LMFDB - Embedded newform 756.2.be.e.107.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(107,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("756.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.be (of order $6$, degree $2$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.3
Character	$\chi$	$=$	756.107
Dual form			756.2.be.e.431.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37308 + 0.338582i) q^{2} +(1.77072 - 0.929803i) q^{4} +(-3.53194 - 2.03916i) q^{5} +(1.92589 - 1.81410i) q^{7} +(-2.11654 + 1.87623i) q^{8} +O(q^{10})$	\(q+(-1.37308 + 0.338582i) q^{2} +(1.77072 - 0.929803i) q^{4} +(-3.53194 - 2.03916i) q^{5} +(1.92589 - 1.81410i) q^{7} +(-2.11654 + 1.87623i) q^{8} +(5.54007 + 1.60410i) q^{10} +(0.258599 + 0.447907i) q^{11} -4.00857 q^{13} +(-2.03019 + 3.14298i) q^{14} +(2.27093 - 3.29285i) q^{16} +(5.05144 - 2.91645i) q^{17} +(-4.10015 - 2.36722i) q^{19} +(-8.15011 - 0.326792i) q^{20} +(-0.506732 - 0.527458i) q^{22} +(0.974850 - 1.68849i) q^{23} +(5.81638 + 10.0743i) q^{25} +(5.50411 - 1.35723i) q^{26} +(1.72346 - 5.00297i) q^{28} +2.05067i q^{29} +(-7.53503 + 4.35035i) q^{31} +(-2.00328 + 5.29026i) q^{32} +(-5.94860 + 5.71486i) q^{34} +(-10.5014 + 2.48008i) q^{35} +(-3.53252 + 6.11850i) q^{37} +(6.43135 + 1.86216i) q^{38} +(11.3014 - 2.31077i) q^{40} +2.50300i q^{41} -2.99519i q^{43} +(0.874374 + 0.552674i) q^{44} +(-0.766860 + 2.64851i) q^{46} +(-4.97255 + 8.61270i) q^{47} +(0.418094 - 6.98750i) q^{49} +(-11.3973 - 11.8635i) q^{50} +(-7.09808 + 3.72719i) q^{52} +(-7.05724 + 4.07450i) q^{53} -2.10931i q^{55} +(-0.672548 + 7.45303i) q^{56} +(-0.694319 - 2.81574i) q^{58} +(-6.07396 - 10.5204i) q^{59} +(-1.71003 + 2.96186i) q^{61} +(8.87329 - 8.52463i) q^{62} +(0.959489 - 7.94225i) q^{64} +(14.1580 + 8.17414i) q^{65} +(1.72609 - 0.996560i) q^{67} +(6.23299 - 9.86108i) q^{68} +(13.5795 - 6.96093i) q^{70} -2.86671 q^{71} +(4.04598 + 7.00785i) q^{73} +(2.77883 - 9.59727i) q^{74} +(-9.46129 - 0.379366i) q^{76} +(1.31058 + 0.393495i) q^{77} +(-4.28947 - 2.47652i) q^{79} +(-14.7354 + 6.99934i) q^{80} +(-0.847471 - 3.43683i) q^{82} +1.91175 q^{83} -23.7885 q^{85} +(1.01412 + 4.11266i) q^{86} +(-1.38772 - 0.462821i) q^{88} +(-11.7420 - 6.77926i) q^{89} +(-7.72007 + 7.27195i) q^{91} +(0.156227 - 3.89627i) q^{92} +(3.91162 - 13.5096i) q^{94} +(9.65431 + 16.7218i) q^{95} +4.24721 q^{97} +(1.79176 + 9.73599i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 16 q^{13} + 8 q^{16} - 28 q^{22} + 36 q^{25} + 26 q^{28} - 56 q^{34} - 8 q^{37} + 22 q^{40} - 18 q^{46} + 28 q^{49} - 26 q^{52} - 36 q^{58} + 16 q^{61} - 12 q^{64} - 18 q^{70} + 32 q^{73} - 144 q^{76} + 34 q^{82} + 32 q^{85} - 20 q^{88} - 78 q^{94} + 56 q^{97}+O(q^{100}) $ 64 * q - 16 * q^13 + 8 * q^16 - 28 * q^22 + 36 * q^25 + 26 * q^28 - 56 * q^34 - 8 * q^37 + 22 * q^40 - 18 * q^46 + 28 * q^49 - 26 * q^52 - 36 * q^58 + 16 * q^61 - 12 * q^64 - 18 * q^70 + 32 * q^73 - 144 * q^76 + 34 * q^82 + 32 * q^85 - 20 * q^88 - 78 * q^94 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.37308	+	0.338582i	−0.970918	+	0.239414i
$2$	−1.37308	+	0.338582i	−0.970918	+	0.239414i
$3$		0			0
$3$		0			0
$4$	1.77072	−	0.929803i	0.885362	−	0.464902i
$5$	−3.53194	−	2.03916i	−1.57953	−	0.911942i	−0.994925	−	0.100624i	$-0.967916\pi$
$5$	−3.53194	−	2.03916i	−1.57953	−	0.911942i	−0.584605	−	0.811318i	$-0.698751\pi$
$6$		0			0
$7$	1.92589	−	1.81410i	0.727917	−	0.685665i
$7$	1.92589	−	1.81410i	0.727917	−	0.685665i
$8$	−2.11654	+	1.87623i	−0.748310	+	0.663349i
$9$		0			0
$10$	5.54007	+	1.60410i	1.75192	+	0.507260i
$11$	0.258599	+	0.447907i	0.0779707	+	0.135049i	0.902374	−	0.430953i	$-0.141823\pi$
$11$	0.258599	+	0.447907i	0.0779707	+	0.135049i	−0.824404	+	0.566002i	$0.808489\pi$
$12$		0			0
$13$	−4.00857			−1.11178			−0.555889	−	0.831256i	$-0.687622\pi$
$13$	−4.00857			−1.11178			−0.555889	+	0.831256i	$0.687622\pi$
$14$	−2.03019	+	3.14298i	−0.542590	+	0.839997i
$15$		0			0
$16$	2.27093	−	3.29285i	0.567733	−	0.823213i
$17$	5.05144	−	2.91645i	1.22515	−	0.707343i	0.259142	−	0.965839i	$-0.416560\pi$
$17$	5.05144	−	2.91645i	1.22515	−	0.707343i	0.966012	+	0.258496i	$0.0832268\pi$
$18$		0			0
$19$	−4.10015	−	2.36722i	−0.940639	−	0.543078i	−0.0504782	−	0.998725i	$-0.516075\pi$
$19$	−4.10015	−	2.36722i	−0.940639	−	0.543078i	−0.890160	+	0.455647i	$0.849408\pi$
$20$	−8.15011	−	0.326792i	−1.82242	−	0.0730729i
$21$		0			0
$22$	−0.506732	−	0.527458i	−0.108036	−	0.112454i
$23$	0.974850	−	1.68849i	0.203270	−	0.352074i	−0.746310	−	0.665599i	$-0.768176\pi$
$23$	0.974850	−	1.68849i	0.203270	−	0.352074i	0.949580	+	0.313524i	$0.101510\pi$
$24$		0			0
$25$	5.81638	+	10.0743i	1.16328	+	2.01485i
$26$	5.50411	−	1.35723i	1.07945	−	0.266175i
$27$		0			0
$28$	1.72346	−	5.00297i	0.325704	−	0.945472i
$29$			2.05067i			0.380799i	0.981707	+	0.190400i	$0.0609784\pi$
$29$			2.05067i			0.380799i	−0.981707	+	0.190400i	$0.939022\pi$
$30$		0			0
$31$	−7.53503	+	4.35035i	−1.35333	+	0.781346i	−0.988715	−	0.149811i	$-0.952133\pi$
$31$	−7.53503	+	4.35035i	−1.35333	+	0.781346i	−0.364617	+	0.931158i	$0.618800\pi$
$32$	−2.00328	+	5.29026i	−0.354133	+	0.935195i
$33$		0			0
$34$	−5.94860	+	5.71486i	−1.02018	+	0.980091i
$35$	−10.5014	+	2.48008i	−1.77505	+	0.419209i
$36$		0			0
$37$	−3.53252	+	6.11850i	−0.580743	+	1.00588i	0.414649	+	0.909981i	$0.363904\pi$
$37$	−3.53252	+	6.11850i	−0.580743	+	1.00588i	−0.995392	+	0.0958942i	$0.969429\pi$
$38$	6.43135	+	1.86216i	1.04330	+	0.302082i
$39$		0			0
$40$	11.3014	−	2.31077i	1.78691	−	0.365364i
$41$			2.50300i			0.390903i	0.980713	+	0.195452i	$0.0626172\pi$
$41$			2.50300i			0.390903i	−0.980713	+	0.195452i	$0.937383\pi$
$42$		0			0
$43$		−	2.99519i		−	0.456763i	−0.973572	−	0.228381i	$-0.926657\pi$
$43$		−	2.99519i		−	0.456763i	0.973572	−	0.228381i	$-0.0733433\pi$
$44$	0.874374	+	0.552674i	0.131817	+	0.0833187i
$45$		0			0
$46$	−0.766860	+	2.64851i	−0.113067	+	0.390501i
$47$	−4.97255	+	8.61270i	−0.725321	+	1.25629i	0.233521	+	0.972352i	$0.424975\pi$
$47$	−4.97255	+	8.61270i	−0.725321	+	1.25629i	−0.958842	+	0.283940i	$0.908358\pi$
$48$		0			0
$49$	0.418094	−	6.98750i	0.0597277	−	0.998215i
$50$	−11.3973	−	11.8635i	−1.61183	−	1.67775i
$51$		0			0
$52$	−7.09808	+	3.72719i	−0.984327	+	0.516868i
$53$	−7.05724	+	4.07450i	−0.969386	+	0.559675i	−0.899049	−	0.437848i	$-0.855741\pi$
$53$	−7.05724	+	4.07450i	−0.969386	+	0.559675i	−0.0703372	+	0.997523i	$0.522408\pi$
$54$		0			0
$55$		−	2.10931i		−	0.284419i
$56$	−0.672548	+	7.45303i	−0.0898730	+	0.995953i
$57$		0			0
$58$	−0.694319	−	2.81574i	−0.0911686	−	0.369725i
$59$	−6.07396	−	10.5204i	−0.790762	−	1.36964i	−0.925496	−	0.378758i	$-0.876351\pi$
$59$	−6.07396	−	10.5204i	−0.790762	−	1.36964i	0.134734	−	0.990882i	$-0.456982\pi$
$60$		0			0
$61$	−1.71003	+	2.96186i	−0.218947	+	0.379227i	−0.954486	−	0.298255i	$-0.903596\pi$
$61$	−1.71003	+	2.96186i	−0.218947	+	0.379227i	0.735539	+	0.677482i	$0.236929\pi$
$62$	8.87329	−	8.52463i	1.12691	−	1.08263i
$63$		0			0
$64$	0.959489	−	7.94225i	0.119936	−	0.992782i
$65$	14.1580	+	8.17414i	1.75609	+	1.01388i
$66$		0			0
$67$	1.72609	−	0.996560i	0.210876	−	0.121749i	−0.390843	−	0.920458i	$-0.627816\pi$
$67$	1.72609	−	0.996560i	0.210876	−	0.121749i	0.601718	+	0.798708i	$0.294483\pi$
$68$	6.23299	−	9.86108i	0.755861	−	1.19583i
$69$		0			0
$70$	13.5795	−	6.96093i	1.62307	−	0.831990i
$71$	−2.86671			−0.340216			−0.170108	−	0.985425i	$-0.554412\pi$
$71$	−2.86671			−0.340216			−0.170108	+	0.985425i	$0.554412\pi$
$72$		0			0
