LMFDB - Embedded newform 45.10.b.b.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,10,Mod(19,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("45.19");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	45.b (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:	$23.1766126274$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.49740556.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 45x^{2} + 304 $ x^4 + 45*x^2 + 304
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.2
Root			$-6.05982i$ of defining polynomial
Character	$\chi$	$=$	45.19
Dual form			45.10.b.b.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.843944i q^{2} +511.288 q^{4} +(568.288 - 1276.78i) q^{5} -8712.99i q^{7} -863.597i q^{8} +O(q^{10})$	\(q-0.843944i q^{2} +511.288 q^{4} +(568.288 - 1276.78i) q^{5} -8712.99i q^{7} -863.597i q^{8} +(-1077.53 - 479.603i) q^{10} -44557.8 q^{11} -21430.4i q^{13} -7353.27 q^{14} +261051. q^{16} +300220. i q^{17} -565385. q^{19} +(290559. - 652803. i) q^{20} +37604.2i q^{22} -950727. i q^{23} +(-1.30722e6 - 1.45116e6i) q^{25} -18086.1 q^{26} -4.45485e6i q^{28} -803167. q^{29} -1.99843e6 q^{31} -662474. i q^{32} +253369. q^{34} +(-1.11246e7 - 4.95149e6i) q^{35} -9.53656e6i q^{37} +477153. i q^{38} +(-1.10263e6 - 490772. i) q^{40} +2.54355e7 q^{41} -2.32830e7i q^{43} -2.27818e7 q^{44} -802360. q^{46} -3.77353e7i q^{47} -3.55626e7 q^{49} +(-1.22470e6 + 1.10322e6i) q^{50} -1.09571e7i q^{52} +4.79297e7i q^{53} +(-2.53216e7 + 5.68906e7i) q^{55} -7.52451e6 q^{56} +677827. i q^{58} +7.00069e7 q^{59} +1.26942e8 q^{61} +1.68656e6i q^{62} +1.33099e8 q^{64} +(-2.73620e7 - 1.21787e7i) q^{65} +2.66595e8i q^{67} +1.53499e8i q^{68} +(-4.17877e6 + 9.38853e6i) q^{70} -6.59169e7 q^{71} +1.47516e7i q^{73} -8.04832e6 q^{74} -2.89074e8 q^{76} +3.88231e8i q^{77} +4.66498e7 q^{79} +(1.48352e8 - 3.33305e8i) q^{80} -2.14661e7i q^{82} -2.01840e8i q^{83} +(3.83316e8 + 1.70611e8i) q^{85} -1.96495e7 q^{86} +3.84800e7i q^{88} +5.54039e8 q^{89} -1.86723e8 q^{91} -4.86095e8i q^{92} -3.18465e7 q^{94} +(-3.21301e8 + 7.21874e8i) q^{95} -3.39489e8i q^{97} +3.00128e7i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 1368 q^{4} - 1140 q^{5}+O(q^{10}) $ 4 * q - 1368 * q^4 - 1140 * q^5	$ 4 q - 1368 q^{4} - 1140 q^{5} - 69160 q^{10} - 109968 q^{11} + 424536 q^{14} + 1631264 q^{16} - 636880 q^{19} + 3302280 q^{20} - 1337900 q^{25} - 6618768 q^{26} + 3531720 q^{29} - 10587712 q^{31} + 26434624 q^{34} - 13629840 q^{35} + 43578400 q^{40} + 16788552 q^{41} - 20638944 q^{44} - 61250072 q^{46} - 46921028 q^{49} + 150092400 q^{50} - 26907120 q^{55} - 315178080 q^{56} + 460829040 q^{59} + 360490568 q^{61} + 134995072 q^{64} - 183895680 q^{65} - 508341960 q^{70} + 47611872 q^{71} - 1176861744 q^{74} - 1168489440 q^{76} - 728043520 q^{79} - 965843040 q^{80} + 1275419840 q^{85} + 2375904552 q^{86} + 1582700760 q^{89} + 473322528 q^{91} + 3327101704 q^{94} - 1204791600 q^{95}+O(q^{100}) $ 4 * q - 1368 * q^4 - 1140 * q^5 - 69160 * q^10 - 109968 * q^11 + 424536 * q^14 + 1631264 * q^16 - 636880 * q^19 + 3302280 * q^20 - 1337900 * q^25 - 6618768 * q^26 + 3531720 * q^29 - 10587712 * q^31 + 26434624 * q^34 - 13629840 * q^35 + 43578400 * q^40 + 16788552 * q^41 - 20638944 * q^44 - 61250072 * q^46 - 46921028 * q^49 + 150092400 * q^50 - 26907120 * q^55 - 315178080 * q^56 + 460829040 * q^59 + 360490568 * q^61 + 134995072 * q^64 - 183895680 * q^65 - 508341960 * q^70 + 47611872 * q^71 - 1176861744 * q^74 - 1168489440 * q^76 - 728043520 * q^79 - 965843040 * q^80 + 1275419840 * q^85 + 2375904552 * q^86 + 1582700760 * q^89 + 473322528 * q^91 + 3327101704 * q^94 - 1204791600 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	0.843944i		−	0.0372974i	−0.999826	−	0.0186487i	$-0.994064\pi$
$2$		−	0.843944i		−	0.0372974i	0.999826	−	0.0186487i	$-0.00593641\pi$
$3$		0			0
$3$		0			0
$4$	511.288			0.998609
$5$	568.288	−	1276.78i	0.406634	−	0.913591i
$5$	568.288	−	1276.78i	0.406634	−	0.913591i
$6$		0			0
$7$		−	8712.99i		−	1.37160i	−0.727792	−	0.685798i	$-0.759453\pi$
$7$		−	8712.99i		−	1.37160i	0.727792	−	0.685798i	$-0.240547\pi$
$8$		−	863.597i		−	0.0745429i
$9$		0			0
$10$	−1077.53	−	479.603i	−0.0340746	−	0.0151664i
$11$	−44557.8			−0.917606			−0.458803	−	0.888538i	$-0.651722\pi$
$11$	−44557.8			−0.917606			−0.458803	+	0.888538i	$0.651722\pi$
$12$		0			0
$13$		−	21430.4i		−	0.208107i	−0.994572	−	0.104053i	$-0.966819\pi$
$13$		−	21430.4i		−	0.208107i	0.994572	−	0.104053i	$-0.0331813\pi$
$14$	−7353.27			−0.0511569
$15$		0			0
$16$	261051.			0.995829
$17$			300220.i			0.871805i	0.899994	+	0.435903i	$0.143571\pi$
$17$			300220.i			0.871805i	−0.899994	+	0.435903i	$0.856429\pi$
$18$		0			0
$19$	−565385.			−0.995298			−0.497649	−	0.867379i	$-0.665803\pi$
$19$	−565385.			−0.995298			−0.497649	+	0.867379i	$0.665803\pi$
$20$	290559.	−	652803.i	0.406068	−	0.912320i
$21$		0			0
$22$			37604.2i			0.0342243i
$23$		−	950727.i		−	0.708403i	−0.935169	−	0.354202i	$-0.884753\pi$
$23$		−	950727.i		−	0.708403i	0.935169	−	0.354202i	$-0.115247\pi$
$24$		0			0
$25$	−1.30722e6	−	1.45116e6i	−0.669298	−	0.742994i
$26$	−18086.1			−0.00776183
$27$		0			0
$28$		−	4.45485e6i		−	1.36969i
$29$	−803167.			−0.210870			−0.105435	−	0.994426i	$-0.533623\pi$
$29$	−803167.			−0.210870			−0.105435	+	0.994426i	$0.533623\pi$
$30$		0			0
$31$	−1.99843e6			−0.388652			−0.194326	−	0.980937i	$-0.562252\pi$
$31$	−1.99843e6			−0.388652			−0.194326	+	0.980937i	$0.562252\pi$
$32$		−	662474.i		−	0.111685i
$33$		0			0
$34$	253369.			0.0325161
$35$	−1.11246e7	−	4.95149e6i	−1.25308	−	0.557737i
$36$		0			0
$37$		−	9.53656e6i		−	0.836535i	−0.908324	−	0.418267i	$-0.862637\pi$
$37$		−	9.53656e6i		−	0.836535i	0.908324	−	0.418267i	$-0.137363\pi$
$38$			477153.i			0.0371220i
$39$		0			0
$40$	−1.10263e6	−	490772.i	−0.0681017	−	0.0303116i
$41$	2.54355e7			1.40576			0.702882	−	0.711306i	$-0.251896\pi$
$41$	2.54355e7			1.40576			0.702882	+	0.711306i	$0.251896\pi$
$42$		0			0
$43$		−	2.32830e7i		−	1.03856i	−0.854605	−	0.519279i	$-0.826200\pi$
$43$		−	2.32830e7i		−	1.03856i	0.854605	−	0.519279i	$-0.173800\pi$
$44$	−2.27818e7			−0.916329
$45$		0			0
$46$	−802360.			−0.0264216
$47$		−	3.77353e7i		−	1.12800i	−0.825776	−	0.563998i	$-0.809262\pi$
$47$		−	3.77353e7i		−	1.12800i	0.825776	−	0.563998i	$-0.190738\pi$
$48$		0			0
$49$	−3.55626e7			−0.881274
$50$	−1.22470e6	+	1.10322e6i	−0.0277117	+	0.0249631i
$51$		0			0
$52$		−	1.09571e7i		−	0.207817i
$53$			4.79297e7i			0.834379i	0.908819	+	0.417190i	$0.136985\pi$
$53$			4.79297e7i			0.834379i	−0.908819	+	0.417190i	$0.863015\pi$
$54$		0			0
$55$	−2.53216e7	+	5.68906e7i	−0.373129	+	0.838317i
$56$	−7.52451e6			−0.102243
$57$		0			0
$58$			677827.i			0.00786490i
