LMFDB - Embedded newform 315.2.bq.a.164.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(164,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3, 1]))

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

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

chi := DirichletCharacter("315.164");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bq (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			164.1
Character	$\chi$	$=$	315.164
Dual form			315.2.bq.a.194.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70830 q^{2} +(0.577858 + 1.63281i) q^{3} +5.33489 q^{4} +(-0.422616 + 2.19577i) q^{5} +(-1.56501 - 4.42215i) q^{6} +(-1.01783 + 2.44214i) q^{7} -9.03188 q^{8} +(-2.33216 + 1.88707i) q^{9} +O(q^{10})$	\(q-2.70830 q^{2} +(0.577858 + 1.63281i) q^{3} +5.33489 q^{4} +(-0.422616 + 2.19577i) q^{5} +(-1.56501 - 4.42215i) q^{6} +(-1.01783 + 2.44214i) q^{7} -9.03188 q^{8} +(-2.33216 + 1.88707i) q^{9} +(1.14457 - 5.94680i) q^{10} +(-1.71660 + 0.991081i) q^{11} +(3.08281 + 8.71088i) q^{12} +(-1.09127 - 1.89014i) q^{13} +(2.75659 - 6.61404i) q^{14} +(-3.82949 + 0.578788i) q^{15} +13.7913 q^{16} +(3.56850 + 2.06028i) q^{17} +(6.31619 - 5.11075i) q^{18} +(0.814365 - 0.470174i) q^{19} +(-2.25461 + 11.7142i) q^{20} +(-4.57571 - 0.250719i) q^{21} +(4.64908 - 2.68414i) q^{22} +(3.70432 - 6.41607i) q^{23} +(-5.21914 - 14.7474i) q^{24} +(-4.64279 - 1.85593i) q^{25} +(2.95549 + 5.11906i) q^{26} +(-4.42889 - 2.71753i) q^{27} +(-5.43001 + 13.0285i) q^{28} +(-3.06772 - 1.77115i) q^{29} +(10.3714 - 1.56753i) q^{30} +8.27310i q^{31} -19.2871 q^{32} +(-2.61020 - 2.23019i) q^{33} +(-9.66457 - 5.57984i) q^{34} +(-4.93221 - 3.26700i) q^{35} +(-12.4418 + 10.0673i) q^{36} +(-0.435036 + 0.251168i) q^{37} +(-2.20555 + 1.27337i) q^{38} +(2.45564 - 2.87407i) q^{39} +(3.81702 - 19.8319i) q^{40} +(-1.03473 - 1.79220i) q^{41} +(12.3924 + 0.679021i) q^{42} +(-2.06061 - 1.18970i) q^{43} +(-9.15789 + 5.28731i) q^{44} +(-3.15795 - 5.91839i) q^{45} +(-10.0324 + 17.3767i) q^{46} +3.42460i q^{47} +(7.96939 + 22.5186i) q^{48} +(-4.92805 - 4.97135i) q^{49} +(12.5741 + 5.02643i) q^{50} +(-1.30196 + 7.01724i) q^{51} +(-5.82181 - 10.0837i) q^{52} +(-4.07308 + 7.05479i) q^{53} +(11.9948 + 7.35988i) q^{54} +(-1.45072 - 4.18811i) q^{55} +(9.19291 - 22.0571i) q^{56} +(1.23829 + 1.05801i) q^{57} +(8.30830 + 4.79680i) q^{58} +6.29351 q^{59} +(-20.4299 + 3.08777i) q^{60} -2.69628i q^{61} -22.4060i q^{62} +(-2.23473 - 7.61616i) q^{63} +24.6528 q^{64} +(4.61149 - 1.59738i) q^{65} +(7.06921 + 6.04002i) q^{66} +12.8042i q^{67} +(19.0376 + 10.9913i) q^{68} +(12.6168 + 2.34089i) q^{69} +(13.3579 + 8.84802i) q^{70} +5.02318i q^{71} +(21.0638 - 17.0438i) q^{72} +(3.83786 - 6.64737i) q^{73} +(1.17821 - 0.680239i) q^{74} +(0.347521 - 8.65328i) q^{75} +(4.34455 - 2.50833i) q^{76} +(-0.673146 - 5.20093i) q^{77} +(-6.65062 + 7.78385i) q^{78} -5.33513 q^{79} +(-5.82841 + 30.2824i) q^{80} +(1.87795 - 8.80189i) q^{81} +(2.80235 + 4.85381i) q^{82} +(-0.0907172 - 0.0523756i) q^{83} +(-24.4109 - 1.33756i) q^{84} +(-6.03199 + 6.96489i) q^{85} +(5.58076 + 3.22205i) q^{86} +(1.11925 - 6.03248i) q^{87} +(15.5042 - 8.95133i) q^{88} +(4.17252 + 7.22702i) q^{89} +(8.55269 + 16.0288i) q^{90} +(5.72670 - 0.741195i) q^{91} +(19.7622 - 34.2291i) q^{92} +(-13.5084 + 4.78067i) q^{93} -9.27486i q^{94} +(0.688229 + 1.98686i) q^{95} +(-11.1452 - 31.4923i) q^{96} +(-7.05321 + 12.2165i) q^{97} +(13.3466 + 13.4639i) q^{98} +(2.13316 - 5.55071i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 76 q^{4} - 3 q^{5} - 12 q^{6}+O(q^{10}) $ 88 * q + 76 * q^4 - 3 * q^5 - 12 * q^6	$ 88 q + 76 q^{4} - 3 q^{5} - 12 q^{6} - 6 q^{10} - 12 q^{11} - 12 q^{14} - 6 q^{15} + 52 q^{16} - 12 q^{19} - 6 q^{20} - 12 q^{21} - 48 q^{24} + q^{25} - 12 q^{26} + 6 q^{29} + 33 q^{30} - 12 q^{34} - 36 q^{36} + 12 q^{39} - 30 q^{40} + 6 q^{41} - 84 q^{44} + 21 q^{45} - 18 q^{46} - 8 q^{49} + 30 q^{50} - 24 q^{51} - 60 q^{54} - 78 q^{56} - 12 q^{59} - 45 q^{60} - 8 q^{64} - 24 q^{66} + 60 q^{69} + 15 q^{70} - 30 q^{74} - 48 q^{75} - 48 q^{76} - 16 q^{79} - 69 q^{80} + 36 q^{81} - 90 q^{84} - 7 q^{85} - 12 q^{86} + 72 q^{89} + 33 q^{90} + 20 q^{91} - 60 q^{96} + 30 q^{99}+O(q^{100}) $ 88 * q + 76 * q^4 - 3 * q^5 - 12 * q^6 - 6 * q^10 - 12 * q^11 - 12 * q^14 - 6 * q^15 + 52 * q^16 - 12 * q^19 - 6 * q^20 - 12 * q^21 - 48 * q^24 + q^25 - 12 * q^26 + 6 * q^29 + 33 * q^30 - 12 * q^34 - 36 * q^36 + 12 * q^39 - 30 * q^40 + 6 * q^41 - 84 * q^44 + 21 * q^45 - 18 * q^46 - 8 * q^49 + 30 * q^50 - 24 * q^51 - 60 * q^54 - 78 * q^56 - 12 * q^59 - 45 * q^60 - 8 * q^64 - 24 * q^66 + 60 * q^69 + 15 * q^70 - 30 * q^74 - 48 * q^75 - 48 * q^76 - 16 * q^79 - 69 * q^80 + 36 * q^81 - 90 * q^84 - 7 * q^85 - 12 * q^86 + 72 * q^89 + 33 * q^90 + 20 * q^91 - 60 * q^96 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−2.70830			−1.91506			−0.957529	−	0.288338i	$-0.906897\pi$
$2$	−2.70830			−1.91506			−0.957529	+	0.288338i	$0.906897\pi$
$3$	0.577858	+	1.63281i	0.333626	+	0.942705i
$3$	0.577858	+	1.63281i	0.333626	+	0.942705i
$4$	5.33489			2.66745
$5$	−0.422616	+	2.19577i	−0.189000	+	0.981977i
$5$	−0.422616	+	2.19577i	−0.189000	+	0.981977i
$6$	−1.56501	−	4.42215i	−0.638914	−	1.80534i
$7$	−1.01783	+	2.44214i	−0.384703	+	0.923040i
$7$	−1.01783	+	2.44214i	−0.384703	+	0.923040i
$8$	−9.03188			−3.19325
$9$	−2.33216	+	1.88707i	−0.777387	+	0.629023i
$10$	1.14457	−	5.94680i	0.361945	−	1.88054i
$11$	−1.71660	+	0.991081i	−0.517575	+	0.298822i	−0.735942	−	0.677045i	$-0.763260\pi$
$11$	−1.71660	+	0.991081i	−0.517575	+	0.298822i	0.218367	+	0.975867i	$0.429927\pi$
$12$	3.08281	+	8.71088i	0.889930	+	2.51461i
$13$	−1.09127	−	1.89014i	−0.302664	−	0.524230i	0.674074	−	0.738664i	$-0.264543\pi$
$13$	−1.09127	−	1.89014i	−0.302664	−	0.524230i	−0.976739	+	0.214434i	$0.931209\pi$
$14$	2.75659	−	6.61404i	0.736729	−	1.76768i
$15$	−3.82949	+	0.578788i	−0.988770	+	0.149442i
$16$	13.7913			3.44782
$17$	3.56850	+	2.06028i	0.865489	+	0.499690i	0.865846	−	0.500310i	$-0.166781\pi$
$17$	3.56850	+	2.06028i	0.865489	+	0.499690i	−0.000357731		1.00000i	$0.500114\pi$
$18$	6.31619	−	5.11075i	1.48874	−	1.20461i
$19$	0.814365	−	0.470174i	0.186828	−	0.107865i	−0.403669	−	0.914905i	$-0.632265\pi$
$19$	0.814365	−	0.470174i	0.186828	−	0.107865i	0.590497	+	0.807040i	$0.298932\pi$
$20$	−2.25461	+	11.7142i	−0.504146	+	2.61937i
$21$	−4.57571	−	0.250719i	−0.998502	−	0.0547113i
$22$	4.64908	−	2.68414i	0.991186	−	0.572262i
$23$	3.70432	−	6.41607i	0.772405	−	1.33784i	−0.163837	−	0.986487i	$-0.552387\pi$
$23$	3.70432	−	6.41607i	0.772405	−	1.33784i	0.936242	−	0.351357i	$-0.114279\pi$
$24$	−5.21914	−	14.7474i	−1.06535	−	3.01030i
$25$	−4.64279	−	1.85593i	−0.928558	−	0.371187i
$26$	2.95549	+	5.11906i	0.579619	+	1.00393i
$27$	−4.42889	−	2.71753i	−0.852340	−	0.522988i
$28$	−5.43001	+	13.0285i	−1.02617	+	2.46216i
$29$	−3.06772	−	1.77115i	−0.569661	−	0.328894i	0.187353	−	0.982293i	$-0.440009\pi$
$29$	−3.06772	−	1.77115i	−0.569661	−	0.328894i	−0.757014	+	0.653399i	$0.773343\pi$
$30$	10.3714	−	1.56753i	1.89355	−	0.286191i
$31$			8.27310i			1.48589i	0.669351	+	0.742946i	$0.266572\pi$
$31$			8.27310i			1.48589i	−0.669351	+	0.742946i	$0.733428\pi$
$32$	−19.2871			−3.40952
$33$	−2.61020	−	2.23019i	−0.454378	−	0.388226i
$34$	−9.66457	−	5.57984i	−1.65746	−	0.956935i
$35$	−4.93221	−	3.26700i	−0.833696	−	0.552224i
$36$	−12.4418	+	10.0673i	−2.07364	+	1.67788i
$37$	−0.435036	+	0.251168i	−0.0715195	+	0.0412918i	−0.535333	−	0.844641i	$-0.679814\pi$
$37$	−0.435036	+	0.251168i	−0.0715195	+	0.0412918i	0.463814	+	0.885933i	$0.346481\pi$
$38$	−2.20555	+	1.27337i	−0.357787	+	0.206568i
$39$	2.45564	−	2.87407i	0.393218	−	0.460220i
$40$	3.81702	−	19.8319i	0.603524	−	3.13570i
$41$	−1.03473	−	1.79220i	−0.161597	−	0.279894i	0.773845	−	0.633376i	$-0.218331\pi$
$41$	−1.03473	−	1.79220i	−0.161597	−	0.279894i	−0.935442	+	0.353481i	$0.884998\pi$
$42$	12.3924	+	0.679021i	1.91219	+	0.104775i
$43$	−2.06061	−	1.18970i	−0.314241	−	0.181427i	0.334582	−	0.942367i	$-0.391405\pi$
$43$	−2.06061	−	1.18970i	−0.314241	−	0.181427i	−0.648823	+	0.760940i	$0.724738\pi$
$44$	−9.15789	+	5.28731i	−1.38060	+	0.797092i
$45$	−3.15795	−	5.91839i	−0.470760	−	0.882261i
$46$	−10.0324	+	17.3767i	−1.47920	+	2.56205i
$47$			3.42460i			0.499530i	0.968306	+	0.249765i	$0.0803534\pi$
$47$			3.42460i			0.499530i	−0.968306	+	0.249765i	$0.919647\pi$
$48$	7.96939	+	22.5186i	1.15028	+	3.25028i
$49$	−4.92805	−	4.97135i	−0.704007	−	0.710193i
$50$	12.5741	+	5.02643i	1.77824	+	0.710844i
$51$	−1.30196	+	7.01724i	−0.182311	+	0.982611i
$52$	−5.82181	−	10.0837i	−0.807340	−	1.39835i
$53$	−4.07308	+	7.05479i	−0.559481	+	0.969049i	0.438059	+	0.898946i	$0.355666\pi$
$53$	−4.07308	+	7.05479i	−0.559481	+	0.969049i	−0.997540	+	0.0701030i	$0.977667\pi$
$54$	11.9948	+	7.35988i	1.63228	+	1.00155i
$55$	−1.45072	−	4.18811i	−0.195615	−	0.564724i
$56$	9.19291	−	22.0571i	1.22845	−	2.94750i
$57$	1.23829	+	1.05801i	0.164016	+	0.140137i
$58$	8.30830	+	4.79680i	1.09093	+	0.629851i
$59$	6.29351			0.819345			0.409673	−	0.912233i	$-0.365643\pi$
$59$	6.29351			0.819345			0.409673	+	0.912233i	$0.365643\pi$
$60$	−20.4299	+	3.08777i	−2.63749	+	0.398629i
$61$		−	2.69628i		−	0.345223i	−0.984990	−	0.172612i	$-0.944779\pi$
