Properties

Label 200.4.d.e.101.4
Level 200200
Weight 44
Character 200.101
Analytic conductor 11.80011.800
Analytic rank 00
Dimension 1616
Inner twists 44

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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] = [200,4,Mod(101,200)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(200, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 4, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("200.101"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: N N == 200=2352 200 = 2^{3} \cdot 5^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 200.d (of order 22, degree 11, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [16,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 11.800382001111.8003820011
Analytic rank: 00
Dimension: 1616
Coefficient field: Q[x]/(x16+)\mathbb{Q}[x]/(x^{16} + \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x16+2x14+44x12400x103200x825600x6+180224x4+524288x2+16777216 x^{16} + 2x^{14} + 44x^{12} - 400x^{10} - 3200x^{8} - 25600x^{6} + 180224x^{4} + 524288x^{2} + 16777216 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 22132 2^{21}\cdot 3^{2}
Twist minimal: no (minimal twist has level 40)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 101.4
Root 1.92212+2.07496i-1.92212 + 2.07496i of defining polynomial
Character χ\chi == 200.101
Dual form 200.4.d.e.101.3

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+(1.92212+2.07496i)q26.67494iq3+(0.6109017.97664i)q4+(13.8502+12.8300i)q6+29.8250q7+(17.7254+14.0645i)q817.5548q9+34.8520iq11+(53.2436+4.07773i)q1220.6159iq13+(57.3272+61.8856i)q14+(63.2536+9.74588i)q16+89.9765q17+(33.742436.4254i)q18+0.475810iq19199.080iq21+(72.316466.9897i)q22+100.299q23+(93.8795118.316i)q24+(42.7771+39.6263i)q2663.0462iq27+(18.2201237.903i)q28132.077iq29137.250q31+(101.359149.981i)q32+232.635q33+(172.946+186.697i)q34+(10.7242+140.028i)q36+57.1057iq37+(0.9872850.914564i)q38137.610q39+298.591q41+(413.082+382.656i)q42248.058iq43+(278.00221.2911i)q44+(192.787+208.117i)q46323.827q47+(65.0532+422.214i)q48+546.530q49600.588iq51+(164.446+12.5943i)q52+55.4295iq53+(130.818+121.182i)q54+(528.660+419.473i)q56+3.17600q57+(274.055+253.868i)q58+167.879iq59164.687iq61+(263.810284.787i)q62523.571q63+(116.381+498.597i)q64+(447.152+482.707i)q66666.565iq67+(54.9668717.710i)q68669.491iq69+384.334q71+(311.166246.899i)q72749.119q73+(118.492109.764i)q74+(3.795360.290673i)q76+1039.46iq77+(264.503285.535i)q78582.564q79894.809q81+(573.928+619.564i)q82+636.408iq83+(1587.99+121.618i)q84+(514.710+476.798i)q86881.607q87+(490.175+617.766i)q88759.913q89614.869iq91+(61.2730800.051i)q92+916.133iq93+(622.435671.928i)q94+(1001.12676.563i)q96+1279.63q97+(1050.50+1134.03i)q98611.819iq99+O(q100)q+(-1.92212 + 2.07496i) q^{2} -6.67494i q^{3} +(-0.610901 - 7.97664i) q^{4} +(13.8502 + 12.8300i) q^{6} +29.8250 q^{7} +(17.7254 + 14.0645i) q^{8} -17.5548 q^{9} +34.8520i q^{11} +(-53.2436 + 4.07773i) q^{12} -20.6159i q^{13} +(-57.3272 + 61.8856i) q^{14} +(-63.2536 + 9.74588i) q^{16} +89.9765 q^{17} +(33.7424 - 36.4254i) q^{18} +0.475810i q^{19} -199.080i q^{21} +(-72.3164 - 66.9897i) q^{22} +100.299 q^{23} +(93.8795 - 118.316i) q^{24} +(42.7771 + 39.6263i) q^{26} -63.0462i q^{27} +(-18.2201 - 237.903i) q^{28} -132.077i q^{29} -137.250 q^{31} +(101.359 - 149.981i) q^{32} +232.635 q^{33} +(-172.946 + 186.697i) q^{34} +(10.7242 + 140.028i) q^{36} +57.1057i q^{37} +(-0.987285 - 0.914564i) q^{38} -137.610 q^{39} +298.591 q^{41} +(413.082 + 382.656i) q^{42} -248.058i q^{43} +(278.002 - 21.2911i) q^{44} +(-192.787 + 208.117i) q^{46} -323.827 q^{47} +(65.0532 + 422.214i) q^{48} +546.530 q^{49} -600.588i q^{51} +(-164.446 + 12.5943i) q^{52} +55.4295i q^{53} +(130.818 + 121.182i) q^{54} +(528.660 + 419.473i) q^{56} +3.17600 q^{57} +(274.055 + 253.868i) q^{58} +167.879i q^{59} -164.687i q^{61} +(263.810 - 284.787i) q^{62} -523.571 q^{63} +(116.381 + 498.597i) q^{64} +(-447.152 + 482.707i) q^{66} -666.565i q^{67} +(-54.9668 - 717.710i) q^{68} -669.491i q^{69} +384.334 q^{71} +(-311.166 - 246.899i) q^{72} -749.119 q^{73} +(-118.492 - 109.764i) q^{74} +(3.79536 - 0.290673i) q^{76} +1039.46i q^{77} +(264.503 - 285.535i) q^{78} -582.564 q^{79} -894.809 q^{81} +(-573.928 + 619.564i) q^{82} +636.408i q^{83} +(-1587.99 + 121.618i) q^{84} +(514.710 + 476.798i) q^{86} -881.607 q^{87} +(-490.175 + 617.766i) q^{88} -759.913 q^{89} -614.869i q^{91} +(-61.2730 - 800.051i) q^{92} +916.133i q^{93} +(622.435 - 671.928i) q^{94} +(-1001.12 - 676.563i) q^{96} +1279.63 q^{97} +(-1050.50 + 1134.03i) q^{98} -611.819i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q4q412q6104q928q14168q16+112q24+200q26112q31408q3484q36+736q39+232q41920q44+212q46+200q49+2320q54++3632q96+O(q100) 16 q - 4 q^{4} - 12 q^{6} - 104 q^{9} - 28 q^{14} - 168 q^{16} + 112 q^{24} + 200 q^{26} - 112 q^{31} - 408 q^{34} - 84 q^{36} + 736 q^{39} + 232 q^{41} - 920 q^{44} + 212 q^{46} + 200 q^{49} + 2320 q^{54}+ \cdots + 3632 q^{96}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/200Z)×\left(\mathbb{Z}/200\mathbb{Z}\right)^\times.

nn 101101 151151 177177
χ(n)\chi(n) 1-1 11 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.92212 + 2.07496i −0.679572 + 0.733608i
33 6.67494i 1.28459i −0.766457 0.642296i 0.777982π-0.777982\pi
0.766457 0.642296i 0.222018π-0.222018\pi
44 −0.610901 7.97664i −0.0763627 0.997080i
55 0 0
66 13.8502 + 12.8300i 0.942388 + 0.872973i
77 29.8250 1.61040 0.805199 0.593005i 0.202059π-0.202059\pi
0.805199 + 0.593005i 0.202059π0.202059\pi
88 17.7254 + 14.0645i 0.783360 + 0.621568i
99 −17.5548 −0.650177
1010 0 0
1111 34.8520i 0.955297i 0.878551 + 0.477648i 0.158511π0.158511\pi
−0.878551 + 0.477648i 0.841489π0.841489\pi
1212 −53.2436 + 4.07773i −1.28084 + 0.0980949i
1313 20.6159i 0.439833i −0.975519 0.219916i 0.929422π-0.929422\pi
0.975519 0.219916i 0.0705784π-0.0705784\pi
1414 −57.3272 + 61.8856i −1.09438 + 1.18140i
1515 0 0
1616 −63.2536 + 9.74588i −0.988337 + 0.152279i
1717 89.9765 1.28368 0.641839 0.766840i 0.278172π-0.278172\pi
0.641839 + 0.766840i 0.278172π0.278172\pi
1818 33.7424 36.4254i 0.441842 0.476975i
1919 0.475810i 0.00574517i 0.999996 + 0.00287259i 0.000914374π0.000914374\pi
−0.999996 + 0.00287259i 0.999086π0.999086\pi
2020 0 0
2121 199.080i 2.06870i
2222 −72.3164 66.9897i −0.700814 0.649193i
2323 100.299 0.909298 0.454649 0.890671i 0.349765π-0.349765\pi
0.454649 + 0.890671i 0.349765π0.349765\pi
2424 93.8795 118.316i 0.798461 1.00630i
2525 0 0
