LMFDB - Embedded newform 425.3.t.a.299.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,3,Mod(24,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 11]))

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

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

chi := DirichletCharacter("425.24");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	425.t (of order $16$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.5804112353$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			299.1
Root			$0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	425.299
Dual form			425.3.t.a.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.79690 - 1.15851i) q^{2} +(-0.451406 + 0.675577i) q^{3} +(3.65205 + 3.65205i) q^{4} +(2.04520 - 1.36656i) q^{6} +(1.53233 - 7.70353i) q^{7} +(-1.34942 - 3.25778i) q^{8} +(3.19151 + 7.70500i) q^{9} +O(q^{10})$	\(q+(-2.79690 - 1.15851i) q^{2} +(-0.451406 + 0.675577i) q^{3} +(3.65205 + 3.65205i) q^{4} +(2.04520 - 1.36656i) q^{6} +(1.53233 - 7.70353i) q^{7} +(-1.34942 - 3.25778i) q^{8} +(3.19151 + 7.70500i) q^{9} +(4.48649 + 6.71450i) q^{11} +(-4.11580 + 0.818684i) q^{12} +(0.798835 + 0.798835i) q^{13} +(-13.2104 + 19.7707i) q^{14} -9.98414i q^{16} +(-15.7060 - 6.50562i) q^{17} -25.2475i q^{18} +(-1.07647 + 2.59882i) q^{19} +(4.51262 + 4.51262i) q^{21} +(-4.76941 - 23.9774i) q^{22} +(4.76696 + 7.13426i) q^{23} +(2.81002 + 0.558947i) q^{24} +(-1.30880 - 3.15972i) q^{26} +(-13.8181 - 2.74858i) q^{27} +(33.7298 - 22.5376i) q^{28} +(0.599020 + 3.01148i) q^{29} +(-7.13254 + 10.6746i) q^{31} +(-16.9644 + 40.9557i) q^{32} -6.56139 q^{33} +(36.3911 + 36.3911i) q^{34} +(-16.4835 + 39.7946i) q^{36} +(-13.1509 + 19.6817i) q^{37} +(6.02153 - 6.02153i) q^{38} +(-0.900273 + 0.179075i) q^{39} +(21.4206 + 4.26082i) q^{41} +(-7.39341 - 17.8493i) q^{42} +(-21.4671 + 8.89197i) q^{43} +(-8.13684 + 40.9066i) q^{44} +(-5.06757 - 25.4764i) q^{46} +(55.6597 + 55.6597i) q^{47} +(6.74505 + 4.50690i) q^{48} +(-11.7262 - 4.85715i) q^{49} +(11.4848 - 7.67390i) q^{51} +5.83478i q^{52} +(55.5080 + 22.9922i) q^{53} +(35.4634 + 23.6959i) q^{54} +(-27.1642 + 5.40329i) q^{56} +(-1.26978 - 1.90036i) q^{57} +(1.81344 - 9.11677i) q^{58} +(25.3733 - 10.5100i) q^{59} +(7.11302 - 35.7596i) q^{61} +(32.3156 - 21.5926i) q^{62} +(64.2461 - 12.7793i) q^{63} +(66.6561 - 66.6561i) q^{64} +(18.3515 + 7.60145i) q^{66} +117.219 q^{67} +(-33.6001 - 81.1179i) q^{68} -6.97157 q^{69} +(88.1108 + 58.8738i) q^{71} +(20.7945 - 20.7945i) q^{72} +(11.9073 + 59.8620i) q^{73} +(59.5832 - 39.8122i) q^{74} +(-13.4223 + 5.55971i) q^{76} +(58.6001 - 24.2730i) q^{77} +(2.72543 + 0.542122i) q^{78} +(-52.9382 - 79.2276i) q^{79} +(-44.9799 + 44.9799i) q^{81} +(-54.9749 - 36.7331i) q^{82} +(-45.4770 + 109.791i) q^{83} +32.9607i q^{84} +70.3428 q^{86} +(-2.30489 - 0.954715i) q^{87} +(15.8202 - 23.6767i) q^{88} +(61.4534 + 61.4534i) q^{89} +(7.37792 - 4.92977i) q^{91} +(-8.64551 + 43.4639i) q^{92} +(-3.99184 - 9.63715i) q^{93} +(-91.1920 - 220.157i) q^{94} +(-20.0109 - 29.9484i) q^{96} +(-24.1185 + 4.79748i) q^{97} +(27.1699 + 27.1699i) q^{98} +(-37.4165 + 55.9978i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 8 q^{3} - 8 q^{6} + 8 q^{7} - 40 q^{8} + 16 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 8 * q^3 - 8 * q^6 + 8 * q^7 - 40 * q^8 + 16 * q^9	$ 8 q - 8 q^{2} - 8 q^{3} - 8 q^{6} + 8 q^{7} - 40 q^{8} + 16 q^{9} - 8 q^{11} + 40 q^{12} - 16 q^{13} - 8 q^{14} - 64 q^{21} + 56 q^{22} + 40 q^{23} + 80 q^{24} + 176 q^{26} + 16 q^{27} + 56 q^{28} - 48 q^{29} + 24 q^{31} - 88 q^{32} - 96 q^{33} + 136 q^{34} - 128 q^{36} - 128 q^{37} - 120 q^{38} - 48 q^{39} + 48 q^{41} - 128 q^{42} - 112 q^{43} - 120 q^{44} - 88 q^{46} + 192 q^{47} - 8 q^{48} - 16 q^{49} + 136 q^{51} + 128 q^{53} - 8 q^{54} - 120 q^{56} + 72 q^{57} + 32 q^{58} + 48 q^{59} - 160 q^{61} + 56 q^{62} + 168 q^{63} + 64 q^{64} - 8 q^{66} + 336 q^{67} + 272 q^{68} - 240 q^{69} + 40 q^{71} - 40 q^{72} + 48 q^{73} + 160 q^{74} + 80 q^{76} - 80 q^{77} - 304 q^{78} + 136 q^{79} - 424 q^{81} - 136 q^{82} - 336 q^{83} + 832 q^{86} - 80 q^{87} - 320 q^{88} - 160 q^{89} + 320 q^{91} - 184 q^{92} - 208 q^{93} - 32 q^{94} - 56 q^{96} - 104 q^{97} + 120 q^{98} + 224 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 - 8 * q^3 - 8 * q^6 + 8 * q^7 - 40 * q^8 + 16 * q^9 - 8 * q^11 + 40 * q^12 - 16 * q^13 - 8 * q^14 - 64 * q^21 + 56 * q^22 + 40 * q^23 + 80 * q^24 + 176 * q^26 + 16 * q^27 + 56 * q^28 - 48 * q^29 + 24 * q^31 - 88 * q^32 - 96 * q^33 + 136 * q^34 - 128 * q^36 - 128 * q^37 - 120 * q^38 - 48 * q^39 + 48 * q^41 - 128 * q^42 - 112 * q^43 - 120 * q^44 - 88 * q^46 + 192 * q^47 - 8 * q^48 - 16 * q^49 + 136 * q^51 + 128 * q^53 - 8 * q^54 - 120 * q^56 + 72 * q^57 + 32 * q^58 + 48 * q^59 - 160 * q^61 + 56 * q^62 + 168 * q^63 + 64 * q^64 - 8 * q^66 + 336 * q^67 + 272 * q^68 - 240 * q^69 + 40 * q^71 - 40 * q^72 + 48 * q^73 + 160 * q^74 + 80 * q^76 - 80 * q^77 - 304 * q^78 + 136 * q^79 - 424 * q^81 - 136 * q^82 - 336 * q^83 + 832 * q^86 - 80 * q^87 - 320 * q^88 - 160 * q^89 + 320 * q^91 - 184 * q^92 - 208 * q^93 - 32 * q^94 - 56 * q^96 - 104 * q^97 + 120 * q^98 + 224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{3}{16}\right)$

Coefficient data

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

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

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

$2$	−2.79690	−	1.15851i	−1.39845	−	0.579256i	−0.449100	−	0.893481i	$-0.648255\pi$
$2$	−2.79690	−	1.15851i	−1.39845	−	0.579256i	−0.949348	+	0.314225i	$0.898255\pi$
$3$	−0.451406	+	0.675577i	−0.150469	+	0.225192i	−0.899045	−	0.437857i	$-0.855738\pi$
$3$	−0.451406	+	0.675577i	−0.150469	+	0.225192i	0.748576	+	0.663049i	$0.230738\pi$
$4$	3.65205	+	3.65205i	0.913014	+	0.913014i
$5$		0			0
$5$		0			0
$6$	2.04520	−	1.36656i	0.340867	−	0.227760i
$7$	1.53233	−	7.70353i	0.218904	−	1.10050i	−0.702436	−	0.711746i	$-0.747904\pi$
$7$	1.53233	−	7.70353i	0.218904	−	1.10050i	0.921340	−	0.388757i	$-0.127096\pi$
$8$	−1.34942	−	3.25778i	−0.168677	−	0.407223i
$9$	3.19151	+	7.70500i	0.354613	+	0.856111i
$10$		0			0
$11$	4.48649	+	6.71450i	0.407863	+	0.610410i	0.977360	−	0.211584i	$-0.0678621\pi$
$11$	4.48649	+	6.71450i	0.407863	+	0.610410i	−0.569497	+	0.821993i	$0.692862\pi$
$12$	−4.11580	+	0.818684i	−0.342983	+	0.0682236i
$13$	0.798835	+	0.798835i	0.0614489	+	0.0614489i	0.737163	−	0.675715i	$-0.236165\pi$
$13$	0.798835	+	0.798835i	0.0614489	+	0.0614489i	−0.675715	+	0.737163i	$0.736165\pi$
$14$	−13.2104	+	19.7707i	−0.943599	+	1.41220i
$15$		0			0
$16$		−	9.98414i		−	0.624009i
$17$	−15.7060	−	6.50562i	−0.923880	−	0.382683i
$17$	−15.7060	−	6.50562i	−0.923880	−	0.382683i
$18$		−	25.2475i		−	1.40264i
$19$	−1.07647	+	2.59882i	−0.0566561	+	0.136780i	−0.949673	−	0.313244i	$-0.898584\pi$
$19$	−1.07647	+	2.59882i	−0.0566561	+	0.136780i	0.893017	+	0.450023i	$0.148584\pi$
$20$		0			0
$21$	4.51262	+	4.51262i	0.214887	+	0.214887i
$22$	−4.76941	−	23.9774i	−0.216791	−	1.08988i
$23$	4.76696	+	7.13426i	0.207259	+	0.310185i	0.920507	−	0.390727i	$-0.127776\pi$
$23$	4.76696	+	7.13426i	0.207259	+	0.310185i	−0.713247	+	0.700912i	$0.752776\pi$
$24$	2.81002	+	0.558947i	0.117084	+	0.0232895i
$25$		0			0
$26$	−1.30880	−	3.15972i	−0.0503384	−	0.121528i
$27$	−13.8181	−	2.74858i	−0.511780	−	0.101799i
$28$	33.7298	−	22.5376i	1.20464	−	0.804913i
$29$	0.599020	+	3.01148i	0.0206559	+	0.103844i	0.989738	−	0.142895i	$-0.0456410\pi$
$29$	0.599020	+	3.01148i	0.0206559	+	0.103844i	−0.969082	+	0.246739i	$0.920641\pi$
$30$		0			0
$31$	−7.13254	+	10.6746i	−0.230082	+	0.344342i	−0.928490	−	0.371358i	$-0.878892\pi$
$31$	−7.13254	+	10.6746i	−0.230082	+	0.344342i	0.698408	+	0.715700i	$0.253892\pi$
$32$	−16.9644	+	40.9557i	−0.530138	+	1.27987i
$33$	−6.56139			−0.198830
$34$	36.3911	+	36.3911i	1.07033	+	1.07033i
$35$		0			0
$36$	−16.4835	+	39.7946i	−0.457875	+	1.10541i
$37$	−13.1509	+	19.6817i	−0.355429	+	0.531938i	−0.965498	−	0.260411i	$-0.916142\pi$
$37$	−13.1509	+	19.6817i	−0.355429	+	0.531938i	0.610068	+	0.792349i	$0.291142\pi$
$38$	6.02153	−	6.02153i	0.158461	−	0.158461i
$39$	−0.900273	+	0.179075i	−0.0230839	+	0.00459168i
$40$		0			0
$41$	21.4206	+	4.26082i	0.522453	+	0.103922i	0.449270	−	0.893396i	$-0.351684\pi$
$41$	21.4206	+	4.26082i	0.522453	+	0.103922i	0.0731833	+	0.997319i	$0.476684\pi$
$42$	−7.39341	−	17.8493i	−0.176034	−	0.424982i
$43$	−21.4671	+	8.89197i	−0.499235	+	0.206790i	−0.618069	−	0.786124i	$-0.712085\pi$
$43$	−21.4671	+	8.89197i	−0.499235	+	0.206790i	0.118833	+	0.992914i	$0.462085\pi$
$44$	−8.13684	+	40.9066i	−0.184928	+	0.929696i
$45$		0			0
$46$	−5.06757	−	25.4764i	−0.110164	−	0.553834i
$47$	55.6597	+	55.6597i	1.18425	+	1.18425i	0.978632	+	0.205617i	$0.0659202\pi$
$47$	55.6597	+	55.6597i	1.18425	+	1.18425i	0.205617	+	0.978632i	$0.434080\pi$
