q^{57} - 2 q^{58} + 262 q^{60} + 308 q^{61} + 176 q^{62} + 212 q^{63} + 132 q^{65} + 316 q^{66} + 198 q^{67} + 332 q^{68} - 200 q^{70} - 792 q^{71} + 308 q^{72} + 380 q^{73} - 450 q^{75} - 400 q^{76} - 472 q^{77} - 720 q^{78} - 324 q^{80} - 352 q^{81} - 818 q^{82} - 460 q^{83} + 144 q^{85} - 336 q^{86} - 214 q^{87} - 288 q^{88} + 120 q^{90} + 984 q^{91} + 1372 q^{92} - 68 q^{93} - 88 q^{95} + 816 q^{96} - 72 q^{97} + 482 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.949975 + 3.54535i 0.474987 + 1.77268i 0.621443 + 0.783460i \(0.286547\pi\)
−0.146455 + 0.989217i \(0.546786\pi\)
\(3\) 0.379154 1.41502i 0.126385 0.471674i −0.873501 0.486823i \(-0.838156\pi\)
0.999885 + 0.0151492i \(0.00482234\pi\)
\(4\) −8.20298 + 4.73599i −2.05075 + 1.18400i
\(5\) 4.02777 2.96261i 0.805555 0.592521i
\(6\) 5.37694 0.896156
\(7\) −5.83212 3.87123i −0.833160 0.553033i
\(8\) −14.2019 14.2019i −1.77523 1.77523i
\(9\) 5.93570 + 3.42698i 0.659522 + 0.380775i
\(10\) 14.3298 + 11.4655i 1.43298 + 1.14655i
\(11\) −0.586967 1.01666i −0.0533607 0.0924234i 0.838111 0.545499i \(-0.183660\pi\)
−0.891472 + 0.453076i \(0.850327\pi\)
\(12\) 3.59134 + 13.4031i 0.299278 + 1.11692i
\(13\) 2.48387 + 2.48387i 0.191067 + 0.191067i 0.796157 0.605090i \(-0.206863\pi\)
−0.605090 + 0.796157i \(0.706863\pi\)
\(14\) 8.18451 24.3545i 0.584608 1.73961i
\(15\) −2.66501 6.82267i −0.177667 0.454845i
\(16\) 17.9153 31.0302i 1.11971 1.93939i
\(17\) −15.6797 4.20137i −0.922337 0.247139i −0.233753 0.972296i \(-0.575101\pi\)
−0.688584 + 0.725157i \(0.741767\pi\)
\(18\) −6.51109 + 24.2997i −0.361727 + 1.34998i
\(19\) −2.54557 1.46969i −0.133978 0.0773520i 0.431513 0.902107i \(-0.357980\pi\)
−0.565491 + 0.824755i \(0.691313\pi\)
\(20\) −19.0089 + 43.3777i −0.950443 + 2.16889i
\(21\) −7.68914 + 6.78478i −0.366150 + 0.323085i
\(22\) 3.04681 3.04681i 0.138491 0.138491i
\(23\) −28.4572 + 7.62508i −1.23727 + 0.331525i −0.817406 0.576062i \(-0.804589\pi\)
−0.419863 + 0.907587i \(0.637922\pi\)
\(24\) −25.4807 + 14.7113i −1.06169 + 0.612969i
\(25\) 7.44591 23.8654i 0.297837 0.954617i
\(26\) −6.44658 + 11.1658i −0.247946 + 0.429454i
\(27\) 16.4226 16.4226i 0.608244 0.608244i
\(28\) 66.1749 + 4.13475i 2.36339 + 0.147670i
\(29\) 11.3707i 0.392093i 0.980595 + 0.196046i \(0.0628103\pi\)
−0.980595 + 0.196046i \(0.937190\pi\)
\(30\) 21.6571 15.9298i 0.721903 0.530992i
\(31\) 15.6227 + 27.0593i 0.503959 + 0.872882i 0.999990 + 0.00457701i \(0.00145691\pi\)
−0.496031 + 0.868305i \(0.665210\pi\)
\(32\) 49.4315 + 13.2451i 1.54474 + 0.413911i
\(33\) −1.66114 + 0.445102i −0.0503377 + 0.0134879i
\(34\) 59.5814i 1.75239i
\(35\) −34.9594 + 1.68584i −0.998839 + 0.0481669i
\(36\) −64.9206 −1.80335
\(37\) 9.91842 + 37.0160i 0.268065 + 1.00043i 0.960347 + 0.278806i \(0.0899387\pi\)
−0.692282 + 0.721627i \(0.743395\pi\)
\(38\) 2.79233 10.4211i 0.0734824 0.274240i
\(39\) 4.45650 2.57296i 0.114269 0.0659733i
\(40\) −99.2765 15.1274i −2.48191 0.378184i
\(41\) 59.3486 1.44753 0.723763 0.690048i \(-0.242411\pi\)
0.723763 + 0.690048i \(0.242411\pi\)
\(42\) −31.3589 20.8154i −0.746641 0.495604i
\(43\) 18.7104 + 18.7104i 0.435126 + 0.435126i 0.890368 0.455242i \(-0.150447\pi\)
−0.455242 + 0.890368i \(0.650447\pi\)
\(44\) 9.62976 + 5.55975i 0.218858 + 0.126358i
\(45\) 34.0604 3.78206i 0.756899 0.0840458i
\(46\) −54.0672 93.6472i −1.17537 2.03581i
\(47\) −17.7878 66.3850i −0.378464 1.41245i −0.848217 0.529649i \(-0.822324\pi\)
0.469752 0.882798i \(-0.344343\pi\)
\(48\) −37.1157 37.1157i −0.773244 0.773244i
\(49\) 19.0272 + 45.1549i 0.388310 + 0.921529i
\(50\) 91.6848 + 3.72685i 1.83370 + 0.0745370i
\(51\) −11.8901 + 20.5942i −0.233138 + 0.403807i
\(52\) −32.1387 8.61155i −0.618052 0.165607i
\(53\) 1.94504 7.25898i 0.0366988 0.136962i −0.945146 0.326649i \(-0.894081\pi\)
0.981845 + 0.189687i \(0.0607473\pi\)
\(54\) 73.8250 + 42.6229i 1.36713 + 0.789312i
\(55\) −5.37613 2.35591i −0.0977478 0.0428348i
\(56\) 27.8483 + 137.806i 0.497291 + 2.46082i
\(57\) −3.04480 + 3.04480i −0.0534176 + 0.0534176i
\(58\) −40.3131 + 10.8019i −0.695054 + 0.186239i
\(59\) −5.15171 + 2.97434i −0.0873172 + 0.0504126i −0.543023 0.839718i \(-0.682720\pi\)
0.455706 + 0.890131i \(0.349387\pi\)
\(60\) 54.1731 + 43.3448i 0.902885 + 0.722413i
\(61\) 0.00821757 0.0142333i 0.000134714 0.000233332i −0.865958 0.500117i \(-0.833290\pi\)
0.866093 + 0.499883i \(0.166624\pi\)
\(62\) −81.0937 + 81.0937i −1.30796 + 1.30796i
\(63\) −21.3511 42.9650i −0.338906 0.681984i
\(64\) 44.5126i 0.695509i
\(65\) 17.3632 + 2.64573i 0.267126 + 0.0407036i
\(66\) −3.15609 5.46650i −0.0478195 0.0828258i
\(67\) 40.5504 + 10.8655i 0.605230 + 0.162171i 0.548405 0.836213i \(-0.315235\pi\)
0.0568258 + 0.998384i \(0.481902\pi\)
\(68\) 148.518 39.7953i 2.18409 0.585225i
\(69\) 43.1586i 0.625487i
\(70\) −39.1874 122.342i −0.559820 1.74774i
\(71\) −15.7230 −0.221451 −0.110726 0.993851i \(-0.535317\pi\)
−0.110726 + 0.993851i \(0.535317\pi\)
\(72\) −35.6286 132.968i −0.494841 1.84677i
\(73\) −9.59964 + 35.8263i −0.131502 + 0.490772i −0.999988 0.00494220i \(-0.998427\pi\)
0.868486 + 0.495714i \(0.165094\pi\)
\(74\) −121.813 + 70.3286i −1.64612 + 0.950386i
\(75\) −30.9469 19.5848i −0.412626 0.261131i
\(76\) 27.8417 0.366339
\(77\) −0.512451 + 8.20155i −0.00665521 + 0.106514i
\(78\) 13.3556 + 13.3556i 0.171226 + 0.171226i
\(79\) −60.3579 34.8477i −0.764024 0.441110i 0.0667145 0.997772i \(-0.478748\pi\)
−0.830739 + 0.556663i \(0.812082\pi\)
\(80\) −19.7715 178.059i −0.247144 2.22573i
\(81\) 13.8312 + 23.9563i 0.170755 + 0.295757i
\(82\) 56.3797 + 210.412i 0.687557 + 2.56600i
\(83\) −63.1958 63.1958i −0.761395 0.761395i 0.215180 0.976574i \(-0.430966\pi\)
−0.976574 + 0.215180i \(0.930966\pi\)
\(84\) 30.9412 92.0711i 0.368348 1.09608i
\(85\) −75.6014 + 29.5307i −0.889428 + 0.347420i
\(86\) −48.5606 + 84.1094i −0.564658 + 0.978016i
\(87\) 16.0898 + 4.31124i 0.184940 + 0.0495545i
\(88\) −6.10240 + 22.7745i −0.0693455 + 0.258801i
\(89\) −52.1411 30.1037i −0.585855 0.338243i 0.177602 0.984102i \(-0.443166\pi\)
−0.763457 + 0.645859i \(0.776499\pi\)
\(90\) 45.7653 + 117.163i 0.508503 + 1.30182i
\(91\) −4.87059 24.1018i −0.0535230 0.264855i
\(92\) 197.321 197.321i 2.14480 2.14480i
\(93\) 44.2129 11.8468i 0.475408 0.127385i
\(94\) 218.460 126.128i 2.32405 1.34179i
\(95\) −14.6071 + 1.62197i −0.153759 + 0.0170733i
\(96\) 37.4843 64.9247i 0.390462 0.676299i
\(97\) 51.7791 51.7791i 0.533805 0.533805i −0.387898 0.921702i \(-0.626799\pi\)
0.921702 + 0.387898i \(0.126799\pi\)
\(98\) −142.015 + 110.354i −1.44913 + 1.12606i
\(99\) 8.04610i 0.0812737i
\(100\) 51.9478 + 231.031i 0.519478 + 2.31031i
\(101\) −94.1409 163.057i −0.932088 1.61442i −0.779746 0.626096i \(-0.784652\pi\)
−0.152342 0.988328i \(-0.548682\pi\)
\(102\) −84.3089 22.5905i −0.826558 0.221475i
\(103\) 114.295 30.6253i 1.10966 0.297333i 0.342969 0.939347i \(-0.388567\pi\)
0.766693 + 0.642013i \(0.221901\pi\)
\(104\) 70.5512i 0.678377i
\(105\) −10.8695 + 50.1075i −0.103519 + 0.477214i
\(106\) 27.5834 0.260221
\(107\) 12.0864 + 45.1072i 0.112957 + 0.421563i 0.999126 0.0418001i \(-0.0133093\pi\)
−0.886169 + 0.463363i \(0.846643\pi\)
\(108\) −56.9369 + 212.492i −0.527194 + 1.96751i
\(109\) −29.1458 + 16.8273i −0.267393 + 0.154379i −0.627702 0.778454i \(-0.716004\pi\)
0.360309 + 0.932833i \(0.382671\pi\)
\(110\) 3.24535 21.2983i 0.0295032 0.193621i
\(111\) 56.1391 0.505757
\(112\) −224.609 + 111.617i −2.00544 + 0.996585i
