Properties

Label 75.2.g.b.61.1
Level $75$
Weight $2$
Character 75.61
Analytic conductor $0.599$
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] = [75,2,Mod(16,75)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(75, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.16");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 75.g (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: \(0.598878015160\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.26265625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 61.1
Root \(1.33631 - 0.462894i\) of defining polynomial
Character \(\chi\) \(=\) 75.61
Dual form 75.2.g.b.16.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.18949 + 1.59076i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.64533 - 5.06380i) q^{4} +(0.336312 - 2.21063i) q^{5} +(0.836312 + 2.57390i) q^{6} +0.470294 q^{7} +(2.78023 + 8.55667i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(-2.18949 + 1.59076i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.64533 - 5.06380i) q^{4} +(0.336312 - 2.21063i) q^{5} +(0.836312 + 2.57390i) q^{6} +0.470294 q^{7} +(2.78023 + 8.55667i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(2.78023 + 5.37515i) q^{10} +(2.57387 - 1.87003i) q^{11} +(-4.30753 - 3.12960i) q^{12} +(-0.455836 - 0.331184i) q^{13} +(-1.02971 + 0.748125i) q^{14} +(-1.99851 - 1.00297i) q^{15} +(-11.0839 - 8.05289i) q^{16} +(-0.527295 - 1.62285i) q^{17} +2.70636 q^{18} +(1.15575 + 3.55705i) q^{19} +(-10.6409 - 5.34023i) q^{20} +(0.145329 - 0.447276i) q^{21} +(-2.66071 + 8.18882i) q^{22} +(1.83631 - 1.33416i) q^{23} +8.99702 q^{24} +(-4.77379 - 1.48692i) q^{25} +1.52488 q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.773789 - 2.38148i) q^{28} +(-2.57238 + 7.91697i) q^{29} +(5.97122 - 0.983144i) q^{30} +(1.67999 + 5.17047i) q^{31} +19.0842 q^{32} +(-0.983131 - 3.02577i) q^{33} +(3.73607 + 2.71441i) q^{34} +(0.158166 - 1.03965i) q^{35} +(-4.30753 + 3.12960i) q^{36} +(-0.825886 - 0.600041i) q^{37} +(-8.18892 - 5.94960i) q^{38} +(-0.455836 + 0.331184i) q^{39} +(19.8507 - 3.26836i) q^{40} +(-1.19098 - 0.865300i) q^{41} +(0.393313 + 1.21049i) q^{42} +6.72721 q^{43} +(-5.23458 - 16.1104i) q^{44} +(-1.57146 + 1.59076i) q^{45} +(-1.89827 + 5.84226i) q^{46} +(-1.37005 + 4.21658i) q^{47} +(-11.0839 + 8.05289i) q^{48} -6.77882 q^{49} +(12.8175 - 4.33834i) q^{50} -1.70636 q^{51} +(-2.42705 + 1.76336i) q^{52} +(-2.17907 + 6.70648i) q^{53} +(0.836312 - 2.57390i) q^{54} +(-3.26832 - 6.31879i) q^{55} +(1.30753 + 4.02415i) q^{56} +3.74010 q^{57} +(-6.96179 - 21.4262i) q^{58} +(10.4136 + 7.56596i) q^{59} +(-8.36707 + 8.46984i) q^{60} +(-0.102655 + 0.0745831i) q^{61} +(-11.9033 - 8.64825i) q^{62} +(-0.380476 - 0.276432i) q^{63} +(-19.6170 + 14.2526i) q^{64} +(-0.885429 + 0.896304i) q^{65} +(6.96582 + 5.06097i) q^{66} +(-0.863607 - 2.65791i) q^{67} -9.08535 q^{68} +(-0.701409 - 2.15871i) q^{69} +(1.30753 + 2.52790i) q^{70} +(4.95838 - 15.2603i) q^{71} +(2.78023 - 8.55667i) q^{72} +(7.91925 - 5.75367i) q^{73} +2.76279 q^{74} +(-2.88933 + 4.08066i) q^{75} +19.9138 q^{76} +(1.21048 - 0.879462i) q^{77} +(0.471215 - 1.45025i) q^{78} +(-1.46937 + 4.52227i) q^{79} +(-21.5296 + 21.7940i) q^{80} +(0.309017 + 0.951057i) q^{81} +3.98413 q^{82} +(3.61256 + 11.1183i) q^{83} +(-2.02580 - 1.47183i) q^{84} +(-3.76485 + 0.619872i) q^{85} +(-14.7292 + 10.7014i) q^{86} +(6.73458 + 4.89296i) q^{87} +(23.1572 + 16.8247i) q^{88} +(5.01630 - 3.64456i) q^{89} +(0.910182 - 5.98277i) q^{90} +(-0.214377 - 0.155754i) q^{91} +(-3.73458 - 11.4938i) q^{92} +5.43656 q^{93} +(-3.70785 - 11.4116i) q^{94} +(8.25202 - 1.35867i) q^{95} +(5.89735 - 18.1502i) q^{96} +(2.61256 - 8.04064i) q^{97} +(14.8422 - 10.7835i) q^{98} -3.18148 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - q^{2} - 2 q^{3} + q^{4} - 5 q^{5} - q^{6} + 4 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - q^{2} - 2 q^{3} + q^{4} - 5 q^{5} - q^{6} + 4 q^{7} - 2 q^{9} + 16 q^{11} - 9 q^{12} - 8 q^{13} - 8 q^{14} + 5 q^{15} - 17 q^{16} - q^{17} + 4 q^{18} - 5 q^{19} - 10 q^{20} - 11 q^{21} + 13 q^{22} + 7 q^{23} + 30 q^{24} - 15 q^{25} + 6 q^{26} - 2 q^{27} - 17 q^{28} + 5 q^{29} + 30 q^{30} - 19 q^{31} + 24 q^{32} - 9 q^{33} + 12 q^{34} - 10 q^{35} - 9 q^{36} - q^{37} - 10 q^{38} - 8 q^{39} + 25 q^{40} - 14 q^{41} - 8 q^{42} + 32 q^{43} - 3 q^{44} - 5 q^{45} + 16 q^{46} - q^{47} - 17 q^{48} + 16 q^{49} + 10 q^{50} + 4 q^{51} - 6 q^{52} - 3 q^{53} - q^{54} + 15 q^{55} - 15 q^{56} + 10 q^{57} + 5 q^{58} + 30 q^{59} - 15 q^{60} - 14 q^{61} - 17 q^{62} + 9 q^{63} - 44 q^{64} + 25 q^{65} - 7 q^{66} + 4 q^{67} - 22 q^{68} - 8 q^{69} - 15 q^{70} + 21 q^{71} + 2 q^{73} - 38 q^{74} - 15 q^{75} + 80 q^{76} - 37 q^{77} - 14 q^{78} - 30 q^{79} - 50 q^{80} - 2 q^{81} - 12 q^{82} + 2 q^{83} + 8 q^{84} - 30 q^{85} - 34 q^{86} + 15 q^{87} + 70 q^{88} - 5 q^{90} + 21 q^{91} + 9 q^{92} + 46 q^{93} - 33 q^{94} + 65 q^{95} + 34 q^{96} - 6 q^{97} + 73 q^{98} - 14 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

\(n\) \(26\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.18949 + 1.59076i −1.54821 + 1.12484i −0.603290 + 0.797522i \(0.706144\pi\)
−0.944915 + 0.327315i \(0.893856\pi\)
\(3\) 0.309017 0.951057i 0.178411 0.549093i
\(4\) 1.64533 5.06380i 0.822664 2.53190i
\(5\) 0.336312 2.21063i 0.150403 0.988625i
\(6\) 0.836312 + 2.57390i 0.341423 + 1.05079i
\(7\) 0.470294 0.177754 0.0888772 0.996043i \(-0.471672\pi\)
0.0888772 + 0.996043i \(0.471672\pi\)
\(8\) 2.78023 + 8.55667i 0.982960 + 3.02524i
\(9\) −0.809017 0.587785i −0.269672 0.195928i
\(10\) 2.78023 + 5.37515i 0.879187 + 1.69977i
\(11\) 2.57387 1.87003i 0.776051 0.563834i −0.127740 0.991808i \(-0.540772\pi\)
0.903791 + 0.427974i \(0.140772\pi\)
\(12\) −4.30753 3.12960i −1.24348 0.903438i
\(13\) −0.455836 0.331184i −0.126426 0.0918540i 0.522775 0.852471i \(-0.324897\pi\)
−0.649201 + 0.760617i \(0.724897\pi\)
\(14\) −1.02971 + 0.748125i −0.275200 + 0.199945i
\(15\) −1.99851 1.00297i −0.516013 0.258967i
\(16\) −11.0839 8.05289i −2.77096 2.01322i
\(17\) −0.527295 1.62285i −0.127888 0.393598i 0.866528 0.499128i \(-0.166346\pi\)
−0.994416 + 0.105530i \(0.966346\pi\)
\(18\) 2.70636 0.637896
\(19\) 1.15575 + 3.55705i 0.265148 + 0.816043i 0.991659 + 0.128888i \(0.0411406\pi\)
−0.726511 + 0.687155i \(0.758859\pi\)
\(20\) −10.6409 5.34023i −2.37937 1.19411i
\(21\) 0.145329 0.447276i 0.0317134 0.0976037i
\(22\) −2.66071 + 8.18882i −0.567265 + 1.74586i
\(23\) 1.83631 1.33416i 0.382898 0.278191i −0.379641 0.925134i \(-0.623953\pi\)
0.762539 + 0.646942i \(0.223953\pi\)
\(24\) 8.99702 1.83651
\(25\) −4.77379 1.48692i −0.954758 0.297385i
\(26\) 1.52488 0.299054
\(27\) −0.809017 + 0.587785i −0.155695 + 0.113119i
\(28\) 0.773789 2.38148i 0.146232 0.450057i
\(29\) −2.57238 + 7.91697i −0.477679 + 1.47014i 0.364631 + 0.931152i \(0.381195\pi\)
−0.842310 + 0.538993i \(0.818805\pi\)
\(30\) 5.97122 0.983144i 1.09019 0.179497i
\(31\) 1.67999 + 5.17047i 0.301735 + 0.928644i 0.980876 + 0.194636i \(0.0623526\pi\)
−0.679141 + 0.734008i \(0.737647\pi\)
\(32\) 19.0842 3.37364
\(33\) −0.983131 3.02577i −0.171141 0.526718i
\(34\) 3.73607 + 2.71441i 0.640730 + 0.465518i
\(35\) 0.158166 1.03965i 0.0267349 0.175732i
\(36\) −4.30753 + 3.12960i −0.717921 + 0.521600i
\(37\) −0.825886 0.600041i −0.135775 0.0986462i 0.517825 0.855487i \(-0.326742\pi\)
−0.653600 + 0.756841i \(0.726742\pi\)
\(38\) −8.18892 5.94960i −1.32842 0.965153i
\(39\) −0.455836 + 0.331184i −0.0729922 + 0.0530319i
\(40\) 19.8507 3.26836i 3.13867 0.516773i
\(41\) −1.19098 0.865300i −0.186000 0.135137i 0.490889 0.871222i \(-0.336672\pi\)
−0.676889 + 0.736085i \(0.736672\pi\)
\(42\) 0.393313 + 1.21049i 0.0606895 + 0.186783i
\(43\) 6.72721 1.02589 0.512945 0.858421i \(-0.328554\pi\)
0.512945 + 0.858421i \(0.328554\pi\)
\(44\) −5.23458 16.1104i −0.789142 2.42873i
