Properties

Label 16.7.f.a.11.9
Level $16$
Weight $7$
Character 16.11
Analytic conductor $3.681$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [16,7,Mod(3,16)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(16, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("16.3");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 16.f (of order \(4\), 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: \(3.68086533792\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 11.9
Character \(\chi\) \(=\) 16.11
Dual form 16.7.f.a.3.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(5.94882 + 5.34898i) q^{2} +(25.6946 + 25.6946i) q^{3} +(6.77693 + 63.6402i) q^{4} +(-141.826 - 141.826i) q^{5} +(15.4128 + 290.292i) q^{6} +411.977 q^{7} +(-300.095 + 414.834i) q^{8} +591.425i q^{9} +O(q^{10})\) \(q+(5.94882 + 5.34898i) q^{2} +(25.6946 + 25.6946i) q^{3} +(6.77693 + 63.6402i) q^{4} +(-141.826 - 141.826i) q^{5} +(15.4128 + 290.292i) q^{6} +411.977 q^{7} +(-300.095 + 414.834i) q^{8} +591.425i q^{9} +(-85.0738 - 1602.32i) q^{10} +(-44.9619 + 44.9619i) q^{11} +(-1461.08 + 1809.34i) q^{12} +(2355.48 - 2355.48i) q^{13} +(2450.78 + 2203.65i) q^{14} -7288.34i q^{15} +(-4004.15 + 862.570i) q^{16} -3212.26 q^{17} +(-3163.52 + 3518.28i) q^{18} +(-1628.35 - 1628.35i) q^{19} +(8064.70 - 9986.99i) q^{20} +(10585.6 + 10585.6i) q^{21} +(-507.970 + 26.9702i) q^{22} -8469.99 q^{23} +(-18369.8 + 2948.16i) q^{24} +24604.3i q^{25} +(26611.7 - 1412.92i) q^{26} +(3534.93 - 3534.93i) q^{27} +(2791.94 + 26218.3i) q^{28} +(-8578.85 + 8578.85i) q^{29} +(38985.1 - 43357.0i) q^{30} +17162.0i q^{31} +(-28433.8 - 16286.8i) q^{32} -2310.56 q^{33} +(-19109.2 - 17182.3i) q^{34} +(-58429.1 - 58429.1i) q^{35} +(-37638.4 + 4008.05i) q^{36} +(-39117.2 - 39117.2i) q^{37} +(-976.759 - 18396.8i) q^{38} +121046. q^{39} +(101396. - 16272.9i) q^{40} +68881.9i q^{41} +(6349.71 + 119594. i) q^{42} +(-36872.5 + 36872.5i) q^{43} +(-3166.09 - 2556.68i) q^{44} +(83879.6 - 83879.6i) q^{45} +(-50386.4 - 45305.8i) q^{46} +62591.7i q^{47} +(-125048. - 80721.6i) q^{48} +52075.9 q^{49} +(-131608. + 146367. i) q^{50} +(-82537.8 - 82537.8i) q^{51} +(165866. + 133940. i) q^{52} +(-16287.1 - 16287.1i) q^{53} +(39936.9 - 2120.41i) q^{54} +12753.5 q^{55} +(-123632. + 170902. i) q^{56} -83679.7i q^{57} +(-96922.0 + 5145.98i) q^{58} +(56470.6 - 56470.6i) q^{59} +(463831. - 49392.5i) q^{60} +(242781. - 242781. i) q^{61} +(-91799.4 + 102094. i) q^{62} +243653. i q^{63} +(-82029.9 - 248979. i) q^{64} -668136. q^{65} +(-13745.1 - 12359.1i) q^{66} +(337557. + 337557. i) q^{67} +(-21769.3 - 204429. i) q^{68} +(-217633. - 217633. i) q^{69} +(-35048.4 - 660120. i) q^{70} +355567. q^{71} +(-245343. - 177484. i) q^{72} +341935. i q^{73} +(-23464.3 - 441939. i) q^{74} +(-632199. + 632199. i) q^{75} +(92593.4 - 114664. i) q^{76} +(-18523.3 + 18523.3i) q^{77} +(720081. + 647472. i) q^{78} -439742. i q^{79} +(690228. + 445558. i) q^{80} +612806. q^{81} +(-368448. + 409766. i) q^{82} +(-686399. - 686399. i) q^{83} +(-601931. + 745406. i) q^{84} +(455583. + 455583. i) q^{85} +(-416578. + 22117.8i) q^{86} -440860. q^{87} +(-5158.86 - 32144.5i) q^{88} +599060. i q^{89} +(947654. - 50314.8i) q^{90} +(970401. - 970401. i) q^{91} +(-57400.5 - 539032. i) q^{92} +(-440972. + 440972. i) q^{93} +(-334801. + 372347. i) q^{94} +461886. i q^{95} +(-312112. - 1.14908e6i) q^{96} +997682. q^{97} +(309790. + 278553. i) q^{98} +(-26591.6 - 26591.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8} - 1124 q^{10} + 1358 q^{11} - 2348 q^{12} - 2 q^{13} + 7564 q^{14} - 7976 q^{16} - 4 q^{17} - 1874 q^{18} + 3934 q^{19} - 16564 q^{20} - 1460 q^{21} + 25252 q^{22} - 13124 q^{23} - 32592 q^{24} + 58952 q^{26} + 35776 q^{27} + 45176 q^{28} - 33202 q^{29} + 8452 q^{30} - 39672 q^{32} - 4 q^{33} - 52588 q^{34} - 112420 q^{35} - 138484 q^{36} + 3598 q^{37} - 187280 q^{38} + 254396 q^{39} + 165160 q^{40} + 353496 q^{42} - 267986 q^{43} + 380724 q^{44} + 32706 q^{45} + 248156 q^{46} - 460824 q^{48} + 168066 q^{49} - 719674 q^{50} + 301788 q^{51} - 784892 q^{52} - 221842 q^{53} - 547552 q^{54} - 232708 q^{55} + 366424 q^{56} + 1441912 q^{58} + 39150 q^{59} + 2405600 q^{60} + 326494 q^{61} + 182832 q^{62} - 318656 q^{64} + 186412 q^{65} - 3392732 q^{66} - 122786 q^{67} - 2504400 q^{68} - 543188 q^{69} - 1186816 q^{70} - 267012 q^{71} + 1748596 q^{72} + 3610396 q^{74} - 275278 q^{75} + 4245988 q^{76} + 231180 q^{77} + 3179052 q^{78} - 2898968 q^{80} - 354298 q^{81} - 5004624 q^{82} - 288322 q^{83} - 7602776 q^{84} + 340748 q^{85} - 3240476 q^{86} + 2029884 q^{87} + 3308152 q^{88} + 10273400 q^{90} + 302396 q^{91} + 7253656 q^{92} - 1173344 q^{93} + 3859056 q^{94} - 5689424 q^{96} - 4 q^{97} - 9176950 q^{98} - 271522 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.94882 + 5.34898i 0.743603 + 0.668622i
\(3\) 25.6946 + 25.6946i 0.951652 + 0.951652i 0.998884 0.0472320i \(-0.0150400\pi\)
−0.0472320 + 0.998884i \(0.515040\pi\)
\(4\) 6.77693 + 63.6402i 0.105889 + 0.994378i
\(5\) −141.826 141.826i −1.13461 1.13461i −0.989401 0.145209i \(-0.953615\pi\)
−0.145209 0.989401i \(-0.546385\pi\)
\(6\) 15.4128 + 290.292i 0.0713555 + 1.34395i
\(7\) 411.977 1.20110 0.600549 0.799588i \(-0.294949\pi\)
0.600549 + 0.799588i \(0.294949\pi\)
\(8\) −300.095 + 414.834i −0.586123 + 0.810222i
\(9\) 591.425i 0.811283i
\(10\) −85.0738 1602.32i −0.0850738 1.60232i
\(11\) −44.9619 + 44.9619i −0.0337805 + 0.0337805i −0.723795 0.690015i \(-0.757604\pi\)
0.690015 + 0.723795i \(0.257604\pi\)
\(12\) −1461.08 + 1809.34i −0.845532 + 1.04707i
\(13\) 2355.48 2355.48i 1.07213 1.07213i 0.0749450 0.997188i \(-0.476122\pi\)
0.997188 0.0749450i \(-0.0238781\pi\)
\(14\) 2450.78 + 2203.65i 0.893140 + 0.803081i
\(15\) 7288.34i 2.15951i
\(16\) −4004.15 + 862.570i −0.977575 + 0.210588i
\(17\) −3212.26 −0.653829 −0.326915 0.945054i \(-0.606009\pi\)
−0.326915 + 0.945054i \(0.606009\pi\)
\(18\) −3163.52 + 3518.28i −0.542441 + 0.603272i
\(19\) −1628.35 1628.35i −0.237404 0.237404i 0.578370 0.815774i \(-0.303689\pi\)
−0.815774 + 0.578370i \(0.803689\pi\)
\(20\) 8064.70 9986.99i 1.00809 1.24837i
\(21\) 10585.6 + 10585.6i 1.14303 + 1.14303i
\(22\) −507.970 + 26.9702i −0.0477057 + 0.00253289i
\(23\) −8469.99 −0.696144 −0.348072 0.937468i \(-0.613164\pi\)
−0.348072 + 0.937468i \(0.613164\pi\)
\(24\) −18369.8 + 2948.16i −1.32883 + 0.213264i
\(25\) 24604.3i 1.57468i
\(26\) 26611.7 1412.92i 1.51409 0.0803892i
\(27\) 3534.93 3534.93i 0.179593 0.179593i
\(28\) 2791.94 + 26218.3i 0.127184 + 1.19435i
\(29\) −8578.85 + 8578.85i −0.351751 + 0.351751i −0.860761 0.509010i \(-0.830012\pi\)
0.509010 + 0.860761i \(0.330012\pi\)
\(30\) 38985.1 43357.0i 1.44389 1.60581i
\(31\) 17162.0i 0.576082i 0.957618 + 0.288041i \(0.0930039\pi\)
−0.957618 + 0.288041i \(0.906996\pi\)
\(32\) −28433.8 16286.8i −0.867731 0.497034i
\(33\) −2310.56 −0.0642946
\(34\) −19109.2 17182.3i −0.486189 0.437164i
\(35\) −58429.1 58429.1i −1.36278 1.36278i
\(36\) −37638.4 + 4008.05i −0.806722 + 0.0859063i
\(37\) −39117.2 39117.2i −0.772259 0.772259i 0.206242 0.978501i \(-0.433877\pi\)
−0.978501 + 0.206242i \(0.933877\pi\)
\(38\) −976.759 18396.8i −0.0178007 0.335267i
\(39\) 121046. 2.04059
\(40\) 101396. 16272.9i 1.58431 0.254265i
\(41\) 68881.9i 0.999433i 0.866189 + 0.499716i \(0.166562\pi\)
−0.866189 + 0.499716i \(0.833438\pi\)
\(42\) 6349.71 + 119594.i 0.0857050 + 1.61421i
\(43\) −36872.5 + 36872.5i −0.463764 + 0.463764i −0.899887 0.436123i \(-0.856351\pi\)
0.436123 + 0.899887i \(0.356351\pi\)
\(44\) −3166.09 2556.68i −0.0371676 0.0300136i
\(45\) 83879.6 83879.6i 0.920489 0.920489i
\(46\) −50386.4 45305.8i −0.517655 0.465457i
\(47\) 62591.7i 0.602869i 0.953487 + 0.301435i \(0.0974655\pi\)
−0.953487 + 0.301435i \(0.902534\pi\)
\(48\) −125048. 80721.6i −1.13072 0.729904i
\(49\) 52075.9 0.442638
\(50\) −131608. + 146367.i −1.05286 + 1.17093i
