Properties

Label 825.2.n.f.676.1
Level $825$
Weight $2$
Character 825.676
Analytic conductor $6.588$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [825,2,Mod(301,825)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(825, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("825.301");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.n (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 676.1
Root \(-0.309017 + 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 825.676
Dual form 825.2.n.f.526.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.190983 + 0.587785i) q^{2} +(0.809017 + 0.587785i) q^{3} +(1.30902 - 0.951057i) q^{4} +(-0.190983 + 0.587785i) q^{6} +(2.42705 - 1.76336i) q^{7} +(1.80902 + 1.31433i) q^{8} +(0.309017 + 0.951057i) q^{9} +(1.69098 - 2.85317i) q^{11} +1.61803 q^{12} +(-0.545085 - 1.67760i) q^{13} +(1.50000 + 1.08981i) q^{14} +(0.572949 - 1.76336i) q^{16} +(-0.500000 + 1.53884i) q^{17} +(-0.500000 + 0.363271i) q^{18} +(-4.73607 - 3.44095i) q^{19} +3.00000 q^{21} +(2.00000 + 0.449028i) q^{22} -3.47214 q^{23} +(0.690983 + 2.12663i) q^{24} +(0.881966 - 0.640786i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.50000 - 4.61653i) q^{28} +(-3.61803 + 2.62866i) q^{29} +(0.881966 + 2.71441i) q^{31} +5.61803 q^{32} +(3.04508 - 1.31433i) q^{33} -1.00000 q^{34} +(1.30902 + 0.951057i) q^{36} +(0.190983 - 0.138757i) q^{37} +(1.11803 - 3.44095i) q^{38} +(0.545085 - 1.67760i) q^{39} +(9.66312 + 7.02067i) q^{41} +(0.572949 + 1.76336i) q^{42} -6.23607 q^{43} +(-0.500000 - 5.34307i) q^{44} +(-0.663119 - 2.04087i) q^{46} +(1.30902 + 0.951057i) q^{47} +(1.50000 - 1.08981i) q^{48} +(0.618034 - 1.90211i) q^{49} +(-1.30902 + 0.951057i) q^{51} +(-2.30902 - 1.67760i) q^{52} +(2.97214 + 9.14729i) q^{53} -0.618034 q^{54} +6.70820 q^{56} +(-1.80902 - 5.56758i) q^{57} +(-2.23607 - 1.62460i) q^{58} +(-8.35410 + 6.06961i) q^{59} +(2.42705 - 7.46969i) q^{61} +(-1.42705 + 1.03681i) q^{62} +(2.42705 + 1.76336i) q^{63} +(-0.0729490 - 0.224514i) q^{64} +(1.35410 + 1.53884i) q^{66} +9.56231 q^{67} +(0.809017 + 2.48990i) q^{68} +(-2.80902 - 2.04087i) q^{69} +(-1.71885 + 5.29007i) q^{71} +(-0.690983 + 2.12663i) q^{72} +(-2.61803 + 1.90211i) q^{73} +(0.118034 + 0.0857567i) q^{74} -9.47214 q^{76} +(-0.927051 - 9.90659i) q^{77} +1.09017 q^{78} +(2.92705 + 9.00854i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-2.28115 + 7.02067i) q^{82} +(-0.218847 + 0.673542i) q^{83} +(3.92705 - 2.85317i) q^{84} +(-1.19098 - 3.66547i) q^{86} -4.47214 q^{87} +(6.80902 - 2.93893i) q^{88} +0.527864 q^{89} +(-4.28115 - 3.11044i) q^{91} +(-4.54508 + 3.30220i) q^{92} +(-0.881966 + 2.71441i) q^{93} +(-0.309017 + 0.951057i) q^{94} +(4.54508 + 3.30220i) q^{96} +(4.33688 + 13.3475i) q^{97} +1.23607 q^{98} +(3.23607 + 0.726543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 3 q^{2} + q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{7} + 5 q^{8} - q^{9} + 9 q^{11} + 2 q^{12} + 9 q^{13} + 6 q^{14} + 9 q^{16} - 2 q^{17} - 2 q^{18} - 10 q^{19} + 12 q^{21} + 8 q^{22} + 4 q^{23} + 5 q^{24}+ \cdots + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.190983 + 0.587785i 0.135045 + 0.415627i 0.995597 0.0937362i \(-0.0298810\pi\)
−0.860552 + 0.509363i \(0.829881\pi\)
\(3\) 0.809017 + 0.587785i 0.467086 + 0.339358i
\(4\) 1.30902 0.951057i 0.654508 0.475528i
\(5\) 0 0
\(6\) −0.190983 + 0.587785i −0.0779685 + 0.239962i
\(7\) 2.42705 1.76336i 0.917339 0.666486i −0.0255212 0.999674i \(-0.508125\pi\)
0.942860 + 0.333188i \(0.108125\pi\)
\(8\) 1.80902 + 1.31433i 0.639584 + 0.464685i
\(9\) 0.309017 + 0.951057i 0.103006 + 0.317019i
\(10\) 0 0
\(11\) 1.69098 2.85317i 0.509851 0.860263i
\(12\) 1.61803 0.467086
\(13\) −0.545085 1.67760i −0.151179 0.465282i 0.846574 0.532270i \(-0.178661\pi\)
−0.997754 + 0.0669881i \(0.978661\pi\)
\(14\) 1.50000 + 1.08981i 0.400892 + 0.291265i
\(15\) 0 0
\(16\) 0.572949 1.76336i 0.143237 0.440839i
\(17\) −0.500000 + 1.53884i −0.121268 + 0.373224i −0.993203 0.116398i \(-0.962865\pi\)
0.871935 + 0.489622i \(0.162865\pi\)
\(18\) −0.500000 + 0.363271i −0.117851 + 0.0856239i
\(19\) −4.73607 3.44095i −1.08653 0.789409i −0.107719 0.994181i \(-0.534355\pi\)
−0.978810 + 0.204772i \(0.934355\pi\)
\(20\) 0 0
\(21\) 3.00000 0.654654
\(22\) 2.00000 + 0.449028i 0.426401 + 0.0957331i
\(23\) −3.47214 −0.723990 −0.361995 0.932180i \(-0.617904\pi\)
−0.361995 + 0.932180i \(0.617904\pi\)
\(24\) 0.690983 + 2.12663i 0.141046 + 0.434096i
\(25\) 0 0
\(26\) 0.881966 0.640786i 0.172968 0.125668i
\(27\) −0.309017 + 0.951057i −0.0594703 + 0.183031i
\(28\) 1.50000 4.61653i 0.283473 0.872441i
\(29\) −3.61803 + 2.62866i −0.671852 + 0.488129i −0.870645 0.491912i \(-0.836298\pi\)
0.198793 + 0.980042i \(0.436298\pi\)
\(30\) 0 0
\(31\) 0.881966 + 2.71441i 0.158406 + 0.487523i 0.998490 0.0549331i \(-0.0174946\pi\)
−0.840084 + 0.542456i \(0.817495\pi\)
\(32\) 5.61803 0.993137
\(33\) 3.04508 1.31433i 0.530081 0.228795i
\(34\) −1.00000 −0.171499
\(35\) 0 0
\(36\) 1.30902 + 0.951057i 0.218169 + 0.158509i
\(37\) 0.190983 0.138757i 0.0313974 0.0228116i −0.571976 0.820270i \(-0.693823\pi\)
0.603373 + 0.797459i \(0.293823\pi\)
\(38\) 1.11803 3.44095i 0.181369 0.558197i
\(39\) 0.545085 1.67760i 0.0872835 0.268631i
\(40\) 0 0
\(41\) 9.66312 + 7.02067i 1.50913 + 1.09644i 0.966563 + 0.256428i \(0.0825458\pi\)
0.542562 + 0.840015i \(0.317454\pi\)
\(42\) 0.572949 + 1.76336i 0.0884080 + 0.272092i
\(43\) −6.23607 −0.950991 −0.475496 0.879718i \(-0.657731\pi\)
−0.475496 + 0.879718i \(0.657731\pi\)
\(44\) −0.500000 5.34307i −0.0753778 0.805498i
\(45\) 0 0
\(46\) −0.663119 2.04087i −0.0977716 0.300910i
\(47\) 1.30902 + 0.951057i 0.190940 + 0.138726i 0.679148 0.734001i \(-0.262349\pi\)
−0.488208 + 0.872727i \(0.662349\pi\)
\(48\) 1.50000 1.08981i 0.216506 0.157301i
\(49\) 0.618034 1.90211i 0.0882906 0.271730i
\(50\) 0 0
\(51\) −1.30902 + 0.951057i −0.183299 + 0.133175i
\(52\) −2.30902 1.67760i −0.320203 0.232641i
\(53\) 2.97214 + 9.14729i 0.408254 + 1.25648i 0.918147 + 0.396240i \(0.129685\pi\)
−0.509893 + 0.860238i \(0.670315\pi\)
\(54\) −0.618034 −0.0841038
\(55\) 0 0
\(56\) 6.70820 0.896421
\(57\) −1.80902 5.56758i −0.239610 0.737444i
\(58\) −2.23607 1.62460i −0.293610 0.213320i
\(59\) −8.35410 + 6.06961i −1.08761 + 0.790196i −0.978994 0.203888i \(-0.934642\pi\)
−0.108617 + 0.994084i \(0.534642\pi\)
\(60\) 0 0
\(61\) 2.42705 7.46969i 0.310752 0.956396i −0.666716 0.745312i \(-0.732301\pi\)
0.977468 0.211084i \(-0.0676995\pi\)
\(62\) −1.42705 + 1.03681i −0.181236 + 0.131675i
\(63\) 2.42705 + 1.76336i 0.305780 + 0.222162i
\(64\) −0.0729490 0.224514i −0.00911863 0.0280642i
\(65\) 0 0
\(66\) 1.35410 + 1.53884i 0.166678 + 0.189418i
\(67\) 9.56231 1.16822 0.584111 0.811674i \(-0.301443\pi\)
0.584111 + 0.811674i \(0.301443\pi\)
\(68\) 0.809017 + 2.48990i 0.0981077 + 0.301945i
\(69\) −2.80902 2.04087i −0.338166 0.245692i
\(70\) 0 0
