LMFDB - Embedded newform 756.2.ba.a.71.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(71,756)]

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, 5, 0]))

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

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

chi := DirichletCharacter("756.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ba (of order $6$, degree $2$, not 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:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			71.17
Character	$\chi$	$=$	756.71
Dual form			756.2.ba.a.575.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0878075 - 1.41148i) q^{2} +(-1.98458 + 0.247878i) q^{4} +(-2.57586 - 1.48718i) q^{5} +(0.866025 - 0.500000i) q^{7} +(0.524137 + 2.77944i) q^{8} +O(q^{10})$	\(q+(-0.0878075 - 1.41148i) q^{2} +(-1.98458 + 0.247878i) q^{4} +(-2.57586 - 1.48718i) q^{5} +(0.866025 - 0.500000i) q^{7} +(0.524137 + 2.77944i) q^{8} +(-1.87295 + 3.76638i) q^{10} +(-1.31064 - 2.27009i) q^{11} +(-3.13567 + 5.43114i) q^{13} +(-0.781786 - 1.17848i) q^{14} +(3.87711 - 0.983867i) q^{16} +1.35655i q^{17} +3.40118i q^{19} +(5.48065 + 2.31292i) q^{20} +(-3.08911 + 2.04927i) q^{22} +(1.92084 - 3.32699i) q^{23} +(1.92339 + 3.33140i) q^{25} +(7.94130 + 3.94905i) q^{26} +(-1.59476 + 1.20696i) q^{28} +(-8.00451 + 4.62140i) q^{29} +(1.97895 + 1.14255i) q^{31} +(-1.72915 - 5.38610i) q^{32} +(1.91476 - 0.119116i) q^{34} -2.97435 q^{35} +7.01077 q^{37} +(4.80072 - 0.298649i) q^{38} +(2.78341 - 7.93894i) q^{40} +(7.13684 + 4.12046i) q^{41} +(-1.81712 + 1.04911i) q^{43} +(3.16377 + 4.18029i) q^{44} +(-4.86466 - 2.41910i) q^{46} +(3.82740 + 6.62925i) q^{47} +(0.500000 - 0.866025i) q^{49} +(4.53334 - 3.00735i) q^{50} +(4.87672 - 11.5558i) q^{52} +8.40500i q^{53} +7.79659i q^{55} +(1.84364 + 2.14500i) q^{56} +(7.22590 + 10.8924i) q^{58} +(-3.37021 + 5.83738i) q^{59} +(-1.27813 - 2.21378i) q^{61} +(1.43892 - 2.89359i) q^{62} +(-7.45056 + 2.91361i) q^{64} +(16.1541 - 9.32658i) q^{65} +(1.00605 + 0.580841i) q^{67} +(-0.336260 - 2.69219i) q^{68} +(0.261170 + 4.19825i) q^{70} -15.8417 q^{71} -4.03393 q^{73} +(-0.615599 - 9.89560i) q^{74} +(-0.843078 - 6.74991i) q^{76} +(-2.27009 - 1.31064i) q^{77} +(-9.28946 + 5.36327i) q^{79} +(-11.4501 - 3.23164i) q^{80} +(5.18930 - 10.4354i) q^{82} +(-2.19903 - 3.80883i) q^{83} +(2.01743 - 3.49430i) q^{85} +(1.64036 + 2.47271i) q^{86} +(5.62262 - 4.83267i) q^{88} +0.508542i q^{89} +6.27134i q^{91} +(-2.98737 + 7.07881i) q^{92} +(9.02101 - 5.98442i) q^{94} +(5.05815 - 8.76098i) q^{95} +(-1.83163 - 3.17248i) q^{97} +(-1.26629 - 0.629699i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97}+O(q^{100}) $ 72 * q + 42 * q^20 + 36 * q^25 - 30 * q^32 - 12 * q^34 - 12 * q^40 + 60 * q^41 - 24 * q^46 + 36 * q^49 + 78 * q^50 - 18 * q^52 - 18 * q^58 - 60 * q^64 - 24 * q^65 - 78 * q^68 - 24 * q^73 + 12 * q^76 - 36 * q^82 - 30 * q^86 + 24 * q^88 + 114 * q^92 + 42 * q^94 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.0878075	−	1.41148i	−0.0620893	−	0.998071i
$2$	−0.0878075	−	1.41148i	−0.0620893	−	0.998071i
$3$		0			0
$3$		0			0
$4$	−1.98458	+	0.247878i	−0.992290	+	0.123939i
$5$	−2.57586	−	1.48718i	−1.15196	−	0.665085i	−0.202597	−	0.979262i	$-0.564938\pi$
$5$	−2.57586	−	1.48718i	−1.15196	−	0.665085i	−0.949365	+	0.314177i	$0.898272\pi$
$6$		0			0
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$	0.524137	+	2.77944i	0.185310	+	0.982680i
$9$		0			0
$10$	−1.87295	+	3.76638i	−0.592278	+	1.19103i
$11$	−1.31064	−	2.27009i	−0.395172	−	0.684457i	0.597951	−	0.801532i	$-0.295982\pi$
$11$	−1.31064	−	2.27009i	−0.395172	−	0.684457i	−0.993123	+	0.117075i	$0.962648\pi$
$12$		0			0
$13$	−3.13567	+	5.43114i	−0.869678	+	1.50633i	−0.00735190	+	0.999973i	$0.502340\pi$
$13$	−3.13567	+	5.43114i	−0.869678	+	1.50633i	−0.862326	+	0.506353i	$0.830993\pi$
$14$	−0.781786	−	1.17848i	−0.208941	−	0.314962i
$15$		0			0
$16$	3.87711	−	0.983867i	0.969278	−	0.245967i
$17$			1.35655i			0.329013i	0.986376	+	0.164506i	$0.0526031\pi$
$17$			1.35655i			0.329013i	−0.986376	+	0.164506i	$0.947397\pi$
$18$		0			0
$19$			3.40118i			0.780284i	0.920755	+	0.390142i	$0.127574\pi$
$19$			3.40118i			0.780284i	−0.920755	+	0.390142i	$0.872426\pi$
$20$	5.48065	+	2.31292i	1.22551	+	0.517185i
$21$		0			0
$22$	−3.08911	+	2.04927i	−0.658601	+	0.436907i
$23$	1.92084	−	3.32699i	0.400522	−	0.693725i	−0.593267	−	0.805006i	$-0.702162\pi$
$23$	1.92084	−	3.32699i	0.400522	−	0.693725i	0.993789	+	0.111281i	$0.0354954\pi$
$24$		0			0
$25$	1.92339	+	3.33140i	0.384677	+	0.666281i
$26$	7.94130	+	3.94905i	1.55742	+	0.774473i
$27$		0			0
$28$	−1.59476	+	1.20696i	−0.301381	+	0.228094i
$29$	−8.00451	+	4.62140i	−1.48640	+	0.858173i	−0.999880	−	0.0154968i	$-0.995067\pi$
$29$	−8.00451	+	4.62140i	−1.48640	+	0.858173i	−0.486519	+	0.873670i	$0.661734\pi$
$30$		0			0
$31$	1.97895	+	1.14255i	0.355430	+	0.205208i	0.667074	−	0.744991i	$-0.267546\pi$
$31$	1.97895	+	1.14255i	0.355430	+	0.205208i	−0.311644	+	0.950199i	$0.600880\pi$
$32$	−1.72915	−	5.38610i	−0.305674	−	0.952136i
$33$		0			0
$34$	1.91476	−	0.119116i	0.328378	−	0.0204282i
$35$	−2.97435			−0.502757
$36$		0			0
$37$	7.01077			1.15256			0.576282	−	0.817251i	$-0.304503\pi$
$37$	7.01077			1.15256			0.576282	+	0.817251i	$0.304503\pi$
$38$	4.80072	−	0.298649i	0.778779	−	0.0484473i
$39$		0			0
$40$	2.78341	−	7.93894i	0.440096	−	1.25526i
$41$	7.13684	+	4.12046i	1.11459	+	0.643507i	0.940014	−	0.341137i	$-0.110812\pi$
$41$	7.13684	+	4.12046i	1.11459	+	0.643507i	0.174574	+	0.984644i	$0.444145\pi$
$42$		0			0
$43$	−1.81712	+	1.04911i	−0.277108	+	0.159988i	−0.632113	−	0.774876i	$-0.717812\pi$
$43$	−1.81712	+	1.04911i	−0.277108	+	0.159988i	0.355006	+	0.934864i	$0.384479\pi$
$44$	3.16377	+	4.18029i	0.476956	+	0.630203i
$45$		0			0
$46$	−4.86466	−	2.41910i	−0.717255	−	0.356677i
$47$	3.82740	+	6.62925i	0.558284	+	0.966976i	0.997640	+	0.0686628i	$0.0218733\pi$
$47$	3.82740	+	6.62925i	0.558284	+	0.966976i	−0.439356	+	0.898313i	$0.644793\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	4.53334	−	3.00735i	0.641111	−	0.425304i
$51$		0			0
$52$	4.87672	−	11.5558i	0.676280	−	1.60250i
$53$			8.40500i			1.15452i	0.816562	+	0.577258i	$0.195877\pi$
$53$			8.40500i			1.15452i	−0.816562	+	0.577258i	$0.804123\pi$
$54$		0			0
$55$			7.79659i			1.05129i
$56$	1.84364	+	2.14500i	0.246366	+	0.286637i
$57$		0			0
$58$	7.22590	+	10.8924i	0.948807	+	1.43025i
$59$	−3.37021	+	5.83738i	−0.438764	+	0.759962i	−0.997594	−	0.0693202i	$-0.977917\pi$
$59$	−3.37021	+	5.83738i	−0.438764	+	0.759962i	0.558830	+	0.829282i	$0.311250\pi$
$60$		0			0
$61$	−1.27813	−	2.21378i	−0.163648	−	0.283446i	0.772527	−	0.634982i	$-0.218993\pi$
$61$	−1.27813	−	2.21378i	−0.163648	−	0.283446i	−0.936174	+	0.351537i	$0.885659\pi$
$62$	1.43892	−	2.89359i	0.182744	−	0.367486i
$63$		0			0
$64$	−7.45056	+	2.91361i	−0.931320	+	0.364202i
$65$	16.1541	−	9.32658i	2.00367	−	1.15682i
$66$		0			0
$67$	1.00605	+	0.580841i	0.122908	+	0.0709610i	0.560194	−	0.828362i	$-0.310727\pi$
$67$	1.00605	+	0.580841i	0.122908	+	0.0709610i	−0.437286	+	0.899323i	$0.644060\pi$
$68$	−0.336260	−	2.69219i	−0.0407775	−	0.326476i
$69$		0			0
$70$	0.261170	+	4.19825i	0.0312158	+	0.501787i
$71$	−15.8417			−1.88006			−0.940032	−	0.341088i	$-0.889205\pi$
$71$	−15.8417			−1.88006			−0.940032	+	0.341088i	$0.889205\pi$
$72$		0			0
$73$	−4.03393			−0.472135			−0.236068	−	0.971737i	$-0.575859\pi$