\(51\) −82537.8 82537.8i −0.622218 0.622218i
\(52\) 165866. + 133940.i 1.17963 + 0.952577i
\(53\) −16287.1 16287.1i −0.109400 0.109400i 0.650288 0.759688i \(-0.274648\pi\)
−0.759688 + 0.650288i \(0.774648\pi\)
\(54\) 39936.9 2120.41i 0.253626 0.0134660i
\(55\) 12753.5 0.0766554
\(56\) −123632. + 170902.i −0.703992 + 0.973156i
\(57\) 83679.7i 0.451851i
\(58\) −96922.0 + 5145.98i −0.496751 + 0.0263745i
\(59\) 56470.6 56470.6i 0.274958 0.274958i −0.556134 0.831092i \(-0.687716\pi\)
0.831092 + 0.556134i \(0.187716\pi\)
\(60\) 463831. 49392.5i 2.14737 0.228669i
\(61\) 242781. 242781.i 1.06961 1.06961i 0.0722192 0.997389i \(-0.476992\pi\)
0.997389 0.0722192i \(-0.0230081\pi\)
\(62\) −91799.4 + 102094.i −0.385181 + 0.428376i
\(63\) 243653.i 0.974431i
\(64\) −82029.9 248979.i −0.312919 0.949780i
\(65\) −668136. −2.43290
\(66\) −13745.1 12359.1i −0.0478096 0.0429888i
\(67\) 337557. + 337557.i 1.12234 + 1.12234i 0.991389 + 0.130946i \(0.0418015\pi\)
0.130946 + 0.991389i \(0.458198\pi\)
\(68\) −21769.3 204429.i −0.0692336 0.650153i
\(69\) −217633. 217633.i −0.662487 0.662487i
\(70\) −35048.4 660120.i −0.102182 1.92455i
\(71\) 355567. 0.993452 0.496726 0.867907i \(-0.334535\pi\)
0.496726 + 0.867907i \(0.334535\pi\)
\(72\) −245343. 177484.i −0.657319 0.475512i
\(73\) 341935.i 0.878971i 0.898250 + 0.439486i \(0.144839\pi\)
−0.898250 + 0.439486i \(0.855161\pi\)
\(74\) −23464.3 441939.i −0.0579045 1.09060i
\(75\) −632199. + 632199.i −1.49855 + 1.49855i
\(76\) 92593.4 114664.i 0.210930 0.261208i
\(77\) −18523.3 + 18523.3i −0.0405737 + 0.0405737i
\(78\) 720081. + 647472.i 1.51739 + 1.36439i
\(79\) 439742.i 0.891901i −0.895058 0.445950i \(-0.852866\pi\)
0.895058 0.445950i \(-0.147134\pi\)
\(80\) 690228. + 445558.i 1.34810 + 0.870230i
\(81\) 612806. 1.15310
\(82\) −368448. + 409766.i −0.668243 + 0.743181i
\(83\) −686399. 686399.i −1.20045 1.20045i −0.974031 0.226415i \(-0.927299\pi\)
−0.226415 0.974031i \(-0.572701\pi\)
\(84\) −601931. + 745406.i −1.01557 + 1.25764i
\(85\) 455583. + 455583.i 0.741841 + 0.741841i
\(86\) −416578. + 22117.8i −0.654939 + 0.0347733i
\(87\) −440860. −0.669488
\(88\) −5158.86 32144.5i −0.00757018 0.0471693i
\(89\) 599060.i 0.849768i 0.905248 + 0.424884i \(0.139685\pi\)
−0.905248 + 0.424884i \(0.860315\pi\)
\(90\) 947654. 50314.8i 1.29994 0.0690189i
\(91\) 970401. 970401.i 1.28774 1.28774i
\(92\) −57400.5 539032.i −0.0737144 0.692231i
\(93\) −440972. + 440972.i −0.548229 + 0.548229i
\(94\) −334801. + 372347.i −0.403092 + 0.448295i
\(95\) 461886.i 0.538721i
\(96\) −312112. 1.14908e6i −0.352775 1.29878i
\(97\) 997682. 1.09314 0.546572 0.837412i \(-0.315933\pi\)
0.546572 + 0.837412i \(0.315933\pi\)
\(98\) 309790. + 278553.i 0.329147 + 0.295957i
\(99\) −26591.6 26591.6i −0.0274056 0.0274056i
\(100\) −1.56583e6 + 166742.i −1.56583 + 0.166742i
\(101\) −238723. 238723.i −0.231702 0.231702i 0.581701 0.813403i \(-0.302387\pi\)
−0.813403 + 0.581701i \(0.802387\pi\)
\(102\) −49509.9 932495.i −0.0466543 0.878711i
\(103\) −526787. −0.482085 −0.241042 0.970515i \(-0.577489\pi\)
−0.241042 + 0.970515i \(0.577489\pi\)
\(104\) 270264. + 1.68400e6i 0.240264 + 1.49707i
\(105\) 3.00263e6i 2.59378i
\(106\) −9769.76 184009.i −0.00820288 0.154497i
\(107\) 1.20835e6 1.20835e6i 0.986375 0.986375i −0.0135332 0.999908i \(-0.504308\pi\)
0.999908 + 0.0135332i \(0.00430787\pi\)
\(108\) 248920. + 201008.i 0.197600 + 0.159566i
\(109\) −1.65809e6 + 1.65809e6i −1.28035 + 1.28035i −0.339879 + 0.940469i \(0.610386\pi\)
−0.940469 + 0.339879i \(0.889614\pi\)
\(110\) 75868.6 + 68218.4i 0.0570012 + 0.0512535i
\(111\) 2.01020e6i 1.46984i
\(112\) −1.64962e6 + 355359.i −1.17416 + 0.252937i
\(113\) 57104.5 0.0395763 0.0197881 0.999804i \(-0.493701\pi\)
0.0197881 + 0.999804i \(0.493701\pi\)
\(114\) 447601. 497796.i 0.302118 0.335998i
\(115\) 1.20127e6 + 1.20127e6i 0.789852 + 0.789852i
\(116\) −604098. 487821.i −0.387020 0.312526i
\(117\) 1.39309e6 + 1.39309e6i 0.869803 + 0.869803i
\(118\) 637993. 33873.6i 0.388303 0.0206165i
\(119\) −1.32338e6 −0.785313
\(120\) 3.02345e6 + 2.18719e6i 1.74968 + 1.26574i
\(121\) 1.76752e6i 0.997718i
\(122\) 2.74289e6 145631.i 1.51053 0.0801999i
\(123\) −1.76989e6 + 1.76989e6i −0.951112 + 0.951112i
\(124\) −1.09220e6 + 116306.i −0.572843 + 0.0610010i
\(125\) 1.27351e6 1.27351e6i 0.652035 0.652035i
\(126\) −1.30330e6 + 1.44945e6i −0.651526 + 0.724589i
\(127\) 699514.i 0.341496i 0.985315 + 0.170748i \(0.0546183\pi\)
−0.985315 + 0.170748i \(0.945382\pi\)
\(128\) 843802. 1.91991e6i 0.402356 0.915483i
\(129\) −1.89485e6 −0.882684
\(130\) −3.97462e6 3.57384e6i −1.80911 1.62669i
\(131\) 1.85396e6 + 1.85396e6i 0.824684 + 0.824684i 0.986776 0.162092i \(-0.0518242\pi\)
−0.162092 + 0.986776i \(0.551824\pi\)
\(132\) −15658.5 147044.i −0.00680812 0.0639331i
\(133\) −670843. 670843.i −0.285145 0.285145i
\(134\) 202482. + 3.81365e6i 0.0841534 + 1.58499i
\(135\) −1.00269e6 −0.407536
\(136\) 963984. 1.33255e6i 0.383224 0.529747i
\(137\) 1.00819e6i 0.392086i −0.980595 0.196043i \(-0.937191\pi\)
0.980595 0.196043i \(-0.0628092\pi\)
\(138\) −130546. 2.45877e6i −0.0496737 0.935581i
\(139\) −1.56333e6 + 1.56333e6i −0.582112 + 0.582112i −0.935483 0.353371i \(-0.885035\pi\)
0.353371 + 0.935483i \(0.385035\pi\)
\(140\) 3.32247e6 4.11441e6i 1.21081 1.49942i
\(141\) −1.60827e6 + 1.60827e6i −0.573722 + 0.573722i
\(142\) 2.11521e6 + 1.90192e6i 0.738733 + 0.664244i
\(143\) 211813.i 0.0724344i
\(144\) −510145. 2.36815e6i −0.170847 0.793090i
\(145\) 2.43341e6 0.798199
\(146\) −1.82900e6 + 2.03411e6i −0.587699 + 0.653605i
\(147\) 1.33807e6 + 1.33807e6i 0.421237 + 0.421237i
\(148\) 2.22433e6 2.75452e6i 0.686143 0.849691i
\(149\) −1.96711e6 1.96711e6i −0.594661 0.594661i 0.344226 0.938887i \(-0.388141\pi\)
−0.938887 + 0.344226i \(0.888141\pi\)
\(150\) −7.14245e6 + 379221.i −2.11628 + 0.112362i
\(151\) 431913. 0.125449 0.0627243 0.998031i \(-0.480021\pi\)
0.0627243 + 0.998031i \(0.480021\pi\)
\(152\) 1.16416e6 186835.i 0.331498 0.0532019i
\(153\) 1.89981e6i 0.530440i
\(154\) −209272. + 11111.1i −0.0572992 + 0.00304225i
\(155\) 2.43403e6 2.43403e6i 0.653628 0.653628i
\(156\) 820320. + 7.70339e6i 0.216078 + 2.02912i
\(157\) 4.24849e6 4.24849e6i 1.09783 1.09783i 0.103166 0.994664i \(-0.467103\pi\)
0.994664 0.103166i \(-0.0328974\pi\)
\(158\) 2.35217e6 2.61595e6i 0.596344 0.663220i
\(159\) 836983.i 0.208221i
\(160\) 1.72276e6 + 6.34256e6i 0.420597 + 1.54848i
\(161\) −3.48944e6 −0.836138
\(162\) 3.64547e6 + 3.27789e6i 0.857450 + 0.770990i
\(163\) −2.55603e6 2.55603e6i −0.590206 0.590206i 0.347481 0.937687i \(-0.387037\pi\)
−0.937687 + 0.347481i \(0.887037\pi\)
\(164\) −4.38366e6 + 466808.i −0.993814 + 0.105829i
\(165\) 327697. + 327697.i 0.0729493 + 0.0729493i
\(166\) −411733. 7.75480e6i −0.0900102 1.69530i
\(167\) 646882. 0.138891 0.0694457 0.997586i \(-0.477877\pi\)
0.0694457 + 0.997586i \(0.477877\pi\)
\(168\) −7.56794e6 + 1.21457e6i −1.59606 + 0.256151i
\(169\) 6.26972e6i 1.29894i
\(170\) 273279. + 5.14708e6i 0.0556237 + 1.04765i
\(171\) 963048. 963048.i 0.192602 0.192602i
\(172\) −2.59646e6 2.09669e6i −0.510265 0.412049i
\(173\) −4.10734e6 + 4.10734e6i −0.793273 + 0.793273i −0.982025 0.188752i \(-0.939556\pi\)
0.188752 + 0.982025i \(0.439556\pi\)
\(174\) −2.62260e6 2.35815e6i −0.497833 0.447635i
\(175\) 1.01364e7i 1.89134i
\(176\) 141251. 218817.i 0.0259092 0.0401368i
\(177\) 2.90198e6 0.523329
\(178\) −3.20436e6 + 3.56370e6i −0.568174 + 0.631890i
\(179\) 1.11716e6 + 1.11716e6i 0.194786 + 0.194786i 0.797760 0.602975i \(-0.206018\pi\)
−0.602975 + 0.797760i \(0.706018\pi\)
\(180\) 5.90656e6 + 4.76967e6i 1.01278 + 0.817844i
\(181\) 2.49437e6 + 2.49437e6i 0.420654 + 0.420654i 0.885429 0.464775i \(-0.153865\pi\)
−0.464775 + 0.885429i \(0.653865\pi\)
\(182\) 1.09634e7 582091.i 1.81857 0.0965554i
\(183\) 1.24763e7 2.03579
\(184\) 2.54180e6 3.51364e6i 0.408026 0.564032i
\(185\) 1.10957e7i 1.75243i
