LMFDB - Embedded newform 672.2.bd.a.431.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(431,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("672.431");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bd (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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			431.20
Character	$\chi$	$=$	672.431
Dual form			672.2.bd.a.527.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.987527 + 1.42295i) q^{3} +(1.77783 + 3.07929i) q^{5} +(-0.793456 - 2.52397i) q^{7} +(-1.04958 + 2.81041i) q^{9} +(0.396703 + 0.229036i) q^{11} -0.799063i q^{13} +(-2.62603 + 5.57065i) q^{15} +(5.48456 + 3.16651i) q^{17} +(2.61696 + 4.53272i) q^{19} +(2.80793 - 3.62154i) q^{21} +(-1.55053 - 2.68559i) q^{23} +(-3.82137 + 6.61880i) q^{25} +(-5.03556 + 1.28185i) q^{27} -2.60340 q^{29} +(-4.42520 - 2.55489i) q^{31} +(0.0658472 + 0.790668i) q^{33} +(6.36142 - 6.93048i) q^{35} +(-2.89424 + 1.67099i) q^{37} +(1.13703 - 0.789096i) q^{39} -10.1452i q^{41} -3.56359 q^{43} +(-10.5200 + 1.76446i) q^{45} +(2.15923 + 3.73989i) q^{47} +(-5.74086 + 4.00532i) q^{49} +(0.910362 + 10.9313i) q^{51} +(1.16913 - 2.02499i) q^{53} +1.62875i q^{55} +(-3.86551 + 8.19999i) q^{57} +(1.49741 + 0.864528i) q^{59} +(4.60841 - 2.66067i) q^{61} +(7.92618 + 0.419175i) q^{63} +(2.46055 - 1.42060i) q^{65} +(-0.00979145 + 0.0169593i) q^{67} +(2.29028 - 4.85842i) q^{69} +9.04022 q^{71} +(4.15674 - 7.19969i) q^{73} +(-13.1919 + 1.09863i) q^{75} +(0.263315 - 1.18300i) q^{77} +(10.8825 - 6.28304i) q^{79} +(-6.79677 - 5.89949i) q^{81} +0.694004i q^{83} +22.5181i q^{85} +(-2.57093 - 3.70452i) q^{87} +(7.02189 - 4.05409i) q^{89} +(-2.01681 + 0.634021i) q^{91} +(-0.734523 - 8.81987i) q^{93} +(-9.30504 + 16.1168i) q^{95} +7.05333 q^{97} +(-1.06006 + 0.874504i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{3} - 2 q^{9} + 4 q^{19} - 16 q^{25} + 8 q^{27} - 14 q^{33} + 16 q^{43} - 16 q^{49} + 34 q^{51} + 4 q^{57} + 36 q^{67} + 4 q^{73} - 10 q^{81} - 72 q^{91} - 32 q^{97} + 44 q^{99}+O(q^{100}) $ 56 * q + 2 * q^3 - 2 * q^9 + 4 * q^19 - 16 * q^25 + 8 * q^27 - 14 * q^33 + 16 * q^43 - 16 * q^49 + 34 * q^51 + 4 * q^57 + 36 * q^67 + 4 * q^73 - 10 * q^81 - 72 * q^91 - 32 * q^97 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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
$3$	0.987527	+	1.42295i	0.570149	+	0.821541i
$3$	0.987527	+	1.42295i	0.570149	+	0.821541i
$4$		0			0
$5$	1.77783	+	3.07929i	0.795070	+	1.37710i	0.922795	+	0.385292i	$0.125899\pi$
$5$	1.77783	+	3.07929i	0.795070	+	1.37710i	−0.127724	+	0.991810i	$0.540767\pi$
$6$		0			0
$7$	−0.793456	−	2.52397i	−0.299898	−	0.953971i
$7$	−0.793456	−	2.52397i	−0.299898	−	0.953971i
$8$		0			0
$9$	−1.04958	+	2.81041i	−0.349860	+	0.936802i
$10$		0			0
$11$	0.396703	+	0.229036i	0.119610	+	0.0690571i	0.558612	−	0.829429i	$-0.311334\pi$
$11$	0.396703	+	0.229036i	0.119610	+	0.0690571i	−0.439001	+	0.898486i	$0.644668\pi$
$12$		0			0
$13$		−	0.799063i		−	0.221620i	−0.993842	−	0.110810i	$-0.964655\pi$
$13$		−	0.799063i		−	0.221620i	0.993842	−	0.110810i	$-0.0353445\pi$
$14$		0			0
$15$	−2.62603	+	5.57065i	−0.678037	+	1.43834i
$16$		0			0
$17$	5.48456	+	3.16651i	1.33020	+	0.767993i	0.985330	−	0.170657i	$-0.0545891\pi$
$17$	5.48456	+	3.16651i	1.33020	+	0.767993i	0.344872	+	0.938650i	$0.387922\pi$
$18$		0			0
$19$	2.61696	+	4.53272i	0.600373	+	1.03988i	0.992764	+	0.120078i	$0.0383145\pi$
$19$	2.61696	+	4.53272i	0.600373	+	1.03988i	−0.392392	+	0.919798i	$0.628352\pi$
$20$		0			0
$21$	2.80793	−	3.62154i	0.612740	−	0.790285i
$22$		0			0
$23$	−1.55053	−	2.68559i	−0.323307	−	0.559985i	0.657861	−	0.753139i	$-0.271461\pi$
$23$	−1.55053	−	2.68559i	−0.323307	−	0.559985i	−0.981168	+	0.193155i	$0.938128\pi$
$24$		0			0
$25$	−3.82137	+	6.61880i	−0.764273	+	1.32376i
$26$		0			0
$27$	−5.03556	+	1.28185i	−0.969094	+	0.246693i
$28$		0			0
$29$	−2.60340			−0.483440			−0.241720	−	0.970346i	$-0.577712\pi$
$29$	−2.60340			−0.483440			−0.241720	+	0.970346i	$0.577712\pi$
$30$		0			0
$31$	−4.42520	−	2.55489i	−0.794790	−	0.458872i	0.0468563	−	0.998902i	$-0.485080\pi$
$31$	−4.42520	−	2.55489i	−0.794790	−	0.458872i	−0.841646	+	0.540030i	$0.818413\pi$
$32$		0			0
$33$	0.0658472	+	0.790668i	0.0114625	+	0.137638i
$34$		0			0
$35$	6.36142	−	6.93048i	1.07528	−	1.17146i
$36$		0			0
$37$	−2.89424	+	1.67099i	−0.475810	+	0.274709i	−0.718669	−	0.695352i	$-0.755248\pi$
$37$	−2.89424	+	1.67099i	−0.475810	+	0.274709i	0.242859	+	0.970062i	$0.421915\pi$
$38$		0			0
$39$	1.13703	−	0.789096i	0.182070	−	0.126357i
$40$		0			0
$41$		−	10.1452i		−	1.58441i	−0.610256	−	0.792205i	$-0.708933\pi$
$41$		−	10.1452i		−	1.58441i	0.610256	−	0.792205i	$-0.291067\pi$
$42$		0			0
$43$	−3.56359			−0.543442			−0.271721	−	0.962376i	$-0.587593\pi$
$43$	−3.56359			−0.543442			−0.271721	+	0.962376i	$0.587593\pi$
$44$		0			0
$45$	−10.5200	+	1.76446i	−1.56824	+	0.263031i
$46$		0			0
$47$	2.15923	+	3.73989i	0.314956	+	0.545519i	0.979428	−	0.201794i	$-0.0646770\pi$
$47$	2.15923	+	3.73989i	0.314956	+	0.545519i	−0.664472	+	0.747313i	$0.731344\pi$
$48$		0			0
$49$	−5.74086	+	4.00532i	−0.820122	+	0.572188i
$50$		0			0
$51$	0.910362	+	10.9313i	0.127476	+	1.53069i
$52$		0			0
$53$	1.16913	−	2.02499i	0.160592	−	0.278154i	−0.774489	−	0.632587i	$-0.781993\pi$
$53$	1.16913	−	2.02499i	0.160592	−	0.278154i	0.935081	+	0.354433i	$0.115326\pi$
$54$		0			0
$55$			1.62875i			0.219621i
$56$		0			0
$57$	−3.86551	+	8.19999i	−0.511999	+	1.08612i
$58$		0			0
$59$	1.49741	+	0.864528i	0.194946	+	0.112552i	0.594296	−	0.804247i	$-0.297431\pi$
$59$	1.49741	+	0.864528i	0.194946	+	0.112552i	−0.399350	+	0.916798i	$0.630764\pi$
$60$		0			0
$61$	4.60841	−	2.66067i	0.590047	−	0.340664i	−0.175069	−	0.984556i	$-0.556015\pi$
$61$	4.60841	−	2.66067i	0.590047	−	0.340664i	0.765116	+	0.643892i	$0.222682\pi$
$62$		0			0
$63$	7.92618	+	0.419175i	0.998605	+	0.0528111i
$64$		0			0
$65$	2.46055	−	1.42060i	0.305193	−	0.176204i
$66$		0			0
$67$	−0.00979145	+	0.0169593i	−0.00119622	+	0.00207191i	−0.866623	−	0.498964i	$-0.833714\pi$
$67$	−0.00979145	+	0.0169593i	−0.00119622	+	0.00207191i	0.865427	+	0.501036i	$0.167047\pi$
$68$		0			0
$69$	2.29028	−	4.85842i	0.275717	−	0.584885i
$70$		0			0
$71$	9.04022			1.07288			0.536439	−	0.843939i	$-0.319769\pi$
$71$	9.04022			1.07288			0.536439	+	0.843939i	$0.319769\pi$
$72$		0			0
$73$	4.15674	−	7.19969i	0.486510	−	0.842660i	−0.513370	−	0.858167i	$-0.671603\pi$
$73$	4.15674	−	7.19969i	0.486510	−	0.842660i	0.999880	+	0.0155078i	$0.00493650\pi$
$74$		0			0
$75$	−13.1919	+	1.09863i	−1.52327	+	0.126859i
$76$		0			0
$77$	0.263315	−	1.18300i	0.0300076	−	0.134815i
$78$		0			0
