Properties

Label 275.2.z.c.174.5
Level 275275
Weight 22
Character 275.174
Analytic conductor 2.1962.196
Analytic rank 00
Dimension 3232
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [275,2,Mod(49,275)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(275, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("275.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 275=5211 275 = 5^{2} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 275.z (of order 1010, degree 44, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 2.195886055592.19588605559
Analytic rank: 00
Dimension: 3232
Relative dimension: 88 over Q(ζ10)\Q(\zeta_{10})
Twist minimal: yes
Sato-Tate group: SU(2)[C10]\mathrm{SU}(2)[C_{10}]

Embedding invariants

Embedding label 174.5
Character χ\chi == 275.174
Dual form 275.2.z.c.49.5

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.132580+0.0430779i)q2+(1.755022.41558i)q3+(1.602311.16415i)q4+(0.1286230.395861i)q6+(2.098152.88786i)q7+(0.3261640.448926i)q8+(1.82787+5.62561i)q9+(2.45284+2.23239i)q11+5.91361iq12+(1.137100.369466i)q13+(0.4025760.292489i)q14+(1.20015+3.69369i)q16+(5.16941+1.67964i)q17+(0.484679+0.667104i)q18+(3.885382.82290i)q1910.6581q21+(0.421365+0.190307i)q221.82203iq23+(0.511992+1.57575i)q24+(0.1348410.0979678i)q26+(8.278002.68969i)q27+(6.72378+2.18469i)q28+(3.350442.43424i)q29+(0.3976681.22390i)q31+1.65122iq32+(9.69730+2.00714i)q330.757717q34+(9.477866.88607i)q36+(1.857942.55724i)q37+(0.6367300.206886i)q38+(1.10316+3.39517i)q39+(5.183473.76601i)q41+(1.413060.459131i)q42+4.23557iq43+(6.529050.721514i)q44+(0.07848940.241566i)q46+(4.131035.68588i)q47+(6.816119.38157i)q48+(1.774365.46092i)q49+(13.1297+9.53930i)q51+(1.39187+1.91575i)q52+(10.28183.34076i)q53+1.21337q541.98078q56+(13.63794.43121i)q57+(0.3393400.467062i)q58+(3.249072.36059i)q59+(4.4750013.7726i)q61+(0.1054460.145134i)q62+(12.4108+17.0820i)q63+(2.329187.16847i)q64+(1.19921+0.683847i)q668.14233iq67+(10.2384+3.32664i)q68+(4.40126+3.19770i)q69+(2.63051+8.09589i)q71+(3.121671.01429i)q72+(5.02032+6.90988i)q73+(0.3564880.259003i)q749.51187q76+(1.30039+11.7673i)q77+0.497655iq78+(0.121752+0.374714i)q79+(6.668924.84526i)q81+(0.8494570.276005i)q82+(1.487100.483189i)q83+(17.0777+12.4077i)q84+(0.182460+0.561553i)q86+12.3654iq87+(1.80221+0.373020i)q88+6.90425q89+(3.45277+2.50858i)q91+(2.12112+2.91946i)q92+(3.65434+1.18737i)q93+(0.3027570.931792i)q94+(3.988652.89792i)q96+(8.85604+2.87750i)q970.800446iq98+(8.0750717.8793i)q99+O(q100)q+(0.132580 + 0.0430779i) q^{2} +(-1.75502 - 2.41558i) q^{3} +(-1.60231 - 1.16415i) q^{4} +(-0.128623 - 0.395861i) q^{6} +(2.09815 - 2.88786i) q^{7} +(-0.326164 - 0.448926i) q^{8} +(-1.82787 + 5.62561i) q^{9} +(-2.45284 + 2.23239i) q^{11} +5.91361i q^{12} +(-1.13710 - 0.369466i) q^{13} +(0.402576 - 0.292489i) q^{14} +(1.20015 + 3.69369i) q^{16} +(-5.16941 + 1.67964i) q^{17} +(-0.484679 + 0.667104i) q^{18} +(3.88538 - 2.82290i) q^{19} -10.6581 q^{21} +(-0.421365 + 0.190307i) q^{22} -1.82203i q^{23} +(-0.511992 + 1.57575i) q^{24} +(-0.134841 - 0.0979678i) q^{26} +(8.27800 - 2.68969i) q^{27} +(-6.72378 + 2.18469i) q^{28} +(-3.35044 - 2.43424i) q^{29} +(0.397668 - 1.22390i) q^{31} +1.65122i q^{32} +(9.69730 + 2.00714i) q^{33} -0.757717 q^{34} +(9.47786 - 6.88607i) q^{36} +(1.85794 - 2.55724i) q^{37} +(0.636730 - 0.206886i) q^{38} +(1.10316 + 3.39517i) q^{39} +(5.18347 - 3.76601i) q^{41} +(-1.41306 - 0.459131i) q^{42} +4.23557i q^{43} +(6.52905 - 0.721514i) q^{44} +(0.0784894 - 0.241566i) q^{46} +(-4.13103 - 5.68588i) q^{47} +(6.81611 - 9.38157i) q^{48} +(-1.77436 - 5.46092i) q^{49} +(13.1297 + 9.53930i) q^{51} +(1.39187 + 1.91575i) q^{52} +(-10.2818 - 3.34076i) q^{53} +1.21337 q^{54} -1.98078 q^{56} +(-13.6379 - 4.43121i) q^{57} +(-0.339340 - 0.467062i) q^{58} +(-3.24907 - 2.36059i) q^{59} +(-4.47500 - 13.7726i) q^{61} +(0.105446 - 0.145134i) q^{62} +(12.4108 + 17.0820i) q^{63} +(2.32918 - 7.16847i) q^{64} +(1.19921 + 0.683847i) q^{66} -8.14233i q^{67} +(10.2384 + 3.32664i) q^{68} +(-4.40126 + 3.19770i) q^{69} +(2.63051 + 8.09589i) q^{71} +(3.12167 - 1.01429i) q^{72} +(-5.02032 + 6.90988i) q^{73} +(0.356488 - 0.259003i) q^{74} -9.51187 q^{76} +(1.30039 + 11.7673i) q^{77} +0.497655i q^{78} +(-0.121752 + 0.374714i) q^{79} +(-6.66892 - 4.84526i) q^{81} +(0.849457 - 0.276005i) q^{82} +(1.48710 - 0.483189i) q^{83} +(17.0777 + 12.4077i) q^{84} +(-0.182460 + 0.561553i) q^{86} +12.3654i q^{87} +(1.80221 + 0.373020i) q^{88} +6.90425 q^{89} +(-3.45277 + 2.50858i) q^{91} +(-2.12112 + 2.91946i) q^{92} +(-3.65434 + 1.18737i) q^{93} +(-0.302757 - 0.931792i) q^{94} +(3.98865 - 2.89792i) q^{96} +(8.85604 + 2.87750i) q^{97} -0.800446i q^{98} +(-8.07507 - 17.8793i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 32q+4q46q616q910q116q148q16+26q19+20q21+86q2468q26+22q2920q3140q34+6q366q39+50q41+2q44+80q46++20q99+O(q100) 32 q + 4 q^{4} - 6 q^{6} - 16 q^{9} - 10 q^{11} - 6 q^{14} - 8 q^{16} + 26 q^{19} + 20 q^{21} + 86 q^{24} - 68 q^{26} + 22 q^{29} - 20 q^{31} - 40 q^{34} + 6 q^{36} - 6 q^{39} + 50 q^{41} + 2 q^{44} + 80 q^{46}+ \cdots + 20 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/275Z)×\left(\mathbb{Z}/275\mathbb{Z}\right)^\times.