\(113\) 40.5401 + 40.5401i 0.358762 + 0.358762i 0.863356 0.504595i \(-0.168358\pi\)
−0.504595 + 0.863356i \(0.668358\pi\)
\(114\) −13.6874 7.90242i −0.120065 0.0693195i
\(115\) −92.0290 + 115.020i −0.800252 + 1.00017i
\(116\) −53.8515 93.2736i −0.464237 0.804082i
\(117\) 6.23134 + 23.2557i 0.0532593 + 0.198766i
\(118\) −15.4391 15.4391i −0.130840 0.130840i
\(119\) 75.1815 + 85.2027i 0.631777 + 0.715989i
\(120\) −59.0466 + 134.743i −0.492055 + 1.12286i
\(121\) 59.8109 103.596i 0.494305 0.856162i
\(122\) 0.0582684 + 0.0156130i 0.000477610 + 0.000127975i
\(123\) 22.5022 83.9795i 0.182945 0.682760i
\(124\) −256.306 147.978i −2.06698 1.19337i
\(125\) −40.7134 118.184i −0.325707 0.945471i
\(126\) 132.043 116.513i 1.04796 0.924705i
\(127\) −30.4117 + 30.4117i −0.239462 + 0.239462i −0.816627 0.577165i \(-0.804159\pi\)
0.577165 + 0.816627i \(0.304159\pi\)
\(128\) 39.9133 10.6947i 0.311823 0.0835526i
\(129\) 33.5697 19.3815i 0.260231 0.150244i
\(130\) 7.11454 + 64.0720i 0.0547272 + 0.492862i
\(131\) −28.3295 + 49.0682i −0.216256 + 0.374567i −0.953660 0.300885i \(-0.902718\pi\)
0.737404 + 0.675452i \(0.236051\pi\)
\(132\) 11.5183 11.5183i 0.0872600 0.0872600i
\(133\) 9.15659 + 18.4259i 0.0688465 + 0.138541i
\(134\) 154.088i 1.14991i
\(135\) 17.4928 114.800i 0.129576 0.850372i
\(136\) 163.014 + 282.349i 1.19863 + 2.07609i
\(137\) 208.383 + 55.8359i 1.52104 + 0.407562i 0.920084 0.391721i \(-0.128120\pi\)
0.600956 + 0.799282i \(0.294787\pi\)
\(138\) −153.013 + 40.9996i −1.10879 + 0.297098i
\(139\) 169.451i 1.21907i 0.792760 + 0.609534i \(0.208644\pi\)
−0.792760 + 0.609534i \(0.791356\pi\)
\(140\) 278.787 179.396i 1.99134 1.28140i
\(141\) −100.681 −0.714046
\(142\) −14.9365 55.7438i −0.105187 0.392562i
\(143\) 1.06729 3.98320i 0.00746359 0.0278545i
\(144\) 212.680 122.791i 1.47694 0.852712i
\(145\) 33.6869 + 45.7986i 0.232323 + 0.315852i
\(146\) −136.136 −0.932441
\(147\) 71.1094 9.80319i 0.483737 0.0666884i
\(148\) −256.668 256.668i −1.73424 1.73424i
\(149\) −129.356 74.6835i −0.868159 0.501232i −0.00142291 0.999999i \(-0.500453\pi\)
−0.866736 + 0.498767i \(0.833786\pi\)
\(150\) 40.0362 128.323i 0.266908 0.855486i
\(151\) 76.3156 + 132.182i 0.505401 + 0.875381i 0.999980 + 0.00624813i \(0.00198885\pi\)
−0.494579 + 0.869133i \(0.664678\pi\)
\(152\) 15.2796 + 57.0243i 0.100524 + 0.375160i
\(153\) −78.6721 78.6721i −0.514197 0.514197i
\(154\) −29.5642 + 5.97444i −0.191975 + 0.0387951i
\(155\) 143.091 + 62.7049i 0.923167 + 0.404548i
\(156\) −24.3710 + 42.2119i −0.156225 + 0.270589i
\(157\) −133.650 35.8114i −0.851275 0.228098i −0.193301 0.981139i \(-0.561919\pi\)
−0.657974 + 0.753041i \(0.728586\pi\)
\(158\) 66.2088 247.095i 0.419043 1.56389i
\(159\) −9.53415 5.50454i −0.0599632 0.0346198i
\(160\) 238.339 93.0978i 1.48962 0.581861i
\(161\) 195.484 + 65.6939i 1.21419 + 0.408037i
\(162\) −71.7943 + 71.7943i −0.443175 + 0.443175i
\(163\) 10.4361 2.79634i 0.0640250 0.0171555i −0.226664 0.973973i \(-0.572782\pi\)
0.290689 + 0.956817i \(0.406115\pi\)
\(164\) −486.835 + 281.074i −2.96851 + 1.71387i
\(165\) −5.37204 + 6.71408i −0.0325578 + 0.0406914i
\(166\) 164.017 284.086i 0.988054 1.71136i
\(167\) −80.7727 + 80.7727i −0.483669 + 0.483669i −0.906301 0.422632i \(-0.861106\pi\)
0.422632 + 0.906301i \(0.361106\pi\)
\(168\) 205.557 + 12.8436i 1.22355 + 0.0764503i
\(169\) 156.661i 0.926987i
\(170\) −176.516 239.980i −1.03833 1.41165i
\(171\) −10.0732 17.4473i −0.0589075 0.102031i
\(172\) −242.093 64.8687i −1.40752 0.377144i
\(173\) −218.312 + 58.4966i −1.26192 + 0.338131i −0.826930 0.562304i \(-0.809915\pi\)
−0.434991 + 0.900435i \(0.643248\pi\)
\(174\) 61.1395i 0.351376i
\(175\) −135.814 + 110.361i −0.776080 + 0.630635i
\(176\) −42.0628 −0.238993
\(177\) 2.25547 + 8.41752i 0.0127427 + 0.0475566i
\(178\) 57.1954 213.456i 0.321323 1.19919i
\(179\) 189.777 109.568i 1.06021 0.612112i 0.134719 0.990884i \(-0.456987\pi\)
0.925490 + 0.378772i \(0.123654\pi\)
\(180\) −261.485 + 192.334i −1.45270 + 1.06852i
\(181\) −291.658 −1.61137 −0.805686 0.592343i \(-0.798203\pi\)
−0.805686 + 0.592343i \(0.798203\pi\)
\(182\) 80.8226 40.1641i 0.444080 0.220682i
\(183\) −0.0170246 0.0170246i −9.30308e−5 9.30308e-5i
\(184\) 512.436 + 295.855i 2.78498 + 1.60791i
\(185\) 149.613 + 119.708i 0.808719 + 0.647069i
\(186\) 84.0024 + 145.496i 0.451626 + 0.782239i
\(187\) 4.93213 + 18.4070i 0.0263750 + 0.0984330i
\(188\) 460.312 + 460.312i 2.44847 + 2.44847i
\(189\) −159.354 + 32.2029i −0.843144 + 0.170386i
\(190\) −19.6268 50.2465i −0.103299 0.264455i
\(191\) −55.1786 + 95.5721i −0.288893 + 0.500377i −0.973546 0.228492i \(-0.926621\pi\)
0.684653 + 0.728869i \(0.259954\pi\)
\(192\) 62.9863 + 16.8771i 0.328053 + 0.0879017i
\(193\) −92.7422 + 346.119i −0.480530 + 1.79336i 0.118868 + 0.992910i \(0.462073\pi\)
−0.599398 + 0.800451i \(0.704593\pi\)
\(194\) 232.764 + 134.386i 1.19981 + 0.692713i
\(195\) 10.3271 23.5662i 0.0529594 0.120852i
\(196\) −369.933 280.292i −1.88741 1.43006i
\(197\) −90.6810 + 90.6810i −0.460309 + 0.460309i −0.898757 0.438447i \(-0.855529\pi\)
0.438447 + 0.898757i \(0.355529\pi\)
\(198\) 28.5263 7.64359i 0.144072 0.0386040i
\(199\) 280.150 161.744i 1.40779 0.812786i 0.412613 0.910907i \(-0.364616\pi\)
0.995175 + 0.0981204i \(0.0312830\pi\)
\(200\) −444.680 + 233.188i −2.22340 + 1.16594i
\(201\) 30.7497 53.2601i 0.152984 0.264975i
\(202\) 488.663 488.663i 2.41912 2.41912i
\(203\) 44.0186 66.3152i 0.216840 0.326676i
\(204\) 225.245i 1.10414i
\(205\) 239.043 175.827i 1.16606 0.857691i
\(206\) 217.155 + 376.124i 1.05415 + 1.82584i
\(207\) −195.044 52.2620i −0.942243 0.252473i
\(208\) 121.574 32.5757i 0.584491 0.156614i
\(209\) 3.45064i 0.0165102i
\(210\) −187.974 + 9.06466i −0.895116 + 0.0431650i
\(211\) −32.3501 −0.153318 −0.0766590 0.997057i \(-0.524425\pi\)
−0.0766590 + 0.997057i \(0.524425\pi\)
\(212\) 18.4234 + 68.7570i 0.0869027 + 0.324325i
\(213\) −5.96145 + 22.2484i −0.0279880 + 0.104453i
\(214\) −148.439 + 85.7015i −0.693642 + 0.400474i
\(215\) 130.793 + 19.9297i 0.608339 + 0.0926962i
\(216\) −466.463 −2.15955
\(217\) 13.6394 218.292i 0.0628543 1.00596i
\(218\) −87.3467 87.3467i −0.400673 0.400673i
\(219\) 47.0553 + 27.1674i 0.214864 + 0.124052i
\(220\) 55.2579 6.13581i 0.251172 0.0278901i
\(221\) −28.5107 49.3820i −0.129008 0.223448i
\(222\) 53.3307 + 199.033i 0.240228 + 0.896545i
\(223\) 182.276 + 182.276i 0.817382 + 0.817382i 0.985728 0.168346i \(-0.0538427\pi\)
−0.168346 + 0.985728i \(0.553843\pi\)
\(224\) −237.016 268.608i −1.05811 1.19914i
\(225\) 125.983 116.141i 0.559924 0.516182i
\(226\) −105.217 + 182.241i −0.465561 + 0.806376i
\(227\) −202.109 54.1550i −0.890349 0.238568i −0.215482 0.976508i \(-0.569132\pi\)
−0.674867 + 0.737939i \(0.735799\pi\)
\(228\) 10.5563 39.3966i 0.0462996 0.172792i
\(229\) −91.0319 52.5573i −0.397519 0.229508i 0.287894 0.957662i \(-0.407045\pi\)
−0.685413 + 0.728154i \(0.740378\pi\)
\(230\) −495.210 217.010i −2.15309 0.943520i
\(231\) 11.4111 + 3.83478i 0.0493986 + 0.0166008i
\(232\) 161.485 161.485i 0.696057 0.696057i
\(233\) 49.4071 13.2386i 0.212048 0.0568180i −0.151231 0.988498i \(-0.548324\pi\)
0.363279 + 0.931680i \(0.381657\pi\)
\(234\) −76.5300 + 44.1846i −0.327051 + 0.188823i
\(235\) −268.318 214.686i −1.14178 0.913556i
\(236\) 28.1729 48.7969i 0.119377 0.206767i
\(237\) −72.1951 + 72.1951i −0.304621 + 0.304621i
\(238\) −230.653 + 347.485i −0.969131 + 1.46002i
\(239\) 58.4297i 0.244476i −0.992501 0.122238i \(-0.960993\pi\)
