LMFDB - Embedded newform 354.3.d.a.235.1

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			235.1
Root			$-6.71849 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	354.235
Dual form			354.3.d.a.235.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} -6.71849 q^{5} +2.44949i q^{6} -6.32195 q^{7} +2.82843i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} -6.71849 q^{5} +2.44949i q^{6} -6.32195 q^{7} +2.82843i q^{8} +3.00000 q^{9} +9.50137i q^{10} -8.40471i q^{11} +3.46410 q^{12} +7.72168i q^{13} +8.94059i q^{14} +11.6368 q^{15} +4.00000 q^{16} +18.2397 q^{17} -4.24264i q^{18} +10.8481 q^{19} +13.4370 q^{20} +10.9499 q^{21} -11.8861 q^{22} +3.86104i q^{23} -4.89898i q^{24} +20.1380 q^{25} +10.9201 q^{26} -5.19615 q^{27} +12.6439 q^{28} +23.6370 q^{29} -16.4569i q^{30} +30.7995i q^{31} -5.65685i q^{32} +14.5574i q^{33} -25.7948i q^{34} +42.4739 q^{35} -6.00000 q^{36} +6.95437i q^{37} -15.3415i q^{38} -13.3743i q^{39} -19.0027i q^{40} +15.3451 q^{41} -15.4856i q^{42} -1.63839i q^{43} +16.8094i q^{44} -20.1555 q^{45} +5.46033 q^{46} +2.26085i q^{47} -6.92820 q^{48} -9.03292 q^{49} -28.4795i q^{50} -31.5920 q^{51} -15.4434i q^{52} +4.04429 q^{53} +7.34847i q^{54} +56.4669i q^{55} -17.8812i q^{56} -18.7894 q^{57} -33.4278i q^{58} +(6.04441 - 58.6896i) q^{59} -23.2735 q^{60} +81.7610i q^{61} +43.5570 q^{62} -18.9659 q^{63} -8.00000 q^{64} -51.8780i q^{65} +20.5873 q^{66} +33.8931i q^{67} -36.4793 q^{68} -6.68751i q^{69} -60.0672i q^{70} +106.829 q^{71} +8.48528i q^{72} +30.4115i q^{73} +9.83496 q^{74} -34.8801 q^{75} -21.6961 q^{76} +53.1342i q^{77} -18.9142 q^{78} +22.6143 q^{79} -26.8739 q^{80} +9.00000 q^{81} -21.7013i q^{82} -117.651i q^{83} -21.8999 q^{84} -122.543 q^{85} -2.31703 q^{86} -40.9405 q^{87} +23.7721 q^{88} +91.1221i q^{89} +28.5041i q^{90} -48.8161i q^{91} -7.72207i q^{92} -53.3463i q^{93} +3.19733 q^{94} -72.8825 q^{95} +9.79796i q^{96} +14.5596i q^{97} +12.7745i q^{98} -25.2141i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−6.71849			−1.34370			−0.671849	−	0.740689i	$-0.734499\pi$
$5$	−6.71849			−1.34370			−0.671849	+	0.740689i	$0.734499\pi$
$6$			2.44949i			0.408248i
$7$	−6.32195			−0.903136			−0.451568	−	0.892237i	$-0.649135\pi$
$7$	−6.32195			−0.903136			−0.451568	+	0.892237i	$0.649135\pi$
$8$			2.82843i			0.353553i
$9$	3.00000			0.333333
$10$			9.50137i			0.950137i
$11$		−	8.40471i		−	0.764065i	−0.924149	−	0.382032i	$-0.875224\pi$
$11$		−	8.40471i		−	0.764065i	0.924149	−	0.382032i	$-0.124776\pi$
$12$	3.46410			0.288675
$13$			7.72168i			0.593975i	0.954881	+	0.296988i	$0.0959820\pi$
$13$			7.72168i			0.593975i	−0.954881	+	0.296988i	$0.904018\pi$
$14$			8.94059i			0.638614i
$15$	11.6368			0.775784
$16$	4.00000			0.250000
$17$	18.2397			1.07292			0.536461	−	0.843925i	$-0.319761\pi$
$17$	18.2397			1.07292			0.536461	+	0.843925i	$0.319761\pi$
$18$		−	4.24264i		−	0.235702i
$19$	10.8481			0.570950			0.285475	−	0.958386i	$-0.407849\pi$
$19$	10.8481			0.570950			0.285475	+	0.958386i	$0.407849\pi$
$20$	13.4370			0.671849
$21$	10.9499			0.521426
$22$	−11.8861			−0.540275
$23$			3.86104i			0.167871i	0.996471	+	0.0839356i	$0.0267490\pi$
$23$			3.86104i			0.167871i	−0.996471	+	0.0839356i	$0.973251\pi$
$24$		−	4.89898i		−	0.204124i
$25$	20.1380			0.805522
$26$	10.9201			0.420004
$27$	−5.19615			−0.192450
$28$	12.6439			0.451568
$29$	23.6370			0.815069			0.407534	−	0.913190i	$-0.366389\pi$
$29$	23.6370			0.815069			0.407534	+	0.913190i	$0.366389\pi$
$30$		−	16.4569i		−	0.548562i
$31$			30.7995i			0.993531i	0.867885	+	0.496766i	$0.165479\pi$
$31$			30.7995i			0.993531i	−0.867885	+	0.496766i	$0.834521\pi$
$32$		−	5.65685i		−	0.176777i
$33$			14.5574i			0.441133i
$34$		−	25.7948i		−	0.758670i
$35$	42.4739			1.21354
$36$	−6.00000			−0.166667
$37$			6.95437i			0.187956i	0.995574	+	0.0939780i	$0.0299583\pi$
$37$			6.95437i			0.187956i	−0.995574	+	0.0939780i	$0.970042\pi$
$38$		−	15.3415i		−	0.403723i
$39$		−	13.3743i		−	0.342932i
$40$		−	19.0027i		−	0.475069i
$41$	15.3451			0.374272			0.187136	−	0.982334i	$-0.440080\pi$
$41$	15.3451			0.374272			0.187136	+	0.982334i	$0.440080\pi$
$42$		−	15.4856i		−	0.368704i
$43$		−	1.63839i		−	0.0381021i	−0.999819	−	0.0190510i	$-0.993936\pi$
$43$		−	1.63839i		−	0.0381021i	0.999819	−	0.0190510i	$-0.00606450\pi$
$44$			16.8094i			0.382032i
$45$	−20.1555			−0.447899
$46$	5.46033			0.118703
$47$			2.26085i			0.0481032i	0.999711	+	0.0240516i	$0.00765660\pi$
$47$			2.26085i			0.0481032i	−0.999711	+	0.0240516i	$0.992343\pi$
$48$	−6.92820			−0.144338
$49$	−9.03292			−0.184345
$50$		−	28.4795i		−	0.569590i
$51$	−31.5920			−0.619452
$52$		−	15.4434i		−	0.296988i
$53$	4.04429			0.0763074			0.0381537	−	0.999272i	$-0.487852\pi$
$53$	4.04429			0.0763074			0.0381537	+	0.999272i	$0.487852\pi$
$54$			7.34847i			0.136083i
$55$			56.4669i			1.02667i
$56$		−	17.8812i		−	0.319307i
$57$	−18.7894			−0.329638
$58$		−	33.4278i		−	0.576341i
$59$	6.04441	−	58.6896i	0.102448	−	0.994738i
$59$	6.04441	−	58.6896i	0.102448	−	0.994738i
$60$	−23.2735			−0.387892
$61$			81.7610i			1.34034i	0.742205	+	0.670172i	$0.233780\pi$
$61$			81.7610i			1.34034i	−0.742205	+	0.670172i	$0.766220\pi$
$62$	43.5570			0.702533
$63$	−18.9659			−0.301045
$64$	−8.00000			−0.125000
$65$		−	51.8780i		−	0.798123i
$66$	20.5873			0.311928
$67$			33.8931i			0.505867i	0.967484	+	0.252934i	$0.0813954\pi$
$67$			33.8931i			0.505867i	−0.967484	+	0.252934i	$0.918605\pi$
$68$	−36.4793			−0.536461
$69$		−	6.68751i		−	0.0969204i
$70$		−	60.0672i		−	0.858103i
$71$	106.829			1.50463			0.752316	−	0.658802i	$-0.228937\pi$
$71$	106.829			1.50463			0.752316	+	0.658802i	$0.228937\pi$
$72$			8.48528i			0.117851i
$73$			30.4115i			0.416595i	0.978065	+	0.208298i	$0.0667923\pi$
$73$			30.4115i			0.416595i	−0.978065	+	0.208298i	$0.933208\pi$
$74$	9.83496			0.132905
$75$	−34.8801			−0.465068
$76$	−21.6961			−0.285475
$77$			53.1342i			0.690054i
$78$	−18.9142			−0.242489
$79$	22.6143			0.286257			0.143129	−	0.989704i	$-0.454284\pi$
$79$	22.6143			0.286257			0.143129	+	0.989704i	$0.454284\pi$
$80$	−26.8739			−0.335924
$81$	9.00000			0.111111
$82$		−	21.7013i		−	0.264650i
$83$		−	117.651i		−	1.41749i	−0.705467	−	0.708743i	$-0.749262\pi$
$83$		−	117.651i		−	1.41749i	0.705467	−	0.708743i	$-0.250738\pi$
