Properties

Label 297.2.f.c.190.3
Level 297297
Weight 22
Character 297.190
Analytic conductor 2.3722.372
Analytic rank 00
Dimension 1616
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [297,2,Mod(82,297)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(297, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("297.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 297=3311 297 = 3^{3} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 297.f (of order 55, degree 44, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 2.371556940032.37155694003
Analytic rank: 00
Dimension: 1616
Relative dimension: 44 over Q(ζ5)\Q(\zeta_{5})
Coefficient field: Q[x]/(x16+)\mathbb{Q}[x]/(x^{16} + \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x16+8x14+35x12+108x10+589x8+792x6+465x4+22x2+121 x^{16} + 8x^{14} + 35x^{12} + 108x^{10} + 589x^{8} + 792x^{6} + 465x^{4} + 22x^{2} + 121 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C5]\mathrm{SU}(2)[C_{5}]

Embedding invariants

Embedding label 190.3
Root 0.3296431.01454i0.329643 - 1.01454i of defining polynomial
Character χ\chi == 297.190
Dual form 297.2.f.c.136.3

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.8630170.627019i)q2+(0.266388+0.819857i)q4+(0.993168+0.721579i)q5+(0.473654+1.45776i)q7+(0.943455+2.90366i)q8+1.30957q10+(3.003371.40704i)q11+(1.89482+1.37667i)q13+(0.505269+1.55506i)q14+(1.24004+0.900943i)q16+(2.87322+2.08752i)q17+(0.8844222.72197i)q19+(0.856159+0.622036i)q20+(1.709723.09747i)q22+2.29437q23+(1.079383.32198i)q25+(0.772068+2.37618i)q26+(1.068980.776656i)q28+(2.562577.88677i)q29+(3.91111+2.84159i)q314.47108q32+3.78855q34+(1.52230+1.10602i)q35+(1.244013.82868i)q37+(2.470001.79456i)q38+(1.15821+3.56460i)q40+(1.49582+4.60365i)q417.52483q43+(0.353510+2.83715i)q44+(1.980081.43861i)q46+(2.827758.70291i)q47+(3.76241+2.73355i)q49+(3.014472.19014i)q50+(0.6239151.92021i)q52+(5.00934+3.63950i)q53+(3.99814+0.769743i)q554.67969q56+(2.733618.41319i)q58+(3.3637410.3525i)q59+(0.496027+0.360385i)q61+(1.59363+4.90467i)q62+(6.33871+4.60534i)q642.87526q65+8.65964q67+(2.47686+1.79954i)q68+(0.620280+1.90903i)q70+(12.63529.18000i)q71+(4.68358+14.4146i)q73+(1.327054.08424i)q74+2.46722q76+(0.628562+5.04463i)q77+(1.571431.14171i)q79+(0.581468+1.78958i)q80+(4.17749+3.03513i)q82+(4.31509+3.13509i)q83+(1.34728+4.14651i)q85+(6.49406+4.71821i)q86+(6.91910+7.39328i)q88+5.84063q89+(1.109363.41426i)q91+(0.611192+1.88106i)q92+(7.897285.73771i)q94+(1.085743.34155i)q95+(6.881344.99958i)q97+4.96102q98+O(q100)q+(0.863017 - 0.627019i) q^{2} +(-0.266388 + 0.819857i) q^{4} +(0.993168 + 0.721579i) q^{5} +(-0.473654 + 1.45776i) q^{7} +(0.943455 + 2.90366i) q^{8} +1.30957 q^{10} +(3.00337 - 1.40704i) q^{11} +(-1.89482 + 1.37667i) q^{13} +(0.505269 + 1.55506i) q^{14} +(1.24004 + 0.900943i) q^{16} +(2.87322 + 2.08752i) q^{17} +(-0.884422 - 2.72197i) q^{19} +(-0.856159 + 0.622036i) q^{20} +(1.70972 - 3.09747i) q^{22} +2.29437 q^{23} +(-1.07938 - 3.32198i) q^{25} +(-0.772068 + 2.37618i) q^{26} +(-1.06898 - 0.776656i) q^{28} +(2.56257 - 7.88677i) q^{29} +(-3.91111 + 2.84159i) q^{31} -4.47108 q^{32} +3.78855 q^{34} +(-1.52230 + 1.10602i) q^{35} +(1.24401 - 3.82868i) q^{37} +(-2.47000 - 1.79456i) q^{38} +(-1.15821 + 3.56460i) q^{40} +(1.49582 + 4.60365i) q^{41} -7.52483 q^{43} +(0.353510 + 2.83715i) q^{44} +(1.98008 - 1.43861i) q^{46} +(-2.82775 - 8.70291i) q^{47} +(3.76241 + 2.73355i) q^{49} +(-3.01447 - 2.19014i) q^{50} +(-0.623915 - 1.92021i) q^{52} +(-5.00934 + 3.63950i) q^{53} +(3.99814 + 0.769743i) q^{55} -4.67969 q^{56} +(-2.73361 - 8.41319i) q^{58} +(3.36374 - 10.3525i) q^{59} +(0.496027 + 0.360385i) q^{61} +(-1.59363 + 4.90467i) q^{62} +(-6.33871 + 4.60534i) q^{64} -2.87526 q^{65} +8.65964 q^{67} +(-2.47686 + 1.79954i) q^{68} +(-0.620280 + 1.90903i) q^{70} +(-12.6352 - 9.18000i) q^{71} +(-4.68358 + 14.4146i) q^{73} +(-1.32705 - 4.08424i) q^{74} +2.46722 q^{76} +(0.628562 + 5.04463i) q^{77} +(1.57143 - 1.14171i) q^{79} +(0.581468 + 1.78958i) q^{80} +(4.17749 + 3.03513i) q^{82} +(4.31509 + 3.13509i) q^{83} +(1.34728 + 4.14651i) q^{85} +(-6.49406 + 4.71821i) q^{86} +(6.91910 + 7.39328i) q^{88} +5.84063 q^{89} +(-1.10936 - 3.41426i) q^{91} +(-0.611192 + 1.88106i) q^{92} +(-7.89728 - 5.73771i) q^{94} +(1.08574 - 3.34155i) q^{95} +(6.88134 - 4.99958i) q^{97} +4.96102 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q+2q4+8q712q10+8q132q16+10q1924q2216q2530q286q31+32q34+12q3740q4080q4312q46+40q49+12q52+46q94+O(q100) 16 q + 2 q^{4} + 8 q^{7} - 12 q^{10} + 8 q^{13} - 2 q^{16} + 10 q^{19} - 24 q^{22} - 16 q^{25} - 30 q^{28} - 6 q^{31} + 32 q^{34} + 12 q^{37} - 40 q^{40} - 80 q^{43} - 12 q^{46} + 40 q^{49} + 12 q^{52}+ \cdots - 46 q^{94}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/297Z)×\left(\mathbb{Z}/297\mathbb{Z}\right)^\times.

