Properties

Label 630.2.j.l.211.3
Level $630$
Weight $2$
Character 630.211
Analytic conductor $5.031$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [630,2,Mod(211,630)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(630, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("630.211");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.j (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.03057532734\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.856615824.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 211.3
Root \(2.33086i\) of defining polynomial
Character \(\chi\) \(=\) 630.211
Dual form 630.2.j.l.421.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.657430 - 1.60243i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.05903 + 1.37057i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-2.13557 + 2.10697i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.657430 - 1.60243i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.05903 + 1.37057i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-2.13557 + 2.10697i) q^{9} -1.00000 q^{10} +(-1.37389 - 2.37965i) q^{11} +(1.71646 + 0.231865i) q^{12} +(2.01859 - 3.49629i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-1.71646 - 0.231865i) q^{15} +(-0.500000 - 0.866025i) q^{16} -7.58816 q^{17} +(2.89248 + 0.795973i) q^{18} -4.27114 q^{19} +(0.500000 + 0.866025i) q^{20} +(1.05903 - 1.37057i) q^{21} +(-1.37389 + 2.37965i) q^{22} +(0.873891 - 1.51362i) q^{23} +(-0.657430 - 1.60243i) q^{24} +(-0.500000 - 0.866025i) q^{25} -4.03717 q^{26} +(4.78027 + 2.03692i) q^{27} -1.00000 q^{28} +(-4.67709 - 8.10096i) q^{29} +(0.657430 + 1.60243i) q^{30} +(-5.27114 + 9.12989i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.90999 + 3.76602i) q^{33} +(3.79408 + 6.57154i) q^{34} +1.00000 q^{35} +(-0.756906 - 2.90295i) q^{36} +7.30832 q^{37} +(2.13557 + 3.69892i) q^{38} +(-6.92965 - 0.936078i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-1.51859 + 2.63027i) q^{41} +(-1.71646 - 0.231865i) q^{42} +(0.644696 + 1.11665i) q^{43} +2.74778 q^{44} +(0.756906 + 2.90295i) q^{45} -1.74778 q^{46} +(0.378666 + 0.655869i) q^{47} +(-1.05903 + 1.37057i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(4.98868 + 12.1595i) q^{51} +(2.01859 + 3.49629i) q^{52} +7.23397 q^{53} +(-0.626109 - 5.15829i) q^{54} -2.74778 q^{55} +(0.500000 + 0.866025i) q^{56} +(2.80798 + 6.84421i) q^{57} +(-4.67709 + 8.10096i) q^{58} +(0.612210 - 1.06038i) q^{59} +(1.05903 - 1.37057i) q^{60} +(-6.16797 - 10.6832i) q^{61} +10.5423 q^{62} +(-2.89248 - 0.795973i) q^{63} +1.00000 q^{64} +(-2.01859 - 3.49629i) q^{65} +(4.71646 + 0.637113i) q^{66} +(-6.64938 + 11.5171i) q^{67} +(3.79408 - 6.57154i) q^{68} +(-3.00000 - 0.405249i) q^{69} +(-0.500000 - 0.866025i) q^{70} -0.550985 q^{71} +(-2.13557 + 2.10697i) q^{72} -9.07435 q^{73} +(-3.65416 - 6.32919i) q^{74} +(-1.05903 + 1.37057i) q^{75} +(2.13557 - 3.69892i) q^{76} +(1.37389 - 2.37965i) q^{77} +(2.65416 + 6.46929i) q^{78} +(-3.14470 - 5.44677i) q^{79} -1.00000 q^{80} +(0.121334 - 8.99918i) q^{81} +3.03717 q^{82} +(-6.18187 - 10.7073i) q^{83} +(0.657430 + 1.60243i) q^{84} +(-3.79408 + 6.57154i) q^{85} +(0.644696 - 1.11665i) q^{86} +(-9.90638 + 12.8205i) q^{87} +(-1.37389 - 2.37965i) q^{88} +7.02762 q^{89} +(2.13557 - 2.10697i) q^{90} +4.03717 q^{91} +(0.873891 + 1.51362i) q^{92} +(18.0954 + 2.44438i) q^{93} +(0.378666 - 0.655869i) q^{94} +(-2.13557 + 3.69892i) q^{95} +(1.71646 + 0.231865i) q^{96} +(7.79877 + 13.5079i) q^{97} +1.00000 q^{98} +(7.94790 + 2.18716i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} + 4 q^{5} + 4 q^{7} + 8 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} + 4 q^{5} + 4 q^{7} + 8 q^{8} + 3 q^{9} - 8 q^{10} + 2 q^{11} + 3 q^{12} + 3 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} + 4 q^{20} + 2 q^{22} - 6 q^{23} - 3 q^{24} - 4 q^{25} - 6 q^{26} + 18 q^{27} - 8 q^{28} - 12 q^{29} + 3 q^{30} - 2 q^{31} - 4 q^{32} + 6 q^{33} - 2 q^{34} + 8 q^{35} - 8 q^{37} - 3 q^{38} - 3 q^{39} + 4 q^{40} + q^{41} - 3 q^{42} + 5 q^{43} - 4 q^{44} + 12 q^{46} - 11 q^{47} - 4 q^{49} - 4 q^{50} - 21 q^{51} + 3 q^{52} + 44 q^{53} - 18 q^{54} + 4 q^{55} + 4 q^{56} + 9 q^{57} - 12 q^{58} - q^{59} - 4 q^{61} + 4 q^{62} + 3 q^{63} + 8 q^{64} - 3 q^{65} + 27 q^{66} - 21 q^{67} - 2 q^{68} - 24 q^{69} - 4 q^{70} + 34 q^{71} + 3 q^{72} - 20 q^{73} + 4 q^{74} - 3 q^{76} - 2 q^{77} - 12 q^{78} - 25 q^{79} - 8 q^{80} + 15 q^{81} - 2 q^{82} - 23 q^{83} + 3 q^{84} + 2 q^{85} + 5 q^{86} - 72 q^{87} + 2 q^{88} + 32 q^{89} - 3 q^{90} + 6 q^{91} - 6 q^{92} + 6 q^{93} - 11 q^{94} + 3 q^{95} + 3 q^{96} - 2 q^{97} + 8 q^{98} + 51 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −0.657430 1.60243i −0.379567 0.925164i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) −1.05903 + 1.37057i −0.432348 + 0.559531i
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i
\(8\) 1.00000 0.353553
\(9\) −2.13557 + 2.10697i −0.711857 + 0.702324i
\(10\) −1.00000 −0.316228
\(11\) −1.37389 2.37965i −0.414244 0.717491i 0.581105 0.813829i \(-0.302621\pi\)
−0.995349 + 0.0963374i \(0.969287\pi\)
\(12\) 1.71646 + 0.231865i 0.495500 + 0.0669335i
\(13\) 2.01859 3.49629i 0.559855 0.969698i −0.437653 0.899144i \(-0.644190\pi\)
0.997508 0.0705536i \(-0.0224766\pi\)
\(14\) 0.500000 0.866025i 0.133631 0.231455i
\(15\) −1.71646 0.231865i −0.443188 0.0598672i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −7.58816 −1.84040 −0.920199 0.391450i \(-0.871974\pi\)
−0.920199 + 0.391450i \(0.871974\pi\)
\(18\) 2.89248 + 0.795973i 0.681764 + 0.187613i
\(19\) −4.27114 −0.979868 −0.489934 0.871760i \(-0.662979\pi\)
−0.489934 + 0.871760i \(0.662979\pi\)
\(20\) 0.500000 + 0.866025i 0.111803 + 0.193649i
\(21\) 1.05903 1.37057i 0.231100 0.299082i
\(22\) −1.37389 + 2.37965i −0.292915 + 0.507343i
\(23\) 0.873891 1.51362i 0.182219 0.315612i −0.760417 0.649435i \(-0.775005\pi\)
0.942636 + 0.333823i \(0.108339\pi\)
\(24\) −0.657430 1.60243i −0.134197 0.327095i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −4.03717 −0.791755
\(27\) 4.78027 + 2.03692i 0.919963 + 0.392005i
\(28\) −1.00000 −0.188982
\(29\) −4.67709 8.10096i −0.868514 1.50431i −0.863515 0.504324i \(-0.831742\pi\)
−0.00499981 0.999988i \(-0.501591\pi\)
\(30\) 0.657430 + 1.60243i 0.120030 + 0.292563i
\(31\) −5.27114 + 9.12989i −0.946725 + 1.63978i −0.194466 + 0.980909i \(0.562297\pi\)
−0.752259 + 0.658867i \(0.771036\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −2.90999 + 3.76602i −0.506564 + 0.655580i
\(34\) 3.79408 + 6.57154i 0.650679 + 1.12701i
\(35\) 1.00000 0.169031
\(36\) −0.756906 2.90295i −0.126151 0.483824i
\(37\) 7.30832 1.20148 0.600740 0.799445i \(-0.294873\pi\)
0.600740 + 0.799445i \(0.294873\pi\)
\(38\) 2.13557 + 3.69892i 0.346435 + 0.600044i
\(39\) −6.92965 0.936078i −1.10963 0.149892i
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) −1.51859 + 2.63027i −0.237163 + 0.410779i −0.959899 0.280345i \(-0.909551\pi\)
0.722736 + 0.691124i \(0.242884\pi\)
\(42\) −1.71646 0.231865i −0.264856 0.0357775i
\(43\) 0.644696 + 1.11665i 0.0983151 + 0.170287i 0.910987 0.412434i \(-0.135321\pi\)
−0.812672 + 0.582721i \(0.801988\pi\)
\(44\) 2.74778 0.414244
\(45\) 0.756906 + 2.90295i 0.112833 + 0.432746i
\(46\) −1.74778 −0.257696
\(47\) 0.378666 + 0.655869i 0.0552341 + 0.0956683i 0.892320 0.451403i \(-0.149076\pi\)
−0.837086 + 0.547071i \(0.815743\pi\)
\(48\) −1.05903 + 1.37057i −0.152858 + 0.197824i
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) −0.500000 + 0.866025i −0.0707107 + 0.122474i
\(51\) 4.98868 + 12.1595i 0.698555 + 1.70267i
