Properties

Label 33.8.e.b.16.3
Level $33$
Weight $8$
Character 33.16
Analytic conductor $10.309$
Analytic rank $0$
Dimension $28$
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] = [33,8,Mod(4,33)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(33, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("33.4");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 33.e (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(10.3087058410\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 16.3
Character \(\chi\) \(=\) 33.16
Dual form 33.8.e.b.31.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.99223 - 9.20914i) q^{2} +(-21.8435 - 15.8702i) q^{3} +(27.6994 - 20.1248i) q^{4} +(-60.2993 + 185.582i) q^{5} +(-80.7902 + 248.647i) q^{6} +(-765.654 + 556.280i) q^{7} +(-1270.94 - 923.389i) q^{8} +(225.273 + 693.320i) q^{9} +O(q^{10})\) \(q+(-2.99223 - 9.20914i) q^{2} +(-21.8435 - 15.8702i) q^{3} +(27.6994 - 20.1248i) q^{4} +(-60.2993 + 185.582i) q^{5} +(-80.7902 + 248.647i) q^{6} +(-765.654 + 556.280i) q^{7} +(-1270.94 - 923.389i) q^{8} +(225.273 + 693.320i) q^{9} +1889.48 q^{10} +(3334.28 + 2893.05i) q^{11} -924.437 q^{12} +(1590.49 + 4895.03i) q^{13} +(7413.88 + 5386.50i) q^{14} +(4262.37 - 3096.79i) q^{15} +(-3346.41 + 10299.2i) q^{16} +(2416.81 - 7438.18i) q^{17} +(5710.81 - 4149.15i) q^{18} +(43492.8 + 31599.4i) q^{19} +(2064.55 + 6354.03i) q^{20} +25552.8 q^{21} +(16665.6 - 39362.5i) q^{22} -105008. q^{23} +(13107.3 + 40340.0i) q^{24} +(32399.7 + 23539.8i) q^{25} +(40319.9 - 29294.1i) q^{26} +(6082.38 - 18719.6i) q^{27} +(-10013.2 + 30817.3i) q^{28} +(-74398.1 + 54053.4i) q^{29} +(-41272.8 - 29986.4i) q^{30} +(11436.9 + 35199.2i) q^{31} -96223.4 q^{32} +(-26918.9 - 116110. i) q^{33} -75730.9 q^{34} +(-57067.3 - 175635. i) q^{35} +(20192.9 + 14671.0i) q^{36} +(-426418. + 309811. i) q^{37} +(160863. - 495084. i) q^{38} +(42943.3 - 132166. i) q^{39} +(248001. - 180183. i) q^{40} +(-276352. - 200781. i) q^{41} +(-76459.9 - 235319. i) q^{42} +137623. q^{43} +(150580. + 13034.2i) q^{44} -142252. q^{45} +(314207. + 967030. i) q^{46} +(-13964.8 - 10146.0i) q^{47} +(236548. - 171862. i) q^{48} +(22289.9 - 68601.3i) q^{49} +(119834. - 368810. i) q^{50} +(-170837. + 124120. i) q^{51} +(142567. + 103581. i) q^{52} +(385602. + 1.18676e6i) q^{53} -190592. q^{54} +(-737953. + 444334. i) q^{55} +1.48676e6 q^{56} +(-448545. - 1.38048e6i) q^{57} +(720401. + 523402. i) q^{58} +(-216226. + 157098. i) q^{59} +(55742.9 - 171559. i) q^{60} +(-656652. + 2.02097e6i) q^{61} +(289932. - 210648. i) q^{62} +(-558162. - 405528. i) q^{63} +(716263. + 2.20443e6i) q^{64} -1.00434e6 q^{65} +(-988725. + 595327. i) q^{66} -648851. q^{67} +(-82747.7 - 254671. i) q^{68} +(2.29373e6 + 1.66649e6i) q^{69} +(-1.44669e6 + 1.05108e6i) q^{70} +(1.32284e6 - 4.07129e6i) q^{71} +(353896. - 1.08918e6i) q^{72} +(3.51360e6 - 2.55278e6i) q^{73} +(4.12903e6 + 2.99992e6i) q^{74} +(-334141. - 1.02838e6i) q^{75} +1.84066e6 q^{76} +(-4.16225e6 - 360284. i) q^{77} -1.34563e6 q^{78} +(-1.57582e6 - 4.84988e6i) q^{79} +(-1.70956e6 - 1.24207e6i) q^{80} +(-429945. + 312373. i) q^{81} +(-1.02211e6 + 3.14574e6i) q^{82} +(473739. - 1.45802e6i) q^{83} +(707799. - 514246. i) q^{84} +(1.23466e6 + 897034. i) q^{85} +(-411800. - 1.26739e6i) q^{86} +2.48295e6 q^{87} +(-1.56624e6 - 6.75572e6i) q^{88} -9.14985e6 q^{89} +(425650. + 1.31001e6i) q^{90} +(-3.94078e6 - 2.86314e6i) q^{91} +(-2.90865e6 + 2.11326e6i) q^{92} +(308797. - 950378. i) q^{93} +(-51650.2 + 158963. i) q^{94} +(-8.48687e6 + 6.16607e6i) q^{95} +(2.10185e6 + 1.52709e6i) q^{96} +(-1.01983e6 - 3.13870e6i) q^{97} -698455. q^{98} +(-1.25469e6 + 2.96345e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 6 q^{2} - 189 q^{3} + 160 q^{4} + 773 q^{5} - 162 q^{6} + 1289 q^{7} + 2956 q^{8} - 5103 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 6 q^{2} - 189 q^{3} + 160 q^{4} + 773 q^{5} - 162 q^{6} + 1289 q^{7} + 2956 q^{8} - 5103 q^{9} - 10640 q^{10} + 13209 q^{11} + 45630 q^{12} + 13499 q^{13} - 3318 q^{14} - 22734 q^{15} - 113196 q^{16} + 30296 q^{17} + 21141 q^{18} - 6858 q^{19} + 76725 q^{20} - 177012 q^{21} - 48859 q^{22} - 166984 q^{23} + 44442 q^{24} + 99832 q^{25} + 340424 q^{26} - 137781 q^{27} + 657387 q^{28} + 192014 q^{29} - 184410 q^{30} + 396068 q^{31} - 303498 q^{32} + 168453 q^{33} - 1229124 q^{34} - 725859 q^{35} + 116640 q^{36} + 811053 q^{37} + 1548798 q^{38} + 364473 q^{39} - 1427263 q^{40} + 1041497 q^{41} + 300024 q^{42} - 5265288 q^{43} - 5341085 q^{44} + 100602 q^{45} + 1198651 q^{46} + 1667505 q^{47} + 730593 q^{48} + 2968140 q^{49} + 11247432 q^{50} + 340767 q^{51} + 2325763 q^{52} - 1625736 q^{53} - 905418 q^{54} - 8338690 q^{55} - 18201906 q^{56} + 1546479 q^{57} + 14965553 q^{58} - 2587454 q^{59} + 2071575 q^{60} + 5801619 q^{61} + 15631121 q^{62} + 939681 q^{63} - 3732846 q^{64} - 15368174 q^{65} - 235683 q^{66} - 7141262 q^{67} + 17394545 q^{68} - 5063553 q^{69} - 4329200 q^{70} + 3569199 q^{71} + 1199934 q^{72} + 125008 q^{73} - 13691530 q^{74} - 11794221 q^{75} - 19690428 q^{76} - 6038739 q^{77} + 12684438 q^{78} + 17075485 q^{79} + 26606436 q^{80} - 3720087 q^{81} + 19886007 q^{82} - 4645575 q^{83} + 1074519 q^{84} + 12002715 q^{85} - 12296287 q^{86} - 12259512 q^{87} - 50905990 q^{88} + 9601664 q^{89} + 8857350 q^{90} - 14129477 q^{91} - 90776021 q^{92} + 10693836 q^{93} + 1047679 q^{94} + 58935661 q^{95} + 26156304 q^{96} - 22170261 q^{97} + 140532178 q^{98} - 6579954 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.99223 9.20914i −0.264478 0.813980i −0.991813 0.127698i \(-0.959241\pi\)
0.727335 0.686283i \(-0.240759\pi\)
\(3\) −21.8435 15.8702i −0.467086 0.339358i
\(4\) 27.6994 20.1248i 0.216402 0.157225i
\(5\) −60.2993 + 185.582i −0.215733 + 0.663959i 0.783367 + 0.621559i \(0.213500\pi\)
−0.999101 + 0.0423999i \(0.986500\pi\)
\(6\) −80.7902 + 248.647i −0.152697 + 0.469952i
\(7\) −765.654 + 556.280i −0.843703 + 0.612986i −0.923403 0.383833i \(-0.874604\pi\)
0.0796995 + 0.996819i \(0.474604\pi\)
\(8\) −1270.94 923.389i −0.877625 0.637632i
\(9\) 225.273 + 693.320i 0.103006 + 0.317019i
\(10\) 1889.48 0.597506
\(11\) 3334.28 + 2893.05i 0.755314 + 0.655363i
\(12\) −924.437 −0.154434
\(13\) 1590.49 + 4895.03i 0.200784 + 0.617951i 0.999860 + 0.0167204i \(0.00532253\pi\)
−0.799076 + 0.601230i \(0.794677\pi\)
\(14\) 7413.88 + 5386.50i 0.722100 + 0.524636i
\(15\) 4262.37 3096.79i 0.326086 0.236915i
\(16\) −3346.41 + 10299.2i −0.204249 + 0.628613i
\(17\) 2416.81 7438.18i 0.119309 0.367194i −0.873513 0.486801i \(-0.838164\pi\)
0.992821 + 0.119607i \(0.0381636\pi\)
\(18\) 5710.81 4149.15i 0.230804 0.167689i
\(19\) 43492.8 + 31599.4i 1.45472 + 1.05692i 0.984699 + 0.174263i \(0.0557543\pi\)
0.470023 + 0.882654i \(0.344246\pi\)
\(20\) 2064.55 + 6354.03i 0.0577059 + 0.177601i
\(21\) 25552.8 0.602104
\(22\) 16665.6 39362.5i 0.333688 0.788140i
\(23\) −105008. −1.79959 −0.899795 0.436312i \(-0.856284\pi\)
−0.899795 + 0.436312i \(0.856284\pi\)
\(24\) 13107.3 + 40340.0i 0.193541 + 0.595658i
\(25\) 32399.7 + 23539.8i 0.414717 + 0.301309i
\(26\) 40319.9 29294.1i 0.449897 0.326869i
\(27\) 6082.38 18719.6i 0.0594703 0.183031i
\(28\) −10013.2 + 30817.3i −0.0862021 + 0.265303i
\(29\) −74398.1 + 54053.4i −0.566460 + 0.411557i −0.833817 0.552040i \(-0.813849\pi\)
0.267358 + 0.963597i \(0.413849\pi\)
\(30\) −41272.8 29986.4i −0.279087 0.202768i
\(31\) 11436.9 + 35199.2i 0.0689514 + 0.212210i 0.979595 0.200983i \(-0.0644135\pi\)
−0.910643 + 0.413193i \(0.864413\pi\)
\(32\) −96223.4 −0.519106
\(33\) −26918.9 116110.i −0.130394 0.562433i
\(34\) −75730.9 −0.330443
\(35\) −57067.3 175635.i −0.224983 0.692426i
\(36\) 20192.9 + 14671.0i 0.0721340 + 0.0524084i
\(37\) −426418. + 309811.i −1.38398 + 1.00552i −0.387485 + 0.921876i \(0.626656\pi\)
−0.996496 + 0.0836443i \(0.973344\pi\)
\(38\) 160863. 495084.i 0.475568 1.46365i
\(39\) 42943.3 132166.i 0.115923 0.356774i
\(40\) 248001. 180183.i 0.612694 0.445148i
\(41\) −276352. 200781.i −0.626208 0.454967i 0.228876 0.973455i \(-0.426495\pi\)
−0.855084 + 0.518489i \(0.826495\pi\)
\(42\) −76459.9 235319.i −0.159243 0.490101i
\(43\) 137623. 0.263968 0.131984 0.991252i \(-0.457865\pi\)
0.131984 + 0.991252i \(0.457865\pi\)