\(45\) −1.57146 + 1.59076i −0.234259 + 0.237136i
\(46\) −1.89827 + 5.84226i −0.279884 + 0.861395i
\(47\) −1.37005 + 4.21658i −0.199842 + 0.615052i 0.800043 + 0.599942i \(0.204810\pi\)
−0.999886 + 0.0151095i \(0.995190\pi\)
\(48\) −11.0839 + 8.05289i −1.59982 + 1.16234i
\(49\) −6.77882 −0.968403
\(50\) 12.8175 4.33834i 1.81267 0.613534i
\(51\) −1.70636 −0.238938
\(52\) −2.42705 + 1.76336i −0.336571 + 0.244533i
\(53\) −2.17907 + 6.70648i −0.299318 + 0.921206i 0.682419 + 0.730961i \(0.260928\pi\)
−0.981737 + 0.190244i \(0.939072\pi\)
\(54\) 0.836312 2.57390i 0.113808 0.350264i
\(55\) −3.26832 6.31879i −0.440700 0.852026i
\(56\) 1.30753 + 4.02415i 0.174726 + 0.537750i
\(57\) 3.74010 0.495388
\(58\) −6.96179 21.4262i −0.914128 2.81340i
\(59\) 10.4136 + 7.56596i 1.35574 + 0.985004i 0.998703 + 0.0509138i \(0.0162134\pi\)
0.357038 + 0.934090i \(0.383787\pi\)
\(60\) −8.36707 + 8.46984i −1.08018 + 1.09345i
\(61\) −0.102655 + 0.0745831i −0.0131436 + 0.00954939i −0.594338 0.804216i \(-0.702586\pi\)
0.581194 + 0.813765i \(0.302586\pi\)
\(62\) −11.9033 8.64825i −1.51172 1.09833i
\(63\) −0.380476 0.276432i −0.0479355 0.0348272i
\(64\) −19.6170 + 14.2526i −2.45213 + 1.78158i
\(65\) −0.885429 + 0.896304i −0.109824 + 0.111173i
\(66\) 6.96582 + 5.06097i 0.857434 + 0.622962i
\(67\) −0.863607 2.65791i −0.105506 0.324715i 0.884343 0.466838i \(-0.154607\pi\)
−0.989849 + 0.142123i \(0.954607\pi\)
\(68\) −9.08535 −1.10176
\(69\) −0.701409 2.15871i −0.0844397 0.259879i
\(70\) 1.30753 + 2.52790i 0.156279 + 0.302142i
\(71\) 4.95838 15.2603i 0.588451 1.81107i 0.00350617 0.999994i \(-0.498884\pi\)
0.584945 0.811073i \(-0.301116\pi\)
\(72\) 2.78023 8.55667i 0.327653 1.00841i
\(73\) 7.91925 5.75367i 0.926878 0.673416i −0.0183484 0.999832i \(-0.505841\pi\)
0.945226 + 0.326415i \(0.105841\pi\)
\(74\) 2.76279 0.321168
\(75\) −2.88933 + 4.08066i −0.333631 + 0.471194i
\(76\) 19.9138 2.28427
\(77\) 1.21048 0.879462i 0.137947 0.100224i
\(78\) 0.471215 1.45025i 0.0533546 0.164209i
\(79\) −1.46937 + 4.52227i −0.165317 + 0.508795i −0.999060 0.0433593i \(-0.986194\pi\)
0.833742 + 0.552154i \(0.186194\pi\)
\(80\) −21.5296 + 21.7940i −2.40708 + 2.43665i
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) 3.98413 0.439974
\(83\) 3.61256 + 11.1183i 0.396530 + 1.22039i 0.927763 + 0.373169i \(0.121729\pi\)
−0.531233 + 0.847226i \(0.678271\pi\)
\(84\) −2.02580 1.47183i −0.221033 0.160590i
\(85\) −3.76485 + 0.619872i −0.408356 + 0.0672346i
\(86\) −14.7292 + 10.7014i −1.58829 + 1.15396i
\(87\) 6.73458 + 4.89296i 0.722023 + 0.524580i
\(88\) 23.1572 + 16.8247i 2.46856 + 1.79351i
\(89\) 5.01630 3.64456i 0.531727 0.386322i −0.289277 0.957246i \(-0.593415\pi\)
0.821003 + 0.570923i \(0.193415\pi\)
\(90\) 0.910182 5.98277i 0.0959416 0.630639i
\(91\) −0.214377 0.155754i −0.0224728 0.0163275i
\(92\) −3.73458 11.4938i −0.389357 1.19832i
\(93\) 5.43656 0.563745
\(94\) −3.70785 11.4116i −0.382436 1.17702i
\(95\) 8.25202 1.35867i 0.846639 0.139397i
\(96\) 5.89735 18.1502i 0.601895 1.85244i
\(97\) 2.61256 8.04064i 0.265265 0.816403i −0.726367 0.687307i \(-0.758793\pi\)
0.991632 0.129096i \(-0.0412074\pi\)
\(98\) 14.8422 10.7835i 1.49929 1.08930i
\(99\) −3.18148 −0.319751
\(100\) −15.3839 + 21.7270i −1.53839 + 2.17270i
\(101\) −5.83325 −0.580430 −0.290215 0.956961i \(-0.593727\pi\)
−0.290215 + 0.956961i \(0.593727\pi\)
\(102\) 3.73607 2.71441i 0.369926 0.268767i
\(103\) −4.35077 + 13.3903i −0.428694 + 1.31938i 0.470718 + 0.882284i \(0.343995\pi\)
−0.899412 + 0.437101i \(0.856005\pi\)
\(104\) 1.56651 4.82121i 0.153609 0.472758i
\(105\) −0.939888 0.471693i −0.0917236 0.0460325i
\(106\) −5.89735 18.1502i −0.572801 1.76290i
\(107\) −8.61207 −0.832561 −0.416280 0.909236i \(-0.636666\pi\)
−0.416280 + 0.909236i \(0.636666\pi\)
\(108\) 1.64533 + 5.06380i 0.158322 + 0.487265i
\(109\) −13.5005 9.80868i −1.29311 0.939501i −0.293249 0.956036i \(-0.594736\pi\)
−0.999863 + 0.0165355i \(0.994736\pi\)
\(110\) 17.2076 + 8.63584i 1.64068 + 0.823395i
\(111\) −0.825886 + 0.600041i −0.0783896 + 0.0569534i
\(112\) −5.21267 3.78723i −0.492551 0.357860i
\(113\) −9.52686 6.92167i −0.896211 0.651136i 0.0412787 0.999148i \(-0.486857\pi\)
−0.937490 + 0.348012i \(0.886857\pi\)
\(114\) −8.18892 + 5.94960i −0.766963 + 0.557231i
\(115\) −2.33176 4.50810i −0.217438 0.420383i
\(116\) 35.8576 + 26.0520i 3.32929 + 2.41887i
\(117\) 0.174114 + 0.535867i 0.0160968 + 0.0495409i
\(118\) −34.8362 −3.20693
\(119\) −0.247984 0.763215i −0.0227326 0.0699638i
\(120\) 3.02580 19.8891i 0.276217 1.81562i
\(121\) −0.271378 + 0.835215i −0.0246707 + 0.0759286i
\(122\) 0.106118 0.326598i 0.00960749 0.0295688i
\(123\) −1.19098 + 0.865300i −0.107387 + 0.0780215i
\(124\) 28.9464 2.59946
\(125\) −4.89252 + 10.0530i −0.437601 + 0.899169i
\(126\) 1.27279 0.113389
\(127\) −1.43910 + 1.04557i −0.127699 + 0.0927790i −0.649801 0.760104i \(-0.725148\pi\)
0.522102 + 0.852883i \(0.325148\pi\)
\(128\) 8.48418 26.1116i 0.749903 2.30796i
\(129\) 2.07882 6.39796i 0.183030 0.563309i
\(130\) 0.512837 3.37096i 0.0449787 0.295653i
\(131\) −1.82895 5.62892i −0.159796 0.491801i 0.838819 0.544410i \(-0.183246\pi\)
−0.998615 + 0.0526087i \(0.983246\pi\)
\(132\) −16.9395 −1.47439
\(133\) 0.543545 + 1.67286i 0.0471313 + 0.145055i
\(134\) 6.11895 + 4.44568i 0.528597 + 0.384048i
\(135\) 1.02729 + 1.98612i 0.0884155 + 0.170938i
\(136\) 12.4202 9.02378i 1.06502 0.773783i
\(137\) 4.13902 + 3.00717i 0.353620 + 0.256920i 0.750386 0.661000i \(-0.229868\pi\)
−0.396766 + 0.917920i \(0.629868\pi\)
\(138\) 4.96973 + 3.61072i 0.423051 + 0.307365i
\(139\) 6.66482 4.84228i 0.565303 0.410717i −0.268093 0.963393i \(-0.586393\pi\)
0.833396 + 0.552676i \(0.186393\pi\)
\(140\) −5.00433 2.51148i −0.422943 0.212259i
\(141\) 3.58684 + 2.60599i 0.302066 + 0.219464i
\(142\) 13.4192 + 41.3000i 1.12611 + 3.46581i
\(143\) −1.79259 −0.149904
\(144\) 4.23366 + 13.0299i 0.352805 + 1.08582i
\(145\) 16.6364 + 8.34916i 1.38158 + 0.693360i
\(146\) −8.18643 + 25.1952i −0.677514 + 2.08517i
\(147\) −2.09477 + 6.44704i −0.172774 + 0.531743i
\(148\) −4.39735 + 3.19486i −0.361460 + 0.262616i
\(149\) −10.0585 −0.824027 −0.412014 0.911178i \(-0.635174\pi\)
−0.412014 + 0.911178i \(0.635174\pi\)
\(150\) −0.165178 13.5308i −0.0134867 1.10479i
\(151\) −11.9810 −0.974999 −0.487500 0.873123i \(-0.662091\pi\)
−0.487500 + 0.873123i \(0.662091\pi\)
\(152\) −27.2232 + 19.7788i −2.20810 + 1.60428i
\(153\) −0.527295 + 1.62285i −0.0426293 + 0.131199i
\(154\) −1.25132 + 3.85115i −0.100834 + 0.310335i
\(155\) 11.9950 1.97494i 0.963462 0.158631i
\(156\) 0.927051 + 2.85317i 0.0742235 + 0.228436i
\(157\) 19.5960 1.56393 0.781967 0.623319i \(-0.214216\pi\)
0.781967 + 0.623319i \(0.214216\pi\)
\(158\) −3.97666 12.2389i −0.316366 0.973674i
\(159\) 5.70487 + 4.14483i 0.452426 + 0.328707i
\(160\) 6.41825 42.1882i 0.507407 3.33527i
\(161\) 0.863607 0.627447i 0.0680618 0.0494498i
\(162\) −2.18949 1.59076i −0.172023 0.124982i
\(163\) −9.62137 6.99033i −0.753604 0.547525i 0.143338 0.989674i \(-0.454216\pi\)
−0.896942 + 0.442149i \(0.854216\pi\)
\(164\) −6.34127 + 4.60720i −0.495170 + 0.359762i
\(165\) −7.01949 + 1.15574i −0.546467 + 0.0899742i
\(166\) −25.5963 18.5968i −1.98665 1.44339i
\(167\) −1.85218 5.70042i −0.143326 0.441112i 0.853466 0.521149i \(-0.174496\pi\)
−0.996792 + 0.0800367i \(0.974496\pi\)
\(168\) 4.23125 0.326448
\(169\) −3.91912 12.0618i −0.301471 0.927831i
\(170\) 7.25705 7.34618i 0.556590 0.563426i
\(171\) 1.15575 3.55705i 0.0883828 0.272014i
\(172\) 11.0685 34.0653i 0.843964 2.59745i
\(173\) −14.0157 + 10.1830i −1.06560 + 0.774201i −0.975116 0.221697i \(-0.928840\pi\)
−0.0904807 + 0.995898i \(0.528840\pi\)
\(174\) −22.5288 −1.70791
\(175\) −2.24509 0.699292i −0.169712 0.0528615i
\(176\) −43.5875 −3.28553
\(177\) 10.4136 7.56596i 0.782738 0.568692i
\(178\) −5.18554 + 15.9595i −0.388673 + 1.19621i
