Properties

Label 75.6.i.a.4.6
Level $75$
Weight $6$
Character 75.4
Analytic conductor $12.029$
Analytic rank $0$
Dimension $96$
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] = [75,6,Mod(4,75)]
 
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, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.4");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 75.i (of order \(10\), 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: \(12.0287864860\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(24\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 4.6
Character \(\chi\) \(=\) 75.4
Dual form 75.6.i.a.19.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-6.37631 - 2.07179i) q^{2} +(5.29007 - 7.28115i) q^{3} +(10.4765 + 7.61160i) q^{4} +(-54.0427 + 14.2963i) q^{5} +(-48.8161 + 35.4670i) q^{6} -23.6018i q^{7} +(75.0733 + 103.329i) q^{8} +(-25.0304 - 77.0356i) q^{9} +O(q^{10})\) \(q+(-6.37631 - 2.07179i) q^{2} +(5.29007 - 7.28115i) q^{3} +(10.4765 + 7.61160i) q^{4} +(-54.0427 + 14.2963i) q^{5} +(-48.8161 + 35.4670i) q^{6} -23.6018i q^{7} +(75.0733 + 103.329i) q^{8} +(-25.0304 - 77.0356i) q^{9} +(374.212 + 20.8074i) q^{10} +(-110.177 + 339.091i) q^{11} +(110.842 - 36.0149i) q^{12} +(-253.189 + 82.2660i) q^{13} +(-48.8979 + 150.492i) q^{14} +(-181.796 + 469.122i) q^{15} +(-392.666 - 1208.50i) q^{16} +(-2.65440 - 3.65347i) q^{17} +543.060i q^{18} +(843.372 - 612.745i) q^{19} +(-674.994 - 261.577i) q^{20} +(-171.848 - 124.855i) q^{21} +(1405.05 - 1933.89i) q^{22} +(3963.82 + 1287.92i) q^{23} +1149.50 q^{24} +(2716.23 - 1545.22i) q^{25} +1784.85 q^{26} +(-693.320 - 225.273i) q^{27} +(179.647 - 247.263i) q^{28} +(2105.93 + 1530.05i) q^{29} +(2131.11 - 2614.62i) q^{30} +(8379.64 - 6088.16i) q^{31} +4432.20i q^{32} +(1886.13 + 2596.04i) q^{33} +(9.35607 + 28.7950i) q^{34} +(337.418 + 1275.50i) q^{35} +(324.134 - 997.582i) q^{36} +(-4255.25 + 1382.61i) q^{37} +(-6647.08 + 2159.77i) q^{38} +(-740.394 + 2278.70i) q^{39} +(-5534.39 - 4510.94i) q^{40} +(-1897.07 - 5838.58i) q^{41} +(837.084 + 1152.15i) q^{42} +12085.8i q^{43} +(-3735.30 + 2713.85i) q^{44} +(2454.03 + 3805.37i) q^{45} +(-22606.2 - 16424.4i) q^{46} +(-6551.40 + 9017.23i) q^{47} +(-10876.5 - 3534.00i) q^{48} +16250.0 q^{49} +(-20520.9 + 4225.36i) q^{50} -40.6435 q^{51} +(-3278.70 - 1065.31i) q^{52} +(-10888.8 + 14987.1i) q^{53} +(3954.10 + 2872.83i) q^{54} +(1106.54 - 19900.6i) q^{55} +(2438.76 - 1771.86i) q^{56} -9382.18i q^{57} +(-10258.1 - 14119.1i) q^{58} +(15228.6 + 46868.9i) q^{59} +(-5475.35 + 3530.98i) q^{60} +(4337.41 - 13349.2i) q^{61} +(-66044.5 + 21459.2i) q^{62} +(-1818.18 + 590.761i) q^{63} +(-3382.75 + 10411.0i) q^{64} +(12506.9 - 8065.54i) q^{65} +(-6648.11 - 20460.8i) q^{66} +(16539.0 + 22764.0i) q^{67} -58.4797i q^{68} +(30346.4 - 22048.0i) q^{69} +(491.092 - 8832.07i) q^{70} +(-18699.3 - 13585.8i) q^{71} +(6080.93 - 8369.69i) q^{72} +(-3196.41 - 1038.58i) q^{73} +29997.3 q^{74} +(3118.04 - 27951.6i) q^{75} +13499.5 q^{76} +(8003.16 + 2600.38i) q^{77} +(9441.96 - 12995.7i) q^{78} +(35405.9 + 25723.9i) q^{79} +(38497.9 + 59697.1i) q^{80} +(-5307.96 + 3856.46i) q^{81} +41158.9i q^{82} +(5606.56 + 7716.76i) q^{83} +(-850.015 - 2616.08i) q^{84} +(195.682 + 159.495i) q^{85} +(25039.3 - 77063.0i) q^{86} +(22281.1 - 7239.55i) q^{87} +(-43309.5 + 14072.1i) q^{88} +(27824.7 - 85635.5i) q^{89} +(-7763.76 - 29348.5i) q^{90} +(1941.62 + 5975.70i) q^{91} +(31723.7 + 43663.9i) q^{92} -93220.2i q^{93} +(60455.6 - 43923.5i) q^{94} +(-36818.1 + 45171.5i) q^{95} +(32271.5 + 23446.6i) q^{96} +(-15427.5 + 21234.2i) q^{97} +(-103615. - 33666.5i) q^{98} +28879.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q + 352 q^{4} - 120 q^{5} + 72 q^{6} - 1230 q^{8} + 1944 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 96 q + 352 q^{4} - 120 q^{5} + 72 q^{6} - 1230 q^{8} + 1944 q^{9} - 890 q^{10} + 474 q^{11} + 2748 q^{14} - 780 q^{16} + 1910 q^{17} - 5522 q^{19} - 19220 q^{20} + 1764 q^{21} + 6170 q^{22} + 21980 q^{23} + 13824 q^{24} + 11790 q^{25} - 11028 q^{26} - 9120 q^{28} - 24304 q^{29} - 22860 q^{30} + 1566 q^{31} - 3690 q^{33} + 24224 q^{34} + 10250 q^{35} - 28512 q^{36} + 16490 q^{37} + 68730 q^{38} - 12168 q^{39} - 106480 q^{40} + 26126 q^{41} - 43560 q^{42} - 10814 q^{44} + 9720 q^{45} + 22956 q^{46} + 66440 q^{47} - 123480 q^{49} + 329620 q^{50} - 83232 q^{51} + 251240 q^{52} - 91690 q^{53} - 5832 q^{54} - 123470 q^{55} + 116100 q^{56} - 483290 q^{58} - 97428 q^{59} + 119610 q^{60} + 91560 q^{61} - 138410 q^{62} + 47790 q^{63} + 127738 q^{64} - 235130 q^{65} + 118296 q^{66} + 163960 q^{67} - 73332 q^{69} + 209520 q^{70} + 155672 q^{71} - 99630 q^{72} + 18980 q^{73} + 100588 q^{74} - 464032 q^{76} + 119560 q^{77} - 112020 q^{79} - 66300 q^{80} - 157464 q^{81} + 148010 q^{83} - 61128 q^{84} + 346980 q^{85} - 295956 q^{86} - 371160 q^{87} - 189090 q^{88} - 494082 q^{89} - 144180 q^{90} - 79494 q^{91} + 599810 q^{92} + 234622 q^{94} + 605800 q^{95} + 210744 q^{96} + 372140 q^{97} + 891060 q^{98} + 25596 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(26\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.37631 2.07179i −1.12718 0.366244i −0.314678 0.949198i \(-0.601897\pi\)
−0.812505 + 0.582955i \(0.801897\pi\)
\(3\) 5.29007 7.28115i 0.339358 0.467086i
\(4\) 10.4765 + 7.61160i 0.327390 + 0.237862i
\(5\) −54.0427 + 14.2963i −0.966746 + 0.255740i
\(6\) −48.8161 + 35.4670i −0.553586 + 0.402204i
\(7\) 23.6018i 0.182054i −0.995848 0.0910268i \(-0.970985\pi\)
0.995848 0.0910268i \(-0.0290149\pi\)
\(8\) 75.0733 + 103.329i 0.414725 + 0.570820i
\(9\) −25.0304 77.0356i −0.103006 0.317019i
\(10\) 374.212 + 20.8074i 1.18336 + 0.0657988i
\(11\) −110.177 + 339.091i −0.274543 + 0.844958i 0.714796 + 0.699333i \(0.246519\pi\)
−0.989340 + 0.145625i \(0.953481\pi\)
\(12\) 110.842 36.0149i 0.222204 0.0721986i
\(13\) −253.189 + 82.2660i −0.415514 + 0.135009i −0.509311 0.860583i \(-0.670100\pi\)
0.0937966 + 0.995591i \(0.470100\pi\)
\(14\) −48.8979 + 150.492i −0.0666761 + 0.205208i
\(15\) −181.796 + 469.122i −0.208620 + 0.538341i
\(16\) −392.666 1208.50i −0.383463 1.18018i
\(17\) −2.65440 3.65347i −0.00222764 0.00306608i 0.807902 0.589317i \(-0.200603\pi\)
−0.810129 + 0.586251i \(0.800603\pi\)
\(18\) 543.060i 0.395063i
\(19\) 843.372 612.745i 0.535963 0.389400i −0.286620 0.958044i \(-0.592532\pi\)
0.822584 + 0.568644i \(0.192532\pi\)
\(20\) −674.994 261.577i −0.377333 0.146226i
\(21\) −171.848 124.855i −0.0850348 0.0617814i
\(22\) 1405.05 1933.89i 0.618921 0.851872i
\(23\) 3963.82 + 1287.92i 1.56241 + 0.507657i 0.957450 0.288600i \(-0.0931899\pi\)
0.604958 + 0.796257i \(0.293190\pi\)
\(24\) 1149.50 0.407362
\(25\) 2716.23 1545.22i 0.869194 0.494471i
\(26\) 1784.85 0.517807
\(27\) −693.320 225.273i −0.183031 0.0594703i
\(28\) 179.647 247.263i 0.0433037 0.0596025i
\(29\) 2105.93 + 1530.05i 0.464996 + 0.337840i 0.795488 0.605969i \(-0.207215\pi\)
−0.330492 + 0.943809i \(0.607215\pi\)
\(30\) 2131.11 2614.62i 0.432317 0.530403i
\(31\) 8379.64 6088.16i 1.56611 1.13784i 0.635336 0.772236i \(-0.280862\pi\)
0.930770 0.365606i \(-0.119138\pi\)
\(32\) 4432.20i 0.765146i
\(33\) 1886.13 + 2596.04i 0.301500 + 0.414979i
\(34\) 9.35607 + 28.7950i 0.00138802 + 0.00427189i
\(35\) 337.418 + 1275.50i 0.0465584 + 0.176000i
\(36\) 324.134 997.582i 0.0416839 0.128290i
\(37\) −4255.25 + 1382.61i −0.511000 + 0.166034i −0.553157 0.833077i \(-0.686577\pi\)
0.0421572 + 0.999111i \(0.486577\pi\)
\(38\) −6647.08 + 2159.77i −0.746744 + 0.242632i
\(39\) −740.394 + 2278.70i −0.0779474 + 0.239897i
\(40\) −5534.39 4510.94i −0.546915 0.445776i
\(41\) −1897.07 5838.58i −0.176248 0.542435i 0.823440 0.567403i \(-0.192052\pi\)
−0.999688 + 0.0249676i \(0.992052\pi\)
\(42\) 837.084 + 1152.15i 0.0732227 + 0.100782i
\(43\) 12085.8i 0.996793i 0.866949 + 0.498397i \(0.166078\pi\)
−0.866949 + 0.498397i \(0.833922\pi\)
\(44\) −3735.30 + 2713.85i −0.290866 + 0.211327i
\(45\) 2454.03 + 3805.37i 0.180655 + 0.280134i
\(46\) −22606.2 16424.4i −1.57519 1.14444i
