Properties

Label 845.2.o.g.587.1
Level 845845
Weight 22
Character 845.587
Analytic conductor 6.7476.747
Analytic rank 00
Dimension 2020
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] = [845,2,Mod(258,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 7])) 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("845.258"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 845=5132 845 = 5 \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 845.o (of order 1212, degree 44, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [20,4,-2,-6,6,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 6.747358970806.74735897080
Analytic rank: 00
Dimension: 2020
Relative dimension: 55 over Q(ζ12)\Q(\zeta_{12})
Coefficient field: Q[x]/(x20+)\mathbb{Q}[x]/(x^{20} + \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x20+26x18+279x16+1604x14+5353x12+10466x10+11441x8+6176x6++1 x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 587.1
Root 1.51805i-1.51805i of defining polynomial
Character χ\chi == 845.587
Dual form 845.2.o.g.488.1

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+(0.7590231.31467i)q2+(0.6533670.175069i)q3+(0.152233+0.263675i)q4+(0.6002312.15400i)q5+(0.265763+0.991842i)q6+(2.24723+1.29744i)q72.57390q8+(2.201841.27123i)q9+(2.37621+2.42404i)q10+(1.29395+4.82908i)q11+(0.1456250.145625i)q123.93915iq14+(0.0150717+1.51244i)q15+(2.25812+3.91117i)q16+(0.0211881+0.0790751i)q17+3.85958iq18+(2.71143+0.726525i)q19+(0.659330+0.169644i)q20+(1.241131.24113i)q21+(7.330771.96427i)q22+(1.05016+3.91925i)q23+(1.68170+0.450611i)q24+(4.27945+2.58580i)q25+(2.65095+2.65095i)q27+(0.684205+0.395026i)q28+(4.31701+2.49243i)q29+(1.976911.16779i)q30+(2.321242.32124i)q31+(0.8540241.47921i)q32+(1.690852.92863i)q33+(0.08787510.0878751i)q34+(1.445835.61931i)q35+(0.6703830.387046i)q36+(0.494934+0.285750i)q37+(3.01318+3.01318i)q38+(1.54493+5.54419i)q40+(10.05632.69458i)q41+(0.689624+2.57371i)q42+(0.1321210.0354017i)q43+(1.076331.07633i)q44+(1.41662+5.50579i)q45+(5.949601.59419i)q46+2.30053iq47+(0.7906532.95076i)q48+(0.1332930.230870i)q49+(6.64766+3.66337i)q500.0553744iq51+(6.707356.70735i)q53+(1.472985.49724i)q54+(11.17850.111396i)q55+(5.784163.33948i)q56+1.89875q57+(6.55343+3.78362i)q58+(0.6941092.59045i)q59+(0.4010850.226268i)q60+(2.74237+4.74992i)q61+(4.813521.28978i)q62+(3.298705.71351i)q63+6.43957q645.13357q66+(7.89339+13.6718i)q67+(0.02407560.00645104i)q68+(1.372282.37686i)q69+(8.48494+2.36440i)q70+(1.98951+7.42495i)q71+(5.66731+3.27202i)q72+6.61894q73+(0.751333+0.433783i)q74+(3.248740.940275i)q75+(0.2212020.825536i)q76+(9.17326+9.17326i)q77+5.71054iq79+(7.069287.21159i)q80+(2.54575+4.40937i)q81+(4.09050+15.2660i)q82+3.70736iq83+(0.5161940.138314i)q84+(0.1576100.0931025i)q85+(0.1468240.146824i)q86+(3.256940.872695i)q87+(3.3305012.4296i)q88+(17.28294.63094i)q89+(8.313532.31664i)q90+(0.8735380.873538i)q92+(1.92300+1.11024i)q93+(3.024431.74616i)q94+(3.19242+5.40434i)q95+(0.816956+0.816956i)q96+(2.684934.65043i)q97+(0.202345+0.350471i)q98+(8.987948.98794i)q99+O(q100)q+(-0.759023 - 1.31467i) q^{2} +(-0.653367 - 0.175069i) q^{3} +(-0.152233 + 0.263675i) q^{4} +(-0.600231 - 2.15400i) q^{5} +(0.265763 + 0.991842i) q^{6} +(2.24723 + 1.29744i) q^{7} -2.57390 q^{8} +(-2.20184 - 1.27123i) q^{9} +(-2.37621 + 2.42404i) q^{10} +(-1.29395 + 4.82908i) q^{11} +(0.145625 - 0.145625i) q^{12} -3.93915i q^{14} +(0.0150717 + 1.51244i) q^{15} +(2.25812 + 3.91117i) q^{16} +(0.0211881 + 0.0790751i) q^{17} +3.85958i q^{18} +(-2.71143 + 0.726525i) q^{19} +(0.659330 + 0.169644i) q^{20} +(-1.24113 - 1.24113i) q^{21} +(7.33077 - 1.96427i) q^{22} +(-1.05016 + 3.91925i) q^{23} +(1.68170 + 0.450611i) q^{24} +(-4.27945 + 2.58580i) q^{25} +(2.65095 + 2.65095i) q^{27} +(-0.684205 + 0.395026i) q^{28} +(-4.31701 + 2.49243i) q^{29} +(1.97691 - 1.16779i) q^{30} +(2.32124 - 2.32124i) q^{31} +(0.854024 - 1.47921i) q^{32} +(1.69085 - 2.92863i) q^{33} +(0.0878751 - 0.0878751i) q^{34} +(1.44583 - 5.61931i) q^{35} +(0.670383 - 0.387046i) q^{36} +(-0.494934 + 0.285750i) q^{37} +(3.01318 + 3.01318i) q^{38} +(1.54493 + 5.54419i) q^{40} +(-10.0563 - 2.69458i) q^{41} +(-0.689624 + 2.57371i) q^{42} +(0.132121 - 0.0354017i) q^{43} +(-1.07633 - 1.07633i) q^{44} +(-1.41662 + 5.50579i) q^{45} +(5.94960 - 1.59419i) q^{46} +2.30053i q^{47} +(-0.790653 - 2.95076i) q^{48} +(-0.133293 - 0.230870i) q^{49} +(6.64766 + 3.66337i) q^{50} -0.0553744i q^{51} +(6.70735 - 6.70735i) q^{53} +(1.47298 - 5.49724i) q^{54} +(11.1785 - 0.111396i) q^{55} +(-5.78416 - 3.33948i) q^{56} +1.89875 q^{57} +(6.55343 + 3.78362i) q^{58} +(-0.694109 - 2.59045i) q^{59} +(-0.401085 - 0.226268i) q^{60} +(-2.74237 + 4.74992i) q^{61} +(-4.81352 - 1.28978i) q^{62} +(-3.29870 - 5.71351i) q^{63} +6.43957 q^{64} -5.13357 q^{66} +(7.89339 + 13.6718i) q^{67} +(-0.0240756 - 0.00645104i) q^{68} +(1.37228 - 2.37686i) q^{69} +(-8.48494 + 2.36440i) q^{70} +(1.98951 + 7.42495i) q^{71} +(5.66731 + 3.27202i) q^{72} +6.61894 q^{73} +(0.751333 + 0.433783i) q^{74} +(3.24874 - 0.940275i) q^{75} +(0.221202 - 0.825536i) q^{76} +(-9.17326 + 9.17326i) q^{77} +5.71054i q^{79} +(7.06928 - 7.21159i) q^{80} +(2.54575 + 4.40937i) q^{81} +(4.09050 + 15.2660i) q^{82} +3.70736i q^{83} +(0.516194 - 0.138314i) q^{84} +(0.157610 - 0.0931025i) q^{85} +(-0.146824 - 0.146824i) q^{86} +(3.25694 - 0.872695i) q^{87} +(3.33050 - 12.4296i) q^{88} +(-17.2829 - 4.63094i) q^{89} +(8.31353 - 2.31664i) q^{90} +(-0.873538 - 0.873538i) q^{92} +(-1.92300 + 1.11024i) q^{93} +(3.02443 - 1.74616i) q^{94} +(3.19242 + 5.40434i) q^{95} +(-0.816956 + 0.816956i) q^{96} +(2.68493 - 4.65043i) q^{97} +(-0.202345 + 0.350471i) q^{98} +(8.98794 - 8.98794i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q+4q22q36q4+6q5+8q6+6q712q812q910q10+16q11+24q1212q152q1610q1720q1914q204q21+16q22++60q99+O(q100) 20 q + 4 q^{2} - 2 q^{3} - 6 q^{4} + 6 q^{5} + 8 q^{6} + 6 q^{7} - 12 q^{8} - 12 q^{9} - 10 q^{10} + 16 q^{11} + 24 q^{12} - 12 q^{15} - 2 q^{16} - 10 q^{17} - 20 q^{19} - 14 q^{20} - 4 q^{21} + 16 q^{22}+ \cdots + 60 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/845Z)×\left(\mathbb{Z}/845\mathbb{Z}\right)^\times.