\(52\) 2.01859 + 3.49629i 0.279928 + 0.484849i
\(53\) 7.23397 0.993662 0.496831 0.867847i \(-0.334497\pi\)
0.496831 + 0.867847i \(0.334497\pi\)
\(54\) −0.626109 5.15829i −0.0852026 0.701955i
\(55\) −2.74778 −0.370511
\(56\) 0.500000 + 0.866025i 0.0668153 + 0.115728i
\(57\) 2.80798 + 6.84421i 0.371926 + 0.906538i
\(58\) −4.67709 + 8.10096i −0.614132 + 1.06371i
\(59\) 0.612210 1.06038i 0.0797030 0.138050i −0.823419 0.567434i \(-0.807936\pi\)
0.903122 + 0.429385i \(0.141269\pi\)
\(60\) 1.05903 1.37057i 0.136720 0.176939i
\(61\) −6.16797 10.6832i −0.789728 1.36785i −0.926134 0.377195i \(-0.876889\pi\)
0.136406 0.990653i \(-0.456445\pi\)
\(62\) 10.5423 1.33887
\(63\) −2.89248 0.795973i −0.364418 0.100283i
\(64\) 1.00000 0.125000
\(65\) −2.01859 3.49629i −0.250375 0.433662i
\(66\) 4.71646 + 0.637113i 0.580556 + 0.0784232i
\(67\) −6.64938 + 11.5171i −0.812351 + 1.40703i 0.0988627 + 0.995101i \(0.468480\pi\)
−0.911214 + 0.411933i \(0.864854\pi\)
\(68\) 3.79408 6.57154i 0.460100 0.796916i
\(69\) −3.00000 0.405249i −0.361158 0.0487862i
\(70\) −0.500000 0.866025i −0.0597614 0.103510i
\(71\) −0.550985 −0.0653899 −0.0326949 0.999465i \(-0.510409\pi\)
−0.0326949 + 0.999465i \(0.510409\pi\)
\(72\) −2.13557 + 2.10697i −0.251680 + 0.248309i
\(73\) −9.07435 −1.06207 −0.531036 0.847349i \(-0.678197\pi\)
−0.531036 + 0.847349i \(0.678197\pi\)
\(74\) −3.65416 6.32919i −0.424787 0.735753i
\(75\) −1.05903 + 1.37057i −0.122286 + 0.158259i
\(76\) 2.13557 3.69892i 0.244967 0.424295i
\(77\) 1.37389 2.37965i 0.156569 0.271186i
\(78\) 2.65416 + 6.46929i 0.300524 + 0.732503i
\(79\) −3.14470 5.44677i −0.353806 0.612810i 0.633107 0.774064i \(-0.281779\pi\)
−0.986913 + 0.161255i \(0.948446\pi\)
\(80\) −1.00000 −0.111803
\(81\) 0.121334 8.99918i 0.0134816 0.999909i
\(82\) 3.03717 0.335400
\(83\) −6.18187 10.7073i −0.678548 1.17528i −0.975418 0.220362i \(-0.929276\pi\)
0.296870 0.954918i \(-0.404057\pi\)
\(84\) 0.657430 + 1.60243i 0.0717315 + 0.174840i
\(85\) −3.79408 + 6.57154i −0.411526 + 0.712783i
\(86\) 0.644696 1.11665i 0.0695193 0.120411i
\(87\) −9.90638 + 12.8205i −1.06208 + 1.37451i
\(88\) −1.37389 2.37965i −0.146457 0.253671i
\(89\) 7.02762 0.744927 0.372463 0.928047i \(-0.378513\pi\)
0.372463 + 0.928047i \(0.378513\pi\)
\(90\) 2.13557 2.10697i 0.225109 0.222094i
\(91\) 4.03717 0.423211
\(92\) 0.873891 + 1.51362i 0.0911094 + 0.157806i
\(93\) 18.0954 + 2.44438i 1.87641 + 0.253471i
\(94\) 0.378666 0.655869i 0.0390564 0.0676477i
\(95\) −2.13557 + 3.69892i −0.219105 + 0.379501i
\(96\) 1.71646 + 0.231865i 0.175186 + 0.0236646i
\(97\) 7.79877 + 13.5079i 0.791845 + 1.37152i 0.924823 + 0.380397i \(0.124212\pi\)
−0.132979 + 0.991119i \(0.542454\pi\)
\(98\) 1.00000 0.101015
\(99\) 7.94790 + 2.18716i 0.798794 + 0.219818i
\(100\) 1.00000 0.100000
\(101\) −7.98175 13.8248i −0.794214 1.37562i −0.923337 0.383991i \(-0.874550\pi\)
0.129123 0.991629i \(-0.458784\pi\)
\(102\) 8.03610 10.4001i 0.795692 1.02976i
\(103\) 7.36477 12.7562i 0.725672 1.25690i −0.233025 0.972471i \(-0.574862\pi\)
0.958697 0.284430i \(-0.0918044\pi\)
\(104\) 2.01859 3.49629i 0.197939 0.342840i
\(105\) −0.657430 1.60243i −0.0641586 0.156381i
\(106\) −3.61699 6.26480i −0.351313 0.608491i
\(107\) 8.66474 0.837652 0.418826 0.908067i \(-0.362442\pi\)
0.418826 + 0.908067i \(0.362442\pi\)
\(108\) −4.15416 + 3.12137i −0.399734 + 0.300354i
\(109\) 3.56923 0.341870 0.170935 0.985282i \(-0.445321\pi\)
0.170935 + 0.985282i \(0.445321\pi\)
\(110\) 1.37389 + 2.37965i 0.130995 + 0.226891i
\(111\) −4.80471 11.7111i −0.456043 1.11157i
\(112\) 0.500000 0.866025i 0.0472456 0.0818317i
\(113\) 4.04186 7.00071i 0.380226 0.658571i −0.610868 0.791732i \(-0.709179\pi\)
0.991094 + 0.133161i \(0.0425128\pi\)
\(114\) 4.52327 5.85389i 0.423643 0.548267i
\(115\) −0.873891 1.51362i −0.0814908 0.141146i
\(116\) 9.35419 0.868514
\(117\) 3.05576 + 11.7197i 0.282505 + 1.08349i
\(118\) −1.22442 −0.112717
\(119\) −3.79408 6.57154i −0.347803 0.602412i
\(120\) −1.71646 0.231865i −0.156691 0.0211662i
\(121\) 1.72485 2.98752i 0.156804 0.271593i
\(122\) −6.16797 + 10.6832i −0.558422 + 0.967215i
\(123\) 5.21319 + 0.704213i 0.470057 + 0.0634967i
\(124\) −5.27114 9.12989i −0.473363 0.819888i
\(125\) −1.00000 −0.0894427
\(126\) 0.756906 + 2.90295i 0.0674305 + 0.258615i
\(127\) −3.74778 −0.332562 −0.166281 0.986078i \(-0.553176\pi\)
−0.166281 + 0.986078i \(0.553176\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 1.36551 1.76720i 0.120226 0.155593i
\(130\) −2.01859 + 3.49629i −0.177042 + 0.306645i
\(131\) −6.25691 + 10.8373i −0.546668 + 0.946857i 0.451831 + 0.892103i \(0.350771\pi\)
−0.998500 + 0.0547541i \(0.982563\pi\)
\(132\) −1.80647 4.40313i −0.157233 0.383243i
\(133\) −2.13557 3.69892i −0.185178 0.320737i
\(134\) 13.2988 1.14884
\(135\) 4.15416 3.12137i 0.357533 0.268645i
\(136\) −7.58816 −0.650679
\(137\) −8.77549 15.1996i −0.749741 1.29859i −0.947947 0.318429i \(-0.896845\pi\)
0.198206 0.980160i \(-0.436489\pi\)
\(138\) 1.14904 + 2.80070i 0.0978131 + 0.238411i
\(139\) 0.195680 0.338928i 0.0165974 0.0287475i −0.857607 0.514305i \(-0.828050\pi\)
0.874205 + 0.485557i \(0.161383\pi\)
\(140\) −0.500000 + 0.866025i −0.0422577 + 0.0731925i
\(141\) 0.802038 1.03797i 0.0675438 0.0874132i
\(142\) 0.275492 + 0.477167i 0.0231188 + 0.0400429i
\(143\) −11.0933 −0.927666
\(144\) 2.89248 + 0.795973i 0.241040 + 0.0663311i
\(145\) −9.35419 −0.776823
\(146\) 4.53717 + 7.85861i 0.375499 + 0.650384i
\(147\) 1.71646 + 0.231865i 0.141571 + 0.0191239i
\(148\) −3.65416 + 6.32919i −0.300370 + 0.520256i
\(149\) 1.61264 2.79317i 0.132112 0.228825i −0.792378 0.610030i \(-0.791157\pi\)
0.924491 + 0.381205i \(0.124491\pi\)
\(150\) 1.71646 + 0.231865i 0.140148 + 0.0189317i
\(151\) 2.69568 + 4.66906i 0.219371 + 0.379962i 0.954616 0.297840i \(-0.0962660\pi\)
−0.735245 + 0.677802i \(0.762933\pi\)
\(152\) −4.27114 −0.346435
\(153\) 16.2051 15.9880i 1.31010 1.29256i
\(154\) −2.74778 −0.221423
\(155\) 5.27114 + 9.12989i 0.423388 + 0.733330i
\(156\) 4.27549 5.53321i 0.342313 0.443012i
\(157\) 11.5696 20.0391i 0.923352 1.59929i 0.129162 0.991623i \(-0.458771\pi\)
0.794190 0.607670i \(-0.207896\pi\)
\(158\) −3.14470 + 5.44677i −0.250179 + 0.433322i
\(159\) −4.75583 11.5919i −0.377162 0.919301i
\(160\) 0.500000 + 0.866025i 0.0395285 + 0.0684653i
\(161\) 1.74778 0.137745
\(162\) −7.85419 + 4.39451i −0.617083 + 0.345266i
\(163\) −4.58816 −0.359372 −0.179686 0.983724i \(-0.557508\pi\)
−0.179686 + 0.983724i \(0.557508\pi\)
\(164\) −1.51859 2.63027i −0.118582 0.205390i
\(165\) 1.80647 + 4.40313i 0.140634 + 0.342783i
\(166\) −6.18187 + 10.7073i −0.479806 + 0.831048i
\(167\) 4.74343 8.21587i 0.367058 0.635763i −0.622046 0.782981i \(-0.713698\pi\)
0.989104 + 0.147218i \(0.0470318\pi\)
\(168\) 1.05903 1.37057i 0.0817060 0.105742i
\(169\) −1.64938 2.85682i −0.126876 0.219755i
\(170\) 7.58816 0.581985
\(171\) 9.12133 8.99918i 0.697526 0.688185i
\(172\) −1.28939 −0.0983151
\(173\) −5.27114 9.12989i −0.400758 0.694133i 0.593060 0.805158i \(-0.297920\pi\)
−0.993818 + 0.111026i \(0.964586\pi\)
\(174\) 16.0561 + 2.16891i 1.21721 + 0.164424i
\(175\) 0.500000 0.866025i 0.0377964 0.0654654i
\(176\) −1.37389 + 2.37965i −0.103561 + 0.179373i
\(177\) −2.10167 0.283900i −0.157971 0.0213392i
\(178\) −3.51381 6.08610i −0.263371 0.456172i
\(179\) −11.9052 −0.889834 −0.444917 0.895572i \(-0.646767\pi\)
−0.444917 + 0.895572i \(0.646767\pi\)
\(180\) −2.89248 0.795973i −0.215593 0.0593283i
\(181\) 10.5232 0.782182 0.391091 0.920352i \(-0.372098\pi\)
0.391091 + 0.920352i \(0.372098\pi\)
\(182\) −2.01859 3.49629i −0.149628 0.259163i
