LMFDB - Embedded newform 1008.2.bh.c.95.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(95,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5, 4]))

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

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

chi := DirichletCharacter("1008.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.bh (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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			95.4
Character	$\chi$	$=$	1008.95
Dual form			1008.2.bh.c.191.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19485 - 1.25393i) q^{3} -2.36899i q^{5} +(-0.783237 - 2.52716i) q^{7} +(-0.144689 + 2.99651i) q^{9} +O(q^{10})$	\(q+(-1.19485 - 1.25393i) q^{3} -2.36899i q^{5} +(-0.783237 - 2.52716i) q^{7} +(-0.144689 + 2.99651i) q^{9} -4.14140 q^{11} +(-1.38752 + 2.40326i) q^{13} +(-2.97055 + 2.83058i) q^{15} +(-1.58369 - 0.914347i) q^{17} +(-2.73242 + 1.57756i) q^{19} +(-2.23304 + 4.00169i) q^{21} -1.02166 q^{23} -0.612123 q^{25} +(3.93030 - 3.39894i) q^{27} +(1.59887 - 0.923106i) q^{29} +(8.06524 - 4.65647i) q^{31} +(4.94834 + 5.19304i) q^{33} +(-5.98682 + 1.85548i) q^{35} +(3.15039 + 5.45663i) q^{37} +(4.67139 - 1.13166i) q^{39} +(8.53919 + 4.93010i) q^{41} +(-9.54137 + 5.50871i) q^{43} +(7.09871 + 0.342766i) q^{45} +(-1.59009 + 2.75412i) q^{47} +(-5.77308 + 3.95873i) q^{49} +(0.745743 + 3.07835i) q^{51} +(-10.2889 - 5.94029i) q^{53} +9.81095i q^{55} +(5.24298 + 1.54132i) q^{57} +(-1.62351 - 2.81200i) q^{59} +(-0.426723 + 0.739106i) q^{61} +(7.68598 - 1.98132i) q^{63} +(5.69329 + 3.28702i) q^{65} +(-0.259676 + 0.149924i) q^{67} +(1.22073 + 1.28109i) q^{69} -15.6672 q^{71} +(-0.419551 + 0.726684i) q^{73} +(0.731392 + 0.767560i) q^{75} +(3.24370 + 10.4660i) q^{77} +(9.69258 + 5.59601i) q^{79} +(-8.95813 - 0.867121i) q^{81} +(-2.64353 - 4.57872i) q^{83} +(-2.16608 + 3.75176i) q^{85} +(-3.06791 - 0.901900i) q^{87} +(-1.62851 + 0.940223i) q^{89} +(7.16017 + 1.62417i) q^{91} +(-15.4756 - 4.54950i) q^{93} +(3.73724 + 6.47308i) q^{95} +(-8.03665 - 13.9199i) q^{97} +(0.599214 - 12.4098i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} - 2 q^{7} - q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 - 2 * q^7 - q^9	$ 30 q - 3 q^{3} - 2 q^{7} - q^{9} + 6 q^{11} + 12 q^{17} + 9 q^{19} + 14 q^{21} - 24 q^{23} - 36 q^{25} + 27 q^{27} + 27 q^{29} + 6 q^{31} - 20 q^{33} - 6 q^{35} + 6 q^{37} - 15 q^{39} + 9 q^{41} - 21 q^{43} - 8 q^{45} + 12 q^{49} - 15 q^{51} - 3 q^{53} + 20 q^{57} + 3 q^{59} - 3 q^{61} + 24 q^{63} - 39 q^{67} + 10 q^{69} + 18 q^{71} + 21 q^{73} + 21 q^{75} + 36 q^{77} - 33 q^{79} - 17 q^{81} - 15 q^{83} - 3 q^{85} + 78 q^{87} + 6 q^{89} - 26 q^{91} - 3 q^{93} - 27 q^{95} - 6 q^{97} - 48 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 - 2 * q^7 - q^9 + 6 * q^11 + 12 * q^17 + 9 * q^19 + 14 * q^21 - 24 * q^23 - 36 * q^25 + 27 * q^27 + 27 * q^29 + 6 * q^31 - 20 * q^33 - 6 * q^35 + 6 * q^37 - 15 * q^39 + 9 * q^41 - 21 * q^43 - 8 * q^45 + 12 * q^49 - 15 * q^51 - 3 * q^53 + 20 * q^57 + 3 * q^59 - 3 * q^61 + 24 * q^63 - 39 * q^67 + 10 * q^69 + 18 * q^71 + 21 * q^73 + 21 * q^75 + 36 * q^77 - 33 * q^79 - 17 * q^81 - 15 * q^83 - 3 * q^85 + 78 * q^87 + 6 * q^89 - 26 * q^91 - 3 * q^93 - 27 * q^95 - 6 * q^97 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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			0
$2$		0			0
$3$	−1.19485	−	1.25393i	−0.689844	−	0.723958i
$3$	−1.19485	−	1.25393i	−0.689844	−	0.723958i
$4$		0			0
$5$		−	2.36899i		−	1.05945i	−0.848171	−	0.529723i	$-0.822296\pi$
$5$		−	2.36899i		−	1.05945i	0.848171	−	0.529723i	$-0.177704\pi$
$6$		0			0
$7$	−0.783237	−	2.52716i	−0.296036	−	0.955177i
$7$	−0.783237	−	2.52716i	−0.296036	−	0.955177i
$8$		0			0
$9$	−0.144689	+	2.99651i	−0.0482295	+	0.998836i
$10$		0			0
$11$	−4.14140			−1.24868			−0.624340	−	0.781153i	$-0.714632\pi$
$11$	−4.14140			−1.24868			−0.624340	+	0.781153i	$0.714632\pi$
$12$		0			0
$13$	−1.38752	+	2.40326i	−0.384829	+	0.666543i	−0.991745	−	0.128222i	$-0.959073\pi$
$13$	−1.38752	+	2.40326i	−0.384829	+	0.666543i	0.606917	+	0.794766i	$0.292406\pi$
$14$		0			0
$15$	−2.97055	+	2.83058i	−0.766994	+	0.730852i
$16$		0			0
$17$	−1.58369	−	0.914347i	−0.384102	−	0.221762i	0.295499	−	0.955343i	$-0.404514\pi$
$17$	−1.58369	−	0.914347i	−0.384102	−	0.221762i	−0.679602	+	0.733581i	$0.737847\pi$
$18$		0			0
$19$	−2.73242	+	1.57756i	−0.626860	+	0.361918i	−0.779535	−	0.626358i	$-0.784545\pi$
$19$	−2.73242	+	1.57756i	−0.626860	+	0.361918i	0.152675	+	0.988276i	$0.451211\pi$
$20$		0			0
$21$	−2.23304	+	4.00169i	−0.487289	+	0.873241i
$22$		0			0
$23$	−1.02166			−0.213031			−0.106516	−	0.994311i	$-0.533969\pi$
$23$	−1.02166			−0.213031			−0.106516	+	0.994311i	$0.533969\pi$
$24$		0			0
$25$	−0.612123			−0.122425
$26$		0			0
$27$	3.93030	−	3.39894i	0.756386	−	0.654125i
$28$		0			0
$29$	1.59887	−	0.923106i	0.296902	−	0.171417i	−0.344148	−	0.938915i	$-0.611832\pi$
$29$	1.59887	−	0.923106i	0.296902	−	0.171417i	0.641050	+	0.767499i	$0.278499\pi$
$30$		0			0
$31$	8.06524	−	4.65647i	1.44856	−	0.836327i	0.450165	−	0.892946i	$-0.351365\pi$
$31$	8.06524	−	4.65647i	1.44856	−	0.836327i	0.998396	+	0.0566188i	$0.0180320\pi$
$32$		0			0
$33$	4.94834	+	5.19304i	0.861395	+	0.903992i
$34$		0			0
$35$	−5.98682	+	1.85548i	−1.01196	+	0.313634i
$36$		0			0
$37$	3.15039	+	5.45663i	0.517920	+	0.897064i	0.999783	+	0.0208175i	$0.00662691\pi$
$37$	3.15039	+	5.45663i	0.517920	+	0.897064i	−0.481863	+	0.876246i	$0.660040\pi$
$38$		0			0
$39$	4.67139	−	1.13166i	0.748021	−	0.181211i
$40$		0			0
$41$	8.53919	+	4.93010i	1.33360	+	0.769953i	0.985849	−	0.167635i	$-0.0536131\pi$
$41$	8.53919	+	4.93010i	1.33360	+	0.769953i	0.347748	+	0.937588i	$0.386946\pi$
$42$		0			0
$43$	−9.54137	+	5.50871i	−1.45505	+	0.840071i	−0.998761	−	0.0497632i	$-0.984153\pi$
$43$	−9.54137	+	5.50871i	−1.45505	+	0.840071i	−0.456284	+	0.889834i	$0.650820\pi$
$44$		0			0
$45$	7.09871	+	0.342766i	1.05821	+	0.0510965i
$46$		0			0
$47$	−1.59009	+	2.75412i	−0.231939	+	0.401729i	−0.958379	−	0.285500i	$-0.907840\pi$
$47$	−1.59009	+	2.75412i	−0.231939	+	0.401729i	0.726440	+	0.687230i	$0.241174\pi$
$48$		0			0
$49$	−5.77308	+	3.95873i	−0.824726	+	0.565533i
$50$		0			0
$51$	0.745743	+	3.07835i	0.104425	+	0.431055i
$52$		0			0
$53$	−10.2889	−	5.94029i	−1.41329	−	0.815962i	−0.417591	−	0.908635i	$-0.637125\pi$
$53$	−10.2889	−	5.94029i	−1.41329	−	0.815962i	−0.995697	+	0.0926733i	$0.970459\pi$
$54$		0			0
$55$			9.81095i			1.32291i
$56$		0			0
$57$	5.24298	+	1.54132i	0.694450	+	0.204153i
$58$		0			0
$59$	−1.62351	−	2.81200i	−0.211363	−	0.366092i	0.740778	−	0.671750i	$-0.234457\pi$
$59$	−1.62351	−	2.81200i	−0.211363	−	0.366092i	−0.952141	+	0.305658i	$0.901124\pi$
$60$		0			0
$61$	−0.426723	+	0.739106i	−0.0546363	+	0.0946328i	−0.892050	−	0.451937i	$-0.850733\pi$
$61$	−0.426723	+	0.739106i	−0.0546363	+	0.0946328i	0.837414	+	0.546570i	$0.184067\pi$
