Properties

Label 150.3.d.c.101.4
Level 150150
Weight 33
Character 150.101
Analytic conductor 4.0874.087
Analytic rank 00
Dimension 44
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] = [150,3,Mod(101,150)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(150, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("150.101"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Level: N N == 150=2352 150 = 2 \cdot 3 \cdot 5^{2}
Weight: k k == 3 3
Character orbit: [χ][\chi] == 150.d (of order 22, degree 11, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.087203965404.08720396540
Analytic rank: 00
Dimension: 44
Coefficient field: Q(2,5)\Q(\sqrt{-2}, \sqrt{-5})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x44x2+9 x^{4} - 4x^{2} + 9 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 3 3
Twist minimal: no (minimal twist has level 30)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 101.4
Root 1.58114+0.707107i-1.58114 + 0.707107i of defining polynomial
Character χ\chi == 150.101
Dual form 150.3.d.c.101.2

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+1.41421iq2+(0.581139+2.94317i)q32.00000q4+(4.16228+0.821854i)q611.4868q72.82843iq8+(8.32456+3.42079i)q9+8.48528iq11+(1.162285.88635i)q12+10.0000q1316.2448iq14+4.00000q16+3.55415iq17+(4.8377211.7727i)q1810.9737q19+(6.6754433.8078i)q2112.0000q22+17.6590iq23+(8.324561.64371i)q24+14.1421iq26+(14.905722.5127i)q27+22.9737q28+26.8328iq29+8.00000q31+5.65685iq32+(24.9737+4.93113i)q335.02633q34+(16.64916.84157i)q36+59.9473q3715.5191iq38+(5.81139+29.4317i)q39+20.5247iq41+(47.81149.44050i)q4242.4605q4316.9706iq4424.9737q46+88.2952iq47+(2.32456+11.7727i)q48+82.9473q49+(10.4605+2.06546i)q5120.0000q52+3.55415iq53+(31.837721.0798i)q54+32.4897iq56+(6.3772232.2974i)q5737.9473q5877.7445iq59+21.9473q61+11.3137iq62+(95.622839.2940i)q638.00000q64+(6.9736735.3181i)q66+53.5395q677.10831iq68+(51.9737+10.2624i)q69+69.2592iq71+(9.67544+23.5454i)q7212.0527q73+84.7783iq74+21.9473q7697.4690iq77+(41.6228+8.21854i)q789.02633q79+(57.596456.9530i)q8129.0263q82+0.688486iq83+(13.3509+67.6155i)q8460.0482iq86+(78.9737+15.5936i)q87+24.0000q88+7.10831iq89114.868q9135.3181iq92+(4.64911+23.5454i)q93124.868q94+(16.6491+3.28742i)q96111.947q97+117.305iq98+(29.026370.6362i)q99+O(q100)q+1.41421i q^{2} +(0.581139 + 2.94317i) q^{3} -2.00000 q^{4} +(-4.16228 + 0.821854i) q^{6} -11.4868 q^{7} -2.82843i q^{8} +(-8.32456 + 3.42079i) q^{9} +8.48528i q^{11} +(-1.16228 - 5.88635i) q^{12} +10.0000 q^{13} -16.2448i q^{14} +4.00000 q^{16} +3.55415i q^{17} +(-4.83772 - 11.7727i) q^{18} -10.9737 q^{19} +(-6.67544 - 33.8078i) q^{21} -12.0000 q^{22} +17.6590i q^{23} +(8.32456 - 1.64371i) q^{24} +14.1421i q^{26} +(-14.9057 - 22.5127i) q^{27} +22.9737 q^{28} +26.8328i q^{29} +8.00000 q^{31} +5.65685i q^{32} +(-24.9737 + 4.93113i) q^{33} -5.02633 q^{34} +(16.6491 - 6.84157i) q^{36} +59.9473 q^{37} -15.5191i q^{38} +(5.81139 + 29.4317i) q^{39} +20.5247i q^{41} +(47.8114 - 9.44050i) q^{42} -42.4605 q^{43} -16.9706i q^{44} -24.9737 q^{46} +88.2952i q^{47} +(2.32456 + 11.7727i) q^{48} +82.9473 q^{49} +(-10.4605 + 2.06546i) q^{51} -20.0000 q^{52} +3.55415i q^{53} +(31.8377 - 21.0798i) q^{54} +32.4897i q^{56} +(-6.37722 - 32.2974i) q^{57} -37.9473 q^{58} -77.7445i q^{59} +21.9473 q^{61} +11.3137i q^{62} +(95.6228 - 39.2940i) q^{63} -8.00000 q^{64} +(-6.97367 - 35.3181i) q^{66} +53.5395 q^{67} -7.10831i q^{68} +(-51.9737 + 10.2624i) q^{69} +69.2592i q^{71} +(9.67544 + 23.5454i) q^{72} -12.0527 q^{73} +84.7783i q^{74} +21.9473 q^{76} -97.4690i q^{77} +(-41.6228 + 8.21854i) q^{78} -9.02633 q^{79} +(57.5964 - 56.9530i) q^{81} -29.0263 q^{82} +0.688486i q^{83} +(13.3509 + 67.6155i) q^{84} -60.0482i q^{86} +(-78.9737 + 15.5936i) q^{87} +24.0000 q^{88} +7.10831i q^{89} -114.868 q^{91} -35.3181i q^{92} +(4.64911 + 23.5454i) q^{93} -124.868 q^{94} +(-16.6491 + 3.28742i) q^{96} -111.947 q^{97} +117.305i q^{98} +(-29.0263 - 70.6362i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q4q38q44q68q78q9+8q12+40q13+16q1632q18+32q1952q2148q22+8q2428q27+16q28+32q3124q3396q34+192q99+O(q100) 4 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 8 q^{9} + 8 q^{12} + 40 q^{13} + 16 q^{16} - 32 q^{18} + 32 q^{19} - 52 q^{21} - 48 q^{22} + 8 q^{24} - 28 q^{27} + 16 q^{28} + 32 q^{31} - 24 q^{33} - 96 q^{34}+ \cdots - 192 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/150Z)×\left(\mathbb{Z}/150\mathbb{Z}\right)^\times.

nn 101101 127127
χ(n)\chi(n) 1-1 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.41421i 0.707107i
33 0.581139 + 2.94317i 0.193713 + 0.981058i
44 −2.00000 −0.500000
55 0 0
66 −4.16228 + 0.821854i −0.693713 + 0.136976i
77 −11.4868 −1.64098 −0.820488 0.571664i 0.806298π-0.806298\pi
−0.820488 + 0.571664i 0.806298π0.806298\pi
88 2.82843i 0.353553i
99 −8.32456 + 3.42079i −0.924951 + 0.380087i
1010 0 0
1111 8.48528i 0.771389i 0.922627 + 0.385695i 0.126038π0.126038\pi
−0.922627 + 0.385695i 0.873962π0.873962\pi
1212 −1.16228 5.88635i −0.0968565 0.490529i
1313 10.0000 0.769231 0.384615 0.923077i 0.374334π-0.374334\pi
0.384615 + 0.923077i 0.374334π0.374334\pi
1414 16.2448i 1.16035i
1515 0 0
1616 4.00000 0.250000
1717 3.55415i 0.209068i 0.994521 + 0.104534i 0.0333351π0.0333351\pi
−0.994521 + 0.104534i 0.966665π0.966665\pi
1818 −4.83772 11.7727i −0.268762 0.654039i
1919 −10.9737 −0.577561 −0.288781 0.957395i 0.593250π-0.593250\pi
−0.288781 + 0.957395i 0.593250π0.593250\pi
2020 0 0
2121 −6.67544 33.8078i −0.317878 1.60989i
2222 −12.0000 −0.545455
2323 17.6590i 0.767785i 0.923378 + 0.383892i 0.125417π0.125417\pi
−0.923378 + 0.383892i 0.874583π0.874583\pi
2424 8.32456 1.64371i 0.346856 0.0684879i
2525 0 0
2626 14.1421i 0.543928i
2727 −14.9057 22.5127i −0.552063 0.833803i
2828 22.9737 0.820488
2929 26.8328i 0.925270i 0.886549 + 0.462635i 0.153096π0.153096\pi
−0.886549 + 0.462635i 0.846904π0.846904\pi
3030 0 0
3131 8.00000 0.258065 0.129032 0.991640i 0.458813π-0.458813\pi
0.129032 + 0.991640i 0.458813π0.458813\pi
3232 5.65685i 0.176777i
3333 −24.9737 + 4.93113i −0.756778 + 0.149428i
