Properties

Label 13.7.d.a.5.4
Level $13$
Weight $7$
Character 13.5
Analytic conductor $2.991$
Analytic rank $0$
Dimension $12$
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] = [13,7,Mod(5,13)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(13, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("13.5");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 13 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 13.d (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: \(2.99070308706\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 18 x^{10} + 488 x^{9} + 36205 x^{8} - 155430 x^{7} + 399962 x^{6} + 9502784 x^{5} + 275595012 x^{4} - 541321656 x^{3} + 523196552 x^{2} + \cdots + 56070144 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 5^{2}\cdot 13^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.4
Root \(0.388469 + 0.388469i\) of defining polynomial
Character \(\chi\) \(=\) 13.5
Dual form 13.7.d.a.8.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.611531 - 0.611531i) q^{2} +18.7379 q^{3} +63.2521i q^{4} +(134.607 - 134.607i) q^{5} +(11.4588 - 11.4588i) q^{6} +(241.226 + 241.226i) q^{7} +(77.8186 + 77.8186i) q^{8} -377.891 q^{9} +O(q^{10})\) \(q+(0.611531 - 0.611531i) q^{2} +18.7379 q^{3} +63.2521i q^{4} +(134.607 - 134.607i) q^{5} +(11.4588 - 11.4588i) q^{6} +(241.226 + 241.226i) q^{7} +(77.8186 + 77.8186i) q^{8} -377.891 q^{9} -164.633i q^{10} +(-1796.54 - 1796.54i) q^{11} +1185.21i q^{12} +(-375.320 + 2164.70i) q^{13} +295.034 q^{14} +(2522.26 - 2522.26i) q^{15} -3952.95 q^{16} -789.421i q^{17} +(-231.092 + 231.092i) q^{18} +(4083.16 - 4083.16i) q^{19} +(8514.18 + 8514.18i) q^{20} +(4520.07 + 4520.07i) q^{21} -2197.28 q^{22} -1432.88i q^{23} +(1458.16 + 1458.16i) q^{24} -20613.2i q^{25} +(1094.26 + 1553.30i) q^{26} -20740.8 q^{27} +(-15258.0 + 15258.0i) q^{28} +6913.74 q^{29} -3084.88i q^{30} +(-11888.4 + 11888.4i) q^{31} +(-7397.75 + 7397.75i) q^{32} +(-33663.3 - 33663.3i) q^{33} +(-482.756 - 482.756i) q^{34} +64941.4 q^{35} -23902.4i q^{36} +(29823.4 + 29823.4i) q^{37} -4993.96i q^{38} +(-7032.71 + 40562.0i) q^{39} +20949.9 q^{40} +(-29513.5 + 29513.5i) q^{41} +5528.32 q^{42} -33537.0i q^{43} +(113635. - 113635. i) q^{44} +(-50866.8 + 50866.8i) q^{45} +(-876.249 - 876.249i) q^{46} +(76861.6 + 76861.6i) q^{47} -74070.1 q^{48} -1269.32i q^{49} +(-12605.6 - 12605.6i) q^{50} -14792.1i q^{51} +(-136922. - 23739.8i) q^{52} +142559. q^{53} +(-12683.7 + 12683.7i) q^{54} -483653. q^{55} +37543.7i q^{56} +(76509.9 - 76509.9i) q^{57} +(4227.97 - 4227.97i) q^{58} +(-82531.1 - 82531.1i) q^{59} +(159538. + 159538. i) q^{60} +305962. q^{61} +14540.3i q^{62} +(-91156.9 - 91156.9i) q^{63} -243941. i q^{64} +(240864. + 341906. i) q^{65} -41172.3 q^{66} +(53061.6 - 53061.6i) q^{67} +49932.5 q^{68} -26849.1i q^{69} +(39713.7 - 39713.7i) q^{70} +(-192797. + 192797. i) q^{71} +(-29406.9 - 29406.9i) q^{72} +(390480. + 390480. i) q^{73} +36475.9 q^{74} -386248. i q^{75} +(258268. + 258268. i) q^{76} -866741. i q^{77} +(20504.2 + 29105.7i) q^{78} -531901. q^{79} +(-532096. + 532096. i) q^{80} -113157. q^{81} +36096.9i q^{82} +(188950. - 188950. i) q^{83} +(-285903. + 285903. i) q^{84} +(-106262. - 106262. i) q^{85} +(-20508.9 - 20508.9i) q^{86} +129549. q^{87} -279608. i q^{88} +(-45096.2 - 45096.2i) q^{89} +62213.3i q^{90} +(-612719. + 431645. i) q^{91} +90632.4 q^{92} +(-222764. + 222764. i) q^{93} +94006.6 q^{94} -1.09925e6i q^{95} +(-138618. + 138618. i) q^{96} +(730591. - 730591. i) q^{97} +(-776.232 - 776.232i) q^{98} +(678894. + 678894. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{2} - 4 q^{3} + 108 q^{5} - 640 q^{6} + 398 q^{7} - 912 q^{8} + 1940 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{2} - 4 q^{3} + 108 q^{5} - 640 q^{6} + 398 q^{7} - 912 q^{8} + 1940 q^{9} + 1686 q^{11} - 3926 q^{13} + 5484 q^{14} - 15268 q^{15} + 2132 q^{16} + 15254 q^{18} + 1766 q^{19} - 19044 q^{20} + 3428 q^{21} + 28832 q^{22} + 31608 q^{24} - 58266 q^{26} - 20464 q^{27} + 4092 q^{28} - 90108 q^{29} + 61014 q^{31} - 64932 q^{32} - 44452 q^{33} + 259896 q^{34} + 158772 q^{35} - 40212 q^{37} + 137852 q^{39} - 104196 q^{40} - 190416 q^{41} - 959204 q^{42} + 489372 q^{44} - 151444 q^{45} - 44412 q^{46} + 562446 q^{47} + 930308 q^{48} + 82422 q^{50} - 578500 q^{52} + 509136 q^{53} - 871432 q^{54} - 1264036 q^{55} + 939908 q^{57} - 1019980 q^{58} - 994458 q^{59} + 2407804 q^{60} + 1013696 q^{61} + 865778 q^{63} - 1130064 q^{65} - 418352 q^{66} - 1442386 q^{67} - 2313132 q^{68} + 2958968 q^{70} - 655866 q^{71} - 1706508 q^{72} + 2588228 q^{73} + 3373752 q^{74} + 246984 q^{76} + 77480 q^{78} - 75316 q^{79} - 2685408 q^{80} - 4016140 q^{81} + 894966 q^{83} - 3220504 q^{84} + 105396 q^{85} + 3704832 q^{86} + 2109064 q^{87} - 977376 q^{89} + 1088750 q^{91} + 3682872 q^{92} - 216268 q^{93} - 6238300 q^{94} + 896384 q^{96} + 983388 q^{97} + 1039302 q^{98} + 2894714 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.611531 0.611531i 0.0764414 0.0764414i −0.667852 0.744294i \(-0.732786\pi\)
0.744294 + 0.667852i \(0.232786\pi\)
\(3\) 18.7379 0.693997 0.346998 0.937866i \(-0.387201\pi\)
0.346998 + 0.937866i \(0.387201\pi\)
\(4\) 63.2521i 0.988313i
\(5\) 134.607 134.607i 1.07686 1.07686i 0.0800682 0.996789i \(-0.474486\pi\)
0.996789 0.0800682i \(-0.0255138\pi\)
\(6\) 11.4588 11.4588i 0.0530501 0.0530501i
\(7\) 241.226 + 241.226i 0.703282 + 0.703282i 0.965114 0.261832i \(-0.0843265\pi\)
−0.261832 + 0.965114i \(0.584327\pi\)
\(8\) 77.8186 + 77.8186i 0.151990 + 0.151990i
\(9\) −377.891 −0.518369
\(10\) 164.633i 0.164633i
\(11\) −1796.54 1796.54i −1.34976 1.34976i −0.885914 0.463849i \(-0.846468\pi\)
−0.463849 0.885914i \(-0.653532\pi\)
\(12\) 1185.21i 0.685886i
\(13\) −375.320 + 2164.70i −0.170833 + 0.985300i
\(14\) 295.034 0.107520
\(15\) 2522.26 2522.26i 0.747336 0.747336i
\(16\) −3952.95 −0.965077
\(17\) 789.421i 0.160680i −0.996768 0.0803400i \(-0.974399\pi\)
0.996768 0.0803400i \(-0.0256006\pi\)
\(18\) −231.092 + 231.092i −0.0396248 + 0.0396248i
\(19\) 4083.16 4083.16i 0.595299 0.595299i −0.343759 0.939058i \(-0.611700\pi\)
0.939058 + 0.343759i \(0.111700\pi\)
\(20\) 8514.18 + 8514.18i 1.06427 + 1.06427i
\(21\) 4520.07 + 4520.07i 0.488075 + 0.488075i
\(22\) −2197.28 −0.206356
\(23\) 1432.88i 0.117767i −0.998265 0.0588837i \(-0.981246\pi\)
0.998265 0.0588837i \(-0.0187541\pi\)
\(24\) 1458.16 + 1458.16i 0.105480 + 0.105480i
\(25\) 20613.2i 1.31924i
\(26\) 1094.26 + 1553.30i 0.0622590 + 0.0883765i
\(27\) −20740.8 −1.05374
\(28\) −15258.0 + 15258.0i −0.695063 + 0.695063i
\(29\) 6913.74 0.283478 0.141739 0.989904i \(-0.454731\pi\)
0.141739 + 0.989904i \(0.454731\pi\)
\(30\) 3084.88i 0.114255i
\(31\) −11888.4 + 11888.4i −0.399060 + 0.399060i −0.877902 0.478841i \(-0.841057\pi\)
0.478841 + 0.877902i \(0.341057\pi\)
\(32\) −7397.75 + 7397.75i −0.225761 + 0.225761i
\(33\) −33663.3 33663.3i −0.936731 0.936731i
\(34\) −482.756 482.756i −0.0122826 0.0122826i
\(35\) 64941.4 1.51467
\(36\) 23902.4i 0.512311i
\(37\) 29823.4 + 29823.4i 0.588779 + 0.588779i 0.937301 0.348521i \(-0.113316\pi\)
−0.348521 + 0.937301i \(0.613316\pi\)
\(38\) 4993.96i 0.0910111i
\(39\) −7032.71 + 40562.0i −0.118558 + 0.683795i
\(40\) 20949.9 0.327342
\(41\) −29513.5 + 29513.5i −0.428222 + 0.428222i −0.888022 0.459800i \(-0.847921\pi\)
