LMFDB - Embedded newform 925.2.y.b.393.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(193,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.193"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.y (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [68] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			393.10
Character	$\chi$	$=$	925.393
Dual form			925.2.y.b.732.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.305683 + 0.176486i) q^{2} +(-2.52485 - 0.676530i) q^{3} +(-0.937705 - 1.62415i) q^{4} +(-0.652403 - 0.652403i) q^{6} +(1.50833 + 0.404156i) q^{7} -1.36791i q^{8} +(3.31908 + 1.91627i) q^{9} -2.57054i q^{11} +(1.26877 + 4.73512i) q^{12} +(4.41433 - 2.54861i) q^{13} +(0.389743 + 0.389743i) q^{14} +(-1.63399 + 2.83016i) q^{16} +(0.342624 - 0.593443i) q^{17} +(0.676389 + 1.17154i) q^{18} +(4.59908 + 1.23232i) q^{19} +(-3.53488 - 2.04087i) q^{21} +(0.453664 - 0.785768i) q^{22} -5.83340i q^{23} +(-0.925433 + 3.45376i) q^{24} +1.79918 q^{26} +(-1.53879 - 1.53879i) q^{27} +(-0.757959 - 2.82874i) q^{28} +(-4.71673 - 4.71673i) q^{29} +(-1.40786 + 1.40786i) q^{31} +(-3.36826 + 1.94466i) q^{32} +(-1.73905 + 6.49021i) q^{33} +(0.209469 - 0.120937i) q^{34} -7.18758i q^{36} +(-4.74646 + 3.80409i) q^{37} +(1.18837 + 1.18837i) q^{38} +(-12.8697 + 3.44843i) q^{39} +(-6.82923 + 3.94286i) q^{41} +(-0.720368 - 1.24771i) q^{42} -2.28668i q^{43} +(-4.17495 + 2.41041i) q^{44} +(1.02951 - 1.78317i) q^{46} +(7.99119 - 7.99119i) q^{47} +(6.04027 - 6.04027i) q^{48} +(-3.95045 - 2.28080i) q^{49} +(-1.26656 + 1.26656i) q^{51} +(-8.27868 - 4.77970i) q^{52} +(-4.37275 + 1.17167i) q^{53} +(-0.198807 - 0.741957i) q^{54} +(0.552850 - 2.06326i) q^{56} +(-10.7783 - 6.22283i) q^{57} +(-0.609385 - 2.27426i) q^{58} +(-2.43277 - 9.07924i) q^{59} +(-2.49030 - 0.667274i) q^{61} +(-0.678826 + 0.181891i) q^{62} +(4.23180 + 4.23180i) q^{63} +5.16315 q^{64} +(-1.67703 + 1.67703i) q^{66} +(-0.100851 + 0.376380i) q^{67} -1.28512 q^{68} +(-3.94647 + 14.7284i) q^{69} +(0.0695659 + 0.120492i) q^{71} +(2.62128 - 4.54020i) q^{72} +(-6.70047 + 6.70047i) q^{73} +(-2.12228 + 0.325159i) q^{74} +(-2.31111 - 8.62517i) q^{76} +(1.03890 - 3.87723i) q^{77} +(-4.54265 - 1.21720i) q^{78} +(0.455083 + 0.121939i) q^{79} +(-2.90463 - 5.03097i) q^{81} -2.78343 q^{82} +(3.06472 - 0.821188i) q^{83} +7.65492i q^{84} +(0.403567 - 0.698999i) q^{86} +(8.71800 + 15.1000i) q^{87} -3.51627 q^{88} +(15.2422 - 4.08413i) q^{89} +(7.68831 - 2.06008i) q^{91} +(-9.47433 + 5.47001i) q^{92} +(4.50709 - 2.60217i) q^{93} +(3.85310 - 1.03243i) q^{94} +(9.81995 - 2.63125i) q^{96} -13.7731 q^{97} +(-0.805056 - 1.39440i) q^{98} +(4.92584 - 8.53181i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) $ 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.305683	+	0.176486i	0.216150	+	0.124794i	0.604166	−	0.796858i	$-0.293506\pi$
$2$	0.305683	+	0.176486i	0.216150	+	0.124794i	−0.388016	+	0.921653i	$0.626840\pi$
$3$	−2.52485	−	0.676530i	−1.45772	−	0.390595i	−0.559018	−	0.829155i	$-0.688822\pi$
$3$	−2.52485	−	0.676530i	−1.45772	−	0.390595i	−0.898702	+	0.438560i	$0.855489\pi$
$4$	−0.937705	−	1.62415i	−0.468853	−	0.812077i
$5$		0			0
$5$		0			0
$6$	−0.652403	−	0.652403i	−0.266342	−	0.266342i
$7$	1.50833	+	0.404156i	0.570096	+	0.152757i	0.532341	−	0.846530i	$-0.321313\pi$
$7$	1.50833	+	0.404156i	0.570096	+	0.152757i	0.0377554	+	0.999287i	$0.487979\pi$
$8$		−	1.36791i		−	0.483629i
$9$	3.31908	+	1.91627i	1.10636	+	0.638756i
$10$		0			0
$11$		−	2.57054i		−	0.775046i	−0.921860	−	0.387523i	$-0.873331\pi$
$11$		−	2.57054i		−	0.775046i	0.921860	−	0.387523i	$-0.126669\pi$
$12$	1.26877	+	4.73512i	0.366263	+	1.36691i
$13$	4.41433	−	2.54861i	1.22431	−	0.706858i	0.258480	−	0.966017i	$-0.416778\pi$
$13$	4.41433	−	2.54861i	1.22431	−	0.706858i	0.965835	+	0.259158i	$0.0834451\pi$
$14$	0.389743	+	0.389743i	0.104163	+	0.104163i
$15$		0			0
$16$	−1.63399	+	2.83016i	−0.408499	+	0.707540i
$17$	0.342624	−	0.593443i	0.0830986	−	0.143931i	−0.821481	−	0.570236i	$-0.806852\pi$
$17$	0.342624	−	0.593443i	0.0830986	−	0.143931i	0.904579	+	0.426305i	$0.140185\pi$
$18$	0.676389	+	1.17154i	0.159426	+	0.276135i
$19$	4.59908	+	1.23232i	1.05510	+	0.282714i	0.744358	−	0.667780i	$-0.232755\pi$
$19$	4.59908	+	1.23232i	1.05510	+	0.282714i	0.310743	+	0.950494i	$0.399422\pi$
$20$		0			0
$21$	−3.53488	−	2.04087i	−0.771374	−	0.445353i
$22$	0.453664	−	0.785768i	0.0967214	−	0.167526i
$23$		−	5.83340i		−	1.21635i	−0.793804	−	0.608174i	$-0.791902\pi$
$23$		−	5.83340i		−	1.21635i	0.793804	−	0.608174i	$-0.208098\pi$
$24$	−0.925433	+	3.45376i	−0.188903	+	0.704996i
$25$		0			0
$26$	1.79918			0.352848
$27$	−1.53879	−	1.53879i	−0.296141	−	0.296141i
$28$	−0.757959	−	2.82874i	−0.143241	−	0.534582i
$29$	−4.71673	−	4.71673i	−0.875874	−	0.875874i	0.117231	−	0.993105i	$-0.462598\pi$
$29$	−4.71673	−	4.71673i	−0.875874	−	0.875874i	−0.993105	+	0.117231i	$0.962598\pi$
$30$		0			0
$31$	−1.40786	+	1.40786i	−0.252859	+	0.252859i	−0.822142	−	0.569283i	$-0.807221\pi$
$31$	−1.40786	+	1.40786i	−0.252859	+	0.252859i	0.569283	+	0.822142i	$0.307221\pi$
$32$	−3.36826	+	1.94466i	−0.595429	+	0.343771i
$33$	−1.73905	+	6.49021i	−0.302729	+	1.12980i
$34$	0.209469	−	0.120937i	0.0359236	−	0.0207405i
$35$		0			0
$36$		−	7.18758i		−	1.19793i
$37$	−4.74646	+	3.80409i	−0.780314	+	0.625388i
$37$	−4.74646	+	3.80409i	−0.780314	+	0.625388i
$38$	1.18837	+	1.18837i	0.192779	+	0.192779i
$39$	−12.8697	+	3.44843i	−2.06080	+	0.552191i
$40$		0			0
$41$	−6.82923	+	3.94286i	−1.06655	+	0.615771i	−0.927236	−	0.374478i	$-0.877822\pi$
$41$	−6.82923	+	3.94286i	−1.06655	+	0.615771i	−0.139311	+	0.990249i	$0.544489\pi$
$42$	−0.720368	−	1.24771i	−0.111155	−	0.192526i
$43$		−	2.28668i		−	0.348716i	−0.984682	−	0.174358i	$-0.944215\pi$
$43$		−	2.28668i		−	0.348716i	0.984682	−	0.174358i	$-0.0557850\pi$
$44$	−4.17495	+	2.41041i	−0.629397	+	0.363383i
$45$		0			0
$46$	1.02951	−	1.78317i	0.151793	−	0.262914i
$47$	7.99119	−	7.99119i	1.16563	−	1.16563i	0.182412	−	0.983222i	$-0.441610\pi$
$47$	7.99119	−	7.99119i	1.16563	−	1.16563i	0.983222	−	0.182412i	$-0.0583905\pi$
$48$	6.04027	−	6.04027i	0.871838	−	0.871838i
$49$	−3.95045	−	2.28080i	−0.564351	−	0.325828i
$50$		0			0
$51$	−1.26656	+	1.26656i	−0.177353	+	0.177353i
$52$	−8.27868	−	4.77970i	−1.14805	−	0.662825i
$53$	−4.37275	+	1.17167i	−0.600643	+	0.160942i	−0.546313	−	0.837581i	$-0.683969\pi$
$53$	−4.37275	+	1.17167i	−0.600643	+	0.160942i	−0.0543303	+	0.998523i	$0.517302\pi$
$54$	−0.198807	−	0.741957i	−0.0270542	−	0.100968i
$55$		0			0
$56$	0.552850	−	2.06326i	0.0738777	−	0.275715i
$57$	−10.7783	−	6.22283i	−1.42762	−	0.824235i
$58$	−0.609385	−	2.27426i	−0.0800162	−	0.298624i
$59$	−2.43277	−	9.07924i	−0.316720	−	1.18202i	−0.922377	−	0.386290i	$-0.873756\pi$
$59$	−2.43277	−	9.07924i	−0.316720	−	1.18202i	0.605657	−	0.795726i	$-0.292910\pi$
$60$		0			0
$61$	−2.49030	−	0.667274i	−0.318850	−	0.0854357i	0.0958442	−	0.995396i	$-0.469445\pi$
$61$	−2.49030	−	0.667274i	−0.318850	−	0.0854357i	−0.414695	+	0.909961i	$0.636112\pi$
$62$	−0.678826	+	0.181891i	−0.0862110	+	0.0231002i
$63$	4.23180	+	4.23180i	0.533156	+	0.533156i
$64$	5.16315			0.645394
$65$		0			0
$66$	−1.67703	+	1.67703i	−0.206428	+	0.206428i
$67$	−0.100851	+	0.376380i	−0.0123209	+	0.0459822i	−0.971813	−	0.235755i	$-0.924244\pi$
$67$	−0.100851	+	0.376380i	−0.0123209	+	0.0459822i	0.959492	+	0.281737i	$0.0909105\pi$
$68$	−1.28512			−0.155844
$69$	−3.94647	+	14.7284i	−0.475099	+	1.77309i
$70$		0			0
$71$	0.0695659	+	0.120492i	0.00825595	+	0.0142997i	0.870124	−	0.492833i	$-0.164039\pi$
$71$	0.0695659	+	0.120492i	0.00825595	+	0.0142997i	−0.861868	+	0.507133i	$0.830705\pi$
$72$	2.62128	−	4.54020i	0.308921	−	0.535067i
$73$	−6.70047	+	6.70047i	−0.784231	+	0.784231i	−0.980542	−	0.196311i	$-0.937104\pi$
$73$	−6.70047	+	6.70047i	−0.784231	+	0.784231i	0.196311	+	0.980542i	$0.437104\pi$
$74$	−2.12228	+	0.325159i	−0.246710	+	0.0377989i
$75$		0			0
$76$	−2.31111	−	8.62517i	−0.265102	−	0.989374i
$77$	1.03890	−	3.87723i	0.118394	−	0.441851i
