LMFDB - Embedded newform 354.3.d.a.235.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,3,Mod(235,354)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("354.235");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	354.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.64580135835$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 300 x^{18} - 88 x^{17} + 37952 x^{16} + 27000 x^{15} - 2574056 x^{14} - 3295208 x^{13} + \cdots + 2455573689828 $ x^20 - 300x^18 - 88x^17 + 37952x^16 + 27000x^15 - 2574056x^14 - 3295208x^13 + 98138134x^12 + 195465720x^11 - 1935828112x^10 - 5590976152x^9 + 12661641204x^8 + 55962519336x^7 + 75365256136x^6 + 219349710792x^5 + 570681930321x^4 + 614778274152x^3 + 1559028888924x^2 + 534075251472x + 2455573689828
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{11}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			235.13
Root			$0.383479 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	354.235
Dual form			354.3.d.a.235.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +0.383479 q^{5} -2.44949i q^{6} +1.10699 q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +0.383479 q^{5} -2.44949i q^{6} +1.10699 q^{7} -2.82843i q^{8} +3.00000 q^{9} +0.542321i q^{10} +6.78708i q^{11} +3.46410 q^{12} +11.1907i q^{13} +1.56552i q^{14} -0.664205 q^{15} +4.00000 q^{16} -23.0209 q^{17} +4.24264i q^{18} -25.1752 q^{19} -0.766958 q^{20} -1.91737 q^{21} -9.59839 q^{22} -33.4057i q^{23} +4.89898i q^{24} -24.8529 q^{25} -15.8260 q^{26} -5.19615 q^{27} -2.21398 q^{28} +25.0107 q^{29} -0.939328i q^{30} -15.6660i q^{31} +5.65685i q^{32} -11.7556i q^{33} -32.5565i q^{34} +0.424508 q^{35} -6.00000 q^{36} -15.7219i q^{37} -35.6031i q^{38} -19.3828i q^{39} -1.08464i q^{40} -77.9309 q^{41} -2.71156i q^{42} +78.2183i q^{43} -13.5742i q^{44} +1.15044 q^{45} +47.2428 q^{46} -22.0128i q^{47} -6.92820 q^{48} -47.7746 q^{49} -35.1474i q^{50} +39.8734 q^{51} -22.3813i q^{52} -9.99084 q^{53} -7.34847i q^{54} +2.60271i q^{55} -3.13104i q^{56} +43.6047 q^{57} +35.3705i q^{58} +(-35.1111 - 47.4153i) q^{59} +1.32841 q^{60} +38.9195i q^{61} +22.1550 q^{62} +3.32097 q^{63} -8.00000 q^{64} +4.29138i q^{65} +16.6249 q^{66} +0.743062i q^{67} +46.0418 q^{68} +57.8604i q^{69} +0.600345i q^{70} -34.1225 q^{71} -8.48528i q^{72} +56.2491i q^{73} +22.2341 q^{74} +43.0466 q^{75} +50.3504 q^{76} +7.51324i q^{77} +27.4114 q^{78} +112.686 q^{79} +1.53392 q^{80} +9.00000 q^{81} -110.211i q^{82} -92.0358i q^{83} +3.83473 q^{84} -8.82804 q^{85} -110.617 q^{86} -43.3199 q^{87} +19.1968 q^{88} +133.439i q^{89} +1.62696i q^{90} +12.3880i q^{91} +66.8114i q^{92} +27.1342i q^{93} +31.1308 q^{94} -9.65416 q^{95} -9.79796i q^{96} +120.295i q^{97} -67.5634i q^{98} +20.3613i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 40 q^{4} + 8 q^{7} + 60 q^{9}+O(q^{10}) $ 20 * q - 40 * q^4 + 8 * q^7 + 60 * q^9	$ 20 q - 40 q^{4} + 8 q^{7} + 60 q^{9} - 24 q^{15} + 80 q^{16} + 72 q^{19} + 16 q^{22} + 140 q^{25} + 64 q^{26} - 16 q^{28} + 56 q^{29} - 80 q^{35} - 120 q^{36} - 8 q^{41} + 16 q^{46} + 52 q^{49} + 32 q^{53} - 48 q^{57} + 192 q^{59} + 48 q^{60} - 16 q^{62} + 24 q^{63} - 160 q^{64} + 96 q^{66} - 568 q^{71} - 288 q^{74} - 96 q^{75} - 144 q^{76} + 192 q^{78} + 528 q^{79} + 180 q^{81} + 568 q^{85} - 416 q^{86} - 216 q^{87} - 32 q^{88} - 480 q^{94} - 456 q^{95}+O(q^{100}) $ 20 * q - 40 * q^4 + 8 * q^7 + 60 * q^9 - 24 * q^15 + 80 * q^16 + 72 * q^19 + 16 * q^22 + 140 * q^25 + 64 * q^26 - 16 * q^28 + 56 * q^29 - 80 * q^35 - 120 * q^36 - 8 * q^41 + 16 * q^46 + 52 * q^49 + 32 * q^53 - 48 * q^57 + 192 * q^59 + 48 * q^60 - 16 * q^62 + 24 * q^63 - 160 * q^64 + 96 * q^66 - 568 * q^71 - 288 * q^74 - 96 * q^75 - 144 * q^76 + 192 * q^78 + 528 * q^79 + 180 * q^81 + 568 * q^85 - 416 * q^86 - 216 * q^87 - 32 * q^88 - 480 * q^94 - 456 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−2.00000			−0.500000
$5$	0.383479			0.0766958			0.0383479	−	0.999264i	$-0.487790\pi$
$5$	0.383479			0.0766958			0.0383479	+	0.999264i	$0.487790\pi$
$6$		−	2.44949i		−	0.408248i
$7$	1.10699			0.158142			0.0790708	−	0.996869i	$-0.474805\pi$
$7$	1.10699			0.158142			0.0790708	+	0.996869i	$0.474805\pi$
$8$		−	2.82843i		−	0.353553i
$9$	3.00000			0.333333
$10$			0.542321i			0.0542321i
$11$			6.78708i			0.617008i	0.951223	+	0.308504i	$0.0998283\pi$
$11$			6.78708i			0.617008i	−0.951223	+	0.308504i	$0.900172\pi$
$12$	3.46410			0.288675
$13$			11.1907i			0.860820i	0.902634	+	0.430410i	$0.141631\pi$
$13$			11.1907i			0.860820i	−0.902634	+	0.430410i	$0.858369\pi$
$14$			1.56552i			0.111823i
$15$	−0.664205			−0.0442804
$16$	4.00000			0.250000
$17$	−23.0209			−1.35417			−0.677085	−	0.735905i	$-0.736757\pi$
$17$	−23.0209			−1.35417			−0.677085	+	0.735905i	$0.736757\pi$
$18$			4.24264i			0.235702i
$19$	−25.1752			−1.32501			−0.662505	−	0.749058i	$-0.730507\pi$
$19$	−25.1752			−1.32501			−0.662505	+	0.749058i	$0.730507\pi$
$20$	−0.766958			−0.0383479
$21$	−1.91737			−0.0913031
$22$	−9.59839			−0.436290
$23$		−	33.4057i		−	1.45242i	−0.687472	−	0.726211i	$-0.741279\pi$
$23$		−	33.4057i		−	1.45242i	0.687472	−	0.726211i	$-0.258721\pi$
$24$			4.89898i			0.204124i
$25$	−24.8529			−0.994118
$26$	−15.8260			−0.608691
$27$	−5.19615			−0.192450
$28$	−2.21398			−0.0790708
$29$	25.0107			0.862439			0.431220	−	0.902247i	$-0.358083\pi$
$29$	25.0107			0.862439			0.431220	+	0.902247i	$0.358083\pi$
$30$		−	0.939328i		−	0.0313109i
$31$		−	15.6660i		−	0.505353i	−0.967551	−	0.252677i	$-0.918689\pi$
$31$		−	15.6660i		−	0.505353i	0.967551	−	0.252677i	$-0.0813109\pi$
$32$			5.65685i			0.176777i
$33$		−	11.7556i		−	0.356230i
$34$		−	32.5565i		−	0.957543i
$35$	0.424508			0.0121288
$36$	−6.00000			−0.166667
$37$		−	15.7219i		−	0.424917i	−0.977170	−	0.212458i	$-0.931853\pi$
$37$		−	15.7219i		−	0.424917i	0.977170	−	0.212458i	$-0.0681470\pi$
$38$		−	35.6031i		−	0.936923i
$39$		−	19.3828i		−	0.496994i
$40$		−	1.08464i		−	0.0271161i
$41$	−77.9309			−1.90075			−0.950377	−	0.311101i	$-0.899302\pi$
$41$	−77.9309			−1.90075			−0.950377	+	0.311101i	$0.899302\pi$
$42$		−	2.71156i		−	0.0645610i
$43$			78.2183i			1.81903i	0.415670	+	0.909516i	$0.363547\pi$
$43$			78.2183i			1.81903i	−0.415670	+	0.909516i	$0.636453\pi$
$44$		−	13.5742i		−	0.308504i
$45$	1.15044			0.0255653
$46$	47.2428			1.02702
$47$		−	22.0128i		−	0.468357i	−0.972194	−	0.234179i	$-0.924760\pi$
$47$		−	22.0128i		−	0.468357i	0.972194	−	0.234179i	$-0.0752401\pi$
$48$	−6.92820			−0.144338
$49$	−47.7746			−0.974991
$50$		−	35.1474i		−	0.702947i
$51$	39.8734			0.781831
$52$		−	22.3813i		−	0.430410i
$53$	−9.99084			−0.188506			−0.0942532	−	0.995548i	$-0.530046\pi$