$79$	10.8825	−	6.28304i	1.22438	−	0.706897i	0.258533	−	0.966003i	$-0.416761\pi$
$79$	10.8825	−	6.28304i	1.22438	−	0.706897i	0.965849	+	0.259105i	$0.0834277\pi$
$80$		0			0
$81$	−6.79677	−	5.89949i	−0.755196	−	0.655499i
$82$		0			0
$83$			0.694004i			0.0761768i	0.999274	+	0.0380884i	$0.0121268\pi$
$83$			0.694004i			0.0761768i	−0.999274	+	0.0380884i	$0.987873\pi$
$84$		0			0
$85$			22.5181i			2.44243i
$86$		0			0
$87$	−2.57093	−	3.70452i	−0.275633	−	0.397166i
$88$		0			0
$89$	7.02189	−	4.05409i	0.744319	−	0.429733i	−0.0793185	−	0.996849i	$-0.525274\pi$
$89$	7.02189	−	4.05409i	0.744319	−	0.429733i	0.823638	+	0.567116i	$0.191941\pi$
$90$		0			0
$91$	−2.01681	+	0.634021i	−0.211419	+	0.0664634i
$92$		0			0
$93$	−0.734523	−	8.81987i	−0.0761664	−	0.914578i
$94$		0			0
$95$	−9.30504	+	16.1168i	−0.954677	+	1.65355i
$96$		0			0
$97$	7.05333			0.716157			0.358078	−	0.933692i	$-0.383432\pi$
$97$	7.05333			0.716157			0.358078	+	0.933692i	$0.383432\pi$
$98$		0			0
$99$	−1.06006	+	0.874504i	−0.106540	+	0.0878909i
$100$		0			0
$101$	3.34348	−	5.79108i	0.332689	−	0.576234i	−0.650349	−	0.759635i	$-0.725378\pi$
$101$	3.34348	−	5.79108i	0.332689	−	0.576234i	0.983038	+	0.183402i	$0.0587108\pi$
$102$		0			0
$103$	−5.48751	+	3.16822i	−0.540701	+	0.312174i	−0.745363	−	0.666659i	$-0.767724\pi$
$103$	−5.48751	+	3.16822i	−0.540701	+	0.312174i	0.204662	+	0.978833i	$0.434390\pi$
$104$		0			0
$105$	16.1438	+	2.20795i	1.57547	+	0.215474i
$106$		0			0
$107$	3.09681	−	1.78795i	0.299380	−	0.172847i	−0.342784	−	0.939414i	$-0.611370\pi$
$107$	3.09681	−	1.78795i	0.299380	−	0.172847i	0.642164	+	0.766567i	$0.278037\pi$
$108$		0			0
$109$	0.488061	+	0.281782i	0.0467478	+	0.0269899i	0.523192	−	0.852215i	$-0.324741\pi$
$109$	0.488061	+	0.281782i	0.0467478	+	0.0269899i	−0.476444	+	0.879205i	$0.658074\pi$
$110$		0			0
$111$	−5.23588	−	2.46821i	−0.496968	−	0.234273i
$112$		0			0
$113$			1.41462i			0.133076i	0.997784	+	0.0665381i	$0.0211954\pi$
$113$			1.41462i			0.133076i	−0.997784	+	0.0665381i	$0.978805\pi$
$114$		0			0
$115$	5.51315	−	9.54906i	0.514104	−	0.890454i
$116$		0			0
$117$	2.24569	+	0.838680i	0.207614	+	0.0775360i
$118$		0			0
$119$	3.64043	−	16.3554i	0.333718	−	1.49929i
$120$		0			0
$121$	−5.39508	−	9.34456i	−0.490462	−	0.849506i
$122$		0			0
$123$	14.4361	−	10.0186i	1.30166	−	0.903350i
$124$		0			0
$125$	−9.39666			−0.840463
$126$		0			0
$127$			15.7043i			1.39353i	0.717299	+	0.696766i	$0.245378\pi$
$127$			15.7043i			1.39353i	−0.717299	+	0.696766i	$0.754622\pi$
$128$		0			0
$129$	−3.51914	−	5.07081i	−0.309843	−	0.446460i
$130$		0			0
$131$	−1.16617	+	0.673290i	−0.101889	+	0.0588256i	−0.550079	−	0.835113i	$-0.685402\pi$
$131$	−1.16617	+	0.673290i	−0.101889	+	0.0588256i	0.448190	+	0.893938i	$0.352069\pi$
$132$		0			0
$133$	9.36400	−	10.2016i	0.811961	−	0.884595i
$134$		0			0
$135$	−12.8996	−	13.2270i	−1.11022	−	1.13840i
$136$		0			0
$137$	−7.79136	−	4.49834i	−0.665661	−	0.384320i	0.128770	−	0.991675i	$-0.458897\pi$
$137$	−7.79136	−	4.49834i	−0.665661	−	0.384320i	−0.794431	+	0.607355i	$0.792231\pi$
$138$		0			0
$139$	16.0176			1.35859			0.679296	−	0.733864i	$-0.262285\pi$
$139$	16.0176			1.35859			0.679296	+	0.733864i	$0.262285\pi$
$140$		0			0
$141$	−3.18939	+	6.76572i	−0.268595	+	0.569777i
$142$		0			0
$143$	0.183014	−	0.316990i	0.0153044	−	0.0265081i
$144$		0			0
$145$	−4.62841	−	8.01664i	−0.384369	−	0.665746i
$146$		0			0
$147$	−11.3686	−	4.21360i	−0.937668	−	0.347532i
$148$		0			0
$149$	3.34348	+	5.79108i	0.273909	+	0.474424i	0.969859	−	0.243666i	$-0.0783501\pi$
$149$	3.34348	+	5.79108i	0.273909	+	0.474424i	−0.695951	+	0.718090i	$0.745017\pi$
$150$		0			0
$151$	−3.66278	−	2.11471i	−0.298073	−	0.172093i	0.343504	−	0.939151i	$-0.388386\pi$
$151$	−3.66278	−	2.11471i	−0.298073	−	0.172093i	−0.641577	+	0.767059i	$0.721719\pi$
$152$		0			0
$153$	−14.6557	+	12.0903i	−1.18484	+	0.977446i
$154$		0			0
$155$		−	18.1687i		−	1.45934i
$156$		0			0
$157$	−19.9382	−	11.5113i	−1.59124	−	0.918702i	−0.993095	−	0.117313i	$-0.962572\pi$
$157$	−19.9382	−	11.5113i	−1.59124	−	0.918702i	−0.598144	−	0.801389i	$-0.704095\pi$
$158$		0			0
$159$	4.03601	−	0.336121i	0.320077	−	0.0266561i
$160$		0			0
$161$	−5.54808	+	6.04438i	−0.437250	+	0.476364i
$162$		0			0
$163$	−10.4009	−	18.0148i	−0.814658	−	1.41103i	−0.909573	−	0.415544i	$-0.863591\pi$
$163$	−10.4009	−	18.0148i	−0.814658	−	1.41103i	0.0949145	−	0.995485i	$-0.469742\pi$
$164$		0			0
$165$	−2.31763	+	1.60844i	−0.180428	+	0.125217i
$166$		0			0
$167$	−7.53905			−0.583390			−0.291695	−	0.956511i	$-0.594219\pi$
$167$	−7.53905			−0.583390			−0.291695	+	0.956511i	$0.594219\pi$
$168$		0			0
$169$	12.3615			0.950885
$170$		0			0
$171$	−15.4855	+	2.59729i	−1.18420	+	0.198620i
$172$		0			0
$173$	7.77603	+	13.4685i	0.591201	+	1.02399i	0.994071	+	0.108733i	$0.0346793\pi$
$173$	7.77603	+	13.4685i	0.591201	+	1.02399i	−0.402870	+	0.915257i	$0.631987\pi$
$174$		0			0
$175$	19.7377	+	4.39329i	1.49203	+	0.332102i
$176$		0			0
$177$	0.248549	+	2.98448i	0.0186821	+	0.224327i
$178$		0			0
$179$	7.81218	+	4.51037i	0.583910	+	0.337121i	0.762686	−	0.646769i	$-0.223880\pi$
$179$	7.81218	+	4.51037i	0.583910	+	0.337121i	−0.178776	+	0.983890i	$0.557214\pi$
$180$		0			0
$181$		−	10.4041i		−	0.773330i	−0.922220	−	0.386665i	$-0.873627\pi$
$181$		−	10.4041i		−	0.773330i	0.922220	−	0.386665i	$-0.126373\pi$
$182$		0			0
$183$	8.33693	+	3.93006i	0.616284	+	0.290519i
$184$		0			0
$185$	−10.2909	−	5.94148i	−0.756605	−	0.436826i
$186$		0			0
$187$	1.45049	+	2.51233i	0.106071	+	0.183720i
$188$		0			0
$189$	7.23085	+	11.6925i	0.525967	+	0.850505i
$190$		0			0
$191$	7.33838	+	12.7104i	0.530986	+	0.919695i	0.999346	+	0.0361574i	$0.0115118\pi$
$191$	7.33838	+	12.7104i	0.530986	+	0.919695i	−0.468360	+	0.883538i	$0.655155\pi$
$192$		0			0
$193$	8.06569	−	13.9702i	0.580581	−	1.00560i	−0.414829	−	0.909899i	$-0.636159\pi$
$193$	8.06569	−	13.9702i	0.580581	−	1.00560i	0.995411	−	0.0956969i	$-0.0305080\pi$
$194$		0			0
$195$	4.45130	+	2.09836i	0.318764	+	0.150267i
$196$		0			0
$197$	21.9480			1.56373			0.781863	−	0.623450i	$-0.214269\pi$
$197$	21.9480			1.56373			0.781863	+	0.623450i	$0.214269\pi$
$198$		0			0
$199$	−13.8171	−	7.97732i	−0.979470	−	0.565497i	−0.0773599	−	0.997003i	$-0.524649\pi$
$199$	−13.8171	−	7.97732i	−0.979470	−	0.565497i	−0.902110	+	0.431506i	$0.857982\pi$
$200$		0			0
$201$	−0.0338016	+	0.00281501i	−0.00238418	+	0.000198555i
$202$		0			0
$203$	2.06568	+	6.57091i	0.144983	+	0.461188i
$204$		0			0
$205$	31.2400	−	18.0364i	2.18189	−	1.25972i
$206$		0			0
$207$	9.17500	−	1.53887i	0.637707	−	0.106959i
$208$		0			0
$209$			2.39752i			0.165840i
$210$		0			0
$211$	−20.9923			−1.44517			−0.722586	−	0.691281i	$-0.757047\pi$
