LMFDB - Embedded newform 483.3.f.a.22.46

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,3,Mod(22,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("483.22");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	483.f (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:	$13.1607967686$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			22.46
Character	$\chi$	$=$	483.22
Dual form			483.3.f.a.22.45

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.66398 q^{2} -1.73205 q^{3} +9.42474 q^{4} -6.75938i q^{5} -6.34620 q^{6} -2.64575i q^{7} +19.8761 q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+3.66398 q^{2} -1.73205 q^{3} +9.42474 q^{4} -6.75938i q^{5} -6.34620 q^{6} -2.64575i q^{7} +19.8761 q^{8} +3.00000 q^{9} -24.7662i q^{10} -15.9194i q^{11} -16.3241 q^{12} -22.9414 q^{13} -9.69398i q^{14} +11.7076i q^{15} +35.1267 q^{16} +7.83072i q^{17} +10.9919 q^{18} +21.4544i q^{19} -63.7054i q^{20} +4.58258i q^{21} -58.3283i q^{22} +(22.2791 - 5.71325i) q^{23} -34.4265 q^{24} -20.6893 q^{25} -84.0567 q^{26} -5.19615 q^{27} -24.9355i q^{28} +42.1679 q^{29} +42.8964i q^{30} +34.5332 q^{31} +49.1991 q^{32} +27.5732i q^{33} +28.6916i q^{34} -17.8836 q^{35} +28.2742 q^{36} +17.1979i q^{37} +78.6083i q^{38} +39.7356 q^{39} -134.350i q^{40} +43.6569 q^{41} +16.7905i q^{42} -55.0901i q^{43} -150.036i q^{44} -20.2782i q^{45} +(81.6302 - 20.9332i) q^{46} +16.2312 q^{47} -60.8413 q^{48} -7.00000 q^{49} -75.8050 q^{50} -13.5632i q^{51} -216.217 q^{52} +101.442i q^{53} -19.0386 q^{54} -107.605 q^{55} -52.5873i q^{56} -37.1600i q^{57} +154.502 q^{58} +12.8539 q^{59} +110.341i q^{60} -69.6589i q^{61} +126.529 q^{62} -7.93725i q^{63} +39.7575 q^{64} +155.070i q^{65} +101.028i q^{66} +62.4811i q^{67} +73.8025i q^{68} +(-38.5886 + 9.89563i) q^{69} -65.5253 q^{70} -130.073 q^{71} +59.6284 q^{72} +42.3220 q^{73} +63.0127i q^{74} +35.8349 q^{75} +202.202i q^{76} -42.1188 q^{77} +145.591 q^{78} +124.851i q^{79} -237.435i q^{80} +9.00000 q^{81} +159.958 q^{82} +54.3845i q^{83} +43.1896i q^{84} +52.9308 q^{85} -201.849i q^{86} -73.0369 q^{87} -316.416i q^{88} -132.737i q^{89} -74.2987i q^{90} +60.6972i q^{91} +(209.975 - 53.8459i) q^{92} -59.8133 q^{93} +59.4709 q^{94} +145.018 q^{95} -85.2154 q^{96} +5.45915i q^{97} -25.6478 q^{98} -47.7582i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9}+O(q^{10}) $ 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9	$ 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9} + 16 q^{13} + 324 q^{16} + 12 q^{18} - 4 q^{23} - 24 q^{24} - 176 q^{25} + 136 q^{26} - 128 q^{29} - 8 q^{31} - 252 q^{32} - 56 q^{35} + 348 q^{36} + 96 q^{39} - 24 q^{41} - 148 q^{46} - 408 q^{47} - 96 q^{48} - 336 q^{49} + 236 q^{50} - 32 q^{52} - 72 q^{54} - 24 q^{55} - 56 q^{58} + 136 q^{59} + 184 q^{62} + 716 q^{64} - 48 q^{69} - 112 q^{70} + 48 q^{71} - 12 q^{72} - 224 q^{73} - 48 q^{75} + 224 q^{77} - 96 q^{78} + 432 q^{81} + 640 q^{82} - 424 q^{85} + 312 q^{87} + 1060 q^{92} + 192 q^{93} + 216 q^{94} + 624 q^{95} + 48 q^{96} - 28 q^{98}+O(q^{100}) $ 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9 + 16 * q^13 + 324 * q^16 + 12 * q^18 - 4 * q^23 - 24 * q^24 - 176 * q^25 + 136 * q^26 - 128 * q^29 - 8 * q^31 - 252 * q^32 - 56 * q^35 + 348 * q^36 + 96 * q^39 - 24 * q^41 - 148 * q^46 - 408 * q^47 - 96 * q^48 - 336 * q^49 + 236 * q^50 - 32 * q^52 - 72 * q^54 - 24 * q^55 - 56 * q^58 + 136 * q^59 + 184 * q^62 + 716 * q^64 - 48 * q^69 - 112 * q^70 + 48 * q^71 - 12 * q^72 - 224 * q^73 - 48 * q^75 + 224 * q^77 - 96 * q^78 + 432 * q^81 + 640 * q^82 - 424 * q^85 + 312 * q^87 + 1060 * q^92 + 192 * q^93 + 216 * q^94 + 624 * q^95 + 48 * q^96 - 28 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	3.66398			1.83199			0.915995	−	0.401191i	$-0.131403\pi$
$2$	3.66398			1.83199			0.915995	+	0.401191i	$0.131403\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	9.42474			2.35618
$5$		−	6.75938i		−	1.35188i	−0.736958	−	0.675938i	$-0.763739\pi$
$5$		−	6.75938i		−	1.35188i	0.736958	−	0.675938i	$-0.236261\pi$
$6$	−6.34620			−1.05770
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	19.8761			2.48452
$9$	3.00000			0.333333
$10$		−	24.7662i		−	2.47662i
$11$		−	15.9194i		−	1.44722i	−0.690210	−	0.723609i	$-0.742482\pi$
$11$		−	15.9194i		−	1.44722i	0.690210	−	0.723609i	$-0.257518\pi$
$12$	−16.3241			−1.36034
$13$	−22.9414			−1.76472			−0.882361	−	0.470573i	$-0.844047\pi$
$13$	−22.9414			−1.76472			−0.882361	+	0.470573i	$0.844047\pi$
$14$		−	9.69398i		−	0.692427i
$15$			11.7076i			0.780506i
$16$	35.1267			2.19542
$17$			7.83072i			0.460631i	0.973116	+	0.230315i	$0.0739757\pi$
$17$			7.83072i			0.460631i	−0.973116	+	0.230315i	$0.926024\pi$
$18$	10.9919			0.610663
$19$			21.4544i			1.12918i	0.825373	+	0.564588i	$0.190965\pi$
$19$			21.4544i			1.12918i	−0.825373	+	0.564588i	$0.809035\pi$
$20$		−	63.7054i		−	3.18527i
$21$			4.58258i			0.218218i
$22$		−	58.3283i		−	2.65129i
$23$	22.2791	−	5.71325i	0.968657	−	0.248402i
$23$	22.2791	−	5.71325i	0.968657	−	0.248402i
$24$	−34.4265			−1.43444
$25$	−20.6893			−0.827571
$26$	−84.0567			−3.23295
$27$	−5.19615			−0.192450
$28$		−	24.9355i		−	0.890554i
$29$	42.1679			1.45407			0.727033	−	0.686603i	$-0.240899\pi$
$29$	42.1679			1.45407			0.727033	+	0.686603i	$0.240899\pi$
$30$			42.8964i			1.42988i
$31$	34.5332			1.11398			0.556988	−	0.830521i	$-0.311957\pi$
$31$	34.5332			1.11398			0.556988	+	0.830521i	$0.311957\pi$
$32$	49.1991			1.53747
$33$			27.5732i			0.835552i
$34$			28.6916i			0.843870i
$35$	−17.8836			−0.510961
$36$	28.2742			0.785395
$37$			17.1979i			0.464808i	0.972619	+	0.232404i	$0.0746591\pi$
$37$			17.1979i			0.464808i	−0.972619	+	0.232404i	$0.925341\pi$
$38$			78.6083i			2.06864i
$39$	39.7356			1.01886
$40$		−	134.350i		−	3.35876i
$41$	43.6569			1.06480			0.532401	−	0.846492i	$-0.321290\pi$
$41$	43.6569			1.06480			0.532401	+	0.846492i	$0.321290\pi$
$42$			16.7905i			0.399773i
$43$		−	55.0901i		−	1.28117i	−0.767889	−	0.640583i	$-0.778693\pi$
$43$		−	55.0901i		−	1.28117i	0.767889	−	0.640583i	$-0.221307\pi$
$44$		−	150.036i		−	3.40991i
$45$		−	20.2782i		−	0.450626i
$46$	81.6302	−	20.9332i	1.77457	−	0.455070i
$47$	16.2312			0.345346			0.172673	−	0.984979i	$-0.444760\pi$
$47$	16.2312			0.345346			0.172673	+	0.984979i	$0.444760\pi$
$48$	−60.8413			−1.26753
$49$	−7.00000			−0.142857
$50$	−75.8050			−1.51610
$51$		−	13.5632i		−	0.265945i
$52$	−216.217			−4.15801
$53$			101.442i			1.91401i	0.290074	+	0.957004i	$0.406320\pi$
$53$			101.442i			1.91401i	−0.290074	+	0.957004i	$0.593680\pi$
$54$	−19.0386			−0.352566
$55$	−107.605			−1.95646
$56$		−	52.5873i		−	0.939059i
$57$		−	37.1600i		−	0.651930i