2626 42.7771 + 39.6263i 0.322665 + 0.298898i
2727 63.0462i 0.449380i
2828 −18.2201 237.903i −0.122974 1.60570i
2929 132.077i 0.845729i −0.906193 0.422864i 0.861025π-0.861025\pi
0.906193 0.422864i 0.138975π-0.138975\pi
3030 0 0
3131 −137.250 −0.795186 −0.397593 0.917562i 0.630154π-0.630154\pi
−0.397593 + 0.917562i 0.630154π0.630154\pi
3232 101.359 149.981i 0.559933 0.828538i
3333 232.635 1.22717
3434 −172.946 + 186.697i −0.872351 + 0.941716i
3535 0 0
3636 10.7242 + 140.028i 0.0496493 + 0.648279i
3737 57.1057i 0.253733i 0.991920 + 0.126866i 0.0404920π0.0404920\pi
−0.991920 + 0.126866i 0.959508π0.959508\pi
3838 −0.987285 0.914564i −0.00421471 0.00390426i
3939 −137.610 −0.565005
4040 0 0
4141 298.591 1.13737 0.568684 0.822556i 0.307453π-0.307453\pi
0.568684 + 0.822556i 0.307453π0.307453\pi
4242 413.082 + 382.656i 1.51762 + 1.40583i
4343 248.058i 0.879733i −0.898063 0.439866i 0.855026π-0.855026\pi
0.898063 0.439866i 0.144974π-0.144974\pi
4444 278.002 21.2911i 0.952507 0.0729490i
4545 0 0
4646 −192.787 + 208.117i −0.617934 + 0.667068i
4747 −323.827 −1.00500 −0.502501 0.864577i 0.667587π-0.667587\pi
−0.502501 + 0.864577i 0.667587π0.667587\pi
4848 65.0532 + 422.214i 0.195617 + 1.26961i
4949 546.530 1.59338
5050 0 0
5151 600.588i 1.64900i
5252 −164.446 + 12.5943i −0.438548 + 0.0335868i
5353 55.4295i 0.143657i 0.997417 + 0.0718285i 0.0228834π0.0228834\pi
−0.997417 + 0.0718285i 0.977117π0.977117\pi
5454 130.818 + 121.182i 0.329669 + 0.305386i
5555 0 0
5656 528.660 + 419.473i 1.26152 + 1.00097i
5757 3.17600 0.00738020
5858 274.055 + 253.868i 0.620434 + 0.574734i
5959 167.879i 0.370440i 0.982697 + 0.185220i 0.0592998π0.0592998\pi
−0.982697 + 0.185220i 0.940700π0.940700\pi
6060 0 0
6161 164.687i 0.345672i −0.984951 0.172836i 0.944707π-0.944707\pi
0.984951 0.172836i 0.0552930π-0.0552930\pi
6262 263.810 284.787i 0.540386 0.583355i
6363 −523.571 −1.04704
6464 116.381 + 498.597i 0.227307 + 0.973823i
6565 0 0
6666 −447.152 + 482.707i −0.833949 + 0.900260i
6767 666.565i 1.21543i −0.794155 0.607715i 0.792086π-0.792086\pi
0.794155 0.607715i 0.207914π-0.207914\pi
6868 −54.9668 717.710i −0.0980250 1.27993i
6969 669.491i 1.16808i
7070 0 0
7171 384.334 0.642424 0.321212 0.947007i 0.395910π-0.395910\pi
0.321212 + 0.947007i 0.395910π0.395910\pi
7272 −311.166 246.899i −0.509323 0.404129i
7373 −749.119 −1.20107 −0.600533 0.799600i 0.705045π-0.705045\pi
−0.600533 + 0.799600i 0.705045π0.705045\pi
7474 −118.492 109.764i −0.186141 0.172430i
7575 0 0
7676 3.79536 0.290673i 0.00572840 0.000438717i
7777 1039.46i 1.53841i
7878 264.503 285.535i 0.383962 0.414493i
7979 −582.564 −0.829666 −0.414833 0.909898i 0.636160π-0.636160\pi
−0.414833 + 0.909898i 0.636160π0.636160\pi
8080 0 0
8181 −894.809 −1.22745
8282 −573.928 + 619.564i −0.772924 + 0.834383i
8383 636.408i 0.841625i 0.907148 + 0.420813i 0.138255π0.138255\pi
−0.907148 + 0.420813i 0.861745π0.861745\pi
8484 −1587.99 + 121.618i −2.06266 + 0.157972i
8585 0 0
8686 514.710 + 476.798i 0.645379 + 0.597842i
8787 −881.607 −1.08642
8888 −490.175 + 617.766i −0.593782 + 0.748341i
8989 −759.913 −0.905064 −0.452532 0.891748i 0.649479π-0.649479\pi
−0.452532 + 0.891748i 0.649479π0.649479\pi
9090 0 0
9191 614.869i 0.708305i
9292 −61.2730 800.051i −0.0694364 0.906643i
9393 916.133i 1.02149i
9494 622.435 671.928i 0.682971 0.737278i
9595 0 0
9696 −1001.12 676.563i −1.06433 0.719286i
9797 1279.63 1.33945 0.669723 0.742611i 0.266413π-0.266413\pi
0.669723 + 0.742611i 0.266413π0.266413\pi
9898 −1050.50 + 1134.03i −1.08282 + 1.16892i
9999 611.819i 0.621112i
100100 0 0
101101 806.217i 0.794273i −0.917760 0.397137i 0.870004π-0.870004\pi
0.917760 0.397137i 0.129996π-0.129996\pi
102102 1246.19 + 1154.40i 1.20972 + 1.12062i
103103 −497.704 −0.476119 −0.238059 0.971251i 0.576511π-0.576511\pi
−0.238059 + 0.971251i 0.576511π0.576511\pi
104104 289.952 365.426i 0.273386 0.344547i
105105 0 0
106106 −115.014 106.542i −0.105388 0.0976254i
107107 111.714i 0.100933i −0.998726 0.0504666i 0.983929π-0.983929\pi
0.998726 0.0504666i 0.0160708π-0.0160708\pi
108108 −502.897 + 38.5150i −0.448068 + 0.0343158i
109109 1098.19i 0.965022i 0.875890 + 0.482511i 0.160275π0.160275\pi
−0.875890 + 0.482511i 0.839725π0.839725\pi
110110 0 0
111111 381.177 0.325943
112112 −1886.54 + 290.671i −1.59162 + 0.245230i
113113 2118.96 1.76403 0.882015 0.471221i 0.156187π-0.156187\pi
0.882015 + 0.471221i 0.156187π0.156187\pi
114114 −6.10466 + 6.59007i −0.00501538 + 0.00541418i
115115 0 0
116116 −1053.53 + 80.6862i −0.843259 + 0.0645821i
117117 361.908i 0.285969i
118118 −348.341 322.683i −0.271758 0.251741i
119119 2683.55 2.06723
120120 0 0
121121 116.341 0.0874084
122122 341.718 + 316.548i 0.253588 + 0.234909i
123123 1993.08i 1.46105i
124124 83.8460 + 1094.79i 0.0607225 + 0.792864i
125125 0 0
126126 1006.37 1086.39i 0.711542 0.768120i
127127 −567.970 −0.396844 −0.198422 0.980117i 0.563582π-0.563582\pi
−0.198422 + 0.980117i 0.563582π0.563582\pi
128128 −1258.27 716.879i −0.868876 0.495029i
129129 −1655.77 −1.13010
130130 0 0
131131 2238.84i 1.49319i 0.665278 + 0.746596i 0.268313π0.268313\pi
−0.665278 + 0.746596i 0.731687π0.731687\pi
132132 −142.117 1855.64i −0.0937097 1.22358i
133133 14.1910i 0.00925201i
134134 1383.09 + 1281.22i 0.891650 + 0.825973i
135135 0 0
136136 1594.87 + 1265.47i 1.00558 + 0.797892i
137137 1428.64 0.890925 0.445462 0.895301i 0.353039π-0.353039\pi
0.445462 + 0.895301i 0.353039π0.353039\pi
138138 1389.17 + 1286.84i 0.856911 + 0.793793i
139139 1467.79i 0.895659i −0.894119 0.447829i 0.852197π-0.852197\pi
0.894119 0.447829i 0.147803π-0.147803\pi
140140 0 0
141141 2161.53i 1.29102i
142142 −738.737 + 797.478i −0.436574 + 0.471288i
143143 718.505 0.420171
144144 1110.40 171.087i 0.642594 0.0990086i
145145 0 0
146146 1439.90 1554.39i 0.816211 0.881112i
147147 3648.05i 2.04684i
148148 455.512 34.8860i 0.252992 0.0193757i
149149 2881.15i 1.58411i 0.610449 + 0.792056i 0.290989π0.290989\pi
−0.610449 + 0.792056i 0.709011π0.709011\pi
150150 0 0
151151 −949.291 −0.511604 −0.255802 0.966729i 0.582340π-0.582340\pi
−0.255802 + 0.966729i 0.582340π0.582340\pi
152152 −6.69202 + 8.43393i −0.00357101 + 0.00450054i
153153 −1579.52 −0.834617
154154 −2156.83 1997.97i −1.12859 1.04546i
155155 0 0
156156 84.0661 + 1097.66i 0.0431453 + 0.563356i
157157 3159.30i 1.60599i 0.595988 + 0.802993i 0.296761π0.296761\pi
−0.595988 + 0.802993i 0.703239π0.703239\pi
158158 1119.76 1208.80i 0.563818 0.608650i
159159 369.988 0.184541
160160 0 0
161161 2991.42 1.46433