\(47\) −6551.40 + 9017.23i −0.432603 + 0.595427i −0.968548 0.248826i \(-0.919955\pi\)
0.535945 + 0.844253i \(0.319955\pi\)
\(48\) −10876.5 3534.00i −0.681376 0.221393i
\(49\) 16250.0 0.966856
\(50\) −20520.9 + 4225.36i −1.16084 + 0.239023i
\(51\) −40.6435 −0.00218809
\(52\) −3278.70 1065.31i −0.168149 0.0546348i
\(53\) −10888.8 + 14987.1i −0.532463 + 0.732872i −0.987503 0.157599i \(-0.949625\pi\)
0.455041 + 0.890471i \(0.349625\pi\)
\(54\) 3954.10 + 2872.83i 0.184529 + 0.134068i
\(55\) 1106.54 19900.6i 0.0493240 0.887071i
\(56\) 2438.76 1771.86i 0.103920 0.0755022i
\(57\) 9382.18i 0.382487i
\(58\) −10258.1 14119.1i −0.400404 0.551109i
\(59\) 15228.6 + 46868.9i 0.569549 + 1.75289i 0.654033 + 0.756466i \(0.273076\pi\)
−0.0844847 + 0.996425i \(0.526924\pi\)
\(60\) −5475.35 + 3530.98i −0.196351 + 0.126624i
\(61\) 4337.41 13349.2i 0.149247 0.459335i −0.848286 0.529539i \(-0.822365\pi\)
0.997533 + 0.0702036i \(0.0223649\pi\)
\(62\) −66044.5 + 21459.2i −2.18202 + 0.708980i
\(63\) −1818.18 + 590.761i −0.0577144 + 0.0187526i
\(64\) −3382.75 + 10411.0i −0.103233 + 0.317720i
\(65\) 12506.9 8065.54i 0.367169 0.236783i
\(66\) −6648.11 20460.8i −0.187862 0.578179i
\(67\) 16539.0 + 22764.0i 0.450113 + 0.619528i 0.972422 0.233229i \(-0.0749290\pi\)
−0.522308 + 0.852757i \(0.674929\pi\)
\(68\) 58.4797i 0.00153367i
\(69\) 30346.4 22048.0i 0.767335 0.557502i
\(70\) 491.092 8832.07i 0.0119789 0.215435i
\(71\) −18699.3 13585.8i −0.440229 0.319845i 0.345497 0.938420i \(-0.387710\pi\)
−0.785726 + 0.618575i \(0.787710\pi\)
\(72\) 6080.93 8369.69i 0.138242 0.190273i
\(73\) −3196.41 1038.58i −0.0702030 0.0228103i 0.273705 0.961814i \(-0.411751\pi\)
−0.343908 + 0.939003i \(0.611751\pi\)
\(74\) 29997.3 0.636799
\(75\) 3118.04 27951.6i 0.0640072 0.573791i
\(76\) 13499.5 0.268092
\(77\) 8003.16 + 2600.38i 0.153828 + 0.0499817i
\(78\) 9441.96 12995.7i 0.175722 0.241860i
\(79\) 35405.9 + 25723.9i 0.638276 + 0.463734i 0.859257 0.511544i \(-0.170926\pi\)
−0.220982 + 0.975278i \(0.570926\pi\)
\(80\) 38497.9 + 59697.1i 0.672530 + 1.04287i
\(81\) −5307.96 + 3856.46i −0.0898908 + 0.0653095i
\(82\) 41158.9i 0.675973i
\(83\) 5606.56 + 7716.76i 0.0893307 + 0.122953i 0.851343 0.524609i \(-0.175789\pi\)
−0.762012 + 0.647562i \(0.775789\pi\)
\(84\) −850.015 2616.08i −0.0131440 0.0404531i
\(85\) 195.682 + 159.495i 0.00293768 + 0.00239442i
\(86\) 25039.3 77063.0i 0.365070 1.12357i
\(87\) 22281.1 7239.55i 0.315600 0.102545i
\(88\) −43309.5 + 14072.1i −0.596179 + 0.193710i
\(89\) 27824.7 85635.5i 0.372353 1.14598i −0.572894 0.819629i \(-0.694179\pi\)
0.945247 0.326355i \(-0.105821\pi\)
\(90\) −7763.76 29348.5i −0.101034 0.381926i
\(91\) 1941.62 + 5975.70i 0.0245788 + 0.0756459i
\(92\) 31723.7 + 43663.9i 0.390763 + 0.537840i
\(93\) 93220.2i 1.11764i
\(94\) 60455.6 43923.5i 0.705694 0.512717i
\(95\) −36818.1 + 45171.5i −0.418555 + 0.513518i
\(96\) 32271.5 + 23446.6i 0.357389 + 0.259658i
\(97\) −15427.5 + 21234.2i −0.166482 + 0.229142i −0.884104 0.467290i \(-0.845230\pi\)
0.717622 + 0.696432i \(0.245230\pi\)
\(98\) −103615. 33666.5i −1.08982 0.354105i
\(99\) 28879.9 0.296147
\(100\) 40218.1 + 4486.39i 0.402181 + 0.0448639i
\(101\) 8162.68 0.0796213 0.0398107 0.999207i \(-0.487325\pi\)
0.0398107 + 0.999207i \(0.487325\pi\)
\(102\) 259.155 + 84.2046i 0.00246638 + 0.000801375i
\(103\) −67167.9 + 92448.7i −0.623834 + 0.858633i −0.997625 0.0688796i \(-0.978058\pi\)
0.373791 + 0.927513i \(0.378058\pi\)
\(104\) −27508.2 19985.9i −0.249390 0.181192i
\(105\) 11072.1 + 4290.71i 0.0980070 + 0.0379801i
\(106\) 100480. 73003.2i 0.868593 0.631070i
\(107\) 61359.8i 0.518113i 0.965862 + 0.259057i \(0.0834117\pi\)
−0.965862 + 0.259057i \(0.916588\pi\)
\(108\) −5548.85 7637.34i −0.0457766 0.0630061i
\(109\) 44958.9 + 138369.i 0.362451 + 1.11551i 0.951562 + 0.307457i \(0.0994781\pi\)
−0.589111 + 0.808052i \(0.700522\pi\)
\(110\) −48285.4 + 124600.i −0.380482 + 0.981827i
\(111\) −12443.5 + 38297.2i −0.0958597 + 0.295026i
\(112\) −28522.8 + 9267.62i −0.214856 + 0.0698109i
\(113\) 136893. 44479.3i 1.00852 0.327689i 0.242256 0.970212i \(-0.422112\pi\)
0.766266 + 0.642524i \(0.222112\pi\)
\(114\) −19437.9 + 59823.7i −0.140084 + 0.431133i
\(115\) −232628. 12934.9i −1.64028 0.0912048i
\(116\) 10416.6 + 32059.0i 0.0718756 + 0.221210i
\(117\) 12674.8 + 17445.4i 0.0856007 + 0.117819i
\(118\) 330401.i 2.18442i
\(119\) −86.2284 + 62.6486i −0.000558191 + 0.000405550i
\(120\) −62122.1 + 16433.6i −0.393816 + 0.104179i
\(121\) 27449.1 + 19942.9i 0.170437 + 0.123830i
\(122\) −55313.3 + 76132.3i −0.336458 + 0.463094i
\(123\) −52547.3 17073.6i −0.313175 0.101757i
\(124\) 134130. 0.783376
\(125\) −124702. + 122340.i −0.713833 + 0.700316i
\(126\) 12817.2 0.0719227
\(127\) 215149. + 69906.1i 1.18367 + 0.384597i 0.833728 0.552175i \(-0.186202\pi\)
0.349940 + 0.936772i \(0.386202\pi\)
\(128\) 126505. 174119.i 0.682467 0.939335i
\(129\) 87998.7 + 63934.8i 0.465588 + 0.338270i
\(130\) −96458.0 + 25516.7i −0.500587 + 0.132424i
\(131\) 303583. 220566.i 1.54561 1.12295i 0.598915 0.800813i \(-0.295599\pi\)
0.946693 0.322137i \(-0.104401\pi\)
\(132\) 41553.7i 0.207575i
\(133\) −14461.9 19905.1i −0.0708917 0.0975741i
\(134\) −58295.6 179415.i −0.280462 0.863173i
\(135\) 40689.5 + 2262.47i 0.192153 + 0.0106843i
\(136\) 178.237 548.556i 0.000826323 0.00254316i
\(137\) −77097.1 + 25050.4i −0.350943 + 0.114028i −0.479183 0.877715i \(-0.659067\pi\)
0.128240 + 0.991743i \(0.459067\pi\)
\(138\) −239177. + 77713.3i −1.06911 + 0.347374i
\(139\) 71503.8 220066.i 0.313901 0.966087i −0.662304 0.749235i \(-0.730421\pi\)
0.976205 0.216851i \(-0.0695787\pi\)
\(140\) −6173.67 + 15931.1i −0.0266209 + 0.0686949i
\(141\) 30998.5 + 95403.5i 0.131308 + 0.404126i
\(142\) 91085.4 + 125368.i 0.379077 + 0.521755i
\(143\) 94918.0i 0.388158i
\(144\) −83269.1 + 60498.6i −0.334640 + 0.243130i
\(145\) −135684. 52581.0i −0.535932 0.207687i
\(146\) 18229.6 + 13244.6i 0.0707775 + 0.0514228i
\(147\) 85963.4 118318.i 0.328110 0.451605i
\(148\) −55103.9 17904.3i −0.206789 0.0671899i
\(149\) −232241. −0.856986 −0.428493 0.903545i \(-0.640955\pi\)
−0.428493 + 0.903545i \(0.640955\pi\)
\(150\) −77791.5 + 171768.i −0.282295 + 0.623325i
\(151\) −286435. −1.02231 −0.511157 0.859488i \(-0.670783\pi\)
−0.511157 + 0.859488i \(0.670783\pi\)
\(152\) 126629. + 41144.4i 0.444555 + 0.144445i
\(153\) −215.007 + 295.931i −0.000742546 + 0.00102203i
\(154\) −45643.2 33161.7i −0.155086 0.112677i
\(155\) −365820. + 448819.i −1.22303 + 1.50052i
\(156\) −25101.2 + 18237.1i −0.0825817 + 0.0599991i
\(157\) 76045.1i 0.246219i −0.992393 0.123110i \(-0.960713\pi\)
0.992393 0.123110i \(-0.0392867\pi\)
\(158\) −172465. 237377.i −0.549614 0.756478i
\(159\) 51521.1 + 158566.i 0.161619 + 0.497412i
\(160\) −63364.1 239528.i −0.195678 0.739701i
\(161\) 30397.3 93553.2i 0.0924208 0.284442i
\(162\) 41835.0 13593.0i 0.125243 0.0406938i
\(163\) −50679.9 + 16466.9i −0.149405 + 0.0485448i −0.382765 0.923846i \(-0.625028\pi\)
0.233360 + 0.972391i \(0.425028\pi\)
\(164\) 24566.3 75607.5i 0.0713232 0.219510i
\(165\) −139045. 113332.i −0.397600 0.324073i
\(166\) −19761.6 60820.1i −0.0556612 0.171308i
\(167\) 53426.9 + 73535.8i 0.148241 + 0.204036i 0.876679 0.481075i \(-0.159754\pi\)
−0.728438 + 0.685111i \(0.759754\pi\)
\(168\) 27130.2i 0.0741618i
\(169\) −243046. + 176583.i −0.654592 + 0.475589i
\(170\) −917.290 1422.40i −0.00243436 0.00377486i
\(171\) −68313.1 49632.4i −0.178654 0.129800i
\(172\) −91992.4 + 126617.i −0.237100 + 0.326340i
\(173\) 636089. + 206678.i 1.61586 + 0.525024i 0.970959 0.239245i \(-0.0769000\pi\)
0.644898 + 0.764269i \(0.276900\pi\)
\(174\) −157070. −0.393296
\(175\) −36470.0 64107.9i −0.0900203 0.158240i
\(176\) 453056. 1.10248
\(177\) 421820. + 137058.i 1.01203 + 0.328829i
\(178\) −354837. + 488392.i −0.839420 + 1.15536i
\(179\) −473683. 344151.i −1.10498 0.802817i −0.123116 0.992392i \(-0.539289\pi\)
−0.981866 + 0.189576i \(0.939289\pi\)
\(180\) −3255.34 + 58545.9i −0.00748886 + 0.134684i
\(181\) −292498. + 212512.i −0.663631 + 0.482156i −0.867887 0.496762i \(-0.834522\pi\)