$58$	154.502			2.66383
$59$	12.8539			0.217862			0.108931	−	0.994049i	$-0.465257\pi$
$59$	12.8539			0.217862			0.108931	+	0.994049i	$0.465257\pi$
$60$			110.341i			1.83902i
$61$		−	69.6589i		−	1.14195i	−0.820968	−	0.570975i	$-0.806565\pi$
$61$		−	69.6589i		−	1.14195i	0.820968	−	0.570975i	$-0.193435\pi$
$62$	126.529			2.04079
$63$		−	7.93725i		−	0.125988i
$64$	39.7575			0.621212
$65$			155.070i			2.38569i
$66$			101.028i			1.53072i
$67$			62.4811i			0.932553i	0.884639	+	0.466277i	$0.154405\pi$
$67$			62.4811i			0.932553i	−0.884639	+	0.466277i	$0.845595\pi$
$68$			73.8025i			1.08533i
$69$	−38.5886	+	9.89563i	−0.559254	+	0.143415i
$70$	−65.5253			−0.936076
$71$	−130.073			−1.83201			−0.916007	−	0.401161i	$-0.868607\pi$
$71$	−130.073			−1.83201			−0.916007	+	0.401161i	$0.868607\pi$
$72$	59.6284			0.828172
$73$	42.3220			0.579754			0.289877	−	0.957064i	$-0.406386\pi$
$73$	42.3220			0.579754			0.289877	+	0.957064i	$0.406386\pi$
$74$			63.0127i			0.851523i
$75$	35.8349			0.477798
$76$			202.202i			2.66055i
$77$	−42.1188			−0.546997
$78$	145.591			1.86655
$79$			124.851i			1.58039i	0.612856	+	0.790195i	$0.290021\pi$
$79$			124.851i			1.58039i	−0.612856	+	0.790195i	$0.709979\pi$
$80$		−	237.435i		−	2.96794i
$81$	9.00000			0.111111
$82$	159.958			1.95071
$83$			54.3845i			0.655235i	0.944811	+	0.327617i	$0.106246\pi$
$83$			54.3845i			0.655235i	−0.944811	+	0.327617i	$0.893754\pi$
$84$			43.1896i			0.514162i
$85$	52.9308			0.622716
$86$		−	201.849i		−	2.34708i
$87$	−73.0369			−0.839505
$88$		−	316.416i		−	3.59564i
$89$		−	132.737i		−	1.49143i	−0.666266	−	0.745714i	$-0.732109\pi$
$89$		−	132.737i		−	1.49143i	0.666266	−	0.745714i	$-0.267891\pi$
$90$		−	74.2987i		−	0.825541i
$91$			60.6972i			0.667002i
$92$	209.975	−	53.8459i	2.28233	−	0.585281i
$93$	−59.8133			−0.643154
$94$	59.4709			0.632670
$95$	145.018			1.52651
$96$	−85.2154			−0.887660
$97$			5.45915i			0.0562799i	0.999604	+	0.0281400i	$0.00895841\pi$
$97$			5.45915i			0.0562799i	−0.999604	+	0.0281400i	$0.991042\pi$
$98$	−25.6478			−0.261713
$99$		−	47.7582i		−	0.482406i
$100$	−194.991			−1.94991
$101$	10.1860			0.100852			0.0504259	−	0.998728i	$-0.483942\pi$
$101$	10.1860			0.100852			0.0504259	+	0.998728i	$0.483942\pi$
$102$		−	49.6953i		−	0.487209i
$103$			163.691i			1.58924i	0.607110	+	0.794618i	$0.292329\pi$
$103$			163.691i			1.58924i	−0.607110	+	0.794618i	$0.707671\pi$
$104$	−455.986			−4.38448
$105$	30.9754			0.295004
$106$			371.683i			3.50644i
$107$		−	11.6860i		−	0.109215i	−0.998508	−	0.0546074i	$-0.982609\pi$
$107$		−	11.6860i		−	0.109215i	0.998508	−	0.0546074i	$-0.0173907\pi$
$108$	−48.9724			−0.453448
$109$		−	88.5263i		−	0.812168i	−0.913836	−	0.406084i	$-0.866894\pi$
$109$		−	88.5263i		−	0.812168i	0.913836	−	0.406084i	$-0.133106\pi$
$110$	−394.264			−3.58421
$111$		−	29.7876i		−	0.268357i
$112$		−	92.9366i		−	0.829791i
$113$			85.4249i			0.755973i	0.925811	+	0.377986i	$0.123383\pi$
$113$			85.4249i			0.755973i	−0.925811	+	0.377986i	$0.876617\pi$
$114$		−	136.154i		−	1.19433i
$115$	−38.6180	−	150.593i	−0.335809	−	1.30950i
$116$	397.421			3.42605
$117$	−68.8242			−0.588241
$118$	47.0962			0.399121
$119$	20.7181			0.174102
$120$			232.702i			1.93918i
$121$	−132.427			−1.09444
$122$		−	255.229i		−	2.09204i
$123$	−75.6159			−0.614764
$124$	325.467			2.62473
$125$		−	29.1379i		−	0.233103i
$126$		−	29.0819i		−	0.230809i
$127$	79.7140			0.627669			0.313834	−	0.949478i	$-0.398386\pi$
$127$	79.7140			0.627669			0.313834	+	0.949478i	$0.398386\pi$
$128$	−51.1257			−0.399419
$129$			95.4188i			0.739681i
$130$			568.172i			4.37055i
$131$	−15.3252			−0.116986			−0.0584930	−	0.998288i	$-0.518630\pi$
$131$	−15.3252			−0.116986			−0.0584930	+	0.998288i	$0.518630\pi$
$132$			259.870i			1.96871i
$133$	56.7629			0.426789
$134$			228.929i			1.70843i
$135$			35.1228i			0.260169i
$136$			155.644i			1.14444i
$137$		−	95.4779i		−	0.696919i	−0.937324	−	0.348460i	$-0.886705\pi$
$137$		−	95.4779i		−	0.696919i	0.937324	−	0.348460i	$-0.113295\pi$
$138$	−141.388	+	36.2574i	−1.02455	+	0.262735i
$139$	−13.7489			−0.0989130			−0.0494565	−	0.998776i	$-0.515749\pi$
$139$	−13.7489			−0.0989130			−0.0494565	+	0.998776i	$0.515749\pi$
$140$	−168.549			−1.20392
$141$	−28.1133			−0.199385
$142$	−476.585			−3.35623
$143$			365.213i			2.55394i
$144$	105.380			0.731807
$145$		−	285.029i		−	1.96572i
$146$	155.067			1.06210
$147$	12.1244			0.0824786
$148$			162.086i			1.09517i
$149$		−	71.5980i		−	0.480524i	−0.970708	−	0.240262i	$-0.922767\pi$
$149$		−	71.5980i		−	0.480524i	0.970708	−	0.240262i	$-0.0772333\pi$
$150$	131.298			0.875321
$151$	−93.0295			−0.616090			−0.308045	−	0.951372i	$-0.599675\pi$
$151$	−93.0295			−0.616090			−0.308045	+	0.951372i	$0.599675\pi$
$152$			426.429i			2.80546i
$153$			23.4922i			0.153544i
$154$	−154.322			−1.00209
$155$		−	233.423i		−	1.50596i
$156$	374.498			2.40063
$157$			11.0989i			0.0706934i	0.999375	+	0.0353467i	$0.0112535\pi$
$157$			11.0989i			0.0706934i	−0.999375	+	0.0353467i	$0.988746\pi$
$158$			457.451i			2.89526i
$159$		−	175.703i		−	1.10505i
$160$		−	332.556i		−	2.07847i
$161$	−15.1158	−	58.9450i	−0.0938871	−	0.366118i
$162$	32.9758			0.203554
$163$	−195.920			−1.20196			−0.600981	−	0.799264i	$-0.705223\pi$
$163$	−195.920			−1.20196			−0.600981	+	0.799264i	$0.705223\pi$
$164$	411.455			2.50887
$165$	186.378			1.12956
$166$			199.264i			1.20038i
$167$	−170.028			−1.01813			−0.509067	−	0.860727i	$-0.670009\pi$
$167$	−170.028			−1.01813			−0.509067	+	0.860727i	$0.670009\pi$
$168$			91.0838i			0.542166i
$169$	357.307			2.11424
$170$	193.937			1.14081
$171$			64.3631i			0.376392i
$172$		−	519.210i		−	3.01866i
$173$	−55.1476			−0.318772			−0.159386	−	0.987216i	$-0.550951\pi$
$173$	−55.1476			−0.318772			−0.159386	+	0.987216i	$0.550951\pi$
$174$	−267.606			−1.53796
$175$			54.7387i			0.312792i
$176$		−	559.197i		−	3.17725i
$177$	−22.2635			−0.125783
$178$		−	486.346i		−	2.73228i
$179$	−122.922			−0.686717			−0.343359	−	0.939204i	$-0.611565\pi$
$179$	−122.922			−0.686717			−0.343359	+	0.939204i	$0.611565\pi$
$180$		−	191.116i		−	1.06176i
$181$		−	239.915i		−	1.32550i	−0.748841	−	0.662749i	$-0.769390\pi$
$181$		−	239.915i		−	1.32550i	0.748841	−	0.662749i	$-0.230610\pi$
$182$			222.393i			1.22194i
$183$			120.653i			0.659305i
$184$	442.822	−	113.557i	2.40664	−	0.617159i
$185$	116.247			0.628363
$186$	−219.155			−1.17825
$187$	124.660			0.666633
$188$	152.975			0.813698
$189$			13.7477i			0.0727393i
$190$	531.344			2.79655
$191$			120.725i			0.632070i	0.948747	+	0.316035i	$0.102352\pi$
$191$			120.725i			0.632070i	−0.948747	+	0.316035i	$0.897648\pi$
$192$	−68.8621			−0.358657
