Properties

Label 930.2.z.c.349.1
Level $930$
Weight $2$
Character 930.349
Analytic conductor $7.426$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,2,Mod(109,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 5, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.z (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 349.1
Character \(\chi\) \(=\) 930.349
Dual form 930.2.z.c.469.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.951057 - 0.309017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.618034 - 2.14896i) q^{5} -1.00000 q^{6} +(-1.53347 + 2.11064i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(-0.951057 - 0.309017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.618034 - 2.14896i) q^{5} -1.00000 q^{6} +(-1.53347 + 2.11064i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-1.25185 + 1.85280i) q^{10} +(-1.18111 - 0.858129i) q^{11} +(0.951057 + 0.309017i) q^{12} +(-4.52499 + 1.47026i) q^{13} +(2.11064 - 1.53347i) q^{14} +(-0.0762803 - 2.23477i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.98439 - 4.10766i) q^{17} +(-0.951057 + 0.309017i) q^{18} +(0.574481 - 1.76807i) q^{19} +(1.76313 - 1.37527i) q^{20} +(-0.806193 + 2.48121i) q^{21} +(0.858129 + 1.18111i) q^{22} +(-2.59484 - 3.57150i) q^{23} +(-0.809017 - 0.587785i) q^{24} +(-4.23607 - 2.65626i) q^{25} +4.75786 q^{26} +(0.587785 - 0.809017i) q^{27} +(-2.48121 + 0.806193i) q^{28} +(0.334189 - 1.02853i) q^{29} +(-0.618034 + 2.14896i) q^{30} +(-1.69375 - 5.30389i) q^{31} -1.00000i q^{32} +(-1.38848 - 0.451145i) q^{33} +(1.56899 + 4.82884i) q^{34} +(3.58795 + 4.59982i) q^{35} +1.00000 q^{36} -4.67804i q^{37} +(-1.09273 + 1.50401i) q^{38} +(-3.84919 + 2.79660i) q^{39} +(-2.10182 + 0.763128i) q^{40} +(-2.57073 + 7.91189i) q^{41} +(1.53347 - 2.11064i) q^{42} +(-4.48308 - 1.45664i) q^{43} +(-0.451145 - 1.38848i) q^{44} +(-0.763128 - 2.10182i) q^{45} +(1.36419 + 4.19855i) q^{46} +(9.18597 - 2.98470i) q^{47} +(0.587785 + 0.809017i) q^{48} +(0.0598438 + 0.184180i) q^{49} +(3.20791 + 3.83527i) q^{50} +(-4.10766 - 2.98439i) q^{51} +(-4.52499 - 1.47026i) q^{52} +(0.866223 + 1.19225i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(-2.57405 + 2.00781i) q^{55} +2.60890 q^{56} -1.85906i q^{57} +(-0.635666 + 0.874919i) q^{58} +(-1.33847 - 4.11940i) q^{59} +(1.25185 - 1.85280i) q^{60} -0.894288 q^{61} +(-0.0281347 + 5.56769i) q^{62} +2.60890i q^{63} +(-0.309017 + 0.951057i) q^{64} +(0.362931 + 10.6327i) q^{65} +(1.18111 + 0.858129i) q^{66} -2.19683i q^{67} -5.07734i q^{68} +(-3.57150 - 2.59484i) q^{69} +(-1.99092 - 5.48342i) q^{70} +(9.22722 - 6.70397i) q^{71} +(-0.951057 - 0.309017i) q^{72} +(-7.37431 + 10.1499i) q^{73} +(-1.44559 + 4.44908i) q^{74} +(-4.84957 - 1.21724i) q^{75} +(1.50401 - 1.09273i) q^{76} +(3.62240 - 1.17699i) q^{77} +(4.52499 - 1.47026i) q^{78} +(-2.95125 + 2.14421i) q^{79} +(2.23477 - 0.0762803i) q^{80} +(0.309017 - 0.951057i) q^{81} +(4.88982 - 6.73026i) q^{82} +(-1.39630 - 0.453685i) q^{83} +(-2.11064 + 1.53347i) q^{84} +(-10.6716 + 3.87466i) q^{85} +(3.81353 + 2.77069i) q^{86} -1.08146i q^{87} +1.45994i q^{88} +(-1.40650 - 1.02188i) q^{89} +(0.0762803 + 2.23477i) q^{90} +(3.83575 - 11.8052i) q^{91} -4.41461i q^{92} +(-3.24985 - 4.52090i) q^{93} -9.65870 q^{94} +(-3.44446 - 2.32726i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(1.18626 - 1.63274i) q^{97} -0.193659i q^{98} -1.45994 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 8 q^{4} - 16 q^{5} - 32 q^{6} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 8 q^{4} - 16 q^{5} - 32 q^{6} + 8 q^{9} - 4 q^{11} - 4 q^{14} - 8 q^{16} - 16 q^{19} + 16 q^{20} - 4 q^{21} - 8 q^{24} - 64 q^{25} - 16 q^{26} + 4 q^{29} + 16 q^{30} - 24 q^{31} - 12 q^{34} + 32 q^{36} + 4 q^{39} - 48 q^{41} + 4 q^{44} + 16 q^{45} + 8 q^{46} - 28 q^{49} + 8 q^{51} - 8 q^{54} - 8 q^{55} - 16 q^{56} - 8 q^{59} + 32 q^{61} + 8 q^{64} - 8 q^{65} + 4 q^{66} - 12 q^{69} - 8 q^{70} + 32 q^{71} + 4 q^{74} - 24 q^{76} + 64 q^{79} + 24 q^{80} - 8 q^{81} + 4 q^{84} + 28 q^{85} + 84 q^{86} - 128 q^{89} - 28 q^{91} + 40 q^{94} + 8 q^{95} + 8 q^{96} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.951057 0.309017i −0.672499 0.218508i
\(3\) 0.951057 0.309017i 0.549093 0.178411i
\(4\) 0.809017 + 0.587785i 0.404508 + 0.293893i
\(5\) 0.618034 2.14896i 0.276393 0.961045i
\(6\) −1.00000 −0.408248
\(7\) −1.53347 + 2.11064i −0.579598 + 0.797748i −0.993651 0.112505i \(-0.964113\pi\)
0.414054 + 0.910252i \(0.364113\pi\)
\(8\) −0.587785 0.809017i −0.207813 0.286031i
\(9\) 0.809017 0.587785i 0.269672 0.195928i
\(10\) −1.25185 + 1.85280i −0.395870 + 0.585907i
\(11\) −1.18111 0.858129i −0.356119 0.258735i 0.395313 0.918547i \(-0.370636\pi\)
−0.751431 + 0.659811i \(0.770636\pi\)
\(12\) 0.951057 + 0.309017i 0.274546 + 0.0892055i
\(13\) −4.52499 + 1.47026i −1.25501 + 0.407776i −0.859713 0.510778i \(-0.829357\pi\)
−0.395294 + 0.918555i \(0.629357\pi\)
\(14\) 2.11064 1.53347i 0.564093 0.409837i
\(15\) −0.0762803 2.23477i −0.0196955 0.577014i
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) −2.98439 4.10766i −0.723820 0.996253i −0.999388 0.0349716i \(-0.988866\pi\)
0.275568 0.961282i \(-0.411134\pi\)
\(18\) −0.951057 + 0.309017i −0.224166 + 0.0728360i
\(19\) 0.574481 1.76807i 0.131795 0.405623i −0.863283 0.504720i \(-0.831596\pi\)
0.995078 + 0.0990975i \(0.0315956\pi\)
\(20\) 1.76313 1.37527i 0.394247 0.307521i
\(21\) −0.806193 + 2.48121i −0.175926 + 0.541444i
\(22\) 0.858129 + 1.18111i 0.182954 + 0.251814i
\(23\) −2.59484 3.57150i −0.541062 0.744708i 0.447703 0.894182i \(-0.352242\pi\)
−0.988766 + 0.149474i \(0.952242\pi\)
\(24\) −0.809017 0.587785i −0.165140 0.119981i
\(25\) −4.23607 2.65626i −0.847214 0.531252i
\(26\) 4.75786 0.933093
\(27\) 0.587785 0.809017i 0.113119 0.155695i
\(28\) −2.48121 + 0.806193i −0.468904 + 0.152356i
\(29\) 0.334189 1.02853i 0.0620574 0.190993i −0.915221 0.402952i \(-0.867984\pi\)
0.977279 + 0.211959i \(0.0679842\pi\)
\(30\) −0.618034 + 2.14896i −0.112837 + 0.392345i
\(31\) −1.69375 5.30389i −0.304207 0.952606i
\(32\) 1.00000i 0.176777i
\(33\) −1.38848 0.451145i −0.241704 0.0785342i
\(34\) 1.56899 + 4.82884i 0.269079 + 0.828139i
\(35\) 3.58795 + 4.59982i 0.606474 + 0.777511i
\(36\) 1.00000 0.166667
\(37\) 4.67804i 0.769064i −0.923112 0.384532i \(-0.874363\pi\)
0.923112 0.384532i \(-0.125637\pi\)
\(38\) −1.09273 + 1.50401i −0.177264 + 0.243983i
\(39\) −3.84919 + 2.79660i −0.616363 + 0.447814i
\(40\) −2.10182 + 0.763128i −0.332327 + 0.120661i
\(41\) −2.57073 + 7.91189i −0.401481 + 1.23563i 0.522318 + 0.852751i \(0.325068\pi\)
−0.923798 + 0.382879i \(0.874932\pi\)
\(42\) 1.53347 2.11064i 0.236620 0.325679i
\(43\) −4.48308 1.45664i −0.683663 0.222136i −0.0534646 0.998570i \(-0.517026\pi\)
−0.630198 + 0.776434i \(0.717026\pi\)
\(44\) −0.451145 1.38848i −0.0680126 0.209321i
\(45\) −0.763128 2.10182i −0.113760 0.313320i
\(46\) 1.36419 + 4.19855i 0.201139 + 0.619042i
\(47\) 9.18597 2.98470i 1.33991 0.435364i 0.450624 0.892714i \(-0.351201\pi\)
0.889287 + 0.457350i \(0.151201\pi\)
\(48\) 0.587785 + 0.809017i 0.0848395 + 0.116772i
\(49\) 0.0598438 + 0.184180i 0.00854912 + 0.0263115i
\(50\) 3.20791 + 3.83527i 0.453667 + 0.542389i
\(51\) −4.10766 2.98439i −0.575187 0.417898i
\(52\) −4.52499 1.47026i −0.627503 0.203888i
\(53\) 0.866223 + 1.19225i 0.118985 + 0.163769i 0.864355 0.502882i \(-0.167727\pi\)
−0.745370 + 0.666651i \(0.767727\pi\)
\(54\) −0.809017 + 0.587785i −0.110093 + 0.0799874i
\(55\) −2.57405 + 2.00781i −0.347085 + 0.270733i
\(56\) 2.60890 0.348628
\(57\) 1.85906i 0.246238i
\(58\) −0.635666 + 0.874919i −0.0834670 + 0.114883i
\(59\) −1.33847 4.11940i −0.174254 0.536300i 0.825344 0.564630i \(-0.190981\pi\)
−0.999599 + 0.0283300i \(0.990981\pi\)
