Properties

Label 572.2.bq.a.49.3
Level $572$
Weight $2$
Character 572.49
Analytic conductor $4.567$
Analytic rank $0$
Dimension $112$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [572,2,Mod(49,572)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(572, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 12, 25]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("572.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 572.bq (of order \(30\), degree \(8\), 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: \(4.56744299562\)
Analytic rank: \(0\)
Dimension: \(112\)
Relative dimension: \(14\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 49.3
Character \(\chi\) \(=\) 572.49
Dual form 572.2.bq.a.537.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.228377 + 2.17287i) q^{3} +(-1.96627 - 0.638880i) q^{5} +(0.214213 - 0.0225147i) q^{7} +(-1.73475 - 0.368732i) q^{9} +O(q^{10})\) \(q+(-0.228377 + 2.17287i) q^{3} +(-1.96627 - 0.638880i) q^{5} +(0.214213 - 0.0225147i) q^{7} +(-1.73475 - 0.368732i) q^{9} +(-2.60415 + 2.05387i) q^{11} +(-3.55220 - 0.617985i) q^{13} +(1.83725 - 4.12654i) q^{15} +(-3.14172 - 3.48924i) q^{17} +(1.28304 + 2.88176i) q^{19} +0.470598i q^{21} +(-3.14916 - 5.45450i) q^{23} +(-0.587028 - 0.426501i) q^{25} +(-0.828072 + 2.54854i) q^{27} +(0.874739 + 0.389459i) q^{29} +(1.14922 - 0.373404i) q^{31} +(-3.86806 - 6.12753i) q^{33} +(-0.435585 - 0.0925865i) q^{35} +(-1.25197 + 2.81197i) q^{37} +(2.15404 - 7.57731i) q^{39} +(-4.26163 - 0.447915i) q^{41} +(1.22456 - 2.12100i) q^{43} +(3.17541 + 1.83332i) q^{45} +(3.68927 - 5.07784i) q^{47} +(-6.80165 + 1.44574i) q^{49} +(8.29914 - 6.02968i) q^{51} +(-1.27940 - 3.93759i) q^{53} +(6.43265 - 2.37473i) q^{55} +(-6.55470 + 2.12975i) q^{57} +(0.807588 - 0.0848809i) q^{59} +(1.94746 + 2.16287i) q^{61} +(-0.379907 - 0.0399298i) q^{63} +(6.58976 + 3.48455i) q^{65} +(-7.02583 + 4.05637i) q^{67} +(12.5711 - 5.59701i) q^{69} +(-8.90772 + 8.02055i) q^{71} +(8.70946 + 11.9875i) q^{73} +(1.06079 - 1.17813i) q^{75} +(-0.511601 + 0.498598i) q^{77} +(1.81378 + 5.58224i) q^{79} +(-10.2091 - 4.54536i) q^{81} +(8.54045 + 2.77496i) q^{83} +(3.94828 + 8.86797i) q^{85} +(-1.04601 + 1.81175i) q^{87} +(-13.6365 + 7.87302i) q^{89} +(-0.774840 - 0.0524038i) q^{91} +(0.548901 + 2.58238i) q^{93} +(-0.681710 - 6.48604i) q^{95} +(-1.98727 + 9.34936i) q^{97} +(5.27487 - 2.60272i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 112 q + 20 q^{9} - 6 q^{11} + 11 q^{13} + 30 q^{15} + 16 q^{17} - 12 q^{19} + 6 q^{23} + 40 q^{25} - 12 q^{27} - 5 q^{29} + 9 q^{33} - 33 q^{35} - 45 q^{39} - 18 q^{41} + 30 q^{45} - 16 q^{49} + 48 q^{51} - 2 q^{53} - 20 q^{55} - 39 q^{59} + 4 q^{61} - 102 q^{63} - 6 q^{65} + 48 q^{67} + 34 q^{69} + 84 q^{71} - 56 q^{75} - 22 q^{77} - 24 q^{79} + 16 q^{81} + 60 q^{85} - 34 q^{87} - 66 q^{89} - 41 q^{91} + 123 q^{93} + 12 q^{95} - 15 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(353\) \(365\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{5}\right)\)

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
\(3\) −0.228377 + 2.17287i −0.131854 + 1.25450i 0.705843 + 0.708369i \(0.250568\pi\)
−0.837697 + 0.546136i \(0.816098\pi\)
\(4\) 0 0
\(5\) −1.96627 0.638880i −0.879344 0.285716i −0.165659 0.986183i \(-0.552975\pi\)
−0.713685 + 0.700467i \(0.752975\pi\)
\(6\) 0 0
\(7\) 0.214213 0.0225147i 0.0809649 0.00850976i −0.0639594 0.997953i \(-0.520373\pi\)
0.144924 + 0.989443i \(0.453706\pi\)
\(8\) 0 0
\(9\) −1.73475 0.368732i −0.578249 0.122911i
\(10\) 0 0
\(11\) −2.60415 + 2.05387i −0.785181 + 0.619266i
\(12\) 0 0
\(13\) −3.55220 0.617985i −0.985202 0.171398i
\(14\) 0 0
\(15\) 1.83725 4.12654i 0.474377 1.06547i
\(16\) 0 0
\(17\) −3.14172 3.48924i −0.761980 0.846264i 0.229930 0.973207i \(-0.426150\pi\)
−0.991910 + 0.126943i \(0.959484\pi\)
\(18\) 0 0
\(19\) 1.28304 + 2.88176i 0.294350 + 0.661122i 0.998818 0.0486147i \(-0.0154806\pi\)
−0.704467 + 0.709737i \(0.748814\pi\)
\(20\) 0 0
\(21\) 0.470598i 0.102693i
\(22\) 0 0
\(23\) −3.14916 5.45450i −0.656644 1.13734i −0.981479 0.191570i \(-0.938642\pi\)
0.324835 0.945771i \(-0.394691\pi\)
\(24\) 0 0
\(25\) −0.587028 0.426501i −0.117406 0.0853002i
\(26\) 0 0
\(27\) −0.828072 + 2.54854i −0.159362 + 0.490467i
\(28\) 0 0
\(29\) 0.874739 + 0.389459i 0.162435 + 0.0723207i 0.486344 0.873768i \(-0.338330\pi\)
−0.323909 + 0.946088i \(0.604997\pi\)
\(30\) 0 0
\(31\) 1.14922 0.373404i 0.206406 0.0670654i −0.203989 0.978973i \(-0.565391\pi\)
0.410395 + 0.911908i \(0.365391\pi\)
\(32\) 0 0
\(33\) −3.86806 6.12753i −0.673343 1.06667i
\(34\) 0 0
\(35\) −0.435585 0.0925865i −0.0736273 0.0156500i
\(36\) 0 0
\(37\) −1.25197 + 2.81197i −0.205823 + 0.462286i −0.986732 0.162359i \(-0.948090\pi\)
0.780909 + 0.624645i \(0.214756\pi\)
\(38\) 0 0
\(39\) 2.15404 7.57731i 0.344922 1.21334i
\(40\) 0 0
\(41\) −4.26163 0.447915i −0.665554 0.0699526i −0.234274 0.972171i \(-0.575271\pi\)
−0.431280 + 0.902218i \(0.641938\pi\)
\(42\) 0 0
\(43\) 1.22456 2.12100i 0.186744 0.323449i −0.757419 0.652929i \(-0.773540\pi\)
0.944163 + 0.329480i \(0.106873\pi\)
\(44\) 0 0
\(45\) 3.17541 + 1.83332i 0.473362 + 0.273296i
\(46\) 0 0
\(47\) 3.68927 5.07784i 0.538135 0.740680i −0.450208 0.892924i \(-0.648650\pi\)
0.988343 + 0.152244i \(0.0486501\pi\)
\(48\) 0 0
\(49\) −6.80165 + 1.44574i −0.971665 + 0.206534i
\(50\) 0 0
\(51\) 8.29914 6.02968i 1.16211 0.844324i
\(52\) 0 0
\(53\) −1.27940 3.93759i −0.175739 0.540870i 0.823927 0.566696i \(-0.191779\pi\)
−0.999666 + 0.0258257i \(0.991779\pi\)
\(54\) 0 0
\(55\) 6.43265 2.37473i 0.867378 0.320209i
\(56\) 0 0
\(57\) −6.55470 + 2.12975i −0.868192 + 0.282093i
\(58\) 0 0
