Properties

Label 704.2.m.i.577.2
Level 704704
Weight 22
Character 704.577
Analytic conductor 5.6215.621
Analytic rank 00
Dimension 88
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [704,2,Mod(257,704)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(704, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("704.257"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 704=2611 704 = 2^{6} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 704.m (of order 55, degree 44, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [8,0,-1,0,3,0,-7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 5.621468302305.62146830230
Analytic rank: 00
Dimension: 88
Relative dimension: 22 over Q(ζ5)\Q(\zeta_{5})
Coefficient field: 8.0.682515625.5
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x83x7+5x6+2x5+19x4+28x3+100x2+88x+121 x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 88)
Sato-Tate group: SU(2)[C5]\mathrm{SU}(2)[C_{5}]

Embedding invariants

Embedding label 577.2
Root 1.203160.874145i-1.20316 - 0.874145i of defining polynomial
Character χ\chi == 704.577
Dual form 704.2.m.i.449.2

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(0.743592+0.540251i)q3+(1.243593.82738i)q5+(3.01217+2.18847i)q7+(0.6659932.04972i)q9+(1.971742.66688i)q11+(0.3244620.998590i)q13+(2.992482.17416i)q15+(0.291947+0.898521i)q17+(1.927051.40008i)q193.42216q21+1.73830q23+(9.057266.58048i)q25+(1.464224.50639i)q27+(2.22389+1.61575i)q29+(1.479664.55393i)q31+(0.02538583.04831i)q33+(4.63021+14.2503i)q35+(1.711081.24317i)q37+(0.2982230.917835i)q39+(7.38598+5.36623i)q41+0.431946q438.67327q45+(5.11739+3.71800i)q47+(2.120666.52673i)q49+(0.702517+0.510409i)q51+(0.09769430.300672i)q53+(12.6592+4.23010i)q55+(0.6765432.08218i)q57+(6.54508+4.75528i)q59+(4.2127012.9654i)q61+(6.49184+4.71659i)q634.22549q65+5.68178q67+(1.29259+0.939120i)q69+(3.9766412.2388i)q71+(2.848812.06978i)q73+(3.179799.78640i)q75+(11.7756+3.71800i)q77+(2.73078+8.40447i)q79+(1.70741+1.24051i)q81+(4.5322713.9489i)q83+(3.07592+2.23479i)q852.52658q87+2.43195q89+(3.16272+2.29785i)q91+(1.360004.18565i)q93+(7.75513+5.63443i)q95+(0.457940+1.40940i)q97+(4.15318+5.81763i)q99+O(q100)q+(0.743592 + 0.540251i) q^{3} +(1.24359 - 3.82738i) q^{5} +(-3.01217 + 2.18847i) q^{7} +(-0.665993 - 2.04972i) q^{9} +(-1.97174 - 2.66688i) q^{11} +(-0.324462 - 0.998590i) q^{13} +(2.99248 - 2.17416i) q^{15} +(-0.291947 + 0.898521i) q^{17} +(-1.92705 - 1.40008i) q^{19} -3.42216 q^{21} +1.73830 q^{23} +(-9.05726 - 6.58048i) q^{25} +(1.46422 - 4.50639i) q^{27} +(-2.22389 + 1.61575i) q^{29} +(-1.47966 - 4.55393i) q^{31} +(-0.0253858 - 3.04831i) q^{33} +(4.63021 + 14.2503i) q^{35} +(1.71108 - 1.24317i) q^{37} +(0.298223 - 0.917835i) q^{39} +(7.38598 + 5.36623i) q^{41} +0.431946 q^{43} -8.67327 q^{45} +(5.11739 + 3.71800i) q^{47} +(2.12066 - 6.52673i) q^{49} +(-0.702517 + 0.510409i) q^{51} +(-0.0976943 - 0.300672i) q^{53} +(-12.6592 + 4.23010i) q^{55} +(-0.676543 - 2.08218i) q^{57} +(-6.54508 + 4.75528i) q^{59} +(4.21270 - 12.9654i) q^{61} +(6.49184 + 4.71659i) q^{63} -4.22549 q^{65} +5.68178 q^{67} +(1.29259 + 0.939120i) q^{69} +(3.97664 - 12.2388i) q^{71} +(2.84881 - 2.06978i) q^{73} +(-3.17979 - 9.78640i) q^{75} +(11.7756 + 3.71800i) q^{77} +(2.73078 + 8.40447i) q^{79} +(-1.70741 + 1.24051i) q^{81} +(4.53227 - 13.9489i) q^{83} +(3.07592 + 2.23479i) q^{85} -2.52658 q^{87} +2.43195 q^{89} +(3.16272 + 2.29785i) q^{91} +(1.36000 - 4.18565i) q^{93} +(-7.75513 + 5.63443i) q^{95} +(0.457940 + 1.40940i) q^{97} +(-4.15318 + 5.81763i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8qq3+3q57q713q9+7q117q13+13q15+q172q19+2q21+4q2333q2522q2717q29+13q31+16q33+11q35q37+27q99+O(q100) 8 q - q^{3} + 3 q^{5} - 7 q^{7} - 13 q^{9} + 7 q^{11} - 7 q^{13} + 13 q^{15} + q^{17} - 2 q^{19} + 2 q^{21} + 4 q^{23} - 33 q^{25} - 22 q^{27} - 17 q^{29} + 13 q^{31} + 16 q^{33} + 11 q^{35} - q^{37}+ \cdots - 27 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/704Z)×\left(\mathbb{Z}/704\mathbb{Z}\right)^\times.

nn 133133 321321 639639
χ(n)\chi(n) 11 e(25)e\left(\frac{2}{5}\right) 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 0.743592 + 0.540251i 0.429313 + 0.311914i 0.781374 0.624063i 0.214519π-0.214519\pi
−0.352061 + 0.935977i 0.614519π0.614519\pi
44 0 0
55 1.24359 3.82738i 0.556151 1.71166i −0.136732 0.990608i 0.543660π-0.543660\pi
0.692883 0.721050i 0.256340π-0.256340\pi
66 0 0
77 −3.01217 + 2.18847i −1.13850 + 0.827165i −0.986909 0.161279i 0.948438π-0.948438\pi
−0.151586 + 0.988444i 0.548438π0.548438\pi
88 0 0
99 −0.665993 2.04972i −0.221998 0.683239i
1010 0 0
1111 −1.97174 2.66688i −0.594502 0.804094i
1212 0 0
1313 −0.324462 0.998590i −0.0899895 0.276959i 0.895926 0.444203i 0.146513π-0.146513\pi
−0.985916 + 0.167244i 0.946513π0.946513\pi
1414 0 0
1515 2.99248 2.17416i 0.772654 0.561366i
1616 0 0
1717 −0.291947 + 0.898521i −0.0708076 + 0.217923i −0.980198 0.198020i 0.936549π-0.936549\pi
0.909390 + 0.415944i 0.136549π0.136549\pi
1818 0 0
1919 −1.92705 1.40008i −0.442096 0.321201i 0.344371 0.938834i 0.388092π-0.388092\pi
−0.786467 + 0.617632i 0.788092π0.788092\pi
2020 0 0
2121 −3.42216 −0.746776
2222 0 0
2323 1.73830 0.362461 0.181230 0.983441i 0.441992π-0.441992\pi
0.181230 + 0.983441i 0.441992π0.441992\pi
2424 0 0
2525 −9.05726 6.58048i −1.81145 1.31610i
2626 0 0
2727 1.46422 4.50639i 0.281788 0.867256i
2828 0 0
2929 −2.22389 + 1.61575i −0.412967 + 0.300038i −0.774802 0.632204i 0.782150π-0.782150\pi
0.361835 + 0.932242i 0.382150π0.382150\pi
3030 0 0
3131 −1.47966 4.55393i −0.265755 0.817909i −0.991519 0.129965i 0.958513π-0.958513\pi
0.725764 0.687944i 0.241487π-0.241487\pi
3232 0 0
3333 −0.0253858 3.04831i −0.00441911 0.530642i
3434 0 0
3535 4.63021 + 14.2503i 0.782648 + 2.40874i
3636 0 0
3737 1.71108 1.24317i 0.281299 0.204376i −0.438185 0.898885i 0.644378π-0.644378\pi