nn 5656 244244
χ(n)\chi(n) 11 e(45)e\left(\frac{4}{5}\right)

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.863017 0.627019i 0.610245 0.443369i −0.239255 0.970957i 0.576903π-0.576903\pi
0.849501 + 0.527587i 0.176903π0.176903\pi
33 0 0
44 −0.266388 + 0.819857i −0.133194 + 0.409928i
55 0.993168 + 0.721579i 0.444158 + 0.322700i 0.787285 0.616589i 0.211486π-0.211486\pi
−0.343127 + 0.939289i 0.611486π0.611486\pi
66 0 0
77 −0.473654 + 1.45776i −0.179024 + 0.550980i −0.999794 0.0202787i 0.993545π-0.993545\pi
0.820770 + 0.571259i 0.193545π0.193545\pi
88 0.943455 + 2.90366i 0.333562 + 1.02660i
99 0 0
1010 1.30957 0.414121
1111 3.00337 1.40704i 0.905551 0.424238i
1212 0 0
1313 −1.89482 + 1.37667i −0.525530 + 0.381820i −0.818683 0.574246i 0.805295π-0.805295\pi
0.293153 + 0.956065i 0.405295π0.405295\pi
1414 0.505269 + 1.55506i 0.135039 + 0.415607i
1515 0 0
1616 1.24004 + 0.900943i 0.310010 + 0.225236i
1717 2.87322 + 2.08752i 0.696858 + 0.506297i 0.878908 0.476992i 0.158273π-0.158273\pi
−0.182049 + 0.983289i 0.558273π0.558273\pi
1818 0 0
1919 −0.884422 2.72197i −0.202900 0.624463i −0.999793 0.0203420i 0.993524π-0.993524\pi
0.796893 0.604121i 0.206476π-0.206476\pi
2020 −0.856159 + 0.622036i −0.191443 + 0.139092i
2121 0 0
2222 1.70972 3.09747i 0.364514 0.660383i
2323 2.29437 0.478410 0.239205 0.970969i 0.423113π-0.423113\pi
0.239205 + 0.970969i 0.423113π0.423113\pi
2424 0 0
2525 −1.07938 3.32198i −0.215876 0.664397i
2626 −0.772068 + 2.37618i −0.151415 + 0.466007i
2727 0 0
2828 −1.06898 0.776656i −0.202017 0.146774i
2929 2.56257 7.88677i 0.475857 1.46454i −0.368943 0.929452i 0.620280π-0.620280\pi
0.844799 0.535084i 0.179720π-0.179720\pi
3030 0 0
3131 −3.91111 + 2.84159i −0.702456 + 0.510364i −0.880731 0.473617i 0.842948π-0.842948\pi
0.178276 + 0.983981i 0.442948π0.442948\pi
3232 −4.47108 −0.790384
3333 0 0
3434 3.78855 0.649731
3535 −1.52230 + 1.10602i −0.257316 + 0.186951i
3636 0 0
3737 1.24401 3.82868i 0.204515 0.629432i −0.795218 0.606323i 0.792644π-0.792644\pi
0.999733 0.0231083i 0.00735626π-0.00735626\pi
3838 −2.47000 1.79456i −0.400687 0.291116i
3939 0 0
4040 −1.15821 + 3.56460i −0.183129 + 0.563612i
4141 1.49582 + 4.60365i 0.233608 + 0.718970i 0.997303 + 0.0733934i 0.0233829π0.0233829\pi
−0.763696 + 0.645577i 0.776617π0.776617\pi
4242 0 0
4343 −7.52483 −1.14753 −0.573763 0.819022i 0.694517π-0.694517\pi
−0.573763 + 0.819022i 0.694517π0.694517\pi
4444 0.353510 + 2.83715i 0.0532936 + 0.427717i
4545 0 0
4646 1.98008 1.43861i 0.291947 0.212112i
4747 −2.82775 8.70291i −0.412469 1.26945i −0.914495 0.404597i 0.867412π-0.867412\pi
0.502026 0.864853i 0.332588π-0.332588\pi
4848 0 0
4949 3.76241 + 2.73355i 0.537488 + 0.390508i
5050 −3.01447 2.19014i −0.426310 0.309732i
5151 0 0
5252 −0.623915 1.92021i −0.0865214 0.266286i
5353 −5.00934 + 3.63950i −0.688085 + 0.499923i −0.876030 0.482256i 0.839817π-0.839817\pi
0.187945 + 0.982180i 0.439817π0.439817\pi
5454 0 0
5555 3.99814 + 0.769743i 0.539110 + 0.103792i
5656 −4.67969 −0.625350
5757 0 0
5858 −2.73361 8.41319i −0.358941 1.10471i
5959 3.36374 10.3525i 0.437922 1.34778i −0.452141 0.891946i 0.649340π-0.649340\pi
0.890063 0.455838i 0.150660π-0.150660\pi
6060 0 0
6161 0.496027 + 0.360385i 0.0635097 + 0.0461425i 0.619087 0.785322i 0.287503π-0.287503\pi
−0.555577 + 0.831465i 0.687503π0.687503\pi
6262 −1.59363 + 4.90467i −0.202391 + 0.622894i
6363 0 0
6464 −6.33871 + 4.60534i −0.792338 + 0.575667i
6565 −2.87526 −0.356632
6666 0 0
6767 8.65964 1.05794 0.528972 0.848639i 0.322578π-0.322578\pi
0.528972 + 0.848639i 0.322578π0.322578\pi
6868 −2.47686 + 1.79954i −0.300363 + 0.218226i
6969 0 0
7070 −0.620280 + 1.90903i −0.0741377 + 0.228172i
7171 −12.6352 9.18000i −1.49952 1.08947i −0.970572 0.240813i 0.922586π-0.922586\pi
−0.528950 0.848653i 0.677414π-0.677414\pi
7272 0 0
7373 −4.68358 + 14.4146i −0.548172 + 1.68710i 0.165154 + 0.986268i 0.447188π0.447188\pi
−0.713326 + 0.700832i 0.752812π0.752812\pi
7474 −1.32705 4.08424i −0.154266 0.474783i
7575 0 0
7676 2.46722 0.283010
7777 0.628562 + 5.04463i 0.0716313 + 0.574889i
7878 0 0
7979 1.57143 1.14171i 0.176800 0.128453i −0.495866 0.868399i 0.665149π-0.665149\pi
0.672666 + 0.739947i 0.265149π0.265149\pi
8080 0.581468 + 1.78958i 0.0650101 + 0.200081i
8181 0 0
8282 4.17749 + 3.03513i 0.461327 + 0.335174i
8383 4.31509 + 3.13509i 0.473642 + 0.344121i 0.798859 0.601518i 0.205437π-0.205437\pi
−0.325217 + 0.945639i 0.605437π0.605437\pi
8484 0 0
8585 1.34728 + 4.14651i 0.146133 + 0.449752i
8686 −6.49406 + 4.71821i −0.700272 + 0.508778i
8787 0 0
8888 6.91910 + 7.39328i 0.737579 + 0.788126i
8989 5.84063 0.619105 0.309553 0.950882i 0.399821π-0.399821\pi
0.309553 + 0.950882i 0.399821π0.399821\pi
9090 0 0
9191 −1.10936 3.41426i −0.116292 0.357911i
9292 −0.611192 + 1.88106i −0.0637212 + 0.196114i
9393 0 0
9494 −7.89728 5.73771i −0.814542 0.591800i
9595 1.08574 3.34155i 0.111394 0.342836i
9696 0 0
9797 6.88134 4.99958i 0.698694 0.507631i −0.180813 0.983518i 0.557873π-0.557873\pi
0.879507 + 0.475887i 0.157873π0.157873\pi
9898 4.96102 0.501139
9999 0 0
100100 3.01108 0.301108
101101 0.606954 0.440978i 0.0603942 0.0438789i −0.557179 0.830393i 0.688116π-0.688116\pi
0.617573 + 0.786514i 0.288116π0.288116\pi
102102 0 0
103103 3.33934 10.2774i 0.329035 1.01266i −0.640552 0.767915i 0.721294π-0.721294\pi
0.969586 0.244749i 0.0787057π-0.0787057\pi
104104 −5.78506 4.20309i −0.567272 0.412147i
105105 0 0
106106 −2.04111 + 6.28190i −0.198250 + 0.610152i
107107 −1.23326 3.79558i −0.119224 0.366932i 0.873581 0.486679i 0.161792π-0.161792\pi
−0.992804 + 0.119747i 0.961792π0.961792\pi
108108 0 0
109109 −13.1110 −1.25580 −0.627902 0.778293i 0.716086π-0.716086\pi
−0.627902 + 0.778293i 0.716086π0.716086\pi
110110 3.93311 1.84261i 0.375007 0.175686i
111111 0 0
112112 −1.90070 + 1.38094i −0.179600 + 0.130487i
113113 0.705985 + 2.17280i 0.0664135 + 0.204400i 0.978756 0.205028i 0.0657285π-0.0657285\pi
−0.912343 + 0.409428i 0.865728π0.865728\pi
114114 0 0
115115 2.27870 + 1.65557i 0.212490 + 0.154383i
116116 5.78338 + 4.20187i 0.536974 + 0.390134i
117117 0 0
118118 −3.58826 11.0435i −0.330326 1.01664i
119119 −4.40400 + 3.19969i −0.403714 + 0.293315i
120120 0 0
121121 7.04048 8.45172i 0.640044 0.768338i
122122 0.654048 0.0592147
123123 0 0
124124 −1.28782 3.96351i −0.115650 0.355934i
125125 3.22185 9.91584i 0.288171 0.886900i
126126 0 0
127127 −1.28021 0.930131i −0.113601 0.0825357i 0.529534 0.848288i 0.322367π-0.322367\pi
−0.643135 + 0.765753i 0.722367π0.722367\pi
128128 0.180503 0.555533i 0.0159544 0.0491026i
129129 0 0
130130 −2.48140 + 1.80284i −0.217633 + 0.158119i
131131 5.64250 0.492987 0.246494 0.969144i 0.420722π-0.420722\pi
0.246494 + 0.969144i 0.420722π0.420722\pi
132132 0 0
133133 4.38688 0.380391
134134 7.47342 5.42976i 0.645605 0.469060i
135135 0 0
