LMFDB - Embedded newform 17.3.e.a.12.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,3,Mod(3,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(16))

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

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

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

chi := DirichletCharacter("17.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	17.e (of order $16$, degree $8$, 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:	$0.463216449413$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			12.1
Root			$0.382683 - 0.923880i$ of defining polynomial
Character	$\chi$	$=$	17.12
Dual form			17.3.e.a.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15851 - 2.79690i) q^{2} +(-0.675577 + 0.451406i) q^{3} +(-3.65205 + 3.65205i) q^{4} +(7.87510 + 1.56645i) q^{5} +(2.04520 + 1.36656i) q^{6} +(-7.70353 + 1.53233i) q^{7} +(3.25778 + 1.34942i) q^{8} +(-3.19151 + 7.70500i) q^{9} +O(q^{10})$	\(q+(-1.15851 - 2.79690i) q^{2} +(-0.675577 + 0.451406i) q^{3} +(-3.65205 + 3.65205i) q^{4} +(7.87510 + 1.56645i) q^{5} +(2.04520 + 1.36656i) q^{6} +(-7.70353 + 1.53233i) q^{7} +(3.25778 + 1.34942i) q^{8} +(-3.19151 + 7.70500i) q^{9} +(-4.74219 - 23.8406i) q^{10} +(4.48649 - 6.71450i) q^{11} +(0.818684 - 4.11580i) q^{12} +(-0.798835 - 0.798835i) q^{13} +(13.2104 + 19.7707i) q^{14} +(-6.02734 + 2.49661i) q^{15} +9.98414i q^{16} +(-6.50562 - 15.7060i) q^{17} +25.2475 q^{18} +(1.07647 + 2.59882i) q^{19} +(-34.4811 + 23.0395i) q^{20} +(4.51262 - 4.51262i) q^{21} +(-23.9774 - 4.76941i) q^{22} +(-7.13426 - 4.76696i) q^{23} +(-2.81002 + 0.558947i) q^{24} +(36.4664 + 15.1049i) q^{25} +(-1.30880 + 3.15972i) q^{26} +(-2.74858 - 13.8181i) q^{27} +(22.5376 - 33.7298i) q^{28} +(-0.599020 + 3.01148i) q^{29} +(13.9655 + 13.9655i) q^{30} +(-7.13254 - 10.6746i) q^{31} +(40.9557 - 16.9644i) q^{32} +6.56139i q^{33} +(-36.3911 + 36.3911i) q^{34} -63.0663 q^{35} +(-16.4835 - 39.7946i) q^{36} +(19.6817 - 13.1509i) q^{37} +(6.02153 - 6.02153i) q^{38} +(0.900273 + 0.179075i) q^{39} +(23.5416 + 15.7300i) q^{40} +(21.4206 - 4.26082i) q^{41} +(-17.8493 - 7.39341i) q^{42} +(-8.89197 + 21.4671i) q^{43} +(8.13684 + 40.9066i) q^{44} +(-37.2030 + 55.6783i) q^{45} +(-5.06757 + 25.4764i) q^{46} +(55.6597 + 55.6597i) q^{47} +(-4.50690 - 6.74505i) q^{48} +(11.7262 - 4.85715i) q^{49} -119.492i q^{50} +(11.4848 + 7.67390i) q^{51} +5.83478 q^{52} +(-22.9922 - 55.5080i) q^{53} +(-35.4634 + 23.6959i) q^{54} +(45.8495 - 45.8495i) q^{55} +(-27.1642 - 5.40329i) q^{56} +(-1.90036 - 1.26978i) q^{57} +(9.11677 - 1.81344i) q^{58} +(-25.3733 - 10.5100i) q^{59} +(12.8944 - 31.1299i) q^{60} +(7.11302 + 35.7596i) q^{61} +(-21.5926 + 32.3156i) q^{62} +(12.7793 - 64.2461i) q^{63} +(-66.6561 - 66.6561i) q^{64} +(-5.03957 - 7.54224i) q^{65} +(18.3515 - 7.60145i) q^{66} +117.219i q^{67} +(81.1179 + 33.6001i) q^{68} +6.97157 q^{69} +(73.0632 + 176.390i) q^{70} +(88.1108 - 58.8738i) q^{71} +(-20.7945 + 20.7945i) q^{72} +(-59.8620 - 11.9073i) q^{73} +(-59.5832 - 39.8122i) q^{74} +(-31.4543 + 6.25665i) q^{75} +(-13.4223 - 5.55971i) q^{76} +(-24.2730 + 58.6001i) q^{77} +(-0.542122 - 2.72543i) q^{78} +(52.9382 - 79.2276i) q^{79} +(-15.6397 + 78.6261i) q^{80} +(-44.9799 - 44.9799i) q^{81} +(-36.7331 - 54.9749i) q^{82} +(-109.791 + 45.4770i) q^{83} +32.9607i q^{84} +(-26.6297 - 133.877i) q^{85} +70.3428 q^{86} +(-0.954715 - 2.30489i) q^{87} +(23.6767 - 15.8202i) q^{88} +(-61.4534 + 61.4534i) q^{89} +(198.826 + 39.5490i) q^{90} +(7.37792 + 4.92977i) q^{91} +(43.4639 - 8.64551i) q^{92} +(9.63715 + 3.99184i) q^{93} +(91.1920 - 220.157i) q^{94} +(4.40634 + 22.1522i) q^{95} +(-20.0109 + 29.9484i) q^{96} +(4.79748 - 24.1185i) 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} + 16 q^{5} - 8 q^{6} + 8 q^{7} - 24 q^{8} - 16 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 8 * q^3 + 16 * q^5 - 8 * q^6 + 8 * q^7 - 24 * q^8 - 16 * q^9	\( 8 q - 8 q^{2} - 8 q^{3} + 16 q^{5} - 8 q^{6} + 8 q^{7} - 24 q^{8} - 16 q^{9} + 16 q^{10} - 8 q^{11} + 48 q^{12} + 16 q^{13} + 8 q^{14} - 16 q^{15} + 56 q^{18} - 80 q^{20} - 64 q^{21} - 104 q^{22} - 56 q^{23} - 80 q^{24} + 64 q^{25} + 176 q^{26} + 40 q^{27} + 152 q^{28} + 48 q^{29} + 16 q^{30} + 24 q^{31} + 88 q^{32} - 136 q^{34} - 160 q^{35} - 128 q^{36} + 32 q^{37} - 120 q^{38} + 48 q^{39} + 64 q^{40} + 48 q^{41} + 16 q^{42} - 232 q^{43} + 120 q^{44} - 88 q^{46} + 192 q^{47} + 136 q^{48} + 16 q^{49} + 136 q^{51} - 384 q^{52} - 32 q^{53} + 8 q^{54} + 224 q^{55} - 120 q^{56} + 24 q^{57} + 240 q^{58} - 48 q^{59} + 64 q^{60} - 160 q^{61} - 168 q^{62} + 56 q^{63} - 64 q^{64} - 96 q^{65} - 8 q^{66} + 272 q^{68} + 240 q^{69} + 224 q^{70} + 40 q^{71} + 40 q^{72} + 48 q^{73} - 160 q^{74} - 296 q^{75} + 80 q^{76} - 48 q^{77} - 400 q^{78} - 136 q^{79} - 240 q^{80} - 424 q^{81} - 64 q^{82} - 264 q^{83} - 272 q^{85} + 832 q^{86} + 208 q^{87} + 264 q^{88} + 160 q^{89} + 448 q^{90} + 320 q^{91} + 24 q^{92} - 64 q^{93} + 32 q^{94} + 272 q^{95} - 56 q^{96} + 48 q^{97} - 120 q^{98} - 224 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 8 * q^3 + 16 * q^5 - 8 * q^6 + 8 * q^7 - 24 * q^8 - 16 * q^9 + 16 * q^10 - 8 * q^11 + 48 * q^12 + 16 * q^13 + 8 * q^14 - 16 * q^15 + 56 * q^18 - 80 * q^20 - 64 * q^21 - 104 * q^22 - 56 * q^23 - 80 * q^24 + 64 * q^25 + 176 * q^26 + 40 * q^27 + 152 * q^28 + 48 * q^29 + 16 * q^30 + 24 * q^31 + 88 * q^32 - 136 * q^34 - 160 * q^35 - 128 * q^36 + 32 * q^37 - 120 * q^38 + 48 * q^39 + 64 * q^40 + 48 * q^41 + 16 * q^42 - 232 * q^43 + 120 * q^44 - 88 * q^46 + 192 * q^47 + 136 * q^48 + 16 * q^49 + 136 * q^51 - 384 * q^52 - 32 * q^53 + 8 * q^54 + 224 * q^55 - 120 * q^56 + 24 * q^57 + 240 * q^58 - 48 * q^59 + 64 * q^60 - 160 * q^61 - 168 * q^62 + 56 * q^63 - 64 * q^64 - 96 * q^65 - 8 * q^66 + 272 * q^68 + 240 * q^69 + 224 * q^70 + 40 * q^71 + 40 * q^72 + 48 * q^73 - 160 * q^74 - 296 * q^75 + 80 * q^76 - 48 * q^77 - 400 * q^78 - 136 * q^79 - 240 * q^80 - 424 * q^81 - 64 * q^82 - 264 * q^83 - 272 * q^85 + 832 * q^86 + 208 * q^87 + 264 * q^88 + 160 * q^89 + 448 * q^90 + 320 * q^91 + 24 * q^92 - 64 * q^93 + 32 * q^94 + 272 * q^95 - 56 * q^96 + 48 * q^97 - 120 * q^98 - 224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{13}{16}\right)$

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 $

$2$	−1.15851	−	2.79690i	−0.579256	−	1.39845i	−0.893481	−	0.449100i	$-0.851745\pi$
$2$	−1.15851	−	2.79690i	−0.579256	−	1.39845i	0.314225	−	0.949348i	$-0.398255\pi$
$3$	−0.675577	+	0.451406i	−0.225192	+	0.150469i	−0.663049	−	0.748576i	$-0.730738\pi$
$3$	−0.675577	+	0.451406i	−0.225192	+	0.150469i	0.437857	+	0.899045i	$0.355738\pi$
$4$	−3.65205	+	3.65205i	−0.913014	+	0.913014i
$5$	7.87510	+	1.56645i	1.57502	+	0.313291i	0.903796	−	0.427964i	$-0.140769\pi$
$5$	7.87510	+	1.56645i	1.57502	+	0.313291i	0.671224	+	0.741255i	$0.265769\pi$
$6$	2.04520	+	1.36656i	0.340867	+	0.227760i
$7$	−7.70353	+	1.53233i	−1.10050	+	0.218904i	−0.711746	−	0.702436i	$-0.752096\pi$
$7$	−7.70353	+	1.53233i	−1.10050	+	0.218904i	−0.388757	+	0.921340i	$0.627096\pi$
$8$	3.25778	+	1.34942i	0.407223	+	0.168677i
$9$	−3.19151	+	7.70500i	−0.354613	+	0.856111i
$10$	−4.74219	−	23.8406i	−0.474219	−	2.38406i
$11$	4.48649	−	6.71450i	0.407863	−	0.610410i	−0.569497	−	0.821993i	$-0.692862\pi$
$11$	4.48649	−	6.71450i	0.407863	−	0.610410i	0.977360	+	0.211584i	$0.0678621\pi$
$12$	0.818684	−	4.11580i	0.0682236	−	0.342983i
$13$	−0.798835	−	0.798835i	−0.0614489	−	0.0614489i	0.675715	−	0.737163i	$-0.263835\pi$
$13$	−0.798835	−	0.798835i	−0.0614489	−	0.0614489i	−0.737163	+	0.675715i	$0.763835\pi$
$14$	13.2104	+	19.7707i	0.943599	+	1.41220i
$15$	−6.02734	+	2.49661i	−0.401823	+	0.166440i
$16$			9.98414i			0.624009i
$17$	−6.50562	−	15.7060i	−0.382683	−	0.923880i
$17$	−6.50562	−	15.7060i	−0.382683	−	0.923880i
$18$	25.2475			1.40264
$19$	1.07647	+	2.59882i	0.0566561	+	0.136780i	0.949673	−	0.313244i	$-0.101416\pi$
$19$	1.07647	+	2.59882i	0.0566561	+	0.136780i	−0.893017	+	0.450023i	$0.851416\pi$
$20$	−34.4811	+	23.0395i	−1.72405	+	1.15198i
$21$	4.51262	−	4.51262i	0.214887	−	0.214887i
$22$	−23.9774	−	4.76941i	−1.08988	−	0.216791i
$23$	−7.13426	−	4.76696i	−0.310185	−	0.207259i	0.390727	−	0.920507i	$-0.372224\pi$
$23$	−7.13426	−	4.76696i	−0.310185	−	0.207259i	−0.700912	+	0.713247i	$0.747224\pi$
$24$	−2.81002	+	0.558947i	−0.117084	+	0.0232895i
$25$	36.4664	+	15.1049i	1.45866	+	0.604195i
$26$	−1.30880	+	3.15972i	−0.0503384	+	0.121528i
$27$	−2.74858	−	13.8181i	−0.101799	−	0.511780i
$28$	22.5376	−	33.7298i	0.804913	−	1.20464i
$29$	−0.599020	+	3.01148i	−0.0206559	+	0.103844i	−0.989738	−	0.142895i	$-0.954359\pi$
$29$	−0.599020	+	3.01148i	−0.0206559	+	0.103844i	0.969082	+	0.246739i	$0.0793590\pi$
$30$	13.9655	+	13.9655i	0.465517	+	0.465517i
$31$	−7.13254	−	10.6746i	−0.230082	−	0.344342i	0.698408	−	0.715700i	$-0.253892\pi$
$31$	−7.13254	−	10.6746i	−0.230082	−	0.344342i	−0.928490	+	0.371358i	$0.878892\pi$
$32$	40.9557	−	16.9644i	1.27987	−	0.530138i
$33$			6.56139i			0.198830i
$34$	−36.3911	+	36.3911i	−1.07033	+	1.07033i
$35$	−63.0663			−1.80190
$36$	−16.4835	−	39.7946i	−0.457875	−	1.10541i
$37$	19.6817	−	13.1509i	0.531938	−	0.355429i	−0.260411	−	0.965498i	$-0.583858\pi$
$37$	19.6817	−	13.1509i	0.531938	−	0.355429i	0.792349	+	0.610068i	$0.208858\pi$
$38$	6.02153	−	6.02153i	0.158461	−	0.158461i
$39$	0.900273	+	0.179075i	0.0230839	+	0.00459168i
$40$	23.5416	+	15.7300i	0.588539	+	0.393249i
$41$	21.4206	−	4.26082i	0.522453	−	0.103922i	0.0731833	−	0.997319i	$-0.476684\pi$
$41$	21.4206	−	4.26082i	0.522453	−	0.103922i	0.449270	+	0.893396i	$0.351684\pi$
$42$	−17.8493	−	7.39341i	−0.424982	−	0.176034i
$43$	−8.89197	+	21.4671i	−0.206790	+	0.499235i	−0.992914	−	0.118833i	$-0.962085\pi$
$43$	−8.89197	+	21.4671i	−0.206790	+	0.499235i	0.786124	+	0.618069i	$0.212085\pi$