$59$	7.00069e7			0.752154			0.376077	−	0.926588i	$-0.377273\pi$
$59$	7.00069e7			0.752154			0.376077	+	0.926588i	$0.377273\pi$
$60$		0			0
$61$	1.26942e8			1.17387			0.586936	−	0.809633i	$-0.300334\pi$
$61$	1.26942e8			1.17387			0.586936	+	0.809633i	$0.300334\pi$
$62$			1.68656e6i			0.0144957i
$63$		0			0
$64$	1.33099e8			0.991663
$65$	−2.73620e7	−	1.21787e7i	−0.190124	−	0.0846231i
$66$		0			0
$67$			2.66595e8i			1.61628i	0.588993	+	0.808138i	$0.299525\pi$
$67$			2.66595e8i			1.61628i	−0.588993	+	0.808138i	$0.700475\pi$
$68$			1.53499e8i			0.870593i
$69$		0			0
$70$	−4.17877e6	+	9.38853e6i	−0.0208021	+	0.0467365i
$71$	−6.59169e7			−0.307846			−0.153923	−	0.988083i	$-0.549191\pi$
$71$	−6.59169e7			−0.307846			−0.153923	+	0.988083i	$0.549191\pi$
$72$		0			0
$73$			1.47516e7i			0.0607977i	0.999538	+	0.0303989i	$0.00967775\pi$
$73$			1.47516e7i			0.0607977i	−0.999538	+	0.0303989i	$0.990322\pi$
$74$	−8.04832e6			−0.0312006
$75$		0			0
$76$	−2.89074e8			−0.993913
$77$			3.88231e8i			1.25858i
$78$		0			0
$79$	4.66498e7			0.134750			0.0673748	−	0.997728i	$-0.478538\pi$
$79$	4.66498e7			0.134750			0.0673748	+	0.997728i	$0.478538\pi$
$80$	1.48352e8	−	3.33305e8i	0.404937	−	0.909780i
$81$		0			0
$82$		−	2.14661e7i		−	0.0524313i
$83$		−	2.01840e8i		−	0.466826i	−0.972378	−	0.233413i	$-0.925011\pi$
$83$		−	2.01840e8i		−	0.466826i	0.972378	−	0.233413i	$-0.0749895\pi$
$84$		0			0
$85$	3.83316e8	+	1.70611e8i	0.796474	+	0.354505i
$86$	−1.96495e7			−0.0387355
$87$		0			0
$88$			3.84800e7i			0.0684010i
$89$	5.54039e8			0.936020			0.468010	−	0.883723i	$-0.344971\pi$
$89$	5.54039e8			0.936020			0.468010	+	0.883723i	$0.344971\pi$
$90$		0			0
$91$	−1.86723e8			−0.285438
$92$		−	4.86095e8i		−	0.707418i
$93$		0			0
$94$	−3.18465e7			−0.0420713
$95$	−3.21301e8	+	7.21874e8i	−0.404722	+	0.909295i
$96$		0			0
$97$		−	3.39489e8i		−	0.389361i	−0.980867	−	0.194681i	$-0.937633\pi$
$97$		−	3.39489e8i		−	0.389361i	0.980867	−	0.194681i	$-0.0623670\pi$
$98$			3.00128e7i			0.0328692i
$99$		0			0
$100$	−6.68367e8	−	7.41960e8i	−0.668367	−	0.741960i
$101$	−1.33921e9			−1.28056			−0.640282	−	0.768140i	$-0.721183\pi$
$101$	−1.33921e9			−1.28056			−0.640282	+	0.768140i	$0.721183\pi$
$102$		0			0
$103$		−	3.84306e8i		−	0.336442i	−0.985749	−	0.168221i	$-0.946198\pi$
$103$		−	3.84306e8i		−	0.336442i	0.985749	−	0.168221i	$-0.0538022\pi$
$104$	−1.85073e7			−0.0155129
$105$		0			0
$106$	4.04500e7			0.0311202
$107$		−	7.97379e8i		−	0.588082i	−0.955793	−	0.294041i	$-0.905000\pi$
$107$		−	7.97379e8i		−	0.588082i	0.955793	−	0.294041i	$-0.0950002\pi$
$108$		0			0
$109$	6.63230e8			0.450034			0.225017	−	0.974355i	$-0.427756\pi$
$109$	6.63230e8			0.450034			0.225017	+	0.974355i	$0.427756\pi$
$110$	4.80124e7	+	2.13700e7i	0.0312670	+	0.0139168i
$111$		0			0
$112$		−	2.27453e9i		−	1.36587i
$113$		−	1.48164e9i		−	0.854847i	−0.904051	−	0.427424i	$-0.859421\pi$
$113$		−	1.48164e9i		−	0.854847i	0.904051	−	0.427424i	$-0.140579\pi$
$114$		0			0
$115$	−1.21387e9	−	5.40286e8i	−0.647191	−	0.288060i
$116$	−4.10649e8			−0.210577
$117$		0			0
$118$		−	5.90819e7i		−	0.0280534i
$119$	2.61581e9			1.19576
$120$		0			0
$121$	−3.72554e8			−0.157999
$122$		−	1.07132e8i		−	0.0437824i
$123$		0			0
$124$	−1.02177e9			−0.388112
$125$	−2.59569e9	+	8.44363e8i	−0.950952	+	0.309339i
$126$		0			0
$127$			2.28772e9i			0.780344i	0.920742	+	0.390172i	$0.127584\pi$
$127$			2.28772e9i			0.780344i	−0.920742	+	0.390172i	$0.872416\pi$
$128$		−	4.51514e8i		−	0.148671i
$129$		0			0
$130$	−1.02781e7	+	2.30920e7i	−0.00315622	+	0.00709114i
$131$	3.83999e9			1.13922			0.569612	−	0.821914i	$-0.307094\pi$
$131$	3.83999e9			1.13922			0.569612	+	0.821914i	$0.307094\pi$
$132$		0			0
$133$			4.92619e9i			1.36515i
$134$	2.24991e8			0.0602829
$135$		0			0
$136$	2.59269e8			0.0649869
$137$			5.82666e9i			1.41311i	0.707657	+	0.706556i	$0.249752\pi$
$137$			5.82666e9i			1.41311i	−0.707657	+	0.706556i	$0.750248\pi$
$138$		0			0
$139$	5.89895e9			1.34032			0.670159	−	0.742217i	$-0.266226\pi$
$139$	5.89895e9			1.34032			0.670159	+	0.742217i	$0.266226\pi$
$140$	−5.68787e9	−	2.53163e9i	−1.25133	−	0.556961i
$141$		0			0
$142$			5.56301e7i			0.0114819i
$143$			9.54892e8i			0.190960i
$144$		0			0
$145$	−4.56430e8	+	1.02547e9i	−0.0857468	+	0.192649i
$146$	1.24495e7			0.00226760
$147$		0			0
$148$		−	4.87593e9i		−	0.835371i
$149$	5.39333e9			0.896436			0.448218	−	0.893924i	$-0.352059\pi$
$149$	5.39333e9			0.896436			0.448218	+	0.893924i	$0.352059\pi$
$150$		0			0
$151$	7.92204e8			0.124005			0.0620027	−	0.998076i	$-0.480251\pi$
$151$	7.92204e8			0.124005			0.0620027	+	0.998076i	$0.480251\pi$
$152$			4.88265e8i			0.0741924i
$153$		0			0
$154$	3.27645e8			0.0469419
$155$	−1.13568e9	+	2.55156e9i	−0.158039	+	0.355069i
$156$		0			0
$157$			1.18606e10i			1.55797i	0.627042	+	0.778985i	$0.284265\pi$
$157$			1.18606e10i			1.55797i	−0.627042	+	0.778985i	$0.715735\pi$
$158$		−	3.93698e7i		−	0.00502581i
$159$		0			0
$160$	−8.45835e8	−	3.76476e8i	−0.102034	−	0.0454148i
$161$	−8.28367e9			−0.971642
$162$		0			0
$163$			3.99906e9i			0.443724i	0.975078	+	0.221862i	$0.0712135\pi$
$163$			3.99906e9i			0.443724i	−0.975078	+	0.221862i	$0.928787\pi$
$164$	1.30048e10			1.40381
$165$		0			0
$166$	−1.70341e8			−0.0174114
$167$		−	1.09118e10i		−	1.08560i	−0.839861	−	0.542802i	$-0.817363\pi$
$167$		−	1.09118e10i		−	1.08560i	0.839861	−	0.542802i	$-0.182637\pi$
$168$		0			0
$169$	1.01452e10			0.956692
$170$	1.43986e8	−	3.23497e8i	0.0132221	−	0.0297064i
$171$		0			0
$172$		−	1.19043e10i		−	1.03711i
$173$			1.89328e10i			1.60696i	0.595329	+	0.803482i	$0.297022\pi$
$173$			1.89328e10i			1.60696i	−0.595329	+	0.803482i	$0.702978\pi$
$174$		0			0
$175$	−1.26439e10	+	1.13898e10i	−1.01909	+	0.918006i
$176$	−1.16318e10			−0.913778
$177$		0			0
$178$		−	4.67577e8i		−	0.0349111i
$179$	2.09763e10			1.52718			0.763592	−	0.645699i	$-0.223434\pi$
$179$	2.09763e10			1.52718			0.763592	+	0.645699i	$0.223434\pi$
$180$		0			0
$181$	−7.16950e9			−0.496518			−0.248259	−	0.968694i	$-0.579858\pi$
$181$	−7.16950e9			−0.496518			−0.248259	+	0.968694i	$0.579858\pi$
$182$			1.57584e8i			0.0106461i
$183$		0			0
$184$	−8.21045e8			−0.0528064
$185$	−1.21761e10	−	5.41951e9i	−0.764251	−	0.340163i
$186$		0			0
$187$		−	1.33771e10i		−	0.799974i
$188$		−	1.92936e10i		−	1.12643i
$189$		0			0
$190$	6.09221e8	+	2.71160e8i	0.0339143	+	0.0150951i
$191$	−1.75301e10			−0.953091			−0.476545	−	0.879150i	$-0.658111\pi$
$191$	−1.75301e10			−0.953091			−0.476545	+	0.879150i	$0.658111\pi$
$192$		0			0
$193$		−	3.13528e10i		−	1.62655i	−0.581877	−	0.813277i	$-0.697681\pi$
$193$		−	3.13528e10i		−	1.62655i	0.581877	−	0.813277i	$-0.302319\pi$
$194$	−2.86509e8			−0.0145222