$78$	−4.54265	−	1.21720i	−0.514353	−	0.137821i
$79$	0.455083	+	0.121939i	0.0512008	+	0.0137192i	0.284329	−	0.958727i	$-0.408229\pi$
$79$	0.455083	+	0.121939i	0.0512008	+	0.0137192i	−0.233128	+	0.972446i	$0.574896\pi$
$80$		0			0
$81$	−2.90463	−	5.03097i	−0.322737	−	0.558997i
$82$	−2.78343			−0.307379
$83$	3.06472	−	0.821188i	0.336396	−	0.0901371i	−0.0866667	−	0.996237i	$-0.527622\pi$
$83$	3.06472	−	0.821188i	0.336396	−	0.0901371i	0.423063	+	0.906100i	$0.360955\pi$
$84$			7.65492i			0.835220i
$85$		0			0
$86$	0.403567	−	0.698999i	0.0435178	−	0.0753750i
$87$	8.71800	+	15.1000i	0.934667	+	1.61889i
$88$	−3.51627			−0.374835
$89$	15.2422	−	4.08413i	1.61567	−	0.432917i	0.665944	−	0.746002i	$-0.268029\pi$
$89$	15.2422	−	4.08413i	1.61567	−	0.432917i	0.949725	+	0.313084i	$0.101362\pi$
$90$		0			0
$91$	7.68831	−	2.06008i	0.805954	−	0.215955i
$92$	−9.47433	+	5.47001i	−0.987768	+	0.570288i
$93$	4.50709	−	2.60217i	0.467364	−	0.269832i
$94$	3.85310	−	1.03243i	0.397417	−	0.106487i
$95$		0			0
$96$	9.81995	−	2.63125i	1.00224	−	0.268551i
$97$	−13.7731			−1.39845			−0.699224	−	0.714902i	$-0.746471\pi$
$97$	−13.7731			−1.39845			−0.699224	+	0.714902i	$0.746471\pi$
$98$	−0.805056	−	1.39440i	−0.0813230	−	0.140856i
$99$	4.92584	−	8.53181i	0.495066	−	0.857479i
$100$		0			0
$101$		−	12.9947i		−	1.29302i	−0.762904	−	0.646512i	$-0.776227\pi$
$101$		−	12.9947i		−	1.29302i	0.762904	−	0.646512i	$-0.223773\pi$
$102$	−0.610693	+	0.163635i	−0.0604676	+	0.0162023i
$103$	−15.5723			−1.53439			−0.767194	−	0.641415i	$-0.778348\pi$
$103$	−15.5723			−1.53439			−0.767194	+	0.641415i	$0.778348\pi$
$104$	−3.48628	−	6.03841i	−0.341858	−	0.592115i
$105$		0			0
$106$	−1.54346	−	0.413568i	−0.149914	−	0.0401693i
$107$	15.0746	+	4.03924i	1.45732	+	0.390488i	0.898564	−	0.438843i	$-0.144612\pi$
$107$	15.0746	+	4.03924i	1.45732	+	0.390488i	0.558758	+	0.829331i	$0.311278\pi$
$108$	−1.05630	+	3.94217i	−0.101643	+	0.379335i
$109$	4.41374	+	16.4723i	0.422760	+	1.57776i	0.768767	+	0.639530i	$0.220871\pi$
$109$	4.41374	+	16.4723i	0.422760	+	1.57776i	−0.346007	+	0.938232i	$0.612463\pi$
$110$		0			0
$111$	14.5577	−	6.39360i	1.38175	−	0.606854i
$112$	−3.60843	+	3.60843i	−0.340965	+	0.340965i
$113$	−4.95674	+	8.58533i	−0.466291	+	0.807640i	−0.999259	−	0.0384957i	$-0.987743\pi$
$113$	−4.95674	+	8.58533i	−0.466291	+	0.807640i	0.532968	+	0.846136i	$0.321077\pi$
$114$	−2.19649	−	3.80442i	−0.205720	−	0.356317i
$115$		0			0
$116$	−3.23779	+	12.0836i	−0.300621	+	1.12193i
$117$	19.5353			1.80604
$118$	0.858701	−	3.20471i	0.0790498	−	0.295018i
$119$	0.756635	−	0.756635i	0.0693606	−	0.0693606i
$120$		0			0
$121$	4.39234			0.399303
$122$	−0.643477	−	0.643477i	−0.0582577	−	0.0582577i
$123$	19.9102	−	5.33493i	1.79524	−	0.481034i
$124$	3.60674	+	0.966423i	0.323895	+	0.0867874i
$125$		0			0
$126$	0.546734	+	2.04044i	0.0487069	+	0.181777i
$127$	−3.49690	−	13.0506i	−0.310299	−	1.15805i	−0.928287	−	0.371865i	$-0.878718\pi$
$127$	−3.49690	−	13.0506i	−0.310299	−	1.15805i	0.617987	−	0.786188i	$-0.287948\pi$
$128$	8.31480	+	4.80055i	0.734931	+	0.424313i
$129$	−1.54701	+	5.77352i	−0.136207	+	0.508330i
$130$		0			0
$131$	2.35244	+	8.77941i	0.205533	+	0.767061i	0.989286	+	0.145988i	$0.0466362\pi$
$131$	2.35244	+	8.77941i	0.205533	+	0.767061i	−0.783753	+	0.621073i	$0.786697\pi$
$132$	12.1718	−	3.26143i	1.05942	−	0.283871i
$133$	6.43889	+	3.71750i	0.558323	+	0.322348i
$134$	−0.0972542	+	0.0972542i	−0.00840148	+	0.00840148i
$135$		0			0
$136$	−0.811777	−	0.468680i	−0.0696093	−	0.0401889i
$137$	3.39738	−	3.39738i	0.290258	−	0.290258i	−0.546924	−	0.837182i	$-0.684201\pi$
$137$	3.39738	−	3.39738i	0.290258	−	0.290258i	0.837182	+	0.546924i	$0.184201\pi$
$138$	−3.80573	+	3.80573i	−0.323965	+	0.323965i
$139$	5.14118	−	8.90478i	0.436069	−	0.755293i	−0.561313	−	0.827603i	$-0.689704\pi$
$139$	5.14118	−	8.90478i	0.436069	−	0.755293i	0.997382	+	0.0723099i	$0.0230371\pi$
$140$		0			0
$141$	−25.5828	+	14.7702i	−2.15446	+	1.24388i
$142$			0.0491096i			0.00412119i
$143$	−6.55131	−	11.3472i	−0.547848	−	0.948901i
$144$	−10.8467	+	6.26234i	−0.903891	+	0.521862i
$145$		0			0
$146$	−3.23075	+	0.865678i	−0.267379	+	0.0716440i
$147$	8.43126	+	8.43126i	0.695398	+	0.695398i
$148$	10.6292	+	4.14187i	0.873715	+	0.340460i
$149$		−	13.8216i		−	1.13231i	−0.824298	−	0.566156i	$-0.808430\pi$
$149$		−	13.8216i		−	1.13231i	0.824298	−	0.566156i	$-0.191570\pi$
$150$		0			0
$151$	−18.7800	+	10.8426i	−1.52829	+	0.882359i	−0.528857	+	0.848711i	$0.677379\pi$
$151$	−18.7800	+	10.8426i	−1.52829	+	0.882359i	−0.999434	+	0.0336485i	$0.989287\pi$
$152$	1.68570	−	6.29113i	0.136729	−	0.510278i
$153$	2.27439	−	1.31312i	0.183874	−	0.106160i
$154$	1.00185	−	1.00185i	0.0807313	−	0.0807313i
$155$		0			0
$156$	17.6688	+	17.6688i	1.41463	+	1.41463i
$157$	2.49678	+	9.31810i	0.199265	+	0.743665i	0.991122	+	0.132959i	$0.0424478\pi$
$157$	2.49678	+	9.31810i	0.199265	+	0.743665i	−0.791857	+	0.610706i	$0.790886\pi$
$158$	0.117590	+	0.117590i	0.00935498	+	0.00935498i
$159$	11.8332			0.938433
$160$		0			0
$161$	2.35761	−	8.79870i	0.185805	−	0.693435i
$162$		−	2.05051i		−	0.161103i
$163$	9.72549	−	16.8451i	0.761760	−	1.31941i	−0.180183	−	0.983633i	$-0.557669\pi$
$163$	9.72549	−	16.8451i	0.761760	−	1.31941i	0.941943	−	0.335773i	$-0.108998\pi$
$164$	12.8076	+	7.39448i	1.00011	+	0.577412i
$165$		0			0
$166$	1.08176	+	0.289856i	0.0839607	+	0.0224972i
$167$	2.03581	+	3.52613i	0.157536	+	0.272860i	0.933980	−	0.357326i	$-0.116312\pi$
$167$	2.03581	+	3.52613i	0.157536	+	0.272860i	−0.776444	+	0.630187i	$0.782978\pi$
$168$	−2.79172	+	4.83540i	−0.215386	+	0.373059i
$169$	6.49087	−	11.2425i	0.499297	−	0.864809i
$170$		0			0
$171$	12.9032	+	12.9032i	0.986735	+	0.986735i
$172$	−3.71392	+	2.14423i	−0.283184	+	0.163496i
$173$	0.919404	+	3.43126i	0.0699010	+	0.260874i	0.992029	−	0.126011i	$-0.0402176\pi$
$173$	0.919404	+	3.43126i	0.0699010	+	0.260874i	−0.922128	+	0.386885i	$0.873551\pi$
$174$			6.15441i			0.466565i
$175$		0			0
$176$	7.27504	+	4.20024i	0.548376	+	0.316605i
$177$			24.5695i			1.84676i
$178$	5.38006	+	1.44158i	0.403253	+	0.108051i
$179$	−5.13938	−	5.13938i	−0.384135	−	0.384135i	0.488454	−	0.872590i	$-0.337561\pi$
$179$	−5.13938	−	5.13938i	−0.384135	−	0.384135i	−0.872590	+	0.488454i	$0.837561\pi$
$180$		0			0
$181$	4.66518	+	8.08032i	0.346760	+	0.600606i	0.985672	−	0.168674i	$-0.0539485\pi$
$181$	4.66518	+	8.08032i	0.346760	+	0.600606i	−0.638912	+	0.769280i	$0.720615\pi$
$182$	2.71376	+	0.727149i	0.201157	+	0.0538999i
$183$	5.83620	+	3.36953i	0.431424	+	0.249083i
$184$	−7.97957			−0.588261
$185$		0			0
$186$	1.83699			0.134694
$187$	−1.52547	−	0.880729i	−0.111553	−	0.0644053i
$188$	−20.4723	−	5.48553i	−1.49310	−	0.400074i
$189$	−1.69910	−	2.94292i	−0.123591	−	0.214066i
$190$		0			0
$191$	1.71277	+	1.71277i	0.123932	+	0.123932i	0.766352	−	0.642420i	$-0.222070\pi$
$191$	1.71277	+	1.71277i	0.123932	+	0.123932i	−0.642420	+	0.766352i	$0.722070\pi$
$192$	−13.0362	−	3.49303i	−0.940804	−	0.252088i
$193$			9.20371i			0.662498i	0.943543	+	0.331249i	$0.107470\pi$
$193$			9.20371i			0.662498i	−0.943543	+	0.331249i	$0.892530\pi$
$194$	−4.21020	−	2.43076i	−0.302275	−	0.174518i
$195$		0			0
$196$			8.55486i			0.611061i
$197$	0.594910	+	2.22023i	0.0423856	+	0.158185i	0.983875	−	0.178857i	$-0.0572401\pi$
$197$	0.594910	+	2.22023i	0.0423856	+	0.158185i	−0.941489	+	0.337043i	$0.890573\pi$
$198$	3.01149	−	1.73868i	0.214017	−	0.123563i
$199$	−13.0048	−	13.0048i	−0.921884	−	0.921884i	0.0752787	−	0.997163i	$-0.476015\pi$
$199$	−13.0048	−	13.0048i	−0.921884	−	0.921884i	−0.997163	+	0.0752787i	$0.976015\pi$
$200$		0			0
$201$	0.509266	−	0.882074i	0.0359208	−	0.0622167i
$202$	2.29339	−	3.97226i	0.161362	−	0.279487i
$203$	−5.20810	−	9.02069i	−0.365537	−	0.633128i
$204$	3.24474	+	0.869425i	0.227177	+	0.0608719i
$205$		0			0
$206$	−4.76019	−	2.74830i	−0.331658	−	0.191483i
$207$	11.1784	−	19.3615i	0.776950	−	1.34572i
$208$			16.6577i			1.15500i
$209$	3.16773	−	11.8221i	0.219116	−	0.817753i
$210$		0			0
$211$	18.9546			1.30489			0.652445	−	0.757836i	$-0.273744\pi$