0.992501 0.122238i \(-0.0390071\pi\)
\(240\) −259.453 39.5344i −1.08105 0.164727i
\(241\) −103.305 178.930i −0.428653 0.742449i 0.568101 0.822959i \(-0.307678\pi\)
−0.996754 + 0.0805104i \(0.974345\pi\)
\(242\) 424.102 + 113.638i 1.75249 + 0.469578i
\(243\) 241.046 64.5881i 0.991959 0.265795i
\(244\) 0.155673i 0.000638006i
\(245\) 210.413 + 125.504i 0.858830 + 0.512260i
\(246\) 319.114 1.29721
\(247\) −2.67236 9.97339i −0.0108193 0.0403781i
\(248\) 162.421 606.165i 0.654925 2.44421i
\(249\) −113.384 + 65.4624i −0.455359 + 0.262901i
\(250\) 380.327 256.615i 1.52131 1.02646i
\(251\) 357.500 1.42430 0.712151 0.702026i \(-0.247721\pi\)
0.712151 + 0.702026i \(0.247721\pi\)
\(252\) 378.624 + 251.322i 1.50248 + 0.997311i
\(253\) 24.4555 + 24.4555i 0.0966622 + 0.0966622i
\(254\) −136.711 78.9299i −0.538231 0.310748i
\(255\) 13.1220 + 118.174i 0.0514589 + 0.463428i
\(256\) 164.858 + 285.543i 0.643978 + 1.11540i
\(257\) −3.80238 14.1907i −0.0147953 0.0552167i 0.958134 0.286322i \(-0.0924326\pi\)
−0.972929 + 0.231105i \(0.925766\pi\)
\(258\) 100.605 + 100.605i 0.389941 + 0.389941i
\(259\) 85.4522 254.278i 0.329931 0.981769i
\(260\) −154.960 + 60.5291i −0.596000 + 0.232804i
\(261\) −38.9671 + 67.4930i −0.149299 + 0.258594i
\(262\) −200.877 53.8247i −0.766704 0.205438i
\(263\) 68.4088 255.305i 0.260109 0.970741i −0.705067 0.709141i \(-0.749083\pi\)
0.965176 0.261601i \(-0.0842503\pi\)
\(264\) 29.9126 + 17.2701i 0.113305 + 0.0654169i
\(265\) −13.6713 34.9999i −0.0515900 0.132075i
\(266\) −56.6278 + 49.9675i −0.212886 + 0.187848i
\(267\) −62.3668 + 62.3668i −0.233583 + 0.233583i
\(268\) −384.093 + 102.917i −1.43318 + 0.384020i
\(269\) 225.615 130.259i 0.838717 0.484234i −0.0181109 0.999836i \(-0.505765\pi\)
0.856828 + 0.515602i \(0.172432\pi\)
\(270\) 423.625 47.0392i 1.56898 0.174219i
\(271\) −177.157 + 306.844i −0.653715 + 1.13227i 0.328500 + 0.944504i \(0.393457\pi\)
−0.982214 + 0.187763i \(0.939876\pi\)
\(272\) −411.276 + 411.276i −1.51204 + 1.51204i
\(273\) −35.9513 2.24632i −0.131690 0.00822828i
\(274\) 791.833i 2.88990i
\(275\) −28.6335 + 6.43828i −0.104122 + 0.0234119i
\(276\) −204.399 354.029i −0.740576 1.28271i
\(277\) −89.4100 23.9573i −0.322780 0.0864886i 0.0937909 0.995592i \(-0.470101\pi\)
−0.416571 + 0.909103i \(0.636768\pi\)
\(278\) −600.762 + 160.974i −2.16102 + 0.579042i
\(279\) 214.155i 0.767580i
\(280\) 520.431 + 472.547i 1.85868 + 1.68767i
\(281\) 14.0935 0.0501547 0.0250774 0.999686i \(-0.492017\pi\)
0.0250774 + 0.999686i \(0.492017\pi\)
\(282\) −95.6440 356.948i −0.339163 1.26577i
\(283\) −105.700 + 394.478i −0.373499 + 1.39392i 0.482027 + 0.876156i \(0.339901\pi\)
−0.855526 + 0.517760i \(0.826766\pi\)
\(284\) 128.976 74.4642i 0.454140 0.262198i
\(285\) −3.24322 + 21.2843i −0.0113797 + 0.0746819i
\(286\) 15.1357 0.0529222
\(287\) −346.128 229.752i −1.20602 0.800530i
\(288\) 248.020 + 248.020i 0.861181 + 0.861181i
\(289\) −22.0791 12.7474i −0.0763984 0.0441086i
\(290\) −130.370 + 162.939i −0.449553 + 0.561860i
\(291\) −53.6362 92.9007i −0.184317 0.319246i
\(292\) −90.9276 339.346i −0.311396 1.16215i
\(293\) −272.948 272.948i −0.931564 0.931564i 0.0662402 0.997804i \(-0.478900\pi\)
−0.997804 + 0.0662402i \(0.978900\pi\)
\(294\) 102.308 + 242.795i 0.347986 + 0.825834i
\(295\) −11.9381 + 27.2425i −0.0404682 + 0.0923474i
\(296\) 384.837 666.557i 1.30013 2.25188i
\(297\) −26.3357 7.05663i −0.0886723 0.0237597i
\(298\) 141.895 529.559i 0.476158 1.77704i
\(299\) −89.6237 51.7442i −0.299745 0.173058i
\(300\) 346.611 + 14.0892i 1.15537 + 0.0469640i
\(301\) −36.6890 181.553i −0.121890 0.603168i
\(302\) −396.136 + 396.136i −1.31171 + 1.31171i
\(303\) −266.423 + 71.3878i −0.879283 + 0.235603i
\(304\) −91.2094 + 52.6598i −0.300031 + 0.173223i
\(305\) −0.00906902 0.0816738i −2.97345e−5 0.000267783i
\(306\) 204.184 353.657i 0.667268 1.15574i
\(307\) 149.471 149.471i 0.486877 0.486877i −0.420442 0.907319i \(-0.638125\pi\)
0.907319 + 0.420442i \(0.138125\pi\)
\(308\) −34.6389 69.7041i −0.112464 0.226312i
\(309\) 173.342i 0.560977i
\(310\) −86.3783 + 566.876i −0.278640 + 1.82863i
\(311\) 60.8111 + 105.328i 0.195534 + 0.338675i 0.947075 0.321011i \(-0.104023\pi\)
−0.751541 + 0.659686i \(0.770689\pi\)
\(312\) −99.8315 26.7498i −0.319973 0.0857364i
\(313\) 186.211 49.8952i 0.594924 0.159409i 0.0512215 0.998687i \(-0.483689\pi\)
0.543703 + 0.839278i \(0.317022\pi\)
\(314\) 507.857i 1.61738i
\(315\) −213.286 109.798i −0.677098 0.348566i
\(316\) 660.153 2.08909
\(317\) 142.521 + 531.897i 0.449594 + 1.67791i 0.703513 + 0.710682i \(0.251614\pi\)
−0.253919 + 0.967225i \(0.581720\pi\)
\(318\) 10.4583 39.0311i 0.0328879 0.122739i
\(319\) 11.5601 6.67423i 0.0362386 0.0209223i
\(320\) 131.873 + 179.287i 0.412104 + 0.560271i
\(321\) 68.4103 0.213116
\(322\) −47.2033 + 755.468i −0.146594 + 2.34617i
\(323\) 33.7392 + 33.7392i 0.104456 + 0.104456i
\(324\) −226.914 131.009i −0.700351 0.404348i
\(325\) 77.7733 40.7839i 0.239302 0.125489i
\(326\) 19.8280 + 34.3431i 0.0608222 + 0.105347i
\(327\) 12.7603 + 47.6221i 0.0390223 + 0.145633i
\(328\) −842.861 842.861i −2.56970 2.56970i
\(329\) −153.251 + 456.026i −0.465809 + 1.38610i
\(330\) −28.9071 12.6676i −0.0875973 0.0383866i
\(331\) −311.306 + 539.198i −0.940501 + 1.62900i −0.175983 + 0.984393i \(0.556310\pi\)
−0.764518 + 0.644602i \(0.777023\pi\)
\(332\) 817.688 + 219.099i 2.46292 + 0.659937i
\(333\) −67.9804 + 253.706i −0.204145 + 0.761881i
\(334\) −363.100 209.636i −1.08713 0.627652i
\(335\) 195.518 76.3714i 0.583636 0.227974i
\(336\) 72.7798 + 360.147i 0.216606 + 1.07187i
\(337\) 298.924 298.924i 0.887015 0.887015i −0.107220 0.994235i \(-0.534195\pi\)
0.994235 + 0.107220i \(0.0341949\pi\)
\(338\) 555.418 148.824i 1.64325 0.440307i
\(339\) 72.7360 41.9941i 0.214560 0.123877i
\(340\) 480.299 600.287i 1.41265 1.76555i
\(341\) 18.3401 31.7659i 0.0537831 0.0931551i
\(342\) 52.2874 52.2874i 0.152887 0.152887i
\(343\) 63.8364 337.007i 0.186112 0.982529i
\(344\) 531.446i 1.54490i
\(345\) 127.862 + 173.833i 0.370615 + 0.503864i
\(346\) −414.782 718.424i −1.19879 2.07637i
\(347\) −21.8083 5.84351i −0.0628480 0.0168401i 0.227258 0.973835i \(-0.427024\pi\)
−0.290106 + 0.956994i \(0.593691\pi\)
\(348\) −152.402 + 40.8360i −0.437937 + 0.117345i
\(349\) 267.249i 0.765758i 0.923799 + 0.382879i \(0.125067\pi\)
−0.923799 + 0.382879i \(0.874933\pi\)
\(350\) −520.289 376.668i −1.48654 1.07620i
\(351\) 81.5832 0.232431
\(352\) −15.5489 58.0294i −0.0441731 0.164856i
\(353\) −82.2594 + 306.996i −0.233030 + 0.869678i 0.745998 + 0.665949i \(0.231973\pi\)
−0.979027 + 0.203730i \(0.934694\pi\)
\(354\) −27.7004 + 15.9929i −0.0782498 + 0.0451776i
\(355\) −63.3289 + 46.5812i −0.178391 + 0.131215i
\(356\) 570.283 1.60192
\(357\) 149.069 74.0785i 0.417560 0.207503i
\(358\) 568.741 + 568.741i 1.58866 + 1.58866i
\(359\) −327.578 189.127i −0.912473 0.526816i −0.0312469 0.999512i \(-0.509948\pi\)
−0.881226 + 0.472695i \(0.843281\pi\)
\(360\) −537.435 430.010i −1.49287 1.19447i
\(361\) −176.180 305.153i −0.488033 0.845299i
\(362\) −277.068 1034.03i −0.765381 2.85644i
\(363\) −123.912 123.912i −0.341357 0.341357i
\(364\) 154.100 + 174.640i 0.423350 + 0.479780i
\(365\) 67.4742 + 172.740i 0.184861 + 0.473261i
\(366\) 0.0441854 0.0765313i 0.000120725 0.000209102i
\(367\) 424.235 + 113.673i 1.15595 + 0.309737i 0.785348 0.619054i \(-0.212484\pi\)
0.370605 + 0.928791i \(0.379150\pi\)