nn 171171 677677
χ(n)\chi(n) e(112)e\left(\frac{1}{12}\right) e(14)e\left(\frac{1}{4}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.759023 1.31467i −0.536710 0.929610i −0.999078 0.0429217i 0.986333π-0.986333\pi
0.462368 0.886688i 0.347000π-0.347000\pi
33 −0.653367 0.175069i −0.377222 0.101076i 0.0652261 0.997871i 0.479223π-0.479223\pi
−0.442448 + 0.896794i 0.645890π0.645890\pi
44 −0.152233 + 0.263675i −0.0761163 + 0.131837i
55 −0.600231 2.15400i −0.268431 0.963299i
66 0.265763 + 0.991842i 0.108497 + 0.404918i
77 2.24723 + 1.29744i 0.849375 + 0.490387i 0.860440 0.509552i 0.170189π-0.170189\pi
−0.0110652 + 0.999939i 0.503522π0.503522\pi
88 −2.57390 −0.910011
99 −2.20184 1.27123i −0.733946 0.423744i
1010 −2.37621 + 2.42404i −0.751422 + 0.766549i
1111 −1.29395 + 4.82908i −0.390140 + 1.45602i 0.439762 + 0.898114i 0.355063π0.355063\pi
−0.829902 + 0.557909i 0.811604π0.811604\pi
1212 0.145625 0.145625i 0.0420383 0.0420383i
1313 0 0
1414 3.93915i 1.05278i
1515 0.0150717 + 1.51244i 0.00389149 + 0.390509i
1616 2.25812 + 3.91117i 0.564529 + 0.977793i
1717 0.0211881 + 0.0790751i 0.00513887 + 0.0191785i 0.968448 0.249217i 0.0801732π-0.0801732\pi
−0.963309 + 0.268396i 0.913507π0.913507\pi
1818 3.85958i 0.909711i
1919 −2.71143 + 0.726525i −0.622045 + 0.166676i −0.556057 0.831144i 0.687686π-0.687686\pi
−0.0659876 + 0.997820i 0.521020π0.521020\pi
2020 0.659330 + 0.169644i 0.147431 + 0.0379335i
2121 −1.24113 1.24113i −0.270836 0.270836i
2222 7.33077 1.96427i 1.56293 0.418785i
2323 −1.05016 + 3.91925i −0.218973 + 0.817220i 0.765756 + 0.643131i 0.222365π0.222365\pi
−0.984730 + 0.174089i 0.944302π0.944302\pi
2424 1.68170 + 0.450611i 0.343276 + 0.0919805i
2525 −4.27945 + 2.58580i −0.855889 + 0.517159i
2626 0 0
2727 2.65095 + 2.65095i 0.510175 + 0.510175i
2828 −0.684205 + 0.395026i −0.129303 + 0.0746528i
2929 −4.31701 + 2.49243i −0.801649 + 0.462833i −0.844048 0.536268i 0.819834π-0.819834\pi
0.0423981 + 0.999101i 0.486500π0.486500\pi
3030 1.97691 1.16779i 0.360933 0.213208i
3131 2.32124 2.32124i 0.416906 0.416906i −0.467230 0.884136i 0.654748π-0.654748\pi
0.884136 + 0.467230i 0.154748π0.154748\pi
3232 0.854024 1.47921i 0.150972 0.261490i
3333 1.69085 2.92863i 0.294339 0.509809i
3434 0.0878751 0.0878751i 0.0150705 0.0150705i
3535 1.44583 5.61931i 0.244390 0.949837i
3636 0.670383 0.387046i 0.111730 0.0645076i
3737 −0.494934 + 0.285750i −0.0813667 + 0.0469771i −0.540131 0.841581i 0.681625π-0.681625\pi
0.458765 + 0.888558i 0.348292π0.348292\pi
3838 3.01318 + 3.01318i 0.488802 + 0.488802i
3939 0 0
4040 1.54493 + 5.54419i 0.244276 + 0.876613i
4141 −10.0563 2.69458i −1.57053 0.420823i −0.634554 0.772879i 0.718816π-0.718816\pi
−0.935979 + 0.352056i 0.885483π0.885483\pi
4242 −0.689624 + 2.57371i −0.106411 + 0.397132i
4343 0.132121 0.0354017i 0.0201483 0.00539871i −0.248731 0.968573i 0.580013π-0.580013\pi
0.268879 + 0.963174i 0.413347π0.413347\pi
4444 −1.07633 1.07633i −0.162262 0.162262i
4545 −1.41662 + 5.50579i −0.211178 + 0.820755i
4646 5.94960 1.59419i 0.877221 0.235051i
4747 2.30053i 0.335567i 0.985824 + 0.167784i 0.0536610π0.0536610\pi
−0.985824 + 0.167784i 0.946339π0.946339\pi
4848 −0.790653 2.95076i −0.114121 0.425905i
4949 −0.133293 0.230870i −0.0190418 0.0329814i
5050 6.64766 + 3.66337i 0.940121 + 0.518078i
5151 0.0553744i 0.00775397i
5252 0 0
5353 6.70735 6.70735i 0.921326 0.921326i −0.0757974 0.997123i 0.524150π-0.524150\pi
0.997123 + 0.0757974i 0.0241502π0.0241502\pi
5454 1.47298 5.49724i 0.200447 0.748080i
5555 11.1785 0.111396i 1.50731 0.0150206i
5656 −5.78416 3.33948i −0.772941 0.446257i
5757 1.89875 0.251496
5858 6.55343 + 3.78362i 0.860507 + 0.496814i
5959 −0.694109 2.59045i −0.0903653 0.337248i 0.905911 0.423469i 0.139188π-0.139188\pi
−0.996276 + 0.0862207i 0.972521π0.972521\pi
6060 −0.401085 0.226268i −0.0517799 0.0292111i
6161 −2.74237 + 4.74992i −0.351124 + 0.608165i −0.986447 0.164082i 0.947534π-0.947534\pi
0.635322 + 0.772247i 0.280867π0.280867\pi
6262 −4.81352 1.28978i −0.611318 0.163802i
6363 −3.29870 5.71351i −0.415597 0.719834i
6464 6.43957 0.804946
6565 0 0
6666 −5.13357 −0.631899
6767 7.89339 + 13.6718i 0.964331 + 1.67027i 0.711401 + 0.702786i 0.248061π0.248061\pi
0.252930 + 0.967485i 0.418606π0.418606\pi
6868 −0.0240756 0.00645104i −0.00291960 0.000782303i
6969 1.37228 2.37686i 0.165203 0.286140i
7070 −8.48494 + 2.36440i −1.01414 + 0.282600i
7171 1.98951 + 7.42495i 0.236111 + 0.881180i 0.977645 + 0.210264i 0.0674322π0.0674322\pi
−0.741533 + 0.670916i 0.765901π0.765901\pi
7272 5.66731 + 3.27202i 0.667899 + 0.385612i
7373 6.61894 0.774688 0.387344 0.921935i 0.373393π-0.373393\pi
0.387344 + 0.921935i 0.373393π0.373393\pi
7474 0.751333 + 0.433783i 0.0873407 + 0.0504262i
7575 3.24874 0.940275i 0.375132 0.108574i
7676 0.221202 0.825536i 0.0253736 0.0946955i
7777 −9.17326 + 9.17326i −1.04539 + 1.04539i
7878 0 0
7979 5.71054i 0.642486i 0.946997 + 0.321243i 0.104101π0.104101\pi
−0.946997 + 0.321243i 0.895899π0.895899\pi
8080 7.06928 7.21159i 0.790369 0.806280i
8181 2.54575 + 4.40937i 0.282861 + 0.489930i
8282 4.09050 + 15.2660i 0.451720 + 1.68584i
8383 3.70736i 0.406936i 0.979082 + 0.203468i 0.0652213π0.0652213\pi
−0.979082 + 0.203468i 0.934779π0.934779\pi
8484 0.516194 0.138314i 0.0563213 0.0150913i
8585 0.157610 0.0931025i 0.0170952 0.0100984i
8686 −0.146824 0.146824i −0.0158325 0.0158325i
8787 3.25694 0.872695i 0.349181 0.0935627i
8888 3.33050 12.4296i 0.355032 1.32500i
8989 −17.2829 4.63094i −1.83198 0.490878i −0.833851 0.551989i 0.813869π-0.813869\pi
−0.998131 + 0.0611111i 0.980536π0.980536\pi
9090 8.31353 2.31664i 0.876323 0.244195i
9191 0 0
9292 −0.873538 0.873538i −0.0910726 0.0910726i
9393 −1.92300 + 1.11024i −0.199405 + 0.115127i
9494 3.02443 1.74616i 0.311946 0.180102i
9595 3.19242 + 5.40434i 0.327535 + 0.554474i
9696 −0.816956 + 0.816956i −0.0833802 + 0.0833802i
9797 2.68493 4.65043i 0.272613 0.472180i −0.696917 0.717152i 0.745445π-0.745445\pi
0.969530 + 0.244972i 0.0787787π0.0787787\pi
9898 −0.202345 + 0.350471i −0.0204399 + 0.0354029i
9999 8.98794 8.98794i 0.903322 0.903322i
100100 −0.0303375 1.52202i −0.00303375 0.152202i
101101 2.17443 1.25541i 0.216363 0.124918i −0.387902 0.921701i 0.626800π-0.626800\pi
0.604265 + 0.796783i 0.293467π0.293467\pi
102102 −0.0727989 + 0.0420305i −0.00720817 + 0.00416164i
103103 −4.71738 4.71738i −0.464817 0.464817i 0.435414 0.900230i 0.356602π-0.356602\pi
−0.900230 + 0.435414i 0.856602π0.856602\pi
104104 0 0
105105 −1.92843 + 3.41835i −0.188195 + 0.333597i
106106 −13.9090 3.72690i −1.35096 0.361988i
107107 0.939155 3.50497i 0.0907915 0.338838i −0.905556 0.424226i 0.860546π-0.860546\pi
0.996348 + 0.0853876i 0.0272129π0.0272129\pi
108108 −1.10255 + 0.295427i −0.106093 + 0.0284275i
109109 1.58528 + 1.58528i 0.151843 + 0.151843i 0.778941 0.627098i 0.215757π-0.215757\pi
−0.627098 + 0.778941i 0.715757π0.715757\pi
110110 −8.63120 14.6115i −0.822953 1.39315i
111111 0.373400 0.100052i 0.0354416 0.00949653i
112112 11.7191i 1.10735i
113113 1.48231 + 5.53206i 0.139444 + 0.520412i 0.999940 + 0.0109551i 0.00348719π0.00348719\pi
−0.860496 + 0.509457i 0.829846π0.829846\pi
114114 −1.44120 2.49623i −0.134980 0.233793i
115115 9.07241 0.0904081i 0.846006 0.00843060i
116116 1.51772i 0.140916i
117117 0 0
118118 −2.87873 + 2.87873i −0.265009 + 0.265009i
119119 −0.0549806 + 0.205190i −0.00504007 + 0.0188098i
120120 −0.0387930 3.89286i −0.00354130 0.355368i
121121 −12.1195 6.99717i −1.10177 0.636106i
122122 8.32609 0.753809
123123 6.09873 + 3.52110i 0.549904 + 0.317487i
124124 0.258683 + 0.965419i 0.0232304 + 0.0866972i
125125 8.13846 + 7.66586i 0.727926 + 0.685655i
126126 −5.00757 + 8.67337i −0.446110 + 0.772685i
127127 0.786718 + 0.210801i 0.0698100 + 0.0187055i 0.293555 0.955942i 0.405162π-0.405162\pi
−0.223745 + 0.974648i 0.571828π0.571828\pi
128128 −6.59583 11.4243i −0.582994 1.00978i
129129 −0.0925213 −0.00814605
130130 0 0
131131 −16.1062 −1.40721 −0.703604 0.710592i 0.748427π-0.748427\pi
−0.703604 + 0.710592i 0.748427π0.748427\pi
132132 0.514804 + 0.891667i 0.0448079 + 0.0776096i
133133 −7.03584 1.88525i −0.610085 0.163472i
134134 11.9825 20.7544i 1.03513 1.79290i
135135 4.11897 7.30133i 0.354504 0.628398i
136136 −0.0545361 0.203531i −0.00467643 0.0174527i
137137 −16.6601 9.61871i −1.42337 0.821782i −0.426783 0.904354i 0.640353π-0.640353\pi
−0.996585 + 0.0825721i 0.973687π0.973687\pi