0.204256 + 0.978917i \(0.434522\pi\)
\(182\) 42125.6i 0.0942686i
\(183\) −74252.2 102199.i −0.163901 0.225590i
\(184\) 164496. + 506268.i 0.358189 + 1.10239i
\(185\) 210199. 135555.i 0.451545 0.291196i
\(186\) −193133. + 594401.i −0.409330 + 1.25979i
\(187\) 1531.32 497.555i 0.00320229 0.00104049i
\(188\) −137271. + 44602.1i −0.283260 + 0.0920366i
\(189\) −5316.85 + 16363.6i −0.0108268 + 0.0333215i
\(190\) 328350. 211748.i 0.659861 0.425536i
\(191\) −234900. 722948.i −0.465907 1.43392i −0.857838 0.513920i \(-0.828193\pi\)
0.391930 0.919995i \(-0.371807\pi\)
\(192\) 57909.4 + 79705.4i 0.113369 + 0.156040i
\(193\) 198105.i 0.382827i −0.981509 0.191414i \(-0.938693\pi\)
0.981509 0.191414i \(-0.0613072\pi\)
\(194\) 142363. 103433.i 0.271577 0.197313i
\(195\) 7435.93 133732.i 0.0140039 0.251854i
\(196\) 170242. + 123688.i 0.316539 + 0.229979i
\(197\) 99279.6 136647.i 0.182261 0.250861i −0.708104 0.706108i \(-0.750449\pi\)
0.890365 + 0.455247i \(0.150449\pi\)
\(198\) −184147. 59833.0i −0.333812 0.108462i
\(199\) 809878. 1.44973 0.724865 0.688891i \(-0.241902\pi\)
0.724865 + 0.688891i \(0.241902\pi\)
\(200\) 363583. + 164662.i 0.642731 + 0.291084i
\(201\) 253240. 0.442123
\(202\) −52047.8 16911.4i −0.0897478 0.0291608i
\(203\) 36111.9 49703.7i 0.0615049 0.0846543i
\(204\) −425.800 309.362i −0.000716358 0.000520464i
\(205\) 185993. + 288412.i 0.309109 + 0.479323i
\(206\) 619817. 450324.i 1.01764 0.739361i
\(207\) 337592.i 0.547604i
\(208\) 198837. + 273676.i 0.318669 + 0.438610i
\(209\) 114856. + 353491.i 0.181882 + 0.559774i
\(210\) −61709.7 50297.9i −0.0965618 0.0787049i
\(211\) −84500.5 + 260066.i −0.130663 + 0.402140i −0.994890 0.100962i \(-0.967808\pi\)
0.864227 + 0.503102i \(0.167808\pi\)
\(212\) −228152. + 74131.0i −0.348645 + 0.113282i
\(213\) −197841. + 64282.4i −0.298790 + 0.0970829i
\(214\) 127125. 391249.i 0.189756 0.584009i
\(215\) −172783. 653151.i −0.254920 0.963646i
\(216\) −28772.4 88552.4i −0.0419606 0.129142i
\(217\) −143691. 197774.i −0.207148 0.285115i
\(218\) 975430.i 1.39013i
\(219\) −24471.3 + 17779.4i −0.0344783 + 0.0250500i
\(220\) 163068. 200065.i 0.227149 0.278685i
\(221\) 972.621 + 706.651i 0.00133956 + 0.000973250i
\(222\) 158688. 218415.i 0.216103 0.297440i
\(223\) 864602. + 280926.i 1.16427 + 0.378294i 0.826501 0.562935i \(-0.190328\pi\)
0.337769 + 0.941229i \(0.390328\pi\)
\(224\) 104608. 0.139298
\(225\) −187025. 170569.i −0.246289 0.224618i
\(226\) −965024. −1.25680
\(227\) −1.26759e6 411864.i −1.63272 0.530504i −0.657829 0.753167i \(-0.728525\pi\)
−0.974896 + 0.222663i \(0.928525\pi\)
\(228\) 71413.4 98292.1i 0.0909793 0.125222i
\(229\) 764496. + 555439.i 0.963355 + 0.699919i 0.953928 0.300037i \(-0.0969990\pi\)
0.00942773 + 0.999956i \(0.496999\pi\)
\(230\) 1.45651e6 + 564433.i 1.81549 + 0.703547i
\(231\) 61271.0 44516.0i 0.0755484 0.0548891i
\(232\) 332471.i 0.405540i
\(233\) 834933. + 1.14919e6i 1.00754 + 1.38676i 0.920583 + 0.390546i \(0.127714\pi\)
0.0869557 + 0.996212i \(0.472286\pi\)
\(234\) −44675.4 137497.i −0.0533370 0.164155i
\(235\) 225143. 580977.i 0.265943 0.686261i
\(236\) −197205. + 606935.i −0.230482 + 0.709352i
\(237\) 374600. 121715.i 0.433208 0.140758i
\(238\) 679.614 220.820i 0.000777714 0.000252694i
\(239\) 54693.4 168329.i 0.0619356 0.190618i −0.915301 0.402770i \(-0.868047\pi\)
0.977237 + 0.212152i \(0.0680473\pi\)
\(240\) 638320. + 35492.7i 0.715337 + 0.0397750i
\(241\) −232023. 714095.i −0.257329 0.791978i −0.993362 0.115032i \(-0.963303\pi\)
0.736033 0.676946i \(-0.236697\pi\)
\(242\) −133706. 184031.i −0.146762 0.202000i
\(243\) 59049.0i 0.0641500i
\(244\) 147049. 106838.i 0.158121 0.114881i
\(245\) −878192. + 232314.i −0.934704 + 0.247264i
\(246\) 299685. + 217734.i 0.315738 + 0.229397i
\(247\) −163124. + 224521.i −0.170128 + 0.234161i
\(248\) 1.25817e6 + 408805.i 1.29901 + 0.422073i
\(249\) 85846.0 0.0877449
\(250\) 1.04860e6 521723.i 1.06111 0.527947i
\(251\) 564356. 0.565417 0.282708 0.959206i \(-0.408767\pi\)
0.282708 + 0.959206i \(0.408767\pi\)
\(252\) −23544.7 7650.13i −0.0233556 0.00758871i
\(253\) −873448. + 1.20220e6i −0.857898 + 1.18079i
\(254\) −1.22703e6 891486.i −1.19335 0.867022i
\(255\) 2196.48 581.051i 0.00211533 0.000559582i
\(256\) −883973. + 642244.i −0.843023 + 0.612492i
\(257\) 617482.i 0.583165i −0.956546 0.291582i \(-0.905818\pi\)
0.956546 0.291582i \(-0.0941817\pi\)
\(258\) −428648. 589983.i −0.400914 0.551811i
\(259\) 32632.1 + 100431.i 0.0302271 + 0.0930294i
\(260\) 192420. + 10699.2i 0.176529 + 0.00981560i
\(261\) 65156.0 200529.i 0.0592043 0.182212i
\(262\) −2.39271e6 + 777437.i −2.15346 + 0.699700i
\(263\) −1.78445e6 + 579802.i −1.59080 + 0.516881i −0.964809 0.262953i \(-0.915304\pi\)
−0.625987 + 0.779834i \(0.715304\pi\)
\(264\) −126649. + 389786.i −0.111839 + 0.344204i
\(265\) 374198. 965613.i 0.327331 0.844673i
\(266\) 50974.3 + 156883.i 0.0441720 + 0.135948i
\(267\) −476331. 655613.i −0.408913 0.562820i
\(268\) 364374.i 0.309892i
\(269\) −1.19954e6 + 871520.i −1.01073 + 0.734339i −0.964362 0.264585i \(-0.914765\pi\)
−0.0463686 + 0.998924i \(0.514765\pi\)
\(270\) −254761. 98726.2i −0.212679 0.0824182i
\(271\) −1.16350e6 845335.i −0.962376 0.699207i −0.00867457 0.999962i \(-0.502761\pi\)
−0.953701 + 0.300755i \(0.902761\pi\)
\(272\) −3372.94 + 4642.45i −0.00276430 + 0.00380474i
\(273\) 53781.3 + 17474.6i 0.0436742 + 0.0141906i
\(274\) 543494. 0.437339
\(275\) 224704. + 1.09130e6i 0.179176 + 0.870186i
\(276\) 485744. 0.383826
\(277\) −816123. 265174.i −0.639081 0.207650i −0.0284876 0.999594i \(-0.509069\pi\)
−0.610594 + 0.791944i \(0.709069\pi\)
\(278\) −911861. + 1.25507e6i −0.707647 + 0.973992i
\(279\) −678751. 493141.i −0.522035 0.379281i
\(280\) −106466. + 130621.i −0.0811552 + 0.0995679i
\(281\) −1.86488e6 + 1.35492e6i −1.40892 + 1.02364i −0.415440 + 0.909621i \(0.636372\pi\)
−0.993479 + 0.114019i \(0.963628\pi\)
\(282\) 672545.i 0.503615i
\(283\) 1.01613e6 + 1.39859e6i 0.754196 + 1.03806i 0.997675 + 0.0681553i \(0.0217113\pi\)
−0.243479 + 0.969906i \(0.578289\pi\)
\(284\) −92492.5 284663.i −0.0680472 0.209428i
\(285\) 134131. + 507039.i 0.0978173 + 0.369768i
\(286\) −196650. + 605226.i −0.142160 + 0.437525i
\(287\) −137801. + 44774.2i −0.0987523 + 0.0320866i
\(288\) 341437. 110940.i 0.242566 0.0788143i
\(289\) 438754. 1.35034e6i 0.309013 0.951043i
\(290\) 756229. + 616382.i 0.528030 + 0.430383i
\(291\) 72996.5 + 224660.i 0.0505324 + 0.155523i
\(292\) −25581.9 35210.4i −0.0175580 0.0241665i
\(293\) 713965.i 0.485856i −0.970044 0.242928i \(-0.921892\pi\)
0.970044 0.242928i \(-0.0781079\pi\)
\(294\) −793260. + 576337.i −0.535238 + 0.388873i
\(295\) −1.49305e6 2.31521e6i −0.998893 1.54894i
\(296\) −462320. 335895.i −0.306700 0.222830i
\(297\) 152777. 210279.i 0.100500 0.138326i
\(298\) 1.48084e6 + 481155.i 0.965980 + 0.313866i
\(299\) −1.10955e6 −0.717741
\(300\) 245423. 269101.i 0.157439 0.172628i
\(301\) 285247. 0.181470
\(302\) 1.82640e6 + 593433.i 1.15233 + 0.374416i
\(303\) 43181.1 59433.7i 0.0270201 0.0371900i
\(304\) −1.07167e6 778613.i −0.665084 0.483212i
\(305\) −43561.5 + 783435.i −0.0268135 + 0.482229i
\(306\) 1984.06 1441.50i 0.00121130 0.000880058i
\(307\) 2.88457e6i 1.74677i −0.487033 0.873383i \(-0.661921\pi\)
0.487033 0.873383i \(-0.338079\pi\)
\(308\) 64051.7 + 88159.6i 0.0384728 + 0.0529533i
\(309\) 317810. + 978119.i 0.189353 + 0.582768i
\(310\) 3.26244e6 2.10391e6i 1.92814 1.24343i
\(311\) −651829. + 2.00612e6i −0.382149 + 1.17613i 0.556379 + 0.830929i \(0.312190\pi\)
−0.938528 + 0.345204i \(0.887810\pi\)
\(312\) −291041. + 94564.8i −0.169265 + 0.0549975i
\(313\) 123219. 40036.1i 0.0710911 0.0230989i −0.273256 0.961941i \(-0.588100\pi\)
0.344347 + 0.938843i \(0.388100\pi\)
\(314\) −157549. + 484887.i −0.0901763 + 0.277534i
\(315\) 89813.5 57919.5i 0.0509994 0.0328889i
\(316\) 175129. + 538991.i 0.0986598 + 0.303644i
\(317\) −157324. 216538.i −0.0879320 0.121028i 0.762785 0.646653i \(-0.223832\pi\)
−0.850717 + 0.525625i \(0.823832\pi\)