\(183\) −13.0641 + 16.9072i −0.965729 + 1.24982i
\(184\) 0.873891 1.51362i 0.0644241 0.111586i
\(185\) 3.65416 6.32919i 0.268659 0.465331i
\(186\) −6.93082 16.8933i −0.508192 1.23868i
\(187\) 10.4253 + 18.0572i 0.762374 + 1.32047i
\(188\) −0.757332 −0.0552341
\(189\) 0.626109 + 5.15829i 0.0455427 + 0.375211i
\(190\) 4.27114 0.309861
\(191\) 9.37311 + 16.2347i 0.678215 + 1.17470i 0.975518 + 0.219919i \(0.0705794\pi\)
−0.297303 + 0.954783i \(0.596087\pi\)
\(192\) −0.657430 1.60243i −0.0474459 0.115646i
\(193\) 5.81267 10.0678i 0.418405 0.724698i −0.577374 0.816480i \(-0.695923\pi\)
0.995779 + 0.0917811i \(0.0292560\pi\)
\(194\) 7.79877 13.5079i 0.559919 0.969808i
\(195\) −4.27549 + 5.53321i −0.306174 + 0.396242i
\(196\) −0.500000 0.866025i −0.0357143 0.0618590i
\(197\) 22.8039 1.62471 0.812355 0.583164i \(-0.198185\pi\)
0.812355 + 0.583164i \(0.198185\pi\)
\(198\) −2.07981 7.97666i −0.147806 0.566877i
\(199\) 14.8498 1.05267 0.526335 0.850277i \(-0.323566\pi\)
0.526335 + 0.850277i \(0.323566\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) 22.8268 + 3.08351i 1.61008 + 0.217494i
\(202\) −7.98175 + 13.8248i −0.561594 + 0.972710i
\(203\) 4.67709 8.10096i 0.328268 0.568576i
\(204\) −13.0248 1.75943i −0.911917 0.123184i
\(205\) 1.51859 + 2.63027i 0.106063 + 0.183706i
\(206\) −14.7295 −1.02626
\(207\) 1.32291 + 5.07372i 0.0919483 + 0.352648i
\(208\) −4.03717 −0.279928
\(209\) 5.86809 + 10.1638i 0.405904 + 0.703046i
\(210\) −1.05903 + 1.37057i −0.0730801 + 0.0945781i
\(211\) 4.90203 8.49056i 0.337469 0.584514i −0.646487 0.762925i \(-0.723762\pi\)
0.983956 + 0.178411i \(0.0570957\pi\)
\(212\) −3.61699 + 6.26480i −0.248416 + 0.430268i
\(213\) 0.362234 + 0.882915i 0.0248199 + 0.0604963i
\(214\) −4.33237 7.50388i −0.296155 0.512955i
\(215\) 1.28939 0.0879357
\(216\) 4.78027 + 2.03692i 0.325256 + 0.138595i
\(217\) −10.5423 −0.715657
\(218\) −1.78462 3.09105i −0.120869 0.209352i
\(219\) 5.96575 + 14.5410i 0.403128 + 0.982591i
\(220\) 1.37389 2.37965i 0.0926277 0.160436i
\(221\) −15.3174 + 26.5304i −1.03036 + 1.78463i
\(222\) −7.73974 + 10.0165i −0.519457 + 0.672266i
\(223\) −1.28504 2.22576i −0.0860528 0.149048i 0.819787 0.572669i \(-0.194092\pi\)
−0.905839 + 0.423621i \(0.860759\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 2.89248 + 0.795973i 0.192832 + 0.0530649i
\(226\) −8.08372 −0.537721
\(227\) −4.37858 7.58392i −0.290616 0.503363i 0.683339 0.730101i \(-0.260527\pi\)
−0.973956 + 0.226739i \(0.927194\pi\)
\(228\) −7.33125 0.990327i −0.485524 0.0655860i
\(229\) 0.0936237 0.162161i 0.00618683 0.0107159i −0.862915 0.505348i \(-0.831364\pi\)
0.869102 + 0.494632i \(0.164697\pi\)
\(230\) −0.873891 + 1.51362i −0.0576227 + 0.0998054i
\(231\) −4.71646 0.637113i −0.310320 0.0419190i
\(232\) −4.67709 8.10096i −0.307066 0.531854i
\(233\) 15.5795 1.02064 0.510322 0.859983i \(-0.329526\pi\)
0.510322 + 0.859983i \(0.329526\pi\)
\(234\) 8.62167 8.50621i 0.563616 0.556069i
\(235\) 0.757332 0.0494029
\(236\) 0.612210 + 1.06038i 0.0398515 + 0.0690248i
\(237\) −6.66066 + 8.62003i −0.432656 + 0.559931i
\(238\) −3.79408 + 6.57154i −0.245934 + 0.425970i
\(239\) −2.46794 + 4.27460i −0.159638 + 0.276501i −0.934738 0.355337i \(-0.884366\pi\)
0.775100 + 0.631838i \(0.217699\pi\)
\(240\) 0.657430 + 1.60243i 0.0424369 + 0.103436i
\(241\) −12.6348 21.8841i −0.813879 1.40968i −0.910130 0.414322i \(-0.864019\pi\)
0.0962517 0.995357i \(-0.469315\pi\)
\(242\) −3.44969 −0.221755
\(243\) −14.5003 + 5.72190i −0.930197 + 0.367060i
\(244\) 12.3359 0.789728
\(245\) 0.500000 + 0.866025i 0.0319438 + 0.0553283i
\(246\) −1.99673 4.86686i −0.127307 0.310300i
\(247\) −8.62167 + 14.9332i −0.548584 + 0.950175i
\(248\) −5.27114 + 9.12989i −0.334718 + 0.579749i
\(249\) −13.0936 + 16.9453i −0.829772 + 1.07387i
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) −16.6741 −1.05246 −0.526230 0.850342i \(-0.676395\pi\)
−0.526230 + 0.850342i \(0.676395\pi\)
\(252\) 2.13557 2.10697i 0.134528 0.132727i
\(253\) −4.80252 −0.301932
\(254\) 1.87389 + 3.24567i 0.117578 + 0.203652i
\(255\) 13.0248 + 1.75943i 0.815643 + 0.110179i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −11.0699 + 19.1736i −0.690522 + 1.19602i 0.281145 + 0.959665i \(0.409286\pi\)
−0.971667 + 0.236354i \(0.924048\pi\)
\(258\) −2.21319 0.298964i −0.137787 0.0186127i
\(259\) 3.65416 + 6.32919i 0.227058 + 0.393277i
\(260\) 4.03717 0.250375
\(261\) 27.0568 + 7.44568i 1.67477 + 0.460876i
\(262\) 12.5138 0.773106
\(263\) 0.911064 + 1.57801i 0.0561786 + 0.0973042i 0.892747 0.450558i \(-0.148775\pi\)
−0.836568 + 0.547862i \(0.815442\pi\)
\(264\) −2.90999 + 3.76602i −0.179097 + 0.231782i
\(265\) 3.61699 6.26480i 0.222190 0.384844i
\(266\) −2.13557 + 3.69892i −0.130940 + 0.226795i
\(267\) −4.62017 11.2613i −0.282750 0.689179i
\(268\) −6.64938 11.5171i −0.406176 0.703517i
\(269\) −6.26159 −0.381776 −0.190888 0.981612i \(-0.561137\pi\)
−0.190888 + 0.981612i \(0.561137\pi\)
\(270\) −4.78027 2.03692i −0.290918 0.123963i
\(271\) −5.91387 −0.359242 −0.179621 0.983736i \(-0.557487\pi\)
−0.179621 + 0.983736i \(0.557487\pi\)
\(272\) 3.79408 + 6.57154i 0.230050 + 0.398458i
\(273\) −2.65416 6.46929i −0.160637 0.391539i
\(274\) −8.77549 + 15.1996i −0.530147 + 0.918241i
\(275\) −1.37389 + 2.37965i −0.0828487 + 0.143498i
\(276\) 1.85096 2.39545i 0.111414 0.144189i
\(277\) 7.98175 + 13.8248i 0.479577 + 0.830652i 0.999726 0.0234240i \(-0.00745677\pi\)
−0.520149 + 0.854076i \(0.674123\pi\)
\(278\) −0.391360 −0.0234722
\(279\) −7.97952 30.6037i −0.477721 1.83219i
\(280\) 1.00000 0.0597614
\(281\) −1.60795 2.78505i −0.0959222 0.166142i 0.814071 0.580765i \(-0.197247\pi\)
−0.909993 + 0.414623i \(0.863913\pi\)
\(282\) −1.29993 0.175599i −0.0774098 0.0104567i
\(283\) 0.621334 1.07618i 0.0369345 0.0639724i −0.846967 0.531645i \(-0.821574\pi\)
0.883902 + 0.467673i \(0.154907\pi\)
\(284\) 0.275492 0.477167i 0.0163475 0.0283146i
\(285\) 7.33125 + 0.990327i 0.434266 + 0.0586619i
\(286\) 5.54664 + 9.60706i 0.327979 + 0.568077i
\(287\) −3.03717 −0.179279
\(288\) −0.756906 2.90295i −0.0446011 0.171058i
\(289\) 40.5801 2.38707
\(290\) 4.67709 + 8.10096i 0.274648 + 0.475705i
\(291\) 16.5183 21.3775i 0.968318 1.25317i
\(292\) 4.53717 7.85861i 0.265518 0.459891i
\(293\) −10.7419 + 18.6055i −0.627548 + 1.08694i 0.360494 + 0.932761i \(0.382608\pi\)
−0.988042 + 0.154183i \(0.950725\pi\)
\(294\) −0.657430 1.60243i −0.0383421 0.0934557i
\(295\) −0.612210 1.06038i −0.0356443 0.0617377i
\(296\) 7.30832 0.424787
\(297\) −1.72041 14.1739i −0.0998284 0.822451i
\(298\) −3.22527 −0.186835
\(299\) −3.52805 6.11076i −0.204032 0.353394i
\(300\) −0.657430 1.60243i −0.0379567 0.0925164i
\(301\) −0.644696 + 1.11665i −0.0371596 + 0.0643624i
\(302\) 2.69568 4.66906i 0.155119 0.268674i
\(303\) −16.9059 + 21.8790i −0.971216 + 1.25692i
\(304\) 2.13557 + 3.69892i 0.122483 + 0.212148i
\(305\) −12.3359 −0.706354
\(306\) −21.9486 6.03997i −1.25472 0.345282i
\(307\) 31.1369 1.77708 0.888539 0.458802i \(-0.151721\pi\)
0.888539 + 0.458802i \(0.151721\pi\)
\(308\) 1.37389 + 2.37965i 0.0782847 + 0.135593i
\(309\) −25.2827 3.41526i −1.43828 0.194287i
\(310\) 5.27114 9.12989i 0.299381 0.518543i
\(311\) −12.8498 + 22.2564i −0.728643 + 1.26205i 0.228814 + 0.973470i \(0.426515\pi\)
−0.957457 + 0.288576i \(0.906818\pi\)
\(312\) −6.92965 0.936078i −0.392314 0.0529950i
\(313\) −11.2375 19.4640i −0.635183 1.10017i −0.986476 0.163904i \(-0.947591\pi\)
0.351293 0.936266i \(-0.385742\pi\)
\(314\) −23.1391 −1.30582
\(315\) −2.13557 + 2.10697i −0.120326 + 0.118714i
\(316\) 6.28939 0.353806