$44$	8.13684	+	40.9066i	0.184928	+	0.929696i
$45$	−37.2030	+	55.6783i	−0.826734	+	1.23729i
$46$	−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	$0.434080\pi$
$48$	−4.50690	−	6.74505i	−0.0938937	−	0.140522i
$49$	11.7262	−	4.85715i	0.239310	−	0.0991254i
$50$		−	119.492i		−	2.38984i
$51$	11.4848	+	7.67390i	0.225192	+	0.150469i
$52$	5.83478			0.112207
$53$	−22.9922	−	55.5080i	−0.433815	−	1.04732i	−0.978047	−	0.208386i	$-0.933179\pi$
$53$	−22.9922	−	55.5080i	−0.433815	−	1.04732i	0.544232	−	0.838935i	$-0.316821\pi$
$54$	−35.4634	+	23.6959i	−0.656730	+	0.438813i
$55$	45.8495	−	45.8495i	0.833627	−	0.833627i
$56$	−27.1642	−	5.40329i	−0.485074	−	0.0964873i
$57$	−1.90036	−	1.26978i	−0.0333396	−	0.0222768i
$58$	9.11677	−	1.81344i	0.157186	−	0.0312662i
$59$	−25.3733	−	10.5100i	−0.430057	−	0.178135i	0.157146	−	0.987575i	$-0.449771\pi$
$59$	−25.3733	−	10.5100i	−0.430057	−	0.178135i	−0.587202	+	0.809440i	$0.699771\pi$
$60$	12.8944	−	31.1299i	0.214907	−	0.518832i
$61$	7.11302	+	35.7596i	0.116607	+	0.586223i	0.994266	+	0.106937i	$0.0341043\pi$
$61$	7.11302	+	35.7596i	0.116607	+	0.586223i	−0.877659	+	0.479286i	$0.840896\pi$
$62$	−21.5926	+	32.3156i	−0.348268	+	0.521220i
$63$	12.7793	−	64.2461i	0.202847	−	1.01978i
$64$	−66.6561	−	66.6561i	−1.04150	−	1.04150i
$65$	−5.03957	−	7.54224i	−0.0775318	−	0.116035i
$66$	18.3515	−	7.60145i	0.278054	−	0.115174i
$67$			117.219i			1.74953i	0.484544	+	0.874767i	$0.338985\pi$
$67$			117.219i			1.74953i	−0.484544	+	0.874767i	$0.661015\pi$
$68$	81.1179	+	33.6001i	1.19291	+	0.494119i
$69$	6.97157			0.101037
$70$	73.0632	+	176.390i	1.04376	+	2.51986i
$71$	88.1108	−	58.8738i	1.24100	−	0.829208i	0.250685	−	0.968069i	$-0.419344\pi$
$71$	88.1108	−	58.8738i	1.24100	−	0.829208i	0.990312	+	0.138861i	$0.0443440\pi$
$72$	−20.7945	+	20.7945i	−0.288813	+	0.288813i
$73$	−59.8620	−	11.9073i	−0.820028	−	0.163114i	−0.232789	−	0.972527i	$-0.574785\pi$
$73$	−59.8620	−	11.9073i	−0.820028	−	0.163114i	−0.587239	+	0.809414i	$0.699785\pi$
$74$	−59.5832	−	39.8122i	−0.805178	−	0.538003i
$75$	−31.4543	+	6.25665i	−0.419390	+	0.0834220i
$76$	−13.4223	−	5.55971i	−0.176610	−	0.0731541i
$77$	−24.2730	+	58.6001i	−0.315233	+	0.761041i
$78$	−0.542122	−	2.72543i	−0.00695029	−	0.0349414i
$79$	52.9382	−	79.2276i	0.670103	−	1.00288i	−0.328197	−	0.944609i	$-0.606441\pi$
$79$	52.9382	−	79.2276i	0.670103	−	1.00288i	0.998301	−	0.0582714i	$-0.0185589\pi$
$80$	−15.6397	+	78.6261i	−0.195496	+	0.982826i
$81$	−44.9799	−	44.9799i	−0.555308	−	0.555308i
$82$	−36.7331	−	54.9749i	−0.447964	−	0.670426i
$83$	−109.791	+	45.4770i	−1.32279	+	0.547916i	−0.928589	−	0.371110i	$-0.878977\pi$
$83$	−109.791	+	45.4770i	−1.32279	+	0.547916i	−0.394197	+	0.919026i	$0.628977\pi$
$84$			32.9607i			0.392389i
$85$	−26.6297	−	133.877i	−0.313291	−	1.57502i
$86$	70.3428			0.817939
$87$	−0.954715	−	2.30489i	−0.0109737	−	0.0264929i
$88$	23.6767	−	15.8202i	0.269053	−	0.179776i
$89$	−61.4534	+	61.4534i	−0.690488	+	0.690488i	−0.962339	−	0.271851i	$-0.912364\pi$
$89$	−61.4534	+	61.4534i	−0.690488	+	0.690488i	0.271851	+	0.962339i	$0.412364\pi$
$90$	198.826	+	39.5490i	2.20918	+	0.439434i
$91$	7.37792	+	4.92977i	0.0810761	+	0.0541733i
$92$	43.4639	−	8.64551i	0.472434	−	0.0939729i
$93$	9.63715	+	3.99184i	0.103625	+	0.0429230i
$94$	91.1920	−	220.157i	0.970128	−	2.34210i
$95$	4.40634	+	22.1522i	0.0463826	+	0.233181i
$96$	−20.0109	+	29.9484i	−0.208447	+	0.311963i
$97$	4.79748	−	24.1185i	0.0494585	−	0.248645i	−0.948145	−	0.317839i	$-0.897043\pi$
$97$	4.79748	−	24.1185i	0.0494585	−	0.248645i	0.997603	+	0.0691943i	$0.0220428\pi$
$98$	−27.1699	−	27.1699i	−0.277244	−	0.277244i
$99$	37.4165	+	55.9978i	0.377945	+	0.565635i
$100$	−188.341	+	78.0135i	−1.88341	+	0.780135i
$101$		−	7.70266i		−	0.0762640i	−0.999273	−	0.0381320i	$-0.987859\pi$
$101$		−	7.70266i		−	0.0762640i	0.999273	−	0.0381320i	$-0.0121407\pi$
$102$	8.15782	−	41.0121i	0.0799786	−	0.402080i
$103$	41.5688			0.403581			0.201790	−	0.979429i	$-0.435324\pi$
$103$	41.5688			0.403581			0.201790	+	0.979429i	$0.435324\pi$
$104$	−1.52447	−	3.68039i	−0.0146584	−	0.0353884i
$105$	42.6061	−	28.4685i	0.405773	−	0.271129i
$106$	−128.614	+	128.614i	−1.21333	+	1.21333i
$107$	86.7136	+	17.2484i	0.810407	+	0.161200i	0.582866	−	0.812568i	$-0.301931\pi$
$107$	86.7136	+	17.2484i	0.810407	+	0.161200i	0.227541	+	0.973768i	$0.426931\pi$
$108$	60.5023	+	40.4263i	0.560206	+	0.374318i
$109$	18.2754	−	3.63521i	0.167665	−	0.0333506i	−0.110544	−	0.993871i	$-0.535259\pi$
$109$	18.2754	−	3.63521i	0.167665	−	0.0333506i	0.278209	+	0.960521i	$0.410259\pi$
$110$	−181.354	−	75.1191i	−1.64867	−	0.682901i
$111$	−7.36011	+	17.7689i	−0.0663073	+	0.160080i
$112$	−15.2990	−	76.9131i	−0.136598	−	0.686724i
$113$	−33.6909	+	50.4220i	−0.298150	+	0.446212i	−0.950053	−	0.312090i	$-0.898971\pi$
$113$	−33.6909	+	50.4220i	−0.298150	+	0.446212i	0.651903	+	0.758302i	$0.273971\pi$
$114$	−1.34985	+	6.78616i	−0.0118408	+	0.0595277i
$115$	−48.7158	−	48.7158i	−0.423615	−	0.423615i
$116$	−8.81043	−	13.1857i	−0.0759520	−	0.113670i
$117$	8.70452	−	3.60553i	0.0743976	−	0.0308165i
$118$			83.1426i			0.704598i
$119$	74.1828	+	111.022i	0.623385	+	0.932962i
$120$	−23.0047			−0.191706
$121$	21.3487	+	51.5403i	0.176436	+	0.425953i
$122$	91.7753	−	61.3223i	0.752257	−	0.502642i
$123$	−12.5479	+	12.5479i	−0.102015	+	0.102015i
$124$	65.0326	+	12.9358i	0.524456	+	0.104321i
$125$	96.6108	+	64.5533i	0.772886	+	0.516426i
$126$	−194.495	+	38.6874i	−1.54361	+	0.307043i
$127$	110.168	+	45.6333i	0.867468	+	0.359317i	0.771624	−	0.636079i	$-0.219445\pi$
$127$	110.168	+	45.6333i	0.867468	+	0.359317i	0.0958444	+	0.995396i	$0.469445\pi$
$128$	−41.3506	+	99.8291i	−0.323051	+	0.779915i
$129$	−3.68317	−	18.5166i	−0.0285517	−	0.143539i
$130$	−15.2565	+	22.8329i	−0.117358	+	0.175638i
$131$	33.4238	−	168.033i	0.255144	−	1.28269i	−0.614461	−	0.788947i	$-0.710627\pi$
$131$	33.4238	−	168.033i	0.255144	−	1.28269i	0.869605	−	0.493748i	$-0.164373\pi$
$132$	−23.9626	−	23.9626i	−0.181534	−	0.181534i
$133$	−12.2748	−	18.3706i	−0.0922919	−	0.138125i
$134$	327.849	−	135.799i	2.44663	−	1.01343i
$135$		−	113.124i		−	0.837956i
$136$		−	59.9454i		−	0.440775i
$137$	−173.113			−1.26360			−0.631799	−	0.775132i	$-0.717683\pi$
$137$	−173.113			−1.26360			−0.631799	+	0.775132i	$0.717683\pi$
$138$	−8.07666	−	19.4988i	−0.0585265	−	0.141295i
$139$	−149.307	+	99.7637i	−1.07415	+	0.717724i	−0.961193	−	0.275876i	$-0.911032\pi$
$139$	−149.307	+	99.7637i	−1.07415	+	0.717724i	−0.112957	+	0.993600i	$0.536032\pi$
$140$	230.322	−	230.322i	1.64515	−	1.64515i
$141$	−62.7276	−	12.4773i	−0.444876	−	0.0884914i
$142$	−266.741	−	178.231i	−1.87846	−	1.25515i
$143$	−8.94775	+	1.77982i	−0.0625717	+	0.0124463i
$144$	−76.9278	−	31.8645i	−0.534221	−	0.221281i
$145$	−9.43469	+	22.7774i	−0.0650668	+	0.157085i
$146$	36.0474	+	181.223i	0.246900	+	1.24125i
$147$	−5.72939	+	8.57464i	−0.0389755	+	0.0583309i
$148$	−23.8509	+	119.906i	−0.161154	+	0.810178i
$149$	31.6842	+	31.6842i	0.212646	+	0.212646i	0.805391	−	0.592745i	$-0.201956\pi$
$149$	31.6842	+	31.6842i	0.212646	+	0.212646i	−0.592745	+	0.805391i	$0.701956\pi$
$150$	53.9394	+	80.7260i	0.359596	+	0.538173i
$151$	−121.384	+	50.2789i	−0.803868	+	0.332973i	−0.746504	−	0.665380i	$-0.768269\pi$
$151$	−121.384	+	50.2789i	−0.803868	+	0.332973i	−0.0573634	+	0.998353i	$0.518269\pi$
$152$			9.91898i			0.0652565i
$153$	141.777			0.926648
$154$	192.019			1.24688
$155$	−39.4482	−	95.2363i	−0.254504	−	0.614428i
$156$	−3.94184	+	2.63385i	−0.0252682	+	0.0168837i
$157$	25.4694	−	25.4694i	0.162225	−	0.162225i	−0.621327	−	0.783552i	$-0.713406\pi$
$157$	25.4694	−	25.4694i	0.162225	−	0.162225i	0.783552	+	0.621327i	$0.213406\pi$
$158$	−282.921	−	56.2765i	−1.79064	−	0.356180i
$159$	40.5896	+	27.1211i	0.255281	+	0.170573i
$160$	349.104	−	69.4412i	2.18190	−	0.434007i
$161$	62.2635	+	25.7904i	0.386730	+	0.160189i
$162$	−73.6944	+	177.914i	−0.454904	+	1.09823i
$163$	31.1596	+	156.650i	0.191163	+	0.961041i	0.950590	+	0.310449i	$0.100479\pi$
$163$	31.1596	+	156.650i	0.191163	+	0.961041i	−0.759427	+	0.650592i	$0.774521\pi$
$164$	−62.6684	+	93.7898i	−0.382124	+	0.571889i
$165$	−10.2781	+	51.6716i	−0.0622916	+	0.313161i
$166$	254.389	+	254.389i	1.53246	+	1.53246i
$167$	−61.5214	−	92.0734i	−0.368392	−	0.551337i	0.600246	−	0.799816i	$-0.295070\pi$
$167$	−61.5214	−	92.0734i	−0.368392	−	0.551337i	−0.968637	+	0.248478i	$0.920070\pi$
$168$	20.7905	−	8.61173i	0.123753	−	0.0512603i
$169$		−	167.724i		−	0.992448i
$170$	−343.588	+	229.578i	−2.02111	+	1.35046i
$171$	−23.4594			−0.137190
$172$	−45.9251	−	110.873i	−0.267006	−	0.644611i
$173$	−148.047	+	98.9216i	−0.855761	+	0.571801i	−0.904241	−	0.427023i	$-0.859562\pi$
$173$	−148.047	+	98.9216i	−0.855761	+	0.571801i	0.0484797	+	0.998824i	$0.484562\pi$
$174$	−5.34048	+	5.34048i	−0.0306924	+	0.0306924i
$175$	−304.066	−	60.4824i	−1.73752	−	0.345614i
$176$	67.0386	+	44.7937i	0.380901	+	0.254510i
$177$	21.8859	−	4.35338i	0.123649	−	0.0245954i
$178$	243.074	+	100.684i	1.36558	+	0.565642i
$179$	96.5028	−	232.978i	0.539122	−	1.30155i	−0.386215	−	0.922409i	$-0.626218\pi$
$179$	96.5028	−	232.978i	0.539122	−	1.30155i	0.925337	−	0.379146i	$-0.123782\pi$
$180$	−67.4725	−	339.207i	−0.374847	−	1.88449i
$181$	167.421	−	250.563i	0.924977	−	1.38433i	0.00178027	−	0.999998i	$-0.499433\pi$
$181$	167.421	−	250.563i	0.924977	−	1.38433i	0.923197	−	0.384328i	$-0.125567\pi$
$182$	5.24064	−	26.3465i	0.0287947	−	0.144761i
$183$	−20.9475	−	20.9475i	−0.114467	−	0.114467i
$184$	−16.8092	−	25.1568i	−0.0913546	−	0.136722i
$185$	175.596	−	72.7341i	0.949165	−	0.393157i
$186$		−	31.5787i		−	0.169778i
$187$	−134.645	−	26.7826i	−0.720027	−	0.143222i
$188$	−406.545			−2.16247
$189$	42.3476	+	102.236i	0.224061	+	0.540931i
$190$	56.8526	−	37.9877i	0.299224	−	0.199935i