$53$	−9.99084			−0.188506			−0.0942532	+	0.995548i	$0.530046\pi$
$54$		−	7.34847i		−	0.136083i
$55$			2.60271i			0.0473219i
$56$		−	3.13104i		−	0.0559115i
$57$	43.6047			0.764995
$58$			35.3705i			0.609837i
$59$	−35.1111	−	47.4153i	−0.595103	−	0.803650i
$59$	−35.1111	−	47.4153i	−0.595103	−	0.803650i
$60$	1.32841			0.0221402
$61$			38.9195i			0.638025i	0.947750	+	0.319013i	$0.103351\pi$
$61$			38.9195i			0.638025i	−0.947750	+	0.319013i	$0.896649\pi$
$62$	22.1550			0.357339
$63$	3.32097			0.0527139
$64$	−8.00000			−0.125000
$65$			4.29138i			0.0660213i
$66$	16.6249			0.251892
$67$			0.743062i			0.0110905i	0.999985	+	0.00554524i	$0.00176511\pi$
$67$			0.743062i			0.0110905i	−0.999985	+	0.00554524i	$0.998235\pi$
$68$	46.0418			0.677085
$69$			57.8604i			0.838557i
$70$			0.600345i			0.00857636i
$71$	−34.1225			−0.480599			−0.240299	−	0.970699i	$-0.577246\pi$
$71$	−34.1225			−0.480599			−0.240299	+	0.970699i	$0.577246\pi$
$72$		−	8.48528i		−	0.117851i
$73$			56.2491i			0.770536i	0.922805	+	0.385268i	$0.125891\pi$
$73$			56.2491i			0.770536i	−0.922805	+	0.385268i	$0.874109\pi$
$74$	22.2341			0.300461
$75$	43.0466			0.573954
$76$	50.3504			0.662505
$77$			7.51324i			0.0975746i
$78$	27.4114			0.351428
$79$	112.686			1.42641			0.713205	−	0.700956i	$-0.247243\pi$
$79$	112.686			1.42641			0.713205	+	0.700956i	$0.247243\pi$
$80$	1.53392			0.0191740
$81$	9.00000			0.111111
$82$		−	110.211i		−	1.34404i
$83$		−	92.0358i		−	1.10886i	−0.832229	−	0.554432i	$-0.812935\pi$
$83$		−	92.0358i		−	1.10886i	0.832229	−	0.554432i	$-0.187065\pi$
$84$	3.83473			0.0456516
$85$	−8.82804			−0.103859
$86$	−110.617			−1.28625
$87$	−43.3199			−0.497929
$88$	19.1968			0.218145
$89$			133.439i			1.49931i	0.661827	+	0.749656i	$0.269781\pi$
$89$			133.439i			1.49931i	−0.661827	+	0.749656i	$0.730219\pi$
$90$			1.62696i			0.0180774i
$91$			12.3880i			0.136131i
$92$			66.8114i			0.726211i
$93$			27.1342i			0.291766i
$94$	31.1308			0.331179
$95$	−9.65416			−0.101623
$96$		−	9.79796i		−	0.102062i
$97$			120.295i			1.24016i	0.784540	+	0.620078i	$0.212899\pi$
$97$			120.295i			1.24016i	−0.784540	+	0.620078i	$0.787101\pi$
$98$		−	67.5634i		−	0.689423i
$99$			20.3613i			0.205669i
$100$	49.7059			0.497059
$101$		−	163.105i		−	1.61490i	−0.589937	−	0.807449i	$-0.700847\pi$
$101$		−	163.105i		−	1.61490i	0.589937	−	0.807449i	$-0.299153\pi$
$102$			56.3895i			0.552838i
$103$			149.150i			1.44806i	0.689770	+	0.724029i	$0.257712\pi$
$103$			149.150i			1.44806i	−0.689770	+	0.724029i	$0.742288\pi$
$104$	31.6520			0.304346
$105$	−0.735270			−0.00700257
$106$		−	14.1292i		−	0.133294i
$107$	28.5629			0.266943			0.133472	−	0.991053i	$-0.457388\pi$
$107$	28.5629			0.266943			0.133472	+	0.991053i	$0.457388\pi$
$108$	10.3923			0.0962250
$109$			31.9018i			0.292677i	0.989235	+	0.146338i	$0.0467488\pi$
$109$			31.9018i			0.292677i	−0.989235	+	0.146338i	$0.953251\pi$
$110$	−3.68078			−0.0334617
$111$			27.2312i			0.245326i
$112$	4.42797			0.0395354
$113$			95.0303i			0.840976i	0.907298	+	0.420488i	$0.138141\pi$
$113$			95.0303i			0.840976i	−0.907298	+	0.420488i	$0.861859\pi$
$114$			61.6663i			0.540933i
$115$		−	12.8104i		−	0.111395i
$116$	−50.0215			−0.431220
$117$			33.5720i			0.286940i
$118$	67.0554	−	49.6545i	0.568266	−	0.420801i
$119$	−25.4839			−0.214151
$120$			1.87866i			0.0156555i
$121$	74.9355			0.619302
$122$	−55.0405			−0.451152
$123$	134.980			1.09740
$124$			31.3319i			0.252677i
$125$	−19.1176			−0.152941
$126$			4.69657i			0.0372743i
$127$	−127.882			−1.00694			−0.503471	−	0.864012i	$-0.667944\pi$
$127$	−127.882			−1.00694			−0.503471	+	0.864012i	$0.667944\pi$
$128$		−	11.3137i		−	0.0883883i
$129$		−	135.478i		−	1.05022i
$130$	−6.06893			−0.0466841
$131$		−	15.6265i		−	0.119286i	−0.998220	−	0.0596432i	$-0.981004\pi$
$131$		−	15.6265i		−	0.119286i	0.998220	−	0.0596432i	$-0.0189963\pi$
$132$			23.5112i			0.178115i
$133$	−27.8687			−0.209539
$134$	−1.05085			−0.00784215
$135$	−1.99262			−0.0147601
$136$			65.1129i			0.478772i
$137$	−103.769			−0.757435			−0.378717	−	0.925512i	$-0.623635\pi$
$137$	−103.769			−0.757435			−0.378717	+	0.925512i	$0.623635\pi$
$138$	−81.8270			−0.592949
$139$	256.867			1.84797			0.923983	−	0.382435i	$-0.124914\pi$
$139$	256.867			1.84797			0.923983	+	0.382435i	$0.124914\pi$
$140$	−0.849016			−0.00606440
$141$			38.1273i			0.270406i
$142$		−	48.2565i		−	0.339834i
$143$	−75.9519			−0.531132
$144$	12.0000			0.0833333
$145$	9.59110			0.0661455
$146$	−79.5483			−0.544851
$147$	82.7480			0.562911
$148$			31.4438i			0.212458i
$149$			170.448i			1.14395i	0.820272	+	0.571974i	$0.193822\pi$
$149$			170.448i			1.14395i	−0.820272	+	0.571974i	$0.806178\pi$
$150$			60.8770i			0.405847i
$151$		−	228.576i		−	1.51375i	−0.653560	−	0.756875i	$-0.726725\pi$
$151$		−	228.576i		−	1.51375i	0.653560	−	0.756875i	$-0.273275\pi$
$152$			71.2062i			0.468462i
$153$	−69.0627			−0.451390
$154$	−10.6253			−0.0689957
$155$		−	6.00757i		−	0.0387585i
$156$			38.7656i			0.248497i
$157$			159.049i			1.01305i	0.862225	+	0.506526i	$0.169071\pi$
$157$			159.049i			1.01305i	−0.862225	+	0.506526i	$0.830929\pi$
$158$			159.363i			1.00862i
$159$	17.3046			0.108834
$160$			2.16929i			0.0135580i
$161$		−	36.9798i		−	0.229688i
$162$			12.7279i			0.0785674i
$163$	−90.7850			−0.556963			−0.278482	−	0.960442i	$-0.589831\pi$
$163$	−90.7850			−0.556963			−0.278482	+	0.960442i	$0.589831\pi$
$164$	155.862			0.950377
$165$		−	4.50802i		−	0.0273213i
$166$	130.158			0.784086
$167$	291.326			1.74447			0.872234	−	0.489088i	$-0.162670\pi$
$167$	291.326			1.74447			0.872234	+	0.489088i	$0.162670\pi$
$168$			5.42313i			0.0322805i
$169$	43.7692			0.258989
$170$		−	12.4847i		−	0.0734396i
$171$	−75.5255			−0.441670
$172$		−	156.437i		−	0.909516i
$173$		−	118.062i		−	0.682438i	−0.939984	−	0.341219i	$-0.889160\pi$
$173$		−	118.062i		−	0.682438i	0.939984	−	0.341219i	$-0.110840\pi$
$174$		−	61.2635i		−	0.352089i
$175$	−27.5120			−0.157211
$176$			27.1483i			0.154252i
$177$	60.8141	+	82.1258i	0.343583	+	0.463987i
$178$	−188.711			−1.06017
$179$		−	319.412i		−	1.78442i	−0.451618	−	0.892211i	$-0.649153\pi$
$179$		−	319.412i		−	1.78442i	0.451618	−	0.892211i	$-0.350847\pi$
$180$	−2.30088			−0.0127826
$181$	−164.088			−0.906561			−0.453281	−	0.891368i	$-0.649746\pi$
$181$	−164.088			−0.906561			−0.453281	+	0.891368i	$0.649746\pi$
$182$	−17.5192			−0.0962595
$183$		−	67.4106i		−	0.368364i
$184$	−94.4856			−0.513509
$185$		−	6.02903i		−	0.0325893i
$186$	−38.3736			−0.206310
$187$		−	156.245i		−	0.835534i
$188$			44.0256i			0.234179i
$189$	−5.75210			−0.0304344
$190$		−	13.6530i		−	0.0718581i
