LMFDB - Embedded newform 224.3.w.a.99.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(43,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 0]))

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

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

chi := DirichletCharacter("224.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.w (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			99.16
Character	$\chi$	$=$	224.99
Dual form			224.3.w.a.43.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00544 + 1.72890i) q^{2} +(-0.343872 + 0.830180i) q^{3} +(-1.97818 - 3.47661i) q^{4} +(-1.68929 - 4.07830i) q^{5} +(-1.08955 - 1.42922i) q^{6} +(-1.87083 - 1.87083i) q^{7} +(7.99964 + 0.0754426i) q^{8} +(5.79301 + 5.79301i) q^{9} +O(q^{10})$	\(q+(-1.00544 + 1.72890i) q^{2} +(-0.343872 + 0.830180i) q^{3} +(-1.97818 - 3.47661i) q^{4} +(-1.68929 - 4.07830i) q^{5} +(-1.08955 - 1.42922i) q^{6} +(-1.87083 - 1.87083i) q^{7} +(7.99964 + 0.0754426i) q^{8} +(5.79301 + 5.79301i) q^{9} +(8.74944 + 1.17988i) q^{10} +(1.83307 + 4.42543i) q^{11} +(3.56645 - 0.446740i) q^{12} +(-5.16372 + 12.4663i) q^{13} +(5.11548 - 1.35347i) q^{14} +3.96662 q^{15} +(-8.17359 + 13.7547i) q^{16} +25.5323i q^{17} +(-15.8401 + 4.19101i) q^{18} +(20.0221 + 8.29342i) q^{19} +(-10.8369 + 13.9406i) q^{20} +(2.19645 - 0.909799i) q^{21} +(-9.49417 - 1.28031i) q^{22} +(19.0131 - 19.0131i) q^{23} +(-2.81348 + 6.61520i) q^{24} +(3.89886 - 3.89886i) q^{25} +(-16.3612 - 21.4617i) q^{26} +(-14.2729 + 5.91203i) q^{27} +(-2.80330 + 10.2050i) q^{28} +(-28.8850 - 11.9646i) q^{29} +(-3.98819 + 6.85788i) q^{30} +20.2039i q^{31} +(-15.5625 - 27.9609i) q^{32} -4.30425 q^{33} +(-44.1428 - 25.6712i) q^{34} +(-4.46943 + 10.7902i) q^{35} +(8.68039 - 31.5996i) q^{36} +(20.6185 + 49.7775i) q^{37} +(-34.4695 + 26.2776i) q^{38} +(-8.57363 - 8.57363i) q^{39} +(-13.2060 - 32.7524i) q^{40} +(48.4204 + 48.4204i) q^{41} +(-0.635447 + 4.71219i) q^{42} +(-1.98997 - 4.80421i) q^{43} +(11.7593 - 15.1272i) q^{44} +(13.8396 - 33.4117i) q^{45} +(13.7552 + 51.9884i) q^{46} -0.301912 q^{47} +(-8.60823 - 11.5154i) q^{48} +7.00000i q^{49} +(2.82066 + 10.6608i) q^{50} +(-21.1964 - 8.77984i) q^{51} +(53.5552 - 6.70842i) q^{52} +(-57.5410 + 23.8343i) q^{53} +(4.12925 - 30.6206i) q^{54} +(14.9516 - 14.9516i) q^{55} +(-14.8248 - 15.1071i) q^{56} +(-13.7701 + 13.7701i) q^{57} +(49.7277 - 37.9097i) q^{58} +(10.1059 - 4.18602i) q^{59} +(-7.84669 - 13.7904i) q^{60} +(41.4624 + 17.1743i) q^{61} +(-34.9305 - 20.3138i) q^{62} -21.6755i q^{63} +(63.9886 + 1.20703i) q^{64} +59.5643 q^{65} +(4.32766 - 7.44161i) q^{66} +(20.6489 - 49.8508i) q^{67} +(88.7658 - 50.5076i) q^{68} +(9.24625 + 22.3224i) q^{69} +(-14.1613 - 18.5760i) q^{70} +(-61.3241 - 61.3241i) q^{71} +(45.9050 + 46.7791i) q^{72} +(41.1271 + 41.1271i) q^{73} +(-106.791 - 14.4009i) q^{74} +(1.89605 + 4.57746i) q^{75} +(-10.7744 - 86.0148i) q^{76} +(4.84986 - 11.7086i) q^{77} +(23.4432 - 6.20267i) q^{78} +68.4372 q^{79} +(69.9034 + 10.0987i) q^{80} +59.8509i q^{81} +(-132.398 + 35.0302i) q^{82} +(-105.678 - 43.7731i) q^{83} +(-7.50799 - 5.83644i) q^{84} +(104.128 - 43.1314i) q^{85} +(10.3068 + 1.38989i) q^{86} +(19.8655 - 19.8655i) q^{87} +(14.3301 + 35.5402i) q^{88} +(48.8993 - 48.8993i) q^{89} +(43.8505 + 57.5206i) q^{90} +(32.9828 - 13.6619i) q^{91} +(-103.713 - 28.4898i) q^{92} +(-16.7729 - 6.94756i) q^{93} +(0.303555 - 0.521976i) q^{94} -95.6659i q^{95} +(28.5640 - 3.30470i) q^{96} -140.318 q^{97} +(-12.1023 - 7.03808i) q^{98} +(-15.0176 + 36.2556i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q + 80 q^{10} + 96 q^{12} - 20 q^{16} - 60 q^{18} - 260 q^{22} + 64 q^{23} - 144 q^{24} - 200 q^{26} + 192 q^{27} - 40 q^{30} + 40 q^{32} + 120 q^{34} + 464 q^{36} + 504 q^{38} - 384 q^{39} + 360 q^{40} - 96 q^{43} + 52 q^{44} + 64 q^{46} - 104 q^{48} - 312 q^{50} - 384 q^{51} - 320 q^{52} + 160 q^{53} - 576 q^{54} - 512 q^{55} - 196 q^{56} - 360 q^{58} - 872 q^{60} + 128 q^{61} - 408 q^{62} + 832 q^{66} + 160 q^{67} + 856 q^{68} - 384 q^{69} + 336 q^{70} + 1488 q^{72} + 308 q^{74} + 768 q^{75} + 1024 q^{76} - 224 q^{77} - 408 q^{78} + 1024 q^{79} - 1040 q^{80} - 240 q^{82} - 1384 q^{86} + 896 q^{87} - 560 q^{88} - 1320 q^{90} - 380 q^{92} - 936 q^{94} - 1088 q^{96} - 512 q^{99}+O(q^{100}) $ 192 * q + 80 * q^10 + 96 * q^12 - 20 * q^16 - 60 * q^18 - 260 * q^22 + 64 * q^23 - 144 * q^24 - 200 * q^26 + 192 * q^27 - 40 * q^30 + 40 * q^32 + 120 * q^34 + 464 * q^36 + 504 * q^38 - 384 * q^39 + 360 * q^40 - 96 * q^43 + 52 * q^44 + 64 * q^46 - 104 * q^48 - 312 * q^50 - 384 * q^51 - 320 * q^52 + 160 * q^53 - 576 * q^54 - 512 * q^55 - 196 * q^56 - 360 * q^58 - 872 * q^60 + 128 * q^61 - 408 * q^62 + 832 * q^66 + 160 * q^67 + 856 * q^68 - 384 * q^69 + 336 * q^70 + 1488 * q^72 + 308 * q^74 + 768 * q^75 + 1024 * q^76 - 224 * q^77 - 408 * q^78 + 1024 * q^79 - 1040 * q^80 - 240 * q^82 - 1384 * q^86 + 896 * q^87 - 560 * q^88 - 1320 * q^90 - 380 * q^92 - 936 * q^94 - 1088 * q^96 - 512 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−1.00544	+	1.72890i	−0.502720	+	0.864449i
$2$	−1.00544	+	1.72890i	−0.502720	+	0.864449i
$3$	−0.343872	+	0.830180i	−0.114624	+	0.276727i	−0.970772	−	0.240004i	$-0.922851\pi$
$3$	−0.343872	+	0.830180i	−0.114624	+	0.276727i	0.856148	+	0.516731i	$0.172851\pi$
$4$	−1.97818	−	3.47661i	−0.494545	−	0.869152i
$5$	−1.68929	−	4.07830i	−0.337857	−	0.815659i	−0.997921	−	0.0644497i	$-0.979471\pi$
$5$	−1.68929	−	4.07830i	−0.337857	−	0.815659i	0.660064	−	0.751209i	$-0.270529\pi$
$6$	−1.08955	−	1.42922i	−0.181592	−	0.238203i
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$8$	7.99964	+	0.0754426i	0.999956	+	0.00943033i
$9$	5.79301	+	5.79301i	0.643668	+	0.643668i
$10$	8.74944	+	1.17988i	0.874944	+	0.117988i
$11$	1.83307	+	4.42543i	0.166643	+	0.402312i	0.985036	−	0.172346i	$-0.0551348\pi$
$11$	1.83307	+	4.42543i	0.166643	+	0.402312i	−0.818393	+	0.574659i	$0.805135\pi$
$12$	3.56645	−	0.446740i	0.297204	−	0.0372283i
$13$	−5.16372	+	12.4663i	−0.397209	+	0.958947i	0.591116	+	0.806587i	$0.298688\pi$
$13$	−5.16372	+	12.4663i	−0.397209	+	0.958947i	−0.988325	+	0.152361i	$0.951312\pi$
$14$	5.11548	−	1.35347i	0.365391	−	0.0966763i
$15$	3.96662			0.264441
$16$	−8.17359	+	13.7547i	−0.510850	+	0.859670i
$17$			25.5323i			1.50190i	0.660359	+	0.750950i	$0.270404\pi$
$17$			25.5323i			1.50190i	−0.660359	+	0.750950i	$0.729596\pi$
$18$	−15.8401	+	4.19101i	−0.880003	+	0.232834i
$19$	20.0221	+	8.29342i	1.05379	+	0.436496i	0.841245	−	0.540655i	$-0.181823\pi$
$19$	20.0221	+	8.29342i	1.05379	+	0.436496i	0.212549	+	0.977150i	$0.431823\pi$
$20$	−10.8369	+	13.9406i	−0.541846	+	0.697030i
$21$	2.19645	−	0.909799i	0.104593	−	0.0433238i
$22$	−9.49417	−	1.28031i	−0.431553	−	0.0581958i
$23$	19.0131	−	19.0131i	0.826658	−	0.826658i	−0.160395	−	0.987053i	$-0.551277\pi$
$23$	19.0131	−	19.0131i	0.826658	−	0.826658i	0.987053	+	0.160395i	$0.0512766\pi$
$24$	−2.81348	+	6.61520i	−0.117228	+	0.275633i
$25$	3.89886	−	3.89886i	0.155954	−	0.155954i
$26$	−16.3612	−	21.4617i	−0.629276	−	0.825449i
$27$	−14.2729	+	5.91203i	−0.528626	+	0.218964i
$28$	−2.80330	+	10.2050i	−0.100118	+	0.364463i
$29$	−28.8850	−	11.9646i	−0.996036	−	0.412572i	−0.175694	−	0.984445i	$-0.556217\pi$
$29$	−28.8850	−	11.9646i	−0.996036	−	0.412572i	−0.820342	+	0.571873i	$0.806217\pi$
$30$	−3.98819	+	6.85788i	−0.132940	+	0.228596i
$31$			20.2039i			0.651739i	0.945415	+	0.325870i	$0.105657\pi$
$31$			20.2039i			0.651739i	−0.945415	+	0.325870i	$0.894343\pi$
$32$	−15.5625	−	27.9609i	−0.486327	−	0.873777i
$33$	−4.30425			−0.130432
$34$	−44.1428	−	25.6712i	−1.29832	−	0.755035i
$35$	−4.46943	+	10.7902i	−0.127698	+	0.308290i
$36$	8.68039	−	31.5996i	0.241122	−	0.877768i
$37$	20.6185	+	49.7775i	0.557257	+	1.34534i	0.911930	+	0.410346i	$0.134592\pi$
$37$	20.6185	+	49.7775i	0.557257	+	1.34534i	−0.354673	+	0.934990i	$0.615408\pi$
$38$	−34.4695	+	26.2776i	−0.907091	+	0.691516i
$39$	−8.57363	−	8.57363i	−0.219837	−	0.219837i
$40$	−13.2060	−	32.7524i	−0.330150	−	0.818809i
$41$	48.4204	+	48.4204i	1.18098	+	1.18098i	0.979489	+	0.201495i	$0.0645801\pi$
$41$	48.4204	+	48.4204i	1.18098	+	1.18098i	0.201495	+	0.979489i	$0.435420\pi$
$42$	−0.635447	+	4.71219i	−0.0151297	+	0.112195i
$43$	−1.98997	−	4.80421i	−0.0462783	−	0.111726i	0.899050	−	0.437846i	$-0.144259\pi$
$43$	−1.98997	−	4.80421i	−0.0462783	−	0.111726i	−0.945328	+	0.326120i	$0.894259\pi$
$44$	11.7593	−	15.1272i	0.267258	−	0.343800i
$45$	13.8396	−	33.4117i	0.307546	−	0.742481i
$46$	13.7552	+	51.9884i	0.299027	+	1.13018i
$47$	−0.301912			−0.00642367			−0.00321183	−	0.999995i	$-0.501022\pi$
$47$	−0.301912			−0.00642367			−0.00321183	+	0.999995i	$0.501022\pi$
$48$	−8.60823	−	11.5154i	−0.179338	−	0.239904i
$49$			7.00000i			0.142857i
$50$	2.82066	+	10.6608i	0.0564133	+	0.213216i
$51$	−21.1964	−	8.77984i	−0.415616	−	0.172154i
$52$	53.5552	−	6.70842i	1.02991	−	0.129008i
$53$	−57.5410	+	23.8343i	−1.08568	+	0.449703i	−0.852498	−	0.522730i	$-0.824913\pi$
$53$	−57.5410	+	23.8343i	−1.08568	+	0.449703i	−0.233181	+	0.972433i	$0.574913\pi$
$54$	4.12925	−	30.6206i	0.0764675	−	0.567048i
$55$	14.9516	−	14.9516i	0.271848	−	0.271848i
$56$	−14.8248	−	15.1071i	−0.264729	−	0.269770i
$57$	−13.7701	+	13.7701i	−0.241580	+	0.241580i
$58$	49.7277	−	37.9097i	0.857374	−	0.653615i
$59$	10.1059	−	4.18602i	0.171287	−	0.0709494i	−0.295392	−	0.955376i	$-0.595450\pi$