\(60\) 1.25185 1.85280i 0.161613 0.239196i
\(61\) −0.894288 −0.114502 −0.0572509 0.998360i \(-0.518234\pi\)
−0.0572509 + 0.998360i \(0.518234\pi\)
\(62\) −0.0281347 + 5.56769i −0.00357311 + 0.707098i
\(63\) 2.60890i 0.328690i
\(64\) −0.309017 + 0.951057i −0.0386271 + 0.118882i
\(65\) 0.362931 + 10.6327i 0.0450160 + 1.31882i
\(66\) 1.18111 + 0.858129i 0.145385 + 0.105628i
\(67\) 2.19683i 0.268385i −0.990955 0.134193i \(-0.957156\pi\)
0.990955 0.134193i \(-0.0428441\pi\)
\(68\) 5.07734i 0.615718i
\(69\) −3.57150 2.59484i −0.429958 0.312382i
\(70\) −1.99092 5.48342i −0.237961 0.655395i
\(71\) 9.22722 6.70397i 1.09507 0.795615i 0.114822 0.993386i \(-0.463370\pi\)
0.980248 + 0.197771i \(0.0633703\pi\)
\(72\) −0.951057 0.309017i −0.112083 0.0364180i
\(73\) −7.37431 + 10.1499i −0.863098 + 1.18795i 0.117724 + 0.993046i \(0.462440\pi\)
−0.980822 + 0.194906i \(0.937560\pi\)
\(74\) −1.44559 + 4.44908i −0.168047 + 0.517195i
\(75\) −4.84957 1.21724i −0.559980 0.140555i
\(76\) 1.50401 1.09273i 0.172522 0.125344i
\(77\) 3.62240 1.17699i 0.412811 0.134130i
\(78\) 4.52499 1.47026i 0.512354 0.166474i
\(79\) −2.95125 + 2.14421i −0.332042 + 0.241242i −0.741296 0.671178i \(-0.765789\pi\)
0.409255 + 0.912420i \(0.365789\pi\)
\(80\) 2.23477 0.0762803i 0.249854 0.00852839i
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 4.88982 6.73026i 0.539990 0.743233i
\(83\) −1.39630 0.453685i −0.153264 0.0497984i 0.231380 0.972863i \(-0.425676\pi\)
−0.384644 + 0.923065i \(0.625676\pi\)
\(84\) −2.11064 + 1.53347i −0.230290 + 0.167315i
\(85\) −10.6716 + 3.87466i −1.15750 + 0.420266i
\(86\) 3.81353 + 2.77069i 0.411224 + 0.298772i
\(87\) 1.08146i 0.115945i
\(88\) 1.45994i 0.155630i
\(89\) −1.40650 1.02188i −0.149089 0.108319i 0.510740 0.859735i \(-0.329371\pi\)
−0.659829 + 0.751416i \(0.729371\pi\)
\(90\) 0.0762803 + 2.23477i 0.00804065 + 0.235565i
\(91\) 3.83575 11.8052i 0.402096 1.23752i
\(92\) 4.41461i 0.460255i
\(93\) −3.24985 4.52090i −0.336993 0.468795i
\(94\) −9.65870 −0.996219
\(95\) −3.44446 2.32726i −0.353395 0.238772i
\(96\) −0.309017 0.951057i −0.0315389 0.0970668i
\(97\) 1.18626 1.63274i 0.120446 0.165780i −0.744536 0.667582i \(-0.767329\pi\)
0.864983 + 0.501802i \(0.167329\pi\)
\(98\) 0.193659i 0.0195625i
\(99\) −1.45994 −0.146729
\(100\) −1.86574 4.63886i −0.186574 0.463886i
\(101\) 5.04616 3.66625i 0.502112 0.364806i −0.307711 0.951480i \(-0.599563\pi\)
0.809823 + 0.586674i \(0.199563\pi\)
\(102\) 2.98439 + 4.10766i 0.295498 + 0.406719i
\(103\) 2.87221 + 0.933237i 0.283007 + 0.0919546i 0.447081 0.894493i \(-0.352464\pi\)
−0.164074 + 0.986448i \(0.552464\pi\)
\(104\) 3.84919 + 2.79660i 0.377444 + 0.274229i
\(105\) 4.83376 + 3.26595i 0.471727 + 0.318724i
\(106\) −0.455400 1.40158i −0.0442324 0.136133i
\(107\) −1.39348 1.91797i −0.134713 0.185417i 0.736331 0.676622i \(-0.236557\pi\)
−0.871044 + 0.491205i \(0.836557\pi\)
\(108\) 0.951057 0.309017i 0.0915155 0.0297352i
\(109\) −0.533694 1.64254i −0.0511186 0.157327i 0.922238 0.386622i \(-0.126358\pi\)
−0.973357 + 0.229295i \(0.926358\pi\)
\(110\) 3.06852 1.11412i 0.292572 0.106227i
\(111\) −1.44559 4.44908i −0.137210 0.422288i
\(112\) −2.48121 0.806193i −0.234452 0.0761781i
\(113\) −9.36957 + 12.8961i −0.881415 + 1.21316i 0.0946114 + 0.995514i \(0.469839\pi\)
−0.976027 + 0.217650i \(0.930161\pi\)
\(114\) −0.574481 + 1.76807i −0.0538050 + 0.165595i
\(115\) −9.27871 + 3.36891i −0.865244 + 0.314153i
\(116\) 0.874919 0.635666i 0.0812342 0.0590201i
\(117\) −2.79660 + 3.84919i −0.258546 + 0.355858i
\(118\) 4.33139i 0.398737i
\(119\) 13.2463 1.21428
\(120\) −1.76313 + 1.37527i −0.160951 + 0.125545i
\(121\) −2.74054 8.43453i −0.249140 0.766775i
\(122\) 0.850518 + 0.276350i 0.0770023 + 0.0250196i
\(123\) 8.31906i 0.750104i
\(124\) 1.74727 5.28650i 0.156909 0.474741i
\(125\) −8.32624 + 7.46149i −0.744721 + 0.667376i
\(126\) 0.806193 2.48121i 0.0718214 0.221044i
\(127\) 2.33670 0.759239i 0.207348 0.0673716i −0.203501 0.979075i \(-0.565232\pi\)
0.410850 + 0.911703i \(0.365232\pi\)
\(128\) 0.587785 0.809017i 0.0519534 0.0715077i
\(129\) −4.71379 −0.415026
\(130\) 2.94052 10.2245i 0.257900 0.896744i
\(131\) −12.2671 8.91259i −1.07178 0.778697i −0.0955522 0.995424i \(-0.530462\pi\)
−0.976232 + 0.216728i \(0.930462\pi\)
\(132\) −0.858129 1.18111i −0.0746905 0.102803i
\(133\) 2.85081 + 3.92381i 0.247197 + 0.340237i
\(134\) −0.678857 + 2.08931i −0.0586443 + 0.180489i
\(135\) −1.37527 1.76313i −0.118365 0.151746i
\(136\) −1.56899 + 4.82884i −0.134539 + 0.414070i
\(137\) −0.913334 + 0.296760i −0.0780314 + 0.0253539i −0.347773 0.937579i \(-0.613062\pi\)
0.269741 + 0.962933i \(0.413062\pi\)
\(138\) 2.59484 + 3.57150i 0.220888 + 0.304026i
\(139\) 1.59641 + 4.91325i 0.135406 + 0.416736i 0.995653 0.0931411i \(-0.0296908\pi\)
−0.860247 + 0.509877i \(0.829691\pi\)
\(140\) 0.199007 + 5.83027i 0.0168192 + 0.492748i
\(141\) 7.81405 5.67724i 0.658062 0.478110i
\(142\) −10.8473 + 3.52449i −0.910281 + 0.295768i
\(143\) 6.60620 + 2.14648i 0.552438 + 0.179498i
\(144\) 0.809017 + 0.587785i 0.0674181 + 0.0489821i
\(145\) −2.00373 1.35383i −0.166401 0.112429i
\(146\) 10.1499 7.37431i 0.840009 0.610302i
\(147\) 0.113830 + 0.156673i 0.00938852 + 0.0129222i
\(148\) 2.74968 3.78461i 0.226022 0.311093i
\(149\) −8.79127 −0.720209 −0.360104 0.932912i \(-0.617259\pi\)
−0.360104 + 0.932912i \(0.617259\pi\)
\(150\) 4.23607 + 2.65626i 0.345874 + 0.216883i
\(151\) −15.2240 11.0609i −1.23891 0.900124i −0.241389 0.970429i \(-0.577603\pi\)
−0.997526 + 0.0703048i \(0.977603\pi\)
\(152\) −1.76807 + 0.574481i −0.143409 + 0.0465965i
\(153\) −4.82884 1.56899i −0.390389 0.126845i
\(154\) −3.80882 −0.306924
\(155\) −12.4446 + 0.361831i −0.999578 + 0.0290629i
\(156\) −4.75786 −0.380933
\(157\) 21.8225 + 7.09056i 1.74163 + 0.565888i 0.995047 0.0994091i \(-0.0316953\pi\)
0.746578 + 0.665297i \(0.231695\pi\)
\(158\) 3.46940 1.12728i 0.276011 0.0896814i
\(159\) 1.19225 + 0.866223i 0.0945519 + 0.0686960i
\(160\) −2.14896 0.618034i −0.169890 0.0488599i
\(161\) 11.5173 0.907688
\(162\) −0.587785 + 0.809017i −0.0461808 + 0.0635624i
\(163\) 12.9023 + 17.7584i 1.01058 + 1.39095i 0.918600 + 0.395188i \(0.129321\pi\)
0.0919830 + 0.995761i \(0.470679\pi\)
\(164\) −6.73026 + 4.88982i −0.525545 + 0.381831i
\(165\) −1.82762 + 2.70497i −0.142280 + 0.210582i
\(166\) 1.18776 + 0.862961i 0.0921883 + 0.0669787i
\(167\) −11.5829 3.76350i −0.896308 0.291228i −0.175596 0.984462i \(-0.556185\pi\)
−0.720712 + 0.693234i \(0.756185\pi\)
\(168\) 2.48121 0.806193i 0.191429 0.0621992i
\(169\) 7.79667 5.66461i 0.599744 0.435739i
\(170\) 11.3467 0.387301i 0.870250 0.0297046i
\(171\) −0.574481 1.76807i −0.0439316 0.135208i
\(172\) −2.77069 3.81353i −0.211263 0.290779i
\(173\) 22.8869 7.43640i 1.74006 0.565379i 0.745217 0.666822i \(-0.232346\pi\)
0.994841 + 0.101443i \(0.0323459\pi\)
\(174\) −0.334189 + 1.02853i −0.0253348 + 0.0779726i
\(175\) 12.1023 4.86752i 0.914848 0.367950i
\(176\) 0.451145 1.38848i 0.0340063 0.104661i
\(177\) −2.54593 3.50417i −0.191364 0.263389i
\(178\) 1.02188 + 1.40650i 0.0765933 + 0.105422i
\(179\) 8.82509 + 6.41180i 0.659618 + 0.479241i 0.866534 0.499118i \(-0.166343\pi\)
−0.206916 + 0.978359i \(0.566343\pi\)
\(180\) 0.618034 2.14896i 0.0460655 0.160174i
\(181\) 4.16517 0.309595 0.154797 0.987946i \(-0.450528\pi\)
0.154797 + 0.987946i \(0.450528\pi\)
\(182\) −7.29604 + 10.0421i −0.540818 + 0.744372i
\(183\) −0.850518 + 0.276350i −0.0628721 + 0.0204284i
\(184\) −1.36419 + 4.19855i −0.100569 + 0.309521i
\(185\) −10.0529 2.89118i −0.739105 0.212564i
\(186\) 1.69375 + 5.30389i 0.124192 + 0.388900i
\(187\) 7.41259i 0.542063i
\(188\) 9.18597 + 2.98470i 0.669956 + 0.217682i
\(189\) 0.806193 + 2.48121i 0.0586419 + 0.180481i