$195$		0			0
$196$	−1.81827e10			−0.880048
$197$		−	1.85971e10i		−	0.879725i	−0.898065	−	0.439862i	$-0.855027\pi$
$197$		−	1.85971e10i		−	0.879725i	0.898065	−	0.439862i	$-0.144973\pi$
$198$		0			0
$199$	1.26662e10			0.572544			0.286272	−	0.958148i	$-0.407584\pi$
$199$	1.26662e10			0.572544			0.286272	+	0.958148i	$0.407584\pi$
$200$	−1.25322e9	+	1.12891e9i	−0.0553849	+	0.0498914i
$201$		0			0
$202$			1.13021e9i			0.0477617i
$203$			6.99798e9i			0.289228i
$204$		0			0
$205$	1.44547e10	−	3.24756e10i	0.571631	−	1.28429i
$206$	−3.24333e8			−0.0125484
$207$		0			0
$208$		−	5.59443e9i		−	0.207239i
$209$	2.51923e10			0.913291
$210$		0			0
$211$	−6.20579e9			−0.215539			−0.107770	−	0.994176i	$-0.534371\pi$
$211$	−6.20579e9			−0.215539			−0.107770	+	0.994176i	$0.534371\pi$
$212$			2.45059e10i			0.833218i
$213$		0			0
$214$	−6.72943e8			−0.0219339
$215$	−2.97273e10	−	1.32314e10i	−0.948818	−	0.422313i
$216$		0			0
$217$			1.74123e10i			0.533074i
$218$		−	5.59729e8i		−	0.0167851i
$219$		0			0
$220$	−1.29466e10	+	2.90875e10i	−0.372610	+	0.837151i
$221$	6.43385e9			0.181428
$222$		0			0
$223$			4.30855e10i			1.16670i	0.812221	+	0.583350i	$0.198258\pi$
$223$			4.30855e10i			1.16670i	−0.812221	+	0.583350i	$0.801742\pi$
$224$	−5.77213e9			−0.153186
$225$		0			0
$226$	−1.25042e9			−0.0318836
$227$			2.28857e10i			0.572068i	0.958219	+	0.286034i	$0.0923371\pi$
$227$			2.28857e10i			0.572068i	−0.958219	+	0.286034i	$0.907663\pi$
$228$		0			0
$229$	5.26747e9			0.126573			0.0632867	−	0.997995i	$-0.479842\pi$
$229$	5.26747e9			0.126573			0.0632867	+	0.997995i	$0.479842\pi$
$230$	−4.55971e8	+	1.02444e9i	−0.0107439	+	0.0241385i
$231$		0			0
$232$			6.93612e8i			0.0157189i
$233$		−	3.55179e10i		−	0.789488i	−0.918791	−	0.394744i	$-0.870833\pi$
$233$		−	3.55179e10i		−	0.789488i	0.918791	−	0.394744i	$-0.129167\pi$
$234$		0			0
$235$	−4.81798e10	−	2.14445e10i	−1.03053	−	0.458681i
$236$	3.57937e10			0.751108
$237$		0			0
$238$		−	2.20760e9i		−	0.0445989i
$239$	5.72471e10			1.13491			0.567457	−	0.823403i	$-0.307927\pi$
$239$	5.72471e10			1.13491			0.567457	+	0.823403i	$0.307927\pi$
$240$		0			0
$241$	3.89830e10			0.744386			0.372193	−	0.928155i	$-0.378606\pi$
$241$	3.89830e10			0.744386			0.372193	+	0.928155i	$0.378606\pi$
$242$			3.14415e8i			0.00589296i
$243$		0			0
$244$	6.49039e10			1.17224
$245$	−2.02098e10	+	4.54057e10i	−0.358356	+	0.805124i
$246$		0			0
$247$			1.21164e10i			0.207128i
$248$			1.72584e9i			0.0289713i
$249$		0			0
$250$	7.12595e8	+	2.19062e9i	0.0115375	+	0.0354680i
$251$	−4.56895e10			−0.726581			−0.363291	−	0.931676i	$-0.618347\pi$
$251$	−4.56895e10			−0.726581			−0.363291	+	0.931676i	$0.618347\pi$
$252$		0			0
$253$			4.23622e10i			0.650035i
$254$	1.93071e9			0.0291048
$255$		0			0
$256$	6.77655e10			0.986118
$257$		−	1.29955e10i		−	0.185821i	−0.995674	−	0.0929104i	$-0.970383\pi$
$257$		−	1.29955e10i		−	0.185821i	0.995674	−	0.0929104i	$-0.0296170\pi$
$258$		0			0
$259$	−8.30920e10			−1.14739
$260$	−1.39899e10	−	6.22680e9i	−0.189860	−	0.0845054i
$261$		0			0
$262$		−	3.24073e9i		−	0.0424901i
$263$			4.80103e10i			0.618776i	0.950936	+	0.309388i	$0.100124\pi$
$263$			4.80103e10i			0.618776i	−0.950936	+	0.309388i	$0.899876\pi$
$264$		0			0
$265$	6.11958e10	+	2.72379e10i	0.762282	+	0.339287i
$266$	4.15743e9			0.0509164
$267$		0			0
$268$			1.36307e11i			1.61403i
$269$	−9.98823e10			−1.16306			−0.581531	−	0.813524i	$-0.697546\pi$
$269$	−9.98823e10			−1.16306			−0.581531	+	0.813524i	$0.697546\pi$
$270$		0			0
$271$	−4.80217e10			−0.540849			−0.270424	−	0.962741i	$-0.587164\pi$
$271$	−4.80217e10			−0.540849			−0.270424	+	0.962741i	$0.587164\pi$
$272$			7.83726e10i			0.868169i
$273$		0			0
$274$	4.91737e9			0.0527054
$275$	5.82469e10	+	6.46604e10i	0.614152	+	0.681776i
$276$		0			0
$277$		−	1.77838e10i		−	0.181495i	−0.995874	−	0.0907477i	$-0.971074\pi$
$277$		−	1.77838e10i		−	0.181495i	0.995874	−	0.0907477i	$-0.0289257\pi$
$278$		−	4.97838e9i		−	0.0499904i
$279$		0			0
$280$	−4.27609e9	+	9.60717e9i	−0.0415753	+	0.0934080i
$281$	1.52044e11			1.45476			0.727379	−	0.686236i	$-0.240738\pi$
$281$	1.52044e11			1.45476			0.727379	+	0.686236i	$0.240738\pi$
$282$		0			0
$283$		−	1.86733e11i		−	1.73055i	−0.501301	−	0.865273i	$-0.667145\pi$
$283$		−	1.86733e11i		−	1.73055i	0.501301	−	0.865273i	$-0.332855\pi$
$284$	−3.37025e10			−0.307418
$285$		0			0
$286$	8.05875e8			0.00712230
$287$		−	2.21619e11i		−	1.92814i
$288$		0			0
$289$	2.84558e10			0.239955
$290$	8.65438e8	+	3.85201e8i	0.00718530	+	0.00319813i
$291$		0			0
$292$			7.54233e9i			0.0607132i
$293$		−	1.28928e11i		−	1.02198i	−0.859586	−	0.510991i	$-0.829278\pi$
$293$		−	1.28928e11i		−	1.02198i	0.859586	−	0.510991i	$-0.170722\pi$
$294$		0			0
$295$	3.97841e10	−	8.93836e10i	0.305851	−	0.687161i
$296$	−8.23575e9			−0.0623577
$297$		0			0
$298$		−	4.55167e9i		−	0.0334347i
$299$	−2.03745e10			−0.147423
$300$		0			0
$301$	−2.02865e11			−1.42448
$302$		−	6.68575e8i		−	0.00462508i
$303$		0			0
$304$	−1.47594e11			−0.991146
$305$	7.21396e10	−	1.62077e11i	0.477336	−	1.07244i
$306$		0			0
$307$		−	8.78331e10i		−	0.564333i	−0.959365	−	0.282167i	$-0.908947\pi$
$307$		−	8.78331e10i		−	0.564333i	0.959365	−	0.282167i	$-0.0910531\pi$
$308$			1.98498e11i			1.25683i
$309$		0			0
$310$	2.15337e9	+	9.58452e8i	0.0132432	+	0.00589444i
$311$	−2.76204e11			−1.67420			−0.837101	−	0.547049i	$-0.815751\pi$
$311$	−2.76204e11			−1.67420			−0.837101	+	0.547049i	$0.815751\pi$
$312$		0			0
$313$		−	1.84107e11i		−	1.08423i	−0.840304	−	0.542115i	$-0.817624\pi$
$313$		−	1.84107e11i		−	1.08423i	0.840304	−	0.542115i	$-0.182376\pi$
$314$	1.00097e10			0.0581082
$315$		0			0
$316$	2.38515e10			0.134562
$317$			3.48865e11i			1.94040i	0.242313	+	0.970198i	$0.422094\pi$
$317$			3.48865e11i			1.94040i	−0.242313	+	0.970198i	$0.577906\pi$
$318$		0			0
$319$	3.57873e10			0.193496
$320$	7.56384e10	−	1.69938e11i	0.403244	−	0.905975i
$321$		0			0
$322$			6.99095e9i			0.0362397i
$323$		−	1.69740e11i		−	0.867706i
$324$		0			0
$325$	−3.10990e10	+	2.80144e10i	−0.154622	+	0.139285i
$326$	3.37498e9			0.0165498
$327$		0			0
$328$		−	2.19660e10i		−	0.104790i
$329$	−3.28788e11			−1.54716
$330$		0			0
$331$	2.88744e11			1.32217			0.661084	−	0.750312i	$-0.270097\pi$
$331$	2.88744e11			1.32217			0.661084	+	0.750312i	$0.270097\pi$
$332$		−	1.03198e11i		−	0.466177i
$333$		0			0
$334$	−9.20892e9			−0.0404902
$335$	3.40384e11	+	1.51503e11i	1.47662	+	0.657232i
$336$		0			0
$337$			1.25882e11i			0.531654i	0.964021	+	0.265827i	$0.0856450\pi$
$337$			1.25882e11i			0.531654i	−0.964021	+	0.265827i	$0.914355\pi$
$338$		−	8.56201e9i		−	0.0356821i
$339$		0			0
$340$	1.95985e11	+	8.72315e10i	0.795366	+	0.354012i