\(71\) −1.71885 + 5.29007i −0.203990 + 0.627815i 0.795764 + 0.605607i \(0.207070\pi\)
−0.999753 + 0.0222083i \(0.992930\pi\)
\(72\) −0.690983 + 2.12663i −0.0814331 + 0.250625i
\(73\) −2.61803 + 1.90211i −0.306418 + 0.222625i −0.730358 0.683065i \(-0.760647\pi\)
0.423940 + 0.905690i \(0.360647\pi\)
\(74\) 0.118034 + 0.0857567i 0.0137212 + 0.00996902i
\(75\) 0 0
\(76\) −9.47214 −1.08653
\(77\) −0.927051 9.90659i −0.105647 1.12896i
\(78\) 1.09017 0.123437
\(79\) 2.92705 + 9.00854i 0.329319 + 1.01354i 0.969453 + 0.245276i \(0.0788787\pi\)
−0.640134 + 0.768263i \(0.721121\pi\)
\(80\) 0 0
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) −2.28115 + 7.02067i −0.251911 + 0.775303i
\(83\) −0.218847 + 0.673542i −0.0240216 + 0.0739308i −0.962349 0.271818i \(-0.912375\pi\)
0.938327 + 0.345749i \(0.112375\pi\)
\(84\) 3.92705 2.85317i 0.428476 0.311306i
\(85\) 0 0
\(86\) −1.19098 3.66547i −0.128427 0.395258i
\(87\) −4.47214 −0.479463
\(88\) 6.80902 2.93893i 0.725844 0.313291i
\(89\) 0.527864 0.0559535 0.0279767 0.999609i \(-0.491094\pi\)
0.0279767 + 0.999609i \(0.491094\pi\)
\(90\) 0 0
\(91\) −4.28115 3.11044i −0.448787 0.326063i
\(92\) −4.54508 + 3.30220i −0.473858 + 0.344278i
\(93\) −0.881966 + 2.71441i −0.0914556 + 0.281471i
\(94\) −0.309017 + 0.951057i −0.0318727 + 0.0980940i
\(95\) 0 0
\(96\) 4.54508 + 3.30220i 0.463881 + 0.337029i
\(97\) 4.33688 + 13.3475i 0.440344 + 1.35524i 0.887510 + 0.460788i \(0.152433\pi\)
−0.447167 + 0.894451i \(0.647567\pi\)
\(98\) 1.23607 0.124862
\(99\) 3.23607 + 0.726543i 0.325237 + 0.0730203i
\(100\) 0 0
\(101\) −0.927051 2.85317i −0.0922450 0.283901i 0.894281 0.447506i \(-0.147688\pi\)
−0.986526 + 0.163605i \(0.947688\pi\)
\(102\) −0.809017 0.587785i −0.0801046 0.0581994i
\(103\) −4.85410 + 3.52671i −0.478289 + 0.347497i −0.800663 0.599115i \(-0.795519\pi\)
0.322374 + 0.946612i \(0.395519\pi\)
\(104\) 1.21885 3.75123i 0.119518 0.367838i
\(105\) 0 0
\(106\) −4.80902 + 3.49396i −0.467093 + 0.339363i
\(107\) −3.42705 2.48990i −0.331306 0.240708i 0.409679 0.912230i \(-0.365641\pi\)
−0.740984 + 0.671522i \(0.765641\pi\)
\(108\) 0.500000 + 1.53884i 0.0481125 + 0.148075i
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0.236068 0.0224066
\(112\) −1.71885 5.29007i −0.162416 0.499864i
\(113\) 0.572949 + 0.416272i 0.0538985 + 0.0391596i 0.614408 0.788988i \(-0.289395\pi\)
−0.560510 + 0.828148i \(0.689395\pi\)
\(114\) 2.92705 2.12663i 0.274143 0.199177i
\(115\) 0 0
\(116\) −2.23607 + 6.88191i −0.207614 + 0.638969i
\(117\) 1.42705 1.03681i 0.131931 0.0958534i
\(118\) −5.16312 3.75123i −0.475304 0.345328i
\(119\) 1.50000 + 4.61653i 0.137505 + 0.423196i
\(120\) 0 0
\(121\) −5.28115 9.64932i −0.480105 0.877211i
\(122\) 4.85410 0.439470
\(123\) 3.69098 + 11.3597i 0.332805 + 1.02427i
\(124\) 3.73607 + 2.71441i 0.335509 + 0.243761i
\(125\) 0 0
\(126\) −0.572949 + 1.76336i −0.0510424 + 0.157092i
\(127\) 1.14590 3.52671i 0.101682 0.312945i −0.887255 0.461279i \(-0.847391\pi\)
0.988937 + 0.148333i \(0.0473909\pi\)
\(128\) 9.20820 6.69015i 0.813898 0.591331i
\(129\) −5.04508 3.66547i −0.444195 0.322727i
\(130\) 0 0
\(131\) −7.14590 −0.624340 −0.312170 0.950026i \(-0.601056\pi\)
−0.312170 + 0.950026i \(0.601056\pi\)
\(132\) 2.73607 4.61653i 0.238144 0.401817i
\(133\) −17.5623 −1.52285
\(134\) 1.82624 + 5.62058i 0.157763 + 0.485544i
\(135\) 0 0
\(136\) −2.92705 + 2.12663i −0.250993 + 0.182357i
\(137\) −2.30902 + 7.10642i −0.197273 + 0.607143i 0.802670 + 0.596424i \(0.203412\pi\)
−0.999943 + 0.0107192i \(0.996588\pi\)
\(138\) 0.663119 2.04087i 0.0564484 0.173730i
\(139\) 0.690983 0.502029i 0.0586084 0.0425815i −0.558095 0.829777i \(-0.688468\pi\)
0.616704 + 0.787195i \(0.288468\pi\)
\(140\) 0 0
\(141\) 0.500000 + 1.53884i 0.0421076 + 0.129594i
\(142\) −3.43769 −0.288485
\(143\) −5.70820 1.28157i −0.477344 0.107170i
\(144\) 1.85410 0.154508
\(145\) 0 0
\(146\) −1.61803 1.17557i −0.133909 0.0972909i
\(147\) 1.61803 1.17557i 0.133453 0.0969594i
\(148\) 0.118034 0.363271i 0.00970233 0.0298607i
\(149\) 4.63525 14.2658i 0.379735 1.16870i −0.560493 0.828159i \(-0.689388\pi\)
0.940228 0.340545i \(-0.110612\pi\)
\(150\) 0 0
\(151\) −1.61803 1.17557i −0.131674 0.0956666i 0.519999 0.854167i \(-0.325932\pi\)
−0.651673 + 0.758500i \(0.725932\pi\)
\(152\) −4.04508 12.4495i −0.328100 1.00979i
\(153\) −1.61803 −0.130810
\(154\) 5.64590 2.43690i 0.454959 0.196371i
\(155\) 0 0
\(156\) −0.881966 2.71441i −0.0706138 0.217327i
\(157\) −3.00000 2.17963i −0.239426 0.173953i 0.461601 0.887087i \(-0.347275\pi\)
−0.701028 + 0.713134i \(0.747275\pi\)
\(158\) −4.73607 + 3.44095i −0.376781 + 0.273748i
\(159\) −2.97214 + 9.14729i −0.235706 + 0.725428i
\(160\) 0 0
\(161\) −8.42705 + 6.12261i −0.664145 + 0.482529i
\(162\) −0.500000 0.363271i −0.0392837 0.0285413i
\(163\) −5.64590 17.3763i −0.442221 1.36102i −0.885503 0.464634i \(-0.846186\pi\)
0.443282 0.896382i \(-0.353814\pi\)
\(164\) 19.3262 1.50913
\(165\) 0 0
\(166\) −0.437694 −0.0339717
\(167\) −3.10081 9.54332i −0.239948 0.738484i −0.996426 0.0844656i \(-0.973082\pi\)
0.756478 0.654019i \(-0.226918\pi\)
\(168\) 5.42705 + 3.94298i 0.418706 + 0.304208i
\(169\) 8.00000 5.81234i 0.615385 0.447103i
\(170\) 0 0
\(171\) 1.80902 5.56758i 0.138339 0.425764i
\(172\) −8.16312 + 5.93085i −0.622432 + 0.452223i
\(173\) 12.4443 + 9.04129i 0.946120 + 0.687397i 0.949886 0.312596i \(-0.101199\pi\)
−0.00376565 + 0.999993i \(0.501199\pi\)
\(174\) −0.854102 2.62866i −0.0647493 0.199278i
\(175\) 0 0
\(176\) −4.06231 4.61653i −0.306208 0.347984i
\(177\) −10.3262 −0.776168
\(178\) 0.100813 + 0.310271i 0.00755626 + 0.0232558i
\(179\) 1.80902 + 1.31433i 0.135212 + 0.0982375i 0.653335 0.757069i \(-0.273369\pi\)
−0.518123 + 0.855306i \(0.673369\pi\)
\(180\) 0 0
\(181\) −5.39919 + 16.6170i −0.401318 + 1.23513i 0.522612 + 0.852571i \(0.324958\pi\)
−0.923930 + 0.382560i \(0.875042\pi\)
\(182\) 1.01064 3.11044i 0.0749139 0.230561i
\(183\) 6.35410 4.61653i 0.469709 0.341263i
\(184\) −6.28115 4.56352i −0.463053 0.336428i
\(185\) 0 0
\(186\) −1.76393 −0.129338
\(187\) 3.54508 + 4.02874i 0.259242 + 0.294611i
\(188\) 2.61803 0.190940
\(189\) 0.927051 + 2.85317i 0.0674330 + 0.207538i
\(190\) 0 0
\(191\) 6.04508 4.39201i 0.437407 0.317795i −0.347197 0.937792i \(-0.612866\pi\)
0.784604 + 0.619998i \(0.212866\pi\)
\(192\) 0.0729490 0.224514i 0.00526464 0.0162029i
\(193\) 5.73607 17.6538i 0.412891 1.27075i −0.501232 0.865313i \(-0.667120\pi\)
0.914124 0.405436i \(-0.132880\pi\)
\(194\) −7.01722 + 5.09831i −0.503807 + 0.366037i
\(195\) 0 0
\(196\) −1.00000 3.07768i −0.0714286 0.219835i
\(197\) −24.3820 −1.73714 −0.868572 0.495564i \(-0.834961\pi\)
−0.868572 + 0.495564i \(0.834961\pi\)
\(198\) 0.190983 + 2.04087i 0.0135726 + 0.145038i
\(199\) −16.7082 −1.18441 −0.592207 0.805786i \(-0.701743\pi\)
−0.592207 + 0.805786i \(0.701743\pi\)
\(200\) 0 0
\(201\) 7.73607 + 5.62058i 0.545660 + 0.396445i
\(202\) 1.50000 1.08981i 0.105540 0.0766790i
