LMFDB - Embedded newform 225.3.o.b.193.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,3,Mod(7,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("225.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	225.o (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.13080594811$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.5
Character	$\chi$	$=$	225.193
Dual form			225.3.o.b.7.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.183646 + 0.0492077i) q^{2} +(1.82902 + 2.37796i) q^{3} +(-3.43280 - 1.98193i) q^{4} +(0.218877 + 0.526704i) q^{6} +(-8.70492 - 2.33248i) q^{7} +(-1.07064 - 1.07064i) q^{8} +(-2.30940 + 8.69866i) q^{9} +(-7.04110 - 12.1955i) q^{11} +(-1.56570 - 11.7880i) q^{12} +(-12.9444 + 3.46845i) q^{13} +(-1.48385 - 0.856699i) q^{14} +(7.78377 + 13.4819i) q^{16} +(0.740694 - 0.740694i) q^{17} +(-0.852153 + 1.48383i) q^{18} -7.09073i q^{19} +(-10.3749 - 24.9661i) q^{21} +(-0.692953 - 2.58614i) q^{22} +(-19.0499 + 5.10441i) q^{23} +(0.587726 - 4.50418i) q^{24} -2.54786 q^{26} +(-24.9090 + 10.4183i) q^{27} +(25.2594 + 25.2594i) q^{28} +(6.18301 - 3.56976i) q^{29} +(13.0783 - 22.6522i) q^{31} +(2.33357 + 8.70902i) q^{32} +(16.1223 - 39.0493i) q^{33} +(0.172473 - 0.0995774i) q^{34} +(25.1678 - 25.2837i) q^{36} +(23.0151 - 23.0151i) q^{37} +(0.348919 - 1.30218i) q^{38} +(-31.9234 - 24.4375i) q^{39} +(-36.0387 + 62.4209i) q^{41} +(-0.676780 - 5.09544i) q^{42} +(-3.22835 + 12.0484i) q^{43} +55.8198i q^{44} -3.74961 q^{46} +(-51.8935 - 13.9048i) q^{47} +(-17.8228 + 43.1681i) q^{48} +(27.9000 + 16.1081i) q^{49} +(3.11608 + 0.406601i) q^{51} +(51.3098 + 13.7484i) q^{52} +(-17.2907 - 17.2907i) q^{53} +(-5.08709 + 0.687563i) q^{54} +(6.82262 + 11.8171i) q^{56} +(16.8615 - 12.9691i) q^{57} +(1.31114 - 0.351320i) q^{58} +(27.5407 + 15.9006i) q^{59} +(40.7317 + 70.5494i) q^{61} +(3.51643 - 3.51643i) q^{62} +(40.3926 - 70.3345i) q^{63} -60.5560i q^{64} +(4.88231 - 6.37790i) q^{66} +(17.1864 + 64.1404i) q^{67} +(-4.01065 + 1.07465i) q^{68} +(-46.9807 - 35.9639i) q^{69} -36.3928 q^{71} +(11.7857 - 6.84062i) q^{72} +(-2.90991 - 2.90991i) q^{73} +(5.35915 - 3.09411i) q^{74} +(-14.0533 + 24.3410i) q^{76} +(32.8464 + 122.584i) q^{77} +(-4.66008 - 6.05872i) q^{78} +(71.8823 - 41.5012i) q^{79} +(-70.3333 - 40.1774i) q^{81} +(-9.68994 + 9.68994i) q^{82} +(13.7671 - 51.3796i) q^{83} +(-13.8661 + 106.266i) q^{84} +(-1.18574 + 2.05377i) q^{86} +(19.7976 + 8.17381i) q^{87} +(-5.51857 + 20.5956i) q^{88} -22.5436i q^{89} +120.770 q^{91} +(75.5111 + 20.2331i) q^{92} +(77.7864 - 10.3316i) q^{93} +(-8.84580 - 5.10712i) q^{94} +(-16.4416 + 21.4781i) q^{96} +(-33.7192 - 9.03502i) q^{97} +(4.33107 + 4.33107i) q^{98} +(122.346 - 33.0837i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 2 q^{2} + 6 q^{3} - 24 q^{6} + 2 q^{7} + 24 q^{8} + 8 q^{11} + 30 q^{12} + 2 q^{13} + 28 q^{16} - 28 q^{17} - 48 q^{18} + 12 q^{21} - 14 q^{22} - 82 q^{23} - 112 q^{26} + 198 q^{27} + 88 q^{28} - 4 q^{31}+ \cdots + 1876 q^{98}+O(q^{100}) $ 40 * q + 2 * q^2 + 6 * q^3 - 24 * q^6 + 2 * q^7 + 24 * q^8 + 8 * q^11 + 30 * q^12 + 2 * q^13 + 28 * q^16 - 28 * q^17 - 48 * q^18 + 12 * q^21 - 14 * q^22 - 82 * q^23 - 112 * q^26 + 198 * q^27 + 88 * q^28 - 4 * q^31 + 14 * q^32 - 96 * q^33 + 264 * q^36 + 92 * q^37 - 330 * q^38 - 28 * q^41 - 498 * q^42 + 2 * q^43 - 136 * q^46 - 64 * q^47 + 510 * q^48 - 396 * q^51 + 74 * q^52 + 608 * q^53 - 192 * q^56 + 114 * q^57 - 30 * q^58 + 92 * q^61 + 100 * q^62 - 24 * q^63 + 588 * q^66 + 80 * q^67 - 626 * q^68 + 248 * q^71 + 162 * q^72 + 8 * q^73 - 96 * q^76 - 338 * q^77 - 1062 * q^78 + 204 * q^81 - 104 * q^82 - 370 * q^83 - 328 * q^86 - 534 * q^87 + 210 * q^88 + 152 * q^91 - 388 * q^92 + 1062 * q^93 - 876 * q^96 - 292 * q^97 + 1876 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.183646	+	0.0492077i	0.0918228	+	0.0246039i	0.304438	−	0.952532i	$-0.401531\pi$
$2$	0.183646	+	0.0492077i	0.0918228	+	0.0246039i	−0.212615	+	0.977136i	$0.568198\pi$
$3$	1.82902	+	2.37796i	0.609672	+	0.792654i
$3$	1.82902	+	2.37796i	0.609672	+	0.792654i
$4$	−3.43280	−	1.98193i	−0.858199	−	0.495482i
$5$		0			0
$5$		0			0
$6$	0.218877	+	0.526704i	0.0364795	+	0.0877840i
$7$	−8.70492	−	2.33248i	−1.24356	−	0.333211i	−0.423715	−	0.905796i	$-0.639274\pi$
$7$	−8.70492	−	2.33248i	−1.24356	−	0.333211i	−0.819846	+	0.572585i	$0.805941\pi$
$8$	−1.07064	−	1.07064i	−0.133831	−	0.133831i
$9$	−2.30940	+	8.69866i	−0.256600	+	0.966518i
$10$		0			0
$11$	−7.04110	−	12.1955i	−0.640100	−	1.10869i	−0.985410	−	0.170197i	$-0.945560\pi$
$11$	−7.04110	−	12.1955i	−0.640100	−	1.10869i	0.345310	−	0.938489i	$-0.387774\pi$
$12$	−1.56570	−	11.7880i	−0.130475	−	0.982336i
$13$	−12.9444	+	3.46845i	−0.995725	+	0.266804i	−0.719653	−	0.694333i	$-0.755699\pi$
$13$	−12.9444	+	3.46845i	−0.995725	+	0.266804i	−0.276071	+	0.961137i	$0.589033\pi$
$14$	−1.48385	−	0.856699i	−0.105989	−	0.0611928i
$15$		0			0
$16$	7.78377	+	13.4819i	0.486486	+	0.842618i
$17$	0.740694	−	0.740694i	0.0435702	−	0.0435702i	−0.684986	−	0.728556i	$-0.740192\pi$
$17$	0.740694	−	0.740694i	0.0435702	−	0.0435702i	0.728556	+	0.684986i	$0.240192\pi$
$18$	−0.852153	+	1.48383i	−0.0473418	+	0.0824350i
$19$		−	7.09073i		−	0.373196i	−0.982436	−	0.186598i	$-0.940254\pi$
$19$		−	7.09073i		−	0.373196i	0.982436	−	0.186598i	$-0.0597463\pi$
$20$		0			0
$21$	−10.3749	−	24.9661i	−0.494043	−	1.18886i
$22$	−0.692953	−	2.58614i	−0.0314979	−	0.117552i
$23$	−19.0499	+	5.10441i	−0.828257	+	0.221931i	−0.647953	−	0.761680i	$-0.724375\pi$
$23$	−19.0499	+	5.10441i	−0.828257	+	0.221931i	−0.180304	+	0.983611i	$0.557708\pi$
$24$	0.587726	−	4.50418i	0.0244886	−	0.187674i
$25$		0			0
$26$	−2.54786			−0.0979947
$27$	−24.9090	+	10.4183i	−0.922556	+	0.385863i
$28$	25.2594	+	25.2594i	0.902123	+	0.902123i
$29$	6.18301	−	3.56976i	0.213207	−	0.123095i	−0.389594	−	0.920987i	$-0.627385\pi$
$29$	6.18301	−	3.56976i	0.213207	−	0.123095i	0.602801	+	0.797892i	$0.294051\pi$
$30$		0			0
$31$	13.0783	−	22.6522i	0.421879	−	0.730716i	−0.574244	−	0.818684i	$-0.694704\pi$
$31$	13.0783	−	22.6522i	0.421879	−	0.730716i	0.996123	+	0.0879678i	$0.0280373\pi$
$32$	2.33357	+	8.70902i	0.0729242	+	0.272157i
$33$	16.1223	−	39.0493i	0.488553	−	1.18331i
$34$	0.172473	−	0.0995774i	0.00507274	−	0.00292875i
$35$		0			0
$36$	25.1678	−	25.2837i	0.699106	−	0.702324i
$37$	23.0151	−	23.0151i	0.622031	−	0.622031i	−0.324020	−	0.946050i	$-0.605034\pi$
$37$	23.0151	−	23.0151i	0.622031	−	0.622031i	0.946050	+	0.324020i	$0.105034\pi$
$38$	0.348919	−	1.30218i	0.00918207	−	0.0342680i
$39$	−31.9234	−	24.4375i	−0.818548	−	0.626602i
$40$		0			0
$41$	−36.0387	+	62.4209i	−0.878993	+	1.52246i	−0.0265459	+	0.999648i	$0.508451\pi$
$41$	−36.0387	+	62.4209i	−0.878993	+	1.52246i	−0.852447	+	0.522813i	$0.824883\pi$
$42$	−0.676780	−	5.09544i	−0.0161138	−	0.121320i
$43$	−3.22835	+	12.0484i	−0.0750779	+	0.280195i	−0.993251	−	0.115985i	$-0.962998\pi$
$43$	−3.22835	+	12.0484i	−0.0750779	+	0.280195i	0.918173	+	0.396180i	$0.129664\pi$
$44$			55.8198i			1.26863i
$45$		0			0
$46$	−3.74961			−0.0815133
$47$	−51.8935	−	13.9048i	−1.10412	−	0.295847i	−0.339677	−	0.940542i	$-0.610318\pi$
$47$	−51.8935	−	13.9048i	−1.10412	−	0.295847i	−0.764440	+	0.644695i	$0.776985\pi$
$48$	−17.8228	+	43.1681i	−0.371308	+	0.899335i
$49$	27.9000	+	16.1081i	0.569388	+	0.328736i
$50$		0			0
$51$	3.11608	+	0.406601i	0.0610997	+	0.00797257i
$52$	51.3098	+	13.7484i	0.986727	+	0.264393i
$53$	−17.2907	−	17.2907i	−0.326240	−	0.326240i	0.524915	−	0.851155i	$-0.324097\pi$
$53$	−17.2907	−	17.2907i	−0.326240	−	0.326240i	−0.851155	+	0.524915i	$0.824097\pi$
$54$	−5.08709	+	0.687563i	−0.0942054	+	0.0127326i
$55$		0			0
$56$	6.82262	+	11.8171i	0.121833	+	0.211020i
$57$	16.8615	−	12.9691i	0.295816	−	0.227527i
$58$	1.31114	−	0.351320i	0.0226059	−	0.00605724i
$59$	27.5407	+	15.9006i	0.466792	+	0.269502i	0.714896	−	0.699231i	$-0.246474\pi$
$59$	27.5407	+	15.9006i	0.466792	+	0.269502i	−0.248104	+	0.968733i	$0.579807\pi$
$60$		0			0
$61$	40.7317	+	70.5494i	0.667733	+	1.15655i	0.978537	+	0.206073i	$0.0660684\pi$
$61$	40.7317	+	70.5494i	0.667733	+	1.15655i	−0.310804	+	0.950474i	$0.600598\pi$
$62$	3.51643	−	3.51643i	0.0567166	−	0.0567166i
$63$	40.3926	−	70.3345i	0.641152	−	1.11642i
$64$		−	60.5560i		−	0.946187i
$65$		0			0
$66$	4.88231	−	6.37790i	0.0739744	−	0.0966348i
$67$	17.1864	+	64.1404i	0.256513	+	0.957319i	0.967243	+	0.253854i	$0.0816983\pi$
$67$	17.1864	+	64.1404i	0.256513	+	0.957319i	−0.710730	+	0.703465i	$0.751635\pi$
