Properties

Label 35.6.e.a.11.2
Level $35$
Weight $6$
Character 35.11
Analytic conductor $5.613$
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] = [35,6,Mod(11,35)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(35, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("35.11");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 35.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.61343369345\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} + 110 x^{10} + 27 x^{9} + 9714 x^{8} - 3257 x^{7} + 240269 x^{6} - 608504 x^{5} + 5067668 x^{4} - 7120352 x^{3} + 9029136 x^{2} - 1794240 x + 313600 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 11.2
Root \(2.06025 + 3.56846i\) of defining polynomial
Character \(\chi\) \(=\) 35.11
Dual form 35.6.e.a.16.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.56025 - 2.70243i) q^{2} +(-13.9359 + 24.1376i) q^{3} +(11.1312 - 19.2799i) q^{4} +(12.5000 + 21.6506i) q^{5} +86.9736 q^{6} +(-89.4698 - 93.8198i) q^{7} -169.326 q^{8} +(-266.916 - 462.312i) q^{9} +O(q^{10})\) \(q+(-1.56025 - 2.70243i) q^{2} +(-13.9359 + 24.1376i) q^{3} +(11.1312 - 19.2799i) q^{4} +(12.5000 + 21.6506i) q^{5} +86.9736 q^{6} +(-89.4698 - 93.8198i) q^{7} -169.326 q^{8} +(-266.916 - 462.312i) q^{9} +(39.0062 - 67.5608i) q^{10} +(202.629 - 350.963i) q^{11} +(310.247 + 537.363i) q^{12} -931.313 q^{13} +(-113.946 + 388.168i) q^{14} -696.793 q^{15} +(-92.0091 - 159.364i) q^{16} +(368.146 - 637.648i) q^{17} +(-832.912 + 1442.65i) q^{18} +(497.114 + 861.027i) q^{19} +556.562 q^{20} +(3511.42 - 852.127i) q^{21} -1264.61 q^{22} +(-612.416 - 1060.74i) q^{23} +(2359.70 - 4087.13i) q^{24} +(-312.500 + 541.266i) q^{25} +(1453.08 + 2516.81i) q^{26} +8106.00 q^{27} +(-2804.75 + 680.635i) q^{28} -5585.88 q^{29} +(1087.17 + 1883.03i) q^{30} +(-1574.79 + 2727.61i) q^{31} +(-2996.33 + 5189.80i) q^{32} +(5647.61 + 9781.95i) q^{33} -2297.60 q^{34} +(912.887 - 3109.83i) q^{35} -11884.4 q^{36} +(4806.89 + 8325.78i) q^{37} +(1551.24 - 2686.83i) q^{38} +(12978.6 - 22479.7i) q^{39} +(-2116.58 - 3666.02i) q^{40} -14680.2 q^{41} +(-7781.51 - 8159.85i) q^{42} +3526.05 q^{43} +(-4511.02 - 7813.32i) q^{44} +(6672.91 - 11557.8i) q^{45} +(-1911.04 + 3310.03i) q^{46} +(-9283.82 - 16080.1i) q^{47} +5128.90 q^{48} +(-797.318 + 16788.1i) q^{49} +1950.31 q^{50} +(10260.9 + 17772.4i) q^{51} +(-10366.7 + 17955.6i) q^{52} +(2728.99 - 4726.75i) q^{53} +(-12647.4 - 21905.9i) q^{54} +10131.4 q^{55} +(15149.6 + 15886.1i) q^{56} -27710.9 q^{57} +(8715.36 + 15095.5i) q^{58} +(3883.98 - 6727.24i) q^{59} +(-7756.17 + 13434.1i) q^{60} +(-9437.36 - 16346.0i) q^{61} +9828.25 q^{62} +(-19493.1 + 66405.0i) q^{63} +12811.5 q^{64} +(-11641.4 - 20163.5i) q^{65} +(17623.4 - 30524.6i) q^{66} +(33352.2 - 57767.7i) q^{67} +(-8195.86 - 14195.6i) q^{68} +34138.2 q^{69} +(-9828.42 + 2385.09i) q^{70} +30994.2 q^{71} +(45195.9 + 78281.5i) q^{72} +(-18657.3 + 32315.3i) q^{73} +(14999.9 - 25980.6i) q^{74} +(-8709.91 - 15086.0i) q^{75} +22134.0 q^{76} +(-51056.5 + 12390.0i) q^{77} -80999.7 q^{78} +(7830.73 + 13563.2i) q^{79} +(2300.23 - 3984.11i) q^{80} +(-48103.4 + 83317.5i) q^{81} +(22904.7 + 39672.2i) q^{82} +70001.9 q^{83} +(22657.6 - 77185.1i) q^{84} +18407.3 q^{85} +(-5501.52 - 9528.90i) q^{86} +(77844.0 - 134830. i) q^{87} +(-34310.3 + 59427.2i) q^{88} +(3952.08 + 6845.21i) q^{89} -41645.6 q^{90} +(83324.4 + 87375.6i) q^{91} -27267.8 q^{92} +(-43892.0 - 76023.3i) q^{93} +(-28970.2 + 50177.8i) q^{94} +(-12427.9 + 21525.7i) q^{95} +(-83512.9 - 144649. i) q^{96} -149459. q^{97} +(46612.6 - 24038.9i) q^{98} -216340. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 5 q^{2} - 20 q^{3} - 31 q^{4} + 150 q^{5} + 192 q^{6} - 20 q^{7} - 270 q^{8} - 378 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 5 q^{2} - 20 q^{3} - 31 q^{4} + 150 q^{5} + 192 q^{6} - 20 q^{7} - 270 q^{8} - 378 q^{9} - 125 q^{10} + 924 q^{11} - 370 q^{12} - 300 q^{13} + 3409 q^{14} - 1000 q^{15} - 435 q^{16} - 1540 q^{17} - 195 q^{18} - 92 q^{19} - 1550 q^{20} + 7288 q^{21} - 13710 q^{22} + 3920 q^{23} + 7200 q^{24} - 3750 q^{25} - 2635 q^{26} + 4120 q^{27} - 6015 q^{28} + 2528 q^{29} + 2400 q^{30} + 7160 q^{31} - 9105 q^{32} - 4460 q^{33} + 4332 q^{34} - 2500 q^{35} - 52750 q^{36} + 14170 q^{37} + 46215 q^{38} + 15376 q^{39} - 3375 q^{40} + 8196 q^{41} + 10500 q^{42} - 48920 q^{43} + 27873 q^{44} + 9450 q^{45} - 6815 q^{46} - 42940 q^{47} + 23220 q^{48} - 17856 q^{49} - 6250 q^{50} + 42008 q^{51} + 36115 q^{52} + 2450 q^{53} - 19566 q^{54} + 46200 q^{55} + 67998 q^{56} - 194200 q^{57} + 36110 q^{58} + 64600 q^{59} + 9250 q^{60} - 73620 q^{61} + 222880 q^{62} - 57780 q^{63} - 315994 q^{64} - 3750 q^{65} + 139138 q^{66} + 142620 q^{67} - 124330 q^{68} + 34688 q^{69} + 34475 q^{70} - 308512 q^{71} + 117495 q^{72} + 5120 q^{73} - 2785 q^{74} - 12500 q^{75} + 15550 q^{76} + 44230 q^{77} - 428180 q^{78} + 222504 q^{79} + 10875 q^{80} + 43986 q^{81} - 31665 q^{82} + 359160 q^{83} - 19966 q^{84} - 77000 q^{85} + 207160 q^{86} + 209300 q^{87} + 45145 q^{88} - 41648 q^{89} - 9750 q^{90} - 31376 q^{91} - 584370 q^{92} + 198520 q^{93} + 333699 q^{94} + 2300 q^{95} - 61824 q^{96} - 147960 q^{97} - 101815 q^{98} - 381544 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.56025 2.70243i −0.275816 0.477727i 0.694525 0.719469i \(-0.255615\pi\)
−0.970341 + 0.241742i \(0.922281\pi\)
\(3\) −13.9359 + 24.1376i −0.893986 + 1.54843i −0.0589307 + 0.998262i \(0.518769\pi\)
−0.835055 + 0.550166i \(0.814564\pi\)
\(4\) 11.1312 19.2799i 0.347851 0.602496i
\(5\) 12.5000 + 21.6506i 0.223607 + 0.387298i
\(6\) 86.9736 0.986301
\(7\) −89.4698 93.8198i −0.690131 0.723685i
\(8\) −169.326 −0.935403
\(9\) −266.916 462.312i −1.09842 1.90252i
\(10\) 39.0062 67.5608i 0.123349 0.213646i
\(11\) 202.629 350.963i 0.504916 0.874541i −0.495067 0.868855i \(-0.664857\pi\)
0.999984 0.00568632i \(-0.00181002\pi\)
\(12\) 310.247 + 537.363i 0.621948 + 1.07725i
\(13\) −931.313 −1.52840 −0.764200 0.644979i \(-0.776866\pi\)
−0.764200 + 0.644979i \(0.776866\pi\)
\(14\) −113.946 + 388.168i −0.155375 + 0.529298i
\(15\) −696.793 −0.799605
\(16\) −92.0091 159.364i −0.0898526 0.155629i
\(17\) 368.146 637.648i 0.308957 0.535130i −0.669177 0.743103i \(-0.733353\pi\)
0.978135 + 0.207973i \(0.0666867\pi\)
\(18\) −832.912 + 1442.65i −0.605923 + 1.04949i
\(19\) 497.114 + 861.027i 0.315917 + 0.547184i 0.979632 0.200802i \(-0.0643547\pi\)
−0.663715 + 0.747985i \(0.731021\pi\)
\(20\) 556.562 0.311128
\(21\) 3511.42 852.127i 1.73754 0.421654i
\(22\) −1264.61 −0.557055
\(23\) −612.416 1060.74i −0.241394 0.418107i 0.719717 0.694267i \(-0.244271\pi\)
−0.961112 + 0.276160i \(0.910938\pi\)
\(24\) 2359.70 4087.13i 0.836237 1.44840i
\(25\) −312.500 + 541.266i −0.100000 + 0.173205i
\(26\) 1453.08 + 2516.81i 0.421557 + 0.730158i
\(27\) 8106.00 2.13992
\(28\) −2804.75 + 680.635i −0.676080 + 0.164066i
\(29\) −5585.88 −1.23338 −0.616689 0.787207i \(-0.711527\pi\)
−0.616689 + 0.787207i \(0.711527\pi\)
\(30\) 1087.17 + 1883.03i 0.220544 + 0.381993i
\(31\) −1574.79 + 2727.61i −0.294319 + 0.509775i −0.974826 0.222966i \(-0.928426\pi\)
0.680507 + 0.732741i \(0.261759\pi\)
\(32\) −2996.33 + 5189.80i −0.517267 + 0.895933i
\(33\) 5647.61 + 9781.95i 0.902776 + 1.56365i
\(34\) −2297.60 −0.340861
\(35\) 912.887 3109.83i 0.125964 0.429107i
\(36\) −11884.4 −1.52835
\(37\) 4806.89 + 8325.78i 0.577245 + 0.999817i 0.995794 + 0.0916228i \(0.0292054\pi\)
−0.418549 + 0.908194i \(0.637461\pi\)
\(38\) 1551.24 2686.83i 0.174269 0.301844i
\(39\) 12978.6 22479.7i 1.36637 2.36662i
\(40\) −2116.58 3666.02i −0.209162 0.362280i
\(41\) −14680.2 −1.36387 −0.681933 0.731414i \(-0.738861\pi\)
