Properties

Label 14.6.c.b.11.2
Level $14$
Weight $6$
Character 14.11
Analytic conductor $2.245$
Analytic rank $0$
Dimension $4$
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] = [14,6,Mod(9,14)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(14, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("14.9");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 14.c (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.24537347738\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{130})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 130x^{2} + 16900 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 11.2
Root \(-5.70088 + 9.87421i\) of defining polynomial
Character \(\chi\) \(=\) 14.11
Dual form 14.6.c.b.9.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.00000 + 3.46410i) q^{2} +(14.9018 - 25.8106i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(10.5000 + 18.1865i) q^{5} +119.214 q^{6} +(-10.4105 + 129.223i) q^{7} -64.0000 q^{8} +(-322.625 - 558.802i) q^{9} +O(q^{10})\) \(q+(2.00000 + 3.46410i) q^{2} +(14.9018 - 25.8106i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(10.5000 + 18.1865i) q^{5} +119.214 q^{6} +(-10.4105 + 129.223i) q^{7} -64.0000 q^{8} +(-322.625 - 558.802i) q^{9} +(-42.0000 + 72.7461i) q^{10} +(-165.937 + 287.411i) q^{11} +(238.428 + 412.970i) q^{12} +66.8211 q^{13} +(-468.463 + 222.383i) q^{14} +625.874 q^{15} +(-128.000 - 221.703i) q^{16} +(-120.268 + 208.311i) q^{17} +(1290.50 - 2235.21i) q^{18} +(-220.989 - 382.765i) q^{19} -336.000 q^{20} +(3180.19 + 2194.35i) q^{21} -1327.49 q^{22} +(535.684 + 927.832i) q^{23} +(-953.712 + 1651.88i) q^{24} +(1342.00 - 2324.41i) q^{25} +(133.642 + 231.475i) q^{26} -11988.4 q^{27} +(-1707.28 - 1178.04i) q^{28} +1791.75 q^{29} +(1251.75 + 2168.09i) q^{30} +(2844.37 - 4926.59i) q^{31} +(512.000 - 886.810i) q^{32} +(4945.50 + 8565.86i) q^{33} -962.147 q^{34} +(-2459.43 + 1167.51i) q^{35} +10324.0 q^{36} +(-5605.36 - 9708.77i) q^{37} +(883.958 - 1531.06i) q^{38} +(995.751 - 1724.69i) q^{39} +(-672.000 - 1163.94i) q^{40} +12077.9 q^{41} +(-1241.08 + 15405.2i) q^{42} -9921.98 q^{43} +(-2654.99 - 4598.58i) q^{44} +(6775.12 - 11734.8i) q^{45} +(-2142.74 + 3711.33i) q^{46} +(8434.62 + 14609.2i) q^{47} -7629.70 q^{48} +(-16590.2 - 2690.56i) q^{49} +10736.0 q^{50} +(3584.42 + 6208.40i) q^{51} +(-534.568 + 925.900i) q^{52} +(-2649.38 + 4588.87i) q^{53} +(-23976.9 - 41529.2i) q^{54} -6969.35 q^{55} +(666.274 - 8270.28i) q^{56} -13172.5 q^{57} +(3583.49 + 6206.79i) q^{58} +(-20692.4 + 35840.3i) q^{59} +(-5006.99 + 8672.36i) q^{60} +(10761.6 + 18639.7i) q^{61} +22754.9 q^{62} +(75568.9 - 35873.1i) q^{63} +4096.00 q^{64} +(701.621 + 1215.24i) q^{65} +(-19782.0 + 34263.4i) q^{66} +(13309.4 - 23052.5i) q^{67} +(-1924.29 - 3332.98i) q^{68} +31930.5 q^{69} +(-8963.24 - 6184.70i) q^{70} -58096.5 q^{71} +(20648.0 + 35763.3i) q^{72} +(19993.8 - 34630.2i) q^{73} +(22421.5 - 38835.1i) q^{74} +(-39996.3 - 69275.6i) q^{75} +7071.66 q^{76} +(-35412.7 - 24435.0i) q^{77} +7966.01 q^{78} +(21974.9 + 38061.7i) q^{79} +(2688.00 - 4655.75i) q^{80} +(-100251. + 173640. i) q^{81} +(24155.7 + 41838.9i) q^{82} +22421.4 q^{83} +(-55847.4 + 26511.2i) q^{84} -5051.27 q^{85} +(-19844.0 - 34370.7i) q^{86} +(26700.2 - 46246.1i) q^{87} +(10620.0 - 18394.3i) q^{88} +(-12031.0 - 20838.3i) q^{89} +54200.9 q^{90} +(-695.642 + 8634.83i) q^{91} -17141.9 q^{92} +(-84772.2 - 146830. i) q^{93} +(-33738.5 + 58436.8i) q^{94} +(4640.78 - 8038.06i) q^{95} +(-15259.4 - 26430.0i) q^{96} +71896.4 q^{97} +(-23860.1 - 62851.4i) q^{98} +214141. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 8 q^{2} + 14 q^{3} - 32 q^{4} + 42 q^{5} + 112 q^{6} + 232 q^{7} - 256 q^{8} - 652 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 8 q^{2} + 14 q^{3} - 32 q^{4} + 42 q^{5} + 112 q^{6} + 232 q^{7} - 256 q^{8} - 652 q^{9} - 168 q^{10} + 294 q^{11} + 224 q^{12} - 280 q^{13} - 232 q^{14} + 588 q^{15} - 512 q^{16} - 1302 q^{17} + 2608 q^{18} + 1442 q^{19} - 1344 q^{20} + 5150 q^{21} + 2352 q^{22} - 2646 q^{23} - 896 q^{24} + 5368 q^{25} - 560 q^{26} - 31444 q^{27} - 4640 q^{28} + 3336 q^{29} + 1176 q^{30} + 14798 q^{31} + 2048 q^{32} + 19782 q^{33} - 10416 q^{34} - 1218 q^{35} + 20864 q^{36} - 5182 q^{37} - 5768 q^{38} + 5260 q^{39} - 2688 q^{40} - 10248 q^{41} - 18464 q^{42} - 9040 q^{43} + 4704 q^{44} + 13692 q^{45} + 10584 q^{46} + 14994 q^{47} - 7168 q^{48} - 2876 q^{49} + 42944 q^{50} - 9606 q^{51} + 2240 q^{52} - 24006 q^{53} - 62888 q^{54} + 12348 q^{55} - 14848 q^{56} - 85892 q^{57} + 6672 q^{58} - 38850 q^{59} - 4704 q^{60} + 23618 q^{61} + 118384 q^{62} + 149948 q^{63} + 16384 q^{64} - 2940 q^{65} - 79128 q^{66} - 32002 q^{67} - 20832 q^{68} + 181356 q^{69} - 24360 q^{70} - 178752 q^{71} + 41728 q^{72} + 47138 q^{73} + 20728 q^{74} - 37576 q^{75} - 46144 q^{76} - 22890 q^{77} + 42080 q^{78} + 40970 q^{79} + 10752 q^{80} - 139858 q^{81} - 20496 q^{82} + 136752 q^{83} - 156256 q^{84} - 54684 q^{85} - 18080 q^{86} + 55356 q^{87} - 18816 q^{88} - 123102 q^{89} + 109536 q^{90} - 53680 q^{91} + 84672 q^{92} - 25586 q^{93} - 59976 q^{94} - 30282 q^{95} - 14336 q^{96} - 87304 q^{97} + 63272 q^{98} + 419832 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 + 3.46410i 0.353553 + 0.612372i
\(3\) 14.9018 25.8106i 0.955948 1.65575i 0.223764 0.974643i \(-0.428165\pi\)
0.732184 0.681107i \(-0.238501\pi\)
\(4\) −8.00000 + 13.8564i −0.250000 + 0.433013i
\(5\) 10.5000 + 18.1865i 0.187830 + 0.325331i 0.944526 0.328436i \(-0.106521\pi\)
−0.756697 + 0.653766i \(0.773188\pi\)
\(6\) 119.214 1.35191
\(7\) −10.4105 + 129.223i −0.0803022 + 0.996771i
\(8\) −64.0000 −0.353553
\(9\) −322.625 558.802i −1.32767 2.29960i
\(10\) −42.0000 + 72.7461i −0.132816 + 0.230043i
\(11\) −165.937 + 287.411i −0.413486 + 0.716179i −0.995268 0.0971656i \(-0.969022\pi\)
0.581782 + 0.813345i \(0.302356\pi\)
\(12\) 238.428 + 412.970i 0.477974 + 0.827875i
\(13\) 66.8211 0.109662 0.0548308 0.998496i \(-0.482538\pi\)
0.0548308 + 0.998496i \(0.482538\pi\)
\(14\) −468.463 + 222.383i −0.638786 + 0.303237i
\(15\) 625.874 0.718222
\(16\) −128.000 221.703i −0.125000 0.216506i
\(17\) −120.268 + 208.311i −0.100932 + 0.174820i −0.912069 0.410037i \(-0.865516\pi\)
0.811137 + 0.584856i \(0.198849\pi\)
\(18\) 1290.50 2235.21i 0.938807 1.62606i
\(19\) −220.989 382.765i −0.140439 0.243247i 0.787223 0.616668i \(-0.211518\pi\)
−0.927662 + 0.373421i \(0.878185\pi\)
\(20\) −336.000 −0.187830
\(21\) 3180.19 + 2194.35i 1.57364 + 1.08582i
\(22\) −1327.49 −0.584758
\(23\) 535.684 + 927.832i 0.211149 + 0.365721i 0.952074 0.305866i \(-0.0989461\pi\)
−0.740925 + 0.671587i \(0.765613\pi\)
\(24\) −953.712 + 1651.88i −0.337979 + 0.585396i
\(25\) 1342.00 2324.41i 0.429440 0.743812i
\(26\) 133.642 + 231.475i 0.0387713 + 0.0671538i
\(27\) −11988.4 −3.16485
\(28\) −1707.28 1178.04i −0.411539 0.283965i
\(29\) 1791.75 0.395623 0.197812 0.980240i \(-0.436617\pi\)
0.197812 + 0.980240i \(0.436617\pi\)
\(30\) 1251.75 + 2168.09i 0.253930 + 0.439819i
\(31\) 2844.37 4926.59i 0.531596 0.920751i −0.467724 0.883875i \(-0.654926\pi\)
0.999320 0.0368765i \(-0.0117408\pi\)
\(32\) 512.000 886.810i 0.0883883 0.153093i
\(33\) 4945.50 + 8565.86i 0.790543 + 1.36926i
\(34\) −962.147 −0.142740
\(35\) −2459.43 + 1167.51i −0.339363 + 0.161098i
\(36\) 10324.0 1.32767
\(37\) −5605.36 9708.77i −0.673131 1.16590i −0.977012 0.213187i \(-0.931616\pi\)
0.303881 0.952710i \(-0.401718\pi\)
\(38\) 883.958 1531.06i 0.0993053 0.172002i
\(39\) 995.751 1724.69i 0.104831 0.181572i
\(40\) −672.000 1163.94i −0.0664078 0.115022i
\(41\) 12077.9 1.12210 0.561048 0.827783i \(-0.310398\pi\)
0.561048 + 0.827783i \(0.310398\pi\)
\(42\) −1241.08 + 15405.2i −0.108562 + 1.34755i