$211$	−20.9923			−1.44517			−0.722586	+	0.691281i	$0.757047\pi$
$212$		0			0
$213$	8.92747	+	12.8638i	0.611700	+	0.881413i
$214$		0			0
$215$	−6.33546	−	10.9733i	−0.432074	−	0.748375i
$216$		0			0
$217$	−2.93727	+	13.1963i	−0.199395	+	0.895821i
$218$		0			0
$219$	14.3497	−	1.19505i	0.969663	−	0.0807539i
$220$		0			0
$221$	2.53024	−	4.38251i	0.170203	−	0.294800i
$222$		0			0
$223$		−	7.05072i		−	0.472151i	−0.971735	−	0.236075i	$-0.924139\pi$
$223$		−	7.05072i		−	0.472151i	0.971735	−	0.236075i	$-0.0758613\pi$
$224$		0			0
$225$	−14.5907	−	17.6865i	−0.972713	−	1.17910i
$226$		0			0
$227$	−17.9681	−	10.3739i	−1.19258	−	0.688539i	−0.233693	−	0.972310i	$-0.575081\pi$
$227$	−17.9681	−	10.3739i	−1.19258	−	0.688539i	−0.958892	+	0.283771i	$0.908414\pi$
$228$		0			0
$229$	−19.0453	+	10.9958i	−1.25855	+	0.726623i	−0.972792	−	0.231680i	$-0.925578\pi$
$229$	−19.0453	+	10.9958i	−1.25855	+	0.726623i	−0.285756	+	0.958302i	$0.592245\pi$
$230$		0			0
$231$	1.94338	−	0.793556i	0.127865	−	0.0522122i
$232$		0			0
$233$	15.1401	−	8.74112i	0.991858	−	0.572650i	0.0860289	−	0.996293i	$-0.472582\pi$
$233$	15.1401	−	8.74112i	0.991858	−	0.572650i	0.905829	+	0.423643i	$0.139249\pi$
$234$		0			0
$235$	−7.67748	+	13.2978i	−0.500824	+	0.867452i
$236$		0			0
$237$	19.6873	+	9.28065i	1.27883	+	0.602843i
$238$		0			0
$239$	6.60546			0.427271			0.213636	−	0.976913i	$-0.431469\pi$
$239$	6.60546			0.427271			0.213636	+	0.976913i	$0.431469\pi$
$240$		0			0
$241$	−5.27959	+	9.14453i	−0.340089	+	0.589051i	−0.984449	−	0.175671i	$-0.943790\pi$
$241$	−5.27959	+	9.14453i	−0.340089	+	0.589051i	0.644360	+	0.764722i	$0.277124\pi$
$242$		0			0
$243$	1.68269	−	15.4974i	0.107945	−	0.994157i
$244$		0			0
$245$	−22.5398	−	10.5570i	−1.44002	−	0.674462i
$246$		0			0
$247$	3.62192	−	2.09112i	0.230457	−	0.133055i
$248$		0			0
$249$	−0.987533	+	0.685347i	−0.0625824	+	0.0434321i
$250$		0			0
$251$			6.66647i			0.420784i	0.977617	+	0.210392i	$0.0674741\pi$
$251$			6.66647i			0.420784i	−0.977617	+	0.210392i	$0.932526\pi$
$252$		0			0
$253$		−	1.42051i		−	0.0893066i
$254$		0			0
$255$	−32.0422	+	22.2373i	−2.00656	+	1.39255i
$256$		0			0
$257$	−0.887844	+	0.512597i	−0.0553822	+	0.0319749i	−0.527435	−	0.849595i	$-0.676846\pi$
$257$	−0.887844	+	0.512597i	−0.0553822	+	0.0319749i	0.472053	+	0.881570i	$0.343513\pi$
$258$		0			0
$259$	6.51398	+	5.97912i	0.404759	+	0.371525i
$260$		0			0
$261$	2.73248	−	7.31662i	0.169136	−	0.452887i
$262$		0			0
$263$	8.60208	−	14.8992i	0.530427	−	0.918726i	−0.468943	−	0.883228i	$-0.655365\pi$
$263$	8.60208	−	14.8992i	0.530427	−	0.918726i	0.999370	−	0.0354978i	$-0.0113017\pi$
$264$		0			0
$265$	8.31406			0.510729
$266$		0			0
$267$	12.7031	+	5.98828i	0.777416	+	0.366477i
$268$		0			0
$269$	−3.92637	+	6.80068i	−0.239395	+	0.414644i	−0.960541	−	0.278139i	$-0.910282\pi$
$269$	−3.92637	+	6.80068i	−0.239395	+	0.414644i	0.721146	+	0.692783i	$0.243616\pi$
$270$		0			0
$271$	−15.7096	+	9.06993i	−0.954289	+	0.550959i	−0.894411	−	0.447247i	$-0.852405\pi$
$271$	−15.7096	+	9.06993i	−0.954289	+	0.550959i	−0.0598783	+	0.998206i	$0.519071\pi$
$272$		0			0
$273$	−2.89384	−	2.24371i	−0.175143	−	0.135796i
$274$		0			0
$275$	−3.03189	+	1.75046i	−0.182830	+	0.105557i
$276$		0			0
$277$	−19.2898	−	11.1370i	−1.15901	−	0.669157i	−0.207946	−	0.978140i	$-0.566678\pi$
$277$	−19.2898	−	11.1370i	−1.15901	−	0.669157i	−0.951067	+	0.308983i	$0.900011\pi$
$278$		0			0
$279$	11.8249	−	9.75505i	0.707937	−	0.584020i
$280$		0			0
$281$			17.9109i			1.06847i	0.845335	+	0.534236i	$0.179401\pi$
$281$			17.9109i			1.06847i	−0.845335	+	0.534236i	$0.820599\pi$
$282$		0			0
$283$	2.24283	−	3.88469i	0.133322	−	0.230921i	−0.791633	−	0.610997i	$-0.790769\pi$
$283$	2.24283	−	3.88469i	0.133322	−	0.230921i	0.924955	+	0.380076i	$0.124102\pi$
$284$		0			0
$285$	−32.1224	+	2.67517i	−1.90277	+	0.158463i
$286$		0			0
$287$	−25.6061	+	8.04974i	−1.51148	+	0.475161i
$288$		0			0
$289$	11.5536	+	20.0115i	0.679625	+	1.17715i
$290$		0			0
$291$	6.96535	+	10.0365i	0.408316	+	0.588352i
$292$		0			0
$293$	−24.7711			−1.44714			−0.723570	−	0.690251i	$-0.757500\pi$
$293$	−24.7711			−1.44714			−0.723570	+	0.690251i	$0.757500\pi$
$294$		0			0
$295$			6.14794i			0.357947i
$296$		0			0
$297$	−2.29121	−	0.644812i	−0.132950	−	0.0374158i
$298$		0			0
$299$	−2.14596	+	1.23897i	−0.124104	+	0.0716514i
$300$		0			0
$301$	2.82755	+	8.99439i	0.162977	+	0.518428i
$302$		0			0
$303$	11.5422	−	0.961239i	0.663082	−	0.0552217i
$304$		0			0
$305$	16.3860	+	9.46044i	0.938257	+	0.541703i
$306$		0			0
$307$	−7.72188			−0.440711			−0.220355	−	0.975420i	$-0.570722\pi$
$307$	−7.72188			−0.440711			−0.220355	+	0.975420i	$0.570722\pi$
$308$		0			0
$309$	−9.92729	−	4.67976i	−0.564744	−	0.266222i
$310$		0			0
$311$	10.0093	−	17.3367i	0.567577	−	0.983072i	−0.429228	−	0.903196i	$-0.641214\pi$
$311$	10.0093	−	17.3367i	0.567577	−	0.983072i	0.996805	−	0.0798757i	$-0.0254523\pi$
$312$		0			0
$313$	−8.54501	−	14.8004i	−0.482993	−	0.836568i	0.516817	−	0.856096i	$-0.327117\pi$
$313$	−8.54501	−	14.8004i	−0.482993	−	0.836568i	−0.999809	+	0.0195284i	$0.993784\pi$
$314$		0			0
$315$	12.8006	+	25.1523i	0.721234	+	1.41717i
$316$		0			0
$317$	−7.67062	−	13.2859i	−0.430825	−	0.746210i	0.566120	−	0.824323i	$-0.308444\pi$
$317$	−7.67062	−	13.2859i	−0.430825	−	0.746210i	−0.996945	+	0.0781127i	$0.975111\pi$
$318$		0			0
$319$	−1.03278	−	0.596274i	−0.0578244	−	0.0333849i
$320$		0			0
$321$	5.60235	+	2.64097i	0.312693	+	0.147405i
$322$		0			0
$323$			33.1466i			1.84433i
$324$		0			0
$325$	5.28884	+	3.05351i	0.293372	+	0.169378i
$326$		0			0
$327$	0.0810115	+	0.972755i	0.00447994	+	0.0537935i
$328$		0			0
$329$	7.72613	−	8.41727i	0.425955	−	0.464059i
$330$		0			0
$331$	6.86143	+	11.8844i	0.377138	+	0.653223i	0.990645	−	0.136467i	$-0.0435748\pi$
$331$	6.86143	+	11.8844i	0.377138	+	0.653223i	−0.613506	+	0.789690i	$0.710241\pi$
$332$		0			0
$333$	−1.65843	−	9.88783i	−0.0908813	−	0.541850i
$334$		0			0
$335$	−0.0696302			−0.00380430
$336$		0			0
$337$	−15.7338			−0.857074			−0.428537	−	0.903524i	$-0.640971\pi$
$337$	−15.7338			−0.857074			−0.428537	+	0.903524i	$0.640971\pi$
$338$		0			0
$339$	−2.01293	+	1.39698i	−0.109328	+	0.0758733i
$340$		0			0
$341$	−1.17033	−	2.02706i	−0.0633767	−	0.109772i
$342$		0			0
$343$	14.6644	+	11.3117i	0.791804	+	0.610775i
$344$		0			0
$345$	19.0322	−	1.58501i	1.02466	−	0.0853342i
$346$		0			0
$347$	−18.5301	−	10.6984i	−0.994748	−	0.574318i	−0.0880576	−	0.996115i	$-0.528066\pi$
$347$	−18.5301	−	10.6984i	−0.994748	−	0.574318i	−0.906690	+	0.421798i	$0.861399\pi$
$348$		0			0
$349$			15.7266i			0.841826i	0.907101	+	0.420913i	$0.138290\pi$