\(59\) 0.807588 0.0848809i 0.105139 0.0110505i −0.0518129 0.998657i \(-0.516500\pi\)
0.156952 + 0.987606i \(0.449833\pi\)
\(60\) 0 0
\(61\) 1.94746 + 2.16287i 0.249346 + 0.276927i 0.854805 0.518950i \(-0.173677\pi\)
−0.605458 + 0.795877i \(0.707010\pi\)
\(62\) 0 0
\(63\) −0.379907 0.0399298i −0.0478638 0.00503069i
\(64\) 0 0
\(65\) 6.58976 + 3.48455i 0.817360 + 0.432206i
\(66\) 0 0
\(67\) −7.02583 + 4.05637i −0.858342 + 0.495564i −0.863457 0.504423i \(-0.831705\pi\)
0.00511480 + 0.999987i \(0.498372\pi\)
\(68\) 0 0
\(69\) 12.5711 5.59701i 1.51338 0.673801i
\(70\) 0 0
\(71\) −8.90772 + 8.02055i −1.05715 + 0.951864i −0.998921 0.0464395i \(-0.985213\pi\)
−0.0582306 + 0.998303i \(0.518546\pi\)
\(72\) 0 0
\(73\) 8.70946 + 11.9875i 1.01937 + 1.40304i 0.912648 + 0.408747i \(0.134034\pi\)
0.106718 + 0.994289i \(0.465966\pi\)
\(74\) 0 0
\(75\) 1.06079 1.17813i 0.122490 0.136039i
\(76\) 0 0
\(77\) −0.511601 + 0.498598i −0.0583023 + 0.0568205i
\(78\) 0 0
\(79\) 1.81378 + 5.58224i 0.204066 + 0.628051i 0.999750 + 0.0223392i \(0.00711139\pi\)
−0.795684 + 0.605711i \(0.792889\pi\)
\(80\) 0 0
\(81\) −10.2091 4.54536i −1.13434 0.505040i
\(82\) 0 0
\(83\) 8.54045 + 2.77496i 0.937436 + 0.304591i 0.737600 0.675238i \(-0.235959\pi\)
0.199836 + 0.979829i \(0.435959\pi\)
\(84\) 0 0
\(85\) 3.94828 + 8.86797i 0.428251 + 0.961867i
\(86\) 0 0
\(87\) −1.04601 + 1.81175i −0.112144 + 0.194240i
\(88\) 0 0
\(89\) −13.6365 + 7.87302i −1.44546 + 0.834539i −0.998206 0.0598665i \(-0.980933\pi\)
−0.447257 + 0.894405i \(0.647599\pi\)
\(90\) 0 0
\(91\) −0.774840 0.0524038i −0.0812253 0.00549341i
\(92\) 0 0
\(93\) 0.548901 + 2.58238i 0.0569184 + 0.267780i
\(94\) 0 0
\(95\) −0.681710 6.48604i −0.0699420 0.665454i
\(96\) 0 0
\(97\) −1.98727 + 9.34936i −0.201777 + 0.949284i 0.754382 + 0.656435i \(0.227937\pi\)
−0.956159 + 0.292849i \(0.905397\pi\)
\(98\) 0 0
\(99\) 5.27487 2.60272i 0.530144 0.261583i
\(100\) 0 0
\(101\) −10.0804 + 11.1954i −1.00303 + 1.11398i −0.00955647 + 0.999954i \(0.503042\pi\)
−0.993478 + 0.114028i \(0.963625\pi\)
\(102\) 0 0
\(103\) 7.93002 5.76150i 0.781368 0.567697i −0.124021 0.992280i \(-0.539579\pi\)
0.905389 + 0.424582i \(0.139579\pi\)
\(104\) 0 0
\(105\) 0.300656 0.925324i 0.0293410 0.0903023i
\(106\) 0 0
\(107\) 0.433830 4.12761i 0.0419399 0.399031i −0.953334 0.301919i \(-0.902373\pi\)
0.995273 0.0971122i \(-0.0309606\pi\)
\(108\) 0 0
\(109\) 0.584563i 0.0559909i −0.999608 0.0279955i \(-0.991088\pi\)
0.999608 0.0279955i \(-0.00891240\pi\)
\(110\) 0 0
\(111\) −5.82412 3.36256i −0.552801 0.319160i
\(112\) 0 0
\(113\) 4.96356 2.20992i 0.466932 0.207892i −0.159764 0.987155i \(-0.551073\pi\)
0.626696 + 0.779264i \(0.284407\pi\)
\(114\) 0 0
\(115\) 2.70732 + 12.7370i 0.252459 + 1.18773i
\(116\) 0 0
\(117\) 5.93429 + 2.38185i 0.548625 + 0.220202i
\(118\) 0 0
\(119\) −0.751557 0.676705i −0.0688951 0.0620335i
\(120\) 0 0
\(121\) 2.56321 10.6972i 0.233019 0.972472i
\(122\) 0 0
\(123\) 1.94652 9.15765i 0.175512 0.825717i
\(124\) 0 0
\(125\) 6.95789 + 9.57671i 0.622332 + 0.856567i
\(126\) 0 0
\(127\) 4.88501 1.03834i 0.433475 0.0921379i 0.0139940 0.999902i \(-0.495545\pi\)
0.419481 + 0.907764i \(0.362212\pi\)
\(128\) 0 0
\(129\) 4.32898 + 3.14519i 0.381146 + 0.276919i
\(130\) 0 0
\(131\) −14.6262 −1.27790 −0.638949 0.769249i \(-0.720630\pi\)
−0.638949 + 0.769249i \(0.720630\pi\)
\(132\) 0 0
\(133\) 0.339727 + 0.588424i 0.0294580 + 0.0510228i
\(134\) 0 0
\(135\) 3.25643 4.48209i 0.280269 0.385757i
\(136\) 0 0
\(137\) −8.71667 + 7.84852i −0.744715 + 0.670544i −0.951433 0.307856i \(-0.900388\pi\)
0.206718 + 0.978401i \(0.433722\pi\)
\(138\) 0 0
\(139\) 2.21669 + 21.0904i 0.188017 + 1.78887i 0.528823 + 0.848732i \(0.322634\pi\)
−0.340806 + 0.940134i \(0.610700\pi\)
\(140\) 0 0
\(141\) 10.1909 + 9.17595i 0.858231 + 0.772754i
\(142\) 0 0
\(143\) 10.5197 5.68643i 0.879703 0.475524i
\(144\) 0 0
\(145\) −1.47116 1.32464i −0.122173 0.110005i
\(146\) 0 0
\(147\) −1.58805 15.1093i −0.130980 1.24619i
\(148\) 0 0
\(149\) −6.31303 + 5.68428i −0.517183 + 0.465674i −0.885906 0.463866i \(-0.846462\pi\)
0.368722 + 0.929540i \(0.379795\pi\)
\(150\) 0 0
\(151\) −2.83548 + 3.90271i −0.230748 + 0.317598i −0.908653 0.417552i \(-0.862888\pi\)
0.677905 + 0.735150i \(0.262888\pi\)
\(152\) 0 0
\(153\) 4.16350 + 7.21139i 0.336599 + 0.583007i
\(154\) 0 0
\(155\) −2.49824 −0.200663
\(156\) 0 0
\(157\) 2.63395 + 1.91367i 0.210212 + 0.152728i 0.687909 0.725797i \(-0.258529\pi\)
−0.477698 + 0.878524i \(0.658529\pi\)
\(158\) 0 0
\(159\) 8.84805 1.88071i 0.701696 0.149150i
\(160\) 0 0
\(161\) −0.797396 1.09752i −0.0628436 0.0864969i
\(162\) 0 0
\(163\) 3.25989 15.3366i 0.255334 1.20125i −0.644357 0.764725i \(-0.722875\pi\)
0.899691 0.436527i \(-0.143792\pi\)
\(164\) 0 0
\(165\) 3.69090 + 14.5196i 0.287336 + 1.13035i
\(166\) 0 0
\(167\) 5.15982 + 4.64593i 0.399279 + 0.359513i 0.844173 0.536071i \(-0.180092\pi\)
−0.444894 + 0.895583i \(0.646759\pi\)
\(168\) 0 0
\(169\) 12.2362 + 4.39041i 0.941245 + 0.337724i
\(170\) 0 0
\(171\) −1.16316 5.47223i −0.0889489 0.418472i
\(172\) 0 0
\(173\) 16.6900 7.43088i 1.26892 0.564960i 0.341817 0.939767i \(-0.388958\pi\)
0.927103 + 0.374807i \(0.122291\pi\)
\(174\) 0 0
\(175\) −0.135352 0.0781453i −0.0102316 0.00590723i
\(176\) 0 0
\(177\) 1.77416i 0.133354i
\(178\) 0 0
\(179\) 1.29917 12.3608i 0.0971046 0.923888i −0.832176 0.554512i \(-0.812905\pi\)
0.929280 0.369376i \(-0.120429\pi\)
\(180\) 0 0
\(181\) 5.95237 18.3195i 0.442436 1.36168i −0.442835 0.896603i \(-0.646027\pi\)
0.885271 0.465075i \(-0.153973\pi\)
\(182\) 0 0
\(183\) −5.14438 + 3.73761i −0.380284 + 0.276292i
\(184\) 0 0
\(185\) 4.25823 4.72925i 0.313071 0.347701i
