LMFDB - Embedded newform 354.3.d.a.235.17

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			235.17
Root			$-2.72105 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	354.235
Dual form			354.3.d.a.235.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} -2.72105 q^{5} +2.44949i q^{6} -3.73640 q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} -2.72105 q^{5} +2.44949i q^{6} -3.73640 q^{7} -2.82843i q^{8} +3.00000 q^{9} -3.84815i q^{10} +14.1470i q^{11} -3.46410 q^{12} +1.27623i q^{13} -5.28407i q^{14} -4.71300 q^{15} +4.00000 q^{16} -24.7226 q^{17} +4.24264i q^{18} -17.2238 q^{19} +5.44210 q^{20} -6.47164 q^{21} -20.0069 q^{22} +4.11414i q^{23} -4.89898i q^{24} -17.5959 q^{25} -1.80487 q^{26} +5.19615 q^{27} +7.47281 q^{28} -30.6705 q^{29} -6.66518i q^{30} -11.8987i q^{31} +5.65685i q^{32} +24.5033i q^{33} -34.9631i q^{34} +10.1669 q^{35} -6.00000 q^{36} +24.6133i q^{37} -24.3581i q^{38} +2.21050i q^{39} +7.69629i q^{40} +36.7356 q^{41} -9.15229i q^{42} -23.4627i q^{43} -28.2940i q^{44} -8.16315 q^{45} -5.81828 q^{46} +64.7858i q^{47} +6.92820 q^{48} -35.0393 q^{49} -24.8843i q^{50} -42.8209 q^{51} -2.55247i q^{52} +77.6433 q^{53} +7.34847i q^{54} -38.4947i q^{55} +10.5681i q^{56} -29.8325 q^{57} -43.3746i q^{58} +(11.6261 + 57.8432i) q^{59} +9.42599 q^{60} +25.2423i q^{61} +16.8273 q^{62} -11.2092 q^{63} -8.00000 q^{64} -3.47270i q^{65} -34.6529 q^{66} -72.9225i q^{67} +49.4453 q^{68} +7.12591i q^{69} +14.3782i q^{70} +18.1155 q^{71} -8.48528i q^{72} -99.9234i q^{73} -34.8084 q^{74} -30.4770 q^{75} +34.4476 q^{76} -52.8589i q^{77} -3.12612 q^{78} -34.1973 q^{79} -10.8842 q^{80} +9.00000 q^{81} +51.9519i q^{82} +48.3744i q^{83} +12.9433 q^{84} +67.2715 q^{85} +33.1812 q^{86} -53.1228 q^{87} +40.0137 q^{88} -51.8676i q^{89} -11.5444i q^{90} -4.76853i q^{91} -8.22829i q^{92} -20.6092i q^{93} -91.6210 q^{94} +46.8668 q^{95} +9.79796i q^{96} +68.4744i q^{97} -49.5530i q^{98} +42.4410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.72105			−0.544210			−0.272105	−	0.962268i	$-0.587720\pi$
$5$	−2.72105			−0.544210			−0.272105	+	0.962268i	$0.587720\pi$
$6$			2.44949i			0.408248i
$7$	−3.73640			−0.533772			−0.266886	−	0.963728i	$-0.585995\pi$
$7$	−3.73640			−0.533772			−0.266886	+	0.963728i	$0.585995\pi$
$8$		−	2.82843i		−	0.353553i
$9$	3.00000			0.333333
$10$		−	3.84815i		−	0.384815i
$11$			14.1470i			1.28609i	0.765828	+	0.643045i	$0.222329\pi$
$11$			14.1470i			1.28609i	−0.765828	+	0.643045i	$0.777671\pi$
$12$	−3.46410			−0.288675
$13$			1.27623i			0.0981719i	0.998795	+	0.0490859i	$0.0156308\pi$
$13$			1.27623i			0.0981719i	−0.998795	+	0.0490859i	$0.984369\pi$
$14$		−	5.28407i		−	0.377434i
$15$	−4.71300			−0.314200
$16$	4.00000			0.250000
$17$	−24.7226			−1.45427			−0.727137	−	0.686493i	$-0.759149\pi$
$17$	−24.7226			−1.45427			−0.727137	+	0.686493i	$0.759149\pi$
$18$			4.24264i			0.235702i
$19$	−17.2238			−0.906516			−0.453258	−	0.891379i	$-0.649738\pi$
$19$	−17.2238			−0.906516			−0.453258	+	0.891379i	$0.649738\pi$
$20$	5.44210			0.272105
$21$	−6.47164			−0.308173
$22$	−20.0069			−0.909403
$23$			4.11414i			0.178876i	0.995992	+	0.0894379i	$0.0285071\pi$
$23$			4.11414i			0.178876i	−0.995992	+	0.0894379i	$0.971493\pi$
$24$		−	4.89898i		−	0.204124i
$25$	−17.5959			−0.703836
$26$	−1.80487			−0.0694180
$27$	5.19615			0.192450
$28$	7.47281			0.266886
$29$	−30.6705			−1.05760			−0.528801	−	0.848746i	$-0.677358\pi$
$29$	−30.6705			−1.05760			−0.528801	+	0.848746i	$0.677358\pi$
$30$		−	6.66518i		−	0.222173i
$31$		−	11.8987i		−	0.383829i	−0.981412	−	0.191915i	$-0.938530\pi$
$31$		−	11.8987i		−	0.383829i	0.981412	−	0.191915i	$-0.0614697\pi$
$32$			5.65685i			0.176777i
$33$			24.5033i			0.742524i
$34$		−	34.9631i		−	1.02833i
$35$	10.1669			0.290484
$36$	−6.00000			−0.166667
$37$			24.6133i			0.665223i	0.943064	+	0.332612i	$0.107930\pi$
$37$			24.6133i			0.665223i	−0.943064	+	0.332612i	$0.892070\pi$
$38$		−	24.3581i		−	0.641004i
$39$			2.21050i			0.0566796i
$40$			7.69629i			0.192407i
$41$	36.7356			0.895990			0.447995	−	0.894036i	$-0.352138\pi$
$41$	36.7356			0.895990			0.447995	+	0.894036i	$0.352138\pi$
$42$		−	9.15229i		−	0.217912i
$43$		−	23.4627i		−	0.545643i	−0.962065	−	0.272822i	$-0.912043\pi$
$43$		−	23.4627i		−	0.545643i	0.962065	−	0.272822i	$-0.0879569\pi$
$44$		−	28.2940i		−	0.643045i
$45$	−8.16315			−0.181403
$46$	−5.81828			−0.126484
$47$			64.7858i			1.37842i	0.724561	+	0.689211i	$0.242043\pi$
$47$			64.7858i			1.37842i	−0.724561	+	0.689211i	$0.757957\pi$
$48$	6.92820			0.144338
$49$	−35.0393			−0.715087
$50$		−	24.8843i		−	0.497687i
$51$	−42.8209			−0.839625
$52$		−	2.55247i		−	0.0490859i
$53$	77.6433			1.46497			0.732484	−	0.680785i	$-0.238361\pi$
$53$	77.6433			1.46497			0.732484	+	0.680785i	$0.238361\pi$
$54$			7.34847i			0.136083i
$55$		−	38.4947i		−	0.699903i
$56$			10.5681i			0.188717i
$57$	−29.8325			−0.523377
$58$		−	43.3746i		−	0.747838i
$59$	11.6261	+	57.8432i	0.197052	+	0.980393i
$59$	11.6261	+	57.8432i	0.197052	+	0.980393i
$60$	9.42599			0.157100
$61$			25.2423i			0.413808i	0.978361	+	0.206904i	$0.0663388\pi$
$61$			25.2423i			0.413808i	−0.978361	+	0.206904i	$0.933661\pi$
$62$	16.8273			0.271408
$63$	−11.2092			−0.177924
$64$	−8.00000			−0.125000
$65$		−	3.47270i		−	0.0534261i
$66$	−34.6529			−0.525044
$67$		−	72.9225i		−	1.08839i	−0.838957	−	0.544197i	$-0.816834\pi$
$67$		−	72.9225i		−	1.08839i	0.838957	−	0.544197i	$-0.183166\pi$
$68$	49.4453			0.727137
$69$			7.12591i			0.103274i
$70$			14.3782i			0.205403i
$71$	18.1155			0.255148			0.127574	−	0.991829i	$-0.459281\pi$
$71$	18.1155			0.255148			0.127574	+	0.991829i	$0.459281\pi$
$72$		−	8.48528i		−	0.117851i
$73$		−	99.9234i		−	1.36881i	−0.729100	−	0.684407i	$-0.760061\pi$
$73$		−	99.9234i		−	1.36881i	0.729100	−	0.684407i	$-0.239939\pi$
$74$	−34.8084			−0.470384
$75$	−30.4770			−0.406360
$76$	34.4476			0.453258
$77$		−	52.8589i		−	0.686479i
$78$	−3.12612			−0.0400785
$79$	−34.1973			−0.432877			−0.216439	−	0.976296i	$-0.569444\pi$
$79$	−34.1973			−0.432877			−0.216439	+	0.976296i	$0.569444\pi$
$80$	−10.8842			−0.136052
$81$	9.00000			0.111111
$82$			51.9519i			0.633560i
$83$			48.3744i			0.582824i	0.956598	+	0.291412i	$0.0941250\pi$
$83$			48.3744i			0.582824i	−0.956598	+	0.291412i	$0.905875\pi$