$349$			15.7266i			0.841826i	−0.907101	+	0.420913i	$0.861710\pi$
$350$		0			0
$351$	1.02428	+	4.02373i	0.0546721	+	0.214771i
$352$		0			0
$353$	10.1824	+	5.87883i	0.541956	+	0.312898i	0.745871	−	0.666090i	$-0.232033\pi$
$353$	10.1824	+	5.87883i	0.541956	+	0.312898i	−0.203915	+	0.978989i	$0.565367\pi$
$354$		0			0
$355$	16.0720	+	27.8375i	0.853013	+	1.47746i
$356$		0			0
$357$	26.8679	−	10.9712i	1.42200	−	0.580658i
$358$		0			0
$359$	10.2639	+	17.7776i	0.541709	+	0.938268i	0.998806	+	0.0488509i	$0.0155559\pi$
$359$	10.2639	+	17.7776i	0.541709	+	0.938268i	−0.457097	+	0.889417i	$0.651111\pi$
$360$		0			0
$361$	−4.19701	+	7.26943i	−0.220895	+	0.382601i
$362$		0			0
$363$	7.96906	−	16.9050i	0.418267	−	0.887280i
$364$		0			0
$365$	29.5599			1.54724
$366$		0			0
$367$	19.9290	+	11.5060i	1.04029	+	0.600609i	0.919914	−	0.392120i	$-0.128258\pi$
$367$	19.9290	+	11.5060i	1.04029	+	0.600609i	0.120372	+	0.992729i	$0.461591\pi$
$368$		0			0
$369$	28.5120	+	10.6482i	1.48428	+	0.554321i
$370$		0			0
$371$	−6.03867	−	1.34411i	−0.313512	−	0.0697826i
$372$		0			0
$373$	−21.6640	+	12.5077i	−1.12172	+	0.647624i	−0.941839	−	0.336065i	$-0.890904\pi$
$373$	−21.6640	+	12.5077i	−1.12172	+	0.647624i	−0.179878	+	0.983689i	$0.557570\pi$
$374$		0			0
$375$	−9.27946	−	13.3710i	−0.479189	−	0.690475i
$376$		0			0
$377$			2.08028i			0.107140i
$378$		0			0
$379$	11.7405			0.603071			0.301535	−	0.953455i	$-0.402501\pi$
$379$	11.7405			0.603071			0.301535	+	0.953455i	$0.402501\pi$
$380$		0			0
$381$	−22.3464	+	15.5084i	−1.14484	+	0.794521i
$382$		0			0
$383$	8.93250	+	15.4715i	0.456430	+	0.790559i	0.998769	−	0.0496002i	$-0.0157947\pi$
$383$	8.93250	+	15.4715i	0.456430	+	0.790559i	−0.542340	+	0.840159i	$0.682461\pi$
$384$		0			0
$385$	4.11092	−	1.29234i	0.209512	−	0.0658639i
$386$		0			0
$387$	3.74027	−	10.0151i	0.190128	−	0.509098i
$388$		0			0
$389$	−12.9460	+	22.4231i	−0.656386	+	1.13689i	0.325158	+	0.945660i	$0.394582\pi$
$389$	−12.9460	+	22.4231i	−0.656386	+	1.13689i	−0.981544	+	0.191235i	$0.938751\pi$
$390$		0			0
$391$		−	19.6391i		−	0.993190i
$392$		0			0
$393$	−2.10969	−	0.994514i	−0.106420	−	0.0501666i
$394$		0			0
$395$	38.6946	+	22.3404i	1.94694	+	1.12407i
$396$		0			0
$397$	17.5040	−	10.1060i	0.878502	−	0.507203i	0.00833784	−	0.999965i	$-0.497346\pi$
$397$	17.5040	−	10.1060i	0.878502	−	0.507203i	0.870164	+	0.492762i	$0.164013\pi$
$398$		0			0
$399$	23.7637	+	3.25010i	1.18967	+	0.162708i
$400$		0			0
$401$	−32.0937	+	18.5293i	−1.60268	+	0.925309i	−0.611735	+	0.791063i	$0.709528\pi$
$401$	−32.0937	+	18.5293i	−1.60268	+	0.925309i	−0.990948	+	0.134247i	$0.957139\pi$
$402$		0			0
$403$	−2.04152	+	3.53601i	−0.101695	+	0.176141i
$404$		0			0
$405$	6.08275	−	31.4175i	0.302255	−	1.56115i
$406$		0			0
$407$	−1.53087			−0.0758825
$408$		0			0
$409$	−14.5304	+	25.1675i	−0.718484	+	1.24445i	0.243117	+	0.969997i	$0.421830\pi$
$409$	−14.5304	+	25.1675i	−0.718484	+	1.24445i	−0.961600	+	0.274453i	$0.911503\pi$
$410$		0			0
$411$	−1.29326	−	15.5290i	−0.0637918	−	0.765987i
$412$		0			0
$413$	0.993917	−	4.46537i	0.0489075	−	0.219727i
$414$		0			0
$415$	−2.13704	+	1.23382i	−0.104903	+	0.0605659i
$416$		0			0
$417$	15.8178	+	22.7922i	0.774600	+	1.11614i
$418$		0			0
$419$		−	1.27248i		−	0.0621647i	−0.999517	−	0.0310823i	$-0.990105\pi$
$419$		−	1.27248i		−	0.0621647i	0.999517	−	0.0310823i	$-0.00989541\pi$
$420$		0			0
$421$			12.1006i			0.589749i	0.955536	+	0.294875i	$0.0952779\pi$
$421$			12.1006i			0.589749i	−0.955536	+	0.294875i	$0.904722\pi$
$422$		0			0
$423$	−12.7769	+	2.14299i	−0.621234	+	0.104196i
$424$		0			0
$425$	−41.9171	+	24.2008i	−2.03328	+	1.17391i
$426$		0			0
$427$	−10.3720	−	9.52038i	−0.501937	−	0.460723i
$428$		0			0
$429$	0.631793	−	0.0526160i	0.0305033	−	0.00254033i
$430$		0			0
$431$	−8.36354	+	14.4861i	−0.402858	+	0.697770i	−0.994070	−	0.108746i	$-0.965316\pi$
$431$	−8.36354	+	14.4861i	−0.402858	+	0.697770i	0.591212	+	0.806516i	$0.298650\pi$
$432$		0			0
$433$	−14.1708			−0.681007			−0.340503	−	0.940243i	$-0.610597\pi$
$433$	−14.1708			−0.681007			−0.340503	+	0.940243i	$0.610597\pi$
$434$		0			0
$435$	6.83661	−	14.5027i	0.327790	−	0.695349i
$436$		0			0
$437$	8.11535	−	14.0562i	0.388210	−	0.672399i
$438$		0			0
$439$	−22.3364	+	12.8959i	−1.06606	+	0.615489i	−0.927102	−	0.374809i	$-0.877708\pi$
$439$	−22.3364	+	12.8959i	−1.06606	+	0.615489i	−0.138957	+	0.990298i	$0.544375\pi$
$440$		0			0
$441$	−5.23108	−	20.3380i	−0.249099	−	0.968478i
$442$		0			0
$443$	−30.3993	+	17.5510i	−1.44431	+	0.833875i	−0.998134	−	0.0610673i	$-0.980550\pi$
$443$	−30.3993	+	17.5510i	−1.44431	+	0.833875i	−0.446181	+	0.894943i	$0.647216\pi$
$444$		0			0
$445$	24.9675	+	14.4150i	1.18357	+	0.683336i
$446$		0			0
$447$	−4.93864	+	10.4765i	−0.233590	+	0.495519i
$448$		0			0
$449$		−	13.8891i		−	0.655467i	−0.944770	−	0.327733i	$-0.893715\pi$
$449$		−	13.8891i		−	0.655467i	0.944770	−	0.327733i	$-0.106285\pi$
$450$		0			0
$451$	2.32361	−	4.02462i	0.109415	−	0.189512i
$452$		0			0
$453$	−0.607972	−	7.30029i	−0.0285650	−	0.342998i
$454$		0			0
$455$	−5.53788	−	5.08317i	−0.259620	−	0.238303i
$456$		0			0
$457$	3.77280	+	6.53468i	0.176484	+	0.305679i	0.940674	−	0.339312i	$-0.110194\pi$
$457$	3.77280	+	6.53468i	0.176484	+	0.305679i	−0.764190	+	0.644991i	$0.776861\pi$
$458$		0			0
$459$	−31.6769	−	8.91476i	−1.47855	−	0.416106i
$460$		0			0
$461$	17.6339			0.821292			0.410646	−	0.911795i	$-0.365303\pi$
$461$	17.6339			0.821292			0.410646	+	0.911795i	$0.365303\pi$
$462$		0			0
$463$		−	29.5192i		−	1.37187i	−0.727661	−	0.685937i	$-0.759393\pi$
$463$		−	29.5192i		−	1.37187i	0.727661	−	0.685937i	$-0.240607\pi$
$464$		0			0
$465$	25.8531	−	17.9420i	1.19891	−	0.832043i
$466$		0			0
$467$	26.4319	−	15.2605i	1.22312	−	0.706170i	0.257539	−	0.966268i	$-0.417088\pi$
$467$	26.4319	−	15.2605i	1.22312	−	0.706170i	0.965582	+	0.260098i	$0.0837549\pi$
$468$		0			0
$469$	0.0505738	+	0.0112569i	0.00233528	+	0.000519795i
$470$		0			0
$471$	−3.30946	−	39.7388i	−0.152492	−	1.83107i
$472$		0			0
$473$	−1.41368	−	0.816191i	−0.0650013	−	0.0375285i
$474$		0			0
$475$	−40.0015			−1.83540
$476$		0			0
$477$	4.46396	+	5.41112i	0.204391	+	0.247758i
$478$		0			0
$479$	−0.0969618	+	0.167943i	−0.00443030	+	0.00767350i	−0.868232	−	0.496158i	$-0.834744\pi$
$479$	−0.0969618	+	0.167943i	−0.00443030	+	0.00767350i	0.863802	+	0.503832i	$0.168077\pi$
$480$		0			0
$481$	1.33523	+	2.31268i	0.0608811	+	0.105449i
$482$		0			0
$483$	−14.0797	−	1.92565i	−0.640650	−	0.0876203i
$484$		0			0
$485$	12.5396	+	21.7193i	0.569395	+	0.986221i
$486$		0			0
$487$	−17.4486	−	10.0740i	−0.790673	−	0.456496i	0.0495261	−	0.998773i	$-0.484229\pi$
$487$	−17.4486	−	10.0740i	−0.790673	−	0.456496i	−0.840200	+	0.542277i	$0.817562\pi$