$61$		−	2.69628i		−	0.345223i	0.984990	−	0.172612i	$-0.0552205\pi$
$62$		−	22.4060i		−	2.84557i
$63$	−2.23473	−	7.61616i	−0.281550	−	0.959547i
$64$	24.6528			3.08160
$65$	4.61149	−	1.59738i	0.571985	−	0.198130i
$66$	7.06921	+	6.04002i	0.870160	+	0.743475i
$67$			12.8042i			1.56429i	0.623098	+	0.782144i	$0.285874\pi$
$67$			12.8042i			1.56429i	−0.623098	+	0.782144i	$0.714126\pi$
$68$	19.0376	+	10.9913i	2.30864	+	1.33290i
$69$	12.6168	+	2.34089i	1.51889	+	0.281810i
$70$	13.3579	+	8.84802i	1.59658	+	1.05754i
$71$			5.02318i			0.596142i	0.954544	+	0.298071i	$0.0963432\pi$
$71$			5.02318i			0.596142i	−0.954544	+	0.298071i	$0.903657\pi$
$72$	21.0638	−	17.0438i	2.48239	−	2.00863i
$73$	3.83786	−	6.64737i	0.449188	−	0.778016i	−0.549145	−	0.835727i	$-0.685047\pi$
$73$	3.83786	−	6.64737i	0.449188	−	0.778016i	0.998333	+	0.0577105i	$0.0183800\pi$
$74$	1.17821	−	0.680239i	0.136964	−	0.0790762i
$75$	0.347521	−	8.65328i	0.0401283	−	0.999195i
$76$	4.34455	−	2.50833i	0.498354	−	0.287725i
$77$	−0.673146	−	5.20093i	−0.0767121	−	0.592701i
$78$	−6.65062	+	7.78385i	−0.753034	+	0.881348i
$79$	−5.33513			−0.600249			−0.300125	−	0.953900i	$-0.597028\pi$
$79$	−5.33513			−0.600249			−0.300125	+	0.953900i	$0.597028\pi$
$80$	−5.82841	+	30.2824i	−0.651637	+	3.38568i
$81$	1.87795	−	8.80189i	0.208661	−	0.977988i
$82$	2.80235	+	4.85381i	0.309468	+	0.536014i
$83$	−0.0907172	−	0.0523756i	−0.00995751	−	0.00574897i	0.495013	−	0.868886i	$-0.335163\pi$
$83$	−0.0907172	−	0.0523756i	−0.00995751	−	0.00574897i	−0.504970	+	0.863137i	$0.668497\pi$
$84$	−24.4109	−	1.33756i	−2.66345	−	0.145939i
$85$	−6.03199	+	6.96489i	−0.654261	+	0.755449i
$86$	5.58076	+	3.22205i	0.601789	+	0.347443i
$87$	1.11925	−	6.03248i	0.119996	−	0.646750i
$88$	15.5042	−	8.95133i	1.65275	−	0.954215i
$89$	4.17252	+	7.22702i	0.442287	+	0.766063i	0.997859	−	0.0654055i	$-0.0208341\pi$
$89$	4.17252	+	7.22702i	0.442287	+	0.766063i	−0.555572	+	0.831468i	$0.687501\pi$
$90$	8.55269	+	16.0288i	0.901532	+	1.68958i
$91$	5.72670	−	0.741195i	0.600321	−	0.0776984i
$92$	19.7622	−	34.2291i	2.06035	−	3.56863i
$93$	−13.5084	+	4.78067i	−1.40076	+	0.495733i
$94$		−	9.27486i		−	0.956629i
$95$	0.688229	+	1.98686i	0.0706108	+	0.203848i
$96$	−11.1452	−	31.4923i	−1.13750	−	3.21417i
$97$	−7.05321	+	12.2165i	−0.716145	+	1.24040i	0.246371	+	0.969176i	$0.420762\pi$
$97$	−7.05321	+	12.2165i	−0.716145	+	1.24040i	−0.962516	+	0.271224i	$0.912572\pi$
$98$	13.3466	+	13.4639i	1.34821	+	1.36006i
$99$	2.13316	−	5.55071i	0.214390	−	0.557867i
$100$	−24.7688	−	9.90120i	−2.47688	−	0.990120i
$101$	−2.54244	−	4.40364i	−0.252983	−	0.438179i	0.711363	−	0.702825i	$-0.248078\pi$
$101$	−2.54244	−	4.40364i	−0.252983	−	0.438179i	−0.964346	+	0.264646i	$0.914745\pi$
$102$	3.52610	−	19.0048i	0.349136	−	1.88176i
$103$	−3.86536	+	6.69499i	−0.380865	+	0.659677i	−0.991186	−	0.132477i	$-0.957707\pi$
$103$	−3.86536	+	6.69499i	−0.380865	+	0.659677i	0.610321	+	0.792154i	$0.291040\pi$
$104$	9.85624	+	17.0715i	0.966483	+	1.67400i
$105$	2.48429	−	9.94124i	0.242442	−	0.970166i
$106$	11.0311	−	19.1065i	1.07144	−	1.85579i
$107$	1.61993	+	2.80580i	0.156604	+	0.271247i	0.933642	−	0.358207i	$-0.116612\pi$
$107$	1.61993	+	2.80580i	0.156604	+	0.271247i	−0.777038	+	0.629454i	$0.783279\pi$
$108$	−23.6276	−	14.4977i	−2.27357	−	1.39504i
$109$	−0.812760	+	1.40774i	−0.0778483	+	0.134837i	−0.902321	−	0.431064i	$-0.858138\pi$
$109$	−0.812760	+	1.40774i	−0.0778483	+	0.134837i	0.824473	+	0.565901i	$0.191472\pi$
$110$	3.92898	+	11.3427i	0.374614	+	1.08148i
$111$	−0.661500	−	0.565194i	−0.0627868	−	0.0536458i
$112$	−14.0372	+	33.6802i	−1.32639	+	3.18248i
$113$	6.15224	+	10.6560i	0.578754	+	1.00243i	0.995623	+	0.0934643i	$0.0297941\pi$
$113$	6.15224	+	10.6560i	0.578754	+	1.00243i	−0.416869	+	0.908967i	$0.636873\pi$
$114$	−3.35367	−	2.86542i	−0.314100	−	0.268371i
$115$	12.5227	+	10.8454i	1.16775	+	1.01134i
$116$	−16.3659	−	9.44888i	−1.51954	−	0.877307i
$117$	6.11184	+	2.34880i	0.565040	+	0.217147i
$118$	−17.0447			−1.56909
$119$	−8.66360	+	6.61775i	−0.794190	+	0.606649i
$120$	34.5875	−	5.22755i	3.15739	−	0.477207i
$121$	−3.53552	+	6.12370i	−0.321411	+	0.556700i
$122$			7.30233i			0.661122i
$123$	2.32840	−	2.72515i	0.209945	−	0.245718i
$124$			44.1361i			3.96353i
$125$	6.03732	−	9.41014i	0.539994	−	0.841669i
$126$	6.05233	+	20.6269i	0.539184	+	1.83759i
$127$			9.16158i			0.812959i	0.913660	+	0.406479i	$0.133244\pi$
$127$			9.16158i			0.812959i	−0.913660	+	0.406479i	$0.866756\pi$
$128$	−28.1930			−2.49193
$129$	0.751810	−	4.05207i	0.0661932	−	0.356765i
$130$	−12.4893	+	4.32617i	−1.09538	+	0.379430i
$131$	1.28443	−	2.22470i	0.112221	−	0.194373i	−0.804444	−	0.594028i	$-0.797537\pi$
$131$	1.28443	−	2.22470i	0.112221	−	0.194373i	0.916666	+	0.399655i	$0.130870\pi$
$132$	−13.9251	−	11.8978i	−1.21203	−	1.03557i
$133$	0.319344	+	2.46735i	0.0276906	+	0.213946i
$134$		−	34.6777i		−	2.99570i
$135$	7.83878	−	8.57634i	0.674655	−	0.738134i
$136$	−32.2303	−	18.6082i	−2.76372	−	1.59564i
$137$	−2.08537	−	3.61197i	−0.178165	−	0.308591i	0.763087	−	0.646296i	$-0.223683\pi$
$137$	−2.08537	−	3.61197i	−0.178165	−	0.308591i	−0.941252	+	0.337705i	$0.890350\pi$
$138$	−34.1701	−	6.33983i	−2.90876	−	0.539682i
$139$	16.4254	−	9.48320i	1.39318	−	0.804354i	0.399517	−	0.916726i	$-0.369178\pi$
$139$	16.4254	−	9.48320i	1.39318	−	0.804354i	0.993666	+	0.112372i	$0.0358447\pi$
$140$	−26.3128	−	17.4291i	−2.22384	−	1.47303i
$141$	−5.59174	+	1.97893i	−0.470910	+	0.166656i
$142$		−	13.6043i		−	1.14165i
$143$	3.74656	+	2.16308i	0.313303	+	0.180886i
$144$	−32.1635	+	26.0251i	−2.68029	+	2.16876i
$145$	5.18550	−	5.98748i	0.430632	−	0.497233i
$146$	−10.3941	+	18.0031i	−0.860221	+	1.48995i
$147$	5.26958	−	10.9193i	0.434628	−	0.900610i
$148$	−2.32087	+	1.33996i	−0.190774	+	0.110144i
$149$	−4.68628	−	2.70563i	−0.383915	−	0.221654i	0.295605	−	0.955310i	$-0.404479\pi$
$149$	−4.68628	−	2.70563i	−0.383915	−	0.221654i	−0.679520	+	0.733657i	$0.737812\pi$
$150$	−0.941191	+	23.4357i	−0.0768479	+	1.91351i
$151$	5.03721	+	8.72471i	0.409923	+	0.710007i	0.994881	−	0.101057i	$-0.0322224\pi$
$151$	5.03721	+	8.72471i	0.409923	+	0.710007i	−0.584958	+	0.811064i	$0.698889\pi$
$152$	−7.35525	+	4.24656i	−0.596590	+	0.344441i
$153$	−12.2102	+	1.92911i	−0.987136	+	0.155959i
$154$	1.82308	+	14.0857i	0.146908	+	1.13506i
$155$	−18.1658	−	3.49634i	−1.45911	−	0.280833i
$156$	13.1006	−	15.3329i	1.04889	−	1.22761i
$157$	1.24834			0.0996283			0.0498141	−	0.998759i	$-0.484137\pi$
$157$	1.24834			0.0996283			0.0498141	+	0.998759i	$0.484137\pi$
$158$	14.4491			1.14951
$159$	−13.8728	−	2.57392i	−1.10019	−	0.204125i
$160$	8.15106	−	42.3501i	0.644398	−	3.34807i
$161$	11.8986	+	15.5769i	0.937737	+	1.22763i
$162$	−5.08605	+	23.8382i	−0.399598	+	1.87290i
$163$	16.8002	−	9.69962i	1.31590	−	0.759733i	0.332831	−	0.942987i	$-0.391996\pi$
$163$	16.8002	−	9.69962i	1.31590	−	0.759733i	0.983066	+	0.183253i	$0.0586629\pi$
$164$	−5.52015	−	9.56118i	−0.431051	−	0.746603i
$165$	6.00009	−	4.78888i	0.467106	−	0.372814i
$166$	0.245689	+	0.141849i	0.0190692	+	0.0110096i
$167$	4.48863	−	2.59151i	0.347340	−	0.200537i	−0.316173	−	0.948702i	$-0.602398\pi$
$167$	4.48863	−	2.59151i	0.347340	−	0.200537i	0.663513	+	0.748165i	$0.269065\pi$
$168$	41.3273	+	2.26446i	3.18847	+	0.174707i
$169$	4.11825	−	7.13303i	0.316789	−	0.548694i
$170$	16.3364	−	18.8630i	1.25295	−	1.44673i
$171$	−1.01198	+	2.63328i	−0.0773881	+	0.201372i
$172$	−10.9931	−	6.34690i	−0.838220	−	0.483946i
$173$		−	4.76548i		−	0.362313i	−0.983454	−	0.181156i	$-0.942016\pi$
$173$		−	4.76548i		−	0.362313i	0.983454	−	0.181156i	$-0.0579840\pi$
$174$	−3.03127	+	16.3378i	−0.229800	+	1.23856i
$175$	9.25801	−	9.44930i	0.699840	−	0.714300i
$176$	−23.6741	+	13.6683i	−1.78451	+	1.03028i
$177$	3.63675	+	10.2761i	0.273355	+	0.772401i
$178$	−11.3004	−	19.5729i	−0.847004	−	1.46705i
$179$	20.4483	+	11.8058i	1.52838	+	0.882408i	0.999430	+	0.0337528i	$0.0107459\pi$
$179$	20.4483	+	11.8058i	1.52838	+	0.882408i	0.528946	+	0.848656i	$0.322587\pi$
$180$	−16.8473	−	31.5740i	−1.25573	−	2.35338i
$181$		−	2.72600i		−	0.202622i	−0.994855	−	0.101311i	$-0.967696\pi$
$181$		−	2.72600i		−	0.202622i	0.994855	−	0.101311i	$-0.0323037\pi$
$182$	−15.5096	+	2.00738i	−1.14965	+	0.148797i
$183$	4.40252	−	1.55806i	0.325444	−	0.115175i
$184$	−33.4570	+	57.9492i	−2.46648	+	4.27207i
$185$	−0.367654	−	1.06139i	−0.0270305	−	0.0780347i
$186$	36.5849	−	12.9475i	2.68253	−	0.949356i
$187$	−8.16760			−0.597274
$188$			18.2699i			1.33247i
$189$	11.1444	−	8.04996i	0.810637	−	0.585549i
$190$	−1.86393	−	5.38101i	−0.135224	−	0.390380i
$191$			22.4598i			1.62514i	0.582867	+	0.812568i	$0.301931\pi$
$191$			22.4598i			1.62514i	−0.582867	+	0.812568i	$0.698069\pi$
$192$	14.2458	+	40.2535i	1.02810	+	2.90504i
$193$		−	10.0800i		−	0.725572i	−0.931872	−	0.362786i	$-0.881826\pi$
$193$		−	10.0800i		−	0.725572i	0.931872	−	0.362786i	$-0.118174\pi$
$194$	19.1022	−	33.0860i	1.37146	−	2.37544i
$195$	5.27300	+	6.60665i	0.377608	+	0.473112i
$196$	−26.2906	−	26.5216i	−1.87790	−	1.89440i
$197$	−25.3735			−1.80779			−0.903895	−	0.427755i	$-0.859305\pi$
$197$	−25.3735			−1.80779			−0.903895	+	0.427755i	$0.859305\pi$
$198$	−5.77723	+	15.0330i	−0.410570	+	1.06835i
$199$	15.4584	+	8.92491i	1.09582	+	0.632670i	0.935119	−	0.354334i	$-0.115292\pi$