3434 −5.02633 −0.147833
3535 0 0
3636 16.6491 6.84157i 0.462475 0.190044i
3737 59.9473 1.62020 0.810099 0.586293i 0.199413π-0.199413\pi
0.810099 + 0.586293i 0.199413π0.199413\pi
3838 15.5191i 0.408398i
3939 5.81139 + 29.4317i 0.149010 + 0.754660i
4040 0 0
4141 20.5247i 0.500603i 0.968168 + 0.250301i 0.0805297π0.0805297\pi
−0.968168 + 0.250301i 0.919470π0.919470\pi
4242 47.8114 9.44050i 1.13837 0.224774i
4343 −42.4605 −0.987453 −0.493727 0.869617i 0.664366π-0.664366\pi
−0.493727 + 0.869617i 0.664366π0.664366\pi
4444 16.9706i 0.385695i
4545 0 0
4646 −24.9737 −0.542906
4747 88.2952i 1.87862i 0.343067 + 0.939311i 0.388534π0.388534\pi
−0.343067 + 0.939311i 0.611466π0.611466\pi
4848 2.32456 + 11.7727i 0.0484282 + 0.245265i
4949 82.9473 1.69280
5050 0 0
5151 −10.4605 + 2.06546i −0.205108 + 0.0404992i
5252 −20.0000 −0.384615
5353 3.55415i 0.0670595i 0.999438 + 0.0335298i 0.0106749π0.0106749\pi
−0.999438 + 0.0335298i 0.989325π0.989325\pi
5454 31.8377 21.0798i 0.589587 0.390367i
5555 0 0
5656 32.4897i 0.580173i
5757 −6.37722 32.2974i −0.111881 0.566621i
5858 −37.9473 −0.654264
5959 77.7445i 1.31770i −0.752273 0.658852i 0.771042π-0.771042\pi
0.752273 0.658852i 0.228958π-0.228958\pi
6060 0 0
6161 21.9473 0.359792 0.179896 0.983686i 0.442424π-0.442424\pi
0.179896 + 0.983686i 0.442424π0.442424\pi
6262 11.3137i 0.182479i
6363 95.6228 39.2940i 1.51782 0.623714i
6464 −8.00000 −0.125000
6565 0 0
6666 −6.97367 35.3181i −0.105662 0.535123i
6767 53.5395 0.799097 0.399549 0.916712i 0.369167π-0.369167\pi
0.399549 + 0.916712i 0.369167π0.369167\pi
6868 7.10831i 0.104534i
6969 −51.9737 + 10.2624i −0.753242 + 0.148730i
7070 0 0
7171 69.2592i 0.975482i 0.872988 + 0.487741i 0.162179π0.162179\pi
−0.872988 + 0.487741i 0.837821π0.837821\pi
7272 9.67544 + 23.5454i 0.134381 + 0.327019i
7373 −12.0527 −0.165105 −0.0825525 0.996587i 0.526307π-0.526307\pi
−0.0825525 + 0.996587i 0.526307π0.526307\pi
7474 84.7783i 1.14565i
7575 0 0
7676 21.9473 0.288781
7777 97.4690i 1.26583i
7878 −41.6228 + 8.21854i −0.533625 + 0.105366i
7979 −9.02633 −0.114257 −0.0571287 0.998367i 0.518195π-0.518195\pi
−0.0571287 + 0.998367i 0.518195π0.518195\pi
8080 0 0
8181 57.5964 56.9530i 0.711067 0.703124i
8282 −29.0263 −0.353980
8383 0.688486i 0.00829501i 0.999991 + 0.00414750i 0.00132020π0.00132020\pi
−0.999991 + 0.00414750i 0.998680π0.998680\pi
8484 13.3509 + 67.6155i 0.158939 + 0.804947i
8585 0 0
8686 60.0482i 0.698235i
8787 −78.9737 + 15.5936i −0.907743 + 0.179237i
8888 24.0000 0.272727
8989 7.10831i 0.0798686i 0.999202 + 0.0399343i 0.0127149π0.0127149\pi
−0.999202 + 0.0399343i 0.987285π0.987285\pi
9090 0 0
9191 −114.868 −1.26229
9292 35.3181i 0.383892i
9393 4.64911 + 23.5454i 0.0499904 + 0.253176i
9494 −124.868 −1.32839
9595 0 0
9696 −16.6491 + 3.28742i −0.173428 + 0.0342439i
9797 −111.947 −1.15410 −0.577048 0.816710i 0.695795π-0.695795\pi
−0.577048 + 0.816710i 0.695795π0.695795\pi
9898 117.305i 1.19699i
9999 −29.0263 70.6362i −0.293195 0.713497i
100100 0 0
101101 155.489i 1.53950i −0.638348 0.769748i 0.720382π-0.720382\pi
0.638348 0.769748i 0.279618π-0.279618\pi
102102 −2.92100 14.7934i −0.0286372 0.145033i
103103 −7.59217 −0.0737104 −0.0368552 0.999321i 0.511734π-0.511734\pi
−0.0368552 + 0.999321i 0.511734π0.511734\pi
104104 28.2843i 0.271964i
105105 0 0
106106 −5.02633 −0.0474182
107107 16.2821i 0.152169i 0.997101 + 0.0760845i 0.0242419π0.0242419\pi
−0.997101 + 0.0760845i 0.975758π0.975758\pi
108108 29.8114 + 45.0253i 0.276031 + 0.416901i
109109 −93.8420 −0.860936 −0.430468 0.902606i 0.641651π-0.641651\pi
−0.430468 + 0.902606i 0.641651π0.641651\pi
110110 0 0
111111 34.8377 + 176.435i 0.313853 + 1.58951i
112112 −45.9473 −0.410244
113113 195.738i 1.73220i −0.499874 0.866098i 0.666620π-0.666620\pi
0.499874 0.866098i 0.333380π-0.333380\pi
114114 45.6754 9.01876i 0.400662 0.0791119i
115115 0 0
116116 53.6656i 0.462635i
117117 −83.2456 + 34.2079i −0.711500 + 0.292375i
118118 109.947 0.931757
119119 40.8260i 0.343075i
120120 0 0
121121 49.0000 0.404959
122122 31.0382i 0.254412i
123123 −60.4078 + 11.9277i −0.491121 + 0.0969733i
124124 −16.0000 −0.129032
125125 0 0
126126 55.5701 + 135.231i 0.441033 + 1.07326i
127127 77.5395 0.610547 0.305274 0.952265i 0.401252π-0.401252\pi
0.305274 + 0.952265i 0.401252π0.401252\pi
128128 11.3137i 0.0883883i
129129 −24.6754 124.969i −0.191283 0.968749i
130130 0 0
131131 101.600i 0.775572i 0.921749 + 0.387786i 0.126760π0.126760\pi
−0.921749 + 0.387786i 0.873240π0.873240\pi
132132 49.9473 9.86225i 0.378389 0.0747140i
133133 126.053 0.947764
134134 75.7163i 0.565047i
135135 0 0
136136 10.0527 0.0739167
137137 176.014i 1.28477i −0.766381 0.642386i 0.777945π-0.777945\pi
0.766381 0.642386i 0.222055π-0.222055\pi
138138 −14.5132 73.5019i −0.105168 0.532622i
139139 188.816 1.35839 0.679193 0.733960i 0.262330π-0.262330\pi
0.679193 + 0.733960i 0.262330π0.262330\pi
140140 0 0
141141 −259.868 + 51.3118i −1.84304 + 0.363913i
142142 −97.9473 −0.689770
143143 84.8528i 0.593376i
144144 −33.2982 + 13.6831i −0.231238 + 0.0950218i
145145 0 0
146146 17.0450i 0.116747i
147147 48.2039 + 244.128i 0.327918 + 1.66074i
148148 −119.895 −0.810099
149149 72.5899i 0.487181i 0.969878 + 0.243590i 0.0783252π0.0783252\pi
−0.969878 + 0.243590i 0.921675π0.921675\pi
150150 0 0
151151 93.9473 0.622168 0.311084 0.950382i 0.399308π-0.399308\pi
0.311084 + 0.950382i 0.399308π0.399308\pi
152152 31.0382i 0.204199i
153153 −12.1580 29.5868i −0.0794641 0.193378i
154154 137.842 0.895078
155155 0 0
156156 −11.6228 58.8635i −0.0745050 0.377330i
157157 123.842 0.788803 0.394401 0.918938i 0.370952π-0.370952\pi
0.394401 + 0.918938i 0.370952π0.370952\pi
158158 12.7652i 0.0807922i
159159 −10.4605 + 2.06546i −0.0657893 + 0.0129903i
160160 0 0
161161 202.847i 1.25992i
162162 80.5438 + 81.4537i 0.497184 + 0.502800i
163163 −159.381 −0.977801 −0.488900 0.872340i 0.662602π-0.662602\pi
−0.488900 + 0.872340i 0.662602π0.662602\pi
164164 41.0494i 0.250301i
165165 0 0
166166 −0.973666 −0.00586546
167167 10.7742i 0.0645161i −0.999480 0.0322581i 0.989730π-0.989730\pi