0.719484 + 0.694509i 0.244378π0.244378\pi
3838 0 0
3939 0.298223 0.917835i 0.0477538 0.146971i
4040 0 0
4141 7.38598 + 5.36623i 1.15350 + 0.838064i 0.988942 0.148304i 0.0473816π-0.0473816\pi
0.164554 + 0.986368i 0.447382π0.447382\pi
4242 0 0
4343 0.431946 0.0658711 0.0329356 0.999457i 0.489514π-0.489514\pi
0.0329356 + 0.999457i 0.489514π0.489514\pi
4444 0 0
4545 −8.67327 −1.29294
4646 0 0
4747 5.11739 + 3.71800i 0.746449 + 0.542327i 0.894724 0.446619i 0.147372π-0.147372\pi
−0.148275 + 0.988946i 0.547372π0.547372\pi
4848 0 0
4949 2.12066 6.52673i 0.302952 0.932390i
5050 0 0
5151 −0.702517 + 0.510409i −0.0983721 + 0.0714715i
5252 0 0
5353 −0.0976943 0.300672i −0.0134194 0.0413005i 0.944123 0.329594i 0.106912π-0.106912\pi
−0.957542 + 0.288294i 0.906912π0.906912\pi
5454 0 0
5555 −12.6592 + 4.23010i −1.70697 + 0.570386i
5656 0 0
5757 −0.676543 2.08218i −0.0896103 0.275792i
5858 0 0
5959 −6.54508 + 4.75528i −0.852097 + 0.619085i −0.925724 0.378201i 0.876543π-0.876543\pi
0.0736261 + 0.997286i 0.476543π0.476543\pi
6060 0 0
6161 4.21270 12.9654i 0.539381 1.66005i −0.194606 0.980882i 0.562343π-0.562343\pi
0.733987 0.679164i 0.237657π-0.237657\pi
6262 0 0
6363 6.49184 + 4.71659i 0.817894 + 0.594235i
6464 0 0
6565 −4.22549 −0.524107
6666 0 0
6767 5.68178 0.694140 0.347070 0.937839i 0.387177π-0.387177\pi
0.347070 + 0.937839i 0.387177π0.387177\pi
6868 0 0
6969 1.29259 + 0.939120i 0.155609 + 0.113057i
7070 0 0
7171 3.97664 12.2388i 0.471940 1.45248i −0.378101 0.925764i 0.623423π-0.623423\pi
0.850041 0.526717i 0.176577π-0.176577\pi
7272 0 0
7373 2.84881 2.06978i 0.333428 0.242250i −0.408456 0.912778i 0.633933π-0.633933\pi
0.741884 + 0.670528i 0.233933π0.233933\pi
7474 0 0
7575 −3.17979 9.78640i −0.367171 1.13004i
7676 0 0
7777 11.7756 + 3.71800i 1.34196 + 0.423706i
7878 0 0
7979 2.73078 + 8.40447i 0.307236 + 0.945577i 0.978833 + 0.204660i 0.0656088π0.0656088\pi
−0.671597 + 0.740917i 0.734391π0.734391\pi
8080 0 0
8181 −1.70741 + 1.24051i −0.189712 + 0.137834i
8282 0 0
8383 4.53227 13.9489i 0.497481 1.53109i −0.315573 0.948901i 0.602197π-0.602197\pi
0.813054 0.582188i 0.197803π-0.197803\pi
8484 0 0
8585 3.07592 + 2.23479i 0.333631 + 0.242397i
8686 0 0
8787 −2.52658 −0.270878
8888 0 0
8989 2.43195 0.257786 0.128893 0.991659i 0.458858π-0.458858\pi
0.128893 + 0.991659i 0.458858π0.458858\pi
9090 0 0
9191 3.16272 + 2.29785i 0.331543 + 0.240880i
9292 0 0
9393 1.36000 4.18565i 0.141026 0.434032i
9494 0 0
9595 −7.75513 + 5.63443i −0.795659 + 0.578080i
9696 0 0
9797 0.457940 + 1.40940i 0.0464968 + 0.143102i 0.971610 0.236590i 0.0760298π-0.0760298\pi
−0.925113 + 0.379692i 0.876030π0.876030\pi
9898 0 0
9999 −4.15318 + 5.81763i −0.417410 + 0.584694i
100100 0 0
101101 1.34355 + 4.13503i 0.133688 + 0.411451i 0.995384 0.0959754i 0.0305970π-0.0305970\pi
−0.861695 + 0.507426i 0.830597π0.830597\pi
102102 0 0
103103 8.97150 6.51817i 0.883988 0.642255i −0.0503157 0.998733i 0.516023π-0.516023\pi
0.934303 + 0.356479i 0.116023π0.116023\pi
104104 0 0
105105 −4.25577 + 13.0979i −0.415320 + 1.27822i
106106 0 0
107107 −7.72854 5.61512i −0.747147 0.542834i 0.147795 0.989018i 0.452783π-0.452783\pi
−0.894941 + 0.446184i 0.852783π0.852783\pi
108108 0 0
109109 −4.14866 −0.397369 −0.198685 0.980063i 0.563667π-0.563667\pi
−0.198685 + 0.980063i 0.563667π0.563667\pi
110110 0 0
111111 1.94397 0.184513
112112 0 0
113113 7.51945 + 5.46320i 0.707371 + 0.513935i 0.882324 0.470642i 0.155978π-0.155978\pi
−0.174954 + 0.984577i 0.555978π0.555978\pi
114114 0 0
115115 2.16174 6.65315i 0.201583 0.620409i
116116 0 0
117117 −1.83074 + 1.33011i −0.169252 + 0.122969i
118118 0 0
119119 −1.08699 3.34542i −0.0996445 0.306674i
120120 0 0
121121 −3.22448 + 10.5168i −0.293135 + 0.956071i
122122 0 0
123123 2.59304 + 7.98057i 0.233807 + 0.719584i
124124 0 0
125125 −20.1707 + 14.6549i −1.80413 + 1.31077i
126126 0 0
127127 −2.45856 + 7.56667i −0.218162 + 0.671434i 0.780752 + 0.624841i 0.214836π0.214836\pi
−0.998914 + 0.0465926i 0.985164π0.985164\pi
128128 0 0
129129 0.321192 + 0.233359i 0.0282794 + 0.0205462i
130130 0 0
131131 12.2670 1.07177 0.535885 0.844291i 0.319978π-0.319978\pi
0.535885 + 0.844291i 0.319978π0.319978\pi
132132 0 0
133133 8.86866 0.769010
134134 0 0
135135 −15.4268 11.2082i −1.32773 0.964651i
136136 0 0
137137 −0.778128 + 2.39483i −0.0664799 + 0.204604i −0.978778 0.204922i 0.934306π-0.934306\pi
0.912298 + 0.409526i 0.134306π0.134306\pi
138138 0 0
139139 −11.4034 + 8.28509i −0.967227 + 0.702732i −0.954818 0.297191i 0.903950π-0.903950\pi
−0.0124093 + 0.999923i 0.503950π0.503950\pi
140140 0 0
141141 1.79660 + 5.52936i 0.151301 + 0.465656i
142142 0 0
143143 −2.02336 + 2.83426i −0.169202 + 0.237013i
144144 0 0
145145 3.41849 + 10.5210i 0.283890 + 0.873724i
146146 0 0
147147 5.10299 3.70754i 0.420887 0.305792i
148148 0 0
149149 −3.29883 + 10.1528i −0.270251 + 0.831746i 0.720186 + 0.693781i 0.244056π0.244056\pi
−0.990437 + 0.137966i 0.955944π0.955944\pi
150150 0 0
151151 −16.3778 11.8992i −1.33281 0.968341i −0.999676 0.0254609i 0.991895π-0.991895\pi
−0.333132 0.942880i 0.608105π-0.608105\pi
152152 0 0
153153 2.03615 0.164613
154154 0 0
155155 −19.2697 −1.54778
156156 0 0
157157 15.7033 + 11.4091i 1.25326 + 0.910544i 0.998406 0.0564365i 0.0179738π-0.0179738\pi
0.254850 + 0.966981i 0.417974π0.417974\pi
158158 0 0
159159 0.0897939 0.276357i 0.00712112 0.0219165i
160160 0 0
161161 −5.23607 + 3.80423i −0.412660 + 0.299815i
162162 0 0
163163 5.83236 + 17.9502i 0.456826 + 1.40597i 0.868978 + 0.494850i 0.164777π0.164777\pi
−0.412152 + 0.911115i 0.635223π0.635223\pi
164164 0 0
165165 −11.6986 3.69369i −0.910735 0.287553i
166166 0 0
167167 5.48945 + 16.8948i 0.424786 + 1.30736i 0.903199 + 0.429223i 0.141212π0.141212\pi
−0.478412 + 0.878135i 0.658788π0.658788\pi
168168 0 0
169169 9.62531 6.99320i 0.740409 0.537938i
170170 0 0
171171 −1.58637 + 4.88235i −0.121313 + 0.373363i
