Properties

Label 300.2.o.a.289.4
Level $300$
Weight $2$
Character 300.289
Analytic conductor $2.396$
Analytic rank $0$
Dimension $24$
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] = [300,2,Mod(109,300)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(300, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("300.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.o (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 289.4
Character \(\chi\) \(=\) 300.289
Dual form 300.2.o.a.109.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.951057 + 0.309017i) q^{3} +(-1.98828 + 1.02311i) q^{5} +3.54704i q^{7} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(0.951057 + 0.309017i) q^{3} +(-1.98828 + 1.02311i) q^{5} +3.54704i q^{7} +(0.809017 + 0.587785i) q^{9} +(1.78482 - 1.29675i) q^{11} +(-4.21895 + 5.80689i) q^{13} +(-2.20712 + 0.358624i) q^{15} +(6.05378 - 1.96699i) q^{17} +(0.715151 + 2.20101i) q^{19} +(-1.09610 + 3.37344i) q^{21} +(-1.27899 - 1.76038i) q^{23} +(2.90649 - 4.06845i) q^{25} +(0.587785 + 0.809017i) q^{27} +(-0.262008 + 0.806379i) q^{29} +(-1.32905 - 4.09040i) q^{31} +(2.09819 - 0.681742i) q^{33} +(-3.62901 - 7.05250i) q^{35} +(4.24968 - 5.84918i) q^{37} +(-5.80689 + 4.21895i) q^{39} +(1.08778 + 0.790317i) q^{41} +8.18973i q^{43} +(-2.20992 - 0.340966i) q^{45} +(-5.75820 - 1.87095i) q^{47} -5.58150 q^{49} +6.36532 q^{51} +(11.3730 + 3.69530i) q^{53} +(-2.22201 + 4.40437i) q^{55} +2.31428i q^{57} +(-10.0896 - 7.33050i) q^{59} +(5.59873 - 4.06772i) q^{61} +(-2.08490 + 2.86962i) q^{63} +(2.44736 - 15.8622i) q^{65} +(4.50239 - 1.46291i) q^{67} +(-0.672404 - 2.06945i) q^{69} +(4.25799 - 13.1047i) q^{71} +(-0.640196 - 0.881155i) q^{73} +(4.02146 - 2.97117i) q^{75} +(4.59963 + 6.33085i) q^{77} +(1.80542 - 5.55650i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-11.9145 + 3.87127i) q^{83} +(-10.0241 + 10.1046i) q^{85} +(-0.498370 + 0.685947i) q^{87} +(-5.68424 + 4.12984i) q^{89} +(-20.5973 - 14.9648i) q^{91} -4.30090i q^{93} +(-3.67379 - 3.64454i) q^{95} +(17.2564 + 5.60695i) q^{97} +2.20616 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 2 q^{5} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 2 q^{5} + 6 q^{9} - 6 q^{11} + 4 q^{15} + 10 q^{17} + 10 q^{19} - 4 q^{21} + 40 q^{23} - 4 q^{25} + 4 q^{29} + 6 q^{31} + 10 q^{33} - 6 q^{35} - 10 q^{41} + 2 q^{45} - 40 q^{47} - 56 q^{49} + 16 q^{51} - 60 q^{53} - 62 q^{55} - 36 q^{59} - 12 q^{61} - 10 q^{63} + 20 q^{67} + 4 q^{69} + 40 q^{71} + 60 q^{73} + 8 q^{75} - 40 q^{77} + 8 q^{79} - 6 q^{81} - 50 q^{83} + 34 q^{85} - 20 q^{87} - 30 q^{91} - 60 q^{95} - 40 q^{97} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{10}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.951057 + 0.309017i 0.549093 + 0.178411i
\(4\) 0 0
\(5\) −1.98828 + 1.02311i −0.889185 + 0.457549i
\(6\) 0 0
\(7\) 3.54704i 1.34066i 0.742065 + 0.670328i \(0.233846\pi\)
−0.742065 + 0.670328i \(0.766154\pi\)
\(8\) 0 0
\(9\) 0.809017 + 0.587785i 0.269672 + 0.195928i
\(10\) 0 0
\(11\) 1.78482 1.29675i 0.538145 0.390985i −0.285251 0.958453i \(-0.592077\pi\)
0.823396 + 0.567468i \(0.192077\pi\)
\(12\) 0 0
\(13\) −4.21895 + 5.80689i −1.17013 + 1.61054i −0.507301 + 0.861769i \(0.669357\pi\)
−0.662827 + 0.748773i \(0.730643\pi\)
\(14\) 0 0
\(15\) −2.20712 + 0.358624i −0.569877 + 0.0925964i
\(16\) 0 0
\(17\) 6.05378 1.96699i 1.46826 0.477066i 0.537676 0.843151i \(-0.319302\pi\)
0.930581 + 0.366086i \(0.119302\pi\)
\(18\) 0 0
\(19\) 0.715151 + 2.20101i 0.164067 + 0.504946i 0.998966 0.0454566i \(-0.0144743\pi\)
−0.834899 + 0.550402i \(0.814474\pi\)
\(20\) 0 0
\(21\) −1.09610 + 3.37344i −0.239188 + 0.736144i
\(22\) 0 0
\(23\) −1.27899 1.76038i −0.266687 0.367064i 0.654580 0.755992i \(-0.272845\pi\)
−0.921268 + 0.388929i \(0.872845\pi\)
\(24\) 0 0
\(25\) 2.90649 4.06845i 0.581298 0.813691i
\(26\) 0 0
\(27\) 0.587785 + 0.809017i 0.113119 + 0.155695i
\(28\) 0 0
\(29\) −0.262008 + 0.806379i −0.0486538 + 0.149741i −0.972432 0.233188i \(-0.925084\pi\)
0.923778 + 0.382928i \(0.125084\pi\)
\(30\) 0 0
\(31\) −1.32905 4.09040i −0.238705 0.734657i −0.996608 0.0822910i \(-0.973776\pi\)
0.757904 0.652367i \(-0.226224\pi\)
\(32\) 0 0
\(33\) 2.09819 0.681742i 0.365248 0.118676i
\(34\) 0 0
\(35\) −3.62901 7.05250i −0.613415 1.19209i
\(36\) 0 0
\(37\) 4.24968 5.84918i 0.698643 0.961599i −0.301325 0.953522i \(-0.597429\pi\)
0.999967 0.00807756i \(-0.00257119\pi\)
\(38\) 0 0
\(39\) −5.80689 + 4.21895i −0.929847 + 0.675573i
\(40\) 0 0
\(41\) 1.08778 + 0.790317i 0.169882 + 0.123427i 0.669478 0.742832i \(-0.266518\pi\)
−0.499595 + 0.866259i \(0.666518\pi\)
\(42\) 0 0
\(43\) 8.18973i 1.24892i 0.781056 + 0.624461i \(0.214681\pi\)
−0.781056 + 0.624461i \(0.785319\pi\)
\(44\) 0 0
\(45\) −2.20992 0.340966i −0.329435 0.0508283i
\(46\) 0 0
\(47\) −5.75820 1.87095i −0.839920 0.272907i −0.142702 0.989766i \(-0.545579\pi\)
−0.697218 + 0.716859i \(0.745579\pi\)
\(48\) 0 0
\(49\) −5.58150 −0.797357
\(50\) 0 0
\(51\) 6.36532 0.891323
\(52\) 0 0
\(53\) 11.3730 + 3.69530i 1.56220 + 0.507589i 0.957394 0.288785i \(-0.0932512\pi\)
0.604805 + 0.796374i \(0.293251\pi\)
\(54\) 0 0
\(55\) −2.22201 + 4.40437i −0.299615 + 0.593886i
\(56\) 0 0
\(57\) 2.31428i 0.306533i
\(58\) 0 0
\(59\) −10.0896 7.33050i −1.31355 0.954350i −0.999989 0.00478202i \(-0.998478\pi\)
−0.313561 0.949568i \(-0.601522\pi\)
\(60\) 0 0
\(61\) 5.59873 4.06772i 0.716844 0.520818i −0.168530 0.985696i \(-0.553902\pi\)
0.885374 + 0.464879i \(0.153902\pi\)
\(62\) 0 0
\(63\) −2.08490 + 2.86962i −0.262672 + 0.361538i