$211$	18.9546			1.30489			0.652445	+	0.757836i	$0.273744\pi$
$212$	6.00333	+	6.00333i	0.412310	+	0.412310i
$213$	−0.0941269	−	0.351286i	−0.00644947	−	0.0240697i
$214$	3.89519	+	3.89519i	0.266270	+	0.266270i
$215$		0			0
$216$	−2.10493	+	2.10493i	−0.143222	+	0.143222i
$217$	−2.69252	+	1.55453i	−0.182780	+	0.105528i
$218$	−1.55793	+	5.81426i	−0.105516	+	0.393792i
$219$	21.4507	−	12.3846i	1.44951	−	0.836872i
$220$		0			0
$221$		−	3.49287i		−	0.234956i
$222$	5.57841	+	0.614811i	0.374398	+	0.0412634i
$223$	−12.6125	−	12.6125i	−0.844597	−	0.844597i	0.144856	−	0.989453i	$-0.453728\pi$
$223$	−12.6125	−	12.6125i	−0.844597	−	0.844597i	−0.989453	+	0.144856i	$0.953728\pi$
$224$	−5.86640	+	1.57190i	−0.391965	+	0.105027i
$225$		0			0
$226$	−3.03038	+	1.74959i	−0.201578	+	0.116381i
$227$	−7.55203	−	13.0805i	−0.501246	−	0.868183i	−0.999999	−	0.00143883i	$-0.999542\pi$
$227$	−7.55203	−	13.0805i	−0.501246	−	0.868183i	0.498753	−	0.866744i	$-0.333791\pi$
$228$			23.3407i			1.54578i
$229$	−17.9565	+	10.3672i	−1.18660	+	0.685083i	−0.957532	−	0.288328i	$-0.906901\pi$
$229$	−17.9565	+	10.3672i	−1.18660	+	0.685083i	−0.229067	+	0.973411i	$0.573567\pi$
$230$		0			0
$231$	−5.24612	+	9.08655i	−0.345169	+	0.597851i
$232$	−6.45206	+	6.45206i	−0.423598	+	0.423598i
$233$	0.0618698	−	0.0618698i	0.00405322	−	0.00405322i	−0.705077	−	0.709130i	$-0.749088\pi$
$233$	0.0618698	−	0.0618698i	0.00405322	−	0.00405322i	0.709130	+	0.705077i	$0.249088\pi$
$234$	5.97161	+	3.44771i	0.390376	+	0.225384i
$235$		0			0
$236$	−12.4648	+	12.4648i	−0.811393	+	0.811393i
$237$	−1.06652	−	0.615754i	−0.0692778	−	0.0399975i
$238$	0.364826	−	0.0977547i	0.0236481	−	0.00633650i
$239$	3.92002	+	14.6297i	0.253565	+	0.946318i	0.968883	+	0.247519i	$0.0796152\pi$
$239$	3.92002	+	14.6297i	0.253565	+	0.946318i	−0.715318	+	0.698799i	$0.753718\pi$
$240$		0			0
$241$	3.24330	−	12.1042i	0.208919	−	0.779697i	−0.779300	−	0.626651i	$-0.784425\pi$
$241$	3.24330	−	12.1042i	0.208919	−	0.779697i	0.988219	−	0.153046i	$-0.0489083\pi$
$242$	1.34266	+	0.775185i	0.0863095	+	0.0498308i
$243$	5.61986	+	20.9736i	0.360514	+	1.34546i
$244$	1.25141	+	4.67034i	0.0801135	+	0.298988i
$245$		0			0
$246$	7.02774	+	1.88308i	0.448072	+	0.120061i
$247$	23.4426	−	6.28142i	1.49161	−	0.399677i
$248$	1.92583	+	1.92583i	0.122290	+	0.122290i
$249$	−8.29350			−0.525579
$250$		0			0
$251$	0.772329	−	0.772329i	0.0487490	−	0.0487490i	−0.682312	−	0.731061i	$-0.739025\pi$
$251$	0.772329	−	0.772329i	0.0487490	−	0.0487490i	0.731061	+	0.682312i	$0.239025\pi$
$252$	2.90491	−	10.8413i	0.182992	−	0.682935i
$253$	−14.9950			−0.942726
$254$	1.23431	−	4.60649i	0.0774472	−	0.289037i
$255$		0			0
$256$	−3.46869	−	6.00795i	−0.216793	−	0.375497i
$257$	−0.226136	+	0.391679i	−0.0141060	+	0.0244322i	−0.872992	−	0.487734i	$-0.837824\pi$
$257$	−0.226136	+	0.391679i	−0.0141060	+	0.0244322i	0.858886	+	0.512166i	$0.171157\pi$
$258$	−1.49184	+	1.49184i	−0.0928778	+	0.0928778i
$259$	−8.69669	+	3.81951i	−0.540386	+	0.237333i
$260$		0			0
$261$	−6.61665	−	24.6937i	−0.409561	−	1.52850i
$262$	−0.830344	+	3.09889i	−0.0512988	+	0.191450i
$263$	14.5598	+	3.90128i	0.897794	+	0.240563i	0.678069	−	0.734999i	$-0.262817\pi$
$263$	14.5598	+	3.90128i	0.897794	+	0.240563i	0.219725	+	0.975562i	$0.429484\pi$
$264$	8.87803	+	2.37886i	0.546405	+	0.146409i
$265$		0			0
$266$	1.31217	+	2.27275i	0.0804544	+	0.139351i
$267$	−41.2472			−2.52429
$268$	0.705868	−	0.189137i	0.0431177	−	0.0115534i
$269$		−	17.7593i		−	1.08280i	−0.840764	−	0.541402i	$-0.817894\pi$
$269$		−	17.7593i		−	1.08280i	0.840764	−	0.541402i	$-0.182106\pi$
$270$		0			0
$271$	5.45528	−	9.44882i	0.331385	−	0.573975i	−0.651399	−	0.758735i	$-0.725818\pi$
$271$	5.45528	−	9.44882i	0.331385	−	0.573975i	0.982784	+	0.184760i	$0.0591509\pi$
$272$	1.11969	+	1.93936i	0.0678913	+	0.117591i
$273$	−20.8055			−1.25921
$274$	1.63811	−	0.438930i	0.0989618	−	0.0265167i
$275$		0			0
$276$	27.6219	−	7.40125i	1.66264	−	0.445503i
$277$	−11.1460	+	6.43516i	−0.669700	+	0.386652i	−0.795963	−	0.605345i	$-0.793035\pi$
$277$	−11.1460	+	6.43516i	−0.669700	+	0.386652i	0.126263	+	0.991997i	$0.459702\pi$
$278$	3.14314	−	1.81469i	0.188513	−	0.108838i
$279$	−7.37063	+	1.97496i	−0.441268	+	0.118238i
$280$		0			0
$281$	−25.0501	+	6.71215i	−1.49436	+	0.400413i	−0.911208	−	0.411947i	$-0.864849\pi$
$281$	−25.0501	+	6.71215i	−1.49436	+	0.400413i	−0.583155	+	0.812361i	$0.698182\pi$
$282$	−10.4269			−0.620916
$283$	−2.54545	−	4.40886i	−0.151312	−	0.262079i	0.780398	−	0.625283i	$-0.215016\pi$
$283$	−2.54545	−	4.40886i	−0.151312	−	0.262079i	−0.931710	+	0.363203i	$0.881683\pi$
$284$	0.130465	−	0.225971i	0.00774165	−	0.0134089i
$285$		0			0
$286$		−	4.62485i		−	0.273473i
$287$	−11.8943	+	3.18706i	−0.702097	+	0.188126i
$288$	−14.9060			−0.878344
$289$	8.26522	+	14.3158i	0.486189	+	0.842104i
$290$		0			0
$291$	34.7750	+	9.31793i	2.03855	+	0.546227i
$292$	17.1657	+	4.59952i	1.00454	+	0.269167i
$293$	6.05444	−	22.5955i	0.353704	−	1.32004i	−0.528403	−	0.848993i	$-0.677209\pi$
$293$	6.05444	−	22.5955i	0.353704	−	1.32004i	0.882108	−	0.471048i	$-0.156124\pi$
$294$	1.08929	+	4.06529i	0.0635287	+	0.237092i
$295$		0			0
$296$	5.20365	+	6.49274i	0.302456	+	0.377383i
$297$	−3.95552	+	3.95552i	−0.229523	+	0.229523i
$298$	2.43932	−	4.22503i	0.141306	−	0.244749i
$299$	−14.8671	−	25.7505i	−0.859785	−	1.48919i
$300$		0			0
$301$	0.924177	−	3.44908i	0.0532687	−	0.198801i
$302$	−7.65427			−0.440454
$303$	−8.79133	+	32.8097i	−0.505049	+	1.88487i
$304$	−11.0025	+	11.0025i	−0.631039	+	0.631039i
$305$		0			0
$306$	0.926989			0.0529925
$307$	2.66991	+	2.66991i	0.152380	+	0.152380i	0.779180	−	0.626800i	$-0.215636\pi$
$307$	2.66991	+	2.66991i	0.152380	+	0.152380i	−0.626800	+	0.779180i	$0.715636\pi$
$308$	−7.27139	+	1.94836i	−0.414326	+	0.111018i
$309$	39.3177	+	10.5352i	2.23671	+	0.599324i
$310$		0			0
$311$	−2.32734	−	8.68575i	−0.131971	−	0.492524i	0.868021	−	0.496528i	$-0.165392\pi$
$311$	−2.32734	−	8.68575i	−0.131971	−	0.492524i	−0.999992	+	0.00400430i	$0.998725\pi$
$312$	4.71714	+	17.6046i	0.267056	+	0.996665i
$313$	−1.29441	−	0.747326i	−0.0731642	−	0.0422414i	0.462972	−	0.886373i	$-0.346783\pi$
$313$	−1.29441	−	0.747326i	−0.0731642	−	0.0422414i	−0.536136	+	0.844132i	$0.680117\pi$
$314$	−0.881292	+	3.28903i	−0.0497342	+	0.185610i
$315$		0			0
$316$	−0.228686	−	0.853467i	−0.0128646	−	0.0480113i
$317$	18.1650	−	4.86730i	1.02025	−	0.273375i	0.290343	−	0.956923i	$-0.406230\pi$
$317$	18.1650	−	4.86730i	1.02025	−	0.273375i	0.729906	+	0.683548i	$0.239564\pi$
$318$	3.61720	+	2.08839i	0.202842	+	0.117111i
$319$	−12.1245	+	12.1245i	−0.678843	+	0.678843i
$320$		0			0
$321$	−35.3285	−	20.3969i	−1.97184	−	1.13844i
$322$	2.27353	−	2.27353i	0.126699	−	0.126699i
$323$	2.30707	−	2.30707i	0.128369	−	0.128369i
$324$	−5.44738	+	9.43514i	−0.302632	+	0.524175i
$325$		0			0
$326$	5.94583	−	3.43282i	0.329309	−	0.190127i
$327$		−	44.5761i		−	2.46506i
$328$	5.39348	+	9.34178i	0.297805	+	0.515813i
$329$	15.2831	−	8.82367i	0.842582	−	0.486465i
$330$		0			0
$331$	−3.69837	+	0.990975i	−0.203281	+	0.0544689i	−0.359023	−	0.933329i	$-0.616890\pi$
$331$	−3.69837	+	0.990975i	−0.203281	+	0.0544689i	0.155742	+	0.987798i	$0.450223\pi$
$332$	−4.20754	−	4.20754i	−0.230919	−	0.230919i
$333$	−23.0435	+	3.53055i	−1.26278	+	0.193473i
$334$			1.43717i			0.0786384i
$335$		0			0
$336$	11.5520	−	6.66952i	0.630211	−	0.363852i
$337$	1.37651	−	5.13720i	0.0749832	−	0.279841i	−0.918246	−	0.396010i	$-0.870395\pi$
$337$	1.37651	−	5.13720i	0.0749832	−	0.279841i	0.993230	+	0.116169i	$0.0370613\pi$
$338$	3.96829	−	2.29109i	0.215846	−	0.124619i
$339$	18.3232	−	18.3232i	0.995182	−	0.995182i
$340$		0			0
$341$	3.61896	+	3.61896i	0.195978	+	0.195978i
$342$	1.66705	+	6.22153i	0.0901440	+	0.336422i
$343$	−12.7660	−	12.7660i	−0.689301	−	0.689301i
$344$	−3.12798			−0.168649
$345$		0			0
$346$	−0.324524	+	1.21114i	−0.0174465	+	0.0651112i
$347$		−	17.6817i		−	0.949201i	−0.880201	−	0.474600i	$-0.842593\pi$
$347$		−	17.6817i		−	0.949201i	0.880201	−	0.474600i	$-0.157407\pi$