\(186\) 0 0
\(187\) 15.3480 + 2.63380i 1.12236 + 0.192603i
\(188\) 0 0
\(189\) −0.120004 + 0.564575i −0.00872901 + 0.0410668i
\(190\) 0 0
\(191\) −1.88876 17.9704i −0.136666 1.30029i −0.820918 0.571046i \(-0.806538\pi\)
0.684252 0.729246i \(-0.260129\pi\)
\(192\) 0 0
\(193\) −2.05196 9.65373i −0.147704 0.694891i −0.988212 0.153092i \(-0.951077\pi\)
0.840508 0.541799i \(-0.182256\pi\)
\(194\) 0 0
\(195\) −9.07642 + 13.5229i −0.649976 + 0.968393i
\(196\) 0 0
\(197\) 13.2502 7.65003i 0.944041 0.545042i 0.0528160 0.998604i \(-0.483180\pi\)
0.891225 + 0.453562i \(0.149847\pi\)
\(198\) 0 0
\(199\) 3.31325 5.73872i 0.234870 0.406807i −0.724365 0.689417i \(-0.757867\pi\)
0.959235 + 0.282610i \(0.0912002\pi\)
\(200\) 0 0
\(201\) −7.20940 16.1926i −0.508512 1.14214i
\(202\) 0 0
\(203\) 0.196149 + 0.0637327i 0.0137670 + 0.00447316i
\(204\) 0 0
\(205\) 8.09335 + 3.60339i 0.565264 + 0.251672i
\(206\) 0 0
\(207\) 3.45174 + 10.6234i 0.239912 + 0.738375i
\(208\) 0 0
\(209\) −9.26002 4.86934i −0.640529 0.336819i
\(210\) 0 0
\(211\) −17.2282 + 19.1339i −1.18604 + 1.31723i −0.248799 + 0.968555i \(0.580036\pi\)
−0.937243 + 0.348677i \(0.886631\pi\)
\(212\) 0 0
\(213\) −15.3932 21.1870i −1.05473 1.45171i
\(214\) 0 0
\(215\) −3.76288 + 3.38811i −0.256626 + 0.231067i
\(216\) 0 0
\(217\) 0.237771 0.105862i 0.0161409 0.00718641i
\(218\) 0 0
\(219\) −28.0364 + 16.1868i −1.89452 + 1.09380i
\(220\) 0 0
\(221\) 9.00372 + 14.3360i 0.605656 + 0.964343i
\(222\) 0 0
\(223\) −6.22435 0.654206i −0.416813 0.0438088i −0.106199 0.994345i \(-0.533868\pi\)
−0.310614 + 0.950536i \(0.600535\pi\)
\(224\) 0 0
\(225\) 0.861080 + 0.956326i 0.0574053 + 0.0637551i
\(226\) 0 0
\(227\) 12.5031 1.31413i 0.829860 0.0872218i 0.319934 0.947440i \(-0.396339\pi\)
0.509926 + 0.860218i \(0.329673\pi\)
\(228\) 0 0
\(229\) −9.88744 + 3.21262i −0.653380 + 0.212296i −0.616904 0.787038i \(-0.711613\pi\)
−0.0364763 + 0.999335i \(0.511613\pi\)
\(230\) 0 0
\(231\) −0.966549 1.22551i −0.0635942 0.0806325i
\(232\) 0 0
\(233\) −2.37768 7.31776i −0.155767 0.479402i 0.842471 0.538742i \(-0.181100\pi\)
−0.998238 + 0.0593402i \(0.981100\pi\)
\(234\) 0 0
\(235\) −10.4982 + 7.62742i −0.684830 + 0.497558i
\(236\) 0 0
\(237\) −12.5437 + 2.66624i −0.814799 + 0.173191i
\(238\) 0 0
\(239\) 10.9578 15.0822i 0.708804 0.975584i −0.291018 0.956717i \(-0.593994\pi\)
0.999822 0.0188670i \(-0.00600590\pi\)
\(240\) 0 0
\(241\) −7.41176 4.27918i −0.477433 0.275646i 0.241913 0.970298i \(-0.422225\pi\)
−0.719346 + 0.694652i \(0.755558\pi\)
\(242\) 0 0
\(243\) 8.18843 14.1828i 0.525288 0.909826i
\(244\) 0 0
\(245\) 14.2976 + 1.50273i 0.913437 + 0.0960061i
\(246\) 0 0
\(247\) −2.77674 11.0295i −0.176680 0.701790i
\(248\) 0 0
\(249\) −7.98006 + 17.9235i −0.505716 + 1.13586i
\(250\) 0 0
\(251\) −10.5811 2.24907i −0.667870 0.141960i −0.138515 0.990360i \(-0.544233\pi\)
−0.529355 + 0.848400i \(0.677566\pi\)
\(252\) 0 0
\(253\) 19.4037 + 7.73637i 1.21990 + 0.486381i
\(254\) 0 0
\(255\) −20.1706 + 6.55383i −1.26313 + 0.410417i
\(256\) 0 0
\(257\) −17.0590 7.59516i −1.06411 0.473773i −0.201421 0.979505i \(-0.564556\pi\)
−0.862691 + 0.505732i \(0.831223\pi\)
\(258\) 0 0
\(259\) −0.204878 + 0.630549i −0.0127305 + 0.0391804i
\(260\) 0 0
\(261\) −1.37384 0.998156i −0.0850388 0.0617843i
\(262\) 0 0
\(263\) 7.07115 + 12.2476i 0.436026 + 0.755219i 0.997379 0.0723577i \(-0.0230523\pi\)
−0.561353 + 0.827577i \(0.689719\pi\)
\(264\) 0 0
\(265\) 8.55977i 0.525822i
\(266\) 0 0
\(267\) −13.9928 31.4283i −0.856343 1.92338i
\(268\) 0 0
\(269\) −8.54114 9.48590i −0.520763 0.578365i 0.424190 0.905573i \(-0.360559\pi\)
−0.944952 + 0.327208i \(0.893892\pi\)
\(270\) 0 0
\(271\) −1.70380 + 3.82679i −0.103498 + 0.232461i −0.957870 0.287201i \(-0.907275\pi\)
0.854372 + 0.519662i \(0.173942\pi\)
\(272\) 0 0
\(273\) 0.290822 1.67166i 0.0176014 0.101173i
\(274\) 0 0
\(275\) 2.40469 0.0950084i 0.145008 0.00572922i
\(276\) 0 0
\(277\) −24.6696 5.24369i −1.48225 0.315063i −0.605439 0.795891i \(-0.707003\pi\)
−0.876815 + 0.480829i \(0.840336\pi\)
\(278\) 0 0
\(279\) −2.13129 + 0.224008i −0.127597 + 0.0134110i
\(280\) 0 0
\(281\) −8.51290 2.76601i −0.507837 0.165006i 0.0438812 0.999037i \(-0.486028\pi\)
−0.551718 + 0.834030i \(0.686028\pi\)
\(282\) 0 0
\(283\) −2.29630 + 21.8478i −0.136501 + 1.29872i 0.685014 + 0.728530i \(0.259796\pi\)
−0.821515 + 0.570187i \(0.806871\pi\)
\(284\) 0 0
\(285\) 14.2490 0.844037
\(286\) 0 0
\(287\) −0.922980 −0.0544818
\(288\) 0 0
\(289\) −0.527367 + 5.01756i −0.0310216 + 0.295151i
\(290\) 0 0
\(291\) −19.8611 6.45325i −1.16428 0.378296i
\(292\) 0 0
\(293\) −23.7125 + 2.49229i −1.38530 + 0.145601i −0.767658 0.640859i \(-0.778578\pi\)
−0.617641 + 0.786460i \(0.711912\pi\)
\(294\) 0 0
\(295\) −1.64217 0.349053i −0.0956106 0.0203227i
\(296\) 0 0
\(297\) −3.07796 8.33755i −0.178601 0.483794i
\(298\) 0 0
\(299\) 7.81562 + 21.3216i 0.451989 + 1.23306i
\(300\) 0 0
\(301\) 0.214563 0.481916i 0.0123672 0.0277772i
\(302\) 0 0
\(303\) −22.0239 24.4601i −1.26524 1.40519i
\(304\) 0 0
\(305\) −2.44741 5.49698i −0.140139 0.314756i
\(306\) 0 0
\(307\) 20.4606i 1.16775i 0.811843 + 0.583875i \(0.198464\pi\)
−0.811843 + 0.583875i \(0.801536\pi\)
\(308\) 0 0
\(309\) 10.7079 + 18.5467i 0.609152 + 1.05508i
\(310\) 0 0
\(311\) 10.2191 + 7.42463i 0.579473 + 0.421012i 0.838534 0.544849i \(-0.183413\pi\)
−0.259061 + 0.965861i \(0.583413\pi\)
\(312\) 0 0
\(313\) 8.78493 27.0372i 0.496554 1.52823i −0.317968 0.948101i \(-0.603000\pi\)
0.814521 0.580133i \(-0.197000\pi\)
\(314\) 0 0
\(315\) 0.721490 + 0.321228i 0.0406514 + 0.0180992i
\(316\) 0 0
\(317\) −6.33817 + 2.05940i −0.355987 + 0.115667i −0.481550 0.876418i \(-0.659926\pi\)