\(190\) 2.55672 + 3.27776i 0.185484 + 0.237793i
\(191\) 13.8431 1.00165 0.500826 0.865548i \(-0.333030\pi\)
0.500826 + 0.865548i \(0.333030\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) −7.50660 + 10.3319i −0.540337 + 0.743710i −0.988662 0.150161i \(-0.952021\pi\)
0.448325 + 0.893871i \(0.352021\pi\)
\(194\) −1.63274 + 1.18626i −0.117224 + 0.0851684i
\(195\) 3.63085 + 10.0001i 0.260011 + 0.716125i
\(196\) −0.0598438 + 0.184180i −0.00427456 + 0.0131557i
\(197\) 9.40690 12.9475i 0.670214 0.922470i −0.329551 0.944138i \(-0.606897\pi\)
0.999765 + 0.0216673i \(0.00689744\pi\)
\(198\) 1.38848 + 0.451145i 0.0986751 + 0.0320615i
\(199\) −4.33373 13.3378i −0.307210 0.945495i −0.978843 0.204611i \(-0.934407\pi\)
0.671633 0.740884i \(-0.265593\pi\)
\(200\) 0.340937 + 4.98836i 0.0241079 + 0.352731i
\(201\) −0.678857 2.08931i −0.0478829 0.147368i
\(202\) −5.93212 + 1.92746i −0.417382 + 0.135616i
\(203\) 1.65839 + 2.28257i 0.116396 + 0.160205i
\(204\) −1.56899 4.82884i −0.109851 0.338086i
\(205\) 15.4136 + 10.4142i 1.07653 + 0.727361i
\(206\) −2.44325 1.77512i −0.170229 0.123679i
\(207\) −4.19855 1.36419i −0.291819 0.0948178i
\(208\) −2.79660 3.84919i −0.193909 0.266893i
\(209\) −2.19576 + 1.59531i −0.151884 + 0.110350i
\(210\) −3.58795 4.59982i −0.247592 0.317418i
\(211\) −0.562969 −0.0387564 −0.0193782 0.999812i \(-0.506169\pi\)
−0.0193782 + 0.999812i \(0.506169\pi\)
\(212\) 1.47371i 0.101215i
\(213\) 6.70397 9.22722i 0.459348 0.632239i
\(214\) 0.732598 + 2.25470i 0.0500794 + 0.154128i
\(215\) −5.90096 + 8.73371i −0.402442 + 0.595634i
\(216\) −1.00000 −0.0680414
\(217\) 13.7919 + 4.55845i 0.936257 + 0.309447i
\(218\) 1.72707i 0.116972i
\(219\) −3.87690 + 11.9319i −0.261977 + 0.806282i
\(220\) −3.26261 + 0.111364i −0.219965 + 0.00750818i
\(221\) 19.5436 + 14.1993i 1.31465 + 0.955148i
\(222\) 4.67804i 0.313969i
\(223\) 2.28518i 0.153027i 0.997069 + 0.0765136i \(0.0243789\pi\)
−0.997069 + 0.0765136i \(0.975621\pi\)
\(224\) 2.11064 + 1.53347i 0.141023 + 0.102459i
\(225\) −4.98836 + 0.340937i −0.332558 + 0.0227291i
\(226\) 12.8961 9.36957i 0.857837 0.623255i
\(227\) 26.2931 + 8.54313i 1.74513 + 0.567028i 0.995494 0.0948217i \(-0.0302281\pi\)
0.749637 + 0.661849i \(0.230228\pi\)
\(228\) 1.09273 1.50401i 0.0723676 0.0996055i
\(229\) −5.72909 + 17.6323i −0.378589 + 1.16518i 0.562436 + 0.826841i \(0.309864\pi\)
−0.941025 + 0.338337i \(0.890136\pi\)
\(230\) 9.86563 0.336748i 0.650520 0.0222045i
\(231\) 3.08140 2.23877i 0.202741 0.147300i
\(232\) −1.02853 + 0.334189i −0.0675263 + 0.0219406i
\(233\) 22.2747 7.23747i 1.45926 0.474143i 0.531417 0.847110i \(-0.321660\pi\)
0.927844 + 0.372968i \(0.121660\pi\)
\(234\) 3.84919 2.79660i 0.251629 0.182819i
\(235\) −0.736768 21.5849i −0.0480614 1.40805i
\(236\) 1.33847 4.11940i 0.0871272 0.268150i
\(237\) −2.14421 + 2.95125i −0.139281 + 0.191704i
\(238\) −12.5979 4.09332i −0.816603 0.265331i
\(239\) 9.55003 6.93850i 0.617740 0.448814i −0.234392 0.972142i \(-0.575310\pi\)
0.852131 + 0.523328i \(0.175310\pi\)
\(240\) 2.10182 0.763128i 0.135672 0.0492597i
\(241\) 16.8369 + 12.2327i 1.08456 + 0.787979i 0.978472 0.206377i \(-0.0661675\pi\)
0.106088 + 0.994357i \(0.466167\pi\)
\(242\) 8.86859i 0.570094i
\(243\) 1.00000i 0.0641500i
\(244\) −0.723494 0.525649i −0.0463170 0.0336512i
\(245\) 0.432782 0.0147723i 0.0276494 0.000943770i
\(246\) 2.57073 7.91189i 0.163904 0.504444i
\(247\) 8.84513i 0.562802i
\(248\) −3.29537 + 4.48782i −0.209256 + 0.284977i
\(249\) −1.46816 −0.0930406
\(250\) 10.2244 4.52335i 0.646651 0.286081i
\(251\) −1.44571 4.44945i −0.0912527 0.280847i 0.895006 0.446054i \(-0.147171\pi\)
−0.986259 + 0.165207i \(0.947171\pi\)
\(252\) −1.53347 + 2.11064i −0.0965996 + 0.132958i
\(253\) 6.44505i 0.405197i
\(254\) −2.45695 −0.154163
\(255\) −8.95200 + 6.98274i −0.560596 + 0.437276i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) −11.6077 15.9767i −0.724071 0.996598i −0.999379 0.0352422i \(-0.988780\pi\)
0.275308 0.961356i \(-0.411220\pi\)
\(258\) 4.48308 + 1.45664i 0.279104 + 0.0906865i
\(259\) 9.87366 + 7.17363i 0.613519 + 0.445748i
\(260\) −5.95613 + 8.81536i −0.369383 + 0.546705i
\(261\) −0.334189 1.02853i −0.0206858 0.0636644i
\(262\) 8.91259 + 12.2671i 0.550622 + 0.757866i
\(263\) −23.7210 + 7.70742i −1.46270 + 0.475260i −0.928894 0.370347i \(-0.879239\pi\)
−0.533807 + 0.845607i \(0.679239\pi\)
\(264\) 0.451145 + 1.38848i 0.0277660 + 0.0854551i
\(265\) 3.09746 1.12463i 0.190276 0.0690853i
\(266\) −1.49876 4.61271i −0.0918949 0.282823i
\(267\) −1.65344 0.537236i −0.101189 0.0328783i
\(268\) 1.29126 1.77727i 0.0788764 0.108564i
\(269\) 5.83891 17.9703i 0.356004 1.09567i −0.599420 0.800434i \(-0.704602\pi\)
0.955425 0.295235i \(-0.0953978\pi\)
\(270\) 0.763128 + 2.10182i 0.0464425 + 0.127913i
\(271\) 21.3250 15.4935i 1.29540 0.941162i 0.295499 0.955343i \(-0.404514\pi\)
0.999899 + 0.0141810i \(0.00451409\pi\)
\(272\) 2.98439 4.10766i 0.180955 0.249063i
\(273\) 12.4128i 0.751254i
\(274\) 0.960337 0.0580161
\(275\) 2.72386 + 6.77244i 0.164255 + 0.408393i
\(276\) −1.36419 4.19855i −0.0821146 0.252723i
\(277\) 20.9454 + 6.80557i 1.25849 + 0.408907i 0.860955 0.508682i \(-0.169867\pi\)
0.397532 + 0.917589i \(0.369867\pi\)
\(278\) 5.16610i 0.309842i
\(279\) −4.48782 3.29537i −0.268679 0.197289i
\(280\) 1.61239 5.60642i 0.0963585 0.335048i
\(281\) 2.45248 7.54795i 0.146303 0.450273i −0.850874 0.525370i \(-0.823927\pi\)
0.997176 + 0.0750973i \(0.0239267\pi\)
\(282\) −9.18597 + 2.98470i −0.547016 + 0.177736i
\(283\) 4.03165 5.54909i 0.239657 0.329859i −0.672199 0.740371i \(-0.734650\pi\)
0.911855 + 0.410512i \(0.134650\pi\)
\(284\) 11.4055 0.676790
\(285\) −3.99504 1.14896i −0.236646 0.0680586i
\(286\) −5.61957 4.08285i −0.332292 0.241424i
\(287\) −12.7570 17.5586i −0.753024 1.03645i
\(288\) −0.587785 0.809017i −0.0346356 0.0476718i
\(289\) −2.71299 + 8.34972i −0.159588 + 0.491160i
\(290\) 1.48730 + 1.90675i 0.0873375 + 0.111968i
\(291\) 0.623653 1.91941i 0.0365592 0.112518i
\(292\) −11.9319 + 3.87690i −0.698261 + 0.226879i
\(293\) −19.1762 26.3937i −1.12028 1.54194i −0.805327 0.592831i \(-0.798010\pi\)
−0.314957 0.949106i \(-0.601990\pi\)
\(294\) −0.0598438 0.184180i −0.00349016 0.0107416i
\(295\) −9.67965 + 0.330400i −0.563571 + 0.0192366i
\(296\) −3.78461 + 2.74968i −0.219976 + 0.159822i
\(297\) −1.38848 + 0.451145i −0.0805678 + 0.0261781i
\(298\) 8.36099 + 2.71665i 0.484339 + 0.157371i
\(299\) 16.9927 + 12.3459i 0.982711 + 0.713982i
\(300\) −3.20791 3.83527i −0.185209 0.221430i
\(301\) 9.94911 7.22845i 0.573457 0.416641i
\(302\) 11.0609 + 15.2240i 0.636484 + 0.876045i
\(303\) 3.66625 5.04616i 0.210621 0.289894i
\(304\) 1.85906 0.106624
\(305\) −0.552700 + 1.92179i −0.0316475 + 0.110041i
\(306\) 4.10766 + 2.98439i 0.234819 + 0.170606i
\(307\) −3.05911 + 0.993966i −0.174593 + 0.0567286i −0.395009 0.918677i \(-0.629258\pi\)
0.220416 + 0.975406i \(0.429258\pi\)
\(308\) 3.62240 + 1.17699i 0.206406 + 0.0670652i
\(309\) 3.02002 0.171803
\(310\) 11.9474 + 3.50148i 0.678565 + 0.198871i
\(311\) −4.19986 −0.238152 −0.119076 0.992885i \(-0.537993\pi\)
−0.119076 + 0.992885i \(0.537993\pi\)
\(312\) 4.52499 + 1.47026i 0.256177 + 0.0832370i
\(313\) 2.87211 0.933206i 0.162341 0.0527479i −0.226719 0.973960i \(-0.572800\pi\)
0.389060 + 0.921212i \(0.372800\pi\)
\(314\) −18.5633 13.4870i −1.04759 0.761118i
\(315\) 5.60642 + 1.61239i 0.315886 + 0.0908477i
\(316\) −3.64795 −0.205213
\(317\) −7.38243 + 10.1610i −0.414639 + 0.570701i −0.964342 0.264659i \(-0.914741\pi\)
0.549703 + 0.835360i \(0.314741\pi\)
\(318\) −0.866223 1.19225i −0.0485754 0.0668583i
\(319\) −1.27733 + 0.928031i −0.0715165 + 0.0519598i
\(320\) 1.85280 + 1.25185i 0.103575 + 0.0699806i
\(321\) −1.91797 1.39348i −0.107050 0.0777767i