\(203\) −4.14590 + 12.7598i −0.290985 + 0.895560i
\(204\) −0.809017 + 2.48990i −0.0566425 + 0.174328i
\(205\) 0 0
\(206\) −3.00000 2.17963i −0.209020 0.151862i
\(207\) −1.07295 3.30220i −0.0745751 0.229519i
\(208\) −3.27051 −0.226769
\(209\) −17.8262 + 7.69421i −1.23307 + 0.532220i
\(210\) 0 0
\(211\) −6.88197 21.1805i −0.473774 1.45813i −0.847604 0.530629i \(-0.821956\pi\)
0.373830 0.927497i \(-0.378044\pi\)
\(212\) 12.5902 + 9.14729i 0.864696 + 0.628239i
\(213\) −4.50000 + 3.26944i −0.308335 + 0.224018i
\(214\) 0.809017 2.48990i 0.0553033 0.170206i
\(215\) 0 0
\(216\) −1.80902 + 1.31433i −0.123088 + 0.0894287i
\(217\) 6.92705 + 5.03280i 0.470239 + 0.341649i
\(218\) 0 0
\(219\) −3.23607 −0.218673
\(220\) 0 0
\(221\) 2.85410 0.191988
\(222\) 0.0450850 + 0.138757i 0.00302591 + 0.00931278i
\(223\) 0.572949 + 0.416272i 0.0383675 + 0.0278756i 0.606804 0.794852i \(-0.292451\pi\)
−0.568436 + 0.822727i \(0.692451\pi\)
\(224\) 13.6353 9.90659i 0.911044 0.661912i
\(225\) 0 0
\(226\) −0.135255 + 0.416272i −0.00899702 + 0.0276900i
\(227\) −20.1353 + 14.6291i −1.33642 + 0.970969i −0.336856 + 0.941556i \(0.609364\pi\)
−0.999567 + 0.0294127i \(0.990636\pi\)
\(228\) −7.66312 5.56758i −0.507502 0.368722i
\(229\) 3.09017 + 9.51057i 0.204204 + 0.628476i 0.999745 + 0.0225760i \(0.00718678\pi\)
−0.795541 + 0.605900i \(0.792813\pi\)
\(230\) 0 0
\(231\) 5.07295 8.55951i 0.333776 0.563174i
\(232\) −10.0000 −0.656532
\(233\) −7.51722 23.1356i −0.492470 1.51567i −0.820863 0.571124i \(-0.806507\pi\)
0.328394 0.944541i \(-0.393493\pi\)
\(234\) 0.881966 + 0.640786i 0.0576559 + 0.0418895i
\(235\) 0 0
\(236\) −5.16312 + 15.8904i −0.336090 + 1.03438i
\(237\) −2.92705 + 9.00854i −0.190132 + 0.585167i
\(238\) −2.42705 + 1.76336i −0.157322 + 0.114301i
\(239\) −2.07295 1.50609i −0.134088 0.0974206i 0.518719 0.854945i \(-0.326409\pi\)
−0.652807 + 0.757524i \(0.726409\pi\)
\(240\) 0 0
\(241\) −23.1246 −1.48959 −0.744794 0.667295i \(-0.767452\pi\)
−0.744794 + 0.667295i \(0.767452\pi\)
\(242\) 4.66312 4.94704i 0.299757 0.318008i
\(243\) −1.00000 −0.0641500
\(244\) −3.92705 12.0862i −0.251404 0.773741i
\(245\) 0 0
\(246\) −5.97214 + 4.33901i −0.380769 + 0.276645i
\(247\) −3.19098 + 9.82084i −0.203037 + 0.624885i
\(248\) −1.97214 + 6.06961i −0.125231 + 0.385421i
\(249\) −0.572949 + 0.416272i −0.0363092 + 0.0263802i
\(250\) 0 0
\(251\) −2.40983 7.41669i −0.152107 0.468138i 0.845749 0.533581i \(-0.179154\pi\)
−0.997856 + 0.0654431i \(0.979154\pi\)
\(252\) 4.85410 0.305780
\(253\) −5.87132 + 9.90659i −0.369127 + 0.622822i
\(254\) 2.29180 0.143800
\(255\) 0 0
\(256\) 5.30902 + 3.85723i 0.331814 + 0.241077i
\(257\) −9.44427 + 6.86167i −0.589117 + 0.428019i −0.842000 0.539478i \(-0.818622\pi\)
0.252882 + 0.967497i \(0.418622\pi\)
\(258\) 1.19098 3.66547i 0.0741474 0.228202i
\(259\) 0.218847 0.673542i 0.0135985 0.0418519i
\(260\) 0 0
\(261\) −3.61803 2.62866i −0.223951 0.162710i
\(262\) −1.36475 4.20025i −0.0843142 0.259493i
\(263\) 16.3262 1.00672 0.503359 0.864077i \(-0.332097\pi\)
0.503359 + 0.864077i \(0.332097\pi\)
\(264\) 7.23607 + 1.62460i 0.445349 + 0.0999871i
\(265\) 0 0
\(266\) −3.35410 10.3229i −0.205653 0.632935i
\(267\) 0.427051 + 0.310271i 0.0261351 + 0.0189883i
\(268\) 12.5172 9.09429i 0.764611 0.555522i
\(269\) 4.79837 14.7679i 0.292562 0.900413i −0.691467 0.722408i \(-0.743035\pi\)
0.984029 0.178006i \(-0.0569645\pi\)
\(270\) 0 0
\(271\) 22.0623 16.0292i 1.34019 0.973705i 0.340753 0.940153i \(-0.389318\pi\)
0.999437 0.0335518i \(-0.0106819\pi\)
\(272\) 2.42705 + 1.76336i 0.147162 + 0.106919i
\(273\) −1.63525 5.03280i −0.0989701 0.304599i
\(274\) −4.61803 −0.278986
\(275\) 0 0
\(276\) −5.61803 −0.338166
\(277\) −9.44427 29.0665i −0.567451 1.74644i −0.660554 0.750779i \(-0.729678\pi\)
0.0931022 0.995657i \(-0.470322\pi\)
\(278\) 0.427051 + 0.310271i 0.0256128 + 0.0186088i
\(279\) −2.30902 + 1.67760i −0.138237 + 0.100435i
\(280\) 0 0
\(281\) −0.236068 + 0.726543i −0.0140826 + 0.0433419i −0.957851 0.287266i \(-0.907254\pi\)
0.943768 + 0.330608i \(0.107254\pi\)
\(282\) −0.809017 + 0.587785i −0.0481763 + 0.0350021i
\(283\) 0.145898 + 0.106001i 0.00867274 + 0.00630111i 0.592113 0.805855i \(-0.298294\pi\)
−0.583440 + 0.812156i \(0.698294\pi\)
\(284\) 2.78115 + 8.55951i 0.165031 + 0.507913i
\(285\) 0 0
\(286\) −0.336881 3.59996i −0.0199202 0.212870i
\(287\) 35.8328 2.11514
\(288\) 1.73607 + 5.34307i 0.102299 + 0.314843i
\(289\) 11.6353 + 8.45351i 0.684427 + 0.497265i
\(290\) 0 0
\(291\) −4.33688 + 13.3475i −0.254232 + 0.782447i
\(292\) −1.61803 + 4.97980i −0.0946883 + 0.291421i
\(293\) 0.0450850 0.0327561i 0.00263389 0.00191363i −0.586468 0.809973i \(-0.699482\pi\)
0.589101 + 0.808059i \(0.299482\pi\)
\(294\) 1.00000 + 0.726543i 0.0583212 + 0.0423728i
\(295\) 0 0
\(296\) 0.527864 0.0306815
\(297\) 2.19098 + 2.48990i 0.127134 + 0.144479i
\(298\) 9.27051 0.537026
\(299\) 1.89261 + 5.82485i 0.109452 + 0.336860i
\(300\) 0 0
\(301\) −15.1353 + 10.9964i −0.872382 + 0.633822i
\(302\) 0.381966 1.17557i 0.0219797 0.0676465i
\(303\) 0.927051 2.85317i 0.0532577 0.163910i
\(304\) −8.78115 + 6.37988i −0.503634 + 0.365911i
\(305\) 0 0
\(306\) −0.309017 0.951057i −0.0176653 0.0543683i
\(307\) −0.562306 −0.0320925 −0.0160462 0.999871i \(-0.505108\pi\)
−0.0160462 + 0.999871i \(0.505108\pi\)
\(308\) −10.6353 12.0862i −0.606000 0.688676i
\(309\) −6.00000 −0.341328
\(310\) 0 0
\(311\) −2.04508 1.48584i −0.115966 0.0842543i 0.528291 0.849064i \(-0.322833\pi\)
−0.644257 + 0.764809i \(0.722833\pi\)
\(312\) 3.19098 2.31838i 0.180654 0.131253i
\(313\) −7.98278 + 24.5685i −0.451213 + 1.38869i 0.424310 + 0.905517i \(0.360517\pi\)
−0.875524 + 0.483175i \(0.839483\pi\)
\(314\) 0.708204 2.17963i 0.0399663 0.123004i
\(315\) 0 0
\(316\) 12.3992 + 9.00854i 0.697509 + 0.506770i
\(317\) 5.98278 + 18.4131i 0.336026 + 1.03418i 0.966214 + 0.257740i \(0.0829778\pi\)
−0.630188 + 0.776443i \(0.717022\pi\)
\(318\) −5.94427 −0.333338
\(319\) 1.38197 + 14.7679i 0.0773752 + 0.826842i
\(320\) 0 0
\(321\) −1.30902 4.02874i −0.0730622 0.224862i
\(322\) −5.20820 3.78398i −0.290242 0.210873i
\(323\) 7.66312 5.56758i 0.426387 0.309789i
\(324\) −0.500000 + 1.53884i −0.0277778 + 0.0854912i
\(325\) 0 0
\(326\) 9.13525 6.63715i 0.505955 0.367598i
\(327\) 0 0
\(328\) 8.25329 + 25.4010i 0.455712 + 1.40254i
\(329\) 4.85410 0.267615
\(330\) 0 0
\(331\) 26.5967 1.46189 0.730945 0.682437i \(-0.239080\pi\)
0.730945 + 0.682437i \(0.239080\pi\)
\(332\) 0.354102 + 1.08981i 0.0194339 + 0.0598113i
\(333\) 0.190983 + 0.138757i 0.0104658 + 0.00760385i
\(334\) 5.01722 3.64522i 0.274530 0.199458i
\(335\) 0 0
\(336\) 1.71885 5.29007i 0.0937708 0.288597i
\(337\) −0.236068 + 0.171513i −0.0128594 + 0.00934293i −0.594196 0.804320i \(-0.702530\pi\)
0.581337 + 0.813663i \(0.302530\pi\)
\(338\) 4.94427 + 3.59222i 0.268933 + 0.195391i
\(339\) 0.218847 + 0.673542i 0.0118861 + 0.0365818i
\(340\) 0 0
\(341\) 9.23607 + 2.07363i 0.500161 + 0.112293i