0.125563 + 0.992086i \(0.459926\pi\)
\(318\) 0 0
\(319\) −3.07785 + 0.782393i −0.172327 + 0.0438056i
\(320\) 0 0
\(321\) 8.86967 + 1.88531i 0.495057 + 0.105228i
\(322\) 0 0
\(323\) 6.02419 13.5305i 0.335195 0.752860i
\(324\) 0 0
\(325\) 1.82167 + 1.87779i 0.101048 + 0.104161i
\(326\) 0 0
\(327\) 1.27018 + 0.133501i 0.0702409 + 0.00738261i
\(328\) 0 0
\(329\) 0.675963 1.17080i 0.0372671 0.0645485i
\(330\) 0 0
\(331\) 24.9410 + 14.3997i 1.37088 + 0.791479i 0.991039 0.133573i \(-0.0426450\pi\)
0.379842 + 0.925051i \(0.375978\pi\)
\(332\) 0 0
\(333\) 3.20872 4.41642i 0.175837 0.242018i
\(334\) 0 0
\(335\) 16.4062 3.48725i 0.896368 0.190529i
\(336\) 0 0
\(337\) 7.20243 5.23287i 0.392341 0.285053i −0.374073 0.927399i \(-0.622039\pi\)
0.766414 + 0.642347i \(0.222039\pi\)
\(338\) 0 0
\(339\) 3.66829 + 11.2898i 0.199234 + 0.613180i
\(340\) 0 0
\(341\) −2.22582 + 3.33275i −0.120535 + 0.180479i
\(342\) 0 0
\(343\) −2.85841 + 0.928753i −0.154340 + 0.0501480i
\(344\) 0 0
\(345\) −28.2940 + 2.97382i −1.52330 + 0.160105i
\(346\) 0 0
\(347\) −16.4999 18.3250i −0.885761 0.983738i 0.114191 0.993459i \(-0.463572\pi\)
−0.999953 + 0.00972116i \(0.996906\pi\)
\(348\) 0 0
\(349\) −14.5353 1.52772i −0.778055 0.0817769i −0.292828 0.956165i \(-0.594596\pi\)
−0.485227 + 0.874388i \(0.661263\pi\)
\(350\) 0 0
\(351\) 4.51643 8.54119i 0.241069 0.455895i
\(352\) 0 0
\(353\) −22.0809 + 12.7484i −1.17525 + 0.678531i −0.954911 0.296893i \(-0.904050\pi\)
−0.220339 + 0.975423i \(0.570716\pi\)
\(354\) 0 0
\(355\) 22.6392 10.0796i 1.20156 0.534970i
\(356\) 0 0
\(357\) 1.64203 1.47849i 0.0869053 0.0782499i
\(358\) 0 0
\(359\) 11.4586 + 15.7714i 0.604761 + 0.832382i 0.996134 0.0878505i \(-0.0279998\pi\)
−0.391373 + 0.920232i \(0.628000\pi\)
\(360\) 0 0
\(361\) 6.05512 6.72490i 0.318691 0.353942i
\(362\) 0 0
\(363\) 22.6582 + 8.01251i 1.18925 + 0.420548i
\(364\) 0 0
\(365\) −9.46656 29.1351i −0.495503 1.52500i
\(366\) 0 0
\(367\) 15.0458 + 6.69881i 0.785383 + 0.349675i 0.759933 0.650001i \(-0.225232\pi\)
0.0254499 + 0.999676i \(0.491898\pi\)
\(368\) 0 0
\(369\) 7.22768 + 2.34841i 0.376258 + 0.122254i
\(370\) 0 0
\(371\) −0.362718 0.814679i −0.0188314 0.0422960i
\(372\) 0 0
\(373\) 15.3712 26.6238i 0.795892 1.37853i −0.126379 0.991982i \(-0.540335\pi\)
0.922271 0.386544i \(-0.126331\pi\)
\(374\) 0 0
\(375\) −22.3979 + 12.9315i −1.15662 + 0.667777i
\(376\) 0 0
\(377\) −2.86656 1.92401i −0.147636 0.0990915i
\(378\) 0 0
\(379\) 0.828625 + 3.89837i 0.0425636 + 0.200246i 0.994292 0.106697i \(-0.0340274\pi\)
−0.951728 + 0.306943i \(0.900694\pi\)
\(380\) 0 0
\(381\) 1.14055 + 10.8516i 0.0584322 + 0.555945i
\(382\) 0 0
\(383\) 3.48240 16.3834i 0.177943 0.837154i −0.795091 0.606490i \(-0.792577\pi\)
0.973034 0.230664i \(-0.0740897\pi\)
\(384\) 0 0
\(385\) 1.32449 0.653528i 0.0675023 0.0333069i
\(386\) 0 0
\(387\) −2.90638 + 3.22786i −0.147740 + 0.164081i
\(388\) 0 0
\(389\) −18.0210 + 13.0930i −0.913699 + 0.663841i −0.941948 0.335760i \(-0.891007\pi\)
0.0282489 + 0.999601i \(0.491007\pi\)
\(390\) 0 0
\(391\) −9.13826 + 28.1247i −0.462142 + 1.42233i
\(392\) 0 0
\(393\) 3.34030 31.7808i 0.168496 1.60313i
\(394\) 0 0
\(395\) 12.1350i 0.610577i
\(396\) 0 0
\(397\) 7.48520 + 4.32158i 0.375671 + 0.216894i 0.675933 0.736963i \(-0.263741\pi\)
−0.300262 + 0.953857i \(0.597074\pi\)
\(398\) 0 0
\(399\) −1.35615 + 0.603798i −0.0678925 + 0.0302277i
\(400\) 0 0
\(401\) −4.95020 23.2889i −0.247201 1.16299i −0.910135 0.414312i \(-0.864022\pi\)
0.662934 0.748678i \(-0.269311\pi\)
\(402\) 0 0
\(403\) −4.31301 + 0.616204i −0.214846 + 0.0306953i
\(404\) 0 0
\(405\) 17.1698 + 15.4598i 0.853176 + 0.768203i
\(406\) 0 0
\(407\) −2.51511 9.89420i −0.124670 0.490437i
\(408\) 0 0
\(409\) 6.41574 30.1837i 0.317238 1.49249i −0.473753 0.880658i \(-0.657101\pi\)
0.790990 0.611829i \(-0.209566\pi\)
\(410\) 0 0
\(411\) −15.0631 20.7326i −0.743008 1.02266i
\(412\) 0 0
\(413\) 0.171085 0.0363652i 0.00841853 0.00178941i
\(414\) 0 0
\(415\) −15.0200 10.9127i −0.737302 0.535681i
\(416\) 0 0
\(417\) −46.3329 −2.26893
\(418\) 0 0
\(419\) 12.8114 + 22.1899i 0.625876 + 1.08405i 0.988371 + 0.152064i \(0.0485918\pi\)
−0.362494 + 0.931986i \(0.618075\pi\)
\(420\) 0 0
\(421\) 12.8422 17.6758i 0.625892 0.861466i −0.371874 0.928283i \(-0.621285\pi\)
0.997765 + 0.0668176i \(0.0212846\pi\)
\(422\) 0 0
\(423\) −8.27231 + 7.44842i −0.402213 + 0.362154i
\(424\) 0 0
\(425\) 0.356117 + 3.38823i 0.0172742 + 0.164353i
\(426\) 0 0
\(427\) 0.465867 + 0.419469i 0.0225449 + 0.0202995i
\(428\) 0 0
\(429\) 9.95339 + 24.1566i 0.480554 + 1.16629i
\(430\) 0 0
\(431\) −14.0743 12.6726i −0.677936 0.610417i 0.256501 0.966544i \(-0.417430\pi\)
−0.934437 + 0.356127i \(0.884097\pi\)
\(432\) 0 0
\(433\) 0.862143 + 8.20274i 0.0414319 + 0.394199i 0.995511 + 0.0946442i \(0.0301713\pi\)
−0.954079 + 0.299554i \(0.903162\pi\)
\(434\) 0 0
\(435\) 3.21423 2.89411i 0.154111 0.138762i
\(436\) 0 0
\(437\) 11.6781 16.0735i 0.558638 0.768899i
\(438\) 0 0
\(439\) 18.6127 + 32.2381i 0.888335 + 1.53864i 0.841843 + 0.539722i \(0.181471\pi\)
0.0464914 + 0.998919i \(0.485196\pi\)
\(440\) 0 0
\(441\) 12.3322 0.587249
\(442\) 0 0
\(443\) 13.3791 + 9.72045i 0.635658 + 0.461833i 0.858356 0.513055i \(-0.171486\pi\)
−0.222698 + 0.974888i \(0.571486\pi\)
\(444\) 0 0
\(445\) 31.8429 6.76843i 1.50950 0.320854i
\(446\) 0 0
\(447\) −10.9094 15.0155i −0.515998 0.710210i
\(448\) 0 0
\(449\) 1.98423 9.33509i 0.0936418 0.440550i −0.906201 0.422846i \(-0.861031\pi\)
0.999843 0.0177039i \(-0.00563561\pi\)
\(450\) 0 0
\(451\) 12.0179 7.58640i 0.565900 0.357230i
\(452\) 0 0
\(453\) −7.83250 7.05241i −0.368003 0.331351i
\(454\) 0 0