$73$	−4.03393			−0.472135			−0.236068	+	0.971737i	$0.575859\pi$
$74$	−0.615599	−	9.89560i	−0.0715619	−	1.15034i
$75$		0			0
$76$	−0.843078	−	6.74991i	−0.0967076	−	0.774268i
$77$	−2.27009	−	1.31064i	−0.258701	−	0.149361i
$78$		0			0
$79$	−9.28946	+	5.36327i	−1.04515	+	0.603415i	−0.921286	−	0.388885i	$-0.872860\pi$
$79$	−9.28946	+	5.36327i	−1.04515	+	0.603415i	−0.123859	+	0.992300i	$0.539527\pi$
$80$	−11.4501	−	3.23164i	−1.28016	−	0.361309i
$81$		0			0
$82$	5.18930	−	10.4354i	0.573062	−	1.15239i
$83$	−2.19903	−	3.80883i	−0.241375	−	0.418073i	0.719731	−	0.694253i	$-0.244265\pi$
$83$	−2.19903	−	3.80883i	−0.241375	−	0.418073i	−0.961106	+	0.276179i	$0.910932\pi$
$84$		0			0
$85$	2.01743	−	3.49430i	0.218822	−	0.379010i
$86$	1.64036	+	2.47271i	0.176885	+	0.266640i
$87$		0			0
$88$	5.62262	−	4.83267i	0.599373	−	0.515164i
$89$			0.508542i			0.0539054i	0.999637	+	0.0269527i	$0.00858034\pi$
$89$			0.508542i			0.0539054i	−0.999637	+	0.0269527i	$0.991420\pi$
$90$		0			0
$91$			6.27134i			0.657415i
$92$	−2.98737	+	7.07881i	−0.311455	+	0.738017i
$93$		0			0
$94$	9.02101	−	5.98442i	0.930447	−	0.617245i
$95$	5.05815	−	8.76098i	0.518956	−	0.898858i
$96$		0			0
$97$	−1.83163	−	3.17248i	−0.185974	−	0.322116i	0.757930	−	0.652335i	$-0.226211\pi$
$97$	−1.83163	−	3.17248i	−0.185974	−	0.322116i	−0.943904	+	0.330219i	$0.892877\pi$
$98$	−1.26629	−	0.629699i	−0.127914	−	0.0636092i
$99$		0			0
$100$	−4.64289	−	6.13467i	−0.464289	−	0.613467i
$101$	−3.96515	+	2.28928i	−0.394547	+	0.227792i	−0.684128	−	0.729362i	$-0.739817\pi$
$101$	−3.96515	+	2.28928i	−0.394547	+	0.227792i	0.289581	+	0.957153i	$0.406484\pi$
$102$		0			0
$103$	−14.2254	−	8.21307i	−1.40168	−	0.809257i	−0.407110	−	0.913379i	$-0.633464\pi$
$103$	−14.2254	−	8.21307i	−1.40168	−	0.809257i	−0.994565	+	0.104121i	$0.966797\pi$
$104$	−16.7390	−	5.86874i	−1.64140	−	0.575477i
$105$		0			0
$106$	11.8635	−	0.738022i	1.15229	−	0.0716830i
$107$	−6.90534			−0.667564			−0.333782	−	0.942650i	$-0.608325\pi$
$107$	−6.90534			−0.667564			−0.333782	+	0.942650i	$0.608325\pi$
$108$		0			0
$109$	−10.0627			−0.963835			−0.481918	−	0.876216i	$-0.660060\pi$
$109$	−10.0627			−0.963835			−0.481918	+	0.876216i	$0.660060\pi$
$110$	11.0048	−	0.684599i	1.04926	−	0.0652739i
$111$		0			0
$112$	2.86574	−	2.79061i	0.270787	−	0.263688i
$113$	1.57280	+	0.908055i	0.147956	+	0.0854227i	0.572151	−	0.820149i	$-0.306109\pi$
$113$	1.57280	+	0.908055i	0.147956	+	0.0854227i	−0.424194	+	0.905571i	$0.639443\pi$
$114$		0			0
$115$	−9.89564	+	5.71325i	−0.922773	+	0.532763i
$116$	14.7400	−	11.1557i	1.36858	−	1.03578i
$117$		0			0
$118$	8.53530	+	4.24444i	0.785738	+	0.390732i
$119$	0.678277	+	1.17481i	0.0621776	+	0.107695i
$120$		0			0
$121$	2.06447	−	3.57576i	0.187679	−	0.325069i
$122$	−3.01249	+	1.99845i	−0.272738	+	0.180931i
$123$		0			0
$124$	−4.21060	−	1.77694i	−0.378123	−	0.159574i
$125$			3.43010i			0.306798i
$126$		0			0
$127$		−	14.1234i		−	1.25325i	−0.779321	−	0.626625i	$-0.784436\pi$
$127$		−	14.1234i		−	1.25325i	0.779321	−	0.626625i	$-0.215564\pi$
$128$	4.76674	+	10.2605i	0.421324	+	0.906910i
$129$		0			0
$130$	−14.5828	−	21.9823i	−1.27899	−	1.92798i
$131$	4.15097	−	7.18969i	0.362672	−	0.628166i	−0.625728	−	0.780042i	$-0.715198\pi$
$131$	4.15097	−	7.18969i	0.362672	−	0.628166i	0.988400	+	0.151875i	$0.0485312\pi$
$132$		0			0
$133$	1.70059	+	2.94551i	0.147460	+	0.255408i
$134$	0.731510	−	1.47102i	0.0631928	−	0.127077i
$135$		0			0
$136$	−3.77046	+	0.711020i	−0.323314	+	0.0609695i
$137$	−3.00493	+	1.73490i	−0.256728	+	0.148222i	−0.622841	−	0.782348i	$-0.714022\pi$
$137$	−3.00493	+	1.73490i	−0.256728	+	0.148222i	0.366113	+	0.930570i	$0.380688\pi$
$138$		0			0
$139$	13.7363	+	7.93067i	1.16510	+	0.672671i	0.952521	−	0.304473i	$-0.0984803\pi$
$139$	13.7363	+	7.93067i	1.16510	+	0.672671i	0.212579	+	0.977144i	$0.431814\pi$
$140$	5.90284	−	0.737276i	0.498881	−	0.0623112i
$141$		0			0
$142$	1.39102	+	22.3603i	0.116732	+	1.87644i
$143$	16.4389			1.37469
$144$		0			0
$145$	27.4914			2.28303
$146$	0.354209	+	5.69383i	0.0293146	+	0.471224i
$147$		0			0
$148$	−13.9134	+	1.73782i	−1.14368	+	0.142848i
$149$	−4.63352	−	2.67517i	−0.379593	−	0.219158i	0.298048	−	0.954551i	$-0.403664\pi$
$149$	−4.63352	−	2.67517i	−0.379593	−	0.219158i	−0.677641	+	0.735393i	$0.736998\pi$
$150$		0			0
$151$	7.29470	−	4.21159i	0.593634	−	0.342735i	−0.172899	−	0.984940i	$-0.555313\pi$
$151$	7.29470	−	4.21159i	0.593634	−	0.342735i	0.766533	+	0.642205i	$0.221980\pi$
$152$	−9.45337	+	1.78268i	−0.766770	+	0.144595i
$153$		0			0
$154$	−1.65061	+	3.31928i	−0.133010	+	0.267475i
$155$	−3.39834	−	5.88610i	−0.272962	−	0.472783i
$156$		0			0
$157$	−11.4355	+	19.8069i	−0.912652	+	1.58076i	−0.102350	+	0.994748i	$0.532636\pi$
$157$	−11.4355	+	19.8069i	−0.912652	+	1.58076i	−0.810302	+	0.586012i	$0.800697\pi$
$158$	8.38586	+	12.6410i	0.667143	+	1.00566i
$159$		0			0
$160$	−3.55601	+	16.4454i	−0.281127	+	1.30012i
$161$		−	3.84167i		−	0.302766i
$162$		0			0
$163$		−	6.73289i		−	0.527361i	−0.964610	−	0.263680i	$-0.915064\pi$
$163$		−	6.73289i		−	0.527361i	0.964610	−	0.263680i	$-0.0849364\pi$
$164$	−15.1850	−	6.40831i	−1.18575	−	0.500405i
$165$		0			0
$166$	−5.18301	+	3.43834i	−0.402280	+	0.266867i
$167$	−7.90810	+	13.6972i	−0.611947	+	1.05992i	0.378965	+	0.925411i	$0.376280\pi$
$167$	−7.90810	+	13.6972i	−0.611947	+	1.05992i	−0.990912	+	0.134513i	$0.957053\pi$
$168$		0			0
$169$	−13.1648	−	22.8022i	−1.01268	−	1.75401i
$170$	−5.10930	−	2.54075i	−0.391865	−	0.194867i
$171$		0			0
$172$	3.34616	−	2.53247i	0.255143	−	0.193099i
$173$	2.41981	−	1.39708i	0.183975	−	0.106218i	−0.405184	−	0.914235i	$-0.632793\pi$
$173$	2.41981	−	1.39708i	0.183975	−	0.106218i	0.589159	+	0.808017i	$0.299459\pi$
$174$		0			0
$175$	3.33140	+	1.92339i	0.251830	+	0.145394i
$176$	−7.31495	−	7.51190i	−0.551385	−	0.566231i
$177$		0			0
$178$	0.717800	−	0.0446538i	0.0538014	−	0.00334695i
$179$	−17.2057			−1.28601			−0.643007	−	0.765860i	$-0.722314\pi$
$179$	−17.2057			−1.28601			−0.643007	+	0.765860i	$0.722314\pi$
$180$		0			0
$181$	18.3608			1.36475			0.682375	−	0.731002i	$-0.260947\pi$
$181$	18.3608			1.36475			0.682375	+	0.731002i	$0.260947\pi$
$182$	8.85190	−	0.550670i	0.656146	−	0.0408184i
$183$		0			0
$184$	10.2539	+	3.59505i	0.755931	+	0.265031i
$185$	−18.0588	−	10.4263i	−1.32771	−	0.766554i
$186$		0			0
$187$	3.07950	−	1.77795i	0.225195	−	0.130016i
$188$	−9.23903	−	12.2076i	−0.673825	−	0.890327i
$189$		0			0
$190$	−12.8101	−	6.37023i	−0.929345	−	0.462145i
$191$	0.00610386	+	0.0105722i	0.000441660	+	0.000764978i	0.866246	−	0.499617i	$-0.166526\pi$
$191$	0.00610386	+	0.0105722i	0.000441660	+	0.000764978i	−0.865804	+	0.500382i	$0.833193\pi$
$192$		0			0
$193$	−0.402602	+	0.697327i	−0.0289799	+	0.0501947i	−0.880152	−	0.474693i	$-0.842559\pi$
$193$	−0.402602	+	0.697327i	−0.0289799	+	0.0501947i	0.851172	+	0.524887i	$0.175893\pi$
$194$	−4.31707	+	2.86389i	−0.309948	+	0.205615i
$195$		0			0
$196$	−0.777621	+	1.84264i	−0.0555444	+	0.131617i
$197$			6.58229i			0.468968i	0.972120	+	0.234484i	$0.0753401\pi$
$197$			6.58229i			0.468968i	−0.972120	+	0.234484i	$0.924660\pi$
$198$		0			0
$199$		−	4.53659i		−	0.321591i	−0.986988	−	0.160795i	$-0.948594\pi$
$199$		−	4.53659i		−	0.321591i	0.986988	−	0.160795i	$-0.0514059\pi$
$200$	−8.25131	+	7.09205i	−0.583456	+	0.501483i
$201$		0			0
$202$	3.57945	+	5.39573i	0.251849	+	0.379642i
$203$	−4.62140	+	8.00451i	−0.324359	+	0.561806i