$73$	4.04598	+	7.00785i	0.473547	+	0.820207i	0.999541	−	0.0302810i	$-0.00964022\pi$
$73$	4.04598	+	7.00785i	0.473547	+	0.820207i	−0.525995	+	0.850488i	$0.676307\pi$
$74$	2.77883	−	9.59727i	0.323033	−	1.11566i
$75$		0			0
$76$	−9.46129	−	0.379366i	−1.08528	−	0.0435162i
$77$	1.31058	+	0.393495i	0.149355	+	0.0448429i
$78$		0			0
$79$	−4.28947	−	2.47652i	−0.482603	−	0.278631i	0.238898	−	0.971045i	$-0.423214\pi$
$79$	−4.28947	−	2.47652i	−0.482603	−	0.278631i	−0.721500	+	0.692414i	$0.756547\pi$
$80$	−14.7354	+	6.99934i	−1.64747	+	0.782550i
$81$		0			0
$82$	−0.847471	−	3.43683i	−0.0935875	−	0.379535i
$83$	1.91175			0.209842			0.104921	−	0.994481i	$-0.466541\pi$
$83$	1.91175			0.209842			0.104921	+	0.994481i	$0.466541\pi$
$84$		0			0
$85$	−23.7885			−2.58022
$86$	1.01412	+	4.11266i	0.109355	+	0.443479i
$87$		0			0
$88$	−1.38772	−	0.462821i	−0.147931	−	0.0493369i
$89$	−11.7420	−	6.77926i	−1.24465	−	0.718600i	−0.274614	−	0.961555i	$-0.588550\pi$
$89$	−11.7420	−	6.77926i	−1.24465	−	0.718600i	−0.970038	+	0.242955i	$0.921883\pi$
$90$		0			0
$91$	−7.72007	+	7.27195i	−0.809283	+	0.762307i
$92$	0.156227	−	3.89627i	0.0162878	−	0.406214i
$93$		0			0
$94$	3.91162	−	13.5096i	0.403453	−	1.39341i
$95$	9.65431	+	16.7218i	0.990511	+	1.71562i
$96$		0			0
$97$	4.24721			0.431238			0.215619	−	0.976478i	$-0.430823\pi$
$97$	4.24721			0.431238			0.215619	+	0.976478i	$0.430823\pi$
$98$	1.79176	+	9.73599i	0.180995	+	0.983484i
$99$		0			0
$100$	19.6663	+	12.4307i	1.96663	+	1.24307i
$101$	−0.668392	+	0.385896i	−0.0665075	+	0.0383981i	−0.532885	−	0.846188i	$-0.678892\pi$
$101$	−0.668392	+	0.385896i	−0.0665075	+	0.0383981i	0.466378	+	0.884586i	$0.345559\pi$
$102$		0			0
$103$	−13.8054	−	7.97056i	−1.36029	−	0.785363i	−0.370626	−	0.928782i	$-0.620857\pi$
$103$	−13.8054	−	7.97056i	−1.36029	−	0.785363i	−0.989662	+	0.143420i	$0.954190\pi$
$104$	8.48431	−	7.52103i	0.831955	−	0.737497i
$105$		0			0
$106$	8.31064	−	7.98409i	0.807200	−	0.775483i
$107$	0.733470	−	1.27041i	0.0709072	−	0.122815i	−0.828392	−	0.560149i	$-0.810744\pi$
$107$	0.733470	−	1.27041i	0.0709072	−	0.122815i	0.899299	+	0.437334i	$0.144077\pi$
$108$		0			0
$109$	3.23374	+	5.60100i	0.309736	+	0.536479i	0.978305	−	0.207172i	$-0.0664259\pi$
$109$	3.23374	+	5.60100i	0.309736	+	0.536479i	−0.668568	+	0.743651i	$0.733093\pi$
$110$	0.714173	+	2.89626i	0.0680937	+	0.276147i
$111$		0			0
$112$	−1.60000	−	10.4614i	−0.151185	−	0.988505i
$113$			11.3550i			1.06819i	0.845424	+	0.534095i	$0.179348\pi$
$113$			11.3550i			1.06819i	−0.845424	+	0.534095i	$0.820652\pi$
$114$		0			0
$115$	−6.88621	+	3.97576i	−0.642143	+	0.370741i
$116$	1.90672	+	3.63117i	0.177034	+	0.337145i
$117$		0			0
$118$	11.9021	+	12.3889i	1.09567	+	1.14049i
$119$	4.43778	−	14.7806i	0.406811	−	1.35493i
$120$		0			0
$121$	5.36625	−	9.29462i	0.487841	−	0.844966i
$122$	1.34519	−	4.64587i	0.121787	−	0.420617i
$123$		0			0
$124$	−9.29749	+	14.7094i	−0.834939	+	1.32094i
$125$		−	27.0506i		−	2.41948i
$126$		0			0
$127$			4.46382i			0.396100i	0.980192	+	0.198050i	$0.0634609\pi$
$127$			4.46382i			0.396100i	−0.980192	+	0.198050i	$0.936539\pi$
$128$	1.37164	+	11.2303i	0.121237	+	0.992624i
$129$		0			0
$130$	−22.2078	−	6.43014i	−1.94775	−	0.563960i
$131$	3.89148	−	6.74025i	0.340001	−	0.588898i	−0.644432	−	0.764662i	$-0.722906\pi$
$131$	3.89148	−	6.74025i	0.340001	−	0.588898i	0.984432	+	0.175764i	$0.0562394\pi$
$132$		0			0
$133$	−12.1908	+	2.87907i	−1.05708	+	0.249647i
$134$	−2.03265	+	1.95279i	−0.175595	+	0.168695i
$135$		0			0
$136$	−5.21964	+	15.6505i	−0.447580	+	1.34202i
$137$	−7.70211	+	4.44682i	−0.658036	+	0.379917i	−0.791528	−	0.611133i	$-0.790714\pi$
$137$	−7.70211	+	4.44682i	−0.658036	+	0.379917i	0.133492	+	0.991050i	$0.457381\pi$
$138$		0			0
$139$			0.116187i			0.00985482i	0.999988	+	0.00492741i	$0.00156845\pi$
$139$			0.116187i			0.00985482i	−0.999988	+	0.00492741i	$0.998432\pi$
$140$	−16.2890	+	14.1557i	−1.37667	+	1.19638i
$141$		0			0
$142$	3.93624	−	0.970617i	0.330322	−	0.0814524i
$143$	−1.03662	−	1.79547i	−0.0866861	−	0.150145i
$144$		0			0
$145$	4.18165	−	7.24283i	0.347267	−	0.601484i
$146$	−7.92821	−	8.25248i	−0.656143	−	0.682980i
$147$		0			0
$148$	−0.566114	+	14.1187i	−0.0465343	+	1.16055i
$149$	3.58054	+	2.06723i	0.293329	+	0.169354i	0.639442	−	0.768839i	$-0.279165\pi$
$149$	3.58054	+	2.06723i	0.293329	+	0.169354i	−0.346113	+	0.938193i	$0.612499\pi$
$150$		0			0
$151$	−3.94574	+	2.27807i	−0.321100	+	0.185387i	−0.651883	−	0.758320i	$-0.726021\pi$
$151$	−3.94574	+	2.27807i	−0.321100	+	0.185387i	0.330783	+	0.943707i	$0.392687\pi$
$152$	13.1196	−	2.68252i	1.06414	−	0.217581i
$153$		0			0
$154$	−1.93277	−	0.0965626i	−0.155747	−	0.00778123i
$155$	35.4843			2.85017
$156$		0			0
$157$	8.18445	+	14.1759i	0.653190	+	1.13136i	0.982344	+	0.187082i	$0.0599031\pi$
$157$	8.18445	+	14.1759i	0.653190	+	1.13136i	−0.329154	+	0.944276i	$0.606764\pi$
$158$	6.72831	+	1.94814i	0.535275	+	0.154986i
$159$		0			0
$160$	17.8632	−	14.5998i	1.41221	−	1.15422i
$161$	−1.18563	−	5.02032i	−0.0934410	−	0.395656i
$162$		0			0
$163$	0.616691	+	0.356047i	0.0483030	+	0.0278877i	0.523957	−	0.851745i	$-0.324455\pi$
$163$	0.616691	+	0.356047i	0.0483030	+	0.0278877i	−0.475654	+	0.879632i	$0.657789\pi$
$164$	2.32730	+	4.43213i	0.181731	+	0.346091i
$165$		0			0
$166$	−2.62499	+	0.647284i	−0.203739	+	0.0502390i
$167$	14.8541			1.14944			0.574721	−	0.818349i	$-0.305111\pi$
$167$	14.8541			1.14944			0.574721	+	0.818349i	$0.305111\pi$
$168$		0			0
$169$	3.06867			0.236052
$170$	32.6636	−	8.05435i	2.50519	−	0.617741i
$171$		0			0
$172$	−2.78494	−	5.30366i	−0.212350	−	0.404401i
$173$	−3.66034	−	2.11330i	−0.278291	−	0.160671i	0.354359	−	0.935110i	$-0.384699\pi$
$173$	−3.66034	−	2.11330i	−0.278291	−	0.160671i	−0.632649	+	0.774438i	$0.718033\pi$
$174$		0			0
$175$	29.4774	+	8.85043i	2.22828	+	0.669029i
$176$	2.06215	+	0.165637i	0.155441	+	0.0124854i
$177$		0			0
$178$	18.4181	+	5.33286i	1.38050	+	0.399715i
$179$	−1.11308	−	1.92790i	−0.0831952	−	0.144098i	0.821426	−	0.570316i	$-0.193179\pi$
$179$	−1.11308	−	1.92790i	−0.0831952	−	0.144098i	−0.904621	+	0.426218i	$0.859846\pi$
$180$		0			0
$181$	11.4376			0.850150			0.425075	−	0.905158i	$-0.360248\pi$
$181$	11.4376			0.850150			0.425075	+	0.905158i	$0.360248\pi$
$182$	8.13816	−	12.5989i	0.603240	−	0.933891i
$183$		0			0
$184$	1.10469	+	5.40280i	0.0814390	+	0.398300i
$185$	24.9533	−	14.4068i	1.83460	−	1.05921i
$186$		0			0
$187$	2.61260	+	1.50839i	0.191052	+	0.110304i
$188$	−0.796890	+	19.8742i	−0.0581191	+	1.44948i
$189$		0			0
$190$	−18.9179	−	19.6916i	−1.37245	−	1.42858i
$191$	6.16406	−	10.6765i	0.446016	−	0.772522i	−0.552107	−	0.833774i	$-0.686176\pi$
$191$	6.16406	−	10.6765i	0.446016	−	0.772522i	0.998122	+	0.0612515i	$0.0195092\pi$
$192$		0			0
$193$	−0.872412	−	1.51106i	−0.0627976	−	0.108769i	0.832917	−	0.553397i	$-0.186669\pi$
$193$	−0.872412	−	1.51106i	−0.0627976	−	0.108769i	−0.895715	+	0.444629i	$0.853336\pi$
$194$	−5.83177	+	1.43803i	−0.418697	+	0.103244i
$195$		0			0
$196$	−5.75668	−	12.7617i	−0.411191	−	0.911549i
$197$		−	5.29064i		−	0.376943i	−0.982079	−	0.188471i	$-0.939647\pi$
$197$		−	5.29064i		−	0.376943i	0.982079	−	0.188471i	$-0.0603533\pi$
$198$		0			0
$199$	9.73931	−	5.62299i	0.690401	−	0.398603i	−0.113361	−	0.993554i	$-0.536162\pi$
$199$	9.73931	−	5.62299i	0.690401	−	0.398603i	0.803762	+	0.594950i	$0.202828\pi$
$200$	−31.2123	−	10.4097i	−2.20704	−	0.736077i
$201$		0			0
$202$	0.787102	−	0.756174i	0.0553803	−	0.0532042i