$191$			227.817i			1.19276i	0.802703	+	0.596379i	$0.203394\pi$
$191$			227.817i			1.19276i	−0.802703	+	0.596379i	$0.796606\pi$
$192$	13.8564			0.0721688
$193$	26.2331			0.135923			0.0679615	−	0.997688i	$-0.478350\pi$
$193$	26.2331			0.135923			0.0679615	+	0.997688i	$0.478350\pi$
$194$	−170.123			−0.876923
$195$		−	7.43289i		−	0.0381174i
$196$	95.5491			0.487496
$197$	192.073			0.974990			0.487495	−	0.873126i	$-0.337911\pi$
$197$	192.073			0.974990			0.487495	+	0.873126i	$0.337911\pi$
$198$	−28.7952			−0.145430
$199$	150.033			0.753937			0.376968	−	0.926226i	$-0.376967\pi$
$199$	150.033			0.753937			0.376968	+	0.926226i	$0.376967\pi$
$200$			70.2947i			0.351474i
$201$		−	1.28702i		−	0.00640309i
$202$	230.665			1.14191
$203$	27.6867			0.136388
$204$	−79.7467			−0.390915
$205$	−29.8849			−0.145780
$206$	−210.930			−1.02393
$207$		−	100.217i		−	0.484141i
$208$			44.7626i			0.215205i
$209$		−	170.866i		−	0.817541i
$210$		−	1.03983i		−	0.00495156i
$211$		−	63.2345i		−	0.299690i	−0.988710	−	0.149845i	$-0.952123\pi$
$211$		−	63.2345i		−	0.299690i	0.988710	−	0.149845i	$-0.0478774\pi$
$212$	19.9817			0.0942532
$213$	59.1019			0.277474
$214$			40.3941i			0.188757i
$215$			29.9951i			0.139512i
$216$			14.6969i			0.0680414i
$217$		−	17.3421i		−	0.0799174i
$218$	−45.1159			−0.206954
$219$		−	97.4263i		−	0.444869i
$220$		−	5.20541i		−	0.0236610i
$221$		−	257.619i		−	1.16570i
$222$	−38.5107			−0.173471
$223$	−31.0977			−0.139451			−0.0697257	−	0.997566i	$-0.522212\pi$
$223$	−31.0977			−0.139451			−0.0697257	+	0.997566i	$0.522212\pi$
$224$			6.26209i			0.0279558i
$225$	−74.5588			−0.331373
$226$	−134.393			−0.594660
$227$		−	142.283i		−	0.626799i	−0.949621	−	0.313400i	$-0.898532\pi$
$227$		−	142.283i		−	0.626799i	0.949621	−	0.313400i	$-0.101468\pi$
$228$	−87.2094			−0.382497
$229$		−	212.664i		−	0.928663i	−0.885662	−	0.464331i	$-0.846295\pi$
$229$		−	212.664i		−	0.928663i	0.885662	−	0.464331i	$-0.153705\pi$
$230$	18.1166			0.0787680
$231$		−	13.0133i		−	0.0563347i
$232$		−	70.7410i		−	0.304918i
$233$			44.0973i			0.189259i	0.995513	+	0.0946295i	$0.0301666\pi$
$233$			44.0973i			0.189259i	−0.995513	+	0.0946295i	$0.969833\pi$
$234$	−47.4779			−0.202897
$235$		−	8.44145i		−	0.0359211i
$236$	70.2221	+	94.8307i	0.297551	+	0.401825i
$237$	−195.178			−0.823538
$238$		−	36.0397i		−	0.151427i
$239$	160.020			0.669540			0.334770	−	0.942300i	$-0.391341\pi$
$239$	160.020			0.669540			0.334770	+	0.942300i	$0.391341\pi$
$240$	−2.65682			−0.0110701
$241$	−230.909			−0.958128			−0.479064	−	0.877780i	$-0.659024\pi$
$241$	−230.909			−0.958128			−0.479064	+	0.877780i	$0.659024\pi$
$242$			105.975i			0.437912i
$243$	−15.5885			−0.0641500
$244$		−	77.8391i		−	0.319013i
$245$	−18.3206			−0.0747778
$246$			190.891i			0.775979i
$247$		−	281.727i		−	1.14059i
$248$	−44.3100			−0.178669
$249$			159.411i			0.640203i
$250$		−	27.0363i		−	0.108145i
$251$	−155.063			−0.617782			−0.308891	−	0.951097i	$-0.599958\pi$
$251$	−155.063			−0.617782			−0.308891	+	0.951097i	$0.599958\pi$
$252$	−6.64195			−0.0263569
$253$	226.727			0.896156
$254$		−	180.852i		−	0.712016i
$255$	15.2906			0.0599632
$256$	16.0000			0.0625000
$257$	−416.359			−1.62007			−0.810037	−	0.586378i	$-0.800553\pi$
$257$	−416.359			−1.62007			−0.810037	+	0.586378i	$0.800553\pi$
$258$	191.595			0.742616
$259$		−	17.4040i		−	0.0671970i
$260$		−	8.58277i		−	0.0330106i
$261$	75.0322			0.287480
$262$	22.0992			0.0843483
$263$	136.163			0.517729			0.258865	−	0.965914i	$-0.416652\pi$
$263$	136.163			0.517729			0.258865	+	0.965914i	$0.416652\pi$
$264$	−33.2498			−0.125946
$265$	−3.83128			−0.0144577
$266$		−	39.4123i		−	0.148167i
$267$		−	231.123i		−	0.865629i
$268$		−	1.48612i		−	0.00554524i
$269$			384.216i			1.42831i	0.699987	+	0.714155i	$0.253189\pi$
$269$			384.216i			1.42831i	−0.699987	+	0.714155i	$0.746811\pi$
$270$		−	2.81799i		−	0.0104370i
$271$	−492.798			−1.81844			−0.909222	−	0.416312i	$-0.863323\pi$
$271$	−492.798			−1.81844			−0.909222	+	0.416312i	$0.863323\pi$
$272$	−92.0836			−0.338543
$273$		−	21.4566i		−	0.0785955i
$274$		−	146.751i		−	0.535587i
$275$		−	168.679i		−	0.613378i
$276$		−	115.721i		−	0.419278i
$277$	−370.983			−1.33929			−0.669644	−	0.742682i	$-0.733553\pi$
$277$	−370.983			−1.33929			−0.669644	+	0.742682i	$0.733553\pi$
$278$			363.265i			1.30671i
$279$		−	46.9979i		−	0.168451i
$280$		−	1.20069i		−	0.00428818i
$281$	95.0085			0.338108			0.169054	−	0.985607i	$-0.445929\pi$
$281$	95.0085			0.338108			0.169054	+	0.985607i	$0.445929\pi$
$282$	−53.9201			−0.191206
$283$			527.259i			1.86311i	0.363606	+	0.931553i	$0.381546\pi$
$283$			527.259i			1.86311i	−0.363606	+	0.931553i	$0.618454\pi$
$284$	68.2450			0.240299
$285$	16.7215			0.0586719
$286$		−	107.412i		−	0.375567i
$287$	−86.2688			−0.300588
$288$			16.9706i			0.0589256i
$289$	240.962			0.833778
$290$			13.5639i			0.0467719i
$291$		−	208.357i		−	0.716004i
$292$		−	112.498i		−	0.385268i
$293$	−142.940			−0.487849			−0.243924	−	0.969794i	$-0.578435\pi$
$293$	−142.940			−0.487849			−0.243924	+	0.969794i	$0.578435\pi$
$294$			117.023i			0.398039i
$295$	−13.4644	−	18.1828i	−0.0456419	−	0.0616366i
$296$	−44.4683			−0.150231
$297$		−	35.2667i		−	0.118743i
$298$	−241.050			−0.808893
$299$	373.832			1.25027
$300$	−86.0931			−0.286977
$301$			86.5870i			0.287665i
$302$	323.256			1.07038
$303$			282.506i			0.932362i
$304$	−100.701			−0.331252
$305$			14.9248i			0.0489339i
$306$		−	97.6694i		−	0.319181i
$307$	−64.0119			−0.208508			−0.104254	−	0.994551i	$-0.533245\pi$
$307$	−64.0119			−0.208508			−0.104254	+	0.994551i	$0.533245\pi$
$308$		−	15.0265i		−	0.0487873i
$309$		−	258.335i		−	0.836036i
$310$	8.49598			0.0274064
$311$	−14.3630			−0.0461834			−0.0230917	−	0.999733i	$-0.507351\pi$
$311$	−14.3630			−0.0461834			−0.0230917	+	0.999733i	$0.507351\pi$
$312$	−54.8228			−0.175714
$313$			97.7175i			0.312197i	0.987742	+	0.156098i	$0.0498917\pi$
$313$			97.7175i			0.312197i	−0.987742	+	0.156098i	$0.950108\pi$
$314$	−224.930			−0.716336
$315$	1.27352			0.00404293
$316$	−225.373			−0.713205
$317$	−119.165			−0.375915			−0.187957	−	0.982177i	$-0.560187\pi$
$317$	−119.165			−0.375915			−0.187957	+	0.982177i	$0.560187\pi$
$318$			24.4725i			0.0769574i
$319$			169.750i			0.532132i
$320$	−3.06783			−0.00958698
$321$	−49.4724			−0.154120
$322$	52.2974			0.162414
$323$	579.555			1.79429
$324$	−18.0000			−0.0555556
$325$		−	278.121i		−	0.855756i
$326$		−	128.389i		−	0.393832i
$327$		−	55.2555i		−	0.168977i
$328$			220.422i			0.672018i
$329$		−	24.3680i		−	0.0740668i
$330$	6.37530			0.0193191
$331$	−358.877			−1.08422			−0.542110	−	0.840307i	$-0.682375\pi$