$84$	−21.8999			−0.260713
$85$	−122.543			−1.44168
$86$	−2.31703			−0.0269422
$87$	−40.9405			−0.470580
$88$	23.7721			0.270138
$89$			91.1221i			1.02384i	0.859032	+	0.511922i	$0.171066\pi$
$89$			91.1221i			1.02384i	−0.859032	+	0.511922i	$0.828934\pi$
$90$			28.5041i			0.316712i
$91$		−	48.8161i		−	0.536440i
$92$		−	7.72207i		−	0.0839356i
$93$		−	53.3463i		−	0.573616i
$94$	3.19733			0.0340141
$95$	−72.8825			−0.767184
$96$			9.79796i			0.102062i
$97$			14.5596i			0.150099i	0.997180	+	0.0750494i	$0.0239115\pi$
$97$			14.5596i			0.150099i	−0.997180	+	0.0750494i	$0.976089\pi$
$98$			12.7745i			0.130352i
$99$		−	25.2141i		−	0.254688i
$100$	−40.2761			−0.402761
$101$			69.4585i			0.687708i	0.939023	+	0.343854i	$0.111733\pi$
$101$			69.4585i			0.687708i	−0.939023	+	0.343854i	$0.888267\pi$
$102$			44.6779i			0.438019i
$103$			164.097i			1.59317i	0.604524	+	0.796587i	$0.293363\pi$
$103$			164.097i			1.59317i	−0.604524	+	0.796587i	$0.706637\pi$
$104$	−21.8402			−0.210002
$105$	−73.5670			−0.700638
$106$		−	5.71950i		−	0.0539575i
$107$	55.0409			0.514401			0.257201	−	0.966358i	$-0.417200\pi$
$107$	55.0409			0.514401			0.257201	+	0.966358i	$0.417200\pi$
$108$	10.3923			0.0962250
$109$		−	102.405i		−	0.939498i	−0.882800	−	0.469749i	$-0.844344\pi$
$109$		−	102.405i		−	0.939498i	0.882800	−	0.469749i	$-0.155656\pi$
$110$	79.8563			0.725966
$111$		−	12.0453i		−	0.108516i
$112$	−25.2878			−0.225784
$113$			137.513i			1.21693i	0.793579	+	0.608467i	$0.208215\pi$
$113$			137.513i			1.21693i	−0.793579	+	0.608467i	$0.791785\pi$
$114$			26.5722i			0.233089i
$115$		−	25.9403i		−	0.225568i
$116$	−47.2740			−0.407534
$117$			23.1650i			0.197992i
$118$	−82.9996	−	8.54808i	−0.703386	−	0.0724414i
$119$	−115.310			−0.968994
$120$			32.9137i			0.274281i
$121$	50.3609			0.416205
$122$	115.628			0.947767
$123$	−26.5785			−0.216086
$124$		−	61.5990i		−	0.496766i
$125$	32.6650			0.261320
$126$			26.8218i			0.212871i
$127$	−182.778			−1.43919			−0.719597	−	0.694392i	$-0.755673\pi$
$127$	−182.778			−1.43919			−0.719597	+	0.694392i	$0.755673\pi$
$128$			11.3137i			0.0883883i
$129$			2.83777i			0.0219982i
$130$	−73.3665			−0.564358
$131$			7.08310i			0.0540694i	0.999634	+	0.0270347i	$0.00860647\pi$
$131$			7.08310i			0.0540694i	−0.999634	+	0.0270347i	$0.991394\pi$
$132$		−	29.1148i		−	0.220566i
$133$	−68.5809			−0.515646
$134$	47.9321			0.357702
$135$	34.9103			0.258595
$136$			51.5896i			0.379335i
$137$	69.0148			0.503758			0.251879	−	0.967759i	$-0.418952\pi$
$137$	69.0148			0.503758			0.251879	+	0.967759i	$0.418952\pi$
$138$	−9.45757			−0.0685331
$139$	−8.18474			−0.0588830			−0.0294415	−	0.999567i	$-0.509373\pi$
$139$	−8.18474			−0.0588830			−0.0294415	+	0.999567i	$0.509373\pi$
$140$	−84.9479			−0.606771
$141$		−	3.91591i		−	0.0277724i
$142$		−	151.079i		−	1.06394i
$143$	64.8985			0.453835
$144$	12.0000			0.0833333
$145$	−158.805			−1.09521
$146$	43.0083			0.294577
$147$	15.6455			0.106432
$148$		−	13.9087i		−	0.0939780i
$149$			118.892i			0.797930i	0.916966	+	0.398965i	$0.130631\pi$
$149$			118.892i			0.797930i	−0.916966	+	0.398965i	$0.869369\pi$
$150$			49.3279i			0.328853i
$151$			152.523i			1.01008i	0.863095	+	0.505042i	$0.168523\pi$
$151$			152.523i			1.01008i	−0.863095	+	0.505042i	$0.831477\pi$
$152$			30.6829i			0.201861i
$153$	54.7190			0.357641
$154$	75.1431			0.487942
$155$		−	206.926i		−	1.33501i
$156$			26.7487i			0.171466i
$157$			3.83421i			0.0244217i	0.999925	+	0.0122109i	$0.00388693\pi$
$157$			3.83421i			0.0244217i	−0.999925	+	0.0122109i	$0.996113\pi$
$158$		−	31.9815i		−	0.202415i
$159$	−7.00492			−0.0440561
$160$			38.0055i			0.237534i
$161$		−	24.4093i		−	0.151610i
$162$		−	12.7279i		−	0.0785674i
$163$	−147.912			−0.907435			−0.453718	−	0.891146i	$-0.649902\pi$
$163$	−147.912			−0.907435			−0.453718	+	0.891146i	$0.649902\pi$
$164$	−30.6903			−0.187136
$165$		−	97.8036i		−	0.592749i
$166$	−166.384			−1.00231
$167$	102.027			0.610940			0.305470	−	0.952202i	$-0.401186\pi$
$167$	102.027			0.610940			0.305470	+	0.952202i	$0.401186\pi$
$168$			30.9711i			0.184352i
$169$	109.376			0.647193
$170$			173.302i			1.01942i
$171$	32.5442			0.190317
$172$			3.27678i			0.0190510i
$173$			322.990i			1.86700i	0.358581	+	0.933498i	$0.383261\pi$
$173$			322.990i			1.86700i	−0.358581	+	0.933498i	$0.616739\pi$
$174$			57.8986i			0.332750i
$175$	−127.312			−0.727496
$176$		−	33.6188i		−	0.191016i
$177$	−10.4692	+	101.653i	−0.0591481	+	0.574312i
$178$	128.866			0.723967
$179$		−	317.930i		−	1.77615i	−0.459702	−	0.888073i	$-0.652044\pi$
$179$		−	317.930i		−	1.77615i	0.459702	−	0.888073i	$-0.347956\pi$
$180$	40.3109			0.223950
$181$	205.551			1.13564			0.567820	−	0.823152i	$-0.307787\pi$
$181$	205.551			1.13564			0.567820	+	0.823152i	$0.307787\pi$
$182$	−69.0364			−0.379321
$183$		−	141.614i		−	0.773849i
$184$	−10.9207			−0.0593514
$185$		−	46.7228i		−	0.252556i
$186$	−75.4430			−0.405608
$187$		−	153.299i		−	0.819782i
$188$		−	4.52170i		−	0.0240516i
$189$	32.8498			0.173809
$190$			103.071i			0.542481i
$191$		−	368.762i		−	1.93069i	−0.260979	−	0.965344i	$-0.584045\pi$
$191$		−	368.762i		−	1.93069i	0.260979	−	0.965344i	$-0.415955\pi$
$192$	13.8564			0.0721688
$193$	−35.0207			−0.181454			−0.0907271	−	0.995876i	$-0.528919\pi$
$193$	−35.0207			−0.181454			−0.0907271	+	0.995876i	$0.528919\pi$
$194$	20.5904			0.106136
$195$			89.8553i			0.460796i
$196$	18.0658			0.0921727
$197$	183.762			0.932803			0.466402	−	0.884573i	$-0.345550\pi$
$197$	183.762			0.932803			0.466402	+	0.884573i	$0.345550\pi$
$198$	−35.6582			−0.180092
$199$	299.099			1.50301			0.751506	−	0.659726i	$-0.229328\pi$
$199$	299.099			1.50301			0.751506	+	0.659726i	$0.229328\pi$
$200$			56.9590i			0.284795i
$201$		−	58.7046i		−	0.292063i
$202$	98.2292			0.486283
$203$	−149.432			−0.736118
$204$	63.1841			0.309726
$205$	−103.096			−0.502908
$206$	232.068			1.12654
$207$			11.5831i			0.0559570i
$208$			30.8867i			0.148494i
$209$		−	91.1748i		−	0.436243i
$210$			104.039i			0.495426i
$211$		−	369.888i		−	1.75302i	−0.481380	−	0.876512i	$-0.659864\pi$
$211$		−	369.888i		−	1.75302i	0.481380	−	0.876512i	$-0.340136\pi$
$212$	−8.08859			−0.0381537
$213$	−185.033			−0.868700
$214$		−	77.8396i		−	0.363737i
$215$			11.0075i			0.0511976i