0.459800 + 0.888022i \(0.347921\pi\)
\(42\) 5528.32 0.0746183
\(43\) 33537.0i 0.421811i −0.977506 0.210906i \(-0.932359\pi\)
0.977506 0.210906i \(-0.0676413\pi\)
\(44\) 113635. 113635.i 1.33399 1.33399i
\(45\) −50866.8 + 50866.8i −0.558209 + 0.558209i
\(46\) −876.249 876.249i −0.00900232 0.00900232i
\(47\) 76861.6 + 76861.6i 0.740314 + 0.740314i 0.972638 0.232325i \(-0.0746331\pi\)
−0.232325 + 0.972638i \(0.574633\pi\)
\(48\) −74070.1 −0.669760
\(49\) 1269.32i 0.0107891i
\(50\) −12605.6 12605.6i −0.100845 0.100845i
\(51\) 14792.1i 0.111511i
\(52\) −136922. 23739.8i −0.973785 0.168837i
\(53\) 142559. 0.957564 0.478782 0.877934i \(-0.341078\pi\)
0.478782 + 0.877934i \(0.341078\pi\)
\(54\) −12683.7 + 12683.7i −0.0805496 + 0.0805496i
\(55\) −483653. −2.90701
\(56\) 37543.7i 0.213783i
\(57\) 76509.9 76509.9i 0.413136 0.413136i
\(58\) 4227.97 4227.97i 0.0216695 0.0216695i
\(59\) −82531.1 82531.1i −0.401848 0.401848i 0.477036 0.878884i \(-0.341711\pi\)
−0.878884 + 0.477036i \(0.841711\pi\)
\(60\) 159538. + 159538.i 0.738602 + 0.738602i
\(61\) 305962. 1.34796 0.673982 0.738748i \(-0.264582\pi\)
0.673982 + 0.738748i \(0.264582\pi\)
\(62\) 14540.3i 0.0610095i
\(63\) −91156.9 91156.9i −0.364559 0.364559i
\(64\) 243941.i 0.930562i
\(65\) 240864. + 341906.i 0.877065 + 1.24499i
\(66\) −41172.3 −0.143210
\(67\) 53061.6 53061.6i 0.176423 0.176423i −0.613371 0.789795i \(-0.710187\pi\)
0.789795 + 0.613371i \(0.210187\pi\)
\(68\) 49932.5 0.158802
\(69\) 26849.1i 0.0817303i
\(70\) 39713.7 39713.7i 0.115783 0.115783i
\(71\) −192797. + 192797.i −0.538672 + 0.538672i −0.923139 0.384467i \(-0.874385\pi\)
0.384467 + 0.923139i \(0.374385\pi\)
\(72\) −29406.9 29406.9i −0.0787866 0.0787866i
\(73\) 390480. + 390480.i 1.00376 + 1.00376i 0.999993 + 0.00376728i \(0.00119916\pi\)
0.00376728 + 0.999993i \(0.498801\pi\)
\(74\) 36475.9 0.0900143
\(75\) 386248.i 0.915551i
\(76\) 258268. + 258268.i 0.588342 + 0.588342i
\(77\) 866741.i 1.89853i
\(78\) 20504.2 + 29105.7i 0.0432076 + 0.0613330i
\(79\) −531901. −1.07882 −0.539411 0.842043i \(-0.681353\pi\)
−0.539411 + 0.842043i \(0.681353\pi\)
\(80\) −532096. + 532096.i −1.03925 + 1.03925i
\(81\) −113157. −0.212925
\(82\) 36096.9i 0.0654679i
\(83\) 188950. 188950.i 0.330455 0.330455i −0.522305 0.852759i \(-0.674928\pi\)
0.852759 + 0.522305i \(0.174928\pi\)
\(84\) −285903. + 285903.i −0.482371 + 0.482371i
\(85\) −106262. 106262.i −0.173029 0.173029i
\(86\) −20508.9 20508.9i −0.0322439 0.0322439i
\(87\) 129549. 0.196733
\(88\) 279608.i 0.410300i
\(89\) −45096.2 45096.2i −0.0639691 0.0639691i 0.674398 0.738368i \(-0.264403\pi\)
−0.738368 + 0.674398i \(0.764403\pi\)
\(90\) 62213.3i 0.0853406i
\(91\) −612719. + 431645.i −0.813087 + 0.572800i
\(92\) 90632.4 0.116391
\(93\) −222764. + 222764.i −0.276947 + 0.276947i
\(94\) 94006.6 0.113181
\(95\) 1.09925e6i 1.28211i
\(96\) −138618. + 138618.i −0.156678 + 0.156678i
\(97\) 730591. 730591.i 0.800496 0.800496i −0.182677 0.983173i \(-0.558476\pi\)
0.983173 + 0.182677i \(0.0584762\pi\)
\(98\) −776.232 776.232i −0.000824732 0.000824732i
\(99\) 678894. + 678894.i 0.699675 + 0.699675i
\(100\) 1.30383e6 1.30383
\(101\) 957084.i 0.928937i 0.885590 + 0.464468i \(0.153755\pi\)
−0.885590 + 0.464468i \(0.846245\pi\)
\(102\) −9045.83 9045.83i −0.00852409 0.00852409i
\(103\) 1.00285e6i 0.917746i 0.888502 + 0.458873i \(0.151747\pi\)
−0.888502 + 0.458873i \(0.848253\pi\)
\(104\) −197661. + 139247.i −0.175720 + 0.123790i
\(105\) 1.21687e6 1.05118
\(106\) 87179.4 87179.4i 0.0731975 0.0731975i
\(107\) −949187. −0.774820 −0.387410 0.921908i \(-0.626630\pi\)
−0.387410 + 0.921908i \(0.626630\pi\)
\(108\) 1.31190e6i 1.04143i
\(109\) 850682. 850682.i 0.656882 0.656882i −0.297759 0.954641i \(-0.596239\pi\)
0.954641 + 0.297759i \(0.0962391\pi\)
\(110\) −295769. + 295769.i −0.222216 + 0.222216i
\(111\) 558829. + 558829.i 0.408611 + 0.408611i
\(112\) −953554. 953554.i −0.678721 0.678721i
\(113\) −2.43128e6 −1.68500 −0.842498 0.538699i \(-0.818916\pi\)
−0.842498 + 0.538699i \(0.818916\pi\)
\(114\) 93576.4i 0.0631614i
\(115\) −192876. 192876.i −0.126819 0.126819i
\(116\) 437308.i 0.280165i
\(117\) 141830. 818021.i 0.0885544 0.510749i
\(118\) −100941. −0.0614357
\(119\) 190429. 190429.i 0.113003 0.113003i
\(120\) 392557. 0.227174
\(121\) 4.68352e6i 2.64372i
\(122\) 187106. 187106.i 0.103040 0.103040i
\(123\) −553022. + 553022.i −0.297185 + 0.297185i
\(124\) −751966. 751966.i −0.394397 0.394397i
\(125\) −671447. 671447.i −0.343781 0.343781i
\(126\) −111491. −0.0557349
\(127\) 2.27446e6i 1.11037i −0.831728 0.555184i \(-0.812648\pi\)
0.831728 0.555184i \(-0.187352\pi\)
\(128\) −622634. 622634.i −0.296895 0.296895i
\(129\) 628413.i 0.292736i
\(130\) 356382. + 61790.1i 0.162213 + 0.0281248i
\(131\) −1.76457e6 −0.784919 −0.392460 0.919769i \(-0.628376\pi\)
−0.392460 + 0.919769i \(0.628376\pi\)
\(132\) 2.12927e6 2.12927e6i 0.925784 0.925784i
\(133\) 1.96993e6 0.837327
\(134\) 64897.7i 0.0269721i
\(135\) −2.79186e6 + 2.79186e6i −1.13473 + 1.13473i
\(136\) 61431.6 61431.6i 0.0244217 0.0244217i
\(137\) 136280. + 136280.i 0.0529994 + 0.0529994i 0.733110 0.680110i \(-0.238068\pi\)
−0.680110 + 0.733110i \(0.738068\pi\)
\(138\) −16419.1 16419.1i −0.00624758 0.00624758i
\(139\) 960906. 0.357797 0.178898 0.983868i \(-0.442747\pi\)
0.178898 + 0.983868i \(0.442747\pi\)
\(140\) 4.10768e6i 1.49697i
\(141\) 1.44023e6 + 1.44023e6i 0.513775 + 0.513775i
\(142\) 235803.i 0.0823538i
\(143\) 4.56324e6 3.21469e6i 1.56051 1.09934i
\(144\) 1.49378e6 0.500265
\(145\) 930639. 930639.i 0.305265 0.305265i
\(146\) 477581. 0.153458
\(147\) 23784.5i 0.00748758i
\(148\) −1.88639e6 + 1.88639e6i −0.581899 + 0.581899i
\(149\) 2.10179e6 2.10179e6i 0.635374 0.635374i −0.314036 0.949411i \(-0.601681\pi\)
0.949411 + 0.314036i \(0.101681\pi\)
\(150\) −236203. 236203.i −0.0699860 0.0699860i
\(151\) −3.16039e6 3.16039e6i −0.917930 0.917930i 0.0789491 0.996879i \(-0.474844\pi\)
−0.996879 + 0.0789491i \(0.974844\pi\)
\(152\) 635492. 0.180959
\(153\) 298315.i 0.0832915i
\(154\) −530039. 530039.i −0.145126 0.145126i
\(155\) 3.20053e6i 0.859462i
\(156\) −2.56563e6 444834.i −0.675804 0.117172i
\(157\) −2.14207e6 −0.553522 −0.276761 0.960939i \(-0.589261\pi\)
−0.276761 + 0.960939i \(0.589261\pi\)
\(158\) −325274. + 325274.i −0.0824667 + 0.0824667i
\(159\) 2.67126e6 0.664546
\(160\) 1.99158e6i 0.486226i
\(161\) 345647. 345647.i 0.0828238 0.0828238i
\(162\) −69199.3 + 69199.3i −0.0162763 + 0.0162763i
\(163\) 1.17045e6 + 1.17045e6i 0.270266 + 0.270266i 0.829207 0.558941i \(-0.188792\pi\)
−0.558941 + 0.829207i \(0.688792\pi\)
\(164\) −1.86679e6 1.86679e6i −0.423218 0.423218i
\(165\) −9.06265e6 −2.01745
\(166\) 231097.i 0.0505208i
\(167\) 471034. + 471034.i 0.101135 + 0.101135i 0.755864 0.654729i \(-0.227217\pi\)
−0.654729 + 0.755864i \(0.727217\pi\)
\(168\) 703491.i 0.148365i
\(169\) −4.54508e6 1.62491e6i −0.941632 0.336643i
\(170\) −129965. −0.0264532
\(171\) −1.54299e6 + 1.54299e6i −0.308585 + 0.308585i
\(172\) 2.12128e6 0.416882
\(173\) 7.65909e6i 1.47924i −0.673025 0.739620i \(-0.735005\pi\)
0.673025 0.739620i \(-0.264995\pi\)
\(174\) 79223.3 79223.3i 0.0150385 0.0150385i
\(175\) 4.97243e6 4.97243e6i 0.927801 0.927801i
\(176\) 7.10162e6 + 7.10162e6i 1.30263 + 1.30263i
\(177\) −1.54646e6 1.54646e6i −0.278881 0.278881i
\(178\) −55155.5 −0.00977978