\(318\) 1.11780e6i 0.619866i
\(319\) −750853. + 545527.i −0.413122 + 0.300151i
\(320\) 33973.7 611001.i 0.0185467 0.333555i
\(321\) 446770. + 324598.i 0.242004 + 0.175826i
\(322\) −387645. + 533547.i −0.208350 + 0.286770i
\(323\) −4477.30 1454.76i −0.00238786 0.000775864i
\(324\) −84962.5 −0.0449640
\(325\) −560600. + 614687.i −0.294405 + 0.322809i
\(326\) 357266. 0.186187
\(327\) 1.24532e6 + 404630.i 0.644040 + 0.209261i
\(328\) 460879. 634345.i 0.236539 0.325567i
\(329\) 212823. + 154625.i 0.108400 + 0.0787570i
\(330\) 651796. + 1.01071e6i 0.329478 + 0.510908i
\(331\) 2.93640e6 2.13342e6i 1.47315 1.07030i 0.493459 0.869769i \(-0.335732\pi\)
0.979687 0.200534i \(-0.0642677\pi\)
\(332\) 123519.i 0.0615020i
\(333\) 213021. + 293198.i 0.105272 + 0.144894i
\(334\) −188316. 579576.i −0.0923677 0.284279i
\(335\) −1.21925e6 993780.i −0.593583 0.483814i
\(336\) −83408.6 + 256705.i −0.0403053 + 0.124047i
\(337\) 3.19478e6 1.03805e6i 1.53238 0.497900i 0.583118 0.812387i \(-0.301832\pi\)
0.949262 + 0.314487i \(0.101832\pi\)
\(338\) 1.91558e6 622408.i 0.912027 0.296335i
\(339\) 400313. 1.23204e6i 0.189191 0.582271i
\(340\) 836.044 + 3160.40i 0.000392222 + 0.00148267i
\(341\) 1.14120e6 + 3.51224e6i 0.531465 + 1.63568i
\(342\) 332758. + 458002.i 0.153838 + 0.211739i
\(343\) 780203.i 0.358073i
\(344\) −1.24882e6 + 907322.i −0.568990 + 0.413395i
\(345\) −1.32480e6 + 1.62537e6i −0.599242 + 0.735201i
\(346\) −3.62771e6 2.63569e6i −1.62908 1.18360i
\(347\) 2.42774e6 3.34150e6i 1.08238 1.48977i 0.225502 0.974243i \(-0.427598\pi\)
0.856876 0.515522i \(-0.172402\pi\)
\(348\) 288531. + 93749.5i 0.127716 + 0.0414974i
\(349\) 2.62110e6 1.15191 0.575957 0.817480i \(-0.304629\pi\)
0.575957 + 0.817480i \(0.304629\pi\)
\(350\) 99726.0 + 484330.i 0.0435149 + 0.211335i
\(351\) 194073. 0.0840810
\(352\) −1.50292e6 488328.i −0.646516 0.210066i
\(353\) −1.02124e6 + 1.40562e6i −0.436205 + 0.600385i −0.969363 0.245631i \(-0.921005\pi\)
0.533158 + 0.846015i \(0.321005\pi\)
\(354\) −2.40570e6 1.74784e6i −1.02031 0.741301i
\(355\) 1.20479e6 + 466884.i 0.507387 + 0.196625i
\(356\) 943327. 685367.i 0.394491 0.286615i
\(357\) 959.258i 0.000398350i
\(358\) 2.30734e6 + 3.17578e6i 0.951490 + 1.30961i
\(359\) 504648. + 1.55315e6i 0.206658 + 0.636028i 0.999641 + 0.0267847i \(0.00852685\pi\)
−0.792983 + 0.609244i \(0.791473\pi\)
\(360\) −208975. + 539256.i −0.0849840 + 0.219300i
\(361\) −429338. + 1.32137e6i −0.173393 + 0.533648i
\(362\) 2.30534e6 749050.i 0.924620 0.300427i
\(363\) 290415. 94361.5i 0.115678 0.0375862i
\(364\) −25143.3 + 77383.1i −0.00994646 + 0.0306121i
\(365\) 187591. + 10430.6i 0.0737020 + 0.00409807i
\(366\) 261720. + 805490.i 0.102125 + 0.314309i
\(367\) 1.41443e6 + 1.94679e6i 0.548170 + 0.754492i 0.989763 0.142724i \(-0.0455862\pi\)
−0.441592 + 0.897216i \(0.645586\pi\)
\(368\) 5.29601e6i 2.03859i
\(369\) −402294. + 292284.i −0.153808 + 0.111748i
\(370\) −1.62113e6 + 428850.i −0.615622 + 0.162855i
\(371\) 353722. + 256994.i 0.133422 + 0.0969368i
\(372\) 709555. 976618.i 0.265845 0.365904i
\(373\) 1.22030e6 + 396501.i 0.454147 + 0.147561i 0.527153 0.849770i \(-0.323259\pi\)
−0.0730066 + 0.997331i \(0.523259\pi\)
\(374\) −10795.0 −0.00399064
\(375\) 231098. + 1.55516e6i 0.0848628 + 0.571079i
\(376\) −1.42358e6 −0.519293
\(377\) −659070. 214145.i −0.238824 0.0775986i
\(378\) 67803.8 93323.9i 0.0244076 0.0335941i
\(379\) −326439. 237172.i −0.116736 0.0848134i 0.527886 0.849315i \(-0.322985\pi\)
−0.644621 + 0.764502i \(0.722985\pi\)
\(380\) −729551. + 192993.i −0.259177 + 0.0685620i
\(381\) 1.64715e6 1.19672e6i 0.581327 0.422359i
\(382\) 5.09640e6i 1.78692i
\(383\) −1.12144e6 1.54353e6i −0.390642 0.537673i 0.567722 0.823220i \(-0.307825\pi\)
−0.958365 + 0.285547i \(0.907825\pi\)
\(384\) −598567. 1.84220e6i −0.207150 0.637542i
\(385\) −469688. 26116.2i −0.161495 0.00897962i
\(386\) −410432. + 1.26318e6i −0.140208 + 0.431517i
\(387\) 931039. 302513.i 0.316002 0.102675i
\(388\) −323252. + 105031.i −0.109009 + 0.0354191i
\(389\) −357528. + 1.10036e6i −0.119794 + 0.368689i −0.992917 0.118812i \(-0.962091\pi\)
0.873122 + 0.487501i \(0.162091\pi\)
\(390\) −324478. + 837311.i −0.108025 + 0.278757i
\(391\) −5816.18 17900.4i −0.00192396 0.00592134i
\(392\) 1.21994e6 + 1.67910e6i 0.400980 + 0.551901i
\(393\) 3.37724e6i 1.10301i
\(394\) −916140. + 665615.i −0.297318 + 0.216014i
\(395\) −2.28119e6 884016.i −0.735646 0.285081i
\(396\) 302559. + 219822.i 0.0969555 + 0.0704423i
\(397\) −2.95386e6 + 4.06563e6i −0.940617 + 1.29465i 0.0149538 + 0.999888i \(0.495240\pi\)
−0.955571 + 0.294761i \(0.904760\pi\)
\(398\) −5.16403e6 1.67790e6i −1.63411 0.530954i
\(399\) −221436. −0.0696332
\(400\) −2.93398e6 2.67582e6i −0.916868 0.836193i
\(401\) 5.58145e6 1.73335 0.866674 0.498874i \(-0.166253\pi\)
0.866674 + 0.498874i \(0.166253\pi\)
\(402\) −1.61474e6 524660.i −0.498353 0.161925i
\(403\) −1.62078e6 + 2.23081e6i −0.497121 + 0.684228i
\(404\) 85516.1 + 62131.1i 0.0260672 + 0.0189389i
\(405\) 231723. 284298.i 0.0701993 0.0861263i
\(406\) −333236. + 242110.i −0.100331 + 0.0728951i
\(407\) 1.59525e6i 0.477357i
\(408\) −3051.24 4199.67i −0.000907456 0.00124901i
\(409\) −569380. 1.75237e6i −0.168304 0.517986i 0.830961 0.556331i \(-0.187791\pi\)
−0.999265 + 0.0383453i \(0.987791\pi\)
\(410\) −588421. 2.22434e6i −0.172874 0.653494i
\(411\) −225453. + 693874.i −0.0658343 + 0.202617i
\(412\) −1.40736e6 + 457280.i −0.408473 + 0.132721i
\(413\) 1.10619e6 359423.i 0.319120 0.103688i
\(414\) −699420. + 2.15259e6i −0.200557 + 0.617250i
\(415\) −413315. 336882.i −0.117804 0.0960190i
\(416\) −364619. 1.12218e6i −0.103301 0.317929i
\(417\) −1.22407e6 1.68479e6i −0.344721 0.474468i
\(418\) 2.49192e6i 0.697580i
\(419\) 970920. 705415.i 0.270177 0.196295i −0.444445 0.895806i \(-0.646599\pi\)
0.714622 + 0.699511i \(0.246599\pi\)
\(420\) 83337.4 + 129228.i 0.0230524 + 0.0357464i
\(421\) 1.60016e6 + 1.16258e6i 0.440005 + 0.319682i 0.785637 0.618688i \(-0.212336\pi\)
−0.345632 + 0.938370i \(0.612336\pi\)
\(422\) 1.07760e6 1.48319e6i 0.294563 0.405431i
\(423\) 858632. + 278986.i 0.233322 + 0.0758110i
\(424\) −2.36607e6 −0.639164
\(425\) −12855.4 5822.03i −0.00345234 0.00156352i
\(426\) 1.39467e6 0.372348
\(427\) −315064. 102371.i −0.0836237 0.0271710i
\(428\) −467046. + 642834.i −0.123240 + 0.169625i
\(429\) −691112. 502123.i −0.181303 0.131724i
\(430\) −251475. + 4.52266e6i −0.0655878 + 1.17957i
\(431\) −1.09586e6 + 796187.i −0.284159 + 0.206453i −0.720729 0.693217i \(-0.756193\pi\)
0.436571 + 0.899670i \(0.356193\pi\)
\(432\) 926337.i 0.238814i
\(433\) 2.57152e6 + 3.53940e6i 0.659130 + 0.907214i 0.999452 0.0330948i \(-0.0105363\pi\)
−0.340323 + 0.940309i \(0.610536\pi\)
\(434\) 506474. + 1.55877e6i 0.129072 + 0.397244i
\(435\) −1.10063e6 + 709782.i −0.278880 + 0.179846i
\(436\) −582201. + 1.79183e6i −0.146675 + 0.451420i
\(437\) 4.13214e6 1.34261e6i 1.03507 0.336316i
\(438\) 192872. 62667.8i 0.0480378 0.0156084i
\(439\) 1.93584e6 5.95791e6i 0.479411 1.47548i −0.360503 0.932758i \(-0.617395\pi\)
0.839915 0.542719i \(-0.182605\pi\)
\(440\) 2.13939e6 1.37966e6i 0.526814 0.339736i
\(441\) −406743. 1.25182e6i −0.0995917 0.306512i
\(442\) −4737.70 6520.89i −0.00115349 0.00158764i
\(443\) 1.70812e6i 0.413532i −0.978390 0.206766i \(-0.933706\pi\)
0.978390 0.206766i \(-0.0662938\pi\)
\(444\) −421867. + 306504.i −0.101559 + 0.0737869i
\(445\) −279449. + 5.02577e6i −0.0668963 + 1.20310i
\(446\) −4.93095e6 3.58254e6i −1.17380 0.852814i
\(447\) −1.22857e6 + 1.69098e6i −0.290825 + 0.400286i
\(448\) 245719. + 79838.9i 0.0578420 + 0.0187940i
\(449\) 6.98874e6 1.63600 0.817999 0.575219i \(-0.195083\pi\)
0.817999 + 0.575219i \(0.195083\pi\)
\(450\) 839149. + 1.47508e6i 0.195347 + 0.343387i
\(451\) 2.18883e6 0.506723
\(452\) 1.77271e6 + 575990.i 0.408124 + 0.132608i
\(453\) −1.51526e6 + 2.08558e6i −0.346930 + 0.477509i
\(454\) 7.22923e6 + 5.25234e6i 1.64609 + 1.19595i
\(455\) −190361. 295185.i −0.0431072 0.0668446i
\(456\) 969456. 704351.i 0.218331 0.158627i