$331$	−358.877			−1.08422			−0.542110	+	0.840307i	$0.682375\pi$
$332$			184.072i			0.554432i
$333$		−	47.1657i		−	0.141639i
$334$			411.997i			1.23353i
$335$			0.284949i			0.000850594i
$336$	−7.66946			−0.0228258
$337$			282.696i			0.838859i	0.907788	+	0.419430i	$0.137770\pi$
$337$			282.696i			0.838859i	−0.907788	+	0.419430i	$0.862230\pi$
$338$			61.8990i			0.183133i
$339$		−	164.597i		−	0.485538i
$340$	17.6561			0.0519296
$341$	106.326			0.311807
$342$		−	106.809i		−	0.312308i
$343$	−107.129			−0.312328
$344$	221.235			0.643125
$345$			22.1883i			0.0643138i
$346$	166.964			0.482556
$347$		−	146.110i		−	0.421067i	−0.977587	−	0.210533i	$-0.932480\pi$
$347$		−	146.110i		−	0.421067i	0.977587	−	0.210533i	$-0.0675200\pi$
$348$	86.6397			0.248965
$349$		−	146.122i		−	0.418689i	−0.977842	−	0.209344i	$-0.932867\pi$
$349$		−	146.122i		−	0.418689i	0.977842	−	0.209344i	$-0.0671330\pi$
$350$		−	38.9078i		−	0.111165i
$351$		−	58.1484i		−	0.165665i
$352$	−38.3935			−0.109073
$353$			506.069i			1.43362i	0.697266	+	0.716812i	$0.254399\pi$
$353$			506.069i			1.43362i	−0.697266	+	0.716812i	$0.745601\pi$
$354$	−116.143	+	86.0042i	−0.328089	+	0.242950i
$355$	−13.0853			−0.0368599
$356$		−	266.878i		−	0.749656i
$357$	44.1395			0.123640
$358$	451.716			1.26178
$359$	−205.700			−0.572982			−0.286491	−	0.958083i	$-0.592489\pi$
$359$	−205.700			−0.572982			−0.286491	+	0.958083i	$0.592489\pi$
$360$		−	3.25393i		−	0.00903869i
$361$	272.790			0.755650
$362$		−	232.055i		−	0.641036i
$363$	−129.792			−0.357554
$364$		−	24.7759i		−	0.0680657i
$365$			21.5704i			0.0590969i
$366$	95.3330			0.260473
$367$			131.342i			0.357879i	0.983860	+	0.178940i	$0.0572667\pi$
$367$			131.342i			0.357879i	−0.983860	+	0.178940i	$0.942733\pi$
$368$		−	133.623i		−	0.363106i
$369$	−233.793			−0.633585
$370$	8.52633			0.0230441
$371$	−11.0598			−0.0298107
$372$		−	54.2685i		−	0.145883i
$373$	370.148			0.992354			0.496177	−	0.868221i	$-0.334737\pi$
$373$	370.148			0.992354			0.496177	+	0.868221i	$0.334737\pi$
$374$	220.963			0.590811
$375$	33.1126			0.0883003
$376$	−62.2616			−0.165589
$377$			279.887i			0.742405i
$378$		−	8.13469i		−	0.0215203i
$379$	−410.269			−1.08250			−0.541252	−	0.840860i	$-0.682049\pi$
$379$	−410.269			−1.08250			−0.541252	+	0.840860i	$0.682049\pi$
$380$	19.3083			0.0508114
$381$	221.498			0.581359
$382$	−322.181			−0.843407
$383$	711.022			1.85645			0.928227	−	0.372015i	$-0.121333\pi$
$383$	711.022			1.85645			0.928227	+	0.372015i	$0.121333\pi$
$384$			19.5959i			0.0510310i
$385$			2.88117i			0.00748357i
$386$			37.0993i			0.0961121i
$387$			234.655i			0.606344i
$388$		−	240.590i		−	0.620078i
$389$	243.610			0.626248			0.313124	−	0.949712i	$-0.398624\pi$
$389$	243.610			0.626248			0.313124	+	0.949712i	$0.398624\pi$
$390$	10.5117			0.0269531
$391$			769.030i			1.96683i
$392$			135.127i			0.344711i
$393$			27.0659i			0.0688701i
$394$			271.632i			0.689422i
$395$	43.2129			0.109400
$396$		−	40.7225i		−	0.102835i
$397$			277.564i			0.699153i	0.936908	+	0.349577i	$0.113675\pi$
$397$			277.564i			0.699153i	−0.936908	+	0.349577i	$0.886325\pi$
$398$			212.179i			0.533114i
$399$	48.2700			0.120977
$400$	−99.4118			−0.248529
$401$			489.765i			1.22136i	0.791877	+	0.610680i	$0.209104\pi$
$401$			489.765i			1.22136i	−0.791877	+	0.610680i	$0.790896\pi$
$402$	1.82012			0.00452767
$403$	175.312			0.435018
$404$			326.210i			0.807449i
$405$	3.45131			0.00852176
$406$			39.1549i			0.0964405i
$407$	106.706			0.262177
$408$		−	112.779i		−	0.276419i
$409$		−	745.617i		−	1.82303i	−0.411272	−	0.911513i	$-0.634915\pi$
$409$		−	745.617i		−	1.82303i	0.411272	−	0.911513i	$-0.365085\pi$
$410$		−	42.2636i		−	0.103082i
$411$	179.732			0.437305
$412$		−	298.300i		−	0.724029i
$413$	−38.8676	−	52.4884i	−0.0941105	−	0.127090i
$414$	141.728			0.342339
$415$		−	35.2938i		−	0.0850453i
$416$	−63.3039			−0.152173
$417$	−444.907			−1.06692
$418$	241.641			0.578089
$419$		−	68.3223i		−	0.163060i	−0.996671	−	0.0815302i	$-0.974019\pi$
$419$		−	68.3223i		−	0.163060i	0.996671	−	0.0815302i	$-0.0259807\pi$
$420$	1.47054			0.00350128
$421$		−	584.969i		−	1.38948i	−0.719263	−	0.694738i	$-0.755520\pi$
$421$		−	584.969i		−	1.38948i	0.719263	−	0.694738i	$-0.244480\pi$
$422$	89.4271			0.211913
$423$		−	66.0384i		−	0.156119i
$424$			28.2584i			0.0666471i
$425$	572.137			1.34620
$426$			83.5827i			0.196204i
$427$			43.0836i			0.100898i
$428$	−57.1258			−0.133472
$429$	131.553			0.306649
$430$	−42.4195			−0.0986500
$431$		−	618.641i		−	1.43536i	−0.696372	−	0.717681i	$-0.745204\pi$
$431$		−	618.641i		−	1.43536i	0.696372	−	0.717681i	$-0.254796\pi$
$432$	−20.7846			−0.0481125
$433$	−368.464			−0.850956			−0.425478	−	0.904969i	$-0.639894\pi$
$433$	−368.464			−0.850956			−0.425478	+	0.904969i	$0.639894\pi$
$434$	24.5254			0.0565101
$435$	−16.6123			−0.0381891
$436$		−	63.8036i		−	0.146338i
$437$			840.995i			1.92447i
$438$	137.782			0.314570
$439$	−148.866			−0.339102			−0.169551	−	0.985521i	$-0.554232\pi$
$439$	−148.866			−0.339102			−0.169551	+	0.985521i	$0.554232\pi$
$440$	7.36156			0.0167308
$441$	−143.324			−0.324997
$442$	364.328			0.824272
$443$			126.016i			0.284461i	0.989834	+	0.142230i	$0.0454274\pi$
$443$			126.016i			0.284461i	−0.989834	+	0.142230i	$0.954573\pi$
$444$		−	54.4623i		−	0.122663i
$445$			51.1710i			0.114991i
$446$		−	43.9787i		−	0.0986070i
$447$		−	295.225i		−	0.660458i
$448$	−8.85593			−0.0197677
$449$	608.478			1.35519			0.677593	−	0.735437i	$-0.263023\pi$
$449$	608.478			1.35519			0.677593	+	0.735437i	$0.263023\pi$
$450$		−	105.442i		−	0.234316i
$451$		−	528.924i		−	1.17278i
$452$		−	190.061i		−	0.420488i
$453$			395.906i			0.873964i
$454$	201.219			0.443214
$455$			4.75052i			0.0104407i
$456$		−	123.333i		−	0.270466i
$457$			347.364i			0.760096i	0.924967	+	0.380048i	$0.124093\pi$
$457$			347.364i			0.760096i	−0.924967	+	0.380048i	$0.875907\pi$
$458$	300.752			0.656664
$459$	119.620			0.260610
$460$			25.6208i			0.0556974i
$461$	459.494			0.996733			0.498366	−	0.866967i	$-0.333933\pi$
$461$	459.494			0.996733			0.498366	+	0.866967i	$0.333933\pi$
$462$	18.4036			0.0398347
$463$			519.915i			1.12293i	0.827501	+	0.561464i	$0.189762\pi$
$463$			519.915i			1.12293i	−0.827501	+	0.561464i	$0.810238\pi$
$464$	100.043			0.215610
$465$			10.4054i			0.0223772i
$466$	−62.3631			−0.133826
$467$			406.834i			0.871165i	0.900149	+	0.435583i	$0.143458\pi$
$467$			406.834i			0.871165i	−0.900149	+	0.435583i	$0.856542\pi$
$468$		−	67.1439i		−	0.143470i
$469$			0.822563i			0.00175387i
$470$	11.9380			0.0254000
$471$		−	275.481i		−	0.584886i
$472$	−134.111	+	99.3091i	−0.284133	+	0.210401i
$473$	−530.875			−1.12236