$204$		0			0
$205$	−12.2557	−	21.2275i	−0.855975	−	1.48259i
$206$	−10.3435	+	20.8002i	−0.720667	+	1.44922i
$207$		0			0
$208$	−6.81382	+	24.1422i	−0.472454	+	1.67396i
$209$	7.72098	−	4.45771i	0.534071	−	0.308346i
$210$		0			0
$211$	11.1537	+	6.43957i	0.767850	+	0.443319i	0.832107	−	0.554615i	$-0.187134\pi$
$211$	11.1537	+	6.43957i	0.767850	+	0.443319i	−0.0642570	+	0.997933i	$0.520468\pi$
$212$	−2.08341	−	16.6804i	−0.143089	−	1.14561i
$213$		0			0
$214$	0.606340	+	9.74678i	0.0414486	+	0.666276i
$215$	6.24087			0.425624
$216$		0			0
$217$	2.28510			0.155123
$218$	0.883584	+	14.2034i	0.0598439	+	0.961976i
$219$		0			0
$220$	−1.93260	−	15.4729i	−0.130296	−	1.04319i
$221$	−7.36763	−	4.25370i	−0.495600	−	0.286135i
$222$		0			0
$223$	−16.7013	+	9.64247i	−1.11840	+	0.645708i	−0.940992	−	0.338430i	$-0.890104\pi$
$223$	−16.7013	+	9.64247i	−1.11840	+	0.645708i	−0.177407	+	0.984138i	$0.556771\pi$
$224$	−4.19054	−	3.79992i	−0.279992	−	0.253893i
$225$		0			0
$226$	1.14360	−	2.29971i	0.0760713	−	0.152975i
$227$	−5.21610	−	9.03455i	−0.346205	−	0.599644i	0.639367	−	0.768902i	$-0.279196\pi$
$227$	−5.21610	−	9.03455i	−0.346205	−	0.599644i	−0.985572	+	0.169257i	$0.945863\pi$
$228$		0			0
$229$	−13.0067	+	22.5282i	−0.859504	+	1.48870i	0.0128983	+	0.999917i	$0.495894\pi$
$229$	−13.0067	+	22.5282i	−0.859504	+	1.48870i	−0.872403	+	0.488788i	$0.837439\pi$
$230$	8.93307	+	13.4659i	0.589029	+	0.887913i
$231$		0			0
$232$	−17.0404	−	19.8258i	−1.11875	−	1.30163i
$233$		−	14.0621i		−	0.921239i	−0.887598	−	0.460620i	$-0.847627\pi$
$233$		−	14.0621i		−	0.921239i	0.887598	−	0.460620i	$-0.152373\pi$
$234$		0			0
$235$		−	22.7681i		−	1.48523i
$236$	5.24150	−	12.4201i	0.341192	−	0.808482i
$237$		0			0
$238$	1.59867	−	1.06054i	0.103626	−	0.0687443i
$239$	0.100067	−	0.173322i	0.00647281	−	0.0112112i	−0.862771	−	0.505595i	$-0.831273\pi$
$239$	0.100067	−	0.173322i	0.00647281	−	0.0112112i	0.869244	+	0.494384i	$0.164606\pi$
$240$		0			0
$241$	11.6261	+	20.1370i	0.748905	+	1.29714i	0.948348	+	0.317231i	$0.102753\pi$
$241$	11.6261	+	20.1370i	0.748905	+	1.29714i	−0.199444	+	0.979909i	$0.563913\pi$
$242$	−5.22841	−	2.59998i	−0.336095	−	0.167133i
$243$		0			0
$244$	3.08529	+	4.07661i	0.197516	+	0.260978i
$245$	−2.57586	+	1.48718i	−0.164566	+	0.0950122i
$246$		0			0
$247$	−18.4723	−	10.6650i	−1.17536	−	0.678596i
$248$	−2.13840	+	6.09923i	−0.135789	+	0.387302i
$249$		0			0
$250$	4.84154	−	0.301189i	0.306206	−	0.0190489i
$251$	15.0210			0.948120			0.474060	−	0.880493i	$-0.342788\pi$
$251$	15.0210			0.948120			0.474060	+	0.880493i	$0.342788\pi$
$252$		0			0
$253$	−10.0701			−0.633100
$254$	−19.9350	+	1.24014i	−1.25083	+	0.0778134i
$255$		0			0
$256$	14.0640	−	7.62913i	0.879001	−	0.476821i
$257$	−5.72495	−	3.30530i	−0.357112	−	0.206179i	0.310701	−	0.950508i	$-0.399436\pi$
$257$	−5.72495	−	3.30530i	−0.357112	−	0.206179i	−0.667813	+	0.744329i	$0.732770\pi$
$258$		0			0
$259$	6.07151	−	3.50539i	0.377265	−	0.217814i
$260$	−29.7473	+	22.5136i	−1.84485	+	1.39623i
$261$		0			0
$262$	−10.5126	−	5.22772i	−0.649472	−	0.322970i
$263$	8.73342	+	15.1267i	0.538526	+	0.932754i	0.998984	+	0.0450728i	$0.0143520\pi$
$263$	8.73342	+	15.1267i	0.538526	+	0.932754i	−0.460458	+	0.887682i	$0.652315\pi$
$264$		0			0
$265$	12.4997	−	21.6501i	0.767851	−	1.32996i
$266$	4.00822	−	2.65900i	0.245760	−	0.163033i
$267$		0			0
$268$	−2.14056	−	0.903348i	−0.130755	−	0.0551808i
$269$			13.3540i			0.814208i	0.913382	+	0.407104i	$0.133461\pi$
$269$			13.3540i			0.814208i	−0.913382	+	0.407104i	$0.866539\pi$
$270$		0			0
$271$			3.89358i			0.236518i	0.992983	+	0.118259i	$0.0377314\pi$
$271$			3.89358i			0.236518i	−0.992983	+	0.118259i	$0.962269\pi$
$272$	1.33467	+	5.25951i	0.0809262	+	0.318905i
$273$		0			0
$274$	2.71264	+	4.08908i	0.163876	+	0.247030i
$275$	5.04172	−	8.73251i	0.304027	−	0.526590i
$276$		0			0
$277$	0.728816	+	1.26235i	0.0437903	+	0.0758471i	0.887090	−	0.461597i	$-0.152723\pi$
$277$	0.728816	+	1.26235i	0.0437903	+	0.0758471i	−0.843300	+	0.537444i	$0.819390\pi$
$278$	9.98787	−	20.0850i	0.599033	−	1.20462i
$279$		0			0
$280$	−1.55897	−	8.26703i	−0.0931662	−	0.494050i
$281$	8.13587	−	4.69725i	0.485346	−	0.280214i	−0.237296	−	0.971437i	$-0.576261\pi$
$281$	8.13587	−	4.69725i	0.485346	−	0.280214i	0.722641	+	0.691223i	$0.242928\pi$
$282$		0			0
$283$	−5.86177	−	3.38429i	−0.348446	−	0.201175i	0.315555	−	0.948907i	$-0.397809\pi$
$283$	−5.86177	−	3.38429i	−0.348446	−	0.201175i	−0.664001	+	0.747732i	$0.731143\pi$
$284$	31.4391	−	3.92681i	1.86557	−	0.233013i
$285$		0			0
$286$	−1.44346	−	23.2032i	−0.0853534	−	1.37204i
$287$	8.24092			0.486446
$288$		0			0
$289$	15.1598			0.891751
$290$	−2.41395	−	38.8036i	−0.141752	−	2.27863i
$291$		0			0
$292$	8.00565	−	0.999922i	0.468495	−	0.0585160i
$293$	2.02438	+	1.16877i	0.118265	+	0.0682805i	0.557966	−	0.829864i	$-0.311582\pi$
$293$	2.02438	+	1.16877i	0.118265	+	0.0682805i	−0.439700	+	0.898145i	$0.644915\pi$
$294$		0			0
$295$	17.3624	−	10.0242i	1.01088	−	0.583631i
$296$	3.67461	+	19.4860i	0.213582	+	1.13260i
$297$		0			0
$298$	−3.36910	+	6.77505i	−0.195167	+	0.392468i
$299$	12.0462	+	20.8647i	0.696651	+	1.20663i
$300$		0			0
$301$	−1.04911	+	1.81712i	−0.0604699	+	0.104737i
$302$	−6.58513	−	9.92654i	−0.378932	−	0.571208i
$303$		0			0
$304$	3.34631	+	13.1868i	0.191924	+	0.756313i
$305$			7.60321i			0.435358i
$306$		0			0
$307$		−	27.7944i		−	1.58631i	−0.609020	−	0.793155i	$-0.708437\pi$
$307$		−	27.7944i		−	1.58631i	0.609020	−	0.793155i	$-0.291563\pi$
$308$	4.83005	+	2.03836i	0.275218	+	0.116146i
$309$		0			0
$310$	−8.00975	+	5.31356i	−0.454923	+	0.301790i
$311$	−9.35590	+	16.2049i	−0.530524	+	0.918895i	0.468841	+	0.883282i	$0.344672\pi$
$311$	−9.35590	+	16.2049i	−0.530524	+	0.918895i	−0.999366	+	0.0356128i	$0.988662\pi$
$312$		0			0
$313$	2.86836	+	4.96815i	0.162129	+	0.280816i	0.935632	−	0.352977i	$-0.114830\pi$
$313$	2.86836	+	4.96815i	0.162129	+	0.280816i	−0.773503	+	0.633793i	$0.781497\pi$
$314$	28.9612	+	14.4018i	1.63438	+	0.812743i
$315$		0			0
$316$	17.1062	−	12.9465i	0.962301	−	0.728297i
$317$	14.1223	−	8.15353i	0.793189	−	0.457948i	−0.0478952	−	0.998852i	$-0.515251\pi$
$317$	14.1223	−	8.15353i	0.793189	−	0.457948i	0.841084	+	0.540905i	$0.181918\pi$
$318$		0			0
$319$	20.9820	+	12.1140i	1.17477	+	0.678251i
$320$	23.5247	+	3.57522i	1.31507	+	0.199861i
$321$		0			0
$322$	−5.42247	+	0.337328i	−0.302182	+	0.0187985i
$323$	−4.61389			−0.256723
$324$		0			0
$325$	−24.1244			−1.33818
$326$	−9.50338	+	0.591199i	−0.526343	+	0.0327435i
$327$		0			0
$328$	−7.71188	+	21.9961i	−0.425817	+	1.21453i
$329$	6.62925	+	3.82740i	0.365482	+	0.211011i
$330$		0			0
$331$	−8.17068	+	4.71735i	−0.449101	+	0.259289i	−0.707451	−	0.706763i	$-0.750155\pi$
$331$	−8.17068	+	4.71735i	−0.449101	+	0.259289i	0.258349	+	0.966052i	$0.416821\pi$
$332$	5.30827	+	7.01383i	0.291329	+	0.384934i
$333$		0			0
$334$	20.0278	+	9.95945i	1.09587	+	0.544957i
$335$	−1.72763	−	2.99233i	−0.0943902	−	0.163489i
$336$		0			0
$337$	−16.4975	+	28.5745i	−0.898675	+	1.55655i	−0.0694862	+	0.997583i	$0.522136\pi$
$337$	−16.4975	+	28.5745i	−0.898675	+	1.55655i	−0.829189	+	0.558968i	$0.811197\pi$
$338$	−31.0289	+	20.5842i	−1.68775	+	1.11963i
$339$		0			0
$340$	−3.13760	+	7.43479i	−0.170160	+	0.403208i
$341$		−	5.98986i		−	0.324369i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	−3.86837	−	4.50069i	−0.208568	−	0.242661i
$345$		0			0