\(179\) 1.06052e6i 0.184910i 0.995717 + 0.0924552i \(0.0294715\pi\)
−0.995717 + 0.0924552i \(0.970529\pi\)
\(180\) −3.21743e6 3.21743e6i −0.551686 0.551686i
\(181\) 1.01426e7i 1.71046i 0.518253 + 0.855228i \(0.326583\pi\)
−0.518253 + 0.855228i \(0.673417\pi\)
\(182\) −110732. + 638662.i −0.0183679 + 0.105939i
\(183\) 5.73310e6 0.935483
\(184\) 111505. 111505.i 0.0178994 0.0178994i
\(185\) 8.02890e6 1.26806
\(186\) 272454.i 0.0423404i
\(187\) −1.41822e6 + 1.41822e6i −0.216880 + 0.216880i
\(188\) −4.86165e6 + 4.86165e6i −0.731662 + 0.731662i
\(189\) −5.00322e6 5.00322e6i −0.741078 0.741078i
\(190\) −672223. 672223.i −0.0980060 0.0980060i
\(191\) 6.10706e6 0.876460 0.438230 0.898863i \(-0.355606\pi\)
0.438230 + 0.898863i \(0.355606\pi\)
\(192\) 4.57095e6i 0.645807i
\(193\) −1.87431e6 1.87431e6i −0.260717 0.260717i 0.564628 0.825345i \(-0.309020\pi\)
−0.825345 + 0.564628i \(0.809020\pi\)
\(194\) 893559.i 0.122382i
\(195\) 4.51329e6 + 6.40660e6i 0.608680 + 0.864019i
\(196\) 80287.4 0.0106630
\(197\) 3.59068e6 3.59068e6i 0.469654 0.469654i −0.432148 0.901802i \(-0.642244\pi\)
0.901802 + 0.432148i \(0.142244\pi\)
\(198\) 830330. 0.106968
\(199\) 2.17903e6i 0.276506i −0.990397 0.138253i \(-0.955851\pi\)
0.990397 0.138253i \(-0.0441487\pi\)
\(200\) 1.60409e6 1.60409e6i 0.200511 0.200511i
\(201\) 994263. 994263.i 0.122437 0.122437i
\(202\) 585287. + 585287.i 0.0710092 + 0.0710092i
\(203\) 1.66777e6 + 1.66777e6i 0.199365 + 0.199365i
\(204\) 935631. 0.110208
\(205\) 7.94546e6i 0.922269i
\(206\) 613272. + 613272.i 0.0701538 + 0.0701538i
\(207\) 541471.i 0.0610470i
\(208\) 1.48362e6 8.55698e6i 0.164867 0.950890i
\(209\) −1.46711e7 −1.60703
\(210\) 744152. 744152.i 0.0803533 0.0803533i
\(211\) −1.24296e7 −1.32315 −0.661574 0.749880i \(-0.730111\pi\)
−0.661574 + 0.749880i \(0.730111\pi\)
\(212\) 9.01716e6i 0.946373i
\(213\) −3.61261e6 + 3.61261e6i −0.373837 + 0.373837i
\(214\) −580458. + 580458.i −0.0592283 + 0.0592283i
\(215\) −4.51432e6 4.51432e6i −0.454231 0.454231i
\(216\) −1.61402e6 1.61402e6i −0.160158 0.160158i
\(217\) −5.73558e6 −0.561304
\(218\) 1.04044e6i 0.100426i
\(219\) 7.31678e6 + 7.31678e6i 0.696606 + 0.696606i
\(220\) 3.05921e7i 2.87303i
\(221\) 1.70886e6 + 296285.i 0.158318 + 0.0274494i
\(222\) 683483. 0.0624696
\(223\) −8.35639e6 + 8.35639e6i −0.753537 + 0.753537i −0.975137 0.221601i \(-0.928872\pi\)
0.221601 + 0.975137i \(0.428872\pi\)
\(224\) −3.56905e6 −0.317548
\(225\) 7.78953e6i 0.683855i
\(226\) −1.48680e6 + 1.48680e6i −0.128804 + 0.128804i
\(227\) 540807. 540807.i 0.0462343 0.0462343i −0.683612 0.729846i \(-0.739592\pi\)
0.729846 + 0.683612i \(0.239592\pi\)
\(228\) 4.83941e6 + 4.83941e6i 0.408308 + 0.408308i
\(229\) 1.52151e7 + 1.52151e7i 1.26697 + 1.26697i 0.947643 + 0.319332i \(0.103458\pi\)
0.319332 + 0.947643i \(0.396542\pi\)
\(230\) −235899. −0.0193884
\(231\) 1.62409e7i 1.31757i
\(232\) 538018. + 538018.i 0.0430857 + 0.0430857i
\(233\) 1.83092e6i 0.144744i 0.997378 + 0.0723720i \(0.0230569\pi\)
−0.997378 + 0.0723720i \(0.976943\pi\)
\(234\) −413512. 586979.i −0.0322731 0.0458116i
\(235\) 2.06922e7 1.59442
\(236\) 5.22026e6 5.22026e6i 0.397152 0.397152i
\(237\) −9.96672e6 −0.748699
\(238\) 232906.i 0.0172763i
\(239\) 9.23971e6 9.23971e6i 0.676806 0.676806i −0.282470 0.959276i \(-0.591154\pi\)
0.959276 + 0.282470i \(0.0911537\pi\)
\(240\) −9.97037e6 + 9.97037e6i −0.721236 + 0.721236i
\(241\) −1.23613e7 1.23613e7i −0.883107 0.883107i 0.110743 0.993849i \(-0.464677\pi\)
−0.993849 + 0.110743i \(0.964677\pi\)
\(242\) 2.86412e6 + 2.86412e6i 0.202090 + 0.202090i
\(243\) 1.29997e7 0.905973
\(244\) 1.93527e7i 1.33221i
\(245\) −170860. 170860.i −0.0116183 0.0116183i
\(246\) 676380.i 0.0454345i
\(247\) 7.30634e6 + 1.03713e7i 0.484852 + 0.688245i
\(248\) −1.85028e6 −0.121306
\(249\) 3.54052e6 3.54052e6i 0.229334 0.229334i
\(250\) −821222. −0.0525582
\(251\) 1.03150e7i 0.652300i −0.945318 0.326150i \(-0.894248\pi\)
0.945318 0.326150i \(-0.105752\pi\)
\(252\) 5.76586e6 5.76586e6i 0.360299 0.360299i
\(253\) −2.57421e6 + 2.57421e6i −0.158958 + 0.158958i
\(254\) −1.39090e6 1.39090e6i −0.0848780 0.0848780i
\(255\) −1.99112e6 1.99112e6i −0.120082 0.120082i
\(256\) 1.48507e7 0.885172
\(257\) 1.57226e7i 0.926244i −0.886294 0.463122i \(-0.846729\pi\)
0.886294 0.463122i \(-0.153271\pi\)
\(258\) −384294. 384294.i −0.0223771 0.0223771i
\(259\) 1.43884e7i 0.828156i
\(260\) −2.16262e7 + 1.52351e7i −1.23044 + 0.866815i
\(261\) −2.61264e6 −0.146946
\(262\) −1.07909e6 + 1.07909e6i −0.0600004 + 0.0600004i
\(263\) −2.43214e7 −1.33697 −0.668484 0.743727i \(-0.733056\pi\)
−0.668484 + 0.743727i \(0.733056\pi\)
\(264\) 5.23927e6i 0.284747i
\(265\) 1.91895e7 1.91895e7i 1.03116 1.03116i
\(266\) 1.20467e6 1.20467e6i 0.0640064 0.0640064i
\(267\) −845009. 845009.i −0.0443943 0.0443943i
\(268\) 3.35626e6 + 3.35626e6i 0.174361 + 0.174361i
\(269\) −974208. −0.0500489 −0.0250245 0.999687i \(-0.507966\pi\)
−0.0250245 + 0.999687i \(0.507966\pi\)
\(270\) 3.41462e6i 0.173481i
\(271\) −8.06718e6 8.06718e6i −0.405335 0.405335i 0.474773 0.880108i \(-0.342530\pi\)
−0.880108 + 0.474773i \(0.842530\pi\)
\(272\) 3.12054e6i 0.155069i
\(273\) −1.14811e7 + 8.08813e6i −0.564280 + 0.397521i
\(274\) 166679. 0.00810270
\(275\) −3.70323e7 + 3.70323e7i −1.78067 + 1.78067i
\(276\) 1.69826e6 0.0807751
\(277\) 1.85917e7i 0.874741i −0.899281 0.437371i \(-0.855910\pi\)
0.899281 0.437371i \(-0.144090\pi\)
\(278\) 587624. 587624.i 0.0273505 0.0273505i
\(279\) 4.49252e6 4.49252e6i 0.206860 0.206860i
\(280\) 5.05365e6 + 5.05365e6i 0.230214 + 0.230214i
\(281\) 1.38680e7 + 1.38680e7i 0.625020 + 0.625020i 0.946811 0.321791i \(-0.104285\pi\)
−0.321791 + 0.946811i \(0.604285\pi\)
\(282\) 1.76149e6 0.0785474
\(283\) 2.29361e7i 1.01195i −0.862547 0.505976i \(-0.831132\pi\)
0.862547 0.505976i \(-0.168868\pi\)
\(284\) −1.21948e7 1.21948e7i −0.532377 0.532377i
\(285\) 2.05976e7i 0.889777i
\(286\) 824681. 4.75645e6i 0.0352524 0.203322i
\(287\) −1.42388e7 −0.602322
\(288\) 2.79554e6 2.79554e6i 0.117028 0.117028i
\(289\) 2.35144e7 0.974182
\(290\) 1.13823e6i 0.0466698i
\(291\) 1.36898e7 1.36898e7i 0.555542 0.555542i
\(292\) −2.46986e7 + 2.46986e7i −0.992030 + 0.992030i
\(293\) 4.68843e6 + 4.68843e6i 0.186391 + 0.186391i 0.794134 0.607743i \(-0.207925\pi\)
−0.607743 + 0.794134i \(0.707925\pi\)
\(294\) −14545.0 14545.0i −0.000572362 0.000572362i
\(295\) −2.22186e7 −0.865466
\(296\) 4.64164e6i 0.178977i
\(297\) 3.72616e7 + 3.72616e7i 1.42230 + 1.42230i
\(298\) 2.57062e6i 0.0971379i
\(299\) 3.10176e6 + 537788.i 0.116036 + 0.0201186i
\(300\) 2.44310e7 0.904852
\(301\) 8.08998e6 8.08998e6i 0.296652 0.296652i
\(302\) −3.86535e6 −0.140336
\(303\) 1.79338e7i 0.644679i
\(304\) −1.61405e7 + 1.61405e7i −0.574510 + 0.574510i
\(305\) 4.11847e7 4.11847e7i 1.45157 1.45157i
\(306\) 182429. + 182429.i 0.00636692 + 0.00636692i
\(307\) 2.66439e7 + 2.66439e7i 0.920838 + 0.920838i 0.997089 0.0762504i \(-0.0242948\pi\)
−0.0762504 + 0.997089i \(0.524295\pi\)
\(308\) 5.48231e7 1.87634
\(309\) 1.87912e7i 0.636913i
\(310\) 1.95723e6 + 1.95723e6i 0.0656985 + 0.0656985i
\(311\) 4.76858e7i 1.58529i −0.609685 0.792644i \(-0.708704\pi\)
0.609685 0.792644i \(-0.291296\pi\)
\(312\) −3.70376e6 + 2.60921e6i −0.121949 + 0.0859102i
\(313\) −3.30144e7 −1.07664 −0.538320 0.842741i \(-0.680941\pi\)
−0.538320 + 0.842741i \(0.680941\pi\)