136136 −3.35068 + 10.3123i −0.287318 + 0.884274i
137137 17.5144 + 12.7249i 1.49635 + 1.08716i 0.971805 + 0.235784i 0.0757659π0.0757659\pi
0.524549 + 0.851380i 0.324234π0.324234\pi
138138 0 0
139139 −6.50795 + 20.0294i −0.551997 + 1.69887i 0.151748 + 0.988419i 0.451510π0.451510\pi
−0.703745 + 0.710452i 0.748490π0.748490\pi
140140 −0.501254 1.54270i −0.0423637 0.130382i
141141 0 0
142142 −16.6604 −1.39811
143143 −3.75383 + 6.80074i −0.313911 + 0.568707i
144144 0 0
145145 8.23599 5.98379i 0.683961 0.496927i
146146 4.99620 + 15.3767i 0.413489 + 1.27259i
147147 0 0
148148 2.80758 + 2.03983i 0.230782 + 0.167673i
149149 11.3235 + 8.22699i 0.927655 + 0.673981i 0.945418 0.325861i 0.105654π-0.105654\pi
−0.0177624 + 0.999842i 0.505654π0.505654\pi
150150 0 0
151151 −6.47911 19.9407i −0.527263 1.62275i −0.759798 0.650160i 0.774702π-0.774702\pi
0.232535 0.972588i 0.425298π-0.425298\pi
152152 7.06925 5.13611i 0.573392 0.416594i
153153 0 0
154154 3.70554 + 3.95948i 0.298601 + 0.319064i
155155 −5.93482 −0.476696
156156 0 0
157157 −5.41090 16.6530i −0.431837 1.32906i −0.896294 0.443461i 0.853751π-0.853751\pi
0.464457 0.885596i 0.346249π-0.346249\pi
158158 0.640298 1.97063i 0.0509394 0.156775i
159159 0 0
160160 −4.44054 3.22624i −0.351055 0.255057i
161161 −1.08674 + 3.34463i −0.0856469 + 0.263594i
162162 0 0
163163 −0.154783 + 0.112456i −0.0121235 + 0.00880824i −0.593831 0.804590i 0.702385π-0.702385\pi
0.581707 + 0.813398i 0.302385π0.302385\pi
164164 −4.17280 −0.325841
165165 0 0
166166 5.68976 0.441611
167167 −0.775722 + 0.563595i −0.0600271 + 0.0436123i −0.617394 0.786654i 0.711812π-0.711812\pi
0.557367 + 0.830266i 0.311812π0.311812\pi
168168 0 0
169169 −2.32208 + 7.14664i −0.178622 + 0.549742i
170170 3.76267 + 2.73374i 0.288584 + 0.209668i
171171 0 0
172172 2.00452 6.16928i 0.152843 0.470403i
173173 6.68664 + 20.5794i 0.508376 + 1.56462i 0.795021 + 0.606582i 0.207460π0.207460\pi
−0.286645 + 0.958037i 0.592540π0.592540\pi
174174 0 0
175175 5.35389 0.404716
176176 4.99197 + 0.961079i 0.376284 + 0.0724440i
177177 0 0
178178 5.04056 3.66218i 0.377806 0.274492i
179179 −6.33539 19.4983i −0.473529 1.45737i −0.847931 0.530106i 0.822152π-0.822152\pi
0.374402 0.927266i 0.377848π-0.377848\pi
180180 0 0
181181 8.43682 + 6.12971i 0.627104 + 0.455618i 0.855396 0.517975i 0.173314π-0.173314\pi
−0.228292 + 0.973593i 0.573314π0.573314\pi
182182 −3.09820 2.25097i −0.229654 0.166853i
183183 0 0
184184 2.16464 + 6.66207i 0.159579 + 0.491134i
185185 3.99821 2.90487i 0.293954 0.213570i
186186 0 0
187187 11.5666 + 2.22685i 0.845831 + 0.162844i
188188 7.88841 0.575322
189189 0 0
190190 −1.15821 3.56460i −0.0840252 0.258603i
191191 −6.37924 + 19.6333i −0.461586 + 1.42061i 0.401640 + 0.915797i 0.368440π0.368440\pi
−0.863226 + 0.504817i 0.831560π0.831560\pi
192192 0 0
193193 4.84767 + 3.52204i 0.348943 + 0.253522i 0.748426 0.663219i 0.230810π-0.230810\pi
−0.399482 + 0.916741i 0.630810π0.630810\pi
194194 2.80388 8.62945i 0.201307 0.619559i
195195 0 0
196196 −3.24338 + 2.35646i −0.231670 + 0.168318i
197197 1.41800 0.101028 0.0505141 0.998723i 0.483914π-0.483914\pi
0.0505141 + 0.998723i 0.483914π0.483914\pi
198198 0 0
199199 6.07350 0.430539 0.215269 0.976555i 0.430937π-0.430937\pi
0.215269 + 0.976555i 0.430937π0.430937\pi
200200 8.62755 6.26828i 0.610060 0.443235i
201201 0 0
202202 0.247310 0.761143i 0.0174007 0.0535538i
203203 10.2832 + 7.47119i 0.721740 + 0.524375i
204204 0 0
205205 −1.83630 + 5.65155i −0.128253 + 0.394722i
206206 −3.56223 10.9634i −0.248192 0.763858i
207207 0 0
208208 −3.58996 −0.248919
209209 −6.48617 6.93067i −0.448657 0.479405i
210210 0 0
211211 −12.8992 + 9.37181i −0.888017 + 0.645182i −0.935360 0.353697i 0.884924π-0.884924\pi
0.0473435 + 0.998879i 0.484924π0.484924\pi
212212 −1.64944 5.07646i −0.113284 0.348652i
213213 0 0
214214 −3.44422 2.50237i −0.235442 0.171059i
215215 −7.47342 5.42976i −0.509683 0.370306i
216216 0 0
217217 −2.28983 7.04737i −0.155444 0.478406i
218218 −11.3150 + 8.22083i −0.766348 + 0.556785i
219219 0 0
220220 −1.69614 + 3.07286i −0.114353 + 0.207172i
221221 −8.31807 −0.559534
222222 0 0
223223 8.12958 + 25.0203i 0.544397 + 1.67548i 0.722419 + 0.691456i 0.243030π0.243030\pi
−0.178022 + 0.984027i 0.556970π0.556970\pi
224224 2.11775 6.51775i 0.141498 0.435485i
225225 0 0
226226 1.97166 + 1.43250i 0.131153 + 0.0952883i
227227 0.859779 2.64613i 0.0570656 0.175630i −0.918461 0.395512i 0.870567π-0.870567\pi
0.975526 + 0.219882i 0.0705672π0.0705672\pi
228228 0 0
229229 −17.0058 + 12.3554i −1.12377 + 0.816470i −0.984777 0.173823i 0.944388π-0.944388\pi
−0.138998 + 0.990293i 0.544388π0.544388\pi
230230 3.00463 0.198119
231231 0 0
232232 25.3181 1.66222
233233 −11.0308 + 8.01437i −0.722654 + 0.525039i −0.887231 0.461326i 0.847374π-0.847374\pi
0.164577 + 0.986364i 0.447374π0.447374\pi
234234 0 0
235235 3.47141 10.6839i 0.226450 0.696940i
236236 7.59153 + 5.51557i 0.494167 + 0.359033i
237237 0 0
238238 −1.79446 + 5.52278i −0.116318 + 0.357989i
239239 −6.26582 19.2842i −0.405302 1.24739i −0.920643 0.390407i 0.872334π-0.872334\pi
0.515340 0.856986i 0.327666π-0.327666\pi
240240 0 0
241241 −26.3931 −1.70013 −0.850066 0.526676i 0.823438π-0.823438\pi
−0.850066 + 0.526676i 0.823438π0.823438\pi
242242 0.776668 11.7085i 0.0499261 0.752651i
243243 0 0
244244 −0.427599 + 0.310669i −0.0273742 + 0.0198885i
245245 1.76424 + 5.42976i 0.112713 + 0.346895i
246246 0 0
247247 5.42308 + 3.94010i 0.345062 + 0.250702i
248248 −11.9409 8.67560i −0.758250 0.550901i
249249 0 0
250250 −3.43691 10.5777i −0.217369 0.668993i
251251 4.51620 3.28121i 0.285060 0.207108i −0.436062 0.899917i 0.643627π-0.643627\pi
0.721121 + 0.692809i 0.243627π0.243627\pi
252252 0 0
253253 6.89085 3.22827i 0.433224 0.202960i
254254 −1.68806 −0.105918
255255 0 0
256256 −5.03489 15.4958i −0.314681 0.968488i
257257 −8.53233 + 26.2598i −0.532232 + 1.63804i 0.217322 + 0.976100i 0.430268π0.430268\pi
−0.749555 + 0.661943i 0.769732π0.769732\pi
258258 0 0
259259 4.99205 + 3.62694i 0.310191 + 0.225367i
260260 0.765932 2.35730i 0.0475011 0.146193i
261261 0 0
262262 4.86957 3.53795i 0.300843 0.218575i
263263 −29.4556 −1.81631 −0.908156 0.418632i 0.862510π-0.862510\pi
−0.908156 + 0.418632i 0.862510π0.862510\pi
264264 0 0
265265 −7.60130 −0.466944
266266 3.78595 2.75065i 0.232132 0.168653i
267267 0 0
268268 −2.30682 + 7.09967i −0.140912 + 0.433681i
269269 −14.7566 10.7213i −0.899723 0.653687i 0.0386718 0.999252i 0.487687π-0.487687\pi
−0.938395 + 0.345565i 0.887687π0.887687\pi
270270 0 0
271271 −2.16675 + 6.66858i −0.131621 + 0.405087i −0.995049 0.0993842i 0.968313π-0.968313\pi
0.863428 + 0.504472i 0.168313π0.168313\pi
272272 1.68218 + 5.17721i 0.101997 + 0.313915i
273273 0 0
274274 23.0940 1.39516
275275 −7.91593 8.45842i −0.477349 0.510062i
276276 0 0