$199$	15.4584	+	8.92491i	1.09582	+	0.632670i	0.160698	+	0.987004i	$0.448626\pi$
$200$	41.9332	+	16.7626i	2.96512	+	1.18529i
$201$	−20.9069	+	7.39903i	−1.47466	+	0.521887i
$202$	6.88570	+	11.9264i	0.484476	+	0.839138i
$203$	7.44780	−	5.68906i	0.522733	−	0.399294i
$204$	−6.94581	+	37.4362i	−0.486304	+	2.62106i
$205$	4.37254	−	1.51461i	0.305392	−	0.105785i
$206$	10.4685	−	18.1321i	0.729378	−	1.26332i
$207$	3.46849	+	21.9536i	0.241077	+	1.52588i
$208$	−15.0500	−	26.0674i	−1.04353	−	1.80745i
$209$	−0.931961	+	1.61420i	−0.0644651	+	0.111657i
$210$	−6.72820	+	26.9239i	−0.464290	+	1.85792i
$211$	5.08259	+	8.80330i	0.349900	+	0.606044i	0.986231	−	0.165372i	$-0.0528824\pi$
$211$	5.08259	+	8.80330i	0.349900	+	0.606044i	−0.636332	+	0.771416i	$0.719549\pi$
$212$	−21.7294	+	37.6365i	−1.49238	+	2.58489i
$213$	−8.20192	+	2.90268i	−0.561986	+	0.198889i
$214$	−4.38725	−	7.59895i	−0.299906	−	0.519453i
$215$	3.48314	−	4.02184i	0.237548	−	0.274287i
$216$	40.0012	+	24.5444i	2.72174	+	1.67003i
$217$	−20.2040	−	8.42060i	−1.37154	−	0.571627i
$218$	2.20120	−	3.81259i	0.149084	−	0.258221i
$219$	13.0717	+	2.42528i	0.883301	+	0.163885i
$220$	−7.73943	−	22.3431i	−0.521792	−	1.50637i
$221$		−	8.99328i		−	0.604953i
$222$	1.79154	+	1.53071i	0.120240	+	0.102735i
$223$	11.5531	−	20.0106i	0.773654	−	1.34001i	−0.161894	−	0.986808i	$-0.551760\pi$
$223$	11.5531	−	20.0106i	0.773654	−	1.34001i	0.935548	−	0.353200i	$-0.114906\pi$
$224$	19.6310	−	47.1018i	1.31165	−	3.14712i
$225$	14.3300	−	4.43293i	0.955334	−	0.295528i
$226$	−16.6621	−	28.8596i	−1.10835	−	1.91971i
$227$	5.78877	−	3.34215i	0.384214	−	0.221826i	−0.295436	−	0.955363i	$-0.595465\pi$
$227$	5.78877	−	3.34215i	0.384214	−	0.221826i	0.679650	+	0.733536i	$0.262132\pi$
$228$	6.60616	+	5.64439i	0.437504	+	0.373809i
$229$	−9.98658	−	5.76576i	−0.659932	−	0.381012i	0.132319	−	0.991207i	$-0.457758\pi$
$229$	−9.98658	−	5.76576i	−0.659932	−	0.381012i	−0.792251	+	0.610195i	$0.791091\pi$
$230$	−33.9152	−	29.3725i	−2.23630	−	1.93677i
$231$	8.10316	−	4.10452i	0.533149	−	0.270057i
$232$	27.7073	+	15.9968i	1.81907	+	1.05024i
$233$	5.22252	+	9.04568i	0.342139	+	0.592602i	0.984830	−	0.173524i	$-0.0555153\pi$
$233$	5.22252	+	9.04568i	0.342139	+	0.592602i	−0.642691	+	0.766126i	$0.722182\pi$
$234$	−16.5527	−	6.36126i	−1.08208	−	0.415849i
$235$	−7.51964	−	1.44729i	−0.490527	−	0.0944110i
$236$	33.5752			2.18556
$237$	−3.08295	−	8.71127i	−0.200259	−	0.565858i
$238$	23.4636	−	17.9229i	1.52092	−	1.16177i
$239$	−15.2471	+	8.80294i	−0.986256	+	0.569415i	−0.904153	−	0.427209i	$-0.859497\pi$
$239$	−15.2471	+	8.80294i	−0.986256	+	0.569415i	−0.0821028	+	0.996624i	$0.526164\pi$
$240$	−52.8136	+	7.98222i	−3.40910	+	0.515250i
$241$	−18.8305	+	10.8718i	−1.21298	+	0.700314i	−0.963407	−	0.268042i	$-0.913623\pi$
$241$	−18.8305	+	10.8718i	−1.21298	+	0.700314i	−0.249572	+	0.968356i	$0.580290\pi$
$242$	9.57524	−	16.5848i	0.615520	−	1.06611i
$243$	15.4570	−	2.01990i	0.991569	−	0.129577i
$244$		−	14.3843i		−	0.920863i
$245$	12.9986	−	8.71988i	0.830451	−	0.557092i
$246$	−6.30601	+	7.38052i	−0.402056	+	0.470565i
$247$	−1.77739	−	1.02618i	−0.113092	−	0.0652940i
$248$		−	74.7216i		−	4.74483i
$249$	0.0330980	−	0.178390i	0.00209750	−	0.0113050i
$250$	−16.3509	+	25.4855i	−1.03412	+	1.61184i
$251$	−26.3947			−1.66602			−0.833009	−	0.553260i	$-0.813384\pi$
$251$	−26.3947			−1.66602			−0.833009	+	0.553260i	$0.813384\pi$
$252$	−11.9221	−	40.6314i	−0.751019	−	2.55954i
$253$			14.6851i			0.923246i
$254$		−	24.8123i		−	1.55686i
$255$	−14.8580	−	5.82440i	−0.930445	−	0.364738i
$256$	27.0494			1.69059
$257$	4.68970	+	2.70760i	0.292535	+	0.168895i	0.639085	−	0.769136i	$-0.279313\pi$
$257$	4.68970	+	2.70760i	0.292535	+	0.168895i	−0.346549	+	0.938032i	$0.612647\pi$
$258$	−2.03613	+	10.9742i	−0.126764	+	0.683226i
$259$	−0.170594	−	1.31806i	−0.0106002	−	0.0819005i
$260$	24.6018	−	8.52182i	1.52574	−	0.528501i
$261$	10.4967	−	1.65839i	0.649729	−	0.102652i
$262$	−3.47862	+	6.02515i	−0.214910	+	0.372235i
$263$	3.78397	+	6.55403i	0.233330	+	0.404139i	0.958786	−	0.284129i	$-0.0917045\pi$
$263$	3.78397	+	6.55403i	0.233330	+	0.404139i	−0.725456	+	0.688268i	$0.758371\pi$
$264$	23.5750	+	20.1428i	1.45094	+	1.23970i
$265$	−13.7693	−	11.9250i	−0.845843	−	0.732547i
$266$	−0.864879	−	6.68232i	−0.0530291	−	0.409719i
$267$	−9.38926	+	10.9891i	−0.574613	+	0.672525i
$268$			68.3092i			4.17265i
$269$	−4.70695	+	8.15268i	−0.286988	+	0.497077i	−0.973089	−	0.230428i	$-0.925987\pi$
$269$	−4.70695	+	8.15268i	−0.286988	+	0.497077i	0.686101	+	0.727506i	$0.259321\pi$
$270$	−21.2298	+	23.2273i	−1.29200	+	1.41357i
$271$	11.1877	−	6.45922i	0.679605	−	0.392370i	−0.120102	−	0.992762i	$-0.538322\pi$
$271$	11.1877	−	6.45922i	0.679605	−	0.392370i	0.799706	+	0.600392i	$0.204989\pi$
$272$	49.2142	+	28.4138i	2.98405	+	1.72284i
$273$	4.51945	+	8.92233i	0.273530	+	0.540004i
$274$	5.64781	+	9.78230i	0.341197	+	0.590970i
$275$	9.80921	−	1.41548i	0.591517	−	0.0853568i
$276$	67.3094	+	12.4884i	4.05155	+	0.751713i
$277$	10.0762	−	5.81750i	0.605420	−	0.349540i	−0.165751	−	0.986168i	$-0.553005\pi$
$277$	10.0762	−	5.81750i	0.605420	−	0.349540i	0.771171	+	0.636628i	$0.219671\pi$
$278$	−44.4849	+	25.6834i	−2.66803	+	1.54039i
$279$	−15.6119	−	19.2942i	−0.934660	−	1.15511i
$280$	44.5472	+	29.5072i	2.66220	+	1.76339i
$281$	8.75060	+	5.05216i	0.522017	+	0.301387i	0.737759	−	0.675064i	$-0.235884\pi$
$281$	8.75060	+	5.05216i	0.522017	+	0.301387i	−0.215743	+	0.976450i	$0.569217\pi$
$282$	15.1441	−	5.35955i	0.901819	−	0.319156i
$283$	−15.3386			−0.911788			−0.455894	−	0.890034i	$-0.650680\pi$
$283$	−15.3386			−0.911788			−0.455894	+	0.890034i	$0.650680\pi$
$284$			26.7981i			1.59018i
$285$	−2.84647	+	2.27187i	−0.168611	+	0.134574i
$286$	−10.1468	−	5.85826i	−0.599993	−	0.346406i
$287$	5.42996	−	0.702790i	0.320521	−	0.0414844i
$288$	44.9807	−	36.3961i	2.65051	−	2.14466i
$289$	−0.0105312	−	0.0182405i	−0.000619481	−	0.00107297i
$290$	−14.0439	+	16.2159i	−0.824685	+	0.952230i
$291$	−24.0231	−	4.45717i	−1.40826	−	0.261284i
$292$	20.4746	−	35.4630i	1.19818	−	2.07532i
$293$	−14.9270	+	8.61810i	−0.872043	+	0.503475i	−0.868027	−	0.496517i	$-0.834612\pi$
$293$	−14.9270	+	8.61810i	−0.872043	+	0.503475i	−0.00401671	+	0.999992i	$0.501279\pi$
$294$	−14.2716	+	29.5728i	−0.832337	+	1.72472i
$295$	−2.65974	+	13.8191i	−0.154856	+	0.804578i
$296$	3.92920	−	2.26852i	0.228380	−	0.131855i
$297$	10.2959	+	0.275529i	0.597430	+	0.0159878i
$298$	12.6919	+	7.32765i	0.735220	+	0.424479i
$299$	−16.1697			−0.935117
$300$	1.85399	−	46.1643i	0.107040	−	2.66530i
$301$	5.00275	−	3.82139i	0.288354	−	0.220261i
$302$	−13.6423	−	23.6291i	−0.785025	−	1.35970i
$303$	5.72116	−	6.69602i	0.328672	−	0.384676i
$304$	11.2311	−	6.48430i	0.644150	−	0.371900i
$305$	5.92040	+	1.13949i	0.339001	+	0.0652470i
$306$	33.0689	−	5.22461i	1.89042	−	0.298671i
$307$	22.0324			1.25746			0.628729	−	0.777625i	$-0.283576\pi$
$307$	22.0324			1.25746			0.628729	+	0.777625i	$0.283576\pi$
$308$	−3.59116	−	27.7464i	−0.204625	−	1.58100i
$309$	−13.1653	−	2.44265i	−0.748948	−	0.138958i
$310$	49.1984	+	9.46915i	2.79428	+	0.537811i
$311$	14.1455			0.802115			0.401058	−	0.916053i	$-0.368643\pi$
$311$	14.1455			0.802115			0.401058	+	0.916053i	$0.368643\pi$
$312$	−22.1791	+	25.9583i	−1.25564	+	1.46960i
$313$	20.2242			1.14314			0.571569	−	0.820554i	$-0.306335\pi$
$313$	20.2242			1.14314			0.571569	+	0.820554i	$0.306335\pi$
$314$	−3.38088			−0.190794
$315$	17.6678	−	1.68824i	0.995466	−	0.0951216i
$316$	−28.4623			−1.60113
$317$	−16.3648			−0.919140			−0.459570	−	0.888142i	$-0.651996\pi$
$317$	−16.3648			−0.919140			−0.459570	+	0.888142i	$0.651996\pi$
$318$	37.5717	+	6.97095i	2.10692	+	0.390912i
$319$	7.02140			0.393123
$320$	−10.4187	+	54.1319i	−0.582422	+	3.02606i
$321$	−3.64526	+	4.26639i	−0.203458	+	0.238127i
$322$	−32.2249	−	42.1870i	−1.79582	−	2.35099i
$323$	3.87475			0.215597
$324$	10.0187	−	46.9571i	0.556592	−	2.60873i
$325$	1.55858	+	10.8008i	0.0864542	+	0.599123i
$326$	−45.5001	+	26.2695i	−2.52002	+	1.45493i
$327$	−2.76824	−	0.513612i	−0.153084	−	0.0284028i
$328$	9.34553	+	16.1869i	0.516020	+	0.893773i
$329$	−8.36335	−	3.48566i	−0.461086	−	0.192171i
$330$	−16.2500	+	12.9697i	−0.894535	+	0.713961i
$331$	7.35349			0.404184			0.202092	−	0.979367i	$-0.435226\pi$
$331$	7.35349			0.404184			0.202092	+	0.979367i	$0.435226\pi$
$332$	−0.483966	−	0.279418i	−0.0265611	−	0.0153351i
$333$	0.540603	−	1.40671i	0.0296249	−	0.0770871i
$334$	−12.1566	+	7.01859i	−0.665177	+	0.384040i
$335$	−28.1151	−	5.41128i	−1.53609	−	0.295650i
$336$	−63.1049	−	3.45773i	−3.44265	−	0.188635i
$337$	7.66922	−	4.42783i	0.417769	−	0.241199i	−0.276353	−	0.961056i	$-0.589126\pi$
$337$	7.66922	−	4.42783i	0.417769	−	0.241199i	0.694122	+	0.719857i	$0.255793\pi$
$338$	−11.1535	+	19.3184i	−0.606669	+	1.05078i
$339$	−13.8441	+	16.2031i	−0.751910	+	0.880032i
$340$	−32.1800	+	37.1569i	−1.74521	+	2.01512i
$341$	−8.19931	−	14.2016i	−0.444017	−	0.769061i
$342$	2.74075	−	7.13173i	0.148203	−	0.385640i
$343$	17.1566	−	6.97497i	0.926371	−	0.376613i
$344$	18.6112	+	10.7452i	1.00345	+	0.579342i
$345$	−10.4721	+	26.7143i	−0.563800	+	1.43825i
$346$			12.9064i			0.693850i
$347$	−15.5872			−0.836765			−0.418383	−	0.908271i	$-0.637403\pi$