\(64\) 0 0
\(65\) 2.44736 15.8622i 0.303558 1.96746i
\(66\) 0 0
\(67\) 4.50239 1.46291i 0.550054 0.178723i −0.0207870 0.999784i \(-0.506617\pi\)
0.570841 + 0.821060i \(0.306617\pi\)
\(68\) 0 0
\(69\) −0.672404 2.06945i −0.0809479 0.249132i
\(70\) 0 0
\(71\) 4.25799 13.1047i 0.505330 1.55525i −0.294884 0.955533i \(-0.595281\pi\)
0.800214 0.599714i \(-0.204719\pi\)
\(72\) 0 0
\(73\) −0.640196 0.881155i −0.0749293 0.103131i 0.769907 0.638156i \(-0.220302\pi\)
−0.844837 + 0.535024i \(0.820302\pi\)
\(74\) 0 0
\(75\) 4.02146 2.97117i 0.464358 0.343082i
\(76\) 0 0
\(77\) 4.59963 + 6.33085i 0.524176 + 0.721467i
\(78\) 0 0
\(79\) 1.80542 5.55650i 0.203125 0.625156i −0.796660 0.604428i \(-0.793402\pi\)
0.999785 0.0207276i \(-0.00659828\pi\)
\(80\) 0 0
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) 0 0
\(83\) −11.9145 + 3.87127i −1.30779 + 0.424927i −0.878285 0.478137i \(-0.841312\pi\)
−0.429505 + 0.903064i \(0.641312\pi\)
\(84\) 0 0
\(85\) −10.0241 + 10.1046i −1.08727 + 1.09600i
\(86\) 0 0
\(87\) −0.498370 + 0.685947i −0.0534308 + 0.0735412i
\(88\) 0 0
\(89\) −5.68424 + 4.12984i −0.602528 + 0.437762i −0.846775 0.531951i \(-0.821459\pi\)
0.244247 + 0.969713i \(0.421459\pi\)
\(90\) 0 0
\(91\) −20.5973 14.9648i −2.15918 1.56874i
\(92\) 0 0
\(93\) 4.30090i 0.445983i
\(94\) 0 0
\(95\) −3.67379 3.64454i −0.376923 0.373921i
\(96\) 0 0
\(97\) 17.2564 + 5.60695i 1.75212 + 0.569299i 0.996337 0.0855183i \(-0.0272546\pi\)
0.755787 + 0.654818i \(0.227255\pi\)
\(98\) 0 0
\(99\) 2.20616 0.221728
\(100\) 0 0
\(101\) 5.97473 0.594508 0.297254 0.954798i \(-0.403929\pi\)
0.297254 + 0.954798i \(0.403929\pi\)
\(102\) 0 0
\(103\) −0.437076 0.142014i −0.0430663 0.0139931i 0.287405 0.957809i \(-0.407208\pi\)
−0.330471 + 0.943816i \(0.607208\pi\)
\(104\) 0 0
\(105\) −1.27205 7.82875i −0.124140 0.764008i
\(106\) 0 0
\(107\) 2.47862i 0.239617i −0.992797 0.119809i \(-0.961772\pi\)
0.992797 0.119809i \(-0.0382281\pi\)
\(108\) 0 0
\(109\) −2.70314 1.96394i −0.258914 0.188112i 0.450754 0.892648i \(-0.351155\pi\)
−0.709668 + 0.704536i \(0.751155\pi\)
\(110\) 0 0
\(111\) 5.84918 4.24968i 0.555180 0.403362i
\(112\) 0 0
\(113\) 10.3438 14.2370i 0.973059 1.33930i 0.0325728 0.999469i \(-0.489630\pi\)
0.940486 0.339832i \(-0.110370\pi\)
\(114\) 0 0
\(115\) 4.34404 + 2.19157i 0.405084 + 0.204365i
\(116\) 0 0
\(117\) −6.82641 + 2.21804i −0.631102 + 0.205057i
\(118\) 0 0
\(119\) 6.97700 + 21.4730i 0.639581 + 1.96843i
\(120\) 0 0
\(121\) −1.89515 + 5.83267i −0.172286 + 0.530243i
\(122\) 0 0
\(123\) 0.790317 + 1.08778i 0.0712605 + 0.0980816i
\(124\) 0 0
\(125\) −1.61643 + 11.0629i −0.144578 + 0.989493i
\(126\) 0 0
\(127\) 7.29555 + 10.0415i 0.647376 + 0.891036i 0.998982 0.0451118i \(-0.0143644\pi\)
−0.351606 + 0.936148i \(0.614364\pi\)
\(128\) 0 0
\(129\) −2.53077 + 7.78890i −0.222822 + 0.685774i
\(130\) 0 0
\(131\) 4.88963 + 15.0487i 0.427209 + 1.31481i 0.900863 + 0.434104i \(0.142935\pi\)
−0.473654 + 0.880711i \(0.657065\pi\)
\(132\) 0 0
\(133\) −7.80706 + 2.53667i −0.676958 + 0.219957i
\(134\) 0 0
\(135\) −1.99639 1.00718i −0.171822 0.0866843i
\(136\) 0 0
\(137\) −4.34663 + 5.98262i −0.371358 + 0.511130i −0.953269 0.302122i \(-0.902305\pi\)
0.581912 + 0.813252i \(0.302305\pi\)
\(138\) 0 0
\(139\) 3.18667 2.31525i 0.270290 0.196377i −0.444381 0.895838i \(-0.646576\pi\)
0.714671 + 0.699461i \(0.246576\pi\)
\(140\) 0 0
\(141\) −4.89822 3.55876i −0.412504 0.299702i
\(142\) 0 0
\(143\) 15.8352i 1.32421i
\(144\) 0 0
\(145\) −0.304069 1.87137i −0.0252516 0.155409i
\(146\) 0 0
\(147\) −5.30832 1.72478i −0.437823 0.142257i
\(148\) 0 0
\(149\) −3.92892 −0.321870 −0.160935 0.986965i \(-0.551451\pi\)
−0.160935 + 0.986965i \(0.551451\pi\)
\(150\) 0 0
\(151\) 7.93418 0.645674 0.322837 0.946455i \(-0.395363\pi\)
0.322837 + 0.946455i \(0.395363\pi\)
\(152\) 0 0
\(153\) 6.05378 + 1.96699i 0.489419 + 0.159022i
\(154\) 0 0
\(155\) 6.82745 + 6.77308i 0.548394 + 0.544027i
\(156\) 0 0
\(157\) 6.09738i 0.486624i 0.969948 + 0.243312i \(0.0782339\pi\)
−0.969948 + 0.243312i \(0.921766\pi\)
\(158\) 0 0
\(159\) 9.67443 + 7.02889i 0.767232 + 0.557427i
\(160\) 0 0
\(161\) 6.24413 4.53662i 0.492106 0.357536i
\(162\) 0 0
\(163\) −0.00150257 + 0.00206811i −0.000117690 + 0.000161987i −0.809076 0.587704i \(-0.800032\pi\)
0.808958 + 0.587866i \(0.200032\pi\)
\(164\) 0 0
\(165\) −3.47428 + 3.50217i −0.270472 + 0.272644i
\(166\) 0 0
\(167\) −9.60630 + 3.12128i −0.743358 + 0.241532i −0.656121 0.754656i \(-0.727804\pi\)
−0.0872372 + 0.996188i \(0.527804\pi\)
\(168\) 0 0
\(169\) −11.9032 36.6343i −0.915631 2.81802i
\(170\) 0 0
\(171\) −0.715151 + 2.20101i −0.0546889 + 0.168315i
\(172\) 0 0
\(173\) 3.63244 + 4.99963i 0.276169 + 0.380115i 0.924460 0.381278i \(-0.124516\pi\)
−0.648291 + 0.761393i \(0.724516\pi\)
\(174\) 0 0
\(175\) 14.4310 + 10.3094i 1.09088 + 0.779321i
\(176\) 0 0
\(177\) −7.33050 10.0896i −0.550994 0.758378i
\(178\) 0 0
\(179\) −4.45991 + 13.7262i −0.333349 + 1.02594i 0.634181 + 0.773185i \(0.281338\pi\)
−0.967530 + 0.252758i \(0.918662\pi\)
\(180\) 0 0
\(181\) 2.08366 + 6.41283i 0.154877 + 0.476662i 0.998148 0.0608258i \(-0.0193734\pi\)
−0.843272 + 0.537488i \(0.819373\pi\)
\(182\) 0 0
\(183\) 6.58170 2.13853i 0.486534 0.158084i
\(184\) 0 0
\(185\) −2.46518 + 15.9777i −0.181244 + 1.17470i
\(186\) 0 0
\(187\) 8.25424 11.3610i 0.603610 0.830798i
\(188\) 0 0
\(189\) −2.86962 + 2.08490i −0.208734 + 0.151654i
\(190\) 0 0
\(191\) −12.4512 9.04634i −0.900938 0.654570i 0.0377687 0.999287i \(-0.487975\pi\)
−0.938707 + 0.344717i \(0.887975\pi\)