\(368\) −273.211 + 1019.64i −0.742421 + 2.77075i
\(369\) 352.275 + 203.386i 0.954676 + 0.551183i
\(370\) −282.278 + 644.151i −0.762913 + 1.74095i
\(371\) −39.4449 + 34.8055i −0.106320 + 0.0938155i
\(372\) −306.571 + 306.571i −0.824117 + 0.824117i
\(373\) 505.079 135.336i 1.35410 0.362830i 0.492454 0.870339i \(-0.336100\pi\)
0.861647 + 0.507509i \(0.169433\pi\)
\(374\) −60.5738 + 34.9723i −0.161962 + 0.0935089i
\(375\) −182.669 + 12.8005i −0.487118 + 0.0341347i
\(376\) −690.172 + 1195.41i −1.83556 + 3.17929i
\(377\) −28.2433 + 28.2433i −0.0749160 + 0.0749160i
\(378\) −265.553 534.375i −0.702521 1.41369i
\(379\) 438.406i 1.15674i −0.815773 0.578372i \(-0.803688\pi\)
0.815773 0.578372i \(-0.196312\pi\)
\(380\) 112.140 82.4841i 0.295106 0.217063i
\(381\) 31.5025 + 54.5639i 0.0826837 + 0.143212i
\(382\) −391.255 104.836i −1.02423 0.274441i
\(383\) 200.789 53.8012i 0.524253 0.140473i 0.0130198 0.999915i \(-0.495856\pi\)
0.511233 + 0.859442i \(0.329189\pi\)
\(384\) 60.5331i 0.157638i
\(385\) 22.2339 + 34.5522i 0.0577505 + 0.0897459i
\(386\) −1315.22 −3.40730
\(387\) 46.9392 + 175.179i 0.121290 + 0.452660i
\(388\) −179.517 + 669.968i −0.462674 + 1.72672i
\(389\) −217.843 + 125.772i −0.560007 + 0.323320i −0.753148 0.657851i \(-0.771466\pi\)
0.193141 + 0.981171i \(0.438132\pi\)
\(390\) 93.3608 + 14.2259i 0.239387 + 0.0364768i
\(391\) 478.237 1.22311
\(392\) 371.063 911.506i 0.946590 2.32527i
\(393\) 58.6913 + 58.6913i 0.149342 + 0.149342i
\(394\) −407.641 235.351i −1.03462 0.597339i
\(395\) −346.348 + 38.4583i −0.876830 + 0.0973629i
\(396\) 38.1063 + 66.0020i 0.0962280 + 0.166672i
\(397\) 69.2050 + 258.277i 0.174320 + 0.650571i 0.996666 + 0.0815838i \(0.0259978\pi\)
−0.822347 + 0.568987i \(0.807336\pi\)
\(398\) 839.576 + 839.576i 2.10949 + 2.10949i
\(399\) 29.5448 5.97052i 0.0740471 0.0149637i
\(400\) −607.153 658.604i −1.51788 1.64651i
\(401\) 331.345 573.906i 0.826296 1.43119i −0.0746287 0.997211i \(-0.523777\pi\)
0.900925 0.433975i \(-0.142890\pi\)
\(402\) 218.037 + 58.4229i 0.542381 + 0.145331i
\(403\) −28.4071 + 106.017i −0.0704890 + 0.263069i
\(404\) 1544.47 + 891.701i 3.82295 + 2.20718i
\(405\) 126.682 + 55.5142i 0.312795 + 0.137072i
\(406\) 276.927 + 93.0636i 0.682087 + 0.229221i
\(407\) 31.8108 31.8108i 0.0781593 0.0781593i
\(408\) 461.337 123.615i 1.13073 0.302978i
\(409\) 217.013 125.293i 0.530595 0.306339i −0.210664 0.977559i \(-0.567562\pi\)
0.741259 + 0.671219i \(0.234229\pi\)
\(410\) 850.452 + 680.460i 2.07427 + 1.65966i
\(411\) 158.018 273.695i 0.384472 0.665925i
\(412\) −792.520 + 792.520i −1.92359 + 1.92359i
\(413\) 41.5597 + 2.59675i 0.100629 + 0.00628752i
\(414\) 741.149i 1.79021i
\(415\) −441.763 67.3140i −1.06449 0.162202i
\(416\) 89.8823 + 155.681i 0.216063 + 0.374233i
\(417\) 239.776 + 64.2478i 0.575003 + 0.154072i
\(418\) −12.2337 + 3.27802i −0.0292673 + 0.00784215i
\(419\) 195.592i 0.466807i 0.972380 + 0.233403i \(0.0749862\pi\)
−0.972380 + 0.233403i \(0.925014\pi\)
\(420\) −148.146 462.508i −0.352730 1.10121i
\(421\) −134.668 −0.319877 −0.159939 0.987127i \(-0.551130\pi\)
−0.159939 + 0.987127i \(0.551130\pi\)
\(422\) −30.7318 114.692i −0.0728241 0.271783i
\(423\) 121.917 455.000i 0.288220 1.07565i
\(424\) −130.714 + 75.4680i −0.308289 + 0.177991i
\(425\) −217.017 + 342.920i −0.510629 + 0.806871i
\(426\) −84.5418 −0.198455
\(427\) −0.103026 + 0.0511979i −0.000241279 + 0.000119901i
\(428\) −312.772 312.772i −0.730777 0.730777i
\(429\) −5.23164 3.02049i −0.0121950 0.00704076i
\(430\) 53.5921 + 482.640i 0.124633 + 1.12242i
\(431\) −259.076 448.733i −0.601105 1.04114i −0.992654 0.120987i \(-0.961394\pi\)
0.391549 0.920157i \(-0.371939\pi\)
\(432\) −215.381 803.812i −0.498566 1.86068i
\(433\) −370.568 370.568i −0.855815 0.855815i 0.135027 0.990842i \(-0.456888\pi\)
−0.990842 + 0.135027i \(0.956888\pi\)
\(434\) 786.881 159.016i 1.81309 0.366396i
\(435\) 77.5785 30.3030i 0.178341 0.0696620i
\(436\) 159.388 276.069i 0.365570 0.633185i
\(437\) 83.6464 + 22.4130i 0.191410 + 0.0512883i
\(438\) −51.6166 + 192.636i −0.117846 + 0.439808i
\(439\) −129.219 74.6045i −0.294348 0.169942i 0.345553 0.938399i \(-0.387691\pi\)
−0.639901 + 0.768457i \(0.721025\pi\)
\(440\) 42.8928 + 109.809i 0.0974835 + 0.249567i
\(441\) −41.8053 + 333.232i −0.0947967 + 0.755628i
\(442\) 147.992 147.992i 0.334824 0.334824i
\(443\) −586.733 + 157.215i −1.32445 + 0.354886i −0.850645 0.525741i \(-0.823788\pi\)
−0.473809 + 0.880627i \(0.657121\pi\)
\(444\) −460.508 + 265.874i −1.03718 + 0.598816i
\(445\) −299.198 + 33.2228i −0.672354 + 0.0746580i
\(446\) −473.076 + 819.391i −1.06071 + 1.83720i
\(447\) −154.724 + 154.724i −0.346140 + 0.346140i
\(448\) 172.318 259.603i 0.384639 0.579470i
\(449\) 653.166i 1.45471i 0.686259 + 0.727357i \(0.259251\pi\)
−0.686259 + 0.727357i \(0.740749\pi\)
\(450\) 531.442 + 336.323i 1.18098 + 0.747385i
\(451\) −34.8357 60.3372i −0.0772410 0.133785i
\(452\) −524.547 140.552i −1.16050 0.310956i
\(453\) 215.976 57.8707i 0.476769 0.127750i
\(454\) 767.995i 1.69162i
\(455\) −91.0219 82.6471i −0.200048 0.181642i
\(456\) 86.4839 0.189658
\(457\) −26.9808 100.694i −0.0590390 0.220336i 0.930103 0.367298i \(-0.119717\pi\)
−0.989142 + 0.146962i \(0.953051\pi\)
\(458\) 99.8562 372.668i 0.218027 0.813687i
\(459\) −326.499 + 188.504i −0.711327 + 0.410685i
\(460\) 210.180 1379.35i 0.456913 2.99859i
\(461\) −51.4142 −0.111527 −0.0557637 0.998444i \(-0.517759\pi\)
−0.0557637 + 0.998444i \(0.517759\pi\)
\(462\) −2.75542 + 44.0992i −0.00596411 + 0.0954529i
\(463\) −47.6581 47.6581i −0.102933 0.102933i 0.653765 0.756698i \(-0.273189\pi\)
−0.756698 + 0.653765i \(0.773189\pi\)
\(464\) 352.835 + 203.709i 0.760420 + 0.439028i
\(465\) 142.982 178.702i 0.307489 0.384305i
\(466\) 93.8710 + 162.589i 0.201440 + 0.348904i
\(467\) −52.3282 195.292i −0.112052 0.418183i 0.886998 0.461774i \(-0.152787\pi\)
−0.999049 + 0.0435908i \(0.986120\pi\)
\(468\) −161.254 161.254i −0.344560 0.344560i
\(469\) −194.432 220.349i −0.414568 0.469827i
\(470\) 506.241 1155.23i 1.07711 2.45793i
\(471\) −101.348 + 175.540i −0.215176 + 0.372696i
\(472\) 115.405 + 30.9227i 0.244503 + 0.0655143i
\(473\) 8.03967 30.0045i 0.0169972 0.0634344i
\(474\) −324.541 187.374i −0.684685 0.395303i
\(475\) −54.0289 + 49.8080i −0.113745 + 0.104859i
\(476\) −1020.23 342.857i −2.14334 0.720287i
\(477\) 36.4215 36.4215i 0.0763554 0.0763554i
\(478\) 207.154 55.5068i 0.433377 0.116123i
\(479\) −560.143 + 323.399i −1.16940 + 0.675154i −0.953539 0.301270i \(-0.902590\pi\)
−0.215862 + 0.976424i \(0.569256\pi\)
\(480\) −41.3682 372.553i −0.0861837 0.776153i
\(481\) −67.3069 + 116.579i −0.139931 + 0.242368i
\(482\) 536.233 536.233i 1.11252 1.11252i
\(483\) 167.077 251.706i 0.345915 0.521130i
\(484\) 1133.06i 2.34103i
\(485\) 55.1533 361.955i 0.113718 0.746300i
\(486\) 457.975 + 793.236i 0.942336 + 1.63217i
\(487\) 501.060 + 134.259i 1.02887 + 0.275685i 0.733494 0.679695i \(-0.237888\pi\)
0.295377 + 0.955381i \(0.404555\pi\)
\(488\) −0.318844 + 0.0854340i −0.000653369 + 0.000175070i
\(489\) 15.8275i 0.0323671i
\(490\) −245.068 + 865.215i −0.500138 + 1.76575i
\(491\) 142.382 0.289984 0.144992 0.989433i \(-0.453684\pi\)
0.144992 + 0.989433i \(0.453684\pi\)
\(492\) 213.141 + 795.453i 0.433213 + 1.61677i
\(493\) 47.7725 178.289i 0.0969016 0.361642i
\(494\) 32.8205 18.9489i 0.0664383 0.0383582i
\(495\) −23.8374 32.4079i −0.0481564 0.0654704i
\(496\) 1119.54 2.25714
\(497\) 91.6986 + 60.8675i 0.184504 + 0.122470i