$203$	3.72011	+	3.94936i	0.261101	+	0.277191i
$204$		0			0
$205$	5.10403	−	8.84044i	0.356481	−	0.617443i
$206$	21.6547	+	6.26999i	1.50875	+	0.436851i
$207$		0			0
$208$	−9.10320	+	13.1996i	−0.631193	+	0.915230i
$209$		−	2.44865i		−	0.169377i
$210$		0			0
$211$		−	25.0975i		−	1.72778i	−0.503677	−	0.863892i	$-0.668020\pi$
$211$		−	25.0975i		−	1.72778i	0.503677	−	0.863892i	$-0.331980\pi$
$212$	−8.70794	+	13.7767i	−0.598064	+	0.946185i
$213$		0			0
$214$	−0.576980	+	1.99272i	−0.0394415	+	0.136219i
$215$	−6.10769	+	10.5788i	−0.416541	+	0.721470i
$216$		0			0
$217$	−6.61966	+	22.0476i	−0.449372	+	1.49669i
$218$	−6.33660	−	6.59577i	−0.429169	−	0.446722i
$219$		0			0
$220$	−1.96124	−	3.73500i	−0.132227	−	0.251814i
$221$	−20.2491	+	11.6908i	−1.36210	+	0.786409i
$222$		0			0
$223$		−	17.9029i		−	1.19887i	−0.800423	−	0.599435i	$-0.795392\pi$
$223$		−	17.9029i		−	1.19887i	0.800423	−	0.599435i	$-0.204608\pi$
$224$	5.73896	+	13.8226i	0.383450	+	0.923562i
$225$		0			0
$226$	−3.84460	−	15.5914i	−0.255739	−	1.03712i
$227$	7.08833	+	12.2774i	0.470469	+	0.814877i	0.999430	−	0.0337699i	$-0.0107513\pi$
$227$	7.08833	+	12.2774i	0.470469	+	0.814877i	−0.528960	+	0.848647i	$0.677418\pi$
$228$		0			0
$229$	1.86807	−	3.23559i	0.123446	−	0.213814i	−0.797679	−	0.603083i	$-0.793939\pi$
$229$	1.86807	−	3.23559i	0.123446	−	0.213814i	0.921124	+	0.389269i	$0.127272\pi$
$230$	8.10924	−	7.79060i	0.534707	−	0.513697i
$231$		0			0
$232$	−3.84753	−	4.34032i	−0.252603	−	0.284956i
$233$	23.9146	+	13.8071i	1.56670	+	0.904532i	0.996551	+	0.0829878i	$0.0264463\pi$
$233$	23.9146	+	13.8071i	1.56670	+	0.904532i	0.570145	+	0.821544i	$0.306887\pi$
$234$		0			0
$235$	35.1254	−	20.2797i	2.29133	−	1.32290i
$236$	−20.5372	−	12.9811i	−1.33686	−	0.845001i
$237$		0			0
$238$	−1.08902	+	21.7975i	−0.0705907	+	1.41292i
$239$	−13.8753			−0.897520			−0.448760	−	0.893652i	$-0.648134\pi$
$239$	−13.8753			−0.897520			−0.448760	+	0.893652i	$0.648134\pi$
$240$		0			0
$241$	−12.8683	−	22.2886i	−0.828921	−	1.43573i	−0.898885	−	0.438184i	$-0.855622\pi$
$241$	−12.8683	−	22.2886i	−0.828921	−	1.43573i	0.0699642	−	0.997550i	$-0.477711\pi$
$242$	−4.22133	+	14.5792i	−0.271357	+	0.937188i
$243$		0			0
$244$	−0.274046	+	6.83463i	−0.0175440	+	0.437542i
$245$	−15.7253	+	23.8268i	−1.00466	+	1.52224i
$246$		0			0
$247$	16.4358	+	9.48919i	1.04578	+	0.603782i
$248$	7.78592	−	23.3452i	0.494406	−	1.48242i
$249$		0			0
$250$	9.15883	+	37.1427i	0.579255	+	2.34911i
$251$	−21.4777			−1.35566			−0.677829	−	0.735219i	$-0.737079\pi$
$251$	−21.4777			−1.35566			−0.677829	+	0.735219i	$0.737079\pi$
$252$		0			0
$253$	1.00838			0.0633965
$254$	−1.51137	−	6.12921i	−0.0948318	−	0.384581i
$255$		0			0
$256$	−5.68574	−	14.9557i	−0.355359	−	0.934730i
$257$	−4.93576	−	2.84966i	−0.307884	−	0.177757i	0.338095	−	0.941112i	$-0.390217\pi$
$257$	−4.93576	−	2.84966i	−0.307884	−	0.177757i	−0.645979	+	0.763355i	$0.723551\pi$
$258$		0			0
$259$	4.29633	+	18.1919i	0.266961	+	1.13039i
$260$	32.6703	+	1.30997i	2.02613	+	0.0812409i
$261$		0			0
$262$	−3.06121	+	10.5725i	−0.189122	+	0.653172i
$263$	−14.8083	−	25.6487i	−0.913117	−	1.58157i	−0.809635	−	0.586934i	$-0.800335\pi$
$263$	−14.8083	−	25.6487i	−0.913117	−	1.58157i	−0.103482	−	0.994631i	$-0.532998\pi$
$264$		0			0
$265$	33.2343			2.04157
$266$	15.7642	−	8.08079i	0.966566	−	0.495465i
$267$		0			0
$268$	2.12983	−	3.36956i	0.130100	−	0.205829i
$269$	−5.49978	+	3.17530i	−0.335328	+	0.193601i	−0.658204	−	0.752840i	$-0.728684\pi$
$269$	−5.49978	+	3.17530i	−0.335328	+	0.193601i	0.322876	+	0.946441i	$0.395350\pi$
$270$		0			0
$271$	−17.5939	−	10.1579i	−1.06876	−	0.617046i	−0.140914	−	0.990022i	$-0.545004\pi$
$271$	−17.5939	−	10.1579i	−1.06876	−	0.617046i	−0.927841	+	0.372976i	$0.878337\pi$
$272$	1.86804	−	23.2567i	0.113266	−	1.41015i
$273$		0			0
$274$	9.07004	−	8.71365i	0.547941	−	0.526411i
$275$	−3.00823	+	5.21040i	−0.181403	+	0.314199i
$276$		0			0
$277$	−2.95274	−	5.11429i	−0.177413	−	0.307288i	0.763581	−	0.645712i	$-0.223439\pi$
$277$	−2.95274	−	5.11429i	−0.177413	−	0.307288i	−0.940994	+	0.338424i	$0.890106\pi$
$278$	−0.0393387	−	0.159534i	−0.00235938	−	0.00956822i
$279$		0			0
$280$	17.5733	−	24.9522i	1.05021	−	1.49118i
$281$		−	7.21240i		−	0.430256i	−0.976586	−	0.215128i	$-0.930983\pi$
$281$		−	7.21240i		−	0.430256i	0.976586	−	0.215128i	$-0.0690169\pi$
$282$		0			0
$283$	−18.9031	+	10.9137i	−1.12367	+	0.648751i	−0.942335	−	0.334670i	$-0.891375\pi$
$283$	−18.9031	+	10.9137i	−1.12367	+	0.648751i	−0.181335	+	0.983421i	$0.558042\pi$
$284$	−5.07616	+	2.66548i	−0.301215	+	0.158167i
$285$		0			0
$286$	2.03127	+	2.11435i	0.120112	+	0.125024i
$287$	4.54069	+	4.82050i	0.268028	+	0.284545i
$288$		0			0
$289$	8.51138	−	14.7421i	0.500669	−	0.867184i
$290$	−3.28947	+	11.3608i	−0.193164	+	0.667132i
$291$		0			0
$292$	13.6802	+	8.64700i	0.800576	+	0.506027i
$293$			10.6245i			0.620690i	0.950624	+	0.310345i	$0.100445\pi$
$293$			10.6245i			0.620690i	−0.950624	+	0.310345i	$0.899555\pi$
$294$		0			0
$295$			49.5432i			2.88452i
$296$	−4.00302	−	19.5779i	−0.232671	−	1.13794i
$297$		0			0
$298$	−5.61631	−	1.62617i	−0.325344	−	0.0942015i
$299$	−3.90776	+	6.76844i	−0.225992	+	0.391429i
$300$		0			0
$301$	−5.43358	−	5.76841i	−0.313186	−	0.332486i
$302$	4.64652	−	4.46394i	0.267377	−	0.256871i
$303$		0			0
$304$	−17.1061	+	8.12538i	−0.981100	+	0.466023i
$305$	12.0794	−	6.97407i	0.691666	−	0.399334i
$306$		0			0
$307$			28.9860i			1.65432i	0.561967	+	0.827160i	$0.310045\pi$
$307$			28.9860i			1.65432i	−0.561967	+	0.827160i	$0.689955\pi$
$308$	2.68655	−	0.521812i	0.153081	−	0.0297330i
$309$		0			0
$310$	−48.7230	+	12.0144i	−2.76728	+	0.682369i
$311$	3.60735	+	6.24811i	0.204554	+	0.354298i	0.949990	−	0.312279i	$-0.101092\pi$
$311$	3.60735	+	6.24811i	0.204554	+	0.354298i	−0.745437	+	0.666576i	$0.767759\pi$
$312$		0			0
$313$	3.16439	−	5.48089i	0.178862	−	0.309798i	−0.762629	−	0.646836i	$-0.776092\pi$
$313$	3.16439	−	5.48089i	0.178862	−	0.309798i	0.941491	+	0.337038i	$0.109425\pi$
$314$	−16.0376	−	16.6936i	−0.905056	−	0.942073i
$315$		0			0
$316$	−9.89814	−	0.396882i	−0.556814	−	0.0223264i
$317$	−7.29993	−	4.21462i	−0.410005	−	0.236717i	0.280787	−	0.959770i	$-0.409405\pi$
$317$	−7.29993	−	4.21462i	−0.410005	−	0.236717i	−0.690792	+	0.723054i	$0.742738\pi$
$318$		0			0
$319$	−0.918509	+	0.530302i	−0.0514266	+	0.0296912i
$320$	−19.5844	+	26.0950i	−1.09480	+	1.45875i
$321$		0			0
$322$	3.32776	+	6.49189i	0.185449	+	0.361779i
$323$	−27.6156			−1.53657
$324$		0			0
$325$	−23.3154	−	40.3834i	−1.29331	−	2.24007i
$326$	−0.967320	−	0.280082i	−0.0535749	−	0.0155123i
$327$		0			0
$328$	−4.69622	−	5.29770i	−0.259305	−	0.292517i
$329$	6.04772	+	25.6078i	0.333422	+	1.41180i
$330$		0			0
$331$	−8.94368	−	5.16363i	−0.491589	−	0.283819i	0.233644	−	0.972322i	$-0.424935\pi$
$331$	−8.94368	−	5.16363i	−0.491589	−	0.283819i	−0.725233	+	0.688503i	$0.758268\pi$
$332$	3.38518	−	1.77755i	0.185786	−	0.0975558i
$333$		0			0
$334$	−20.3959	+	5.02932i	−1.11601	+	0.275192i
$335$	−8.12860			−0.444113
$336$		0			0
$337$	−36.2097			−1.97247			−0.986235	−	0.165351i	$-0.947124\pi$
$337$	−36.2097			−1.97247			−0.986235	+	0.165351i	$0.947124\pi$
$338$	−4.21355	+	1.03900i	−0.229187	+	0.0565139i
$339$		0			0
$340$	−42.1229	+	22.1186i	−2.28443	+	1.19955i
$341$	−3.89711	−	2.25000i	−0.211040	−	0.121844i
$342$		0			0
$343$	−11.8708	−	14.2156i	−0.640964	−	0.767571i
$344$	5.61969	+	6.33945i	0.302993	+	0.341800i
$345$		0			0
$346$	5.74149	+	1.66241i	0.308664	+	0.0893719i