\(192\) 0 0
\(193\) 16.3875i 1.17960i 0.807550 + 0.589799i \(0.200793\pi\)
−0.807550 + 0.589799i \(0.799207\pi\)
\(194\) 0 0
\(195\) 7.22926 14.3295i 0.517698 1.02616i
\(196\) 0 0
\(197\) −9.36824 3.04392i −0.667459 0.216871i −0.0443625 0.999015i \(-0.514126\pi\)
−0.623097 + 0.782145i \(0.714126\pi\)
\(198\) 0 0
\(199\) 4.96275 0.351800 0.175900 0.984408i \(-0.443716\pi\)
0.175900 + 0.984408i \(0.443716\pi\)
\(200\) 0 0
\(201\) 4.73409 0.333917
\(202\) 0 0
\(203\) −2.86026 0.929355i −0.200751 0.0652279i
\(204\) 0 0
\(205\) −2.97139 0.458452i −0.207531 0.0320197i
\(206\) 0 0
\(207\) 2.17594i 0.151239i
\(208\) 0 0
\(209\) 4.13058 + 3.00104i 0.285718 + 0.207586i
\(210\) 0 0
\(211\) −2.83140 + 2.05713i −0.194921 + 0.141619i −0.680965 0.732316i \(-0.738440\pi\)
0.486044 + 0.873934i \(0.338440\pi\)
\(212\) 0 0
\(213\) 8.09918 11.1476i 0.554947 0.763818i
\(214\) 0 0
\(215\) −8.37900 16.2835i −0.571443 1.11052i
\(216\) 0 0
\(217\) 14.5088 4.71420i 0.984923 0.320021i
\(218\) 0 0
\(219\) −0.336571 1.03586i −0.0227434 0.0699969i
\(220\) 0 0
\(221\) −14.1185 + 43.4523i −0.949714 + 2.92292i
\(222\) 0 0
\(223\) −13.5653 18.6710i −0.908397 1.25030i −0.967711 0.252062i \(-0.918891\pi\)
0.0593138 0.998239i \(-0.481109\pi\)
\(224\) 0 0
\(225\) 4.74278 1.58305i 0.316185 0.105537i
\(226\) 0 0
\(227\) −3.43889 4.73323i −0.228247 0.314155i 0.679498 0.733677i \(-0.262198\pi\)
−0.907745 + 0.419522i \(0.862198\pi\)
\(228\) 0 0
\(229\) 1.97484 6.07793i 0.130501 0.401641i −0.864362 0.502870i \(-0.832277\pi\)
0.994863 + 0.101229i \(0.0322775\pi\)
\(230\) 0 0
\(231\) 2.41817 + 7.44236i 0.159104 + 0.489671i
\(232\) 0 0
\(233\) −4.32076 + 1.40390i −0.283062 + 0.0919725i −0.447107 0.894480i \(-0.647546\pi\)
0.164045 + 0.986453i \(0.447546\pi\)
\(234\) 0 0
\(235\) 13.3631 2.17130i 0.871712 0.141640i
\(236\) 0 0
\(237\) 3.43411 4.72664i 0.223069 0.307029i
\(238\) 0 0
\(239\) 18.6407 13.5432i 1.20576 0.876040i 0.210926 0.977502i \(-0.432352\pi\)
0.994839 + 0.101463i \(0.0323522\pi\)
\(240\) 0 0
\(241\) −13.3064 9.66766i −0.857140 0.622749i 0.0699655 0.997549i \(-0.477711\pi\)
−0.927105 + 0.374801i \(0.877711\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) 11.0976 5.71049i 0.708997 0.364830i
\(246\) 0 0
\(247\) −15.7982 5.13315i −1.00522 0.326614i
\(248\) 0 0
\(249\) −12.5277 −0.793910
\(250\) 0 0
\(251\) 4.66327 0.294343 0.147171 0.989111i \(-0.452983\pi\)
0.147171 + 0.989111i \(0.452983\pi\)
\(252\) 0 0
\(253\) −4.56554 1.48343i −0.287033 0.0932627i
\(254\) 0 0
\(255\) −12.6560 + 6.51243i −0.792551 + 0.407824i
\(256\) 0 0
\(257\) 5.78734i 0.361004i 0.983575 + 0.180502i \(0.0577723\pi\)
−0.983575 + 0.180502i \(0.942228\pi\)
\(258\) 0 0
\(259\) 20.7473 + 15.0738i 1.28917 + 0.936639i
\(260\) 0 0
\(261\) −0.685947 + 0.498370i −0.0424591 + 0.0308483i
\(262\) 0 0
\(263\) 13.4896 18.5668i 0.831803 1.14488i −0.155781 0.987792i \(-0.549790\pi\)
0.987585 0.157087i \(-0.0502105\pi\)
\(264\) 0 0
\(265\) −26.3933 + 4.28852i −1.62133 + 0.263442i
\(266\) 0 0
\(267\) −6.68222 + 2.17119i −0.408945 + 0.132874i
\(268\) 0 0
\(269\) 1.39366 + 4.28923i 0.0849727 + 0.261519i 0.984511 0.175323i \(-0.0560969\pi\)
−0.899538 + 0.436842i \(0.856097\pi\)
\(270\) 0 0
\(271\) −3.06895 + 9.44525i −0.186425 + 0.573758i −0.999970 0.00774433i \(-0.997535\pi\)
0.813545 + 0.581502i \(0.197535\pi\)
\(272\) 0 0
\(273\) −14.9648 20.5973i −0.905711 1.24660i
\(274\) 0 0
\(275\) −0.0881931 11.0305i −0.00531824 0.665163i
\(276\) 0 0
\(277\) −13.5280 18.6197i −0.812821 1.11875i −0.990882 0.134732i \(-0.956983\pi\)
0.178061 0.984019i \(-0.443017\pi\)
\(278\) 0 0
\(279\) 1.32905 4.09040i 0.0795682 0.244886i
\(280\) 0 0
\(281\) 0.226820 + 0.698080i 0.0135309 + 0.0416439i 0.957594 0.288121i \(-0.0930305\pi\)
−0.944063 + 0.329765i \(0.893031\pi\)
\(282\) 0 0
\(283\) −20.4402 + 6.64144i −1.21505 + 0.394793i −0.845276 0.534330i \(-0.820564\pi\)
−0.369771 + 0.929123i \(0.620564\pi\)
\(284\) 0 0
\(285\) −2.36776 4.60142i −0.140254 0.272565i
\(286\) 0 0
\(287\) −2.80329 + 3.85839i −0.165473 + 0.227754i
\(288\) 0 0
\(289\) 19.0259 13.8231i 1.11917 0.813126i
\(290\) 0 0
\(291\) 14.6792 + 10.6651i 0.860509 + 0.625196i
\(292\) 0 0
\(293\) 26.5961i 1.55376i −0.629649 0.776880i \(-0.716801\pi\)
0.629649 0.776880i \(-0.283199\pi\)
\(294\) 0 0
\(295\) 27.5608 + 4.25233i 1.60465 + 0.247580i
\(296\) 0 0
\(297\) 2.09819 + 0.681742i 0.121749 + 0.0395587i
\(298\) 0 0
\(299\) 15.6183 0.903230
\(300\) 0 0
\(301\) −29.0493 −1.67437
\(302\) 0 0
\(303\) 5.68231 + 1.84629i 0.326440 + 0.106067i
\(304\) 0 0
\(305\) −6.97011 + 13.8159i −0.399107 + 0.791094i
\(306\) 0 0
\(307\) 12.1736i 0.694785i −0.937720 0.347393i \(-0.887067\pi\)
0.937720 0.347393i \(-0.112933\pi\)
\(308\) 0 0
\(309\) −0.371799 0.270128i −0.0211509 0.0153670i
\(310\) 0 0
\(311\) 20.0330 14.5548i 1.13597 0.825327i 0.149414 0.988775i \(-0.452261\pi\)
0.986552 + 0.163447i \(0.0522614\pi\)
\(312\) 0 0
\(313\) 8.72589 12.0102i 0.493216 0.678854i −0.487761 0.872977i \(-0.662186\pi\)
0.980977 + 0.194123i \(0.0621862\pi\)
\(314\) 0 0
\(315\) 1.20942 7.83867i 0.0681432 0.441659i
\(316\) 0 0
\(317\) 1.84725 0.600207i 0.103752 0.0337110i −0.256681 0.966496i \(-0.582629\pi\)
0.360433 + 0.932785i \(0.382629\pi\)
\(318\) 0 0
\(319\) 0.578034 + 1.77901i 0.0323637 + 0.0996052i
\(320\) 0 0
\(321\) 0.765935 2.35731i 0.0427503 0.131572i
\(322\) 0 0
\(323\) 8.65873 + 11.9177i 0.481785 + 0.663120i
\(324\) 0 0
\(325\) 11.3627 + 34.0423i 0.630290 + 1.88833i
\(326\) 0 0
\(327\) −1.96394 2.70314i −0.108606 0.149484i