$341$	8.90455e10			0.356630
$342$		0			0
$343$		−	4.17441e10i		−	0.162844i
$344$	−2.01071e10			−0.0774172
$345$		0			0
$346$	1.59782e10			0.0599356
$347$		−	2.95822e11i		−	1.09534i	−0.836695	−	0.547669i	$-0.815515\pi$
$347$		−	2.95822e11i		−	1.09534i	0.836695	−	0.547669i	$-0.184485\pi$
$348$		0			0
$349$	−3.73474e11			−1.34755			−0.673777	−	0.738934i	$-0.735329\pi$
$349$	−3.73474e11			−1.34755			−0.673777	+	0.738934i	$0.735329\pi$
$350$	9.61237e9	+	1.06708e10i	0.0342392	+	0.0380093i
$351$		0			0
$352$			2.95183e10i			0.102483i
$353$			4.89872e11i			1.67918i	0.543223	+	0.839589i	$0.317204\pi$
$353$			4.89872e11i			1.67918i	−0.543223	+	0.839589i	$0.682796\pi$
$354$		0			0
$355$	−3.74598e10	+	8.41615e10i	−0.125181	+	0.281246i
$356$	2.83273e11			0.934718
$357$		0			0
$358$		−	1.77029e10i		−	0.0569600i
$359$	−4.27559e11			−1.35854			−0.679268	−	0.733891i	$-0.737702\pi$
$359$	−4.27559e11			−1.35854			−0.679268	+	0.733891i	$0.737702\pi$
$360$		0			0
$361$	−3.02753e9			−0.00938223
$362$			6.05065e9i			0.0185188i
$363$		0			0
$364$	−9.54693e10			−0.285041
$365$	1.88346e10	+	8.38317e9i	0.0555443	+	0.0247224i
$366$		0			0
$367$		−	2.54403e10i		−	0.0732023i	−0.999330	−	0.0366012i	$-0.988347\pi$
$367$		−	2.54403e10i		−	0.0732023i	0.999330	−	0.0366012i	$-0.0116531\pi$
$368$		−	2.48188e11i		−	0.705448i
$369$		0			0
$370$	−4.57376e9	+	1.02760e10i	−0.0126872	+	0.0285046i
$371$	4.17611e11			1.14443
$372$		0			0
$373$			7.26003e11i			1.94200i	0.239087	+	0.970998i	$0.423152\pi$
$373$			7.26003e11i			1.94200i	−0.239087	+	0.970998i	$0.576848\pi$
$374$	−1.12895e10			−0.0298369
$375$		0			0
$376$	−3.25881e10			−0.0840842
$377$			1.72122e10i			0.0438834i
$378$		0			0
$379$	2.76699e11			0.688859			0.344430	−	0.938812i	$-0.388072\pi$
$379$	2.76699e11			0.688859			0.344430	+	0.938812i	$0.388072\pi$
$380$	−1.64277e11	+	3.69085e11i	−0.404159	+	0.908031i
$381$		0			0
$382$			1.47944e10i			0.0355478i
$383$			1.71143e11i			0.406410i	0.979136	+	0.203205i	$0.0651358\pi$
$383$			1.71143e11i			0.406410i	−0.979136	+	0.203205i	$0.934864\pi$
$384$		0			0
$385$	4.95687e11	+	2.20627e11i	1.14983	+	0.511783i
$386$	−2.64600e10			−0.0606662
$387$		0			0
$388$		−	1.73576e11i		−	0.388819i
$389$	3.92384e10			0.0868837			0.0434419	−	0.999056i	$-0.486168\pi$
$389$	3.92384e10			0.0868837			0.0434419	+	0.999056i	$0.486168\pi$
$390$		0			0
$391$	2.85427e11			0.617590
$392$			3.07117e10i			0.0656927i
$393$		0			0
$394$	−1.56949e10			−0.0328114
$395$	2.65105e10	−	5.95616e10i	0.0547937	−	0.123106i
$396$		0			0
$397$			3.91381e11i			0.790756i	0.918519	+	0.395378i	$0.129386\pi$
$397$			3.91381e11i			0.790756i	−0.918519	+	0.395378i	$0.870614\pi$
$398$		−	1.06896e10i		−	0.0213544i
$399$		0			0
$400$	−3.41251e11	−	3.78826e11i	−0.666506	−	0.739895i
$401$	5.04969e11			0.975248			0.487624	−	0.873054i	$-0.337864\pi$
$401$	5.04969e11			0.975248			0.487624	+	0.873054i	$0.337864\pi$
$402$		0			0
$403$			4.28272e10i			0.0808811i
$404$	−6.84720e11			−1.27878
$405$		0			0
$406$	5.90590e9			0.0107875
$407$			4.24928e11i			0.767609i
$408$		0			0
$409$	−9.44998e9			−0.0166985			−0.00834923	−	0.999965i	$-0.502658\pi$
$409$	−9.44998e9			−0.0166985			−0.00834923	+	0.999965i	$0.502658\pi$
$410$	−2.74075e10	−	1.21989e10i	−0.0479008	−	0.0213203i
$411$		0			0
$412$		−	1.96491e11i		−	0.335974i
$413$		−	6.09969e11i		−	1.03165i
$414$		0			0
$415$	−2.57706e11	−	1.14703e11i	−0.426488	−	0.189827i
$416$	−1.41971e10			−0.0232423
$417$		0			0
$418$		−	2.12609e10i		−	0.0340634i
$419$	−5.77328e10			−0.0915081			−0.0457541	−	0.998953i	$-0.514569\pi$
$419$	−5.77328e10			−0.0915081			−0.0457541	+	0.998953i	$0.514569\pi$
$420$		0			0
$421$	4.38976e9			0.00681038			0.00340519	−	0.999994i	$-0.498916\pi$
$421$	4.38976e9			0.00681038			0.00340519	+	0.999994i	$0.498916\pi$
$422$			5.23734e9i			0.00803905i
$423$		0			0
$424$	4.13920e10			0.0621970
$425$	4.35667e11	−	3.92455e11i	0.647746	−	0.583498i
$426$		0			0
$427$		−	1.10604e12i		−	1.61008i
$428$		−	4.07690e11i		−	0.587264i
$429$		0			0
$430$	−1.11666e10	+	2.50882e10i	−0.0157512	+	0.0353884i
$431$	−9.94476e11			−1.38818			−0.694091	−	0.719887i	$-0.744193\pi$
$431$	−9.94476e11			−1.38818			−0.694091	+	0.719887i	$0.744193\pi$
$432$		0			0
$433$			1.91618e11i			0.261963i	0.991385	+	0.130982i	$0.0418129\pi$
$433$			1.91618e11i			0.261963i	−0.991385	+	0.130982i	$0.958187\pi$
$434$	1.46950e10			0.0198823
$435$		0			0
$436$	3.39101e11			0.449407
$437$			5.37527e11i			0.705072i
$438$		0			0
$439$	−1.38202e12			−1.77592			−0.887962	−	0.459917i	$-0.847879\pi$
$439$	−1.38202e12			−1.77592			−0.887962	+	0.459917i	$0.847879\pi$
$440$	4.91305e10	+	2.18677e10i	0.0624906	+	0.0278141i
$441$		0			0
$442$		−	5.42980e9i		−	0.00676681i
$443$		−	3.05660e11i		−	0.377070i	−0.982066	−	0.188535i	$-0.939626\pi$
$443$		−	3.05660e11i		−	0.377070i	0.982066	−	0.188535i	$-0.0603740\pi$
$444$		0			0
$445$	3.14853e11	−	7.07387e11i	0.380617	−	0.855139i
$446$	3.63617e10			0.0435148
$447$		0			0
$448$		−	1.15969e12i		−	1.36016i
$449$	1.49518e12			1.73614			0.868069	−	0.496444i	$-0.165361\pi$
$449$	1.49518e12			1.73614			0.868069	+	0.496444i	$0.165361\pi$
$450$		0			0
$451$	−1.13335e12			−1.28994
$452$		−	7.57542e11i		−	0.853658i
$453$		0			0
$454$	1.93142e10			0.0213367
$455$	−1.06112e11	+	2.38405e11i	−0.116069	+	0.260774i
$456$		0			0
$457$			1.17977e12i			1.26525i	0.774459	+	0.632624i	$0.218022\pi$
$457$			1.17977e12i			1.26525i	−0.774459	+	0.632624i	$0.781978\pi$
$458$		−	4.44545e9i		−	0.00472086i
$459$		0			0
$460$	−6.20638e11	−	2.76242e11i	−0.646291	−	0.287660i
$461$	−1.54415e12			−1.59234			−0.796170	−	0.605074i	$-0.793144\pi$
$461$	−1.54415e12			−1.59234			−0.796170	+	0.605074i	$0.793144\pi$
$462$		0			0
$463$			4.55769e11i			0.460926i	0.973081	+	0.230463i	$0.0740240\pi$
$463$			4.55769e11i			0.460926i	−0.973081	+	0.230463i	$0.925976\pi$
$464$	−2.09667e11			−0.209990
$465$		0			0
$466$	−2.99751e10			−0.0294458
$467$		−	6.97342e11i		−	0.678454i	−0.940705	−	0.339227i	$-0.889835\pi$
$467$		−	6.97342e11i		−	0.678454i	0.940705	−	0.339227i	$-0.110165\pi$
$468$		0			0
$469$	2.32284e12			2.21688
$470$	−1.80980e10	+	4.06611e10i	−0.0171076	+	0.0384360i
$471$		0			0
$472$		−	6.04578e10i		−	0.0560677i
$473$			1.03744e12i			0.952987i
$474$		0			0
$475$	7.39084e11	+	8.20464e11i	0.666151	+	0.739500i
$476$	1.33743e12			1.19410
$477$		0			0
$478$		−	4.83134e10i		−	0.0423294i
$479$	2.43471e11			0.211318			0.105659	−	0.994402i	$-0.466305\pi$
$479$	2.43471e11			0.211318			0.105659	+	0.994402i	$0.466305\pi$
$480$		0			0
$481$	−2.04373e11			−0.174088
$482$		−	3.28994e10i		−	0.0277637i
$483$		0			0
$484$	−1.90482e11			−0.157780
$485$	−4.33453e11	−	1.92927e11i	−0.355717	−	0.158327i