172172 0 0
173173 −5.14174 3.73569i −0.390919 0.284020i 0.374913 0.927060i 0.377673π-0.377673\pi
−0.765832 + 0.643040i 0.777673π0.777673\pi
174174 0 0
175175 41.6833 3.15096
176176 0 0
177177 −7.43592 −0.558918
178178 0 0
179179 1.13877 + 0.827364i 0.0851156 + 0.0618401i 0.629529 0.776977i 0.283248π-0.283248\pi
−0.544414 + 0.838817i 0.683248π0.683248\pi
180180 0 0
181181 −5.35860 + 16.4921i −0.398302 + 1.22585i 0.528059 + 0.849208i 0.322920π0.322920\pi
−0.926360 + 0.376639i 0.877080π0.877080\pi
182182 0 0
183183 10.1371 7.36503i 0.749355 0.544439i
184184 0 0
185185 −2.63021 8.09495i −0.193377 0.595153i
186186 0 0
187187 2.97189 0.993063i 0.217326 0.0726199i
188188 0 0
189189 5.45165 + 16.7784i 0.396549 + 1.22045i
190190 0 0
191191 −5.65456 + 4.10828i −0.409149 + 0.297264i −0.773257 0.634092i 0.781374π-0.781374\pi
0.364108 + 0.931357i 0.381374π0.381374\pi
192192 0 0
193193 7.21221 22.1969i 0.519147 1.59777i −0.256462 0.966554i 0.582557π-0.582557\pi
0.775608 0.631214i 0.217443π-0.217443\pi
194194 0 0
195195 −3.14204 2.28283i −0.225006 0.163477i
196196 0 0
197197 10.8142 0.770481 0.385240 0.922816i 0.374119π-0.374119\pi
0.385240 + 0.922816i 0.374119π0.374119\pi
198198 0 0
199199 −9.07433 −0.643262 −0.321631 0.946865i 0.604231π-0.604231\pi
−0.321631 + 0.946865i 0.604231π0.604231\pi
200200 0 0
201201 4.22493 + 3.06959i 0.298004 + 0.216512i
202202 0 0
203203 3.16272 9.73386i 0.221980 0.683183i
204204 0 0
205205 29.7237 21.5956i 2.07600 1.50830i
206206 0 0
207207 −1.15770 3.56302i −0.0804655 0.247647i
208208 0 0
209209 0.0657885 + 7.89981i 0.00455068 + 0.546442i
210210 0 0
211211 −0.737448 2.26963i −0.0507680 0.156248i 0.922458 0.386097i 0.126177π-0.126177\pi
−0.973226 + 0.229849i 0.926177π0.926177\pi
212212 0 0
213213 9.56904 6.95231i 0.655660 0.476365i
214214 0 0
215215 0.537165 1.65322i 0.0366343 0.112749i
216216 0 0
217217 14.4231 + 10.4790i 0.979107 + 0.711363i
218218 0 0
219219 3.23656 0.218706
220220 0 0
221221 0.991980 0.0667278
222222 0 0
223223 −12.4428 9.04025i −0.833234 0.605380i 0.0872383 0.996187i 0.472196π-0.472196\pi
−0.920472 + 0.390807i 0.872196π0.872196\pi
224224 0 0
225225 −7.45605 + 22.9474i −0.497070 + 1.52982i
226226 0 0
227227 10.1460 7.37150i 0.673414 0.489264i −0.197753 0.980252i 0.563364π-0.563364\pi
0.871166 + 0.490988i 0.163364π0.163364\pi
228228 0 0
229229 −4.12253 12.6879i −0.272425 0.838437i −0.989889 0.141842i 0.954698π-0.954698\pi
0.717465 0.696595i 0.245302π-0.245302\pi
230230 0 0
231231 6.74760 + 9.12647i 0.443960 + 0.600478i
232232 0 0
233233 −7.25552 22.3302i −0.475325 1.46290i −0.845519 0.533946i 0.820709π-0.820709\pi
0.370194 0.928955i 0.379291π-0.379291\pi
234234 0 0
235235 20.5942 14.9625i 1.34342 0.976049i
236236 0 0
237237 −2.50994 + 7.72480i −0.163038 + 0.501780i
238238 0 0
239239 3.02068 + 2.19466i 0.195392 + 0.141960i 0.681180 0.732116i 0.261467π-0.261467\pi
−0.485788 + 0.874077i 0.661467π0.661467\pi
240240 0 0
241241 15.9621 1.02821 0.514104 0.857728i 0.328125π-0.328125\pi
0.514104 + 0.857728i 0.328125π0.328125\pi
242242 0 0
243243 −16.1547 −1.03633
244244 0 0
245245 −22.3431 16.2332i −1.42745 1.03710i
246246 0 0
247247 −0.772857 + 2.37861i −0.0491757 + 0.151347i
248248 0 0
249249 10.9061 7.92372i 0.691144 0.502146i
250250 0 0
251251 −3.42442 10.5393i −0.216148 0.665234i −0.999070 0.0431147i 0.986272π-0.986272\pi
0.782923 0.622119i 0.213728π-0.213728\pi
252252 0 0
253253 −3.42748 4.63584i −0.215484 0.291453i
254254 0 0
255255 1.07988 + 3.32354i 0.0676250 + 0.208128i
256256 0 0
257257 −12.1230 + 8.80787i −0.756212 + 0.549420i −0.897746 0.440513i 0.854796π-0.854796\pi
0.141534 + 0.989933i 0.454796π0.454796\pi
258258 0 0
259259 −2.43342 + 7.48930i −0.151205 + 0.465362i
260260 0 0
261261 4.79293 + 3.48227i 0.296675 + 0.215547i
262262 0 0
263263 −8.96129 −0.552577 −0.276288 0.961075i 0.589104π-0.589104\pi
−0.276288 + 0.961075i 0.589104π0.589104\pi
264264 0 0
265265 −1.27228 −0.0781555
266266 0 0
267267 1.80838 + 1.31386i 0.110671 + 0.0804071i
268268 0 0
269269 −0.324462 + 0.998590i −0.0197828 + 0.0608851i −0.960461 0.278416i 0.910191π-0.910191\pi
0.940678 + 0.339301i 0.110191π0.110191\pi
270270 0 0
271271 14.6960 10.6773i 0.892720 0.648599i −0.0438656 0.999037i 0.513967π-0.513967\pi
0.936586 + 0.350438i 0.113967π0.113967\pi
272272 0 0
273273 1.11036 + 3.41733i 0.0672019 + 0.206826i
274274 0 0
275275 0.309210 + 37.1296i 0.0186461 + 2.23900i
276276 0 0
277277 −6.16272 18.9669i −0.370282 1.13961i −0.946607 0.322390i 0.895514π-0.895514\pi
0.576325 0.817221i 0.304486π-0.304486\pi
278278 0 0
279279 −8.34881 + 6.06577i −0.499830 + 0.363148i
280280 0 0
281281 −6.49159 + 19.9791i −0.387256 + 1.19185i 0.547575 + 0.836757i 0.315551π0.315551\pi
−0.934831 + 0.355094i 0.884449π0.884449\pi
282282 0 0
283283 −5.29615 3.84788i −0.314823 0.228733i 0.419140 0.907922i 0.362332π-0.362332\pi
−0.733963 + 0.679189i 0.762332π0.762332\pi
284284 0 0
285285 −8.81066 −0.521899
286286 0 0
287287 −33.9917 −2.00647
288288 0 0
289289 13.0312 + 9.46771i 0.766540 + 0.556924i
290290 0 0
291291 −0.420907 + 1.29542i −0.0246740 + 0.0759388i
292292 0 0
293293 −12.9630 + 9.41816i −0.757306 + 0.550215i −0.898083 0.439826i 0.855040π-0.855040\pi
0.140777 + 0.990041i 0.455040π0.455040\pi
294294 0 0
295295 10.0609 + 30.9642i 0.585767 + 1.80280i
296296 0 0
297297 −14.9051 + 4.98055i −0.864879 + 0.289001i
298298 0 0
299299 −0.564012 1.73585i −0.0326177 0.100387i
300300 0 0
301301 −1.30110 + 0.945302i −0.0749940 + 0.0544863i
302302 0 0
303303 −1.23490 + 3.80063i −0.0709432 + 0.218341i
304304 0 0
305305 −44.3845 32.2473i −2.54145 1.84647i
306306 0 0
307307 10.8016 0.616478 0.308239 0.951309i 0.400260π-0.400260\pi
0.308239 + 0.951309i 0.400260π0.400260\pi
308308 0 0
309309 10.1926 0.579836
310310 0 0
311311 2.58023 + 1.87465i 0.146311 + 0.106301i 0.658533 0.752552i 0.271177π-0.271177\pi