−0.681933 + 0.731414i \(0.738861\pi\)
\(42\) −7781.51 8159.85i −0.680677 0.713771i
\(43\) 3526.05 0.290815 0.145408 0.989372i \(-0.453551\pi\)
0.145408 + 0.989372i \(0.453551\pi\)
\(44\) −4511.02 7813.32i −0.351272 0.608421i
\(45\) 6672.91 11557.8i 0.491229 0.850833i
\(46\) −1911.04 + 3310.03i −0.133161 + 0.230641i
\(47\) −9283.82 16080.1i −0.613031 1.06180i −0.990727 0.135870i \(-0.956617\pi\)
0.377696 0.925930i \(-0.376716\pi\)
\(48\) 5128.90 0.321308
\(49\) −797.318 + 16788.1i −0.0474396 + 0.998874i
\(50\) 1950.31 0.110326
\(51\) 10260.9 + 17772.4i 0.552407 + 0.956796i
\(52\) −10366.7 + 17955.6i −0.531656 + 0.920856i
\(53\) 2728.99 4726.75i 0.133448 0.231139i −0.791555 0.611097i \(-0.790728\pi\)
0.925004 + 0.379958i \(0.124062\pi\)
\(54\) −12647.4 21905.9i −0.590223 1.02230i
\(55\) 10131.4 0.451611
\(56\) 15149.6 + 15886.1i 0.645550 + 0.676937i
\(57\) −27710.9 −1.12970
\(58\) 8715.36 + 15095.5i 0.340185 + 0.589218i
\(59\) 3883.98 6727.24i 0.145260 0.251598i −0.784210 0.620496i \(-0.786931\pi\)
0.929470 + 0.368898i \(0.120265\pi\)
\(60\) −7756.17 + 13434.1i −0.278144 + 0.481759i
\(61\) −9437.36 16346.0i −0.324733 0.562453i 0.656726 0.754130i \(-0.271941\pi\)
−0.981458 + 0.191676i \(0.938608\pi\)
\(62\) 9828.25 0.324711
\(63\) −19493.1 + 66405.0i −0.618772 + 2.10790i
\(64\) 12811.5 0.390976
\(65\) −11641.4 20163.5i −0.341761 0.591947i
\(66\) 17623.4 30524.6i 0.498000 0.862561i
\(67\) 33352.2 57767.7i 0.907691 1.57217i 0.0904261 0.995903i \(-0.471177\pi\)
0.817264 0.576263i \(-0.195490\pi\)
\(68\) −8195.86 14195.6i −0.214942 0.372291i
\(69\) 34138.2 0.863212
\(70\) −9828.42 + 2385.09i −0.239739 + 0.0581781i
\(71\) 30994.2 0.729683 0.364842 0.931070i \(-0.381123\pi\)
0.364842 + 0.931070i \(0.381123\pi\)
\(72\) 45195.9 + 78281.5i 1.02747 + 1.77962i
\(73\) −18657.3 + 32315.3i −0.409771 + 0.709743i −0.994864 0.101223i \(-0.967725\pi\)
0.585093 + 0.810966i \(0.301058\pi\)
\(74\) 14999.9 25980.6i 0.318426 0.551530i
\(75\) −8709.91 15086.0i −0.178797 0.309686i
\(76\) 22134.0 0.439568
\(77\) −51056.5 + 12390.0i −0.981350 + 0.238147i
\(78\) −80999.7 −1.50746
\(79\) 7830.73 + 13563.2i 0.141167 + 0.244509i 0.927937 0.372738i \(-0.121581\pi\)
−0.786769 + 0.617247i \(0.788248\pi\)
\(80\) 2300.23 3984.11i 0.0401833 0.0695995i
\(81\) −48103.4 + 83317.5i −0.814635 + 1.41099i
\(82\) 22904.7 + 39672.2i 0.376176 + 0.651556i
\(83\) 70001.9 1.11536 0.557679 0.830057i \(-0.311692\pi\)
0.557679 + 0.830057i \(0.311692\pi\)
\(84\) 22657.6 77185.1i 0.350361 1.19354i
\(85\) 18407.3 0.276340
\(86\) −5501.52 9528.90i −0.0802114 0.138930i
\(87\) 77844.0 134830.i 1.10262 1.90980i
\(88\) −34310.3 + 59427.2i −0.472300 + 0.818048i
\(89\) 3952.08 + 6845.21i 0.0528873 + 0.0916034i 0.891257 0.453499i \(-0.149824\pi\)
−0.838370 + 0.545102i \(0.816491\pi\)
\(90\) −41645.6 −0.541954
\(91\) 83324.4 + 87375.6i 1.05480 + 1.10608i
\(92\) −27267.8 −0.335877
\(93\) −43892.0 76023.3i −0.526233 0.911463i
\(94\) −28970.2 + 50177.8i −0.338167 + 0.585722i
\(95\) −12427.9 + 21525.7i −0.141282 + 0.244708i
\(96\) −83512.9 144649.i −0.924858 1.60190i
\(97\) −149459. −1.61284 −0.806420 0.591343i \(-0.798598\pi\)
−0.806420 + 0.591343i \(0.798598\pi\)
\(98\) 46612.6 24038.9i 0.490274 0.252842i
\(99\) −216340. −2.21844
\(100\) 6957.03 + 12049.9i 0.0695703 + 0.120499i
\(101\) 63466.3 109927.i 0.619070 1.07226i −0.370586 0.928798i \(-0.620843\pi\)
0.989656 0.143462i \(-0.0458235\pi\)
\(102\) 32019.0 55458.6i 0.304725 0.527799i
\(103\) −6750.25 11691.8i −0.0626941 0.108589i 0.832975 0.553311i \(-0.186636\pi\)
−0.895669 + 0.444722i \(0.853303\pi\)
\(104\) 157696. 1.42967
\(105\) 62341.9 + 65373.0i 0.551832 + 0.578662i
\(106\) −17031.6 −0.147228
\(107\) −37215.8 64459.6i −0.314245 0.544287i 0.665032 0.746815i \(-0.268418\pi\)
−0.979277 + 0.202527i \(0.935085\pi\)
\(108\) 90229.9 156283.i 0.744373 1.28929i
\(109\) −68840.7 + 119236.i −0.554982 + 0.961257i 0.442923 + 0.896560i \(0.353942\pi\)
−0.997905 + 0.0646973i \(0.979392\pi\)
\(110\) −15807.6 27379.5i −0.124561 0.215747i
\(111\) −267953. −2.06419
\(112\) −6719.51 + 22890.6i −0.0506165 + 0.172429i
\(113\) 62258.8 0.458674 0.229337 0.973347i \(-0.426344\pi\)
0.229337 + 0.973347i \(0.426344\pi\)
\(114\) 43235.9 + 74886.7i 0.311589 + 0.539688i
\(115\) 15310.4 26518.4i 0.107955 0.186983i
\(116\) −62177.8 + 107695.i −0.429033 + 0.743106i
\(117\) 248583. + 430558.i 1.67883 + 2.90781i
\(118\) −24239.9 −0.160260
\(119\) −92762.0 + 22510.8i −0.600486 + 0.145722i
\(120\) 117985. 0.747953
\(121\) −1591.37 2756.34i −0.00988117 0.0171147i
\(122\) −29449.3 + 51007.6i −0.179133 + 0.310267i
\(123\) 204581. 354345.i 1.21928 2.11185i
\(124\) 35058.7 + 60723.5i 0.204758 + 0.354652i
\(125\) −15625.0 −0.0894427
\(126\) 209869. 50929.5i 1.17767 0.285788i
\(127\) −264361. −1.45442 −0.727208 0.686417i \(-0.759183\pi\)
−0.727208 + 0.686417i \(0.759183\pi\)
\(128\) 75893.4 + 131451.i 0.409430 + 0.709153i
\(129\) −49138.5 + 85110.4i −0.259985 + 0.450307i
\(130\) −36327.0 + 62920.2i −0.188526 + 0.326537i
\(131\) −54997.2 95258.0i −0.280003 0.484979i 0.691382 0.722489i \(-0.257002\pi\)
−0.971385 + 0.237510i \(0.923669\pi\)
\(132\) 251460. 1.25613
\(133\) 36304.7 123675.i 0.177965 0.606252i
\(134\) −208151. −1.00142
\(135\) 101325. + 175500.i 0.478500 + 0.828787i
\(136\) −62336.8 + 107970.i −0.288999 + 0.500562i
\(137\) 140940. 244115.i 0.641552 1.11120i −0.343535 0.939140i \(-0.611624\pi\)
0.985086 0.172060i \(-0.0550424\pi\)
\(138\) −53264.1 92256.1i −0.238088 0.412380i
\(139\) 236209. 1.03696 0.518478 0.855091i \(-0.326499\pi\)
0.518478 + 0.855091i \(0.326499\pi\)
\(140\) −49795.5 52216.6i −0.214719 0.225158i
\(141\) 517512. 2.19216
\(142\) −48358.6 83759.6i −0.201258 0.348589i
\(143\) −188711. + 326857.i −0.771715 + 1.33665i
\(144\) −49117.4 + 85073.9i −0.197392 + 0.341893i
\(145\) −69823.5 120938.i −0.275792 0.477686i
\(146\) 116440. 0.452085
\(147\) −394113. 253202.i −1.50427 0.966436i
\(148\) 214027. 0.803181
\(149\) 12819.9 + 22204.8i 0.0473064 + 0.0819371i 0.888709 0.458472i \(-0.151603\pi\)
−0.841403 + 0.540409i \(0.818270\pi\)
\(150\) −27179.3 + 47075.9i −0.0986301 + 0.170832i
\(151\) −131289. + 227399.i −0.468581 + 0.811606i −0.999355 0.0359071i \(-0.988568\pi\)
0.530774 + 0.847513i \(0.321901\pi\)
\(152\) −84174.4 145794.i −0.295509 0.511837i
\(153\) −393057. −1.35746
\(154\) 113144. + 118645.i 0.384441 + 0.403133i
\(155\) −78739.4 −0.263247
\(156\) −288937. 500453.i −0.950586 1.64646i
\(157\) −131131. + 227126.i −0.424578 + 0.735391i −0.996381 0.0849999i \(-0.972911\pi\)
0.571803 + 0.820391i \(0.306244\pi\)
\(158\) 24435.8 42324.0i 0.0778724 0.134879i
\(159\) 76061.7 + 131743.i 0.238602 + 0.413270i
\(160\) −149817. −0.462658
\(161\) −44725.3 + 152361.i −0.135984 + 0.463242i
\(162\) 300213. 0.898757
\(163\) −142691. 247148.i −0.420656 0.728598i 0.575348 0.817909i \(-0.304867\pi\)
−0.996004 + 0.0893112i \(0.971533\pi\)
\(164\) −163409. + 283032.i −0.474423 + 0.821725i
\(165\) −141190. + 244549.i −0.403734 + 0.699287i
\(166\) −109220. 189175.i −0.307633 0.532837i
\(167\) 467133. 1.29613 0.648067 0.761583i \(-0.275578\pi\)
0.648067 + 0.761583i \(0.275578\pi\)
\(168\) −594576. + 144287.i −1.62530 + 0.394416i
\(169\) 496051. 1.33601
\(170\) −28720.0 49744.5i −0.0762188 0.132015i
\(171\) 265376. 459644.i 0.694019 1.20208i
\(172\) 39249.3 67981.8i 0.101161 0.175215i
\(173\) 15082.1 + 26123.0i 0.0383132 + 0.0663603i 0.884546 0.466453i \(-0.154468\pi\)
−0.846233 + 0.532813i \(0.821135\pi\)
\(174\) −485824. −1.21648
\(175\) 78740.8 19108.2i 0.194359 0.0471656i
\(176\) −74574.8 −0.181472
\(177\) 108253. + 187500.i 0.259721 + 0.449850i
\(178\) 12332.5 21360.5i 0.0291743 0.0505313i