$62$		0			0
$63$	7.68598	−	1.98132i	0.968343	−	0.249623i
$64$		0			0
$65$	5.69329	+	3.28702i	0.706166	+	0.407705i
$66$		0			0
$67$	−0.259676	+	0.149924i	−0.0317245	+	0.0183161i	−0.515778	−	0.856722i	$-0.672497\pi$
$67$	−0.259676	+	0.149924i	−0.0317245	+	0.0183161i	0.484054	+	0.875038i	$0.339164\pi$
$68$		0			0
$69$	1.22073	+	1.28109i	0.146958	+	0.154226i
$70$		0			0
$71$	−15.6672			−1.85936			−0.929678	−	0.368373i	$-0.879915\pi$
$71$	−15.6672			−1.85936			−0.929678	+	0.368373i	$0.879915\pi$
$72$		0			0
$73$	−0.419551	+	0.726684i	−0.0491048	+	0.0850520i	−0.889533	−	0.456871i	$-0.848970\pi$
$73$	−0.419551	+	0.726684i	−0.0491048	+	0.0850520i	0.840428	+	0.541923i	$0.182303\pi$
$74$		0			0
$75$	0.731392	+	0.767560i	0.0844539	+	0.0886302i
$76$		0			0
$77$	3.24370	+	10.4660i	0.369654	+	1.19271i
$78$		0			0
$79$	9.69258	+	5.59601i	1.09050	+	0.629601i	0.933710	−	0.358031i	$-0.116552\pi$
$79$	9.69258	+	5.59601i	1.09050	+	0.629601i	0.156791	+	0.987632i	$0.449885\pi$
$80$		0			0
$81$	−8.95813	−	0.867121i	−0.995348	−	0.0963468i
$82$		0			0
$83$	−2.64353	−	4.57872i	−0.290165	−	0.502580i	0.683684	−	0.729778i	$-0.260377\pi$
$83$	−2.64353	−	4.57872i	−0.290165	−	0.502580i	−0.973849	+	0.227198i	$0.927043\pi$
$84$		0			0
$85$	−2.16608	+	3.75176i	−0.234944	+	0.406936i
$86$		0			0
$87$	−3.06791	−	0.901900i	−0.328915	−	0.0966939i
$88$		0			0
$89$	−1.62851	+	0.940223i	−0.172622	+	0.0996635i	−0.583822	−	0.811882i	$-0.698443\pi$
$89$	−1.62851	+	0.940223i	−0.172622	+	0.0996635i	0.411200	+	0.911545i	$0.365110\pi$
$90$		0			0
$91$	7.16017	+	1.62417i	0.750590	+	0.170259i
$92$		0			0
$93$	−15.4756	−	4.54950i	−1.60475	−	0.471761i
$94$		0			0
$95$	3.73724	+	6.47308i	0.383432	+	0.664124i
$96$		0			0
$97$	−8.03665	−	13.9199i	−0.815999	−	1.41335i	−0.908609	−	0.417649i	$-0.862854\pi$
$97$	−8.03665	−	13.9199i	−0.815999	−	1.41335i	0.0926100	−	0.995702i	$-0.470479\pi$
$98$		0			0
$99$	0.599214	−	12.4098i	0.0602232	−	1.24723i
$100$		0			0
$101$			9.65156i			0.960366i	0.877168	+	0.480183i	$0.159430\pi$
$101$			9.65156i			0.960366i	−0.877168	+	0.480183i	$0.840570\pi$
$102$		0			0
$103$			9.51229i			0.937274i	0.883391	+	0.468637i	$0.155255\pi$
$103$			9.51229i			0.937274i	−0.883391	+	0.468637i	$0.844745\pi$
$104$		0			0
$105$	9.47997	+	5.29005i	0.925151	+	0.516256i
$106$		0			0
$107$	−4.53673	−	7.85784i	−0.438582	−	0.759646i	0.558998	−	0.829169i	$-0.311186\pi$
$107$	−4.53673	−	7.85784i	−0.438582	−	0.759646i	−0.997580	+	0.0695224i	$0.977852\pi$
$108$		0			0
$109$	−6.96808	+	12.0691i	−0.667421	+	1.15601i	0.311202	+	0.950344i	$0.399268\pi$
$109$	−6.96808	+	12.0691i	−0.667421	+	1.15601i	−0.978623	+	0.205663i	$0.934065\pi$
$110$		0			0
$111$	3.07801	−	10.4702i	0.292152	−	0.993787i
$112$		0			0
$113$	−12.4701	−	7.19961i	−1.17309	−	0.677282i	−0.218682	−	0.975796i	$-0.570176\pi$
$113$	−12.4701	−	7.19961i	−1.17309	−	0.677282i	−0.954405	+	0.298514i	$0.903509\pi$
$114$		0			0
$115$			2.42031i			0.225695i
$116$		0			0
$117$	−7.00062	−	4.50544i	−0.647207	−	0.416528i
$118$		0			0
$119$	−1.07029	+	4.71840i	−0.0981136	+	0.432535i
$120$		0			0
$121$	6.15122			0.559202
$122$		0			0
$123$	−4.02100	−	16.5983i	−0.362561	−	1.49662i
$124$		0			0
$125$		−	10.3948i		−	0.929743i
$126$		0			0
$127$			17.3111i			1.53611i	0.640383	+	0.768056i	$0.278776\pi$
$127$			17.3111i			1.53611i	−0.640383	+	0.768056i	$0.721224\pi$
$128$		0			0
$129$	18.3080	+	5.38216i	1.61193	+	0.473873i
$130$		0			0
$131$	14.5663			1.27266			0.636331	−	0.771417i	$-0.280451\pi$
$131$	14.5663			1.27266			0.636331	+	0.771417i	$0.280451\pi$
$132$		0			0
$133$	6.12689	+	5.66966i	0.531269	+	0.491622i
$134$		0			0
$135$	−8.05205	−	9.31084i	−0.693010	−	0.801350i
$136$		0			0
$137$		−	8.44753i		−	0.721721i	−0.932620	−	0.360861i	$-0.882483\pi$
$137$		−	8.44753i		−	0.721721i	0.932620	−	0.360861i	$-0.117517\pi$
$138$		0			0
$139$	2.44796	+	1.41333i	0.207633	+	0.119877i	0.600211	−	0.799842i	$-0.295083\pi$
$139$	2.44796	+	1.41333i	0.207633	+	0.119877i	−0.392578	+	0.919719i	$0.628417\pi$
$140$		0			0
$141$	5.35339	−	1.29688i	0.450837	−	0.109217i
$142$		0			0
$143$	5.74628	−	9.95285i	0.480528	−	0.832299i
$144$		0			0
$145$	−2.18683	−	3.78770i	−0.181606	−	0.314552i
$146$		0			0
$147$	11.8619	+	2.50898i	0.978354	+	0.206937i
$148$		0			0
$149$		−	19.0143i		−	1.55771i	−0.627205	−	0.778854i	$-0.715801\pi$
$149$		−	19.0143i		−	1.55771i	0.627205	−	0.778854i	$-0.284199\pi$
$150$		0			0
$151$		−	2.82893i		−	0.230215i	−0.993353	−	0.115107i	$-0.963279\pi$
$151$		−	2.82893i		−	0.230215i	0.993353	−	0.115107i	$-0.0367212\pi$
$152$		0			0
$153$	2.96899	−	4.61326i	0.240029	−	0.372960i
$154$		0			0
$155$	−11.0311	−	19.1065i	−0.886043	−	1.53467i
$156$		0			0
$157$	−1.26644	−	2.19354i	−0.101073	−	0.175063i	0.811054	−	0.584971i	$-0.198894\pi$
$157$	−1.26644	−	2.19354i	−0.101073	−	0.175063i	−0.912127	+	0.409908i	$0.865561\pi$
$158$		0			0
$159$	4.84491	+	19.9993i	0.384226	+	1.58605i
$160$		0			0
$161$	0.800204	+	2.58191i	0.0630649	+	0.203483i
$162$		0			0
$163$	−7.47930	+	4.31818i	−0.585824	+	0.338226i	−0.763445	−	0.645873i	$-0.776493\pi$
$163$	−7.47930	+	4.31818i	−0.585824	+	0.338226i	0.177620	+	0.984099i	$0.443160\pi$
$164$		0			0
$165$	12.3023	−	11.7226i	0.957730	−	0.912601i
$166$		0			0
$167$	−6.35289	+	11.0035i	−0.491602	+	0.851479i	−0.999953	−	0.00967054i	$-0.996922\pi$
$167$	−6.35289	+	11.0035i	−0.491602	+	0.851479i	0.508352	+	0.861150i	$0.330255\pi$
$168$		0			0
$169$	2.64957	+	4.58920i	0.203813	+	0.353015i
$170$		0			0
$171$	−4.33184	−	8.41598i	−0.331264	−	0.643586i
$172$		0			0
$173$	−0.0225933	−	0.0130443i	−0.00171774	−	0.000991738i	0.499141	−	0.866521i	$-0.333649\pi$
$173$	−0.0225933	−	0.0130443i	−0.00171774	−	0.000991738i	−0.500859	+	0.865529i	$0.666982\pi$
$174$		0			0
$175$	0.479437	+	1.54693i	0.0362420	+	0.116937i
$176$		0			0
$177$	−1.58622	+	5.39568i	−0.119227	+	0.405564i
$178$		0			0
$179$	−4.11673	+	7.13038i	−0.307699	+	0.532950i	−0.977859	−	0.209267i	$-0.932892\pi$
$179$	−4.11673	+	7.13038i	−0.307699	+	0.532950i	0.670160	+	0.742217i	$0.266226\pi$
$180$		0			0
$181$	−9.49775			−0.705962			−0.352981	−	0.935630i	$-0.614832\pi$
$181$	−9.49775			−0.705962			−0.352981	+	0.935630i	$0.614832\pi$
$182$		0			0
$183$	1.43666	−	0.348036i	0.106201	−	0.0257276i
$184$		0			0
$185$	12.9267	−	7.46324i	0.950390	−	0.548708i
$186$		0			0
$187$	6.55872	+	3.78668i	0.479621	+	0.276909i
$188$		0			0
$189$	−11.6680	−	7.27032i	−0.848723	−	0.528838i
$190$		0			0
$191$	4.96530	−	8.60015i	0.359276	−	0.622285i	−0.628564	−	0.777758i	$-0.716357\pi$
$191$	4.96530	−	8.60015i	0.359276	−	0.622285i	0.987840	+	0.155473i	$0.0496902\pi$
$192$		0			0
$193$	−7.83098	−	13.5637i	−0.563686	−	0.976333i	−0.997171	−	0.0751721i	$-0.976049\pi$
$193$	−7.83098	−	13.5637i	−0.563686	−	0.976333i	0.433484	−	0.901161i	$-0.357284\pi$
$194$		0			0
$195$	−2.68090	−	11.0665i	−0.191983	−	0.792488i
$196$		0			0