$347$	−9.40691	−	16.2933i	−0.504990	−	0.874668i	−0.999983	−	0.00577106i	$-0.998163\pi$
$347$	−9.40691	−	16.2933i	−0.504990	−	0.874668i	0.494994	−	0.868897i	$-0.335170\pi$
$348$		0			0
$349$	11.5487			0.618186			0.309093	−	0.951032i	$-0.399975\pi$
$349$	11.5487			0.618186			0.309093	+	0.951032i	$0.399975\pi$
$350$	−43.4716	−	2.17187i	−2.32365	−	0.116091i
$351$		0			0
$352$	−2.88759	+	0.470774i	−0.153909	+	0.0250923i
$353$	−7.46456	+	4.30967i	−0.397298	+	0.229380i	−0.685318	−	0.728244i	$-0.740337\pi$
$353$	−7.46456	+	4.30967i	−0.397298	+	0.229380i	0.288019	+	0.957625i	$0.407003\pi$
$354$		0			0
$355$	10.1250	+	5.84570i	0.537382	+	0.310257i
$356$	−27.0953	−	1.08643i	−1.43605	−	0.0575806i
$357$		0			0
$358$	2.18110	+	2.27031i	0.115275	+	0.119989i
$359$	−10.5681	+	18.3045i	−0.557765	+	0.966077i	0.439918	+	0.898038i	$0.355008\pi$
$359$	−10.5681	+	18.3045i	−0.557765	+	0.966077i	−0.997683	+	0.0680390i	$0.978326\pi$
$360$		0			0
$361$	1.70748	+	2.95745i	0.0898675	+	0.155655i
$362$	−15.7048	+	3.87257i	−0.825426	+	0.203538i
$363$		0			0
$364$	−6.90863	+	20.0548i	−0.362111	+	1.05116i
$365$		−	33.0017i		−	1.72739i
$366$		0			0
$367$	20.0270	−	11.5626i	1.04540	−	0.603561i	0.124041	−	0.992277i	$-0.460414\pi$
$367$	20.0270	−	11.5626i	1.04540	−	0.603561i	0.921358	+	0.388716i	$0.127081\pi$
$368$	−3.34613	−	7.04448i	−0.174429	−	0.367219i
$369$		0			0
$370$	−29.3851	+	28.2304i	−1.52766	+	1.46763i
$371$	−6.19991	+	20.6496i	−0.321883	+	1.07207i
$372$		0			0
$373$	13.1467	−	22.7708i	0.680711	−	1.17903i	−0.294054	−	0.955789i	$-0.595004\pi$
$373$	13.1467	−	22.7708i	0.680711	−	1.17903i	0.974764	−	0.223236i	$-0.0716622\pi$
$374$	−4.09803	−	1.18656i	−0.211904	−	0.0613557i
$375$		0			0
$376$	−5.63485	−	27.5588i	−0.290595	−	1.42124i
$377$		−	8.22026i		−	0.423365i
$378$		0			0
$379$			28.0266i			1.43963i	0.694167	+	0.719814i	$0.255773\pi$
$379$			28.0266i			1.43963i	−0.694167	+	0.719814i	$0.744227\pi$
$380$	32.6431	+	20.6330i	1.67455	+	1.05845i
$381$		0			0
$382$	−4.84892	+	16.7467i	−0.248092	+	0.856838i
$383$	4.60294	−	7.97253i	0.235199	−	0.407377i	−0.724131	−	0.689662i	$-0.757759\pi$
$383$	4.60294	−	7.97253i	0.235199	−	0.407377i	0.959331	+	0.282285i	$0.0910923\pi$
$384$		0			0
$385$	−3.82649	−	4.06229i	−0.195016	−	0.207033i
$386$	1.70951	+	1.77943i	0.0870120	+	0.0905708i
$387$		0			0
$388$	7.52063	−	3.94907i	0.381802	−	0.200483i
$389$	7.16218	−	4.13509i	0.363137	−	0.209657i	−0.307319	−	0.951607i	$-0.599432\pi$
$389$	7.16218	−	4.13509i	0.363137	−	0.209657i	0.670456	+	0.741949i	$0.266099\pi$
$390$		0			0
$391$		−	11.3724i		−	0.575127i
$392$	12.2253	+	15.5738i	0.617470	+	0.786594i
$393$		0			0
$394$	1.79132	+	7.26450i	0.0902452	+	0.365980i
$395$	10.1001	+	17.4938i	0.508190	+	0.880211i
$396$		0			0
$397$	16.6044	−	28.7597i	0.833353	−	1.44341i	−0.0620122	−	0.998075i	$-0.519752\pi$
$397$	16.6044	−	28.7597i	0.833353	−	1.44341i	0.895365	−	0.445334i	$-0.146915\pi$
$398$	−11.4691	+	11.0184i	−0.574892	+	0.552303i
$399$		0			0
$400$	46.3817	+	3.72549i	2.31908	+	0.186274i
$401$	11.4810	+	6.62858i	0.573336	+	0.331015i	0.758480	−	0.651696i	$-0.225942\pi$
$401$	11.4810	+	6.62858i	0.573336	+	0.331015i	−0.185145	+	0.982711i	$0.559275\pi$
$402$		0			0
$403$	30.2047	−	17.4387i	1.50460	−	0.868684i
$404$	−0.824731	+	1.30479i	−0.0410319	+	0.0649157i
$405$		0			0
$406$	−6.44521	−	4.16324i	−0.319871	−	0.206618i
$407$	−3.65403			−0.181124
$408$		0			0
$409$	3.75064	+	6.49630i	0.185457	+	0.321222i	0.943731	−	0.330715i	$-0.107290\pi$
$409$	3.75064	+	6.49630i	0.185457	+	0.321222i	−0.758273	+	0.651937i	$0.773957\pi$
$410$	−4.01505	+	13.8668i	−0.198289	+	0.684833i
$411$		0			0
$412$	−31.8566	−	1.27734i	−1.56946	−	0.0629302i
$413$	−30.7828	−	9.24237i	−1.51472	−	0.454787i
$414$		0			0
$415$	−6.75218	−	3.89837i	−0.331451	−	0.191363i
$416$	8.03030	−	21.2064i	0.393718	−	1.03973i
$417$		0			0
$418$	0.829068	+	3.36220i	0.0405511	+	0.164451i
$419$	−1.05849			−0.0517104			−0.0258552	−	0.999666i	$-0.508231\pi$
$419$	−1.05849			−0.0517104			−0.0258552	+	0.999666i	$0.508231\pi$
$420$		0			0
$421$	15.7988			0.769988			0.384994	−	0.922919i	$-0.374203\pi$
$421$	15.7988			0.769988			0.384994	+	0.922919i	$0.374203\pi$
$422$	8.49757	+	34.4610i	0.413655	+	1.67754i
$423$		0			0
$424$	7.29222	−	21.8649i	0.354141	−	1.06185i
$425$	58.7622	+	33.9264i	2.85039	+	1.64567i
$426$		0			0
$427$	2.07978	+	8.80638i	0.100647	+	0.426170i
$428$	0.117544	−	2.93152i	0.00568172	−	0.141701i
$429$		0			0
$430$	4.80458	−	16.5936i	0.231697	−	0.800214i
$431$	−6.94337	−	12.0263i	−0.334450	−	0.579285i	0.648929	−	0.760849i	$-0.275217\pi$
$431$	−6.94337	−	12.0263i	−0.334450	−	0.579285i	−0.983379	+	0.181564i	$0.941884\pi$
$432$		0			0
$433$	−37.7930			−1.81622			−0.908109	−	0.418734i	$-0.862474\pi$
$433$	−37.7930			−1.81622			−0.908109	+	0.418734i	$0.862474\pi$
$434$	1.62445	−	32.5145i	0.0779760	−	1.56075i
$435$		0			0
$436$	10.9339	+	6.91109i	0.523639	+	0.330981i
$437$	−7.99406	+	4.61537i	−0.382408	+	0.220783i
$438$		0			0
$439$	0.157376	+	0.0908612i	0.00751116	+	0.00433657i	0.503751	−	0.863849i	$-0.331953\pi$
$439$	0.157376	+	0.0908612i	0.00751116	+	0.00433657i	−0.496240	+	0.868186i	$0.665286\pi$
$440$	3.95755	+	4.46443i	0.188669	+	0.212834i
$441$		0			0
$442$	23.8454	−	22.9085i	1.13421	−	1.08964i
$443$	5.02268	−	8.69954i	0.238635	−	0.413327i	−0.721688	−	0.692218i	$-0.756633\pi$
$443$	5.02268	−	8.69954i	0.238635	−	0.413327i	0.960323	+	0.278891i	$0.0899668\pi$
$444$		0			0
$445$	27.6480	+	47.8878i	1.31064	+	2.27010i
$446$	6.06161	+	24.5823i	0.287026	+	1.16400i
$447$		0			0
$448$	−12.5602	−	17.0365i	−0.593412	−	0.804899i
$449$		−	9.54508i		−	0.450460i	−0.974306	−	0.225230i	$-0.927687\pi$
$449$		−	9.54508i		−	0.450460i	0.974306	−	0.225230i	$-0.0723134\pi$
$450$		0			0
$451$	−1.12111	+	0.647275i	−0.0527911	+	0.0304790i
$452$	10.5579	+	20.1066i	0.496603	+	0.945735i
$453$		0			0
$454$	−13.8898	−	14.4579i	−0.651879	−	0.678541i
$455$	42.0955	−	9.94157i	1.97347	−	0.466068i
$456$		0			0
$457$	−13.6611	+	23.6617i	−0.639039	+	1.10685i	0.346605	+	0.938011i	$0.387334\pi$
$457$	−13.6611	+	23.6617i	−0.639039	+	1.10685i	−0.985644	+	0.168836i	$0.945999\pi$
$458$	−1.46951	+	5.07524i	−0.0686655	+	0.237150i
$459$		0			0
$460$	−8.49692	+	13.4428i	−0.396171	+	0.626774i
$461$		−	32.7076i		−	1.52335i	−0.647961	−	0.761673i	$-0.724378\pi$
$461$		−	32.7076i		−	1.52335i	0.647961	−	0.761673i	$-0.275622\pi$
$462$		0			0
$463$			29.7571i			1.38293i	0.722411	+	0.691464i	$0.243034\pi$
$463$			29.7571i			1.38293i	−0.722411	+	0.691464i	$0.756966\pi$
$464$	6.75255	+	4.65693i	0.313479	+	0.216192i
$465$		0			0
$466$	−37.5116	−	10.8613i	−1.73769	−	0.503138i
$467$	17.4458	−	30.2171i	0.807297	−	1.39828i	−0.107432	−	0.994212i	$-0.534263\pi$
$467$	17.4458	−	30.2171i	0.807297	−	1.39828i	0.914729	−	0.404067i	$-0.132404\pi$
$468$		0			0
$469$	1.51640	−	5.05057i	0.0700210	−	0.233213i
$470$	−41.3639	+	39.7386i	−1.90797	+	1.83300i
$471$		0			0
$472$	32.5945	+	10.8707i	1.50028	+	0.500364i
$473$	1.34157	−	0.774556i	0.0616854	−	0.0356141i
$474$		0			0
$475$		−	55.0747i		−	2.52700i
$476$	−5.88493	−	30.2986i	−0.269735	−	1.38873i
$477$		0			0
$478$	19.0520	−	4.69793i	0.871418	−	0.214878i
$479$	−17.1476	−	29.7004i	−0.783492	−	1.35705i	−0.929896	−	0.367823i	$-0.880103\pi$
$479$	−17.1476	−	29.7004i	−0.783492	−	1.35705i	0.146404	−	0.989225i	$-0.453230\pi$
$480$		0			0
$481$	14.1604	−	24.5265i	0.645657	−	1.11831i
$482$	25.2158	+	26.2471i	1.14855	+	1.19552i
$483$		0			0