\(457\) 1.32555e6i 0.296897i 0.988920 + 0.148448i \(0.0474279\pi\)
−0.988920 + 0.148448i \(0.952572\pi\)
\(458\) −3.72391e6 5.12552e6i −0.829537 1.14176i
\(459\) 1017.32 + 3130.99i 0.000225386 + 0.000693666i
\(460\) −2.33867e6 1.90618e6i −0.515316 0.420020i
\(461\) −695306. + 2.13993e6i −0.152378 + 0.468973i −0.997886 0.0649911i \(-0.979298\pi\)
0.845507 + 0.533964i \(0.179298\pi\)
\(462\) −482911. + 156907.i −0.105260 + 0.0342009i
\(463\) −2.20509e6 + 716477.i −0.478050 + 0.155328i −0.538124 0.842866i \(-0.680867\pi\)
0.0600731 + 0.998194i \(0.480867\pi\)
\(464\) 1.02214e6 3.14583e6i 0.220402 0.678328i
\(465\) 1.33270e6 + 5.03787e6i 0.285826 + 1.08048i
\(466\) −2.94292e6 9.05737e6i −0.627789 1.93214i
\(467\) −3.24110e6 4.46099e6i −0.687702 0.946540i 0.312292 0.949986i \(-0.398903\pi\)
−0.999994 + 0.00344596i \(0.998903\pi\)
\(468\) 279242.i 0.0589340i
\(469\) 537270. 390349.i 0.112787 0.0819448i
\(470\) −2.63924e6 + 3.23804e6i −0.551105 + 0.676141i
\(471\) −553696. 402284.i −0.115006 0.0835565i
\(472\) −3.69968e6 + 5.09217e6i −0.764379 + 1.05208i
\(473\) −4.09820e6 1.33159e6i −0.842249 0.273663i
\(474\) −2.64073e6 −0.539856
\(475\) 1.34396e6 2.96756e6i 0.273309 0.603483i
\(476\) −1380.22 −0.000279211
\(477\) 1.42709e6 + 463690.i 0.287181 + 0.0933107i
\(478\) −697484. + 960004.i −0.139625 + 0.192178i
\(479\) −2.81251e6 2.04341e6i −0.560087 0.406927i 0.271404 0.962466i \(-0.412512\pi\)
−0.831491 + 0.555539i \(0.812512\pi\)
\(480\) −2.07924e6 805756.i −0.411909 0.159625i
\(481\) 963639. 700125.i 0.189912 0.137979i
\(482\) 5.03399e6i 0.986949i
\(483\) −520371. 716230.i −0.101495 0.139696i
\(484\) 135772. + 417863.i 0.0263449 + 0.0810812i
\(485\) 530175. 1.36811e6i 0.102345 0.264099i
\(486\) 122337. 376515.i 0.0234946 0.0723088i
\(487\) −6.52812e6 + 2.12112e6i −1.24729 + 0.405268i −0.856947 0.515404i \(-0.827642\pi\)
−0.390338 + 0.920671i \(0.627642\pi\)
\(488\) 1.70499e6 553984.i 0.324094 0.105305i
\(489\) −148202. + 456119.i −0.0280273 + 0.0862593i
\(490\) 6.08093e6 + 338119.i 1.14414 + 0.0636180i
\(491\) 1.97282e6 + 6.07171e6i 0.369303 + 1.13660i 0.947242 + 0.320519i \(0.103857\pi\)
−0.577939 + 0.816080i \(0.696143\pi\)
\(492\) −420552. 578840.i −0.0783261 0.107807i
\(493\) 11755.3i 0.00217830i
\(494\) 1.50529e6 1.09366e6i 0.277525 0.201634i
\(495\) −1.56075e6 + 412876.i −0.286299 + 0.0757367i
\(496\) −1.06480e7 7.73620e6i −1.94340 1.41196i
\(497\) −320649. + 441336.i −0.0582290 + 0.0801453i
\(498\) −547381. 177855.i −0.0989045 0.0321360i
\(499\) 5.44905e6 0.979647 0.489823 0.871822i \(-0.337061\pi\)
0.489823 + 0.871822i \(0.337061\pi\)
\(500\) −2.23763e6 + 332514.i −0.400280 + 0.0594819i
\(501\) 818057. 0.145609
\(502\) −3.59851e6 1.16923e6i −0.637328 0.207080i
\(503\) −2.22314e6 + 3.05989e6i −0.391784 + 0.539245i −0.958658 0.284560i \(-0.908153\pi\)
0.566874 + 0.823804i \(0.308153\pi\)
\(504\) −197539. 143521.i −0.0346400 0.0251674i
\(505\) −441134. + 116696.i −0.0769736 + 0.0203624i
\(506\) 8.06007e6 5.85598e6i 1.39947 1.01677i
\(507\) 2.70379e6i 0.467146i
\(508\) 1.72190e6 + 2.37000e6i 0.296039 + 0.407463i
\(509\) 1.68229e6 + 5.17757e6i 0.287811 + 0.885791i 0.985542 + 0.169431i \(0.0541930\pi\)
−0.697731 + 0.716360i \(0.745807\pi\)
\(510\) −15209.3 845.685i −0.00258930 0.000143974i
\(511\) −24512.3 + 75441.0i −0.00415271 + 0.0127807i
\(512\) 417036. 135503.i 0.0703070 0.0228441i
\(513\) −722762. + 234840.i −0.121256 + 0.0393983i
\(514\) −1.27929e6 + 3.93725e6i −0.213581 + 0.657333i
\(515\) 2.30826e6 5.95643e6i 0.383501 0.989619i
\(516\) 435270. + 1.33962e6i 0.0719671 + 0.221492i
\(517\) −2.33585e6 3.21502e6i −0.384343 0.529002i
\(518\) 707988.i 0.115932i
\(519\) 4.86981e6 3.53812e6i 0.793585 0.576573i
\(520\) 1.77234e6 + 686826.i 0.287435 + 0.111388i
\(521\) −5.14351e6 3.73698e6i −0.830167 0.603151i 0.0894398 0.995992i \(-0.471492\pi\)
−0.919606 + 0.392841i \(0.871492\pi\)
\(522\) −830909. + 1.14365e6i −0.133468 + 0.183703i
\(523\) −1.06088e7 3.44702e6i −1.69595 0.551048i −0.708053 0.706159i \(-0.750426\pi\)
−0.987897 + 0.155111i \(0.950426\pi\)
\(524\) 4.85934e6 0.773123
\(525\) −659708. 73591.3i −0.104461 0.0116527i
\(526\) 1.25794e7 1.98242
\(527\) −44485.9 14454.3i −0.00697743 0.00226710i
\(528\) 2.39670e6 3.29877e6i 0.374135 0.514953i
\(529\) 8.84601e6 + 6.42701e6i 1.37439 + 0.998549i
\(530\) −4.38655e6 + 5.38179e6i −0.678318 + 0.832218i
\(531\) 3.22939e6 2.34629e6i 0.497033 0.361115i
\(532\) 318613.i 0.0488072i
\(533\) 960634. + 1.32220e6i 0.146467 + 0.201595i
\(534\) 1.67894e6 + 5.16725e6i 0.254790 + 0.784163i
\(535\) −877219. 3.31605e6i −0.132502 0.500884i
\(536\) −1.11055e6 + 3.41793e6i −0.166966 + 0.513868i
\(537\) −5.01163e6 + 1.62838e6i −0.749969 + 0.243680i
\(538\) 9.45427e6 3.07188e6i 1.40823 0.457560i
\(539\) −1.79038e6 + 5.51022e6i −0.265444 + 0.816953i
\(540\) 409061. + 333415.i 0.0603676 + 0.0492040i
\(541\) −696546. 2.14375e6i −0.102319 0.314906i 0.886773 0.462206i \(-0.152942\pi\)
−0.989092 + 0.147300i \(0.952942\pi\)
\(542\) 5.66751e6 + 7.80065e6i 0.828693 + 1.14060i
\(543\) 3.25393e6i 0.473596i
\(544\) 16192.9 11764.8i 0.00234600 0.00170447i
\(545\) −4.40787e6 6.83510e6i −0.635678 0.985721i
\(546\) −306723. 222847.i −0.0440316 0.0319908i
\(547\) −4.30556e6 + 5.92609e6i −0.615263 + 0.846837i −0.996997 0.0774349i \(-0.975327\pi\)
0.381734 + 0.924272i \(0.375327\pi\)
\(548\) −998379. 324393.i −0.142018 0.0461445i
\(549\) −1.13693e6 −0.160991
\(550\) 828158. 7.42400e6i 0.116736 1.04648i
\(551\) 2.71362e6 0.380776
\(552\) 4.55641e6 + 1.48047e6i 0.636466 + 0.206800i
\(553\) 607130. 835643.i 0.0844246 0.116200i
\(554\) 4.65447e6 + 3.38167e6i 0.644311 + 0.468119i
\(555\) 124973. 2.24758e6i 0.0172220 0.309730i
\(556\) 2.42416e6 1.76126e6i 0.332563 0.241621i
\(557\) 6.53496e6i 0.892493i 0.894910 + 0.446246i \(0.147239\pi\)
−0.894910 + 0.446246i \(0.852761\pi\)
\(558\) 3.30624e6 + 4.55065e6i 0.449520 + 0.618711i
\(559\) −994253. 3.05999e6i −0.134576 0.414182i
\(560\) 1.40896e6 908618.i 0.189858 0.122437i
\(561\) 4477.99 13781.8i 0.000600726 0.00184884i
\(562\) 1.46982e7 4.77573e6i 1.96301 0.637821i
\(563\) −200607. + 65181.1i −0.0266732 + 0.00866664i −0.322323 0.946630i \(-0.604464\pi\)
0.295650 + 0.955296i \(0.404464\pi\)
\(564\) −401419. + 1.23544e6i −0.0531374 + 0.163540i
\(565\) −6.76219e6 + 4.36085e6i −0.891181 + 0.574711i
\(566\) −3.58160e6 1.10230e7i −0.469933 1.44630i
\(567\) 91019.3 + 125277.i 0.0118898 + 0.0163649i
\(568\) 2.95212e6i 0.383939i
\(569\) 8.67079e6 6.29970e6i 1.12274 0.815716i 0.138115 0.990416i \(-0.455896\pi\)
0.984622 + 0.174700i \(0.0558956\pi\)
\(570\) 195219. 3.51093e6i 0.0251672 0.452621i
\(571\) −3.10008e6 2.25234e6i −0.397908 0.289097i 0.370780 0.928721i \(-0.379090\pi\)
−0.768688 + 0.639624i \(0.779090\pi\)
\(572\) 722478. 994405.i 0.0923282 0.127079i
\(573\) −6.50653e6 2.11410e6i −0.827871 0.268992i
\(574\) 971424. 0.123063
\(575\) 1.27568e7 2.62669e6i 1.60906 0.331313i
\(576\) 886692. 0.111357
\(577\) −2.51482e6 817114.i −0.314461 0.102175i 0.147534 0.989057i \(-0.452866\pi\)
−0.461995 + 0.886882i \(0.652866\pi\)
\(578\) −5.59526e6 + 7.70121e6i −0.696627 + 0.958825i
\(579\) −1.44244e6 1.04799e6i −0.178813 0.129916i
\(580\) −1.02127e6 1.58364e6i −0.126058 0.195473i
\(581\) 182129. 132325.i 0.0223841 0.0162630i
\(582\) 1.58374e6i 0.193810i
\(583\) −3.88230e6 5.34353e6i −0.473062 0.651114i
\(584\) −132649. 408253.i −0.0160943 0.0495333i
\(585\) −934386. 761593.i −0.112885 0.0920097i
\(586\) −1.47918e6 + 4.55246e6i −0.177942 + 0.547649i
\(587\) 472421. 153499.i 0.0565892 0.0183870i −0.280586 0.959829i \(-0.590529\pi\)
0.337175 + 0.941442i \(0.390529\pi\)
\(588\) 1.80118e6 585240.i 0.214840 0.0698057i
\(589\) 3.33666e6 1.02692e7i 0.396299 1.21968i
\(590\) 4.72352e6 + 1.78558e7i 0.558644 + 2.11178i
\(591\) −469749. 1.44574e6i −0.0553219 0.170263i
\(592\) 3.34179e6 + 4.59957e6i 0.391899 + 0.539403i
\(593\) 8.71807e6i 1.01808i 0.860742 + 0.509042i \(0.170000\pi\)
−0.860742 + 0.509042i \(0.830000\pi\)
\(594\) −1.40980e6 + 1.02428e6i −0.163943 + 0.119111i