$197$		−	12.1289i		−	0.864148i	−0.901838	−	0.432074i	$-0.857782\pi$
$197$		−	12.1289i		−	0.864148i	0.901838	−	0.432074i	$-0.142218\pi$
$198$		0			0
$199$	10.5404	+	6.08552i	0.747191	+	0.431391i	0.824678	−	0.565602i	$-0.191356\pi$
$199$	10.5404	+	6.08552i	0.747191	+	0.431391i	−0.0774869	+	0.996993i	$0.524690\pi$
$200$		0			0
$201$	0.498267	+	0.146480i	0.0351450	+	0.0103319i
$202$		0			0
$203$	−3.58513	−	3.31758i	−0.251627	−	0.232849i
$204$		0			0
$205$	11.6794	−	20.2293i	0.815723	−	1.41287i
$206$		0			0
$207$	0.147823	−	3.06142i	0.0102744	−	0.212783i
$208$		0			0
$209$	11.3161	−	6.53333i	0.782748	−	0.451920i
$210$		0			0
$211$	−7.33542	−	4.23511i	−0.504991	−	0.291557i	0.225781	−	0.974178i	$-0.427507\pi$
$211$	−7.33542	−	4.23511i	−0.504991	−	0.291557i	−0.730772	+	0.682621i	$0.760840\pi$
$212$		0			0
$213$	18.7199	+	19.6456i	1.28267	+	1.34610i
$214$		0			0
$215$	13.0501	+	22.6034i	0.890009	+	1.54154i
$216$		0			0
$217$	−18.0846	−	16.7350i	−1.22767	−	1.13605i
$218$		0			0
$219$	1.41251	−	0.342187i	0.0954487	−	0.0231228i
$220$		0			0
$221$	4.39482	−	2.53735i	0.295627	−	0.170681i
$222$		0			0
$223$	−7.76299	+	4.48197i	−0.519848	+	0.300135i	−0.736873	−	0.676032i	$-0.763698\pi$
$223$	−7.76299	+	4.48197i	−0.519848	+	0.300135i	0.217024	+	0.976166i	$0.430365\pi$
$224$		0			0
$225$	0.0885671	−	1.83423i	0.00590448	−	0.122282i
$226$		0			0
$227$	−17.9514			−1.19148			−0.595738	−	0.803179i	$-0.703140\pi$
$227$	−17.9514			−1.19148			−0.595738	+	0.803179i	$0.703140\pi$
$228$		0			0
$229$	−2.21449			−0.146338			−0.0731689	−	0.997320i	$-0.523311\pi$
$229$	−2.21449			−0.146338			−0.0731689	+	0.997320i	$0.523311\pi$
$230$		0			0
$231$	9.24792	−	16.5726i	0.608468	−	1.09040i
$232$		0			0
$233$	2.98834	−	1.72532i	0.195773	−	0.113029i	−0.398910	−	0.916990i	$-0.630611\pi$
$233$	2.98834	−	1.72532i	0.195773	−	0.113029i	0.594682	+	0.803961i	$0.297278\pi$
$234$		0			0
$235$	6.52448	+	3.76691i	0.425610	+	0.245726i
$236$		0			0
$237$	−4.56412	−	18.8402i	−0.296471	−	1.22380i
$238$		0			0
$239$	3.67035	−	6.35723i	0.237415	−	0.411215i	−0.722557	−	0.691312i	$-0.757033\pi$
$239$	3.67035	−	6.35723i	0.237415	−	0.411215i	0.959972	+	0.280097i	$0.0903665\pi$
$240$		0			0
$241$	−17.3446			−1.11726			−0.558631	−	0.829416i	$-0.688673\pi$
$241$	−17.3446			−1.11726			−0.558631	+	0.829416i	$0.688673\pi$
$242$		0			0
$243$	9.61627	+	12.2690i	0.616884	+	0.787054i
$244$		0			0
$245$	9.37820	+	13.6764i	0.599151	+	0.873752i
$246$		0			0
$247$		−	8.75561i		−	0.557106i
$248$		0			0
$249$	−2.58280	+	8.78567i	−0.163678	+	0.556769i
$250$		0			0
$251$	−13.9816			−0.882511			−0.441255	−	0.897382i	$-0.645467\pi$
$251$	−13.9816			−0.882511			−0.441255	+	0.897382i	$0.645467\pi$
$252$		0			0
$253$	4.23112			0.266008
$254$		0			0
$255$	7.29258	−	1.76666i	0.456679	−	0.110632i
$256$		0			0
$257$		−	28.0261i		−	1.74822i	−0.485730	−	0.874109i	$-0.661446\pi$
$257$		−	28.0261i		−	1.74822i	0.485730	−	0.874109i	$-0.338554\pi$
$258$		0			0
$259$	11.3223	−	12.2354i	0.703532	−	0.760268i
$260$		0			0
$261$	2.53476	+	4.92458i	0.156898	+	0.304824i
$262$		0			0
$263$	−16.9791			−1.04697			−0.523487	−	0.852034i	$-0.675369\pi$
$263$	−16.9791			−1.04697			−0.523487	+	0.852034i	$0.675369\pi$
$264$		0			0
$265$	−14.0725	+	24.3743i	−0.864467	+	1.49730i
$266$		0			0
$267$	3.12480	+	0.918624i	0.191235	+	0.0562189i
$268$		0			0
$269$	−23.7601	−	13.7179i	−1.44868	−	0.836396i	−0.450277	−	0.892889i	$-0.648675\pi$
$269$	−23.7601	−	13.7179i	−1.44868	−	0.836396i	−0.998403	+	0.0564933i	$0.982008\pi$
$270$		0			0
$271$	3.93599	−	2.27244i	0.239094	−	0.138041i	−0.375666	−	0.926755i	$-0.622586\pi$
$271$	3.93599	−	2.27244i	0.239094	−	0.138041i	0.614760	+	0.788714i	$0.289253\pi$
$272$		0			0
$273$	−6.51870	−	10.9190i	−0.394530	−	0.660847i
$274$		0			0
$275$	2.53505			0.152869
$276$		0			0
$277$	6.58357			0.395568			0.197784	−	0.980246i	$-0.436625\pi$
$277$	6.58357			0.395568			0.197784	+	0.980246i	$0.436625\pi$
$278$		0			0
$279$	12.7862	+	24.8413i	0.765490	+	1.48721i
$280$		0			0
$281$	−23.0468	+	13.3061i	−1.37486	+	0.793775i	−0.991535	−	0.129839i	$-0.958554\pi$
$281$	−23.0468	+	13.3061i	−1.37486	+	0.793775i	−0.383324	+	0.923614i	$0.625221\pi$
$282$		0			0
$283$	26.7323	−	15.4339i	1.58907	−	0.917449i	0.595607	−	0.803276i	$-0.296912\pi$
$283$	26.7323	−	15.4339i	1.58907	−	0.917449i	0.993461	−	0.114173i	$-0.0364218\pi$
$284$		0			0
$285$	3.65138	−	12.4206i	0.216289	−	0.735731i
$286$		0			0
$287$	5.77095	−	25.4413i	0.340649	−	1.50175i
$288$		0			0
$289$	−6.82794	−	11.8263i	−0.401644	−	0.695667i
$290$		0			0
$291$	−7.85203	+	26.7095i	−0.460294	+	1.56574i
$292$		0			0
$293$	−4.92535	−	2.84365i	−0.287742	−	0.166128i	0.349181	−	0.937055i	$-0.386460\pi$
$293$	−4.92535	−	2.84365i	−0.287742	−	0.166128i	−0.636923	+	0.770927i	$0.719793\pi$
$294$		0			0
$295$	−6.66162	+	3.84609i	−0.387854	+	0.223928i
$296$		0			0
$297$	−16.2769	+	14.0764i	−0.944484	+	0.816793i
$298$		0			0
$299$	1.41758	−	2.45532i	0.0819806	−	0.141995i
$300$		0			0
$301$	21.3946	+	19.7979i	1.23316	+	1.14113i
$302$		0			0
$303$	12.1024	−	11.5321i	0.695264	−	0.662503i
$304$		0			0
$305$	1.75094	+	1.01090i	0.100258	+	0.0578842i
$306$		0			0
$307$		−	27.9000i		−	1.59234i	−0.605075	−	0.796168i	$-0.706857\pi$
$307$		−	27.9000i		−	1.59234i	0.605075	−	0.796168i	$-0.293143\pi$
$308$		0			0
$309$	11.9278	−	11.3657i	0.678547	−	0.646573i
$310$		0			0
$311$	14.5572	+	25.2138i	0.825463	+	1.42974i	0.901565	+	0.432644i	$0.142419\pi$
$311$	14.5572	+	25.2138i	0.825463	+	1.42974i	−0.0761021	+	0.997100i	$0.524247\pi$
$312$		0			0
$313$	−14.2072	+	24.6075i	−0.803037	+	1.39090i	0.114572	+	0.993415i	$0.463450\pi$
$313$	−14.2072	+	24.6075i	−0.803037	+	1.39090i	−0.917608	+	0.397486i	$0.869883\pi$
$314$		0			0
$315$	−4.69374	−	18.2080i	−0.264462	−	1.02591i
$316$		0			0
$317$	21.3899	+	12.3495i	1.20138	+	0.693615i	0.960861	−	0.277030i	$-0.0893502\pi$
$317$	21.3899	+	12.3495i	1.20138	+	0.693615i	0.240515	+	0.970645i	$0.422684\pi$
$318$		0			0
$319$	−6.62155	+	3.82296i	−0.370736	+	0.214044i
$320$		0			0
$321$	−4.43251	+	15.0777i	−0.247399	+	0.841553i
$322$		0			0
$323$	5.76976			0.321038
$324$		0			0
$325$	0.849332	−	1.47109i	0.0471125	−	0.0816012i
$326$		0			0
$327$	23.4596	−	5.68318i	1.29732	−	0.314280i
$328$		0			0
$329$	8.20552	+	1.86129i	0.452385	+	0.102616i
$330$		0			0
$331$	−12.8194	−	7.40130i	−0.704620	−	0.406812i	0.104446	−	0.994531i	$-0.466693\pi$
$331$	−12.8194	−	7.40130i	−0.704620	−	0.406812i	−0.809066	+	0.587718i	$0.800026\pi$
$332$		0			0
$333$	−16.8067	+	8.65065i	−0.920999	+	0.474052i
$334$		0			0
$335$	0.355169	+	0.615170i	0.0194049	+	0.0336103i
$336$		0			0
$337$	14.3380	−	24.8342i	0.781042	−	1.35280i	−0.150293	−	0.988642i	$-0.548022\pi$
$337$	14.3380	−	24.8342i	0.781042	−	1.35280i	0.931335	−	0.364163i	$-0.118645\pi$
$338$		0			0
$339$	5.87201	+	24.2391i	0.318924	+	1.31649i
$340$		0			0
$341$	−33.4014	+	19.2843i	−1.80879	+	1.04430i