$216$		−	14.6969i		−	0.0680414i
$217$		−	194.713i		−	0.897294i
$218$	−144.823			−0.664325
$219$		−	52.6742i		−	0.240521i
$220$		−	112.934i		−	0.513336i
$221$			140.841i			0.637289i
$222$	−17.0347			−0.0767327
$223$	173.383			0.777504			0.388752	−	0.921342i	$-0.372906\pi$
$223$	173.383			0.777504			0.388752	+	0.921342i	$0.372906\pi$
$224$			35.7624i			0.159653i
$225$	60.4141			0.268507
$226$	194.473			0.860502
$227$		−	192.654i		−	0.848694i	−0.905500	−	0.424347i	$-0.860504\pi$
$227$		−	192.654i		−	0.848694i	0.905500	−	0.424347i	$-0.139496\pi$
$228$	37.5788			0.164819
$229$			20.4005i			0.0890850i	0.999007	+	0.0445425i	$0.0141830\pi$
$229$			20.4005i			0.0890850i	−0.999007	+	0.0445425i	$0.985817\pi$
$230$	−36.6851			−0.159501
$231$		−	92.0311i		−	0.398403i
$232$			66.8555i			0.288170i
$233$			306.918i			1.31725i	0.752473	+	0.658623i	$0.228861\pi$
$233$			306.918i			1.31725i	−0.752473	+	0.658623i	$0.771139\pi$
$234$	32.7603			0.140001
$235$		−	15.1895i		−	0.0646361i
$236$	−12.0888	+	117.379i	−0.0512238	+	0.497369i
$237$	−39.1692			−0.165271
$238$			163.073i			0.685183i
$239$	−154.595			−0.646840			−0.323420	−	0.946256i	$-0.604833\pi$
$239$	−154.595			−0.646840			−0.323420	+	0.946256i	$0.604833\pi$
$240$	46.5470			0.193946
$241$	295.225			1.22500			0.612500	−	0.790470i	$-0.290164\pi$
$241$	295.225			1.22500			0.612500	+	0.790470i	$0.290164\pi$
$242$		−	71.2210i		−	0.294302i
$243$	−15.5885			−0.0641500
$244$		−	163.522i		−	0.670172i
$245$	60.6876			0.247704
$246$			37.5877i			0.152796i
$247$			83.7652i			0.339130i
$248$	−87.1141			−0.351266
$249$			203.778i			0.818386i
$250$		−	46.1953i		−	0.184781i
$251$	21.5372			0.0858056			0.0429028	−	0.999079i	$-0.486339\pi$
$251$	21.5372			0.0858056			0.0429028	+	0.999079i	$0.486339\pi$
$252$	37.9317			0.150523
$253$	32.4509			0.128264
$254$			258.487i			1.01766i
$255$	212.251			0.832356
$256$	16.0000			0.0625000
$257$	−183.273			−0.713125			−0.356563	−	0.934271i	$-0.616051\pi$
$257$	−183.273			−0.713125			−0.356563	+	0.934271i	$0.616051\pi$
$258$	4.01322			0.0155551
$259$		−	43.9652i		−	0.169750i
$260$			103.756i			0.399061i
$261$	70.9110			0.271690
$262$	10.0170			0.0382329
$263$	−136.482			−0.518943			−0.259471	−	0.965751i	$-0.583548\pi$
$263$	−136.482			−0.518943			−0.259471	+	0.965751i	$0.583548\pi$
$264$	−41.1745			−0.155964
$265$	−27.1715			−0.102534
$266$			96.9880i			0.364617i
$267$		−	157.828i		−	0.591116i
$268$		−	67.7862i		−	0.252934i
$269$		−	83.6039i		−	0.310795i	−0.987852	−	0.155398i	$-0.950334\pi$
$269$		−	83.6039i		−	0.310795i	0.987852	−	0.155398i	$-0.0496658\pi$
$270$		−	49.3706i		−	0.182854i
$271$	212.308			0.783425			0.391712	−	0.920088i	$-0.371883\pi$
$271$	212.308			0.783425			0.391712	+	0.920088i	$0.371883\pi$
$272$	72.9587			0.268231
$273$			84.5519i			0.309714i
$274$		−	97.6017i		−	0.356211i
$275$		−	169.254i		−	0.615471i
$276$			13.3750i			0.0484602i
$277$	255.299			0.921655			0.460828	−	0.887490i	$-0.347553\pi$
$277$	255.299			0.921655			0.460828	+	0.887490i	$0.347553\pi$
$278$			11.5750i			0.0416366i
$279$			92.3984i			0.331177i
$280$			120.134i			0.429052i
$281$	−87.4368			−0.311163			−0.155581	−	0.987823i	$-0.549725\pi$
$281$	−87.4368			−0.311163			−0.155581	+	0.987823i	$0.549725\pi$
$282$	−5.53793			−0.0196381
$283$			52.9223i			0.187004i	0.995619	+	0.0935022i	$0.0298062\pi$
$283$			52.9223i			0.187004i	−0.995619	+	0.0935022i	$0.970194\pi$
$284$	−213.658			−0.752316
$285$	126.236			0.442934
$286$		−	91.7803i		−	0.320910i
$287$	−97.0112			−0.338018
$288$		−	16.9706i		−	0.0589256i
$289$	43.6857			0.151162
$290$			224.584i			0.774427i
$291$		−	25.2179i		−	0.0866596i
$292$		−	60.8229i		−	0.208298i
$293$	−136.130			−0.464609			−0.232305	−	0.972643i	$-0.574627\pi$
$293$	−136.130			−0.464609			−0.232305	+	0.972643i	$0.574627\pi$
$294$		−	22.1261i		−	0.0752587i
$295$	−40.6092	+	394.305i	−0.137658	+	1.33663i
$296$	−19.6699			−0.0664524
$297$			43.6722i			0.147044i
$298$	168.138			0.564222
$299$	−29.8137			−0.0997113
$300$	69.7602			0.232534
$301$			10.3578i			0.0344113i
$302$	215.699			0.714237
$303$		−	120.306i		−	0.397048i
$304$	43.3922			0.142738
$305$		−	549.310i		−	1.80102i
$306$		−	77.3844i		−	0.252890i
$307$	428.998			1.39739			0.698693	−	0.715421i	$-0.253765\pi$
$307$	428.998			1.39739			0.698693	+	0.715421i	$0.253765\pi$
$308$		−	106.268i		−	0.345027i
$309$		−	284.224i		−	0.919819i
$310$	−292.637			−0.943991
$311$	271.117			0.871760			0.435880	−	0.900005i	$-0.356437\pi$
$311$	271.117			0.871760			0.435880	+	0.900005i	$0.356437\pi$
$312$	37.8283			0.121245
$313$			586.304i			1.87317i	0.350435	+	0.936587i	$0.386034\pi$
$313$			586.304i			1.87317i	−0.350435	+	0.936587i	$0.613966\pi$
$314$	5.42239			0.0172688
$315$	127.422			0.404514
$316$	−45.2287			−0.143129
$317$	−195.425			−0.616482			−0.308241	−	0.951308i	$-0.599740\pi$
$317$	−195.425			−0.616482			−0.308241	+	0.951308i	$0.599740\pi$
$318$			9.90646i			0.0311524i
$319$		−	198.662i		−	0.622765i
$320$	53.7479			0.167962
$321$	−95.3337			−0.296990
$322$	−34.5199			−0.107205
$323$	197.865			0.612585
$324$	−18.0000			−0.0555556
$325$			155.499i			0.478460i
$326$			209.179i			0.641653i
$327$			177.371i			0.542419i
$328$			43.4026i			0.132325i
$329$		−	14.2930i		−	0.0434437i
$330$	−138.315			−0.419137
$331$	143.285			0.432886			0.216443	−	0.976295i	$-0.430555\pi$
$331$	143.285			0.432886			0.216443	+	0.976295i	$0.430555\pi$
$332$			235.303i			0.708743i
$333$			20.8631i			0.0626520i
$334$		−	144.288i		−	0.432000i
$335$		−	227.710i		−	0.679732i
$336$	43.7998			0.130356
$337$			460.010i			1.36502i	0.730879	+	0.682508i	$0.239111\pi$
$337$			460.010i			1.36502i	−0.730879	+	0.682508i	$0.760889\pi$
$338$		−	154.681i		−	0.457635i
$339$		−	238.180i		−	0.702597i
$340$	245.086			0.720841
$341$	258.861			0.759122
$342$		−	46.0244i		−	0.134574i
$343$	366.881			1.06962
$344$	4.63406			0.0134711
$345$			44.9299i			0.130232i
$346$	456.778			1.32017
$347$			601.325i			1.73293i	0.499242	+	0.866463i	$0.333612\pi$
$347$			601.325i			1.73293i	−0.499242	+	0.866463i	$0.666388\pi$
$348$	81.8809			0.235290
$349$			198.428i			0.568560i	0.958741	+	0.284280i	$0.0917546\pi$
$349$			198.428i			0.568560i	−0.958741	+	0.284280i	$0.908245\pi$
$350$			180.046i			0.514417i