$348$	16.3498	−	28.3187i	0.876443	−	1.51804i
$349$	−12.9795	−	7.49374i	−0.694779	−	0.401131i	0.110621	−	0.993863i	$-0.464716\pi$
$349$	−12.9795	−	7.49374i	−0.694779	−	0.401131i	−0.805400	+	0.592732i	$0.798049\pi$
$350$		0			0
$351$	−10.7145	−	2.87095i	−0.571899	−	0.153240i
$352$	4.99883	+	8.65823i	0.266439	+	0.461485i
$353$	5.89156	−	10.2045i	0.313576	−	0.543130i	−0.665558	−	0.746347i	$-0.731806\pi$
$353$	5.89156	−	10.2045i	0.313576	−	0.543130i	0.979134	+	0.203216i	$0.0651395\pi$
$354$	−4.33617	+	7.51047i	−0.230465	+	0.399177i
$355$		0			0
$356$	−20.9260	−	20.9260i	−1.10907	−	1.10907i
$357$	−2.42227	+	1.39850i	−0.128200	+	0.0740165i
$358$	−0.663991	−	2.47805i	−0.0350930	−	0.130969i
$359$			3.55034i			0.187380i	0.995601	+	0.0936900i	$0.0298663\pi$
$359$			3.55034i			0.187380i	−0.995601	+	0.0936900i	$0.970134\pi$
$360$		0			0
$361$	3.17845	+	1.83508i	0.167287	+	0.0965831i
$362$			3.29335i			0.173095i
$363$	−11.0900	−	2.97155i	−0.582072	−	0.155966i
$364$	−10.5553	−	10.5553i	−0.553246	−	0.553246i
$365$		0			0
$366$	1.18935	+	2.06001i	0.0621683	+	0.107679i
$367$	5.68539	+	1.52339i	0.296775	+	0.0795206i	0.404134	−	0.914700i	$-0.367573\pi$
$367$	5.68539	+	1.52339i	0.296775	+	0.0795206i	−0.107359	+	0.994220i	$0.534240\pi$
$368$	16.5095	+	9.53174i	0.860615	+	0.496876i
$369$	−30.2223			−1.57331
$370$		0			0
$371$	−7.06910			−0.367009
$372$	−8.45265	−	4.88014i	−0.438249	−	0.253023i
$373$	25.7256	+	6.89317i	1.33202	+	0.356915i	0.853469	−	0.521143i	$-0.174494\pi$
$373$	25.7256	+	6.89317i	1.33202	+	0.356915i	0.478554	+	0.878058i	$0.341161\pi$
$374$	−0.310872	−	0.538447i	−0.0160748	−	0.0278424i
$375$		0			0
$376$	−10.9312	−	10.9312i	−0.563735	−	0.563735i
$377$	−32.8423	−	8.80007i	−1.69146	−	0.453226i
$378$		−	1.19947i		−	0.0616939i
$379$	21.5060	+	12.4165i	1.10469	+	0.637793i	0.937449	−	0.348123i	$-0.113181\pi$
$379$	21.5060	+	12.4165i	1.10469	+	0.637793i	0.167241	+	0.985916i	$0.446514\pi$
$380$		0			0
$381$			35.3165i			1.80932i
$382$	0.221284	+	0.825845i	0.0113219	+	0.0422539i
$383$	0.836267	−	0.482819i	0.0427312	−	0.0246709i	−0.478482	−	0.878097i	$-0.658813\pi$
$383$	0.836267	−	0.482819i	0.0427312	−	0.0246709i	0.521213	+	0.853426i	$0.325480\pi$
$384$	−17.7459	−	17.7459i	−0.905590	−	0.905590i
$385$		0			0
$386$	−1.62433	+	2.81341i	−0.0826760	+	0.143199i
$387$	4.38190	−	7.58967i	0.222744	−	0.385805i
$388$	12.9151	+	22.3697i	0.655666	+	1.13565i
$389$	17.1704	+	4.60080i	0.870574	+	0.233270i	0.666336	−	0.745651i	$-0.267862\pi$
$389$	17.1704	+	4.60080i	0.870574	+	0.233270i	0.204238	+	0.978921i	$0.434528\pi$
$390$		0			0
$391$	−3.46179	−	1.99866i	−0.175070	−	0.101077i
$392$	−3.11992	+	5.40387i	−0.157580	+	0.272937i
$393$		−	23.7582i		−	1.19844i
$394$	−0.209986	+	0.783680i	−0.0105790	+	0.0394812i
$395$		0			0
$396$	−18.4760			−0.928452
$397$	24.5436	+	24.5436i	1.23181	+	1.23181i	0.963268	+	0.268541i	$0.0865414\pi$
$397$	24.5436	+	24.5436i	1.23181	+	1.23181i	0.268541	+	0.963268i	$0.413459\pi$
$398$	−1.68017	−	6.27049i	−0.0842194	−	0.314311i
$399$	−13.7422	−	13.7422i	−0.687971	−	0.687971i
$400$		0			0
$401$	−12.2360	+	12.2360i	−0.611036	+	0.611036i	−0.943216	−	0.332180i	$-0.892216\pi$
$401$	−12.2360	+	12.2360i	−0.611036	+	0.611036i	0.332180	+	0.943216i	$0.392216\pi$
$402$	0.311347	−	0.179756i	0.0155286	−	0.00896543i
$403$	−2.62667	+	9.80285i	−0.130844	+	0.488315i
$404$	−21.1054	+	12.1852i	−1.05003	+	0.606238i
$405$		0			0
$406$		−	3.67662i		−	0.182468i
$407$	9.77855	+	12.2010i	0.484705	+	0.604780i
$408$	1.73254	+	1.73254i	0.0857733	+	0.0857733i
$409$	32.7833	−	8.78426i	1.62103	−	0.434354i	0.669727	−	0.742608i	$-0.266411\pi$
$409$	32.7833	−	8.78426i	1.62103	−	0.434354i	0.951304	+	0.308254i	$0.0997446\pi$
$410$		0			0
$411$	−10.8763	+	6.27943i	−0.536488	+	0.309742i
$412$	14.6023	+	25.2919i	0.719402	+	1.24604i
$413$		−	14.6777i		−	0.722244i
$414$	6.83406	−	3.94565i	0.335876	−	0.193918i
$415$		0			0
$416$	−9.91240	+	17.1688i	−0.485995	+	0.841769i
$417$	−19.0050	+	19.0050i	−0.930680	+	0.930680i
$418$	3.05475	−	3.05475i	0.149413	−	0.149413i
$419$	18.2797	+	10.5538i	0.893023	+	0.515587i	0.874930	−	0.484249i	$-0.160907\pi$
$419$	18.2797	+	10.5538i	0.893023	+	0.515587i	0.0180930	+	0.999836i	$0.494241\pi$
$420$		0			0
$421$	21.7979	−	21.7979i	1.06237	−	1.06237i	0.0644457	−	0.997921i	$-0.479472\pi$
$421$	21.7979	−	21.7979i	1.06237	−	1.06237i	0.997921	−	0.0644457i	$-0.0205279\pi$
$422$	5.79409	+	3.34522i	0.282052	+	0.162843i
$423$	41.8366	−	11.2101i	2.03417	−	0.545053i
$424$	1.60275	+	5.98153i	0.0778362	+	0.290489i
$425$		0			0
$426$	0.0332241	−	0.123994i	0.00160971	−	0.00600754i
$427$	−3.48652	−	2.01294i	−0.168725	−	0.0974131i
$428$	−7.57523	−	28.2712i	−0.366163	−	1.36654i
$429$	8.86432	+	33.0821i	0.427973	+	1.59722i
$430$		0			0
$431$	30.9974	+	8.30574i	1.49309	+	0.400073i	0.910781	−	0.412891i	$-0.135481\pi$
$431$	30.9974	+	8.30574i	1.49309	+	0.400073i	0.582314	+	0.812964i	$0.302147\pi$
$432$	6.86941	−	1.84065i	0.330504	−	0.0885584i
$433$	−6.59714	−	6.59714i	−0.317038	−	0.317038i	0.530590	−	0.847628i	$-0.321970\pi$
$433$	−6.59714	−	6.59714i	−0.317038	−	0.317038i	−0.847628	+	0.530590i	$0.821970\pi$
$434$	−1.09741			−0.0526772
$435$		0			0
$436$	22.6148	−	22.6148i	1.08305	−	1.08305i
$437$	7.18861	−	26.8283i	0.343878	−	1.28337i
$438$	8.74281			0.417748
$439$	−1.83248	+	6.83892i	−0.0874597	+	0.326404i	−0.995769	−	0.0918961i	$-0.970707\pi$
$439$	−1.83248	+	6.83892i	−0.0874597	+	0.326404i	0.908309	+	0.418300i	$0.137374\pi$
$440$		0			0
$441$	−8.74124	−	15.1403i	−0.416249	−	0.720965i
$442$	0.616442	−	1.06771i	0.0293212	−	0.0507857i
$443$	−18.7004	+	18.7004i	−0.888481	+	0.888481i	−0.994377	−	0.105896i	$-0.966229\pi$
$443$	−18.7004	+	18.7004i	−0.888481	+	0.888481i	0.105896	+	0.994377i	$0.466229\pi$
$444$	−24.0350	−	17.6486i	−1.14065	−	0.837564i
$445$		0			0
$446$	−1.62950	−	6.08136i	−0.0771588	−	0.287961i
$447$	−9.35075	+	34.8975i	−0.442275	+	1.65059i
$448$	7.78775	+	2.08672i	0.367937	+	0.0985883i
$449$	−14.0578	−	3.76677i	−0.663427	−	0.177765i	−0.0886349	−	0.996064i	$-0.528250\pi$
$449$	−14.0578	−	3.76677i	−0.663427	−	0.177765i	−0.574792	+	0.818299i	$0.694917\pi$
$450$		0			0
$451$	10.1353	+	17.5548i	0.477251	+	0.826623i
$452$	18.5919			0.874488
$453$	54.7518	−	14.6707i	2.57247	−	0.689290i
$454$		−	5.33130i		−	0.250210i
$455$		0			0
$456$	−8.51228	+	14.7437i	−0.398624	+	0.690437i
$457$	−8.63291	−	14.9526i	−0.403831	−	0.699455i	0.590354	−	0.807145i	$-0.298988\pi$
$457$	−8.63291	−	14.9526i	−0.403831	−	0.699455i	−0.994185	+	0.107689i	$0.965655\pi$
$458$	−7.31865			−0.341978
$459$	−1.44041	+	0.385958i	−0.0672327	+	0.0180150i
$460$		0			0
$461$	−12.8182	+	3.43463i	−0.597004	+	0.159967i	−0.544652	−	0.838662i	$-0.683338\pi$
$461$	−12.8182	+	3.43463i	−0.597004	+	0.159967i	−0.0523519	+	0.998629i	$0.516672\pi$
$462$	−3.20729	+	1.85173i	−0.149217	+	0.0861504i
$463$	20.6820	−	11.9408i	0.961176	−	0.554935i	0.0646411	−	0.997909i	$-0.479410\pi$
$463$	20.6820	−	11.9408i	0.961176	−	0.554935i	0.896535	+	0.442973i	$0.146076\pi$
$464$	21.0562	−	5.64199i	0.977509	−	0.261923i
$465$		0			0
$466$	0.0298317	−	0.00799337i	0.00138192	−	0.000370286i
$467$	20.4259			0.945199			0.472600	−	0.881277i	$-0.343316\pi$
$467$	20.4259			0.945199			0.472600	+	0.881277i	$0.343316\pi$
$468$	−18.3184	−	31.7284i	−0.846767	−	1.46664i
$469$	−0.304233	+	0.526947i	−0.0140482	+	0.0243322i
$470$		0			0
$471$		−	25.2159i		−	1.16189i
$472$	−12.4196	+	3.32782i	−0.571658	+	0.153175i
$473$	−5.87800			−0.270271
$474$	−0.217344	−	0.376451i	−0.00998293	−	0.0172910i
$475$		0			0
$476$	−1.93839	−	0.519391i	−0.0888461	−	0.0238062i
$477$	−16.7587	−	4.49049i	−0.767329	−	0.205605i
$478$	−1.38366	+	5.16388i	−0.0632870	+	0.236190i
$479$	−3.51612	−	13.1223i	−0.160655	−	0.599574i	−0.998554	−	0.0537489i	$-0.982883\pi$
$479$	−3.51612	−	13.1223i	−0.160655	−	0.599574i	0.837899	−	0.545825i	$-0.183784\pi$
$480$		0			0
$481$	−11.2573	+	28.8894i	−0.513289	+	1.31724i
$482$	3.12763	−	3.12763i	0.142460	−	0.142460i
$483$	−11.9052	+	20.6204i	−0.541704	+	0.938259i
$484$	−4.11872	−	7.13383i	−0.187214	−	0.324265i