$346$	−2.18443	−	3.29285i	−0.117436	−	0.177025i
$347$	9.65449	−	16.7221i	0.518280	−	0.897688i	−0.481494	−	0.876449i	$-0.659906\pi$
$347$	9.65449	−	16.7221i	0.518280	−	0.897688i	0.999774	−	0.0212384i	$-0.00676089\pi$
$348$		0			0
$349$	−9.11469	−	15.7871i	−0.487898	−	0.845065i	0.512005	−	0.858983i	$-0.328903\pi$
$349$	−9.11469	−	15.7871i	−0.487898	−	0.845065i	−0.999903	+	0.0139178i	$0.995570\pi$
$350$	2.42231	−	4.87111i	0.129478	−	0.260372i
$351$		0			0
$352$	−9.96062	+	10.9845i	−0.530903	+	0.585478i
$353$	−10.9398	+	6.31609i	−0.582266	+	0.336172i	−0.762033	−	0.647538i	$-0.775799\pi$
$353$	−10.9398	+	6.31609i	−0.582266	+	0.336172i	0.179767	+	0.983709i	$0.442466\pi$
$354$		0			0
$355$	40.8061	+	23.5594i	2.16576	+	1.25040i
$356$	−0.126056	−	1.00924i	−0.00668098	−	0.0534897i
$357$		0			0
$358$	1.51079	+	24.2856i	0.0798477	+	1.28353i
$359$	36.8318			1.94391			0.971954	−	0.235173i	$-0.0755657\pi$
$359$	36.8318			1.94391			0.971954	+	0.235173i	$0.0755657\pi$
$360$		0			0
$361$	7.43197			0.391156
$362$	−1.61222	−	25.9160i	−0.0847363	−	1.36212i
$363$		0			0
$364$	−1.55453	−	12.4460i	−0.0814793	−	0.652346i
$365$	10.3908	+	5.99916i	0.543882	+	0.314010i
$366$		0			0
$367$	22.5189	−	13.0013i	1.17548	−	0.678663i	0.220514	−	0.975384i	$-0.429226\pi$
$367$	22.5189	−	13.0013i	1.17548	−	0.678663i	0.954964	+	0.296721i	$0.0958932\pi$
$368$	4.17399	−	14.7890i	0.217584	−	0.770928i
$369$		0			0
$370$	−13.1308	+	26.4052i	−0.682638	+	1.37274i
$371$	4.20250	+	7.27894i	0.218183	+	0.377904i
$372$		0			0
$373$	15.7454	−	27.2718i	0.815265	−	1.41208i	−0.0938733	−	0.995584i	$-0.529925\pi$
$373$	15.7454	−	27.2718i	0.815265	−	1.41208i	0.909138	−	0.416495i	$-0.136742\pi$
$374$	−2.77995	−	4.19055i	−0.143748	−	0.216688i
$375$		0			0
$376$	−16.4195	+	14.1127i	−0.846772	+	0.727805i
$377$		−	57.9648i		−	2.98534i
$378$		0			0
$379$			16.1164i			0.827846i	0.910312	+	0.413923i	$0.135842\pi$
$379$			16.1164i			0.827846i	−0.910312	+	0.413923i	$0.864158\pi$
$380$	−7.86666	+	18.6407i	−0.403551	+	0.956246i
$381$		0			0
$382$	0.0143865	−	0.00954383i	0.000736079	−	0.000488305i
$383$	−1.57404	+	2.72631i	−0.0804296	+	0.139308i	−0.903435	−	0.428726i	$-0.858963\pi$
$383$	−1.57404	+	2.72631i	−0.0804296	+	0.139308i	0.823005	+	0.568034i	$0.192296\pi$
$384$		0			0
$385$	3.89829	+	6.75204i	0.198675	+	0.344116i
$386$	1.01962	+	0.507036i	0.0518972	+	0.0258075i
$387$		0			0
$388$	4.42140	+	5.84201i	0.224463	+	0.296583i
$389$	−10.9162	+	6.30247i	−0.553473	+	0.319548i	−0.750522	−	0.660846i	$-0.770198\pi$
$389$	−10.9162	+	6.30247i	−0.553473	+	0.319548i	0.197049	+	0.980394i	$0.436864\pi$
$390$		0			0
$391$	4.51324	+	2.60572i	0.228244	+	0.131777i
$392$	2.66913	+	0.935803i	0.134812	+	0.0472652i
$393$		0			0
$394$	9.29080	−	0.577974i	0.468064	−	0.0291179i
$395$	31.9045			1.60529
$396$		0			0
$397$	−13.0492			−0.654922			−0.327461	−	0.944865i	$-0.606193\pi$
$397$	−13.0492			−0.654922			−0.327461	+	0.944865i	$0.606193\pi$
$398$	−6.40333	+	0.398347i	−0.320970	+	0.0199673i
$399$		0			0
$400$	10.7348	+	11.0239i	0.536742	+	0.551193i
$401$	26.4195	+	15.2533i	1.31933	+	0.761714i	0.983620	−	0.180252i	$-0.0576915\pi$
$401$	26.4195	+	15.2533i	1.31933	+	0.761714i	0.335707	+	0.941966i	$0.391025\pi$
$402$		0			0
$403$	−12.4107	+	7.16531i	−0.618220	+	0.356930i
$404$	7.30169	−	5.52613i	0.363273	−	0.274935i
$405$		0			0
$406$	11.7040	+	5.82019i	0.580861	+	0.288851i
$407$	−9.18857	−	15.9151i	−0.455461	−	0.788881i
$408$		0			0
$409$	6.54461	−	11.3356i	0.323610	−	0.560509i	−0.657620	−	0.753350i	$-0.728437\pi$
$409$	6.54461	−	11.3356i	0.323610	−	0.560509i	0.981230	+	0.192840i	$0.0617700\pi$
$410$	−28.8861	+	19.1627i	−1.42658	+	0.946376i
$411$		0			0
$412$	30.2674	+	12.7733i	1.49117	+	0.629296i
$413$			6.74042i			0.331675i
$414$		0			0
$415$			13.0814i			0.642139i
$416$	34.6747	+	7.49774i	1.70007	+	0.367607i
$417$		0			0
$418$	−6.96995	−	10.5066i	−0.340911	−	0.513896i
$419$	8.31349	−	14.3994i	0.406141	−	0.703456i	−0.588313	−	0.808633i	$-0.700208\pi$
$419$	8.31349	−	14.3994i	0.406141	−	0.703456i	0.994453	+	0.105177i	$0.0335410\pi$
$420$		0			0
$421$	−10.2816	−	17.8082i	−0.501094	−	0.867919i	−0.999999	−	0.00126316i	$-0.999598\pi$
$421$	−10.2816	−	17.8082i	−0.501094	−	0.867919i	0.498906	−	0.866656i	$-0.333735\pi$
$422$	8.10999	−	16.3087i	0.394788	−	0.793894i
$423$		0			0
$424$	−23.3612	+	4.40537i	−1.13452	+	0.213944i
$425$	−4.51923	+	2.60918i	−0.219215	+	0.126564i
$426$		0			0
$427$	−2.21378	−	1.27813i	−0.107132	−	0.0618529i
$428$	13.7042	−	1.71168i	0.662417	−	0.0827372i
$429$		0			0
$430$	−0.547995	−	8.80889i	−0.0264267	−	0.424802i
$431$	−6.45678			−0.311012			−0.155506	−	0.987835i	$-0.549701\pi$
$431$	−6.45678			−0.311012			−0.155506	+	0.987835i	$0.549701\pi$
$432$		0			0
$433$	−17.5593			−0.843847			−0.421924	−	0.906631i	$-0.638645\pi$
$433$	−17.5593			−0.843847			−0.421924	+	0.906631i	$0.638645\pi$
$434$	−0.200649	−	3.22538i	−0.00963145	−	0.154823i
$435$		0			0
$436$	19.9703	−	2.49433i	0.956404	−	0.119457i
$437$	11.3157	+	6.53311i	0.541303	+	0.312521i
$438$		0			0
$439$	13.8975	−	8.02371i	0.663291	−	0.382951i	−0.130239	−	0.991483i	$-0.541574\pi$
$439$	13.8975	−	8.02371i	0.663291	−	0.382951i	0.793530	+	0.608532i	$0.208241\pi$
$440$	−21.6701	+	4.08648i	−1.03308	+	0.194815i
$441$		0			0
$442$	−5.35711	+	10.7728i	−0.254812	+	0.512410i
$443$	−2.84537	−	4.92833i	−0.135188	−	0.234152i	0.790481	−	0.612486i	$-0.209830\pi$
$443$	−2.84537	−	4.92833i	−0.135188	−	0.234152i	−0.925669	+	0.378334i	$0.876497\pi$
$444$		0			0
$445$	0.756292	−	1.30994i	0.0358517	−	0.0620969i
$446$	15.0767	+	22.7269i	0.713903	+	1.07615i
$447$		0			0
$448$	−4.99557	+	6.24854i	−0.236018	+	0.295216i
$449$			3.71055i			0.175112i	0.996160	+	0.0875558i	$0.0279056\pi$
$449$			3.71055i			0.175112i	−0.996160	+	0.0875558i	$0.972094\pi$
$450$		0			0
$451$		−	21.6017i		−	1.01718i
$452$	−3.34643	−	1.41225i	−0.157403	−	0.0664265i
$453$		0			0
$454$	−12.2941	+	8.15575i	−0.576992	+	0.382768i
$455$	9.32658	−	16.1541i	0.437237	−	0.757317i
$456$		0			0
$457$	−2.22552	−	3.85472i	−0.104106	−	0.180316i	0.809267	−	0.587441i	$-0.199865\pi$
$457$	−2.22552	−	3.85472i	−0.104106	−	0.180316i	−0.913372	+	0.407125i	$0.866531\pi$
$458$	32.9403	+	16.3806i	1.53920	+	0.765413i
$459$		0			0
$460$	18.2225	−	13.7913i	0.849628	−	0.643023i
$461$	2.91427	−	1.68255i	0.135731	−	0.0783642i	−0.430597	−	0.902544i	$-0.641697\pi$
$461$	2.91427	−	1.68255i	0.135731	−	0.0783642i	0.566328	+	0.824180i	$0.308364\pi$
$462$		0			0
$463$	−37.1756	−	21.4633i	−1.72770	−	0.997486i	−0.899278	−	0.437377i	$-0.855908\pi$
$463$	−37.1756	−	21.4633i	−1.72770	−	0.997486i	−0.828419	−	0.560109i	$-0.810759\pi$
$464$	−26.4875	+	25.7931i	−1.22965	+	1.19741i
$465$		0			0
$466$	−19.8485	+	1.23476i	−0.919462	+	0.0571991i
$467$	−6.73800			−0.311798			−0.155899	−	0.987773i	$-0.549827\pi$
$467$	−6.73800			−0.311798			−0.155899	+	0.987773i	$0.549827\pi$
$468$		0			0
$469$	1.16168			0.0536415
$470$	−32.1368	+	1.99921i	−1.48236	+	0.0922166i
$471$		0			0
$472$	−17.9911	−	6.30771i	−0.828107	−	0.290336i
$473$	4.76316	+	2.75001i	0.219010	+	0.126446i
$474$		0			0
$475$	−11.3307	+	6.54178i	−0.519888	+	0.300158i
$476$	−1.63730	−	2.16337i	−0.0750457	−	0.0991581i
$477$		0			0
$478$	−0.253427	−	0.126024i	−0.0115915	−	0.00576423i
$479$	−6.39740	−	11.0806i	−0.292305	−	0.506287i	0.682050	−	0.731306i	$-0.261089\pi$
$479$	−6.39740	−	11.0806i	−0.292305	−	0.506287i	−0.974354	+	0.225019i	$0.927755\pi$