$351$		−	40.1230i		−	0.114311i
$352$	−47.5442			−0.135069
$353$		−	173.993i		−	0.492898i	−0.969156	−	0.246449i	$-0.920736\pi$
$353$		−	173.993i		−	0.492898i	0.969156	−	0.246449i	$-0.0792637\pi$
$354$	143.759	+	14.8057i	0.406100	+	0.0418240i
$355$	−717.728			−2.02177
$356$		−	182.244i		−	0.511922i
$357$	199.723			0.559449
$358$	−449.621			−1.25592
$359$	−678.524			−1.89004			−0.945020	−	0.327013i	$-0.893958\pi$
$359$	−678.524			−1.89004			−0.945020	+	0.327013i	$0.893958\pi$
$360$		−	57.0082i		−	0.158356i
$361$	−243.320			−0.674016
$362$		−	290.693i		−	0.803019i
$363$	−87.2276			−0.240296
$364$			97.6322i			0.268220i
$365$		−	204.319i		−	0.559778i
$366$	−200.273			−0.547194
$367$			570.539i			1.55460i	0.629128	+	0.777301i	$0.283412\pi$
$367$			570.539i			1.55460i	−0.629128	+	0.777301i	$0.716588\pi$
$368$			15.4441i			0.0419678i
$369$	46.0354			0.124757
$370$	−66.0760			−0.178584
$371$	−25.5678			−0.0689160
$372$			106.693i			0.286808i
$373$	−559.834			−1.50089			−0.750447	−	0.660931i	$-0.770162\pi$
$373$	−559.834			−1.50089			−0.750447	+	0.660931i	$0.770162\pi$
$374$	−216.798			−0.579673
$375$	−56.5774			−0.150873
$376$	−6.39465			−0.0170071
$377$			182.517i			0.484131i
$378$		−	46.4567i		−	0.122901i
$379$	−287.529			−0.758651			−0.379325	−	0.925263i	$-0.623844\pi$
$379$	−287.529			−0.758651			−0.379325	+	0.925263i	$0.623844\pi$
$380$	145.765			0.383592
$381$	316.580			0.830919
$382$	−521.508			−1.36520
$383$	−411.973			−1.07565			−0.537823	−	0.843058i	$-0.680753\pi$
$383$	−411.973			−1.07565			−0.537823	+	0.843058i	$0.680753\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		−	356.981i		−	0.927224i
$386$			49.5267i			0.128308i
$387$		−	4.91517i		−	0.0127007i
$388$		−	29.1192i		−	0.0750494i
$389$	−758.698			−1.95038			−0.975190	−	0.221370i	$-0.928947\pi$
$389$	−758.698			−1.95038			−0.975190	+	0.221370i	$0.928947\pi$
$390$	127.075			0.325832
$391$			70.4240i			0.180113i
$392$		−	25.5490i		−	0.0651759i
$393$		−	12.2683i		−	0.0312170i
$394$		−	259.879i		−	0.659592i
$395$	−151.934			−0.384643
$396$			50.4283i			0.127344i
$397$		−	636.181i		−	1.60247i	−0.598349	−	0.801236i	$-0.704176\pi$
$397$		−	636.181i		−	1.60247i	0.598349	−	0.801236i	$-0.295824\pi$
$398$		−	422.990i		−	1.06279i
$399$	118.786			0.297708
$400$	80.5522			0.201380
$401$		−	201.337i		−	0.502087i	−0.967976	−	0.251043i	$-0.919226\pi$
$401$		−	201.337i		−	0.502087i	0.967976	−	0.251043i	$-0.0807737\pi$
$402$	−83.0208			−0.206519
$403$	−237.824			−0.590133
$404$		−	138.917i		−	0.343854i
$405$	−60.4664			−0.149300
$406$			211.329i			0.520514i
$407$	58.4494			0.143610
$408$		−	89.3558i		−	0.219009i
$409$			411.947i			1.00721i	0.863935	+	0.503603i	$0.167992\pi$
$409$			411.947i			1.00721i	−0.863935	+	0.503603i	$0.832008\pi$
$410$			145.800i			0.355609i
$411$	−119.537			−0.290845
$412$		−	328.194i		−	0.796587i
$413$	−38.2124	+	371.033i	−0.0925241	+	0.898384i
$414$	16.3810			0.0395676
$415$			790.439i			1.90467i
$416$	43.6804			0.105001
$417$	14.1764			0.0339961
$418$	−128.941			−0.308470
$419$		−	391.117i		−	0.933453i	−0.884402	−	0.466727i	$-0.845433\pi$
$419$		−	391.117i		−	0.933453i	0.884402	−	0.466727i	$-0.154567\pi$
$420$	147.134			0.350319
$421$		−	235.386i		−	0.559112i	−0.960129	−	0.279556i	$-0.909813\pi$
$421$		−	235.386i		−	0.559112i	0.960129	−	0.279556i	$-0.0901873\pi$
$422$	−523.101			−1.23958
$423$			6.78255i			0.0160344i
$424$			11.4390i			0.0269788i
$425$	367.311			0.864262
$426$			261.676i			0.614264i
$427$		−	516.889i		−	1.21051i
$428$	−110.082			−0.257201
$429$	−112.407			−0.262022
$430$	15.5669			0.0362022
$431$			493.830i			1.14578i	0.819634	+	0.572888i	$0.194177\pi$
$431$			493.830i			1.14578i	−0.819634	+	0.572888i	$0.805823\pi$
$432$	−20.7846			−0.0481125
$433$	38.9100			0.0898614			0.0449307	−	0.998990i	$-0.485693\pi$
$433$	38.9100			0.0898614			0.0449307	+	0.998990i	$0.485693\pi$
$434$	−275.365			−0.634483
$435$	275.058			0.632317
$436$			204.811i			0.469749i
$437$			41.8847i			0.0958461i
$438$	−74.4926			−0.170074
$439$	−342.035			−0.779123			−0.389561	−	0.921001i	$-0.627373\pi$
$439$	−342.035			−0.779123			−0.389561	+	0.921001i	$0.627373\pi$
$440$	−159.713			−0.362983
$441$	−27.0988			−0.0614485
$442$	199.179			0.450631
$443$			292.902i			0.661179i	0.943775	+	0.330590i	$0.107248\pi$
$443$			292.902i			0.661179i	−0.943775	+	0.330590i	$0.892752\pi$
$444$			24.0906i			0.0542582i
$445$		−	612.202i		−	1.37574i
$446$		−	245.201i		−	0.549778i
$447$		−	205.926i		−	0.460685i
$448$	50.5756			0.112892
$449$	−704.557			−1.56917			−0.784585	−	0.620021i	$-0.787124\pi$
$449$	−704.557			−1.56917			−0.784585	+	0.620021i	$0.787124\pi$
$450$		−	85.4385i		−	0.189863i
$451$		−	128.971i		−	0.285968i
$452$		−	275.027i		−	0.608467i
$453$		−	264.177i		−	0.583172i
$454$	−272.453			−0.600117
$455$			327.970i			0.720813i
$456$		−	53.1444i		−	0.116545i
$457$			162.426i			0.355417i	0.984083	+	0.177708i	$0.0568684\pi$
$457$			162.426i			0.355417i	−0.984083	+	0.177708i	$0.943132\pi$
$458$	28.8506			0.0629926
$459$	−94.7761			−0.206484
$460$			51.8806i			0.112784i
$461$	756.772			1.64159			0.820794	−	0.571224i	$-0.193531\pi$
$461$	756.772			1.64159			0.820794	+	0.571224i	$0.193531\pi$
$462$	−130.152			−0.281713
$463$		−	194.394i		−	0.419858i	−0.977717	−	0.209929i	$-0.932677\pi$
$463$		−	194.394i		−	0.419858i	0.977717	−	0.209929i	$-0.0673233\pi$
$464$	94.5480			0.203767
$465$			358.406i			0.770766i
$466$	434.048			0.931434
$467$			434.501i			0.930409i	0.885203	+	0.465205i	$0.154019\pi$
$467$			434.501i			0.930409i	−0.885203	+	0.465205i	$0.845981\pi$
$468$		−	46.3301i		−	0.0989959i
$469$		−	214.271i		−	0.456867i
$470$	−21.4812			−0.0457046
$471$		−	6.64104i		−	0.0140999i
$472$	165.999	+	17.0962i	0.351693	+	0.0362207i
$473$	−13.7702			−0.0291124
$474$			55.3936i			0.116864i
$475$	218.459			0.459913
$476$	230.621			0.484497
$477$	12.1329			0.0254358
$478$			218.630i			0.457385i
$479$	323.183			0.674704			0.337352	−	0.941379i	$-0.390469\pi$
$479$	323.183			0.674704			0.337352	+	0.941379i	$0.390469\pi$
$480$		−	65.8274i		−	0.137141i
$481$	−53.6994			−0.111641
$482$		−	417.511i		−	0.866206i
$483$			42.2781i			0.0875323i
$484$	−100.722			−0.208103
$485$		−	97.8184i		−	0.201687i
$486$			22.0454i			0.0453609i