\(186\) −4.98201e6 + 264515.i −0.774223 + 0.0411066i
\(187\) 144429. 144429.i 0.0220867 0.0220867i
\(188\) −3.98335e6 + 424179.i −0.599480 + 0.0638375i
\(189\) 1.45631e6 1.45631e6i 0.215709 0.215709i
\(190\) −2.47062e6 + 2.74768e6i −0.360201 + 0.400594i
\(191\) 7.12374e6i 1.02237i −0.859471 0.511185i \(-0.829207\pi\)
0.859471 0.511185i \(-0.170793\pi\)
\(192\) 4.28969e6 8.50514e6i 0.606069 1.20165i
\(193\) 1.63763e6 0.227795 0.113898 0.993492i \(-0.463666\pi\)
0.113898 + 0.993492i \(0.463666\pi\)
\(194\) 5.93503e6 + 5.33658e6i 0.812864 + 0.730899i
\(195\) −1.71675e7 1.71675e7i −2.31528 2.31528i
\(196\) 352915. + 3.31412e6i 0.0468707 + 0.440149i
\(197\) −8.02811e6 8.02811e6i −1.05006 1.05006i −0.998679 0.0513818i \(-0.983637\pi\)
−0.0513818 0.998679i \(-0.516363\pi\)
\(198\) −15950.8 300426.i −0.00205489 0.0387028i
\(199\) −1.07094e7 −1.35896 −0.679481 0.733693i \(-0.737795\pi\)
−0.679481 + 0.733693i \(0.737795\pi\)
\(200\) −1.02067e7 7.38364e6i −1.27584 0.922955i
\(201\) 1.73468e7i 2.13615i
\(202\) −143197. 2.69704e6i −0.0173732 0.327215i
\(203\) −3.53429e6 + 3.53429e6i −0.422487 + 0.422487i
\(204\) 4.69337e6 5.81207e6i 0.552833 0.684606i
\(205\) 9.76926e6 9.76926e6i 1.13397 1.13397i
\(206\) −3.13376e6 2.81777e6i −0.358480 0.322332i
\(207\) 5.00936e6i 0.564770i
\(208\) −7.39991e6 + 1.14634e7i −0.822311 + 1.27387i
\(209\) 146428. 0.0160392
\(210\) 1.60610e7 1.78621e7i 1.73426 1.92874i
\(211\) −599213. 599213.i −0.0637872 0.0637872i 0.674494 0.738281i \(-0.264362\pi\)
−0.738281 + 0.674494i \(0.764362\pi\)
\(212\) 926140. 1.14689e6i 0.0972006 0.120369i
\(213\) 9.13616e6 + 9.13616e6i 0.945420 + 0.945420i
\(214\) 1.36517e7 724824.i 1.39298 0.0739591i
\(215\) 1.04590e7 1.05238
\(216\) 405593. + 2.52722e6i 0.0402466 + 0.250774i
\(217\) 7.07037e6i 0.691931i
\(218\) −1.87327e7 + 994596.i −1.80814 + 0.0960013i
\(219\) −8.78588e6 + 8.78588e6i −0.836475 + 0.836475i
\(220\) 86429.9 + 811638.i 0.00811700 + 0.0762245i
\(221\) −7.56641e6 + 7.56641e6i −0.700992 + 0.700992i
\(222\) 1.07525e7 1.19583e7i 0.982770 1.09298i
\(223\) 4.79044e6i 0.431977i 0.976396 + 0.215989i \(0.0692975\pi\)
−0.976396 + 0.215989i \(0.930703\pi\)
\(224\) −1.17141e7 6.70979e6i −1.04223 0.596987i
\(225\) −1.45516e7 −1.27751
\(226\) 339704. + 305451.i 0.0294290 + 0.0264616i
\(227\) 1.24849e7 + 1.24849e7i 1.06735 + 1.06735i 0.997562 + 0.0697866i \(0.0222318\pi\)
0.0697866 + 0.997562i \(0.477768\pi\)
\(228\) 5.32539e6 567091.i 0.449311 0.0478463i
\(229\) 4.70901e6 + 4.70901e6i 0.392123 + 0.392123i 0.875444 0.483320i \(-0.160569\pi\)
−0.483320 + 0.875444i \(0.660569\pi\)
\(230\) 720574. + 1.35717e7i 0.0592236 + 1.11545i
\(231\) −951895. −0.0772242
\(232\) −984325. 6.13326e6i −0.0788269 0.491165i
\(233\) 7.62544e6i 0.602833i −0.953493 0.301417i \(-0.902540\pi\)
0.953493 0.301417i \(-0.0974595\pi\)
\(234\) 835637. + 1.57388e7i 0.0652184 + 1.22836i
\(235\) 8.87714e6 8.87714e6i 0.684021 0.684021i
\(236\) 3.97650e6 + 3.21110e6i 0.302527 + 0.244297i
\(237\) 1.12990e7 1.12990e7i 0.848779 0.848779i
\(238\) −7.87254e6 7.07871e6i −0.583961 0.525078i
\(239\) 1.14653e7i 0.839830i −0.907563 0.419915i \(-0.862060\pi\)
0.907563 0.419915i \(-0.137940\pi\)
\(240\) 6.28670e6 + 2.91836e7i 0.454767 + 2.11108i
\(241\) −1.91183e7 −1.36583 −0.682916 0.730497i \(-0.739289\pi\)
−0.682916 + 0.730497i \(0.739289\pi\)
\(242\) −9.45441e6 + 1.05146e7i −0.667096 + 0.741905i
\(243\) 1.31688e7 + 1.31688e7i 0.917760 + 0.917760i
\(244\) 1.70959e7 + 1.38053e7i 1.17685 + 0.950334i
\(245\) −7.38573e6 7.38573e6i −0.502221 0.502221i
\(246\) −1.99959e7 + 1.06166e6i −1.34318 + 0.0713150i
\(247\) −7.67109e6 −0.509057
\(248\) −7.11939e6 5.15025e6i −0.466754 0.337655i
\(249\) 3.52735e7i 2.28481i
\(250\) 1.43878e7 763907.i 0.920820 0.0488900i
\(251\) 1.23788e7 1.23788e7i 0.782810 0.782810i −0.197494 0.980304i \(-0.563280\pi\)
0.980304 + 0.197494i \(0.0632804\pi\)
\(252\) −1.55061e7 + 1.65122e6i −0.968952 + 0.103182i
\(253\) 380827. 380827.i 0.0235161 0.0235161i
\(254\) −3.74168e6 + 4.16128e6i −0.228331 + 0.253937i
\(255\) 2.34120e7i 1.41195i
\(256\) 1.52892e7 6.90771e6i 0.911305 0.411732i
\(257\) 2.58515e7 1.52295 0.761475 0.648194i \(-0.224475\pi\)
0.761475 + 0.648194i \(0.224475\pi\)
\(258\) −1.12721e7 1.01355e7i −0.656366 0.590182i
\(259\) −1.61154e7 1.61154e7i −0.927559 0.927559i
\(260\) −4.52791e6 4.25203e7i −0.257619 2.41923i
\(261\) −5.07374e6 5.07374e6i −0.285369 0.285369i
\(262\) 1.11209e6 + 2.09457e7i 0.0618353 + 1.16464i
\(263\) 4.58883e6 0.252252 0.126126 0.992014i \(-0.459746\pi\)
0.126126 + 0.992014i \(0.459746\pi\)
\(264\) 693386. 958496.i 0.0376846 0.0520929i
\(265\) 4.61989e6i 0.248252i
\(266\) −402402. 7.57905e6i −0.0213804 0.402689i
\(267\) −1.53926e7 + 1.53926e7i −0.808684 + 0.808684i
\(268\) −1.91946e7 + 2.37698e7i −0.997182 + 1.23487i
\(269\) −1.43832e7 + 1.43832e7i −0.738921 + 0.738921i −0.972369 0.233448i \(-0.924999\pi\)
0.233448 + 0.972369i \(0.424999\pi\)
\(270\) −5.96483e6 5.36337e6i −0.303045 0.272488i
\(271\) 1.56022e7i 0.783932i −0.919980 0.391966i \(-0.871795\pi\)
0.919980 0.391966i \(-0.128205\pi\)
\(272\) 1.28624e7 2.77080e6i 0.639167 0.137689i
\(273\) 4.98682e7 2.45095
\(274\) 5.39279e6 5.99755e6i 0.262157 0.291556i
\(275\) −1.10626e6 1.10626e6i −0.0531935 0.0531935i
\(276\) 1.23753e7 1.53251e7i 0.588612 0.728913i
\(277\) −1.49968e7 1.49968e7i −0.705600 0.705600i 0.260007 0.965607i \(-0.416275\pi\)
−0.965607 + 0.260007i \(0.916275\pi\)
\(278\) −1.76622e7 + 937756.i −0.822072 + 0.0436471i
\(279\) −1.01501e7 −0.467365
\(280\) 4.17726e7 6.70407e6i 1.90291 0.305397i
\(281\) 5.16260e6i 0.232675i −0.993210 0.116338i \(-0.962885\pi\)
0.993210 0.116338i \(-0.0371154\pi\)
\(282\) −1.81699e7 + 964712.i −0.810224 + 0.0430180i
\(283\) 7.74606e6 7.74606e6i 0.341760 0.341760i −0.515269 0.857029i \(-0.672308\pi\)
0.857029 + 0.515269i \(0.172308\pi\)
\(284\) 2.40965e6 + 2.26284e7i 0.105196 + 0.987867i
\(285\) −1.18680e7 + 1.18680e7i −0.512675 + 0.512675i
\(286\) −1.13298e6 + 1.26004e6i −0.0484312 + 0.0538624i
\(287\) 2.83777e7i 1.20042i
\(288\) 9.63243e6 1.68165e7i 0.403235 0.703975i
\(289\) −1.38189e7 −0.572508
\(290\) 1.44759e7 + 1.30163e7i 0.593543 + 0.533694i
\(291\) 2.56350e7 + 2.56350e7i 1.04029 + 1.04029i
\(292\) −2.17608e7 + 2.31727e6i −0.874030 + 0.0930738i
\(293\) 1.94355e7 + 1.94355e7i 0.772668 + 0.772668i 0.978572 0.205904i \(-0.0660136\pi\)
−0.205904 + 0.978572i \(0.566014\pi\)
\(294\) 802635. + 1.51172e7i 0.0315846 + 0.594881i
\(295\) −1.60180e7 −0.623940
\(296\) 2.79660e7 4.48826e6i 1.07834 0.173062i
\(297\) 317874.i 0.0121335i
\(298\) −1.17996e6 2.22240e7i −0.0445880 0.839794i
\(299\) −1.99509e7 + 1.99509e7i −0.746359 + 0.746359i
\(300\) −4.45176e7 3.59489e7i −1.64880 1.33144i
\(301\) −1.51906e7 + 1.51906e7i −0.557027 + 0.557027i
\(302\) 2.56937e6 + 2.31029e6i 0.0932839 + 0.0838777i
\(303\) 1.22678e7i 0.441000i
\(304\) 7.92473e6 + 5.11559e6i 0.282074 + 0.182085i
\(305\) −6.88653e7 −2.42718
\(306\) 1.01621e7 1.13016e7i 0.354664 0.394437i
\(307\) 1.20617e7 + 1.20617e7i 0.416861 + 0.416861i 0.884120 0.467259i \(-0.154758\pi\)
−0.467259 + 0.884120i \(0.654758\pi\)
\(308\) −1.30435e6 1.05329e6i −0.0446420 0.0360493i
\(309\) −1.35356e7 1.35356e7i −0.458777 0.458777i
\(310\) 2.74992e7 1.46004e6i 0.923069 0.0490094i
\(311\) 2.86256e7 0.951642 0.475821 0.879542i \(-0.342151\pi\)
0.475821 + 0.879542i \(0.342151\pi\)
\(312\) −3.63253e7 + 5.02140e7i −1.19604 + 1.65333i
\(313\) 4.36158e7i 1.42236i −0.703009 0.711181i \(-0.748160\pi\)
0.703009 0.711181i \(-0.251840\pi\)
\(314\) 4.79985e7 2.54843e6i 1.55038 0.0823160i
\(315\) 3.45564e7 3.45564e7i 1.10560 1.10560i
\(316\) 2.79853e7 2.98010e6i 0.886886 0.0944429i
\(317\) −1.79251e7 + 1.79251e7i −0.562708 + 0.562708i −0.930076 0.367368i \(-0.880259\pi\)
0.367368 + 0.930076i \(0.380259\pi\)
\(318\) 4.47700e6 4.97906e6i 0.139221 0.154834i
\(319\) 771442.i 0.0237646i