162162 1719.93 1856.69i 0.834139 0.900465i
163163 1361.75i 0.654360i 0.944962 + 0.327180i 0.106098π0.106098\pi
−0.944962 + 0.327180i 0.893902π0.893902\pi
164164 −182.410 2381.75i −0.0868525 1.13405i
165165 0 0
166166 −1320.52 1223.25i −0.617423 0.571945i
167167 −641.323 −0.297168 −0.148584 0.988900i 0.547472π-0.547472\pi
−0.148584 + 0.988900i 0.547472π0.547472\pi
168168 2799.95 3528.77i 1.28584 1.62054i
169169 1771.98 0.806547
170170 0 0
171171 8.35274i 0.00373538i
172172 −1978.67 + 151.539i −0.877164 + 0.0671787i
173173 57.9969i 0.0254880i 0.999919 + 0.0127440i 0.00405665π0.00405665\pi
−0.999919 + 0.0127440i 0.995943π0.995943\pi
174174 1694.56 1829.30i 0.738299 0.797004i
175175 0 0
176176 −339.663 2204.51i −0.145472 0.944155i
177177 1120.58 0.475864
178178 1460.65 1576.79i 0.615056 0.663962i
179179 1608.75i 0.671753i 0.941906 + 0.335876i 0.109032π0.109032\pi
−0.941906 + 0.335876i 0.890968π0.890968\pi
180180 0 0
181181 2665.60i 1.09465i 0.836919 + 0.547327i 0.184354π0.184354\pi
−0.836919 + 0.547327i 0.815646π0.815646\pi
182182 1275.83 + 1181.85i 0.519619 + 0.481345i
183183 −1099.27 −0.444047
184184 1777.85 + 1410.66i 0.712308 + 0.565190i
185185 0 0
186186 −1900.94 1760.92i −0.749373 0.694176i
187187 3135.86i 1.22629i
188188 197.827 + 2583.05i 0.0767446 + 1.00207i
189189 1880.35i 0.723680i
190190 0 0
191191 −2879.60 −1.09089 −0.545446 0.838146i 0.683640π-0.683640\pi
−0.545446 + 0.838146i 0.683640π0.683640\pi
192192 3328.11 776.837i 1.25097 0.291997i
193193 2401.35 0.895611 0.447805 0.894131i 0.352206π-0.352206\pi
0.447805 + 0.894131i 0.352206π0.352206\pi
194194 −2459.60 + 2655.17i −0.910251 + 0.982629i
195195 0 0
196196 −333.876 4359.47i −0.121675 1.58873i
197197 4454.03i 1.61085i −0.592700 0.805423i 0.701938π-0.701938\pi
0.592700 0.805423i 0.298062π-0.298062\pi
198198 1269.50 + 1175.99i 0.455653 + 0.422091i
199199 −4903.81 −1.74684 −0.873422 0.486964i 0.838104π-0.838104\pi
−0.873422 + 0.486964i 0.838104π0.838104\pi
200200 0 0
201201 −4449.28 −1.56133
202202 1672.87 + 1549.65i 0.582685 + 0.539766i
203203 3939.20i 1.36196i
204204 −4790.67 + 366.900i −1.64419 + 0.125922i
205205 0 0
206206 956.647 1032.72i 0.323557 0.349285i
207207 −1760.73 −0.591205
208208 200.920 + 1304.03i 0.0669774 + 0.434703i
209209 −16.5829 −0.00548834
210210 0 0
211211 1226.59i 0.400200i 0.979776 + 0.200100i 0.0641266π0.0641266\pi
−0.979776 + 0.200100i 0.935873π0.935873\pi
212212 442.141 33.8620i 0.143238 0.0109700i
213213 2565.41i 0.825253i
214214 231.803 + 214.729i 0.0740454 + 0.0685914i
215215 0 0
216216 886.712 1117.52i 0.279320 0.352026i
217217 −4093.47 −1.28057
218218 −2278.69 2110.85i −0.707948 0.655802i
219219 5000.32i 1.54288i
220220 0 0
221221 1854.95i 0.564603i
222222 −732.668 + 790.926i −0.221502 + 0.239115i
223223 1542.77 0.463281 0.231641 0.972801i 0.425591π-0.425591\pi
0.231641 + 0.972801i 0.425591π0.425591\pi
224224 3023.02 4473.19i 0.901716 1.33428i
225225 0 0
226226 −4072.91 + 4396.76i −1.19879 + 1.29411i
227227 3851.34i 1.12609i −0.826426 0.563045i 0.809630π-0.809630\pi
0.826426 0.563045i 0.190370π-0.190370\pi
228228 −1.94022 25.3338i −0.000563572 0.00735865i
229229 5232.61i 1.50996i −0.655748 0.754980i 0.727647π-0.727647\pi
0.655748 0.754980i 0.272353π-0.272353\pi
230230 0 0
231231 6938.32 1.97623
232232 1857.60 2341.13i 0.525678 0.662510i
233233 181.419 0.0510094 0.0255047 0.999675i 0.491881π-0.491881\pi
0.0255047 + 0.999675i 0.491881π0.491881\pi
234234 −750.943 695.630i −0.209789 0.194337i
235235 0 0
236236 1339.11 102.557i 0.369358 0.0282878i
237237 3888.58i 1.06578i
238238 −5158.10 + 5568.25i −1.40483 + 1.51654i
239239 −2507.75 −0.678716 −0.339358 0.940657i 0.610210π-0.610210\pi
−0.339358 + 0.940657i 0.610210π0.610210\pi
240240 0 0
241241 −1089.46 −0.291196 −0.145598 0.989344i 0.546511π-0.546511\pi
−0.145598 + 0.989344i 0.546511π0.546511\pi
242242 −223.621 + 241.402i −0.0594003 + 0.0641235i
243243 4270.54i 1.12739i
244244 −1313.65 + 100.607i −0.344662 + 0.0263964i
245245 0 0
246246 4135.55 + 3830.93i 1.07184 + 0.992892i
247247 9.80925 0.00252691
248248 −2432.81 1930.34i −0.622917 0.494262i
249249 4247.99 1.08115
250250 0 0
251251 5380.02i 1.35292i 0.736478 + 0.676461i 0.236487π0.236487\pi
−0.736478 + 0.676461i 0.763513π0.763513\pi
252252 319.850 + 4176.34i 0.0799551 + 1.04399i
253253 3495.63i 0.868649i
254254 1091.71 1178.51i 0.269684 0.291128i
255255 0 0
256256 3906.04 1232.92i 0.953622 0.301007i
257257 1377.98 0.334458 0.167229 0.985918i 0.446518π-0.446518\pi
0.167229 + 0.985918i 0.446518π0.446518\pi
258258 3182.59 3435.66i 0.767983 0.829049i
259259 1703.18i 0.408611i
260260 0 0
261261 2318.59i 0.549873i
262262 −4645.49 4303.32i −1.09542 1.01473i
263263 411.340 0.0964422 0.0482211 0.998837i 0.484645π-0.484645\pi
0.0482211 + 0.998837i 0.484645π0.484645\pi
264264 4123.55 + 3271.88i 0.961314 + 0.762767i
265265 0 0
266266 −29.4458 27.2769i −0.00678735 0.00628741i
267267 5072.37i 1.16264i
268268 −5316.95 + 407.205i −1.21188 + 0.0928135i
269269 407.204i 0.0922961i 0.998935 + 0.0461481i 0.0146946π0.0146946\pi
−0.998935 + 0.0461481i 0.985305π0.985305\pi
270270 0 0
271271 −1329.04 −0.297909 −0.148954 0.988844i 0.547591π-0.547591\pi
−0.148954 + 0.988844i 0.547591π0.547591\pi
272272 −5691.34 + 876.900i −1.26871 + 0.195478i
273273 −4104.21 −0.909884
274274 −2746.01 + 2964.36i −0.605448 + 0.653590i
275275 0 0
276276 −5340.29 + 408.993i −1.16467 + 0.0891975i
277277 4411.34i 0.956866i −0.878124 0.478433i 0.841205π-0.841205\pi
0.878124 0.478433i 0.158795π-0.158795\pi
278278 3045.61 + 2821.28i 0.657063 + 0.608665i
279279 2409.39 0.517012
280280 0 0
281281 5134.23 1.08997 0.544986 0.838445i 0.316535π-0.316535\pi
0.544986 + 0.838445i 0.316535π0.316535\pi
282282 −4485.08 4154.72i −0.947101 0.877340i
283283 3093.54i 0.649794i 0.945749 + 0.324897i 0.105330π0.105330\pi
−0.945749 + 0.324897i 0.894670π0.894670\pi
284284 −234.790 3065.70i −0.0490572 0.640548i
285285 0 0
286286 −1381.05 + 1490.87i −0.285536 + 0.308241i
287287 8905.47 1.83161
288288 −1779.33 + 2632.89i −0.364056 + 0.538696i
289289 3182.77 0.647827
290290 0 0
291291 8541.42i 1.72064i
292292 457.638 + 5975.45i 0.0917166 + 1.19756i
293293 671.319i 0.133853i 0.997758 + 0.0669264i 0.0213193π0.0213193\pi
−0.997758 + 0.0669264i 0.978681π0.978681\pi
294294 7569.55 + 7011.99i 1.50158 + 1.39098i
295295 0 0
296296 −803.162 + 1012.22i −0.157712 + 0.198764i
297297 2197.28 0.429291
298298 −5978.26 5537.91i −1.16212 1.07652i
299299 2067.76i 0.399939i
300300 0 0
301301 7398.33i 1.41672i
