Properties

Label 592.2.bc.g.49.4
Level 592592
Weight 22
Character 592.49
Analytic conductor 4.7274.727
Analytic rank 00
Dimension 3030
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [592,2,Mod(33,592)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(592, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("592.33");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 592=2437 592 = 2^{4} \cdot 37
Weight: k k == 2 2
Character orbit: [χ][\chi] == 592.bc (of order 99, degree 66, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.727143799664.72714379966
Analytic rank: 00
Dimension: 3030
Relative dimension: 55 over Q(ζ9)\Q(\zeta_{9})
Twist minimal: no (minimal twist has level 296)
Sato-Tate group: SU(2)[C9]\mathrm{SU}(2)[C_{9}]

Embedding invariants

Embedding label 49.4
Character χ\chi == 592.49
Dual form 592.2.bc.g.145.4

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+(0.714590+0.599612i)q3+(2.46699+0.897912i)q5+(3.18160+1.15801i)q7+(0.3698412.09747i)q9+(0.622664+1.07848i)q11+(0.5643863.20079i)q13+(2.301290.837600i)q15+(1.308497.42080i)q17+(0.8039670.674609i)q19+(2.967891.08022i)q21+(0.1137100.196952i)q23+(1.449591.21635i)q25+(2.392634.14416i)q27+(2.961365.12922i)q297.32779q31+(0.201724+1.14403i)q33+(6.809195.71359i)q35+(1.52734+5.88789i)q37+(2.322541.94884i)q39+(1.30197+7.38387i)q413.93777q43+(2.79574+4.84236i)q45+(3.87141+6.70548i)q47+(3.419282.86912i)q49+(3.514576.08742i)q51+(7.65285+2.78541i)q53+(2.504492.10152i)q55+(0.1700030.964137i)q57+(8.89397+3.23714i)q59+(0.4537862.57355i)q61+(3.60557+6.24503i)q63+(1.48169+8.40310i)q65+(6.57694+2.39381i)q67+(0.1993510.0725578i)q69+(10.65758.94266i)q7112.7621q73+1.76520q75+(3.229962.71026i)q77+(6.775702.46615i)q79+(1.80951+0.658608i)q81+(2.2400712.7041i)q83+(9.89126+17.1322i)q85+(0.9593875.44095i)q87+(2.470990.899365i)q89+(1.91089+10.8372i)q91+(5.236364.39383i)q93+(2.58912+0.942363i)q95+(1.63655+2.83459i)q97+(2.031801.70489i)q99+O(q100)q+(0.714590 + 0.599612i) q^{3} +(-2.46699 + 0.897912i) q^{5} +(-3.18160 + 1.15801i) q^{7} +(-0.369841 - 2.09747i) q^{9} +(0.622664 + 1.07848i) q^{11} +(0.564386 - 3.20079i) q^{13} +(-2.30129 - 0.837600i) q^{15} +(-1.30849 - 7.42080i) q^{17} +(-0.803967 - 0.674609i) q^{19} +(-2.96789 - 1.08022i) q^{21} +(0.113710 - 0.196952i) q^{23} +(1.44959 - 1.21635i) q^{25} +(2.39263 - 4.14416i) q^{27} +(-2.96136 - 5.12922i) q^{29} -7.32779 q^{31} +(-0.201724 + 1.14403i) q^{33} +(6.80919 - 5.71359i) q^{35} +(-1.52734 + 5.88789i) q^{37} +(2.32254 - 1.94884i) q^{39} +(-1.30197 + 7.38387i) q^{41} -3.93777 q^{43} +(2.79574 + 4.84236i) q^{45} +(-3.87141 + 6.70548i) q^{47} +(3.41928 - 2.86912i) q^{49} +(3.51457 - 6.08742i) q^{51} +(7.65285 + 2.78541i) q^{53} +(-2.50449 - 2.10152i) q^{55} +(-0.170003 - 0.964137i) q^{57} +(8.89397 + 3.23714i) q^{59} +(0.453786 - 2.57355i) q^{61} +(3.60557 + 6.24503i) q^{63} +(1.48169 + 8.40310i) q^{65} +(-6.57694 + 2.39381i) q^{67} +(0.199351 - 0.0725578i) q^{69} +(-10.6575 - 8.94266i) q^{71} -12.7621 q^{73} +1.76520 q^{75} +(-3.22996 - 2.71026i) q^{77} +(6.77570 - 2.46615i) q^{79} +(-1.80951 + 0.658608i) q^{81} +(-2.24007 - 12.7041i) q^{83} +(9.89126 + 17.1322i) q^{85} +(0.959387 - 5.44095i) q^{87} +(-2.47099 - 0.899365i) q^{89} +(1.91089 + 10.8372i) q^{91} +(-5.23636 - 4.39383i) q^{93} +(2.58912 + 0.942363i) q^{95} +(-1.63655 + 2.83459i) q^{97} +(2.03180 - 1.70489i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 30q6q5+3q7+3q11+9q133q1527q179q19+15q21+3q2312q25+3q27+9q29+6q316q339q35+9q37+12q39+48q43++6q99+O(q100) 30 q - 6 q^{5} + 3 q^{7} + 3 q^{11} + 9 q^{13} - 3 q^{15} - 27 q^{17} - 9 q^{19} + 15 q^{21} + 3 q^{23} - 12 q^{25} + 3 q^{27} + 9 q^{29} + 6 q^{31} - 6 q^{33} - 9 q^{35} + 9 q^{37} + 12 q^{39} + 48 q^{43}+ \cdots + 6 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/592Z)×\left(\mathbb{Z}/592\mathbb{Z}\right)^\times.

nn 113113 149149 223223
χ(n)\chi(n) e(79)e\left(\frac{7}{9}\right) 11 11

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 0
33 0.714590 + 0.599612i 0.412569 + 0.346186i 0.825328 0.564654i 0.190990π-0.190990\pi
−0.412759 + 0.910840i 0.635435π0.635435\pi
44 0 0
55 −2.46699 + 0.897912i −1.10327 + 0.401558i −0.828522 0.559957i 0.810818π-0.810818\pi
−0.274751 + 0.961515i 0.588595π0.588595\pi
66 0 0
77 −3.18160 + 1.15801i −1.20253 + 0.437686i −0.864107 0.503308i 0.832116π-0.832116\pi
−0.338424 + 0.940994i 0.609894π0.609894\pi
88 0 0
99 −0.369841 2.09747i −0.123280 0.699157i
1010 0 0
1111 0.622664 + 1.07848i 0.187740 + 0.325175i 0.944496 0.328522i 0.106550π-0.106550\pi
−0.756756 + 0.653697i 0.773217π0.773217\pi
1212 0 0
1313 0.564386 3.20079i 0.156532 0.887740i −0.800839 0.598880i 0.795613π-0.795613\pi
0.957371 0.288860i 0.0932762π-0.0932762\pi
1414 0 0
1515 −2.30129 0.837600i −0.594190 0.216267i
1616 0 0
1717 −1.30849 7.42080i −0.317355 1.79981i −0.558700 0.829370i 0.688700π-0.688700\pi
0.241345 0.970439i 0.422411π-0.422411\pi
1818 0 0
1919 −0.803967 0.674609i −0.184443 0.154766i 0.545891 0.837856i 0.316191π-0.316191\pi
−0.730334 + 0.683090i 0.760636π0.760636\pi
2020 0 0
2121 −2.96789 1.08022i −0.647647 0.235724i
2222 0 0
2323 0.113710 0.196952i 0.0237102 0.0410673i −0.853927 0.520393i 0.825785π-0.825785\pi
0.877637 + 0.479326i 0.159119π0.159119\pi
2424 0 0
2525 1.44959 1.21635i 0.289917 0.243269i
2626 0 0
2727 2.39263 4.14416i 0.460462 0.797543i
2828 0 0
2929 −2.96136 5.12922i −0.549910 0.952472i −0.998280 0.0586242i 0.981329π-0.981329\pi
0.448370 0.893848i 0.352005π-0.352005\pi
3030 0 0
3131 −7.32779 −1.31611 −0.658055 0.752970i 0.728620π-0.728620\pi
−0.658055 + 0.752970i 0.728620π0.728620\pi
3232 0 0
3333 −0.201724 + 1.14403i −0.0351156 + 0.199150i
3434 0 0
3535 6.80919 5.71359i 1.15096 0.965773i
3636 0 0
3737 −1.52734 + 5.88789i −0.251093 + 0.967963i