$484$	0.859984	−	21.4478i	0.0390902	−	0.974899i
$485$	−15.0009	−	8.66075i	−0.681154	−	0.393264i
$486$		0			0
$487$	27.0016	−	15.5894i	1.22356	−	0.706423i	0.257885	−	0.966176i	$-0.416974\pi$
$487$	27.0016	−	15.5894i	1.22356	−	0.706423i	0.965675	+	0.259753i	$0.0836411\pi$
$488$	−1.93779	−	9.47731i	−0.0877198	−	0.429018i
$489$		0			0
$490$	13.5249	−	38.0406i	0.610992	−	1.71850i
$491$	−29.3983			−1.32673			−0.663363	−	0.748297i	$-0.730872\pi$
$491$	−29.3983			−1.32673			−0.663363	+	0.748297i	$0.730872\pi$
$492$		0			0
$493$	5.98067	+	10.3588i	0.269356	+	0.466538i
$494$	−25.7806	−	7.46461i	−1.15992	−	0.335849i
$495$		0			0
$496$	−2.78647	+	34.6911i	−0.125116	+	1.55768i
$497$	−5.52097	+	5.20050i	−0.247649	+	0.233274i
$498$		0			0
$499$	−4.13651	−	2.38822i	−0.185176	−	0.106911i	0.404546	−	0.914517i	$-0.367429\pi$
$499$	−4.13651	−	2.38822i	−0.185176	−	0.106911i	−0.589722	+	0.807606i	$0.700763\pi$
$500$	−25.1517	−	47.8991i	−1.12482	−	2.14211i
$501$		0			0
$502$	29.4907	−	7.27195i	1.31623	−	0.324563i
$503$	−18.2902			−0.815519			−0.407760	−	0.913089i	$-0.633690\pi$
$503$	−18.2902			−0.815519			−0.407760	+	0.913089i	$0.633690\pi$
$504$		0			0
$505$	3.14762			0.140067
$506$	−1.38459	+	0.341420i	−0.0615528	+	0.0151780i
$507$		0			0
$508$	4.15048	+	7.90420i	0.184148	+	0.350692i
$509$	−22.1503	−	12.7885i	−0.981795	−	0.566840i	−0.0789836	−	0.996876i	$-0.525167\pi$
$509$	−22.1503	−	12.7885i	−0.981795	−	0.566840i	−0.902812	+	0.430036i	$0.858501\pi$
$510$		0			0
$511$	20.5050	+	6.15652i	0.907090	+	0.272349i
$512$	12.8707	+	18.6103i	0.568811	+	0.822468i
$513$		0			0
$514$	7.74206	+	2.24167i	0.341488	+	0.0988758i
$515$	32.5066	+	56.3030i	1.43241	+	2.48101i
$516$		0			0
$517$	−5.14359			−0.226215
$518$	−12.0587	−	23.5244i	−0.529827	−	1.03360i
$519$		0			0
$520$	−45.3026	+	9.26288i	−1.98665	+	0.406204i
$521$	−10.2479	+	5.91663i	−0.448969	+	0.259212i	−0.707395	−	0.706819i	$-0.750130\pi$
$521$	−10.2479	+	5.91663i	−0.448969	+	0.259212i	0.258426	+	0.966031i	$0.416796\pi$
$522$		0			0
$523$	11.6681	+	6.73657i	0.510210	+	0.294570i	0.732920	−	0.680315i	$-0.238157\pi$
$523$	11.6681	+	6.73657i	0.510210	+	0.294570i	−0.222710	+	0.974885i	$0.571490\pi$
$524$	0.623641	−	15.5534i	0.0272439	−	0.679455i
$525$		0			0
$526$	29.0172	+	30.2040i	1.26521	+	1.31696i
$527$	−25.3752	+	43.9511i	−1.10536	+	1.91454i
$528$		0			0
$529$	9.59934	+	16.6265i	0.417362	+	0.722893i
$530$	−45.6335	+	11.2525i	−1.98219	+	0.488779i
$531$		0			0
$532$	−18.9096	+	16.4331i	−0.819835	+	0.712465i
$533$		−	10.0335i		−	0.434598i
$534$		0			0
$535$	−5.18114	+	2.99133i	−0.224000	+	0.129327i
$536$	−1.78357	+	5.34781i	−0.0770383	+	0.230990i
$537$		0			0
$538$	6.47657	−	6.22208i	0.279225	−	0.268253i
$539$	3.23787	−	1.61970i	0.139465	−	0.0697653i
$540$		0			0
$541$	−15.8103	+	27.3843i	−0.679740	+	1.17734i	0.295320	+	0.955398i	$0.404574\pi$
$541$	−15.8103	+	27.3843i	−0.679740	+	1.17734i	−0.975059	+	0.221945i	$0.928759\pi$
$542$	27.5972	+	7.99062i	1.18540	+	0.343226i
$543$		0			0
$544$	5.30933	+	32.5659i	0.227636	+	1.39625i
$545$		−	26.3765i		−	1.12985i
$546$		0			0
$547$		−	23.9671i		−	1.02476i	−0.858759	−	0.512381i	$-0.828764\pi$
$547$		−	23.9671i		−	1.02476i	0.858759	−	0.512381i	$-0.171236\pi$
$548$	−9.50365	+	15.0355i	−0.405976	+	0.642286i
$549$		0			0
$550$	2.36640	−	8.17285i	0.100904	−	0.348492i
$551$	4.85439	−	8.40804i	0.206804	−	0.358195i
$552$		0			0
$553$	−12.7537	+	3.01200i	−0.542342	+	0.128083i
$554$	5.78596	+	6.02261i	0.245822	+	0.255876i
$555$		0			0
$556$	0.108031	+	0.205735i	0.00458152	+	0.00872509i
$557$	−2.55943	+	1.47769i	−0.108446	+	0.0626116i	−0.553242	−	0.833020i	$-0.686610\pi$
$557$	−2.55943	+	1.47769i	−0.108446	+	0.0626116i	0.444796	+	0.895632i	$0.353276\pi$
$558$		0			0
$559$			12.0065i			0.507819i
$560$	−15.6813	+	40.2115i	−0.662658	+	1.69925i
$561$		0			0
$562$	2.44199	+	9.90324i	0.103009	+	0.417743i
$563$	5.73102	+	9.92642i	0.241534	+	0.418349i	0.961151	−	0.276022i	$-0.0890162\pi$
$563$	5.73102	+	9.92642i	0.241534	+	0.418349i	−0.719618	+	0.694371i	$0.755683\pi$
$564$		0			0
$565$	23.1547	−	40.1052i	0.974127	−	1.68724i
$566$	22.2603	−	21.3856i	0.935671	−	0.898906i
$567$		0			0
$568$	6.06751	−	5.37862i	0.254587	−	0.225682i
$569$	1.53807	+	0.888004i	0.0644792	+	0.0372271i	0.531893	−	0.846812i	$-0.321481\pi$
$569$	1.53807	+	0.888004i	0.0644792	+	0.0372271i	−0.467414	+	0.884039i	$0.654814\pi$
$570$		0			0
$571$	2.13249	−	1.23120i	0.0892421	−	0.0515239i	−0.454715	−	0.890637i	$-0.650259\pi$
$571$	2.13249	−	1.23120i	0.0892421	−	0.0515239i	0.543957	+	0.839113i	$0.316925\pi$
$572$	−3.50499	−	2.21543i	−0.146551	−	0.0926320i
$573$		0			0
$574$	−7.86689	−	5.08156i	−0.328358	−	0.212100i
$575$	22.6804			0.945838
$576$		0			0
$577$	−6.51529	−	11.2848i	−0.271235	−	0.469793i	0.697943	−	0.716153i	$-0.254099\pi$
$577$	−6.51529	−	11.2848i	−0.271235	−	0.469793i	−0.969178	+	0.246360i	$0.920765\pi$
$578$	−6.69542	+	23.1240i	−0.278493	+	0.961832i
$579$		0			0
$580$	0.670142	−	16.7132i	0.0278261	−	0.693976i
$581$	3.68182	−	3.46810i	0.152747	−	0.143881i
$582$		0			0
$583$	−3.65000	−	2.10733i	−0.151167	−	0.0872765i
$584$	−21.7119	−	7.24118i	−0.898443	−	0.299642i
$585$		0			0
$586$	−3.59727	−	14.5883i	−0.148602	−	0.602639i
$587$	27.5904			1.13878			0.569389	−	0.822068i	$-0.307180\pi$
$587$	27.5904			1.13878			0.569389	+	0.822068i	$0.307180\pi$
$588$		0			0
$589$	41.1930			1.69733
$590$	−16.7744	−	68.0270i	−0.690592	−	2.80063i
$591$		0			0
$592$	12.1252	+	25.5268i	0.498343	+	1.04914i
$593$	12.6506	+	7.30385i	0.519500	+	0.299933i	0.736730	−	0.676187i	$-0.236369\pi$
$593$	12.6506	+	7.30385i	0.519500	+	0.299933i	−0.217230	+	0.976120i	$0.569702\pi$
$594$		0			0
$595$	−45.8140	+	43.1547i	−1.87819	+	1.76917i
$596$	8.26226	+	0.331289i	0.338435	+	0.0135701i
$597$		0			0
$598$	3.07401	−	10.6167i	0.125706	−	0.434151i
$599$	−19.2913	−	33.4136i	−0.788222	−	1.36524i	−0.927055	−	0.374925i	$-0.877668\pi$
$599$	−19.2913	−	33.4136i	−0.788222	−	1.36524i	0.138833	−	0.990316i	$-0.455665\pi$
$600$		0			0
$601$	−29.5034			−1.20347			−0.601735	−	0.798696i	$-0.705524\pi$
$601$	−29.5034			−1.20347			−0.601735	+	0.798696i	$0.705524\pi$
$602$	9.41384	+	6.08081i	0.383680	+	0.247835i
$603$		0			0
$604$	−4.86866	+	7.70260i	−0.198103	+	0.313414i
$605$	−37.9065	+	21.8853i	−1.54112	+	0.889766i
$606$		0			0
$607$	−33.9174	−	19.5822i	−1.37666	−	0.794817i	−0.384907	−	0.922955i	$-0.625767\pi$
$607$	−33.9174	−	19.5822i	−1.37666	−	0.794817i	−0.991756	+	0.128138i	$0.959100\pi$
$608$	20.7370	−	16.9486i	0.840995	−	0.687358i
$609$		0			0
$610$	−14.2248	+	13.6659i	−0.575945	+	0.553315i
$611$	19.9328	−	34.5247i	0.806396	−	1.39672i
$612$		0			0
$613$	3.93298	+	6.81212i	0.158851	+	0.275139i	0.934455	−	0.356082i	$-0.115888\pi$
$613$	3.93298	+	6.81212i	0.158851	+	0.275139i	−0.775603	+	0.631221i	$0.782554\pi$
$614$	−9.81414	−	39.8003i	−0.396066	−	1.60621i
$615$		0			0
$616$	−3.51219	+	1.62611i	−0.141510	+	0.0655179i
$617$			42.0669i			1.69355i	0.531950	+	0.846776i	$0.321459\pi$
$617$			42.0669i			1.69355i	−0.531950	+	0.846776i	$0.678541\pi$
$618$		0			0
$619$	−30.0148	+	17.3290i	−1.20639	+	0.696512i	−0.961970	−	0.273156i	$-0.911933\pi$
$619$	−30.0148	+	17.3290i	−1.20639	+	0.696512i	−0.244425	+	0.969668i	$0.578599\pi$
$620$	62.8330	−	32.9934i	2.52343	−	1.32505i
$621$		0			0
$622$	−7.06869	−	7.35780i	−0.283429	−	0.295021i
$623$	−34.9121	+	8.24508i	−1.39872	+	0.330332i
$624$		0			0
$625$	−26.0786	+	45.1695i	−1.04315	+	1.80678i
$626$	−2.48925	+	8.59714i	−0.0994905	+	0.343611i