$474$		−	276.024i		−	0.582329i
$475$	625.677			1.31722
$476$	50.9679			0.107075
$477$	−29.9725			−0.0628355
$478$			226.302i			0.473436i
$479$	−255.225			−0.532828			−0.266414	−	0.963859i	$-0.585839\pi$
$479$	−255.225			−0.532828			−0.266414	+	0.963859i	$0.585839\pi$
$480$		−	3.75731i		−	0.00782774i
$481$	175.939			0.365777
$482$		−	326.555i		−	0.677499i
$483$			64.0510i			0.132611i
$484$	−149.871			−0.309651
$485$			46.1307i			0.0951148i
$486$		−	22.0454i		−	0.0453609i
$487$	666.071			1.36770			0.683851	−	0.729622i	$-0.260304\pi$
$487$	666.071			1.36770			0.683851	+	0.729622i	$0.260304\pi$
$488$	110.081			0.225576
$489$	157.244			0.321563
$490$		−	25.9092i		−	0.0528759i
$491$	−249.250			−0.507637			−0.253818	−	0.967252i	$-0.581687\pi$
$491$	−249.250			−0.507637			−0.253818	+	0.967252i	$0.581687\pi$
$492$	−269.961			−0.548700
$493$	−575.770			−1.16789
$494$	398.422			0.806522
$495$			7.80812i			0.0157740i
$496$		−	62.6638i		−	0.126338i
$497$	−37.7733			−0.0760026
$498$	−225.441			−0.452692
$499$	111.311			0.223068			0.111534	−	0.993761i	$-0.464424\pi$
$499$	111.311			0.223068			0.111534	+	0.993761i	$0.464424\pi$
$500$	38.2351			0.0764703
$501$	−504.592			−1.00717
$502$		−	219.293i		−	0.436838i
$503$		−	218.130i		−	0.433657i	−0.976210	−	0.216829i	$-0.930429\pi$
$503$		−	218.130i		−	0.433657i	0.976210	−	0.216829i	$-0.0695713\pi$
$504$		−	9.39313i		−	0.0186372i
$505$		−	62.5473i		−	0.123856i
$506$			320.641i			0.633678i
$507$	−75.8105			−0.149528
$508$	255.763			0.503471
$509$			114.526i			0.225002i	0.993652	+	0.112501i	$0.0358862\pi$
$509$			114.526i			0.225002i	−0.993652	+	0.112501i	$0.964114\pi$
$510$			21.6242i			0.0424004i
$511$			62.2673i			0.121854i
$512$			22.6274i			0.0441942i
$513$	130.814			0.254998
$514$		−	588.821i		−	1.14557i
$515$			57.1959i			0.111060i
$516$			270.956i			0.525109i
$517$	149.403			0.288980
$518$	24.6130			0.0475155
$519$			204.489i			0.394006i
$520$	12.1379			0.0233421
$521$	−884.868			−1.69840			−0.849201	−	0.528069i	$-0.822916\pi$
$521$	−884.868			−1.69840			−0.849201	+	0.528069i	$0.822916\pi$
$522$			106.112i			0.203279i
$523$	733.955			1.40336			0.701678	−	0.712494i	$-0.252434\pi$
$523$	733.955			1.40336			0.701678	+	0.712494i	$0.252434\pi$
$524$			31.2531i			0.0596432i
$525$	47.6522			0.0907660
$526$			192.563i			0.366090i
$527$			360.644i			0.684335i
$528$		−	47.0223i		−	0.0890574i
$529$	−586.942			−1.10953
$530$		−	5.41825i		−	0.0102231i
$531$	−105.333	−	142.246i	−0.198368	−	0.267883i
$532$	55.7374			0.104770
$533$		−	872.098i		−	1.63621i
$534$	326.857			0.612092
$535$	10.9533			0.0204734
$536$	2.10170			0.00392108
$537$			553.237i			1.03024i
$538$	−543.363			−1.00997
$539$		−	324.250i		−	0.601577i
$540$	3.98523			0.00738006
$541$			35.8067i			0.0661861i	0.999452	+	0.0330931i	$0.0105358\pi$
$541$			35.8067i			0.0661861i	−0.999452	+	0.0330931i	$0.989464\pi$
$542$		−	696.922i		−	1.28583i
$543$	284.208			0.523403
$544$		−	130.226i		−	0.239386i
$545$			12.2337i			0.0224471i
$546$	30.3442			0.0555754
$547$	−270.369			−0.494276			−0.247138	−	0.968980i	$-0.579490\pi$
$547$	−270.369			−0.494276			−0.247138	+	0.968980i	$0.579490\pi$
$548$	207.537			0.378717
$549$			116.759i			0.212675i
$550$	238.548			0.433724
$551$	−629.650			−1.14274
$552$	163.654			0.296475
$553$	124.743			0.225575
$554$		−	524.649i		−	0.947020i
$555$			10.4426i			0.0188155i
$556$	−513.734			−0.923983
$557$	−662.266			−1.18899			−0.594494	−	0.804100i	$-0.702647\pi$
$557$	−662.266			−1.18899			−0.594494	+	0.804100i	$0.702647\pi$
$558$	66.4650			0.119113
$559$	−875.315			−1.56586
$560$	1.69803			0.00303220
$561$			270.624i			0.482396i
$562$			134.362i			0.239079i
$563$			222.212i			0.394693i	0.980334	+	0.197346i	$0.0632324\pi$
$563$			222.212i			0.394693i	−0.980334	+	0.197346i	$0.936768\pi$
$564$		−	76.2546i		−	0.135203i
$565$			36.4422i			0.0644994i
$566$	−745.657			−1.31741
$567$	9.96292			0.0175713
$568$			96.5130i			0.169917i
$569$		−	202.567i		−	0.356005i	−0.984030	−	0.178002i	$-0.943037\pi$
$569$		−	202.567i		−	0.356005i	0.984030	−	0.178002i	$-0.0569635\pi$
$570$			23.6478i			0.0414873i
$571$		−	89.2806i		−	0.156358i	−0.996939	−	0.0781792i	$-0.975089\pi$
$571$		−	89.2806i		−	0.156358i	0.996939	−	0.0781792i	$-0.0249106\pi$
$572$	151.904			0.265566
$573$		−	394.590i		−	0.688639i
$574$		−	122.003i		−	0.212548i
$575$			830.230i			1.44388i
$576$	−24.0000			−0.0416667
$577$	−28.4362			−0.0492828			−0.0246414	−	0.999696i	$-0.507844\pi$
$577$	−28.4362			−0.0492828			−0.0246414	+	0.999696i	$0.507844\pi$
$578$			340.771i			0.589570i
$579$	−45.4371			−0.0784752
$580$	−19.1822			−0.0330727
$581$		−	101.883i		−	0.175358i
$582$	294.662			0.506292
$583$		−	67.8087i		−	0.116310i
$584$	159.097			0.272426
$585$			12.8742i			0.0220071i
$586$		−	202.147i		−	0.344961i
$587$		−	180.587i		−	0.307643i	−0.988099	−	0.153822i	$-0.950842\pi$
$587$		−	180.587i		−	0.307643i	0.988099	−	0.153822i	$-0.0491581\pi$
$588$	−165.496			−0.281456
$589$			394.393i			0.669598i
$590$	25.7144	−	19.0415i	0.0435837	−	0.0322737i
$591$	−332.680			−0.562911
$592$		−	62.8877i		−	0.106229i
$593$	−558.379			−0.941618			−0.470809	−	0.882235i	$-0.656038\pi$
$593$	−558.379			−0.941618			−0.470809	+	0.882235i	$0.656038\pi$
$594$	49.8747			0.0839641
$595$	−9.77256			−0.0164245
$596$		−	340.896i		−	0.571974i
$597$	−259.865			−0.435286
$598$			528.678i			0.884077i
$599$	−1044.80			−1.74424			−0.872118	−	0.489296i	$-0.837254\pi$
$599$	−1044.80			−1.74424			−0.872118	+	0.489296i	$0.837254\pi$
$600$		−	121.754i		−	0.202923i
$601$		−	730.430i		−	1.21536i	−0.794183	−	0.607679i	$-0.792101\pi$
$601$		−	730.430i		−	1.21536i	0.794183	−	0.607679i	$-0.207899\pi$
$602$	−122.453			−0.203410
$603$			2.22919i			0.00369683i
$604$			457.152i			0.756875i
$605$	28.7362			0.0474978
$606$	−399.523			−0.659280
$607$	−87.9621			−0.144913			−0.0724564	−	0.997372i	$-0.523084\pi$
$607$	−87.9621			−0.144913			−0.0724564	+	0.997372i	$0.523084\pi$
$608$		−	142.412i		−	0.234231i
$609$	−47.9547			−0.0787434
$610$	−21.1069			−0.0346015
$611$	246.338			0.403171
$612$	138.125			0.225695
$613$			27.1344i			0.0442649i	0.999755	+	0.0221325i	$0.00704555\pi$
$613$			27.1344i			0.0442649i	−0.999755	+	0.0221325i	$0.992954\pi$
$614$		−	90.5265i		−	0.147437i
$615$	51.7621			0.0841661
$616$	21.2507			0.0344978
$617$	409.795			0.664174			0.332087	−	0.943249i	$-0.392247\pi$
$617$	409.795			0.664174			0.332087	+	0.943249i	$0.392247\pi$
$618$	365.341			0.591167
$619$	−533.623			−0.862073			−0.431037	−	0.902334i	$-0.641852\pi$
$619$	−533.623			−0.862073			−0.431037	+	0.902334i	$0.641852\pi$
$620$			12.0151i			0.0193793i