$84$	12.9433			0.154087
$85$	67.2715			0.791430
$86$	33.1812			0.385828
$87$	−53.1228			−0.610607
$88$	40.0137			0.454701
$89$		−	51.8676i		−	0.582782i	−0.956604	−	0.291391i	$-0.905882\pi$
$89$		−	51.8676i		−	0.582782i	0.956604	−	0.291391i	$-0.0941181\pi$
$90$		−	11.5444i		−	0.128272i
$91$		−	4.76853i		−	0.0524014i
$92$		−	8.22829i		−	0.0894379i
$93$		−	20.6092i		−	0.221604i
$94$	−91.6210			−0.974691
$95$	46.8668			0.493335
$96$			9.79796i			0.102062i
$97$			68.4744i			0.705921i	0.935638	+	0.352961i	$0.114825\pi$
$97$			68.4744i			0.705921i	−0.935638	+	0.352961i	$0.885175\pi$
$98$		−	49.5530i		−	0.505643i
$99$			42.4410i			0.428697i
$100$	35.1918			0.351918
$101$			182.659i			1.80850i	0.426999	+	0.904252i	$0.359571\pi$
$101$			182.659i			1.80850i	−0.426999	+	0.904252i	$0.640429\pi$
$102$		−	60.5579i		−	0.593705i
$103$			46.9891i			0.456205i	0.973637	+	0.228103i	$0.0732521\pi$
$103$			46.9891i			0.456205i	−0.973637	+	0.228103i	$0.926748\pi$
$104$	3.60974			0.0347090
$105$	17.6097			0.167711
$106$			109.804i			1.03589i
$107$	146.071			1.36515			0.682576	−	0.730815i	$-0.260860\pi$
$107$	146.071			1.36515			0.682576	+	0.730815i	$0.260860\pi$
$108$	−10.3923			−0.0962250
$109$			53.3291i			0.489258i	0.969617	+	0.244629i	$0.0786661\pi$
$109$			53.3291i			0.489258i	−0.969617	+	0.244629i	$0.921334\pi$
$110$	54.4397			0.494906
$111$			42.6314i			0.384067i
$112$	−14.9456			−0.133443
$113$			97.4696i			0.862563i	0.902218	+	0.431281i	$0.141938\pi$
$113$			97.4696i			0.862563i	−0.902218	+	0.431281i	$0.858062\pi$
$114$		−	42.1895i		−	0.370084i
$115$		−	11.1948i		−	0.0973460i
$116$	61.3409			0.528801
$117$			3.82870i			0.0327240i
$118$	−81.8026	+	16.4418i	−0.693243	+	0.139337i
$119$	92.3738			0.776251
$120$			13.3304i			0.111086i
$121$	−79.1373			−0.654028
$122$	−35.6980			−0.292607
$123$	63.6279			0.517300
$124$			23.7974i			0.191915i
$125$	115.906			0.927244
$126$		−	15.8522i		−	0.125811i
$127$	−8.87801			−0.0699056			−0.0349528	−	0.999389i	$-0.511128\pi$
$127$	−8.87801			−0.0699056			−0.0349528	+	0.999389i	$0.511128\pi$
$128$		−	11.3137i		−	0.0883883i
$129$		−	40.6385i		−	0.315027i
$130$	4.91113			0.0377780
$131$		−	80.2663i		−	0.612720i	−0.951916	−	0.306360i	$-0.900889\pi$
$131$		−	80.2663i		−	0.612720i	0.951916	−	0.306360i	$-0.0991111\pi$
$132$		−	49.0066i		−	0.371262i
$133$	64.3551			0.483873
$134$	103.128			0.769611
$135$	−14.1390			−0.104733
$136$			69.9262i			0.514163i
$137$	57.8676			0.422391			0.211196	−	0.977444i	$-0.432264\pi$
$137$	57.8676			0.422391			0.211196	+	0.977444i	$0.432264\pi$
$138$	−10.0776			−0.0730257
$139$	−38.6930			−0.278367			−0.139183	−	0.990267i	$-0.544448\pi$
$139$	−38.6930			−0.278367			−0.139183	+	0.990267i	$0.544448\pi$
$140$	−20.3339			−0.145242
$141$			112.212i			0.795832i
$142$			25.6192i			0.180417i
$143$	−18.0549			−0.126258
$144$	12.0000			0.0833333
$145$	83.4559			0.575558
$146$	141.313			0.967897
$147$	−60.6898			−0.412856
$148$		−	49.2265i		−	0.332612i
$149$		−	156.045i		−	1.04728i	−0.851940	−	0.523640i	$-0.824574\pi$
$149$		−	156.045i		−	1.04728i	0.851940	−	0.523640i	$-0.175426\pi$
$150$		−	43.1010i		−	0.287340i
$151$		−	53.7792i		−	0.356154i	−0.984017	−	0.178077i	$-0.943012\pi$
$151$		−	53.7792i		−	0.356154i	0.984017	−	0.178077i	$-0.0569876\pi$
$152$			48.7163i			0.320502i
$153$	−74.1679			−0.484758
$154$	74.7537			0.485414
$155$			32.3770i			0.208884i
$156$		−	4.42101i		−	0.0283398i
$157$			112.116i			0.714112i	0.934083	+	0.357056i	$0.116220\pi$
$157$			112.116i			0.714112i	−0.934083	+	0.357056i	$0.883780\pi$
$158$		−	48.3623i		−	0.306090i
$159$	134.482			0.845799
$160$		−	15.3926i		−	0.0962036i
$161$		−	15.3721i		−	0.0954789i
$162$			12.7279i			0.0785674i
$163$	163.428			1.00263			0.501313	−	0.865266i	$-0.332850\pi$
$163$	163.428			1.00263			0.501313	+	0.865266i	$0.332850\pi$
$164$	−73.4711			−0.447995
$165$		−	66.6747i		−	0.404089i
$166$	−68.4117			−0.412119
$167$	−103.482			−0.619650			−0.309825	−	0.950794i	$-0.600270\pi$
$167$	−103.482			−0.619650			−0.309825	+	0.950794i	$0.600270\pi$
$168$			18.3046i			0.108956i
$169$	167.371			0.990362
$170$			95.1363i			0.559625i
$171$	−51.6714			−0.302172
$172$			46.9253i			0.272822i
$173$			307.992i			1.78030i	0.455668	+	0.890150i	$0.349400\pi$
$173$			307.992i			1.78030i	−0.455668	+	0.890150i	$0.650600\pi$
$174$		−	75.1270i		−	0.431764i
$175$	65.7454			0.375688
$176$			56.5880i			0.321523i
$177$	20.1370	+	100.187i	0.113768	+	0.566030i
$178$	73.3519			0.412089
$179$		−	148.016i		−	0.826906i	−0.910526	−	0.413453i	$-0.864323\pi$
$179$		−	148.016i		−	0.826906i	0.910526	−	0.413453i	$-0.135677\pi$
$180$	16.3263			0.0907016
$181$	−272.612			−1.50614			−0.753072	−	0.657938i	$-0.771429\pi$
$181$	−272.612			−1.50614			−0.753072	+	0.657938i	$0.771429\pi$
$182$	6.74372			0.0370534
$183$			43.7210i			0.238912i
$184$	11.6366			0.0632421
$185$		−	66.9739i		−	0.362021i
$186$	29.1458			0.156698
$187$		−	349.751i		−	1.87033i
$188$		−	129.572i		−	0.689211i
$189$	−19.4149			−0.102724
$190$			66.2797i			0.348841i
$191$		−	5.52692i		−	0.0289368i	−0.999895	−	0.0144684i	$-0.995394\pi$
$191$		−	5.52692i		−	0.0289368i	0.999895	−	0.0144684i	$-0.00460559\pi$
$192$	−13.8564			−0.0721688
$193$	−319.116			−1.65345			−0.826726	−	0.562604i	$-0.809800\pi$
$193$	−319.116			−1.65345			−0.826726	+	0.562604i	$0.809800\pi$
$194$	−96.8374			−0.499162
$195$		−	6.01489i		−	0.0308456i
$196$	70.0786			0.357544
$197$	−218.702			−1.11016			−0.555080	−	0.831797i	$-0.687312\pi$
$197$	−218.702			−1.11016			−0.555080	+	0.831797i	$0.687312\pi$
$198$	−60.0206			−0.303134
$199$	−65.7431			−0.330367			−0.165184	−	0.986263i	$-0.552822\pi$
$199$	−65.7431			−0.330367			−0.165184	+	0.986263i	$0.552822\pi$
$200$			49.7687i			0.248843i
$201$		−	126.305i		−	0.628385i
$202$	−258.319			−1.27881
$203$	114.597			0.564519
$204$	85.6418			0.419813
$205$	−99.9593			−0.487606
$206$	−66.4527			−0.322586
$207$			12.3424i			0.0596253i
$208$			5.10494i			0.0245430i
$209$		−	243.665i		−	1.16586i
$210$			24.9038i			0.118590i
$211$		−	305.488i		−	1.44781i	−0.689899	−	0.723906i	$-0.742345\pi$
$211$		−	305.488i		−	1.44781i	0.689899	−	0.723906i	$-0.257655\pi$
$212$	−155.287			−0.732484
$213$	31.3770			0.147310