\(328\) 0 0
\(329\) 6.63635 20.4246i 0.365874 1.12604i
\(330\) 0 0
\(331\) −8.56924 26.3734i −0.471008 1.44961i −0.851266 0.524734i \(-0.824165\pi\)
0.380258 0.924880i \(-0.375835\pi\)
\(332\) 0 0
\(333\) 6.87612 2.23419i 0.376809 0.122433i
\(334\) 0 0
\(335\) −7.45527 + 7.51512i −0.407325 + 0.410595i
\(336\) 0 0
\(337\) −6.40119 + 8.81048i −0.348695 + 0.479937i −0.946956 0.321364i \(-0.895859\pi\)
0.598261 + 0.801301i \(0.295859\pi\)
\(338\) 0 0
\(339\) 14.2370 10.3438i 0.773246 0.561796i
\(340\) 0 0
\(341\) −7.67636 5.57720i −0.415698 0.302022i
\(342\) 0 0
\(343\) 5.03148i 0.271675i
\(344\) 0 0
\(345\) 3.45420 + 3.42669i 0.185968 + 0.184487i
\(346\) 0 0
\(347\) −21.7353 7.06224i −1.16681 0.379121i −0.339361 0.940656i \(-0.610211\pi\)
−0.827453 + 0.561536i \(0.810211\pi\)
\(348\) 0 0
\(349\) 28.8539 1.54451 0.772256 0.635311i \(-0.219128\pi\)
0.772256 + 0.635311i \(0.219128\pi\)
\(350\) 0 0
\(351\) −7.17771 −0.383118
\(352\) 0 0
\(353\) −25.9079 8.41799i −1.37894 0.448045i −0.476619 0.879110i \(-0.658138\pi\)
−0.902321 + 0.431065i \(0.858138\pi\)
\(354\) 0 0
\(355\) 4.94153 + 30.4123i 0.262269 + 1.61412i
\(356\) 0 0
\(357\) 22.5781i 1.19496i
\(358\) 0 0
\(359\) −19.3648 14.0694i −1.02204 0.742553i −0.0553373 0.998468i \(-0.517623\pi\)
−0.966699 + 0.255915i \(0.917623\pi\)
\(360\) 0 0
\(361\) 11.0383 8.01981i 0.580965 0.422096i
\(362\) 0 0
\(363\) −3.60479 + 4.96157i −0.189202 + 0.260415i
\(364\) 0 0
\(365\) 2.17441 + 1.09699i 0.113814 + 0.0574190i
\(366\) 0 0
\(367\) −6.38465 + 2.07450i −0.333276 + 0.108288i −0.470875 0.882200i \(-0.656062\pi\)
0.137599 + 0.990488i \(0.456062\pi\)
\(368\) 0 0
\(369\) 0.415494 + 1.27876i 0.0216298 + 0.0665696i
\(370\) 0 0
\(371\) −13.1074 + 40.3404i −0.680502 + 2.09437i
\(372\) 0 0
\(373\) −7.99923 11.0100i −0.414184 0.570076i 0.550048 0.835133i \(-0.314609\pi\)
−0.964233 + 0.265057i \(0.914609\pi\)
\(374\) 0 0
\(375\) −4.95594 + 10.0219i −0.255923 + 0.517529i
\(376\) 0 0
\(377\) −3.57715 4.92353i −0.184233 0.253575i
\(378\) 0 0
\(379\) −0.137272 + 0.422481i −0.00705120 + 0.0217014i −0.954520 0.298146i \(-0.903632\pi\)
0.947469 + 0.319848i \(0.103632\pi\)
\(380\) 0 0
\(381\) 3.83550 + 11.8045i 0.196499 + 0.604760i
\(382\) 0 0
\(383\) −9.72980 + 3.16140i −0.497170 + 0.161540i −0.546859 0.837224i \(-0.684177\pi\)
0.0496897 + 0.998765i \(0.484177\pi\)
\(384\) 0 0
\(385\) −15.6225 7.88155i −0.796196 0.401681i
\(386\) 0 0
\(387\) −4.81380 + 6.62563i −0.244699 + 0.336800i
\(388\) 0 0
\(389\) −19.5834 + 14.2282i −0.992919 + 0.721398i −0.960558 0.278078i \(-0.910303\pi\)
−0.0323607 + 0.999476i \(0.510303\pi\)
\(390\) 0 0
\(391\) −11.2054 8.14117i −0.566679 0.411717i
\(392\) 0 0
\(393\) 15.8232i 0.798174i
\(394\) 0 0
\(395\) 2.09525 + 12.8950i 0.105423 + 0.648818i
\(396\) 0 0
\(397\) −2.58871 0.841124i −0.129924 0.0422148i 0.243333 0.969943i \(-0.421759\pi\)
−0.373257 + 0.927728i \(0.621759\pi\)
\(398\) 0 0
\(399\) −8.20883 −0.410956
\(400\) 0 0
\(401\) 31.3538 1.56573 0.782867 0.622189i \(-0.213756\pi\)
0.782867 + 0.622189i \(0.213756\pi\)
\(402\) 0 0
\(403\) 29.3597 + 9.53955i 1.46251 + 0.475199i
\(404\) 0 0
\(405\) −1.58745 1.57481i −0.0788809 0.0782527i
\(406\) 0 0
\(407\) 15.9505i 0.790639i
\(408\) 0 0
\(409\) 2.68805 + 1.95298i 0.132916 + 0.0965688i 0.652256 0.757998i \(-0.273823\pi\)
−0.519341 + 0.854567i \(0.673823\pi\)
\(410\) 0 0
\(411\) −5.98262 + 4.34663i −0.295101 + 0.214404i
\(412\) 0 0
\(413\) 26.0016 35.7881i 1.27945 1.76102i
\(414\) 0 0
\(415\) 19.7287 19.8870i 0.968442 0.976216i
\(416\) 0 0
\(417\) 3.74615 1.21720i 0.183450 0.0596065i
\(418\) 0 0
\(419\) 3.41347 + 10.5056i 0.166759 + 0.513231i 0.999162 0.0409399i \(-0.0130352\pi\)
−0.832403 + 0.554171i \(0.813035\pi\)
\(420\) 0 0
\(421\) −7.56044 + 23.2686i −0.368473 + 1.13404i 0.579304 + 0.815111i \(0.303324\pi\)
−0.947777 + 0.318932i \(0.896676\pi\)
\(422\) 0 0
\(423\) −3.55876 4.89822i −0.173033 0.238160i
\(424\) 0 0
\(425\) 9.59264 30.3466i 0.465312 1.47202i
\(426\) 0 0
\(427\) 14.4284 + 19.8589i 0.698237 + 0.961041i
\(428\) 0 0
\(429\) −4.89335 + 15.0602i −0.236253 + 0.727113i
\(430\) 0 0
\(431\) 0.354621 + 1.09141i 0.0170815 + 0.0525715i 0.959234 0.282613i \(-0.0912013\pi\)
−0.942152 + 0.335185i \(0.891201\pi\)
\(432\) 0 0
\(433\) −5.56802 + 1.80916i −0.267582 + 0.0869427i −0.439735 0.898128i \(-0.644928\pi\)
0.172153 + 0.985070i \(0.444928\pi\)
\(434\) 0 0
\(435\) 0.289098 1.87374i 0.0138612 0.0898390i
\(436\) 0 0
\(437\) 2.95993 4.07400i 0.141593 0.194886i
\(438\) 0 0
\(439\) −16.4473 + 11.9497i −0.784988 + 0.570328i −0.906472 0.422266i \(-0.861235\pi\)
0.121484 + 0.992593i \(0.461235\pi\)
\(440\) 0 0
\(441\) −4.51553 3.28072i −0.215025 0.156225i
\(442\) 0 0
\(443\) 17.5912i 0.835783i −0.908497 0.417891i \(-0.862769\pi\)
0.908497 0.417891i \(-0.137231\pi\)
\(444\) 0 0
\(445\) 7.07656 14.0269i 0.335461 0.664937i
\(446\) 0 0
\(447\) −3.73662 1.21410i −0.176736 0.0574251i
\(448\) 0 0
\(449\) 2.83956 0.134007 0.0670037 0.997753i \(-0.478656\pi\)
0.0670037 + 0.997753i \(0.478656\pi\)
\(450\) 0 0
\(451\) 2.96634 0.139679
\(452\) 0 0
\(453\) 7.54585 + 2.45180i 0.354535 + 0.115195i
\(454\) 0 0
\(455\) 56.2637 + 8.68088i 2.63768 + 0.406966i
\(456\) 0 0
\(457\) 8.12004i 0.379840i −0.981800 0.189920i \(-0.939177\pi\)
0.981800 0.189920i \(-0.0608228\pi\)
\(458\) 0 0
\(459\) 5.14965 + 3.74144i 0.240365 + 0.174636i
\(460\) 0 0
\(461\) −14.5629 + 10.5806i −0.678261 + 0.492786i −0.872780 0.488113i \(-0.837685\pi\)
0.194519 + 0.980899i \(0.437685\pi\)
\(462\) 0 0