$59$	10.1059	−	4.18602i	0.171287	−	0.0709494i	0.466679	+	0.884427i	$0.345450\pi$
$60$	−7.84669	−	13.7904i	−0.130778	−	0.229840i
$61$	41.4624	+	17.1743i	0.679712	+	0.281546i	0.695706	−	0.718326i	$-0.255091\pi$
$61$	41.4624	+	17.1743i	0.679712	+	0.281546i	−0.0159947	+	0.999872i	$0.505091\pi$
$62$	−34.9305	−	20.3138i	−0.563396	−	0.327642i
$63$		−	21.6755i		−	0.344055i
$64$	63.9886	+	1.20703i	0.999822	+	0.0188598i
$65$	59.5643			0.916374
$66$	4.32766	−	7.44161i	0.0655707	−	0.112752i
$67$	20.6489	−	49.8508i	0.308192	−	0.744042i	−0.691571	−	0.722308i	$-0.743081\pi$
$67$	20.6489	−	49.8508i	0.308192	−	0.744042i	0.999764	−	0.0217341i	$-0.00691874\pi$
$68$	88.7658	−	50.5076i	1.30538	−	0.742758i
$69$	9.24625	+	22.3224i	0.134004	+	0.323513i
$70$	−14.1613	−	18.5760i	−0.202305	−	0.265372i
$71$	−61.3241	−	61.3241i	−0.863720	−	0.863720i	0.128048	−	0.991768i	$-0.459129\pi$
$71$	−61.3241	−	61.3241i	−0.863720	−	0.863720i	−0.991768	+	0.128048i	$0.959129\pi$
$72$	45.9050	+	46.7791i	0.637569	+	0.649709i
$73$	41.1271	+	41.1271i	0.563385	+	0.563385i	0.930267	−	0.366882i	$-0.119575\pi$
$73$	41.1271	+	41.1271i	0.563385	+	0.563385i	−0.366882	+	0.930267i	$0.619575\pi$
$74$	−106.791	−	14.4009i	−1.44312	−	0.194607i
$75$	1.89605	+	4.57746i	0.0252806	+	0.0610328i
$76$	−10.7744	−	86.0148i	−0.141768	−	1.13177i
$77$	4.84986	−	11.7086i	0.0629852	−	0.152060i
$78$	23.4432	−	6.20267i	0.300554	−	0.0795214i
$79$	68.4372			0.866294			0.433147	−	0.901323i	$-0.357403\pi$
$79$	68.4372			0.866294			0.433147	+	0.901323i	$0.357403\pi$
$80$	69.9034	+	10.0987i	0.873792	+	0.126233i
$81$			59.8509i			0.738900i
$82$	−132.398	+	35.0302i	−1.61461	+	0.427197i
$83$	−105.678	−	43.7731i	−1.27323	−	0.527387i	−0.359282	−	0.933229i	$-0.616978\pi$
$83$	−105.678	−	43.7731i	−1.27323	−	0.527387i	−0.913943	+	0.405842i	$0.866978\pi$
$84$	−7.50799	−	5.83644i	−0.0893809	−	0.0694815i
$85$	104.128	−	43.1314i	1.22504	−	0.507428i
$86$	10.3068	+	1.38989i	0.119846	+	0.0161615i
$87$	19.8655	−	19.8655i	0.228339	−	0.228339i
$88$	14.3301	+	35.5402i	0.162842	+	0.403866i
$89$	48.8993	−	48.8993i	0.549430	−	0.549430i	−0.376846	−	0.926276i	$-0.622991\pi$
$89$	48.8993	−	48.8993i	0.549430	−	0.549430i	0.926276	+	0.376846i	$0.122991\pi$
$90$	43.8505	+	57.5206i	0.487228	+	0.639118i
$91$	32.9828	−	13.6619i	0.362448	−	0.150131i
$92$	−103.713	−	28.4898i	−1.12731	−	0.309671i
$93$	−16.7729	−	6.94756i	−0.180354	−	0.0747049i
$94$	0.303555	−	0.521976i	0.00322931	−	0.00555294i
$95$		−	95.6659i		−	1.00701i
$96$	28.5640	−	3.30470i	0.297542	−	0.0344239i
$97$	−140.318			−1.44658			−0.723289	−	0.690545i	$-0.757371\pi$
$97$	−140.318			−1.44658			−0.723289	+	0.690545i	$0.757371\pi$
$98$	−12.1023	−	7.03808i	−0.123493	−	0.0718171i
$99$	−15.0176	+	36.2556i	−0.151693	+	0.366218i
$100$	−21.2674	−	5.84215i	−0.212674	−	0.0584215i
$101$	−15.6876	−	37.8733i	−0.155323	−	0.374983i	0.826993	−	0.562212i	$-0.190050\pi$
$101$	−15.6876	−	37.8733i	−0.155323	−	0.374983i	−0.982316	+	0.187229i	$0.940050\pi$
$102$	36.4912	−	27.8189i	0.357757	−	0.272734i
$103$	138.293	+	138.293i	1.34265	+	1.34265i	0.893408	+	0.449247i	$0.148308\pi$
$103$	138.293	+	138.293i	1.34265	+	1.34265i	0.449247	+	0.893408i	$0.351692\pi$
$104$	−42.2484	+	99.3365i	−0.406234	+	0.955159i
$105$	−7.42086	−	7.42086i	−0.0706749	−	0.0706749i
$106$	16.6470	−	123.446i	0.157047	−	1.16459i
$107$	−69.6503	−	168.151i	−0.650938	−	1.57150i	−0.811420	−	0.584464i	$-0.801305\pi$
$107$	−69.6503	−	168.151i	−0.650938	−	1.57150i	0.160482	−	0.987039i	$-0.448695\pi$
$108$	48.7882	+	37.9262i	0.451743	+	0.351169i
$109$	33.9441	−	81.9483i	0.311414	−	0.751819i	−0.688239	−	0.725484i	$-0.741616\pi$
$109$	33.9441	−	81.9483i	0.311414	−	0.751819i	0.999653	−	0.0263355i	$-0.00838383\pi$
$110$	10.8169	+	40.8829i	0.0983355	+	0.371662i
$111$	−48.4144			−0.436165
$112$	41.0241	−	10.4413i	0.366287	−	0.0932262i
$113$			197.649i			1.74911i	0.484926	+	0.874555i	$0.338847\pi$
$113$			197.649i			1.74911i	−0.484926	+	0.874555i	$0.661153\pi$
$114$	−9.96207	−	37.6520i	−0.0873866	−	0.330281i
$115$	−109.660	−	45.4226i	−0.953564	−	0.394979i
$116$	15.5437	+	124.090i	0.133998	+	1.06974i
$117$	−102.131	+	42.3040i	−0.872914	+	0.361573i
$118$	−2.92371	+	21.6809i	−0.0247772	+	0.183737i
$119$	47.7666	−	47.7666i	0.401400	−	0.401400i
$120$	31.7315	+	0.299252i	0.264429	+	0.00249377i
$121$	69.3356	−	69.3356i	0.573022	−	0.573022i
$122$	−71.3806	+	54.4166i	−0.585087	+	0.446038i
$123$	−56.8480	+	23.5472i	−0.462179	+	0.191441i
$124$	70.2411	−	39.9670i	0.566460	−	0.322315i
$125$	−124.444	−	51.5465i	−0.995555	−	0.412372i
$126$	37.4747	+	21.7934i	0.297418	+	0.172963i
$127$		−	75.1216i		−	0.591509i	−0.955264	−	0.295754i	$-0.904429\pi$
$127$		−	75.1216i		−	0.591509i	0.955264	−	0.295754i	$-0.0955710\pi$
$128$	−66.4235	+	109.416i	−0.518934	+	0.854814i
$129$	4.67265			0.0362221
$130$	−59.8883	+	102.981i	−0.460679	+	0.792159i
$131$	−38.2947	+	92.4517i	−0.292326	+	0.705738i	−1.00000		0.000801796i	$-0.999745\pi$
$131$	−38.2947	+	92.4517i	−0.292326	+	0.705738i	0.707674	+	0.706540i	$0.249745\pi$
$132$	8.51459	+	14.9642i	0.0645045	+	0.113365i
$133$	−21.9423	−	52.9734i	−0.164980	−	0.398297i
$134$	65.4258	+	85.8218i	0.488252	+	0.640462i
$135$	48.2221	+	48.2221i	0.357200	+	0.357200i
$136$	−1.92622	+	204.249i	−0.0141634	+	1.50183i
$137$	−43.7701	−	43.7701i	−0.319489	−	0.319489i	0.529082	−	0.848571i	$-0.322537\pi$
$137$	−43.7701	−	43.7701i	−0.319489	−	0.319489i	−0.848571	+	0.529082i	$0.822537\pi$
$138$	−47.8897	−	6.45802i	−0.347027	−	0.0467972i
$139$	41.2233	+	99.5219i	0.296571	+	0.715985i	0.999986	+	0.00520627i	$0.00165722\pi$
$139$	41.2233	+	99.5219i	0.296571	+	0.715985i	−0.703416	+	0.710779i	$0.748343\pi$
$140$	46.3545	−	5.80644i	0.331103	−	0.0414746i
$141$	0.103819	−	0.250642i	0.000736306	−	0.00177760i
$142$	167.681	−	44.3655i	1.18085	−	0.312433i
$143$	−64.6343			−0.451988
$144$	−127.031	+	32.3315i	−0.882159	+	0.224525i
$145$			138.013i			0.951816i
$146$	−112.455	+	29.7538i	−0.770243	+	0.203793i
$147$	−5.81126	−	2.40710i	−0.0395324	−	0.0163748i
$148$	132.270	−	170.151i	0.893713	−	1.14967i
$149$	42.4781	−	17.5950i	0.285088	−	0.118087i	−0.235557	−	0.971861i	$-0.575691\pi$
$149$	42.4781	−	17.5950i	0.285088	−	0.118087i	0.520645	+	0.853773i	$0.325691\pi$
$150$	−9.82033	−	1.32429i	−0.0654688	−	0.00882859i
$151$	7.69062	−	7.69062i	0.0509313	−	0.0509313i	−0.681182	−	0.732114i	$-0.738534\pi$
$151$	7.69062	−	7.69062i	0.0509313	−	0.0509313i	0.732114	+	0.681182i	$0.238534\pi$
$152$	159.544	+	67.8549i	1.04963	+	0.446414i
$153$	−147.909	+	147.909i	−0.966725	+	0.966725i
$154$	15.3667	+	20.1572i	0.0997840	+	0.130891i
$155$	82.3975	−	34.1302i	0.531597	−	0.220195i
$156$	−12.8469	+	46.7673i	−0.0823522	+	0.299791i
$157$	−198.237	−	82.1123i	−1.26265	−	0.523008i	−0.351931	−	0.936026i	$-0.614475\pi$
$157$	−198.237	−	82.1123i	−1.26265	−	0.523008i	−0.910723	+	0.413018i	$0.864475\pi$
$158$	−68.8095	+	118.321i	−0.435503	+	0.748867i
$159$		−	55.9653i		−	0.351983i
$160$	−87.7432	+	110.702i	−0.548395	+	0.691889i
$161$	−71.1407			−0.441868
$162$	−103.476	−	60.1765i	−0.638742	−	0.371460i
$163$	−27.7685	+	67.0390i	−0.170359	+	0.411282i	−0.985882	−	0.167442i	$-0.946449\pi$
$163$	−27.7685	+	67.0390i	−0.170359	+	0.411282i	0.815523	+	0.578724i	$0.196449\pi$
$164$	72.5543	−	264.123i	0.442404	−	1.61051i
$165$	7.27111	+	17.5540i	0.0440673	+	0.106388i
$166$	181.932	−	138.695i	1.09598	−	0.835511i
$167$	−36.9123	−	36.9123i	−0.221032	−	0.221032i	0.587901	−	0.808933i	$-0.299954\pi$
$167$	−36.9123	−	36.9123i	−0.221032	−	0.221032i	−0.808933	+	0.587901i	$0.799954\pi$
$168$	17.6395	−	7.11236i	0.104997	−	0.0423355i
$169$	−9.24397	−	9.24397i	−0.0546980	−	0.0546980i
$170$	−30.1250	+	223.393i	−0.177206	+	1.31408i
$171$	67.9443	+	164.032i	0.397335	+	0.959251i
$172$	−12.7658	+	16.4219i	−0.0742199	+	0.0954764i
$173$	−26.2498	+	63.3727i	−0.151733	+	0.366316i	−0.981409	−	0.191930i	$-0.938525\pi$
$173$	−26.2498	+	63.3727i	−0.151733	+	0.366316i	0.829676	+	0.558246i	$0.188525\pi$
$174$	14.3719	+	54.3190i	0.0825970	+	0.312178i
$175$	−14.5882			−0.0833611
$176$	−75.8534	−	10.9583i	−0.430985	−	0.0622629i
$177$			9.82920i			0.0555322i
$178$	35.3766	+	133.707i	0.198745	+	0.751164i
$179$	−254.465	−	105.403i	−1.42159	−	0.588842i	−0.466331	−	0.884610i	$-0.654425\pi$
$179$	−254.465	−	105.403i	−1.42159	−	0.588842i	−0.955260	+	0.295768i	$0.904425\pi$
$180$	−143.536	+	17.9796i	−0.797424	+	0.0998868i
$181$	37.7918	−	15.6539i	0.208794	−	0.0864855i	−0.275835	−	0.961205i	$-0.588954\pi$
$181$	37.7918	−	15.6539i	0.208794	−	0.0864855i	0.484630	+	0.874719i	$0.338954\pi$
$182$	−9.54213	+	70.7601i	−0.0524293	+	0.388792i
$183$	−28.5155	+	28.5155i	−0.155822	+	0.155822i
$184$	153.533	−	150.664i	0.834417	−	0.818826i
$185$	168.177	−	168.177i	0.909063	−	0.909063i
$186$	28.8757	−	22.0133i	0.155246	−	0.118351i
$187$	−112.992	+	46.8026i	−0.604233	+	0.250282i
$188$	0.597238	+	1.04963i	0.00317680	+	0.00558314i
$189$	37.7626	+	15.6418i	0.199802	+	0.0827607i
$190$	165.397	+	96.1863i	0.870509	+	0.506244i
$191$		−	370.891i		−	1.94184i	−0.239409	−	0.970919i	$-0.576954\pi$
$191$		−	370.891i		−	1.94184i	0.239409	−	0.970919i	$-0.423046\pi$
$192$	−23.0059	+	52.7070i	−0.119823	+	0.274516i
$193$	173.819			0.900617			0.450308	−	0.892873i	$-0.351314\pi$
$193$	173.819			0.900617			0.450308	+	0.892873i	$0.351314\pi$
$194$	141.081	−	242.596i	0.727224	−	1.25049i