\(317\) −1.18622 2.05459i −0.0666246 0.115397i 0.830789 0.556588i \(-0.187890\pi\)
−0.897413 + 0.441190i \(0.854556\pi\)
\(318\) −7.66100 + 9.91464i −0.429608 + 0.555985i
\(319\) −12.8516 + 22.2597i −0.719553 + 1.24630i
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) −5.69646 13.8846i −0.317945 0.774965i
\(322\) −0.873891 1.51362i −0.0487000 0.0843510i
\(323\) 32.4101 1.80335
\(324\) 7.73285 + 4.60467i 0.429603 + 0.255815i
\(325\) −4.03717 −0.223942
\(326\) 2.29408 + 3.97346i 0.127057 + 0.220070i
\(327\) −2.34652 5.71945i −0.129763 0.316286i
\(328\) −1.51859 + 2.63027i −0.0838499 + 0.145232i
\(329\) −0.378666 + 0.655869i −0.0208765 + 0.0361592i
\(330\) 2.90999 3.76602i 0.160190 0.207312i
\(331\) 0.649810 + 1.12550i 0.0357168 + 0.0618633i 0.883331 0.468749i \(-0.155295\pi\)
−0.847614 + 0.530613i \(0.821962\pi\)
\(332\) 12.3637 0.678548
\(333\) −15.6074 + 15.3984i −0.855282 + 0.843828i
\(334\) −9.48687 −0.519098
\(335\) 6.64938 + 11.5171i 0.363295 + 0.629245i
\(336\) −1.71646 0.231865i −0.0936406 0.0126493i
\(337\) −1.29885 + 2.24968i −0.0707531 + 0.122548i −0.899232 0.437473i \(-0.855874\pi\)
0.828478 + 0.560021i \(0.189207\pi\)
\(338\) −1.64938 + 2.85682i −0.0897146 + 0.155390i
\(339\) −13.8754 1.87433i −0.753608 0.101800i
\(340\) −3.79408 6.57154i −0.205763 0.356392i
\(341\) 28.9679 1.56870
\(342\) −12.3542 3.39972i −0.668038 0.183836i
\(343\) −1.00000 −0.0539949
\(344\) 0.644696 + 1.11665i 0.0347597 + 0.0602055i
\(345\) −1.85096 + 2.39545i −0.0996521 + 0.128967i
\(346\) −5.27114 + 9.12989i −0.283378 + 0.490826i
\(347\) 6.16319 10.6750i 0.330858 0.573062i −0.651823 0.758371i \(-0.725995\pi\)
0.982680 + 0.185309i \(0.0593287\pi\)
\(348\) −6.14972 14.9894i −0.329660 0.803518i
\(349\) 6.79554 + 11.7702i 0.363757 + 0.630045i 0.988576 0.150724i \(-0.0481606\pi\)
−0.624819 + 0.780770i \(0.714827\pi\)
\(350\) −1.00000 −0.0534522
\(351\) 16.7711 12.6015i 0.895173 0.672620i
\(352\) 2.74778 0.146457
\(353\) 4.71904 + 8.17362i 0.251169 + 0.435038i 0.963848 0.266453i \(-0.0858516\pi\)
−0.712679 + 0.701491i \(0.752518\pi\)
\(354\) 0.804971 + 1.96205i 0.0427837 + 0.104282i
\(355\) −0.275492 + 0.477167i −0.0146216 + 0.0253254i
\(356\) −3.51381 + 6.08610i −0.186232 + 0.322563i
\(357\) −8.03610 + 10.4001i −0.425315 + 0.550430i
\(358\) 5.95259 + 10.3102i 0.314604 + 0.544910i
\(359\) −14.2251 −0.750772 −0.375386 0.926869i \(-0.622490\pi\)
−0.375386 + 0.926869i \(0.622490\pi\)
\(360\) 0.756906 + 2.90295i 0.0398924 + 0.152999i
\(361\) −0.757332 −0.0398596
\(362\) −5.26159 9.11335i −0.276543 0.478987i
\(363\) −5.92127 0.799862i −0.310786 0.0419819i
\(364\) −2.01859 + 3.49629i −0.105803 + 0.183256i
\(365\) −4.53717 + 7.85861i −0.237486 + 0.411339i
\(366\) 21.1742 + 2.86027i 1.10679 + 0.149509i
\(367\) −12.3870 21.4549i −0.646597 1.11994i −0.983930 0.178553i \(-0.942858\pi\)
0.337334 0.941385i \(-0.390475\pi\)
\(368\) −1.74778 −0.0911094
\(369\) −2.29885 8.81675i −0.119674 0.458982i
\(370\) −7.30832 −0.379941
\(371\) 3.61699 + 6.26480i 0.187785 + 0.325252i
\(372\) −11.1646 + 14.4489i −0.578858 + 0.749141i
\(373\) 8.00000 13.8564i 0.414224 0.717458i −0.581122 0.813816i \(-0.697386\pi\)
0.995347 + 0.0963587i \(0.0307196\pi\)
\(374\) 10.4253 18.0572i 0.539080 0.933713i
\(375\) 0.657430 + 1.60243i 0.0339495 + 0.0827492i
\(376\) 0.378666 + 0.655869i 0.0195282 + 0.0338239i
\(377\) −37.7645 −1.94497
\(378\) 4.15416 3.12137i 0.213667 0.160546i
\(379\) −24.4570 −1.25627 −0.628136 0.778103i \(-0.716182\pi\)
−0.628136 + 0.778103i \(0.716182\pi\)
\(380\) −2.13557 3.69892i −0.109553 0.189751i
\(381\) 2.46390 + 6.00556i 0.126230 + 0.307674i
\(382\) 9.37311 16.2347i 0.479570 0.830640i
\(383\) 0.461710 0.799705i 0.0235923 0.0408630i −0.853988 0.520292i \(-0.825823\pi\)
0.877580 + 0.479429i \(0.159156\pi\)
\(384\) −1.05903 + 1.37057i −0.0540435 + 0.0699414i
\(385\) −1.37389 2.37965i −0.0700200 0.121278i
\(386\) −11.6253 −0.591714
\(387\) −3.72953 1.02632i −0.189583 0.0521708i
\(388\) −15.5975 −0.791845
\(389\) 8.68698 + 15.0463i 0.440448 + 0.762877i 0.997723 0.0674504i \(-0.0214865\pi\)
−0.557275 + 0.830328i \(0.688153\pi\)
\(390\) 6.92965 + 0.936078i 0.350897 + 0.0474001i
\(391\) −6.63122 + 11.4856i −0.335355 + 0.580853i
\(392\) −0.500000 + 0.866025i −0.0252538 + 0.0437409i
\(393\) 21.4795 + 2.90151i 1.08350 + 0.146362i
\(394\) −11.4019 19.7487i −0.574421 0.994927i
\(395\) −6.28939 −0.316454
\(396\) −5.86809 + 5.78950i −0.294882 + 0.290933i
\(397\) −28.4562 −1.42817 −0.714087 0.700057i \(-0.753158\pi\)
−0.714087 + 0.700057i \(0.753158\pi\)
\(398\) −7.42488 12.8603i −0.372175 0.644627i
\(399\) −4.52327 + 5.85389i −0.226447 + 0.293061i
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) −7.55210 + 13.0806i −0.377134 + 0.653215i −0.990644 0.136472i \(-0.956424\pi\)
0.613510 + 0.789687i \(0.289757\pi\)
\(402\) −8.74301 21.3104i −0.436062 1.06286i
\(403\) 21.2805 + 36.8589i 1.06006 + 1.83607i
\(404\) 15.9635 0.794214
\(405\) −7.73285 4.60467i −0.384249 0.228808i
\(406\) −9.35419 −0.464241
\(407\) −10.0408 17.3912i −0.497706 0.862051i
\(408\) 4.98868 + 12.1595i 0.246977 + 0.601985i
\(409\) 16.1257 27.9305i 0.797363 1.38107i −0.123965 0.992287i \(-0.539561\pi\)
0.921328 0.388787i \(-0.127106\pi\)
\(410\) 1.51859 2.63027i 0.0749976 0.129900i
\(411\) −18.5870 + 24.0548i −0.916831 + 1.18654i
\(412\) 7.36477 + 12.7562i 0.362836 + 0.628450i
\(413\) 1.22442 0.0602498
\(414\) 3.73251 3.68253i 0.183443 0.180986i
\(415\) −12.3637 −0.606912
\(416\) 2.01859 + 3.49629i 0.0989693 + 0.171420i
\(417\) −0.671755 0.0907426i −0.0328960 0.00444369i
\(418\) 5.86809 10.1638i 0.287017 0.497129i
\(419\) −3.31300 + 5.73829i −0.161851 + 0.280334i −0.935532 0.353241i \(-0.885080\pi\)
0.773682 + 0.633575i \(0.218413\pi\)
\(420\) 1.71646 + 0.231865i 0.0837547 + 0.0113138i
\(421\) 0.335601 + 0.581277i 0.0163562 + 0.0283297i 0.874088 0.485768i \(-0.161460\pi\)
−0.857731 + 0.514098i \(0.828127\pi\)
\(422\) −9.80406 −0.477254
\(423\) −2.19057 0.602816i −0.106509 0.0293099i
\(424\) 7.23397 0.351313
\(425\) 3.79408 + 6.57154i 0.184040 + 0.318766i
\(426\) 0.583510 0.755161i 0.0282712 0.0365877i
\(427\) 6.16797 10.6832i 0.298489 0.516998i
\(428\) −4.33237 + 7.50388i −0.209413 + 0.362714i
\(429\) 7.29305 + 17.7762i 0.352112 + 0.858243i
\(430\) −0.644696 1.11665i −0.0310900 0.0538494i
\(431\) 25.3914 1.22306 0.611529 0.791222i \(-0.290555\pi\)
0.611529 + 0.791222i \(0.290555\pi\)
\(432\) −0.626109 5.15829i −0.0301237 0.248178i
\(433\) 31.1376 1.49638 0.748188 0.663486i \(-0.230924\pi\)
0.748188 + 0.663486i \(0.230924\pi\)
\(434\) 5.27114 + 9.12989i 0.253023 + 0.438249i
\(435\) 6.14972 + 14.9894i 0.294857 + 0.718689i
\(436\) −1.78462 + 3.09105i −0.0854676 + 0.148034i
\(437\) −3.73251 + 6.46490i −0.178550 + 0.309258i
\(438\) 9.61002 12.4370i 0.459184 0.594263i
\(439\) 0.368777 + 0.638740i 0.0176008 + 0.0304854i 0.874692 0.484680i \(-0.161064\pi\)
−0.857091 + 0.515165i \(0.827731\pi\)
\(440\) −2.74778 −0.130995
\(441\) −0.756906 2.90295i −0.0360431 0.138236i
\(442\) 30.6347 1.45714
\(443\) −13.5499 23.4691i −0.643774 1.11505i −0.984583 0.174916i \(-0.944035\pi\)
0.340810 0.940132i \(-0.389299\pi\)
\(444\) 12.5444 + 1.69454i 0.595333 + 0.0804193i
\(445\) 3.51381 6.08610i 0.166571 0.288509i
\(446\) −1.28504 + 2.22576i −0.0608485 + 0.105393i
\(447\) −5.53606 0.747827i −0.261846 0.0353710i
\(448\) 0.500000 + 0.866025i 0.0236228 + 0.0409159i
\(449\) −5.16917 −0.243948 −0.121974 0.992533i \(-0.538923\pi\)
−0.121974 + 0.992533i \(0.538923\pi\)
\(450\) −0.756906 2.90295i −0.0356809 0.136846i
\(451\) 8.34549 0.392974