$214$			206.576i			0.965308i
$215$			63.8431i			0.296945i
$216$		−	14.6969i		−	0.0680414i
$217$			44.4584i			0.204877i
$218$	−75.4187			−0.345957
$219$		−	173.072i		−	0.790285i
$220$			76.9893i			0.349951i
$221$		−	31.5519i		−	0.142769i
$222$	−60.2899			−0.271576
$223$	40.6000			0.182063			0.0910313	−	0.995848i	$-0.470984\pi$
$223$	40.6000			0.182063			0.0910313	+	0.995848i	$0.470984\pi$
$224$		−	21.1363i		−	0.0943585i
$225$	−52.7877			−0.234612
$226$	−137.843			−0.609924
$227$		−	415.724i		−	1.83138i	−0.401880	−	0.915692i	$-0.631643\pi$
$227$		−	415.724i		−	1.83138i	0.401880	−	0.915692i	$-0.368357\pi$
$228$	59.6650			0.261689
$229$			236.035i			1.03072i	0.856973	+	0.515361i	$0.172342\pi$
$229$			236.035i			1.03072i	−0.856973	+	0.515361i	$0.827658\pi$
$230$	15.8318			0.0688340
$231$		−	91.5543i		−	0.396339i
$232$			86.7492i			0.373919i
$233$			116.205i			0.498733i	0.968409	+	0.249366i	$0.0802224\pi$
$233$			116.205i			0.498733i	−0.968409	+	0.249366i	$0.919778\pi$
$234$	−5.41460			−0.0231393
$235$		−	176.285i		−	0.750151i
$236$	−23.2522	−	115.686i	−0.0985261	−	0.490197i
$237$	−59.2315			−0.249922
$238$			130.636i			0.548892i
$239$	−333.878			−1.39698			−0.698489	−	0.715621i	$-0.746144\pi$
$239$	−333.878			−1.39698			−0.698489	+	0.715621i	$0.746144\pi$
$240$	−18.8520			−0.0785499
$241$	198.651			0.824277			0.412138	−	0.911121i	$-0.364782\pi$
$241$	198.651			0.824277			0.412138	+	0.911121i	$0.364782\pi$
$242$		−	111.917i		−	0.462467i
$243$	15.5885			0.0641500
$244$		−	50.4846i		−	0.206904i
$245$	95.3436			0.389158
$246$			89.9834i			0.365786i
$247$		−	21.9816i		−	0.0889944i
$248$	−33.6546			−0.135704
$249$			83.7869i			0.336494i
$250$			163.915i			0.655661i
$251$	−182.811			−0.728331			−0.364165	−	0.931334i	$-0.618646\pi$
$251$	−182.811			−0.728331			−0.364165	+	0.931334i	$0.618646\pi$
$252$	22.4184			0.0889620
$253$	−58.2027			−0.230050
$254$		−	12.5554i		−	0.0494307i
$255$	116.518			0.456932
$256$	16.0000			0.0625000
$257$	−183.962			−0.715807			−0.357904	−	0.933759i	$-0.616508\pi$
$257$	−183.962			−0.715807			−0.357904	+	0.933759i	$0.616508\pi$
$258$	57.4716			0.222758
$259$		−	91.9651i		−	0.355078i
$260$			6.94539i			0.0267131i
$261$	−92.0114			−0.352534
$262$	113.514			0.433258
$263$	−225.233			−0.856399			−0.428200	−	0.903684i	$-0.640852\pi$
$263$	−225.233			−0.856399			−0.428200	+	0.903684i	$0.640852\pi$
$264$	69.3058			0.262522
$265$	−211.271			−0.797250
$266$			91.0119i			0.342150i
$267$		−	89.8373i		−	0.336469i
$268$			145.845i			0.544197i
$269$			357.919i			1.33055i	0.746597	+	0.665276i	$0.231686\pi$
$269$			357.919i			1.33055i	−0.746597	+	0.665276i	$0.768314\pi$
$270$		−	19.9955i		−	0.0740576i
$271$	381.899			1.40922			0.704610	−	0.709595i	$-0.251122\pi$
$271$	381.899			1.40922			0.704610	+	0.709595i	$0.251122\pi$
$272$	−98.8906			−0.363568
$273$		−	8.25933i		−	0.0302540i
$274$			81.8371i			0.298676i
$275$		−	248.929i		−	0.905196i
$276$		−	14.2518i		−	0.0516370i
$277$	122.896			0.443666			0.221833	−	0.975085i	$-0.428796\pi$
$277$	122.896			0.443666			0.221833	+	0.975085i	$0.428796\pi$
$278$		−	54.7201i		−	0.196835i
$279$		−	35.6961i		−	0.127943i
$280$		−	28.7565i		−	0.102702i
$281$	107.927			0.384082			0.192041	−	0.981387i	$-0.438489\pi$
$281$	107.927			0.384082			0.192041	+	0.981387i	$0.438489\pi$
$282$	−158.692			−0.562738
$283$		−	259.666i		−	0.917549i	−0.888553	−	0.458774i	$-0.848289\pi$
$283$		−	259.666i		−	0.917549i	0.888553	−	0.458774i	$-0.151711\pi$
$284$	−36.2310			−0.127574
$285$	81.1757			0.284827
$286$		−	25.5334i		−	0.0892778i
$287$	−137.259			−0.478254
$288$			16.9706i			0.0589256i
$289$	322.209			1.11491
$290$			118.024i			0.406981i
$291$			118.601i			0.407564i
$292$			199.847i			0.684407i
$293$	−30.4980			−0.104089			−0.0520443	−	0.998645i	$-0.516574\pi$
$293$	−30.4980			−0.104089			−0.0520443	+	0.998645i	$0.516574\pi$
$294$		−	85.8284i		−	0.291933i
$295$	−31.6351	−	157.394i	−0.107238	−	0.533540i
$296$	69.6168			0.235192
$297$			73.5099i			0.247508i
$298$	220.680			0.740538
$299$	−5.25061			−0.0175606
$300$	60.9539			0.203180
$301$			87.6660i			0.291249i
$302$	76.0553			0.251839
$303$			316.375i			1.04414i
$304$	−68.8952			−0.226629
$305$		−	68.6856i		−	0.225199i
$306$		−	104.889i		−	0.342775i
$307$	−266.924			−0.869461			−0.434730	−	0.900561i	$-0.643156\pi$
$307$	−266.924			−0.869461			−0.434730	+	0.900561i	$0.643156\pi$
$308$			105.718i			0.343240i
$309$			81.3876i			0.263390i
$310$	−45.7879			−0.147703
$311$	−194.246			−0.624585			−0.312292	−	0.949986i	$-0.601097\pi$
$311$	−194.246			−0.624585			−0.312292	+	0.949986i	$0.601097\pi$
$312$	6.25225			0.0200392
$313$			400.329i			1.27901i	0.768788	+	0.639503i	$0.220860\pi$
$313$			400.329i			1.27901i	−0.768788	+	0.639503i	$0.779140\pi$
$314$	−158.555			−0.504954
$315$	30.5008			0.0968280
$316$	68.3946			0.216439
$317$	−418.689			−1.32079			−0.660393	−	0.750920i	$-0.729610\pi$
$317$	−418.689			−1.32079			−0.660393	+	0.750920i	$0.729610\pi$
$318$			190.186i			0.598070i
$319$		−	433.895i		−	1.36017i
$320$	21.7684			0.0680262
$321$	253.003			0.788171
$322$	21.7394			0.0675138
$323$	425.818			1.31832
$324$	−18.0000			−0.0555556
$325$		−	22.4565i		−	0.0690969i
$326$			231.122i			0.708964i
$327$			92.3687i			0.282473i
$328$		−	103.904i		−	0.316780i
$329$		−	242.066i		−	0.735763i
$330$	94.2923			0.285734
$331$	−9.63193			−0.0290995			−0.0145497	−	0.999894i	$-0.504631\pi$
$331$	−9.63193			−0.0290995			−0.0145497	+	0.999894i	$0.504631\pi$
$332$		−	96.7488i		−	0.291412i
$333$			73.8398i			0.221741i
$334$		−	146.345i		−	0.438159i
$335$			198.426i			0.592315i
$336$	−25.8866			−0.0770434
$337$		−	147.914i		−	0.438914i	−0.975622	−	0.219457i	$-0.929571\pi$
$337$		−	147.914i		−	0.438914i	0.975622	−	0.219457i	$-0.0704286\pi$
$338$			236.699i			0.700292i
$339$			168.822i			0.498001i
$340$	−134.543			−0.395715
$341$	168.331			0.493639
$342$		−	73.0744i		−	0.213668i
$343$	314.005			0.915466
$344$	−66.3625			−0.192914
$345$		−	19.3899i		−	0.0562027i
$346$	−435.566			−1.25886
$347$			392.318i			1.13060i	0.824885	+	0.565300i	$0.191240\pi$
$347$			392.318i			1.13060i	−0.824885	+	0.565300i	$0.808760\pi$
$348$	106.246			0.305304
$349$		−	442.305i		−	1.26735i	−0.773600	−	0.633674i	$-0.781546\pi$