$627$		0			0
$628$	27.6732	+	17.4917i	1.10428	+	0.697993i
$629$			41.2097i			1.64314i
$630$		0			0
$631$		−	13.1561i		−	0.523737i	−0.965104	−	0.261868i	$-0.915661\pi$
$631$		−	13.1561i		−	0.523737i	0.965104	−	0.261868i	$-0.0843387\pi$
$632$	13.7254	−	2.80638i	0.545966	−	0.111632i
$633$		0			0
$634$	11.4504	+	3.31540i	0.454754	+	0.131672i
$635$	9.10247	−	15.7659i	0.361220	−	0.625652i
$636$		0			0
$637$	−1.67596	+	28.0099i	−0.0664039	+	1.10979i
$638$	1.08164	−	1.03914i	0.0428226	−	0.0411399i
$639$		0			0
$640$	18.0558	−	42.4615i	0.713717	−	1.67844i
$641$	21.0414	−	12.1482i	0.831084	−	0.479827i	−0.0231396	−	0.999732i	$-0.507366\pi$
$641$	21.0414	−	12.1482i	0.831084	−	0.479827i	0.854224	+	0.519906i	$0.174033\pi$
$642$		0			0
$643$		−	25.3313i		−	0.998968i	−0.866323	−	0.499484i	$-0.833523\pi$
$643$		−	25.3313i		−	0.998968i	0.866323	−	0.499484i	$-0.166477\pi$
$644$	−6.76734	−	7.78719i	−0.266670	−	0.306858i
$645$		0			0
$646$	37.9185	−	9.35013i	1.49188	−	0.367876i
$647$	18.5185	+	32.0749i	0.728036	+	1.26100i	0.957712	+	0.287728i	$0.0928999\pi$
$647$	18.5185	+	32.0749i	0.728036	+	1.26100i	−0.229676	+	0.973267i	$0.573767\pi$
$648$		0			0
$649$	3.14144	−	5.44114i	0.123312	−	0.213583i
$650$	45.6871	+	47.5557i	1.79200	+	1.86529i
$651$		0			0
$652$	1.42304	+	0.0570593i	0.0557307	+	0.00223461i
$653$	−7.04637	−	4.06822i	−0.275746	−	0.159202i	0.355750	−	0.934581i	$-0.384225\pi$
$653$	−7.04637	−	4.06822i	−0.275746	−	0.159202i	−0.631496	+	0.775379i	$0.717559\pi$
$654$		0			0
$655$	−27.4889	+	15.8707i	−1.07408	+	0.620121i
$656$	8.24201	+	5.68414i	0.321796	+	0.221928i
$657$		0			0
$658$	−16.9744	−	33.1140i	−0.661730	−	1.29092i
$659$	−46.2323			−1.80095			−0.900477	−	0.434904i	$-0.856782\pi$
$659$	−46.2323			−1.80095			−0.900477	+	0.434904i	$0.856782\pi$
$660$		0			0
$661$	−4.95426	−	8.58103i	−0.192698	−	0.333764i	0.753445	−	0.657511i	$-0.228391\pi$
$661$	−4.95426	−	8.58103i	−0.192698	−	0.333764i	−0.946144	+	0.323747i	$0.895057\pi$
$662$	14.0287	+	4.06194i	0.545242	+	0.157872i
$663$		0			0
$664$	−4.04630	+	3.58689i	−0.157027	+	0.139198i
$665$	48.9280	+	14.6904i	1.89735	+	0.569668i
$666$		0			0
$667$	3.46253	+	1.99909i	0.134070	+	0.0774052i
$668$	26.3025	−	13.8114i	1.01767	−	0.534378i
$669$		0			0
$670$	11.1613	−	2.75220i	0.431197	−	0.106327i
$671$	−1.76885			−0.0682858
$672$		0			0
$673$	−14.7303			−0.567811			−0.283906	−	0.958852i	$-0.591630\pi$
$673$	−14.7303			−0.567811			−0.283906	+	0.958852i	$0.591630\pi$
$674$	49.7190	−	12.2600i	1.91511	−	0.472236i
$675$		0			0
$676$	5.43377	−	2.85326i	0.208991	−	0.109741i
$677$	−4.80739	−	2.77555i	−0.184763	−	0.106673i	0.404766	−	0.914420i	$-0.367353\pi$
$677$	−4.80739	−	2.77555i	−0.184763	−	0.106673i	−0.589529	+	0.807748i	$0.700686\pi$
$678$		0			0
$679$	8.17964	−	7.70485i	0.313906	−	0.295685i
$680$	50.3493	−	44.6328i	1.93081	−	1.71159i
$681$		0			0
$682$	6.11287	+	1.76995i	0.234074	+	0.0677748i
$683$	0.804069	+	1.39269i	0.0307669	+	0.0532898i	0.880999	−	0.473118i	$-0.156872\pi$
$683$	0.804069	+	1.39269i	0.0307669	+	0.0532898i	−0.850232	+	0.526408i	$0.823538\pi$
$684$		0			0
$685$	36.2711			1.38585
$686$	21.1128	+	15.5000i	0.806090	+	0.591793i
$687$		0			0
$688$	−9.86273	−	6.80188i	−0.376013	−	0.259319i
$689$	28.2895	−	16.3329i	1.07774	−	0.622235i
$690$		0			0
$691$	−5.92991	−	3.42364i	−0.225584	−	0.130241i	0.382949	−	0.923770i	$-0.374909\pi$
$691$	−5.92991	−	3.42364i	−0.225584	−	0.130241i	−0.608533	+	0.793528i	$0.708242\pi$
$692$	−8.44641	−	0.338673i	−0.321084	−	0.0128744i
$693$		0			0
$694$	18.4331	+	19.1870i	0.699711	+	0.728329i
$695$	0.236924	−	0.410364i	0.00898703	−	0.0155660i
$696$		0			0
$697$	7.29988	+	12.6438i	0.276503	+	0.478917i
$698$	−15.8573	+	3.91017i	−0.600208	+	0.148002i
$699$		0			0
$700$	60.4255	−	11.7365i	2.28387	−	0.443599i
$701$			22.3346i			0.843567i	0.906697	+	0.421784i	$0.138596\pi$
$701$			22.3346i			0.843567i	−0.906697	+	0.421784i	$0.861404\pi$
$702$		0			0
$703$	28.9677	−	16.7245i	1.09254	−	0.630777i
$704$	3.80552	−	1.62410i	0.143426	−	0.0612106i
$705$		0			0
$706$	8.79030	−	8.44490i	0.330827	−	0.317828i
$707$	−0.587195	+	1.95572i	−0.0220837	+	0.0735525i
$708$		0			0
$709$	0.883842	−	1.53086i	0.0331934	−	0.0574926i	−0.848951	−	0.528471i	$-0.822766\pi$
$709$	0.883842	−	1.53086i	0.0331934	−	0.0574926i	0.882145	+	0.470978i	$0.156099\pi$
$710$	−15.8818	−	4.59848i	−0.596033	−	0.172578i
$711$		0			0
$712$	37.5719	−	7.68220i	1.40807	−	0.287903i
$713$			16.9638i			0.635298i
$714$		0			0
$715$			8.45531i			0.316211i
$716$	−3.76352	−	2.37884i	−0.140649	−	0.0889016i
$717$		0			0
$718$	8.31336	−	28.7119i	0.310252	−	1.07152i
$719$	15.3487	−	26.5848i	0.572411	−	0.991446i	−0.423906	−	0.905706i	$-0.639341\pi$
$719$	15.3487	−	26.5848i	0.572411	−	0.991446i	0.996318	−	0.0857396i	$-0.0273253\pi$
$720$		0			0
$721$	−41.0471	+	9.69397i	−1.52867	+	0.361022i
$722$	−3.34586	−	3.48270i	−0.124520	−	0.129613i
$723$		0			0
$724$	20.2528	−	10.6347i	0.752691	−	0.395236i
$725$	−20.6590	+	11.9275i	−0.767255	+	0.442975i
$726$		0			0
$727$			25.2505i			0.936488i	0.883599	+	0.468244i	$0.155113\pi$
$727$			25.2505i			0.936488i	−0.883599	+	0.468244i	$0.844887\pi$
$728$	2.69596	−	29.8760i	0.0999188	−	1.10728i
$729$		0			0
$730$	11.1738	+	45.3141i	0.413560	+	1.67715i
$731$	−8.73534	−	15.1300i	−0.323088	−	0.559605i
$732$		0			0
$733$	−17.1670	+	29.7341i	−0.634077	+	1.09825i	0.352632	+	0.935762i	$0.385287\pi$
$733$	−17.1670	+	29.7341i	−0.634077	+	1.09825i	−0.986710	+	0.162492i	$0.948047\pi$
$734$	−23.5838	+	22.6572i	−0.870496	+	0.836291i
$735$		0			0
$736$	6.97965	+	8.53973i	0.257273	+	0.314779i
$737$	0.892733	+	0.515420i	0.0328842	+	0.0189857i
$738$		0			0
$739$	17.6194	−	10.1725i	0.648139	−	0.374203i	−0.139604	−	0.990207i	$-0.544583\pi$
$739$	17.6194	−	10.1725i	0.648139	−	0.374203i	0.787743	+	0.616004i	$0.211250\pi$
$740$	30.7899	−	48.7120i	1.13186	−	1.79069i
$741$		0			0
$742$	1.52144	−	30.4528i	0.0558539	−	1.11796i
$743$	34.6692			1.27189			0.635945	−	0.771734i	$-0.280610\pi$
$743$	34.6692			1.27189			0.635945	+	0.771734i	$0.280610\pi$
$744$		0			0
$745$	−8.43082	−	14.6026i	−0.308881	−	0.534998i
$746$	−10.3418	+	35.7174i	−0.378639	+	1.30771i
$747$		0			0
$748$	6.02870	+	0.241731i	0.220431	+	0.00883854i
$749$	−0.892062	−	3.77725i	−0.0325953	−	0.138018i
$750$		0			0
$751$	−27.9988	−	16.1651i	−1.02169	−	0.589872i	−0.107096	−	0.994249i	$-0.534155\pi$
$751$	−27.9988	−	16.1651i	−1.02169	−	0.589872i	−0.914593	+	0.404376i	$0.867489\pi$
$752$	17.0680	+	35.9327i	0.622408	+	1.31033i
$753$		0			0
$754$	2.78323	+	11.2871i	0.101359	+	0.411052i
$755$	18.5815			0.676248
$756$		0			0
$757$	−17.0256			−0.618806			−0.309403	−	0.950931i	$-0.600129\pi$
$757$	−17.0256			−0.618806			−0.309403	+	0.950931i	$0.600129\pi$
$758$	−9.48929	−	38.4829i	−0.344666	−	1.39776i
$759$		0			0
$760$	−51.8077	−	17.2785i	−1.87926	−	0.626758i
$761$	10.5633	+	6.09870i	0.382918	+	0.221078i	0.679087	−	0.734058i	$-0.262376\pi$
$761$	10.5633	+	6.09870i	0.382918	+	0.221078i	−0.296169	+	0.955135i	$0.595709\pi$
$762$		0			0
$763$	16.3886	+	4.92058i	0.593307	+	0.178137i
$764$	0.987839	−	24.6365i	0.0357388	−	0.891315i
$765$		0			0
$766$	−3.62088	+	12.5054i	−0.130828	+	0.451840i
$767$	24.3479	+	42.1718i	0.879152	+	1.52274i
$768$		0			0
$769$	−5.45133			−0.196580			−0.0982899	−	0.995158i	$-0.531337\pi$
$769$	−5.45133			−0.196580			−0.0982899	+	0.995158i	$0.531337\pi$
$770$	6.62951	+	4.28229i	0.238911	+	0.154323i
$771$		0			0
$772$	−2.94979	−	1.86450i	−0.106165	−	0.0671049i