\(595\) 3764.37 4618.45i 0.000435914 0.000534815i
\(596\) −2.43307e6 1.76773e6i −0.280568 0.203845i
\(597\) 4.28431e6 5.89685e6i 0.491977 0.677148i
\(598\) 7.07481e6 + 2.29875e6i 0.809025 + 0.262868i
\(599\) −1.51097e7 −1.72064 −0.860318 0.509757i \(-0.829735\pi\)
−0.860318 + 0.509757i \(0.829735\pi\)
\(600\) 3.12231e6 1.77623e6i 0.354077 0.201429i
\(601\) 4.20197e6 0.474534 0.237267 0.971444i \(-0.423748\pi\)
0.237267 + 0.971444i \(0.423748\pi\)
\(602\) −1.81882e6 590971.i −0.204550 0.0664622i
\(603\) 1.33966e6 1.84388e6i 0.150038 0.206509i
\(604\) −3.00083e6 2.18023e6i −0.334695 0.243170i
\(605\) −1.76853e6 685349.i −0.196438 0.0761243i
\(606\) −398470. + 289506.i −0.0440773 + 0.0320240i
\(607\) 1.28146e6i 0.141167i −0.997506 0.0705837i \(-0.977514\pi\)
0.997506 0.0705837i \(-0.0224862\pi\)
\(608\) 2.71581e6 + 3.73799e6i 0.297948 + 0.410090i
\(609\) −170866. 525872.i −0.0186687 0.0574562i
\(610\) 1.90087e6 4.90517e6i 0.206837 0.533740i
\(611\) 916930. 2.82202e6i 0.0993649 0.305814i
\(612\) −4505.02 + 1463.77i −0.000486203 + 0.000157977i
\(613\) −2.70609e6 + 879262.i −0.290865 + 0.0945076i −0.450815 0.892617i \(-0.648867\pi\)
0.159950 + 0.987125i \(0.448867\pi\)
\(614\) −5.97621e6 + 1.83929e7i −0.639743 + 1.96893i
\(615\) 3.08389e6 + 171474.i 0.328784 + 0.0182815i
\(616\) 332127. + 1.02218e6i 0.0352657 + 0.108537i
\(617\) −8.86094e6 1.21960e7i −0.937059 1.28975i −0.957042 0.289951i \(-0.906361\pi\)
0.0199826 0.999800i \(-0.493639\pi\)
\(618\) 6.89523e6i 0.726235i
\(619\) 1.56722e6 1.13865e6i 0.164400 0.119444i −0.502543 0.864552i \(-0.667602\pi\)
0.666943 + 0.745108i \(0.267602\pi\)
\(620\) −7.24873e6 + 1.91756e6i −0.757326 + 0.200341i
\(621\) −2.45806e6 1.78589e6i −0.255778 0.185834i
\(622\) 8.31252e6 1.14412e7i 0.861503 1.18576i
\(623\) −2.02115e6 656711.i −0.208631 0.0677882i
\(624\) 3.04454e6 0.313012
\(625\) 4.99020e6 8.39436e6i 0.510996 0.859583i
\(626\) −868626. −0.0885925
\(627\) 3.18142e6 + 1.03371e6i 0.323186 + 0.105009i
\(628\) 578824. 796684.i 0.0585663 0.0806096i
\(629\) 16346.5 + 11876.4i 0.00164739 + 0.00119690i
\(630\) −692675. + 183238.i −0.0695310 + 0.0183935i
\(631\) −4.52410e6 + 3.28695e6i −0.452333 + 0.328639i −0.790516 0.612441i \(-0.790188\pi\)
0.338183 + 0.941080i \(0.390188\pi\)
\(632\) 5.58966e6i 0.556663i
\(633\) 1.44657e6 + 1.99103e6i 0.143492 + 0.197500i
\(634\) 554526. + 1.70665e6i 0.0547897 + 0.168625i
\(635\) −1.26266e7 702082.i −1.24266 0.0690961i
\(636\) −667179. + 2.05336e6i −0.0654033 + 0.201291i
\(637\) −4.11431e6 + 1.33682e6i −0.401743 + 0.130534i
\(638\) 5.91789e6 1.92284e6i 0.575592 0.187021i
\(639\) −578541. + 1.78057e6i −0.0560508 + 0.172507i
\(640\) −4.34740e6 + 1.12184e7i −0.419546 + 1.08263i
\(641\) 2.91810e6 + 8.98099e6i 0.280514 + 0.863334i 0.987707 + 0.156314i \(0.0499611\pi\)
−0.707193 + 0.707020i \(0.750039\pi\)
\(642\) −2.17625e6 2.99535e6i −0.208387 0.286820i
\(643\) 1.17321e7i 1.11905i 0.828815 + 0.559523i \(0.189016\pi\)
−0.828815 + 0.559523i \(0.810984\pi\)
\(644\) 1.03054e6 748735.i 0.0979157 0.0711399i
\(645\) −5.66972e6 2.19715e6i −0.536615 0.207951i
\(646\) 25534.7 + 18552.0i 0.00240740 + 0.00174908i
\(647\) 1.77629e6 2.44485e6i 0.166822 0.229610i −0.717419 0.696642i \(-0.754677\pi\)
0.884241 + 0.467032i \(0.154677\pi\)
\(648\) −796972. 258952.i −0.0745599 0.0242260i
\(649\) −1.75707e7 −1.63748
\(650\) 4.84806e6 2.75799e6i 0.450075 0.256041i
\(651\) −2.20016e6 −0.203471
\(652\) −656285. 213240.i −0.0604608 0.0196449i
\(653\) 8.65626e6 1.19143e7i 0.794415 1.09342i −0.199130 0.979973i \(-0.563812\pi\)
0.993544 0.113445i \(-0.0361885\pi\)
\(654\) −7.10226e6 5.16009e6i −0.649310 0.471751i
\(655\) −1.32532e7 + 1.62601e7i −1.20703 + 1.48088i
\(656\) −6.31103e6 + 4.58523e6i −0.572586 + 0.416008i
\(657\) 272233.i 0.0246053i
\(658\) −1.03667e6 1.42686e6i −0.0933420 0.128474i
\(659\) −6.09576e6 1.87608e7i −0.546782 1.68282i −0.716715 0.697367i \(-0.754355\pi\)
0.169933 0.985456i \(-0.445645\pi\)
\(660\) −594065. 2.24568e6i −0.0530853 0.200672i
\(661\) −6.26237e6 + 1.92736e7i −0.557487 + 1.71577i 0.131795 + 0.991277i \(0.457926\pi\)
−0.689282 + 0.724493i \(0.742074\pi\)
\(662\) −2.31434e7 + 7.51975e6i −2.05250 + 0.666897i
\(663\) 10290.5 3343.58i 0.000909183 0.000295411i
\(664\) −376467. + 1.15865e6i −0.0331365 + 0.101984i
\(665\) 1.06613e6 + 868973.i 0.0934879 + 0.0761995i
\(666\) −750843. 2.31086e6i −0.0655939 0.201877i
\(667\) 6.37695e6 + 8.77712e6i 0.555007 + 0.763902i
\(668\) 1.17706e6i 0.102060i
\(669\) 6.61927e6 4.80918e6i 0.571801 0.415437i
\(670\) 5.71543e6 + 8.86268e6i 0.491883 + 0.762743i
\(671\) 4.04871e6 + 2.94156e6i 0.347144 + 0.252215i
\(672\) 553382. 761665.i 0.0472717 0.0650640i
\(673\) −2.06365e7 6.70520e6i −1.75630 0.570656i −0.759491 0.650517i \(-0.774552\pi\)
−0.996806 + 0.0798619i \(0.974552\pi\)
\(674\) −2.25215e7 −1.90963
\(675\) −2.23132e6 + 459440.i −0.188496 + 0.0388123i
\(676\) −3.89034e6 −0.327431
\(677\) −4.58473e6 1.48967e6i −0.384452 0.124916i 0.110413 0.993886i \(-0.464783\pi\)
−0.494865 + 0.868970i \(0.664783\pi\)
\(678\) −5.10504e6 + 7.02649e6i −0.426506 + 0.587035i
\(679\) 501164. + 364117.i 0.0417162 + 0.0303086i
\(680\) −1790.07 + 32193.6i −0.000148456 + 0.00266991i
\(681\) −9.70446e6 + 7.05070e6i −0.801869 + 0.582592i
\(682\) 2.47595e7i 2.03836i
\(683\) 1.12282e7 + 1.54543e7i 0.920998 + 1.26765i 0.963269 + 0.268539i \(0.0865409\pi\)
−0.0422703 + 0.999106i \(0.513459\pi\)
\(684\) −337898. 1.03994e6i −0.0276150 0.0849904i
\(685\) 3.80841e6 2.45600e6i 0.310111 0.199987i
\(686\) −1.61641e6 + 4.97481e6i −0.131142 + 0.403614i
\(687\) 8.08847e6 2.62810e6i 0.653845 0.212447i
\(688\) 1.46058e7 4.74570e6i 1.17639 0.382234i
\(689\) 1.52398e6 4.69034e6i 0.122302 0.376406i
\(690\) 1.18148e7 7.61919e6i 0.944718 0.609237i
\(691\) 4.67521e6 + 1.43888e7i 0.372483 + 1.14638i 0.945161 + 0.326604i \(0.105904\pi\)
−0.572678 + 0.819780i \(0.694096\pi\)
\(692\) 5.09082e6 + 7.00691e6i 0.404131 + 0.556239i
\(693\) 681616.i 0.0539147i
\(694\) −2.24029e7 + 1.62767e7i −1.76565 + 1.28282i
\(695\) −718128. + 1.29152e7i −0.0563949 + 1.01424i
\(696\) 2.42077e6 + 1.75879e6i 0.189422 + 0.137623i
\(697\) −16295.5 + 22428.8i −0.00127053 + 0.00174874i
\(698\) −1.67130e7 5.43037e6i −1.29842 0.421882i
\(699\) 1.27843e7 0.989652
\(700\) 105887. 949219.i 0.00816763 0.0732186i
\(701\) 1.68307e7 1.29362 0.646812 0.762649i \(-0.276102\pi\)
0.646812 + 0.762649i \(0.276102\pi\)
\(702\) −1.23747e6 402079.i −0.0947746 0.0307941i
\(703\) −2.74157e6 + 3.77344e6i −0.209223 + 0.287971i
\(704\) −3.15759e6 2.29412e6i −0.240118 0.174456i
\(705\) −3.03916e6 4.71270e6i −0.230293 0.357106i
\(706\) 9.42387e6 6.84685e6i 0.711570 0.516986i
\(707\) 192654.i 0.0144954i
\(708\) 3.37596e6 + 4.64660e6i 0.253113 + 0.348380i
\(709\) −924238. 2.84451e6i −0.0690507 0.212516i 0.910577 0.413340i \(-0.135638\pi\)
−0.979627 + 0.200824i \(0.935638\pi\)
\(710\) −6.71480e6 5.47306e6i −0.499905 0.407459i
\(711\) 1.09543e6 3.37140e6i 0.0812665 0.250113i
\(712\) 1.09376e7 3.55383e6i 0.808575 0.262722i
\(713\) 4.10565e7 1.33401e7i 3.02453 0.982729i
\(714\) 1987.38 6116.52i 0.000145893 0.000449013i
\(715\) 1.35698e6 + 5.12963e6i 0.0992676 + 0.375250i
\(716\) −2.34299e6 7.21097e6i −0.170800 0.525667i
\(717\) −936297. 1.28870e6i −0.0680167 0.0936170i
\(718\) 1.09489e7i 0.792607i
\(719\) 6.38522e6 4.63914e6i 0.460632 0.334669i −0.333147 0.942875i \(-0.608111\pi\)
0.793779 + 0.608206i \(0.208111\pi\)
\(720\) 3.63518e6 4.45995e6i 0.261334 0.320626i
\(721\) 2.18195e6 + 1.58528e6i 0.156317 + 0.113571i
\(722\) 5.47518e6 7.53594e6i 0.390891 0.538015i
\(723\) −6.42685e6 2.08821e6i −0.457249 0.148569i
\(724\) −4.68190e6 −0.331952
\(725\) 8.08447e6 + 901834.i 0.571224 + 0.0637208i
\(726\) −2.04727e6 −0.144156
\(727\) 1.89701e7 + 6.16377e6i 1.33117 + 0.432524i 0.886317 0.463079i \(-0.153255\pi\)
0.444855 + 0.895603i \(0.353255\pi\)
\(728\) −471702. + 649242.i −0.0329867 + 0.0454024i
\(729\) 429945. + 312373.i 0.0299636 + 0.0217698i
\(730\) −1.17453e6 455157.i −0.0815747 0.0316122i