$621$			173.581i			0.279519i
$622$		−	20.3124i		−	0.0326566i
$623$			147.716i			0.237104i
$624$		−	77.5311i		−	0.124249i
$625$	613.992			0.982388
$626$	−138.193			−0.220756
$627$			295.949i			0.472008i
$628$		−	318.098i		−	0.506526i
$629$			361.933i			0.575410i
$630$			1.80104i			0.00285879i
$631$	−114.982			−0.182221			−0.0911106	−	0.995841i	$-0.529042\pi$
$631$	−114.982			−0.182221			−0.0911106	+	0.995841i	$0.529042\pi$
$632$		−	318.725i		−	0.504312i
$633$			109.525i			0.173026i
$634$		−	168.525i		−	0.265812i
$635$	−49.0400			−0.0772283
$636$	−34.6093			−0.0544171
$637$		−	534.629i		−	0.839292i
$638$	−240.063			−0.376274
$639$	−102.367			−0.160200
$640$		−	4.33857i		−	0.00677902i
$641$	234.297			0.365518			0.182759	−	0.983158i	$-0.441497\pi$
$641$	234.297			0.365518			0.182759	+	0.983158i	$0.441497\pi$
$642$		−	69.9646i		−	0.108979i
$643$	382.044			0.594159			0.297080	−	0.954853i	$-0.403987\pi$
$643$	382.044			0.594159			0.297080	+	0.954853i	$0.403987\pi$
$644$			73.9597i			0.114844i
$645$		−	51.9531i		−	0.0805474i
$646$			819.615i			1.26875i
$647$	−668.577			−1.03335			−0.516675	−	0.856182i	$-0.672830\pi$
$647$	−668.577			−1.03335			−0.516675	+	0.856182i	$0.672830\pi$
$648$		−	25.4558i		−	0.0392837i
$649$	321.812	−	238.302i	0.495858	−	0.367183i
$650$	393.322			0.605111
$651$			30.0374i			0.0461403i
$652$	181.570			0.278482
$653$	−165.925			−0.254097			−0.127048	−	0.991897i	$-0.540550\pi$
$653$	−165.925			−0.254097			−0.127048	+	0.991897i	$0.540550\pi$
$654$	78.1431			0.119485
$655$		−	5.99245i		−	0.00914878i
$656$	−311.724			−0.475188
$657$			168.747i			0.256845i
$658$	34.4615			0.0523731
$659$			149.073i			0.226210i	0.993583	+	0.113105i	$0.0360797\pi$
$659$			149.073i			0.226210i	−0.993583	+	0.113105i	$0.963920\pi$
$660$			9.01604i			0.0136607i
$661$	287.939			0.435612			0.217806	−	0.975992i	$-0.430110\pi$
$661$	287.939			0.435612			0.217806	+	0.975992i	$0.430110\pi$
$662$		−	507.529i		−	0.766660i
$663$			446.209i			0.673015i
$664$	−260.316			−0.392043
$665$	−10.6871			−0.0160708
$666$	66.7024			0.100154
$667$		−	835.502i		−	1.25263i
$668$	−582.652			−0.872234
$669$	53.8627			0.0805123
$670$	−0.402979			−0.000601461
$671$	−264.150			−0.393667
$672$		−	10.8463i		−	0.0161403i
$673$		−	711.875i		−	1.05776i	−0.848696	−	0.528882i	$-0.822612\pi$
$673$		−	711.875i		−	1.05776i	0.848696	−	0.528882i	$-0.177388\pi$
$674$	−399.792			−0.593163
$675$	129.140			0.191318
$676$	−87.5384			−0.129495
$677$	−665.770			−0.983412			−0.491706	−	0.870761i	$-0.663626\pi$
$677$	−665.770			−0.983412			−0.491706	+	0.870761i	$0.663626\pi$
$678$	232.776			0.343327
$679$			133.166i			0.196120i
$680$			24.9695i			0.0367198i
$681$			246.442i			0.361883i
$682$			150.368i			0.220481i
$683$			189.224i			0.277048i	0.990359	+	0.138524i	$0.0442358\pi$
$683$			189.224i			0.277048i	−0.990359	+	0.138524i	$0.955764\pi$
$684$	151.051			0.220835
$685$	−39.7931			−0.0580921
$686$		−	151.503i		−	0.220849i
$687$			368.344i			0.536164i
$688$			312.873i			0.454758i
$689$		−	111.804i		−	0.162270i
$690$	−31.3789			−0.0454767
$691$		−	963.176i		−	1.39389i	−0.717126	−	0.696944i	$-0.754543\pi$
$691$		−	963.176i		−	1.39389i	0.717126	−	0.696944i	$-0.245457\pi$
$692$			236.123i			0.341219i
$693$			22.5397i			0.0325249i
$694$	206.631			0.297739
$695$	98.5032			0.141731
$696$			122.527i			0.176045i
$697$	1794.04			2.57394
$698$	206.648			0.296058
$699$		−	76.3788i		−	0.109269i
$700$	55.0240			0.0786057
$701$		−	521.185i		−	0.743488i	−0.928335	−	0.371744i	$-0.878760\pi$
$701$		−	521.185i		−	0.743488i	0.928335	−	0.371744i	$-0.121240\pi$
$702$	82.2342			0.117143
$703$			395.802i			0.563019i
$704$		−	54.2967i		−	0.0771260i
$705$			14.6210i			0.0207390i
$706$	−715.690			−1.01373
$707$		−	180.556i		−	0.255383i
$708$	−121.628	−	164.252i	−0.171791	−	0.231994i
$709$	435.515			0.614266			0.307133	−	0.951667i	$-0.400630\pi$
$709$	435.515			0.614266			0.307133	+	0.951667i	$0.400630\pi$
$710$		−	18.5054i		−	0.0260639i
$711$	338.059			0.475470
$712$	377.422			0.530087
$713$	−523.333			−0.733987
$714$			62.4226i			0.0874267i
$715$	−29.1260			−0.0407356
$716$			638.823i			0.892211i
$717$	−277.163			−0.386559
$718$		−	290.904i		−	0.405159i
$719$		−	1026.95i		−	1.42830i	−0.699991	−	0.714151i	$-0.746813\pi$
$719$		−	1026.95i		−	1.42830i	0.699991	−	0.714151i	$-0.253187\pi$
$720$	4.60175			0.00639132
$721$			165.108i			0.228998i
$722$			385.783i			0.534325i
$723$	399.946			0.553176
$724$	328.175			0.453281
$725$	−621.590			−0.857366
$726$		−	183.554i		−	0.252829i
$727$	−981.371			−1.34989			−0.674946	−	0.737867i	$-0.735833\pi$
$727$	−981.371			−1.34989			−0.674946	+	0.737867i	$0.735833\pi$
$728$	35.0384			0.0481297
$729$	27.0000			0.0370370
$730$	−30.5051			−0.0417878
$731$		−	1800.66i		−	2.46328i
$732$			134.821i			0.184182i
$733$	1198.97			1.63571			0.817854	−	0.575426i	$-0.195164\pi$
$733$	1198.97			1.63571			0.817854	+	0.575426i	$0.195164\pi$
$734$	−185.745			−0.253059
$735$	31.7321			0.0431730
$736$	188.971			0.256754
$737$	−5.04323			−0.00684291
$738$		−	330.633i		−	0.448012i
$739$			67.2399i			0.0909877i	0.998965	+	0.0454938i	$0.0144861\pi$
$739$			67.2399i			0.0909877i	−0.998965	+	0.0454938i	$0.985514\pi$
$740$			12.0581i			0.0162947i
$741$			487.965i			0.658522i
$742$		−	15.6409i		−	0.0210794i
$743$	−256.835			−0.345673			−0.172837	−	0.984951i	$-0.555293\pi$
$743$	−256.835			−0.345673			−0.172837	+	0.984951i	$0.555293\pi$
$744$	76.7472			0.103155
$745$			65.3633i			0.0877360i
$746$			523.468i			0.701700i
$747$		−	276.107i		−	0.369622i
$748$			312.490i			0.417767i
$749$	31.6189			0.0422148
$750$			46.8283i			0.0624377i
$751$			1452.43i			1.93400i	0.254778	+	0.966999i	$0.417998\pi$
$751$			1452.43i			1.93400i	−0.254778	+	0.966999i	$0.582002\pi$
$752$		−	88.0512i		−	0.117089i
$753$	268.578			0.356677
$754$	−395.819			−0.524959
$755$		−	87.6542i		−	0.116098i
$756$	11.5042			0.0152172
$757$	90.1525			0.119092			0.0595459	−	0.998226i	$-0.481035\pi$
$757$	90.1525			0.119092			0.0595459	+	0.998226i	$0.481035\pi$
$758$		−	580.208i		−	0.765446i
$759$	−392.703			−0.517396
$760$			27.3061i			0.0359291i
$761$	−906.629			−1.19137			−0.595683	−	0.803220i	$-0.703118\pi$
$761$	−906.629			−1.19137			−0.595683	+	0.803220i	$0.703118\pi$
$762$			313.245i			0.411083i
$763$			35.3150i			0.0462844i
$764$		−	455.633i		−	0.596379i
$765$	−26.4841			−0.0346197
$766$			1005.54i			1.31271i
$767$	530.609	−	392.916i	0.691798	−	0.512276i
$768$	−27.7128			−0.0360844
$769$		−	1067.74i		−	1.38848i	−0.719744	−	0.694240i	$-0.755741\pi$
$769$		−	1067.74i		−	1.38848i	0.719744	−	0.694240i	$-0.244259\pi$