−0.512222 + 0.858853i 0.671177π0.671177\pi
312312 0 0
313313 4.65232 14.3184i 0.262965 0.809323i −0.729190 0.684311i 0.760103π-0.760103\pi
0.992155 0.125012i 0.0398969π-0.0398969\pi
314314 0 0
315315 26.1254 18.9812i 1.47200 1.06947i
316316 0 0
317317 −4.09444 12.6014i −0.229967 0.707765i −0.997749 0.0670547i 0.978640π-0.978640\pi
0.767782 0.640711i 0.221360π-0.221360\pi
318318 0 0
319319 8.69396 + 2.74501i 0.486768 + 0.153691i
320320 0 0
321321 −2.71331 8.35071i −0.151442 0.466091i
322322 0 0
323323 1.82060 1.32275i 0.101301 0.0735995i
324324 0 0
325325 −3.63247 + 11.1796i −0.201493 + 0.620133i
326326 0 0
327327 −3.08491 2.24132i −0.170596 0.123945i
328328 0 0
329329 −23.5512 −1.29842
330330 0 0
331331 −33.5540 −1.84429 −0.922147 0.386839i 0.873567π-0.873567\pi
−0.922147 + 0.386839i 0.873567π0.873567\pi
332332 0 0
333333 −3.68771 2.67928i −0.202085 0.146824i
334334 0 0
335335 7.06582 21.7464i 0.386047 1.18813i
336336 0 0
337337 −5.58656 + 4.05887i −0.304319 + 0.221101i −0.729455 0.684029i 0.760226π-0.760226\pi
0.425136 + 0.905129i 0.360226π0.360226\pi
338338 0 0
339339 2.63991 + 8.12479i 0.143380 + 0.441278i
340340 0 0
341341 −9.22726 + 12.9252i −0.499684 + 0.699941i
342342 0 0
343343 −0.158073 0.486498i −0.00853513 0.0262684i
344344 0 0
345345 5.20182 3.77935i 0.280057 0.203473i
346346 0 0
347347 −6.39637 + 19.6860i −0.343375 + 1.05680i 0.619072 + 0.785334i 0.287509π0.287509\pi
−0.962448 + 0.271467i 0.912491π0.912491\pi
348348 0 0
349349 −8.94507 6.49898i −0.478819 0.347882i 0.322049 0.946723i 0.395628π-0.395628\pi
−0.800868 + 0.598841i 0.795628π0.795628\pi
350350 0 0
351351 −4.97512 −0.265552
352352 0 0
353353 13.5005 0.718557 0.359279 0.933230i 0.383023π-0.383023\pi
0.359279 + 0.933230i 0.383023π0.383023\pi
354354 0 0
355355 −41.8974 30.4402i −2.22368 1.61560i
356356 0 0
357357 0.999089 3.07488i 0.0528774 0.162740i
358358 0 0
359359 27.0425 19.6475i 1.42725 1.03696i 0.436726 0.899595i 0.356138π-0.356138\pi
0.990521 0.137361i 0.0438621π-0.0438621\pi
360360 0 0
361361 −4.11803 12.6740i −0.216739 0.667053i
362362 0 0
363363 −8.07941 + 6.07817i −0.424059 + 0.319021i
364364 0 0
365365 −4.37909 13.4775i −0.229212 0.705442i
366366 0 0
367367 16.2563 11.8109i 0.848570 0.616522i −0.0761814 0.997094i 0.524273π-0.524273\pi
0.924751 + 0.380572i 0.124273π0.124273\pi
368368 0 0
369369 6.08023 18.7130i 0.316524 0.974161i
370370 0 0
371371 0.952286 + 0.691876i 0.0494402 + 0.0359204i
372372 0 0
373373 26.4379 1.36890 0.684451 0.729059i 0.260042π-0.260042\pi
0.684451 + 0.729059i 0.260042π0.260042\pi
374374 0 0
375375 −22.9161 −1.18338
376376 0 0
377377 2.33504 + 1.69651i 0.120261 + 0.0873746i
378378 0 0
379379 6.26005 19.2665i 0.321557 0.989652i −0.651413 0.758723i 0.725824π-0.725824\pi
0.972971 0.230929i 0.0741764π-0.0741764\pi
380380 0 0
381381 −5.91607 + 4.29828i −0.303090 + 0.220208i
382382 0 0
383383 1.42442 + 4.38392i 0.0727845 + 0.224008i 0.980831 0.194863i 0.0624261π-0.0624261\pi
−0.908046 + 0.418870i 0.862426π0.862426\pi
384384 0 0
385385 28.8743 40.4461i 1.47157 2.06133i
386386 0 0
387387 −0.287673 0.885366i −0.0146232 0.0450057i
388388 0 0
389389 24.9393 18.1195i 1.26447 0.918694i 0.265506 0.964109i 0.414461π-0.414461\pi
0.998968 + 0.0454151i 0.0144611π0.0144611\pi
390390 0 0
391391 −0.507492 + 1.56190i −0.0256650 + 0.0789887i
392392 0 0
393393 9.12162 + 6.62724i 0.460125 + 0.334300i
394394 0 0
395395 35.5631 1.78937
396396 0 0
397397 −15.9382 −0.799916 −0.399958 0.916533i 0.630975π-0.630975\pi
−0.399958 + 0.916533i 0.630975π0.630975\pi
398398 0 0
399399 6.59467 + 4.79131i 0.330146 + 0.239865i
400400 0 0
401401 7.12841 21.9390i 0.355976 1.09558i −0.599466 0.800401i 0.704620π-0.704620\pi
0.955441 0.295181i 0.0953799π-0.0953799\pi
402402 0 0
403403 −4.06741 + 2.95515i −0.202612 + 0.147206i
404404 0 0
405405 2.62457 + 8.07761i 0.130416 + 0.401380i
406406 0 0
407407 −6.68919 2.11203i −0.331571 0.104689i
408408 0 0
409409 4.49146 + 13.8233i 0.222088 + 0.683518i 0.998574 + 0.0533829i 0.0170004π0.0170004\pi
−0.776486 + 0.630135i 0.783000π0.783000\pi
410410 0 0
411411 −1.87242 + 1.36039i −0.0923597 + 0.0671033i
412412 0 0
413413 9.30813 28.6475i 0.458023 1.40965i
414414 0 0
415415 −47.7515 34.6935i −2.34403 1.70304i
416416 0 0
417417 −12.9555 −0.634436
418418 0 0
419419 7.34710 0.358929 0.179465 0.983764i 0.442563π-0.442563\pi
0.179465 + 0.983764i 0.442563π0.442563\pi
420420 0 0
421421 1.43035 + 1.03921i 0.0697111 + 0.0506481i 0.622095 0.782942i 0.286282π-0.286282\pi
−0.552384 + 0.833590i 0.686282π0.686282\pi
422422 0 0
423423 4.21270 12.9654i 0.204829 0.630398i
424424 0 0
425425 8.55695 6.21699i 0.415073 0.301568i
426426 0 0
427427 15.6850 + 48.2733i 0.759048 + 2.33611i
428428 0 0
429429 −3.03577 + 1.01441i −0.146568 + 0.0489761i
430430 0 0
431431 5.03267 + 15.4890i 0.242415 + 0.746077i 0.996051 + 0.0887844i 0.0282982π0.0282982\pi
−0.753636 + 0.657292i 0.771702π0.771702\pi
432432 0 0
433433 1.81976 1.32213i 0.0874521 0.0635376i −0.543200 0.839603i 0.682787π-0.682787\pi
0.630652 + 0.776066i 0.282787π0.282787\pi
434434 0 0
435435 −3.14204 + 9.67020i −0.150649 + 0.463651i
436436 0 0
437437 −3.34980 2.43377i −0.160242 0.116423i
438438 0 0
439439 8.85337 0.422549 0.211274 0.977427i 0.432239π-0.432239\pi
0.211274 + 0.977427i 0.432239π0.432239\pi
440440 0 0
441441 −14.7903 −0.704300
442442 0 0
443443 −12.9159 9.38396i −0.613654 0.445845i 0.237045 0.971499i 0.423821π-0.423821\pi
−0.850699 + 0.525653i 0.823821π0.823821\pi
444444 0 0
445445 3.02435 9.30799i 0.143368 0.441241i
446446 0 0
447447 −7.93803 + 5.76732i −0.375456 + 0.272785i
448448 0 0
449449 7.35448 + 22.6348i 0.347079 + 1.06820i 0.960461 + 0.278414i 0.0898086π0.0898086\pi
−0.613382 + 0.789786i 0.710191π0.710191\pi
450450 0 0
451451 −0.252153 30.2783i −0.0118734 1.42575i
452452 0 0
453453 −5.74987 17.6963i −0.270152 0.831443i