$191$	93.7287	−	93.7287i	0.490726	−	0.490726i	−0.417809	−	0.908535i	$-0.637202\pi$
$191$	93.7287	−	93.7287i	0.490726	−	0.490726i	0.908535	+	0.417809i	$0.137202\pi$
$192$	75.1202	+	14.9423i	0.391251	+	0.0778247i
$193$	264.917	+	177.012i	1.37263	+	0.917161i	0.999942	−	0.0107958i	$-0.00343648\pi$
$193$	264.917	+	177.012i	1.37263	+	0.917161i	0.372687	+	0.927957i	$0.378436\pi$
$194$	−73.0150	+	14.5236i	−0.376366	+	0.0748639i
$195$	6.80923	+	2.82047i	0.0349191	+	0.0144640i
$196$	−25.0861	+	60.5632i	−0.127990	+	0.308996i
$197$	22.5650	+	113.442i	0.114543	+	0.575847i	0.994843	+	0.101429i	$0.0323415\pi$
$197$	22.5650	+	113.442i	0.114543	+	0.575847i	−0.880300	+	0.474418i	$0.842659\pi$
$198$	113.273	−	169.524i	0.572084	−	0.856184i
$199$	−57.7166	+	290.161i	−0.290033	+	1.45809i	0.511055	+	0.859548i	$0.329255\pi$
$199$	−57.7166	+	290.161i	−0.290033	+	1.45809i	−0.801088	+	0.598547i	$0.795745\pi$
$200$	98.4168	+	98.4168i	0.492084	+	0.492084i
$201$	−52.9132	−	79.1902i	−0.263250	−	0.393981i
$202$	−21.5436	+	8.92363i	−0.106651	+	0.0441764i
$203$		−	24.1169i		−	0.118802i
$204$	−69.9686	+	13.9176i	−0.342983	+	0.0682236i
$205$	175.364			0.855432
$206$	−48.1580	−	116.264i	−0.233777	−	0.564387i
$207$	59.4985	−	39.7556i	0.287432	−	0.192056i
$208$	7.97568	−	7.97568i	0.0383446	−	0.0383446i
$209$	22.2793	+	4.43163i	0.106600	+	0.0212040i
$210$	−128.983	−	86.1839i	−0.614206	−	0.410399i
$211$	−225.325	+	44.8199i	−1.06789	+	0.212417i	−0.697592	−	0.716495i	$-0.745745\pi$
$211$	−225.325	+	44.8199i	−1.06789	+	0.212417i	−0.370300	+	0.928912i	$0.620745\pi$
$212$	286.687	+	118.750i	1.35230	+	0.560140i
$213$	−32.9496	+	79.5475i	−0.154693	+	0.373462i
$214$	−52.2168	−	262.511i	−0.244004	−	1.22669i
$215$	−103.652	+	155.127i	−0.482104	+	0.721520i
$216$	9.69205	−	48.7252i	0.0448706	−	0.225580i
$217$	71.3026	+	71.3026i	0.328584	+	0.328584i
$218$	−31.3396	−	46.9031i	−0.143760	−	0.215152i
$219$	45.8164	−	18.9778i	0.209207	−	0.0866565i
$220$			334.890i			1.52223i
$221$	−7.34955	+	17.7434i	−0.0332559	+	0.0802868i
$222$	58.2245			0.262272
$223$	−139.061	−	335.723i	−0.623593	−	1.50549i	−0.847456	−	0.530865i	$-0.821867\pi$
$223$	−139.061	−	335.723i	−0.623593	−	1.50549i	0.223863	−	0.974621i	$-0.428133\pi$
$224$	−289.509	+	193.443i	−1.29245	+	0.863587i
$225$	−232.766	+	232.766i	−1.03452	+	1.03452i
$226$	180.056	+	35.8155i	0.796710	+	0.158475i
$227$	−80.5890	−	53.8478i	−0.355017	−	0.237215i	0.365253	−	0.930908i	$-0.380982\pi$
$227$	−80.5890	−	53.8478i	−0.355017	−	0.237215i	−0.720271	+	0.693693i	$0.755982\pi$
$228$	11.5775	−	2.30291i	0.0507785	−	0.0101005i
$229$	−334.120	−	138.397i	−1.45904	−	0.604353i	−0.494708	−	0.869059i	$-0.664725\pi$
$229$	−334.120	−	138.397i	−1.45904	−	0.604353i	−0.964329	+	0.264706i	$0.914725\pi$
$230$	−79.8152	+	192.691i	−0.347022	+	0.837786i
$231$	−10.0542	−	50.5458i	−0.0435246	−	0.218813i
$232$	−6.01522	+	9.00241i	−0.0259277	+	0.0388035i
$233$	54.6542	−	274.765i	0.234567	−	1.17925i	−0.666478	−	0.745525i	$-0.732199\pi$
$233$	54.6542	−	274.765i	0.234567	−	1.17925i	0.901045	−	0.433725i	$-0.142801\pi$
$234$	−20.1686	−	20.1686i	−0.0861905	−	0.0861905i
$235$	351.137	+	525.514i	1.49420	+	2.23623i
$236$	131.048	−	54.2818i	0.555288	−	0.230008i
$237$			77.4209i			0.326670i
$238$	224.577	−	336.103i	0.943599	−	1.41220i
$239$	328.551			1.37469			0.687345	−	0.726331i	$-0.258776\pi$
$239$	328.551			1.37469			0.687345	+	0.726331i	$0.258776\pi$
$240$	−24.9265	−	60.1778i	−0.103860	−	0.250741i
$241$	−201.560	+	134.678i	−0.836349	+	0.558831i	−0.898368	−	0.439244i	$-0.855246\pi$
$241$	−201.560	+	134.678i	−0.836349	+	0.558831i	0.0620186	+	0.998075i	$0.480246\pi$
$242$	119.420	−	119.420i	0.493472	−	0.493472i
$243$	175.054	+	34.8204i	0.720387	+	0.143294i
$244$	−156.573	−	104.619i	−0.641693	−	0.428765i
$245$	99.9534	−	19.8820i	0.407973	−	0.0811509i
$246$	49.6320	+	20.5583i	0.201756	+	0.0835701i
$247$	1.21611	−	2.93595i	0.00492352	−	0.0118864i
$248$	−8.83176	−	44.4003i	−0.0356119	−	0.179033i
$249$	53.6438	−	80.2836i	0.215437	−	0.322424i
$250$	68.6240	−	344.996i	0.274496	−	1.37999i
$251$	−155.463	−	155.463i	−0.619375	−	0.619375i	0.325996	−	0.945371i	$-0.394300\pi$
$251$	−155.463	−	155.463i	−0.619375	−	0.619375i	−0.945371	+	0.325996i	$0.894300\pi$
$252$	187.959	+	281.301i	0.745870	+	1.11627i
$253$	−64.0155	+	26.5161i	−0.253026	+	0.104807i
$254$		−	360.996i		−	1.42125i
$255$	78.4231	+	78.4231i	0.307542	+	0.307542i
$256$	−49.9468			−0.195105
$257$	124.463	+	300.480i	0.484292	+	1.16918i	0.957552	+	0.288261i	$0.0930772\pi$
$257$	124.463	+	300.480i	0.484292	+	1.16918i	−0.473260	+	0.880923i	$0.656923\pi$
$258$	−47.5219	+	31.7531i	−0.184194	+	0.123074i
$259$	−131.467	+	131.467i	−0.507595	+	0.507595i
$260$	45.9494	+	9.13991i	0.176729	+	0.0351535i
$261$	−21.2917	−	14.2266i	−0.0815772	−	0.0545082i
$262$	−508.693	+	101.185i	−1.94158	+	0.386203i
$263$	128.172	+	53.0907i	0.487347	+	0.201866i	0.612806	−	0.790233i	$-0.290041\pi$
$263$	128.172	+	53.0907i	0.487347	+	0.201866i	−0.125460	+	0.992099i	$0.540041\pi$
$264$	−8.85405	+	21.3756i	−0.0335381	+	0.0809681i
$265$	−94.1149	−	473.147i	−0.355150	−	1.78546i
$266$	−37.1600	+	55.6139i	−0.139699	+	0.209075i
$267$	13.7761	−	69.2570i	0.0515957	−	0.259389i
$268$	−428.089	−	428.089i	−1.59735	−	1.59735i
$269$	−180.493	−	270.126i	−0.670976	−	1.00419i	−0.998243	−	0.0592547i	$-0.981128\pi$
$269$	−180.493	−	270.126i	−0.670976	−	1.00419i	0.327267	−	0.944932i	$-0.393872\pi$
$270$	−316.396	+	131.056i	−1.17184	+	0.485391i
$271$		−	19.1867i		−	0.0707996i	−0.999373	−	0.0353998i	$-0.988730\pi$
$271$		−	19.1867i		−	0.0707996i	0.999373	−	0.0353998i	$-0.0112705\pi$
$272$	156.810	−	64.9530i	0.576509	−	0.238798i
$273$	−7.20968			−0.0264091
$274$	200.554	+	484.179i	0.731947	+	1.76708i
$275$	265.028	−	177.086i	0.963738	−	0.643949i
$276$	−25.4606	+	25.4606i	−0.0922484	+	0.0922484i
$277$	302.084	+	60.0883i	1.09056	+	0.216925i	0.707439	−	0.706774i	$-0.249850\pi$
$277$	302.084	+	60.0883i	1.09056	+	0.216925i	0.383118	+	0.923700i	$0.374850\pi$
$278$	452.003	+	302.018i	1.62591	+	1.08640i
$279$	105.011	−	20.8880i	0.376385	−	0.0748676i
$280$	−205.456	−	85.1028i	−0.733773	−	0.303939i
$281$	−33.1106	+	79.9361i	−0.117831	+	0.284470i	−0.971781	−	0.235886i	$-0.924201\pi$
$281$	−33.1106	+	79.9361i	−0.117831	+	0.284470i	0.853949	+	0.520356i	$0.174201\pi$
$282$	37.7730	+	189.898i	0.133947	+	0.673396i
$283$	4.15656	−	6.22073i	0.0146875	−	0.0219814i	−0.824053	−	0.566512i	$-0.808292\pi$
$283$	4.15656	−	6.22073i	0.0146875	−	0.0219814i	0.838741	+	0.544531i	$0.183292\pi$
$284$	−106.775	+	536.796i	−0.375969	+	1.89013i
$285$	−12.9764	−	12.9764i	−0.0455314	−	0.0455314i
$286$	15.3440	+	22.9640i	0.0536505	+	0.0802937i
$287$	−158.485	+	65.6466i	−0.552213	+	0.228734i
$288$			369.706i			1.28370i
$289$	−204.354	+	204.354i	−0.707107	+	0.707107i
$290$	74.6361			0.257366
$291$	7.64619	+	18.4595i	0.0262756	+	0.0634348i
$292$	262.105	−	175.133i	0.897621	−	0.599771i
$293$	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
$295$	−183.354	−	122.513i	−0.621540	−	0.415300i
$296$	81.8647	−	16.2839i	0.276570	−	0.0550132i
$297$	−105.113	−	43.5392i	−0.353915	−	0.146597i
$298$	51.9110	−	125.324i	0.174198	−	0.420551i
$299$	1.89108	+	9.50711i	0.00632469	+	0.0317964i
$300$	92.0231	−	137.722i	0.306744	−	0.459075i
$301$	35.6049	−	178.998i	0.118289	−	0.594677i
$302$	281.250	+	281.250i	0.931291	+	0.931291i
$303$	3.47703	+	5.20374i	0.0114753	+	0.0171741i
$304$	−25.9470	+	10.7476i	−0.0853519	+	0.0353539i
$305$			292.752i			0.959844i
$306$	−164.251	−	396.536i	−0.536767	−	1.29587i
$307$	−159.680			−0.520132			−0.260066	−	0.965591i	$-0.583744\pi$
$307$	−159.680			−0.520132			−0.260066	+	0.965591i	$0.583744\pi$
$308$	−125.365	−	302.657i	−0.407028	−	0.982653i
$309$	−28.0829	+	18.7644i	−0.0908832	+	0.0607262i
$310$	−220.665	+	220.665i	−0.711822	+	0.711822i
$311$	−326.615	−	64.9678i	−1.05021	−	0.208900i	−0.360331	−	0.932825i	$-0.617336\pi$
$311$	−326.615	−	64.9678i	−1.05021	−	0.208900i	−0.689879	+	0.723925i	$0.742336\pi$
$312$	2.69125	+	1.79823i	0.00862579	+	0.00576357i
$313$	386.986	−	76.9763i	1.23638	−	0.245931i	0.466729	−	0.884400i	$-0.345432\pi$
$313$	386.986	−	76.9763i	1.23638	−	0.245931i	0.769647	+	0.638470i	$0.220432\pi$
$314$	−100.742	−	41.7286i	−0.320834	−	0.132894i
$315$	201.277	−	485.926i	0.638975	−	1.54262i
$316$	96.0103	+	482.676i	0.303830	+	1.52746i
$317$	−77.2775	+	115.654i	−0.243778	+	0.364839i	−0.933101	−	0.359615i	$-0.882908\pi$
$317$	−77.2775	+	115.654i	−0.243778	+	0.364839i	0.689323	+	0.724454i	$0.257908\pi$
$318$	28.8314	−	144.945i	0.0906647	−	0.455802i
$319$	17.5331	+	17.5331i	0.0549627	+	0.0549627i
$320$	−420.509	−	629.337i	−1.31409	−	1.96668i
$321$	−66.3677	+	27.4904i	−0.206753	+	0.0856399i
$322$		−	204.023i		−	0.633612i
$323$	33.8138	−	33.8138i	0.104687	−	0.104687i
$324$	328.538			1.01401
$325$	−17.0643	−	41.1970i	−0.0525057	−	0.126760i
$326$	402.034	−	268.631i	1.23323	−	0.824021i
$327$	−10.7055	+	10.7055i	−0.0327385	+	0.0327385i
$328$	75.5332	+	15.0245i	0.230284	+	0.0458064i
$329$	−514.065	−	343.487i	−1.56251	−	1.04403i
$330$	156.427	−	31.1154i	0.474023	−	0.0942890i
$331$	146.717	+	60.7720i	0.443252	+	0.183601i	0.593136	−	0.805103i	$-0.297890\pi$
$331$	146.717	+	60.7720i	0.443252	+	0.183601i	−0.149883	+	0.988704i	$0.547890\pi$
$332$	234.879	−	567.048i	0.707467	−	1.70798i
$333$	38.5132	+	193.619i	0.115655	+	0.581438i
$334$	−186.246	+	278.737i	−0.557624	+	0.834543i
$335$	−183.618	+	923.109i	−0.548113	+	2.75555i
$336$	45.0546	+	45.0546i	0.134091	+	0.134091i
$337$	−267.981	−	401.062i	−0.795195	−	1.19009i	−0.978339	−	0.207008i	$-0.933628\pi$
$337$	−267.981	−	401.062i	−0.795195	−	1.19009i	0.183144	−	0.983086i	$-0.441372\pi$
$338$	−469.106	+	194.310i	−1.38789	+	0.574882i
$339$		−	49.2722i		−	0.145346i
$340$	586.178	+	391.672i	1.72405	+	1.15198i
$341$	−103.675			−0.304031