277277 9.31029 6.76432i 0.559401 0.406429i −0.271838 0.962343i 0.587632π-0.587632\pi
0.831240 + 0.555914i 0.187632π0.187632\pi
278278 6.94234 + 21.3663i 0.416374 + 1.28147i
279279 0 0
280280 −4.64772 3.37677i −0.277755 0.201801i
281281 −9.16977 6.66223i −0.547022 0.397435i 0.279664 0.960098i 0.409777π-0.409777\pi
−0.826686 + 0.562663i 0.809777π0.809777\pi
282282 0 0
283283 1.41474 + 4.35413i 0.0840976 + 0.258826i 0.984259 0.176730i 0.0565519π-0.0565519\pi
−0.900162 + 0.435556i 0.856552π0.856552\pi
284284 10.8921 7.91361i 0.646330 0.469586i
285285 0 0
286286 1.02457 + 8.22288i 0.0605842 + 0.486229i
287287 −7.41950 −0.437959
288288 0 0
289289 −1.35562 4.17217i −0.0797423 0.245422i
290290 3.35585 10.3282i 0.197062 0.606495i
291291 0 0
292292 −10.5703 7.67974i −0.618577 0.449423i
293293 −8.12850 + 25.0170i −0.474872 + 1.46151i 0.371258 + 0.928530i 0.378927π0.378927\pi
−0.846130 + 0.532977i 0.821073π0.821073\pi
294294 0 0
295295 10.8109 7.85460i 0.629436 0.457312i
296296 12.2909 0.714391
297297 0 0
298298 14.9308 0.864920
299299 −4.34743 + 3.15859i −0.251418 + 0.182666i
300300 0 0
301301 3.56416 10.9694i 0.205435 0.632264i
302302 −18.0948 13.1466i −1.04124 0.756502i
303303 0 0
304304 1.35562 4.17217i 0.0777501 0.239290i
305305 0.232592 + 0.715845i 0.0133182 + 0.0409892i
306306 0 0
307307 −14.7093 −0.839504 −0.419752 0.907639i 0.637883π-0.637883\pi
−0.419752 + 0.907639i 0.637883π0.637883\pi
308308 −4.30332 0.828497i −0.245204 0.0472080i
309309 0 0
310310 −5.12185 + 3.72124i −0.290901 + 0.211352i
311311 −2.40653 7.40655i −0.136462 0.419987i 0.859353 0.511384i 0.170867π-0.170867\pi
−0.995815 + 0.0913967i 0.970867π0.970867\pi
312312 0 0
313313 −14.6754 10.6623i −0.829504 0.602670i 0.0899148 0.995949i 0.471341π-0.471341\pi
−0.919419 + 0.393279i 0.871341π0.871341\pi
314314 −15.1115 10.9791i −0.852789 0.619588i
315315 0 0
316316 0.517430 + 1.59249i 0.0291077 + 0.0895844i
317317 15.7364 11.4331i 0.883843 0.642149i −0.0504227 0.998728i 0.516057π-0.516057\pi
0.934265 + 0.356579i 0.116057π0.116057\pi
318318 0 0
319319 −3.40065 27.2925i −0.190400 1.52809i
320320 −9.61852 −0.537692
321321 0 0
322322 1.15928 + 3.56788i 0.0646039 + 0.198830i
323323 3.14102 9.66706i 0.174771 0.537890i
324324 0 0
325325 6.61851 + 4.80863i 0.367129 + 0.266735i
326326 −0.0630679 + 0.194103i −0.00349301 + 0.0107504i
327327 0 0
328328 −11.9562 + 8.68668i −0.660170 + 0.479642i
329329 14.0261 0.773283
330330 0 0
331331 −20.6236 −1.13358 −0.566788 0.823863i 0.691814π-0.691814\pi
−0.566788 + 0.823863i 0.691814π0.691814\pi
332332 −3.71981 + 2.70260i −0.204151 + 0.148325i
333333 0 0
334334 −0.316077 + 0.972784i −0.0172949 + 0.0532284i
335335 8.60048 + 6.24862i 0.469895 + 0.341398i
336336 0 0
337337 −1.01877 + 3.13545i −0.0554959 + 0.170799i −0.974963 0.222369i 0.928621π-0.928621\pi
0.919467 + 0.393168i 0.128621π0.128621\pi
338338 2.47708 + 7.62366i 0.134735 + 0.414673i
339339 0 0
340340 −3.75845 −0.203830
341341 −7.74828 + 14.0374i −0.419593 + 0.760169i
342342 0 0
343343 −14.4472 + 10.4965i −0.780077 + 0.566759i
344344 −7.09934 21.8495i −0.382771 1.17805i
345345 0 0
346346 18.6743 + 13.5677i 1.00394 + 0.729404i
347347 −6.50317 4.72483i −0.349109 0.253642i 0.399386 0.916783i 0.369223π-0.369223\pi
−0.748495 + 0.663140i 0.769223π0.769223\pi
348348 0 0
349349 0.924934 + 2.84665i 0.0495106 + 0.152378i 0.972755 0.231835i 0.0744729π-0.0744729\pi
−0.923245 + 0.384213i 0.874473π0.874473\pi
350350 4.62050 3.35699i 0.246976 0.179439i
351351 0 0
352352 −13.4283 + 6.29099i −0.715732 + 0.335311i
353353 9.91473 0.527708 0.263854 0.964563i 0.415006π-0.415006\pi
0.263854 + 0.964563i 0.415006π0.415006\pi
354354 0 0
355355 −5.92477 18.2346i −0.314454 0.967791i
356356 −1.55587 + 4.78848i −0.0824610 + 0.253789i
357357 0 0
358358 −17.6934 12.8550i −0.935123 0.679407i
359359 −4.69829 + 14.4598i −0.247966 + 0.763161i 0.747168 + 0.664635i 0.231413π0.231413\pi
−0.995134 + 0.0985263i 0.968587π0.968587\pi
360360 0 0
361361 8.74440 6.35318i 0.460232 0.334378i
362362 11.1246 0.584694
363363 0 0
364364 3.09472 0.162207
365365 −15.0529 + 10.9365i −0.787902 + 0.572445i
366366 0 0
367367 −0.428907 + 1.32004i −0.0223888 + 0.0689056i −0.961627 0.274361i 0.911534π-0.911534\pi
0.939238 + 0.343267i 0.111534π0.111534\pi
368368 2.84512 + 2.06710i 0.148312 + 0.107755i
369369 0 0
370370 1.62912 5.01391i 0.0846938 0.260661i
371371 −2.93281 9.02625i −0.152264 0.468620i
372372 0 0
373373 19.1341 0.990725 0.495362 0.868686i 0.335035π-0.335035\pi
0.495362 + 0.868686i 0.335035π0.335035\pi
374374 11.3784 5.33064i 0.588364 0.275641i
375375 0 0
376376 22.6024 16.4216i 1.16563 0.846879i
377377 6.00187 + 18.4718i 0.309112 + 0.951348i
378378 0 0
379379 0.383874 + 0.278900i 0.0197183 + 0.0143262i 0.597601 0.801794i 0.296121π-0.296121\pi
−0.577882 + 0.816120i 0.696121π0.696121\pi
380380 2.45037 + 1.78030i 0.125701 + 0.0913273i
381381 0 0
382382 6.80504 + 20.9438i 0.348176 + 1.07158i
383383 16.8630 12.2517i 0.861658 0.626031i −0.0666775 0.997775i 0.521240π-0.521240\pi
0.928336 + 0.371743i 0.121240π0.121240\pi
384384 0 0
385385 −3.01583 + 5.46373i −0.153701 + 0.278457i
386386 6.39201 0.325345
387387 0 0
388388 2.26584 + 6.97354i 0.115031 + 0.354028i
389389 0.823795 2.53538i 0.0417681 0.128549i −0.927998 0.372585i 0.878472π-0.878472\pi
0.969766 + 0.244036i 0.0784715π0.0784715\pi
390390 0 0
391391 6.59224 + 4.78954i 0.333384 + 0.242217i
392392 −4.38763 + 13.5037i −0.221609 + 0.682042i
393393 0 0
394394 1.22376 0.889112i 0.0616521 0.0447928i
395395 2.38453 0.119979
396396 0 0
397397 −15.5756 −0.781716 −0.390858 0.920451i 0.627822π-0.627822\pi
−0.390858 + 0.920451i 0.627822π0.627822\pi
398398 5.24153 3.80820i 0.262734 0.190888i
399399 0 0
400400 1.65444 5.09185i 0.0827222 0.254593i
401401 6.67194 + 4.84745i 0.333181 + 0.242070i 0.741779 0.670644i 0.233982π-0.233982\pi
−0.408598 + 0.912714i 0.633982π0.633982\pi
402402 0 0
403403 3.49893 10.7686i 0.174294 0.536423i
404404 0.199854 + 0.615086i 0.00994309 + 0.0306017i
405405 0 0
406406 13.5592 0.672930
407407 −1.65087 13.2493i −0.0818306 0.656745i
408408 0 0
409409 −3.25502 + 2.36491i −0.160950 + 0.116937i −0.665345 0.746536i 0.731716π-0.731716\pi
0.504395 + 0.863473i 0.331716π0.331716\pi
410410 1.95887 + 6.02878i 0.0967417 + 0.297740i
411411 0 0
412412 7.53646 + 5.47556i 0.371295 + 0.269761i
413413 13.4982 + 9.80702i 0.664203 + 0.482572i
414414 0 0
415415 2.02339 + 6.22735i 0.0993243 + 0.305689i
416416 8.47192 6.15521i 0.415370 0.301784i
417417 0 0
418418 −9.94333 1.91434i −0.486344 0.0936335i
419419 32.0411 1.56531 0.782654 0.622456i 0.213865π-0.213865\pi
0.782654 + 0.622456i 0.213865π0.213865\pi
420420 0 0
421421 7.87554 + 24.2384i 0.383830 + 1.18131i 0.937325 + 0.348455i 0.113294π0.113294\pi
−0.553495 + 0.832852i 0.686706π0.686706\pi
422422 −5.25592 + 16.1761i −0.255854 + 0.787439i