$195$	−20.4825	+	49.4491i	−0.105038	+	0.253585i
$196$	24.3362	−	13.8473i	0.124165	−	0.0706494i
$197$	64.4972	+	155.710i	0.327397	+	0.790406i	0.998784	+	0.0492994i	$0.0156988\pi$
$197$	64.4972	+	155.710i	0.327397	+	0.790406i	−0.671387	+	0.741107i	$0.734301\pi$
$198$	−47.5830	−	62.4167i	−0.240318	−	0.315236i
$199$	−1.38471	−	1.38471i	−0.00695836	−	0.00695836i	0.703619	−	0.710577i	$-0.251566\pi$
$199$	−1.38471	−	1.38471i	−0.00695836	−	0.00695836i	−0.710577	+	0.703619i	$0.751566\pi$
$200$	31.4836	−	30.8953i	0.157418	−	0.154477i
$201$	34.2846	+	34.2846i	0.170570	+	0.170570i
$202$	81.2521	+	10.9570i	0.402238	+	0.0542426i
$203$	31.6553	+	76.4226i	0.155937	+	0.376466i
$204$	11.4063	+	91.0597i	0.0559132	+	0.446371i
$205$	115.677	−	279.268i	0.564277	−	1.36229i
$206$	−378.141	+	100.050i	−1.83564	+	0.485678i
$207$	220.287			1.06419
$208$	−129.265	−	172.920i	−0.621464	−	0.831346i
$209$			103.809i			0.496693i
$210$	20.2911	−	5.36869i	0.0966245	−	0.0255652i
$211$	15.7733	+	6.53352i	0.0747551	+	0.0309646i	0.419748	−	0.907641i	$-0.362119\pi$
$211$	15.7733	+	6.53352i	0.0747551	+	0.0309646i	−0.344993	+	0.938605i	$0.612119\pi$
$212$	196.689	+	152.899i	0.927778	+	0.721221i
$213$	71.9977	−	29.8224i	0.338017	−	0.140011i
$214$	360.745	+	48.6471i	1.68572	+	0.227323i
$215$	−16.2314	+	16.2314i	−0.0754947	+	0.0754947i
$216$	−114.624	+	46.2174i	−0.530668	+	0.213969i
$217$	37.7981	−	37.7981i	0.174185	−	0.174185i
$218$	107.552	+	141.080i	0.493356	+	0.647156i
$219$	−48.2853	+	20.0004i	−0.220481	+	0.0913262i
$220$	−81.5581	−	22.4039i	−0.370718	−	0.101836i
$221$	−318.294	−	131.842i	−1.44024	−	0.596568i
$222$	48.6777	−	83.7035i	0.219269	−	0.377043i
$223$			54.6541i			0.245085i	0.992463	+	0.122543i	$0.0391049\pi$
$223$			54.6541i			0.245085i	−0.992463	+	0.122543i	$0.960895\pi$
$224$	−23.1953	+	81.4247i	−0.103550	+	0.363503i
$225$	45.1722			0.200765
$226$	−341.716	−	198.725i	−1.51202	−	0.879313i
$227$	−83.2494	+	200.982i	−0.366737	+	0.885382i	0.627543	+	0.778582i	$0.284061\pi$
$227$	−83.2494	+	200.982i	−0.366737	+	0.885382i	−0.994280	+	0.106801i	$0.965939\pi$
$228$	75.1128	+	20.6334i	0.329442	+	0.0904974i
$229$	−9.36982	−	22.6207i	−0.0409162	−	0.0987805i	0.902100	−	0.431526i	$-0.142025\pi$
$229$	−9.36982	−	22.6207i	−0.0409162	−	0.0987805i	−0.943017	+	0.332746i	$0.892025\pi$
$230$	188.787	−	143.921i	0.820815	−	0.625744i
$231$	8.05251	+	8.05251i	0.0348594	+	0.0348594i
$232$	−230.167	−	97.8915i	−0.992101	−	0.421946i
$233$	−25.7958	−	25.7958i	−0.110712	−	0.110712i	0.649581	−	0.760293i	$-0.274944\pi$
$233$	−25.7958	−	25.7958i	−0.110712	−	0.110712i	−0.760293	+	0.649581i	$0.774944\pi$
$234$	29.5471	−	219.108i	0.126270	−	0.936360i
$235$	0.510016	+	1.23129i	0.00217028	+	0.00523952i
$236$	−34.5445	−	26.8537i	−0.146375	−	0.113787i
$237$	−23.5336	+	56.8152i	−0.0992980	+	0.239727i
$238$	34.5572	+	130.610i	0.145198	+	0.548782i
$239$	452.784			1.89450			0.947248	−	0.320502i	$-0.103852\pi$
$239$	452.784			1.89450			0.947248	+	0.320502i	$0.103852\pi$
$240$	−32.4215	+	54.5597i	−0.135090	+	0.227332i
$241$		−	234.751i		−	0.974071i	−0.873382	−	0.487035i	$-0.838078\pi$
$241$		−	234.751i		−	0.974071i	0.873382	−	0.487035i	$-0.161922\pi$
$242$	50.1615	+	189.587i	0.207279	+	0.783418i
$243$	−178.143	−	73.7894i	−0.733100	−	0.303660i
$244$	−22.3119	−	178.122i	−0.0914423	−	0.730010i
$245$	28.5481	−	11.8250i	0.116523	−	0.0482653i
$246$	16.4465	−	121.960i	0.0668557	−	0.495772i
$247$	−206.777	+	206.777i	−0.837153	+	0.837153i
$248$	−1.52424	+	161.624i	−0.00614612	+	0.651710i
$249$	72.6792	−	72.6792i	0.291884	−	0.291884i
$250$	214.240	−	163.325i	0.856960	−	0.653299i
$251$	287.832	−	119.224i	1.14674	−	0.474995i	0.273301	−	0.961929i	$-0.411885\pi$
$251$	287.832	−	119.224i	1.14674	−	0.474995i	0.873439	+	0.486933i	$0.161885\pi$
$252$	−75.3571	+	42.8780i	−0.299036	+	0.170151i
$253$	118.994	+	49.2889i	0.470332	+	0.194818i
$254$	129.878	+	75.5302i	0.511329	+	0.297363i
$255$			101.277i			0.397164i
$256$	−122.385	−	224.851i	−0.478065	−	0.878324i
$257$	−99.8626			−0.388571			−0.194285	−	0.980945i	$-0.562239\pi$
$257$	−99.8626			−0.388571			−0.194285	+	0.980945i	$0.562239\pi$
$258$	−4.69807	+	8.07854i	−0.0182096	+	0.0313122i
$259$	54.5514	−	131.699i	0.210623	−	0.508489i
$260$	−117.829	−	207.082i	−0.453189	−	0.796468i
$261$	−98.0204	−	236.642i	−0.375557	−	0.906675i
$262$	−121.337	−	159.162i	−0.463116	−	0.607490i
$263$	304.367	+	304.367i	1.15729	+	1.15729i	0.985057	+	0.172231i	$0.0550976\pi$
$263$	304.367	+	304.367i	1.15729	+	1.15729i	0.172231	+	0.985057i	$0.444902\pi$
$264$	−34.4325	−	0.324724i	−0.130426	−	0.00123002i
$265$	194.406	+	194.406i	0.733609	+	0.733609i
$266$	113.647	+	15.3256i	0.427246	+	0.0576149i
$267$	23.7801	+	57.4103i	0.0890641	+	0.215020i
$268$	−214.159	+	26.8259i	−0.799101	+	0.100097i
$269$	152.192	−	367.424i	0.565769	−	1.36589i	−0.339323	−	0.940670i	$-0.610198\pi$
$269$	152.192	−	367.424i	0.565769	−	1.36589i	0.905092	−	0.425217i	$-0.139802\pi$
$270$	−131.855	+	34.8867i	−0.488353	+	0.129210i
$271$	79.5484			0.293537			0.146768	−	0.989171i	$-0.453113\pi$
$271$	79.5484			0.293537			0.146768	+	0.989171i	$0.453113\pi$
$272$	−351.190	−	208.691i	−1.29114	−	0.767245i
$273$			32.0796i			0.117508i
$274$	119.682	−	31.6658i	0.436796	−	0.115569i
$275$	24.4010	+	10.1072i	0.0887310	+	0.0367536i
$276$	59.3155	−	76.3034i	0.214911	−	0.276461i
$277$	−10.6248	+	4.40094i	−0.0383567	+	0.0158879i	−0.401779	−	0.915737i	$-0.631608\pi$
$277$	−10.6248	+	4.40094i	−0.0383567	+	0.0158879i	0.363423	+	0.931624i	$0.381608\pi$
$278$	−213.511	−	28.7923i	−0.768025	−	0.103570i
$279$	−117.041	+	117.041i	−0.419504	+	0.419504i
$280$	−36.5679	+	85.9802i	−0.130600	+	0.307072i
$281$	−141.000	+	141.000i	−0.501778	+	0.501778i	−0.911990	−	0.410212i	$-0.865455\pi$
$281$	−141.000	+	141.000i	−0.501778	+	0.501778i	0.410212	+	0.911990i	$0.365455\pi$
$282$	0.328950	+	0.431498i	0.00116649	+	0.00153013i
$283$	−44.3666	+	18.3773i	−0.156773	+	0.0649373i	−0.459690	−	0.888080i	$-0.652039\pi$
$283$	−44.3666	+	18.3773i	−0.156773	+	0.0649373i	0.302917	+	0.953017i	$0.402039\pi$
$284$	−91.8896	+	334.510i	−0.323555	+	1.17785i
$285$	79.4199	+	32.8968i	0.278666	+	0.115427i
$286$	64.9859	−	111.746i	0.227224	−	0.390721i
$287$		−	181.172i		−	0.631263i
$288$	71.8240	−	252.131i	0.249389	−	0.875455i
$289$	−362.899			−1.25571
$290$	−238.611	−	138.764i	−0.822797	−	0.478497i
$291$	48.2514	−	116.489i	0.165813	−	0.400307i
$292$	61.6259	−	224.340i	0.211048	−	0.768286i
$293$	−25.9248	−	62.5879i	−0.0884804	−	0.213611i	0.873445	−	0.486923i	$-0.161881\pi$
$293$	−25.9248	−	62.5879i	−0.0884804	−	0.213611i	−0.961925	+	0.273312i	$0.911881\pi$
$294$	10.0045	−	7.62688i	0.0340289	−	0.0259418i
$295$	−34.1436	−	34.1436i	−0.115741	−	0.115741i
$296$	161.185	+	399.757i	0.544545	+	1.35053i
$297$	−52.3266	−	52.3266i	−0.176184	−	0.176184i
$298$	−12.2892	+	91.1311i	−0.0412389	+	0.305809i
$299$	138.845	+	335.202i	0.464366	+	1.12108i
$300$	12.1633	−	15.6469i	0.0405444	−	0.0521562i
$301$	−5.26496	+	12.7107i	−0.0174916	+	0.0422284i
$302$	5.56385	+	21.0288i	0.0184233	+	0.0696317i
$303$	36.8362			0.121572
$304$	−277.726	+	207.611i	−0.913572	+	0.682931i
$305$		−	198.108i		−	0.649535i
$306$	−107.006	−	404.433i	−0.349693	−	1.32168i
$307$	92.0170	+	38.1147i	0.299730	+	0.124152i	0.527480	−	0.849568i	$-0.323137\pi$
$307$	92.0170	+	38.1147i	0.299730	+	0.124152i	−0.227750	+	0.973720i	$0.573137\pi$
$308$	−50.3001	+	6.30068i	−0.163312	+	0.0204568i
$309$	−162.364	+	67.2532i	−0.525449	+	0.217648i
$310$	−23.8381	+	176.773i	−0.0768972	+	0.570235i
$311$	−86.5020	+	86.5020i	−0.278142	+	0.278142i	−0.832367	−	0.554225i	$-0.813015\pi$
$311$	−86.5020	+	86.5020i	−0.278142	+	0.278142i	0.554225	+	0.832367i	$0.313015\pi$
$312$	−67.9392	−	69.2328i	−0.217754	−	0.221900i
$313$	232.344	−	232.344i	0.742314	−	0.742314i	−0.230709	−	0.973023i	$-0.574104\pi$
$313$	232.344	−	232.344i	0.742314	−	0.742314i	0.973023	+	0.230709i	$0.0741044\pi$
$314$	341.279	−	260.172i	1.08688	−	0.828574i
$315$	−88.3989	+	36.6160i	−0.280632	+	0.116241i
$316$	−135.381	−	237.929i	−0.428422	−	0.752941i
$317$	−18.0052	−	7.45801i	−0.0567989	−	0.0235269i	0.354103	−	0.935206i	$-0.384786\pi$
$317$	−18.0052	−	7.45801i	−0.0567989	−	0.0235269i	−0.410902	+	0.911680i	$0.634786\pi$
$318$	96.7584	+	56.2697i	0.304272	+	0.176949i
$319$		−	149.761i		−	0.469470i
$320$	−103.172	−	263.004i	−0.322414	−	0.821886i
$321$	163.546			0.509490
$322$	71.5277	−	122.995i	0.222136	−	0.381972i
$323$	−211.750	+	511.210i	−0.655573	+	1.58269i
$324$	208.078	−	118.396i	0.642216	−	0.365420i
$325$	28.4718	+	68.7370i	0.0876055	+	0.211498i
$326$	−87.9841	−	115.413i	−0.269890	−	0.354026i
$327$	56.3594	+	56.3594i	0.172353	+	0.172353i
$328$	383.693	+	390.999i	1.16980	+	1.19207i
$329$	0.564826	+	0.564826i	0.00171680	+	0.00171680i
$330$	−37.6598	−	5.07849i	−0.114120	−	0.0153894i
$331$	178.431	+	430.771i	0.539067	+	1.30142i	0.925375	+	0.379053i	$0.123750\pi$
$331$	178.431	+	430.771i	0.539067	+	1.30142i	−0.386308	+	0.922370i	$0.626250\pi$
$332$	56.8677	+	453.991i	0.171288	+	1.36744i
$333$	−168.918	+	407.804i	−0.507262	+	1.22464i
$334$	100.931	−	26.7046i	0.302188	−	0.0799538i
$335$	−238.188			−0.711010
$336$	−5.43885	+	37.6479i	−0.0161871	+	0.112047i
$337$			32.6233i			0.0968051i	0.998828	+	0.0484025i	$0.0154130\pi$
$337$			32.6233i			0.0968051i	−0.998828	+	0.0484025i	$0.984587\pi$