\(44\) 150580. + 13034.2i 0.266491 + 0.0230674i
\(45\) −142252. −0.232709
\(46\) 314207. + 967030.i 0.475952 + 1.46483i
\(47\) −13964.8 10146.0i −0.0196197 0.0142545i 0.577932 0.816085i \(-0.303860\pi\)
−0.597552 + 0.801830i \(0.703860\pi\)
\(48\) 236548. 171862.i 0.308727 0.224303i
\(49\) 22289.9 68601.3i 0.0270659 0.0833002i
\(50\) 119834. 368810.i 0.135576 0.417261i
\(51\) −170837. + 124120.i −0.180338 + 0.131023i
\(52\) 142567. + 103581.i 0.140608 + 0.102157i
\(53\) 385602. + 1.18676e6i 0.355774 + 1.09496i 0.955559 + 0.294799i \(0.0952526\pi\)
−0.599785 + 0.800161i \(0.704747\pi\)
\(54\) −190592. −0.164712
\(55\) −737953. + 444334.i −0.598080 + 0.360114i
\(56\) 1.48676e6 1.13131
\(57\) −448545. 1.38048e6i −0.320807 0.987343i
\(58\) 720401. + 523402.i 0.484816 + 0.352239i
\(59\) −216226. + 157098.i −0.137065 + 0.0995836i −0.654205 0.756317i \(-0.726997\pi\)
0.517140 + 0.855901i \(0.326997\pi\)
\(60\) 55742.9 171559.i 0.0333165 0.102538i
\(61\) −656652. + 2.02097e6i −0.370408 + 1.14000i 0.576116 + 0.817368i \(0.304568\pi\)
−0.946525 + 0.322632i \(0.895432\pi\)
\(62\) 289932. 210648.i 0.154499 0.112250i
\(63\) −558162. 405528.i −0.281234 0.204329i
\(64\) 716263. + 2.20443e6i 0.341541 + 1.05116i
\(65\) −1.00434e6 −0.453610
\(66\) −988725. + 595327.i −0.423323 + 0.254889i
\(67\) −648851. −0.263562 −0.131781 0.991279i \(-0.542070\pi\)
−0.131781 + 0.991279i \(0.542070\pi\)
\(68\) −82747.7 254671.i −0.0319135 0.0982198i
\(69\) 2.29373e6 + 1.66649e6i 0.840564 + 0.610705i
\(70\) −1.44669e6 + 1.05108e6i −0.504118 + 0.366263i
\(71\) 1.32284e6 4.07129e6i 0.438636 1.34998i −0.450679 0.892686i \(-0.648818\pi\)
0.889315 0.457296i \(-0.151182\pi\)
\(72\) 353896. 1.08918e6i 0.111741 0.343903i
\(73\) 3.51360e6 2.55278e6i 1.05711 0.768039i 0.0835622 0.996503i \(-0.473370\pi\)
0.973552 + 0.228464i \(0.0733703\pi\)
\(74\) 4.12903e6 + 2.99992e6i 1.18451 + 0.860594i
\(75\) −334141. 1.02838e6i −0.0914567 0.281475i
\(76\) 1.84066e6 0.480979
\(77\) −4.16225e6 360284.i −1.03899 0.0899347i
\(78\) −1.34563e6 −0.321066
\(79\) −1.57582e6 4.84988e6i −0.359594 1.10672i −0.953298 0.302032i \(-0.902335\pi\)
0.593704 0.804683i \(-0.297665\pi\)
\(80\) −1.70956e6 1.24207e6i −0.373310 0.271226i
\(81\) −429945. + 312373.i −0.0898908 + 0.0653095i
\(82\) −1.02211e6 + 3.14574e6i −0.204716 + 0.630050i
\(83\) 473739. 1.45802e6i 0.0909423 0.279892i −0.895233 0.445599i \(-0.852991\pi\)
0.986175 + 0.165707i \(0.0529907\pi\)
\(84\) 707799. 514246.i 0.130296 0.0946659i
\(85\) 1.23466e6 + 897034.i 0.218063 + 0.158432i
\(86\) −411800. 1.26739e6i −0.0698139 0.214865i
\(87\) 2.48295e6 0.404251
\(88\) −1.56624e6 6.75572e6i −0.245002 1.05677i
\(89\) −9.14985e6 −1.37578 −0.687890 0.725815i \(-0.741463\pi\)
−0.687890 + 0.725815i \(0.741463\pi\)
\(90\) 425650. + 1.31001e6i 0.0615465 + 0.189421i
\(91\) −3.94078e6 2.86314e6i −0.548198 0.398289i
\(92\) −2.90865e6 + 2.11326e6i −0.389435 + 0.282941i
\(93\) 308797. 950378.i 0.0398091 0.122520i
\(94\) −51650.2 + 158963.i −0.00641393 + 0.0197400i
\(95\) −8.48687e6 + 6.16607e6i −1.01558 + 0.737863i
\(96\) 2.10185e6 + 1.52709e6i 0.242467 + 0.176163i
\(97\) −1.01983e6 3.13870e6i −0.113455 0.349179i 0.878166 0.478355i \(-0.158767\pi\)
−0.991622 + 0.129176i \(0.958767\pi\)
\(98\) −698455. −0.0749630
\(99\) −1.25469e6 + 2.96345e6i −0.129961 + 0.306955i
\(100\) 1.37119e6 0.137119
\(101\) −1.56926e6 4.82968e6i −0.151555 0.466438i 0.846241 0.532801i \(-0.178861\pi\)
−0.997796 + 0.0663628i \(0.978861\pi\)
\(102\) 1.65422e6 + 1.20186e6i 0.154345 + 0.112139i
\(103\) −1.01428e7 + 7.36916e6i −0.914590 + 0.664489i −0.942172 0.335131i \(-0.891220\pi\)
0.0275812 + 0.999620i \(0.491220\pi\)
\(104\) 2.49861e6 7.68992e6i 0.217812 0.670355i
\(105\) −1.54082e6 + 4.74215e6i −0.129894 + 0.399772i
\(106\) 9.77524e6 7.10213e6i 0.797181 0.579186i
\(107\) 1.69660e7 + 1.23265e7i 1.33886 + 0.972740i 0.999485 + 0.0320888i \(0.0102159\pi\)
0.339376 + 0.940651i \(0.389784\pi\)
\(108\) −208251. 640931.i −0.0159076 0.0489585i
\(109\) 7.90843e6 0.584922 0.292461 0.956277i \(-0.405526\pi\)
0.292461 + 0.956277i \(0.405526\pi\)
\(110\) 6.30005e6 + 5.46637e6i 0.451305 + 0.391583i
\(111\) 1.42312e7 0.987669
\(112\) −3.16705e6 9.74717e6i −0.213006 0.655565i
\(113\) 1.08150e7 + 7.85759e6i 0.705105 + 0.512289i 0.881591 0.472015i \(-0.156473\pi\)
−0.176486 + 0.984303i \(0.556473\pi\)
\(114\) −1.13709e7 + 8.26142e6i −0.718831 + 0.522261i
\(115\) 6.33189e6 1.94875e7i 0.388232 1.19485i
\(116\) −972971. + 2.99450e6i −0.0578758 + 0.178123i
\(117\) −3.03553e6 + 2.20544e6i −0.175220 + 0.127305i
\(118\) 2.09373e6 + 1.52119e6i 0.117310 + 0.0852305i
\(119\) 2.28727e6 + 7.03950e6i 0.124424 + 0.382937i
\(120\) −8.27675e6 −0.437246
\(121\) 2.74766e6 + 1.92925e7i 0.140999 + 0.990010i
\(122\) 2.05762e7 1.02590
\(123\) 2.85004e6 + 8.77151e6i 0.138097 + 0.425017i
\(124\) 1.02517e6 + 744832.i 0.0482860 + 0.0350819i
\(125\) −1.86555e7 + 1.35540e7i −0.854322 + 0.620701i
\(126\) −2.06442e6 + 6.35362e6i −0.0919392 + 0.282960i
\(127\) 1.15717e7 3.56142e7i 0.501286 1.54280i −0.305640 0.952147i \(-0.598870\pi\)
0.806926 0.590653i \(-0.201130\pi\)
\(128\) 8.19335e6 5.95282e6i 0.345324 0.250892i
\(129\) −3.00617e6 2.18411e6i −0.123296 0.0895798i
\(130\) 3.00520e6 + 9.24907e6i 0.119970 + 0.369229i
\(131\) 1.64849e7 0.640674 0.320337 0.947304i \(-0.396204\pi\)
0.320337 + 0.947304i \(0.396204\pi\)
\(132\) −3.08233e6 2.67444e6i −0.116646 0.101210i
\(133\) −5.08786e7 −1.87523
\(134\) 1.94151e6 + 5.97536e6i 0.0697065 + 0.214535i
\(135\) 3.10727e6 + 2.25756e6i 0.108695 + 0.0789717i
\(136\) −9.93995e6 + 7.22180e6i −0.338843 + 0.246184i
\(137\) −1.49745e6 + 4.60869e6i −0.0497544 + 0.153128i −0.972847 0.231450i \(-0.925653\pi\)
0.923092 + 0.384578i \(0.125653\pi\)
\(138\) 8.48359e6 2.61098e7i 0.274791 0.845721i
\(139\) 1.61002e7 1.16975e7i 0.508486 0.369436i −0.303763 0.952748i \(-0.598243\pi\)
0.812249 + 0.583311i \(0.198243\pi\)
\(140\) −5.11536e6 3.71652e6i −0.157553 0.114469i
\(141\) 144020. + 443248.i 0.00432669 + 0.0133162i
\(142\) −4.14513e7 −1.21487
\(143\) −8.85844e6 + 2.09228e7i −0.253327 + 0.598333i
\(144\) −7.89450e6 −0.220321
\(145\) −5.54519e6 1.70663e7i −0.151053 0.464892i
\(146\) −3.40224e7 2.47187e7i −0.904752 0.657341i
\(147\) −1.57560e6 + 1.14474e6i −0.0409107 + 0.0297233i
\(148\) −5.57666e6 + 1.71632e7i −0.141403 + 0.435193i
\(149\) 1.49272e6 4.59411e6i 0.0369680 0.113776i −0.930870 0.365352i \(-0.880949\pi\)
0.967838 + 0.251576i \(0.0809488\pi\)
\(150\) −8.47067e6 + 6.15430e6i −0.204927 + 0.148888i
\(151\) 4.99202e7 + 3.62691e7i 1.17993 + 0.857271i 0.992164 0.124943i \(-0.0398747\pi\)
0.187768 + 0.982213i \(0.439875\pi\)
\(152\) −2.60981e7 8.03216e7i −0.602776 1.85515i
\(153\) 5.70148e6 0.128697
\(154\) 9.13652e6 + 3.94088e7i 0.201585 + 0.869503i
\(155\) −7.22198e6 −0.155774
\(156\) −1.47031e6 4.52515e6i −0.0310079 0.0954326i
\(157\) 7.60562e6 + 5.52581e6i 0.156851 + 0.113959i 0.663442 0.748227i \(-0.269095\pi\)
−0.506592 + 0.862186i \(0.669095\pi\)
\(158\) −3.99480e7 + 2.90239e7i −0.805740 + 0.585404i
\(159\) 1.04113e7 3.20426e7i 0.205406 0.632175i
\(160\) 5.80220e6 1.78573e7i 0.111988 0.344665i
\(161\) 8.03996e7 5.84137e7i 1.51832 1.10312i
\(162\) 4.16318e6 + 3.02473e6i 0.0769348 + 0.0558964i
\(163\) −1.76875e7 5.44367e7i −0.319898 0.984544i −0.973691 0.227871i \(-0.926824\pi\)
0.653794 0.756673i \(-0.273176\pi\)
\(164\) −1.16955e7 −0.207045
\(165\) 2.31711e7 + 2.00569e6i 0.401563 + 0.0347592i
\(166\) −1.48446e7 −0.251878
\(167\) 1.17755e7 + 3.62413e7i 0.195647 + 0.602139i 0.999968 + 0.00794472i \(0.00252891\pi\)
−0.804322 + 0.594194i \(0.797471\pi\)
\(168\) −3.24760e7 2.35952e7i −0.528421 0.383920i
\(169\) 2.93329e7 2.13116e7i 0.467468 0.339636i
\(170\) 4.56652e6 1.40543e7i 0.0712876 0.219401i
\(171\) −1.21107e7 + 3.72730e7i −0.185218 + 0.570043i
\(172\) 3.81209e6 2.76964e6i 0.0571233 0.0415025i
\(173\) −1.42751e7 1.03714e7i −0.209612 0.152292i 0.478026 0.878346i \(-0.341353\pi\)
−0.687638 + 0.726053i \(0.741353\pi\)
\(174\) −7.42956e6 2.28658e7i −0.106915 0.329052i
\(175\) −3.79017e7 −0.534596
\(176\) −4.09540e7 + 2.46591e7i −0.566242 + 0.340943i
\(177\) 7.21630e6 0.0978157
\(178\) 2.73785e7 + 8.42622e7i 0.363864 + 1.11986i