$347$	−15.5872			−0.836765			−0.418383	+	0.908271i	$0.637403\pi$
$348$	5.97108	−	32.1826i	0.320083	−	1.72517i
$349$	−7.63902	−	4.41039i	−0.408908	−	0.236083i	0.281413	−	0.959587i	$-0.409197\pi$
$349$	−7.63902	−	4.41039i	−0.408908	−	0.236083i	−0.690320	+	0.723504i	$0.742530\pi$
$350$	−25.0735	+	25.5915i	−1.34023	+	1.36793i
$351$	−0.303383	+	11.3368i	−0.0161934	+	0.605112i
$352$	33.1084	−	19.1151i	1.76468	−	1.01884i
$353$	3.63467	−	2.09848i	0.193454	−	0.111691i	−0.400144	−	0.916452i	$-0.631040\pi$
$353$	3.63467	−	2.09848i	0.193454	−	0.111691i	0.593599	+	0.804761i	$0.297707\pi$
$354$	−9.84942	−	27.8308i	−0.523491	−	1.47919i
$355$	−11.0297	−	2.12288i	−0.585398	−	0.112671i
$356$	22.2600	+	38.5554i	1.17978	+	2.04343i
$357$	−15.8119	−	10.3219i	−0.836854	−	0.546294i
$358$	−55.3801	−	31.9737i	−2.92693	−	1.68986i
$359$	−4.15127	+	2.39673i	−0.219095	+	0.126495i	−0.605531	−	0.795821i	$-0.707039\pi$
$359$	−4.15127	+	2.39673i	−0.219095	+	0.126495i	0.386436	+	0.922316i	$0.373706\pi$
$360$	28.5223	+	53.4542i	1.50326	+	2.81728i
$361$	−9.05787	+	15.6887i	−0.476730	+	0.825721i
$362$			7.38282i			0.388033i
$363$	−12.0419	−	2.23422i	−0.632035	−	0.117266i
$364$	30.5513	−	3.95420i	1.60132	−	0.207256i
$365$	12.9741	+	11.2363i	0.679098	+	0.588137i
$366$	−11.9233	+	4.21971i	−0.623243	+	0.220568i
$367$	1.07963	+	1.86997i	0.0563560	+	0.0976115i	0.892827	−	0.450400i	$-0.148718\pi$
$367$	1.07963	+	1.86997i	0.0563560	+	0.0976115i	−0.836471	+	0.548011i	$0.815385\pi$
$368$	51.0873	−	88.4858i	2.66311	−	4.61264i
$369$	5.79515	+	2.22710i	0.301683	+	0.115938i
$370$	0.995718	+	2.87455i	0.0517649	+	0.149441i
$371$	−13.0830	−	17.1276i	−0.679237	−	0.889220i
$372$	−72.0660	+	25.5044i	−3.73645	+	1.32234i
$373$	−27.5510	−	15.9066i	−1.42654	−	0.823612i	−0.429691	−	0.902976i	$-0.641378\pi$
$373$	−27.5510	−	15.9066i	−1.42654	−	0.823612i	−0.996846	+	0.0793643i	$0.974711\pi$
$374$	22.1203			1.14381
$375$	18.8537	+	4.42009i	0.973602	+	0.228252i
$376$		−	30.9306i		−	1.59513i
$377$			7.73121i			0.398178i
$378$	−30.1824	+	21.8017i	−1.55242	+	1.12136i
$379$	2.25020			0.115585			0.0577926	−	0.998329i	$-0.481594\pi$
$379$	2.25020			0.115585			0.0577926	+	0.998329i	$0.481594\pi$
$380$	3.67163	+	10.5997i	0.188351	+	0.543752i
$381$	−14.9592	+	5.29409i	−0.766381	+	0.271224i
$382$		−	60.8279i		−	3.11223i
$383$	−22.7055	−	13.1090i	−1.16020	−	0.669840i	−0.208845	−	0.977949i	$-0.566970\pi$
$383$	−22.7055	−	13.1090i	−1.16020	−	0.669840i	−0.951351	+	0.308109i	$0.900304\pi$
$384$	−16.2915	−	46.0339i	−0.831373	−	2.34916i
$385$	11.7045	+	0.719924i	0.596517	+	0.0366907i
$386$			27.2996i			1.38951i
$387$	7.05072	−	1.11396i	0.358408	−	0.0566255i
$388$	−37.6281	+	65.1738i	−1.91028	+	3.30870i
$389$	7.59761	−	4.38648i	0.385214	−	0.222404i	−0.294870	−	0.955537i	$-0.595276\pi$
$389$	7.59761	−	4.38648i	0.385214	−	0.222404i	0.680084	+	0.733134i	$0.261943\pi$
$390$	−14.2809	−	17.8928i	−0.723140	−	0.906037i
$391$	26.4378	−	15.2638i	1.33701	−	0.771926i
$392$	44.5096	+	44.9007i	2.24807	+	2.26783i
$393$	4.37473	+	0.811676i	0.220676	+	0.0409436i
$394$	68.7192			3.46202
$395$	2.25471	−	11.7147i	0.113447	−	0.589431i
$396$	11.3802	−	29.6124i	0.571874	−	1.48808i
$397$	9.65652	+	16.7256i	0.484647	+	0.839433i	0.999844	−	0.0176387i	$-0.00561486\pi$
$397$	9.65652	+	16.7256i	0.484647	+	0.839433i	−0.515198	+	0.857071i	$0.672282\pi$
$398$	−41.8660	−	24.1713i	−2.09855	−	1.21160i
$399$	−3.84418	+	1.94720i	−0.192450	+	0.0974822i
$400$	−64.0300	−	25.5957i	−3.20150	−	1.27978i
$401$	−33.5161	−	19.3506i	−1.67372	−	0.966320i	−0.965529	−	0.260296i	$-0.916180\pi$
$401$	−33.5161	−	19.3506i	−1.67372	−	0.966320i	−0.708187	−	0.706025i	$-0.750487\pi$
$402$	56.6223	−	20.0388i	2.82406	−	0.999444i
$403$	15.6373	−	9.02819i	0.778949	−	0.449726i
$404$	−13.5637	−	23.4930i	−0.674817	−	1.16882i
$405$	18.5333	+	7.84336i	0.920925	+	0.389740i
$406$	−20.1709	+	15.4077i	−1.00106	+	0.764670i
$407$	0.497856	−	0.862313i	0.0246778	−	0.0427432i
$408$	11.7591	−	63.3789i	0.582165	−	3.13772i
$409$			38.2982i			1.89372i	0.321640	+	0.946862i	$0.395766\pi$
$409$			38.2982i			1.89372i	−0.321640	+	0.946862i	$0.604234\pi$
$410$	−11.8422	+	4.10201i	−0.584842	+	0.202584i
$411$	4.69263	−	5.49223i	0.231470	−	0.270912i
$412$	−20.6213	+	35.7171i	−1.01594	+	1.75965i
$413$	−6.40572	+	15.3696i	−0.315205	+	0.756289i
$414$	−9.39372	−	59.4570i	−0.461676	−	2.92215i
$415$	0.153343	−	0.177059i	0.00752732	−	0.00869149i
$416$	21.0475	+	36.4553i	1.03194	+	1.78737i
$417$	24.9758	+	21.3397i	1.22307	+	1.04501i
$418$	2.52403	−	4.37175i	0.123454	−	0.213829i
$419$	−12.0080	−	20.7984i	−0.586628	−	1.01607i	−0.994670	−	0.103107i	$-0.967122\pi$
$419$	−12.0080	−	20.7984i	−0.586628	−	1.01607i	0.408042	−	0.912963i	$-0.366212\pi$
$420$	13.2534	−	53.0354i	0.646700	−	2.58786i
$421$	6.22471	−	10.7815i	0.303374	−	0.525459i	−0.673524	−	0.739165i	$-0.735220\pi$
$421$	6.22471	−	10.7815i	0.303374	−	0.525459i	0.976898	+	0.213706i	$0.0685536\pi$
$422$	−13.7652	−	23.8420i	−0.670078	−	1.16061i
$423$	−6.46246	−	7.98673i	−0.314216	−	0.388328i
$424$	36.7876	−	63.7180i	1.78656	−	3.09442i
$425$	−12.7441	−	16.1883i	−0.618178	−	0.785249i
$426$	22.2133	−	7.86134i	1.07624	−	0.380883i
$427$	6.58468	+	2.74435i	0.318655	+	0.132808i
$428$	8.64214	+	14.9686i	0.417734	+	0.723536i
$429$	−1.36692	+	7.36738i	−0.0659957	+	0.355701i
$430$	−9.43340	+	10.8924i	−0.454919	+	0.525276i
$431$	30.8069	+	17.7864i	1.48392	+	0.856740i	0.999833	−	0.0182809i	$-0.00581932\pi$
$431$	30.8069	+	17.7864i	1.48392	+	0.856740i	0.484085	+	0.875021i	$0.339153\pi$
$432$	−61.0800	−	37.4782i	−2.93871	−	1.80317i
$433$	10.0391			0.482450			0.241225	−	0.970469i	$-0.422451\pi$
$433$	10.0391			0.482450			0.241225	+	0.970469i	$0.422451\pi$
$434$	54.7185	+	22.8055i	2.62657	+	1.09470i
$435$	12.7729	+	5.00704i	0.612415	+	0.240069i
$436$	−4.33599	+	7.51015i	−0.207656	+	0.359671i
$437$		−	6.96671i		−	0.333263i
$438$	−35.4020	−	6.56838i	−1.69157	−	0.313850i
$439$		−	0.856611i		−	0.0408838i	−0.999791	−	0.0204419i	$-0.993493\pi$
$439$		−	0.856611i		−	0.0408838i	0.999791	−	0.0204419i	$-0.00650732\pi$
$440$	13.1027	+	37.8265i	0.624648	+	1.80331i
$441$	20.8743	+	2.29443i	0.994013	+	0.109259i
$442$			24.3565i			1.15852i
$443$	36.0987			1.71510			0.857550	−	0.514401i	$-0.171986\pi$
$443$	36.0987			1.71510			0.857550	+	0.514401i	$0.171986\pi$
$444$	−3.52903	−	3.01525i	−0.167480	−	0.143097i
$445$	−17.6322	+	6.10764i	−0.835848	+	0.289530i
$446$	−31.2893	+	54.1947i	−1.48159	+	2.56619i
$447$	1.70978	−	9.21529i	0.0808698	−	0.435868i
$448$	−25.0924	+	60.2055i	−1.18550	+	2.84444i
$449$		−	10.5870i		−	0.499630i	−0.968294	−	0.249815i	$-0.919630\pi$
$449$		−	10.5870i		−	0.499630i	0.968294	−	0.249815i	$-0.0803698\pi$
$450$	−38.8100	+	12.0057i	−1.82952	+	0.565954i
$451$	3.55243	+	2.05099i	0.167277	+	0.0965775i
$452$	32.8215	+	56.8485i	1.54379	+	2.67393i
$453$	−11.3350	+	13.2665i	−0.532566	+	0.623313i
$454$	−15.6777	+	9.05154i	−0.735792	+	0.424810i
$455$	−0.792702	+	12.8877i	−0.0371625	+	0.604187i
$456$	−11.1841	−	9.55585i	−0.523745	−	0.447494i
$457$			5.87417i			0.274782i	0.990517	+	0.137391i	$0.0438717\pi$
$457$			5.87417i			0.274782i	−0.990517	+	0.137391i	$0.956128\pi$
$458$	27.0467	+	15.6154i	1.26381	+	0.729660i
$459$	−10.2056	−	18.8222i	−0.476358	−	0.878546i
$460$	66.8072	+	57.8588i	3.11490	+	2.69768i
$461$	5.48808	−	9.50563i	0.255605	−	0.442722i	−0.709454	−	0.704751i	$-0.751059\pi$
$461$	5.48808	−	9.50563i	0.255605	−	0.442722i	0.965060	+	0.262030i	$0.0843919\pi$
$462$	−21.9458	+	11.1163i	−1.02101	+	0.517175i
$463$	−0.698463	+	0.403258i	−0.0324603	+	0.0187410i	−0.516142	−	0.856503i	$-0.672632\pi$
$463$	−0.698463	+	0.403258i	−0.0324603	+	0.0187410i	0.483682	+	0.875244i	$0.339299\pi$
$464$	−42.3077	−	24.4264i	−1.96409	−	1.13397i
$465$	−4.78837	−	31.6817i	−0.222055	−	1.46921i
$466$	−14.1442	−	24.4984i	−0.655216	−	1.13487i
$467$	25.0808	−	14.4804i	1.16060	−	0.670073i	0.209153	−	0.977883i	$-0.432929\pi$
$467$	25.0808	−	14.4804i	1.16060	−	0.670073i	0.951448	+	0.307809i	$0.0995959\pi$
$468$	32.6060	+	12.5306i	1.50721	+	0.579227i
$469$	−31.2697	−	13.0325i	−1.44390	−	0.601786i
$470$	20.3654	+	3.91970i	0.939387	+	0.180802i
$471$	0.721362	+	2.03830i	0.0332386	+	0.0939201i
$472$	−56.8422			−2.61638
$473$	4.71634			0.216858
$474$	8.34954	+	23.5927i	0.383507	+	1.08365i
$475$	−4.65354	+	0.671512i	−0.213519	+	0.0308111i
$476$	−46.2193	+	35.3050i	−2.11846	+	1.61820i
$477$	−3.81377	−	24.1391i	−0.174621	−	1.10525i
$478$	41.2938	−	23.8410i	1.88874	−	1.09046i
$479$	2.14521	+	3.71561i	0.0980170	+	0.169770i	0.910864	−	0.412707i	$-0.135417\pi$
$479$	2.14521	+	3.71561i	0.0980170	+	0.169770i	−0.812847	+	0.582478i	$0.802083\pi$
$480$	73.8599	−	11.1632i	3.37123	−	0.509526i
$481$	0.949485	+	0.548186i	0.0432928	+	0.0249951i
$482$	50.9987	−	29.4441i	2.32293	−	1.34114i
$483$	−18.5585	+	28.4294i	−0.844443	+	1.29358i
$484$	−18.8616	+	32.6692i	−0.857345	+	1.48497i
$485$	−23.8438	−	20.6501i	−1.08269	−	0.937673i
$486$	−41.8623	+	5.47049i	−1.89891	+	0.248147i
$487$	−24.9509	−	14.4054i	−1.13064	−	0.652772i	−0.186541	−	0.982447i	$-0.559728\pi$
$487$	−24.9509	−	14.4054i	−1.13064	−	0.652772i	−0.944095	+	0.329675i	$0.893061\pi$
$488$			24.3525i			1.10238i
$489$	25.5458	+	21.8267i	1.15522	+	0.987036i
$490$	−35.2041	+	23.6160i	−1.59036	+	1.06686i