3838 0 0
3939 2.32254 1.94884i 0.371904 0.312064i
4040 0 0
4141 −1.30197 + 7.38387i −0.203334 + 1.15317i 0.696705 + 0.717358i 0.254649π0.254649\pi
−0.900039 + 0.435809i 0.856462π0.856462\pi
4242 0 0
4343 −3.93777 −0.600505 −0.300253 0.953860i 0.597071π-0.597071\pi
−0.300253 + 0.953860i 0.597071π0.597071\pi
4444 0 0
4545 2.79574 + 4.84236i 0.416764 + 0.721856i
4646 0 0
4747 −3.87141 + 6.70548i −0.564703 + 0.978095i 0.432374 + 0.901694i 0.357676π0.357676\pi
−0.997077 + 0.0764005i 0.975657π0.975657\pi
4848 0 0
4949 3.41928 2.86912i 0.488468 0.409874i
5050 0 0
5151 3.51457 6.08742i 0.492138 0.852409i
5252 0 0
5353 7.65285 + 2.78541i 1.05120 + 0.382606i 0.809116 0.587650i 0.199947π-0.199947\pi
0.242085 + 0.970255i 0.422169π0.422169\pi
5454 0 0
5555 −2.50449 2.10152i −0.337706 0.283369i
5656 0 0
5757 −0.170003 0.964137i −0.0225175 0.127703i
5858 0 0
5959 8.89397 + 3.23714i 1.15790 + 0.421440i 0.848345 0.529443i 0.177599π-0.177599\pi
0.309551 + 0.950883i 0.399821π0.399821\pi
6060 0 0
6161 0.453786 2.57355i 0.0581014 0.329509i −0.941878 0.335955i 0.890941π-0.890941\pi
0.999979 + 0.00644632i 0.00205194π0.00205194\pi
6262 0 0
6363 3.60557 + 6.24503i 0.454259 + 0.786800i
6464 0 0
6565 1.48169 + 8.40310i 0.183781 + 1.04228i
6666 0 0
6767 −6.57694 + 2.39381i −0.803501 + 0.292450i −0.710936 0.703256i 0.751729π-0.751729\pi
−0.0925645 + 0.995707i 0.529506π0.529506\pi
6868 0 0
6969 0.199351 0.0725578i 0.0239990 0.00873493i
7070 0 0
7171 −10.6575 8.94266i −1.26481 1.06130i −0.995153 0.0983415i 0.968646π-0.968646\pi
−0.269654 0.962957i 0.586909π-0.586909\pi
7272 0 0
7373 −12.7621 −1.49369 −0.746843 0.665000i 0.768431π-0.768431\pi
−0.746843 + 0.665000i 0.768431π0.768431\pi
7474 0 0
7575 1.76520 0.203827
7676 0 0
7777 −3.22996 2.71026i −0.368088 0.308863i
7878 0 0
7979 6.77570 2.46615i 0.762326 0.277464i 0.0685433 0.997648i 0.478165π-0.478165\pi
0.693783 + 0.720184i 0.255943π0.255943\pi
8080 0 0
8181 −1.80951 + 0.658608i −0.201057 + 0.0731787i
8282 0 0
8383 −2.24007 12.7041i −0.245880 1.39445i −0.818441 0.574591i 0.805161π-0.805161\pi
0.572561 0.819862i 0.305950π-0.305950\pi
8484 0 0
8585 9.89126 + 17.1322i 1.07286 + 1.85824i
8686 0 0
8787 0.959387 5.44095i 0.102857 0.583332i
8888 0 0
8989 −2.47099 0.899365i −0.261924 0.0953325i 0.207720 0.978188i 0.433396π-0.433396\pi
−0.469644 + 0.882856i 0.655618π0.655618\pi
9090 0 0
9191 1.91089 + 10.8372i 0.200316 + 1.13605i
9292 0 0
9393 −5.23636 4.39383i −0.542985 0.455619i
9494 0 0
9595 2.58912 + 0.942363i 0.265638 + 0.0966844i
9696 0 0
9797 −1.63655 + 2.83459i −0.166167 + 0.287809i −0.937069 0.349144i 0.886472π-0.886472\pi
0.770902 + 0.636953i 0.219806π0.219806\pi
9898 0 0
9999 2.03180 1.70489i 0.204204 0.171347i
100100 0 0
101101 2.31341 4.00694i 0.230193 0.398706i −0.727672 0.685925i 0.759398π-0.759398\pi
0.957865 + 0.287220i 0.0927310π0.0927310\pi
102102 0 0
103103 5.85346 + 10.1385i 0.576759 + 0.998976i 0.995848 + 0.0910308i 0.0290162π0.0290162\pi
−0.419089 + 0.907945i 0.637651π0.637651\pi
104104 0 0
105105 8.29172 0.809189
106106 0 0
107107 2.25971 12.8155i 0.218455 1.23892i −0.656355 0.754452i 0.727903π-0.727903\pi
0.874810 0.484467i 0.160986π-0.160986\pi
108108 0 0
109109 −0.104826 + 0.0879597i −0.0100405 + 0.00842501i −0.647794 0.761815i 0.724308π-0.724308\pi
0.637754 + 0.770240i 0.279864π0.279864\pi
110110 0 0
111111 −4.62187 + 3.29162i −0.438688 + 0.312426i
112112 0 0
113113 5.70275 4.78518i 0.536470 0.450152i −0.333859 0.942623i 0.608351π-0.608351\pi
0.870329 + 0.492471i 0.163906π0.163906\pi
114114 0 0
115115 −0.103677 + 0.587981i −0.00966792 + 0.0548295i
116116 0 0
117117 −6.92230 −0.639966
118118 0 0
119119 12.7564 + 22.0948i 1.16938 + 2.02543i
120120 0 0
121121 4.72458 8.18321i 0.429507 0.743928i
122122 0 0
123123 −5.35783 + 4.49576i −0.483100 + 0.405369i
124124 0 0
125125 4.07935 7.06564i 0.364868 0.631970i
126126 0 0
127127 −19.1828 6.98197i −1.70220 0.619550i −0.706127 0.708085i 0.749559π-0.749559\pi
−0.996073 + 0.0885354i 0.971781π0.971781\pi
128128 0 0
129129 −2.81389 2.36114i −0.247750 0.207887i
130130 0 0
131131 1.65466 + 9.38404i 0.144568 + 0.819887i 0.967713 + 0.252055i 0.0811065π0.0811065\pi
−0.823145 + 0.567832i 0.807782π0.807782\pi
132132 0 0
133133 3.33910 + 1.21533i 0.289537 + 0.105383i
134134 0 0
135135 −2.18151 + 12.3720i −0.187755 + 1.06481i
136136 0 0
137137 4.74114 + 8.21190i 0.405063 + 0.701590i 0.994329 0.106349i 0.0339162π-0.0339162\pi
−0.589266 + 0.807939i 0.700583π0.700583\pi
138138 0 0
139139 3.23003 + 18.3184i 0.273968 + 1.55375i 0.742222 + 0.670154i 0.233772π0.233772\pi
−0.468255 + 0.883593i 0.655117π0.655117\pi
140140 0 0
141141 −6.78716 + 2.47032i −0.571582 + 0.208039i
142142 0 0
143143 3.80343 1.38433i 0.318059 0.115764i
144144 0 0
145145 11.9112 + 9.99471i 0.989174 + 0.830016i
146146 0 0
147147 4.16374 0.343419
148148 0 0
149149 8.02290 0.657261 0.328631 0.944458i 0.393413π-0.393413\pi
0.328631 + 0.944458i 0.393413π0.393413\pi
150150 0 0
151151 2.04800 + 1.71848i 0.166664 + 0.139848i 0.722305 0.691575i 0.243083π-0.243083\pi
−0.555641 + 0.831422i 0.687527π0.687527\pi
152152 0 0
153153 −15.0810 + 5.48903i −1.21922 + 0.443762i
154154 0 0
155155 18.0776 6.57971i 1.45203 0.528495i
156156 0 0
157157 −1.40926 7.99229i −0.112471 0.637854i −0.987971 0.154637i 0.950579π-0.950579\pi
0.875501 0.483217i 0.160532π-0.160532\pi
158158 0 0
159159 3.79848 + 6.57917i 0.301239 + 0.521762i
160160 0 0
161161 −0.133709 + 0.758299i −0.0105377 + 0.0597623i
162162 0 0
163163 −8.54919 3.11165i −0.669624 0.243723i −0.0152382 0.999884i 0.504851π-0.504851\pi
−0.654386 + 0.756161i 0.727073π0.727073\pi
164164 0 0
165165 −0.529589 3.00345i −0.0412284 0.233818i
166166 0 0
167167 −15.5178 13.0210i −1.20081 1.00760i −0.999607 0.0280460i 0.991071π-0.991071\pi