\(179\) 3.00392e7 + 2.18248e7i 0.391474 + 0.284423i 0.766059 0.642770i \(-0.222215\pi\)
−0.374585 + 0.927193i \(0.622215\pi\)
\(180\) −3.94029e6 + 2.86279e6i −0.0503587 + 0.0365877i
\(181\) −2.94301e7 + 9.05767e7i −0.368907 + 1.13538i 0.578591 + 0.815618i \(0.303603\pi\)
−0.947498 + 0.319762i \(0.896397\pi\)
\(182\) −1.45754e7 + 4.48583e7i −0.179213 + 0.551561i
\(183\) 4.64167e7 3.37237e7i 0.559880 0.406777i
\(184\) 1.33458e8 + 9.69630e7i 1.57937 + 1.14748i
\(185\) −3.17827e7 9.78170e7i −0.369054 1.13583i
\(186\) −9.67615e6 −0.110257
\(187\) 2.95774e7 1.78090e7i 0.330761 0.199156i
\(188\) −591004. −0.00648691
\(189\) 5.75637e6 + 1.77163e7i 0.0620201 + 0.190878i
\(190\) 8.21788e7 + 5.97064e7i 0.869205 + 0.631515i
\(191\) 3.58902e7 2.60757e7i 0.372699 0.270782i −0.385630 0.922653i \(-0.626016\pi\)
0.758329 + 0.651872i \(0.226016\pi\)
\(192\) 1.93391e7 5.95197e7i 0.197189 0.606885i
\(193\) −2.82485e7 + 8.69401e7i −0.282843 + 0.870501i 0.704194 + 0.710008i \(0.251309\pi\)
−0.987037 + 0.160494i \(0.948691\pi\)
\(194\) −2.58532e7 + 1.87834e7i −0.254219 + 0.184701i
\(195\) 2.19382e7 + 1.59390e7i 0.211875 + 0.153936i
\(196\) −763170. 2.34880e6i −0.00723978 0.0222817i
\(197\) −1.07289e8 −0.999826 −0.499913 0.866075i \(-0.666635\pi\)
−0.499913 + 0.866075i \(0.666635\pi\)
\(198\) 3.10451e7 + 2.68726e6i 0.284227 + 0.0246026i
\(199\) −1.03701e8 −0.932815 −0.466408 0.884570i \(-0.654452\pi\)
−0.466408 + 0.884570i \(0.654452\pi\)
\(200\) −1.94416e7 5.98351e7i −0.171841 0.528873i
\(201\) 1.41732e7 + 1.02974e7i 0.123106 + 0.0894420i
\(202\) −3.97816e7 + 2.89030e7i −0.339588 + 0.246725i
\(203\) 2.68944e7 8.27725e7i 0.225645 0.694464i
\(204\) −2.23419e6 + 6.87613e6i −0.0184253 + 0.0567072i
\(205\) 5.39252e7 3.91790e7i 0.437173 0.317625i
\(206\) 9.82131e7 + 7.13560e7i 0.782770 + 0.568716i
\(207\) −2.36554e7 7.28040e7i −0.185368 0.570504i
\(208\) −5.57373e7 −0.429462
\(209\) 5.35985e7 + 2.31188e8i 0.406107 + 1.75168i
\(210\) 4.82816e7 0.359761
\(211\) 4.46928e7 + 1.37550e8i 0.327529 + 1.00803i 0.970286 + 0.241960i \(0.0777902\pi\)
−0.642758 + 0.766070i \(0.722210\pi\)
\(212\) 3.45643e7 + 2.51125e7i 0.249145 + 0.181015i
\(213\) −9.35077e7 + 6.79373e7i −0.663008 + 0.481703i
\(214\) 6.27503e7 1.93126e8i 0.437691 1.34707i
\(215\) −8.29858e6 + 2.55404e7i −0.0569468 + 0.175264i
\(216\) −2.50158e7 + 1.81751e7i −0.168899 + 0.122712i
\(217\) −2.83374e7 2.05883e7i −0.188257 0.136776i
\(218\) −2.36639e7 7.28298e7i −0.154699 0.476115i
\(219\) −1.17262e8 −0.754404
\(220\) −1.14988e7 + 2.71590e7i −0.0728068 + 0.171963i
\(221\) 4.02541e7 0.250863
\(222\) −4.25831e7 1.31057e8i −0.261217 0.803943i
\(223\) −2.31073e8 1.67884e8i −1.39535 1.01378i −0.995255 0.0973042i \(-0.968978\pi\)
−0.400092 0.916475i \(-0.631022\pi\)
\(224\) 7.36739e7 5.35272e7i 0.437971 0.318205i
\(225\) −9.02181e6 + 2.77663e7i −0.0528026 + 0.162510i
\(226\) 4.00005e7 1.23109e8i 0.230508 0.709431i
\(227\) 2.27204e8 1.65073e8i 1.28921 0.936668i 0.289424 0.957201i \(-0.406536\pi\)
0.999789 + 0.0205333i \(0.00653640\pi\)
\(228\) −4.02064e7 2.92116e7i −0.224658 0.163224i
\(229\) −7.61633e7 2.34406e8i −0.419104 1.28987i −0.908528 0.417823i \(-0.862793\pi\)
0.489425 0.872045i \(-0.337207\pi\)
\(230\) −1.98410e8 −1.07527
\(231\) 8.52002e7 + 7.39257e7i 0.454777 + 0.394597i
\(232\) 1.44468e8 0.759561
\(233\) 8.05573e6 + 2.47930e7i 0.0417214 + 0.128405i 0.969748 0.244109i \(-0.0784956\pi\)
−0.928026 + 0.372515i \(0.878496\pi\)
\(234\) 2.93932e7 + 2.13554e7i 0.149966 + 0.108956i
\(235\) 2.72499e6 1.97982e6i 0.0136970 0.00995148i
\(236\) −2.82779e6 + 8.70304e6i −0.0140041 + 0.0431001i
\(237\) −4.25472e7 + 1.30947e8i −0.207611 + 0.638962i
\(238\) 5.79837e7 4.21276e7i 0.278796 0.202557i
\(239\) −7.34464e7 5.33619e7i −0.347999 0.252836i 0.400030 0.916502i \(-0.369000\pi\)
−0.748029 + 0.663666i \(0.769000\pi\)
\(240\) 1.76308e7 + 5.42621e7i 0.0823254 + 0.253371i
\(241\) −3.24333e8 −1.49256 −0.746279 0.665634i \(-0.768161\pi\)
−0.746279 + 0.665634i \(0.768161\pi\)
\(242\) 1.69446e8 8.30312e7i 0.768557 0.376606i
\(243\) 1.43489e7 0.0641500
\(244\) 2.24827e7 + 6.91946e7i 0.0990796 + 0.304936i
\(245\) 1.13871e7 + 8.27321e6i 0.0494689 + 0.0359412i
\(246\) 7.22501e7 5.24928e7i 0.309432 0.224816i
\(247\) −8.55050e7 + 2.63157e8i −0.361037 + 1.11116i
\(248\) 1.79670e7 5.52967e7i 0.0747987 0.230207i
\(249\) −3.34872e7 + 2.43298e7i −0.137461 + 0.0998715i
\(250\) 1.80642e8 + 1.31244e8i 0.731188 + 0.531239i
\(251\) 8.27567e7 + 2.54699e8i 0.330328 + 1.01664i 0.968978 + 0.247147i \(0.0794931\pi\)
−0.638650 + 0.769497i \(0.720507\pi\)
\(252\) −2.36220e7 −0.0929853
\(253\) −3.50125e8 3.03793e8i −1.35926 1.17939i
\(254\) −3.62601e8 −1.38839
\(255\) −1.27332e7 3.91886e7i −0.0480890 0.148003i
\(256\) 1.60689e8 + 1.16747e8i 0.598614 + 0.434918i
\(257\) −3.08314e8 + 2.24003e8i −1.13299 + 0.823167i −0.986127 0.165990i \(-0.946918\pi\)
−0.146864 + 0.989157i \(0.546918\pi\)
\(258\) −1.11186e7 + 3.42195e7i −0.0403071 + 0.124052i
\(259\) 1.54147e8 4.74416e8i 0.551298 1.69672i
\(260\) −2.78195e7 + 2.02121e7i −0.0981620 + 0.0713189i
\(261\) −5.42362e7 3.94049e7i −0.188820 0.137186i
\(262\) −4.93267e7 1.51812e8i −0.169444 0.521496i
\(263\) 1.10991e8 0.376221 0.188111 0.982148i \(-0.439764\pi\)
0.188111 + 0.982148i \(0.439764\pi\)
\(264\) −7.30025e7 + 1.72425e8i −0.244188 + 0.576748i
\(265\) −2.43493e8 −0.803760
\(266\) 1.52240e8 + 4.68548e8i 0.495957 + 1.52640i
\(267\) 1.99864e8 + 1.45210e8i 0.642608 + 0.466882i
\(268\) −1.79728e7 + 1.30580e7i −0.0570354 + 0.0414386i
\(269\) 1.03737e8 3.19269e8i 0.324937 1.00005i −0.646532 0.762887i \(-0.723781\pi\)
0.971469 0.237167i \(-0.0762187\pi\)
\(270\) 1.14925e7 3.53704e7i 0.0355339 0.109362i
\(271\) 4.67769e8 3.39854e8i 1.42771 1.03729i 0.437267 0.899332i \(-0.355947\pi\)
0.990438 0.137957i \(-0.0440535\pi\)
\(272\) 6.85197e7 + 4.97824e7i 0.206454 + 0.149998i
\(273\) 4.06416e7 + 1.25082e8i 0.120893 + 0.372070i
\(274\) 4.69227e7 0.137802
\(275\) 3.99279e7 + 1.72222e8i 0.115774 + 0.499373i
\(276\) 9.70730e7 0.277918
\(277\) −5.28154e7 1.62549e8i −0.149307 0.459521i 0.848232 0.529624i \(-0.177667\pi\)
−0.997540 + 0.0701033i \(0.977667\pi\)
\(278\) −1.55899e8 1.13267e8i −0.435197 0.316189i
\(279\) −2.18279e7 + 1.58589e7i −0.0601723 + 0.0437178i
\(280\) −8.96507e7 + 2.75916e8i −0.244062 + 0.751146i
\(281\) −1.20768e8 + 3.71685e8i −0.324698 + 0.999317i 0.646879 + 0.762593i \(0.276074\pi\)
−0.971577 + 0.236724i \(0.923926\pi\)
\(282\) 3.65099e6 2.65260e6i 0.00969480 0.00704368i
\(283\) 3.75698e8 + 2.72960e8i 0.985339 + 0.715891i 0.958896 0.283759i \(-0.0915817\pi\)
0.0264439 + 0.999650i \(0.491582\pi\)
\(284\) −4.52920e7 1.39394e8i −0.117330 0.361103i
\(285\) 2.83239e8 0.724764
\(286\) 2.19187e8 + 1.89728e7i 0.554031 + 0.0479568i
\(287\) 3.23281e8 0.807222
\(288\) −2.16766e7 6.67136e7i −0.0534708 0.164566i
\(289\) 2.82485e8 + 2.05238e8i 0.688420 + 0.500167i
\(290\) −1.40574e8 + 1.02133e8i −0.338463 + 0.245908i
\(291\) −2.75353e7 + 8.47449e7i −0.0655034 + 0.201599i
\(292\) 4.59505e7 1.41421e8i 0.108007 0.332410i
\(293\) −4.62544e8 + 3.36058e8i −1.07428 + 0.780508i −0.976676 0.214717i \(-0.931117\pi\)
−0.0976012 + 0.995226i \(0.531117\pi\)
\(294\) 1.52567e7 + 1.10846e7i 0.0350142 + 0.0254393i
\(295\) −1.61162e7 4.96006e7i −0.0365499 0.112489i
\(296\) 8.28027e8 1.85577
\(297\) 7.44373e7 4.48199e7i 0.164870 0.0992712i
\(298\) −4.67744e7 −0.102388
\(299\) −1.67014e8 5.14016e8i −0.361330 1.11206i
\(300\) −2.99515e7 2.17610e7i −0.0640463 0.0465324i
\(301\) −1.05372e8 + 7.65571e7i −0.222711 + 0.161809i
\(302\) 1.84635e8 5.68247e8i 0.385735 1.18717i
\(303\) −4.23700e7 + 1.30401e8i −0.0875003 + 0.269298i
\(304\) −4.70993e8 + 3.42197e8i −0.961517 + 0.698583i
\(305\) −3.35460e8 2.43726e8i −0.677003 0.491872i
\(306\) −1.70601e7 5.25057e7i −0.0340375 0.104757i
\(307\) 5.55579e8 1.09588 0.547938 0.836519i \(-0.315413\pi\)
0.547938 + 0.836519i \(0.315413\pi\)
\(308\) −1.22543e8 + 7.37850e7i −0.238979 + 0.143893i
\(309\) 3.38503e8 0.652692
\(310\) 2.16098e7 + 6.65082e7i 0.0411989 + 0.126797i
\(311\) 6.23535e7 + 4.53025e7i 0.117544 + 0.0854006i 0.645004 0.764179i \(-0.276856\pi\)
−0.527460 + 0.849580i \(0.676856\pi\)
\(312\) −1.76619e8 + 1.28321e8i −0.329227 + 0.239198i