\(179\) 3.26832 10.0588i 0.244285 0.751833i −0.751468 0.659770i \(-0.770654\pi\)
0.995753 0.0920634i \(-0.0293462\pi\)
\(180\) 5.46973 + 10.5749i 0.407689 + 0.788205i
\(181\) 3.70198 + 11.3935i 0.275166 + 0.846873i 0.989175 + 0.146738i \(0.0468773\pi\)
−0.714010 + 0.700136i \(0.753123\pi\)
\(182\) 0.717144 0.0531583
\(183\) 0.0392107 + 0.120678i 0.00289854 + 0.00892077i
\(184\) 16.5213 + 12.0035i 1.21797 + 0.884906i
\(185\) −1.60423 + 1.62393i −0.117945 + 0.119394i
\(186\) −11.9033 + 8.64825i −0.872792 + 0.634121i
\(187\) −4.39195 3.19094i −0.321172 0.233345i
\(188\) 19.0977 + 13.8753i 1.39285 + 1.01196i
\(189\) −0.380476 + 0.276432i −0.0276756 + 0.0201075i
\(190\) −15.9064 + 16.1018i −1.15397 + 1.16815i
\(191\) −14.7773 10.7363i −1.06924 0.776852i −0.0934681 0.995622i \(-0.529795\pi\)
−0.975776 + 0.218771i \(0.929795\pi\)
\(192\) 7.49304 + 23.0612i 0.540763 + 1.66430i
\(193\) 25.2063 1.81439 0.907194 0.420713i \(-0.138220\pi\)
0.907194 + 0.420713i \(0.138220\pi\)
\(194\) 7.07054 + 21.7609i 0.507635 + 1.56234i
\(195\) 0.578823 + 1.11907i 0.0414504 + 0.0801380i
\(196\) −11.1534 + 34.3266i −0.796671 + 2.45190i
\(197\) 3.73672 11.5004i 0.266230 0.819372i −0.725177 0.688562i \(-0.758242\pi\)
0.991407 0.130810i \(-0.0417578\pi\)
\(198\) 6.96582 5.06097i 0.495040 0.359667i
\(199\) −0.544434 −0.0385939 −0.0192970 0.999814i \(-0.506143\pi\)
−0.0192970 + 0.999814i \(0.506143\pi\)
\(200\) −0.549118 44.9817i −0.0388285 3.18069i
\(201\) −2.79469 −0.197122
\(202\) 12.7719 9.27930i 0.898625 0.652889i
\(203\) −1.20978 + 3.72331i −0.0849096 + 0.261325i
\(204\) −2.80753 + 8.64068i −0.196566 + 0.604969i
\(205\) −2.31340 + 2.34181i −0.161575 + 0.163559i
\(206\) −11.7748 36.2390i −0.820386 2.52489i
\(207\) −2.26981 −0.157762
\(208\) 2.38543 + 7.34160i 0.165400 + 0.509048i
\(209\) 9.62653 + 6.99409i 0.665881 + 0.483791i
\(210\) 2.80823 0.462367i 0.193786 0.0319063i
\(211\) 2.52580 1.83510i 0.173884 0.126334i −0.497439 0.867499i \(-0.665726\pi\)
0.671323 + 0.741165i \(0.265726\pi\)
\(212\) 30.3750 + 22.0687i 2.08616 + 1.51569i
\(213\) −12.9812 9.43140i −0.889457 0.646229i
\(214\) 18.8561 13.6997i 1.28897 0.936495i
\(215\) 2.26244 14.8714i 0.154297 1.01422i
\(216\) −7.27874 5.28832i −0.495256 0.359824i
\(217\) 0.790089 + 2.43164i 0.0536347 + 0.165071i
\(218\) 45.1625 3.05879
\(219\) −3.02488 9.30964i −0.204403 0.629087i
\(220\) −37.3746 + 6.15362i −2.51979 + 0.414877i
\(221\) −0.297101 + 0.914384i −0.0199852 + 0.0615081i
\(222\) 0.853750 2.62757i 0.0573000 0.176351i
\(223\) −0.274358 + 0.199333i −0.0183724 + 0.0133483i −0.596934 0.802291i \(-0.703614\pi\)
0.578561 + 0.815639i \(0.303614\pi\)
\(224\) 8.97519 0.599680
\(225\) 2.98808 + 4.00891i 0.199206 + 0.267261i
\(226\) 31.8697 2.11994
\(227\) 1.44690 1.05123i 0.0960341 0.0697729i −0.538732 0.842477i \(-0.681096\pi\)
0.634766 + 0.772704i \(0.281096\pi\)
\(228\) 6.15370 18.9391i 0.407538 1.25427i
\(229\) −8.64730 + 26.6137i −0.571430 + 1.75868i 0.0765965 + 0.997062i \(0.475595\pi\)
−0.648026 + 0.761618i \(0.724405\pi\)
\(230\) 12.2767 + 6.16119i 0.809500 + 0.406257i
\(231\) −0.462361 1.42300i −0.0304211 0.0936265i
\(232\) −74.8948 −4.91708
\(233\) −2.09328 6.44246i −0.137135 0.422059i 0.858781 0.512343i \(-0.171223\pi\)
−0.995916 + 0.0902840i \(0.971223\pi\)
\(234\) −1.23366 0.896304i −0.0806467 0.0585932i
\(235\) 8.86055 + 4.44676i 0.577998 + 0.290075i
\(236\) 55.4464 40.2841i 3.60925 2.62227i
\(237\) 3.84687 + 2.79491i 0.249881 + 0.181549i
\(238\) 1.75705 + 1.27657i 0.113893 + 0.0827479i
\(239\) 5.24514 3.81081i 0.339280 0.246501i −0.405078 0.914282i \(-0.632756\pi\)
0.744358 + 0.667781i \(0.232756\pi\)
\(240\) 14.0744 + 27.2106i 0.908496 + 1.75644i
\(241\) 6.02602 + 4.37816i 0.388170 + 0.282022i 0.764705 0.644380i \(-0.222885\pi\)
−0.376535 + 0.926402i \(0.622885\pi\)
\(242\) −0.734446 2.26039i −0.0472120 0.145304i
\(243\) 1.00000 0.0641500
\(244\) 0.208773 + 0.642537i 0.0133653 + 0.0411342i
\(245\) −2.27980 + 14.9855i −0.145651 + 0.957387i
\(246\) 1.23116 3.78914i 0.0784962 0.241586i
\(247\) 0.651203 2.00420i 0.0414351 0.127524i
\(248\) −39.5713 + 28.7502i −2.51278 + 1.82564i
\(249\) 11.6905 0.740855
\(250\) −5.27979 29.7938i −0.333924 1.88433i
\(251\) −4.60217 −0.290486 −0.145243 0.989396i \(-0.546396\pi\)
−0.145243 + 0.989396i \(0.546396\pi\)
\(252\) −2.02580 + 1.47183i −0.127614 + 0.0927168i
\(253\) 2.23152 6.86790i 0.140294 0.431781i
\(254\) 1.48765 4.57852i 0.0933435 0.287282i
\(255\) −0.573870 + 3.77214i −0.0359371 + 0.236221i
\(256\) 7.97520 + 24.5451i 0.498450 + 1.53407i
\(257\) −5.79485 −0.361473 −0.180736 0.983532i \(-0.557848\pi\)
−0.180736 + 0.983532i \(0.557848\pi\)
\(258\) 5.62605 + 17.3152i 0.350262 + 1.07800i
\(259\) −0.388409 0.282196i −0.0241346 0.0175348i
\(260\) 3.08188 + 5.95835i 0.191130 + 0.369521i
\(261\) 6.73458 4.89296i 0.416860 0.302866i
\(262\) 12.9587 + 9.41507i 0.800593 + 0.581665i
\(263\) −11.5680 8.40467i −0.713316 0.518254i 0.170926 0.985284i \(-0.445324\pi\)
−0.884242 + 0.467030i \(0.845324\pi\)
\(264\) 23.1572 16.8247i 1.42522 1.03549i
\(265\) 14.0927 + 7.07258i 0.865708 + 0.434465i
\(266\) −3.85120 2.79806i −0.236132 0.171560i
\(267\) −1.91606 5.89701i −0.117261 0.360891i
\(268\) −14.8800 −0.908943
\(269\) −5.93945 18.2797i −0.362135 1.11454i −0.951756 0.306856i \(-0.900723\pi\)
0.589621 0.807680i \(-0.299277\pi\)
\(270\) −5.40869 2.71441i −0.329162 0.165194i
\(271\) −7.18256 + 22.1057i −0.436310 + 1.34282i 0.455429 + 0.890272i \(0.349486\pi\)
−0.891739 + 0.452551i \(0.850514\pi\)
\(272\) −7.22415 + 22.2337i −0.438029 + 1.34811i
\(273\) −0.214377 + 0.155754i −0.0129747 + 0.00942666i
\(274\) −13.8460 −0.836470
\(275\) −15.0677 + 5.09996i −0.908616 + 0.307539i
\(276\) −12.0853 −0.727452
\(277\) −17.7102 + 12.8672i −1.06410 + 0.773115i −0.974843 0.222894i \(-0.928450\pi\)
−0.0892586 + 0.996008i \(0.528450\pi\)
\(278\) −6.88968 + 21.2043i −0.413216 + 1.27175i
\(279\) 1.67999 5.17047i 0.100578 0.309548i
\(280\) 9.33566 1.53709i 0.557912 0.0918587i
\(281\) 8.37863 + 25.7868i 0.499827 + 1.53831i 0.809296 + 0.587401i \(0.199849\pi\)
−0.309469 + 0.950910i \(0.600151\pi\)
\(282\) −11.9989 −0.714522
\(283\) 5.03926 + 15.5093i 0.299553 + 0.921929i 0.981654 + 0.190671i \(0.0610664\pi\)
−0.682101 + 0.731258i \(0.738934\pi\)
\(284\) −69.1171 50.2165i −4.10134 2.97980i
\(285\) 1.25784 8.26799i 0.0745080 0.489753i
\(286\) 3.92485 2.85157i 0.232081 0.168617i
\(287\) −0.560112 0.406945i −0.0330624 0.0240212i
\(288\) −15.4395 11.2174i −0.909778 0.660993i
\(289\) 11.3977 8.28091i 0.670453 0.487112i
\(290\) −49.7068 + 8.18408i −2.91888 + 0.480586i
\(291\) −6.83978 4.96939i −0.400955 0.291311i
\(292\) −16.1057 49.5682i −0.942514 2.90076i
\(293\) 5.46407 0.319214 0.159607 0.987181i \(-0.448977\pi\)
0.159607 + 0.987181i \(0.448977\pi\)
\(294\) −5.66921 17.4480i −0.330635 1.01759i
\(295\) 20.2278 20.4762i 1.17771 1.19217i
\(296\) 2.83820 8.73509i 0.164967 0.507717i
\(297\) −0.983131 + 3.02577i −0.0570470 + 0.175573i
\(298\) 22.0231 16.0007i 1.27576 0.926897i
\(299\) −1.27891 −0.0739612
\(300\) 15.9097 + 21.3450i 0.918550 + 1.23236i
\(301\) 3.16377 0.182357
\(302\) 26.2323 19.0589i 1.50950 1.09672i
\(303\) −1.80257 + 5.54775i −0.103555 + 0.318710i
\(304\) 15.8343 48.7330i 0.908160 2.79503i
\(305\) 0.130352 + 0.252015i 0.00746392 + 0.0144304i
\(306\) −1.42705 4.39201i −0.0815791 0.251075i
\(307\) −21.4194 −1.22247 −0.611235 0.791450i \(-0.709327\pi\)
−0.611235 + 0.791450i \(0.709327\pi\)
\(308\) −2.46179 7.57662i −0.140274 0.431718i
\(309\) 11.3905 + 8.27566i 0.647981 + 0.470786i
\(310\) −23.1213 + 23.4053i −1.31320 + 1.32933i
\(311\) 2.30731 1.67636i 0.130836 0.0950578i −0.520443 0.853897i \(-0.674233\pi\)
0.651278 + 0.758839i \(0.274233\pi\)
\(312\) −4.10116 2.97967i −0.232183 0.168691i
\(313\) −11.6802 8.48616i −0.660204 0.479666i 0.206528 0.978441i \(-0.433784\pi\)
−0.866732 + 0.498774i \(0.833784\pi\)