$491$	36.6618	−	21.1667i	1.65452	−	0.955239i	0.679344	−	0.733820i	$-0.262264\pi$
$491$	36.6618	−	21.1667i	1.65452	−	0.955239i	0.975179	−	0.221419i	$-0.0710689\pi$
$492$	12.4218	−	14.5384i	0.560016	−	0.655441i
$493$	−7.29811	−	12.6407i	−0.328690	−	0.569308i
$494$	4.81370	+	2.77919i	0.216579	+	0.125042i
$495$	11.2866	+	7.02973i	0.507293	+	0.315963i
$496$			114.097i			5.12309i
$497$	−12.2673	−	5.11274i	−0.550263	−	0.229338i
$498$	−0.0896393	+	0.483134i	−0.00401683	+	0.0216497i
$499$	14.7535	−	25.5539i	0.660460	−	1.14395i	−0.320035	−	0.947406i	$-0.603695\pi$
$499$	14.7535	−	25.5539i	0.660460	−	1.14395i	0.980495	−	0.196544i	$-0.0629718\pi$
$500$	32.2084	−	50.2021i	1.44040	−	2.24511i
$501$	6.82524	+	5.83157i	0.304929	+	0.260535i
$502$	71.4847			3.19052
$503$			33.3227i			1.48578i	0.669411	+	0.742892i	$0.266546\pi$
$503$			33.3227i			1.48578i	−0.669411	+	0.742892i	$0.733454\pi$
$504$	20.1839	+	68.7883i	0.899060	+	3.06408i
$505$	10.7439	−	3.72157i	0.478095	−	0.165608i
$506$		−	39.7717i		−	1.76807i
$507$	14.0267	+	2.60247i	0.622946	+	0.115580i
$508$			48.8760i			2.16852i
$509$	14.3722	−	24.8934i	0.637038	−	1.10338i	−0.349042	−	0.937107i	$-0.613493\pi$
$509$	14.3722	−	24.8934i	0.637038	−	1.10338i	0.986080	−	0.166274i	$-0.0531737\pi$
$510$	40.2399	+	15.7742i	1.78185	+	0.698495i
$511$	12.3275	+	16.1385i	0.545336	+	0.713924i
$512$	−16.8719			−0.745639
$513$	−4.88444	−	0.130713i	−0.215653	−	0.00577110i
$514$	−12.7011	−	7.33299i	−0.560222	−	0.323444i
$515$	−13.0671	−	11.3168i	−0.575805	−	0.498679i
$516$	4.01082	−	21.6174i	0.176567	−	0.951651i
$517$	−3.39406	−	5.87868i	−0.149271	−	0.258544i
$518$	0.462021	+	3.56971i	0.0203000	+	0.156844i
$519$	7.78114	−	2.75377i	0.341554	−	0.120877i
$520$	−41.6505	+	14.4273i	−1.82649	+	0.632680i
$521$	18.3222	−	31.7350i	0.802710	−	1.39033i	−0.115116	−	0.993352i	$-0.536724\pi$
$521$	18.3222	−	31.7350i	0.802710	−	1.39033i	0.917826	−	0.396982i	$-0.129943\pi$
$522$	−28.4282	+	4.49142i	−1.24427	+	0.196584i
$523$	−22.5406	−	39.0415i	−0.985633	−	1.70717i	−0.639090	−	0.769132i	$-0.720689\pi$
$523$	−22.5406	−	39.0415i	−0.985633	−	1.70717i	−0.346542	−	0.938034i	$-0.612644\pi$
$524$	6.85229	−	11.8685i	0.299344	−	0.518479i
$525$	20.7788	+	9.65625i	0.906859	+	0.421433i
$526$	−10.2481	−	17.7503i	−0.446840	−	0.773949i
$527$	−17.0449	+	29.5226i	−0.742486	+	1.28602i
$528$	−35.9980	−	30.7571i	−1.56661	−	1.33853i
$529$	−15.9440	−	27.6158i	−0.693218	−	1.20069i
$530$	37.2915	+	32.2965i	1.61984	+	1.40287i
$531$	−14.6775	+	11.8763i	−0.636948	+	0.515387i
$532$	1.70366	+	13.1630i	0.0738632	+	0.570690i
$533$	−2.25833	+	3.91155i	−0.0978193	+	0.169428i
$534$	25.4289	−	29.7619i	1.10042	−	1.28792i
$535$	−6.84549	+	2.37121i	−0.295956	+	0.102516i
$536$		−	115.646i		−	4.99517i
$537$	−7.46051	+	40.2103i	−0.321945	+	1.73520i
$538$	12.7478	−	22.0799i	0.549598	−	0.951932i
$539$	13.3865	+	3.64974i	0.576598	+	0.157205i
$540$	41.8190	−	45.7538i	1.79960	−	1.96893i
$541$	5.58471	+	9.67300i	0.240105	+	0.415875i	0.960744	−	0.277436i	$-0.0894846\pi$
$541$	5.58471	+	9.67300i	0.240105	+	0.415875i	−0.720639	+	0.693311i	$0.756151\pi$
$542$	−30.2997	+	17.4935i	−1.30148	+	0.751411i
$543$	4.45105	−	1.57524i	0.191013	−	0.0676000i
$544$	−68.8262	−	39.7368i	−2.95090	−	1.70370i
$545$	−2.74759	−	2.37957i	−0.117694	−	0.101929i
$546$	−12.2400	−	24.1643i	−0.523825	−	1.03414i
$547$	23.2739	+	13.4372i	0.995119	+	0.574532i	0.906800	−	0.421560i	$-0.138517\pi$
$547$	23.2739	+	13.4372i	0.995119	+	0.574532i	0.0883184	+	0.996092i	$0.471851\pi$
$548$	−11.1252	−	19.2695i	−0.475246	−	0.823151i
$549$	5.08806	+	6.28815i	0.217153	+	0.268372i
$550$	−26.5663	+	3.83355i	−1.13279	+	0.163463i
$551$	−3.33099			−0.141905
$552$	−113.954	−	21.1426i	−4.85019	−	0.899891i
$553$	5.43025	−	13.0291i	0.230918	−	0.554054i
$554$	−27.2894	+	15.7555i	−1.15941	+	0.669388i
$555$	1.52059	−	1.21364i	0.0645457	−	0.0515162i
$556$	87.6276	−	50.5918i	3.71624	−	2.14557i
$557$	−16.2064	+	28.0702i	−0.686685	+	1.18937i	0.286219	+	0.958164i	$0.407602\pi$
$557$	−16.2064	+	28.0702i	−0.686685	+	1.18937i	−0.972904	+	0.231210i	$0.925732\pi$
$558$	42.2817	+	52.2545i	1.78993	+	2.21211i
$559$			5.19312i			0.219646i
$560$	−68.0215	−	45.0561i	−2.87443	−	1.90397i
$561$	−4.71971	−	13.3362i	−0.199266	−	0.563053i
$562$	−23.6992	−	13.6828i	−0.999692	−	0.577173i
$563$			15.5122i			0.653762i	0.945065	+	0.326881i	$0.105998\pi$
$563$			15.5122i			0.653762i	−0.945065	+	0.326881i	$0.894002\pi$
$564$	−29.8313	+	10.5574i	−1.25613	+	0.444547i
$565$	−25.9981	+	9.00549i	−1.09375	+	0.378864i
$566$	41.5416			1.74613
$567$	19.5840	+	13.5450i	0.822450	+	0.568838i
$568$		−	45.3688i		−	1.90363i
$569$			21.9666i			0.920887i	0.887689	+	0.460444i	$0.152310\pi$
$569$			21.9666i			0.920887i	−0.887689	+	0.460444i	$0.847690\pi$
$570$	7.70911	−	6.15291i	0.322899	−	0.257717i
$571$	−5.97323			−0.249972			−0.124986	−	0.992159i	$-0.539889\pi$
$571$	−5.97323			−0.249972			−0.124986	+	0.992159i	$0.539889\pi$
$572$	19.9875	+	11.5398i	0.835718	+	0.482502i
$573$	−36.6727	+	12.9786i	−1.53202	+	0.542188i
$574$	−14.7060	+	1.90336i	−0.613815	+	0.0794449i
$575$	−29.1062	+	22.9135i	−1.21381	+	0.955560i
$576$	−57.4944	+	46.5216i	−2.39560	+	1.93840i
$577$	14.6664	−	25.4030i	0.610570	−	1.05754i	−0.380574	−	0.924750i	$-0.624274\pi$
$577$	14.6664	−	25.4030i	0.610570	−	1.05754i	0.991144	−	0.132789i	$-0.0423931\pi$
$578$	0.0285216	+	0.0494008i	0.00118634	+	0.00205480i
$579$	16.4587	−	5.82479i	0.684001	−	0.242070i
$580$	27.6641	−	31.9426i	1.14869	−	1.32634i
$581$	0.220243	−	0.168234i	0.00913722	−	0.00697954i
$582$	65.0616	+	12.0714i	2.69689	+	0.500374i
$583$		−	16.1470i		−	0.668741i
$584$	−34.6631	+	60.0383i	−1.43437	+	2.48440i
$585$	−7.74038	+	12.4275i	−0.320025	+	0.513815i
$586$	40.4267	−	23.3404i	1.67001	−	0.964183i
$587$	0.298786	+	0.172504i	0.0123322	+	0.00712002i	0.506153	−	0.862443i	$-0.331067\pi$
$587$	0.298786	+	0.172504i	0.0123322	+	0.00712002i	−0.493821	+	0.869563i	$0.664400\pi$
$588$	28.1126	−	58.2534i	1.15935	−	2.40233i
$589$	3.88980	+	6.73732i	0.160276	+	0.277607i
$590$	7.20337	−	37.4262i	0.296558	−	1.54081i
$591$	−14.6623	−	41.4303i	−0.603126	−	1.70421i
$592$	−5.99971	+	3.46393i	−0.246586	+	0.142367i
$593$	35.2553	−	20.3547i	1.44776	−	0.835866i	0.449414	−	0.893324i	$-0.351633\pi$
$593$	35.2553	−	20.3547i	1.44776	−	0.835866i	0.998348	+	0.0574577i	$0.0182994\pi$
$594$	−27.8845	−	0.746216i	−1.14411	−	0.0306176i
$595$	−10.8697	−	21.8200i	−0.445613	−	0.894533i
$596$	−25.0008	−	14.4342i	−1.02407	−	0.591249i
$597$	−5.63996	+	30.3980i	−0.230828	+	1.24411i
$598$	43.7924			1.79080
$599$			34.5560i			1.41192i	0.708251	+	0.705960i	$0.249484\pi$
$599$			34.5560i			1.41192i	−0.708251	+	0.705960i	$0.750516\pi$
$600$	−3.13877	+	78.1554i	−0.128140	+	3.19068i
$601$	33.6121	+	19.4059i	1.37106	+	0.791585i	0.991062	−	0.133401i	$-0.0425897\pi$
$601$	33.6121	+	19.4059i	1.37106	+	0.791585i	0.380003	+	0.924985i	$0.375923\pi$
$602$	−13.5489	+	10.3495i	−0.552214	+	0.421813i
$603$	−24.1625	−	29.8616i	−0.983972	−	1.21606i
$604$	26.8730	+	46.5454i	1.09345	+	1.89390i
$605$	−11.9520	−	10.3511i	−0.485920	−	0.420834i
$606$	−15.4946	+	18.1348i	−0.629426	+	0.736677i
$607$	−15.5424	+	26.9203i	−0.630848	+	1.09266i	0.356531	+	0.934284i	$0.383959\pi$
$607$	−15.5424	+	26.9203i	−0.630848	+	1.09266i	−0.987379	+	0.158377i	$0.949374\pi$
$608$	−15.7068	+	9.06832i	−0.636994	+	0.367769i
$609$	13.5929	+	8.87340i	0.550814	+	0.359568i
$610$	−16.0342	−	3.08608i	−0.649207	−	0.124952i
$611$	6.47297	−	3.73717i	0.261868	−	0.151190i
$612$	−65.1401	+	10.2916i	−2.63313	+	0.416013i
$613$	3.64643	+	2.10527i	0.147278	+	0.0850310i	0.571828	−	0.820373i	$-0.306234\pi$
$613$	3.64643	+	2.10527i	0.147278	+	0.0850310i	−0.424550	+	0.905404i	$0.639568\pi$
$614$	−59.6705			−2.40810
$615$	4.99978	+	6.26432i	0.201610	+	0.252602i
$616$	6.07977	+	46.9742i	0.244961	+	1.89264i
$617$	−0.173845	−	0.301109i	−0.00699875	−	0.0121222i	0.862505	−	0.506049i	$-0.168894\pi$
$617$	−0.173845	−	0.301109i	−0.00699875	−	0.0121222i	−0.869504	+	0.493927i	$0.835561\pi$
$618$	35.6556	+	6.61544i	1.43428	+	0.266112i
$619$	−2.12306	+	1.22575i	−0.0853332	+	0.0492671i	−0.542059	−	0.840340i	$-0.682355\pi$
$619$	−2.12306	+	1.22575i	−0.0853332	+	0.0492671i	0.456726	+	0.889607i	$0.349022\pi$
$620$	−96.9125	−	18.6526i	−3.89210	−	0.749107i
$621$	−33.8419	+	18.3495i	−1.35803	+	0.736339i
$622$	−38.3101			−1.53610
$623$	−21.8963	+	2.83399i	−0.877256	+	0.113542i
$624$	33.8664	−	39.6371i	1.35574	−	1.58676i
$625$	18.1110	+	17.2334i	0.724441	+	0.689337i
$626$	−54.7731			−2.18918
$627$	−3.17424	−	0.588939i	−0.126767	−	0.0235199i
$628$	6.65975			0.265753
$629$	−2.06990			−0.0825325
$630$	−47.8496	+	4.57227i	−1.90637	+	0.182163i
$631$	−28.7347			−1.14391			−0.571956	−	0.820284i	$-0.693815\pi$
$631$	−28.7347			−1.14391			−0.571956	+	0.820284i	$0.693815\pi$
$632$	48.1863			1.91675
$633$	−11.4371	+	13.3860i	−0.454585	+	0.532044i
$634$	44.3208			1.76021
$635$	−20.1167	−	3.87183i	−0.798307	−	0.153649i
$636$	−74.0099	−	13.7316i	−2.93468	−	0.544493i
$637$	−4.01870	+	14.7398i	−0.159227	+	0.584011i
$638$	−19.0161			−0.752853
$639$	−9.47909	−	11.7149i	−0.374987	−	0.463433i
$640$	11.9148	−	61.9052i	0.470974	−	2.44702i
$641$	39.8812	−	23.0254i	1.57521	−	0.909449i	0.579699	−	0.814831i	$-0.303170\pi$