0.999480 0.0322581i 0.0102698π-0.0102698\pi
168168 −95.6228 + 18.8810i −0.569183 + 0.112387i
169169 −69.0000 −0.408284
170170 0 0
171171 91.3509 37.5386i 0.534216 0.219524i
172172 84.9210 0.493727
173173 283.345i 1.63783i 0.573913 + 0.818916i 0.305425π0.305425\pi
−0.573913 + 0.818916i 0.694575π0.694575\pi
174174 −22.0527 111.686i −0.126739 0.641871i
175175 0 0
176176 33.9411i 0.192847i
177177 228.816 45.1804i 1.29274 0.255256i
178178 −10.0527 −0.0564757
179179 306.624i 1.71298i 0.516163 + 0.856491i 0.327360π0.327360\pi
−0.516163 + 0.856491i 0.672640π0.672640\pi
180180 0 0
181181 265.684 1.46787 0.733934 0.679221i 0.237682π-0.237682\pi
0.733934 + 0.679221i 0.237682π0.237682\pi
182182 162.448i 0.892573i
183183 12.7544 + 64.5948i 0.0696964 + 0.352977i
184184 49.9473 0.271453
185185 0 0
186186 −33.2982 + 6.57484i −0.179023 + 0.0353486i
187187 −30.1580 −0.161273
188188 176.590i 0.939311i
189189 171.219 + 258.599i 0.905922 + 1.36825i
190190 0 0
191191 159.620i 0.835706i −0.908515 0.417853i 0.862783π-0.862783\pi
0.908515 0.417853i 0.137217π-0.137217\pi
192192 −4.64911 23.5454i −0.0242141 0.122632i
193193 92.0527 0.476957 0.238478 0.971148i 0.423351π-0.423351\pi
0.238478 + 0.971148i 0.423351π0.423351\pi
194194 158.317i 0.816069i
195195 0 0
196196 −165.895 −0.846401
197197 69.8360i 0.354497i 0.984166 + 0.177249i 0.0567197π0.0567197\pi
−0.984166 + 0.177249i 0.943280π0.943280\pi
198198 99.8947 41.0494i 0.504519 0.207320i
199199 148.921 0.748347 0.374173 0.927359i 0.377926π-0.377926\pi
0.374173 + 0.927359i 0.377926π0.377926\pi
200200 0 0
201201 31.1139 + 157.576i 0.154795 + 0.783961i
202202 219.895 1.08859
203203 308.224i 1.51835i
204204 20.9210 4.13091i 0.102554 0.0202496i
205205 0 0
206206 10.7369i 0.0521211i
207207 −60.4078 147.004i −0.291825 0.710163i
208208 40.0000 0.192308
209209 93.1146i 0.445525i
210210 0 0
211211 −285.842 −1.35470 −0.677351 0.735660i 0.736872π-0.736872\pi
−0.677351 + 0.735660i 0.736872π0.736872\pi
212212 7.10831i 0.0335298i
213213 −203.842 + 40.2492i −0.957005 + 0.188963i
214214 −23.0263 −0.107600
215215 0 0
216216 −63.6754 + 42.1597i −0.294794 + 0.195184i
217217 −91.8947 −0.423478
218218 132.713i 0.608774i
219219 −7.00427 35.4731i −0.0319830 0.161978i
220220 0 0
221221 35.5415i 0.160821i
222222 −249.517 + 49.2680i −1.12395 + 0.221928i
223223 71.3815 0.320096 0.160048 0.987109i 0.448835π-0.448835\pi
0.160048 + 0.987109i 0.448835π0.448835\pi
224224 64.9793i 0.290086i
225225 0 0
226226 276.816 1.22485
227227 29.1217i 0.128290i 0.997941 + 0.0641448i 0.0204319π0.0204319\pi
−0.997941 + 0.0641448i 0.979568π0.979568\pi
228228 12.7544 + 64.5948i 0.0559406 + 0.283311i
229229 −129.684 −0.566306 −0.283153 0.959075i 0.591380π-0.591380\pi
−0.283153 + 0.959075i 0.591380π0.591380\pi
230230 0 0
231231 286.868 56.6430i 1.24185 0.245208i
232232 75.8947 0.327132
233233 185.876i 0.797751i 0.917005 + 0.398875i 0.130599π0.130599\pi
−0.917005 + 0.398875i 0.869401π0.869401\pi
234234 −48.3772 117.727i −0.206740 0.503107i
235235 0 0
236236 155.489i 0.658852i
237237 −5.24555 26.5661i −0.0221331 0.112093i
238238 57.7367 0.242591
239239 302.716i 1.26659i −0.773908 0.633297i 0.781701π-0.781701\pi
0.773908 0.633297i 0.218299π-0.218299\pi
240240 0 0
241241 −237.526 −0.985585 −0.492793 0.870147i 0.664024π-0.664024\pi
−0.492793 + 0.870147i 0.664024π0.664024\pi
242242 69.2965i 0.286349i
243243 201.094 + 136.419i 0.827549 + 0.561394i
244244 −43.8947 −0.179896
245245 0 0
246246 −16.8683 85.4296i −0.0685704 0.347275i
247247 −109.737 −0.444278
248248 22.6274i 0.0912396i
249249 −2.02633 + 0.400106i −0.00813789 + 0.00160685i
250250 0 0
251251 84.6294i 0.337169i 0.985687 + 0.168584i 0.0539196π0.0539196\pi
−0.985687 + 0.168584i 0.946080π0.946080\pi
252252 −191.246 + 78.5880i −0.758911 + 0.311857i
253253 −149.842 −0.592261
254254 109.657i 0.431722i
255255 0 0
256256 16.0000 0.0625000
257257 292.054i 1.13640i 0.822892 + 0.568198i 0.192359π0.192359\pi
−0.822892 + 0.568198i 0.807641π0.807641\pi
258258 176.732 34.8963i 0.685009 0.135257i
259259 −688.605 −2.65871
260260 0 0
261261 −91.7893 223.371i −0.351683 0.855829i
262262 −143.684 −0.548412
263263 277.725i 1.05599i 0.849247 + 0.527995i 0.177056π0.177056\pi
−0.849247 + 0.527995i 0.822944π0.822944\pi
264264 13.9473 + 70.6362i 0.0528308 + 0.267561i
265265 0 0
266266 178.265i 0.670171i
267267 −20.9210 + 4.13091i −0.0783558 + 0.0154716i
268268 −107.079 −0.399549
269269 286.546i 1.06523i 0.846359 + 0.532613i 0.178790π0.178790\pi
−0.846359 + 0.532613i 0.821210π0.821210\pi
270270 0 0
271271 −324.105 −1.19596 −0.597980 0.801511i 0.704030π-0.704030\pi
−0.597980 + 0.801511i 0.704030π0.704030\pi
272272 14.2166i 0.0522670i
273273 −66.7544 338.078i −0.244522 1.23838i
274274 248.921 0.908471
275275 0 0
276276 103.947 20.5247i 0.376621 0.0743649i
277277 −415.842 −1.50123 −0.750617 0.660737i 0.770244π-0.770244\pi
−0.750617 + 0.660737i 0.770244π0.770244\pi
278278 267.026i 0.960524i
279279 −66.5964 + 27.3663i −0.238697 + 0.0980871i
280280 0 0
281281 431.726i 1.53639i 0.640216 + 0.768195i 0.278845π0.278845\pi
−0.640216 + 0.768195i 0.721155π0.721155\pi
282282 −72.5658 367.509i −0.257326 1.30322i
283283 −141.540 −0.500140 −0.250070 0.968228i 0.580454π-0.580454\pi
−0.250070 + 0.968228i 0.580454π0.580454\pi
284284 138.518i 0.487741i
285285 0 0
286286 −120.000 −0.419580
287287 235.764i 0.821477i
288288 −19.3509 47.0908i −0.0671906 0.163510i
289289 276.368 0.956291
290290 0 0
291291 −65.0569 329.481i −0.223563 1.13224i
292292 24.1053 0.0825525
293293 164.998i 0.563133i −0.959542 0.281566i 0.909146π-0.909146\pi
0.959542 0.281566i 0.0908540π-0.0908540\pi
294294 −345.250 + 68.1706i −1.17432 + 0.231873i
295295 0 0
296296 169.557i 0.572827i
297297 191.026 126.479i 0.643186 0.425855i
298298 −102.658 −0.344489
299299 176.590i 0.590604i
300300 0 0
301301 487.737 1.62039
302302 132.862i 0.439939i
303303 457.631 90.3607i 1.51033 0.298220i
304304 −43.8947 −0.144390
305305 0 0
306306 41.8420 17.1940i 0.136739 0.0561896i
307307 −159.381 −0.519158 −0.259579 0.965722i 0.583584π-0.583584\pi