\(342\) 3.61803 0.195641
\(343\) 4.63525 + 14.2658i 0.250280 + 0.770283i
\(344\) −11.2812 8.19624i −0.608239 0.441912i
\(345\) 0 0
\(346\) −2.93769 + 9.04129i −0.157931 + 0.486063i
\(347\) 6.47214 19.9192i 0.347442 1.06932i −0.612821 0.790222i \(-0.709965\pi\)
0.960263 0.279096i \(-0.0900348\pi\)
\(348\) −5.85410 + 4.25325i −0.313813 + 0.227998i
\(349\) 8.19098 + 5.95110i 0.438453 + 0.318555i 0.785020 0.619470i \(-0.212653\pi\)
−0.346567 + 0.938025i \(0.612653\pi\)
\(350\) 0 0
\(351\) 1.76393 0.0941517
\(352\) 9.50000 16.0292i 0.506352 0.854359i
\(353\) 10.4721 0.557376 0.278688 0.960382i \(-0.410101\pi\)
0.278688 + 0.960382i \(0.410101\pi\)
\(354\) −1.97214 6.06961i −0.104818 0.322596i
\(355\) 0 0
\(356\) 0.690983 0.502029i 0.0366220 0.0266075i
\(357\) −1.50000 + 4.61653i −0.0793884 + 0.244332i
\(358\) −0.427051 + 1.31433i −0.0225703 + 0.0694644i
\(359\) 10.3262 7.50245i 0.544998 0.395964i −0.280940 0.959725i \(-0.590646\pi\)
0.825938 + 0.563761i \(0.190646\pi\)
\(360\) 0 0
\(361\) 4.71885 + 14.5231i 0.248360 + 0.764375i
\(362\) −10.7984 −0.567550
\(363\) 1.39919 10.9106i 0.0734383 0.572661i
\(364\) −8.56231 −0.448787
\(365\) 0 0
\(366\) 3.92705 + 2.85317i 0.205270 + 0.149138i
\(367\) 4.50000 3.26944i 0.234898 0.170663i −0.464109 0.885778i \(-0.653625\pi\)
0.699007 + 0.715115i \(0.253625\pi\)
\(368\) −1.98936 + 6.12261i −0.103702 + 0.319163i
\(369\) −3.69098 + 11.3597i −0.192145 + 0.591361i
\(370\) 0 0
\(371\) 23.3435 + 16.9600i 1.21193 + 0.880520i
\(372\) 1.42705 + 4.39201i 0.0739891 + 0.227715i
\(373\) 4.41641 0.228673 0.114336 0.993442i \(-0.463526\pi\)
0.114336 + 0.993442i \(0.463526\pi\)
\(374\) −1.69098 + 2.85317i −0.0874386 + 0.147534i
\(375\) 0 0
\(376\) 1.11803 + 3.44095i 0.0576582 + 0.177454i
\(377\) 6.38197 + 4.63677i 0.328688 + 0.238806i
\(378\) −1.50000 + 1.08981i −0.0771517 + 0.0560540i
\(379\) 0.489357 1.50609i 0.0251366 0.0773624i −0.937701 0.347443i \(-0.887050\pi\)
0.962838 + 0.270080i \(0.0870502\pi\)
\(380\) 0 0
\(381\) 3.00000 2.17963i 0.153695 0.111666i
\(382\) 3.73607 + 2.71441i 0.191154 + 0.138881i
\(383\) −8.30902 25.5725i −0.424571 1.30669i −0.903405 0.428789i \(-0.858940\pi\)
0.478834 0.877906i \(-0.341060\pi\)
\(384\) 11.3820 0.580834
\(385\) 0 0
\(386\) 11.4721 0.583916
\(387\) −1.92705 5.93085i −0.0979575 0.301482i
\(388\) 18.3713 + 13.3475i 0.932663 + 0.677619i
\(389\) −19.6353 + 14.2658i −0.995547 + 0.723307i −0.961129 0.276100i \(-0.910958\pi\)
−0.0344181 + 0.999408i \(0.510958\pi\)
\(390\) 0 0
\(391\) 1.73607 5.34307i 0.0877967 0.270211i
\(392\) 3.61803 2.62866i 0.182738 0.132767i
\(393\) −5.78115 4.20025i −0.291621 0.211875i
\(394\) −4.65654 14.3314i −0.234593 0.722003i
\(395\) 0 0
\(396\) 4.92705 2.12663i 0.247594 0.106867i
\(397\) 38.7082 1.94271 0.971355 0.237635i \(-0.0763722\pi\)
0.971355 + 0.237635i \(0.0763722\pi\)
\(398\) −3.19098 9.82084i −0.159950 0.492274i
\(399\) −14.2082 10.3229i −0.711300 0.516790i
\(400\) 0 0
\(401\) −8.06231 + 24.8132i −0.402612 + 1.23911i 0.520260 + 0.854008i \(0.325835\pi\)
−0.922873 + 0.385106i \(0.874165\pi\)
\(402\) −1.82624 + 5.62058i −0.0910845 + 0.280329i
\(403\) 4.07295 2.95917i 0.202888 0.147407i
\(404\) −3.92705 2.85317i −0.195378 0.141950i
\(405\) 0 0
\(406\) −8.29180 −0.411515
\(407\) −0.0729490 0.779543i −0.00361595 0.0386405i
\(408\) −3.61803 −0.179119
\(409\) −3.41641 10.5146i −0.168930 0.519915i 0.830374 0.557207i \(-0.188127\pi\)
−0.999304 + 0.0372920i \(0.988127\pi\)
\(410\) 0 0
\(411\) −6.04508 + 4.39201i −0.298182 + 0.216642i
\(412\) −3.00000 + 9.23305i −0.147799 + 0.454880i
\(413\) −9.57295 + 29.4625i −0.471054 + 1.44976i
\(414\) 1.73607 1.26133i 0.0853231 0.0619909i
\(415\) 0 0
\(416\) −3.06231 9.42481i −0.150142 0.462089i
\(417\) 0.854102 0.0418256
\(418\) −7.92705 9.00854i −0.387725 0.440622i
\(419\) 16.5066 0.806399 0.403200 0.915112i \(-0.367898\pi\)
0.403200 + 0.915112i \(0.367898\pi\)
\(420\) 0 0
\(421\) 30.1525 + 21.9071i 1.46954 + 1.06768i 0.980746 + 0.195286i \(0.0625636\pi\)
0.488795 + 0.872398i \(0.337436\pi\)
\(422\) 11.1353 8.09024i 0.542056 0.393827i
\(423\) −0.500000 + 1.53884i −0.0243108 + 0.0748210i
\(424\) −6.64590 + 20.4540i −0.322753 + 0.993333i
\(425\) 0 0
\(426\) −2.78115 2.02063i −0.134747 0.0978996i
\(427\) −7.28115 22.4091i −0.352360 1.08445i
\(428\) −6.85410 −0.331306
\(429\) −3.86475 4.39201i −0.186592 0.212048i
\(430\) 0 0
\(431\) −12.2082 37.5730i −0.588048 1.80983i −0.586667 0.809828i \(-0.699560\pi\)
−0.00138127 0.999999i \(-0.500440\pi\)
\(432\) 1.50000 + 1.08981i 0.0721688 + 0.0524337i
\(433\) −4.85410 + 3.52671i −0.233273 + 0.169483i −0.698281 0.715824i \(-0.746051\pi\)
0.465008 + 0.885307i \(0.346051\pi\)
\(434\) −1.63525 + 5.03280i −0.0784947 + 0.241582i
\(435\) 0 0
\(436\) 0 0
\(437\) 16.4443 + 11.9475i 0.786636 + 0.571525i
\(438\) −0.618034 1.90211i −0.0295308 0.0908865i
\(439\) 3.29180 0.157109 0.0785544 0.996910i \(-0.474970\pi\)
0.0785544 + 0.996910i \(0.474970\pi\)
\(440\) 0 0
\(441\) 2.00000 0.0952381
\(442\) 0.545085 + 1.67760i 0.0259270 + 0.0797952i
\(443\) −33.2705 24.1724i −1.58073 1.14847i −0.915853 0.401514i \(-0.868484\pi\)
−0.664877 0.746953i \(-0.731516\pi\)
\(444\) 0.309017 0.224514i 0.0146653 0.0106550i
\(445\) 0 0
\(446\) −0.135255 + 0.416272i −0.00640451 + 0.0197110i
\(447\) 12.1353 8.81678i 0.573978 0.417019i
\(448\) −0.572949 0.416272i −0.0270693 0.0196670i
\(449\) −7.56231 23.2744i −0.356887 1.09839i −0.954907 0.296905i \(-0.904046\pi\)
0.598020 0.801481i \(-0.295954\pi\)
\(450\) 0 0
\(451\) 36.3713 15.6987i 1.71266 0.739222i
\(452\) 1.14590 0.0538985
\(453\) −0.618034 1.90211i −0.0290378 0.0893691i
\(454\) −12.4443 9.04129i −0.584039 0.424329i
\(455\) 0 0
\(456\) 4.04508 12.4495i 0.189428 0.583001i
\(457\) −2.53444 + 7.80021i −0.118556 + 0.364878i −0.992672 0.120839i \(-0.961442\pi\)
0.874116 + 0.485717i \(0.161442\pi\)
\(458\) −5.00000 + 3.63271i −0.233635 + 0.169746i
\(459\) −1.30902 0.951057i −0.0610997 0.0443915i
\(460\) 0 0
\(461\) −21.0902 −0.982267 −0.491134 0.871084i \(-0.663417\pi\)
−0.491134 + 0.871084i \(0.663417\pi\)
\(462\) 6.00000 + 1.34708i 0.279145 + 0.0626720i
\(463\) 15.7984 0.734213 0.367106 0.930179i \(-0.380349\pi\)
0.367106 + 0.930179i \(0.380349\pi\)
\(464\) 2.56231 + 7.88597i 0.118952 + 0.366097i
\(465\) 0 0
\(466\) 12.1631 8.83702i 0.563446 0.409367i
\(467\) 3.01722 9.28605i 0.139620 0.429707i −0.856660 0.515882i \(-0.827464\pi\)
0.996280 + 0.0861747i \(0.0274643\pi\)
\(468\) 0.881966 2.71441i 0.0407689 0.125474i
\(469\) 23.2082 16.8617i 1.07166 0.778603i
\(470\) 0 0
\(471\) −1.14590 3.52671i −0.0528002 0.162502i
\(472\) −23.0902 −1.06281
\(473\) −10.5451 + 17.7926i −0.484864 + 0.818103i
\(474\) −5.85410 −0.268888
\(475\) 0 0
\(476\) 6.35410 + 4.61653i 0.291240 + 0.211598i
\(477\) −7.78115 + 5.65334i −0.356275 + 0.258849i
\(478\) 0.489357 1.50609i 0.0223827 0.0688868i
\(479\) −8.68034 + 26.7153i −0.396615 + 1.22066i 0.531082 + 0.847320i \(0.321786\pi\)