\(322\) −10.9536 3.55903i −0.610419 0.198337i
\(323\) −8.97710 + 2.91684i −0.499499 + 0.162297i
\(324\) 0.809017 0.587785i 0.0449454 0.0326547i
\(325\) 23.0736 + 5.79145i 1.27989 + 0.321252i
\(326\) −6.78312 20.8763i −0.375682 1.15623i
\(327\) −1.01515 1.39723i −0.0561377 0.0772670i
\(328\) 7.91189 2.57073i 0.436861 0.141945i
\(329\) −7.78678 + 23.9652i −0.429299 + 1.32125i
\(330\) 2.57405 2.00781i 0.141697 0.110526i
\(331\) 0.117391 0.361292i 0.00645238 0.0198584i −0.947778 0.318929i \(-0.896677\pi\)
0.954231 + 0.299071i \(0.0966767\pi\)
\(332\) −0.862961 1.18776i −0.0473611 0.0651870i
\(333\) −2.74968 3.78461i −0.150682 0.207395i
\(334\) 9.85296 + 7.15860i 0.539130 + 0.391701i
\(335\) −4.72090 1.35771i −0.257930 0.0741798i
\(336\) −2.60890 −0.142327
\(337\) 12.7064 17.4889i 0.692162 0.952679i −0.307838 0.951439i \(-0.599605\pi\)
0.999999 0.00123971i \(-0.000394612\pi\)
\(338\) −9.16553 + 2.97806i −0.498539 + 0.161985i
\(339\) −4.92588 + 15.1603i −0.267537 + 0.823394i
\(340\) −10.9110 3.13797i −0.591733 0.170180i
\(341\) −2.55090 + 7.71794i −0.138139 + 0.417950i
\(342\) 1.85906i 0.100526i
\(343\) −17.8490 5.79948i −0.963753 0.313142i
\(344\) 1.45664 + 4.48308i 0.0785368 + 0.241711i
\(345\) −7.78352 + 6.07130i −0.419051 + 0.326868i
\(346\) −24.0647 −1.29373
\(347\) 12.7424i 0.684047i 0.939691 + 0.342023i \(0.111112\pi\)
−0.939691 + 0.342023i \(0.888888\pi\)
\(348\) 0.635666 0.874919i 0.0340753 0.0469006i
\(349\) −28.5687 + 20.7564i −1.52925 + 1.11106i −0.572591 + 0.819841i \(0.694062\pi\)
−0.956656 + 0.291222i \(0.905938\pi\)
\(350\) −13.0141 + 0.889470i −0.695634 + 0.0475442i
\(351\) −1.47026 + 4.52499i −0.0784766 + 0.241526i
\(352\) −0.858129 + 1.18111i −0.0457384 + 0.0629535i
\(353\) −21.2468 6.90352i −1.13086 0.367437i −0.316954 0.948441i \(-0.602660\pi\)
−0.813901 + 0.581004i \(0.802660\pi\)
\(354\) 1.33847 + 4.11940i 0.0711390 + 0.218943i
\(355\) −8.70383 23.9722i −0.461951 1.27231i
\(356\) −0.537236 1.65344i −0.0284734 0.0876322i
\(357\) 12.5979 4.09332i 0.666754 0.216641i
\(358\) −6.41180 8.82509i −0.338874 0.466420i
\(359\) −8.69462 26.7593i −0.458884 1.41230i −0.866514 0.499153i \(-0.833644\pi\)
0.407629 0.913148i \(-0.366356\pi\)
\(360\) −1.25185 + 1.85280i −0.0659783 + 0.0976512i
\(361\) 12.5753 + 9.13648i 0.661857 + 0.480867i
\(362\) −3.96132 1.28711i −0.208202 0.0676490i
\(363\) −5.21283 7.17484i −0.273602 0.376581i
\(364\) 10.0421 7.29604i 0.526351 0.382416i
\(365\) 17.2541 + 22.1201i 0.903121 + 1.15782i
\(366\) 0.894288 0.0467452
\(367\) 17.4128i 0.908943i −0.890761 0.454471i \(-0.849828\pi\)
0.890761 0.454471i \(-0.150172\pi\)
\(368\) 2.59484 3.57150i 0.135266 0.186177i
\(369\) 2.57073 + 7.91189i 0.133827 + 0.411877i
\(370\) 8.66747 + 5.85620i 0.450600 + 0.304449i
\(371\) −3.84475 −0.199609
\(372\) 0.0281347 5.56769i 0.00145872 0.288671i
\(373\) 33.9694i 1.75887i 0.476020 + 0.879435i \(0.342079\pi\)
−0.476020 + 0.879435i \(0.657921\pi\)
\(374\) 2.29062 7.04980i 0.118445 0.364536i
\(375\) −5.61300 + 9.66924i −0.289854 + 0.499318i
\(376\) −7.81405 5.67724i −0.402979 0.292781i
\(377\) 5.14543i 0.265003i
\(378\) 2.60890i 0.134187i
\(379\) 5.35456 + 3.89031i 0.275045 + 0.199832i 0.716753 0.697327i \(-0.245627\pi\)
−0.441708 + 0.897159i \(0.645627\pi\)
\(380\) −1.41870 3.90740i −0.0727777 0.200445i
\(381\) 1.98771 1.44416i 0.101834 0.0739865i
\(382\) −13.1656 4.27776i −0.673610 0.218869i
\(383\) 8.33438 11.4713i 0.425867 0.586156i −0.541131 0.840938i \(-0.682004\pi\)
0.966998 + 0.254782i \(0.0820038\pi\)
\(384\) 0.309017 0.951057i 0.0157695 0.0485334i
\(385\) −0.290538 8.51182i −0.0148072 0.433803i
\(386\) 10.3319 7.50660i 0.525882 0.382076i
\(387\) −4.48308 + 1.45664i −0.227888 + 0.0740452i
\(388\) 1.91941 0.623653i 0.0974431 0.0316612i
\(389\) −9.25458 + 6.72385i −0.469226 + 0.340913i −0.797140 0.603795i \(-0.793654\pi\)
0.327914 + 0.944708i \(0.393654\pi\)
\(390\) −0.362931 10.6327i −0.0183777 0.538408i
\(391\) −6.92646 + 21.3175i −0.350286 + 1.07807i
\(392\) 0.113830 0.156673i 0.00574927 0.00791319i
\(393\) −14.4209 4.68563i −0.727437 0.236359i
\(394\) −12.9475 + 9.40690i −0.652285 + 0.473913i
\(395\) 2.78385 + 7.66732i 0.140071 + 0.385785i
\(396\) −1.18111 0.858129i −0.0593531 0.0431226i
\(397\) 6.08289i 0.305291i −0.988281 0.152646i \(-0.951221\pi\)
0.988281 0.152646i \(-0.0487793\pi\)
\(398\) 14.0242i 0.702972i
\(399\) 3.92381 + 2.85081i 0.196436 + 0.142719i
\(400\) 1.21724 4.84957i 0.0608619 0.242479i
\(401\) −10.6744 + 32.8524i −0.533054 + 1.64057i 0.214764 + 0.976666i \(0.431102\pi\)
−0.747817 + 0.663905i \(0.768898\pi\)
\(402\) 2.19683i 0.109568i
\(403\) 15.4623 + 21.5098i 0.770232 + 1.07148i
\(404\) 6.23740 0.310322
\(405\) −1.85280 1.25185i −0.0920664 0.0622050i
\(406\) −0.871866 2.68333i −0.0432700 0.133171i
\(407\) −4.01436 + 5.52529i −0.198984 + 0.273878i
\(408\) 5.07734i 0.251366i
\(409\) 5.99496 0.296432 0.148216 0.988955i \(-0.452647\pi\)
0.148216 + 0.988955i \(0.452647\pi\)
\(410\) −11.4410 14.6676i −0.565030 0.724379i
\(411\) −0.776929 + 0.564472i −0.0383231 + 0.0278433i
\(412\) 1.77512 + 2.44325i 0.0874540 + 0.120370i
\(413\) 10.7471 + 3.49194i 0.528829 + 0.171827i
\(414\) 3.57150 + 2.59484i 0.175529 + 0.127530i
\(415\) −1.83791 + 2.72020i −0.0902196 + 0.133529i
\(416\) 1.47026 + 4.52499i 0.0720854 + 0.221856i
\(417\) 3.03655 + 4.17946i 0.148701 + 0.204669i
\(418\) 2.58127 0.838705i 0.126254 0.0410224i
\(419\) −8.78260 27.0301i −0.429058 1.32051i −0.899054 0.437837i \(-0.855745\pi\)
0.469996 0.882669i \(-0.344255\pi\)
\(420\) 1.99092 + 5.48342i 0.0971470 + 0.267564i
\(421\) −7.38365 22.7245i −0.359857 1.10753i −0.953139 0.302531i \(-0.902168\pi\)
0.593282 0.804994i \(-0.297832\pi\)
\(422\) 0.535415 + 0.173967i 0.0260636 + 0.00846858i
\(423\) 5.67724 7.81405i 0.276037 0.379932i
\(424\) 0.455400 1.40158i 0.0221162 0.0680667i
\(425\) 1.73105 + 25.3276i 0.0839685 + 1.22857i
\(426\) −9.22722 + 6.70397i −0.447060 + 0.324808i
\(427\) 1.37136 1.88752i 0.0663650 0.0913436i
\(428\) 2.37074i 0.114594i
\(429\) 6.94617 0.335364
\(430\) 8.31101 6.48275i 0.400792 0.312626i
\(431\) 2.00824 + 6.18073i 0.0967335 + 0.297715i 0.987702 0.156351i \(-0.0499731\pi\)
−0.890968 + 0.454066i \(0.849973\pi\)
\(432\) 0.951057 + 0.309017i 0.0457577 + 0.0148676i
\(433\) 19.6221i 0.942979i 0.881872 + 0.471490i \(0.156284\pi\)
−0.881872 + 0.471490i \(0.843716\pi\)
\(434\) −11.7083 8.59728i −0.562015 0.412683i
\(435\) −2.32401 0.668379i −0.111428 0.0320463i
\(436\) 0.533694 1.64254i 0.0255593 0.0786635i
\(437\) −7.80534 + 2.53611i −0.373380 + 0.121319i
\(438\) 7.37431 10.1499i 0.352358 0.484979i
\(439\) −20.2699 −0.967428 −0.483714 0.875226i \(-0.660713\pi\)
−0.483714 + 0.875226i \(0.660713\pi\)
\(440\) 3.13734 + 0.902290i 0.149567 + 0.0430150i
\(441\) 0.156673 + 0.113830i 0.00746063 + 0.00542046i
\(442\) −14.1993 19.5436i −0.675391 0.929597i
\(443\) 0.392196 + 0.539812i 0.0186338 + 0.0256472i 0.818232 0.574888i \(-0.194954\pi\)
−0.799598 + 0.600535i \(0.794954\pi\)
\(444\) 1.44559 4.44908i 0.0686048 0.211144i
\(445\) −3.06525 + 2.39096i −0.145307 + 0.113342i
\(446\) 0.706161 2.17334i 0.0334377 0.102911i
\(447\) −8.36099 + 2.71665i −0.395461 + 0.128493i
\(448\) −1.53347 2.11064i −0.0724497 0.0997184i
\(449\) −6.52879 20.0936i −0.308113 0.948274i −0.978497 0.206260i \(-0.933871\pi\)
0.670384 0.742014i \(-0.266129\pi\)
\(450\) 4.84957 + 1.21724i 0.228611 + 0.0573812i
\(451\) 9.82574 7.13882i 0.462676 0.336154i
\(452\) −15.1603 + 4.92588i −0.713080 + 0.231694i
\(453\) −17.8969 5.81506i −0.840871 0.273215i
\(454\) −22.3662 16.2500i −1.04970 0.762650i
\(455\) −22.9984 15.5389i −1.07818 0.728476i
\(456\) −1.50401 + 1.09273i −0.0704317 + 0.0511716i
\(457\) 7.42348 + 10.2175i 0.347256 + 0.477957i 0.946543 0.322577i \(-0.104549\pi\)