$486$		0			0
$487$		−	1.56961e12i		−	1.26448i	−0.774773	−	0.632239i	$-0.782136\pi$
$487$		−	1.56961e12i		−	1.26448i	0.774773	−	0.632239i	$-0.217864\pi$
$488$		−	1.09627e11i		−	0.0875039i
$489$		0			0
$490$	3.83198e10	+	1.70559e10i	0.0300290	+	0.0133657i
$491$	−6.52870e11			−0.506944			−0.253472	−	0.967343i	$-0.581573\pi$
$491$	−6.52870e11			−0.506944			−0.253472	+	0.967343i	$0.581573\pi$
$492$		0			0
$493$		−	2.41127e11i		−	0.183838i
$494$	1.02256e10			0.00772534
$495$		0			0
$496$	−5.21691e11			−0.387031
$497$			5.74333e11i			0.422241i
$498$		0			0
$499$	7.51465e11			0.542571			0.271285	−	0.962499i	$-0.412551\pi$
$499$	7.51465e11			0.542571			0.271285	+	0.962499i	$0.412551\pi$
$500$	−1.32715e12	+	4.31713e11i	−0.949629	+	0.308908i
$501$		0			0
$502$			3.85593e10i			0.0270996i
$503$			1.31120e12i			0.913299i	0.889647	+	0.456649i	$0.150951\pi$
$503$			1.31120e12i			0.913299i	−0.889647	+	0.456649i	$0.849049\pi$
$504$		0			0
$505$	−7.61055e11	+	1.70988e12i	−0.520721	+	1.16991i
$506$	3.57513e10			0.0242446
$507$		0			0
$508$			1.16968e12i			0.779259i
$509$	1.78629e12			1.17957			0.589783	−	0.807561i	$-0.299213\pi$
$509$	1.78629e12			1.17957			0.589783	+	0.807561i	$0.299213\pi$
$510$		0			0
$511$	1.28531e11			0.0833899
$512$		−	2.88366e11i		−	0.185451i
$513$		0			0
$514$	−1.09675e10			−0.00693063
$515$	−4.90676e11	−	2.18397e11i	−0.307370	−	0.136809i
$516$		0			0
$517$			1.68140e12i			1.03506i
$518$			7.01249e10i			0.0427946i
$519$		0			0
$520$	−1.05175e10	+	2.36298e10i	−0.00630805	+	0.0141724i
$521$	−5.88627e11			−0.350002			−0.175001	−	0.984568i	$-0.555993\pi$
$521$	−5.88627e11			−0.350002			−0.175001	+	0.984568i	$0.555993\pi$
$522$		0			0
$523$		−	6.01202e11i		−	0.351369i	−0.984447	−	0.175684i	$-0.943786\pi$
$523$		−	6.01202e11i		−	0.351369i	0.984447	−	0.175684i	$-0.0562138\pi$
$524$	1.96334e12			1.13764
$525$		0			0
$526$	4.05180e10			0.0230787
$527$		−	5.99968e11i		−	0.338829i
$528$		0			0
$529$	8.97272e11			0.498165
$530$	2.29872e10	−	5.16458e10i	0.0126545	−	0.0284311i
$531$		0			0
$532$			2.51870e12i			1.36325i
$533$		−	5.45093e11i		−	0.292549i
$534$		0			0
$535$	−1.01808e12	−	4.53141e11i	−0.537266	−	0.239134i
$536$	2.30231e11			0.120482
$537$		0			0
$538$			8.42950e10i			0.0433792i
$539$	1.58459e12			0.808662
$540$		0			0
$541$	1.40863e12			0.706982			0.353491	−	0.935438i	$-0.384995\pi$
$541$	1.40863e12			0.706982			0.353491	+	0.935438i	$0.384995\pi$
$542$			4.05276e10i			0.0201723i
$543$		0			0
$544$	1.98888e11			0.0973673
$545$	3.76905e11	−	8.46800e11i	0.182999	−	0.411147i
$546$		0			0
$547$		−	8.05933e10i		−	0.0384907i	−0.999815	−	0.0192454i	$-0.993874\pi$
$547$		−	8.05933e10i		−	0.0384907i	0.999815	−	0.0192454i	$-0.00612636\pi$
$548$			2.97910e12i			1.41115i
$549$		0			0
$550$	5.45698e10	−	4.91571e10i	0.0254285	−	0.0229063i
$551$	4.54098e11			0.209878
$552$		0			0
$553$		−	4.06459e11i		−	0.184822i
$554$	−1.50085e10			−0.00676930
$555$		0			0
$556$	3.01606e12			1.33845
$557$			3.92066e12i			1.72588i	0.505305	+	0.862941i	$0.331380\pi$
$557$			3.92066e12i			1.72588i	−0.505305	+	0.862941i	$0.668620\pi$
$558$		0			0
$559$	−4.98965e11			−0.216131
$560$	−2.90408e12	−	1.29259e12i	−1.24785	−	0.555410i
$561$		0			0
$562$		−	1.28317e11i		−	0.0542587i
$563$		−	3.86627e12i		−	1.62182i	−0.585168	−	0.810912i	$-0.698971\pi$
$563$		−	3.86627e12i		−	1.62182i	0.585168	−	0.810912i	$-0.301029\pi$
$564$		0			0
$565$	−1.89173e12	−	8.41996e11i	−0.780981	−	0.347610i
$566$	−1.57592e11			−0.0645448
$567$		0			0
$568$			5.69256e10i			0.0229478i
$569$	−1.87990e12			−0.751849			−0.375924	−	0.926650i	$-0.622675\pi$
$569$	−1.87990e12			−0.751849			−0.375924	+	0.926650i	$0.622675\pi$
$570$		0			0
$571$	−3.44726e12			−1.35710			−0.678550	−	0.734554i	$-0.737391\pi$
$571$	−3.44726e12			−1.35710			−0.678550	+	0.734554i	$0.737391\pi$
$572$			4.88225e11i			0.190694i
$573$		0			0
$574$	−1.87034e11			−0.0719146
$575$	−1.37966e12	+	1.24281e12i	−0.526339	+	0.474133i
$576$		0			0
$577$		−	1.68433e12i		−	0.632608i	−0.948658	−	0.316304i	$-0.897558\pi$
$577$		−	1.68433e12i		−	0.632608i	0.948658	−	0.316304i	$-0.102442\pi$
$578$		−	2.40151e10i		−	0.00894971i
$579$		0			0
$580$	−2.33367e11	+	5.24310e11i	−0.0856275	+	0.192381i
$581$	−1.75863e12			−0.640297
$582$		0			0
$583$		−	2.13564e12i		−	0.765631i
$584$	1.27395e10			0.00453204
$585$		0			0
$586$	−1.08808e11			−0.0381173
$587$		−	5.04715e12i		−	1.75458i	−0.479956	−	0.877292i	$-0.659348\pi$
$587$		−	5.04715e12i		−	1.75458i	0.479956	−	0.877292i	$-0.340652\pi$
$588$		0			0
$589$	1.12988e12			0.386825
$590$	−7.54347e10	−	3.35755e10i	−0.0256293	−	0.0114074i
$591$		0			0
$592$		−	2.48952e12i		−	0.833045i
$593$		−	6.66924e11i		−	0.221478i	−0.993850	−	0.110739i	$-0.964678\pi$
$593$		−	6.66924e11i		−	0.221478i	0.993850	−	0.110739i	$-0.0353217\pi$
$594$		0			0
$595$	1.48654e12	−	3.33983e12i	0.486238	−	1.09244i
$596$	2.75755e12			0.895189
$597$		0			0
$598$			1.71949e10i			0.00549851i
$599$	3.36479e12			1.06792			0.533958	−	0.845511i	$-0.320704\pi$
$599$	3.36479e12			1.06792			0.533958	+	0.845511i	$0.320704\pi$
$600$		0			0
$601$	−2.79891e12			−0.875092			−0.437546	−	0.899196i	$-0.644152\pi$
$601$	−2.79891e12			−0.875092			−0.437546	+	0.899196i	$0.644152\pi$
$602$			1.71206e11i			0.0531295i
$603$		0			0
$604$	4.05044e11			0.123833
$605$	−2.11718e11	+	4.75671e11i	−0.0642478	+	0.144347i
$606$		0			0
$607$		−	3.38683e12i		−	1.01261i	−0.862353	−	0.506307i	$-0.831010\pi$
$607$		−	3.38683e12i		−	1.01261i	0.862353	−	0.506307i	$-0.168990\pi$
$608$			3.74553e11i			0.111160i
$609$		0			0
$610$	−1.36784e11	−	6.08817e10i	−0.0399992	−	0.0178034i
$611$	−8.08685e11			−0.234744
$612$		0			0
$613$			7.53866e11i			0.215636i	0.994171	+	0.107818i	$0.0343864\pi$
$613$			7.53866e11i			0.215636i	−0.994171	+	0.107818i	$0.965614\pi$
$614$	−7.41262e10			−0.0210482
$615$		0			0
$616$	3.35275e11			0.0938185
$617$		−	1.42132e11i		−	0.0394827i	−0.999805	−	0.0197414i	$-0.993716\pi$
$617$		−	1.42132e11i		−	0.0394827i	0.999805	−	0.0197414i	$-0.00628428\pi$
$618$		0			0
$619$	1.03073e12			0.282186			0.141093	−	0.989996i	$-0.454938\pi$
$619$	1.03073e12			0.282186			0.141093	+	0.989996i	$0.454938\pi$
$620$	−5.80661e11	+	1.30458e12i	−0.157819	+	0.354575i
$621$		0			0
$622$			2.33100e11i			0.0624433i
$623$		−	4.82733e12i		−	1.28384i
$624$		0			0
$625$	−3.97033e11	+	3.79398e12i	−0.104080	+	0.994569i
$626$	−1.55376e11			−0.0404390
$627$		0			0
$628$			6.06419e12i			1.55580i
$629$	2.86307e12			0.729296
$630$		0			0
$631$	−4.61780e12			−1.15959			−0.579793	−	0.814764i	$-0.696867\pi$
$631$	−4.61780e12			−1.15959			−0.579793	+	0.814764i	$0.696867\pi$
$632$		−	4.02866e10i		−	0.0100446i
$633$		0			0
$634$	2.94422e11			0.0723717