$342$		0			0
$343$	14.5260	+	11.4889i	0.784332	+	0.620341i
$344$		0			0
$345$	3.03490	−	2.89190i	0.163394	−	0.155694i
$346$		0			0
$347$	9.31831	+	16.1398i	0.500233	+	0.866429i	1.00000		0.000269083i	$8.56516e-5\pi$
$347$	9.31831	+	16.1398i	0.500233	+	0.866429i	−0.499767	+	0.866160i	$0.666581\pi$
$348$		0			0
$349$	−8.10052	−	14.0305i	−0.433611	−	0.751036i	0.563570	−	0.826068i	$-0.309427\pi$
$349$	−8.10052	−	14.0305i	−0.433611	−	0.751036i	−0.997181	+	0.0750321i	$0.976094\pi$
$350$		0			0
$351$	2.71514	+	14.1616i	0.144924	+	0.755890i
$352$		0			0
$353$		−	11.4817i		−	0.611110i	−0.952174	−	0.305555i	$-0.901158\pi$
$353$		−	11.4817i		−	0.611110i	0.952174	−	0.305555i	$-0.0988421\pi$
$354$		0			0
$355$			37.1155i			1.96989i
$356$		0			0
$357$	7.19539	−	4.29569i	0.380820	−	0.227352i
$358$		0			0
$359$	8.31363	+	14.3996i	0.438777	+	0.759983i	0.997595	−	0.0693065i	$-0.0220786\pi$
$359$	8.31363	+	14.3996i	0.438777	+	0.759983i	−0.558819	+	0.829290i	$0.688745\pi$
$360$		0			0
$361$	−4.52258	+	7.83334i	−0.238031	+	0.412281i
$362$		0			0
$363$	−7.34976	−	7.71321i	−0.385762	−	0.404838i
$364$		0			0
$365$	1.72151	+	0.993914i	0.0901079	+	0.0520238i
$366$		0			0
$367$		−	20.1028i		−	1.04936i	−0.851300	−	0.524680i	$-0.824185\pi$
$367$		−	20.1028i		−	1.04936i	0.851300	−	0.524680i	$-0.175815\pi$
$368$		0			0
$369$	−16.0086	+	24.8744i	−0.833375	+	1.29491i
$370$		0			0
$371$	−6.95344	+	30.6543i	−0.361004	+	1.59149i
$372$		0			0
$373$	33.4298			1.73093			0.865465	−	0.500969i	$-0.167023\pi$
$373$	33.4298			1.73093			0.865465	+	0.500969i	$0.167023\pi$
$374$		0			0
$375$	−13.0344	+	12.4202i	−0.673095	+	0.641378i
$376$		0			0
$377$			5.12331i			0.263864i
$378$		0			0
$379$		−	15.2571i		−	0.783704i	−0.920028	−	0.391852i	$-0.871834\pi$
$379$		−	15.2571i		−	0.783704i	0.920028	−	0.391852i	$-0.128166\pi$
$380$		0			0
$381$	21.7069	−	20.6841i	1.11208	−	1.05968i
$382$		0			0
$383$	−19.2018			−0.981168			−0.490584	−	0.871394i	$-0.663217\pi$
$383$	−19.2018			−0.981168			−0.490584	+	0.871394i	$0.663217\pi$
$384$		0			0
$385$	24.7938	−	7.68430i	1.26361	−	0.391628i
$386$		0			0
$387$	−15.1264	−	29.3878i	−0.768917	−	1.49387i
$388$		0			0
$389$			13.2664i			0.672632i	0.941749	+	0.336316i	$0.109181\pi$
$389$			13.2664i			0.672632i	−0.941749	+	0.336316i	$0.890819\pi$
$390$		0			0
$391$	1.61800	+	0.934154i	0.0818259	+	0.0472422i
$392$		0			0
$393$	−17.4044	−	18.2651i	−0.877938	−	0.921353i
$394$		0			0
$395$	13.2569	−	22.9616i	0.667028	−	1.15533i
$396$		0			0
$397$	5.15559	+	8.92974i	0.258752	+	0.448171i	0.965908	−	0.258887i	$-0.0833556\pi$
$397$	5.15559	+	8.92974i	0.258752	+	0.448171i	−0.707156	+	0.707057i	$0.750022\pi$
$398$		0			0
$399$	−0.211321	−	14.4571i	−0.0105793	−	0.723759i
$400$		0			0
$401$			4.21540i			0.210507i	0.994445	+	0.105253i	$0.0335654\pi$
$401$			4.21540i			0.210507i	−0.994445	+	0.105253i	$0.966435\pi$
$402$		0			0
$403$			25.8438i			1.28737i
$404$		0			0
$405$	−2.05420	+	21.2217i	−0.102074	+	1.05452i
$406$		0			0
$407$	−13.0470	−	22.5981i	−0.646717	−	1.12015i
$408$		0			0
$409$	−8.29502	−	14.3674i	−0.410163	−	0.710422i	0.584745	−	0.811217i	$-0.301195\pi$
$409$	−8.29502	−	14.3674i	−0.410163	−	0.710422i	−0.994907	+	0.100795i	$0.967861\pi$
$410$		0			0
$411$	−10.5926	+	10.0935i	−0.522496	+	0.497875i
$412$		0			0
$413$	−5.83479	+	6.30534i	−0.287111	+	0.310266i
$414$		0			0
$415$	−10.8470	+	6.26249i	−0.532456	+	0.307414i
$416$		0			0
$417$	−1.15271	−	4.75828i	−0.0564486	−	0.233014i
$418$		0			0
$419$	3.14140	−	5.44107i	0.153467	−	0.265813i	−0.779032	−	0.626984i	$-0.784289\pi$
$419$	3.14140	−	5.44107i	0.153467	−	0.265813i	0.932500	+	0.361170i	$0.117623\pi$
$420$		0			0
$421$	14.9372	+	25.8720i	0.727995	+	1.26092i	0.957729	+	0.287670i	$0.0928808\pi$
$421$	14.9372	+	25.8720i	0.727995	+	1.26092i	−0.229735	+	0.973253i	$0.573786\pi$
$422$		0			0
$423$	−8.02267	−	5.16321i	−0.390076	−	0.251044i
$424$		0			0
$425$	0.969415	+	0.559692i	0.0470236	+	0.0271491i
$426$		0			0
$427$	2.20206	+	0.499503i	0.106565	+	0.0241726i
$428$		0			0
$429$	−19.3461	+	4.68668i	−0.934039	+	0.226275i
$430$		0			0
$431$	6.76371	−	11.7151i	0.325796	−	0.564296i	−0.655877	−	0.754868i	$-0.727701\pi$
$431$	6.76371	−	11.7151i	0.325796	−	0.564296i	0.981673	+	0.190572i	$0.0610343\pi$
$432$		0			0
$433$	39.5892			1.90254			0.951269	−	0.308363i	$-0.0997813\pi$
$433$	39.5892			1.90254			0.951269	+	0.308363i	$0.0997813\pi$
$434$		0			0
$435$	−2.13659	+	7.26786i	−0.102442	+	0.348467i
$436$		0			0
$437$	2.79161	−	1.61174i	0.133541	−	0.0770999i
$438$		0			0
$439$	−14.0314	−	8.10104i	−0.669683	−	0.386642i	0.126274	−	0.991995i	$-0.459698\pi$
$439$	−14.0314	−	8.10104i	−0.669683	−	0.386642i	−0.795956	+	0.605354i	$0.793032\pi$
$440$		0			0
$441$	−11.0271	−	17.8719i	−0.525099	−	0.851041i
$442$		0			0
$443$	−13.6100	+	23.5732i	−0.646630	+	1.12000i	0.337293	+	0.941400i	$0.390489\pi$
$443$	−13.6100	+	23.5732i	−0.646630	+	1.12000i	−0.983923	+	0.178596i	$0.942845\pi$
$444$		0			0
$445$	2.22738	+	3.85794i	0.105588	+	0.182884i
$446$		0			0
$447$	−23.8426	+	22.7191i	−1.12772	+	1.07458i
$448$		0			0
$449$		−	17.8656i		−	0.843130i	−0.906798	−	0.421565i	$-0.861481\pi$
$449$		−	17.8656i		−	0.843130i	0.906798	−	0.421565i	$-0.138519\pi$
$450$		0			0
$451$	−35.3642	−	20.4175i	−1.66524	−	0.961425i
$452$		0			0
$453$	−3.54728	+	3.38013i	−0.166666	+	0.158812i
$454$		0			0
$455$	3.84764	−	16.9624i	0.180380	−	0.795209i
$456$		0			0
$457$	−7.12400	+	12.3391i	−0.333246	+	0.577200i	−0.983146	−	0.182820i	$-0.941477\pi$
$457$	−7.12400	+	12.3391i	−0.333246	+	0.577200i	0.649900	+	0.760020i	$0.274811\pi$
$458$		0			0
$459$	−9.33220	+	1.78922i	−0.435590	+	0.0835138i
$460$		0			0
$461$	−3.37315	+	1.94749i	−0.157103	+	0.0907036i	−0.576491	−	0.817104i	$-0.695578\pi$
$461$	−3.37315	+	1.94749i	−0.157103	+	0.0907036i	0.419387	+	0.907807i	$0.362245\pi$
$462$		0			0
$463$	−4.28829	−	2.47585i	−0.199294	−	0.115062i	0.397032	−	0.917805i	$-0.370040\pi$
$463$	−4.28829	−	2.47585i	−0.199294	−	0.115062i	−0.596326	+	0.802742i	$0.703373\pi$
$464$		0			0
$465$	−10.7777	+	36.6616i	−0.499805	+	1.70014i
$466$		0			0
$467$	−10.3358	−	17.9021i	−0.478282	−	0.828409i	0.521408	−	0.853307i	$-0.325407\pi$
$467$	−10.3358	−	17.9021i	−0.478282	−	0.828409i	−0.999690	+	0.0248989i	$0.992074\pi$
$468$		0			0
$469$	0.582270	+	0.538817i	0.0268867	+	0.0248802i
$470$		0			0
$471$	−1.23734	+	4.20896i	−0.0570138	+	0.193939i
$472$		0			0
$473$	39.5147	−	22.8138i	1.81689	−	1.04898i
$474$		0			0
$475$	1.67258	−	0.965663i	0.0767431	−	0.0443076i
$476$		0			0
$477$	19.2888	−	29.9713i	0.883175	−	1.37229i
$478$		0			0
$479$	26.4349			1.20784			0.603920	−	0.797045i	$-0.293605\pi$
$479$	26.4349			1.20784			0.603920	+	0.797045i	$0.293605\pi$
$480$		0			0
$481$	−17.4849			−0.797243
$482$		0			0
$483$	2.28141	−	4.08838i	0.103808	−	0.186028i
$484$		0			0
$485$	−32.9761	+	19.0388i	−1.49737	+	0.864506i
$486$		0			0