\(43\) −9921.98 −0.818328 −0.409164 0.912461i \(-0.634180\pi\)
−0.409164 + 0.912461i \(0.634180\pi\)
\(44\) −2654.99 4598.58i −0.206743 0.358090i
\(45\) 6775.12 11734.8i 0.498753 0.863865i
\(46\) −2142.74 + 3711.33i −0.149305 + 0.258604i
\(47\) 8434.62 + 14609.2i 0.556956 + 0.964676i 0.997748 + 0.0670671i \(0.0213642\pi\)
−0.440792 + 0.897609i \(0.645303\pi\)
\(48\) −7629.70 −0.477974
\(49\) −16590.2 2690.56i −0.987103 0.160086i
\(50\) 10736.0 0.607320
\(51\) 3584.42 + 6208.40i 0.192972 + 0.334237i
\(52\) −534.568 + 925.900i −0.0274154 + 0.0474849i
\(53\) −2649.38 + 4588.87i −0.129555 + 0.224396i −0.923504 0.383588i \(-0.874688\pi\)
0.793949 + 0.607984i \(0.208022\pi\)
\(54\) −23976.9 41529.2i −1.11894 1.93807i
\(55\) −6969.35 −0.310660
\(56\) 666.274 8270.28i 0.0283911 0.352412i
\(57\) −13172.5 −0.537009
\(58\) 3583.49 + 6206.79i 0.139874 + 0.242269i
\(59\) −20692.4 + 35840.3i −0.773892 + 1.34042i 0.161522 + 0.986869i \(0.448360\pi\)
−0.935415 + 0.353552i \(0.884974\pi\)
\(60\) −5006.99 + 8672.36i −0.179555 + 0.310999i
\(61\) 10761.6 + 18639.7i 0.370300 + 0.641379i 0.989612 0.143766i \(-0.0459214\pi\)
−0.619311 + 0.785146i \(0.712588\pi\)
\(62\) 22754.9 0.751790
\(63\) 75568.9 35873.1i 2.39879 1.13872i
\(64\) 4096.00 0.125000
\(65\) 701.621 + 1215.24i 0.0205977 + 0.0356763i
\(66\) −19782.0 + 34263.4i −0.558998 + 0.968213i
\(67\) 13309.4 23052.5i 0.362219 0.627381i −0.626107 0.779737i \(-0.715353\pi\)
0.988326 + 0.152356i \(0.0486860\pi\)
\(68\) −1924.29 3332.98i −0.0504661 0.0874098i
\(69\) 31930.5 0.807390
\(70\) −8963.24 6184.70i −0.218635 0.150860i
\(71\) −58096.5 −1.36774 −0.683870 0.729603i \(-0.739705\pi\)
−0.683870 + 0.729603i \(0.739705\pi\)
\(72\) 20648.0 + 35763.3i 0.469403 + 0.813030i
\(73\) 19993.8 34630.2i 0.439124 0.760585i −0.558498 0.829506i \(-0.688622\pi\)
0.997622 + 0.0689204i \(0.0219555\pi\)
\(74\) 22421.5 38835.1i 0.475975 0.824413i
\(75\) −39996.3 69275.6i −0.821045 1.42209i
\(76\) 7071.66 0.140439
\(77\) −35412.7 24435.0i −0.680663 0.469662i
\(78\) 7966.01 0.148253
\(79\) 21974.9 + 38061.7i 0.396150 + 0.686151i 0.993247 0.116017i \(-0.0370128\pi\)
−0.597098 + 0.802169i \(0.703679\pi\)
\(80\) 2688.00 4655.75i 0.0469574 0.0813327i
\(81\) −100251. + 173640.i −1.69776 + 2.94060i
\(82\) 24155.7 + 41838.9i 0.396721 + 0.687141i
\(83\) 22421.4 0.357246 0.178623 0.983918i \(-0.442836\pi\)
0.178623 + 0.983918i \(0.442836\pi\)
\(84\) −55847.4 + 26511.2i −0.863584 + 0.409950i
\(85\) −5051.27 −0.0758322
\(86\) −19844.0 34370.7i −0.289322 0.501121i
\(87\) 26700.2 46246.1i 0.378195 0.655053i
\(88\) 10620.0 18394.3i 0.146189 0.253208i
\(89\) −12031.0 20838.3i −0.161001 0.278861i 0.774227 0.632908i \(-0.218139\pi\)
−0.935228 + 0.354047i \(0.884805\pi\)
\(90\) 54200.9 0.705343
\(91\) −695.642 + 8634.83i −0.00880608 + 0.109308i
\(92\) −17141.9 −0.211149
\(93\) −84772.2 146830.i −1.01636 1.76038i
\(94\) −33738.5 + 58436.8i −0.393827 + 0.682129i
\(95\) 4640.78 8038.06i 0.0527572 0.0913782i
\(96\) −15259.4 26430.0i −0.168989 0.292698i
\(97\) 71896.4 0.775850 0.387925 0.921691i \(-0.373192\pi\)
0.387925 + 0.921691i \(0.373192\pi\)
\(98\) −23860.1 62851.4i −0.250962 0.661074i
\(99\) 214141. 2.19590
\(100\) 21472.0 + 37190.6i 0.214720 + 0.371906i
\(101\) 7932.73 13739.9i 0.0773783 0.134023i −0.824740 0.565512i \(-0.808678\pi\)
0.902118 + 0.431489i \(0.142012\pi\)
\(102\) −14337.7 + 24833.6i −0.136452 + 0.236341i
\(103\) 80286.8 + 139061.i 0.745677 + 1.29155i 0.949878 + 0.312622i \(0.101207\pi\)
−0.204200 + 0.978929i \(0.565459\pi\)
\(104\) −4276.55 −0.0387713
\(105\) −6515.67 + 80877.4i −0.0576748 + 0.715902i
\(106\) −21195.1 −0.183219
\(107\) 102523. + 177576.i 0.865693 + 1.49942i 0.866357 + 0.499425i \(0.166455\pi\)
−0.000664234 1.00000i \(0.500211\pi\)
\(108\) 95907.5 166117.i 0.791212 1.37042i
\(109\) 56272.1 97466.2i 0.453657 0.785756i −0.544953 0.838466i \(-0.683453\pi\)
0.998610 + 0.0527102i \(0.0167860\pi\)
\(110\) −13938.7 24142.5i −0.109835 0.190240i
\(111\) −334119. −2.57391
\(112\) 29981.6 14232.5i 0.225845 0.107210i
\(113\) −118332. −0.871782 −0.435891 0.900000i \(-0.643567\pi\)
−0.435891 + 0.900000i \(0.643567\pi\)
\(114\) −26345.0 45631.0i −0.189861 0.328850i
\(115\) −11249.4 + 19484.5i −0.0793202 + 0.137387i
\(116\) −14334.0 + 24827.2i −0.0989058 + 0.171310i
\(117\) −21558.1 37339.7i −0.145595 0.252178i
\(118\) −165539. −1.09445
\(119\) −25666.5 17710.1i −0.166150 0.114645i
\(120\) −40055.9 −0.253930
\(121\) 25455.4 + 44090.1i 0.158058 + 0.273765i
\(122\) −43046.6 + 74558.9i −0.261842 + 0.453524i
\(123\) 179981. 311737.i 1.07267 1.85791i
\(124\) 45509.9 + 78825.5i 0.265798 + 0.460376i
\(125\) 121989. 0.698306
\(126\) 275406. + 190032.i 1.54542 + 1.06635i
\(127\) −245195. −1.34897 −0.674485 0.738289i \(-0.735634\pi\)
−0.674485 + 0.738289i \(0.735634\pi\)
\(128\) 8192.00 + 14189.0i 0.0441942 + 0.0765466i
\(129\) −147855. + 256092.i −0.782279 + 1.35495i
\(130\) −2806.48 + 4860.97i −0.0145648 + 0.0252270i
\(131\) −34996.9 60616.3i −0.178177 0.308611i 0.763079 0.646305i \(-0.223687\pi\)
−0.941256 + 0.337694i \(0.890353\pi\)
\(132\) −158256. −0.790543
\(133\) 51762.7 24572.2i 0.253739 0.120452i
\(134\) 106475. 0.512254
\(135\) −125879. 218028.i −0.594453 1.02962i
\(136\) 7697.18 13331.9i 0.0356849 0.0618080i
\(137\) 93831.9 162522.i 0.427119 0.739792i −0.569496 0.821994i \(-0.692862\pi\)
0.996616 + 0.0822015i \(0.0261951\pi\)
\(138\) 63861.1 + 110611.i 0.285456 + 0.494424i
\(139\) −78272.7 −0.343616 −0.171808 0.985130i \(-0.554961\pi\)
−0.171808 + 0.985130i \(0.554961\pi\)
\(140\) 3497.94 43419.0i 0.0150831 0.187223i
\(141\) 502763. 2.12968
\(142\) −116193. 201252.i −0.483569 0.837567i
\(143\) −11088.1 + 19205.1i −0.0453436 + 0.0785374i
\(144\) −82591.9 + 143053.i −0.331918 + 0.574899i
\(145\) 18813.3 + 32585.7i 0.0743098 + 0.128708i
\(146\) 159950. 0.621015
\(147\) −316669. + 388110.i −1.20868 + 1.48136i
\(148\) 179372. 0.673131
\(149\) 46083.2 + 79818.5i 0.170050 + 0.294536i 0.938437 0.345450i \(-0.112274\pi\)
−0.768387 + 0.639985i \(0.778940\pi\)
\(150\) 159985. 277103.i 0.580566 1.00557i
\(151\) −26708.0 + 46259.6i −0.0953232 + 0.165105i −0.909743 0.415171i \(-0.863722\pi\)
0.814420 + 0.580276i \(0.197055\pi\)
\(152\) 14143.3 + 24497.0i 0.0496527 + 0.0860009i
\(153\) 155206. 0.536019
\(154\) 13819.9 171543.i 0.0469574 0.582869i
\(155\) 119463. 0.399398
\(156\) 15932.0 + 27595.1i 0.0524154 + 0.0907862i
\(157\) 140250. 242921.i 0.454103 0.786530i −0.544533 0.838739i \(-0.683293\pi\)
0.998636 + 0.0522096i \(0.0166264\pi\)
\(158\) −87899.6 + 152247.i −0.280120 + 0.485182i
\(159\) 78960.9 + 136764.i 0.247696 + 0.429023i
\(160\) 21504.0 0.0664078
\(161\) −125474. + 59563.6i −0.381496 + 0.181099i
\(162\) −802008. −2.40099
\(163\) −313405. 542833.i −0.923925 1.60028i −0.793281 0.608855i \(-0.791629\pi\)
−0.130643 0.991429i \(-0.541704\pi\)
\(164\) −96622.8 + 167356.i −0.280524 + 0.485882i
\(165\) −103856. + 179883.i −0.296975 + 0.514375i
\(166\) 44842.8 + 77670.0i 0.126306 + 0.218768i
\(167\) 293997. 0.815741 0.407870 0.913040i \(-0.366272\pi\)
0.407870 + 0.913040i \(0.366272\pi\)
\(168\) −203532. 140439.i −0.556365 0.383896i
\(169\) −366828. −0.987974
\(170\) −10102.5 17498.1i −0.0268107 0.0464375i
\(171\) −142593. + 246979.i −0.372914 + 0.645906i
\(172\) 79375.8 137483.i 0.204582 0.354346i
\(173\) −357093. 618504.i −0.907124 1.57118i −0.818041 0.575160i \(-0.804940\pi\)
−0.0890831 0.996024i \(-0.528394\pi\)
\(174\) 213601. 0.534849
\(175\) 286397. + 197616.i 0.706925 + 0.487783i
\(176\) 84959.7 0.206743
\(177\) 616706. + 1.06817e6i 1.47960 + 2.56275i
\(178\) 48124.1 83353.3i 0.113845 0.197185i
\(179\) −290025. + 502338.i −0.676554 + 1.17183i 0.299458 + 0.954110i \(0.403194\pi\)
−0.976012 + 0.217717i \(0.930139\pi\)