nn 101101 177177
χ(n)\chi(n) e(35)e\left(\frac{3}{5}\right) 1-1

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 0.132580 + 0.0430779i 0.0937484 + 0.0304607i 0.355516 0.934670i 0.384305π-0.384305\pi
−0.261767 + 0.965131i 0.584305π0.584305\pi
33 −1.75502 2.41558i −1.01326 1.39463i −0.916822 0.399296i 0.869255π-0.869255\pi
−0.0964394 0.995339i 0.530745π-0.530745\pi
44 −1.60231 1.16415i −0.801156 0.582074i
55 0 0
66 −0.128623 0.395861i −0.0525101 0.161609i
77 2.09815 2.88786i 0.793026 1.09151i −0.200698 0.979653i 0.564321π-0.564321\pi
0.993725 0.111854i 0.0356789π-0.0356789\pi
88 −0.326164 0.448926i −0.115316 0.158719i
99 −1.82787 + 5.62561i −0.609290 + 1.87520i
1010 0 0
1111 −2.45284 + 2.23239i −0.739560 + 0.673091i
1212 5.91361i 1.70711i
1313 −1.13710 0.369466i −0.315375 0.102471i 0.147053 0.989129i 0.453021π-0.453021\pi
−0.462427 + 0.886657i 0.653021π0.653021\pi
1414 0.402576 0.292489i 0.107593 0.0781709i
1515 0 0
1616 1.20015 + 3.69369i 0.300038 + 0.923423i
1717 −5.16941 + 1.67964i −1.25377 + 0.407373i −0.859269 0.511524i 0.829081π-0.829081\pi
−0.394496 + 0.918897i 0.629081π0.629081\pi
1818 −0.484679 + 0.667104i −0.114240 + 0.157238i
1919 3.88538 2.82290i 0.891368 0.647617i −0.0448661 0.998993i 0.514286π-0.514286\pi
0.936234 + 0.351376i 0.114286π0.114286\pi
2020 0 0
2121 −10.6581 −2.32580
2222 −0.421365 + 0.190307i −0.0898354 + 0.0405737i
2323 1.82203i 0.379920i −0.981792 0.189960i 0.939164π-0.939164\pi
0.981792 0.189960i 0.0608358π-0.0608358\pi
2424 −0.511992 + 1.57575i −0.104510 + 0.321649i
2525 0 0
2626 −0.134841 0.0979678i −0.0264445 0.0192131i
2727 8.27800 2.68969i 1.59310 0.517630i
2828 −6.72378 + 2.18469i −1.27068 + 0.412868i
2929 −3.35044 2.43424i −0.622161 0.452026i 0.231515 0.972831i 0.425632π-0.425632\pi
−0.853676 + 0.520805i 0.825632π0.825632\pi
3030 0 0
3131 0.397668 1.22390i 0.0714233 0.219818i −0.908973 0.416856i 0.863132π-0.863132\pi
0.980396 + 0.197037i 0.0631320π0.0631320\pi
3232 1.65122i 0.291897i
3333 9.69730 + 2.00714i 1.68808 + 0.349399i
3434 −0.757717 −0.129947
3535 0 0
3636 9.47786 6.88607i 1.57964 1.14768i
3737 1.85794 2.55724i 0.305444 0.420408i −0.628509 0.777802i 0.716335π-0.716335\pi
0.933954 + 0.357394i 0.116335π0.116335\pi
3838 0.636730 0.206886i 0.103291 0.0335614i
3939 1.10316 + 3.39517i 0.176647 + 0.543663i
4040 0 0
4141 5.18347 3.76601i 0.809522 0.588152i −0.104170 0.994559i 0.533219π-0.533219\pi
0.913692 + 0.406408i 0.133219π0.133219\pi
4242 −1.41306 0.459131i −0.218040 0.0708454i
4343 4.23557i 0.645919i 0.946413 + 0.322959i 0.104678π0.104678\pi
−0.946413 + 0.322959i 0.895322π0.895322\pi
4444 6.52905 0.721514i 0.984291 0.108772i
4545 0 0
4646 0.0784894 0.241566i 0.0115726 0.0356169i
4747 −4.13103 5.68588i −0.602573 0.829371i 0.393368 0.919381i 0.371310π-0.371310\pi
−0.995941 + 0.0900107i 0.971310π0.971310\pi
4848 6.81611 9.38157i 0.983821 1.35411i
4949 −1.77436 5.46092i −0.253480 0.780131i
5050 0 0
5151 13.1297 + 9.53930i 1.83853 + 1.33577i
5252 1.39187 + 1.91575i 0.193018 + 0.265667i
5353 −10.2818 3.34076i −1.41232 0.458889i −0.499164 0.866508i 0.666359π-0.666359\pi
−0.913152 + 0.407618i 0.866359π0.866359\pi
5454 1.21337 0.165118
5555 0 0
5656 −1.98078 −0.264692
5757 −13.6379 4.43121i −1.80638 0.586928i
5858 −0.339340 0.467062i −0.0445575 0.0613282i
5959 −3.24907 2.36059i −0.422993 0.307323i 0.355848 0.934544i 0.384192π-0.384192\pi
−0.778841 + 0.627221i 0.784192π0.784192\pi
6060 0 0
6161 −4.47500 13.7726i −0.572964 1.76340i −0.643008 0.765859i 0.722314π-0.722314\pi
0.0700436 0.997544i 0.477686π-0.477686\pi
6262 0.105446 0.145134i 0.0133916 0.0184320i
6363 12.4108 + 17.0820i 1.56361 + 2.15213i
6464 2.32918 7.16847i 0.291147 0.896058i
6565 0 0
6666 1.19921 + 0.683847i 0.147612 + 0.0841758i
6767 8.14233i 0.994744i −0.867537 0.497372i 0.834298π-0.834298\pi
0.867537 0.497372i 0.165702π-0.165702\pi
6868 10.2384 + 3.32664i 1.24158 + 0.403415i
6969 −4.40126 + 3.19770i −0.529850 + 0.384958i
7070 0 0
7171 2.63051 + 8.09589i 0.312185 + 0.960806i 0.976898 + 0.213707i 0.0685538π0.0685538\pi
−0.664713 + 0.747099i 0.731446π0.731446\pi
7272 3.12167 1.01429i 0.367892 0.119535i
7373 −5.02032 + 6.90988i −0.587584 + 0.808740i −0.994501 0.104725i 0.966604π-0.966604\pi
0.406917 + 0.913465i 0.366604π0.366604\pi
7474 0.356488 0.259003i 0.0414408 0.0301085i
7575 0 0
7676 −9.51187 −1.09109
7777 1.30039 + 11.7673i 0.148193 + 1.34101i
7878 0.497655i 0.0563483i
7979 −0.121752 + 0.374714i −0.0136982 + 0.0421586i −0.957672 0.287862i 0.907056π-0.907056\pi
0.943974 + 0.330020i 0.107056π0.107056\pi
8080 0 0
8181 −6.66892 4.84526i −0.740992 0.538362i
8282 0.849457 0.276005i 0.0938069 0.0304797i
8383 1.48710 0.483189i 0.163231 0.0530369i −0.226262 0.974067i 0.572650π-0.572650\pi
0.389492 + 0.921030i 0.372650π0.372650\pi
8484 17.0777 + 12.4077i 1.86333 + 1.35379i
8585 0 0
8686 −0.182460 + 0.561553i −0.0196751 + 0.0605538i
8787 12.3654i 1.32571i
8888 1.80221 + 0.373020i 0.192116 + 0.0397641i
8989 6.90425 0.731849 0.365925 0.930645i 0.380753π-0.380753\pi
0.365925 + 0.930645i 0.380753π0.380753\pi
9090 0 0
9191 −3.45277 + 2.50858i −0.361949 + 0.262971i
9292 −2.12112 + 2.91946i −0.221142 + 0.304375i
9393 −3.65434 + 1.18737i −0.378937 + 0.123124i
9494 −0.302757 0.931792i −0.0312270 0.0961070i
9595 0 0
9696 3.98865 2.89792i 0.407089 0.295768i
9797 8.85604 + 2.87750i 0.899195 + 0.292166i 0.721905 0.691993i 0.243267π-0.243267\pi
0.177290 + 0.984159i 0.443267π0.443267\pi
9898 0.800446i 0.0808572i
9999 −8.07507 17.8793i −0.811575 1.79693i
100100 0 0
101101 −0.810256 + 2.49371i −0.0806235 + 0.248134i −0.983241 0.182309i 0.941643π-0.941643\pi
0.902618 + 0.430443i 0.141643π0.141643\pi
102102 1.32981 + 1.83032i 0.131671 + 0.181229i
103103 3.88267 5.34404i 0.382571 0.526564i −0.573692 0.819071i 0.694490π-0.694490\pi
0.956263 + 0.292507i 0.0944895π0.0944895\pi
104104 0.205018 + 0.630980i 0.0201037 + 0.0618727i
105105 0 0
106106 −1.21925 0.885839i −0.118424 0.0860403i
107107 −8.26556 11.3766i −0.799062 1.09981i −0.992920 0.118785i 0.962100π-0.962100\pi
0.193858 0.981030i 0.437900π-0.437900\pi
108108 −16.3951 5.32710i −1.57762 0.512601i
109109 −12.3514 −1.18305 −0.591525 0.806286i 0.701474π-0.701474\pi
−0.591525 + 0.806286i 0.701474π0.701474\pi
110110 0 0
111111 −9.43795 −0.895810
112112 13.1850 + 4.28405i 1.24586 + 0.404805i
113113 2.09760 + 2.88710i 0.197326 + 0.271596i 0.896201 0.443648i 0.146316π-0.146316\pi
−0.698875 + 0.715243i 0.746316π0.746316\pi
114114 −1.61722 1.17498i −0.151467 0.110047i
115115 0 0
116116 2.53464 + 7.80081i 0.235335 + 0.724287i
117117 4.15694 5.72154i 0.384309 0.528956i
118118 −0.329074 0.452931i −0.0302937 0.0416957i
119119 −5.99563 + 18.4526i −0.549618 + 1.69155i
120120 0 0
121121 1.03287 10.9514i 0.0938974 0.995582i
122122 2.01875i 0.182769i
123123 −18.1942 5.91165i −1.64051 0.533035i
124124 −2.06199 + 1.49812i −0.185172 + 0.134535i
125125 0 0
126126 0.909570 + 2.79937i 0.0810309 + 0.249388i
127127 5.97215 1.94047i 0.529943 0.172189i −0.0318100 0.999494i 0.510127π-0.510127\pi
0.561753 + 0.827305i 0.310127π0.310127\pi
128128 2.55873 3.52179i 0.226162 0.311285i
129129 10.2314 7.43352i 0.900821 0.654485i
130130 0 0
131131 18.4755 1.61421 0.807105 0.590408i 0.201033π-0.201033\pi
0.807105 + 0.590408i 0.201033π0.201033\pi
132132 −13.2015 14.5052i −1.14904 1.26251i
133133 17.1433i 1.48651i
134134 0.350755 1.07951i 0.0303006 0.0932557i
135135 0 0