302302 1824.65 1969.74i 0.347672 0.375317i
303303 −5381.45 −1.02032
304304 −4.63719 30.0967i −0.000874871 0.00567817i
305305 0 0
306306 3036.02 3277.43i 0.567183 0.612282i
307307 5810.78i 1.08026i 0.841583 + 0.540128i 0.181624π0.181624\pi
−0.841583 + 0.540128i 0.818376π0.818376\pi
308308 8291.39 635.007i 1.53392 0.117477i
309309 3322.14i 0.611619i
310310 0 0
311311 −7223.30 −1.31703 −0.658514 0.752568i 0.728815π-0.728815\pi
−0.658514 + 0.752568i 0.728815π0.728815\pi
312312 −2439.19 1935.41i −0.442603 0.351189i
313313 −1804.40 −0.325849 −0.162925 0.986638i 0.552093π-0.552093\pi
−0.162925 + 0.986638i 0.552093π0.552093\pi
314314 −6555.42 6072.56i −1.17817 1.09138i
315315 0 0
316316 355.889 + 4646.91i 0.0633555 + 0.827244i
317317 1593.07i 0.282259i 0.989991 + 0.141129i 0.0450733π0.0450733\pi
−0.989991 + 0.141129i 0.954927π0.954927\pi
318318 −711.162 + 767.710i −0.125409 + 0.135381i
319319 4603.15 0.807922
320320 0 0
321321 −745.687 −0.129658
322322 −5749.88 + 6207.08i −0.995119 + 1.07425i
323323 42.8117i 0.00737495i
324324 546.640 + 7137.57i 0.0937311 + 1.22386i
325325 0 0
326326 −2825.58 2617.45i −0.480044 0.444685i
327327 7330.34 1.23966
328328 5292.65 + 4199.53i 0.890969 + 0.706951i
329329 −9658.14 −1.61845
330330 0 0
331331 6213.17i 1.03174i −0.856666 0.515871i 0.827468π-0.827468\pi
0.856666 0.515871i 0.172532π-0.172532\pi
332332 5076.40 388.783i 0.839168 0.0642688i
333333 1002.48i 0.164971i
334334 1232.70 1330.72i 0.201947 0.218005i
335335 0 0
336336 1940.21 + 12592.5i 0.315021 + 2.04458i
337337 −11379.1 −1.83935 −0.919673 0.392686i 0.871546π-0.871546\pi
−0.919673 + 0.392686i 0.871546π0.871546\pi
338338 −3405.97 + 3676.79i −0.548107 + 0.591690i
339339 14144.0i 2.26606i
340340 0 0
341341 4783.42i 0.759638i
342342 17.3316 + 16.0550i 0.00274031 + 0.00253846i
343343 6070.27 0.955579
344344 3488.81 4396.93i 0.546814 0.689148i
345345 0 0
346346 −120.341 111.477i −0.0186982 0.0173209i
347347 2528.79i 0.391217i 0.980682 + 0.195609i 0.0626682π0.0626682\pi
−0.980682 + 0.195609i 0.937332π0.937332\pi
348348 538.575 + 7032.27i 0.0829617 + 1.08324i
349349 110.562i 0.0169577i 0.999964 + 0.00847885i 0.00269893π0.00269893\pi
−0.999964 + 0.00847885i 0.997301π0.997301\pi
350350 0 0
351351 −1299.76 −0.197652
352352 5227.14 + 3532.55i 0.791499 + 0.534903i
353353 −7118.00 −1.07324 −0.536619 0.843825i 0.680299π-0.680299\pi
−0.536619 + 0.843825i 0.680299π0.680299\pi
354354 −2153.89 + 2325.16i −0.323384 + 0.349098i
355355 0 0
356356 464.232 + 6061.56i 0.0691131 + 0.902421i
357357 17912.5i 2.65555i
358358 −3338.09 3092.22i −0.492804 0.456505i
359359 3118.04 0.458396 0.229198 0.973380i 0.426390π-0.426390\pi
0.229198 + 0.973380i 0.426390π0.426390\pi
360360 0 0
361361 6858.77 0.999967
362362 −5531.00 5123.60i −0.803047 0.743896i
363363 776.566i 0.112284i
364364 −4904.59 + 375.624i −0.706237 + 0.0540881i
365365 0 0
366366 2112.94 2280.95i 0.301762 0.325757i
367367 −11007.8 −1.56567 −0.782835 0.622230i 0.786227π-0.786227\pi
−0.782835 + 0.622230i 0.786227π0.786227\pi
368368 −6344.29 + 977.505i −0.898693 + 0.138467i
369369 −5241.70 −0.739491
370370 0 0
371371 1653.18i 0.231345i
372372 7307.66 559.667i 1.01851 0.0780037i
373373 12872.3i 1.78687i −0.449190 0.893436i 0.648287π-0.648287\pi
0.449190 0.893436i 0.351713π-0.351713\pi
374374 −6506.77 6027.50i −0.899618 0.833354i
375375 0 0
376376 −5739.98 4554.46i −0.787278 0.624677i
377377 −2722.89 −0.371979
378378 3901.65 + 3614.27i 0.530898 + 0.491793i
379379 6010.29i 0.814586i −0.913298 0.407293i 0.866473π-0.866473\pi
0.913298 0.407293i 0.133527π-0.133527\pi
380380 0 0
381381 3791.16i 0.509783i
382382 5534.93 5975.04i 0.741340 0.800287i
383383 4012.72 0.535354 0.267677 0.963509i 0.413744π-0.413744\pi
0.267677 + 0.963509i 0.413744π0.413744\pi
384384 −4785.12 + 8398.86i −0.635911 + 1.11615i
385385 0 0
386386 −4615.68 + 4982.70i −0.608632 + 0.657028i
387387 4354.61i 0.571982i
388388 −781.725 10207.1i −0.102284 1.33554i
389389 9488.02i 1.23666i 0.785918 + 0.618331i 0.212191π0.212191\pi
−0.785918 + 0.618331i 0.787809π0.787809\pi
390390 0 0
391391 9024.58 1.16724
392392 9687.47 + 7686.65i 1.24819 + 0.990394i
393393 14944.1 1.91814
394394 9241.93 + 8561.19i 1.18173 + 1.09469i
395395 0 0
396396 −4880.26 + 373.761i −0.619298 + 0.0474298i
397397 4950.44i 0.625832i 0.949781 + 0.312916i 0.101306π0.101306\pi
−0.949781 + 0.312916i 0.898694π0.898694\pi
398398 9425.72 10175.2i 1.18711 1.28150i
399399 94.7242 0.0118851
400400 0 0
401401 −8799.56 −1.09583 −0.547917 0.836533i 0.684579π-0.684579\pi
−0.547917 + 0.836533i 0.684579π0.684579\pi
402402 8552.05 9232.06i 1.06104 1.14541i
403403 2829.53i 0.349749i
404404 −6430.90 + 492.519i −0.791954 + 0.0606528i
405405 0 0
406406 8173.68 + 7571.62i 0.999145 + 0.925550i
407407 −1990.25 −0.242390
408408 8446.95 10645.7i 1.02497 1.29176i
409409 −7179.75 −0.868009 −0.434005 0.900911i 0.642900π-0.642900\pi
−0.434005 + 0.900911i 0.642900π0.642900\pi
410410 0 0
411411 9536.06i 1.14447i
412412 304.048 + 3970.01i 0.0363577 + 0.474729i
413413 5006.98i 0.596556i
414414 3384.34 3653.44i 0.401766 0.433713i
415415 0 0
416416 −3092.00 2089.60i −0.364418 0.246277i
417417 −9797.42 −1.15056
418418 31.8744 34.4088i 0.00372973 0.00402629i
419419 13557.2i 1.58070i 0.612657 + 0.790349i 0.290101π0.290101\pi
−0.612657 + 0.790349i 0.709899π0.709899\pi
420420 0 0
421421 7428.36i 0.859943i −0.902843 0.429971i 0.858524π-0.858524\pi
0.902843 0.429971i 0.141476π-0.141476\pi
422422 −2545.13 2357.66i −0.293590 0.271965i
423423 5684.72 0.653429
424424 −779.587 + 982.511i −0.0892926 + 0.112535i
425425 0 0
426426 5323.11 + 4931.02i 0.605412 + 0.560819i
427427 4911.78i 0.556669i
428428 −891.106 + 68.2465i −0.100638 + 0.00770752i
429429 4795.97i 0.539748i
430430 0 0
431431 −1591.77 −0.177895 −0.0889475 0.996036i 0.528350π-0.528350\pi
−0.0889475 + 0.996036i 0.528350π0.528350\pi
432432 614.441 + 3987.90i 0.0684313 + 0.444139i
433433 −10811.6 −1.19994 −0.599970 0.800023i 0.704821π-0.704821\pi
−0.599970 + 0.800023i 0.704821π0.704821\pi
434434 7868.14 8493.77i 0.870237 0.939434i
435435 0 0
436436 8759.85 670.885i 0.962204 0.0736916i
437437 47.7234i 0.00522407i
438438 −10375.5 9611.23i −1.13187 1.04850i
439439 4891.74 0.531823 0.265911 0.963997i 0.414327π-0.414327\pi
0.265911 + 0.963997i 0.414327π0.414327\pi
440440 0 0
441441 −9594.21 −1.03598
442442 3848.94 + 3565.43i 0.414197 + 0.383689i
443443 2116.86i 0.227032i 0.993536 + 0.113516i 0.0362113π0.0362113\pi
−0.993536 + 0.113516i 0.963789π0.963789\pi
444444 −232.862 3040.51i −0.0248899 0.324992i