$342$	27.1781	+	65.6136i	0.0794680	+	0.191853i
$343$	237.116	−	158.436i	0.691299	−	0.461912i
$344$	−57.9362	+	57.9362i	−0.168419	+	0.168419i
$345$	54.9018	+	10.9207i	0.159136	+	0.0316541i
$346$	448.188	+	299.469i	1.29534	+	0.865518i
$347$	−19.4096	+	3.86080i	−0.0559353	+	0.0111262i	−0.222979	−	0.974823i	$-0.571578\pi$
$347$	−19.4096	+	3.86080i	−0.0559353	+	0.0111262i	0.167043	+	0.985950i	$0.446578\pi$
$348$	11.9042	+	4.93090i	0.0342076	+	0.0141692i
$349$	−149.801	+	361.651i	−0.429229	+	1.03625i	0.550304	+	0.834965i	$0.314512\pi$
$349$	−149.801	+	361.651i	−0.429229	+	1.03625i	−0.979533	+	0.201286i	$0.935488\pi$
$350$	183.101	+	920.510i	0.523145	+	2.63003i
$351$	−8.84268	+	13.2340i	−0.0251928	+	0.0377037i
$352$	69.8398	−	351.108i	0.198408	−	0.997466i
$353$	138.024	+	138.024i	0.391003	+	0.391003i	0.875045	−	0.484042i	$-0.160832\pi$
$353$	138.024	+	138.024i	0.391003	+	0.391003i	−0.484042	+	0.875045i	$0.660832\pi$
$354$	−37.5311	−	56.1692i	−0.106020	−	0.158670i
$355$	786.104	−	325.615i	2.21438	−	0.917226i
$356$		−	448.863i		−	1.26085i
$357$	−100.232	−	41.5176i	−0.280763	−	0.116296i
$358$	−763.416			−2.13245
$359$	136.163	+	328.726i	0.379284	+	0.915672i	0.992100	+	0.125447i	$0.0400364\pi$
$359$	136.163	+	328.726i	0.379284	+	0.915672i	−0.612817	+	0.790225i	$0.709964\pi$
$360$	−196.333	+	131.185i	−0.545368	+	0.364403i
$361$	249.670	−	249.670i	0.691608	−	0.691608i
$362$	−894.758	−	177.978i	−2.47171	−	0.491653i
$363$	−37.6883	−	25.1825i	−0.103824	−	0.0693733i
$364$	−44.9484	+	8.94078i	−0.123485	+	0.0245626i
$365$	−452.767	−	187.542i	−1.24046	−	0.513814i
$366$	−34.3200	+	82.8558i	−0.0937705	+	0.226382i
$367$	−15.9442	−	80.1568i	−0.0434446	−	0.218411i	0.952964	−	0.303083i	$-0.0980158\pi$
$367$	−15.9442	−	80.1568i	−0.0434446	−	0.218411i	−0.996409	+	0.0846717i	$0.973016\pi$
$368$	47.5940	−	71.2294i	0.129331	−	0.193558i
$369$	−35.5345	+	178.644i	−0.0962994	+	0.484130i
$370$	−406.859	−	406.859i	−1.09962	−	1.09962i
$371$	262.177	+	392.376i	0.706677	+	1.05762i
$372$	−49.7738	+	20.6170i	−0.133801	+	0.0554220i
$373$		−	76.8209i		−	0.205954i	−0.994684	−	0.102977i	$-0.967163\pi$
$373$		−	76.8209i		−	0.205954i	0.994684	−	0.102977i	$-0.0328368\pi$
$374$	81.0799	+	407.616i	0.216791	+	1.08988i
$375$	−94.4077			−0.251754
$376$	106.219	+	256.436i	0.282498	+	0.682009i
$377$	2.88419	−	1.92716i	0.00765038	−	0.00511182i
$378$	236.883	−	236.883i	0.626676	−	0.626676i
$379$	577.940	+	114.959i	1.52491	+	0.303323i	0.885169	−	0.465269i	$-0.154043\pi$
$379$	577.940	+	114.959i	1.52491	+	0.303323i	0.639739	+	0.768592i	$0.279043\pi$
$380$	−96.9932	−	64.8088i	−0.255245	−	0.170549i
$381$	−95.0264	+	18.9019i	−0.249413	+	0.0496113i
$382$	−370.735	−	153.564i	−0.970511	−	0.401999i
$383$	−89.4016	+	215.834i	−0.233424	+	0.563537i	−0.996576	−	0.0826832i	$-0.973651\pi$
$383$	−89.4016	+	215.834i	−0.233424	+	0.563537i	0.763151	+	0.646220i	$0.223651\pi$
$384$	−17.1280	−	86.1081i	−0.0446041	−	0.224240i
$385$	−282.946	+	423.459i	−0.734926	+	1.09989i
$386$	188.175	−	946.017i	0.487499	−	2.45082i
$387$	−137.025	−	137.025i	−0.354070	−	0.354070i
$388$	70.5616	+	105.603i	0.181860	+	0.272172i
$389$	372.916	−	154.467i	0.958653	−	0.397087i	0.152177	−	0.988353i	$-0.451372\pi$
$389$	372.916	−	154.467i	0.958653	−	0.397087i	0.806477	+	0.591266i	$0.201372\pi$
$390$		−	22.3123i		−	0.0572109i
$391$	−28.4569	+	143.062i	−0.0727797	+	0.365888i
$392$	44.7557			0.114173
$393$	53.2707	+	128.607i	0.135549	+	0.327244i
$394$	291.143	−	194.536i	0.738943	−	0.493746i
$395$	541.000	−	541.000i	1.36962	−	1.36962i
$396$	−341.154	−	67.8598i	−0.861501	−	0.171363i
$397$	219.332	+	146.553i	0.552474	+	0.369151i	0.800251	−	0.599666i	$-0.204700\pi$
$397$	219.332	+	146.553i	0.552474	+	0.369151i	−0.247776	+	0.968817i	$0.579700\pi$
$398$	878.415	−	174.728i	2.20707	−	0.439014i
$399$	16.5852	+	6.86980i	0.0415668	+	0.0172175i
$400$	−150.809	+	364.086i	−0.377023	+	0.910214i
$401$	46.6830	+	234.691i	0.116416	+	0.585265i	0.994320	+	0.106428i	$0.0339414\pi$
$401$	46.6830	+	234.691i	0.116416	+	0.585265i	−0.877904	+	0.478837i	$0.841059\pi$
$402$	−160.186	+	239.736i	−0.398473	+	0.596358i
$403$	−2.82952	+	14.2250i	−0.00702114	+	0.0352977i
$404$	28.1305	+	28.1305i	0.0696300	+	0.0696300i
$405$	−283.762	−	424.680i	−0.700648	−	1.04859i
$406$	−67.4525	+	27.9397i	−0.166139	+	0.0688171i
$407$		−	191.154i		−	0.469666i
$408$	27.0597	+	40.4977i	0.0663228	+	0.0992590i
$409$	259.903			0.635461			0.317730	−	0.948181i	$-0.397079\pi$
$409$	259.903			0.635461			0.317730	+	0.948181i	$0.397079\pi$
$410$	−203.161	−	490.474i	−0.495514	−	1.19628i
$411$	116.951	−	78.1442i	0.284552	−	0.190132i
$412$	−151.812	+	151.812i	−0.368475	+	0.368475i
$413$	211.569	+	42.0837i	0.512274	+	0.101898i
$414$	−180.122	−	120.354i	−0.435078	−	0.290710i
$415$	−935.855	+	186.153i	−2.25507	+	0.448562i
$416$	−46.2687	−	19.1651i	−0.111223	−	0.0460700i
$417$	55.8343	−	134.796i	0.133895	−	0.323252i
$418$	−13.4161	−	67.4471i	−0.0320958	−	0.161357i
$419$	−95.3087	+	142.640i	−0.227467	+	0.340429i	−0.927594	−	0.373590i	$-0.878127\pi$
$419$	−95.3087	+	142.640i	−0.227467	+	0.340429i	0.700127	+	0.714018i	$0.253127\pi$
$420$	−51.6314	+	259.569i	−0.122932	+	0.618020i
$421$	443.214	+	443.214i	1.05276	+	1.05276i	0.998528	+	0.0542356i	$0.0172722\pi$
$421$	443.214	+	443.214i	1.05276	+	1.05276i	0.0542356	+	0.998528i	$0.482728\pi$
$422$	386.399	+	578.287i	0.915637	+	1.37035i
$423$	−606.497	+	251.219i	−1.43380	+	0.593899i
$424$		−	211.859i		−	0.499668i
$425$		−	671.006i		−	1.57884i
$426$	260.659			0.611875
$427$	−109.591	−	264.575i	−0.256653	−	0.619614i
$428$	−379.675	+	253.691i	−0.887090	+	0.592735i
$429$	5.24147	−	5.24147i	0.0122179	−	0.0122179i
$430$	553.956	+	110.189i	1.28827	+	0.256253i
$431$	−633.734	−	423.447i	−1.47038	−	0.982477i	−0.994696	−	0.102860i	$-0.967201\pi$
$431$	−633.734	−	423.447i	−1.47038	−	0.982477i	−0.475684	−	0.879616i	$-0.657799\pi$
$432$	137.961	−	27.4422i	0.319355	−	0.0635237i
$433$	87.4681	+	36.2305i	0.202005	+	0.0836732i	0.481392	−	0.876505i	$-0.340131\pi$
$433$	87.4681	+	36.2305i	0.202005	+	0.0836732i	−0.279387	+	0.960179i	$0.590131\pi$
$434$	116.821	−	282.031i	0.269173	−	0.649841i
$435$	−3.90798	−	19.6467i	−0.00898385	−	0.0451649i
$436$	−53.4669	+	80.0189i	−0.122630	+	0.183530i
$437$	4.70868	−	23.6721i	0.0107750	−	0.0541696i
$438$	−106.158	−	106.158i	−0.242369	−	0.242369i
$439$	−20.5441	−	30.7465i	−0.0467976	−	0.0700375i	0.807333	−	0.590096i	$-0.200910\pi$
$439$	−20.5441	−	30.7465i	−0.0467976	−	0.0700375i	−0.854131	+	0.520059i	$0.825910\pi$
$440$	211.238	−	87.4976i	0.480086	−	0.198858i
$441$			105.852i			0.240027i
$442$	58.1410			0.131541
$443$	−634.146			−1.43148			−0.715740	−	0.698367i	$-0.753911\pi$
$443$	−634.146			−1.43148			−0.715740	+	0.698367i	$0.753911\pi$
$444$	−38.0134	−	91.7724i	−0.0856157	−	0.206695i
$445$	−580.216	+	387.688i	−1.30386	+	0.871209i
$446$	−777.880	+	777.880i	−1.74412	+	1.74412i
$447$	−35.7076	−	7.10268i	−0.0798828	−	0.0158897i
$448$	615.626	+	411.348i	1.37416	+	0.918187i
$449$	433.336	−	86.1959i	0.965114	−	0.191973i	0.312713	−	0.949848i	$-0.398762\pi$
$449$	433.336	−	86.1959i	0.965114	−	0.191973i	0.652400	+	0.757874i	$0.273762\pi$
$450$	920.685	+	381.360i	2.04597	+	0.847468i
$451$	67.4939	−	162.945i	0.149654	−	0.361296i
$452$	−61.1029	−	307.185i	−0.135183	−	0.679613i
$453$	59.3080	−	88.7607i	0.130923	−	0.195940i
$454$	−57.2435	+	287.782i	−0.126087	+	0.633882i
$455$	50.3796	+	50.3796i	0.110724	+	0.110724i
$456$	−4.47749	−	6.70103i	−0.00981905	−	0.0146953i
$457$	246.501	−	102.104i	0.539390	−	0.223423i	−0.0963202	−	0.995350i	$-0.530707\pi$
$457$	246.501	−	102.104i	0.539390	−	0.223423i	0.635710	+	0.771928i	$0.280707\pi$
$458$			1094.83i			2.39046i
$459$	−199.145	+	133.064i	−0.433866	+	0.289900i
$460$	355.825			0.773533
$461$	172.768	+	417.100i	0.374769	+	0.904772i	0.992928	+	0.118719i	$0.0378787\pi$
$461$	172.768	+	417.100i	0.374769	+	0.904772i	−0.618159	+	0.786053i	$0.712121\pi$
$462$	−129.724	+	86.6785i	−0.280787	+	0.187616i
$463$	−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
$465$	69.6405	+	46.5323i	0.149764	+	0.100069i
$466$	−831.808	+	165.457i	−1.78499	+	0.355058i
$467$	76.1879	+	31.5580i	0.163143	+	0.0675761i	0.462760	−	0.886483i	$-0.346859\pi$
$467$	76.1879	+	31.5580i	0.163143	+	0.0675761i	−0.299617	+	0.954059i	$0.596859\pi$
$468$	−18.6218	+	44.9569i	−0.0397901	+	0.0960619i
$469$	−179.617	−	902.998i	−0.382979	−	1.92537i
$470$	1063.01	−	1590.91i	2.26173	−	3.38492i
$471$	−5.70949	+	28.7035i	−0.0121221	+	0.0609417i
$472$	−68.4785	−	68.4785i	−0.145082	−	0.145082i
$473$	104.247	+	156.017i	0.220396	+	0.329846i
$474$	216.538	−	89.6931i	0.456832	−	0.189226i
$475$			111.029i			0.233746i
$476$	−676.380	−	134.540i	−1.42097	−	0.282648i
$477$	501.069			1.05046
$478$	−380.630	−	918.923i	−0.796298	−	1.92243i
$479$	382.794	−	255.775i	0.799153	−	0.533977i	−0.0876357	−	0.996153i	$-0.527931\pi$
$479$	382.794	−	255.775i	0.799153	−	0.533977i	0.886788	+	0.462176i	$0.152931\pi$
$480$	−204.501	+	204.501i	−0.426043	+	0.426043i
$481$	−26.2278	−	5.21704i	−0.0545277	−	0.0108462i
$482$	610.191	+	407.717i	1.26596	+	0.845885i
$483$	−53.7057	+	10.6827i	−0.111192	+	0.0221174i
$484$	−266.195	−	110.261i	−0.549989	−	0.227813i
$485$	75.5612	−	182.421i	0.155796	−	0.376125i
$486$	−105.413	−	529.948i	−0.216900	−	1.09043i
$487$	290.646	−	434.982i	0.596809	−	0.893187i	−0.402948	−	0.915223i	$-0.632015\pi$
$487$	290.646	−	434.982i	0.596809	−	0.893187i	0.999757	+	0.0220352i	$0.00701459\pi$
$488$	−25.0819	+	126.095i	−0.0513974	+	0.258392i
$489$	−91.7633	−	91.7633i	−0.187655	−	0.187655i
$490$	−171.405	−	256.526i	−0.349806	−	0.523522i
$491$	−451.862	+	187.167i	−0.920289	+	0.381196i	−0.791986	−	0.610539i	$-0.790953\pi$
$491$	−451.862	+	187.167i	−0.920289	+	0.381196i	−0.128303	+	0.991735i	$0.540953\pi$
$492$		−	91.6511i		−	0.186283i