$635$	2.92092e12	+	1.30008e12i	0.712916	+	0.317314i
$636$		0			0
$637$			7.62122e11i			0.183399i
$638$		−	3.02025e10i		−	0.00721688i
$639$		0			0
$640$	−5.76486e11	−	2.56590e11i	−0.135825	−	0.0604547i
$641$	−7.51099e12			−1.75726			−0.878630	−	0.477503i	$-0.841542\pi$
$641$	−7.51099e12			−1.75726			−0.878630	+	0.477503i	$0.841542\pi$
$642$		0			0
$643$		−	4.42841e12i		−	1.02164i	−0.859687	−	0.510821i	$-0.829341\pi$
$643$		−	4.42841e12i		−	1.02164i	0.859687	−	0.510821i	$-0.170659\pi$
$644$	−4.23534e12			−0.970291
$645$		0			0
$646$	−1.43251e11			−0.0323632
$647$			1.09396e12i			0.245432i	0.992442	+	0.122716i	$0.0391604\pi$
$647$			1.09396e12i			0.245432i	−0.992442	+	0.122716i	$0.960840\pi$
$648$		0			0
$649$	−3.11935e12			−0.690181
$650$	2.36425e10	+	2.62458e10i	0.00519498	+	0.00576699i
$651$		0			0
$652$			2.04467e12i			0.443107i
$653$			8.24881e12i			1.77534i	0.460477	+	0.887671i	$0.347678\pi$
$653$			8.24881e12i			1.77534i	−0.460477	+	0.887671i	$0.652322\pi$
$654$		0			0
$655$	2.18222e12	−	4.90283e12i	0.463247	−	1.04078i
$656$	6.63994e12			1.39990
$657$		0			0
$658$			2.77478e11i			0.0577049i
$659$	−2.64086e12			−0.545458			−0.272729	−	0.962091i	$-0.587926\pi$
$659$	−2.64086e12			−0.545458			−0.272729	+	0.962091i	$0.587926\pi$
$660$		0			0
$661$	8.94654e12			1.82284			0.911420	−	0.411478i	$-0.134987\pi$
$661$	8.94654e12			1.82284			0.911420	+	0.411478i	$0.134987\pi$
$662$		−	2.43683e11i		−	0.0493134i
$663$		0			0
$664$	−1.74308e11			−0.0347986
$665$	6.28968e12	+	2.79950e12i	1.24719	+	0.555114i
$666$		0			0
$667$			7.63592e11i			0.149381i
$668$		−	5.57906e12i		−	1.08409i
$669$		0			0
$670$	1.27860e11	−	2.87265e11i	0.0245130	−	0.0550739i
$671$	−5.65625e12			−1.07715
$672$		0			0
$673$			6.40541e12i			1.20359i	0.798650	+	0.601796i	$0.205548\pi$
$673$			6.40541e12i			1.20359i	−0.798650	+	0.601796i	$0.794452\pi$
$674$	1.06237e11			0.0198293
$675$		0			0
$676$	5.18713e12			0.955361
$677$		−	6.41491e12i		−	1.17366i	−0.809711	−	0.586829i	$-0.800376\pi$
$677$		−	6.41491e12i		−	1.17366i	0.809711	−	0.586829i	$-0.199624\pi$
$678$		0			0
$679$	−2.95796e12			−0.534046
$680$	1.47339e11	−	3.31030e11i	0.0264259	−	0.0593715i
$681$		0			0
$682$		−	7.51494e10i		−	0.0133014i
$683$			2.15592e12i			0.379088i	0.981872	+	0.189544i	$0.0607009\pi$
$683$			2.15592e12i			0.379088i	−0.981872	+	0.189544i	$0.939299\pi$
$684$		0			0
$685$	7.43937e12	+	3.31122e12i	1.29101	+	0.574619i
$686$	−3.52297e10			−0.00607366
$687$		0			0
$688$		−	6.07804e12i		−	1.03423i
$689$	1.02715e12			0.173640
$690$		0			0
$691$	−4.58074e12			−0.764336			−0.382168	−	0.924093i	$-0.624822\pi$
$691$	−4.58074e12			−0.764336			−0.382168	+	0.924093i	$0.624822\pi$
$692$			9.68009e12i			1.60473i
$693$		0			0
$694$	−2.49657e11			−0.0408533
$695$	3.35230e12	−	7.53168e12i	0.545019	−	1.22450i
$696$		0			0
$697$			7.63624e12i			1.22555i
$698$			3.15191e11i			0.0502603i
$699$		0			0
$700$	−6.46469e12	+	5.82348e12i	−1.01767	+	0.916729i
$701$	1.22474e12			0.191564			0.0957819	−	0.995402i	$-0.469465\pi$
$701$	1.22474e12			0.191564			0.0957819	+	0.995402i	$0.469465\pi$
$702$		0			0
$703$			5.39183e12i			0.832601i
$704$	−5.93058e12			−0.909956
$705$		0			0
$706$	4.13424e11			0.0626289
$707$			1.16685e13i			1.75642i
$708$		0			0
$709$	5.65887e12			0.841049			0.420525	−	0.907281i	$-0.361846\pi$
$709$	5.65887e12			0.841049			0.420525	+	0.907281i	$0.361846\pi$
$710$	7.10276e10	+	3.16139e10i	0.0104897	+	0.00466891i
$711$		0			0
$712$		−	4.78466e11i		−	0.0697736i
$713$			1.89996e12i			0.275322i
$714$		0			0
$715$	1.21919e12	+	5.42653e11i	0.174459	+	0.0776507i
$716$	1.07250e13			1.52506
$717$		0			0
$718$			3.60836e11i			0.0506698i
$719$	−6.02904e12			−0.841333			−0.420667	−	0.907215i	$-0.638204\pi$
$719$	−6.02904e12			−0.841333			−0.420667	+	0.907215i	$0.638204\pi$
$720$		0			0
$721$	−3.34846e12			−0.461462
$722$			2.55506e9i			0.000349933i
$723$		0			0
$724$	−3.66568e12			−0.495827
$725$	1.04992e12	+	1.16552e12i	0.141135	+	0.156675i
$726$		0			0
$727$			2.63469e12i			0.349805i	0.984586	+	0.174902i	$0.0559609\pi$
$727$			2.63469e12i			0.349805i	−0.984586	+	0.174902i	$0.944039\pi$
$728$			1.61254e11i			0.0212774i
$729$		0			0
$730$	7.07493e9	−	1.58954e10i	0.000922081	−	0.00207166i
$731$	6.99002e12			0.905421
$732$		0			0
$733$		−	5.28609e12i		−	0.676343i	−0.941085	−	0.338171i	$-0.890192\pi$
$733$		−	5.28609e12i		−	0.676343i	0.941085	−	0.338171i	$-0.109808\pi$
$734$	−2.14702e10			−0.00273026
$735$		0			0
$736$	−6.29831e11			−0.0791178
$737$		−	1.18789e13i		−	1.48310i
$738$		0			0
$739$	−2.51810e12			−0.310580			−0.155290	−	0.987869i	$-0.549631\pi$
$739$	−2.51810e12			−0.310580			−0.155290	+	0.987869i	$0.549631\pi$
$740$	−6.22550e12	−	2.77093e12i	−0.763188	−	0.339690i
$741$		0			0
$742$		−	3.52440e11i		−	0.0426843i
$743$			7.02537e11i			0.0845706i	0.999106	+	0.0422853i	$0.0134638\pi$
$743$			7.02537e11i			0.0845706i	−0.999106	+	0.0422853i	$0.986536\pi$
$744$		0			0
$745$	3.06497e12	−	6.88612e12i	0.364521	−	0.818976i
$746$	6.12705e11			0.0724314
$747$		0			0
$748$		−	6.83956e12i		−	0.798861i
$749$	−6.94755e12			−0.806610
$750$		0			0
$751$	4.60108e12			0.527813			0.263907	−	0.964548i	$-0.414989\pi$
$751$	4.60108e12			0.527813			0.263907	+	0.964548i	$0.414989\pi$
$752$		−	9.85083e12i		−	1.12329i
$753$		0			0
$754$	1.45261e10			0.00163674
$755$	4.50200e11	−	1.01147e12i	0.0504248	−	0.113290i
$756$		0			0
$757$		−	3.05764e12i		−	0.338419i	−0.985580	−	0.169210i	$-0.945878\pi$
$757$		−	3.05764e12i		−	0.338419i	0.985580	−	0.169210i	$-0.0541215\pi$
$758$		−	2.33518e11i		−	0.0256927i
$759$		0			0
$760$	6.23408e11	+	2.77475e11i	0.0677815	+	0.0301691i
$761$	9.86753e12			1.06654			0.533270	−	0.845945i	$-0.320963\pi$
$761$	9.86753e12			1.06654			0.533270	+	0.845945i	$0.320963\pi$
$762$		0			0
$763$		−	5.77872e12i		−	0.617264i
$764$	−8.96293e12			−0.951765
$765$		0			0
$766$	1.44435e11			0.0151580
$767$		−	1.50028e12i		−	0.156528i
$768$		0			0
$769$	−1.65694e13			−1.70859			−0.854294	−	0.519790i	$-0.826010\pi$
$769$	−1.65694e13			−1.70859			−0.854294	+	0.519790i	$0.826010\pi$
$770$	1.86197e11	−	4.18332e11i	0.0190882	−	0.0428857i
$771$		0			0
$772$		−	1.60303e13i		−	1.62429i
$773$			1.10674e13i			1.11490i	0.830210	+	0.557451i	$0.188221\pi$
$773$			1.10674e13i			1.11490i	−0.830210	+	0.557451i	$0.811779\pi$
$774$		0			0
$775$	2.61239e12	+	2.90004e12i	0.260124	+	0.288766i
$776$	−2.93181e11			−0.0290241
$777$		0			0
$778$		−	3.31150e10i		−	0.00324054i
$779$	−1.43808e13			−1.39915
$780$		0			0
$781$	2.93711e12			0.282482
$782$		−	2.40884e11i		−	0.0230345i
$783$		0			0
$784$	−9.28363e12			−0.877598
$785$	1.51434e13	+	6.74025e12i	1.42335	+	0.633523i
$786$		0			0