$193$	−171.968			−0.891028			−0.445514	−	0.895275i	$-0.646979\pi$
$193$	−171.968			−0.891028			−0.445514	+	0.895275i	$0.646979\pi$
$194$			20.0022i			0.103104i
$195$		−	268.588i		−	1.37738i
$196$	−65.9732			−0.336598
$197$	−62.1180			−0.315320			−0.157660	−	0.987493i	$-0.550395\pi$
$197$	−62.1180			−0.315320			−0.157660	+	0.987493i	$0.550395\pi$
$198$		−	174.985i		−	0.883763i
$199$		−	182.710i		−	0.918140i	−0.888400	−	0.459070i	$-0.848183\pi$
$199$		−	182.710i		−	0.918140i	0.888400	−	0.459070i	$-0.151817\pi$
$200$	−411.222			−2.05611
$201$		−	108.220i		−	0.538410i
$202$	37.3214			0.184759
$203$		−	111.566i		−	0.549585i
$204$		−	127.830i		−	0.626616i
$205$		−	295.094i		−	1.43948i
$206$			599.761i			2.91146i
$207$	66.8373	−	17.1397i	0.322886	−	0.0828007i
$208$	−805.856			−3.87431
$209$	341.541			1.63417
$210$	113.493			0.540444
$211$	181.380			0.859623			0.429811	−	0.902919i	$-0.358580\pi$
$211$	181.380			0.859623			0.429811	+	0.902919i	$0.358580\pi$
$212$			956.068i			4.50976i
$213$	225.293			1.05771
$214$		−	42.8172i		−	0.200080i
$215$	−372.375			−1.73198
$216$	−103.279			−0.478145
$217$		−	91.3664i		−	0.421043i
$218$		−	324.358i		−	1.48788i
$219$	−73.3039			−0.334721
$220$	−1014.15			−4.60978
$221$		−	179.648i		−	0.812885i
$222$		−	109.141i		−	0.491627i
$223$	357.247			1.60200			0.801001	−	0.598662i	$-0.204301\pi$
$223$	357.247			1.60200			0.801001	+	0.598662i	$0.204301\pi$
$224$		−	130.169i		−	0.581110i
$225$	−62.0678			−0.275857
$226$			312.995i			1.38493i
$227$			72.1054i			0.317645i	0.987307	+	0.158822i	$0.0507698\pi$
$227$			72.1054i			0.317645i	−0.987307	+	0.158822i	$0.949230\pi$
$228$		−	350.224i		−	1.53607i
$229$		−	132.355i		−	0.577970i	−0.957334	−	0.288985i	$-0.906682\pi$
$229$		−	132.355i		−	0.577970i	0.957334	−	0.288985i	$-0.0933178\pi$
$230$	−141.496	−	551.770i	−0.615198	−	2.39900i
$231$	72.9519			0.315809
$232$	838.134			3.61265
$233$	53.9100			0.231373			0.115687	−	0.993286i	$-0.463093\pi$
$233$	53.9100			0.231373			0.115687	+	0.993286i	$0.463093\pi$
$234$	−252.170			−1.07765
$235$		−	109.713i		−	0.466865i
$236$	121.144			0.513323
$237$		−	216.248i		−	0.912438i
$238$	75.9108			0.318953
$239$	148.264			0.620351			0.310176	−	0.950679i	$-0.399612\pi$
$239$	148.264			0.620351			0.310176	+	0.950679i	$0.399612\pi$
$240$			411.250i			1.71354i
$241$			403.221i			1.67312i	0.547878	+	0.836558i	$0.315436\pi$
$241$			403.221i			1.67312i	−0.547878	+	0.836558i	$0.684564\pi$
$242$	−485.211			−2.00500
$243$	−15.5885			−0.0641500
$244$		−	656.517i		−	2.69064i
$245$			47.3157i			0.193125i
$246$	−277.055			−1.12624
$247$		−	492.193i		−	1.99268i
$248$	686.387			2.76769
$249$		−	94.1967i		−	0.378300i
$250$		−	106.761i		−	0.427042i
$251$			441.190i			1.75773i	0.477072	+	0.878864i	$0.341698\pi$
$251$			441.190i			1.75773i	−0.477072	+	0.878864i	$0.658302\pi$
$252$		−	74.8065i		−	0.296851i
$253$	−90.9515	−	354.670i	−0.359492	−	1.40186i
$254$	292.070			1.14988
$255$	−91.6789			−0.359525
$256$	−346.354			−1.35294
$257$	25.9239			0.100871			0.0504357	−	0.998727i	$-0.483939\pi$
$257$	25.9239			0.100871			0.0504357	+	0.998727i	$0.483939\pi$
$258$			349.613i			1.35509i
$259$	45.5013			0.175681
$260$			1461.49i			5.62112i
$261$	126.504			0.484688
$262$	−56.1511			−0.214317
$263$			145.292i			0.552440i	0.961094	+	0.276220i	$0.0890818\pi$
$263$			145.292i			0.552440i	−0.961094	+	0.276220i	$0.910918\pi$
$264$			548.049i			2.07594i
$265$	685.688			2.58750
$266$	207.978			0.781872
$267$			229.907i			0.861076i
$268$			588.868i			2.19727i
$269$	234.704			0.872506			0.436253	−	0.899824i	$-0.356305\pi$
$269$	234.704			0.872506			0.436253	+	0.899824i	$0.356305\pi$
$270$			128.689i			0.476626i
$271$	−157.268			−0.580324			−0.290162	−	0.956978i	$-0.593709\pi$
$271$	−157.268			−0.580324			−0.290162	+	0.956978i	$0.593709\pi$
$272$			275.068i			1.01128i
$273$		−	105.131i		−	0.385094i
$274$		−	349.829i		−	1.27675i
$275$			329.361i			1.19768i
$276$	−363.687	+	93.2638i	−1.31771	+	0.337912i
$277$	22.3759			0.0807793			0.0403897	−	0.999184i	$-0.487140\pi$
$277$	22.3759			0.0807793			0.0403897	+	0.999184i	$0.487140\pi$
$278$	−50.3757			−0.181207
$279$	103.600			0.371325
$280$	−355.458			−1.26949
$281$			464.857i			1.65429i	0.561985	+	0.827147i	$0.310038\pi$
$281$			464.857i			1.65429i	−0.561985	+	0.827147i	$0.689962\pi$
$282$	−103.007			−0.365272
$283$		−	154.066i		−	0.544404i	−0.962240	−	0.272202i	$-0.912248\pi$
$283$		−	154.066i		−	0.544404i	0.962240	−	0.272202i	$-0.0877520\pi$
$284$	−1225.90			−4.31656
$285$	−251.179			−0.881330
$286$			1338.13i			4.67879i
$287$		−	115.505i		−	0.402457i
$288$	147.597			0.512491
$289$	227.680			0.787819
$290$		−	1044.34i		−	3.60117i
$291$		−	9.45553i		−	0.0324932i
$292$	398.874			1.36601
$293$			130.260i			0.444575i	0.974981	+	0.222287i	$0.0713523\pi$
$293$			130.260i			0.444575i	−0.974981	+	0.222287i	$0.928648\pi$
$294$	44.4234			0.151100
$295$		−	86.8841i		−	0.294522i
$296$			341.827i			1.15482i
$297$			82.7196i			0.278517i
$298$		−	262.334i		−	0.880314i
$299$	−511.114	+	131.070i	−1.70941	+	0.438361i
$300$	337.734			1.12578
$301$	−145.755			−0.484235
$302$	−340.858			−1.12867
$303$	−17.6427			−0.0582268
$304$			753.622i			2.47902i
$305$	−470.851			−1.54377
$306$			86.0748i			0.281290i
$307$	13.3879			0.0436087			0.0218043	−	0.999762i	$-0.493059\pi$
$307$	13.3879			0.0436087			0.0218043	+	0.999762i	$0.493059\pi$
$308$	−396.958			−1.28883
$309$		−	283.522i		−	0.917546i
$310$		−	855.259i		−	2.75890i
$311$	−215.114			−0.691684			−0.345842	−	0.938293i	$-0.612407\pi$
$311$	−215.114			−0.691684			−0.345842	+	0.938293i	$0.612407\pi$
$312$	789.791			2.53138
$313$			137.417i			0.439032i	0.975609	+	0.219516i	$0.0704478\pi$
$313$			137.417i			0.439032i	−0.975609	+	0.219516i	$0.929552\pi$
$314$			40.6660i			0.129510i
$315$	−53.6509			−0.170320
$316$			1176.69i			3.72369i
$317$	36.4218			0.114895			0.0574477	−	0.998349i	$-0.481704\pi$
$317$	36.4218			0.114895			0.0574477	+	0.998349i	$0.481704\pi$
$318$		−	643.774i		−	2.02445i
$319$		−	671.288i		−	2.10435i
$320$		−	268.736i		−	0.839801i
$321$			20.2407i			0.0630552i
$322$	−55.3841	−	215.973i	−0.172000	−	0.670724i
$323$	−168.003			−0.520133
$324$	84.8226			0.261798
$325$	474.640			1.46043
$326$	−717.846			−2.20198
$327$			153.332i			0.468905i
$328$	867.730			2.64552
$329$		−	42.9438i		−	0.130528i
$330$	682.885			2.06935
$331$	−632.786			−1.91174			−0.955869	−	0.293792i	$-0.905083\pi$
$331$	−632.786			−1.91174			−0.955869	+	0.293792i	$0.905083\pi$
$332$			512.559i			1.54385i
$333$			51.5937i			0.154936i
$334$	−622.980			−1.86521
$335$	422.334			1.26070
$336$			160.971i			0.479080i