−0.259579 + 0.965722i 0.583584π0.583584\pi
308308 194.938i 0.632916i
309309 −4.41210 22.3451i −0.0142787 0.0723142i
310310 0 0
311311 143.096i 0.460117i 0.973177 + 0.230058i 0.0738917π0.0738917\pi
−0.973177 + 0.230058i 0.926108π0.926108\pi
312312 83.2456 16.4371i 0.266813 0.0526830i
313313 501.684 1.60282 0.801412 0.598113i 0.204082π-0.204082\pi
0.801412 + 0.598113i 0.204082π0.204082\pi
314314 175.139i 0.557768i
315315 0 0
316316 18.0527 0.0571287
317317 334.257i 1.05444i 0.849730 + 0.527219i 0.176765π0.176765\pi
−0.849730 + 0.527219i 0.823235π0.823235\pi
318318 −2.92100 14.7934i −0.00918553 0.0465201i
319319 −227.684 −0.713743
320320 0 0
321321 −47.9210 + 9.46215i −0.149287 + 0.0294771i
322322 286.868 0.890895
323323 39.0021i 0.120750i
324324 −115.193 + 113.906i −0.355534 + 0.351562i
325325 0 0
326326 225.399i 0.691409i
327327 −54.5352 276.193i −0.166774 0.844628i
328328 58.0527 0.176990
329329 1014.23i 3.08277i
330330 0 0
331331 389.421 1.17650 0.588249 0.808680i 0.299818π-0.299818\pi
0.588249 + 0.808680i 0.299818π0.299818\pi
332332 1.37697i 0.00414750i
333333 −499.035 + 205.067i −1.49860 + 0.615817i
334334 15.2370 0.0456198
335335 0 0
336336 −26.7018 135.231i −0.0794696 0.402473i
337337 129.684 0.384819 0.192409 0.981315i 0.438370π-0.438370\pi
0.192409 + 0.981315i 0.438370π0.438370\pi
338338 97.5807i 0.288700i
339339 576.092 113.751i 1.69939 0.335549i
340340 0 0
341341 67.8823i 0.199068i
342342 53.0875 + 129.190i 0.155227 + 0.377748i
343343 −389.947 −1.13687
344344 120.096i 0.349118i
345345 0 0
346346 −400.710 −1.15812
347347 346.985i 0.999956i −0.866038 0.499978i 0.833341π-0.833341\pi
0.866038 0.499978i 0.166659π-0.166659\pi
348348 157.947 31.1872i 0.453872 0.0896183i
349349 509.579 1.46011 0.730055 0.683388i 0.239494π-0.239494\pi
0.730055 + 0.683388i 0.239494π0.239494\pi
350350 0 0
351351 −149.057 225.127i −0.424664 0.641387i
352352 −48.0000 −0.136364
353353 637.679i 1.80646i −0.429159 0.903229i 0.641190π-0.641190\pi
0.429159 0.903229i 0.358810π-0.358810\pi
354354 63.8947 + 323.594i 0.180493 + 0.914108i
355355 0 0
356356 14.2166i 0.0399343i
357357 120.158 23.7256i 0.336577 0.0664582i
358358 −433.631 −1.21126
359359 166.952i 0.465046i 0.972591 + 0.232523i 0.0746982π0.0746982\pi
−0.972591 + 0.232523i 0.925302π0.925302\pi
360360 0 0
361361 −240.579 −0.666423
362362 375.734i 1.03794i
363363 28.4758 + 144.216i 0.0784457 + 0.397288i
364364 229.737 0.631145
365365 0 0
366366 −91.3509 + 18.0375i −0.249593 + 0.0492828i
367367 505.828 1.37828 0.689140 0.724629i 0.257989π-0.257989\pi
0.689140 + 0.724629i 0.257989π0.257989\pi
368368 70.6362i 0.191946i
369369 −70.2107 170.859i −0.190273 0.463033i
370370 0 0
371371 40.8260i 0.110043i
372372 −9.29822 47.0908i −0.0249952 0.126588i
373373 416.053 1.11542 0.557711 0.830035i 0.311680π-0.311680\pi
0.557711 + 0.830035i 0.311680π0.311680\pi
374374 42.6499i 0.114037i
375375 0 0
376376 249.737 0.664193
377377 268.328i 0.711746i
378378 −365.715 + 242.141i −0.967499 + 0.640583i
379379 82.7630 0.218372 0.109186 0.994021i 0.465176π-0.465176\pi
0.109186 + 0.994021i 0.465176π0.465176\pi
380380 0 0
381381 45.0612 + 228.212i 0.118271 + 0.598982i
382382 225.737 0.590934
383383 334.592i 0.873608i −0.899557 0.436804i 0.856110π-0.856110\pi
0.899557 0.436804i 0.143890π-0.143890\pi
384384 33.2982 6.57484i 0.0867141 0.0171220i
385385 0 0
386386 130.182i 0.337259i
387387 353.465 145.248i 0.913346 0.375319i
388388 223.895 0.577048
389389 542.964i 1.39580i 0.716197 + 0.697898i 0.245881π0.245881\pi
−0.716197 + 0.697898i 0.754119π0.754119\pi
390390 0 0
391391 −62.7630 −0.160519
392392 234.610i 0.598496i
393393 −299.026 + 59.0437i −0.760881 + 0.150238i
394394 −98.7630 −0.250667
395395 0 0
396396 58.0527 + 141.272i 0.146598 + 0.356748i
397397 214.000 0.539043 0.269521 0.962994i 0.413135π-0.413135\pi
0.269521 + 0.962994i 0.413135π0.413135\pi
398398 210.606i 0.529161i
399399 73.2541 + 370.995i 0.183594 + 0.929812i
400400 0 0
401401 726.086i 1.81069i 0.424677 + 0.905345i 0.360387π0.360387\pi
−0.424677 + 0.905345i 0.639613π0.639613\pi
402402 −222.846 + 44.0017i −0.554344 + 0.109457i
403403 80.0000 0.198511
404404 310.978i 0.769748i
405405 0 0
406406 435.895 1.07363
407407 508.670i 1.24980i
408408 5.84200 + 29.5868i 0.0143186 + 0.0725166i
409409 −346.158 −0.846352 −0.423176 0.906047i 0.639085π-0.639085\pi
−0.423176 + 0.906047i 0.639085π0.639085\pi
410410 0 0
411411 518.039 102.288i 1.26044 0.248877i
412412 15.1843 0.0368552
413413 893.038i 2.16232i
414414 207.895 85.4296i 0.502161 0.206352i
415415 0 0
416416 56.5685i 0.135982i
417417 109.728 + 555.717i 0.263137 + 1.33266i
418418 131.684 0.315033
419419 580.907i 1.38641i −0.720740 0.693206i 0.756198π-0.756198\pi
0.720740 0.693206i 0.243802π-0.243802\pi
420420 0 0
421421 −269.315 −0.639704 −0.319852 0.947468i 0.603633π-0.603633\pi
−0.319852 + 0.947468i 0.603633π0.603633\pi
422422 404.242i 0.957919i
423423 −302.039 735.019i −0.714041 1.73763i
424424 10.0527 0.0237091
425425 0 0
426426 −56.9210 288.276i −0.133617 0.676704i
427427 −252.105 −0.590411
428428 32.5642i 0.0760845i
429429 −249.737 + 49.3113i −0.582137 + 0.114945i
430430 0 0
431431 776.068i 1.80062i −0.435247 0.900311i 0.643339π-0.643339\pi
0.435247 0.900311i 0.356661π-0.356661\pi
432432 −59.6228 90.0507i −0.138016 0.208451i
433433 195.526 0.451561 0.225781 0.974178i 0.427507π-0.427507\pi
0.225781 + 0.974178i 0.427507π0.427507\pi
434434 129.959i 0.299444i
435435 0 0
436436 187.684 0.430468
437437 193.785i 0.443443i
438438 50.1666 9.90554i 0.114536 0.0226154i
439439 598.763 1.36392 0.681962 0.731387i 0.261127π-0.261127\pi
0.681962 + 0.731387i 0.261127π0.261127\pi
440440 0 0
441441 −690.500 + 283.745i −1.56576 + 0.643413i
442442 −50.2633 −0.113718
443443 216.728i 0.489228i 0.969621 + 0.244614i 0.0786612π0.0786612\pi
−0.969621 + 0.244614i 0.921339π0.921339\pi
444444 −69.6754 352.871i −0.156927 0.794754i
445445 0 0
446446 100.949i 0.226342i
447447 −213.645 + 42.1848i −0.477953 + 0.0943732i
448448 91.8947 0.205122
449449 246.203i 0.548336i −0.961682 0.274168i 0.911598π-0.911598\pi