\(731\) 44155.2 32080.6i 0.00305625 0.00222049i
\(732\) 1.63587e6i 0.112842i
\(733\) −5.06576e6 6.97242e6i −0.348245 0.479318i 0.598582 0.801062i \(-0.295731\pi\)
−0.946827 + 0.321744i \(0.895731\pi\)
\(734\) −4.98548e6 1.53437e7i −0.341560 1.05121i
\(735\) −2.95418e6 + 7.62321e6i −0.201706 + 0.520498i
\(736\) −5.70833e6 + 1.75684e7i −0.388432 + 1.19547i
\(737\) −9.54129e6 + 3.10015e6i −0.647051 + 0.210240i
\(738\) 3.17070e6 1.03022e6i 0.214296 0.0696291i
\(739\) 3.19527e6 9.83403e6i 0.215227 0.662400i −0.783911 0.620874i \(-0.786778\pi\)
0.999137 0.0415264i \(-0.0132221\pi\)
\(740\) 3.23393e6 + 179817.i 0.217096 + 0.0120712i
\(741\) 771835. + 2.37546e6i 0.0516391 + 0.158929i
\(742\) −1.72300e6 2.37151e6i −0.114889 0.158130i
\(743\) 1.05147e7i 0.698753i 0.936982 + 0.349377i \(0.113607\pi\)
−0.936982 + 0.349377i \(0.886393\pi\)
\(744\) 9.63240e6 6.99835e6i 0.637973 0.463514i
\(745\) 1.25510e7 3.32019e6i 0.828488 0.219166i
\(746\) −6.95957e6 5.05642e6i −0.457863 0.332657i
\(747\) 454131. 625058.i 0.0297769 0.0409844i
\(748\) 19830.0 + 6443.15i 0.00129589 + 0.000421060i
\(749\) 1.44820e6 0.0943245
\(750\) 1.74841e6 1.03950e7i 0.113498 0.674791i
\(751\) 1.64943e7 1.06717 0.533584 0.845747i \(-0.320845\pi\)
0.533584 + 0.845747i \(0.320845\pi\)
\(752\) 1.34699e7 + 4.37663e6i 0.868598 + 0.282225i
\(753\) 2.98548e6 4.10916e6i 0.191879 0.264098i
\(754\) 3.75877e6 + 2.73091e6i 0.240778 + 0.174936i
\(755\) 1.54797e7 4.09497e6i 0.988317 0.261447i
\(756\) −180255. + 130963.i −0.0114705 + 0.00833381i
\(757\) 2.35077e7i 1.49098i −0.666520 0.745488i \(-0.732217\pi\)
0.666520 0.745488i \(-0.267783\pi\)
\(758\) 1.59010e6 + 2.18859e6i 0.100520 + 0.138354i
\(759\) 4.13279e6 + 1.27194e7i 0.260399 + 0.801424i
\(760\) −7.43161e6 413221.i −0.466712 0.0259507i
\(761\) −6.01594e6 + 1.85151e7i −0.376566 + 1.15895i 0.565849 + 0.824509i \(0.308548\pi\)
−0.942416 + 0.334444i \(0.891452\pi\)
\(762\) −1.29821e7 + 4.21814e6i −0.809948 + 0.263168i
\(763\) 3.26576e6 1.06111e6i 0.203083 0.0659855i
\(764\) 3.04187e6 9.36190e6i 0.188541 0.580271i
\(765\) 7388.82 19066.7i 0.000456480 0.00117794i
\(766\) 3.95278e6 + 1.21654e7i 0.243406 + 0.749126i
\(767\) −7.71144e6 1.06139e7i −0.473311 0.651457i
\(768\) 9.83386e6i 0.601618i
\(769\) −2.27139e7 + 1.65026e7i −1.38509 + 1.00632i −0.388702 + 0.921364i \(0.627076\pi\)
−0.996384 + 0.0849604i \(0.972924\pi\)
\(770\) 2.94077e6 + 1.13962e6i 0.178745 + 0.0692681i
\(771\) −4.49598e6 3.26652e6i −0.272388 0.197902i
\(772\) 1.50790e6 2.07544e6i 0.0910603 0.125334i
\(773\) 1.05091e7 + 3.41461e6i 0.632582 + 0.205538i 0.607718 0.794153i \(-0.292085\pi\)
0.0248634 + 0.999691i \(0.492085\pi\)
\(774\) −6.56333e6 −0.393797
\(775\) 1.33535e7 2.94853e7i 0.798619 1.76340i
\(776\) −3.35231e6 −0.199843
\(777\) 903882. + 293689.i 0.0537105 + 0.0174516i
\(778\) 4.55942e6 6.27550e6i 0.270060 0.371706i
\(779\) −5.17750e6 3.76168e6i −0.305687 0.222094i
\(780\) 1.09582e6 1.34444e6i 0.0644913 0.0791233i
\(781\) 6.66707e6 4.84391e6i 0.391118 0.284164i
\(782\) 126188.i 0.00737907i
\(783\) −1.11541e6 1.53523e6i −0.0650173 0.0894886i
\(784\) −6.38081e6 1.96381e7i −0.370754 1.14106i
\(785\) 1.08716e6 + 4.10968e6i 0.0629681 + 0.238031i
\(786\) −6.99693e6 + 2.15343e7i −0.403972 + 1.24330i
\(787\) 2.82817e7 9.18929e6i 1.62768 0.528866i 0.653944 0.756543i \(-0.273113\pi\)
0.973737 + 0.227677i \(0.0731131\pi\)
\(788\) 2.08020e6 675897.i 0.119341 0.0387762i
\(789\) −5.21822e6 + 1.60600e7i −0.298421 + 0.918446i
\(790\) 1.27141e7 + 1.03629e7i 0.724798 + 0.590764i
\(791\) −1.04979e6 3.23092e6i −0.0596569 0.183605i
\(792\) 2.16811e6 + 2.98414e6i 0.122820 + 0.169047i
\(793\) 3.73668e6i 0.211010i
\(794\) 2.72578e7 1.98040e7i 1.53440 1.11481i
\(795\) −5.05124e6 7.83276e6i −0.283453 0.439538i
\(796\) 8.48466e6 + 6.16446e6i 0.474626 + 0.344836i
\(797\) −7.61627e6 + 1.04829e7i −0.424714 + 0.584569i −0.966730 0.255800i \(-0.917661\pi\)
0.542016 + 0.840368i \(0.317661\pi\)
\(798\) 1.41195e6 + 458769.i 0.0784893 + 0.0255027i
\(799\) 50334.3 0.00278931
\(800\) 6.84873e6 + 1.20389e7i 0.378343 + 0.665060i
\(801\) −7.29344e6 −0.401653
\(802\) −3.55890e7 1.15636e7i −1.95380 0.634828i
\(803\) 704345. 969448.i 0.0385476 0.0530562i
\(804\) 2.65306e6 + 1.92756e6i 0.144746 + 0.105164i
\(805\) −305286. + 5.49044e6i −0.0166042 + 0.298619i
\(806\) 1.49564e7 1.08664e7i 0.810940 0.589182i
\(807\) 1.33445e7i 0.721302i
\(808\) 612799. + 843446.i 0.0330210 + 0.0454495i
\(809\) 1.58308e6 + 4.87221e6i 0.0850414 + 0.261731i 0.984531 0.175212i \(-0.0560612\pi\)
−0.899489 + 0.436943i \(0.856061\pi\)
\(810\) −2.06655e6 + 1.33269e6i −0.110671 + 0.0713701i
\(811\) −1.62307e6 + 4.99530e6i −0.0866533 + 0.266692i −0.984989 0.172619i \(-0.944777\pi\)
0.898335 + 0.439310i \(0.144777\pi\)
\(812\) 756650. 245850.i 0.0402721 0.0130852i
\(813\) −1.23100e7 + 3.99977e6i −0.653180 + 0.212231i
\(814\) −3.30502e6 + 1.01718e7i −0.174829 + 0.538068i
\(815\) 2.50346e6 1.61445e6i 0.132022 0.0851394i
\(816\) 15959.3 + 49117.7i 0.000839052 + 0.00258234i
\(817\) 7.40553e6 + 1.01928e7i 0.388152 + 0.534245i
\(818\) 1.23533e7i 0.645505i
\(819\) 411742. 299148.i 0.0214494 0.0155839i
\(820\) −246725. + 4.43724e6i −0.0128138 + 0.230451i
\(821\) −2.21878e7 1.61203e7i −1.14883 0.834673i −0.160505 0.987035i \(-0.551312\pi\)
−0.988325 + 0.152362i \(0.951312\pi\)
\(822\) 2.87512e6 3.95726e6i 0.148415 0.204275i
\(823\) −1.50766e7 4.89870e6i −0.775898 0.252105i −0.105810 0.994386i \(-0.533744\pi\)
−0.670088 + 0.742282i \(0.733744\pi\)
\(824\) −1.45952e7 −0.748845
\(825\) 9.13462e6 + 4.13694e6i 0.467257 + 0.211614i
\(826\) −7.79805e6 −0.397682
\(827\) −5.82888e6 1.89392e6i −0.296361 0.0962937i 0.157062 0.987589i \(-0.449798\pi\)
−0.453424 + 0.891295i \(0.649798\pi\)
\(828\) 2.56962e6 3.53677e6i 0.130254 0.179280i
\(829\) 1.41458e7 + 1.02775e7i 0.714892 + 0.519399i 0.884748 0.466070i \(-0.154330\pi\)
−0.169856 + 0.985469i \(0.554330\pi\)
\(830\) 1.93747e6 + 3.00436e6i 0.0976205 + 0.151376i
\(831\) −6.24812e6 + 4.53952e6i −0.313868 + 0.228038i
\(832\) 2.91424e6i 0.145954i
\(833\) −43133.9 59368.8i −0.00215381 0.00296446i
\(834\) 4.31454e6 + 1.32788e7i 0.214793 + 0.661064i
\(835\) −3.93862e6 3.21027e6i −0.195492 0.159340i
\(836\) −1.48734e6 + 4.57757e6i −0.0736030 + 0.226527i
\(837\) −7.18127e6 + 2.33334e6i −0.354314 + 0.115123i
\(838\) −7.65235e6 + 2.48640e6i −0.376431 + 0.122310i
\(839\) −8.84145e6 + 2.72112e7i −0.433629 + 1.33457i 0.460856 + 0.887475i \(0.347542\pi\)
−0.894485 + 0.447098i \(0.852458\pi\)
\(840\) 387862. + 1.46619e6i 0.0189662 + 0.0716956i
\(841\) −4.24439e6 1.30629e7i −0.206931 0.636868i
\(842\) −7.79447e6 1.07282e7i −0.378884 0.521489i
\(843\) 2.07461e7i 1.00547i
\(844\) −2.86478e6 + 2.08139e6i −0.138432 + 0.100577i
\(845\) 1.06104e7 1.30177e7i 0.511197 0.627179i
\(846\) −4.89690e6 3.55781e6i −0.235231 0.170906i
\(847\) 470688. 647847.i 0.0225437 0.0310287i
\(848\) 2.23876e7 + 7.27418e6i 1.06910 + 0.347372i
\(849\) 1.55587e7 0.740807
\(850\) 69908.0 + 63756.7i 0.00331879 + 0.00302677i
\(851\) −1.86477e7 −0.882678
\(852\) −2.56196e6 832432.i −0.120913 0.0392871i
\(853\) 6.22008e6 8.56120e6i 0.292700 0.402867i −0.637189 0.770708i \(-0.719903\pi\)
0.929889 + 0.367841i \(0.119903\pi\)
\(854\) 1.79686e6 + 1.30549e6i 0.0843080 + 0.0612533i
\(855\) 4.40139e6 + 1.70564e6i 0.205908 + 0.0797945i
\(856\) −6.34028e6 + 4.60648e6i −0.295750 + 0.214875i
\(857\) 2.86803e7i 1.33392i −0.745092 0.666962i \(-0.767594\pi\)
0.745092 0.666962i \(-0.232406\pi\)
\(858\) 3.36645e6 + 4.63353e6i 0.156119 + 0.214879i
\(859\) −6.75344e6 2.07850e7i −0.312279 0.961095i −0.976860 0.213879i \(-0.931390\pi\)
0.664582 0.747216i \(-0.268610\pi\)
\(860\) 3.16137e6 8.15786e6i 0.145757 0.376123i
\(861\) −402968. + 1.24021e6i −0.0185252 + 0.0570147i
\(862\) 8.63705e6 2.80635e6i 0.395911 0.128639i
\(863\) 6.49913e6 2.11170e6i 0.297049 0.0965171i −0.156701 0.987646i \(-0.550086\pi\)
0.453750 + 0.891129i \(0.350086\pi\)
\(864\) 998456. 3.07293e6i 0.0455035 0.140045i
\(865\) −3.73307e7 2.07571e6i −1.69639 0.0943249i