\(463\) −16.8529 + 23.1960i −0.783219 + 1.07801i 0.211700 + 0.977335i \(0.432100\pi\)
−0.994919 + 0.100674i \(0.967900\pi\)
\(464\) 0 0
\(465\) 4.40030 + 8.55138i 0.204059 + 0.396561i
\(466\) 0 0
\(467\) −19.0638 + 6.19421i −0.882169 + 0.286634i −0.714858 0.699270i \(-0.753509\pi\)
−0.167311 + 0.985904i \(0.553509\pi\)
\(468\) 0 0
\(469\) 5.18902 + 15.9702i 0.239607 + 0.737433i
\(470\) 0 0
\(471\) −1.88419 + 5.79896i −0.0868191 + 0.267202i
\(472\) 0 0
\(473\) 10.6200 + 14.6172i 0.488310 + 0.672101i
\(474\) 0 0
\(475\) 11.0333 + 3.48765i 0.506241 + 0.160024i
\(476\) 0 0
\(477\) 7.02889 + 9.67443i 0.321831 + 0.442962i
\(478\) 0 0
\(479\) 4.78232 14.7185i 0.218510 0.672505i −0.780376 0.625311i \(-0.784972\pi\)
0.998886 0.0471937i \(-0.0150278\pi\)
\(480\) 0 0
\(481\) 16.0364 + 49.3548i 0.731195 + 2.25039i
\(482\) 0 0
\(483\) 7.34041 2.38504i 0.334000 0.108523i
\(484\) 0 0
\(485\) −40.0471 + 6.50704i −1.81844 + 0.295470i
\(486\) 0 0
\(487\) −22.0222 + 30.3110i −0.997923 + 1.37352i −0.0713312 + 0.997453i \(0.522725\pi\)
−0.926591 + 0.376070i \(0.877275\pi\)
\(488\) 0 0
\(489\) −0.00206811 + 0.00150257i −9.35232e−5 + 6.79486e-5i
\(490\) 0 0
\(491\) −32.3517 23.5049i −1.46001 1.06076i −0.983360 0.181667i \(-0.941851\pi\)
−0.476651 0.879093i \(-0.658149\pi\)
\(492\) 0 0
\(493\) 5.39701i 0.243069i
\(494\) 0 0
\(495\) −4.38647 + 2.25715i −0.197157 + 0.101451i
\(496\) 0 0
\(497\) 46.4831 + 15.1033i 2.08505 + 0.677474i
\(498\) 0 0
\(499\) −28.3040 −1.26706 −0.633530 0.773718i \(-0.718395\pi\)
−0.633530 + 0.773718i \(0.718395\pi\)
\(500\) 0 0
\(501\) −10.1007 −0.451264
\(502\) 0 0
\(503\) 31.0839 + 10.0998i 1.38596 + 0.450327i 0.904625 0.426208i \(-0.140151\pi\)
0.481338 + 0.876535i \(0.340151\pi\)
\(504\) 0 0
\(505\) −11.8794 + 6.11281i −0.528627 + 0.272016i
\(506\) 0 0
\(507\) 38.5196i 1.71071i
\(508\) 0 0
\(509\) 13.8620 + 10.0713i 0.614422 + 0.446404i 0.850969 0.525217i \(-0.176016\pi\)
−0.236547 + 0.971620i \(0.576016\pi\)
\(510\) 0 0
\(511\) 3.12549 2.27080i 0.138264 0.100454i
\(512\) 0 0
\(513\) −1.36030 + 1.87229i −0.0600586 + 0.0826636i
\(514\) 0 0
\(515\) 1.01432 0.164812i 0.0446964 0.00726250i
\(516\) 0 0
\(517\) −12.7035 + 4.12763i −0.558701 + 0.181533i
\(518\) 0 0
\(519\) 1.90969 + 5.87741i 0.0838260 + 0.257990i
\(520\) 0 0
\(521\) 6.22259 19.1512i 0.272617 0.839028i −0.717223 0.696843i \(-0.754587\pi\)
0.989840 0.142185i \(-0.0454128\pi\)
\(522\) 0 0
\(523\) −16.4036 22.5777i −0.717281 0.987253i −0.999610 0.0279349i \(-0.991107\pi\)
0.282329 0.959318i \(-0.408893\pi\)
\(524\) 0 0
\(525\) 10.5389 + 14.2643i 0.459954 + 0.622544i
\(526\) 0 0
\(527\) −16.0916 22.1482i −0.700960 0.964789i
\(528\) 0 0
\(529\) 5.64428 17.3713i 0.245403 0.755274i
\(530\) 0 0
\(531\) −3.85387 11.8610i −0.167244 0.514724i
\(532\) 0 0
\(533\) −9.17857 + 2.98230i −0.397568 + 0.129178i
\(534\) 0 0
\(535\) 2.53590 + 4.92818i 0.109636 + 0.213064i
\(536\) 0 0
\(537\) −8.48325 + 11.6762i −0.366079 + 0.503865i
\(538\) 0 0
\(539\) −9.96200 + 7.23781i −0.429094 + 0.311755i
\(540\) 0 0
\(541\) 9.00089 + 6.53953i 0.386979 + 0.281156i 0.764216 0.644960i \(-0.223126\pi\)
−0.377238 + 0.926116i \(0.623126\pi\)
\(542\) 0 0
\(543\) 6.74285i 0.289363i
\(544\) 0 0
\(545\) 7.38392 + 1.13926i 0.316292 + 0.0488004i
\(546\) 0 0
\(547\) 26.4684 + 8.60009i 1.13171 + 0.367713i 0.814224 0.580551i \(-0.197163\pi\)
0.317482 + 0.948264i \(0.397163\pi\)
\(548\) 0 0
\(549\) 6.92041 0.295356
\(550\) 0 0
\(551\) −1.96222 −0.0835935
\(552\) 0 0
\(553\) 19.7091 + 6.40389i 0.838118 + 0.272321i
\(554\) 0 0
\(555\) −7.28190 + 14.4339i −0.309099 + 0.612685i
\(556\) 0 0
\(557\) 6.36580i 0.269728i −0.990864 0.134864i \(-0.956940\pi\)
0.990864 0.134864i \(-0.0430597\pi\)
\(558\) 0 0
\(559\) −47.5569 34.5521i −2.01144 1.46140i
\(560\) 0 0
\(561\) 11.3610 8.25424i 0.479661 0.348494i
\(562\) 0 0
\(563\) −10.0676 + 13.8569i −0.424301 + 0.584000i −0.966633 0.256164i \(-0.917541\pi\)
0.542333 + 0.840164i \(0.317541\pi\)
\(564\) 0 0
\(565\) −6.00028 + 38.8898i −0.252434 + 1.63611i
\(566\) 0 0
\(567\) −3.37344 + 1.09610i −0.141671 + 0.0460317i
\(568\) 0 0
\(569\) −4.75461 14.6332i −0.199324 0.613455i −0.999899 0.0142229i \(-0.995473\pi\)
0.800575 0.599232i \(-0.204527\pi\)
\(570\) 0 0
\(571\) 2.63760 8.11770i 0.110380 0.339715i −0.880575 0.473906i \(-0.842844\pi\)
0.990955 + 0.134191i \(0.0428435\pi\)
\(572\) 0 0
\(573\) −9.04634 12.4512i −0.377916 0.520157i
\(574\) 0 0
\(575\) −10.8794 + 0.0869850i −0.453701 + 0.00362752i
\(576\) 0 0
\(577\) 1.35494 + 1.86491i 0.0564068 + 0.0776374i 0.836289 0.548290i \(-0.184721\pi\)
−0.779882 + 0.625927i \(0.784721\pi\)
\(578\) 0 0
\(579\) −5.06402 + 15.5854i −0.210453 + 0.647709i
\(580\) 0 0
\(581\) −13.7315 42.2614i −0.569681 1.75330i
\(582\) 0 0
\(583\) 25.0907 8.15245i 1.03915 0.337640i
\(584\) 0 0
\(585\) 11.3035 11.3942i 0.467342 0.471094i
\(586\) 0 0
\(587\) 0.540303 0.743663i 0.0223007 0.0306943i −0.797721 0.603027i \(-0.793961\pi\)
0.820022 + 0.572332i \(0.193961\pi\)
\(588\) 0 0
\(589\) 8.05253 5.85051i 0.331799 0.241066i
\(590\) 0 0
\(591\) −7.96910 5.78989i −0.327805 0.238164i
\(592\) 0 0
\(593\) 25.5925i 1.05096i 0.850807 + 0.525478i \(0.176114\pi\)
−0.850807 + 0.525478i \(0.823886\pi\)
\(594\) 0 0
\(595\) −35.8415 35.5560i −1.46936 1.45766i
\(596\) 0 0
\(597\) 4.71985 + 1.53357i 0.193171 + 0.0627650i
\(598\) 0 0
\(599\) 37.0204 1.51261 0.756307 0.654217i \(-0.227002\pi\)
0.756307 + 0.654217i \(0.227002\pi\)
\(600\) 0 0
\(601\) 33.4191 1.36319 0.681597 0.731728i \(-0.261286\pi\)
0.681597 + 0.731728i \(0.261286\pi\)
\(602\) 0 0