$337$		−	214.913i		−	0.637725i	−0.947801	−	0.318862i	$-0.896699\pi$
$337$		−	214.913i		−	0.637725i	0.947801	−	0.318862i	$-0.103301\pi$
$338$	1309.17			3.87327
$339$		−	147.960i		−	0.436461i
$340$	498.859			1.46723
$341$		−	549.749i		−	1.61217i
$342$			235.825i			0.689547i
$343$			18.5203i			0.0539949i
$344$		−	1094.98i		−	3.18307i
$345$	66.8884	+	260.835i	0.193879	+	0.756043i
$346$	−202.060			−0.583987
$347$	423.545			1.22059			0.610295	−	0.792174i	$-0.291051\pi$
$347$	423.545			1.22059			0.610295	+	0.792174i	$0.291051\pi$
$348$	−688.354			−1.97803
$349$	−174.759			−0.500741			−0.250370	−	0.968150i	$-0.580552\pi$
$349$	−174.759			−0.500741			−0.250370	+	0.968150i	$0.580552\pi$
$350$			200.561i			0.573032i
$351$	119.207			0.339621
$352$		−	783.220i		−	2.22506i
$353$	54.4727			0.154314			0.0771568	−	0.997019i	$-0.475416\pi$
$353$	54.4727			0.154314			0.0771568	+	0.997019i	$0.475416\pi$
$354$	−81.5731			−0.230432
$355$			879.214i			2.47666i
$356$		−	1251.01i		−	3.51408i
$357$	−35.8849			−0.100518
$358$	−450.385			−1.25806
$359$		−	90.3676i		−	0.251720i	−0.992048	−	0.125860i	$-0.959831\pi$
$359$		−	90.3676i		−	0.251720i	0.992048	−	0.125860i	$-0.0401691\pi$
$360$		−	403.051i		−	1.11959i
$361$	−99.2895			−0.275040
$362$		−	879.044i		−	2.42830i
$363$	229.371			0.631876
$364$			572.055i			1.57158i
$365$		−	286.071i		−	0.783756i
$366$			442.069i			1.20784i
$367$		−	26.3314i		−	0.0717478i	−0.999356	−	0.0358739i	$-0.988579\pi$
$367$		−	26.3314i		−	0.0717478i	0.999356	−	0.0358739i	$-0.0114215\pi$
$368$	782.592	−	200.688i	2.12661	−	0.545347i
$369$	130.971			0.354934
$370$	425.927			1.15115
$371$	268.391			0.723427
$372$	−563.725			−1.51539
$373$		−	299.336i		−	0.802510i	−0.915966	−	0.401255i	$-0.868574\pi$
$373$		−	299.336i		−	0.802510i	0.915966	−	0.401255i	$-0.131426\pi$
$374$	456.753			1.22126
$375$			50.4683i			0.134582i
$376$	322.614			0.858017
$377$	−967.390			−2.56602
$378$			50.3714i			0.133258i
$379$		−	62.8146i		−	0.165738i	−0.996560	−	0.0828689i	$-0.973592\pi$
$379$		−	62.8146i		−	0.165738i	0.996560	−	0.0828689i	$-0.0264083\pi$
$380$	1366.76			3.59673
$381$	−138.069			−0.362385
$382$			442.335i			1.15795i
$383$		−	148.157i		−	0.386833i	−0.981117	−	0.193417i	$-0.938043\pi$
$383$		−	148.157i		−	0.386833i	0.981117	−	0.193417i	$-0.0619569\pi$
$384$	88.5523			0.230605
$385$			284.697i			0.739473i
$386$	−630.089			−1.63235
$387$		−	165.270i		−	0.427055i
$388$			51.4511i			0.132606i
$389$		−	83.5447i		−	0.214768i	−0.994218	−	0.107384i	$-0.965753\pi$
$389$		−	83.5447i		−	0.214768i	0.994218	−	0.107384i	$-0.0342474\pi$
$390$		−	984.102i		−	2.52334i
$391$	44.7388	+	174.461i	0.114422	+	0.446193i
$392$	−139.133			−0.354931
$393$	26.5440			0.0675419
$394$	−227.599			−0.577662
$395$	843.914			2.13649
$396$		−	450.109i		−	1.13664i
$397$	−381.332			−0.960533			−0.480267	−	0.877123i	$-0.659460\pi$
$397$	−381.332			−0.960533			−0.480267	+	0.877123i	$0.659460\pi$
$398$		−	669.445i		−	1.68202i
$399$	−98.3162			−0.246407
$400$	−726.746			−1.81687
$401$		−	324.031i		−	0.808058i	−0.914746	−	0.404029i	$-0.867609\pi$
$401$		−	324.031i		−	0.808058i	0.914746	−	0.404029i	$-0.132391\pi$
$402$		−	396.517i		−	0.986361i
$403$	−792.241			−1.96586
$404$	96.0006			0.237625
$405$		−	60.8345i		−	0.150209i
$406$		−	408.775i		−	1.00683i
$407$	273.780			0.672678
$408$		−	269.584i		−	0.660745i
$409$	773.748			1.89181			0.945903	−	0.324451i	$-0.105179\pi$
$409$	773.748			1.89181			0.945903	+	0.324451i	$0.105179\pi$
$410$		−	1081.22i		−	2.63711i
$411$			165.373i			0.402367i
$412$			1542.75i			3.74453i
$413$		−	34.0081i		−	0.0823441i
$414$	244.891	−	62.7996i	0.591523	−	0.151690i
$415$	367.605			0.885796
$416$	−1128.70			−2.71321
$417$	23.8138			0.0571074
$418$	1251.40			2.99377
$419$		−	537.522i		−	1.28287i	−0.767178	−	0.641435i	$-0.778340\pi$
$419$		−	537.522i		−	1.28287i	0.767178	−	0.641435i	$-0.221660\pi$
$420$	291.935			0.695083
$421$		−	304.690i		−	0.723730i	−0.932231	−	0.361865i	$-0.882140\pi$
$421$		−	304.690i		−	0.723730i	0.932231	−	0.361865i	$-0.117860\pi$
$422$	664.574			1.57482
$423$	48.6937			0.115115
$424$			2016.28i			4.75538i
$425$		−	162.012i		−	0.381204i
$426$	825.469			1.93772
$427$	−184.300			−0.431616
$428$		−	110.137i		−	0.257330i
$429$		−	632.568i		−	1.47452i
$430$	−1364.37			−3.17296
$431$			387.933i			0.900078i	0.893009	+	0.450039i	$0.148590\pi$
$431$			387.933i			0.900078i	−0.893009	+	0.450039i	$0.851410\pi$
$432$	−182.524			−0.422509
$433$		−	163.863i		−	0.378438i	−0.981935	−	0.189219i	$-0.939404\pi$
$433$		−	163.863i		−	0.378438i	0.981935	−	0.189219i	$-0.0605955\pi$
$434$		−	334.764i		−	0.771347i
$435$			493.685i			1.13491i
$436$		−	834.337i		−	1.91362i
$437$	122.574	+	477.984i	0.280490	+	1.09378i
$438$	−268.584			−0.613205
$439$	−572.494			−1.30409			−0.652043	−	0.758182i	$-0.726088\pi$
$439$	−572.494			−1.30409			−0.652043	+	0.758182i	$0.726088\pi$
$440$	−2138.78			−4.86086
$441$	−21.0000			−0.0476190
$442$		−	658.225i		−	1.48920i
$443$	−665.397			−1.50203			−0.751013	−	0.660288i	$-0.770434\pi$
$443$	−665.397			−1.50203			−0.751013	+	0.660288i	$0.770434\pi$
$444$		−	280.741i		−	0.632298i
$445$	−897.221			−2.01623
$446$	1308.94			2.93485
$447$			124.011i			0.277430i
$448$		−	105.189i		−	0.234796i
$449$	−13.0058			−0.0289662			−0.0144831	−	0.999895i	$-0.504610\pi$
$449$	−13.0058			−0.0289662			−0.0144831	+	0.999895i	$0.504610\pi$
$450$	−227.415			−0.505367
$451$		−	694.991i		−	1.54100i
$452$			805.108i			1.78121i
$453$	161.132			0.355700
$454$			264.193i			0.581922i
$455$	410.276			0.901705
$456$		−	738.597i		−	1.61973i
$457$			582.896i			1.27548i	0.770250	+	0.637742i	$0.220131\pi$
$457$			582.896i			1.27548i	−0.770250	+	0.637742i	$0.779869\pi$
$458$		−	484.946i		−	1.05883i
$459$		−	40.6896i		−	0.0886484i
$460$	−363.965	−	1419.30i	−0.791228	−	3.08544i
$461$	−512.499			−1.11171			−0.555856	−	0.831278i	$-0.687610\pi$
$461$	−512.499			−1.11171			−0.555856	+	0.831278i	$0.687610\pi$
$462$	267.294			0.578559
$463$	−99.8043			−0.215560			−0.107780	−	0.994175i	$-0.534374\pi$
$463$	−99.8043			−0.215560			−0.107780	+	0.994175i	$0.534374\pi$
$464$	1481.22			3.19229
$465$			404.301i			0.869465i
$466$	197.525			0.423873
$467$			835.479i			1.78903i	0.447034	+	0.894517i	$0.352480\pi$
$467$			835.479i			1.78903i	−0.447034	+	0.894517i	$0.647520\pi$
$468$	−648.650			−1.38600
$469$	165.309			0.352472
$470$		−	401.987i		−	0.855291i
$471$		−	19.2238i		−	0.0408149i
$472$	255.485			0.541281
$473$	−877.001			−1.85413
$474$		−	792.328i		−	1.67158i
$475$		−	443.875i		−	0.934474i
$476$	195.263			0.410216
$477$			304.327i			0.638003i
$478$	543.236			1.13648