136136 2.44011 + 1.77284i 0.209238 + 0.152020i
137137 −3.97216 + 1.29063i −0.339364 + 0.110266i −0.473741 0.880664i 0.657097π-0.657097\pi
0.134377 + 0.990930i 0.457097π0.457097\pi
138138 −0.721271 + 0.234355i −0.0613987 + 0.0199496i
139139 −2.20927 1.60513i −0.187388 0.136145i 0.490136 0.871646i 0.336947π-0.336947\pi
−0.677524 + 0.735501i 0.736947π0.736947\pi
140140 0 0
141141 −6.48464 + 19.9577i −0.546105 + 1.68074i
142142 1.18667i 0.0995834i
143143 3.61392 1.63221i 0.302211 0.136492i
144144 −22.9730 −1.91442
145145 0 0
146146 −0.963258 + 0.699848i −0.0797198 + 0.0579199i
147147 −10.0772 + 13.8701i −0.831156 + 1.14399i
148148 −5.95401 + 1.93458i −0.489417 + 0.159021i
149149 5.48466 + 16.8800i 0.449321 + 1.38287i 0.877675 + 0.479256i 0.159094π0.159094\pi
−0.428354 + 0.903611i 0.640906π0.640906\pi
150150 0 0
151151 1.17615 0.854522i 0.0957136 0.0695400i −0.538899 0.842370i 0.681160π-0.681160\pi
0.634613 + 0.772830i 0.281160π0.281160\pi
152152 −2.53455 0.823524i −0.205579 0.0667966i
153153 32.1512i 2.59927i
154154 −0.334507 + 1.61614i −0.0269554 + 0.130232i
155155 0 0
156156 2.18488 6.72437i 0.174930 0.538380i
157157 1.97318 + 2.71585i 0.157477 + 0.216749i 0.880464 0.474113i 0.157231π-0.157231\pi
−0.722987 + 0.690862i 0.757231π0.757231\pi
158158 −0.0322838 + 0.0444348i −0.00256836 + 0.00353504i
159159 9.97492 + 30.6996i 0.791062 + 2.43464i
160160 0 0
161161 −5.26177 3.82290i −0.414685 0.301287i
162162 −0.675444 0.929669i −0.0530679 0.0730417i
163163 6.47640 + 2.10431i 0.507271 + 0.164822i 0.551461 0.834201i 0.314071π-0.314071\pi
−0.0441897 + 0.999023i 0.514071π0.514071\pi
164164 −12.6897 −0.990901
165165 0 0
166166 0.217975 0.0169182
167167 18.6804 + 6.06962i 1.44553 + 0.469681i 0.923616 0.383318i 0.125219π-0.125219\pi
0.521913 + 0.852999i 0.325219π0.325219\pi
168168 3.47630 + 4.78472i 0.268203 + 0.369149i
169169 −9.36073 6.80097i −0.720056 0.523152i
170170 0 0
171171 8.77853 + 27.0175i 0.671311 + 2.06608i
172172 4.93083 6.78671i 0.375972 0.517482i
173173 −0.137634 0.189438i −0.0104642 0.0144027i 0.803753 0.594963i 0.202833π-0.202833\pi
−0.814217 + 0.580561i 0.802833π0.802833\pi
174174 −0.532675 + 1.63941i −0.0403820 + 0.124283i
175175 0 0
176176 −11.1895 6.38084i −0.843444 0.480974i
177177 11.9913i 0.901319i
178178 0.915367 + 0.297421i 0.0686097 + 0.0222926i
179179 13.7416 9.98383i 1.02709 0.746227i 0.0593679 0.998236i 0.481091π-0.481091\pi
0.967725 + 0.252010i 0.0810915π0.0810915\pi
180180 0 0
181181 −5.36003 16.4965i −0.398408 1.22617i −0.926275 0.376847i 0.877008π-0.877008\pi
0.527867 0.849327i 0.322992π-0.322992\pi
182182 −0.565834 + 0.183851i −0.0419424 + 0.0136279i
183183 −25.4151 + 34.9809i −1.87874 + 2.58586i
184184 −0.817958 + 0.594282i −0.0603007 + 0.0438110i
185185 0 0
186186 −0.535642 −0.0392752
187187 8.93012 15.6600i 0.653035 1.14517i
188188 13.9197i 1.01520i
189189 9.60107 29.5490i 0.698375 2.14938i
190190 0 0
191191 −16.8029 12.2080i −1.21582 0.883342i −0.220070 0.975484i 0.570629π-0.570629\pi
−0.995746 + 0.0921420i 0.970629π0.970629\pi
192192 −21.4037 + 6.95450i −1.54468 + 0.501898i
193193 8.09586 2.63050i 0.582752 0.189348i −0.00278083 0.999996i 0.500885π-0.500885\pi
0.585533 + 0.810648i 0.300885π0.300885\pi
194194 1.05018 + 0.763000i 0.0753985 + 0.0547802i
195195 0 0
196196 −3.51424 + 10.8157i −0.251017 + 0.772551i
197197 2.60251i 0.185421i −0.995693 0.0927106i 0.970447π-0.970447\pi
0.995693 0.0927106i 0.0295531π-0.0295531\pi
198198 −0.300394 2.71829i −0.0213481 0.193181i
199199 8.77731 0.622207 0.311104 0.950376i 0.399301π-0.399301\pi
0.311104 + 0.950376i 0.399301π0.399301\pi
200200 0 0
201201 −19.6684 + 14.2900i −1.38730 + 1.00794i
202202 −0.214848 + 0.295713i −0.0151167 + 0.0208063i
203203 −14.0594 + 4.56819i −0.986780 + 0.320624i
204204 −9.93275 30.5699i −0.695432 2.14032i
205205 0 0
206206 0.744976 0.541256i 0.0519049 0.0377111i
207207 10.2500 + 3.33044i 0.712427 + 0.231482i
208208 4.64351i 0.321970i
209209 −3.22843 + 15.5978i −0.223315 + 1.07892i
210210 0 0
211211 3.34024 10.2802i 0.229952 0.707718i −0.767799 0.640690i 0.778648π-0.778648\pi
0.997751 0.0670281i 0.0213517π-0.0213517\pi
212212 12.5855 + 17.3225i 0.864378 + 1.18971i
213213 14.9397 20.5627i 1.02365 1.40893i
214214 −0.605771 1.86437i −0.0414097 0.127446i
215215 0 0
216216 −3.90746 2.83893i −0.265869 0.193165i
217217 −2.70007 3.71633i −0.183293 0.252281i
218218 −1.63755 0.532073i −0.110909 0.0360366i
219219 25.5021 1.72327
220220 0 0
221221 6.49870 0.437150
222222 −1.25129 0.406567i −0.0839808 0.0272870i
223223 4.73085 + 6.51146i 0.316801 + 0.436040i 0.937487 0.348020i 0.113146π-0.113146\pi
−0.620686 + 0.784059i 0.713146π0.713146\pi
224224 4.76848 + 3.46450i 0.318607 + 0.231482i
225225 0 0
226226 0.153730 + 0.473133i 0.0102260 + 0.0314724i
227227 −12.1786 + 16.7624i −0.808323 + 1.11256i 0.183257 + 0.983065i 0.441336π0.441336\pi
−0.991580 + 0.129496i 0.958664π0.958664\pi
228228 16.6935 + 22.9767i 1.10556 + 1.52167i
229229 −2.47597 + 7.62024i −0.163616 + 0.503560i −0.998932 0.0462117i 0.985285π-0.985285\pi
0.835315 + 0.549771i 0.185285π0.185285\pi
230230 0 0
231231 26.1427 23.7931i 1.72007 1.56547i
232232 2.29806i 0.150875i
233233 24.2133 + 7.86737i 1.58626 + 0.515408i 0.963661 0.267129i 0.0860750π-0.0860750\pi
0.622603 + 0.782538i 0.286075π0.286075\pi
234234 0.797601 0.579491i 0.0521408 0.0378825i
235235 0 0
236236 2.45795 + 7.56480i 0.159999 + 0.492427i
237237 1.11883 0.363529i 0.0726756 0.0236137i
238238 −1.58980 + 2.18818i −0.103052 + 0.141838i
239239 0.442580 0.321553i 0.0286281 0.0207995i −0.573379 0.819290i 0.694368π-0.694368\pi
0.602007 + 0.798491i 0.294368π0.294368\pi
240240 0 0
241241 21.9600 1.41457 0.707285 0.706929i 0.249920π-0.249920\pi
0.707285 + 0.706929i 0.249920π0.249920\pi
242242 0.608702 1.40745i 0.0391289 0.0904740i
243243 1.49919i 0.0961728i
244244 −8.86303 + 27.2776i −0.567397 + 1.74627i
245245 0 0
246246 −2.15753 1.56754i −0.137559 0.0999424i
247247 −5.46103 + 1.77440i −0.347477 + 0.112902i
248248 −0.679145 + 0.220668i −0.0431257 + 0.0140124i
249249 −3.77708 2.74421i −0.239362 0.173907i
250250 0 0
251251 1.87041 5.75652i 0.118059 0.363348i −0.874514 0.485001i 0.838819π-0.838819\pi
0.992573 + 0.121653i 0.0388194π0.0388194\pi
252252 41.8187i 2.63433i
253253 4.06749 + 4.46916i 0.255721 + 0.280974i
254254 0.875381 0.0549263
255255 0 0
256256 −11.7048 + 8.50402i −0.731548 + 0.531501i
257257 1.79724 2.47369i 0.112109 0.154305i −0.749275 0.662259i 0.769598π-0.769598\pi
0.861384 + 0.507954i 0.169598π0.169598\pi
258258 1.67670 0.544792i 0.104387 0.0339172i
259259 −3.48670 10.7310i −0.216653 0.666789i
260260 0 0
261261 19.8182 14.3988i 1.22672 0.891263i
262262 2.44948 + 0.795885i 0.151330 + 0.0491699i
263263 18.1365i 1.11835i −0.829050 0.559174i 0.811118π-0.811118\pi
0.829050 0.559174i 0.188882π-0.188882\pi
264264 −2.26185 5.00803i −0.139207 0.308223i
265265 0 0
266266 0.738498 2.27286i 0.0452802 0.139358i
267267 −12.1171 16.6778i −0.741555 1.02066i
268268 −9.47888 + 13.0466i −0.579015 + 0.796945i
269269 −5.38987 16.5883i −0.328626 1.01141i −0.969777 0.243993i 0.921543π-0.921543\pi
0.641151 0.767415i 0.278457π-0.278457\pi
270270 0 0
271271 5.70006 + 4.14134i 0.346254 + 0.251568i 0.747296 0.664492i 0.231352π-0.231352\pi
−0.401042 + 0.916060i 0.631352π0.631352\pi
272272 −12.4082 17.0784i −0.752355 1.03553i
273273 12.1194 + 3.93782i 0.733497 + 0.238328i
274274 −0.582227 −0.0351736
275275 0 0