$488$		0			0
$489$	15.3631	−	32.5900i	0.694742	−	1.47377i
$490$		0			0
$491$			4.30244i			0.194167i	0.995276	+	0.0970833i	$0.0309513\pi$
$491$			4.30244i			0.194167i	−0.995276	+	0.0970833i	$0.969049\pi$
$492$		0			0
$493$	−14.2785	−	8.24371i	−0.643073	−	0.371278i
$494$		0			0
$495$	−4.57745	−	1.70950i	−0.205741	−	0.0768365i
$496$		0			0
$497$	−7.17302	−	22.8173i	−0.321754	−	1.02349i
$498$		0			0
$499$	13.0198	+	22.5510i	0.582848	+	1.00952i	0.995140	+	0.0984710i	$0.0313952\pi$
$499$	13.0198	+	22.5510i	0.582848	+	1.00952i	−0.412292	+	0.911052i	$0.635272\pi$
$500$		0			0
$501$	−7.44502	−	10.7277i	−0.332619	−	0.479279i
$502$		0			0
$503$	−22.7182			−1.01295			−0.506476	−	0.862254i	$-0.669052\pi$
$503$	−22.7182			−1.01295			−0.506476	+	0.862254i	$0.669052\pi$
$504$		0			0
$505$	23.7766			1.05804
$506$		0			0
$507$	12.2073	+	17.5898i	0.542146	+	0.781191i
$508$		0			0
$509$	−18.1915	−	31.5087i	−0.806326	−	1.39660i	−0.915392	−	0.402563i	$-0.868120\pi$
$509$	−18.1915	−	31.5087i	−0.806326	−	1.39660i	0.109067	−	0.994034i	$-0.465214\pi$
$510$		0			0
$511$	−21.4700	−	4.77886i	−0.949776	−	0.211404i
$512$		0			0
$513$	−18.9882	−	19.4702i	−0.838347	−	0.859630i
$514$		0			0
$515$	−19.5117	−	11.2651i	−0.859790	−	0.496400i
$516$		0			0
$517$			1.97817i			0.0869997i
$518$		0			0
$519$	−11.4860	+	24.3654i	−0.504177	+	1.06952i
$520$		0			0
$521$	4.25083	+	2.45422i	0.186232	+	0.107521i	0.590218	−	0.807244i	$-0.299042\pi$
$521$	4.25083	+	2.45422i	0.186232	+	0.107521i	−0.403985	+	0.914765i	$0.632375\pi$
$522$		0			0
$523$	−20.4680	−	35.4516i	−0.895002	−	1.55019i	−0.833802	−	0.552064i	$-0.813841\pi$
$523$	−20.4680	−	35.4516i	−0.895002	−	1.55019i	−0.0612000	−	0.998126i	$-0.519493\pi$
$524$		0			0
$525$	13.2401	+	32.4243i	0.577846	+	1.41511i
$526$		0			0
$527$	−16.1802	−	28.0249i	−0.704821	−	1.22079i
$528$		0			0
$529$	6.69173	−	11.5904i	0.290945	−	0.503931i
$530$		0			0
$531$	−4.00132	+	3.30093i	−0.173642	+	0.143248i
$532$		0			0
$533$	−8.10662			−0.351137
$534$		0			0
$535$	11.0112	+	6.35733i	0.476057	+	0.274852i
$536$		0			0
$537$	1.29671	+	15.5705i	0.0559574	+	0.671915i
$538$		0			0
$539$	−3.19478	+	0.274055i	−0.137609	+	0.0118044i
$540$		0			0
$541$	7.39731	−	4.27084i	0.318035	−	0.183618i	−0.332481	−	0.943110i	$-0.607886\pi$
$541$	7.39731	−	4.27084i	0.318035	−	0.183618i	0.650517	+	0.759492i	$0.274552\pi$
$542$		0			0
$543$	14.8045	−	10.2743i	0.635322	−	0.440913i
$544$		0			0
$545$			2.00385i			0.0858353i
$546$		0			0
$547$	0.501652			0.0214491			0.0107245	−	0.999942i	$-0.496586\pi$
$547$	0.501652			0.0214491			0.0107245	+	0.999942i	$0.496586\pi$
$548$		0			0
$549$	2.64066	+	15.7441i	0.112701	+	0.671942i
$550$		0			0
$551$	−6.81301	−	11.8005i	−0.290244	−	0.502718i
$552$		0			0
$553$	−24.4930	−	22.4819i	−1.04155	−	0.956028i
$554$		0			0
$555$	−1.70815	−	20.5109i	−0.0725071	−	0.870638i
$556$		0			0
$557$	−8.85048	+	15.3295i	−0.375007	+	0.649531i	−0.990328	−	0.138745i	$-0.955693\pi$
$557$	−8.85048	+	15.3295i	−0.375007	+	0.649531i	0.615321	+	0.788277i	$0.289026\pi$
$558$		0			0
$559$			2.84753i			0.120438i
$560$		0			0
$561$	−2.14252	+	4.54498i	−0.0904572	+	0.191889i
$562$		0			0
$563$	0.214083	+	0.123601i	0.00902251	+	0.00520915i	0.504504	−	0.863409i	$-0.331675\pi$
$563$	0.214083	+	0.123601i	0.00902251	+	0.00520915i	−0.495482	+	0.868618i	$0.665009\pi$
$564$		0			0
$565$	−4.35603	+	2.51495i	−0.183260	+	0.105805i
$566$		0			0
$567$	−9.49720	+	21.8358i	−0.398845	+	0.917018i
$568$		0			0
$569$	−22.8950	+	13.2184i	−0.959809	+	0.554146i	−0.896114	−	0.443824i	$-0.853622\pi$
$569$	−22.8950	+	13.2184i	−0.959809	+	0.554146i	−0.0636947	+	0.997969i	$0.520288\pi$
$570$		0			0
$571$	16.4357	−	28.4675i	0.687814	−	1.19133i	−0.284730	−	0.958608i	$-0.591904\pi$
$571$	16.4357	−	28.4675i	0.687814	−	1.19133i	0.972544	−	0.232721i	$-0.0747629\pi$
$572$		0			0
$573$	−10.8395	+	22.9941i	−0.452826	+	0.960591i
$574$		0			0
$575$	23.7005			0.988380
$576$		0			0
$577$	13.3055	−	23.0459i	0.553917	−	0.959413i	−0.444070	−	0.895992i	$-0.646466\pi$
$577$	13.3055	−	23.0459i	0.553917	−	0.959413i	0.997987	−	0.0634205i	$-0.0202009\pi$
$578$		0			0
$579$	27.8440	−	2.31886i	1.15716	−	0.0963685i
$580$		0			0
$581$	1.75164	−	0.550661i	0.0726705	−	0.0228453i
$582$		0			0
$583$	0.927594	−	0.535547i	0.0384170	−	0.0221801i
$584$		0			0
$585$	1.40992	+	8.40617i	0.0582929	+	0.347552i
$586$		0			0
$587$		−	23.5447i		−	0.971792i	−0.874017	−	0.485896i	$-0.838493\pi$
$587$		−	23.5447i		−	0.971792i	0.874017	−	0.485896i	$-0.161507\pi$
$588$		0			0
$589$		−	26.7442i		−	1.10198i
$590$		0			0
$591$	21.6742	+	31.2309i	0.891558	+	1.28467i
$592$		0			0
$593$	4.37266	−	2.52456i	0.179564	−	0.103671i	−0.407524	−	0.913195i	$-0.633608\pi$
$593$	4.37266	−	2.52456i	0.179564	−	0.103671i	0.587088	+	0.809523i	$0.300274\pi$
$594$		0			0
$595$	56.8351	−	17.8671i	2.33001	−	0.732480i
$596$		0			0
$597$	−2.29345	−	27.5389i	−0.0938648	−	1.12709i
$598$		0			0
$599$	7.88687	−	13.6605i	0.322249	−	0.558151i	−0.658703	−	0.752403i	$-0.728895\pi$
$599$	7.88687	−	13.6605i	0.322249	−	0.558151i	0.980952	+	0.194252i	$0.0622280\pi$
$600$		0			0
$601$	−3.65359			−0.149033			−0.0745165	−	0.997220i	$-0.523741\pi$
$601$	−3.65359			−0.149033			−0.0745165	+	0.997220i	$0.523741\pi$
$602$		0			0
$603$	−0.0373856	−	0.0453181i	−0.00152246	−	0.00184550i
$604$		0			0
$605$	19.1831	−	33.2261i	0.779904	−	1.35083i
$606$		0			0
$607$	40.3527	−	23.2976i	1.63786	−	0.945622i	0.656298	−	0.754502i	$-0.272122\pi$
$607$	40.3527	−	23.2976i	1.63786	−	0.945622i	0.981567	−	0.191120i	$-0.0612118\pi$
$608$		0			0
$609$	−7.31017	+	9.42833i	−0.296223	+	0.382055i
$610$		0			0
$611$	2.98841	−	1.72536i	0.120898	−	0.0698005i
$612$		0			0
$613$	18.5964	+	10.7366i	0.751102	+	0.433649i	0.826092	−	0.563536i	$-0.190559\pi$
$613$	18.5964	+	10.7366i	0.751102	+	0.433649i	−0.0749902	+	0.997184i	$0.523893\pi$
$614$		0			0
$615$	56.5152	+	26.6415i	2.27891	+	1.07429i
$616$		0			0
$617$			23.7350i			0.955536i	0.878486	+	0.477768i	$0.158554\pi$
$617$			23.7350i			0.955536i	−0.878486	+	0.477768i	$0.841446\pi$
$618$		0			0
$619$	10.3184	−	17.8719i	0.414730	−	0.718334i	−0.580670	−	0.814139i	$-0.697209\pi$
$619$	10.3184	−	17.8719i	0.414730	−	0.718334i	0.995400	+	0.0958052i	$0.0305426\pi$
$620$		0			0
$621$	11.2503	+	11.5359i	0.451459	+	0.462920i
$622$		0			0
$623$	−15.8040	−	14.5063i	−0.633173	−	0.581183i
$624$		0			0
$625$	2.40116	+	4.15892i	0.0960462	+	0.166357i
$626$		0			0
$627$	−3.41155	+	2.36762i	−0.136244	+	0.0945535i
$628$		0			0
$629$	−21.1649			−0.843899
$630$		0			0
$631$			1.83946i			0.0732279i	0.999329	+	0.0366139i	$0.0116572\pi$
$631$			1.83946i			0.0732279i	−0.999329	+	0.0366139i	$0.988343\pi$