\(180\) 108402. + 187758.i 0.249376 + 0.431933i
\(181\) −308046. −0.698907 −0.349454 0.936954i \(-0.613633\pi\)
−0.349454 + 0.936954i \(0.613633\pi\)
\(182\) −31303.2 + 14859.9i −0.0700503 + 0.0332535i
\(183\) 641470. 1.41595
\(184\) −34283.8 59381.3i −0.0746525 0.129302i
\(185\) 117713. 203884.i 0.252868 0.437980i
\(186\) 339089. 587319.i 0.718672 1.24478i
\(187\) −39913.9 69132.9i −0.0834681 0.144571i
\(188\) −269908. −0.556956
\(189\) 124806. 1.54918e6i 0.254144 3.15463i
\(190\) 37126.2 0.0746100
\(191\) 101395. + 175621.i 0.201109 + 0.348331i 0.948886 0.315619i \(-0.102212\pi\)
−0.747777 + 0.663950i \(0.768879\pi\)
\(192\) 61037.6 105720.i 0.119493 0.206969i
\(193\) −302994. + 524801.i −0.585519 + 1.01415i 0.409292 + 0.912403i \(0.365776\pi\)
−0.994811 + 0.101744i \(0.967558\pi\)
\(194\) 143793. + 249057.i 0.274305 + 0.475109i
\(195\) 41821.5 0.0787614
\(196\) 170003. 208357.i 0.316095 0.387407i
\(197\) −310.819 −0.000570614 −0.000285307 1.00000i \(-0.500091\pi\)
−0.000285307 1.00000i \(0.500091\pi\)
\(198\) 428282. + 741807.i 0.776367 + 1.34471i
\(199\) 204833. 354782.i 0.366664 0.635080i −0.622378 0.782717i \(-0.713833\pi\)
0.989042 + 0.147637i \(0.0471667\pi\)
\(200\) −85888.0 + 148762.i −0.151830 + 0.262977i
\(201\) −396666. 687046.i −0.692524 1.19949i
\(202\) 63461.9 0.109429
\(203\) −18653.0 + 231535.i −0.0317694 + 0.394346i
\(204\) −114701. −0.192972
\(205\) 126817. + 219654.i 0.210763 + 0.365052i
\(206\) −321147. + 556243.i −0.527274 + 0.913265i
\(207\) 345650. 598683.i 0.560674 0.971116i
\(208\) −8553.09 14814.4i −0.0137077 0.0237425i
\(209\) 146681. 0.232278
\(210\) −293199. + 139184.i −0.458790 + 0.217791i
\(211\) −441339. −0.682442 −0.341221 0.939983i \(-0.610840\pi\)
−0.341221 + 0.939983i \(0.610840\pi\)
\(212\) −42390.1 73421.9i −0.0647777 0.112198i
\(213\) −865739. + 1.49950e6i −1.30749 + 2.26464i
\(214\) −410094. + 710304.i −0.612137 + 1.06025i
\(215\) −104181. 180446.i −0.153706 0.266227i
\(216\) 767260. 1.11894
\(217\) 607018. + 418847.i 0.875089 + 0.603817i
\(218\) 450177. 0.641567
\(219\) −595884. 1.03210e6i −0.839560 1.45416i
\(220\) 55754.8 96570.1i 0.0776650 0.134520i
\(221\) −8036.46 + 13919.6i −0.0110684 + 0.0191710i
\(222\) −668238. 1.15742e6i −0.910015 1.57619i
\(223\) 265133. 0.357028 0.178514 0.983937i \(-0.442871\pi\)
0.178514 + 0.983937i \(0.442871\pi\)
\(224\) 109266. + 75394.4i 0.145501 + 0.100397i
\(225\) −1.73185e6 −2.28062
\(226\) −236665. 409916.i −0.308221 0.533855i
\(227\) 715220. 1.23880e6i 0.921244 1.59564i 0.123751 0.992313i \(-0.460508\pi\)
0.797493 0.603328i \(-0.206159\pi\)
\(228\) 105380. 182524.i 0.134252 0.232532i
\(229\) 629025. + 1.08950e6i 0.792646 + 1.37290i 0.924323 + 0.381610i \(0.124630\pi\)
−0.131678 + 0.991293i \(0.542036\pi\)
\(230\) −89994.9 −0.112176
\(231\) −1.15839e6 + 549898.i −1.42832 + 0.678035i
\(232\) −114672. −0.139874
\(233\) −112362. 194616.i −0.135590 0.234849i 0.790233 0.612807i \(-0.209960\pi\)
−0.925823 + 0.377958i \(0.876626\pi\)
\(234\) 86232.4 149359.i 0.102951 0.178317i
\(235\) −177127. + 306793.i −0.209226 + 0.362390i
\(236\) −331078. 573444.i −0.386946 0.670211i
\(237\) 1.30986e6 1.51479
\(238\) 10016.5 124332.i 0.0114623 0.142279i
\(239\) 1.28193e6 1.45167 0.725837 0.687867i \(-0.241453\pi\)
0.725837 + 0.687867i \(0.241453\pi\)
\(240\) −80111.8 138758.i −0.0897777 0.155500i
\(241\) 288062. 498939.i 0.319480 0.553356i −0.660899 0.750475i \(-0.729825\pi\)
0.980380 + 0.197118i \(0.0631583\pi\)
\(242\) −101822. + 176360.i −0.111764 + 0.193581i
\(243\) 1.53124e6 + 2.65218e6i 1.66351 + 2.88129i
\(244\) −344373. −0.370300
\(245\) −125266. 329970.i −0.133326 0.351204i
\(246\) 1.43985e6 1.51698
\(247\) −14766.7 25576.8i −0.0154008 0.0266749i
\(248\) −182040. + 315302.i −0.187948 + 0.325535i
\(249\) 334118. 578709.i 0.341509 0.591510i
\(250\) 243978. + 422582.i 0.246888 + 0.427623i
\(251\) −609040. −0.610185 −0.305092 0.952323i \(-0.598687\pi\)
−0.305092 + 0.952323i \(0.598687\pi\)
\(252\) −107478. + 1.33410e6i −0.106615 + 1.32339i
\(253\) −355559. −0.349229
\(254\) −490390. 849380.i −0.476933 0.826072i
\(255\) −75272.8 + 130376.i −0.0724916 + 0.125559i
\(256\) −32768.0 + 56755.8i −0.0312500 + 0.0541266i
\(257\) −515335. 892586.i −0.486695 0.842980i 0.513188 0.858276i \(-0.328464\pi\)
−0.999883 + 0.0152961i \(0.995131\pi\)
\(258\) −1.18284e6 −1.10631
\(259\) 1.31295e6 623269.i 1.21619 0.577333i
\(260\) −22451.9 −0.0205977
\(261\) −578062. 1.00123e6i −0.525258 0.909774i
\(262\) 139987. 242465.i 0.125990 0.218221i
\(263\) 455293. 788590.i 0.405883 0.703011i −0.588540 0.808468i \(-0.700297\pi\)
0.994424 + 0.105457i \(0.0336306\pi\)
\(264\) −316512. 548215.i −0.279499 0.484107i
\(265\) −111274. −0.0973374
\(266\) 188646. + 130167.i 0.163472 + 0.112797i
\(267\) −717133. −0.615633
\(268\) 212950. + 368840.i 0.181109 + 0.313691i
\(269\) −710499. + 1.23062e6i −0.598663 + 1.03692i 0.394355 + 0.918958i \(0.370968\pi\)
−0.993019 + 0.117957i \(0.962365\pi\)
\(270\) 503514. 872112.i 0.420342 0.728053i
\(271\) 148765. + 257668.i 0.123049 + 0.213127i 0.920969 0.389637i \(-0.127400\pi\)
−0.797920 + 0.602764i \(0.794066\pi\)
\(272\) 61577.4 0.0504661
\(273\) 212504. + 146629.i 0.172568 + 0.119073i
\(274\) 750655. 0.604038
\(275\) 445374. + 771411.i 0.355135 + 0.615112i
\(276\) −255444. + 442442.i −0.201848 + 0.349610i
\(277\) −424806. + 735785.i −0.332653 + 0.576171i −0.983031 0.183439i \(-0.941277\pi\)
0.650378 + 0.759610i \(0.274610\pi\)
\(278\) −156545. 271144.i −0.121487 0.210421i
\(279\) −3.67065e6 −2.82314
\(280\) 157404. 74720.7i 0.119983 0.0569569i
\(281\) −7680.49 −0.00580261 −0.00290130 0.999996i \(-0.500924\pi\)
−0.00290130 + 0.999996i \(0.500924\pi\)
\(282\) 1.00553e6 + 1.74162e6i 0.752957 + 1.30416i
\(283\) 492684. 853353.i 0.365681 0.633378i −0.623204 0.782059i \(-0.714170\pi\)
0.988885 + 0.148681i \(0.0475029\pi\)
\(284\) 464772. 805008.i 0.341935 0.592249i
\(285\) −138311. 239563.i −0.100866 0.174706i
\(286\) −88704.6 −0.0641255
\(287\) −125737. + 1.56074e6i −0.0901068 + 1.11847i
\(288\) −660735. −0.469403
\(289\) 681000. + 1.17953e6i 0.479625 + 0.830736i
\(290\) −75253.4 + 130343.i −0.0525450 + 0.0910105i
\(291\) 1.07138e6 1.85569e6i 0.741673 1.28461i
\(292\) 319900. + 554083.i 0.219562 + 0.380293i
\(293\) −2.16934e6 −1.47625 −0.738124 0.674665i \(-0.764288\pi\)
−0.738124 + 0.674665i \(0.764288\pi\)
\(294\) −1.97779e6 320753.i −1.33448 0.216422i
\(295\) −869080. −0.581440
\(296\) 358743. + 621362.i 0.237988 + 0.412207i
\(297\) 1.98932e6 3.44561e6i 1.30862 2.26660i
\(298\) −184333. + 319274.i −0.120244 + 0.208268i
\(299\) 35795.0 + 61998.7i 0.0231550 + 0.0401056i
\(300\) 1.27988e6 0.821045
\(301\) 103293. 1.28215e6i 0.0657135 0.815685i
\(302\) −213664. −0.134807
\(303\) −236423. 409497.i −0.147939 0.256238i
\(304\) −56573.3 + 97987.8i −0.0351097 + 0.0608118i
\(305\) −225995. + 391434.i −0.139107 + 0.240940i
\(306\) 310412. + 537650.i 0.189511 + 0.328243i
\(307\) −1.39093e6 −0.842287 −0.421143 0.906994i \(-0.638371\pi\)
−0.421143 + 0.906994i \(0.638371\pi\)
\(308\) 621882. 295212.i 0.373535 0.177320i
\(309\) 4.78566e6 2.85132
\(310\) 238927. + 413834.i 0.141209 + 0.244580i
\(311\) −1.01897e6 + 1.76491e6i −0.597394 + 1.03472i 0.395810 + 0.918332i \(0.370464\pi\)
−0.993204 + 0.116385i \(0.962869\pi\)
\(312\) −63728.1 + 110380.i −0.0370633 + 0.0641955i
\(313\) 584789. + 1.01288e6i 0.337395 + 0.584385i 0.983942 0.178489i \(-0.0571210\pi\)
−0.646547 + 0.762874i \(0.723788\pi\)
\(314\) 1.12200e6 0.642199
\(315\) 1.44588e6 + 997668.i 0.821025 + 0.566513i
\(316\) −703197. −0.396150
\(317\) −400568. 693805.i −0.223887 0.387783i 0.732098 0.681199i \(-0.238541\pi\)
−0.955985 + 0.293416i \(0.905208\pi\)
\(318\) −315844. + 547057.i −0.175148 + 0.303365i