\(455\) 1.49007 + 0.598070i 0.0698554 + 0.0280380i
\(456\) 0 0
\(457\) 8.75610 + 41.1942i 0.409593 + 1.92698i 0.373487 + 0.927636i \(0.378162\pi\)
0.0361065 + 0.999348i \(0.488504\pi\)
\(458\) 0 0
\(459\) 11.4940 5.11748i 0.536496 0.238863i
\(460\) 0 0
\(461\) 8.56300 + 4.94385i 0.398819 + 0.230258i 0.685974 0.727626i \(-0.259376\pi\)
−0.287155 + 0.957884i \(0.592710\pi\)
\(462\) 0 0
\(463\) 18.0734i 0.839944i −0.907537 0.419972i \(-0.862040\pi\)
0.907537 0.419972i \(-0.137960\pi\)
\(464\) 0 0
\(465\) 0.570541 5.42834i 0.0264582 0.251733i
\(466\) 0 0
\(467\) −3.32979 + 10.2480i −0.154084 + 0.474222i −0.998067 0.0621480i \(-0.980205\pi\)
0.843983 + 0.536370i \(0.180205\pi\)
\(468\) 0 0
\(469\) −1.41370 + 1.02711i −0.0652785 + 0.0474276i
\(470\) 0 0
\(471\) −4.75969 + 5.28617i −0.219315 + 0.243574i
\(472\) 0 0
\(473\) 1.16733 + 8.03849i 0.0536737 + 0.369610i
\(474\) 0 0
\(475\) 0.475892 2.23890i 0.0218354 0.102728i
\(476\) 0 0
\(477\) 0.767522 + 7.30248i 0.0351424 + 0.334358i
\(478\) 0 0
\(479\) 3.51879 + 16.5546i 0.160778 + 0.756400i 0.982463 + 0.186458i \(0.0597009\pi\)
−0.821685 + 0.569942i \(0.806966\pi\)
\(480\) 0 0
\(481\) 6.18501 9.21498i 0.282012 0.420167i
\(482\) 0 0
\(483\) 2.56688 1.48199i 0.116797 0.0674327i
\(484\) 0 0
\(485\) 9.88064 17.1138i 0.448657 0.777096i
\(486\) 0 0
\(487\) 3.19878 + 7.18458i 0.144951 + 0.325564i 0.971401 0.237445i \(-0.0763100\pi\)
−0.826450 + 0.563010i \(0.809643\pi\)
\(488\) 0 0
\(489\) 32.5798 + 10.5858i 1.47331 + 0.478707i
\(490\) 0 0
\(491\) 24.5903 + 10.9483i 1.10975 + 0.494091i 0.877988 0.478682i \(-0.158885\pi\)
0.231759 + 0.972773i \(0.425552\pi\)
\(492\) 0 0
\(493\) −1.38927 4.27574i −0.0625697 0.192570i
\(494\) 0 0
\(495\) −12.0347 + 1.74764i −0.540917 + 0.0785504i
\(496\) 0 0
\(497\) −1.72757 + 1.91866i −0.0774921 + 0.0860637i
\(498\) 0 0
\(499\) −22.2023 30.5588i −0.993912 1.36800i −0.928987 0.370112i \(-0.879319\pi\)
−0.0649243 0.997890i \(-0.520681\pi\)
\(500\) 0 0
\(501\) −11.2734 + 10.1506i −0.503657 + 0.453494i
\(502\) 0 0
\(503\) −16.4832 + 7.33881i −0.734951 + 0.327221i −0.739855 0.672767i \(-0.765106\pi\)
0.00490373 + 0.999988i \(0.498439\pi\)
\(504\) 0 0
\(505\) 26.9733 15.5730i 1.20029 0.692990i
\(506\) 0 0
\(507\) −12.3342 + 25.5849i −0.547782 + 1.13627i
\(508\) 0 0
\(509\) −14.2783 1.50071i −0.632876 0.0665180i −0.217342 0.976096i \(-0.569739\pi\)
−0.415534 + 0.909578i \(0.636405\pi\)
\(510\) 0 0
\(511\) 2.13558 + 2.37180i 0.0944723 + 0.104922i
\(512\) 0 0
\(513\) −8.40675 + 0.883585i −0.371167 + 0.0390112i
\(514\) 0 0
\(515\) −19.2735 + 6.26234i −0.849291 + 0.275951i
\(516\) 0 0
\(517\) 0.821831 + 20.8008i 0.0361441 + 0.914817i
\(518\) 0 0
\(519\) 12.3347 + 37.9622i 0.541432 + 1.66636i
\(520\) 0 0
\(521\) −10.3672 + 7.53218i −0.454194 + 0.329991i −0.791249 0.611494i \(-0.790569\pi\)
0.337056 + 0.941485i \(0.390569\pi\)
\(522\) 0 0
\(523\) −11.2098 + 2.38271i −0.490169 + 0.104189i −0.446364 0.894851i \(-0.647281\pi\)
−0.0438052 + 0.999040i \(0.513948\pi\)
\(524\) 0 0
\(525\) 0.200710 0.276254i 0.00875972 0.0120567i
\(526\) 0 0
\(527\) −4.91343 2.83677i −0.214032 0.123572i
\(528\) 0 0
\(529\) −8.33436 + 14.4355i −0.362363 + 0.627632i
\(530\) 0 0
\(531\) −1.43226 0.150536i −0.0621547 0.00653272i
\(532\) 0 0
\(533\) 14.8613 + 4.22470i 0.643715 + 0.182992i
\(534\) 0 0
\(535\) −3.49008 + 7.83884i −0.150889 + 0.338903i
\(536\) 0 0
\(537\) 26.5616 + 5.64585i 1.14622 + 0.243636i
\(538\) 0 0
\(539\) 14.7432 17.7346i 0.635034 0.763885i
\(540\) 0 0
\(541\) −8.58844 + 2.79055i −0.369246 + 0.119975i −0.487761 0.872977i \(-0.662186\pi\)
0.118516 + 0.992952i \(0.462186\pi\)
\(542\) 0 0
\(543\) 38.4464 + 17.1175i 1.64989 + 0.734580i
\(544\) 0 0
\(545\) −0.373466 + 1.14941i −0.0159975 + 0.0492353i
\(546\) 0 0
\(547\) −0.275694 0.200303i −0.0117878 0.00856435i 0.581876 0.813278i \(-0.302319\pi\)
−0.593664 + 0.804713i \(0.702319\pi\)
\(548\) 0 0
\(549\) −2.58082 4.47012i −0.110147 0.190780i
\(550\) 0 0
\(551\) 3.02048i 0.128677i
\(552\) 0 0
\(553\) 0.514217 + 1.15495i 0.0218667 + 0.0491135i
\(554\) 0 0
\(555\) 9.30353 + 10.3326i 0.394913 + 0.438595i
\(556\) 0 0
\(557\) 4.46111 10.0198i 0.189023 0.424553i −0.794029 0.607880i \(-0.792020\pi\)
0.983052 + 0.183327i \(0.0586867\pi\)
\(558\) 0 0
\(559\) −5.66062 + 6.77745i −0.239419 + 0.286655i
\(560\) 0 0
\(561\) −9.22803 + 32.7476i −0.389608 + 1.38260i
\(562\) 0 0
\(563\) 10.6624 + 2.26636i 0.449365 + 0.0955156i 0.427035 0.904235i \(-0.359558\pi\)
0.0223304 + 0.999751i \(0.492891\pi\)
\(564\) 0 0
\(565\) −11.1716 + 1.17418i −0.469992 + 0.0493981i
\(566\) 0 0
\(567\) −2.28925 0.743822i −0.0961394 0.0312376i
\(568\) 0 0
\(569\) 1.84012 17.5075i 0.0771417 0.733954i −0.885768 0.464129i \(-0.846367\pi\)
0.962909 0.269825i \(-0.0869659\pi\)
\(570\) 0 0
\(571\) −20.3911 −0.853339 −0.426670 0.904408i \(-0.640313\pi\)
−0.426670 + 0.904408i \(0.640313\pi\)
\(572\) 0 0
\(573\) 39.4786 1.64924
\(574\) 0 0
\(575\) −0.477705 + 4.54506i −0.0199217 + 0.189542i
\(576\) 0 0
\(577\) −25.8649 8.40400i −1.07677 0.349863i −0.283648 0.958928i \(-0.591545\pi\)
−0.793120 + 0.609065i \(0.791545\pi\)
\(578\) 0 0
\(579\) 21.4449 2.25395i 0.891219 0.0936709i
\(580\) 0 0
\(581\) 1.89195 + 0.402147i 0.0784914 + 0.0166839i
\(582\) 0 0
\(583\) 11.4191 + 7.62636i 0.472930 + 0.315852i
\(584\) 0 0
\(585\) −10.1467 8.47467i −0.419514 0.350385i
\(586\) 0 0
\(587\) 10.2237 22.9628i 0.421977 0.947776i −0.570033 0.821621i \(-0.693070\pi\)
0.992011 0.126155i \(-0.0402636\pi\)
\(588\) 0 0
\(589\) 2.55056 + 2.83269i 0.105094 + 0.116719i
\(590\) 0 0
\(591\) 13.5964 + 30.5381i 0.559283 + 1.25617i
\(592\) 0 0
\(593\) 19.1843i 0.787803i 0.919153 + 0.393901i \(0.128875\pi\)