\(314\) −1.30994e6 + 1.30994e6i −0.0423120 + 0.0423120i
\(315\) −2.45408e7 −0.785157
\(316\) 3.36438e7i 1.06621i
\(317\) −4.35163e7 + 4.35163e7i −1.36607 + 1.36607i −0.500112 + 0.865961i \(0.666708\pi\)
−0.865961 + 0.500112i \(0.833292\pi\)
\(318\) 1.63356e6 1.63356e6i 0.0507989 0.0507989i
\(319\) −1.24208e7 1.24208e7i −0.382628 0.382628i
\(320\) −3.28362e7 3.28362e7i −1.00208 1.00208i
\(321\) −1.77858e7 −0.537722
\(322\) 422748.i 0.0126623i
\(323\) −3.22333e6 3.22333e6i −0.0956527 0.0956527i
\(324\) 7.15743e6i 0.210437i
\(325\) 4.46215e7 + 7.73655e6i 1.29985 + 0.225370i
\(326\) 1.43154e6 0.0413190
\(327\) 1.59400e7 1.59400e7i 0.455874 0.455874i
\(328\) −4.59340e6 −0.130171
\(329\) 3.70820e7i 1.04130i
\(330\) −5.54209e6 + 5.54209e6i −0.154217 + 0.154217i
\(331\) −3.16932e7 + 3.16932e7i −0.873940 + 0.873940i −0.992899 0.118959i \(-0.962044\pi\)
0.118959 + 0.992899i \(0.462044\pi\)
\(332\) 1.19515e7 + 1.19515e7i 0.326593 + 0.326593i
\(333\) −1.12700e7 1.12700e7i −0.305205 0.305205i
\(334\) 576105. 0.0154619
\(335\) 1.42849e7i 0.379965i
\(336\) −1.78676e7 1.78676e7i −0.471030 0.471030i
\(337\) 4.31706e7i 1.12797i 0.825784 + 0.563986i \(0.190733\pi\)
−0.825784 + 0.563986i \(0.809267\pi\)
\(338\) −3.77314e6 + 1.78577e6i −0.0977132 + 0.0462462i
\(339\) −4.55571e7 −1.16938
\(340\) 6.72127e6 6.72127e6i 0.171007 0.171007i
\(341\) 4.27159e7 1.07727
\(342\) 1.88717e6i 0.0471773i
\(343\) 2.86862e7 2.86862e7i 0.710870 0.710870i
\(344\) 2.60980e6 2.60980e6i 0.0641109 0.0641109i
\(345\) −3.61409e6 3.61409e6i −0.0880118 0.0880118i
\(346\) −4.68377e6 4.68377e6i −0.113075 0.113075i
\(347\) −5.94985e7 −1.42403 −0.712013 0.702167i \(-0.752216\pi\)
−0.712013 + 0.702167i \(0.752216\pi\)
\(348\) 8.19425e6i 0.194434i
\(349\) −3.01005e7 3.01005e7i −0.708105 0.708105i 0.258032 0.966136i \(-0.416926\pi\)
−0.966136 + 0.258032i \(0.916926\pi\)
\(350\) 6.08160e6i 0.141845i
\(351\) 7.78445e6 4.48977e7i 0.180014 1.03825i
\(352\) 2.65806e7 0.609449
\(353\) 1.53500e7 1.53500e7i 0.348966 0.348966i −0.510758 0.859725i \(-0.670635\pi\)
0.859725 + 0.510758i \(0.170635\pi\)
\(354\) −1.89142e6 −0.0426361
\(355\) 5.19037e7i 1.16015i
\(356\) 2.85243e6 2.85243e6i 0.0632215 0.0632215i
\(357\) 3.56823e6 3.56823e6i 0.0784239 0.0784239i
\(358\) 648544. + 648544.i 0.0141348 + 0.0141348i
\(359\) 2.38598e7 + 2.38598e7i 0.515685 + 0.515685i 0.916263 0.400578i \(-0.131191\pi\)
−0.400578 + 0.916263i \(0.631191\pi\)
\(360\) −7.91677e6 −0.169684
\(361\) 1.37015e7i 0.291237i
\(362\) 6.20249e6 + 6.20249e6i 0.130750 + 0.130750i
\(363\) 8.77593e7i 1.83473i
\(364\) −2.73025e7 3.87557e7i −0.566106 0.803585i
\(365\) 1.05123e8 2.16181
\(366\) 3.50597e6 3.50597e6i 0.0715096 0.0715096i
\(367\) 1.73262e6 0.0350514 0.0175257 0.999846i \(-0.494421\pi\)
0.0175257 + 0.999846i \(0.494421\pi\)
\(368\) 5.66410e6i 0.113655i
\(369\) 1.11529e7 1.11529e7i 0.221977 0.221977i
\(370\) 4.90992e6 4.90992e6i 0.0969325 0.0969325i
\(371\) 3.43890e7 + 3.43890e7i 0.673437 + 0.673437i
\(372\) −1.40903e7 1.40903e7i −0.273710 0.273710i
\(373\) −2.27039e7 −0.437496 −0.218748 0.975781i \(-0.570197\pi\)
−0.218748 + 0.975781i \(0.570197\pi\)
\(374\) 1.73457e6i 0.0331572i
\(375\) −1.25815e7 1.25815e7i −0.238583 0.238583i
\(376\) 1.19625e7i 0.225040i
\(377\) −2.59487e6 + 1.49662e7i −0.0484274 + 0.279311i
\(378\) −6.11925e6 −0.113298
\(379\) 2.57526e7 2.57526e7i 0.473046 0.473046i −0.429853 0.902899i \(-0.641435\pi\)
0.902899 + 0.429853i \(0.141435\pi\)
\(380\) 6.95295e7 1.26712
\(381\) 4.26186e7i 0.770591i
\(382\) 3.73466e6 3.73466e6i 0.0669978 0.0669978i
\(383\) 4.71374e7 4.71374e7i 0.839014 0.839014i −0.149715 0.988729i \(-0.547836\pi\)
0.988729 + 0.149715i \(0.0478355\pi\)
\(384\) −1.16669e7 1.16669e7i −0.206044 0.206044i
\(385\) −1.16670e8 1.16670e8i −2.04444 2.04444i
\(386\) −2.29240e6 −0.0398592
\(387\) 1.26733e7i 0.218654i
\(388\) 4.62114e7 + 4.62114e7i 0.791141 + 0.791141i
\(389\) 9.05585e7i 1.53844i 0.638985 + 0.769219i \(0.279355\pi\)
−0.638985 + 0.769219i \(0.720645\pi\)
\(390\) 6.67785e6 + 1.15782e6i 0.112575 + 0.0195185i
\(391\) −1.13114e6 −0.0189229
\(392\) 98777.1 98777.1i 0.00163983 0.00163983i
\(393\) −3.30644e7 −0.544732
\(394\) 4.39163e6i 0.0718021i
\(395\) −7.15977e7 + 7.15977e7i −1.16174 + 1.16174i
\(396\) −4.29414e7 + 4.29414e7i −0.691498 + 0.691498i
\(397\) −2.22106e7 2.22106e7i −0.354968 0.354968i 0.506986 0.861954i \(-0.330760\pi\)
−0.861954 + 0.506986i \(0.830760\pi\)
\(398\) −1.33255e6 1.33255e6i −0.0211365 0.0211365i
\(399\) 3.69123e7 0.581102
\(400\) 8.14830e7i 1.27317i
\(401\) −1.67907e7 1.67907e7i −0.260397 0.260397i 0.564819 0.825215i \(-0.308946\pi\)
−0.825215 + 0.564819i \(0.808946\pi\)
\(402\) 1.21605e6i 0.0187185i
\(403\) −2.12729e7 3.01968e7i −0.325022 0.461367i
\(404\) −6.05376e7 −0.918081
\(405\) −1.52318e7 + 1.52318e7i −0.229290 + 0.229290i
\(406\) 2.03979e6 0.0304795
\(407\) 1.07158e8i 1.58943i
\(408\) 1.15110e6 1.15110e6i 0.0169486 0.0169486i
\(409\) 3.72819e7 3.72819e7i 0.544914 0.544914i −0.380051 0.924965i \(-0.624094\pi\)
0.924965 + 0.380051i \(0.124094\pi\)
\(410\) 4.85890e6 + 4.85890e6i 0.0704996 + 0.0704996i
\(411\) 2.55361e6 + 2.55361e6i 0.0367814 + 0.0367814i
\(412\) −6.34321e7 −0.907021
\(413\) 3.98173e7i 0.565225i
\(414\) 331126. + 331126.i 0.00466652 + 0.00466652i
\(415\) 5.08680e7i 0.711705i
\(416\) −1.32374e7 1.87905e7i −0.183875 0.261010i
\(417\) 1.80054e7 0.248310
\(418\) −8.97182e6 + 8.97182e6i −0.122843 + 0.122843i
\(419\) 8.72939e7 1.18670 0.593351 0.804944i \(-0.297804\pi\)
0.593351 + 0.804944i \(0.297804\pi\)
\(420\) 7.69693e7i 1.03889i
\(421\) −5.41486e7 + 5.41486e7i −0.725673 + 0.725673i −0.969755 0.244081i \(-0.921514\pi\)
0.244081 + 0.969755i \(0.421514\pi\)
\(422\) −7.60106e6 + 7.60106e6i −0.101143 + 0.101143i
\(423\) −2.90453e7 2.90453e7i −0.383755 0.383755i
\(424\) 1.10938e7 + 1.10938e7i 0.145540 + 0.145540i
\(425\) −1.62725e7 −0.211976
\(426\) 4.41845e6i 0.0571532i
\(427\) 7.38060e7 + 7.38060e7i 0.947999 + 0.947999i
\(428\) 6.00381e7i 0.765765i
\(429\) 8.55056e7 6.02366e7i 1.08299 0.762937i
\(430\) −5.52129e6 −0.0694441
\(431\) 3.81041e6 3.81041e6i 0.0475926 0.0475926i −0.682910 0.730503i \(-0.739286\pi\)
0.730503 + 0.682910i \(0.239286\pi\)
\(432\) 8.19875e7 1.01694
\(433\) 9.85826e7i 1.21433i 0.794576 + 0.607165i \(0.207693\pi\)
−0.794576 + 0.607165i \(0.792307\pi\)
\(434\) −3.50749e6 + 3.50749e6i −0.0429069 + 0.0429069i
\(435\) 1.74382e7 1.74382e7i 0.211853 0.211853i
\(436\) 5.38074e7 + 5.38074e7i 0.649206 + 0.649206i
\(437\) −5.85067e6 5.85067e6i −0.0701069 0.0701069i
\(438\) 8.94888e6 0.106499
\(439\) 5.14314e6i 0.0607903i −0.999538 0.0303952i \(-0.990323\pi\)
0.999538 0.0303952i \(-0.00967657\pi\)
\(440\) −3.76372e7 3.76372e7i −0.441834 0.441834i
\(441\) 479666.i 0.00559272i
\(442\) 1.22621e6 863835.i 0.0142003 0.0100038i
\(443\) −1.52839e8 −1.75802 −0.879008 0.476808i \(-0.841794\pi\)
−0.879008 + 0.476808i \(0.841794\pi\)
\(444\) −3.53471e7 + 3.53471e7i −0.403836 + 0.403836i
\(445\) −1.21406e7 −0.137771
\(446\) 1.02204e7i 0.115203i
\(447\) 3.93831e7 3.93831e7i 0.440948 0.440948i
\(448\) 5.88449e7 5.88449e7i 0.654447 0.654447i
\(449\) 8.12560e7 + 8.12560e7i 0.897669 + 0.897669i 0.995230 0.0975605i \(-0.0311039\pi\)
−0.0975605 + 0.995230i \(0.531104\pi\)
\(450\) 4.76354e6 + 4.76354e6i 0.0522748 + 0.0522748i