$68$	−4.01065	+	1.07465i	−0.0589802	+	0.0158037i
$69$	−46.9807	−	35.9639i	−0.680880	−	0.521216i
$70$		0			0
$71$	−36.3928			−0.512574			−0.256287	−	0.966601i	$-0.582499\pi$
$71$	−36.3928			−0.512574			−0.256287	+	0.966601i	$0.582499\pi$
$72$	11.7857	−	6.84062i	0.163691	−	0.0950086i
$73$	−2.90991	−	2.90991i	−0.0398617	−	0.0398617i	0.686895	−	0.726757i	$-0.258973\pi$
$73$	−2.90991	−	2.90991i	−0.0398617	−	0.0398617i	−0.726757	+	0.686895i	$0.758973\pi$
$74$	5.35915	−	3.09411i	0.0724210	−	0.0418123i
$75$		0			0
$76$	−14.0533	+	24.3410i	−0.184912	+	0.320277i
$77$	32.8464	+	122.584i	0.426577	+	1.59201i
$78$	−4.66008	−	6.05872i	−0.0597446	−	0.0776759i
$79$	71.8823	−	41.5012i	0.909902	−	0.525332i	0.0295025	−	0.999565i	$-0.490608\pi$
$79$	71.8823	−	41.5012i	0.909902	−	0.525332i	0.880400	+	0.474232i	$0.157274\pi$
$80$		0			0
$81$	−70.3333	−	40.1774i	−0.868313	−	0.496017i
$82$	−9.68994	+	9.68994i	−0.118170	+	0.118170i
$83$	13.7671	−	51.3796i	0.165869	−	0.619031i	−0.832059	−	0.554687i	$-0.812838\pi$
$83$	13.7671	−	51.3796i	0.165869	−	0.619031i	0.997928	−	0.0643438i	$-0.0204954\pi$
$84$	−13.8661	+	106.266i	−0.165072	+	1.26507i
$85$		0			0
$86$	−1.18574	+	2.05377i	−0.0137877	+	0.0238811i
$87$	19.7976	+	8.17381i	0.227558	+	0.0939518i
$88$	−5.51857	+	20.5956i	−0.0627111	+	0.234041i
$89$		−	22.5436i		−	0.253299i	−0.991948	−	0.126650i	$-0.959578\pi$
$89$		−	22.5436i		−	0.253299i	0.991948	−	0.126650i	$-0.0404224\pi$
$90$		0			0
$91$	120.770			1.32715
$92$	75.5111	+	20.2331i	0.820773	+	0.219925i
$93$	77.7864	−	10.3316i	0.836413	−	0.111093i
$94$	−8.84580	−	5.10712i	−0.0941042	−	0.0543311i
$95$		0			0
$96$	−16.4416	+	21.4781i	−0.171266	+	0.223730i
$97$	−33.7192	−	9.03502i	−0.347620	−	0.0931446i	0.0807843	−	0.996732i	$-0.474258\pi$
$97$	−33.7192	−	9.03502i	−0.347620	−	0.0931446i	−0.428405	+	0.903587i	$0.640924\pi$
$98$	4.33107	+	4.33107i	0.0441946	+	0.0441946i
$99$	122.346	−	33.0837i	1.23581	−	0.334179i
$100$		0			0
$101$	−29.7283	−	51.4909i	−0.294340	−	0.509811i	0.680491	−	0.732756i	$-0.261766\pi$
$101$	−29.7283	−	51.4909i	−0.294340	−	0.509811i	−0.974831	+	0.222945i	$0.928433\pi$
$102$	0.552247	+	0.228006i	0.00541419	+	0.00223535i
$103$	76.0184	−	20.3691i	0.738043	−	0.197758i	0.129835	−	0.991536i	$-0.458555\pi$
$103$	76.0184	−	20.3691i	0.738043	−	0.197758i	0.608208	+	0.793778i	$0.291889\pi$
$104$	17.5723	+	10.1454i	0.168965	+	0.0975519i
$105$		0			0
$106$	−2.32453	−	4.02620i	−0.0219295	−	0.0379830i
$107$	50.6865	−	50.6865i	0.473706	−	0.473706i	−0.429406	−	0.903112i	$-0.641277\pi$
$107$	50.6865	−	50.6865i	0.473706	−	0.473706i	0.903112	+	0.429406i	$0.141277\pi$
$108$	106.156	+	13.6039i	0.982925	+	0.125962i
$109$			47.8364i			0.438866i	0.975628	+	0.219433i	$0.0704208\pi$
$109$			47.8364i			0.438866i	−0.975628	+	0.219433i	$0.929579\pi$
$110$		0			0
$111$	96.8241	+	12.6341i	0.872289	+	0.113820i
$112$	−36.3109	−	135.514i	−0.324205	−	1.20995i
$113$	−168.318	+	45.1005i	−1.48954	+	0.399120i	−0.909580	−	0.415529i	$-0.863597\pi$
$113$	−168.318	+	45.1005i	−1.48954	+	0.399120i	−0.579955	+	0.814648i	$0.696930\pi$
$114$	3.73472	−	1.55200i	0.0327607	−	0.0136140i
$115$		0			0
$116$	−28.3000			−0.243966
$117$	−0.276954	−	120.609i	−0.00236713	−	1.03085i
$118$	4.27530	+	4.27530i	0.0362313	+	0.0362313i
$119$	−8.17534	+	4.72003i	−0.0687003	+	0.0396641i
$120$		0			0
$121$	−38.6542	+	66.9510i	−0.319456	+	0.553314i
$122$	4.00863	+	14.9604i	0.0328576	+	0.122626i
$123$	−214.350	+	28.4701i	−1.74268	+	0.231464i
$124$	−89.7900	+	51.8403i	−0.724113	+	0.418067i
$125$		0			0
$126$	10.8789	−	10.9290i	0.0863407	−	0.0867381i
$127$	−16.3333	+	16.3333i	−0.128608	+	0.128608i	−0.768481	−	0.639873i	$-0.778987\pi$
$127$	−16.3333	+	16.3333i	−0.128608	+	0.128608i	0.639873	+	0.768481i	$0.278987\pi$
$128$	12.3141	−	45.9569i	0.0962041	−	0.359038i
$129$	−34.5553	+	14.3598i	−0.267870	+	0.111316i
$130$		0			0
$131$	−27.6049	+	47.8130i	−0.210724	+	0.364985i	−0.951941	−	0.306280i	$-0.900916\pi$
$131$	−27.6049	+	47.8130i	−0.210724	+	0.364985i	0.741217	+	0.671265i	$0.234249\pi$
$132$	−132.737	+	102.095i	−1.00559	+	0.773449i
$133$	−16.5390	+	61.7243i	−0.124353	+	0.464092i
$134$			12.6248i			0.0942150i
$135$		0			0
$136$	−1.58604			−0.0116621
$137$	−189.371	−	50.7417i	−1.38227	−	0.370377i	−0.510323	−	0.859983i	$-0.670474\pi$
$137$	−189.371	−	50.7417i	−1.38227	−	0.370377i	−0.871944	+	0.489606i	$0.837141\pi$
$138$	−6.85810	−	8.91643i	−0.0496964	−	0.0646118i
$139$	−82.5364	−	47.6524i	−0.593787	−	0.342823i	0.172806	−	0.984956i	$-0.444717\pi$
$139$	−82.5364	−	47.6524i	−0.593787	−	0.342823i	−0.766594	+	0.642133i	$0.778050\pi$
$140$		0			0
$141$	−61.8489	−	148.833i	−0.438645	−	1.05555i
$142$	−6.68338	−	1.79081i	−0.0470660	−	0.0126113i
$143$	133.443	+	133.443i	0.933165	+	0.933165i
$144$	−135.250	+	36.5733i	−0.939237	+	0.253981i
$145$		0			0
$146$	−0.391202	−	0.677581i	−0.00267946	−	0.00464097i
$147$	12.7252	+	95.8070i	0.0865657	+	0.651748i
$148$	−124.621	+	33.3920i	−0.842031	+	0.225622i
$149$	−225.341	−	130.101i	−1.51235	−	0.873158i	−0.999896	−	0.0144460i	$-0.995402\pi$
$149$	−225.341	−	130.101i	−1.51235	−	0.873158i	−0.512458	−	0.858712i	$-0.671265\pi$
$150$		0			0
$151$	−128.914	−	223.285i	−0.853735	−	1.47871i	−0.877814	−	0.479002i	$-0.840999\pi$
$151$	−128.914	−	223.285i	−0.853735	−	1.47871i	0.0240792	−	0.999710i	$-0.492335\pi$
$152$	−7.59165	+	7.59165i	−0.0499451	+	0.0499451i
$153$	4.73248	+	8.15361i	0.0309313	+	0.0532915i
$154$			24.1284i			0.156678i
$155$		0			0
$156$	61.1532	+	147.159i	0.392008	+	0.943325i
$157$	12.0301	+	44.8971i	0.0766251	+	0.285969i	0.993597	−	0.112983i	$-0.0360407\pi$
$157$	12.0301	+	44.8971i	0.0766251	+	0.285969i	−0.916972	+	0.398952i	$0.869374\pi$
$158$	15.2431	−	4.08436i	0.0964750	−	0.0258504i
$159$	9.49166	−	72.7416i	0.0596960	−	0.457494i
$160$		0			0
$161$	177.734			1.10394
$162$	−10.9394	−	10.8393i	−0.0675270	−	0.0669096i
$163$	−76.8331	−	76.8331i	−0.471369	−	0.471369i	0.430989	−	0.902357i	$-0.358165\pi$
$163$	−76.8331	−	76.8331i	−0.471369	−	0.471369i	−0.902357	+	0.430989i	$0.858165\pi$
$164$	247.427	−	142.852i	1.50870	−	0.871050i
$165$		0			0
$166$	5.05654	−	8.75819i	0.0304611	−	0.0527602i
$167$	−80.7212	−	301.256i	−0.483360	−	1.80393i	−0.587333	−	0.809346i	$-0.699822\pi$
$167$	−80.7212	−	301.256i	−0.483360	−	1.80393i	0.103972	−	0.994580i	$-0.466845\pi$
$168$	−15.6220	+	37.8376i	−0.0929881	+	0.225224i
$169$	9.16964	−	5.29409i	0.0542582	−	0.0313260i
$170$		0			0
$171$	61.6799	+	16.3754i	0.360701	+	0.0957623i
$172$	34.9612	−	34.9612i	0.203263	−	0.203263i
$173$	51.6158	−	192.633i	0.298357	−	1.11348i	−0.640157	−	0.768244i	$-0.721131\pi$
$173$	51.6158	−	192.633i	0.298357	−	1.11348i	0.938514	−	0.345240i	$-0.112203\pi$
$174$	3.23353	+	2.47528i	0.0185835	+	0.0142257i
$175$		0			0
$176$	109.613	−	189.855i	0.622799	−	1.07872i
$177$	12.5613	+	94.5733i	0.0709677	+	0.534312i
$178$	1.10932	−	4.14004i	0.00623214	−	0.0232587i
$179$			254.120i			1.41967i	0.704370	+	0.709833i	$0.251230\pi$
$179$			254.120i			1.41967i	−0.704370	+	0.709833i	$0.748770\pi$
$180$		0			0
$181$	−236.998			−1.30938			−0.654691	−	0.755896i	$-0.727201\pi$
$181$	−236.998			−1.30938			−0.654691	+	0.755896i	$0.727201\pi$
$182$	22.1789	+	5.94283i	0.121862	+	0.0326529i
$183$	−93.2648	+	225.894i	−0.509644	+	1.23440i
$184$	25.8607	+	14.9307i	0.140547	+	0.0811450i
$185$		0			0
$186$	14.7935	+	1.93033i	0.0795351	+	0.0103781i
$187$	−14.2485	−	3.81787i	−0.0761950	−	0.0204164i
$188$	150.582	+	150.582i	0.800966	+	0.800966i
$189$	241.131	−	32.5909i	1.27583	−	0.172439i
$190$		0			0
$191$	27.2962	+	47.2784i	0.142912	+	0.247531i	0.928592	−	0.371102i	$-0.121020\pi$
$191$	27.2962	+	47.2784i	0.142912	+	0.247531i	−0.785680	+	0.618633i	$0.787687\pi$
$192$	144.000	−	110.758i	0.749999	−	0.576864i
$193$	193.408	−	51.8234i	1.00211	−	0.268515i	0.279782	−	0.960063i	$-0.409738\pi$
$193$	193.408	−	51.8234i	1.00211	−	0.268515i	0.722330	+	0.691548i	$0.243071\pi$
$194$	−5.74779	−	3.31849i	−0.0296278	−	0.0171056i
$195$		0			0
$196$	−63.8500	−	110.591i	−0.325765	−	0.564242i
$197$	−18.5367	+	18.5367i	−0.0940948	+	0.0940948i	−0.752587	−	0.658492i	$-0.771194\pi$
$197$	−18.5367	+	18.5367i	−0.0940948	+	0.0940948i	0.658492	+	0.752587i	$0.271194\pi$
$198$	24.0962	−	0.0553320i	0.121698	−	0.000279454i
$199$			206.081i			1.03558i	0.855507	+	0.517792i	$0.173246\pi$
$199$			206.081i			1.03558i	−0.855507	+	0.517792i	$0.826754\pi$
$200$		0			0
$201$	−121.089	+	158.182i	−0.602434	+	0.786977i