−0.201200 0.979550i 0.564484π-0.564484\pi
168168 0 0
169169 2.28947 + 0.833299i 0.176113 + 0.0640999i
170170 0 0
171171 −1.11763 + 1.93579i −0.0854674 + 0.148034i
172172 0 0
173173 14.4874 12.1563i 1.10145 0.924229i 0.103931 0.994584i 0.466858π-0.466858\pi
0.997522 + 0.0703555i 0.0224134π0.0224134\pi
174174 0 0
175175 −3.20346 + 5.54856i −0.242159 + 0.419432i
176176 0 0
177177 4.41451 + 7.64616i 0.331815 + 0.574721i
178178 0 0
179179 13.4598 1.00604 0.503018 0.864276i 0.332223π-0.332223\pi
0.503018 + 0.864276i 0.332223π0.332223\pi
180180 0 0
181181 −2.34928 + 13.3234i −0.174621 + 0.990323i 0.763960 + 0.645263i 0.223252π0.223252\pi
−0.938581 + 0.345060i 0.887859π0.887859\pi
182182 0 0
183183 1.86740 1.56694i 0.138042 0.115831i
184184 0 0
185185 −1.51888 15.8968i −0.111670 1.16876i
186186 0 0
187187 7.18848 6.03185i 0.525673 0.441092i
188188 0 0
189189 −2.81343 + 15.9557i −0.204647 + 1.16061i
190190 0 0
191191 2.36093 0.170831 0.0854155 0.996345i 0.472778π-0.472778\pi
0.0854155 + 0.996345i 0.472778π0.472778\pi
192192 0 0
193193 4.63768 + 8.03270i 0.333827 + 0.578206i 0.983259 0.182214i 0.0583264π-0.0583264\pi
−0.649431 + 0.760420i 0.724993π0.724993\pi
194194 0 0
195195 −3.97980 + 6.89321i −0.284999 + 0.493633i
196196 0 0
197197 −1.05645 + 0.886469i −0.0752691 + 0.0631583i −0.679646 0.733540i 0.737867π-0.737867\pi
0.604377 + 0.796699i 0.293422π0.293422\pi
198198 0 0
199199 −1.97499 + 3.42079i −0.140003 + 0.242493i −0.927498 0.373829i 0.878045π-0.878045\pi
0.787494 + 0.616322i 0.211378π0.211378\pi
200200 0 0
201201 −6.13517 2.23302i −0.432742 0.157505i
202202 0 0
203203 15.3615 + 12.8898i 1.07817 + 0.904690i
204204 0 0
205205 −3.41810 19.3850i −0.238730 1.35391i
206206 0 0
207207 −0.455155 0.165663i −0.0316355 0.0115144i
208208 0 0
209209 0.226954 1.28712i 0.0156987 0.0890320i
210210 0 0
211211 10.4164 + 18.0417i 0.717095 + 1.24204i 0.962146 + 0.272534i 0.0878619π0.0878619\pi
−0.245051 + 0.969510i 0.578805π0.578805\pi
212212 0 0
213213 −2.25358 12.7807i −0.154413 0.875717i
214214 0 0
215215 9.71446 3.53578i 0.662521 0.241138i
216216 0 0
217217 23.3141 8.48563i 1.58266 0.576042i
218218 0 0
219219 −9.11964 7.65229i −0.616248 0.517094i
220220 0 0
221221 −24.4909 −1.64744
222222 0 0
223223 −24.9633 −1.67166 −0.835832 0.548985i 0.815014π-0.815014\pi
−0.835832 + 0.548985i 0.815014π0.815014\pi
224224 0 0
225225 −3.08737 2.59061i −0.205824 0.172707i
226226 0 0
227227 −0.996856 + 0.362826i −0.0661637 + 0.0240816i −0.374890 0.927069i 0.622320π-0.622320\pi
0.308726 + 0.951151i 0.400097π0.400097\pi
228228 0 0
229229 5.99574 2.18227i 0.396210 0.144209i −0.136228 0.990677i 0.543498π-0.543498\pi
0.532438 + 0.846469i 0.321276π0.321276\pi
230230 0 0
231231 −0.682993 3.87345i −0.0449376 0.254854i
232232 0 0
233233 4.79443 + 8.30419i 0.314093 + 0.544026i 0.979244 0.202683i 0.0649662π-0.0649662\pi
−0.665151 + 0.746709i 0.731633π0.731633\pi
234234 0 0
235235 3.52981 20.0186i 0.230260 1.30587i
236236 0 0
237237 6.32059 + 2.30051i 0.410566 + 0.149434i
238238 0 0
239239 −2.28199 12.9418i −0.147610 0.837138i −0.965234 0.261386i 0.915821π-0.915821\pi
0.817624 0.575752i 0.195291π-0.195291\pi
240240 0 0
241241 −3.56189 2.98878i −0.229441 0.192524i 0.520818 0.853668i 0.325627π-0.325627\pi
−0.750259 + 0.661143i 0.770071π0.770071\pi
242242 0 0
243243 −15.1780 5.52434i −0.973668 0.354386i
244244 0 0
245245 −5.85912 + 10.1483i −0.374326 + 0.648351i
246246 0 0
247247 −2.61303 + 2.19259i −0.166263 + 0.139511i
248248 0 0
249249 6.01678 10.4214i 0.381298 0.660427i
250250 0 0
251251 −8.89316 15.4034i −0.561331 0.972254i −0.997381 0.0723317i 0.976956π-0.976956\pi
0.436049 0.899923i 0.356377π-0.356377\pi
252252 0 0
253253 0.283213 0.0178054
254254 0 0
255255 −3.20446 + 18.1734i −0.200671 + 1.13806i
256256 0 0
257257 −13.3966 + 11.2411i −0.835660 + 0.701202i −0.956583 0.291460i 0.905859π-0.905859\pi
0.120923 + 0.992662i 0.461414π0.461414\pi
258258 0 0
259259 −1.95885 20.5016i −0.121717 1.27391i
260260 0 0
261261 −9.66316 + 8.10835i −0.598134 + 0.501894i
262262 0 0
263263 1.37219 7.78206i 0.0846127 0.479862i −0.912827 0.408347i 0.866105π-0.866105\pi
0.997439 0.0715154i 0.0227835π-0.0227835\pi
264264 0 0
265265 −21.3806 −1.31340
266266 0 0
267267 −1.22647 2.12431i −0.0750588 0.130006i
268268 0 0
269269 3.22251 5.58155i 0.196480 0.340313i −0.750905 0.660410i 0.770382π-0.770382\pi
0.947385 + 0.320097i 0.103716π0.103716\pi
270270 0 0
271271 13.8349 11.6089i 0.840410 0.705187i −0.117246 0.993103i 0.537407π-0.537407\pi
0.957656 + 0.287915i 0.0929622π0.0929622\pi
272272 0 0
273273 −5.13261 + 8.88994i −0.310640 + 0.538044i
274274 0 0
275275 2.21442 + 0.805982i 0.133534 + 0.0486025i
276276 0 0
277277 20.4091 + 17.1252i 1.22626 + 1.02896i 0.998473 + 0.0552461i 0.0175943π0.0175943\pi
0.227790 + 0.973710i 0.426850π0.426850\pi
278278 0 0
279279 2.71011 + 15.3698i 0.162250 + 0.920166i
280280 0 0
281281 3.47714 + 1.26558i 0.207429 + 0.0754979i 0.443645 0.896203i 0.353685π-0.353685\pi
−0.236216 + 0.971701i 0.575907π0.575907\pi
282282 0 0
283283 3.63239 20.6003i 0.215923 1.22456i −0.663375 0.748287i 0.730876π-0.730876\pi
0.879298 0.476272i 0.158012π-0.158012\pi
284284 0 0
285285 1.28511 + 2.22587i 0.0761232 + 0.131849i
286286 0 0
287287 −4.40821 25.0002i −0.260208 1.47572i
288288 0 0
289289 −37.3814 + 13.6057i −2.19891 + 0.800336i
290290 0 0
291291 −2.86912 + 1.04427i −0.168191 + 0.0612164i
292292 0 0
293293 −19.2124 16.1211i −1.12240 0.941805i −0.123676 0.992323i 0.539468π-0.539468\pi
−0.998723 + 0.0505175i 0.983913π0.983913\pi
294294 0 0
295295 −24.8480 −1.44671
296296 0 0
297297 5.95921 0.345789
298298 0 0
299299 −0.566225 0.475120i −0.0327457 0.0274769i
300300 0 0
301301 12.5284 4.55997i 0.722126 0.262832i
302302 0 0
303303 4.05575 1.47617i 0.232997 0.0848039i