\(319\) −297317. + 514968.i −0.163585 + 0.283337i
\(320\) 43008.0 + 74492.0i 0.0234787 + 0.0406663i
\(321\) 6.11112e6 3.31023
\(322\) −457283. 315528.i −0.245779 0.169589i
\(323\) 106312. 0.0566992
\(324\) −1.60402e6 2.77824e6i −0.848879 1.47030i
\(325\) 89673.9 155320.i 0.0470931 0.0815677i
\(326\) 1.25362e6 2.17133e6i 0.653313 1.13157i
\(327\) −1.67711e6 2.90483e6i −0.867344 1.50228i
\(328\) −772983. −0.396721
\(329\) −1.97565e6 + 937859.i −1.00629 + 0.477692i
\(330\) −830844. −0.419986
\(331\) −1.32476e6 2.29454e6i −0.664608 1.15114i −0.979391 0.201972i \(-0.935265\pi\)
0.314783 0.949164i \(-0.398068\pi\)
\(332\) −179371. + 310680.i −0.0893115 + 0.154692i
\(333\) −3.61686e6 + 6.26458e6i −1.78740 + 3.09586i
\(334\) 587994. + 1.01844e6i 0.288408 + 0.499537i
\(335\) 558994. 0.272142
\(336\) 79429.2 985934.i 0.0383824 0.476430i
\(337\) −3.40056e6 −1.63108 −0.815541 0.578699i \(-0.803560\pi\)
−0.815541 + 0.578699i \(0.803560\pi\)
\(338\) −733656. 1.27073e6i −0.349302 0.605008i
\(339\) −1.76336e6 + 3.05423e6i −0.833378 + 1.44345i
\(340\) 40410.2 69992.5i 0.0189580 0.0328363i
\(341\) 943971. + 1.63501e6i 0.439615 + 0.761436i
\(342\) −1.14075e6 −0.527380
\(343\) 520396. 2.11583e6i 0.238835 0.971060i
\(344\) 635007. 0.289322
\(345\) 335271. + 580706.i 0.151652 + 0.262669i
\(346\) 1.42837e6 2.47402e6i 0.641433 1.11100i
\(347\) 308855. 534952.i 0.137699 0.238501i −0.788926 0.614488i \(-0.789363\pi\)
0.926625 + 0.375986i \(0.122696\pi\)
\(348\) 427203. + 739937.i 0.189098 + 0.327527i
\(349\) 2.70539e6 1.18896 0.594479 0.804111i \(-0.297358\pi\)
0.594479 + 0.804111i \(0.297358\pi\)
\(350\) −111767. + 1.38734e6i −0.0487691 + 0.605359i
\(351\) −801080. −0.347063
\(352\) 169919. + 294309.i 0.0730947 + 0.126604i
\(353\) 1.59032e6 2.75452e6i 0.679279 1.17655i −0.295919 0.955213i \(-0.595626\pi\)
0.975198 0.221333i \(-0.0710407\pi\)
\(354\) −2.46682e6 + 4.27266e6i −1.04624 + 1.81213i
\(355\) −610013. 1.05657e6i −0.256902 0.444968i
\(356\) 384993. 0.161001
\(357\) −839585. + 398557.i −0.348653 + 0.165509i
\(358\) −2.32020e6 −0.956792
\(359\) 2.22985e6 + 3.86222e6i 0.913145 + 1.58161i 0.809595 + 0.586989i \(0.199687\pi\)
0.103550 + 0.994624i \(0.466980\pi\)
\(360\) −433607. + 751030.i −0.176336 + 0.305423i
\(361\) 1.14038e6 1.97519e6i 0.460554 0.797703i
\(362\) −616093. 1.06710e6i −0.247101 0.427992i
\(363\) 1.51732e6 0.604382
\(364\) −114083. 78717.7i −0.0451300 0.0311400i
\(365\) 839738. 0.329922
\(366\) 1.28294e6 + 2.22212e6i 0.500615 + 0.867090i
\(367\) −230623. + 399451.i −0.0893795 + 0.154810i −0.907249 0.420594i \(-0.861822\pi\)
0.817869 + 0.575404i \(0.195155\pi\)
\(368\) 137135. 237525.i 0.0527873 0.0914302i
\(369\) −3.89661e6 6.74913e6i −1.48978 2.58037i
\(370\) 941701. 0.357609
\(371\) −565406. 390134.i −0.213268 0.147156i
\(372\) 2.71271e6 1.01636
\(373\) −1.70977e6 2.96141e6i −0.636305 1.10211i −0.986237 0.165338i \(-0.947129\pi\)
0.349932 0.936775i \(-0.386205\pi\)
\(374\) 159656. 276532.i 0.0590208 0.102227i
\(375\) 1.81785e6 3.14861e6i 0.667544 1.15622i
\(376\) −539816. 934988.i −0.196914 0.341065i
\(377\) 119726. 0.0433847
\(378\) 5.61614e6 2.66603e6i 2.02166 0.959699i
\(379\) 16355.6 0.00584882 0.00292441 0.999996i \(-0.499069\pi\)
0.00292441 + 0.999996i \(0.499069\pi\)
\(380\) 74252.5 + 128609.i 0.0263786 + 0.0456891i
\(381\) −3.65383e6 + 6.32863e6i −1.28954 + 2.23356i
\(382\) −405579. + 702483.i −0.142206 + 0.246308i
\(383\) 1.71822e6 + 2.97604e6i 0.598523 + 1.03667i 0.993039 + 0.117784i \(0.0375789\pi\)
−0.394516 + 0.918889i \(0.629088\pi\)
\(384\) 488301. 0.168989
\(385\) 72554.6 900601.i 0.0249467 0.309657i
\(386\) −2.42395e6 −0.828048
\(387\) 3.20107e6 + 5.54442e6i 1.08647 + 1.88182i
\(388\) −575171. + 996226.i −0.193963 + 0.335953i
\(389\) 2.40526e6 4.16604e6i 0.805914 1.39588i −0.109759 0.993958i \(-0.535008\pi\)
0.915673 0.401925i \(-0.131659\pi\)
\(390\) 83643.1 + 144874.i 0.0278464 + 0.0482313i
\(391\) −257704. −0.0852469
\(392\) 1.06178e6 + 172196.i 0.348994 + 0.0565989i
\(393\) −2.08606e6 −0.681310
\(394\) −621.638 1076.71i −0.000201742 0.000349428i
\(395\) −461473. + 799295.i −0.148817 + 0.257759i
\(396\) −1.71313e6 + 2.96723e6i −0.548975 + 0.950852i
\(397\) 1.64924e6 + 2.85657e6i 0.525180 + 0.909638i 0.999570 + 0.0293232i \(0.00933522\pi\)
−0.474390 + 0.880315i \(0.657331\pi\)
\(398\) 1.63867e6 0.518540
\(399\) 137133. 1.70219e6i 0.0431230 0.535275i
\(400\) −687104. −0.214720
\(401\) −68082.0 117921.i −0.0211432 0.0366211i 0.855260 0.518199i \(-0.173397\pi\)
−0.876403 + 0.481578i \(0.840064\pi\)
\(402\) 1.58666e6 2.74818e6i 0.489689 0.848166i
\(403\) 190064. 329200.i 0.0582957 0.100971i
\(404\) 126924. + 219838.i 0.0386892 + 0.0670116i
\(405\) −4.21054e6 −1.27556
\(406\) −839368. + 398454.i −0.252719 + 0.119967i
\(407\) 3.72054e6 1.11332
\(408\) −229403. 397338.i −0.0682258 0.118171i
\(409\) −1.37435e6 + 2.38044e6i −0.406245 + 0.703637i −0.994466 0.105064i \(-0.966495\pi\)
0.588220 + 0.808701i \(0.299829\pi\)
\(410\) −507270. + 878617.i −0.149032 + 0.258131i
\(411\) −2.79652e6 4.84372e6i −0.816608 1.41441i
\(412\) −2.56918e6 −0.745677
\(413\) −4.41597e6 3.04705e6i −1.27395 0.879032i
\(414\) 2.76520e6 0.792913
\(415\) 235425. + 407767.i 0.0671014 + 0.116223i
\(416\) 34212.4 59257.6i 0.00969282 0.0167884i
\(417\) −1.16640e6 + 2.02026e6i −0.328479 + 0.568942i
\(418\) 293362. + 508118.i 0.0821228 + 0.142241i
\(419\) −1.87219e6 −0.520973 −0.260486 0.965478i \(-0.583883\pi\)
−0.260486 + 0.965478i \(0.583883\pi\)
\(420\) −1.06854e6 737303.i −0.295576 0.203949i
\(421\) 655225. 0.180171 0.0900856 0.995934i \(-0.471286\pi\)
0.0900856 + 0.995934i \(0.471286\pi\)
\(422\) −882677. 1.52884e6i −0.241280 0.417909i
\(423\) 5.44243e6 9.42657e6i 1.47891 2.56155i
\(424\) 169561. 293688.i 0.0458047 0.0793361i
\(425\) 322800. + 559107.i 0.0866886 + 0.150149i
\(426\) −6.92591e6 −1.84907
\(427\) −2.52072e6 + 1.19660e6i −0.669044 + 0.317600i
\(428\) −3.28075e6 −0.865693
\(429\) 330464. + 572380.i 0.0866923 + 0.150155i
\(430\) 416723. 721786.i 0.108687 0.188251i
\(431\) −3.18845e6 + 5.52256e6i −0.826773 + 1.43201i 0.0737832 + 0.997274i \(0.476493\pi\)
−0.900556 + 0.434739i \(0.856841\pi\)
\(432\) 1.53452e6 + 2.65787e6i 0.395606 + 0.685210i
\(433\) 4.80003e6 1.23034 0.615168 0.788396i \(-0.289088\pi\)
0.615168 + 0.788396i \(0.289088\pi\)
\(434\) −236891. + 2.94047e6i −0.0603704 + 0.749362i
\(435\) 1.12141e6 0.284145
\(436\) 900354. + 1.55946e6i 0.226828 + 0.392878i
\(437\) 236761. 410082.i 0.0593071 0.102723i
\(438\) 2.38354e6 4.12841e6i 0.593658 1.02825i
\(439\) 2.79754e6 + 4.84548e6i 0.692811 + 1.19998i 0.970913 + 0.239432i \(0.0769612\pi\)
−0.278102 + 0.960551i \(0.589705\pi\)
\(440\) 446038. 0.109835
\(441\) 3.84893e6 + 1.01387e7i 0.942417 + 2.48248i
\(442\) −64291.7 −0.0156531
\(443\) −2.07005e6 3.58543e6i −0.501154 0.868024i −0.999999 0.00133297i \(-0.999576\pi\)
0.498845 0.866691i \(-0.333758\pi\)
\(444\) 2.67295e6 4.62969e6i 0.643478 1.11454i
\(445\) 252651. 437605.i 0.0604814 0.104757i
\(446\) 530267. + 918449.i 0.126228 + 0.218634i
\(447\) 2.74688e6 0.650237
\(448\) −42641.5 + 529298.i −0.0100378 + 0.124596i
\(449\) −305966. −0.0716239 −0.0358119 0.999359i \(-0.511402\pi\)
−0.0358119 + 0.999359i \(0.511402\pi\)
\(450\) −3.46370e6 5.99930e6i −0.806322 1.39659i
\(451\) −2.00416e6 + 3.47131e6i −0.463971 + 0.803622i
\(452\) 946660. 1.63966e6i 0.217945 0.377493i
\(453\) 795992. + 1.37870e6i 0.182248 + 0.315663i
\(454\) 5.72176e6 1.30284
\(455\) −164342. + 78014.4i −0.0372151 + 0.0176663i
\(456\) 843041. 0.189861
\(457\) −446304. 773021.i −0.0999632 0.173141i 0.811706 0.584066i \(-0.198539\pi\)
−0.911669 + 0.410925i \(0.865206\pi\)
\(458\) −2.51610e6 + 4.35801e6i −0.560485 + 0.970789i
\(459\) 1.44183e6 2.49732e6i 0.319435 0.553278i