$487$	448.134			0.920193			0.460096	−	0.887869i	$-0.347815\pi$
$487$	448.134			0.920193			0.460096	+	0.887869i	$0.347815\pi$
$488$	−231.255			−0.473884
$489$	256.191			0.523908
$490$		−	85.8252i		−	0.175153i
$491$	−325.053			−0.662023			−0.331011	−	0.943627i	$-0.607390\pi$
$491$	−325.053			−0.662023			−0.331011	+	0.943627i	$0.607390\pi$
$492$	53.1571			0.108043
$493$	431.131			0.874505
$494$	118.462			0.239801
$495$			169.401i			0.342224i
$496$			123.198i			0.248383i
$497$	−675.367			−1.35889
$498$	288.186			0.578686
$499$	488.083			0.978122			0.489061	−	0.872250i	$-0.337340\pi$
$499$	488.083			0.978122			0.489061	+	0.872250i	$0.337340\pi$
$500$	−65.3300			−0.130660
$501$	−176.716			−0.352726
$502$		−	30.4582i		−	0.0606737i
$503$			341.428i			0.678783i	0.940645	+	0.339391i	$0.110221\pi$
$503$			341.428i			0.678783i	−0.940645	+	0.339391i	$0.889779\pi$
$504$		−	53.6435i		−	0.106436i
$505$		−	466.656i		−	0.924071i
$506$		−	45.8925i		−	0.0906966i
$507$	−189.444			−0.373657
$508$	365.555			0.719597
$509$		−	263.158i		−	0.517009i	−0.966010	−	0.258504i	$-0.916770\pi$
$509$		−	263.158i		−	0.517009i	0.966010	−	0.258504i	$-0.0832297\pi$
$510$		−	300.168i		−	0.588564i
$511$		−	192.260i		−	0.376242i
$512$		−	22.6274i		−	0.0441942i
$513$	−56.3681			−0.109879
$514$			259.187i			0.504256i
$515$		−	1102.48i		−	2.14074i
$516$		−	5.67555i		−	0.0109991i
$517$	19.0018			0.0367540
$518$	−62.1762			−0.120031
$519$		−	559.436i		−	1.07791i
$520$	146.733			0.282179
$521$	−248.128			−0.476254			−0.238127	−	0.971234i	$-0.576533\pi$
$521$	−248.128			−0.476254			−0.238127	+	0.971234i	$0.576533\pi$
$522$		−	100.283i		−	0.192114i
$523$	−529.919			−1.01323			−0.506615	−	0.862173i	$-0.669103\pi$
$523$	−529.919			−1.01323			−0.506615	+	0.862173i	$0.669103\pi$
$524$		−	14.1662i		−	0.0270347i
$525$	220.510			0.420020
$526$			193.015i			0.366948i
$527$			561.772i			1.06598i
$528$			58.2295i			0.110283i
$529$	514.092			0.971819
$530$			38.4263i			0.0725025i
$531$	18.1332	−	176.069i	0.0341492	−	0.331579i
$532$	137.162			0.257823
$533$			118.490i			0.222308i
$534$	−223.203			−0.417982
$535$	−369.792			−0.691199
$536$	−95.8642			−0.178851
$537$			550.671i			1.02546i
$538$	−118.234			−0.219765
$539$			75.9191i			0.140852i
$540$	−69.8205			−0.129297
$541$			531.704i			0.982817i	0.870929	+	0.491409i	$0.163518\pi$
$541$			531.704i			0.982817i	−0.870929	+	0.491409i	$0.836482\pi$
$542$		−	300.249i		−	0.553965i
$543$	−356.025			−0.655663
$544$		−	103.179i		−	0.189668i
$545$			688.008i			1.26240i
$546$	119.574			0.219001
$547$	618.649			1.13099			0.565493	−	0.824753i	$-0.308686\pi$
$547$	618.649			1.13099			0.565493	+	0.824753i	$0.308686\pi$
$548$	−138.030			−0.251879
$549$			245.283i			0.446782i
$550$	−239.362			−0.435203
$551$	256.415			0.465364
$552$	18.9151			0.0342666
$553$	−142.967			−0.258529
$554$		−	361.047i		−	0.651709i
$555$			80.9263i			0.145813i
$556$	16.3695			0.0294415
$557$	−10.3321			−0.0185495			−0.00927477	−	0.999957i	$-0.502952\pi$
$557$	−10.3321			−0.0185495			−0.00927477	+	0.999957i	$0.502952\pi$
$558$	130.671			0.234178
$559$	12.6511			0.0226317
$560$	169.896			0.303385
$561$			265.522i			0.473301i
$562$			123.654i			0.220025i
$563$		−	317.116i		−	0.563261i	−0.959523	−	0.281631i	$-0.909125\pi$
$563$		−	317.116i		−	0.563261i	0.959523	−	0.281631i	$-0.0908753\pi$
$564$			7.83182i			0.0138862i
$565$		−	923.882i		−	1.63519i
$566$	74.8434			0.132232
$567$	−56.8976			−0.100348
$568$			302.158i			0.531968i
$569$			500.143i			0.878986i	0.898246	+	0.439493i	$0.144842\pi$
$569$			500.143i			0.878986i	−0.898246	+	0.439493i	$0.855158\pi$
$570$		−	178.525i		−	0.313202i
$571$			40.3223i			0.0706170i	0.999376	+	0.0353085i	$0.0112414\pi$
$571$			40.3223i			0.0706170i	−0.999376	+	0.0353085i	$0.988759\pi$
$572$	−129.797			−0.226918
$573$			638.714i			1.11468i
$574$			137.195i			0.239015i
$575$			77.7537i			0.135224i
$576$	−24.0000			−0.0416667
$577$	549.767			0.952803			0.476401	−	0.879228i	$-0.341941\pi$
$577$	549.767			0.952803			0.476401	+	0.879228i	$0.341941\pi$
$578$		−	61.7809i		−	0.106887i
$579$	60.6576			0.104763
$580$	317.610			0.547603
$581$			743.786i			1.28018i
$582$	−35.6636			−0.0612776
$583$		−	33.9911i		−	0.0583038i
$584$	−86.0166			−0.147289
$585$		−	155.634i		−	0.266041i
$586$			192.518i			0.328528i
$587$			988.465i			1.68393i	0.539534	+	0.841964i	$0.318600\pi$
$587$			988.465i			1.68393i	−0.539534	+	0.841964i	$0.681400\pi$
$588$	−31.2910			−0.0532159
$589$			334.114i			0.567257i
$590$	557.631	+	57.4301i	0.945138	+	0.0973392i
$591$	−318.286			−0.538554
$592$			27.8175i			0.0469890i
$593$	70.2063			0.118392			0.0591958	−	0.998246i	$-0.481146\pi$
$593$	70.2063			0.118392			0.0591958	+	0.998246i	$0.481146\pi$
$594$	61.7618			0.103976
$595$	774.711			1.30204
$596$		−	237.783i		−	0.398965i
$597$	−518.055			−0.867764
$598$			42.1629i			0.0705065i
$599$	1118.20			1.86678			0.933392	−	0.358860i	$-0.116834\pi$
$599$	1118.20			1.86678			0.933392	+	0.358860i	$0.116834\pi$
$600$		−	98.6559i		−	0.164426i
$601$			563.262i			0.937208i	0.883408	+	0.468604i	$0.155243\pi$
$601$			563.262i			0.937208i	−0.883408	+	0.468604i	$0.844757\pi$
$602$	14.6482			0.0243325
$603$			101.679i			0.168622i
$604$		−	305.045i		−	0.505042i
$605$	−338.349			−0.559254
$606$	−170.138			−0.280756
$607$	−626.332			−1.03185			−0.515924	−	0.856634i	$-0.672551\pi$
$607$	−626.332			−1.03185			−0.515924	+	0.856634i	$0.672551\pi$
$608$		−	61.3659i		−	0.100931i
$609$	258.824			0.424998
$610$	−776.842			−1.27351
$611$	−17.4576			−0.0285721
$612$	−109.438			−0.178820
$613$		−	473.871i		−	0.773036i	−0.922282	−	0.386518i	$-0.873678\pi$
$613$		−	473.871i		−	0.773036i	0.922282	−	0.386518i	$-0.126322\pi$
$614$		−	606.694i		−	0.988102i
$615$	178.568			0.290354
$616$	−150.286			−0.243971
$617$	1071.74			1.73702			0.868512	−	0.495668i	$-0.165077\pi$
$617$	1071.74			1.73702			0.868512	+	0.495668i	$0.165077\pi$
$618$	−401.954			−0.650410
$619$	279.836			0.452078			0.226039	−	0.974118i	$-0.427422\pi$
$619$	279.836			0.452078			0.226039	+	0.974118i	$0.427422\pi$
$620$			413.852i			0.667503i
$621$		−	20.0625i		−	0.0323068i
$622$		−	383.418i		−	0.616428i
$623$		−	576.069i		−	0.924670i
$624$		−	53.4974i		−	0.0857329i
$625$	−722.910			−1.15666
$626$	829.158			1.32453