445445 0 0
446446 −2965.40 + 3201.19i −0.314833 + 0.339867i
447447 19231.5 2.03494
448448 3471.06 + 14870.7i 0.366054 + 1.56824i
449449 13253.6 1.39305 0.696523 0.717535i 0.254730π-0.254730\pi
0.696523 + 0.717535i 0.254730π0.254730\pi
450450 0 0
451451 10406.5i 1.08652i
452452 −1294.48 16902.2i −0.134706 1.75888i
453453 6336.46i 0.657202i
454454 7991.37 + 7402.74i 0.826109 + 0.765260i
455455 0 0
456456 56.2960 + 44.6688i 0.00578136 + 0.00458730i
457457 3969.19 0.406282 0.203141 0.979150i 0.434885π-0.434885\pi
0.203141 + 0.979150i 0.434885π0.434885\pi
458458 10857.4 + 10057.7i 1.10772 + 1.02613i
459459 5672.68i 0.576858i
460460 0 0
461461 7068.99i 0.714177i 0.934071 + 0.357089i 0.116231π0.116231\pi
−0.934071 + 0.357089i 0.883769π0.883769\pi
462462 −13336.3 + 14396.7i −1.34299 + 1.44978i
463463 −178.581 −0.0179251 −0.00896257 0.999960i 0.502853π-0.502853\pi
−0.00896257 + 0.999960i 0.502853π0.502853\pi
464464 1287.21 + 8354.36i 0.128787 + 0.835865i
465465 0 0
466466 −348.710 + 376.438i −0.0346646 + 0.0374209i
467467 11576.2i 1.14707i 0.819180 + 0.573536i 0.194429π0.194429\pi
−0.819180 + 0.573536i 0.805571π0.805571\pi
468468 2886.81 221.090i 0.285134 0.0218374i
469469 19880.3i 1.95733i
470470 0 0
471471 21088.2 2.06304
472472 −2361.13 + 2975.72i −0.230254 + 0.290188i
473473 8645.31 0.840406
474474 −8068.64 7474.32i −0.781867 0.724276i
475475 0 0
476476 −1639.38 21405.7i −0.157859 2.06119i
477477 973.053i 0.0934025i
478478 4820.20 5203.48i 0.461236 0.497911i
479479 −12742.0 −1.21544 −0.607720 0.794152i 0.707916π-0.707916\pi
−0.607720 + 0.794152i 0.707916π0.707916\pi
480480 0 0
481481 1177.29 0.111600
482482 2094.07 2260.58i 0.197889 0.213624i
483483 19967.6i 1.88107i
484484 −71.0726 928.007i −0.00667474 0.0871532i
485485 0 0
486486 −8861.20 8208.50i −0.827062 0.766142i
487487 13309.0 1.23838 0.619188 0.785243i 0.287462π-0.287462\pi
0.619188 + 0.785243i 0.287462π0.287462\pi
488488 2316.23 2919.14i 0.214858 0.270785i
489489 9089.62 0.840586
490490 0 0
491491 216.689i 0.0199166i 0.999950 + 0.00995830i 0.00316988π0.00316988\pi
−0.999950 + 0.00995830i 0.996830π0.996830\pi
492492 −15898.1 + 1217.57i −1.45679 + 0.111570i
493493 11883.9i 1.08564i
494494 −18.8546 + 20.3538i −0.00171722 + 0.00185377i
495495 0 0
496496 8681.53 1337.62i 0.785912 0.121090i
497497 11462.8 1.03456
498498 −8165.14 + 8814.39i −0.734716 + 0.793137i
499499 10800.4i 0.968921i 0.874813 + 0.484460i 0.160984π0.160984\pi
−0.874813 + 0.484460i 0.839016π0.839016\pi
500500 0 0
501501 4280.79i 0.381740i
502502 −11163.3 10341.0i −0.992516 0.919409i
503503 −16697.6 −1.48013 −0.740067 0.672533i 0.765206π-0.765206\pi
−0.740067 + 0.672533i 0.765206π0.765206\pi
504504 −9280.52 7363.75i −0.820213 0.650809i
505505 0 0
506506 −7253.28 6719.02i −0.637248 0.590310i
507507 11827.9i 1.03608i
508508 346.974 + 4530.49i 0.0303041 + 0.395685i
509509 13066.1i 1.13781i 0.822402 + 0.568906i 0.192633π0.192633\pi
−0.822402 + 0.568906i 0.807367π0.807367\pi
510510 0 0
511511 −22342.5 −1.93419
512512 −4949.61 + 10474.7i −0.427234 + 0.904141i
513513 29.9980 0.00258176
514514 −2648.64 + 2859.24i −0.227289 + 0.245361i
515515 0 0
516516 1011.51 + 13207.5i 0.0862973 + 1.12680i
517517 11286.0i 0.960075i
518518 −3534.02 3273.71i −0.299760 0.277681i
519519 387.126 0.0327417
520520 0 0
521521 −269.920 −0.0226975 −0.0113488 0.999936i 0.503613π-0.503613\pi
−0.0113488 + 0.999936i 0.503613π0.503613\pi
522522 −4810.97 4456.61i −0.403392 0.373679i
523523 19287.7i 1.61260i 0.591506 + 0.806300i 0.298533π0.298533\pi
−0.591506 + 0.806300i 0.701467π0.701467\pi
524524 17858.4 1367.71i 1.48883 0.114024i
525525 0 0
526526 −790.645 + 853.513i −0.0655395 + 0.0707508i
527527 −12349.2 −1.02076
528528 −14715.0 + 2267.23i −1.21285 + 0.186872i
529529 −2107.06 −0.173178
530530 0 0
531531 2947.08i 0.240852i
532532 113.197 8.66931i 0.00922500 0.000706508i
533533 6155.72i 0.500251i
534534 −10525.0 9749.72i −0.852921 0.790096i
535535 0 0
536536 9374.88 11815.1i 0.755472 0.952120i
537537 10738.3 0.862928
538538 −844.931 782.695i −0.0677092 0.0627219i
539539 19047.6i 1.52215i
540540 0 0
541541 8722.31i 0.693164i 0.938020 + 0.346582i 0.112658π0.112658\pi
−0.938020 + 0.346582i 0.887342π0.887342\pi
542542 2554.57 2757.70i 0.202450 0.218548i
543543 17792.7 1.40618
544544 9119.91 13494.8i 0.718774 1.06357i
545545 0 0
546546 7888.79 8516.07i 0.618332 0.667498i
547547 8718.86i 0.681520i 0.940150 + 0.340760i 0.110684π0.110684\pi
−0.940150 + 0.340760i 0.889316π0.889316\pi
548548 −872.756 11395.7i −0.0680334 0.888323i
549549 2891.04i 0.224748i
550550 0 0
551551 62.8437 0.00485886
552552 9416.04 11867.0i 0.726039 0.915025i
553553 −17375.0 −1.33609
554554 9153.35 + 8479.13i 0.701965 + 0.650260i
555555 0 0
556556 −11708.1 + 896.677i −0.893043 + 0.0683949i
557557 11758.7i 0.894489i 0.894412 + 0.447245i 0.147595π0.147595\pi
−0.894412 + 0.447245i 0.852405π0.852405\pi
558558 −4631.13 + 4999.38i −0.351347 + 0.379284i
559559 −5113.94 −0.386935
560560 0 0
561561 20931.7 1.57529
562562 −9868.60 + 10653.3i −0.740715 + 0.799613i
563563 5260.52i 0.393791i 0.980424 + 0.196896i 0.0630860π0.0630860\pi
−0.980424 + 0.196896i 0.936914π0.936914\pi
564564 17241.7 1320.48i 1.28725 0.0985855i
565565 0 0
566566 −6418.96 5946.16i −0.476695 0.441582i
567567 −26687.7 −1.97668
568568 6812.49 + 5405.46i 0.503250 + 0.399310i
569569 19030.4 1.40210 0.701050 0.713112i 0.252715π-0.252715\pi
0.701050 + 0.713112i 0.252715π0.252715\pi
570570 0 0
571571 23227.4i 1.70234i 0.524887 + 0.851172i 0.324108π0.324108\pi
−0.524887 + 0.851172i 0.675892π0.675892\pi
572572 −438.936 5731.25i −0.0320853 0.418944i
573573 19221.1i 1.40135i
574574 −17117.4 + 18478.5i −1.24471 + 1.34369i
575575 0 0
576576 −2043.05 8752.77i −0.147790 0.633158i
577577 −526.632 −0.0379965 −0.0189983 0.999820i 0.506048π-0.506048\pi
−0.0189983 + 0.999820i 0.506048π0.506048\pi
578578 −6117.67 + 6604.12i −0.440245 + 0.475251i
579579 16028.9i 1.15049i
580580 0 0
581581 18980.9i 1.35535i
582582 17723.1 + 16417.6i 1.26228 + 1.16930i
583583 −1931.83 −0.137235
584584 −13278.5 10536.0i −0.940867 0.746544i
585585 0 0
586586 −1392.96 1290.36i −0.0981956 0.0909627i
587587 14220.5i 0.999902i −0.866054 0.499951i 0.833351π-0.833351\pi
0.866054 0.499951i 0.166649π-0.166649\pi
588588 −29099.2 + 2228.60i −2.04087 + 0.156303i
589589 65.3047i 0.00456848i
590590 0 0
591591 −29730.4 −2.06928
592592 −556.545 3612.14i −0.0386383 0.250774i
593593 10794.3 0.747500 0.373750 0.927529i 0.378072π-0.378072\pi