$338$	25.2761	−	6.68763i	0.0747815	−	0.0197859i
$339$	−164.085	−	67.9661i	−0.484026	−	0.200490i
$340$	−355.936	−	276.692i	−1.04687	−	0.813799i
$341$	−89.4111	+	37.0353i	−0.262203	+	0.108608i
$342$	−351.908	−	47.4555i	−1.02897	−	0.138759i
$343$	13.0958	−	13.0958i	0.0381802	−	0.0381802i
$344$	−15.5566	−	38.5821i	−0.0452227	−	0.112157i
$345$	75.4179	−	75.4179i	0.218603	−	0.218603i
$346$	−83.1724	−	109.101i	−0.240383	−	0.315320i
$347$	484.922	−	200.861i	1.39747	−	0.578851i	0.448377	−	0.893845i	$-0.352002\pi$
$347$	484.922	−	200.861i	1.39747	−	0.578851i	0.949094	+	0.314993i	$0.102002\pi$
$348$	−108.362	−	29.7670i	−0.311385	−	0.0855373i
$349$	−445.236	−	184.423i	−1.27575	−	0.528432i	−0.361041	−	0.932550i	$-0.617579\pi$
$349$	−445.236	−	184.423i	−1.27575	−	0.528432i	−0.914707	+	0.404118i	$0.867579\pi$
$350$	14.6675	−	25.2215i	0.0419073	−	0.0720614i
$351$		−	208.459i		−	0.593899i
$352$	95.2118	−	120.125i	0.270488	−	0.341264i
$353$	34.9060			0.0988838			0.0494419	−	0.998777i	$-0.484256\pi$
$353$	34.9060			0.0988838			0.0494419	+	0.998777i	$0.484256\pi$
$354$	−16.9937	−	9.88267i	−0.0480048	−	0.0279171i
$355$	−146.504	+	353.692i	−0.412687	+	0.996315i
$356$	−266.735	−	73.2719i	−0.749256	−	0.205820i
$357$	23.2293	+	56.0804i	0.0650680	+	0.157088i
$358$	438.080	−	333.968i	1.22369	−	0.932871i
$359$	192.166	+	192.166i	0.535281	+	0.535281i	0.922139	−	0.386858i	$-0.126440\pi$
$359$	192.166	+	192.166i	0.535281	+	0.535281i	−0.386858	+	0.922139i	$0.626440\pi$
$360$	113.232	−	266.237i	0.314534	−	0.739548i
$361$	76.8373	+	76.8373i	0.212846	+	0.212846i
$362$	−10.9334	+	81.0772i	−0.0302028	+	0.223970i
$363$	33.7185	+	81.4036i	0.0928884	+	0.224252i
$364$	−112.743	−	87.6424i	−0.309734	−	0.240776i
$365$	98.2531	−	237.204i	0.269186	−	0.649874i
$366$	−20.6298	−	77.9711i	−0.0563656	−	0.213036i
$367$	−293.297			−0.799174			−0.399587	−	0.916695i	$-0.630846\pi$
$367$	−293.297			−0.799174			−0.399587	+	0.916695i	$0.630846\pi$
$368$	106.115	+	416.926i	0.288355	+	1.13295i
$369$			560.999i			1.52032i
$370$	121.669	+	459.852i	0.328835	+	1.24284i
$371$	152.239	+	63.0595i	0.410348	+	0.169972i
$372$	9.02589	+	72.0563i	0.0242632	+	0.193700i
$373$	416.935	−	172.700i	1.11779	−	0.463003i	0.254175	−	0.967158i	$-0.418196\pi$
$373$	416.935	−	172.700i	1.11779	−	0.463003i	0.863613	+	0.504155i	$0.168196\pi$
$374$	32.6892	−	242.408i	0.0874042	−	0.648150i
$375$	85.5858	−	85.5858i	0.228229	−	0.228229i
$376$	−2.41519	−	0.0227771i	−0.00642338	−	6.05773e-5i
$377$	298.308	−	298.308i	0.791269	−	0.791269i
$378$	−65.0110	+	49.5608i	−0.171987	+	0.131113i
$379$	204.554	−	84.7289i	0.539719	−	0.223559i	−0.0961347	−	0.995368i	$-0.530648\pi$
$379$	204.554	−	84.7289i	0.539719	−	0.223559i	0.635854	+	0.771809i	$0.280648\pi$
$380$	−332.593	+	189.245i	−0.875244	+	0.498012i
$381$	62.3645	+	25.8322i	0.163686	+	0.0678011i
$382$	641.233	+	372.909i	1.67862	+	0.976200i
$383$			160.267i			0.418451i	0.977867	+	0.209226i	$0.0670943\pi$
$383$			160.267i			0.418451i	−0.977867	+	0.209226i	$0.932906\pi$
$384$	−67.9940	−	92.7686i	−0.177068	−	0.241585i
$385$	−55.9439			−0.145309
$386$	−174.765	+	300.516i	−0.452758	+	0.778538i
$387$	16.3029	−	39.3587i	0.0421264	−	0.101702i
$388$	277.575	+	487.831i	0.715399	+	1.25730i
$389$	72.3872	+	174.758i	0.186085	+	0.449250i	0.989200	−	0.146575i	$-0.0468251\pi$
$389$	72.3872	+	174.758i	0.186085	+	0.449250i	−0.803114	+	0.595825i	$0.796825\pi$
$390$	−64.8986	−	85.1302i	−0.166407	−	0.218283i
$391$	485.450	+	485.450i	1.24156	+	1.24156i
$392$	−0.528098	+	55.9975i	−0.00134719	+	0.142851i
$393$	−63.5830	−	63.5830i	−0.161789	−	0.161789i
$394$	−334.055	−	45.0479i	−0.847855	−	0.114335i
$395$	−115.610	−	279.107i	−0.292683	−	0.706600i
$396$	155.754	−	19.5100i	0.393318	−	0.0492677i
$397$	−98.0919	+	236.815i	−0.247083	+	0.596511i	−0.997954	−	0.0639381i	$-0.979634\pi$
$397$	−98.0919	+	236.815i	−0.247083	+	0.596511i	0.750871	+	0.660449i	$0.229634\pi$
$398$	3.78628	−	1.00178i	0.00951326	−	0.00251705i
$399$	51.5228			0.129130
$400$	21.7600	+	85.4954i	0.0544001	+	0.213738i
$401$		−	515.282i		−	1.28499i	−0.766289	−	0.642496i	$-0.777899\pi$
$401$		−	515.282i		−	1.28499i	0.766289	−	0.642496i	$-0.222101\pi$
$402$	−93.7457	+	24.8035i	−0.233198	+	0.0617002i
$403$	−251.868	−	104.327i	−0.624983	−	0.258877i
$404$	−100.638	+	129.460i	−0.249103	+	0.320446i
$405$	244.090	−	101.105i	0.602691	−	0.249643i
$406$	−163.955	−	22.1096i	−0.403829	−	0.0544571i
$407$	−182.492	+	182.492i	−0.448382	+	0.448382i
$408$	−168.901	−	71.8347i	−0.413974	−	0.176066i
$409$	119.731	−	119.731i	0.292740	−	0.292740i	−0.545422	−	0.838162i	$-0.683631\pi$
$409$	119.731	−	119.731i	0.292740	−	0.292740i	0.838162	+	0.545422i	$0.183631\pi$
$410$	366.521	+	480.781i	0.893953	+	1.17264i
$411$	51.3883	−	21.2857i	0.125032	−	0.0517901i
$412$	207.222	−	754.361i	0.502967	−	1.83097i
$413$	−26.7378	−	11.0752i	−0.0647404	−	0.0268164i
$414$	−221.485	+	380.853i	−0.534988	+	0.919936i
$415$			504.930i			1.21670i
$416$	428.929	−	49.6247i	1.03108	−	0.119290i
$417$	−96.7966			−0.232126
$418$	−179.475	−	104.374i	−0.429366	−	0.249697i
$419$	310.756	−	750.231i	0.741661	−	1.79053i	0.142671	−	0.989770i	$-0.454431\pi$
$419$	310.756	−	750.231i	0.741661	−	1.79053i	0.598990	−	0.800757i	$-0.295569\pi$
$420$	−11.1196	+	40.4792i	−0.0264753	+	0.0963791i
$421$	312.840	+	755.262i	0.743087	+	1.79397i	0.592836	+	0.805323i	$0.298008\pi$
$421$	312.840	+	755.262i	0.743087	+	1.79397i	0.150251	+	0.988648i	$0.451992\pi$
$422$	−27.1549	+	20.7014i	−0.0643482	+	0.0490555i
$423$	−1.74898	−	1.74898i	−0.00413471	−	0.00413471i
$424$	−462.106	+	186.325i	−1.08987	+	0.439445i
$425$	99.5468	+	99.5468i	0.234228	+	0.234228i
$426$	−20.8294	+	154.461i	−0.0488953	+	0.362585i
$427$	−45.4389	−	109.699i	−0.106414	−	0.256907i
$428$	−446.813	+	574.780i	−1.04396	+	1.34294i
$429$	22.2259	−	53.6581i	0.0518087	−	0.125077i
$430$	−11.7427	−	44.3820i	−0.0273087	−	0.103214i
$431$	−510.423			−1.18428			−0.592138	−	0.805837i	$-0.701716\pi$
$431$	−510.423			−1.18428			−0.592138	+	0.805837i	$0.701716\pi$
$432$	35.3426	−	244.643i	0.0818116	−	0.566302i
$433$			415.076i			0.958604i	0.877650	+	0.479302i	$0.159110\pi$
$433$			415.076i			0.958604i	−0.877650	+	0.479302i	$0.840890\pi$
$434$	27.3454	+	103.353i	0.0630077	+	0.238140i
$435$	−114.576	−	47.4589i	−0.263393	−	0.109101i
$436$	−352.050	+	44.0983i	−0.807453	+	0.101143i
$437$	538.367	−	222.999i	1.23196	−	0.510295i
$438$	13.9693	−	103.590i	0.0318933	−	0.236506i
$439$	−558.451	+	558.451i	−1.27210	+	1.27210i	−0.327114	+	0.944985i	$0.606076\pi$
$439$	−558.451	+	558.451i	−1.27210	+	1.27210i	−0.944985	+	0.327114i	$0.893924\pi$
$440$	120.736	−	118.480i	0.274400	−	0.269272i
$441$	−40.5511	+	40.5511i	−0.0919525	+	0.0919525i
$442$	547.966	−	417.739i	1.23974	−	0.945111i
$443$	−2.02208	+	0.837574i	−0.00456452	+	0.00189069i	−0.384965	−	0.922931i	$-0.625786\pi$
$443$	−2.02208	+	0.837574i	−0.00456452	+	0.00189069i	0.380400	+	0.924822i	$0.375786\pi$
$444$	95.7724	+	168.318i	0.215704	+	0.379094i
$445$	−282.031	−	116.821i	−0.633777	−	0.262519i
$446$	−94.4913	−	54.9514i	−0.211864	−	0.123209i
$447$			41.3149i			0.0924271i
$448$	−117.454	−	121.970i	−0.262173	−	0.272254i
$449$	−524.185			−1.16745			−0.583725	−	0.811951i	$-0.698405\pi$
$449$	−524.185			−1.16745			−0.583725	+	0.811951i	$0.698405\pi$
$450$	−45.4180	+	78.0982i	−0.100929	+	0.173552i
$451$	−125.523	+	303.039i	−0.278322	+	0.671928i
$452$	687.150	−	390.987i	1.52024	−	0.865015i
$453$	3.74001	+	9.02919i	0.00825610	+	0.0199320i
$454$	−263.775	−	346.005i	−0.581002	−	0.762125i
$455$	−111.435	−	111.435i	−0.244911	−	0.244911i
$456$	−111.194	+	109.117i	−0.243847	+	0.239291i
$457$	−438.185	−	438.185i	−0.958830	−	0.958830i	0.0403551	−	0.999185i	$-0.487151\pi$
$457$	−438.185	−	438.185i	−0.958830	−	0.958830i	−0.999185	+	0.0403551i	$0.987151\pi$
$458$	48.5298	+	6.54433i	0.105960	+	0.0142889i
$459$	−150.948	−	364.421i	−0.328863	−	0.793944i
$460$	59.0106	+	471.098i	0.128284	+	1.02413i
$461$	−51.5226	+	124.387i	−0.111763	+	0.269819i	−0.969858	−	0.243672i	$-0.921648\pi$
$461$	−51.5226	+	124.387i	−0.111763	+	0.269819i	0.858095	+	0.513491i	$0.171648\pi$
$462$	−22.0183	+	5.82566i	−0.0476587	+	0.0126097i
$463$	37.5531			0.0811082			0.0405541	−	0.999177i	$-0.487088\pi$
$463$	37.5531			0.0811082			0.0405541	+	0.999177i	$0.487088\pi$
$464$	400.664	−	299.512i	0.863500	−	0.645500i
$465$			80.1412i			0.172347i
$466$	70.5346	−	18.6622i	0.151362	−	0.0400477i
$467$	333.417	+	138.106i	0.713954	+	0.295729i	0.709940	−	0.704262i	$-0.248722\pi$
$467$	333.417	+	138.106i	0.713954	+	0.295729i	0.00401440	+	0.999992i	$0.498722\pi$
$468$	349.108	+	271.384i	0.745957	+	0.579881i
$469$	−131.893	+	54.6318i	−0.281222	+	0.116486i
$470$	−2.64156	−	0.356220i	−0.00562035	−	0.000757914i
$471$	136.336	−	136.336i	0.289461	−	0.289461i
$472$	81.1597	−	32.7242i	0.171948	−	0.0693310i
$473$	17.6130	−	17.6130i	0.0372367	−	0.0372367i
$474$	−74.5661	−	97.8115i	−0.157312	−	0.206353i
$475$	110.398	−	45.7284i	0.232417	−	0.0962703i
$476$	−260.557	−	71.5746i	−0.547388	−	0.150367i
$477$	−471.408	−	195.263i	−0.988276	−	0.409357i
$478$	−455.247	+	782.819i	−0.952401	+	1.63770i
$479$		−	388.188i		−	0.810413i	−0.914225	−	0.405206i	$-0.867200\pi$
$479$		−	388.188i		−	0.810413i	0.914225	−	0.405206i	$-0.132800\pi$
$480$	−61.7304	−	110.910i	−0.128605	−	0.231063i
$481$	−727.009			−1.51145
$482$	405.861	+	236.028i	0.842035	+	0.489685i