−0.599287 + 0.800534i \(0.704549\pi\)
\(458\) 10.8974 14.9990i 0.509201 0.700855i
\(459\) −5.07734 −0.236990
\(460\) −9.48683 2.72838i −0.442326 0.127211i
\(461\) −11.0161 8.00364i −0.513069 0.372767i 0.300917 0.953650i \(-0.402707\pi\)
−0.813987 + 0.580884i \(0.802707\pi\)
\(462\) −3.62240 + 1.17699i −0.168529 + 0.0547585i
\(463\) −22.4421 7.29188i −1.04297 0.338883i −0.263066 0.964778i \(-0.584734\pi\)
−0.779907 + 0.625895i \(0.784734\pi\)
\(464\) 1.08146 0.0502055
\(465\) −11.7237 + 4.18973i −0.543676 + 0.194294i
\(466\) −23.4210 −1.08495
\(467\) 2.13216 + 0.692779i 0.0986644 + 0.0320580i 0.357933 0.933747i \(-0.383482\pi\)
−0.259269 + 0.965805i \(0.583482\pi\)
\(468\) −4.52499 + 1.47026i −0.209168 + 0.0679627i
\(469\) 4.63671 + 3.36877i 0.214104 + 0.155555i
\(470\) −5.96940 + 20.7562i −0.275348 + 0.957411i
\(471\) 22.9455 1.05727
\(472\) −2.54593 + 3.50417i −0.117186 + 0.161292i
\(473\) 4.04503 + 5.56751i 0.185991 + 0.255994i
\(474\) 2.95125 2.14421i 0.135555 0.0984868i
\(475\) −7.12999 + 5.96369i −0.327147 + 0.273633i
\(476\) 10.7165 + 7.78596i 0.491188 + 0.356869i
\(477\) 1.40158 + 0.455400i 0.0641739 + 0.0208514i
\(478\) −11.2267 + 3.64779i −0.513499 + 0.166846i
\(479\) −22.0284 + 16.0046i −1.00650 + 0.731268i −0.963473 0.267806i \(-0.913701\pi\)
−0.0430312 + 0.999074i \(0.513701\pi\)
\(480\) −2.23477 + 0.0762803i −0.102003 + 0.00348170i
\(481\) 6.87792 + 21.1681i 0.313606 + 0.965181i
\(482\) −12.2327 16.8369i −0.557186 0.766900i
\(483\) 10.9536 3.55903i 0.498405 0.161942i
\(484\) 2.74054 8.43453i 0.124570 0.383388i
\(485\) −2.77556 3.55831i −0.126032 0.161575i
\(486\) −0.309017 + 0.951057i −0.0140173 + 0.0431408i
\(487\) −24.2935 33.4372i −1.10084 1.51518i −0.834261 0.551370i \(-0.814105\pi\)
−0.266584 0.963812i \(-0.585895\pi\)
\(488\) 0.525649 + 0.723494i 0.0237950 + 0.0327510i
\(489\) 17.7584 + 12.9023i 0.803065 + 0.583461i
\(490\) −0.416165 0.119688i −0.0188004 0.00540694i
\(491\) −17.4627 −0.788080 −0.394040 0.919093i \(-0.628923\pi\)
−0.394040 + 0.919093i \(0.628923\pi\)
\(492\) −4.88982 + 6.73026i −0.220450 + 0.303424i
\(493\) −5.22220 + 1.69679i −0.235196 + 0.0764198i
\(494\) 2.73330 8.41222i 0.122977 0.378484i
\(495\) −0.902290 + 3.13734i −0.0405549 + 0.141013i
\(496\) 4.52090 3.24985i 0.202994 0.145922i
\(497\) 29.7557i 1.33473i
\(498\) 1.39630 + 0.453685i 0.0625697 + 0.0203301i
\(499\) 0.869270 + 2.67534i 0.0389139 + 0.119765i 0.968626 0.248522i \(-0.0799447\pi\)
−0.929713 + 0.368286i \(0.879945\pi\)
\(500\) −11.1218 + 1.14243i −0.497383 + 0.0510910i
\(501\) −12.1789 −0.544115
\(502\) 4.67843i 0.208809i
\(503\) 23.6481 32.5488i 1.05441 1.45128i 0.169497 0.985531i \(-0.445786\pi\)
0.884918 0.465747i \(-0.154214\pi\)
\(504\) 2.11064 1.53347i 0.0940155 0.0683062i
\(505\) −4.75993 13.1099i −0.211814 0.583382i
\(506\) 1.99163 6.12960i 0.0885387 0.272494i
\(507\) 5.66461 7.79667i 0.251574 0.346262i
\(508\) 2.33670 + 0.759239i 0.103674 + 0.0336858i
\(509\) −2.53618 7.80555i −0.112414 0.345975i 0.878985 0.476850i \(-0.158221\pi\)
−0.991399 + 0.130875i \(0.958221\pi\)
\(510\) 10.6716 3.87466i 0.472549 0.171573i
\(511\) −10.1144 31.1290i −0.447437 1.37707i
\(512\) 0.951057 0.309017i 0.0420312 0.0136568i
\(513\) −1.09273 1.50401i −0.0482451 0.0664036i
\(514\) 6.10255 + 18.7817i 0.269172 + 0.828426i
\(515\) 3.78061 5.59549i 0.166594 0.246567i
\(516\) −3.81353 2.77069i −0.167881 0.121973i
\(517\) −13.4109 4.35747i −0.589812 0.191641i
\(518\) −7.17363 9.87366i −0.315191 0.433824i
\(519\) 19.4688 14.1449i 0.854583 0.620891i
\(520\) 8.38871 6.54336i 0.367869 0.286945i
\(521\) −21.1992 −0.928755 −0.464377 0.885637i \(-0.653722\pi\)
−0.464377 + 0.885637i \(0.653722\pi\)
\(522\) 1.08146i 0.0473342i
\(523\) 24.9394 34.3261i 1.09052 1.50098i 0.243144 0.969990i \(-0.421821\pi\)
0.847380 0.530988i \(-0.178179\pi\)
\(524\) −4.68563 14.4209i −0.204693 0.629979i
\(525\) 10.0058 8.36911i 0.436690 0.365258i
\(526\) 24.9417 1.08751
\(527\) −16.7317 + 22.7862i −0.728845 + 0.992583i
\(528\) 1.45994i 0.0635355i
\(529\) 1.08502 3.33935i 0.0471749 0.145189i
\(530\) −3.29339 + 0.112415i −0.143056 + 0.00488298i
\(531\) −3.50417 2.54593i −0.152068 0.110484i
\(532\) 4.85009i 0.210278i
\(533\) 39.5809i 1.71444i
\(534\) 1.40650 + 1.02188i 0.0608652 + 0.0442212i
\(535\) −4.98285 + 1.80917i −0.215428 + 0.0782174i
\(536\) −1.77727 + 1.29126i −0.0767664 + 0.0557740i
\(537\) 10.3745 + 3.37088i 0.447693 + 0.145464i
\(538\) −11.1063 + 15.2865i −0.478825 + 0.659046i
\(539\) 0.0873681 0.268891i 0.00376321 0.0115820i
\(540\) −0.0762803 2.23477i −0.00328258 0.0961690i
\(541\) 29.0823 21.1295i 1.25035 0.908429i 0.252104 0.967700i \(-0.418878\pi\)
0.998242 + 0.0592708i \(0.0188776\pi\)
\(542\) −25.0690 + 8.14541i −1.07680 + 0.349875i
\(543\) 3.96132 1.28711i 0.169996 0.0552351i
\(544\) −4.10766 + 2.98439i −0.176114 + 0.127955i
\(545\) −3.85960 + 0.131741i −0.165327 + 0.00564318i
\(546\) −3.83575 + 11.8052i −0.164155 + 0.505217i
\(547\) 14.9307 20.5503i 0.638389 0.878668i −0.360139 0.932899i \(-0.617271\pi\)
0.998528 + 0.0542310i \(0.0172707\pi\)
\(548\) −0.913334 0.296760i −0.0390157 0.0126770i
\(549\) −0.723494 + 0.525649i −0.0308780 + 0.0224342i
\(550\) −0.497746 7.28269i −0.0212240 0.310535i
\(551\) −1.62653 1.18174i −0.0692923 0.0503438i
\(552\) 4.41461i 0.187898i
\(553\) 9.51712i 0.404709i
\(554\) −17.8172 12.9450i −0.756981 0.549979i
\(555\) −10.4543 + 0.356842i −0.443761 + 0.0151471i
\(556\) −1.59641 + 4.91325i −0.0677029 + 0.208368i
\(557\) 12.1202i 0.513548i −0.966471 0.256774i \(-0.917340\pi\)
0.966471 0.256774i \(-0.0826596\pi\)
\(558\) 3.24985 + 4.52090i 0.137577 + 0.191385i
\(559\) 22.4275 0.948583
\(560\) −3.26595 + 4.83376i −0.138012 + 0.204264i
\(561\) 2.29062 + 7.04980i 0.0967099 + 0.297643i
\(562\) −4.66489 + 6.42067i −0.196777 + 0.270840i
\(563\) 23.6343i 0.996068i −0.867157 0.498034i \(-0.834055\pi\)
0.867157 0.498034i \(-0.165945\pi\)
\(564\) 9.65870 0.406705
\(565\) 21.9225 + 28.1051i 0.922288 + 1.18239i
\(566\) −5.54909 + 4.03165i −0.233245 + 0.169463i
\(567\) 1.53347 + 2.11064i 0.0643997 + 0.0886386i
\(568\) −10.8473 3.52449i −0.455141 0.147884i
\(569\) 14.7873 + 10.7436i 0.619915 + 0.450395i 0.852892 0.522087i \(-0.174847\pi\)
−0.232977 + 0.972482i \(0.574847\pi\)
\(570\) 3.44446 + 2.32726i 0.144273 + 0.0974783i
\(571\) −2.63673 8.11503i −0.110344 0.339603i 0.880604 0.473854i \(-0.157137\pi\)
−0.990947 + 0.134250i \(0.957137\pi\)
\(572\) 4.08285 + 5.61957i 0.170713 + 0.234966i
\(573\) 13.1656 4.27776i 0.550000 0.178706i
\(574\) 6.70677 + 20.6413i 0.279935 + 0.861552i
\(575\) 1.50511 + 22.0217i 0.0627672 + 0.918368i
\(576\) 0.309017 + 0.951057i 0.0128757 + 0.0396274i
\(577\) −32.2896 10.4915i −1.34423 0.436768i −0.453484 0.891264i \(-0.649819\pi\)
−0.890749 + 0.454496i \(0.849819\pi\)
\(578\) 5.16041 7.10270i 0.214645 0.295433i
\(579\) −3.94645 + 12.1459i −0.164009 + 0.504768i
\(580\) −0.825292 2.27303i −0.0342684 0.0943825i
\(581\) 3.09875 2.25138i 0.128558 0.0934028i
\(582\) −1.18626 + 1.63274i −0.0491720 + 0.0676794i
\(583\) 2.15152i 0.0891067i
\(584\) 12.5459 0.519154
\(585\) 6.54336 + 8.38871i 0.270535 + 0.346830i
\(586\) 10.0815 + 31.0277i 0.416463 + 1.28174i
\(587\) 23.2577 + 7.55690i 0.959950 + 0.311907i 0.746752 0.665103i \(-0.231612\pi\)
0.213198 + 0.977009i \(0.431612\pi\)
\(588\) 0.193659i 0.00798635i
\(589\) −10.3507 0.0523040i −0.426492 0.00215515i
\(590\) 9.30799 + 2.67695i 0.383204 + 0.110208i
\(591\) 4.94550 15.2207i 0.203431 0.626095i
\(592\) 4.44908 1.44559i 0.182856 0.0594135i
\(593\) −7.65636 + 10.5381i −0.314409 + 0.432747i −0.936750 0.350000i \(-0.886182\pi\)
0.622341 + 0.782746i \(0.286182\pi\)
\(594\) 1.45994 0.0599019
\(595\) 8.18664 28.4657i 0.335620 1.16698i