\(451\) 1.06044e8 1.15600
\(452\) 1.53783e8i 1.66531i
\(453\) −5.92190e7 5.92190e7i −0.637040 0.637040i
\(454\) 661441.i 0.00706844i
\(455\) −2.43738e7 + 1.40579e8i −0.258755 + 1.49240i
\(456\) 1.19078e7 0.125585
\(457\) 6.60613e7 6.60613e7i 0.692148 0.692148i −0.270556 0.962704i \(-0.587208\pi\)
0.962704 + 0.270556i \(0.0872077\pi\)
\(458\) 1.86090e7 0.193699
\(459\) 1.63732e7i 0.169315i
\(460\) 1.21998e7 1.21998e7i 0.125337 0.125337i
\(461\) −7.29238e7 + 7.29238e7i −0.744332 + 0.744332i −0.973408 0.229077i \(-0.926429\pi\)
0.229077 + 0.973408i \(0.426429\pi\)
\(462\) −9.93183e6 9.93183e6i −0.100717 0.100717i
\(463\) 2.88794e7 + 2.88794e7i 0.290968 + 0.290968i 0.837463 0.546495i \(-0.184038\pi\)
−0.546495 + 0.837463i \(0.684038\pi\)
\(464\) −2.73297e7 −0.273578
\(465\) 5.99713e7i 0.596464i
\(466\) 1.11966e6 + 1.11966e6i 0.0110644 + 0.0110644i
\(467\) 2.98298e7i 0.292886i −0.989219 0.146443i \(-0.953217\pi\)
0.989219 0.146443i \(-0.0467825\pi\)
\(468\) 5.17415e7 + 8.97104e6i 0.504780 + 0.0875195i
\(469\) 2.55996e7 0.248151
\(470\) 1.26540e7 1.26540e7i 0.121880 0.121880i
\(471\) −4.01379e7 −0.384142
\(472\) 1.28449e7i 0.122153i
\(473\) −6.02503e7 + 6.02503e7i −0.569346 + 0.569346i
\(474\) −6.09496e6 + 6.09496e6i −0.0572316 + 0.0572316i
\(475\) −8.41670e7 8.41670e7i −0.785346 0.785346i
\(476\) 1.20450e7 + 1.20450e7i 0.111683 + 0.111683i
\(477\) −5.38718e7 −0.496371
\(478\) 1.13007e7i 0.103472i
\(479\) −6.33389e7 6.33389e7i −0.576320 0.576320i 0.357567 0.933887i \(-0.383606\pi\)
−0.933887 + 0.357567i \(0.883606\pi\)
\(480\) 3.73181e7i 0.337439i
\(481\) −7.57523e7 + 5.33656e7i −0.680707 + 0.479541i
\(482\) −1.51186e7 −0.135012
\(483\) 6.47670e6 6.47670e6i 0.0574794 0.0574794i
\(484\) −2.96242e8 −2.61283
\(485\) 1.96686e8i 1.72404i
\(486\) 7.94974e6 7.94974e6i 0.0692539 0.0692539i
\(487\) −4.86653e6 + 4.86653e6i −0.0421340 + 0.0421340i −0.727860 0.685726i \(-0.759485\pi\)
0.685726 + 0.727860i \(0.259485\pi\)
\(488\) 2.38096e7 + 2.38096e7i 0.204876 + 0.204876i
\(489\) 2.19318e7 + 2.19318e7i 0.187564 + 0.187564i
\(490\) −208973. −0.00177624
\(491\) 1.92918e8i 1.62977i 0.579620 + 0.814887i \(0.303201\pi\)
−0.579620 + 0.814887i \(0.696799\pi\)
\(492\) −3.49798e7 3.49798e7i −0.293712 0.293712i
\(493\) 5.45785e6i 0.0455492i
\(494\) 1.08104e7 + 1.87433e6i 0.0896732 + 0.0155477i
\(495\) 1.82768e8 1.50690
\(496\) 4.69943e7 4.69943e7i 0.385124 0.385124i
\(497\) −9.30151e7 −0.757677
\(498\) 4.33028e6i 0.0350613i
\(499\) 1.55886e8 1.55886e8i 1.25460 1.25460i 0.300962 0.953636i \(-0.402692\pi\)
0.953636 0.300962i \(-0.0973077\pi\)
\(500\) 4.24704e7 4.24704e7i 0.339763 0.339763i
\(501\) 8.82620e6 + 8.82620e6i 0.0701876 + 0.0701876i
\(502\) −6.30794e6 6.30794e6i −0.0498628 0.0498628i
\(503\) 9.61748e6 0.0755714 0.0377857 0.999286i \(-0.487970\pi\)
0.0377857 + 0.999286i \(0.487970\pi\)
\(504\) 1.41874e7i 0.110818i
\(505\) 1.28830e8 + 1.28830e8i 1.00033 + 1.00033i
\(506\) 3.14843e6i 0.0243020i
\(507\) −8.51653e7 3.04475e7i −0.653490 0.233629i
\(508\) 1.43864e8 1.09739
\(509\) −1.48532e8 + 1.48532e8i −1.12633 + 1.12633i −0.135560 + 0.990769i \(0.543283\pi\)
−0.990769 + 0.135560i \(0.956717\pi\)
\(510\) −2.43527e6 −0.0183585
\(511\) 1.88388e8i 1.41185i
\(512\) 4.89302e7 4.89302e7i 0.364559 0.364559i
\(513\) −8.46881e7 + 8.46881e7i −0.627293 + 0.627293i
\(514\) −9.61487e6 9.61487e6i −0.0708034 0.0708034i
\(515\) 1.34990e8 + 1.34990e8i 0.988282 + 0.988282i
\(516\) 3.97484e7 0.289315
\(517\) 2.76169e8i 1.99850i
\(518\) 8.79893e6 + 8.79893e6i 0.0633054 + 0.0633054i
\(519\) 1.43515e8i 1.02659i
\(520\) −7.86292e6 + 4.53503e7i −0.0559208 + 0.322530i
\(521\) −1.16210e8 −0.821731 −0.410865 0.911696i \(-0.634773\pi\)
−0.410865 + 0.911696i \(0.634773\pi\)
\(522\) −1.59771e6 + 1.59771e6i −0.0112328 + 0.0112328i
\(523\) 1.16773e8 0.816274 0.408137 0.912921i \(-0.366179\pi\)
0.408137 + 0.912921i \(0.366179\pi\)
\(524\) 1.11613e8i 0.775746i
\(525\) 9.31730e7 9.31730e7i 0.643891 0.643891i
\(526\) −1.48733e7 + 1.48733e7i −0.102200 + 0.102200i
\(527\) 9.38496e6 + 9.38496e6i 0.0641210 + 0.0641210i
\(528\) 1.33070e8 + 1.33070e8i 0.904018 + 0.904018i
\(529\) 1.45983e8 0.986131
\(530\) 2.34700e7i 0.157647i
\(531\) 3.11877e7 + 3.11877e7i 0.208305 + 0.208305i
\(532\) 1.24602e8i 0.827541i
\(533\) −5.28110e7 7.49651e7i −0.348773 0.495082i
\(534\) −1.03350e6 −0.00678713
\(535\) −1.27767e8 + 1.27767e8i −0.834370 + 0.834370i
\(536\) 8.25836e6 0.0536290
\(537\) 1.98720e7i 0.128327i
\(538\) −595759. + 595759.i −0.00382581 + 0.00382581i
\(539\) −2.28039e6 + 2.28039e6i −0.0145627 + 0.0145627i
\(540\) −1.76591e8 1.76591e8i −1.12147 1.12147i
\(541\) −5.07826e7 5.07826e7i −0.320718 0.320718i 0.528325 0.849042i \(-0.322820\pi\)
−0.849042 + 0.528325i \(0.822820\pi\)
\(542\) −9.86667e6 −0.0619687
\(543\) 1.90050e8i 1.18705i
\(544\) 5.83994e6 + 5.83994e6i 0.0362753 + 0.0362753i
\(545\) 2.29016e8i 1.41474i
\(546\) −2.07489e6 + 1.19672e7i −0.0127473 + 0.0735215i
\(547\) 3.77483e7 0.230640 0.115320 0.993328i \(-0.463211\pi\)
0.115320 + 0.993328i \(0.463211\pi\)
\(548\) −8.62000e6 + 8.62000e6i −0.0523800 + 0.0523800i
\(549\) −1.15620e8 −0.698742
\(550\) 4.52929e7i 0.272234i
\(551\) 2.82299e7 2.82299e7i 0.168754 0.168754i
\(552\) 2.08936e6 2.08936e6i 0.0124221 0.0124221i
\(553\) −1.28308e8 1.28308e8i −0.758716 0.758716i
\(554\) −1.13694e7 1.13694e7i −0.0668665 0.0668665i
\(555\) 1.50445e8 0.880032
\(556\) 6.07793e7i 0.353615i
\(557\) 1.59658e8 + 1.59658e8i 0.923903 + 0.923903i 0.997303 0.0733997i \(-0.0233849\pi\)
−0.0733997 + 0.997303i \(0.523385\pi\)
\(558\) 5.49463e6i 0.0316254i
\(559\) 7.25976e7 + 1.25871e7i 0.415611 + 0.0720593i
\(560\) −2.56711e8 −1.46177
\(561\) −2.65745e7 + 2.65745e7i −0.150514 + 0.150514i
\(562\) 1.69614e7 0.0955548
\(563\) 2.76920e8i 1.55177i −0.630872 0.775887i \(-0.717303\pi\)
0.630872 0.775887i \(-0.282697\pi\)
\(564\) −9.10972e7 + 9.10972e7i −0.507771 + 0.507771i
\(565\) −3.27267e8 + 3.27267e8i −1.81450 + 1.81450i
\(566\) −1.40261e7 1.40261e7i −0.0773551 0.0773551i
\(567\) −2.72965e7 2.72965e7i −0.149747 0.149747i
\(568\) −3.00064e7 −0.163745
\(569\) 2.43629e8i 1.32249i −0.750170 0.661245i \(-0.770029\pi\)
0.750170 0.661245i \(-0.229971\pi\)
\(570\) −1.25961e7 1.25961e7i −0.0680158 0.0680158i
\(571\) 1.59255e8i 0.855432i −0.903913 0.427716i \(-0.859318\pi\)
0.903913 0.427716i \(-0.140682\pi\)
\(572\) 2.03336e8 + 2.88634e8i 1.08649 + 1.54227i
\(573\) 1.14433e8 0.608260
\(574\) −8.70750e6 + 8.70750e6i −0.0460424 + 0.0460424i
\(575\) −2.95362e7 −0.155364
\(576\) 9.21831e7i 0.482374i
\(577\) −7.58084e6 + 7.58084e6i −0.0394630 + 0.0394630i −0.726563 0.687100i \(-0.758883\pi\)
0.687100 + 0.726563i \(0.258883\pi\)
\(578\) 1.43798e7 1.43798e7i 0.0744679 0.0744679i
\(579\) −3.51206e7 3.51206e7i −0.180937 0.180937i
\(580\) 5.88649e7 + 5.88649e7i 0.301698 + 0.301698i
\(581\) 9.11590e7 0.464805
\(582\) 1.67434e7i 0.0849328i
\(583\) −2.56113e8 2.56113e8i −1.29248 1.29248i
\(584\) 6.07732e7i 0.305122i
\(585\) −9.10202e7 1.29203e8i −0.454643 0.645364i
\(586\) 5.73424e6 0.0284960
\(587\) 2.37473e7 2.37473e7i 0.117409 0.117409i −0.645961 0.763370i \(-0.723543\pi\)
0.763370 + 0.645961i \(0.223543\pi\)
\(588\) 1.50442e6 0.00740008
\(589\) 9.70845e7i 0.475121i
\(590\) −1.35874e7 + 1.35874e7i −0.0661575 + 0.0661575i
\(591\) 6.72819e7 6.72819e7i 0.325938 0.325938i