454454 0 0
455455 12.7279 9.24736i 0.596693 0.433523i
456456 0 0
457457 9.16009 28.1919i 0.428491 1.31876i −0.471120 0.882069i 0.656150π-0.656150\pi
0.899612 0.436691i 0.143850π-0.143850\pi
458458 0 0
459459 3.62162 + 2.63126i 0.169043 + 0.122817i
460460 0 0
461461 −9.00605 −0.419454 −0.209727 0.977760i 0.567257π-0.567257\pi
−0.209727 + 0.977760i 0.567257π0.567257\pi
462462 0 0
463463 −16.0634 −0.746528 −0.373264 0.927725i 0.621761π-0.621761\pi
−0.373264 + 0.927725i 0.621761π0.621761\pi
464464 0 0
465465 −14.3288 10.4105i −0.664483 0.482775i
466466 0 0
467467 −1.25913 + 3.87521i −0.0582656 + 0.179323i −0.975953 0.217979i 0.930054π-0.930054\pi
0.917688 + 0.397302i 0.130054π0.130054\pi
468468 0 0
469469 −17.1145 + 12.4344i −0.790275 + 0.574168i
470470 0 0
471471 5.51305 + 16.9674i 0.254028 + 0.781817i
472472 0 0
473473 −0.851685 1.15195i −0.0391605 0.0529666i
474474 0 0
475475 8.24057 + 25.3619i 0.378103 + 1.16368i
476476 0 0
477477 −0.551229 + 0.400491i −0.0252390 + 0.0183372i
478478 0 0
479479 −0.107974 + 0.332309i −0.00493344 + 0.0151836i −0.953493 0.301415i 0.902541π-0.902541\pi
0.948559 + 0.316599i 0.102541π0.102541\pi
480480 0 0
481481 −1.79660 1.30530i −0.0819178 0.0595168i
482482 0 0
483483 −5.94874 −0.270677
484484 0 0
485485 5.96379 0.270802
486486 0 0
487487 31.6732 + 23.0119i 1.43525 + 1.04277i 0.989009 + 0.147855i 0.0472368π0.0472368\pi
0.446239 + 0.894914i 0.352763π0.352763\pi
488488 0 0
489489 −5.36070 + 16.4985i −0.242419 + 0.746090i
490490 0 0
491491 7.10844 5.16458i 0.320799 0.233074i −0.415717 0.909494i 0.636469π-0.636469\pi
0.736516 + 0.676420i 0.236469π0.236469\pi
492492 0 0
493493 −0.802529 2.46993i −0.0361441 0.111240i
494494 0 0
495495 17.1014 + 23.1306i 0.768653 + 1.03964i
496496 0 0
497497 14.8060 + 45.5682i 0.664141 + 2.04401i
498498 0 0
499499 20.8304 15.1342i 0.932497 0.677499i −0.0141058 0.999901i 0.504490π-0.504490\pi
0.946603 + 0.322402i 0.104490π0.104490\pi
500500 0 0
501501 −5.04552 + 15.5285i −0.225417 + 0.693763i
502502 0 0
503503 12.0267 + 8.73793i 0.536246 + 0.389605i 0.822689 0.568492i 0.192473π-0.192473\pi
−0.286443 + 0.958097i 0.592473π0.592473\pi
504504 0 0
505505 17.4972 0.778614
506506 0 0
507507 10.9354 0.485658
508508 0 0
509509 2.78541 + 2.02372i 0.123461 + 0.0896997i 0.647802 0.761809i 0.275688π-0.275688\pi
−0.524341 + 0.851508i 0.675688π0.675688\pi
510510 0 0
511511 −4.05145 + 12.4691i −0.179226 + 0.551600i
512512 0 0
513513 −9.13095 + 6.63402i −0.403141 + 0.292899i
514514 0 0
515515 −13.7907 42.4433i −0.607689 1.87028i
516516 0 0
517517 −0.174705 20.9784i −0.00768352 0.922629i
518518 0 0
519519 −1.80515 5.55567i −0.0792371 0.243867i
520520 0 0
521521 −32.5393 + 23.6412i −1.42557 + 1.03574i −0.434755 + 0.900549i 0.643165π0.643165\pi
−0.990820 + 0.135191i 0.956835π0.956835\pi
522522 0 0
523523 −10.6385 + 32.7419i −0.465189 + 1.43170i 0.393556 + 0.919301i 0.371245π0.371245\pi
−0.858745 + 0.512403i 0.828755π0.828755\pi
524524 0 0
525525 30.9954 + 22.5194i 1.35275 + 0.982829i
526526 0 0
527527 4.52378 0.197059
528528 0 0
529529 −19.9783 −0.868622
530530 0 0
531531 14.1060 + 10.2486i 0.612146 + 0.444750i
532532 0 0
533533 2.96219 9.11670i 0.128307 0.394888i
534534 0 0
535535 −31.1024 + 22.5972i −1.34467 + 0.976962i
536536 0 0
537537 0.399795 + 1.23044i 0.0172524 + 0.0530976i
538538 0 0
539539 −21.5874 + 7.21347i −0.929835 + 0.310706i
540540 0 0
541541 5.84779 + 17.9977i 0.251416 + 0.773780i 0.994515 + 0.104598i 0.0333555π0.0333555\pi
−0.743098 + 0.669182i 0.766645π0.766645\pi
542542 0 0
543543 −12.8945 + 9.36839i −0.553355 + 0.402036i
544544 0 0
545545 −5.15924 + 15.8785i −0.220998 + 0.680161i
546546 0 0
547547 −26.5669 19.3020i −1.13592 0.825292i −0.149372 0.988781i 0.547725π-0.547725\pi
−0.986545 + 0.163489i 0.947725π0.947725\pi
548548 0 0
549549 −29.3809 −1.25395
550550 0 0
551551 6.54775 0.278943
552552 0 0
553553 −26.6185 19.3395i −1.13194 0.822399i
554554 0 0
555555 2.41751 7.44032i 0.102617 0.315824i
556556 0 0
557557 −25.9380 + 18.8451i −1.09903 + 0.798492i −0.980901 0.194506i 0.937690π-0.937690\pi
−0.118129 + 0.992998i 0.537690π0.537690\pi
558558 0 0
559559 −0.140150 0.431337i −0.00592771 0.0182436i
560560 0 0
561561 2.74638 + 0.867135i 0.115952 + 0.0366105i
562562 0 0
563563 0.387163 + 1.19157i 0.0163170 + 0.0502185i 0.958883 0.283800i 0.0915952π-0.0915952\pi
−0.942567 + 0.334019i 0.891595π0.891595\pi
564564 0 0
565565 30.2609 21.9858i 1.27309 0.924951i
566566 0 0
567567 2.42821 7.47325i 0.101975 0.313847i
568568 0 0
569569 −4.17610 3.03411i −0.175071 0.127197i 0.496799 0.867866i 0.334509π-0.334509\pi
−0.671870 + 0.740669i 0.734509π0.734509\pi
570570 0 0
571571 1.46767 0.0614200 0.0307100 0.999528i 0.490223π-0.490223\pi
0.0307100 + 0.999528i 0.490223π0.490223\pi
572572 0 0
573573 −6.42419 −0.268374
574574 0 0
575575 −15.7442 11.4389i −0.656581 0.477034i
576576 0 0
577577 −5.93354 + 18.2616i −0.247016 + 0.760238i 0.748282 + 0.663381i 0.230879π0.230879\pi
−0.995298 + 0.0968575i 0.969121π0.969121\pi
578578 0 0
579579 17.3549 12.6090i 0.721243 0.524014i
580580 0 0
581581 16.8748 + 51.9353i 0.700084 + 2.15464i
582582 0 0
583583 −0.609229 + 0.853387i −0.0252317 + 0.0353437i
584584 0 0
585585 2.81414 + 8.66105i 0.116351 + 0.358090i
586586 0 0
587587 4.62070 3.35713i 0.190717 0.138564i −0.488330 0.872659i 0.662394π-0.662394\pi
0.679046 + 0.734096i 0.262394π0.262394\pi
588588 0 0
589589 −3.52450 + 10.8473i −0.145225 + 0.446955i
590590 0 0
591591 8.04137 + 5.84240i 0.330778 + 0.240324i
592592 0 0
593593 36.3301 1.49190 0.745949 0.666003i 0.231996π-0.231996\pi
0.745949 + 0.666003i 0.231996π0.231996\pi
594594 0 0
595595 −14.1560 −0.580339
596596 0 0
597597 −6.74760 4.90242i −0.276161 0.200643i
598598 0 0
599599 12.7458 39.2276i 0.520780 1.60280i −0.251732 0.967797i 0.581000π-0.581000\pi
0.772512 0.635000i 0.219000π-0.219000\pi
600600 0 0