\(596\) −7.11228 5.16738i −0.291330 0.211664i
\(597\) −8.24324 11.3459i −0.337373 0.464355i
\(598\) −12.3459 16.9927i −0.504861 0.694882i
\(599\) 11.0471 33.9993i 0.451370 1.38918i −0.423974 0.905675i \(-0.639365\pi\)
0.875344 0.483501i \(-0.160635\pi\)
\(600\) 1.86574 + 4.63886i 0.0761685 + 0.189381i
\(601\) 3.47202 10.6858i 0.141627 0.435882i −0.854935 0.518735i \(-0.826403\pi\)
0.996562 + 0.0828529i \(0.0264032\pi\)
\(602\) −11.6959 + 3.80022i −0.476689 + 0.154886i
\(603\) −1.29126 1.77727i −0.0525843 0.0723760i
\(604\) −5.81506 17.8969i −0.236612 0.728215i
\(605\) −19.8192 + 0.676498i −0.805766 + 0.0275036i
\(606\) −5.04616 + 3.66625i −0.204986 + 0.148931i
\(607\) 31.7362 10.3117i 1.28813 0.418540i 0.416696 0.909046i \(-0.363188\pi\)
0.871438 + 0.490505i \(0.163188\pi\)
\(608\) −1.76807 0.574481i −0.0717047 0.0232983i
\(609\) 2.28257 + 1.65839i 0.0924946 + 0.0672012i
\(610\) 1.11952 1.65694i 0.0453278 0.0670874i
\(611\) −37.1781 + 27.0115i −1.50407 + 1.09277i
\(612\) −2.98439 4.10766i −0.120637 0.166042i
\(613\) −19.3732 + 26.6650i −0.782477 + 1.07699i 0.212527 + 0.977155i \(0.431831\pi\)
−0.995004 + 0.0998322i \(0.968169\pi\)
\(614\) 3.21654 0.129809
\(615\) 17.8773 + 5.14146i 0.720884 + 0.207324i
\(616\) −3.08140 2.23877i −0.124153 0.0902026i
\(617\) −25.3159 + 8.22563i −1.01918 + 0.331152i −0.770504 0.637435i \(-0.779995\pi\)
−0.248676 + 0.968587i \(0.579995\pi\)
\(618\) −2.87221 0.933237i −0.115537 0.0375403i
\(619\) −22.4470 −0.902219 −0.451110 0.892469i \(-0.648972\pi\)
−0.451110 + 0.892469i \(0.648972\pi\)
\(620\) −10.2806 7.02205i −0.412879 0.282012i
\(621\) −4.41461 −0.177152
\(622\) 3.99431 + 1.29783i 0.160157 + 0.0520382i
\(623\) 4.31366 1.40159i 0.172823 0.0561536i
\(624\) −3.84919 2.79660i −0.154091 0.111954i
\(625\) 10.8885 + 22.5042i 0.435542 + 0.900169i
\(626\) −3.01992 −0.120700
\(627\) −1.59531 + 2.19576i −0.0637106 + 0.0876901i
\(628\) 13.4870 + 18.5633i 0.538192 + 0.740757i
\(629\) −19.2158 + 13.9611i −0.766183 + 0.556664i
\(630\) −4.83376 3.26595i −0.192582 0.130119i
\(631\) 20.3171 + 14.7612i 0.808811 + 0.587636i 0.913486 0.406871i \(-0.133380\pi\)
−0.104675 + 0.994507i \(0.533380\pi\)
\(632\) 3.46940 + 1.12728i 0.138005 + 0.0448407i
\(633\) −0.535415 + 0.173967i −0.0212809 + 0.00691457i
\(634\) 10.1610 7.38243i 0.403547 0.293194i
\(635\) −0.187417 5.49071i −0.00743741 0.217892i
\(636\) 0.455400 + 1.40158i 0.0180578 + 0.0555762i
\(637\) −0.541586 0.745429i −0.0214584 0.0295350i
\(638\) 1.50159 0.487895i 0.0594484 0.0193159i
\(639\) 3.52449 10.8473i 0.139426 0.429111i
\(640\) −1.37527 1.76313i −0.0543625 0.0696937i
\(641\) −7.24021 + 22.2831i −0.285971 + 0.880129i 0.700135 + 0.714011i \(0.253123\pi\)
−0.986106 + 0.166118i \(0.946877\pi\)
\(642\) 1.39348 + 1.91797i 0.0549964 + 0.0756961i
\(643\) 12.2372 + 16.8430i 0.482587 + 0.664225i 0.979000 0.203862i \(-0.0653495\pi\)
−0.496412 + 0.868087i \(0.665350\pi\)
\(644\) 9.31766 + 6.76968i 0.367167 + 0.266763i
\(645\) −2.91328 + 10.1297i −0.114710 + 0.398858i
\(646\) 9.43908 0.371375
\(647\) 17.4051 23.9560i 0.684264 0.941809i −0.315711 0.948855i \(-0.602243\pi\)
0.999975 + 0.00704651i \(0.00224299\pi\)
\(648\) −0.951057 + 0.309017i −0.0373610 + 0.0121393i
\(649\) −1.95408 + 6.01405i −0.0767045 + 0.236072i
\(650\) −20.1546 12.6381i −0.790529 0.495708i
\(651\) 14.5255 + 0.0734005i 0.569301 + 0.00287679i
\(652\) 21.9506i 0.859654i
\(653\) 11.1471 + 3.62191i 0.436219 + 0.141736i 0.518890 0.854841i \(-0.326345\pi\)
−0.0826716 + 0.996577i \(0.526345\pi\)
\(654\) 0.533694 + 1.64254i 0.0208691 + 0.0642285i
\(655\) −26.7343 + 20.8533i −1.04460 + 0.814806i
\(656\) −8.31906 −0.324805
\(657\) 12.5459i 0.489463i
\(658\) 14.8113 20.3861i 0.577406 0.794731i
\(659\) −1.47672 + 1.07290i −0.0575247 + 0.0417941i −0.616176 0.787608i \(-0.711319\pi\)
0.558651 + 0.829403i \(0.311319\pi\)
\(660\) −3.06852 + 1.11412i −0.119442 + 0.0433669i
\(661\) −8.71960 + 26.8362i −0.339153 + 1.04381i 0.625487 + 0.780235i \(0.284900\pi\)
−0.964640 + 0.263571i \(0.915100\pi\)
\(662\) −0.223291 + 0.307333i −0.00867844 + 0.0119448i
\(663\) 22.9749 + 7.46501i 0.892273 + 0.289917i
\(664\) 0.453685 + 1.39630i 0.0176064 + 0.0541869i
\(665\) 10.1940 3.70124i 0.395307 0.143528i
\(666\) 1.44559 + 4.44908i 0.0560156 + 0.172398i
\(667\) −4.54056 + 1.47532i −0.175811 + 0.0571245i
\(668\) −7.15860 9.85296i −0.276974 0.381223i
\(669\) 0.706161 + 2.17334i 0.0273017 + 0.0840261i
\(670\) 4.07028 + 2.75010i 0.157249 + 0.106246i
\(671\) 1.05625 + 0.767414i 0.0407763 + 0.0296257i
\(672\) 2.48121 + 0.806193i 0.0957147 + 0.0310996i
\(673\) −14.1205 19.4353i −0.544307 0.749174i 0.444919 0.895571i \(-0.353232\pi\)
−0.989226 + 0.146397i \(0.953232\pi\)
\(674\) −17.4889 + 12.7064i −0.673645 + 0.489432i
\(675\) −4.63886 + 1.86574i −0.178550 + 0.0718123i
\(676\) 9.63721 0.370662
\(677\) 35.4285i 1.36163i −0.732457 0.680813i \(-0.761627\pi\)
0.732457 0.680813i \(-0.238373\pi\)
\(678\) 9.36957 12.8961i 0.359836 0.495272i
\(679\) 1.62705 + 5.00753i 0.0624403 + 0.192171i
\(680\) 9.40730 + 6.35608i 0.360754 + 0.243744i
\(681\) 27.6462 1.05940
\(682\) 4.81103 6.55193i 0.184224 0.250886i
\(683\) 12.5875i 0.481645i −0.970569 0.240823i \(-0.922583\pi\)
0.970569 0.240823i \(-0.0774172\pi\)
\(684\) 0.574481 1.76807i 0.0219658 0.0676038i
\(685\) 0.0732547 + 2.14613i 0.00279892 + 0.0819993i
\(686\) 15.1832 + 11.0313i 0.579699 + 0.421176i
\(687\) 18.5397i 0.707335i
\(688\) 4.71379i 0.179711i
\(689\) −5.67257 4.12137i −0.216108 0.157012i
\(690\) 9.27871 3.36891i 0.353234 0.128252i
\(691\) −26.9201 + 19.5586i −1.02409 + 0.744043i −0.967117 0.254333i \(-0.918144\pi\)
−0.0569709 + 0.998376i \(0.518144\pi\)
\(692\) 22.8869 + 7.43640i 0.870029 + 0.282690i
\(693\) 2.23877 3.08140i 0.0850438 0.117053i
\(694\) 3.93761 12.1187i 0.149470 0.460020i
\(695\) 11.5450 0.394071i 0.437927 0.0149480i
\(696\) −0.874919 + 0.635666i −0.0331637 + 0.0240949i
\(697\) 40.1714 13.0525i 1.52160 0.494398i
\(698\) 33.5845 10.9123i 1.27119 0.413035i
\(699\) 18.9480 13.7665i 0.716677 0.520697i
\(700\) 12.6520 + 3.17565i 0.478202 + 0.120028i
\(701\) −7.61791 + 23.4455i −0.287725 + 0.885525i 0.697844 + 0.716250i \(0.254143\pi\)
−0.985569 + 0.169276i \(0.945857\pi\)
\(702\) 2.79660 3.84919i 0.105551 0.145278i
\(703\) −8.27109 2.68744i −0.311950 0.101359i
\(704\) 1.18111 0.858129i 0.0445149 0.0323419i
\(705\) −7.37082 20.3008i −0.277601 0.764573i
\(706\) 18.0736 + 13.1313i 0.680211 + 0.494202i
\(707\) 16.2727i 0.611999i
\(708\) 4.33139i 0.162784i
\(709\) 7.27724 + 5.28722i 0.273302 + 0.198566i 0.715991 0.698110i \(-0.245975\pi\)
−0.442688 + 0.896676i \(0.645975\pi\)
\(710\) 0.870013 + 25.4886i 0.0326510 + 0.956569i
\(711\) −1.12728 + 3.46940i −0.0422762 + 0.130113i
\(712\) 1.73853i 0.0651542i
\(713\) −14.5478 + 19.8120i −0.544819 + 0.741965i
\(714\) −13.2463 −0.495729
\(715\) 8.69556 12.8699i 0.325196 0.481305i
\(716\) 3.37088 + 10.3745i 0.125976 + 0.387714i
\(717\) 6.93850 9.55003i 0.259123 0.356652i
\(718\) 28.1364i 1.05004i
\(719\) 8.11160 0.302512 0.151256 0.988495i \(-0.451668\pi\)
0.151256 + 0.988495i \(0.451668\pi\)
\(720\) 1.76313 1.37527i 0.0657079 0.0512535i
\(721\) −6.37418 + 4.63111i −0.237387 + 0.172472i
\(722\) −9.13648 12.5753i −0.340024 0.468004i
\(723\) 19.7930 + 6.43113i 0.736109 + 0.239176i
\(724\) 3.36970 + 2.44823i 0.125234 + 0.0909877i
\(725\) −4.14769 + 3.46922i −0.154041 + 0.128844i
\(726\) 2.74054 + 8.43453i 0.101711 + 0.313035i
\(727\) −5.62794 7.74619i −0.208729 0.287290i 0.691798 0.722091i \(-0.256819\pi\)
−0.900527 + 0.434801i \(0.856819\pi\)
\(728\) −11.8052 + 3.83575i −0.437531 + 0.142162i
\(729\) −0.309017 0.951057i −0.0114451 0.0352243i
\(730\) −9.57414 26.3692i −0.354355 0.975969i