\(592\) −1.17891e8 1.17891e8i −0.568217 0.568217i
\(593\) 7.15224e7 + 7.15224e7i 0.342987 + 0.342987i 0.857489 0.514502i \(-0.172023\pi\)
−0.514502 + 0.857489i \(0.672023\pi\)
\(594\) 4.55733e7 0.217446
\(595\) 5.12661e7i 0.243377i
\(596\) 1.32942e8 + 1.32942e8i 0.627949 + 0.627949i
\(597\) 4.08305e7i 0.191894i
\(598\) 2.22569e6 1.56795e6i 0.0104079 0.00733209i
\(599\) −4.67139e7 −0.217353 −0.108677 0.994077i \(-0.534661\pi\)
−0.108677 + 0.994077i \(0.534661\pi\)
\(600\) 3.00573e7 3.00573e7i 0.139154 0.139154i
\(601\) 4.90865e7 0.226120 0.113060 0.993588i \(-0.463935\pi\)
0.113060 + 0.993588i \(0.463935\pi\)
\(602\) 9.89455e6i 0.0453531i
\(603\) −2.00515e7 + 2.00515e7i −0.0914523 + 0.0914523i
\(604\) 1.99901e8 1.99901e8i 0.907202 0.907202i
\(605\) 6.30435e8 + 6.30435e8i 2.84691 + 2.84691i
\(606\) 1.09671e7 + 1.09671e7i 0.0492802 + 0.0492802i
\(607\) −1.43011e8 −0.639446 −0.319723 0.947511i \(-0.603590\pi\)
−0.319723 + 0.947511i \(0.603590\pi\)
\(608\) 6.04124e7i 0.268791i
\(609\) 3.12506e7 + 3.12506e7i 0.138359 + 0.138359i
\(610\) 5.03715e7i 0.221920i
\(611\) −1.95230e8 + 1.37535e8i −0.855901 + 0.602961i
\(612\) −1.88690e7 −0.0823181
\(613\) 1.01429e8 1.01429e8i 0.440333 0.440333i −0.451791 0.892124i \(-0.649215\pi\)
0.892124 + 0.451791i \(0.149215\pi\)
\(614\) 3.25872e7 0.140780
\(615\) 1.48881e8i 0.640052i
\(616\) 6.74486e7 6.74486e7i 0.288556 0.288556i
\(617\) 3.13102e8 3.13102e8i 1.33300 1.33300i 0.430328 0.902673i \(-0.358398\pi\)
0.902673 0.430328i \(-0.141602\pi\)
\(618\) 1.14914e7 + 1.14914e7i 0.0486865 + 0.0486865i
\(619\) 5.14300e7 + 5.14300e7i 0.216843 + 0.216843i 0.807167 0.590324i \(-0.201000\pi\)
−0.590324 + 0.807167i \(0.701000\pi\)
\(620\) −2.02440e8 −0.849418
\(621\) 2.97190e7i 0.124097i
\(622\) −2.91614e7 2.91614e7i −0.121182 0.121182i
\(623\) 2.17567e7i 0.0899766i
\(624\) 2.78000e7 1.60340e8i 0.114417 0.659915i
\(625\) 1.41318e8 0.578839
\(626\) −2.01893e7 + 2.01893e7i −0.0822998 + 0.0822998i
\(627\) −2.74905e8 −1.11527
\(628\) 1.35490e8i 0.547053i
\(629\) 2.35432e7 2.35432e7i 0.0946051 0.0946051i
\(630\) −1.50074e7 + 1.50074e7i −0.0600185 + 0.0600185i
\(631\) 2.06799e7 + 2.06799e7i 0.0823114 + 0.0823114i 0.747064 0.664752i \(-0.231463\pi\)
−0.664752 + 0.747064i \(0.731463\pi\)
\(632\) −4.13918e7 4.13918e7i −0.163970 0.163970i
\(633\) −2.32904e8 −0.918260
\(634\) 5.32231e7i 0.208849i
\(635\) −3.06158e8 3.06158e8i −1.19571 1.19571i
\(636\) 1.68963e8i 0.656780i
\(637\) 2.74771e6 + 476403.i 0.0106305 + 0.00184313i
\(638\) −1.51914e7 −0.0584973
\(639\) 7.28561e7 7.28561e7i 0.279231 0.279231i
\(640\) −1.67622e8 −0.639427
\(641\) 7.40571e7i 0.281185i −0.990068 0.140593i \(-0.955099\pi\)
0.990068 0.140593i \(-0.0449008\pi\)
\(642\) −1.08766e7 + 1.08766e7i −0.0411043 + 0.0411043i
\(643\) −1.94452e8 + 1.94452e8i −0.731442 + 0.731442i −0.970905 0.239463i \(-0.923028\pi\)
0.239463 + 0.970905i \(0.423028\pi\)
\(644\) 2.18629e7 + 2.18629e7i 0.0818558 + 0.0818558i
\(645\) −8.45889e7 8.45889e7i −0.315235 0.315235i
\(646\) −3.94234e6 −0.0146237
\(647\) 4.53504e8i 1.67444i 0.546870 + 0.837218i \(0.315819\pi\)
−0.546870 + 0.837218i \(0.684181\pi\)
\(648\) −8.80575e6 8.80575e6i −0.0323624 0.0323624i
\(649\) 2.96540e8i 1.08480i
\(650\) 3.20186e7 2.25563e7i 0.116590 0.0821349i
\(651\) −1.07473e8 −0.389543
\(652\) −7.40335e7 + 7.40335e7i −0.267107 + 0.267107i
\(653\) 3.57842e8 1.28515 0.642573 0.766225i \(-0.277867\pi\)
0.642573 + 0.766225i \(0.277867\pi\)
\(654\) 1.94956e7i 0.0696954i
\(655\) −2.37524e8 + 2.37524e8i −0.845246 + 0.845246i
\(656\) 1.16666e8 1.16666e8i 0.413268 0.413268i
\(657\) −1.47559e8 1.47559e8i −0.520318 0.520318i
\(658\) 2.26768e7 + 2.26768e7i 0.0795983 + 0.0795983i
\(659\) 2.30929e8 0.806904 0.403452 0.915001i \(-0.367810\pi\)
0.403452 + 0.915001i \(0.367810\pi\)
\(660\) 5.73231e8i 1.99388i
\(661\) −7.81262e7 7.81262e7i −0.270516 0.270516i 0.558792 0.829308i \(-0.311265\pi\)
−0.829308 + 0.558792i \(0.811265\pi\)
\(662\) 3.87627e7i 0.133610i
\(663\) 3.20205e7 + 5.55177e6i 0.109872 + 0.0190498i
\(664\) 2.94076e7 0.100451
\(665\) 2.65166e8 2.65166e8i 0.901682 0.901682i
\(666\) −1.37839e7 −0.0466606
\(667\) 9.90654e6i 0.0333845i
\(668\) −2.97939e7 + 2.97939e7i −0.0999535 + 0.0999535i
\(669\) −1.56581e8 + 1.56581e8i −0.522952 + 0.522952i
\(670\) −8.73569e6 8.73569e6i −0.0290451 0.0290451i
\(671\) −5.49672e8 5.49672e8i −1.81943 1.81943i
\(672\) −6.68766e7 −0.220377
\(673\) 3.05242e8i 1.00138i 0.865627 + 0.500690i \(0.166920\pi\)
−0.865627 + 0.500690i \(0.833080\pi\)
\(674\) 2.64002e7 + 2.64002e7i 0.0862238 + 0.0862238i
\(675\) 4.27535e8i 1.39014i
\(676\) 1.02779e8 2.87486e8i 0.332709 0.930628i
\(677\) −1.80909e8 −0.583033 −0.291517 0.956566i \(-0.594160\pi\)
−0.291517 + 0.956566i \(0.594160\pi\)
\(678\) −2.78596e7 + 2.78596e7i −0.0893893 + 0.0893893i
\(679\) 3.52475e8 1.12595
\(680\) 1.65383e7i 0.0525973i
\(681\) 1.01336e7 1.01336e7i 0.0320865 0.0320865i
\(682\) 2.61221e7 2.61221e7i 0.0823484 0.0823484i
\(683\) −8.95873e7 8.95873e7i −0.281180 0.281180i 0.552400 0.833579i \(-0.313712\pi\)
−0.833579 + 0.552400i \(0.813712\pi\)
\(684\) −9.75972e7 9.75972e7i −0.304978 0.304978i
\(685\) 3.66886e7 0.114146
\(686\) 3.50850e7i 0.108680i
\(687\) 2.85099e8 + 2.85099e8i 0.879276 + 0.879276i
\(688\) 1.32570e8i 0.407080i
\(689\) −5.35053e7 + 3.08599e8i −0.163583 + 0.943488i
\(690\) −4.42025e6 −0.0134555
\(691\) 1.52213e8 1.52213e8i 0.461336 0.461336i −0.437757 0.899093i \(-0.644227\pi\)
0.899093 + 0.437757i \(0.144227\pi\)
\(692\) 4.84453e8 1.46195
\(693\) 3.27533e8i 0.984137i
\(694\) −3.63852e7 + 3.63852e7i −0.108855 + 0.108855i
\(695\) 1.29345e8 1.29345e8i 0.385296 0.385296i
\(696\) 1.00813e7 + 1.00813e7i 0.0299013 + 0.0299013i
\(697\) 2.32986e7 + 2.32986e7i 0.0688068 + 0.0688068i
\(698\) −3.68148e7 −0.108257
\(699\) 3.43076e7i 0.100452i
\(700\) 3.14517e8 + 3.14517e8i 0.916958 + 0.916958i
\(701\) 5.41363e8i 1.57157i −0.618498 0.785786i \(-0.712259\pi\)
0.618498 0.785786i \(-0.287741\pi\)
\(702\) −2.26959e7 3.22168e7i −0.0656050 0.0931260i
\(703\) 2.43548e8 0.701000
\(704\) −4.38249e8 + 4.38249e8i −1.25604 + 1.25604i
\(705\) 3.87730e8 1.10653
\(706\) 1.87740e7i 0.0533510i
\(707\) −2.30873e8 + 2.30873e8i −0.653304 + 0.653304i
\(708\) 9.78168e7 9.78168e7i 0.275622 0.275622i
\(709\) −1.17076e8 1.17076e8i −0.328494 0.328494i 0.523520 0.852014i \(-0.324619\pi\)
−0.852014 + 0.523520i \(0.824619\pi\)
\(710\) 3.17407e7 + 3.17407e7i 0.0886833 + 0.0886833i
\(711\) 2.01001e8 0.559227
\(712\) 7.01865e6i 0.0194453i
\(713\) 1.70346e7 + 1.70346e7i 0.0469963 + 0.0469963i
\(714\) 4.36417e6i 0.0119897i
\(715\) 1.81525e8 1.04697e9i 0.496612 2.86427i
\(716\) −6.70803e7 −0.182749
\(717\) 1.73133e8 1.73133e8i 0.469701 0.469701i
\(718\) 2.91821e7 0.0788393
\(719\) 3.08710e8i 0.830548i 0.909696 + 0.415274i \(0.136314\pi\)
−0.909696 + 0.415274i \(0.863686\pi\)
\(720\) 2.01074e8 2.01074e8i 0.538715 0.538715i
\(721\) −2.41912e8 + 2.41912e8i −0.645434 + 0.645434i
\(722\) 8.37890e6 + 8.37890e6i 0.0222626 + 0.0222626i
\(723\) −2.31625e8 2.31625e8i −0.612873 0.612873i
\(724\) −6.41538e8 −1.69047
\(725\) 1.42514e8i 0.373977i
\(726\) 5.36676e7 + 5.36676e7i 0.140250 + 0.140250i
\(727\) 2.05083e8i 0.533737i 0.963733 + 0.266868i \(0.0859889\pi\)
−0.963733 + 0.266868i \(0.914011\pi\)
\(728\) −8.12710e7 1.40909e7i −0.210640 0.0365212i