\(179\) 297188. 514745.i 0.693265 1.20077i −0.277497 0.960727i \(-0.589505\pi\)
0.970762 0.240044i \(-0.0771618\pi\)
\(180\) −148555. 257306.i −0.341749 0.591927i
\(181\) 155232. 0.352197 0.176099 0.984373i \(-0.443652\pi\)
0.176099 + 0.984373i \(0.443652\pi\)
\(182\) 106120. 361506.i 0.237475 0.808979i
\(183\) 526071. 1.16123
\(184\) 103698. + 179610.i 0.225801 + 0.391099i
\(185\) −120172. + 208144.i −0.258152 + 0.447132i
\(186\) −136965. + 237230.i −0.290287 + 0.502792i
\(187\) −149194. 258412.i −0.311995 0.540391i
\(188\) −413362. −0.852974
\(189\) −725242. 760503.i −1.47682 1.54863i
\(190\) 77562.2 0.155871
\(191\) −160480. 277960.i −0.318302 0.551314i 0.661832 0.749652i \(-0.269779\pi\)
−0.980134 + 0.198338i \(0.936446\pi\)
\(192\) −178539. + 309239.i −0.349527 + 0.605399i
\(193\) 363618. 629804.i 0.702670 1.21706i −0.264855 0.964288i \(-0.585324\pi\)
0.967526 0.252773i \(-0.0813424\pi\)
\(194\) 233193. + 403901.i 0.444847 + 0.770497i
\(195\) 648932. 1.22212
\(196\) 314797. + 202244.i 0.585316 + 0.376042i
\(197\) −752919. −1.38224 −0.691119 0.722741i \(-0.742882\pi\)
−0.691119 + 0.722741i \(0.742882\pi\)
\(198\) 337544. + 584643.i 0.611881 + 1.05981i
\(199\) −48317.7 + 83688.7i −0.0864915 + 0.149808i −0.906026 0.423222i \(-0.860899\pi\)
0.819534 + 0.573030i \(0.194232\pi\)
\(200\) 52914.4 91650.4i 0.0935403 0.162017i
\(201\) 929584. + 1.61009e6i 1.62292 + 2.81099i
\(202\) −396093. −0.682996
\(203\) 499767. + 524066.i 0.851193 + 0.892578i
\(204\) 456865. 0.768622
\(205\) −183502. 317835.i −0.304970 0.528223i
\(206\) −21064.2 + 36484.2i −0.0345841 + 0.0599013i
\(207\) −326928. + 566255.i −0.530305 + 0.918515i
\(208\) 85689.2 + 148418.i 0.137331 + 0.237864i
\(209\) 402919. 0.638046
\(210\) 79397.1 270473.i 0.124239 0.423229i
\(211\) −373868. −0.578112 −0.289056 0.957312i \(-0.593341\pi\)
−0.289056 + 0.957312i \(0.593341\pi\)
\(212\) −60754.2 105229.i −0.0928403 0.160804i
\(213\) −431930. + 748126.i −0.652326 + 1.12986i
\(214\) −116132. + 201146.i −0.173347 + 0.300246i
\(215\) 44075.6 + 76341.2i 0.0650283 + 0.112632i
\(216\) −1.37256e6 −2.00169
\(217\) 396800. 96292.6i 0.572035 0.138817i
\(218\) 429634. 0.612291
\(219\) −520010. 900684.i −0.732658 1.26900i
\(220\) 112776. 195333.i 0.157094 0.272094i
\(221\) −342860. + 593850.i −0.472210 + 0.817892i
\(222\) 418073. + 724123.i 0.569337 + 0.986121i
\(223\) 545786. 0.734954 0.367477 0.930033i \(-0.380222\pi\)
0.367477 + 0.930033i \(0.380222\pi\)
\(224\) 754987. 183215.i 1.00535 0.243972i
\(225\) 333645. 0.439368
\(226\) −97139.2 168250.i −0.126510 0.219121i
\(227\) 61638.3 106761.i 0.0793937 0.137514i −0.823595 0.567179i \(-0.808035\pi\)
0.902989 + 0.429665i \(0.141368\pi\)
\(228\) −308456. + 534262.i −0.392968 + 0.680640i
\(229\) −539166. 933862.i −0.679412 1.17678i −0.975158 0.221510i \(-0.928901\pi\)
0.295746 0.955267i \(-0.404432\pi\)
\(230\) −95552.2 −0.119103
\(231\) 412450. 1.40505e6i 0.508559 1.73245i
\(232\) 945835. 1.15371
\(233\) −70604.2 122290.i −0.0852002 0.147571i 0.820276 0.571967i \(-0.193820\pi\)
−0.905476 + 0.424396i \(0.860486\pi\)
\(234\) 775701. 1.34355e6i 0.926094 1.60404i
\(235\) 232096. 402001.i 0.274156 0.474851i
\(236\) −86467.0 149765.i −0.101058 0.175037i
\(237\) −436512. −0.504807
\(238\) 205566. + 215560.i 0.235239 + 0.246676i
\(239\) −508655. −0.576008 −0.288004 0.957629i \(-0.592992\pi\)
−0.288004 + 0.957629i \(0.592992\pi\)
\(240\) 64111.3 + 111044.i 0.0718466 + 0.124442i
\(241\) 12848.0 22253.5i 0.0142493 0.0246806i −0.858813 0.512290i \(-0.828797\pi\)
0.873062 + 0.487609i \(0.162131\pi\)
\(242\) −4965.87 + 8601.15i −0.00545076 + 0.00944100i
\(243\) −355845. 616342.i −0.386586 0.669586i
\(244\) −420198. −0.451835
\(245\) −373439. + 192589.i −0.397470 + 0.204982i
\(246\) −1.27679e6 −1.34518
\(247\) −462969. 801886.i −0.482847 0.836316i
\(248\) 266653. 461856.i 0.275307 0.476845i
\(249\) −975536. + 1.68968e6i −0.997114 + 1.72705i
\(250\) 24378.9 + 42225.5i 0.0246697 + 0.0427292i
\(251\) −30939.4 −0.0309975 −0.0154988 0.999880i \(-0.504934\pi\)
−0.0154988 + 0.999880i \(0.504934\pi\)
\(252\) 1.06330e6 + 1.11500e6i 1.05476 + 1.10604i
\(253\) −496373. −0.487536
\(254\) 412470. + 714419.i 0.401151 + 0.694814i
\(255\) −256522. + 444309.i −0.247044 + 0.427892i
\(256\) 441809. 765236.i 0.421342 0.729786i
\(257\) −128055. 221797.i −0.120938 0.209471i 0.799200 0.601065i \(-0.205257\pi\)
−0.920138 + 0.391595i \(0.871924\pi\)
\(258\) 306673. 0.286831
\(259\) 351052. 1.19589e6i 0.325178 1.10775i
\(260\) −518334. −0.475528
\(261\) 1.49096e6 + 2.58242e6i 1.35477 + 2.34653i
\(262\) −171619. + 297252.i −0.154458 + 0.267530i
\(263\) −510371. + 883989.i −0.454985 + 0.788056i −0.998687 0.0512214i \(-0.983689\pi\)
0.543703 + 0.839278i \(0.317022\pi\)
\(264\) −956288. 1.65634e6i −0.844459 1.46265i
\(265\) 136450. 0.119360
\(266\) −390868. + 94853.0i −0.338708 + 0.0821953i
\(267\) −220303. −0.189122
\(268\) −742504. 1.28605e6i −0.631483 1.09376i
\(269\) 246883. 427613.i 0.208022 0.360305i −0.743069 0.669215i \(-0.766631\pi\)
0.951091 + 0.308909i \(0.0999640\pi\)
\(270\) 316184. 547648.i 0.263956 0.457185i
\(271\) 737896. + 1.27807e6i 0.610340 + 1.05714i 0.991183 + 0.132500i \(0.0423004\pi\)
−0.380843 + 0.924640i \(0.624366\pi\)
\(272\) −135491. −0.111042
\(273\) −3.27024e6 + 793597.i −2.65566 + 0.644456i
\(274\) −879604. −0.707800
\(275\) 126643. + 219352.i 0.100983 + 0.174908i
\(276\) 380000. 658180.i 0.300270 0.520082i
\(277\) 438956. 760293.i 0.343733 0.595363i −0.641390 0.767215i \(-0.721642\pi\)
0.985123 + 0.171852i \(0.0549752\pi\)
\(278\) −368546. 638340.i −0.286009 0.495382i
\(279\) 1.68135e6 1.29314
\(280\) −154575. + 526574.i −0.117827 + 0.401388i
\(281\) −1.46598e6 −1.10755 −0.553774 0.832667i \(-0.686813\pi\)
−0.553774 + 0.832667i \(0.686813\pi\)
\(282\) −807448. 1.39854e6i −0.604633 1.04725i
\(283\) −865539. + 1.49916e6i −0.642422 + 1.11271i 0.342468 + 0.939530i \(0.388737\pi\)
−0.984890 + 0.173179i \(0.944596\pi\)
\(284\) 345004. 597564.i 0.253821 0.439631i
\(285\) −346386. 599958.i −0.252608 0.437531i
\(286\) 1.17774e6 0.851404
\(287\) 1.31343e6 + 1.37729e6i 0.941246 + 0.987010i
\(288\) 3.19908e6 2.27271
\(289\) 438865. + 760136.i 0.309091 + 0.535361i
\(290\) −217884. + 377386.i −0.152135 + 0.263506i
\(291\) 2.08283e6 3.60757e6i 1.44186 2.49737i
\(292\) 415357. + 719420.i 0.285079 + 0.493771i
\(293\) −623726. −0.424449 −0.212224 0.977221i \(-0.568071\pi\)
−0.212224 + 0.977221i \(0.568071\pi\)
\(294\) −69345.7 + 1.46012e6i −0.0467898 + 0.985191i
\(295\) 194199. 0.129925
\(296\) −813931. 1.40977e6i −0.539956 0.935232i
\(297\) 1.64251e6 2.84491e6i 1.08048 1.87145i
\(298\) 40004.6 69289.9i 0.0260957 0.0451991i
\(299\) 570351. + 987877.i 0.368947 + 0.639036i
\(300\) −387809. −0.248779
\(301\) −315475. 330813.i −0.200701 0.210459i
\(302\) 819372. 0.516968
\(303\) 1.76891e6 + 3.06385e6i 1.10688 + 1.91717i
\(304\) 91478.1 158445.i 0.0567718 0.0983317i
\(305\) 235934. 408650.i 0.145225 0.251537i
\(306\) 613267. + 1.06221e6i 0.374409 + 0.648495i
\(307\) −1.92297e6 −1.16446 −0.582232 0.813022i \(-0.697821\pi\)
−0.582232 + 0.813022i \(0.697821\pi\)
\(308\) −329444. + 1.12228e6i −0.197881 + 0.674100i
\(309\) 376282. 0.224191
\(310\) 122853. + 212788.i 0.0726076 + 0.125760i
\(311\) −1.05152e6 + 1.82129e6i −0.616478 + 1.06777i 0.373645 + 0.927572i \(0.378108\pi\)
−0.990123 + 0.140200i \(0.955226\pi\)
\(312\) −2.19762e6 + 3.80639e6i −1.27810 + 2.21374i
\(313\) −1.37176e6 2.37595e6i −0.791437 1.37081i −0.925077 0.379779i \(-0.876000\pi\)
0.133640 0.991030i \(-0.457333\pi\)
\(314\) 818391. 0.468422
\(315\) −1.68138e6 + 408024.i −0.954747 + 0.231691i
\(316\) 348663. 0.196421