$483$	24.4633	−	59.0596i	0.0506486	−	0.122277i
$484$	−378.211	−	103.894i	−0.781428	−	0.214657i
$485$	237.037	+	572.259i	0.488737	+	1.17992i
$486$	306.687	−	233.801i	0.631042	−	0.481072i
$487$	−553.441	−	553.441i	−1.13643	−	1.13643i	−0.989085	−	0.147343i	$-0.952928\pi$
$487$	−553.441	−	553.441i	−1.13643	−	1.13643i	−0.147343	−	0.989085i	$-0.547072\pi$
$488$	330.389	+	140.516i	0.677026	+	0.287943i
$489$	−46.1056	−	46.1056i	−0.0942856	−	0.0942856i
$490$	−8.25914	+	61.2460i	−0.0168554	+	0.124992i
$491$	−308.837	−	745.599i	−0.628996	−	1.51853i	−0.840872	−	0.541235i	$-0.817957\pi$
$491$	−308.837	−	745.599i	−0.628996	−	1.51853i	0.211875	−	0.977297i	$-0.432043\pi$
$492$	194.320	+	151.058i	0.394960	+	0.307028i
$493$	305.483	−	737.502i	0.619642	−	1.49595i
$494$	−149.594	−	565.397i	−0.302823	−	1.14453i
$495$	173.230			0.349960
$496$	−277.899	−	165.139i	−0.560281	−	0.332941i
$497$			229.454i			0.461678i
$498$	52.5804	+	198.729i	0.105583	+	0.399055i
$499$	−511.365	−	211.814i	−1.02478	−	0.424477i	−0.193953	−	0.981011i	$-0.562131\pi$
$499$	−511.365	−	211.814i	−1.02478	−	0.424477i	−0.830825	+	0.556534i	$0.812131\pi$
$500$	66.9665	+	534.613i	0.133933	+	1.06923i
$501$	43.3370	−	17.9508i	0.0865010	−	0.0358299i
$502$	−83.2716	+	617.504i	−0.165880	+	1.23009i
$503$	208.061	−	208.061i	0.413641	−	0.413641i	−0.469364	−	0.883005i	$-0.655517\pi$
$503$	208.061	−	208.061i	0.413641	−	0.413641i	0.883005	+	0.469364i	$0.155517\pi$
$504$	1.63525	−	173.396i	0.00324455	−	0.344040i
$505$	−127.958	+	127.958i	−0.253382	+	0.253382i
$506$	−204.857	+	156.171i	−0.404855	+	0.308639i
$507$	10.8529	−	4.49542i	0.0214061	−	0.00886670i
$508$	−261.168	+	148.604i	−0.514111	+	0.292528i
$509$	189.208	+	78.3725i	0.371725	+	0.153974i	0.560722	−	0.828004i	$-0.310524\pi$
$509$	189.208	+	78.3725i	0.371725	+	0.153974i	−0.188997	+	0.981978i	$0.560524\pi$
$510$	−175.098	−	101.828i	−0.343329	−	0.199662i
$511$		−	153.884i		−	0.301142i
$512$	511.795	+	14.4833i	0.999600	+	0.0282876i
$513$	−334.804			−0.652640
$514$	100.406	−	172.652i	0.195342	−	0.335900i
$515$	330.384	−	797.618i	0.641523	−	1.54877i
$516$	−9.24336	−	16.2450i	−0.0179135	−	0.0314825i
$517$	−0.553428	−	1.33609i	−0.00107046	−	0.00258432i
$518$	172.846	+	226.729i	0.333679	+	0.437701i
$519$	−43.5842	−	43.5842i	−0.0839772	−	0.0839772i
$520$	476.493	+	4.49369i	0.916333	+	0.00864171i
$521$	0.665308	+	0.665308i	0.00127698	+	0.00127698i	0.707745	−	0.706468i	$-0.249713\pi$
$521$	0.665308	+	0.665308i	0.00127698	+	0.00127698i	−0.706468	+	0.707745i	$0.749713\pi$
$522$	507.684	+	68.4621i	0.972575	+	0.131154i
$523$	90.6904	+	218.946i	0.173404	+	0.418635i	0.986557	−	0.163415i	$-0.0522509\pi$
$523$	90.6904	+	218.946i	0.173404	+	0.418635i	−0.813153	+	0.582050i	$0.802251\pi$
$524$	397.172	−	49.7505i	0.757962	−	0.0949436i
$525$	5.01647	−	12.1108i	0.00955517	−	0.0230682i
$526$	−832.242	+	220.197i	−1.58221	+	0.418625i
$527$	−515.853			−0.978848
$528$	35.1812	−	59.2038i	0.0666310	−	0.112128i
$529$		−	193.999i		−	0.366728i
$530$	−531.573	+	140.645i	−1.00297	+	0.265368i
$531$	82.7934	+	34.2942i	0.155920	+	0.0645841i
$532$	−140.762	+	181.076i	−0.264590	+	0.340368i
$533$	−853.653	+	353.595i	−1.60160	+	0.663404i
$534$	−123.166	−	16.6092i	−0.230648	−	0.0311033i
$535$	−568.109	+	568.109i	−1.06189	+	1.06189i
$536$	168.945	−	397.231i	0.315195	−	0.741103i
$537$	175.007	−	175.007i	0.325897	−	0.325897i
$538$	482.218	+	632.546i	0.896317	+	1.17574i
$539$	−30.9780	+	12.8315i	−0.0574732	+	0.0238062i
$540$	72.2571	−	263.041i	0.133810	−	0.487113i
$541$	329.527	+	136.495i	0.609108	+	0.252301i	0.665847	−	0.746088i	$-0.268070\pi$
$541$	329.527	+	136.495i	0.609108	+	0.252301i	−0.0567391	+	0.998389i	$0.518070\pi$
$542$	−79.9812	+	137.531i	−0.147567	+	0.253748i
$543$			36.7569i			0.0676923i
$544$	713.905	−	397.346i	1.31233	−	0.730415i
$545$	−391.551			−0.718441
$546$	−55.4623	−	32.2541i	−0.101579	−	0.0590734i
$547$	4.56056	−	11.0102i	0.00833741	−	0.0201283i	−0.919656	−	0.392725i	$-0.871532\pi$
$547$	4.56056	−	11.0102i	0.00833741	−	0.0201283i	0.927993	+	0.372597i	$0.121532\pi$
$548$	−65.5861	+	238.756i	−0.119683	+	0.435687i
$549$	140.701	+	339.683i	0.256287	+	0.618730i
$550$	−42.0082	+	32.0247i	−0.0763785	+	0.0582267i
$551$	−479.111	−	479.111i	−0.869531	−	0.869531i
$552$	72.2826	+	179.269i	0.130947	+	0.324763i
$553$	−128.034	−	128.034i	−0.231527	−	0.231527i
$554$	3.07382	−	22.7941i	0.00554842	−	0.0411446i
$555$	81.7857	+	197.448i	0.147362	+	0.355762i
$556$	264.451	−	340.190i	0.475632	−	0.611852i
$557$	10.2476	−	24.7400i	0.0183979	−	0.0444165i	−0.914414	−	0.404781i	$-0.867348\pi$
$557$	10.2476	−	24.7400i	0.0183979	−	0.0444165i	0.932812	+	0.360365i	$0.117348\pi$
$558$	−84.6747	−	320.031i	−0.151747	−	0.573532i
$559$	70.1664			0.125521
$560$	−111.884	−	149.670i	−0.199793	−	0.267268i
$561$		−	109.897i		−	0.195896i
$562$	−102.007	−	385.541i	−0.181508	−	0.686015i
$563$	973.853	+	403.383i	1.72976	+	0.716488i	0.999443	+	0.0333758i	$0.0106258\pi$
$563$	973.853	+	403.383i	1.72976	+	0.716488i	0.730313	+	0.683113i	$0.239374\pi$
$564$	−1.07676	+	0.134876i	−0.00190914	+	0.000239142i
$565$	806.073	−	333.886i	1.42668	−	0.590949i
$566$	12.8355	−	95.1826i	0.0226777	−	0.168167i
$567$	111.971	−	111.971i	0.197479	−	0.197479i
$568$	−485.944	−	495.197i	−0.855536	−	0.871826i
$569$	178.840	−	178.840i	0.314306	−	0.314306i	−0.532269	−	0.846575i	$-0.678660\pi$
$569$	178.840	−	178.840i	0.314306	−	0.314306i	0.846575	+	0.532269i	$0.178660\pi$
$570$	−136.727	+	104.233i	−0.239872	+	0.182865i
$571$	862.975	−	357.456i	1.51134	−	0.626018i	0.535507	−	0.844531i	$-0.320121\pi$
$571$	862.975	−	357.456i	1.51134	−	0.626018i	0.975834	+	0.218513i	$0.0701207\pi$
$572$	127.858	+	224.708i	0.223529	+	0.392846i
$573$	307.906	+	127.539i	0.537358	+	0.222581i
$574$	313.229	+	182.158i	0.545695	+	0.317348i
$575$		−	148.259i		−	0.257842i
$576$	363.694	+	377.679i	0.631414	+	0.655693i
$577$	831.605			1.44126			0.720628	−	0.693322i	$-0.243853\pi$
$577$	831.605			1.44126			0.720628	+	0.693322i	$0.243853\pi$
$578$	364.873	−	627.416i	0.631268	−	1.08549i
$579$	−59.7715	+	144.301i	−0.103232	+	0.249225i
$580$	479.818	−	273.016i	0.827273	−	0.470716i
$581$	115.813	+	279.597i	0.199334	+	0.481234i
$582$	152.884	+	200.545i	0.262688	+	0.344579i
$583$	−210.954	−	210.954i	−0.361842	−	0.361842i
$584$	325.899	+	332.105i	0.558047	+	0.568673i
$585$	345.057	+	345.057i	0.589840	+	0.589840i
$586$	134.274	+	18.1071i	0.229136	+	0.0308995i
$587$	−392.678	−	948.008i	−0.668957	−	1.61500i	−0.783359	−	0.621570i	$-0.786495\pi$
$587$	−392.678	−	948.008i	−0.668957	−	1.61500i	0.114402	−	0.993435i	$-0.463505\pi$
$588$	3.12718	+	24.9652i	0.00531833	+	0.0424577i
$589$	−167.559	+	404.524i	−0.284481	+	0.686799i
$590$	93.3602	−	24.7015i	0.158238	−	0.0418670i
$591$	−151.446			−0.256254
$592$	−853.202	−	123.259i	−1.44122	−	0.208208i
$593$		−	812.822i		−	1.37069i	−0.728217	−	0.685347i	$-0.759651\pi$
$593$		−	812.822i		−	1.37069i	0.728217	−	0.685347i	$-0.240349\pi$
$594$	143.079	−	37.8562i	0.240873	−	0.0637309i
$595$	−275.498	−	114.115i	−0.463021	−	0.191790i
$596$	−145.200	−	112.874i	−0.243625	−	0.189385i
$597$	1.62573	−	0.673398i	0.00272316	−	0.00112797i
$598$	−719.131	−	96.9762i	−1.20256	−	0.162168i
$599$	81.6751	−	81.6751i	0.136352	−	0.136352i	−0.635636	−	0.771989i	$-0.719262\pi$
$599$	81.6751	−	81.6751i	0.136352	−	0.136352i	0.771989	+	0.635636i	$0.219262\pi$
$600$	14.8224	+	36.7611i	0.0247039	+	0.0612685i
$601$	835.585	−	835.585i	1.39032	−	1.39032i	0.565742	−	0.824582i	$-0.308590\pi$
$601$	835.585	−	835.585i	1.39032	−	1.39032i	0.824582	−	0.565742i	$-0.191410\pi$
$602$	−16.6820	−	21.8825i	−0.0277109	−	0.0363496i
$603$	408.406	−	169.167i	0.677290	−	0.280543i
$604$	−41.9507	−	11.5238i	−0.0694548	−	0.0190792i
$605$	−399.899	−	165.644i	−0.660990	−	0.273791i
$606$	−37.0366	+	63.6861i	−0.0611165	+	0.105093i
$607$		−	808.461i		−	1.33190i	−0.745998	−	0.665948i	$-0.768027\pi$
$607$		−	808.461i		−	1.33190i	0.745998	−	0.665948i	$-0.231973\pi$
$608$	−79.7019	−	688.901i	−0.131089	−	1.13306i
$609$	−74.3299			−0.122052
$610$	342.509	+	199.186i	0.561490	+	0.326534i
$611$	1.55899	−	3.76373i	0.00255154	−	0.00615996i
$612$	806.812	+	221.630i	1.31832	+	0.362141i
$613$	100.376	+	242.329i	0.163745	+	0.395317i	0.984361	−	0.176165i	$-0.0563691\pi$
$613$	100.376	+	242.329i	0.163745	+	0.395317i	−0.820615	+	0.571481i	$0.806369\pi$
$614$	−158.414	+	120.766i	−0.258003	+	0.196687i
$615$	192.065	+	192.065i	0.312301	+	0.312301i
$616$	39.6805	−	93.2987i	0.0644164	−	0.151459i
$617$	−423.912	−	423.912i	−0.687053	−	0.687053i	0.274527	−	0.961580i	$-0.411479\pi$
$617$	−423.912	−	423.912i	−0.687053	−	0.687053i	−0.961580	+	0.274527i	$0.911479\pi$
$618$	46.9728	−	348.329i	0.0760078	−	0.563640i
$619$	247.099	+	596.550i	0.399191	+	0.963733i	0.987858	+	0.155357i	$0.0496528\pi$
$619$	247.099	+	596.550i	0.399191	+	0.963733i	−0.588667	+	0.808375i	$0.700347\pi$
$620$	−281.655	−	218.948i	−0.454282	−	0.353142i
$621$	−158.967	+	383.779i	−0.255985	+	0.618002i
$622$	−62.5807	−	236.526i	−0.100612	−	0.380267i
$623$	−182.964			−0.293683
$624$	188.005	−	47.8505i	0.301290	−	0.0766835i
$625$			456.752i			0.730804i
$626$	168.092	+	635.308i	0.268517	+	1.01487i
$627$	−86.1800	−	35.6969i	−0.137448	−	0.0569329i
$628$	106.676	+	851.624i	0.169866	+	1.35609i
$629$	−1270.93	+	526.438i	−2.02056	+	0.836944i
$630$	25.5744	−	189.648i	0.0405943	−	0.301029i