601601 −17.3591 + 12.6121i −0.708091 + 0.514458i −0.882557 0.470205i 0.844180π-0.844180\pi
0.174466 + 0.984663i 0.444180π0.444180\pi
602602 0 0
603603 −3.78403 11.6460i −0.154097 0.474263i
604604 0 0
605605 36.2418 + 25.4199i 1.47344 + 1.03347i
606606 0 0
607607 −1.15092 3.54218i −0.0467146 0.143773i 0.924979 0.380019i 0.124083π-0.124083\pi
−0.971693 + 0.236247i 0.924083π0.924083\pi
608608 0 0
609609 7.61051 5.52936i 0.308393 0.224061i
610610 0 0
611611 2.05236 6.31653i 0.0830298 0.255539i
612612 0 0
613613 −11.5250 8.37340i −0.465490 0.338198i 0.330191 0.943914i 0.392887π-0.392887\pi
−0.795681 + 0.605716i 0.792887π0.792887\pi
614614 0 0
615615 33.7694 1.36171
616616 0 0
617617 33.2403 1.33821 0.669103 0.743170i 0.266678π-0.266678\pi
0.669103 + 0.743170i 0.266678π0.266678\pi
618618 0 0
619619 12.6726 + 9.20717i 0.509354 + 0.370067i 0.812578 0.582852i 0.198063π-0.198063\pi
−0.303224 + 0.952919i 0.598063π0.598063\pi
620620 0 0
621621 2.54525 7.83347i 0.102137 0.314346i
622622 0 0
623623 −7.32545 + 5.32225i −0.293488 + 0.213231i
624624 0 0
625625 13.7079 + 42.1887i 0.548317 + 1.68755i
626626 0 0
627627 −4.21897 + 5.90978i −0.168489 + 0.236014i
628628 0 0
629629 0.617471 + 1.90038i 0.0246202 + 0.0757731i
630630 0 0
631631 6.17588 4.48704i 0.245858 0.178626i −0.458031 0.888936i 0.651445π-0.651445\pi
0.703889 + 0.710310i 0.251445π0.251445\pi
632632 0 0
633633 0.677811 2.08609i 0.0269406 0.0829146i
634634 0 0
635635 25.9031 + 18.8197i 1.02793 + 0.746838i
636636 0 0
637637 −7.20560 −0.285496
638638 0 0
639639 −27.7345 −1.09716
640640 0 0
641641 15.3559 + 11.1567i 0.606521 + 0.440663i 0.848187 0.529696i 0.177694π-0.177694\pi
−0.241667 + 0.970359i 0.577694π0.577694\pi
642642 0 0
643643 5.09102 15.6686i 0.200770 0.617908i −0.799090 0.601211i 0.794685π-0.794685\pi
0.999861 0.0166965i 0.00531491π-0.00531491\pi
644644 0 0
645645 1.29259 0.939120i 0.0508956 0.0369778i
646646 0 0
647647 −12.3054 37.8720i −0.483774 1.48890i −0.833749 0.552144i 0.813810π-0.813810\pi
0.349975 0.936759i 0.386190π-0.386190\pi
648648 0 0
649649 25.5870 + 8.07877i 1.00438 + 0.317119i
650650 0 0
651651 5.06363 + 15.5842i 0.198459 + 0.610795i
652652 0 0
653653 −19.9459 + 14.4915i −0.780542 + 0.567097i −0.905142 0.425110i 0.860235π-0.860235\pi
0.124600 + 0.992207i 0.460235π0.460235\pi
654654 0 0
655655 15.2551 46.9504i 0.596066 1.83450i
656656 0 0
657657 −6.13975 4.46079i −0.239535 0.174032i
658658 0 0
659659 −11.3599 −0.442518 −0.221259 0.975215i 0.571017π-0.571017\pi
−0.221259 + 0.975215i 0.571017π0.571017\pi
660660 0 0
661661 5.05889 0.196768 0.0983841 0.995149i 0.468633π-0.468633\pi
0.0983841 + 0.995149i 0.468633π0.468633\pi
662662 0 0
663663 0.737629 + 0.535919i 0.0286471 + 0.0208134i
664664 0 0
665665 11.0290 33.9438i 0.427686 1.31628i
666666 0 0
667667 −3.86580 + 2.80867i −0.149684 + 0.108752i
668668 0 0
669669 −4.36839 13.4445i −0.168892 0.519795i
670670 0 0
671671 −42.8834 + 14.3296i −1.65550 + 0.553187i
672672 0 0
673673 −12.4707 38.3809i −0.480710 1.47947i −0.838099 0.545518i 0.816333π-0.816333\pi
0.357389 0.933956i 0.383667π-0.383667\pi
674674 0 0
675675 −42.9160 + 31.1803i −1.65184 + 1.20013i
676676 0 0
677677 −9.72753 + 29.9382i −0.373859 + 1.15062i 0.570386 + 0.821377i 0.306794π0.306794\pi
−0.944245 + 0.329244i 0.893206π0.893206\pi
678678 0 0
679679 −4.46382 3.24315i −0.171306 0.124461i
680680 0 0
681681 11.5269 0.441714
682682 0 0
683683 40.0582 1.53279 0.766393 0.642372i 0.222050π-0.222050\pi
0.766393 + 0.642372i 0.222050π0.222050\pi
684684 0 0
685685 8.19826 + 5.95639i 0.313240 + 0.227582i
686686 0 0
687687 3.78915 11.6618i 0.144565 0.444925i
688688 0 0
689689 −0.268550 + 0.195113i −0.0102310 + 0.00743322i
690690 0 0
691691 −4.00915 12.3389i −0.152515 0.469394i 0.845385 0.534157i 0.179371π-0.179371\pi
−0.997901 + 0.0647632i 0.979371π0.979371\pi
692692 0 0
693693 −0.221628 26.6128i −0.00841894 1.01094i
694694 0 0
695695 17.5290 + 53.9486i 0.664912 + 2.04639i
696696 0 0
697697 −6.97798 + 5.06980i −0.264310 + 0.192032i
698698 0 0
699699 6.66877 20.5244i 0.252236 0.776303i
700700 0 0
701701 10.6664 + 7.74961i 0.402865 + 0.292699i 0.770707 0.637190i 0.219903π-0.219903\pi
−0.367842 + 0.929888i 0.619903π0.619903\pi
702702 0 0
703703 −5.03788 −0.190007
704704 0 0
705705 23.3972 0.881190
706706 0 0
707707 −13.0964 9.51510i −0.492541 0.357852i
708708 0 0
709709 −5.05048 + 15.5438i −0.189675 + 0.583758i −0.999998 0.00222523i 0.999292π-0.999292\pi
0.810323 + 0.585984i 0.199292π0.199292\pi
710710 0 0
711711 15.4081 11.1946i 0.577849 0.419832i
712712 0 0
713713 −2.57210 7.91610i −0.0963257 0.296460i
714714 0 0
715715 8.33156 + 11.2689i 0.311583 + 0.421431i
716716 0 0
717717 1.06049 + 3.26386i 0.0396048 + 0.121891i
718718 0 0
719719 −4.53222 + 3.29285i −0.169023 + 0.122803i −0.669081 0.743189i 0.733312π-0.733312\pi
0.500058 + 0.865992i 0.333312π0.333312\pi
720720 0 0
721721 −12.7589 + 39.2678i −0.475165 + 1.46241i
722722 0 0
723723 11.8693 + 8.62354i 0.441423 + 0.320713i
724724 0 0
725725 30.7748 1.14295
726726 0 0
727727 29.1822 1.08231 0.541155 0.840923i 0.317987π-0.317987\pi
0.541155 + 0.840923i 0.317987π0.317987\pi
728728 0 0
729729 −6.89028 5.00608i −0.255196 0.185410i
730730 0 0
731731 −0.126105 + 0.388113i −0.00466418 + 0.0143549i
732732 0 0
733733 20.0564 14.5718i 0.740800 0.538223i −0.152161 0.988356i 0.548623π-0.548623\pi
0.892962 + 0.450133i 0.148623π0.148623\pi
734734 0 0
735735 −7.84413 24.1417i −0.289335 0.890482i
736736 0 0
737737 −11.2030 15.1526i −0.412668 0.558154i
738738 0 0
739739 8.26632 + 25.4411i 0.304081 + 0.935866i 0.980018 + 0.198907i 0.0637391π0.0637391\pi
−0.675937 + 0.736959i 0.736261π0.736261\pi
740740 0 0
741741 −1.85974 + 1.35118i −0.0683191 + 0.0496368i
742742 0 0
743743 −11.3483 + 34.9265i −0.416330 + 1.28133i 0.494727 + 0.869049i 0.335268π0.335268\pi
−0.911056 + 0.412282i 0.864732π0.864732\pi