\(498\) −339.800 339.800i −0.682329 0.682329i
\(499\) 847.182 + 489.121i 1.69776 + 0.980202i 0.947880 + 0.318627i \(0.103222\pi\)
0.749879 + 0.661575i \(0.230112\pi\)
\(500\) 893.689 + 776.641i 1.78738 + 1.55328i
\(501\) 83.6698 + 144.920i 0.167006 + 0.289262i
\(502\) 339.616 + 1267.46i 0.676526 + 2.52483i
\(503\) −233.167 233.167i −0.463553 0.463553i 0.436265 0.899818i \(-0.356301\pi\)
−0.899818 + 0.436265i \(0.856301\pi\)
\(504\) −306.958 + 913.409i −0.609044 + 1.81232i
\(505\) −862.252 377.853i −1.70743 0.748224i
\(506\) −63.4714 + 109.936i −0.125438 + 0.217264i
\(507\) −221.678 59.3985i −0.437235 0.117157i
\(508\) 105.437 393.496i 0.207553 0.774599i
\(509\) −838.493 484.104i −1.64733 0.951089i −0.978126 0.208014i \(-0.933300\pi\)
−0.669208 0.743075i \(-0.733366\pi\)
\(510\) −406.504 + 158.785i −0.797066 + 0.311343i
\(511\) 194.678 171.781i 0.380975 0.336166i
\(512\) −738.866 + 738.866i −1.44310 + 1.44310i
\(513\) −65.9410 + 17.6688i −0.128540 + 0.0344422i
\(514\) 46.6988 26.9616i 0.0908538 0.0524544i
\(515\) 369.625 461.964i 0.717718 0.897017i
\(516\) −183.581 + 317.972i −0.355778 + 0.616225i
\(517\) −57.0500 + 57.0500i −0.110348 + 0.110348i
\(518\) 982.684 + 61.4003i 1.89707 + 0.118533i
\(519\) 331.096i 0.637949i
\(520\) −209.016 284.164i −0.401953 0.546470i
\(521\) 13.0561 + 22.6139i 0.0250597 + 0.0434048i 0.878283 0.478141i \(-0.158689\pi\)
−0.853224 + 0.521545i \(0.825356\pi\)
\(522\) −276.304 74.0355i −0.529319 0.141831i
\(523\) −55.3556 + 14.8325i −0.105842 + 0.0283604i −0.311351 0.950295i \(-0.600782\pi\)
0.205509 + 0.978655i \(0.434115\pi\)
\(524\) 536.674i 1.02419i
\(525\) 104.669 + 234.023i 0.199369 + 0.445759i
\(526\) 970.133 1.84436
\(527\) −131.274 489.920i −0.249096 0.929639i
\(528\) −15.9483 + 59.5197i −0.0302050 + 0.112727i
\(529\) 293.542 169.477i 0.554900 0.320372i
\(530\) 111.100 81.7188i 0.209622 0.154186i
\(531\) −40.7720 −0.0767835
\(532\) −162.376 107.782i −0.305218 0.202597i
\(533\) 147.414 + 147.414i 0.276574 + 0.276574i
\(534\) −280.359 161.865i −0.525017 0.303119i
\(535\) 182.317 + 145.874i 0.340779 + 0.272662i
\(536\) −421.582 730.202i −0.786534 1.36232i
\(537\) −83.0862 310.082i −0.154723 0.577434i
\(538\) 676.142 + 676.142i 1.25677 + 1.25677i
\(539\) 34.7388 45.8486i 0.0644504 0.0850623i
\(540\) 400.200 + 1024.55i 0.741111 + 1.89731i
\(541\) 290.337 502.879i 0.536667 0.929535i −0.462413 0.886665i \(-0.653016\pi\)
0.999081 0.0428707i \(-0.0136504\pi\)
\(542\) −1256.17 336.589i −2.31765 0.621012i
\(543\) −110.583 + 412.703i −0.203653 + 0.760042i
\(544\) −719.425 415.360i −1.32247 0.763530i
\(545\) −67.5399 + 154.124i −0.123926 + 0.282797i
\(546\) −26.1889 129.594i −0.0479649 0.237352i
\(547\) 200.743 200.743i 0.366988 0.366988i −0.499389 0.866378i \(-0.666442\pi\)
0.866378 + 0.499389i \(0.166442\pi\)
\(548\) −1973.80 + 528.877i −3.60182 + 0.965104i
\(549\) 0.0975541 0.0563229i 0.000177694 0.000102592i
\(550\) −50.0271 95.3996i −0.0909583 0.173454i
\(551\) 16.7114 28.9449i 0.0303292 0.0525317i
\(552\) 612.933 612.933i 1.11039 1.11039i
\(553\) 217.111 + 436.895i 0.392606 + 0.790045i
\(554\) 339.749i 0.613265i
\(555\) 226.115 166.318i 0.407415 0.299672i
\(556\) −802.517 1390.00i −1.44338 2.50000i
\(557\) 456.872 + 122.418i 0.820236 + 0.219782i 0.644450 0.764647i \(-0.277087\pi\)
0.175786 + 0.984428i \(0.443753\pi\)
\(558\) −759.255 + 203.442i −1.36067 + 0.364591i
\(559\) 92.9484i 0.166276i
\(560\) −573.995 + 1115.00i −1.02499 + 1.99107i
\(561\) 27.9163 0.0497617
\(562\) 13.3884 + 49.9664i 0.0238229 + 0.0889081i
\(563\) 98.1984 366.481i 0.174420 0.650944i −0.822230 0.569156i \(-0.807270\pi\)
0.996650 0.0817883i \(-0.0260631\pi\)
\(564\) 825.881 476.822i 1.46433 0.845430i
\(565\) 283.391 + 43.1819i 0.501576 + 0.0764281i
\(566\) −1498.98 −2.64837
\(567\) 12.0753 193.260i 0.0212968 0.340846i
\(568\) 223.297 + 223.297i 0.393128 + 0.393128i
\(569\) 416.460 + 240.443i 0.731916 + 0.422572i 0.819123 0.573619i \(-0.194461\pi\)
−0.0872069 + 0.996190i \(0.527794\pi\)
\(570\) −78.5415 + 8.72122i −0.137792 + 0.0153004i
\(571\) 419.663 + 726.877i 0.734961 + 1.27299i 0.954740 + 0.297440i \(0.0961329\pi\)
−0.219779 + 0.975550i \(0.570534\pi\)
\(572\) 10.1094 + 37.7288i 0.0176738 + 0.0659594i
\(573\) 114.315 + 114.315i 0.199503 + 0.199503i
\(574\) 485.739 1445.40i 0.846236 2.51813i
\(575\) −29.9140 + 735.919i −0.0520244 + 1.27986i
\(576\) −152.544 + 264.213i −0.264833 + 0.458704i
\(577\) −697.804 186.976i −1.20937 0.324049i −0.402853 0.915265i \(-0.631981\pi\)
−0.806513 + 0.591216i \(0.798648\pi\)
\(578\) 24.2194 90.3881i 0.0419021 0.156381i
\(579\) 454.602 + 262.464i 0.785150 + 0.453306i
\(580\) −493.235 216.144i −0.850405 0.372662i
\(581\) 123.920 + 613.210i 0.213287 + 1.05544i
\(582\) 278.413 278.413i 0.478372 0.478372i
\(583\) −8.52157 + 2.28335i −0.0146168 + 0.00391655i
\(584\) 645.134 372.468i 1.10468 0.637788i
\(585\) 93.9959 + 75.2076i 0.160677 + 0.128560i
\(586\) 708.404 1226.99i 1.20888 2.09384i
\(587\) −421.963 + 421.963i −0.718847 + 0.718847i −0.968369 0.249522i \(-0.919726\pi\)
0.249522 + 0.968369i \(0.419726\pi\)
\(588\) −536.881 + 417.189i −0.913063 + 0.709505i
\(589\) 91.8421i 0.155929i
\(590\) −107.925 16.4452i −0.182924 0.0278732i
\(591\) 93.9335 + 162.698i 0.158940 + 0.275292i
\(592\) 1326.31 + 355.382i 2.24038 + 0.600308i
\(593\) −376.987 + 101.013i −0.635728 + 0.170343i −0.562268 0.826955i \(-0.690071\pi\)
−0.0734605 + 0.997298i \(0.523404\pi\)
\(594\) 100.073i 0.168473i
\(595\) 555.236 + 120.444i 0.933170 + 0.202426i
\(596\) 1414.80 2.37383
\(597\) −122.652 457.744i −0.205447 0.766740i
\(598\) 98.3114 366.903i 0.164400 0.613551i
\(599\) 909.142 524.893i 1.51777 0.876283i 0.517984 0.855390i \(-0.326683\pi\)
0.999782 0.0208923i \(-0.00665070\pi\)
\(600\) 161.364 + 717.645i 0.268940 + 1.19608i
\(601\) −205.229 −0.341479 −0.170739 0.985316i \(-0.554616\pi\)
−0.170739 + 0.985316i \(0.554616\pi\)
\(602\) 608.818 302.547i 1.01133 0.502569i
\(603\) 203.460 + 203.460i 0.337412 + 0.337412i
\(604\) −1252.03 722.860i −2.07290 1.19679i
\(605\) −66.0082 594.456i −0.109104 0.982572i
\(606\) −506.190 876.746i −0.835297 1.44678i
\(607\) −36.6899 136.929i −0.0604447 0.225583i 0.929096 0.369840i \(-0.120587\pi\)
−0.989540 + 0.144257i \(0.953921\pi\)
\(608\) −106.365 106.365i −0.174943 0.174943i
\(609\) −77.1476 87.4308i −0.126679 0.143565i
\(610\) 0.280947 0.109741i 0.000460569 0.000179903i
\(611\) 120.709 209.074i 0.197560 0.342184i
\(612\) 1017.94 + 272.755i 1.66330 + 0.445679i
\(613\) −61.7096 + 230.303i −0.100668 + 0.375699i −0.997818 0.0660280i \(-0.978967\pi\)
0.897150 + 0.441727i \(0.145634\pi\)
\(614\) 671.922 + 387.934i 1.09434 + 0.631815i
\(615\) −158.164 404.916i −0.257178 0.658400i
\(616\) 123.755 109.200i 0.200901 0.177272i
\(617\) −96.9272 + 96.9272i −0.157094 + 0.157094i −0.781278 0.624183i \(-0.785432\pi\)
0.624183 + 0.781278i \(0.285432\pi\)
\(618\) 614.558 164.670i 0.994431 0.266457i
\(619\) −853.884 + 492.990i −1.37946 + 0.796430i −0.992094 0.125498i \(-0.959947\pi\)
−0.387363 + 0.921927i \(0.626614\pi\)
\(620\) −1470.74 + 163.311i −2.37216 + 0.263404i
\(621\) −342.117 + 592.565i −0.550914 + 0.954210i
\(622\) −315.656 + 315.656i −0.507485 + 0.507485i
\(623\) 187.555 + 377.418i 0.301051 + 0.605807i
\(624\) 184.381i 0.295483i
\(625\) −514.117 355.400i −0.822587 0.568640i
\(626\) 353.792 + 612.786i 0.565163 + 0.978891i
\(627\) 4.88272 + 1.30832i 0.00778744 + 0.00208664i