138138 −4.16637 −0.354665
139139 −13.7257 7.92451i −1.16419 0.672148i −0.211889 0.977294i 0.567962π-0.567962\pi
−0.952306 + 0.305146i 0.901295π0.901295\pi
140140 1.26157 + 1.23667i 0.106622 + 0.104518i
141141 0.402752 1.50309i 0.0339178 0.126583i
142142 8.25125 8.25125i 0.692430 0.692430i
143143 0 0
144144 11.4823i 0.956862i
145145 7.95990 + 7.80282i 0.661034 + 0.647989i
146146 −5.02393 8.70170i −0.415783 0.720158i
147147 0.0466709 + 0.174178i 0.00384935 + 0.0143660i
148148 0.174002i 0.0143029i
149149 −1.39120 + 0.372772i −0.113972 + 0.0305387i −0.315354 0.948974i 0.602123π-0.602123\pi
0.201382 + 0.979513i 0.435457π0.435457\pi
150150 −3.70202 3.55732i −0.302269 0.290454i
151151 −13.9253 13.9253i −1.13322 1.13322i −0.989638 0.143585i 0.954137π-0.954137\pi
−0.143585 0.989638i 0.545863π-0.545863\pi
152152 6.97895 1.87000i 0.566068 0.151677i
153153 0.0538699 0.201045i 0.00435513 0.0162536i
154154 19.0225 + 5.09706i 1.53288 + 0.410733i
155155 −6.39322 3.60667i −0.513516 0.289695i
156156 0 0
157157 4.54644 + 4.54644i 0.362845 + 0.362845i 0.864859 0.502014i 0.167408π-0.167408\pi
−0.502014 + 0.864859i 0.667408π0.667408\pi
158158 7.50746 4.33444i 0.597262 0.344829i
159159 −5.55661 + 3.20811i −0.440668 + 0.254420i
160160 −3.69884 0.951700i −0.292419 0.0752385i
161161 −7.44495 + 7.44495i −0.586744 + 0.586744i
162162 3.86457 6.69363i 0.303629 0.525901i
163163 −6.56789 + 11.3759i −0.514437 + 0.891031i 0.485423 + 0.874280i 0.338666π0.338666\pi
−0.999860 + 0.0167516i 0.994668π0.994668\pi
164164 2.24139 2.24139i 0.175023 0.175023i
165165 −7.32318 1.88423i −0.570109 0.146687i
166166 4.87395 2.81398i 0.378292 0.218407i
167167 −2.84503 + 1.64258i −0.220155 + 0.127107i −0.606022 0.795448i 0.707236π-0.707236\pi
0.385867 + 0.922554i 0.373902π0.373902\pi
168168 3.19454 + 3.19454i 0.246464 + 0.246464i
169169 0 0
170170 −0.242028 0.136538i −0.0185627 0.0104720i
171171 6.89371 + 1.84716i 0.527175 + 0.141256i
172172 −0.0107786 + 0.0402263i −0.000821860 + 0.00306722i
173173 −4.09367 + 1.09689i −0.311236 + 0.0833953i −0.411056 0.911610i 0.634840π-0.634840\pi
0.0998202 + 0.995005i 0.468173π0.468173\pi
174174 −3.61940 3.61940i −0.274386 0.274386i
175175 −12.9718 + 0.258559i −0.980579 + 0.0195452i
176176 −21.8093 + 5.84377i −1.64393 + 0.440491i
177177 1.81403i 0.136351i
178178 7.02997 + 26.2362i 0.526919 + 1.96649i
179179 6.98083 + 12.0912i 0.521772 + 0.903735i 0.999679 + 0.0253252i 0.00806213π0.00806213\pi
−0.477907 + 0.878410i 0.658605π0.658605\pi
180180 −1.23608 1.21169i −0.0921321 0.0903139i
181181 8.64775i 0.642782i −0.946947 0.321391i 0.895850π-0.895850\pi
0.946947 0.321391i 0.104150π-0.104150\pi
182182 0 0
183183 2.62334 2.62334i 0.193923 0.193923i
184184 2.70301 10.0878i 0.199268 0.743680i
185185 0.912582 + 0.894573i 0.0670944 + 0.0657703i
186186 2.91920 + 1.68540i 0.214046 + 0.123579i
187187 −0.409276 −0.0299292
188188 −0.606592 0.350216i −0.0442402 0.0255421i
189189 2.51785 + 9.39675i 0.183147 + 0.683513i
190190 4.68179 8.29899i 0.339653 0.602072i
191191 −8.45647 + 14.6470i −0.611889 + 1.05982i 0.379033 + 0.925383i 0.376257π0.376257\pi
−0.990922 + 0.134439i 0.957077π0.957077\pi
192192 −4.20740 1.12737i −0.303643 0.0813609i
193193 4.27780 + 7.40936i 0.307923 + 0.533338i 0.977908 0.209037i 0.0670329π-0.0670329\pi
−0.669985 + 0.742375i 0.733700π0.733700\pi
194194 −8.15169 −0.585257
195195 0 0
196196 0.0811660 0.00579757
197197 3.82842 + 6.63101i 0.272764 + 0.472440i 0.969568 0.244820i 0.0787290π-0.0787290\pi
−0.696805 + 0.717261i 0.745396π0.745396\pi
198198 −18.6382 4.99409i −1.32456 0.354915i
199199 −7.66380 + 13.2741i −0.543272 + 0.940975i 0.455441 + 0.890266i 0.349481π0.349481\pi
−0.998713 + 0.0507092i 0.983852π0.983852\pi
200200 11.0149 6.65558i 0.778869 0.470621i
201201 −2.76378 10.3146i −0.194942 0.727533i
202202 −3.30088 1.90576i −0.232249 0.134089i
203203 −12.9351 −0.907868
204204 0.0146008 + 0.00842979i 0.00102226 + 0.000590203i
205205 0.231976 + 23.2787i 0.0162019 + 1.62585i
206206 −2.62118 + 9.78238i −0.182626 + 0.681570i
207207 7.29455 7.29455i 0.507006 0.507006i
208208 0 0
209209 14.0338i 0.970739i
210210 5.95771 0.0593697i 0.411121 0.00409690i
211211 −9.91788 17.1783i −0.682775 1.18260i −0.974130 0.225986i 0.927440π-0.927440\pi
0.291355 0.956615i 0.405894π-0.405894\pi
212212 0.747481 + 2.78964i 0.0513372 + 0.191593i
213213 5.19952i 0.356265i
214214 −5.32071 + 1.42568i −0.363716 + 0.0974575i
215215 −0.155559 0.263340i −0.0106090 0.0179596i
216216 −6.82328 6.82328i −0.464265 0.464265i
217217 8.22803 2.20469i 0.558555 0.149664i
218218 0.880853 3.28739i 0.0596589 0.222650i
219219 −4.32460 1.15877i −0.292229 0.0783025i
220220 −1.67236 + 2.96445i −0.112751 + 0.199863i
221221 0 0
222222 −0.414955 0.414955i −0.0278499 0.0278499i
223223 −16.4311 + 9.48653i −1.10031 + 0.635265i −0.936303 0.351194i 0.885776π-0.885776\pi
−0.164008 + 0.986459i 0.552442π0.552442\pi
224224 3.83838 2.21609i 0.256463 0.148069i
225225 12.7098 0.253336i 0.847319 0.0168890i
226226 6.14771 6.14771i 0.408939 0.408939i
227227 13.4794 23.3469i 0.894656 1.54959i 0.0604265 0.998173i 0.480754π-0.480754\pi
0.834230 0.551417i 0.185913π-0.185913\pi
228228 −0.289052 + 0.500652i −0.0191429 + 0.0331565i
229229 −11.1801 + 11.1801i −0.738799 + 0.738799i −0.972346 0.233547i 0.924967π-0.924967\pi
0.233547 + 0.972346i 0.424967π0.424967\pi
230230 −7.00503 11.8586i −0.461898 0.781931i
231231 7.59946 4.38755i 0.500008 0.288680i
232232 11.1116 6.41527i 0.729510 0.421183i
233233 −6.75797 6.75797i −0.442729 0.442729i 0.450199 0.892928i 0.351353π-0.351353\pi
−0.892928 + 0.450199i 0.851353π0.851353\pi
234234 0 0
235235 4.95535 1.38085i 0.323251 0.0900767i
236236 0.788702 + 0.211332i 0.0513401 + 0.0137565i
237237 0.999740 3.73108i 0.0649401 0.242360i
238238 0.311489 0.0834631i 0.0201908 0.00541011i
239239 1.98766 + 1.98766i 0.128571 + 0.128571i 0.768464 0.639893i 0.221021π-0.221021\pi
−0.639893 + 0.768464i 0.721021π0.721021\pi
240240 −5.88136 + 3.47420i −0.379640 + 0.224259i
241241 2.65141 0.710443i 0.170792 0.0457637i −0.172409 0.985025i 0.555155π-0.555155\pi
0.343202 + 0.939262i 0.388489π0.388489\pi
242242 21.2441i 1.36562i
243243 −3.80231 14.1904i −0.243918 0.910315i
244244 −0.834956 1.44619i −0.0534526 0.0925826i
245245 −0.417287 + 0.425688i −0.0266595 + 0.0271962i
246246 10.6904i 0.681595i
247247 0 0
248248 −5.97463 + 5.97463i −0.379389 + 0.379389i
249249 0.649045 2.42227i 0.0411316 0.153505i
250250 3.90077 16.5179i 0.246706 1.04469i
251251 −2.45414 1.41690i −0.154904 0.0894337i 0.420545 0.907272i 0.361839π-0.361839\pi
−0.575448 + 0.817838i 0.695172π0.695172\pi
252252 2.00868 0.126535
253253 −17.5675 10.1426i −1.10446 0.637661i
254254 −0.320005 1.19428i −0.0200789 0.0749355i
255255 −0.119277 + 0.0332374i −0.00746939 + 0.00208141i
256256 −3.57321 + 6.18898i −0.223325 + 0.386811i
257257 −19.3784 5.19242i −1.20879 0.323894i −0.402502 0.915419i 0.631859π-0.631859\pi
−0.806287 + 0.591525i 0.798526π0.798526\pi
258258 0.0702258 + 0.121635i 0.00437207 + 0.00757265i
259259 −1.48298 −0.0921478
260260 0 0
261261 12.6738 0.784490
262262 12.2250 + 21.1743i 0.755264 + 1.30815i
263263 −9.10077 2.43854i −0.561177 0.150367i −0.0329302 0.999458i 0.510484π-0.510484\pi
−0.528247 + 0.849091i 0.677151π0.677151\pi
264264 −4.35207 + 7.53801i −0.267851 + 0.463932i
265265 −18.4736 10.4217i −1.13482 0.640199i
266266 2.86189 + 10.6807i 0.175474 + 0.654878i
267267 10.4813 + 6.05140i 0.641447 + 0.370340i
268268 −4.80653 −0.293605
269269 2.78417 + 1.60744i 0.169754 + 0.0980075i 0.582470 0.812852i 0.302086π-0.302086\pi
−0.412716 + 0.910860i 0.635420π0.635420\pi
270270 −12.7252 + 0.126809i −0.774431 + 0.00771734i
271271 3.93065 14.6694i 0.238770 0.891102i −0.737643 0.675191i 0.764061π-0.764061\pi
0.976413 0.215911i 0.0692721π-0.0692721\pi
272272 −0.261431 + 0.261431i −0.0158516 + 0.0158516i
273273 0 0
274274 29.2033i 1.76424i
275275 −6.94964 24.0117i −0.419079 1.44796i
276276 0.417811 + 0.723671i 0.0251493 + 0.0435598i
277277 2.76028 + 10.3015i 0.165849 + 0.618956i 0.997930 + 0.0643031i 0.0204824π0.0204824\pi
−0.832082 + 0.554653i 0.812851π0.812851\pi
278278 24.0595i 1.44300i
279279 −8.06181 + 2.16016i −0.482648 + 0.129325i
280280 −3.72143 + 14.4635i −0.222398 + 0.864362i
281281 12.7630 + 12.7630i 0.761379 + 0.761379i 0.976572 0.215193i 0.0690380π-0.0690380\pi