$48$	6.74505	+	4.50690i	0.140522	+	0.0938937i
$49$	−11.7262	−	4.85715i	−0.239310	−	0.0991254i
$50$		0			0
$51$	11.4848	−	7.67390i	0.225192	−	0.150469i
$52$			5.83478i			0.112207i
$53$	55.5080	+	22.9922i	1.04732	+	0.433815i	0.838935	−	0.544232i	$-0.183179\pi$
$53$	55.5080	+	22.9922i	1.04732	+	0.433815i	0.208386	+	0.978047i	$0.433179\pi$
$54$	35.4634	+	23.6959i	0.656730	+	0.438813i
$55$		0			0
$56$	−27.1642	+	5.40329i	−0.485074	+	0.0964873i
$57$	−1.26978	−	1.90036i	−0.0222768	−	0.0333396i
$58$	1.81344	−	9.11677i	0.0312662	−	0.157186i
$59$	25.3733	−	10.5100i	0.430057	−	0.178135i	−0.157146	−	0.987575i	$-0.550229\pi$
$59$	25.3733	−	10.5100i	0.430057	−	0.178135i	0.587202	+	0.809440i	$0.300229\pi$
$60$		0			0
$61$	7.11302	−	35.7596i	0.116607	−	0.586223i	−0.877659	−	0.479286i	$-0.840896\pi$
$61$	7.11302	−	35.7596i	0.116607	−	0.586223i	0.994266	−	0.106937i	$-0.0341043\pi$
$62$	32.3156	−	21.5926i	0.521220	−	0.348268i
$63$	64.2461	−	12.7793i	1.01978	−	0.202847i
$64$	66.6561	−	66.6561i	1.04150	−	1.04150i
$65$		0			0
$66$	18.3515	+	7.60145i	0.278054	+	0.115174i
$67$	117.219			1.74953			0.874767	−	0.484544i	$-0.161015\pi$
$67$	117.219			1.74953			0.874767	+	0.484544i	$0.161015\pi$
$68$	−33.6001	−	81.1179i	−0.494119	−	1.19291i
$69$	−6.97157			−0.101037
$70$		0			0
$71$	88.1108	+	58.8738i	1.24100	+	0.829208i	0.990312	−	0.138861i	$-0.0443440\pi$
$71$	88.1108	+	58.8738i	1.24100	+	0.829208i	0.250685	+	0.968069i	$0.419344\pi$
$72$	20.7945	−	20.7945i	0.288813	−	0.288813i
$73$	11.9073	+	59.8620i	0.163114	+	0.820028i	0.972527	+	0.232789i	$0.0747851\pi$
$73$	11.9073	+	59.8620i	0.163114	+	0.820028i	−0.809414	+	0.587239i	$0.800215\pi$
$74$	59.5832	−	39.8122i	0.805178	−	0.538003i
$75$		0			0
$76$	−13.4223	+	5.55971i	−0.176610	+	0.0731541i
$77$	58.6001	−	24.2730i	0.761041	−	0.315233i
$78$	2.72543	+	0.542122i	0.0349414	+	0.00695029i
$79$	−52.9382	−	79.2276i	−0.670103	−	1.00288i	−0.998301	−	0.0582714i	$-0.981441\pi$
$79$	−52.9382	−	79.2276i	−0.670103	−	1.00288i	0.328197	−	0.944609i	$-0.393559\pi$
$80$		0			0
$81$	−44.9799	+	44.9799i	−0.555308	+	0.555308i
$82$	−54.9749	−	36.7331i	−0.670426	−	0.447964i
$83$	−45.4770	+	109.791i	−0.547916	+	1.32279i	0.371110	+	0.928589i	$0.378977\pi$
$83$	−45.4770	+	109.791i	−0.547916	+	1.32279i	−0.919026	+	0.394197i	$0.871023\pi$
$84$			32.9607i			0.392389i
$85$		0			0
$86$	70.3428			0.817939
$87$	−2.30489	−	0.954715i	−0.0264929	−	0.0109737i
$88$	15.8202	−	23.6767i	0.179776	−	0.269053i
$89$	61.4534	+	61.4534i	0.690488	+	0.690488i	0.962339	−	0.271851i	$-0.0876359\pi$
$89$	61.4534	+	61.4534i	0.690488	+	0.690488i	−0.271851	+	0.962339i	$0.587636\pi$
$90$		0			0
$91$	7.37792	−	4.92977i	0.0810761	−	0.0541733i
$92$	−8.64551	+	43.4639i	−0.0939729	+	0.472434i
$93$	−3.99184	−	9.63715i	−0.0429230	−	0.103625i
$94$	−91.1920	−	220.157i	−0.970128	−	2.34210i
$95$		0			0
$96$	−20.0109	−	29.9484i	−0.208447	−	0.311963i
$97$	−24.1185	+	4.79748i	−0.248645	+	0.0494585i	−0.317839	−	0.948145i	$-0.602957\pi$
$97$	−24.1185	+	4.79748i	−0.248645	+	0.0494585i	0.0691943	+	0.997603i	$0.477957\pi$
$98$	27.1699	+	27.1699i	0.277244	+	0.277244i
$99$	−37.4165	+	55.9978i	−0.377945	+	0.565635i
$100$		0			0
$101$			7.70266i			0.0762640i	0.999273	+	0.0381320i	$0.0121407\pi$
$101$			7.70266i			0.0762640i	−0.999273	+	0.0381320i	$0.987859\pi$
$102$	−41.0121	+	8.15782i	−0.402080	+	0.0799786i
$103$		−	41.5688i		−	0.403581i	−0.979429	−	0.201790i	$-0.935324\pi$
$103$		−	41.5688i		−	0.403581i	0.979429	−	0.201790i	$-0.0646760\pi$
$104$	1.52447	−	3.68039i	0.0146584	−	0.0353884i
$105$		0			0
$106$	−128.614	−	128.614i	−1.21333	−	1.21333i
$107$	17.2484	+	86.7136i	0.161200	+	0.810407i	0.973768	+	0.227541i	$0.0730687\pi$
$107$	17.2484	+	86.7136i	0.161200	+	0.810407i	−0.812568	+	0.582866i	$0.801931\pi$
$108$	−40.4263	−	60.5023i	−0.374318	−	0.560206i
$109$	−18.2754	−	3.63521i	−0.167665	−	0.0333506i	0.110544	−	0.993871i	$-0.464741\pi$
$109$	−18.2754	−	3.63521i	−0.167665	−	0.0333506i	−0.278209	+	0.960521i	$0.589741\pi$
$110$		0			0
$111$	−7.36011	−	17.7689i	−0.0663073	−	0.160080i
$112$	−76.9131	−	15.2990i	−0.686724	−	0.136598i
$113$	−50.4220	+	33.6909i	−0.446212	+	0.298150i	−0.758302	−	0.651903i	$-0.773971\pi$
$113$	−50.4220	+	33.6909i	−0.446212	+	0.298150i	0.312090	+	0.950053i	$0.398971\pi$
$114$	1.34985	+	6.78616i	0.0118408	+	0.0595277i
$115$		0			0
$116$	−8.81043	+	13.1857i	−0.0759520	+	0.113670i
$117$	−3.60553	+	8.70452i	−0.0308165	+	0.0743976i
$118$	−83.1426			−0.704598
$119$	−74.1828	+	111.022i	−0.623385	+	0.932962i
$120$		0			0
$121$	21.3487	−	51.5403i	0.176436	−	0.425953i
$122$	−61.3223	+	91.7753i	−0.502642	+	0.752257i
$123$	−12.5479	+	12.5479i	−0.102015	+	0.102015i
$124$	−65.0326	+	12.9358i	−0.524456	+	0.104321i
$125$		0			0
$126$	−194.495	−	38.6874i	−1.54361	−	0.307043i
$127$	45.6333	+	110.168i	0.359317	+	0.867468i	0.995396	+	0.0958444i	$0.0305551\pi$
$127$	45.6333	+	110.168i	0.359317	+	0.867468i	−0.636079	+	0.771624i	$0.719445\pi$
$128$	−99.8291	+	41.3506i	−0.779915	+	0.323051i
$129$	3.68317	−	18.5166i	0.0285517	−	0.143539i
$130$		0			0
$131$	33.4238	+	168.033i	0.255144	+	1.28269i	0.869605	+	0.493748i	$0.164373\pi$
$131$	33.4238	+	168.033i	0.255144	+	1.28269i	−0.614461	+	0.788947i	$0.710627\pi$
$132$	−23.9626	−	23.9626i	−0.181534	−	0.181534i
$133$	18.3706	+	12.2748i	0.138125	+	0.0922919i
$134$	−327.849	−	135.799i	−2.44663	−	1.01343i
$135$		0			0
$136$			59.9454i			0.440775i
$137$		−	173.113i		−	1.26360i	−0.775132	−	0.631799i	$-0.782317\pi$
$137$		−	173.113i		−	1.26360i	0.775132	−	0.631799i	$-0.217683\pi$
$138$	19.4988	+	8.07666i	0.141295	+	0.0585265i
$139$	149.307	+	99.7637i	1.07415	+	0.717724i	0.961193	−	0.275876i	$-0.0889678\pi$
$139$	149.307	+	99.7637i	1.07415	+	0.717724i	0.112957	+	0.993600i	$0.463968\pi$
$140$		0			0
$141$	−62.7276	+	12.4773i	−0.444876	+	0.0884914i
$142$	−178.231	−	266.741i	−1.25515	−	1.87846i
$143$	−1.77982	+	8.94775i	−0.0124463	+	0.0625717i
$144$	76.9278	−	31.8645i	0.534221	−	0.221281i
$145$		0			0
$146$	36.0474	−	181.223i	0.246900	−	1.24125i
$147$	8.57464	−	5.72939i	0.0583309	−	0.0389755i
$148$	−119.906	+	23.8509i	−0.810178	+	0.161154i
$149$	−31.6842	+	31.6842i	−0.212646	+	0.212646i	−0.805391	−	0.592745i	$-0.798044\pi$
$149$	−31.6842	+	31.6842i	−0.212646	+	0.212646i	0.592745	+	0.805391i	$0.298044\pi$
$150$		0			0
$151$	−121.384	−	50.2789i	−0.803868	−	0.332973i	−0.0573634	−	0.998353i	$-0.518269\pi$
$151$	−121.384	−	50.2789i	−0.803868	−	0.332973i	−0.746504	+	0.665380i	$0.768269\pi$
$152$	9.91898			0.0652565
$153$		−	141.777i		−	0.926648i
$154$	−192.019			−1.24688
$155$		0			0
$156$	−3.94184	−	2.63385i	−0.0252682	−	0.0168837i
$157$	−25.4694	+	25.4694i	−0.162225	+	0.162225i	−0.783552	−	0.621327i	$-0.786594\pi$
$157$	−25.4694	+	25.4694i	−0.162225	+	0.162225i	0.621327	+	0.783552i	$0.286594\pi$
$158$	56.2765	+	282.921i	0.356180	+	1.79064i
$159$	−40.5896	+	27.1211i	−0.255281	+	0.170573i
$160$		0			0
$161$	62.2635	−	25.7904i	0.386730	−	0.160189i
$162$	177.914	−	73.6944i	1.09823	−	0.454904i
$163$	−156.650	−	31.1596i	−0.961041	−	0.191163i	−0.310449	−	0.950590i	$-0.600479\pi$
$163$	−156.650	−	31.1596i	−0.961041	−	0.191163i	−0.650592	+	0.759427i	$0.725479\pi$
$164$	62.6684	+	93.7898i	0.382124	+	0.571889i
$165$		0			0
$166$	254.389	−	254.389i	1.53246	−	1.53246i
$167$	−92.0734	−	61.5214i	−0.551337	−	0.368392i	0.248478	−	0.968637i	$-0.420070\pi$
$167$	−92.0734	−	61.5214i	−0.551337	−	0.368392i	−0.799816	+	0.600246i	$0.795070\pi$
$168$	8.61173	−	20.7905i	0.0512603	−	0.123753i
$169$		−	167.724i		−	0.992448i
$170$		0			0
$171$	−23.4594			−0.137190
$172$	−110.873	−	45.9251i	−0.644611	−	0.267006i
$173$	−98.9216	+	148.047i	−0.571801	+	0.855761i	−0.998824	−	0.0484797i	$-0.984562\pi$
$173$	−98.9216	+	148.047i	−0.571801	+	0.855761i	0.427023	+	0.904241i	$0.359562\pi$
$174$	5.34048	+	5.34048i	0.0306924	+	0.0306924i
$175$		0			0
$176$	67.0386	−	44.7937i	0.380901	−	0.254510i
$177$	−4.35338	+	21.8859i	−0.0245954	+	0.123649i
$178$	−100.684	−	243.074i	−0.565642	−	1.36558i
$179$	−96.5028	−	232.978i	−0.539122	−	1.30155i	−0.925337	−	0.379146i	$-0.876218\pi$
$179$	−96.5028	−	232.978i	−0.539122	−	1.30155i	0.386215	−	0.922409i	$-0.373782\pi$
$180$		0			0
$181$	167.421	+	250.563i	0.924977	+	1.38433i	0.923197	+	0.384328i	$0.125567\pi$
$181$	167.421	+	250.563i	0.924977	+	1.38433i	0.00178027	+	0.999998i	$0.499433\pi$
$182$	−26.3465	+	5.24064i	−0.144761	+	0.0287947i
$183$	20.9475	+	20.9475i	0.114467	+	0.114467i
$184$	16.8092	−	25.1568i	0.0913546	−	0.136722i
$185$		0			0
$186$			31.5787i			0.169778i
$187$	−26.7826	−	134.645i	−0.143222	−	0.720027i
$188$			406.545i			2.16247i
$189$	−42.3476	+	102.236i	−0.224061	+	0.540931i
$190$		0			0
$191$	93.7287	+	93.7287i	0.490726	+	0.490726i	0.908535	−	0.417809i	$-0.137202\pi$
$191$	93.7287	+	93.7287i	0.490726	+	0.490726i	−0.417809	+	0.908535i	$0.637202\pi$