−0.927697 + 0.373335i \(0.878214\pi\)
\(480\) 0 0
\(481\) −0.336881 0.244758i −0.0153605 0.0111600i
\(482\) −4.41641 13.5923i −0.201162 0.619113i
\(483\) −10.4164 −0.473963
\(484\) −16.0902 7.60845i −0.731371 0.345839i
\(485\) 0 0
\(486\) −0.190983 0.587785i −0.00866317 0.0266625i
\(487\) 13.6074 + 9.88635i 0.616610 + 0.447993i 0.851736 0.523972i \(-0.175550\pi\)
−0.235126 + 0.971965i \(0.575550\pi\)
\(488\) 14.2082 10.3229i 0.643175 0.467294i
\(489\) 5.64590 17.3763i 0.255316 0.785783i
\(490\) 0 0
\(491\) −20.3992 + 14.8209i −0.920602 + 0.668857i −0.943674 0.330877i \(-0.892655\pi\)
0.0230715 + 0.999734i \(0.492655\pi\)
\(492\) 15.6353 + 11.3597i 0.704892 + 0.512134i
\(493\) −2.23607 6.88191i −0.100707 0.309946i
\(494\) −6.38197 −0.287138
\(495\) 0 0
\(496\) 5.29180 0.237609
\(497\) 5.15654 + 15.8702i 0.231302 + 0.711876i
\(498\) −0.354102 0.257270i −0.0158677 0.0115286i
\(499\) 14.2082 10.3229i 0.636047 0.462115i −0.222443 0.974946i \(-0.571403\pi\)
0.858490 + 0.512831i \(0.171403\pi\)
\(500\) 0 0
\(501\) 3.10081 9.54332i 0.138534 0.426364i
\(502\) 3.89919 2.83293i 0.174029 0.126440i
\(503\) 22.7082 + 16.4985i 1.01251 + 0.735631i 0.964734 0.263227i \(-0.0847870\pi\)
0.0477750 + 0.998858i \(0.484787\pi\)
\(504\) 2.07295 + 6.37988i 0.0923365 + 0.284182i
\(505\) 0 0
\(506\) −6.94427 1.55909i −0.308711 0.0693098i
\(507\) 9.88854 0.439166
\(508\) −1.85410 5.70634i −0.0822625 0.253178i
\(509\) −19.1074 13.8823i −0.846920 0.615324i 0.0773749 0.997002i \(-0.475346\pi\)
−0.924295 + 0.381679i \(0.875346\pi\)
\(510\) 0 0
\(511\) −3.00000 + 9.23305i −0.132712 + 0.408446i
\(512\) 5.78115 17.7926i 0.255493 0.786327i
\(513\) 4.73607 3.44095i 0.209103 0.151922i
\(514\) −5.83688 4.24074i −0.257454 0.187051i
\(515\) 0 0
\(516\) −10.0902 −0.444195
\(517\) 4.92705 2.12663i 0.216691 0.0935289i
\(518\) 0.437694 0.0192312
\(519\) 4.75329 + 14.6291i 0.208646 + 0.642147i
\(520\) 0 0
\(521\) 12.0000 8.71851i 0.525730 0.381965i −0.293028 0.956104i \(-0.594663\pi\)
0.818758 + 0.574139i \(0.194663\pi\)
\(522\) 0.854102 2.62866i 0.0373830 0.115053i
\(523\) 3.70163 11.3924i 0.161861 0.498156i −0.836930 0.547309i \(-0.815652\pi\)
0.998791 + 0.0491529i \(0.0156522\pi\)
\(524\) −9.35410 + 6.79615i −0.408636 + 0.296891i
\(525\) 0 0
\(526\) 3.11803 + 9.59632i 0.135953 + 0.418420i
\(527\) −4.61803 −0.201165
\(528\) −0.572949 6.12261i −0.0249344 0.266452i
\(529\) −10.9443 −0.475838
\(530\) 0 0
\(531\) −8.35410 6.06961i −0.362537 0.263399i
\(532\) −22.9894 + 16.7027i −0.996715 + 0.724156i
\(533\) 6.51064 20.0377i 0.282007 0.867929i
\(534\) −0.100813 + 0.310271i −0.00436261 + 0.0134267i
\(535\) 0 0
\(536\) 17.2984 + 12.5680i 0.747176 + 0.542855i
\(537\) 0.690983 + 2.12663i 0.0298181 + 0.0917707i
\(538\) 9.59675 0.413745
\(539\) −4.38197 4.97980i −0.188745 0.214495i
\(540\) 0 0
\(541\) 6.04508 + 18.6049i 0.259899 + 0.799885i 0.992825 + 0.119577i \(0.0381540\pi\)
−0.732926 + 0.680308i \(0.761846\pi\)
\(542\) 13.6353 + 9.90659i 0.585684 + 0.425525i
\(543\) −14.1353 + 10.2699i −0.606602 + 0.440722i
\(544\) −2.80902 + 8.64527i −0.120436 + 0.370663i
\(545\) 0 0
\(546\) 2.64590 1.92236i 0.113234 0.0822693i
\(547\) 17.4894 + 12.7068i 0.747791 + 0.543302i 0.895141 0.445782i \(-0.147075\pi\)
−0.147350 + 0.989084i \(0.547075\pi\)
\(548\) 3.73607 + 11.4984i 0.159597 + 0.491189i
\(549\) 7.85410 0.335205
\(550\) 0 0
\(551\) 26.1803 1.11532
\(552\) −2.39919 7.38394i −0.102116 0.314281i
\(553\) 22.9894 + 16.7027i 0.977607 + 0.710273i
\(554\) 15.2812 11.1024i 0.649234 0.471696i
\(555\) 0 0
\(556\) 0.427051 1.31433i 0.0181110 0.0557399i
\(557\) 12.0623 8.76378i 0.511096 0.371333i −0.302143 0.953263i \(-0.597702\pi\)
0.813239 + 0.581929i \(0.197702\pi\)
\(558\) −1.42705 1.03681i −0.0604119 0.0438918i
\(559\) 3.39919 + 10.4616i 0.143770 + 0.442479i
\(560\) 0 0
\(561\) 0.500000 + 5.34307i 0.0211100 + 0.225585i
\(562\) −0.472136 −0.0199159
\(563\) 2.74671 + 8.45351i 0.115760 + 0.356273i 0.992105 0.125412i \(-0.0400251\pi\)
−0.876345 + 0.481684i \(0.840025\pi\)
\(564\) 2.11803 + 1.53884i 0.0891853 + 0.0647969i
\(565\) 0 0
\(566\) −0.0344419 + 0.106001i −0.00144770 + 0.00445556i
\(567\) −0.927051 + 2.85317i −0.0389325 + 0.119822i
\(568\) −10.0623 + 7.31069i −0.422205 + 0.306750i
\(569\) 19.4721 + 14.1473i 0.816314 + 0.593087i 0.915654 0.401966i \(-0.131673\pi\)
−0.0993400 + 0.995054i \(0.531673\pi\)
\(570\) 0 0
\(571\) 34.6869 1.45160 0.725801 0.687905i \(-0.241469\pi\)
0.725801 + 0.687905i \(0.241469\pi\)
\(572\) −8.69098 + 3.75123i −0.363388 + 0.156847i
\(573\) 7.47214 0.312153
\(574\) 6.84346 + 21.0620i 0.285640 + 0.879111i
\(575\) 0 0
\(576\) 0.190983 0.138757i 0.00795763 0.00578155i
\(577\) −3.32624 + 10.2371i −0.138473 + 0.426176i −0.996114 0.0880726i \(-0.971929\pi\)
0.857641 + 0.514249i \(0.171929\pi\)
\(578\) −2.74671 + 8.45351i −0.114248 + 0.351620i
\(579\) 15.0172 10.9106i 0.624094 0.453431i
\(580\) 0 0
\(581\) 0.656541 + 2.02063i 0.0272379 + 0.0838297i
\(582\) −8.67376 −0.359539
\(583\) 31.1246 + 6.98791i 1.28905 + 0.289410i
\(584\) −7.23607 −0.299431
\(585\) 0 0
\(586\) 0.0278640 + 0.0202444i 0.00115105 + 0.000836289i
\(587\) −30.9894 + 22.5151i −1.27907 + 0.929297i −0.999524 0.0308361i \(-0.990183\pi\)
−0.279543 + 0.960133i \(0.590183\pi\)
\(588\) 1.00000 3.07768i 0.0412393 0.126922i
\(589\) 5.16312 15.8904i 0.212743 0.654754i
\(590\) 0 0
\(591\) −19.7254 14.3314i −0.811396 0.589513i
\(592\) −0.135255 0.416272i −0.00555894 0.0171087i
\(593\) −22.2148 −0.912252 −0.456126 0.889915i \(-0.650763\pi\)
−0.456126 + 0.889915i \(0.650763\pi\)
\(594\) −1.04508 + 1.76336i −0.0428804 + 0.0723514i
\(595\) 0 0
\(596\) −7.50000 23.0826i −0.307212 0.945501i
\(597\) −13.5172 9.82084i −0.553223 0.401940i
\(598\) −3.06231 + 2.22490i −0.125227 + 0.0909827i
\(599\) −2.56231 + 7.88597i −0.104693 + 0.322212i −0.989658 0.143445i \(-0.954182\pi\)
0.884965 + 0.465657i \(0.154182\pi\)
\(600\) 0 0
\(601\) −27.3713 + 19.8864i −1.11650 + 0.811184i −0.983675 0.179955i \(-0.942405\pi\)
−0.132825 + 0.991140i \(0.542405\pi\)
\(602\) −9.35410 6.79615i −0.381245 0.276991i
\(603\) 2.95492 + 9.09429i 0.120333 + 0.370348i
\(604\) −3.23607 −0.131674
\(605\) 0 0
\(606\) 1.85410 0.0753177
\(607\) −4.11803 12.6740i −0.167146 0.514422i 0.832042 0.554712i \(-0.187172\pi\)
−0.999188 + 0.0402904i \(0.987172\pi\)
\(608\) −26.6074 19.3314i −1.07907 0.783992i
\(609\) −10.8541 + 7.88597i −0.439830 + 0.319555i
\(610\) 0 0
\(611\) 0.881966 2.71441i 0.0356805 0.109813i
\(612\) −2.11803 + 1.53884i −0.0856164 + 0.0622040i
\(613\) 28.0344 + 20.3682i 1.13230 + 0.822664i 0.986028 0.166580i \(-0.0532724\pi\)
0.146272 + 0.989244i \(0.453272\pi\)
\(614\) −0.107391 0.330515i −0.00433394 0.0133385i
\(615\) 0 0
\(616\) 11.3435 19.1396i 0.457041 0.771158i
\(617\) −19.5836 −0.788406 −0.394203 0.919023i \(-0.628979\pi\)
−0.394203 + 0.919023i \(0.628979\pi\)
\(618\) −1.14590 3.52671i −0.0460948 0.141865i