\(313\) −8.39828e7 + 2.58472e8i −0.154805 + 0.476441i −0.998141 0.0609457i \(-0.980588\pi\)
0.843336 + 0.537387i \(0.180588\pi\)
\(314\) 2.81302e7 8.65757e7i 0.0512765 0.157813i
\(315\) 1.08916e8 7.91318e7i 0.196337 0.142648i
\(316\) −1.41252e8 1.02626e8i −0.251820 0.182958i
\(317\) 2.56475e7 + 7.89348e7i 0.0452207 + 0.139175i 0.971118 0.238601i \(-0.0766889\pi\)
−0.925897 + 0.377776i \(0.876689\pi\)
\(318\) −3.26237e8 −0.568904
\(319\) −4.04443e8 3.50086e7i −0.697574 0.0603819i
\(320\) −4.52293e8 −0.771605
\(321\) −1.74971e8 5.38507e8i −0.295257 0.908706i
\(322\) −7.78514e8 5.65623e8i −1.29948 0.944130i
\(323\) 3.40156e8 2.47138e8i 0.561654 0.408066i
\(324\) −5.62278e6 + 1.73051e7i −0.00918424 + 0.0282662i
\(325\) −6.36965e7 + 1.96038e8i −0.102926 + 0.316773i
\(326\) −4.48389e8 + 3.25774e8i −0.716793 + 0.520781i
\(327\) −1.72748e8 1.25508e8i −0.273209 0.198498i
\(328\) 1.65826e8 + 5.10360e8i 0.259474 + 0.798580i
\(329\) 1.63362e7 0.0252910
\(330\) −5.08627e7 2.19387e8i −0.0779113 0.336057i
\(331\) −3.80917e8 −0.577341 −0.288671 0.957428i \(-0.593213\pi\)
−0.288671 + 0.957428i \(0.593213\pi\)
\(332\) −1.62201e7 4.99202e7i −0.0243259 0.0748675i
\(333\) −3.10859e8 2.25852e8i −0.461327 0.335173i
\(334\) 2.98516e8 2.16885e8i 0.438385 0.318505i
\(335\) 3.91253e7 1.20415e8i 0.0568592 0.174994i
\(336\) −8.55103e7 + 2.63174e8i −0.122979 + 0.378490i
\(337\) −1.83692e8 + 1.33460e8i −0.261448 + 0.189953i −0.710785 0.703409i \(-0.751660\pi\)
0.449337 + 0.893362i \(0.351660\pi\)
\(338\) −2.84033e8 2.06362e8i −0.400092 0.290684i
\(339\) −1.11536e8 3.43274e8i −0.155495 0.478566i
\(340\) 5.22521e7 0.0720987
\(341\) −6.36993e7 + 1.50452e8i −0.0869950 + 0.205474i
\(342\) 3.79490e8 0.512990
\(343\) −2.19753e8 6.76331e8i −0.294040 0.904961i
\(344\) −1.74910e8 1.27080e8i −0.231665 0.168315i
\(345\) −4.47582e8 + 3.25187e8i −0.586821 + 0.426350i
\(346\) −5.27978e7 + 1.62495e8i −0.0685250 + 0.210898i
\(347\) 1.61279e8 4.96367e8i 0.207217 0.637749i −0.792398 0.610005i \(-0.791168\pi\)
0.999615 0.0277444i \(-0.00883245\pi\)
\(348\) 6.87764e7 4.99689e7i 0.0874806 0.0635584i
\(349\) 4.99161e8 + 3.62661e8i 0.628567 + 0.456680i 0.855903 0.517136i \(-0.173002\pi\)
−0.227337 + 0.973816i \(0.573002\pi\)
\(350\) 1.13411e8 + 3.49042e8i 0.141389 + 0.435151i
\(351\) 1.01307e8 0.125045
\(352\) −3.20836e8 2.78379e8i −0.392088 0.340203i
\(353\) 3.96429e8 0.479683 0.239841 0.970812i \(-0.422905\pi\)
0.239841 + 0.970812i \(0.422905\pi\)
\(354\) −2.15928e7 6.64559e7i −0.0258701 0.0796200i
\(355\) 6.75792e8 + 4.90992e8i 0.801704 + 0.582472i
\(356\) −2.53446e8 + 1.84139e8i −0.297721 + 0.216307i
\(357\) 6.17564e7 1.90067e8i 0.0718361 0.221089i
\(358\) 1.11103e8 3.41940e8i 0.127978 0.393876i
\(359\) 7.85013e8 5.70346e8i 0.895461 0.650590i −0.0418355 0.999125i \(-0.513321\pi\)
0.937296 + 0.348534i \(0.113321\pi\)
\(360\) 1.80793e8 + 1.31354e8i 0.204231 + 0.148383i
\(361\) 6.16883e8 + 1.89857e9i 0.690125 + 2.12399i
\(362\) 9.22194e8 1.02174
\(363\) 2.46157e8 4.65021e8i 0.270109 0.510269i
\(364\) −1.66778e8 −0.181252
\(365\) 2.61883e8 + 8.05992e8i 0.281891 + 0.867572i
\(366\) −4.49455e8 3.26548e8i −0.479185 0.348148i
\(367\) 9.12253e8 6.62791e8i 0.963350 0.699915i 0.00942401 0.999956i \(-0.497000\pi\)
0.953926 + 0.300041i \(0.0970002\pi\)
\(368\) 3.51399e8 1.08150e9i 0.367564 1.13125i
\(369\) 7.69510e7 2.36831e8i 0.0797301 0.245384i
\(370\) −8.05709e8 + 5.85382e8i −0.826937 + 0.600805i
\(371\) −9.55411e8 6.94146e8i −0.971363 0.705736i
\(372\) −1.05727e7 3.25394e7i −0.0106484 0.0327725i
\(373\) 3.49901e8 0.349111 0.174556 0.984647i \(-0.444151\pi\)
0.174556 + 0.984647i \(0.444151\pi\)
\(374\) −2.52508e8 2.19093e8i −0.249588 0.216560i
\(375\) 6.22605e8 0.609682
\(376\) 8.37964e6 + 2.57899e7i 0.00812957 + 0.0250203i
\(377\) −3.82923e8 2.78210e8i −0.368058 0.267410i
\(378\) 1.45927e8 1.06022e8i 0.138968 0.100966i
\(379\) −5.16659e8 + 1.59011e9i −0.487491 + 1.50034i 0.340849 + 0.940118i \(0.389286\pi\)
−0.828340 + 0.560226i \(0.810714\pi\)
\(380\) −1.10990e8 + 3.41593e8i −0.103763 + 0.319350i
\(381\) −8.17971e8 + 5.94290e8i −0.757705 + 0.550505i
\(382\) −3.47526e8 2.52493e8i −0.318982 0.231754i
\(383\) 4.16765e8 + 1.28267e9i 0.379049 + 1.16659i 0.940706 + 0.339223i \(0.110164\pi\)
−0.561657 + 0.827370i \(0.689836\pi\)
\(384\) −2.73444e8 −0.246438
\(385\) 3.17843e8 7.50715e8i 0.283858 0.670444i
\(386\) 8.85169e8 0.783377
\(387\) 3.10028e7 + 9.54169e7i 0.0271902 + 0.0836830i
\(388\) −9.14144e7 6.64164e7i −0.0794517 0.0577251i
\(389\) 7.42260e8 5.39283e8i 0.639341 0.464508i −0.220283 0.975436i \(-0.570698\pi\)
0.859624 + 0.510928i \(0.170698\pi\)
\(390\) 8.11405e7 2.49725e8i 0.0692646 0.213175i
\(391\) −2.53784e8 + 7.81066e8i −0.214707 + 0.660799i
\(392\) −9.16747e7 + 6.66056e7i −0.0768685 + 0.0558482i
\(393\) −3.60088e8 2.61619e8i −0.299250 0.217418i
\(394\) 3.21034e8 + 9.88042e8i 0.264432 + 0.813839i
\(395\) 9.95071e8 0.812390
\(396\) 2.48848e7 + 1.07336e8i 0.0201373 + 0.0868587i
\(397\) 1.86088e8 0.149263 0.0746316 0.997211i \(-0.476222\pi\)
0.0746316 + 0.997211i \(0.476222\pi\)
\(398\) 3.10296e8 + 9.54993e8i 0.246709 + 0.759293i
\(399\) 1.11136e9 + 8.07454e8i 0.875894 + 0.636374i
\(400\) −3.50864e8 + 2.54917e8i −0.274112 + 0.199154i
\(401\) −5.91487e8 + 1.82041e9i −0.458079 + 1.40982i 0.409404 + 0.912353i \(0.365737\pi\)
−0.867482 + 0.497468i \(0.834263\pi\)
\(402\) 5.24208e7 1.61335e8i 0.0402451 0.123862i
\(403\) −1.54111e8 + 1.11968e8i −0.117291 + 0.0852171i
\(404\) −1.40664e8 1.02199e8i −0.106133 0.0771098i
\(405\) −3.20455e7 9.86259e7i −0.0239704 0.0737732i
\(406\) −8.42737e8 −0.624958
\(407\) −2.31810e9 2.00654e8i −1.70432 0.147526i
\(408\) 3.31734e8 0.241813
\(409\) −5.23956e8 1.61257e9i −0.378672 1.16543i −0.940968 0.338496i \(-0.890082\pi\)
0.562296 0.826936i \(-0.309918\pi\)
\(410\) −5.22161e8 3.79372e8i −0.374163 0.271845i
\(411\) 1.05850e8 7.69048e7i 0.0752048 0.0546395i
\(412\) −1.32646e8 + 4.08243e8i −0.0934447 + 0.287593i
\(413\) 7.81643e7 2.40565e8i 0.0545988 0.168038i
\(414\) −5.99679e8 + 4.35692e8i −0.415353 + 0.301772i
\(415\) 2.42016e8 + 1.75835e8i 0.166217 + 0.120764i
\(416\) −1.53043e8 4.71017e8i −0.104228 0.320782i
\(417\) −5.37325e8 −0.362878
\(418\) 1.96866e9 1.18536e9i 1.31842 0.793843i
\(419\) −2.66551e9 −1.77024 −0.885118 0.465366i \(-0.845923\pi\)
−0.885118 + 0.465366i \(0.845923\pi\)
\(420\) 5.27551e7 + 1.62363e8i 0.0347450 + 0.106934i
\(421\) 1.75111e9 + 1.27226e9i 1.14374 + 0.830974i 0.987636 0.156766i \(-0.0501070\pi\)
0.156102 + 0.987741i \(0.450107\pi\)
\(422\) 1.13299e9 8.23165e8i 0.733892 0.533204i
\(423\) 3.88854e6 1.19677e7i 0.00249802 0.00768811i
\(424\) 6.05767e8 1.86436e9i 0.385945 1.18782i
\(425\) 2.53397e8 1.84104e8i 0.160118 0.116333i
\(426\) 9.05440e8 + 6.57841e8i 0.567448 + 0.412275i
\(427\) −6.21456e8 1.91264e9i −0.386289 1.18888i
\(428\) 7.18017e8 0.442671
\(429\) 5.25548e8 3.16441e8i 0.321375 0.193505i
\(430\) 2.60036e8 0.157723
\(431\) 5.91080e8 + 1.81916e9i 0.355611 + 1.09446i 0.955654 + 0.294491i \(0.0951502\pi\)
−0.600043 + 0.799968i \(0.704850\pi\)
\(432\) 1.72443e8 + 1.25287e8i 0.102909 + 0.0747677i
\(433\) 9.14595e8 6.64492e8i 0.541403 0.393353i −0.283203 0.959060i \(-0.591397\pi\)
0.824606 + 0.565708i \(0.191397\pi\)
\(434\) −1.04808e8 + 3.22567e8i −0.0615435 + 0.189412i
\(435\) −1.49720e8 + 4.60791e8i −0.0872103 + 0.268406i
\(436\) 2.19059e8 1.59156e8i 0.126578 0.0919644i
\(437\) −4.56708e9 3.31818e9i −2.61790 1.90202i
\(438\) 3.50876e8 + 1.07988e9i 0.199523 + 0.614070i
\(439\) −1.88272e9 −1.06209 −0.531045 0.847344i \(-0.678200\pi\)
−0.531045 + 0.847344i \(0.678200\pi\)
\(440\) 1.34818e9 + 1.16699e8i 0.754510 + 0.0653103i
\(441\) 5.25840e7 0.0291957
\(442\) −1.20449e8 3.70705e8i −0.0663478 0.204198i
\(443\) 1.92066e9 + 1.39544e9i 1.04963 + 0.762602i 0.972142 0.234391i \(-0.0753097\pi\)
0.0774890 + 0.996993i \(0.475310\pi\)
\(444\) 3.94197e8 2.86401e8i 0.213734 0.155287i
\(445\) 5.51729e8 1.69805e9i 0.296802 0.913461i
\(446\) −8.54647e8 + 2.63033e9i −0.456157 + 1.40391i
\(447\) −1.05516e8 + 7.66616e7i −0.0558780 + 0.0405977i
\(448\) −1.77469e9 1.28939e9i −0.932503 0.677503i
\(449\) −3.77319e8 1.16127e9i −0.196719 0.605440i −0.999952 0.00977464i \(-0.996889\pi\)
0.803233 0.595665i \(-0.203111\pi\)