\(603\) 4.50239 + 1.46291i 0.183351 + 0.0595745i
\(604\) 0 0
\(605\) −2.19938 13.5359i −0.0894176 0.550313i
\(606\) 0 0
\(607\) 4.34502i 0.176359i 0.996105 + 0.0881795i \(0.0281049\pi\)
−0.996105 + 0.0881795i \(0.971895\pi\)
\(608\) 0 0
\(609\) −2.43308 1.76774i −0.0985935 0.0716323i
\(610\) 0 0
\(611\) 35.1580 25.5438i 1.42234 1.03339i
\(612\) 0 0
\(613\) −2.32761 + 3.20367i −0.0940111 + 0.129395i −0.853431 0.521205i \(-0.825483\pi\)
0.759420 + 0.650600i \(0.225483\pi\)
\(614\) 0 0
\(615\) −2.68429 1.35422i −0.108241 0.0546075i
\(616\) 0 0
\(617\) −19.2721 + 6.26189i −0.775866 + 0.252094i −0.670074 0.742294i \(-0.733738\pi\)
−0.105792 + 0.994388i \(0.533738\pi\)
\(618\) 0 0
\(619\) 4.65930 + 14.3398i 0.187273 + 0.576367i 0.999980 0.00630532i \(-0.00200706\pi\)
−0.812707 + 0.582672i \(0.802007\pi\)
\(620\) 0 0
\(621\) 0.672404 2.06945i 0.0269826 0.0830440i
\(622\) 0 0
\(623\) −14.6487 20.1622i −0.586888 0.807782i
\(624\) 0 0
\(625\) −8.10462 23.6498i −0.324185 0.945994i
\(626\) 0 0
\(627\) 3.00104 + 4.13058i 0.119850 + 0.164959i
\(628\) 0 0
\(629\) 14.2213 43.7687i 0.567041 1.74517i
\(630\) 0 0
\(631\) −0.755761 2.32599i −0.0300864 0.0925963i 0.934886 0.354949i \(-0.115502\pi\)
−0.964972 + 0.262352i \(0.915502\pi\)
\(632\) 0 0
\(633\) −3.32851 + 1.08150i −0.132296 + 0.0429857i
\(634\) 0 0
\(635\) −24.7791 12.5011i −0.983329 0.496090i
\(636\) 0 0
\(637\) 23.5481 32.4112i 0.933009 1.28418i
\(638\) 0 0
\(639\) 11.1476 8.09918i 0.440991 0.320399i
\(640\) 0 0
\(641\) −10.8353 7.87228i −0.427967 0.310936i 0.352868 0.935673i \(-0.385206\pi\)
−0.780836 + 0.624737i \(0.785206\pi\)
\(642\) 0 0
\(643\) 35.4836i 1.39934i −0.714467 0.699669i \(-0.753331\pi\)
0.714467 0.699669i \(-0.246669\pi\)
\(644\) 0 0
\(645\) −2.93704 18.0757i −0.115646 0.711731i
\(646\) 0 0
\(647\) 21.2886 + 6.91707i 0.836940 + 0.271938i 0.695966 0.718075i \(-0.254977\pi\)
0.140974 + 0.990013i \(0.454977\pi\)
\(648\) 0 0
\(649\) −27.5140 −1.08002
\(650\) 0 0
\(651\) 15.2555 0.597909
\(652\) 0 0
\(653\) −18.0021 5.84923i −0.704476 0.228898i −0.0651961 0.997872i \(-0.520767\pi\)
−0.639279 + 0.768974i \(0.720767\pi\)
\(654\) 0 0
\(655\) −25.1185 24.9184i −0.981460 0.973644i
\(656\) 0 0
\(657\) 1.08917i 0.0424925i
\(658\) 0 0
\(659\) 4.58371 + 3.33026i 0.178556 + 0.129729i 0.673473 0.739212i \(-0.264802\pi\)
−0.494917 + 0.868940i \(0.664802\pi\)
\(660\) 0 0
\(661\) 20.4225 14.8378i 0.794342 0.577123i −0.114907 0.993376i \(-0.536657\pi\)
0.909249 + 0.416253i \(0.136657\pi\)
\(662\) 0 0
\(663\) −26.8550 + 36.9627i −1.04296 + 1.43551i
\(664\) 0 0
\(665\) 12.9273 13.0311i 0.501300 0.505324i
\(666\) 0 0
\(667\) 1.75464 0.570116i 0.0679398 0.0220750i
\(668\) 0 0
\(669\) −7.13168 21.9491i −0.275727 0.848600i
\(670\) 0 0
\(671\) 4.71794 14.5203i 0.182134 0.560551i
\(672\) 0 0
\(673\) −7.74044 10.6538i −0.298372 0.410674i 0.633339 0.773875i \(-0.281684\pi\)
−0.931711 + 0.363201i \(0.881684\pi\)
\(674\) 0 0
\(675\) 4.99984 0.0399757i 0.192444 0.00153867i
\(676\) 0 0
\(677\) 15.8487 + 21.8139i 0.609115 + 0.838375i 0.996504 0.0835409i \(-0.0266229\pi\)
−0.387389 + 0.921916i \(0.626623\pi\)
\(678\) 0 0
\(679\) −19.8881 + 61.2092i −0.763234 + 2.34899i
\(680\) 0 0
\(681\) −1.80793 5.56424i −0.0692801 0.213222i
\(682\) 0 0
\(683\) −49.2454 + 16.0008i −1.88432 + 0.612254i −0.899996 + 0.435897i \(0.856431\pi\)
−0.984326 + 0.176356i \(0.943569\pi\)
\(684\) 0 0
\(685\) 2.52142 16.3422i 0.0963386 0.624403i
\(686\) 0 0
\(687\) 3.75637 5.17019i 0.143314 0.197255i
\(688\) 0 0
\(689\) −69.4403 + 50.4513i −2.64546 + 1.92204i
\(690\) 0 0
\(691\) 3.00647 + 2.18432i 0.114371 + 0.0830956i 0.643501 0.765446i \(-0.277481\pi\)
−0.529129 + 0.848541i \(0.677481\pi\)
\(692\) 0 0
\(693\) 7.82536i 0.297261i
\(694\) 0 0
\(695\) −3.96722 + 7.86367i −0.150485 + 0.298286i
\(696\) 0 0
\(697\) 8.13972 + 2.64475i 0.308314 + 0.100177i
\(698\) 0 0
\(699\) −4.54311 −0.171836
\(700\) 0 0
\(701\) −28.4299 −1.07378 −0.536890 0.843652i \(-0.680401\pi\)
−0.536890 + 0.843652i \(0.680401\pi\)
\(702\) 0 0
\(703\) 15.9132 + 5.17053i 0.600180 + 0.195010i
\(704\) 0 0
\(705\) 13.3800 + 2.06439i 0.503921 + 0.0777495i
\(706\) 0 0
\(707\) 21.1926i 0.797030i
\(708\) 0 0
\(709\) 33.1126 + 24.0577i 1.24357 + 0.903507i 0.997831 0.0658288i \(-0.0209691\pi\)
0.245740 + 0.969336i \(0.420969\pi\)
\(710\) 0 0
\(711\) 4.72664 3.43411i 0.177263 0.128789i
\(712\) 0 0
\(713\) −5.50080 + 7.57120i −0.206007 + 0.283544i
\(714\) 0 0
\(715\) −16.2012 31.4848i −0.605890 1.17746i
\(716\) 0 0
\(717\) 21.9134 7.12010i 0.818372 0.265905i
\(718\) 0 0
\(719\) −1.46368 4.50475i −0.0545861 0.167999i 0.920047 0.391809i \(-0.128151\pi\)
−0.974633 + 0.223810i \(0.928151\pi\)
\(720\) 0 0
\(721\) 0.503731 1.55032i 0.0187599 0.0577371i
\(722\) 0 0
\(723\) −9.66766 13.3064i −0.359544 0.494870i
\(724\) 0 0
\(725\) 2.51919 + 3.40970i 0.0935604 + 0.126633i
\(726\) 0 0
\(727\) −3.27447 4.50692i −0.121443 0.167153i 0.743967 0.668217i \(-0.232942\pi\)
−0.865410 + 0.501064i \(0.832942\pi\)
\(728\) 0 0
\(729\) −0.309017 + 0.951057i −0.0114451 + 0.0352243i
\(730\) 0 0
\(731\) 16.1091 + 49.5788i 0.595818 + 1.83374i
\(732\) 0 0
\(733\) 28.8738 9.38166i 1.06648 0.346520i 0.277363 0.960765i \(-0.410540\pi\)
0.789115 + 0.614246i \(0.210540\pi\)
\(734\) 0 0
\(735\) 12.3190 2.00166i 0.454395 0.0738323i
\(736\) 0 0
\(737\) 6.13894 8.44952i 0.226131 0.311242i
\(738\) 0 0
\(739\) 39.6127 28.7803i 1.45718 1.05870i 0.473089 0.881015i \(-0.343139\pi\)
0.984087 0.177686i \(-0.0568611\pi\)
\(740\) 0 0
\(741\) −13.4388 9.76383i −0.493685 0.358683i