$632$		0			0
$633$	−20.7305	−	29.8711i	−0.823964	−	1.18727i
$634$		0			0
$635$	−48.3581	+	27.9196i	−1.91903	+	1.10796i
$636$		0			0
$637$	3.20050	+	4.58730i	0.126808	+	0.181756i
$638$		0			0
$639$	−9.48843	+	25.4067i	−0.375357	+	1.00507i
$640$		0			0
$641$	−21.1148	−	12.1906i	−0.833983	−	0.481500i	0.0212316	−	0.999775i	$-0.493241\pi$
$641$	−21.1148	−	12.1906i	−0.833983	−	0.481500i	−0.855214	+	0.518274i	$0.826575\pi$
$642$		0			0
$643$	7.88201			0.310836			0.155418	−	0.987849i	$-0.450328\pi$
$643$	7.88201			0.310836			0.155418	+	0.987849i	$0.450328\pi$
$644$		0			0
$645$	9.35808	−	19.8515i	0.368474	−	0.781652i
$646$		0			0
$647$	2.44506	−	4.23496i	0.0961251	−	0.166494i	−0.813953	−	0.580931i	$-0.802688\pi$
$647$	2.44506	−	4.23496i	0.0961251	−	0.166494i	0.910078	+	0.414438i	$0.136022\pi$
$648$		0			0
$649$	0.396017	+	0.685921i	0.0155450	+	0.0269247i
$650$		0			0
$651$	−21.6783	+	8.85209i	−0.849639	+	0.346941i
$652$		0			0
$653$	21.3381	+	36.9587i	0.835024	+	1.44630i	0.894011	+	0.448045i	$0.147880\pi$
$653$	21.3381	+	36.9587i	0.835024	+	1.44630i	−0.0589868	+	0.998259i	$0.518787\pi$
$654$		0			0
$655$	−4.14651	−	2.39399i	−0.162018	−	0.0935410i
$656$		0			0
$657$	15.8712	+	19.2388i	0.619195	+	0.750576i
$658$		0			0
$659$			33.4550i			1.30322i	0.758553	+	0.651611i	$0.225907\pi$
$659$			33.4550i			1.30322i	−0.758553	+	0.651611i	$0.774093\pi$
$660$		0			0
$661$	11.2595	+	6.50067i	0.437944	+	0.252847i	0.702725	−	0.711462i	$-0.251966\pi$
$661$	11.2595	+	6.50067i	0.437944	+	0.252847i	−0.264781	+	0.964308i	$0.585300\pi$
$662$		0			0
$663$	8.73478	−	0.727436i	0.339231	−	0.0282513i
$664$		0			0
$665$	48.0615	+	10.6977i	1.86374	+	0.414838i
$666$		0			0
$667$	4.03665	+	6.99168i	0.156300	+	0.270719i
$668$		0			0
$669$	10.0328	−	6.96278i	0.387891	−	0.269197i
$670$		0			0
$671$	2.43756			0.0941009
$672$		0			0
$673$	−12.3531			−0.476179			−0.238089	−	0.971243i	$-0.576521\pi$
$673$	−12.3531			−0.476179			−0.238089	+	0.971243i	$0.576521\pi$
$674$		0			0
$675$	10.7584	−	38.2278i	0.414090	−	1.47139i
$676$		0			0
$677$	2.07866	+	3.60034i	0.0798894	+	0.138372i	0.903202	−	0.429216i	$-0.141210\pi$
$677$	2.07866	+	3.60034i	0.0798894	+	0.138372i	−0.823313	+	0.567588i	$0.807877\pi$
$678$		0			0
$679$	−5.59650	−	17.8024i	−0.214774	−	0.683193i
$680$		0			0
$681$	−2.98246	−	35.8122i	−0.114288	−	1.37233i
$682$		0			0
$683$	11.5310	+	6.65741i	0.441221	+	0.254739i	0.704115	−	0.710086i	$-0.251344\pi$
$683$	11.5310	+	6.65741i	0.441221	+	0.254739i	−0.262895	+	0.964825i	$0.584677\pi$
$684$		0			0
$685$		−	31.9892i		−	1.22224i
$686$		0			0
$687$	−34.4542	−	16.2419i	−1.31451	−	0.619665i
$688$		0			0
$689$	−1.61810	−	0.934208i	−0.0616445	−	0.0355905i
$690$		0			0
$691$	−7.57239	−	13.1158i	−0.288067	−	0.498947i	0.685281	−	0.728279i	$-0.259679\pi$
$691$	−7.57239	−	13.1158i	−0.288067	−	0.498947i	−0.973348	+	0.229332i	$0.926346\pi$
$692$		0			0
$693$	3.04833	+	1.98167i	0.115796	+	0.0752775i
$694$		0			0
$695$	28.4765	+	49.3228i	1.08018	+	1.87092i
$696$		0			0
$697$	32.1248	−	55.6418i	1.21681	−	2.10758i
$698$		0			0
$699$	27.3894	+	12.9115i	1.03596	+	0.488357i
$700$		0			0
$701$	−51.6538			−1.95094			−0.975468	−	0.220142i	$-0.929348\pi$
$701$	−51.6538			−1.95094			−0.975468	+	0.220142i	$0.929348\pi$
$702$		0			0
$703$	−15.1483	−	8.74585i	−0.571327	−	0.329856i
$704$		0			0
$705$	−26.5038	+	2.20725i	−0.998192	+	0.0831299i
$706$		0			0
$707$	−17.2694	−	3.84388i	−0.649483	−	0.144564i
$708$		0			0
$709$	−44.7941	+	25.8619i	−1.68228	+	0.971263i	−0.722134	+	0.691753i	$0.756839\pi$
$709$	−44.7941	+	25.8619i	−1.68228	+	0.971263i	−0.960143	+	0.279510i	$0.909828\pi$
$710$		0			0
$711$	6.23580	+	37.1789i	0.233861	+	1.39432i
$712$		0			0
$713$			15.8457i			0.593427i
$714$		0			0
$715$	1.30147			0.0486724
$716$		0			0
$717$	6.52307	+	9.39924i	0.243608	+	0.351021i
$718$		0			0
$719$	18.9896	+	32.8909i	0.708191	+	1.22662i	0.965527	+	0.260302i	$0.0838220\pi$
$719$	18.9896	+	32.8909i	0.708191	+	1.22662i	−0.257336	+	0.966322i	$0.582845\pi$
$720$		0			0
$721$	12.3506	+	11.3365i	0.459960	+	0.422193i
$722$		0			0
$723$	−18.2260	+	1.51787i	−0.677831	+	0.0564500i
$724$		0			0
$725$	9.94856	−	17.2314i	0.369480	−	0.639958i
$726$		0			0
$727$			15.9886i			0.592984i	0.955035	+	0.296492i	$0.0958167\pi$
$727$			15.9886i			0.592984i	−0.955035	+	0.296492i	$0.904183\pi$
$728$		0			0
$729$	23.7137	−	12.9097i	0.878285	−	0.478137i
$730$		0			0
$731$	−19.5447	−	11.2842i	−0.722888	−	0.417359i
$732$		0			0
$733$	10.1169	−	5.84098i	0.373675	−	0.215741i	−0.301388	−	0.953502i	$-0.597450\pi$
$733$	10.1169	−	5.84098i	0.373675	−	0.215741i	0.675063	+	0.737760i	$0.264117\pi$
$734$		0			0
$735$	−7.23659	−	42.4984i	−0.266925	−	1.56758i
$736$		0			0
$737$	−0.00776859	+	0.00448520i	−0.000286160	+	0.000165214i
$738$		0			0
$739$	−8.47946	+	14.6869i	−0.311922	+	0.540265i	−0.978778	−	0.204922i	$-0.934306\pi$
$739$	−8.47946	+	14.6869i	−0.311922	+	0.540265i	0.666857	+	0.745186i	$0.267639\pi$
$740$		0			0
$741$	6.55231	+	3.08878i	0.240705	+	0.113469i
$742$		0			0
$743$	−14.5437			−0.533558			−0.266779	−	0.963758i	$-0.585959\pi$
$743$	−14.5437			−0.533558			−0.266779	+	0.963758i	$0.585959\pi$
$744$		0			0
$745$	−11.8883	+	20.5911i	−0.435553	+	0.754400i
$746$		0			0
$747$	−1.95043	−	0.728412i	−0.0713626	−	0.0266512i
$748$		0			0
$749$	−6.96991	−	6.39761i	−0.254675	−	0.233764i
$750$		0			0
$751$	−9.37421	+	5.41220i	−0.342070	+	0.197494i	−0.661187	−	0.750221i	$-0.729947\pi$
$751$	−9.37421	+	5.41220i	−0.342070	+	0.197494i	0.319117	+	0.947715i	$0.396614\pi$
$752$		0			0
$753$	−9.48607	+	6.58333i	−0.345692	+	0.239910i
$754$		0			0
$755$		−	15.0384i		−	0.547303i
$756$		0			0
$757$			13.5121i			0.491105i	0.969383	+	0.245552i	$0.0789694\pi$
$757$			13.5121i			0.491105i	−0.969383	+	0.245552i	$0.921031\pi$
$758$		0			0
$759$	2.02131	−	1.40279i	0.0733690	−	0.0509181i
$760$		0			0
$761$	22.5165	−	12.9999i	0.816221	−	0.471245i	−0.0328907	−	0.999459i	$-0.510471\pi$
$761$	22.5165	−	12.9999i	0.816221	−	0.471245i	0.849111	+	0.528214i	$0.177138\pi$
$762$		0			0
$763$	0.323955	−	1.45543i	0.0117280	−	0.0526903i
$764$		0			0
$765$	−63.2850	−	23.6345i	−2.28808	−	0.854509i
$766$		0			0
$767$	0.690812	−	1.19652i	0.0249438	−	0.0432039i
$768$		0			0
$769$	3.84206			0.138548			0.0692741	−	0.997598i	$-0.477932\pi$
$769$	3.84206			0.138548			0.0692741	+	0.997598i	$0.477932\pi$
$770$		0			0
$771$	−1.60617	−	0.757155i	−0.0578449	−	0.0272683i
$772$		0			0
$773$	18.3710	−	31.8195i	0.660760	−	1.14447i	−0.319657	−	0.947533i	$-0.603568\pi$
$773$	18.3710	−	31.8195i	0.660760	−	1.14447i	0.980416	−	0.196936i	$-0.0630991\pi$
$774$		0			0
$775$	33.8206	−	19.5263i	1.21487	−	0.701407i