0.961682 0.274168i 0.0884025π-0.0884025\pi
450450 0 0
451451 −174.158 −0.386160
452452 391.476i 0.866098i
453453 54.5964 + 276.503i 0.120522 + 0.610383i
454454 −41.1843 −0.0907144
455455 0 0
456456 −91.3509 + 18.0375i −0.200331 + 0.0395559i
457457 −553.052 −1.21018 −0.605090 0.796157i 0.706863π-0.706863\pi
−0.605090 + 0.796157i 0.706863π0.706863\pi
458458 183.401i 0.400439i
459459 80.0135 52.9771i 0.174321 0.115419i
460460 0 0
461461 124.749i 0.270605i −0.990804 0.135302i 0.956799π-0.956799\pi
0.990804 0.135302i 0.0432006π-0.0432006\pi
462462 80.1053 + 405.693i 0.173388 + 0.878124i
463463 −669.723 −1.44649 −0.723243 0.690593i 0.757349π-0.757349\pi
−0.723243 + 0.690593i 0.757349π0.757349\pi
464464 107.331i 0.231317i
465465 0 0
466466 −262.868 −0.564095
467467 486.880i 1.04257i −0.853383 0.521285i 0.825453π-0.825453\pi
0.853383 0.521285i 0.174547π-0.174547\pi
468468 166.491 68.4157i 0.355750 0.146187i
469469 −614.999 −1.31130
470470 0 0
471471 71.9694 + 364.489i 0.152801 + 0.773861i
472472 −219.895 −0.465879
473473 360.289i 0.761711i
474474 37.5701 7.41833i 0.0792618 0.0156505i
475475 0 0
476476 81.6520i 0.171538i
477477 −12.1580 29.5868i −0.0254885 0.0620267i
478478 428.105 0.895618
479479 520.580i 1.08680i 0.839472 + 0.543402i 0.182864π0.182864\pi
−0.839472 + 0.543402i 0.817136π0.817136\pi
480480 0 0
481481 599.473 1.24631
482482 335.912i 0.696914i
483483 597.013 117.882i 1.23605 0.244062i
484484 −98.0000 −0.202479
485485 0 0
486486 −192.925 + 284.390i −0.396966 + 0.585165i
487487 263.381 0.540824 0.270412 0.962745i 0.412840π-0.412840\pi
0.270412 + 0.962745i 0.412840π0.412840\pi
488488 62.0764i 0.127206i
489489 −92.6228 469.088i −0.189413 0.959279i
490490 0 0
491491 711.646i 1.44938i −0.689074 0.724691i 0.741983π-0.741983\pi
0.689074 0.724691i 0.258017π-0.258017\pi
492492 120.816 23.8554i 0.245560 0.0484866i
493493 −95.3680 −0.193444
494494 155.191i 0.314152i
495495 0 0
496496 32.0000 0.0645161
497497 795.569i 1.60074i
498498 −0.565835 2.86567i −0.00113622 0.00575436i
499499 23.0790 0.0462505 0.0231253 0.999733i 0.492638π-0.492638\pi
0.0231253 + 0.999733i 0.492638π0.492638\pi
500500 0 0
501501 31.7103 6.26130i 0.0632941 0.0124976i
502502 −119.684 −0.238414
503503 40.5844i 0.0806847i −0.999186 0.0403423i 0.987155π-0.987155\pi
0.999186 0.0403423i 0.0128449π-0.0128449\pi
504504 −111.140 270.462i −0.220516 0.536631i
505505 0 0
506506 211.909i 0.418792i
507507 −40.0986 203.079i −0.0790899 0.400550i
508508 −155.079 −0.305274
509509 484.591i 0.952045i 0.879433 + 0.476023i 0.157922π0.157922\pi
−0.879433 + 0.476023i 0.842078π0.842078\pi
510510 0 0
511511 138.447 0.270933
512512 22.6274i 0.0441942i
513513 163.570 + 247.047i 0.318850 + 0.481572i
514514 −413.026 −0.803553
515515 0 0
516516 49.3509 + 249.937i 0.0956413 + 0.484375i
517517 −749.210 −1.44915
518518 973.835i 1.87999i
519519 −833.934 + 164.663i −1.60681 + 0.317269i
520520 0 0
521521 539.857i 1.03619i −0.855322 0.518097i 0.826641π-0.826641\pi
0.855322 0.518097i 0.173359π-0.173359\pi
522522 315.895 129.810i 0.605162 0.248678i
523523 266.644 0.509836 0.254918 0.966963i 0.417952π-0.417952\pi
0.254918 + 0.966963i 0.417952π0.417952\pi
524524 203.200i 0.387786i
525525 0 0
526526 −392.763 −0.746698
527527 28.4332i 0.0539530i
528528 −99.8947 + 19.7245i −0.189194 + 0.0373570i
529529 217.158 0.410507
530530 0 0
531531 265.947 + 647.188i 0.500842 + 1.21881i
532532 −252.105 −0.473882
533533 205.247i 0.385079i
534534 −5.84200 29.5868i −0.0109401 0.0554059i
535535 0 0
536536 151.433i 0.282523i
537537 −902.447 + 178.191i −1.68053 + 0.331827i
538538 −405.237 −0.753229
539539 703.831i 1.30581i
540540 0 0
541541 −337.895 −0.624574 −0.312287 0.949988i 0.601095π-0.601095\pi
−0.312287 + 0.949988i 0.601095π0.601095\pi
542542 458.354i 0.845672i
543543 154.399 + 781.954i 0.284345 + 1.44006i
544544 −20.1053 −0.0369583
545545 0 0
546546 478.114 94.4050i 0.875666 0.172903i
547547 214.566 0.392259 0.196130 0.980578i 0.437163π-0.437163\pi
0.196130 + 0.980578i 0.437163π0.437163\pi
548548 352.027i 0.642386i
549549 −182.702 + 75.0771i −0.332790 + 0.136753i
550550 0 0
551551 294.454i 0.534400i
552552 29.0263 + 147.004i 0.0525839 + 0.266311i
553553 103.684 0.187494
554554 588.089i 1.06153i
555555 0 0
556556 −377.631 −0.679193
557557 674.821i 1.21153i 0.795644 + 0.605764i 0.207133π0.207133\pi
−0.795644 + 0.605764i 0.792867π0.792867\pi
558558 −38.7018 94.1816i −0.0693580 0.168784i
559559 −424.605 −0.759580
560560 0 0
561561 −17.5260 88.7603i −0.0312406 0.158218i
562562 −610.552 −1.08639
563563 718.513i 1.27622i 0.769944 + 0.638111i 0.220284π0.220284\pi
−0.769944 + 0.638111i 0.779716π0.779716\pi
564564 519.737 102.624i 0.921519 0.181957i
565565 0 0
566566 200.167i 0.353652i
567567 −661.601 + 654.210i −1.16684 + 1.15381i
568568 195.895 0.344885
569569 183.122i 0.321831i 0.986968 + 0.160916i 0.0514447π0.0514447\pi
−0.986968 + 0.160916i 0.948555π0.948555\pi
570570 0 0
571571 −295.895 −0.518204 −0.259102 0.965850i 0.583427π-0.583427\pi
−0.259102 + 0.965850i 0.583427π0.583427\pi
572572 169.706i 0.296688i
573573 469.789 92.7613i 0.819877 0.161887i
574574 333.421 0.580872
575575 0 0
576576 66.5964 27.3663i 0.115619 0.0475109i
577577 984.947 1.70701 0.853507 0.521082i 0.174471π-0.174471\pi
0.853507 + 0.521082i 0.174471π0.174471\pi
578578 390.843i 0.676200i
579579 53.4954 + 270.927i 0.0923927 + 0.467922i
580580 0 0
581581 7.90852i 0.0136119i
582582 465.956 92.0044i 0.800611 0.158083i
583583 −30.1580 −0.0517290
584584 34.0901i 0.0583734i
585585 0 0
586586 233.342 0.398195
587587 378.172i 0.644245i −0.946698 0.322122i 0.895604π-0.895604\pi
0.946698 0.322122i 0.104396π-0.104396\pi
588588 −96.4078 488.257i −0.163959 0.830369i
589589 −87.7893 −0.149048
590590 0 0
591591 −205.540 + 40.5844i −0.347783 + 0.0686707i
592592 239.789 0.405050
593593 265.221i 0.447253i −0.974675 0.223626i 0.928210π-0.928210\pi
0.974675 0.223626i 0.0717895π-0.0717895\pi
594594 178.868 + 270.152i 0.301125 + 0.454801i
595595 0 0
596596 145.180i 0.243590i