423423 0 0
424424 −15.2939 11.1117i −0.742739 0.539631i
425425 3.83341 11.7980i 0.185948 0.572288i
426426 0 0
427427 −0.760297 + 0.552388i −0.0367934 + 0.0267320i
428428 3.44035 0.166296
429429 0 0
430430 −9.85425 −0.475214
431431 −16.7429 + 12.1644i −0.806477 + 0.585940i −0.912807 0.408391i 0.866090π-0.866090\pi
0.106330 + 0.994331i 0.466090π0.466090\pi
432432 0 0
433433 −4.45957 + 13.7251i −0.214313 + 0.659588i 0.784889 + 0.619637i 0.212720π0.212720\pi
−0.999202 + 0.0399509i 0.987280π0.987280\pi
434434 −6.39499 4.64623i −0.306969 0.223026i
435435 0 0
436436 3.49260 10.7491i 0.167265 0.514790i
437437 −2.02919 6.24521i −0.0970694 0.298749i
438438 0 0
439439 8.95399 0.427351 0.213675 0.976905i 0.431457π-0.431457\pi
0.213675 + 0.976905i 0.431457π0.431457\pi
440440 1.53700 + 12.3355i 0.0732736 + 0.588070i
441441 0 0
442442 −7.17864 + 5.21559i −0.341453 + 0.248080i
443443 3.16988 + 9.75589i 0.150606 + 0.463516i 0.997689 0.0679433i 0.0216437π-0.0216437\pi
−0.847084 + 0.531460i 0.821644π0.821644\pi
444444 0 0
445445 5.80073 + 4.21448i 0.274981 + 0.199785i
446446 22.7042 + 16.4955i 1.07507 + 0.781086i
447447 0 0
448448 −3.71111 11.4216i −0.175333 0.539621i
449449 16.5355 12.0137i 0.780359 0.566964i −0.124728 0.992191i 0.539806π-0.539806\pi
0.905087 + 0.425227i 0.139806π0.139806\pi
450450 0 0
451451 10.9700 + 11.7218i 0.516558 + 0.551958i
452452 −1.96945 −0.0926351
453453 0 0
454454 −0.917168 2.82275i −0.0430448 0.132478i
455455 1.36188 4.19142i 0.0638457 0.196497i
456456 0 0
457457 31.1364 + 22.6219i 1.45650 + 1.05821i 0.984258 + 0.176739i 0.0565550π0.0565550\pi
0.472242 + 0.881469i 0.343445π0.343445\pi
458458 −6.92921 + 21.3259i −0.323781 + 0.996494i
459459 0 0
460460 −1.96435 + 1.42718i −0.0915882 + 0.0665427i
461461 19.5409 0.910110 0.455055 0.890463i 0.349620π-0.349620\pi
0.455055 + 0.890463i 0.349620π0.349620\pi
462462 0 0
463463 −16.5263 −0.768042 −0.384021 0.923324i 0.625461π-0.625461\pi
−0.384021 + 0.923324i 0.625461π0.625461\pi
464464 10.2832 7.47119i 0.477386 0.346841i
465465 0 0
466466 −4.49464 + 13.8331i −0.208210 + 0.640805i
467467 23.7147 + 17.2297i 1.09739 + 0.797297i 0.980631 0.195864i 0.0627510π-0.0627510\pi
0.116754 + 0.993161i 0.462751π0.462751\pi
468468 0 0
469469 −4.10167 + 12.6236i −0.189398 + 0.582906i
470470 −3.70312 11.3970i −0.170812 0.525705i
471471 0 0
472472 33.2337 1.52971
473473 −22.5999 + 10.5877i −1.03914 + 0.486824i
474474 0 0
475475 −8.08771 + 5.87607i −0.371090 + 0.269613i
476476 −1.45012 4.46301i −0.0664661 0.204562i
477477 0 0
478478 −17.4991 12.7138i −0.800389 0.581517i
479479 −12.5305 9.10393i −0.572533 0.415969i 0.263492 0.964662i 0.415126π-0.415126\pi
−0.836024 + 0.548692i 0.815126π0.815126\pi
480480 0 0
481481 2.91365 + 8.96728i 0.132851 + 0.408873i
482482 −22.7777 + 16.5490i −1.03750 + 0.753786i
483483 0 0
484484 5.05371 + 8.02362i 0.229714 + 0.364710i
485485 10.4419 0.474143
486486 0 0
487487 −1.19788 3.68670i −0.0542811 0.167060i 0.920241 0.391353i 0.127993π-0.127993\pi
−0.974522 + 0.224293i 0.927993π0.927993\pi
488488 −0.578454 + 1.78030i −0.0261854 + 0.0805903i
489489 0 0
490490 4.92713 + 3.57977i 0.222585 + 0.161717i
491491 2.24264 6.90215i 0.101209 0.311490i −0.887613 0.460590i 0.847638π-0.847638\pi
0.988822 + 0.149101i 0.0476378π0.0476378\pi
492492 0 0
493493 23.8266 17.3110i 1.07310 0.779649i
494494 7.15072 0.321726
495495 0 0
496496 −7.41004 −0.332721
497497 19.3669 14.0709i 0.868725 0.631165i
498498 0 0
499499 11.0928 34.1400i 0.496580 1.52832i −0.317900 0.948124i 0.602978π-0.602978\pi
0.814480 0.580192i 0.197022π-0.197022\pi
500500 7.27131 + 5.28292i 0.325183 + 0.236259i
501501 0 0
502502 1.84018 5.66348i 0.0821311 0.252774i
503503 4.52869 + 13.9379i 0.201924 + 0.621459i 0.999826 + 0.0186711i 0.00594354π0.00594354\pi
−0.797901 + 0.602788i 0.794056π0.794056\pi
504504 0 0
505505 0.921008 0.0409843
506506 3.92274 7.10675i 0.174387 0.315933i
507507 0 0
508508 1.10361 0.801818i 0.0489647 0.0355749i
509509 −0.124689 0.383752i −0.00552673 0.0170095i 0.948255 0.317509i 0.102847π-0.102847\pi
−0.953782 + 0.300500i 0.902847π0.902847\pi
510510 0 0
511511 −18.7946 13.6550i −0.831422 0.604064i
512512 −13.1162 9.52950i −0.579661 0.421148i
513513 0 0
514514 9.10185 + 28.0126i 0.401465 + 1.23558i
515515 10.7325 7.79761i 0.472930 0.343604i
516516 0 0
517517 −20.7381 22.1593i −0.912061 0.974565i
518518 6.58239 0.289214
519519 0 0
520520 −2.71267 8.34875i −0.118959 0.366117i
521521 −3.50114 + 10.7754i −0.153388 + 0.472079i −0.997994 0.0633089i 0.979835π-0.979835\pi
0.844606 + 0.535388i 0.179835π0.179835\pi
522522 0 0
523523 11.6876 + 8.49154i 0.511063 + 0.371309i 0.813227 0.581947i 0.197709π-0.197709\pi
−0.302164 + 0.953256i 0.597709π0.597709\pi
524524 −1.50309 + 4.62604i −0.0656629 + 0.202090i
525525 0 0
526526 −25.4207 + 18.4692i −1.10840 + 0.805297i
527527 −17.1693 −0.747908
528528 0 0
529529 −17.7359 −0.771124
530530 −6.56005 + 4.76616i −0.284950 + 0.207029i
531531 0 0
532532 −1.16861 + 3.59661i −0.0506657 + 0.155933i
533533 −9.17202 6.66387i −0.397284 0.288644i
534534 0 0
535535 1.51398 4.65954i 0.0654549 0.201449i
536536 8.16998 + 25.1446i 0.352890 + 1.08608i
537537 0 0
538538 −19.4576 −0.838877
539539 15.1461 + 2.91601i 0.652391 + 0.125602i
540540 0 0
541541 18.9044 13.7349i 0.812765 0.590509i −0.101866 0.994798i 0.532481π-0.532481\pi
0.914631 + 0.404290i 0.132481π0.132481\pi
542542 2.31138 + 7.11370i 0.0992823 + 0.305559i
543543 0 0
544544 −12.8464 9.33346i −0.550785 0.400169i
545545 −13.0214 9.46060i −0.557776 0.405248i
546546 0 0
547547 1.13277 + 3.48630i 0.0484337 + 0.149063i 0.972348 0.233535i 0.0750293π-0.0750293\pi
−0.923915 + 0.382598i 0.875029π0.875029\pi
548548 −15.0982 + 10.9695i −0.644965 + 0.468594i
549549 0 0
550550 −12.1352 2.33633i −0.517446 0.0996213i
551551 −23.7339 −1.01110
552552 0 0
553553 0.920023 + 2.83154i 0.0391234 + 0.120409i
554554 3.79359 11.6755i 0.161174 0.496043i
555555 0 0
556556 −14.6876 10.6712i −0.622893 0.452558i
557557 10.6998 32.9306i 0.453365 1.39531i −0.419680 0.907672i 0.637858π-0.637858\pi
0.873044 0.487641i 0.162142π-0.162142\pi
558558 0 0
559559 14.2582 10.3592i 0.603059 0.438148i
560560 −2.88418 −0.121879
561561 0 0
562562 −12.0910 −0.510028
563563 31.1564 22.6364i 1.31309 0.954012i 0.313095 0.949722i 0.398634π-0.398634\pi
0.999991 0.00429056i 0.00136573π-0.00136573\pi
564564 0 0
565565 −0.866684 + 2.66738i −0.0364617 + 0.112218i
566566 3.95107 + 2.87062i 0.166076 + 0.120661i
567567 0 0
568568 14.7348 45.3492i 0.618260 1.90281i
569569 −7.93065 24.4080i −0.332470 1.02324i −0.967955 0.251124i 0.919200π-0.919200\pi
0.635485 0.772114i 0.280800π-0.280800\pi
570570 0 0
571571 22.4284 0.938600 0.469300 0.883039i 0.344506π-0.344506\pi
0.469300 + 0.883039i 0.344506π0.344506\pi
572572 −4.57566 4.88924i −0.191318 0.204429i