$776$		0			0
$777$	−2.07526	+	15.1736i	−0.0744496	+	0.544351i
$778$		0			0
$779$	45.9852	−	26.5495i	1.64759	−	0.951236i
$780$		0			0
$781$	3.58628	+	2.07054i	0.128327	+	0.0740897i
$782$		0			0
$783$	13.1096	−	3.33718i	0.468499	−	0.119261i
$784$		0			0
$785$		−	81.8606i		−	2.92173i
$786$		0			0
$787$	−19.1854	+	33.2301i	−0.683886	+	1.18453i	0.289899	+	0.957057i	$0.406378\pi$
$787$	−19.1854	+	33.2301i	−0.683886	+	1.18453i	−0.973785	+	0.227469i	$0.926955\pi$
$788$		0			0
$789$	29.6957	−	2.47307i	1.05719	−	0.0880436i
$790$		0			0
$791$	3.57046	−	1.12244i	0.126951	−	0.0399093i
$792$		0			0
$793$	−2.12604	−	3.68241i	−0.0754979	−	0.130766i
$794$		0			0
$795$	8.21036	+	11.8305i	0.291192	+	0.419585i
$796$		0			0
$797$	−25.0108			−0.885927			−0.442964	−	0.896540i	$-0.646073\pi$
$797$	−25.0108			−0.885927			−0.442964	+	0.896540i	$0.646073\pi$
$798$		0			0
$799$			27.3489i			0.967535i
$800$		0			0
$801$	4.02361	+	23.9895i	0.142167	+	0.847626i
$802$		0			0
$803$	3.29798	−	1.90409i	0.116383	−	0.0671939i
$804$		0			0
$805$	−28.4760	−	6.33828i	−1.00365	−	0.223395i
$806$		0			0
$807$	−13.5544	+	1.12882i	−0.477138	+	0.0397363i
$808$		0			0
$809$	32.0756	+	18.5188i	1.12772	+	0.651087i	0.943360	−	0.331772i	$-0.107646\pi$
$809$	32.0756	+	18.5188i	1.12772	+	0.651087i	0.184357	+	0.982859i	$0.440980\pi$
$810$		0			0
$811$	−1.97747			−0.0694383			−0.0347192	−	0.999397i	$-0.511054\pi$
$811$	−1.97747			−0.0694383			−0.0347192	+	0.999397i	$0.511054\pi$
$812$		0			0
$813$	−28.4197	−	13.3972i	−0.996722	−	0.469859i
$814$		0			0
$815$	36.9820	−	64.0546i	1.29542	−	2.24374i
$816$		0			0
$817$	−9.32578	−	16.1527i	−0.326268	−	0.565112i
$818$		0			0
$819$	0.334947	−	6.33351i	0.0117040	−	0.221311i
$820$		0			0
$821$	6.85902	+	11.8802i	0.239382	+	0.414621i	0.960537	−	0.278152i	$-0.0897220\pi$
$821$	6.85902	+	11.8802i	0.239382	+	0.414621i	−0.721155	+	0.692773i	$0.756389\pi$
$822$		0			0
$823$	34.0169	+	19.6397i	1.18575	+	0.684596i	0.957339	−	0.288968i	$-0.0933122\pi$
$823$	34.0169	+	19.6397i	1.18575	+	0.684596i	0.228416	+	0.973564i	$0.426646\pi$
$824$		0			0
$825$	−5.48490	−	2.58560i	−0.190960	−	0.0900191i
$826$		0			0
$827$		−	26.9376i		−	0.936713i	−0.883540	−	0.468356i	$-0.844846\pi$
$827$		−	26.9376i		−	0.936713i	0.883540	−	0.468356i	$-0.155154\pi$
$828$		0			0
$829$	17.5320	+	10.1221i	0.608910	+	0.351554i	0.772539	−	0.634968i	$-0.218987\pi$
$829$	17.5320	+	10.1221i	0.608910	+	0.351554i	−0.163629	+	0.986522i	$0.552320\pi$
$830$		0			0
$831$	−3.20185	−	38.4466i	−0.111071	−	1.33370i
$832$		0			0
$833$	−44.1690	+	3.78891i	−1.53036	+	0.131278i
$834$		0			0
$835$	−13.4032	−	23.2150i	−0.463836	−	0.803387i
$836$		0			0
$837$	25.5584	+	7.19285i	0.883426	+	0.248621i
$838$		0			0
$839$	−45.3448			−1.56548			−0.782738	−	0.622352i	$-0.786177\pi$
$839$	−45.3448			−1.56548			−0.782738	+	0.622352i	$0.786177\pi$
$840$		0			0
$841$	−22.2223			−0.766286
$842$		0			0
$843$	−25.4863	+	17.6875i	−0.877794	+	0.609189i
$844$		0			0
$845$	21.9767	+	38.0647i	0.756020	+	1.30946i
$846$		0			0
$847$	−19.3046	+	21.0315i	−0.663315	+	0.722652i
$848$		0			0
$849$	7.74258	−	0.644805i	0.265725	−	0.0221297i
$850$		0			0
$851$	8.97520	+	5.18183i	0.307666	+	0.177631i
$852$		0			0
$853$			37.8961i			1.29754i	0.760986	+	0.648769i	$0.224716\pi$
$853$			37.8961i			1.29754i	−0.760986	+	0.648769i	$0.775284\pi$
$854$		0			0
$855$	−35.5284	−	43.0668i	−1.21505	−	1.47285i
$856$		0			0
$857$	−30.1090	−	17.3834i	−1.02850	−	0.593806i	−0.111947	−	0.993714i	$-0.535709\pi$
$857$	−30.1090	−	17.3834i	−1.02850	−	0.593806i	−0.916555	+	0.399908i	$0.869042\pi$
$858$		0			0
$859$	17.5062	+	30.3217i	0.597305	+	1.03456i	0.993217	+	0.116274i	$0.0370951\pi$
$859$	17.5062	+	30.3217i	0.597305	+	1.03456i	−0.395912	+	0.918288i	$0.629572\pi$
$860$		0			0
$861$	−36.7411	−	28.4869i	−1.25213	−	0.970831i
$862$		0			0
$863$	−11.8510	−	20.5265i	−0.403413	−	0.698732i	0.590722	−	0.806875i	$-0.298843\pi$
$863$	−11.8510	−	20.5265i	−0.403413	−	0.698732i	−0.994135	+	0.108143i	$0.965509\pi$
$864$		0			0
$865$	−27.6490	+	47.8894i	−0.940093	+	1.62829i
$866$		0			0
$867$	−17.0658	+	36.2021i	−0.579586	+	1.22949i
$868$		0			0
$869$	5.75618			0.195265
$870$		0			0
$871$	0.0135515	+	0.00782398i	0.000459176	+	0.000265106i
$872$		0			0
$873$	−7.40303	+	19.8227i	−0.250554	+	0.670897i
$874$		0			0
$875$	7.45583	+	23.7169i	0.252053	+	0.801777i
$876$		0			0
$877$	6.02275	−	3.47724i	0.203374	−	0.117418i	−0.394854	−	0.918744i	$-0.629205\pi$
$877$	6.02275	−	3.47724i	0.203374	−	0.117418i	0.598228	+	0.801326i	$0.295872\pi$
$878$		0			0
$879$	−24.4621	−	35.2480i	−0.825086	−	1.18889i
$880$		0			0
$881$			23.8500i			0.803528i	0.915743	+	0.401764i	$0.131603\pi$
$881$			23.8500i			0.803528i	−0.915743	+	0.401764i	$0.868397\pi$
$882$		0			0
$883$	−32.0357			−1.07809			−0.539044	−	0.842278i	$-0.681214\pi$
$883$	−32.0357			−1.07809			−0.539044	+	0.842278i	$0.681214\pi$
$884$		0			0
$885$	−8.74821	+	6.07125i	−0.294068	+	0.204083i
$886$		0			0
$887$	25.4399	+	44.0633i	0.854190	+	1.47950i	0.877395	+	0.479769i	$0.159280\pi$
$887$	25.4399	+	44.0633i	0.854190	+	1.47950i	−0.0232053	+	0.999731i	$0.507387\pi$
$888$		0			0
$889$	39.6372	−	12.4607i	1.32939	−	0.417917i
$890$		0			0
$891$	−1.34510	−	3.89705i	−0.0450625	−	0.130556i
$892$		0			0
$893$	−11.3012	+	19.5743i	−0.378182	+	0.655030i
$894$		0			0
$895$			32.0747i			1.07214i
$896$		0			0
$897$	−3.88218	−	1.83007i	−0.129622	−	0.0611044i
$898$		0			0
$899$	11.5206	+	6.65141i	0.384233	+	0.221837i
$900$		0			0
$901$	12.8243	−	7.40413i	0.427241	−	0.246667i
$902$		0			0
$903$	−10.0063	+	12.9057i	−0.332989	+	0.429474i
$904$		0			0
$905$	32.0372	−	18.4967i	1.06495	−	0.614851i
$906$		0			0
$907$	−5.21438	+	9.03157i	−0.173141	+	0.299888i	−0.939516	−	0.342504i	$-0.888725\pi$
$907$	−5.21438	+	9.03157i	−0.173141	+	0.299888i	0.766376	+	0.642393i	$0.222058\pi$
$908$		0			0
$909$	12.7660	+	15.4747i	0.423423	+	0.513264i
$910$		0			0
$911$	−9.95365			−0.329779			−0.164889	−	0.986312i	$-0.552727\pi$
$911$	−9.95365			−0.329779			−0.164889	+	0.986312i	$0.552727\pi$
$912$		0			0
$913$	−0.158952	+	0.275313i	−0.00526055	+	0.00911153i
$914$		0			0
$915$	2.71984	+	32.6589i	0.0899152	+	1.07967i
$916$		0			0
$917$	2.62467	+	2.40916i	0.0866742	+	0.0795574i
$918$		0			0
$919$	−7.23519	+	4.17724i	−0.238667	+	0.137794i	−0.614564	−	0.788867i	$-0.710668\pi$
$919$	−7.23519	+	4.17724i	−0.238667	+	0.137794i	0.375897	+	0.926661i	$0.377335\pi$
$920$		0			0
$921$	−7.62556	−	10.9879i	−0.251271	−	0.362062i
$922$		0			0
$923$		−	7.22370i		−	0.237771i
$924$		0			0
$925$		−	25.5419i		−	0.839812i
$926$		0			0
$927$	−3.14440	−	18.7474i	−0.103276	−	0.615747i
$928$		0			0