$631$	381.014	−	381.014i	0.603826	−	0.603826i	−0.337500	−	0.941326i	$-0.609581\pi$
$631$	381.014	−	381.014i	0.603826	−	0.603826i	0.941326	+	0.337500i	$0.109581\pi$
$632$	547.473	+	5.16308i	0.866255	+	0.00816943i
$633$	−10.8480	+	10.8480i	−0.0171374	+	0.0171374i
$634$	30.9973	−	23.6307i	0.0488917	−	0.0372723i
$635$	−306.368	+	126.902i	−0.482469	+	0.199845i
$636$	−194.569	+	110.710i	−0.305927	+	0.174072i
$637$	−87.2642	−	36.1460i	−0.136992	−	0.0567441i
$638$	258.921	+	150.576i	0.405833	+	0.236012i
$639$		−	710.502i		−	1.11190i
$640$	558.440	+	86.0595i	0.872563	+	0.134468i
$641$	599.749			0.935646			0.467823	−	0.883822i	$-0.345039\pi$
$641$	599.749			0.935646			0.467823	+	0.883822i	$0.345039\pi$
$642$	−164.436	+	282.755i	−0.256131	+	0.440428i
$643$	358.249	−	864.888i	0.557152	−	1.34508i	−0.354860	−	0.934919i	$-0.615472\pi$
$643$	358.249	−	864.888i	0.557152	−	1.34508i	0.912012	−	0.410164i	$-0.134528\pi$
$644$	140.729	+	247.328i	0.218524	+	0.384050i
$645$	−7.89345	−	19.0565i	−0.0122379	−	0.0295449i
$646$	−670.928	−	880.085i	−1.03859	−	1.36236i
$647$	−49.6972	−	49.6972i	−0.0768117	−	0.0768117i	0.667657	−	0.744469i	$-0.267297\pi$
$647$	−49.6972	−	49.6972i	−0.0768117	−	0.0768117i	−0.744469	+	0.667657i	$0.767297\pi$
$648$	−4.51531	+	478.786i	−0.00696807	+	0.738867i
$649$	37.0499	+	37.0499i	0.0570876	+	0.0570876i
$650$	−147.466	−	19.8860i	−0.226871	−	0.0305939i
$651$	18.3815	+	44.3769i	0.0282358	+	0.0681673i
$652$	287.999	−	36.0753i	0.441717	−	0.0553302i
$653$	−190.695	+	460.379i	−0.292030	+	0.705022i	−0.999999	−	0.00122104i	$-0.999611\pi$
$653$	−190.695	+	460.379i	−0.292030	+	0.705022i	0.707970	+	0.706243i	$0.249611\pi$
$654$	−154.106	+	40.7737i	−0.235636	+	0.0623451i
$655$	441.736			0.674406
$656$	−1061.78	+	270.240i	−1.61856	+	0.411952i
$657$			476.499i			0.725265i
$658$	−1.54443	+	0.408629i	−0.00234715	+	0.000621016i
$659$	383.261	+	158.752i	0.581580	+	0.240898i	0.654023	−	0.756474i	$-0.273080\pi$
$659$	383.261	+	158.752i	0.581580	+	0.240898i	−0.0724437	+	0.997373i	$0.523080\pi$
$660$	46.6448	−	60.0038i	0.0706740	−	0.0909148i
$661$	−301.062	+	124.704i	−0.455465	+	0.188660i	−0.598608	−	0.801042i	$-0.704279\pi$
$661$	−301.062	+	124.704i	−0.455465	+	0.188660i	0.143143	+	0.989702i	$0.454279\pi$
$662$	−924.161	−	124.625i	−1.39601	−	0.188255i
$663$	218.905	−	218.905i	0.330173	−	0.330173i
$664$	−842.082	−	358.142i	−1.26820	−	0.539371i
$665$	−178.975	+	178.975i	−0.269135	+	0.269135i
$666$	−535.216	−	702.065i	−0.803627	−	1.05415i
$667$	−776.680	+	321.711i	−1.16444	+	0.482326i
$668$	−55.3104	+	201.349i	−0.0828000	+	0.301421i
$669$	−45.3727	−	18.7940i	−0.0678217	−	0.0280927i
$670$	239.484	−	411.803i	0.357439	−	0.614632i
$671$			214.971i			0.320374i
$672$	−59.6209	−	47.2559i	−0.0887216	−	0.0703213i
$673$	−355.511			−0.528248			−0.264124	−	0.964489i	$-0.585083\pi$
$673$	−355.511			−0.528248			−0.264124	+	0.964489i	$0.585083\pi$
$674$	−56.4024	−	32.8008i	−0.0836831	−	0.0486658i
$675$	−32.5979	+	78.6982i	−0.0482931	+	0.116590i
$676$	−13.8514	+	50.4239i	−0.0204902	+	0.0745915i
$677$	−69.8055	−	168.525i	−0.103110	−	0.248930i	0.863902	−	0.503660i	$-0.168013\pi$
$677$	−69.8055	−	168.525i	−0.103110	−	0.248930i	−0.967012	+	0.254730i	$0.918013\pi$
$678$	282.484	−	215.350i	0.416643	−	0.317625i
$679$	262.511	+	262.511i	0.386614	+	0.386614i
$680$	836.244	−	337.180i	1.22977	−	0.495853i
$681$	−138.224	−	138.224i	−0.202972	−	0.202972i
$682$	25.8672	−	191.819i	0.0379285	−	0.281260i
$683$	166.452	+	401.851i	0.243707	+	0.588361i	0.997645	−	0.0685841i	$-0.0218481\pi$
$683$	166.452	+	401.851i	0.243707	+	0.588361i	−0.753938	+	0.656946i	$0.771848\pi$
$684$	435.869	−	560.701i	0.637235	−	0.819738i
$685$	−104.567	+	252.447i	−0.152653	+	0.368536i
$686$	9.47428	+	35.8084i	0.0138109	+	0.0521988i
$687$	22.0013			0.0320252
$688$	82.3458	+	11.8962i	0.119689	+	0.0172910i
$689$		−	840.397i		−	1.21974i
$690$	54.5617	+	206.218i	0.0790750	+	0.298867i
$691$	−364.926	−	151.157i	−0.528113	−	0.218752i	0.102663	−	0.994716i	$-0.467264\pi$
$691$	−364.926	−	151.157i	−0.528113	−	0.218752i	−0.630777	+	0.775964i	$0.717264\pi$
$692$	272.249	−	34.1024i	0.393423	−	0.0492809i
$693$	95.9233	−	39.7327i	0.138417	−	0.0573344i
$694$	−140.291	+	1040.34i	−0.202149	+	1.49904i
$695$	336.242	−	336.242i	0.483801	−	0.483801i
$696$	160.416	−	157.418i	0.230482	−	0.226176i
$697$	−1236.28	+	1236.28i	−1.77372	+	1.77372i
$698$	766.507	−	584.342i	1.09815	−	0.837167i
$699$	30.2857	−	12.5447i	0.0433271	−	0.0179467i
$700$	28.8581	+	50.7174i	0.0412258	+	0.0724534i
$701$	876.664	+	363.126i	1.25059	+	0.518012i	0.907009	−	0.421111i	$-0.138360\pi$
$701$	876.664	+	363.126i	1.25059	+	0.518012i	0.343582	+	0.939123i	$0.388360\pi$
$702$	360.404	+	209.593i	0.513396	+	0.298565i
$703$			1167.65i			1.66095i
$704$	111.954	+	285.390i	0.159026	+	0.405384i
$705$	−1.19757			−0.00169868
$706$	−35.0959	+	60.3489i	−0.0497109	+	0.0854801i
$707$	−41.5056	+	100.203i	−0.0587067	+	0.141730i
$708$	34.1723	−	19.4439i	0.0482659	−	0.0274632i
$709$	−27.2742	−	65.8459i	−0.0384686	−	0.0928714i	0.903478	−	0.428635i	$-0.141006\pi$
$709$	−27.2742	−	65.8459i	−0.0384686	−	0.0928714i	−0.941946	+	0.335764i	$0.891006\pi$
$710$	−464.196	−	608.906i	−0.653798	−	0.857614i
$711$	396.457	+	396.457i	0.557605	+	0.557605i
$712$	394.866	−	387.488i	0.554587	−	0.544224i
$713$	384.140	+	384.140i	0.538766	+	0.538766i
$714$	−120.313	−	16.2244i	−0.168506	−	0.0227233i
$715$	109.186	+	263.598i	0.152707	+	0.368668i
$716$	136.934	+	1093.18i	0.191248	+	1.52679i
$717$	−155.700	+	375.893i	−0.217155	+	0.524257i
$718$	−525.447	+	139.024i	−0.731820	+	0.193627i
$719$	−482.081			−0.670489			−0.335244	−	0.942131i	$-0.608819\pi$
$719$	−482.081			−0.670489			−0.335244	+	0.942131i	$0.608819\pi$
$720$	346.449	+	463.453i	0.481179	+	0.643684i
$721$		−	517.447i		−	0.717679i
$722$	−210.099	+	55.5887i	−0.290996	+	0.0769926i
$723$	194.886	+	80.7243i	0.269551	+	0.111652i
$724$	−129.181	−	100.421i	−0.178427	−	0.138703i
$725$	−159.267	+	65.9705i	−0.219678	+	0.0909938i
$726$	−174.640	−	23.5506i	−0.240552	−	0.0324388i
$727$	−958.078	+	958.078i	−1.31785	+	1.31785i	−0.402378	+	0.915474i	$0.631816\pi$
$727$	−958.078	+	958.078i	−1.31785	+	1.31785i	−0.915474	+	0.402378i	$0.868184\pi$
$728$	264.881	−	106.802i	0.363848	−	0.146706i
$729$	−258.372	+	258.372i	−0.354420	+	0.354420i
$730$	311.314	+	408.364i	0.426457	+	0.559402i
$731$	122.663	−	50.8085i	0.167801	−	0.0695055i
$732$	155.546	+	42.7284i	0.212495	+	0.0583721i
$733$	1139.64	+	472.054i	1.55476	+	0.644002i	0.984169	−	0.177233i	$-0.0567145\pi$
$733$	1139.64	+	472.054i	1.55476	+	0.644002i	0.570590	+	0.821235i	$0.306714\pi$
$734$	294.892	−	507.081i	0.401761	−	0.690845i
$735$			27.7663i			0.0377773i
$736$	−827.515	−	235.732i	−1.12434	−	0.320289i
$737$	258.463			0.350695
$738$	−969.911	−	564.051i	−1.31424	−	0.764297i
$739$	−231.276	+	558.350i	−0.312958	+	0.755548i	0.686634	+	0.727003i	$0.259087\pi$
$739$	−231.276	+	558.350i	−0.312958	+	0.755548i	−0.999593	+	0.0285453i	$0.990913\pi$
$740$	−917.368	−	252.000i	−1.23969	−	0.340541i
$741$	−100.557	−	242.767i	−0.135705	−	0.327620i
$742$	−262.091	+	199.804i	−0.353222	+	0.269277i
$743$	−633.588	−	633.588i	−0.852743	−	0.852743i	0.137727	−	0.990470i	$-0.456020\pi$
$743$	−633.588	−	633.588i	−0.852743	−	0.852743i	−0.990470	+	0.137727i	$0.956020\pi$
$744$	−133.653	−	56.8434i	−0.179641	−	0.0764024i
$745$	−143.515	−	143.515i	−0.192638	−	0.192638i
$746$	−120.622	+	894.478i	−0.161692	+	1.19903i
$747$	−358.614	−	865.770i	−0.480072	−	1.15900i
$748$	386.232	+	300.243i	0.516353	+	0.401395i
$749$	−184.277	+	444.885i	−0.246031	+	0.593972i
$750$	61.9178	+	234.021i	0.0825571	+	0.312027i
$751$	−970.408			−1.29215			−0.646077	−	0.763272i	$-0.723592\pi$
$751$	−970.408			−1.29215			−0.646077	+	0.763272i	$0.723592\pi$
$752$	2.46771	−	4.15272i	0.00328153	−	0.00552224i
$753$			279.950i			0.371779i
$754$	215.814	+	815.676i	0.286225	+	1.08180i
$755$	−44.3563	−	18.3730i	−0.0587500	−	0.0243351i
$756$	−20.3210	−	162.228i	−0.0268796	−	0.214587i
$757$	1169.52	−	484.433i	1.54495	−	0.639937i	0.562552	−	0.826762i	$-0.309819\pi$
$757$	1169.52	−	484.433i	1.54495	−	0.639937i	0.982393	+	0.186824i	$0.0598195\pi$
$758$	−59.1787	+	438.842i	−0.0780721	+	0.578948i
$759$	−81.8373	+	81.8373i	−0.107823	+	0.107823i
$760$	7.21729	−	765.293i	0.00949643	−	1.00696i
$761$	30.5801	−	30.5801i	0.0401841	−	0.0401841i	−0.686729	−	0.726913i	$-0.740954\pi$
$761$	30.5801	−	30.5801i	0.0401841	−	0.0401841i	0.726913	+	0.686729i	$0.240954\pi$
$762$	−107.365	+	81.8491i	−0.140899	+	0.107414i
$763$	−216.815	+	89.8076i	−0.284161	+	0.117703i
$764$	−1289.44	+	733.690i	−1.68775	+	0.960327i
$765$	853.077	+	353.356i	1.11513	+	0.461903i
$766$	−277.085	−	161.139i	−0.361730	−	0.210364i
$767$			147.599i			0.192437i
$768$	228.751	−	24.2815i	0.297853	−	0.0316165i
$769$	939.017			1.22109			0.610544	−	0.791982i	$-0.290951\pi$
$769$	939.017			1.22109			0.610544	+	0.791982i	$0.290951\pi$
$770$	56.2483	−	96.7214i	0.0730497	−	0.125612i
$771$	34.3399	−	82.9040i	0.0445395	−	0.107528i
$772$	−343.846	−	604.301i	−0.445396	−	0.782773i
$773$	80.5180	+	194.388i	0.104163	+	0.251472i	0.967365	−	0.253387i	$-0.0815446\pi$
$773$	80.5180	+	194.388i	0.104163	+	0.251472i	−0.863202	+	0.504859i	$0.831545\pi$
$774$	51.6557	+	67.7590i	0.0667386	+	0.0875439i
$775$	78.7722	+	78.7722i	0.101642	+	0.101642i