$641$	39.8812	−	23.0254i	1.57521	−	0.909449i	0.995514	−	0.0946187i	$-0.0301632\pi$
$642$	9.87245	−	11.5547i	0.389635	−	0.456027i
$643$	9.09346	+	15.7503i	0.358611	+	0.621133i	0.987729	−	0.156177i	$-0.0499171\pi$
$643$	9.09346	+	15.7503i	0.358611	+	0.621133i	−0.629118	+	0.777310i	$0.716584\pi$
$644$	63.4775	+	83.1012i	2.50136	+	3.27464i
$645$	8.57968	+	3.36327i	0.337825	+	0.132429i
$646$	−10.4940			−0.412881
$647$	−3.52125	−	2.03300i	−0.138435	−	0.0799253i	0.429183	−	0.903218i	$-0.358802\pi$
$647$	−3.52125	−	2.03300i	−0.138435	−	0.0799253i	−0.567618	+	0.823292i	$0.692135\pi$
$648$	−16.9614	+	79.4977i	−0.666308	+	3.12296i
$649$	−10.8035	+	6.23738i	−0.424073	+	0.244838i
$650$	−4.22109	−	29.2519i	−0.165565	−	1.14735i
$651$	2.07422	−	37.8553i	0.0812951	−	1.48367i
$652$	89.6274	−	51.7464i	3.51008	−	2.02655i
$653$	−11.3321	+	19.6278i	−0.443461	+	0.768097i	−0.997944	−	0.0640983i	$-0.979583\pi$
$653$	−11.3321	+	19.6278i	−0.443461	+	0.768097i	0.554483	+	0.832195i	$0.312916\pi$
$654$	7.49723	+	1.39101i	0.293165	+	0.0543930i
$655$	4.34210	+	3.76050i	0.169660	+	0.146935i
$656$	−14.2702	−	24.7167i	−0.557157	−	0.965025i
$657$	3.59353	+	22.7451i	0.140197	+	0.887369i
$658$	22.6505	+	9.44022i	0.883007	+	0.368018i
$659$	3.07951	+	1.77796i	0.119961	+	0.0692594i	0.558780	−	0.829316i	$-0.311270\pi$
$659$	3.07951	+	1.77796i	0.119961	+	0.0692594i	−0.438819	+	0.898576i	$0.644603\pi$
$660$	32.0098	−	25.5482i	1.24598	−	0.994461i
$661$		−	11.9661i		−	0.465426i	−0.972546	−	0.232713i	$-0.925240\pi$
$661$		−	11.9661i		−	0.465426i	0.972546	−	0.232713i	$-0.0747602\pi$
$662$	−19.9155			−0.774036
$663$	14.6843	−	5.19683i	0.570293	−	0.201828i
$664$	0.819348	+	0.473051i	0.0317969	+	0.0183579i
$665$	−5.55268	−	0.341536i	−0.215324	−	0.0132442i
$666$	−1.46412	+	3.80979i	−0.0567333	+	0.147626i
$667$	−22.7276	+	13.1218i	−0.880018	+	0.508078i
$668$	23.9463	−	13.8254i	0.926512	−	0.534922i
$669$	39.3496	+	7.30082i	1.52134	+	0.282266i
$670$	76.1443	+	14.6554i	2.94171	+	0.566186i
$671$	2.67223	+	4.62844i	0.103160	+	0.178679i
$672$	88.2524	+	4.83565i	3.40441	+	0.186539i
$673$	13.3294	+	7.69573i	0.513810	+	0.296648i	0.734398	−	0.678719i	$-0.237464\pi$
$673$	13.3294	+	7.69573i	0.513810	+	0.296648i	−0.220588	+	0.975367i	$0.570798\pi$
$674$	−20.7706	+	11.9919i	−0.800052	+	0.461910i
$675$	15.5188	+	20.8366i	0.597321	+	0.802002i
$676$	21.9704	−	38.0539i	0.845017	−	1.46361i
$677$			16.0996i			0.618759i	0.950939	+	0.309380i	$0.100121\pi$
$677$			16.0996i			0.618759i	−0.950939	+	0.309380i	$0.899879\pi$
$678$	37.4940	−	43.8829i	1.43995	−	1.68531i
$679$	−22.6554	−	29.6592i	−0.869436	−	1.13822i
$680$	54.4803	−	62.9061i	2.08922	−	2.41234i
$681$	8.80219	+	7.52070i	0.337301	+	0.288194i
$682$	22.2062	+	38.4622i	0.850319	+	1.47280i
$683$	−0.288302	+	0.499354i	−0.0110316	+	0.0191073i	−0.871488	−	0.490416i	$-0.836845\pi$
$683$	−0.288302	+	0.499354i	−0.0110316	+	0.0191073i	0.860457	+	0.509523i	$0.170178\pi$
$684$	−5.39881	+	14.0483i	−0.206429	+	0.537150i
$685$	8.81236	−	3.05251i	0.336703	−	0.116631i
$686$	−46.4653	+	18.8903i	−1.77405	+	0.721236i
$687$	3.64358	−	19.6380i	0.139011	−	0.749237i
$688$	−28.4185	−	16.4074i	−1.08344	−	0.625527i
$689$	17.7793			0.677339
$690$	28.3617	−	72.3504i	1.07971	−	2.75433i
$691$			29.3997i			1.11842i	0.829027	+	0.559208i	$0.188895\pi$
$691$			29.3997i			1.11842i	−0.829027	+	0.559208i	$0.811105\pi$
$692$		−	25.4233i		−	0.966450i
$693$	11.3844	+	10.8591i	0.432457	+	0.412504i
$694$	42.2148			1.60245
$695$	13.8813	+	40.0741i	0.526547	+	1.52010i
$696$	−10.1089	+	54.4847i	−0.383178	+	2.06524i
$697$		−	8.52728i		−	0.322994i
$698$	20.6888	+	11.9447i	0.783081	+	0.452112i
$699$	−11.7520	+	13.7545i	−0.444503	+	0.520244i
$700$	49.3905	−	50.4110i	1.86678	−	1.90536i
$701$		−	25.4130i		−	0.959836i	−0.877313	−	0.479918i	$-0.840666\pi$
$701$		−	25.4130i		−	0.959836i	0.877313	−	0.479918i	$-0.159334\pi$
$702$	0.821652	−	30.7034i	0.0310113	−	1.15882i
$703$	−0.236186	+	0.409086i	−0.00890791	+	0.0154290i
$704$	−42.3191	+	24.4329i	−1.59496	+	0.920851i
$705$	−1.98212	−	13.1145i	−0.0746509	−	0.493920i
$706$	−9.84378	+	5.68331i	−0.370476	+	0.213894i
$707$	13.3421	−	1.72684i	0.501780	−	0.0649444i
$708$	19.4017	+	54.8220i	0.729160	+	2.06034i
$709$	−26.3702			−0.990354			−0.495177	−	0.868792i	$-0.664897\pi$
$709$	−26.3702			−0.990354			−0.495177	+	0.868792i	$0.664897\pi$
$710$	29.8719	+	5.74939i	1.12107	+	0.215771i
$711$	12.4424	−	10.0678i	0.466626	−	0.377570i
$712$	−37.6857	−	65.2736i	−1.41233	−	2.44623i
$713$	53.0808	+	30.6462i	1.98789	+	1.14771i
$714$	42.8233	+	27.9548i	1.60262	+	1.04618i
$715$	−6.33297	+	7.31242i	−0.236840	+	0.273469i
$716$	109.089	+	62.9828i	4.07686	+	2.35378i
$717$	−23.1842	−	19.8089i	−0.865832	−	0.739777i
$718$	11.2429	−	6.49108i	0.419580	−	0.242245i
$719$	−18.5755	−	32.1737i	−0.692749	−	1.19988i	−0.970934	−	0.239348i	$-0.923066\pi$
$719$	−18.5755	−	32.1737i	−0.692749	−	1.19988i	0.278185	−	0.960527i	$-0.410267\pi$
$720$	−43.5522	−	81.6221i	−1.62309	−	3.04188i
$721$	−12.4158	−	16.2541i	−0.462389	−	0.605334i
$722$	24.5314	−	42.4897i	0.912966	−	1.58130i
$723$	−28.6330	−	24.4644i	−1.06487	−	0.909839i
$724$		−	14.5429i		−	0.540483i
$725$	10.9556	+	13.9166i	0.406882	+	0.516848i
$726$	32.6130	+	6.05093i	1.21038	+	0.224571i
$727$	−0.879130	+	1.52270i	−0.0326051	+	0.0564738i	−0.881868	−	0.471497i	$-0.843714\pi$
$727$	−0.879130	+	1.52270i	−0.0326051	+	0.0564738i	0.849262	+	0.527971i	$0.177047\pi$
$728$	−51.7229	+	6.69439i	−1.91698	+	0.248111i
$729$	12.2301	+	24.0712i	0.452966	+	0.891528i
$730$	−35.1379	−	30.4314i	−1.30051	−	1.12632i
$731$	−4.90220	−	8.49086i	−0.181314	−	0.314046i
$732$	23.4870	−	8.31211i	0.868103	−	0.307224i
$733$	−13.6646	+	23.6678i	−0.504713	+	0.874189i	0.495272	+	0.868738i	$0.335068\pi$
$733$	−13.6646	+	23.6678i	−0.504713	+	0.874189i	−0.999985	+	0.00545112i	$0.998265\pi$
$734$	−2.92395	−	5.06443i	−0.107925	−	0.186932i
$735$	21.7493	+	16.1855i	0.802234	+	0.597010i
$736$	−71.4458	+	123.748i	−2.63353	+	4.56140i
$737$	−12.6900	−	21.9798i	−0.467444	−	0.809636i
$738$	−15.6950	−	6.03164i	−0.577741	−	0.222028i
$739$	−25.0078	+	43.3147i	−0.919926	+	1.59336i	−0.120402	+	0.992725i	$0.538418\pi$
$739$	−25.0078	+	43.3147i	−0.919926	+	1.59336i	−0.799525	+	0.600633i	$0.794915\pi$
$740$	−1.96139	−	5.66238i	−0.0721023	−	0.208153i
$741$	0.648476	−	3.49513i	0.0238224	−	0.128397i
$742$	35.4328	+	46.3866i	1.30078	+	1.70291i
$743$	−14.5046	−	25.1227i	−0.532123	−	0.921664i	−0.999297	−	0.0374983i	$-0.988061\pi$
$743$	−14.5046	−	25.1227i	−0.532123	−	0.921664i	0.467174	−	0.884165i	$-0.345272\pi$
$744$	122.007	−	43.1785i	4.47298	−	1.58300i
$745$	7.92142	−	9.14654i	0.290219	−	0.335103i
$746$	74.6164	+	43.0798i	2.73190	+	1.57726i
$747$	0.310404	−	0.0490412i	0.0113571	−	0.00179432i
$748$	−43.5732			−1.59320
$749$	−8.50095	+	1.10026i	−0.310618	+	0.0402027i
$750$	−51.0615	−	11.9709i	−1.86450	−	0.437117i
$751$	0.0580908	−	0.100616i	0.00211976	−	0.00367154i	−0.864964	−	0.501835i	$-0.832659\pi$
$751$	0.0580908	−	0.100616i	0.00211976	−	0.00367154i	0.867083	+	0.498163i	$0.165992\pi$
$752$			47.2297i			1.72229i
$753$	−15.2524	−	43.0976i	−0.555827	−	1.57056i
$754$		−	20.9384i		−	0.762533i
$755$	−21.2862	+	7.37335i	−0.774686	+	0.268344i
$756$	59.4543	−	42.9457i	2.16233	−	1.56192i
$757$		−	30.3033i		−	1.10139i	−0.834706	−	0.550696i	$-0.814362\pi$
$757$		−	30.3033i		−	1.10139i	0.834706	−	0.550696i	$-0.185638\pi$
$758$	−6.09423			−0.221352
$759$	−23.9781	+	8.48592i	−0.870349	+	0.308019i
$760$	−6.21601	−	17.9451i	−0.225478	−	0.650937i
$761$	11.9715	−	20.7352i	0.433966	−	0.751651i	−0.563245	−	0.826290i	$-0.690447\pi$
$761$	11.9715	−	20.7352i	0.433966	−	0.751651i	0.997211	+	0.0746390i	$0.0237805\pi$
$762$	40.5139	−	14.3380i	1.46766	−	0.519410i
$763$	−2.61065	−	3.41771i	−0.0945117	−	0.123729i
$764$			119.821i			4.33496i
$765$	0.924348	−	27.6260i	0.0334199	−	0.998821i
$766$	61.4933	+	35.5032i	2.22184	+	1.28278i
$767$	−6.86793	−	11.8956i	−0.247986	−	0.429525i
$768$	15.6307	+	44.1666i	0.564024	+	1.59372i
$769$	16.0377	−	9.25936i	0.578334	−	0.333901i	−0.182137	−	0.983273i	$-0.558301\pi$
$769$	16.0377	−	9.25936i	0.578334	−	0.333901i	0.760471	+	0.649372i	$0.224968\pi$
$770$	−31.6993	−	1.94977i	−1.14236	−	0.0702648i
$771$	−1.71103	+	9.22201i	−0.0616211	+	0.332123i
$772$		−	53.7756i		−	1.93542i
$773$	11.0043	+	6.35331i	0.395795	+	0.228513i	0.684668	−	0.728855i	$-0.259947\pi$
$773$	11.0043	+	6.35331i	0.395795	+	0.228513i	−0.288873	+	0.957367i	$0.593280\pi$
$774$	−19.0955	+	3.01693i	−0.686372	+	0.108441i
$775$	15.3543	−	38.4103i	0.551543	−	1.37974i
$776$	63.7038	−	110.338i	2.28683	−	3.96091i
$777$	2.05357	−	1.04020i	0.0736716	−	0.0373171i
$778$	−20.5766	+	11.8799i	−0.737707	+	0.425916i
$779$	−1.68529	−	0.973003i	−0.0603818	−	0.0348614i
$780$	28.1309	+	35.2458i	1.00725	+	1.26200i
$781$	−4.97838	−	8.62281i	−0.178140	−	0.308548i
$782$	−71.6014	+	41.3391i	−2.56046	+	1.47828i
$783$	8.77344	+	16.1808i	0.313537	+	0.578256i
$784$	−67.9641	−	68.5613i	−2.42729	−	2.44862i
$785$	−0.527568	+	2.74106i	−0.0188297	+	0.0978327i
$786$	−11.8481	−	2.19826i	−0.422608	−	0.0784094i
$787$	−17.2967			−0.616559			−0.308280	−	0.951296i	$-0.599753\pi$
$787$	−17.2967			−0.616559			−0.308280	+	0.951296i	$0.599753\pi$
$788$	−135.365			−4.82218