$929$	45.0777	−	26.0256i	1.47895	−	0.853872i	0.479234	−	0.877687i	$-0.340915\pi$
$929$	45.0777	−	26.0256i	1.47895	−	0.853872i	0.999716	+	0.0238151i	$0.00758131\pi$
$930$		0			0
$931$	−33.1786	−	15.5399i	−1.08738	−	0.509300i
$932$		0			0
$933$	34.5537	−	2.87765i	1.13124	−	0.0942099i
$934$		0			0
$935$	−5.15747	+	8.93299i	−0.168667	+	0.292140i
$936$		0			0
$937$	−35.8998			−1.17280			−0.586398	−	0.810023i	$-0.699455\pi$
$937$	−35.8998			−1.17280			−0.586398	+	0.810023i	$0.699455\pi$
$938$		0			0
$939$	12.6218	−	26.7749i	0.411897	−	0.873767i
$940$		0			0
$941$	−2.74621	+	4.75657i	−0.0895238	+	0.155060i	−0.907310	−	0.420462i	$-0.861868\pi$
$941$	−2.74621	+	4.75657i	−0.0895238	+	0.155060i	0.817786	+	0.575522i	$0.195201\pi$
$942$		0			0
$943$	−27.2458	+	15.7304i	−0.887245	+	0.512251i
$944$		0			0
$945$	−23.1494	+	43.0532i	−0.753051	+	1.40052i
$946$		0			0
$947$	−1.99491	+	1.15176i	−0.0648257	+	0.0374272i	−0.532063	−	0.846705i	$-0.678583\pi$
$947$	−1.99491	+	1.15176i	−0.0648257	+	0.0374272i	0.467237	+	0.884132i	$0.345250\pi$
$948$		0			0
$949$	−5.75300	−	3.32150i	−0.186750	−	0.107820i
$950$		0			0
$951$	11.3302	−	24.0351i	0.367408	−	0.779391i
$952$		0			0
$953$			27.0751i			0.877047i	0.898720	+	0.438524i	$0.144498\pi$
$953$			27.0751i			0.877047i	−0.898720	+	0.438524i	$0.855502\pi$
$954$		0			0
$955$	−26.0928	+	45.1940i	−0.844343	+	1.46244i
$956$		0			0
$957$	−0.171427	−	2.05843i	−0.00554144	−	0.0665395i
$958$		0			0
$959$	−5.17159	+	23.2344i	−0.166999	+	0.750278i
$960$		0			0
$961$	−2.44506	−	4.23497i	−0.0788729	−	0.136612i
$962$		0			0
$963$	1.77450	+	10.5799i	0.0571826	+	0.340932i
$964$		0			0
$965$	57.3577			1.84641
$966$		0			0
$967$		−	33.0009i		−	1.06124i	−0.847611	−	0.530618i	$-0.821960\pi$
$967$		−	33.0009i		−	1.06124i	0.847611	−	0.530618i	$-0.178040\pi$
$968$		0			0
$969$	−47.1660	+	32.7332i	−1.51519	+	1.05154i
$970$		0			0
$971$	31.6718	−	18.2857i	1.01640	−	0.586817i	0.103339	−	0.994646i	$-0.467047\pi$
$971$	31.6718	−	18.2857i	1.01640	−	0.586817i	0.913058	+	0.407829i	$0.133714\pi$
$972$		0			0
$973$	−12.7092	−	40.4279i	−0.407439	−	1.29606i
$974$		0			0
$975$	0.877874	+	10.5412i	0.0281145	+	0.337588i
$976$		0			0
$977$	−2.71660	−	1.56843i	−0.0869117	−	0.0501785i	0.455914	−	0.890024i	$-0.349312\pi$
$977$	−2.71660	−	1.56843i	−0.0869117	−	0.0501785i	−0.542826	+	0.839845i	$0.682646\pi$
$978$		0			0
$979$	3.71414			0.118704
$980$		0			0
$981$	−1.30418	+	1.07590i	−0.0416393	+	0.0343508i
$982$		0			0
$983$	−5.06871	+	8.77927i	−0.161667	+	0.280015i	−0.935467	−	0.353415i	$-0.885020\pi$
$983$	−5.06871	+	8.77927i	−0.161667	+	0.280015i	0.773800	+	0.633430i	$0.218354\pi$
$984$		0			0
$985$	39.0197	+	67.5842i	1.24327	+	2.15341i
$986$		0			0
$987$	19.6071	+	2.68162i	0.624102	+	0.0853569i
$988$		0			0
$989$	5.52544	+	9.57034i	0.175699	+	0.304319i
$990$		0			0
$991$	22.8644	+	13.2008i	0.726313	+	0.419337i	0.817072	−	0.576536i	$-0.195596\pi$
$991$	22.8644	+	13.2008i	0.726313	+	0.419337i	−0.0907589	+	0.995873i	$0.528929\pi$
$992$		0			0
$993$	−10.1350	+	21.4996i	−0.321624	+	0.682269i
$994$		0			0
$995$		−	56.7293i		−	1.79844i
$996$		0			0
$997$	0.842124	+	0.486200i	0.0266703	+	0.0153981i	0.513276	−	0.858224i	$-0.328432\pi$
$997$	0.842124	+	0.486200i	0.0266703	+	0.0153981i	−0.486606	+	0.873622i	$0.661765\pi$
$998$		0			0
$999$	12.4322	−	12.1244i	0.393336	−	0.383598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bd.a.431.20		56
3.2	odd	2	inner	672.2.bd.a.431.1		56
4.3	odd	2		168.2.v.a.11.7	✓	56
7.2	even	3	inner	672.2.bd.a.527.2		56
8.3	odd	2	inner	672.2.bd.a.431.19		56
8.5	even	2		168.2.v.a.11.17	yes	56
12.11	even	2		168.2.v.a.11.22	yes	56
21.2	odd	6	inner	672.2.bd.a.527.19		56
24.5	odd	2		168.2.v.a.11.12	yes	56
24.11	even	2	inner	672.2.bd.a.431.2		56
28.23	odd	6		168.2.v.a.107.12	yes	56
56.37	even	6		168.2.v.a.107.22	yes	56
56.51	odd	6	inner	672.2.bd.a.527.1		56
84.23	even	6		168.2.v.a.107.17	yes	56
168.107	even	6	inner	672.2.bd.a.527.20		56
168.149	odd	6		168.2.v.a.107.7	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.v.a.11.7	✓	56	4.3	odd	2
168.2.v.a.11.12	yes	56	24.5	odd	2
168.2.v.a.11.17	yes	56	8.5	even	2
168.2.v.a.11.22	yes	56	12.11	even	2
168.2.v.a.107.7	yes	56	168.149	odd	6
168.2.v.a.107.12	yes	56	28.23	odd	6
168.2.v.a.107.17	yes	56	84.23	even	6
168.2.v.a.107.22	yes	56	56.37	even	6
672.2.bd.a.431.1		56	3.2	odd	2	inner
672.2.bd.a.431.2		56	24.11	even	2	inner
672.2.bd.a.431.19		56	8.3	odd	2	inner
672.2.bd.a.431.20		56	1.1	even	1	trivial
672.2.bd.a.527.1		56	56.51	odd	6	inner
672.2.bd.a.527.2		56	7.2	even	3	inner
672.2.bd.a.527.19		56	21.2	odd	6	inner
672.2.bd.a.527.20		56	168.107	even	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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bd (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.987527 + 1.42295i) q^{3} +(1.77783 + 3.07929i) q^{5} +(-0.793456 - 2.52397i) q^{7} +(-1.04958 + 2.81041i) q^{9} +(0.396703 + 0.229036i) q^{11} -0.799063i q^{13} +(-2.62603 + 5.57065i) q^{15} +(5.48456 + 3.16651i) q^{17} +(2.61696 + 4.53272i) q^{19} +(2.80793 - 3.62154i) q^{21} +(-1.55053 - 2.68559i) q^{23} +(-3.82137 + 6.61880i) q^{25} +(-5.03556 + 1.28185i) q^{27} -2.60340 q^{29} +(-4.42520 - 2.55489i) q^{31} +(0.0658472 + 0.790668i) q^{33} +(6.36142 - 6.93048i) q^{35} +(-2.89424 + 1.67099i) q^{37} +(1.13703 - 0.789096i) q^{39} -10.1452i q^{41} -3.56359 q^{43} +(-10.5200 + 1.76446i) q^{45} +(2.15923 + 3.73989i) q^{47} +(-5.74086 + 4.00532i) q^{49} +(0.910362 + 10.9313i) q^{51} +(1.16913 - 2.02499i) q^{53} +1.62875i q^{55} +(-3.86551 + 8.19999i) q^{57} +(1.49741 + 0.864528i) q^{59} +(4.60841 - 2.66067i) q^{61} +(7.92618 + 0.419175i) q^{63} +(2.46055 - 1.42060i) q^{65} +(-0.00979145 + 0.0169593i) q^{67} +(2.29028 - 4.85842i) q^{69} +9.04022 q^{71} +(4.15674 - 7.19969i) q^{73} +(-13.1919 + 1.09863i) q^{75} +(0.263315 - 1.18300i) q^{77} +(10.8825 - 6.28304i) q^{79} +(-6.79677 - 5.89949i) q^{81} +0.694004i q^{83} +22.5181i q^{85} +(-2.57093 - 3.70452i) q^{87} +(7.02189 - 4.05409i) q^{89} +(-2.01681 + 0.634021i) q^{91} +(-0.734523 - 8.81987i) q^{93} +(-9.30504 + 16.1168i) q^{95} +7.05333 q^{97} +(-1.06006 + 0.874504i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{3} - 2 q^{9} + 4 q^{19} - 16 q^{25} + 8 q^{27} - 14 q^{33} + 16 q^{43} - 16 q^{49} + 34 q^{51} + 4 q^{57} + 36 q^{67} + 4 q^{73} - 10 q^{81} - 72 q^{91} - 32 q^{97} + 44 q^{99}+O(q^{100}) \) 56 * q + 2 * q^3 - 2 * q^9 + 4 * q^19 - 16 * q^25 + 8 * q^27 - 14 * q^33 + 16 * q^43 - 16 * q^49 + 34 * q^51 + 4 * q^57 + 36 * q^67 + 4 * q^73 - 10 * q^81 - 72 * q^91 - 32 * q^97 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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