$493$	51.1951	−	10.1833i	0.103844	−	0.0206559i
$494$	−9.62041			−0.0194745
$495$	206.941	+	499.600i	0.418063	+	1.00929i
$496$	106.577	−	71.2122i	0.214872	−	0.143573i
$497$	−588.550	+	588.550i	−1.18421	+	1.18421i
$498$	−286.692	−	57.0266i	−0.575687	−	0.114511i
$499$	−421.610	−	281.711i	−0.844910	−	0.564551i	0.0560623	−	0.998427i	$-0.482145\pi$
$499$	−421.610	−	281.711i	−0.844910	−	0.564551i	−0.900972	+	0.433876i	$0.857145\pi$
$500$	−588.580	+	117.076i	−1.17716	+	0.234152i
$501$	83.1249	+	34.4315i	0.165918	+	0.0687255i
$502$	−254.709	+	614.921i	−0.507388	+	1.22494i
$503$	−131.577	−	661.484i	−0.261585	−	1.31508i	−0.858517	−	0.512785i	$-0.828614\pi$
$503$	−131.577	−	661.484i	−0.261585	−	1.31508i	0.596932	−	0.802292i	$-0.296386\pi$
$504$	128.327	−	192.055i	0.254617	−	0.381062i
$505$	12.0659	−	60.6592i	0.0238928	−	0.120117i
$506$	148.326	+	148.326i	0.293134	+	0.293134i
$507$	75.7115	+	113.310i	0.149332	+	0.223492i
$508$	−568.996	+	235.686i	−1.12007	+	0.463949i
$509$			349.504i			0.686648i	0.939217	+	0.343324i	$0.111553\pi$
$509$			349.504i			0.686648i	−0.939217	+	0.343324i	$0.888447\pi$
$510$	128.487	−	310.196i	0.251936	−	0.608227i
$511$	479.395			0.938150
$512$	223.266	+	539.012i	0.436067	+	1.05276i
$513$	32.9519	−	22.0177i	0.0642337	−	0.0429196i
$514$	696.221	−	696.221i	1.35451	−	1.35451i
$515$	327.358	+	65.1157i	0.635648	+	0.126438i
$516$	81.0747	+	54.1724i	0.157121	+	0.104985i
$517$	623.444	−	124.011i	1.20589	−	0.239866i
$518$	520.006	+	215.393i	1.00387	+	0.415818i
$519$	55.3631	−	133.658i	0.106673	−	0.257530i
$520$	−6.24017	−	31.3715i	−0.0120003	−	0.0603297i
$521$	−175.223	+	262.240i	−0.336320	+	0.503339i	−0.960627	−	0.277840i	$-0.910381\pi$
$521$	−175.223	+	262.240i	−0.336320	+	0.503339i	0.624307	+	0.781179i	$0.285381\pi$
$522$	−15.1238	+	76.0323i	−0.0289727	+	0.145656i
$523$	−145.221	−	145.221i	−0.277669	−	0.277669i	0.554509	−	0.832178i	$-0.312906\pi$
$523$	−145.221	−	145.221i	−0.277669	−	0.277669i	−0.832178	+	0.554509i	$0.812906\pi$
$524$	491.600	+	735.731i	0.938168	+	1.40407i
$525$	232.722	−	96.3965i	0.443279	−	0.183612i
$526$		−	419.991i		−	0.798461i
$527$	−121.253	+	181.468i	−0.230082	+	0.344342i
$528$	−65.5098			−0.124072
$529$	−174.266	−	420.715i	−0.329425	−	0.795302i
$530$	−1214.31	+	811.377i	−2.29115	+	1.53090i
$531$	161.959	−	161.959i	0.305007	−	0.305007i
$532$	111.919	+	22.2620i	0.210373	+	0.0418459i
$533$	−20.5152	−	13.7078i	−0.0384901	−	0.0257182i
$534$	−209.664	+	41.7048i	−0.392630	+	0.0780989i
$535$	655.859	+	271.666i	1.22590	+	0.507786i
$536$	−158.177	+	381.873i	−0.295106	+	0.712450i
$537$	39.9728	+	200.957i	0.0744372	+	0.374221i
$538$	−546.412	+	817.764i	−1.01564	+	1.52001i
$539$	19.9961	−	100.527i	0.0370985	−	0.186507i
$540$	413.135	+	413.135i	0.765065	+	0.765065i
$541$	439.282	+	657.431i	0.811981	+	1.21522i	0.973577	+	0.228358i	$0.0733358\pi$
$541$	439.282	+	657.431i	0.811981	+	1.21522i	−0.161596	+	0.986857i	$0.551664\pi$
$542$	−53.6632	+	22.2280i	−0.0990096	+	0.0410111i
$543$			244.849i			0.450919i
$544$	−532.885	−	532.885i	−0.979568	−	0.979568i
$545$	149.615			0.274523
$546$	8.35251	+	20.1647i	0.0152976	+	0.0369317i
$547$	−783.860	+	523.758i	−1.43302	+	0.957511i	−0.434637	+	0.900606i	$0.643123\pi$
$547$	−783.860	+	523.758i	−1.43302	+	0.957511i	−0.998380	+	0.0569051i	$0.981877\pi$
$548$	632.218	−	632.218i	1.15368	−	1.15368i
$549$	−298.229	−	59.3214i	−0.543222	−	0.108054i
$550$	−802.330	−	536.099i	−1.45878	−	0.974726i
$551$	−8.47111	+	1.68501i	−0.0153741	+	0.00305809i
$552$	22.7119	+	9.40756i	0.0411447	+	0.0170427i
$553$	−286.408	+	691.450i	−0.517917	+	1.25036i
$554$	−181.908	−	914.512i	−0.328353	−	1.65074i
$555$	−85.7957	+	128.402i	−0.154587	+	0.231356i
$556$	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	$0.875804\pi$
$558$	−180.079	−	269.507i	−0.322722	−	0.482987i
$559$	24.2519	−	10.0455i	0.0433844	−	0.0179704i
$560$		−	629.663i		−	1.12440i
$561$	103.053	−	42.6859i	0.183695	−	0.0760889i
$562$	261.932			0.466071
$563$	−264.879	−	639.473i	−0.470477	−	1.13583i	−0.963953	−	0.266072i	$-0.914274\pi$
$563$	−264.879	−	639.473i	−0.470477	−	1.13583i	0.493476	−	0.869759i	$-0.335726\pi$
$564$	274.652	−	183.517i	0.486972	−	0.325384i
$565$	−344.303	+	344.303i	−0.609386	+	0.609386i
$566$	−22.2142	−	4.41867i	−0.0392476	−	0.00780684i
$567$	415.428	+	277.580i	0.732677	+	0.489559i
$568$	366.491	−	72.8996i	0.645231	−	0.128344i
$569$	−370.173	−	153.331i	−0.650567	−	0.269474i	0.0328958	−	0.999459i	$-0.489527\pi$
$569$	−370.173	−	153.331i	−0.650567	−	0.269474i	−0.683463	+	0.729985i	$0.739527\pi$
$570$	−21.2604	+	51.3272i	−0.0372990	+	0.0900477i
$571$	127.142	+	639.187i	0.222666	+	1.11942i	0.916731	+	0.399505i	$0.130818\pi$
$571$	127.142	+	639.187i	0.222666	+	1.11942i	−0.694065	+	0.719912i	$0.744182\pi$
$572$	26.1777	−	39.1776i	0.0457651	−	0.0684924i
$573$	−21.0112	+	105.631i	−0.0366688	+	0.184347i
$574$	367.214	+	367.214i	0.639745	+	0.639745i
$575$	−188.156	−	281.596i	−0.327229	−	0.489732i
$576$	726.319	−	300.851i	1.26097	−	0.522311i
$577$		−	684.109i		−	1.18563i	−0.805339	−	0.592815i	$-0.798017\pi$
$577$		−	684.109i		−	1.18563i	0.805339	−	0.592815i	$-0.201983\pi$
$578$	808.303	+	334.810i	1.39845	+	0.579256i
$579$	−258.876			−0.447109
$580$	−48.7281	−	117.640i	−0.0840140	−	0.202828i
$581$	776.094	−	518.569i	1.33579	−	0.892546i
$582$	42.7712	−	42.7712i	0.0734900	−	0.0734900i
$583$	−475.863	−	94.6550i	−0.816232	−	0.162359i
$584$	−178.950	−	119.570i	−0.306420	−	0.204744i
$585$	74.1968	−	14.7587i	0.126832	−	0.0252285i
$586$	−215.405	−	89.2236i	−0.367585	−	0.152259i
$587$	−141.750	+	342.216i	−0.241483	+	0.582991i	−0.997430	−	0.0716408i	$-0.977176\pi$
$587$	−141.750	+	342.216i	−0.241483	+	0.582991i	0.755948	+	0.654632i	$0.227176\pi$
$588$	−10.3910	−	52.2391i	−0.0176718	−	0.0888420i
$589$	20.0634	−	30.0270i	0.0340635	−	0.0509796i
$590$	−130.239	+	654.756i	−0.220744	+	1.10976i
$591$	−66.4527	−	66.4527i	−0.112441	−	0.112441i
$592$	131.300	+	196.505i	0.221791	+	0.331934i
$593$	585.245	−	242.416i	0.986922	−	0.408797i	0.169937	−	0.985455i	$-0.445644\pi$
$593$	585.245	−	242.416i	0.986922	−	0.408797i	0.816985	+	0.576658i	$0.195644\pi$
$594$			344.431i			0.579850i
$595$	410.286	+	990.517i	0.689556	+	1.66473i
$596$	−231.425			−0.388297
$597$	−91.9883	−	222.080i	−0.154084	−	0.371992i
$598$	24.3996	−	16.3033i	0.0408020	−	0.0272630i
$599$	315.855	−	315.855i	0.527304	−	0.527304i	−0.392463	−	0.919768i	$-0.628377\pi$
$599$	315.855	−	315.855i	0.527304	−	0.527304i	0.919768	+	0.392463i	$0.128377\pi$
$600$	−110.914	−	22.0622i	−0.184857	−	0.0367703i
$601$	362.279	+	242.067i	0.602794	+	0.402774i	0.819182	−	0.573533i	$-0.194428\pi$
$601$	362.279	+	242.067i	0.602794	+	0.402774i	−0.216388	+	0.976307i	$0.569428\pi$
$602$	−541.887	+	107.788i	−0.900145	+	0.179050i
$603$	−903.170	−	374.105i	−1.49779	−	0.620407i
$604$	259.680	−	626.922i	0.429933	−	1.03795i
$605$	87.3876	+	439.327i	0.144442	+	0.726160i
$606$	10.5261	−	15.7535i	0.0173699	−	0.0259958i
$607$	123.803	−	622.400i	0.203959	−	1.02537i	−0.734139	−	0.679000i	$-0.762414\pi$
$607$	123.803	−	622.400i	0.203959	−	1.02537i	0.938098	−	0.346371i	$-0.112586\pi$
$608$	88.1749	+	88.1749i	0.145025	+	0.145025i
$609$	10.8865	+	16.2928i	0.0178760	+	0.0267534i
$610$	818.798	−	339.157i	1.34229	−	0.555996i
$611$		−	88.9259i		−	0.145542i
$612$	−517.778	+	517.778i	−0.846042	+	0.846042i
$613$	−692.422			−1.12956			−0.564782	−	0.825240i	$-0.691040\pi$
$613$	−692.422			−1.12956			−0.564782	+	0.825240i	$0.691040\pi$
$614$	184.992	+	446.610i	0.301290	+	0.727377i
$615$	−118.472	+	79.1601i	−0.192637	+	0.128716i
$616$	−158.152	+	158.152i	−0.256740	+	0.256740i
$617$	−263.077	−	52.3292i	−0.426381	−	0.0848124i	−0.0227645	−	0.999741i	$-0.507247\pi$
$617$	−263.077	−	52.3292i	−0.426381	−	0.0848124i	−0.403616	+	0.914928i	$0.632247\pi$
$618$	85.0165	+	56.8062i	0.137567	+	0.0919195i
$619$	−153.549	+	30.5428i	−0.248060	+	0.0493422i	−0.317554	−	0.948240i	$-0.602862\pi$
$619$	−153.549	+	30.5428i	−0.248060	+	0.0493422i	0.0694940	+	0.997582i	$0.477862\pi$
$620$	491.875	+	203.741i	0.793346	+	0.328615i
$621$	−46.2610	+	111.684i	−0.0744944	+	0.179845i
$622$	196.680	+	988.775i	0.316205	+	1.58967i
$623$	379.241	−	567.575i	0.608734	−	0.911035i
$624$	−1.78791	+	8.98845i	−0.00286525	+	0.0144046i
$625$	−38.0547	−	38.0547i	−0.0608875	−	0.0608875i
$626$	−663.623	−	993.182i	−1.06010	−	1.58655i
$627$	−17.0519	+	7.06311i	−0.0271959	+	0.0112649i
$628$			186.031i			0.296228i
$629$	−334.589	−	223.565i	−0.531938	−	0.355429i
$630$	−1592.27			−2.52741
$631$	−119.803	−	289.230i	−0.189862	−	0.458368i	0.800071	−	0.599906i	$-0.204795\pi$
$631$	−119.803	−	289.230i	−0.189862	−	0.458368i	−0.989933	+	0.141538i	$0.954795\pi$
$632$	279.372	−	186.670i	0.442044	−	0.295365i
$633$	131.992	−	131.992i	0.208519	−	0.208519i
$634$	412.999	+	82.1506i	0.651418	+	0.129575i
$635$	796.105	+	531.940i	1.25371	+	0.837701i
$636$	−247.283	+	49.1877i	−0.388810	+	0.0773392i
$637$	−13.2473	−	5.48723i	−0.0207965	−	0.00861418i
$638$	28.7259	−	69.3506i	0.0450250	−	0.108700i
$639$	172.415	+	866.790i	0.269820	+	1.35648i
$640$	−482.018	+	721.390i	−0.753153	+	1.12717i
$641$	−72.2074	+	363.011i	−0.112648	+	0.566320i	0.882697	+	0.469943i	$0.155725\pi$
$641$	−72.2074	+	363.011i	−0.112648	+	0.566320i	−0.995345	+	0.0963771i	$0.969275\pi$
$642$	153.776	+	153.776i	0.239526	+	0.239526i
$643$	−122.220	−	182.915i	−0.190077	−	0.284471i	0.724175	−	0.689616i	$-0.242221\pi$
$643$	−122.220	−	182.915i	−0.190077	−	0.284471i	−0.914252	+	0.405146i	$0.867221\pi$
$644$	−321.577	+	133.202i	−0.499344	+	0.206835i
$645$		−	151.589i		−	0.235022i
$646$	−133.748	−	55.4001i	−0.207040	−	0.0857586i
$647$	769.098			1.18871			0.594357	−	0.804201i	$-0.297407\pi$
$647$	769.098			1.18871			0.594357	+	0.804201i	$0.297407\pi$
$648$	−85.8381	−	207.231i	−0.132466	−	0.319802i
$649$	−184.407	+	123.217i	−0.284140	+	0.189856i