\(317\) 756053. + 1.30952e6i 0.422575 + 0.731922i 0.996191 0.0872031i \(-0.0277929\pi\)
−0.573615 + 0.819125i \(0.694460\pi\)
\(318\) 237350. 411103.i 0.131620 0.227973i
\(319\) −1.13186e6 + 1.96044e6i −0.622753 + 1.07864i
\(320\) 160144. + 277377.i 0.0874249 + 0.151424i
\(321\) 2.07454e6 1.12372
\(322\) 481527. 116853.i 0.258810 0.0628061i
\(323\) 732044. 0.390419
\(324\) 1.07090e6 + 1.85486e6i 0.566744 + 0.981630i
\(325\) 291035. 504088.i 0.152840 0.264727i
\(326\) −445267. + 771225.i −0.232047 + 0.401917i
\(327\) −1.91871e6 3.32330e6i −0.992292 1.71870i
\(328\) 2.48574e6 1.27576
\(329\) −678006. + 2.30969e6i −0.345338 + 1.17642i
\(330\) 881168. 0.445424
\(331\) −391389. 677905.i −0.196353 0.340094i 0.750990 0.660314i \(-0.229577\pi\)
−0.947343 + 0.320220i \(0.896243\pi\)
\(332\) 779208. 1.34963e6i 0.387979 0.671999i
\(333\) 2.56607e6 4.44457e6i 1.26811 2.19644i
\(334\) −728845. 1.26240e6i −0.357494 0.619198i
\(335\) 1.66761e6 0.811863
\(336\) −458882. 481193.i −0.221744 0.232526i
\(337\) −2.98847e6 −1.43342 −0.716711 0.697370i \(-0.754354\pi\)
−0.716711 + 0.697370i \(0.754354\pi\)
\(338\) −773963. 1.34054e6i −0.368492 0.638247i
\(339\) −867630. + 1.50278e6i −0.410048 + 0.710225i
\(340\) 204896. 354891.i 0.0961252 0.166494i
\(341\) 638195. + 1.10539e6i 0.297213 + 0.514788i
\(342\) −1.65621e6 −0.765685
\(343\) 1.64639e6 1.42722e6i 0.755610 0.655022i
\(344\) −597052. −0.272029
\(345\) 426727. + 739113.i 0.193020 + 0.334321i
\(346\) 47063.8 81516.9i 0.0211347 0.0366064i
\(347\) 307031. 531794.i 0.136886 0.237094i −0.789430 0.613840i \(-0.789624\pi\)
0.926316 + 0.376747i \(0.122957\pi\)
\(348\) −1.73300e6 3.00165e6i −0.767098 1.32865i
\(349\) −3.34125e6 −1.46841 −0.734203 0.678930i \(-0.762444\pi\)
−0.734203 + 0.678930i \(0.762444\pi\)
\(350\) −174494. 182978.i −0.0761395 0.0798415i
\(351\) −7.54922e6 −3.27065
\(352\) 1.21429e6 + 2.10320e6i 0.522353 + 0.904742i
\(353\) 1.81062e6 3.13608e6i 0.773374 1.33952i −0.162329 0.986737i \(-0.551901\pi\)
0.935704 0.352787i \(-0.114766\pi\)
\(354\) 337804. 585093.i 0.143270 0.248151i
\(355\) 387427. + 671044.i 0.163162 + 0.282605i
\(356\) 175966. 0.0735876
\(357\) 749361. 2.55276e6i 0.311186 1.06008i
\(358\) −1.85475e6 −0.764854
\(359\) −1.79122e6 3.10248e6i −0.733522 1.27050i −0.955369 0.295415i \(-0.904542\pi\)
0.221847 0.975081i \(-0.428791\pi\)
\(360\) −1.12990e6 + 1.95704e6i −0.459497 + 0.795872i
\(361\) 743804. 1.28831e6i 0.300393 0.520297i
\(362\) −242201. 419505.i −0.0971415 0.168254i
\(363\) 88708.6 0.0353345
\(364\) 2.61210e6 633884.i 1.03332 0.250759i
\(365\) −932863. −0.366510
\(366\) −820802. 1.42167e6i −0.320284 0.554748i
\(367\) −1.44015e6 + 2.49441e6i −0.558138 + 0.966723i 0.439514 + 0.898236i \(0.355151\pi\)
−0.997652 + 0.0684875i \(0.978183\pi\)
\(368\) −112696. + 195195.i −0.0433798 + 0.0751361i
\(369\) 3.91838e6 + 6.78683e6i 1.49810 + 2.59478i
\(370\) 749995. 0.284809
\(371\) −687626. + 166868.i −0.259369 + 0.0629417i
\(372\) −1.95429e6 −0.732204
\(373\) 1.95904e6 + 3.39315e6i 0.729071 + 1.26279i 0.957276 + 0.289176i \(0.0933812\pi\)
−0.228205 + 0.973613i \(0.573285\pi\)
\(374\) −465560. + 806374.i −0.172106 + 0.298097i
\(375\) 217748. 377150.i 0.0799605 0.138496i
\(376\) 1.57199e6 + 2.72277e6i 0.573431 + 0.993211i
\(377\) 5.20220e6 1.88510
\(378\) −923650. + 3.14649e6i −0.332489 + 1.13265i
\(379\) −795965. −0.284640 −0.142320 0.989821i \(-0.545456\pi\)
−0.142320 + 0.989821i \(0.545456\pi\)
\(380\) 276675. + 479215.i 0.0982904 + 0.170244i
\(381\) 3.68410e6 6.38105e6i 1.30023 2.25206i
\(382\) −500779. + 867375.i −0.175585 + 0.304122i
\(383\) −1.01288e6 1.75435e6i −0.352825 0.611111i 0.633918 0.773400i \(-0.281446\pi\)
−0.986743 + 0.162289i \(0.948112\pi\)
\(384\) −4.23056e6 −1.46410
\(385\) −906458. 950530.i −0.311671 0.326824i
\(386\) −2.26934e6 −0.775230
\(387\) −941160. 1.63014e6i −0.319438 0.553282i
\(388\) −1.66366e6 + 2.88154e6i −0.561029 + 0.971730i
\(389\) 1.30160e6 2.25443e6i 0.436117 0.755376i −0.561269 0.827633i \(-0.689687\pi\)
0.997386 + 0.0722571i \(0.0230202\pi\)
\(390\) −1.01250e6 1.75369e6i −0.337079 0.583838i
\(391\) −901836. −0.298322
\(392\) 135007. 2.84266e6i 0.0443752 0.934350i
\(393\) 3.06573e6 1.00127
\(394\) 1.17474e6 + 2.03471e6i 0.381243 + 0.660332i
\(395\) −195768. + 339081.i −0.0631320 + 0.109348i
\(396\) −2.40813e6 + 4.17100e6i −0.771688 + 1.33660i
\(397\) 2.58387e6 + 4.47539e6i 0.822800 + 1.42513i 0.903589 + 0.428400i \(0.140923\pi\)
−0.0807894 + 0.996731i \(0.525744\pi\)
\(398\) 301550. 0.0954228
\(399\) 2.47928e6 + 2.59983e6i 0.779640 + 0.817546i
\(400\) 115011. 0.0359410
\(401\) −675308. 1.16967e6i −0.209720 0.363247i 0.741906 0.670504i \(-0.233922\pi\)
−0.951626 + 0.307257i \(0.900589\pi\)
\(402\) 2.90076e6 5.02427e6i 0.895256 1.55063i
\(403\) 1.46662e6 2.54026e6i 0.449837 0.779141i
\(404\) −1.41292e6 2.44724e6i −0.430688 0.745974i
\(405\) −2.40517e6 −0.728632
\(406\) 636491. 2.16826e6i 0.191636 0.652824i
\(407\) 3.89606e6 1.16584
\(408\) −1.73743e6 3.00932e6i −0.516723 0.894990i
\(409\) 1.38902e6 2.40585e6i 0.410581 0.711148i −0.584372 0.811486i \(-0.698659\pi\)
0.994953 + 0.100338i \(0.0319925\pi\)
\(410\) −572619. + 991805.i −0.168231 + 0.291385i
\(411\) 3.92823e6 + 6.80389e6i 1.14708 + 1.98679i
\(412\) −300555. −0.0872330
\(413\) −978647. + 237491.i −0.282326 + 0.0685129i
\(414\) 2.04035e6 0.585066
\(415\) 875023. + 1.51558e6i 0.249402 + 0.431976i
\(416\) 2.79052e6 4.83332e6i 0.790591 1.36934i
\(417\) −3.29178e6 + 5.70153e6i −0.927024 + 1.60565i
\(418\) −628654. 1.08886e6i −0.175983 0.304812i
\(419\) 1.67370e6 0.465739 0.232869 0.972508i \(-0.425189\pi\)
0.232869 + 0.972508i \(0.425189\pi\)
\(420\) 1.95433e6 474262.i 0.540597 0.131188i
\(421\) 3.23947e6 0.890776 0.445388 0.895338i \(-0.353066\pi\)
0.445388 + 0.895338i \(0.353066\pi\)
\(422\) 583327. + 1.01035e6i 0.159452 + 0.276179i
\(423\) −4.95601e6 + 8.58405e6i −1.34673 + 2.33261i
\(424\) −462090. + 800363.i −0.124828 + 0.216208i
\(425\) 230092. + 398530.i 0.0617914 + 0.107026i
\(426\) 2.69568e6 0.719687
\(427\) −689219. + 2.34788e6i −0.182931 + 0.623170i
\(428\) −1.65703e6 −0.437242
\(429\) −5.25969e6 9.11006e6i −1.37980 2.38989i
\(430\) 137538. 238223.i 0.0358716 0.0621315i
\(431\) −1.58160e6 + 2.73941e6i −0.410112 + 0.710335i −0.994902 0.100850i \(-0.967844\pi\)
0.584789 + 0.811185i \(0.301177\pi\)
\(432\) −745825. 1.29181e6i −0.192277 0.333034i
\(433\) −5.42491e6 −1.39050 −0.695252 0.718766i \(-0.744707\pi\)
−0.695252 + 0.718766i \(0.744707\pi\)
\(434\) −879331. 922085.i −0.224093 0.234988i
\(435\) 3.89220e6 0.986216
\(436\) 1.53256e6 + 2.65448e6i 0.386103 + 0.668749i
\(437\) 608882. 1.05461e6i 0.152521 0.264174i
\(438\) −1.62269e6 + 2.81058e6i −0.404157 + 0.700021i
\(439\) −253716. 439449.i −0.0628328 0.108830i 0.832898 0.553427i \(-0.186680\pi\)
−0.895731 + 0.444597i \(0.853347\pi\)
\(440\) −1.71552e6 −0.422438
\(441\) 7.97415e6 4.11240e6i 1.95249 1.00693i
\(442\) 2.13979e6 0.520972
\(443\) 1.69198e6 + 2.93059e6i 0.409624 + 0.709490i 0.994848 0.101382i \(-0.0323266\pi\)
−0.585223 + 0.810872i \(0.698993\pi\)
\(444\) −2.98265e6 + 5.16609e6i −0.718033 + 1.24367i
\(445\) −98802.1 + 171130.i −0.0236519 + 0.0409663i
\(446\) −851562. 1.47495e6i −0.202712 0.351107i
\(447\) −714627. −0.169165
\(448\) −1.14624e6 1.20197e6i −0.269825 0.282944i
\(449\) 2.00014e6 0.468215 0.234108 0.972211i \(-0.424783\pi\)
0.234108 + 0.972211i \(0.424783\pi\)
\(450\) −520570. 901653.i −0.121185 0.209898i
\(451\) −2.97463e6 + 5.15221e6i −0.688639 + 1.19276i
\(452\) 693018. 1.20034e6i 0.159551 0.276350i
\(453\) −3.65924e6 6.33799e6i −0.837810 1.45113i
\(454\) −384685. −0.0875922
\(455\) −850183. + 2.89622e6i −0.192524 + 0.655848i