0.373750 + 0.927529i 0.378072π0.378072\pi
594594 −4223.45 + 4559.27i −0.291734 + 0.314931i
595595 0 0
596596 22981.9 1760.10i 1.57949 0.120967i
597597 32732.6i 2.24398i
598598 4290.52 + 3974.49i 0.293398 + 0.271787i
599599 −10036.9 −0.684634 −0.342317 0.939584i 0.611212π-0.611212\pi
−0.342317 + 0.939584i 0.611212π0.611212\pi
600600 0 0
601601 8251.09 0.560015 0.280008 0.959998i 0.409663π-0.409663\pi
0.280008 + 0.959998i 0.409663π0.409663\pi
602602 15351.2 + 14220.5i 1.03932 + 0.962764i
603603 11701.4i 0.790245i
604604 579.923 + 7572.15i 0.0390674 + 0.510110i
605605 0 0
606606 10343.8 11166.3i 0.693379 0.748513i
607607 8119.05 0.542903 0.271451 0.962452i 0.412496π-0.412496\pi
0.271451 + 0.962452i 0.412496π0.412496\pi
608608 71.3626 + 48.2275i 0.00476009 + 0.00321691i
609609 −26293.9 −1.74956
610610 0 0
611611 6675.99i 0.442032i
612612 964.930 + 12599.2i 0.0637336 + 0.832180i
613613 20527.3i 1.35251i 0.736668 + 0.676255i 0.236398π0.236398\pi
−0.736668 + 0.676255i 0.763602π0.763602\pi
614614 −12057.1 11169.0i −0.792485 0.734112i
615615 0 0
616616 −14619.4 + 18424.9i −0.956225 + 1.20513i
617617 −27545.7 −1.79732 −0.898661 0.438643i 0.855459π-0.855459\pi
−0.898661 + 0.438643i 0.855459π0.855459\pi
618618 −6893.31 6385.56i −0.448689 0.415639i
619619 1777.17i 0.115396i −0.998334 0.0576982i 0.981624π-0.981624\pi
0.998334 0.0576982i 0.0183761π-0.0183761\pi
620620 0 0
621621 6323.49i 0.408620i
622622 13884.1 14988.1i 0.895016 0.966183i
623623 −22664.4 −1.45751
624624 8704.32 1341.13i 0.558416 0.0860387i
625625 0 0
626626 3468.28 3744.06i 0.221438 0.239046i
627627 110.690i 0.00705028i
628628 25200.6 1930.02i 1.60130 0.122637i
629629 5138.17i 0.325711i
630630 0 0
631631 16484.4 1.03999 0.519995 0.854169i 0.325934π-0.325934\pi
0.519995 + 0.854169i 0.325934π0.325934\pi
632632 −10326.2 8193.46i −0.649927 0.515694i
633633 8187.43 0.514093
634634 −3305.56 3062.08i −0.207067 0.191815i
635635 0 0
636636 −226.026 2951.26i −0.0140920 0.184002i
637637 11267.2i 0.700821i
638638 −8847.82 + 9551.35i −0.549041 + 0.592698i
639639 −6746.91 −0.417689
640640 0 0
641641 −24.7805 −0.00152694 −0.000763470 1.00000i 0.500243π-0.500243\pi
−0.000763470 1.00000i 0.500243π0.500243\pi
642642 1433.30 1547.27i 0.0881119 0.0951181i
643643 29107.1i 1.78518i −0.450870 0.892590i 0.648886π-0.648886\pi
0.450870 0.892590i 0.351114π-0.351114\pi
644644 −1827.47 23861.5i −0.111820 1.46006i
645645 0 0
646646 −88.8325 82.2893i −0.00541032 0.00501181i
647647 −13419.6 −0.815421 −0.407711 0.913111i 0.633673π-0.633673\pi
−0.407711 + 0.913111i 0.633673π0.633673\pi
648648 −15860.9 12585.0i −0.961533 0.762941i
649649 −5850.91 −0.353880
650650 0 0
651651 27323.6i 1.64500i
652652 10862.2 831.897i 0.652450 0.0499687i
653653 1926.26i 0.115437i 0.998333 + 0.0577186i 0.0183826π0.0183826\pi
−0.998333 + 0.0577186i 0.981617π0.981617\pi
654654 −14089.8 + 15210.1i −0.842438 + 0.909425i
655655 0 0
656656 −18887.0 + 2910.03i −1.12410 + 0.173198i
657657 13150.6 0.780905
658658 18564.1 20040.2i 1.09986 1.18731i
659659 13158.1i 0.777797i 0.921281 + 0.388899i 0.127144π0.127144\pi
−0.921281 + 0.388899i 0.872856π0.872856\pi
660660 0 0
661661 27392.1i 1.61184i −0.592023 0.805921i 0.701670π-0.701670\pi
0.592023 0.805921i 0.298330π-0.298330\pi
662662 12892.1 + 11942.5i 0.756895 + 0.701143i
663663 −12381.7 −0.725285
664664 −8950.75 + 11280.6i −0.523127 + 0.659296i
665665 0 0
666666 2080.10 + 1926.88i 0.121024 + 0.112110i
667667 13247.3i 0.769019i
668668 391.785 + 5115.61i 0.0226926 + 0.296301i
669669 10297.9i 0.595128i
670670 0 0
671671 5739.65 0.330219
672672 −29858.3 20178.5i −1.71400 1.15834i
673673 −5569.75 −0.319017 −0.159508 0.987197i 0.550991π-0.550991\pi
−0.159508 + 0.987197i 0.550991π0.550991\pi
674674 21872.0 23611.2i 1.24997 1.34936i
675675 0 0
676676 −1082.51 14134.5i −0.0615901 0.804192i
677677 4130.23i 0.234472i −0.993104 0.117236i 0.962597π-0.962597\pi
0.993104 0.117236i 0.0374034π-0.0374034\pi
678678 29348.1 + 27186.4i 1.66240 + 1.53995i
679679 38164.8 2.15704
680680 0 0
681681 −25707.5 −1.44657
682682 9925.39 + 9194.31i 0.557277 + 0.516229i
683683 22875.3i 1.28155i −0.767728 0.640776i 0.778613π-0.778613\pi
0.767728 0.640776i 0.221387π-0.221387\pi
684684 −66.6268 + 5.10270i −0.00372447 + 0.000285244i
685685 0 0
686686 −11667.8 + 12595.5i −0.649385 + 0.701021i
687687 −34927.3 −1.93968
688688 2417.55 + 15690.6i 0.133965 + 0.869473i
689689 1142.73 0.0631851
690690 0 0
691691 19910.4i 1.09613i −0.836435 0.548066i 0.815364π-0.815364\pi
0.836435 0.548066i 0.184636π-0.184636\pi
692692 462.620 35.4304i 0.0254136 0.00194633i
693693 18247.5i 1.00024i
694694 −5247.12 4860.63i −0.287000 0.265860i
695695 0 0
696696 −15626.9 12399.3i −0.851056 0.675282i
697697 26866.2 1.46001
698698 −229.411 212.513i −0.0124403 0.0115240i
699699 1210.96i 0.0655262i
700700 0 0
701701 3428.44i 0.184722i 0.995726 + 0.0923612i 0.0294414π0.0294414\pi
−0.995726 + 0.0923612i 0.970559π0.970559\pi
702702 2498.29 2696.94i 0.134319 0.144999i
703703 −27.1715 −0.00145774
704704 −17377.1 + 4056.11i −0.930290 + 0.217145i
705705 0 0
706706 13681.7 14769.6i 0.729343 0.787337i
707707 24045.4i 1.27910i
708708 −684.564 8938.47i −0.0363383 0.474475i
709709 15608.3i 0.826771i 0.910556 + 0.413385i 0.135654π0.135654\pi
−0.910556 + 0.413385i 0.864346π0.864346\pi
710710 0 0
711711 10226.8 0.539430
712712 −13469.8 10687.8i −0.708991 0.562558i
713713 −13766.0 −0.723061
714714 37167.7 + 34430.0i 1.94813 + 1.80464i
715715 0 0
716716 12832.4 982.789i 0.669791 0.0512968i
717717 16739.1i 0.871873i
718718 −5993.26 + 6469.81i −0.311513 + 0.336283i
719719 −8282.41 −0.429599 −0.214800 0.976658i 0.568910π-0.568910\pi
−0.214800 + 0.976658i 0.568910π0.568910\pi
720720 0 0
721721 −14844.0 −0.766741
722722 −13183.4 + 14231.7i −0.679550 + 0.733584i
723723 7272.08i 0.374068i
724724 21262.5 1628.42i 1.09146 0.0835907i
725725 0 0
726726 1611.34 + 1492.65i 0.0823726 + 0.0763052i
727727 20590.4 1.05042 0.525210 0.850973i 0.323987π-0.323987\pi
0.525210 + 0.850973i 0.323987π0.323987\pi
728728 8647.81 10898.8i 0.440260 0.554858i
729729 4345.77 0.220788
730730 0 0
731731 22319.4i 1.12929i
732732 671.548 + 8768.51i 0.0339086 + 0.442751i
733733 24257.3i 1.22232i −0.791506 0.611162i 0.790703π-0.790703\pi
0.791506 0.611162i 0.209297π-0.209297\pi
734734 21158.3 22840.6i 1.06399 1.14859i
735735 0 0
736736 10166.2 15043.0i 0.509146 0.753387i
737737 23231.1 1.16110
738738 10075.2 10876.3i 0.502537 0.542497i
739739 25426.8i 1.26569i −0.774280 0.632843i 0.781888π-0.781888\pi