$650$	−95.4544	+	95.4544i	−0.146853	+	0.146853i
$651$	−80.3568	−	15.9840i	−0.123436	−	0.0245529i
$652$	−685.889	−	458.297i	−1.05198	−	0.702909i
$653$	−41.6201	+	8.27876i	−0.0637368	+	0.0126780i	−0.226856	−	0.973928i	$-0.572845\pi$
$653$	−41.6201	+	8.27876i	−0.0637368	+	0.0126780i	0.163119	+	0.986606i	$0.447845\pi$
$654$	42.3446	+	17.5397i	0.0647472	+	0.0268192i
$655$	526.432	−	1270.92i	0.803713	−	1.94033i
$656$	42.5406	+	213.866i	0.0648485	+	0.326015i
$657$	282.796	−	423.234i	0.430436	−	0.644192i
$658$	−365.148	+	1835.72i	−0.554936	+	2.78985i
$659$	472.719	+	472.719i	0.717328	+	0.717328i	0.968057	−	0.250729i	$-0.0806703\pi$
$659$	472.719	+	472.719i	0.717328	+	0.717328i	−0.250729	+	0.968057i	$0.580670\pi$
$660$	−151.171	−	226.244i	−0.229047	−	0.342793i
$661$	−380.158	+	157.467i	−0.575126	+	0.238225i	−0.651237	−	0.758874i	$-0.725750\pi$
$661$	−380.158	+	157.467i	−0.575126	+	0.238225i	0.0761113	+	0.997099i	$0.475750\pi$
$662$		−	480.756i		−	0.726218i
$663$	−3.04428	−	15.3046i	−0.00459168	−	0.0230839i
$664$	−419.043			−0.631089
$665$	−67.8888	−	163.898i	−0.102088	−	0.246463i
$666$	496.914	−	332.027i	0.746116	−	0.498539i
$667$	18.6292	−	18.6292i	0.0279298	−	0.0279298i
$668$	560.937	+	111.577i	0.839725	+	0.167032i
$669$	245.494	+	164.034i	0.366957	+	0.245193i
$670$	2794.56	−	555.873i	4.17099	−	0.829662i
$671$	272.020	+	112.675i	0.405395	+	0.167920i
$672$	108.264	−	261.372i	0.161107	−	0.388946i
$673$	3.16371	+	15.9051i	0.00470091	+	0.0236331i	0.983065	−	0.183260i	$-0.0586649\pi$
$673$	3.16371	+	15.9051i	0.00470091	+	0.0236331i	−0.978364	+	0.206893i	$0.933665\pi$
$674$	−811.269	+	1214.15i	−1.20366	+	1.80141i
$675$	108.489	−	545.412i	0.160725	−	0.808018i
$676$	612.536	+	612.536i	0.906119	+	0.906119i
$677$	−571.240	−	854.921i	−0.843782	−	1.26281i	−0.962881	−	0.269926i	$-0.913001\pi$
$677$	−571.240	−	854.921i	−0.843782	−	1.26281i	0.119099	−	0.992882i	$-0.461999\pi$
$678$	−137.809	+	57.0825i	−0.203258	+	0.0841924i
$679$			193.149i			0.284461i
$680$	93.9017	−	472.076i	0.138091	−	0.694229i
$681$	78.7512			0.115641
$682$	120.108	+	289.967i	0.176112	+	0.425172i
$683$	188.201	−	125.752i	0.275551	−	0.184117i	−0.410114	−	0.912034i	$-0.634511\pi$
$683$	188.201	−	125.752i	0.275551	−	0.184117i	0.685666	+	0.727917i	$0.259511\pi$
$684$	85.6752	−	85.6752i	0.125256	−	0.125256i
$685$	−1363.28	−	271.173i	−1.99019	−	0.395874i
$686$	−717.830	−	479.639i	−1.04640	−	0.699181i
$687$	288.197	−	57.3259i	0.419500	−	0.0834438i
$688$	−214.331	−	88.7787i	−0.311527	−	0.129039i
$689$	−25.9748	+	62.7087i	−0.0376993	+	0.0910141i
$690$	−33.0605	−	166.206i	−0.0479138	−	0.240879i
$691$	−21.7058	+	32.4851i	−0.0314122	+	0.0470117i	−0.846843	−	0.531842i	$-0.821500\pi$
$691$	−21.7058	+	32.4851i	−0.0314122	+	0.0470117i	0.815431	+	0.578854i	$0.196500\pi$
$692$	179.407	−	901.942i	0.259259	−	1.30338i
$693$	−374.046	−	374.046i	−0.539749	−	0.539749i
$694$	33.2845	+	49.8138i	0.0479604	+	0.0717778i
$695$	−1332.08	+	551.766i	−1.91666	+	0.793908i
$696$		−	8.79713i		−	0.0126395i
$697$	−206.274	−	308.711i	−0.295946	−	0.442914i
$698$	1185.05			1.69778
$699$	87.1075	+	210.296i	0.124617	+	0.300853i
$700$	1331.35	−	889.579i	1.90193	−	1.27083i
$701$	−401.261	+	401.261i	−0.572412	+	0.572412i	−0.932802	−	0.360390i	$-0.882644\pi$
$701$	−401.261	+	401.261i	−0.572412	+	0.572412i	0.360390	+	0.932802i	$0.382644\pi$
$702$	47.2585	+	9.40031i	0.0673198	+	0.0133908i
$703$	55.3634	+	36.9927i	0.0787531	+	0.0526212i
$704$	−746.614	+	148.511i	−1.06053	+	0.210953i
$705$	−474.441	−	196.520i	−0.672965	−	0.278751i
$706$	226.136	−	545.941i	0.320306	−	0.773288i
$707$	11.8030	+	59.3377i	0.0166945	+	0.0839288i
$708$	−64.0298	+	95.8273i	−0.0904375	+	0.135349i
$709$	55.6759	−	279.901i	0.0785273	−	0.394783i	−0.921453	−	0.388490i	$-0.872997\pi$
$709$	55.6759	−	279.901i	0.0785273	−	0.394783i	0.999980	−	0.00629329i	$-0.00200323\pi$
$710$	−1821.42	−	1821.42i	−2.56539	−	2.56539i
$711$	441.495	+	660.744i	0.620950	+	0.929317i
$712$	−283.128	+	117.276i	−0.397652	+	0.164713i
$713$			110.156i			0.154496i
$714$			328.438i			0.459998i
$715$	−73.2524			−0.102451
$716$	498.416	+	1203.28i	0.696112	+	1.68056i
$717$	−221.961	+	148.310i	−0.309569	+	0.206848i
$718$	761.667	−	761.667i	1.06082	−	1.06082i
$719$	601.644	+	119.674i	0.836779	+	0.166446i	0.594838	−	0.803845i	$-0.297216\pi$
$719$	601.644	+	119.674i	0.836779	+	0.166446i	0.241941	+	0.970291i	$0.422216\pi$
$720$	−555.899	−	371.440i	−0.772083	−	0.515889i
$721$	−320.226	+	63.6970i	−0.444142	+	0.0883453i
$722$	−987.549	−	409.056i	−1.36780	−	0.566560i
$723$	75.3748	−	181.971i	0.104253	−	0.251689i
$724$	303.640	+	1526.50i	0.419392	+	2.10842i
$725$	−67.3322	+	100.770i	−0.0928719	+	0.138993i
$726$	−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	$0.673598\pi$
$728$	17.3833	+	26.0160i	0.0238782	+	0.0357363i
$729$	394.941	−	163.590i	0.541758	−	0.224403i
$730$			1483.61i			2.03235i
$731$	395.009			0.540368
$732$	153.003			0.209020
$733$	516.266	+	1246.38i	0.704319	+	1.70038i	0.713730	+	0.700421i	$0.247004\pi$
$733$	516.266	+	1246.38i	0.704319	+	1.70038i	−0.00941053	+	0.999956i	$0.502996\pi$
$734$	−205.719	+	137.457i	−0.280271	+	0.187271i
$735$	−58.5513	+	58.5513i	−0.0796617	+	0.0796617i
$736$	−373.058	−	74.2058i	−0.506872	−	0.100823i
$737$	787.066	+	525.901i	1.06793	+	0.713569i
$738$	540.816	−	107.575i	0.732813	−	0.145766i
$739$	602.925	+	249.740i	0.815866	+	0.337943i	0.751292	−	0.659970i	$-0.229431\pi$
$739$	602.925	+	249.740i	0.815866	+	0.337943i	0.0645741	+	0.997913i	$0.479431\pi$
$740$	−375.656	+	906.913i	−0.507643	+	1.22556i
$741$	0.503729	+	2.53241i	0.000679796	+	0.00341756i
$742$	793.700	−	1187.86i	1.06968	−	1.60088i
$743$	−43.5044	+	218.711i	−0.0585523	+	0.294362i	−0.998955	−	0.0456999i	$-0.985448\pi$
$743$	−43.5044	+	218.711i	−0.0585523	+	0.294362i	0.940403	+	0.340062i	$0.110448\pi$
$744$	26.0091	+	26.0091i	0.0349584	+	0.0349584i
$745$	199.885	+	299.149i	0.268302	+	0.401542i
$746$	−214.860	+	88.9980i	−0.288016	+	0.119300i
$747$		−	991.082i		−	1.32675i
$748$	589.542	−	393.920i	0.788158	−	0.526631i
$749$	−694.430			−0.927143
$750$	109.373	+	264.049i	0.145830	+	0.352065i
$751$	−373.353	+	249.467i	−0.497142	+	0.332180i	−0.778734	−	0.627355i	$-0.784138\pi$
$751$	−373.353	+	249.467i	−0.497142	+	0.332180i	0.281592	+	0.959534i	$0.409138\pi$
$752$	−555.715	+	555.715i	−0.738982	+	0.738982i
$753$	175.204	+	34.8503i	0.232675	+	0.0462820i
$754$	−8.73143	−	5.83416i	−0.0115802	−	0.00773761i
$755$	−1034.67	+	205.809i	−1.37043	+	0.272595i
$756$	−528.027	−	218.716i	−0.698449	−	0.289307i
$757$	−17.6369	+	42.5792i	−0.0232984	+	0.0562473i	−0.935101	−	0.354382i	$-0.884691\pi$
$757$	−17.6369	+	42.5792i	−0.0232984	+	0.0562473i	0.911802	+	0.410630i	$0.134691\pi$
$758$	−348.021	−	1749.62i	−0.459131	−	2.30821i
$759$	31.2779	−	46.8107i	0.0412093	−	0.0616741i
$760$	−15.5376	+	78.1130i	−0.0204443	+	0.102780i
$761$	−552.081	−	552.081i	−0.725467	−	0.725467i	0.244246	−	0.969713i	$-0.421460\pi$
$761$	−552.081	−	552.081i	−0.725467	−	0.725467i	−0.969713	+	0.244246i	$0.921460\pi$
$762$	162.956	+	243.881i	0.213853	+	0.320054i
$763$	−135.215	+	56.0079i	−0.177215	+	0.0734048i
$764$			684.604i			0.896079i
$765$	1116.51	+	222.087i	1.45949	+	0.290310i
$766$	707.240			0.923289
$767$	11.8734	+	28.6649i	0.0154803	+	0.0373727i
$768$	33.7429	−	22.5463i	0.0439360	−	0.0293571i
$769$	−625.504	+	625.504i	−0.813400	+	0.813400i	−0.985142	−	0.171742i	$-0.945060\pi$
$769$	−625.504	+	625.504i	−0.813400	+	0.813400i	0.171742	+	0.985142i	$0.445060\pi$
$770$	1512.17	+	300.789i	1.96386	+	0.390635i
$771$	−219.723	−	146.814i	−0.284984	−	0.190420i
$772$	−1613.95	+	321.035i	−2.09061	+	0.415848i
$773$	1123.75	+	465.474i	1.45376	+	0.602166i	0.963090	−	0.269181i	$-0.0867531\pi$
$773$	1123.75	+	465.474i	1.45376	+	0.602166i	0.490667	+	0.871347i	$0.336753\pi$
$774$	−224.500	+	541.991i	−0.290052	+	0.700247i
$775$	−98.8595	−	497.000i	−0.127561	−	0.641291i
$776$	48.1751	−	72.0992i	0.0620813	−	0.0929113i
$777$	29.4711	−	148.161i	0.0379293	−	0.190683i
$778$	−864.056	−	864.056i	−1.11061	−	1.11061i
$779$	34.1316	+	51.0816i	0.0438146	+	0.0655733i
$780$	−35.1682	+	14.5671i	−0.0450874	+	0.0186758i
$781$		−	855.757i		−	1.09572i
$782$	433.098	−	86.1486i	0.553834	−	0.110164i
$783$	43.2592			0.0552481
$784$	48.4944	+	117.076i	0.0618551	+	0.149331i
$785$	240.470	−	160.677i	0.306332	−	0.204684i
$786$	297.985	−	297.985i	0.379116	−	0.379116i
$787$	−190.336	−	37.8601i	−0.241850	−	0.0481069i	0.0726771	−	0.997356i	$-0.476846\pi$
$787$	−190.336	−	37.8601i	−0.241850	−	0.0481069i	−0.314527	+	0.949249i	$0.601846\pi$
$788$	−496.704	−	331.887i	−0.630336	−	0.421177i
$789$	−110.556	+	21.9909i	−0.140121	+	0.0278718i
$790$	−2139.88	−	886.365i	−2.70870	−	1.12198i
$791$	182.276	−	440.053i	0.230437	−	0.556324i
$792$	46.3305	+	232.919i	0.0584981	+	0.294090i
$793$	22.8839	−	34.2481i	0.0288573	−	0.0431881i
$794$	155.795	−	783.233i	0.196215	−	0.986440i
$795$	277.163	+	277.163i	0.348633	+	0.348633i
$796$	−848.899	−	1270.47i	−1.06646	−	1.59606i
$797$	118.577	−	49.1164i	0.148780	−	0.0616266i	−0.307051	−	0.951693i	$-0.599342\pi$
$797$	118.577	−	49.1164i	0.148780	−	0.0616266i	0.455831	+	0.890066i	$0.349342\pi$
$798$		−	54.3457i		−	0.0681024i
$799$	512.088	−	1236.29i	0.640911	−	1.54730i
$800$	1749.75			2.18719
$801$	−277.369	−	669.628i	−0.346278	−	0.835990i
$802$	602.324	−	402.460i	0.751028	−	0.501821i
$803$	−348.522	+	348.522i	−0.434025	+	0.434025i
$804$	482.449	+	95.9651i	0.600061	+	0.119360i
$805$	449.932	+	300.635i	0.558921	+	0.373459i
$806$	43.0638	−	8.56592i	0.0534290	−	0.0106277i
$807$	243.873	+	101.016i	0.302197	+	0.125174i
$808$	10.3941	−	25.0936i	0.0128640	−	0.0310564i
$809$	68.1098	+	342.411i	0.0841902	+	0.423253i	0.999777	+	0.0211316i	$0.00672688\pi$
$809$	68.1098	+	342.411i	0.0841902	+	0.423253i	−0.915587	+	0.402121i	$0.868273\pi$