−0.215193 + 0.976572i 0.569038π0.569038\pi
282282 −2.28176 + 0.611396i −0.135877 + 0.0364081i
283283 −1.49018 + 5.56143i −0.0885820 + 0.330592i −0.995968 0.0897050i 0.971408π-0.971408\pi
0.907386 + 0.420297i 0.138074π0.138074\pi
284284 −2.26064 0.605736i −0.134144 0.0359438i
285285 −1.13969 4.08991i −0.0675093 0.242266i
286286 0 0
287287 −19.1028 19.1028i −1.12760 1.12760i
288288 −3.76084 + 2.17132i −0.221610 + 0.127946i
289289 14.7166 8.49665i 0.865684 0.499803i
290290 4.21636 16.3871i 0.247593 0.962286i
291291 −2.56839 + 2.56839i −0.150562 + 0.150562i
292292 −1.00762 + 1.74525i −0.0589664 + 0.102133i
293293 −1.59804 + 2.76788i −0.0933583 + 0.161701i −0.908922 0.416966i 0.863094π-0.863094\pi
0.815564 + 0.578667i 0.196427π0.196427\pi
294294 0.193562 0.193562i 0.0112888 0.0112888i
295295 −5.16321 + 3.04998i −0.300614 + 0.177577i
296296 1.27391 0.735493i 0.0740446 0.0427497i
297297 −16.2318 + 9.37145i −0.941867 + 0.543787i
298298 1.54603 + 1.54603i 0.0895590 + 0.0895590i
299299 0 0
300300 −0.246638 + 0.999751i −0.0142396 + 0.0577207i
301301 0.342839 + 0.0918633i 0.0197609 + 0.00529491i
302302 −7.73749 + 28.8767i −0.445243 + 1.66167i
303303 −1.64048 + 0.439566i −0.0942432 + 0.0252524i
304304 −8.96429 8.96429i −0.514137 0.514137i
305305 11.8774 + 3.05602i 0.680098 + 0.174987i
306306 −0.305196 + 0.0817771i −0.0174469 + 0.00467488i
307307 24.2740i 1.38539i −0.721231 0.692695i 0.756423π-0.756423\pi
0.721231 0.692695i 0.243577π-0.243577\pi
308308 −1.02229 3.81522i −0.0582501 0.217393i
309309 2.25631 + 3.90804i 0.128357 + 0.222321i
310310 0.111037 + 11.1425i 0.00630648 + 0.632852i
311311 16.9053i 0.958614i 0.877647 + 0.479307i 0.159112π0.159112\pi
−0.877647 + 0.479307i 0.840888π0.840888\pi
312312 0 0
313313 −8.40997 + 8.40997i −0.475359 + 0.475359i −0.903644 0.428285i 0.859118π-0.859118\pi
0.428285 + 0.903644i 0.359118π0.359118\pi
314314 2.52620 9.42790i 0.142562 0.532047i
315315 −10.3269 + 10.5348i −0.581856 + 0.593570i
316316 −1.50573 0.869331i −0.0847037 0.0489037i
317317 −11.9484 −0.671087 −0.335543 0.942025i 0.608920π-0.608920\pi
−0.335543 + 0.942025i 0.608920π0.608920\pi
318318 8.43520 + 4.87006i 0.473022 + 0.273100i
319319 −6.45015 24.0723i −0.361139 1.34779i
320320 −3.86523 13.8708i −0.216073 0.775403i
321321 −1.22723 + 2.12562i −0.0684970 + 0.118640i
322322 15.4385 + 4.13674i 0.860355 + 0.230531i
323323 −0.114900 0.199013i −0.00639321 0.0110734i
324324 −1.55018 −0.0861214
325325 0 0
326326 19.9407 1.10442
327327 −0.758238 1.31331i −0.0419307 0.0726260i
328328 25.8840 + 6.93559i 1.42920 + 0.382954i
329329 −2.98480 + 5.16983i −0.164558 + 0.285022i
330330 3.08133 + 11.0577i 0.169621 + 0.608707i
331331 5.55136 + 20.7179i 0.305130 + 1.13876i 0.932833 + 0.360308i 0.117329π0.117329\pi
−0.627703 + 0.778453i 0.716005π0.716005\pi
332332 −0.977538 0.564382i −0.0536494 0.0309745i
333333 1.45302 0.0796250
334334 4.31889 + 2.49351i 0.236319 + 0.136439i
335335 24.7111 25.2086i 1.35011 1.37729i
336336 2.05165 7.65687i 0.111927 0.417716i
337337 −14.1264 + 14.1264i −0.769514 + 0.769514i −0.978021 0.208507i 0.933140π-0.933140\pi
0.208507 + 0.978021i 0.433140π0.433140\pi
338338 0 0
339339 3.87397i 0.210405i
340340 0.000555369 0.0557310i 3.01191e−5 0.00302244i
341341 8.20588 + 14.2130i 0.444373 + 0.769677i
342342 −2.80408 10.4650i −0.151627 0.565881i
343343 18.8559i 1.01812i
344344 −0.340067 + 0.0911205i −0.0183352 + 0.00491289i
345345 −5.94344 1.52923i −0.319984 0.0823309i
346346 4.54924 + 4.54924i 0.244569 + 0.244569i
347347 23.7906 6.37467i 1.27715 0.342210i 0.444382 0.895837i 0.353423π-0.353423\pi
0.832765 + 0.553627i 0.186757π0.186757\pi
348348 −0.265705 + 0.991626i −0.0142433 + 0.0531567i
349349 26.3190 + 7.05214i 1.40882 + 0.377493i 0.881504 0.472176i 0.156531π-0.156531\pi
0.527317 + 0.849669i 0.323198π0.323198\pi
350350 10.1858 + 16.8574i 0.544456 + 0.901065i
351351 0 0
352352 6.03818 + 6.03818i 0.321836 + 0.321836i
353353 −7.62038 + 4.39963i −0.405592 + 0.234169i −0.688894 0.724862i 0.741903π-0.741903\pi
0.283302 + 0.959031i 0.408570π0.408570\pi
354354 2.38485 1.37689i 0.126753 0.0731810i
355355 14.7992 8.74209i 0.785460 0.463982i
356356 3.85208 3.85208i 0.204160 0.204160i
357357 0.0718451 0.124439i 0.00380244 0.00658603i
358358 10.5972 18.3549i 0.560081 0.970089i
359359 11.1256 11.1256i 0.587186 0.587186i −0.349683 0.936868i 0.613711π-0.613711\pi
0.936868 + 0.349683i 0.113711π0.113711\pi
360360 3.64625 14.1714i 0.192174 0.746896i
361361 −9.63047 + 5.56015i −0.506867 + 0.292640i
362362 −11.3689 + 6.56385i −0.597537 + 0.344988i
363363 6.69346 + 6.69346i 0.351316 + 0.351316i
364364 0 0
365365 −3.97289 14.2572i −0.207951 0.746256i
366366 −5.43999 1.45764i −0.284353 0.0761921i
367367 2.84144 10.6044i 0.148322 0.553545i −0.851263 0.524739i 0.824163π-0.824163\pi
0.999585 0.0288057i 0.00917042π-0.00917042\pi
368368 −17.7002 + 4.74276i −0.922689 + 0.247234i
369369 18.7169 + 18.7169i 0.974365 + 0.974365i
370370 0.483395 1.87874i 0.0251305 0.0976712i
371371 23.7754 6.37060i 1.23436 0.330745i
372372 0.676060i 0.0350521i
373373 2.73825 + 10.2193i 0.141781 + 0.529135i 0.999878 + 0.0156462i 0.00498054π0.00498054\pi
−0.858096 + 0.513489i 0.828353π0.828353\pi
374374 0.310650 + 0.538062i 0.0160633 + 0.0278225i
375375 −3.97535 6.43341i −0.205286 0.332220i
376376 5.92134i 0.305370i
377377 0 0
378378 10.4425 10.4425i 0.537104 0.537104i
379379 −2.53694 + 9.46800i −0.130314 + 0.486338i −0.999973 0.00731411i 0.997672π-0.997672\pi
0.869659 + 0.493652i 0.164338π0.164338\pi
380380 −1.91098 + 0.0190432i −0.0980311 + 0.000976897i
381381 −0.477111 0.275460i −0.0244431 0.0141123i
382382 25.6746 1.31363
383383 22.5658 + 13.0283i 1.15306 + 0.665718i 0.949630 0.313373i 0.101459π-0.101459\pi
0.203426 + 0.979090i 0.434792π0.434792\pi
384384 2.30945 + 8.61899i 0.117854 + 0.439836i
385385 25.2653 + 14.2531i 1.28764 + 0.726407i
386386 6.49390 11.2478i 0.330531 0.572496i
387387 −0.335913 0.0900076i −0.0170754 0.00457534i
388388 0.817467 + 1.41589i 0.0415006 + 0.0718812i
389389 32.4888 1.64725 0.823623 0.567138i 0.191950π-0.191950\pi
0.823623 + 0.567138i 0.191950π0.191950\pi
390390 0 0
391391 −0.332166 −0.0167983
392392 0.343082 + 0.594236i 0.0173283 + 0.0300134i
393393 10.5233 + 2.81971i 0.530830 + 0.142235i
394394 5.81172 10.0662i 0.292790 0.507127i
395395 12.3005 3.42764i 0.618906 0.172463i
396396 1.00163 + 3.73815i 0.0503340 + 0.187849i
397397 20.9451 + 12.0927i 1.05121 + 0.606914i 0.922987 0.384832i 0.125741π-0.125741\pi
0.128219 + 0.991746i 0.459074π0.459074\pi
398398 23.2680 1.16632
399399 4.26694 + 2.46352i 0.213614 + 0.123330i
400400 −19.7770 10.8986i −0.988849 0.544931i
401401 8.49918 31.7194i 0.424429 1.58399i −0.340738 0.940158i 0.610677π-0.610677\pi
0.765167 0.643832i 0.222657π-0.222657\pi
402402 −11.4624 + 11.4624i −0.571695 + 0.571695i
403403 0 0
404404 0.764454i 0.0380330i
405405 7.96975 8.13019i 0.396020 0.403992i
406406 9.81806 + 17.0054i 0.487262 + 0.843963i
407407 −0.739493 2.75983i −0.0366553 0.136799i
408408 0.142528i 0.00705620i
409409 13.4843 3.61312i 0.666758 0.178657i 0.0904639 0.995900i 0.471165π-0.471165\pi
0.576294 + 0.817243i 0.304498π0.304498\pi
410410 30.4277 17.9740i 1.50271 0.887675i
411411 9.20122 + 9.20122i 0.453863 + 0.453863i
412412 1.96199 0.525714i 0.0966603 0.0259001i
413413 1.80113 6.72192i 0.0886279 0.330764i
414414 −15.1266 4.05317i −0.743434 0.199203i
415415 7.98567 2.22527i 0.392001 0.109234i
416416 0 0
417417 7.58055 + 7.58055i 0.371221 + 0.371221i
418418 −18.4498 + 10.6520i −0.902408 + 0.521006i
419419 1.92240 1.10990i 0.0939155 0.0542221i −0.452307 0.891862i 0.649399π-0.649399\pi
0.546222 + 0.837640i 0.316065π0.316065\pi
420420 −0.607763 1.02886i −0.0296558 0.0502033i
421421 −24.4795 + 24.4795i −1.19306 + 1.19306i −0.216853 + 0.976204i 0.569579π0.569579\pi
−0.976204 + 0.216853i 0.930421π0.930421\pi
422422 −15.0558 + 26.0774i −0.732905 + 1.26943i
423423 2.92451 5.06540i 0.142194 0.246288i
424424 −17.2641 + 17.2641i −0.838417 + 0.838417i
425425 −0.295145 0.283609i −0.0143166 0.0137571i
426426 −6.83564 + 3.94656i −0.331188 + 0.191211i
427427 −12.3255 + 7.11613i −0.596472 + 0.344374i
428428 0.781202 + 0.781202i 0.0377608 + 0.0377608i
429429 0 0
430430 −0.228132 + 0.404389i −0.0110015 + 0.0195014i
431431 −1.59621 0.427704i −0.0768868 0.0206018i 0.220171 0.975461i 0.429339π-0.429339\pi
−0.297057 + 0.954860i 0.596005π0.596005\pi