$349$		−	442.305i		−	1.26735i	0.773600	−	0.633674i	$-0.218454\pi$
$350$			92.9780i			0.265651i
$351$			6.63151i			0.0188932i
$352$	−80.0275			−0.227351
$353$			538.145i			1.52449i	0.647289	+	0.762245i	$0.275903\pi$
$353$			538.145i			1.52449i	−0.647289	+	0.762245i	$0.724097\pi$
$354$	−141.686	+	28.4780i	−0.400244	+	0.0804462i
$355$	−49.2932			−0.138854
$356$			103.735i			0.291391i
$357$	159.996			0.448168
$358$	209.326			0.584711
$359$	−416.732			−1.16081			−0.580406	−	0.814327i	$-0.697106\pi$
$359$	−416.732			−1.16081			−0.580406	+	0.814327i	$0.697106\pi$
$360$			23.0889i			0.0641358i
$361$	−64.3404			−0.178228
$362$		−	385.532i		−	1.06500i
$363$	−137.070			−0.377603
$364$			9.53706i			0.0262007i
$365$			271.896i			0.744922i
$366$	−61.8308			−0.168937
$367$		−	45.4815i		−	0.123928i	−0.998078	−	0.0619639i	$-0.980264\pi$
$367$		−	45.4815i		−	0.123928i	0.998078	−	0.0619639i	$-0.0197364\pi$
$368$			16.4566i			0.0447189i
$369$	110.207			0.298663
$370$	94.7154			0.255988
$371$	−290.107			−0.781959
$372$			41.2183i			0.110802i
$373$	137.361			0.368259			0.184130	−	0.982902i	$-0.441053\pi$
$373$	137.361			0.368259			0.184130	+	0.982902i	$0.441053\pi$
$374$	494.623			1.32252
$375$	200.754			0.535345
$376$	183.242			0.487346
$377$		−	39.1427i		−	0.103827i
$378$		−	27.4569i		−	0.0726372i
$379$	448.138			1.18242			0.591212	−	0.806516i	$-0.298650\pi$
$379$	448.138			1.18242			0.591212	+	0.806516i	$0.298650\pi$
$380$	−93.7337			−0.246668
$381$	−15.3772			−0.0403600
$382$	7.81625			0.0204614
$383$	619.017			1.61623			0.808116	−	0.589024i	$-0.200488\pi$
$383$	619.017			1.61623			0.808116	+	0.589024i	$0.200488\pi$
$384$		−	19.5959i		−	0.0510310i
$385$			143.832i			0.373589i
$386$		−	451.299i		−	1.16917i
$387$		−	70.3880i		−	0.181881i
$388$		−	136.949i		−	0.352961i
$389$	−183.899			−0.472749			−0.236375	−	0.971662i	$-0.575959\pi$
$389$	−183.899			−0.472749			−0.236375	+	0.971662i	$0.575959\pi$
$390$	8.50633			0.0218111
$391$		−	101.713i		−	0.260134i
$392$			99.1060i			0.252822i
$393$		−	139.025i		−	0.353754i
$394$		−	309.291i		−	0.785002i
$395$	93.0526			0.235576
$396$		−	84.8819i		−	0.214348i
$397$			645.394i			1.62568i	0.582489	+	0.812839i	$0.302079\pi$
$397$			645.394i			1.62568i	−0.582489	+	0.812839i	$0.697921\pi$
$398$		−	92.9748i		−	0.233605i
$399$	111.466			0.279364
$400$	−70.3836			−0.175959
$401$		−	210.707i		−	0.525454i	−0.964870	−	0.262727i	$-0.915378\pi$
$401$		−	210.707i		−	0.525454i	0.964870	−	0.262727i	$-0.0846218\pi$
$402$	178.623			0.444335
$403$	15.1855			0.0376812
$404$		−	365.318i		−	0.904252i
$405$	−24.4894			−0.0604678
$406$			162.065i			0.399175i
$407$	−348.204			−0.855537
$408$			121.116i			0.296852i
$409$			472.791i			1.15597i	0.816048	+	0.577984i	$0.196160\pi$
$409$			472.791i			1.15597i	−0.816048	+	0.577984i	$0.803840\pi$
$410$		−	141.364i		−	0.344790i
$411$	100.230			0.243868
$412$		−	93.9782i		−	0.228103i
$413$	−43.4397	−	216.126i	−0.105181	−	0.523306i
$414$	−17.4548			−0.0421614
$415$		−	131.629i		−	0.317179i
$416$	−7.21947			−0.0173545
$417$	−67.0182			−0.160715
$418$	344.594			0.824389
$419$		−	52.1580i		−	0.124482i	−0.998061	−	0.0622410i	$-0.980175\pi$
$419$		−	52.1580i		−	0.124482i	0.998061	−	0.0622410i	$-0.0198247\pi$
$420$	−35.2193			−0.0838555
$421$		−	498.624i		−	1.18438i	−0.805798	−	0.592190i	$-0.798263\pi$
$421$		−	498.624i		−	1.18438i	0.805798	−	0.592190i	$-0.201737\pi$
$422$	432.026			1.02376
$423$			194.357i			0.459474i
$424$		−	219.608i		−	0.517944i
$425$	435.017			1.02357
$426$			44.3737i			0.104164i
$427$		−	94.3155i		−	0.220879i
$428$	−292.142			−0.682576
$429$	−31.2720			−0.0728950
$430$	−90.2878			−0.209972
$431$			31.5974i			0.0733119i	0.999328	+	0.0366559i	$0.0116706\pi$
$431$			31.5974i			0.0733119i	−0.999328	+	0.0366559i	$0.988329\pi$
$432$	20.7846			0.0481125
$433$	97.2975			0.224705			0.112353	−	0.993668i	$-0.464161\pi$
$433$	97.2975			0.224705			0.112353	+	0.993668i	$0.464161\pi$
$434$	−62.8736			−0.144870
$435$	144.550			0.332298
$436$		−	106.658i		−	0.244629i
$437$		−	70.8612i		−	0.162154i
$438$	244.761			0.558816
$439$	141.413			0.322125			0.161063	−	0.986944i	$-0.448508\pi$
$439$	141.413			0.322125			0.161063	+	0.986944i	$0.448508\pi$
$440$	−108.879			−0.247453
$441$	−105.118			−0.238362
$442$	44.6211			0.100953
$443$			225.411i			0.508828i	0.967095	+	0.254414i	$0.0818826\pi$
$443$			225.411i			0.508828i	−0.967095	+	0.254414i	$0.918117\pi$
$444$		−	85.2628i		−	0.192033i
$445$			141.134i			0.317156i
$446$			57.4170i			0.128738i
$447$		−	270.277i		−	0.604647i
$448$	29.8912			0.0667215
$449$	−246.301			−0.548554			−0.274277	−	0.961651i	$-0.588438\pi$
$449$	−246.301			−0.548554			−0.274277	+	0.961651i	$0.588438\pi$
$450$		−	74.6530i		−	0.165896i
$451$			519.698i			1.15232i
$452$		−	194.939i		−	0.431281i
$453$		−	93.1484i		−	0.205626i
$454$	587.923			1.29498
$455$			12.9754i			0.0285174i
$456$			84.3791i			0.185042i
$457$			628.105i			1.37441i	0.726464	+	0.687204i	$0.241162\pi$
$457$			628.105i			1.37441i	−0.726464	+	0.687204i	$0.758838\pi$
$458$	−333.804			−0.728831
$459$	−128.463			−0.279875
$460$			22.3896i			0.0486730i
$461$	−673.243			−1.46040			−0.730198	−	0.683235i	$-0.760572\pi$
$461$	−673.243			−1.46040			−0.730198	+	0.683235i	$0.760572\pi$
$462$	129.477			0.280254
$463$		−	118.885i		−	0.256770i	−0.991724	−	0.128385i	$-0.959021\pi$
$463$		−	118.885i		−	0.256770i	0.991724	−	0.128385i	$-0.0409794\pi$
$464$	−122.682			−0.264401
$465$			56.0785i			0.120599i
$466$	−164.338			−0.352657
$467$		−	131.921i		−	0.282487i	−0.989975	−	0.141243i	$-0.954890\pi$
$467$		−	131.921i		−	0.282487i	0.989975	−	0.141243i	$-0.0451100\pi$
$468$		−	7.65741i		−	0.0163620i
$469$			272.468i			0.580955i
$470$	249.305			0.530437
$471$			194.190i			0.412293i
$472$	163.605	−	32.8835i	0.346621	−	0.0696685i
$473$	331.926			0.701747
$474$		−	83.7660i		−	0.176721i
$475$	303.068			0.638038
$476$	−184.748			−0.388125
$477$	232.930			0.488322
$478$		−	472.174i		−	0.987812i
$479$	377.534			0.788172			0.394086	−	0.919074i	$-0.371061\pi$
$479$	377.534			0.788172			0.394086	+	0.919074i	$0.371061\pi$
$480$		−	26.6607i		−	0.0555432i
$481$	−31.4123			−0.0653062
$482$			280.935i			0.582852i
$483$		−	26.6253i		−	0.0551248i
$484$	158.275			0.327014
$485$		−	186.322i		−	0.384169i