\(450\) 2.82699e8 0.146245
\(451\) −3.40563e8 1.46896e9i −0.174815 0.754036i
\(452\) 4.57703e8 0.233131
\(453\) −5.14831e8 1.58449e9i −0.260208 0.800839i
\(454\) −2.20002e9 1.59841e9i −1.10340 0.801665i
\(455\) 7.68974e8 5.58692e8i 0.382712 0.278056i
\(456\) −7.04648e8 + 2.16868e9i −0.348013 + 1.07107i
\(457\) −9.29074e8 + 2.85940e9i −0.455348 + 1.40142i 0.415378 + 0.909649i \(0.363649\pi\)
−0.870726 + 0.491768i \(0.836351\pi\)
\(458\) −1.93078e9 + 1.40280e9i −0.939084 + 0.682284i
\(459\) −1.24540e8 9.04837e7i −0.0601125 0.0436743i
\(460\) −2.16794e8 6.67222e8i −0.103847 0.319608i
\(461\) 1.83552e8 0.0872583 0.0436292 0.999048i \(-0.486108\pi\)
0.0436292 + 0.999048i \(0.486108\pi\)
\(462\) 4.25853e8 1.00582e9i 0.200915 0.474542i
\(463\) 1.75882e9 0.823548 0.411774 0.911286i \(-0.364909\pi\)
0.411774 + 0.911286i \(0.364909\pi\)
\(464\) −3.07740e8 9.47126e8i −0.143011 0.440144i
\(465\) 1.57753e8 + 1.14614e8i 0.0727599 + 0.0528632i
\(466\) 2.04217e8 1.48373e8i 0.0934851 0.0679209i
\(467\) 1.20138e9 3.69746e9i 0.545846 1.67994i −0.173125 0.984900i \(-0.555386\pi\)
0.718971 0.695040i \(-0.244614\pi\)
\(468\) −3.96984e7 + 1.22179e8i −0.0179024 + 0.0550980i
\(469\) 4.96796e8 3.60943e8i 0.222368 0.161560i
\(470\) −2.63862e7 1.91707e7i −0.0117229 0.00851717i
\(471\) −7.84374e7 2.41406e8i −0.0345900 0.106457i
\(472\) 4.19872e8 0.183789
\(473\) 4.58874e8 + 3.98151e8i 0.199379 + 0.172995i
\(474\) 1.33322e9 0.575012
\(475\) 6.65313e8 + 2.04762e9i 0.284838 + 0.876642i
\(476\) 2.05025e8 + 1.48959e8i 0.0871329 + 0.0633058i
\(477\) −7.35940e8 + 5.34692e8i −0.310476 + 0.225574i
\(478\) −2.71649e8 + 8.36048e8i −0.113765 + 0.350134i
\(479\) −3.98165e8 + 1.22543e9i −0.165534 + 0.509463i −0.999075 0.0429952i \(-0.986310\pi\)
0.833541 + 0.552458i \(0.186310\pi\)
\(480\) −4.10140e8 + 2.97984e8i −0.169273 + 0.122984i
\(481\) −2.19475e9 1.59458e9i −0.899244 0.653339i
\(482\) 9.70478e8 + 2.98682e9i 0.394749 + 1.21491i
\(483\) −2.68324e9 −1.08354
\(484\) 4.64367e8 + 4.79095e8i 0.186167 + 0.192071i
\(485\) 6.43981e8 0.256317
\(486\) −4.29352e7 1.32141e8i −0.0169663 0.0522169i
\(487\) −2.98851e9 2.17128e9i −1.17248 0.851854i −0.181173 0.983451i \(-0.557989\pi\)
−0.991303 + 0.131598i \(0.957989\pi\)
\(488\) 2.70070e9 1.96217e9i 1.05198 0.764308i
\(489\) −4.77564e8 + 1.46979e9i −0.184693 + 0.568427i
\(490\) 4.21163e7 1.29621e8i 0.0161720 0.0497723i
\(491\) −1.13894e9 + 8.27486e8i −0.434225 + 0.315483i −0.783336 0.621599i \(-0.786484\pi\)
0.349111 + 0.937081i \(0.386484\pi\)
\(492\) 2.55470e8 + 1.85610e8i 0.0967078 + 0.0702623i
\(493\) 2.22253e8 + 6.84024e8i 0.0835378 + 0.257103i
\(494\) 2.67930e9 0.999948
\(495\) −4.74307e8 4.11542e8i −0.175769 0.152509i
\(496\) −4.00796e8 −0.147482
\(497\) 1.25194e9 + 3.85307e9i 0.457442 + 1.40786i
\(498\) 3.24258e8 + 2.35587e8i 0.117649 + 0.0854770i
\(499\) −5.32287e8 + 3.86729e8i −0.191776 + 0.139333i −0.679530 0.733648i \(-0.737816\pi\)
0.487754 + 0.872981i \(0.337816\pi\)
\(500\) −2.43975e8 + 7.50877e8i −0.0872870 + 0.268642i
\(501\) 3.17939e8 9.78516e8i 0.112957 0.347645i
\(502\) 2.09793e9 1.52424e9i 0.740164 0.537761i
\(503\) 3.84398e9 + 2.79282e9i 1.34677 + 0.978486i 0.999166 + 0.0408449i \(0.0130049\pi\)
0.347605 + 0.937641i \(0.386995\pi\)
\(504\) 3.34928e8 + 1.03080e9i 0.116532 + 0.358648i
\(505\) 9.90928e8 0.342391
\(506\) −1.75001e9 + 4.13337e9i −0.600503 + 1.41833i
\(507\) −9.78953e8 −0.333606
\(508\) −3.96198e8 1.21937e9i −0.134088 0.412680i
\(509\) −1.85607e9 1.34851e9i −0.623852 0.453255i 0.230413 0.973093i \(-0.425992\pi\)
−0.854265 + 0.519838i \(0.825992\pi\)
\(510\) −3.22793e8 + 2.34523e8i −0.107753 + 0.0782870i
\(511\) −1.27014e9 + 3.90909e9i −0.421094 + 1.29599i
\(512\) 9.94911e8 3.06202e9i 0.327597 1.00824i
\(513\) 8.56069e8 6.21971e8i 0.279961 0.203404i
\(514\) 2.98542e9 + 2.16903e9i 0.969693 + 0.704523i
\(515\) −7.55982e8 2.32667e9i −0.243886 0.750603i
\(516\) −1.27224e8 −0.0407657
\(517\) −1.72096e7 7.42305e7i −0.00547713 0.0236247i
\(518\) −4.83021e9 −1.52690
\(519\) 1.47220e8 + 4.53097e8i 0.0462254 + 0.142267i
\(520\) 1.27645e9 + 9.27393e8i 0.398099 + 0.289236i
\(521\) 4.39201e9 3.19098e9i 1.36060 0.988535i 0.362196 0.932102i \(-0.382027\pi\)
0.998406 0.0564334i \(-0.0179728\pi\)
\(522\) −2.00598e8 + 6.17377e8i −0.0617277 + 0.189978i
\(523\) 2.74962e7 8.46246e7i 0.00840459 0.0258667i −0.946766 0.321922i \(-0.895671\pi\)
0.955171 + 0.296055i \(0.0956712\pi\)
\(524\) 4.56623e8 3.31756e8i 0.138643 0.100730i
\(525\) 8.27905e8 + 6.01508e8i 0.249702 + 0.181419i
\(526\) −3.32111e8 1.02213e9i −0.0995023 0.306237i
\(527\) 2.89459e8 0.0861489
\(528\) 1.28592e9 + 1.11309e8i 0.380186 + 0.0329088i
\(529\) 7.62179e9 2.23853
\(530\) 7.28588e8 + 2.24236e9i 0.212577 + 0.654245i
\(531\) −1.57629e8 1.14524e8i −0.0456883 0.0331945i
\(532\) −1.40931e9 + 1.02392e9i −0.405803 + 0.294833i
\(533\) 5.43295e8 1.67209e9i 0.155414 0.478316i
\(534\) 7.39218e8 2.27508e9i 0.210077 0.646550i
\(535\) −3.31061e9 + 2.40530e9i −0.934696 + 0.679096i
\(536\) 8.24649e8 + 5.99142e8i 0.231309 + 0.168056i
\(537\) −3.09797e8 9.53457e8i −0.0863311 0.265700i
\(538\) −3.25059e9 −0.899963
\(539\) 2.72788e8 1.64250e8i 0.0750351 0.0451798i
\(540\) 1.31503e8 0.0359382
\(541\) 6.76855e7 + 2.08314e8i 0.0183783 + 0.0565625i 0.959825 0.280599i \(-0.0905331\pi\)
−0.941447 + 0.337162i \(0.890533\pi\)
\(542\) −4.52943e9 3.29082e9i −1.22193 0.887784i
\(543\) 2.08033e9 1.51145e9i 0.557612 0.405129i
\(544\) −2.32554e8 + 7.15727e8i −0.0619338 + 0.190612i
\(545\) −4.76873e8 + 1.46766e9i −0.126187 + 0.388364i
\(546\) 1.03029e9 7.48547e8i 0.270884 0.196809i
\(547\) −1.10300e9 8.01376e8i −0.288151 0.209354i 0.434314 0.900762i \(-0.356991\pi\)
−0.722465 + 0.691408i \(0.756991\pi\)
\(548\) 5.12704e7 + 1.57794e8i 0.0133087 + 0.0409599i
\(549\) −1.54910e9 −0.399555
\(550\) 1.46655e9 8.83030e8i 0.375860 0.226311i
\(551\) −4.94384e9 −1.25902
\(552\) −1.37636e9 4.23601e9i −0.348294 1.07194i
\(553\) 3.90443e9 + 2.83673e9i 0.981792 + 0.713313i
\(554\) −1.33890e9 + 9.72768e8i −0.334552 + 0.243067i
\(555\) −8.58132e8 + 2.64106e9i −0.213073 + 0.655772i
\(556\) 2.10557e8 6.48026e8i 0.0519526 0.159894i
\(557\) 4.55898e9 3.31229e9i 1.11783 0.812149i 0.133949 0.990988i \(-0.457234\pi\)
0.983878 + 0.178839i \(0.0572343\pi\)
\(558\) 2.11361e8 + 1.53563e8i 0.0514997 + 0.0374167i
\(559\) 2.18889e8 + 6.73670e8i 0.0530007 + 0.163119i
\(560\) 1.99987e9 0.481220
\(561\) −9.28705e8 8.03885e7i −0.222079 0.0192231i
\(562\) 3.78427e9 0.899300
\(563\) 1.23574e9 + 3.80322e9i 0.291842 + 0.898197i 0.984264 + 0.176705i \(0.0565437\pi\)
−0.692422 + 0.721493i \(0.743456\pi\)
\(564\) 1.29096e7 + 9.37935e6i 0.00302994 + 0.00220138i
\(565\) −2.11037e9 + 1.53327e9i −0.492253 + 0.357643i
\(566\) 1.38955e9 4.27661e9i 0.322120 0.991384i
\(567\) 1.55422e8 4.78340e8i 0.0358073 0.110204i
\(568\) −5.44064e9 + 3.95285e9i −1.24575 + 0.905090i
\(569\) −4.39317e9 3.19183e9i −0.999736 0.726351i −0.0377048 0.999289i \(-0.512005\pi\)
−0.962032 + 0.272938i \(0.912005\pi\)
\(570\) −8.47517e8 2.60839e9i −0.191684 0.589943i
\(571\) −1.67210e9 −0.375869 −0.187934 0.982182i \(-0.560179\pi\)
−0.187934 + 0.982182i \(0.560179\pi\)
\(572\) 1.75693e8 + 7.57824e8i 0.0392527 + 0.169310i
\(573\) −1.19779e9 −0.265975
\(574\) −9.67330e8 2.97713e9i −0.213493 0.657063i
\(575\) −3.40222e9 2.47186e9i −0.746320 0.542233i
\(576\) −1.36702e9 + 9.93200e8i −0.298055 + 0.216550i
\(577\) 1.41177e9 4.34499e9i 0.305949 0.941616i −0.673372 0.739304i \(-0.735155\pi\)
0.979321 0.202312i \(-0.0648454\pi\)
\(578\) 1.04480e9 3.21556e9i 0.225054 0.692644i
\(579\) 1.99680e9 1.45076e9i 0.427524 0.310614i
\(580\) −4.97056e8 3.61132e8i −0.105781 0.0768543i
\(581\) 4.48347e8 + 1.37987e9i 0.0948414 + 0.291892i
\(582\) 8.62819e8 0.181422
\(583\) −2.14766e9 + 5.07256e9i −0.448875 + 1.06020i
\(584\) −6.82277e9 −1.41748
\(585\) −2.26250e8 6.96326e8i −0.0467244 0.143803i
\(586\) 4.47884e9 + 3.25407e9i 0.919441 + 0.668013i
\(587\) −5.95676e9 + 4.32784e9i −1.21556 + 0.883157i −0.995724 0.0923794i \(-0.970553\pi\)
−0.219838 + 0.975536i \(0.570553\pi\)
\(588\) −2.06056e7 + 6.34175e7i −0.00417989 + 0.0128644i
\(589\) −6.14849e8 + 1.89231e9i −0.123984 + 0.381583i
\(590\) −4.08555e8 + 2.96833e8i −0.0818972 + 0.0595018i