$480$		0			0
$481$	−21.9835	+	38.0765i	−1.00236	+	1.73614i
$482$	27.4023	−	18.1783i	1.24814	−	0.827998i
$483$		0			0
$484$	−3.21075	+	7.60812i	−0.145943	+	0.345824i
$485$			10.8958i			0.494754i
$486$		0			0
$487$			9.80009i			0.444084i	0.975037	+	0.222042i	$0.0712723\pi$
$487$			9.80009i			0.444084i	−0.975037	+	0.222042i	$0.928728\pi$
$488$	5.48316	−	4.71280i	0.248211	−	0.213339i
$489$		0			0
$490$	2.32531	+	3.50521i	0.105047	+	0.158349i
$491$	14.8302	−	25.6866i	0.669277	−	1.15922i	−0.308830	−	0.951117i	$-0.599937\pi$
$491$	14.8302	−	25.6866i	0.669277	−	1.15922i	0.978107	−	0.208104i	$-0.0667294\pi$
$492$		0			0
$493$	−6.26918	−	10.8585i	−0.282350	−	0.489044i
$494$	−13.4314	+	27.0098i	−0.604309	+	1.21523i
$495$		0			0
$496$	8.79674	+	2.48277i	0.394985	+	0.111479i
$497$	−13.7193	+	7.92085i	−0.615395	+	0.355299i
$498$		0			0
$499$	3.59135	+	2.07347i	0.160771	+	0.0928212i	0.578227	−	0.815876i	$-0.303745\pi$
$499$	3.59135	+	2.07347i	0.160771	+	0.0928212i	−0.417456	+	0.908697i	$0.637078\pi$
$500$	−0.850247	−	6.80732i	−0.0380242	−	0.304432i
$501$		0			0
$502$	−1.31896	−	21.2020i	−0.0588681	−	0.946290i
$503$	−5.09747			−0.227285			−0.113643	−	0.993522i	$-0.536252\pi$
$503$	−5.09747			−0.227285			−0.113643	+	0.993522i	$0.536252\pi$
$504$		0			0
$505$	13.6182			0.606004
$506$	0.884228	+	14.2138i	0.0393087	+	0.631879i
$507$		0			0
$508$	3.50088	+	28.0290i	0.155327	+	1.24359i
$509$	−3.57195	−	2.06226i	−0.158324	−	0.0914083i	0.418745	−	0.908104i	$-0.362470\pi$
$509$	−3.57195	−	2.06226i	−0.158324	−	0.0914083i	−0.577069	+	0.816696i	$0.695803\pi$
$510$		0			0
$511$	−3.49348	+	2.01696i	−0.154543	+	0.0892252i
$512$	−12.0033	−	19.1812i	−0.530477	−	0.847699i
$513$		0			0
$514$	−4.16269	+	8.37090i	−0.183608	+	0.369225i
$515$	24.4286	+	42.3115i	1.07645	+	1.86447i
$516$		0			0
$517$	10.0327	−	17.3771i	0.441236	−	0.764243i
$518$	−5.48093	−	8.26204i	−0.240818	−	0.363013i
$519$		0			0
$520$	34.3896	+	40.0110i	1.50809	+	1.75460i
$521$			6.45917i			0.282981i	0.989940	+	0.141491i	$0.0451895\pi$
$521$			6.45917i			0.282981i	−0.989940	+	0.141491i	$0.954810\pi$
$522$		0			0
$523$			25.3340i			1.10778i	0.832590	+	0.553889i	$0.186857\pi$
$523$			25.3340i			1.10778i	−0.832590	+	0.553889i	$0.813143\pi$
$524$	−6.45577	+	15.2974i	−0.282021	+	0.668272i
$525$		0			0
$526$	20.5843	−	13.6553i	0.897518	−	0.595401i
$527$	−1.54993	+	2.68456i	−0.0675160	+	0.116941i
$528$		0			0
$529$	4.12077	+	7.13738i	0.179164	+	0.310321i
$530$	−31.6564	−	15.7421i	−1.37507	−	0.683794i
$531$		0			0
$532$	−4.10508	−	5.42406i	−0.177978	−	0.235163i
$533$	−44.7575	+	25.8408i	−1.93866	+	1.11929i
$534$		0			0
$535$	17.7872	+	10.2695i	0.769008	+	0.443987i
$536$	−1.08711	+	3.10068i	−0.0469558	+	0.133929i
$537$		0			0
$538$	18.8490	−	1.17258i	0.812637	−	0.0505536i
$539$	−2.62127			−0.112906
$540$		0			0
$541$	−34.0278			−1.46297			−0.731484	−	0.681859i	$-0.761172\pi$
$541$	−34.0278			−1.46297			−0.731484	+	0.681859i	$0.761172\pi$
$542$	5.49574	−	0.341886i	0.236062	−	0.0146853i
$543$		0			0
$544$	7.30653	−	2.34569i	0.313265	−	0.100571i
$545$	25.9203	+	14.9651i	1.11030	+	0.641033i
$546$		0			0
$547$	16.3200	−	9.42235i	0.697792	−	0.402870i	−0.108732	−	0.994071i	$-0.534679\pi$
$547$	16.3200	−	9.42235i	0.697792	−	0.402870i	0.806525	+	0.591201i	$0.201346\pi$
$548$	5.53348	−	4.18790i	0.236379	−	0.178898i
$549$		0			0
$550$	−12.7685	−	6.34953i	−0.544451	−	0.270745i
$551$	−15.7182	−	27.2248i	−0.669619	−	1.15981i
$552$		0			0
$553$	−5.36327	+	9.28946i	−0.228069	+	0.395028i
$554$	1.71779	−	1.13956i	0.0729818	−	0.0484151i
$555$		0			0
$556$	−29.2267	−	12.3341i	−1.23949	−	0.523083i
$557$		−	25.4658i		−	1.07902i	−0.841979	−	0.539511i	$-0.818609\pi$
$557$		−	25.4658i		−	1.07902i	0.841979	−	0.539511i	$-0.181391\pi$
$558$		0			0
$559$		−	13.1587i		−	0.556553i
$560$	−11.5319	+	2.92637i	−0.487312	+	0.123662i
$561$		0			0
$562$	−7.34449	−	11.0712i	−0.309808	−	0.467011i
$563$	−7.78050	+	13.4762i	−0.327909	+	0.567955i	−0.982097	−	0.188377i	$-0.939677\pi$
$563$	−7.78050	+	13.4762i	−0.327909	+	0.567955i	0.654188	+	0.756332i	$0.273011\pi$
$564$		0			0
$565$	−2.70088	−	4.67806i	−0.113627	−	0.196807i
$566$	−4.26217	+	8.57096i	−0.179152	+	0.360264i
$567$		0			0
$568$	−8.30322	−	44.0310i	−0.348395	−	1.84750i
$569$	19.3293	−	11.1598i	0.810325	−	0.467841i	−0.0367437	−	0.999325i	$-0.511699\pi$
$569$	19.3293	−	11.1598i	0.810325	−	0.467841i	0.847069	+	0.531483i	$0.178365\pi$
$570$		0			0
$571$	−11.7672	−	6.79382i	−0.492444	−	0.284313i	0.233144	−	0.972442i	$-0.425099\pi$
$571$	−11.7672	−	6.79382i	−0.492444	−	0.284313i	−0.725588	+	0.688130i	$0.758432\pi$
$572$	−32.6243	+	4.07484i	−1.36409	+	0.170377i
$573$		0			0
$574$	−0.723614	−	11.6319i	−0.0302031	−	0.485507i
$575$	14.7780			0.616287
$576$		0			0
$577$	32.2367			1.34203			0.671015	−	0.741444i	$-0.265859\pi$
$577$	32.2367			1.34203			0.671015	+	0.741444i	$0.265859\pi$
$578$	−1.33114	−	21.3978i	−0.0553682	−	0.890030i
$579$		0			0
$580$	−54.5588	+	6.81450i	−2.26543	+	0.282957i
$581$	−3.80883	−	2.19903i	−0.158017	−	0.0912310i
$582$		0			0
$583$	19.0801	−	11.0159i	0.790216	−	0.456232i
$584$	−2.11433	−	11.2121i	−0.0874916	−	0.463958i
$585$		0			0
$586$	1.47195	−	2.96000i	0.0608058	−	0.122277i
$587$	−14.0249	−	24.2919i	−0.578870	−	1.00263i	−0.995609	−	0.0936065i	$-0.970160\pi$
$587$	−14.0249	−	24.2919i	−0.578870	−	1.00263i	0.416739	−	0.909026i	$-0.363173\pi$
$588$		0			0
$589$	−3.88602	+	6.73078i	−0.160120	+	0.277337i
$590$	−15.6736	−	23.6266i	−0.645270	−	0.972692i
$591$		0			0
$592$	27.1816	−	6.89767i	1.11716	−	0.283493i
$593$			7.23268i			0.297011i	0.988912	+	0.148505i	$0.0474462\pi$
$593$			7.23268i			0.297011i	−0.988912	+	0.148505i	$0.952554\pi$
$594$		0			0
$595$		−	4.03487i		−	0.165414i
$596$	9.85871	+	4.16053i	0.403829	+	0.170422i
$597$		0			0
$598$	28.3924	−	18.8351i	1.16105	−	0.770226i
$599$	−22.1421	+	38.3513i	−0.904702	+	1.56699i	−0.0833860	+	0.996517i	$0.526573\pi$
$599$	−22.1421	+	38.3513i	−0.904702	+	1.56699i	−0.821316	+	0.570473i	$0.806760\pi$
$600$		0			0
$601$	17.0506	+	29.5325i	0.695508	+	1.20466i	0.970009	+	0.243068i	$0.0781540\pi$
$601$	17.0506	+	29.5325i	0.695508	+	1.20466i	−0.274501	+	0.961587i	$0.588513\pi$
$602$	2.65695	+	1.32125i	0.108289	+	0.0538502i
$603$		0			0
$604$	−13.4329	+	10.1664i	−0.546579	+	0.413667i
$605$	−10.6356	+	6.14045i	−0.432397	+	0.249645i
$606$		0			0
$607$	−11.5054	−	6.64263i	−0.466988	−	0.269616i	0.247990	−	0.968763i	$-0.420230\pi$
$607$	−11.5054	−	6.64263i	−0.466988	−	0.269616i	−0.714978	+	0.699147i	$0.753563\pi$
$608$	18.3191	−	5.88116i	0.742937	−	0.238513i
$609$		0			0
$610$	10.7318	−	0.667619i	0.434518	−	0.0270311i
$611$	−48.0058			−1.94211
$612$		0			0
$613$	−19.8379			−0.801245			−0.400622	−	0.916243i	$-0.631206\pi$
$613$	−19.8379			−0.801245			−0.400622	+	0.916243i	$0.631206\pi$
$614$	−39.2314	+	2.44056i	−1.58325	+	0.0984929i
$615$		0			0
$616$	2.45300	−	6.99652i	0.0988340	−	0.281898i
$617$	9.02809	+	5.21237i	0.363457	+	0.209842i	0.670596	−	0.741823i	$-0.266038\pi$
$617$	9.02809	+	5.21237i	0.363457	+	0.209842i	−0.307139	+	0.951665i	$0.599372\pi$
$618$		0			0
$619$	3.93059	−	2.26933i	0.157984	−	0.0912119i	−0.418924	−	0.908021i	$-0.637593\pi$
$619$	3.93059	−	2.26933i	0.157984	−	0.0912119i	0.576908	+	0.816809i	$0.304259\pi$
$620$	8.20332	+	10.8391i	0.329453	+	0.435307i
$621$		0			0
$622$	23.6945	+	11.7828i	0.950062	+	0.472447i