$202$	−2.92572	−	10.9190i	−0.0144838	−	0.0540542i
$203$	−62.1490	+	16.6528i	−0.306153	+	0.0820334i
$204$	−9.89103	−	7.57163i	−0.0484854	−	0.0371158i
$205$		0			0
$206$	14.9628			0.0726348
$207$	−0.407585	−	177.497i	−0.00196901	−	0.857473i
$208$	−147.518	−	147.518i	−0.709219	−	0.709219i
$209$	−86.4753	+	49.9266i	−0.413758	+	0.238883i
$210$		0			0
$211$	121.373	−	210.225i	0.575230	−	0.996327i	−0.420787	−	0.907159i	$-0.638246\pi$
$211$	121.373	−	210.225i	0.575230	−	0.996327i	0.996017	−	0.0891675i	$-0.0284206\pi$
$212$	25.0866	+	93.6244i	0.118333	+	0.441625i
$213$	−66.5630	−	86.5406i	−0.312502	−	0.406294i
$214$	11.8025	−	6.81419i	0.0551520	−	0.0318420i
$215$		0			0
$216$	37.8230	+	15.5144i	0.175106	+	0.0718258i
$217$	−166.681	+	166.681i	−0.768115	+	0.768115i
$218$	−2.35392	+	8.78496i	−0.0107978	+	0.0402980i
$219$	1.59738	−	12.2419i	0.00729397	−	0.0558991i
$220$		0			0
$221$	−7.01880	+	12.1569i	−0.0317593	+	0.0550087i
$222$	17.1596	+	7.08468i	0.0772957	+	0.0319130i
$223$	53.2572	−	198.758i	0.238821	−	0.891293i	−0.737568	−	0.675273i	$-0.764026\pi$
$223$	53.2572	−	198.758i	0.238821	−	0.891293i	0.976389	−	0.216020i	$-0.0693077\pi$
$224$		−	81.2544i		−	0.362743i
$225$		0			0
$226$	−33.1301			−0.146593
$227$	179.821	+	48.1829i	0.792163	+	0.212259i	0.632140	−	0.774854i	$-0.282177\pi$
$227$	179.821	+	48.1829i	0.792163	+	0.212259i	0.160022	+	0.987113i	$0.448843\pi$
$228$	−83.5858	+	11.1019i	−0.366604	+	0.0486927i
$229$	156.704	+	90.4733i	0.684298	+	0.395080i	0.801473	−	0.598031i	$-0.204050\pi$
$229$	156.704	+	90.4733i	0.684298	+	0.395080i	−0.117174	+	0.993111i	$0.537384\pi$
$230$		0			0
$231$	−231.425	+	302.316i	−1.00184	+	1.30873i
$232$	−10.4417	−	2.79786i	−0.0450075	−	0.0120597i
$233$	120.230	+	120.230i	0.516010	+	0.516010i	0.916362	−	0.400351i	$-0.131112\pi$
$233$	120.230	+	120.230i	0.516010	+	0.516010i	−0.400351	+	0.916362i	$0.631112\pi$
$234$	5.88404	−	22.1630i	0.0251455	−	0.0947136i
$235$		0			0
$236$	−63.0278	−	109.167i	−0.267067	−	0.462573i
$237$	230.162	+	95.0268i	0.971148	+	0.400957i
$238$	−1.73363	+	0.464524i	−0.00728415	+	0.00195178i
$239$	−332.123	−	191.751i	−1.38963	−	0.802306i	−0.396360	−	0.918095i	$-0.629727\pi$
$239$	−332.123	−	191.751i	−1.38963	−	0.802306i	−0.993274	+	0.115790i	$0.963060\pi$
$240$		0			0
$241$	162.944	+	282.226i	0.676114	+	1.17106i	0.976142	+	0.217134i	$0.0696708\pi$
$241$	162.944	+	282.226i	0.676114	+	1.17106i	−0.300028	+	0.953931i	$0.596996\pi$
$242$	−10.3932	+	10.3932i	−0.0429470	+	0.0429470i
$243$	−33.1004	−	240.735i	−0.136216	−	0.990679i
$244$		−	322.909i		−	1.32340i
$245$		0			0
$246$	−40.7654	−	5.31925i	−0.165713	−	0.0216230i
$247$	24.5938	+	91.7854i	0.0995702	+	0.371601i
$248$	−38.2546	+	10.2503i	−0.154252	+	0.0413318i
$249$	147.359	−	61.2364i	0.591803	−	0.245929i
$250$		0			0
$251$	428.941			1.70893			0.854465	−	0.519509i	$-0.173885\pi$
$251$	428.941			1.70893			0.854465	+	0.519509i	$0.173885\pi$
$252$	−278.057	+	161.389i	−1.10340	+	0.640433i
$253$	196.383	+	196.383i	0.776219	+	0.776219i
$254$	−3.80325	+	2.19581i	−0.0149734	+	0.00864492i
$255$		0			0
$256$	−116.589	+	201.938i	−0.455426	+	0.788821i
$257$	95.3527	+	355.861i	0.371022	+	1.38467i	0.859070	+	0.511857i	$0.171042\pi$
$257$	95.3527	+	355.861i	0.371022	+	1.38467i	−0.488048	+	0.872817i	$0.662291\pi$
$258$	−7.05253	+	0.936723i	−0.0273354	+	0.00363071i
$259$	−254.027	+	146.663i	−0.980800	+	0.566265i
$260$		0			0
$261$	16.7731	+	62.0279i	0.0642647	+	0.237655i
$262$	−7.42228	+	7.42228i	−0.0283293	+	0.0283293i
$263$	−17.0763	+	63.7296i	−0.0649289	+	0.242318i	−0.990761	−	0.135616i	$-0.956699\pi$
$263$	−17.0763	+	63.7296i	−0.0649289	+	0.242318i	0.925833	+	0.377934i	$0.123365\pi$
$264$	−59.0691	+	24.5467i	−0.223747	+	0.0929800i
$265$		0			0
$266$	−6.07462	+	10.5216i	−0.0228369	+	0.0395547i
$267$	53.6079	−	41.2327i	0.200779	−	0.154429i
$268$	68.1242	−	254.243i	0.254195	−	0.948668i
$269$		−	146.927i		−	0.546197i	−0.961986	−	0.273099i	$-0.911951\pi$
$269$		−	146.927i		−	0.546197i	0.961986	−	0.273099i	$-0.0880485\pi$
$270$		0			0
$271$	−45.0155			−0.166109			−0.0830544	−	0.996545i	$-0.526468\pi$
$271$	−45.0155			−0.166109			−0.0830544	+	0.996545i	$0.526468\pi$
$272$	15.7513	+	4.22056i	0.0579094	+	0.0155168i
$273$	220.891	+	287.187i	0.809124	+	1.05197i
$274$	−32.2802	−	18.6370i	−0.117811	−	0.0680182i
$275$		0			0
$276$	89.9973	+	216.569i	0.326077	+	0.784671i
$277$	−153.339	−	41.0870i	−0.553570	−	0.148329i	−0.0288193	−	0.999585i	$-0.509175\pi$
$277$	−153.339	−	41.0870i	−0.553570	−	0.148329i	−0.524751	+	0.851256i	$0.675841\pi$
$278$	−12.8126	−	12.8126i	−0.0460885	−	0.0460885i
$279$	166.841	+	166.076i	0.597996	+	0.595256i
$280$		0			0
$281$	−33.0937	−	57.3199i	−0.117771	−	0.203986i	0.801113	−	0.598513i	$-0.204242\pi$
$281$	−33.0937	−	57.3199i	−0.117771	−	0.203986i	−0.918884	+	0.394528i	$0.870908\pi$
$282$	−4.03456	−	30.3760i	−0.0143069	−	0.107716i
$283$	−388.793	+	104.177i	−1.37383	+	0.368116i	−0.868875	−	0.495032i	$-0.835156\pi$
$283$	−388.793	+	104.177i	−1.37383	+	0.368116i	−0.504952	+	0.863148i	$0.668490\pi$
$284$	124.929	+	72.1278i	0.439891	+	0.253971i
$285$		0			0
$286$	17.9397	+	31.0726i	0.0627264	+	0.108645i
$287$	459.310	−	459.310i	1.60038	−	1.60038i
$288$	−81.1460	+	0.186335i	−0.281757	+	0.000646996i
$289$			287.903i			0.996203i
$290$		0			0
$291$	−40.1880	−	96.7081i	−0.138103	−	0.332330i
$292$	4.22190	+	15.7563i	0.0144586	+	0.0539600i
$293$	209.736	−	56.1985i	0.715821	−	0.191804i	0.117515	−	0.993071i	$-0.462507\pi$
$293$	209.736	−	56.1985i	0.715821	−	0.191804i	0.598306	+	0.801267i	$0.295841\pi$
$294$	−2.37752	+	18.2207i	−0.00808682	+	0.0619752i
$295$		0			0
$296$	−49.2820			−0.166493
$297$	302.444	+	230.423i	1.01833	+	0.775833i
$298$	−34.9809	−	34.9809i	−0.117386	−	0.117386i
$299$	228.886	−	132.147i	0.765504	−	0.441964i
$300$		0			0
$301$	56.2051	−	97.3500i	0.186728	−	0.323422i
$302$	−12.6871	−	47.3490i	−0.0420103	−	0.156785i
$303$	68.0699	−	164.871i	0.224653	−	0.544127i
$304$	95.5965	−	55.1926i	0.314462	−	0.181555i
$305$		0			0
$306$	0.467880	+	1.73025i	0.00152902	+	0.00565441i
$307$	219.096	−	219.096i	0.713666	−	0.713666i	−0.253634	−	0.967300i	$-0.581626\pi$
$307$	219.096	−	219.096i	0.713666	−	0.713666i	0.967300	+	0.253634i	$0.0816258\pi$
$308$	130.198	−	485.907i	0.422722	−	1.57762i
$309$	187.476	+	143.513i	0.606717	+	0.464445i
$310$		0			0
$311$	−68.8478	+	119.248i	−0.221376	+	0.383434i	−0.955226	−	0.295877i	$-0.904388\pi$
$311$	−68.8478	+	119.248i	−0.221376	+	0.383434i	0.733850	+	0.679311i	$0.237721\pi$
$312$	8.01473	+	60.3424i	0.0256882	+	0.193405i
$313$	−1.70804	+	6.37451i	−0.00545701	+	0.0203658i	−0.968601	−	0.248622i	$-0.920022\pi$
$313$	−1.70804	+	6.37451i	−0.00545701	+	0.0203658i	0.963144	+	0.268988i	$0.0866891\pi$
$314$			8.83713i			0.0281437i
$315$		0			0
$316$	−329.010			−1.04117
$317$	−427.280	−	114.489i	−1.34789	−	0.361165i	−0.488532	−	0.872546i	$-0.662467\pi$
$317$	−427.280	−	114.489i	−1.34789	−	0.361165i	−0.859354	+	0.511381i	$0.829134\pi$
$318$	5.32255	−	12.8916i	0.0167376	−	0.0405397i
$319$	−87.0704	−	50.2701i	−0.272948	−	0.157587i
$320$		0			0
$321$	213.237	+	27.8241i	0.664290	+	0.0866796i
$322$	32.6401	+	8.74588i	0.101367	+	0.0271611i
$323$	−5.25206	−	5.25206i	−0.0162603	−	0.0162603i
$324$	161.811	+	277.316i	0.499418	+	0.855915i
$325$		0			0
$326$	−10.3293	−	17.8909i	−0.0316849	−	0.0548799i
$327$	−113.753	+	87.4936i	−0.347869	+	0.267565i
$328$	105.415	−	28.2459i	0.321388	−	0.0861156i
$329$	419.296	+	242.081i	1.27446	+	0.735808i
$330$		0			0
$331$	−130.851	−	226.641i	−0.395321	−	0.684716i	0.597821	−	0.801630i	$-0.296033\pi$
$331$	−130.851	−	226.641i	−0.395321	−	0.684716i	−0.993142	+	0.116913i	$0.962700\pi$
$332$	−149.090	+	149.090i	−0.449067	+	0.449067i
$333$	147.050	+	253.352i	0.441590	+	0.760817i
$334$		−	59.2964i		−	0.177534i
$335$		0			0
$336$	255.834	−	334.204i	0.761412	−	0.994654i
$337$	37.7355	+	140.831i	0.111975	+	0.417895i	0.999043	−	0.0437433i	$-0.0139284\pi$
$337$	37.7355	+	140.831i	0.111975	+	0.417895i	−0.887068	+	0.461639i	$0.847262\pi$
$338$	1.94447	−	0.521020i	0.00575288	−	0.00154148i
$339$	−415.103	−	317.763i	−1.22449	−	0.937354i
$340$		0			0
$341$	−368.341			−1.08018
$342$	10.5214	+	6.04239i	0.0307645	+	0.0176678i
$343$	106.954	+	106.954i	0.311820	+	0.311820i
$344$	16.3559	−	9.44310i	0.0475463	−	0.0274509i
$345$		0			0
$346$	18.9580	−	32.8363i	0.0547920	−	0.0949025i
$347$	2.62052	+	9.77990i	0.00755192	+	0.0281842i	0.969599	−	0.244699i	$-0.0786893\pi$