$486$			22.0454i			0.0453609i
$487$	16.2787			0.0334266			0.0167133	−	0.999860i	$-0.494680\pi$
$487$	16.2787			0.0334266			0.0167133	+	0.999860i	$0.494680\pi$
$488$	71.3960			0.146303
$489$	283.066			0.578867
$490$			134.836i			0.275176i
$491$	300.838			0.612706			0.306353	−	0.951918i	$-0.400891\pi$
$491$	300.838			0.612706			0.306353	+	0.951918i	$0.400891\pi$
$492$	−127.256			−0.258650
$493$	758.255			1.53804
$494$	31.0867			0.0629285
$495$		−	115.484i		−	0.233301i
$496$		−	47.5948i		−	0.0959573i
$497$	−67.6868			−0.136191
$498$	−118.493			−0.237937
$499$	−716.300			−1.43547			−0.717736	−	0.696316i	$-0.754821\pi$
$499$	−716.300			−1.43547			−0.717736	+	0.696316i	$0.754821\pi$
$500$	−231.811			−0.463622
$501$	−179.235			−0.357755
$502$		−	258.534i		−	0.515008i
$503$			279.450i			0.555568i	0.960644	+	0.277784i	$0.0895999\pi$
$503$			279.450i			0.555568i	−0.960644	+	0.277784i	$0.910400\pi$
$504$			31.7044i			0.0629056i
$505$		−	497.024i		−	0.984206i
$506$		−	82.3111i		−	0.162670i
$507$	289.895			0.571786
$508$	17.7560			0.0349528
$509$		−	236.261i		−	0.464168i	−0.972696	−	0.232084i	$-0.925446\pi$
$509$		−	236.261i		−	0.464168i	0.972696	−	0.232084i	$-0.0745544\pi$
$510$			164.781i			0.323100i
$511$			373.354i			0.730634i
$512$			22.6274i			0.0441942i
$513$	−89.4975			−0.174459
$514$		−	260.162i		−	0.506152i
$515$		−	127.860i		−	0.248271i
$516$			81.2771i			0.157514i
$517$	−916.524			−1.77277
$518$	130.058			0.251078
$519$			533.457i			1.02786i
$520$	−9.82227			−0.0188890
$521$	−232.825			−0.446881			−0.223440	−	0.974718i	$-0.571729\pi$
$521$	−232.825			−0.446881			−0.223440	+	0.974718i	$0.571729\pi$
$522$		−	130.124i		−	0.249279i
$523$	378.759			0.724204			0.362102	−	0.932139i	$-0.382059\pi$
$523$	378.759			0.724204			0.362102	+	0.932139i	$0.382059\pi$
$524$			160.533i			0.306360i
$525$	113.874			0.216903
$526$		−	318.528i		−	0.605566i
$527$			294.167i			0.558192i
$528$			98.0132i			0.185631i
$529$	512.074			0.968003
$530$		−	298.783i		−	0.563741i
$531$	34.8782	+	173.530i	0.0656840	+	0.326798i
$532$	−128.710			−0.241937
$533$			46.8832i			0.0879610i
$534$	127.049			0.237920
$535$	−397.467			−0.742929
$536$	−206.256			−0.384806
$537$		−	256.371i		−	0.477414i
$538$	−506.173			−0.940843
$539$		−	495.700i		−	0.919667i
$540$	28.2780			0.0523666
$541$			238.647i			0.441122i	0.975373	+	0.220561i	$0.0707887\pi$
$541$			238.647i			0.441122i	−0.975373	+	0.220561i	$0.929211\pi$
$542$			540.086i			0.996469i
$543$	−472.178			−0.869573
$544$		−	139.852i		−	0.257082i
$545$		−	145.111i		−	0.266259i
$546$	11.6805			0.0213928
$547$	260.803			0.476788			0.238394	−	0.971169i	$-0.423379\pi$
$547$	260.803			0.476788			0.238394	+	0.971169i	$0.423379\pi$
$548$	−115.735			−0.211196
$549$			75.7269i			0.137936i
$550$	352.039			0.640070
$551$	528.262			0.958734
$552$	20.1551			0.0365129
$553$	127.775			0.231058
$554$			173.801i			0.313719i
$555$		−	116.002i		−	0.209013i
$556$	77.3859			0.139183
$557$	535.279			0.961004			0.480502	−	0.876994i	$-0.340455\pi$
$557$	535.279			0.961004			0.480502	+	0.876994i	$0.340455\pi$
$558$	50.4819			0.0904694
$559$	29.9439			0.0535668
$560$	40.6678			0.0726210
$561$		−	605.787i		−	1.07983i
$562$			152.632i			0.271587i
$563$		−	454.775i		−	0.807770i	−0.914810	−	0.403885i	$-0.867660\pi$
$563$		−	454.775i		−	0.807770i	0.914810	−	0.403885i	$-0.132340\pi$
$564$		−	224.425i		−	0.397916i
$565$		−	265.220i		−	0.469415i
$566$	367.224			0.648805
$567$	−33.6276			−0.0593080
$568$		−	51.2384i		−	0.0902084i
$569$			565.449i			0.993760i	0.867819	+	0.496880i	$0.165521\pi$
$569$			565.449i			0.993760i	−0.867819	+	0.496880i	$0.834479\pi$
$570$			114.800i			0.201403i
$571$			247.022i			0.432614i	0.976325	+	0.216307i	$0.0694011\pi$
$571$			247.022i			0.432614i	−0.976325	+	0.216307i	$0.930599\pi$
$572$	36.1097			0.0631289
$573$		−	9.57291i		−	0.0167067i
$574$		−	194.113i		−	0.338177i
$575$		−	72.3920i		−	0.125899i
$576$	−24.0000			−0.0416667
$577$	−492.619			−0.853759			−0.426880	−	0.904308i	$-0.640387\pi$
$577$	−492.619			−0.853759			−0.426880	+	0.904308i	$0.640387\pi$
$578$			455.673i			0.788361i
$579$	−552.726			−0.954621
$580$	−166.912			−0.287779
$581$		−	180.746i		−	0.311095i
$582$	−167.727			−0.288191
$583$			1098.42i			1.88408i
$584$	−282.626			−0.483949
$585$		−	10.4181i		−	0.0178087i
$586$		−	43.1306i		−	0.0736018i
$587$			411.107i			0.700353i	0.936684	+	0.350177i	$0.113878\pi$
$587$			411.107i			0.700353i	−0.936684	+	0.350177i	$0.886122\pi$
$588$	121.380			0.206428
$589$			204.941i			0.347947i
$590$	222.589	−	44.7388i	0.377269	−	0.0758285i
$591$	−378.802			−0.640951
$592$			98.4530i			0.166306i
$593$	−827.945			−1.39620			−0.698098	−	0.716002i	$-0.745970\pi$
$593$	−827.945			−1.39620			−0.698098	+	0.716002i	$0.745970\pi$
$594$	−103.959			−0.175015
$595$	−251.354			−0.422443
$596$			312.089i			0.523640i
$597$	−113.870			−0.190738
$598$		−	7.42548i		−	0.0124172i
$599$	−654.327			−1.09237			−0.546183	−	0.837666i	$-0.683920\pi$
$599$	−654.327			−1.09237			−0.546183	+	0.837666i	$0.683920\pi$
$600$			86.2019i			0.143670i
$601$			16.9123i			0.0281403i	0.999901	+	0.0140702i	$0.00447882\pi$
$601$			16.9123i			0.0281403i	−0.999901	+	0.0140702i	$0.995521\pi$
$602$	−123.978			−0.205944
$603$		−	218.767i		−	0.362798i
$604$			107.558i			0.178077i
$605$	215.337			0.355928
$606$	−447.421			−0.738319
$607$	−232.346			−0.382778			−0.191389	−	0.981514i	$-0.561299\pi$
$607$	−232.346			−0.382778			−0.191389	+	0.981514i	$0.561299\pi$
$608$		−	97.4326i		−	0.160251i
$609$	198.488			0.325925
$610$	97.1361			0.159239
$611$	−82.6819			−0.135322
$612$	148.336			0.242379
$613$			1159.80i			1.89201i	0.324158	+	0.946003i	$0.394919\pi$
$613$			1159.80i			1.89201i	−0.324158	+	0.946003i	$0.605081\pi$
$614$		−	377.488i		−	0.614802i
$615$	−173.135			−0.281520
$616$	−149.507			−0.242707
$617$	−648.182			−1.05054			−0.525269	−	0.850936i	$-0.676035\pi$
$617$	−648.182			−1.05054			−0.525269	+	0.850936i	$0.676035\pi$
$618$	−115.099			−0.186245
$619$	−32.0778			−0.0518220			−0.0259110	−	0.999664i	$-0.508249\pi$
$619$	−32.0778			−0.0518220			−0.0259110	+	0.999664i	$0.508249\pi$
$620$		−	64.7539i		−	0.104442i
$621$			21.3777i			0.0344247i
$622$		−	274.705i		−	0.441648i
$623$			193.798i			0.311073i