\(452\) 4.04186 + 7.00071i 0.190113 + 0.329286i
\(453\) 5.70962 7.38922i 0.268261 0.347176i
\(454\) −4.37858 + 7.58392i −0.205497 + 0.355931i
\(455\) 2.01859 3.49629i 0.0946328 0.163909i
\(456\) 2.80798 + 6.84421i 0.131496 + 0.320510i
\(457\) 2.56446 + 4.44177i 0.119960 + 0.207777i 0.919752 0.392501i \(-0.128390\pi\)
−0.799791 + 0.600278i \(0.795057\pi\)
\(458\) −0.187247 −0.00874950
\(459\) −36.2734 15.4565i −1.69310 0.721446i
\(460\) 1.74778 0.0814908
\(461\) 6.54040 + 11.3283i 0.304617 + 0.527612i 0.977176 0.212431i \(-0.0681382\pi\)
−0.672559 + 0.740044i \(0.734805\pi\)
\(462\) 1.80647 + 4.40313i 0.0840448 + 0.204852i
\(463\) 9.76671 16.9164i 0.453897 0.786173i −0.544727 0.838614i \(-0.683367\pi\)
0.998624 + 0.0524403i \(0.0166999\pi\)
\(464\) −4.67709 + 8.10096i −0.217129 + 0.376078i
\(465\) 11.1646 14.4489i 0.517746 0.670052i
\(466\) −7.78973 13.4922i −0.360852 0.625014i
\(467\) −0.510899 −0.0236416 −0.0118208 0.999930i \(-0.503763\pi\)
−0.0118208 + 0.999930i \(0.503763\pi\)
\(468\) −11.6774 3.21348i −0.539790 0.148543i
\(469\) −13.2988 −0.614080
\(470\) −0.378666 0.655869i −0.0174666 0.0302530i
\(471\) −39.7174 5.36515i −1.83008 0.247213i
\(472\) 0.612210 1.06038i 0.0281793 0.0488079i
\(473\) 1.77148 3.06830i 0.0814529 0.141081i
\(474\) 10.7955 + 1.45829i 0.495854 + 0.0669814i
\(475\) 2.13557 + 3.69892i 0.0979868 + 0.169718i
\(476\) 7.58816 0.347803
\(477\) −15.4487 + 15.2418i −0.707346 + 0.697873i
\(478\) 4.93588 0.225762
\(479\) −4.17283 7.22756i −0.190662 0.330236i 0.754808 0.655946i \(-0.227730\pi\)
−0.945470 + 0.325710i \(0.894397\pi\)
\(480\) 1.05903 1.37057i 0.0483379 0.0625575i
\(481\) 14.7525 25.5520i 0.672655 1.16507i
\(482\) −12.6348 + 21.8841i −0.575499 + 0.996794i
\(483\) −1.14904 2.80070i −0.0522833 0.127436i
\(484\) 1.72485 + 2.98752i 0.0784021 + 0.135796i
\(485\) 15.5975 0.708248
\(486\) 12.2055 + 9.69671i 0.553652 + 0.439852i
\(487\) 21.8847 0.991690 0.495845 0.868411i \(-0.334858\pi\)
0.495845 + 0.868411i \(0.334858\pi\)
\(488\) −6.16797 10.6832i −0.279211 0.483607i
\(489\) 3.01639 + 7.35221i 0.136406 + 0.332478i
\(490\) 0.500000 0.866025i 0.0225877 0.0391230i
\(491\) 14.2103 24.6129i 0.641300 1.11076i −0.343843 0.939027i \(-0.611729\pi\)
0.985143 0.171737i \(-0.0549379\pi\)
\(492\) −3.21646 + 4.16265i −0.145009 + 0.187667i
\(493\) 35.4905 + 61.4714i 1.59841 + 2.76853i
\(494\) 17.2433 0.775815
\(495\) 5.86809 5.78950i 0.263751 0.260219i
\(496\) 10.5423 0.473363
\(497\) −0.275492 0.477167i −0.0123575 0.0214039i
\(498\) 21.2219 + 2.86671i 0.950975 + 0.128460i
\(499\) 7.70983 13.3538i 0.345139 0.597799i −0.640240 0.768175i \(-0.721165\pi\)
0.985379 + 0.170376i \(0.0544983\pi\)
\(500\) 0.500000 0.866025i 0.0223607 0.0387298i
\(501\) −16.2838 2.19967i −0.727508 0.0982740i
\(502\) 8.33706 + 14.4402i 0.372101 + 0.644498i
\(503\) 39.0058 1.73918 0.869590 0.493774i \(-0.164383\pi\)
0.869590 + 0.493774i \(0.164383\pi\)
\(504\) −2.89248 0.795973i −0.128841 0.0354555i
\(505\) −15.9635 −0.710367
\(506\) 2.40126 + 4.15911i 0.106749 + 0.184895i
\(507\) −3.49350 + 4.52118i −0.155152 + 0.200793i
\(508\) 1.87389 3.24567i 0.0831405 0.144004i
\(509\) −6.16797 + 10.6832i −0.273390 + 0.473526i −0.969728 0.244188i \(-0.921478\pi\)
0.696337 + 0.717715i \(0.254812\pi\)
\(510\) −4.98868 12.1595i −0.220903 0.538432i
\(511\) −4.53717 7.85861i −0.200713 0.347645i
\(512\) 1.00000 0.0441942
\(513\) −20.4172 8.69998i −0.901442 0.384113i
\(514\) 22.1398 0.976546
\(515\) −7.36477 12.7562i −0.324530 0.562103i
\(516\) 0.847684 + 2.06616i 0.0373172 + 0.0909576i
\(517\) 1.04049 1.80218i 0.0457608 0.0792600i
\(518\) 3.65416 6.32919i 0.160555 0.278089i
\(519\) −11.1646 + 14.4489i −0.490072 + 0.634237i
\(520\) −2.01859 3.49629i −0.0885209 0.153323i
\(521\) 6.55986 0.287393 0.143696 0.989622i \(-0.454101\pi\)
0.143696 + 0.989622i \(0.454101\pi\)
\(522\) −7.08024 27.1547i −0.309894 1.18853i
\(523\) −10.2070 −0.446322 −0.223161 0.974782i \(-0.571638\pi\)
−0.223161 + 0.974782i \(0.571638\pi\)
\(524\) −6.25691 10.8373i −0.273334 0.473429i
\(525\) −1.71646 0.231865i −0.0749125 0.0101194i
\(526\) 0.911064 1.57801i 0.0397243 0.0688045i
\(527\) 39.9983 69.2790i 1.74235 3.01784i
\(528\) 4.71646 + 0.637113i 0.205258 + 0.0277268i
\(529\) 9.97263 + 17.2731i 0.433593 + 0.751004i
\(530\) −7.23397 −0.314224
\(531\) 0.926771 + 3.55443i 0.0402184 + 0.154249i
\(532\) 4.27114 0.185178
\(533\) 6.13080 + 10.6189i 0.265554 + 0.459954i
\(534\) −7.44247 + 9.63183i −0.322067 + 0.416810i
\(535\) 4.33237 7.50388i 0.187305 0.324421i
\(536\) −6.64938 + 11.5171i −0.287210 + 0.497462i
\(537\) 7.82682 + 19.0772i 0.337752 + 0.823243i
\(538\) 3.13080 + 5.42270i 0.134978 + 0.233789i
\(539\) 2.74778 0.118355
\(540\) 0.626109 + 5.15829i 0.0269434 + 0.221978i
\(541\) −22.1741 −0.953338 −0.476669 0.879083i \(-0.658156\pi\)
−0.476669 + 0.879083i \(0.658156\pi\)
\(542\) 2.95693 + 5.12156i 0.127011 + 0.219990i
\(543\) −6.91826 16.8627i −0.296891 0.723647i
\(544\) 3.79408 6.57154i 0.162670 0.281752i
\(545\) 1.78462 3.09105i 0.0764446 0.132406i
\(546\) −4.27549 + 5.53321i −0.182974 + 0.236800i
\(547\) 0.364002 + 0.630470i 0.0155636 + 0.0269569i 0.873702 0.486461i \(-0.161712\pi\)
−0.858139 + 0.513418i \(0.828379\pi\)
\(548\) 17.5510 0.749741
\(549\) 35.6814 + 9.81908i 1.52285 + 0.419068i
\(550\) 2.74778 0.117166
\(551\) 19.9765 + 34.6004i 0.851029 + 1.47403i
\(552\) −3.00000 0.405249i −0.127688 0.0172485i
\(553\) 3.14470 5.44677i 0.133726 0.231620i
\(554\) 7.98175 13.8248i 0.339112 0.587360i
\(555\) −12.5444 1.69454i −0.532482 0.0719292i
\(556\) 0.195680 + 0.338928i 0.00829869 + 0.0143738i
\(557\) −9.64426 −0.408640 −0.204320 0.978904i \(-0.565498\pi\)
−0.204320 + 0.978904i \(0.565498\pi\)
\(558\) −22.5138 + 22.2123i −0.953086 + 0.940322i
\(559\) 5.20549 0.220169
\(560\) −0.500000 0.866025i −0.0211289 0.0365963i
\(561\) 22.0814 28.5771i 0.932279 1.20653i
\(562\) −1.60795 + 2.78505i −0.0678272 + 0.117480i
\(563\) −9.84183 + 17.0466i −0.414784 + 0.718427i −0.995406 0.0957467i \(-0.969476\pi\)
0.580622 + 0.814173i \(0.302809\pi\)
\(564\) 0.497893 + 1.21357i 0.0209651 + 0.0511006i
\(565\) −4.04186 7.00071i −0.170042 0.294522i
\(566\) −1.24267 −0.0522332
\(567\) 7.85419 4.39451i 0.329845 0.184552i
\(568\) −0.550985 −0.0231188
\(569\) 12.0928 + 20.9454i 0.506958 + 0.878078i 0.999968 + 0.00805366i \(0.00256359\pi\)
−0.493009 + 0.870024i \(0.664103\pi\)
\(570\) −2.80798 6.84421i −0.117613 0.286673i
\(571\) −6.62125 + 11.4683i −0.277091 + 0.479935i −0.970660 0.240454i \(-0.922704\pi\)
0.693570 + 0.720389i \(0.256037\pi\)
\(572\) 5.54664 9.60706i 0.231917 0.401691i
\(573\) 19.8528 25.6930i 0.829364 1.07334i
\(574\) 1.51859 + 2.63027i 0.0633846 + 0.109785i
\(575\) −1.74778 −0.0728876
\(576\) −2.13557 + 2.10697i −0.0889822 + 0.0877905i
\(577\) 7.45822 0.310490 0.155245 0.987876i \(-0.450383\pi\)
0.155245 + 0.987876i \(0.450383\pi\)
\(578\) −20.2901 35.1434i −0.843956 1.46177i
\(579\) −19.9544 2.69550i −0.829278 0.112021i
\(580\) 4.67709 8.10096i 0.194206 0.336374i
\(581\) 6.18187 10.7073i 0.256467 0.444214i
\(582\) −26.7726 3.61652i −1.10976 0.149909i
\(583\) −9.93869 17.2143i −0.411618 0.712944i
\(584\) −9.07435 −0.375499
\(585\) 11.6774 + 3.21348i 0.482802 + 0.132861i
\(586\) 21.4838 0.887487
\(587\) −4.56514 7.90705i −0.188423 0.326359i 0.756301 0.654223i \(-0.227004\pi\)
−0.944725 + 0.327865i \(0.893671\pi\)
\(588\) −1.05903 + 1.37057i −0.0436737 + 0.0565212i
\(589\) 22.5138 38.9951i 0.927665 1.60676i
\(590\) −0.612210 + 1.06038i −0.0252043 + 0.0436551i
\(591\) −14.9920 36.5417i −0.616687 1.50312i
\(592\) −3.65416 6.32919i −0.150185 0.260128i