$627$			157.919i			0.251865i
$628$		−	7.66842i		−	0.0122109i
$629$			126.845i			0.201662i
$630$		−	180.202i		−	0.286034i
$631$	−163.714			−0.259451			−0.129726	−	0.991550i	$-0.541410\pi$
$631$	−163.714			−0.259451			−0.129726	+	0.991550i	$0.541410\pi$
$632$			63.9630i			0.101207i
$633$			640.665i			1.01211i
$634$			276.372i			0.435918i
$635$	1227.99			1.93384
$636$	14.0098			0.0220281
$637$		−	69.7493i		−	0.109497i
$638$	−280.951			−0.440361
$639$	320.487			0.501544
$640$		−	76.0110i		−	0.118767i
$641$	1053.26			1.64315			0.821573	−	0.570103i	$-0.193097\pi$
$641$	1053.26			1.64315			0.821573	+	0.570103i	$0.193097\pi$
$642$			134.822i			0.210003i
$643$	−540.426			−0.840477			−0.420238	−	0.907414i	$-0.638054\pi$
$643$	−540.426			−0.840477			−0.420238	+	0.907414i	$0.638054\pi$
$644$			48.8186i			0.0758052i
$645$		−	19.0655i		−	0.0295590i
$646$		−	279.823i		−	0.433163i
$647$	−391.365			−0.604892			−0.302446	−	0.953167i	$-0.597803\pi$
$647$	−391.365			−0.604892			−0.302446	+	0.953167i	$0.597803\pi$
$648$			25.4558i			0.0392837i
$649$	−493.269	−	50.8015i	−0.760044	−	0.0782765i
$650$	219.909			0.338322
$651$			337.252i			0.518053i
$652$	295.824			0.453718
$653$	−96.0994			−0.147166			−0.0735830	−	0.997289i	$-0.523443\pi$
$653$	−96.0994			−0.147166			−0.0735830	+	0.997289i	$0.523443\pi$
$654$	250.841			0.383548
$655$		−	47.5877i		−	0.0726530i
$656$	61.3805			0.0935679
$657$			91.2344i			0.138865i
$658$	−20.2133			−0.0307194
$659$		−	424.244i		−	0.643769i	−0.946779	−	0.321884i	$-0.895684\pi$
$659$		−	424.244i		−	0.643769i	0.946779	−	0.321884i	$-0.104316\pi$
$660$			195.607i			0.296374i
$661$	478.955			0.724592			0.362296	−	0.932063i	$-0.381993\pi$
$661$	478.955			0.724592			0.362296	+	0.932063i	$0.381993\pi$
$662$		−	202.636i		−	0.306096i
$663$		−	243.944i		−	0.367939i
$664$	332.768			0.501157
$665$	460.760			0.692872
$666$	29.5049			0.0443016
$667$			91.2633i			0.136826i
$668$	−204.054			−0.305470
$669$	−300.309			−0.448892
$670$	−322.031			−0.480643
$671$	687.178			1.02411
$672$		−	61.9422i		−	0.0921759i
$673$		−	1228.23i		−	1.82501i	−0.409063	−	0.912506i	$-0.634144\pi$
$673$		−	1228.23i		−	1.82501i	0.409063	−	0.912506i	$-0.365856\pi$
$674$	650.552			0.965211
$675$	−104.640			−0.155023
$676$	−218.751			−0.323597
$677$	667.785			0.986389			0.493194	−	0.869919i	$-0.335829\pi$
$677$	667.785			0.986389			0.493194	+	0.869919i	$0.335829\pi$
$678$	−336.838			−0.496811
$679$		−	92.0450i		−	0.135560i
$680$		−	346.604i		−	0.509712i
$681$			333.686i			0.489994i
$682$		−	366.084i		−	0.536780i
$683$			104.445i			0.152921i	0.997073	+	0.0764607i	$0.0243620\pi$
$683$			104.445i			0.152921i	−0.997073	+	0.0764607i	$0.975638\pi$
$684$	−65.0883			−0.0951584
$685$	−463.675			−0.676898
$686$		−	518.849i		−	0.756339i
$687$		−	35.3346i		−	0.0514332i
$688$		−	6.55355i		−	0.00952552i
$689$			31.2287i			0.0453247i
$690$	63.5405			0.0920877
$691$			211.060i			0.305441i	0.988269	+	0.152720i	$0.0488034\pi$
$691$			211.060i			0.305441i	−0.988269	+	0.152720i	$0.951197\pi$
$692$		−	645.981i		−	0.933498i
$693$			159.403i			0.230018i
$694$	850.402			1.22536
$695$	54.9890			0.0791209
$696$		−	115.797i		−	0.166375i
$697$	279.890			0.401564
$698$	280.619			0.402033
$699$		−	531.598i		−	0.760513i
$700$	254.623			0.363748
$701$			383.970i			0.547746i	0.961766	+	0.273873i	$0.0883047\pi$
$701$			383.970i			0.547746i	−0.961766	+	0.273873i	$0.911695\pi$
$702$	−56.7425			−0.0808298
$703$			75.4414i			0.107313i
$704$			67.2377i			0.0955081i
$705$			26.3090i			0.0373177i
$706$	−246.063			−0.348531
$707$		−	439.113i		−	0.621094i
$708$	20.9384	−	203.307i	0.0295741	−	0.287156i
$709$	337.393			0.475871			0.237936	−	0.971281i	$-0.423529\pi$
$709$	337.393			0.475871			0.237936	+	0.971281i	$0.423529\pi$
$710$			1015.02i			1.42961i
$711$	67.8430			0.0954191
$712$	−257.732			−0.361983
$713$	−118.918			−0.166785
$714$		−	282.452i		−	0.395590i
$715$	−436.019			−0.609817
$716$			635.860i			0.888073i
$717$	267.766			0.373453
$718$			959.578i			1.33646i
$719$			352.097i			0.489703i	0.969561	+	0.244852i	$0.0787393\pi$
$719$			352.097i			0.489703i	−0.969561	+	0.244852i	$0.921261\pi$
$720$	−80.6218			−0.111975
$721$		−	1037.41i		−	1.43885i
$722$			344.106i			0.476601i
$723$	−511.345			−0.707254
$724$	−411.102			−0.567820
$725$	476.003			0.656555
$726$			123.358i			0.169915i
$727$	252.642			0.347514			0.173757	−	0.984789i	$-0.444409\pi$
$727$	252.642			0.347514			0.173757	+	0.984789i	$0.444409\pi$
$728$	138.073			0.189660
$729$	27.0000			0.0370370
$730$	−288.951			−0.395823
$731$		−	29.8837i		−	0.0408805i
$732$			283.229i			0.386924i
$733$	−1316.81			−1.79647			−0.898236	−	0.439512i	$-0.855151\pi$
$733$	−1316.81			−1.79647			−0.898236	+	0.439512i	$0.855151\pi$
$734$	806.864			1.09927
$735$	−105.114			−0.143012
$736$	21.8413			0.0296757
$737$	284.862			0.386515
$738$		−	65.1039i		−	0.0882166i
$739$			49.9599i			0.0676047i	0.999429	+	0.0338024i	$0.0107617\pi$
$739$			49.9599i			0.0676047i	−0.999429	+	0.0338024i	$0.989238\pi$
$740$			93.4456i			0.126278i
$741$		−	145.086i		−	0.195797i
$742$			36.1584i			0.0487310i
$743$	−1084.88			−1.46014			−0.730068	−	0.683375i	$-0.760512\pi$
$743$	−1084.88			−1.46014			−0.730068	+	0.683375i	$0.760512\pi$
$744$	150.886			0.202804
$745$		−	798.771i		−	1.07218i
$746$			791.724i			1.06129i
$747$		−	352.954i		−	0.472495i
$748$			306.598i			0.409891i
$749$	−347.966			−0.464574
$750$			80.0125i			0.106683i
$751$		−	601.675i		−	0.801165i	−0.916261	−	0.400582i	$-0.868808\pi$
$751$		−	601.675i		−	0.801165i	0.916261	−	0.400582i	$-0.131192\pi$
$752$			9.04340i			0.0120258i
$753$	−37.3035			−0.0495399
$754$	258.118			0.342332
$755$		−	1024.72i		−	1.35725i
$756$	−65.6997			−0.0869043
$757$	−1403.20			−1.85364			−0.926818	−	0.375511i	$-0.877467\pi$
$757$	−1403.20			−1.85364			−0.926818	+	0.375511i	$0.877467\pi$
$758$			406.627i			0.536447i
$759$	−56.2066			−0.0740535
$760$		−	206.143i		−	0.271241i
$761$	323.035			0.424488			0.212244	−	0.977217i	$-0.431923\pi$
$761$	323.035			0.424488			0.212244	+	0.977217i	$0.431923\pi$
$762$		−	447.712i		−	0.587548i
$763$			647.401i			0.848494i
$764$			737.523i			0.965344i
$765$	−367.629			−0.480561
$766$			582.617i			0.760597i
$767$	453.182	+	46.6730i	0.590850	+	0.0608513i