$347$	2.62052	+	9.77990i	0.00755192	+	0.0281842i	−0.962047	+	0.272884i	$0.912023\pi$
$348$	−51.7612	−	67.2964i	−0.148739	−	0.193380i
$349$	94.1070	−	54.3327i	0.269648	−	0.155681i	−0.359080	−	0.933307i	$-0.616909\pi$
$349$	94.1070	−	54.3327i	0.269648	−	0.155681i	0.628727	+	0.777626i	$0.283576\pi$
$350$		0			0
$351$	286.297	−	221.255i	0.815662	−	0.630355i
$352$	89.7803	−	89.7803i	0.255058	−	0.255058i
$353$	−125.168	+	467.133i	−0.354583	+	1.32332i	0.526425	+	0.850221i	$0.323532\pi$
$353$	−125.168	+	467.133i	−0.354583	+	1.32332i	−0.881008	+	0.473101i	$0.843135\pi$
$354$	−2.34691	+	17.9861i	−0.00662968	+	0.0508082i
$355$		0			0
$356$	−44.6798	+	77.3877i	−0.125505	+	0.217381i
$357$	−26.1769	−	10.8076i	−0.0733246	−	0.0302735i
$358$	−12.5047	+	46.6681i	−0.0349293	+	0.130358i
$359$		−	279.063i		−	0.777333i	−0.921378	−	0.388667i	$-0.872936\pi$
$359$		−	279.063i		−	0.777333i	0.921378	−	0.388667i	$-0.127064\pi$
$360$		0			0
$361$	310.722			0.860724
$362$	−43.5237	−	11.6621i	−0.120231	−	0.0322159i
$363$	−229.906	+	30.5363i	−0.633350	+	0.0841220i
$364$	−414.580	−	239.358i	−1.13896	−	0.657576i
$365$		0			0
$366$	−28.2434	+	36.8952i	−0.0771678	+	0.100806i
$367$	172.547	+	46.2339i	0.470156	+	0.125978i	0.486115	−	0.873895i	$-0.338414\pi$
$367$	172.547	+	46.2339i	0.470156	+	0.125978i	−0.0159593	+	0.999873i	$0.505080\pi$
$368$	−217.097	−	217.097i	−0.589938	−	0.589938i
$369$	−459.750	−	457.643i	−1.24594	−	1.24023i
$370$		0			0
$371$	110.184	+	190.844i	0.296992	+	0.514406i
$372$	−287.502	−	118.701i	−0.772854	−	0.319087i
$373$	−84.7938	+	22.7204i	−0.227329	+	0.0609127i	−0.370685	−	0.928758i	$-0.620877\pi$
$373$	−84.7938	+	22.7204i	−0.227329	+	0.0609127i	0.143356	+	0.989671i	$0.454211\pi$
$374$	−2.42880	−	1.40227i	−0.00649412	−	0.00374938i
$375$		0			0
$376$	40.6724	+	70.4466i	0.108171	+	0.187358i
$377$	−67.6540	+	67.6540i	−0.179453	+	0.179453i
$378$	45.8865	+	5.88035i	0.121393	+	0.0155565i
$379$		−	10.3793i		−	0.0273860i	−0.999906	−	0.0136930i	$-0.995641\pi$
$379$		−	10.3793i		−	0.0273860i	0.999906	−	0.0136930i	$-0.00435875\pi$
$380$		0			0
$381$	−68.7136	−	8.96607i	−0.180351	−	0.0235330i
$382$	2.68637	+	10.0257i	0.00703238	+	0.0262452i
$383$	−124.435	+	33.3422i	−0.324895	+	0.0870554i	−0.417580	−	0.908640i	$-0.637122\pi$
$383$	−124.435	+	33.3422i	−0.324895	+	0.0870554i	0.0926850	+	0.995695i	$0.470455\pi$
$384$	131.807	−	54.7734i	0.343246	−	0.142639i
$385$		0			0
$386$	38.0686			0.0986233
$387$	−97.3490	−	55.9068i	−0.251548	−	0.144462i
$388$	97.8443	+	97.8443i	0.252176	+	0.252176i
$389$	−635.357	+	366.824i	−1.63331	+	0.942991i	−0.650245	+	0.759724i	$0.725334\pi$
$389$	−635.357	+	366.824i	−1.63331	+	0.942991i	−0.983063	+	0.183267i	$0.941333\pi$
$390$		0			0
$391$	−10.3294	+	17.8910i	−0.0264178	+	0.0457570i
$392$	−12.6250	−	47.1170i	−0.0322065	−	0.120196i
$393$	−164.187	+	21.8075i	−0.417779	+	0.0554898i
$394$	−4.31633	+	2.49203i	−0.0109552	+	0.00632496i
$395$		0			0
$396$	−485.557	−	128.910i	−1.22615	−	0.325531i
$397$	−151.257	+	151.257i	−0.381000	+	0.381000i	−0.871462	−	0.490463i	$-0.836828\pi$
$397$	−151.257	+	151.257i	−0.381000	+	0.381000i	0.490463	+	0.871462i	$0.336828\pi$
$398$	−10.1408	+	37.8459i	−0.0254794	+	0.0950903i
$399$	−177.028	+	73.5656i	−0.443679	+	0.184375i
$400$		0			0
$401$	−3.27254	+	5.66821i	−0.00816096	+	0.0141352i	−0.870077	−	0.492916i	$-0.835931\pi$
$401$	−3.27254	+	5.66821i	−0.00816096	+	0.0141352i	0.861916	+	0.507051i	$0.169264\pi$
$402$	−30.0213	+	23.0910i	−0.0746799	+	0.0574402i
$403$	−90.7225	+	338.581i	−0.225118	+	0.840151i
$404$			235.677i			0.583360i
$405$		0			0
$406$	−12.2328			−0.0301302
$407$	−442.734	−	118.630i	−1.08780	−	0.291475i
$408$	−2.90089	−	3.77154i	−0.00711003	−	0.00924397i
$409$	639.259	+	369.076i	1.56298	+	0.902387i	0.996953	+	0.0779993i	$0.0248532\pi$
$409$	639.259	+	369.076i	1.56298	+	0.902387i	0.566026	+	0.824387i	$0.308480\pi$
$410$		0			0
$411$	−225.700	−	543.123i	−0.549148	−	1.32147i
$412$	−301.326	−	80.7400i	−0.731373	−	0.195971i
$413$	−202.652	−	202.652i	−0.490683	−	0.490683i
$414$	8.65937	−	32.6166i	0.0209163	−	0.0787840i
$415$		0			0
$416$	−60.4136	−	104.639i	−0.145225	−	0.251537i
$417$	−37.6448	−	283.426i	−0.0902753	−	0.679678i
$418$	−18.3376	+	4.91354i	−0.0438698	+	0.0117549i
$419$	−235.376	−	135.894i	−0.561756	−	0.324330i	0.192094	−	0.981377i	$-0.438472\pi$
$419$	−235.376	−	135.894i	−0.561756	−	0.324330i	−0.753850	+	0.657047i	$0.771805\pi$
$420$		0			0
$421$	102.996	+	178.395i	0.244647	+	0.423741i	0.962032	−	0.272936i	$-0.0879947\pi$
$421$	102.996	+	178.395i	0.244647	+	0.423741i	−0.717386	+	0.696676i	$0.754661\pi$
$422$	32.6344	−	32.6344i	0.0773327	−	0.0773327i
$423$	240.796	−	419.292i	0.569259	−	0.991235i
$424$			37.0244i			0.0873217i
$425$		0			0
$426$	−7.96553	−	19.1682i	−0.0186984	−	0.0449958i
$427$	−190.011	−	709.133i	−0.444992	−	1.66073i
$428$	−274.453	+	73.5396i	−0.641246	+	0.171821i
$429$	−73.2528	+	561.390i	−0.170752	+	1.30860i
$430$		0			0
$431$	−238.470			−0.553294			−0.276647	−	0.960972i	$-0.589223\pi$
$431$	−238.470			−0.553294			−0.276647	+	0.960972i	$0.589223\pi$
$432$	−334.345	−	254.727i	−0.773946	−	0.589645i
$433$	−79.6977	−	79.6977i	−0.184059	−	0.184059i	0.609063	−	0.793122i	$-0.291546\pi$
$433$	−79.6977	−	79.6977i	−0.184059	−	0.184059i	−0.793122	+	0.609063i	$0.791546\pi$
$434$	−38.8122	+	22.4083i	−0.0894291	+	0.0516319i
$435$		0			0
$436$	94.8083	−	164.213i	0.217450	−	0.376635i
$437$	36.1940	+	135.078i	0.0828238	+	0.309103i
$438$	0.895748	−	2.16957i	0.00204509	−	0.00495336i
$439$	280.123	−	161.729i	0.638094	−	0.368404i	−0.145786	−	0.989316i	$-0.546571\pi$
$439$	280.123	−	161.729i	0.638094	−	0.368404i	0.783880	+	0.620912i	$0.213238\pi$
$440$		0			0
$441$	−204.551	+	205.492i	−0.463834	+	0.465969i
$442$	−1.88719	+	1.88719i	−0.00426965	+	0.00426965i
$443$	−195.518	+	729.682i	−0.441349	+	1.64714i	0.284051	+	0.958809i	$0.408322\pi$
$443$	−195.518	+	729.682i	−0.441349	+	1.64714i	−0.725400	+	0.688328i	$0.758345\pi$
$444$	−307.338	−	235.268i	−0.692202	−	0.529884i
$445$		0			0
$446$	19.5609	−	33.8805i	0.0438585	−	0.0759652i
$447$	−102.778	−	773.808i	−0.229928	−	1.73111i
$448$	−141.245	+	527.135i	−0.315280	+	1.17664i
$449$			514.733i			1.14640i	0.819416	+	0.573199i	$0.194298\pi$
$449$			514.733i			1.14640i	−0.819416	+	0.573199i	$0.805702\pi$
$450$		0			0
$451$	1015.01			2.25057
$452$	667.186	+	178.772i	1.47607	+	0.395513i
$453$	295.179	−	714.945i	0.651609	−	1.57825i
$454$	30.6524	+	17.6972i	0.0675162	+	0.0389805i
$455$		0			0
$456$	−31.9379	−	4.16741i	−0.0700393	−	0.00913905i
$457$	550.455	+	147.494i	1.20450	+	0.322744i	0.804601	−	0.593816i	$-0.202379\pi$
$457$	550.455	+	147.494i	1.20450	+	0.322744i	0.399897	+	0.916560i	$0.369046\pi$
$458$	24.3261	+	24.3261i	0.0531137	+	0.0531137i
$459$	−10.7332	+	26.1667i	−0.0233838	+	0.0570081i
$460$		0			0
$461$	−119.334	−	206.693i	−0.258860	−	0.448358i	0.707077	−	0.707137i	$-0.250013\pi$
$461$	−119.334	−	206.693i	−0.258860	−	0.448358i	−0.965937	+	0.258778i	$0.916680\pi$
$462$	−57.3764	+	44.1312i	−0.124191	+	0.0955222i
$463$	796.822	−	213.508i	1.72100	−	0.461140i	0.742921	−	0.669380i	$-0.233440\pi$
$463$	796.822	−	213.508i	1.72100	−	0.461140i	0.978078	+	0.208239i	$0.0667733\pi$
$464$	96.2543	+	55.5724i	0.207445	+	0.119768i
$465$		0			0
$466$	16.1635	+	27.9961i	0.0346857	+	0.0600774i
$467$	−489.265	+	489.265i	−1.04768	+	1.04768i	−0.0488707	+	0.998805i	$0.515562\pi$
$467$	−489.265	+	489.265i	−1.04768	+	1.04768i	−0.998805	+	0.0488707i	$0.984438\pi$
$468$	−238.088	+	414.576i	−0.508734	+	0.885845i
$469$		−	598.424i		−	1.27596i
$470$		0			0
$471$	−84.7602	+	110.725i	−0.179958	+	0.235084i
$472$	−12.4624	−	46.5102i	−0.0264033	−	0.0985386i
$473$	169.667	−	45.4623i	0.358705	−	0.0961147i
$474$	37.5922	+	28.7770i	0.0793085	+	0.0607110i
$475$		0			0
$476$	37.4190			0.0786114
$477$	190.337	−	110.475i	0.399030	−	0.231603i
$478$	−51.5572	−	51.5572i	−0.107860	−	0.107860i
$479$	142.795	−	82.4426i	0.298110	−	0.172114i	−0.343483	−	0.939159i	$-0.611607\pi$
$479$	142.795	−	82.4426i	0.298110	−	0.172114i	0.641594	+	0.767045i	$0.278274\pi$
$480$		0			0
$481$	−218.091	+	377.744i	−0.453411	+	0.785331i
$482$	16.0362	+	59.8478i	0.0332700	+	0.124165i
$483$	325.078	+	422.645i	0.673040	+	0.875041i
$484$	265.384	−	153.220i	0.548314	−	0.316569i
$485$		0			0
$486$	5.76728	−	45.8387i	0.0118668	−	0.0943184i
$487$	−326.960	+	326.960i	−0.671376	+	0.671376i	−0.958033	−	0.286657i	$-0.907456\pi$
$487$	−326.960	+	326.960i	−0.671376	+	0.671376i	0.286657	+	0.958033i	$0.407456\pi$