−0.919153 + 0.393901i \(0.871125\pi\)
\(594\) 0 0
\(595\) 1.04543 + 1.81074i 0.0428585 + 0.0742332i
\(596\) 0 0
\(597\) 11.7128 + 8.50984i 0.479373 + 0.348285i
\(598\) 0 0
\(599\) −12.5142 + 38.5148i −0.511318 + 1.57367i 0.278566 + 0.960417i \(0.410141\pi\)
−0.789884 + 0.613257i \(0.789859\pi\)
\(600\) 0 0
\(601\) 17.5346 + 7.80689i 0.715249 + 0.318450i 0.731900 0.681412i \(-0.238634\pi\)
−0.0166508 + 0.999861i \(0.505300\pi\)
\(602\) 0 0
\(603\) 13.6837 4.44612i 0.557245 0.181060i
\(604\) 0 0
\(605\) −11.8742 + 19.3960i −0.482755 + 0.788560i
\(606\) 0 0
\(607\) 5.49204 + 1.16737i 0.222915 + 0.0473821i 0.318015 0.948086i \(-0.396984\pi\)
−0.0950999 + 0.995468i \(0.530317\pi\)
\(608\) 0 0
\(609\) −0.183279 + 0.411650i −0.00742682 + 0.0166809i
\(610\) 0 0
\(611\) −16.2430 + 15.7576i −0.657123 + 0.637483i
\(612\) 0 0
\(613\) −28.6966 3.01613i −1.15904 0.121820i −0.494574 0.869136i \(-0.664676\pi\)
−0.664470 + 0.747315i \(0.731342\pi\)
\(614\) 0 0
\(615\) −9.67802 + 16.7628i −0.390256 + 0.675943i
\(616\) 0 0
\(617\) 38.6065 + 22.2895i 1.55424 + 0.897341i 0.997789 + 0.0664604i \(0.0211706\pi\)
0.556451 + 0.830880i \(0.312163\pi\)
\(618\) 0 0
\(619\) −0.499541 + 0.687559i −0.0200783 + 0.0276353i −0.818938 0.573882i \(-0.805437\pi\)
0.798860 + 0.601517i \(0.205437\pi\)
\(620\) 0 0
\(621\) 16.5087 3.50904i 0.662473 0.140813i
\(622\) 0 0
\(623\) −2.74385 + 1.99353i −0.109930 + 0.0798689i
\(624\) 0 0
\(625\) −6.44160 19.8252i −0.257664 0.793008i
\(626\) 0 0
\(627\) 12.6952 19.0087i 0.506997 0.759135i
\(628\) 0 0
\(629\) 13.7450 4.46602i 0.548049 0.178072i
\(630\) 0 0
\(631\) −24.0708 + 2.52995i −0.958245 + 0.100716i −0.570721 0.821144i \(-0.693336\pi\)
−0.387524 + 0.921860i \(0.626670\pi\)
\(632\) 0 0
\(633\) −37.6409 41.8044i −1.49609 1.66158i
\(634\) 0 0
\(635\) −10.2686 1.07928i −0.407499 0.0428298i
\(636\) 0 0
\(637\) 25.0542 0.932219i 0.992685 0.0369359i
\(638\) 0 0
\(639\) 18.4101 10.6291i 0.728291 0.420479i
\(640\) 0 0
\(641\) 12.3791 5.51154i 0.488946 0.217693i −0.147429 0.989073i \(-0.547100\pi\)
0.636375 + 0.771380i \(0.280433\pi\)
\(642\) 0 0
\(643\) −32.2152 + 29.0067i −1.27044 + 1.14391i −0.287943 + 0.957647i \(0.592971\pi\)
−0.982500 + 0.186264i \(0.940362\pi\)
\(644\) 0 0
\(645\) −6.50256 8.95000i −0.256038 0.352406i
\(646\) 0 0
\(647\) 28.2189 31.3402i 1.10940 1.23211i 0.139079 0.990281i \(-0.455586\pi\)
0.970319 0.241829i \(-0.0777475\pi\)
\(648\) 0 0
\(649\) −1.92875 + 1.87973i −0.0757099 + 0.0737857i
\(650\) 0 0
\(651\) 0.175723 + 0.540821i 0.00688714 + 0.0211964i
\(652\) 0 0
\(653\) −28.6767 12.7677i −1.12220 0.499638i −0.240127 0.970741i \(-0.577189\pi\)
−0.882078 + 0.471104i \(0.843856\pi\)
\(654\) 0 0
\(655\) 28.7591 + 9.34440i 1.12371 + 0.365116i
\(656\) 0 0
\(657\) −10.6885 24.0068i −0.416999 0.936595i
\(658\) 0 0
\(659\) 2.38651 4.13356i 0.0929653 0.161021i −0.815792 0.578345i \(-0.803699\pi\)
0.908758 + 0.417324i \(0.137032\pi\)
\(660\) 0 0
\(661\) 24.4782 14.1325i 0.952090 0.549690i 0.0583608 0.998296i \(-0.481413\pi\)
0.893730 + 0.448606i \(0.148079\pi\)
\(662\) 0 0
\(663\) −33.2064 + 16.2899i −1.28963 + 0.632646i
\(664\) 0 0
\(665\) −0.292063 1.37405i −0.0113257 0.0532832i
\(666\) 0 0
\(667\) −0.630387 5.99773i −0.0244087 0.232233i
\(668\) 0 0
\(669\) 2.84300 13.3753i 0.109917 0.517118i
\(670\) 0 0
\(671\) −9.51373 1.63261i −0.367274 0.0630263i
\(672\) 0 0
\(673\) −1.00264 + 1.11355i −0.0386490 + 0.0429241i −0.762159 0.647389i \(-0.775861\pi\)
0.723510 + 0.690314i \(0.242527\pi\)
\(674\) 0 0
\(675\) 1.57306 1.14289i 0.0605470 0.0439900i
\(676\) 0 0
\(677\) −9.62285 + 29.6161i −0.369836 + 1.13824i 0.577061 + 0.816701i \(0.304200\pi\)
−0.946897 + 0.321537i \(0.895800\pi\)
\(678\) 0 0
\(679\) −0.215201 + 2.04750i −0.00825865 + 0.0785758i
\(680\) 0 0
\(681\) 27.4677i 1.05256i
\(682\) 0 0
\(683\) −22.2923 12.8705i −0.852992 0.492475i 0.00866729 0.999962i \(-0.497241\pi\)
−0.861659 + 0.507487i \(0.830574\pi\)
\(684\) 0 0
\(685\) 22.1536 9.86342i 0.846446 0.376862i
\(686\) 0 0
\(687\) −4.72253 22.2178i −0.180176 0.847661i
\(688\) 0 0
\(689\) 2.11131 + 14.7778i 0.0804346 + 0.562988i
\(690\) 0 0
\(691\) −19.9580 17.9702i −0.759236 0.683619i 0.195623 0.980679i \(-0.437327\pi\)
−0.954859 + 0.297060i \(0.903994\pi\)
\(692\) 0 0
\(693\) 1.07135 0.676298i 0.0406971 0.0256904i
\(694\) 0 0
\(695\) 9.11564 42.8857i 0.345776 1.62675i
\(696\) 0 0
\(697\) 11.8260 + 16.2770i 0.447940 + 0.616537i
\(698\) 0 0
\(699\) 16.4435 3.49518i 0.621951 0.132200i
\(700\) 0 0
\(701\) −20.8123 15.1210i −0.786069 0.571112i 0.120726 0.992686i \(-0.461478\pi\)
−0.906794 + 0.421574i \(0.861478\pi\)
\(702\) 0 0
\(703\) −9.70978 −0.366211
\(704\) 0 0
\(705\) −14.1758 24.5532i −0.533891 0.924727i
\(706\) 0 0
\(707\) −1.90729 + 2.62515i −0.0717309 + 0.0987290i
\(708\) 0 0
\(709\) 3.67842 3.31207i 0.138146 0.124387i −0.597161 0.802121i \(-0.703705\pi\)
0.735307 + 0.677734i \(0.237038\pi\)
\(710\) 0 0
\(711\) −1.08810 10.3526i −0.0408069 0.388251i
\(712\) 0 0
\(713\) −5.65580 5.09251i −0.211812 0.190716i
\(714\) 0 0
\(715\) −24.3176 + 4.46023i −0.909426 + 0.166803i
\(716\) 0 0
\(717\) 30.2690 + 27.2543i 1.13042 + 1.01783i
\(718\) 0 0
\(719\) 2.60868 + 24.8200i 0.0972875 + 0.925629i 0.928915 + 0.370294i \(0.120743\pi\)
−0.831627 + 0.555335i \(0.812590\pi\)
\(720\) 0 0
\(721\) 1.56900 1.41273i 0.0584325 0.0526128i
\(722\) 0 0
\(723\) 10.9908 15.1275i 0.408751 0.562597i
\(724\) 0 0
\(725\) −0.347392 0.601700i −0.0129018 0.0223466i
\(726\) 0 0
\(727\) −44.9405 −1.66675 −0.833375 0.552709i \(-0.813594\pi\)
−0.833375 + 0.552709i \(0.813594\pi\)
\(728\) 0 0
\(729\) 1.82445 + 1.32554i 0.0675723 + 0.0490941i
\(730\) 0 0