$768$	−27.7128			−0.0360844
$769$			756.001i			0.983096i	0.870850	+	0.491548i	$0.163569\pi$
$769$			756.001i			0.983096i	−0.870850	+	0.491548i	$0.836431\pi$
$770$	−504.848			−0.655646
$771$	317.438			0.411723
$772$	70.0413			0.0907271
$773$		−	1296.56i		−	1.67731i	−0.544662	−	0.838656i	$-0.683342\pi$
$773$		−	1296.56i		−	1.67731i	0.544662	−	0.838656i	$-0.316658\pi$
$774$	−6.95109			−0.00898074
$775$			620.241i			0.800311i
$776$	−41.1807			−0.0530680
$777$			76.1499i			0.0980051i
$778$			1072.96i			1.37913i
$779$	166.465			0.213690
$780$		−	179.711i		−	0.230398i
$781$		−	897.866i		−	1.14964i
$782$	99.5946			0.127359
$783$	−122.821			−0.156860
$784$	−36.1317			−0.0460863
$785$		−	25.7601i		−	0.0328154i
$786$	−17.3500			−0.0220738
$787$	−410.466			−0.521557			−0.260779	−	0.965399i	$-0.583979\pi$
$787$	−410.466			−0.521557			−0.260779	+	0.965399i	$0.583979\pi$
$788$	−367.525			−0.466402
$789$	236.394			0.299612
$790$			214.867i			0.271984i
$791$		−	869.354i		−	1.09906i
$792$	71.3163			0.0900459
$793$	−631.332			−0.796132
$794$	−899.696			−1.13312
$795$	47.0625			0.0591981
$796$	−598.199			−0.751506
$797$		−	16.1965i		−	0.0203219i	−0.999948	−	0.0101609i	$-0.996766\pi$
$797$		−	16.1965i		−	0.0203219i	0.999948	−	0.0101609i	$-0.00323438\pi$
$798$		−	167.988i		−	0.210511i
$799$			41.2372i			0.0516110i
$800$		−	113.918i		−	0.142397i
$801$			273.366i			0.341281i
$802$	−284.733			−0.355029
$803$	255.600			0.318306
$804$			117.409i			0.146031i
$805$			163.993i			0.203719i
$806$			336.333i			0.417287i
$807$			144.806i			0.179438i
$808$	−196.458			−0.243141
$809$		−	673.314i		−	0.832279i	−0.909301	−	0.416140i	$-0.863383\pi$
$809$		−	673.314i		−	0.832279i	0.909301	−	0.416140i	$-0.136617\pi$
$810$			85.5124i			0.105571i
$811$		−	1299.49i		−	1.60234i	−0.598440	−	0.801168i	$-0.704212\pi$
$811$		−	1299.49i		−	1.60234i	0.598440	−	0.801168i	$-0.295788\pi$
$812$	298.864			0.368059
$813$	−367.728			−0.452311
$814$		−	82.6600i		−	0.101548i
$815$	993.744			1.21932
$816$	−126.368			−0.154863
$817$		−	17.7733i		−	0.0217544i
$818$	582.581			0.712202
$819$		−	146.448i		−	0.178813i
$820$	206.192			0.251454
$821$		−	986.048i		−	1.20103i	−0.799613	−	0.600516i	$-0.794962\pi$
$821$		−	986.048i		−	1.20103i	0.799613	−	0.600516i	$-0.205038\pi$
$822$			169.051i			0.205658i
$823$		−	142.520i		−	0.173171i	−0.996244	−	0.0865854i	$-0.972404\pi$
$823$		−	142.520i		−	0.173171i	0.996244	−	0.0865854i	$-0.0275955\pi$
$824$	−464.136			−0.563272
$825$			293.157i			0.355342i
$826$	524.719	+	54.0405i	0.635253	+	0.0654244i
$827$	−974.357			−1.17818			−0.589091	−	0.808067i	$-0.700514\pi$
$827$	−974.357			−1.17818			−0.589091	+	0.808067i	$0.700514\pi$
$828$		−	23.1662i		−	0.0279785i
$829$	1361.74			1.64263			0.821314	−	0.570476i	$-0.193241\pi$
$829$	1361.74			1.64263			0.821314	+	0.570476i	$0.193241\pi$
$830$	1117.85			1.34681
$831$	−442.190			−0.532118
$832$		−	61.7734i		−	0.0742469i
$833$	−164.758			−0.197788
$834$		−	20.0484i		−	0.0240389i
$835$	−685.467			−0.820918
$836$			182.350i			0.218121i
$837$		−	160.039i		−	0.191205i
$838$	−553.123			−0.660051
$839$		−	546.392i		−	0.651242i	−0.945500	−	0.325621i	$-0.894427\pi$
$839$		−	546.392i		−	0.651242i	0.945500	−	0.325621i	$-0.105573\pi$
$840$		−	208.079i		−	0.247713i
$841$	−282.293			−0.335663
$842$	−332.886			−0.395352
$843$	151.445			0.179650
$844$			739.776i			0.876512i
$845$	−734.839			−0.869632
$846$	9.59198			0.0113380
$847$	−318.379			−0.375890
$848$	16.1772			0.0190769
$849$		−	91.6641i		−	0.107967i
$850$		−	519.457i		−	0.611126i
$851$	−26.8511			−0.0315524
$852$	370.066			0.434350
$853$	1343.26			1.57475			0.787376	−	0.616473i	$-0.211439\pi$
$853$	1343.26			1.57475			0.787376	+	0.616473i	$0.211439\pi$
$854$	−730.992			−0.855962
$855$	−218.647			−0.255728
$856$			155.679i			0.181868i
$857$			601.087i			0.701385i	0.936491	+	0.350692i	$0.114054\pi$
$857$			601.087i			0.701385i	−0.936491	+	0.350692i	$0.885946\pi$
$858$			158.968i			0.185278i
$859$			418.957i			0.487726i	0.969810	+	0.243863i	$0.0784147\pi$
$859$			418.957i			0.487726i	−0.969810	+	0.243863i	$0.921585\pi$
$860$		−	22.0150i		−	0.0255988i
$861$	168.028			0.195155
$862$	698.380			0.810186
$863$		−	734.911i		−	0.851576i	−0.904823	−	0.425788i	$-0.859997\pi$
$863$		−	734.911i		−	0.851576i	0.904823	−	0.425788i	$-0.140003\pi$
$864$			29.3939i			0.0340207i
$865$		−	2170.01i		−	2.50868i
$866$		−	55.0270i		−	0.0635416i
$867$	−75.6659			−0.0872732
$868$			389.426i			0.448647i
$869$		−	190.067i		−	0.218719i
$870$		−	388.991i		−	0.447116i
$871$	−261.712			−0.300473
$872$	289.646			0.332163
$873$			43.6788i			0.0500329i
$874$	59.2340			0.0677734
$875$	−206.506			−0.236007
$876$			105.348i			0.120261i
$877$	247.251			0.281929			0.140964	−	0.990015i	$-0.454980\pi$
$877$	247.251			0.281929			0.140964	+	0.990015i	$0.454980\pi$
$878$			483.710i			0.550923i
$879$	235.785			0.268242
$880$			225.868i			0.256668i
$881$		−	512.144i		−	0.581321i	−0.956826	−	0.290661i	$-0.906125\pi$
$881$		−	512.144i		−	0.581321i	0.956826	−	0.290661i	$-0.0938751\pi$
$882$			38.3234i			0.0434506i
$883$	−698.113			−0.790615			−0.395308	−	0.918549i	$-0.629362\pi$
$883$	−698.113			−0.790615			−0.395308	+	0.918549i	$0.629362\pi$
$884$		−	281.682i		−	0.318645i
$885$	70.3373	−	682.956i	0.0794771	−	0.771702i
$886$	414.227			0.467524
$887$			161.403i			0.181965i	0.995852	+	0.0909826i	$0.0290008\pi$
$887$			161.403i			0.181965i	−0.995852	+	0.0909826i	$0.970999\pi$
$888$	34.0693			0.0383663
$889$	1155.51			1.29979
$890$	−865.785			−0.972792
$891$		−	75.6424i		−	0.0848961i
$892$	−346.767			−0.388752
$893$			24.5258i			0.0274645i
$894$	−291.224			−0.325754
$895$			2136.01i			2.38660i
$896$		−	71.5247i		−	0.0798267i
$897$	51.6388			0.0575683
$898$			996.395i			1.10957i
$899$			728.007i			0.809796i
$900$	−120.828			−0.134254
$901$	73.7666			0.0818719
$902$	−182.393			−0.202210
$903$		−	17.9403i		−	0.0198674i
$904$	−388.947			−0.430251
$905$	−1380.99			−1.52596
$906$	−373.602			−0.412365
$907$	1193.38			1.31574			0.657871	−	0.753131i	$-0.271457\pi$
$907$	1193.38			1.31574			0.657871	+	0.753131i	$0.271457\pi$
$908$			385.307i			0.424347i
$909$			208.376i			0.229236i
$910$	463.820			0.509692
$911$	−1142.28			−1.25387			−0.626937	−	0.779070i	$-0.715692\pi$