744744 0 0
745745 34.7561 + 25.2518i 1.27337 + 0.925154i
746746 0 0
747747 −31.6097 −1.15654
748748 0 0
749749 35.5683 1.29964
750750 0 0
751751 −18.4555 13.4087i −0.673451 0.489290i 0.197728 0.980257i 0.436644π-0.436644\pi
−0.871178 + 0.490966i 0.836644π0.836644\pi
752752 0 0
753753 3.14749 9.68698i 0.114701 0.353013i
754754 0 0
755755 −65.9100 + 47.8864i −2.39871 + 1.74277i
756756 0 0
757757 8.25614 + 25.4098i 0.300075 + 0.923535i 0.981469 + 0.191619i 0.0613737π0.0613737\pi
−0.681395 + 0.731916i 0.738626π0.738626\pi
758758 0 0
759759 −0.0441282 5.29888i −0.00160175 0.192337i
760760 0 0
761761 6.71252 + 20.6590i 0.243329 + 0.748889i 0.995907 + 0.0903857i 0.0288100π0.0288100\pi
−0.752578 + 0.658503i 0.771190π0.771190\pi
762762 0 0
763763 12.4965 9.07923i 0.452403 0.328690i
764764 0 0
765765 2.53214 7.79312i 0.0915497 0.281761i
766766 0 0
767767 6.87221 + 4.99295i 0.248141 + 0.180285i
768768 0 0
769769 −53.7688 −1.93895 −0.969476 0.245185i 0.921151π-0.921151\pi
−0.969476 + 0.245185i 0.921151π0.921151\pi
770770 0 0
771771 −13.7730 −0.496024
772772 0 0
773773 7.87350 + 5.72044i 0.283190 + 0.205750i 0.720308 0.693655i 0.244001π-0.244001\pi
−0.437117 + 0.899404i 0.644001π0.644001\pi
774774 0 0
775775 −16.5654 + 50.9830i −0.595046 + 1.83136i
776776 0 0
777777 −5.85558 + 4.25432i −0.210068 + 0.152623i
778778 0 0
779779 −6.71998 20.6820i −0.240768 0.741009i
780780 0 0
781781 −40.4803 + 13.5266i −1.44850 + 0.484019i
782782 0 0
783783 4.02496 + 12.3875i 0.143840 + 0.442695i
784784 0 0
785785 63.1954 45.9141i 2.25554 1.63875i
786786 0 0
787787 11.8092 36.3451i 0.420954 1.29556i −0.485862 0.874035i 0.661494π-0.661494\pi
0.906816 0.421527i 0.138506π-0.138506\pi
788788 0 0
789789 −6.66355 4.84135i −0.237229 0.172357i
790790 0 0
791791 −34.6060 −1.23045
792792 0 0
793793 −14.3139 −0.508303
794794 0 0
795795 −0.946058 0.687351i −0.0335532 0.0243778i
796796 0 0
797797 −6.72473 + 20.6966i −0.238202 + 0.733110i 0.758478 + 0.651698i 0.225943π0.225943\pi
−0.996681 + 0.0814124i 0.974057π0.974057\pi
798798 0 0
799799 −4.83471 + 3.51263i −0.171040 + 0.124268i
800800 0 0
801801 −1.61966 4.98480i −0.0572278 0.176129i
802802 0 0
803803 −11.1370 3.51636i −0.393015 0.124090i
804804 0 0
805805 8.04870 + 24.7713i 0.283679 + 0.873075i
806806 0 0
807807 −0.780757 + 0.567253i −0.0274840 + 0.0199683i
808808 0 0
809809 −4.22367 + 12.9991i −0.148496 + 0.457025i −0.997444 0.0714523i 0.977237π-0.977237\pi
0.848948 + 0.528477i 0.177237π0.177237\pi
810810 0 0
811811 −28.7004 20.8520i −1.00781 0.732214i −0.0440580 0.999029i 0.514029π-0.514029\pi
−0.963748 + 0.266815i 0.914029π0.914029\pi
812812 0 0
813813 16.6963 0.585564
814814 0 0
815815 75.9553 2.66060
816816 0 0
817817 −0.832382 0.604761i −0.0291214 0.0211579i
818818 0 0
819819 2.60359 8.01304i 0.0909769 0.279998i
820820 0 0
821821 −12.1076 + 8.79669i −0.422558 + 0.307007i −0.778666 0.627438i 0.784103π-0.784103\pi
0.356108 + 0.934445i 0.384103π0.384103\pi
822822 0 0
823823 −3.77471 11.6174i −0.131578 0.404955i 0.863464 0.504410i 0.168290π-0.168290\pi
−0.995042 + 0.0994549i 0.968290π0.968290\pi
824824 0 0
825825 −19.8294 + 27.7764i −0.690371 + 0.967048i
826826 0 0
827827 4.29641 + 13.2230i 0.149401 + 0.459809i 0.997551 0.0699477i 0.0222833π-0.0222833\pi
−0.848150 + 0.529757i 0.822283π0.822283\pi
828828 0 0
829829 −9.98862 + 7.25716i −0.346919 + 0.252051i −0.747575 0.664177i 0.768782π-0.768782\pi
0.400656 + 0.916228i 0.368782π0.368782\pi
830830 0 0
831831 5.66435 17.4331i 0.196494 0.604747i
832832 0 0
833833 5.24528 + 3.81092i 0.181738 + 0.132041i
834834 0 0
835835 71.4895 2.47400
836836 0 0
837837 −22.6883 −0.784223
838838 0 0
839839 16.4757 + 11.9703i 0.568804 + 0.413260i 0.834671 0.550749i 0.185658π-0.185658\pi
−0.265866 + 0.964010i 0.585658π0.585658\pi
840840 0 0
841841 −6.62645 + 20.3941i −0.228498 + 0.703245i
842842 0 0
843843 −15.6208 + 11.3492i −0.538009 + 0.390887i
844844 0 0
845845 −14.7957 45.5365i −0.508987 1.56650i
846846 0 0
847847 −13.3030 38.7351i −0.457096 1.33095i
848848 0 0
849849 −1.85935 5.72251i −0.0638129 0.196396i
850850 0 0
851851 2.97437 2.16101i 0.101960 0.0740783i
852852 0 0
853853 16.1419 49.6795i 0.552687 1.70100i −0.149288 0.988794i 0.547698π-0.547698\pi
0.701975 0.712201i 0.252302π-0.252302\pi
854854 0 0
855855 16.7138 + 12.1433i 0.571601 + 0.415293i
856856 0 0
857857 −38.4691 −1.31408 −0.657041 0.753855i 0.728192π-0.728192\pi
−0.657041 + 0.753855i 0.728192π0.728192\pi
858858 0 0
859859 33.3955 1.13944 0.569720 0.821839i 0.307052π-0.307052\pi
0.569720 + 0.821839i 0.307052π0.307052\pi
860860 0 0
861861 −25.2760 18.3641i −0.861402 0.625846i
862862 0 0
863863 4.67070 14.3750i 0.158993 0.489329i −0.839551 0.543281i 0.817182π-0.817182\pi
0.998544 + 0.0539520i 0.0171818π0.0171818\pi
864864 0 0
865865 −20.6922 + 15.0337i −0.703555 + 0.511163i
866866 0 0
867867 4.57494 + 14.0802i 0.155373 + 0.478190i
868868 0 0
869869 17.0293 23.8541i 0.577680 0.809194i
870870 0 0
871871 −1.84352 5.67377i −0.0624653 0.192248i
872872 0 0
873873 2.58387 1.87729i 0.0874509 0.0635368i
874874 0 0
875875 28.6859 88.2863i 0.969762 2.98462i
876876 0 0
877877 12.9419 + 9.40283i 0.437016 + 0.317511i 0.784448 0.620194i 0.212946π-0.212946\pi
−0.347432 + 0.937705i 0.612946π0.612946\pi
878878 0 0
879879 −14.7274 −0.496741
880880 0 0
881881 −43.0908 −1.45177 −0.725883 0.687818i 0.758569π-0.758569\pi
−0.725883 + 0.687818i 0.758569π0.758569\pi
882882 0 0
883883 36.3842 + 26.4347i 1.22443 + 0.889598i 0.996460 0.0840715i 0.0267924π-0.0267924\pi
0.227966 + 0.973669i 0.426792π0.426792\pi
884884 0 0
885885 −9.24726 + 28.4601i −0.310843 + 0.956677i
886886 0 0
887887 −36.6560 + 26.6322i −1.23079 + 0.894221i −0.996949 0.0780543i 0.975129π-0.975129\pi
−0.233840 + 0.972275i 0.575129π0.575129\pi
888888 0 0
889889 −9.15384 28.1726i −0.307010 0.944880i
890890 0 0