\(731\) −11.2479 + 2.39081i −0.416018 + 0.0884275i
\(732\) 0 0
\(733\) −17.5586 24.1673i −0.648541 0.892641i 0.350494 0.936565i \(-0.386014\pi\)
−0.999035 + 0.0439246i \(0.986014\pi\)
\(734\) 0 0
\(735\) −6.53047 + 30.7235i −0.240880 + 1.13325i
\(736\) 0 0
\(737\) 9.96507 24.9936i 0.367068 0.920649i
\(738\) 0 0
\(739\) 17.8088 + 16.0351i 0.655106 + 0.589860i 0.928179 0.372133i \(-0.121374\pi\)
−0.273073 + 0.961993i \(0.588040\pi\)
\(740\) 0 0
\(741\) 24.5997 3.51459i 0.903694 0.129112i
\(742\) 0 0
\(743\) −4.22980 19.8996i −0.155176 0.730046i −0.985074 0.172131i \(-0.944935\pi\)
0.829898 0.557915i \(-0.188399\pi\)
\(744\) 0 0
\(745\) 16.0447 7.14356i 0.587832 0.261720i
\(746\) 0 0
\(747\) −13.7923 7.96299i −0.504634 0.291350i
\(748\) 0 0
\(749\) 0.893956i 0.0326644i
\(750\) 0 0
\(751\) 3.03681 28.8933i 0.110815 1.05433i −0.787902 0.615801i \(-0.788833\pi\)
0.898716 0.438530i \(-0.144501\pi\)
\(752\) 0 0
\(753\) 7.30341 22.4776i 0.266151 0.819128i
\(754\) 0 0
\(755\) 8.06869 5.86225i 0.293650 0.213349i
\(756\) 0 0
\(757\) −20.2597 + 22.5007i −0.736353 + 0.817803i −0.988712 0.149831i \(-0.952127\pi\)
0.252359 + 0.967634i \(0.418794\pi\)
\(758\) 0 0
\(759\) −21.2415 + 40.3949i −0.771016 + 1.46624i
\(760\) 0 0
\(761\) 0.898128 4.22536i 0.0325571 0.153169i −0.958866 0.283858i \(-0.908386\pi\)
0.991423 + 0.130689i \(0.0417189\pi\)
\(762\) 0 0
\(763\) −0.0131612 0.125221i −0.000476469 0.00453330i
\(764\) 0 0
\(765\) −3.57935 16.8395i −0.129412 0.608835i
\(766\) 0 0
\(767\) −2.92116 0.197563i −0.105477 0.00713360i
\(768\) 0 0
\(769\) 0.429491 0.247967i 0.0154879 0.00894192i −0.492236 0.870462i \(-0.663820\pi\)
0.507724 + 0.861520i \(0.330487\pi\)
\(770\) 0 0
\(771\) 20.3992 35.3324i 0.734658 1.27246i
\(772\) 0 0
\(773\) 13.4898 + 30.2986i 0.485195 + 1.08977i 0.975856 + 0.218415i \(0.0700887\pi\)
−0.490661 + 0.871351i \(0.663245\pi\)
\(774\) 0 0
\(775\) −0.833882 0.270945i −0.0299539 0.00973262i
\(776\) 0 0
\(777\) −1.32331 0.589175i −0.0474735 0.0211365i
\(778\) 0 0
\(779\) −4.17707 12.8557i −0.149659 0.460603i
\(780\) 0 0
\(781\) 6.72386 39.1820i 0.240599 1.40204i
\(782\) 0 0
\(783\) −1.71690 + 1.90681i −0.0613570 + 0.0681438i
\(784\) 0 0
\(785\) −3.95644 5.44558i −0.141212 0.194361i
\(786\) 0 0
\(787\) 35.1060 31.6096i 1.25139 1.12676i 0.264671 0.964339i \(-0.414737\pi\)
0.986722 0.162420i \(-0.0519299\pi\)
\(788\) 0 0
\(789\) −28.2273 + 12.5676i −1.00492 + 0.447418i
\(790\) 0 0
\(791\) 1.01350 0.585146i 0.0360360 0.0208054i
\(792\) 0 0
\(793\) −5.58113 8.88644i −0.198192 0.315567i
\(794\) 0 0
\(795\) −18.5992 1.95486i −0.659646 0.0693316i
\(796\) 0 0
\(797\) 34.2092 + 37.9932i 1.21175 + 1.34579i 0.921278 + 0.388905i \(0.127146\pi\)
0.290475 + 0.956883i \(0.406187\pi\)
\(798\) 0 0
\(799\) −29.3085 + 3.08044i −1.03686 + 0.108978i
\(800\) 0 0
\(801\) 26.5589 8.62950i 0.938411 0.304908i
\(802\) 0 0
\(803\) −47.3017 13.3293i −1.66924 0.470379i
\(804\) 0 0
\(805\) 0.866713 + 2.66747i 0.0305476 + 0.0940159i
\(806\) 0 0
\(807\) 22.5622 16.3924i 0.794226 0.577039i
\(808\) 0 0
\(809\) 32.0415 6.81064i 1.12652 0.239449i 0.393280 0.919419i \(-0.371340\pi\)
0.733240 + 0.679970i \(0.238007\pi\)
\(810\) 0 0
\(811\) −2.64333 + 3.63824i −0.0928200 + 0.127756i −0.852901 0.522072i \(-0.825159\pi\)
0.760081 + 0.649828i \(0.225159\pi\)
\(812\) 0 0
\(813\) −7.92599 4.57607i −0.277976 0.160490i
\(814\) 0 0
\(815\) −16.2081 + 28.0732i −0.567743 + 0.983360i
\(816\) 0 0
\(817\) 7.68338 + 0.807556i 0.268807 + 0.0282528i
\(818\) 0 0
\(819\) 1.32483 + 0.376615i 0.0462932 + 0.0131600i
\(820\) 0 0
\(821\) 1.40040 3.14534i 0.0488742 0.109773i −0.887458 0.460889i \(-0.847531\pi\)
0.936332 + 0.351115i \(0.114197\pi\)
\(822\) 0 0
\(823\) −39.9231 8.48591i −1.39163 0.295800i −0.549689 0.835369i \(-0.685254\pi\)
−0.841941 + 0.539569i \(0.818587\pi\)
\(824\) 0 0
\(825\) −0.342736 + 5.24676i −0.0119325 + 0.182669i
\(826\) 0 0
\(827\) −40.7562 + 13.2425i −1.41723 + 0.460487i −0.914722 0.404084i \(-0.867590\pi\)
−0.502511 + 0.864571i \(0.667590\pi\)
\(828\) 0 0
\(829\) 6.52264 + 2.90407i 0.226541 + 0.100862i 0.516868 0.856065i \(-0.327098\pi\)
−0.290328 + 0.956927i \(0.593764\pi\)
\(830\) 0 0
\(831\) 17.0278 52.4062i 0.590688 1.81795i
\(832\) 0 0
\(833\) 26.4134 + 19.1905i 0.915171 + 0.664911i
\(834\) 0 0
\(835\) −7.17743 12.4317i −0.248385 0.430216i
\(836\) 0 0
\(837\) 3.23804i 0.111923i
\(838\) 0 0
\(839\) 21.3721 + 48.0025i 0.737846 + 1.65723i 0.753582 + 0.657354i \(0.228324\pi\)
−0.0157356 + 0.999876i \(0.505009\pi\)
\(840\) 0 0
\(841\) −18.7913 20.8699i −0.647976 0.719650i
\(842\) 0 0
\(843\) 7.95432 17.8657i 0.273961 0.615327i
\(844\) 0 0
\(845\) −21.2547 16.4502i −0.731185 0.565904i
\(846\) 0 0
\(847\) 0.308229 2.34919i 0.0105909 0.0807191i
\(848\) 0 0
\(849\) −46.9479 9.97909i −1.61125 0.342481i
\(850\) 0 0
\(851\) 19.2806 2.02647i 0.660929 0.0694664i
\(852\) 0 0
\(853\) −8.43928 2.74209i −0.288955 0.0938873i 0.160953 0.986962i \(-0.448543\pi\)
−0.449908 + 0.893075i \(0.648543\pi\)
\(854\) 0 0
\(855\) −1.20901 + 11.5030i −0.0413474 + 0.393394i
\(856\) 0 0
\(857\) 35.1714 1.20143 0.600715 0.799463i \(-0.294883\pi\)
0.600715 + 0.799463i \(0.294883\pi\)
\(858\) 0 0
\(859\) −43.6032 −1.48772 −0.743861 0.668335i \(-0.767007\pi\)
−0.743861 + 0.668335i \(0.767007\pi\)
\(860\) 0 0
\(861\) 0.210788 2.00551i 0.00718363 0.0683477i
\(862\) 0 0
\(863\) −39.6363 12.8786i −1.34924 0.438393i −0.456801 0.889569i \(-0.651005\pi\)
−0.892435 + 0.451176i \(0.851005\pi\)
\(864\) 0 0
\(865\) −37.5646 + 3.94820i −1.27723 + 0.134243i
\(866\) 0 0
\(867\) −10.7821 2.29180i −0.366178 0.0778335i
\(868\) 0 0
\(869\) −16.1886 10.8117i −0.549159 0.366762i
\(870\) 0 0