$488$	31.9241	−	119.142i	0.0654183	−	0.244144i
$489$	42.1772	−	323.235i	0.0862520	−	0.661013i
$490$		0			0
$491$	−182.011	+	315.253i	−0.370695	+	0.642063i	−0.989673	−	0.143346i	$-0.954214\pi$
$491$	−182.011	+	315.253i	−0.370695	+	0.642063i	0.618977	+	0.785409i	$0.287547\pi$
$492$	792.245	+	327.094i	1.61025	+	0.664824i
$493$	1.93562	−	7.22382i	0.00392620	−	0.0146528i
$494$			18.0662i			0.0365713i
$495$		0			0
$496$	407.193			0.820953
$497$	316.796	+	84.8853i	0.637417	+	0.170795i
$498$	30.0751	−	3.99460i	0.0603918	−	0.00802129i
$499$	−353.578	−	204.138i	−0.708573	−	0.409095i	0.101960	−	0.994789i	$-0.467489\pi$
$499$	−353.578	−	204.138i	−0.708573	−	0.409095i	−0.810532	+	0.585694i	$0.800822\pi$
$500$		0			0
$501$	568.734	−	742.953i	1.13520	−	1.48294i
$502$	78.7732	+	21.1072i	0.156919	+	0.0420463i
$503$	−555.921	−	555.921i	−1.10521	−	1.10521i	−0.993771	−	0.111440i	$-0.964454\pi$
$503$	−555.921	−	555.921i	−1.10521	−	1.10521i	−0.111440	−	0.993771i	$-0.535546\pi$
$504$	−118.549	+	32.0571i	−0.235217	+	0.0636055i
$505$		0			0
$506$	26.4014	+	45.7286i	0.0521767	+	0.0903726i
$507$	29.3606	+	12.1221i	0.0579104	+	0.0239094i
$508$	88.4400	−	23.6974i	0.174095	−	0.0466485i
$509$	453.968	+	262.098i	0.891882	+	0.514928i	0.874558	−	0.484922i	$-0.161152\pi$
$509$	453.968	+	262.098i	0.891882	+	0.514928i	0.0173243	+	0.999850i	$0.494485\pi$
$510$		0			0
$511$	18.5432	+	32.1178i	0.0362881	+	0.0628528i
$512$	−165.919	+	165.919i	−0.324061	+	0.324061i
$513$	73.8735	+	176.623i	0.144003	+	0.344295i
$514$			70.0445i			0.136273i
$515$		0			0
$516$	147.081	+	19.1918i	0.285041	+	0.0371935i
$517$	195.811	+	730.775i	0.378744	+	1.41349i
$518$	−53.8679	+	14.4339i	−0.103992	+	0.0278646i
$519$	552.479	−	229.588i	1.06451	−	0.442366i
$520$		0			0
$521$	−694.042			−1.33213			−0.666067	−	0.745892i	$-0.732023\pi$
$521$	−694.042			−1.33213			−0.666067	+	0.745892i	$0.732023\pi$
$522$	0.0280527	+	12.2165i	5.37408e−5	+	0.0234033i
$523$	−244.233	−	244.233i	−0.466985	−	0.466985i	0.433951	−	0.900936i	$-0.357119\pi$
$523$	−244.233	−	244.233i	−0.466985	−	0.466985i	−0.900936	+	0.433951i	$0.857119\pi$
$524$	189.524	−	109.422i	0.361687	−	0.208820i
$525$		0			0
$526$	−6.27198	+	10.8634i	−0.0119239	+	0.0206528i
$527$	−7.09137	−	26.4653i	−0.0134561	−	0.0502189i
$528$	651.950	−	86.5925i	1.23475	−	0.164001i
$529$	−121.283	+	70.0227i	−0.229268	+	0.132368i
$530$		0			0
$531$	−201.917	+	202.846i	−0.380258	+	0.382008i
$532$	179.108	−	179.108i	0.336669	−	0.336669i
$533$	249.997	−	933.001i	0.469037	−	1.75047i
$534$	11.8738	−	4.93428i	0.0222356	−	0.00924022i
$535$		0			0
$536$	50.2711	−	87.0720i	0.0937893	−	0.162448i
$537$	−604.288	+	464.790i	−1.12530	+	0.865531i
$538$	7.22994	−	26.9825i	0.0134386	−	0.0501534i
$539$		−	453.674i		−	0.841696i
$540$		0			0
$541$	−682.588			−1.26172			−0.630858	−	0.775899i	$-0.717297\pi$
$541$	−682.588			−1.26172			−0.630858	+	0.775899i	$0.717297\pi$
$542$	−8.26689	−	2.21511i	−0.0152526	−	0.00408691i
$543$	−433.474	−	563.573i	−0.798294	−	1.03789i
$544$	8.17918	+	4.72225i	0.0150353	+	0.00868061i
$545$		0			0
$546$	26.4338	+	63.6102i	0.0484136	+	0.116502i
$547$	−62.4694	−	16.7386i	−0.114204	−	0.0306008i	0.201265	−	0.979537i	$-0.435495\pi$
$547$	−62.4694	−	16.7386i	−0.114204	−	0.0306008i	−0.315468	+	0.948936i	$0.602162\pi$
$548$	549.504	+	549.504i	1.00275	+	1.00275i
$549$	−707.751	+	191.384i	−1.28916	+	0.348605i
$550$		0			0
$551$	−25.3122	−	43.8421i	−0.0459387	−	0.0795682i
$552$	11.7950	+	88.8042i	0.0213678	+	0.160877i
$553$	−722.530	+	193.601i	−1.30656	+	0.350093i
$554$	−26.1382	−	15.0909i	−0.0471809	−	0.0272399i
$555$		0			0
$556$	188.887	+	327.162i	0.339725	+	0.588421i
$557$	66.9124	−	66.9124i	0.120130	−	0.120130i	−0.644486	−	0.764616i	$-0.722929\pi$
$557$	66.9124	−	66.9124i	0.120130	−	0.120130i	0.764616	+	0.644486i	$0.222929\pi$
$558$	22.4674	+	38.7091i	0.0402641	+	0.0693711i
$559$		−	167.156i		−	0.299028i
$560$		0			0
$561$	−16.9819	−	40.8652i	−0.0302708	−	0.0728436i
$562$	−3.25693	−	12.1550i	−0.00579525	−	0.0216282i
$563$	137.436	−	36.8258i	0.244113	−	0.0654099i	−0.134688	−	0.990888i	$-0.543003\pi$
$563$	137.436	−	36.8258i	0.244113	−	0.0654099i	0.378801	+	0.925478i	$0.376337\pi$
$564$	−82.6612	+	633.493i	−0.146562	+	1.12322i
$565$		0			0
$566$	−76.5264			−0.135206
$567$	518.533	+	513.792i	0.914521	+	0.906159i
$568$	38.9637	+	38.9637i	0.0685981	+	0.0685981i
$569$	276.828	−	159.827i	0.486517	−	0.280891i	−0.236611	−	0.971604i	$-0.576037\pi$
$569$	276.828	−	159.827i	0.486517	−	0.280891i	0.723128	+	0.690714i	$0.242703\pi$
$570$		0			0
$571$	−324.309	+	561.720i	−0.567967	+	0.983748i	0.428800	+	0.903400i	$0.358937\pi$
$571$	−324.309	+	561.720i	−0.567967	+	0.983748i	−0.996767	+	0.0803483i	$0.974397\pi$
$572$	−193.608	−	722.555i	−0.338475	−	1.26321i
$573$	−62.5011	+	151.382i	−0.109077	+	0.264193i
$574$	106.952	−	61.7486i	0.186327	−	0.107576i
$575$		0			0
$576$	526.756	+	139.848i	0.914506	+	0.242792i
$577$	519.616	−	519.616i	0.900548	−	0.900548i	−0.0949353	−	0.995483i	$-0.530264\pi$
$577$	519.616	−	519.616i	0.900548	−	0.900548i	0.995483	+	0.0949353i	$0.0302644\pi$
$578$	−14.1670	+	52.8721i	−0.0245104	+	0.0914742i
$579$	476.980	+	365.130i	0.823800	+	0.630622i
$580$		0			0
$581$	−239.683	+	415.144i	−0.412536	+	0.714533i
$582$	−2.62156	−	19.7376i	−0.00450440	−	0.0339134i
$583$	−89.1240	+	332.615i	−0.152871	+	0.570523i
$584$			6.23095i			0.0106694i
$585$		0			0
$586$	41.2824			0.0704478
$587$	797.684	+	213.739i	1.35892	+	0.364120i	0.863418	−	0.504489i	$-0.168319\pi$
$587$	797.684	+	213.739i	1.35892	+	0.364120i	0.495498	+	0.868609i	$0.334986\pi$
$588$	146.200	−	354.106i	0.248639	−	0.602222i
$589$	−160.621	−	92.7344i	−0.272701	−	0.157444i
$590$		0			0
$591$	−77.9834	−	10.1756i	−0.131952	−	0.0172177i
$592$	489.432	+	131.143i	0.826743	+	0.221525i
$593$	−329.014	−	329.014i	−0.554829	−	0.554829i	0.373002	−	0.927831i	$-0.378329\pi$
$593$	−329.014	−	329.014i	−0.554829	−	0.554829i	−0.927831	+	0.373002i	$0.878329\pi$
$594$	44.2039	+	57.1987i	0.0744174	+	0.0962941i
$595$		0			0
$596$	515.699	+	893.218i	0.865267	+	1.49869i
$597$	−490.053	+	376.926i	−0.820860	+	0.631366i
$598$	48.5366	−	13.0053i	0.0811648	−	0.0217480i
$599$	445.587	+	257.260i	0.743885	+	0.429482i	0.823480	−	0.567345i	$-0.192029\pi$
$599$	445.587	+	257.260i	0.743885	+	0.429482i	−0.0795952	+	0.996827i	$0.525363\pi$
$600$		0			0
$601$	−19.7478	−	34.2041i	−0.0328582	−	0.0569121i	0.849129	−	0.528186i	$-0.177128\pi$
$601$	−19.7478	−	34.2041i	−0.0328582	−	0.0569121i	−0.881987	+	0.471274i	$0.843794\pi$
$602$	15.1122	−	15.1122i	0.0251033	−	0.0251033i
$603$	−597.626	+	1.37232i	−0.991087	+	0.00227583i
$604$			1021.99i			1.69204i
$605$		0			0
$606$	20.6137	−	26.9282i	0.0340159	−	0.0444360i
$607$	−104.659	−	390.594i	−0.172421	−	0.643483i	−0.996977	−	0.0777026i	$-0.975242\pi$
$607$	−104.659	−	390.594i	−0.172421	−	0.643483i	0.824556	−	0.565781i	$-0.191425\pi$
$608$	61.7533	−	16.5468i	0.101568	−	0.0272151i
$609$	−153.271	−	117.330i	−0.251677	−	0.192660i
$610$		0			0
$611$	719.960			1.17833
$612$	−0.0858104	−	37.3691i	−0.000140213	−	0.0610606i
$613$	559.593	+	559.593i	0.912876	+	0.912876i	0.996498	−	0.0836213i	$-0.0266486\pi$
$613$	559.593	+	559.593i	0.912876	+	0.912876i	−0.0836213	+	0.996498i	$0.526649\pi$
$614$	51.0172	−	29.4548i	0.0830898	−	0.0479719i
$615$		0			0
$616$	96.0775	−	166.411i	0.155970	−	0.270148i
$617$	−90.4285	−	337.484i	−0.146562	−	0.546976i	−0.999681	−	0.0252596i	$-0.991959\pi$
$617$	−90.4285	−	337.484i	−0.146562	−	0.546976i	0.853119	−	0.521716i	$-0.174708\pi$
$618$	27.3671	+	35.5809i	0.0442834	+	0.0575742i
$619$	−384.591	+	222.044i	−0.621311	+	0.358714i	−0.777379	−	0.629032i	$-0.783451\pi$
$619$	−384.591	+	222.044i	−0.621311	+	0.358714i	0.156068	+	0.987746i	$0.450118\pi$
$620$		0			0
$621$	421.335	−	325.614i	0.678479	−	0.524338i
$622$	−18.5115	+	18.5115i	−0.0297613	+	0.0297613i
$623$	−52.5825	+	196.241i	−0.0844021	+	0.314993i
$624$	80.9792	−	620.603i	0.129774	−	0.994557i
$625$		0			0
$626$	−0.627350	+	1.08660i	−0.00100216	+	0.00173579i
$627$	−276.888	−	114.319i	−0.441608	−	0.182326i
$628$	47.6857	−	177.965i	0.0759326	−	0.283384i
$629$		−	34.0943i		−	0.0542040i
$630$		0			0
$631$	−181.428			−0.287524			−0.143762	−	0.989612i	$-0.545920\pi$
$631$	−181.428			−0.287524			−0.143762	+	0.989612i	$0.545920\pi$
$632$	−121.393	−	32.5273i	−0.192078	−	0.0514672i
$633$	721.901	−	95.8834i	1.14044	−	0.151475i
$634$	−72.8343	−	42.0509i	−0.114881	−	0.0663264i
$635$		0			0