\(314\) −42.9054 + 31.1726i −2.42129 + 1.75917i
\(315\) −0.739048 + 0.748125i −0.0416406 + 0.0421521i
\(316\) 20.4823 + 14.8812i 1.15222 + 0.837135i
\(317\) 6.98695 + 21.5036i 0.392426 + 1.20776i 0.930948 + 0.365152i \(0.118983\pi\)
−0.538522 + 0.842611i \(0.681017\pi\)
\(318\) −19.0842 −1.07019
\(319\) 8.18397 + 25.1877i 0.458214 + 1.41024i
\(320\) 24.9098 + 48.1594i 1.39250 + 2.69219i
\(321\) −2.66128 + 8.19057i −0.148538 + 0.457153i
\(322\) −0.892743 + 2.74758i −0.0497506 + 0.153117i
\(323\) 5.16312 3.75123i 0.287284 0.208724i
\(324\) 5.32440 0.295800
\(325\) 1.68362 + 2.25880i 0.0933904 + 0.125295i
\(326\) 32.1859 1.78261
\(327\) −13.5005 + 9.80868i −0.746578 + 0.542421i
\(328\) 4.09288 12.5966i 0.225991 0.695530i
\(329\) −0.644327 + 1.98303i −0.0355229 + 0.109328i
\(330\) 13.5306 13.6968i 0.744836 0.753985i
\(331\) 1.19480 + 3.67721i 0.0656720 + 0.202118i 0.978508 0.206209i \(-0.0661125\pi\)
−0.912836 + 0.408326i \(0.866113\pi\)
\(332\) 62.2448 3.41613
\(333\) 0.315460 + 0.970887i 0.0172871 + 0.0532043i
\(334\) 13.1233 + 9.53466i 0.718077 + 0.521713i
\(335\) −6.16610 + 1.01523i −0.336890 + 0.0554680i
\(336\) −5.21267 + 3.78723i −0.284375 + 0.206610i
\(337\) −14.1459 10.2776i −0.770576 0.559856i 0.131560 0.991308i \(-0.458001\pi\)
−0.902136 + 0.431452i \(0.858001\pi\)
\(338\) 27.7683 + 20.1749i 1.51040 + 1.09737i
\(339\) −9.52686 + 6.92167i −0.517428 + 0.375933i
\(340\) −3.05551 + 20.0844i −0.165708 + 1.08923i
\(341\) 13.9930 + 10.1665i 0.757763 + 0.550547i
\(342\) 3.12789 + 9.62666i 0.169137 + 0.520550i
\(343\) −6.48010 −0.349893
\(344\) 18.7032 + 57.5626i 1.00841 + 3.10357i
\(345\) −5.00801 + 0.824555i −0.269622 + 0.0443926i
\(346\) 14.4886 44.5913i 0.778912 2.39724i
\(347\) −7.13647 + 21.9638i −0.383106 + 1.17908i 0.554739 + 0.832024i \(0.312818\pi\)
−0.937845 + 0.347055i \(0.887182\pi\)
\(348\) 35.8576 26.0520i 1.92217 1.39654i
\(349\) −9.32650 −0.499236 −0.249618 0.968344i \(-0.580305\pi\)
−0.249618 + 0.968344i \(0.580305\pi\)
\(350\) 6.02800 2.04030i 0.322210 0.109058i
\(351\) 0.563444 0.0300744
\(352\) 49.1203 35.6880i 2.61812 1.90218i
\(353\) 9.87219 30.3835i 0.525444 1.61715i −0.237993 0.971267i \(-0.576490\pi\)
0.763437 0.645883i \(-0.223510\pi\)
\(354\) −10.7650 + 33.1312i −0.572152 + 1.76090i
\(355\) −32.0674 16.0934i −1.70196 0.854148i
\(356\) −10.2018 31.3980i −0.540697 1.66409i
\(357\) −0.802492 −0.0424724
\(358\) 8.84525 + 27.2229i 0.467486 + 1.43877i
\(359\) 7.75810 + 5.63659i 0.409457 + 0.297488i 0.773382 0.633940i \(-0.218564\pi\)
−0.363925 + 0.931428i \(0.618564\pi\)
\(360\) −17.9806 9.02378i −0.947663 0.475595i
\(361\) 4.05451 2.94577i 0.213395 0.155041i
\(362\) −26.2298 19.0571i −1.37861 1.00162i
\(363\) 0.710476 + 0.516191i 0.0372903 + 0.0270930i
\(364\) −1.14143 + 0.829296i −0.0598271 + 0.0434669i
\(365\) −10.0559 19.4416i −0.526351 1.01762i
\(366\) −0.277821 0.201849i −0.0145219 0.0105508i
\(367\) 0.328866 + 1.01215i 0.0171667 + 0.0528336i 0.959273 0.282481i \(-0.0911574\pi\)
−0.942106 + 0.335315i \(0.891157\pi\)
\(368\) −31.0973 −1.62106
\(369\) 0.454915 + 1.40008i 0.0236819 + 0.0728855i
\(370\) 0.929160 6.10752i 0.0483047 0.317515i
\(371\) −1.02480 + 3.15402i −0.0532051 + 0.163748i
\(372\) 8.94492 27.5296i 0.463773 1.42735i
\(373\) 3.33333 2.42181i 0.172593 0.125396i −0.498135 0.867099i \(-0.665982\pi\)
0.670728 + 0.741703i \(0.265982\pi\)
\(374\) 14.6922 0.759714
\(375\) 8.04912 + 7.75962i 0.415655 + 0.400705i
\(376\) −39.8890 −2.05712
\(377\) 3.79456 2.75691i 0.195430 0.141988i
\(378\) 0.393313 1.21049i 0.0202298 0.0622610i
\(379\) 3.20027 9.84942i 0.164387 0.505931i −0.834604 0.550851i \(-0.814303\pi\)
0.998991 + 0.0449201i \(0.0143033\pi\)
\(380\) 6.69724 44.0220i 0.343561 2.25828i
\(381\) 0.549687 + 1.69176i 0.0281613 + 0.0866716i
\(382\) 49.4336 2.52924
\(383\) 0.370619 + 1.14065i 0.0189378 + 0.0582845i 0.960079 0.279730i \(-0.0902448\pi\)
−0.941141 + 0.338014i \(0.890245\pi\)
\(384\) −22.2119 16.1379i −1.13350 0.823533i
\(385\) −1.53707 2.97169i −0.0783363 0.151451i
\(386\) −55.1890 + 40.0971i −2.80904 + 2.04089i
\(387\) −5.44243 3.95416i −0.276654 0.201001i
\(388\) −36.4177 26.4590i −1.84883 1.34325i
\(389\) −10.1971 + 7.40861i −0.517012 + 0.375631i −0.815477 0.578789i \(-0.803525\pi\)
0.298465 + 0.954421i \(0.403525\pi\)
\(390\) −3.04750 1.52942i −0.154316 0.0774452i
\(391\) −3.13341 2.27656i −0.158464 0.115130i
\(392\) −18.8467 58.0042i −0.951902 2.92965i
\(393\) −5.91860 −0.298554
\(394\) 10.1129 + 31.1243i 0.509481 + 1.56802i
\(395\) 9.50290 + 4.76914i 0.478143 + 0.239961i
\(396\) −5.23458 + 16.1104i −0.263047 + 0.809577i
\(397\) −0.405848 + 1.24907i −0.0203689 + 0.0626891i −0.960724 0.277505i \(-0.910493\pi\)
0.940355 + 0.340194i \(0.110493\pi\)
\(398\) 1.19204 0.866064i 0.0597513 0.0434119i
\(399\) 1.75895 0.0880575
\(400\) 40.9380 + 54.9237i 2.04690 + 2.74618i
\(401\) 16.1042 0.804205 0.402102 0.915595i \(-0.368280\pi\)
0.402102 + 0.915595i \(0.368280\pi\)
\(402\) 6.11895 4.44568i 0.305186 0.221730i
\(403\) 0.946580 2.91327i 0.0471525 0.145120i
\(404\) −9.59762 + 29.5384i −0.477499 + 1.46959i
\(405\) 2.20636 0.363271i 0.109635 0.0180511i
\(406\) −3.27409 10.0766i −0.162490 0.500094i
\(407\) −3.24782 −0.160988
\(408\) −4.74408 14.6008i −0.234867 0.722847i
\(409\) −17.1188 12.4375i −0.846471 0.614997i 0.0776999 0.996977i \(-0.475242\pi\)
−0.924171 + 0.381980i \(0.875242\pi\)
\(410\) 1.33991 8.80745i 0.0661735 0.434969i
\(411\) 4.13902 3.00717i 0.204163 0.148333i
\(412\) 60.6473 + 44.0629i 2.98788 + 2.17082i
\(413\) 4.89748 + 3.55823i 0.240989 + 0.175089i
\(414\) 4.96973 3.61072i 0.244249 0.177457i
\(415\) 25.7935 4.24682i 1.26615 0.208468i
\(416\) −8.69927 6.32039i −0.426517 0.309883i
\(417\) −2.54574 7.83497i −0.124665 0.383680i
\(418\) −32.2031 −1.57511
\(419\) −2.06144 6.34445i −0.100708 0.309946i 0.887991 0.459860i \(-0.152100\pi\)
−0.988699 + 0.149914i \(0.952100\pi\)
\(420\) −3.93498 + 3.98331i −0.192008 + 0.194366i
\(421\) 8.43555 25.9620i 0.411124 1.26531i −0.504549 0.863383i \(-0.668341\pi\)
0.915673 0.401925i \(-0.131659\pi\)
\(422\) −2.61102 + 8.03590i −0.127103 + 0.391181i
\(423\) 3.58684 2.60599i 0.174398 0.126708i
\(424\) −63.4435 −3.08109
\(425\) 0.104145 + 8.53118i 0.00505177 + 0.413823i
\(426\) 43.4253 2.10396
\(427\) −0.0482780 + 0.0350760i −0.00233633 + 0.00169745i
\(428\) −14.1697 + 43.6098i −0.684918 + 2.10796i
\(429\) −0.553939 + 1.70485i −0.0267444 + 0.0823109i
\(430\) 18.7032 + 36.1598i 0.901949 + 1.74378i
\(431\) 3.80011 + 11.6955i 0.183045 + 0.563354i 0.999909 0.0134755i \(-0.00428951\pi\)
−0.816864 + 0.576830i \(0.804290\pi\)
\(432\) 13.7004 0.659161
\(433\) −10.4587 32.1887i −0.502614 1.54689i −0.804744 0.593622i \(-0.797698\pi\)
0.302130 0.953267i \(-0.402302\pi\)
\(434\) −5.59805 4.06722i −0.268715 0.195233i
\(435\) 13.0814 13.2421i 0.627207 0.634911i
\(436\) −71.8819 + 52.2253i −3.44252 + 2.50114i
\(437\) 6.86799 + 4.98989i 0.328541 + 0.238699i
\(438\) 21.4324 + 15.5715i 1.02408 + 0.744036i
\(439\) 16.9614 12.3231i 0.809521 0.588152i −0.104171 0.994559i \(-0.533219\pi\)
0.913692 + 0.406408i \(0.133219\pi\)
\(440\) 44.9812 45.5336i 2.14439 2.17073i
\(441\) 5.48418 + 3.98449i 0.261152 + 0.189738i
\(442\) −0.804064 2.47465i −0.0382454 0.117707i
\(443\) 6.04847 0.287371 0.143686 0.989623i \(-0.454105\pi\)
0.143686 + 0.989623i \(0.454105\pi\)
\(444\) 1.67964 + 5.16939i 0.0797120 + 0.245328i
\(445\) −6.36973 12.3149i −0.301954 0.583782i
\(446\) 0.283614 0.872875i 0.0134295 0.0413318i
\(447\) −3.10826 + 9.56624i −0.147016 + 0.452467i
\(448\) −9.22577 + 6.70292i −0.435877 + 0.316683i
\(449\) 15.5896 0.735721 0.367860 0.929881i \(-0.380090\pi\)
0.367860 + 0.929881i \(0.380090\pi\)
\(450\) −12.9196 4.02415i −0.609036 0.189700i
\(451\) −4.68357 −0.220541
\(452\) −50.7248 + 36.8537i −2.38589 + 1.73345i
\(453\) −3.70233 + 11.3946i −0.173951 + 0.535365i