304304 0 0
305305 1.19133 + 6.75639i 0.0682155 + 0.386870i
306306 0 0
307307 −10.9498 18.9656i −0.624939 1.08243i −0.988553 0.150876i 0.951791π-0.951791\pi
0.363614 0.931550i 0.381543π-0.381543\pi
308308 0 0
309309 −1.89634 + 10.7547i −0.107879 + 0.611812i
310310 0 0
311311 −0.490564 0.178551i −0.0278173 0.0101247i 0.328074 0.944652i 0.393600π-0.393600\pi
−0.355891 + 0.934527i 0.615823π0.615823\pi
312312 0 0
313313 −4.67797 26.5301i −0.264415 1.49957i −0.770696 0.637202i 0.780092π-0.780092\pi
0.506282 0.862368i 0.331020π-0.331020\pi
314314 0 0
315315 −14.5024 12.1690i −0.817118 0.685643i
316316 0 0
317317 12.9323 + 4.70698i 0.726352 + 0.264370i 0.678620 0.734490i 0.262578π-0.262578\pi
0.0477320 + 0.998860i 0.484801π0.484801\pi
318318 0 0
319319 3.68786 6.38756i 0.206480 0.357635i
320320 0 0
321321 9.29909 7.80286i 0.519024 0.435513i
322322 0 0
323323 −3.95416 + 6.84880i −0.220015 + 0.381077i
324324 0 0
325325 −3.07515 5.32631i −0.170578 0.295451i
326326 0 0
327327 −0.127649 −0.00705903
328328 0 0
329329 4.55228 25.8173i 0.250975 1.42335i
330330 0 0
331331 −15.5503 + 13.0482i −0.854719 + 0.717194i −0.960824 0.277161i 0.910607π-0.910607\pi
0.106105 + 0.994355i 0.466162π0.466162\pi
332332 0 0
333333 12.9145 + 1.02596i 0.707713 + 0.0562224i
334334 0 0
335335 14.0758 11.8110i 0.769045 0.645305i
336336 0 0
337337 −5.77178 + 32.7334i −0.314409 + 1.78310i 0.261107 + 0.965310i 0.415913π0.415913\pi
−0.575516 + 0.817791i 0.695199π0.695199\pi
338338 0 0
339339 6.94438 0.377167
340340 0 0
341341 −4.56275 7.90291i −0.247087 0.427966i
342342 0 0
343343 4.29394 7.43732i 0.231851 0.401577i
344344 0 0
345345 −0.426647 + 0.357999i −0.0229699 + 0.0192740i
346346 0 0
347347 −11.2032 + 19.4045i −0.601418 + 1.04169i 0.391188 + 0.920311i 0.372064π0.372064\pi
−0.992607 + 0.121377i 0.961269π0.961269\pi
348348 0 0
349349 −28.6222 10.4176i −1.53211 0.557644i −0.567975 0.823046i 0.692273π-0.692273\pi
−0.964138 + 0.265402i 0.914495π0.914495\pi
350350 0 0
351351 −11.9142 9.99721i −0.635934 0.533612i
352352 0 0
353353 −3.47525 19.7091i −0.184969 1.04901i −0.925995 0.377536i 0.876772π-0.876772\pi
0.741026 0.671476i 0.234340π-0.234340\pi
354354 0 0
355355 34.3216 + 12.4920i 1.82160 + 0.663008i
356356 0 0
357357 −4.13268 + 23.4376i −0.218725 + 1.24045i
358358 0 0
359359 12.6779 + 21.9587i 0.669113 + 1.15894i 0.978152 + 0.207889i 0.0666592π0.0666592\pi
−0.309039 + 0.951049i 0.600007π0.600007\pi
360360 0 0
361361 −3.10805 17.6266i −0.163582 0.927717i
362362 0 0
363363 8.28289 3.01473i 0.434739 0.158232i
364364 0 0
365365 31.4839 11.4592i 1.64794 0.599802i
366366 0 0
367367 3.13156 + 2.62769i 0.163466 + 0.137164i 0.720852 0.693090i 0.243751π-0.243751\pi
−0.557385 + 0.830254i 0.688195π0.688195\pi
368368 0 0
369369 15.9690 0.831311
370370 0 0
371371 −27.5738 −1.43156
372372 0 0
373373 −7.03559 5.90356i −0.364289 0.305675i 0.442208 0.896912i 0.354195π-0.354195\pi
−0.806498 + 0.591237i 0.798640π0.798640\pi
374374 0 0
375375 7.15171 2.60301i 0.369313 0.134419i
376376 0 0
377377 −18.0889 + 6.58383i −0.931626 + 0.339084i
378378 0 0
379379 0.949204 + 5.38320i 0.0487573 + 0.276516i 0.999433 0.0336702i 0.0107196π-0.0107196\pi
−0.950676 + 0.310187i 0.899608π0.899608\pi
380380 0 0
381381 −9.52137 16.4915i −0.487795 0.844885i
382382 0 0
383383 5.04396 28.6057i 0.257734 1.46168i −0.531222 0.847233i 0.678267π-0.678267\pi
0.788956 0.614450i 0.210622π-0.210622\pi
384384 0 0
385385 10.4019 + 3.78597i 0.530128 + 0.192951i
386386 0 0
387387 1.45635 + 8.25936i 0.0740304 + 0.419847i
388388 0 0
389389 15.6096 + 13.0980i 0.791438 + 0.664095i 0.946101 0.323872i 0.104985π-0.104985\pi
−0.154663 + 0.987967i 0.549429π0.549429\pi
390390 0 0
391391 −1.61033 0.586112i −0.0814379 0.0296410i
392392 0 0
393393 −4.44438 + 7.69789i −0.224189 + 0.388307i
394394 0 0
395395 −14.5012 + 12.1680i −0.729636 + 0.612237i
396396 0 0
397397 −3.84463 + 6.65910i −0.192957 + 0.334211i −0.946229 0.323498i 0.895141π-0.895141\pi
0.753272 + 0.657709i 0.228474π0.228474\pi
398398 0 0
399399 1.65736 + 2.87063i 0.0829718 + 0.143711i
400400 0 0
401401 14.7251 0.735338 0.367669 0.929957i 0.380156π-0.380156\pi
0.367669 + 0.929957i 0.380156π0.380156\pi
402402 0 0
403403 −4.13570 + 23.4547i −0.206014 + 1.16836i
404404 0 0
405405 3.87268 3.24956i 0.192435 0.161472i
406406 0 0
407407 −7.30102 + 2.01896i −0.361898 + 0.100076i
408408 0 0
409409 2.63421 2.21037i 0.130253 0.109296i −0.575334 0.817919i 0.695128π-0.695128\pi
0.705587 + 0.708623i 0.250683π0.250683\pi
410410 0 0
411411 −1.53598 + 8.71099i −0.0757644 + 0.429681i
412412 0 0
413413 −32.0457 −1.57686
414414 0 0
415415 16.9334 + 29.3295i 0.831226 + 1.43973i
416416 0 0
417417 −8.67579 + 15.0269i −0.424855 + 0.735871i
418418 0 0
419419 −23.9931 + 20.1326i −1.17214 + 0.983541i −0.999999 0.00153152i 0.999513π-0.999513\pi
−0.172140 + 0.985073i 0.555068π0.555068\pi
420420 0 0
421421 −0.199850 + 0.346151i −0.00974011 + 0.0168704i −0.870854 0.491541i 0.836434π-0.836434\pi
0.861114 + 0.508411i 0.169767π0.169767\pi
422422 0 0
423423 15.4963 + 5.64021i 0.753458 + 0.274236i
424424 0 0
425425 −10.9230 9.16552i −0.529845 0.444593i
426426 0 0
427427 1.53642 + 8.71349i 0.0743527 + 0.421675i
428428 0 0
429429 3.54795 + 1.29135i 0.171297 + 0.0623470i
430430 0 0
431431 0.839936 4.76352i 0.0404583 0.229450i −0.957873 0.287191i 0.907279π-0.907279\pi
0.998332 + 0.0577406i 0.0183896π0.0183896\pi
432432 0 0
433433 −4.89095 8.47137i −0.235044 0.407108i 0.724241 0.689546i 0.242190π-0.242190\pi
−0.959285 + 0.282438i 0.908857π0.908857\pi
434434 0 0
435435 2.51870 + 14.2842i 0.120762 + 0.684877i
436436 0 0
437437 −0.224285 + 0.0816330i −0.0107290 + 0.00390504i
438438 0 0
439439 37.0174 13.4732i 1.76674 0.643042i 0.766744 0.641952i 0.221875π-0.221875\pi