276276 10.7748 0.648567
277277 −17.6181 5.72446i −1.05857 0.343949i −0.272542 0.962144i 0.587864π-0.587864\pi
−0.786025 + 0.618195i 0.787864π0.787864\pi
278278 −0.223760 0.307979i −0.0134202 0.0184714i
279279 6.15828 + 4.47425i 0.368687 + 0.267866i
280280 0 0
281281 6.49461 + 19.9884i 0.387436 + 1.19241i 0.934698 + 0.355444i 0.115670π0.115670\pi
−0.547262 + 0.836962i 0.684330π0.684330\pi
282282 −1.71947 + 2.36665i −0.102393 + 0.140932i
283283 0.955030 + 1.31449i 0.0567706 + 0.0781381i 0.836458 0.548030i 0.184622π-0.184622\pi
−0.779688 + 0.626169i 0.784622π0.784622\pi
284284 5.20991 16.0345i 0.309151 0.951470i
285285 0 0
286286 0.549446 0.0607183i 0.0324894 0.00359035i
287287 22.8708i 1.35002i
288288 −9.28911 3.01821i −0.547366 0.177850i
289289 10.1483 7.37316i 0.596957 0.433715i
290290 0 0
291291 −8.59170 26.4425i −0.503654 1.55009i
292292 16.0882 5.22738i 0.941493 0.305910i
293293 7.41008 10.1991i 0.432901 0.595838i −0.535715 0.844399i 0.679958π-0.679958\pi
0.968616 + 0.248561i 0.0799578π0.0799578\pi
294294 −1.93354 + 1.40480i −0.112766 + 0.0819295i
295295 0 0
296296 −1.75401 −0.101950
297297 −14.3002 + 25.0771i −0.829782 + 1.45512i
298298 2.47423i 0.143328i
299299 −0.673179 + 2.07183i −0.0389309 + 0.119817i
300300 0 0
301301 12.2317 + 8.88687i 0.705025 + 0.512230i
302302 0.192745 0.0626267i 0.0110912 0.00360376i
303303 7.44578 2.41928i 0.427749 0.138984i
304304 15.0900 + 10.9635i 0.865469 + 0.628800i
305305 0 0
306306 1.38501 4.26262i 0.0791757 0.243678i
307307 22.6055i 1.29017i 0.764112 + 0.645083i 0.223177π0.223177\pi
−0.764112 + 0.645083i 0.776823π0.776823\pi
308308 11.6153 20.3688i 0.661843 1.16062i
309309 −19.7231 −1.12201
310310 0 0
311311 15.0909 10.9642i 0.855729 0.621723i −0.0709908 0.997477i 0.522616π-0.522616\pi
0.926720 + 0.375754i 0.122616π0.122616\pi
312312 1.16437 1.60262i 0.0659196 0.0907305i
313313 −16.6286 + 5.40298i −0.939907 + 0.305394i −0.738608 0.674136i 0.764516π-0.764516\pi
−0.201299 + 0.979530i 0.564516π0.564516\pi
314314 0.144612 + 0.445069i 0.00816091 + 0.0251167i
315315 0 0
316316 0.631307 0.458671i 0.0355138 0.0258023i
317317 10.6373 + 3.45627i 0.597450 + 0.194123i 0.592103 0.805862i 0.298298π-0.298298\pi
0.00534745 + 0.999986i 0.498298π0.498298\pi
318318 4.49987i 0.252340i
319319 13.6523 1.50869i 0.764380 0.0844703i
320320 0 0
321321 −12.9748 + 39.9322i −0.724181 + 2.22880i
322322 −0.532924 0.733507i −0.0296987 0.0408767i
323323 −15.3437 + 21.1188i −0.853745 + 1.17508i
324324 5.04510 + 15.5272i 0.280283 + 0.862624i
325325 0 0
326326 0.767994 + 0.557980i 0.0425353 + 0.0309037i
327327 21.6770 + 29.8358i 1.19874 + 1.64992i
328328 −3.38132 1.09866i −0.186702 0.0606632i
329329 −25.0875 −1.38312
330330 0 0
331331 −25.7621 −1.41602 −0.708008 0.706205i 0.750406π-0.750406\pi
−0.708008 + 0.706205i 0.750406π0.750406\pi
332332 −2.94531 0.956988i −0.161645 0.0525215i
333333 10.9900 + 15.1264i 0.602246 + 0.828920i
334334 2.21518 + 1.60942i 0.121209 + 0.0880637i
335335 0 0
336336 −12.7914 39.3679i −0.697828 2.14769i
337337 −6.75842 + 9.30216i −0.368154 + 0.506721i −0.952398 0.304857i 0.901391π-0.901391\pi
0.584244 + 0.811578i 0.301391π0.301391\pi
338338 −0.948077 1.30492i −0.0515686 0.0709780i
339339 3.29269 10.1339i 0.178834 0.550395i
340340 0 0
341341 1.75680 + 3.88978i 0.0951359 + 0.210643i
342342 3.96015i 0.214141i
343343 4.27093 + 1.38771i 0.230609 + 0.0749293i
344344 1.90146 1.38149i 0.102520 0.0744850i
345345 0 0
346346 −0.0100870 0.0310447i −0.000542282 0.00166897i
347347 0.823501 0.267572i 0.0442079 0.0143640i −0.286830 0.957982i 0.592601π-0.592601\pi
0.331037 + 0.943618i 0.392601π0.392601\pi
348348 14.3951 19.8132i 0.771660 1.06210i
349349 14.3937 10.4576i 0.770476 0.559784i −0.131630 0.991299i 0.542021π-0.542021\pi
0.902106 + 0.431515i 0.142021π0.142021\pi
350350 0 0
351351 −10.4067 −0.555466
352352 −3.68616 4.05018i −0.196473 0.215875i
353353 1.11550i 0.0593723i −0.999559 0.0296862i 0.990549π-0.990549\pi
0.999559 0.0296862i 0.00945079π-0.00945079\pi
354354 −0.516559 + 1.58981i −0.0274548 + 0.0844972i
355355 0 0
356356 −11.0628 8.03757i −0.586325 0.425990i
357357 55.0963 17.9019i 2.91600 0.947467i
358358 2.25194 0.731701i 0.119019 0.0386716i
359359 1.22945 + 0.893247i 0.0648878 + 0.0471438i 0.619756 0.784794i 0.287231π-0.287231\pi
−0.554869 + 0.831938i 0.687231π0.687231\pi
360360 0 0
361361 1.25614 3.86601i 0.0661127 0.203474i
362362 2.41801i 0.127088i
363363 −28.2667 + 16.7250i −1.48362 + 0.877832i
364364 8.45278 0.443046
365365 0 0
366366 −4.87645 + 3.54295i −0.254896 + 0.185193i
367367 −6.24587 + 8.59670i −0.326032 + 0.448744i −0.940297 0.340356i 0.889453π-0.889453\pi
0.614265 + 0.789100i 0.289453π0.289453\pi
368368 6.73003 2.18672i 0.350827 0.113991i
369369 11.7114 + 36.0439i 0.609670 + 1.87637i
370370 0 0
371371 −31.2204 + 22.6830i −1.62088 + 1.17764i
372372 7.23765 + 2.35166i 0.375255 + 0.121928i
373373 27.9435i 1.44686i 0.690399 + 0.723429i 0.257435π0.257435\pi
−0.690399 + 0.723429i 0.742565π0.742565\pi
374374 1.85856 1.69152i 0.0961038 0.0874664i
375375 0 0
376376 −1.20515 + 3.70906i −0.0621507 + 0.191280i
377377 2.91041 + 4.00584i 0.149894 + 0.206311i
378378 2.54582 3.50403i 0.130943 0.180228i
379379 −5.76969 17.7573i −0.296369 0.912130i −0.982758 0.184896i 0.940805π-0.940805\pi
0.686389 0.727235i 0.259195π-0.259195\pi
380380 0 0
381381 −15.1686 11.0206i −0.777111 0.564605i
382382 −1.70184 2.34238i −0.0870736 0.119847i
383383 −20.6018 6.69393i −1.05270 0.342044i −0.268974 0.963147i 0.586685π-0.586685\pi
−0.783729 + 0.621104i 0.786685π0.786685\pi
384384 −12.9978 −0.663290
385385 0 0
386386 1.18667 0.0603998
387387 −23.8277 7.74208i −1.21123 0.393552i
388388 −10.8403 14.9204i −0.550333 0.757468i
389389 −30.3224 22.0305i −1.53740 1.11699i −0.951937 0.306294i 0.900911π-0.900911\pi
−0.585468 0.810696i 0.699089π-0.699089\pi
390390 0 0
391391 3.06036 + 9.41883i 0.154769 + 0.476331i
392392 −1.87282 + 2.57771i −0.0945916 + 0.130194i
393393 −32.4248 44.6289i −1.63562 2.25123i
394394 0.112111 0.345042i 0.00564806 0.0173829i
395395 0 0
396396 −7.87531 + 38.0487i −0.395749 + 1.91202i
397397 18.3084i 0.918873i 0.888211 + 0.459437i 0.151949π0.151949\pi
−0.888211 + 0.459437i 0.848051π0.848051\pi
398398 1.16370 + 0.378109i 0.0583309 + 0.0189529i
399399 −41.4110 + 30.0868i −2.07314 + 1.50623i
400400 0 0
401401 4.04434 + 12.4472i 0.201965 + 0.621583i 0.999824 + 0.0187401i 0.00596551π0.00596551\pi
−0.797860 + 0.602843i 0.794034π0.794034\pi
402402 −3.22323 + 1.04729i −0.160760 + 0.0522341i
403403 −0.904376 + 1.24477i −0.0450502 + 0.0620063i
404404 4.20133 3.05245i 0.209024 0.151865i
405405 0 0
406406 −2.06079 −0.102275
407407 1.15151 + 10.4202i 0.0570785 + 0.516509i
408408 9.00566i 0.445846i
409409 −6.57096 + 20.2233i −0.324913 + 0.999980i 0.646567 + 0.762857i 0.276204π0.276204\pi
−0.971480 + 0.237122i 0.923796π0.923796\pi
410410 0 0
411411 10.0888 + 7.32997i 0.497646 + 0.361561i
412412 −12.4425 + 4.04281i −0.612998 + 0.199175i
413413 −13.6341 + 4.42998i −0.670889 + 0.217985i
414414 1.21548 + 0.883101i 0.0597378 + 0.0434021i
415415 0 0
416416 0.610069 1.87760i 0.0299111 0.0920568i
417417 8.15371i 0.399289i
418418 −1.09995 + 1.92889i −0.0538002 + 0.0943450i
419419 37.5627 1.83506 0.917528 0.397670i 0.130181π-0.130181\pi
0.917528 + 0.397670i 0.130181π0.130181\pi
420420 0 0
421421 7.41340 5.38615i 0.361307 0.262505i −0.392290 0.919842i 0.628317π-0.628317\pi