\(619\) 7.13525 + 5.18407i 0.286790 + 0.208365i 0.721874 0.692025i \(-0.243281\pi\)
−0.435084 + 0.900390i \(0.643281\pi\)
\(620\) 0 0
\(621\) 1.07295 3.30220i 0.0430560 0.132513i
\(622\) 0.482779 1.48584i 0.0193577 0.0595768i
\(623\) 1.28115 0.930812i 0.0513283 0.0372922i
\(624\) −2.64590 1.92236i −0.105921 0.0769559i
\(625\) 0 0
\(626\) −15.9656 −0.638112
\(627\) −18.9443 4.25325i −0.756561 0.169859i
\(628\) −6.00000 −0.239426
\(629\) 0.118034 + 0.363271i 0.00470632 + 0.0144846i
\(630\) 0 0
\(631\) −37.4336 + 27.1971i −1.49021 + 1.08270i −0.516125 + 0.856513i \(0.672626\pi\)
−0.974084 + 0.226187i \(0.927374\pi\)
\(632\) −6.54508 + 20.1437i −0.260350 + 0.801273i
\(633\) 6.88197 21.1805i 0.273534 0.841850i
\(634\) −9.68034 + 7.03318i −0.384455 + 0.279323i
\(635\) 0 0
\(636\) 4.80902 + 14.8006i 0.190690 + 0.586883i
\(637\) −3.52786 −0.139779
\(638\) −8.41641 + 3.63271i −0.333209 + 0.143820i
\(639\) −5.56231 −0.220041
\(640\) 0 0
\(641\) −28.9164 21.0090i −1.14213 0.829806i −0.154715 0.987959i \(-0.549446\pi\)
−0.987415 + 0.158154i \(0.949446\pi\)
\(642\) 2.11803 1.53884i 0.0835921 0.0607332i
\(643\) 11.9164 36.6749i 0.469937 1.44632i −0.382728 0.923861i \(-0.625015\pi\)
0.852666 0.522457i \(-0.174985\pi\)
\(644\) −5.20820 + 16.0292i −0.205232 + 0.631639i
\(645\) 0 0
\(646\) 4.73607 + 3.44095i 0.186338 + 0.135383i
\(647\) −8.59017 26.4378i −0.337714 1.03938i −0.965369 0.260887i \(-0.915985\pi\)
0.627655 0.778492i \(-0.284015\pi\)
\(648\) −2.23607 −0.0878410
\(649\) 3.19098 + 34.0993i 0.125257 + 1.33851i
\(650\) 0 0
\(651\) 2.64590 + 8.14324i 0.103701 + 0.319159i
\(652\) −23.9164 17.3763i −0.936639 0.680508i
\(653\) 41.2877 29.9973i 1.61571 1.17388i 0.776390 0.630252i \(-0.217049\pi\)
0.839323 0.543632i \(-0.182951\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 17.9164 13.0170i 0.699518 0.508230i
\(657\) −2.61803 1.90211i −0.102139 0.0742085i
\(658\) 0.927051 + 2.85317i 0.0361402 + 0.111228i
\(659\) −10.6525 −0.414962 −0.207481 0.978239i \(-0.566526\pi\)
−0.207481 + 0.978239i \(0.566526\pi\)
\(660\) 0 0
\(661\) −9.90983 −0.385448 −0.192724 0.981253i \(-0.561732\pi\)
−0.192724 + 0.981253i \(0.561732\pi\)
\(662\) 5.07953 + 15.6332i 0.197421 + 0.607601i
\(663\) 2.30902 + 1.67760i 0.0896748 + 0.0651525i
\(664\) −1.28115 + 0.930812i −0.0497184 + 0.0361225i
\(665\) 0 0
\(666\) −0.0450850 + 0.138757i −0.00174701 + 0.00537674i
\(667\) 12.5623 9.12705i 0.486414 0.353401i
\(668\) −13.1353 9.54332i −0.508218 0.369242i
\(669\) 0.218847 + 0.673542i 0.00846112 + 0.0260406i
\(670\) 0 0
\(671\) −17.2082 19.5559i −0.664315 0.754948i
\(672\) 16.8541 0.650161
\(673\) −3.83688 11.8087i −0.147901 0.455192i 0.849472 0.527634i \(-0.176921\pi\)
−0.997373 + 0.0724420i \(0.976921\pi\)
\(674\) −0.145898 0.106001i −0.00561978 0.00408301i
\(675\) 0 0
\(676\) 4.94427 15.2169i 0.190164 0.585266i
\(677\) −4.18034 + 12.8658i −0.160664 + 0.494471i −0.998691 0.0511572i \(-0.983709\pi\)
0.838027 + 0.545629i \(0.183709\pi\)
\(678\) −0.354102 + 0.257270i −0.0135992 + 0.00988040i
\(679\) 34.0623 + 24.7477i 1.30719 + 0.949730i
\(680\) 0 0
\(681\) −24.8885 −0.953731
\(682\) 0.545085 + 5.82485i 0.0208724 + 0.223045i
\(683\) 3.11146 0.119057 0.0595283 0.998227i \(-0.481040\pi\)
0.0595283 + 0.998227i \(0.481040\pi\)
\(684\) −2.92705 9.00854i −0.111919 0.344450i
\(685\) 0 0
\(686\) −7.50000 + 5.44907i −0.286351 + 0.208046i
\(687\) −3.09017 + 9.51057i −0.117897 + 0.362851i
\(688\) −3.57295 + 10.9964i −0.136217 + 0.419234i
\(689\) 13.7254 9.97210i 0.522897 0.379907i
\(690\) 0 0
\(691\) −8.12461 25.0050i −0.309075 0.951234i −0.978125 0.208017i \(-0.933299\pi\)
0.669050 0.743217i \(-0.266701\pi\)
\(692\) 24.8885 0.946120
\(693\) 9.13525 3.94298i 0.347020 0.149782i
\(694\) 12.9443 0.491358
\(695\) 0 0
\(696\) −8.09017 5.87785i −0.306657 0.222799i
\(697\) −15.6353 + 11.3597i −0.592228 + 0.430278i
\(698\) −1.93363 + 5.95110i −0.0731889 + 0.225252i
\(699\) 7.51722 23.1356i 0.284327 0.875070i
\(700\) 0 0
\(701\) 8.64590 + 6.28161i 0.326551 + 0.237253i 0.738966 0.673743i \(-0.235315\pi\)
−0.412415 + 0.910996i \(0.635315\pi\)
\(702\) 0.336881 + 1.03681i 0.0127148 + 0.0391320i
\(703\) −1.38197 −0.0521218
\(704\) −0.763932 0.171513i −0.0287918 0.00646416i
\(705\) 0 0
\(706\) 2.00000 + 6.15537i 0.0752710 + 0.231660i
\(707\) −7.28115 5.29007i −0.273836 0.198953i
\(708\) −13.5172 + 9.82084i −0.508008 + 0.369090i
\(709\) 15.0623 46.3570i 0.565677 1.74097i −0.100255 0.994962i \(-0.531966\pi\)
0.665932 0.746012i \(-0.268034\pi\)
\(710\) 0 0
\(711\) −7.66312 + 5.56758i −0.287389 + 0.208801i
\(712\) 0.954915 + 0.693786i 0.0357870 + 0.0260007i
\(713\) −3.06231 9.42481i −0.114684 0.352962i
\(714\) −3.00000 −0.112272
\(715\) 0 0
\(716\) 3.61803 0.135212
\(717\) −0.791796 2.43690i −0.0295702 0.0910076i
\(718\) 6.38197 + 4.63677i 0.238173 + 0.173043i
\(719\) 1.28115 0.930812i 0.0477789 0.0347134i −0.563639 0.826021i \(-0.690599\pi\)
0.611418 + 0.791307i \(0.290599\pi\)
\(720\) 0 0
\(721\) −5.56231 + 17.1190i −0.207151 + 0.637546i
\(722\) −7.63525 + 5.54734i −0.284155 + 0.206451i
\(723\) −18.7082 13.5923i −0.695766 0.505503i
\(724\) 8.73607 + 26.8869i 0.324673 + 0.999242i
\(725\) 0 0
\(726\) 6.68034 1.26133i 0.247931 0.0468122i
\(727\) −38.8541 −1.44102 −0.720509 0.693445i \(-0.756092\pi\)
−0.720509 + 0.693445i \(0.756092\pi\)
\(728\) −3.65654 11.2537i −0.135520 0.417089i
\(729\) −0.809017 0.587785i −0.0299636 0.0217698i
\(730\) 0 0
\(731\) 3.11803 9.59632i 0.115325 0.354933i
\(732\) 3.92705 12.0862i 0.145148 0.446720i
\(733\) −30.5066 + 22.1643i −1.12679 + 0.818658i −0.985224 0.171271i \(-0.945213\pi\)
−0.141562 + 0.989929i \(0.545213\pi\)
\(734\) 2.78115 + 2.02063i 0.102654 + 0.0745827i
\(735\) 0 0
\(736\) −19.5066 −0.719022
\(737\) 16.1697 27.2829i 0.595618 1.00498i
\(738\) −7.38197 −0.271734
\(739\) −7.72542 23.7764i −0.284184 0.874629i −0.986642 0.162904i \(-0.947914\pi\)
0.702458 0.711726i \(-0.252086\pi\)
\(740\) 0 0
\(741\) −8.35410 + 6.06961i −0.306896 + 0.222973i
\(742\) −5.51064 + 16.9600i −0.202302 + 0.622622i
\(743\) −10.8713 + 33.4585i −0.398830 + 1.22747i 0.527108 + 0.849798i \(0.323276\pi\)
−0.925938 + 0.377675i \(0.876724\pi\)
\(744\) −5.16312 + 3.75123i −0.189289 + 0.137527i
\(745\) 0 0
\(746\) 0.843459 + 2.59590i 0.0308812 + 0.0950426i
\(747\) −0.708204 −0.0259118
\(748\) 8.47214 + 1.90211i 0.309772 + 0.0695481i
\(749\) −12.7082 −0.464348
\(750\) 0 0
\(751\) −9.64590 7.00816i −0.351984 0.255731i 0.397717 0.917508i \(-0.369803\pi\)
−0.749701 + 0.661777i \(0.769803\pi\)
\(752\) 2.42705 1.76336i 0.0885054 0.0643030i
\(753\) 2.40983 7.41669i 0.0878191 0.270279i
\(754\) −1.50658 + 4.63677i −0.0548663 + 0.168861i
\(755\) 0 0
\(756\) 3.92705 + 2.85317i 0.142825 + 0.103769i
\(757\) −0.600813 1.84911i −0.0218369 0.0672071i 0.939544 0.342428i \(-0.111249\pi\)
−0.961381 + 0.275220i \(0.911249\pi\)
\(758\) 0.978714 0.0355485
\(759\) −10.5729 + 4.56352i −0.383774 + 0.165645i