$487$	−13.9150	−	8.03383i	−0.630549	−	0.364048i	0.150415	−	0.988623i	$-0.451939\pi$
$487$	−13.9150	−	8.03383i	−0.630549	−	0.364048i	−0.780965	+	0.624575i	$0.785272\pi$
$488$		0			0
$489$	14.3513	+	4.21898i	0.648989	+	0.190789i
$490$		0			0
$491$	−3.70049	+	6.40944i	−0.167001	+	0.289254i	−0.937364	−	0.348351i	$-0.886742\pi$
$491$	−3.70049	+	6.40944i	−0.167001	+	0.289254i	0.770363	+	0.637605i	$0.220075\pi$
$492$		0			0
$493$	−3.37616			−0.152054
$494$		0			0
$495$	−29.3986	−	1.41953i	−1.32137	−	0.0638032i
$496$		0			0
$497$	12.2711	+	39.5936i	0.550436	+	1.77601i
$498$		0			0
$499$		−	10.0862i		−	0.451521i	−0.974183	−	0.225760i	$-0.927513\pi$
$499$		−	10.0862i		−	0.451521i	0.974183	−	0.225760i	$-0.0724866\pi$
$500$		0			0
$501$	21.3884	−	5.18143i	0.955564	−	0.231489i
$502$		0			0
$503$	2.11362			0.0942416			0.0471208	−	0.998889i	$-0.484995\pi$
$503$	2.11362			0.0942416			0.0471208	+	0.998889i	$0.484995\pi$
$504$		0			0
$505$	22.8645			1.01746
$506$		0			0
$507$	2.58871	−	8.80577i	0.114969	−	0.391078i
$508$		0			0
$509$			29.9445i			1.32727i	0.748058	+	0.663633i	$0.230986\pi$
$509$			29.9445i			1.32727i	−0.748058	+	0.663633i	$0.769014\pi$
$510$		0			0
$511$	2.16506	+	0.491108i	0.0957764	+	0.0217253i
$512$		0			0
$513$	−5.37719	+	15.4876i	−0.237409	+	0.683795i
$514$		0			0
$515$	22.5345			0.992990
$516$		0			0
$517$	6.58521	−	11.4059i	0.289617	−	0.501632i
$518$		0			0
$519$	0.0106389	+	0.0439164i	0.000466997	+	0.00192772i
$520$		0			0
$521$	31.6120	+	18.2512i	1.38495	+	0.799599i	0.992740	−	0.120278i	$-0.0383786\pi$
$521$	31.6120	+	18.2512i	1.38495	+	0.799599i	0.392206	+	0.919877i	$0.371712\pi$
$522$		0			0
$523$	9.22636	−	5.32684i	0.403440	−	0.232926i	−0.284527	−	0.958668i	$-0.591837\pi$
$523$	9.22636	−	5.32684i	0.403440	−	0.232926i	0.687967	+	0.725742i	$0.258503\pi$
$524$		0			0
$525$	1.36689	−	2.44953i	0.0596561	−	0.106906i
$526$		0			0
$527$	−17.0305			−0.741861
$528$		0			0
$529$	−21.9562			−0.954618
$530$		0			0
$531$	8.66110	−	4.45800i	0.375860	−	0.193461i
$532$		0			0
$533$	−23.6966	+	13.6812i	−1.02641	+	0.592600i
$534$		0			0
$535$	−18.6152	+	10.7475i	−0.804804	+	0.464654i
$536$		0			0
$537$	13.8599	−	3.35761i	0.598097	−	0.144892i
$538$		0			0
$539$	23.9087	−	16.3947i	1.02982	−	0.706170i
$540$		0			0
$541$	−14.8060	−	25.6447i	−0.636558	−	1.10255i	−0.986183	−	0.165661i	$-0.947024\pi$
$541$	−14.8060	−	25.6447i	−0.636558	−	1.10255i	0.349625	−	0.936890i	$-0.386309\pi$
$542$		0			0
$543$	11.3483	+	11.9095i	0.487004	+	0.511087i
$544$		0			0
$545$	28.5915	+	16.5073i	1.22473	+	0.707096i
$546$		0			0
$547$	−36.4637	+	21.0523i	−1.55908	+	0.900133i	−0.561731	+	0.827320i	$0.689864\pi$
$547$	−36.4637	+	21.0523i	−1.55908	+	0.900133i	−0.997346	+	0.0728131i	$0.976802\pi$
$548$		0			0
$549$	−2.15300	−	1.38562i	−0.0918876	−	0.0591368i
$550$		0			0
$551$	−2.91252	+	5.04463i	−0.124077	+	0.214909i
$552$		0			0
$553$	6.55044	−	28.8777i	0.278553	−	1.22801i
$554$		0			0
$555$	−24.8038	−	7.29179i	−1.05286	−	0.309519i
$556$		0			0
$557$	−3.87538	−	2.23745i	−0.164205	−	0.0948039i	0.415645	−	0.909527i	$-0.363556\pi$
$557$	−3.87538	−	2.23745i	−0.164205	−	0.0948039i	−0.579851	+	0.814723i	$0.696889\pi$
$558$		0			0
$559$		−	30.5738i		−	1.29313i
$560$		0			0
$561$	−3.08842	−	12.7487i	−0.130393	−	0.538250i
$562$		0			0
$563$	5.37514	+	9.31001i	0.226535	+	0.392370i	0.956779	−	0.290816i	$-0.0939269\pi$
$563$	5.37514	+	9.31001i	0.226535	+	0.392370i	−0.730244	+	0.683187i	$0.760594\pi$
$564$		0			0
$565$	−17.0558	+	29.5415i	−0.717544	+	1.24282i
$566$		0			0
$567$	4.82498	+	23.3178i	0.202630	+	0.979255i
$568$		0			0
$569$	19.8609	+	11.4667i	0.832614	+	0.480710i	0.854747	−	0.519045i	$-0.173712\pi$
$569$	19.8609	+	11.4667i	0.832614	+	0.480710i	−0.0221329	+	0.999755i	$0.507046\pi$
$570$		0			0
$571$	−14.6608	+	8.46444i	−0.613537	+	0.354226i	−0.774348	−	0.632759i	$-0.781922\pi$
$571$	−14.6608	+	8.46444i	−0.613537	+	0.354226i	0.160812	+	0.986985i	$0.448589\pi$
$572$		0			0
$573$	−16.7168	+	4.04971i	−0.698353	+	0.169179i
$574$		0			0
$575$	0.625383			0.0260803
$576$		0			0
$577$	−9.14015	+	15.8312i	−0.380509	+	0.659062i	−0.991135	−	0.132858i	$-0.957585\pi$
$577$	−9.14015	+	15.8312i	−0.380509	+	0.659062i	0.610626	+	0.791919i	$0.290918\pi$
$578$		0			0
$579$	−7.65108	+	26.0260i	−0.317968	+	1.08160i
$580$		0			0
$581$	−9.50066	+	10.2668i	−0.394154	+	0.425940i
$582$		0			0
$583$	42.6104	+	24.6011i	1.76474	+	1.01888i
$584$		0			0
$585$	−10.6734	+	16.5844i	−0.441289	+	0.685681i
$586$		0			0
$587$	20.2944	+	35.1509i	0.837638	+	1.45083i	0.891864	+	0.452303i	$0.149397\pi$
$587$	20.2944	+	35.1509i	0.837638	+	1.45083i	−0.0542266	+	0.998529i	$0.517269\pi$
$588$		0			0
$589$	−14.6918	+	25.4469i	−0.605364	+	1.04852i
$590$		0			0
$591$	−15.2088	+	14.4921i	−0.625606	+	0.596127i
$592$		0			0
$593$	−7.56487	+	4.36758i	−0.310652	+	0.179355i	−0.647218	−	0.762305i	$-0.724068\pi$
$593$	−7.56487	+	4.36758i	−0.310652	+	0.179355i	0.336566	+	0.941660i	$0.390734\pi$
$594$		0			0
$595$	11.1779	+	2.53551i	0.458247	+	0.103946i
$596$		0			0
$597$	−4.96336	−	20.4882i	−0.203137	−	0.838528i
$598$		0			0
$599$	−6.31444	−	10.9369i	−0.258001	−	0.446871i	0.707705	−	0.706508i	$-0.249731\pi$
$599$	−6.31444	−	10.9369i	−0.258001	−	0.446871i	−0.965706	+	0.259637i	$0.916397\pi$
$600$		0			0
$601$	11.3142	+	19.5968i	0.461516	+	0.799369i	0.999037	−	0.0438818i	$-0.0139725\pi$
$601$	11.3142	+	19.5968i	0.461516	+	0.799369i	−0.537521	+	0.843250i	$0.680639\pi$
$602$		0			0
$603$	−0.411676	−	0.799813i	−0.0167648	−	0.0325709i
$604$		0			0
$605$		−	14.5722i		−	0.592444i
$606$		0			0
$607$		−	32.1415i		−	1.30458i	−0.757968	−	0.652292i	$-0.773808\pi$
$607$		−	32.1415i		−	1.30458i	0.757968	−	0.652292i	$-0.226192\pi$
$608$		0			0
$609$	0.123654	+	8.45951i	0.00501071	+	0.342796i
$610$		0			0
$611$	−4.41257	−	7.64279i	−0.178513	−	0.309194i
$612$		0			0
$613$	6.49677	−	11.2527i	0.262402	−	0.454494i	−0.704478	−	0.709726i	$-0.748819\pi$
$613$	6.49677	−	11.2527i	0.262402	−	0.454494i	0.966880	+	0.255232i	$0.0821520\pi$
$614$		0			0
$615$	−39.3212	+	9.52571i	−1.58558	+	0.384114i
$616$		0			0
$617$	−32.4105	−	18.7122i	−1.30480	−	0.753325i	−0.323575	−	0.946203i	$-0.604885\pi$
$617$	−32.4105	−	18.7122i	−1.30480	−	0.753325i	−0.981223	+	0.192877i	$0.938218\pi$
$618$		0			0
$619$		−	33.9526i		−	1.36467i	−0.731039	−	0.682335i	$-0.760964\pi$
$619$		−	33.9526i		−	1.36467i	0.731039	−	0.682335i	$-0.239036\pi$
$620$		0			0
$621$	−4.01544	+	3.47257i	−0.161134	+	0.139349i
$622$		0			0
$623$	3.65161	+	3.37910i	0.146299	+	0.135381i
$624$		0			0
$625$	−27.6859			−1.10744
$626$		0			0
$627$	−21.7133	−	6.38324i	−0.867145	−	0.254922i
$628$		0			0
$629$		−	11.5222i		−	0.459419i
$630$		0			0
$631$		−	20.5424i		−	0.817780i	−0.912584	−	0.408890i	$-0.865916\pi$
$631$		−	20.5424i		−	0.817780i	0.912584	−	0.408890i	$-0.134084\pi$
$632$		0			0
$633$	3.45416	+	14.2584i	0.137291	+	0.566721i
$634$		0			0
$635$	41.0099			1.62743