\(593\) −34.3068 −1.40881 −0.704405 0.709798i \(-0.748786\pi\)
−0.704405 + 0.709798i \(0.748786\pi\)
\(594\) −11.4147 + 8.57685i −0.468352 + 0.351913i
\(595\) −7.58816 −0.311084
\(596\) 1.61264 + 2.79317i 0.0660562 + 0.114413i
\(597\) −9.76267 23.7957i −0.399560 0.973893i
\(598\) −3.52805 + 6.11076i −0.144273 + 0.249888i
\(599\) −12.9573 + 22.4427i −0.529420 + 0.916982i 0.469991 + 0.882671i \(0.344257\pi\)
−0.999411 + 0.0343111i \(0.989076\pi\)
\(600\) −1.05903 + 1.37057i −0.0432348 + 0.0559531i
\(601\) −11.4055 19.7549i −0.465241 0.805820i 0.533972 0.845502i \(-0.320699\pi\)
−0.999212 + 0.0396821i \(0.987365\pi\)
\(602\) 1.28939 0.0525517
\(603\) −10.0659 38.6056i −0.409916 1.57214i
\(604\) −5.39136 −0.219371
\(605\) −1.72485 2.98752i −0.0701250 0.121460i
\(606\) 27.4007 + 3.70137i 1.11308 + 0.150358i
\(607\) −7.10197 + 12.3010i −0.288260 + 0.499281i −0.973395 0.229136i \(-0.926410\pi\)
0.685134 + 0.728417i \(0.259743\pi\)
\(608\) 2.13557 3.69892i 0.0866089 0.150011i
\(609\) −16.0561 2.16891i −0.650626 0.0878885i
\(610\) 6.16797 + 10.6832i 0.249734 + 0.432552i
\(611\) 3.05748 0.123692
\(612\) 5.74352 + 22.0280i 0.232168 + 0.890430i
\(613\) 16.2418 0.656000 0.328000 0.944678i \(-0.393625\pi\)
0.328000 + 0.944678i \(0.393625\pi\)
\(614\) −15.5685 26.9654i −0.628292 1.08823i
\(615\) 3.21646 4.16265i 0.129700 0.167854i
\(616\) 1.37389 2.37965i 0.0553556 0.0958788i
\(617\) 15.4008 26.6750i 0.620014 1.07390i −0.369469 0.929243i \(-0.620460\pi\)
0.989483 0.144652i \(-0.0462063\pi\)
\(618\) 9.68364 + 23.6031i 0.389533 + 0.949455i
\(619\) 12.9157 + 22.3706i 0.519124 + 0.899150i 0.999753 + 0.0222256i \(0.00707520\pi\)
−0.480629 + 0.876924i \(0.659591\pi\)
\(620\) −10.5423 −0.423388
\(621\) 7.26056 5.45548i 0.291356 0.218921i
\(622\) 25.6995 1.03046
\(623\) 3.51381 + 6.08610i 0.140778 + 0.243834i
\(624\) 2.65416 + 6.46929i 0.106251 + 0.258979i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −11.2375 + 19.4640i −0.449142 + 0.777938i
\(627\) 12.4290 16.0852i 0.496365 0.642381i
\(628\) 11.5696 + 20.0391i 0.461676 + 0.799647i
\(629\) −55.4567 −2.21120
\(630\) 2.89248 + 0.795973i 0.115239 + 0.0317123i
\(631\) −29.6908 −1.18197 −0.590986 0.806682i \(-0.701261\pi\)
−0.590986 + 0.806682i \(0.701261\pi\)
\(632\) −3.14470 5.44677i −0.125089 0.216661i
\(633\) −16.8283 2.27321i −0.668864 0.0903521i
\(634\) −1.18622 + 2.05459i −0.0471107 + 0.0815981i
\(635\) −1.87389 + 3.24567i −0.0743631 + 0.128801i
\(636\) 12.4168 + 1.67730i 0.492359 + 0.0665093i
\(637\) 2.01859 + 3.49629i 0.0799793 + 0.138528i
\(638\) 25.7033 1.01760
\(639\) 1.17667 1.16091i 0.0465482 0.0459249i
\(640\) −1.00000 −0.0395285
\(641\) −15.6961 27.1865i −0.619959 1.07380i −0.989493 0.144583i \(-0.953816\pi\)
0.369534 0.929217i \(-0.379517\pi\)
\(642\) −9.17623 + 11.8756i −0.362157 + 0.468693i
\(643\) −5.37858 + 9.31597i −0.212110 + 0.367386i −0.952375 0.304930i \(-0.901367\pi\)
0.740264 + 0.672316i \(0.234700\pi\)
\(644\) −0.873891 + 1.51362i −0.0344361 + 0.0596451i
\(645\) −0.847684 2.06616i −0.0333775 0.0813550i
\(646\) −16.2051 28.0680i −0.637579 1.10432i
\(647\) −3.10438 −0.122046 −0.0610228 0.998136i \(-0.519436\pi\)
−0.0610228 + 0.998136i \(0.519436\pi\)
\(648\) 0.121334 8.99918i 0.00476645 0.353521i
\(649\) −3.36444 −0.132066
\(650\) 2.01859 + 3.49629i 0.0791755 + 0.137136i
\(651\) 6.93082 + 16.8933i 0.271640 + 0.662100i
\(652\) 2.29408 3.97346i 0.0898431 0.155613i
\(653\) −20.4292 + 35.3844i −0.799457 + 1.38470i 0.120513 + 0.992712i \(0.461546\pi\)
−0.919970 + 0.391988i \(0.871787\pi\)
\(654\) −3.77993 + 4.89187i −0.147807 + 0.191287i
\(655\) 6.25691 + 10.8373i 0.244478 + 0.423448i
\(656\) 3.03717 0.118582
\(657\) 19.3789 19.1194i 0.756044 0.745919i
\(658\) 0.757332 0.0295239
\(659\) 15.4158 + 26.7010i 0.600516 + 1.04012i 0.992743 + 0.120256i \(0.0383714\pi\)
−0.392227 + 0.919868i \(0.628295\pi\)
\(660\) −4.71646 0.637113i −0.183588 0.0247996i
\(661\) 22.5795 39.1088i 0.878239 1.52115i 0.0249676 0.999688i \(-0.492052\pi\)
0.853272 0.521467i \(-0.174615\pi\)
\(662\) 0.649810 1.12550i 0.0252556 0.0437439i
\(663\) 52.5833 + 7.10310i 2.04217 + 0.275862i
\(664\) −6.18187 10.7073i −0.239903 0.415524i
\(665\) −4.27114 −0.165628
\(666\) 21.1391 + 5.81722i 0.819125 + 0.225413i
\(667\) −16.3491 −0.633039
\(668\) 4.74343 + 8.21587i 0.183529 + 0.317881i
\(669\) −2.72180 + 3.52247i −0.105231 + 0.136187i
\(670\) 6.64938 11.5171i 0.256888 0.444943i
\(671\) −16.9482 + 29.3552i −0.654279 + 1.13325i
\(672\) 0.657430 + 1.60243i 0.0253609 + 0.0618151i
\(673\) −2.01893 3.49688i −0.0778239 0.134795i 0.824487 0.565881i \(-0.191464\pi\)
−0.902311 + 0.431086i \(0.858131\pi\)
\(674\) 2.59771 0.100060
\(675\) −0.626109 5.15829i −0.0240989 0.198543i
\(676\) 3.29877 0.126876
\(677\) −13.4770 23.3428i −0.517962 0.897137i −0.999782 0.0208668i \(-0.993357\pi\)
0.481820 0.876270i \(-0.339976\pi\)
\(678\) 5.31448 + 12.9536i 0.204101 + 0.497480i
\(679\) −7.79877 + 13.5079i −0.299289 + 0.518384i
\(680\) −3.79408 + 6.57154i −0.145496 + 0.252007i
\(681\) −9.27410 + 12.0023i −0.355384 + 0.459928i
\(682\) −14.4840 25.0869i −0.554619 0.960629i
\(683\) 43.7302 1.67329 0.836645 0.547745i \(-0.184514\pi\)
0.836645 + 0.547745i \(0.184514\pi\)
\(684\) 3.23285 + 12.3989i 0.123611 + 0.474084i
\(685\) −17.5510 −0.670589
\(686\) 0.500000 + 0.866025i 0.0190901 + 0.0330650i
\(687\) −0.321403 0.0434161i −0.0122623 0.00165643i
\(688\) 0.644696 1.11665i 0.0245788 0.0425717i
\(689\) 14.6024 25.2921i 0.556307 0.963552i
\(690\) 3.00000 + 0.405249i 0.114208 + 0.0154276i
\(691\) −4.10420 7.10869i −0.156131 0.270427i 0.777339 0.629082i \(-0.216569\pi\)
−0.933470 + 0.358655i \(0.883236\pi\)
\(692\) 10.5423 0.400758
\(693\) 2.07981 + 7.97666i 0.0790055 + 0.303008i
\(694\) −12.3264 −0.467903
\(695\) −0.195680 0.338928i −0.00742257 0.0128563i
\(696\) −9.90638 + 12.8205i −0.375500 + 0.485961i
\(697\) 11.5233 19.9589i 0.436475 0.755997i
\(698\) 6.79554 11.7702i 0.257215 0.445509i
\(699\) −10.2424 24.9650i −0.387403 0.944264i
\(700\) 0.500000 + 0.866025i 0.0188982 + 0.0327327i
\(701\) −13.9263 −0.525990 −0.262995 0.964797i \(-0.584710\pi\)
−0.262995 + 0.964797i \(0.584710\pi\)
\(702\) −19.2988 8.22340i −0.728385 0.310372i
\(703\) −31.2149 −1.17729
\(704\) −1.37389 2.37965i −0.0517805 0.0896864i
\(705\) −0.497893 1.21357i −0.0187517 0.0457058i
\(706\) 4.71904 8.17362i 0.177603 0.307618i
\(707\) 7.98175 13.8248i 0.300185 0.519935i
\(708\) 1.29670 1.67815i 0.0487330 0.0630687i
\(709\) −8.99411 15.5783i −0.337781 0.585054i 0.646234 0.763139i \(-0.276343\pi\)
−0.984015 + 0.178086i \(0.943010\pi\)
\(710\) 0.550985 0.0206781
\(711\) 18.1919 + 5.00619i 0.682250 + 0.187747i
\(712\) 7.02762 0.263371
\(713\) 9.21281 + 15.9571i 0.345022 + 0.597596i
\(714\) 13.0248 + 1.75943i 0.487440 + 0.0658448i
\(715\) −5.54664 + 9.60706i −0.207432 + 0.359283i
\(716\) 5.95259 10.3102i 0.222459 0.385310i
\(717\) 8.47225 + 1.14446i 0.316402 + 0.0427405i
\(718\) 7.11255 + 12.3193i 0.265438 + 0.459752i
\(719\) 6.41966 0.239413 0.119706 0.992809i \(-0.461805\pi\)
0.119706 + 0.992809i \(0.461805\pi\)
\(720\) 2.13557 2.10697i 0.0795881 0.0785222i
\(721\) 14.7295 0.548557
\(722\) 0.378666 + 0.655869i 0.0140925 + 0.0244089i
\(723\) −26.7613 + 34.6337i −0.995263 + 1.28804i
\(724\) −5.26159 + 9.11335i −0.195546 + 0.338695i
\(725\) −4.67709 + 8.10096i −0.173703 + 0.300862i
\(726\) 2.26793 + 5.52790i 0.0841708 + 0.205159i
\(727\) 7.48830 + 12.9701i 0.277726 + 0.481035i 0.970819 0.239813i \(-0.0770860\pi\)
−0.693093 + 0.720848i \(0.743753\pi\)
\(728\) 4.03717 0.149628
\(729\) 18.7019 + 19.4740i 0.692663 + 0.721261i