0.774280 0.632843i 0.218112π-0.218112\pi
740740 0 0
741741 65.4761i 0.00324605i
742742 −3430.29 3177.62i −0.169717 0.157216i
743743 22658.4 1.11878 0.559391 0.828904i 0.311035π-0.311035\pi
0.559391 + 0.828904i 0.311035π0.311035\pi
744744 −12884.9 + 16238.8i −0.634925 + 0.800194i
745745 0 0
746746 26709.5 + 24742.2i 1.31086 + 1.21431i
747747 11172.0i 0.547205i
748748 25013.6 1915.70i 1.22271 0.0936430i
749749 3331.88i 0.162542i
750750 0 0
751751 −10999.0 −0.534431 −0.267215 0.963637i 0.586104π-0.586104\pi
−0.267215 + 0.963637i 0.586104π0.586104\pi
752752 20483.2 3155.98i 0.993281 0.153041i
753753 35911.3 1.73795
754754 5233.73 5649.89i 0.252787 0.272887i
755755 0 0
756756 −14998.9 + 1148.71i −0.721567 + 0.0552621i
757757 30279.9i 1.45382i 0.686734 + 0.726909i 0.259044π0.259044\pi
−0.686734 + 0.726909i 0.740956π0.740956\pi
758758 12471.1 + 11552.5i 0.597587 + 0.553570i
759759 23333.1 1.11586
760760 0 0
761761 4374.09 0.208358 0.104179 0.994559i 0.466778π-0.466778\pi
0.104179 + 0.994559i 0.466778π0.466778\pi
762762 −7866.50 7287.07i −0.373981 0.346434i
763763 32753.4i 1.55407i
764764 1759.15 + 22969.5i 0.0833034 + 1.08771i
765765 0 0
766766 −7712.93 + 8326.23i −0.363812 + 0.392740i
767767 3460.97 0.162932
768768 −8229.69 26072.5i −0.386671 1.22502i
769769 12982.1 0.608774 0.304387 0.952548i 0.401548π-0.401548\pi
0.304387 + 0.952548i 0.401548π0.401548\pi
770770 0 0
771771 9197.90i 0.429642i
772772 −1466.99 19154.7i −0.0683912 0.892996i
773773 34056.3i 1.58463i 0.610112 + 0.792316i 0.291125π0.291125\pi
−0.610112 + 0.792316i 0.708875π0.708875\pi
774774 −9035.63 8370.08i −0.419611 0.388703i
775775 0 0
776776 22681.9 + 17997.3i 1.04927 + 0.832557i
777777 11368.6 0.524898
778778 −19687.2 18237.1i −0.907226 0.840402i
779779 142.073i 0.00653437i
780780 0 0
781781 13394.8i 0.613706i
782782 −17346.3 + 18725.6i −0.793227 + 0.856300i
783783 −8326.97 −0.380053
784784 −34570.0 + 5326.41i −1.57480 + 0.242639i
785785 0 0
786786 −28724.4 + 31008.4i −1.30352 + 1.40717i
787787 11962.9i 0.541842i 0.962602 + 0.270921i 0.0873282π0.0873282\pi
−0.962602 + 0.270921i 0.912672π0.912672\pi
788788 −35528.2 + 2720.98i −1.60614 + 0.123009i
789789 2745.67i 0.123889i
790790 0 0
791791 63198.1 2.84079
792792 8604.91 10844.7i 0.386063 0.486555i
793793 −3395.17 −0.152038
794794 −10272.0 9515.34i −0.459116 0.425298i
795795 0 0
796796 2995.75 + 39116.0i 0.133394 + 1.74174i
797797 17898.9i 0.795498i −0.917494 0.397749i 0.869791π-0.869791\pi
0.917494 0.397749i 0.130209π-0.130209\pi
798798 −182.071 + 196.549i −0.00807676 + 0.00871898i
799799 −29136.9 −1.29010
800800 0 0
801801 13340.1 0.588452
802802 16913.8 18258.7i 0.744698 0.803913i
803803 26108.3i 1.14737i
804804 2718.07 + 35490.3i 0.119228 + 1.55677i
805805 0 0
806806 −5871.15 5438.69i −0.256579 0.237680i
807807 2718.06 0.118563
808808 11339.0 14290.5i 0.493695 0.622202i
809809 −27690.6 −1.20340 −0.601700 0.798722i 0.705510π-0.705510\pi
−0.601700 + 0.798722i 0.705510π0.705510\pi
810810 0 0
811811 44013.9i 1.90572i −0.303412 0.952859i 0.598126π-0.598126\pi
0.303412 0.952859i 0.401874π-0.401874\pi
812812 −31421.6 + 2406.46i −1.35798 + 0.104003i
813813 8871.24i 0.382691i
814814 3825.49 4129.68i 0.164722 0.177820i
815815 0 0
816816 5853.26 + 37989.3i 0.251109 + 1.62977i
817817 118.028 0.00505422
818818 13800.3 14897.7i 0.589875 0.636779i
819819 10793.9i 0.460524i
820820 0 0
821821 30978.8i 1.31689i 0.752628 + 0.658446i 0.228786π0.228786\pi
−0.752628 + 0.658446i 0.771214π0.771214\pi
822822 19786.9 + 18329.5i 0.839596 + 0.777753i
823823 41684.8 1.76554 0.882771 0.469804i 0.155675π-0.155675\pi
0.882771 + 0.469804i 0.155675π0.155675\pi
824824 −8822.01 6999.95i −0.372973 0.295940i
825825 0 0
826826 −10389.3 9624.03i −0.437638 0.405403i
827827 11988.7i 0.504096i 0.967715 + 0.252048i 0.0811042π0.0811042\pi
−0.967715 + 0.252048i 0.918896π0.918896\pi
828828 1075.63 + 14044.7i 0.0451460 + 0.589478i
829829 2023.64i 0.0847814i 0.999101 + 0.0423907i 0.0134974π0.0134974\pi
−0.999101 + 0.0423907i 0.986503π0.986503\pi
830830 0 0
831831 −29445.4 −1.22918
832832 10279.0 2399.30i 0.428319 0.0999770i
833833 49174.8 2.04539
834834 18831.8 20329.2i 0.781886 0.844058i
835835 0 0
836836 10.1305 + 132.276i 0.000419105 + 0.00547232i
837837 8653.07i 0.357340i
838838 −28130.6 26058.6i −1.15961 1.07420i
839839 10706.3 0.440553 0.220276 0.975438i 0.429304π-0.429304\pi
0.220276 + 0.975438i 0.429304π0.429304\pi
840840 0 0
841841 6944.60 0.284743
842842 15413.5 + 14278.2i 0.630861 + 0.584393i
843843 34270.6i 1.40017i
844844 9784.09 749.327i 0.399031 0.0305603i
845845 0 0
846846 −10926.7 + 11795.6i −0.444052 + 0.479361i
847847 3469.86 0.140762
848848 −540.209 3506.11i −0.0218760 0.141982i
849849 20649.2 0.834721
850850 0 0
851851 5727.66i 0.230719i
852852 −20463.3 + 1567.21i −0.822843 + 0.0630185i
853853 29816.5i 1.19683i −0.801186 0.598416i 0.795797π-0.795797\pi
0.801186 0.598416i 0.204203π-0.204203\pi
854854 10191.7 + 9441.03i 0.408377 + 0.378297i
855855 0 0
856856 1571.21 1980.19i 0.0627368 0.0790670i
857857 −6572.14 −0.261960 −0.130980 0.991385i 0.541812π-0.541812\pi
−0.130980 + 0.991385i 0.541812π0.541812\pi
858858 9951.44 + 9218.44i 0.395964 + 0.366798i
859859 45723.7i 1.81615i −0.418809 0.908075i 0.637552π-0.637552\pi
0.418809 0.908075i 0.362448π-0.362448\pi
860860 0 0
861861 59443.5i 2.35288i
862862 3059.57 3302.85i 0.120893 0.130505i
863863 −13343.7 −0.526331 −0.263166 0.964751i 0.584767π-0.584767\pi
−0.263166 + 0.964751i 0.584767π0.584767\pi
864864 −9455.76 6390.29i −0.372328 0.251623i
865865 0 0
866866 20781.3 22433.7i 0.815446 0.880286i
867867 21244.8i 0.832193i
868868 2500.71 + 32652.1i 0.0977874 + 1.27683i
869869 20303.5i 0.792577i
870870 0 0
871871 −13741.8 −0.534586
872872 −15445.4 + 19465.9i −0.599826 + 0.755960i
873873 −22463.6 −0.870878
874874 −99.0240 91.7301i −0.00383242 0.00355013i
875875 0 0
876876 39885.8 3054.70i 1.53837 0.117818i
877877 41636.8i 1.60317i −0.597884 0.801583i 0.703992π-0.703992\pi
0.597884 0.801583i 0.296008π-0.296008\pi
878878 −9402.52 + 10150.2i −0.361412 + 0.390150i
879879 4481.01 0.171946
880880 0 0
881881 −31220.6 −1.19392 −0.596962 0.802269i 0.703626π-0.703626\pi
−0.596962 + 0.802269i 0.703626π0.703626\pi
882882 18441.2 19907.6i 0.704023 0.760003i
883883 35199.4i 1.34151i 0.741679 + 0.670755i 0.234030π0.234030\pi
−0.741679 + 0.670755i 0.765970π0.765970\pi
884884 −14796.2 + 1133.19i −0.562954 + 0.0431146i
885885 0 0
886886 −4392.40 4068.86i −0.166552 0.154284i