$485$		0			0
$486$	−1.98365	+	7.40309i	−0.0899802	+	0.335811i
$487$	30.9463			1.40231			0.701154	−	0.713009i	$-0.252668\pi$
$487$	30.9463			1.40231			0.701154	+	0.713009i	$0.252668\pi$
$488$	−0.912772	+	3.40651i	−0.0413192	+	0.154205i
$489$	−35.9516	+	35.9516i	−1.62579	+	1.62579i
$490$		0			0
$491$	9.00052			0.406188			0.203094	−	0.979159i	$-0.434900\pi$
$491$	9.00052			0.406188			0.203094	+	0.979159i	$0.434900\pi$
$492$	−27.3347	−	27.3347i	−1.23234	−	1.23234i
$493$	−4.41517	+	1.18304i	−0.198849	+	0.0532815i
$494$	8.27456	+	2.21716i	0.372290	+	0.0997549i
$495$		0			0
$496$	−1.68404	−	6.28491i	−0.0756154	−	0.282201i
$497$	0.0562310	+	0.209857i	0.00252231	+	0.00941337i
$498$	−2.53518	−	1.46368i	−0.113604	−	0.0655893i
$499$	−11.3719	+	42.4404i	−0.509075	+	1.89989i	−0.0795648	+	0.996830i	$0.525353\pi$
$499$	−11.3719	+	42.4404i	−0.509075	+	1.89989i	−0.429510	+	0.903062i	$0.641314\pi$
$500$		0			0
$501$	−2.75458	−	10.2802i	−0.123066	−	0.459287i
$502$	0.372393	−	0.0997823i	0.0166207	−	0.00445350i
$503$	0.523159	+	0.302046i	0.0233265	+	0.0134676i	0.511618	−	0.859213i	$-0.329046\pi$
$503$	0.523159	+	0.302046i	0.0233265	+	0.0134676i	−0.488291	+	0.872681i	$0.662380\pi$
$504$	5.78872	−	5.78872i	0.257850	−	0.257850i
$505$		0			0
$506$	−4.58370	−	2.64640i	−0.203770	−	0.117647i
$507$	−23.9943	+	23.9943i	−1.06563	+	1.06563i
$508$	−17.9171	+	17.9171i	−0.794943	+	0.794943i
$509$	−8.77913	+	15.2059i	−0.389128	+	0.673990i	−0.992333	−	0.123597i	$-0.960557\pi$
$509$	−8.77913	+	15.2059i	−0.389128	+	0.673990i	0.603204	+	0.797587i	$0.293890\pi$
$510$		0			0
$511$	−12.8146	+	7.39850i	−0.566883	+	0.327290i
$512$		−	21.6509i		−	0.956844i
$513$	−5.18075	−	8.97331i	−0.228735	−	0.396181i
$514$	−0.138252	+	0.0798196i	−0.00609801	+	0.00352069i
$515$		0			0
$516$	10.8277	−	2.90128i	0.476664	−	0.127722i
$517$	−20.5416	−	20.5416i	−0.903421	−	0.903421i
$518$	−3.33252	−	0.367285i	−0.146422	−	0.0161376i
$519$		−	9.28541i		−	0.407584i
$520$		0			0
$521$	−19.5517	+	11.2882i	−0.856576	+	0.494545i	−0.862864	−	0.505436i	$-0.831332\pi$
$521$	−19.5517	+	11.2882i	−0.856576	+	0.494545i	0.00628804	+	0.999980i	$0.497998\pi$
$522$	2.33549	−	8.71617i	0.102222	−	0.381497i
$523$	11.0610	−	6.38608i	0.483665	−	0.279244i	−0.238278	−	0.971197i	$-0.576583\pi$
$523$	11.0610	−	6.38608i	0.483665	−	0.279244i	0.721942	+	0.691953i	$0.243250\pi$
$524$	12.0532	−	12.0532i	0.526547	−	0.526547i
$525$		0			0
$526$	3.76215	+	3.76215i	0.164037	+	0.164037i
$527$	0.353117	+	1.31785i	0.0153820	+	0.0574065i
$528$	−15.5267	−	15.5267i	−0.675715	−	0.675715i
$529$	−11.0285			−0.479501
$530$		0			0
$531$	9.32370	−	34.7965i	0.404614	−	1.51004i
$532$		−	13.9437i		−	0.604535i
$533$	−20.0976	+	34.8101i	−0.870526	+	1.50779i
$534$	−12.6086	−	7.27955i	−0.545626	−	0.315017i
$535$		0			0
$536$	0.514855	+	0.137955i	0.0222383	+	0.00595874i
$537$	9.49919	+	16.4531i	0.409920	+	0.710003i
$538$	3.13427	−	5.42871i	0.135128	−	0.234048i
$539$	−5.86287	+	10.1548i	−0.252532	+	0.437398i
$540$		0			0
$541$	20.2821	+	20.2821i	0.871996	+	0.871996i	0.992690	−	0.120694i	$-0.0385120\pi$
$541$	20.2821	+	20.2821i	0.871996	+	0.871996i	−0.120694	+	0.992690i	$0.538512\pi$
$542$	3.33517	−	1.92556i	0.143258	−	0.0827099i
$543$	−6.31227	−	23.5577i	−0.270885	−	1.01096i
$544$			2.66516i			0.114268i
$545$		0			0
$546$	−6.35988	−	3.67188i	−0.272178	−	0.157142i
$547$			1.42392i			0.0608826i	0.999537	+	0.0304413i	$0.00969126\pi$
$547$			1.42392i			0.0608826i	−0.999537	+	0.0304413i	$0.990309\pi$
$548$	−8.70361	−	2.33213i	−0.371800	−	0.0996235i
$549$	−6.98682	−	6.98682i	−0.298190	−	0.298190i
$550$		0			0
$551$	−15.8801	−	27.5051i	−0.676514	−	1.17176i
$552$	20.1472	+	5.39842i	0.857521	+	0.229772i
$553$	0.637133	+	0.367849i	0.0270937	+	0.0156425i
$554$	−4.54286			−0.193008
$555$		0			0
$556$	−19.2836			−0.817808
$557$	−20.2319	−	11.6809i	−0.857251	−	0.494934i	0.00583957	−	0.999983i	$-0.498141\pi$
$557$	−20.2319	−	11.6809i	−0.857251	−	0.494934i	−0.863091	+	0.505049i	$0.831475\pi$
$558$	−2.60163	−	0.697104i	−0.110136	−	0.0295107i
$559$	−5.82787	−	10.0942i	−0.246493	−	0.426938i
$560$		0			0
$561$	3.25573	+	3.25573i	0.137457	+	0.137457i
$562$	−8.84197	−	2.36920i	−0.372976	−	0.0999387i
$563$			33.5056i			1.41209i	0.708166	+	0.706045i	$0.249523\pi$
$563$			33.5056i			1.41209i	−0.708166	+	0.706045i	$0.750477\pi$
$564$	47.9782	+	27.7003i	2.02025	+	1.16639i
$565$		0			0
$566$		−	1.79695i		−	0.0755313i
$567$	−2.34785	−	8.76231i	−0.0986005	−	0.367982i
$568$	0.164822	−	0.0951599i	0.00691577	−	0.00399282i
$569$	−28.8255	−	28.8255i	−1.20843	−	1.20843i	−0.971536	−	0.236893i	$-0.923871\pi$
$569$	−28.8255	−	28.8255i	−1.20843	−	1.20843i	−0.236893	−	0.971536i	$-0.576129\pi$
$570$		0			0
$571$	15.6780	−	27.1551i	0.656105	−	1.13641i	−0.325510	−	0.945538i	$-0.605536\pi$
$571$	15.6780	−	27.1551i	0.656105	−	1.13641i	0.981616	−	0.190869i	$-0.0611306\pi$
$572$	−12.2864	+	21.2807i	−0.513720	+	0.889789i
$573$	−3.16574	−	5.48323i	−0.132251	−	0.229065i
$574$	−4.19834	−	1.12494i	−0.175236	−	0.0469542i
$575$		0			0
$576$	17.1369	+	9.89399i	0.714037	+	0.412250i
$577$	2.25843	−	3.91171i	0.0940195	−	0.162847i	−0.815179	−	0.579208i	$-0.803362\pi$
$577$	2.25843	−	3.91171i	0.0940195	−	0.162847i	0.909199	+	0.416362i	$0.136695\pi$
$578$			5.83478i			0.242695i
$579$	6.22659	−	23.2379i	0.258768	−	0.965736i
$580$		0			0
$581$	4.95450			0.205547
$582$	8.98562	+	8.98562i	0.372466	+	0.372466i
$583$	3.01183	+	11.2403i	0.124737	+	0.465526i
$584$	9.16564	+	9.16564i	0.379277	+	0.379277i
$585$		0			0
$586$	5.83852	−	5.83852i	0.241187	−	0.241187i
$587$	8.52007	−	4.91907i	0.351661	−	0.203032i	−0.313756	−	0.949504i	$-0.601587\pi$
$587$	8.52007	−	4.91907i	0.351661	−	0.203032i	0.665417	+	0.746472i	$0.268254\pi$
$588$	5.78762	−	21.5997i	0.238677	−	0.890756i
$589$	−8.20980	+	4.73993i	−0.338279	+	0.195305i
$590$		0			0
$591$		−	6.00822i		−	0.247145i
$592$	−3.01048	−	19.6491i	−0.123730	−	0.807574i
$593$	−30.7170	−	30.7170i	−1.26139	−	1.26139i	−0.950417	−	0.310977i	$-0.899344\pi$
$593$	−30.7170	−	30.7170i	−1.26139	−	1.26139i	−0.310977	−	0.950417i	$-0.600656\pi$
$594$	−1.90723	+	0.511040i	−0.0782545	+	0.0209682i
$595$		0			0
$596$	−22.4484	+	12.9606i	−0.919524	+	0.530887i
$597$	24.0369	+	41.6332i	0.983765	+	1.70393i
$598$		−	10.4953i		−	0.429186i
$599$	−19.3744	+	11.1858i	−0.791617	+	0.457040i	−0.840532	−	0.541763i	$-0.817757\pi$
$599$	−19.3744	+	11.1858i	−0.791617	+	0.457040i	0.0489144	+	0.998803i	$0.484424\pi$
$600$		0			0
$601$	−1.50390	+	2.60484i	−0.0613456	+	0.106254i	−0.895067	−	0.445931i	$-0.852872\pi$
$601$	−1.50390	+	2.60484i	−0.0613456	+	0.106254i	0.833722	+	0.552185i	$0.186206\pi$
$602$	0.891218	−	0.891218i	0.0363233	−	0.0363233i
$603$	−1.05598	+	1.05598i	−0.0430027	+	0.0430027i
$604$	35.2201	+	20.3344i	1.43309	+	0.827393i
$605$		0			0
$606$	−8.47780	+	8.47780i	−0.344387	+	0.344387i
$607$	14.0611	+	8.11816i	0.570721	+	0.329506i	0.757437	−	0.652908i	$-0.226451\pi$
$607$	14.0611	+	8.11816i	0.570721	+	0.329506i	−0.186716	+	0.982414i	$0.559784\pi$
$608$	−17.8873	+	4.79290i	−0.725427	+	0.194378i
$609$	7.04687	+	26.2993i	0.285554	+	1.06570i
$610$		0			0
$611$	14.9093	−	55.6422i	0.603165	−	2.25104i
$612$	−4.26542	−	2.46264i	−0.172419	−	0.0995464i
$613$	7.57761	+	28.2800i	0.306057	+	1.14222i	0.932032	+	0.362377i	$0.118035\pi$
$613$	7.57761	+	28.2800i	0.306057	+	1.14222i	−0.625975	+	0.779843i	$0.715299\pi$
$614$	0.344943	+	1.28735i	0.0139208	+	0.0519531i
$615$		0			0
$616$	−5.30370	−	1.42112i	−0.213692	−	0.0572586i
$617$	22.8600	−	6.12531i	0.920307	−	0.246596i	0.232591	−	0.972575i	$-0.425280\pi$
$617$	22.8600	−	6.12531i	0.920307	−	0.246596i	0.687717	+	0.725979i	$0.258613\pi$
$618$	10.1594	+	10.1594i	0.408673	+	0.408673i
$619$	29.6822			1.19303			0.596514	−	0.802603i	$-0.296552\pi$
$619$	29.6822			1.19303			0.596514	+	0.802603i	$0.296552\pi$
$620$		0			0
$621$	−8.97639	+	8.97639i	−0.360210	+	0.360210i
$622$	0.821485	−	3.06583i	0.0329386	−	0.122928i
$623$	24.6409			0.987218
$624$	11.2694	−	42.0581i	0.451138	−	1.68367i
$625$		0			0