\(866\) −9.06394e6 2.78960e7i −0.410698 1.26400i
\(867\) −7.51103e6 1.03380e7i −0.339353 0.467079i
\(868\) 3.16570e6i 0.142617i
\(869\) −1.26237e7 + 9.17165e6i −0.567071 + 0.412001i
\(870\) 8.48847e6 2.24552e6i 0.380217 0.100582i
\(871\) −6.06019e6 4.40298e6i −0.270670 0.196653i
\(872\) −1.09224e7 + 1.50334e7i −0.486438 + 0.669524i
\(873\) 2.02194e6 + 656969.i 0.0897910 + 0.0291749i
\(874\) −2.91294e7 −1.28989
\(875\) 2.88744e6 + 2.94318e6i 0.127495 + 0.129956i
\(876\) −391702. −0.0172463
\(877\) 6.27344e6 + 2.03836e6i 0.275427 + 0.0894917i 0.443474 0.896287i \(-0.353746\pi\)
−0.168047 + 0.985779i \(0.553746\pi\)
\(878\) −2.46870e7 + 3.39788e7i −1.08077 + 1.48755i
\(879\) −5.19849e6 3.77692e6i −0.226937 0.164879i
\(880\) −2.44844e7 + 6.47703e6i −1.06582 + 0.281948i
\(881\) 1.66136e7 1.20705e7i 0.721146 0.523943i −0.165604 0.986192i \(-0.552957\pi\)
0.886750 + 0.462249i \(0.152957\pi\)
\(882\) 8.82471e6i 0.381970i
\(883\) 1.88760e7 + 2.59805e7i 0.814718 + 1.12136i 0.990578 + 0.136948i \(0.0437294\pi\)
−0.175860 + 0.984415i \(0.556271\pi\)
\(884\) 4810.89 + 14806.4i 0.000207059 + 0.000637263i
\(885\) −2.47557e7 1.37650e6i −1.06247 0.0590769i
\(886\) −3.53886e6 + 1.08915e7i −0.151453 + 0.466126i
\(887\) −1.26625e7 + 4.11429e6i −0.540393 + 0.175584i −0.566480 0.824075i \(-0.691695\pi\)
0.0260873 + 0.999660i \(0.491695\pi\)
\(888\) −4.89141e6 + 1.58932e6i −0.208162 + 0.0676360i
\(889\) 1.64991e6 5.07790e6i 0.0700173 0.215491i
\(890\) 1.21942e7 3.14669e7i 0.516033 1.33161i
\(891\) −722874. 2.22478e6i −0.0305048 0.0938842i
\(892\) 6.91967e6 + 9.52411e6i 0.291188 + 0.400786i
\(893\) 1.16192e7i 0.487583i
\(894\) 1.13371e7 8.23690e6i 0.474416 0.344683i
\(895\) 3.05192e7 + 1.18269e7i 1.27355 + 0.493531i
\(896\) −4.10951e6 2.98573e6i −0.171009 0.124246i
\(897\) −5.86958e6 + 8.07878e6i −0.243571 + 0.335247i
\(898\) −4.45623e7 1.44792e7i −1.84407 0.599174i
\(899\) 2.69621e7 1.11264
\(900\) −661063. 3.21052e6i −0.0272042 0.132120i
\(901\) 83658.2 0.00343318
\(902\) −1.39566e7 4.53479e6i −0.571169 0.185584i
\(903\) 1.50898e6 2.07693e6i 0.0615833 0.0847621i
\(904\) 1.48730e7 + 1.08059e7i 0.605311 + 0.439784i
\(905\) 1.27692e7 1.56664e7i 0.518255 0.635839i
\(906\) 1.39827e7 1.01590e7i 0.565938 0.411178i
\(907\) 1.52738e7i 0.616492i 0.951307 + 0.308246i \(0.0997420\pi\)
−0.951307 + 0.308246i \(0.900258\pi\)
\(908\) −1.01449e7 1.39632e7i −0.408350 0.562045i
\(909\) −204315. 628817.i −0.00820145 0.0252415i
\(910\) 602240. + 2.27658e6i 0.0241083 + 0.0911338i
\(911\) 2.74727e6 8.45522e6i 0.109674 0.337543i −0.881125 0.472884i \(-0.843213\pi\)
0.990799 + 0.135341i \(0.0432130\pi\)
\(912\) −1.13384e7 + 3.68407e6i −0.451403 + 0.146670i
\(913\) −3.23440e6 + 1.05092e6i −0.128415 + 0.0417247i
\(914\) 2.74626e6 8.45211e6i 0.108737 0.334657i
\(915\) 5.47387e6 + 4.46160e6i 0.216143 + 0.176172i
\(916\) 3.78144e6 + 1.16381e7i 0.148908 + 0.458292i
\(917\) −5.20575e6 7.16510e6i −0.204437 0.281384i
\(918\) 22071.8i 0.000864434i
\(919\) −3.05290e7 + 2.21806e7i −1.19241 + 0.866334i −0.993517 0.113688i \(-0.963734\pi\)
−0.198890 + 0.980022i \(0.563734\pi\)
\(920\) −1.61276e7 2.50084e7i −0.628203 0.974129i
\(921\) −2.10030e7 1.52596e7i −0.815891 0.592779i
\(922\) 8.86697e6 1.22043e7i 0.343517 0.472810i
\(923\) 5.85209e6 + 1.90146e6i 0.226103 + 0.0734654i
\(924\) 980742. 0.0377898
\(925\) −9.42179e6 + 1.03308e7i −0.362059 + 0.396990i
\(926\) 1.55447e7 0.595738
\(927\) 8.80308e6 + 2.86029e6i 0.336461 + 0.109323i
\(928\) −6.78148e6 + 9.33391e6i −0.258497 + 0.355790i
\(929\) −3.39497e6 2.46659e6i −0.129062 0.0937687i 0.521382 0.853324i \(-0.325417\pi\)
−0.650443 + 0.759555i \(0.725417\pi\)
\(930\) 1.93967e6 3.48841e7i 0.0735395 1.32258i
\(931\) 1.37048e7 9.95709e6i 0.518200 0.376494i
\(932\) 1.83946e7i 0.693666i
\(933\) 1.11587e7 + 1.53586e7i 0.419670 + 0.577627i
\(934\) 1.14240e7 + 3.51595e7i 0.428501 + 1.31879i
\(935\) −75643.3 + 48781.4i −0.00282971 + 0.00182484i
\(936\) −851083. + 2.61937e6i −0.0317528 + 0.0977252i
\(937\) −4.45783e6 + 1.44844e6i −0.165873 + 0.0538953i −0.390776 0.920486i \(-0.627793\pi\)
0.224903 + 0.974381i \(0.427793\pi\)
\(938\) −4.23452e6 + 1.37588e6i −0.157144 + 0.0510591i
\(939\) 360325. 1.10897e6i 0.0133362 0.0410445i
\(940\) 6.78086e6 4.37289e6i 0.250302 0.161417i
\(941\) −4.58157e6 1.41006e7i −0.168671 0.519116i 0.830617 0.556844i \(-0.187988\pi\)
−0.999288 + 0.0377279i \(0.987988\pi\)
\(942\) 2.69709e6 + 3.71222e6i 0.0990303 + 0.136304i
\(943\) 2.55864e7i 0.936978i
\(944\) 5.06614e7 3.68077e7i 1.85032 1.34434i
\(945\) 53398.2 960344.i 0.00194512 0.0349822i
\(946\) 2.33726e7 + 1.69812e7i 0.849141 + 0.616937i
\(947\) −7.11684e6 + 9.79548e6i −0.257877 + 0.354937i −0.918250 0.396000i \(-0.870398\pi\)
0.660374 + 0.750937i \(0.270398\pi\)
\(948\) 4.85092e6 + 1.57616e6i 0.175309 + 0.0569613i
\(949\) 894735. 0.0322499
\(950\) −1.47177e7 + 1.61376e7i −0.529091 + 0.580138i
\(951\) −2.40890e6 −0.0863709
\(952\) −12946.9 4206.70i −0.000462992 0.000150435i
\(953\) −8.32388e6 + 1.14568e7i −0.296889 + 0.408632i −0.931236 0.364416i \(-0.881269\pi\)
0.634348 + 0.773048i \(0.281269\pi\)
\(954\) −8.13890e6 5.91326e6i −0.289531 0.210357i
\(955\) 2.30301e7 + 3.57119e7i 0.817124 + 1.26708i
\(956\) 1.85425e6 1.34719e6i 0.0656179 0.0476742i
\(957\) 8.35295e6i 0.294822i
\(958\) 1.36999e7 + 1.88563e7i 0.482286 + 0.663810i
\(959\) 591233. + 1.81963e6i 0.0207593 + 0.0638905i
\(960\) −4.26907e6 3.47961e6i −0.149505 0.121857i
\(961\) 2.43057e7 7.48053e7i 0.848985 2.61291i
\(962\) −7.59497e6 + 2.46775e6i −0.264599 + 0.0859734i
\(963\) 4.72689e6 1.53586e6i 0.164252 0.0533686i
\(964\) 3.00462e6 9.24725e6i 0.104135 0.320494i
\(965\) 2.83218e6 + 1.07062e7i 0.0979043 + 0.370097i
\(966\) 1.83417e6 + 5.64500e6i 0.0632408 + 0.194635i
\(967\) −5.20010e6 7.15732e6i −0.178832 0.246141i 0.710185 0.704015i \(-0.248611\pi\)
−0.889017 + 0.457874i \(0.848611\pi\)
\(968\) 4.33348e6i 0.148644i
\(969\) −34277.5 + 24904.1i −0.00117274 + 0.000852043i
\(970\) −6.21499e6 + 7.62507e6i −0.212086 + 0.260204i
\(971\) −2.02979e7 1.47473e7i −0.690879 0.501953i 0.186070 0.982537i \(-0.440425\pi\)
−0.876949 + 0.480583i \(0.840425\pi\)
\(972\) −449457. + 618625.i −0.0152589 + 0.0210020i
\(973\) −5.19395e6 1.68762e6i −0.175880 0.0571468i
\(974\) 4.60198e7 1.55435
\(975\) 1.51002e6 + 7.33355e6i 0.0508710 + 0.247060i
\(976\) −1.78357e7 −0.599329
\(977\) 5.02135e7 + 1.63153e7i 1.68300 + 0.546839i 0.985490 0.169736i \(-0.0542916\pi\)
0.697509 + 0.716576i \(0.254292\pi\)
\(978\) 1.88996e6 2.60131e6i 0.0631839 0.0869652i
\(979\) 2.59726e7 + 1.88702e7i 0.866082 + 0.629245i
\(980\) −1.09686e7 4.25061e6i −0.364827 0.141379i
\(981\) 9.53402e6 6.92687e6i 0.316303 0.229808i
\(982\) 4.28023e7i 1.41641i
\(983\) −1.52359e7 2.09704e7i −0.502903 0.692186i 0.479800 0.877378i \(-0.340709\pi\)
−0.982702 + 0.185192i \(0.940709\pi\)
\(984\) −2.18068e6 6.71145e6i −0.0717968 0.220968i
\(985\) −3.41180e6 + 8.80408e6i −0.112045 + 0.289130i
\(986\) −24354.6 + 74955.6i −0.000797789 + 0.00245534i
\(987\) 2.25169e6 731619.i 0.0735726 0.0239052i
\(988\) −3.41793e6 + 1.11055e6i −0.111396 + 0.0361948i
\(989\) −1.55656e7 + 4.79060e7i −0.506029 + 1.55740i
\(990\) 1.08072e7 + 600915.i 0.350449 + 0.0194861i
\(991\) 5.87944e6 + 1.80951e7i 0.190174 + 0.585296i 0.999999 0.00137547i \(-0.000437825\pi\)
−0.809825 + 0.586672i \(0.800438\pi\)
\(992\) 2.69839e7 + 3.71402e7i 0.870615 + 1.19830i
\(993\) 3.26663e7i 1.05130i
\(994\) 2.95891e6 2.14978e6i 0.0949874 0.0690124i
\(995\) −4.37680e7 + 1.15783e7i −1.40152 + 0.370754i
\(996\) 899363. + 653425.i 0.0287267 + 0.0208712i
\(997\) −3.10956e7 + 4.27995e7i −0.990744 + 1.36364i −0.0599091 + 0.998204i \(0.519081\pi\)
−0.930835 + 0.365439i \(0.880919\pi\)
\(998\) −3.47448e7 1.12893e7i −1.10424 0.358790i
\(999\) 3.26172e6 0.103403
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 75.6.i.a.4.6 96
25.19 even 10 inner 75.6.i.a.19.6 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.6.i.a.4.6 96 1.1 even 1 trivial
75.6.i.a.19.6 yes 96 25.19 even 10 inner