$192$	14.9423	+	75.1202i	0.0778247	+	0.391251i
$193$	−177.012	−	264.917i	−0.917161	−	1.37263i	−0.927957	−	0.372687i	$-0.878436\pi$
$193$	−177.012	−	264.917i	−0.917161	−	1.37263i	0.0107958	−	0.999942i	$-0.496564\pi$
$194$	73.0150	+	14.5236i	0.376366	+	0.0748639i
$195$		0			0
$196$	−25.0861	−	60.5632i	−0.127990	−	0.308996i
$197$	113.442	+	22.5650i	0.575847	+	0.114543i	0.474418	−	0.880300i	$-0.342659\pi$
$197$	113.442	+	22.5650i	0.575847	+	0.114543i	0.101429	+	0.994843i	$0.467659\pi$
$198$	169.524	−	113.273i	0.856184	−	0.572084i
$199$	57.7166	+	290.161i	0.290033	+	1.45809i	0.801088	+	0.598547i	$0.204255\pi$
$199$	57.7166	+	290.161i	0.290033	+	1.45809i	−0.511055	+	0.859548i	$0.670745\pi$
$200$		0			0
$201$	−52.9132	+	79.1902i	−0.263250	+	0.393981i
$202$	8.92363	−	21.5436i	0.0441764	−	0.106651i
$203$	24.1169			0.118802
$204$	69.9686	+	13.9176i	0.342983	+	0.0682236i
$205$		0			0
$206$	−48.1580	+	116.264i	−0.233777	+	0.564387i
$207$	−39.7556	+	59.4985i	−0.192056	+	0.287432i
$208$	7.97568	−	7.97568i	0.0383446	−	0.0383446i
$209$	−22.2793	+	4.43163i	−0.106600	+	0.0212040i
$210$		0			0
$211$	−225.325	−	44.8199i	−1.06789	−	0.212417i	−0.370300	−	0.928912i	$-0.620745\pi$
$211$	−225.325	−	44.8199i	−1.06789	−	0.212417i	−0.697592	+	0.716495i	$0.745745\pi$
$212$	118.750	+	286.687i	0.560140	+	1.35230i
$213$	−79.5475	+	32.9496i	−0.373462	+	0.154693i
$214$	52.2168	−	262.511i	0.244004	−	1.22669i
$215$		0			0
$216$	9.69205	+	48.7252i	0.0448706	+	0.225580i
$217$	71.3026	+	71.3026i	0.328584	+	0.328584i
$218$	46.9031	+	31.3396i	0.215152	+	0.143760i
$219$	−45.8164	−	18.9778i	−0.209207	−	0.0866565i
$220$		0			0
$221$	−7.34955	−	17.7434i	−0.0332559	−	0.0802868i
$222$			58.2245i			0.262272i
$223$	335.723	+	139.061i	1.50549	+	0.623593i	0.974621	−	0.223863i	$-0.0718669\pi$
$223$	335.723	+	139.061i	1.50549	+	0.623593i	0.530865	+	0.847456i	$0.321867\pi$
$224$	289.509	+	193.443i	1.29245	+	0.863587i
$225$		0			0
$226$	180.056	−	35.8155i	0.796710	−	0.158475i
$227$	−53.8478	−	80.5890i	−0.237215	−	0.355017i	0.693693	−	0.720271i	$-0.255982\pi$
$227$	−53.8478	−	80.5890i	−0.237215	−	0.355017i	−0.930908	+	0.365253i	$0.880982\pi$
$228$	2.30291	−	11.5775i	0.0101005	−	0.0507785i
$229$	334.120	−	138.397i	1.45904	−	0.604353i	0.494708	−	0.869059i	$-0.335275\pi$
$229$	334.120	−	138.397i	1.45904	−	0.604353i	0.964329	+	0.264706i	$0.0852749\pi$
$230$		0			0
$231$	−10.0542	+	50.5458i	−0.0435246	+	0.218813i
$232$	9.00241	−	6.01522i	0.0388035	−	0.0259277i
$233$	274.765	−	54.6542i	1.17925	−	0.234567i	0.433725	−	0.901045i	$-0.357199\pi$
$233$	274.765	−	54.6542i	1.17925	−	0.234567i	0.745525	+	0.666478i	$0.232199\pi$
$234$	20.1686	−	20.1686i	0.0861905	−	0.0861905i
$235$		0			0
$236$	131.048	+	54.2818i	0.555288	+	0.230008i
$237$	77.4209			0.326670
$238$	336.103	−	224.577i	1.41220	−	0.943599i
$239$	−328.551			−1.37469			−0.687345	−	0.726331i	$-0.741224\pi$
$239$	−328.551			−1.37469			−0.687345	+	0.726331i	$0.741224\pi$
$240$		0			0
$241$	−201.560	−	134.678i	−0.836349	−	0.558831i	0.0620186	−	0.998075i	$-0.480246\pi$
$241$	−201.560	−	134.678i	−0.836349	−	0.558831i	−0.898368	+	0.439244i	$0.855246\pi$
$242$	−119.420	+	119.420i	−0.493472	+	0.493472i
$243$	−34.8204	−	175.054i	−0.143294	−	0.720387i
$244$	156.573	−	104.619i	0.641693	−	0.428765i
$245$		0			0
$246$	49.6320	−	20.5583i	0.201756	−	0.0835701i
$247$	−2.93595	+	1.21611i	−0.0118864	+	0.00492352i
$248$	44.4003	+	8.83176i	0.179033	+	0.0356119i
$249$	−53.6438	−	80.2836i	−0.215437	−	0.322424i
$250$		0			0
$251$	−155.463	+	155.463i	−0.619375	+	0.619375i	−0.945371	−	0.325996i	$-0.894300\pi$
$251$	−155.463	+	155.463i	−0.619375	+	0.619375i	0.325996	+	0.945371i	$0.394300\pi$
$252$	281.301	+	187.959i	1.11627	+	0.745870i
$253$	−26.5161	+	64.0155i	−0.104807	+	0.253026i
$254$		−	360.996i		−	1.42125i
$255$		0			0
$256$	−49.9468			−0.195105
$257$	300.480	+	124.463i	1.16918	+	0.484292i	0.880923	−	0.473260i	$-0.156923\pi$
$257$	300.480	+	124.463i	1.16918	+	0.484292i	0.288261	+	0.957552i	$0.406923\pi$
$258$	−31.7531	+	47.5219i	−0.123074	+	0.184194i
$259$	131.467	+	131.467i	0.507595	+	0.507595i
$260$		0			0
$261$	−21.2917	+	14.2266i	−0.0815772	+	0.0545082i
$262$	101.185	−	508.693i	0.386203	−	1.94158i
$263$	−53.0907	−	128.172i	−0.201866	−	0.487347i	0.790233	−	0.612806i	$-0.209959\pi$
$263$	−53.0907	−	128.172i	−0.201866	−	0.487347i	−0.992099	+	0.125460i	$0.959959\pi$
$264$	8.85405	+	21.3756i	0.0335381	+	0.0809681i
$265$		0			0
$266$	−37.1600	−	55.6139i	−0.139699	−	0.209075i
$267$	−69.2570	+	13.7761i	−0.259389	+	0.0515957i
$268$	428.089	+	428.089i	1.59735	+	1.59735i
$269$	180.493	−	270.126i	0.670976	−	1.00419i	−0.327267	−	0.944932i	$-0.606128\pi$
$269$	180.493	−	270.126i	0.670976	−	1.00419i	0.998243	−	0.0592547i	$-0.0188724\pi$
$270$		0			0
$271$			19.1867i			0.0707996i	0.999373	+	0.0353998i	$0.0112705\pi$
$271$			19.1867i			0.0707996i	−0.999373	+	0.0353998i	$0.988730\pi$
$272$	−64.9530	+	156.810i	−0.238798	+	0.576509i
$273$			7.20968i			0.0264091i
$274$	−200.554	+	484.179i	−0.731947	+	1.76708i
$275$		0			0
$276$	−25.4606	−	25.4606i	−0.0922484	−	0.0922484i
$277$	60.0883	+	302.084i	0.216925	+	1.09056i	0.923700	+	0.383118i	$0.125150\pi$
$277$	60.0883	+	302.084i	0.216925	+	1.09056i	−0.706774	+	0.707439i	$0.749850\pi$
$278$	−302.018	−	452.003i	−1.08640	−	1.62591i
$279$	−105.011	−	20.8880i	−0.376385	−	0.0748676i
$280$		0			0
$281$	−33.1106	−	79.9361i	−0.117831	−	0.284470i	0.853949	−	0.520356i	$-0.174201\pi$
$281$	−33.1106	−	79.9361i	−0.117831	−	0.284470i	−0.971781	+	0.235886i	$0.924201\pi$
$282$	189.898	+	37.7730i	0.673396	+	0.133947i
$283$	6.22073	−	4.15656i	0.0219814	−	0.0146875i	−0.544531	−	0.838741i	$-0.683292\pi$
$283$	6.22073	−	4.15656i	0.0219814	−	0.0146875i	0.566512	+	0.824053i	$0.308292\pi$
$284$	106.775	+	536.796i	0.375969	+	1.89013i
$285$		0			0
$286$	15.3440	−	22.9640i	0.0536505	−	0.0802937i
$287$	65.6466	−	158.485i	0.228734	−	0.552213i
$288$	−369.706			−1.28370
$289$	204.354	+	204.354i	0.707107	+	0.707107i
$290$		0			0
$291$	7.64619	−	18.4595i	0.0262756	−	0.0634348i
$292$	−175.133	+	262.105i	−0.599771	+	0.897621i
$293$	54.4583	−	54.4583i	0.185864	−	0.185864i	−0.608041	−	0.793906i	$-0.708044\pi$
$293$	54.4583	−	54.4583i	0.185864	−	0.185864i	0.793906	+	0.608041i	$0.208044\pi$
$294$	−30.6200	+	6.09069i	−0.104150	+	0.0207166i
$295$		0			0
$296$	81.8647	+	16.2839i	0.276570	+	0.0550132i
$297$	−43.5392	−	105.113i	−0.146597	−	0.353915i
$298$	125.324	−	51.9110i	0.420551	−	0.174198i
$299$	−1.89108	+	9.50711i	−0.00632469	+	0.0317964i
$300$		0			0
$301$	35.6049	+	178.998i	0.118289	+	0.594677i
$302$	281.250	+	281.250i	0.931291	+	0.931291i
$303$	−5.20374	−	3.47703i	−0.0171741	−	0.0114753i
$304$	25.9470	+	10.7476i	0.0853519	+	0.0353539i
$305$		0			0
$306$	−164.251	+	396.536i	−0.536767	+	1.29587i
$307$		−	159.680i		−	0.520132i	−0.965591	−	0.260066i	$-0.916256\pi$
$307$		−	159.680i		−	0.520132i	0.965591	−	0.260066i	$-0.0837443\pi$
$308$	302.657	+	125.365i	0.982653	+	0.407028i
$309$	28.0829	+	18.7644i	0.0908832	+	0.0607262i
$310$		0			0
$311$	−326.615	+	64.9678i	−1.05021	+	0.208900i	−0.689879	−	0.723925i	$-0.742336\pi$
$311$	−326.615	+	64.9678i	−1.05021	+	0.208900i	−0.360331	+	0.932825i	$0.617336\pi$
$312$	1.79823	+	2.69125i	0.00576357	+	0.00862579i
$313$	76.9763	−	386.986i	0.245931	−	1.23638i	−0.638470	−	0.769647i	$-0.720432\pi$
$313$	76.9763	−	386.986i	0.245931	−	1.23638i	0.884400	−	0.466729i	$-0.154568\pi$
$314$	100.742	−	41.7286i	0.320834	−	0.132894i
$315$		0			0
$316$	96.0103	−	482.676i	0.303830	−	1.52746i
$317$	115.654	−	77.2775i	0.364839	−	0.243778i	−0.359615	−	0.933101i	$-0.617092\pi$
$317$	115.654	−	77.2775i	0.364839	−	0.243778i	0.724454	+	0.689323i	$0.242092\pi$
$318$	144.945	−	28.8314i	0.455802	−	0.0906647i
$319$	−17.5331	+	17.5331i	−0.0549627	+	0.0549627i
$320$		0			0
$321$	−66.3677	−	27.4904i	−0.206753	−	0.0856399i
$322$	−204.023			−0.633612
$323$	33.8138	−	33.8138i	0.104687	−	0.104687i
$324$	−328.538			−1.01401
$325$		0			0
$326$	402.034	+	268.631i	1.23323	+	0.824021i
$327$	10.7055	−	10.7055i	0.0327385	−	0.0327385i
$328$	−15.0245	−	75.5332i	−0.0458064	−	0.230284i
$329$	514.065	−	343.487i	1.56251	−	1.04403i
$330$		0			0
$331$	146.717	−	60.7720i	0.443252	−	0.183601i	−0.149883	−	0.988704i	$-0.547890\pi$
$331$	146.717	−	60.7720i	0.443252	−	0.183601i	0.593136	+	0.805103i	$0.297890\pi$
$332$	−567.048	+	234.879i	−1.70798	+	0.707467i
$333$	−193.619	−	38.5132i	−0.581438	−	0.115655i
$334$	186.246	+	278.737i	0.557624	+	0.834543i
$335$		0			0
$336$	45.0546	−	45.0546i	0.134091	−	0.134091i
$337$	−401.062	−	267.981i	−1.19009	−	0.795195i	−0.207008	−	0.978339i	$-0.566372\pi$
$337$	−401.062	−	267.981i	−1.19009	−	0.795195i	−0.983086	+	0.183144i	$0.941372\pi$
$338$	−194.310	+	469.106i	−0.574882	+	1.38789i
$339$		−	49.2722i		−	0.145346i
$340$		0			0
$341$	−103.675			−0.304031
$342$	65.6136	+	27.1781i	0.191853	+	0.0794680i