0.753597 + 0.657337i 0.228317π0.228317\pi
422422 0.885700 1.21906i 0.0431152 0.0593430i
423423 39.5375 12.8465i 1.92238 0.624619i
424424 1.85380 + 5.70542i 0.0900286 + 0.277079i
425425 0 0
426426 2.86650 2.08263i 0.138882 0.100904i
427427 −49.1626 15.9739i −2.37914 0.773030i
428428 27.8512i 1.34624i
429429 −10.2852 5.86514i −0.496575 0.283172i
430430 0 0
431431 8.63312 26.5700i 0.415843 1.27983i −0.495653 0.868521i 0.665071π-0.665071\pi
0.911495 0.411311i 0.134929π-0.134929\pi
432432 19.8697 + 27.3484i 0.955984 + 1.31580i
433433 11.9620 16.4642i 0.574856 0.791221i −0.418264 0.908325i 0.637361π-0.637361\pi
0.993120 + 0.117105i 0.0373613π0.0373613\pi
434434 −0.197884 0.609025i −0.00949875 0.0292342i
435435 0 0
436436 19.7908 + 14.3789i 0.947808 + 0.688623i
437437 −5.14341 7.07930i −0.246043 0.338649i
438438 3.38108 + 1.09858i 0.161554 + 0.0524921i
439439 5.87262 0.280285 0.140142 0.990131i 0.455244π-0.455244\pi
0.140142 + 0.990131i 0.455244π0.455244\pi
440440 0 0
441441 33.9643 1.61735
442442 0.861599 + 0.279951i 0.0409821 + 0.0133159i
443443 −21.2309 29.2219i −1.00871 1.38837i −0.919824 0.392332i 0.871668π-0.871668\pi
−0.0888891 0.996042i 0.528332π-0.528332\pi
444444 15.1225 + 10.9872i 0.717684 + 0.521428i
445445 0 0
446446 0.346717 + 1.06709i 0.0164175 + 0.0505280i
447447 31.1494 42.8735i 1.47332 2.02784i
448448 −15.8145 21.7668i −0.747167 1.02839i
449449 −2.11744 + 6.51680i −0.0999281 + 0.307547i −0.988507 0.151177i 0.951694π-0.951694\pi
0.888579 + 0.458724i 0.151694π0.151694\pi
450450 0 0
451451 −4.30703 + 20.8089i −0.202810 + 0.979855i
452452 7.06796i 0.332449i
453453 −4.12833 1.34138i −0.193966 0.0630233i
454454 −2.33674 + 1.69774i −0.109668 + 0.0796788i
455455 0 0
456456 2.45889 + 7.56770i 0.115148 + 0.354390i
457457 −20.2693 + 6.58590i −0.948158 + 0.308075i −0.741967 0.670437i 0.766107π-0.766107\pi
−0.206191 + 0.978512i 0.566107π0.566107\pi
458458 −0.656528 + 0.903634i −0.0306776 + 0.0422240i
459459 −38.2747 + 27.8082i −1.78651 + 1.29797i
460460 0 0
461461 −29.0126 −1.35125 −0.675626 0.737244i 0.736127π-0.736127\pi
−0.675626 + 0.737244i 0.736127π0.736127\pi
462462 4.49097 2.02832i 0.208939 0.0943661i
463463 17.8392i 0.829057i −0.910036 0.414528i 0.863947π-0.863947\pi
0.910036 0.414528i 0.136053π-0.136053\pi
464464 4.97028 15.2969i 0.230739 0.710143i
465465 0 0
466466 2.87129 + 2.08612i 0.133010 + 0.0966374i
467467 −3.80640 + 1.23677i −0.176139 + 0.0572311i −0.395759 0.918354i 0.629518π-0.629518\pi
0.219620 + 0.975586i 0.429518π0.429518\pi
468468 −13.3214 + 4.32840i −0.615784 + 0.200080i
469469 −23.5139 17.0838i −1.08577 0.788858i
470470 0 0
471471 3.09738 9.53275i 0.142720 0.439246i
472472 2.22853i 0.102577i
473473 −9.45545 10.3892i −0.434762 0.477695i
474474 0.163994 0.00753252
475475 0 0
476476 31.0885 22.5871i 1.42494 1.03528i
477477 37.5877 51.7350i 1.72102 2.36878i
478478 0.0725292 0.0235662i 0.00331741 0.00107789i
479479 0.372018 + 1.14495i 0.0169979 + 0.0523143i 0.959196 0.282743i 0.0912443π-0.0912443\pi
−0.942198 + 0.335057i 0.891244π0.891244\pi
480480 0 0
481481 −3.05748 + 2.22139i −0.139409 + 0.101287i
482482 2.91146 + 0.945992i 0.132614 + 0.0430888i
483483 19.4195i 0.883617i
484484 −14.4040 + 16.3451i −0.654729 + 0.742961i
485485 0 0
486486 0.0645818 0.198762i 0.00292949 0.00901605i
487487 −24.8406 34.1902i −1.12564 1.54930i −0.796105 0.605159i 0.793109π-0.793109\pi
−0.329531 0.944145i 0.606891π-0.606891\pi
488488 −4.72331 + 6.50108i −0.213814 + 0.294290i
489489 −6.28309 19.3374i −0.284131 0.874466i
490490 0 0
491491 −14.7908 10.7462i −0.667500 0.484967i 0.201687 0.979450i 0.435358π-0.435358\pi
−0.869188 + 0.494483i 0.835358π0.835358\pi
492492 22.2707 + 30.6530i 1.00404 + 1.38194i
493493 21.4084 + 6.95602i 0.964187 + 0.313283i
494494 −0.800462 −0.0360145
495495 0 0
496496 4.99796 0.224415
497497 28.8990 + 9.38985i 1.29630 + 0.421192i
498498 −0.382551 0.526536i −0.0171425 0.0235947i
499499 18.3522 + 13.3336i 0.821557 + 0.596896i 0.917158 0.398524i 0.130477π-0.130477\pi
−0.0956011 + 0.995420i 0.530477π0.530477\pi
500500 0 0
501501 −18.1228 55.7762i −0.809666 2.49190i
502502 0.495958 0.682627i 0.0221357 0.0304671i
503503 18.9706 + 26.1108i 0.845859 + 1.16422i 0.984760 + 0.173919i 0.0556430π0.0556430\pi
−0.138901 + 0.990306i 0.544357π0.544357\pi
504504 3.62060 11.1431i 0.161274 0.496352i
505505 0 0
506506 0.346746 + 0.767741i 0.0154148 + 0.0341303i
507507 34.5474i 1.53430i
508508 −11.8282 3.84323i −0.524794 0.170516i
509509 17.8771 12.9885i 0.792390 0.575705i −0.116282 0.993216i 0.537098π-0.537098\pi
0.908672 + 0.417512i 0.137098π0.137098\pi
510510 0 0
511511 9.42134 + 28.9959i 0.416776 + 1.28270i
512512 −10.1984 + 3.31365i −0.450709 + 0.146444i
513513 24.5705 33.8184i 1.08481 1.49312i
514514 0.344841 0.250541i 0.0152103 0.0110509i
515515 0 0
516516 −25.0475 −1.10266
517517 22.8259 + 4.72449i 1.00388 + 0.207783i
518518 1.57291i 0.0691098i
519519 −0.216050 + 0.664934i −0.00948355 + 0.0291874i
520520 0 0
521521 13.7909 + 10.0196i 0.604189 + 0.438969i 0.847363 0.531014i 0.178189π-0.178189\pi
−0.243175 + 0.969983i 0.578189π0.578189\pi
522522 3.24778 1.05527i 0.142151 0.0461878i
523523 19.0148 6.17828i 0.831459 0.270157i 0.137799 0.990460i 0.455997π-0.455997\pi
0.693660 + 0.720303i 0.255997π0.255997\pi
524524 −29.6035 21.5082i −1.29323 0.939589i
525525 0 0
526526 0.781285 2.40455i 0.0340657 0.104843i
527527 6.99476i 0.304697i
528528 4.22448 + 38.2277i 0.183847 + 1.66365i
529529 19.6802 0.855661
530530 0 0
531531 19.2186 13.9632i 0.834018 0.605949i
532532 −19.9573 + 27.4689i −0.865260 + 1.19093i
533533 −7.28553 + 2.36721i −0.315571 + 0.102535i
534534 −0.888045 2.73312i −0.0384295 0.118274i
535535 0 0
536536 −3.65531 + 2.65574i −0.157885 + 0.114710i
537537 −48.2334 15.6720i −2.08143 0.676297i
538538 2.43147i 0.104828i
539539 16.5431 + 9.43371i 0.712563 + 0.406338i
540540 0 0
541541 −2.28788 + 7.04138i −0.0983638 + 0.302733i −0.988116 0.153712i 0.950877π-0.950877\pi
0.889752 + 0.456444i 0.150877π0.150877\pi
542542 0.577315 + 0.794606i 0.0247978 + 0.0341313i
543543 −30.4416 + 41.8992i −1.30637 + 1.79807i
544544 −2.77345 8.53582i −0.118911 0.365970i
545545 0 0
546546 1.43716 + 1.04415i 0.0615046 + 0.0446857i
547547 11.5228 + 15.8598i 0.492679 + 0.678115i 0.980879 0.194617i 0.0623464π-0.0623464\pi
−0.488200 + 0.872732i 0.662346π0.662346\pi
548548 7.86712 + 2.55618i 0.336067 + 0.109195i
549549 85.6591 3.65584
550550 0 0
551551 −19.8893 −0.847314
552552 2.87107 + 0.932866i 0.122201 + 0.0397054i
553553 0.826665 + 1.13781i 0.0351534 + 0.0483845i
554554 −2.08921 1.51790i −0.0887620 0.0644894i
555555 0 0
556556 1.67133 + 5.14384i 0.0708804 + 0.218147i
557557 9.93712 13.6773i 0.421049 0.579524i −0.544821 0.838553i 0.683402π-0.683402\pi
0.965870 + 0.259028i 0.0834023π0.0834023\pi
558558 0.623725 + 0.858484i 0.0264044 + 0.0363425i
559559 1.56490 4.81627i 0.0661882 0.203706i
560560 0 0
561561 −53.5006 + 5.91225i −2.25880 + 0.249616i
562562 2.92984i 0.123588i
563563 −18.1665 5.90264i −0.765625 0.248767i −0.0999340 0.994994i 0.531863π-0.531863\pi
−0.665691 + 0.746227i 0.731863π0.731863\pi
564564 33.6241 24.4293i 1.41583 1.02866i
565565 0 0
566566 0.0699928 + 0.215416i 0.00294202 + 0.00905460i
567567 −27.9848 + 9.09282i −1.17525 + 0.381862i
568568 2.77648 3.82150i 0.116499 0.160346i
569569 −14.3191 + 10.4034i −0.600286 + 0.436133i −0.845980 0.533214i 0.820984π-0.820984\pi
0.245694 + 0.969347i 0.420984π0.420984\pi