$624$			8.84201i			0.0141699i
$625$	124.513			0.199220
$626$	−566.151			−0.904394
$627$		−	422.040i		−	0.673110i
$628$		−	224.231i		−	0.357056i
$629$		−	608.505i		−	0.967416i
$630$			43.1347i			0.0684678i
$631$	−842.187			−1.33469			−0.667343	−	0.744751i	$-0.732568\pi$
$631$	−842.187			−1.33469			−0.667343	+	0.744751i	$0.732568\pi$
$632$			96.7246i			0.153045i
$633$		−	529.121i		−	0.835894i
$634$		−	592.116i		−	0.933937i
$635$	24.1575			0.0380433
$636$	−268.964			−0.422900
$637$		−	44.7183i		−	0.0702015i
$638$	613.620			0.961787
$639$	54.3465			0.0850493
$640$			30.7852i			0.0481018i
$641$	−128.167			−0.199949			−0.0999743	−	0.994990i	$-0.531876\pi$
$641$	−128.167			−0.199949			−0.0999743	+	0.994990i	$0.531876\pi$
$642$			357.800i			0.557321i
$643$	−1027.96			−1.59870			−0.799348	−	0.600868i	$-0.794822\pi$
$643$	−1027.96			−1.59870			−0.799348	+	0.600868i	$0.794822\pi$
$644$			30.7442i			0.0477395i
$645$			110.579i			0.171441i
$646$			602.198i			0.932195i
$647$	360.963			0.557902			0.278951	−	0.960305i	$-0.410013\pi$
$647$	360.963			0.557902			0.278951	+	0.960305i	$0.410013\pi$
$648$		−	25.4558i		−	0.0392837i
$649$	−818.307	+	164.474i	−1.26087	+	0.253427i
$650$	31.7583			0.0488589
$651$			77.0042i			0.118286i
$652$	−326.856			−0.501313
$653$	672.237			1.02946			0.514730	−	0.857352i	$-0.327892\pi$
$653$	672.237			1.02946			0.514730	+	0.857352i	$0.327892\pi$
$654$	−130.629			−0.199739
$655$			218.409i			0.333448i
$656$	146.942			0.223997
$657$		−	299.770i		−	0.456271i
$658$	342.333			0.520263
$659$			385.247i			0.584593i	0.956328	+	0.292296i	$0.0944194\pi$
$659$			385.247i			0.584593i	−0.956328	+	0.292296i	$0.905581\pi$
$660$			133.349i			0.202045i
$661$	−900.213			−1.36190			−0.680948	−	0.732332i	$-0.738432\pi$
$661$	−900.213			−1.36190			−0.680948	+	0.732332i	$0.738432\pi$
$662$		−	13.6216i		−	0.0205765i
$663$		−	54.6495i		−	0.0824276i
$664$	136.823			0.206059
$665$	−175.113			−0.263329
$666$	−104.425			−0.156795
$667$		−	126.183i		−	0.189179i
$668$	206.963			0.309825
$669$	70.3212			0.105114
$670$	−280.616			−0.418830
$671$	−357.103			−0.532195
$672$		−	36.6091i		−	0.0544779i
$673$			80.4284i			0.119507i	0.998213	+	0.0597536i	$0.0190315\pi$
$673$			80.4284i			0.119507i	−0.998213	+	0.0597536i	$0.980968\pi$
$674$	209.182			0.310359
$675$	−91.4309			−0.135453
$676$	−334.742			−0.495181
$677$	1262.00			1.86411			0.932054	−	0.362319i	$-0.118015\pi$
$677$	1262.00			1.86411			0.932054	+	0.362319i	$0.118015\pi$
$678$	−238.751			−0.352140
$679$		−	255.848i		−	0.376801i
$680$		−	190.273i		−	0.279813i
$681$		−	720.056i		−	1.05735i
$682$			238.056i			0.349055i
$683$		−	1079.45i		−	1.58045i	−0.612817	−	0.790225i	$-0.709964\pi$
$683$		−	1079.45i		−	1.58045i	0.612817	−	0.790225i	$-0.290036\pi$
$684$	103.343			0.151086
$685$	−157.461			−0.229869
$686$			444.070i			0.647332i
$687$			408.825i			0.595088i
$688$		−	93.8507i		−	0.136411i
$689$			99.0910i			0.143819i
$690$	27.4215			0.0397413
$691$			662.767i			0.959141i	0.877503	+	0.479571i	$0.159208\pi$
$691$			662.767i			0.959141i	−0.877503	+	0.479571i	$0.840792\pi$
$692$		−	615.984i		−	0.890150i
$693$		−	158.577i		−	0.228826i
$694$	−554.822			−0.799455
$695$	105.285			0.151490
$696$			150.254i			0.215882i
$697$	−908.201			−1.30301
$698$	625.513			0.896151
$699$			201.273i			0.287944i
$700$	−131.491			−0.187844
$701$		−	532.634i		−	0.759820i	−0.925023	−	0.379910i	$-0.875955\pi$
$701$		−	532.634i		−	0.759820i	0.925023	−	0.379910i	$-0.124045\pi$
$702$	−9.37837			−0.0133595
$703$		−	423.934i		−	0.603036i
$704$		−	113.176i		−	0.160761i
$705$		−	305.335i		−	0.433100i
$706$	−761.052			−1.07798
$707$		−	682.488i		−	0.965329i
$708$	−40.2739	−	200.375i	−0.0568841	−	0.283015i
$709$	812.591			1.14611			0.573054	−	0.819518i	$-0.305758\pi$
$709$	812.591			1.14611			0.573054	+	0.819518i	$0.305758\pi$
$710$		−	69.7111i		−	0.0981846i
$711$	−102.592			−0.144292
$712$	−146.704			−0.206045
$713$	48.9530			0.0686577
$714$			226.269i			0.316903i
$715$	49.1282			0.0687108
$716$			296.032i			0.413453i
$717$	−578.293			−0.806545
$718$		−	589.347i		−	0.820818i
$719$			1091.09i			1.51751i	0.651374	+	0.758756i	$0.274193\pi$
$719$			1091.09i			1.51751i	−0.651374	+	0.758756i	$0.725807\pi$
$720$	−32.6526			−0.0453508
$721$		−	175.570i		−	0.243510i
$722$		−	90.9911i		−	0.126026i
$723$	344.073			0.475896
$724$	545.224			0.753072
$725$	539.674			0.744378
$726$		−	193.846i		−	0.267006i
$727$	126.444			0.173926			0.0869632	−	0.996212i	$-0.472284\pi$
$727$	126.444			0.173926			0.0869632	+	0.996212i	$0.472284\pi$
$728$	−13.4874			−0.0185267
$729$	27.0000			0.0370370
$730$	−384.520			−0.526739
$731$			580.059i			0.793515i
$732$		−	87.4419i		−	0.119456i
$733$	−299.215			−0.408206			−0.204103	−	0.978949i	$-0.565428\pi$
$733$	−299.215			−0.408206			−0.204103	+	0.978949i	$0.565428\pi$
$734$	64.3205			0.0876301
$735$	165.140			0.224680
$736$	−23.2731			−0.0316211
$737$	1031.63			1.39977
$738$			155.856i			0.211187i
$739$		−	922.111i		−	1.24778i	−0.781511	−	0.623891i	$-0.785551\pi$
$739$		−	922.111i		−	1.24778i	0.781511	−	0.623891i	$-0.214449\pi$
$740$			133.948i			0.181011i
$741$		−	38.0733i		−	0.0513809i
$742$		−	410.273i		−	0.552928i
$743$	1446.15			1.94637			0.973184	−	0.230029i	$-0.0738821\pi$
$743$	1446.15			1.94637			0.973184	+	0.230029i	$0.0738821\pi$
$744$	−58.2915			−0.0783488
$745$			424.605i			0.569940i
$746$			194.257i			0.260399i
$747$			145.123i			0.194275i
$748$			699.502i			0.935163i
$749$	−545.781			−0.728680
$750$			283.909i			0.378546i
$751$		−	569.663i		−	0.758540i	−0.925286	−	0.379270i	$-0.876175\pi$
$751$		−	569.663i		−	0.758540i	0.925286	−	0.379270i	$-0.123825\pi$
$752$			259.143i			0.344605i
$753$	−316.638			−0.420502
$754$	55.3562			0.0734166
$755$			146.336i			0.193822i
$756$	38.8299			0.0513622
$757$	1094.19			1.44542			0.722712	−	0.691149i	$-0.242895\pi$
$757$	1094.19			1.44542			0.722712	+	0.691149i	$0.242895\pi$
$758$			633.764i			0.836100i
$759$	−100.810			−0.132820
$760$		−	132.559i		−	0.174420i
$761$	578.212			0.759806			0.379903	−	0.925026i	$-0.375957\pi$
$761$	578.212			0.759806			0.379903	+	0.925026i	$0.375957\pi$
$762$		−	21.7466i		−	0.0285388i
$763$		−	199.259i		−	0.261152i
$764$			11.0538i			0.0144684i