\(320\) −2.36778e7 + 4.69457e7i −0.722588 + 1.43267i
\(321\) 6.20963e7 1.87737
\(322\) −2.07580e7 1.86649e7i −0.621754 0.559060i
\(323\) 5.23069e6 + 5.23069e6i 0.155221 + 0.155221i
\(324\) 4.15294e6 + 3.89991e7i 0.122102 + 1.14662i
\(325\) 5.79549e7 + 5.79549e7i 1.68826 + 1.68826i
\(326\) −1.53322e6 2.88776e7i −0.0442540 0.833504i
\(327\) −8.52078e7 −2.43689
\(328\) −2.85745e7 2.06711e7i −0.809762 0.585791i
\(329\) 2.57863e7i 0.724106i
\(330\) 196568. + 3.70226e6i 0.00546978 + 0.103021i
\(331\) −1.49668e7 + 1.49668e7i −0.412709 + 0.412709i −0.882681 0.469972i \(-0.844264\pi\)
0.469972 + 0.882681i \(0.344264\pi\)
\(332\) 3.90309e7 4.83343e7i 1.06658 1.32081i
\(333\) 2.31349e7 2.31349e7i 0.626520 0.626520i
\(334\) 3.84818e6 + 3.46016e6i 0.103280 + 0.0928659i
\(335\) 9.57489e7i 2.54683i
\(336\) −5.15170e7 3.32554e7i −1.35810 0.876687i
\(337\) −1.92483e7 −0.502924 −0.251462 0.967867i \(-0.580911\pi\)
−0.251462 + 0.967867i \(0.580911\pi\)
\(338\) 3.35366e7 3.72974e7i 0.868498 0.965893i
\(339\) 1.46728e6 + 1.46728e6i 0.0376629 + 0.0376629i
\(340\) −2.59059e7 + 3.20808e7i −0.659117 + 0.816223i
\(341\) −771638. 771638.i −0.0194603 0.0194603i
\(342\) 1.08803e7 577680.i 0.271997 0.0144414i
\(343\) −2.70146e7 −0.669447
\(344\) −4.23070e6 2.63612e7i −0.103929 0.647575i
\(345\) 6.17321e7i 1.50333i
\(346\) −4.64039e7 + 2.46377e6i −1.12028 + 0.0594801i
\(347\) 5.04931e7 5.04931e7i 1.20849 1.20849i 0.236975 0.971516i \(-0.423844\pi\)
0.971516 0.236975i \(-0.0761560\pi\)
\(348\) −2.98768e6 2.80564e7i −0.0708918 0.665724i
\(349\) 8.31696e6 8.31696e6i 0.195654 0.195654i −0.602480 0.798134i \(-0.705821\pi\)
0.798134 + 0.602480i \(0.205821\pi\)
\(350\) −5.42195e7 + 6.02997e7i −1.26459 + 1.40641i
\(351\) 1.66529e7i 0.385095i
\(352\) 2.01072e6 546152.i 0.0461025 0.0125223i
\(353\) 2.48212e7 0.564284 0.282142 0.959373i \(-0.408955\pi\)
0.282142 + 0.959373i \(0.408955\pi\)
\(354\) 1.72634e7 + 1.55226e7i 0.389149 + 0.349909i
\(355\) −5.04288e7 5.04288e7i −1.12718 1.12718i
\(356\) −3.81243e7 + 4.05979e6i −0.844991 + 0.0899815i
\(357\) −3.40037e7 3.40037e7i −0.747345 0.747345i
\(358\) 670124. + 1.26215e7i 0.0146051 + 0.275081i
\(359\) 8.53598e7 1.84489 0.922444 0.386130i \(-0.126188\pi\)
0.922444 + 0.386130i \(0.126188\pi\)
\(360\) 9.62423e6 + 5.99679e7i 0.206281 + 1.28532i
\(361\) 4.17428e7i 0.887279i
\(362\) 1.49624e6 + 2.81809e7i 0.0315409 + 0.594059i
\(363\) −4.54157e7 + 4.54157e7i −0.949480 + 0.949480i
\(364\) 6.83329e7 + 5.51802e7i 1.41686 + 1.14414i
\(365\) 4.84953e7 4.84953e7i 0.997289 0.997289i
\(366\) 7.42193e7 + 6.67355e7i 1.51382 + 1.36117i
\(367\) 5.07928e7i 1.02755i 0.857924 + 0.513777i \(0.171754\pi\)
−0.857924 + 0.513777i \(0.828246\pi\)
\(368\) 3.39151e7 7.30596e6i 0.680533 0.146600i
\(369\) −4.07385e7 −0.810823
\(370\) −5.93506e7 + 6.60063e7i −1.17171 + 1.30311i
\(371\) −6.70992e6 6.70992e6i −0.131400 0.131400i
\(372\) −3.10520e7 2.50751e7i −0.603199 0.487095i
\(373\) 2.15606e7 + 2.15606e7i 0.415466 + 0.415466i 0.883638 0.468172i \(-0.155087\pi\)
−0.468172 + 0.883638i \(0.655087\pi\)
\(374\) 1.63173e6 86635.3i 0.0311914 0.00165607i
\(375\) 6.54445e7 1.24102
\(376\) −2.59651e7 1.87835e7i −0.488458 0.353356i
\(377\) 4.04145e7i 0.754247i
\(378\) 1.64531e7 873561.i 0.304630 0.0161740i
\(379\) −9.50195e6 + 9.50195e6i −0.174540 + 0.174540i −0.788971 0.614431i \(-0.789386\pi\)
0.614431 + 0.788971i \(0.289386\pi\)
\(380\) −2.93945e7 + 3.13017e6i −0.535692 + 0.0570449i
\(381\) −1.79737e7 + 1.79737e7i −0.324985 + 0.324985i
\(382\) 3.81047e7 4.23778e7i 0.683578 0.760236i
\(383\) 7.09053e7i 1.26207i 0.775755 + 0.631034i \(0.217369\pi\)
−0.775755 + 0.631034i \(0.782631\pi\)
\(384\) 7.10124e7 2.76501e7i 1.25412 0.488319i
\(385\) 5.25417e6 0.0920707
\(386\) 9.74199e6 + 8.75966e6i 0.169389 + 0.152309i
\(387\) −2.18073e7 2.18073e7i −0.376244 0.376244i
\(388\) 6.76122e6 + 6.34927e7i 0.115752 + 1.08700i
\(389\) −2.91857e7 2.91857e7i −0.495816 0.495816i 0.414316 0.910133i \(-0.364021\pi\)
−0.910133 + 0.414316i \(0.864021\pi\)
\(390\) −1.02978e7 1.93955e8i −0.173601 3.26969i
\(391\) 2.72078e7 0.455159
\(392\) −1.56277e7 + 2.16028e7i −0.259440 + 0.358635i
\(393\) 9.52737e7i 1.56962i
\(394\) −4.81562e6 9.06999e7i −0.0787342 1.48292i
\(395\) −6.23669e7 + 6.23669e7i −1.01196 + 1.01196i
\(396\) 1.51208e6 1.87250e6i 0.0243495 0.0301534i
\(397\) −1.98612e7 + 1.98612e7i −0.317420 + 0.317420i −0.847775 0.530356i \(-0.822058\pi\)
0.530356 + 0.847775i \(0.322058\pi\)
\(398\) −6.37085e7 5.72845e7i −1.01053 0.908631i
\(399\) 3.44741e7i 0.542718i
\(400\) −2.12230e7 9.85194e7i −0.331609 1.53937i
\(401\) 3.50138e7 0.543007 0.271504 0.962437i \(-0.412479\pi\)
0.271504 + 0.962437i \(0.412479\pi\)
\(402\) −9.27875e7 + 1.03193e8i −1.42827 + 1.58844i
\(403\) 4.04248e7 + 4.04248e7i 0.617636 + 0.617636i
\(404\) 1.35746e7 1.68102e7i 0.205865 0.254934i
\(405\) −8.69120e7 8.69120e7i −1.30832 1.30832i
\(406\) −3.99296e7 + 2.12002e6i −0.596647 + 0.0316784i
\(407\) 3.51757e6 0.0521746
\(408\) 5.90086e7 9.47027e6i 0.868831 0.139438i
\(409\) 9.66336e7i 1.41240i −0.708011 0.706201i \(-0.750408\pi\)
0.708011 0.706201i \(-0.249592\pi\)
\(410\) 1.10371e8 5.86004e6i 1.60141 0.0850255i
\(411\) 2.59051e7 2.59051e7i 0.373130 0.373130i
\(412\) −3.57000e6 3.35248e7i −0.0510477 0.479375i
\(413\) 2.32646e7 2.32646e7i 0.330252 0.330252i
\(414\) 2.67950e7 2.97998e7i 0.377618 0.419964i
\(415\) 1.94699e8i 2.72407i
\(416\) −1.05338e8 + 2.86120e7i −1.46321 + 0.397437i
\(417\) −8.03383e7 −1.10794
\(418\) 871071. + 783237.i 0.0119268 + 0.0107242i
\(419\) −9.91922e7 9.91922e7i −1.34845 1.34845i −0.887344 0.461109i \(-0.847452\pi\)
−0.461109 0.887344i \(-0.652548\pi\)
\(420\) 1.91088e8 2.03486e7i 2.57920 0.274654i
\(421\) 1.70314e7 + 1.70314e7i 0.228246 + 0.228246i 0.811960 0.583714i \(-0.198401\pi\)
−0.583714 + 0.811960i \(0.698401\pi\)
\(422\) −359435. 6.76978e6i −0.00478281 0.0900819i
\(423\) −3.70183e7 −0.489097
\(424\) 1.16441e7 1.86876e6i 0.152760 0.0245164i
\(425\) 7.90356e7i 1.02957i
\(426\) 5.48028e6 + 1.03218e8i 0.0708882 + 1.33515i
\(427\) 1.00020e8 1.00020e8i 1.28470 1.28470i
\(428\) 8.50887e7 + 6.87108e7i 1.08528 + 0.876383i
\(429\) −5.44246e6 + 5.44246e6i −0.0689324 + 0.0689324i
\(430\) 6.22186e7 + 5.59448e7i 0.782555 + 0.703646i
\(431\) 6.19323e7i 0.773545i 0.922175 + 0.386772i \(0.126410\pi\)
−0.922175 + 0.386772i \(0.873590\pi\)
\(432\) −1.11053e7 + 1.72035e7i −0.137746 + 0.213386i
\(433\) −6.84514e6 −0.0843177 −0.0421588 0.999111i \(-0.513424\pi\)
−0.0421588 + 0.999111i \(0.513424\pi\)
\(434\) −3.78192e7 + 4.20603e7i −0.462640 + 0.514522i
\(435\) 6.25255e7 + 6.25255e7i 0.759608 + 0.759608i
\(436\) −1.16758e8 9.42843e7i −1.40873 1.13757i
\(437\) 1.37921e7 + 1.37921e7i 0.165267 + 0.165267i
\(438\) −9.92611e7 + 5.27017e6i −1.18129 + 0.0627194i
\(439\) 1.48097e8 1.75046 0.875232 0.483703i \(-0.160708\pi\)
0.875232 + 0.483703i \(0.160708\pi\)
\(440\) −3.82728e6 + 5.29060e6i −0.0449295 + 0.0621079i
\(441\) 3.07990e7i 0.359104i
\(442\) −8.54837e7 + 4.53867e6i −0.989957 + 0.0525608i
\(443\) −1.10015e8 + 1.10015e8i −1.26543 + 1.26543i −0.317013 + 0.948421i \(0.602680\pi\)
−0.948421 + 0.317013i \(0.897320\pi\)
\(444\) 1.27930e8 1.36230e7i 1.46158 0.155641i
\(445\) 8.49625e7 8.49625e7i 0.964155 0.964155i
\(446\) −2.56240e7 + 2.84975e7i −0.288830 + 0.321220i
\(447\) 1.01088e8i 1.13182i
\(448\) −3.37944e7 1.02574e8i −0.375847 1.14078i
\(449\) −3.03044e7 −0.334785 −0.167393 0.985890i \(-0.553535\pi\)
−0.167393 + 0.985890i \(0.553535\pi\)
\(450\) −8.65650e7 7.78363e7i −0.949959 0.854171i
\(451\) −3.09706e6 3.09706e6i −0.0337614 0.0337614i
\(452\) 386993. + 3.63414e6i 0.00419071 + 0.0393538i
\(453\) 1.10978e7 + 1.10978e7i 0.119383 + 0.119383i
\(454\) 7.48899e6 + 1.41051e8i 0.0800305 + 1.50734i
\(455\) −2.75257e8 −2.92216
\(456\) 3.47132e7 + 2.51119e7i 0.366100 + 0.264841i
\(457\) 1.61100e8i 1.68790i 0.536424 + 0.843949i \(0.319775\pi\)