\(591\) 2.34357e9 + 1.70270e9i 0.467005 + 0.339299i
\(592\) −1.76383e9 5.42852e9i −0.349407 1.07536i
\(593\) 2.91231e9 0.573516 0.286758 0.958003i \(-0.407422\pi\)
0.286758 + 0.958003i \(0.407422\pi\)
\(594\) −6.35486e8 5.51392e8i −0.124409 0.107946i
\(595\) −1.44433e9 −0.281097
\(596\) −5.11083e7 1.57295e8i −0.00988847 0.0304336i
\(597\) 2.26518e9 + 1.64575e9i 0.435705 + 0.316558i
\(598\) −4.23390e9 + 3.07611e9i −0.809630 + 0.588230i
\(599\) 2.25696e9 6.94620e9i 0.429071 1.32055i −0.469970 0.882682i \(-0.655735\pi\)
0.899041 0.437864i \(-0.144265\pi\)
\(600\) −5.24924e8 + 1.61555e9i −0.0992126 + 0.305345i
\(601\) 1.38012e9 1.00271e9i 0.259332 0.188416i −0.450521 0.892766i \(-0.648762\pi\)
0.709852 + 0.704350i \(0.248762\pi\)
\(602\) 1.02032e9 + 7.41307e8i 0.190612 + 0.138487i
\(603\) −1.46169e8 4.49862e8i −0.0271484 0.0835542i
\(604\) 2.11267e9 0.390124
\(605\) −3.74602e9 6.53406e8i −0.687744 0.119961i
\(606\) 1.32767e9 0.242345
\(607\) −2.34242e9 7.20924e9i −0.425114 1.30837i −0.902886 0.429881i \(-0.858555\pi\)
0.477772 0.878484i \(-0.341445\pi\)
\(608\) −4.18503e9 3.04060e9i −0.755155 0.548652i
\(609\) −1.90108e9 + 1.38122e9i −0.341068 + 0.247800i
\(610\) −1.24073e9 + 3.81858e9i −0.221321 + 0.681157i
\(611\) 2.74542e7 8.44952e7i 0.00486927 0.0149861i
\(612\) 1.57928e8 1.14741e8i 0.0278502 0.0202344i
\(613\) 7.25421e9 + 5.27049e9i 1.27197 + 0.924144i 0.999279 0.0379569i \(-0.0120850\pi\)
0.272695 + 0.962100i \(0.412085\pi\)
\(614\) −1.66242e9 5.11640e9i −0.289835 0.892021i
\(615\) −1.79969e9 −0.311986
\(616\) 4.95728e9 + 4.30128e9i 0.854497 + 0.741421i
\(617\) −2.77632e9 −0.475852 −0.237926 0.971283i \(-0.576468\pi\)
−0.237926 + 0.971283i \(0.576468\pi\)
\(618\) −1.01288e9 3.11732e9i −0.172623 0.531278i
\(619\) 3.82286e9 + 2.77747e9i 0.647845 + 0.470687i 0.862536 0.505995i \(-0.168875\pi\)
−0.214692 + 0.976682i \(0.568875\pi\)
\(620\) −2.00045e8 + 1.45341e8i −0.0337098 + 0.0244916i
\(621\) −6.38697e8 + 1.96571e9i −0.107022 + 0.329381i
\(622\) 2.30621e8 7.09778e8i 0.0384266 0.118265i
\(623\) 7.00562e9 5.08988e9i 1.16075 0.843334i
\(624\) 1.21750e9 + 8.84563e8i 0.200596 + 0.145741i
\(625\) −4.23625e8 1.30378e9i −0.0694067 0.213612i
\(626\) 2.63160e9 0.428756
\(627\) 2.49823e9 5.90057e9i 0.404758 0.955999i
\(628\) 3.21878e8 0.0518599
\(629\) 1.27386e9 + 3.92053e9i 0.204100 + 0.628156i
\(630\) −1.05464e9 7.66238e8i −0.168039 0.122088i
\(631\) −7.89221e9 + 5.73402e9i −1.25053 + 0.908567i −0.998253 0.0590872i \(-0.981181\pi\)
−0.252282 + 0.967654i \(0.581181\pi\)
\(632\) −2.47556e9 + 7.61898e9i −0.390089 + 1.20057i
\(633\) 1.20671e9 3.71386e9i 0.189099 0.581986i
\(634\) 6.50178e8 4.72382e8i 0.101326 0.0736175i
\(635\) 5.91158e9 + 4.29502e9i 0.916211 + 0.665667i
\(636\) −3.56465e8 1.09709e9i −0.0549436 0.169099i
\(637\) 3.71257e8 0.0569098
\(638\) 8.87789e8 + 3.82933e9i 0.135344 + 0.583781i
\(639\) 3.12071e9 0.473152
\(640\) 6.10683e8 + 1.87949e9i 0.0920844 + 0.283407i
\(641\) 9.94752e9 + 7.22730e9i 1.49180 + 1.08386i 0.973507 + 0.228658i \(0.0734337\pi\)
0.518297 + 0.855201i \(0.326566\pi\)
\(642\) −4.43563e9 + 3.22267e9i −0.661580 + 0.480666i
\(643\) 3.78741e9 1.16565e10i 0.561829 1.72913i −0.115361 0.993324i \(-0.536803\pi\)
0.677190 0.735808i \(-0.263197\pi\)
\(644\) 1.05146e9 3.23606e9i 0.155128 0.477436i
\(645\) 5.86601e8 4.26191e8i 0.0860763 0.0625381i
\(646\) −3.29375e9 2.39305e9i −0.480703 0.349251i
\(647\) 3.11875e9 + 9.59852e9i 0.452705 + 1.39328i 0.873808 + 0.486271i \(0.161643\pi\)
−0.421103 + 0.907013i \(0.638357\pi\)
\(648\) 8.34875e8 0.120534
\(649\) −1.17545e9 1.01747e8i −0.168791 0.0146105i
\(650\) 1.99593e9 0.285068
\(651\) 2.92245e8 + 8.99439e8i 0.0415159 + 0.127773i
\(652\) −1.58546e9 1.15191e9i −0.224021 0.162761i
\(653\) 6.38850e8 4.64152e8i 0.0897848 0.0652325i −0.541987 0.840387i \(-0.682328\pi\)
0.631772 + 0.775154i \(0.282328\pi\)
\(654\) −6.38924e8 + 1.96641e9i −0.0893155 + 0.274885i
\(655\) −9.94029e8 + 3.05931e9i −0.138215 + 0.425381i
\(656\) 2.99267e9 2.17430e9i 0.413900 0.300716i
\(657\) 2.56141e9 + 1.86098e9i 0.352372 + 0.256013i
\(658\) −4.88818e7 1.50443e8i −0.00668892 0.0205864i
\(659\) 2.16376e9 0.294517 0.147259 0.989098i \(-0.452955\pi\)
0.147259 + 0.989098i \(0.452955\pi\)
\(660\) 6.82191e8 4.10758e8i 0.0923639 0.0556138i
\(661\) 6.20732e9 0.835986 0.417993 0.908450i \(-0.362734\pi\)
0.417993 + 0.908450i \(0.362734\pi\)
\(662\) 1.13979e9 + 3.50792e9i 0.152694 + 0.469944i
\(663\) −8.79288e8 6.38840e8i −0.117175 0.0851324i
\(664\) −1.94841e9 + 1.41560e9i −0.258281 + 0.187652i
\(665\) 3.06794e9 9.44216e9i 0.404549 1.24507i
\(666\) −1.14974e9 + 3.53854e9i −0.150814 + 0.464157i
\(667\) 7.81238e9 5.67602e9i 1.01940 0.740634i
\(668\) 1.05553e9 + 7.66885e8i 0.137010 + 0.0995434i
\(669\) 2.38308e9 + 7.33435e9i 0.307713 + 0.947044i
\(670\) −1.22599e9 −0.157480
\(671\) −8.03622e9 + 4.83874e9i −1.02689 + 0.618306i
\(672\) −2.45878e9 −0.312556
\(673\) −2.43652e9 7.49885e9i −0.308119 0.948291i −0.978495 0.206270i \(-0.933867\pi\)
0.670377 0.742021i \(-0.266133\pi\)
\(674\) 1.77870e9 + 1.29230e9i 0.223765 + 0.162575i
\(675\) 6.37724e8 4.63334e8i 0.0798122 0.0579870i
\(676\) 3.83613e8 1.18064e9i 0.0477618 0.146996i
\(677\) −8.28255e7 + 2.54911e8i −0.0102590 + 0.0315739i −0.956055 0.293187i \(-0.905284\pi\)
0.945796 + 0.324761i \(0.105284\pi\)
\(678\) −2.82751e9 + 2.05431e9i −0.348418 + 0.253141i
\(679\) 2.52683e9 + 1.83585e9i 0.309765 + 0.225057i
\(680\) −7.40864e8 2.28015e9i −0.0903561 0.278088i
\(681\) −7.58265e9 −0.920039
\(682\) 1.57613e9 + 1.36430e8i 0.190260 + 0.0164689i
\(683\) −7.43196e9 −0.892546 −0.446273 0.894897i \(-0.647249\pi\)
−0.446273 + 0.894897i \(0.647249\pi\)
\(684\) 4.14651e8 + 1.27617e9i 0.0495435 + 0.152479i
\(685\) −7.64994e8 5.55801e8i −0.0909371 0.0660697i
\(686\) −5.57087e9 + 4.04747e9i −0.658853 + 0.478685i
\(687\) −2.05641e9 + 6.32897e9i −0.241970 + 0.744706i
\(688\) −4.60544e8 + 1.41741e9i −0.0539152 + 0.165934i
\(689\) −5.19594e9 + 3.77507e9i −0.605197 + 0.439701i
\(690\) 4.33396e9 + 3.14881e9i 0.502242 + 0.364900i
\(691\) −2.79277e9 8.59527e9i −0.322005 0.991029i −0.972775 0.231754i \(-0.925554\pi\)
0.650770 0.759275i \(-0.274446\pi\)
\(692\) −6.04135e8 −0.0693047
\(693\) −6.87853e8 2.96694e9i −0.0785108 0.338643i
\(694\) −5.05370e9 −0.573920
\(695\) 1.20001e9 + 3.69325e9i 0.135593 + 0.417313i
\(696\) −3.15567e9 2.29273e9i −0.354780 0.257763i
\(697\) −2.16134e9 + 1.57030e9i −0.241773 + 0.175658i
\(698\) 1.84619e9 5.68200e9i 0.205487 0.632423i
\(699\) 2.17505e8 6.69411e8i 0.0240879 0.0741349i
\(700\) −1.04986e9 + 7.62765e8i −0.115688 + 0.0840520i
\(701\) 1.07017e9 + 7.77522e8i 0.117338 + 0.0852510i 0.644907 0.764261i \(-0.276896\pi\)
−0.527569 + 0.849512i \(0.676896\pi\)
\(702\) −3.03135e8 9.32952e8i −0.0330716 0.101784i
\(703\) −2.83360e10 −3.07606
\(704\) −3.98932e9 + 9.42238e9i −0.430917 + 1.01779i
\(705\) −9.09432e7 −0.00977481
\(706\) −1.18621e9 3.65077e9i −0.126866 0.390452i
\(707\) 3.88817e9 + 2.82492e9i 0.413787 + 0.300634i
\(708\) 1.99888e8 1.45227e8i 0.0211675 0.0153791i
\(709\) 3.63664e9 1.11924e10i 0.383212 1.17940i −0.554558 0.832145i \(-0.687113\pi\)
0.937769 0.347259i \(-0.112887\pi\)
\(710\) 2.49949e9 7.69262e9i 0.262088 0.806622i
\(711\) 3.00753e9 2.18510e9i 0.313809 0.227996i
\(712\) 1.16289e10 + 8.44887e9i 1.20742 + 0.877241i
\(713\) −1.20096e9 3.69619e9i −0.124084 0.381892i
\(714\) −1.93514e9 −0.198961
\(715\) −3.34874e9 2.90560e9i −0.342618 0.297279i
\(716\) 1.27129e9 0.129434
\(717\) 7.57458e8 + 2.33122e9i 0.0767435 + 0.236192i
\(718\) −7.60133e9 5.52269e9i −0.766397 0.556820i
\(719\) 7.17458e9 5.21264e9i 0.719856 0.523006i −0.166482 0.986044i \(-0.553241\pi\)
0.886338 + 0.463039i \(0.153241\pi\)
\(720\) 4.76033e8 1.46508e9i 0.0475306 0.146284i
\(721\) 3.66654e9 1.12845e10i 0.364320 1.12126i
\(722\) 1.56383e10 1.13619e10i 1.54636 1.12350i
\(723\) 7.08455e9 + 5.14722e9i 0.697153 + 0.506511i
\(724\) 1.00764e9 + 3.10120e9i 0.0986781 + 0.303700i
\(725\) −3.68289e9 −0.358926
\(726\) −5.01900e9 8.75446e8i −0.486787 0.0849085i
\(727\) −2.84383e8 −0.0274495 −0.0137247 0.999906i \(-0.504369\pi\)
−0.0137247 + 0.999906i \(0.504369\pi\)
\(728\) 2.36468e9 + 7.27774e9i 0.227150 + 0.699096i
\(729\) −3.13430e8 2.27720e8i −0.0299636 0.0217698i