\(460\) −179990. 311752.i −0.0396601 0.0686933i
\(461\) −3.01465e6 −0.660670 −0.330335 0.943864i \(-0.607162\pi\)
−0.330335 + 0.943864i \(0.607162\pi\)
\(462\) −4.22169e6 2.91299e6i −0.920198 0.634943i
\(463\) 3.45497e6 0.749017 0.374508 0.927224i \(-0.377812\pi\)
0.374508 + 0.927224i \(0.377812\pi\)
\(464\) −229344. 397235.i −0.0494529 0.0856549i
\(465\) 1.78022e6 3.08342e6i 0.381804 0.661303i
\(466\) 449446. 778464.i 0.0958767 0.166063i
\(467\) −1.41888e6 2.45757e6i −0.301060 0.521451i 0.675316 0.737528i \(-0.264007\pi\)
−0.976376 + 0.216077i \(0.930674\pi\)
\(468\) 689860. 0.145595
\(469\) 2.84036e6 + 1.95987e6i 0.596268 + 0.411429i
\(470\) −1.41702e6 −0.295890
\(471\) −4.17995e6 7.23989e6i −0.868198 1.50376i
\(472\) 1.32431e6 2.29378e6i 0.273612 0.473910i
\(473\) 1.64642e6 2.85169e6i 0.338367 0.586069i
\(474\) 2.61972e6 + 4.53748e6i 0.535561 + 0.927618i
\(475\) −1.18627e6 −0.241240
\(476\) 450731. 213965.i 0.0911800 0.0432839i
\(477\) 3.41903e6 0.688028
\(478\) 2.56386e6 + 4.44073e6i 0.513244 + 0.888965i
\(479\) 2.35221e6 4.07415e6i 0.468422 0.811331i −0.530926 0.847418i \(-0.678156\pi\)
0.999349 + 0.0360866i \(0.0114892\pi\)
\(480\) 320447. 555031.i 0.0634824 0.109955i
\(481\) −374556. 648750.i −0.0738167 0.127854i
\(482\) 2.30450e6 0.451813
\(483\) −332414. + 4.12616e6i −0.0648352 + 0.804783i
\(484\) −814574. −0.158058
\(485\) 754912. + 1.30755e6i 0.145728 + 0.252408i
\(486\) −6.12494e6 + 1.06087e7i −1.17628 + 2.03738i
\(487\) −2.08317e6 + 3.60816e6i −0.398018 + 0.689387i −0.993481 0.113995i \(-0.963635\pi\)
0.595463 + 0.803383i \(0.296969\pi\)
\(488\) −688745. 1.19294e6i −0.130921 0.226762i
\(489\) −1.86811e7 −3.53290
\(490\) 892518. 1.09387e6i 0.167929 0.205815i
\(491\) 1.57876e6 0.295537 0.147768 0.989022i \(-0.452791\pi\)
0.147768 + 0.989022i \(0.452791\pi\)
\(492\) 2.87970e6 + 4.98779e6i 0.536333 + 0.928956i
\(493\) −215491. + 373241.i −0.0399311 + 0.0691627i
\(494\) 59067.0 102307.i 0.0108900 0.0188620i
\(495\) 2.24848e6 + 3.89449e6i 0.412455 + 0.714393i
\(496\) −1.45632e6 −0.265798
\(497\) 604815. 7.50741e6i 0.109833 1.36332i
\(498\) 2.67294e6 0.482966
\(499\) −778559. 1.34850e6i −0.139972 0.242438i 0.787514 0.616297i \(-0.211368\pi\)
−0.927486 + 0.373859i \(0.878034\pi\)
\(500\) −975912. + 1.69033e6i −0.174576 + 0.302375i
\(501\) 4.38107e6 7.58824e6i 0.779806 1.35066i
\(502\) −1.21808e6 2.10978e6i −0.215733 0.373660i
\(503\) −1.19459e6 −0.210523 −0.105261 0.994445i \(-0.533568\pi\)
−0.105261 + 0.994445i \(0.533568\pi\)
\(504\) −4.83641e6 + 2.29588e6i −0.848099 + 0.402599i
\(505\) 333175. 0.0581358
\(506\) −711118. 1.23169e6i −0.123471 0.213858i
\(507\) −5.46638e6 + 9.46805e6i −0.944452 + 1.63584i
\(508\) 1.96156e6 3.39752e6i 0.337242 0.584121i
\(509\) −1.58428e6 2.74406e6i −0.271043 0.469461i 0.698086 0.716014i \(-0.254035\pi\)
−0.969129 + 0.246553i \(0.920702\pi\)
\(510\) −602183. −0.102519
\(511\) 4.26688e6 + 2.94418e6i 0.722867 + 0.498783i
\(512\) −262144. −0.0441942
\(513\) 2.64932e6 + 4.58875e6i 0.444468 + 0.769841i
\(514\) 2.06134e6 3.57034e6i 0.344145 0.596077i
\(515\) −1.68602e6 + 2.92028e6i −0.280121 + 0.485183i
\(516\) −2.36568e6 4.09747e6i −0.391139 0.677473i
\(517\) −5.59846e6 −0.921175
\(518\) 4.78497e6 + 3.30166e6i 0.783529 + 0.540640i
\(519\) −2.12853e7 −3.46865
\(520\) −44903.7 77775.6i −0.00728239 0.0126135i
\(521\) 503289. 871722.i 0.0812312 0.140697i −0.822548 0.568696i \(-0.807448\pi\)
0.903779 + 0.427999i \(0.140781\pi\)
\(522\) 2.31225e6 4.00493e6i 0.371414 0.643307i
\(523\) −4.39493e6 7.61224e6i −0.702583 1.21691i −0.967557 0.252653i \(-0.918697\pi\)
0.264974 0.964255i \(-0.414637\pi\)
\(524\) 1.11990e6 0.178177
\(525\) 9.36840e6 4.44725e6i 1.48343 0.704196i
\(526\) 3.64234e6 0.574006
\(527\) 684175. + 1.18503e6i 0.107310 + 0.185867i
\(528\) 1.26605e6 2.19286e6i 0.197636 0.342315i
\(529\) 2.64426e6 4.57999e6i 0.410832 0.711582i
\(530\) −222548. 385465.i −0.0344140 0.0596067i
\(531\) 2.67035e7 4.10990
\(532\) −73619.7 + 913823.i −0.0112776 + 0.139985i
\(533\) 807055. 0.123051
\(534\) −1.43427e6 2.48422e6i −0.217659 0.376996i
\(535\) −2.15299e6 + 3.72909e6i −0.325206 + 0.563273i
\(536\) −851800. + 1.47536e6i −0.128064 + 0.221813i
\(537\) 8.64376e6 + 1.49714e7i 1.29350 + 2.24041i
\(538\) −5.68399e6 −0.846638
\(539\) 3.52623e6 4.32176e6i 0.522804 0.640749i
\(540\) 4.02811e6 0.594453
\(541\) 1.77432e6 + 3.07321e6i 0.260639 + 0.451439i 0.966412 0.256999i \(-0.0827336\pi\)
−0.705773 + 0.708438i \(0.749400\pi\)
\(542\) −595059. + 1.03067e6i −0.0870086 + 0.150703i
\(543\) −4.59043e6 + 7.95086e6i −0.668119 + 1.15722i
\(544\) 123155. + 213310.i 0.0178424 + 0.0309040i
\(545\) 2.36343e6 0.340841
\(546\) −82930.3 + 1.02939e6i −0.0119051 + 0.147774i
\(547\) 4.68179e6 0.669027 0.334513 0.942391i \(-0.391428\pi\)
0.334513 + 0.942391i \(0.391428\pi\)
\(548\) 1.50131e6 + 2.60035e6i 0.213560 + 0.369896i
\(549\) 6.94394e6 1.20273e7i 0.983276 1.70308i
\(550\) −1.78150e6 + 3.08564e6i −0.251118 + 0.434950i
\(551\) −395957. 685818.i −0.0555609 0.0962343i
\(552\) −2.04355e6 −0.285456
\(553\) −5.14722e6 + 2.44342e6i −0.715747 + 0.339771i
\(554\) −3.39845e6 −0.470442
\(555\) −3.50825e6 6.07647e6i −0.483457 0.837372i
\(556\) 626181. 1.08458e6i 0.0859040 0.148790i
\(557\) −2.89754e6 + 5.01868e6i −0.395723 + 0.685412i −0.993193 0.116479i \(-0.962839\pi\)
0.597470 + 0.801891i \(0.296173\pi\)
\(558\) −7.34130e6 1.27155e7i −0.998132 1.72881i
\(559\) −662997. −0.0897392
\(560\) 573647. + 395821.i 0.0772992 + 0.0533370i
\(561\) −2.37915e6 −0.319165
\(562\) −15361.0 26606.0i −0.00205153 0.00355336i
\(563\) 3.79852e6 6.57922e6i 0.505060 0.874789i −0.494923 0.868937i \(-0.664804\pi\)
0.999983 0.00585257i \(-0.00186294\pi\)
\(564\) −4.02210e6 + 6.96648e6i −0.532421 + 0.922180i
\(565\) −1.24249e6 2.15206e6i −0.163747 0.283617i
\(566\) 3.94147e6 0.517151
\(567\) −2.13946e7 1.47624e7i −2.79477 1.92841i
\(568\) 3.71817e6 0.483569
\(569\) 4.90850e6 + 8.50176e6i 0.635576 + 1.10085i 0.986393 + 0.164406i \(0.0525708\pi\)
−0.350816 + 0.936444i \(0.614096\pi\)
\(570\) 553246. 958250.i 0.0713232 0.123535i
\(571\) −2.62944e6 + 4.55432e6i −0.337499 + 0.584566i −0.983962 0.178380i \(-0.942914\pi\)
0.646462 + 0.762946i \(0.276248\pi\)
\(572\) −177409. 307282.i −0.0226718 0.0392687i
\(573\) 6.04384e6 0.769000
\(574\) −5.65803e6 + 2.68591e6i −0.716779 + 0.340261i
\(575\) 2.87555e6 0.362703
\(576\) −1.32147e6 2.28885e6i −0.165959 0.287450i
\(577\) −4.31734e6 + 7.47785e6i −0.539855 + 0.935056i 0.459057 + 0.888407i \(0.348187\pi\)
−0.998911 + 0.0466486i \(0.985146\pi\)
\(578\) −2.72400e6 + 4.71810e6i −0.339146 + 0.587419i
\(579\) 9.03028e6 + 1.56409e7i 1.11945 + 1.93895i
\(580\) −602027. −0.0743098
\(581\) −233418. + 2.89736e6i −0.0286876 + 0.356092i
\(582\) 8.57106e6 1.04888
\(583\) −879261. 1.52292e6i −0.107139 0.185570i
\(584\) −1.27960e6 + 2.21633e6i −0.155254 + 0.268908i
\(585\) 452720. 784135.i 0.0546941 0.0947329i
\(586\) −4.33869e6 7.51483e6i −0.521932 0.904014i
\(587\) −3.32014e6 −0.397705 −0.198852 0.980029i \(-0.563721\pi\)
−0.198852 + 0.980029i \(0.563721\pi\)
\(588\) −2.84446e6 7.49277e6i −0.339279 0.893715i
\(589\) −2.51430e6 −0.298627
\(590\) −1.73816e6 3.01058e6i −0.205570 0.356058i
\(591\) −4631.75 + 8022.43i −0.000545477 + 0.000944794i
\(592\) −1.43497e6 + 2.48545e6i −0.168283 + 0.291474i
\(593\) 3.20001e6 + 5.54257e6i 0.373692 + 0.647254i 0.990130 0.140149i \(-0.0447583\pi\)
−0.616438 + 0.787403i \(0.711425\pi\)
\(594\) 1.59146e7 1.85067
\(595\) 52586.4 652741.i 0.00608949 0.0755873i
\(596\) −1.47466e6 −0.170050
\(597\) −6.10475e6 1.05737e7i −0.701022 1.21421i
\(598\) −143180. + 247995.i −0.0163730 + 0.0283589i
\(599\) −3.74931e6 + 6.49400e6i −0.426957 + 0.739512i −0.996601 0.0823800i \(-0.973748\pi\)