−0.536424 + 0.843949i \(0.680225\pi\)
\(458\) 2.82467e6 + 5.32014e7i 0.0294017 + 0.553766i
\(459\) −1.13551e7 + 1.13551e7i −0.117423 + 0.117423i
\(460\) −6.83079e7 + 8.45897e7i −0.701775 + 0.869049i
\(461\) 1.62650e7 1.62650e7i 0.166016 0.166016i −0.619210 0.785226i \(-0.712547\pi\)
0.785226 + 0.619210i \(0.212547\pi\)
\(462\) −5.66265e6 5.09166e6i −0.0574241 0.0516338i
\(463\) 1.68452e8i 1.69720i −0.529038 0.848598i \(-0.677447\pi\)
0.529038 0.848598i \(-0.322553\pi\)
\(464\) 2.69511e7 4.17508e7i 0.269788 0.417937i
\(465\) 1.25083e8 1.24405
\(466\) 4.07883e7 4.53624e7i 0.403068 0.448268i
\(467\) 7.69239e7 + 7.69239e7i 0.755284 + 0.755284i 0.975460 0.220176i \(-0.0706631\pi\)
−0.220176 + 0.975460i \(0.570663\pi\)
\(468\) −7.92155e7 + 9.80972e7i −0.772810 + 0.957016i
\(469\) 1.39066e8 + 1.39066e8i 1.34804 + 1.34804i
\(470\) 1.00292e8 5.32491e6i 0.965992 0.0512884i
\(471\) 2.18326e8 2.08950
\(472\) 6.47936e6 + 4.03725e7i 0.0616178 + 0.383936i
\(473\) 3.31571e6i 0.0313324i
\(474\) 1.27654e8 6.77765e6i 1.19867 0.0636420i
\(475\) 4.00645e7 4.00645e7i 0.373834 0.373834i
\(476\) −8.96843e6 8.42200e7i −0.0831564 0.780898i
\(477\) 9.63262e6 9.63262e6i 0.0887543 0.0887543i
\(478\) 6.13276e7 6.82050e7i 0.561529 0.624500i
\(479\) 1.80538e8i 1.64271i −0.570416 0.821356i \(-0.693218\pi\)
0.570416 0.821356i \(-0.306782\pi\)
\(480\) −1.18704e8 + 2.07235e8i −1.07335 + 1.87387i
\(481\) −1.84279e8 −1.65593
\(482\) −1.13731e8 1.02263e8i −1.01564 0.913225i
\(483\) −8.96598e7 8.96598e7i −0.795712 0.795712i
\(484\) −1.12485e8 + 1.19783e7i −0.992108 + 0.105648i
\(485\) −1.41497e8 1.41497e8i −1.24029 1.24029i
\(486\) 7.89927e6 + 1.48779e8i 0.0688142 + 1.29608i
\(487\) −2.76822e7 −0.239670 −0.119835 0.992794i \(-0.538237\pi\)
−0.119835 + 0.992794i \(0.538237\pi\)
\(488\) 2.78563e7 + 1.73571e8i 0.239698 + 1.49354i
\(489\) 1.31353e8i 1.12334i
\(490\) −4.43029e6 8.34424e7i −0.0376569 0.709249i
\(491\) −1.13442e8 + 1.13442e8i −0.958361 + 0.958361i −0.999167 0.0408060i \(-0.987007\pi\)
0.0408060 + 0.999167i \(0.487007\pi\)
\(492\) −1.24631e8 1.00642e8i −1.04648 0.845052i
\(493\) 2.75575e7 2.75575e7i 0.229985 0.229985i
\(494\) −4.56339e7 4.10325e7i −0.378536 0.340366i
\(495\) 7.54277e6i 0.0621892i
\(496\) −1.48035e7 6.87193e7i −0.121316 0.563163i
\(497\) 1.46486e8 1.19323
\(498\) 1.88677e8 2.09836e8i 1.52768 1.69899i
\(499\) 2.96941e7 + 2.96941e7i 0.238984 + 0.238984i 0.816429 0.577445i \(-0.195950\pi\)
−0.577445 + 0.816429i \(0.695950\pi\)
\(500\) 8.96766e7 + 7.24157e7i 0.717413 + 0.579326i
\(501\) 1.66214e7 + 1.66214e7i 0.132176 + 0.132176i
\(502\) 1.39853e8 7.42534e6i 1.10550 0.0586956i
\(503\) 1.52573e7 0.119888 0.0599438 0.998202i \(-0.480908\pi\)
0.0599438 + 0.998202i \(0.480908\pi\)
\(504\) −1.01076e8 7.31192e7i −0.789505 0.571136i
\(505\) 6.77143e7i 0.525783i
\(506\) 4.30250e6 228437.i 0.0332101 0.00176325i
\(507\) 1.61098e8 1.61098e8i 1.23614 1.23614i
\(508\) −4.45172e7 + 4.74055e6i −0.339576 + 0.0361608i
\(509\) −1.49274e8 + 1.49274e8i −1.13196 + 1.13196i −0.142104 + 0.989852i \(0.545387\pi\)
−0.989852 + 0.142104i \(0.954613\pi\)
\(510\) −1.25230e8 + 1.39274e8i −0.944060 + 1.04993i
\(511\) 1.40869e8i 1.05573i
\(512\) 1.27902e8 + 4.06886e7i 0.952942 + 0.303154i
\(513\) −1.15122e7 −0.0852722
\(514\) 1.53786e8 + 1.38279e8i 1.13247 + 1.01828i
\(515\) 7.47122e7 + 7.47122e7i 0.546978 + 0.546978i
\(516\) −1.28413e7 1.20589e8i −0.0934670 0.877722i
\(517\) −2.81424e6 2.81424e6i −0.0203652 0.0203652i
\(518\) −9.66674e6 1.82068e8i −0.0695490 1.30992i
\(519\) −2.11073e8 −1.50984
\(520\) 2.00504e8 2.77165e8i 1.42598 1.97119i
\(521\) 1.15110e8i 0.813955i −0.913438 0.406977i \(-0.866583\pi\)
0.913438 0.406977i \(-0.133417\pi\)
\(522\) −3.04346e6 5.73221e7i −0.0213972 0.403005i
\(523\) 1.70829e8 1.70829e8i 1.19414 1.19414i 0.218250 0.975893i \(-0.429965\pi\)
0.975893 0.218250i \(-0.0700348\pi\)
\(524\) −1.05422e8 + 1.30551e8i −0.732722 + 0.907372i
\(525\) −2.60451e8 + 2.60451e8i −1.79990 + 1.79990i
\(526\) 2.72981e7 + 2.45455e7i 0.187575 + 0.168661i
\(527\) 5.51290e7i 0.376659i
\(528\) 9.25180e6 1.99302e6i 0.0628528 0.0135397i
\(529\) −7.62952e7 −0.515383
\(530\) −2.47117e7 + 2.74829e7i −0.165987 + 0.184601i
\(531\) 3.33981e7 + 3.33981e7i 0.223069 + 0.223069i
\(532\) 3.81463e7 4.72389e7i 0.253348 0.313736i
\(533\) 1.62250e8 + 1.62250e8i 1.07152 + 1.07152i
\(534\) −1.73903e8 + 9.23319e6i −1.14204 + 0.0606356i
\(535\) −3.42752e8 −2.23830
\(536\) −2.41329e8 + 3.87308e7i −1.56717 + 0.251514i
\(537\) 5.74100e7i 0.370736i
\(538\) −1.62498e8 + 8.62768e6i −1.04352 + 0.0554048i
\(539\) −2.34143e6 + 2.34143e6i −0.0149525 + 0.0149525i
\(540\) −6.79517e6 6.38115e7i −0.0431538 0.405245i
\(541\) −6.73179e7 + 6.73179e7i −0.425147 + 0.425147i −0.886971 0.461825i \(-0.847195\pi\)
0.461825 + 0.886971i \(0.347195\pi\)
\(542\) 8.34558e7 9.28147e7i 0.524154 0.582934i
\(543\) 1.28184e8i 0.800633i
\(544\) 9.13369e7 + 5.23175e7i 0.567348 + 0.324975i
\(545\) 4.70321e8 2.90539
\(546\) 2.96657e8 + 2.66744e8i 1.82254 + 1.63876i
\(547\) −6.44257e7 6.44257e7i −0.393638 0.393638i 0.482344 0.875982i \(-0.339786\pi\)
−0.875982 + 0.482344i \(0.839786\pi\)
\(548\) 6.41615e7 6.83244e6i 0.389882 0.0415178i
\(549\) 1.43587e8 + 1.43587e8i 0.867754 + 0.867754i
\(550\) −663583. 1.24983e7i −0.00398848 0.0751211i
\(551\) 2.79388e7 0.167014
\(552\) 1.55592e8 2.49709e7i 0.925061 0.148463i
\(553\) 1.81163e8i 1.07126i
\(554\) −8.99574e6 1.69430e8i −0.0529063 0.996465i
\(555\) −2.85100e8 + 2.85100e8i −1.66770 + 1.66770i
\(556\) −1.10085e8 8.88960e7i −0.640479 0.517199i
\(557\) −2.81484e7 + 2.81484e7i −0.162888 + 0.162888i −0.783845 0.620957i \(-0.786744\pi\)
0.620957 + 0.783845i \(0.286744\pi\)
\(558\) −6.03809e7 5.42924e7i −0.347534 0.312491i
\(559\) 1.73705e8i 0.994434i
\(560\) 2.84358e8 + 1.83560e8i 1.61920 + 1.04523i
\(561\) 7.42211e6 0.0420377
\(562\) 2.76146e7 3.07114e7i 0.155572 0.173018i
\(563\) −3.25814e7 3.25814e7i −0.182576 0.182576i 0.609901 0.792477i \(-0.291209\pi\)
−0.792477 + 0.609901i \(0.791209\pi\)
\(564\) −1.13250e8 9.14514e7i −0.631247 0.509745i
\(565\) −8.09892e6 8.09892e6i −0.0449036 0.0449036i
\(566\) 8.75134e7 4.64644e6i 0.482642 0.0256254i
\(567\) 2.52462e8 1.38499
\(568\) −1.06704e8 + 1.47501e8i −0.582285 + 0.804917i
\(569\) 6.00764e7i 0.326112i 0.986617 + 0.163056i \(0.0521351\pi\)
−0.986617 + 0.163056i \(0.947865\pi\)
\(570\) −1.34082e8 + 7.11895e6i −0.724012 + 0.0384407i
\(571\) 1.53517e8 1.53517e8i 0.824610 0.824610i −0.162155 0.986765i \(-0.551845\pi\)
0.986765 + 0.162155i \(0.0518446\pi\)
\(572\) −1.34798e7 + 1.43544e6i −0.0720272 + 0.00767004i
\(573\) 1.83042e8 1.83042e8i 0.972939 0.972939i
\(574\) −1.51792e8 + 1.68814e8i −0.802625 + 0.892633i
\(575\) 2.08399e8i 1.09620i
\(576\) 1.47252e8 4.85146e7i 0.770540 0.253866i
\(577\) −3.34357e8 −1.74054 −0.870269 0.492577i \(-0.836055\pi\)
−0.870269 + 0.492577i \(0.836055\pi\)
\(578\) −8.22064e7 7.39172e7i −0.425718 0.382791i
\(579\) 4.20783e7 + 4.20783e7i 0.216782 + 0.216782i
\(580\) 1.64910e7 + 1.54863e8i 0.0845209 + 0.793712i
\(581\) −2.82781e8 2.82781e8i −1.44185 1.44185i
\(582\) 1.53771e7 + 2.89620e8i 0.0780017 + 1.46913i
\(583\) 1.46460e6 0.00739118
\(584\) −1.41846e8 1.02613e8i −0.712162 0.515185i
\(585\) 3.95153e8i 1.97377i
\(586\) 1.16583e7 + 2.19578e8i 0.0579351 + 1.09118i
\(587\) 8.00181e7 8.00181e7i 0.395616 0.395616i −0.481068 0.876684i \(-0.659751\pi\)
0.876684 + 0.481068i \(0.159751\pi\)
\(588\) −7.60870e7 + 9.42230e7i −0.374264 + 0.463474i
\(589\) 2.79459e7 2.79459e7i 0.136764 0.136764i
\(590\) −9.52884e7 8.56800e7i −0.463964 0.417180i
\(591\) 4.12558e8i 1.99858i
\(592\) 1.90373e8 + 1.22890e8i 0.917570 + 0.592312i
\(593\) 5.20669e7 0.249688 0.124844 0.992176i \(-0.460157\pi\)
0.124844 + 0.992176i \(0.460157\pi\)
\(594\) −1.70030e6 + 1.89098e6i −0.00811273 + 0.00902250i
\(595\) 1.87690e8 + 1.87690e8i 0.891024 + 0.891024i