$479$			586.069i			1.22353i	0.791041	+	0.611763i	$0.209539\pi$
$479$			586.069i			1.22353i	−0.791041	+	0.611763i	$0.790461\pi$
$480$			576.003i			1.20001i
$481$		−	394.543i		−	0.820257i
$482$			1477.39i			3.06513i
$483$	26.1814	+	102.096i	0.0542058	+	0.211378i
$484$	−1248.09			−2.57870
$485$	36.9005			0.0760836
$486$	−57.1158			−0.117522
$487$	899.404			1.84683			0.923413	−	0.383808i	$-0.125387\pi$
$487$	899.404			1.84683			0.923413	+	0.383808i	$0.125387\pi$
$488$		−	1384.55i		−	2.83719i
$489$	339.343			0.693953
$490$			173.364i			0.353803i
$491$	686.069			1.39729			0.698645	−	0.715468i	$-0.253787\pi$
$491$	686.069			1.39729			0.698645	+	0.715468i	$0.253787\pi$
$492$	−712.660			−1.44850
$493$			330.205i			0.669787i
$494$		−	1803.38i		−	3.65057i
$495$	−322.816			−0.652154
$496$	1213.04			2.44565
$497$			344.141i			0.692436i
$498$		−	345.135i		−	0.693041i
$499$	−394.814			−0.791211			−0.395605	−	0.918421i	$-0.629465\pi$
$499$	−394.814			−0.791211			−0.395605	+	0.918421i	$0.629465\pi$
$500$		−	274.617i		−	0.549234i
$501$	294.498			0.587820
$502$			1616.51i			3.22014i
$503$			815.621i			1.62151i	0.585384	+	0.810756i	$0.300944\pi$
$503$			815.621i			1.62151i	−0.585384	+	0.810756i	$0.699056\pi$
$504$		−	157.762i		−	0.313020i
$505$		−	68.8513i		−	0.136339i
$506$	−333.244	−	1299.50i	−0.658585	−	2.56819i
$507$	−618.874			−1.22066
$508$	751.283			1.47890
$509$	−112.199			−0.220429			−0.110215	−	0.993908i	$-0.535154\pi$
$509$	−112.199			−0.220429			−0.110215	+	0.993908i	$0.535154\pi$
$510$	−335.910			−0.658646
$511$		−	111.974i		−	0.219126i
$512$	−1064.53			−2.07916
$513$		−	111.480i		−	0.217310i
$514$	94.9848			0.184795
$515$	1106.45			2.14845
$516$			899.298i			1.74282i
$517$		−	258.392i		−	0.499791i
$518$	166.716			0.321845
$519$	95.5184			0.184043
$520$			3082.18i			5.92728i
$521$		−	550.962i		−	1.05751i	−0.848775	−	0.528755i	$-0.822659\pi$
$521$		−	550.962i		−	1.05751i	0.848775	−	0.528755i	$-0.177341\pi$
$522$	463.507			0.887944
$523$			451.072i			0.862471i	0.902239	+	0.431235i	$0.141922\pi$
$523$			451.072i			0.862471i	−0.902239	+	0.431235i	$0.858078\pi$
$524$	−144.436			−0.275641
$525$		−	94.8101i		−	0.180591i
$526$			532.345i			1.01206i
$527$			270.420i			0.513131i
$528$			968.557i			1.83439i
$529$	463.718	−	254.572i	0.876593	−	0.481233i
$530$	2512.35			4.74028
$531$	38.5616			0.0726206
$532$	534.975			1.00559
$533$	−1001.55			−1.87908
$534$			842.376i			1.57748i
$535$	−78.9900			−0.147645
$536$			1241.88i			2.31694i
$537$	212.908			0.396476
$538$	859.951			1.59842
$539$			111.436i			0.206745i
$540$			331.023i			0.613006i
$541$	−622.439			−1.15053			−0.575267	−	0.817966i	$-0.695102\pi$
$541$	−622.439			−1.15053			−0.575267	+	0.817966i	$0.695102\pi$
$542$	−576.225			−1.06315
$543$			415.545i			0.765277i
$544$			385.264i			0.708207i
$545$	−598.383			−1.09795
$546$		−	385.196i		−	0.705488i
$547$	104.189			0.190473			0.0952367	−	0.995455i	$-0.469639\pi$
$547$	104.189			0.190473			0.0952367	+	0.995455i	$0.469639\pi$
$548$		−	899.855i		−	1.64207i
$549$		−	208.977i		−	0.380650i
$550$			1206.77i			2.19413i
$551$			904.685i			1.64190i
$552$	−766.991	+	196.687i	−1.38948	+	0.356317i
$553$	330.324			0.597331
$554$	81.9847			0.147987
$555$	−201.346			−0.362786
$556$	−129.580			−0.233057
$557$		−	60.6168i		−	0.108827i	−0.998518	−	0.0544136i	$-0.982671\pi$
$557$		−	60.6168i		−	0.108827i	0.998518	−	0.0544136i	$-0.0173290\pi$
$558$	379.587			0.680264
$559$			1263.84i			2.26090i
$560$	−628.194			−1.12178
$561$	−215.918			−0.384881
$562$			1703.22i			3.03065i
$563$		−	911.362i		−	1.61876i	−0.587285	−	0.809381i	$-0.699803\pi$
$563$		−	911.362i		−	1.61876i	0.587285	−	0.809381i	$-0.300197\pi$
$564$	−264.961			−0.469789
$565$	577.420			1.02198
$566$		−	564.496i		−	0.997343i
$567$		−	23.8118i		−	0.0419961i
$568$	−2585.35			−4.55167
$569$			97.3238i			0.171044i	0.996336	+	0.0855218i	$0.0272557\pi$
$569$			97.3238i			0.171044i	−0.996336	+	0.0855218i	$0.972744\pi$
$570$	−920.314			−1.61459
$571$		−	382.504i		−	0.669884i	−0.942239	−	0.334942i	$-0.891283\pi$
$571$		−	382.504i		−	0.669884i	0.942239	−	0.334942i	$-0.108717\pi$
$572$			3442.04i			6.01755i
$573$		−	209.103i		−	0.364926i
$574$		−	423.209i		−	0.737298i
$575$	−460.939	+	118.203i	−0.801632	+	0.205570i
$576$	119.273			0.207071
$577$	−462.258			−0.801140			−0.400570	−	0.916266i	$-0.631188\pi$
$577$	−462.258			−0.801140			−0.400570	+	0.916266i	$0.631188\pi$
$578$	834.214			1.44328
$579$	297.858			0.514435
$580$		−	2686.32i		−	4.63159i
$581$	143.888			0.247655
$582$		−	34.6449i		−	0.0595273i
$583$	1614.90			2.76999
$584$	841.198			1.44041
$585$			465.209i			0.795229i
$586$			477.271i			0.814456i
$587$	923.774			1.57372			0.786860	−	0.617131i	$-0.211705\pi$
$587$	923.774			1.57372			0.786860	+	0.617131i	$0.211705\pi$
$588$	114.269			0.194335
$589$			740.889i			1.25788i
$590$		−	318.342i		−	0.539562i
$591$	107.592			0.182050
$592$			604.106i			1.02045i
$593$	85.4942			0.144172			0.0720861	−	0.997398i	$-0.477034\pi$
$593$	85.4942			0.144172			0.0720861	+	0.997398i	$0.477034\pi$
$594$			303.083i			0.510241i
$595$		−	140.042i		−	0.235364i
$596$		−	674.793i		−	1.13220i
$597$			316.463i			0.530088i
$598$	−1872.71	+	480.237i	−3.13162	+	0.803072i
$599$	−4.69193			−0.00783293			−0.00391647	−	0.999992i	$-0.501247\pi$
$599$	−4.69193			−0.00783293			−0.00391647	+	0.999992i	$0.501247\pi$
$600$	712.258			1.18710
$601$	535.980			0.891814			0.445907	−	0.895079i	$-0.352881\pi$
$601$	535.980			0.891814			0.445907	+	0.895079i	$0.352881\pi$
$602$	−534.042			−0.887113
$603$			187.443i			0.310851i
$604$	−876.779			−1.45162
$605$			895.127i			1.47955i
$606$	−64.6425			−0.106671
$607$	−762.383			−1.25599			−0.627993	−	0.778219i	$-0.716123\pi$
$607$	−762.383			−1.25599			−0.627993	+	0.778219i	$0.716123\pi$
$608$			1055.54i			1.73608i
$609$			193.238i			0.317303i
$610$	−1725.19			−2.82818
$611$	−372.367			−0.609439
$612$			221.407i			0.361777i
$613$		−	1181.50i		−	1.92741i	−0.266970	−	0.963705i	$-0.586022\pi$
$613$		−	1181.50i		−	1.92741i	0.266970	−	0.963705i	$-0.413978\pi$
$614$	49.0528			0.0798906
$615$			511.117i			0.831085i
$616$	−837.158			−1.35902
$617$			759.639i			1.23118i	0.788066	+	0.615590i	$0.211082\pi$
$617$			759.639i			1.23118i	−0.788066	+	0.615590i	$0.788918\pi$
$618$		−	1038.82i		−	1.68093i
$619$			818.449i			1.32221i	0.750292	+	0.661106i	$0.229913\pi$
$619$			818.449i			1.32221i	−0.750292	+	0.661106i	$0.770087\pi$
$620$		−	2199.96i		−	3.54831i
$621$	−115.766	+	29.6869i	−0.186418	+	0.0478050i
$622$	−788.172			−1.26716
$623$	−351.189			−0.563707
$624$	1395.78			2.23683
$625$	−714.186			−1.14270
$626$			503.493i			0.804302i