432432 −4.38216 + 16.3545i −0.210837 + 0.786854i
433433 −14.3111 + 3.83465i −0.687748 + 0.184281i −0.585736 0.810502i 0.699195π-0.699195\pi
−0.102012 + 0.994783i 0.532528π0.532528\pi
434434 −9.14370 9.14370i −0.438912 0.438912i
435435 −3.83470 6.49164i −0.183860 0.311250i
436436 −0.659331 + 0.176667i −0.0315762 + 0.00846083i
437437 11.3897i 0.544845i
438438 1.75907 + 6.56494i 0.0840516 + 0.313685i
439439 −10.9363 18.9422i −0.521959 0.904060i −0.999674 0.0255448i 0.991868π-0.991868\pi
0.477714 0.878515i 0.341465π-0.341465\pi
440440 −28.7724 + 0.286722i −1.37167 + 0.0136689i
441441 0.677783i 0.0322754i
442442 0 0
443443 −6.14972 + 6.14972i −0.292182 + 0.292182i −0.837942 0.545760i 0.816241π-0.816241\pi
0.545760 + 0.837942i 0.316241π0.316241\pi
444444 −0.0304624 + 0.113687i −0.00144568 + 0.00539536i
445445 0.398677 + 40.0070i 0.0188991 + 1.89651i
446446 24.9432 + 14.4010i 1.18110 + 0.681907i
447447 0.974228 0.0460794
448448 14.4712 + 8.35496i 0.683701 + 0.394735i
449449 1.20994 + 4.51557i 0.0571008 + 0.213103i 0.988581 0.150688i 0.0481489π-0.0481489\pi
−0.931481 + 0.363791i 0.881482π0.881482\pi
450450 −9.98008 16.5168i −0.470465 0.778612i
451451 26.0247 45.0761i 1.22546 2.12255i
452452 −1.68432 0.451312i −0.0792237 0.0212279i
453453 6.66043 + 11.5362i 0.312934 + 0.542018i
454454 −40.9246 −1.92069
455455 0 0
456456 −4.88720 −0.228864
457457 −15.0180 26.0120i −0.702514 1.21679i −0.967581 0.252560i 0.918727π-0.918727\pi
0.265067 0.964230i 0.414606π-0.414606\pi
458458 23.1840 + 6.21213i 1.08332 + 0.290274i
459459 −0.153455 + 0.265792i −0.00716268 + 0.0124061i
460460 −1.35728 + 2.40593i −0.0632834 + 0.112177i
461461 −0.680045 2.53796i −0.0316729 0.118205i 0.948280 0.317436i 0.102822π-0.102822\pi
−0.979952 + 0.199232i 0.936155π0.936155\pi
462462 −11.5363 6.66050i −0.536719 0.309875i
463463 −25.1475 −1.16870 −0.584352 0.811500i 0.698651π-0.698651\pi
−0.584352 + 0.811500i 0.698651π0.698651\pi
464464 −19.4966 11.2564i −0.905109 0.522565i
465465 3.54570 + 3.47573i 0.164428 + 0.161183i
466466 −3.75502 + 14.0139i −0.173948 + 0.649183i
467467 14.9907 14.9907i 0.693688 0.693688i −0.269354 0.963041i 0.586810π-0.586810\pi
0.963041 + 0.269354i 0.0868100π0.0868100\pi
468468 0 0
469469 40.9648i 1.89158i
470470 −5.57658 5.46654i −0.257229 0.252152i
471471 −2.17455 3.76643i −0.100198 0.173548i
472472 1.78657 + 6.66756i 0.0822335 + 0.306899i
473473 0.683832i 0.0314426i
474474 −5.66395 + 1.51765i −0.260154 + 0.0697081i
475475 9.72477 10.1203i 0.446203 0.464353i
476476 −0.0457337 0.0457337i −0.00209620 0.00209620i
477477 −23.2951 + 6.24190i −1.06661 + 0.285797i
478478 1.10443 4.12178i 0.0505154 0.188526i
479479 2.21157 + 0.592587i 0.101049 + 0.0270760i 0.308989 0.951066i 0.400009π-0.400009\pi
−0.207940 + 0.978142i 0.566676π0.566676\pi
480480 2.25009 + 1.26936i 0.102702 + 0.0579382i
481481 0 0
482482 −2.94648 2.94648i −0.134208 0.134208i
483483 6.16767 3.56090i 0.280639 0.162027i
484484 3.68995 2.13039i 0.167725 0.0968361i
485485 −11.6286 2.99201i −0.528028 0.135860i
486486 −15.7696 + 15.7696i −0.715324 + 0.715324i
487487 −2.78321 + 4.82067i −0.126119 + 0.218445i −0.922170 0.386785i 0.873586π-0.873586\pi
0.796050 + 0.605230i 0.206919π0.206919\pi
488488 7.05859 12.2258i 0.319527 0.553437i
489489 6.28282 6.28282i 0.284119 0.284119i
490490 0.876368 + 0.225487i 0.0395903 + 0.0101865i
491491 5.29139 3.05498i 0.238797 0.137869i −0.375827 0.926690i 0.622641π-0.622641\pi
0.614624 + 0.788820i 0.289308π0.289308\pi
492492 −1.85685 + 1.07205i −0.0837133 + 0.0483319i
493493 −0.288558 0.288558i −0.0129960 0.0129960i
494494 0 0
495495 −24.7549 13.9652i −1.11265 0.627689i
496496 14.3204 + 3.83713i 0.643004 + 0.172292i
497497 −5.16254 + 19.2669i −0.231572 + 0.864237i
498498 −3.67712 + 0.985281i −0.164776 + 0.0441515i
499499 −6.22738 6.22738i −0.278776 0.278776i 0.553844 0.832620i 0.313160π-0.313160\pi
−0.832620 + 0.553844i 0.813160π0.813160\pi
500500 −3.26023 + 0.978912i −0.145802 + 0.0437783i
501501 2.14642 0.575130i 0.0958948 0.0256949i
502502 4.30183i 0.192000i
503503 0.951461 + 3.55090i 0.0424236 + 0.158327i 0.983888 0.178785i 0.0572166π-0.0572166\pi
−0.941465 + 0.337112i 0.890550π0.890550\pi
504504 8.49051 + 14.7060i 0.378198 + 0.655057i
505505 −4.00930 3.93018i −0.178412 0.174891i
506506 30.7939i 1.36896i
507507 0 0
508508 −0.175347 + 0.175347i −0.00777976 + 0.00777976i
509509 −2.90050 + 10.8248i −0.128563 + 0.479802i −0.999942 0.0108085i 0.996559π-0.996559\pi
0.871379 + 0.490610i 0.163226π0.163226\pi
510510 0.134230 + 0.131581i 0.00594380 + 0.00582650i
511511 14.8743 + 8.58768i 0.658000 + 0.379897i
512512 −15.5347 −0.686544
513513 −9.11384 5.26188i −0.402386 0.232318i
514514 7.88233 + 29.4173i 0.347675 + 1.29754i
515515 −7.32972 + 12.9927i −0.322986 + 0.572529i
516516 0.0140848 0.0243955i 0.000620047 0.00107395i
517517 −11.1095 2.97677i −0.488593 0.130918i
518518 1.12561 + 1.94962i 0.0494567 + 0.0856615i
519519 2.86670 0.125834
520520 0 0
521521 35.9604 1.57545 0.787726 0.616026i 0.211258π-0.211258\pi
0.787726 + 0.616026i 0.211258π0.211258\pi
522522 −9.61972 16.6618i −0.421044 0.729269i
523523 8.10636 + 2.17209i 0.354467 + 0.0949790i 0.431658 0.902037i 0.357929π-0.357929\pi
−0.0771917 + 0.997016i 0.524595π0.524595\pi
524524 2.45189 4.24681i 0.107112 0.185523i
525525 8.52064 + 2.10203i 0.371871 + 0.0917403i
526526 3.70182 + 13.8154i 0.161407 + 0.602380i
527527 0.232734 + 0.134369i 0.0101381 + 0.00585322i
528528 15.2725 0.664651
529529 5.66090 + 3.26832i 0.246126 + 0.142101i
530530 0.320848 + 32.1969i 0.0139368 + 1.39855i
531531 −1.76475 + 6.58612i −0.0765835 + 0.285813i
532532 1.56818 1.56818i 0.0679891 0.0679891i
533533 0 0
534534 18.3726i 0.795061i
535535 −8.11343 + 0.0808517i −0.350774 + 0.00349552i
536536 −20.3168 35.1897i −0.877552 1.51997i
537537 −2.44426 9.12209i −0.105477 0.393647i
538538 4.88034i 0.210407i
539539 1.28736 0.344948i 0.0554506 0.0148580i
540540 1.29813 + 2.19757i 0.0558628 + 0.0945682i
541541 −4.13066 4.13066i −0.177591 0.177591i 0.612714 0.790305i 0.290078π-0.290078\pi
−0.790305 + 0.612714i 0.790078π0.790078\pi
542542 −22.2688 + 5.96691i −0.956528 + 0.256301i
543543 −1.51396 + 5.65016i −0.0649700 + 0.242471i
544544 0.135064 + 0.0361903i 0.00579082 + 0.00155165i
545545 2.46317 4.36624i 0.105511 0.187029i
546546 0 0
547547 −7.90229 7.90229i −0.337877 0.337877i 0.517691 0.855568i 0.326792π-0.326792\pi
−0.855568 + 0.517691i 0.826792π0.826792\pi
548548 5.07242 2.92856i 0.216683 0.125102i
549549 12.0765 6.97237i 0.515413 0.297574i
550550 −26.2924 + 27.3619i −1.12111 + 1.16671i
551551 9.89447 9.89447i 0.421519 0.421519i
552552 −3.53211 + 6.11780i −0.150337 + 0.260391i
553553 −7.40909 + 12.8329i −0.315067 + 0.545712i
554554 11.4479 11.4479i 0.486375 0.486375i
555555 −0.439639 0.744250i −0.0186616 0.0315916i
556556 4.17898 2.41274i 0.177228 0.102323i
557557 10.2077 5.89341i 0.432513 0.249712i −0.267903 0.963446i 0.586331π-0.586331\pi
0.700417 + 0.713734i 0.252997π0.252997\pi
558558 8.95899 + 8.95899i 0.379264 + 0.379264i
559559 0 0
560560 25.2429 7.03416i 1.06671 0.297247i
561561 0.267408 + 0.0716517i 0.0112900 + 0.00302514i
562562 7.09170 26.4666i 0.299145 1.11643i
563563 31.0602 8.32255i 1.30903 0.350754i 0.464172 0.885745i 0.346352π-0.346352\pi
0.844858 + 0.534991i 0.179685π0.179685\pi
564564 0.335015 + 0.335015i 0.0141067 + 0.0141067i
565565 11.0263 6.51341i 0.463882 0.274021i
566566 8.44250 2.26216i 0.354865 0.0950858i
567567 13.2118i 0.554845i
568568 −5.12080 19.1111i −0.214864 0.801883i
569569 −4.64237 8.04082i −0.194618 0.337089i 0.752157 0.658984i 0.229013π-0.229013\pi
−0.946775 + 0.321895i 0.895680π0.895680\pi
570570 −4.51182 + 4.60265i −0.188979 + 0.192784i
571571 31.1596i 1.30399i 0.758223 + 0.651995i 0.226068π0.226068\pi
−0.758223 + 0.651995i 0.773932π0.773932\pi
572572 0 0
573573 8.08942 8.08942i 0.337940 0.337940i
574574 −10.6144 + 39.6134i −0.443035 + 1.65343i
575575 −5.64028 19.4877i −0.235216 0.812694i
576576 −14.1789 8.18618i −0.590786 0.341091i
577577 −4.57285 −0.190370 −0.0951852 0.995460i 0.530344π-0.530344\pi
−0.0951852 + 0.995460i 0.530344π0.530344\pi
578578 −22.3405 12.8983i −0.929243 0.536499i
579579 −1.49782 5.58994i −0.0622473 0.232310i
580580 −3.26916 + 0.910980i −0.135745 + 0.0378264i
581581 −4.81009 + 8.33132i −0.199556 + 0.345641i
582582 5.32605 + 1.42711i 0.220772 + 0.0591556i