\(596\) 1.11856e8 1.38518e8i 0.528349 0.654286i
\(597\) −2.75175e8 2.75175e8i −1.29326 1.29326i
\(598\) −2.25401e8 + 1.19674e7i −1.05403 + 0.0559625i
\(599\) 4.82128e6 0.0224327 0.0112164 0.999937i \(-0.496430\pi\)
0.0112164 + 0.999937i \(0.496430\pi\)
\(600\) −7.25376e7 4.51977e8i −0.335822 2.09249i
\(601\) 4.87391e7i 0.224519i 0.993679 + 0.112260i \(0.0358088\pi\)
−0.993679 + 0.112260i \(0.964191\pi\)
\(602\) −1.71621e8 + 9.11202e6i −0.786647 + 0.0417662i
\(603\) −1.99640e8 + 1.99640e8i −0.910532 + 0.910532i
\(604\) 2.92705e6 + 2.74870e7i 0.0132837 + 0.124743i
\(605\) 2.50680e8 2.50680e8i 1.13202 1.13202i
\(606\) 6.56201e7 7.29788e7i 0.294862 0.327928i
\(607\) 3.50813e8i 1.56859i 0.620387 + 0.784296i \(0.286976\pi\)
−0.620387 + 0.784296i \(0.713024\pi\)
\(608\) 1.97796e7 + 7.28209e7i 0.0880049 + 0.324000i
\(609\) −1.81624e8 −0.804121
\(610\) −4.09667e8 3.68359e8i −1.80485 1.62286i
\(611\) 1.47433e8 + 1.47433e8i 0.646356 + 0.646356i
\(612\) 1.20904e8 1.28749e7i 0.527458 0.0561681i
\(613\) 1.59265e7 + 1.59265e7i 0.0691413 + 0.0691413i 0.740832 0.671691i \(-0.234432\pi\)
−0.671691 + 0.740832i \(0.734432\pi\)
\(614\) 7.23512e6 + 1.36270e8i 0.0312565 + 0.588702i
\(615\) 5.02034e8 2.15828
\(616\) −2.12533e6 1.32428e7i −0.00909253 0.0566550i
\(617\) 3.70913e8i 1.57912i 0.613671 + 0.789562i \(0.289692\pi\)
−0.613671 + 0.789562i \(0.710308\pi\)
\(618\) −8.11926e6 1.52922e8i −0.0343994 0.647896i
\(619\) −1.41681e7 + 1.41681e7i −0.0597363 + 0.0597363i −0.736344 0.676608i \(-0.763449\pi\)
0.676608 + 0.736344i \(0.263449\pi\)
\(620\) 1.71397e8 + 1.38407e8i 0.719165 + 0.580741i
\(621\) −2.99408e7 + 2.99408e7i −0.125023 + 0.125023i
\(622\) 1.70289e8 + 1.53118e8i 0.707643 + 0.636289i
\(623\) 2.46799e8i 1.02066i
\(624\) −4.84686e8 + 1.04411e8i −1.99483 + 0.429725i
\(625\) 2.32097e7 0.0950670
\(626\) 2.33300e8 2.59462e8i 0.951023 1.05767i
\(627\) 3.76240e6 + 3.76240e6i 0.0152638 + 0.0152638i
\(628\) 2.99166e8 + 2.41583e8i 1.20791 + 0.975410i
\(629\) 1.25655e8 + 1.25655e8i 0.504925 + 0.504925i
\(630\) 3.90412e8 2.07285e7i 1.56135 0.0828985i
\(631\) −1.53432e8 −0.610699 −0.305350 0.952240i \(-0.598773\pi\)
−0.305350 + 0.952240i \(0.598773\pi\)
\(632\) 1.82420e8 + 1.31964e8i 0.722638 + 0.522764i
\(633\) 3.07931e7i 0.121406i
\(634\) −2.02514e8 + 1.07523e7i −0.794669 + 0.0421922i
\(635\) 9.92094e7 9.92094e7i 0.387464 0.387464i
\(636\) 5.32658e7 5.67217e6i 0.207051 0.0220485i
\(637\) 1.22664e8 1.22664e8i 0.474567 0.474567i
\(638\) 4.12643e6 4.58917e6i 0.0158896 0.0176715i
\(639\) 2.10291e8i 0.805970i
\(640\) −3.91966e8 + 1.52620e8i −1.49523 + 0.582199i
\(641\) −9.63888e7 −0.365976 −0.182988 0.983115i \(-0.558577\pi\)
−0.182988 + 0.983115i \(0.558577\pi\)
\(642\) 3.69399e8 + 3.32151e8i 1.39602 + 1.25525i
\(643\) −2.96341e8 2.96341e8i −1.11470 1.11470i −0.992506 0.122198i \(-0.961006\pi\)
−0.122198 0.992506i \(-0.538994\pi\)
\(644\) −2.36477e7 2.22069e8i −0.0885382 0.831437i
\(645\) 2.68739e8 + 2.68739e8i 1.00150 + 1.00150i
\(646\) 3.13761e6 + 5.90953e7i 0.0116386 + 0.219208i
\(647\) −2.51144e8 −0.927279 −0.463640 0.886024i \(-0.653457\pi\)
−0.463640 + 0.886024i \(0.653457\pi\)
\(648\) −1.83900e8 + 2.54213e8i −0.675860 + 0.934269i
\(649\) 5.07805e6i 0.0185765i
\(650\) 3.47640e7 + 6.54763e8i 0.126587 + 2.38421i
\(651\) −1.81670e8 + 1.81670e8i −0.658477 + 0.658477i
\(652\) 1.45344e8 1.79989e8i 0.524391 0.649385i
\(653\) 1.19499e8 1.19499e8i 0.429165 0.429165i −0.459179 0.888344i \(-0.651856\pi\)
0.888344 + 0.459179i \(0.151856\pi\)
\(654\) −5.06886e8 4.55775e8i −1.81208 1.62936i
\(655\) 5.25881e8i 1.87139i
\(656\) −5.94155e7 2.75813e8i −0.210469 0.977020i
\(657\) −2.02229e8 −0.713094
\(658\) −1.37930e8 + 1.53398e8i −0.484153 + 0.538447i
\(659\) −1.46053e8 1.46053e8i −0.510333 0.510333i 0.404295 0.914629i \(-0.367517\pi\)
−0.914629 + 0.404295i \(0.867517\pi\)
\(660\) −1.86339e7 + 2.30755e7i −0.0648146 + 0.0802637i
\(661\) −1.39338e8 1.39338e8i −0.482464 0.482464i 0.423454 0.905918i \(-0.360818\pi\)
−0.905918 + 0.423454i \(0.860818\pi\)
\(662\) −1.69091e8 + 8.97774e6i −0.582838 + 0.0309452i
\(663\) −3.88832e8 −1.33420
\(664\) 4.90727e8 7.87565e7i 1.67624 0.269019i
\(665\) 1.90286e8i 0.647057i
\(666\) 2.61374e8 1.38774e7i 0.884787 0.0469769i
\(667\) 7.26627e7 7.26627e7i 0.244869 0.244869i
\(668\) 4.38387e6 + 4.11677e7i 0.0147071 + 0.138111i
\(669\) −1.23089e8 + 1.23089e8i −0.411092 + 0.411092i
\(670\) 5.12158e8 5.69593e8i 1.70286 1.89383i
\(671\) 2.18318e7i 0.0722638i
\(672\) −1.28583e8 4.73394e8i −0.423717 1.55996i
\(673\) 1.12659e8 0.369590 0.184795 0.982777i \(-0.440838\pi\)
0.184795 + 0.982777i \(0.440838\pi\)
\(674\) −1.14505e8 1.02959e8i −0.373976 0.336266i
\(675\) 8.69747e7 + 8.69747e7i 0.282801 + 0.282801i
\(676\) 3.99006e8 4.24894e7i 1.29163 0.137544i
\(677\) 2.59382e8 + 2.59382e8i 0.835938 + 0.835938i 0.988321 0.152384i \(-0.0486949\pi\)
−0.152384 + 0.988321i \(0.548695\pi\)
\(678\) 880139. + 1.65770e7i 0.00282398 + 0.0531884i
\(679\) 4.11022e8 1.31297
\(680\) −3.25709e8 + 5.22730e7i −1.03587 + 0.166246i
\(681\) 6.41587e8i 2.03149i
\(682\) −462863. 8.71781e6i −0.00145915 0.0274824i
\(683\) −1.80845e8 + 1.80845e8i −0.567604 + 0.567604i −0.931456 0.363853i \(-0.881461\pi\)
0.363853 + 0.931456i \(0.381461\pi\)
\(684\) 6.78151e7 + 5.47621e7i 0.211913 + 0.171124i
\(685\) −1.42988e8 + 1.42988e8i −0.444865 + 0.444865i
\(686\) −1.60705e8 1.44500e8i −0.497802 0.447607i
\(687\) 2.41992e8i 0.746330i
\(688\) 1.15838e8 1.79448e8i 0.355701 0.551028i
\(689\) −7.67279e7 −0.234583
\(690\) −3.30204e8 + 3.67233e8i −1.00516 + 1.11788i
\(691\) −3.89481e8 3.89481e8i −1.18046 1.18046i −0.979625 0.200838i \(-0.935634\pi\)
−0.200838 0.979625i \(-0.564366\pi\)
\(692\) −2.89227e8 2.33557e8i −0.872812 0.704814i
\(693\) −1.09551e7 1.09551e7i −0.0329168 0.0329168i
\(694\) 5.70460e8 3.02880e7i 1.70666 0.0906134i
\(695\) 4.43442e8 1.32094
\(696\) 1.32300e8 1.82884e8i 0.392403 0.542434i
\(697\) 2.21267e8i 0.653458i
\(698\) 9.39633e7 4.98889e6i 0.276307 0.0146703i
\(699\) 1.95933e8 1.95933e8i 0.573687 0.573687i
\(700\) −6.45084e8 + 6.86938e7i −1.88071 + 0.200273i
\(701\) −1.36109e8 + 1.36109e8i −0.395122 + 0.395122i −0.876509 0.481386i \(-0.840133\pi\)
0.481386 + 0.876509i \(0.340133\pi\)
\(702\) 8.90759e7 9.90651e7i 0.257483 0.286358i
\(703\) 1.27393e8i 0.366674i
\(704\) 1.48828e7 + 7.50635e6i 0.0426546 + 0.0215135i
\(705\) 4.56189e8 1.30190
\(706\) 1.47657e8 + 1.32768e8i 0.419603 + 0.377293i
\(707\) −9.83483e7 9.83483e7i −0.278297 0.278297i
\(708\) 1.96665e7 + 1.84683e8i 0.0554150 + 0.520387i
\(709\) −3.01255e8 3.01255e8i −0.845270 0.845270i 0.144268 0.989539i \(-0.453917\pi\)
−0.989539 + 0.144268i \(0.953917\pi\)
\(710\) −3.02495e7 5.69734e8i −0.0845167 1.59183i
\(711\) 2.60074e8 0.723584
\(712\) −2.48510e8 1.79775e8i −0.688501 0.498069i
\(713\) 1.45362e8i 0.401036i
\(714\) −2.03969e7 3.84166e8i −0.0560364 1.05542i
\(715\) 3.00407e7 3.00407e7i 0.0821848 0.0821848i
\(716\) −6.35254e7 + 7.86672e7i −0.173065 + 0.214316i
\(717\) 2.94596e8 2.94596e8i 0.799226 0.799226i
\(718\) 5.07790e8 + 4.56588e8i 1.37186 + 1.23353i
\(719\) 3.57293e8i 0.961253i 0.876925 + 0.480626i \(0.159591\pi\)
−0.876925 + 0.480626i \(0.840409\pi\)
\(720\) −2.63514e8 + 4.08218e8i −0.706003 + 1.09369i
\(721\) −2.17024e8 −0.579031
\(722\) 2.23281e8 2.48321e8i 0.593254 0.659783i
\(723\) −4.91236e8 4.91236e8i −1.29980 1.29980i
\(724\) −1.41838e8 + 1.75646e8i −0.373747 + 0.462832i
\(725\) −2.11077e8 2.11077e8i −0.553894 0.553894i
\(726\) −5.13097e8 + 2.72424e7i −1.34088 + 0.0711926i
\(727\) 7.94049e7 0.206654 0.103327 0.994647i \(-0.467051\pi\)
0.103327 + 0.994647i \(0.467051\pi\)
\(728\) 1.11342e8 + 6.93768e8i 0.288580 + 1.79813i
\(729\) 2.30001e8i 0.593672i
\(730\) 5.47890e8 2.90897e7i 1.40840 0.0747774i
\(731\) 1.18444e8 1.18444e8i 0.303223 0.303223i
\(732\) 8.45510e7 + 7.93994e8i 0.215569 + 2.02434i