\(742\) 0 0
\(743\) 45.5953i 1.67273i 0.548174 + 0.836364i \(0.315323\pi\)
−0.548174 + 0.836364i \(0.684677\pi\)
\(744\) 0 0
\(745\) 7.81178 4.01972i 0.286201 0.147271i
\(746\) 0 0
\(747\) −11.9145 3.87127i −0.435930 0.141642i
\(748\) 0 0
\(749\) 8.79176 0.321244
\(750\) 0 0
\(751\) −27.9100 −1.01845 −0.509225 0.860633i \(-0.670068\pi\)
−0.509225 + 0.860633i \(0.670068\pi\)
\(752\) 0 0
\(753\) 4.43503 + 1.44103i 0.161621 + 0.0525140i
\(754\) 0 0
\(755\) −15.7753 + 8.11754i −0.574123 + 0.295427i
\(756\) 0 0
\(757\) 27.6680i 1.00561i −0.864400 0.502804i \(-0.832302\pi\)
0.864400 0.502804i \(-0.167698\pi\)
\(758\) 0 0
\(759\) −3.88368 2.82166i −0.140969 0.102420i
\(760\) 0 0
\(761\) 9.80362 7.12275i 0.355381 0.258199i −0.395742 0.918362i \(-0.629513\pi\)
0.751123 + 0.660162i \(0.229513\pi\)
\(762\) 0 0
\(763\) 6.96619 9.58814i 0.252193 0.347114i
\(764\) 0 0
\(765\) −14.0490 + 2.28276i −0.507944 + 0.0825333i
\(766\) 0 0
\(767\) 85.1349 27.6620i 3.07404 0.998817i
\(768\) 0 0
\(769\) 3.13398 + 9.64540i 0.113014 + 0.347822i 0.991528 0.129896i \(-0.0414642\pi\)
−0.878513 + 0.477718i \(0.841464\pi\)
\(770\) 0 0
\(771\) −1.78839 + 5.50409i −0.0644071 + 0.198225i
\(772\) 0 0
\(773\) 29.4908 + 40.5906i 1.06071 + 1.45994i 0.879140 + 0.476563i \(0.158118\pi\)
0.181569 + 0.983378i \(0.441882\pi\)
\(774\) 0 0
\(775\) −20.5045 6.48153i −0.736542 0.232823i
\(776\) 0 0
\(777\) 15.0738 + 20.7473i 0.540769 + 0.744304i
\(778\) 0 0
\(779\) −0.961568 + 2.95940i −0.0344518 + 0.106032i
\(780\) 0 0
\(781\) −9.39383 28.9112i −0.336138 1.03453i
\(782\) 0 0
\(783\) −0.806379 + 0.262008i −0.0288176 + 0.00936342i
\(784\) 0 0
\(785\) −6.23829 12.1233i −0.222654 0.432699i
\(786\) 0 0
\(787\) −9.08606 + 12.5059i −0.323883 + 0.445787i −0.939648 0.342143i \(-0.888847\pi\)
0.615765 + 0.787930i \(0.288847\pi\)
\(788\) 0 0
\(789\) 18.5668 13.4896i 0.660996 0.480242i
\(790\) 0 0
\(791\) 50.4991 + 36.6897i 1.79554 + 1.30454i
\(792\) 0 0
\(793\) 49.6727i 1.76393i
\(794\) 0 0
\(795\) −26.4268 4.07736i −0.937261 0.144609i
\(796\) 0 0
\(797\) −5.45087 1.77110i −0.193080 0.0627354i 0.210881 0.977512i \(-0.432367\pi\)
−0.403961 + 0.914776i \(0.632367\pi\)
\(798\) 0 0
\(799\) −38.5390 −1.36341
\(800\) 0 0
\(801\) −7.02611 −0.248255
\(802\) 0 0
\(803\) −2.28528 0.742531i −0.0806457 0.0262034i
\(804\) 0 0
\(805\) −7.77359 + 15.4085i −0.273983 + 0.543078i
\(806\) 0 0
\(807\) 4.50997i 0.158758i
\(808\) 0 0
\(809\) −22.9907 16.7038i −0.808312 0.587273i 0.105029 0.994469i \(-0.466506\pi\)
−0.913341 + 0.407196i \(0.866506\pi\)
\(810\) 0 0
\(811\) 9.86048 7.16406i 0.346248 0.251564i −0.401045 0.916058i \(-0.631353\pi\)
0.747293 + 0.664494i \(0.231353\pi\)
\(812\) 0 0
\(813\) −5.83748 + 8.03461i −0.204730 + 0.281786i
\(814\) 0 0
\(815\) 0.000871621 0.00564927i 3.05315e−5 0.000197885i
\(816\) 0 0
\(817\) −18.0257 + 5.85689i −0.630638 + 0.204907i
\(818\) 0 0
\(819\) −7.86746 24.2136i −0.274911 0.846090i
\(820\) 0 0
\(821\) 4.51854 13.9066i 0.157698 0.485345i −0.840726 0.541461i \(-0.817872\pi\)
0.998424 + 0.0561157i \(0.0178716\pi\)
\(822\) 0 0
\(823\) 12.7201 + 17.5077i 0.443394 + 0.610280i 0.970962 0.239233i \(-0.0768960\pi\)
−0.527568 + 0.849513i \(0.676896\pi\)
\(824\) 0 0
\(825\) 3.32473 10.5179i 0.115752 0.366185i
\(826\) 0 0
\(827\) −6.56096 9.03038i −0.228147 0.314017i 0.679562 0.733618i \(-0.262170\pi\)
−0.907709 + 0.419601i \(0.862170\pi\)
\(828\) 0 0
\(829\) −8.60563 + 26.4854i −0.298886 + 0.919876i 0.683003 + 0.730416i \(0.260674\pi\)
−0.981888 + 0.189460i \(0.939326\pi\)
\(830\) 0 0
\(831\) −7.11211 21.8888i −0.246716 0.759315i
\(832\) 0 0
\(833\) −33.7892 + 10.9788i −1.17073 + 0.380392i
\(834\) 0 0
\(835\) 15.9066 16.0343i 0.550470 0.554889i
\(836\) 0 0
\(837\) 2.52801 3.47950i 0.0873807 0.120269i
\(838\) 0 0
\(839\) −15.3556 + 11.1565i −0.530133 + 0.385164i −0.820408 0.571779i \(-0.806253\pi\)
0.290274 + 0.956943i \(0.406253\pi\)
\(840\) 0 0
\(841\) 22.8799 + 16.6232i 0.788962 + 0.573214i
\(842\) 0 0
\(843\) 0.734004i 0.0252804i
\(844\) 0 0
\(845\) 61.1478 + 60.6608i 2.10355 + 2.08680i
\(846\) 0 0
\(847\) −20.6887 6.72218i −0.710873 0.230977i
\(848\) 0 0
\(849\) −21.4921 −0.737609
\(850\) 0 0
\(851\) −15.7320 −0.539287
\(852\) 0 0
\(853\) 15.6987 + 5.10082i 0.537513 + 0.174649i 0.565179 0.824969i \(-0.308807\pi\)
−0.0276653 + 0.999617i \(0.508807\pi\)
\(854\) 0 0
\(855\) −0.829955 5.10789i −0.0283839 0.174686i
\(856\) 0 0
\(857\) 28.7615i 0.982475i 0.871026 + 0.491237i \(0.163455\pi\)
−0.871026 + 0.491237i \(0.836545\pi\)
\(858\) 0 0
\(859\) −12.2446 8.89622i −0.417780 0.303535i 0.358964 0.933351i \(-0.383130\pi\)
−0.776744 + 0.629816i \(0.783130\pi\)
\(860\) 0 0
\(861\) −3.85839 + 2.80329i −0.131494 + 0.0955357i
\(862\) 0 0
\(863\) 25.3024 34.8258i 0.861305 1.18549i −0.119951 0.992780i \(-0.538274\pi\)
0.981257 0.192705i \(-0.0617262\pi\)
\(864\) 0 0
\(865\) −12.3375 6.22426i −0.419487 0.211631i
\(866\) 0 0
\(867\) 22.3663 7.26725i 0.759600 0.246809i
\(868\) 0 0
\(869\) −3.98305 12.2586i −0.135116 0.415843i
\(870\) 0 0
\(871\) −10.5004 + 32.3168i −0.355792 + 1.09501i
\(872\) 0 0
\(873\) 10.6651 + 14.6792i 0.360957 + 0.496815i
\(874\) 0 0
\(875\) −39.2405 5.73356i −1.32657 0.193830i
\(876\) 0 0
\(877\) −29.7980 41.0134i −1.00621 1.38492i −0.921439 0.388523i \(-0.872985\pi\)
−0.0847668 0.996401i \(-0.527015\pi\)
\(878\) 0 0
\(879\) 8.21864 25.2944i 0.277208 0.853158i
\(880\) 0 0
\(881\) −0.818966 2.52052i −0.0275917 0.0849184i 0.936312 0.351168i \(-0.114215\pi\)
−0.963904 + 0.266250i \(0.914215\pi\)