\(729\) 3.26079e8 0.841668
\(730\) 6.42859e7 6.42859e7i 0.165252 0.165252i
\(731\) −2.64748e7 −0.0677767
\(732\) 3.62630e8i 0.924550i
\(733\) −2.32596e8 + 2.32596e8i −0.590596 + 0.590596i −0.937792 0.347196i \(-0.887134\pi\)
0.347196 + 0.937792i \(0.387134\pi\)
\(734\) 1.05955e6 1.05955e6i 0.00267938 0.00267938i
\(735\) −3.20156e6 3.20156e6i −0.00806306 0.00806306i
\(736\) 1.06001e7 + 1.06001e7i 0.0265874 + 0.0265874i
\(737\) −1.90654e8 −0.476259
\(738\) 1.36407e7i 0.0339365i
\(739\) −1.11899e8 1.11899e8i −0.277263 0.277263i 0.554752 0.832016i \(-0.312813\pi\)
−0.832016 + 0.554752i \(0.812813\pi\)
\(740\) 5.07844e8i 1.25324i
\(741\) 1.36906e8 + 1.94337e8i 0.336486 + 0.477640i
\(742\) 4.20598e7 0.102957
\(743\) −2.16522e8 + 2.16522e8i −0.527881 + 0.527881i −0.919940 0.392059i \(-0.871763\pi\)
0.392059 + 0.919940i \(0.371763\pi\)
\(744\) −3.46704e7 −0.0841860
\(745\) 5.65831e8i 1.36842i
\(746\) −1.38841e7 + 1.38841e7i −0.0334428 + 0.0334428i
\(747\) −7.14023e7 + 7.14023e7i −0.171297 + 0.171297i
\(748\) −8.97055e7 8.97055e7i −0.214345 0.214345i
\(749\) −2.28968e8 2.28968e8i −0.544917 0.544917i
\(750\) −1.53880e7 −0.0364752
\(751\) 3.77813e8i 0.891983i 0.895037 + 0.445991i \(0.147149\pi\)
−0.895037 + 0.445991i \(0.852851\pi\)
\(752\) −3.03830e8 3.03830e8i −0.714460 0.714460i
\(753\) 1.93281e8i 0.452694i
\(754\) 7.56546e6 + 1.07391e7i 0.0176491 + 0.0250528i
\(755\) −8.50822e8 −1.97696
\(756\) 3.16464e8 3.16464e8i 0.732418 0.732418i
\(757\) −6.99389e8 −1.61225 −0.806123 0.591749i \(-0.798438\pi\)
−0.806123 + 0.591749i \(0.798438\pi\)
\(758\) 3.14971e7i 0.0723207i
\(759\) −4.82354e7 + 4.82354e7i −0.110317 + 0.110317i
\(760\) 8.55418e7 8.55418e7i 0.194867 0.194867i
\(761\) 8.68673e7 + 8.68673e7i 0.197107 + 0.197107i 0.798759 0.601651i \(-0.205490\pi\)
−0.601651 + 0.798759i \(0.705490\pi\)
\(762\) −2.60626e7 2.60626e7i −0.0589051 0.0589051i
\(763\) 4.10413e8 0.923947
\(764\) 3.86284e8i 0.866217i
\(765\) 4.01553e7 + 4.01553e7i 0.0896930 + 0.0896930i
\(766\) 5.76520e7i 0.128271i
\(767\) 2.09631e8 1.47680e8i 0.464590 0.327292i
\(768\) 2.78271e8 0.614306
\(769\) 2.69755e8 2.69755e8i 0.593185 0.593185i −0.345305 0.938490i \(-0.612225\pi\)
0.938490 + 0.345305i \(0.112225\pi\)
\(770\) −1.42694e8 −0.312561
\(771\) 2.94609e8i 0.642810i
\(772\) 1.18554e8 1.18554e8i 0.257670 0.257670i
\(773\) 5.07426e8 5.07426e8i 1.09859 1.09859i 0.104011 0.994576i \(-0.466832\pi\)
0.994576 0.104011i \(-0.0331678\pi\)
\(774\) 7.75012e6 + 7.75012e6i 0.0167142 + 0.0167142i
\(775\) 2.45058e8 + 2.45058e8i 0.526458 + 0.526458i
\(776\) 1.13707e8 0.243334
\(777\) 2.69608e8i 0.574737i
\(778\) 5.53793e7 + 5.53793e7i 0.117600 + 0.117600i
\(779\) 2.41017e8i 0.509841i
\(780\) −4.05230e8 + 2.85475e8i −0.853922 + 0.601567i
\(781\) 6.92732e8 1.45416
\(782\) −691729. + 691729.i −0.00144649 + 0.00144649i
\(783\) −1.43397e8 −0.298713
\(784\) 5.01758e6i 0.0104123i
\(785\) −2.88338e8 + 2.88338e8i −0.596064 + 0.596064i
\(786\) −2.02199e7 + 2.02199e7i −0.0416401 + 0.0416401i
\(787\) 6.10621e8 + 6.10621e8i 1.25270 + 1.25270i 0.954505 + 0.298196i \(0.0963849\pi\)
0.298196 + 0.954505i \(0.403615\pi\)
\(788\) 2.27118e8 + 2.27118e8i 0.464165 + 0.464165i
\(789\) −4.55732e8 −0.927851
\(790\) 8.75685e7i 0.177610i
\(791\) −5.86486e8 5.86486e8i −1.18503 1.18503i
\(792\) 1.05661e8i 0.212686i
\(793\) −1.14834e8 + 6.62318e8i −0.230277 + 1.32815i
\(794\) −2.71650e7 −0.0542685
\(795\) 3.59571e8 3.59571e8i 0.715622 0.715622i
\(796\) 1.37828e8 0.273274
\(797\) 1.40021e8i 0.276578i 0.990392 + 0.138289i \(0.0441602\pi\)
−0.990392 + 0.138289i \(0.955840\pi\)
\(798\) 2.25730e7 2.25730e7i 0.0444203 0.0444203i
\(799\) 6.06761e7 6.06761e7i 0.118954 0.118954i
\(800\) 1.52491e8 + 1.52491e8i 0.297834 + 0.297834i
\(801\) 1.70414e7 + 1.70414e7i 0.0331596 + 0.0331596i
\(802\) −2.05361e7 −0.0398102
\(803\) 1.40302e9i 2.70968i
\(804\) 6.28892e7 + 6.28892e7i 0.121006 + 0.121006i
\(805\) 9.30531e7i 0.178379i
\(806\) −3.14754e7 5.45726e6i −0.0601127 0.0104224i
\(807\) −1.82546e7 −0.0347338
\(808\) −7.44790e7 + 7.44790e7i −0.141189 + 0.141189i
\(809\) 3.87651e8 0.732141 0.366071 0.930587i \(-0.380703\pi\)
0.366071 + 0.930587i \(0.380703\pi\)
\(810\) 1.86294e7i 0.0350546i
\(811\) 6.59086e8 6.59086e8i 1.23561 1.23561i 0.273826 0.961779i \(-0.411711\pi\)
0.961779 0.273826i \(-0.0882892\pi\)
\(812\) −1.05490e8 + 1.05490e8i −0.197035 + 0.197035i
\(813\) −1.51162e8 1.51162e8i −0.281301 0.281301i
\(814\) −6.55303e7 6.55303e7i −0.121498 0.121498i
\(815\) 3.15103e8 0.582075
\(816\) 5.84725e7i 0.107617i
\(817\) −1.36937e8 1.36937e8i −0.251104 0.251104i
\(818\) 4.55981e7i 0.0833080i
\(819\) 2.31541e8 1.63115e8i 0.421479 0.296921i
\(820\) −5.02567e8 −0.911491
\(821\) −3.15682e8 + 3.15682e8i −0.570454 + 0.570454i −0.932255 0.361802i \(-0.882162\pi\)
0.361802 + 0.932255i \(0.382162\pi\)
\(822\) 3.12322e6 0.00562325
\(823\) 9.22357e8i 1.65462i 0.561743 + 0.827312i \(0.310131\pi\)
−0.561743 + 0.827312i \(0.689869\pi\)
\(824\) −7.80401e7 + 7.80401e7i −0.139488 + 0.139488i
\(825\) −6.93908e8 + 6.93908e8i −1.23578 + 1.23578i
\(826\) −2.43495e7 2.43495e7i −0.0432066 0.0432066i
\(827\) 6.23270e8 + 6.23270e8i 1.10194 + 1.10194i 0.994176 + 0.107768i \(0.0343703\pi\)
0.107768 + 0.994176i \(0.465630\pi\)
\(828\) −3.42492e7 −0.0603335
\(829\) 1.44545e8i 0.253712i −0.991921 0.126856i \(-0.959511\pi\)
0.991921 0.126856i \(-0.0404886\pi\)
\(830\) −3.11073e7 3.11073e7i −0.0544037 0.0544037i
\(831\) 3.48369e8i 0.607067i
\(832\) 5.28060e8 + 9.15560e7i 0.916883 + 0.158971i
\(833\) −1.00203e6 −0.00173359
\(834\) 1.10108e7 1.10108e7i 0.0189811 0.0189811i
\(835\) 1.26809e8 0.217817
\(836\) 9.27976e8i 1.58825i
\(837\) 2.46575e8 2.46575e8i 0.420507 0.420507i
\(838\) 5.33830e7 5.33830e7i 0.0907132 0.0907132i
\(839\) 2.13888e8 + 2.13888e8i 0.362160 + 0.362160i 0.864608 0.502448i \(-0.167567\pi\)
−0.502448 + 0.864608i \(0.667567\pi\)
\(840\) 9.46949e7 + 9.46949e7i 0.159768 + 0.159768i
\(841\) −5.47024e8 −0.919640
\(842\) 6.62272e7i 0.110943i
\(843\) 2.59857e8 + 2.59857e8i 0.433762 + 0.433762i
\(844\) 7.86195e8i 1.30768i
\(845\) −8.30525e8 + 3.93075e8i −1.37652 + 0.651487i
\(846\) −3.55242e7 −0.0586696
\(847\) −1.12978e9 + 1.12978e9i −1.85928 + 1.85928i
\(848\) −5.63530e8 −0.924123
\(849\) 4.29774e8i 0.702292i
\(850\) −9.95113e6 + 9.95113e6i −0.0162038 + 0.0162038i
\(851\) 4.27333e7 4.27333e7i 0.0693391 0.0693391i
\(852\) −2.28505e8 2.28505e8i −0.369468 0.369468i
\(853\) −9.88221e7 9.88221e7i −0.159224 0.159224i 0.622999 0.782223i \(-0.285914\pi\)
−0.782223 + 0.622999i \(0.785914\pi\)
\(854\) 9.02693e7 0.144933
\(855\) 4.15395e8i 0.664603i
\(856\) −7.38645e7 7.38645e7i −0.117764 0.117764i
\(857\) 6.90476e8i 1.09700i −0.836151 0.548499i \(-0.815199\pi\)
0.836151 0.548499i \(-0.184801\pi\)
\(858\) 1.54528e7 8.91259e7i 0.0244650 0.141105i
\(859\) −5.34158e8 −0.842734 −0.421367 0.906890i \(-0.638450\pi\)
−0.421367 + 0.906890i \(0.638450\pi\)
\(860\) 2.85540e8 2.85540e8i 0.448922 0.448922i
\(861\) −2.66806e8 −0.418010
\(862\) 4.66037e6i 0.00727610i
\(863\) −2.78251e8 + 2.78251e8i −0.432917 + 0.432917i −0.889619 0.456703i \(-0.849030\pi\)
0.456703 + 0.889619i \(0.349030\pi\)
\(864\) 1.53435e8 1.53435e8i 0.237894 0.237894i
\(865\) −1.03097e9 1.03097e9i −1.59293 1.59293i
\(866\) 6.02863e7 + 6.02863e7i 0.0928251 + 0.0928251i
\(867\) 4.40610e8 0.676079