\(733\) −2.46020e8 + 2.46020e8i −0.624680 + 0.624680i −0.946725 0.322044i \(-0.895630\pi\)
0.322044 + 0.946725i \(0.395630\pi\)
\(734\) −2.71690e8 + 3.02157e8i −0.687045 + 0.764091i
\(735\) 3.79547e8i 0.955879i
\(736\) 2.40834e8 + 1.37949e8i 0.604066 + 0.346007i
\(737\) −3.03544e7 −0.0758262
\(738\) −2.42346e8 2.17909e8i −0.602930 0.542134i
\(739\) 2.05535e8 + 2.05535e8i 0.509276 + 0.509276i 0.914304 0.405028i \(-0.132738\pi\)
−0.405028 + 0.914304i \(0.632738\pi\)
\(740\) −7.06132e8 + 7.51948e7i −1.74257 + 0.185563i
\(741\) −1.97106e8 1.97106e8i −0.484445 0.484445i
\(742\) −4.02491e6 7.58073e7i −0.00985247 0.185566i
\(743\) −1.49313e8 −0.364024 −0.182012 0.983296i \(-0.558261\pi\)
−0.182012 + 0.983296i \(0.558261\pi\)
\(744\) −5.05965e7 3.15264e8i −0.122858 0.765517i
\(745\) 5.57975e8i 1.34942i
\(746\) 1.29330e7 + 2.43588e8i 0.0311519 + 0.586731i
\(747\) 4.05954e8 4.05954e8i 0.973901 0.973901i
\(748\) 1.01703e7 + 8.21272e6i 0.0243013 + 0.0196238i
\(749\) 4.97813e8 4.97813e8i 1.18473 1.18473i
\(750\) 3.89317e8 + 3.50061e8i 0.922827 + 0.829774i
\(751\) 2.61119e8i 0.616478i −0.951309 0.308239i \(-0.900260\pi\)
0.951309 0.308239i \(-0.0997397\pi\)
\(752\) −5.39897e7 2.50626e8i −0.126957 0.589350i
\(753\) 6.36135e8 1.48992
\(754\) −2.16176e8 + 2.40419e8i −0.504306 + 0.560860i
\(755\) −6.12566e7 6.12566e7i −0.142335 0.142335i
\(756\) 1.02549e8 + 8.28105e7i 0.237338 + 0.191655i
\(757\) 4.05024e8 + 4.05024e8i 0.933670 + 0.933670i 0.997933 0.0642632i \(-0.0204697\pi\)
−0.0642632 + 0.997933i \(0.520470\pi\)
\(758\) −1.07351e8 + 5.69970e6i −0.246490 + 0.0130871i
\(759\) 1.95704e7 0.0447583
\(760\) −1.91606e8 1.38610e8i −0.436484 0.315757i
\(761\) 1.35070e8i 0.306481i −0.988189 0.153240i \(-0.951029\pi\)
0.988189 0.153240i \(-0.0489709\pi\)
\(762\) −2.03063e8 + 1.07815e7i −0.458952 + 0.0243676i
\(763\) −6.83094e8 + 6.83094e8i −1.53782 + 1.53782i
\(764\) 4.53356e8 4.82770e7i 1.01662 0.108258i
\(765\) −2.69443e8 + 2.69443e8i −0.601843 + 0.601843i
\(766\) −3.79271e8 + 4.21803e8i −0.843846 + 0.938477i
\(767\) 2.66030e8i 0.589583i
\(768\) 5.70340e8 + 2.15358e8i 1.25907 + 0.475420i
\(769\) 3.00152e8 0.660028 0.330014 0.943976i \(-0.392946\pi\)
0.330014 + 0.943976i \(0.392946\pi\)
\(770\) 3.12561e7 + 2.81044e7i 0.0684640 + 0.0615605i
\(771\) 6.64243e8 + 6.64243e8i 1.44932 + 1.44932i
\(772\) 1.10981e7 + 1.04219e8i 0.0241211 + 0.226515i
\(773\) 3.89585e7 + 3.89585e7i 0.0843458 + 0.0843458i 0.748021 0.663675i \(-0.231004\pi\)
−0.663675 + 0.748021i \(0.731004\pi\)
\(774\) −1.30810e7 2.46375e8i −0.0282110 0.531341i
\(775\) −4.22261e8 −0.907143
\(776\) −2.99399e8 + 4.13872e8i −0.640716 + 0.885689i
\(777\) 8.28157e8i 1.76543i
\(778\) −1.75069e7 3.29734e8i −0.0371766 0.700204i
\(779\) 1.12164e8 1.12164e8i 0.237269 0.237269i
\(780\) 9.76200e8 1.20889e9i 2.05710 2.54742i
\(781\) −1.59870e7 + 1.59870e7i −0.0335593 + 0.0335593i
\(782\) 1.61854e8 + 1.45534e8i 0.338458 + 0.304330i
\(783\) 6.06513e7i 0.126344i
\(784\) −2.08520e8 + 4.49191e7i −0.432712 + 0.0932144i
\(785\) −1.20509e9 −2.49122
\(786\) −5.09617e8 + 5.66766e8i −1.04948 + 1.16718i
\(787\) 4.96033e8 + 4.96033e8i 1.01762 + 1.01762i 0.999842 + 0.0177796i \(0.00565973\pi\)
0.0177796 + 0.999842i \(0.494340\pi\)
\(788\) 4.56504e8 5.65316e8i 0.932967 1.15535i
\(789\) 1.17908e8 + 1.17908e8i 0.240056 + 0.240056i
\(790\) −7.04609e8 + 3.74105e7i −1.42911 + 0.0758774i
\(791\) 2.35257e7 0.0475350
\(792\) 1.90111e7 3.05108e6i 0.0382676 0.00614155i
\(793\) 1.14373e9i 2.29352i
\(794\) −2.24388e8 + 1.19136e7i −0.448268 + 0.0238003i
\(795\) −1.18706e8 + 1.18706e8i −0.236250 + 0.236250i
\(796\) −7.25770e7 6.81550e8i −0.143900 1.35132i
\(797\) −3.36288e8 + 3.36288e8i −0.664257 + 0.664257i −0.956381 0.292123i \(-0.905638\pi\)
0.292123 + 0.956381i \(0.405638\pi\)
\(798\) 1.84401e8 2.05080e8i 0.362873 0.403567i
\(799\) 2.01061e8i 0.394174i
\(800\) 4.00726e8 6.99595e8i 0.782668 1.36640i
\(801\) −3.54299e8 −0.689402
\(802\) 2.08291e8 + 1.87288e8i 0.403782 + 0.363067i
\(803\) −1.53740e7 1.53740e7i −0.0296921 0.0296921i
\(804\) −1.10395e9 + 1.17558e8i −2.12414 + 0.226195i
\(805\) 4.94894e8 + 4.94894e8i 0.948690 + 0.948690i
\(806\) 2.42486e7 + 4.56711e8i 0.0463107 + 0.872241i
\(807\) −7.39140e8 −1.40639
\(808\) 1.70670e8 2.73907e7i 0.323536 0.0519242i
\(809\) 2.41708e8i 0.456506i 0.973602 + 0.228253i \(0.0733013\pi\)
−0.973602 + 0.228253i \(0.926699\pi\)
\(810\) −5.21337e7 9.81914e8i −0.0980988 1.84764i
\(811\) 4.40043e8 4.40043e8i 0.824959 0.824959i −0.161855 0.986814i \(-0.551748\pi\)
0.986814 + 0.161855i \(0.0517478\pi\)
\(812\) −2.48874e8 2.00971e8i −0.464849 0.375375i
\(813\) 4.00893e8 4.00893e8i 0.746030 0.746030i
\(814\) 2.09254e7 + 1.88154e7i 0.0387972 + 0.0348851i
\(815\) 7.25025e8i 1.33931i
\(816\) 4.01688e8 + 2.59299e8i 0.739296 + 0.477233i
\(817\) 1.20083e8 0.220199
\(818\) 5.16891e8 5.74856e8i 0.944363 1.05027i
\(819\) 5.73920e8 + 5.73920e8i 1.04472 + 1.04472i
\(820\) 6.87923e8 + 5.55512e8i 1.24767 + 1.00752i
\(821\) −2.57117e8 2.57117e8i −0.464624 0.464624i 0.435544 0.900168i \(-0.356556\pi\)
−0.900168 + 0.435544i \(0.856556\pi\)
\(822\) 2.92670e8 1.55390e7i 0.526943 0.0279775i
\(823\) −9.19926e8 −1.65026 −0.825132 0.564940i \(-0.808899\pi\)
−0.825132 + 0.564940i \(0.808899\pi\)
\(824\) 1.58086e8 2.18529e8i 0.282561 0.390596i
\(825\) 5.68497e7i 0.101243i
\(826\) 2.62839e8 1.39551e7i 0.466390 0.0247625i
\(827\) −4.44970e8 + 4.44970e8i −0.786709 + 0.786709i −0.980953 0.194245i \(-0.937774\pi\)
0.194245 + 0.980953i \(0.437774\pi\)
\(828\) 3.18797e8 3.39481e7i 0.561595 0.0598032i
\(829\) 3.19132e8 3.19132e8i 0.560153 0.560153i −0.369198 0.929351i \(-0.620368\pi\)
0.929351 + 0.369198i \(0.120368\pi\)
\(830\) −1.04144e9 + 1.15823e9i −1.82138 + 2.02563i
\(831\) 7.70672e8i 1.34297i
\(832\) −7.79684e8 3.93245e8i −1.35378 0.682799i
\(833\) −1.67281e8 −0.289410
\(834\) −4.77918e8 4.29728e8i −0.823864 0.740790i
\(835\) −9.17448e7 9.17448e7i −0.157588 0.157588i
\(836\) 992329. + 9.31868e6i 0.00169839 + 0.0159491i
\(837\) 6.06667e7 + 6.06667e7i 0.103460 + 0.103460i
\(838\) −5.95000e7 1.12065e9i −0.101108 1.90432i
\(839\) 3.41595e8 0.578397 0.289198 0.957269i \(-0.406611\pi\)
0.289198 + 0.957269i \(0.406611\pi\)
\(840\) 1.24559e9 + 9.01073e8i 2.10154 + 1.52027i
\(841\) 4.47630e8i 0.752543i
\(842\) 1.02162e7 + 1.92417e8i 0.0171140 + 0.322335i
\(843\) 1.32651e8 1.32651e8i 0.221426 0.221426i
\(844\) 3.40732e7 4.21948e7i 0.0566742 0.0701830i
\(845\) −8.89211e8 + 8.89211e8i −1.47379 + 1.47379i
\(846\) −2.20215e8 1.98010e8i −0.363694 0.327021i
\(847\) 7.28176e8i 1.19836i
\(848\) 7.92649e7 + 5.11673e7i 0.129985 + 0.0839083i
\(849\) 3.98064e8 0.650473
\(850\) 4.22760e8 4.70169e8i 0.688393 0.765591i
\(851\) 3.31323e8 + 3.31323e8i 0.537604 + 0.537604i
\(852\) −5.19512e8 + 6.43342e8i −0.839995 + 1.04022i
\(853\) −7.26055e8 7.26055e8i −1.16983 1.16983i −0.982249 0.187580i \(-0.939936\pi\)
−0.187580 0.982249i \(-0.560064\pi\)
\(854\) 1.13001e9 5.99965e7i 1.81429 0.0963280i
\(855\) −2.73171e8 −0.437055
\(856\) 1.38645e8 + 8.63886e8i 0.221046 + 1.37732i
\(857\) 1.03657e9i 1.64686i −0.567414 0.823432i \(-0.692056\pi\)
0.567414 0.823432i \(-0.307944\pi\)
\(858\) −6.14878e7 + 3.26463e6i −0.0973480 + 0.00516859i
\(859\) −3.46895e8 + 3.46895e8i −0.547291 + 0.547291i −0.925656 0.378366i \(-0.876486\pi\)
0.378366 + 0.925656i \(0.376486\pi\)
\(860\) 7.08797e7 + 6.65611e8i 0.111436 + 1.04647i
\(861\) −7.29155e8 + 7.29155e8i −1.14238 + 1.14238i
\(862\) −3.31274e8 + 3.68424e8i −0.517209 + 0.575210i
\(863\) 2.30709e8i 0.358948i −0.983763 0.179474i \(-0.942560\pi\)
0.983763 0.179474i \(-0.0574396\pi\)
\(864\) −1.58084e8 + 4.29388e7i −0.245102 + 0.0665747i
\(865\) 1.16506e9 1.80011
\(866\) −4.07205e7 3.66145e7i −0.0626989 0.0563767i
\(867\) −3.55072e8 3.55072e8i −0.544828 0.544828i
\(868\) −4.49959e8 + 4.79154e7i −0.688041 + 0.0732682i
\(869\) 1.97716e7 + 1.97716e7i 0.0301289 + 0.0301289i