\(730\) 9.07435 0.335857
\(731\) −4.89205 8.47328i −0.180939 0.313396i
\(732\) −8.11002 19.7675i −0.299755 0.730628i
\(733\) −15.0320 + 26.0361i −0.555218 + 0.961666i 0.442668 + 0.896685i \(0.354032\pi\)
−0.997887 + 0.0649806i \(0.979301\pi\)
\(734\) −12.3870 + 21.4549i −0.457213 + 0.791916i
\(735\) 1.05903 1.37057i 0.0390630 0.0505541i
\(736\) 0.873891 + 1.51362i 0.0322121 + 0.0557929i
\(737\) 36.5421 1.34605
\(738\) −6.48610 + 6.39924i −0.238757 + 0.235559i
\(739\) 33.4089 1.22897 0.614483 0.788930i \(-0.289365\pi\)
0.614483 + 0.788930i \(0.289365\pi\)
\(740\) 3.65416 + 6.32919i 0.134330 + 0.232666i
\(741\) 29.5975 + 3.99812i 1.08729 + 0.146875i
\(742\) 3.61699 6.26480i 0.132784 0.229988i
\(743\) −0.710609 + 1.23081i −0.0260697 + 0.0451541i −0.878766 0.477253i \(-0.841633\pi\)
0.852696 + 0.522407i \(0.174966\pi\)
\(744\) 18.0954 + 2.44438i 0.663411 + 0.0896154i
\(745\) −1.61264 2.79317i −0.0590824 0.102334i
\(746\) −16.0000 −0.585802
\(747\) 35.7618 + 9.84120i 1.30846 + 0.360071i
\(748\) −20.8506 −0.762374
\(749\) 4.33237 + 7.50388i 0.158301 + 0.274186i
\(750\) 1.05903 1.37057i 0.0386704 0.0500460i
\(751\) −21.0551 + 36.4684i −0.768310 + 1.33075i 0.170168 + 0.985415i \(0.445569\pi\)
−0.938479 + 0.345338i \(0.887764\pi\)
\(752\) 0.378666 0.655869i 0.0138085 0.0239171i
\(753\) 10.9621 + 26.7191i 0.399480 + 0.973699i
\(754\) 18.8822 + 32.7050i 0.687651 + 1.19105i
\(755\) 5.39136 0.196212
\(756\) −4.78027 2.03692i −0.173857 0.0740821i
\(757\) −22.8765 −0.831461 −0.415731 0.909488i \(-0.636474\pi\)
−0.415731 + 0.909488i \(0.636474\pi\)
\(758\) 12.2285 + 21.1804i 0.444159 + 0.769306i
\(759\) 3.15732 + 7.69571i 0.114604 + 0.279337i
\(760\) −2.13557 + 3.69892i −0.0774653 + 0.134174i
\(761\) −2.87978 + 4.98793i −0.104392 + 0.180812i −0.913490 0.406862i \(-0.866623\pi\)
0.809098 + 0.587674i \(0.199956\pi\)
\(762\) 3.96902 5.13659i 0.143782 0.186079i
\(763\) 1.78462 + 3.09105i 0.0646074 + 0.111903i
\(764\) −18.7462 −0.678215
\(765\) −5.74352 22.0280i −0.207657 0.796424i
\(766\) −0.923419 −0.0333645
\(767\) −2.47160 4.28093i −0.0892443 0.154576i
\(768\) 1.71646 + 0.231865i 0.0619375 + 0.00836669i
\(769\) −15.0886 + 26.1342i −0.544108 + 0.942423i 0.454554 + 0.890719i \(0.349799\pi\)
−0.998662 + 0.0517041i \(0.983535\pi\)
\(770\) −1.37389 + 2.37965i −0.0495116 + 0.0857566i
\(771\) 38.0021 + 5.13344i 1.36861 + 0.184876i
\(772\) 5.81267 + 10.0678i 0.209202 + 0.362349i
\(773\) −34.6156 −1.24504 −0.622518 0.782605i \(-0.713890\pi\)
−0.622518 + 0.782605i \(0.713890\pi\)
\(774\) 0.975948 + 3.74303i 0.0350797 + 0.134541i
\(775\) 10.5423 0.378690
\(776\) 7.79877 + 13.5079i 0.279959 + 0.484904i
\(777\) 7.73974 10.0165i 0.277661 0.359341i
\(778\) 8.68698 15.0463i 0.311443 0.539436i
\(779\) 6.48610 11.2343i 0.232389 0.402509i
\(780\) −2.65416 6.46929i −0.0950341 0.231638i
\(781\) 0.756993 + 1.31115i 0.0270873 + 0.0469166i
\(782\) 13.2624 0.474264
\(783\) −5.85674 48.2516i −0.209303 1.72437i
\(784\) 1.00000 0.0357143
\(785\) −11.5696 20.0391i −0.412936 0.715226i
\(786\) −8.22695 20.0525i −0.293446 0.715250i
\(787\) −17.4530 + 30.2295i −0.622133 + 1.07757i 0.366955 + 0.930239i \(0.380400\pi\)
−0.989088 + 0.147327i \(0.952933\pi\)
\(788\) −11.4019 + 19.7487i −0.406177 + 0.703520i
\(789\) 1.92969 2.49735i 0.0686988 0.0889080i
\(790\) 3.14470 + 5.44677i 0.111883 + 0.193787i
\(791\) 8.08372 0.287424
\(792\) 7.94790 + 2.18716i 0.282416 + 0.0777174i
\(793\) −49.8023 −1.76853
\(794\) 14.2281 + 24.6438i 0.504936 + 0.874574i
\(795\) −12.4168 1.67730i −0.440380 0.0594878i
\(796\) −7.42488 + 12.8603i −0.263168 + 0.455820i
\(797\) 22.6403 39.2141i 0.801959 1.38903i −0.116366 0.993206i \(-0.537124\pi\)
0.918325 0.395828i \(-0.129542\pi\)
\(798\) 7.33125 + 0.990327i 0.259524 + 0.0350572i
\(799\) −2.87338 4.97684i −0.101653 0.176068i
\(800\) 1.00000 0.0353553
\(801\) −15.0080 + 14.8070i −0.530281 + 0.523180i
\(802\) 15.1042 0.533348
\(803\) 12.4672 + 21.5938i 0.439957 + 0.762027i
\(804\) −14.0838 + 18.2268i −0.496698 + 0.642811i
\(805\) 0.873891 1.51362i 0.0308006 0.0533482i
\(806\) 21.2805 36.8589i 0.749574 1.29830i
\(807\) 4.11656 + 10.0338i 0.144910 + 0.353206i
\(808\) −7.98175 13.8248i −0.280797 0.486355i
\(809\) 10.1482 0.356791 0.178396 0.983959i \(-0.442909\pi\)
0.178396 + 0.983959i \(0.442909\pi\)
\(810\) −0.121334 + 8.99918i −0.00426324 + 0.316199i
\(811\) −5.76671 −0.202496 −0.101248 0.994861i \(-0.532284\pi\)
−0.101248 + 0.994861i \(0.532284\pi\)
\(812\) 4.67709 + 8.10096i 0.164134 + 0.284288i
\(813\) 3.88795 + 9.47657i 0.136357 + 0.332358i
\(814\) −10.0408 + 17.3912i −0.351931 + 0.609562i
\(815\) −2.29408 + 3.97346i −0.0803581 + 0.139184i
\(816\) 8.03610 10.4001i 0.281320 0.364075i
\(817\) −2.75359 4.76935i −0.0963358 0.166859i
\(818\) −32.2513 −1.12764
\(819\) −8.62167 + 8.50621i −0.301266 + 0.297231i
\(820\) −3.03717 −0.106063
\(821\) 4.68332 + 8.11176i 0.163449 + 0.283102i 0.936103 0.351725i \(-0.114405\pi\)
−0.772654 + 0.634827i \(0.781071\pi\)
\(822\) 30.1256 + 4.06945i 1.05075 + 0.141938i
\(823\) 25.5088 44.1825i 0.889180 1.54010i 0.0483333 0.998831i \(-0.484609\pi\)
0.840847 0.541273i \(-0.182058\pi\)
\(824\) 7.36477 12.7562i 0.256564 0.444382i
\(825\) 4.71646 + 0.637113i 0.164206 + 0.0221814i
\(826\) −0.612210 1.06038i −0.0213015 0.0368953i
\(827\) 20.4582 0.711402 0.355701 0.934600i \(-0.384242\pi\)
0.355701 + 0.934600i \(0.384242\pi\)
\(828\) −5.05542 1.39119i −0.175688 0.0483471i
\(829\) −36.5801 −1.27048 −0.635240 0.772314i \(-0.719099\pi\)
−0.635240 + 0.772314i \(0.719099\pi\)
\(830\) 6.18187 + 10.7073i 0.214576 + 0.371656i
\(831\) 16.9059 21.8790i 0.586457 0.758976i
\(832\) 2.01859 3.49629i 0.0699819 0.121212i
\(833\) 3.79408 6.57154i 0.131457 0.227690i
\(834\) 0.257292 + 0.627128i 0.00890929 + 0.0217157i
\(835\) −4.74343 8.21587i −0.164153 0.284322i
\(836\) −11.7362 −0.405904
\(837\) −43.7943 + 32.9064i −1.51375 + 1.13741i
\(838\) 6.62601 0.228892
\(839\) 6.89214 + 11.9375i 0.237943 + 0.412129i 0.960124 0.279575i \(-0.0901935\pi\)
−0.722181 + 0.691704i \(0.756860\pi\)
\(840\) −0.657430 1.60243i −0.0226835 0.0552891i
\(841\) −29.2504 + 50.6632i −1.00863 + 1.74701i
\(842\) 0.335601 0.581277i 0.0115656 0.0200321i
\(843\) −3.40574 + 4.40760i −0.117300 + 0.151806i
\(844\) 4.90203 + 8.49056i 0.168735 + 0.292257i
\(845\) −3.29877 −0.113481
\(846\) 0.573229 + 2.19849i 0.0197080 + 0.0755858i
\(847\) 3.44969 0.118533
\(848\) −3.61699 6.26480i −0.124208 0.215134i
\(849\) −2.13299 0.288131i −0.0732041 0.00988862i
\(850\) 3.79408 6.57154i 0.130136 0.225402i
\(851\) 6.38667 11.0620i 0.218932 0.379202i
\(852\) −0.945744 0.127754i −0.0324006 0.00437677i
\(853\) 9.06480 + 15.7007i 0.310373 + 0.537581i 0.978443 0.206517i \(-0.0662128\pi\)
−0.668070 + 0.744098i \(0.732879\pi\)
\(854\) −12.3359 −0.422127
\(855\) −3.23285 12.3989i −0.110561 0.424033i
\(856\) 8.66474 0.296155
\(857\) −10.9993 19.0514i −0.375729 0.650782i 0.614707 0.788756i \(-0.289274\pi\)
−0.990436 + 0.137974i \(0.955941\pi\)
\(858\) 11.7481 15.2041i 0.401074 0.519058i
\(859\) −1.15364 + 1.99817i −0.0393619 + 0.0681767i −0.885035 0.465524i \(-0.845866\pi\)
0.845673 + 0.533701i \(0.179199\pi\)
\(860\) −0.644696 + 1.11665i −0.0219839 + 0.0380773i
\(861\) 1.99673 + 4.86686i 0.0680483 + 0.165862i
\(862\) −12.6957 21.9896i −0.432417 0.748967i
\(863\) −56.2987 −1.91643 −0.958216 0.286047i \(-0.907659\pi\)
−0.958216 + 0.286047i \(0.907659\pi\)
\(864\) −4.15416 + 3.12137i −0.141327 + 0.106191i
\(865\) −10.5423 −0.358449
\(866\) −15.5688 26.9659i −0.529049 0.916340i
\(867\) −26.6786 65.0269i −0.906053 2.20843i