$810$	−859.045	+	1285.65i	−1.06055	+	1.58722i
$811$	36.2150	−	182.065i	0.0446547	−	0.224494i	−0.952014	−	0.306056i	$-0.900991\pi$
$811$	36.2150	−	182.065i	0.0446547	−	0.224494i	0.996668	+	0.0815613i	$0.0259906\pi$
$812$	88.0762	+	88.0762i	0.108468	+	0.108468i
$813$	8.66099	+	12.9621i	0.0106531	+	0.0159435i
$814$	−534.639	+	221.455i	−0.656804	+	0.272057i
$815$			1282.44i			1.57355i
$816$	−76.6173	+	114.666i	−0.0938937	+	0.140522i
$817$	−65.3610			−0.0800013
$818$	−301.101	−	726.923i	−0.368095	−	0.888659i
$819$	−61.5306	+	41.1134i	−0.0751290	+	0.0501996i
$820$	−640.437	+	640.437i	−0.781021	+	0.781021i
$821$	1545.78	+	307.474i	1.88280	+	0.374512i	0.996130	−	0.0878920i	$-0.0280130\pi$
$821$	1545.78	+	307.474i	1.88280	+	0.374512i	0.886669	+	0.462404i	$0.153013\pi$
$822$	−354.051	−	236.569i	−0.430718	−	0.287797i
$823$	986.291	−	196.185i	1.19841	−	0.238378i	0.444757	−	0.895651i	$-0.353290\pi$
$823$	986.291	−	196.185i	1.19841	−	0.238378i	0.753653	+	0.657273i	$0.228290\pi$
$824$	135.422	+	56.0937i	0.164347	+	0.0680749i
$825$	−99.1090	+	239.270i	−0.120132	+	0.290025i
$826$	−127.402	−	640.491i	−0.154239	−	0.775413i
$827$	−883.014	+	1321.52i	−1.06773	+	1.59797i	−0.303731	+	0.952758i	$0.598232\pi$
$827$	−883.014	+	1321.52i	−1.06773	+	1.59797i	−0.764001	+	0.645216i	$0.776768\pi$
$828$	−72.1020	+	362.481i	−0.0870798	+	0.437780i
$829$	−269.747	−	269.747i	−0.325388	−	0.325388i	0.525442	−	0.850830i	$-0.323900\pi$
$829$	−269.747	−	269.747i	−0.325388	−	0.325388i	−0.850830	+	0.525442i	$0.823900\pi$
$830$	1604.85	+	2401.83i	1.93355	+	2.89377i
$831$	−231.205	+	95.7684i	−0.278225	+	0.115245i
$832$			106.494i			0.127998i
$833$	−152.572	−	152.572i	−0.183160	−	0.183160i
$834$	−441.695			−0.529611
$835$	−340.259	−	821.457i	−0.407495	−	0.983781i
$836$	−97.5499	+	65.1807i	−0.116686	+	0.0779674i
$837$	−127.898	+	127.898i	−0.152805	+	0.152805i
$838$	509.365	+	101.319i	0.607834	+	0.120906i
$839$	−30.7798	−	20.5664i	−0.0366862	−	0.0245130i	0.537092	−	0.843524i	$-0.319523\pi$
$839$	−30.7798	−	20.5664i	−0.0366862	−	0.0245130i	−0.573778	+	0.819011i	$0.694523\pi$
$840$	177.217	−	35.2507i	0.210973	−	0.0419652i
$841$	768.273	+	318.229i	0.913523	+	0.378393i
$842$	726.154	−	1753.09i	0.862416	−	2.08206i
$843$	−13.7149	−	68.9493i	−0.0162691	−	0.0817904i
$844$	659.215	−	986.584i	0.781060	−	1.16894i
$845$	262.732	−	1320.84i	0.310925	−	1.56313i
$846$	1405.27	+	1405.27i	1.66107	+	1.66107i
$847$	−243.437	−	364.329i	−0.287411	−	0.430141i
$848$	554.200	−	229.557i	0.653538	−	0.270704i
$849$			6.07887i			0.00716004i
$850$	−1876.74	+	777.369i	−2.20792	+	0.914552i
$851$	−203.104			−0.238665
$852$	−170.178	−	410.846i	−0.199739	−	0.482213i
$853$	−65.5718	+	43.8137i	−0.0768720	+	0.0513642i	−0.593412	−	0.804899i	$-0.702220\pi$
$853$	−65.5718	+	43.8137i	−0.0768720	+	0.0513642i	0.516540	+	0.856263i	$0.327220\pi$
$854$	−613.028	+	613.028i	−0.717831	+	0.717831i
$855$	−184.745	−	36.7481i	−0.216077	−	0.0429803i
$856$	259.219	+	173.204i	0.302825	+	0.202342i
$857$	−653.288	+	129.947i	−0.762297	+	0.151630i	−0.560905	−	0.827880i	$-0.689547\pi$
$857$	−653.288	+	129.947i	−0.762297	+	0.151630i	−0.201392	+	0.979511i	$0.564547\pi$
$858$	−20.7322	−	8.58754i	−0.0241634	−	0.0100088i
$859$	−530.649	+	1281.10i	−0.617752	+	1.49138i	0.236556	+	0.971618i	$0.423981\pi$
$859$	−530.649	+	1281.10i	−0.617752	+	1.49138i	−0.854308	+	0.519767i	$0.826019\pi$
$860$	−187.987	−	945.076i	−0.218590	−	1.09893i
$861$	77.4355	−	115.890i	0.0899367	−	0.134600i
$862$	−450.150	+	2263.06i	−0.522216	+	2.62536i
$863$	−375.548	−	375.548i	−0.435166	−	0.435166i	0.455215	−	0.890381i	$-0.349562\pi$
$863$	−375.548	−	375.548i	−0.435166	−	0.435166i	−0.890381	+	0.455215i	$0.849562\pi$
$864$	−346.986	−	519.301i	−0.401604	−	0.601042i
$865$	−1320.84	+	547.109i	−1.52698	+	0.632496i
$866$		−	286.613i		−	0.330962i
$867$	45.8102	−	230.303i	0.0528376	−	0.265632i
$868$	−520.802			−0.600002
$869$	−294.467	−	710.907i	−0.338858	−	0.818075i
$870$	−50.4224	+	33.6912i	−0.0579568	+	0.0387255i
$871$	93.6384	−	93.6384i	0.107507	−	0.107507i
$872$	64.4428	+	12.8185i	0.0739023	+	0.0147001i
$873$	170.522	+	113.939i	0.195329	+	0.130515i
$874$	−71.6635	+	14.2548i	−0.0819949	+	0.0163098i
$875$	−843.160	−	349.249i	−0.963612	−	0.399141i
$876$	−98.0161	+	236.632i	−0.111891	+	0.270128i
$877$	−48.4908	−	243.780i	−0.0552917	−	0.277970i	0.943242	−	0.332107i	$-0.107759\pi$
$877$	−48.4908	−	243.780i	−0.0552917	−	0.277970i	−0.998534	+	0.0541366i	$0.982759\pi$
$878$	−62.1940	+	93.0800i	−0.0708360	+	0.106014i
$879$	−12.2080	+	61.3735i	−0.0138885	+	0.0698220i
$880$	457.768	+	457.768i	0.520191	+	0.520191i
$881$	−81.3688	−	121.777i	−0.0923595	−	0.138226i	0.782412	−	0.622761i	$-0.213989\pi$
$881$	−81.3688	−	121.777i	−0.0923595	−	0.138226i	−0.874772	+	0.484535i	$0.838989\pi$
$882$	296.057	−	122.631i	0.335665	−	0.139037i
$883$		−	322.505i		−	0.365237i	−0.983184	−	0.182619i	$-0.941543\pi$
$883$		−	322.505i		−	0.365237i	0.983184	−	0.182619i	$-0.0584574\pi$
$884$	−37.9588	−	91.6407i	−0.0429399	−	0.103666i
$885$	179.173			0.202455
$886$	734.666	+	1773.64i	0.829194	+	2.00185i
$887$	−52.2618	+	34.9202i	−0.0589197	+	0.0393689i	−0.584681	−	0.811263i	$-0.698780\pi$
$887$	−52.2618	+	34.9202i	−0.0589197	+	0.0393689i	0.525762	+	0.850632i	$0.323780\pi$
$888$	−47.9552	+	47.9552i	−0.0540037	+	0.0540037i
$889$	−918.610	−	182.723i	−1.03331	−	0.205538i
$890$	1756.51	+	1173.66i	1.97361	+	1.31872i
$891$	−503.820	+	100.216i	−0.565454	+	0.112476i
$892$	1733.94	+	718.221i	1.94388	+	0.805180i
$893$	−84.7337	+	204.565i	−0.0948866	+	0.229077i
$894$	21.5022	+	108.099i	0.0240517	+	0.120916i
$895$	1124.92	−	1683.56i	1.25689	−	1.88107i
$896$	165.574	−	832.399i	0.184793	−	0.929016i
$897$	−5.56914	−	5.56914i	−0.00620863	−	0.00620863i
$898$	−743.106	−	1112.14i	−0.827513	−	1.23846i
$899$	36.4189	−	15.0852i	0.0405104	−	0.0167800i
$900$		−	1700.15i		−	1.88905i
$901$	−722.228	+	722.228i	−0.801585	+	0.801585i
$902$	−533.932			−0.591942
$903$	56.7469	+	136.999i	0.0628426	+	0.151715i
$904$	−177.798	+	118.801i	−0.196679	+	0.131417i
$905$	1710.95	−	1710.95i	1.89055	−	1.89055i
$906$	−316.964	−	63.0480i	−0.349850	−	0.0695894i
$907$	−182.765	−	122.120i	−0.201505	−	0.134641i	0.450724	−	0.892663i	$-0.351166\pi$
$907$	−182.765	−	122.120i	−0.201505	−	0.134641i	−0.652229	+	0.758022i	$0.726166\pi$
$908$	490.970	−	97.6601i	0.540716	−	0.107555i
$909$	59.3490	+	24.5832i	0.0652904	+	0.0270442i
$910$	82.5412	−	199.272i	0.0907046	−	0.218980i
$911$	98.5913	+	495.652i	0.108223	+	0.544074i	0.996415	+	0.0846014i	$0.0269617\pi$
$911$	98.5913	+	495.652i	0.108223	+	0.544074i	−0.888192	+	0.459473i	$0.848038\pi$
$912$	12.6776	−	18.9734i	0.0139009	−	0.0208042i
$913$	−187.221	+	941.226i	−0.205062	+	1.03092i
$914$	−571.150	−	571.150i	−0.624890	−	0.624890i
$915$	−132.150	−	197.777i	−0.144426	−	0.216149i
$916$	1725.66	−	714.790i	1.88390	−	0.780338i
$917$			1345.66i			1.46746i
$918$	602.878	+	402.830i	0.656730	+	0.438813i
$919$	−930.196			−1.01218			−0.506091	−	0.862480i	$-0.668910\pi$
$919$	−930.196			−1.01218			−0.506091	+	0.862480i	$0.668910\pi$
$920$	−92.9674	−	224.443i	−0.101052	−	0.243960i
$921$	107.876	−	72.0807i	0.117130	−	0.0782635i
$922$	966.431	−	966.431i	1.04819	−	1.04819i
$923$	−117.416	−	23.3556i	−0.127212	−	0.0253040i
$924$	221.315	+	147.878i	0.239518	+	0.160041i
$925$	916.364	−	182.276i	0.990663	−	0.197055i
$926$	225.922	+	93.5798i	0.243976	+	0.101058i
$927$	−132.667	+	320.288i	−0.143115	+	0.345510i
$928$	26.5547	+	133.499i	0.0286150	+	0.143857i
$929$	637.592	−	954.224i	0.686321	−	1.02715i	−0.310737	−	0.950496i	$-0.600576\pi$
$929$	637.592	−	954.224i	0.686321	−	1.02715i	0.997058	−	0.0766557i	$-0.0244242\pi$
$930$	49.4666	−	248.685i	0.0531899	−	0.267404i
$931$	25.2457	+	25.2457i	0.0271167	+	0.0271167i
$932$	803.857	+	1203.06i	0.862508	+	1.29083i
$933$	249.980	−	103.545i	0.267932	−	0.110981i
$934$		−	249.650i		−	0.267291i
$935$	−1018.39	−	421.831i	−1.08919	−	0.451156i
$936$	33.2228			0.0354944
$937$	517.380	+	1249.07i	0.552166	+	1.33305i	0.915848	+	0.401524i	$0.131519\pi$
$937$	517.380	+	1249.07i	0.552166	+	1.33305i	−0.363682	+	0.931523i	$0.618481\pi$
$938$	−2317.50	+	1548.51i	−2.47068	+	1.65086i
$939$	−226.691	+	226.691i	−0.241418	+	0.241418i
$940$	−3201.58	−	636.834i	−3.40594	−	0.677483i
$941$	−1529.70	−	1022.11i	−1.62561	−	1.08620i	−0.929864	−	0.367905i	$-0.880075\pi$
$941$	−1529.70	−	1022.11i	−1.62561	−	1.08620i	−0.695743	−	0.718291i	$-0.744925\pi$
$942$	86.8953	−	17.2846i	0.0922455	−	0.0183488i
$943$	−173.131	−	71.7133i	−0.183596	−	0.0760480i
$944$	104.933	−	253.331i	0.111158	−	0.268359i
$945$	173.343	+	871.454i	0.183432	+	0.922174i
$946$	315.592	−	472.317i	0.333607	−	0.499278i
$947$	−7.67691	+	38.5945i	−0.00810656	+	0.0407544i	−0.984627	−	0.174671i	$-0.944114\pi$
$947$	−7.67691	+	38.5945i	−0.00810656	+	0.0407544i	0.976520	+	0.215425i	$0.0691138\pi$
$948$	−282.745	−	282.745i	−0.298255	−	0.298255i
$949$	38.3079	+	57.3319i	0.0403666	+	0.0604129i
$950$	310.538	−	128.629i	0.326882	−	0.135399i
$951$		−	113.017i		−	0.118840i
$952$	91.8559	+	461.791i	0.0964873	+	0.485074i
$953$	183.445			0.192492			0.0962458	−	0.995358i	$-0.469317\pi$
$953$	183.445			0.192492			0.0962458	+	0.995358i	$0.469317\pi$
$954$	−580.495	−	1401.44i	−0.608485	−	1.46901i
$955$	884.944	−	591.301i	0.926643	−	0.619163i
$956$	−1199.89	+	1199.89i	−1.25511	+	1.25511i
$957$	−19.7595	−	3.93041i	−0.0206473	−	0.00410701i
$958$	−1158.85	−	774.317i	−1.20965	−	0.808264i
$959$	1333.58	−	265.266i	1.39059	−	0.276606i
$960$	568.173	+	235.345i	0.591847	+	0.245151i
$961$	304.685	−	735.574i	0.317050	−	0.765426i
$962$	15.7937	+	79.4005i	0.0164176	+	0.0825369i
$963$	−409.646	+	613.079i	−0.425386	+	0.636635i
$964$	244.257	−	1227.96i	0.253378	−	1.27382i
$965$	1808.97	+	1808.97i	1.87458	+	1.87458i