$776$	−1122.49	−	10.5860i	−1.44651	−	0.0136417i
$777$	90.5750	+	90.5750i	0.116570	+	0.116570i
$778$	−374.920	−	50.5587i	−0.481903	−	0.0649854i
$779$	567.906	+	1371.05i	0.729020	+	1.76001i
$780$	212.433	−	26.6098i	0.272350	−	0.0341151i
$781$	158.974	−	383.797i	0.203552	−	0.491418i
$782$	−1327.38	+	351.203i	−1.69742	+	0.449109i
$783$	483.009			0.616869
$784$	−96.2831	−	57.2152i	−0.122810	−	0.0729785i
$785$			947.179i			1.20660i
$786$	173.858	−	45.9997i	0.221193	−	0.0585238i
$787$	−1409.72	−	583.926i	−1.79126	−	0.741965i	−0.989539	−	0.144269i	$-0.953917\pi$
$787$	−1409.72	−	583.926i	−1.79126	−	0.741965i	−0.801723	−	0.597696i	$-0.796083\pi$
$788$	413.755	−	532.254i	0.525070	−	0.675450i
$789$	−357.342	+	148.016i	−0.452905	+	0.187600i
$790$	598.787	+	80.7475i	0.757958	+	0.102212i
$791$	369.768	−	369.768i	0.467469	−	0.467469i
$792$	−122.870	+	288.899i	−0.155139	+	0.364771i
$793$	−428.200	+	428.200i	−0.539975	+	0.539975i
$794$	−310.803	−	407.694i	−0.391440	−	0.513468i
$795$	−228.243	+	94.5414i	−0.287098	+	0.118920i
$796$	−2.07489	+	7.55332i	−0.00260665	+	0.00948910i
$797$	349.792	+	144.889i	0.438886	+	0.181792i	0.591175	−	0.806544i	$-0.298664\pi$
$797$	349.792	+	144.889i	0.438886	+	0.181792i	−0.152289	+	0.988336i	$0.548664\pi$
$798$	−51.8031	+	89.0778i	−0.0649162	+	0.111626i
$799$		−	7.70852i		−	0.00964771i
$800$	−169.691	−	48.3396i	−0.212114	−	0.0604244i
$801$	566.548			0.707301
$802$	890.871	+	518.085i	1.11081	+	0.645991i
$803$	−106.616	+	257.394i	−0.132772	+	0.320541i
$804$	51.3729	−	187.015i	0.0638966	−	0.232606i
$805$	120.177	+	290.133i	0.149288	+	0.360413i
$806$	433.610	−	330.560i	0.537977	−	0.410124i
$807$	252.693	+	252.693i	0.313127	+	0.313127i
$808$	−122.638	−	304.157i	−0.151780	−	0.376432i
$809$	−6.76445	−	6.76445i	−0.00836149	−	0.00836149i	0.702914	−	0.711275i	$-0.251882\pi$
$809$	−6.76445	−	6.76445i	−0.00836149	−	0.00836149i	−0.711275	+	0.702914i	$0.751882\pi$
$810$	−70.6167	+	523.662i	−0.0871811	+	0.646496i
$811$	−310.210	−	748.913i	−0.382503	−	0.923443i	−0.991480	−	0.130256i	$-0.958420\pi$
$811$	−310.210	−	748.913i	−0.382503	−	0.923443i	0.608978	−	0.793187i	$-0.291580\pi$
$812$	203.072	−	261.231i	0.250088	−	0.321713i
$813$	−27.3545	+	66.0395i	−0.0336463	+	0.0812294i
$814$	−132.025	−	498.994i	−0.162193	−	0.613015i
$815$	320.314			0.393023
$816$	294.015	−	219.788i	0.360313	−	0.269348i
$817$		−	112.694i		−	0.137936i
$818$	86.6202	+	327.384i	0.105893	+	0.400225i
$819$	270.213	+	111.926i	0.329930	+	0.136662i
$820$	−1199.74	+	150.281i	−1.46309	+	0.183270i
$821$	778.657	−	322.530i	0.948425	−	0.392850i	0.145786	−	0.989316i	$-0.453429\pi$
$821$	778.657	−	322.530i	0.948425	−	0.392850i	0.802639	+	0.596466i	$0.203429\pi$
$822$	−14.8670	+	110.247i	−0.0180863	+	0.134120i
$823$	−650.790	+	650.790i	−0.790753	+	0.790753i	−0.981617	−	0.190863i	$-0.938871\pi$
$823$	−650.790	+	650.790i	−0.790753	+	0.790753i	0.190863	+	0.981617i	$0.438871\pi$
$824$	1095.86	+	1116.73i	1.32993	+	1.35526i
$825$	−16.7817	+	16.7817i	−0.0203414	+	0.0203414i
$826$	46.0311	−	35.0915i	0.0557277	−	0.0424837i
$827$	399.575	−	165.509i	0.483162	−	0.200132i	−0.127788	−	0.991801i	$-0.540788\pi$
$827$	399.575	−	165.509i	0.483162	−	0.200132i	0.610950	+	0.791669i	$0.290788\pi$
$828$	−435.767	−	765.850i	−0.526289	−	0.924940i
$829$	−260.369	−	107.848i	−0.314076	−	0.130094i	0.220077	−	0.975483i	$-0.429369\pi$
$829$	−260.369	−	107.848i	−0.314076	−	0.130094i	−0.534153	+	0.845388i	$0.679369\pi$
$830$	−872.973	−	507.677i	−1.05177	−	0.611659i
$831$		−	10.3339i		−	0.0124355i
$832$	−345.466	+	791.469i	−0.415224	+	0.951285i
$833$	−178.726			−0.214557
$834$	97.3232	−	167.352i	0.116694	−	0.200661i
$835$	−88.1840	+	212.895i	−0.105610	+	0.254964i
$836$	360.903	−	205.353i	0.431702	−	0.245637i
$837$	−119.446	−	288.369i	−0.142708	−	0.344527i
$838$	984.627	+	1291.58i	1.17497	+	1.54126i
$839$	−894.643	−	894.643i	−1.06632	−	1.06632i	−0.997639	−	0.0686826i	$-0.978120\pi$
$839$	−894.643	−	894.643i	−1.06632	−	1.06632i	−0.0686826	−	0.997639i	$-0.521880\pi$
$840$	−58.8044	−	59.9241i	−0.0700052	−	0.0713382i
$841$	96.5180	+	96.5180i	0.114766	+	0.114766i
$842$	−1620.31	−	218.502i	−1.92436	−	0.259504i
$843$	−68.5693	−	165.541i	−0.0813396	−	0.196371i
$844$	−8.48801	−	67.7621i	−0.0100569	−	0.0802869i
$845$	−22.0839	+	53.3153i	−0.0261348	+	0.0630951i
$846$	4.78231	−	1.26532i	0.00565285	−	0.00149565i
$847$	−259.430			−0.306293
$848$	142.483	−	986.272i	0.168022	−	1.16306i
$849$		−	43.1517i		−	0.0508265i
$850$	−272.195	+	72.0181i	−0.320229	+	0.0847271i
$851$	1338.45	+	554.403i	1.57279	+	0.651473i
$852$	−246.105	−	191.313i	−0.288856	−	0.224546i
$853$	−1101.73	+	456.353i	−1.29160	+	0.534998i	−0.919462	−	0.393180i	$-0.871375\pi$
$853$	−1101.73	+	456.353i	−1.29160	+	0.534998i	−0.372137	+	0.928178i	$0.621375\pi$
$854$	235.345	+	31.7367i	0.275580	+	0.0371624i
$855$	554.194	−	554.194i	0.648180	−	0.648180i
$856$	−544.492	−	1350.40i	−0.636089	−	1.57757i
$857$	320.192	−	320.192i	0.373619	−	0.373619i	−0.495174	−	0.868794i	$-0.664896\pi$
$857$	320.192	−	320.192i	0.373619	−	0.373619i	0.868794	+	0.495174i	$0.164896\pi$
$858$	70.4226	+	92.3764i	0.0820777	+	0.107665i
$859$	975.935	−	404.245i	1.13613	−	0.470600i	0.266269	−	0.963899i	$-0.414209\pi$
$859$	975.935	−	404.245i	1.13613	−	0.470600i	0.869860	+	0.493299i	$0.164209\pi$
$860$	88.5387	+	24.3215i	0.102952	+	0.0282808i
$861$	150.406	+	62.3001i	0.174687	+	0.0723578i
$862$	513.199	−	882.469i	0.595359	−	1.02375i
$863$			558.346i			0.646983i	0.946231	+	0.323492i	$0.104857\pi$
$863$			558.346i			0.646983i	−0.946231	+	0.323492i	$0.895143\pi$
$864$	387.427	+	307.077i	0.448411	+	0.355413i
$865$	302.796			0.350053
$866$	−717.624	−	417.334i	−0.828665	−	0.481909i
$867$	124.791	−	301.271i	0.143934	−	0.347487i
$868$	−206.180	−	56.6376i	−0.237535	−	0.0652507i
$869$	125.451	+	302.864i	0.144362	+	0.348521i
$870$	197.251	−	150.373i	0.226725	−	0.172843i
$871$	514.831	+	514.831i	0.591080	+	0.591080i
$872$	277.723	−	652.996i	0.318490	−	0.748849i
$873$	−812.864	−	812.864i	−0.931116	−	0.931116i
$874$	−155.753	+	1154.99i	−0.178207	+	1.32150i
$875$	136.379	+	329.249i	0.155862	+	0.376284i
$876$	165.051	+	128.305i	0.188414	+	0.146466i
$877$	214.061	−	516.788i	0.244083	−	0.589268i	−0.753598	−	0.657336i	$-0.771683\pi$
$877$	214.061	−	516.788i	0.244083	−	0.589268i	0.997681	+	0.0680678i	$0.0216834\pi$
$878$	−404.017	−	1527.00i	−0.460156	−	1.73917i
$879$	60.8740			0.0692537
$880$	83.4471	+	327.864i	0.0948262	+	0.372573i
$881$		−	786.792i		−	0.893067i	−0.894767	−	0.446533i	$-0.852658\pi$
$881$		−	786.792i		−	0.893067i	0.894767	−	0.446533i	$-0.147342\pi$
$882$	−29.3370	−	110.880i	−0.0332619	−	0.125715i
$883$	431.473	+	178.722i	0.488644	+	0.202403i	0.613381	−	0.789787i	$-0.289809\pi$
$883$	431.473	+	178.722i	0.488644	+	0.202403i	−0.124737	+	0.992190i	$0.539809\pi$
$884$	171.282	+	1367.39i	0.193757	+	1.54682i
$885$	40.0864	−	16.6043i	0.0452953	−	0.0187619i
$886$	0.585001	−	4.33810i	0.000660272	−	0.00489628i
$887$	146.612	−	146.612i	0.165289	−	0.165289i	−0.619616	−	0.784905i	$-0.712712\pi$
$887$	146.612	−	146.612i	0.165289	−	0.165289i	0.784905	+	0.619616i	$0.212712\pi$
$888$	−387.298	−	3.65251i	−0.436146	−	0.00411318i
$889$	−140.540	+	140.540i	−0.158087	+	0.158087i
$890$	485.536	−	370.146i	0.545546	−	0.415894i
$891$	−264.866	+	109.711i	−0.297269	+	0.123133i
$892$	190.011	−	108.116i	0.213016	−	0.121206i
$893$	−6.04491	−	2.50389i	−0.00676922	−	0.00280390i
$894$	−71.4293	−	41.5397i	−0.0798986	−	0.0464650i
$895$			1215.84i			1.35848i
$896$	328.966	−	80.4320i	0.367150	−	0.0897679i
$897$	−326.023			−0.363460
$898$	527.037	−	906.263i	0.586900	−	1.00920i
$899$	241.731	−	583.591i	0.268889	−	0.649156i
$900$	−89.3589	−	157.046i	−0.0992877	−	0.174496i
$901$	−608.544	−	1469.15i	−0.675409	−	1.63058i
$902$	−397.719	−	521.704i	−0.440930	−	0.578386i
$903$	−8.74173	−	8.74173i	−0.00968077	−	0.00968077i
$904$	−14.9112	+	1581.13i	−0.0164947	+	1.74903i
$905$	−127.682	−	127.682i	−0.141085	−	0.141085i
$906$	−19.3709	−	2.61220i	−0.0213807	−	0.00288322i
$907$	214.470	+	517.776i	0.236461	+	0.570866i	0.996912	−	0.0785287i	$-0.0250222\pi$
$907$	214.470	+	517.776i	0.236461	+	0.570866i	−0.760451	+	0.649395i	$0.775022\pi$
$908$	863.417	−	108.153i	0.950900	−	0.119111i
$909$	128.522	−	310.279i	0.141388	−	0.341341i
$910$	304.700	−	80.6184i	0.334835	−	0.0885916i
$911$	830.737			0.911896			0.455948	−	0.890006i	$-0.349300\pi$
$911$	830.737			0.911896			0.455948	+	0.890006i	$0.349300\pi$
$912$	−76.8525	−	301.954i	−0.0842681	−	0.331090i
$913$		−	547.909i		−	0.600120i
$914$	1198.15	−	317.009i	1.31088	−	0.346837i
$915$	164.466	+	68.1239i	0.179744	+	0.0744523i
$916$	−60.1082	+	77.3231i	−0.0656203	+	0.0844139i
$917$	244.604	−	101.318i	0.266744	−	0.110489i
$918$	781.815	+	105.429i	0.851651	+	0.114847i
$919$	459.455	−	459.455i	0.499951	−	0.499951i	−0.411472	−	0.911422i	$-0.634985\pi$
$919$	459.455	−	459.455i	0.499951	−	0.499951i	0.911422	+	0.411472i	$0.134985\pi$
$920$	−873.813	−	371.638i	−0.949797	−	0.403954i
$921$	−63.2841	+	63.2841i	−0.0687124	+	0.0687124i
$922$	−163.249	−	214.141i	−0.177060	−	0.232257i
$923$	1081.15	−	447.825i	1.17134	−	0.485184i
$924$	12.0661	−	43.9248i	0.0130585	−	0.0475376i
$925$	274.464	+	113.687i	0.296718	+	0.122904i
$926$	−37.7574	+	64.9255i	−0.0407747	+	0.0701140i
$927$			1602.27i			1.72845i
$928$	114.983	+	993.849i	0.123904	+	1.07096i