887887 −12744.8 −0.482444 −0.241222 0.970470i 0.577548π-0.577548\pi
−0.241222 + 0.970470i 0.577548π0.577548\pi
888888 6756.52 + 5361.05i 0.255331 + 0.202596i
889889 −16939.7 −0.639076
890890 0 0
891891 31185.8i 1.17258i
892892 −942.482 12306.1i −0.0353774 0.461929i
893893 154.080i 0.00577391i
894894 −36965.2 + 39904.5i −1.38289 + 1.49285i
895895 0 0
896896 −37527.8 21380.9i −1.39924 0.797194i
897897 −13802.2 −0.513758
898898 −25475.1 + 27500.7i −0.946675 + 1.02195i
899899 18127.6i 0.672512i
900900 0 0
901901 4987.35i 0.184409i
902902 −21593.0 20002.5i −0.797083 0.738372i
903903 −49383.4 −1.81991
904904 37559.5 + 29802.1i 1.38187 + 1.09646i
905905 0 0
906906 −13147.9 12179.4i −0.482129 0.446617i
907907 16588.8i 0.607299i −0.952784 0.303650i 0.901795π-0.901795\pi
0.952784 0.303650i 0.0982052π-0.0982052\pi
908908 −30720.8 + 2352.79i −1.12280 + 0.0859912i
909909 14153.0i 0.516418i
910910 0 0
911911 −46114.7 −1.67711 −0.838555 0.544816i 0.816599π-0.816599\pi
−0.838555 + 0.544816i 0.816599π0.816599\pi
912912 −200.893 + 30.9529i −0.00729413 + 0.00112385i
913913 −22180.1 −0.804002
914914 −7629.26 + 8235.90i −0.276098 + 0.298052i
915915 0 0
916916 −41738.7 + 3196.61i −1.50555 + 0.115305i
917917 66773.3i 2.40463i
918918 11770.6 + 10903.6i 0.423188 + 0.392017i
919919 −47522.6 −1.70580 −0.852898 0.522077i 0.825157π-0.825157\pi
−0.852898 + 0.522077i 0.825157π0.825157\pi
920920 0 0
921921 38786.6 1.38769
922922 −14667.9 13587.5i −0.523926 0.485335i
923923 7923.40i 0.282559i
924924 −4238.63 55344.5i −0.150910 1.97046i
925925 0 0
926926 343.253 370.547i 0.0121814 0.0131500i
927927 8737.09 0.309562
928928 −19809.1 13387.2i −0.700718 0.473552i
929929 −13494.3 −0.476570 −0.238285 0.971195i 0.576585π-0.576585\pi
−0.238285 + 0.971195i 0.576585π0.576585\pi
930930 0 0
931931 260.044i 0.00915425i
932932 −110.829 1447.12i −0.00389521 0.0508604i
933933 48215.1i 1.69184i
934934 −24020.1 22250.9i −0.841502 0.779519i
935935 0 0
936936 −5090.04 + 6414.97i −0.177749 + 0.224017i
937937 −12453.1 −0.434179 −0.217089 0.976152i 0.569656π-0.569656\pi
−0.217089 + 0.976152i 0.569656π0.569656\pi
938938 41250.7 + 38212.3i 1.43591 + 1.33014i
939939 12044.3i 0.418584i
940940 0 0
941941 40466.5i 1.40188i −0.713220 0.700940i 0.752764π-0.752764\pi
0.713220 0.700940i 0.247236π-0.247236\pi
942942 −40534.0 + 43757.0i −1.40198 + 1.51346i
943943 29948.5 1.03421
944944 −1636.13 10618.9i −0.0564104 0.366120i
945945 0 0
946946 −16617.3 + 17938.7i −0.571117 + 0.616529i
947947 2645.96i 0.0907943i 0.998969 + 0.0453971i 0.0144553π0.0144553\pi
−0.998969 + 0.0453971i 0.985545π0.985545\pi
948948 31017.8 2375.54i 1.06267 0.0813860i
949949 15443.8i 0.528268i
950950 0 0
951951 10633.7 0.362587
952952 47567.0 + 37742.7i 1.61939 + 1.28492i
953953 −40045.8 −1.36119 −0.680593 0.732662i 0.738278π-0.738278\pi
−0.680593 + 0.732662i 0.738278π0.738278\pi
954954 2019.04 + 1870.32i 0.0685209 + 0.0634738i
955955 0 0
956956 1531.99 + 20003.4i 0.0518285 + 0.676734i
957957 30725.8i 1.03785i
958958 24491.6 26439.1i 0.825979 0.891657i
959959 42609.1 1.43474
960960 0 0
961961 −10953.5 −0.367679
962962 −2262.89 + 2442.82i −0.0758403 + 0.0818707i
963963 1961.12i 0.0656244i
964964 665.553 + 8690.23i 0.0222365 + 0.290346i
965965 0 0
966966 41431.9 + 38380.1i 1.37997 + 1.27832i
967967 −11049.0 −0.367439 −0.183719 0.982979i 0.558814π-0.558814\pi
−0.183719 + 0.982979i 0.558814π0.558814\pi
968968 2062.19 + 1636.27i 0.0684723 + 0.0543302i
969969 285.765 0.00947380
970970 0 0
971971 26708.5i 0.882717i 0.897331 + 0.441358i 0.145503π0.145503\pi
−0.897331 + 0.441358i 0.854497π0.854497\pi
972972 34064.6 2608.88i 1.12410 0.0860904i
973973 43776.9i 1.44237i
974974 −25581.5 + 27615.7i −0.841566 + 0.908483i
975975 0 0
976976 1605.02 + 10417.0i 0.0526387 + 0.341640i
977977 11102.6 0.363566 0.181783 0.983339i 0.441813π-0.441813\pi
0.181783 + 0.983339i 0.441813π0.441813\pi
978978 −17471.3 + 18860.6i −0.571239 + 0.616661i
979979 26484.5i 0.864604i
980980 0 0
981981 19278.5i 0.627435i
982982 −449.621 416.503i −0.0146110 0.0135348i
983983 −33544.2 −1.08840 −0.544198 0.838957i 0.683166π-0.683166\pi
−0.544198 + 0.838957i 0.683166π0.683166\pi
984984 28031.6 35328.1i 0.908144 1.14453i
985985 0 0
986986 24658.5 + 22842.2i 0.796436 + 0.737773i
987987 64467.5i 2.07905i
988988 −5.99249 78.2449i −0.000192962 0.00251954i
989989 24880.0i 0.799939i
990990 0 0
991991 5538.20 0.177524 0.0887622 0.996053i 0.471709π-0.471709\pi
0.0887622 + 0.996053i 0.471709π0.471709\pi
992992 −13911.5 + 20584.9i −0.445251 + 0.658841i
993993 −41472.5 −1.32537
994994 −22032.8 + 23784.8i −0.703057 + 0.758961i
995995 0 0
996996 −2595.10 33884.7i −0.0825591 1.07799i
997997 24192.6i 0.768492i −0.923231 0.384246i 0.874461π-0.874461\pi
0.923231 0.384246i 0.125539π-0.125539\pi
998998 −22410.3 20759.6i −0.710808 0.658452i
999999 3600.30 0.114022
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 200.4.d.e.101.4 16
4.3 odd 2 800.4.d.e.401.13 16
5.2 odd 4 40.4.f.a.29.5 16
5.3 odd 4 40.4.f.a.29.12 yes 16
5.4 even 2 inner 200.4.d.e.101.13 16
8.3 odd 2 800.4.d.e.401.3 16
8.5 even 2 inner 200.4.d.e.101.3 16
15.2 even 4 360.4.d.d.109.12 16
15.8 even 4 360.4.d.d.109.5 16
20.3 even 4 160.4.f.a.49.3 16
20.7 even 4 160.4.f.a.49.13 16
20.19 odd 2 800.4.d.e.401.4 16
40.3 even 4 160.4.f.a.49.14 16
40.13 odd 4 40.4.f.a.29.6 yes 16
40.19 odd 2 800.4.d.e.401.14 16
40.27 even 4 160.4.f.a.49.4 16
40.29 even 2 inner 200.4.d.e.101.14 16
40.37 odd 4 40.4.f.a.29.11 yes 16
60.23 odd 4 1440.4.d.d.1009.16 16
60.47 odd 4 1440.4.d.d.1009.2 16
120.53 even 4 360.4.d.d.109.11 16
120.77 even 4 360.4.d.d.109.6 16
120.83 odd 4 1440.4.d.d.1009.1 16
120.107 odd 4 1440.4.d.d.1009.15 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.4.f.a.29.5 16 5.2 odd 4
40.4.f.a.29.6 yes 16 40.13 odd 4
40.4.f.a.29.11 yes 16 40.37 odd 4
40.4.f.a.29.12 yes 16 5.3 odd 4
160.4.f.a.49.3 16 20.3 even 4
160.4.f.a.49.4 16 40.27 even 4
160.4.f.a.49.13 16 20.7 even 4
160.4.f.a.49.14 16 40.3 even 4
200.4.d.e.101.3 16 8.5 even 2 inner
200.4.d.e.101.4 16 1.1 even 1 trivial
200.4.d.e.101.13 16 5.4 even 2 inner
200.4.d.e.101.14 16 40.29 even 2 inner
360.4.d.d.109.5 16 15.8 even 4
360.4.d.d.109.6 16 120.77 even 4
360.4.d.d.109.11 16 120.53 even 4
360.4.d.d.109.12 16 15.2 even 4
800.4.d.e.401.3 16 8.3 odd 2
800.4.d.e.401.4 16 20.19 odd 2
800.4.d.e.401.13 16 4.3 odd 2
800.4.d.e.401.14 16 40.19 odd 2
1440.4.d.d.1009.1 16 120.83 odd 4
1440.4.d.d.1009.2 16 60.47 odd 4
1440.4.d.d.1009.15 16 120.107 odd 4
1440.4.d.d.1009.16 16 60.23 odd 4