583583 23.7114 + 41.0693i 0.982025 + 1.70092i
584584 −17.0365 −0.704975
585585 0 0
586586 4.85179 0.200425
587587 −3.59590 6.22829i −0.148419 0.257069i 0.782224 0.622997i 0.214085π-0.214085\pi
−0.930643 + 0.365928i 0.880752π0.880752\pi
588588 −0.0530312 0.0142097i −0.00218697 0.000585997i
589589 −4.60743 + 7.98031i −0.189846 + 0.328823i
590590 7.92870 + 4.47289i 0.326420 + 0.184146i
591591 −1.34048 5.00272i −0.0551398 0.205785i
592592 −2.23524 1.29052i −0.0918677 0.0530399i
593593 −28.0561 −1.15212 −0.576062 0.817406i 0.695411π-0.695411\pi
−0.576062 + 0.817406i 0.695411π0.695411\pi
594594 24.6407 + 14.2263i 1.01102 + 0.583712i
595595 0.474982 0.00473328i 0.0194724 0.000194045i
596596 0.113496 0.423573i 0.00464898 0.0173502i
597597 7.33116 7.33116i 0.300044 0.300044i
598598 0 0
599599 0.912959i 0.0373025i 0.999826 + 0.0186513i 0.00593722π0.00593722\pi
−0.999826 + 0.0186513i 0.994063π0.994063\pi
600600 −8.36194 + 2.42017i −0.341375 + 0.0988032i
601601 −6.22691 10.7853i −0.254001 0.439943i 0.710623 0.703573i 0.248413π-0.248413\pi
−0.964624 + 0.263631i 0.915080π0.915080\pi
602602 −0.139453 0.520445i −0.00568367 0.0212118i
603603 40.1373i 1.63452i
604604 5.79162 1.55186i 0.235658 0.0631443i
605605 −7.79745 + 30.3052i −0.317011 + 1.23208i
606606 1.82305 + 1.82305i 0.0740562 + 0.0740562i
607607 37.4512 10.0350i 1.52010 0.407309i 0.600324 0.799757i 0.295038π-0.295038\pi
0.919774 + 0.392448i 0.128372π0.128372\pi
608608 −1.24094 + 4.63125i −0.0503268 + 0.187822i
609609 8.45138 + 2.26454i 0.342467 + 0.0917638i
610610 −4.99757 17.9344i −0.202346 0.726143i
611611 0 0
612612 0.0448098 + 0.0448098i 0.00181133 + 0.00181133i
613613 21.3140 12.3057i 0.860865 0.497021i −0.00343656 0.999994i 0.501094π-0.501094\pi
0.864302 + 0.502973i 0.167761π0.167761\pi
614614 −31.9122 + 18.4245i −1.28787 + 0.743553i
615615 3.92382 15.2501i 0.158224 0.614945i
616616 23.6110 23.6110i 0.951316 0.951316i
617617 −7.70769 + 13.3501i −0.310300 + 0.537455i −0.978427 0.206592i 0.933763π-0.933763\pi
0.668127 + 0.744047i 0.267096π0.267096\pi
618618 3.42518 5.93259i 0.137781 0.238644i
619619 −20.7915 + 20.7915i −0.835683 + 0.835683i −0.988287 0.152604i 0.951234π-0.951234\pi
0.152604 + 0.988287i 0.451234π0.451234\pi
620620 1.92424 1.13668i 0.0772795 0.0456501i
621621 −13.1736 + 7.60581i −0.528640 + 0.305211i
622622 22.2249 12.8316i 0.891137 0.514498i
623623 −32.8303 32.8303i −1.31532 1.31532i
624624 0 0
625625 11.6273 22.1315i 0.465093 0.885262i
626626 17.4397 + 4.67294i 0.697029 + 0.186768i
627627 −2.45689 + 9.16923i −0.0981186 + 0.366184i
628628 −1.89090 + 0.506664i −0.0754549 + 0.0202181i
629629 −0.0330825 0.0330825i −0.00131908 0.00131908i
630630 21.6882 + 5.58030i 0.864077 + 0.222324i
631631 −12.1738 + 3.26195i −0.484631 + 0.129856i −0.492858 0.870110i 0.664048π-0.664048\pi
0.00822739 + 0.999966i 0.497381π0.497381\pi
632632 14.6984i 0.584670i
633633 3.47263 + 12.9600i 0.138025 + 0.515115i
634634 9.06908 + 15.7081i 0.360179 + 0.623849i
635635 −0.0181478 1.82112i −0.000720173 0.0722690i
636636 1.95352i 0.0774620i
637637 0 0
638638 −26.7512 + 26.7512i −1.05909 + 1.05909i
639639 5.05825 18.8777i 0.200101 0.746789i
640640 −20.6490 + 21.0646i −0.816222 + 0.832653i
641641 −8.45341 4.88058i −0.333890 0.192771i 0.323677 0.946168i 0.395081π-0.395081\pi
−0.657567 + 0.753396i 0.728414π0.728414\pi
642642 3.72597 0.147052
643643 −24.0854 13.9057i −0.949834 0.548387i −0.0568044 0.998385i 0.518091π-0.518091\pi
−0.893029 + 0.449999i 0.851424π0.851424\pi
644644 −0.829680 3.09641i −0.0326940 0.122016i
645645 0.0555341 + 0.199291i 0.00218665 + 0.00784708i
646646 −0.174424 + 0.302111i −0.00686261 + 0.0118864i
647647 −17.7967 4.76862i −0.699662 0.187474i −0.108583 0.994087i 0.534631π-0.534631\pi
−0.591079 + 0.806613i 0.701298π0.701298\pi
648648 −6.55251 11.3493i −0.257407 0.445842i
649649 13.4076 0.526296
650650 0 0
651651 −5.76190 −0.225826
652652 −1.99970 3.46357i −0.0783141 0.135644i
653653 −7.12491 1.90911i −0.278819 0.0747094i 0.116700 0.993167i 0.462769π-0.462769\pi
−0.395519 + 0.918458i 0.629435π0.629435\pi
654654 −1.15104 + 1.99366i −0.0450093 + 0.0779583i
655655 9.66746 + 34.6929i 0.377739 + 1.35556i
656656 −12.1694 45.4167i −0.475134 1.77322i
657657 −14.5738 8.41420i −0.568579 0.328269i
658658 9.06214 0.353279
659659 12.0786 + 6.97358i 0.470515 + 0.271652i 0.716455 0.697633i 0.245763π-0.245763\pi
−0.245940 + 0.969285i 0.579097π0.579097\pi
660660 1.61165 1.64409i 0.0627334 0.0639963i
661661 −0.0586648 + 0.218940i −0.00228180 + 0.00851578i −0.967057 0.254559i 0.918070π-0.918070\pi
0.964776 + 0.263074i 0.0847365π0.0847365\pi
662662 23.0236 23.0236i 0.894837 0.894837i
663663 0 0
664664 9.54239i 0.370317i
665665 0.162301 + 16.2868i 0.00629375 + 0.631575i
666666 −1.10288 1.91024i −0.0427356 0.0740202i
667667 −5.23490 19.5369i −0.202696 0.756472i
668668 1.00022i 0.0386996i
669669 12.3964 3.32160i 0.479271 0.128420i
670670 −51.8972 13.3530i −2.00496 0.515871i
671671 −19.3893 19.3893i −0.748515 0.748515i
672672 −2.89584 + 0.775939i −0.111710 + 0.0299325i
673673 −8.70112 + 32.4730i −0.335404 + 1.25174i 0.568027 + 0.823010i 0.307707π0.307707\pi
−0.903431 + 0.428734i 0.858960π0.858960\pi
674674 29.2938 + 7.84924i 1.12835 + 0.302341i
675675 −18.1994 4.48978i −0.700495 0.172812i
676676 0 0
677677 25.1691 + 25.1691i 0.967326 + 0.967326i 0.999483 0.0321566i 0.0102375π-0.0102375\pi
−0.0321566 + 0.999483i 0.510238π0.510238\pi
678678 −5.09298 + 2.94044i −0.195595 + 0.112927i
679679 12.0673 6.96707i 0.463101 0.267372i
680680 −0.405673 + 0.239637i −0.0155568 + 0.00918964i
681681 −12.8943 + 12.8943i −0.494110 + 0.494110i
682682 12.4569 21.5760i 0.477000 0.826187i
683683 −15.3784 + 26.6361i −0.588437 + 1.01920i 0.406001 + 0.913873i 0.366923π0.366923\pi
−0.994437 + 0.105329i 0.966410π0.966410\pi
684684 −1.53650 + 1.53650i −0.0587494 + 0.0587494i
685685 −10.7188 + 41.6593i −0.409545 + 1.59172i
686686 −24.7893 + 14.3121i −0.946459 + 0.546438i
687687 9.26197 5.34740i 0.353366 0.204016i
688688 0.436807 + 0.436807i 0.0166531 + 0.0166531i
689689 0 0
690690 2.50078 + 8.97436i 0.0952032 + 0.341648i
691691 37.4215 + 10.0271i 1.42358 + 0.381447i 0.886753 0.462244i 0.152956π-0.152956\pi
0.536828 + 0.843692i 0.319622π0.319622\pi
692692 0.333966 1.24638i 0.0126955 0.0473802i
693693 31.8593 8.53668i 1.21024 0.324282i
694694 −26.4382 26.4382i −1.00358 1.00358i
695695 −8.83085 + 34.3216i −0.334973 + 1.30189i
696696 −8.38305 + 2.24623i −0.317759 + 0.0851432i
697697 0.852297i 0.0322831i
698698 −10.7055 39.9534i −0.405208 1.51226i
699699 3.23232 + 5.59854i 0.122258 + 0.211756i
700700 1.90656 3.45970i 0.0720612 0.130765i
701701 19.8876i 0.751143i −0.926793 0.375571i 0.877447π-0.877447\pi
0.926793 0.375571i 0.122553π-0.122553\pi
702702 0 0
703703 1.13437 1.13437i 0.0427838 0.0427838i
704704 −8.33247 + 31.0972i −0.314042 + 1.17202i
705705 −3.47941 + 0.0346729i −0.131042 + 0.00130586i
706706 11.5681 + 6.67884i 0.435371 + 0.251361i
707707 6.51526 0.245032
708708 −0.478314 0.276155i −0.0179761 0.0103785i
709709 −8.24828 30.7830i −0.309771 1.15608i −0.928760 0.370680i 0.879125π-0.879125\pi
0.618990 0.785399i 0.287542π-0.287542\pi
710710 −22.7259 12.8206i −0.852887 0.481147i
711711 7.25942 12.5737i 0.272250 0.471550i
712712 44.4844 + 11.9196i 1.66712 + 0.446705i
713713 6.65983 + 11.5352i 0.249413 + 0.431996i
714714 −0.218128 −0.00816325
715715 0 0
716716 −4.25084 −0.158861
717717 −0.950692 1.64665i −0.0355042 0.0614951i
718718 −23.0710 6.18186i −0.861002 0.230705i
719719 −15.4818 + 26.8152i −0.577372 + 1.00004i 0.418407 + 0.908260i 0.362589π0.362589\pi
−0.995779 + 0.0917785i 0.970745π0.970745\pi
720720 −24.7330 + 6.89206i −0.921744 + 0.256852i
721721 −4.48053 16.7216i −0.166864 0.622744i
722722 14.6195 + 8.44057i 0.544081 + 0.314126i
723723 −1.85672 −0.0690522
724724 2.28019 + 1.31647i 0.0847427 + 0.0489262i
725725 12.0295 21.8291i 0.446765 0.810714i
726726 3.71918 13.8802i 0.138032 0.515141i
727727 −16.2588 + 16.2588i −0.603007 + 0.603007i −0.941109 0.338103i 0.890215π-0.890215\pi
0.338103 + 0.941109i 0.390215π0.390215\pi
728728 0 0
729729 5.33729i 0.197678i
730730 −15.7280 + 16.0446i −0.582118 + 0.593836i
731731 0.00559879 + 0.00969739i 0.000207079 + 0.000358671i
732732 0.292350 + 1.09107i 0.0108056 + 0.0403269i
733733 31.2515i 1.15430i 0.816638 + 0.577150i 0.195835π0.195835\pi