573573 0 0
574574 −6.40316 + 4.65217i −0.267263 + 0.194178i
575575 −2.47649 7.62187i −0.103277 0.317854i
576576 0 0
577577 −16.4972 11.9859i −0.686786 0.498979i 0.188816 0.982013i 0.439535π-0.439535\pi
−0.875602 + 0.483033i 0.839535π0.839535\pi
578578 −3.78595 2.75065i −0.157475 0.114412i
579579 0 0
580580 2.71189 + 8.34634i 0.112605 + 0.346563i
581581 −6.61406 + 4.80539i −0.274397 + 0.199361i
582582 0 0
583583 −9.92398 + 17.9791i −0.411009 + 0.744618i
584584 −46.2738 −1.91482
585585 0 0
586586 8.67107 + 26.6868i 0.358198 + 1.10242i
587587 −2.07403 + 6.38320i −0.0856043 + 0.263463i −0.984691 0.174307i 0.944232π-0.944232\pi
0.899087 + 0.437770i 0.144232π0.144232\pi
588588 0 0
589589 11.1938 + 8.13276i 0.461232 + 0.335104i
590590 4.40504 13.5573i 0.181352 0.558145i
591591 0 0
592592 4.99205 3.62694i 0.205172 0.149066i
593593 −12.4707 −0.512110 −0.256055 0.966662i 0.582423π-0.582423\pi
−0.256055 + 0.966662i 0.582423π0.582423\pi
594594 0 0
595595 −6.68275 −0.273966
596596 −9.76138 + 7.09206i −0.399842 + 0.290502i
597597 0 0
598598 −1.77141 + 5.45184i −0.0724384 + 0.222942i
599599 −4.35794 3.16623i −0.178061 0.129369i 0.495185 0.868788i 0.335100π-0.335100\pi
−0.673246 + 0.739419i 0.735100π0.735100\pi
600600 0 0
601601 12.5533 38.6351i 0.512059 1.57596i −0.276510 0.961011i 0.589178π-0.589178\pi
0.788569 0.614946i 0.210822π-0.210822\pi
602602 −3.80206 11.7015i −0.154961 0.476919i
603603 0 0
604604 18.0744 0.735439
605605 13.0910 3.31372i 0.532224 0.134722i
606606 0 0
607607 −30.1803 + 21.9272i −1.22498 + 0.889999i −0.996504 0.0835505i 0.973374π-0.973374\pi
−0.228475 + 0.973550i 0.573374π0.573374\pi
608608 3.95432 + 12.1702i 0.160369 + 0.493565i
609609 0 0
610610 0.649579 + 0.471947i 0.0263007 + 0.0191086i
611611 17.3391 + 12.5976i 0.701465 + 0.509644i
612612 0 0
613613 −2.35013 7.23295i −0.0949208 0.292136i 0.892312 0.451419i 0.149082π-0.149082\pi
−0.987233 + 0.159283i 0.949082π0.949082\pi
614614 −12.6944 + 9.22301i −0.512304 + 0.372210i
615615 0 0
616616 −14.0549 + 6.58451i −0.566286 + 0.265298i
617617 −38.2642 −1.54046 −0.770229 0.637767i 0.779858π-0.779858\pi
−0.770229 + 0.637767i 0.779858π0.779858\pi
618618 0 0
619619 9.54846 + 29.3871i 0.383785 + 1.18117i 0.937358 + 0.348368i 0.113264π0.113264\pi
−0.553573 + 0.832801i 0.686736π0.686736\pi
620620 1.58096 4.86570i 0.0634929 0.195411i
621621 0 0
622622 −6.72093 4.88304i −0.269485 0.195792i
623623 −2.76643 + 8.51421i −0.110835 + 0.341115i
624624 0 0
625625 −3.77433 + 2.74221i −0.150973 + 0.109689i
626626 −19.3506 −0.773407
627627 0 0
628628 15.0945 0.602336
629629 11.5668 8.40375i 0.461197 0.335079i
630630 0 0
631631 1.73983 5.35465i 0.0692616 0.213165i −0.910435 0.413653i 0.864253π-0.864253\pi
0.979696 + 0.200488i 0.0642527π0.0642527\pi
632632 4.79771 + 3.48574i 0.190843 + 0.138655i
633633 0 0
634634 6.41196 19.7340i 0.254652 0.783737i
635635 −0.600306 1.84755i −0.0238224 0.0733179i
636636 0 0
637637 −10.8923 −0.431569
638638 −20.0477 21.4216i −0.793698 0.848091i
639639 0 0
640640 0.580131 0.421490i 0.0229317 0.0166609i
641641 −13.0681 40.2195i −0.516159 1.58857i −0.781163 0.624327i 0.785373π-0.785373\pi
0.265004 0.964247i 0.414627π-0.414627\pi
642642 0 0
643643 9.80010 + 7.12019i 0.386478 + 0.280793i 0.764011 0.645203i 0.223227π-0.223227\pi
−0.377533 + 0.925996i 0.623227π0.623227\pi
644644 −2.45263 1.78194i −0.0966471 0.0702182i
645645 0 0
646646 −3.35068 10.3123i −0.131831 0.405733i
647647 −33.3540 + 24.2331i −1.31128 + 0.952703i −0.311286 + 0.950316i 0.600760π0.600760\pi
−0.999997 + 0.00238648i 0.999240π0.999240\pi
648648 0 0
649649 −4.46385 35.8254i −0.175221 1.40627i
650650 8.72698 0.342301
651651 0 0
652652 −0.0509658 0.156856i −0.00199597 0.00614297i
653653 4.25924 13.1086i 0.166677 0.512979i −0.832479 0.554056i 0.813079π-0.813079\pi
0.999156 + 0.0410778i 0.0130792π0.0130792\pi
654654 0 0
655655 5.60395 + 4.07151i 0.218964 + 0.159087i
656656 −2.29275 + 7.05637i −0.0895170 + 0.275505i
657657 0 0
658658 12.1048 8.79462i 0.471892 0.342850i
659659 7.42881 0.289385 0.144693 0.989477i 0.453781π-0.453781\pi
0.144693 + 0.989477i 0.453781π0.453781\pi
660660 0 0
661661 −10.6949 −0.415984 −0.207992 0.978130i 0.566693π-0.566693\pi
−0.207992 + 0.978130i 0.566693π0.566693\pi
662662 −17.7985 + 12.9314i −0.691760 + 0.502593i
663663 0 0
664664 −5.03214 + 15.4873i −0.195285 + 0.601026i
665665 4.35691 + 3.16548i 0.168954 + 0.122752i
666666 0 0
667667 5.87948 18.0952i 0.227654 0.700648i
668668 −0.255424 0.786115i −0.00988266 0.0304157i
669669 0 0
670670 11.3404 0.438117
671671 1.99683 + 0.384439i 0.0770867 + 0.0148411i
672672 0 0
673673 15.7103 11.4142i 0.605588 0.439986i −0.242270 0.970209i 0.577892π-0.577892\pi
0.847858 + 0.530223i 0.177892π0.177892\pi
674674 1.08677 + 3.34474i 0.0418609 + 0.128834i
675675 0 0
676676 −5.24065 3.80755i −0.201563 0.146444i
677677 26.2504 + 19.0720i 1.00888 + 0.732997i 0.963975 0.265994i 0.0857001π-0.0857001\pi
0.0449095 + 0.998991i 0.485700π0.485700\pi
678678 0 0
679679 4.02880 + 12.3994i 0.154611 + 0.475844i
680680 −10.7689 + 7.82409i −0.412970 + 0.300040i
681681 0 0
682682 2.11482 + 16.9729i 0.0809807 + 0.649924i
683683 20.5244 0.785344 0.392672 0.919679i 0.371551π-0.371551\pi
0.392672 + 0.919679i 0.371551π0.371551\pi
684684 0 0
685685 8.21267 + 25.2760i 0.313790 + 0.965747i
686686 −5.88669 + 18.1174i −0.224755 + 0.691724i
687687 0 0
688688 −9.33110 6.77944i −0.355745 0.258464i
689689 4.48142 13.7924i 0.170729 0.525449i
690690 0 0
691691 23.9062 17.3688i 0.909433 0.660742i −0.0314381 0.999506i 0.510009π-0.510009\pi
0.940871 + 0.338764i 0.110009π0.110009\pi
692692 −18.6534 −0.709094
693693 0 0
694694 −8.57491 −0.325499
695695 −20.9163 + 15.1966i −0.793400 + 0.576439i
696696 0 0
697697 −5.31239 + 16.3499i −0.201221 + 0.619295i
698698 2.58314 + 1.87676i 0.0977733 + 0.0710365i
699699 0 0
700700 −1.42621 + 4.38943i −0.0539057 + 0.165905i
701701 −6.24195 19.2108i −0.235755 0.725580i −0.997020 0.0771395i 0.975421π-0.975421\pi
0.761265 0.648441i 0.224579π-0.224579\pi
702702 0 0
703703 −11.5218 −0.434553
704704 −12.5576 + 22.7504i −0.473282 + 0.857436i
705705 0 0
706706 8.55658 6.21672i 0.322031 0.233969i
707707 0.355352 + 1.09366i 0.0133644 + 0.0411314i
708708 0 0
709709 −8.44613 6.13647i −0.317201 0.230460i 0.417779 0.908549i 0.362809π-0.362809\pi
−0.734980 + 0.678089i 0.762809π0.762809\pi
710710 −16.5466 12.0218i −0.620983 0.451171i
711711 0 0
712712 5.51037 + 16.9592i 0.206510 + 0.635572i
713713 −8.97353 + 6.51965i −0.336061 + 0.244163i
714714 0 0
715715 −8.63546 + 4.04560i −0.322948 + 0.151297i
716716 17.6735 0.660489
717717 0 0
718718 5.01189 + 15.4250i 0.187042 + 0.575656i
719719 5.23808 16.1212i 0.195348 0.601218i −0.804625 0.593784i 0.797634π-0.797634\pi
0.999972 0.00743448i 0.00236649π-0.00236649\pi
720720 0 0