$787$		−	1.67201e12i		−	0.155365i	−0.996978	−	0.0776825i	$-0.975248\pi$
$787$		−	1.67201e12i		−	0.155365i	0.996978	−	0.0776825i	$-0.0247520\pi$
$788$		−	9.50846e12i		−	0.878501i
$789$		0			0
$790$	−5.02666e10	−	2.23734e10i	−0.00459154	−	0.00204366i
$791$	−1.29095e13			−1.17250
$792$		0			0
$793$		−	2.72042e12i		−	0.244291i
$794$	3.30303e11			0.0294931
$795$		0			0
$796$	6.47609e12			0.571748
$797$		−	6.97864e12i		−	0.612644i	−0.951928	−	0.306322i	$-0.900902\pi$
$797$		−	6.97864e12i		−	0.612644i	0.951928	−	0.306322i	$-0.0990985\pi$
$798$		0			0
$799$	1.13289e13			0.983394
$800$	−9.61355e11	+	8.66001e11i	−0.0829811	+	0.0747504i
$801$		0			0
$802$		−	4.26165e11i		−	0.0363742i
$803$		−	6.57300e11i		−	0.0557884i
$804$		0			0
$805$	−4.70751e12	+	1.05764e13i	−0.395102	+	0.887684i
$806$	3.61437e10			0.00301665
$807$		0			0
$808$			1.15654e12i			0.0954570i
$809$	5.27673e12			0.433108			0.216554	−	0.976271i	$-0.430518\pi$
$809$	5.27673e12			0.433108			0.216554	+	0.976271i	$0.430518\pi$
$810$		0			0
$811$	−1.43675e12			−0.116624			−0.0583118	−	0.998298i	$-0.518572\pi$
$811$	−1.43675e12			−0.116624			−0.0583118	+	0.998298i	$0.518572\pi$
$812$			3.57798e12i			0.288826i
$813$		0			0
$814$	3.58615e11			0.0286298
$815$	5.10592e12	+	2.27261e12i	0.405383	+	0.180433i
$816$		0			0
$817$			1.31639e13i			1.03367i
$818$			7.97525e9i			0.000622809i
$819$		0			0
$820$	7.39049e12	−	1.66044e13i	0.570836	−	1.28251i
$821$	−9.44899e12			−0.725840			−0.362920	−	0.931820i	$-0.618220\pi$
$821$	−9.44899e12			−0.725840			−0.362920	+	0.931820i	$0.618220\pi$
$822$		0			0
$823$			1.20237e13i			0.913562i	0.889579	+	0.456781i	$0.150998\pi$
$823$			1.20237e13i			0.913562i	−0.889579	+	0.456781i	$0.849002\pi$
$824$	−3.31886e11			−0.0250794
$825$		0			0
$826$	−5.14780e11			−0.0384779
$827$			7.86848e12i			0.584947i	0.956274	+	0.292473i	$0.0944782\pi$
$827$			7.86848e12i			0.584947i	−0.956274	+	0.292473i	$0.905522\pi$
$828$		0			0
$829$	−4.86184e12			−0.357524			−0.178762	−	0.983892i	$-0.557209\pi$
$829$	−4.86184e12			−0.357524			−0.178762	+	0.983892i	$0.557209\pi$
$830$	−9.68029e10	+	2.17489e11i	−0.00708006	+	0.0159069i
$831$		0			0
$832$		−	2.85236e12i		−	0.206372i
$833$		−	1.06766e13i		−	0.768299i
$834$		0			0
$835$	−1.39320e13	−	6.20103e12i	−0.991798	−	0.441443i
$836$	1.28805e13			0.912021
$837$		0			0
$838$			4.87232e10i			0.00341301i
$839$	1.76025e13			1.22644			0.613218	−	0.789914i	$-0.289875\pi$
$839$	1.76025e13			1.22644			0.613218	+	0.789914i	$0.289875\pi$
$840$		0			0
$841$	−1.38621e13			−0.955534
$842$		−	3.70471e9i		−	0.000254009i
$843$		0			0
$844$	−3.17294e12			−0.215239
$845$	5.76541e12	−	1.29533e13i	0.389023	−	0.874025i
$846$		0			0
$847$			3.24606e12i			0.216711i
$848$			1.25121e13i			0.830899i
$849$		0			0
$850$	−3.31209e11	−	3.67679e11i	−0.0217629	−	0.0241592i
$851$	−9.06666e12			−0.592604
$852$		0			0
$853$		−	9.20458e11i		−	0.0595296i	−0.999557	−	0.0297648i	$-0.990524\pi$
$853$		−	9.20458e11i		−	0.0595296i	0.999557	−	0.0297648i	$-0.00947584\pi$
$854$	−9.33439e11			−0.0600517
$855$		0			0
$856$	−6.88614e11			−0.0438373
$857$			2.35047e13i			1.48847i	0.667915	+	0.744237i	$0.267187\pi$
$857$			2.35047e13i			1.48847i	−0.667915	+	0.744237i	$0.732813\pi$
$858$		0			0
$859$	2.02385e13			1.26826			0.634132	−	0.773225i	$-0.281357\pi$
$859$	2.02385e13			1.26826			0.634132	+	0.773225i	$0.281357\pi$
$860$	−1.51992e13	−	6.76508e12i	−0.947498	−	0.421725i
$861$		0			0
$862$			8.39281e11i			0.0517756i
$863$		−	3.07364e13i		−	1.88627i	−0.332406	−	0.943136i	$-0.607860\pi$
$863$		−	3.07364e13i		−	1.88627i	0.332406	−	0.943136i	$-0.392140\pi$
$864$		0			0
$865$	2.41730e13	+	1.07593e13i	1.46811	+	0.653446i
$866$	1.61715e11			0.00977055
$867$		0			0
$868$			8.90269e12i			0.532332i
$869$	−2.07861e12			−0.123647
$870$		0			0
$871$	5.71325e12			0.336358
$872$		−	5.72763e11i		−	0.0335468i
$873$		0			0
$874$	4.53642e11			0.0262973
$875$	7.35693e12	+	2.26163e13i	0.424288	+	1.30432i
$876$		0			0
$877$		−	6.65840e12i		−	0.380077i	−0.981777	−	0.190039i	$-0.939139\pi$
$877$		−	6.65840e12i		−	0.380077i	0.981777	−	0.190039i	$-0.0608613\pi$
$878$			1.16635e12i			0.0662373i
$879$		0			0
$880$	−6.61022e12	+	1.48513e13i	−0.371573	+	0.834820i
$881$	−3.41842e12			−0.191176			−0.0955882	−	0.995421i	$-0.530473\pi$
$881$	−3.41842e12			−0.191176			−0.0955882	+	0.995421i	$0.530473\pi$
$882$		0			0
$883$			1.92500e13i			1.06563i	0.846231	+	0.532815i	$0.178866\pi$
$883$			1.92500e13i			1.06563i	−0.846231	+	0.532815i	$0.821134\pi$
$884$	3.28955e12			0.181176
$885$		0			0
$886$	−2.57960e11			−0.0140637
$887$			1.48977e13i			0.808095i	0.914738	+	0.404048i	$0.132397\pi$
$887$			1.48977e13i			0.808095i	−0.914738	+	0.404048i	$0.867603\pi$
$888$		0			0
$889$	1.99329e13			1.07032
$890$	−5.96995e11	−	2.65718e11i	−0.0318945	−	0.0141960i
$891$		0			0
$892$			2.20291e13i			1.16508i
$893$			2.13350e13i			1.12269i
$894$		0			0
$895$	1.19206e13	−	2.67822e13i	0.621004	−	1.39522i
$896$	−3.93404e12			−0.203917
$897$		0			0
$898$		−	1.26185e12i		−	0.0647534i
$899$	1.60507e12			0.0819551
$900$		0			0
$901$	−1.43895e13			−0.727416
$902$			9.56481e11i			0.0481113i
$903$		0			0
$904$	−1.27954e12			−0.0637228
$905$	−4.07434e12	+	9.15389e12i	−0.201901	+	0.453615i
$906$		0			0
$907$			1.11529e13i			0.547210i	0.961842	+	0.273605i	$0.0882162\pi$
$907$			1.11529e13i			0.547210i	−0.961842	+	0.273605i	$0.911784\pi$
$908$			1.17012e13i			0.571273i
$909$		0			0
$910$	2.01200e11	+	8.95530e10i	0.00972618	+	0.00432906i
$911$	2.25248e12			0.108350			0.0541750	−	0.998531i	$-0.482747\pi$
$911$	2.25248e12			0.108350			0.0541750	+	0.998531i	$0.482747\pi$
$912$		0			0
$913$			8.99353e12i			0.428363i
$914$	9.95663e11			0.0471905
$915$		0			0
$916$	2.69319e12			0.126397
$917$		−	3.34578e13i		−	1.56255i
$918$		0			0
$919$	−1.40633e13			−0.650380			−0.325190	−	0.945649i	$-0.605428\pi$
$919$	−1.40633e13			−0.650380			−0.325190	+	0.945649i	$0.605428\pi$
$920$	−4.66590e11	+	1.04830e12i	−0.0214729	+	0.0482435i
$921$		0			0
$922$			1.30318e12i			0.0593901i
$923$			1.41263e12i			0.0640649i
$924$		0			0
$925$	−1.38391e13	+	1.24664e13i	−0.621540	+	0.559891i
$926$	3.84644e11			0.0171913
$927$		0			0
$928$			5.32077e11i			0.0235509i
$929$	1.04912e13			0.462118			0.231059	−	0.972940i	$-0.425781\pi$
$929$	1.04912e13			0.462118			0.231059	+	0.972940i	$0.425781\pi$
$930$		0			0
$931$	2.01066e13			0.877130
$932$		−	1.81599e13i		−	0.788389i
$933$		0			0
$934$	−5.88518e11			−0.0253045
$935$	−1.70797e13	−	7.60206e12i	−0.730849	−	0.325296i
$936$		0			0
$937$		−	3.77841e13i		−	1.60133i	−0.599111	−	0.800666i	$-0.704479\pi$
$937$		−	3.77841e13i		−	1.60133i	0.599111	−	0.800666i	$-0.295521\pi$
$938$		−	1.96035e12i		−	0.0826837i