−0.816638 + 0.577150i 0.804165π0.804165\pi
734734 −16.0980 + 4.31344i −0.594187 + 0.159212i
735735 0.347167 0.205076i 0.0128054 0.00756435i
736736 4.90054 + 4.90054i 0.180636 + 0.180636i
737737 −76.2357 + 20.4273i −2.80818 + 0.752449i
738738 10.3999 38.8131i 0.382827 1.42873i
739739 −26.3668 7.06496i −0.969918 0.259889i −0.261125 0.965305i 0.584093π-0.584093\pi
−0.708793 + 0.705416i 0.750760π0.750760\pi
740740 −0.374801 + 0.104441i −0.0137780 + 0.00383934i
741741 0 0
742742 −26.4213 26.4213i −0.969956 0.969956i
743743 28.5494 16.4830i 1.04738 0.604703i 0.125463 0.992098i 0.459958π-0.459958\pi
0.921914 + 0.387395i 0.126625π0.126625\pi
744744 4.94960 2.85765i 0.181461 0.104767i
745745 1.63800 + 2.77291i 0.0600115 + 0.101591i
746746 11.3566 11.3566i 0.415794 0.415794i
747747 4.71292 8.16301i 0.172437 0.298669i
748748 0.0623052 0.107916i 0.00227810 0.00394579i
749749 6.65800 6.65800i 0.243278 0.243278i
750750 −5.44041 + 10.1094i −0.198656 + 0.369142i
751751 26.8241 15.4869i 0.978826 0.565125i 0.0769103 0.997038i 0.475494π-0.475494\pi
0.901915 + 0.431913i 0.142161π0.142161\pi
752752 −8.99777 + 5.19487i −0.328115 + 0.189437i
753753 1.35540 + 1.35540i 0.0493934 + 0.0493934i
754754 0 0
755755 −21.6367 + 38.3535i −0.787440 + 1.39583i
756756 −2.86098 0.766598i −0.104053 0.0278809i
757757 13.2249 49.3561i 0.480668 1.79388i −0.118154 0.992995i 0.537698π-0.537698\pi
0.598822 0.800882i 0.295636π-0.295636\pi
758758 14.3729 3.85120i 0.522046 0.139882i
759759 9.70238 + 9.70238i 0.352174 + 0.352174i
760760 −8.21697 13.9102i −0.298061 0.504577i
761761 −1.11809 + 0.299592i −0.0405308 + 0.0108602i −0.279027 0.960283i 0.590012π-0.590012\pi
0.238497 + 0.971143i 0.423345π0.423345\pi
762762 0.836323i 0.0302968i
763763 1.50569 + 5.61932i 0.0545097 + 0.203433i
764764 −2.57470 4.45951i −0.0931494 0.161339i
765765 −0.465386 + 0.00463766i −0.0168261 + 0.000167675i
766766 39.5553i 1.42919i
767767 0 0
768768 3.41812 3.41812i 0.123341 0.123341i
769769 7.82422 29.2004i 0.282148 1.05299i −0.668750 0.743488i 0.733170π-0.733170\pi
0.950898 0.309505i 0.100163π-0.100163\pi
770770 −0.438805 44.0339i −0.0158134 1.58687i
771771 11.7522 + 6.78511i 0.423243 + 0.244360i
772772 −2.60488 −0.0937517
773773 −6.22916 3.59641i −0.224047 0.129354i 0.383776 0.923426i 0.374624π-0.374624\pi
−0.607823 + 0.794073i 0.707957π0.707957\pi
774774 0.136636 + 0.509931i 0.00491127 + 0.0183291i
775775 −3.93136 + 15.9358i −0.141219 + 0.572432i
776776 −6.91074 + 11.9698i −0.248081 + 0.429689i
777777 0.968929 + 0.259624i 0.0347601 + 0.00931395i
778778 −24.6597 42.7119i −0.884094 1.53130i
779779 29.2247 1.04708
780780 0 0
781781 −38.4300 −1.37513
782782 0.252122 + 0.436687i 0.00901585 + 0.0156159i
783783 −18.0515 4.83688i −0.645107 0.172856i
784784 0.601981 1.04266i 0.0214993 0.0372379i
785785 7.06412 12.5219i 0.252129 0.446927i
786786 −4.28044 15.9748i −0.152678 0.569804i
787787 6.21708 + 3.58943i 0.221615 + 0.127949i 0.606698 0.794933i 0.292494π-0.292494\pi
−0.385083 + 0.922882i 0.625827π0.625827\pi
788788 −2.33124 −0.0830470
789789 5.51923 + 3.18653i 0.196490 + 0.113443i
790790 −13.8426 13.5694i −0.492497 0.482778i
791791 −3.84642 + 14.3550i −0.136763 + 0.510407i
792792 −23.1341 + 23.1341i −0.822034 + 0.822034i
793793 0 0
794794 36.7145i 1.30295i
795795 10.2455 + 10.0433i 0.363372 + 0.356201i
796796 −2.33336 4.04150i −0.0827037 0.143247i
797797 −10.1969 38.0553i −0.361192 1.34799i −0.872510 0.488596i 0.837509π-0.837509\pi
0.511318 0.859391i 0.329157π-0.329157\pi
798798 7.47947i 0.264770i
799799 −0.181915 + 0.0487439i −0.00643568 + 0.00172443i
800800 0.170193 + 8.53854i 0.00601723 + 0.301883i
801801 32.1671 + 32.1671i 1.13657 + 1.13657i
802802 −48.1515 + 12.9022i −1.70029 + 0.455591i
803803 −8.56456 + 31.9634i −0.302237 + 1.12796i
804804 3.14043 + 0.841474i 0.110754 + 0.0296765i
805805 20.5051 + 11.5677i 0.722711 + 0.407710i
806806 0 0
807807 −1.53767 1.53767i −0.0541286 0.0541286i
808808 −5.59676 + 3.23129i −0.196893 + 0.113676i
809809 −24.2062 + 13.9754i −0.851043 + 0.491350i −0.861003 0.508600i 0.830163π-0.830163\pi
0.00995956 + 0.999950i 0.496830π0.496830\pi
810810 −16.7377 4.30656i −0.588103 0.151317i
811811 23.2784 23.2784i 0.817415 0.817415i −0.168317 0.985733i 0.553833π-0.553833\pi
0.985733 + 0.168317i 0.0538334π0.0538334\pi
812812 1.96915 3.41066i 0.0691035 0.119691i
813813 −5.13632 + 8.89636i −0.180138 + 0.312009i
814814 −3.06696 + 3.06696i −0.107497 + 0.107497i
815815 28.4460 + 7.31907i 0.996420 + 0.256376i
816816 0.216579 0.125042i 0.00758178 0.00437734i
817817 −0.332517 + 0.191979i −0.0116333 + 0.00671648i
818818 −14.9850 14.9850i −0.523937 0.523937i
819819 0 0
820820 −6.17331 3.48261i −0.215582 0.121618i
821821 −18.8872 5.06082i −0.659169 0.176624i −0.0862981 0.996269i 0.527504π-0.527504\pi
−0.572871 + 0.819646i 0.694170π0.694170\pi
822822 5.11260 19.0805i 0.178322 0.665508i
823823 −39.4302 + 10.5653i −1.37445 + 0.368283i −0.869102 0.494633i 0.835303π-0.835303\pi
−0.505348 + 0.862915i 0.668636π0.668636\pi
824824 12.1421 + 12.1421i 0.422989 + 0.422989i
825825 0.336958 + 16.9051i 0.0117314 + 0.588560i
826826 −10.2042 + 2.73420i −0.355049 + 0.0951350i
827827 31.8649i 1.10805i −0.832499 0.554026i 0.813091π-0.813091\pi
0.832499 0.554026i 0.186909π-0.186909\pi
828828 0.812920 + 3.03386i 0.0282509 + 0.105434i
829829 −27.6391 47.8724i −0.959946 1.66268i −0.722620 0.691246i 0.757062π-0.757062\pi
−0.237326 0.971430i 0.576271π-0.576271\pi
830830 −8.98680 8.80946i −0.311937 0.305781i
831831 7.21389i 0.250247i
832832 0 0
833833 0.0154318 0.0154318i 0.000534681 0.000534681i
834834 4.21208 15.7197i 0.145853 0.544329i
835835 5.24580 + 5.14228i 0.181538 + 0.177956i
836836 3.70036 + 2.13640i 0.127980 + 0.0738890i
837837 12.3070 0.425390
838838 −2.91830 1.68488i −0.100811 0.0582032i
839839 1.00953 + 3.76762i 0.0348528 + 0.130073i 0.981160 0.193195i 0.0618851π-0.0618851\pi
−0.946307 + 0.323268i 0.895218π0.895218\pi
840840 4.96358 8.79850i 0.171260 0.303577i
841841 −2.07559 + 3.59503i −0.0715721 + 0.123966i
842842 50.7629 + 13.6019i 1.74940 + 0.468751i
843843 −6.10453 10.5734i −0.210251 0.364166i
844844 6.03930 0.207881
845845 0 0
846846 −8.87908 −0.305269
847847 −18.1568 31.4485i −0.623876 1.08058i
848848 41.3796 + 11.0876i 1.42098 + 0.380751i
849849 1.94727 3.37277i 0.0668301 0.115753i
850850 −0.148830 + 0.603284i −0.00510482 + 0.0206925i
851851 −0.600167 2.23986i −0.0205735 0.0767812i
852852 1.37098 + 0.791536i 0.0469690 + 0.0271176i
853853 53.5726 1.83429 0.917145 0.398554i 0.130488π-0.130488\pi
0.917145 + 0.398554i 0.130488π0.130488\pi
854854 18.7107 + 10.8026i 0.640266 + 0.369658i
855855 −0.159022 15.9578i −0.00543844 0.545745i
856856 −2.41729 + 9.02145i −0.0826213 + 0.308347i
857857 18.9164 18.9164i 0.646171 0.646171i −0.305894 0.952066i 0.598955π-0.598955\pi
0.952066 + 0.305894i 0.0989554π0.0989554\pi
858858 0 0
859859 18.1203i 0.618258i 0.951020 + 0.309129i 0.100037π0.100037\pi
−0.951020 + 0.309129i 0.899963π0.899963\pi
860860 0.0931171 0.000927928i 0.00317527 3.16421e-5i
861861 9.13685 + 15.8255i 0.311383 + 0.539331i
862862 0.649274 + 2.42312i 0.0221144 + 0.0825320i
863863 21.4967i 0.731757i 0.930663 + 0.365879i 0.119232π0.119232\pi
−0.930663 + 0.365879i 0.880768π0.880768\pi
864864 6.18529 1.65734i 0.210428 0.0563840i
865865 4.81986 + 8.15937i 0.163880 + 0.277427i
866866 15.9037 + 15.9037i 0.540431 + 0.540431i
867867 −11.1029 + 2.97500i −0.377073 + 0.101036i
868868 −0.671252 + 2.50515i −0.0227838 + 0.0850303i
869869 −27.5767 7.38915i −0.935475 0.250660i
870870 −5.62372 + 9.96866i −0.190662 + 0.337969i
871871 0 0
872872 −4.08036 4.08036i −0.138179 0.138179i
873873 −11.8235 + 6.82633i −0.400167 + 0.231036i
874874 −14.9737 + 8.64508i −0.506493 + 0.292424i
875875 8.34303 + 27.7862i 0.282046 + 0.939344i
876876 0.963883 0.963883i 0.0325666 0.0325666i
877877 −10.6745 + 18.4889i −0.360454 + 0.624324i −0.988036 0.154226i 0.950711π-0.950711\pi
0.627582 + 0.778551i 0.284045π0.284045\pi
878878 −16.6018 + 28.7551i −0.560282 + 0.970437i
879879 1.52867 1.52867i 0.0515609 0.0515609i
880880 25.6781 + 43.4696i 0.865608 + 1.46536i
881881 11.4703 6.62238i 0.386444 0.223114i −0.294174 0.955752i 0.595045π-0.595045\pi
0.680618 + 0.732638i 0.261711π0.261711\pi
882882 0.891059 0.514453i 0.0300035 0.0173225i
883883 32.5668 + 32.5668i 1.09596 + 1.09596i 0.994878 + 0.101082i 0.0322304π0.0322304\pi