597597 86.5438 + 438.301i 0.144964 + 0.734172i
598598 −249.737 −0.417620
599599 382.061i 0.637832i −0.947783 0.318916i 0.896681π-0.896681\pi
0.947783 0.318916i 0.103319π-0.103319\pi
600600 0 0
601601 1021.53 1.69971 0.849855 0.527016i 0.176689π-0.176689\pi
0.849855 + 0.527016i 0.176689π0.176689\pi
602602 689.764i 1.14579i
603603 −445.693 + 183.147i −0.739125 + 0.303727i
604604 −187.895 −0.311084
605605 0 0
606606 127.789 + 647.188i 0.210873 + 1.06797i
607607 835.487 1.37642 0.688210 0.725512i 0.258397π-0.258397\pi
0.688210 + 0.725512i 0.258397π0.258397\pi
608608 62.0764i 0.102099i
609609 907.157 179.121i 1.48959 0.294123i
610610 0 0
611611 882.952i 1.44509i
612612 24.3160 + 59.1735i 0.0397320 + 0.0966888i
613613 −833.263 −1.35932 −0.679660 0.733528i 0.737872π-0.737872\pi
−0.679660 + 0.733528i 0.737872π0.737872\pi
614614 225.399i 0.367100i
615615 0 0
616616 −275.684 −0.447539
617617 455.098i 0.737598i −0.929509 0.368799i 0.879769π-0.879769\pi
0.929509 0.368799i 0.120231π-0.120231\pi
618618 31.6007 6.23966i 0.0511338 0.0100965i
619619 336.710 0.543959 0.271979 0.962303i 0.412322π-0.412322\pi
0.271979 + 0.962303i 0.412322π0.412322\pi
620620 0 0
621621 397.552 263.220i 0.640181 0.423865i
622622 −202.369 −0.325352
623623 81.6520i 0.131063i
624624 23.2456 + 117.727i 0.0372525 + 0.188665i
625625 0 0
626626 709.488i 1.13337i
627627 274.053 54.1125i 0.437086 0.0863039i
628628 −247.684 −0.394401
629629 213.062i 0.338731i
630630 0 0
631631 −1100.89 −1.74468 −0.872341 0.488898i 0.837399π-0.837399\pi
−0.872341 + 0.488898i 0.837399π0.837399\pi
632632 25.5303i 0.0403961i
633633 −166.114 841.283i −0.262423 1.32904i
634634 −472.710 −0.745600
635635 0 0
636636 20.9210 4.13091i 0.0328947 0.00649515i
637637 829.473 1.30216
638638 321.994i 0.504692i
639639 −236.921 576.552i −0.370768 0.902273i
640640 0 0
641641 337.011i 0.525758i 0.964829 + 0.262879i 0.0846719π0.0846719\pi
−0.964829 + 0.262879i 0.915328π0.915328\pi
642642 −13.3815 67.7705i −0.0208435 0.105562i
643643 599.381 0.932164 0.466082 0.884742i 0.345665π-0.345665\pi
0.466082 + 0.884742i 0.345665π0.345665\pi
644644 405.693i 0.629958i
645645 0 0
646646 55.1573 0.0853828
647647 47.0224i 0.0726775i 0.999340 + 0.0363388i 0.0115695π0.0115695\pi
−0.999340 + 0.0363388i 0.988430π0.988430\pi
648648 −161.088 162.907i −0.248592 0.251400i
649649 659.684 1.01646
650650 0 0
651651 −53.4036 270.462i −0.0820331 0.415456i
652652 318.763 0.488900
653653 559.228i 0.856399i −0.903684 0.428199i 0.859148π-0.859148\pi
0.903684 0.428199i 0.140852π-0.140852\pi
654654 390.596 77.1245i 0.597242 0.117927i
655655 0 0
656656 82.0989i 0.125151i
657657 100.333 41.2296i 0.152714 0.0627543i
658658 1434.34 2.17985
659659 665.759i 1.01026i −0.863044 0.505129i 0.831445π-0.831445\pi
0.863044 0.505129i 0.168555π-0.168555\pi
660660 0 0
661661 −557.947 −0.844096 −0.422048 0.906574i 0.638689π-0.638689\pi
−0.422048 + 0.906574i 0.638689π0.638689\pi
662662 550.724i 0.831909i
663663 −104.605 + 20.6546i −0.157775 + 0.0311532i
664664 1.94733 0.00293273
665665 0 0
666666 −290.009 705.742i −0.435448 1.05967i
667667 −473.842 −0.710408
668668 21.5484i 0.0322581i
669669 41.4826 + 210.088i 0.0620068 + 0.314033i
670670 0 0
671671 186.229i 0.277540i
672672 191.246 37.7620i 0.284592 0.0561935i
673673 −1019.42 −1.51474 −0.757370 0.652985i 0.773516π-0.773516\pi
−0.757370 + 0.652985i 0.773516π0.773516\pi
674674 183.401i 0.272108i
675675 0 0
676676 138.000 0.204142
677677 624.616i 0.922624i −0.887238 0.461312i 0.847379π-0.847379\pi
0.887238 0.461312i 0.152621π-0.152621\pi
678678 160.868 + 814.717i 0.237269 + 1.20165i
679679 1285.92 1.89384
680680 0 0
681681 −85.7103 + 16.9238i −0.125860 + 0.0248513i
682682 −96.0000 −0.140762
683683 525.882i 0.769959i −0.922925 0.384980i 0.874208π-0.874208\pi
0.922925 0.384980i 0.125792π-0.125792\pi
684684 −182.702 + 75.0771i −0.267108 + 0.109762i
685685 0 0
686686 551.469i 0.803890i
687687 −75.3644 381.683i −0.109701 0.555579i
688688 −169.842 −0.246863
689689 35.5415i 0.0515843i
690690 0 0
691691 932.000 1.34877 0.674385 0.738380i 0.264409π-0.264409\pi
0.674385 + 0.738380i 0.264409π0.264409\pi
692692 566.690i 0.818916i
693693 333.421 + 811.386i 0.481126 + 1.17083i
694694 490.710 0.707075
695695 0 0
696696 44.1053 + 223.371i 0.0633697 + 0.320936i
697697 −72.9480 −0.104660
698698 720.653i 1.03245i
699699 −547.065 + 108.020i −0.782640 + 0.154535i
700700 0 0
701701 606.045i 0.864544i −0.901743 0.432272i 0.857712π-0.857712\pi
0.901743 0.432272i 0.142288π-0.142288\pi
702702 318.377 210.798i 0.453529 0.300283i
703703 −657.842 −0.935764
704704 67.8823i 0.0964237i
705705 0 0
706706 901.815 1.27736
707707 1786.08i 2.52627i
708708 −457.631 + 90.3607i −0.646372 + 0.127628i
709709 489.473 0.690371 0.345186 0.938534i 0.387816π-0.387816\pi
0.345186 + 0.938534i 0.387816π0.387816\pi
710710 0 0
711711 75.1402 30.8772i 0.105682 0.0434278i
712712 20.1053 0.0282378
713713 141.272i 0.198138i
714714 33.5530 + 169.929i 0.0469930 + 0.237996i
715715 0 0
716716 613.247i 0.856491i
717717 890.947 175.920i 1.24260 0.245356i
718718 −236.105 −0.328838
719719 107.778i 0.149900i −0.997187 0.0749500i 0.976120π-0.976120\pi
0.997187 0.0749500i 0.0238797π-0.0238797\pi
720720 0 0
721721 87.2100 0.120957
722722 340.230i 0.471232i
723723 −138.036 699.080i −0.190921 0.966916i
724724 −531.368 −0.733934
725725 0 0
726726 −203.952 + 40.2709i −0.280925 + 0.0554695i
727727 150.172 0.206563 0.103282 0.994652i 0.467066π-0.467066\pi
0.103282 + 0.994652i 0.467066π0.467066\pi
728728 324.897i 0.446287i
729729 −284.641 + 671.134i −0.390453 + 0.920623i
730730 0 0
731731 150.911i 0.206445i
732732 −25.5089 129.190i −0.0348482 0.176489i
733733 675.526 0.921591 0.460795 0.887506i 0.347564π-0.347564\pi
0.460795 + 0.887506i 0.347564π0.347564\pi
734734 715.349i 0.974591i
735735 0 0
736736 −99.8947 −0.135726
737737 454.298i 0.616415i
738738 241.631 99.2929i 0.327414 0.134543i
739739 −936.921 −1.26782 −0.633911 0.773406i 0.718552π-0.718552\pi
−0.633911 + 0.773406i 0.718552π0.718552\pi
740740 0 0
741741 −63.7722 322.974i −0.0860624 0.435863i