$773$	23.9152	−	13.8075i	0.860171	−	0.496620i	−0.00389822	−	0.999992i	$-0.501241\pi$
$773$	23.9152	−	13.8075i	0.860171	−	0.496620i	0.864070	+	0.503372i	$0.167908\pi$
$774$		0			0
$775$	−87.6532	−	50.6066i	−3.14860	−	1.81784i
$776$	−8.98938	+	7.96875i	−0.322700	+	0.286062i
$777$		0			0
$778$	−8.43421	+	8.10281i	−0.302381	+	0.290500i
$779$	5.92516	−	10.2627i	0.212291	−	0.367699i
$780$		0			0
$781$	−0.741330	−	1.28402i	−0.0265269	−	0.0459459i
$782$	3.85049	+	15.6153i	0.137693	+	0.558401i
$783$		0			0
$784$	−22.0593	−	17.2449i	−0.787834	−	0.615888i
$785$		−	66.7577i		−	2.38269i
$786$		0			0
$787$	16.6863	−	9.63386i	0.594804	−	0.343410i	−0.172191	−	0.985064i	$-0.555085\pi$
$787$	16.6863	−	9.63386i	0.594804	−	0.343410i	0.766995	+	0.641654i	$0.221751\pi$
$788$	−4.91926	−	9.36827i	−0.175241	−	0.333731i
$789$		0			0
$790$	−19.7914	−	20.6008i	−0.704145	−	0.732945i
$791$	20.5991	+	21.8685i	0.732420	+	0.777554i
$792$		0			0
$793$	6.85478	−	11.8728i	0.243421	−	0.421617i
$794$	−13.0618	+	45.1115i	−0.463545	+	1.60095i
$795$		0			0
$796$	12.0174	−	19.0124i	0.425944	−	0.673877i
$797$			16.1419i			0.571776i	0.958263	+	0.285888i	$0.0922886\pi$
$797$			16.1419i			0.571776i	−0.958263	+	0.285888i	$0.907711\pi$
$798$		0			0
$799$			58.0088i			2.05220i
$800$	−64.9473	+	10.5886i	−2.29624	+	0.374363i
$801$		0			0
$802$	−18.0088	−	5.21433i	−0.635911	−	0.184124i
$803$	−2.09258	+	3.62445i	−0.0738455	+	0.127904i
$804$		0			0
$805$	−6.04967	+	20.1491i	−0.213223	+	0.710164i
$806$	−35.5692	+	34.1716i	−1.25287	+	1.20364i
$807$		0			0
$808$	0.690647	−	2.07083i	0.0242969	−	0.0728514i
$809$	−13.5671	+	7.83297i	−0.476994	+	0.275392i	−0.719163	−	0.694842i	$-0.755474\pi$
$809$	−13.5671	+	7.83297i	−0.476994	+	0.275392i	0.242169	+	0.970234i	$0.422141\pi$
$810$		0			0
$811$		−	7.64906i		−	0.268595i	−0.990941	−	0.134297i	$-0.957122\pi$
$811$		−	7.64906i		−	0.268595i	0.990941	−	0.134297i	$-0.0428778\pi$
$812$	10.2594	+	3.53425i	0.360035	+	0.124028i
$813$		0			0
$814$	5.01729	−	1.23719i	0.175856	−	0.0433634i
$815$	−1.45208	−	2.51507i	−0.0508640	−	0.0880990i
$816$		0			0
$817$	−7.09029	+	12.2807i	−0.248058	+	0.429649i
$818$	−7.34948	−	7.65008i	−0.256969	−	0.267479i
$819$		0			0
$820$	0.817961	−	20.3997i	0.0285644	−	0.712389i
$821$	−31.7178	−	18.3123i	−1.10696	−	0.639104i	−0.168920	−	0.985630i	$-0.554028\pi$
$821$	−31.7178	−	18.3123i	−1.10696	−	0.639104i	−0.938040	+	0.346526i	$0.887361\pi$
$822$		0			0
$823$	8.04562	−	4.64514i	0.280453	−	0.161919i	−0.353176	−	0.935557i	$-0.614898\pi$
$823$	8.04562	−	4.64514i	0.280453	−	0.161919i	0.633628	+	0.773638i	$0.281565\pi$
$824$	44.1744	−	9.03218i	1.53889	−	0.314651i
$825$		0			0
$826$	45.3967	+	2.26805i	1.57955	+	0.0789156i
$827$	30.5486			1.06228			0.531139	−	0.847285i	$-0.321764\pi$
$827$	30.5486			1.06228			0.531139	+	0.847285i	$0.321764\pi$
$828$		0			0
$829$	17.9375	+	31.0687i	0.622997	+	1.07906i	0.988925	+	0.148419i	$0.0474183\pi$
$829$	17.9375	+	31.0687i	0.622997	+	1.07906i	−0.365928	+	0.930643i	$0.619248\pi$
$830$	10.5912	+	3.06663i	0.367627	+	0.106444i
$831$		0			0
$832$	−3.84618	+	31.8371i	−0.133342	+	1.10375i
$833$	−18.2667	−	36.5163i	−0.632905	−	1.26522i
$834$		0			0
$835$	−52.4636	−	30.2899i	−1.81558	−	1.04822i
$836$	−2.27676	−	4.33588i	−0.0787435	−	0.149960i
$837$		0			0
$838$	1.45339	−	0.358384i	0.0502065	−	0.0123802i
$839$	3.56665			0.123134			0.0615672	−	0.998103i	$-0.480390\pi$
$839$	3.56665			0.123134			0.0615672	+	0.998103i	$0.480390\pi$
$840$		0			0
$841$	24.7948			0.854992
$842$	−21.6932	+	5.34920i	−0.747595	+	0.184346i
$843$		0			0
$844$	−23.3358	−	44.4408i	−0.803250	−	1.52972i
$845$	−10.8383	−	6.25752i	−0.372850	−	0.215265i
$846$		0			0
$847$	−6.52656	−	27.6353i	−0.224255	−	0.949561i
$848$	−2.60978	+	32.4913i	−0.0896204	+	1.11576i
$849$		0			0
$850$	−92.1724	−	26.6880i	−3.16149	−	0.915390i
$851$	6.88735	+	11.9292i	0.236095	+	0.408929i
$852$		0			0
$853$	−17.6192			−0.603270			−0.301635	−	0.953423i	$-0.597532\pi$
$853$	−17.6192			−0.603270			−0.301635	+	0.953423i	$0.597532\pi$
$854$	−5.83739	−	11.3877i	−0.199751	−	0.389680i
$855$		0			0
$856$	0.831163	+	4.06503i	0.0284086	+	0.138940i
$857$	−5.09277	+	2.94031i	−0.173966	+	0.100439i	−0.584455	−	0.811426i	$-0.698691\pi$
$857$	−5.09277	+	2.94031i	−0.173966	+	0.100439i	0.410489	+	0.911866i	$0.365358\pi$
$858$		0			0
$859$	39.4828	+	22.7954i	1.34714	+	0.777769i	0.987843	−	0.155455i	$-0.0496845\pi$
$859$	39.4828	+	22.7954i	1.34714	+	0.777769i	0.359293	+	0.933225i	$0.383018\pi$
$860$	−0.978805	+	24.4112i	−0.0333770	+	0.832413i
$861$		0			0
$862$	13.6057	+	14.1622i	0.463412	+	0.482366i
$863$	17.8840	−	30.9760i	0.608778	−	1.05443i	−0.382664	−	0.923887i	$-0.624993\pi$
$863$	17.8840	−	30.9760i	0.608778	−	1.05443i	0.991442	−	0.130547i	$-0.0416733\pi$
$864$		0			0
$865$	8.61873	+	14.9281i	0.293046	+	0.507570i
$866$	51.8931	−	12.7960i	1.76340	−	0.434827i
$867$		0			0
$868$	8.77832	+	45.1952i	0.297955	+	1.53402i
$869$		−	2.56171i		−	0.0869001i
$870$		0			0
$871$	−6.91917	+	3.99479i	−0.234447	+	0.135358i
$872$	−17.3531	−	5.78750i	−0.587651	−	0.195989i
$873$		0			0
$874$	9.41384	−	9.04394i	0.318428	−	0.305916i
$875$	−49.0724	−	52.0964i	−1.65895	−	1.76118i
$876$		0			0
$877$	20.8302	−	36.0790i	0.703387	−	1.21830i	−0.263884	−	0.964554i	$-0.585004\pi$
$877$	20.8302	−	36.0790i	0.703387	−	1.21830i	0.967271	−	0.253747i	$-0.0816631\pi$
$878$	−0.246855	−	0.0714754i	−0.00833095	−	0.00241218i
$879$		0			0
$880$	−6.94563	−	4.79009i	−0.234137	−	0.161474i
$881$			29.0197i			0.977700i	0.872368	+	0.488850i	$0.162583\pi$
$881$			29.0197i			0.977700i	−0.872368	+	0.488850i	$0.837417\pi$
$882$		0			0
$883$		−	6.30954i		−	0.212333i	−0.994348	−	0.106166i	$-0.966142\pi$
$883$		−	6.30954i		−	0.212333i	0.994348	−	0.106166i	$-0.0338576\pi$
$884$	−24.9854	+	39.5289i	−0.840350	+	1.32950i
$885$		0			0
$886$	−3.95106	+	13.6458i	−0.132738	+	0.458439i
$887$	−9.23650	+	15.9981i	−0.310131	+	0.537163i	−0.978391	−	0.206765i	$-0.933706\pi$
$887$	−9.23650	+	15.9981i	−0.310131	+	0.537163i	0.668259	+	0.743929i	$0.267040\pi$
$888$		0			0
$889$	8.09781	+	8.59683i	0.271592	+	0.288328i
$890$	−54.1770	−	56.3929i	−1.81602	−	1.89029i
$891$		0			0
$892$	−16.6462	−	31.7012i	−0.557357	−	1.06143i
$893$	40.7764	−	23.5422i	1.36453	−	0.787811i
$894$		0			0
$895$			9.07897i			0.303477i
$896$	23.0144	+	19.1399i	0.768858	+	0.639420i
$897$		0			0
$898$	3.23179	+	13.1062i	0.107846	+	0.437360i
$899$	−8.92113	−	15.4518i	−0.297536	−	0.515348i
$900$		0			0
$901$	−23.7662	+	41.1642i	−0.791765	+	1.37138i
$902$	1.32023	−	1.26835i	0.0439588	−	0.0422315i
$903$		0			0
$904$	−21.3047	−	24.0334i	−0.708583	−	0.799338i
$905$	−40.3969	−	23.3231i	−1.34284	−	0.775288i
$906$		0			0
$907$	−37.2566	+	21.5101i	−1.23709	+	0.714232i	−0.968497	−	0.249023i	$-0.919890\pi$
$907$	−37.2566	+	21.5101i	−1.23709	+	0.714232i	−0.268588	+	0.963255i	$0.586557\pi$
$908$	23.9670	+	15.1491i	0.795373	+	0.502739i
$909$		0			0
$910$	−54.4346	+	27.9034i	−1.80449	+	0.924988i
$911$	50.4366			1.67104			0.835519	−	0.549461i	$-0.185167\pi$
$911$	50.4366			1.67104			0.835519	+	0.549461i	$0.185167\pi$
$912$		0			0
$913$	0.494377	+	0.856287i	0.0163615	+	0.0283390i
$914$	10.7464	−	37.1149i	0.355460	−	1.22765i
$915$		0			0
$916$	0.299373	−	7.46628i	0.00989156	−	0.246693i
$917$	−4.73291	−	20.0405i	−0.156294	−	0.661796i
$918$		0			0
$919$	36.7035	+	21.1908i	1.21074	+	0.699019i	0.962920	−	0.269787i	$-0.0869534\pi$
$919$	36.7035	+	21.1908i	1.21074	+	0.699019i	0.247817	+	0.968807i	$0.420287\pi$