721721 13.4003 + 9.73588i 0.499053 + 0.362583i
722722 3.56301 10.9658i 0.132601 0.408105i
723723 0 0
724724 −7.27295 + 5.28411i −0.270297 + 0.196382i
725725 −28.9657 −1.07576
726726 0 0
727727 −26.2077 −0.971991 −0.485996 0.873961i 0.661543π-0.661543\pi
−0.485996 + 0.873961i 0.661543π0.661543\pi
728728 8.86719 6.44239i 0.328640 0.238771i
729729 0 0
730730 −6.13346 + 18.8768i −0.227010 + 0.698663i
731731 −21.6205 15.7082i −0.799663 0.580989i
732732 0 0
733733 −5.18559 + 15.9596i −0.191534 + 0.589481i 0.808465 + 0.588544i 0.200299π0.200299\pi
−1.00000 0.000937776i 0.999701π0.999701\pi
734734 0.457536 + 1.40815i 0.0168880 + 0.0519758i
735735 0 0
736736 −10.2583 −0.378127
737737 26.0081 12.1845i 0.958022 0.448820i
738738 0 0
739739 −7.71218 + 5.60322i −0.283697 + 0.206118i −0.720528 0.693425i 0.756101π-0.756101\pi
0.436831 + 0.899543i 0.356101π0.356101\pi
740740 1.31650 + 4.05178i 0.0483957 + 0.148947i
741741 0 0
742742 −8.19069 5.95089i −0.300690 0.218464i
743743 −2.22765 1.61848i −0.0817246 0.0593764i 0.546173 0.837673i 0.316084π-0.316084\pi
−0.627897 + 0.778296i 0.716084π0.716084\pi
744744 0 0
745745 5.30970 + 16.3416i 0.194532 + 0.598709i
746746 16.5130 11.9974i 0.604585 0.439257i
747747 0 0
748748 −4.90689 + 8.88972i −0.179414 + 0.325040i
749749 6.11716 0.223516
750750 0 0
751751 10.7058 + 32.9491i 0.390661 + 1.20233i 0.932289 + 0.361713i 0.117808π0.117808\pi
−0.541628 + 0.840618i 0.682192π0.682192\pi
752752 4.33430 13.3396i 0.158056 0.486445i
753753 0 0
754754 16.7619 + 12.1782i 0.610433 + 0.443505i
755755 7.95391 24.4796i 0.289472 0.890905i
756756 0 0
757757 −3.15478 + 2.29208i −0.114663 + 0.0833072i −0.643639 0.765329i 0.722576π-0.722576\pi
0.528976 + 0.848637i 0.322576π0.322576\pi
758758 0.506165 0.0183848
759759 0 0
760760 10.7271 0.389112
761761 1.77801 1.29180i 0.0644527 0.0468276i −0.555092 0.831789i 0.687317π-0.687317\pi
0.619545 + 0.784961i 0.287317π0.287317\pi
762762 0 0
763763 6.21006 19.1126i 0.224819 0.691923i
764764 −14.3971 10.4601i −0.520870 0.378434i
765765 0 0
766766 6.87102 21.1468i 0.248260 0.764065i
767767 7.87832 + 24.2470i 0.284470 + 0.875507i
768768 0 0
769769 39.6598 1.43017 0.715085 0.699037i 0.246388π-0.246388\pi
0.715085 + 0.699037i 0.246388π0.246388\pi
770770 0.823143 + 6.60627i 0.0296640 + 0.238074i
771771 0 0
772772 −4.17893 + 3.03617i −0.150403 + 0.109274i
773773 −4.55217 14.0102i −0.163730 0.503910i 0.835210 0.549931i 0.185346π-0.185346\pi
−0.998940 + 0.0460208i 0.985346π0.985346\pi
774774 0 0
775775 13.6613 + 9.92549i 0.490727 + 0.356534i
776776 21.0093 + 15.2641i 0.754190 + 0.547951i
777777 0 0
778778 −0.878782 2.70461i −0.0315059 0.0969650i
779779 11.2081 8.14314i 0.401571 0.291758i
780780 0 0
781781 −50.8648 9.79275i −1.82009 0.350412i
782782 8.69234 0.310838
783783 0 0
784784 2.20277 + 6.77944i 0.0786705 + 0.242123i
785785 6.64255 20.4437i 0.237083 0.729665i
786786 0 0
787787 0.426247 + 0.309686i 0.0151941 + 0.0110391i 0.595356 0.803462i 0.297011π-0.297011\pi
−0.580162 + 0.814501i 0.697011π0.697011\pi
788788 −0.377738 + 1.16256i −0.0134563 + 0.0414144i
789789 0 0
790790 2.05789 1.49515i 0.0732165 0.0531949i
791791 −3.50180 −0.124510
792792 0 0
793793 −1.43601 −0.0509943
794794 −13.4420 + 9.76618i −0.477039 + 0.346589i
795795 0 0
796796 −1.61790 + 4.97940i −0.0573451 + 0.176490i
797797 −4.55735 3.31111i −0.161429 0.117285i 0.504138 0.863623i 0.331810π-0.331810\pi
−0.665567 + 0.746338i 0.731810π0.731810\pi
798798 0 0
799799 10.0427 30.9083i 0.355286 1.09346i
800800 4.82599 + 14.8529i 0.170625 + 0.525128i
801801 0 0
802802 8.79744 0.310649
803803 6.21535 + 49.8824i 0.219335 + 1.76031i
804804 0 0
805805 −3.49273 + 2.53762i −0.123103 + 0.0894393i
806806 −3.73248 11.4874i −0.131471 0.404626i
807807 0 0
808808 1.85308 + 1.34634i 0.0651912 + 0.0473642i
809809 19.1292 + 13.8982i 0.672549 + 0.488635i 0.870877 0.491500i 0.163551π-0.163551\pi
−0.198329 + 0.980136i 0.563551π0.563551\pi
810810 0 0
811811 −4.98249 15.3345i −0.174959 0.538468i 0.824673 0.565610i 0.191359π-0.191359\pi
−0.999632 + 0.0271423i 0.991359π0.991359\pi
812812 −8.86463 + 6.44053i −0.311087 + 0.226018i
813813 0 0
814814 −9.73231 10.3993i −0.341117 0.364495i
815815 −0.234871 −0.00822718
816816 0 0
817817 6.65512 + 20.4824i 0.232833 + 0.716587i
818818 −1.32629 + 4.08191i −0.0463728 + 0.142721i
819819 0 0
820820 −4.14430 3.01101i −0.144725 0.105149i
821821 −6.40533 + 19.7136i −0.223548 + 0.688009i 0.774888 + 0.632098i 0.217806π0.217806\pi
−0.998436 + 0.0559105i 0.982194π0.982194\pi
822822 0 0
823823 21.3970 15.5458i 0.745852 0.541893i −0.148686 0.988884i 0.547504π-0.547504\pi
0.894538 + 0.446991i 0.147504π0.147504\pi
824824 32.9926 1.14935
825825 0 0
826826 17.7984 0.619285
827827 42.3796 30.7905i 1.47368 1.07069i 0.494156 0.869373i 0.335477π-0.335477\pi
0.979526 0.201319i 0.0645227π-0.0645227\pi
828828 0 0
829829 8.69589 26.7632i 0.302021 0.929525i −0.678751 0.734368i 0.737479π-0.737479\pi
0.980772 0.195156i 0.0625215π-0.0625215\pi
830830 5.65089 + 4.10561i 0.196145 + 0.142508i
831831 0 0
832832 5.67070 17.4526i 0.196596 0.605061i
833833 5.10391 + 15.7082i 0.176840 + 0.544257i
834834 0 0
835835 −1.17710 −0.0407352
836836 7.40999 3.47148i 0.256280 0.120064i
837837 0 0
838838 27.6520 20.0904i 0.955223 0.694010i
839839 13.5192 + 41.6078i 0.466735 + 1.43646i 0.856788 + 0.515669i 0.172457π0.172457\pi
−0.390053 + 0.920792i 0.627543π0.627543\pi
840840 0 0
841841 −32.1729 23.3750i −1.10941 0.806033i
842842 21.9947 + 15.9801i 0.757986 + 0.550709i
843843 0 0
844844 −4.24736 13.0720i −0.146200 0.449958i
845845 −7.46309 + 5.42225i −0.256738 + 0.186531i
846846 0 0
847847 8.98580 + 14.2665i 0.308756 + 0.490202i
848848 −9.49076 −0.325914
849849 0 0
850850 −4.08928 12.5855i −0.140261 0.431679i
851851 2.85423 8.78442i 0.0978418 0.301126i
852852 0 0
853853 17.0427 + 12.3822i 0.583530 + 0.423960i 0.839995 0.542594i 0.182558π-0.182558\pi
−0.256465 + 0.966554i 0.582558π0.582558\pi
854854 −0.309792 + 0.953442i −0.0106009 + 0.0326261i
855855 0 0
856856 9.85753 7.16191i 0.336923 0.244789i
857857 18.8828 0.645025 0.322512 0.946565i 0.395473π-0.395473\pi
0.322512 + 0.946565i 0.395473π0.395473\pi
858858 0 0
859859 −43.0833 −1.46998 −0.734992 0.678075i 0.762814π-0.762814\pi
−0.734992 + 0.678075i 0.762814π0.762814\pi
860860 6.44245 4.68072i 0.219686 0.159611i
861861 0 0
862862 −6.82208 + 20.9962i −0.232361 + 0.715134i
863863 −12.9855 9.43449i −0.442030 0.321154i 0.344411 0.938819i 0.388079π-0.388079\pi
−0.786441 + 0.617665i 0.788079π0.788079\pi
864864 0 0
865865 −8.20867 + 25.2637i −0.279103 + 0.858992i
866866 4.75723 + 14.6413i 0.161657 + 0.497530i
867867 0 0
868868 6.38781 0.216817
869869 3.11316 5.64005i 0.105607 0.191326i
870870 0 0
871871 −16.4085 + 11.9215i −0.555981 + 0.403944i
872872 −12.3696 38.0698i −0.418888 1.28920i