0.569644 + 0.821892i \(0.307081\pi\)
\(600\) 2.55976e6 + 4.43364e6i 0.290283 + 0.502785i
\(601\) −227052. −0.0256412 −0.0128206 0.999918i \(-0.504081\pi\)
−0.0128206 + 0.999918i \(0.504081\pi\)
\(602\) 4.64808e6 2.20648e6i 0.522736 0.248147i
\(603\) −1.71757e7 −1.92363
\(604\) −427328. 740153.i −0.0476616 0.0825523i
\(605\) −534564. + 925892.i −0.0593761 + 0.102842i
\(606\) 945693. 1.63799e6i 0.104609 0.181188i
\(607\) −8.15183e6 1.41194e7i −0.898015 1.55541i −0.830029 0.557721i \(-0.811676\pi\)
−0.0679862 0.997686i \(-0.521657\pi\)
\(608\) −452586. −0.0496527
\(609\) 5.69810e6 + 3.93173e6i 0.622568 + 0.429576i
\(610\) −1.80796e6 −0.196727
\(611\) 563610. + 976202.i 0.0610767 + 0.105788i
\(612\) −1.24165e6 + 2.15060e6i −0.134005 + 0.232103i
\(613\) 5.20312e6 9.01207e6i 0.559259 0.968664i −0.438300 0.898829i \(-0.644419\pi\)
0.997559 0.0698355i \(-0.0222474\pi\)
\(614\) −2.78186e6 4.81833e6i −0.297793 0.515793i
\(615\) 7.55921e6 0.805914
\(616\) 2.26641e6 + 1.56384e6i 0.240651 + 0.166050i
\(617\) 4.74140e6 0.501411 0.250705 0.968063i \(-0.419337\pi\)
0.250705 + 0.968063i \(0.419337\pi\)
\(618\) 9.57131e6 + 1.65780e7i 1.00809 + 1.74607i
\(619\) 5.42668e6 9.39929e6i 0.569256 0.985981i −0.427383 0.904070i \(-0.640565\pi\)
0.996640 0.0819103i \(-0.0261021\pi\)
\(620\) −955708. + 1.65533e6i −0.0998495 + 0.172944i
\(621\) −6.42202e6 1.11233e7i −0.668255 1.15745i
\(622\) −8.15177e6 −0.844843
\(623\) 2.81804e6 1.33775e6i 0.290889 0.138087i
\(624\) −509824. −0.0524154
\(625\) −2.91287e6 5.04523e6i −0.298277 0.516632i
\(626\) −2.33915e6 + 4.05154e6i −0.238574 + 0.413222i
\(627\) 2.18581e6 3.78593e6i 0.222046 0.384595i
\(628\) 2.24400e6 + 3.88673e6i 0.227052 + 0.393265i
\(629\) 2.69659e6 0.271762
\(630\) −564260. + 7.00401e6i −0.0566406 + 0.703065i
\(631\) 1.58978e7 1.58951 0.794757 0.606928i \(-0.207598\pi\)
0.794757 + 0.606928i \(0.207598\pi\)
\(632\) −1.40639e6 2.43595e6i −0.140060 0.242591i
\(633\) −6.57672e6 + 1.13912e7i −0.652379 + 1.12995i
\(634\) 1.60227e6 2.77522e6i 0.158312 0.274204i
\(635\) −2.57455e6 4.45925e6i −0.253377 0.438861i
\(636\) −2.52675e6 −0.247696
\(637\) −1.10858e6 179786.i −0.108247 0.0175553i
\(638\) −2.37854e6 −0.231344
\(639\) 1.87433e7 + 3.24644e7i 1.81591 + 3.14525i
\(640\) −172032. + 297968.i −0.0166020 + 0.0287554i
\(641\) −5.59139e6 + 9.68457e6i −0.537496 + 0.930970i 0.461543 + 0.887118i \(0.347296\pi\)
−0.999038 + 0.0438515i \(0.986037\pi\)
\(642\) 1.22222e7 + 2.11695e7i 1.17034 + 2.02709i
\(643\) 1.55983e6 0.148782 0.0743909 0.997229i \(-0.476299\pi\)
0.0743909 + 0.997229i \(0.476299\pi\)
\(644\) 178456. 2.21513e6i 0.0169557 0.210467i
\(645\) −6.20991e6 −0.587741
\(646\) 212624. + 368276.i 0.0200462 + 0.0347210i
\(647\) 7.74118e6 1.34081e7i 0.727020 1.25924i −0.231117 0.972926i \(-0.574238\pi\)
0.958137 0.286310i \(-0.0924286\pi\)
\(648\) 6.41606e6 1.11129e7i 0.600248 1.03966i
\(649\) −6.86726e6 1.18944e7i −0.639988 1.10849i
\(650\) 717391. 0.0665997
\(651\) 1.98563e7 9.42595e6i 1.83631 0.871711i
\(652\) 1.00290e7 0.923925
\(653\) −307376. 532391.i −0.0282090 0.0488593i 0.851576 0.524231i \(-0.175647\pi\)
−0.879785 + 0.475371i \(0.842314\pi\)
\(654\) 6.70843e6 1.16193e7i 0.613305 1.06228i
\(655\) 734934. 1.27294e6i 0.0669337 0.115933i
\(656\) −1.54597e6 2.67769e6i −0.140262 0.242941i
\(657\) −2.58019e7 −2.33205
\(658\) −7.20015e6 4.96815e6i −0.648301 0.447332i
\(659\) −1.32697e7 −1.19028 −0.595139 0.803623i \(-0.702903\pi\)
−0.595139 + 0.803623i \(0.702903\pi\)
\(660\) −1.66169e6 2.87813e6i −0.148487 0.257188i
\(661\) −2.51792e6 + 4.36116e6i −0.224150 + 0.388238i −0.956064 0.293158i \(-0.905294\pi\)
0.731914 + 0.681397i \(0.238627\pi\)
\(662\) 5.29902e6 9.17817e6i 0.469949 0.813975i
\(663\) 239515. + 414852.i 0.0211616 + 0.0366530i
\(664\) −1.43497e6 −0.126306
\(665\) 990391. + 683377.i 0.0868466 + 0.0599247i
\(666\) −2.89348e7 −2.52776
\(667\) 959811. + 1.66244e6i 0.0835355 + 0.144688i
\(668\) −2.35198e6 + 4.07375e6i −0.203935 + 0.353226i
\(669\) 3.95095e6 6.84325e6i 0.341300 0.591149i
\(670\) 1.11799e6 + 1.93641e6i 0.0962166 + 0.166652i
\(671\) −7.14301e6 −0.612457
\(672\) 3.57423e6 1.69672e6i 0.305323 0.144939i
\(673\) 8.28068e6 0.704739 0.352369 0.935861i \(-0.385376\pi\)
0.352369 + 0.935861i \(0.385376\pi\)
\(674\) −6.80112e6 1.17799e7i −0.576675 0.998830i
\(675\) −1.60885e7 + 2.78661e7i −1.35911 + 2.35405i
\(676\) 2.93462e6 5.08292e6i 0.246994 0.427805i
\(677\) 7.62563e6 + 1.32080e7i 0.639446 + 1.10755i 0.985554 + 0.169359i \(0.0541698\pi\)
−0.346108 + 0.938195i \(0.612497\pi\)
\(678\) −1.41069e7 −1.17857
\(679\) −748480. + 9.29068e6i −0.0623025 + 0.773345i
\(680\) 323282. 0.0268107
\(681\) −2.13161e7 3.69205e7i −1.76132 3.05070i
\(682\) −3.77588e6 + 6.54002e6i −0.310855 + 0.538416i
\(683\) −3.94337e6 + 6.83011e6i −0.323456 + 0.560243i −0.981199 0.193000i \(-0.938178\pi\)
0.657743 + 0.753243i \(0.271511\pi\)
\(684\) −2.28149e6 3.95166e6i −0.186457 0.322953i
\(685\) 3.94094e6 0.320903
\(686\) 8.37025e6 2.42896e6i 0.679091 0.197065i
\(687\) 3.74943e7 3.03091
\(688\) 1.27001e6 + 2.19973e6i 0.102291 + 0.177173i
\(689\) −177035. + 306633.i −0.0142073 + 0.0246077i
\(690\) −1.34108e6 + 2.32282e6i −0.107234 + 0.185735i
\(691\) 830950. + 1.43925e6i 0.0662033 + 0.114667i 0.897227 0.441569i \(-0.145578\pi\)
−0.831024 + 0.556237i \(0.812245\pi\)
\(692\) 1.14270e7 0.907124
\(693\) −2.22932e6 + 2.76720e7i −0.176336 + 2.18881i
\(694\) 2.47084e6 0.194736
\(695\) −821863. 1.42351e6i −0.0645413 0.111789i
\(696\) −1.70881e6 + 2.95975e6i −0.133712 + 0.231596i
\(697\) −1.45258e6 + 2.51595e6i −0.113256 + 0.196164i
\(698\) 5.41078e6 + 9.37175e6i 0.420360 + 0.728085i
\(699\) −6.69754e6 −0.518469
\(700\) −5.02942e6 + 2.38751e6i −0.387947 + 0.184162i
\(701\) −1.39364e7 −1.07117 −0.535583 0.844483i \(-0.679908\pi\)
−0.535583 + 0.844483i \(0.679908\pi\)
\(702\) −1.60216e6 2.77502e6i −0.122705 0.212532i
\(703\) −2.47745e6 + 4.29107e6i −0.189068 + 0.327475i
\(704\) −679677. + 1.17724e6i −0.0516858 + 0.0895224i
\(705\) 5.27901e6 + 9.14351e6i 0.400018 + 0.692851i
\(706\) 1.27226e7 0.960646
\(707\) 1.69293e6 + 1.16813e6i 0.127377 + 0.0878908i
\(708\) −1.97346e7 −1.47960
\(709\) 5.09368e6 + 8.82252e6i 0.380554 + 0.659139i 0.991142 0.132810i \(-0.0424000\pi\)
−0.610587 + 0.791949i \(0.709067\pi\)
\(710\) 2.44005e6 4.22629e6i 0.181657 0.314640i
\(711\) 1.41793e7 2.45592e7i 1.05191 1.82197i
\(712\) 769985. + 1.33365e6i 0.0569223 + 0.0985923i
\(713\) 6.09473e6 0.448984
\(714\) −3.05981e6 2.11129e6i −0.224620 0.154990i
\(715\) −465699. −0.0340675
\(716\) −4.64040e6 8.03740e6i −0.338277 0.585913i
\(717\) 1.91030e7 3.30874e7i 1.38773 2.40361i
\(718\) −8.91940e6 + 1.54489e7i −0.645691 + 1.11837i
\(719\) −6.95844e6 1.20524e7i −0.501983 0.869461i −0.999997 0.00229184i \(-0.999270\pi\)
0.498014 0.867169i \(-0.334063\pi\)
\(720\) −3.46886e6 −0.249376
\(721\) −1.88057e7 + 8.92721e6i −1.34726 + 0.639555i
\(722\) 9.12301e6 0.651321
\(723\) −8.58527e6 1.48701e7i −0.610813 1.05796i
\(724\) 2.46437e6 4.26841e6i 0.174727 0.302636i
\(725\) 2.40452e6 4.16476e6i 0.169896 0.294269i
\(726\) 3.03464e6 + 5.25616e6i 0.213681 + 0.370107i
\(727\) 3.42063e6 0.240033 0.120016 0.992772i \(-0.461705\pi\)
0.120016 + 0.992772i \(0.461705\pi\)
\(728\) 44521.1 552629.i 0.00311342 0.0386461i
\(729\) 4.25504e7 2.96541
\(730\) 1.67948e6 + 2.90894e6i 0.116645 + 0.202035i
\(731\) 1.19330e6 2.06686e6i 0.0825955 0.143060i
\(732\) −5.13176e6 + 8.88846e6i −0.353988 + 0.613125i
\(733\) 5.15810e6 + 8.93410e6i 0.354593 + 0.614173i 0.987048 0.160424i \(-0.0512861\pi\)
−0.632455 + 0.774597i \(0.717953\pi\)
\(734\) −1.84499e6 −0.126402
\(735\) −1.03834e7 1.68395e6i −0.708959 0.114977i
\(736\) 1.09708e6 0.0746525
\(737\) 4.41703e6 + 7.65052e6i 0.299545 + 0.518827i