$920$	7.11550	−	21.3350i	0.234591	−	0.703394i
$921$		0			0
$922$	11.0742	+	44.9104i	0.364710	+	1.47904i
$923$	11.4914			0.378245
$924$		0			0
$925$	−82.1859			−2.70226
$926$	−10.0752	−	40.8590i	−0.331092	−	1.34271i
$927$		0			0
$928$	−10.8486	−	4.10807i	−0.356122	−	0.134854i
$929$	−5.26910	−	3.04211i	−0.172873	−	0.0998085i	0.411067	−	0.911605i	$-0.365156\pi$
$929$	−5.26910	−	3.04211i	−0.172873	−	0.0998085i	−0.583940	+	0.811797i	$0.698490\pi$
$930$		0			0
$931$	−18.2552	+	27.6601i	−0.598291	+	0.906523i
$932$	55.1840	+	2.21269i	1.80761	+	0.0724792i
$933$		0			0
$934$	−13.7237	+	47.3975i	−0.449052	+	1.55089i
$935$	−6.15169	−	10.6550i	−0.201182	−	0.348457i
$936$		0			0
$937$	36.0029			1.17616			0.588081	−	0.808802i	$-0.299884\pi$
$937$	36.0029			1.17616			0.588081	+	0.808802i	$0.299884\pi$
$938$	−0.372122	+	7.44828i	−0.0121502	+	0.243195i
$939$		0			0
$940$	43.3414	−	68.5695i	1.41364	−	2.23649i
$941$	8.57725	−	4.95208i	0.279610	−	0.161433i	−0.353637	−	0.935383i	$-0.615055\pi$
$941$	8.57725	−	4.95208i	0.279610	−	0.161433i	0.633247	+	0.773950i	$0.281722\pi$
$942$		0			0
$943$	4.22629	+	2.44005i	0.137627	+	0.0794590i
$944$	−48.4357	−	3.89047i	−1.57645	−	0.126624i
$945$		0			0
$946$	−1.57984	+	1.51776i	−0.0513650	+	0.0493467i
$947$	6.84359	−	11.8534i	0.222387	−	0.385185i	−0.733145	−	0.680072i	$-0.761949\pi$
$947$	6.84359	−	11.8534i	0.222387	−	0.385185i	0.955532	+	0.294887i	$0.0952819\pi$
$948$		0			0
$949$	−16.2186	−	28.0915i	−0.526479	−	0.911888i
$950$	18.6473	+	75.6222i	0.604998	+	2.45351i
$951$		0			0
$952$	18.3391	+	39.6100i	0.594373	+	1.28377i
$953$			50.1927i			1.62590i	0.582333	+	0.812950i	$0.302140\pi$
$953$			50.1927i			1.62590i	−0.582333	+	0.812950i	$0.697860\pi$
$954$		0			0
$955$	−43.5421	+	25.1391i	−1.40899	+	0.813481i
$956$	−24.5694	+	12.9013i	−0.794630	+	0.417258i
$957$		0			0
$958$	33.6011	+	34.9754i	1.08560	+	1.13000i
$959$	−6.76645	+	22.5365i	−0.218500	+	0.727740i
$960$		0			0
$961$	22.3511	−	38.7133i	0.721004	−	1.24882i
$962$	−11.1392	+	38.4714i	−0.359141	+	1.24037i
$963$		0			0
$964$	−43.5102	−	27.5019i	−1.40137	−	0.885777i
$965$			7.11596i			0.229071i
$966$		0			0
$967$			24.0131i			0.772209i	0.922455	+	0.386104i	$0.126180\pi$
$967$			24.0131i			0.772209i	−0.922455	+	0.386104i	$0.873820\pi$
$968$	6.08100	+	29.7408i	0.195451	+	0.955905i
$969$		0			0
$970$	23.5298	+	6.81292i	0.755497	+	0.218750i
$971$	−24.0246	+	41.6118i	−0.770986	+	1.33539i	0.166037	+	0.986119i	$0.446903\pi$
$971$	−24.0246	+	41.6118i	−0.770986	+	1.33539i	−0.937023	+	0.349267i	$0.886431\pi$
$972$		0			0
$973$	0.210774	+	0.223763i	0.00675711	+	0.00717350i
$974$	−31.7972	+	30.5478i	−1.01885	+	0.978815i
$975$		0			0
$976$	5.86960	+	12.3571i	0.187881	+	0.395540i
$977$	44.5417	−	25.7162i	1.42502	−	0.822734i	0.428295	−	0.903639i	$-0.359114\pi$
$977$	44.5417	−	25.7162i	1.42502	−	0.822734i	0.996722	+	0.0809051i	$0.0257811\pi$
$978$		0			0
$979$		−	7.01245i		−	0.224119i
$980$	−5.69097	+	56.8123i	−0.181791	+	1.81480i
$981$		0			0
$982$	40.3664	−	9.95373i	1.28814	−	0.317636i
$983$	−5.28876	−	9.16039i	−0.168685	−	0.292171i	0.769273	−	0.638921i	$-0.220619\pi$
$983$	−5.28876	−	9.16039i	−0.168685	−	0.292171i	−0.937958	+	0.346749i	$0.887285\pi$
$984$		0			0
$985$	−10.7885	+	18.6862i	−0.343750	+	0.595392i
$986$	−11.7193	−	12.1986i	−0.373218	−	0.388483i
$987$		0			0
$988$	37.9263	+	1.52072i	1.20660	+	0.0483804i
$989$	−5.05735	−	2.91986i	−0.160814	−	0.0928463i
$990$		0			0
$991$	9.82987	−	5.67528i	0.312256	−	0.180281i	−0.335680	−	0.941976i	$-0.608966\pi$
$991$	9.82987	−	5.67528i	0.312256	−	0.180281i	0.647936	+	0.761695i	$0.275633\pi$
$992$	−7.91971	−	48.5773i	−0.251451	−	1.54233i
$993$		0			0
$994$	5.81996	−	9.01003i	0.184598	−	0.285781i
$995$	−45.8648			−1.45401
$996$		0			0
$997$	15.0483	+	26.0644i	0.476585	+	0.825469i	0.999640	−	0.0268300i	$-0.00854128\pi$
$997$	15.0483	+	26.0644i	0.476585	+	0.825469i	−0.523055	+	0.852299i	$0.675208\pi$
$998$	6.48839	+	1.87868i	0.205386	+	0.0594684i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.be.e.107.3	✓	64
3.2	odd	2	inner	756.2.be.e.107.30	yes	64
4.3	odd	2	inner	756.2.be.e.107.13	yes	64
7.4	even	3	inner	756.2.be.e.431.20	yes	64
12.11	even	2	inner	756.2.be.e.107.20	yes	64
21.11	odd	6	inner	756.2.be.e.431.13	yes	64
28.11	odd	6	inner	756.2.be.e.431.30	yes	64
84.11	even	6	inner	756.2.be.e.431.3	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.be.e.107.3	✓	64	1.1	even	1	trivial
756.2.be.e.107.13	yes	64	4.3	odd	2	inner
756.2.be.e.107.20	yes	64	12.11	even	2	inner
756.2.be.e.107.30	yes	64	3.2	odd	2	inner
756.2.be.e.431.3	yes	64	84.11	even	6	inner
756.2.be.e.431.13	yes	64	21.11	odd	6	inner
756.2.be.e.431.20	yes	64	7.4	even	3	inner
756.2.be.e.431.30	yes	64	28.11	odd	6	inner

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37308 + 0.338582i) q^{2} +(1.77072 - 0.929803i) q^{4} +(-3.53194 - 2.03916i) q^{5} +(1.92589 - 1.81410i) q^{7} +(-2.11654 + 1.87623i) q^{8} +O(q^{10})\)	\(q+(-1.37308 + 0.338582i) q^{2} +(1.77072 - 0.929803i) q^{4} +(-3.53194 - 2.03916i) q^{5} +(1.92589 - 1.81410i) q^{7} +(-2.11654 + 1.87623i) q^{8} +(5.54007 + 1.60410i) q^{10} +(0.258599 + 0.447907i) q^{11} -4.00857 q^{13} +(-2.03019 + 3.14298i) q^{14} +(2.27093 - 3.29285i) q^{16} +(5.05144 - 2.91645i) q^{17} +(-4.10015 - 2.36722i) q^{19} +(-8.15011 - 0.326792i) q^{20} +(-0.506732 - 0.527458i) q^{22} +(0.974850 - 1.68849i) q^{23} +(5.81638 + 10.0743i) q^{25} +(5.50411 - 1.35723i) q^{26} +(1.72346 - 5.00297i) q^{28} +2.05067i q^{29} +(-7.53503 + 4.35035i) q^{31} +(-2.00328 + 5.29026i) q^{32} +(-5.94860 + 5.71486i) q^{34} +(-10.5014 + 2.48008i) q^{35} +(-3.53252 + 6.11850i) q^{37} +(6.43135 + 1.86216i) q^{38} +(11.3014 - 2.31077i) q^{40} +2.50300i q^{41} -2.99519i q^{43} +(0.874374 + 0.552674i) q^{44} +(-0.766860 + 2.64851i) q^{46} +(-4.97255 + 8.61270i) q^{47} +(0.418094 - 6.98750i) q^{49} +(-11.3973 - 11.8635i) q^{50} +(-7.09808 + 3.72719i) q^{52} +(-7.05724 + 4.07450i) q^{53} -2.10931i q^{55} +(-0.672548 + 7.45303i) q^{56} +(-0.694319 - 2.81574i) q^{58} +(-6.07396 - 10.5204i) q^{59} +(-1.71003 + 2.96186i) q^{61} +(8.87329 - 8.52463i) q^{62} +(0.959489 - 7.94225i) q^{64} +(14.1580 + 8.17414i) q^{65} +(1.72609 - 0.996560i) q^{67} +(6.23299 - 9.86108i) q^{68} +(13.5795 - 6.96093i) q^{70} -2.86671 q^{71} +(4.04598 + 7.00785i) q^{73} +(2.77883 - 9.59727i) q^{74} +(-9.46129 - 0.379366i) q^{76} +(1.31058 + 0.393495i) q^{77} +(-4.28947 - 2.47652i) q^{79} +(-14.7354 + 6.99934i) q^{80} +(-0.847471 - 3.43683i) q^{82} +1.91175 q^{83} -23.7885 q^{85} +(1.01412 + 4.11266i) q^{86} +(-1.38772 - 0.462821i) q^{88} +(-11.7420 - 6.77926i) q^{89} +(-7.72007 + 7.27195i) q^{91} +(0.156227 - 3.89627i) q^{92} +(3.91162 - 13.5096i) q^{94} +(9.65431 + 16.7218i) q^{95} +4.24721 q^{97} +(1.79176 + 9.73599i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 16 q^{13} + 8 q^{16} - 28 q^{22} + 36 q^{25} + 26 q^{28} - 56 q^{34} - 8 q^{37} + 22 q^{40} - 18 q^{46} + 28 q^{49} - 26 q^{52} - 36 q^{58} + 16 q^{61} - 12 q^{64} - 18 q^{70} + 32 q^{73} - 144 q^{76} + 34 q^{82} + 32 q^{85} - 20 q^{88} - 78 q^{94} + 56 q^{97}+O(q^{100}) \) 64 * q - 16 * q^13 + 8 * q^16 - 28 * q^22 + 36 * q^25 + 26 * q^28 - 56 * q^34 - 8 * q^37 + 22 * q^40 - 18 * q^46 + 28 * q^49 - 26 * q^52 - 36 * q^58 + 16 * q^61 - 12 * q^64 - 18 * q^70 + 32 * q^73 - 144 * q^76 + 34 * q^82 + 32 * q^85 - 20 * q^88 - 78 * q^94 + 56 * q^97

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