0.999999 0.00108969i 0.000346859π-0.000346859\pi
440440 0 0
441441 −7.28247 6.11072i −0.346784 0.290987i
442442 0 0
443443 15.2550 0.724788 0.362394 0.932025i 0.381960π-0.381960\pi
0.362394 + 0.932025i 0.381960π0.381960\pi
444444 0 0
445445 6.90345 0.327255
446446 0 0
447447 5.73308 + 4.81063i 0.271165 + 0.227535i
448448 0 0
449449 30.8222 11.2184i 1.45459 0.529428i 0.510721 0.859746i 0.329378π-0.329378\pi
0.943869 + 0.330319i 0.107156π0.107156\pi
450450 0 0
451451 −8.77408 + 3.19350i −0.413155 + 0.150376i
452452 0 0
453453 0.433062 + 2.45601i 0.0203470 + 0.115394i
454454 0 0
455455 −14.4450 25.0195i −0.677192 1.17293i
456456 0 0
457457 6.46679 36.6750i 0.302504 1.71558i −0.332525 0.943095i 0.607900π-0.607900\pi
0.635028 0.772489i 0.280988π-0.280988\pi
458458 0 0
459459 −33.8837 12.3327i −1.58156 0.575639i
460460 0 0
461461 4.75723 + 26.9796i 0.221566 + 1.25657i 0.869141 + 0.494564i 0.164672π0.164672\pi
−0.647575 + 0.762002i 0.724217π0.724217\pi
462462 0 0
463463 −0.676688 0.567808i −0.0314483 0.0263883i 0.626928 0.779077i 0.284312π-0.284312\pi
−0.658376 + 0.752689i 0.728756π0.728756\pi
464464 0 0
465465 16.8633 + 6.13775i 0.782019 + 0.284632i
466466 0 0
467467 1.83634 3.18064i 0.0849758 0.147182i −0.820405 0.571783i 0.806252π-0.806252\pi
0.905381 + 0.424600i 0.139585π0.139585\pi
468468 0 0
469469 18.1531 15.2323i 0.838234 0.703362i
470470 0 0
471471 3.78523 6.55621i 0.174414 0.302094i
472472 0 0
473473 −2.45191 4.24683i −0.112739 0.195269i
474474 0 0
475475 −1.98598 −0.0911229
476476 0 0
477477 3.01198 17.0818i 0.137909 0.782121i
478478 0 0
479479 18.2228 15.2908i 0.832623 0.698654i −0.123268 0.992373i 0.539338π-0.539338\pi
0.955892 + 0.293720i 0.0948932π0.0948932\pi
480480 0 0
481481 17.9839 + 8.21173i 0.819995 + 0.374423i
482482 0 0
483483 −0.550232 + 0.461700i −0.0250364 + 0.0210081i
484484 0 0
485485 1.49215 8.46240i 0.0677550 0.384258i
486486 0 0
487487 15.7470 0.713565 0.356782 0.934188i 0.383874π-0.383874\pi
0.356782 + 0.934188i 0.383874π0.383874\pi
488488 0 0
489489 −4.24338 7.34975i −0.191892 0.332367i
490490 0 0
491491 −0.943381 + 1.63398i −0.0425742 + 0.0737406i −0.886527 0.462676i 0.846889π-0.846889\pi
0.843953 + 0.536417i 0.180223π0.180223\pi
492492 0 0
493493 −34.1880 + 28.6872i −1.53975 + 1.29200i
494494 0 0
495495 −3.48161 + 6.03032i −0.156487 + 0.271043i
496496 0 0
497497 44.2634 + 16.1106i 1.98548 + 0.722657i
498498 0 0
499499 27.1748 + 22.8023i 1.21651 + 1.02077i 0.999000 + 0.0447151i 0.0142380π0.0142380\pi
0.217510 + 0.976058i 0.430206π0.430206\pi
500500 0 0
501501 −3.28133 18.6094i −0.146599 0.831405i
502502 0 0
503503 −30.7970 11.2092i −1.37317 0.499793i −0.453070 0.891475i 0.649671π-0.649671\pi
−0.920101 + 0.391682i 0.871893π0.871893\pi
504504 0 0
505505 −2.10928 + 11.9623i −0.0938618 + 0.532317i
506506 0 0
507507 1.13638 + 1.96826i 0.0504682 + 0.0874136i
508508 0 0
509509 −4.56507 25.8898i −0.202343 1.14755i −0.901566 0.432642i 0.857581π-0.857581\pi
0.699222 0.714904i 0.253530π-0.253530\pi
510510 0 0
511511 40.6038 14.7786i 1.79620 0.653765i
512512 0 0
513513 −4.71928 + 1.71768i −0.208361 + 0.0758373i
514514 0 0
515515 −23.5439 19.7557i −1.03747 0.870540i
516516 0 0
517517 −9.64235 −0.424070
518518 0 0
519519 17.6416 0.774380
520520 0 0
521521 −20.9631 17.5902i −0.918412 0.770639i 0.0552886 0.998470i 0.482392π-0.482392\pi
−0.973701 + 0.227831i 0.926837π0.926837\pi
522522 0 0
523523 −37.7012 + 13.7221i −1.64856 + 0.600026i −0.988505 0.151191i 0.951689π-0.951689\pi
−0.660054 + 0.751218i 0.729467π0.729467\pi
524524 0 0
525525 −5.61615 + 2.04411i −0.245109 + 0.0892123i
526526 0 0
527527 9.58832 + 54.3781i 0.417674 + 2.36875i
528528 0 0
529529 11.4741 + 19.8738i 0.498876 + 0.864078i
530530 0 0
531531 3.50045 19.8521i 0.151907 0.861506i
532532 0 0
533533 22.8994 + 8.33470i 0.991883 + 0.361016i
534534 0 0
535535 5.93247 + 33.6447i 0.256483 + 1.45459i
536536 0 0
537537 9.61827 + 8.07069i 0.415059 + 0.348276i
538538 0 0
539539 5.22336 + 1.90115i 0.224986 + 0.0818882i
540540 0 0
541541 −13.2494 + 22.9486i −0.569635 + 0.986636i 0.426967 + 0.904267i 0.359582π0.359582\pi
−0.996602 + 0.0823693i 0.973751π0.973751\pi
542542 0 0
543543 −9.66766 + 8.11213i −0.414879 + 0.348125i
544544 0 0
545545 0.179626 0.311121i 0.00769431 0.0133269i
546546 0 0
547547 −14.8012 25.6364i −0.632853 1.09613i −0.986966 0.160931i 0.948550π-0.948550\pi
0.354113 0.935203i 0.384783π-0.384783\pi
548548 0 0
549549 −5.56577 −0.237541
550550 0 0
551551 −1.07938 + 6.12148i −0.0459832 + 0.260784i
552552 0 0
553553 −18.7017 + 15.6926i −0.795279 + 0.667319i
554554 0 0
555555 8.44654 12.2704i 0.358535 0.520851i
556556 0 0
557557 1.56151 1.31026i 0.0661633 0.0555176i −0.609106 0.793089i 0.708472π-0.708472\pi
0.675270 + 0.737571i 0.264027π0.264027\pi
558558 0 0
559559 −2.22242 + 12.6040i −0.0939985 + 0.533092i
560560 0 0
561561 8.75358 0.369576
562562 0 0
563563 21.5625 + 37.3473i 0.908751 + 1.57400i 0.815802 + 0.578332i 0.196296π0.196296\pi
0.0929493 + 0.995671i 0.470371π0.470371\pi
564564 0 0
565565 −9.77198 + 16.9256i −0.411110 + 0.712064i
566566 0 0
567567 4.99446 4.19085i 0.209748 0.175999i
568568 0 0
569569 2.16570 3.75110i 0.0907908 0.157254i −0.817053 0.576562i 0.804394π-0.804394\pi
0.907844 + 0.419308i 0.137727π0.137727\pi
570570 0 0
571571 −25.9464 9.44371i −1.08582 0.395207i −0.263751 0.964591i 0.584960π-0.584960\pi
−0.822072 + 0.569384i 0.807182π0.807182\pi
572572 0 0
573573 1.68710 + 1.41564i 0.0704795 + 0.0591393i
574574 0 0
575575 −0.0747291 0.423810i −0.00311642 0.0176741i
576576 0 0
577577 −28.6487 10.4273i −1.19266 0.434093i −0.332004 0.943278i 0.607725π-0.607725\pi
−0.860657 + 0.509185i 0.829947π0.829947\pi
578578 0 0
579579 −1.50246 + 8.52089i −0.0624402 + 0.354116i
580580 0 0
581581 21.8384 + 37.8252i 0.906010 + 1.56925i