$911$	−1142.28			−1.25387			−0.626937	+	0.779070i	$0.715692\pi$
$912$	−75.1575			−0.0824096
$913$	−988.826			−1.08305
$914$	229.704			0.251318
$915$			951.433i			1.03982i
$916$		−	40.8009i		−	0.0445425i
$917$		−	44.7790i		−	0.0488321i
$918$			134.034i			0.146006i
$919$			1283.61i			1.39675i	0.715731	+	0.698376i	$0.246094\pi$
$919$			1283.61i			1.39675i	−0.715731	+	0.698376i	$0.753906\pi$
$920$	73.3703			0.0797503
$921$	−743.046			−0.806782
$922$		−	1070.24i		−	1.16078i
$923$			824.898i			0.893714i
$924$			184.062i			0.199201i
$925$			140.047i			0.151403i
$926$	−274.915			−0.296884
$927$			492.291i			0.531058i
$928$		−	133.711i		−	0.144085i
$929$		−	152.101i		−	0.163725i	−0.996644	−	0.0818627i	$-0.973913\pi$
$929$		−	152.101i		−	0.163725i	0.996644	−	0.0818627i	$-0.0260869\pi$
$930$	506.863			0.545014
$931$	−97.9896			−0.105252
$932$		−	613.837i		−	0.658623i
$933$	−469.589			−0.503311
$934$	614.477			0.657899
$935$			1029.94i			1.10154i
$936$	−65.5206			−0.0700007
$937$		−	1028.98i		−	1.09817i	−0.835767	−	0.549084i	$-0.814977\pi$
$937$		−	1028.98i		−	1.09817i	0.835767	−	0.549084i	$-0.185023\pi$
$938$	−303.024			−0.323054
$939$		−	1015.51i		−	1.08148i
$940$			30.3790i			0.0323181i
$941$			1325.28i			1.40837i	0.710016	+	0.704186i	$0.248688\pi$
$941$			1325.28i			1.40837i	−0.710016	+	0.704186i	$0.751312\pi$
$942$	−9.39186			−0.00997012
$943$			59.2481i			0.0628294i
$944$	24.1776	−	234.758i	0.0256119	−	0.248685i
$945$	−220.701			−0.233546
$946$			19.4740i			0.0205856i
$947$	−688.238			−0.726756			−0.363378	−	0.931642i	$-0.618377\pi$
$947$	−688.238			−0.726756			−0.363378	+	0.931642i	$0.618377\pi$
$948$	78.3384			0.0826354
$949$	−234.828			−0.247447
$950$		−	308.947i		−	0.325207i
$951$	338.485			0.355926
$952$		−	326.147i		−	0.342591i
$953$	281.053			0.294914			0.147457	−	0.989068i	$-0.452891\pi$
$953$	281.053			0.294914			0.147457	+	0.989068i	$0.452891\pi$
$954$		−	17.1585i		−	0.0179858i
$955$			2477.52i			2.59426i
$956$	309.189			0.323420
$957$			344.093i			0.359554i
$958$		−	457.050i		−	0.477088i
$959$	−436.308			−0.454962
$960$	−93.0941			−0.0969730
$961$	12.3923			0.0128952
$962$			75.9424i			0.0789422i
$963$	165.123			0.171467
$964$	−590.450			−0.612500
$965$	235.286			0.243820
$966$	59.7903			0.0618947
$967$			565.280i			0.584571i	0.956331	+	0.292286i	$0.0944158\pi$
$967$			565.280i			0.584571i	−0.956331	+	0.292286i	$0.905584\pi$
$968$			142.442i			0.147151i
$969$	−342.712			−0.353676
$970$	−138.336			−0.142614
$971$	741.348			0.763489			0.381744	−	0.924268i	$-0.375323\pi$
$971$	741.348			0.763489			0.381744	+	0.924268i	$0.375323\pi$
$972$	31.1769			0.0320750
$973$	51.7435			0.0531794
$974$		−	633.757i		−	0.650675i
$975$		−	269.333i		−	0.276239i
$976$			327.044i			0.335086i
$977$		−	1790.19i		−	1.83234i	−0.400796	−	0.916168i	$-0.631266\pi$
$977$		−	1790.19i		−	1.83234i	0.400796	−	0.916168i	$-0.368734\pi$
$978$		−	362.309i		−	0.370459i
$979$	765.854			0.782282
$980$	−121.375			−0.123852
$981$		−	307.216i		−	0.313166i
$982$			459.695i			0.468121i
$983$			1578.62i			1.60593i	0.596029	+	0.802963i	$0.296744\pi$
$983$			1578.62i			1.60593i	−0.596029	+	0.802963i	$0.703256\pi$
$984$		−	75.1755i		−	0.0763979i
$985$	−1234.60			−1.25341
$986$		−	609.711i		−	0.618368i
$987$			24.7562i			0.0250823i
$988$		−	167.530i		−	0.169565i
$989$	6.32588			0.00639624
$990$	239.569			0.241989
$991$			1391.11i			1.40374i	0.712303	+	0.701872i	$0.247652\pi$
$991$			1391.11i			1.40374i	−0.712303	+	0.701872i	$0.752348\pi$
$992$	174.228			0.175633
$993$	−248.177			−0.249927
$994$			955.113i			0.960879i
$995$	−2009.49			−2.01959
$996$		−	407.556i		−	0.409193i
$997$	−989.963			−0.992942			−0.496471	−	0.868053i	$-0.665371\pi$
$997$	−989.963			−0.992942			−0.496471	+	0.868053i	$0.665371\pi$
$998$		−	690.253i		−	0.691636i
$999$		−	36.1360i		−	0.0361721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.3.d.a.235.1	✓	20
3.2	odd	2		1062.3.d.f.235.19		20
59.58	odd	2	inner	354.3.d.a.235.11	yes	20
177.176	even	2		1062.3.d.f.235.9		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.3.d.a.235.1	✓	20	1.1	even	1	trivial
354.3.d.a.235.11	yes	20	59.58	odd	2	inner
1062.3.d.f.235.9		20	177.176	even	2
1062.3.d.f.235.19		20	3.2	odd	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)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} -6.71849 q^{5} +2.44949i q^{6} -6.32195 q^{7} +2.82843i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} -6.71849 q^{5} +2.44949i q^{6} -6.32195 q^{7} +2.82843i q^{8} +3.00000 q^{9} +9.50137i q^{10} -8.40471i q^{11} +3.46410 q^{12} +7.72168i q^{13} +8.94059i q^{14} +11.6368 q^{15} +4.00000 q^{16} +18.2397 q^{17} -4.24264i q^{18} +10.8481 q^{19} +13.4370 q^{20} +10.9499 q^{21} -11.8861 q^{22} +3.86104i q^{23} -4.89898i q^{24} +20.1380 q^{25} +10.9201 q^{26} -5.19615 q^{27} +12.6439 q^{28} +23.6370 q^{29} -16.4569i q^{30} +30.7995i q^{31} -5.65685i q^{32} +14.5574i q^{33} -25.7948i q^{34} +42.4739 q^{35} -6.00000 q^{36} +6.95437i q^{37} -15.3415i q^{38} -13.3743i q^{39} -19.0027i q^{40} +15.3451 q^{41} -15.4856i q^{42} -1.63839i q^{43} +16.8094i q^{44} -20.1555 q^{45} +5.46033 q^{46} +2.26085i q^{47} -6.92820 q^{48} -9.03292 q^{49} -28.4795i q^{50} -31.5920 q^{51} -15.4434i q^{52} +4.04429 q^{53} +7.34847i q^{54} +56.4669i q^{55} -17.8812i q^{56} -18.7894 q^{57} -33.4278i q^{58} +(6.04441 - 58.6896i) q^{59} -23.2735 q^{60} +81.7610i q^{61} +43.5570 q^{62} -18.9659 q^{63} -8.00000 q^{64} -51.8780i q^{65} +20.5873 q^{66} +33.8931i q^{67} -36.4793 q^{68} -6.68751i q^{69} -60.0672i q^{70} +106.829 q^{71} +8.48528i q^{72} +30.4115i q^{73} +9.83496 q^{74} -34.8801 q^{75} -21.6961 q^{76} +53.1342i q^{77} -18.9142 q^{78} +22.6143 q^{79} -26.8739 q^{80} +9.00000 q^{81} -21.7013i q^{82} -117.651i q^{83} -21.8999 q^{84} -122.543 q^{85} -2.31703 q^{86} -40.9405 q^{87} +23.7721 q^{88} +91.1221i q^{89} +28.5041i q^{90} -48.8161i q^{91} -7.72207i q^{92} -53.3463i q^{93} +3.19733 q^{94} -72.8825 q^{95} +9.79796i q^{96} +14.5596i q^{97} +12.7745i q^{98} -25.2141i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 40 q^{4} + 8 q^{7} + 60 q^{9}+O(q^{10}) \) 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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