742742 57.7367 0.0778122
743743 452.939i 0.609608i −0.952415 0.304804i 0.901409π-0.901409\pi
0.952415 0.304804i 0.0985910π-0.0985910\pi
744744 66.5964 13.1497i 0.0895113 0.0176743i
745745 0 0
746746 588.387i 0.788723i
747747 −2.35516 5.73134i −0.00315283 0.00767247i
748748 60.3160 0.0806364
749749 187.029i 0.249706i
750750 0 0
751751 654.369 0.871330 0.435665 0.900109i 0.356513π-0.356513\pi
0.435665 + 0.900109i 0.356513π0.356513\pi
752752 353.181i 0.469656i
753753 −249.079 + 49.1814i −0.330782 + 0.0653140i
754754 −379.473 −0.503280
755755 0 0
756756 −342.438 517.199i −0.452961 0.684125i
757757 −123.315 −0.162900 −0.0814500 0.996677i 0.525955π-0.525955\pi
−0.0814500 + 0.996677i 0.525955π0.525955\pi
758758 117.045i 0.154412i
759759 −87.0790 441.011i −0.114729 0.581042i
760760 0 0
761761 502.715i 0.660598i −0.943876 0.330299i 0.892850π-0.892850\pi
0.943876 0.330299i 0.107150π-0.107150\pi
762762 −322.741 + 63.7262i −0.423545 + 0.0836302i
763763 1077.95 1.41278
764764 319.240i 0.417853i
765765 0 0
766766 473.184 0.617734
767767 777.445i 1.01362i
768768 9.29822 + 47.0908i 0.0121071 + 0.0613161i
769769 −286.316 −0.372323 −0.186161 0.982519i 0.559605π-0.559605\pi
−0.186161 + 0.982519i 0.559605π0.559605\pi
770770 0 0
771771 −859.565 + 169.724i −1.11487 + 0.220135i
772772 −184.105 −0.238478
773773 972.030i 1.25748i 0.777617 + 0.628739i 0.216428π0.216428\pi
−0.777617 + 0.628739i 0.783572π0.783572\pi
774774 205.412 + 499.875i 0.265390 + 0.645833i
775775 0 0
776776 316.635i 0.408035i
777777 −400.175 2026.68i −0.515026 2.60835i
778778 −767.868 −0.986976
779779 225.231i 0.289129i
780780 0 0
781781 −587.684 −0.752476
782782 88.7603i 0.113504i
783783 604.078 399.962i 0.771492 0.510807i
784784 331.789 0.423201
785785 0 0
786786 −83.5003 422.887i −0.106235 0.538024i
787787 −1492.70 −1.89669 −0.948346 0.317237i 0.897245π-0.897245\pi
−0.948346 + 0.317237i 0.897245π0.897245\pi
788788 139.672i 0.177249i
789789 −817.394 + 161.397i −1.03599 + 0.204559i
790790 0 0
791791 2248.41i 2.84249i
792792 −199.789 + 82.0989i −0.252259 + 0.103660i
793793 219.473 0.276763
794794 302.642i 0.381161i
795795 0 0
796796 −297.842 −0.374173
797797 94.3618i 0.118396i 0.998246 + 0.0591981i 0.0188544π0.0188544\pi
−0.998246 + 0.0591981i 0.981146π0.981146\pi
798798 −524.666 + 103.597i −0.657476 + 0.129821i
799799 −313.815 −0.392760
800800 0 0
801801 −24.3160 59.1735i −0.0303571 0.0738746i
802802 −1026.84 −1.28035
803803 102.270i 0.127360i
804804 −62.2278 315.152i −0.0773977 0.391980i
805805 0 0
806806 113.137i 0.140369i
807807 −843.354 + 166.523i −1.04505 + 0.206348i
808808 −439.789 −0.544294
809809 1103.35i 1.36384i −0.731427 0.681920i 0.761145π-0.761145\pi
0.731427 0.681920i 0.238855π-0.238855\pi
810810 0 0
811811 −10.1580 −0.0125253 −0.00626264 0.999980i 0.501993π-0.501993\pi
−0.00626264 + 0.999980i 0.501993π0.501993\pi
812812 616.448i 0.759173i
813813 −188.350 953.899i −0.231673 1.17331i
814814 −719.368 −0.883744
815815 0 0
816816 −41.8420 + 8.26183i −0.0512770 + 0.0101248i
817817 465.947 0.570315
818818 489.541i 0.598461i
819819 956.228 392.940i 1.16756 0.479780i
820820 0 0
821821 337.011i 0.410488i 0.978711 + 0.205244i 0.0657988π0.0657988\pi
−0.978711 + 0.205244i 0.934201π0.934201\pi
822822 144.658 + 732.618i 0.175983 + 0.891263i
823823 901.512 1.09540 0.547699 0.836675i 0.315504π-0.315504\pi
0.547699 + 0.836675i 0.315504π0.315504\pi
824824 21.4739i 0.0260606i
825825 0 0
826826 −1262.95 −1.52899
827827 531.354i 0.642508i 0.946993 + 0.321254i 0.104104π0.104104\pi
−0.946993 + 0.321254i 0.895896π0.895896\pi
828828 120.816 + 294.007i 0.145913 + 0.355081i
829829 −197.631 −0.238397 −0.119199 0.992870i 0.538033π-0.538033\pi
−0.119199 + 0.992870i 0.538033π0.538033\pi
830830 0 0
831831 −241.662 1223.90i −0.290809 1.47280i
832832 −80.0000 −0.0961538
833833 294.808i 0.353911i
834834 −785.903 + 155.179i −0.942330 + 0.186066i
835835 0 0
836836 186.229i 0.222762i
837837 −119.246 180.101i −0.142468 0.215175i
838838 821.526 0.980341
839839 943.950i 1.12509i −0.826767 0.562545i 0.809822π-0.809822\pi
0.826767 0.562545i 0.190178π-0.190178\pi
840840 0 0
841841 121.000 0.143876
842842 380.869i 0.452339i
843843 −1270.64 + 250.893i −1.50729 + 0.297619i
844844 571.684 0.677351
845845 0 0
846846 1039.47 427.148i 1.22869 0.504903i
847847 −562.855 −0.664528
848848 14.2166i 0.0167649i
849849 −82.2541 416.575i −0.0968835 0.490666i
850850 0 0
851851 1058.61i 1.24396i
852852 407.684 80.4984i 0.478502 0.0944817i
853853 1196.42 1.40260 0.701301 0.712865i 0.252603π-0.252603\pi
0.701301 + 0.712865i 0.252603π0.252603\pi
854854 356.531i 0.417483i
855855 0 0
856856 46.0527 0.0537998
857857 1266.04i 1.47729i 0.674095 + 0.738645i 0.264534π0.264534\pi
−0.674095 + 0.738645i 0.735466π0.735466\pi
858858 −69.7367 353.181i −0.0812782 0.411633i
859859 −470.868 −0.548159 −0.274079 0.961707i 0.588373π-0.588373\pi
−0.274079 + 0.961707i 0.588373π0.588373\pi
860860 0 0
861861 693.895 137.012i 0.805917 0.159131i
862862 1097.53 1.27323
863863 285.057i 0.330310i 0.986268 + 0.165155i 0.0528124π0.0528124\pi
−0.986268 + 0.165155i 0.947188π0.947188\pi
864864 127.351 84.3193i 0.147397 0.0975918i
865865 0 0
866866 276.516i 0.319302i
867867 160.608 + 813.399i 0.185246 + 0.938177i
868868 183.789 0.211739
869869 76.5910i 0.0881369i
870870 0 0
871871 535.395 0.614690
872872 265.425i 0.304387i
873873 931.912 382.948i 1.06748 0.438657i
874874 274.053 0.313561
875875 0 0
876876 14.0085 + 70.9462i 0.0159915 + 0.0809888i
877877 −244.579 −0.278882 −0.139441 0.990230i 0.544531π-0.544531\pi
−0.139441 + 0.990230i 0.544531π0.544531\pi
878878 846.779i 0.964440i
879879 485.618 95.8867i 0.552466 0.109086i
880880 0 0
881881 137.271i 0.155813i −0.996961 0.0779065i 0.975176π-0.975176\pi
0.996961 0.0779065i 0.0248236π-0.0248236\pi
882882 −401.276 976.514i −0.454962 1.10716i
883883 −1647.75 −1.86608 −0.933040 0.359772i 0.882854π-0.882854\pi
−0.933040 + 0.359772i 0.882854π0.882854\pi
884884 71.0831i 0.0804107i
885885 0 0
886886 −306.500 −0.345936
887887 514.419i 0.579954i −0.957034 0.289977i 0.906352π-0.906352\pi