582582 0 0
583583 1.76113 + 9.98786i 0.0729385 + 0.413655i
584584 0 0
585585 17.0773 6.21561i 0.706058 0.256984i
586586 0 0
587587 −3.46775 + 1.26216i −0.143129 + 0.0520948i −0.412591 0.910916i 0.635376π-0.635376\pi
0.269462 + 0.963011i 0.413154π0.413154\pi
588588 0 0
589589 5.89130 + 4.94339i 0.242747 + 0.203689i
590590 0 0
591591 −1.28647 −0.0529182
592592 0 0
593593 −0.261315 −0.0107309 −0.00536546 0.999986i 0.501708π-0.501708\pi
−0.00536546 + 0.999986i 0.501708π0.501708\pi
594594 0 0
595595 −51.3092 43.0535i −2.10347 1.76502i
596596 0 0
597597 −3.46245 + 1.26023i −0.141709 + 0.0515778i
598598 0 0
599599 8.61184 3.13445i 0.351870 0.128070i −0.160037 0.987111i 0.551161π-0.551161\pi
0.511907 + 0.859041i 0.328939π0.328939\pi
600600 0 0
601601 1.02400 + 5.80742i 0.0417700 + 0.236890i 0.998544 0.0539429i 0.0171789π-0.0171789\pi
−0.956774 + 0.290832i 0.906068π0.906068\pi
602602 0 0
603603 7.45336 + 12.9096i 0.303524 + 0.525720i
604604 0 0
605605 −4.30770 + 24.4302i −0.175133 + 0.993228i
606606 0 0
607607 28.7256 + 10.4552i 1.16593 + 0.424365i 0.851214 0.524819i 0.175867π-0.175867\pi
0.314721 + 0.949184i 0.398089π0.398089\pi
608608 0 0
609609 3.24828 + 18.4219i 0.131627 + 0.746494i
610610 0 0
611611 19.2779 + 16.1761i 0.779899 + 0.654413i
612612 0 0
613613 −1.91751 0.697915i −0.0774473 0.0281885i 0.303006 0.952989i 0.402010π-0.402010\pi
−0.380453 + 0.924800i 0.624232π0.624232\pi
614614 0 0
615615 9.18095 15.9019i 0.370211 0.641225i
616616 0 0
617617 6.14266 5.15431i 0.247294 0.207505i −0.510712 0.859752i 0.670618π-0.670618\pi
0.758006 + 0.652247i 0.226174π0.226174\pi
618618 0 0
619619 −5.81923 + 10.0792i −0.233895 + 0.405118i −0.958951 0.283572i 0.908480π-0.908480\pi
0.725056 + 0.688690i 0.241814π0.241814\pi
620620 0 0
621621 −0.544133 0.942466i −0.0218353 0.0378199i
622622 0 0
623623 8.90316 0.356697
624624 0 0
625625 −5.36238 + 30.4116i −0.214495 + 1.21646i
626626 0 0
627627 0.933953 0.783679i 0.0372985 0.0312971i
628628 0 0
629629 45.6914 + 3.62983i 1.82183 + 0.144731i
630630 0 0
631631 23.8402 20.0043i 0.949063 0.796358i −0.0300766 0.999548i 0.509575π-0.509575\pi
0.979139 + 0.203189i 0.0651307π0.0651307\pi
632632 0 0
633633 −3.37459 + 19.1382i −0.134128 + 0.760677i
634634 0 0
635635 53.5931 2.12678
636636 0 0
637637 −7.25365 12.5637i −0.287400 0.497791i
638638 0 0
639639 −14.8154 + 25.6610i −0.586088 + 1.01514i
640640 0 0
641641 −25.2141 + 21.1571i −0.995897 + 0.835657i −0.986411 0.164298i 0.947464π-0.947464\pi
−0.00948626 + 0.999955i 0.503020π0.503020\pi
642642 0 0
643643 5.30025 9.18031i 0.209022 0.362036i −0.742385 0.669974i 0.766305π-0.766305\pi
0.951407 + 0.307937i 0.0996388π0.0996388\pi
644644 0 0
645645 9.06195 + 3.29828i 0.356814 + 0.129870i
646646 0 0
647647 −31.5917 26.5086i −1.24200 1.04216i −0.997365 0.0725450i 0.976888π-0.976888\pi
−0.244634 0.969616i 0.578668π-0.578668\pi
648648 0 0
649649 2.04674 + 11.6077i 0.0803417 + 0.455641i
650650 0 0
651651 21.7481 + 7.91566i 0.852375 + 0.310239i
652652 0 0
653653 7.29955 41.3978i 0.285653 1.62002i −0.417289 0.908774i 0.637020π-0.637020\pi
0.702943 0.711247i 0.251869π-0.251869\pi
654654 0 0
655655 −12.5081 21.6646i −0.488731 0.846506i
656656 0 0
657657 4.71993 + 26.7680i 0.184142 + 1.04432i
658658 0 0
659659 19.7147 7.17557i 0.767977 0.279521i 0.0718269 0.997417i 0.477117π-0.477117\pi
0.696150 + 0.717896i 0.254895π0.254895\pi
660660 0 0
661661 11.7123 4.26293i 0.455556 0.165809i −0.104042 0.994573i 0.533178π-0.533178\pi
0.559598 + 0.828764i 0.310955π0.310955\pi
662662 0 0
663663 −17.5010 14.6851i −0.679681 0.570320i
664664 0 0
665665 −9.32881 −0.361756
666666 0 0
667667 −1.34695 −0.0521540
668668 0 0
669669 −17.8385 14.9683i −0.689676 0.578707i
670670 0 0
671671 3.05809 1.11305i 0.118056 0.0429690i
672672 0 0
673673 −44.2357 + 16.1005i −1.70516 + 0.620628i −0.996397 0.0848166i 0.972970π-0.972970\pi
−0.708765 + 0.705445i 0.750747π0.750747\pi
674674 0 0
675675 −1.57241 8.91758i −0.0605221 0.343238i
676676 0 0
677677 16.6746 + 28.8812i 0.640856 + 1.10999i 0.985242 + 0.171166i 0.0547536π0.0547536\pi
−0.344387 + 0.938828i 0.611913π0.611913\pi
678678 0 0
679679 1.92437 10.9137i 0.0738507 0.418828i
680680 0 0
681681 −0.929898 0.338455i −0.0356338 0.0129696i
682682 0 0
683683 1.03627 + 5.87697i 0.0396517 + 0.224876i 0.998194 0.0600747i 0.0191339π-0.0191339\pi
−0.958542 + 0.284951i 0.908023π0.908023\pi
684684 0 0
685685 −19.0699 16.0016i −0.728625 0.611389i
686686 0 0
687687 5.59301 + 2.03569i 0.213387 + 0.0776664i
688688 0 0
689689 13.2347 22.9231i 0.504201 0.873302i
690690 0 0
691691 −7.73164 + 6.48761i −0.294125 + 0.246800i −0.777894 0.628395i 0.783712π-0.783712\pi
0.483769 + 0.875196i 0.339268π0.339268\pi
692692 0 0
693693 −4.49011 + 7.77710i −0.170565 + 0.295428i
694694 0 0
695695 −24.4168 42.2911i −0.926181 1.60419i
696696 0 0
697697 56.4978 2.14001
698698 0 0
699699 −1.55324 + 8.80889i −0.0587491 + 0.333183i
700700 0 0
701701 −18.3592 + 15.4052i −0.693416 + 0.581845i −0.919892 0.392172i 0.871724π-0.871724\pi
0.226476 + 0.974017i 0.427279π0.427279\pi
702702 0 0
703703 5.19995 3.70332i 0.196120 0.139673i
704704 0 0
705705 14.5257 12.1885i 0.547071 0.459047i
706706 0 0
707707 −2.72027 + 15.4274i −0.102306 + 0.580208i
708708 0 0
709709 3.33993 0.125434 0.0627168 0.998031i 0.480024π-0.480024\pi
0.0627168 + 0.998031i 0.480024π0.480024\pi
710710 0 0
711711 −7.67862 13.2998i −0.287971 0.498780i
712712 0 0
713713 −0.833244 + 1.44322i −0.0312052 + 0.0540491i
714714 0 0
715715 −8.14002 + 6.83029i −0.304419 + 0.255438i
716716 0 0
717717 6.12939 10.6164i 0.228906 0.396477i
718718 0 0
719719 −29.0244 10.5640i −1.08243 0.393972i −0.261617 0.965172i 0.584256π-0.584256\pi
−0.820811 + 0.571200i 0.806478π0.806478\pi
720720 0 0
721721 −30.3638 25.4783i −1.13081 0.948861i