$636$		0			0
$637$	−1.50357	−	19.3670i	−0.0595738	−	0.767349i
$638$		0			0
$639$	2.26687	−	46.9469i	0.0896759	−	1.85719i
$640$		0			0
$641$			36.9825i			1.46072i	0.683062	+	0.730360i	$0.260648\pi$
$641$			36.9825i			1.46072i	−0.683062	+	0.730360i	$0.739352\pi$
$642$		0			0
$643$	−7.41539	−	4.28128i	−0.292435	−	0.168837i	0.346605	−	0.938011i	$-0.387335\pi$
$643$	−7.41539	−	4.28128i	−0.292435	−	0.168837i	−0.639039	+	0.769174i	$0.720668\pi$
$644$		0			0
$645$	12.7503	−	43.3715i	0.502043	−	1.70775i
$646$		0			0
$647$	15.8126	−	27.3882i	0.621658	−	1.07674i	−0.367519	−	0.930016i	$-0.619793\pi$
$647$	15.8126	−	27.3882i	0.621658	−	1.07674i	0.989177	−	0.146727i	$-0.0468739\pi$
$648$		0			0
$649$	6.72362	+	11.6456i	0.263925	+	0.457132i
$650$		0			0
$651$	0.623753	+	42.6727i	0.0244468	+	1.67247i
$652$		0			0
$653$			27.3648i			1.07087i	0.844577	+	0.535435i	$0.179852\pi$
$653$			27.3648i			1.07087i	−0.844577	+	0.535435i	$0.820148\pi$
$654$		0			0
$655$		−	34.5074i		−	1.34831i
$656$		0			0
$657$	−2.11681	−	1.36233i	−0.0825847	−	0.0531497i
$658$		0			0
$659$	17.2635	+	29.9012i	0.672489	+	1.16478i	0.977196	+	0.212339i	$0.0681081\pi$
$659$	17.2635	+	29.9012i	0.672489	+	1.16478i	−0.304707	+	0.952446i	$0.598559\pi$
$660$		0			0
$661$	5.43775	+	9.41846i	0.211504	+	0.366336i	0.952185	−	0.305521i	$-0.0988305\pi$
$661$	5.43775	+	9.41846i	0.211504	+	0.366336i	−0.740681	+	0.671856i	$0.765497\pi$
$662$		0			0
$663$	−8.43279	−	2.47906i	−0.327502	−	0.0962787i
$664$		0			0
$665$	13.4314	−	14.5146i	0.520847	−	0.562850i
$666$		0			0
$667$	−1.63350	+	0.943103i	−0.0632495	+	0.0365171i
$668$		0			0
$669$	14.8957	+	4.37900i	0.575899	+	0.169302i
$670$		0			0
$671$	1.76723	−	3.06094i	0.0682232	−	0.118166i
$672$		0			0
$673$	12.4897	+	21.6327i	0.481441	+	0.833880i	0.999773	−	0.0212993i	$-0.00678029\pi$
$673$	12.4897	+	21.6327i	0.481441	+	0.833880i	−0.518332	+	0.855179i	$0.673447\pi$
$674$		0			0
$675$	−2.40582	+	2.08057i	−0.0926002	+	0.0800810i
$676$		0			0
$677$	−27.6377	−	15.9566i	−1.06220	−	0.613263i	−0.136162	−	0.990687i	$-0.543477\pi$
$677$	−27.6377	−	15.9566i	−1.06220	−	0.613263i	−0.926041	+	0.377423i	$0.876810\pi$
$678$		0			0
$679$	−28.8832	+	31.2125i	−1.10844	+	1.19783i
$680$		0			0
$681$	21.4492	+	22.5098i	0.821933	+	0.862579i
$682$		0			0
$683$	0.154508	−	0.267616i	0.00591210	−	0.0102401i	−0.863054	−	0.505111i	$-0.831451\pi$
$683$	0.154508	−	0.267616i	0.00591210	−	0.0102401i	0.868966	+	0.494871i	$0.164785\pi$
$684$		0			0
$685$	−20.0121			−0.764624
$686$		0			0
$687$	2.64598	+	2.77682i	0.100950	+	0.105942i
$688$		0			0
$689$	28.5521	−	16.4846i	1.08775	−	0.628011i
$690$		0			0
$691$	−2.36984	−	1.36823i	−0.0901530	−	0.0520499i	0.454246	−	0.890876i	$-0.349909\pi$
$691$	−2.36984	−	1.36823i	−0.0901530	−	0.0520499i	−0.544399	+	0.838827i	$0.683242\pi$
$692$		0			0
$693$	−31.8308	+	8.20546i	−1.20915	+	0.311700i
$694$		0			0
$695$	3.34816	−	5.79919i	0.127003	−	0.219976i
$696$		0			0
$697$	−9.01565	−	15.6156i	−0.341492	−	0.591481i
$698$		0			0
$699$	−5.73403	−	1.68568i	−0.216881	−	0.0637584i
$700$		0			0
$701$			34.1114i			1.28837i	0.764869	+	0.644185i	$0.222803\pi$
$701$			34.1114i			1.28837i	−0.764869	+	0.644185i	$0.777197\pi$
$702$		0			0
$703$	−17.2164	−	9.93987i	−0.649327	−	0.374889i
$704$		0			0
$705$	−3.07230	−	12.6821i	−0.115710	−	0.477637i
$706$		0			0
$707$	24.3910	−	7.55946i	0.917319	−	0.284303i
$708$		0			0
$709$	2.86828	−	4.96800i	0.107720	−	0.186577i	−0.807126	−	0.590379i	$-0.798978\pi$
$709$	2.86828	−	4.96800i	0.107720	−	0.186577i	0.914846	+	0.403802i	$0.132312\pi$
$710$		0			0
$711$	−18.1709	+	28.2342i	−0.681462	+	1.05887i
$712$		0			0
$713$	−8.23996	+	4.75734i	−0.308589	+	0.178164i
$714$		0			0
$715$	−23.5782	−	13.6129i	−0.881776	−	0.509093i
$716$		0			0
$717$	−12.3570	+	2.99354i	−0.461482	+	0.111796i
$718$		0			0
$719$	14.5211	+	25.1513i	0.541545	+	0.937983i	0.998816	+	0.0486559i	$0.0154938\pi$
$719$	14.5211	+	25.1513i	0.541545	+	0.937983i	−0.457271	+	0.889328i	$0.651173\pi$
$720$		0			0
$721$	24.0391	−	7.45038i	0.895262	−	0.277467i
$722$		0			0
$723$	20.7241	+	21.7489i	0.770737	+	0.808850i
$724$		0			0
$725$	−0.978703	+	0.565054i	−0.0363481	+	0.0209856i
$726$		0			0
$727$	10.3221	−	5.95949i	0.382827	−	0.221025i	−0.296220	−	0.955120i	$-0.595726\pi$
$727$	10.3221	−	5.95949i	0.382827	−	0.221025i	0.679048	+	0.734094i	$0.262393\pi$
$728$		0			0
$729$	3.89447	−	26.7177i	0.144240	−	0.989543i
$730$		0			0
$731$	20.1475			0.745182
$732$		0			0
$733$	−7.89924			−0.291765			−0.145883	−	0.989302i	$-0.546602\pi$
$733$	−7.89924			−0.291765			−0.145883	+	0.989302i	$0.546602\pi$
$734$		0			0
$735$	5.94375	−	28.1008i	0.219238	−	1.03651i
$736$		0			0
$737$	1.07542	−	0.620895i	0.0396137	−	0.0228710i
$738$		0			0
$739$	20.6202	+	11.9051i	0.758525	+	0.437934i	0.828766	−	0.559596i	$-0.189044\pi$
$739$	20.6202	+	11.9051i	0.758525	+	0.437934i	−0.0702410	+	0.997530i	$0.522377\pi$
$740$		0			0
$741$	−10.9789	+	10.4616i	−0.403321	+	0.384317i
$742$		0			0
$743$	1.16678	−	2.02092i	0.0428050	−	0.0741404i	−0.843829	−	0.536612i	$-0.819704\pi$
$743$	1.16678	−	2.02092i	0.0428050	−	0.0741404i	0.886634	+	0.462472i	$0.153037\pi$
$744$		0			0
$745$	−45.0446			−1.65031
$746$		0			0
$747$	14.1027	−	7.25886i	0.515990	−	0.265588i
$748$		0			0
$749$	−16.3047	+	17.6196i	−0.595761	+	0.643806i
$750$		0			0
$751$		−	32.9806i		−	1.20348i	−0.798692	−	0.601740i	$-0.794474\pi$
$751$		−	32.9806i		−	1.20348i	0.798692	−	0.601740i	$-0.205526\pi$
$752$		0			0
$753$	16.7059	+	17.5320i	0.608795	+	0.638901i
$754$		0			0
$755$	−6.70170			−0.243900
$756$		0			0
$757$	46.1289			1.67658			0.838291	−	0.545223i	$-0.183555\pi$
$757$	46.1289			1.67658			0.838291	+	0.545223i	$0.183555\pi$
$758$		0			0
$759$	−5.05553	−	5.30553i	−0.183504	−	0.192579i
$760$		0			0
$761$		−	49.2394i		−	1.78493i	−0.451121	−	0.892463i	$-0.648976\pi$
$761$		−	49.2394i		−	1.78493i	0.451121	−	0.892463i	$-0.351024\pi$
$762$		0			0
$763$	35.9581	+	8.15652i	1.30177	+	0.295286i
$764$		0			0
$765$	−10.9288	−	7.03351i	−0.395131	−	0.254297i
$766$		0			0
$767$	9.01062			0.325355
$768$		0			0
$769$	24.2219	−	41.9536i	0.873465	−	1.51289i	0.0150758	−	0.999886i	$-0.495201\pi$
$769$	24.2219	−	41.9536i	0.873465	−	1.51289i	0.858389	−	0.512999i	$-0.171466\pi$
$770$		0			0
$771$	−35.1428	+	33.4868i	−1.26564	+	1.20600i
$772$		0			0
$773$	10.8701	+	6.27584i	0.390970	+	0.225726i	0.682580	−	0.730811i	$-0.260858\pi$
$773$	10.8701	+	6.27584i	0.390970	+	0.225726i	−0.291611	+	0.956537i	$0.594191\pi$
$774$		0			0
$775$	−4.93692	+	2.85033i	−0.177339	+	0.102387i
$776$		0			0
$777$	−28.8707	+	0.422007i	−1.03573	+	0.0151394i
$778$		0			0
$779$	−31.1102			−1.11464
$780$		0			0
$781$	64.8843			2.32174
$782$		0			0
$783$	3.14644	−	9.06253i	0.112445	−	0.323868i
$784$		0			0
$785$	−5.19647	+	3.00018i	−0.185470	+	0.107081i
$786$		0			0
$787$	14.2967	−	8.25421i	0.509623	−	0.294231i	−0.223056	−	0.974806i	$-0.571603\pi$