\(628\) 1265.93 339.206i 2.01582 0.540136i
\(629\) 622.072i 0.988986i
\(630\) 186.658 860.479i 0.296283 1.36584i
\(631\) −930.705 −1.47497 −0.737484 0.675365i \(-0.763986\pi\)
−0.737484 + 0.675365i \(0.763986\pi\)
\(632\) 362.294 + 1352.10i 0.573249 + 2.13940i
\(633\) −12.2657 + 45.7760i −0.0193770 + 0.0723160i
\(634\) −1750.37 + 1010.58i −2.76084 + 1.59397i
\(635\) −32.3935 + 212.589i −0.0510134 + 0.334786i
\(636\) 104.278 0.163959
\(637\) −64.8979 + 159.420i −0.101881 + 0.250267i
\(638\) 34.6443 + 34.6443i 0.0543014 + 0.0543014i
\(639\) −93.3273 53.8825i −0.146052 0.0843232i
\(640\) 129.077 161.323i 0.201683 0.252068i
\(641\) 177.889 + 308.112i 0.277518 + 0.480674i 0.970767 0.240023i \(-0.0771550\pi\)
−0.693250 + 0.720698i \(0.743822\pi\)
\(642\) 64.9881 + 242.539i 0.101228 + 0.377786i
\(643\) 366.310 + 366.310i 0.569689 + 0.569689i 0.932041 0.362352i \(-0.118026\pi\)
−0.362352 + 0.932041i \(0.618026\pi\)
\(644\) −1914.68 + 386.925i −2.97310 + 0.600815i
\(645\) 77.7915 177.518i 0.120607 0.275222i
\(646\) −87.5660 + 151.669i −0.135551 + 0.234781i
\(647\) 790.128 + 211.714i 1.22122 + 0.327225i 0.811154 0.584832i \(-0.198840\pi\)
0.410064 + 0.912057i \(0.365506\pi\)
\(648\) 143.796 536.653i 0.221907 0.828168i
\(649\) 6.04777 + 3.49168i 0.00931860 + 0.00538010i
\(650\) 218.476 + 236.990i 0.336117 + 0.364600i
\(651\) −303.717 102.066i −0.466539 0.156784i
\(652\) −72.3635 + 72.3635i −0.110987 + 0.110987i
\(653\) −30.7771 + 8.24671i −0.0471319 + 0.0126290i −0.282308 0.959324i \(-0.591100\pi\)
0.235176 + 0.971953i \(0.424433\pi\)
\(654\) −156.715 + 90.4796i −0.239626 + 0.138348i
\(655\) 31.2649 + 281.565i 0.0477326 + 0.429870i
\(656\) 1063.25 1841.60i 1.62080 2.80731i
\(657\) −179.757 + 179.757i −0.273602 + 0.273602i
\(658\) −1762.36 110.116i −2.67836 0.167350i
\(659\) 495.313i 0.751612i −0.926698 0.375806i \(-0.877366\pi\)
0.926698 0.375806i \(-0.122634\pi\)
\(660\) 12.2689 80.5175i 0.0185893 0.121996i
\(661\) 428.787 + 742.682i 0.648695 + 1.12357i 0.983435 + 0.181262i \(0.0580182\pi\)
−0.334740 + 0.942311i \(0.608648\pi\)
\(662\) −2207.38 591.465i −3.33441 0.893452i
\(663\) −80.6866 + 21.6199i −0.121699 + 0.0326092i
\(664\) 1795.00i 2.70331i
\(665\) 91.4694 + 47.0879i 0.137548 + 0.0708089i
\(666\) −964.058 −1.44753
\(667\) −86.7024 323.578i −0.129989 0.485124i
\(668\) 280.038 1045.12i 0.419219 1.56455i
\(669\) 327.035 188.814i 0.488842 0.282233i
\(670\) 456.501 + 620.630i 0.681345 + 0.926313i
\(671\) −0.0192938 −2.87538e−5
\(672\) −469.951 + 233.538i −0.699333 + 0.347527i
\(673\) −692.154 692.154i −1.02846 1.02846i −0.999583 0.0288771i \(-0.990807\pi\)
−0.0288771 0.999583i \(-0.509193\pi\)
\(674\) 1343.76 + 775.822i 1.99371 + 1.15107i
\(675\) −269.651 514.213i −0.399483 0.761798i
\(676\) 741.944 + 1285.09i 1.09755 + 1.90101i
\(677\) −116.061 433.146i −0.171435 0.639802i −0.997132 0.0756885i \(-0.975885\pi\)
0.825697 0.564114i \(-0.190782\pi\)
\(678\) 217.981 + 217.981i 0.321507 + 0.321507i
\(679\) −502.430 + 101.533i −0.739956 + 0.149533i
\(680\) 1493.07 + 654.290i 2.19570 + 0.962191i
\(681\) −153.261 + 265.456i −0.225053 + 0.389803i
\(682\) 130.044 + 34.8452i 0.190680 + 0.0510926i
\(683\) −134.721 + 502.785i −0.197249 + 0.736142i 0.794425 + 0.607363i \(0.207772\pi\)
−0.991673 + 0.128779i \(0.958894\pi\)
\(684\) 165.260 + 95.4130i 0.241608 + 0.139493i
\(685\) 1004.74 392.461i 1.46677 0.572936i
\(686\) 1255.45 93.8259i 1.83011 0.136772i
\(687\) −108.885 + 108.885i −0.158493 + 0.158493i
\(688\) 915.789 245.385i 1.33109 0.356664i
\(689\) 22.8616 13.1991i 0.0331808 0.0191570i
\(690\) −494.834 + 618.453i −0.717151 + 0.896309i
\(691\) 124.505 215.649i 0.180181 0.312083i −0.761761 0.647858i \(-0.775665\pi\)
0.941942 + 0.335775i \(0.108998\pi\)
\(692\) 1513.77 1513.77i 2.18753 2.18753i
\(693\) −31.1483 + 46.9258i −0.0449470 + 0.0677140i
\(694\) 82.8692i 0.119408i
\(695\) 502.016 + 682.508i 0.722324 + 0.982027i
\(696\) −167.277 289.733i −0.240341 0.416283i
\(697\) −930.569 249.345i −1.33511 0.357741i
\(698\) −947.494 + 253.880i −1.35744 + 0.363725i
\(699\) 74.9316i 0.107198i
\(700\) 591.410 1548.50i 0.844871 2.21215i
\(701\) 954.149 1.36113 0.680563 0.732690i \(-0.261735\pi\)
0.680563 + 0.732690i \(0.261735\pi\)
\(702\) 77.5020 + 289.241i 0.110402 + 0.412025i
\(703\) 29.1540 108.804i 0.0414708 0.154771i
\(704\) 45.2541 26.1274i 0.0642813 0.0371128i
\(705\) −405.518 + 298.277i −0.575203 + 0.423088i
\(706\) −1166.56 −1.65234
\(707\) −82.1896 + 1315.41i −0.116251 + 1.86055i
\(708\) −58.3668 58.3668i −0.0824390 0.0824390i
\(709\) 19.0690 + 11.0095i 0.0268957 + 0.0155282i 0.513388 0.858157i \(-0.328390\pi\)
−0.486492 + 0.873685i \(0.661724\pi\)
\(710\) −225.308 180.272i −0.317335 0.253905i
\(711\) −238.844 413.691i −0.335927 0.581843i
\(712\) 312.972 + 1168.03i 0.439568 + 1.64049i
\(713\) −650.908 650.908i −0.912915 0.912915i
\(714\) 404.246 + 458.129i 0.566171 + 0.641638i
\(715\) −7.50183 19.2054i −0.0104921 0.0268607i
\(716\) −1037.83 + 1797.57i −1.44948 + 2.51057i
\(717\) −82.6793 22.1539i −0.115313 0.0308980i
\(718\) 359.332 1341.04i 0.500462 1.86775i
\(719\) 217.588 + 125.625i 0.302626 + 0.174721i 0.643622 0.765343i \(-0.277431\pi\)
−0.340996 + 0.940065i \(0.610764\pi\)
\(720\) 492.845 1124.66i 0.684506 1.56203i
\(721\) −785.141 263.853i −1.08896 0.365954i
\(722\) 914.508 914.508i 1.26663 1.26663i
\(723\) −292.359 + 78.3372i −0.404369 + 0.108350i
\(724\) 2392.47 1381.29i 3.30451 1.90786i
\(725\) 271.366 + 84.6652i 0.374298 + 0.116780i
\(726\) 321.600 557.027i 0.442975 0.767255i
\(727\) −157.277 + 157.277i −0.216338 + 0.216338i −0.806953 0.590615i \(-0.798885\pi\)
0.590615 + 0.806953i \(0.298885\pi\)
\(728\) −273.120 + 411.463i −0.375165 + 0.565196i
\(729\) 116.613i 0.159963i
\(730\) −548.327 + 403.319i −0.751132 + 0.552491i
\(731\) −214.765 371.983i −0.293796 0.508869i
\(732\) 0.220281 + 0.0590242i 0.000300931 + 8.06341e-5i
\(733\) 322.220 86.3385i 0.439590 0.117788i −0.0322341 0.999480i \(-0.510262\pi\)
0.471825 + 0.881692i \(0.343596\pi\)
\(734\) 1612.05i 2.19625i
\(735\) 257.370 250.154i 0.350163 0.340346i
\(736\) −1507.68 −2.04848
\(737\) −12.7553 47.6036i −0.0173071 0.0645910i
\(738\) −386.424 + 1442.15i −0.523609 + 1.95414i
\(739\) 342.328 197.643i 0.463231 0.267446i −0.250171 0.968202i \(-0.580487\pi\)
0.713402 + 0.700755i \(0.247153\pi\)
\(740\) −1794.21 273.394i −2.42461 0.369452i
\(741\) −15.1258 −0.0204127
\(742\) −160.870 106.782i −0.216805 0.143911i
\(743\) 500.455 + 500.455i 0.673560 + 0.673560i 0.958535 0.284975i \(-0.0919853\pi\)
−0.284975 + 0.958535i \(0.591985\pi\)
\(744\) −796.154 459.660i −1.07010 0.617822i
\(745\) −742.273 + 82.4218i −0.996340 + 0.110633i
\(746\) 959.625 + 1662.12i 1.28636 + 2.22804i
\(747\) −158.541 591.682i −0.212236 0.792077i
\(748\) −127.633 127.633i −0.170633 0.170633i
\(749\) 104.131 309.860i 0.139027 0.413698i
\(750\) −218.914 635.467i −0.291885 0.847289i
\(751\) 399.343 691.683i 0.531749 0.921016i −0.467564 0.883959i \(-0.654868\pi\)
0.999313 0.0370570i \(-0.0117983\pi\)
\(752\) −2378.61 637.348i −3.16305 0.847537i
\(753\) 135.547 505.870i 0.180010 0.671806i
\(754\) −126.963 73.3021i −0.168386 0.0972177i
\(755\) 698.987 + 306.308i 0.925810 + 0.405706i
\(756\) 1154.67 1018.86i 1.52734 1.34770i
\(757\) −456.836 + 456.836i −0.603482 + 0.603482i −0.941235 0.337753i \(-0.890333\pi\)
0.337753 + 0.941235i \(0.390333\pi\)
\(758\) 1554.31 416.475i 2.05053 0.549439i