722722 0 0
723723 −0.753181 4.27150i −0.0280111 0.158859i
724724 0 0
725725 −10.5317 3.83321i −0.391136 0.142362i
726726 0 0
727727 −0.0553353 + 0.313822i −0.00205227 + 0.0116390i −0.985817 0.167826i 0.946325π-0.946325\pi
0.983764 + 0.179465i 0.0574365π0.0574365\pi
728728 0 0
729729 −4.64512 8.04558i −0.172041 0.297984i
730730 0 0
731731 5.15253 + 29.2214i 0.190573 + 1.08079i
732732 0 0
733733 30.2544 11.0117i 1.11747 0.406726i 0.283742 0.958901i 0.408424π-0.408424\pi
0.833728 + 0.552175i 0.186202π0.186202\pi
734734 0 0
735735 −10.2719 + 3.73867i −0.378885 + 0.137903i
736736 0 0
737737 −6.67691 5.60259i −0.245947 0.206374i
738738 0 0
739739 31.0155 1.14092 0.570461 0.821325i 0.306765π-0.306765\pi
0.570461 + 0.821325i 0.306765π0.306765\pi
740740 0 0
741741 −3.18195 −0.116892
742742 0 0
743743 −2.11789 1.77712i −0.0776980 0.0651964i 0.603111 0.797657i 0.293927π-0.293927\pi
−0.680809 + 0.732461i 0.738372π0.738372\pi
744744 0 0
745745 −19.7924 + 7.20386i −0.725139 + 0.263929i
746746 0 0
747747 −25.8179 + 9.39696i −0.944629 + 0.343817i
748748 0 0
749749 7.65091 + 43.3905i 0.279558 + 1.58545i
750750 0 0
751751 −14.0482 24.3323i −0.512628 0.887897i −0.999893 0.0146429i 0.995339π-0.995339\pi
0.487265 0.873254i 0.337994π-0.337994\pi
752752 0 0
753753 2.88111 16.3396i 0.104993 0.595447i
754754 0 0
755755 −6.59545 2.40055i −0.240033 0.0873649i
756756 0 0
757757 −5.72565 32.4718i −0.208102 1.18021i −0.892483 0.451082i 0.851038π-0.851038\pi
0.684380 0.729125i 0.260073π-0.260073\pi
758758 0 0
759759 0.202381 + 0.169818i 0.00734597 + 0.00616400i
760760 0 0
761761 5.00448 + 1.82148i 0.181412 + 0.0660286i 0.431129 0.902290i 0.358115π-0.358115\pi
−0.249717 + 0.968319i 0.580338π0.580338\pi
762762 0 0
763763 0.231657 0.401242i 0.00838655 0.0145259i
764764 0 0
765765 32.2760 27.0828i 1.16694 0.979180i
766766 0 0
767767 15.3810 26.6407i 0.555377 0.961942i
768768 0 0
769769 −17.9353 31.0648i −0.646762 1.12022i −0.983892 0.178766i 0.942789π-0.942789\pi
0.337130 0.941458i 0.390544π-0.390544\pi
770770 0 0
771771 −16.3134 −0.587513
772772 0 0
773773 0.584521 3.31498i 0.0210238 0.119232i −0.972490 0.232946i 0.925164π-0.925164\pi
0.993514 + 0.113714i 0.0362747π0.0362747\pi
774774 0 0
775775 −10.6223 + 8.91313i −0.381563 + 0.320169i
776776 0 0
777777 10.8932 15.8248i 0.390792 0.567710i
778778 0 0
779779 6.02797 5.05806i 0.215974 0.181224i
780780 0 0
781781 3.00852 17.0622i 0.107653 0.610532i
782782 0 0
783783 −28.3417 −1.01285
784784 0 0
785785 10.6530 + 18.4515i 0.380222 + 0.658563i
786786 0 0
787787 20.2776 35.1219i 0.722820 1.25196i −0.237045 0.971499i 0.576179π-0.576179\pi
0.959865 0.280462i 0.0904878π-0.0904878\pi
788788 0 0
789789 5.64677 4.73820i 0.201030 0.168684i
790790 0 0
791791 −12.6026 + 21.8283i −0.448097 + 0.776127i
792792 0 0
793793 −7.98128 2.90495i −0.283424 0.103158i
794794 0 0
795795 −15.2783 12.8201i −0.541867 0.454681i
796796 0 0
797797 −7.10571 40.2985i −0.251697 1.42745i −0.804410 0.594075i 0.797518π-0.797518\pi
0.552713 0.833372i 0.313593π-0.313593\pi
798798 0 0
799799 54.8257 + 19.9549i 1.93960 + 0.705955i
800800 0 0
801801 −0.972521 + 5.51544i −0.0343623 + 0.194878i
802802 0 0
803803 −7.94647 13.7637i −0.280425 0.485710i
804804 0 0
805805 −0.351028 1.99078i −0.0123721 0.0701657i
806806 0 0
807807 5.64954 2.05626i 0.198873 0.0723839i
808808 0 0
809809 −43.8247 + 15.9509i −1.54079 + 0.560803i −0.966235 0.257661i 0.917048π-0.917048\pi
−0.574558 + 0.818464i 0.694826π0.694826\pi
810810 0 0
811811 −19.0963 16.0237i −0.670562 0.562668i 0.242670 0.970109i 0.421977π-0.421977\pi
−0.913232 + 0.407441i 0.866421π0.866421\pi
812812 0 0
813813 16.8471 0.590853
814814 0 0
815815 23.8848 0.836647
816816 0 0
817817 3.16584 + 2.65646i 0.110759 + 0.0929377i
818818 0 0
819819 22.0240 8.01607i 0.769580 0.280104i
820820 0 0
821821 −32.2949 + 11.7544i −1.12710 + 0.410231i −0.837238 0.546838i 0.815831π-0.815831\pi
−0.289861 + 0.957069i 0.593609π0.593609\pi
822822 0 0
823823 3.74718 + 21.2513i 0.130619 + 0.740774i 0.977811 + 0.209488i 0.0671799π0.0671799\pi
−0.847193 + 0.531286i 0.821709π0.821709\pi
824824 0 0
825825 1.09912 + 1.90374i 0.0382666 + 0.0662796i
826826 0 0
827827 4.05290 22.9852i 0.140933 0.799272i −0.829610 0.558344i 0.811437π-0.811437\pi
0.970543 0.240928i 0.0774519π-0.0774519\pi
828828 0 0
829829 17.5307 + 6.38067i 0.608868 + 0.221610i 0.628008 0.778207i 0.283871π-0.283871\pi
−0.0191401 + 0.999817i 0.506093π0.506093\pi
830830 0 0
831831 4.31561 + 24.4751i 0.149707 + 0.849030i
832832 0 0
833833 −25.7652 21.6196i −0.892712 0.749074i
834834 0 0
835835 49.9741 + 18.1891i 1.72943 + 0.629460i
836836 0 0
837837 −17.5327 + 30.3675i −0.606018 + 1.04965i
838838 0 0
839839 −19.0280 + 15.9664i −0.656919 + 0.551220i −0.909161 0.416444i 0.863276π-0.863276\pi
0.252243 + 0.967664i 0.418832π0.418832\pi
840840 0 0
841841 −3.03927 + 5.26417i −0.104802 + 0.181523i
842842 0 0
843843 1.72587 + 2.98930i 0.0594423 + 0.102957i
844844 0 0
845845 −6.39634 −0.220041
846846 0 0
847847 −5.55550 + 31.5068i −0.190889 + 1.08259i
848848 0 0
849849 14.9478 12.5427i 0.513009 0.430465i
850850 0 0
851851 0.985957 + 0.970325i 0.0337982 + 0.0332623i
852852 0 0
853853 −27.6465 + 23.1982i −0.946599 + 0.794291i −0.978722 0.205193i 0.934218π-0.934218\pi
0.0321226 + 0.999484i 0.489773π0.489773\pi
854854 0 0
855855 1.01902 5.77913i 0.0348496 0.197642i
856856 0 0
857857 −23.1215 −0.789814 −0.394907 0.918721i 0.629223π-0.629223\pi
−0.394907 + 0.918721i 0.629223π0.629223\pi
858858 0 0
859859 −17.2312 29.8454i −0.587922 1.01831i −0.994504 0.104697i 0.966613π-0.966613\pi
0.406582 0.913614i 0.366721π-0.366721\pi
860860 0 0
861861 11.8404 20.5081i 0.403518 0.698914i
862862 0 0
863863 −28.1125 + 23.5892i −0.956960 + 0.802985i −0.980456 0.196739i 0.936965π-0.936965\pi