$787$	14.2967	−	8.25421i	0.509623	−	0.294231i	0.732678	+	0.680575i	$0.238270\pi$
$788$		0			0
$789$	20.2874	+	21.2906i	0.722249	+	0.757965i
$790$		0			0
$791$	−8.42754	+	37.1529i	−0.299649	+	1.32101i
$792$		0			0
$793$	−1.18417	−	2.05105i	−0.0420512	−	0.0728349i
$794$		0			0
$795$	47.3782	−	11.4776i	1.68033	−	0.407067i
$796$		0			0
$797$	2.09669	+	1.21053i	0.0742687	+	0.0428791i	0.536674	−	0.843789i	$-0.319680\pi$
$797$	2.09669	+	1.21053i	0.0742687	+	0.0428791i	−0.462406	+	0.886668i	$0.653014\pi$
$798$		0			0
$799$	5.03644	−	2.90779i	0.178176	−	0.102870i
$800$		0			0
$801$	−2.58176	−	5.01590i	−0.0912220	−	0.177228i
$802$		0			0
$803$	1.73753	−	3.00949i	0.0613162	−	0.106203i
$804$		0			0
$805$	6.11651	−	1.89568i	0.215579	−	0.0668138i
$806$		0			0
$807$	11.1883	+	46.1843i	0.393848	+	1.62577i
$808$		0			0
$809$	−27.8540	−	16.0815i	−0.979293	−	0.565395i	−0.0772364	−	0.997013i	$-0.524610\pi$
$809$	−27.8540	−	16.0815i	−0.979293	−	0.565395i	−0.902057	+	0.431618i	$0.857943\pi$
$810$		0			0
$811$			31.5999i			1.10962i	0.831976	+	0.554812i	$0.187210\pi$
$811$			31.5999i			1.10962i	−0.831976	+	0.554812i	$0.812790\pi$
$812$		0			0
$813$	−7.55238	−	2.22024i	−0.264874	−	0.0778672i
$814$		0			0
$815$	10.2297	+	17.7184i	0.358332	+	0.620649i
$816$		0			0
$817$	17.3807	−	30.1043i	0.608074	−	1.05321i
$818$		0			0
$819$	−5.90283	+	21.2205i	−0.206262	+	0.741505i
$820$		0			0
$821$	34.8215	+	20.1042i	1.21528	+	0.701642i	0.963905	−	0.266248i	$-0.0857839\pi$
$821$	34.8215	+	20.1042i	1.21528	+	0.701642i	0.251375	+	0.967890i	$0.419117\pi$
$822$		0			0
$823$	−20.2108	+	11.6687i	−0.704505	+	0.406746i	−0.809023	−	0.587777i	$-0.800003\pi$
$823$	−20.2108	+	11.6687i	−0.704505	+	0.406746i	0.104518	+	0.994523i	$0.466670\pi$
$824$		0			0
$825$	−3.02899	−	3.17877i	−0.105456	−	0.110671i
$826$		0			0
$827$	32.8733			1.14312			0.571558	−	0.820561i	$-0.306339\pi$
$827$	32.8733			1.14312			0.571558	+	0.820561i	$0.306339\pi$
$828$		0			0
$829$	−9.89105	+	17.1318i	−0.343530	+	0.595012i	−0.985086	−	0.172065i	$-0.944956\pi$
$829$	−9.89105	+	17.1318i	−0.343530	+	0.595012i	0.641555	+	0.767077i	$0.278289\pi$
$830$		0			0
$831$	−7.86635	−	8.25535i	−0.272881	−	0.286375i
$832$		0			0
$833$	12.7625	−	0.990824i	0.442193	−	0.0343300i
$834$		0			0
$835$	26.0673	+	15.0500i	0.902096	+	0.520825i
$836$		0			0
$837$	15.8718	−	45.7146i	0.548608	−	1.58013i
$838$		0			0
$839$	9.16013	+	15.8658i	0.316243	+	0.547748i	0.979701	−	0.200465i	$-0.0642453\pi$
$839$	9.16013	+	15.8658i	0.316243	+	0.547748i	−0.663458	+	0.748213i	$0.730912\pi$
$840$		0			0
$841$	−12.7957	+	22.1629i	−0.441233	+	0.764238i
$842$		0			0
$843$	44.2223	+	13.0004i	1.52310	+	0.447758i
$844$		0			0
$845$	10.8718	−	6.27682i	0.374000	−	0.215929i
$846$		0			0
$847$	−4.81786	−	15.5451i	−0.165544	−	0.534137i
$848$		0			0
$849$	−51.2939	−	15.0793i	−1.76040	−	0.517521i
$850$		0			0
$851$	−3.21863	−	5.57483i	−0.110333	−	0.191103i
$852$		0			0
$853$	−22.1236	−	38.3192i	−0.757498	−	1.31203i	−0.944123	−	0.329594i	$-0.893088\pi$
$853$	−22.1236	−	38.3192i	−0.757498	−	1.31203i	0.186625	−	0.982431i	$-0.440245\pi$
$854$		0			0
$855$	−19.9374	+	10.2621i	−0.681844	+	0.350956i
$856$		0			0
$857$		−	50.7367i		−	1.73313i	−0.499063	−	0.866566i	$-0.666322\pi$
$857$		−	50.7367i		−	1.73313i	0.499063	−	0.866566i	$-0.333678\pi$
$858$		0			0
$859$		−	4.30738i		−	0.146966i	−0.997296	−	0.0734829i	$-0.976589\pi$
$859$		−	4.30738i		−	0.146966i	0.997296	−	0.0734829i	$-0.0234114\pi$
$860$		0			0
$861$	−38.7971	+	23.1621i	−1.32220	+	0.789362i
$862$		0			0
$863$	9.42163	+	16.3187i	0.320716	+	0.555496i	0.980636	−	0.195840i	$-0.0627432\pi$
$863$	9.42163	+	16.3187i	0.320716	+	0.555496i	−0.659920	+	0.751336i	$0.729410\pi$
$864$		0			0
$865$	−0.0309018	+	0.0535234i	−0.00105069	+	0.00181985i
$866$		0			0
$867$	−6.67109	+	22.6924i	−0.226562	+	0.770675i
$868$		0			0
$869$	−40.1409	−	23.1754i	−1.36169	−	0.786170i
$870$		0			0
$871$		−	0.832090i		−	0.0281943i
$872$		0			0
$873$	42.8739	−	22.0679i	1.45106	−	0.746884i
$874$		0			0
$875$	−26.2694	+	8.14163i	−0.888069	+	0.275237i
$876$		0			0
$877$	29.1118			0.983037			0.491519	−	0.870867i	$-0.336442\pi$
$877$	29.1118			0.983037			0.491519	+	0.870867i	$0.336442\pi$
$878$		0			0
$879$	2.31929	+	9.57378i	0.0782277	+	0.322916i
$880$		0			0
$881$			21.7911i			0.734161i	0.930189	+	0.367081i	$0.119643\pi$
$881$			21.7911i			0.734161i	−0.930189	+	0.367081i	$0.880357\pi$
$882$		0			0
$883$			8.18321i			0.275387i	0.990475	+	0.137693i	$0.0439689\pi$
$883$			8.18321i			0.275387i	−0.990475	+	0.137693i	$0.956031\pi$
$884$		0			0
$885$	12.7823	+	3.75773i	0.429673	+	0.126315i
$886$		0			0
$887$	−3.61322			−0.121320			−0.0606600	−	0.998158i	$-0.519321\pi$
$887$	−3.61322			−0.121320			−0.0606600	+	0.998158i	$0.519321\pi$
$888$		0			0
$889$	43.7479	−	13.5587i	1.46726	−	0.454744i
$890$		0			0
$891$	37.0992	+	3.59110i	1.24287	+	0.120306i
$892$		0			0
$893$		−	10.0339i		−	0.335771i
$894$		0			0
$895$	16.8918	+	9.75249i	0.564631	+	0.325990i
$896$		0			0
$897$	−4.77258	+	1.15618i	−0.159352	+	0.0386037i
$898$		0			0
$899$	8.59683	−	14.8902i	0.286720	−	0.496614i
$900$		0			0
$901$	10.8630	+	18.8152i	0.361898	+	0.626826i
$902$		0			0
$903$	−0.737914	−	50.4828i	−0.0245563	−	1.67996i
$904$		0			0
$905$			22.5001i			0.747928i
$906$		0			0
$907$		−	50.8788i		−	1.68940i	−0.535237	−	0.844702i	$-0.679778\pi$
$907$		−	50.8788i		−	1.68940i	0.535237	−	0.844702i	$-0.320222\pi$
$908$		0			0
$909$	−28.9210	−	1.39647i	−0.959248	−	0.0463180i
$910$		0			0
$911$	−29.4958	−	51.0882i	−0.977238	−	1.69263i	−0.672342	−	0.740240i	$-0.734712\pi$
$911$	−29.4958	−	51.0882i	−0.977238	−	1.69263i	−0.304896	−	0.952386i	$-0.598622\pi$
$912$		0			0
$913$	10.9479	+	18.9623i	0.362323	+	0.627562i
$914$		0			0
$915$	−0.824494	−	3.40343i	−0.0272569	−	0.112514i
$916$		0			0
$917$	−11.4088	−	36.8113i	−0.376753	−	1.21562i
$918$		0			0
$919$	26.6301	−	15.3749i	0.878447	−	0.507172i	0.00830118	−	0.999966i	$-0.497358\pi$
$919$	26.6301	−	15.3749i	0.878447	−	0.507172i	0.870146	+	0.492794i	$0.164024\pi$
$920$		0			0
$921$	−34.9847	+	33.3362i	−1.15278	+	1.09846i
$922$		0			0
$923$	21.7386	−	37.6523i	0.715534	−	1.23934i
$924$		0			0
$925$	−1.92842	−	3.34012i	−0.0634061	−	0.109823i
$926$		0			0
$927$	−28.5037	−	1.37632i	−0.936183	−	0.0452043i
$928$		0			0
$929$	−5.13839	−	2.96665i	−0.168585	−	0.0973327i	0.413333	−	0.910580i	$-0.364364\pi$
$929$	−5.13839	−	2.96665i	−0.168585	−	0.0973327i	−0.581919	+	0.813247i	$0.697698\pi$
$930$		0			0
$931$	9.52934	−	19.9243i	0.312311	−	0.652993i
$932$		0			0
$933$	14.2228	−	48.3803i	0.465633	−	1.58390i
$934$		0			0
$935$	8.97061	−	15.5376i	0.293370	−	0.508132i
$936$		0			0
$937$	−6.00231			−0.196087			−0.0980435	−	0.995182i	$-0.531258\pi$
$937$	−6.00231			−0.196087			−0.0980435	+	0.995182i	$0.531258\pi$
$938$		0			0
$939$	47.8316	−	11.5874i	1.56092	−	0.378140i
$940$		0			0