$627$	−591.566			−0.943486
$628$			104.604i			0.166567i
$629$	−134.672			−0.214105
$630$	−196.576			−0.312025
$631$		−	870.019i		−	1.37879i	−0.724384	−	0.689397i	$-0.757876\pi$
$631$		−	870.019i		−	1.37879i	0.724384	−	0.689397i	$-0.242124\pi$
$632$			2481.55i			3.92650i
$633$	−314.160			−0.496303
$634$	133.449			0.210487
$635$		−	538.817i		−	0.848531i
$636$		−	1655.96i		−	2.60371i
$637$	160.590			0.252103
$638$		−	2459.58i		−	3.85515i
$639$	−390.219			−0.610672
$640$			345.578i			0.539966i
$641$			426.398i			0.665208i	0.943067	+	0.332604i	$0.107927\pi$
$641$			426.398i			0.665208i	−0.943067	+	0.332604i	$0.892073\pi$
$642$			74.1615i			0.115516i
$643$			336.988i			0.524087i	0.965056	+	0.262044i	$0.0843964\pi$
$643$			336.988i			0.524087i	−0.965056	+	0.262044i	$0.915604\pi$
$644$	−142.463	−	555.541i	−0.221215	−	0.862641i
$645$	644.973			0.999957
$646$	−615.560			−0.952879
$647$	383.437			0.592638			0.296319	−	0.955089i	$-0.404241\pi$
$647$	383.437			0.592638			0.296319	+	0.955089i	$0.404241\pi$
$648$	178.885			0.276057
$649$		−	204.626i		−	0.315294i
$650$	1739.07			2.67550
$651$			158.251i			0.243089i
$652$	−1846.49			−2.83204
$653$	366.277			0.560914			0.280457	−	0.959867i	$-0.409514\pi$
$653$	366.277			0.560914			0.280457	+	0.959867i	$0.409514\pi$
$654$			561.805i			0.859029i
$655$			103.589i			0.158151i
$656$	1533.52			2.33769
$657$	126.966			0.193251
$658$		−	157.345i		−	0.239127i
$659$			926.855i			1.40646i	0.710964	+	0.703229i	$0.248259\pi$
$659$			926.855i			1.40646i	−0.710964	+	0.703229i	$0.751741\pi$
$660$	1756.56			2.66146
$661$			406.139i			0.614431i	0.951640	+	0.307215i	$0.0993972\pi$
$661$			406.139i			0.614431i	−0.951640	+	0.307215i	$0.900603\pi$
$662$	−2318.51			−3.50228
$663$			311.159i			0.469319i
$664$			1080.95i			1.62794i
$665$		−	383.682i		−	0.576966i
$666$			189.038i			0.283841i
$667$	939.463	−	240.916i	1.40849	−	0.361193i
$668$	−1602.47			−2.39891
$669$	−618.769			−0.924917
$670$	1547.42			2.30958
$671$	−1108.93			−1.65265
$672$			225.459i			0.335504i
$673$	343.906			0.511004			0.255502	−	0.966808i	$-0.417759\pi$
$673$	343.906			0.511004			0.255502	+	0.966808i	$0.417759\pi$
$674$		−	787.437i		−	1.16830i
$675$	107.505			0.159266
$676$	3367.53			4.98155
$677$		−	932.182i		−	1.37693i	−0.725269	−	0.688465i	$-0.758285\pi$
$677$		−	932.182i		−	1.37693i	0.725269	−	0.688465i	$-0.241715\pi$
$678$		−	542.123i		−	0.799592i
$679$	14.4436			0.0212718
$680$	1052.06			1.54715
$681$		−	124.890i		−	0.183392i
$682$		−	2014.27i		−	2.95347i
$683$	−875.009			−1.28113			−0.640563	−	0.767906i	$-0.721299\pi$
$683$	−875.009			−1.28113			−0.640563	+	0.767906i	$0.721299\pi$
$684$			606.605i			0.886850i
$685$	−645.372			−0.942149
$686$			67.8578i			0.0989181i
$687$			229.246i			0.333691i
$688$		−	1935.14i		−	2.81270i
$689$		−	2327.23i		−	3.37769i
$690$	245.078	+	955.693i	0.355185	+	1.38506i
$691$	201.947			0.292253			0.146126	−	0.989266i	$-0.453319\pi$
$691$	201.947			0.292253			0.146126	+	0.989266i	$0.453319\pi$
$692$	−519.752			−0.751086
$693$	−126.356			−0.182332
$694$	1551.86			2.23611
$695$			92.9341i			0.133718i
$696$	−1451.69			−2.08576
$697$			341.865i			0.490480i
$698$	−640.312			−0.917352
$699$	−93.3748			−0.133583
$700$			515.898i			0.736996i
$701$		−	315.976i		−	0.450751i	−0.974272	−	0.225375i	$-0.927639\pi$
$701$		−	315.976i		−	0.450751i	0.974272	−	0.225375i	$-0.0723608\pi$
$702$	436.772			0.622182
$703$	−368.970			−0.524850
$704$		−	632.916i		−	0.899029i
$705$			190.029i			0.269545i
$706$	199.587			0.282701
$707$		−	26.9497i		−	0.0381184i
$708$	−209.828			−0.296367
$709$		−	200.378i		−	0.282621i	−0.989965	−	0.141310i	$-0.954868\pi$
$709$		−	200.378i		−	0.282621i	0.989965	−	0.141310i	$-0.0451316\pi$
$710$			3221.42i			4.53721i
$711$			374.552i			0.526797i
$712$		−	2638.30i		−	3.70548i
$713$	769.370	−	197.297i	1.07906	−	0.276714i
$714$	−131.481			−0.184148
$715$	2468.62			3.45261
$716$	−1158.51			−1.61803
$717$	−256.801			−0.358160
$718$		−	331.105i		−	0.461149i
$719$	−1296.09			−1.80262			−0.901311	−	0.433172i	$-0.857394\pi$
$719$	−1296.09			−1.80262			−0.901311	+	0.433172i	$0.857394\pi$
$720$		−	712.305i		−	0.989313i
$721$	433.086			0.600675
$722$	−363.794			−0.503870
$723$		−	698.399i		−	0.965974i
$724$		−	2261.14i		−	3.12312i
$725$	−872.423			−1.20334
$726$	840.410			1.15759
$727$		−	597.000i		−	0.821183i	−0.911819	−	0.410591i	$-0.865322\pi$
$727$		−	597.000i		−	0.821183i	0.911819	−	0.410591i	$-0.134678\pi$
$728$			1206.43i			1.65718i
$729$	27.0000			0.0370370
$730$		−	1048.16i		−	1.43583i
$731$	431.395			0.590144
$732$			1137.12i			1.55344i
$733$		−	72.2110i		−	0.0985143i	−0.998786	−	0.0492572i	$-0.984315\pi$
$733$		−	72.2110i		−	0.0985143i	0.998786	−	0.0492572i	$-0.0156854\pi$
$734$		−	96.4778i		−	0.131441i
$735$		−	81.9532i		−	0.111501i
$736$	1096.11	−	281.087i	1.48928	−	0.381911i
$737$	994.661			1.34961
$738$	479.874			0.650235
$739$	−740.480			−1.00200			−0.501002	−	0.865446i	$-0.667035\pi$
$739$	−740.480			−1.00200			−0.501002	+	0.865446i	$0.667035\pi$
$740$	1095.60			1.48054
$741$			852.503i			1.15048i
$742$	983.381			1.32531
$743$			741.435i			0.997894i	0.866632	+	0.498947i	$0.166280\pi$
$743$			741.435i			0.997894i	−0.866632	+	0.498947i	$0.833720\pi$
$744$	−1188.86			−1.59793
$745$	−483.958			−0.649609
$746$		−	1096.76i		−	1.47019i
$747$			163.153i			0.218412i
$748$	1174.89			1.57071
$749$	−30.9182			−0.0412793
$750$			184.915i			0.246553i
$751$			465.752i			0.620176i	0.950708	+	0.310088i	$0.100358\pi$
$751$			465.752i			0.620176i	−0.950708	+	0.310088i	$0.899642\pi$
$752$	570.151			0.758179
$753$		−	764.163i		−	1.01482i
$754$	−3544.50			−4.70092
$755$			628.822i			0.832877i
$756$			129.569i			0.171387i
$757$			743.346i			0.981964i	0.871170	+	0.490982i	$0.163362\pi$
$757$			743.346i			0.981964i	−0.871170	+	0.490982i	$0.836638\pi$
$758$		−	230.151i		−	0.303630i
$759$	157.533	+	614.307i	0.207553	+	0.809363i
$760$	2882.40			3.79263
$761$	−353.882			−0.465023			−0.232511	−	0.972594i	$-0.574694\pi$
$761$	−353.882			−0.465023			−0.232511	+	0.972594i	$0.574694\pi$
$762$	−505.880			−0.663885
$763$	−234.218			−0.306970
$764$			1137.81i			1.48927i
$765$	158.793			0.207572
$766$		−	542.845i		−	0.708674i
$767$	−294.885			−0.384466
$768$	599.902			0.781122
$769$		−	410.265i		−	0.533505i	−0.963765	−	0.266752i	$-0.914049\pi$
$769$		−	410.265i		−	0.533505i	0.963765	−	0.266752i	$-0.0859506\pi$
$770$			1043.12i			1.35471i
$771$	−44.9016			−0.0582381
$772$	−1620.76			−2.09943
$773$			972.411i			1.25797i	0.777417	+	0.628985i	$0.216529\pi$
$773$			972.411i			1.25797i	−0.777417	+	0.628985i	$0.783471\pi$
$774$		−	605.547i		−	0.782360i