\(759\) 43.8775 25.3327i 0.0578096 0.0333764i
\(760\) 230.483 + 184.413i 0.303268 + 0.242649i
\(761\) 523.481 906.696i 0.687886 1.19145i −0.284635 0.958636i \(-0.591872\pi\)
0.972521 0.232817i \(-0.0747943\pi\)
\(762\) −163.522 + 163.522i −0.214596 + 0.214596i
\(763\) 235.124 + 14.6911i 0.308158 + 0.0192544i
\(764\) 1045.30i 1.36820i
\(765\) −549.948 83.7989i −0.718887 0.109541i
\(766\) 381.489 + 660.758i 0.498027 + 0.862608i
\(767\) −20.1841 5.40830i −0.0263156 0.00705124i
\(768\) 466.556 125.013i 0.607495 0.162778i
\(769\) 627.616i 0.816146i 0.912949 + 0.408073i \(0.133799\pi\)
−0.912949 + 0.408073i \(0.866201\pi\)
\(770\) −101.378 + 111.651i −0.131660 + 0.145001i
\(771\) −21.5218 −0.0279141
\(772\) −878.453 3278.43i −1.13789 4.24667i
\(773\) −47.5625 + 177.506i −0.0615297 + 0.229632i −0.989843 0.142168i \(-0.954593\pi\)
0.928313 + 0.371800i \(0.121259\pi\)
\(774\) −576.482 + 332.832i −0.744809 + 0.430016i
\(775\) 762.108 171.361i 0.983365 0.221111i
\(776\) −1470.72 −1.89526
\(777\) −327.410 217.327i −0.421377 0.279700i
\(778\) −652.850 652.850i −0.839139 0.839139i
\(779\) −151.076 87.2239i −0.193936 0.111969i
\(780\) 26.8962 + 242.222i 0.0344823 + 0.310541i
\(781\) 9.22891 + 15.9849i 0.0118168 + 0.0204673i
\(782\) 454.313 + 1695.52i 0.580962 + 2.16818i
\(783\) 186.736 + 186.736i 0.238488 + 0.238488i
\(784\) 1742.04 + 218.547i 2.22199 + 0.278758i
\(785\) −644.408 + 251.713i −0.820902 + 0.320653i
\(786\) −152.326 + 263.837i −0.193799 + 0.335670i
\(787\) 1048.26 + 280.881i 1.33197 + 0.356901i 0.853451 0.521173i \(-0.174506\pi\)
0.478523 + 0.878075i \(0.341172\pi\)
\(788\) 314.390 1173.32i 0.398972 1.48898i
\(789\) −335.325 193.600i −0.424999 0.245374i
\(790\) −465.370 1191.39i −0.589076 1.50809i
\(791\) −79.4945 393.374i −0.100499 0.497313i
\(792\) −114.270 + 114.270i −0.144280 + 0.144280i
\(793\) 0.0557649 0.0149422i 7.03215e−5 1.88426e-5i
\(794\) −849.939 + 490.712i −1.07045 + 0.618026i
\(795\) −54.7092 + 6.07489i −0.0688166 + 0.00764137i
\(796\) −1532.04 + 2653.57i −1.92467 + 3.33363i
\(797\) 174.158 174.158i 0.218516 0.218516i −0.589357 0.807873i \(-0.700619\pi\)
0.807873 + 0.589357i \(0.200619\pi\)
\(798\) 49.2344 + 99.0749i 0.0616972 + 0.124154i
\(799\) 1115.63i 1.39629i
\(800\) 684.164 1081.08i 0.855205 1.35135i
\(801\) −206.329 357.373i −0.257589 0.446158i
\(802\) 2349.47 + 629.538i 2.92951 + 0.784960i
\(803\) 42.0578 11.2693i 0.0523758 0.0140341i
\(804\) 582.522i 0.724529i
\(805\) 981.991 314.542i 1.21986 0.390736i
\(806\) −402.853 −0.499817
\(807\) −98.7763 368.638i −0.122399 0.456800i
\(808\) −978.735 + 3652.69i −1.21131 + 4.52066i
\(809\) 394.796 227.936i 0.488005 0.281750i −0.235741 0.971816i \(-0.575752\pi\)
0.723746 + 0.690066i \(0.242418\pi\)
\(810\) −76.4728 + 501.869i −0.0944109 + 0.619592i
\(811\) −509.754 −0.628550 −0.314275 0.949332i \(-0.601761\pi\)
−0.314275 + 0.949332i \(0.601761\pi\)
\(812\) −47.0150 + 752.454i −0.0579002 + 0.926667i
\(813\) 367.022 + 367.022i 0.451441 + 0.451441i
\(814\) 143.000 + 82.5612i 0.175676 + 0.101427i
\(815\) 33.7497 42.1810i 0.0414107 0.0517559i
\(816\) 426.027 + 737.901i 0.522092 + 0.904291i
\(817\) −20.1303 75.1272i −0.0246392 0.0919549i
\(818\) 650.365 + 650.365i 0.795067 + 0.795067i
\(819\) 53.6862 159.753i 0.0655509 0.195058i
\(820\) −1128.15 + 2574.41i −1.37579 + 3.13952i
\(821\) −534.939 + 926.542i −0.651571 + 1.12855i 0.331171 + 0.943571i \(0.392556\pi\)
−0.982742 + 0.184983i \(0.940777\pi\)
\(822\) 1120.46 + 300.226i 1.36309 + 0.365239i
\(823\) 115.190 429.895i 0.139964 0.522351i −0.859964 0.510354i \(-0.829514\pi\)
0.999928 0.0119972i \(-0.00381891\pi\)
\(824\) −2058.14 1188.27i −2.49775 1.44208i
\(825\) −1.74618 + 42.9581i −0.00211658 + 0.0520704i
\(826\) 30.2743 + 149.811i 0.0366517 + 0.181369i
\(827\) 645.053 645.053i 0.779992 0.779992i −0.199837 0.979829i \(-0.564041\pi\)
0.979829 + 0.199837i \(0.0640414\pi\)
\(828\) 1847.46 495.025i 2.23123 0.597856i
\(829\) −30.6402 + 17.6901i −0.0369604 + 0.0213391i −0.518366 0.855159i \(-0.673460\pi\)
0.481406 + 0.876498i \(0.340126\pi\)
\(830\) −181.011 1630.15i −0.218086 1.96404i
\(831\) −67.8003 + 117.434i −0.0815888 + 0.141316i
\(832\) −110.563 + 110.563i −0.132889 + 0.132889i
\(833\) −108.628 787.957i −0.130406 0.945927i
\(834\) 911.125i 1.09248i
\(835\) −86.0363 + 564.632i −0.103038 + 0.676206i
\(836\) −16.3422 28.3055i −0.0195481 0.0338583i
\(837\) 700.950 + 187.819i 0.837455 + 0.224396i
\(838\) −693.443 + 185.807i −0.827497 + 0.221727i
\(839\) 1257.73i 1.49908i −0.661957 0.749541i \(-0.730274\pi\)
0.661957 0.749541i \(-0.269726\pi\)
\(840\) 865.987 557.253i 1.03094 0.663396i
\(841\) 711.707 0.846263
\(842\) −127.932 477.447i −0.151938 0.567039i
\(843\) 5.34360 19.9426i 0.00633878 0.0236567i
\(844\) 265.367 153.210i 0.314416 0.181528i
\(845\) −464.124 630.994i −0.549260 0.746739i
\(846\) 1728.95 2.04368
\(847\) −749.867 + 372.640i −0.885321 + 0.439952i
\(848\) −190.402 190.402i −0.224530 0.224530i
\(849\) 518.119 + 299.136i 0.610269 + 0.352339i
\(850\) −1421.93 443.638i −1.67286 0.521927i
\(851\) −564.500 977.743i −0.663338 1.14893i
\(852\) −56.4668 210.737i −0.0662756 0.247344i
\(853\) 703.443 + 703.443i 0.824669 + 0.824669i 0.986774 0.162105i \(-0.0518282\pi\)
−0.162105 + 0.986774i \(0.551828\pi\)
\(854\) −0.279387 0.316627i −0.000327151 0.000370758i
\(855\) −92.2619 40.4307i −0.107909 0.0472874i
\(856\) 468.957 812.258i 0.547847 0.948899i
\(857\) 54.1673 + 14.5141i 0.0632057 + 0.0169359i 0.290283 0.956941i \(-0.406250\pi\)
−0.227078 + 0.973877i \(0.572917\pi\)
\(858\) 5.73877 21.4174i 0.00668855 0.0249620i
\(859\) −1435.21 828.621i −1.67080 0.964635i −0.967193 0.254042i \(-0.918240\pi\)
−0.703603 0.710593i \(-0.748427\pi\)
\(860\) −1167.28 + 455.951i −1.35730 + 0.530176i
\(861\) −456.340 + 402.667i −0.530011 + 0.467674i
\(862\) 1344.80 1344.80i 1.56009 1.56009i
\(863\) −251.406 + 67.3640i −0.291316 + 0.0780580i −0.401518 0.915851i \(-0.631517\pi\)
0.110201 + 0.993909i \(0.464850\pi\)
\(864\) 1029.31 594.275i 1.19134 0.687818i
\(865\) −706.010 + 882.385i −0.816197 + 1.02010i
\(866\) 961.764 1665.82i 1.11058 1.92358i
\(867\) −26.4092 + 26.4092i −0.0304605 + 0.0304605i
\(868\) 921.947 + 1855.24i 1.06215 + 2.13738i
\(869\) 81.8178i 0.0941516i
\(870\) 181.132 + 246.256i 0.208198 + 0.283053i
\(871\) 73.7336 + 127.710i 0.0846540 + 0.146625i
\(872\) 652.905 + 174.945i 0.748745 + 0.200626i
\(873\) 484.791 129.899i 0.555316 0.148796i
\(874\) 317.848i 0.363670i
\(875\) −220.071 + 846.873i −0.251510 + 0.967855i
\(876\) −514.658 −0.587509
\(877\) 390.105 + 1455.89i 0.444817 + 1.66008i 0.716418 + 0.697671i \(0.245780\pi\)
−0.271601 + 0.962410i \(0.587553\pi\)
\(878\) 141.745 528.999i 0.161440 0.602504i
\(879\) −489.717 + 282.738i −0.557129 + 0.321659i
\(880\) −169.419 + 124.615i −0.192522 + 0.141608i
\(881\) −87.7715 −0.0996272 −0.0498136 0.998759i \(-0.515863\pi\)
−0.0498136 + 0.998759i \(0.515863\pi\)
\(882\) −1221.14 + 168.347i −1.38451 + 0.190870i
\(883\) −472.621 472.621i −0.535245 0.535245i 0.386884 0.922129i \(-0.373551\pi\)
−0.922129 + 0.386884i \(0.873551\pi\)
\(884\) 467.746 + 270.053i 0.529124 + 0.305490i
\(885\) 34.0223 + 27.2218i 0.0384433 + 0.0307591i
\(886\) −1114.76 1930.83i −1.25820 2.17926i
\(887\) 309.901 + 1156.57i 0.349381 + 1.30391i 0.887409 + 0.460982i \(0.152503\pi\)
−0.538028 + 0.842927i \(0.680831\pi\)
\(888\) −797.280 797.280i −0.897838 0.897838i
\(889\) 295.095 59.6339i 0.331941 0.0670798i