$765$	201.815			0.263810
$766$			875.422i			1.14285i
$767$	−73.8215	+	14.8376i	−0.0962470	+	0.0193450i
$768$	27.7128			0.0360844
$769$		−	240.005i		−	0.312101i	−0.987749	−	0.156050i	$-0.950124\pi$
$769$		−	240.005i		−	0.312101i	0.987749	−	0.156050i	$-0.0498762\pi$
$770$	−203.409			−0.264167
$771$	−318.632			−0.413271
$772$	638.233			0.826726
$773$			216.612i			0.280223i	0.990136	+	0.140112i	$0.0447461\pi$
$773$			216.612i			0.280223i	−0.990136	+	0.140112i	$0.955254\pi$
$774$	99.5437			0.128609
$775$			209.368i			0.270153i
$776$	193.675			0.249581
$777$		−	159.288i		−	0.205004i
$778$		−	260.073i		−	0.334284i
$779$	−632.726			−0.812229
$780$			12.0298i			0.0154228i
$781$			256.280i			0.328143i
$782$	143.843			0.183943
$783$	−159.368			−0.203536
$784$	−140.157			−0.178772
$785$		−	305.072i		−	0.388627i
$786$	196.611			0.250142
$787$	497.030			0.631550			0.315775	−	0.948834i	$-0.397736\pi$
$787$	497.030			0.631550			0.315775	+	0.948834i	$0.397736\pi$
$788$	437.403			0.555080
$789$	−390.115			−0.494442
$790$			131.596i			0.166577i
$791$		−	364.186i		−	0.460412i
$792$	120.041			0.151567
$793$	−32.2151			−0.0406243
$794$	−912.725			−1.14953
$795$	−365.932			−0.460292
$796$	131.486			0.165184
$797$		−	989.594i		−	1.24165i	−0.783950	−	0.620824i	$-0.786798\pi$
$797$		−	989.594i		−	1.24165i	0.783950	−	0.620824i	$-0.213202\pi$
$798$			157.637i			0.197540i
$799$		−	1601.68i		−	2.00460i
$800$		−	99.5374i		−	0.124422i
$801$		−	155.603i		−	0.194261i
$802$	297.985			0.371552
$803$	1413.62			1.76042
$804$			252.611i			0.314193i
$805$			41.8283i			0.0519606i
$806$			21.4756i			0.0266446i
$807$			619.933i			0.768195i
$808$	516.638			0.639403
$809$			520.741i			0.643685i	0.946793	+	0.321842i	$0.104302\pi$
$809$			520.741i			0.643685i	−0.946793	+	0.321842i	$0.895698\pi$
$810$		−	34.6333i		−	0.0427572i
$811$		−	1471.85i		−	1.81486i	−0.420204	−	0.907430i	$-0.638042\pi$
$811$		−	1471.85i		−	1.81486i	0.420204	−	0.907430i	$-0.361958\pi$
$812$	−229.195			−0.282259
$813$	661.468			0.813614
$814$		−	492.434i		−	0.604956i
$815$	−444.696			−0.545639
$816$	−171.284			−0.209906
$817$			404.117i			0.494635i
$818$	−668.627			−0.817392
$819$		−	14.3056i		−	0.0174671i
$820$	199.919			0.243803
$821$		−	1355.73i		−	1.65131i	−0.564172	−	0.825657i	$-0.690805\pi$
$821$		−	1355.73i		−	1.65131i	0.564172	−	0.825657i	$-0.309195\pi$
$822$			141.746i			0.172440i
$823$			1383.36i			1.68088i	0.541904	+	0.840440i	$0.317704\pi$
$823$			1383.36i			1.68088i	−0.541904	+	0.840440i	$0.682296\pi$
$824$	132.905			0.161293
$825$		−	431.157i		−	0.522615i
$826$	305.648	−	61.4331i	0.370034	−	0.0743742i
$827$	111.274			0.134551			0.0672754	−	0.997734i	$-0.478569\pi$
$827$	111.274			0.134551			0.0672754	+	0.997734i	$0.478569\pi$
$828$		−	24.6849i		−	0.0298126i
$829$	142.082			0.171389			0.0856946	−	0.996321i	$-0.472689\pi$
$829$	142.082			0.171389			0.0856946	+	0.996321i	$0.472689\pi$
$830$	186.152			0.224279
$831$	212.861			0.256151
$832$		−	10.2099i		−	0.0122715i
$833$	866.264			1.03993
$834$		−	94.7780i		−	0.113643i
$835$	281.578			0.337220
$836$			487.330i			0.582931i
$837$		−	61.8275i		−	0.0738680i
$838$	73.7625			0.0880221
$839$			698.475i			0.832509i	0.909248	+	0.416255i	$0.136657\pi$
$839$			698.475i			0.832509i	−0.909248	+	0.416255i	$0.863343\pi$
$840$		−	49.8076i		−	0.0592948i
$841$	99.6779			0.118523
$842$	705.161			0.837483
$843$	186.935			0.221750
$844$			610.976i			0.723906i
$845$	−455.425			−0.538965
$846$	−274.863			−0.324897
$847$	295.689			0.349102
$848$	310.573			0.366242
$849$		−	449.755i		−	0.529747i
$850$			615.207i			0.723773i
$851$	−101.262			−0.118992
$852$	−62.7539			−0.0736548
$853$	553.971			0.649438			0.324719	−	0.945811i	$-0.394730\pi$
$853$	553.971			0.649438			0.324719	+	0.945811i	$0.394730\pi$
$854$	133.382			0.156185
$855$	140.601			0.164445
$856$		−	413.152i		−	0.482654i
$857$		−	1014.46i		−	1.18374i	−0.806034	−	0.591869i	$-0.798390\pi$
$857$		−	1014.46i		−	1.18374i	0.806034	−	0.591869i	$-0.201610\pi$
$858$		−	44.2252i		−	0.0515446i
$859$		−	342.527i		−	0.398751i	−0.979923	−	0.199375i	$-0.936109\pi$
$859$		−	342.527i		−	0.398751i	0.979923	−	0.199375i	$-0.0638913\pi$
$860$		−	127.686i		−	0.148472i
$861$	−237.739			−0.276120
$862$	−44.6855			−0.0518393
$863$			1174.93i			1.36144i	0.732542	+	0.680722i	$0.238334\pi$
$863$			1174.93i			1.36144i	−0.732542	+	0.680722i	$0.761666\pi$
$864$			29.3939i			0.0340207i
$865$		−	838.061i		−	0.968856i
$866$			137.599i			0.158891i
$867$	558.083			0.643694
$868$		−	88.9167i		−	0.102439i
$869$		−	483.789i		−	0.556719i
$870$			204.424i			0.234970i
$871$	93.0661			0.106850
$872$	150.837			0.172979
$873$			205.423i			0.235307i
$874$	100.213			0.114660
$875$	−433.070			−0.494937
$876$			346.145i			0.395142i
$877$	−520.131			−0.593079			−0.296540	−	0.955021i	$-0.595833\pi$
$877$	−520.131			−0.593079			−0.296540	+	0.955021i	$0.595833\pi$
$878$			199.988i			0.227777i
$879$	−52.8240			−0.0600956
$880$		−	153.979i		−	0.174976i
$881$			542.355i			0.615613i	0.951449	+	0.307806i	$0.0995949\pi$
$881$			542.355i			0.615613i	−0.951449	+	0.307806i	$0.900405\pi$
$882$		−	148.659i		−	0.168548i
$883$	1315.76			1.49010			0.745051	−	0.667007i	$-0.232425\pi$
$883$	1315.76			1.49010			0.745051	+	0.667007i	$0.232425\pi$
$884$			63.1038i			0.0713844i
$885$	−54.7937	−	272.615i	−0.0619137	−	0.308039i
$886$	−318.779			−0.359796
$887$			1691.36i			1.90683i	0.301661	+	0.953415i	$0.402459\pi$
$887$			1691.36i			1.90683i	−0.301661	+	0.953415i	$0.597541\pi$
$888$	120.580			0.135788
$889$	33.1718			0.0373137
$890$	−199.594			−0.224263
$891$			127.323i			0.142899i
$892$	−81.1999			−0.0910313
$893$		−	1115.86i		−	1.24956i
$894$	382.230			0.427550
$895$			402.759i			0.450010i
$896$			42.2726i			0.0471792i
$897$	−9.09432			−0.0101386
$898$		−	348.322i		−	0.387886i
$899$			364.939i			0.405939i
$900$	105.575			0.117306
$901$	−1919.55			−2.13046
$902$	−734.964			−0.814816
$903$			151.842i			0.168153i
$904$	275.686			0.304962
$905$	741.791			0.819658
$906$	131.732			0.145399
$907$	−89.6888			−0.0988851			−0.0494426	−	0.998777i	$-0.515744\pi$
$907$	−89.6888			−0.0988851			−0.0494426	+	0.998777i	$0.515744\pi$
$908$			831.449i			0.915692i
$909$			547.977i			0.602835i
$910$	−18.3500			−0.0201648