$343$	158.436	−	237.116i	0.461912	−	0.691299i
$344$	57.9362	+	57.9362i	0.168419	+	0.168419i
$345$		0			0
$346$	448.188	−	299.469i	1.29534	−	0.865518i
$347$	3.86080	−	19.4096i	0.0111262	−	0.0559353i	−0.974823	−	0.222979i	$-0.928422\pi$
$347$	3.86080	−	19.4096i	0.0111262	−	0.0559353i	0.985950	+	0.167043i	$0.0534220\pi$
$348$	−4.93090	−	11.9042i	−0.0141692	−	0.0342076i
$349$	149.801	+	361.651i	0.429229	+	1.03625i	0.979533	+	0.201286i	$0.0645120\pi$
$349$	149.801	+	361.651i	0.429229	+	1.03625i	−0.550304	+	0.834965i	$0.685488\pi$
$350$		0			0
$351$	−8.84268	−	13.2340i	−0.0251928	−	0.0377037i
$352$	−351.108	+	69.8398i	−0.997466	+	0.198408i
$353$	−138.024	−	138.024i	−0.391003	−	0.391003i	0.484042	−	0.875045i	$-0.339168\pi$
$353$	−138.024	−	138.024i	−0.391003	−	0.391003i	−0.875045	+	0.484042i	$0.839168\pi$
$354$	37.5311	−	56.1692i	0.106020	−	0.158670i
$355$		0			0
$356$			448.863i			1.26085i
$357$	−41.5176	−	100.232i	−0.116296	−	0.280763i
$358$			763.416i			2.13245i
$359$	−136.163	+	328.726i	−0.379284	+	0.915672i	0.612817	+	0.790225i	$0.290036\pi$
$359$	−136.163	+	328.726i	−0.379284	+	0.915672i	−0.992100	+	0.125447i	$0.959964\pi$
$360$		0			0
$361$	249.670	+	249.670i	0.691608	+	0.691608i
$362$	−177.978	−	894.758i	−0.491653	−	2.47171i
$363$	25.1825	+	37.6883i	0.0693733	+	0.103824i
$364$	44.9484	+	8.94078i	0.123485	+	0.0245626i
$365$		0			0
$366$	−34.3200	−	82.8558i	−0.0937705	−	0.226382i
$367$	−80.1568	−	15.9442i	−0.218411	−	0.0434446i	0.0846717	−	0.996409i	$-0.473016\pi$
$367$	−80.1568	−	15.9442i	−0.218411	−	0.0434446i	−0.303083	+	0.952964i	$0.598016\pi$
$368$	71.2294	−	47.5940i	0.193558	−	0.129331i
$369$	35.5345	+	178.644i	0.0962994	+	0.484130i
$370$		0			0
$371$	262.177	−	392.376i	0.706677	−	1.05762i
$372$	20.6170	−	49.7738i	0.0554220	−	0.133801i
$373$	76.8209			0.205954			0.102977	−	0.994684i	$-0.467163\pi$
$373$	76.8209			0.205954			0.102977	+	0.994684i	$0.467163\pi$
$374$	−81.0799	+	407.616i	−0.216791	+	1.08988i
$375$		0			0
$376$	106.219	−	256.436i	0.282498	−	0.682009i
$377$	−1.92716	+	2.88419i	−0.00511182	+	0.00765038i
$378$	236.883	−	236.883i	0.626676	−	0.626676i
$379$	−577.940	+	114.959i	−1.52491	+	0.303323i	−0.885169	−	0.465269i	$-0.845957\pi$
$379$	−577.940	+	114.959i	−1.52491	+	0.303323i	−0.639739	+	0.768592i	$0.720957\pi$
$380$		0			0
$381$	−95.0264	−	18.9019i	−0.249413	−	0.0496113i
$382$	−153.564	−	370.735i	−0.401999	−	0.970511i
$383$	−215.834	+	89.4016i	−0.563537	+	0.233424i	−0.646220	−	0.763151i	$-0.723651\pi$
$383$	−215.834	+	89.4016i	−0.563537	+	0.233424i	0.0826832	+	0.996576i	$0.473651\pi$
$384$	17.1280	−	86.1081i	0.0446041	−	0.224240i
$385$		0			0
$386$	188.175	+	946.017i	0.487499	+	2.45082i
$387$	−137.025	−	137.025i	−0.354070	−	0.354070i
$388$	−105.603	−	70.5616i	−0.272172	−	0.181860i
$389$	−372.916	−	154.467i	−0.958653	−	0.397087i	−0.152177	−	0.988353i	$-0.548628\pi$
$389$	−372.916	−	154.467i	−0.958653	−	0.397087i	−0.806477	+	0.591266i	$0.798628\pi$
$390$		0			0
$391$	−28.4569	−	143.062i	−0.0727797	−	0.365888i
$392$			44.7557i			0.114173i
$393$	−128.607	−	53.2707i	−0.327244	−	0.135549i
$394$	−291.143	−	194.536i	−0.738943	−	0.493746i
$395$		0			0
$396$	−341.154	+	67.8598i	−0.861501	+	0.171363i
$397$	146.553	+	219.332i	0.369151	+	0.552474i	0.968817	−	0.247776i	$-0.0796998\pi$
$397$	146.553	+	219.332i	0.369151	+	0.552474i	−0.599666	+	0.800251i	$0.704700\pi$
$398$	174.728	−	878.415i	0.439014	−	2.20707i
$399$	−16.5852	+	6.86980i	−0.0415668	+	0.0172175i
$400$		0			0
$401$	46.6830	−	234.691i	0.116416	−	0.585265i	−0.877904	−	0.478837i	$-0.841059\pi$
$401$	46.6830	−	234.691i	0.116416	−	0.585265i	0.994320	−	0.106428i	$-0.0339414\pi$
$402$	239.736	−	160.186i	0.596358	−	0.398473i
$403$	−14.2250	+	2.82952i	−0.0352977	+	0.00702114i
$404$	−28.1305	+	28.1305i	−0.0696300	+	0.0696300i
$405$		0			0
$406$	−67.4525	−	27.9397i	−0.166139	−	0.0688171i
$407$	−191.154			−0.469666
$408$	−40.4977	−	27.0597i	−0.0992590	−	0.0663228i
$409$	−259.903			−0.635461			−0.317730	−	0.948181i	$-0.602921\pi$
$409$	−259.903			−0.635461			−0.317730	+	0.948181i	$0.602921\pi$
$410$		0			0
$411$	116.951	+	78.1442i	0.284552	+	0.190132i
$412$	151.812	−	151.812i	0.368475	−	0.368475i
$413$	−42.0837	−	211.569i	−0.101898	−	0.512274i
$414$	180.122	−	120.354i	0.435078	−	0.290710i
$415$		0			0
$416$	−46.2687	+	19.1651i	−0.111223	+	0.0460700i
$417$	−134.796	+	55.8343i	−0.323252	+	0.133895i
$418$	67.4471	+	13.4161i	0.161357	+	0.0320958i
$419$	95.3087	+	142.640i	0.227467	+	0.340429i	0.927594	−	0.373590i	$-0.121873\pi$
$419$	95.3087	+	142.640i	0.227467	+	0.340429i	−0.700127	+	0.714018i	$0.746873\pi$
$420$		0			0
$421$	443.214	−	443.214i	1.05276	−	1.05276i	0.0542356	−	0.998528i	$-0.482728\pi$
$421$	443.214	−	443.214i	1.05276	−	1.05276i	0.998528	−	0.0542356i	$-0.0172722\pi$
$422$	578.287	+	386.399i	1.37035	+	0.915637i
$423$	−251.219	+	606.497i	−0.593899	+	1.43380i
$424$		−	211.859i		−	0.499668i
$425$		0			0
$426$	260.659			0.611875
$427$	−264.575	−	109.591i	−0.619614	−	0.256653i
$428$	−253.691	+	379.675i	−0.592735	+	0.887090i
$429$	−5.24147	−	5.24147i	−0.0122179	−	0.0122179i
$430$		0			0
$431$	−633.734	+	423.447i	−1.47038	+	0.982477i	−0.475684	+	0.879616i	$0.657799\pi$
$431$	−633.734	+	423.447i	−1.47038	+	0.982477i	−0.994696	+	0.102860i	$0.967201\pi$
$432$	−27.4422	+	137.961i	−0.0635237	+	0.319355i
$433$	−36.2305	−	87.4681i	−0.0836732	−	0.202005i	0.876505	−	0.481392i	$-0.159869\pi$
$433$	−36.2305	−	87.4681i	−0.0836732	−	0.202005i	−0.960179	+	0.279387i	$0.909869\pi$
$434$	−116.821	−	282.031i	−0.269173	−	0.649841i
$435$		0			0
$436$	−53.4669	−	80.0189i	−0.122630	−	0.183530i
$437$	−23.6721	+	4.70868i	−0.0541696	+	0.0107750i
$438$	106.158	+	106.158i	0.242369	+	0.242369i
$439$	20.5441	−	30.7465i	0.0467976	−	0.0700375i	−0.807333	−	0.590096i	$-0.799090\pi$
$439$	20.5441	−	30.7465i	0.0467976	−	0.0700375i	0.854131	+	0.520059i	$0.174090\pi$
$440$		0			0
$441$		−	105.852i		−	0.240027i
$442$			58.1410i			0.131541i
$443$			634.146i			1.43148i	0.698367	+	0.715740i	$0.253911\pi$
$443$			634.146i			1.43148i	−0.698367	+	0.715740i	$0.746089\pi$
$444$	38.0134	−	91.7724i	0.0856157	−	0.206695i
$445$		0			0
$446$	−777.880	−	777.880i	−1.74412	−	1.74412i
$447$	−7.10268	−	35.7076i	−0.0158897	−	0.0798828i
$448$	−411.348	−	615.626i	−0.918187	−	1.37416i
$449$	−433.336	−	86.1959i	−0.965114	−	0.191973i	−0.312713	−	0.949848i	$-0.601238\pi$
$449$	−433.336	−	86.1959i	−0.965114	−	0.191973i	−0.652400	+	0.757874i	$0.726238\pi$
$450$		0			0
$451$	67.4939	+	162.945i	0.149654	+	0.361296i
$452$	−307.185	−	61.1029i	−0.679613	−	0.135183i
$453$	88.7607	−	59.3080i	0.195940	−	0.130923i
$454$	57.2435	+	287.782i	0.126087	+	0.633882i
$455$		0			0
$456$	−4.47749	+	6.70103i	−0.00981905	+	0.0146953i
$457$	−102.104	+	246.501i	−0.223423	+	0.539390i	−0.995350	−	0.0963202i	$-0.969293\pi$
$457$	−102.104	+	246.501i	−0.223423	+	0.539390i	0.771928	+	0.635710i	$0.219293\pi$
$458$	−1094.83			−2.39046
$459$	199.145	+	133.064i	0.433866	+	0.289900i
$460$		0			0
$461$	172.768	−	417.100i	0.374769	−	0.904772i	−0.618159	−	0.786053i	$-0.712121\pi$
$461$	172.768	−	417.100i	0.374769	−	0.904772i	0.992928	−	0.118719i	$-0.0378787\pi$
$462$	86.6785	−	129.724i	0.187616	−	0.280787i
$463$	−57.1171	+	57.1171i	−0.123363	+	0.123363i	−0.766093	−	0.642730i	$-0.777802\pi$
$463$	−57.1171	+	57.1171i	−0.123363	+	0.123363i	0.642730	+	0.766093i	$0.277802\pi$
$464$	30.0670	−	5.98070i	0.0647996	−	0.0128894i
$465$		0			0
$466$	−831.808	−	165.457i	−1.78499	−	0.355058i
$467$	31.5580	+	76.1879i	0.0675761	+	0.163143i	0.954059	−	0.299617i	$-0.0968590\pi$
$467$	31.5580	+	76.1879i	0.0675761	+	0.163143i	−0.886483	+	0.462760i	$0.846859\pi$
$468$	−44.9569	+	18.6218i	−0.0960619	+	0.0397901i
$469$	179.617	−	902.998i	0.382979	−	1.92537i
$470$		0			0
$471$	−5.70949	−	28.7035i	−0.0121221	−	0.0609417i
$472$	−68.4785	−	68.4785i	−0.145082	−	0.145082i
$473$	−156.017	−	104.247i	−0.329846	−	0.220396i
$474$	−216.538	−	89.6931i	−0.456832	−	0.189226i
$475$		0			0
$476$	−676.380	+	134.540i	−1.42097	+	0.282648i
$477$			501.069i			1.05046i
$478$	918.923	+	380.630i	1.92243	+	0.796298i
$479$	−382.794	−	255.775i	−0.799153	−	0.533977i	0.0876357	−	0.996153i	$-0.472069\pi$
$479$	−382.794	−	255.775i	−0.799153	−	0.533977i	−0.886788	+	0.462176i	$0.847069\pi$
$480$		0			0
$481$	−26.2278	+	5.21704i	−0.0545277	+	0.0108462i
$482$	407.717	+	610.191i	0.845885	+	1.26596i
$483$	−10.6827	+	53.7057i	−0.0221174	+	0.111192i
$484$	266.195	−	110.261i	0.549989	−	0.227813i
$485$		0			0
$486$	−105.413	+	529.948i	−0.216900	+	1.09043i
$487$	−434.982	+	290.646i	−0.893187	+	0.596809i	−0.915223	−	0.402948i	$-0.867985\pi$
$487$	−434.982	+	290.646i	−0.893187	+	0.596809i	0.0220352	+	0.999757i	$0.492985\pi$
$488$	−126.095	+	25.0819i	−0.258392	+	0.0513974i
$489$	91.7633	−	91.7633i	0.187655	−	0.187655i
$490$		0			0