$623$	0.254271	+	0.440410i	0.0101872	+	0.0176447i
$624$		0			0
$625$	14.7181	−	25.4925i	0.588724	−	1.01970i
$626$	6.76060	−	4.48489i	0.270208	−	0.179252i
$627$		0			0
$628$	17.7850	−	42.1429i	0.709698	−	1.68169i
$629$			9.51049i			0.379208i
$630$		0			0
$631$			12.7139i			0.506132i	0.967449	+	0.253066i	$0.0814390\pi$
$631$			12.7139i			0.506132i	−0.967449	+	0.253066i	$0.918561\pi$
$632$	−19.7758	−	23.0084i	−0.786640	−	0.915225i
$633$		0			0
$634$	−12.7486	−	19.2175i	−0.506313	−	0.763225i
$635$	−21.0040	+	36.3800i	−0.833518	+	1.44370i
$636$		0			0
$637$	3.13567	+	5.43114i	0.124240	+	0.215189i
$638$	15.2563	−	30.6795i	0.604002	−	1.21461i
$639$		0			0
$640$	2.98073	−	33.5187i	0.117824	−	1.32494i
$641$	−17.1431	+	9.89758i	−0.677112	+	0.390931i	−0.798766	−	0.601642i	$-0.794514\pi$
$641$	−17.1431	+	9.89758i	−0.677112	+	0.390931i	0.121654	+	0.992573i	$0.461180\pi$
$642$		0			0
$643$	−32.0861	−	18.5249i	−1.26535	−	0.730551i	−0.291247	−	0.956648i	$-0.594070\pi$
$643$	−32.0861	−	18.5249i	−1.26535	−	0.730551i	−0.974105	+	0.226097i	$0.927403\pi$
$644$	0.952267	+	7.62411i	0.0375246	+	0.300432i
$645$		0			0
$646$	0.405134	+	6.51243i	0.0159398	+	0.256228i
$647$	−21.1167			−0.830182			−0.415091	−	0.909780i	$-0.636250\pi$
$647$	−21.1167			−0.830182			−0.415091	+	0.909780i	$0.636250\pi$
$648$		0			0
$649$	17.6685			0.693549
$650$	2.11830	+	34.0512i	0.0830867	+	1.33560i
$651$		0			0
$652$	1.66894	+	13.3620i	0.0653606	+	0.523295i
$653$	30.0641	+	17.3575i	1.17650	+	0.679253i	0.955202	−	0.295953i	$-0.0956373\pi$
$653$	30.0641	+	17.3575i	1.17650	+	0.679253i	0.221298	+	0.975206i	$0.428971\pi$
$654$		0			0
$655$	−21.3847	+	12.3464i	−0.835568	+	0.482416i
$656$	31.7243	+	8.95378i	1.23863	+	0.349586i
$657$		0			0
$658$	4.82022	−	9.69316i	0.187912	−	0.377879i
$659$	15.5616	+	26.9535i	0.606193	+	1.04996i	0.991862	+	0.127320i	$0.0406376\pi$
$659$	15.5616	+	26.9535i	0.606193	+	1.04996i	−0.385668	+	0.922637i	$0.626029\pi$
$660$		0			0
$661$	4.33105	−	7.50160i	0.168458	−	0.291779i	−0.769420	−	0.638744i	$-0.779454\pi$
$661$	4.33105	−	7.50160i	0.168458	−	0.291779i	0.937878	+	0.346965i	$0.112788\pi$
$662$	7.37591	+	11.1186i	0.286673	+	0.432136i
$663$		0			0
$664$	9.43381	−	8.10841i	0.366103	−	0.314667i
$665$		−	10.1163i		−	0.392294i
$666$		0			0
$667$			35.5079i			1.37487i
$668$	12.2990	−	29.1435i	0.475863	−	1.12760i
$669$		0			0
$670$	−4.07194	+	2.70127i	−0.157313	+	0.104359i
$671$	−3.35032	+	5.80293i	−0.129338	+	0.224019i
$672$		0			0
$673$	9.60975	+	16.6446i	0.370429	+	0.641601i	0.989631	−	0.143630i	$-0.0458774\pi$
$673$	9.60975	+	16.6446i	0.370429	+	0.641601i	−0.619203	+	0.785231i	$0.712544\pi$
$674$	41.7811	+	20.7769i	1.60935	+	0.800296i
$675$		0			0
$676$	31.7788	+	41.9894i	1.22226	+	1.61498i
$677$	−9.44997	+	5.45594i	−0.363192	+	0.209689i	−0.670480	−	0.741928i	$-0.733912\pi$
$677$	−9.44997	+	5.45594i	−0.363192	+	0.209689i	0.307288	+	0.951616i	$0.400578\pi$
$678$		0			0
$679$	−3.17248	−	1.83163i	−0.121749	−	0.0702915i
$680$	10.7696	+	3.77585i	0.412996	+	0.144797i
$681$		0			0
$682$	−8.45460	+	0.525955i	−0.323743	+	0.0201399i
$683$	−11.3989			−0.436167			−0.218084	−	0.975930i	$-0.569981\pi$
$683$	−11.3989			−0.436167			−0.218084	+	0.975930i	$0.569981\pi$
$684$		0			0
$685$	10.3204			0.394322
$686$	−1.41148	+	0.0878075i	−0.0538907	+	0.00335251i
$687$		0			0
$688$	−6.01298	+	5.85533i	−0.229243	+	0.223233i
$689$	−45.6487	−	26.3553i	−1.73908	−	1.00406i
$690$		0			0
$691$	−10.8929	+	6.28904i	−0.414387	+	0.239247i	−0.692673	−	0.721252i	$-0.743567\pi$
$691$	−10.8929	+	6.28904i	−0.414387	+	0.239247i	0.278286	+	0.960498i	$0.410234\pi$
$692$	−4.45600	+	3.37243i	−0.169392	+	0.128200i
$693$		0			0
$694$	−24.4507	−	12.1588i	−0.928135	−	0.461543i
$695$	−23.5886	−	40.8567i	−0.894767	−	1.54978i
$696$		0			0
$697$	−5.58962	+	9.68151i	−0.211722	+	0.366713i
$698$	−21.4829	+	14.2515i	−0.813141	+	0.539427i
$699$		0			0
$700$	−7.08820	−	2.99133i	−0.267909	−	0.113062i
$701$		−	42.0852i		−	1.58953i	−0.606914	−	0.794767i	$-0.707593\pi$
$701$		−	42.0852i		−	1.58953i	0.606914	−	0.794767i	$-0.292407\pi$
$702$		0			0
$703$			23.8449i			0.899328i
$704$	16.3791	+	13.0947i	0.617312	+	0.493527i
$705$		0			0
$706$	9.87566	+	14.8867i	0.371675	+	0.560270i
$707$	−2.28928	+	3.96515i	−0.0860972	+	0.149125i
$708$		0			0
$709$	7.73531	+	13.3980i	0.290506	+	0.503171i	0.973929	−	0.226851i	$-0.0728431\pi$
$709$	7.73531	+	13.3980i	0.290506	+	0.503171i	−0.683424	+	0.730022i	$0.739510\pi$
$710$	29.6706	−	59.6658i	1.11352	−	2.23922i
$711$		0			0
$712$	−1.41346	+	0.266546i	−0.0529717	+	0.00998923i
$713$	7.60249	−	4.38930i	0.284716	−	0.164381i
$714$		0			0
$715$	−42.3443	−	24.4475i	−1.58359	−	0.914285i
$716$	34.1461	−	4.26491i	1.27610	−	0.159387i
$717$		0			0
$718$	−3.23411	−	51.9875i	−0.120696	−	1.94016i
$719$	18.6607			0.695927			0.347964	−	0.937508i	$-0.386873\pi$
$719$	18.6607			0.695927			0.347964	+	0.937508i	$0.386873\pi$
$720$		0			0
$721$	−16.4261			−0.611741
$722$	−0.652583	−	10.4901i	−0.0242866	−	0.390402i
$723$		0			0
$724$	−36.4385	+	4.55125i	−1.35423	+	0.169146i
$725$	−30.7915	−	17.7775i	−1.14357	−	0.660239i
$726$		0			0
$727$	−31.9960	+	18.4729i	−1.18667	+	0.685122i	−0.957547	−	0.288276i	$-0.906918\pi$
$727$	−31.9960	+	18.4729i	−1.18667	+	0.685122i	−0.229119	+	0.973398i	$0.573584\pi$
$728$	−17.4308	+	3.28704i	−0.646028	+	0.121826i
$729$		0			0
$730$	7.55533	−	15.1933i	0.279635	−	0.562329i
$731$	−1.42318	−	2.46502i	−0.0526382	−	0.0911720i
$732$		0			0
$733$	13.1754	−	22.8205i	0.486645	−	0.842893i	−0.513238	−	0.858247i	$-0.671554\pi$
$733$	13.1754	−	22.8205i	0.486645	−	0.842893i	0.999882	+	0.0153535i	$0.00488735\pi$
$734$	−20.3285	−	30.6435i	−0.750338	−	1.13107i
$735$		0			0
$736$	−21.2409	−	4.59294i	−0.782950	−	0.169298i
$737$		−	3.04508i		−	0.112167i
$738$		0			0
$739$			24.6208i			0.905690i	0.891589	+	0.452845i	$0.149591\pi$
$739$			24.6208i			0.905690i	−0.891589	+	0.452845i	$0.850409\pi$
$740$	38.4236	+	16.2154i	1.41248	+	0.596088i
$741$		0			0
$742$	9.90511	−	6.57091i	0.363628	−	0.241226i
$743$	−2.34064	+	4.05411i	−0.0858697	+	0.148731i	−0.905761	−	0.423788i	$-0.860700\pi$
$743$	−2.34064	+	4.05411i	−0.0858697	+	0.148731i	0.819892	+	0.572519i	$0.194034\pi$
$744$		0			0
$745$	7.95689	+	13.7817i	0.291518	+	0.504924i
$746$	−39.8763	−	19.8297i	−1.45997	−	0.726017i
$747$		0			0
$748$	−5.67079	+	4.29182i	−0.207345	+	0.156924i
$749$	−5.98020	+	3.45267i	−0.218512	+	0.126158i
$750$		0			0
$751$	−30.6788	−	17.7124i	−1.11949	−	0.646335i	−0.178216	−	0.983991i	$-0.557033\pi$
$751$	−30.6788	−	17.7124i	−1.11949	−	0.646335i	−0.941270	+	0.337656i	$0.890366\pi$
$752$	21.3616	+	21.9367i	0.778976	+	0.799949i
$753$		0			0
$754$	−81.8164	+	5.08974i	−2.97958	+	0.185357i
$755$	−25.0535			−0.911791
$756$		0			0
$757$	43.2924			1.57349			0.786744	−	0.617280i	$-0.211765\pi$
$757$	43.2924			1.57349			0.786744	+	0.617280i	$0.211765\pi$
$758$	22.7481	−	1.41515i	0.826249	−	0.0514004i
$759$		0			0
$760$	27.0018	+	9.46688i	0.979457	+	0.343400i
$761$	−18.6652	−	10.7763i	−0.676612	−	0.390642i	0.121965	−	0.992534i	$-0.461080\pi$
$761$	−18.6652	−	10.7763i	−0.676612	−	0.390642i	−0.798577	+	0.601892i	$0.794414\pi$
$762$		0			0
$763$	−8.71459	+	5.03137i	−0.315489	+	0.182148i
$764$	−0.0147342	−	0.0194684i	−0.000533065	−	0.000704341i
$765$		0			0
$766$	3.98636	+	1.98234i	0.144033	+	0.0716248i
$767$	−21.1357	−	36.6082i	−0.763167	−	1.32184i
$768$		0			0