570570 0 0
571571 −5.15632 −0.215785 −0.107893 0.994163i 0.534410π-0.534410\pi
−0.107893 + 0.994163i 0.534410π0.534410\pi
572572 −7.69075 1.59183i −0.321567 0.0665577i
573573 62.0141i 2.59068i
574574 0.985225 3.03221i 0.0411225 0.126562i
575575 0 0
576576 36.0696 + 26.2061i 1.50290 + 1.09192i
577577 −19.1835 + 6.23309i −0.798619 + 0.259487i −0.679770 0.733425i 0.737920π-0.737920\pi
−0.118849 + 0.992912i 0.537920π0.537920\pi
578578 1.66308 0.540368i 0.0691751 0.0224763i
579579 −20.5626 14.9396i −0.854552 0.620868i
580580 0 0
581581 1.72478 5.30834i 0.0715561 0.220227i
582582 3.87587i 0.160660i
583583 32.6776 14.7587i 1.35337 0.611241i
584584 4.73947 0.196121
585585 0 0
586586 1.42179 1.03299i 0.0587334 0.0426723i
587587 20.8185 28.6541i 0.859270 1.18268i −0.122474 0.992472i 0.539083π-0.539083\pi
0.981743 0.190211i 0.0609173π-0.0609173\pi
588588 32.2938 10.4929i 1.33177 0.432719i
589589 −1.90984 5.87789i −0.0786936 0.242194i
590590 0 0
591591 −6.28657 + 4.56746i −0.258595 + 0.187880i
592592 11.6755 + 3.79359i 0.479859 + 0.155916i
593593 38.2459i 1.57057i 0.619134 + 0.785285i 0.287484π0.287484\pi
−0.619134 + 0.785285i 0.712516π0.712516\pi
594594 −2.97620 + 2.70871i −0.122115 + 0.111140i
595595 0 0
596596 10.8627 33.4321i 0.444955 1.36943i
597597 −15.4044 21.2023i −0.630459 0.867752i
598598 −0.178500 + 0.245685i −0.00729943 + 0.0100468i
599599 −7.32601 22.5471i −0.299333 0.921251i −0.981732 0.190271i 0.939063π-0.939063\pi
0.682399 0.730980i 0.260937π-0.260937\pi
600600 0 0
601601 −7.93032 5.76172i −0.323485 0.235025i 0.414176 0.910197i 0.364070π-0.364070\pi
−0.737661 + 0.675171i 0.764070π0.764070\pi
602602 1.23886 + 1.70514i 0.0504920 + 0.0694963i
603603 45.8056 + 14.8831i 1.86535 + 0.606088i
604604 −2.87935 −0.117159
605605 0 0
606606 1.09138 0.0443343
607607 2.00862 + 0.652640i 0.0815273 + 0.0264898i 0.349497 0.936938i 0.386353π-0.386353\pi
−0.267969 + 0.963427i 0.586353π0.586353\pi
608608 4.66122 + 6.41562i 0.189037 + 0.260188i
609609 35.7094 + 25.9444i 1.44702 + 1.05132i
610610 0 0
611611 2.59666 + 7.99168i 0.105049 + 0.323309i
612612 −37.4288 + 51.5163i −1.51297 + 2.08242i
613613 −1.66624 2.29338i −0.0672986 0.0926286i 0.774041 0.633136i 0.218232π-0.218232\pi
−0.841340 + 0.540507i 0.818232π0.818232\pi
614614 −0.973800 + 2.99705i −0.0392994 + 0.120951i
615615 0 0
616616 4.85853 4.42186i 0.195756 0.178162i
617617 43.2099i 1.73957i −0.493434 0.869783i 0.664259π-0.664259\pi
0.493434 0.869783i 0.335741π-0.335741\pi
618618 −2.61489 0.849631i −0.105187 0.0341772i
619619 −37.9078 + 27.5416i −1.52364 + 1.10699i −0.563998 + 0.825776i 0.690738π0.690738\pi
−0.959645 + 0.281216i 0.909262π0.909262\pi
620620 0 0
621621 −4.90070 15.0828i −0.196658 0.605252i
622622 2.47308 0.803551i 0.0991613 0.0322195i
623623 14.4862 19.9385i 0.580376 0.798818i
624624 −11.2168 + 8.14946i −0.449030 + 0.326239i
625625 0 0
626626 −2.43738 −0.0974173
627627 43.3437 19.5760i 1.73098 0.781789i
628628 6.64872i 0.265313i
629629 −5.30922 + 16.3401i −0.211693 + 0.651523i
630630 0 0
631631 −4.16305 3.02463i −0.165728 0.120409i 0.501830 0.864966i 0.332660π-0.332660\pi
−0.667558 + 0.744558i 0.732660π0.732660\pi
632632 0.207930 0.0675605i 0.00827101 0.00268741i
633633 −30.6948 + 9.97335i −1.22001 + 0.396405i
634634 1.26141 + 0.916466i 0.0500969 + 0.0363975i
635635 0 0
636636 19.7560 60.8027i 0.783376 2.41098i
637637 6.86517i 0.272008i
638638 1.87501 + 0.388089i 0.0742324 + 0.0153646i
639639 −50.3526 −1.99192
640640 0 0
641641 −13.4838 + 9.79658i −0.532580 + 0.386942i −0.821322 0.570465i 0.806763π-0.806763\pi
0.288742 + 0.957407i 0.406763π0.406763\pi
642642 −3.44040 + 4.73530i −0.135782 + 0.186887i
643643 34.0436 11.0614i 1.34255 0.436220i 0.452368 0.891831i 0.350579π-0.350579\pi
0.890179 + 0.455611i 0.150579π0.150579\pi
644644 3.98058 + 12.2510i 0.156857 + 0.482755i
645645 0 0
646646 −2.94402 + 2.13896i −0.115831 + 0.0841561i
647647 30.3007 + 9.84530i 1.19124 + 0.387059i 0.836533 0.547917i 0.184579π-0.184579\pi
0.354712 + 0.934976i 0.384579π0.384579\pi
648648 4.57421i 0.179692i
649649 13.2392 1.46304i 0.519685 0.0574295i
650650 0 0
651651 −4.23840 + 13.0445i −0.166116 + 0.511253i
652652 −7.92749 10.9113i −0.310465 0.427318i
653653 −1.19071 + 1.63887i −0.0465961 + 0.0641340i −0.831679 0.555256i 0.812620π-0.812620\pi
0.785083 + 0.619390i 0.212620π0.212620\pi
654654 1.58867 + 4.88944i 0.0621221 + 0.191192i
655655 0 0
656656 20.1314 + 14.6263i 0.786001 + 0.571063i
657657 −29.6958 40.8727i −1.15854 1.59460i
658658 −3.32611 1.08072i −0.129665 0.0421308i
659659 14.3580 0.559308 0.279654 0.960101i 0.409780π-0.409780\pi
0.279654 + 0.960101i 0.409780π0.409780\pi
660660 0 0
661661 28.0721 1.09188 0.545938 0.837825i 0.316173π-0.316173\pi
0.545938 + 0.837825i 0.316173π0.316173\pi
662662 −3.41555 1.10978i −0.132749 0.0431328i
663663 −11.4053 15.6981i −0.442947 0.609664i
664664 −0.701956 0.510001i −0.0272412 0.0197919i
665665 0 0
666666 0.805438 + 2.47888i 0.0312101 + 0.0960548i
667667 −4.43526 + 6.10461i −0.171734 + 0.236371i
668668 −22.8658 31.4721i −0.884706 1.21769i
669669 7.42620 22.8555i 0.287113 0.883644i
670670 0 0
671671 41.7223 + 23.7921i 1.61067 + 0.918485i
672672 17.5989i 0.678893i
673673 37.3122 + 12.1235i 1.43828 + 0.467326i 0.921361 0.388708i 0.127079π-0.127079\pi
0.516919 + 0.856034i 0.327079π0.327079\pi
674674 −1.29675 + 0.942144i −0.0499490 + 0.0362900i
675675 0 0
676676 7.08148 + 21.7946i 0.272365 + 0.838252i
677677 −46.9682 + 15.2609i −1.80513 + 0.586524i −0.999979 0.00653953i 0.997918π-0.997918\pi
−0.805156 + 0.593063i 0.797918π0.797918\pi
678678 0.873091 1.20171i 0.0335309 0.0461513i
679679 26.8911 19.5375i 1.03199 0.749782i
680680 0 0
681681 61.8647 2.37066
682682 0.0653531 + 0.591387i 0.00250250 + 0.0226454i
683683 29.7973i 1.14016i 0.821589 + 0.570081i 0.193088π0.193088\pi
−0.821589 + 0.570081i 0.806912π0.806912\pi
684684 17.3865 53.5101i 0.664788 2.04601i
685685 0 0
686686 0.506462 + 0.367966i 0.0193368 + 0.0140490i
687687 22.7527 7.39279i 0.868068 0.282052i
688688 −15.6449 + 5.08334i −0.596456 + 0.193800i
689689 10.4571 + 7.59756i 0.398386 + 0.289444i
690690 0 0
691691 9.94364 30.6034i 0.378274 1.16421i −0.562970 0.826478i 0.690341π-0.690341\pi
0.941243 0.337729i 0.109659π-0.109659\pi
692692 0.463765i 0.0176297i
693693 −68.5754 14.1937i −2.60497 0.539175i
694694 0.120706 0.00458195
695695 0 0
696696 5.55115 4.03314i 0.210416 0.152876i
697697 −20.4699 + 28.1744i −0.775353 + 1.06718i
698698 2.35881 0.766424i 0.0892823 0.0290096i
699699 −23.4905 72.2964i −0.888494 2.73450i
700700 0 0
701701 −10.8560 + 7.88737i −0.410027 + 0.297902i −0.773613 0.633659i 0.781552π-0.781552\pi
0.363586 + 0.931561i 0.381552π0.381552\pi
702702 −1.37972 0.448297i −0.0520741 0.0169199i
703703 15.1807i 0.572549i
704704 10.2897 + 22.7827i 0.387808 + 0.858657i
705705 0 0
706706 0.0480537 0.147894i 0.00180852 0.00556606i
707707 5.50144 + 7.57209i 0.206903 + 0.284778i
708708 13.9596 19.2138i 0.524634 0.722097i
709709 6.97855 + 21.4778i 0.262085 + 0.806615i 0.992351 + 0.123451i 0.0393963π0.0393963\pi
−0.730266 + 0.683163i 0.760604π0.760604\pi
710710 0 0
711711 −1.88545 1.36986i −0.0707097 0.0513736i
712712 −2.25192 3.09950i −0.0843942 0.116159i
713713 −2.22998 0.724565i −0.0835134 0.0271352i
714714 8.07585 0.302231
715715 0 0
716716 −33.6409 −1.25722
717717 −1.55347 0.504754i −0.0580155 0.0188504i