\(731\) 7.39586 + 22.7621i 0.273546 + 0.841887i
\(732\) −0.850518 0.276350i −0.0314361 0.0102142i
\(733\) −27.7464 + 38.1897i −1.02484 + 1.41057i −0.116083 + 0.993239i \(0.537034\pi\)
−0.908755 + 0.417330i \(0.862966\pi\)
\(734\) −5.38086 + 16.5606i −0.198611 + 0.611263i
\(735\) 0.407035 0.147786i 0.0150137 0.00545118i
\(736\) −3.57150 + 2.59484i −0.131647 + 0.0956472i
\(737\) −1.88516 + 2.59470i −0.0694407 + 0.0955770i
\(738\) 8.31906i 0.306229i
\(739\) 45.0761 1.65815 0.829075 0.559137i \(-0.188868\pi\)
0.829075 + 0.559137i \(0.188868\pi\)
\(740\) −6.43358 8.24797i −0.236503 0.303202i
\(741\) 2.73330 + 8.41222i 0.100410 + 0.309031i
\(742\) 3.65657 + 1.18809i 0.134237 + 0.0436163i
\(743\) 52.2621i 1.91731i 0.284569 + 0.958656i \(0.408149\pi\)
−0.284569 + 0.958656i \(0.591851\pi\)
\(744\) −1.74727 + 5.28650i −0.0640580 + 0.193812i
\(745\) −5.43330 + 18.8921i −0.199061 + 0.692153i
\(746\) 10.4971 32.3068i 0.384327 1.18284i
\(747\) −1.39630 + 0.453685i −0.0510879 + 0.0165995i
\(748\) −4.35701 + 5.99691i −0.159308 + 0.219269i
\(749\) 6.18501 0.225995
\(750\) 8.32624 7.46149i 0.304031 0.272455i
\(751\) 17.7962 + 12.9297i 0.649392 + 0.471811i 0.863064 0.505095i \(-0.168542\pi\)
−0.213672 + 0.976905i \(0.568542\pi\)
\(752\) 5.67724 + 7.81405i 0.207028 + 0.284949i
\(753\) −2.74991 3.78493i −0.100212 0.137931i
\(754\) 1.59003 4.89360i 0.0579053 0.178214i
\(755\) −33.1784 + 25.8798i −1.20749 + 0.941864i
\(756\) −0.806193 + 2.48121i −0.0293210 + 0.0902407i
\(757\) 21.1136 6.86021i 0.767385 0.249339i 0.100940 0.994893i \(-0.467815\pi\)
0.666445 + 0.745554i \(0.267815\pi\)
\(758\) −3.89031 5.35456i −0.141303 0.194486i
\(759\) 1.99163 + 6.12960i 0.0722916 + 0.222491i
\(760\) 0.141809 + 4.15456i 0.00514397 + 0.150702i
\(761\) −28.0817 + 20.4025i −1.01796 + 0.739591i −0.965864 0.259051i \(-0.916590\pi\)
−0.0520960 + 0.998642i \(0.516590\pi\)
\(762\) −2.33670 + 0.759239i −0.0846497 + 0.0275043i
\(763\) 4.28522 + 1.39235i 0.155135 + 0.0504066i
\(764\) 11.1993 + 8.13678i 0.405177 + 0.294378i
\(765\) −6.35608 + 9.40730i −0.229804 + 0.340122i
\(766\) −11.4713 + 8.33438i −0.414475 + 0.301134i
\(767\) 12.1132 + 16.6723i 0.437381 + 0.602003i
\(768\) −0.587785 + 0.809017i −0.0212099 + 0.0291929i
\(769\) 38.9753 1.40549 0.702743 0.711443i \(-0.251958\pi\)
0.702743 + 0.711443i \(0.251958\pi\)
\(770\) −2.35398 + 8.18501i −0.0848316 + 0.294967i
\(771\) −15.9767 11.6077i −0.575386 0.418043i
\(772\) −12.1459 + 3.94645i −0.437142 + 0.142036i
\(773\) 6.82707 + 2.21825i 0.245553 + 0.0797849i 0.429208 0.903206i \(-0.358793\pi\)
−0.183655 + 0.982991i \(0.558793\pi\)
\(774\) 4.71379 0.169434
\(775\) −6.91365 + 26.9667i −0.248346 + 0.968671i
\(776\) −2.01818 −0.0724486
\(777\) 11.6072 + 3.77140i 0.416405 + 0.135298i
\(778\) 10.8794 3.53494i 0.390046 0.126734i
\(779\) 12.5119 + 9.09046i 0.448287 + 0.325700i
\(780\) −2.94052 + 10.2245i −0.105287 + 0.366094i
\(781\) −16.6513 −0.595829
\(782\) 13.1749 18.1337i 0.471134 0.648460i
\(783\) −0.635666 0.874919i −0.0227168 0.0312671i
\(784\) −0.156673 + 0.113830i −0.00559547 + 0.00406535i
\(785\) 28.7244 42.5135i 1.02522 1.51737i
\(786\) 12.2671 + 8.91259i 0.437554 + 0.317902i
\(787\) −34.2730 11.1360i −1.22170 0.396954i −0.373999 0.927429i \(-0.622013\pi\)
−0.847700 + 0.530475i \(0.822013\pi\)
\(788\) 15.2207 4.94550i 0.542215 0.176176i
\(789\) −20.1783 + 14.6604i −0.718366 + 0.521924i
\(790\) −0.278266 8.15231i −0.00990027 0.290046i
\(791\) −12.8511 39.5516i −0.456933 1.40629i
\(792\) 0.858129 + 1.18111i 0.0304923 + 0.0419690i
\(793\) 4.04665 1.31483i 0.143701 0.0466912i
\(794\) −1.87972 + 5.78517i −0.0667086 + 0.205308i
\(795\) 2.59833 2.02675i 0.0921534 0.0718815i
\(796\) 4.33373 13.3378i 0.153605 0.472747i
\(797\) 24.3472 + 33.5111i 0.862424 + 1.18702i 0.980986 + 0.194078i \(0.0621714\pi\)
−0.118563 + 0.992947i \(0.537829\pi\)
\(798\) −2.85081 3.92381i −0.100918 0.138901i
\(799\) −39.6746 28.8253i −1.40359 1.01977i
\(800\) −2.65626 + 4.23607i −0.0939130 + 0.149768i
\(801\) −1.73853 −0.0614280
\(802\) 20.3039 27.9459i 0.716956 0.986805i
\(803\) 17.4198 5.66003i 0.614731 0.199738i
\(804\) 0.678857 2.08931i 0.0239414 0.0736842i
\(805\) 7.11806 24.7502i 0.250879 0.872328i
\(806\) −8.05864 25.2351i −0.283854 0.888870i
\(807\) 18.8951i 0.665139i
\(808\) −5.93212 1.92746i −0.208691 0.0678079i
\(809\) −10.2628 31.5858i −0.360822 1.11050i −0.952556 0.304363i \(-0.901557\pi\)
0.591734 0.806133i \(-0.298443\pi\)
\(810\) 1.37527 + 1.76313i 0.0483222 + 0.0619500i
\(811\) −23.4552 −0.823623 −0.411811 0.911269i \(-0.635104\pi\)
−0.411811 + 0.911269i \(0.635104\pi\)
\(812\) 2.82142i 0.0990123i
\(813\) 15.4935 21.3250i 0.543380 0.747899i
\(814\) 5.52529 4.01436i 0.193661 0.140703i
\(815\) 46.1362 16.7511i 1.61608 0.586767i
\(816\) 1.56899 4.82884i 0.0549255 0.169043i
\(817\) −5.15088 + 7.08958i −0.180207 + 0.248033i
\(818\) −5.70155 1.85255i −0.199350 0.0647728i
\(819\) −3.83575 11.8052i −0.134032 0.412508i
\(820\) 6.34850 + 17.4851i 0.221699 + 0.610608i
\(821\) −9.64494 29.6841i −0.336611 1.03598i −0.965923 0.258829i \(-0.916663\pi\)
0.629313 0.777152i \(-0.283337\pi\)
\(822\) 0.913334 0.296760i 0.0318562 0.0103507i
\(823\) 26.4718 + 36.4353i 0.922749 + 1.27006i 0.962621 + 0.270850i \(0.0873049\pi\)
−0.0398723 + 0.999205i \(0.512695\pi\)
\(824\) −0.933237 2.87221i −0.0325108 0.100058i
\(825\) 4.68334 + 5.59925i 0.163053 + 0.194941i
\(826\) −9.14201 6.64206i −0.318091 0.231107i
\(827\) 28.2092 + 9.16573i 0.980930 + 0.318723i 0.755220 0.655471i \(-0.227530\pi\)
0.225710 + 0.974195i \(0.427530\pi\)
\(828\) −2.59484 3.57150i −0.0901771 0.124118i
\(829\) 35.9303 26.1049i 1.24791 0.906660i 0.249812 0.968294i \(-0.419631\pi\)
0.998099 + 0.0616345i \(0.0196313\pi\)
\(830\) 2.58855 2.01912i 0.0898498 0.0700846i
\(831\) 22.0233 0.763979
\(832\) 4.75786i 0.164949i
\(833\) 0.577953 0.795484i 0.0200249 0.0275619i
\(834\) −1.59641 4.91325i −0.0552792 0.170132i
\(835\) −15.2462 + 22.5651i −0.527617 + 0.780899i
\(836\) −2.71410 −0.0938693
\(837\) −5.28650 1.74727i −0.182728 0.0603945i
\(838\) 28.4211i 0.981791i
\(839\) 5.30216 16.3184i 0.183051 0.563372i −0.816859 0.576838i \(-0.804286\pi\)
0.999909 + 0.0134657i \(0.00428641\pi\)
\(840\) −0.199007 5.83027i −0.00686640 0.201164i
\(841\) 22.5153 + 16.3583i 0.776390 + 0.564080i
\(842\) 23.8940i 0.823441i
\(843\) 7.93639i 0.273344i
\(844\) −0.455452 0.330905i −0.0156773 0.0113902i
\(845\) −7.35442 20.2557i −0.253000 0.696816i
\(846\) −7.81405 + 5.67724i −0.268653 + 0.195188i
\(847\) 22.0048 + 7.14980i 0.756094 + 0.245670i
\(848\) −0.866223 + 1.19225i −0.0297462 + 0.0409422i
\(849\) 2.11956 6.52334i 0.0727432 0.223880i
\(850\) 6.18034 24.6229i 0.211984 0.844560i
\(851\) −16.7076 + 12.1388i −0.572729 + 0.416112i
\(852\) 10.8473 3.52449i 0.371621 0.120747i
\(853\) −40.3181 + 13.1002i −1.38047 + 0.448541i −0.902823 0.430013i \(-0.858509\pi\)
−0.477644 + 0.878554i \(0.658509\pi\)
\(854\) −1.88752 + 1.37136i −0.0645897 + 0.0469271i
\(855\) −4.15456 + 0.141809i −0.142083 + 0.00484978i
\(856\) −0.732598 + 2.25470i −0.0250397 + 0.0770642i
\(857\) 22.2137 30.5745i 0.758804 1.04440i −0.238509 0.971140i \(-0.576659\pi\)
0.997313 0.0732637i \(-0.0233415\pi\)
\(858\) −6.60620 2.14648i −0.225532 0.0732797i
\(859\) −31.9424 + 23.2075i −1.08986 + 0.791830i −0.979376 0.202048i \(-0.935240\pi\)
−0.110485 + 0.993878i \(0.535240\pi\)
\(860\) −9.90752 + 3.59722i −0.337844 + 0.122664i
\(861\) −17.5586 12.7570i −0.598394 0.434759i
\(862\) 6.49880i 0.221350i
\(863\) 37.2565i 1.26823i 0.773241 + 0.634113i \(0.218634\pi\)
−0.773241 + 0.634113i \(0.781366\pi\)
\(864\) −0.809017 0.587785i −0.0275233 0.0199969i
\(865\) −1.83566 53.7790i −0.0624144 1.82854i
\(866\) 6.06357 18.6618i 0.206049 0.634152i