$769$	12.7509	−	22.0852i	0.459809	−	0.796412i	−0.539142	−	0.842215i	$-0.681251\pi$
$769$	12.7509	−	22.0852i	0.459809	−	0.796412i	0.998951	+	0.0458027i	$0.0145846\pi$
$770$	9.18811	−	6.09526i	0.331116	−	0.219658i
$771$		0			0
$772$	0.626144	−	1.48370i	0.0225354	−	0.0533995i
$773$			18.9133i			0.680263i	0.940378	+	0.340131i	$0.110472\pi$
$773$			18.9133i			0.680263i	−0.940378	+	0.340131i	$0.889528\pi$
$774$		0			0
$775$			8.79025i			0.315755i
$776$	7.85768	−	6.75372i	0.282074	−	0.242444i
$777$		0			0
$778$	9.85436	+	14.8546i	0.353296	+	0.532565i
$779$	−14.0144	+	24.2737i	−0.502119	+	0.869695i
$780$		0			0
$781$	20.7627	+	35.9620i	0.742948	+	1.28682i
$782$	3.28164	−	6.59917i	0.117351	−	0.235986i
$783$		0			0
$784$	1.08650	−	3.84961i	0.0388037	−	0.137486i
$785$	58.9126	−	34.0132i	2.10268	−	1.21398i
$786$		0			0
$787$	13.4770	+	7.78097i	0.480404	+	0.277362i	0.720585	−	0.693367i	$-0.243873\pi$
$787$	13.4770	+	7.78097i	0.480404	+	0.277362i	−0.240181	+	0.970728i	$0.577207\pi$
$788$	−1.63160	−	13.0631i	−0.0581235	−	0.465353i
$789$		0			0
$790$	−2.80146	−	45.0327i	−0.0996713	−	1.60219i
$791$	1.81611			0.0645735
$792$		0			0
$793$	16.0311			0.569283
$794$	1.14582	+	18.4188i	0.0406636	+	0.653658i
$795$		0			0
$796$	1.12452	+	9.00323i	0.0398576	+	0.319111i
$797$	−22.8419	−	13.1878i	−0.809102	−	0.467135i	0.0375418	−	0.999295i	$-0.488047\pi$
$797$	−22.8419	−	13.1878i	−0.809102	−	0.467135i	−0.846644	+	0.532160i	$0.821381\pi$
$798$		0			0
$799$	−8.99294	+	5.19208i	−0.318147	+	0.183682i
$800$	14.6174	−	16.1200i	0.516804	−	0.569930i
$801$		0			0
$802$	19.2100	−	38.6301i	0.678328	−	1.36408i
$803$	5.28701	+	9.15737i	0.186575	+	0.323157i
$804$		0			0
$805$	−5.71325	+	9.89564i	−0.201366	+	0.348775i
$806$	11.2035	+	16.8883i	0.394626	+	0.594866i
$807$		0			0
$808$	−8.44119	−	9.82099i	−0.296960	−	0.345501i
$809$		−	21.9975i		−	0.773390i	−0.922208	−	0.386695i	$-0.873617\pi$
$809$		−	21.9975i		−	0.773390i	0.922208	−	0.386695i	$-0.126383\pi$
$810$		0			0
$811$		−	41.7569i		−	1.46628i	−0.680076	−	0.733142i	$-0.738053\pi$
$811$		−	41.7569i		−	1.46628i	0.680076	−	0.733142i	$-0.261947\pi$
$812$	7.18740	−	17.0311i	0.252228	−	0.597675i
$813$		0			0
$814$	−21.6571	+	14.3670i	−0.759080	+	0.503563i
$815$	−10.0130	+	17.3430i	−0.350740	+	0.607500i
$816$		0			0
$817$	−3.56822	−	6.18035i	−0.124836	−	0.216223i
$818$	−16.5747	−	8.24227i	−0.579521	−	0.288184i
$819$		0			0
$820$	29.5842	+	39.0897i	1.03313	+	1.36507i
$821$	40.3172	−	23.2772i	1.40708	−	0.812379i	0.411976	−	0.911195i	$-0.364839\pi$
$821$	40.3172	−	23.2772i	1.40708	−	0.812379i	0.995106	+	0.0988159i	$0.0315055\pi$
$822$		0			0
$823$	30.7365	+	17.7457i	1.07141	+	0.618577i	0.928565	−	0.371169i	$-0.121043\pi$
$823$	30.7365	+	17.7457i	1.07141	+	0.618577i	0.142841	+	0.989746i	$0.454376\pi$
$824$	15.3716	−	43.8435i	0.535496	−	1.52736i
$825$		0			0
$826$	9.51401	−	0.591860i	0.331035	−	0.0205934i
$827$	1.34326			0.0467099			0.0233549	−	0.999727i	$-0.492565\pi$
$827$	1.34326			0.0467099			0.0233549	+	0.999727i	$0.492565\pi$
$828$		0			0
$829$	−28.3580			−0.984915			−0.492458	−	0.870336i	$-0.663901\pi$
$829$	−28.3580			−0.984915			−0.492458	+	0.870336i	$0.663901\pi$
$830$	18.4641	−	1.14864i	0.640900	−	0.0398699i
$831$		0			0
$832$	7.53825	−	49.6011i	0.261342	−	1.71961i
$833$	1.17481	+	0.678277i	0.0407048	+	0.0235009i
$834$		0			0
$835$	40.7404	−	23.5215i	1.40988	−	0.813994i
$836$	−14.2179	+	10.7605i	−0.491737	+	0.372161i
$837$		0			0
$838$	−21.0545	−	10.4700i	−0.727316	−	0.361680i
$839$	21.0669	+	36.4890i	0.727311	+	1.25974i	0.958016	+	0.286716i	$0.0925635\pi$
$839$	21.0669	+	36.4890i	0.727311	+	1.25974i	−0.230705	+	0.973024i	$0.574103\pi$
$840$		0			0
$841$	28.2147	−	48.8694i	0.972922	−	1.68515i
$842$	−24.2332	+	16.0760i	−0.835132	+	0.554015i
$843$		0			0
$844$	−23.7316	−	10.0151i	−0.816874	−	0.344734i
$845$			78.3137i			2.69407i
$846$		0			0
$847$		−	4.12893i		−	0.141872i
$848$	8.26940	+	32.5871i	0.283972	+	1.11905i
$849$		0			0
$850$	4.07964	+	6.14972i	0.139930	+	0.210934i
$851$	13.4666	−	23.3248i	0.461628	−	0.799563i
$852$		0			0
$853$	−3.70142	−	6.41105i	−0.126734	−	0.219510i	0.795675	−	0.605723i	$-0.207116\pi$
$853$	−3.70142	−	6.41105i	−0.126734	−	0.219510i	−0.922410	+	0.386213i	$0.873783\pi$
$854$	−1.60967	+	3.23695i	−0.0550818	+	0.110766i
$855$		0			0
$856$	−3.61934	−	19.1930i	−0.123707	−	0.656002i
$857$	3.45961	−	1.99741i	0.118178	−	0.0682302i	−0.439746	−	0.898122i	$-0.644931\pi$
$857$	3.45961	−	1.99741i	0.118178	−	0.0682302i	0.557924	+	0.829892i	$0.311598\pi$
$858$		0			0
$859$	−30.4494	−	17.5800i	−1.03892	−	0.599822i	−0.119394	−	0.992847i	$-0.538095\pi$
$859$	−30.4494	−	17.5800i	−1.03892	−	0.599822i	−0.919528	+	0.393025i	$0.871428\pi$
$860$	−12.3855	+	1.54697i	−0.422342	+	0.0527514i
$861$		0			0
$862$	0.566954	+	9.11364i	0.0193105	+	0.310412i
$863$	−7.96071			−0.270986			−0.135493	−	0.990778i	$-0.543262\pi$
$863$	−7.96071			−0.270986			−0.135493	+	0.990778i	$0.543262\pi$
$864$		0			0
$865$	−8.31080			−0.282576
$866$	1.54184	+	24.7847i	0.0523939	+	0.842219i
$867$		0			0
$868$	−4.53496	+	0.566425i	−0.153927	+	0.0192257i
$869$	24.3502	+	14.0586i	0.826024	+	0.476905i
$870$		0			0
$871$	−6.30925	+	3.64265i	−0.213781	+	0.123426i
$872$	−5.27425	−	27.9688i	−0.178609	−	0.947142i
$873$		0			0
$874$	8.22779	−	16.5456i	0.278309	−	0.559663i
$875$	1.71505	+	2.97056i	0.0579794	+	0.100423i
$876$		0			0
$877$	−6.13852	+	10.6322i	−0.207283	+	0.359025i	−0.950858	−	0.309628i	$-0.899795\pi$
$877$	−6.13852	+	10.6322i	−0.207283	+	0.359025i	0.743575	+	0.668653i	$0.233129\pi$
$878$	−12.5457	−	18.9115i	−0.423395	−	0.638234i
$879$		0			0
$880$	7.67081	+	30.2282i	0.258583	+	1.01899i
$881$			48.2439i			1.62538i	0.582697	+	0.812689i	$0.301997\pi$
$881$			48.2439i			1.62538i	−0.582697	+	0.812689i	$0.698003\pi$
$882$		0			0
$883$			30.2152i			1.01682i	0.861114	+	0.508412i	$0.169767\pi$
$883$			30.2152i			1.01682i	−0.861114	+	0.508412i	$0.830233\pi$
$884$	15.6761	+	6.61554i	0.527243	+	0.222505i
$885$		0			0
$886$	−6.70642	+	4.44895i	−0.225307	+	0.149465i
$887$	−0.828398	+	1.43483i	−0.0278149	+	0.0481768i	−0.879598	−	0.475718i	$-0.842188\pi$
$887$	−0.828398	+	1.43483i	−0.0278149	+	0.0481768i	0.851783	+	0.523895i	$0.175522\pi$
$888$		0			0
$889$	−7.06171	−	12.2312i	−0.236842	−	0.410222i
$890$	−1.91536	−	0.952472i	−0.0642031	−	0.0319269i
$891$		0			0
$892$	30.7548	−	23.2761i	1.02975	−	0.779343i
$893$	−22.5473	+	13.0177i	−0.754516	+	0.435620i
$894$		0			0
$895$	44.3196	+	25.5879i	1.48144	+	0.855310i
$896$	9.25837	+	6.50250i	0.309301	+	0.217233i
$897$		0			0
$898$	5.23739	−	0.325814i	0.174774	−	0.0108726i
$899$	−21.1207			−0.704415
$900$		0			0
$901$	−11.4018			−0.379850
$902$	−30.4905	+	1.89679i	−1.01522	+	0.0631562i
$903$		0			0
$904$	−1.69952	+	4.84744i	−0.0565253	+	0.161224i
$905$	−47.2950	−	27.3058i	−1.57214	−	0.907675i
$906$		0			0
$907$	−1.70693	+	0.985495i	−0.0566776	+	0.0327228i	−0.528071	−	0.849200i	$-0.677085\pi$
$907$	−1.70693	+	0.985495i	−0.0566776	+	0.0327228i	0.471393	+	0.881923i	$0.343751\pi$
$908$	12.5912	+	16.6368i	0.417855	+	0.552113i
$909$		0			0
$910$	−23.6202	−	11.7459i	−0.783003	−	0.389372i
$911$	12.1631	+	21.0670i	0.402980	+	0.697982i	0.994084	−	0.108614i	$-0.0346411\pi$
$911$	12.1631	+	21.0670i	0.402980	+	0.697982i	−0.591104	+	0.806595i	$0.701308\pi$
$912$		0			0
$913$	−5.76425	+	9.98397i	−0.190769	+	0.330421i
$914$	−5.24546	+	3.47977i	−0.173504	+	0.115100i