$636$	−176.751	+	230.895i	−0.277911	+	0.363043i
$637$	−417.019	−	111.740i	−0.654661	−	0.175416i
$638$	−13.5164	−	13.5164i	−0.0211856	−	0.0211856i
$639$	84.0456	−	316.568i	0.131527	−	0.495412i
$640$		0			0
$641$	44.3645	+	76.8416i	0.0692114	+	0.119878i	0.898554	−	0.438862i	$-0.144618\pi$
$641$	44.3645	+	76.8416i	0.0692114	+	0.119878i	−0.829343	+	0.558740i	$0.811285\pi$
$642$	37.7909	+	15.6027i	0.0588643	+	0.0243032i
$643$	414.879	−	111.166i	0.645224	−	0.172887i	0.0786553	−	0.996902i	$-0.474937\pi$
$643$	414.879	−	111.166i	0.645224	−	0.172887i	0.566568	+	0.824015i	$0.308271\pi$
$644$	−610.125	−	352.256i	−0.947399	−	0.546981i
$645$		0			0
$646$	−0.706077	−	1.22296i	−0.00109300	−	0.00189313i
$647$	−237.290	+	237.290i	−0.366755	+	0.366755i	−0.866292	−	0.499537i	$-0.833503\pi$
$647$	−237.290	+	237.290i	−0.366755	+	0.366755i	0.499537	+	0.866292i	$0.333503\pi$
$648$	32.2862	+	118.318i	0.0498244	+	0.182589i
$649$		−	447.832i		−	0.690034i
$650$		0			0
$651$	−701.223	−	91.4988i	−1.07715	−	0.140551i
$652$	111.475	+	416.030i	0.170974	+	0.638083i
$653$	777.291	−	208.275i	1.19034	−	0.318950i	0.391319	−	0.920255i	$-0.372019\pi$
$653$	777.291	−	208.275i	1.19034	−	0.318950i	0.799020	+	0.601305i	$0.205352\pi$
$654$	−25.1956	+	10.4703i	−0.0385255	+	0.0160096i
$655$		0			0
$656$	−1122.07			−1.71047
$657$	32.0324	−	18.5921i	0.0487556	−	0.0282985i
$658$	65.0897	+	65.0897i	0.0989206	+	0.0989206i
$659$	−407.245	+	235.123i	−0.617974	+	0.356787i	−0.776080	−	0.630635i	$-0.782795\pi$
$659$	−407.245	+	235.123i	−0.617974	+	0.356787i	0.158106	+	0.987422i	$0.449461\pi$
$660$		0			0
$661$	379.580	−	657.451i	0.574251	−	0.994631i	−0.421872	−	0.906655i	$-0.638627\pi$
$661$	379.580	−	657.451i	0.574251	−	0.994631i	0.996123	−	0.0879760i	$-0.0280399\pi$
$662$	−12.8778	−	48.0606i	−0.0194528	−	0.0725990i
$663$	−41.7462	+	5.54476i	−0.0629656	+	0.00836313i
$664$	−69.7489	+	40.2696i	−0.105044	+	0.0606469i
$665$		0			0
$666$	14.5381	+	53.7630i	0.0218290	+	0.0807252i
$667$	−99.5643	+	99.5643i	−0.149272	+	0.149272i
$668$	−319.967	+	1194.13i	−0.478992	+	1.78762i
$669$	570.048	−	236.889i	0.852090	−	0.354094i
$670$		0			0
$671$	573.592	−	993.490i	0.854832	−	1.48061i
$672$	193.220	−	148.616i	0.287529	−	0.221154i
$673$	326.337	−	1217.91i	0.484899	−	1.80967i	−0.0956152	−	0.995418i	$-0.530482\pi$
$673$	326.337	−	1217.91i	0.484899	−	1.80967i	0.580514	−	0.814250i	$-0.302852\pi$
$674$			27.7198i			0.0411273i
$675$		0			0
$676$	−41.9700			−0.0620858
$677$	96.3967	+	25.8294i	0.142388	+	0.0381528i	0.329309	−	0.944222i	$-0.393184\pi$
$677$	96.3967	+	25.8294i	0.142388	+	0.0381528i	−0.186921	+	0.982375i	$0.559851\pi$
$678$	−60.5954	−	78.7820i	−0.0893738	−	0.116198i
$679$	272.449	+	157.298i	0.401250	+	0.231662i
$680$		0			0
$681$	214.318	+	515.734i	0.314711	+	0.757319i
$682$	−67.6443	−	18.1252i	−0.0991852	−	0.0265766i
$683$	−366.381	−	366.381i	−0.536430	−	0.536430i	0.386049	−	0.922478i	$-0.373840\pi$
$683$	−366.381	−	366.381i	−0.536430	−	0.536430i	−0.922478	+	0.386049i	$0.873840\pi$
$684$	−179.280	−	178.458i	−0.262105	−	0.260904i
$685$		0			0
$686$	14.3787	+	24.9047i	0.0209602	+	0.0363042i
$687$	71.4727	+	538.114i	0.104036	+	0.783281i
$688$	−187.563	+	50.2575i	−0.272621	+	0.0730486i
$689$	283.790	+	163.846i	0.411887	+	0.237803i
$690$		0			0
$691$	−298.133	−	516.381i	−0.431451	−	0.747296i	0.565547	−	0.824716i	$-0.308665\pi$
$691$	−298.133	−	516.381i	−0.431451	−	0.747296i	−0.996999	+	0.0774204i	$0.975332\pi$
$692$	−558.971	+	558.971i	−0.807761	+	0.807761i
$693$	−1142.18	+	2.62277i	−1.64816	+	0.00378466i
$694$			1.92499i			0.00277376i
$695$		0			0
$696$	−12.4449	−	29.9474i	−0.0178806	−	0.0430279i
$697$	19.5411	+	72.9284i	0.0280360	+	0.104632i
$698$	19.9559	−	5.34718i	0.0285902	−	0.00766071i
$699$	−66.0000	+	505.806i	−0.0944206	+	0.723614i
$700$		0			0
$701$	147.235			0.210036			0.105018	−	0.994470i	$-0.466510\pi$
$701$	147.235			0.210036			0.105018	+	0.994470i	$0.466510\pi$
$702$	63.4647	−	26.5444i	0.0904056	−	0.0378126i
$703$	−163.194	−	163.194i	−0.232140	−	0.232140i
$704$	−738.513	+	426.381i	−1.04902	+	0.605654i
$705$		0			0
$706$	−45.9731	+	79.6277i	−0.0651177	+	0.112787i
$707$	138.681	+	517.565i	0.196154	+	0.732058i
$708$	144.317	−	349.546i	0.203837	−	0.493710i
$709$	−123.232	+	71.1480i	−0.173811	+	0.100350i	−0.584382	−	0.811479i	$-0.698663\pi$
$709$	−123.232	+	71.1480i	−0.173811	+	0.100350i	0.410571	+	0.911829i	$0.365330\pi$
$710$		0			0
$711$	195.000	+	721.122i	0.274262	+	1.01424i
$712$	−24.1362	+	24.1362i	−0.0338992	+	0.0338992i
$713$	−133.514	+	498.280i	−0.187256	+	0.698849i
$714$	−4.27545	−	3.27288i	−0.00598803	−	0.00458386i
$715$		0			0
$716$	503.648	−	872.343i	0.703418	−	1.21836i
$717$	−151.481	−	1140.49i	−0.211270	−	1.59064i
$718$	13.7320	−	51.2486i	0.0191254	−	0.0713769i
$719$		−	1075.81i		−	1.49626i	−0.663555	−	0.748128i	$-0.730953\pi$
$719$		−	1075.81i		−	1.49626i	0.663555	−	0.748128i	$-0.269047\pi$
$720$		0			0
$721$	−709.245			−0.983696
$722$	57.0627	+	15.2899i	0.0790342	+	0.0211771i
$723$	−373.097	+	903.670i	−0.516041	+	1.24989i
$724$	813.567	+	469.713i	1.12371	+	0.648775i
$725$		0			0
$726$	−43.7239	−	5.70530i	−0.0602257	−	0.00785853i
$727$	−696.238	−	186.556i	−0.957687	−	0.256611i	−0.254066	−	0.967187i	$-0.581768\pi$
$727$	−696.238	−	186.556i	−0.957687	−	0.256611i	−0.703621	+	0.710576i	$0.748435\pi$
$728$	−129.302	−	129.302i	−0.177613	−	0.177613i
$729$	511.918	−	519.020i	0.702219	−	0.711961i
$730$		0			0
$731$	6.53293	+	11.3154i	0.00893698	+	0.0154793i
$732$	767.865	−	590.605i	1.04900	−	0.806838i
$733$	−1179.49	+	316.043i	−1.60913	+	0.431164i	−0.947782	−	0.318918i	$-0.896681\pi$
$733$	−1179.49	+	316.043i	−1.60913	+	0.431164i	−0.661345	+	0.750082i	$0.730014\pi$
$734$	29.4125	+	16.9813i	0.0400715	+	0.0231353i
$735$		0			0
$736$	−88.9088	−	153.995i	−0.120800	−	0.209232i
$737$	661.216	−	661.216i	0.897173	−	0.897173i
$738$	−61.9115	−	106.668i	−0.0838910	−	0.144536i
$739$		−	683.603i		−	0.925038i	−0.886609	−	0.462519i	$-0.846946\pi$
$739$		−	683.603i		−	0.925038i	0.886609	−	0.462519i	$-0.153054\pi$
$740$		0			0
$741$	−173.280	+	226.360i	−0.233846	+	0.305479i
$742$	10.8438	+	40.4697i	0.0146143	+	0.0545413i
$743$	763.713	−	204.636i	1.02788	−	0.275419i	0.294797	−	0.955560i	$-0.404748\pi$
$743$	763.713	−	204.636i	1.02788	−	0.275419i	0.733081	+	0.680141i	$0.238081\pi$
$744$	−94.3431	−	72.2201i	−0.126805	−	0.0970700i
$745$		0			0
$746$	−16.6900			−0.0223727
$747$	415.140	+	238.412i	0.555742	+	0.319159i
$748$	41.3454	+	41.3454i	0.0552746	+	0.0552746i
$749$	−559.447	+	322.997i	−0.746925	+	0.431238i
$750$		0			0
$751$	326.862	−	566.142i	0.435236	−	0.753851i	−0.562079	−	0.827084i	$-0.689998\pi$
$751$	326.862	−	566.142i	0.435236	−	0.753851i	0.997315	+	0.0732329i	$0.0233317\pi$
$752$	−216.464	−	807.855i	−0.287851	−	1.07427i
$753$	784.541	+	1020.01i	1.04189	+	1.35459i
$754$	−15.7535	+	9.09526i	−0.0208932	+	0.0120627i
$755$		0			0
$756$	−892.348	−	366.027i	−1.18035	−	0.484163i
$757$	−668.868	+	668.868i	−0.883577	+	0.883577i	−0.993896	−	0.110319i	$-0.964813\pi$
$757$	−668.868	+	668.868i	−0.883577	+	0.883577i	0.110319	+	0.993896i	$0.464813\pi$
$758$	0.510741	−	1.90611i	0.000673800	−	0.00251466i
$759$	−107.804	+	826.181i	−0.142034	+	1.08851i
$760$		0			0
$761$	478.705	−	829.141i	0.629047	−	1.08954i	−0.358696	−	0.933454i	$-0.616779\pi$
$761$	478.705	−	829.141i	0.629047	−	1.08954i	0.987743	−	0.156087i	$-0.0498881\pi$
$762$	−12.1778	−	5.02782i	−0.0159813	−	0.00659819i
$763$	111.577	−	416.413i	0.146235	−	0.545757i
$764$		−	216.396i		−	0.283241i
$765$		0			0
$766$	−24.4926			−0.0319747
$767$	−411.649	−	110.301i	−0.536700	−	0.143808i
$768$	−693.444	+	92.1038i	−0.902922	+	0.119927i
$769$	−435.970	−	251.708i	−0.566932	−	0.327318i	0.188991	−	0.981979i	$-0.439478\pi$
$769$	−435.970	−	251.708i	−0.566932	−	0.327318i	−0.755923	+	0.654661i	$0.772812\pi$
$770$		0			0
$771$	−671.823	+	877.621i	−0.871365	+	1.13829i
$772$	−766.640	−	205.421i	−0.993057	−	0.266089i
$773$	362.267	+	362.267i	0.468651	+	0.468651i	0.901477	−	0.432827i	$-0.142484\pi$
$773$	362.267	+	362.267i	0.468651	+	0.468651i	−0.432827	+	0.901477i	$0.642484\pi$
$774$	−15.1267	−	15.0574i	−0.0195435	−	0.0194540i
$775$		0			0
$776$	26.4279	+	45.7745i	0.0340566	+	0.0589878i
$777$	−813.378	−	335.819i	−1.04682	−	0.432199i
$778$	−134.731	+	36.1011i	−0.173176	+	0.0464024i
$779$	442.610	+	255.541i	0.568177	+	0.328037i
$780$		0			0
$781$	256.245	+	443.830i	0.328099	+	0.568284i
$782$	−2.77732	+	2.77732i	−0.00355155	+	0.00355155i