\(738\) 1.55864e7 2.69965e7i 1.05343 1.82460i
\(739\) 5.19448e6 8.99710e6i 0.349889 0.606026i −0.636340 0.771409i \(-0.719553\pi\)
0.986229 + 0.165383i \(0.0528859\pi\)
\(740\) 1.88340e6 + 3.26215e6i 0.126434 + 0.218990i
\(741\) −880202. −0.0588893
\(742\) 220652. 2.73889e6i 0.0147129 0.182627i
\(743\) −1.04738e7 −0.696035 −0.348018 0.937488i \(-0.613145\pi\)
−0.348018 + 0.937488i \(0.613145\pi\)
\(744\) 5.42542e6 + 9.39710e6i 0.359336 + 0.622388i
\(745\) −967748. + 1.67619e6i −0.0638810 + 0.110645i
\(746\) 6.83908e6 1.18456e7i 0.449936 0.779312i
\(747\) −7.23369e6 1.25291e7i −0.474306 0.821522i
\(748\) 1.27725e6 0.0834681
\(749\) −2.40142e7 + 1.13997e7i −1.56410 + 0.742490i
\(750\) 1.45428e7 0.944050
\(751\) 4.70223e6 + 8.14449e6i 0.304231 + 0.526944i 0.977090 0.212827i \(-0.0682671\pi\)
−0.672859 + 0.739771i \(0.734934\pi\)
\(752\) 2.15926e6 3.73995e6i 0.139239 0.241169i
\(753\) −9.07576e6 + 1.57197e7i −0.583305 + 1.01031i
\(754\) 239453. + 414745.i 0.0153388 + 0.0265676i
\(755\) −1.12174e6 −0.0716181
\(756\) 2.04677e7 + 1.41228e7i 1.30246 + 0.898705i
\(757\) −1.33677e7 −0.847848 −0.423924 0.905698i \(-0.639348\pi\)
−0.423924 + 0.905698i \(0.639348\pi\)
\(758\) 32711.2 + 56657.5i 0.00206787 + 0.00358166i
\(759\) −5.29845e6 + 9.17719e6i −0.333845 + 0.578236i
\(760\) −297010. + 514436.i −0.0186525 + 0.0323071i
\(761\) 1.11312e7 + 1.92797e7i 0.696752 + 1.20681i 0.969586 + 0.244749i \(0.0787057\pi\)
−0.272834 + 0.962061i \(0.587961\pi\)
\(762\) −2.92307e7 −1.82369
\(763\) 1.20091e7 + 8.28634e6i 0.746789 + 0.515289i
\(764\) −3.24463e6 −0.201109
\(765\) 1.62966e6 + 2.82266e6i 0.100680 + 0.174383i
\(766\) −6.87287e6 + 1.19042e7i −0.423220 + 0.733038i
\(767\) −1.38269e6 + 2.39488e6i −0.0848664 + 0.146993i
\(768\) 976601. + 1.69152e6i 0.0597467 + 0.103484i
\(769\) 9.65833e6 0.588961 0.294480 0.955658i \(-0.404853\pi\)
0.294480 + 0.955658i \(0.404853\pi\)
\(770\) 3.26488e6 1.54987e6i 0.198445 0.0942035i
\(771\) −3.07176e7 −1.86102
\(772\) −4.84790e6 8.39681e6i −0.292759 0.507074i
\(773\) 2.55476e6 4.42497e6i 0.153780 0.266355i −0.778834 0.627230i \(-0.784189\pi\)
0.932614 + 0.360875i \(0.117522\pi\)
\(774\) −1.28043e7 + 2.21777e7i −0.768251 + 1.33065i
\(775\) −7.63428e6 1.32230e7i −0.456577 0.790815i
\(776\) −4.60137e6 −0.274305
\(777\) 3.47835e6 4.31759e7i 0.206691 2.56560i
\(778\) 1.92421e7 1.13973
\(779\) −2.66908e6 4.62298e6i −0.157586 0.272947i
\(780\) −334572. + 579496.i −0.0196904 + 0.0341047i
\(781\) 9.64034e6 1.66976e7i 0.565542 0.979548i
\(782\) −515407. 892711.i −0.0301393 0.0522028i
\(783\) −2.14802e7 −1.25209
\(784\) 1.52705e6 + 4.02249e6i 0.0887283 + 0.233725i
\(785\) 5.89051e6 0.341176
\(786\) −4.17212e6 7.22632e6i −0.240880 0.417216i
\(787\) −1.25796e7 + 2.17885e7i −0.723984 + 1.25398i 0.235406 + 0.971897i \(0.424358\pi\)
−0.959391 + 0.282081i \(0.908975\pi\)
\(788\) 2486.55 4306.84i 0.000142653 0.000247083i
\(789\) −1.35693e7 2.35028e7i −0.776007 1.34408i
\(790\) −3.69178e6 −0.210460
\(791\) 1.23190e6 1.52913e7i 0.0700060 0.868966i
\(792\) −1.37050e7 −0.776367
\(793\) 719105. + 1.24553e6i 0.0406078 + 0.0703347i
\(794\) −6.59696e6 + 1.14263e7i −0.371358 + 0.643211i
\(795\) −1.65818e6 + 2.87205e6i −0.0930495 + 0.161166i
\(796\) 3.27733e6 + 5.67650e6i 0.183332 + 0.317540i
\(797\) −3.35976e6 −0.187354 −0.0936768 0.995603i \(-0.529862\pi\)
−0.0936768 + 0.995603i \(0.529862\pi\)
\(798\) 6.17084e6 2.92935e6i 0.343034 0.162841i
\(799\) −4.05767e6 −0.224859
\(800\) −1.37421e6 2.38020e6i −0.0759150 0.131489i
\(801\) −7.76300e6 + 1.34459e7i −0.427512 + 0.740473i
\(802\) 272328. 471686.i 0.0149505 0.0258951i
\(803\) 6.63540e6 + 1.14929e7i 0.363144 + 0.628983i
\(804\) 1.26933e7 0.692524
\(805\) −2.40073e6 1.65652e6i −0.130573 0.0900964i
\(806\) 1.52051e6 0.0824426
\(807\) 2.11754e7 + 3.66768e7i 1.14458 + 1.98247i
\(808\) −507695. + 879353.i −0.0273574 + 0.0473844i
\(809\) 1.48525e7 2.57253e7i 0.797862 1.38194i −0.123143 0.992389i \(-0.539297\pi\)
0.921006 0.389549i \(-0.127369\pi\)
\(810\) −8.42108e6 1.45857e7i −0.450978 0.781117i
\(811\) 1.26386e7 0.674757 0.337379 0.941369i \(-0.390460\pi\)
0.337379 + 0.941369i \(0.390460\pi\)
\(812\) −3.05902e6 2.11075e6i −0.162814 0.112343i
\(813\) 8.86743e6 0.470513
\(814\) 7.44109e6 + 1.28883e7i 0.393619 + 0.681767i
\(815\) 6.58150e6 1.13995e7i 0.347081 0.601162i
\(816\) 917612. 1.58935e6i 0.0482429 0.0835592i
\(817\) 2.19265e6 + 3.79779e6i 0.114925 + 0.199056i
\(818\) −1.09948e7 −0.574517
\(819\) 5.04959e6 2.39708e6i 0.263055 0.124874i
\(820\) −4.05816e6 −0.210763
\(821\) 1.30880e7 + 2.26691e7i 0.677666 + 1.17375i 0.975682 + 0.219190i \(0.0703416\pi\)
−0.298017 + 0.954561i \(0.596325\pi\)
\(822\) 1.11861e7 1.93749e7i 0.577429 1.00014i
\(823\) 3.64922e6 6.32063e6i 0.187802 0.325283i −0.756715 0.653745i \(-0.773197\pi\)
0.944517 + 0.328462i \(0.106530\pi\)
\(824\) −5.13835e6 8.89989e6i −0.263637 0.456632i
\(825\) 2.65474e7 1.35796
\(826\) 1.72335e6 2.13915e7i 0.0878867 1.09091i
\(827\) 1.18681e7 0.603418 0.301709 0.953400i \(-0.402443\pi\)
0.301709 + 0.953400i \(0.402443\pi\)
\(828\) 5.53040e6 + 9.57893e6i 0.280337 + 0.485558i
\(829\) 5.21689e6 9.03593e6i 0.263649 0.456653i −0.703560 0.710636i \(-0.748407\pi\)
0.967209 + 0.253983i \(0.0817407\pi\)
\(830\) −941698. + 1.63107e6i −0.0474479 + 0.0821821i
\(831\) 1.26607e7 + 2.19290e7i 0.635997 + 1.10158i
\(832\) 273699. 0.0137077
\(833\) 2.55576e6 3.13234e6i 0.127617 0.156407i
\(834\) −9.33120e6 −0.464539
\(835\) 3.08697e6 + 5.34679e6i 0.153220 + 0.265385i
\(836\) −1.17345e6 + 2.03247e6i −0.0580696 + 0.100579i
\(837\) −3.40995e7 + 5.90621e7i −1.68242 + 2.91404i
\(838\) −3.74438e6 6.48546e6i −0.184192 0.319029i
\(839\) −2.91444e7 −1.42939 −0.714695 0.699436i \(-0.753435\pi\)
−0.714695 + 0.699436i \(0.753435\pi\)
\(840\) 417003. 5.17615e6i 0.0203911 0.253110i
\(841\) −1.73008e7 −0.843482
\(842\) 1.31045e6 + 2.26977e6i 0.0637001 + 0.110332i
\(843\) −114453. + 198238.i −0.00554699 + 0.00960767i
\(844\) 3.53071e6 6.11537e6i 0.170610 0.295506i
\(845\) −3.85169e6 6.67133e6i −0.185571 0.321418i
\(846\) 4.35395e7 2.09150
\(847\) −5.96247e6 + 2.83043e6i −0.285573 + 0.135564i
\(848\) 1.35648e6 0.0647777
\(849\) −1.46837e7 2.54329e7i −0.699144 1.21095i
\(850\) −1.29120e6 + 2.23643e6i −0.0612981 + 0.106171i
\(851\) 6.00541e6 1.04017e7i 0.284262 0.492356i
\(852\) −1.38518e7 2.39921e7i −0.653745 1.13232i
\(853\) 2.63032e7 1.23776 0.618879 0.785487i \(-0.287587\pi\)
0.618879 + 0.785487i \(0.287587\pi\)
\(854\) −9.18660e6 6.33881e6i −0.431032 0.297415i
\(855\) −5.98892e6 −0.280177
\(856\) −6.56150e6 1.13649e7i −0.306069 0.530127i
\(857\) −1.71799e6 + 2.97565e6i −0.0799040 + 0.138398i −0.903208 0.429202i \(-0.858795\pi\)
0.823304 + 0.567600i \(0.192128\pi\)
\(858\) −1.32185e6 + 2.28952e6i −0.0613007 + 0.106176i
\(859\) −5.45696e6 9.45173e6i −0.252329 0.437047i 0.711837 0.702344i \(-0.247863\pi\)
−0.964167 + 0.265297i \(0.914530\pi\)
\(860\) 3.33378e6 0.153706
\(861\) 3.84099e7 + 2.65031e7i 1.76577 + 1.21840i
\(862\) −2.55076e7 −1.16923
\(863\) −1.09529e7 1.89710e7i −0.500614 0.867088i −1.00000 0.000708873i \(-0.999774\pi\)
0.499386 0.866380i \(-0.333559\pi\)
\(864\) −6.13808e6 + 1.06315e7i −0.279736 + 0.484517i
\(865\) 7.49896e6 1.29886e7i 0.340770 0.590230i
\(866\) 9.60005e6 + 1.66278e7i 0.434990 + 0.753424i
\(867\) 4.05923e7 1.83399
\(868\) −1.06599e7 + 5.06032e6i −0.480233 + 0.227970i
\(869\) −1.45858e7 −0.655210
\(870\) 2.24282e6 + 3.88467e6i 0.100460 + 0.174003i
\(871\) 889347. 1.54039e6i 0.0397215 0.0687997i
\(872\) −3.60142e6 + 6.23784e6i −0.160392 + 0.277807i
\(873\) −2.31956e7 4.01759e7i −1.03008 1.78414i
\(874\) 1.89409e6 0.0838729
\(875\) −1.26997e6 + 1.57638e7i −0.0560755 + 0.696051i
\(876\) 1.90683e7 0.839560
\(877\) −3.23464e6 5.60256e6i −0.142012 0.245973i 0.786242 0.617919i \(-0.212024\pi\)