$491$	−451.862	−	187.167i	−0.920289	−	0.381196i	−0.128303	−	0.991735i	$-0.540953\pi$
$491$	−451.862	−	187.167i	−0.920289	−	0.381196i	−0.791986	+	0.610539i	$0.790953\pi$
$492$	−91.6511			−0.186283
$493$	10.1833	−	51.1951i	0.0206559	−	0.103844i
$494$	9.62041			0.0194745
$495$		0			0
$496$	106.577	+	71.2122i	0.214872	+	0.143573i
$497$	588.550	−	588.550i	1.18421	−	1.18421i
$498$	57.0266	+	286.692i	0.114511	+	0.575687i
$499$	421.610	−	281.711i	0.844910	−	0.564551i	−0.0560623	−	0.998427i	$-0.517855\pi$
$499$	421.610	−	281.711i	0.844910	−	0.564551i	0.900972	+	0.433876i	$0.142855\pi$
$500$		0			0
$501$	83.1249	−	34.4315i	0.165918	−	0.0687255i
$502$	614.921	−	254.709i	1.22494	−	0.507388i
$503$	661.484	+	131.577i	1.31508	+	0.261585i	0.802292	−	0.596932i	$-0.203614\pi$
$503$	661.484	+	131.577i	1.31508	+	0.261585i	0.512785	+	0.858517i	$0.328614\pi$
$504$	−128.327	−	192.055i	−0.254617	−	0.381062i
$505$		0			0
$506$	148.326	−	148.326i	0.293134	−	0.293134i
$507$	113.310	+	75.7115i	0.223492	+	0.149332i
$508$	−235.686	+	568.996i	−0.463949	+	1.12007i
$509$			349.504i			0.686648i	0.939217	+	0.343324i	$0.111553\pi$
$509$			349.504i			0.686648i	−0.939217	+	0.343324i	$0.888447\pi$
$510$		0			0
$511$	479.395			0.938150
$512$	539.012	+	223.266i	1.05276	+	0.436067i
$513$	22.0177	−	32.9519i	0.0429196	−	0.0642337i
$514$	−696.221	−	696.221i	−1.35451	−	1.35451i
$515$		0			0
$516$	81.0747	−	54.1724i	0.157121	−	0.104985i
$517$	−124.011	+	623.444i	−0.239866	+	1.20589i
$518$	−215.393	−	520.006i	−0.415818	−	1.00387i
$519$	−55.3631	−	133.658i	−0.106673	−	0.257530i
$520$		0			0
$521$	−175.223	−	262.240i	−0.336320	−	0.503339i	0.624307	−	0.781179i	$-0.285381\pi$
$521$	−175.223	−	262.240i	−0.336320	−	0.503339i	−0.960627	+	0.277840i	$0.910381\pi$
$522$	76.0323	−	15.1238i	0.145656	−	0.0289727i
$523$	145.221	+	145.221i	0.277669	+	0.277669i	0.832178	−	0.554509i	$-0.187094\pi$
$523$	145.221	+	145.221i	0.277669	+	0.277669i	−0.554509	+	0.832178i	$0.687094\pi$
$524$	−491.600	+	735.731i	−0.938168	+	1.40407i
$525$		0			0
$526$			419.991i			0.798461i
$527$	181.468	−	121.253i	0.344342	−	0.230082i
$528$			65.5098i			0.124072i
$529$	174.266	−	420.715i	0.329425	−	0.795302i
$530$		0			0
$531$	161.959	+	161.959i	0.305007	+	0.305007i
$532$	22.2620	+	111.919i	0.0418459	+	0.210373i
$533$	13.7078	+	20.5152i	0.0257182	+	0.0384901i
$534$	209.664	+	41.7048i	0.392630	+	0.0780989i
$535$		0			0
$536$	−158.177	−	381.873i	−0.295106	−	0.712450i
$537$	200.957	+	39.9728i	0.374221	+	0.0744372i
$538$	−817.764	+	546.412i	−1.52001	+	1.01564i
$539$	−19.9961	−	100.527i	−0.0370985	−	0.186507i
$540$		0			0
$541$	439.282	−	657.431i	0.811981	−	1.21522i	−0.161596	−	0.986857i	$-0.551664\pi$
$541$	439.282	−	657.431i	0.811981	−	1.21522i	0.973577	−	0.228358i	$-0.0733358\pi$
$542$	22.2280	−	53.6632i	0.0410111	−	0.0990096i
$543$	−244.849			−0.450919
$544$	532.885	−	532.885i	0.979568	−	0.979568i
$545$		0			0
$546$	8.35251	−	20.1647i	0.0152976	−	0.0369317i
$547$	523.758	−	783.860i	0.957511	−	1.43302i	0.0569051	−	0.998380i	$-0.481877\pi$
$547$	523.758	−	783.860i	0.957511	−	1.43302i	0.900606	−	0.434637i	$-0.143123\pi$
$548$	632.218	−	632.218i	1.15368	−	1.15368i
$549$	298.229	−	59.3214i	0.543222	−	0.108054i
$550$		0			0
$551$	−8.47111	−	1.68501i	−0.0153741	−	0.00305809i
$552$	9.40756	+	22.7119i	0.0170427	+	0.0411447i
$553$	−691.450	+	286.408i	−1.25036	+	0.517917i
$554$	181.908	−	914.512i	0.328353	−	1.65074i
$555$		0			0
$556$	180.934	+	909.619i	0.325422	+	1.63601i
$557$	−303.284	−	303.284i	−0.544495	−	0.544495i	0.380348	−	0.924843i	$-0.375804\pi$
$557$	−303.284	−	303.284i	−0.544495	−	0.544495i	−0.924843	+	0.380348i	$0.875804\pi$
$558$	269.507	+	180.079i	0.482987	+	0.322722i
$559$	−24.2519	−	10.0455i	−0.0433844	−	0.0179704i
$560$		0			0
$561$	103.053	+	42.6859i	0.183695	+	0.0760889i
$562$			261.932i			0.466071i
$563$	639.473	+	264.879i	1.13583	+	0.470477i	0.869759	−	0.493476i	$-0.164274\pi$
$563$	639.473	+	264.879i	1.13583	+	0.470477i	0.266072	+	0.963953i	$0.414274\pi$
$564$	−274.652	−	183.517i	−0.486972	−	0.325384i
$565$		0			0
$566$	−22.2142	+	4.41867i	−0.0392476	+	0.00780684i
$567$	277.580	+	415.428i	0.489559	+	0.732677i
$568$	72.8996	−	366.491i	0.128344	−	0.645231i
$569$	370.173	−	153.331i	0.650567	−	0.269474i	−0.0328958	−	0.999459i	$-0.510473\pi$
$569$	370.173	−	153.331i	0.650567	−	0.269474i	0.683463	+	0.729985i	$0.260473\pi$
$570$		0			0
$571$	127.142	−	639.187i	0.222666	−	1.11942i	−0.694065	−	0.719912i	$-0.744182\pi$
$571$	127.142	−	639.187i	0.222666	−	1.11942i	0.916731	−	0.399505i	$-0.130818\pi$
$572$	−39.1776	+	26.1777i	−0.0684924	+	0.0457651i
$573$	−105.631	+	21.0112i	−0.184347	+	0.0366688i
$574$	−367.214	+	367.214i	−0.639745	+	0.639745i
$575$		0			0
$576$	726.319	+	300.851i	1.26097	+	0.522311i
$577$	−684.109			−1.18563			−0.592815	−	0.805339i	$-0.701983\pi$
$577$	−684.109			−1.18563			−0.592815	+	0.805339i	$0.701983\pi$
$578$	−334.810	−	808.303i	−0.579256	−	1.39845i
$579$	258.876			0.447109
$580$		0			0
$581$	776.094	+	518.569i	1.33579	+	0.892546i
$582$	−42.7712	+	42.7712i	−0.0734900	+	0.0734900i
$583$	94.6550	+	475.863i	0.162359	+	0.816232i
$584$	178.950	−	119.570i	0.306420	−	0.204744i
$585$		0			0
$586$	−215.405	+	89.2236i	−0.367585	+	0.152259i
$587$	342.216	−	141.750i	0.582991	−	0.241483i	−0.0716408	−	0.997430i	$-0.522824\pi$
$587$	342.216	−	141.750i	0.582991	−	0.241483i	0.654632	+	0.755948i	$0.272824\pi$
$588$	52.2391	+	10.3910i	0.0888420	+	0.0176718i
$589$	−20.0634	−	30.0270i	−0.0340635	−	0.0509796i
$590$		0			0
$591$	−66.4527	+	66.4527i	−0.112441	+	0.112441i
$592$	196.505	+	131.300i	0.331934	+	0.221791i
$593$	242.416	−	585.245i	0.408797	−	0.986922i	−0.576658	−	0.816985i	$-0.695644\pi$
$593$	242.416	−	585.245i	0.408797	−	0.986922i	0.985455	−	0.169937i	$-0.0543564\pi$
$594$			344.431i			0.579850i
$595$		0			0
$596$	−231.425			−0.388297
$597$	−222.080	−	91.9883i	−0.371992	−	0.154084i
$598$	16.3033	−	24.3996i	0.0272630	−	0.0408020i
$599$	−315.855	−	315.855i	−0.527304	−	0.527304i	0.392463	−	0.919768i	$-0.371623\pi$
$599$	−315.855	−	315.855i	−0.527304	−	0.527304i	−0.919768	+	0.392463i	$0.871623\pi$
$600$		0			0
$601$	362.279	−	242.067i	0.602794	−	0.402774i	−0.216388	−	0.976307i	$-0.569428\pi$
$601$	362.279	−	242.067i	0.602794	−	0.402774i	0.819182	+	0.573533i	$0.194428\pi$
$602$	107.788	−	541.887i	0.179050	−	0.900145i
$603$	374.105	+	903.170i	0.620407	+	1.49779i
$604$	−259.680	−	626.922i	−0.429933	−	1.03795i
$605$		0			0
$606$	10.5261	+	15.7535i	0.0173699	+	0.0259958i
$607$	−622.400	+	123.803i	−1.02537	+	0.203959i	−0.679000	−	0.734139i	$-0.737586\pi$
$607$	−622.400	+	123.803i	−1.02537	+	0.203959i	−0.346371	+	0.938098i	$0.612586\pi$
$608$	−88.1749	−	88.1749i	−0.145025	−	0.145025i
$609$	−10.8865	+	16.2928i	−0.0178760	+	0.0267534i
$610$		0			0
$611$			88.9259i			0.145542i
$612$	517.778	−	517.778i	0.846042	−	0.846042i
$613$			692.422i			1.12956i	0.825240	+	0.564782i	$0.191040\pi$
$613$			692.422i			1.12956i	−0.825240	+	0.564782i	$0.808960\pi$
$614$	−184.992	+	446.610i	−0.301290	+	0.727377i
$615$		0			0
$616$	−158.152	−	158.152i	−0.256740	−	0.256740i
$617$	−52.3292	−	263.077i	−0.0848124	−	0.426381i	−0.999741	−	0.0227645i	$-0.992753\pi$
$617$	−52.3292	−	263.077i	−0.0848124	−	0.426381i	0.914928	−	0.403616i	$-0.132247\pi$
$618$	−56.8062	−	85.0165i	−0.0919195	−	0.137567i
$619$	153.549	+	30.5428i	0.248060	+	0.0493422i	0.317554	−	0.948240i	$-0.397138\pi$
$619$	153.549	+	30.5428i	0.248060	+	0.0493422i	−0.0694940	+	0.997582i	$0.522138\pi$
$620$		0			0
$621$	−46.2610	−	111.684i	−0.0744944	−	0.179845i
$622$	988.775	+	196.680i	1.58967	+	0.316205i
$623$	567.575	−	379.241i	0.911035	−	0.608734i
$624$	1.78791	+	8.98845i	0.00286525	+	0.0144046i
$625$		0			0
$626$	−663.623	+	993.182i	−1.06010	+	1.58655i
$627$	7.06311	−	17.0519i	0.0112649	−	0.0271959i
$628$	−186.031			−0.296228
$629$	334.589	−	223.565i	0.531938	−	0.355429i
$630$		0			0
$631$	−119.803	+	289.230i	−0.189862	+	0.458368i	−0.989933	−	0.141538i	$-0.954795\pi$
$631$	−119.803	+	289.230i	−0.189862	+	0.458368i	0.800071	+	0.599906i	$0.204795\pi$
$632$	−186.670	+	279.372i	−0.295365	+	0.442044i
$633$	131.992	−	131.992i	0.208519	−	0.208519i
$634$	−412.999	+	82.1506i	−0.651418	+	0.129575i
$635$		0			0
$636$	−247.283	−	49.1877i	−0.388810	−	0.0773392i
$637$	−5.48723	−	13.2473i	−0.00861418	−	0.0207965i
$638$	69.3506	−	28.7259i	0.108700	−	0.0450250i
$639$	−172.415	+	866.790i	−0.269820	+	1.35648i
$640$		0			0
$641$	−72.2074	−	363.011i	−0.112648	−	0.566320i	−0.995345	−	0.0963771i	$-0.969275\pi$
$641$	−72.2074	−	363.011i	−0.112648	−	0.566320i	0.882697	−	0.469943i	$-0.155725\pi$
$642$	153.776	+	153.776i	0.239526	+	0.239526i
$643$	182.915	+	122.220i	0.284471	+	0.190077i	0.689616	−	0.724175i	$-0.257779\pi$
$643$	182.915	+	122.220i	0.284471	+	0.190077i	−0.405146	+	0.914252i	$0.632779\pi$
$644$	321.577	+	133.202i	0.499344	+	0.206835i