891891 6.67486 + 2.10750i 0.223616 + 0.0706040i
892892 0 0
893893 −4.65596 14.3296i −0.155806 0.479521i
894894 0 0
895895 4.58281 3.32960i 0.153186 0.111296i
896896 0 0
897897 0.518401 1.59547i 0.0173089 0.0532713i
898898 0 0
899899 10.6486 + 7.73668i 0.355152 + 0.258033i
900900 0 0
901901 0.298682 0.00995054
902902 0 0
903903 −1.47819 −0.0491910
904904 0 0
905905 56.4576 + 41.0188i 1.87671 + 1.36351i
906906 0 0
907907 −6.55486 + 20.1738i −0.217651 + 0.669860i 0.781304 + 0.624150i 0.214555π0.214555\pi
−0.998955 + 0.0457093i 0.985445π0.985445\pi
908908 0 0
909909 7.58084 5.50780i 0.251441 0.182682i
910910 0 0
911911 5.91191 + 18.1950i 0.195870 + 0.602827i 0.999965 + 0.00832598i 0.00265027π0.00265027\pi
−0.804095 + 0.594501i 0.797350π0.797350\pi
912912 0 0
913913 −46.1365 + 15.4166i −1.52689 + 0.510214i
914914 0 0
915915 −15.5824 47.9576i −0.515138 1.58543i
916916 0 0
917917 −36.9502 + 26.8459i −1.22020 + 0.886530i
918918 0 0
919919 −12.7027 + 39.0949i −0.419023 + 1.28962i 0.489580 + 0.871959i 0.337150π0.337150\pi
−0.908603 + 0.417662i 0.862850π0.862850\pi
920920 0 0
921921 8.03196 + 5.83556i 0.264662 + 0.192288i
922922 0 0
923923 −13.5118 −0.444748
924924 0 0
925925 −23.6783 −0.778539
926926 0 0
927927 −19.3354 14.0480i −0.635056 0.461395i
928928 0 0
929929 −14.6696 + 45.1485i −0.481295 + 1.48128i 0.355980 + 0.934494i 0.384147π0.384147\pi
−0.837275 + 0.546781i 0.815853π0.815853\pi
930930 0 0
931931 −13.2246 + 9.60824i −0.433419 + 0.314897i
932932 0 0
933933 0.905858 + 2.78794i 0.0296565 + 0.0912732i
934934 0 0
935935 −0.105010 12.6095i −0.00343420 0.412376i
936936 0 0
937937 −8.48605 26.1174i −0.277227 0.853218i −0.988621 0.150425i 0.951936π-0.951936\pi
0.711394 0.702793i 0.248064π-0.248064\pi
938938 0 0
939939 11.1950 8.13362i 0.365334 0.265430i
940940 0 0
941941 4.99497 15.3729i 0.162831 0.501144i −0.836038 0.548671i 0.815134π-0.815134\pi
0.998870 + 0.0475271i 0.0151340π0.0151340\pi
942942 0 0
943943 12.8391 + 9.32812i 0.418097 + 0.303765i
944944 0 0
945945 70.9971 2.30954
946946 0 0
947947 −28.3252 −0.920445 −0.460223 0.887804i 0.652230π-0.652230\pi
−0.460223 + 0.887804i 0.652230π0.652230\pi
948948 0 0
949949 −2.99119 2.17323i −0.0970983 0.0705460i
950950 0 0
951951 3.76333 11.5823i 0.122034 0.375583i
952952 0 0
953953 43.1890 31.3787i 1.39903 1.01645i 0.404224 0.914660i 0.367542π-0.367542\pi
0.994805 0.101794i 0.0324584π-0.0324584\pi
954954 0 0
955955 8.69199 + 26.7512i 0.281266 + 0.865648i
956956 0 0
957957 4.98177 + 6.73809i 0.161038 + 0.217812i
958958 0 0
959959 −2.89717 8.91656i −0.0935544 0.287931i
960960 0 0
961961 6.53068 4.74481i 0.210667 0.153059i
962962 0 0
963963 −6.36223 + 19.5809i −0.205020 + 0.630987i
964964 0 0
965965 −75.9870 55.2078i −2.44611 1.77720i
966966 0 0
967967 45.0985 1.45027 0.725136 0.688606i 0.241777π-0.241777\pi
0.725136 + 0.688606i 0.241777π0.241777\pi
968968 0 0
969969 2.06840 0.0664466
970970 0 0
971971 38.4582 + 27.9415i 1.23418 + 0.896686i 0.997197 0.0748274i 0.0238406π-0.0238406\pi
0.236986 + 0.971513i 0.423841π0.423841\pi
972972 0 0
973973 16.2175 49.9122i 0.519908 1.60011i
974974 0 0
975975 −8.74088 + 6.35062i −0.279932 + 0.203383i
976976 0 0
977977 −1.64262 5.05545i −0.0525519 0.161738i 0.921336 0.388767i 0.127099π-0.127099\pi
−0.973888 + 0.227029i 0.927099π0.927099\pi
978978 0 0
979979 −4.79517 6.48570i −0.153254 0.207284i
980980 0 0
981981 2.76298 + 8.50357i 0.0882151 + 0.271498i
982982 0 0
983983 2.87735 2.09052i 0.0917731 0.0666771i −0.540952 0.841053i 0.681936π-0.681936\pi
0.632726 + 0.774376i 0.281936π0.281936\pi
984984 0 0
985985 13.4485 41.3901i 0.428504 1.31880i
986986 0 0
987987 −17.5125 12.7236i −0.557430 0.404996i
988988 0 0
989989 0.750852 0.0238757
990990 0 0
991991 38.1592 1.21217 0.606083 0.795401i 0.292740π-0.292740\pi
0.606083 + 0.795401i 0.292740π0.292740\pi
992992 0 0
993993 −24.9505 18.1276i −0.791780 0.575262i
994994 0 0
995995 −11.2848 + 34.7309i −0.357751 + 1.10104i
996996 0 0
997997 23.5980 17.1450i 0.747357 0.542987i −0.147649 0.989040i 0.547171π-0.547171\pi
0.895007 + 0.446053i 0.147171π0.147171\pi
998998 0 0
999999 −3.09683 9.53106i −0.0979793 0.301549i
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 704.2.m.i.577.2 8
4.3 odd 2 704.2.m.l.577.1 8
8.3 odd 2 88.2.i.b.49.2 yes 8
8.5 even 2 176.2.m.d.49.1 8
11.3 even 5 7744.2.a.dr.1.2 4
11.8 odd 10 7744.2.a.ds.1.2 4
11.9 even 5 inner 704.2.m.i.449.2 8
24.11 even 2 792.2.r.g.577.2 8
44.3 odd 10 7744.2.a.di.1.3 4
44.19 even 10 7744.2.a.dh.1.3 4
44.31 odd 10 704.2.m.l.449.1 8
88.3 odd 10 968.2.a.n.1.2 4
88.19 even 10 968.2.a.m.1.2 4
88.27 odd 10 968.2.i.s.81.1 8
88.35 even 10 968.2.i.p.9.2 8
88.43 even 2 968.2.i.p.753.2 8
88.51 even 10 968.2.i.t.729.1 8
88.53 even 10 176.2.m.d.97.1 8
88.59 odd 10 968.2.i.s.729.1 8
88.69 even 10 1936.2.a.bb.1.3 4
88.75 odd 10 88.2.i.b.9.2 8
88.83 even 10 968.2.i.t.81.1 8
88.85 odd 10 1936.2.a.bc.1.3 4
264.107 odd 10 8712.2.a.cd.1.4 4
264.179 even 10 8712.2.a.ce.1.4 4
264.251 even 10 792.2.r.g.361.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
88.2.i.b.9.2 8 88.75 odd 10
88.2.i.b.49.2 yes 8 8.3 odd 2
176.2.m.d.49.1 8 8.5 even 2
176.2.m.d.97.1 8 88.53 even 10
704.2.m.i.449.2 8 11.9 even 5 inner
704.2.m.i.577.2 8 1.1 even 1 trivial
704.2.m.l.449.1 8 44.31 odd 10
704.2.m.l.577.1 8 4.3 odd 2
792.2.r.g.361.2 8 264.251 even 10
792.2.r.g.577.2 8 24.11 even 2
968.2.a.m.1.2 4 88.19 even 10
968.2.a.n.1.2 4 88.3 odd 10
968.2.i.p.9.2 8 88.35 even 10
968.2.i.p.753.2 8 88.43 even 2
968.2.i.s.81.1 8 88.27 odd 10
968.2.i.s.729.1 8 88.59 odd 10
968.2.i.t.81.1 8 88.83 even 10
968.2.i.t.729.1 8 88.51 even 10
1936.2.a.bb.1.3 4 88.69 even 10
1936.2.a.bc.1.3 4 88.85 odd 10
7744.2.a.dh.1.3 4 44.19 even 10
7744.2.a.di.1.3 4 44.3 odd 10
7744.2.a.dr.1.2 4 11.3 even 5
7744.2.a.ds.1.2 4 11.8 odd 10
8712.2.a.cd.1.4 4 264.107 odd 10
8712.2.a.ce.1.4 4 264.179 even 10