$775$	−714.468			−0.921894
$776$			108.507i			0.139828i
$777$	−78.8106			−0.101429
$778$		−	306.106i		−	0.393452i
$779$			936.630i			1.20235i
$780$		−	2531.38i		−	3.24535i
$781$			2070.68i			2.65133i
$782$	163.922	+	639.223i	0.209619	+	0.817421i
$783$	−219.111			−0.279835
$784$	−245.887			−0.313632
$785$	75.0215			0.0955688
$786$	97.2565			0.123736
$787$			277.056i			0.352040i	0.984387	+	0.176020i	$0.0563224\pi$
$787$			277.056i			0.352040i	−0.984387	+	0.176020i	$0.943678\pi$
$788$	−585.446			−0.742952
$789$		−	251.652i		−	0.318951i
$790$	3092.08			3.91403
$791$	226.013			0.285731
$792$		−	949.248i		−	1.19855i
$793$			1598.07i			2.01522i
$794$	−1397.19			−1.75969
$795$	−1187.65			−1.49390
$796$		−	1721.99i		−	2.16331i
$797$		−	668.830i		−	0.839184i	−0.907713	−	0.419592i	$-0.862173\pi$
$797$		−	668.830i		−	0.839184i	0.907713	−	0.419592i	$-0.137827\pi$
$798$	−360.229			−0.451414
$799$			127.102i			0.159077i
$800$	−1017.89			−1.27237
$801$		−	398.211i		−	0.497143i
$802$		−	1187.24i		−	1.48035i
$803$		−	673.741i		−	0.839030i
$804$		−	1019.95i		−	1.26859i
$805$	−398.432	+	102.174i	−0.494946	+	0.126924i
$806$	−2902.75			−3.60143
$807$	−406.520			−0.503742
$808$	202.459			0.250568
$809$	785.371			0.970792			0.485396	−	0.874294i	$-0.338675\pi$
$809$	785.371			0.970792			0.485396	+	0.874294i	$0.338675\pi$
$810$		−	222.896i		−	0.275180i
$811$	−213.692			−0.263492			−0.131746	−	0.991284i	$-0.542058\pi$
$811$	−213.692			−0.263492			−0.131746	+	0.991284i	$0.542058\pi$
$812$		−	1051.48i		−	1.29492i
$813$	272.396			0.335050
$814$	1003.12			1.23234
$815$			1324.30i			1.62490i
$816$		−	476.431i		−	0.583862i
$817$	1181.92			1.44666
$818$	2835.00			3.46577
$819$			182.092i			0.222334i
$820$		−	2781.18i		−	3.39168i
$821$	1012.73			1.23354			0.616768	−	0.787145i	$-0.288442\pi$
$821$	1012.73			1.23354			0.616768	+	0.787145i	$0.288442\pi$
$822$			605.922i			0.737131i
$823$	−1269.45			−1.54247			−0.771233	−	0.636553i	$-0.780360\pi$
$823$	−1269.45			−1.54247			−0.771233	+	0.636553i	$0.780360\pi$
$824$			3253.55i			3.94848i
$825$		−	570.470i		−	0.691478i
$826$		−	124.605i		−	0.150853i
$827$			672.019i			0.812599i	0.913740	+	0.406299i	$0.133181\pi$
$827$			672.019i			0.812599i	−0.913740	+	0.406299i	$0.866819\pi$
$828$	629.924	−	161.538i	0.760778	−	0.195094i
$829$	27.0238			0.0325981			0.0162991	−	0.999867i	$-0.494812\pi$
$829$	27.0238			0.0325981			0.0162991	+	0.999867i	$0.494812\pi$
$830$	1346.90			1.62277
$831$	−38.7561			−0.0466380
$832$	−912.093			−1.09627
$833$		−	54.8150i		−	0.0658044i
$834$	87.2532			0.104620
$835$			1149.29i			1.37639i
$836$	3218.93			3.85039
$837$	−179.440			−0.214385
$838$		−	1969.47i		−	2.35020i
$839$			247.980i			0.295566i	0.989020	+	0.147783i	$0.0472138\pi$
$839$			247.980i			0.295566i	−0.989020	+	0.147783i	$0.952786\pi$
$840$	615.671			0.732941
$841$	937.131			1.11431
$842$		−	1116.38i		−	1.32587i
$843$		−	805.155i		−	0.955107i
$844$	1709.46			2.02543
$845$		−	2415.18i		−	2.85820i
$846$	178.413			0.210890
$847$			350.370i			0.413660i
$848$			3563.34i			4.20205i
$849$			266.851i			0.314312i
$850$		−	593.608i		−	0.698362i
$851$	98.2558	+	383.154i	0.115459	+	0.450239i
$852$	2123.33			2.49217
$853$	−1580.09			−1.85239			−0.926197	−	0.377040i	$-0.876942\pi$
$853$	−1580.09			−1.85239			−0.926197	+	0.377040i	$0.876942\pi$
$854$	−675.272			−0.790716
$855$	435.055			0.508836
$856$		−	232.272i		−	0.271346i
$857$	1316.07			1.53568			0.767838	−	0.640644i	$-0.221333\pi$
$857$	1316.07			1.53568			0.767838	+	0.640644i	$0.221333\pi$
$858$		−	2317.71i		−	2.70130i
$859$	−296.834			−0.345557			−0.172779	−	0.984961i	$-0.555275\pi$
$859$	−296.834			−0.345557			−0.172779	+	0.984961i	$0.555275\pi$
$860$	−3509.54			−4.08086
$861$			200.061i			0.232359i
$862$			1421.38i			1.64893i
$863$	89.2043			0.103365			0.0516827	−	0.998664i	$-0.483542\pi$
$863$	89.2043			0.103365			0.0516827	+	0.998664i	$0.483542\pi$
$864$	−255.646			−0.295887
$865$			372.764i			0.430941i
$866$		−	600.392i		−	0.693294i
$867$	−394.353			−0.454848
$868$		−	861.104i		−	0.992056i
$869$	1987.55			2.28717
$870$			1808.85i			2.07914i
$871$		−	1433.40i		−	1.64570i
$872$		−	1759.56i		−	2.01784i
$873$			16.3775i			0.0187600i
$874$	449.109	+	1751.32i	0.513854	+	2.00380i
$875$	−77.0916			−0.0881047
$876$	−690.870			−0.788665
$877$	−983.991			−1.12200			−0.560998	−	0.827817i	$-0.689583\pi$
$877$	−983.991			−1.12200			−0.560998	+	0.827817i	$0.689583\pi$
$878$	−2097.61			−2.38907
$879$		−	225.618i		−	0.256675i
$880$	−3779.82			−4.29525
$881$		−	199.834i		−	0.226826i	−0.993548	−	0.113413i	$-0.963822\pi$
$881$		−	199.834i		−	0.226826i	0.993548	−	0.113413i	$-0.0361783\pi$
$882$	−76.9435			−0.0872376
$883$	−333.363			−0.377535			−0.188767	−	0.982022i	$-0.560449\pi$
$883$	−333.363			−0.377535			−0.188767	+	0.982022i	$0.560449\pi$
$884$		−	1693.13i		−	1.91531i
$885$			150.488i			0.170043i
$886$	−2438.00			−2.75170
$887$	−493.686			−0.556580			−0.278290	−	0.960497i	$-0.589768\pi$
$887$	−493.686			−0.556580			−0.278290	+	0.960497i	$0.589768\pi$
$888$		−	592.062i		−	0.666737i
$889$		−	210.903i		−	0.237237i
$890$	−3287.40			−3.69371
$891$		−	143.275i		−	0.160802i
$892$	3366.96			3.77461
$893$			348.231i			0.389956i
$894$			454.375i			0.508250i
$895$			830.880i			0.928357i
$896$			135.266i			0.150966i
$897$	885.275	−	227.020i	0.986929	−	0.253088i
$898$	−47.6531			−0.0530658
$899$	1456.19			1.61979
$900$	−584.973			−0.649970
$901$	−794.367			−0.881651
$902$		−	2546.43i		−	2.82310i
$903$	252.455			0.279573
$904$			1697.92i			1.87823i
$905$	−1621.68			−1.79191
$906$	590.384			0.651638
$907$		−	248.878i		−	0.274397i	−0.990544	−	0.137198i	$-0.956190\pi$
$907$		−	248.878i		−	0.274397i	0.990544	−	0.137198i	$-0.0438098\pi$
$908$			679.575i			0.748430i
$909$	30.5581			0.0336172
$910$	1503.24			1.65191
$911$		−	981.755i		−	1.07767i	−0.842412	−	0.538834i	$-0.818865\pi$
$911$		−	981.755i		−	1.07767i	0.842412	−	0.538834i	$-0.181135\pi$
$912$		−	1305.31i		−	1.43126i
$913$	865.768			0.948267
$914$			2135.72i			2.33667i
$915$	815.538			0.891299
$916$		−	1247.41i		−	1.36180i
$917$			40.5466i			0.0442165i
$918$		−	149.086i		−	0.162403i
$919$		−	1393.58i		−	1.51640i	−0.652020	−	0.758202i	$-0.726078\pi$
$919$		−	1393.58i		−	1.51640i	0.652020	−	0.758202i	$-0.273922\pi$
$920$	−767.577	−	2993.21i	−0.834322	−	3.25349i
$921$	−23.1885			−0.0251775
$922$	−1877.79			−2.03665
$923$	2984.06			3.23300
$924$	687.552			0.744104
$925$		−	355.812i		−	0.384661i
$926$	−365.681			−0.394904
$927$			491.074i			0.529745i
$928$	2074.62			2.23559
$929$	−606.923			−0.653308			−0.326654	−	0.945144i	$-0.605921\pi$
$929$	−606.923			−0.653308			−0.326654	+	0.945144i	$0.605921\pi$