$645$		0			0
$646$	−133.748	+	55.4001i	−0.207040	+	0.0857586i
$647$			769.098i			1.18871i	0.804201	+	0.594357i	$0.202593\pi$
$647$			769.098i			1.18871i	−0.804201	+	0.594357i	$0.797407\pi$
$648$	207.231	+	85.8381i	0.319802	+	0.132466i
$649$	184.407	+	123.217i	0.284140	+	0.189856i
$650$		0			0
$651$	−80.3568	+	15.9840i	−0.123436	+	0.0245529i
$652$	−458.297	−	685.889i	−0.702909	−	1.05198i
$653$	−8.27876	+	41.6201i	−0.0126780	+	0.0637368i	−0.986606	−	0.163119i	$-0.947845\pi$
$653$	−8.27876	+	41.6201i	−0.0126780	+	0.0637368i	0.973928	+	0.226856i	$0.0728446\pi$
$654$	−42.3446	+	17.5397i	−0.0647472	+	0.0268192i
$655$		0			0
$656$	42.5406	−	213.866i	0.0648485	−	0.326015i
$657$	−423.234	+	282.796i	−0.644192	+	0.430436i
$658$	−1835.72	+	365.148i	−2.78985	+	0.554936i
$659$	−472.719	+	472.719i	−0.717328	+	0.717328i	−0.968057	−	0.250729i	$-0.919330\pi$
$659$	−472.719	+	472.719i	−0.717328	+	0.717328i	0.250729	+	0.968057i	$0.419330\pi$
$660$		0			0
$661$	−380.158	−	157.467i	−0.575126	−	0.238225i	0.0761113	−	0.997099i	$-0.475750\pi$
$661$	−380.158	−	157.467i	−0.575126	−	0.238225i	−0.651237	+	0.758874i	$0.725750\pi$
$662$	−480.756			−0.726218
$663$	15.3046	+	3.04428i	0.0230839	+	0.00459168i
$664$	419.043			0.631089
$665$		0			0
$666$	496.914	+	332.027i	0.746116	+	0.498539i
$667$	−18.6292	+	18.6292i	−0.0279298	+	0.0279298i
$668$	−111.577	−	560.937i	−0.167032	−	0.839725i
$669$	−245.494	+	164.034i	−0.366957	+	0.245193i
$670$		0			0
$671$	272.020	−	112.675i	0.405395	−	0.167920i
$672$	−261.372	+	108.264i	−0.388946	+	0.161107i
$673$	−15.9051	−	3.16371i	−0.0236331	−	0.00470091i	0.183260	−	0.983065i	$-0.441335\pi$
$673$	−15.9051	−	3.16371i	−0.0236331	−	0.00470091i	−0.206893	+	0.978364i	$0.566335\pi$
$674$	811.269	+	1214.15i	1.20366	+	1.80141i
$675$		0			0
$676$	612.536	−	612.536i	0.906119	−	0.906119i
$677$	−854.921	−	571.240i	−1.26281	−	0.843782i	−0.269926	−	0.962881i	$-0.586999\pi$
$677$	−854.921	−	571.240i	−1.26281	−	0.843782i	−0.992882	+	0.119099i	$0.961999\pi$
$678$	−57.0825	+	137.809i	−0.0841924	+	0.203258i
$679$			193.149i			0.284461i
$680$		0			0
$681$	78.7512			0.115641
$682$	289.967	+	120.108i	0.425172	+	0.176112i
$683$	125.752	−	188.201i	0.184117	−	0.275551i	−0.727917	−	0.685666i	$-0.759511\pi$
$683$	125.752	−	188.201i	0.184117	−	0.275551i	0.912034	+	0.410114i	$0.134511\pi$
$684$	−85.6752	−	85.6752i	−0.125256	−	0.125256i
$685$		0			0
$686$	−717.830	+	479.639i	−1.04640	+	0.699181i
$687$	−57.3259	+	288.197i	−0.0834438	+	0.419500i
$688$	88.7787	+	214.331i	0.129039	+	0.311527i
$689$	25.9748	+	62.7087i	0.0376993	+	0.0910141i
$690$		0			0
$691$	−21.7058	−	32.4851i	−0.0314122	−	0.0470117i	0.815431	−	0.578854i	$-0.196500\pi$
$691$	−21.7058	−	32.4851i	−0.0314122	−	0.0470117i	−0.846843	+	0.531842i	$0.821500\pi$
$692$	−901.942	+	179.407i	−1.30338	+	0.259259i
$693$	374.046	+	374.046i	0.539749	+	0.539749i
$694$	−33.2845	+	49.8138i	−0.0479604	+	0.0717778i
$695$		0			0
$696$			8.79713i			0.0126395i
$697$	−308.711	−	206.274i	−0.442914	−	0.295946i
$698$		−	1185.05i		−	1.69778i
$699$	−87.1075	+	210.296i	−0.124617	+	0.300853i
$700$		0			0
$701$	−401.261	−	401.261i	−0.572412	−	0.572412i	0.360390	−	0.932802i	$-0.382644\pi$
$701$	−401.261	−	401.261i	−0.572412	−	0.572412i	−0.932802	+	0.360390i	$0.882644\pi$
$702$	9.40031	+	47.2585i	0.0133908	+	0.0673198i
$703$	−36.9927	−	55.3634i	−0.0526212	−	0.0787531i
$704$	746.614	+	148.511i	1.06053	+	0.210953i
$705$		0			0
$706$	226.136	+	545.941i	0.320306	+	0.773288i
$707$	59.3377	+	11.8030i	0.0839288	+	0.0166945i
$708$	−95.8273	+	64.0298i	−0.135349	+	0.0904375i
$709$	−55.6759	−	279.901i	−0.0785273	−	0.394783i	−0.999980	−	0.00629329i	$-0.997997\pi$
$709$	−55.6759	−	279.901i	−0.0785273	−	0.394783i	0.921453	−	0.388490i	$-0.127003\pi$
$710$		0			0
$711$	441.495	−	660.744i	0.620950	−	0.929317i
$712$	117.276	−	283.128i	0.164713	−	0.397652i
$713$	−110.156			−0.154496
$714$			328.438i			0.459998i
$715$		0			0
$716$	498.416	−	1203.28i	0.696112	−	1.68056i
$717$	148.310	−	221.961i	0.206848	−	0.309569i
$718$	761.667	−	761.667i	1.06082	−	1.06082i
$719$	−601.644	+	119.674i	−0.836779	+	0.166446i	−0.594838	−	0.803845i	$-0.702784\pi$
$719$	−601.644	+	119.674i	−0.836779	+	0.166446i	−0.241941	+	0.970291i	$0.577784\pi$
$720$		0			0
$721$	−320.226	−	63.6970i	−0.444142	−	0.0883453i
$722$	−409.056	−	987.549i	−0.566560	−	1.36780i
$723$	181.971	−	75.3748i	0.251689	−	0.104253i
$724$	−303.640	+	1526.50i	−0.419392	+	2.10842i
$725$		0			0
$726$	−26.7705	−	134.585i	−0.0368740	−	0.185378i
$727$	244.413	+	244.413i	0.336194	+	0.336194i	0.854933	−	0.518739i	$-0.173598\pi$
$727$	244.413	+	244.413i	0.336194	+	0.336194i	−0.518739	+	0.854933i	$0.673598\pi$
$728$	−26.0160	−	17.3833i	−0.0357363	−	0.0238782i
$729$	−394.941	−	163.590i	−0.541758	−	0.224403i
$730$		0			0
$731$	395.009			0.540368
$732$			153.003i			0.209020i
$733$	−1246.38	−	516.266i	−1.70038	−	0.704319i	−0.700421	−	0.713730i	$-0.747004\pi$
$733$	−1246.38	−	516.266i	−1.70038	−	0.704319i	−0.999956	+	0.00941053i	$0.997004\pi$
$734$	205.719	+	137.457i	0.280271	+	0.187271i
$735$		0			0
$736$	−373.058	+	74.2058i	−0.506872	+	0.100823i
$737$	525.901	+	787.066i	0.713569	+	1.06793i
$738$	107.575	−	540.816i	0.145766	−	0.732813i
$739$	−602.925	+	249.740i	−0.815866	+	0.337943i	−0.751292	−	0.659970i	$-0.770569\pi$
$739$	−602.925	+	249.740i	−0.815866	+	0.337943i	−0.0645741	+	0.997913i	$0.520569\pi$
$740$		0			0
$741$	0.503729	−	2.53241i	0.000679796	−	0.00341756i
$742$	−1187.86	+	793.700i	−1.60088	+	1.06968i
$743$	−218.711	+	43.5044i	−0.294362	+	0.0585523i	−0.340062	−	0.940403i	$-0.610448\pi$
$743$	−218.711	+	43.5044i	−0.294362	+	0.0585523i	0.0456999	+	0.998955i	$0.485448\pi$
$744$	−26.0091	+	26.0091i	−0.0349584	+	0.0349584i
$745$		0			0
$746$	−214.860	−	88.9980i	−0.288016	−	0.119300i
$747$	−991.082			−1.32675
$748$	393.920	−	589.542i	0.526631	−	0.788158i
$749$	694.430			0.927143
$750$		0			0
$751$	−373.353	−	249.467i	−0.497142	−	0.332180i	0.281592	−	0.959534i	$-0.409138\pi$
$751$	−373.353	−	249.467i	−0.497142	−	0.332180i	−0.778734	+	0.627355i	$0.784138\pi$
$752$	555.715	−	555.715i	0.738982	−	0.738982i
$753$	−34.8503	−	175.204i	−0.0462820	−	0.232675i
$754$	8.73143	−	5.83416i	0.0115802	−	0.00773761i
$755$		0			0
$756$	−528.027	+	218.716i	−0.698449	+	0.289307i
$757$	42.5792	−	17.6369i	0.0562473	−	0.0232984i	−0.354382	−	0.935101i	$-0.615309\pi$
$757$	42.5792	−	17.6369i	0.0562473	−	0.0232984i	0.410630	+	0.911802i	$0.365309\pi$
$758$	1749.62	+	348.021i	2.30821	+	0.459131i
$759$	−31.2779	−	46.8107i	−0.0412093	−	0.0616741i
$760$		0			0
$761$	−552.081	+	552.081i	−0.725467	+	0.725467i	−0.969713	−	0.244246i	$-0.921460\pi$
$761$	−552.081	+	552.081i	−0.725467	+	0.725467i	0.244246	+	0.969713i	$0.421460\pi$
$762$	243.881	+	162.956i	0.320054	+	0.213853i
$763$	−56.0079	+	135.215i	−0.0734048	+	0.177215i
$764$			684.604i			0.896079i
$765$		0			0
$766$	707.240			0.923289
$767$	28.6649	+	11.8734i	0.0373727	+	0.0154803i
$768$	22.5463	−	33.7429i	0.0293571	−	0.0439360i
$769$	625.504	+	625.504i	0.813400	+	0.813400i	0.985142	−	0.171742i	$-0.0549396\pi$
$769$	625.504	+	625.504i	0.813400	+	0.813400i	−0.171742	+	0.985142i	$0.554940\pi$
$770$		0			0
$771$	−219.723	+	146.814i	−0.284984	+	0.190420i
$772$	321.035	−	1613.95i	0.415848	−	2.09061i
$773$	−465.474	−	1123.75i	−0.602166	−	1.45376i	−0.871347	−	0.490667i	$-0.836753\pi$
$773$	−465.474	−	1123.75i	−0.602166	−	1.45376i	0.269181	−	0.963090i	$-0.413247\pi$
$774$	224.500	+	541.991i	0.290052	+	0.700247i
$775$		0			0
$776$	48.1751	+	72.0992i	0.0620813	+	0.0929113i
$777$	−148.161	+	29.4711i	−0.190683	+	0.0379293i
$778$	864.056	+	864.056i	1.11061	+	1.11061i
$779$	−34.1316	+	51.0816i	−0.0438146	+	0.0655733i
$780$		0			0
$781$			855.757i			1.09572i
$782$	−86.1486	+	433.098i	−0.110164	+	0.553834i
$783$		−	43.2592i		−	0.0552481i
$784$	−48.4944	+	117.076i	−0.0618551	+	0.149331i
$785$		0			0
$786$	297.985	+	297.985i	0.379116	+	0.379116i
$787$	−37.8601	−	190.336i	−0.0481069	−	0.241850i	0.949249	−	0.314527i	$-0.101846\pi$
$787$	−37.8601	−	190.336i	−0.0481069	−	0.241850i	−0.997356	+	0.0726771i	$0.976846\pi$
$788$	331.887	+	496.704i	0.421177	+	0.630336i
$789$	110.556	+	21.9909i	0.140121	+	0.0278718i
$790$		0			0
$791$	182.276	+	440.053i	0.230437	+	0.556324i
$792$	232.919	+	46.3305i	0.294090	+	0.0584981i
$793$	34.2481	−	22.8839i	0.0431881	−	0.0288573i
$794$	−155.795	−	783.233i	−0.196215	−	0.986440i
$795$		0			0
$796$	−848.899	+	1270.47i	−1.06646	+	1.59606i
$797$	−49.1164	+	118.577i	−0.0616266	+	0.148780i	−0.951693	−	0.307051i	$-0.900658\pi$
$797$	−49.1164	+	118.577i	−0.0616266	+	0.148780i	0.890066	+	0.455831i	$0.150658\pi$
$798$	54.3457			0.0681024
$799$	−512.088	−	1236.29i	−0.640911	−	1.54730i
$800$		0			0
$801$	−277.369	+	669.628i	−0.346278	+	0.835990i
$802$	−402.460	+	602.324i	−0.501821	+	0.751028i