\(454\) −1.49572 + 4.60334i −0.0701974 + 0.216046i
\(455\) −0.416412 + 0.421527i −0.0195217 + 0.0197615i
\(456\) 10.3983 + 32.0028i 0.486947 + 1.49867i
\(457\) −2.50193 −0.117035 −0.0585176 0.998286i \(-0.518637\pi\)
−0.0585176 + 0.998286i \(0.518637\pi\)
\(458\) −23.4027 72.0262i −1.09354 3.36556i
\(459\) 1.38048 + 1.00297i 0.0644351 + 0.0468148i
\(460\) −26.6647 + 4.39026i −1.24325 + 0.204697i
\(461\) 0.124559 0.0904973i 0.00580128 0.00421488i −0.584881 0.811119i \(-0.698859\pi\)
0.590682 + 0.806904i \(0.298859\pi\)
\(462\) 3.27599 + 2.38014i 0.152413 + 0.110734i
\(463\) 9.41102 + 6.83751i 0.437367 + 0.317766i 0.784588 0.620018i \(-0.212875\pi\)
−0.347221 + 0.937783i \(0.612875\pi\)
\(464\) 92.2664 67.0355i 4.28336 3.11204i
\(465\) 1.82838 12.0182i 0.0847890 0.557332i
\(466\) 14.8316 + 10.7758i 0.687062 + 0.499180i
\(467\) 0.145329 + 0.447276i 0.00672502 + 0.0206975i 0.954363 0.298650i \(-0.0965363\pi\)
−0.947638 + 0.319347i \(0.896536\pi\)
\(468\) 3.00000 0.138675
\(469\) −0.406149 1.25000i −0.0187542 0.0577196i
\(470\) −26.4738 + 4.35884i −1.22115 + 0.201058i
\(471\) 6.05551 18.6369i 0.279023 0.858745i
\(472\) −35.7871 + 110.141i −1.64723 + 5.06966i
\(473\) 17.3150 12.5801i 0.796143 0.578432i
\(474\) −12.8687 −0.591080
\(475\) −0.228271 18.6991i −0.0104738 0.857974i
\(476\) −4.27279 −0.195843
\(477\) 5.70487 4.14483i 0.261208 0.189779i
\(478\) −5.42210 + 16.6875i −0.248001 + 0.763269i
\(479\) 3.83534 11.8040i 0.175241 0.539337i −0.824403 0.566003i \(-0.808489\pi\)
0.999644 + 0.0266660i \(0.00848907\pi\)
\(480\) −38.1400 19.1410i −1.74084 0.873662i
\(481\) 0.177744 + 0.547041i 0.00810444 + 0.0249429i
\(482\) −20.1585 −0.918196
\(483\) −0.329868 1.01523i −0.0150095 0.0461946i
\(484\) 3.78286 + 2.74841i 0.171948 + 0.124928i
\(485\) −16.8963 8.47958i −0.767220 0.385038i
\(486\) −2.18949 + 1.59076i −0.0993174 + 0.0721583i
\(487\) −27.9633 20.3165i −1.26714 0.920631i −0.268055 0.963404i \(-0.586381\pi\)
−0.999085 + 0.0427731i \(0.986381\pi\)
\(488\) −0.923588 0.671026i −0.0418088 0.0303759i
\(489\) −9.62137 + 6.99033i −0.435093 + 0.316114i
\(490\) −18.8467 36.4372i −0.851407 1.64607i
\(491\) 20.1168 + 14.6157i 0.907859 + 0.659598i 0.940473 0.339870i \(-0.110383\pi\)
−0.0326134 + 0.999468i \(0.510383\pi\)
\(492\) 2.42215 + 7.45460i 0.109199 + 0.336080i
\(493\) 14.2044 0.639736
\(494\) 1.76239 + 5.42408i 0.0792938 + 0.244041i
\(495\) −1.06997 + 7.03308i −0.0480915 + 0.316113i
\(496\) 23.0165 70.8375i 1.03347 3.18070i
\(497\) 2.33190 7.17684i 0.104600 0.321925i
\(498\) −25.5963 + 18.5968i −1.14700 + 0.833341i
\(499\) 12.6037 0.564220 0.282110 0.959382i \(-0.408966\pi\)
0.282110 + 0.959382i \(0.408966\pi\)
\(500\) 42.8567 + 41.3153i 1.91661 + 1.84768i
\(501\) −5.99378 −0.267782
\(502\) 10.0764 7.32094i 0.449732 0.326750i
\(503\) 9.26827 28.5248i 0.413252 1.27186i −0.500554 0.865705i \(-0.666870\pi\)
0.913805 0.406152i \(-0.133130\pi\)
\(504\) 1.30753 4.02415i 0.0582419 0.179250i
\(505\) −1.96179 + 12.8952i −0.0872986 + 0.573828i
\(506\) 6.03929 + 18.5870i 0.268479 + 0.826294i
\(507\) −12.6825 −0.563251
\(508\) 2.92675 + 9.00761i 0.129854 + 0.399648i
\(509\) 0.377802 + 0.274489i 0.0167458 + 0.0121665i 0.596127 0.802890i \(-0.296706\pi\)
−0.579381 + 0.815057i \(0.696706\pi\)
\(510\) −4.74408 9.17196i −0.210072 0.406141i
\(511\) 3.72438 2.70592i 0.164757 0.119703i
\(512\) −12.0833 8.77902i −0.534011 0.387982i
\(513\) −3.02580 2.19838i −0.133593 0.0970607i
\(514\) 12.6878 9.21822i 0.559634 0.406598i
\(515\) 28.1378 + 14.1213i 1.23990 + 0.622257i
\(516\) −28.9777 21.0535i −1.27567 0.926829i
\(517\) 4.35878 + 13.4150i 0.191699 + 0.589989i
\(518\) 1.29933 0.0570891
\(519\) 5.35353 + 16.4765i 0.234994 + 0.723237i
\(520\) −10.1311 5.08440i −0.444277 0.222966i
\(521\) −5.34039 + 16.4360i −0.233967 + 0.720076i 0.763290 + 0.646056i \(0.223583\pi\)
−0.997257 + 0.0740200i \(0.976417\pi\)
\(522\) −6.96179 + 21.4262i −0.304709 + 0.937799i
\(523\) −32.8849 + 23.8922i −1.43795 + 1.04473i −0.449489 + 0.893286i \(0.648394\pi\)
−0.988465 + 0.151449i \(0.951606\pi\)
\(524\) −31.5130 −1.37665
\(525\) −1.35884 + 1.91911i −0.0593044 + 0.0837568i
\(526\) 38.6980 1.68731
\(527\) 7.50503 5.45273i 0.326924 0.237525i
\(528\) −13.4693 + 41.4542i −0.586175 + 1.80406i
\(529\) −5.51533 + 16.9744i −0.239797 + 0.738019i
\(530\) −42.1067 + 6.93275i −1.82900 + 0.301139i
\(531\) −3.97766 12.2420i −0.172616 0.531256i
\(532\) 9.36533 0.406039
\(533\) 0.256319 + 0.788869i 0.0111024 + 0.0341697i
\(534\) 13.5759 + 9.86349i 0.587488 + 0.426835i
\(535\) −2.89634 + 19.0381i −0.125220 + 0.823090i
\(536\) 20.3418 14.7792i 0.878633 0.638364i
\(537\) −8.55656 6.21671i −0.369243 0.268271i
\(538\) 42.0831 + 30.5751i 1.81433 + 1.31819i
\(539\) −17.4478 + 12.6766i −0.751530 + 0.546019i
\(540\) 11.7475 1.93420i 0.505534 0.0832347i
\(541\) 1.60265 + 1.16440i 0.0689035 + 0.0500613i 0.621704 0.783252i \(-0.286441\pi\)
−0.552800 + 0.833314i \(0.686441\pi\)
\(542\) −19.4386 59.8259i −0.834960 2.56974i
\(543\) 11.9799 0.514105
\(544\) −10.0630 30.9707i −0.431448 1.32786i
\(545\) −26.2237 + 26.5458i −1.12330 + 1.13710i
\(546\) 0.221610 0.682045i 0.00948402 0.0291888i
\(547\) 10.8324 33.3386i 0.463158 1.42545i −0.398126 0.917331i \(-0.630339\pi\)
0.861284 0.508124i \(-0.169661\pi\)
\(548\) 22.0378 16.0114i 0.941407 0.683972i
\(549\) 0.126888 0.00541546
\(550\) 24.8778 35.1354i 1.06079 1.49818i
\(551\) −31.1341 −1.32636
\(552\) 16.5213 12.0035i 0.703195 0.510901i
\(553\) −0.691038 + 2.12680i −0.0293859 + 0.0904405i
\(554\) 18.3077 56.3453i 0.777819 2.39388i
\(555\) 1.04872 + 2.02753i 0.0445155 + 0.0860639i
\(556\) −13.5545 41.7165i −0.574839 1.76917i
\(557\) 19.2383 0.815154 0.407577 0.913171i \(-0.366374\pi\)
0.407577 + 0.913171i \(0.366374\pi\)
\(558\) 4.54666 + 13.9932i 0.192475 + 0.592378i
\(559\) −3.06651 2.22795i −0.129699 0.0942321i
\(560\) −10.1253 + 10.2496i −0.427870 + 0.433125i
\(561\) −4.39195 + 3.19094i −0.185428 + 0.134722i
\(562\) −59.3655 43.1316i −2.50418 1.81940i
\(563\) 23.6023 + 17.1481i 0.994720 + 0.722707i 0.960950 0.276723i \(-0.0892485\pi\)
0.0337705 + 0.999430i \(0.489248\pi\)
\(564\) 19.0977 13.8753i 0.804160 0.584257i
\(565\) −18.5053 + 18.7325i −0.778522 + 0.788084i
\(566\) −35.7049 25.9411i −1.50079 1.09039i
\(567\) 0.145329 + 0.447276i 0.00610324 + 0.0187838i
\(568\) 144.363 6.05734
\(569\) −10.1701 31.3004i −0.426354 1.31218i −0.901692 0.432380i \(-0.857674\pi\)
0.475338 0.879803i \(-0.342326\pi\)
\(570\) 10.3983 + 20.1036i 0.435539 + 0.842048i
\(571\) 8.23065 25.3313i 0.344442 1.06008i −0.617440 0.786618i \(-0.711830\pi\)
0.961882 0.273465i \(-0.0881698\pi\)
\(572\) −2.94939 + 9.07730i −0.123320 + 0.379541i
\(573\) −14.7773 + 10.7363i −0.617329 + 0.448515i
\(574\) 1.87371 0.0782073
\(575\) −10.7500 + 3.63854i −0.448304 + 0.151737i
\(576\) 24.2480 1.01033
\(577\) −27.9237 + 20.2878i −1.16248 + 0.844591i −0.990089 0.140438i \(-0.955149\pi\)
−0.172390 + 0.985029i \(0.555149\pi\)
\(578\) −11.7822 + 36.2620i −0.490076 + 1.50830i
\(579\) 7.78917 23.9726i 0.323707 0.996267i
\(580\) 69.6508 70.5063i 2.89209 2.92761i
\(581\) 1.69897 + 5.22888i 0.0704850 + 0.216931i
\(582\) 22.8807 0.948437
\(583\) 6.93265 + 21.3365i 0.287121 + 0.883668i
\(584\) 71.2496 + 51.7659i 2.94833 + 2.14209i
\(585\) 1.24316 0.204683i 0.0513984 0.00846260i
\(586\) −11.9635 + 8.69202i −0.494209 + 0.359064i
\(587\) 18.0213 + 13.0932i 0.743817 + 0.540414i 0.893904 0.448258i \(-0.147955\pi\)
−0.150087 + 0.988673i \(0.547955\pi\)
\(588\) 29.2000 + 21.2150i 1.20419 + 0.874893i
\(589\) −16.4500 + 11.9516i −0.677809 + 0.492457i
\(590\) −11.7158 + 77.0101i −0.482333 + 3.17045i
\(591\) −9.78286 7.10766i −0.402413 0.292370i
\(592\) 4.32193 + 13.3015i 0.177630 + 0.546690i
\(593\) −30.9158 −1.26956 −0.634779 0.772693i \(-0.718909\pi\)
−0.634779 + 0.772693i \(0.718909\pi\)
\(594\) −2.66071 8.18882i −0.109170 0.335991i