$930$			1481.35i			1.59285i
$931$		−	150.181i		−	0.161311i
$932$	508.087			0.545158
$933$	372.588			0.399344
$934$			3061.18i			3.27749i
$935$		−	842.627i		−	0.901206i
$936$	−1367.96			−1.46149
$937$		−	878.710i		−	0.937791i	−0.883254	−	0.468895i	$-0.844652\pi$
$937$		−	878.710i		−	0.937791i	0.883254	−	0.468895i	$-0.155348\pi$
$938$	605.690			0.645725
$939$		−	238.013i		−	0.253475i
$940$		−	1034.02i		−	1.10002i
$941$			382.353i			0.406326i	0.979145	+	0.203163i	$0.0651221\pi$
$941$			382.353i			0.406326i	−0.979145	+	0.203163i	$0.934878\pi$
$942$		−	70.4356i		−	0.0747724i
$943$	972.637	−	249.423i	1.03143	−	0.264499i
$944$	451.514			0.478299
$945$	92.9262			0.0983346
$946$	−3213.31			−3.39674
$947$	296.477			0.313070			0.156535	−	0.987672i	$-0.449968\pi$
$947$	296.477			0.313070			0.156535	+	0.987672i	$0.449968\pi$
$948$		−	2038.08i		−	2.14987i
$949$	−970.926			−1.02310
$950$		−	1626.35i		−	1.71195i
$951$	−63.0845			−0.0663349
$952$	411.796			0.432559
$953$		−	311.161i		−	0.326507i	−0.986584	−	0.163253i	$-0.947801\pi$
$953$		−	311.161i		−	0.326507i	0.986584	−	0.163253i	$-0.0521988\pi$
$954$			1115.05i			1.16881i
$955$	816.029			0.854481
$956$	1397.35			1.46166
$957$			1162.70i			1.21495i
$958$			2147.34i			2.24149i
$959$	−252.611			−0.263411
$960$			465.465i			0.484860i
$961$	231.545			0.240942
$962$		−	1445.60i		−	1.50270i
$963$		−	35.0579i		−	0.0364049i
$964$			3800.25i			3.94217i
$965$			1162.40i			1.20456i
$966$	95.9280	+	374.077i	0.0993044	+	0.387243i
$967$	−1703.54			−1.76168			−0.880839	−	0.473417i	$-0.843021\pi$
$967$	−1703.54			−1.76168			−0.880839	+	0.473417i	$0.843021\pi$
$968$	−2632.14			−2.71915
$969$	290.990			0.300299
$970$	135.203			0.139384
$971$			827.966i			0.852695i	0.904560	+	0.426347i	$0.140200\pi$
$971$			827.966i			0.852695i	−0.904560	+	0.426347i	$0.859800\pi$
$972$	−146.917			−0.151149
$973$			36.3762i			0.0373856i
$974$	3295.40			3.38337
$975$	−822.101			−0.843181
$976$		−	2446.89i		−	2.50706i
$977$			694.742i			0.711097i	0.934658	+	0.355549i	$0.115706\pi$
$977$			694.742i			0.711097i	−0.934658	+	0.355549i	$0.884294\pi$
$978$	1243.34			1.27131
$979$	−2113.09			−2.15842
$980$			445.938i			0.455039i
$981$		−	265.579i		−	0.270723i
$982$	2513.74			2.55982
$983$		−	1669.54i		−	1.69842i	−0.528058	−	0.849208i	$-0.677080\pi$
$983$		−	1669.54i		−	1.69842i	0.528058	−	0.849208i	$-0.322920\pi$
$984$	−1502.95			−1.52739
$985$			419.879i			0.426274i
$986$			1209.86i			1.22704i
$987$			74.3809i			0.0753606i
$988$		−	4638.79i		−	4.69513i
$989$	−314.743	−	1227.36i	−0.318244	−	1.24101i
$990$	−1182.79			−1.19474
$991$	150.532			0.151899			0.0759495	−	0.997112i	$-0.475801\pi$
$991$	150.532			0.151899			0.0759495	+	0.997112i	$0.475801\pi$
$992$	1699.01			1.71271
$993$	1096.02			1.10374
$994$			1260.92i			1.26854i
$995$	−1235.01			−1.24121
$996$		−	887.779i		−	0.891344i
$997$	1779.39			1.78475			0.892374	−	0.451297i	$-0.149039\pi$
$997$	1779.39			1.78475			0.892374	+	0.451297i	$0.149039\pi$
$998$	−1446.59			−1.44949
$999$		−	89.3629i		−	0.0894523i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.f.a.22.46	yes	48
23.22	odd	2	inner	483.3.f.a.22.45	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.f.a.22.45	✓	48	23.22	odd	2	inner
483.3.f.a.22.46	yes	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	483.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.66398 q^{2} -1.73205 q^{3} +9.42474 q^{4} -6.75938i q^{5} -6.34620 q^{6} -2.64575i q^{7} +19.8761 q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+3.66398 q^{2} -1.73205 q^{3} +9.42474 q^{4} -6.75938i q^{5} -6.34620 q^{6} -2.64575i q^{7} +19.8761 q^{8} +3.00000 q^{9} -24.7662i q^{10} -15.9194i q^{11} -16.3241 q^{12} -22.9414 q^{13} -9.69398i q^{14} +11.7076i q^{15} +35.1267 q^{16} +7.83072i q^{17} +10.9919 q^{18} +21.4544i q^{19} -63.7054i q^{20} +4.58258i q^{21} -58.3283i q^{22} +(22.2791 - 5.71325i) q^{23} -34.4265 q^{24} -20.6893 q^{25} -84.0567 q^{26} -5.19615 q^{27} -24.9355i q^{28} +42.1679 q^{29} +42.8964i q^{30} +34.5332 q^{31} +49.1991 q^{32} +27.5732i q^{33} +28.6916i q^{34} -17.8836 q^{35} +28.2742 q^{36} +17.1979i q^{37} +78.6083i q^{38} +39.7356 q^{39} -134.350i q^{40} +43.6569 q^{41} +16.7905i q^{42} -55.0901i q^{43} -150.036i q^{44} -20.2782i q^{45} +(81.6302 - 20.9332i) q^{46} +16.2312 q^{47} -60.8413 q^{48} -7.00000 q^{49} -75.8050 q^{50} -13.5632i q^{51} -216.217 q^{52} +101.442i q^{53} -19.0386 q^{54} -107.605 q^{55} -52.5873i q^{56} -37.1600i q^{57} +154.502 q^{58} +12.8539 q^{59} +110.341i q^{60} -69.6589i q^{61} +126.529 q^{62} -7.93725i q^{63} +39.7575 q^{64} +155.070i q^{65} +101.028i q^{66} +62.4811i q^{67} +73.8025i q^{68} +(-38.5886 + 9.89563i) q^{69} -65.5253 q^{70} -130.073 q^{71} +59.6284 q^{72} +42.3220 q^{73} +63.0127i q^{74} +35.8349 q^{75} +202.202i q^{76} -42.1188 q^{77} +145.591 q^{78} +124.851i q^{79} -237.435i q^{80} +9.00000 q^{81} +159.958 q^{82} +54.3845i q^{83} +43.1896i q^{84} +52.9308 q^{85} -201.849i q^{86} -73.0369 q^{87} -316.416i q^{88} -132.737i q^{89} -74.2987i q^{90} +60.6972i q^{91} +(209.975 - 53.8459i) q^{92} -59.8133 q^{93} +59.4709 q^{94} +145.018 q^{95} -85.2154 q^{96} +5.45915i q^{97} -25.6478 q^{98} -47.7582i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9}+O(q^{10}) \) 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9} + 16 q^{13} + 324 q^{16} + 12 q^{18} - 4 q^{23} - 24 q^{24} - 176 q^{25} + 136 q^{26} - 128 q^{29} - 8 q^{31} - 252 q^{32} - 56 q^{35} + 348 q^{36} + 96 q^{39} - 24 q^{41} - 148 q^{46} - 408 q^{47} - 96 q^{48} - 336 q^{49} + 236 q^{50} - 32 q^{52} - 72 q^{54} - 24 q^{55} - 56 q^{58} + 136 q^{59} + 184 q^{62} + 716 q^{64} - 48 q^{69} - 112 q^{70} + 48 q^{71} - 12 q^{72} - 224 q^{73} - 48 q^{75} + 224 q^{77} - 96 q^{78} + 432 q^{81} + 640 q^{82} - 424 q^{85} + 312 q^{87} + 1060 q^{92} + 192 q^{93} + 216 q^{94} + 624 q^{95} + 48 q^{96} - 28 q^{98}+O(q^{100}) \) 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9 + 16 * q^13 + 324 * q^16 + 12 * q^18 - 4 * q^23 - 24 * q^24 - 176 * q^25 + 136 * q^26 - 128 * q^29 - 8 * q^31 - 252 * q^32 - 56 * q^35 + 348 * q^36 + 96 * q^39 - 24 * q^41 - 148 * q^46 - 408 * q^47 - 96 * q^48 - 336 * q^49 + 236 * q^50 - 32 * q^52 - 72 * q^54 - 24 * q^55 - 56 * q^58 + 136 * q^59 + 184 * q^62 + 716 * q^64 - 48 * q^69 - 112 * q^70 + 48 * q^71 - 12 * q^72 - 224 * q^73 - 48 * q^75 + 224 * q^77 - 96 * q^78 + 432 * q^81 + 640 * q^82 - 424 * q^85 + 312 * q^87 + 1060 * q^92 + 192 * q^93 + 216 * q^94 + 624 * q^95 + 48 * q^96 - 28 * q^98

Introduction

L-functions

Modular forms

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