$803$	−348.522	+	348.522i	−0.434025	+	0.434025i
$804$	−482.449	+	95.9651i	−0.600061	+	0.119360i
$805$		0			0
$806$	43.0638	+	8.56592i	0.0534290	+	0.0106277i
$807$	101.016	+	243.873i	0.125174	+	0.302197i
$808$	25.0936	−	10.3941i	0.0310564	−	0.0128640i
$809$	−68.1098	+	342.411i	−0.0841902	+	0.423253i	0.915587	+	0.402121i	$0.131727\pi$
$809$	−68.1098	+	342.411i	−0.0841902	+	0.423253i	−0.999777	+	0.0211316i	$0.993273\pi$
$810$		0			0
$811$	36.2150	+	182.065i	0.0446547	+	0.224494i	0.996668	−	0.0815613i	$-0.0259906\pi$
$811$	36.2150	+	182.065i	0.0446547	+	0.224494i	−0.952014	+	0.306056i	$0.900991\pi$
$812$	88.0762	+	88.0762i	0.108468	+	0.108468i
$813$	−12.9621	−	8.66099i	−0.0159435	−	0.0106531i
$814$	534.639	+	221.455i	0.656804	+	0.272057i
$815$		0			0
$816$	−76.6173	−	114.666i	−0.0938937	−	0.140522i
$817$		−	65.3610i		−	0.0800013i
$818$	726.923	+	301.101i	0.888659	+	0.368095i
$819$	61.5306	+	41.1134i	0.0751290	+	0.0501996i
$820$		0			0
$821$	1545.78	−	307.474i	1.88280	−	0.374512i	0.886669	−	0.462404i	$-0.153013\pi$
$821$	1545.78	−	307.474i	1.88280	−	0.374512i	0.996130	+	0.0878920i	$0.0280130\pi$
$822$	−236.569	−	354.051i	−0.287797	−	0.430718i
$823$	196.185	−	986.291i	0.238378	−	1.19841i	−0.657273	−	0.753653i	$-0.728290\pi$
$823$	196.185	−	986.291i	0.238378	−	1.19841i	0.895651	−	0.444757i	$-0.146710\pi$
$824$	−135.422	+	56.0937i	−0.164347	+	0.0680749i
$825$		0			0
$826$	−127.402	+	640.491i	−0.154239	+	0.775413i
$827$	1321.52	−	883.014i	1.59797	−	1.06773i	0.645216	−	0.764001i	$-0.276768\pi$
$827$	1321.52	−	883.014i	1.59797	−	1.06773i	0.952758	−	0.303731i	$-0.0982324\pi$
$828$	−362.481	+	72.1020i	−0.437780	+	0.0870798i
$829$	269.747	−	269.747i	0.325388	−	0.325388i	−0.525442	−	0.850830i	$-0.676100\pi$
$829$	269.747	−	269.747i	0.325388	−	0.325388i	0.850830	+	0.525442i	$0.176100\pi$
$830$		0			0
$831$	−231.205	−	95.7684i	−0.278225	−	0.115245i
$832$	106.494			0.127998
$833$	152.572	+	152.572i	0.183160	+	0.183160i
$834$	441.695			0.529611
$835$		0			0
$836$	−97.5499	−	65.1807i	−0.116686	−	0.0779674i
$837$	127.898	−	127.898i	0.152805	−	0.152805i
$838$	−101.319	−	509.365i	−0.120906	−	0.607834i
$839$	30.7798	−	20.5664i	0.0366862	−	0.0245130i	−0.537092	−	0.843524i	$-0.680477\pi$
$839$	30.7798	−	20.5664i	0.0366862	−	0.0245130i	0.573778	+	0.819011i	$0.305477\pi$
$840$		0			0
$841$	768.273	−	318.229i	0.913523	−	0.378393i
$842$	−1753.09	+	726.154i	−2.08206	+	0.862416i
$843$	68.9493	+	13.7149i	0.0817904	+	0.0162691i
$844$	−659.215	−	986.584i	−0.781060	−	1.16894i
$845$		0			0
$846$	1405.27	−	1405.27i	1.66107	−	1.66107i
$847$	−364.329	−	243.437i	−0.430141	−	0.287411i
$848$	229.557	−	554.200i	0.270704	−	0.653538i
$849$			6.07887i			0.00716004i
$850$		0			0
$851$	−203.104			−0.238665
$852$	−410.846	−	170.178i	−0.482213	−	0.199739i
$853$	−43.8137	+	65.5718i	−0.0513642	+	0.0768720i	−0.856263	−	0.516540i	$-0.827220\pi$
$853$	−43.8137	+	65.5718i	−0.0513642	+	0.0768720i	0.804899	+	0.593412i	$0.202220\pi$
$854$	613.028	+	613.028i	0.717831	+	0.717831i
$855$		0			0
$856$	259.219	−	173.204i	0.302825	−	0.202342i
$857$	129.947	−	653.288i	0.151630	−	0.762297i	−0.827880	−	0.560905i	$-0.810453\pi$
$857$	129.947	−	653.288i	0.151630	−	0.762297i	0.979511	−	0.201392i	$-0.0645465\pi$
$858$	8.58754	+	20.7322i	0.0100088	+	0.0241634i
$859$	530.649	+	1281.10i	0.617752	+	1.49138i	0.854308	+	0.519767i	$0.173981\pi$
$859$	530.649	+	1281.10i	0.617752	+	1.49138i	−0.236556	+	0.971618i	$0.576019\pi$
$860$		0			0
$861$	77.4355	+	115.890i	0.0899367	+	0.134600i
$862$	2263.06	−	450.150i	2.62536	−	0.522216i
$863$	375.548	+	375.548i	0.435166	+	0.435166i	0.890381	−	0.455215i	$-0.150438\pi$
$863$	375.548	+	375.548i	0.435166	+	0.435166i	−0.455215	+	0.890381i	$0.650438\pi$
$864$	346.986	−	519.301i	0.401604	−	0.601042i
$865$		0			0
$866$			286.613i			0.330962i
$867$	−230.303	+	45.8102i	−0.265632	+	0.0528376i
$868$			520.802i			0.600002i
$869$	294.467	−	710.907i	0.338858	−	0.818075i
$870$		0			0
$871$	93.6384	+	93.6384i	0.107507	+	0.107507i
$872$	12.8185	+	64.4428i	0.0147001	+	0.0739023i
$873$	−113.939	−	170.522i	−0.130515	−	0.195329i
$874$	71.6635	+	14.2548i	0.0819949	+	0.0163098i
$875$		0			0
$876$	−98.0161	−	236.632i	−0.111891	−	0.270128i
$877$	−243.780	−	48.4908i	−0.277970	−	0.0552917i	0.0541366	−	0.998534i	$-0.482759\pi$
$877$	−243.780	−	48.4908i	−0.277970	−	0.0552917i	−0.332107	+	0.943242i	$0.607759\pi$
$878$	−93.0800	+	62.1940i	−0.106014	+	0.0708360i
$879$	12.2080	+	61.3735i	0.0138885	+	0.0698220i
$880$		0			0
$881$	−81.3688	+	121.777i	−0.0923595	+	0.138226i	−0.874772	−	0.484535i	$-0.838989\pi$
$881$	−81.3688	+	121.777i	−0.0923595	+	0.138226i	0.782412	+	0.622761i	$0.213989\pi$
$882$	−122.631	+	296.057i	−0.139037	+	0.335665i
$883$	322.505			0.365237			0.182619	−	0.983184i	$-0.441543\pi$
$883$	322.505			0.365237			0.182619	+	0.983184i	$0.441543\pi$
$884$	37.9588	−	91.6407i	0.0429399	−	0.103666i
$885$		0			0
$886$	734.666	−	1773.64i	0.829194	−	2.00185i
$887$	34.9202	−	52.2618i	0.0393689	−	0.0589197i	−0.811263	−	0.584681i	$-0.801220\pi$
$887$	34.9202	−	52.2618i	0.0393689	−	0.0589197i	0.850632	+	0.525762i	$0.176220\pi$
$888$	−47.9552	+	47.9552i	−0.0540037	+	0.0540037i
$889$	918.610	−	182.723i	1.03331	−	0.205538i
$890$		0			0
$891$	−503.820	−	100.216i	−0.565454	−	0.112476i
$892$	718.221	+	1733.94i	0.805180	+	1.94388i
$893$	−204.565	+	84.7337i	−0.229077	+	0.0948866i
$894$	−21.5022	+	108.099i	−0.0240517	+	0.120916i
$895$		0			0
$896$	165.574	+	832.399i	0.184793	+	0.929016i
$897$	−5.56914	−	5.56914i	−0.00620863	−	0.00620863i
$898$	1112.14	+	743.106i	1.23846	+	0.827513i
$899$	−36.4189	−	15.0852i	−0.0405104	−	0.0167800i
$900$		0			0
$901$	−722.228	−	722.228i	−0.801585	−	0.801585i
$902$		−	533.932i		−	0.591942i
$903$	−136.999	−	56.7469i	−0.151715	−	0.0628426i
$904$	177.798	+	118.801i	0.196679	+	0.131417i
$905$		0			0
$906$	−316.964	+	63.0480i	−0.349850	+	0.0695894i
$907$	−122.120	−	182.765i	−0.134641	−	0.201505i	0.758022	−	0.652229i	$-0.226166\pi$
$907$	−122.120	−	182.765i	−0.134641	−	0.201505i	−0.892663	+	0.450724i	$0.851166\pi$
$908$	97.6601	−	490.970i	0.107555	−	0.540716i
$909$	−59.3490	+	24.5832i	−0.0652904	+	0.0270442i
$910$		0			0
$911$	98.5913	−	495.652i	0.108223	−	0.544074i	−0.888192	−	0.459473i	$-0.848038\pi$
$911$	98.5913	−	495.652i	0.108223	−	0.544074i	0.996415	−	0.0846014i	$-0.0269617\pi$
$912$	−18.9734	+	12.6776i	−0.0208042	+	0.0139009i
$913$	−941.226	+	187.221i	−1.03092	+	0.205062i
$914$	571.150	−	571.150i	0.624890	−	0.624890i
$915$		0			0
$916$	1725.66	+	714.790i	1.88390	+	0.780338i
$917$	1345.66			1.46746
$918$	−402.830	−	602.878i	−0.438813	−	0.656730i
$919$	930.196			1.01218			0.506091	−	0.862480i	$-0.331090\pi$
$919$	930.196			1.01218			0.506091	+	0.862480i	$0.331090\pi$
$920$		0			0
$921$	107.876	+	72.0807i	0.117130	+	0.0782635i
$922$	−966.431	+	966.431i	−1.04819	+	1.04819i
$923$	23.3556	+	117.416i	0.0253040	+	0.127212i
$924$	−221.315	+	147.878i	−0.239518	+	0.160041i
$925$		0			0
$926$	225.922	−	93.5798i	0.243976	−	0.101058i
$927$	320.288	−	132.667i	0.345510	−	0.143115i
$928$	−133.499	−	26.5547i	−0.143857	−	0.0286150i
$929$	−637.592	−	954.224i	−0.686321	−	1.02715i	−0.997058	−	0.0766557i	$-0.975576\pi$
$929$	−637.592	−	954.224i	−0.686321	−	1.02715i	0.310737	−	0.950496i	$-0.399424\pi$
$930$		0			0
$931$	25.2457	−	25.2457i	0.0271167	−	0.0271167i
$932$	1203.06	+	803.857i	1.29083	+	0.862508i
$933$	103.545	−	249.980i	0.110981	−	0.267932i
$934$		−	249.650i		−	0.267291i
$935$		0			0
$936$	33.2228			0.0354944
$937$	1249.07	+	517.380i	1.33305	+	0.552166i	0.931523	−	0.363682i	$-0.118481\pi$
$937$	1249.07	+	517.380i	1.33305	+	0.552166i	0.401524	+	0.915848i	$0.368481\pi$
$938$	−1548.51	+	2317.50i	−1.65086	+	2.47068i
$939$	226.691	+	226.691i	0.241418	+	0.241418i
$940$		0			0
$941$	−1529.70	+	1022.11i	−1.62561	+	1.08620i	−0.695743	+	0.718291i	$0.744925\pi$
$941$	−1529.70	+	1022.11i	−1.62561	+	1.08620i	−0.929864	+	0.367905i	$0.880075\pi$
$942$	−17.2846	+	86.8953i	−0.0183488	+	0.0922455i
$943$	71.7133	+	173.131i	0.0760480	+	0.183596i
$944$	−104.933	−	253.331i	−0.111158	−	0.268359i
$945$		0			0
$946$	315.592	+	472.317i	0.333607	+	0.499278i
$947$	38.5945	−	7.67691i	0.0407544	−	0.00810656i	−0.174671	−	0.984627i	$-0.555886\pi$
$947$	38.5945	−	7.67691i	0.0407544	−	0.00810656i	0.215425	+	0.976520i	$0.430886\pi$
$948$	282.745	+	282.745i	0.298255	+	0.298255i
$949$	−38.3079	+	57.3319i	−0.0403666	+	0.0604129i
$950$		0			0
$951$			113.017i			0.118840i
$952$	461.791	+	91.8559i	0.485074	+	0.0964873i
$953$		−	183.445i		−	0.192492i	−0.995358	−	0.0962458i	$-0.969317\pi$
$953$		−	183.445i		−	0.192492i	0.995358	−	0.0962458i	$-0.0306835\pi$
$954$	580.495	−	1401.44i	0.608485	−	1.46901i
$955$		0			0
$956$	−1199.89	−	1199.89i	−1.25511	−	1.25511i
$957$	−3.93041	−	19.7595i	−0.00410701	−	0.0206473i
$958$	774.317	+	1158.85i	0.808264	+	1.20965i