\(890\) −402.017 1029.20i −0.451704 1.15641i
\(891\) 16.2369 28.1231i 0.0182232 0.0315636i
\(892\) −2358.47 631.949i −2.64402 0.708463i
\(893\) −52.2851 + 195.131i −0.0585499 + 0.218511i
\(894\) −695.537 401.569i −0.778006 0.449182i
\(895\) 439.773 1003.55i 0.491367 1.12129i
\(896\) −274.181 92.1405i −0.306005 0.102835i
\(897\) −107.200 + 107.200i −0.119510 + 0.119510i
\(898\) −2315.71 + 620.492i −2.57874 + 0.690971i
\(899\) −307.683 + 177.641i −0.342251 + 0.197599i
\(900\) −483.393 + 1549.36i −0.537103 + 1.72151i
\(901\) −60.9953 + 105.647i −0.0676974 + 0.117255i
\(902\) 180.824 180.824i 0.200470 0.200470i
\(903\) −270.813 16.9210i −0.299903 0.0187386i
\(904\) 1151.49i 1.27377i
\(905\) −1174.73 + 864.069i −1.29805 + 0.954772i
\(906\) 410.344 + 710.737i 0.452919 + 0.784478i
\(907\) −720.930 193.173i −0.794851 0.212980i −0.161529 0.986868i \(-0.551643\pi\)
−0.633322 + 0.773888i \(0.718309\pi\)
\(908\) 1914.38 512.955i 2.10834 0.564929i
\(909\) 1290.48i 1.41966i
\(910\) 206.545 401.218i 0.226972 0.440899i
\(911\) −929.888 −1.02073 −0.510366 0.859957i \(-0.670490\pi\)
−0.510366 + 0.859957i \(0.670490\pi\)
\(912\) 39.9323 + 149.029i 0.0437854 + 0.163409i
\(913\) −27.1546 + 101.342i −0.0297422 + 0.110999i
\(914\) 331.364 191.313i 0.362543 0.209314i
\(915\) −0.119009 0.0181341i −0.000130064 1.98186e-5i
\(916\) 995.644 1.08695
\(917\) 355.176 176.501i 0.387323 0.192477i
\(918\) −978.481 978.481i −1.06588 1.06588i
\(919\) 671.557 + 387.724i 0.730748 + 0.421897i 0.818696 0.574228i \(-0.194698\pi\)
−0.0879480 + 0.996125i \(0.528031\pi\)
\(920\) 2940.48 326.510i 3.19617 0.354902i
\(921\) −154.832 268.177i −0.168113 0.291181i
\(922\) −48.8421 182.281i −0.0529741 0.197702i
\(923\) −39.0540 39.0540i −0.0423120 0.0423120i
\(924\) −111.766 + 22.5861i −0.120959 + 0.0244439i
\(925\) 957.255 + 38.9110i 1.03487 + 0.0420660i
\(926\) 123.691 214.239i 0.133576 0.231360i
\(927\) 783.375 + 209.905i 0.845064 + 0.226434i
\(928\) −150.606 + 562.071i −0.162291 + 0.605680i
\(929\) 1303.62 + 752.648i 1.40326 + 0.810170i 0.994725 0.102575i \(-0.0327080\pi\)
0.408531 + 0.912745i \(0.366041\pi\)
\(930\) 769.391 + 337.160i 0.827302 + 0.362538i
\(931\) 17.9286 142.909i 0.0192573 0.153501i
\(932\) −342.588 + 342.588i −0.367583 + 0.367583i
\(933\) 172.098 46.1135i 0.184457 0.0494250i
\(934\) 642.667 371.044i 0.688081 0.397263i
\(935\) 74.3982 + 59.5271i 0.0795702 + 0.0636654i
\(936\) 241.778 418.771i 0.258309 0.447405i
\(937\) 422.890 422.890i 0.451323 0.451323i −0.444471 0.895793i \(-0.646608\pi\)
0.895793 + 0.444471i \(0.146608\pi\)
\(938\) 596.508 898.657i 0.635936 0.958056i
\(939\) 282.411i 0.300757i
\(940\) 3217.76 + 490.309i 3.42315 + 0.521605i
\(941\) 402.993 + 698.004i 0.428260 + 0.741768i 0.996719 0.0809436i \(-0.0257934\pi\)
−0.568459 + 0.822712i \(0.692460\pi\)
\(942\) −718.628 192.556i −0.762875 0.204412i
\(943\) −1688.89 + 452.538i −1.79098 + 0.479892i
\(944\) 213.145i 0.225789i
\(945\) −546.438 + 601.810i −0.578241 + 0.636836i
\(946\) 114.014 0.120522
\(947\) −34.4640 128.621i −0.0363928 0.135820i 0.945339 0.326089i \(-0.105731\pi\)
−0.981732 + 0.190269i \(0.939064\pi\)
\(948\) 250.300 934.131i 0.264029 0.985370i
\(949\) −112.832 + 65.1437i −0.118896 + 0.0686446i
\(950\) −227.913 144.235i −0.239909 0.151826i
\(951\) 806.683 0.848247
\(952\) 142.319 2277.76i 0.149495 2.39260i
\(953\) 25.9574 + 25.9574i 0.0272376 + 0.0272376i 0.720594 0.693357i \(-0.243869\pi\)
−0.693357 + 0.720594i \(0.743869\pi\)
\(954\) 163.727 + 94.5277i 0.171621 + 0.0990856i
\(955\) 60.8958 + 548.415i 0.0637652 + 0.574257i
\(956\) 276.723 + 479.298i 0.289459 + 0.501358i
\(957\) −5.06112 18.8883i −0.00528852 0.0197370i
\(958\) −1678.69 1678.69i −1.75228 1.75228i
\(959\) −999.158 1132.34i −1.04187 1.18075i
\(960\) 303.695 118.626i 0.316349 0.123569i
\(961\) −7.63849 + 13.2303i −0.00794848 + 0.0137672i
\(962\) −477.254 127.880i −0.496106 0.132931i
\(963\) −82.8400 + 309.163i −0.0860228 + 0.321042i
\(964\) 1694.82 + 978.507i 1.75812 + 1.01505i
\(965\) 651.869 + 1668.85i 0.675512 + 1.72937i
\(966\) 1051.11 + 353.232i 1.08810 + 0.365665i
\(967\) −478.254 + 478.254i −0.494575 + 0.494575i −0.909744 0.415169i \(-0.863722\pi\)
0.415169 + 0.909744i \(0.363722\pi\)
\(968\) −2320.68 + 621.824i −2.39740 + 0.642380i
\(969\) 60.5340 34.9493i 0.0624706 0.0360674i
\(970\) 1335.65 148.311i 1.37696 0.152897i
\(971\) 103.956 180.057i 0.107061 0.185435i −0.807517 0.589844i \(-0.799189\pi\)
0.914578 + 0.404409i \(0.132523\pi\)
\(972\) −1671.41 + 1671.41i −1.71955 + 1.71955i
\(973\) 655.982 988.255i 0.674185 1.01568i
\(974\) 1903.98i 1.95480i
\(975\) −28.2221 125.514i −0.0289457 0.128733i
\(976\) −0.294440 0.509986i −0.000301681 0.000522526i
\(977\) −430.304 115.300i −0.440434 0.118014i 0.0317858 0.999495i \(-0.489881\pi\)
−0.472220 + 0.881481i \(0.656547\pi\)
\(978\) 56.1142 15.0357i 0.0573764 0.0153740i
\(979\) 70.6795i 0.0721956i
\(980\) −2320.40 32.9882i −2.36776 0.0336614i
\(981\) −230.668 −0.235135
\(982\) 135.259 + 504.794i 0.137739 + 0.514047i
\(983\) 35.3591 131.962i 0.0359706 0.134244i −0.945606 0.325315i \(-0.894529\pi\)
0.981576 + 0.191071i \(0.0611962\pi\)
\(984\) −1512.24 + 873.093i −1.53683 + 0.887289i
\(985\) −96.5903 + 633.894i −0.0980612 + 0.643548i
\(986\) 677.481 0.687101
\(987\) 587.181 + 389.757i 0.594915 + 0.394891i
\(988\) 69.1552 + 69.1552i 0.0699952 + 0.0699952i
\(989\) −675.114 389.777i −0.682623 0.394112i
\(990\) 92.2524 115.299i 0.0931842 0.116463i
\(991\) 160.541 + 278.066i 0.161999 + 0.280591i 0.935586 0.353100i \(-0.114872\pi\)
−0.773586 + 0.633691i \(0.781539\pi\)
\(992\) 413.850 + 1544.51i 0.417188 + 1.55697i
\(993\) 644.943 + 644.943i 0.649490 + 0.649490i
\(994\) −128.685 + 382.927i −0.129462 + 0.385238i
\(995\) 649.194 1481.44i 0.652456 1.48889i
\(996\) 620.059 1073.97i 0.622550 1.07829i
\(997\) −34.8501 9.33806i −0.0349550 0.00936616i 0.241299 0.970451i \(-0.422426\pi\)
−0.276254 + 0.961085i \(0.589093\pi\)
\(998\) −929.305 + 3468.21i −0.931167 + 3.47516i
\(999\) 770.786 + 445.013i 0.771557 + 0.445459i
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 35.3.l.a.23.6 yes 24
3.2 odd 2 315.3.ca.a.163.1 24
5.2 odd 4 inner 35.3.l.a.2.1 24
5.3 odd 4 175.3.p.c.107.6 24
5.4 even 2 175.3.p.c.93.1 24
7.2 even 3 245.3.g.c.148.6 12
7.3 odd 6 245.3.m.b.18.1 24
7.4 even 3 inner 35.3.l.a.18.1 yes 24
7.5 odd 6 245.3.g.b.148.6 12
7.6 odd 2 245.3.m.b.128.6 24
15.2 even 4 315.3.ca.a.37.6 24
21.11 odd 6 315.3.ca.a.298.6 24
35.2 odd 12 245.3.g.c.197.6 12
35.4 even 6 175.3.p.c.18.6 24
35.12 even 12 245.3.g.b.197.6 12
35.17 even 12 245.3.m.b.67.6 24
35.18 odd 12 175.3.p.c.32.1 24
35.27 even 4 245.3.m.b.177.1 24
35.32 odd 12 inner 35.3.l.a.32.6 yes 24
105.32 even 12 315.3.ca.a.172.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.3.l.a.2.1 24 5.2 odd 4 inner
35.3.l.a.18.1 yes 24 7.4 even 3 inner
35.3.l.a.23.6 yes 24 1.1 even 1 trivial
35.3.l.a.32.6 yes 24 35.32 odd 12 inner
175.3.p.c.18.6 24 35.4 even 6
175.3.p.c.32.1 24 35.18 odd 12
175.3.p.c.93.1 24 5.4 even 2
175.3.p.c.107.6 24 5.3 odd 4
245.3.g.b.148.6 12 7.5 odd 6
245.3.g.b.197.6 12 35.12 even 12
245.3.g.c.148.6 12 7.2 even 3
245.3.g.c.197.6 12 35.2 odd 12
245.3.m.b.18.1 24 7.3 odd 6
245.3.m.b.67.6 24 35.17 even 12
245.3.m.b.128.6 24 7.6 odd 2
245.3.m.b.177.1 24 35.27 even 4
315.3.ca.a.37.6 24 15.2 even 4
315.3.ca.a.163.1 24 3.2 odd 2
315.3.ca.a.172.1 24 105.32 even 12
315.3.ca.a.298.6 24 21.11 odd 6