$939$		0			0
$940$	−2.46338e13	−	1.09643e13i	−1.02909	−	0.458043i
$941$	−1.11142e13			−0.462088			−0.231044	−	0.972943i	$-0.574214\pi$
$941$	−1.11142e13			−0.462088			−0.231044	+	0.972943i	$0.574214\pi$
$942$		0			0
$943$		−	2.41822e13i		−	0.995847i
$944$	1.82753e13			0.749017
$945$		0			0
$946$	8.75539e11			0.0355439
$947$			4.96563e12i			0.200631i	0.994956	+	0.100316i	$0.0319853\pi$
$947$			4.96563e12i			0.200631i	−0.994956	+	0.100316i	$0.968015\pi$
$948$		0			0
$949$	3.16134e11			0.0126524
$950$	6.92425e11	−	6.23745e11i	0.0275814	−	0.0248457i
$951$		0			0
$952$		−	2.25901e12i		−	0.0891357i
$953$		−	3.02750e13i		−	1.18896i	−0.804111	−	0.594479i	$-0.797358\pi$
$953$		−	3.02750e13i		−	1.18896i	0.804111	−	0.594479i	$-0.202642\pi$
$954$		0			0
$955$	−9.96214e12	+	2.23821e13i	−0.387559	+	0.870736i
$956$	2.92698e13			1.13334
$957$		0			0
$958$		−	2.05476e11i		−	0.00788162i
$959$	5.07676e13			1.93822
$960$		0			0
$961$	−2.24459e13			−0.848949
$962$			1.72479e11i			0.00649304i
$963$		0			0
$964$	1.99315e13			0.743351
$965$	−4.00307e13	−	1.78174e13i	−1.48601	−	0.661412i
$966$		0			0
$967$		−	2.48487e13i		−	0.913869i	−0.889500	−	0.456934i	$-0.848947\pi$
$967$		−	2.48487e13i		−	0.913869i	0.889500	−	0.456934i	$-0.151053\pi$
$968$			3.21737e11i			0.0117777i
$969$		0			0
$970$	−1.62820e11	+	3.65810e11i	−0.00590519	+	0.0132673i
$971$	−4.43278e13			−1.60026			−0.800128	−	0.599829i	$-0.795235\pi$
$971$	−4.43278e13			−1.60026			−0.800128	+	0.599829i	$0.795235\pi$
$972$		0			0
$973$		−	5.13975e13i		−	1.83837i
$974$	−1.32466e12			−0.0471618
$975$		0			0
$976$	3.31383e13			1.16898
$977$		−	9.73746e11i		−	0.0341917i	−0.999854	−	0.0170958i	$-0.994558\pi$
$977$		−	9.73746e11i		−	0.0341917i	0.999854	−	0.0170958i	$-0.00544204\pi$
$978$		0			0
$979$	−2.46867e13			−0.858897
$980$	−1.03330e13	+	2.32154e13i	−0.357857	+	0.804004i
$981$		0			0
$982$			5.50985e11i			0.0189077i
$983$			2.85792e13i			0.976247i	0.872775	+	0.488123i	$0.162318\pi$
$983$			2.85792e13i			0.976247i	−0.872775	+	0.488123i	$0.837682\pi$
$984$		0			0
$985$	−2.37444e13	−	1.05685e13i	−0.803709	−	0.357726i
$986$	−2.03497e11			−0.00685666
$987$		0			0
$988$			6.19499e12i			0.206840i
$989$	−2.21358e13			−0.735718
$990$		0			0
$991$	−3.49036e13			−1.14958			−0.574789	−	0.818302i	$-0.694916\pi$
$991$	−3.49036e13			−1.14958			−0.574789	+	0.818302i	$0.694916\pi$
$992$			1.32391e12i			0.0434065i
$993$		0			0
$994$	4.84705e11			0.0157485
$995$	7.19807e12	−	1.61720e13i	0.232816	−	0.523071i
$996$		0			0
$997$			8.78834e12i			0.281695i	0.990031	+	0.140847i	$0.0449827\pi$
$997$			8.78834e12i			0.281695i	−0.990031	+	0.140847i	$0.955017\pi$
$998$		−	6.34194e11i		−	0.0202365i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.10.b.b.19.2		4
3.2	odd	2		5.10.b.a.4.3	yes	4
5.2	odd	4		225.10.a.s.1.3		4
5.3	odd	4		225.10.a.s.1.2		4
5.4	even	2	inner	45.10.b.b.19.3		4
12.11	even	2		80.10.c.c.49.1		4
15.2	even	4		25.10.a.e.1.2		4
15.8	even	4		25.10.a.e.1.3		4
15.14	odd	2		5.10.b.a.4.2	✓	4
60.23	odd	4		400.10.a.ba.1.4		4
60.47	odd	4		400.10.a.ba.1.1		4
60.59	even	2		80.10.c.c.49.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.10.b.a.4.2	✓	4	15.14	odd	2
5.10.b.a.4.3	yes	4	3.2	odd	2
25.10.a.e.1.2		4	15.2	even	4
25.10.a.e.1.3		4	15.8	even	4
45.10.b.b.19.2		4	1.1	even	1	trivial
45.10.b.b.19.3		4	5.4	even	2	inner
80.10.c.c.49.1		4	12.11	even	2
80.10.c.c.49.4		4	60.59	even	2
225.10.a.s.1.2		4	5.3	odd	4
225.10.a.s.1.3		4	5.2	odd	4
400.10.a.ba.1.1		4	60.47	odd	4
400.10.a.ba.1.4		4	60.23	odd	4

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	45.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.843944i q^{2} +511.288 q^{4} +(568.288 - 1276.78i) q^{5} -8712.99i q^{7} -863.597i q^{8} +O(q^{10})\)	\(q-0.843944i q^{2} +511.288 q^{4} +(568.288 - 1276.78i) q^{5} -8712.99i q^{7} -863.597i q^{8} +(-1077.53 - 479.603i) q^{10} -44557.8 q^{11} -21430.4i q^{13} -7353.27 q^{14} +261051. q^{16} +300220. i q^{17} -565385. q^{19} +(290559. - 652803. i) q^{20} +37604.2i q^{22} -950727. i q^{23} +(-1.30722e6 - 1.45116e6i) q^{25} -18086.1 q^{26} -4.45485e6i q^{28} -803167. q^{29} -1.99843e6 q^{31} -662474. i q^{32} +253369. q^{34} +(-1.11246e7 - 4.95149e6i) q^{35} -9.53656e6i q^{37} +477153. i q^{38} +(-1.10263e6 - 490772. i) q^{40} +2.54355e7 q^{41} -2.32830e7i q^{43} -2.27818e7 q^{44} -802360. q^{46} -3.77353e7i q^{47} -3.55626e7 q^{49} +(-1.22470e6 + 1.10322e6i) q^{50} -1.09571e7i q^{52} +4.79297e7i q^{53} +(-2.53216e7 + 5.68906e7i) q^{55} -7.52451e6 q^{56} +677827. i q^{58} +7.00069e7 q^{59} +1.26942e8 q^{61} +1.68656e6i q^{62} +1.33099e8 q^{64} +(-2.73620e7 - 1.21787e7i) q^{65} +2.66595e8i q^{67} +1.53499e8i q^{68} +(-4.17877e6 + 9.38853e6i) q^{70} -6.59169e7 q^{71} +1.47516e7i q^{73} -8.04832e6 q^{74} -2.89074e8 q^{76} +3.88231e8i q^{77} +4.66498e7 q^{79} +(1.48352e8 - 3.33305e8i) q^{80} -2.14661e7i q^{82} -2.01840e8i q^{83} +(3.83316e8 + 1.70611e8i) q^{85} -1.96495e7 q^{86} +3.84800e7i q^{88} +5.54039e8 q^{89} -1.86723e8 q^{91} -4.86095e8i q^{92} -3.18465e7 q^{94} +(-3.21301e8 + 7.21874e8i) q^{95} -3.39489e8i q^{97} +3.00128e7i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 1368 q^{4} - 1140 q^{5}+O(q^{10}) \) 4 * q - 1368 * q^4 - 1140 * q^5	\( 4 q - 1368 q^{4} - 1140 q^{5} - 69160 q^{10} - 109968 q^{11} + 424536 q^{14} + 1631264 q^{16} - 636880 q^{19} + 3302280 q^{20} - 1337900 q^{25} - 6618768 q^{26} + 3531720 q^{29} - 10587712 q^{31} + 26434624 q^{34} - 13629840 q^{35} + 43578400 q^{40} + 16788552 q^{41} - 20638944 q^{44} - 61250072 q^{46} - 46921028 q^{49} + 150092400 q^{50} - 26907120 q^{55} - 315178080 q^{56} + 460829040 q^{59} + 360490568 q^{61} + 134995072 q^{64} - 183895680 q^{65} - 508341960 q^{70} + 47611872 q^{71} - 1176861744 q^{74} - 1168489440 q^{76} - 728043520 q^{79} - 965843040 q^{80} + 1275419840 q^{85} + 2375904552 q^{86} + 1582700760 q^{89} + 473322528 q^{91} + 3327101704 q^{94} - 1204791600 q^{95}+O(q^{100}) \) 4 * q - 1368 * q^4 - 1140 * q^5 - 69160 * q^10 - 109968 * q^11 + 424536 * q^14 + 1631264 * q^16 - 636880 * q^19 + 3302280 * q^20 - 1337900 * q^25 - 6618768 * q^26 + 3531720 * q^29 - 10587712 * q^31 + 26434624 * q^34 - 13629840 * q^35 + 43578400 * q^40 + 16788552 * q^41 - 20638944 * q^44 - 61250072 * q^46 - 46921028 * q^49 + 150092400 * q^50 - 26907120 * q^55 - 315178080 * q^56 + 460829040 * q^59 + 360490568 * q^61 + 134995072 * q^64 - 183895680 * q^65 - 508341960 * q^70 + 47611872 * q^71 - 1176861744 * q^74 - 1168489440 * q^76 - 728043520 * q^79 - 965843040 * q^80 + 1275419840 * q^85 + 2375904552 * q^86 + 1582700760 * q^89 + 473322528 * q^91 + 3327101704 * q^94 - 1204791600 * q^95

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