$959$	−1333.58	−	265.266i	−1.39059	−	0.276606i
$960$		0			0
$961$	304.685	+	735.574i	0.317050	+	0.765426i
$962$	79.4005	+	15.7937i	0.0825369	+	0.0164176i
$963$	−613.079	+	409.646i	−0.636635	+	0.425386i
$964$	−244.257	−	1227.96i	−0.253378	−	1.27382i
$965$		0			0
$966$	92.0972	−	137.833i	0.0953387	−	0.142684i
$967$	−489.471	+	1181.69i	−0.506175	+	1.22201i	0.439894	+	0.898050i	$0.355016\pi$
$967$	−489.471	+	1181.69i	−0.506175	+	1.22201i	−0.946069	+	0.323965i	$0.894984\pi$
$968$	−196.715			−0.203218
$969$	7.58007	+	38.1076i	0.00782257	+	0.0393267i
$970$		0			0
$971$	−349.777	+	844.437i	−0.360224	+	0.869657i	0.635043	+	0.772477i	$0.280982\pi$
$971$	−349.777	+	844.437i	−0.360224	+	0.869657i	−0.995267	+	0.0971803i	$0.969018\pi$
$972$	512.141	−	766.473i	0.526894	−	0.788553i
$973$	997.319	−	997.319i	1.02499	−	1.02499i
$974$	1553.32	−	308.974i	1.59478	−	0.317222i
$975$		0			0
$976$	−357.029	−	71.0174i	−0.365808	−	0.0727637i
$977$	−169.210	−	408.510i	−0.173194	−	0.418126i	0.813318	−	0.581820i	$-0.197659\pi$
$977$	−169.210	−	408.510i	−0.173194	−	0.418126i	−0.986511	+	0.163694i	$0.947659\pi$
$978$	−362.961	+	150.343i	−0.371126	+	0.153725i
$979$	−136.919	+	688.340i	−0.139856	+	0.703105i
$980$		0			0
$981$	−30.3170	−	152.414i	−0.0309042	−	0.155366i
$982$	1046.98	+	1046.98i	1.06617	+	1.06617i
$983$	−553.287	−	369.695i	−0.562856	−	0.376088i	0.241351	−	0.970438i	$-0.422410\pi$
$983$	−553.287	−	369.695i	−0.562856	−	0.376088i	−0.804207	+	0.594350i	$0.797410\pi$
$984$	57.8106	+	23.9459i	0.0587506	+	0.0243353i
$985$		0			0
$986$	−87.7920	+	131.390i	−0.0890385	+	0.133256i
$987$			502.343i			0.508959i
$988$	−15.1635	−	6.28094i	−0.0153477	−	0.00635723i
$989$	−165.770	−	110.764i	−0.167614	−	0.111996i
$990$		0			0
$991$	−1534.80	+	305.291i	−1.54874	+	0.308063i	−0.894096	−	0.447876i	$-0.852181\pi$
$991$	−1534.80	+	305.291i	−1.54874	+	0.308063i	−0.654642	+	0.755939i	$0.727181\pi$
$992$	−316.187	−	473.207i	−0.318736	−	0.477023i
$993$	−25.1726	+	126.551i	−0.0253500	+	0.127443i
$994$	−2327.96	+	964.271i	−2.34201	+	0.970092i
$995$		0			0
$996$	97.2901	−	489.110i	0.0976808	−	0.491075i
$997$	1280.55	−	855.639i	1.28441	−	0.858213i	0.289321	−	0.957232i	$-0.406570\pi$
$997$	1280.55	−	855.639i	1.28441	−	0.858213i	0.995086	+	0.0990189i	$0.0315704\pi$
$998$	−1505.57	+	299.476i	−1.50858	+	0.300076i
$999$	235.817	−	235.817i	0.236053	−	0.236053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.3.t.a.299.1		8
5.2	odd	4		425.3.u.b.401.1		8
5.3	odd	4		17.3.e.a.10.1	✓	8
5.4	even	2		425.3.t.c.299.1		8
15.8	even	4		153.3.p.b.10.1		8
17.12	odd	16		425.3.t.c.199.1		8
20.3	even	4		272.3.bh.c.129.1		8
85.3	even	16		289.3.e.i.158.1		8
85.8	odd	8		289.3.e.l.249.1		8
85.12	even	16		425.3.u.b.301.1		8
85.13	odd	4		289.3.e.m.75.1		8
85.23	even	16		289.3.e.d.224.1		8
85.28	even	16		289.3.e.b.224.1		8
85.29	odd	16	inner	425.3.t.a.199.1		8
85.33	odd	4		289.3.e.c.214.1		8
85.38	odd	4		289.3.e.i.75.1		8
85.43	odd	8		289.3.e.k.249.1		8
85.48	even	16		289.3.e.m.158.1		8
85.53	odd	8		289.3.e.d.40.1		8
85.58	even	16		289.3.e.k.65.1		8
85.63	even	16		17.3.e.a.12.1	yes	8
85.73	even	16		289.3.e.c.131.1		8
85.78	even	16		289.3.e.l.65.1		8
85.83	odd	8		289.3.e.b.40.1		8
255.233	odd	16		153.3.p.b.46.1		8
340.63	odd	16		272.3.bh.c.97.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.a.10.1	✓	8	5.3	odd	4
17.3.e.a.12.1	yes	8	85.63	even	16
153.3.p.b.10.1		8	15.8	even	4
153.3.p.b.46.1		8	255.233	odd	16
272.3.bh.c.97.1		8	340.63	odd	16
272.3.bh.c.129.1		8	20.3	even	4
289.3.e.b.40.1		8	85.83	odd	8
289.3.e.b.224.1		8	85.28	even	16
289.3.e.c.131.1		8	85.73	even	16
289.3.e.c.214.1		8	85.33	odd	4
289.3.e.d.40.1		8	85.53	odd	8
289.3.e.d.224.1		8	85.23	even	16
289.3.e.i.75.1		8	85.38	odd	4
289.3.e.i.158.1		8	85.3	even	16
289.3.e.k.65.1		8	85.58	even	16
289.3.e.k.249.1		8	85.43	odd	8
289.3.e.l.65.1		8	85.78	even	16
289.3.e.l.249.1		8	85.8	odd	8
289.3.e.m.75.1		8	85.13	odd	4
289.3.e.m.158.1		8	85.48	even	16
425.3.t.a.199.1		8	85.29	odd	16	inner
425.3.t.a.299.1		8	1.1	even	1	trivial
425.3.t.c.199.1		8	17.12	odd	16
425.3.t.c.299.1		8	5.4	even	2
425.3.u.b.301.1		8	85.12	even	16
425.3.u.b.401.1		8	5.2	odd	4

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	425.t (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.79690 - 1.15851i) q^{2} +(-0.451406 + 0.675577i) q^{3} +(3.65205 + 3.65205i) q^{4} +(2.04520 - 1.36656i) q^{6} +(1.53233 - 7.70353i) q^{7} +(-1.34942 - 3.25778i) q^{8} +(3.19151 + 7.70500i) q^{9} +O(q^{10})\)	\(q+(-2.79690 - 1.15851i) q^{2} +(-0.451406 + 0.675577i) q^{3} +(3.65205 + 3.65205i) q^{4} +(2.04520 - 1.36656i) q^{6} +(1.53233 - 7.70353i) q^{7} +(-1.34942 - 3.25778i) q^{8} +(3.19151 + 7.70500i) q^{9} +(4.48649 + 6.71450i) q^{11} +(-4.11580 + 0.818684i) q^{12} +(0.798835 + 0.798835i) q^{13} +(-13.2104 + 19.7707i) q^{14} -9.98414i q^{16} +(-15.7060 - 6.50562i) q^{17} -25.2475i q^{18} +(-1.07647 + 2.59882i) q^{19} +(4.51262 + 4.51262i) q^{21} +(-4.76941 - 23.9774i) q^{22} +(4.76696 + 7.13426i) q^{23} +(2.81002 + 0.558947i) q^{24} +(-1.30880 - 3.15972i) q^{26} +(-13.8181 - 2.74858i) q^{27} +(33.7298 - 22.5376i) q^{28} +(0.599020 + 3.01148i) q^{29} +(-7.13254 + 10.6746i) q^{31} +(-16.9644 + 40.9557i) q^{32} -6.56139 q^{33} +(36.3911 + 36.3911i) q^{34} +(-16.4835 + 39.7946i) q^{36} +(-13.1509 + 19.6817i) q^{37} +(6.02153 - 6.02153i) q^{38} +(-0.900273 + 0.179075i) q^{39} +(21.4206 + 4.26082i) q^{41} +(-7.39341 - 17.8493i) q^{42} +(-21.4671 + 8.89197i) q^{43} +(-8.13684 + 40.9066i) q^{44} +(-5.06757 - 25.4764i) q^{46} +(55.6597 + 55.6597i) q^{47} +(6.74505 + 4.50690i) q^{48} +(-11.7262 - 4.85715i) q^{49} +(11.4848 - 7.67390i) q^{51} +5.83478i q^{52} +(55.5080 + 22.9922i) q^{53} +(35.4634 + 23.6959i) q^{54} +(-27.1642 + 5.40329i) q^{56} +(-1.26978 - 1.90036i) q^{57} +(1.81344 - 9.11677i) q^{58} +(25.3733 - 10.5100i) q^{59} +(7.11302 - 35.7596i) q^{61} +(32.3156 - 21.5926i) q^{62} +(64.2461 - 12.7793i) q^{63} +(66.6561 - 66.6561i) q^{64} +(18.3515 + 7.60145i) q^{66} +117.219 q^{67} +(-33.6001 - 81.1179i) q^{68} -6.97157 q^{69} +(88.1108 + 58.8738i) q^{71} +(20.7945 - 20.7945i) q^{72} +(11.9073 + 59.8620i) q^{73} +(59.5832 - 39.8122i) q^{74} +(-13.4223 + 5.55971i) q^{76} +(58.6001 - 24.2730i) q^{77} +(2.72543 + 0.542122i) q^{78} +(-52.9382 - 79.2276i) q^{79} +(-44.9799 + 44.9799i) q^{81} +(-54.9749 - 36.7331i) q^{82} +(-45.4770 + 109.791i) q^{83} +32.9607i q^{84} +70.3428 q^{86} +(-2.30489 - 0.954715i) q^{87} +(15.8202 - 23.6767i) q^{88} +(61.4534 + 61.4534i) q^{89} +(7.37792 - 4.92977i) q^{91} +(-8.64551 + 43.4639i) q^{92} +(-3.99184 - 9.63715i) q^{93} +(-91.1920 - 220.157i) q^{94} +(-20.0109 - 29.9484i) q^{96} +(-24.1185 + 4.79748i) q^{97} +(27.1699 + 27.1699i) q^{98} +(-37.4165 + 55.9978i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 8 q^{3} - 8 q^{6} + 8 q^{7} - 40 q^{8} + 16 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 8 * q^3 - 8 * q^6 + 8 * q^7 - 40 * q^8 + 16 * q^9	\( 8 q - 8 q^{2} - 8 q^{3} - 8 q^{6} + 8 q^{7} - 40 q^{8} + 16 q^{9} - 8 q^{11} + 40 q^{12} - 16 q^{13} - 8 q^{14} - 64 q^{21} + 56 q^{22} + 40 q^{23} + 80 q^{24} + 176 q^{26} + 16 q^{27} + 56 q^{28} - 48 q^{29} + 24 q^{31} - 88 q^{32} - 96 q^{33} + 136 q^{34} - 128 q^{36} - 128 q^{37} - 120 q^{38} - 48 q^{39} + 48 q^{41} - 128 q^{42} - 112 q^{43} - 120 q^{44} - 88 q^{46} + 192 q^{47} - 8 q^{48} - 16 q^{49} + 136 q^{51} + 128 q^{53} - 8 q^{54} - 120 q^{56} + 72 q^{57} + 32 q^{58} + 48 q^{59} - 160 q^{61} + 56 q^{62} + 168 q^{63} + 64 q^{64} - 8 q^{66} + 336 q^{67} + 272 q^{68} - 240 q^{69} + 40 q^{71} - 40 q^{72} + 48 q^{73} + 160 q^{74} + 80 q^{76} - 80 q^{77} - 304 q^{78} + 136 q^{79} - 424 q^{81} - 136 q^{82} - 336 q^{83} + 832 q^{86} - 80 q^{87} - 320 q^{88} - 160 q^{89} + 320 q^{91} - 184 q^{92} - 208 q^{93} - 32 q^{94} - 56 q^{96} - 104 q^{97} + 120 q^{98} + 224 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 8 * q^3 - 8 * q^6 + 8 * q^7 - 40 * q^8 + 16 * q^9 - 8 * q^11 + 40 * q^12 - 16 * q^13 - 8 * q^14 - 64 * q^21 + 56 * q^22 + 40 * q^23 + 80 * q^24 + 176 * q^26 + 16 * q^27 + 56 * q^28 - 48 * q^29 + 24 * q^31 - 88 * q^32 - 96 * q^33 + 136 * q^34 - 128 * q^36 - 128 * q^37 - 120 * q^38 - 48 * q^39 + 48 * q^41 - 128 * q^42 - 112 * q^43 - 120 * q^44 - 88 * q^46 + 192 * q^47 - 8 * q^48 - 16 * q^49 + 136 * q^51 + 128 * q^53 - 8 * q^54 - 120 * q^56 + 72 * q^57 + 32 * q^58 + 48 * q^59 - 160 * q^61 + 56 * q^62 + 168 * q^63 + 64 * q^64 - 8 * q^66 + 336 * q^67 + 272 * q^68 - 240 * q^69 + 40 * q^71 - 40 * q^72 + 48 * q^73 + 160 * q^74 + 80 * q^76 - 80 * q^77 - 304 * q^78 + 136 * q^79 - 424 * q^81 - 136 * q^82 - 336 * q^83 + 832 * q^86 - 80 * q^87 - 320 * q^88 - 160 * q^89 + 320 * q^91 - 184 * q^92 - 208 * q^93 - 32 * q^94 - 56 * q^96 - 104 * q^97 + 120 * q^98 + 224 * q^99

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