$626$	−0.263785	−	0.456889i	−0.0105430	−	0.0182610i
$627$	−15.9960	+	27.7059i	−0.638820	+	1.10647i
$628$	12.7928	−	12.7928i	0.510488	−	0.510488i
$629$	0.631253	+	4.12013i	0.0251697	+	0.164280i
$630$		0			0
$631$	2.72026	+	10.1521i	0.108292	+	0.404151i	0.998698	−	0.0510167i	$-0.0162462\pi$
$631$	2.72026	+	10.1521i	0.108292	+	0.404151i	−0.890406	+	0.455167i	$0.849579\pi$
$632$	0.166802	−	0.622512i	0.00663501	−	0.0247622i
$633$	−47.8575	−	12.8234i	−1.90216	−	0.509683i
$634$	6.41174	+	1.71802i	0.254643	+	0.0682313i
$635$		0			0
$636$	−11.0960	−	19.2189i	−0.439987	−	0.762080i
$637$	−23.2515			−0.921257
$638$	−5.84606	+	1.56645i	−0.231448	+	0.0620163i
$639$			0.533228i			0.0210942i
$640$		0			0
$641$	2.73142	−	4.73096i	0.107885	−	0.186862i	−0.807028	−	0.590513i	$-0.798926\pi$
$641$	2.73142	−	4.73096i	0.107885	−	0.186862i	0.914913	+	0.403651i	$0.132259\pi$
$642$	−7.19953	−	12.4700i	−0.284143	−	0.492150i
$643$	11.2760			0.444683			0.222341	−	0.974969i	$-0.428630\pi$
$643$	11.2760			0.444683			0.222341	+	0.974969i	$0.428630\pi$
$644$	−16.5012	+	4.42148i	−0.650238	+	0.174231i
$645$		0			0
$646$	1.11240	−	0.298066i	0.0437666	−	0.0117272i
$647$	−13.5603	+	7.82906i	−0.533112	+	0.307792i	−0.742283	−	0.670087i	$-0.766257\pi$
$647$	−13.5603	+	7.82906i	−0.533112	+	0.307792i	0.209171	+	0.977879i	$0.432923\pi$
$648$	−6.88192	+	3.97328i	−0.270347	+	0.156085i
$649$	−23.3385	+	6.25354i	−0.916117	+	0.245473i
$650$		0			0
$651$	7.84987	−	2.10337i	0.307661	−	0.0824375i
$652$	−36.4786			−1.42861
$653$	13.0781	+	22.6519i	0.511784	+	0.886436i	0.999907	+	0.0136613i	$0.00434865\pi$
$653$	13.0781	+	22.6519i	0.511784	+	0.886436i	−0.488122	+	0.872775i	$0.662318\pi$
$654$	7.86705	−	13.6261i	0.307626	−	0.532824i
$655$		0			0
$656$		−	25.7704i		−	1.00617i
$657$	−35.0793	+	9.39946i	−1.36857	+	0.366708i
$658$	6.22902			0.242832
$659$	−12.9748	−	22.4730i	−0.505425	−	0.875422i	−0.999980	−	0.00627593i	$-0.998002\pi$
$659$	−12.9748	−	22.4730i	−0.505425	−	0.875422i	0.494555	−	0.869146i	$-0.335331\pi$
$660$		0			0
$661$	20.5645	+	5.51024i	0.799866	+	0.214324i	0.635525	−	0.772080i	$-0.280784\pi$
$661$	20.5645	+	5.51024i	0.799866	+	0.214324i	0.164341	+	0.986404i	$0.447450\pi$
$662$	−1.30542	−	0.349786i	−0.0507366	−	0.0135948i
$663$	−2.36303	+	8.81896i	−0.0917726	+	0.342500i
$664$	−1.12331	−	4.19226i	−0.0435930	−	0.162691i
$665$		0			0
$666$	−7.66709	−	2.98763i	−0.297094	−	0.115768i
$667$	−27.5145	+	27.5145i	−1.06537	+	1.06537i
$668$	3.81799	−	6.61295i	0.147722	−	0.255863i
$669$	23.3119	+	40.3774i	0.901291	+	1.56108i
$670$		0			0
$671$	−1.71525	+	6.40142i	−0.0662166	+	0.247124i
$672$	15.8752			0.612399
$673$	5.01583	−	18.7193i	0.193346	−	0.721577i	−0.799343	−	0.600875i	$-0.794819\pi$
$673$	5.01583	−	18.7193i	0.193346	−	0.721577i	0.992689	−	0.120702i	$-0.0385145\pi$
$674$	1.32742	−	1.32742i	0.0511303	−	0.0511303i
$675$		0			0
$676$	−24.3461			−0.936388
$677$	−16.3844	−	16.3844i	−0.629705	−	0.629705i	0.318289	−	0.947994i	$-0.396892\pi$
$677$	−16.3844	−	16.3844i	−0.629705	−	0.629705i	−0.947994	+	0.318289i	$0.896892\pi$
$678$	8.83489	−	2.36730i	0.339302	−	0.0909157i
$679$	−20.7744	−	5.56649i	−0.797250	−	0.213622i
$680$		0			0
$681$	10.2183	+	38.1354i	0.391568	+	1.46135i
$682$	0.467557	+	1.74495i	0.0179037	+	0.0668175i
$683$	6.50589	+	3.75618i	0.248941	+	0.143726i	0.619279	−	0.785171i	$-0.287425\pi$
$683$	6.50589	+	3.75618i	0.248941	+	0.143726i	−0.370338	+	0.928897i	$0.620758\pi$
$684$	8.85740	−	33.0563i	0.338671	−	1.26394i
$685$		0			0
$686$	−1.64933	−	6.15538i	−0.0629716	−	0.235013i
$687$	52.3511	−	14.0274i	1.99732	−	0.535180i
$688$	6.47168	+	3.73643i	0.246730	+	0.142450i
$689$	−16.3166	+	16.3166i	−0.621613	+	0.621613i
$690$		0			0
$691$	−2.18961	−	1.26417i	−0.0832966	−	0.0480913i	0.457773	−	0.889069i	$-0.348647\pi$
$691$	−2.18961	−	1.26417i	−0.0832966	−	0.0480913i	−0.541070	+	0.840978i	$0.681981\pi$
$692$	4.71077	−	4.71077i	0.179077	−	0.179077i
$693$	10.8780	−	10.8780i	0.413221	−	0.413221i
$694$	3.12056	−	5.40497i	0.118455	−	0.205170i
$695$		0			0
$696$	20.6555	−	11.9254i	0.782943	−	0.452033i
$697$			5.40368i			0.204679i
$698$	−2.64508	−	4.58141i	−0.100118	−	0.173409i
$699$	−0.198068	+	0.114355i	−0.00749164	+	0.00432530i
$700$		0			0
$701$	2.22557	−	0.596340i	0.0840587	−	0.0225235i	−0.216545	−	0.976273i	$-0.569479\pi$
$701$	2.22557	−	0.596340i	0.0840587	−	0.0225235i	0.300603	+	0.953749i	$0.402812\pi$
$702$	−2.76856	−	2.76856i	−0.104493	−	0.104493i
$703$	−26.5172	+	11.6461i	−1.00012	+	0.439242i
$704$		−	13.2721i		−	0.500210i
$705$		0			0
$706$	3.60190	−	2.07956i	0.135559	−	0.0782651i
$707$	5.25190	−	19.6004i	0.197518	−	0.737148i
$708$	39.9047	−	23.0390i	1.49971	−	0.865857i
$709$	−19.7666	+	19.7666i	−0.742350	+	0.742350i	−0.973030	−	0.230680i	$-0.925905\pi$
$709$	−19.7666	+	19.7666i	−0.742350	+	0.742350i	0.230680	+	0.973030i	$0.425905\pi$
$710$		0			0
$711$	1.27679	+	1.27679i	0.0478832	+	0.0478832i
$712$	−5.58673	−	20.8500i	−0.209372	−	0.781385i
$713$	8.21261	+	8.21261i	0.307565	+	0.307565i
$714$	−0.987262			−0.0369474
$715$		0			0
$716$	−3.52792	+	13.1664i	−0.131844	+	0.492050i
$717$		−	39.5898i		−	1.47851i
$718$	−0.626586	+	1.08528i	−0.0233840	+	0.0405022i
$719$	−19.1043	−	11.0299i	−0.712469	−	0.411344i	0.0995054	−	0.995037i	$-0.468274\pi$
$719$	−19.1043	−	11.0299i	−0.712469	−	0.411344i	−0.811975	+	0.583693i	$0.801607\pi$
$720$		0			0
$721$	−23.4883	−	6.29366i	−0.874748	−	0.234388i
$722$	0.647731	+	1.12190i	0.0241060	+	0.0417529i
$723$	−16.3777	+	28.3669i	−0.609092	+	1.05498i
$724$	8.74913	−	15.1539i	0.325159	−	0.563191i
$725$		0			0
$726$	−2.86557	−	2.86557i	−0.106351	−	0.106351i
$727$	30.8570	−	17.8153i	1.14442	−	0.660734i	0.196902	−	0.980423i	$-0.436912\pi$
$727$	30.8570	−	17.8153i	1.14442	−	0.660734i	0.947522	+	0.319689i	$0.103579\pi$
$728$	−2.81800	−	10.5169i	−0.104442	−	0.389783i
$729$		−	39.3293i		−	1.45664i
$730$		0			0
$731$	−1.35702	−	0.783473i	−0.0501910	−	0.0289778i
$732$		−	12.6385i		−	0.467133i
$733$	14.3167	+	3.83616i	0.528801	+	0.141692i	0.513335	−	0.858189i	$-0.328410\pi$
$733$	14.3167	+	3.83616i	0.528801	+	0.141692i	0.0154665	+	0.999880i	$0.495077\pi$
$734$	1.46907	+	1.46907i	0.0542242	+	0.0542242i
$735$		0			0
$736$	11.3440	+	19.6484i	0.418145	+	0.724249i
$737$	0.967500	+	0.259241i	0.0356383	+	0.00954926i
$738$	−9.23843	−	5.33381i	−0.340071	−	0.196340i
$739$	2.13171			0.0784161			0.0392080	−	0.999231i	$-0.487516\pi$
$739$	2.13171			0.0784161			0.0392080	+	0.999231i	$0.487516\pi$
$740$		0			0
$741$	−63.4384			−2.33047
$742$	−2.16090	−	1.24760i	−0.0793291	−	0.0458007i
$743$	3.71803	+	0.996243i	0.136401	+	0.0365486i	0.326374	−	0.945241i	$-0.394173\pi$
$743$	3.71803	+	0.996243i	0.136401	+	0.0365486i	−0.189972	+	0.981789i	$0.560840\pi$
$744$	−3.55954	−	6.16530i	−0.130499	−	0.226031i
$745$		0			0
$746$	6.64733	+	6.64733i	0.243376	+	0.243376i
$747$	11.7456	+	3.14724i	0.429751	+	0.115151i
$748$			3.30346i			0.120786i
$749$	21.1051	+	12.1850i	0.771163	+	0.445231i
$750$		0			0
$751$			1.28407i			0.0468564i	0.999726	+	0.0234282i	$0.00745811\pi$
$751$			1.28407i			0.0468564i	−0.999726	+	0.0234282i	$0.992542\pi$
$752$	9.55879	+	35.6739i	0.348573	+	1.30089i
$753$	−2.47252	+	1.42751i	−0.0901035	+	0.0520213i
$754$	−8.48623	−	8.48623i	−0.309050	−	0.309050i
$755$		0			0
$756$	−3.18651	+	5.51919i	−0.115892	+	0.200731i
$757$	−6.93453	+	12.0110i	−0.252040	+	0.436546i	−0.964087	−	0.265586i	$-0.914435\pi$
$757$	−6.93453	+	12.0110i	−0.252040	+	0.436546i	0.712047	+	0.702131i	$0.247768\pi$
$758$	4.38267	+	7.59101i	0.159186	+	0.275718i
$759$	37.8600	+	10.1446i	1.37423	+	0.368224i
$760$		0			0
$761$	9.48381	+	5.47548i	0.343788	+	0.198486i	0.661946	−	0.749552i	$-0.269731\pi$
$761$	9.48381	+	5.47548i	0.343788	+	0.198486i	−0.318158	+	0.948038i	$0.603064\pi$
$762$	−6.23286	+	10.7956i	−0.225793	+	0.391085i
$763$			26.6296i			0.964055i
$764$	1.17573	−	4.38788i	0.0425364	−	0.158748i
$765$		0			0
$766$	0.340843			0.0123152
$767$	−33.8785	−	33.8785i	−1.22328	−	1.22328i
$768$	4.69335	+	17.5158i	0.169357	+	0.632048i