\(456\) 4.69217e6 1.05672
\(457\) 592334. + 1.02595e6i 0.132671 + 0.229793i 0.924705 0.380684i \(-0.124311\pi\)
−0.792034 + 0.610476i \(0.790978\pi\)
\(458\) −1.68247e6 + 2.91412e6i −0.374785 + 0.649147i
\(459\) 2.98419e6 5.16878e6i 0.661143 1.14513i
\(460\) −340848. 590366.i −0.0751045 0.130085i
\(461\) −8.48869e6 −1.86032 −0.930161 0.367152i \(-0.880333\pi\)
−0.930161 + 0.367152i \(0.880333\pi\)
\(462\) −4.44057e6 + 1.07760e6i −0.967907 + 0.234885i
\(463\) 4.81635e6 1.04416 0.522079 0.852897i \(-0.325157\pi\)
0.522079 + 0.852897i \(0.325157\pi\)
\(464\) 513952. + 890190.i 0.110822 + 0.191950i
\(465\) 1.09730e6 1.90058e6i 0.235339 0.407619i
\(466\) −220320. + 381606.i −0.0469991 + 0.0814048i
\(467\) 2.27367e6 + 3.93812e6i 0.482431 + 0.835596i 0.999797 0.0201689i \(-0.00642040\pi\)
−0.517365 + 0.855765i \(0.673087\pi\)
\(468\) 1.10681e7 2.33593
\(469\) −8.40378e6 + 2.03937e6i −1.76418 + 0.428118i
\(470\) −1.44851e6 −0.302466
\(471\) −3.65486e6 6.33040e6i −0.759134 1.31486i
\(472\) −657658. + 1.13910e6i −0.135877 + 0.235346i
\(473\) 714479. 1.23751e6i 0.146837 0.254330i
\(474\) 681067. + 1.17964e6i 0.139234 + 0.241160i
\(475\) −621393. −0.126367
\(476\) −598551. + 2.03901e6i −0.121083 + 0.412480i
\(477\) −2.91365e6 −0.586329
\(478\) 793629. + 1.37461e6i 0.158872 + 0.275175i
\(479\) 4.37224e6 7.57295e6i 0.870694 1.50809i 0.00941398 0.999956i \(-0.497003\pi\)
0.861280 0.508131i \(-0.169663\pi\)
\(480\) 2.08782e6 3.61621e6i 0.413609 0.716392i
\(481\) −4.47672e6 7.75390e6i −0.882261 1.52812i
\(482\) −80184.6 −0.0157208
\(483\) −3.05434e6 3.20284e6i −0.595729 0.624694i
\(484\) −70855.8 −0.0137487
\(485\) −1.86823e6 3.23587e6i −0.360642 0.624650i
\(486\) −1.11041e6 + 1.92330e6i −0.213253 + 0.369365i
\(487\) 4.52775e6 7.84230e6i 0.865088 1.49838i −0.00187155 0.999998i \(-0.500596\pi\)
0.866960 0.498378i \(-0.166071\pi\)
\(488\) 1.59799e6 + 2.76780e6i 0.303756 + 0.526121i
\(489\) 7.95408e6 1.50424
\(490\) 1.10312e6 + 708707.i 0.207554 + 0.133345i
\(491\) −4.29340e6 −0.803706 −0.401853 0.915704i \(-0.631634\pi\)
−0.401853 + 0.915704i \(0.631634\pi\)
\(492\) −4.55448e6 7.88859e6i −0.848255 1.46922i
\(493\) −2.05642e6 + 3.56183e6i −0.381061 + 0.660018i
\(494\) −1.44469e6 + 2.50228e6i −0.266354 + 0.461338i
\(495\) −2.70425e6 4.68389e6i −0.496059 0.859199i
\(496\) 579579. 0.105781
\(497\) −2.77304e6 2.90787e6i −0.503577 0.528061i
\(498\) 6.08832e6 1.10008
\(499\) 1.82917e6 + 3.16822e6i 0.328855 + 0.569593i 0.982285 0.187394i \(-0.0600041\pi\)
−0.653430 + 0.756987i \(0.726671\pi\)
\(500\) −173926. + 301248.i −0.0311128 + 0.0538889i
\(501\) −6.50990e6 + 1.12755e7i −1.15872 + 2.00697i
\(502\) 48273.1 + 83611.5i 0.00854960 + 0.0148083i
\(503\) −248395. −0.0437746 −0.0218873 0.999760i \(-0.506968\pi\)
−0.0218873 + 0.999760i \(0.506968\pi\)
\(504\) 3.30070e6 1.12441e7i 0.578801 1.97173i
\(505\) 3.17331e6 0.553713
\(506\) 774465. + 1.34141e6i 0.134470 + 0.232909i
\(507\) −6.91289e6 + 1.19735e7i −1.19437 + 2.06871i
\(508\) −2.94267e6 + 5.09686e6i −0.505921 + 0.876281i
\(509\) −4.06027e6 7.03259e6i −0.694640 1.20315i −0.970302 0.241898i \(-0.922230\pi\)
0.275661 0.961255i \(-0.411103\pi\)
\(510\) 1.60095e6 0.272554
\(511\) 4.70108e6 1.14082e6i 0.796426 0.193271i
\(512\) 2.09985e6 0.354008
\(513\) 4.02961e6 + 6.97949e6i 0.676036 + 1.17093i
\(514\) −399594. + 692117.i −0.0667131 + 0.115551i
\(515\) 168756. 292294.i 0.0280377 0.0485627i
\(516\) 1.09395e6 + 1.89477e6i 0.180872 + 0.313280i
\(517\) −7.52468e6 −1.23812
\(518\) −3.77953e6 + 917189.i −0.618890 + 0.150188i
\(519\) −840731. −0.137006
\(520\) 1.97119e6 + 3.41421e6i 0.319684 + 0.553709i
\(521\) −3.51230e6 + 6.08349e6i −0.566889 + 0.981880i 0.429982 + 0.902837i \(0.358520\pi\)
−0.996871 + 0.0790430i \(0.974814\pi\)
\(522\) 4.65254e6 8.05844e6i 0.747333 1.29442i
\(523\) 201663. + 349290.i 0.0322382 + 0.0558382i 0.881694 0.471821i \(-0.156403\pi\)
−0.849456 + 0.527659i \(0.823070\pi\)
\(524\) −2.44875e6 −0.389598
\(525\) −636093. + 2.16690e6i −0.100722 + 0.343116i
\(526\) 3.18522e6 0.501968
\(527\) 1.15951e6 + 2.00832e6i 0.181864 + 0.314997i
\(528\) 1.03926e6 1.80006e6i 0.162234 0.280997i
\(529\) 2.46806e6 4.27481e6i 0.383458 0.664168i
\(530\) −212895. 368746.i −0.0329213 0.0570213i
\(531\) −4.14679e6 −0.638227
\(532\) −1.98033e6 2.07661e6i −0.303359 0.318109i
\(533\) 1.36718e7 2.08453
\(534\) 343727. + 595353.i 0.0521628 + 0.0903486i
\(535\) 930395. 1.61149e6i 0.140534 0.243413i
\(536\) −5.64740e6 + 9.78158e6i −0.849056 + 1.47061i
\(537\) 8.28315e6 + 1.43468e7i 1.23954 + 2.14694i
\(538\) −1.54079e6 −0.229503
\(539\) 5.73044e6 + 3.68158e6i 0.849603 + 0.545836i
\(540\) 4.51149e6 0.665788
\(541\) −643040. 1.11378e6i −0.0944593 0.163608i 0.814924 0.579568i \(-0.196779\pi\)
−0.909383 + 0.415960i \(0.863446\pi\)
\(542\) 2.30260e6 3.98822e6i 0.336683 0.583151i
\(543\) −2.16330e6 + 3.74694e6i −0.314859 + 0.545352i
\(544\) 2.20618e6 + 3.82121e6i 0.319627 + 0.553610i
\(545\) −3.44203e6 −0.496391
\(546\) 7.24702e6 + 7.59938e6i 1.04035 + 1.09093i
\(547\) −7.76839e6 −1.11010 −0.555051 0.831816i \(-0.687301\pi\)
−0.555051 + 0.831816i \(0.687301\pi\)
\(548\) −3.13767e6 5.43460e6i −0.446329 0.773065i
\(549\) −5.03797e6 + 8.72602e6i −0.713386 + 1.23562i
\(550\) 395189. 684488.i 0.0557055 0.0964848i
\(551\) −2.77682e6 4.80960e6i −0.389645 0.674885i
\(552\) −5.78048e6 −0.807451
\(553\) 571885. 1.94818e6i 0.0795236 0.270904i
\(554\) −2.73952e6 −0.379228
\(555\) −3.34941e6 5.80134e6i −0.461568 0.799459i
\(556\) 2.62931e6 4.55409e6i 0.360707 0.624762i
\(557\) 3.33475e6 5.77595e6i 0.455433 0.788834i −0.543280 0.839552i \(-0.682818\pi\)
0.998713 + 0.0507181i \(0.0161510\pi\)
\(558\) −2.62332e6 4.54372e6i −0.356669 0.617769i
\(559\) −3.28386e6 −0.444482
\(560\) −579589. + 140651.i −0.0780999 + 0.0189527i
\(561\) 8.31659e6 1.11568
\(562\) 2.28729e6 + 3.96171e6i 0.305479 + 0.529105i
\(563\) 853267. 1.47790e6i 0.113452 0.196505i −0.803708 0.595024i \(-0.797142\pi\)
0.917160 + 0.398519i \(0.130476\pi\)
\(564\) 5.76055e6 9.97757e6i 0.762547 1.32077i
\(565\) 778235. + 1.34794e6i 0.102563 + 0.177644i
\(566\) 5.40183e6 0.708761
\(567\) 1.21206e7 2.94135e6i 1.58332 0.384228i
\(568\) −5.24812e6 −0.682548
\(569\) 1.10864e6 + 1.92022e6i 0.143552 + 0.248639i 0.928832 0.370502i \(-0.120814\pi\)
−0.785280 + 0.619141i \(0.787481\pi\)
\(570\) −1.08090e6 + 1.87217e6i −0.139347 + 0.241356i
\(571\) 3.18782e6 5.52146e6i 0.409169 0.708702i −0.585628 0.810580i \(-0.699152\pi\)
0.994797 + 0.101878i \(0.0324853\pi\)
\(572\) 4.20117e6 + 7.27665e6i 0.536884 + 0.929910i
\(573\) 8.94573e6 1.13823
\(574\) 1.67275e6 5.69838e6i 0.211911 0.721891i
\(575\) 765520. 0.0965578
\(576\) −3.41960e6 5.92292e6i −0.429456 0.743840i
\(577\) 1.45598e6 2.52184e6i 0.182061 0.315339i −0.760521 0.649313i \(-0.775056\pi\)
0.942582 + 0.333974i \(0.108390\pi\)
\(578\) 1.36948e6 2.37200e6i 0.170504 0.295322i
\(579\) 1.01346e7 + 1.75537e7i 1.25635 + 2.17607i
\(580\) −3.10889e6 −0.383738
\(581\) −6.26305e6 6.56756e6i −0.769743 0.807168i
\(582\) −1.29989e7 −1.59075
\(583\) −1.10595e6 1.91555e6i −0.134760 0.233412i
\(584\) 3.15916e6 5.47183e6i 0.383301 0.663896i
\(585\) −6.21456e6 + 1.07639e7i −0.750794 + 1.30041i
\(586\) 973169. + 1.68558e6i 0.117070 + 0.202770i
\(587\) 1.61871e7 1.93899 0.969494 0.245116i \(-0.0788259\pi\)
0.969494 + 0.245116i \(0.0788259\pi\)
\(588\) −9.26866e6 + 4.78000e6i −1.10554 + 0.570144i
\(589\) −3.13140e6 −0.371921
\(590\) −302999. 524809.i −0.0358353 0.0620685i
\(591\) 1.04926e7 1.81737e7i 1.23570 2.14030i
\(592\) 884555. 1.53209e6i 0.103734 0.179672i
\(593\) 4.17033e6 + 7.22322e6i 0.487005 + 0.843517i 0.999888 0.0149411i \(-0.00475608\pi\)
−0.512884 + 0.858458i \(0.671423\pi\)