$783$	−116.822	+	153.336i	−0.149198	+	0.195831i
$784$			501.526i			0.639701i
$785$		0			0
$786$	−31.2254	−	4.07443i	−0.0397270	−	0.00518376i
$787$	−134.565	−	502.205i	−0.170985	−	0.638126i	−0.997201	−	0.0747716i	$-0.976177\pi$
$787$	−134.565	−	502.205i	−0.170985	−	0.638126i	0.826215	−	0.563354i	$-0.190489\pi$
$788$	100.371	−	26.8943i	0.127374	−	0.0341299i
$789$	−182.779	+	75.9557i	−0.231659	+	0.0962683i
$790$		0			0
$791$	1570.39			1.98532
$792$	−166.409	−	95.5677i	−0.210113	−	0.120666i
$793$	−771.945	−	771.945i	−0.973449	−	0.973449i
$794$	−35.2207	+	20.3347i	−0.0443585	+	0.0256104i
$795$		0			0
$796$	408.438	−	707.435i	0.513113	−	0.888737i
$797$	−72.1737	−	269.356i	−0.0905567	−	0.337962i	0.905752	−	0.423809i	$-0.139307\pi$
$797$	−72.1737	−	269.356i	−0.0905567	−	0.337962i	−0.996308	+	0.0858466i	$0.972640\pi$
$798$	−36.1304	+	4.79887i	−0.0452762	+	0.00601362i
$799$	−48.7365	+	28.1380i	−0.0609968	+	0.0352165i
$800$		0			0
$801$	196.099	+	52.0623i	0.244818	+	0.0649967i
$802$	−0.879908	+	0.879908i	−0.00109714	+	0.00109714i
$803$	−14.9989	+	55.9768i	−0.0186786	+	0.0697096i
$804$	729.181	−	303.018i	0.906941	−	0.376888i
$805$		0			0
$806$	−33.3216	+	57.7147i	−0.0413419	+	0.0716063i
$807$	349.387	−	268.732i	0.432945	−	0.333001i
$808$	−23.3000	+	86.9569i	−0.0288367	+	0.107620i
$809$		−	423.966i		−	0.524062i	−0.965060	−	0.262031i	$-0.915608\pi$
$809$		−	423.966i		−	0.524062i	0.965060	−	0.262031i	$-0.0843922\pi$
$810$		0			0
$811$	−1163.79			−1.43501			−0.717506	−	0.696552i	$-0.754716\pi$
$811$	−1163.79			−1.43501			−0.717506	+	0.696552i	$0.754716\pi$
$812$	246.350	+	66.0092i	0.303386	+	0.0812921i
$813$	−82.3340	−	107.045i	−0.101272	−	0.131667i
$814$	−75.4686	−	43.5718i	−0.0927133	−	0.0535281i
$815$		0			0
$816$	18.7731	+	45.1756i	0.0230063	+	0.0553622i
$817$	85.4317	+	22.8914i	0.104568	+	0.0280188i
$818$	99.2357	+	99.2357i	0.121315	+	0.121315i
$819$	−278.907	+	1050.54i	−0.340546	+	1.28271i
$820$		0			0
$821$	−382.915	−	663.228i	−0.466400	−	0.807829i	0.532863	−	0.846202i	$-0.321116\pi$
$821$	−382.915	−	663.228i	−0.466400	−	0.807829i	−0.999264	+	0.0383722i	$0.987783\pi$
$822$	−14.7230	−	110.848i	−0.0179112	−	0.134852i
$823$	955.510	−	256.028i	1.16101	−	0.311091i	0.373640	−	0.927574i	$-0.378109\pi$
$823$	955.510	−	256.028i	1.16101	−	0.311091i	0.787369	+	0.616482i	$0.211443\pi$
$824$	−103.197	−	59.5806i	−0.125239	−	0.0723066i
$825$		0			0
$826$	−27.2441	−	47.1882i	−0.0329832	−	0.0571286i
$827$	260.100	−	260.100i	0.314510	−	0.314510i	−0.532144	−	0.846654i	$-0.678613\pi$
$827$	260.100	−	260.100i	0.314510	−	0.314510i	0.846654	+	0.532144i	$0.178613\pi$
$828$	−350.387	+	610.119i	−0.423172	+	0.736858i
$829$			325.275i			0.392370i	0.980567	+	0.196185i	$0.0628553\pi$
$829$			325.275i			0.392370i	−0.980567	+	0.196185i	$0.937145\pi$
$830$		0			0
$831$	−182.756	−	439.783i	−0.219923	−	0.529221i
$832$	210.035	+	783.862i	0.252446	+	0.942142i
$833$	32.5965	−	8.73421i	0.0391315	−	0.0104852i
$834$	7.03342	−	53.9023i	0.00843336	−	0.0646310i
$835$		0			0
$836$	395.803			0.473449
$837$	−89.7687	+	700.497i	−0.107251	+	0.836914i
$838$	−36.5387	−	36.5387i	−0.0436022	−	0.0436022i
$839$	−81.4767	+	47.0406i	−0.0971116	+	0.0560674i	−0.547769	−	0.836629i	$-0.684523\pi$
$839$	−81.4767	+	47.0406i	−0.0971116	+	0.0560674i	0.450658	+	0.892697i	$0.351190\pi$
$840$		0			0
$841$	−395.014	+	684.184i	−0.469695	+	0.813536i
$842$	10.1364	+	37.8296i	0.0120385	+	0.0449283i
$843$	75.7757	−	183.535i	0.0898882	−	0.217716i
$844$	−833.301	+	481.107i	−0.987323	+	0.570031i
$845$		0			0
$846$	64.8536	−	65.1522i	0.0766591	−	0.0770120i
$847$	492.644	−	492.644i	0.581633	−	0.581633i
$848$	98.5244	−	367.698i	0.116184	−	0.433606i
$849$	−958.837	−	733.994i	−1.12937	−	0.864539i
$850$		0			0
$851$	−320.958	+	555.915i	−0.377154	+	0.653249i
$852$	56.9800	+	428.999i	0.0668779	+	0.503520i
$853$	−263.924	+	984.979i	−0.309407	+	1.15472i	0.619678	+	0.784856i	$0.287263\pi$
$853$	−263.924	+	984.979i	−0.309407	+	1.15472i	−0.929085	+	0.369867i	$0.879403\pi$
$854$		−	139.579i		−	0.163442i
$855$		0			0
$856$	−108.534			−0.126793
$857$	−1522.95	−	408.073i	−1.77707	−	0.476164i	−0.787026	−	0.616920i	$-0.788380\pi$
$857$	−1522.95	−	408.073i	−1.77707	−	0.476164i	−0.990044	+	0.140756i	$0.955047\pi$
$858$	−41.0773	+	99.4922i	−0.0478756	+	0.115958i
$859$	−507.067	−	292.755i	−0.590299	−	0.340809i	0.174917	−	0.984583i	$-0.444034\pi$
$859$	−507.067	−	292.755i	−0.590299	−	0.340809i	−0.765216	+	0.643774i	$0.777368\pi$
$860$		0			0
$861$	1932.30	+	252.136i	2.24426	+	0.292841i
$862$	−43.7939	−	11.7345i	−0.0508050	−	0.0136132i
$863$	550.423	+	550.423i	0.637802	+	0.637802i	0.950013	−	0.312211i	$-0.101070\pi$
$863$	550.423	+	550.423i	0.637802	+	0.637802i	−0.312211	+	0.950013i	$0.601070\pi$
$864$	−148.860	−	192.621i	−0.172292	−	0.222941i
$865$		0			0
$866$	−10.7144	−	18.5579i	−0.0123723	−	0.0214294i
$867$	−684.622	+	526.579i	−0.789644	+	0.607357i
$868$	902.531	−	241.833i	1.03978	−	0.278609i
$869$	−1012.26	−	584.429i	−1.16486	−	0.672530i
$870$		0			0
$871$	−444.935	−	770.650i	−0.510833	−	0.884788i
$872$	51.2158	−	51.2158i	0.0587337	−	0.0587337i
$873$	156.464	−	272.446i	0.179225	−	0.312080i
$874$			26.5875i			0.0304205i
$875$		0			0
$876$	−29.7460	+	38.8581i	−0.0339567	+	0.0443585i
$877$	−236.500	−	882.630i	−0.269669	−	1.00642i	−0.959330	−	0.282287i	$-0.908907\pi$
$877$	−236.500	−	882.630i	−0.269669	−	1.00642i	0.689661	−	0.724133i	$-0.257760\pi$
$878$	59.4017	−	15.9166i	0.0676557	−	0.0181283i
$879$	517.247	+	395.955i	0.588450	+	0.450461i
$880$		0			0
$881$	−459.689			−0.521781			−0.260891	−	0.965368i	$-0.584016\pi$
$881$	−459.689			−0.521781			−0.260891	+	0.965368i	$0.584016\pi$
$882$	−47.6767	+	27.6723i	−0.0540552	+	0.0313745i
$883$	−107.163	−	107.163i	−0.121362	−	0.121362i	0.643817	−	0.765179i	$-0.277350\pi$
$883$	−107.163	−	107.163i	−0.121362	−	0.121362i	−0.765179	+	0.643817i	$0.777350\pi$
$884$	48.1882	−	27.8215i	0.0545116	−	0.0314723i
$885$		0			0
$886$	−71.8119	+	124.382i	−0.0810519	+	0.140386i
$887$	172.159	+	642.507i	0.194092	+	0.724360i	0.992500	+	0.122244i	$0.0390090\pi$
$887$	172.159	+	642.507i	0.194092	+	0.724360i	−0.798408	+	0.602116i	$0.794324\pi$
$888$	−90.1376	−	117.191i	−0.101506	−	0.131972i
$889$	180.277	−	104.083i	0.202786	−	0.117078i
$890$		0			0
$891$	5.23854	+	1140.65i	0.00587940	+	1.28019i
$892$	−576.746	+	576.746i	−0.646576	+	0.646576i
$893$	−98.5954	+	367.963i	−0.110409	+	0.412053i
$894$	19.2026	−	147.164i	0.0214794	−	0.164613i
$895$		0			0
$896$	−214.387	+	371.329i	−0.239271	+	0.414430i
$897$	732.877	+	302.582i	0.817031	+	0.337327i
$898$	−25.3288	+	94.5284i	−0.0282058	+	0.105266i
$899$		−	186.745i		−	0.207725i
$900$		0			0
$901$	−25.6142			−0.0284287
$902$	186.402	+	49.9463i	0.206654	+	0.0553728i
$903$	334.295	−	44.4012i	0.370204	−	0.0491708i
$904$	228.495	+	131.922i	0.252760	+	0.145931i
$905$		0			0
$906$	89.3891	−	116.772i	0.0986635	−	0.128887i
$907$	804.640	+	215.603i	0.887144	+	0.237710i	0.673487	−	0.739199i	$-0.264796\pi$
$907$	804.640	+	215.603i	0.887144	+	0.237710i	0.213657	+	0.976909i	$0.431462\pi$
$908$	−521.794	−	521.794i	−0.574663	−	0.574663i
$909$	516.557	−	139.683i	0.568269	−	0.153667i
$910$		0			0
$911$	−38.7954	−	67.1955i	−0.0425855	−	0.0737602i	0.843947	−	0.536427i	$-0.180226\pi$
$911$	−38.7954	−	67.1955i	−0.0425855	−	0.0737602i	−0.886533	+	0.462666i	$0.846893\pi$
$912$	306.093	+	126.376i	0.335629	+	0.138571i
$913$	−723.538	+	193.871i	−0.792484	+	0.212345i
$914$	93.8309	+	54.1733i	0.102660	+	0.0592706i
$915$		0			0
$916$	−358.623	−	621.153i	−0.391510	−	0.678115i
$917$	351.821	−	351.821i	0.383665	−	0.383665i
$918$	−3.25871	+	4.27725i	−0.00354979	+	0.00465932i
$919$			1478.95i			1.60930i	0.593750	+	0.804650i	$0.297647\pi$
$919$			1478.95i			1.60930i	−0.593750	+	0.804650i	$0.702353\pi$
$920$		0			0
$921$	921.730	+	120.272i	1.00079	+	0.130588i
$922$	−11.7443	−	43.8305i	−0.0127379	−	0.0475385i
$923$	471.083	−	126.226i	0.510383	−	0.136757i
$924$	1393.60	−	579.125i	1.50823	−	0.626758i
$925$		0			0
$926$	156.839			0.169373
$927$	1.62646	+	708.298i	0.00175454	+	0.764076i
$928$	45.5177	+	45.5177i	0.0490492	+	0.0490492i
$929$	1381.56	−	797.643i	1.48715	−	0.858604i	0.487253	−	0.873261i	$-0.337999\pi$
$929$	1381.56	−	797.643i	1.48715	−	0.858604i	0.999893	+	0.0146572i	$0.00466569\pi$
$930$		0			0
$931$	114.218	−	197.831i	0.122683	−	0.212493i
$932$	−174.439	−	651.014i	−0.187166	−	0.698513i
$933$	−409.491	+	54.3888i	−0.438897	+	0.0582946i