\(760\) 0 0
\(761\) −9.54508 29.3768i −0.346009 1.06491i −0.961041 0.276404i \(-0.910857\pi\)
0.615032 0.788502i \(-0.289143\pi\)
\(762\) 1.85410 + 1.34708i 0.0671670 + 0.0487997i
\(763\) 0 0
\(764\) 3.73607 11.4984i 0.135166 0.415999i
\(765\) 0 0
\(766\) 13.4443 9.76784i 0.485761 0.352926i
\(767\) 14.7361 + 10.7064i 0.532089 + 0.386585i
\(768\) 2.02786 + 6.24112i 0.0731742 + 0.225207i
\(769\) 12.6869 0.457502 0.228751 0.973485i \(-0.426536\pi\)
0.228751 + 0.973485i \(0.426536\pi\)
\(770\) 0 0
\(771\) −11.6738 −0.420420
\(772\) −9.28115 28.5645i −0.334036 1.02806i
\(773\) −25.2812 18.3678i −0.909300 0.660645i 0.0315378 0.999503i \(-0.489960\pi\)
−0.940838 + 0.338858i \(0.889960\pi\)
\(774\) 3.11803 2.26538i 0.112075 0.0814276i
\(775\) 0 0
\(776\) −9.69756 + 29.8460i −0.348122 + 1.07141i
\(777\) 0.572949 0.416272i 0.0205544 0.0149337i
\(778\) −12.1353 8.81678i −0.435070 0.316097i
\(779\) −21.6074 66.5007i −0.774165 2.38264i
\(780\) 0 0
\(781\) 12.1869 + 13.8496i 0.436082 + 0.495577i
\(782\) 3.47214 0.124163
\(783\) −1.38197 4.25325i −0.0493874 0.151999i
\(784\) −3.00000 2.17963i −0.107143 0.0778438i
\(785\) 0 0
\(786\) 1.36475 4.20025i 0.0486788 0.149818i
\(787\) 3.18034 9.78808i 0.113367 0.348907i −0.878236 0.478227i \(-0.841279\pi\)
0.991603 + 0.129320i \(0.0412795\pi\)
\(788\) −31.9164 + 23.1886i −1.13697 + 0.826061i
\(789\) 13.2082 + 9.59632i 0.470225 + 0.341638i
\(790\) 0 0
\(791\) 2.12461 0.0755425
\(792\) 4.89919 + 5.56758i 0.174085 + 0.197835i
\(793\) −13.8541 −0.491974
\(794\) 7.39261 + 22.7521i 0.262354 + 0.807442i
\(795\) 0 0
\(796\) −21.8713 + 15.8904i −0.775208 + 0.563222i
\(797\) −3.32624 + 10.2371i −0.117821 + 0.362617i −0.992525 0.122041i \(-0.961056\pi\)
0.874704 + 0.484658i \(0.161056\pi\)
\(798\) 3.35410 10.3229i 0.118734 0.365425i
\(799\) −2.11803 + 1.53884i −0.0749307 + 0.0544403i
\(800\) 0 0
\(801\) 0.163119 + 0.502029i 0.00576353 + 0.0177383i
\(802\) −16.1246 −0.569380
\(803\) 1.00000 + 10.6861i 0.0352892 + 0.377106i
\(804\) 15.4721 0.545660
\(805\) 0 0
\(806\) 2.51722 + 1.82887i 0.0886653 + 0.0644191i
\(807\) 12.5623 9.12705i 0.442214 0.321287i
\(808\) 2.07295 6.37988i 0.0729261 0.224443i
\(809\) 2.98936 9.20029i 0.105100 0.323465i −0.884654 0.466249i \(-0.845605\pi\)
0.989754 + 0.142783i \(0.0456052\pi\)
\(810\) 0 0
\(811\) −2.63525 1.91462i −0.0925363 0.0672316i 0.540555 0.841309i \(-0.318214\pi\)
−0.633091 + 0.774077i \(0.718214\pi\)
\(812\) 6.70820 + 20.6457i 0.235412 + 0.724523i
\(813\) 27.2705 0.956419
\(814\) 0.444272 0.191758i 0.0155717 0.00672111i
\(815\) 0 0
\(816\) 0.927051 + 2.85317i 0.0324533 + 0.0998809i
\(817\) 29.5344 + 21.4580i 1.03328 + 0.750721i
\(818\) 5.52786 4.01623i 0.193277 0.140424i
\(819\) 1.63525 5.03280i 0.0571404 0.175860i
\(820\) 0 0
\(821\) −32.6976 + 23.7562i −1.14115 + 0.829096i −0.987279 0.158995i \(-0.949175\pi\)
−0.153873 + 0.988091i \(0.549175\pi\)
\(822\) −3.73607 2.71441i −0.130310 0.0946760i
\(823\) 10.9615 + 33.7360i 0.382094 + 1.17596i 0.938567 + 0.345098i \(0.112154\pi\)
−0.556473 + 0.830866i \(0.687846\pi\)
\(824\) −13.4164 −0.467383
\(825\) 0 0
\(826\) −19.1459 −0.666171
\(827\) −16.4164 50.5245i −0.570854 1.75691i −0.649880 0.760037i \(-0.725181\pi\)
0.0790257 0.996873i \(-0.474819\pi\)
\(828\) −4.54508 3.30220i −0.157953 0.114759i
\(829\) −14.3090 + 10.3961i −0.496973 + 0.361072i −0.807859 0.589375i \(-0.799374\pi\)
0.310887 + 0.950447i \(0.399374\pi\)
\(830\) 0 0
\(831\) 9.44427 29.0665i 0.327618 1.00831i
\(832\) −0.336881 + 0.244758i −0.0116792 + 0.00848547i
\(833\) 2.61803 + 1.90211i 0.0907095 + 0.0659043i
\(834\) 0.163119 + 0.502029i 0.00564835 + 0.0173838i
\(835\) 0 0
\(836\) −16.0172 + 27.0256i −0.553967 + 0.934700i
\(837\) −2.85410 −0.0986522
\(838\) 3.15248 + 9.70232i 0.108900 + 0.335161i
\(839\) 29.6976 + 21.5765i 1.02527 + 0.744905i 0.967357 0.253417i \(-0.0815543\pi\)
0.0579164 + 0.998321i \(0.481554\pi\)
\(840\) 0 0
\(841\) −2.78115 + 8.55951i −0.0959018 + 0.295155i
\(842\) −7.11803 + 21.9071i −0.245304 + 0.754967i
\(843\) −0.618034 + 0.449028i −0.0212862 + 0.0154653i
\(844\) −29.1525 21.1805i −1.00347 0.729063i
\(845\) 0 0
\(846\) −1.00000 −0.0343807
\(847\) −29.8328 14.1068i −1.02507 0.484717i
\(848\) 17.8328 0.612381
\(849\) 0.0557281 + 0.171513i 0.00191258 + 0.00588633i
\(850\) 0 0
\(851\) −0.663119 + 0.481784i −0.0227314 + 0.0165153i
\(852\) −2.78115 + 8.55951i −0.0952807 + 0.293244i
\(853\) 3.07295 9.45756i 0.105216 0.323821i −0.884565 0.466416i \(-0.845545\pi\)
0.989781 + 0.142596i \(0.0455448\pi\)
\(854\) 11.7812 8.55951i 0.403143 0.292900i
\(855\) 0 0
\(856\) −2.92705 9.00854i −0.100045 0.307905i
\(857\) −47.7214 −1.63013 −0.815065 0.579369i \(-0.803299\pi\)
−0.815065 + 0.579369i \(0.803299\pi\)
\(858\) 1.84346 3.11044i 0.0629346 0.106189i
\(859\) 7.11146 0.242640 0.121320 0.992613i \(-0.461287\pi\)
0.121320 + 0.992613i \(0.461287\pi\)
\(860\) 0 0
\(861\) 28.9894 + 21.0620i 0.987955 + 0.717791i
\(862\) 19.7533 14.3516i 0.672800 0.488818i
\(863\) −3.67376 + 11.3067i −0.125056 + 0.384884i −0.993911 0.110183i \(-0.964856\pi\)
0.868855 + 0.495067i \(0.164856\pi\)
\(864\) −1.73607 + 5.34307i −0.0590622 + 0.181775i
\(865\) 0 0
\(866\) −3.00000 2.17963i −0.101944 0.0740668i
\(867\) 4.44427 + 13.6781i 0.150935 + 0.464531i
\(868\) 13.8541 0.470239
\(869\) 30.6525 + 6.88191i 1.03981 + 0.233453i
\(870\) 0 0
\(871\) −5.21227 16.0417i −0.176611 0.543553i
\(872\) 0 0
\(873\) −11.3541 + 8.24924i −0.384278 + 0.279194i
\(874\) −3.88197 + 11.9475i −0.131309 + 0.404129i
\(875\) 0 0
\(876\) −4.23607 + 3.07768i −0.143123 + 0.103985i
\(877\) 5.19098 + 3.77147i 0.175287 + 0.127353i 0.671969 0.740579i \(-0.265449\pi\)
−0.496682 + 0.867932i \(0.665449\pi\)
\(878\) 0.628677 + 1.93487i 0.0212168 + 0.0652987i
\(879\) 0.0557281 0.00187966
\(880\) 0 0
\(881\) 13.9098 0.468634 0.234317 0.972160i \(-0.424715\pi\)
0.234317 + 0.972160i \(0.424715\pi\)
\(882\) 0.381966 + 1.17557i 0.0128615 + 0.0395835i
\(883\) 8.56231 + 6.22088i 0.288145 + 0.209349i 0.722462 0.691411i \(-0.243010\pi\)
−0.434318 + 0.900760i \(0.643010\pi\)
\(884\) 3.73607 2.71441i 0.125658 0.0912956i
\(885\) 0 0
\(886\) 7.85410 24.1724i 0.263864 0.812089i
\(887\) 2.42705 1.76336i 0.0814924 0.0592077i −0.546293 0.837594i \(-0.683962\pi\)
0.627785 + 0.778386i \(0.283962\pi\)
\(888\) 0.427051 + 0.310271i 0.0143309 + 0.0104120i
\(889\) −3.43769 10.5801i −0.115297 0.354846i
\(890\) 0 0
\(891\) 0.309017 + 3.30220i 0.0103525 + 0.110628i
\(892\) 1.14590 0.0383675
\(893\) −2.92705 9.00854i −0.0979500 0.301459i
\(894\) 7.50000 + 5.44907i 0.250838 + 0.182244i
\(895\) 0 0
\(896\) 10.5517 32.4747i 0.352506 1.08490i
\(897\) −1.89261 + 5.82485i −0.0631924 + 0.194486i
\(898\) 12.2361 8.89002i 0.408323 0.296664i
\(899\) −10.3262 7.50245i −0.344399 0.250221i
\(900\) 0 0
\(901\) −15.5623 −0.518456
\(902\) 16.1738 + 18.3803i 0.538527 + 0.611999i
\(903\) −18.7082 −0.622570