\(594\) −1.02509e7 −1.19205
\(595\) −1.64690e6 1.72697e6i −0.190710 0.199983i
\(596\) 570807. 0.0658224
\(597\) −1.34670e6 2.33255e6i −0.154644 0.267852i
\(598\) 1.77978e6 3.08267e6i 0.203523 0.352512i
\(599\) −7.04980e6 + 1.22106e7i −0.802805 + 1.39050i 0.114958 + 0.993370i \(0.463327\pi\)
−0.917763 + 0.397128i \(0.870007\pi\)
\(600\) 1.47481e6 + 2.55445e6i 0.167247 + 0.289681i
\(601\) −6.75584e6 −0.762945 −0.381472 0.924380i \(-0.624583\pi\)
−0.381472 + 0.924380i \(0.624583\pi\)
\(602\) −401781. + 1.36870e6i −0.0451854 + 0.153928i
\(603\) −3.56090e7 −3.98810
\(604\) 2.92281e6 + 5.06246e6i 0.325993 + 0.564637i
\(605\) 39784.3 68908.4i 0.00441899 0.00765392i
\(606\) 5.51989e6 9.56073e6i 0.610589 1.05757i
\(607\) −6.01038e6 1.04103e7i −0.662110 1.14681i −0.980060 0.198701i \(-0.936328\pi\)
0.317950 0.948108i \(-0.397006\pi\)
\(608\) −5.95808e6 −0.653653
\(609\) −1.96144e7 + 4.75988e6i −2.14305 + 0.520059i
\(610\) −1.47246e6 −0.160221
\(611\) 8.64614e6 + 1.49756e7i 0.936956 + 1.62286i
\(612\) −4.37521e6 + 7.57809e6i −0.472194 + 0.817865i
\(613\) 729703. 1.26388e6i 0.0784323 0.135849i −0.824141 0.566384i \(-0.808342\pi\)
0.902574 + 0.430535i \(0.141675\pi\)
\(614\) 3.00031e6 + 5.19669e6i 0.321178 + 0.556296i
\(615\) 1.02290e7 1.09055
\(616\) 8.64519e6 2.09795e6i 0.917958 0.222763i
\(617\) −6.88916e6 −0.728540 −0.364270 0.931293i \(-0.618681\pi\)
−0.364270 + 0.931293i \(0.618681\pi\)
\(618\) −587094. 1.01688e6i −0.0618353 0.107102i
\(619\) 5.85438e6 1.01401e7i 0.614121 1.06369i −0.376417 0.926451i \(-0.622844\pi\)
0.990538 0.137239i \(-0.0438228\pi\)
\(620\) −876468. + 1.51809e6i −0.0915707 + 0.158605i
\(621\) −4.96425e6 8.59833e6i −0.516564 0.894715i
\(622\) 6.56255e6 0.680137
\(623\) 288624. 983223.i 0.0297929 0.101492i
\(624\) −4.77661e6 −0.491087
\(625\) −195312. 338291.i −0.0200000 0.0346410i
\(626\) −4.28057e6 + 7.41416e6i −0.436582 + 0.756182i
\(627\) −5.61502e6 + 9.72550e6i −0.570404 + 0.987968i
\(628\) 2.91931e6 + 5.05640e6i 0.295380 + 0.511614i
\(629\) 7.07856e6 0.713375
\(630\) 3.72602e6 + 3.90718e6i 0.374019 + 0.392204i
\(631\) 2.08769e6 0.208734 0.104367 0.994539i \(-0.466718\pi\)
0.104367 + 0.994539i \(0.466718\pi\)
\(632\) −1.32595e6 2.29661e6i −0.132048 0.228715i
\(633\) 5.21017e6 9.02427e6i 0.516824 0.895165i
\(634\) 2.35926e6 4.08636e6i 0.233106 0.403751i
\(635\) −3.30452e6 5.72359e6i −0.325217 0.563293i
\(636\) 3.38665e6 0.331992
\(637\) 742553. 1.56350e7i 0.0725068 1.52668i
\(638\) 7.06394e6 0.687061
\(639\) −8.27285e6 1.43290e7i −0.801499 1.38824i
\(640\) −1.89734e6 + 3.28628e6i −0.183102 + 0.317143i
\(641\) −6.28598e6 + 1.08876e7i −0.604266 + 1.04662i 0.387901 + 0.921701i \(0.373200\pi\)
−0.992167 + 0.124918i \(0.960133\pi\)
\(642\) −3.23679e6 5.60629e6i −0.309940 0.536831i
\(643\) −5.47387e6 −0.522116 −0.261058 0.965323i \(-0.584071\pi\)
−0.261058 + 0.965323i \(0.584071\pi\)
\(644\) 2.43965e6 + 2.55826e6i 0.231799 + 0.243069i
\(645\) −2.45693e6 −0.232537
\(646\) −1.14217e6 1.97830e6i −0.107684 0.186514i
\(647\) −16516.5 + 28607.5i −0.00155116 + 0.00268670i −0.866800 0.498656i \(-0.833827\pi\)
0.865249 + 0.501343i \(0.167160\pi\)
\(648\) 8.14516e6 1.41078e7i 0.762012 1.31984i
\(649\) −1.57401e6 2.72627e6i −0.146688 0.254072i
\(650\) −1.81635e6 −0.168623
\(651\) −3.20548e6 + 1.09197e7i −0.296442 + 1.00986i
\(652\) −6.35331e6 −0.585303
\(653\) −3.39385e6 5.87832e6i −0.311465 0.539473i 0.667215 0.744866i \(-0.267486\pi\)
−0.978680 + 0.205392i \(0.934153\pi\)
\(654\) −5.98732e6 + 1.03703e7i −0.547379 + 0.948089i
\(655\) 1.37493e6 2.38145e6i 0.125221 0.216889i
\(656\) 1.35071e6 + 2.33950e6i 0.122547 + 0.212258i
\(657\) 1.99197e7 1.80040
\(658\) 7.29962e6 1.77142e6i 0.657258 0.159499i
\(659\) 1.30322e7 1.16898 0.584488 0.811403i \(-0.301296\pi\)
0.584488 + 0.811403i \(0.301296\pi\)
\(660\) 3.14325e6 + 5.44426e6i 0.280879 + 0.486496i
\(661\) 7.90405e6 1.36902e7i 0.703632 1.21873i −0.263551 0.964646i \(-0.584894\pi\)
0.967183 0.254081i \(-0.0817731\pi\)
\(662\) −1.22133e6 + 2.11540e6i −0.108315 + 0.187607i
\(663\) −9.55608e6 1.65516e7i −0.844299 1.46237i
\(664\) −1.18531e7 −1.04331
\(665\) 3.13145e6 759919.i 0.274595 0.0666366i
\(666\) −1.60149e7 −1.39906
\(667\) 3.42088e6 + 5.92514e6i 0.297731 + 0.515685i
\(668\) 5.19978e6 9.00628e6i 0.450862 0.780916i
\(669\) −7.60600e6 + 1.31740e7i −0.657039 + 1.13802i
\(670\) −2.60189e6 4.50660e6i −0.223925 0.387849i
\(671\) −7.64912e6 −0.655851
\(672\) −6.09902e6 + 2.07768e7i −0.520999 + 1.77483i
\(673\) 1.94847e7 1.65827 0.829137 0.559045i \(-0.188832\pi\)
0.829137 + 0.559045i \(0.188832\pi\)
\(674\) 4.66276e6 + 8.07614e6i 0.395361 + 0.684784i
\(675\) −2.53312e6 + 4.38750e6i −0.213992 + 0.370645i
\(676\) 5.52166e6 9.56380e6i 0.464733 0.804941i
\(677\) −3.98541e6 6.90293e6i −0.334196 0.578844i 0.649134 0.760674i \(-0.275131\pi\)
−0.983330 + 0.181830i \(0.941798\pi\)
\(678\) 5.41487e6 0.452391
\(679\) 1.33720e7 + 1.40222e7i 1.11307 + 1.16719i
\(680\) −3.11684e6 −0.258489
\(681\) 1.71797e6 + 2.97560e6i 0.141954 + 0.245871i
\(682\) 1.99149e6 3.44936e6i 0.163952 0.283973i
\(683\) 4.96510e6 8.59980e6i 0.407264 0.705402i −0.587318 0.809356i \(-0.699816\pi\)
0.994582 + 0.103954i \(0.0331495\pi\)
\(684\) −5.90793e6 1.02328e7i −0.482831 0.836287i
\(685\) 7.04698e6 0.573821
\(686\) −6.42575e6 2.22244e6i −0.521331 0.180310i
\(687\) 3.00549e7 2.42954
\(688\) −324429. 561927.i −0.0261305 0.0452594i
\(689\) −2.54155e6 + 4.40209e6i −0.203962 + 0.353273i
\(690\) 1.33160e6 2.30640e6i 0.106476 0.184422i
\(691\) −3.19613e6 5.53586e6i −0.254642 0.441053i 0.710156 0.704044i \(-0.248624\pi\)
−0.964798 + 0.262991i \(0.915291\pi\)
\(692\) 671532. 0.0533091
\(693\) 1.93559e7 + 2.02969e7i 1.53101 + 1.60545i
\(694\) −1.91618e6 −0.151021
\(695\) 2.95262e6 + 5.11408e6i 0.231870 + 0.401611i
\(696\) −1.31810e7 + 2.28302e7i −1.03140 + 1.78643i
\(697\) −5.40446e6 + 9.36080e6i −0.421376 + 0.729845i
\(698\) 5.21319e6 + 9.02951e6i 0.405009 + 0.701497i
\(699\) 3.93572e6 0.304671
\(700\) 508078. 1.73081e6i 0.0391909 0.133507i
\(701\) −5.78581e6 −0.444702 −0.222351 0.974967i \(-0.571373\pi\)
−0.222351 + 0.974967i \(0.571373\pi\)
\(702\) 1.17787e7 + 2.04013e7i 0.902097 + 1.56248i
\(703\) −4.77915e6 + 8.27773e6i −0.364722 + 0.631717i
\(704\) 2.59598e6 4.49637e6i 0.197410 0.341925i
\(705\) 6.46890e6 + 1.12045e7i 0.490182 + 0.849021i
\(706\) −1.13001e7 −0.853235
\(707\) −1.59916e7 + 3.88073e6i −1.20322 + 0.291988i
\(708\) 4.81997e6 0.361377
\(709\) 1.21294e7 + 2.10087e7i 0.906198 + 1.56958i 0.819301 + 0.573364i \(0.194362\pi\)
0.0868970 + 0.996217i \(0.472305\pi\)
\(710\) 1.20897e6 2.09399e6i 0.0900053 0.155894i
\(711\) 4.18030e6 7.24049e6i 0.310122 0.537148i
\(712\) −669191. 1.15907e6i −0.0494709 0.0856861i
\(713\) 3.85770e6 0.284188
\(714\) −8.06785e6 + 1.95785e6i −0.592260 + 0.143725i
\(715\) −9.43554e6 −0.690243
\(716\) −6.61615e6 1.14595e7i −0.482306 0.835379i
\(717\) 7.08854e6 1.22777e7i 0.514943 0.891907i
\(718\) −5.58950e6 + 9.68130e6i −0.404634 + 0.700846i
\(719\) −3.35317e6 5.80786e6i −0.241898 0.418980i 0.719357 0.694641i \(-0.244437\pi\)
−0.961255 + 0.275661i \(0.911103\pi\)
\(720\) −2.45587e6 −0.176553
\(721\) −492977. + 1.67937e6i −0.0353174 + 0.120312i
\(722\) −4.64208e6 −0.331413
\(723\) 358097. + 620242.i 0.0254774 + 0.0441281i
\(724\) 1.72793e6 2.99286e6i 0.122512 0.212197i
\(725\) 1.74559e6 3.02345e6i 0.123338 0.213628i
\(726\) −138407. 239729.i −0.00974581 0.0168802i
\(727\) −1.44972e7 −1.01730 −0.508649 0.860974i \(-0.669855\pi\)
−0.508649 + 0.860974i \(0.669855\pi\)
\(728\) −1.41090e7 1.47950e7i −0.986659 1.03463i
\(729\) −3.54221e6 −0.246863
\(730\) 1.45550e6 + 2.52100e6i 0.101089 + 0.175092i