\(595\) −1.77059 + 0.291522i −0.0725870 + 0.0119513i
\(596\) −16.5496 + 50.9344i −0.677898 + 2.08636i
\(597\) −0.168240 + 0.517788i −0.00688558 + 0.0211917i
\(598\) 2.80016 2.03444i 0.114507 0.0831943i
\(599\) −24.0276 −0.981742 −0.490871 0.871232i \(-0.663321\pi\)
−0.490871 + 0.871232i \(0.663321\pi\)
\(600\) −42.9499 13.3779i −1.75342 0.546150i
\(601\) −32.0387 −1.30688 −0.653442 0.756977i \(-0.726676\pi\)
−0.653442 + 0.756977i \(0.726676\pi\)
\(602\) −6.92705 + 5.03280i −0.282326 + 0.205121i
\(603\) −0.863607 + 2.65791i −0.0351688 + 0.108238i
\(604\) −19.7127 + 60.6694i −0.802097 + 2.46860i
\(605\) 1.75508 + 0.880809i 0.0713543 + 0.0358100i
\(606\) −4.87842 15.0142i −0.198172 0.609911i
\(607\) 45.5915 1.85050 0.925251 0.379356i \(-0.123855\pi\)
0.925251 + 0.379356i \(0.123855\pi\)
\(608\) 22.0567 + 67.8834i 0.894516 + 2.75304i
\(609\) 3.16723 + 2.30113i 0.128343 + 0.0932465i
\(610\) −0.686300 0.344427i −0.0277875 0.0139455i
\(611\) 2.02098 1.46833i 0.0817602 0.0594023i
\(612\) 7.35020 + 5.34023i 0.297114 + 0.215866i
\(613\) 8.78299 + 6.38121i 0.354742 + 0.257735i 0.750855 0.660467i \(-0.229641\pi\)
−0.396114 + 0.918201i \(0.629641\pi\)
\(614\) 46.8976 34.0731i 1.89263 1.37508i
\(615\) 1.51232 + 2.92384i 0.0609825 + 0.117900i
\(616\) 10.8907 + 7.91254i 0.438798 + 0.318805i
\(617\) −4.97685 15.3172i −0.200360 0.616646i −0.999872 0.0159954i \(-0.994908\pi\)
0.799512 0.600651i \(-0.205092\pi\)
\(618\) −38.1039 −1.53276
\(619\) 11.8533 + 36.4807i 0.476425 + 1.46628i 0.844026 + 0.536302i \(0.180179\pi\)
−0.367602 + 0.929983i \(0.619821\pi\)
\(620\) 9.73501 63.9898i 0.390967 2.56989i
\(621\) −0.701409 + 2.15871i −0.0281466 + 0.0866262i
\(622\) −2.38516 + 7.34076i −0.0956362 + 0.294338i
\(623\) 2.35914 1.71401i 0.0945168 0.0686705i
\(624\) 7.71941 0.309024
\(625\) 20.5781 + 14.1965i 0.823125 + 0.567861i
\(626\) 39.0732 1.56168
\(627\) 9.62653 6.99409i 0.384447 0.279317i
\(628\) 32.2419 99.2305i 1.28659 3.95973i
\(629\) −0.538290 + 1.65669i −0.0214630 + 0.0660564i
\(630\) 0.428053 2.81366i 0.0170540 0.112099i
\(631\) 7.02370 + 21.6167i 0.279609 + 0.860548i 0.987963 + 0.154690i \(0.0494380\pi\)
−0.708354 + 0.705857i \(0.750562\pi\)
\(632\) −42.7808 −1.70173
\(633\) −0.964772 2.96926i −0.0383462 0.118018i
\(634\) −49.5049 35.9674i −1.96609 1.42845i
\(635\) 1.82738 + 3.53295i 0.0725172 + 0.140201i
\(636\) 30.3750 22.0687i 1.20445 0.875082i
\(637\) 3.09003 + 2.24504i 0.122431 + 0.0889517i
\(638\) −57.9863 42.1295i −2.29570 1.66792i
\(639\) −12.9812 + 9.43140i −0.513528 + 0.373100i
\(640\) −54.8699 27.5371i −2.16892 1.08850i
\(641\) −21.8378 15.8661i −0.862541 0.626673i 0.0660340 0.997817i \(-0.478965\pi\)
−0.928575 + 0.371145i \(0.878965\pi\)
\(642\) −7.20238 22.1666i −0.284255 0.874848i
\(643\) −25.9062 −1.02164 −0.510821 0.859687i \(-0.670659\pi\)
−0.510821 + 0.859687i \(0.670659\pi\)
\(644\) −1.75635 5.40549i −0.0692099 0.213006i
\(645\) −13.4444 6.74722i −0.529373 0.265672i
\(646\) −5.33731 + 16.4266i −0.209994 + 0.646295i
\(647\) −6.69401 + 20.6021i −0.263169 + 0.809950i 0.728941 + 0.684577i \(0.240013\pi\)
−0.992110 + 0.125374i \(0.959987\pi\)
\(648\) −7.27874 + 5.28832i −0.285936 + 0.207745i
\(649\) 40.9519 1.60750
\(650\) −7.27947 2.26739i −0.285524 0.0889342i
\(651\) 2.55678 0.100208
\(652\) −51.2280 + 37.2193i −2.00624 + 1.45762i
\(653\) 3.45405 10.6305i 0.135167 0.416002i −0.860449 0.509537i \(-0.829817\pi\)
0.995616 + 0.0935349i \(0.0298167\pi\)
\(654\) 13.9560 42.9521i 0.545722 1.67956i
\(655\) −13.0586 + 2.15006i −0.510241 + 0.0840097i
\(656\) 6.23252 + 19.1817i 0.243339 + 0.748920i
\(657\) −9.78873 −0.381895
\(658\) −1.74378 5.36681i −0.0679797 0.209220i
\(659\) −10.9010 7.92006i −0.424644 0.308522i 0.354860 0.934919i \(-0.384529\pi\)
−0.779503 + 0.626398i \(0.784529\pi\)
\(660\) −5.69694 + 37.4469i −0.221753 + 1.45762i
\(661\) 18.8195 13.6732i 0.731993 0.531824i −0.158200 0.987407i \(-0.550569\pi\)
0.890193 + 0.455583i \(0.150569\pi\)
\(662\) −8.46556 6.15059i −0.329023 0.239049i
\(663\) 0.777821 + 0.565120i 0.0302081 + 0.0219474i
\(664\) −85.0921 + 61.8230i −3.30221 + 2.39920i
\(665\) 3.88088 0.638975i 0.150494 0.0247784i
\(666\) −2.23515 1.62393i −0.0866102 0.0629260i
\(667\) 5.83880 + 17.9700i 0.226079 + 0.695801i
\(668\) −31.9132 −1.23476
\(669\) 0.104795 + 0.322527i 0.00405162 + 0.0124696i
\(670\) 11.8856 12.0316i 0.459182 0.464822i
\(671\) −0.124748 + 0.383934i −0.00481584 + 0.0148216i
\(672\) 2.77349 8.53592i 0.106990 0.329280i
\(673\) −15.2412 + 11.0734i −0.587507 + 0.426849i −0.841423 0.540378i \(-0.818281\pi\)
0.253916 + 0.967226i \(0.418281\pi\)
\(674\) 47.3215 1.82276
\(675\) 4.73607 1.60302i 0.182291 0.0617001i
\(676\) −67.5268 −2.59719
\(677\) 34.1761 24.8304i 1.31350 0.954310i 0.313507 0.949586i \(-0.398496\pi\)
0.999989 0.00472433i \(-0.00150381\pi\)
\(678\) 9.84828 30.3099i 0.378221 1.16404i
\(679\) 1.22867 3.78147i 0.0471521 0.145119i
\(680\) −15.7712 30.4912i −0.604798 1.16929i
\(681\) −0.552667 1.70093i −0.0211782 0.0651799i
\(682\) −46.8100 −1.79245
\(683\) 15.1264 + 46.5544i 0.578797 + 1.78135i 0.622870 + 0.782325i \(0.285966\pi\)
−0.0440734 + 0.999028i \(0.514034\pi\)
\(684\) −16.1106 11.7050i −0.616004 0.447553i
\(685\) 8.03975 8.13850i 0.307183 0.310956i
\(686\) 14.1881 10.3083i 0.541705 0.393572i
\(687\) 22.6389 + 16.4481i 0.863729 + 0.627536i
\(688\) −74.5635 54.1735i −2.84271 2.06535i
\(689\) 3.21438 2.33538i 0.122458 0.0889710i
\(690\) 9.65334 9.77191i 0.367497 0.372010i
\(691\) 11.4813 + 8.34168i 0.436771 + 0.317332i 0.784350 0.620318i \(-0.212996\pi\)
−0.347580 + 0.937650i \(0.612996\pi\)
\(692\) 28.5043 + 87.7273i 1.08357 + 3.33489i
\(693\) −1.49623 −0.0568371
\(694\) −19.3139 59.4420i −0.733145 2.25639i
\(695\) −8.46303 16.3620i −0.321021 0.620645i
\(696\) −23.1438 + 71.2291i −0.877262 + 2.69993i
\(697\) −0.776250 + 2.38905i −0.0294026 + 0.0904918i
\(698\) 20.4203 14.8362i 0.772920 0.561559i
\(699\) −6.77400 −0.256216
\(700\) −7.23498 + 10.2181i −0.273456 + 0.386208i
\(701\) −9.00786 −0.340222 −0.170111 0.985425i \(-0.554413\pi\)
−0.170111 + 0.985425i \(0.554413\pi\)
\(702\) −1.23366 + 0.896304i −0.0465614 + 0.0338288i
\(703\) 1.17985 3.63122i 0.0444990 0.136954i
\(704\) −23.8389 + 73.3687i −0.898464 + 2.76519i
\(705\) 6.96718 7.05275i 0.262399 0.265622i
\(706\) 26.7177 + 82.2287i 1.00553 + 3.09472i
\(707\) −2.74334 −0.103174
\(708\) −21.1786 65.1811i −0.795942 2.44966i
\(709\) −40.2076 29.2126i −1.51003 1.09710i −0.966164 0.257928i \(-0.916960\pi\)
−0.543865 0.839173i \(-0.683040\pi\)
\(710\) 95.8120 15.7752i 3.59576 0.592032i
\(711\) 3.84687 2.79491i 0.144269 0.104817i
\(712\) 45.1318 + 32.7901i 1.69138 + 1.22886i
\(713\) 9.98321 + 7.25323i 0.373874 + 0.271636i
\(714\) 1.75705 1.27657i 0.0657560 0.0477745i
\(715\) −0.602868 + 3.96275i −0.0225460 + 0.148198i
\(716\) −45.5585 33.1002i −1.70260 1.23701i
\(717\) −2.00346 6.16603i −0.0748207 0.230274i
\(718\) −25.9528 −0.968549
\(719\) −0.660387 2.03246i −0.0246283 0.0757981i 0.937987 0.346671i \(-0.112688\pi\)
−0.962615 + 0.270872i \(0.912688\pi\)
\(720\) 30.2280 4.97696i 1.12653 0.185480i
\(721\) −2.04614 + 6.29738i −0.0762023 + 0.234527i
\(722\) −4.19130 + 12.8995i −0.155984 + 0.480070i
\(723\) 6.02602 4.37816i 0.224110 0.162825i
\(724\) 63.7855 2.37057
\(725\) 24.0519 33.9690i 0.893266 1.26158i
\(726\) −2.37672 −0.0882083
\(727\) 33.5446 24.3716i 1.24410 0.903891i 0.246235 0.969210i \(-0.420807\pi\)
0.997864 + 0.0653195i \(0.0208067\pi\)
\(728\) 0.736718 2.26739i 0.0273046 0.0840349i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) 52.9442 + 26.5706i 1.95955 + 0.983424i
\(731\) −3.54723 10.9172i −0.131199 0.403789i
\(732\) 0.675604 0.0249710
\(733\) 10.0496 + 30.9293i 0.371189 + 1.14240i 0.946014 + 0.324125i \(0.105070\pi\)
−0.574826 + 0.818276i \(0.694930\pi\)
\(734\) −2.33013 1.69294i −0.0860067 0.0624875i
\(735\) 13.5475 + 6.79899i 0.499709 + 0.250784i