\(730\) 6.63887e9 4.82342e9i 0.631632 0.458908i
\(731\) 3.32609e8 1.02367e9i 0.0314937 0.0969276i
\(732\) 6.07033e8 1.86826e9i 0.0572036 0.176055i
\(733\) −6.09071e8 + 4.42516e8i −0.0571221 + 0.0415016i −0.615980 0.787762i \(-0.711240\pi\)
0.558858 + 0.829264i \(0.311240\pi\)
\(734\) −8.83340e9 6.41784e9i −0.824502 0.599036i
\(735\) −1.17436e8 3.61431e8i −0.0109093 0.0335753i
\(736\) 1.01042e10 0.934178
\(737\) −2.16345e9 1.87716e9i −0.199072 0.172729i
\(738\) −2.41126e9 −0.220824
\(739\) −4.47662e9 1.37776e10i −0.408033 1.25580i −0.918336 0.395801i \(-0.870467\pi\)
0.510303 0.859994i \(-0.329533\pi\)
\(740\) −2.84891e9 2.06986e9i −0.258445 0.187771i
\(741\) 6.04408e9 4.39128e9i 0.545716 0.396486i
\(742\) −3.53368e9 + 1.08756e10i −0.317551 + 0.977322i
\(743\) −3.59813e9 + 1.10739e10i −0.321822 + 0.990467i 0.651032 + 0.759050i \(0.274336\pi\)
−0.972855 + 0.231417i \(0.925664\pi\)
\(744\) −1.27003e9 + 9.22731e8i −0.113060 + 0.0821429i
\(745\) 7.62576e8 + 5.54044e8i 0.0675672 + 0.0490904i
\(746\) −1.04698e9 3.22228e9i −0.0923323 0.284170i
\(747\) 1.11759e9 0.0980985
\(748\) 4.60874e8 1.08854e9i 0.0402649 0.0951017i
\(749\) −1.98471e10 −1.72588
\(750\) −1.86298e9 5.73366e9i −0.161248 0.496269i
\(751\) −4.17024e9 3.02985e9i −0.359270 0.261025i 0.393478 0.919334i \(-0.371272\pi\)
−0.752748 + 0.658309i \(0.771272\pi\)
\(752\) 1.51228e8 1.09873e8i 0.0129679 0.00942172i
\(753\) 2.23443e9 6.87687e9i 0.190715 0.586960i
\(754\) −1.41628e9 + 4.35885e9i −0.120323 + 0.370316i
\(755\) −9.74106e9 + 7.07729e9i −0.823743 + 0.598484i
\(756\) 5.15985e8 + 3.74885e8i 0.0434321 + 0.0315553i
\(757\) 3.84346e9 + 1.18289e10i 0.322023 + 0.991084i 0.972767 + 0.231787i \(0.0744572\pi\)
−0.650744 + 0.759297i \(0.725543\pi\)
\(758\) 1.61895e10 1.35018
\(759\) 2.82669e9 + 1.21924e10i 0.234656 + 1.01215i
\(760\) 1.64800e10 1.36178
\(761\) 2.29526e9 + 7.06410e9i 0.188793 + 0.581046i 0.999993 0.00372320i \(-0.00118513\pi\)
−0.811200 + 0.584769i \(0.801185\pi\)
\(762\) 7.92046e9 + 5.75455e9i 0.648497 + 0.471160i
\(763\) −6.05513e9 + 4.39931e9i −0.493500 + 0.358549i
\(764\) 4.69368e8 1.44457e9i 0.0380791 0.117195i
\(765\) −3.43795e8 + 1.05809e9i −0.0277642 + 0.0854494i
\(766\) 1.05652e10 7.67609e9i 0.849334 0.617077i
\(767\) −1.11290e9 8.08572e8i −0.0890582 0.0647046i
\(768\) −1.65720e9 5.10034e9i −0.132011 0.406289i
\(769\) 1.59173e8 0.0126220 0.00631100 0.999980i \(-0.497991\pi\)
0.00631100 + 0.999980i \(0.497991\pi\)
\(770\) −7.86450e9 6.80749e8i −0.620802 0.0537365i
\(771\) 1.02896e10 0.808553
\(772\) 9.67185e8 + 2.97669e9i 0.0756570 + 0.232848i
\(773\) −6.18301e9 4.49222e9i −0.481473 0.349811i 0.320423 0.947275i \(-0.396175\pi\)
−0.801896 + 0.597464i \(0.796175\pi\)
\(774\) 7.85940e8 5.71019e8i 0.0609251 0.0442646i
\(775\) −4.58029e8 + 1.40967e9i −0.0353457 + 0.108783i
\(776\) −1.60211e9 + 4.93078e9i −0.123077 + 0.378791i
\(777\) −1.08962e10 + 7.91655e9i −0.833300 + 0.605428i
\(778\) −7.18735e9 5.22191e9i −0.547192 0.397559i
\(779\) −5.67475e9 1.74651e10i −0.430096 1.32370i
\(780\) 9.28445e8 0.0700527
\(781\) 1.61892e10 9.74777e9i 1.21604 0.732195i
\(782\) 7.95232e9 0.594662
\(783\) 5.59343e8 + 1.72148e9i 0.0416401 + 0.128155i
\(784\) 6.31947e8 + 4.59136e8i 0.0468354 + 0.0340279i
\(785\) −1.48411e9 + 1.07827e9i −0.109502 + 0.0795576i
\(786\) −1.33182e9 + 4.09892e9i −0.0978288 + 0.301086i
\(787\) −7.82266e9 + 2.40757e10i −0.572061 + 1.76062i 0.0739126 + 0.997265i \(0.476451\pi\)
−0.645974 + 0.763359i \(0.723549\pi\)
\(788\) −2.97185e9 + 2.15918e9i −0.216364 + 0.157198i
\(789\) −2.42443e9 1.76145e9i −0.175728 0.127674i
\(790\) −2.97748e9 9.16375e9i −0.214859 0.661269i
\(791\) −1.26516e10 −0.908925
\(792\) 4.33105e9 2.60779e9i 0.309781 0.186524i
\(793\) −1.09371e10 −0.778836
\(794\) −5.56819e8 1.71371e9i −0.0394769 0.121497i
\(795\) 5.31874e9 + 3.86429e9i 0.375425 + 0.272762i
\(796\) −2.87245e9 + 2.08696e9i −0.201863 + 0.146662i
\(797\) −2.45707e9 + 7.56208e9i −0.171915 + 0.529099i −0.999479 0.0322716i \(-0.989726\pi\)
0.827564 + 0.561371i \(0.189726\pi\)
\(798\) 4.11049e9 1.26508e10i 0.286341 0.881267i
\(799\) −1.09218e8 + 7.93516e7i −0.00757497 + 0.00550354i
\(800\) −3.11761e9 2.26508e9i −0.215282 0.156411i
\(801\) −2.06122e9 6.34378e9i −0.141713 0.436148i
\(802\) 1.85343e10 1.26872
\(803\) 1.91006e10 + 1.65335e9i 1.30180 + 0.112683i
\(804\) 5.99822e8 0.0407030
\(805\) 5.99250e9 + 1.84430e10i 0.404877 + 1.24608i
\(806\) 1.49226e9 + 1.08419e9i 0.100386 + 0.0729347i
\(807\) −7.33283e9 + 5.32761e9i −0.491150 + 0.356841i
\(808\) −2.46525e9 + 7.58726e9i −0.164407 + 0.505994i
\(809\) −3.78523e9 + 1.16497e10i −0.251346 + 0.773565i 0.743181 + 0.669090i \(0.233316\pi\)
−0.994528 + 0.104474i \(0.966684\pi\)
\(810\) −8.12372e8 + 5.90223e8i −0.0537103 + 0.0390228i
\(811\) −1.06911e10 7.76757e9i −0.703803 0.511343i 0.177366 0.984145i \(-0.443242\pi\)
−0.881169 + 0.472802i \(0.843242\pi\)
\(812\) −9.20821e8 2.83400e9i −0.0603572 0.185760i
\(813\) −1.56112e10 −1.01887
\(814\) 5.08843e9 + 2.19481e10i 0.330673 + 1.42630i
\(815\) 1.11690e10 0.722709
\(816\) −7.06649e8 2.17484e9i −0.0455290 0.140124i
\(817\) 5.98562e9 + 4.34881e9i 0.384001 + 0.278993i
\(818\) −1.32826e10 + 9.65036e9i −0.848488 + 0.616463i
\(819\) 1.09732e9 3.37721e9i 0.0697976 0.214815i
\(820\) 7.05229e8 2.17047e9i 0.0446665 0.137469i
\(821\) 1.34774e10 9.79194e9i 0.849976 0.617544i −0.0751634 0.997171i \(-0.523948\pi\)
0.925139 + 0.379628i \(0.123948\pi\)
\(822\) −1.02495e9 7.44673e8i −0.0643655 0.0467643i
\(823\) 4.99756e9 + 1.53809e10i 0.312506 + 0.961795i 0.976769 + 0.214296i \(0.0687456\pi\)
−0.664263 + 0.747499i \(0.731254\pi\)
\(824\) 1.96954e10 1.22637
\(825\) 1.86104e9 4.39560e9i 0.115390 0.272539i
\(826\) −2.44928e9 −0.151220
\(827\) 7.60634e8 + 2.34099e9i 0.0467635 + 0.143923i 0.971712 0.236170i \(-0.0758921\pi\)
−0.924948 + 0.380093i \(0.875892\pi\)
\(828\) −2.12041e9 1.54057e9i −0.129812 0.0943136i
\(829\) 9.11368e9 6.62148e9i 0.555588 0.403658i −0.274254 0.961657i \(-0.588431\pi\)
0.829842 + 0.557999i \(0.188431\pi\)
\(830\) 8.95120e8 2.75490e9i 0.0543386 0.167237i
\(831\) −1.42602e9 + 4.38883e9i −0.0862027 + 0.265305i
\(832\) −9.65155e9 + 7.01226e9i −0.580986 + 0.422111i
\(833\) −4.56398e8 3.31593e8i −0.0273581 0.0198768i
\(834\) 1.60780e9 + 4.94829e9i 0.0959733 + 0.295375i
\(835\) −7.43580e9 −0.442003
\(836\) 6.13727e9 + 5.32512e9i 0.363290 + 0.315216i
\(837\) 7.28480e8 0.0429416
\(838\) 7.97582e9 + 2.45470e10i 0.468189 + 1.44094i
\(839\) 1.09654e10 + 7.96684e9i 0.641000 + 0.465714i 0.860194 0.509967i \(-0.170343\pi\)
−0.219193 + 0.975681i \(0.570343\pi\)
\(840\) 6.33713e9 4.60419e9i 0.368905 0.268025i
\(841\) −2.71719e9 + 8.36266e9i −0.157520 + 0.484796i
\(842\) 6.47666e9 1.99331e10i 0.373903 1.15075i
\(843\) 8.53671e9 6.20228e9i 0.490788 0.356578i
\(844\) 4.00614e9 + 2.91063e9i 0.229365 + 0.166644i
\(845\) 2.18630e9 + 6.72875e9i 0.124656 + 0.383650i
\(846\) −1.21848e8 −0.00691864
\(847\) −1.28358e10 1.32429e10i −0.725823 0.748844i
\(848\) −1.35131e10 −0.760972
\(849\) −3.87460e9 1.19248e10i −0.217295 0.668766i
\(850\) −2.45366e9 1.78269e9i −0.137040 0.0995656i
\(851\) 4.47772e10 3.25325e10i 2.49060 1.80953i
\(852\) −1.22288e9 + 3.76365e9i −0.0677403 + 0.208483i
\(853\) −4.18132e8 + 1.28688e9i −0.0230670 + 0.0709930i −0.961927 0.273305i \(-0.911883\pi\)
0.938860 + 0.344298i \(0.111883\pi\)
\(854\) −1.57543e10 + 1.14461e10i −0.865557 + 0.628864i
\(855\) −6.18693e9 4.49506e9i −0.338527 0.245954i
\(856\) −1.01805e10 3.13324e10i −0.554768 1.70740i
\(857\) −1.47329e10 −0.799569 −0.399784 0.916609i \(-0.630915\pi\)
−0.399784 + 0.916609i \(0.630915\pi\)
\(858\) −4.48670e9 3.89298e9i −0.242506 0.210415i
\(859\) 5.80384e9 0.312420 0.156210 0.987724i \(-0.450072\pi\)
0.156210 + 0.987724i \(0.450072\pi\)
\(860\) 2.84130e8 + 8.74462e8i 0.0152325 + 0.0468810i
\(861\) −7.06157e9 5.13053e9i −0.377042 0.273937i
\(862\) 1.49842e10 1.08867e10i 0.796817 0.578921i
\(863\) 1.92933e9 5.93788e9i 0.102181 0.314480i −0.886878 0.462004i \(-0.847130\pi\)
0.989058 + 0.147524i \(0.0471304\pi\)
\(864\) −5.85268e8 + 1.80127e9i −0.0308714 + 0.0950124i
\(865\) 2.78553e9 2.02381e9i 0.146336 0.106319i
\(866\) −8.85607e9 6.43431e9i −0.463371 0.336658i