\(867\) 8.77941i 0.298165i
\(868\) 8.47851 + 11.7945i 0.287780 + 0.400333i
\(869\) 5.32577 0.180664
\(870\) 2.00373 + 1.35383i 0.0679328 + 0.0458990i
\(871\) 3.22990 + 9.94062i 0.109441 + 0.336825i
\(872\) −1.01515 + 1.39723i −0.0343772 + 0.0473162i
\(873\) 2.01818i 0.0683052i
\(874\) 8.20702 0.277607
\(875\) −2.98048 29.0157i −0.100759 0.980909i
\(876\) −10.1499 + 7.37431i −0.342932 + 0.249155i
\(877\) 4.29984 + 5.91822i 0.145195 + 0.199844i 0.875420 0.483363i \(-0.160585\pi\)
−0.730225 + 0.683207i \(0.760585\pi\)
\(878\) 19.2778 + 6.26373i 0.650594 + 0.211391i
\(879\) −26.3937 19.1762i −0.890238 0.646796i
\(880\) −2.70497 1.82762i −0.0911845 0.0616091i
\(881\) −14.7602 45.4272i −0.497283 1.53048i −0.813368 0.581749i \(-0.802368\pi\)
0.316085 0.948731i \(-0.397632\pi\)
\(882\) −0.113830 0.156673i −0.00383285 0.00527546i
\(883\) −43.9748 + 14.2883i −1.47987 + 0.480839i −0.934074 0.357080i \(-0.883772\pi\)
−0.545795 + 0.837918i \(0.683772\pi\)
\(884\) 7.46501 + 22.9749i 0.251075 + 0.772731i
\(885\) −9.10379 + 3.30540i −0.306021 + 0.111110i
\(886\) −0.206190 0.634587i −0.00692708 0.0213194i
\(887\) −17.5663 5.70763i −0.589818 0.191643i −0.00112363 0.999999i \(-0.500358\pi\)
−0.588694 + 0.808356i \(0.700358\pi\)
\(888\) −2.74968 + 3.78461i −0.0922732 + 0.127003i
\(889\) −1.98078 + 6.09620i −0.0664331 + 0.204460i
\(890\) 3.65407 1.32672i 0.122485 0.0444718i
\(891\) −1.18111 + 0.858129i −0.0395688 + 0.0287484i
\(892\) −1.34320 + 1.84875i −0.0449736 + 0.0619008i
\(893\) 17.9561i 0.600877i
\(894\) 8.79127 0.294024
\(895\) 19.2329 15.0021i 0.642885 0.501464i
\(896\) 0.806193 + 2.48121i 0.0269330 + 0.0828913i
\(897\) 19.9761 + 6.49062i 0.666982 + 0.216716i
\(898\) 21.1276i 0.705038i
\(899\) −6.02124 0.0304265i −0.200819 0.00101478i
\(900\) −4.23607 2.65626i −0.141202 0.0885421i
\(901\) 2.31222 7.11630i 0.0770314 0.237078i
\(902\) −11.5509 + 3.75310i −0.384601 + 0.124965i
\(903\) 7.22845 9.94911i 0.240548 0.331086i
\(904\) 15.9405 0.530172
\(905\) 2.57422 8.95080i 0.0855699 0.297535i
\(906\) 15.2240 + 11.0609i 0.505785 + 0.367474i
\(907\) −27.9282 38.4399i −0.927341 1.27638i −0.960888 0.276938i \(-0.910680\pi\)
0.0335465 0.999437i \(-0.489320\pi\)
\(908\) 16.2500 + 22.3662i 0.539275 + 0.742249i
\(909\) 1.92746 5.93212i 0.0639299 0.196756i
\(910\) 17.0710 + 21.8853i 0.565897 + 0.725490i
\(911\) 18.2126 56.0526i 0.603410 1.85710i 0.0960362 0.995378i \(-0.469384\pi\)
0.507373 0.861726i \(-0.330616\pi\)
\(912\) 1.76807 0.574481i 0.0585466 0.0190230i
\(913\) 1.25987 + 1.73406i 0.0416955 + 0.0573889i
\(914\) −3.90276 12.0114i −0.129092 0.397303i
\(915\) 0.0682165 + 1.99852i 0.00225517 + 0.0660692i
\(916\) −14.9990 + 10.8974i −0.495580 + 0.360060i
\(917\) 37.6226 12.2243i 1.24241 0.403683i
\(918\) 4.82884 + 1.56899i 0.159375 + 0.0517842i
\(919\) 13.0684 + 9.49472i 0.431085 + 0.313202i 0.782083 0.623175i \(-0.214157\pi\)
−0.350997 + 0.936376i \(0.614157\pi\)
\(920\) 8.17939 + 5.52644i 0.269667 + 0.182201i
\(921\) −2.60224 + 1.89064i −0.0857466 + 0.0622986i
\(922\) 8.00364 + 11.0161i 0.263586 + 0.362795i
\(923\) −31.8965 + 43.9018i −1.04989 + 1.44505i
\(924\) 3.80882 0.125301
\(925\) −12.4261 + 19.8165i −0.408567 + 0.651562i
\(926\) 19.0904 + 13.8700i 0.627349 + 0.455796i
\(927\) 2.87221 0.933237i 0.0943357 0.0306515i
\(928\) −1.02853 0.334189i −0.0337631 0.0109703i
\(929\) −51.6821 −1.69564 −0.847818 0.530288i \(-0.822084\pi\)
−0.847818 + 0.530288i \(0.822084\pi\)
\(930\) 12.4446 0.361831i 0.408076 0.0118649i
\(931\) 0.360023 0.0117993
\(932\) 22.2747 + 7.23747i 0.729631 + 0.237071i
\(933\) −3.99431 + 1.29783i −0.130768 + 0.0424890i
\(934\) −1.81372 1.31774i −0.0593467 0.0431179i
\(935\) 15.9294 + 4.58123i 0.520946 + 0.149822i
\(936\) 4.75786 0.155515
\(937\) −29.7872 + 40.9985i −0.973104 + 1.33936i −0.0326407 + 0.999467i \(0.510392\pi\)
−0.940463 + 0.339895i \(0.889608\pi\)
\(938\) −3.36877 4.63671i −0.109994 0.151394i
\(939\) 2.44316 1.77506i 0.0797297 0.0579270i
\(940\) 12.0912 17.8956i 0.394373 0.583691i
\(941\) 22.9923 + 16.7049i 0.749529 + 0.544565i 0.895681 0.444698i \(-0.146689\pi\)
−0.146152 + 0.989262i \(0.546689\pi\)
\(942\) −21.8225 7.09056i −0.711015 0.231023i
\(943\) 34.9279 11.3488i 1.13741 0.369567i
\(944\) 3.50417 2.54593i 0.114051 0.0828629i
\(945\) 5.83027 0.199007i 0.189659 0.00647371i
\(946\) −2.12660 6.54500i −0.0691417 0.212796i
\(947\) 17.4818 + 24.0616i 0.568082 + 0.781898i 0.992326 0.123650i \(-0.0394601\pi\)
−0.424244 + 0.905548i \(0.639460\pi\)
\(948\) −3.46940 + 1.12728i −0.112681 + 0.0366123i
\(949\) 18.4458 56.7702i 0.598775 1.84284i
\(950\) 8.62391 3.46852i 0.279797 0.112534i
\(951\) −3.88118 + 11.9450i −0.125856 + 0.387344i
\(952\) −7.78596 10.7165i −0.252344 0.347322i
\(953\) −4.97527 6.84787i −0.161165 0.221824i 0.720796 0.693147i \(-0.243777\pi\)
−0.881961 + 0.471323i \(0.843777\pi\)
\(954\) −1.19225 0.866223i −0.0386006 0.0280450i
\(955\) 8.55551 29.7483i 0.276850 0.962633i
\(956\) 11.8045 0.381784
\(957\) −0.928031 + 1.27733i −0.0299990 + 0.0412901i
\(958\) 25.8960 8.41411i 0.836660 0.271847i
\(959\) 0.774217 2.38279i 0.0250008 0.0769445i
\(960\) 2.14896 + 0.618034i 0.0693574 + 0.0199470i
\(961\) −25.2624 + 17.9670i −0.814916 + 0.579579i
\(962\) 22.2574i 0.717608i
\(963\) −2.25470 0.732598i −0.0726568 0.0236076i
\(964\) 6.43113 + 19.7930i 0.207133 + 0.637489i
\(965\) 17.5636 + 22.5169i 0.565393 + 0.724844i
\(966\) −11.5173 −0.370562
\(967\) 32.1088i 1.03255i −0.856423 0.516274i \(-0.827319\pi\)
0.856423 0.516274i \(-0.172681\pi\)
\(968\) −5.21283 + 7.17484i −0.167547 + 0.230608i
\(969\) −7.63637 + 5.54815i −0.245316 + 0.178232i
\(970\) 1.54013 + 4.24185i 0.0494506 + 0.136198i
\(971\) −12.4203 + 38.2256i −0.398585 + 1.22672i 0.527549 + 0.849525i \(0.323111\pi\)
−0.926134 + 0.377195i \(0.876889\pi\)
\(972\) 0.587785 0.809017i 0.0188532 0.0259492i
\(973\) −12.8182 4.16487i −0.410931 0.133520i
\(974\) 12.7719 + 39.3077i 0.409237 + 1.25950i
\(975\) 23.7339 1.62213i 0.760094 0.0519497i
\(976\) −0.276350 0.850518i −0.00884575 0.0272244i
\(977\) 20.3479 6.61144i 0.650987 0.211519i 0.0351378 0.999382i \(-0.488813\pi\)
0.615849 + 0.787864i \(0.288813\pi\)
\(978\) −12.9023 17.7584i −0.412569 0.567852i
\(979\) 0.784329 + 2.41392i 0.0250673 + 0.0771491i
\(980\) 0.358811 + 0.242432i 0.0114618 + 0.00774420i
\(981\) −1.39723 1.01515i −0.0446101 0.0324111i
\(982\) 16.6080 + 5.39627i 0.529983 + 0.172202i
\(983\) −21.5434 29.6520i −0.687129 0.945752i 0.312863 0.949798i \(-0.398712\pi\)
−0.999992 + 0.00404612i \(0.998712\pi\)
\(984\) 6.73026 4.88982i 0.214553 0.155882i
\(985\) −22.0099 28.2171i −0.701293 0.899070i
\(986\) 5.49094 0.174867
\(987\) 25.1985i 0.802079i
\(988\) −5.19904 + 7.15586i −0.165403 + 0.227658i
\(989\) 6.43050 + 19.7910i 0.204478 + 0.629319i
\(990\) 1.82762 2.70497i 0.0580856 0.0859696i
\(991\) −24.3097 −0.772224 −0.386112 0.922452i \(-0.626182\pi\)
−0.386112 + 0.922452i \(0.626182\pi\)
\(992\) −5.30389 + 1.69375i −0.168399 + 0.0537767i
\(993\) 0.379885i 0.0120553i
\(994\) 9.19502 28.2994i 0.291648 0.897601i
\(995\) −31.3409 + 1.06977i −0.993574 + 0.0339141i
\(996\) −1.18776 0.862961i −0.0376357 0.0273440i
\(997\) 56.2831i 1.78250i 0.453510 + 0.891251i \(0.350172\pi\)
−0.453510 + 0.891251i \(0.649828\pi\)
\(998\) 2.81302i 0.0890445i
\(999\) −3.78461 2.74968i −0.119740 0.0869960i
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 930.2.z.c.349.1 32
5.4 even 2 inner 930.2.z.c.349.8 yes 32
31.4 even 5 inner 930.2.z.c.469.6 yes 32
155.4 even 10 inner 930.2.z.c.469.3 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.z.c.349.1 32 1.1 even 1 trivial
930.2.z.c.349.8 yes 32 5.4 even 2 inner
930.2.z.c.469.3 yes 32 155.4 even 10 inner
930.2.z.c.469.6 yes 32 31.4 even 5 inner