$770$	−4.07459			−0.00529168
$771$	721.155			0.935350
$772$	−52.4663			−0.0679615
$773$			1123.49i			1.45342i	0.686945	+	0.726710i	$0.258951\pi$
$773$			1123.49i			1.45342i	−0.686945	+	0.726710i	$0.741049\pi$
$774$	−331.852			−0.428750
$775$			389.345i			0.502381i
$776$	340.246			0.438461
$777$			30.1447i			0.0387962i
$778$			344.517i			0.442824i
$779$	1961.92			2.51852
$780$			14.8658i			0.0190587i
$781$		−	231.592i		−	0.296533i
$782$	−1087.57			−1.39076
$783$	−129.960			−0.165976
$784$	−191.098			−0.243748
$785$			60.9921i			0.0776969i
$786$	−38.2770			−0.0486985
$787$	−318.214			−0.404338			−0.202169	−	0.979351i	$-0.564799\pi$
$787$	−318.214			−0.404338			−0.202169	+	0.979351i	$0.564799\pi$
$788$	−384.146			−0.487495
$789$	−235.841			−0.298911
$790$			61.1122i			0.0773572i
$791$			105.198i			0.132993i
$792$	57.5903			0.0727151
$793$	−435.535			−0.549225
$794$	−392.534			−0.494376
$795$	6.63597			0.00834714
$796$	−300.067			−0.376968
$797$		−	1099.03i		−	1.37895i	−0.724308	−	0.689477i	$-0.757840\pi$
$797$		−	1099.03i		−	1.37895i	0.724308	−	0.689477i	$-0.242160\pi$
$798$			68.2641i			0.0855440i
$799$			506.754i			0.634236i
$800$		−	140.589i		−	0.175737i
$801$			400.317i			0.499771i
$802$	−692.633			−0.863632
$803$	−381.767			−0.475426
$804$			2.57404i			0.00320155i
$805$		−	14.1810i		−	0.0176161i
$806$			247.929i			0.307604i
$807$		−	665.481i		−	0.824636i
$808$	−461.330			−0.570953
$809$		−	764.943i		−	0.945541i	−0.881186	−	0.472770i	$-0.843254\pi$
$809$		−	764.943i		−	0.945541i	0.881186	−	0.472770i	$-0.156746\pi$
$810$			4.88089i			0.00602579i
$811$			716.038i			0.882908i	0.897284	+	0.441454i	$0.145537\pi$
$811$			716.038i			0.882908i	−0.897284	+	0.441454i	$0.854463\pi$
$812$	−55.3733			−0.0681938
$813$	853.552			1.04988
$814$			150.905i			0.185387i
$815$	−34.8142			−0.0427168
$816$	159.493			0.195458
$817$		−	1969.16i		−	2.41023i
$818$	1054.46			1.28907
$819$			37.1639i			0.0453771i
$820$	59.7698			0.0728899
$821$		−	732.577i		−	0.892298i	−0.894959	−	0.446149i	$-0.852795\pi$
$821$		−	732.577i		−	0.892298i	0.894959	−	0.446149i	$-0.147205\pi$
$822$			254.180i			0.309221i
$823$		−	1396.49i		−	1.69683i	−0.529332	−	0.848415i	$-0.677557\pi$
$823$		−	1396.49i		−	1.69683i	0.529332	−	0.848415i	$-0.322443\pi$
$824$	421.860			0.511966
$825$			292.161i			0.354134i
$826$	74.2298	−	54.9671i	0.0898665	−	0.0665462i
$827$	147.460			0.178307			0.0891536	−	0.996018i	$-0.471584\pi$
$827$	147.460			0.178307			0.0891536	+	0.996018i	$0.471584\pi$
$828$			200.434i			0.242070i
$829$	1083.93			1.30751			0.653755	−	0.756706i	$-0.273193\pi$
$829$	1083.93			1.30751			0.653755	+	0.756706i	$0.273193\pi$
$830$	49.9130			0.0601361
$831$	642.561			0.773238
$832$		−	89.5252i		−	0.107602i
$833$	1099.81			1.32030
$834$		−	629.193i		−	0.754429i
$835$	111.718			0.133793
$836$			341.732i			0.408770i
$837$			81.4027i			0.0972553i
$838$	96.6223			0.115301
$839$			971.489i			1.15791i	0.815358	+	0.578957i	$0.196540\pi$
$839$			971.489i			1.15791i	−0.815358	+	0.578957i	$0.803460\pi$
$840$			2.07966i			0.00247578i
$841$	−215.463			−0.256199
$842$	827.271			0.982508
$843$	−164.559			−0.195207
$844$			126.469i			0.149845i
$845$	16.7846			0.0198634
$846$	93.3924			0.110393
$847$	82.9529			0.0979373
$848$	−39.9634			−0.0471266
$849$		−	913.239i		−	1.07566i
$850$			809.124i			0.951911i
$851$	−525.202			−0.617159
$852$	−118.204			−0.138737
$853$	1340.99			1.57209			0.786044	−	0.618170i	$-0.212126\pi$
$853$	1340.99			1.57209			0.786044	+	0.618170i	$0.212126\pi$
$854$	−60.9294			−0.0713459
$855$	−28.9625			−0.0338742
$856$		−	80.7881i		−	0.0943786i
$857$			939.852i			1.09668i	0.836256	+	0.548339i	$0.184739\pi$
$857$			939.852i			1.09668i	−0.836256	+	0.548339i	$0.815261\pi$
$858$			186.043i			0.216834i
$859$			726.413i			0.845650i	0.906211	+	0.422825i	$0.138961\pi$
$859$			726.413i			0.845650i	−0.906211	+	0.422825i	$0.861039\pi$
$860$		−	59.9902i		−	0.0697561i
$861$	149.422			0.173545
$862$	874.890			1.01495
$863$			744.848i			0.863091i	0.902091	+	0.431546i	$0.142032\pi$
$863$			744.848i			0.863091i	−0.902091	+	0.431546i	$0.857968\pi$
$864$		−	29.3939i		−	0.0340207i
$865$		−	45.2742i		−	0.0523401i
$866$		−	521.087i		−	0.601717i
$867$	−417.358			−0.481382
$868$			34.6842i			0.0399587i
$869$			764.812i			0.880105i
$870$		−	23.4933i		−	0.0270038i
$871$	−8.31535			−0.00954690
$872$	90.2319			0.103477
$873$			360.885i			0.413385i
$874$	−1189.35			−1.36081
$875$	−21.1630			−0.0241863
$876$			194.853i			0.222435i
$877$	−405.205			−0.462036			−0.231018	−	0.972950i	$-0.574206\pi$
$877$	−405.205			−0.462036			−0.231018	+	0.972950i	$0.574206\pi$
$878$		−	210.528i		−	0.239782i
$879$	247.579			0.281660
$880$			10.4108i			0.0118305i
$881$		−	1308.26i		−	1.48498i	−0.669859	−	0.742488i	$-0.733645\pi$
$881$		−	1308.26i		−	1.48498i	0.669859	−	0.742488i	$-0.266355\pi$
$882$		−	202.690i		−	0.229808i
$883$	631.187			0.714821			0.357411	−	0.933947i	$-0.383660\pi$
$883$	631.187			0.714821			0.357411	+	0.933947i	$0.383660\pi$
$884$			515.238i			0.582848i
$885$	23.3210	+	31.4935i	0.0263514	+	0.0355859i
$886$	−178.214			−0.201144
$887$			503.596i			0.567752i	0.958861	+	0.283876i	$0.0916205\pi$
$887$			503.596i			0.567752i	−0.958861	+	0.283876i	$0.908380\pi$
$888$	77.0213			0.0867357
$889$	−141.564			−0.159240
$890$	−72.3668			−0.0813110
$891$			61.0838i			0.0685564i
$892$	62.1953			0.0697257
$893$			554.176i			0.620578i
$894$	417.511			0.467015
$895$		−	122.488i		−	0.136858i
$896$		−	12.5242i		−	0.0139779i
$897$	−647.496			−0.721846
$898$			860.518i			0.958261i
$899$		−	391.817i		−	0.435837i
$900$	149.118			0.165686
$901$	229.998			0.255270
$902$	748.011			0.829280
$903$		−	149.973i		−	0.166083i
$904$	268.786			0.297330
$905$	−62.9242			−0.0695295
$906$	−559.895			−0.617986
$907$	−476.445			−0.525298			−0.262649	−	0.964891i	$-0.584596\pi$
$907$	−476.445			−0.525298			−0.262649	+	0.964891i	$0.584596\pi$
$908$			284.567i			0.313400i
$909$		−	489.314i		−	0.538300i
$910$	−6.71826			−0.00738270
$911$	−103.924			−0.114077			−0.0570384	−	0.998372i	$-0.518166\pi$
$911$	−103.924			−0.114077			−0.0570384	+	0.998372i	$0.518166\pi$
$912$	174.419			0.191249
$913$	624.655			0.684178
$914$	−491.247			−0.537469
$915$		−	25.8506i		−	0.0282520i
$916$			425.327i			0.464331i
$917$		−	17.2984i		−	0.0188642i
$918$			169.168i			0.184279i
$919$			1135.60i			1.23569i	0.786301	+	0.617843i	$0.211993\pi$
$919$			1135.60i			1.23569i	−0.786301	+	0.617843i	$0.788007\pi$
$920$	−36.2333			−0.0393840
$921$	110.872			0.120382
$922$			649.822i			0.704797i
$923$		−	381.853i		−	0.413709i
$924$			26.0266i			0.0281674i
$925$			390.736i			0.422417i