$915$		0			0
$916$	20.2285	−	47.9331i	0.668369	−	1.58375i
$917$		−	8.30194i		−	0.274154i
$918$		0			0
$919$			1.71777i			0.0566639i	0.999599	+	0.0283320i	$0.00901955\pi$
$919$			1.71777i			0.0566639i	−0.999599	+	0.0283320i	$0.990980\pi$
$920$	−21.0663	−	24.5098i	−0.694535	−	0.808064i
$921$		0			0
$922$	−2.63079	−	3.96570i	−0.0866405	−	0.130603i
$923$	49.6743	−	86.0384i	1.63505	−	2.83199i
$924$		0			0
$925$	13.4844	+	23.3557i	0.443365	+	0.767931i
$926$	−27.0309	+	54.3575i	−0.888290	+	1.78630i
$927$		0			0
$928$	38.7323	+	35.1219i	1.27145	+	1.15293i
$929$	−4.74547	+	2.73980i	−0.155694	+	0.0898899i	−0.575823	−	0.817575i	$-0.695318\pi$
$929$	−4.74547	+	2.73980i	−0.155694	+	0.0898899i	0.420129	+	0.907464i	$0.361985\pi$
$930$		0			0
$931$	2.94551	+	1.70059i	0.0965351	+	0.0557346i
$932$	3.48569	+	27.9074i	0.114177	+	0.914136i
$933$		0			0
$934$	0.591647	+	9.51059i	0.0193593	+	0.311196i
$935$	−10.5765			−0.345888
$936$		0			0
$937$	−38.8381			−1.26879			−0.634393	−	0.773010i	$-0.718750\pi$
$937$	−38.8381			−1.26879			−0.634393	+	0.773010i	$0.718750\pi$
$938$	−0.102004	−	1.63970i	−0.00333056	−	0.0535380i
$939$		0			0
$940$	5.64370	+	45.1851i	0.184077	+	1.47377i
$941$	9.24025	+	5.33486i	0.301223	+	0.173911i	0.642992	−	0.765873i	$-0.277693\pi$
$941$	9.24025	+	5.33486i	0.301223	+	0.173911i	−0.341769	+	0.939784i	$0.611026\pi$
$942$		0			0
$943$	27.4174	−	15.8295i	0.892834	−	0.515478i
$944$	−7.32349	+	25.9480i	−0.238359	+	0.844536i
$945$		0			0
$946$	3.46336	−	6.96460i	0.112604	−	0.226439i
$947$	−22.9414	−	39.7356i	−0.745494	−	1.29123i	−0.949964	−	0.312360i	$-0.898880\pi$
$947$	−22.9414	−	39.7356i	−0.745494	−	1.29123i	0.204470	−	0.978873i	$-0.434453\pi$
$948$		0			0
$949$	12.6491	−	21.9088i	0.410606	−	0.711190i
$950$	10.2286	+	15.4187i	0.331858	+	0.500249i
$951$		0			0
$952$	−2.90980	+	2.50099i	−0.0943073	+	0.0810576i
$953$			1.91834i			0.0621411i	0.999517	+	0.0310706i	$0.00989166\pi$
$953$			1.91834i			0.0621411i	−0.999517	+	0.0310706i	$0.990108\pi$
$954$		0			0
$955$		−	0.0363101i		−	0.00117497i
$956$	−0.155629	+	0.368775i	−0.00503340	+	0.0119270i
$957$		0			0
$958$	−15.0784	+	10.0028i	−0.487161	+	0.323176i
$959$	−1.73490	+	3.00493i	−0.0560227	+	0.0970342i
$960$		0			0
$961$	−12.8892	−	22.3247i	−0.415779	−	0.720151i
$962$	55.6747	+	27.6859i	1.79502	+	0.892630i
$963$		0			0
$964$	−28.0645	−	37.0817i	−0.903897	−	1.19432i
$965$	2.07410	−	1.19748i	0.0667676	−	0.0385483i
$966$		0			0
$967$	12.4351	+	7.17941i	0.399886	+	0.230874i	0.686435	−	0.727191i	$-0.259175\pi$
$967$	12.4351	+	7.17941i	0.399886	+	0.230874i	−0.286549	+	0.958066i	$0.592508\pi$
$968$	11.0207	+	3.86387i	0.354218	+	0.124189i
$969$		0			0
$970$	15.3793	−	0.956736i	0.493800	−	0.0307189i
$971$	−13.2945			−0.426640			−0.213320	−	0.976982i	$-0.568428\pi$
$971$	−13.2945			−0.426640			−0.213320	+	0.976982i	$0.568428\pi$
$972$		0			0
$973$	15.8613			0.508491
$974$	13.8327	−	0.860521i	0.443228	−	0.0275729i
$975$		0			0
$976$	−7.13351	−	7.32558i	−0.228338	−	0.234486i
$977$	43.2952	+	24.9965i	1.38514	+	0.799709i	0.992762	−	0.120096i	$-0.0383202\pi$
$977$	43.2952	+	24.9965i	1.38514	+	0.799709i	0.392375	+	0.919805i	$0.371654\pi$
$978$		0			0
$979$	1.15444	−	0.666514i	0.0368959	−	0.0213019i
$980$	4.74337	−	3.58992i	0.151521	−	0.114676i
$981$		0			0
$982$	−37.5585	−	18.6771i	−1.19854	−	0.596010i
$983$	−26.0409	−	45.1042i	−0.830577	−	1.43860i	−0.897582	−	0.440848i	$-0.854678\pi$
$983$	−26.0409	−	45.1042i	−0.830577	−	1.43860i	0.0670049	−	0.997753i	$-0.478656\pi$
$984$		0			0
$985$	9.78902	−	16.9551i	0.311904	−	0.540234i
$986$	−14.7762	+	9.80232i	−0.470570	+	0.312169i
$987$		0			0
$988$	39.3033	+	16.5866i	1.25041	+	0.527691i
$989$			8.06071i			0.256316i
$990$		0			0
$991$		−	27.0227i		−	0.858403i	−0.903209	−	0.429202i	$-0.858795\pi$
$991$		−	27.0227i		−	0.858403i	0.903209	−	0.429202i	$-0.141205\pi$
$992$	2.73197	−	12.6345i	0.0867400	−	0.401145i
$993$		0			0
$994$	12.3848	+	18.6691i	0.392822	+	0.592148i
$995$	−6.74671	+	11.6856i	−0.213885	+	0.370460i
$996$		0			0
$997$	5.18646	+	8.98321i	0.164257	+	0.284501i	0.936391	−	0.350958i	$-0.114144\pi$
$997$	5.18646	+	8.98321i	0.164257	+	0.284501i	−0.772134	+	0.635459i	$0.780811\pi$
$998$	2.61132	−	5.25121i	0.0826600	−	0.166224i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ba.a.71.17		72
3.2	odd	2		252.2.ba.a.239.20	yes	72
4.3	odd	2	inner	756.2.ba.a.71.29		72
9.2	odd	6	inner	756.2.ba.a.575.29		72
9.7	even	3		252.2.ba.a.155.8	✓	72
12.11	even	2		252.2.ba.a.239.8	yes	72
36.7	odd	6		252.2.ba.a.155.20	yes	72
36.11	even	6	inner	756.2.ba.a.575.17		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.8	✓	72	9.7	even	3
252.2.ba.a.155.20	yes	72	36.7	odd	6
252.2.ba.a.239.8	yes	72	12.11	even	2
252.2.ba.a.239.20	yes	72	3.2	odd	2
756.2.ba.a.71.17		72	1.1	even	1	trivial
756.2.ba.a.71.29		72	4.3	odd	2	inner
756.2.ba.a.575.17		72	36.11	even	6	inner
756.2.ba.a.575.29		72	9.2	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.ba (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0878075 - 1.41148i) q^{2} +(-1.98458 + 0.247878i) q^{4} +(-2.57586 - 1.48718i) q^{5} +(0.866025 - 0.500000i) q^{7} +(0.524137 + 2.77944i) q^{8} +O(q^{10})\)	\(q+(-0.0878075 - 1.41148i) q^{2} +(-1.98458 + 0.247878i) q^{4} +(-2.57586 - 1.48718i) q^{5} +(0.866025 - 0.500000i) q^{7} +(0.524137 + 2.77944i) q^{8} +(-1.87295 + 3.76638i) q^{10} +(-1.31064 - 2.27009i) q^{11} +(-3.13567 + 5.43114i) q^{13} +(-0.781786 - 1.17848i) q^{14} +(3.87711 - 0.983867i) q^{16} +1.35655i q^{17} +3.40118i q^{19} +(5.48065 + 2.31292i) q^{20} +(-3.08911 + 2.04927i) q^{22} +(1.92084 - 3.32699i) q^{23} +(1.92339 + 3.33140i) q^{25} +(7.94130 + 3.94905i) q^{26} +(-1.59476 + 1.20696i) q^{28} +(-8.00451 + 4.62140i) q^{29} +(1.97895 + 1.14255i) q^{31} +(-1.72915 - 5.38610i) q^{32} +(1.91476 - 0.119116i) q^{34} -2.97435 q^{35} +7.01077 q^{37} +(4.80072 - 0.298649i) q^{38} +(2.78341 - 7.93894i) q^{40} +(7.13684 + 4.12046i) q^{41} +(-1.81712 + 1.04911i) q^{43} +(3.16377 + 4.18029i) q^{44} +(-4.86466 - 2.41910i) q^{46} +(3.82740 + 6.62925i) q^{47} +(0.500000 - 0.866025i) q^{49} +(4.53334 - 3.00735i) q^{50} +(4.87672 - 11.5558i) q^{52} +8.40500i q^{53} +7.79659i q^{55} +(1.84364 + 2.14500i) q^{56} +(7.22590 + 10.8924i) q^{58} +(-3.37021 + 5.83738i) q^{59} +(-1.27813 - 2.21378i) q^{61} +(1.43892 - 2.89359i) q^{62} +(-7.45056 + 2.91361i) q^{64} +(16.1541 - 9.32658i) q^{65} +(1.00605 + 0.580841i) q^{67} +(-0.336260 - 2.69219i) q^{68} +(0.261170 + 4.19825i) q^{70} -15.8417 q^{71} -4.03393 q^{73} +(-0.615599 - 9.89560i) q^{74} +(-0.843078 - 6.74991i) q^{76} +(-2.27009 - 1.31064i) q^{77} +(-9.28946 + 5.36327i) q^{79} +(-11.4501 - 3.23164i) q^{80} +(5.18930 - 10.4354i) q^{82} +(-2.19903 - 3.80883i) q^{83} +(2.01743 - 3.49430i) q^{85} +(1.64036 + 2.47271i) q^{86} +(5.62262 - 4.83267i) q^{88} +0.508542i q^{89} +6.27134i q^{91} +(-2.98737 + 7.07881i) q^{92} +(9.02101 - 5.98442i) q^{94} +(5.05815 - 8.76098i) q^{95} +(-1.83163 - 3.17248i) q^{97} +(-1.26629 - 0.629699i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97}+O(q^{100}) \) 72 * q + 42 * q^20 + 36 * q^25 - 30 * q^32 - 12 * q^34 - 12 * q^40 + 60 * q^41 - 24 * q^46 + 36 * q^49 + 78 * q^50 - 18 * q^52 - 18 * q^58 - 60 * q^64 - 24 * q^65 - 78 * q^68 - 24 * q^73 + 12 * q^76 - 36 * q^82 - 30 * q^86 + 24 * q^88 + 114 * q^92 + 42 * q^94 - 12 * q^97

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