$769$	9.51657	+	9.51657i	0.343176	+	0.343176i	0.857560	−	0.514384i	$-0.171979\pi$
$769$	9.51657	+	9.51657i	0.343176	+	0.343176i	−0.514384	+	0.857560i	$0.671979\pi$
$770$		0			0
$771$	0.835940	−	0.835940i	0.0301057	−	0.0301057i
$772$	14.9482	−	8.63037i	0.537999	−	0.310614i
$773$	0.370532	−	1.38284i	0.0133271	−	0.0497374i	−0.958942	−	0.283602i	$-0.908471\pi$
$773$	0.370532	−	1.38284i	0.0133271	−	0.0497374i	0.972269	+	0.233865i	$0.0751372\pi$
$774$	2.67894	−	1.54669i	0.0962925	−	0.0555945i
$775$		0			0
$776$			18.8404i			0.676331i
$777$	24.5418	−	3.76010i	0.880433	−	0.134893i
$778$	4.43672	+	4.43672i	0.159064	+	0.159064i
$779$	−36.2670	+	9.71772i	−1.29940	+	0.348174i
$780$		0			0
$781$	0.309728	−	0.178822i	0.0110830	−	0.00639875i
$782$	−0.705472	−	1.22191i	−0.0252276	−	0.0436955i
$783$			14.5161i			0.518764i
$784$	12.9100	−	7.45361i	0.461073	−	0.266200i
$785$		0			0
$786$	4.19298	−	7.26245i	0.149559	−	0.259043i
$787$	−2.47029	+	2.47029i	−0.0880563	+	0.0880563i	−0.749763	−	0.661707i	$-0.769832\pi$
$787$	−2.47029	+	2.47029i	−0.0880563	+	0.0880563i	0.661707	+	0.749763i	$0.269832\pi$
$788$	3.04815	−	3.04815i	0.108586	−	0.108586i
$789$	−34.1218	−	19.7003i	−1.21477	−	0.701348i
$790$		0			0
$791$	−10.9462	+	10.9462i	−0.389203	+	0.389203i
$792$	−11.6708	−	6.73811i	−0.414702	−	0.239428i
$793$	−12.6936	+	3.40125i	−0.450764	+	0.120782i
$794$	3.17095	+	11.8342i	0.112533	+	0.419979i
$795$		0			0
$796$	−8.92710	+	33.3164i	−0.316413	+	1.18087i
$797$	20.6121	+	11.9004i	0.730119	+	0.421534i	0.818466	−	0.574555i	$-0.194825\pi$
$797$	20.6121	+	11.9004i	0.730119	+	0.421534i	−0.0883467	+	0.996090i	$0.528158\pi$
$798$	−1.77545	−	6.62606i	−0.0628501	−	0.234560i
$799$	−2.00434	−	7.48029i	−0.0709083	−	0.264634i
$800$		0			0
$801$	58.4163	+	15.6526i	2.06404	+	0.553057i
$802$	−5.89980	+	1.58085i	−0.208329	+	0.0558217i
$803$	17.2238	+	17.2238i	0.607815	+	0.607815i
$804$	−1.91016			−0.0673663
$805$		0			0
$806$	−2.53299	+	2.53299i	−0.0892208	+	0.0892208i
$807$	−12.0147	+	44.8395i	−0.422938	+	1.57842i
$808$	−17.7756			−0.625344
$809$	−1.72550	+	6.43967i	−0.0606655	+	0.226407i	−0.989602	−	0.143832i	$-0.954057\pi$
$809$	−1.72550	+	6.43967i	−0.0606655	+	0.226407i	0.928937	+	0.370239i	$0.120724\pi$
$810$		0			0
$811$	22.7108	+	39.3363i	0.797486	+	1.38129i	0.921249	+	0.388974i	$0.127170\pi$
$811$	22.7108	+	39.3363i	0.797486	+	1.38129i	−0.123763	+	0.992312i	$0.539496\pi$
$812$	−9.76732	+	16.9175i	−0.342766	+	0.593688i
$813$	−20.1662	+	20.1662i	−0.707258	+	0.707258i
$814$	0.835833	+	5.45540i	0.0292959	+	0.191212i
$815$		0			0
$816$	−1.51501	−	5.65410i	−0.0530360	−	0.197933i
$817$	2.81792	−	10.5166i	0.0985867	−	0.367931i
$818$	11.5716	+	3.10060i	0.404591	+	0.108410i
$819$	29.4658	+	7.89532i	1.02962	+	0.275885i
$820$		0			0
$821$	9.75300	+	16.8927i	0.340382	+	0.589559i	0.984504	−	0.175364i	$-0.0561103\pi$
$821$	9.75300	+	16.8927i	0.340382	+	0.589559i	−0.644122	+	0.764923i	$0.722777\pi$
$822$	−4.43292			−0.154616
$823$	−22.7385	+	6.09277i	−0.792616	+	0.212381i	−0.632339	−	0.774691i	$-0.717905\pi$
$823$	−22.7385	+	6.09277i	−0.792616	+	0.212381i	−0.160276	+	0.987072i	$0.551239\pi$
$824$			21.3016i			0.742075i
$825$		0			0
$826$	2.59041	−	4.48672i	0.0901319	−	0.156113i
$827$	13.6805	+	23.6954i	0.475719	+	0.823970i	0.999613	−	0.0278138i	$-0.00885455\pi$
$827$	13.6805	+	23.6954i	0.475719	+	0.823970i	−0.523894	+	0.851783i	$0.675521\pi$
$828$	−41.9280			−1.45710
$829$	29.7958	−	7.98376i	1.03485	−	0.277287i	0.298873	−	0.954293i	$-0.403389\pi$
$829$	29.7958	−	7.98376i	1.03485	−	0.277287i	0.735978	+	0.677006i	$0.236723\pi$
$830$		0			0
$831$	32.4956	−	8.70717i	1.12726	−	0.302048i
$832$	22.7919	−	13.1589i	0.790165	−	0.456202i
$833$	−2.70704	+	1.56291i	−0.0937935	+	0.0541517i
$834$	−9.16362	+	2.45539i	−0.317310	+	0.0850231i
$835$		0			0
$836$	−22.1713	+	5.94079i	−0.766811	+	0.205466i
$837$	4.33281			0.149764
$838$	3.72520	+	6.45223i	0.128685	+	0.222889i
$839$	20.9908	−	36.3572i	0.724684	−	1.25519i	−0.234420	−	0.972135i	$-0.575319\pi$
$839$	20.9908	−	36.3572i	0.724684	−	1.25519i	0.959104	−	0.283054i	$-0.0913476\pi$
$840$		0			0
$841$			15.4950i			0.534311i
$842$	10.5103	−	2.81622i	0.362208	−	0.0970534i
$843$	67.7886			2.33476
$844$	−17.7738	−	30.7852i	−0.611801	−	1.05967i
$845$		0			0
$846$	14.7671	+	3.95684i	0.507705	+	0.136039i
$847$	6.62510	+	1.77519i	0.227641	+	0.0609963i
$848$	3.82902	−	14.2901i	0.131489	−	0.490724i
$849$	3.44415	+	12.8538i	0.118203	+	0.441140i
$850$		0			0
$851$	22.1907	+	27.6880i	0.760689	+	0.949133i
$852$	−0.482280	+	0.482280i	−0.0165226	+	0.0165226i
$853$	−7.35019	+	12.7309i	−0.251666	+	0.435898i	−0.963985	−	0.265958i	$-0.914312\pi$
$853$	−7.35019	+	12.7309i	−0.251666	+	0.435898i	0.712319	+	0.701856i	$0.247645\pi$
$854$	−0.710512	−	1.23064i	−0.0243132	−	0.0421117i
$855$		0			0
$856$	5.52532	−	20.6208i	0.188852	−	0.704804i
$857$	39.5459			1.35086			0.675431	−	0.737424i	$-0.263958\pi$
$857$	39.5459			1.35086			0.675431	+	0.737424i	$0.263958\pi$
$858$	−3.12885	+	11.6770i	−0.106817	+	0.398648i
$859$	12.0746	−	12.0746i	0.411980	−	0.411980i	−0.470448	−	0.882428i	$-0.655908\pi$
$859$	12.0746	−	12.0746i	0.411980	−	0.411980i	0.882428	+	0.470448i	$0.155908\pi$
$860$		0			0
$861$	32.1874			1.09694
$862$	8.00953	+	8.00953i	0.272806	+	0.272806i
$863$	2.69662	−	0.722557i	0.0917940	−	0.0245961i	−0.212630	−	0.977133i	$-0.568203\pi$
$863$	2.69662	−	0.722557i	0.0917940	−	0.0245961i	0.304424	+	0.952537i	$0.401536\pi$
$864$	8.17548	+	2.19061i	0.278136	+	0.0745262i
$865$		0			0
$866$	−0.852328	−	3.18093i	−0.0289633	−	0.108092i
$867$	−11.1833	−	41.7368i	−0.379806	−	1.41746i
$868$	5.04958	+	2.91537i	0.171394	+	0.0989543i
$869$	0.313449	−	1.16981i	0.0106330	−	0.0396830i
$870$		0			0
$871$	0.514060	+	1.91850i	0.0174182	+	0.0650058i
$872$	22.5327	−	6.03761i	0.763052	−	0.204459i
$873$	−45.7140	−	26.3930i	−1.54719	−	0.893268i
$874$	6.93224	−	6.93224i	0.234487	−	0.234487i
$875$		0			0
$876$	−40.2289	−	23.2262i	−1.35921	−	0.784740i
$877$	−19.2511	+	19.2511i	−0.650064	+	0.650064i	−0.953008	−	0.302944i	$-0.902030\pi$
$877$	−19.2511	+	19.2511i	−0.650064	+	0.650064i	0.302944	+	0.953008i	$0.402030\pi$
$878$	−1.76713	+	1.76713i	−0.0596378	+	0.0596378i
$879$	−30.5730	+	52.9541i	−1.03120	+	1.78610i
$880$		0			0
$881$	43.1969	−	24.9397i	1.45534	−	0.840241i	0.456564	−	0.889691i	$-0.349080\pi$
$881$	43.1969	−	24.9397i	1.45534	−	0.840241i	0.998777	+	0.0494498i	$0.0157468\pi$
$882$		−	6.17082i		−	0.207782i
$883$	−22.8298	−	39.5424i	−0.768285	−	1.33071i	−0.938492	−	0.345300i	$-0.887777\pi$
$883$	−22.8298	−	39.5424i	−0.768285	−	1.33071i	0.170207	−	0.985408i	$-0.445556\pi$
$884$	−5.67296	+	3.27528i	−0.190802	+	0.110160i
$885$		0			0
$886$	−9.01672	+	2.41602i	−0.302923	+	0.0811679i
$887$	−4.12526	−	4.12526i	−0.138513	−	0.138513i	0.634451	−	0.772963i	$-0.281226\pi$
$887$	−4.12526	−	4.12526i	−0.138513	−	0.138513i	−0.772963	+	0.634451i	$0.781226\pi$
$888$	−8.74588	−	19.9136i	−0.293492	−	0.668256i
$889$		−	21.0979i		−	0.707602i
$890$		0			0
$891$	−12.9323	+	7.46647i	−0.433249	+	0.250136i
$892$	−8.65784	+	32.3115i	−0.289886	+	1.08187i
$893$	46.5998	−	26.9044i	1.55940	−	0.900322i
$894$	−9.01727	+	9.01727i	−0.301583	+	0.301583i
$895$		0			0
$896$	10.6013	+	10.6013i	0.354165	+	0.354165i
$897$	20.1161	+	75.0742i	0.671656	+	2.50665i
$898$	−3.63243	−	3.63243i	−0.121216	−	0.121216i
$899$	13.2810			0.442946
$900$		0			0
$901$	−0.802889	+	2.99642i	−0.0267481	+	0.0998253i
$902$			7.15492i			0.238233i
$903$	−4.66681	+	8.08315i	−0.155302	+	0.268990i
$904$	11.7440	+	6.78038i	0.390598	+	0.225512i
$905$		0			0
$906$	19.3259	+	5.17835i	0.642058	+	0.172039i
$907$	2.05682	+	3.56252i	0.0682957	+	0.118292i	0.898151	−	0.439687i	$-0.144911\pi$
$907$	2.05682	+	3.56252i	0.0682957	+	0.118292i	−0.829855	+	0.557978i	$0.811577\pi$
$908$	−14.1632	+	24.5313i	−0.470021	+	0.814100i
$909$	24.9014	−	43.1305i	0.825927	−	1.43055i
$910$		0			0
$911$	23.6772	+	23.6772i	0.784460	+	0.784460i	0.980580	−	0.196120i	$-0.0628341\pi$
$911$	23.6772	+	23.6772i	0.784460	+	0.784460i	−0.196120	+	0.980580i	$0.562834\pi$