\(882\) 0 0
\(883\) 32.1189 10.4361i 1.08089 0.351201i 0.286168 0.958179i \(-0.407618\pi\)
0.794719 + 0.606978i \(0.207618\pi\)
\(884\) 0 0
\(885\) 24.8978 + 12.5609i 0.836931 + 0.422232i
\(886\) 0 0
\(887\) 2.54153 3.49811i 0.0853361 0.117455i −0.764215 0.644962i \(-0.776873\pi\)
0.849551 + 0.527507i \(0.176873\pi\)
\(888\) 0 0
\(889\) −35.6175 + 25.8776i −1.19457 + 0.867908i
\(890\) 0 0
\(891\) 1.78482 + 1.29675i 0.0597939 + 0.0434428i
\(892\) 0 0
\(893\) 14.0119i 0.468889i
\(894\) 0 0
\(895\) −5.17586 31.8544i −0.173010 1.06478i
\(896\) 0 0
\(897\) 14.8539 + 4.82632i 0.495957 + 0.161146i
\(898\) 0 0
\(899\) 3.64664 0.121622
\(900\) 0 0
\(901\) 76.1182 2.53586
\(902\) 0 0
\(903\) −27.6275 8.97673i −0.919387 0.298727i
\(904\) 0 0
\(905\) −10.7039 10.6187i −0.355810 0.352977i
\(906\) 0 0
\(907\) 47.2507i 1.56893i 0.620171 + 0.784467i \(0.287063\pi\)
−0.620171 + 0.784467i \(0.712937\pi\)
\(908\) 0 0
\(909\) 4.83366 + 3.51186i 0.160322 + 0.116481i
\(910\) 0 0
\(911\) −41.1586 + 29.9035i −1.36365 + 0.990747i −0.365443 + 0.930834i \(0.619082\pi\)
−0.998204 + 0.0599132i \(0.980918\pi\)
\(912\) 0 0
\(913\) −16.2453 + 22.3597i −0.537641 + 0.739999i
\(914\) 0 0
\(915\) −10.8983 + 10.9858i −0.360287 + 0.363179i
\(916\) 0 0
\(917\) −53.3785 + 17.3437i −1.76271 + 0.572740i
\(918\) 0 0
\(919\) 11.3396 + 34.8998i 0.374060 + 1.15124i 0.944111 + 0.329629i \(0.106924\pi\)
−0.570051 + 0.821610i \(0.693076\pi\)
\(920\) 0 0
\(921\) 3.76186 11.5778i 0.123957 0.381502i
\(922\) 0 0
\(923\) 58.1336 + 80.0140i 1.91349 + 2.63369i
\(924\) 0 0
\(925\) −11.4455 34.2902i −0.376324 1.12745i
\(926\) 0 0
\(927\) −0.270128 0.371799i −0.00887215 0.0122115i
\(928\) 0 0
\(929\) −14.9269 + 45.9401i −0.489734 + 1.50725i 0.335271 + 0.942122i \(0.391172\pi\)
−0.825005 + 0.565125i \(0.808828\pi\)
\(930\) 0 0
\(931\) −3.99161 12.2849i −0.130820 0.402622i
\(932\) 0 0
\(933\) 23.5502 7.65191i 0.770998 0.250512i
\(934\) 0 0
\(935\) −4.78817 + 31.0338i −0.156590 + 1.01491i
\(936\) 0 0
\(937\) −5.57420 + 7.67223i −0.182101 + 0.250641i −0.890302 0.455370i \(-0.849507\pi\)
0.708201 + 0.706011i \(0.249507\pi\)
\(938\) 0 0
\(939\) 12.0102 8.72589i 0.391937 0.284759i
\(940\) 0 0
\(941\) 17.2272 + 12.5163i 0.561590 + 0.408019i 0.832041 0.554715i \(-0.187173\pi\)
−0.270450 + 0.962734i \(0.587173\pi\)
\(942\) 0 0
\(943\) 2.92570i 0.0952740i
\(944\) 0 0
\(945\) 3.57251 7.08129i 0.116214 0.230354i
\(946\) 0 0
\(947\) 29.9695 + 9.73768i 0.973877 + 0.316432i 0.752380 0.658729i \(-0.228906\pi\)
0.221497 + 0.975161i \(0.428906\pi\)
\(948\) 0 0
\(949\) 7.81773 0.253774
\(950\) 0 0
\(951\) 1.94231 0.0629837
\(952\) 0 0
\(953\) −10.6646 3.46513i −0.345460 0.112247i 0.131148 0.991363i \(-0.458134\pi\)
−0.476608 + 0.879116i \(0.658134\pi\)
\(954\) 0 0
\(955\) 34.0119 + 5.24766i 1.10060 + 0.169810i
\(956\) 0 0
\(957\) 1.87056i 0.0604665i
\(958\) 0 0
\(959\) −21.2206 15.4177i −0.685249 0.497863i
\(960\) 0 0
\(961\) 10.1145 7.34864i 0.326275 0.237053i
\(962\) 0 0
\(963\) 1.45689 2.00524i 0.0469478 0.0646181i
\(964\) 0 0
\(965\) −16.7662 32.5829i −0.539724 1.04888i
\(966\) 0 0
\(967\) 33.8782 11.0077i 1.08945 0.353984i 0.291417 0.956596i \(-0.405873\pi\)
0.798034 + 0.602612i \(0.205873\pi\)
\(968\) 0 0
\(969\) 4.55217 + 14.0101i 0.146237 + 0.450070i
\(970\) 0 0
\(971\) 13.2227 40.6953i 0.424337 1.30598i −0.479290 0.877656i \(-0.659106\pi\)
0.903628 0.428319i \(-0.140894\pi\)
\(972\) 0 0
\(973\) 8.21228 + 11.3032i 0.263274 + 0.362365i
\(974\) 0 0
\(975\) 0.286934 + 35.8874i 0.00918925 + 1.14932i
\(976\) 0 0
\(977\) 23.9119 + 32.9119i 0.765009 + 1.05294i 0.996781 + 0.0801740i \(0.0255476\pi\)
−0.231772 + 0.972770i \(0.574452\pi\)
\(978\) 0 0
\(979\) −4.78999 + 14.7421i −0.153089 + 0.471159i
\(980\) 0 0
\(981\) −1.03251 3.17773i −0.0329654 0.101457i
\(982\) 0 0
\(983\) −46.5713 + 15.1319i −1.48539 + 0.482634i −0.935719 0.352746i \(-0.885248\pi\)
−0.549674 + 0.835379i \(0.685248\pi\)
\(984\) 0 0
\(985\) 21.7409 3.53257i 0.692723 0.112557i
\(986\) 0 0
\(987\) 12.6231 17.3742i 0.401797 0.553026i
\(988\) 0 0
\(989\) 14.4170 10.4746i 0.458434 0.333072i
\(990\) 0 0
\(991\) 1.99334 + 1.44825i 0.0633206 + 0.0460051i 0.618995 0.785395i \(-0.287540\pi\)
−0.555675 + 0.831400i \(0.687540\pi\)
\(992\) 0 0
\(993\) 27.7307i 0.880006i
\(994\) 0 0
\(995\) −9.86732 + 5.07744i −0.312815 + 0.160966i
\(996\) 0 0
\(997\) −51.5975 16.7650i −1.63411 0.530954i −0.658899 0.752232i \(-0.728977\pi\)
−0.975211 + 0.221277i \(0.928977\pi\)
\(998\) 0 0
\(999\) 7.22998 0.228747
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 300.2.o.a.289.4 yes 24
3.2 odd 2 900.2.w.c.289.5 24
5.2 odd 4 1500.2.m.c.301.1 24
5.3 odd 4 1500.2.m.d.301.6 24
5.4 even 2 1500.2.o.c.949.3 24
25.3 odd 20 7500.2.a.m.1.11 12
25.4 even 10 7500.2.d.g.1249.2 24
25.9 even 10 inner 300.2.o.a.109.4 24
25.12 odd 20 1500.2.m.c.1201.1 24
25.13 odd 20 1500.2.m.d.1201.6 24
25.16 even 5 1500.2.o.c.49.3 24
25.21 even 5 7500.2.d.g.1249.23 24
25.22 odd 20 7500.2.a.n.1.2 12
75.59 odd 10 900.2.w.c.109.5 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
300.2.o.a.109.4 24 25.9 even 10 inner
300.2.o.a.289.4 yes 24 1.1 even 1 trivial
900.2.w.c.109.5 24 75.59 odd 10
900.2.w.c.289.5 24 3.2 odd 2
1500.2.m.c.301.1 24 5.2 odd 4
1500.2.m.c.1201.1 24 25.12 odd 20
1500.2.m.d.301.6 24 5.3 odd 4
1500.2.m.d.1201.6 24 25.13 odd 20
1500.2.o.c.49.3 24 25.16 even 5
1500.2.o.c.949.3 24 5.4 even 2
7500.2.a.m.1.11 12 25.3 odd 20
7500.2.a.n.1.2 12 25.22 odd 20
7500.2.d.g.1249.2 24 25.4 even 10
7500.2.d.g.1249.23 24 25.21 even 5