$929$	−789.837			−0.850202			−0.425101	−	0.905146i	$-0.639761\pi$
$929$	−789.837			−0.850202			−0.425101	+	0.905146i	$0.639761\pi$
$930$	−138.556	−	80.5771i	−0.148985	−	0.0866421i
$931$	−58.0539	+	140.155i	−0.0623565	+	0.150542i
$932$	−38.6531	+	140.711i	−0.0414733	+	0.150977i
$933$	−42.0666	−	101.558i	−0.0450875	−	0.108851i
$934$	−574.001	+	437.587i	−0.614562	+	0.468508i
$935$	381.750	+	381.750i	0.408289	+	0.408289i
$936$	−820.203	+	330.712i	−0.876285	+	0.353325i
$937$	887.679	+	887.679i	0.947363	+	0.947363i	0.998682	−	0.0513197i	$-0.0163427\pi$
$937$	887.679	+	887.679i	0.947363	+	0.947363i	−0.0513197	+	0.998682i	$0.516343\pi$
$938$	38.1575	−	282.958i	0.0406796	−	0.301662i
$939$	112.991	+	272.784i	0.120331	+	0.290505i
$940$	3.27180	−	4.20884i	0.00348064	−	0.00447749i
$941$	−158.252	+	382.053i	−0.168174	+	0.406008i	−0.985388	−	0.170327i	$-0.945518\pi$
$941$	−158.252	+	382.053i	−0.168174	+	0.406008i	0.817214	+	0.576335i	$0.195518\pi$
$942$	98.6335	+	372.789i	0.104706	+	0.395742i
$943$	1841.25			1.95254
$944$	−25.0243	+	173.219i	−0.0265088	+	0.183495i
$945$		−	180.430i		−	0.190932i
$946$	12.7423	+	48.1598i	0.0134696	+	0.0509089i
$947$	−389.900	−	161.502i	−0.411721	−	0.170540i	0.167202	−	0.985923i	$-0.446527\pi$
$947$	−389.900	−	161.502i	−0.411721	−	0.170540i	−0.578923	+	0.815382i	$0.696527\pi$
$948$	244.078	−	30.5736i	0.257466	−	0.0322507i
$949$	−725.072	+	300.335i	−0.764038	+	0.316475i
$950$	−31.9389	+	236.844i	−0.0336199	+	0.249310i
$951$	12.3830	−	12.3830i	0.0130210	−	0.0130210i
$952$	385.719	−	378.512i	0.405167	−	0.397597i
$953$	147.793	−	147.793i	0.155081	−	0.155081i	−0.625302	−	0.780383i	$-0.715024\pi$
$953$	147.793	−	147.793i	0.155081	−	0.155081i	0.780383	+	0.625302i	$0.215024\pi$
$954$	811.563	−	618.690i	0.850695	−	0.648523i
$955$	−1512.60	+	626.541i	−1.58388	+	0.656064i
$956$	−895.690	−	1574.15i	−0.936914	−	1.64660i
$957$	124.328	+	51.4985i	0.129915	+	0.0538125i
$958$	671.137	+	390.299i	0.700561	+	0.407411i
$959$			163.773i			0.170774i
$960$	253.818	+	4.78782i	0.264394	+	0.00498731i
$961$	552.802			0.575236
$962$	730.964	−	1256.93i	0.759838	−	1.30658i
$963$	570.614	−	1377.58i	0.592538	−	1.43051i
$964$	−816.137	+	464.380i	−0.846615	+	0.481722i
$965$	−293.630	−	708.886i	−0.304280	−	0.734596i
$966$	77.5117	+	101.675i	0.0802398	+	0.105254i
$967$	−541.417	−	541.417i	−0.559893	−	0.559893i	0.369384	−	0.929277i	$-0.379569\pi$
$967$	−541.417	−	541.417i	−0.559893	−	0.559893i	−0.929277	+	0.369384i	$0.879569\pi$
$968$	559.891	−	549.429i	0.578400	−	0.567592i
$969$	−351.581	−	351.581i	−0.362829	−	0.362829i
$970$	−1227.70	−	165.558i	−1.26567	−	0.170678i
$971$	13.9895	+	33.7736i	0.0144073	+	0.0347823i	0.930919	−	0.365224i	$-0.119008\pi$
$971$	13.9895	+	33.7736i	0.0144073	+	0.0347823i	−0.916512	+	0.400007i	$0.869008\pi$
$972$	95.8632	+	765.303i	0.0986247	+	0.787349i
$973$	109.067	−	263.310i	0.112093	−	0.270617i
$974$	1513.29	−	400.392i	1.55369	−	0.411080i
$975$	−66.8547			−0.0685689
$976$	−575.125	+	429.928i	−0.589267	+	0.440500i
$977$			1346.39i			1.37808i	0.724723	+	0.689041i	$0.241968\pi$
$977$			1346.39i			1.37808i	−0.724723	+	0.689041i	$0.758032\pi$
$978$	126.068	−	33.3555i	0.128904	−	0.0341059i
$979$	306.037	+	126.765i	0.312601	+	0.129484i
$980$	−97.5842	−	75.8584i	−0.0995757	−	0.0774066i
$981$	671.366	−	278.089i	0.684369	−	0.283475i
$982$	1599.58	+	215.707i	1.62890	+	0.219660i
$983$	−603.976	+	603.976i	−0.614422	+	0.614422i	−0.944095	−	0.329673i	$-0.893061\pi$
$983$	−603.976	+	603.976i	−0.614422	+	0.614422i	0.329673	+	0.944095i	$0.393061\pi$
$984$	−456.540	+	184.081i	−0.463964	+	0.187074i
$985$	526.077	−	526.077i	0.534089	−	0.534089i
$986$	967.921	+	1269.66i	0.981665	+	1.28769i
$987$	−0.663135	+	0.274680i	−0.000671870	+	0.000278298i
$988$	1127.92	+	309.839i	1.14162	+	0.313603i
$989$	−129.179	−	53.5076i	−0.130615	−	0.0541027i
$990$	−174.172	+	299.497i	−0.175932	+	0.302522i
$991$		−	685.038i		−	0.691260i	−0.938371	−	0.345630i	$-0.887665\pi$
$991$		−	685.038i		−	0.691260i	0.938371	−	0.345630i	$-0.112335\pi$
$992$	564.919	−	314.423i	0.569475	−	0.316958i
$993$	−418.975			−0.421928
$994$	−396.702	−	230.702i	−0.399097	−	0.232094i
$995$	−3.30810	+	7.98645i	−0.00332472	+	0.00802658i
$996$	−396.449	−	108.904i	−0.398042	−	0.109342i
$997$	−545.439	−	1316.81i	−0.547080	−	1.32077i	−0.919641	−	0.392761i	$-0.871520\pi$
$997$	−545.439	−	1316.81i	−0.547080	−	1.32077i	0.372561	−	0.928008i	$-0.378480\pi$
$998$	880.351	−	671.131i	0.882116	−	0.672476i
$999$	−588.572	−	588.572i	−0.589161	−	0.589161i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.w.a.99.16	yes	192
32.11	odd	8	inner	224.3.w.a.43.16	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.w.a.43.16	✓	192	32.11	odd	8	inner
224.3.w.a.99.16	yes	192	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00544 + 1.72890i) q^{2} +(-0.343872 + 0.830180i) q^{3} +(-1.97818 - 3.47661i) q^{4} +(-1.68929 - 4.07830i) q^{5} +(-1.08955 - 1.42922i) q^{6} +(-1.87083 - 1.87083i) q^{7} +(7.99964 + 0.0754426i) q^{8} +(5.79301 + 5.79301i) q^{9} +O(q^{10})\)	\(q+(-1.00544 + 1.72890i) q^{2} +(-0.343872 + 0.830180i) q^{3} +(-1.97818 - 3.47661i) q^{4} +(-1.68929 - 4.07830i) q^{5} +(-1.08955 - 1.42922i) q^{6} +(-1.87083 - 1.87083i) q^{7} +(7.99964 + 0.0754426i) q^{8} +(5.79301 + 5.79301i) q^{9} +(8.74944 + 1.17988i) q^{10} +(1.83307 + 4.42543i) q^{11} +(3.56645 - 0.446740i) q^{12} +(-5.16372 + 12.4663i) q^{13} +(5.11548 - 1.35347i) q^{14} +3.96662 q^{15} +(-8.17359 + 13.7547i) q^{16} +25.5323i q^{17} +(-15.8401 + 4.19101i) q^{18} +(20.0221 + 8.29342i) q^{19} +(-10.8369 + 13.9406i) q^{20} +(2.19645 - 0.909799i) q^{21} +(-9.49417 - 1.28031i) q^{22} +(19.0131 - 19.0131i) q^{23} +(-2.81348 + 6.61520i) q^{24} +(3.89886 - 3.89886i) q^{25} +(-16.3612 - 21.4617i) q^{26} +(-14.2729 + 5.91203i) q^{27} +(-2.80330 + 10.2050i) q^{28} +(-28.8850 - 11.9646i) q^{29} +(-3.98819 + 6.85788i) q^{30} +20.2039i q^{31} +(-15.5625 - 27.9609i) q^{32} -4.30425 q^{33} +(-44.1428 - 25.6712i) q^{34} +(-4.46943 + 10.7902i) q^{35} +(8.68039 - 31.5996i) q^{36} +(20.6185 + 49.7775i) q^{37} +(-34.4695 + 26.2776i) q^{38} +(-8.57363 - 8.57363i) q^{39} +(-13.2060 - 32.7524i) q^{40} +(48.4204 + 48.4204i) q^{41} +(-0.635447 + 4.71219i) q^{42} +(-1.98997 - 4.80421i) q^{43} +(11.7593 - 15.1272i) q^{44} +(13.8396 - 33.4117i) q^{45} +(13.7552 + 51.9884i) q^{46} -0.301912 q^{47} +(-8.60823 - 11.5154i) q^{48} +7.00000i q^{49} +(2.82066 + 10.6608i) q^{50} +(-21.1964 - 8.77984i) q^{51} +(53.5552 - 6.70842i) q^{52} +(-57.5410 + 23.8343i) q^{53} +(4.12925 - 30.6206i) q^{54} +(14.9516 - 14.9516i) q^{55} +(-14.8248 - 15.1071i) q^{56} +(-13.7701 + 13.7701i) q^{57} +(49.7277 - 37.9097i) q^{58} +(10.1059 - 4.18602i) q^{59} +(-7.84669 - 13.7904i) q^{60} +(41.4624 + 17.1743i) q^{61} +(-34.9305 - 20.3138i) q^{62} -21.6755i q^{63} +(63.9886 + 1.20703i) q^{64} +59.5643 q^{65} +(4.32766 - 7.44161i) q^{66} +(20.6489 - 49.8508i) q^{67} +(88.7658 - 50.5076i) q^{68} +(9.24625 + 22.3224i) q^{69} +(-14.1613 - 18.5760i) q^{70} +(-61.3241 - 61.3241i) q^{71} +(45.9050 + 46.7791i) q^{72} +(41.1271 + 41.1271i) q^{73} +(-106.791 - 14.4009i) q^{74} +(1.89605 + 4.57746i) q^{75} +(-10.7744 - 86.0148i) q^{76} +(4.84986 - 11.7086i) q^{77} +(23.4432 - 6.20267i) q^{78} +68.4372 q^{79} +(69.9034 + 10.0987i) q^{80} +59.8509i q^{81} +(-132.398 + 35.0302i) q^{82} +(-105.678 - 43.7731i) q^{83} +(-7.50799 - 5.83644i) q^{84} +(104.128 - 43.1314i) q^{85} +(10.3068 + 1.38989i) q^{86} +(19.8655 - 19.8655i) q^{87} +(14.3301 + 35.5402i) q^{88} +(48.8993 - 48.8993i) q^{89} +(43.8505 + 57.5206i) q^{90} +(32.9828 - 13.6619i) q^{91} +(-103.713 - 28.4898i) q^{92} +(-16.7729 - 6.94756i) q^{93} +(0.303555 - 0.521976i) q^{94} -95.6659i q^{95} +(28.5640 - 3.30470i) q^{96} -140.318 q^{97} +(-12.1023 - 7.03808i) q^{98} +(-15.0176 + 36.2556i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q + 80 q^{10} + 96 q^{12} - 20 q^{16} - 60 q^{18} - 260 q^{22} + 64 q^{23} - 144 q^{24} - 200 q^{26} + 192 q^{27} - 40 q^{30} + 40 q^{32} + 120 q^{34} + 464 q^{36} + 504 q^{38} - 384 q^{39} + 360 q^{40} - 96 q^{43} + 52 q^{44} + 64 q^{46} - 104 q^{48} - 312 q^{50} - 384 q^{51} - 320 q^{52} + 160 q^{53} - 576 q^{54} - 512 q^{55} - 196 q^{56} - 360 q^{58} - 872 q^{60} + 128 q^{61} - 408 q^{62} + 832 q^{66} + 160 q^{67} + 856 q^{68} - 384 q^{69} + 336 q^{70} + 1488 q^{72} + 308 q^{74} + 768 q^{75} + 1024 q^{76} - 224 q^{77} - 408 q^{78} + 1024 q^{79} - 1040 q^{80} - 240 q^{82} - 1384 q^{86} + 896 q^{87} - 560 q^{88} - 1320 q^{90} - 380 q^{92} - 936 q^{94} - 1088 q^{96} - 512 q^{99}+O(q^{100}) \) 192 * q + 80 * q^10 + 96 * q^12 - 20 * q^16 - 60 * q^18 - 260 * q^22 + 64 * q^23 - 144 * q^24 - 200 * q^26 + 192 * q^27 - 40 * q^30 + 40 * q^32 + 120 * q^34 + 464 * q^36 + 504 * q^38 - 384 * q^39 + 360 * q^40 - 96 * q^43 + 52 * q^44 + 64 * q^46 - 104 * q^48 - 312 * q^50 - 384 * q^51 - 320 * q^52 + 160 * q^53 - 576 * q^54 - 512 * q^55 - 196 * q^56 - 360 * q^58 - 872 * q^60 + 128 * q^61 - 408 * q^62 + 832 * q^66 + 160 * q^67 + 856 * q^68 - 384 * q^69 + 336 * q^70 + 1488 * q^72 + 308 * q^74 + 768 * q^75 + 1024 * q^76 - 224 * q^77 - 408 * q^78 + 1024 * q^79 - 1040 * q^80 - 240 * q^82 - 1384 * q^86 + 896 * q^87 - 560 * q^88 - 1320 * q^90 - 380 * q^92 - 936 * q^94 - 1088 * q^96 - 512 * q^99

Introduction

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