$941$	39.8847	−	23.0275i	1.30020	−	0.750674i	0.319766	−	0.947497i	$-0.396396\pi$
$941$	39.8847	−	23.0275i	1.30020	−	0.750674i	0.980439	+	0.196823i	$0.0630624\pi$
$942$		0			0
$943$	−8.72417	−	5.03690i	−0.284098	−	0.164024i
$944$		0			0
$945$	−17.2233	+	27.6414i	−0.560275	+	0.899175i
$946$		0			0
$947$	−7.27908	+	12.6077i	−0.236538	+	0.409696i	−0.959719	−	0.280963i	$-0.909346\pi$
$947$	−7.27908	+	12.6077i	−0.236538	+	0.409696i	0.723180	+	0.690659i	$0.242680\pi$
$948$		0			0
$949$	−1.16427	−	2.01658i	−0.0377939	−	0.0654609i
$950$		0			0
$951$	−10.0722	−	41.5772i	−0.326615	−	1.34823i
$952$		0			0
$953$			29.0894i			0.942297i	0.882054	+	0.471149i	$0.156160\pi$
$953$			29.0894i			0.942297i	−0.882054	+	0.471149i	$0.843840\pi$
$954$		0			0
$955$	−20.3737	−	11.7628i	−0.659277	−	0.380634i
$956$		0			0
$957$	12.7055	+	3.73513i	0.410709	+	0.120740i
$958$		0			0
$959$	−21.3483	+	6.61642i	−0.689371	+	0.213655i
$960$		0			0
$961$	27.8654	−	48.2644i	0.898885	−	1.55691i
$962$		0			0
$963$	24.2025	−	12.4574i	0.779915	−	0.401434i
$964$		0			0
$965$	−32.1322	+	18.5515i	−1.03437	+	0.597195i
$966$		0			0
$967$	−5.25768	−	3.03552i	−0.169075	−	0.0976158i	0.413074	−	0.910697i	$-0.364455\pi$
$967$	−5.25768	−	3.03552i	−0.169075	−	0.0976158i	−0.582150	+	0.813082i	$0.697788\pi$
$968$		0			0
$969$	−6.89398	−	7.23489i	−0.221466	−	0.232418i
$970$		0			0
$971$	−28.5315	−	49.4180i	−0.915619	−	1.58590i	−0.805992	−	0.591927i	$-0.798368\pi$
$971$	−28.5315	−	49.4180i	−0.915619	−	1.58590i	−0.109627	−	0.993973i	$-0.534966\pi$
$972$		0			0
$973$	1.65438	−	7.29335i	0.0530369	−	0.233814i
$974$		0			0
$975$	−2.85946	+	0.692717i	−0.0915761	+	0.0221847i
$976$		0			0
$977$	−16.6568	+	9.61682i	−0.532899	+	0.307669i	−0.742196	−	0.670183i	$-0.766216\pi$
$977$	−16.6568	+	9.61682i	−0.532899	+	0.307669i	0.209297	+	0.977852i	$0.432882\pi$
$978$		0			0
$979$	6.74433	−	3.89384i	0.215550	−	0.124448i
$980$		0			0
$981$	−35.1569	−	22.6262i	−1.12247	−	0.722398i
$982$		0			0
$983$	−27.1792			−0.866883			−0.433441	−	0.901182i	$-0.642701\pi$
$983$	−27.1792			−0.866883			−0.433441	+	0.901182i	$0.642701\pi$
$984$		0			0
$985$	−28.7332			−0.915517
$986$		0			0
$987$	−7.47040	−	12.5131i	−0.237785	−	0.398297i
$988$		0			0
$989$	9.74806	−	5.62805i	0.309970	−	0.178961i
$990$		0			0
$991$	−29.2381	−	16.8806i	−0.928778	−	0.536230i	−0.0423529	−	0.999103i	$-0.513485\pi$
$991$	−29.2381	−	16.8806i	−0.928778	−	0.536230i	−0.886425	+	0.462873i	$0.846819\pi$
$992$		0			0
$993$	6.03652	+	24.9181i	0.191563	+	0.790752i
$994$		0			0
$995$	14.4165	−	24.9702i	0.457035	−	0.791608i
$996$		0			0
$997$	−2.85134			−0.0903028			−0.0451514	−	0.998980i	$-0.514377\pi$
$997$	−2.85134			−0.0903028			−0.0451514	+	0.998980i	$0.514377\pi$
$998$		0			0
$999$	30.9287	+	10.7382i	0.978540	+	0.339742i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.bh.c.95.4	✓	30
3.2	odd	2		3024.2.bh.c.2447.12		30
4.3	odd	2		1008.2.bh.d.95.12	yes	30
7.2	even	3		1008.2.cj.c.527.14	yes	30
9.2	odd	6		1008.2.cj.d.767.2	yes	30
9.7	even	3		3024.2.cj.d.1439.12		30
12.11	even	2		3024.2.bh.d.2447.12		30
21.2	odd	6		3024.2.cj.c.2879.12		30
28.23	odd	6		1008.2.cj.d.527.2	yes	30
36.7	odd	6		3024.2.cj.c.1439.12		30
36.11	even	6		1008.2.cj.c.767.14	yes	30
63.2	odd	6		1008.2.bh.d.191.12	yes	30
63.16	even	3		3024.2.bh.d.1871.4		30
84.23	even	6		3024.2.cj.d.2879.12		30
252.79	odd	6		3024.2.bh.c.1871.4		30
252.191	even	6	inner	1008.2.bh.c.191.4	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bh.c.95.4	✓	30	1.1	even	1	trivial
1008.2.bh.c.191.4	yes	30	252.191	even	6	inner
1008.2.bh.d.95.12	yes	30	4.3	odd	2
1008.2.bh.d.191.12	yes	30	63.2	odd	6
1008.2.cj.c.527.14	yes	30	7.2	even	3
1008.2.cj.c.767.14	yes	30	36.11	even	6
1008.2.cj.d.527.2	yes	30	28.23	odd	6
1008.2.cj.d.767.2	yes	30	9.2	odd	6
3024.2.bh.c.1871.4		30	252.79	odd	6
3024.2.bh.c.2447.12		30	3.2	odd	2
3024.2.bh.d.1871.4		30	63.16	even	3
3024.2.bh.d.2447.12		30	12.11	even	2
3024.2.cj.c.1439.12		30	36.7	odd	6
3024.2.cj.c.2879.12		30	21.2	odd	6
3024.2.cj.d.1439.12		30	9.7	even	3
3024.2.cj.d.2879.12		30	84.23	even	6

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19485 - 1.25393i) q^{3} -2.36899i q^{5} +(-0.783237 - 2.52716i) q^{7} +(-0.144689 + 2.99651i) q^{9} +O(q^{10})\)	\(q+(-1.19485 - 1.25393i) q^{3} -2.36899i q^{5} +(-0.783237 - 2.52716i) q^{7} +(-0.144689 + 2.99651i) q^{9} -4.14140 q^{11} +(-1.38752 + 2.40326i) q^{13} +(-2.97055 + 2.83058i) q^{15} +(-1.58369 - 0.914347i) q^{17} +(-2.73242 + 1.57756i) q^{19} +(-2.23304 + 4.00169i) q^{21} -1.02166 q^{23} -0.612123 q^{25} +(3.93030 - 3.39894i) q^{27} +(1.59887 - 0.923106i) q^{29} +(8.06524 - 4.65647i) q^{31} +(4.94834 + 5.19304i) q^{33} +(-5.98682 + 1.85548i) q^{35} +(3.15039 + 5.45663i) q^{37} +(4.67139 - 1.13166i) q^{39} +(8.53919 + 4.93010i) q^{41} +(-9.54137 + 5.50871i) q^{43} +(7.09871 + 0.342766i) q^{45} +(-1.59009 + 2.75412i) q^{47} +(-5.77308 + 3.95873i) q^{49} +(0.745743 + 3.07835i) q^{51} +(-10.2889 - 5.94029i) q^{53} +9.81095i q^{55} +(5.24298 + 1.54132i) q^{57} +(-1.62351 - 2.81200i) q^{59} +(-0.426723 + 0.739106i) q^{61} +(7.68598 - 1.98132i) q^{63} +(5.69329 + 3.28702i) q^{65} +(-0.259676 + 0.149924i) q^{67} +(1.22073 + 1.28109i) q^{69} -15.6672 q^{71} +(-0.419551 + 0.726684i) q^{73} +(0.731392 + 0.767560i) q^{75} +(3.24370 + 10.4660i) q^{77} +(9.69258 + 5.59601i) q^{79} +(-8.95813 - 0.867121i) q^{81} +(-2.64353 - 4.57872i) q^{83} +(-2.16608 + 3.75176i) q^{85} +(-3.06791 - 0.901900i) q^{87} +(-1.62851 + 0.940223i) q^{89} +(7.16017 + 1.62417i) q^{91} +(-15.4756 - 4.54950i) q^{93} +(3.73724 + 6.47308i) q^{95} +(-8.03665 - 13.9199i) q^{97} +(0.599214 - 12.4098i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} - 2 q^{7} - q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 - 2 * q^7 - q^9	\( 30 q - 3 q^{3} - 2 q^{7} - q^{9} + 6 q^{11} + 12 q^{17} + 9 q^{19} + 14 q^{21} - 24 q^{23} - 36 q^{25} + 27 q^{27} + 27 q^{29} + 6 q^{31} - 20 q^{33} - 6 q^{35} + 6 q^{37} - 15 q^{39} + 9 q^{41} - 21 q^{43} - 8 q^{45} + 12 q^{49} - 15 q^{51} - 3 q^{53} + 20 q^{57} + 3 q^{59} - 3 q^{61} + 24 q^{63} - 39 q^{67} + 10 q^{69} + 18 q^{71} + 21 q^{73} + 21 q^{75} + 36 q^{77} - 33 q^{79} - 17 q^{81} - 15 q^{83} - 3 q^{85} + 78 q^{87} + 6 q^{89} - 26 q^{91} - 3 q^{93} - 27 q^{95} - 6 q^{97} - 48 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 - 2 * q^7 - q^9 + 6 * q^11 + 12 * q^17 + 9 * q^19 + 14 * q^21 - 24 * q^23 - 36 * q^25 + 27 * q^27 + 27 * q^29 + 6 * q^31 - 20 * q^33 - 6 * q^35 + 6 * q^37 - 15 * q^39 + 9 * q^41 - 21 * q^43 - 8 * q^45 + 12 * q^49 - 15 * q^51 - 3 * q^53 + 20 * q^57 + 3 * q^59 - 3 * q^61 + 24 * q^63 - 39 * q^67 + 10 * q^69 + 18 * q^71 + 21 * q^73 + 21 * q^75 + 36 * q^77 - 33 * q^79 - 17 * q^81 - 15 * q^83 - 3 * q^85 + 78 * q^87 + 6 * q^89 - 26 * q^91 - 3 * q^93 - 27 * q^95 - 6 * q^97 - 48 * q^99

Introduction

L-functions

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