718718 0.124521 + 0.171389i 0.00464710 + 0.00639618i
719719 −21.5922 15.6876i −0.805253 0.585050i 0.107198 0.994238i 0.465812π-0.465812\pi
−0.912450 + 0.409187i 0.865812π0.865812\pi
720720 0 0
721721 −7.28639 22.4252i −0.271359 0.835158i
722722 0.333079 0.458444i 0.0123959 0.0170615i
723723 −38.5403 53.0461i −1.43333 1.97281i
724724 −10.6159 + 32.6724i −0.394537 + 1.21426i
725725 0 0
726726 −4.46808 + 0.999728i −0.165826 + 0.0371034i
727727 10.6151i 0.393693i −0.980434 0.196846i 0.936930π-0.936930\pi
0.980434 0.196846i 0.0630700π-0.0630700\pi
728728 2.25234 + 0.731829i 0.0834772 + 0.0271234i
729729 −23.6282 + 17.1669i −0.875118 + 0.635810i
730730 0 0
731731 −7.11424 21.8954i −0.263130 0.809830i
732732 81.4460 26.4634i 3.01033 0.978115i
733733 7.54772 10.3886i 0.278782 0.383710i −0.646548 0.762873i 0.723788π-0.723788\pi
0.925330 + 0.379163i 0.123788π0.123788\pi
734734 −1.19841 + 0.870694i −0.0442340 + 0.0321379i
735735 0 0
736736 3.00857 0.110897
737737 18.1769 + 19.9719i 0.669553 + 0.735673i
738738 5.28322i 0.194478i
739739 −10.4930 + 32.2942i −0.385992 + 1.18796i 0.549766 + 0.835318i 0.314717π0.314717\pi
−0.935758 + 0.352642i 0.885283π0.885283\pi
740740 0 0
741741 13.8704 + 10.0774i 0.509542 + 0.370204i
742742 −5.11635 + 1.66240i −0.187827 + 0.0610287i
743743 43.8477 14.2470i 1.60862 0.522672i 0.639399 0.768875i 0.279183π-0.279183\pi
0.969218 + 0.246203i 0.0791830π0.0791830\pi
744744 1.72495 + 1.25325i 0.0632398 + 0.0459464i
745745 0 0
746746 −1.20375 + 3.70475i −0.0440723 + 0.135641i
747747 9.24906i 0.338406i
748748 −32.5394 + 14.6963i −1.18976 + 0.537349i
749749 −50.1963 −1.83413
750750 0 0
751751 −33.8831 + 24.6175i −1.23641 + 0.898306i −0.997354 0.0726986i 0.976839π-0.976839\pi
−0.239059 + 0.971005i 0.576839π0.576839\pi
752752 16.0440 22.0827i 0.585065 0.805273i
753753 −17.1879 + 5.58469i −0.626362 + 0.203517i
754754 0.213300 + 0.656470i 0.00776793 + 0.0239072i
755755 0 0
756756 −49.7834 + 36.1697i −1.81060 + 1.31548i
757757 22.1385 + 7.19323i 0.804637 + 0.261442i 0.682325 0.731049i 0.260969π-0.260969\pi
0.122312 + 0.992492i 0.460969π0.460969\pi
758758 2.60281i 0.0945384i
759759 3.65708 17.6688i 0.132744 0.641337i
760760 0 0
761761 6.47737 19.9353i 0.234805 0.722654i −0.762343 0.647174i 0.775951π-0.775951\pi
0.997147 0.0754807i 0.0240491π-0.0240491\pi
762762 −1.53631 2.11455i −0.0556547 0.0766021i
763763 −25.9151 + 35.6691i −0.938190 + 1.29131i
764764 12.7116 + 39.1221i 0.459888 + 1.41539i
765765 0 0
766766 −2.44303 1.77497i −0.0882703 0.0641321i
767767 2.82236 + 3.88465i 0.101910 + 0.140266i
768768 41.0842 + 13.3491i 1.48250 + 0.481693i
769769 −24.9924 −0.901249 −0.450624 0.892714i 0.648799π-0.648799\pi
−0.450624 + 0.892714i 0.648799π0.648799\pi
770770 0 0
771771 −9.12960 −0.328795
772772 −16.0344 5.20989i −0.577090 0.187508i
773773 12.8231 + 17.6495i 0.461215 + 0.634808i 0.974760 0.223254i 0.0716681π-0.0716681\pi
−0.513545 + 0.858063i 0.671668π0.671668\pi
774774 −2.82557 2.05289i −0.101563 0.0737898i
775775 0 0
776776 −1.59674 4.91425i −0.0573195 0.176411i
777777 −19.8022 + 27.2554i −0.710401 + 0.977783i
778778 −3.07112 4.22703i −0.110105 0.151546i
779779 9.50871 29.2648i 0.340685 1.04852i
780780 0 0
781781 −24.5254 13.9856i −0.877589 0.500445i
782782 1.38058i 0.0493696i
783783 −34.2823 11.1390i −1.22515 0.398075i
784784 18.0414 13.1079i 0.644337 0.468138i
785785 0 0
786786 −2.37637 7.31371i −0.0847623 0.260871i
787787 22.6190 7.34937i 0.806281 0.261977i 0.123259 0.992374i 0.460665π-0.460665\pi
0.683022 + 0.730398i 0.260665π0.260665\pi
788788 −3.02971 + 4.17003i −0.107929 + 0.148551i
789789 −43.8103 + 31.8300i −1.55969 + 1.13318i
790790 0 0
791791 12.7386 0.452933
792792 −5.39267 + 9.45668i −0.191620 + 0.336029i
793793 17.3142i 0.614845i
794794 −0.788689 + 2.42733i −0.0279895 + 0.0861429i
795795 0 0
796796 −14.0640 10.2181i −0.498485 0.362171i
797797 −33.9877 + 11.0433i −1.20391 + 0.391173i −0.841197 0.540729i 0.818149π-0.818149\pi
−0.362711 + 0.931902i 0.618149π0.618149\pi
798798 −6.78636 + 2.20502i −0.240234 + 0.0780569i
799799 30.9052 + 22.4540i 1.09335 + 0.794364i
800800 0 0
801801 −12.6201 + 38.8406i −0.445909 + 1.37237i
802802 1.82447i 0.0644244i
803803 −3.11149 28.1561i −0.109802 0.993609i
804804 48.1506 1.69814
805805 0 0
806806 −0.173524 + 0.126073i −0.00611214 + 0.00444073i
807807 −30.6111 + 42.1325i −1.07756 + 1.48313i
808808 1.38377 0.449614i 0.0486809 0.0158174i
809809 12.8563 + 39.5676i 0.452003 + 1.39112i 0.874618 + 0.484812i 0.161112π0.161112\pi
−0.422616 + 0.906309i 0.638888π0.638888\pi
810810 0 0
811811 −19.5592 + 14.2106i −0.686815 + 0.499001i −0.875612 0.483016i 0.839541π-0.839541\pi
0.188796 + 0.982016i 0.439541π0.439541\pi
812812 27.8457 + 9.04761i 0.977192 + 0.317509i
813813 21.0371i 0.737802i
814814 −0.296211 + 1.43111i −0.0103822 + 0.0501605i
815815 0 0
816816 −19.4776 + 59.9458i −0.681851 + 2.09852i
817817 11.9566 + 16.4568i 0.418308 + 0.575751i
818818 −1.74236 + 2.39815i −0.0609202 + 0.0838494i
819819 −7.80109 24.0093i −0.272592 0.838953i
820820 0 0
821821 −27.5371 20.0069i −0.961051 0.698244i −0.00765641 0.999971i 0.502437π-0.502437\pi
−0.953395 + 0.301726i 0.902437π0.902437\pi
822822 1.02182 + 1.40642i 0.0356401 + 0.0490544i
823823 5.26935 + 1.71212i 0.183678 + 0.0596806i 0.399412 0.916772i 0.369214π-0.369214\pi
−0.215734 + 0.976452i 0.569214π0.569214\pi
824824 −3.66547 −0.127693
825825 0 0
826826 −1.99845 −0.0695348
827827 24.4148 + 7.93284i 0.848984 + 0.275852i 0.701021 0.713141i 0.252728π-0.252728\pi
0.147964 + 0.988993i 0.452728π0.452728\pi
828828 −12.5466 17.2690i −0.436026 0.600138i
829829 33.7819 + 24.5440i 1.17329 + 0.852449i 0.991400 0.130869i 0.0417768π-0.0417768\pi
0.181895 + 0.983318i 0.441777π0.441777\pi
830830 0 0
831831 17.0922 + 52.6043i 0.592921 + 1.82482i
832832 −5.29701 + 7.29071i −0.183641 + 0.252760i
833833 18.3448 + 25.2494i 0.635609 + 0.874840i
834834 −0.351245 + 1.08102i −0.0121626 + 0.0374327i
835835 0 0
836836 23.3311 21.2342i 0.806923 0.734400i
837837 11.2010i 0.387164i
838838 4.98007 + 1.61812i 0.172034 + 0.0558971i
839839 8.29817 6.02897i 0.286485 0.208143i −0.435256 0.900307i 0.643342π-0.643342\pi
0.721741 + 0.692163i 0.243342π0.243342\pi
840840 0 0
841841 −3.66156 11.2691i −0.126261 0.388590i
842842 1.21489 0.394743i 0.0418680 0.0136037i
843843 36.8853 50.7682i 1.27040 1.74855i
844844 −17.3198 + 12.5836i −0.596172 + 0.433144i
845845 0 0
846846 5.79530 0.199246
847847 −29.4590 25.9605i −1.01222 0.892012i
848848 41.9873i 1.44185i
849849 1.49915 4.61390i 0.0514506 0.158349i
850850 0 0
851851 −4.65938 3.38524i −0.159721 0.116044i
852852 −47.8760 + 15.5558i −1.64020 + 0.532935i
853853 −27.4331 + 8.91356i −0.939292 + 0.305195i −0.738357 0.674410i 0.764398π-0.764398\pi
−0.200935 + 0.979605i 0.564398π0.564398\pi
854854 −5.82986 4.23564i −0.199494 0.144941i
855855 0 0
856856 −2.41131 + 7.42126i −0.0824170 + 0.253653i
857857 20.7640i 0.709283i 0.935002 + 0.354642i 0.115397π0.115397\pi
−0.935002 + 0.354642i 0.884603π0.884603\pi
858858 −1.11096 1.22067i −0.0379275 0.0416729i
859859 −12.1297 −0.413859 −0.206929 0.978356i 0.566347π-0.566347\pi
−0.206929 + 0.978356i 0.566347π0.566347\pi
860860 0 0
861861 −55.2461 + 40.1386i −1.88278 + 1.36792i
862862 2.28916 3.15076i 0.0779692 0.107315i
863863 −35.5836 + 11.5618i −1.21128 + 0.393568i −0.843899 0.536503i 0.819745π-0.819745\pi
−0.367380 + 0.930071i 0.619745π0.619745\pi
864864 4.44126 + 13.6688i 0.151095 + 0.465022i