$911$	−178.559			−0.196003			−0.0980014	−	0.995186i	$-0.531245\pi$
$911$	−178.559			−0.196003			−0.0980014	+	0.995186i	$0.531245\pi$
$912$	−119.330			−0.130844
$913$	−684.352			−0.749564
$914$	−888.274			−0.971854
$915$		−	118.967i		−	0.130018i
$916$		−	472.071i		−	0.515361i
$917$			299.907i			0.327053i
$918$		−	181.674i		−	0.197902i
$919$			1203.13i			1.30918i	0.755986	+	0.654588i	$0.227158\pi$
$919$			1203.13i			1.30918i	−0.755986	+	0.654588i	$0.772842\pi$
$920$	−31.6636			−0.0344170
$921$	−462.327			−0.501983
$922$		−	952.109i		−	1.03266i
$923$			23.1196i			0.0250483i
$924$			183.109i			0.198169i
$925$		−	433.092i		−	0.468208i
$926$	168.128			0.181564
$927$			140.967i			0.152068i
$928$		−	173.498i		−	0.186959i
$929$		−	516.742i		−	0.556234i	−0.960547	−	0.278117i	$-0.910290\pi$
$929$		−	516.742i		−	0.556234i	0.960547	−	0.278117i	$-0.0897104\pi$
$930$	−79.3070			−0.0852764
$931$	603.510			0.648238
$932$		−	232.409i		−	0.249366i
$933$	−336.444			−0.360604
$934$	186.565			0.199748
$935$			951.690i			1.01785i
$936$	10.8292			0.0115697
$937$			1850.03i			1.97442i	0.159414	+	0.987212i	$0.449039\pi$
$937$			1850.03i			1.97442i	−0.159414	+	0.987212i	$0.550961\pi$
$938$	−385.328			−0.410797
$939$			693.390i			0.738435i
$940$			352.571i			0.375075i
$941$		−	609.751i		−	0.647982i	−0.946060	−	0.323991i	$-0.894975\pi$
$941$		−	609.751i		−	0.647982i	0.946060	−	0.323991i	$-0.105025\pi$
$942$	−274.626			−0.291535
$943$			151.135i			0.160271i
$944$	46.5043	+	231.373i	0.0492630	+	0.245098i
$945$	52.8290			0.0559037
$946$			469.414i			0.496210i
$947$	−1215.00			−1.28300			−0.641499	−	0.767124i	$-0.721687\pi$
$947$	−1215.00			−1.28300			−0.641499	+	0.767124i	$0.721687\pi$
$948$	118.463			0.124961
$949$	127.526			0.134379
$950$			428.603i			0.451161i
$951$	−725.191			−0.762556
$952$		−	261.273i		−	0.274446i
$953$	1357.45			1.42440			0.712199	−	0.701977i	$-0.247699\pi$
$953$	1357.45			1.42440			0.712199	+	0.701977i	$0.247699\pi$
$954$			329.412i			0.345296i
$955$			15.0390i			0.0157477i
$956$	667.755			0.698489
$957$		−	751.528i		−	0.785296i
$958$			533.914i			0.557322i
$959$	−216.217			−0.225461
$960$	37.7040			0.0392750
$961$	819.421			0.852675
$962$		−	44.4237i		−	0.0461785i
$963$	438.214			0.455050
$964$	−397.301			−0.412138
$965$	868.332			0.899825
$966$	37.6538			0.0389791
$967$			1615.44i			1.67057i	0.549815	+	0.835286i	$0.314698\pi$
$967$			1615.44i			1.67057i	−0.549815	+	0.835286i	$0.685302\pi$
$968$			223.834i			0.231234i
$969$	737.539			0.761134
$970$	263.499			0.271649
$971$	988.052			1.01756			0.508781	−	0.860896i	$-0.330096\pi$
$971$	988.052			1.01756			0.508781	+	0.860896i	$0.330096\pi$
$972$	−31.1769			−0.0320750
$973$	144.573			0.148584
$974$			23.0216i			0.0236362i
$975$		−	38.8958i		−	0.0398931i
$976$			100.969i			0.103452i
$977$		−	1085.53i		−	1.11109i	−0.831487	−	0.555544i	$-0.812510\pi$
$977$		−	1085.53i		−	1.11109i	0.831487	−	0.555544i	$-0.187490\pi$
$978$			400.316i			0.409321i
$979$	733.771			0.749510
$980$	−190.687			−0.194579
$981$			159.987i			0.163086i
$982$			425.450i			0.433248i
$983$		−	500.148i		−	0.508797i	−0.967099	−	0.254399i	$-0.918122\pi$
$983$		−	500.148i		−	0.508797i	0.967099	−	0.254399i	$-0.0818775\pi$
$984$		−	179.967i		−	0.182893i
$985$	595.098			0.604160
$986$			1072.33i			1.08756i
$987$		−	419.271i		−	0.424793i
$988$			43.9632i			0.0444972i
$989$	96.5288			0.0976024
$990$	163.319			0.164969
$991$		−	1817.55i		−	1.83406i	−0.398817	−	0.917030i	$-0.630579\pi$
$991$		−	1817.55i		−	1.83406i	0.398817	−	0.917030i	$-0.369421\pi$
$992$	67.3092			0.0678520
$993$	−16.6830			−0.0168006
$994$		−	95.7236i		−	0.0963014i
$995$	178.890			0.179789
$996$		−	167.574i		−	0.168247i
$997$	1343.71			1.34775			0.673875	−	0.738845i	$-0.264629\pi$
$997$	1343.71			1.34775			0.673875	+	0.738845i	$0.264629\pi$
$998$		−	1013.00i		−	1.01503i
$999$			127.894i			0.128022i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.3.d.a.235.17	yes	20
3.2	odd	2		1062.3.d.f.235.7		20
59.58	odd	2	inner	354.3.d.a.235.7	✓	20
177.176	even	2		1062.3.d.f.235.17		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.3.d.a.235.7	✓	20	59.58	odd	2	inner
354.3.d.a.235.17	yes	20	1.1	even	1	trivial
1062.3.d.f.235.7		20	3.2	odd	2
1062.3.d.f.235.17		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)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} -2.72105 q^{5} +2.44949i q^{6} -3.73640 q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} -2.72105 q^{5} +2.44949i q^{6} -3.73640 q^{7} -2.82843i q^{8} +3.00000 q^{9} -3.84815i q^{10} +14.1470i q^{11} -3.46410 q^{12} +1.27623i q^{13} -5.28407i q^{14} -4.71300 q^{15} +4.00000 q^{16} -24.7226 q^{17} +4.24264i q^{18} -17.2238 q^{19} +5.44210 q^{20} -6.47164 q^{21} -20.0069 q^{22} +4.11414i q^{23} -4.89898i q^{24} -17.5959 q^{25} -1.80487 q^{26} +5.19615 q^{27} +7.47281 q^{28} -30.6705 q^{29} -6.66518i q^{30} -11.8987i q^{31} +5.65685i q^{32} +24.5033i q^{33} -34.9631i q^{34} +10.1669 q^{35} -6.00000 q^{36} +24.6133i q^{37} -24.3581i q^{38} +2.21050i q^{39} +7.69629i q^{40} +36.7356 q^{41} -9.15229i q^{42} -23.4627i q^{43} -28.2940i q^{44} -8.16315 q^{45} -5.81828 q^{46} +64.7858i q^{47} +6.92820 q^{48} -35.0393 q^{49} -24.8843i q^{50} -42.8209 q^{51} -2.55247i q^{52} +77.6433 q^{53} +7.34847i q^{54} -38.4947i q^{55} +10.5681i q^{56} -29.8325 q^{57} -43.3746i q^{58} +(11.6261 + 57.8432i) q^{59} +9.42599 q^{60} +25.2423i q^{61} +16.8273 q^{62} -11.2092 q^{63} -8.00000 q^{64} -3.47270i q^{65} -34.6529 q^{66} -72.9225i q^{67} +49.4453 q^{68} +7.12591i q^{69} +14.3782i q^{70} +18.1155 q^{71} -8.48528i q^{72} -99.9234i q^{73} -34.8084 q^{74} -30.4770 q^{75} +34.4476 q^{76} -52.8589i q^{77} -3.12612 q^{78} -34.1973 q^{79} -10.8842 q^{80} +9.00000 q^{81} +51.9519i q^{82} +48.3744i q^{83} +12.9433 q^{84} +67.2715 q^{85} +33.1812 q^{86} -53.1228 q^{87} +40.0137 q^{88} -51.8676i q^{89} -11.5444i q^{90} -4.76853i q^{91} -8.22829i q^{92} -20.6092i q^{93} -91.6210 q^{94} +46.8668 q^{95} +9.79796i q^{96} +68.4744i q^{97} -49.5530i q^{98} +42.4410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 40 q^{4} + 8 q^{7} + 60 q^{9}+O(q^{10}) \) 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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