$934$	−113.927	+	65.7757i	−0.121977	+	0.0704237i
$935$		0			0
$936$	−128.833	+	129.426i	−0.137642	+	0.138276i
$937$	921.265	−	921.265i	0.983207	−	0.983207i	−0.0166542	−	0.999861i	$-0.505301\pi$
$937$	921.265	−	921.265i	0.983207	−	0.983207i	0.999861	+	0.0166542i	$0.00530143\pi$
$938$	29.4471	−	109.898i	0.0313935	−	0.117162i
$939$	−18.2824	+	7.59741i	−0.0194700	+	0.00809096i
$940$		0			0
$941$	−618.185	+	1070.73i	−0.656945	+	1.13786i	0.324458	+	0.945900i	$0.394818\pi$
$941$	−618.185	+	1070.73i	−0.656945	+	1.13786i	−0.981402	+	0.191961i	$0.938515\pi$
$942$	−21.0144	+	16.1632i	−0.0223082	+	0.0171584i
$943$	367.913	−	1373.07i	0.390152	−	1.45607i
$944$			495.068i			0.524436i
$945$		0			0
$946$	33.3958			0.0353021
$947$	1561.01	+	418.272i	1.64838	+	0.441681i	0.959158	−	0.282872i	$-0.0912871\pi$
$947$	1561.01	+	418.272i	1.64838	+	0.441681i	0.689219	+	0.724553i	$0.257954\pi$
$948$	−601.764	−	782.372i	−0.634772	−	0.825287i
$949$	47.7599	+	27.5742i	0.0503265	+	0.0290560i
$950$		0			0
$951$	−509.250	−	1225.46i	−0.535489	−	1.28860i
$952$	13.8064	+	3.69940i	0.0145025	+	0.00388593i
$953$	−1074.57	−	1074.57i	−1.12756	−	1.12756i	−0.990573	−	0.136988i	$-0.956258\pi$
$953$	−1074.57	−	1074.57i	−1.12756	−	1.12756i	−0.136988	−	0.990573i	$-0.543742\pi$
$954$	40.3908	−	10.9222i	0.0423384	−	0.0114488i
$955$		0			0
$956$	760.073	+	1316.48i	0.795055	+	1.37708i
$957$	−39.7127	−	298.995i	−0.0414971	−	0.312429i
$958$	30.2804	−	8.11362i	0.0316080	−	0.00846933i
$959$	1530.10	+	883.405i	1.59552	+	0.921173i
$960$		0			0
$961$	138.418	+	239.748i	0.144036	+	0.249477i
$962$	−58.6394	+	58.6394i	−0.0609557	+	0.0609557i
$963$	323.849	+	557.960i	0.336292	+	0.579398i
$964$		−	1291.77i		−	1.34001i
$965$		0			0
$966$	38.9019	+	93.6132i	0.0402711	+	0.0969081i
$967$	46.6332	+	174.037i	0.0482246	+	0.179977i	0.985837	−	0.167705i	$-0.0536357\pi$
$967$	46.6332	+	174.037i	0.0482246	+	0.179977i	−0.937613	+	0.347682i	$0.886969\pi$
$968$	113.066	−	30.2958i	0.116803	−	0.0312974i
$969$	2.88310	−	22.0953i	0.00297533	−	0.0228022i
$970$		0			0
$971$	−40.8568			−0.0420770			−0.0210385	−	0.999779i	$-0.506697\pi$
$971$	−40.8568			−0.0420770			−0.0210385	+	0.999779i	$0.506697\pi$
$972$	−363.492	+	891.997i	−0.373963	+	0.917693i
$973$	607.325	+	607.325i	0.624178	+	0.624178i
$974$	−76.1338	+	43.9558i	−0.0781661	+	0.0451292i
$975$		0			0
$976$	−634.092	+	1098.28i	−0.649685	+	1.12529i
$977$	202.074	+	754.152i	0.206832	+	0.771906i	0.988883	+	0.148693i	$0.0475065\pi$
$977$	202.074	+	754.152i	0.206832	+	0.771906i	−0.782052	+	0.623213i	$0.785827\pi$
$978$	23.6513	−	57.2853i	0.0241834	−	0.0585739i
$979$	−274.932	+	158.732i	−0.280829	+	0.162137i
$980$		0			0
$981$	−416.113	−	110.474i	−0.424172	−	0.112613i
$982$	−48.9385	+	48.9385i	−0.0498355	+	0.0498355i
$983$	−133.041	+	496.515i	−0.135341	+	0.505101i	0.864655	+	0.502367i	$0.167537\pi$
$983$	−133.041	+	496.515i	−0.135341	+	0.505101i	−0.999996	+	0.00273477i	$0.999129\pi$
$984$	259.974	+	199.011i	0.264201	+	0.202247i
$985$		0			0
$986$	0.710935	−	1.23138i	0.000721030	−	0.00124886i
$987$	191.241	+	1439.84i	0.193760	+	1.45881i
$988$	97.4863	−	363.824i	0.0986704	−	0.368243i
$989$		−	245.999i		−	0.248735i
$990$		0			0
$991$	941.294			0.949843			0.474922	−	0.880028i	$-0.342476\pi$
$991$	941.294			0.949843			0.474922	+	0.880028i	$0.342476\pi$
$992$	227.798	+	61.0382i	0.229635	+	0.0615304i
$993$	299.615	−	725.690i	0.301727	−	0.730805i
$994$	54.0013	+	31.1776i	0.0543272	+	0.0313658i
$995$		0			0
$996$	−627.219	−	81.8425i	−0.629738	−	0.0821712i
$997$	1287.52	+	344.990i	1.29140	+	0.346029i	0.838191	−	0.545377i	$-0.183614\pi$
$997$	1287.52	+	344.990i	1.29140	+	0.346029i	0.453206	+	0.891406i	$0.350280\pi$
$998$	−54.8879	−	54.8879i	−0.0549979	−	0.0549979i
$999$	−333.505	+	813.063i	−0.333839	+	0.813877i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.3.o.b.193.5		40
5.2	odd	4	inner	225.3.o.b.157.6		40
5.3	odd	4		45.3.k.a.22.5	yes	40
5.4	even	2		45.3.k.a.13.6	yes	40
9.7	even	3	inner	225.3.o.b.43.6		40
15.8	even	4		135.3.l.a.37.6		40
15.14	odd	2		135.3.l.a.118.5		40
45.4	even	6		405.3.g.h.163.5		20
45.7	odd	12	inner	225.3.o.b.7.5		40
45.13	odd	12		405.3.g.h.82.5		20
45.14	odd	6		405.3.g.g.163.6		20
45.23	even	12		405.3.g.g.82.6		20
45.29	odd	6		135.3.l.a.73.6		40
45.34	even	6		45.3.k.a.43.5	yes	40
45.38	even	12		135.3.l.a.127.5		40
45.43	odd	12		45.3.k.a.7.6	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.6	✓	40	45.43	odd	12
45.3.k.a.13.6	yes	40	5.4	even	2
45.3.k.a.22.5	yes	40	5.3	odd	4
45.3.k.a.43.5	yes	40	45.34	even	6
135.3.l.a.37.6		40	15.8	even	4
135.3.l.a.73.6		40	45.29	odd	6
135.3.l.a.118.5		40	15.14	odd	2
135.3.l.a.127.5		40	45.38	even	12
225.3.o.b.7.5		40	45.7	odd	12	inner
225.3.o.b.43.6		40	9.7	even	3	inner
225.3.o.b.157.6		40	5.2	odd	4	inner
225.3.o.b.193.5		40	1.1	even	1	trivial
405.3.g.g.82.6		20	45.23	even	12
405.3.g.g.163.6		20	45.14	odd	6
405.3.g.h.82.5		20	45.13	odd	12
405.3.g.h.163.5		20	45.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	225.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.183646 + 0.0492077i) q^{2} +(1.82902 + 2.37796i) q^{3} +(-3.43280 - 1.98193i) q^{4} +(0.218877 + 0.526704i) q^{6} +(-8.70492 - 2.33248i) q^{7} +(-1.07064 - 1.07064i) q^{8} +(-2.30940 + 8.69866i) q^{9} +(-7.04110 - 12.1955i) q^{11} +(-1.56570 - 11.7880i) q^{12} +(-12.9444 + 3.46845i) q^{13} +(-1.48385 - 0.856699i) q^{14} +(7.78377 + 13.4819i) q^{16} +(0.740694 - 0.740694i) q^{17} +(-0.852153 + 1.48383i) q^{18} -7.09073i q^{19} +(-10.3749 - 24.9661i) q^{21} +(-0.692953 - 2.58614i) q^{22} +(-19.0499 + 5.10441i) q^{23} +(0.587726 - 4.50418i) q^{24} -2.54786 q^{26} +(-24.9090 + 10.4183i) q^{27} +(25.2594 + 25.2594i) q^{28} +(6.18301 - 3.56976i) q^{29} +(13.0783 - 22.6522i) q^{31} +(2.33357 + 8.70902i) q^{32} +(16.1223 - 39.0493i) q^{33} +(0.172473 - 0.0995774i) q^{34} +(25.1678 - 25.2837i) q^{36} +(23.0151 - 23.0151i) q^{37} +(0.348919 - 1.30218i) q^{38} +(-31.9234 - 24.4375i) q^{39} +(-36.0387 + 62.4209i) q^{41} +(-0.676780 - 5.09544i) q^{42} +(-3.22835 + 12.0484i) q^{43} +55.8198i q^{44} -3.74961 q^{46} +(-51.8935 - 13.9048i) q^{47} +(-17.8228 + 43.1681i) q^{48} +(27.9000 + 16.1081i) q^{49} +(3.11608 + 0.406601i) q^{51} +(51.3098 + 13.7484i) q^{52} +(-17.2907 - 17.2907i) q^{53} +(-5.08709 + 0.687563i) q^{54} +(6.82262 + 11.8171i) q^{56} +(16.8615 - 12.9691i) q^{57} +(1.31114 - 0.351320i) q^{58} +(27.5407 + 15.9006i) q^{59} +(40.7317 + 70.5494i) q^{61} +(3.51643 - 3.51643i) q^{62} +(40.3926 - 70.3345i) q^{63} -60.5560i q^{64} +(4.88231 - 6.37790i) q^{66} +(17.1864 + 64.1404i) q^{67} +(-4.01065 + 1.07465i) q^{68} +(-46.9807 - 35.9639i) q^{69} -36.3928 q^{71} +(11.7857 - 6.84062i) q^{72} +(-2.90991 - 2.90991i) q^{73} +(5.35915 - 3.09411i) q^{74} +(-14.0533 + 24.3410i) q^{76} +(32.8464 + 122.584i) q^{77} +(-4.66008 - 6.05872i) q^{78} +(71.8823 - 41.5012i) q^{79} +(-70.3333 - 40.1774i) q^{81} +(-9.68994 + 9.68994i) q^{82} +(13.7671 - 51.3796i) q^{83} +(-13.8661 + 106.266i) q^{84} +(-1.18574 + 2.05377i) q^{86} +(19.7976 + 8.17381i) q^{87} +(-5.51857 + 20.5956i) q^{88} -22.5436i q^{89} +120.770 q^{91} +(75.5111 + 20.2331i) q^{92} +(77.7864 - 10.3316i) q^{93} +(-8.84580 - 5.10712i) q^{94} +(-16.4416 + 21.4781i) q^{96} +(-33.7192 - 9.03502i) q^{97} +(4.33107 + 4.33107i) q^{98} +(122.346 - 33.0837i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + 6 q^{3} - 24 q^{6} + 2 q^{7} + 24 q^{8} + 8 q^{11} + 30 q^{12} + 2 q^{13} + 28 q^{16} - 28 q^{17} - 48 q^{18} + 12 q^{21} - 14 q^{22} - 82 q^{23} - 112 q^{26} + 198 q^{27} + 88 q^{28} - 4 q^{31}+ \cdots + 1876 q^{98}+O(q^{100}) \) 40 * q + 2 * q^2 + 6 * q^3 - 24 * q^6 + 2 * q^7 + 24 * q^8 + 8 * q^11 + 30 * q^12 + 2 * q^13 + 28 * q^16 - 28 * q^17 - 48 * q^18 + 12 * q^21 - 14 * q^22 - 82 * q^23 - 112 * q^26 + 198 * q^27 + 88 * q^28 - 4 * q^31 + 14 * q^32 - 96 * q^33 + 264 * q^36 + 92 * q^37 - 330 * q^38 - 28 * q^41 - 498 * q^42 + 2 * q^43 - 136 * q^46 - 64 * q^47 + 510 * q^48 - 396 * q^51 + 74 * q^52 + 608 * q^53 - 192 * q^56 + 114 * q^57 - 30 * q^58 + 92 * q^61 + 100 * q^62 - 24 * q^63 + 588 * q^66 + 80 * q^67 - 626 * q^68 + 248 * q^71 + 162 * q^72 + 8 * q^73 - 96 * q^76 - 338 * q^77 - 1062 * q^78 + 204 * q^81 - 104 * q^82 - 370 * q^83 - 328 * q^86 - 534 * q^87 + 210 * q^88 + 152 * q^91 - 388 * q^92 + 1062 * q^93 - 876 * q^96 - 292 * q^97 + 1876 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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