\(870\) 3.75056e7 + 7.06400e8i 0.0569559 + 1.07274i
\(871\) 1.59021e9 2.40659
\(872\) −1.90247e8 1.18541e9i −0.286925 1.78781i
\(873\) 5.90054e8i 0.886848i
\(874\) 8.27314e6 + 1.55821e8i 0.0123918 + 0.233395i
\(875\) 5.24655e8 5.24655e8i 0.783159 0.783159i
\(876\) −6.18676e8 4.99594e8i −0.920346 0.743198i
\(877\) 1.79911e7 1.79911e7i 0.0266722 0.0266722i −0.693645 0.720317i \(-0.743996\pi\)
0.720317 + 0.693645i \(0.243996\pi\)
\(878\) 8.81004e8 + 7.92168e8i 1.30165 + 1.17040i
\(879\) 9.98775e8i 1.47062i
\(880\) −5.10671e7 + 1.10008e7i −0.0749364 + 0.0161427i
\(881\) 6.42117e8 0.939045 0.469523 0.882920i \(-0.344426\pi\)
0.469523 + 0.882920i \(0.344426\pi\)
\(882\) −1.64743e8 + 1.83218e8i −0.240105 + 0.267031i
\(883\) 4.47721e8 + 4.47721e8i 0.650317 + 0.650317i 0.953069 0.302752i \(-0.0979054\pi\)
−0.302752 + 0.953069i \(0.597905\pi\)
\(884\) −5.32804e8 4.30250e8i −0.771278 0.622823i
\(885\) −4.11577e8 4.11577e8i −0.593774 0.593774i
\(886\) −1.24292e9 + 6.59918e7i −1.78708 + 0.0948831i
\(887\) 5.17347e8 0.741329 0.370664 0.928767i \(-0.379130\pi\)
0.370664 + 0.928767i \(0.379130\pi\)
\(888\) 8.33900e8 + 6.03252e8i 1.19090 + 0.861509i
\(889\) 2.88183e8i 0.410170i
\(890\) 9.59888e8 5.09643e7i 1.36160 0.0722930i
\(891\) −2.75529e7 + 2.75529e7i −0.0389524 + 0.0389524i
\(892\) −3.04865e8 + 3.24645e7i −0.429549 + 0.0457419i
\(893\) 1.01921e8 1.01921e8i 0.143123 0.143123i
\(894\) 5.40718e8 6.01355e8i 0.756760 0.841624i
\(895\) 3.16885e8i 0.442011i
\(896\) 3.47627e8 7.90957e8i 0.483269 1.09959i
\(897\) −1.02526e9 −1.42055
\(898\) −1.80275e8 1.62097e8i −0.248947 0.223845i
\(899\) −1.47231e8 1.47231e8i −0.202637 0.202637i
\(900\) −9.86153e7 9.26068e8i −0.135275 1.27033i
\(901\) 5.23186e7 + 5.23186e7i 0.0715289 + 0.0715289i
\(902\) −1.85776e6 3.49900e7i −0.00253145 0.0476786i
\(903\) −7.80634e8 −1.06019
\(904\) −1.71368e7 + 2.36889e7i −0.0231966 + 0.0320656i
\(905\) 7.07535e8i 0.954557i
\(906\) 6.65699e6 + 1.25381e8i 0.00895144 + 0.168596i
\(907\) −2.47278e8 + 2.47278e8i −0.331409 + 0.331409i −0.853121 0.521713i \(-0.825293\pi\)
0.521713 + 0.853121i \(0.325293\pi\)
\(908\) −7.09930e8 + 8.79148e8i −0.948327 + 1.17437i
\(909\) 1.41187e8 1.41187e8i 0.187976 0.187976i
\(910\) −1.63745e9 1.47234e9i −2.17292 1.95382i
\(911\) 1.40425e9i 1.85733i −0.370919 0.928665i \(-0.620957\pi\)
0.370919 0.928665i \(-0.379043\pi\)
\(912\) 7.21796e7 + 3.35066e8i 0.0951547 + 0.441719i
\(913\) 6.17236e7 0.0811034
\(914\) −8.61718e8 + 9.58353e8i −1.12857 + 1.25512i
\(915\) −1.76947e9 1.76947e9i −2.30983 2.30983i
\(916\) −2.67769e8 + 3.31595e8i −0.348397 + 0.431441i
\(917\) 7.63790e8 + 7.63790e8i 0.990526 + 0.990526i
\(918\) −1.28288e8 + 6.81132e6i −0.165828 + 0.00880447i
\(919\) −8.17828e8 −1.05370 −0.526848 0.849959i \(-0.676626\pi\)
−0.526848 + 0.849959i \(0.676626\pi\)
\(920\) −8.58820e8 + 1.37832e8i −1.10291 + 0.177005i
\(921\) 6.19839e8i 0.793414i
\(922\) 1.83758e8 9.75645e6i 0.234452 0.0124480i
\(923\) 8.37530e8 8.37530e8i 1.06511 1.06511i
\(924\) −6.45093e6 6.05788e7i −0.00817723 0.0767900i
\(925\) 9.62454e8 9.62454e8i 1.21606 1.21606i
\(926\) 9.01043e8 1.00209e9i 1.13478 1.26204i
\(927\) 3.11555e8i 0.391107i
\(928\) 3.83651e8 1.04207e8i 0.480057 0.130393i
\(929\) 9.02460e8 1.12559 0.562796 0.826596i \(-0.309726\pi\)
0.562796 + 0.826596i \(0.309726\pi\)
\(930\) 7.44095e8 + 6.69065e8i 0.925080 + 0.831801i
\(931\) −8.47979e7 8.47979e7i −0.105084 0.105084i
\(932\) 4.85285e8 5.16771e7i 0.599444 0.0638337i
\(933\) 7.35524e8 + 7.35524e8i 0.905632 + 0.905632i
\(934\) 4.61424e7 + 8.69070e8i 0.0566317 + 1.06663i
\(935\) −4.09677e7 −0.0501195
\(936\) −9.95958e8 + 1.59841e8i −1.21454 + 0.194922i
\(937\) 8.55187e8i 1.03954i −0.854305 0.519771i \(-0.826017\pi\)
0.854305 0.519771i \(-0.173983\pi\)
\(938\) 8.34179e7 + 1.57114e9i 0.101077 + 1.90373i
\(939\) 1.12069e9 1.12069e9i 1.35359 1.35359i
\(940\) 6.25103e8 + 5.04783e8i 0.752606 + 0.607745i
\(941\) −6.02375e8 + 6.02375e8i −0.722933 + 0.722933i −0.969202 0.246269i \(-0.920795\pi\)
0.246269 + 0.969202i \(0.420795\pi\)
\(942\) 1.29878e9 + 1.16782e9i 1.55376 + 1.39709i
\(943\) 5.83429e8i 0.695750i
\(944\) −1.77407e8 + 2.74826e8i −0.210889 + 0.326695i
\(945\) −4.13086e8 −0.489491
\(946\) 1.77357e7 1.97246e7i 0.0209495 0.0232989i
\(947\) −4.57925e8 4.57925e8i −0.539193 0.539193i 0.384099 0.923292i \(-0.374512\pi\)
−0.923292 + 0.384099i \(0.874512\pi\)
\(948\) 7.95642e8 + 6.42498e8i 0.933884 + 0.754130i
\(949\) 8.05419e8 + 8.05419e8i 0.942374 + 0.942374i
\(950\) 4.52641e8 2.40325e7i 0.527938 0.0280303i
\(951\) −9.21155e8 −1.07100
\(952\) 3.97139e8 5.48982e8i 0.460290 0.636278i
\(953\) 1.03047e9i 1.19057i 0.803513 + 0.595287i \(0.202962\pi\)
−0.803513 + 0.595287i \(0.797038\pi\)
\(954\) 1.08827e8 5.77808e6i 0.125341 0.00665485i
\(955\) −1.01033e9 + 1.01033e9i −1.15999 + 1.15999i
\(956\) 7.29654e8 7.76995e7i 0.835109 0.0889292i
\(957\) 1.98219e7 1.98219e7i 0.0226157 0.0226157i
\(958\) 9.65692e8 1.07399e9i 1.09835 1.22152i
\(959\) 4.15352e8i 0.470934i
\(960\) −1.81464e9 + 5.97862e8i −2.05106 + 0.675751i
\(961\) 5.92968e8 0.668130
\(962\) −1.09625e9 9.85706e8i −1.23135 1.10719i
\(963\) 7.14650e8 + 7.14650e8i 0.800229 + 0.800229i
\(964\) −1.29563e8 1.21669e9i −0.144627 1.35815i
\(965\) −2.32259e8 2.32259e8i −0.258459 0.258459i
\(966\) −5.37820e7 1.01296e9i −0.0596630 1.12372i
\(967\) 1.42057e9 1.57103 0.785513 0.618845i \(-0.212399\pi\)
0.785513 + 0.618845i \(0.212399\pi\)
\(968\) −7.33226e8 5.30423e8i −0.808373 0.584785i
\(969\) 2.68801e8i 0.295434i
\(970\) −8.48766e7 1.59861e9i −0.0929978 1.75157i
\(971\) −5.17352e8 + 5.17352e8i −0.565104 + 0.565104i −0.930753 0.365649i \(-0.880847\pi\)
0.365649 + 0.930753i \(0.380847\pi\)
\(972\) −7.48824e8 + 9.27312e8i −0.815419 + 1.00978i
\(973\) −6.44056e8 + 6.44056e8i −0.699174 + 0.699174i
\(974\) −1.64677e8 1.48071e8i −0.178219 0.160249i
\(975\) 2.97826e9i 3.21328i
\(976\) −7.62714e8 + 1.18154e9i −0.820375 + 1.27087i
\(977\) −1.73570e9 −1.86119 −0.930594 0.366054i \(-0.880709\pi\)
−0.930594 + 0.366054i \(0.880709\pi\)
\(978\) 7.02602e8 7.81393e8i 0.751091 0.835320i
\(979\) −2.69349e7 2.69349e7i −0.0287056 0.0287056i
\(980\) 4.19977e8 5.20082e8i 0.446218 0.552578i
\(981\) −9.80635e8 9.80635e8i −1.03872 1.03872i
\(982\) −1.28164e9 + 6.80476e7i −1.35342 + 0.0718585i
\(983\) 5.18747e8 0.546129 0.273064 0.961996i \(-0.411963\pi\)
0.273064 + 0.961996i \(0.411963\pi\)
\(984\) −2.03075e8 1.26535e9i −0.213143 1.32808i
\(985\) 2.27719e9i 2.38282i
\(986\) 3.11339e8 1.65302e7i 0.324790 0.0172444i
\(987\) −6.62569e8 + 6.62569e8i −0.689096 + 0.689096i
\(988\) −5.19864e7 4.88189e8i −0.0539038 0.506195i
\(989\) 3.12310e8 3.12310e8i 0.322847 0.322847i
\(990\) −4.03461e7 + 4.48706e7i −0.0415811 + 0.0462441i
\(991\) 6.01846e8i 0.618392i −0.950998 0.309196i \(-0.899940\pi\)
0.950998 0.309196i \(-0.100060\pi\)
\(992\) 2.79515e8 4.87982e8i 0.286332 0.499884i
\(993\) −7.69130e8 −0.785510
\(994\) 8.71416e8 + 7.83547e8i 0.887292 + 0.797822i
\(995\) 1.51888e9 + 1.51888e9i 1.54189 + 1.54189i
\(996\) 2.24481e9 2.39046e8i 2.27197 0.241938i
\(997\) −7.87235e8 7.87235e8i −0.794363 0.794363i 0.187837 0.982200i \(-0.439852\pi\)
−0.982200 + 0.187837i \(0.939852\pi\)
\(998\) 1.78119e7 + 3.35478e8i 0.0179192 + 0.337499i
\(999\) −2.76554e8 −0.277385
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 16.7.f.a.11.9 yes 22
4.3 odd 2 64.7.f.a.15.2 22
8.3 odd 2 128.7.f.a.31.10 22
8.5 even 2 128.7.f.b.31.2 22
16.3 odd 4 inner 16.7.f.a.3.9 22
16.5 even 4 128.7.f.a.95.10 22
16.11 odd 4 128.7.f.b.95.2 22
16.13 even 4 64.7.f.a.47.2 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
16.7.f.a.3.9 22 16.3 odd 4 inner
16.7.f.a.11.9 yes 22 1.1 even 1 trivial
64.7.f.a.15.2 22 4.3 odd 2
64.7.f.a.47.2 22 16.13 even 4
128.7.f.a.31.10 22 8.3 odd 2
128.7.f.a.95.10 22 16.5 even 4
128.7.f.b.31.2 22 8.5 even 2
128.7.f.b.95.2 22 16.11 odd 4