0.0234960 + 0.999724i 0.492520π0.492520\pi
864864 0 0
865865 −24.8249 + 42.9980i −0.844071 + 1.46197i
866866 0 0
867867 −34.8705 12.6918i −1.18426 0.431037i
868868 0 0
869869 6.87870 + 5.77191i 0.233344 + 0.195799i
870870 0 0
871871 3.95015 + 22.4024i 0.133846 + 0.759078i
872872 0 0
873873 6.55073 + 2.38427i 0.221709 + 0.0806954i
874874 0 0
875875 −4.79679 + 27.2040i −0.162161 + 0.919662i
876876 0 0
877877 −7.04975 12.2105i −0.238053 0.412320i 0.722102 0.691786i 0.243176π-0.243176\pi
−0.960156 + 0.279466i 0.909843π0.909843\pi
878878 0 0
879879 −4.06257 23.0400i −0.137027 0.777119i
880880 0 0
881881 34.2171 12.4540i 1.15280 0.419587i 0.306283 0.951940i 0.400915π-0.400915\pi
0.846522 + 0.532354i 0.178692π0.178692\pi
882882 0 0
883883 −3.95749 + 1.44041i −0.133180 + 0.0484736i −0.407750 0.913093i 0.633687π-0.633687\pi
0.274570 + 0.961567i 0.411464π0.411464\pi
884884 0 0
885885 −17.7562 14.8992i −0.596867 0.500830i
886886 0 0
887887 10.5188 0.353188 0.176594 0.984284i 0.443492π-0.443492\pi
0.176594 + 0.984284i 0.443492π0.443492\pi
888888 0 0
889889 69.1172 2.31812
890890 0 0
891891 −1.83702 1.54144i −0.0615423 0.0516402i
892892 0 0
893893 7.63606 2.77930i 0.255531 0.0930057i
894894 0 0
895895 −33.2054 + 12.0858i −1.10993 + 0.403982i
896896 0 0
897897 −0.119732 0.679031i −0.00399772 0.0226722i
898898 0 0
899899 21.7002 + 37.5858i 0.723742 + 1.25356i
900900 0 0
901901 10.6563 60.4350i 0.355013 2.01338i
902902 0 0
903903 11.6869 + 4.25368i 0.388916 + 0.141554i
904904 0 0
905905 −6.16761 34.9783i −0.205018 1.16272i
906906 0 0
907907 23.4994 + 19.7184i 0.780286 + 0.654738i 0.943321 0.331883i 0.107684π-0.107684\pi
−0.163035 + 0.986620i 0.552128π0.552128\pi
908908 0 0
909909 −9.26003 3.37038i −0.307136 0.111788i
910910 0 0
911911 −6.03455 + 10.4521i −0.199934 + 0.346295i −0.948507 0.316757i 0.897406π-0.897406\pi
0.748573 + 0.663052i 0.230739π0.230739\pi
912912 0 0
913913 12.3063 10.3262i 0.407280 0.341749i
914914 0 0
915915 −3.19990 + 5.54238i −0.105785 + 0.183226i
916916 0 0
917917 −16.1312 27.9401i −0.532701 0.922664i
918918 0 0
919919 3.94293 0.130065 0.0650327 0.997883i 0.479285π-0.479285\pi
0.0650327 + 0.997883i 0.479285π0.479285\pi
920920 0 0
921921 3.54740 20.1183i 0.116891 0.662920i
922922 0 0
923923 −34.6385 + 29.0652i −1.14014 + 0.956691i
924924 0 0
925925 4.94771 + 10.3928i 0.162680 + 0.341712i
926926 0 0
927927 19.1003 16.0271i 0.627338 0.526399i
928928 0 0
929929 −7.19718 + 40.8172i −0.236132 + 1.33917i 0.604085 + 0.796920i 0.293539π0.293539\pi
−0.840217 + 0.542250i 0.817573π0.817573\pi
930930 0 0
931931 −4.68452 −0.153529
932932 0 0
933933 −0.243491 0.421738i −0.00797153 0.0138071i
934934 0 0
935935 −12.3179 + 21.3351i −0.402837 + 0.697734i
936936 0 0
937937 −2.45023 + 2.05599i −0.0800455 + 0.0671662i −0.681932 0.731415i 0.738860π-0.738860\pi
0.601887 + 0.798581i 0.294416π0.294416\pi
938938 0 0
939939 12.5649 21.7631i 0.410041 0.710213i
940940 0 0
941941 −4.69883 1.71023i −0.153177 0.0557520i 0.264294 0.964442i 0.414861π-0.414861\pi
−0.417471 + 0.908690i 0.637083π0.637083\pi
942942 0 0
943943 1.30622 + 1.09605i 0.0425363 + 0.0356922i
944944 0 0
945945 −7.38614 41.8889i −0.240271 1.36265i
946946 0 0
947947 −19.3880 7.05667i −0.630026 0.229311i 0.00721636 0.999974i 0.497703π-0.497703\pi
−0.637243 + 0.770663i 0.719925π0.719925\pi
948948 0 0
949949 −7.20273 + 40.8487i −0.233810 + 1.32600i
950950 0 0
951951 6.41895 + 11.1179i 0.208149 + 0.360524i
952952 0 0
953953 0.215365 + 1.22139i 0.00697635 + 0.0395648i 0.988097 0.153831i 0.0491610π-0.0491610\pi
−0.981121 + 0.193396i 0.938050π0.938050\pi
954954 0 0
955955 −5.82440 + 2.11991i −0.188473 + 0.0685986i
956956 0 0
957957 6.46536 2.35320i 0.208996 0.0760681i
958958 0 0
959959 −24.5939 20.6367i −0.794177 0.666394i
960960 0 0
961961 22.6964 0.732143
962962 0 0
963963 −27.7158 −0.893130
964964 0 0
965965 −18.6538 15.6524i −0.600486 0.503868i
966966 0 0
967967 30.3246 11.0373i 0.975173 0.354934i 0.195212 0.980761i 0.437461π-0.437461\pi
0.779962 + 0.625827i 0.215238π0.215238\pi
968968 0 0
969969 −6.93222 + 2.52312i −0.222695 + 0.0810544i
970970 0 0
971971 3.97330 + 22.5337i 0.127509 + 0.723141i 0.979786 + 0.200050i 0.0641103π0.0641103\pi
−0.852276 + 0.523092i 0.824779π0.824779\pi
972972 0 0
973973 −31.4895 54.5414i −1.00951 1.74852i
974974 0 0
975975 0.996252 5.65002i 0.0319056 0.180946i
976976 0 0
977977 −45.0795 16.4076i −1.44222 0.524926i −0.501815 0.864975i 0.667334π-0.667334\pi
−0.940408 + 0.340049i 0.889556π0.889556\pi
978978 0 0
979979 −0.568641 3.22492i −0.0181738 0.103069i
980980 0 0
981981 0.223262 + 0.187339i 0.00712820 + 0.00598127i
982982 0 0
983983 −23.6561 8.61011i −0.754512 0.274620i −0.0640089 0.997949i 0.520389π-0.520389\pi
−0.690503 + 0.723329i 0.742611π0.742611\pi
984984 0 0
985985 1.81029 3.13551i 0.0576806 0.0999058i
986986 0 0
987987 18.7334 15.7192i 0.596290 0.500346i
988988 0 0
989989 −0.447765 + 0.775552i −0.0142381 + 0.0246611i
990990 0 0
991991 −5.92932 10.2699i −0.188351 0.326234i 0.756350 0.654168i 0.226981π-0.226981\pi
−0.944701 + 0.327934i 0.893648π0.893648\pi
992992 0 0
993993 −18.9359 −0.600913
994994 0 0
995995 1.80073 10.2124i 0.0570868 0.323756i
996996 0 0
997997 −9.84239 + 8.25875i −0.311712 + 0.261557i −0.785199 0.619243i 0.787439π-0.787439\pi
0.473487 + 0.880801i 0.342995π0.342995\pi
998998 0 0
999999 20.7460 + 20.4171i 0.656374 + 0.645967i
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 592.2.bc.g.49.4 30
4.3 odd 2 296.2.u.b.49.2 30
37.34 even 9 inner 592.2.bc.g.145.4 30
148.71 odd 18 296.2.u.b.145.2 yes 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
296.2.u.b.49.2 30 4.3 odd 2
296.2.u.b.145.2 yes 30 148.71 odd 18
592.2.bc.g.49.4 30 1.1 even 1 trivial
592.2.bc.g.145.4 30 37.34 even 9 inner