$789$	−8.51492	+	9.96582i	−0.303139	+	0.354793i
$790$	−6.10644	+	31.7269i	−0.217257	+	1.12879i
$791$	−32.2853	+	4.17862i	−1.14793	+	0.148575i
$792$	−19.2664	+	50.1333i	−0.684603	+	1.78141i
$793$	−5.09634	+	2.94237i	−0.180976	+	0.104487i
$794$	−26.1527	−	45.2979i	−0.928126	−	1.60756i
$795$	11.5146	−	29.3737i	0.408381	−	1.04178i
$796$	82.4688	+	47.6134i	2.92303	+	1.68761i
$797$	37.9450	−	21.9076i	1.34408	−	0.776005i	0.356677	−	0.934228i	$-0.383910\pi$
$797$	37.9450	−	21.9076i	1.34408	−	0.776005i	0.987404	+	0.158222i	$0.0505763\pi$
$798$	10.4112	−	5.27362i	0.368553	−	0.186684i
$799$	−7.05563	+	12.2207i	−0.249610	+	0.432338i
$800$	89.5462	+	35.7957i	3.16594	+	1.26557i
$801$	−23.3689	−	8.98074i	−0.825699	−	0.317319i
$802$	90.7718	+	52.4071i	3.20526	+	1.85056i
$803$			15.2145i			0.536909i
$804$	−111.536	+	39.4730i	−3.93358	+	1.39211i
$805$	−39.2318	+	19.5434i	−1.38274	+	0.688814i
$806$	−42.3505	+	24.4511i	−1.49173	+	0.861252i
$807$	−16.0317	−	2.97449i	−0.564344	−	0.104707i
$808$	22.9631	+	39.7732i	0.807838	+	1.39922i
$809$	−9.34173	−	5.39345i	−0.328438	−	0.189624i	0.326710	−	0.945125i	$-0.394060\pi$
$809$	−9.34173	−	5.39345i	−0.328438	−	0.189624i	−0.655147	+	0.755501i	$0.727393\pi$
$810$	−50.1936	−	21.2422i	−1.76362	−	0.746374i
$811$		−	34.9701i		−	1.22797i	−0.789319	−	0.613983i	$-0.789566\pi$
$811$		−	34.9701i		−	1.22797i	0.789319	−	0.613983i	$-0.210434\pi$
$812$	39.7332	−	30.3505i	1.39436	−	1.06509i
$813$	17.0116	+	14.5349i	0.596623	+	0.509762i
$814$	−1.34834	+	2.33540i	−0.0472595	+	0.0818558i
$815$	14.1981	+	40.9886i	0.497337	+	1.43577i
$816$	−17.9557	+	96.7767i	−0.628575	+	3.38786i
$817$	−2.23746			−0.0782787
$818$		−	103.723i		−	3.62659i
$819$	−11.9569	+	12.5353i	−0.417808	+	0.438017i
$820$	23.3270	−	8.08026i	0.814615	−	0.282175i
$821$		−	30.6412i		−	1.06938i	−0.845047	−	0.534692i	$-0.820428\pi$
$821$		−	30.6412i		−	1.06938i	0.845047	−	0.534692i	$-0.179572\pi$
$822$	−12.7090	+	14.8746i	−0.443279	+	0.518811i
$823$		−	9.30078i		−	0.324205i	−0.986774	−	0.162102i	$-0.948173\pi$
$823$		−	9.30078i		−	0.324205i	0.986774	−	0.162102i	$-0.0518275\pi$
$824$	34.9114	−	60.4684i	1.21620	−	2.10652i
$825$	7.97954	+	15.1987i	0.277812	+	0.529149i
$826$	17.3486	−	41.6255i	0.603635	−	1.44834i
$827$	−12.2489			−0.425936			−0.212968	−	0.977059i	$-0.568313\pi$
$827$	−12.2489			−0.425936			−0.212968	+	0.977059i	$0.568313\pi$
$828$	18.5040	+	117.120i	0.643059	+	4.07021i
$829$	29.4948	+	17.0288i	1.02440	+	0.591436i	0.915374	−	0.402604i	$-0.131895\pi$
$829$	29.4948	+	17.0288i	1.02440	+	0.591436i	0.109022	+	0.994039i	$0.465228\pi$
$830$	−0.415300	+	0.479529i	−0.0144153	+	0.0166447i
$831$	15.3215	+	13.0909i	0.531497	+	0.454117i
$832$	−26.9029	−	46.5972i	−0.932691	−	1.61547i
$833$	−7.34339	−	27.8934i	−0.254433	−	0.966450i
$834$	−67.6421	−	57.7942i	−2.34225	−	2.00125i
$835$	3.79339	+	10.9512i	0.131276	+	0.378982i
$836$	−4.97191	+	8.61160i	−0.171957	+	0.297838i
$837$	22.4824	−	36.6406i	0.777104	−	1.26648i
$838$	32.5212	+	56.3284i	1.12343	+	1.94583i
$839$	−2.98348	+	5.16755i	−0.103001	+	0.178404i	−0.912920	−	0.408139i	$-0.866178\pi$
$839$	−2.98348	+	5.16755i	−0.103001	+	0.178404i	0.809919	+	0.586542i	$0.199511\pi$
$840$	−22.4378	+	89.7882i	−0.774178	+	3.09799i
$841$	−8.22607	−	14.2480i	−0.283658	−	0.491309i
$842$	−16.8584	+	29.1996i	−0.580978	+	1.00628i
$843$	−3.19264	+	17.2075i	−0.109960	+	0.592659i
$844$	27.1150	+	46.9646i	0.933338	+	1.61659i
$845$	13.9220	+	12.0573i	0.478932	+	0.414782i
$846$	17.5023	+	21.6305i	0.601741	+	0.743671i
$847$	−11.3563	−	14.8671i	−0.390208	−	0.510839i
$848$	−56.1730	+	97.2945i	−1.92899	+	3.34111i
$849$	−8.86355	−	25.0451i	−0.304196	−	0.859547i
$850$	34.5148	+	43.8429i	1.18385	+	1.50380i
$851$			3.72163i			0.127576i
$852$	−43.7563	+	15.4855i	−1.49907	+	0.530525i
$853$	−8.02176	+	13.8941i	−0.274660	+	0.475725i	−0.970049	−	0.242908i	$-0.921899\pi$
$853$	−8.02176	+	13.8941i	−0.274660	+	0.475725i	0.695389	+	0.718633i	$0.255232\pi$
$854$	−17.8333	−	7.43252i	−0.610242	−	0.254336i
$855$	−5.35440	−	3.33494i	−0.183117	−	0.114053i
$856$	−14.6310	−	25.3416i	−0.500078	−	0.866160i
$857$	21.9165	−	12.6535i	0.748654	−	0.432236i	−0.0765531	−	0.997066i	$-0.524391\pi$
$857$	21.9165	−	12.6535i	0.748654	−	0.432236i	0.825208	+	0.564830i	$0.191058\pi$
$858$	3.70204	−	19.9531i	0.126386	−	0.681187i
$859$	19.1768	+	11.0717i	0.654303	+	0.377762i	0.790103	−	0.612975i	$-0.210027\pi$
$859$	19.1768	+	11.0717i	0.654303	+	0.377762i	−0.135800	+	0.990736i	$0.543361\pi$
$860$	18.5822	−	21.4561i	0.633647	−	0.731647i
$861$	4.28527	+	8.46001i	0.146042	+	0.288316i
$862$	−83.4344	−	48.1709i	−2.84179	−	1.64071i
$863$	−19.5959	−	33.9412i	−0.667053	−	1.15537i	−0.978724	−	0.205180i	$-0.934222\pi$
$863$	−19.5959	−	33.9412i	−0.667053	−	1.15537i	0.311671	−	0.950190i	$-0.399111\pi$
$864$	85.4206	+	52.4133i	2.90607	+	1.78314i
$865$	10.4639	+	2.01397i	0.355783	+	0.0684770i
$866$	−27.1890			−0.923919
$867$	0.0236979	−	0.0277359i	0.000804822	−	0.000941960i
$868$	−107.786	−	44.9230i	−3.65850	−	1.52478i
$869$	9.15830	−	5.28755i	0.310674	−	0.179368i
$870$	−34.5929	−	13.5606i	−1.17281	−	0.459746i
$871$	24.2018	−	13.9729i	0.820046	−	0.473454i
$872$	7.34076	−	12.7146i	0.248589	−	0.430570i
$873$	−6.60418	−	41.8008i	−0.223518	−	1.41474i
$874$			18.8679i			0.638217i
$875$	16.8359	+	24.3219i	0.569157	+	0.822229i
$876$	69.7359	+	12.9386i	2.35616	+	0.437155i
$877$	−6.81574	−	3.93507i	−0.230151	−	0.132878i	0.380491	−	0.924785i	$-0.375755\pi$
$877$	−6.81574	−	3.93507i	−0.230151	−	0.132878i	−0.610642	+	0.791907i	$0.709088\pi$
$878$			2.31996i			0.0782949i
$879$	−22.6974	−	19.3929i	−0.765565	−	0.654108i
$880$	−20.0073	−	57.7593i	−0.674445	−	1.94707i
$881$	−34.9723			−1.17825			−0.589123	−	0.808044i	$-0.700527\pi$
$881$	−34.9723			−1.17825			−0.589123	+	0.808044i	$0.700527\pi$
$882$	−56.5338	−	6.21401i	−1.90359	−	0.209237i
$883$		−	5.45707i		−	0.183645i	−0.995775	−	0.0918225i	$-0.970731\pi$
$883$		−	5.45707i		−	0.183645i	0.995775	−	0.0918225i	$-0.0292692\pi$
$884$		−	47.9781i		−	1.61368i
$885$	−24.1009	+	3.64261i	−0.810144	+	0.122445i
$886$	−97.7660			−3.28451
$887$	10.4494	+	6.03296i	0.350856	+	0.202567i	0.665062	−	0.746788i	$-0.268405\pi$
$887$	10.4494	+	6.03296i	0.350856	+	0.202567i	−0.314206	+	0.949355i	$0.601738\pi$
$888$	5.97459	+	5.10477i	0.200494	+	0.171305i
$889$	−22.3738	−	9.32492i	−0.750394	−	0.312748i
$890$	47.7534	−	16.5413i	1.60070	−	0.554466i
$891$	5.49969	+	16.9706i	0.184247	+	0.568535i
$892$	61.6346	−	106.754i	2.06368	−	3.57440i
$893$	1.61016	+	2.78888i	0.0538820	+	0.0933263i
$894$	−4.63060	+	24.9578i	−0.154870	+	0.834713i
$895$	−34.5646	+	39.9103i	−1.15537	+	1.33406i
$896$	28.6956	−	68.8510i	0.958653	−	2.30015i
$897$	−9.34377	−	26.4021i	−0.311980	−	0.881540i
$898$			28.6727i			0.956821i
$899$	14.6529	−	25.3795i	0.488701	−	0.846455i
$900$	76.4490	−	23.6492i	2.54830	−	0.788306i
$901$	−29.0696	+	16.7833i	−0.968449	+	0.559134i
$902$	−9.62104	−	5.55471i	−0.320345	−	0.184952i
$903$	9.13050	+	5.96034i	0.303844	+	0.198348i
$904$	−55.5663	−	96.2436i	−1.84811	−	3.20102i
$905$	5.98566	+	1.15205i	0.198970	+	0.0382955i
$906$	30.6987	−	35.9296i	1.01990	−	1.19368i
$907$	−5.39392	+	3.11418i	−0.179102	+	0.103405i	−0.586871	−	0.809681i	$-0.699640\pi$
$907$	−5.39392	+	3.11418i	−0.179102	+	0.103405i	0.407769	+	0.913085i	$0.366307\pi$
$908$	30.8824	−	17.8300i	1.02487	−	0.591709i
$909$	14.2394	+	5.47224i	0.472290	+	0.181503i
$910$	2.14688	−	34.9039i	0.0711682	−	1.15705i
$911$	18.8738	+	10.8968i	0.625317	+	0.361027i	0.778936	−	0.627103i	$-0.215760\pi$
$911$	18.8738	+	10.8968i	0.625317	+	0.361027i	−0.153619	+	0.988130i	$0.549093\pi$
$912$	17.0777	+	14.5914i	0.565498	+	0.483168i
$913$	0.207634			0.00687168
$914$		−	15.9090i		−	0.526223i
$915$	1.56057	+	10.3254i	0.0515910	+	0.341346i
$916$	−53.2773	−	30.7597i	−1.76033	−	1.01633i
$917$	4.12568	+	5.40111i	0.136242	+	0.178360i
$918$	27.6399	+	50.9762i	0.912254	+	1.68247i
$919$	25.8180	+	44.7181i	0.851657	+	1.47511i	0.879712	+	0.475507i	$0.157735\pi$
$919$	25.8180	+	44.7181i	0.851657	+	1.47511i	−0.0280547	+	0.999606i	$0.508931\pi$
$920$	−113.104	−	97.9541i	−3.72892	−	3.22945i
$921$	12.7316	+	35.9749i	0.419521	+	1.18541i
$922$	−14.8634	+	25.7441i	−0.489499	+	0.847837i
$923$	9.49450	−	5.48165i	0.312515	−	0.180431i
$924$	43.2295	−	21.8971i	1.42215	−	0.720363i
$925$	2.48594	−	0.358724i	0.0817370	−	0.0117948i
$926$	1.89165	−	1.09214i	0.0621634	−	0.0358901i
$927$	−3.61927	−	22.9080i	−0.118873	−	0.752397i
$928$	59.1675	+	34.1604i	1.94227	+	1.12137i
$929$	33.4575			1.09770			0.548852	−	0.835919i	$-0.315065\pi$
$929$	33.4575			1.09770			0.548852	+	0.835919i	$0.315065\pi$
$930$	12.9683	+	85.8037i	0.425249	+	2.81361i
$931$	−6.35063	−	1.73146i	−0.208134	−	0.0567462i
$932$	27.8616	+	48.2577i	0.912637	+	1.58073i
$933$	8.17406	+	23.0969i	0.267607	+	0.756158i
$934$	−67.9263	+	39.2173i	−2.22262	+	1.28323i
$935$	3.45176	−	17.9341i	0.112885	−	0.586509i
$936$	−55.2014	−	21.2141i	−1.80431	−	0.693405i
$937$	28.2167			0.921799			0.460900	−	0.887452i	$-0.347527\pi$
$937$	28.2167			0.921799			0.460900	+	0.887452i	$0.347527\pi$
$938$	84.6877	+	35.2960i	2.76515	+	1.15246i
$939$	11.6867	+	33.0223i	0.381381	+	1.07764i
$940$	−40.1164	−	7.72115i	−1.30845	−	0.251836i
$941$	−14.2466			−0.464424			−0.232212	−	0.972665i	$-0.574596\pi$