$926$	−735.272			−0.794030
$927$			447.450i			0.482686i
$928$			141.482i			0.152459i
$929$		−	326.277i		−	0.351213i	−0.984460	−	0.175606i	$-0.943811\pi$
$929$		−	326.277i		−	0.351213i	0.984460	−	0.175606i	$-0.0561886\pi$
$930$	−14.7155			−0.0158231
$931$	1202.73			1.29187
$932$		−	88.1947i		−	0.0946295i
$933$	24.8775			0.0266640
$934$	−575.350			−0.616007
$935$		−	59.9166i		−	0.0640820i
$936$	94.9559			0.101449
$937$		−	682.689i		−	0.728590i	−0.931284	−	0.364295i	$-0.881310\pi$
$937$		−	682.689i		−	0.728590i	0.931284	−	0.364295i	$-0.118690\pi$
$938$	−1.16328			−0.00124017
$939$		−	169.252i		−	0.180247i
$940$			16.8829i			0.0179605i
$941$			61.1269i			0.0649595i	0.999472	+	0.0324797i	$0.0103404\pi$
$941$			61.1269i			0.0649595i	−0.999472	+	0.0324797i	$0.989660\pi$
$942$	389.589			0.413577
$943$			2603.34i			2.76070i
$944$	−140.444	−	189.661i	−0.148776	−	0.200912i
$945$	−2.20581			−0.00233419
$946$		−	750.770i		−	0.793626i
$947$	−386.286			−0.407905			−0.203953	−	0.978981i	$-0.565379\pi$
$947$	−386.286			−0.407905			−0.203953	+	0.978981i	$0.565379\pi$
$948$	390.357			0.411769
$949$	−629.464			−0.663292
$950$			884.841i			0.931412i
$951$	206.400			0.217035
$952$			72.0795i			0.0757137i
$953$	662.265			0.694926			0.347463	−	0.937694i	$-0.387043\pi$
$953$	662.265			0.694926			0.347463	+	0.937694i	$0.387043\pi$
$954$		−	42.3876i		−	0.0444314i
$955$			87.3630i			0.0914795i
$956$	−320.040			−0.334770
$957$		−	294.016i		−	0.307226i
$958$		−	360.942i		−	0.376766i
$959$	−114.871			−0.119782
$960$	5.31364			0.00553505
$961$	715.578			0.744618
$962$			248.815i			0.258643i
$963$	85.6887			0.0889810
$964$	461.818			0.479064
$965$	10.0599			0.0104247
$966$	−90.5817			−0.0937699
$967$			1095.46i			1.13285i	0.824114	+	0.566424i	$0.191674\pi$
$967$			1095.46i			1.13285i	−0.824114	+	0.566424i	$0.808326\pi$
$968$		−	211.950i		−	0.218956i
$969$	−1003.82			−1.03593
$970$	−65.2386			−0.0672563
$971$	6.63060			0.00682863			0.00341431	−	0.999994i	$-0.498913\pi$
$971$	6.63060			0.00682863			0.00341431	+	0.999994i	$0.498913\pi$
$972$	31.1769			0.0320750
$973$	284.350			0.292240
$974$			941.966i			0.967111i
$975$			481.719i			0.494071i
$976$			155.678i			0.159506i
$977$			872.049i			0.892578i	0.894889	+	0.446289i	$0.147255\pi$
$977$			872.049i			0.892578i	−0.894889	+	0.446289i	$0.852745\pi$
$978$			222.377i			0.227379i
$979$	−905.661			−0.925088
$980$	36.6411			0.0373889
$981$			95.7053i			0.0975590i
$982$		−	352.492i		−	0.358953i
$983$			1433.25i			1.45803i	0.684496	+	0.729016i	$0.260022\pi$
$983$			1433.25i			1.45803i	−0.684496	+	0.729016i	$0.739978\pi$
$984$		−	381.782i		−	0.387990i
$985$	73.6560			0.0747777
$986$		−	814.261i		−	0.825823i
$987$			42.2066i			0.0427625i
$988$			563.454i			0.570297i
$989$	2612.94			2.64200
$990$	−11.0423			−0.0111539
$991$		−	1255.76i		−	1.26716i	−0.773677	−	0.633580i	$-0.781585\pi$
$991$		−	1255.76i		−	1.26716i	0.773677	−	0.633580i	$-0.218415\pi$
$992$	88.6200			0.0893347
$993$	621.593			0.625975
$994$		−	53.4195i		−	0.0537420i
$995$	57.5347			0.0578238
$996$		−	318.821i		−	0.320102i
$997$	−557.818			−0.559497			−0.279748	−	0.960073i	$-0.590251\pi$
$997$	−557.818			−0.559497			−0.279748	+	0.960073i	$0.590251\pi$
$998$			157.417i			0.157733i
$999$			81.6935i			0.0817752i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.3.d.a.235.13	yes	20
3.2	odd	2		1062.3.d.f.235.5		20
59.58	odd	2	inner	354.3.d.a.235.3	✓	20
177.176	even	2		1062.3.d.f.235.15		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.3.d.a.235.3	✓	20	59.58	odd	2	inner
354.3.d.a.235.13	yes	20	1.1	even	1	trivial
1062.3.d.f.235.5		20	3.2	odd	2
1062.3.d.f.235.15		20	177.176	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	354.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +0.383479 q^{5} -2.44949i q^{6} +1.10699 q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +0.383479 q^{5} -2.44949i q^{6} +1.10699 q^{7} -2.82843i q^{8} +3.00000 q^{9} +0.542321i q^{10} +6.78708i q^{11} +3.46410 q^{12} +11.1907i q^{13} +1.56552i q^{14} -0.664205 q^{15} +4.00000 q^{16} -23.0209 q^{17} +4.24264i q^{18} -25.1752 q^{19} -0.766958 q^{20} -1.91737 q^{21} -9.59839 q^{22} -33.4057i q^{23} +4.89898i q^{24} -24.8529 q^{25} -15.8260 q^{26} -5.19615 q^{27} -2.21398 q^{28} +25.0107 q^{29} -0.939328i q^{30} -15.6660i q^{31} +5.65685i q^{32} -11.7556i q^{33} -32.5565i q^{34} +0.424508 q^{35} -6.00000 q^{36} -15.7219i q^{37} -35.6031i q^{38} -19.3828i q^{39} -1.08464i q^{40} -77.9309 q^{41} -2.71156i q^{42} +78.2183i q^{43} -13.5742i q^{44} +1.15044 q^{45} +47.2428 q^{46} -22.0128i q^{47} -6.92820 q^{48} -47.7746 q^{49} -35.1474i q^{50} +39.8734 q^{51} -22.3813i q^{52} -9.99084 q^{53} -7.34847i q^{54} +2.60271i q^{55} -3.13104i q^{56} +43.6047 q^{57} +35.3705i q^{58} +(-35.1111 - 47.4153i) q^{59} +1.32841 q^{60} +38.9195i q^{61} +22.1550 q^{62} +3.32097 q^{63} -8.00000 q^{64} +4.29138i q^{65} +16.6249 q^{66} +0.743062i q^{67} +46.0418 q^{68} +57.8604i q^{69} +0.600345i q^{70} -34.1225 q^{71} -8.48528i q^{72} +56.2491i q^{73} +22.2341 q^{74} +43.0466 q^{75} +50.3504 q^{76} +7.51324i q^{77} +27.4114 q^{78} +112.686 q^{79} +1.53392 q^{80} +9.00000 q^{81} -110.211i q^{82} -92.0358i q^{83} +3.83473 q^{84} -8.82804 q^{85} -110.617 q^{86} -43.3199 q^{87} +19.1968 q^{88} +133.439i q^{89} +1.62696i q^{90} +12.3880i q^{91} +66.8114i q^{92} +27.1342i q^{93} +31.1308 q^{94} -9.65416 q^{95} -9.79796i q^{96} +120.295i q^{97} -67.5634i q^{98} +20.3613i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 40 q^{4} + 8 q^{7} + 60 q^{9}+O(q^{10}) \) 20 * q - 40 * q^4 + 8 * q^7 + 60 * q^9	\( 20 q - 40 q^{4} + 8 q^{7} + 60 q^{9} - 24 q^{15} + 80 q^{16} + 72 q^{19} + 16 q^{22} + 140 q^{25} + 64 q^{26} - 16 q^{28} + 56 q^{29} - 80 q^{35} - 120 q^{36} - 8 q^{41} + 16 q^{46} + 52 q^{49} + 32 q^{53} - 48 q^{57} + 192 q^{59} + 48 q^{60} - 16 q^{62} + 24 q^{63} - 160 q^{64} + 96 q^{66} - 568 q^{71} - 288 q^{74} - 96 q^{75} - 144 q^{76} + 192 q^{78} + 528 q^{79} + 180 q^{81} + 568 q^{85} - 416 q^{86} - 216 q^{87} - 32 q^{88} - 480 q^{94} - 456 q^{95}+O(q^{100}) \) 20 * q - 40 * q^4 + 8 * q^7 + 60 * q^9 - 24 * q^15 + 80 * q^16 + 72 * q^19 + 16 * q^22 + 140 * q^25 + 64 * q^26 - 16 * q^28 + 56 * q^29 - 80 * q^35 - 120 * q^36 - 8 * q^41 + 16 * q^46 + 52 * q^49 + 32 * q^53 - 48 * q^57 + 192 * q^59 + 48 * q^60 - 16 * q^62 + 24 * q^63 - 160 * q^64 + 96 * q^66 - 568 * q^71 - 288 * q^74 - 96 * q^75 - 144 * q^76 + 192 * q^78 + 528 * q^79 + 180 * q^81 + 568 * q^85 - 416 * q^86 - 216 * q^87 - 32 * q^88 - 480 * q^94 - 456 * q^95

Introduction

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