\(904\) 0.489357 + 1.50609i 0.0162758 + 0.0500917i
\(905\) 0 0
\(906\) 1.00000 0.726543i 0.0332228 0.0241378i
\(907\) 13.2812 40.8752i 0.440993 1.35724i −0.445825 0.895120i \(-0.647090\pi\)
0.886818 0.462118i \(-0.152910\pi\)
\(908\) −12.4443 + 38.2995i −0.412978 + 1.27101i
\(909\) 2.42705 1.76336i 0.0805002 0.0584868i
\(910\) 0 0
\(911\) 5.57953 + 17.1720i 0.184858 + 0.568934i 0.999946 0.0104029i \(-0.00331142\pi\)
−0.815088 + 0.579337i \(0.803311\pi\)
\(912\) −10.8541 −0.359415
\(913\) 1.55166 + 1.76336i 0.0513525 + 0.0583586i
\(914\) −5.06888 −0.167664
\(915\) 0 0
\(916\) 13.0902 + 9.51057i 0.432511 + 0.314238i
\(917\) −17.3435 + 12.6008i −0.572731 + 0.416114i
\(918\) 0.309017 0.951057i 0.0101991 0.0313895i
\(919\) 14.5106 44.6592i 0.478662 1.47317i −0.362293 0.932064i \(-0.618006\pi\)
0.840955 0.541106i \(-0.181994\pi\)
\(920\) 0 0
\(921\) −0.454915 0.330515i −0.0149900 0.0108908i
\(922\) −4.02786 12.3965i −0.132651 0.408257i
\(923\) 9.81153 0.322950
\(924\) −1.50000 16.0292i −0.0493464 0.527322i
\(925\) 0 0
\(926\) 3.01722 + 9.28605i 0.0991520 + 0.305159i
\(927\) −4.85410 3.52671i −0.159430 0.115832i
\(928\) −20.3262 + 14.7679i −0.667241 + 0.484779i
\(929\) −10.1631 + 31.2789i −0.333441 + 1.02623i 0.634044 + 0.773297i \(0.281394\pi\)
−0.967485 + 0.252929i \(0.918606\pi\)
\(930\) 0 0
\(931\) −9.47214 + 6.88191i −0.310437 + 0.225545i
\(932\) −31.8435 23.1356i −1.04307 0.757833i
\(933\) −0.781153 2.40414i −0.0255738 0.0787081i
\(934\) 6.03444 0.197453
\(935\) 0 0
\(936\) 3.94427 0.128923
\(937\) 5.12868 + 15.7844i 0.167547 + 0.515655i 0.999215 0.0396173i \(-0.0126139\pi\)
−0.831668 + 0.555273i \(0.812614\pi\)
\(938\) 14.3435 + 10.4211i 0.468331 + 0.340262i
\(939\) −20.8992 + 15.1841i −0.682019 + 0.495516i
\(940\) 0 0
\(941\) −13.7918 + 42.4468i −0.449600 + 1.38373i 0.427760 + 0.903892i \(0.359303\pi\)
−0.877360 + 0.479833i \(0.840697\pi\)
\(942\) 1.85410 1.34708i 0.0604099 0.0438904i
\(943\) −33.5517 24.3767i −1.09259 0.793815i
\(944\) 5.91641 + 18.2088i 0.192563 + 0.592647i
\(945\) 0 0
\(946\) −12.4721 2.80017i −0.405504 0.0910413i
\(947\) −18.3262 −0.595523 −0.297761 0.954640i \(-0.596240\pi\)
−0.297761 + 0.954640i \(0.596240\pi\)
\(948\) 4.73607 + 14.5761i 0.153820 + 0.473410i
\(949\) 4.61803 + 3.35520i 0.149908 + 0.108914i
\(950\) 0 0
\(951\) −5.98278 + 18.4131i −0.194005 + 0.597086i
\(952\) −3.35410 + 10.3229i −0.108707 + 0.334566i
\(953\) 30.5967 22.2298i 0.991126 0.720095i 0.0309585 0.999521i \(-0.490144\pi\)
0.960167 + 0.279426i \(0.0901440\pi\)
\(954\) −4.80902 3.49396i −0.155698 0.113121i
\(955\) 0 0
\(956\) −4.14590 −0.134088
\(957\) −7.56231 + 12.7598i −0.244455 + 0.412465i
\(958\) −17.3607 −0.560898
\(959\) 6.92705 + 21.3193i 0.223686 + 0.688435i
\(960\) 0 0
\(961\) 18.4894 13.4333i 0.596431 0.433332i
\(962\) 0.0795268 0.244758i 0.00256405 0.00789133i
\(963\) 1.30902 4.02874i 0.0421825 0.129824i
\(964\) −30.2705 + 21.9928i −0.974947 + 0.708341i
\(965\) 0 0
\(966\) −1.98936 6.12261i −0.0640065 0.196992i
\(967\) 34.6869 1.11546 0.557728 0.830024i \(-0.311673\pi\)
0.557728 + 0.830024i \(0.311673\pi\)
\(968\) 3.12868 24.3970i 0.100559 0.784148i
\(969\) 9.47214 0.304289
\(970\) 0 0
\(971\) −30.5623 22.2048i −0.980791 0.712586i −0.0229058 0.999738i \(-0.507292\pi\)
−0.957885 + 0.287151i \(0.907292\pi\)
\(972\) −1.30902 + 0.951057i −0.0419867 + 0.0305052i
\(973\) 0.791796 2.43690i 0.0253838 0.0781234i
\(974\) −3.21227 + 9.88635i −0.102928 + 0.316779i
\(975\) 0 0
\(976\) −11.7812 8.55951i −0.377106 0.273983i
\(977\) 1.43363 + 4.41226i 0.0458658 + 0.141161i 0.971367 0.237585i \(-0.0763557\pi\)
−0.925501 + 0.378745i \(0.876356\pi\)
\(978\) 11.2918 0.361072
\(979\) 0.892609 1.50609i 0.0285279 0.0481347i
\(980\) 0 0
\(981\) 0 0
\(982\) −12.6074 9.15981i −0.402318 0.292301i
\(983\) −22.0902 + 16.0494i −0.704567 + 0.511898i −0.881416 0.472340i \(-0.843409\pi\)
0.176849 + 0.984238i \(0.443409\pi\)
\(984\) −8.25329 + 25.4010i −0.263105 + 0.809755i
\(985\) 0 0
\(986\) 3.61803 2.62866i 0.115222 0.0837134i
\(987\) 3.92705 + 2.85317i 0.124999 + 0.0908174i
\(988\) 5.16312 + 15.8904i 0.164261 + 0.505542i
\(989\) 21.6525 0.688509
\(990\) 0 0
\(991\) 21.2705 0.675680 0.337840 0.941204i \(-0.390304\pi\)
0.337840 + 0.941204i \(0.390304\pi\)
\(992\) 4.95492 + 15.2497i 0.157319 + 0.484177i
\(993\) 21.5172 + 15.6332i 0.682828 + 0.496104i
\(994\) −8.34346 + 6.06188i −0.264638 + 0.192271i
\(995\) 0 0
\(996\) −0.354102 + 1.08981i −0.0112202 + 0.0345321i
\(997\) −10.5000 + 7.62870i −0.332538 + 0.241603i −0.741507 0.670945i \(-0.765889\pi\)
0.408969 + 0.912548i \(0.365889\pi\)
\(998\) 8.78115 + 6.37988i 0.277963 + 0.201952i
\(999\) 0.0729490 + 0.224514i 0.00230800 + 0.00710331i
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 825.2.n.f.676.1 4
5.2 odd 4 825.2.bx.b.49.1 8
5.3 odd 4 825.2.bx.b.49.2 8
5.4 even 2 33.2.e.a.16.1 4
11.3 even 5 9075.2.a.x.1.2 2
11.8 odd 10 9075.2.a.bv.1.1 2
11.9 even 5 inner 825.2.n.f.526.1 4
15.14 odd 2 99.2.f.b.82.1 4
20.19 odd 2 528.2.y.f.49.1 4
45.4 even 6 891.2.n.d.379.1 8
45.14 odd 6 891.2.n.a.379.1 8
45.29 odd 6 891.2.n.a.676.1 8
45.34 even 6 891.2.n.d.676.1 8
55.4 even 10 363.2.e.h.124.1 4
55.9 even 10 33.2.e.a.31.1 yes 4
55.14 even 10 363.2.a.h.1.1 2
55.19 odd 10 363.2.a.e.1.2 2
55.24 odd 10 363.2.e.j.130.1 4
55.29 odd 10 363.2.e.c.124.1 4
55.39 odd 10 363.2.e.c.202.1 4
55.42 odd 20 825.2.bx.b.724.2 8
55.49 even 10 363.2.e.h.202.1 4
55.53 odd 20 825.2.bx.b.724.1 8
55.54 odd 2 363.2.e.j.148.1 4
165.14 odd 10 1089.2.a.m.1.2 2
165.74 even 10 1089.2.a.s.1.1 2
165.119 odd 10 99.2.f.b.64.1 4
220.19 even 10 5808.2.a.bm.1.1 2
220.119 odd 10 528.2.y.f.97.1 4
220.179 odd 10 5808.2.a.bl.1.1 2
495.119 odd 30 891.2.n.a.757.1 8
495.229 even 30 891.2.n.d.460.1 8
495.284 odd 30 891.2.n.a.460.1 8
495.394 even 30 891.2.n.d.757.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.2.e.a.16.1 4 5.4 even 2
33.2.e.a.31.1 yes 4 55.9 even 10
99.2.f.b.64.1 4 165.119 odd 10
99.2.f.b.82.1 4 15.14 odd 2
363.2.a.e.1.2 2 55.19 odd 10
363.2.a.h.1.1 2 55.14 even 10
363.2.e.c.124.1 4 55.29 odd 10
363.2.e.c.202.1 4 55.39 odd 10
363.2.e.h.124.1 4 55.4 even 10
363.2.e.h.202.1 4 55.49 even 10
363.2.e.j.130.1 4 55.24 odd 10
363.2.e.j.148.1 4 55.54 odd 2
528.2.y.f.49.1 4 20.19 odd 2
528.2.y.f.97.1 4 220.119 odd 10
825.2.n.f.526.1 4 11.9 even 5 inner
825.2.n.f.676.1 4 1.1 even 1 trivial
825.2.bx.b.49.1 8 5.2 odd 4
825.2.bx.b.49.2 8 5.3 odd 4
825.2.bx.b.724.1 8 55.53 odd 20
825.2.bx.b.724.2 8 55.42 odd 20
891.2.n.a.379.1 8 45.14 odd 6
891.2.n.a.460.1 8 495.284 odd 30
891.2.n.a.676.1 8 45.29 odd 6
891.2.n.a.757.1 8 495.119 odd 30
891.2.n.d.379.1 8 45.4 even 6
891.2.n.d.460.1 8 495.229 even 30
891.2.n.d.676.1 8 45.34 even 6
891.2.n.d.757.1 8 495.394 even 30
1089.2.a.m.1.2 2 165.14 odd 10
1089.2.a.s.1.1 2 165.74 even 10
5808.2.a.bl.1.1 2 220.179 odd 10
5808.2.a.bm.1.1 2 220.19 even 10
9075.2.a.x.1.2 2 11.3 even 5
9075.2.a.bv.1.1 2 11.8 odd 10