$941$	−14.2466			−0.464424			−0.232212	+	0.972665i	$0.574596\pi$
$942$	−1.95366	−	5.52034i	−0.0636538	−	0.179862i
$943$	−15.3318			−0.499273
$944$	86.7955			2.82495
$945$	12.9660	+	27.8726i	0.421785	+	0.906696i
$946$	−12.7733			−0.415295
$947$	−22.0867			−0.717720			−0.358860	−	0.933391i	$-0.616835\pi$
$947$	−22.0867			−0.717720			−0.358860	+	0.933391i	$0.616835\pi$
$948$	−16.4472	−	46.4737i	−0.534180	−	1.50940i
$949$	−16.7526			−0.543812
$950$	12.6032	−	1.81866i	0.408901	−	0.0590050i
$951$	−9.45654	−	26.7207i	−0.306649	−	0.866478i
$952$	78.2486	−	59.7708i	2.53605	−	1.93718i
$953$	28.0626			0.909036			0.454518	−	0.890737i	$-0.349811\pi$
$953$	28.0626			0.909036			0.454518	+	0.890737i	$0.349811\pi$
$954$	10.3288	+	65.3759i	0.334409	+	2.11662i
$955$	−49.3166	−	9.49188i	−1.59585	−	0.307150i
$956$	−81.3418	+	46.9627i	−2.63078	+	1.51888i
$957$	4.05737	+	11.4646i	0.131156	+	0.370599i
$958$	−5.80986	−	10.0630i	−0.187708	−	0.325120i
$959$	10.9435	−	1.41639i	0.353383	−	0.0457377i
$960$	−94.4078	+	14.2688i	−3.04700	+	0.460522i
$961$	−37.4441			−1.20787
$962$	−2.57149	−	1.48465i	−0.0829082	−	0.0478671i
$963$	−9.07267	−	3.48666i	−0.292363	−	0.112356i
$964$	−100.459	+	57.9999i	−3.23556	+	1.86805i
$965$	22.1333	+	4.25996i	0.712496	+	0.137133i
$966$	50.2621	−	76.9953i	1.61716	−	2.47728i
$967$	1.97508	−	1.14031i	0.0635141	−	0.0366699i	−0.467907	−	0.883778i	$-0.654992\pi$
$967$	1.97508	−	1.14031i	0.0635141	−	0.0366699i	0.531421	+	0.847108i	$0.321658\pi$
$968$	31.9324	−	55.3085i	1.02635	−	1.77768i
$969$	2.23906	+	6.32675i	0.0719288	+	0.203244i
$970$	64.5763	+	55.9267i	2.07342	+	1.79570i
$971$	−2.70152	−	4.67916i	−0.0866958	−	0.150161i	0.819417	−	0.573198i	$-0.194297\pi$
$971$	−2.70152	−	4.67916i	−0.0866958	−	0.150161i	−0.906113	+	0.423037i	$0.860964\pi$
$972$	82.4616	−	10.7759i	2.64496	−	0.345638i
$973$	6.44102	+	49.7653i	0.206490	+	1.59540i
$974$	67.5746	+	39.0142i	2.16523	+	1.25010i
$975$	−16.7351	+	8.78621i	−0.535953	+	0.281384i
$976$		−	37.1851i		−	1.19027i
$977$	37.0400			1.18502			0.592508	−	0.805565i	$-0.298138\pi$
$977$	37.0400			1.18502			0.592508	+	0.805565i	$0.298138\pi$
$978$	−69.1858	−	59.1132i	−2.21232	−	1.89023i
$979$	−14.3251	−	8.27062i	−0.457833	−	0.264330i
$980$	69.3461	−	46.5196i	2.21518	−	1.48601i
$981$	−0.761017	−	4.81682i	−0.0242974	−	0.153789i
$982$	−99.2911	+	57.3257i	−3.16851	+	1.82934i
$983$	−0.334598	+	0.193180i	−0.0106720	+	0.00616149i	−0.505327	−	0.862928i	$-0.668628\pi$
$983$	−0.334598	+	0.193180i	−0.0106720	+	0.00616149i	0.494655	+	0.869090i	$0.335295\pi$
$984$	−21.0298	+	24.6132i	−0.670407	+	0.784641i
$985$	10.7233	−	55.7144i	0.341672	−	1.77521i
$986$	19.7655	+	34.2348i	0.629461	+	1.09026i
$987$	0.858612	−	15.6700i	0.0273299	−	0.498782i
$988$	−9.48217	−	5.47453i	−0.301668	−	0.174168i
$989$	−15.2664	+	8.81403i	−0.485442	+	0.280270i
$990$	−30.5674	−	19.0386i	−0.971495	−	0.605087i
$991$	12.4649	−	21.5899i	0.395961	−	0.685825i	−0.597262	−	0.802046i	$-0.703745\pi$
$991$	12.4649	−	21.5899i	0.395961	−	0.685825i	0.993223	+	0.116221i	$0.0370781\pi$
$992$		−	159.564i		−	5.06617i
$993$	4.24927	+	12.0069i	0.134847	+	0.381027i
$994$	33.2235	+	13.8468i	1.05379	+	0.439195i
$995$	−26.1300	+	30.1712i	−0.828376	+	0.956492i
$996$	0.176574	−	0.951691i	0.00559496	−	0.0301555i
$997$	−8.89839	−	15.4125i	−0.281815	−	0.488118i	0.690017	−	0.723793i	$-0.257603\pi$
$997$	−8.89839	−	15.4125i	−0.281815	−	0.488118i	−0.971832	+	0.235676i	$0.924270\pi$
$998$	−39.9570	+	69.2076i	−1.26482	+	2.19073i
$999$	2.60928	+	0.0698270i	0.0825541	+	0.00220923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bq.a.164.1	yes	88
3.2	odd	2		945.2.bq.a.899.44		88
5.4	even	2	inner	315.2.bq.a.164.44	yes	88
7.5	odd	6		315.2.u.a.299.44	yes	88
9.4	even	3		945.2.u.a.584.44		88
9.5	odd	6		315.2.u.a.59.1	✓	88
15.14	odd	2		945.2.bq.a.899.1		88
21.5	even	6		945.2.u.a.89.1		88
35.19	odd	6		315.2.u.a.299.1	yes	88
45.4	even	6		945.2.u.a.584.1		88
45.14	odd	6		315.2.u.a.59.44	yes	88
63.5	even	6	inner	315.2.bq.a.194.44	yes	88
63.40	odd	6		945.2.bq.a.719.1		88
105.89	even	6		945.2.u.a.89.44		88
315.194	even	6	inner	315.2.bq.a.194.1	yes	88
315.229	odd	6		945.2.bq.a.719.44		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.u.a.59.1	✓	88	9.5	odd	6
315.2.u.a.59.44	yes	88	45.14	odd	6
315.2.u.a.299.1	yes	88	35.19	odd	6
315.2.u.a.299.44	yes	88	7.5	odd	6
315.2.bq.a.164.1	yes	88	1.1	even	1	trivial
315.2.bq.a.164.44	yes	88	5.4	even	2	inner
315.2.bq.a.194.1	yes	88	315.194	even	6	inner
315.2.bq.a.194.44	yes	88	63.5	even	6	inner
945.2.u.a.89.1		88	21.5	even	6
945.2.u.a.89.44		88	105.89	even	6
945.2.u.a.584.1		88	45.4	even	6
945.2.u.a.584.44		88	9.4	even	3
945.2.bq.a.719.1		88	63.40	odd	6
945.2.bq.a.719.44		88	315.229	odd	6
945.2.bq.a.899.1		88	15.14	odd	2
945.2.bq.a.899.44		88	3.2	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bq (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.70830 q^{2} +(0.577858 + 1.63281i) q^{3} +5.33489 q^{4} +(-0.422616 + 2.19577i) q^{5} +(-1.56501 - 4.42215i) q^{6} +(-1.01783 + 2.44214i) q^{7} -9.03188 q^{8} +(-2.33216 + 1.88707i) q^{9} +O(q^{10})\)	\(q-2.70830 q^{2} +(0.577858 + 1.63281i) q^{3} +5.33489 q^{4} +(-0.422616 + 2.19577i) q^{5} +(-1.56501 - 4.42215i) q^{6} +(-1.01783 + 2.44214i) q^{7} -9.03188 q^{8} +(-2.33216 + 1.88707i) q^{9} +(1.14457 - 5.94680i) q^{10} +(-1.71660 + 0.991081i) q^{11} +(3.08281 + 8.71088i) q^{12} +(-1.09127 - 1.89014i) q^{13} +(2.75659 - 6.61404i) q^{14} +(-3.82949 + 0.578788i) q^{15} +13.7913 q^{16} +(3.56850 + 2.06028i) q^{17} +(6.31619 - 5.11075i) q^{18} +(0.814365 - 0.470174i) q^{19} +(-2.25461 + 11.7142i) q^{20} +(-4.57571 - 0.250719i) q^{21} +(4.64908 - 2.68414i) q^{22} +(3.70432 - 6.41607i) q^{23} +(-5.21914 - 14.7474i) q^{24} +(-4.64279 - 1.85593i) q^{25} +(2.95549 + 5.11906i) q^{26} +(-4.42889 - 2.71753i) q^{27} +(-5.43001 + 13.0285i) q^{28} +(-3.06772 - 1.77115i) q^{29} +(10.3714 - 1.56753i) q^{30} +8.27310i q^{31} -19.2871 q^{32} +(-2.61020 - 2.23019i) q^{33} +(-9.66457 - 5.57984i) q^{34} +(-4.93221 - 3.26700i) q^{35} +(-12.4418 + 10.0673i) q^{36} +(-0.435036 + 0.251168i) q^{37} +(-2.20555 + 1.27337i) q^{38} +(2.45564 - 2.87407i) q^{39} +(3.81702 - 19.8319i) q^{40} +(-1.03473 - 1.79220i) q^{41} +(12.3924 + 0.679021i) q^{42} +(-2.06061 - 1.18970i) q^{43} +(-9.15789 + 5.28731i) q^{44} +(-3.15795 - 5.91839i) q^{45} +(-10.0324 + 17.3767i) q^{46} +3.42460i q^{47} +(7.96939 + 22.5186i) q^{48} +(-4.92805 - 4.97135i) q^{49} +(12.5741 + 5.02643i) q^{50} +(-1.30196 + 7.01724i) q^{51} +(-5.82181 - 10.0837i) q^{52} +(-4.07308 + 7.05479i) q^{53} +(11.9948 + 7.35988i) q^{54} +(-1.45072 - 4.18811i) q^{55} +(9.19291 - 22.0571i) q^{56} +(1.23829 + 1.05801i) q^{57} +(8.30830 + 4.79680i) q^{58} +6.29351 q^{59} +(-20.4299 + 3.08777i) q^{60} -2.69628i q^{61} -22.4060i q^{62} +(-2.23473 - 7.61616i) q^{63} +24.6528 q^{64} +(4.61149 - 1.59738i) q^{65} +(7.06921 + 6.04002i) q^{66} +12.8042i q^{67} +(19.0376 + 10.9913i) q^{68} +(12.6168 + 2.34089i) q^{69} +(13.3579 + 8.84802i) q^{70} +5.02318i q^{71} +(21.0638 - 17.0438i) q^{72} +(3.83786 - 6.64737i) q^{73} +(1.17821 - 0.680239i) q^{74} +(0.347521 - 8.65328i) q^{75} +(4.34455 - 2.50833i) q^{76} +(-0.673146 - 5.20093i) q^{77} +(-6.65062 + 7.78385i) q^{78} -5.33513 q^{79} +(-5.82841 + 30.2824i) q^{80} +(1.87795 - 8.80189i) q^{81} +(2.80235 + 4.85381i) q^{82} +(-0.0907172 - 0.0523756i) q^{83} +(-24.4109 - 1.33756i) q^{84} +(-6.03199 + 6.96489i) q^{85} +(5.58076 + 3.22205i) q^{86} +(1.11925 - 6.03248i) q^{87} +(15.5042 - 8.95133i) q^{88} +(4.17252 + 7.22702i) q^{89} +(8.55269 + 16.0288i) q^{90} +(5.72670 - 0.741195i) q^{91} +(19.7622 - 34.2291i) q^{92} +(-13.5084 + 4.78067i) q^{93} -9.27486i q^{94} +(0.688229 + 1.98686i) q^{95} +(-11.1452 - 31.4923i) q^{96} +(-7.05321 + 12.2165i) q^{97} +(13.3466 + 13.4639i) q^{98} +(2.13316 - 5.55071i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 76 q^{4} - 3 q^{5} - 12 q^{6}+O(q^{10}) \) 88 * q + 76 * q^4 - 3 * q^5 - 12 * q^6	\( 88 q + 76 q^{4} - 3 q^{5} - 12 q^{6} - 6 q^{10} - 12 q^{11} - 12 q^{14} - 6 q^{15} + 52 q^{16} - 12 q^{19} - 6 q^{20} - 12 q^{21} - 48 q^{24} + q^{25} - 12 q^{26} + 6 q^{29} + 33 q^{30} - 12 q^{34} - 36 q^{36} + 12 q^{39} - 30 q^{40} + 6 q^{41} - 84 q^{44} + 21 q^{45} - 18 q^{46} - 8 q^{49} + 30 q^{50} - 24 q^{51} - 60 q^{54} - 78 q^{56} - 12 q^{59} - 45 q^{60} - 8 q^{64} - 24 q^{66} + 60 q^{69} + 15 q^{70} - 30 q^{74} - 48 q^{75} - 48 q^{76} - 16 q^{79} - 69 q^{80} + 36 q^{81} - 90 q^{84} - 7 q^{85} - 12 q^{86} + 72 q^{89} + 33 q^{90} + 20 q^{91} - 60 q^{96} + 30 q^{99}+O(q^{100}) \) 88 * q + 76 * q^4 - 3 * q^5 - 12 * q^6 - 6 * q^10 - 12 * q^11 - 12 * q^14 - 6 * q^15 + 52 * q^16 - 12 * q^19 - 6 * q^20 - 12 * q^21 - 48 * q^24 + q^25 - 12 * q^26 + 6 * q^29 + 33 * q^30 - 12 * q^34 - 36 * q^36 + 12 * q^39 - 30 * q^40 + 6 * q^41 - 84 * q^44 + 21 * q^45 - 18 * q^46 - 8 * q^49 + 30 * q^50 - 24 * q^51 - 60 * q^54 - 78 * q^56 - 12 * q^59 - 45 * q^60 - 8 * q^64 - 24 * q^66 + 60 * q^69 + 15 * q^70 - 30 * q^74 - 48 * q^75 - 48 * q^76 - 16 * q^79 - 69 * q^80 + 36 * q^81 - 90 * q^84 - 7 * q^85 - 12 * q^86 + 72 * q^89 + 33 * q^90 + 20 * q^91 - 60 * q^96 + 30 * q^99

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