\(736\) 35.0446 25.4614i 1.29176 0.938518i
\(737\) −7.19317 5.22614i −0.264964 0.192507i
\(738\) −3.22323 2.34181i −0.118649 0.0862034i
\(739\) 28.5724 20.7591i 1.05105 0.763635i 0.0786411 0.996903i \(-0.474942\pi\)
0.972413 + 0.233268i \(0.0749419\pi\)
\(740\) 5.58378 + 10.7954i 0.205264 + 0.396846i
\(741\) −1.70487 1.23866i −0.0626300 0.0455034i
\(742\) −2.77349 8.53592i −0.101818 0.313363i
\(743\) −36.0897 −1.32400 −0.662001 0.749503i \(-0.730292\pi\)
−0.662001 + 0.749503i \(0.730292\pi\)
\(744\) 15.1149 + 46.5188i 0.554139 + 1.70546i
\(745\) −3.38281 + 22.2357i −0.123936 + 0.814654i
\(746\) −3.44579 + 10.6051i −0.126159 + 0.388279i
\(747\) 3.61256 11.1183i 0.132177 0.406798i
\(748\) −23.3845 + 16.9898i −0.855022 + 0.621210i
\(749\) −4.05021 −0.147991
\(750\) −29.9672 4.18542i −1.09425 0.152830i
\(751\) −4.62810 −0.168882 −0.0844409 0.996428i \(-0.526910\pi\)
−0.0844409 + 0.996428i \(0.526910\pi\)
\(752\) 49.1411 35.7031i 1.79199 1.30196i
\(753\) −1.42215 + 4.37692i −0.0518259 + 0.159504i
\(754\) −3.92258 + 12.0725i −0.142852 + 0.439653i
\(755\) −4.02935 + 26.4856i −0.146643 + 0.963908i
\(756\) 0.773789 + 2.38148i 0.0281424 + 0.0866135i
\(757\) 14.6243 0.531530 0.265765 0.964038i \(-0.414375\pi\)
0.265765 + 0.964038i \(0.414375\pi\)
\(758\) 8.66109 + 26.6561i 0.314585 + 0.968193i
\(759\) −5.84219 4.24460i −0.212058 0.154069i
\(760\) 34.5682 + 66.8324i 1.25392 + 2.42427i
\(761\) −9.86133 + 7.16467i −0.357473 + 0.259719i −0.751997 0.659166i \(-0.770909\pi\)
0.394524 + 0.918885i \(0.370909\pi\)
\(762\) −3.89472 2.82968i −0.141091 0.102509i
\(763\) −6.34920 4.61296i −0.229856 0.167000i
\(764\) −78.6799 + 57.1643i −2.84654 + 2.06813i
\(765\) 3.41018 + 1.71144i 0.123295 + 0.0618772i
\(766\) −2.62597 1.90788i −0.0948801 0.0689344i
\(767\) −2.24119 6.89767i −0.0809246 0.249060i
\(768\) 25.8083 0.931276
\(769\) 4.26323 + 13.1209i 0.153736 + 0.473150i 0.998031 0.0627287i \(-0.0199803\pi\)
−0.844295 + 0.535879i \(0.819980\pi\)
\(770\) 8.09265 + 4.06139i 0.291639 + 0.146362i
\(771\) −1.79071 + 5.51123i −0.0644908 + 0.198482i
\(772\) 41.4726 127.640i 1.49263 4.59385i
\(773\) −18.3274 + 13.3156i −0.659190 + 0.478929i −0.866389 0.499369i \(-0.833565\pi\)
0.207199 + 0.978299i \(0.433565\pi\)
\(774\) 18.2063 0.654411
\(775\) −0.331811 27.1808i −0.0119190 0.976362i
\(776\) 76.0647 2.73056
\(777\) −0.388409 + 0.282196i −0.0139341 + 0.0101237i
\(778\) 10.5411 32.4422i 0.377917 1.16311i
\(779\) 1.70143 5.23646i 0.0609600 0.187616i
\(780\) 6.61909 1.08981i 0.237001 0.0390216i
\(781\) −15.7750 48.5504i −0.564473 1.73727i
\(782\) 10.4820 0.374837
\(783\) −2.57238 7.91697i −0.0919294 0.282929i
\(784\) 75.1355 + 54.5891i 2.68341 + 1.94961i
\(785\) 6.59038 43.3196i 0.235221 1.54614i
\(786\) 12.9587 9.41507i 0.462223 0.335824i
\(787\) 38.5785 + 28.0289i 1.37518 + 0.999123i 0.997313 + 0.0732618i \(0.0233409\pi\)
0.377863 + 0.925862i \(0.376659\pi\)
\(788\) −52.0878 37.8440i −1.85555 1.34814i
\(789\) −11.5680 + 8.40467i −0.411833 + 0.299214i
\(790\) −28.3931 + 4.67484i −1.01018 + 0.166323i
\(791\) −4.48043 3.25522i −0.159306 0.115742i
\(792\) −8.84525 27.2229i −0.314302 0.967323i
\(793\) 0.0714945 0.00253884
\(794\) −1.09837 3.38044i −0.0389797 0.119967i
\(795\) 11.0813 11.2174i 0.393014 0.397841i
\(796\) −0.895774 + 2.75691i −0.0317499 + 0.0977160i
\(797\) 8.40931 25.8812i 0.297873 0.916759i −0.684368 0.729137i \(-0.739922\pi\)
0.982241 0.187622i \(-0.0600781\pi\)
\(798\) −3.85120 + 2.79806i −0.136331 + 0.0990504i
\(799\) 7.56529 0.267641
\(800\) −91.1040 28.3768i −3.22101 1.00327i
\(801\) −6.20049 −0.219083
\(802\) −35.2600 + 25.6179i −1.24507 + 0.904599i
\(803\) 9.62360 29.6184i 0.339610 1.04521i
\(804\) −4.59818 + 14.1518i −0.162165 + 0.499094i
\(805\) −1.09661 2.12013i −0.0386505 0.0747249i
\(806\) 2.56179 + 7.88437i 0.0902351 + 0.277715i
\(807\) −19.2205 −0.676592
\(808\) −16.2178 49.9132i −0.570540 1.75594i
\(809\) 15.8693 + 11.5297i 0.557933 + 0.405362i 0.830702 0.556717i \(-0.187939\pi\)
−0.272769 + 0.962080i \(0.587939\pi\)
\(810\) −4.25294 + 4.30517i −0.149433 + 0.151268i
\(811\) −17.0468 + 12.3852i −0.598594 + 0.434904i −0.845380 0.534166i \(-0.820626\pi\)
0.246786 + 0.969070i \(0.420626\pi\)
\(812\) 16.8636 + 12.2521i 0.591796 + 0.429965i
\(813\) 18.8042 + 13.6620i 0.659492 + 0.479149i
\(814\) 7.11107 5.16650i 0.249243 0.181086i
\(815\) −18.6888 + 18.9184i −0.654641 + 0.662682i
\(816\) 18.9131 + 13.7412i 0.662090 + 0.481037i
\(817\) 7.77501 + 23.9290i 0.272013 + 0.837170i
\(818\) 57.2667 2.00228
\(819\) 0.0818847 + 0.252015i 0.00286128 + 0.00880613i
\(820\) 8.05218 + 15.5677i 0.281194 + 0.543646i
\(821\) 12.8039 39.4062i 0.446858 1.37529i −0.433575 0.901117i \(-0.642748\pi\)
0.880433 0.474170i \(-0.157252\pi\)
\(822\) −4.27866 + 13.1684i −0.149235 + 0.459299i
\(823\) −4.88721 + 3.55077i −0.170358 + 0.123772i −0.669697 0.742634i \(-0.733576\pi\)
0.499340 + 0.866406i \(0.333576\pi\)
\(824\) −126.673 −4.41285
\(825\) 0.194176 + 15.9062i 0.00676034 + 0.553783i
\(826\) −16.3833 −0.570047
\(827\) 2.42188 1.75960i 0.0842172 0.0611874i −0.544880 0.838514i \(-0.683425\pi\)
0.629097 + 0.777327i \(0.283425\pi\)
\(828\) −3.73458 + 11.4938i −0.129786 + 0.399439i
\(829\) 8.29802 25.5387i 0.288202 0.886995i −0.697218 0.716859i \(-0.745579\pi\)
0.985421 0.170136i \(-0.0544208\pi\)
\(830\) −49.7189 + 50.3296i −1.72577 + 1.74697i
\(831\) 6.76469 + 20.8196i 0.234664 + 0.722223i
\(832\) 13.6624 0.473658
\(833\) 3.57444 + 11.0010i 0.123847 + 0.381162i
\(834\) 18.0374 + 13.1050i 0.624585 + 0.453787i
\(835\) −13.2244 + 2.17737i −0.457651 + 0.0753509i
\(836\) 51.2555 37.2393i 1.77271 1.28795i
\(837\) −4.39827 3.19553i −0.152026 0.110454i
\(838\) 14.6060 + 10.6119i 0.504555 + 0.366581i
\(839\) −10.0800 + 7.32352i −0.347999 + 0.252836i −0.748029 0.663666i \(-0.769000\pi\)
0.400030 + 0.916502i \(0.369000\pi\)
\(840\) 1.42302 9.35373i 0.0490988 0.322734i
\(841\) −32.5998 23.6851i −1.12413 0.816729i
\(842\) 22.8297 + 70.2624i 0.786762 + 2.42140i
\(843\) 27.1138 0.933850
\(844\) −5.13683 15.8095i −0.176817 0.544186i
\(845\) −27.9823 + 4.60720i −0.962619 + 0.158492i
\(846\) −3.70785 + 11.4116i −0.127479 + 0.392339i
\(847\) −0.127627 + 0.392797i −0.00438533 + 0.0134967i
\(848\) 78.1590 56.7859i 2.68399 1.95003i
\(849\) 16.3074 0.559668
\(850\) −13.7991 18.5133i −0.473304 0.635000i
\(851\) −2.31714 −0.0794304
\(852\) −69.1171 + 50.2165i −2.36791 + 1.72039i
\(853\) −1.76058 + 5.41851i −0.0602811 + 0.185526i −0.976662 0.214780i \(-0.931096\pi\)
0.916381 + 0.400307i \(0.131096\pi\)
\(854\) 0.0499068 0.153597i 0.00170778 0.00525599i
\(855\) −7.47463 3.75123i −0.255627 0.128289i
\(856\) −23.9436 73.6907i −0.818374 2.51870i
\(857\) −7.41982 −0.253456 −0.126728 0.991937i \(-0.540448\pi\)
−0.126728 + 0.991937i \(0.540448\pi\)
\(858\) −1.49916 4.61394i −0.0511805 0.157517i
\(859\) 4.59726 + 3.34011i 0.156857 + 0.113963i 0.663445 0.748225i \(-0.269094\pi\)
−0.506588 + 0.862188i \(0.669094\pi\)
\(860\) −71.5833 35.9249i −2.44097 1.22503i
\(861\) −0.560112 + 0.406945i −0.0190886 + 0.0138687i
\(862\) −26.9251 19.5622i −0.917073 0.666293i
\(863\) 27.9715 + 20.3225i 0.952160 + 0.691785i 0.951317 0.308215i \(-0.0997315\pi\)
0.000843465 1.00000i \(0.499732\pi\)
\(864\) −15.4395 + 11.2174i −0.525261 + 0.381624i
\(865\) 17.7973 + 34.4083i 0.605125 + 1.16992i
\(866\) 74.1037 + 53.8395i 2.51815 + 1.82954i
\(867\) −4.35353 13.3988i −0.147854 0.455047i
\(868\) 13.6133 0.462066
\(869\) 4.67478 + 14.3875i 0.158581 + 0.488062i
\(870\) −7.57671 + 49.8030i −0.256875 + 1.68848i
\(871\) −0.486594 + 1.49758i −0.0164876 + 0.0507437i
\(872\) 46.3952 142.790i 1.57114 4.83547i
\(873\) −6.83978 + 4.96939i −0.231491 + 0.168188i
\(874\) −22.9751 −0.777145
\(875\) −2.30093 + 4.72788i −0.0777855 + 0.159831i
\(876\) −52.1191 −1.76094
\(877\) 4.28790 3.11534i 0.144792 0.105197i −0.513031 0.858370i \(-0.671477\pi\)