$966$	92.0972	+	137.833i	0.0953387	+	0.142684i
$967$	1181.69	−	489.471i	1.22201	−	0.506175i	0.323965	−	0.946069i	$-0.394984\pi$
$967$	1181.69	−	489.471i	1.22201	−	0.506175i	0.898050	+	0.439894i	$0.144984\pi$
$968$			196.715i			0.203218i
$969$	−7.58007	+	38.1076i	−0.00782257	+	0.0393267i
$970$	−597.751			−0.616238
$971$	−349.777	−	844.437i	−0.360224	−	0.869657i	−0.995267	−	0.0971803i	$-0.969018\pi$
$971$	−349.777	−	844.437i	−0.360224	−	0.869657i	0.635043	−	0.772477i	$-0.280982\pi$
$972$	−766.473	+	512.141i	−0.788553	+	0.526894i
$973$	997.319	−	997.319i	1.02499	−	1.02499i
$974$	−1553.32	−	308.974i	−1.59478	−	0.317222i
$975$	30.1248	+	20.1288i	0.0308972	+	0.0206449i
$976$	−357.029	+	71.0174i	−0.365808	+	0.0727637i
$977$	−408.510	−	169.210i	−0.418126	−	0.173194i	0.163694	−	0.986511i	$-0.447659\pi$
$977$	−408.510	−	169.210i	−0.418126	−	0.173194i	−0.581820	+	0.813318i	$0.697659\pi$
$978$	−150.343	+	362.961i	−0.153725	+	0.371126i
$979$	136.919	+	688.340i	0.139856	+	0.703105i
$980$	−292.425	+	437.645i	−0.298393	+	0.446577i
$981$	−30.3170	+	152.414i	−0.0309042	+	0.155366i
$982$	1046.98	+	1046.98i	1.06617	+	1.06617i
$983$	369.695	+	553.287i	0.376088	+	0.562856i	0.970438	−	0.241351i	$-0.0775905\pi$
$983$	369.695	+	553.287i	0.376088	+	0.562856i	−0.594350	+	0.804207i	$0.702590\pi$
$984$	−57.8106	+	23.9459i	−0.0587506	+	0.0243353i
$985$			928.713i			0.942856i
$986$	−87.7920	−	131.390i	−0.0890385	−	0.133256i
$987$	502.343			0.508959
$988$	6.28094	+	15.1635i	0.00635723	+	0.0153477i
$989$	165.770	−	110.764i	0.167614	−	0.111996i
$990$	1157.59	−	1157.59i	1.16928	−	1.16928i
$991$	−1534.80	−	305.291i	−1.54874	−	0.308063i	−0.654642	−	0.755939i	$-0.727181\pi$
$991$	−1534.80	−	305.291i	−1.54874	−	0.308063i	−0.894096	+	0.447876i	$0.852181\pi$
$992$	−473.207	−	316.187i	−0.477023	−	0.318736i
$993$	−126.551	+	25.1726i	−0.127443	+	0.0253500i
$994$	2327.96	+	964.271i	2.34201	+	0.970092i
$995$	−909.048	+	2194.64i	−0.913616	+	2.20566i
$996$	97.2901	+	489.110i	0.0976808	+	0.491075i
$997$	−855.639	+	1280.55i	−0.858213	+	1.28441i	0.0990189	+	0.995086i	$0.468430\pi$
$997$	−855.639	+	1280.55i	−0.858213	+	1.28441i	−0.957232	+	0.289321i	$0.906570\pi$
$998$	−299.476	+	1505.57i	−0.300076	+	1.50858i
$999$	−235.817	−	235.817i	−0.236053	−	0.236053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.3.e.a.12.1	yes	8
3.2	odd	2		153.3.p.b.46.1		8
4.3	odd	2		272.3.bh.c.97.1		8
5.2	odd	4		425.3.t.c.199.1		8
5.3	odd	4		425.3.t.a.199.1		8
5.4	even	2		425.3.u.b.301.1		8
17.2	even	8		289.3.e.k.65.1		8
17.3	odd	16		289.3.e.d.40.1		8
17.4	even	4		289.3.e.m.158.1		8
17.5	odd	16		289.3.e.k.249.1		8
17.6	odd	16		289.3.e.i.75.1		8
17.7	odd	16		289.3.e.c.214.1		8
17.8	even	8		289.3.e.b.224.1		8
17.9	even	8		289.3.e.d.224.1		8
17.10	odd	16	inner	17.3.e.a.10.1	✓	8
17.11	odd	16		289.3.e.m.75.1		8
17.12	odd	16		289.3.e.l.249.1		8
17.13	even	4		289.3.e.i.158.1		8
17.14	odd	16		289.3.e.b.40.1		8
17.15	even	8		289.3.e.l.65.1		8
17.16	even	2		289.3.e.c.131.1		8
51.44	even	16		153.3.p.b.10.1		8
68.27	even	16		272.3.bh.c.129.1		8
85.27	even	16		425.3.t.a.299.1		8
85.44	odd	16		425.3.u.b.401.1		8
85.78	even	16		425.3.t.c.299.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.a.10.1	✓	8	17.10	odd	16	inner
17.3.e.a.12.1	yes	8	1.1	even	1	trivial
153.3.p.b.10.1		8	51.44	even	16
153.3.p.b.46.1		8	3.2	odd	2
272.3.bh.c.97.1		8	4.3	odd	2
272.3.bh.c.129.1		8	68.27	even	16
289.3.e.b.40.1		8	17.14	odd	16
289.3.e.b.224.1		8	17.8	even	8
289.3.e.c.131.1		8	17.16	even	2
289.3.e.c.214.1		8	17.7	odd	16
289.3.e.d.40.1		8	17.3	odd	16
289.3.e.d.224.1		8	17.9	even	8
289.3.e.i.75.1		8	17.6	odd	16
289.3.e.i.158.1		8	17.13	even	4
289.3.e.k.65.1		8	17.2	even	8
289.3.e.k.249.1		8	17.5	odd	16
289.3.e.l.65.1		8	17.15	even	8
289.3.e.l.249.1		8	17.12	odd	16
289.3.e.m.75.1		8	17.11	odd	16
289.3.e.m.158.1		8	17.4	even	4
425.3.t.a.199.1		8	5.3	odd	4
425.3.t.a.299.1		8	85.27	even	16
425.3.t.c.199.1		8	5.2	odd	4
425.3.t.c.299.1		8	85.78	even	16
425.3.u.b.301.1		8	5.4	even	2
425.3.u.b.401.1		8	85.44	odd	16

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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	17.e (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15851 - 2.79690i) q^{2} +(-0.675577 + 0.451406i) q^{3} +(-3.65205 + 3.65205i) q^{4} +(7.87510 + 1.56645i) q^{5} +(2.04520 + 1.36656i) q^{6} +(-7.70353 + 1.53233i) q^{7} +(3.25778 + 1.34942i) q^{8} +(-3.19151 + 7.70500i) q^{9} +O(q^{10})\)	\(q+(-1.15851 - 2.79690i) q^{2} +(-0.675577 + 0.451406i) q^{3} +(-3.65205 + 3.65205i) q^{4} +(7.87510 + 1.56645i) q^{5} +(2.04520 + 1.36656i) q^{6} +(-7.70353 + 1.53233i) q^{7} +(3.25778 + 1.34942i) q^{8} +(-3.19151 + 7.70500i) q^{9} +(-4.74219 - 23.8406i) q^{10} +(4.48649 - 6.71450i) q^{11} +(0.818684 - 4.11580i) q^{12} +(-0.798835 - 0.798835i) q^{13} +(13.2104 + 19.7707i) q^{14} +(-6.02734 + 2.49661i) q^{15} +9.98414i q^{16} +(-6.50562 - 15.7060i) q^{17} +25.2475 q^{18} +(1.07647 + 2.59882i) q^{19} +(-34.4811 + 23.0395i) q^{20} +(4.51262 - 4.51262i) q^{21} +(-23.9774 - 4.76941i) q^{22} +(-7.13426 - 4.76696i) q^{23} +(-2.81002 + 0.558947i) q^{24} +(36.4664 + 15.1049i) q^{25} +(-1.30880 + 3.15972i) q^{26} +(-2.74858 - 13.8181i) q^{27} +(22.5376 - 33.7298i) q^{28} +(-0.599020 + 3.01148i) q^{29} +(13.9655 + 13.9655i) q^{30} +(-7.13254 - 10.6746i) q^{31} +(40.9557 - 16.9644i) q^{32} +6.56139i q^{33} +(-36.3911 + 36.3911i) q^{34} -63.0663 q^{35} +(-16.4835 - 39.7946i) q^{36} +(19.6817 - 13.1509i) q^{37} +(6.02153 - 6.02153i) q^{38} +(0.900273 + 0.179075i) q^{39} +(23.5416 + 15.7300i) q^{40} +(21.4206 - 4.26082i) q^{41} +(-17.8493 - 7.39341i) q^{42} +(-8.89197 + 21.4671i) q^{43} +(8.13684 + 40.9066i) q^{44} +(-37.2030 + 55.6783i) q^{45} +(-5.06757 + 25.4764i) q^{46} +(55.6597 + 55.6597i) q^{47} +(-4.50690 - 6.74505i) q^{48} +(11.7262 - 4.85715i) q^{49} -119.492i q^{50} +(11.4848 + 7.67390i) q^{51} +5.83478 q^{52} +(-22.9922 - 55.5080i) q^{53} +(-35.4634 + 23.6959i) q^{54} +(45.8495 - 45.8495i) q^{55} +(-27.1642 - 5.40329i) q^{56} +(-1.90036 - 1.26978i) q^{57} +(9.11677 - 1.81344i) q^{58} +(-25.3733 - 10.5100i) q^{59} +(12.8944 - 31.1299i) q^{60} +(7.11302 + 35.7596i) q^{61} +(-21.5926 + 32.3156i) q^{62} +(12.7793 - 64.2461i) q^{63} +(-66.6561 - 66.6561i) q^{64} +(-5.03957 - 7.54224i) q^{65} +(18.3515 - 7.60145i) q^{66} +117.219i q^{67} +(81.1179 + 33.6001i) q^{68} +6.97157 q^{69} +(73.0632 + 176.390i) q^{70} +(88.1108 - 58.8738i) q^{71} +(-20.7945 + 20.7945i) q^{72} +(-59.8620 - 11.9073i) q^{73} +(-59.5832 - 39.8122i) q^{74} +(-31.4543 + 6.25665i) q^{75} +(-13.4223 - 5.55971i) q^{76} +(-24.2730 + 58.6001i) q^{77} +(-0.542122 - 2.72543i) q^{78} +(52.9382 - 79.2276i) q^{79} +(-15.6397 + 78.6261i) q^{80} +(-44.9799 - 44.9799i) q^{81} +(-36.7331 - 54.9749i) q^{82} +(-109.791 + 45.4770i) q^{83} +32.9607i q^{84} +(-26.6297 - 133.877i) q^{85} +70.3428 q^{86} +(-0.954715 - 2.30489i) q^{87} +(23.6767 - 15.8202i) q^{88} +(-61.4534 + 61.4534i) q^{89} +(198.826 + 39.5490i) q^{90} +(7.37792 + 4.92977i) q^{91} +(43.4639 - 8.64551i) q^{92} +(9.63715 + 3.99184i) q^{93} +(91.1920 - 220.157i) q^{94} +(4.40634 + 22.1522i) q^{95} +(-20.0109 + 29.9484i) q^{96} +(4.79748 - 24.1185i) q^{97} +(-27.1699 - 27.1699i) q^{98} +(37.4165 + 55.9978i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 8 q^{3} + 16 q^{5} - 8 q^{6} + 8 q^{7} - 24 q^{8} - 16 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 8 * q^3 + 16 * q^5 - 8 * q^6 + 8 * q^7 - 24 * q^8 - 16 * q^9	\( 8 q - 8 q^{2} - 8 q^{3} + 16 q^{5} - 8 q^{6} + 8 q^{7} - 24 q^{8} - 16 q^{9} + 16 q^{10} - 8 q^{11} + 48 q^{12} + 16 q^{13} + 8 q^{14} - 16 q^{15} + 56 q^{18} - 80 q^{20} - 64 q^{21} - 104 q^{22} - 56 q^{23} - 80 q^{24} + 64 q^{25} + 176 q^{26} + 40 q^{27} + 152 q^{28} + 48 q^{29} + 16 q^{30} + 24 q^{31} + 88 q^{32} - 136 q^{34} - 160 q^{35} - 128 q^{36} + 32 q^{37} - 120 q^{38} + 48 q^{39} + 64 q^{40} + 48 q^{41} + 16 q^{42} - 232 q^{43} + 120 q^{44} - 88 q^{46} + 192 q^{47} + 136 q^{48} + 16 q^{49} + 136 q^{51} - 384 q^{52} - 32 q^{53} + 8 q^{54} + 224 q^{55} - 120 q^{56} + 24 q^{57} + 240 q^{58} - 48 q^{59} + 64 q^{60} - 160 q^{61} - 168 q^{62} + 56 q^{63} - 64 q^{64} - 96 q^{65} - 8 q^{66} + 272 q^{68} + 240 q^{69} + 224 q^{70} + 40 q^{71} + 40 q^{72} + 48 q^{73} - 160 q^{74} - 296 q^{75} + 80 q^{76} - 48 q^{77} - 400 q^{78} - 136 q^{79} - 240 q^{80} - 424 q^{81} - 64 q^{82} - 264 q^{83} - 272 q^{85} + 832 q^{86} + 208 q^{87} + 264 q^{88} + 160 q^{89} + 448 q^{90} + 320 q^{91} + 24 q^{92} - 64 q^{93} + 32 q^{94} + 272 q^{95} - 56 q^{96} + 48 q^{97} - 120 q^{98} - 224 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 8 * q^3 + 16 * q^5 - 8 * q^6 + 8 * q^7 - 24 * q^8 - 16 * q^9 + 16 * q^10 - 8 * q^11 + 48 * q^12 + 16 * q^13 + 8 * q^14 - 16 * q^15 + 56 * q^18 - 80 * q^20 - 64 * q^21 - 104 * q^22 - 56 * q^23 - 80 * q^24 + 64 * q^25 + 176 * q^26 + 40 * q^27 + 152 * q^28 + 48 * q^29 + 16 * q^30 + 24 * q^31 + 88 * q^32 - 136 * q^34 - 160 * q^35 - 128 * q^36 + 32 * q^37 - 120 * q^38 + 48 * q^39 + 64 * q^40 + 48 * q^41 + 16 * q^42 - 232 * q^43 + 120 * q^44 - 88 * q^46 + 192 * q^47 + 136 * q^48 + 16 * q^49 + 136 * q^51 - 384 * q^52 - 32 * q^53 + 8 * q^54 + 224 * q^55 - 120 * q^56 + 24 * q^57 + 240 * q^58 - 48 * q^59 + 64 * q^60 - 160 * q^61 - 168 * q^62 + 56 * q^63 - 64 * q^64 - 96 * q^65 - 8 * q^66 + 272 * q^68 + 240 * q^69 + 224 * q^70 + 40 * q^71 + 40 * q^72 + 48 * q^73 - 160 * q^74 - 296 * q^75 + 80 * q^76 - 48 * q^77 - 400 * q^78 - 136 * q^79 - 240 * q^80 - 424 * q^81 - 64 * q^82 - 264 * q^83 - 272 * q^85 + 832 * q^86 + 208 * q^87 + 264 * q^88 + 160 * q^89 + 448 * q^90 + 320 * q^91 + 24 * q^92 - 64 * q^93 + 32 * q^94 + 272 * q^95 - 56 * q^96 + 48 * q^97 - 120 * q^98 - 224 * q^99

Introduction

L-functions

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