\(731\) 1.29810e6 2.24838e6i 0.0898495 0.155624i
\(732\) 5.85582e6 1.01426e7i 0.403934 0.699634i
\(733\) −5.36265e6 9.28837e6i −0.368654 0.638528i 0.620701 0.784047i \(-0.286848\pi\)
−0.989355 + 0.145519i \(0.953515\pi\)
\(734\) 8.98795e6 0.615773
\(735\) 555566. 1.16978e7i 0.0379330 0.798705i
\(736\) 7.34001e6 0.499461
\(737\) −1.35162e7 2.34108e7i −0.916616 1.58762i
\(738\) 1.22273e7 2.11783e7i 0.826399 1.43136i
\(739\) 1.77352e6 3.07182e6i 0.119461 0.206912i −0.800093 0.599875i \(-0.795217\pi\)
0.919554 + 0.392964i \(0.128550\pi\)
\(740\) 2.67533e6 + 4.63381e6i 0.179597 + 0.311071i
\(741\) 2.58075e7 1.72663
\(742\) 1.52382e6 + 1.59791e6i 0.101607 + 0.106547i
\(743\) −8.10764e6 −0.538794 −0.269397 0.963029i \(-0.586824\pi\)
−0.269397 + 0.963029i \(0.586824\pi\)
\(744\) 7.43207e6 + 1.28727e7i 0.492240 + 0.852585i
\(745\) −320498. + 555119.i −0.0211561 + 0.0366434i
\(746\) 6.11317e6 1.05883e7i 0.402179 0.696594i
\(747\) −1.86846e7 3.23627e7i −1.22513 2.12199i
\(748\) −6.64287e6 −0.434112
\(749\) −2.71790e6 + 9.25877e6i −0.177023 + 0.603043i
\(750\) −1.35896e6 −0.0882175
\(751\) 1.21987e7 + 2.11288e7i 0.789250 + 1.36702i 0.926427 + 0.376474i \(0.122864\pi\)
−0.137177 + 0.990547i \(0.543803\pi\)
\(752\) −1.70839e6 + 2.95902e6i −0.110165 + 0.190811i
\(753\) 431166. 746802.i 0.0277113 0.0479975i
\(754\) −8.11673e6 1.40586e7i −0.519939 0.900562i
\(755\) −6.56443e6 −0.419112
\(756\) −2.27353e7 + 5.51723e6i −1.44676 + 0.351088i
\(757\) −9.35579e6 −0.593391 −0.296695 0.954972i \(-0.595885\pi\)
−0.296695 + 0.954972i \(0.595885\pi\)
\(758\) 1.24190e6 + 2.15104e6i 0.0785082 + 0.135980i
\(759\) 6.91738e6 1.19813e7i 0.435850 0.754915i
\(760\) 2.10436e6 3.64486e6i 0.132156 0.228900i
\(761\) 8.68869e6 + 1.50493e7i 0.543867 + 0.942005i 0.998677 + 0.0514170i \(0.0163738\pi\)
−0.454810 + 0.890588i \(0.650293\pi\)
\(762\) −2.29925e7 −1.43449
\(763\) 1.73458e7 4.20936e6i 1.07866 0.261761i
\(764\) −7.14539e6 −0.442886
\(765\) −4.91321e6 8.50993e6i −0.303537 0.525742i
\(766\) −3.16068e6 + 5.47446e6i −0.194630 + 0.337108i
\(767\) −3.61720e6 + 6.26517e6i −0.222016 + 0.384543i
\(768\) 1.23140e7 + 2.13285e7i 0.753348 + 1.30484i
\(769\) 4.58080e6 0.279335 0.139667 0.990198i \(-0.455397\pi\)
0.139667 + 0.990198i \(0.455397\pi\)
\(770\) −1.15444e6 + 3.93270e6i −0.0701690 + 0.239037i
\(771\) 7.13820e6 0.432467
\(772\) −8.09503e6 1.40210e7i −0.488850 0.846713i
\(773\) −1.18714e7 + 2.05619e7i −0.714585 + 1.23770i 0.248534 + 0.968623i \(0.420051\pi\)
−0.963119 + 0.269075i \(0.913282\pi\)
\(774\) −2.93689e6 + 5.08684e6i −0.176212 + 0.305208i
\(775\) −984243. 1.70476e6i −0.0588638 0.101955i
\(776\) 2.53072e7 1.50866
\(777\) 2.39737e7 + 2.51393e7i 1.42456 + 1.49383i
\(778\) −8.12326e6 −0.481151
\(779\) −7.29773e6 1.26400e7i −0.430868 0.746285i
\(780\) 7.22342e6 1.25113e7i 0.425115 0.736321i
\(781\) 6.28031e6 1.08778e7i 0.368429 0.638138i
\(782\) 1.40709e6 + 2.43715e6i 0.0822819 + 0.142516i
\(783\) −4.52791e7 −2.63933
\(784\) 2.74878e6 1.41759e6i 0.159717 0.0823684i
\(785\) −6.55657e6 −0.379754
\(786\) −4.78331e6 8.28494e6i −0.276167 0.478336i
\(787\) −7.41205e6 + 1.28381e7i −0.426581 + 0.738860i −0.996567 0.0827946i \(-0.973615\pi\)
0.569986 + 0.821655i \(0.306949\pi\)
\(788\) −8.38093e6 + 1.45162e7i −0.480813 + 0.832793i
\(789\) −1.42249e7 2.46383e7i −0.813499 1.40902i
\(790\) 1.22179e6 0.0696512
\(791\) −5.57028e6 5.84111e6i −0.316545 0.331936i
\(792\) 3.66319e7 2.07514
\(793\) 8.78914e6 + 1.52232e7i 0.496322 + 0.859654i
\(794\) 8.06296e6 1.39655e7i 0.453882 0.786147i
\(795\) −1.90154e6 + 3.29357e6i −0.106706 + 0.184820i
\(796\) 1.07567e6 + 1.86312e6i 0.0601724 + 0.104222i
\(797\) −1.29629e7 −0.722866 −0.361433 0.932398i \(-0.617712\pi\)
−0.361433 + 0.932398i \(0.617712\pi\)
\(798\) 3.15755e6 1.07565e7i 0.175527 0.597947i
\(799\) −1.36712e7 −0.757601
\(800\) −1.87271e6 3.24362e6i −0.103453 0.179187i
\(801\) 2.10975e6 3.65420e6i 0.116185 0.201238i
\(802\) −2.10730e6 + 3.64995e6i −0.115688 + 0.200378i
\(803\) 7.56100e6 + 1.30960e7i 0.413800 + 0.716722i
\(804\) 4.13897e7 2.25815
\(805\) −3.85777e6 + 936176.i −0.209820 + 0.0509176i
\(806\) −9.15318e6 −0.496288
\(807\) 6.88105e6 + 1.19183e7i 0.371938 + 0.644216i
\(808\) −1.07465e7 + 1.86135e7i −0.579079 + 1.00300i
\(809\) −1.50010e7 + 2.59826e7i −0.805843 + 1.39576i 0.109878 + 0.993945i \(0.464954\pi\)
−0.915721 + 0.401815i \(0.868379\pi\)
\(810\) 3.75266e6 + 6.49981e6i 0.200968 + 0.348087i
\(811\) −9.00717e6 −0.480880 −0.240440 0.970664i \(-0.577292\pi\)
−0.240440 + 0.970664i \(0.577292\pi\)
\(812\) 1.56670e7 3.80195e6i 0.833863 0.202356i
\(813\) −4.11328e7 −2.18254
\(814\) −6.07882e6 1.05288e7i −0.321557 0.556953i
\(815\) 3.56727e6 6.17870e6i 0.188123 0.325839i
\(816\) 1.88819e6 3.27044e6i 0.0992703 0.171941i
\(817\) 1.75285e6 + 3.03603e6i 0.0918734 + 0.159129i
\(818\) −8.66885e6 −0.452979
\(819\) 1.81542e7 6.18439e7i 0.945731 3.22171i
\(820\) −8.17044e6 −0.424337
\(821\) −1.55118e7 2.68672e7i −0.803163 1.39112i −0.917524 0.397679i \(-0.869816\pi\)
0.114362 0.993439i \(-0.463518\pi\)
\(822\) 1.22580e7 2.12315e7i 0.632763 1.09598i
\(823\) −5.91942e6 + 1.02527e7i −0.304635 + 0.527643i −0.977180 0.212413i \(-0.931868\pi\)
0.672545 + 0.740056i \(0.265201\pi\)
\(824\) 1.14299e6 + 1.97972e6i 0.0586443 + 0.101575i
\(825\) −7.05952e6 −0.361110
\(826\) 2.16874e6 + 2.27418e6i 0.110600 + 0.115978i
\(827\) 3.17753e7 1.61557 0.807785 0.589478i \(-0.200666\pi\)
0.807785 + 0.589478i \(0.200666\pi\)
\(828\) 7.27822e6 + 1.26063e7i 0.368935 + 0.639014i
\(829\) −6.56550e6 + 1.13718e7i −0.331804 + 0.574702i −0.982866 0.184323i \(-0.940991\pi\)
0.651062 + 0.759025i \(0.274324\pi\)
\(830\) 2.73051e6 4.72938e6i 0.137578 0.238292i
\(831\) 1.22344e7 + 2.11907e7i 0.614585 + 1.06449i
\(832\) −1.19315e7 −0.597568
\(833\) 1.04114e7 + 6.68888e6i 0.519870 + 0.333996i
\(834\) 2.05440e7 1.02275
\(835\) 5.83917e6 + 1.01137e7i 0.289824 + 0.501990i
\(836\) 4.48499e6 7.76823e6i 0.221945 0.384420i
\(837\) −1.27652e7 + 2.21100e7i −0.629818 + 1.09088i
\(838\) −2.61139e6 4.52306e6i −0.128458 0.222496i
\(839\) 1.51638e7 0.743707 0.371853 0.928291i \(-0.378722\pi\)
0.371853 + 0.928291i \(0.378722\pi\)
\(840\) −1.05561e7 1.10693e7i −0.516185 0.541282i
\(841\) 1.06909e7 0.521224
\(842\) −5.05438e6 8.75444e6i −0.245690 0.425547i
\(843\) 2.04297e7 3.53853e7i 0.990132 1.71496i
\(844\) −4.16161e6 + 7.20812e6i −0.201097 + 0.348310i
\(845\) 6.20064e6 + 1.07398e7i 0.298741 + 0.517434i
\(846\) 3.09304e7 1.48580
\(847\) −116219. + 395911.i −0.00556634 + 0.0189622i
\(848\) −1.00437e6 −0.0479627
\(849\) −2.41241e7 4.17841e7i −1.14863 1.98949i
\(850\) 718000. 1.24361e6i 0.0340861 0.0590389i
\(851\) 5.88764e6 1.01977e7i 0.278687 0.482700i
\(852\) 9.61585e6 + 1.66551e7i 0.453825 + 0.786048i
\(853\) 1.27022e7 0.597733 0.298866 0.954295i \(-0.403392\pi\)
0.298866 + 0.954295i \(0.403392\pi\)
\(854\) 7.42035e6 1.80072e6i 0.348160 0.0844891i
\(855\) 1.32688e7 0.620749
\(856\) 6.30160e6 + 1.09147e7i 0.293945 + 0.509128i
\(857\) −1.26910e6 + 2.19814e6i −0.0590260 + 0.102236i −0.894028 0.448010i \(-0.852133\pi\)
0.835002 + 0.550246i \(0.185466\pi\)
\(858\) −1.64129e7 + 2.84279e7i −0.761143 + 1.31834i
\(859\) 913028. + 1.58141e6i 0.0422184 + 0.0731243i 0.886362 0.462992i \(-0.153224\pi\)
−0.844144 + 0.536116i \(0.819891\pi\)
\(860\) 1.96247e6 0.0904807
\(861\) −5.15484e7 + 1.25094e7i −2.36977 + 0.575080i
\(862\) 9.87075e6 0.452462
\(863\) −1.89628e7 3.28446e7i −0.866714 1.50119i −0.865335 0.501194i \(-0.832894\pi\)
−0.00137974 0.999999i \(-0.500439\pi\)
\(864\) −2.42883e7 + 4.20685e7i −1.10691 + 1.91722i
\(865\) −377054. + 653076.i −0.0171342 + 0.0296772i
\(866\) 8.46421e6 + 1.46604e7i 0.383523 + 0.664281i