0.957034 0.289977i 0.0936477π-0.0936477\pi
888888 499.035 98.5360i 0.561976 0.110964i
889889 −890.683 −1.00189
890890 0 0
891891 483.263 + 488.722i 0.542382 + 0.548510i
892892 −142.763 −0.160048
893893 968.923i 1.08502i
894894 −59.6584 302.139i −0.0667319 0.337964i
895895 0 0
896896 129.959i 0.145043i
897897 −519.737 + 102.624i −0.579417 + 0.114408i
898898 348.184 0.387732
899899 214.663i 0.238779i
900900 0 0
901901 −12.6320 −0.0140200
902902 246.297i 0.273056i
903903 283.443 + 1435.49i 0.313890 + 1.58969i
904904 −553.631 −0.612424
905905 0 0
906906 −391.035 + 77.2110i −0.431606 + 0.0852219i
907907 −347.303 −0.382914 −0.191457 0.981501i 0.561321π-0.561321\pi
−0.191457 + 0.981501i 0.561321π0.561321\pi
908908 58.2434i 0.0641448i
909909 531.895 + 1294.38i 0.585143 + 1.42396i
910910 0 0
911911 304.540i 0.334292i 0.985932 + 0.167146i 0.0534551π0.0534551\pi
−0.985932 + 0.167146i 0.946545π0.946545\pi
912912 −25.5089 129.190i −0.0279703 0.141655i
913913 −5.84200 −0.00639868
914914 782.134i 0.855726i
915915 0 0
916916 259.368 0.283153
917917 1167.06i 1.27270i
918918 74.9210 + 113.156i 0.0816133 + 0.123264i
919919 244.289 0.265820 0.132910 0.991128i 0.457568π-0.457568\pi
0.132910 + 0.991128i 0.457568π0.457568\pi
920920 0 0
921921 −92.6228 469.088i −0.100568 0.509324i
922922 176.421 0.191346
923923 692.592i 0.750371i
924924 −573.737 + 113.286i −0.620927 + 0.122604i
925925 0 0
926926 947.132i 1.02282i
927927 63.2014 25.9712i 0.0681785 0.0280164i
928928 −151.789 −0.163566
929929 1025.96i 1.10437i 0.833723 + 0.552183i 0.186205π0.186205\pi
−0.833723 + 0.552183i 0.813795π0.813795\pi
930930 0 0
931931 −910.236 −0.977697
932932 371.752i 0.398875i
933933 −421.157 + 83.1588i −0.451401 + 0.0891305i
934934 688.552 0.737208
935935 0 0
936936 96.7544 + 235.454i 0.103370 + 0.251553i
937937 332.053 0.354379 0.177189 0.984177i 0.443300π-0.443300\pi
0.177189 + 0.984177i 0.443300π0.443300\pi
938938 869.740i 0.927229i
939939 291.548 + 1476.54i 0.310488 + 1.57246i
940940 0 0
941941 1636.99i 1.73963i −0.493381 0.869813i 0.664239π-0.664239\pi
0.493381 0.869813i 0.335761π-0.335761\pi
942942 −515.465 + 101.780i −0.547203 + 0.108047i
943943 −362.447 −0.384355
944944 310.978i 0.329426i
945945 0 0
946946 509.526 0.538611
947947 1209.32i 1.27700i 0.769622 + 0.638500i 0.220445π0.220445\pi
−0.769622 + 0.638500i 0.779555π0.779555\pi
948948 10.4911 + 53.1322i 0.0110666 + 0.0560466i
949949 −120.527 −0.127004
950950 0 0
951951 −983.776 + 194.250i −1.03446 + 0.204258i
952952 −115.473 −0.121296
953953 1205.26i 1.26470i −0.774681 0.632352i 0.782090π-0.782090\pi
0.774681 0.632352i 0.217910π-0.217910\pi
954954 41.8420 17.1940i 0.0438595 0.0180231i
955955 0 0
956956 605.432i 0.633297i
957957 −132.316 670.114i −0.138261 0.700223i
958958 −736.211 −0.768487
959959 2021.84i 2.10828i
960960 0 0
961961 −897.000 −0.933403
962962 847.783i 0.881272i
963963 −55.6975 135.541i −0.0578375 0.140749i
964964 475.052 0.492793
965965 0 0
966966 166.710 + 844.304i 0.172578 + 0.874020i
967967 1845.93 1.90893 0.954464 0.298325i 0.0964281π-0.0964281\pi
0.954464 + 0.298325i 0.0964281π0.0964281\pi
968968 138.593i 0.143175i
969969 114.790 22.6656i 0.118462 0.0233908i
970970 0 0
971971 1057.91i 1.08950i −0.838598 0.544751i 0.816624π-0.816624\pi
0.838598 0.544751i 0.183376π-0.183376\pi
972972 −402.189 272.838i −0.413774 0.280697i
973973 −2168.89 −2.22908
974974 372.478i 0.382421i
975975 0 0
976976 87.7893 0.0899481
977977 964.028i 0.986722i −0.869825 0.493361i 0.835768π-0.835768\pi
0.869825 0.493361i 0.164232π-0.164232\pi
978978 663.390 130.988i 0.678313 0.133935i
979979 −60.3160 −0.0616098
980980 0 0
981981 781.193 321.013i 0.796323 0.327231i
982982 1006.42 1.02487
983983 460.718i 0.468685i 0.972154 + 0.234343i 0.0752937π0.0752937\pi
−0.972154 + 0.234343i 0.924706π0.924706\pi
984984 33.7367 + 170.859i 0.0342852 + 0.173637i
985985 0 0
986986 134.871i 0.136786i
987987 2985.06 589.410i 3.02438 0.597173i
988988 219.473 0.222139
989989 749.812i 0.758152i
990990 0 0
991991 1237.89 1.24914 0.624568 0.780971i 0.285275π-0.285275\pi
0.624568 + 0.780971i 0.285275π0.285275\pi
992992 45.2548i 0.0456198i
993993 226.307 + 1146.13i 0.227903 + 1.15421i
994994 1125.10 1.13190
995995 0 0
996996 4.05267 0.800212i 0.00406894 0.000803425i
997997 9.36798 0.00939617 0.00469809 0.999989i 0.498505π-0.498505\pi
0.00469809 + 0.999989i 0.498505π0.498505\pi
998998 32.6386i 0.0327040i
999999 −893.557 1349.57i −0.894451 1.35093i
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 150.3.d.c.101.4 4
3.2 odd 2 inner 150.3.d.c.101.2 4
4.3 odd 2 1200.3.l.u.401.1 4
5.2 odd 4 150.3.b.b.149.3 8
5.3 odd 4 150.3.b.b.149.6 8
5.4 even 2 30.3.d.a.11.1 4
12.11 even 2 1200.3.l.u.401.2 4
15.2 even 4 150.3.b.b.149.5 8
15.8 even 4 150.3.b.b.149.4 8
15.14 odd 2 30.3.d.a.11.3 yes 4
20.3 even 4 1200.3.c.k.449.7 8
20.7 even 4 1200.3.c.k.449.2 8
20.19 odd 2 240.3.l.c.161.4 4
40.19 odd 2 960.3.l.f.641.1 4
40.29 even 2 960.3.l.e.641.4 4
45.4 even 6 810.3.h.a.431.4 8
45.14 odd 6 810.3.h.a.431.1 8
45.29 odd 6 810.3.h.a.701.4 8
45.34 even 6 810.3.h.a.701.1 8
60.23 odd 4 1200.3.c.k.449.1 8
60.47 odd 4 1200.3.c.k.449.8 8
60.59 even 2 240.3.l.c.161.3 4
120.29 odd 2 960.3.l.e.641.3 4
120.59 even 2 960.3.l.f.641.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
30.3.d.a.11.1 4 5.4 even 2
30.3.d.a.11.3 yes 4 15.14 odd 2
150.3.b.b.149.3 8 5.2 odd 4
150.3.b.b.149.4 8 15.8 even 4
150.3.b.b.149.5 8 15.2 even 4
150.3.b.b.149.6 8 5.3 odd 4
150.3.d.c.101.2 4 3.2 odd 2 inner
150.3.d.c.101.4 4 1.1 even 1 trivial
240.3.l.c.161.3 4 60.59 even 2
240.3.l.c.161.4 4 20.19 odd 2
810.3.h.a.431.1 8 45.14 odd 6
810.3.h.a.431.4 8 45.4 even 6
810.3.h.a.701.1 8 45.34 even 6
810.3.h.a.701.4 8 45.29 odd 6
960.3.l.e.641.3 4 120.29 odd 2
960.3.l.e.641.4 4 40.29 even 2
960.3.l.f.641.1 4 40.19 odd 2
960.3.l.f.641.2 4 120.59 even 2
1200.3.c.k.449.1 8 60.23 odd 4
1200.3.c.k.449.2 8 20.7 even 4
1200.3.c.k.449.7 8 20.3 even 4
1200.3.c.k.449.8 8 60.47 odd 4
1200.3.l.u.401.1 4 4.3 odd 2
1200.3.l.u.401.2 4 12.11 even 2