873873 0 0
874874 −5.66709 4.11738i −0.191692 0.139273i
875875 12.9288 + 9.39335i 0.437074 + 0.317553i
876876 0 0
877877 4.75721 + 14.6412i 0.160640 + 0.494398i 0.998689 0.0511972i 0.0163037π-0.0163037\pi
−0.838049 + 0.545595i 0.816304π0.816304\pi
878878 7.72745 5.61432i 0.260789 0.189474i
879879 0 0
880880 4.26437 + 4.55661i 0.143752 + 0.153603i
881881 −3.84430 −0.129518 −0.0647589 0.997901i 0.520628π-0.520628\pi
−0.0647589 + 0.997901i 0.520628π0.520628\pi
882882 0 0
883883 6.15742 + 18.9506i 0.207214 + 0.637738i 0.999615 + 0.0277382i 0.00883048π0.00883048\pi
−0.792402 + 0.610000i 0.791170π0.791170\pi
884884 2.21583 6.81963i 0.0745265 0.229369i
885885 0 0
886886 8.85279 + 6.43193i 0.297415 + 0.216085i
887887 −3.59194 + 11.0549i −0.120606 + 0.371186i −0.993075 0.117483i 0.962517π-0.962517\pi
0.872469 + 0.488669i 0.162517π0.162517\pi
888888 0 0
889889 1.96228 1.42568i 0.0658128 0.0478158i
890890 7.64868 0.256384
891891 0 0
892892 −22.6787 −0.759338
893893 −21.1881 + 15.3941i −0.709034 + 0.515143i
894894 0 0
895895 7.77747 23.9366i 0.259972 0.800112i
896896 0.724335 + 0.526260i 0.0241983 + 0.0175811i
897897 0 0
898898 6.73758 20.7361i 0.224836 0.691974i
899899 12.3885 + 38.1277i 0.413178 + 1.27163i
900900 0 0
901901 −21.9904 −0.732608
902902 16.8171 + 3.23772i 0.559949 + 0.107804i
903903 0 0
904904 −5.64300 + 4.09988i −0.187683 + 0.136360i
905905 3.95611 + 12.1757i 0.131506 + 0.404733i
906906 0 0
907907 −24.3910 17.7211i −0.809891 0.588420i 0.103908 0.994587i 0.466865π-0.466865\pi
−0.913799 + 0.406167i 0.866865π0.866865\pi
908908 1.94041 + 1.40979i 0.0643948 + 0.0467856i
909909 0 0
910910 −1.45278 4.47119i −0.0481591 0.148218i
911911 −18.8165 + 13.6710i −0.623419 + 0.452941i −0.854114 0.520086i 0.825900π-0.825900\pi
0.230695 + 0.973026i 0.425900π0.425900\pi
912912 0 0
913913 17.3710 + 3.34436i 0.574896 + 0.110682i
914914 41.0556 1.35800
915915 0 0
916916 −5.59955 17.2337i −0.185014 0.569416i
917917 −2.67259 + 8.22539i −0.0882567 + 0.271626i
918918 0 0
919919 −19.1223 13.8932i −0.630787 0.458294i 0.225886 0.974154i 0.427472π-0.427472\pi
−0.856673 + 0.515860i 0.827472π0.827472\pi
920920 −2.65736 + 8.17851i −0.0876105 + 0.269637i
921921 0 0
922922 16.8641 12.2525i 0.555391 0.403515i
923923 36.5793 1.20402
924924 0 0
925925 −14.0616 −0.462342
926926 −14.2625 + 10.3623i −0.468694 + 0.340526i
927927 0 0
928928 −11.4574 + 35.2624i −0.376109 + 1.15755i
929929 −44.0297 31.9895i −1.44457 1.04954i −0.987063 0.160335i 0.948743π-0.948743\pi
−0.457506 0.889206i 0.651257π-0.651257\pi
930930 0 0
931931 4.11309 12.6588i 0.134801 0.414875i
932932 −3.63216 11.1786i −0.118975 0.366168i
933933 0 0
934934 31.2696 1.02317
935935 9.88070 + 10.5578i 0.323133 + 0.345278i
936936 0 0
937937 −21.9192 + 15.9253i −0.716070 + 0.520255i −0.885126 0.465351i 0.845928π-0.845928\pi
0.169056 + 0.985606i 0.445928π0.445928\pi
938938 4.37545 + 13.4662i 0.142863 + 0.439689i
939939 0 0
940940 7.83452 + 5.69211i 0.255534 + 0.185656i
941941 −29.7676 21.6274i −0.970396 0.705034i −0.0148540 0.999890i 0.504728π-0.504728\pi
−0.955542 + 0.294856i 0.904728π0.904728\pi
942942 0 0
943943 3.43196 + 10.5625i 0.111760 + 0.343962i
944944 13.4982 9.80702i 0.439329 0.319191i
945945 0 0
946946 −12.8654 + 23.3079i −0.418289 + 0.757806i
947947 59.0290 1.91819 0.959093 0.283093i 0.0913604π-0.0913604\pi
0.959093 + 0.283093i 0.0913604π0.0913604\pi
948948 0 0
949949 −10.9696 33.7609i −0.356087 1.09592i
950950 −3.29543 + 10.1423i −0.106918 + 0.329060i
951951 0 0
952952 −13.4458 9.76894i −0.435781 0.316613i
953953 12.3238 37.9287i 0.399206 1.22863i −0.526431 0.850218i 0.676470π-0.676470\pi
0.925637 0.378413i 0.123530π-0.123530\pi
954954 0 0
955955 −20.5026 + 14.8960i −0.663449 + 0.482024i
956956 17.4794 0.565325
957957 0 0
958958 −16.5224 −0.533814
959959 −26.8456 + 19.5045i −0.866890 + 0.629832i
960960 0 0
961961 −2.35738 + 7.25526i −0.0760445 + 0.234041i
962962 8.13718 + 5.91201i 0.262353 + 0.190611i
963963 0 0
964964 7.03081 21.6386i 0.226447 0.696932i
965965 2.27312 + 6.99596i 0.0731745 + 0.225208i
966966 0 0
967967 −22.3285 −0.718037 −0.359019 0.933330i 0.616889π-0.616889\pi
−0.359019 + 0.933330i 0.616889π0.616889\pi
968968 31.1833 + 12.4693i 1.00227 + 0.400779i
969969 0 0
970970 9.01156 6.54728i 0.289344 0.210220i
971971 5.35373 + 16.4771i 0.171809 + 0.528775i 0.999473 0.0324490i 0.0103307π-0.0103307\pi
−0.827664 + 0.561224i 0.810331π0.810331\pi
972972 0 0
973973 −26.1155 18.9740i −0.837223 0.608278i
974974 −3.34542 2.43059i −0.107194 0.0778811i
975975 0 0
976976 0.290408 + 0.893783i 0.00929573 + 0.0286093i
977977 −16.2968 + 11.8404i −0.521382 + 0.378806i −0.817124 0.576461i 0.804433π-0.804433\pi
0.295742 + 0.955268i 0.404433π0.404433\pi
978978 0 0
979979 17.5416 8.21799i 0.560631 0.262648i
980980 −4.92160 −0.157215
981981 0 0
982982 −2.39234 7.36286i −0.0763425 0.234958i
983983 7.71806 23.7537i 0.246168 0.757627i −0.749274 0.662260i 0.769598π-0.769598\pi
0.995442 0.0953671i 0.0304025π-0.0304025\pi
984984 0 0
985985 1.40831 + 1.02320i 0.0448726 + 0.0326018i
986986 9.70841 29.8794i 0.309179 0.951555i
987987 0 0
988988 −4.67496 + 3.39655i −0.148730 + 0.108059i
989989 −17.2648 −0.548987
990990 0 0
991991 −3.49555 −0.111040 −0.0555199 0.998458i 0.517682π-0.517682\pi
−0.0555199 + 0.998458i 0.517682π0.517682\pi
992992 17.4869 12.7050i 0.555209 0.403383i
993993 0 0
994994 7.89127 24.2868i 0.250296 0.770331i
995995 6.03201 + 4.38251i 0.191227 + 0.138935i
996996 0 0
997997 2.27585 7.00435i 0.0720770 0.221830i −0.908528 0.417823i 0.862793π-0.862793\pi
0.980605 + 0.195993i 0.0627931π0.0627931\pi
998998 −11.8332 36.4188i −0.374573 1.15282i
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 297.2.f.c.190.3 yes 16
3.2 odd 2 inner 297.2.f.c.190.2 yes 16
9.2 odd 6 891.2.n.g.190.3 32
9.4 even 3 891.2.n.g.784.3 32
9.5 odd 6 891.2.n.g.784.2 32
9.7 even 3 891.2.n.g.190.2 32
11.2 odd 10 3267.2.a.bh.1.6 8
11.4 even 5 inner 297.2.f.c.136.3 yes 16
11.9 even 5 3267.2.a.bg.1.3 8
33.2 even 10 3267.2.a.bh.1.3 8
33.20 odd 10 3267.2.a.bg.1.6 8
33.26 odd 10 inner 297.2.f.c.136.2 16
99.4 even 15 891.2.n.g.136.2 32
99.59 odd 30 891.2.n.g.136.3 32
99.70 even 15 891.2.n.g.433.3 32
99.92 odd 30 891.2.n.g.433.2 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
297.2.f.c.136.2 16 33.26 odd 10 inner
297.2.f.c.136.3 yes 16 11.4 even 5 inner
297.2.f.c.190.2 yes 16 3.2 odd 2 inner
297.2.f.c.190.3 yes 16 1.1 even 1 trivial
891.2.n.g.136.2 32 99.4 even 15
891.2.n.g.136.3 32 99.59 odd 30
891.2.n.g.190.2 32 9.7 even 3
891.2.n.g.190.3 32 9.2 odd 6
891.2.n.g.433.2 32 99.92 odd 30
891.2.n.g.433.3 32 99.70 even 15
891.2.n.g.784.2 32 9.5 odd 6
891.2.n.g.784.3 32 9.4 even 3
3267.2.a.bg.1.3 8 11.9 even 5
3267.2.a.bg.1.6 8 33.20 odd 10
3267.2.a.bh.1.3 8 33.2 even 10
3267.2.a.bh.1.6 8 11.2 odd 10