865865 0 0
866866 2.29517 1.66754i 0.0779929 0.0566652i
867867 −35.6209 11.5739i −1.20975 0.393071i
868868 9.09800i 0.308806i
869869 −0.537869 1.19091i −0.0182460 0.0403989i
870870 0 0
871871 −3.00831 + 9.25864i −0.101933 + 0.313717i
872872 4.02859 + 5.54487i 0.136425 + 0.187773i
873873 −32.3754 + 44.5609i −1.09574 + 1.50816i
874874 −0.376953 1.16014i −0.0127506 0.0392424i
875875 0 0
876876 −40.8623 29.6882i −1.38061 1.00307i
877877 30.7915 + 42.3808i 1.03975 + 1.43110i 0.897365 + 0.441289i 0.145479π0.145479\pi
0.142389 + 0.989811i 0.454521π0.454521\pi
878878 0.778593 + 0.252980i 0.0262762 + 0.00853767i
879879 −37.6416 −1.26962
880880 0 0
881881 11.0403 0.371956 0.185978 0.982554i 0.440455π-0.440455\pi
0.185978 + 0.982554i 0.440455π0.440455\pi
882882 4.50299 + 1.46311i 0.151624 + 0.0492655i
883883 14.2179 + 19.5693i 0.478470 + 0.658558i 0.978210 0.207618i 0.0665710π-0.0665710\pi
−0.499740 + 0.866176i 0.666571π0.666571\pi
884884 −10.4129 7.56545i −0.350225 0.254453i
885885 0 0
886886 −1.55599 4.78883i −0.0522744 0.160884i
887887 10.2457 14.1020i 0.344016 0.473497i −0.601593 0.798803i 0.705467π-0.705467\pi
0.945609 + 0.325305i 0.105467π0.105467\pi
888888 3.07832 + 4.23694i 0.103302 + 0.142183i
889889 6.92668 21.3181i 0.232313 0.714987i
890890 0 0
891891 27.1743 3.00299i 0.910374 0.100604i
892892 15.9408i 0.533738i
893893 −32.1013 10.4303i −1.07423 0.349038i
894894 5.97669 4.34232i 0.199891 0.145229i
895895 0 0
896896 −4.80182 14.7785i −0.160418 0.493714i
897897 6.18611 2.00999i 0.206548 0.0671116i
898898 −0.561461 + 0.772785i −0.0187362 + 0.0257882i
899899 −4.31162 + 3.13257i −0.143801 + 0.104477i
900900 0 0
901901 58.7622 1.95765
902902 −1.46743 + 2.57332i −0.0488602 + 0.0856821i
903903 45.1433i 1.50228i
904904 0.611934 1.88334i 0.0203526 0.0626389i
905905 0 0
906906 −0.489551 0.355680i −0.0162643 0.0118167i
907907 12.3385 4.00901i 0.409692 0.133117i −0.0969182 0.995292i 0.530899π-0.530899\pi
0.506610 + 0.862176i 0.330899π0.330899\pi
908908 39.0279 12.6809i 1.29519 0.420832i
909909 −12.5476 9.11637i −0.416178 0.302371i
910910 0 0
911911 −6.28687 + 19.3490i −0.208293 + 0.641061i 0.791269 + 0.611468i 0.209421π0.209421\pi
−0.999562 + 0.0295922i 0.990579π0.990579\pi
912912 55.6922i 1.84415i
913913 −2.56896 + 4.50498i −0.0850202 + 0.149093i
914914 −2.97102 −0.0982725
915915 0 0
916916 12.8384 9.32761i 0.424191 0.308193i
917917 38.7643 53.3545i 1.28011 1.76192i
918918 −6.27238 + 2.03802i −0.207019 + 0.0672647i
919919 −2.73013 8.40248i −0.0900587 0.277172i 0.895876 0.444305i 0.146549π-0.146549\pi
−0.985934 + 0.167133i 0.946549π0.946549\pi
920920 0 0
921921 54.6054 39.6732i 1.79931 1.30728i
922922 −3.84650 1.24980i −0.126678 0.0411601i
923923 10.1777i 0.335004i
924924 −69.5875 + 7.69000i −2.28926 + 0.252982i
925925 0 0
926926 0.768475 2.36512i 0.0252537 0.0777228i
927927 22.9664 + 31.6106i 0.754317 + 1.03823i
928928 4.01945 5.53230i 0.131945 0.181607i
929929 −4.77831 14.7061i −0.156771 0.482492i 0.841565 0.540156i 0.181635π-0.181635\pi
−0.998336 + 0.0576639i 0.981635π0.981635\pi
930930 0 0
931931 −22.3097 16.2089i −0.731170 0.531226i
932932 −29.6384 40.7938i −0.970839 1.33625i
933933 −52.9698 17.2109i −1.73415 0.563461i
934934 −0.557931 −0.0182561
935935 0 0
936936 −3.92439 −0.128273
937937 39.6078 + 12.8694i 1.29393 + 0.420424i 0.873466 0.486885i 0.161867π-0.161867\pi
0.420465 + 0.907309i 0.361867π0.361867\pi
938938 −2.38154 3.27791i −0.0777601 0.107028i
939939 42.2349 + 30.6855i 1.37828 + 1.00138i
940940 0 0
941941 14.6364 + 45.0462i 0.477133 + 1.46847i 0.843059 + 0.537821i 0.180753π0.180753\pi
−0.365925 + 0.930644i 0.619247π0.619247\pi
942942 0.821303 1.13043i 0.0267595 0.0368313i
943943 −6.86179 9.44445i −0.223451 0.307553i
944944 4.81991 14.8341i 0.156875 0.482810i
945945 0 0
946946 −0.806061 1.78472i −0.0262073 0.0580263i
947947 41.5599i 1.35052i 0.737581 + 0.675258i 0.235968π0.235968\pi
−0.737581 + 0.675258i 0.764032π0.764032\pi
948948 −2.21591 0.719993i −0.0719695 0.0233843i
949949 8.26156 6.00238i 0.268182 0.194845i
950950 0 0
951951 −10.3198 31.7611i −0.334642 1.02992i
952952 10.2394 3.32699i 0.331862 0.107829i
953953 −16.5498 + 22.7788i −0.536099 + 0.737877i −0.988045 0.154169i 0.950730π-0.950730\pi
0.451946 + 0.892046i 0.350730π0.350730\pi
954954 7.21202 5.23984i 0.233498 0.169646i
955955 0 0
956956 −1.08349 −0.0350425
957957 −27.6044 30.3303i −0.892322 0.980440i
958958 0.167824i 0.00542215i
959959 −4.60702 + 14.1790i −0.148769 + 0.457862i
960960 0 0
961961 23.7397 + 17.2479i 0.765798 + 0.556385i
962962 −0.501055 + 0.162802i −0.0161546 + 0.00524896i
963963 79.1085 25.7039i 2.54924 0.828297i
964964 −35.1868 25.5647i −1.13329 0.823384i
965965 0 0
966966 −0.836551 + 2.57464i −0.0269156 + 0.0828377i
967967 53.8069i 1.73031i −0.501502 0.865157i 0.667219π-0.667219\pi
0.501502 0.865157i 0.332781π-0.332781\pi
968968 −5.25326 + 3.10827i −0.168846 + 0.0999036i
969969 77.9425 2.50387
970970 0 0
971971 9.60235 6.97651i 0.308154 0.223887i −0.422950 0.906153i 0.639005π-0.639005\pi
0.731104 + 0.682266i 0.239005π0.239005\pi
972972 −1.74527 + 2.40216i −0.0559797 + 0.0770494i
973973 −9.27077 + 3.01226i −0.297207 + 0.0965685i
974974 −1.82053 5.60302i −0.0583336 0.179532i
975975 0 0
976976 45.5011 33.0585i 1.45646 1.05818i
977977 −32.9916 10.7196i −1.05550 0.342951i −0.270673 0.962671i 0.587246π-0.587246\pi
−0.784823 + 0.619720i 0.787246π0.787246\pi
978978 2.83442i 0.0906346i
979979 −16.9350 + 15.4130i −0.541246 + 0.492601i
980980 0 0
981981 22.5768 69.4842i 0.720821 2.21846i
982982 −1.49805 2.06189i −0.0478047 0.0657975i
983983 33.4617 46.0561i 1.06726 1.46896i 0.194446 0.980913i 0.437709π-0.437709\pi
0.872817 0.488048i 0.162291π-0.162291\pi
984984 3.28039 + 10.0960i 0.104575 + 0.321849i
985985 0 0
986986 2.53868 + 1.84446i 0.0808482 + 0.0587396i
987987 44.0291 + 60.6009i 1.40146 + 1.92895i
988988 10.8159 + 3.51431i 0.344101 + 0.111805i
989989 7.71735 0.245397
990990 0 0
991991 36.4470 1.15778 0.578889 0.815407i 0.303487π-0.303487\pi
0.578889 + 0.815407i 0.303487π0.303487\pi
992992 2.02092 + 0.656637i 0.0641643 + 0.0208482i
993993 45.2131 + 62.2305i 1.43479 + 1.97482i
994994 3.42694 + 2.48982i 0.108696 + 0.0789722i
995995 0 0
996996 2.85739 + 8.79415i 0.0905399 + 0.278653i
997997 14.1584 19.4874i 0.448402 0.617173i −0.523651 0.851933i 0.675430π-0.675430\pi
0.972053 + 0.234760i 0.0754304π0.0754304\pi
998998 1.85875 + 2.55835i 0.0588378 + 0.0809833i
999999 8.50189 26.1661i 0.268988 0.827860i
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 275.2.z.c.174.5 32
5.2 odd 4 275.2.h.c.251.3 yes 16
5.3 odd 4 275.2.h.e.251.2 yes 16
5.4 even 2 inner 275.2.z.c.174.4 32
11.5 even 5 inner 275.2.z.c.49.4 32
55.7 even 20 3025.2.a.bm.1.4 8
55.18 even 20 3025.2.a.bj.1.5 8
55.27 odd 20 275.2.h.c.126.3 16
55.37 odd 20 3025.2.a.bi.1.5 8
55.38 odd 20 275.2.h.e.126.2 yes 16
55.48 odd 20 3025.2.a.bn.1.4 8
55.49 even 10 inner 275.2.z.c.49.5 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
275.2.h.c.126.3 16 55.27 odd 20
275.2.h.c.251.3 yes 16 5.2 odd 4
275.2.h.e.126.2 yes 16 55.38 odd 20
275.2.h.e.251.2 yes 16 5.3 odd 4
275.2.z.c.49.4 32 11.5 even 5 inner
275.2.z.c.49.5 32 55.49 even 10 inner
275.2.z.c.174.4 32 5.4 even 2 inner
275.2.z.c.174.5 32 1.1 even 1 trivial
3025.2.a.bi.1.5 8 55.37 odd 20
3025.2.a.bj.1.5 8 55.18 even 20
3025.2.a.bm.1.4 8 55.7 even 20
3025.2.a.bn.1.4 8 55.48 odd 20