\(871\) 27.4639 10.0671i 0.930579 0.341112i
\(872\) 0 0
\(873\) 6.89481 15.4860i 0.233354 0.524122i
\(874\) 0 0
\(875\) 1.70609 + 1.89480i 0.0576763 + 0.0640560i
\(876\) 0 0
\(877\) 19.1089 + 42.9193i 0.645261 + 1.44928i 0.878923 + 0.476963i \(0.158262\pi\)
−0.233662 + 0.972318i \(0.575071\pi\)
\(878\) 0 0
\(879\) 52.0933i 1.75706i
\(880\) 0 0
\(881\) −7.39032 12.8004i −0.248986 0.431257i 0.714259 0.699882i \(-0.246764\pi\)
−0.963245 + 0.268625i \(0.913431\pi\)
\(882\) 0 0
\(883\) 18.1323 + 13.1739i 0.610200 + 0.443336i 0.849485 0.527613i \(-0.176913\pi\)
−0.239285 + 0.970949i \(0.576913\pi\)
\(884\) 0 0
\(885\) 1.13348 3.48849i 0.0381015 0.117264i
\(886\) 0 0
\(887\) 28.6818 + 12.7699i 0.963040 + 0.428773i 0.827169 0.561954i \(-0.189950\pi\)
0.135871 + 0.990727i \(0.456617\pi\)
\(888\) 0 0
\(889\) 1.02306 0.332411i 0.0343122 0.0111487i
\(890\) 0 0
\(891\) 35.9215 9.13128i 1.20342 0.305910i
\(892\) 0 0
\(893\) 19.3666 + 4.11651i 0.648080 + 0.137754i
\(894\) 0 0
\(895\) −10.4516 + 23.4746i −0.349358 + 0.784671i
\(896\) 0 0
\(897\) −48.1138 + 12.1129i −1.60647 + 0.404439i
\(898\) 0 0
\(899\) 1.15069 + 0.120943i 0.0383778 + 0.00403366i
\(900\) 0 0
\(901\) −9.71967 + 16.8350i −0.323809 + 0.560854i
\(902\) 0 0
\(903\) 0.998138 + 0.576275i 0.0332160 + 0.0191772i
\(904\) 0 0
\(905\) −23.4079 + 32.2183i −0.778106 + 1.07097i
\(906\) 0 0
\(907\) −3.78079 + 0.803631i −0.125539 + 0.0266841i −0.270253 0.962789i \(-0.587107\pi\)
0.144714 + 0.989474i \(0.453774\pi\)
\(908\) 0 0
\(909\) 21.6150 15.7042i 0.716923 0.520875i
\(910\) 0 0
\(911\) 8.80623 + 27.1028i 0.291763 + 0.897955i 0.984289 + 0.176562i \(0.0564977\pi\)
−0.692526 + 0.721393i \(0.743502\pi\)
\(912\) 0 0
\(913\) −27.9400 + 10.3146i −0.924680 + 0.341363i
\(914\) 0 0
\(915\) 12.5031 4.06252i 0.413341 0.134303i
\(916\) 0 0
\(917\) −3.13312 + 0.329305i −0.103465 + 0.0108746i
\(918\) 0 0
\(919\) 35.0013 + 38.8729i 1.15459 + 1.28230i 0.953049 + 0.302817i \(0.0979272\pi\)
0.201538 + 0.979481i \(0.435406\pi\)
\(920\) 0 0
\(921\) −44.4582 4.67275i −1.46495 0.153972i
\(922\) 0 0
\(923\) 36.5985 22.9857i 1.20466 0.756584i
\(924\) 0 0
\(925\) 1.93425 1.11674i 0.0635978 0.0367182i
\(926\) 0 0
\(927\) −15.8810 + 7.07069i −0.521601 + 0.232232i
\(928\) 0 0
\(929\) −33.6318 + 30.2822i −1.10342 + 0.993528i −0.999999 0.00110966i \(-0.999647\pi\)
−0.103425 + 0.994637i \(0.532980\pi\)
\(930\) 0 0
\(931\) −12.8931 17.7458i −0.422554 0.581595i
\(932\) 0 0
\(933\) −18.4665 + 20.5092i −0.604567 + 0.671440i
\(934\) 0 0
\(935\) −28.4956 14.9843i −0.931906 0.490039i
\(936\) 0 0
\(937\) −2.07826 6.39622i −0.0678937 0.208955i 0.911354 0.411624i \(-0.135038\pi\)
−0.979247 + 0.202669i \(0.935038\pi\)
\(938\) 0 0
\(939\) 56.7420 + 25.2632i 1.85171 + 0.824432i
\(940\) 0 0
\(941\) 14.2430 + 4.62783i 0.464308 + 0.150863i 0.531823 0.846855i \(-0.321507\pi\)
−0.0675152 + 0.997718i \(0.521507\pi\)
\(942\) 0 0
\(943\) 10.9774 + 24.6556i 0.357472 + 0.802896i
\(944\) 0 0
\(945\) 0.596657 1.03344i 0.0194092 0.0336178i
\(946\) 0 0
\(947\) −3.00661 + 1.73587i −0.0977016 + 0.0564080i −0.548055 0.836442i \(-0.684631\pi\)
0.450353 + 0.892851i \(0.351298\pi\)
\(948\) 0 0
\(949\) −23.5296 47.9644i −0.763803 1.55699i
\(950\) 0 0
\(951\) −3.02730 14.2423i −0.0981668 0.461838i
\(952\) 0 0
\(953\) 0.232052 + 2.20783i 0.00751691 + 0.0715186i 0.997637 0.0687016i \(-0.0218856\pi\)
−0.990120 + 0.140220i \(0.955219\pi\)
\(954\) 0 0
\(955\) −7.76711 + 36.5414i −0.251338 + 1.18245i
\(956\) 0 0
\(957\) −0.997123 6.86644i −0.0322324 0.221960i
\(958\) 0 0
\(959\) −1.69052 + 1.87751i −0.0545896 + 0.0606279i
\(960\) 0 0
\(961\) −23.8983 + 17.3631i −0.770911 + 0.560100i
\(962\) 0 0
\(963\) −2.27457 + 7.00039i −0.0732968 + 0.225584i
\(964\) 0 0
\(965\) −2.13286 + 20.2928i −0.0686592 + 0.653249i
\(966\) 0 0
\(967\) 6.98874i 0.224743i −0.993666 0.112371i \(-0.964155\pi\)
0.993666 0.112371i \(-0.0358446\pi\)
\(968\) 0 0
\(969\) 28.0243 + 16.1798i 0.900269 + 0.519771i
\(970\) 0 0
\(971\) −23.3317 + 10.3879i −0.748749 + 0.333364i −0.745389 0.666630i \(-0.767736\pi\)
−0.00335992 + 0.999994i \(0.501069\pi\)
\(972\) 0 0
\(973\) 0.949689 + 4.46793i 0.0304456 + 0.143235i
\(974\) 0 0
\(975\) −4.49621 + 3.52939i −0.143994 + 0.113031i
\(976\) 0 0
\(977\) −7.91651 7.12806i −0.253272 0.228047i 0.532708 0.846299i \(-0.321174\pi\)
−0.785980 + 0.618252i \(0.787841\pi\)
\(978\) 0 0
\(979\) 19.3413 48.5101i 0.618149 1.55039i
\(980\) 0 0
\(981\) −0.215547 + 1.01407i −0.00688188 + 0.0323767i
\(982\) 0 0
\(983\) 10.7573 + 14.8062i 0.343105 + 0.472244i 0.945345 0.326071i \(-0.105725\pi\)
−0.602240 + 0.798315i \(0.705725\pi\)
\(984\) 0 0
\(985\) −30.9410 + 6.57672i −0.985863 + 0.209552i
\(986\) 0 0
\(987\) 2.38962 + 1.73616i 0.0760625 + 0.0552627i
\(988\) 0 0
\(989\) −15.4253 −0.490496
\(990\) 0 0
\(991\) −29.5502 51.1824i −0.938692 1.62586i −0.767914 0.640553i \(-0.778705\pi\)
−0.170779 0.985309i \(-0.554628\pi\)
\(992\) 0 0
\(993\) −36.9846 + 50.9049i −1.17367 + 1.61542i
\(994\) 0 0
\(995\) −10.1811 + 9.16711i −0.322763 + 0.290617i
\(996\) 0 0
\(997\) −2.91760 27.7591i −0.0924013 0.879140i −0.938306 0.345806i \(-0.887606\pi\)
0.845905 0.533334i \(-0.179061\pi\)
\(998\) 0 0
\(999\) −6.12971 5.51922i −0.193936 0.174620i
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 572.2.bq.a.49.3 112
11.9 even 5 inner 572.2.bq.a.361.12 yes 112
13.4 even 6 inner 572.2.bq.a.225.12 yes 112
143.108 even 30 inner 572.2.bq.a.537.3 yes 112
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
572.2.bq.a.49.3 112 1.1 even 1 trivial
572.2.bq.a.225.12 yes 112 13.4 even 6 inner
572.2.bq.a.361.12 yes 112 11.9 even 5 inner
572.2.bq.a.537.3 yes 112 143.108 even 30 inner