0.101082 + 0.994878i 0.467770π0.467770\pi
884884 0 0
885885 3.90743 1.08884i 0.131347 0.0366009i
886886 12.7526 + 3.41705i 0.428432 + 0.114798i
887887 4.13600 15.4358i 0.138873 0.518282i −0.861079 0.508472i 0.830211π-0.830211\pi
0.999952 0.00981024i 0.00312275π-0.00312275\pi
888888 −0.961094 + 0.257524i −0.0322522 + 0.00864195i
889889 1.49444 + 1.49444i 0.0501219 + 0.0501219i
890890 52.2933 30.8904i 1.75287 1.03545i
891891 −24.5873 + 6.58814i −0.823705 + 0.220711i
892892 5.77663i 0.193416i
893893 −1.67139 6.23773i −0.0559311 0.208738i
894894 −0.739462 1.28079i −0.0247313 0.0428359i
895895 21.8543 22.2942i 0.730507 0.745213i
896896 34.2308i 1.14357i
897897 0 0
898898 5.01810 5.01810i 0.167456 0.167456i
899899 −4.23529 + 15.8063i −0.141255 + 0.527170i
900900 −1.86805 + 3.38981i −0.0622682 + 0.112994i
901901 0.672500 + 0.388268i 0.0224042 + 0.0129351i
902902 −79.0135 −2.63086
903903 −0.207917 0.120041i −0.00691905 0.00399471i
904904 −3.81532 14.2390i −0.126896 0.473581i
905905 −18.6273 + 5.19065i −0.619192 + 0.172543i
906906 10.1108 17.5125i 0.335910 0.581814i
907907 5.07458 + 1.35973i 0.168499 + 0.0451491i 0.342082 0.939670i 0.388868π-0.388868\pi
−0.173583 + 0.984819i 0.555535π0.555535\pi
908908 4.10399 + 7.10833i 0.136196 + 0.235898i
909909 −6.38364 −0.211732
910910 0 0
911911 9.49722 0.314657 0.157328 0.987546i 0.449712π-0.449712\pi
0.157328 + 0.987546i 0.449712π0.449712\pi
912912 4.28760 + 7.42634i 0.141977 + 0.245911i
913913 −17.9032 4.79714i −0.592508 0.158762i
914914 −22.7981 + 39.4874i −0.754093 + 1.30613i
915915 −7.22529 4.07607i −0.238861 0.134751i
916916 −1.24593 4.64987i −0.0411666 0.153636i
917917 −36.1945 20.8969i −1.19525 0.690076i
918918 0.465905 0.0153771
919919 −45.6207 26.3391i −1.50489 0.868847i −0.999984 0.00567026i 0.998195π-0.998195\pi
−0.504903 0.863176i 0.668472π-0.668472\pi
920920 −23.3515 + 0.232702i −0.769875 + 0.00767194i
921921 −4.24963 + 15.8598i −0.140030 + 0.522599i
922922 −2.82041 + 2.82041i −0.0928851 + 0.0928851i
923923 0 0
924924 2.67171i 0.0878929i
925925 1.37915 2.50265i 0.0453463 0.0822867i
926926 19.0876 + 33.0606i 0.627256 + 1.08644i
927927 4.39002 + 16.3838i 0.144187 + 0.538114i
928928 8.51438i 0.279498i
929929 −8.04841 + 2.15657i −0.264060 + 0.0707546i −0.388420 0.921483i 0.626979π-0.626979\pi
0.124360 + 0.992237i 0.460312π0.460312\pi
930930 1.87816 7.29958i 0.0615873 0.239363i
931931 0.529147 + 0.529147i 0.0173421 + 0.0173421i
932932 2.81069 0.753121i 0.0920671 0.0246693i
933933 2.95960 11.0454i 0.0968931 0.361610i
934934 −31.0861 8.32950i −1.01717 0.272549i
935935 0.245660 + 0.881582i 0.00803395 + 0.0288308i
936936 0 0
937937 16.3814 + 16.3814i 0.535156 + 0.535156i 0.922102 0.386947i 0.126470π-0.126470\pi
−0.386947 + 0.922102i 0.626470π0.626470\pi
938938 53.8551 31.0933i 1.75843 1.01523i
939939 6.96712 4.02247i 0.227363 0.131268i
940940 −0.390271 + 1.51681i −0.0127292 + 0.0494729i
941941 24.2325 24.2325i 0.789956 0.789956i −0.191530 0.981487i 0.561345π-0.561345\pi
0.981487 + 0.191530i 0.0613451π0.0613451\pi
942942 −3.30107 + 5.71762i −0.107555 + 0.186290i
943943 21.1215 36.5835i 0.687810 1.19132i
944944 8.56432 8.56432i 0.278745 0.278745i
945945 18.7293 11.0637i 0.609265 0.359901i
946946 0.899011 0.519044i 0.0292294 0.0168756i
947947 28.9613 16.7208i 0.941114 0.543353i 0.0508048 0.998709i 0.483821π-0.483821\pi
0.890309 + 0.455356i 0.150488π0.150488\pi
948948 0.831598 + 0.831598i 0.0270091 + 0.0270091i
949949 0 0
950950 −20.6862 5.10327i −0.671149 0.165572i
951951 7.80666 + 2.09179i 0.253148 + 0.0678309i
952952 0.141515 0.528140i 0.00458652 0.0171171i
953953 14.5138 3.88895i 0.470147 0.125975i −0.0159642 0.999873i 0.505082π-0.505082\pi
0.486111 + 0.873897i 0.338415π0.338415\pi
954954 25.8875 + 25.8875i 0.838140 + 0.838140i
955955 36.6256 + 9.42365i 1.18518 + 0.304942i
956956 −0.826681 + 0.221508i −0.0267368 + 0.00716409i
957957 16.8573i 0.544918i
958958 −0.899575 3.35726i −0.0290640 0.108468i
959959 −24.9594 43.2310i −0.805982 1.39600i
960960 0.0970551 + 9.73943i 0.00313244 + 0.314339i
961961 20.2237i 0.652378i
962962 0 0
963963 −6.52350 + 6.52350i −0.210217 + 0.210217i
964964 −0.216305 + 0.807262i −0.00696672 + 0.0260002i
965965 13.3921 13.6617i 0.431107 0.439786i
966966 −9.36281 5.40562i −0.301243 0.173923i
967967 −7.49252 −0.240943 −0.120472 0.992717i 0.538441π-0.538441\pi
−0.120472 + 0.992717i 0.538441π0.538441\pi
968968 31.1943 + 18.0100i 1.00262 + 0.578864i
969969 0.0402309 + 0.150144i 0.00129240 + 0.00482332i
970970 4.89290 + 17.5588i 0.157101 + 0.563778i
971971 −13.9303 + 24.1280i −0.447045 + 0.774304i −0.998192 0.0601036i 0.980857π-0.980857\pi
0.551147 + 0.834408i 0.314190π0.314190\pi
972972 4.32048 + 1.15767i 0.138580 + 0.0371323i
973973 −20.5632 35.6165i −0.659225 1.14181i
974974 8.45010 0.270759
975975 0 0
976976 −24.7704 −0.792880
977977 19.4382 + 33.6679i 0.621883 + 1.07713i 0.989135 + 0.147011i 0.0469654π0.0469654\pi
−0.367252 + 0.930122i 0.619701π0.619701\pi
978978 −13.0286 3.49101i −0.416609 0.111630i
979979 44.7263 77.4683i 1.42946 2.47590i
980980 −0.0487183 0.174832i −0.00155625 0.00558479i
981981 −1.47527 5.50580i −0.0471019 0.175787i
982982 −8.03257 4.63761i −0.256330 0.147992i
983983 −0.207440 −0.00661630 −0.00330815 0.999995i 0.501053π-0.501053\pi
−0.00330815 + 0.999995i 0.501053π0.501053\pi
984984 −15.6975 9.06297i −0.500419 0.288917i
985985 11.9853 12.2266i 0.381883 0.389571i
986986 −0.160336 + 0.598381i −0.00510613 + 0.0190563i
987987 2.85525 2.85525i 0.0908836 0.0908836i
988988 0 0
989989 0.554993i 0.0176477i
990990 0.429941 + 43.1443i 0.0136644 + 1.37122i
991991 12.7480 + 22.0803i 0.404955 + 0.701402i 0.994316 0.106467i 0.0339539π-0.0339539\pi
−0.589361 + 0.807869i 0.700621π0.700621\pi
992992 −1.45121 5.41599i −0.0460760 0.171958i
993993 14.5083i 0.460407i
994994 29.2480 7.83698i 0.927691 0.248574i
995995 33.1924 + 8.54032i 1.05227 + 0.270746i
996996 0.539885 + 0.539885i 0.0171069 + 0.0171069i
997997 33.4743 8.96942i 1.06014 0.284064i 0.313706 0.949520i 0.398429π-0.398429\pi
0.746437 + 0.665456i 0.231763π0.231763\pi
998998 −3.46020 + 12.9137i −0.109531 + 0.408774i
999999 −2.06955 0.554536i −0.0654778 0.0175447i
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 845.2.o.g.587.1 20
5.3 odd 4 845.2.t.g.418.1 20
13.2 odd 12 845.2.f.e.437.2 20
13.3 even 3 845.2.k.d.577.9 20
13.4 even 6 845.2.o.e.357.5 20
13.5 odd 4 845.2.t.f.427.1 20
13.6 odd 12 65.2.t.a.7.5 yes 20
13.7 odd 12 845.2.t.g.657.1 20
13.8 odd 4 845.2.t.e.427.5 20
13.9 even 3 845.2.o.f.357.1 20
13.10 even 6 845.2.k.e.577.2 20
13.11 odd 12 845.2.f.d.437.9 20
13.12 even 2 65.2.o.a.2.5 20
39.32 even 12 585.2.dp.a.397.1 20
39.38 odd 2 585.2.cf.a.262.1 20
65.3 odd 12 845.2.f.d.408.2 20
65.8 even 4 845.2.o.f.258.1 20
65.12 odd 4 325.2.x.b.93.1 20
65.18 even 4 845.2.o.e.258.5 20
65.19 odd 12 325.2.x.b.7.1 20
65.23 odd 12 845.2.f.e.408.9 20
65.28 even 12 845.2.k.e.268.2 20
65.32 even 12 325.2.s.b.293.1 20
65.33 even 12 inner 845.2.o.g.488.1 20
65.38 odd 4 65.2.t.a.28.5 yes 20
65.43 odd 12 845.2.t.f.188.1 20
65.48 odd 12 845.2.t.e.188.5 20
65.58 even 12 65.2.o.a.33.5 yes 20
65.63 even 12 845.2.k.d.268.9 20
65.64 even 2 325.2.s.b.132.1 20
195.38 even 4 585.2.dp.a.28.1 20
195.188 odd 12 585.2.cf.a.163.1 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.o.a.2.5 20 13.12 even 2
65.2.o.a.33.5 yes 20 65.58 even 12
65.2.t.a.7.5 yes 20 13.6 odd 12
65.2.t.a.28.5 yes 20 65.38 odd 4
325.2.s.b.132.1 20 65.64 even 2
325.2.s.b.293.1 20 65.32 even 12
325.2.x.b.7.1 20 65.19 odd 12
325.2.x.b.93.1 20 65.12 odd 4
585.2.cf.a.163.1 20 195.188 odd 12
585.2.cf.a.262.1 20 39.38 odd 2
585.2.dp.a.28.1 20 195.38 even 4
585.2.dp.a.397.1 20 39.32 even 12
845.2.f.d.408.2 20 65.3 odd 12
845.2.f.d.437.9 20 13.11 odd 12
845.2.f.e.408.9 20 65.23 odd 12
845.2.f.e.437.2 20 13.2 odd 12
845.2.k.d.268.9 20 65.63 even 12
845.2.k.d.577.9 20 13.3 even 3
845.2.k.e.268.2 20 65.28 even 12
845.2.k.e.577.2 20 13.10 even 6
845.2.o.e.258.5 20 65.18 even 4
845.2.o.e.357.5 20 13.4 even 6
845.2.o.f.258.1 20 65.8 even 4
845.2.o.f.357.1 20 13.9 even 3
845.2.o.g.488.1 20 65.33 even 12 inner
845.2.o.g.587.1 20 1.1 even 1 trivial
845.2.t.e.188.5 20 65.48 odd 12
845.2.t.e.427.5 20 13.8 odd 4
845.2.t.f.188.1 20 65.43 odd 12
845.2.t.f.427.1 20 13.5 odd 4
845.2.t.g.418.1 20 5.3 odd 4
845.2.t.g.657.1 20 13.7 odd 12