\(868\) 5.27114 9.12989i 0.178914 0.309889i
\(869\) −8.64094 + 14.9665i −0.293124 + 0.507705i
\(870\) 9.90638 12.8205i 0.335858 0.434657i
\(871\) 26.8447 + 46.4964i 0.909598 + 1.57547i
\(872\) 3.56923 0.120869
\(873\) −45.1155 12.4152i −1.52693 0.420191i
\(874\) 7.46503 0.252508
\(875\) −0.500000 0.866025i −0.0169031 0.0292770i
\(876\) −15.5758 2.10402i −0.526256 0.0710882i
\(877\) −18.4754 + 32.0004i −0.623871 + 1.08058i 0.364887 + 0.931052i \(0.381108\pi\)
−0.988758 + 0.149525i \(0.952226\pi\)
\(878\) 0.368777 0.638740i 0.0124456 0.0215564i
\(879\) 36.8761 + 4.98133i 1.24380 + 0.168016i
\(880\) 1.37389 + 2.37965i 0.0463139 + 0.0802180i
\(881\) −41.7471 −1.40649 −0.703247 0.710945i \(-0.748267\pi\)
−0.703247 + 0.710945i \(0.748267\pi\)
\(882\) −2.13557 + 2.10697i −0.0719084 + 0.0709455i
\(883\) −5.69236 −0.191563 −0.0957816 0.995402i \(-0.530535\pi\)
−0.0957816 + 0.995402i \(0.530535\pi\)
\(884\) −15.3174 26.5304i −0.515178 0.892315i
\(885\) −1.29670 + 1.67815i −0.0435881 + 0.0564104i
\(886\) −13.5499 + 23.4691i −0.455217 + 0.788458i
\(887\) −18.9052 + 32.7447i −0.634774 + 1.09946i 0.351790 + 0.936079i \(0.385573\pi\)
−0.986563 + 0.163381i \(0.947760\pi\)
\(888\) −4.80471 11.7111i −0.161235 0.392998i
\(889\) −1.87389 3.24567i −0.0628483 0.108856i
\(890\) −7.02762 −0.235566
\(891\) −21.5816 + 12.0752i −0.723011 + 0.404533i
\(892\) 2.57008 0.0860528
\(893\) −1.61734 2.80131i −0.0541221 0.0937423i
\(894\) 2.12039 + 5.16828i 0.0709165 + 0.172853i
\(895\) −5.95259 + 10.3102i −0.198973 + 0.344631i
\(896\) 0.500000 0.866025i 0.0167038 0.0289319i
\(897\) −7.47263 + 9.67085i −0.249504 + 0.322900i
\(898\) 2.58459 + 4.47664i 0.0862488 + 0.149387i
\(899\) 98.6145 3.28898
\(900\) −2.13557 + 2.10697i −0.0711857 + 0.0702324i
\(901\) −54.8925 −1.82873
\(902\) −4.17274 7.22741i −0.138937 0.240646i
\(903\) 2.21319 + 0.298964i 0.0736503 + 0.00994890i
\(904\) 4.04186 7.00071i 0.134430 0.232840i
\(905\) 5.26159 9.11335i 0.174901 0.302938i
\(906\) −9.25406 1.25007i −0.307446 0.0415307i
\(907\) −20.6779 35.8151i −0.686597 1.18922i −0.972932 0.231091i \(-0.925770\pi\)
0.286335 0.958130i \(-0.407563\pi\)
\(908\) 8.75716 0.290616
\(909\) 46.1741 + 12.7065i 1.53150 + 0.421449i
\(910\) −4.03717 −0.133831
\(911\) −8.48167 14.6907i −0.281010 0.486724i 0.690624 0.723214i \(-0.257336\pi\)
−0.971634 + 0.236491i \(0.924003\pi\)
\(912\) 4.52327 5.85389i 0.149781 0.193842i
\(913\) −16.9864 + 29.4214i −0.562169 + 0.973705i
\(914\) 2.56446 4.44177i 0.0848247 0.146921i
\(915\) 8.11002 + 19.7675i 0.268109 + 0.653493i
\(916\) 0.0936237 + 0.162161i 0.00309341 + 0.00535795i
\(917\) −12.5138 −0.413242
\(918\) 4.75101 + 39.1419i 0.156807 + 1.29188i
\(919\) −3.49350 −0.115240 −0.0576200 0.998339i \(-0.518351\pi\)
−0.0576200 + 0.998339i \(0.518351\pi\)
\(920\) −0.873891 1.51362i −0.0288113 0.0499027i
\(921\) −20.4703 49.8948i −0.674520 1.64409i
\(922\) 6.54040 11.3283i 0.215397 0.373078i
\(923\) −1.11221 + 1.92640i −0.0366088 + 0.0634084i
\(924\) 2.90999 3.76602i 0.0957315 0.123893i
\(925\) −3.65416 6.32919i −0.120148 0.208102i
\(926\) −19.5334 −0.641908
\(927\) 11.1489 + 42.7590i 0.366177 + 1.40439i
\(928\) 9.35419 0.307066
\(929\) 9.76603 + 16.9153i 0.320413 + 0.554972i 0.980573 0.196153i \(-0.0628450\pi\)
−0.660160 + 0.751125i \(0.729512\pi\)
\(930\) −18.0954 2.44438i −0.593372 0.0801545i
\(931\) 2.13557 3.69892i 0.0699905 0.121227i
\(932\) −7.78973 + 13.4922i −0.255161 + 0.441952i
\(933\) 44.1122 + 5.95881i 1.44417 + 0.195083i
\(934\) 0.255449 + 0.442451i 0.00835856 + 0.0144775i
\(935\) 20.8506 0.681888
\(936\) 3.05576 + 11.7197i 0.0998806 + 0.383070i
\(937\) −21.5129 −0.702797 −0.351398 0.936226i \(-0.614294\pi\)
−0.351398 + 0.936226i \(0.614294\pi\)
\(938\) 6.64938 + 11.5171i 0.217110 + 0.376046i
\(939\) −23.8018 + 30.8036i −0.776743 + 1.00524i
\(940\) −0.378666 + 0.655869i −0.0123507 + 0.0213921i
\(941\) −20.3550 + 35.2560i −0.663555 + 1.14931i 0.316119 + 0.948719i \(0.397620\pi\)
−0.979675 + 0.200592i \(0.935713\pi\)
\(942\) 15.2124 + 37.0789i 0.495646 + 1.20810i
\(943\) 2.65416 + 4.59714i 0.0864313 + 0.149703i
\(944\) −1.22442 −0.0398515
\(945\) 4.78027 + 2.03692i 0.155502 + 0.0662610i
\(946\) −3.54297 −0.115192
\(947\) −25.0156 43.3282i −0.812897 1.40798i −0.910828 0.412786i \(-0.864556\pi\)
0.0979313 0.995193i \(-0.468777\pi\)
\(948\) −4.13483 10.0783i −0.134293 0.327329i
\(949\) −18.3174 + 31.7266i −0.594606 + 1.02989i
\(950\) 2.13557 3.69892i 0.0692871 0.120009i
\(951\) −2.51248 + 3.25158i −0.0814728 + 0.105440i
\(952\) −3.79408 6.57154i −0.122967 0.212985i
\(953\) −27.4321 −0.888614 −0.444307 0.895875i \(-0.646550\pi\)
−0.444307 + 0.895875i \(0.646550\pi\)
\(954\) 20.9241 + 5.75805i 0.677443 + 0.186424i
\(955\) 18.7462 0.606614
\(956\) −2.46794 4.27460i −0.0798189 0.138250i
\(957\) 44.1187 + 5.95968i 1.42615 + 0.192649i
\(958\) −4.17283 + 7.22756i −0.134818 + 0.233512i
\(959\) 8.77549 15.1996i 0.283375 0.490821i
\(960\) −1.71646 0.231865i −0.0553985 0.00748340i
\(961\) −40.0699 69.4031i −1.29258 2.23881i
\(962\) −29.5049 −0.951277
\(963\) −18.5042 + 18.2564i −0.596289 + 0.588303i
\(964\) 25.2696 0.813879
\(965\) −5.81267 10.0678i −0.187116 0.324095i
\(966\) −1.85096 + 2.39545i −0.0595535 + 0.0770724i
\(967\) 13.1603 22.7943i 0.423207 0.733016i −0.573044 0.819524i \(-0.694238\pi\)
0.996251 + 0.0865087i \(0.0275710\pi\)
\(968\) 1.72485 2.98752i 0.0554387 0.0960226i
\(969\) −21.3074 51.9350i −0.684492 1.66839i
\(970\) −7.79877 13.5079i −0.250403 0.433711i
\(971\) 12.4301 0.398901 0.199450 0.979908i \(-0.436084\pi\)
0.199450 + 0.979908i \(0.436084\pi\)
\(972\) 2.29486 15.4186i 0.0736076 0.494552i
\(973\) 0.391360 0.0125464
\(974\) −10.9423 18.9527i −0.350615 0.607284i
\(975\) 2.65416 + 6.46929i 0.0850011 + 0.207183i
\(976\) −6.16797 + 10.6832i −0.197432 + 0.341962i
\(977\) −11.3914 + 19.7306i −0.364445 + 0.631237i −0.988687 0.149994i \(-0.952075\pi\)
0.624242 + 0.781231i \(0.285408\pi\)
\(978\) 4.85900 6.28838i 0.155374 0.201080i
\(979\) −9.65519 16.7233i −0.308581 0.534478i
\(980\) −1.00000 −0.0319438
\(981\) −7.62235 + 7.52027i −0.243363 + 0.240104i
\(982\) −28.4205 −0.906935
\(983\) 26.6220 + 46.1107i 0.849110 + 1.47070i 0.882003 + 0.471243i \(0.156195\pi\)
−0.0328929 + 0.999459i \(0.510472\pi\)
\(984\) 5.21319 + 0.704213i 0.166190 + 0.0224495i
\(985\) 11.4019 19.7487i 0.363296 0.629247i
\(986\) 35.4905 61.4714i 1.13025 1.95765i
\(987\) 1.29993 + 0.175599i 0.0413773 + 0.00558936i
\(988\) −8.62167 14.9332i −0.274292 0.475088i
\(989\) 2.25357 0.0716595
\(990\) −7.94790 2.18716i −0.252601 0.0695125i
\(991\) −33.2993 −1.05779 −0.528893 0.848688i \(-0.677393\pi\)
−0.528893 + 0.848688i \(0.677393\pi\)
\(992\) −5.27114 9.12989i −0.167359 0.289874i
\(993\) 1.37634 1.78121i 0.0436767 0.0565251i
\(994\) −0.275492 + 0.477167i −0.00873809 + 0.0151348i
\(995\) 7.42488 12.8603i 0.235384 0.407698i
\(996\) −8.12829 19.8120i −0.257555 0.627768i
\(997\) 4.82230 + 8.35247i 0.152724 + 0.264525i 0.932228 0.361872i \(-0.117862\pi\)
−0.779504 + 0.626397i \(0.784529\pi\)
\(998\) −15.4197 −0.488101
\(999\) 34.9357 + 14.8865i 1.10532 + 0.470987i
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 630.2.j.l.211.3 8
3.2 odd 2 1890.2.j.l.631.3 8
9.2 odd 6 1890.2.j.l.1261.3 8
9.4 even 3 5670.2.a.bw.1.3 4
9.5 odd 6 5670.2.a.bv.1.2 4
9.7 even 3 inner 630.2.j.l.421.3 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.j.l.211.3 8 1.1 even 1 trivial
630.2.j.l.421.3 yes 8 9.7 even 3 inner
1890.2.j.l.631.3 8 3.2 odd 2
1890.2.j.l.1261.3 8 9.2 odd 6
5670.2.a.bv.1.2 4 9.5 odd 6
5670.2.a.bw.1.3 4 9.4 even 3