\(868\) 3.62787e8i 0.554744i
\(869\) 9.55579e8 + 9.55579e8i 1.45615 + 1.45615i
\(870\) 2.13281e7i 0.0323887i
\(871\) 9.49476e7 + 1.34778e8i 0.143691 + 0.203969i
\(872\) 1.32398e8 0.199678
\(873\) −2.76084e8 + 2.76084e8i −0.414952 + 0.414952i
\(874\) −7.15573e6 −0.0107181
\(875\) 3.23940e8i 0.483550i
\(876\) −4.62801e8 + 4.62801e8i −0.688465 + 0.688465i
\(877\) 3.82228e7 3.82228e7i 0.0566661 0.0566661i −0.678206 0.734872i \(-0.737242\pi\)
0.734872 + 0.678206i \(0.237242\pi\)
\(878\) −3.14519e6 3.14519e6i −0.00464690 0.00464690i
\(879\) 8.78514e7 + 8.78514e7i 0.129355 + 0.129355i
\(880\) 1.91186e9 2.80548
\(881\) 2.25232e8i 0.329384i 0.986345 + 0.164692i \(0.0526630\pi\)
−0.986345 + 0.164692i \(0.947337\pi\)
\(882\) 293331. + 293331.i 0.000427515 + 0.000427515i
\(883\) 4.01767e8i 0.583568i 0.956484 + 0.291784i \(0.0942489\pi\)
−0.956484 + 0.291784i \(0.905751\pi\)
\(884\) −1.87407e7 + 1.08089e8i −0.0271287 + 0.156468i
\(885\) −4.16330e8 −0.600631
\(886\) −9.34658e7 + 9.34658e7i −0.134385 + 0.134385i
\(887\) 2.67161e8 0.382826 0.191413 0.981510i \(-0.438693\pi\)
0.191413 + 0.981510i \(0.438693\pi\)
\(888\) 8.69746e7i 0.124209i
\(889\) 5.48658e8 5.48658e8i 0.780901 0.780901i
\(890\) −7.42433e6 + 7.42433e6i −0.0105314 + 0.0105314i
\(891\) 2.03291e8 + 2.03291e8i 0.287399 + 0.287399i
\(892\) −5.28559e8 5.28559e8i −0.744730 0.744730i
\(893\) 6.27676e8 0.881417
\(894\) 4.81680e7i 0.0674134i
\(895\) 1.42754e8 + 1.42754e8i 0.199122 + 0.199122i
\(896\) 3.00390e8i 0.417602i
\(897\) 5.81204e7 + 1.00770e7i 0.0805288 + 0.0139622i
\(898\) 9.93812e7 0.137238
\(899\) −8.21934e7 + 8.21934e7i −0.113125 + 0.113125i
\(900\) −4.92704e8 −0.675863
\(901\) 1.12539e8i 0.153861i
\(902\) 6.48493e7 6.48493e7i 0.0883661 0.0883661i
\(903\) 1.51589e8 1.51589e8i 0.205876 0.205876i
\(904\) −1.89199e8 1.89199e8i −0.256102 0.256102i
\(905\) 1.36526e9 + 1.36526e9i 1.84192 + 1.84192i
\(906\) −7.24286e7 −0.0973925
\(907\) 1.29431e8i 0.173466i 0.996232 + 0.0867332i \(0.0276428\pi\)
−0.996232 + 0.0867332i \(0.972357\pi\)
\(908\) 3.42072e7 + 3.42072e7i 0.0456940 + 0.0456940i
\(909\) 3.61673e8i 0.481532i
\(910\) 7.10631e7 + 1.00874e8i 0.0943018 + 0.133861i
\(911\) 9.09544e8 1.20301 0.601504 0.798870i \(-0.294568\pi\)
0.601504 + 0.798870i \(0.294568\pi\)
\(912\) −3.02440e8 + 3.02440e8i −0.398708 + 0.398708i
\(913\) −6.78909e8 −0.892071
\(914\) 8.07972e7i 0.105818i
\(915\) 7.71716e8 7.71716e8i 1.00738 1.00738i
\(916\) −9.62386e8 + 9.62386e8i −1.25217 + 1.25217i
\(917\) −4.25660e8 4.25660e8i −0.552020 0.552020i
\(918\) 1.00127e7 + 1.00127e7i 0.0129427 + 0.0129427i
\(919\) −5.70701e8 −0.735296 −0.367648 0.929965i \(-0.619837\pi\)
−0.367648 + 0.929965i \(0.619837\pi\)
\(920\) 3.00186e7i 0.0385503i
\(921\) 4.99252e8 + 4.99252e8i 0.639059 + 0.639059i
\(922\) 8.91904e7i 0.113796i
\(923\) −3.44987e8 4.89708e8i −0.438731 0.622777i
\(924\) 1.02727e9 1.30217
\(925\) 6.14756e8 6.14756e8i 0.776744 0.776744i
\(926\) 3.53213e7 0.0444840
\(927\) 3.78966e8i 0.475731i
\(928\) −5.11461e7 + 5.11461e7i −0.0639983 + 0.0639983i
\(929\) −2.60806e8 + 2.60806e8i −0.325290 + 0.325290i −0.850792 0.525502i \(-0.823877\pi\)
0.525502 + 0.850792i \(0.323877\pi\)
\(930\) 3.66743e7 + 3.66743e7i 0.0455946 + 0.0455946i
\(931\) −5.18285e6 5.18285e6i −0.00642273 0.00642273i
\(932\) −1.15809e8 −0.143053
\(933\) 8.93532e8i 1.10018i
\(934\) −1.82418e7 1.82418e7i −0.0223886 0.0223886i
\(935\) 3.81806e8i 0.467098i
\(936\) 7.46943e7 5.26203e7i 0.0910878 0.0641691i
\(937\) −1.85169e8 −0.225086 −0.112543 0.993647i \(-0.535900\pi\)
−0.112543 + 0.993647i \(0.535900\pi\)
\(938\) 1.56550e7 1.56550e7i 0.0189690 0.0189690i
\(939\) −6.18621e8 −0.747184
\(940\) 1.30883e9i 1.57579i
\(941\) 3.91178e8 3.91178e8i 0.469468 0.469468i −0.432274 0.901742i \(-0.642289\pi\)
0.901742 + 0.432274i \(0.142289\pi\)
\(942\) −2.45456e7 + 2.45456e7i −0.0293644 + 0.0293644i
\(943\) 4.22892e7 + 4.22892e7i 0.0504307 + 0.0504307i
\(944\) 3.26242e8 + 3.26242e8i 0.387814 + 0.387814i
\(945\) −1.34694e9 −1.59607
\(946\) 7.36899e7i 0.0870432i
\(947\) −1.03681e9 1.03681e9i −1.22081 1.22081i −0.967343 0.253471i \(-0.918428\pi\)
−0.253471 0.967343i \(-0.581572\pi\)
\(948\) 6.30415e8i 0.739949i
\(949\) −9.91828e8 + 6.98718e8i −1.16048 + 0.817530i
\(950\) −1.02941e8 −0.120066
\(951\) −8.15404e8 + 8.15404e8i −0.948050 + 0.948050i
\(952\) 2.96378e7 0.0343506
\(953\) 2.01631e8i 0.232959i 0.993193 + 0.116479i \(0.0371609\pi\)
−0.993193 + 0.116479i \(0.962839\pi\)
\(954\) −3.29443e7 + 3.29443e7i −0.0379433 + 0.0379433i
\(955\) 8.22054e8 8.22054e8i 0.943822 0.943822i
\(956\) 5.84430e8 + 5.84430e8i 0.668897 + 0.668897i
\(957\) −2.32739e8 2.32739e8i −0.265543 0.265543i
\(958\) −7.74674e7 −0.0881095
\(959\) 6.57486e7i 0.0745470i
\(960\) −6.15283e8 6.15283e8i −0.695442 0.695442i
\(961\) 6.04835e8i 0.681502i
\(962\) −1.36902e7 + 7.89596e7i −0.0153774 + 0.0886911i
\(963\) 3.58689e8 0.401642
\(964\) 7.81878e8 7.81878e8i 0.872786 0.872786i
\(965\) −5.04591e8 −0.561510
\(966\) 7.92141e6i 0.00878762i
\(967\) 8.11848e8 8.11848e8i 0.897832 0.897832i −0.0974120 0.995244i \(-0.531056\pi\)
0.995244 + 0.0974120i \(0.0310565\pi\)
\(968\) −3.64465e8 + 3.64465e8i −0.401818 + 0.401818i
\(969\) −6.03985e7 6.03985e7i −0.0663827 0.0663827i
\(970\) −1.20279e8 1.20279e8i −0.131788 0.131788i
\(971\) −1.57720e8 −0.172278 −0.0861388 0.996283i \(-0.527453\pi\)
−0.0861388 + 0.996283i \(0.527453\pi\)
\(972\) 8.22259e8i 0.895385i
\(973\) 2.31795e8 + 2.31795e8i 0.251632 + 0.251632i
\(974\) 5.95207e6i 0.00644156i
\(975\) 8.36113e8 + 1.44967e8i 0.902093 + 0.156406i
\(976\) −1.20946e9 −1.30089
\(977\) 6.27520e8 6.27520e8i 0.672890 0.672890i −0.285491 0.958381i \(-0.592157\pi\)
0.958381 + 0.285491i \(0.0921568\pi\)
\(978\) 2.68240e7 0.0286752
\(979\) 1.62034e8i 0.172686i
\(980\) 1.08073e7 1.08073e7i 0.0114825 0.0114825i
\(981\) −3.21465e8 + 3.21465e8i −0.340507 + 0.340507i
\(982\) 1.17975e8 + 1.17975e8i 0.124582 + 0.124582i
\(983\) −4.70097e8 4.70097e8i −0.494911 0.494911i 0.414938 0.909849i \(-0.363803\pi\)
−0.909849 + 0.414938i \(0.863803\pi\)
\(984\) −8.60708e7 −0.0903380
\(985\) 9.66663e8i 1.01150i
\(986\) −3.33765e6 3.33765e6i −0.00348185 0.00348185i
\(987\) 6.94839e8i 0.722658i
\(988\) −6.56008e8 + 4.62141e8i −0.680202 + 0.479186i
\(989\) −4.80543e7 −0.0496757
\(990\) 1.11768e8 1.11768e8i 0.115190 0.115190i
\(991\) −7.09755e8 −0.729268 −0.364634 0.931151i \(-0.618806\pi\)
−0.364634 + 0.931151i \(0.618806\pi\)
\(992\) 1.75895e8i 0.180185i
\(993\) −5.93864e8 + 5.93864e8i −0.606512 + 0.606512i
\(994\) −5.68816e7 + 5.68816e7i −0.0579179 + 0.0579179i
\(995\) −2.93313e8 2.93313e8i −0.297757 0.297757i
\(996\) 2.23945e8 + 2.23945e8i 0.226654 + 0.226654i
\(997\) 1.40289e9 1.41559 0.707796 0.706417i \(-0.249690\pi\)
0.707796 + 0.706417i \(0.249690\pi\)
\(998\) 1.90658e8i 0.191807i
\(999\) −6.18563e8 6.18563e8i −0.620422 0.620422i
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 13.7.d.a.5.4 12
3.2 odd 2 117.7.j.b.109.3 12
4.3 odd 2 208.7.t.c.161.3 12
13.8 odd 4 inner 13.7.d.a.8.4 yes 12
39.8 even 4 117.7.j.b.73.3 12
52.47 even 4 208.7.t.c.177.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
13.7.d.a.5.4 12 1.1 even 1 trivial
13.7.d.a.8.4 yes 12 13.8 odd 4 inner
117.7.j.b.73.3 12 39.8 even 4
117.7.j.b.109.3 12 3.2 odd 2
208.7.t.c.161.3 12 4.3 odd 2
208.7.t.c.177.3 12 52.47 even 4