−0.928254 + 0.371946i \(0.878691\pi\)
\(878\) −1.11902e7 + 1.93819e7i −0.489891 + 0.848516i
\(879\) −3.23270e7 + 5.59920e7i −1.41122 + 2.44430i
\(880\) 892076. + 1.54512e6i 0.0388325 + 0.0672599i
\(881\) 2.03983e7 0.885430 0.442715 0.896662i \(-0.354015\pi\)
0.442715 + 0.896662i \(0.354015\pi\)
\(882\) −2.74236e7 + 3.36105e7i −1.18701 + 1.45480i
\(883\) 1.62381e7 0.700862 0.350431 0.936589i \(-0.386035\pi\)
0.350431 + 0.936589i \(0.386035\pi\)
\(884\) −128583. 222713.i −0.00553419 0.00958550i
\(885\) −1.29508e7 + 2.24315e7i −0.555826 + 0.962720i
\(886\) 8.28019e6 1.43417e7i 0.354369 0.613786i
\(887\) 3.39513e6 + 5.88055e6i 0.144893 + 0.250962i 0.929333 0.369242i \(-0.120383\pi\)
−0.784440 + 0.620205i \(0.787049\pi\)
\(888\) 2.13836e7 0.910015
\(889\) 2.55261e6 3.16849e7i 0.108325 1.34461i
\(890\) 2.02121e6 0.0855336
\(891\) −3.32706e7 5.76265e7i −1.40400 2.43180i
\(892\) −2.12107e6 + 3.67380e6i −0.0892570 + 0.154598i
\(893\) 3.72792e6 6.45696e6i 0.156437 0.270956i
\(894\) 5.49377e6 + 9.51548e6i 0.229893 + 0.398187i
\(895\) −1.21810e7 −0.508308
\(896\) −1.91883e6 + 910881.i −0.0798482 + 0.0379046i
\(897\) 2.13363e6 0.0885398
\(898\) −611933. 1.05990e6i −0.0253229 0.0438605i
\(899\) 5.09639e6 8.82721e6i 0.210312 0.364271i
\(900\) 1.38548e7 2.39972e7i 0.570156 0.987539i
\(901\) −637275. 1.10379e6i −0.0261526 0.0452976i
\(902\) −1.60333e7 −0.656155
\(903\) −3.15538e7 2.17723e7i −1.28775 0.888557i
\(904\) 7.57328e6 0.308221
\(905\) −3.23449e6 5.60229e6i −0.131276 0.227376i
\(906\) −3.18397e6 + 5.51479e6i −0.128869 + 0.223207i
\(907\) −1.71071e7 + 2.96304e7i −0.690492 + 1.19597i 0.281185 + 0.959654i \(0.409273\pi\)
−0.971677 + 0.236313i \(0.924061\pi\)
\(908\) 1.14435e7 + 1.98207e7i 0.460622 + 0.797821i
\(909\) −1.02372e7 −0.410932
\(910\) −598933. 413268.i −0.0239759 0.0165435i
\(911\) −4.47390e6 −0.178604 −0.0893019 0.996005i \(-0.528464\pi\)
−0.0893019 + 0.996005i \(0.528464\pi\)
\(912\) 1.68608e6 + 2.92038e6i 0.0671262 + 0.116266i
\(913\) −3.72053e6 + 6.44415e6i −0.147716 + 0.255852i
\(914\) 1.78522e6 3.09208e6i 0.0706846 0.122429i
\(915\) 6.73543e6 + 1.16661e7i 0.265958 + 0.460652i
\(916\) −2.01288e7 −0.792646
\(917\) 8.19737e6 3.89136e6i 0.321922 0.152819i
\(918\) 1.15346e7 0.451749
\(919\) 268950. + 465835.i 0.0105047 + 0.0181946i 0.871230 0.490875i \(-0.163323\pi\)
−0.860725 + 0.509070i \(0.829990\pi\)
\(920\) 719960. 1.24701e6i 0.0280439 0.0485735i
\(921\) −2.07273e7 + 3.59008e7i −0.805182 + 1.39462i
\(922\) −6.02930e6 1.04431e7i −0.233582 0.404576i
\(923\) −3.88207e6 −0.149989
\(924\) 1.64753e6 2.04503e7i 0.0634823 0.787990i
\(925\) −3.00896e7 −1.15628
\(926\) 6.90993e6 + 1.19684e7i 0.264817 + 0.458677i
\(927\) 5.18050e7 8.97288e7i 1.98003 3.42952i
\(928\) 917375. 1.58894e6i 0.0349685 0.0605672i
\(929\) 8.86206e6 + 1.53495e7i 0.336896 + 0.583521i 0.983847 0.179011i \(-0.0572897\pi\)
−0.646951 + 0.762531i \(0.723956\pi\)
\(930\) 1.42417e7 0.539952
\(931\) 2.63642e6 + 6.94475e6i 0.0996873 + 0.262593i
\(932\) 3.59557e6 0.135590
\(933\) 3.03689e7 + 5.26005e7i 1.14216 + 1.97827i
\(934\) 5.67551e6 9.83028e6i 0.212881 0.368722i
\(935\) 838192. 1.45179e6i 0.0313556 0.0543094i
\(936\) 1.37972e6 + 2.38974e6i 0.0514756 + 0.0891583i
\(937\) −3.32444e7 −1.23700 −0.618499 0.785786i \(-0.712259\pi\)
−0.618499 + 0.785786i \(0.712259\pi\)
\(938\) −1.10846e6 + 1.37590e7i −0.0411352 + 0.510600i
\(939\) 3.48575e7 1.29013
\(940\) −2.83403e6 4.90869e6i −0.104613 0.181195i
\(941\) −1.39240e7 + 2.41170e7i −0.512613 + 0.887871i 0.487281 + 0.873245i \(0.337989\pi\)
−0.999893 + 0.0146254i \(0.995344\pi\)
\(942\) 1.67198e7 2.89595e7i 0.613909 1.06332i
\(943\) 6.46991e6 + 1.12062e7i 0.236930 + 0.410374i
\(944\) 1.05945e7 0.386946
\(945\) 2.94847e7 1.39966e7i 1.07403 0.509852i
\(946\) 1.31714e7 0.478523
\(947\) 1.15284e7 + 1.99678e7i 0.417729 + 0.723529i 0.995711 0.0925215i \(-0.0294927\pi\)
−0.577981 + 0.816050i \(0.696159\pi\)
\(948\) −1.04789e7 + 1.81499e7i −0.378698 + 0.655925i
\(949\) 1.33600e6 2.31403e6i 0.0481551 0.0834071i
\(950\) −2.37254e6 4.10936e6i −0.0852914 0.147729i
\(951\) −2.38767e7 −0.856097
\(952\) 1.64266e6 + 1.13345e6i 0.0587429 + 0.0405330i
\(953\) 2.85536e7 1.01843 0.509213 0.860641i \(-0.329937\pi\)
0.509213 + 0.860641i \(0.329937\pi\)
\(954\) 6.83805e6 + 1.18439e7i 0.243255 + 0.421330i
\(955\) −2.12929e6 + 3.68804e6i −0.0755486 + 0.130854i
\(956\) −1.02554e7 + 1.77629e7i −0.362919 + 0.628593i
\(957\) 8.86109e6 + 1.53479e7i 0.312757 + 0.541711i
\(958\) 1.88177e7 0.662449
\(959\) 2.00247e7 + 1.38172e7i 0.703105 + 0.485147i
\(960\) 2.56358e6 0.0897777
\(961\) −1.86629e6 3.23251e6i −0.0651884 0.112910i
\(962\) 1.49823e6 2.59500e6i 0.0521963 0.0904066i
\(963\) 6.61532e7 1.14581e8i 2.29871 3.98149i
\(964\) 4.60900e6 + 7.98302e6i 0.159740 + 0.276678i
\(965\) −1.27257e7 −0.439911
\(966\) −1.49583e7 + 7.10081e6i −0.515750 + 0.244830i
\(967\) −3.45310e7 −1.18753 −0.593763 0.804640i \(-0.702358\pi\)
−0.593763 + 0.804640i \(0.702358\pi\)
\(968\) −1.62915e6 2.82177e6i −0.0558820 0.0967905i
\(969\) 1.58424e6 2.74398e6i 0.0542015 0.0938797i
\(970\) −3.01965e6 + 5.23019e6i −0.103045 + 0.178479i
\(971\) −6.24666e6 1.08195e7i −0.212618 0.368265i 0.739915 0.672700i \(-0.234866\pi\)
−0.952533 + 0.304435i \(0.901532\pi\)
\(972\) −4.89995e7 −1.66351
\(973\) 814860. 1.01146e7i 0.0275931 0.342506i
\(974\) −1.66654e7 −0.562883
\(975\) −2.67260e6 4.62907e6i −0.0900371 0.155949i
\(976\) 2.75498e6 4.77177e6i 0.0925751 0.160345i
\(977\) 1.94720e7 3.37265e7i 0.652641 1.13041i −0.329839 0.944037i \(-0.606994\pi\)
0.982480 0.186370i \(-0.0596723\pi\)
\(978\) −3.73622e7 6.47133e7i −1.24907 2.16345i
\(979\) 7.98556e6 0.266286
\(980\) 5.57432e6 + 904029.i 0.185407 + 0.0300689i
\(981\) −7.26191e7 −2.40923
\(982\) 3.15751e6 + 5.46897e6i 0.104488 + 0.180979i
\(983\) −139950. + 242401.i −0.00461945 + 0.00800112i −0.868326 0.495994i \(-0.834804\pi\)
0.863706 + 0.503995i \(0.168137\pi\)
\(984\) −1.15188e7 + 1.99511e7i −0.379245 + 0.656871i
\(985\) −3263.60 5652.72i −0.000107178 0.000185638i
\(986\) −1.72393e6 −0.0564711
\(987\) −5.23402e6 + 6.49686e7i −0.171018 + 2.12281i
\(988\) 472536. 0.0154008
\(989\) −5.31505e6 9.20593e6i −0.172789 0.299280i
\(990\) −8.99393e6 + 1.55779e7i −0.291650 + 0.505152i
\(991\) −9.81715e6 + 1.70038e7i −0.317542 + 0.549999i −0.979975 0.199122i \(-0.936191\pi\)
0.662432 + 0.749122i \(0.269524\pi\)
\(992\) −2.91263e6 5.04483e6i −0.0939738 0.162767i
\(993\) −7.89647e7 −2.54132
\(994\) 2.72161e7 1.29197e7i 0.873694 0.414749i
\(995\) 8.60299e6 0.275481
\(996\) 5.34589e6 + 9.25935e6i 0.170754 + 0.295755i
\(997\) 1.86687e7 3.23351e7i 0.594807 1.03024i −0.398767 0.917052i \(-0.630562\pi\)
0.993574 0.113184i \(-0.0361050\pi\)
\(998\) 3.11423e6 5.39401e6i 0.0989749 0.171430i
\(999\) 6.71995e7 + 1.16393e8i 2.13036 + 3.68989i
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 14.6.c.b.11.2 yes 4
3.2 odd 2 126.6.g.e.109.1 4
4.3 odd 2 112.6.i.b.81.1 4
7.2 even 3 inner 14.6.c.b.9.2 4
7.3 odd 6 98.6.a.f.1.2 2
7.4 even 3 98.6.a.c.1.1 2
7.5 odd 6 98.6.c.f.79.1 4
7.6 odd 2 98.6.c.f.67.1 4
21.2 odd 6 126.6.g.e.37.1 4
21.11 odd 6 882.6.a.bt.1.1 2
21.17 even 6 882.6.a.bl.1.1 2
28.3 even 6 784.6.a.r.1.1 2
28.11 odd 6 784.6.a.bc.1.2 2
28.23 odd 6 112.6.i.b.65.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.6.c.b.9.2 4 7.2 even 3 inner
14.6.c.b.11.2 yes 4 1.1 even 1 trivial
98.6.a.c.1.1 2 7.4 even 3
98.6.a.f.1.2 2 7.3 odd 6
98.6.c.f.67.1 4 7.6 odd 2
98.6.c.f.79.1 4 7.5 odd 6
112.6.i.b.65.1 4 28.23 odd 6
112.6.i.b.81.1 4 4.3 odd 2
126.6.g.e.37.1 4 21.2 odd 6
126.6.g.e.109.1 4 3.2 odd 2
784.6.a.r.1.1 2 28.3 even 6
784.6.a.bc.1.2 2 28.11 odd 6
882.6.a.bl.1.1 2 21.17 even 6
882.6.a.bt.1.1 2 21.11 odd 6