\(867\) −2.91330e9 8.96620e9i −0.151816 0.467242i
\(868\) −1.19926e9 −0.0622438
\(869\) 8.77673e9 2.07298e10i 0.453694 1.07158i
\(870\) 4.69149e9 0.241542
\(871\) −1.03199e9 3.17615e9i −0.0529192 0.162868i
\(872\) −1.00511e10 7.30256e9i −0.513342 0.372965i
\(873\) 1.94638e9 1.41413e9i 0.0990099 0.0719349i
\(874\) −1.68918e10 + 5.19876e10i −0.855827 + 2.63396i
\(875\) 6.74383e9 2.07554e10i 0.340313 1.04738i
\(876\) −3.24810e9 + 2.35988e9i −0.163254 + 0.118611i
\(877\) −7.64246e9 5.55257e9i −0.382591 0.277968i 0.379822 0.925060i \(-0.375985\pi\)
−0.762413 + 0.647091i \(0.775985\pi\)
\(878\) 5.63354e9 + 1.73383e10i 0.280899 + 0.864520i
\(879\) 1.54369e10 0.766652
\(880\) −2.10678e9 9.08725e9i −0.104215 0.449514i
\(881\) −8.20512e9 −0.404268 −0.202134 0.979358i \(-0.564788\pi\)
−0.202134 + 0.979358i \(0.564788\pi\)
\(882\) −1.57343e8 4.84253e8i −0.00772161 0.0237647i
\(883\) −3.60929e9 2.62231e9i −0.176425 0.128180i 0.496068 0.868284i \(-0.334777\pi\)
−0.672493 + 0.740103i \(0.734777\pi\)
\(884\) 1.11501e9 8.10106e8i 0.0542872 0.0394420i
\(885\) −4.35138e8 + 1.33922e9i −0.0211021 + 0.0649456i
\(886\) 7.10374e9 2.18631e10i 0.343138 1.05607i
\(887\) −1.73009e10 + 1.25698e10i −0.832406 + 0.604779i −0.920239 0.391357i \(-0.872006\pi\)
0.0878328 + 0.996135i \(0.472006\pi\)
\(888\) −1.80870e10 1.31410e10i −0.866803 0.629769i
\(889\) 1.09515e10 + 3.37053e10i 0.522778 + 1.60895i
\(890\) −1.72885e10 −0.822037
\(891\) −2.33727e9 2.02314e8i −0.110697 0.00958193i
\(892\) −9.77924e9 −0.461347
\(893\) −2.86760e8 8.82558e8i −0.0134753 0.0414728i
\(894\) 1.02171e9 + 7.42319e8i 0.0478242 + 0.0347463i
\(895\) −5.86163e9 + 4.25872e9i −0.273299 + 0.198563i
\(896\) −2.96184e9 + 9.11560e9i −0.137557 + 0.423358i
\(897\) −4.50938e9 + 1.38784e10i −0.208614 + 0.642047i
\(898\) −9.56526e9 + 6.94957e9i −0.440788 + 0.320251i
\(899\) −2.75352e9 2.00055e9i −0.126395 0.0918313i
\(900\) 3.08892e8 + 9.50673e8i 0.0141240 + 0.0434693i
\(901\) 9.75928e9 0.444509
\(902\) −1.25088e10 + 7.53176e9i −0.567536 + 0.341722i
\(903\) 3.51666e9 0.158936
\(904\) −6.48962e9 1.99730e10i −0.292166 0.899194i
\(905\) −1.50348e10 1.09234e10i −0.674260 0.489879i
\(906\) −1.30513e10 + 9.48230e9i −0.583047 + 0.423609i
\(907\) 6.33470e9 1.94962e10i 0.281904 0.867610i −0.705406 0.708803i \(-0.749235\pi\)
0.987310 0.158807i \(-0.0507646\pi\)
\(908\) 2.97135e9 9.14486e9i 0.131720 0.405393i
\(909\) 2.99501e9 2.17600e9i 0.132259 0.0960915i
\(910\) −7.44602e9 5.40985e9i −0.327551 0.237980i
\(911\) 3.91851e9 + 1.20599e10i 0.171714 + 0.528482i 0.999468 0.0326090i \(-0.0103816\pi\)
−0.827754 + 0.561091i \(0.810382\pi\)
\(912\) 1.57189e10 0.686181
\(913\) 5.79770e9 3.49089e9i 0.252121 0.151806i
\(914\) 2.91126e10 1.26116
\(915\) 3.45962e9 + 1.06476e10i 0.149298 + 0.459493i
\(916\) −6.82707e9 4.96016e9i −0.293495 0.213236i
\(917\) −1.26218e10 + 9.17024e9i −0.540539 + 0.392725i
\(918\) −4.60624e8 + 1.41765e9i −0.0196516 + 0.0604813i
\(919\) 4.36064e9 1.34207e10i 0.185330 0.570388i −0.814624 0.579990i \(-0.803056\pi\)
0.999954 + 0.00960201i \(0.00305646\pi\)
\(920\) −2.60420e10 + 1.89206e10i −1.10260 + 0.801085i
\(921\) −1.21358e10 8.81714e9i −0.511868 0.371894i
\(922\) −5.49231e8 1.69036e9i −0.0230779 0.0710266i
\(923\) 2.20331e10 0.922293
\(924\) 3.84774e9 + 3.33060e8i 0.160455 + 0.0138890i
\(925\) −2.11087e10 −0.876932
\(926\) −5.26280e9 1.61972e10i −0.217810 0.670352i
\(927\) −7.39409e9 5.37212e9i −0.304863 0.221496i
\(928\) 7.15884e9 5.20120e9i 0.294052 0.213642i
\(929\) 3.58714e9 1.10401e10i 0.146789 0.451770i −0.850448 0.526060i \(-0.823669\pi\)
0.997237 + 0.0742895i \(0.0236689\pi\)
\(930\) 5.83465e8 1.79572e9i 0.0237862 0.0732063i
\(931\) 3.13721e9 2.27932e9i 0.127415 0.0925722i
\(932\) 7.22094e8 + 5.24632e8i 0.0292172 + 0.0212275i
\(933\) −6.43057e8 1.97913e9i −0.0259217 0.0797789i
\(934\) −3.76452e10 −1.51180
\(935\) 1.52154e9 + 6.56290e9i 0.0608755 + 0.262576i
\(936\) 5.89444e9 0.234951
\(937\) 2.19605e9 + 6.75876e9i 0.0872076 + 0.268397i 0.985145 0.171726i \(-0.0549345\pi\)
−0.897937 + 0.440124i \(0.854935\pi\)
\(938\) −4.81050e9 3.49503e9i −0.190318 0.138274i
\(939\) 5.93648e9 4.31311e9i 0.233991 0.170005i
\(940\) 3.56371e7 1.09680e8i 0.00139944 0.00430704i
\(941\) −1.09078e10 + 3.35707e10i −0.426749 + 1.31340i 0.474561 + 0.880223i \(0.342607\pi\)
−0.901310 + 0.433175i \(0.857393\pi\)
\(942\) −1.98843e9 + 1.44468e9i −0.0775056 + 0.0563111i
\(943\) 2.90191e10 + 2.10836e10i 1.12692 + 0.818754i
\(944\) −8.94397e8 2.75267e9i −0.0346042 0.106501i
\(945\) −3.63493e9 −0.140115
\(946\) 2.29357e9 5.41719e9i 0.0880832 0.208044i
\(947\) 5.02190e10 1.92151 0.960755 0.277397i \(-0.0894717\pi\)
0.960755 + 0.277397i \(0.0894717\pi\)
\(948\) 1.45675e9 + 4.48340e9i 0.0555335 + 0.170914i
\(949\) 1.80843e10 + 1.31390e10i 0.686862 + 0.499034i
\(950\) 1.68661e10 1.22539e10i 0.638236 0.463706i
\(951\) 6.92482e8 2.13124e9i 0.0261082 0.0803527i
\(952\) 3.59322e9 1.10588e10i 0.134975 0.415412i
\(953\) 1.30879e9 9.50891e8i 0.0489829 0.0355882i −0.563024 0.826440i \(-0.690362\pi\)
0.612007 + 0.790852i \(0.290362\pi\)
\(954\) 7.12615e9 + 5.17745e9i 0.265727 + 0.193062i
\(955\) 2.67504e9 + 8.23292e9i 0.0993844 + 0.305874i
\(956\) −3.10832e9 −0.115060
\(957\) 8.27885e9 + 7.18331e9i 0.305336 + 0.264931i
\(958\) 1.24765e10 0.458473
\(959\) −1.41719e9 4.36166e9i −0.0518876 0.159693i
\(960\) 9.87965e9 + 7.17799e9i 0.360406 + 0.261850i
\(961\) 2.11500e10 1.53664e10i 0.768738 0.558521i
\(962\) −8.11750e9 + 2.49831e10i −0.293974 + 0.904760i
\(963\) −4.72423e9 + 1.45397e10i −0.170466 + 0.524642i
\(964\) −8.98383e9 + 6.52714e9i −0.322992 + 0.234668i
\(965\) −1.44312e10 1.04848e10i −0.516958 0.375592i
\(966\) 8.02888e9 + 2.47103e10i 0.286573 + 0.881980i
\(967\) 2.91077e10 1.03518 0.517589 0.855629i \(-0.326830\pi\)
0.517589 + 0.855629i \(0.326830\pi\)
\(968\) 1.43224e10 2.70567e10i 0.507518 0.958762i
\(969\) −1.13523e10 −0.400821
\(970\) −1.92694e9 5.93051e9i −0.0677902 0.208637i
\(971\) −1.82314e10 1.32459e10i −0.639076 0.464316i 0.220457 0.975397i \(-0.429245\pi\)
−0.859533 + 0.511081i \(0.829245\pi\)
\(972\) 3.97457e8 2.88769e8i 0.0138822 0.0100860i
\(973\) −5.82010e9 + 1.79124e10i −0.202552 + 0.623389i
\(974\) −1.10533e10 + 3.40186e10i −0.383298 + 1.17967i
\(975\) 4.50251e9 3.27126e9i 0.155574 0.113031i
\(976\) −1.86169e10 1.35260e10i −0.640963 0.465687i
\(977\) 1.48822e10 + 4.58028e10i 0.510549 + 1.57131i 0.791237 + 0.611509i \(0.209437\pi\)
−0.280689 + 0.959799i \(0.590563\pi\)
\(978\) 1.49645e10 0.511535
\(979\) −3.05082e10 2.64710e10i −1.03915 0.901635i
\(980\) 4.81913e8 0.0163560
\(981\) 1.78156e9 + 5.48308e9i 0.0602503 + 0.185431i
\(982\) 1.10284e10 + 8.01260e9i 0.371640 + 0.270012i
\(983\) 2.12281e8 1.54231e8i 0.00712810 0.00517887i −0.584216 0.811599i \(-0.698598\pi\)
0.591344 + 0.806420i \(0.298598\pi\)
\(984\) 4.47731e9 1.37797e10i 0.149808 0.461060i
\(985\) 6.46947e9 1.99110e10i 0.215696 0.663844i
\(986\) 5.63423e9 4.09351e9i 0.187183 0.135996i
\(987\) −3.56840e8 2.59259e8i −0.0118131 0.00858271i
\(988\) 2.92755e9 + 9.01008e9i 0.0965730 + 0.297221i
\(989\) −1.44515e10 −0.475035
\(990\) −2.37071e9 + 5.59938e9i −0.0776524 + 0.183407i
\(991\) −1.46660e10 −0.478688 −0.239344 0.970935i \(-0.576932\pi\)
−0.239344 + 0.970935i \(0.576932\pi\)
\(992\) −1.10050e9 3.38699e9i −0.0357931 0.110160i
\(993\) 8.32055e9 + 6.04523e9i 0.269668 + 0.195925i
\(994\) 3.17374e10 2.30586e10i 1.02499 0.744697i
\(995\) 6.25307e9 1.92450e10i 0.201239 0.619351i
\(996\) −4.37942e8 + 1.34785e9i −0.0140446 + 0.0432248i
\(997\) −1.51854e10 + 1.10328e10i −0.485281 + 0.352577i −0.803367 0.595485i \(-0.796960\pi\)
0.318086 + 0.948062i \(0.396960\pi\)
\(998\) 5.15417e9 + 3.74472e9i 0.164135 + 0.119251i
\(999\) 3.20591e9 + 9.86679e9i 0.101736 + 0.313110i
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 33.8.e.b.16.3 28
3.2 odd 2 99.8.f.b.82.5 28
11.3 even 5 363.8.a.o.1.5 14
11.8 odd 10 363.8.a.r.1.10 14
11.9 even 5 inner 33.8.e.b.31.3 yes 28
33.20 odd 10 99.8.f.b.64.5 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.8.e.b.16.3 28 1.1 even 1 trivial
33.8.e.b.31.3 yes 28 11.9 even 5 inner
99.8.f.b.64.5 28 33.20 odd 10
99.8.f.b.82.5 28 3.2 odd 2
363.8.a.o.1.5 14 11.3 even 5
363.8.a.r.1.10 14 11.8 odd 10