$912$	35.2232	−	20.3361i	1.16636	−	0.673397i
$913$	−2.11090	−	7.87797i	−0.0698605	−	0.260723i
$914$		−	6.09435i		−	0.201583i
$915$		0			0
$916$	33.6758	+	19.4427i	1.11268	+	0.642406i
$917$			14.1930i			0.468695i
$918$	−0.508425	−	0.136232i	−0.0167805	−	0.00449633i
$919$	37.5747	+	37.5747i	1.23947	+	1.23947i	0.960216	+	0.279258i	$0.0900884\pi$
$919$	37.5747	+	37.5747i	1.23947	+	1.23947i	0.279258	+	0.960216i	$0.409912\pi$
$920$		0			0
$921$	−4.93484	−	8.54739i	−0.162608	−	0.281646i
$922$	−4.52447	−	1.21233i	−0.149006	−	0.0399259i
$923$	0.614173	+	0.354593i	0.0202158	+	0.0116716i
$924$	19.6773			0.647334
$925$		0			0
$926$	8.42952			0.277011
$927$	−51.6857	−	29.8408i	−1.69758	−	0.980100i
$928$	25.0596	+	6.71470i	0.822622	+	0.220421i
$929$	1.68883	+	2.92515i	0.0554088	+	0.0959709i	0.892399	−	0.451246i	$-0.149020\pi$
$929$	1.68883	+	2.92515i	0.0554088	+	0.0959709i	−0.836991	+	0.547217i	$0.815687\pi$
$930$		0			0
$931$	−15.3578	−	15.3578i	−0.503331	−	0.503331i
$932$	−0.158502	−	0.0424704i	−0.00519189	−	0.00139116i
$933$			23.5047i			0.769509i
$934$	6.24385	+	3.60489i	0.204305	+	0.117956i
$935$		0			0
$936$		−	26.7226i		−	0.873455i
$937$	13.6061	+	50.7787i	0.444492	+	1.65887i	0.717275	+	0.696791i	$0.245389\pi$
$937$	13.6061	+	50.7787i	0.444492	+	1.65887i	−0.272783	+	0.962076i	$0.587944\pi$
$938$	−0.185997	+	0.107386i	−0.00607303	+	0.00350627i
$939$	2.76259	+	2.76259i	0.0901537	+	0.0901537i
$940$		0			0
$941$	15.5502	−	26.9338i	0.506924	−	0.878017i	−0.493044	−	0.870004i	$-0.664116\pi$
$941$	15.5502	−	26.9338i	0.506924	−	0.878017i	0.999968	−	0.00801323i	$-0.00255072\pi$
$942$	4.45025	−	7.70806i	0.144997	−	0.251142i
$943$	23.0003	+	39.8376i	0.748991	+	1.29729i
$944$	29.6708	+	7.95028i	0.965703	+	0.258759i
$945$		0			0
$946$	−1.79680	−	1.03738i	−0.0584191	−	0.0337283i
$947$	11.3518	−	19.6619i	0.368884	−	0.638926i	−0.620507	−	0.784201i	$-0.713073\pi$
$947$	11.3518	−	19.6619i	0.368884	−	0.638926i	0.989391	+	0.145275i	$0.0464065\pi$
$948$			2.30958i			0.0750118i
$949$	−12.5012	+	46.6550i	−0.405805	+	1.51448i
$950$		0			0
$951$	−49.1568			−1.59402
$952$	−1.03501	−	1.03501i	−0.0335448	−	0.0335448i
$953$	−4.34551	−	16.2177i	−0.140765	−	0.525342i	−0.999907	−	0.0136055i	$-0.995669\pi$
$953$	−4.34551	−	16.2177i	−0.140765	−	0.525342i	0.859142	−	0.511736i	$-0.170998\pi$
$954$	−4.33034	−	4.33034i	−0.140200	−	0.140200i
$955$		0			0
$956$	20.0851	−	20.0851i	0.649598	−	0.649598i
$957$	38.8152	−	22.4099i	1.25472	−	0.724410i
$958$	1.24109	−	4.63181i	0.0400978	−	0.149647i
$959$	6.49745	−	3.75131i	0.209814	−	0.121136i
$960$		0			0
$961$			27.0359i			0.872124i
$962$	−8.53973	+	6.84423i	−0.275332	+	0.220667i
$963$	42.2936	+	42.2936i	1.36289	+	1.36289i
$964$	−22.7003	+	6.08252i	−0.731126	+	0.195905i
$965$		0			0
$966$	−7.27841	+	4.20219i	−0.234179	+	0.135203i
$967$	−18.4488	−	31.9542i	−0.593272	−	1.02758i	−0.993788	−	0.111288i	$-0.964502\pi$
$967$	−18.4488	−	31.9542i	−0.593272	−	1.02758i	0.400516	−	0.916290i	$-0.368831\pi$
$968$		−	6.00832i		−	0.193115i
$969$	−7.38579	+	4.26419i	−0.237266	+	0.136986i
$970$		0			0
$971$	−11.0965	+	19.2197i	−0.356103	+	0.616788i	−0.987306	−	0.158829i	$-0.949228\pi$
$971$	−11.0965	+	19.2197i	−0.356103	+	0.616788i	0.631203	+	0.775618i	$0.282561\pi$
$972$	28.7946	−	28.7946i	0.923586	−	0.923586i
$973$	11.3535	−	11.3535i	0.363977	−	0.363977i
$974$	9.45973	+	5.46158i	0.303109	+	0.175000i
$975$		0			0
$976$	5.95763	−	5.95763i	0.190699	−	0.190699i
$977$	25.8120	+	14.9026i	0.825798	+	0.476775i	0.852412	−	0.522871i	$-0.175139\pi$
$977$	25.8120	+	14.9026i	0.825798	+	0.476775i	−0.0266135	+	0.999646i	$0.508472\pi$
$978$	−17.3347	+	4.64482i	−0.554303	+	0.148525i
$979$	−10.4984	−	39.1806i	−0.335531	−	1.25222i
$980$		0			0
$981$	−16.9158	+	63.1308i	−0.540081	+	2.01561i
$982$	2.75130	+	1.58846i	0.0877975	+	0.0506899i
$983$	−1.36230	−	5.08418i	−0.0434507	−	0.162160i	0.940792	−	0.338986i	$-0.110084\pi$
$983$	−1.36230	−	5.08418i	−0.0434507	−	0.162160i	−0.984242	+	0.176825i	$0.943417\pi$
$984$	−7.29770	−	27.2354i	−0.232642	−	0.868233i
$985$		0			0
$986$	−1.55843	−	0.417580i	−0.0496306	−	0.0132985i
$987$	−44.5568	+	11.9390i	−1.41826	+	0.380021i
$988$	−32.1842	−	32.1842i	−1.02392	−	1.02392i
$989$	−13.3391			−0.424160
$990$		0			0
$991$	−12.3261	+	12.3261i	−0.391550	+	0.391550i	−0.875240	−	0.483690i	$-0.839296\pi$
$991$	−12.3261	+	12.3261i	−0.391550	+	0.391550i	0.483690	+	0.875240i	$0.339296\pi$
$992$	2.00422	−	7.47985i	0.0636341	−	0.237486i
$993$	10.0082			0.317602
$994$	−0.0198480	+	0.0740736i	−0.000629539	+	0.00234947i
$995$		0			0
$996$	7.77686	+	13.4699i	0.246419	+	0.426810i
$997$	25.5597	−	44.2707i	0.809484	−	1.40207i	−0.103738	−	0.994605i	$-0.533080\pi$
$997$	25.5597	−	44.2707i	0.809484	−	1.40207i	0.913222	−	0.407462i	$-0.133586\pi$
$998$	−10.9663	+	10.9663i	−0.347132	+	0.347132i
$999$	13.1575	+	1.45012i	0.416286	+	0.0458799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.y.b.393.10		68
5.2	odd	4		925.2.t.b.282.8		68
5.3	odd	4		185.2.p.a.97.10	✓	68
5.4	even	2		185.2.u.a.23.8	yes	68
37.29	odd	12		925.2.t.b.843.8		68
185.29	odd	12		185.2.p.a.103.10	yes	68
185.103	even	12		185.2.u.a.177.8	yes	68
185.177	even	12	inner	925.2.y.b.732.10		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.97.10	✓	68	5.3	odd	4
185.2.p.a.103.10	yes	68	185.29	odd	12
185.2.u.a.23.8	yes	68	5.4	even	2
185.2.u.a.177.8	yes	68	185.103	even	12
925.2.t.b.282.8		68	5.2	odd	4
925.2.t.b.843.8		68	37.29	odd	12
925.2.y.b.393.10		68	1.1	even	1	trivial
925.2.y.b.732.10		68	185.177	even	12	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.305683 + 0.176486i) q^{2} +(-2.52485 - 0.676530i) q^{3} +(-0.937705 - 1.62415i) q^{4} +(-0.652403 - 0.652403i) q^{6} +(1.50833 + 0.404156i) q^{7} -1.36791i q^{8} +(3.31908 + 1.91627i) q^{9} -2.57054i q^{11} +(1.26877 + 4.73512i) q^{12} +(4.41433 - 2.54861i) q^{13} +(0.389743 + 0.389743i) q^{14} +(-1.63399 + 2.83016i) q^{16} +(0.342624 - 0.593443i) q^{17} +(0.676389 + 1.17154i) q^{18} +(4.59908 + 1.23232i) q^{19} +(-3.53488 - 2.04087i) q^{21} +(0.453664 - 0.785768i) q^{22} -5.83340i q^{23} +(-0.925433 + 3.45376i) q^{24} +1.79918 q^{26} +(-1.53879 - 1.53879i) q^{27} +(-0.757959 - 2.82874i) q^{28} +(-4.71673 - 4.71673i) q^{29} +(-1.40786 + 1.40786i) q^{31} +(-3.36826 + 1.94466i) q^{32} +(-1.73905 + 6.49021i) q^{33} +(0.209469 - 0.120937i) q^{34} -7.18758i q^{36} +(-4.74646 + 3.80409i) q^{37} +(1.18837 + 1.18837i) q^{38} +(-12.8697 + 3.44843i) q^{39} +(-6.82923 + 3.94286i) q^{41} +(-0.720368 - 1.24771i) q^{42} -2.28668i q^{43} +(-4.17495 + 2.41041i) q^{44} +(1.02951 - 1.78317i) q^{46} +(7.99119 - 7.99119i) q^{47} +(6.04027 - 6.04027i) q^{48} +(-3.95045 - 2.28080i) q^{49} +(-1.26656 + 1.26656i) q^{51} +(-8.27868 - 4.77970i) q^{52} +(-4.37275 + 1.17167i) q^{53} +(-0.198807 - 0.741957i) q^{54} +(0.552850 - 2.06326i) q^{56} +(-10.7783 - 6.22283i) q^{57} +(-0.609385 - 2.27426i) q^{58} +(-2.43277 - 9.07924i) q^{59} +(-2.49030 - 0.667274i) q^{61} +(-0.678826 + 0.181891i) q^{62} +(4.23180 + 4.23180i) q^{63} +5.16315 q^{64} +(-1.67703 + 1.67703i) q^{66} +(-0.100851 + 0.376380i) q^{67} -1.28512 q^{68} +(-3.94647 + 14.7284i) q^{69} +(0.0695659 + 0.120492i) q^{71} +(2.62128 - 4.54020i) q^{72} +(-6.70047 + 6.70047i) q^{73} +(-2.12228 + 0.325159i) q^{74} +(-2.31111 - 8.62517i) q^{76} +(1.03890 - 3.87723i) q^{77} +(-4.54265 - 1.21720i) q^{78} +(0.455083 + 0.121939i) q^{79} +(-2.90463 - 5.03097i) q^{81} -2.78343 q^{82} +(3.06472 - 0.821188i) q^{83} +7.65492i q^{84} +(0.403567 - 0.698999i) q^{86} +(8.71800 + 15.1000i) q^{87} -3.51627 q^{88} +(15.2422 - 4.08413i) q^{89} +(7.68831 - 2.06008i) q^{91} +(-9.47433 + 5.47001i) q^{92} +(4.50709 - 2.60217i) q^{93} +(3.85310 - 1.03243i) q^{94} +(9.81995 - 2.63125i) q^{96} -13.7731 q^{97} +(-0.805056 - 1.39440i) q^{98} +(4.92584 - 8.53181i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) \) 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

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Database

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