\(867\) −2.44638e7 −1.10529
\(868\) 2.56037e6 8.72212e6i 0.115346 0.392937i
\(869\) 6.34693e6 0.285111
\(870\) −6.07280e6 1.05184e7i −0.272014 0.471142i
\(871\) −3.10614e7 + 5.37999e7i −1.38731 + 2.40290i
\(872\) 1.16565e7 2.01897e7i 0.519132 0.899163i
\(873\) 3.98929e7 + 6.90965e7i 1.77158 + 3.06846i
\(874\) −3.80003e6 −0.168271
\(875\) 1.39797e6 + 1.46593e6i 0.0617272 + 0.0647283i
\(876\) −2.31534e7 −1.01942
\(877\) 8.02684e6 + 1.39029e7i 0.352408 + 0.610388i 0.986671 0.162729i \(-0.0520297\pi\)
−0.634263 + 0.773117i \(0.718696\pi\)
\(878\) −791720. + 1.37130e6i −0.0346606 + 0.0600338i
\(879\) 8.69216e6 1.50553e7i 0.379451 0.657228i
\(880\) −932184. 1.61459e6i −0.0405784 0.0702839i
\(881\) −2.93698e6 −0.127486 −0.0637428 0.997966i \(-0.520304\pi\)
−0.0637428 + 0.997966i \(0.520304\pi\)
\(882\) −2.35551e7 1.51332e7i −1.01956 0.655029i
\(883\) 5.42066e6 0.233965 0.116982 0.993134i \(-0.462678\pi\)
0.116982 + 0.993134i \(0.462678\pi\)
\(884\) 7.63291e6 + 1.32206e7i 0.328518 + 0.569010i
\(885\) −2.70633e6 + 4.68750e6i −0.116151 + 0.201179i
\(886\) 5.27982e6 9.14491e6i 0.225961 0.391377i
\(887\) −1.96850e6 3.40955e6i −0.0840092 0.145508i 0.820959 0.570987i \(-0.193439\pi\)
−0.904969 + 0.425478i \(0.860106\pi\)
\(888\) 4.53713e7 1.93085
\(889\) 2.36524e7 + 2.48023e7i 1.00374 + 1.05254i
\(890\) 616624. 0.0260943
\(891\) 1.94943e7 + 3.37651e7i 0.822645 + 1.42486i
\(892\) 6.07528e6 1.05227e7i 0.255655 0.442807i
\(893\) 9.23024e6 1.59873e7i 0.387333 0.670880i
\(894\) 1.11500e6 + 1.93123e6i 0.0466584 + 0.0808146i
\(895\) 1.48594e7 0.620075
\(896\) 5.54257e6 1.88812e7i 0.230643 0.785706i
\(897\) −3.17933e7 −1.31933
\(898\) −3.12072e6 5.40525e6i −0.129141 0.223679i
\(899\) 8.79658e6 1.52361e7i 0.363007 0.628746i
\(900\) 3.71389e6 6.43264e6i 0.152835 0.264718i
\(901\) −2.00934e6 3.48028e6i −0.0824596 0.142824i
\(902\) 1.85646e7 0.759749
\(903\) 1.23815e7 3.00464e6i 0.505304 0.122623i
\(904\) −1.05420e7 −0.429045
\(905\) 1.94040e6 + 3.36088e6i 0.0787537 + 0.136405i
\(906\) −1.14187e7 + 1.97777e7i −0.462162 + 0.800488i
\(907\) −976709. + 1.69171e6i −0.0394228 + 0.0682822i −0.885064 0.465470i \(-0.845885\pi\)
0.845641 + 0.533752i \(0.179219\pi\)
\(908\) −1.37222e6 2.37676e6i −0.0552344 0.0956689i
\(909\) −6.77607e7 −2.72000
\(910\) 9.15333e6 2.22126e6i 0.366417 0.0889195i
\(911\) 3.17289e7 1.26666 0.633329 0.773882i \(-0.281688\pi\)
0.633329 + 0.773882i \(0.281688\pi\)
\(912\) 2.54965e6 + 4.41612e6i 0.101506 + 0.175814i
\(913\) 1.41844e7 2.45681e7i 0.563163 0.975426i
\(914\) 1.84838e6 3.20148e6i 0.0731855 0.126761i
\(915\) 6.57589e6 + 1.13898e7i 0.259658 + 0.449741i
\(916\) −2.40063e7 −0.945338
\(917\) −4.01650e6 + 1.36825e7i −0.157734 + 0.537333i
\(918\) −1.86243e7 −0.729415
\(919\) 245575. + 425348.i 0.00959169 + 0.0166133i 0.870781 0.491670i \(-0.163613\pi\)
−0.861190 + 0.508284i \(0.830280\pi\)
\(920\) −2.59245e6 + 4.49026e6i −0.100981 + 0.174905i
\(921\) 2.67982e7 4.64159e7i 1.04101 1.80309i
\(922\) 1.32445e7 + 2.29401e7i 0.513106 + 0.888726i
\(923\) −2.88653e7 −1.11525
\(924\) −2.24981e7 2.35919e7i −0.866892 0.909041i
\(925\) −6.00861e6 −0.230898
\(926\) −7.51471e6 1.30159e7i −0.287995 0.498822i
\(927\) −3.60350e6 + 6.24145e6i −0.137729 + 0.238554i
\(928\) 1.67371e7 2.89896e7i 0.637986 1.10502i
\(929\) −1.38975e7 2.40712e7i −0.528320 0.915077i −0.999455 0.0330157i \(-0.989489\pi\)
0.471135 0.882061i \(-0.343844\pi\)
\(930\) −6.84825e6 −0.259641
\(931\) −1.48514e7 + 7.65908e6i −0.561554 + 0.289603i
\(932\) −3.14365e6 −0.118548
\(933\) −2.93077e7 5.07625e7i −1.10225 1.90914i
\(934\) 7.09499e6 1.22889e7i 0.266124 0.460941i
\(935\) 3.72985e6 6.46030e6i 0.139528 0.241670i
\(936\) −4.20915e7 7.29046e7i −1.57038 2.71998i
\(937\) 2.96127e7 1.10187 0.550934 0.834549i \(-0.314272\pi\)
0.550934 + 0.834549i \(0.314272\pi\)
\(938\) 1.86232e7 + 1.95287e7i 0.691111 + 0.724713i
\(939\) 7.64665e7 2.83013
\(940\) −5.16702e6 8.94955e6i −0.190731 0.330355i
\(941\) −2.46773e7 + 4.27423e7i −0.908497 + 1.57356i −0.0923449 + 0.995727i \(0.529436\pi\)
−0.816152 + 0.577837i \(0.803897\pi\)
\(942\) −1.14050e7 + 1.97540e7i −0.418762 + 0.725317i
\(943\) 8.99039e6 + 1.55718e7i 0.329230 + 0.570243i
\(944\) −1.42944e6 −0.0522080
\(945\) 7.39986e6 2.52082e7i 0.269553 0.918254i
\(946\) −4.45906e6 −0.162000
\(947\) 5.84586e6 + 1.01253e7i 0.211823 + 0.366889i 0.952285 0.305210i \(-0.0987265\pi\)
−0.740462 + 0.672098i \(0.765393\pi\)
\(948\) −4.85892e6 + 8.41589e6i −0.175598 + 0.304144i
\(949\) 1.73758e7 3.00957e7i 0.626294 1.08477i
\(950\) 969528. + 1.67927e6i 0.0348539 + 0.0603687i
\(951\) −4.21450e7 −1.51110
\(952\) 1.57070e7 3.81167e6i 0.561696 0.136308i
\(953\) 5.11241e7 1.82345 0.911725 0.410802i \(-0.134751\pi\)
0.911725 + 0.410802i \(0.134751\pi\)
\(954\) 4.54602e6 + 7.87394e6i 0.161719 + 0.280105i
\(955\) 4.01201e6 6.94901e6i 0.142349 0.246555i
\(956\) −5.66196e6 + 9.80681e6i −0.200365 + 0.347043i
\(957\) −3.15469e7 5.46408e7i −1.11347 1.92858i
\(958\) −2.72872e7 −0.960604
\(959\) −3.55126e7 + 8.61795e6i −1.24691 + 0.302592i
\(960\) −8.92697e6 −0.312627
\(961\) 9.35466e6 + 1.62027e7i 0.326753 + 0.565953i
\(962\) −1.39696e7 + 2.41960e7i −0.486683 + 0.842960i
\(963\) −1.98670e7 + 3.44106e7i −0.690345 + 1.19571i
\(964\) −286029. 495418.i −0.00991330 0.0171703i
\(965\) 1.81809e7 0.628487
\(966\) −3.88992e6 + 1.32514e7i −0.134121 + 0.456896i
\(967\) 3.09492e7 1.06435 0.532173 0.846636i \(-0.321376\pi\)
0.532173 + 0.846636i \(0.321376\pi\)
\(968\) 269461. + 466720.i 0.00924288 + 0.0160091i
\(969\) −1.02017e7 + 1.76698e7i −0.349029 + 0.604536i
\(970\) −5.82981e6 + 1.00975e7i −0.198941 + 0.344577i
\(971\) −2.34720e7 4.06546e7i −0.798917 1.38376i −0.920322 0.391161i \(-0.872073\pi\)
0.121405 0.992603i \(-0.461260\pi\)
\(972\) −1.58440e7 −0.537897
\(973\) −2.11336e7 2.21611e7i −0.715635 0.750429i
\(974\) −2.82577e7 −0.954420
\(975\) 8.11165e6 + 1.40498e7i 0.273274 + 0.473324i
\(976\) −1.73665e6 + 3.00796e6i −0.0583561 + 0.101076i
\(977\) −1.69606e7 + 2.93767e7i −0.568467 + 0.984614i 0.428250 + 0.903660i \(0.359130\pi\)
−0.996718 + 0.0809543i \(0.974203\pi\)
\(978\) −1.24103e7 2.14954e7i −0.414894 0.718617i
\(979\) 3.20322e6 0.106815
\(980\) −443757. + 9.34361e6i −0.0147598 + 0.310777i
\(981\) 7.34988e7 2.43841
\(982\) 6.69877e6 + 1.16026e7i 0.221675 + 0.383952i
\(983\) −7.36307e6 + 1.27532e7i −0.243038 + 0.420955i −0.961578 0.274531i \(-0.911477\pi\)
0.718540 + 0.695486i \(0.244811\pi\)
\(984\) −3.46409e7 + 5.99998e7i −1.14052 + 1.97543i
\(985\) −9.41149e6 1.63012e7i −0.309078 0.535339i
\(986\) 1.28341e7 0.420411
\(987\) −4.63017e7 4.85529e7i −1.51288 1.58643i
\(988\) −2.06137e7 −0.671836
\(989\) −2.15941e6 3.74021e6i −0.0702012 0.121592i
\(990\) −8.43860e6 + 1.46161e7i −0.273642 + 0.473961i
\(991\) −411387. + 712543.i −0.0133066 + 0.0230477i −0.872602 0.488432i \(-0.837569\pi\)
0.859295 + 0.511480i \(0.170902\pi\)
\(992\) −9.43717e6 1.63457e7i −0.304483 0.527380i
\(993\) 2.18174e7 0.702148
\(994\) −3.53168e6 + 1.20310e7i −0.113374 + 0.386219i
\(995\) −2.41588e6 −0.0773603
\(996\) 2.17179e7 + 3.76164e7i 0.693695 + 1.20152i
\(997\) −5.50332e6 + 9.53203e6i −0.175342 + 0.303702i −0.940280 0.340403i \(-0.889437\pi\)
0.764937 + 0.644105i \(0.222770\pi\)
\(998\) 5.70794e6 9.88644e6i 0.181406 0.314205i
\(999\) 3.89646e7 + 6.74887e7i 1.23526 + 2.13953i
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 35.6.e.a.11.2 12
7.2 even 3 inner 35.6.e.a.16.2 yes 12
7.3 odd 6 245.6.a.h.1.5 6
7.4 even 3 245.6.a.i.1.5 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.6.e.a.11.2 12 1.1 even 1 trivial
35.6.e.a.16.2 yes 12 7.2 even 3 inner
245.6.a.h.1.5 6 7.3 odd 6
245.6.a.i.1.5 6 7.4 even 3