0.657823 + 0.753173i \(0.271477\pi\)
\(878\) −17.5336 + 53.9629i −0.591730 + 1.82116i
\(879\) 1.68849 5.19664i 0.0569514 0.175278i
\(880\) −14.6590 + 96.3560i −0.494155 + 3.24816i
\(881\) 2.35251 + 7.24028i 0.0792580 + 0.243931i 0.982833 0.184500i \(-0.0590665\pi\)
−0.903575 + 0.428431i \(0.859067\pi\)
\(882\) −18.3460 −0.617740
\(883\) −16.3264 50.2476i −0.549428 1.69096i −0.710223 0.703977i \(-0.751406\pi\)
0.160795 0.986988i \(-0.448594\pi\)
\(884\) 4.14143 + 3.00892i 0.139291 + 0.101201i
\(885\) −13.2233 25.5653i −0.444497 0.859367i
\(886\) −13.2431 + 9.62166i −0.444910 + 0.323246i
\(887\) −6.23572 4.53052i −0.209375 0.152120i 0.478156 0.878275i \(-0.341305\pi\)
−0.687531 + 0.726155i \(0.741305\pi\)
\(888\) −7.43051 5.39858i −0.249352 0.181165i
\(889\) −0.676800 + 0.491724i −0.0226991 + 0.0164919i
\(890\) 33.5365 + 16.8307i 1.12415 + 0.564166i
\(891\) 2.57387 + 1.87003i 0.0862279 + 0.0626482i
\(892\) 0.557972 + 1.71726i 0.0186823 + 0.0574981i
\(893\) −16.5820 −0.554896
\(894\) −8.41207 25.8897i −0.281342 0.865881i
\(895\) −21.1372 10.6080i −0.706540 0.354585i
\(896\) 3.99006 12.2801i 0.133299 0.410251i
\(897\) −0.395205 + 1.21631i −0.0131955 + 0.0406116i
\(898\) −34.1334 + 24.7994i −1.13905 + 0.827566i
\(899\) −45.2560 −1.50937
\(900\) 25.2167 8.53509i 0.840557 0.284503i
\(901\) 12.0326 0.400864
\(902\) 10.2546 7.45043i 0.341442 0.248072i
\(903\) 0.977659 3.00892i 0.0325344 0.100131i
\(904\) 32.7396 100.762i 1.08890 3.35130i
\(905\) 26.4319 4.35194i 0.878626 0.144663i
\(906\) −10.0198 30.8379i −0.332887 1.02452i
\(907\) −11.3735 −0.377650 −0.188825 0.982011i \(-0.560468\pi\)
−0.188825 + 0.982011i \(0.560468\pi\)
\(908\) −2.94262 9.05644i −0.0976542 0.300549i
\(909\) 4.71920 + 3.42870i 0.156526 + 0.113723i
\(910\) 0.241184 1.58534i 0.00799517 0.0525536i
\(911\) 15.0393 10.9267i 0.498275 0.362018i −0.310082 0.950710i \(-0.600357\pi\)
0.808358 + 0.588691i \(0.200357\pi\)
\(912\) −41.4547 30.1186i −1.37270 0.997328i
\(913\) 30.0898 + 21.8615i 0.995827 + 0.723511i
\(914\) 5.47795 3.97997i 0.181195 0.131646i
\(915\) 0.279962 0.0460949i 0.00925525 0.00152385i
\(916\) 120.539 + 87.5764i 3.98271 + 2.89361i
\(917\) −0.860143 2.64725i −0.0284044 0.0874199i
\(918\) −4.61803 −0.152418
\(919\) 2.36336 + 7.27367i 0.0779600 + 0.239936i 0.982440 0.186581i \(-0.0597405\pi\)
−0.904480 + 0.426517i \(0.859741\pi\)
\(920\) 32.0915 32.4857i 1.05803 1.07102i
\(921\) −6.61895 + 20.3710i −0.218102 + 0.671249i
\(922\) −0.128761 + 0.396286i −0.00424052 + 0.0130510i
\(923\) −7.31418 + 5.31407i −0.240749 + 0.174915i
\(924\) −7.96652 −0.262079
\(925\) 3.05039 + 4.09250i 0.100296 + 0.134561i
\(926\) −31.4822 −1.03457
\(927\) 11.3905 8.27566i 0.374112 0.271808i
\(928\) −49.0918 + 151.089i −1.61152 + 4.95974i
\(929\) −9.56366 + 29.4339i −0.313774 + 0.965696i 0.662483 + 0.749077i \(0.269503\pi\)
−0.976256 + 0.216619i \(0.930497\pi\)
\(930\) 15.1149 + 29.2223i 0.495637 + 0.958238i
\(931\) −7.83466 24.1126i −0.256770 0.790258i
\(932\) −36.0675 −1.18143
\(933\) −0.881316 2.71241i −0.0288530 0.0888003i
\(934\) −1.02971 0.748125i −0.0336930 0.0244794i
\(935\) −8.53106 + 8.63584i −0.278996 + 0.282422i
\(936\) −4.10116 + 2.97967i −0.134051 + 0.0973936i
\(937\) −25.3784 18.4385i −0.829077 0.602360i 0.0902212 0.995922i \(-0.471243\pi\)
−0.919298 + 0.393562i \(0.871243\pi\)
\(938\) 2.87771 + 2.09078i 0.0939605 + 0.0682663i
\(939\) −11.6802 + 8.48616i −0.381169 + 0.276935i
\(940\) 37.0960 37.5517i 1.20994 1.22480i
\(941\) 2.92710 + 2.12666i 0.0954208 + 0.0693273i 0.634473 0.772945i \(-0.281217\pi\)
−0.539052 + 0.842273i \(0.681217\pi\)
\(942\) 16.3884 + 50.4383i 0.533963 + 1.64337i
\(943\) −3.34146 −0.108813
\(944\) −54.4955 167.720i −1.77368 5.45882i
\(945\) 0.483131 + 0.934060i 0.0157162 + 0.0303850i
\(946\) −17.8992 + 55.0879i −0.581952 + 1.79106i
\(947\) −3.49856 + 10.7675i −0.113688 + 0.349896i −0.991671 0.128796i \(-0.958889\pi\)
0.877983 + 0.478692i \(0.158889\pi\)
\(948\) 20.4823 14.8812i 0.665233 0.483320i
\(949\) −5.51540 −0.179038
\(950\) 30.2456 + 40.5784i 0.981296 + 1.31654i
\(951\) 22.6102 0.733187
\(952\) 5.84113 4.24383i 0.189312 0.137543i
\(953\) −5.32071 + 16.3755i −0.172355 + 0.530453i −0.999503 0.0315307i \(-0.989962\pi\)
0.827148 + 0.561984i \(0.189962\pi\)
\(954\) −5.89735 + 18.1502i −0.190934 + 0.587633i
\(955\) −28.7038 + 29.0563i −0.928832 + 0.940240i
\(956\) −10.6672 32.8304i −0.345003 1.06181i
\(957\) 26.4839 0.856102
\(958\) 10.3798 + 31.9458i 0.335357 + 1.03212i
\(959\) 1.94656 + 1.41426i 0.0628576 + 0.0456687i
\(960\) 53.4998 8.80859i 1.72670 0.284296i
\(961\) 1.16811 0.848680i 0.0376809 0.0273768i
\(962\) −1.25938 0.914994i −0.0406041 0.0295006i
\(963\) 6.96731 + 5.06205i 0.224519 + 0.163122i
\(964\) 32.0849 23.3110i 1.03339 0.750798i
\(965\) 8.47717 55.7218i 0.272890 1.79375i
\(966\) 2.33723 + 1.69810i 0.0751992 + 0.0546354i
\(967\) −9.24157 28.4426i −0.297189 0.914653i −0.982477 0.186382i \(-0.940324\pi\)
0.685289 0.728272i \(-0.259676\pi\)
\(968\) −7.90115 −0.253953
\(969\) −1.97214 6.06961i −0.0633541 0.194984i
\(970\) 50.4832 8.31192i 1.62092 0.266880i
\(971\) −7.78497 + 23.9597i −0.249832 + 0.768902i 0.744973 + 0.667095i \(0.232463\pi\)
−0.994804 + 0.101807i \(0.967537\pi\)
\(972\) 1.64533 5.06380i 0.0527739 0.162422i
\(973\) 3.13443 2.27729i 0.100485 0.0730067i
\(974\) 93.5443 2.99735
\(975\) 2.66851 0.903210i 0.0854607 0.0289259i
\(976\) 1.73842 0.0556455
\(977\) −46.1907 + 33.5595i −1.47777 + 1.07366i −0.499504 + 0.866311i \(0.666485\pi\)
−0.978266 + 0.207352i \(0.933515\pi\)
\(978\) 9.94597 30.6106i 0.318037 0.978818i
\(979\) 6.09589 18.7612i 0.194826 0.599611i
\(980\) 72.1325 + 36.2005i 2.30419 + 1.15638i
\(981\) 5.15673 + 15.8708i 0.164642 + 0.506715i
\(982\) −67.2957 −2.14749
\(983\) −8.16325 25.1239i −0.260367 0.801328i −0.992725 0.120407i \(-0.961580\pi\)
0.732357 0.680921i \(-0.238420\pi\)
\(984\) −10.7153 7.78512i −0.341591 0.248181i
\(985\) −24.1665 12.1282i −0.770010 0.386438i
\(986\) −31.1005 + 22.5958i −0.990442 + 0.719598i
\(987\) 1.68687 + 1.22558i 0.0536936 + 0.0390107i
\(988\) −9.07741 6.59513i −0.288791 0.209819i
\(989\) 12.3533 8.97517i 0.392811 0.285394i
\(990\) −8.84525 17.1009i −0.281120 0.543503i
\(991\) 18.2252 + 13.2414i 0.578943 + 0.420626i 0.838343 0.545144i \(-0.183525\pi\)
−0.259400 + 0.965770i \(0.583525\pi\)
\(992\) 32.0612 + 98.6744i 1.01795 + 3.13291i
\(993\) 3.86645 0.122698
\(994\) 6.31096 + 19.4231i 0.200171 + 0.616064i
\(995\) −0.183100 + 1.20354i −0.00580465 + 0.0381549i
\(996\) 19.2347 59.1983i 0.609475 1.87577i
\(997\) −7.44865 + 22.9246i −0.235901 + 0.726029i 0.761099 + 0.648635i \(0.224660\pi\)
−0.997001 + 0.0773940i \(0.975340\pi\)
\(998\) −27.5958 + 20.0495i −0.873529 + 0.634656i
\(999\) 1.02085 0.0322983
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 75.2.g.b.61.1 yes 8
3.2 odd 2 225.2.h.c.136.2 8
5.2 odd 4 375.2.i.b.199.1 16
5.3 odd 4 375.2.i.b.199.4 16
5.4 even 2 375.2.g.b.301.2 8
25.3 odd 20 1875.2.b.c.1249.1 8
25.4 even 10 1875.2.a.e.1.1 4
25.9 even 10 375.2.g.b.76.2 8
25.12 odd 20 375.2.i.b.49.4 16
25.13 odd 20 375.2.i.b.49.1 16
25.16 even 5 inner 75.2.g.b.16.1 8
25.21 even 5 1875.2.a.h.1.4 4
25.22 odd 20 1875.2.b.c.1249.8 8
75.29 odd 10 5625.2.a.n.1.4 4
75.41 odd 10 225.2.h.c.91.2 8
75.71 odd 10 5625.2.a.i.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.2.g.b.16.1 8 25.16 even 5 inner
75.2.g.b.61.1 yes 8 1.1 even 1 trivial
225.2.h.c.91.2 8 75.41 odd 10
225.2.h.c.136.2 8 3.2 odd 2
375.2.g.b.76.2 8 25.9 even 10
375.2.g.b.301.2 8 5.4 even 2
375.2.i.b.49.1 16 25.13 odd 20
375.2.i.b.49.4 16 25.12 odd 20
375.2.i.b.199.1 16 5.2 odd 4
375.2.i.b.199.4 16 5.3 odd 4
1875.2.a.e.1.1 4 25.4 even 10
1875.2.a.h.1.4 4 25.21 even 5
1875.2.b.c.1249.1 8 25.3 odd 20
1875.2.b.c.1249.8 8 25.22 odd 20
5625.2.a.i.1.1 4 75.71 odd 10
5625.2.a.n.1.4 4 75.29 odd 10