LMFDB - Embedded newform 48.3.l.a.43.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,3,Mod(19,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	48.l (of order $4$, degree $2$, 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:	$1.30790526893$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + \cdots + 65536 $ x^16 - 6x^14 - 4x^13 + 10x^12 + 56x^11 + 88x^10 - 128x^9 - 496x^8 - 512x^7 + 1408x^6 + 3584x^5 + 2560x^4 - 4096x^3 - 24576*x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.3
Root			$1.78012 - 0.911682i$ of defining polynomial
Character	$\chi$	$=$	48.43
Dual form			48.3.l.a.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.78012 - 0.911682i) q^{2} +(1.22474 + 1.22474i) q^{3} +(2.33767 + 3.24581i) q^{4} +(1.00772 + 1.00772i) q^{5} +(-1.06362 - 3.29677i) q^{6} +10.0236 q^{7} +(-1.20220 - 7.90915i) q^{8} +3.00000i q^{9} +(-0.875146 - 2.71259i) q^{10} +(2.26517 - 2.26517i) q^{11} +(-1.11224 + 6.83834i) q^{12} +(-6.88229 + 6.88229i) q^{13} +(-17.8432 - 9.13830i) q^{14} +2.46840i q^{15} +(-5.07058 + 15.1753i) q^{16} -22.3801 q^{17} +(2.73505 - 5.34037i) q^{18} +(-16.8918 - 16.8918i) q^{19} +(-0.915151 + 5.62660i) q^{20} +(12.2763 + 12.2763i) q^{21} +(-6.09740 + 1.96717i) q^{22} +33.2007 q^{23} +(8.21431 - 11.1591i) q^{24} -22.9690i q^{25} +(18.5258 - 5.97686i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(23.4318 + 32.5346i) q^{28} +(-24.6412 + 24.6412i) q^{29} +(2.25040 - 4.39406i) q^{30} -41.3761i q^{31} +(22.8613 - 22.3911i) q^{32} +5.54852 q^{33} +(39.8394 + 20.4036i) q^{34} +(10.1010 + 10.1010i) q^{35} +(-9.73743 + 7.01302i) q^{36} +(-6.60031 - 6.60031i) q^{37} +(14.6695 + 45.4693i) q^{38} -16.8581 q^{39} +(6.75875 - 9.18170i) q^{40} -47.1477i q^{41} +(-10.6612 - 33.0454i) q^{42} +(-48.8218 + 48.8218i) q^{43} +(12.6475 + 2.05709i) q^{44} +(-3.02316 + 3.02316i) q^{45} +(-59.1013 - 30.2685i) q^{46} +45.6048i q^{47} +(-24.7960 + 12.3757i) q^{48} +51.4717 q^{49} +(-20.9404 + 40.8876i) q^{50} +(-27.4100 - 27.4100i) q^{51} +(-38.4271 - 6.25007i) q^{52} +(25.1401 + 25.1401i) q^{53} +(9.89032 - 3.19085i) q^{54} +4.56532 q^{55} +(-12.0503 - 79.2779i) q^{56} -41.3762i q^{57} +(66.3292 - 21.3994i) q^{58} +(6.23974 - 6.23974i) q^{59} +(-8.01197 + 5.77032i) q^{60} +(35.9513 - 35.9513i) q^{61} +(-37.7219 + 73.6546i) q^{62} +30.0707i q^{63} +(-61.1095 + 19.0167i) q^{64} -13.8709 q^{65} +(-9.87704 - 5.05848i) q^{66} +(10.2045 + 10.2045i) q^{67} +(-52.3174 - 72.6417i) q^{68} +(40.6624 + 40.6624i) q^{69} +(-8.77208 - 27.1898i) q^{70} +11.9529 q^{71} +(23.7275 - 3.60659i) q^{72} +111.332i q^{73} +(5.73197 + 17.7667i) q^{74} +(28.1312 - 28.1312i) q^{75} +(15.3401 - 94.3149i) q^{76} +(22.7051 - 22.7051i) q^{77} +(30.0095 + 15.3692i) q^{78} +4.46031i q^{79} +(-20.4022 + 10.1827i) q^{80} -9.00000 q^{81} +(-42.9837 + 83.9287i) q^{82} +(10.1751 + 10.1751i) q^{83} +(-11.1486 + 68.5445i) q^{84} +(-22.5530 - 22.5530i) q^{85} +(131.419 - 42.3988i) q^{86} -60.3583 q^{87} +(-20.6388 - 15.1924i) q^{88} -21.9364i q^{89} +(8.13777 - 2.62544i) q^{90} +(-68.9850 + 68.9850i) q^{91} +(77.6124 + 107.763i) q^{92} +(50.6752 - 50.6752i) q^{93} +(41.5771 - 81.1821i) q^{94} -34.0444i q^{95} +(55.4226 + 0.575837i) q^{96} +107.309 q^{97} +(-91.6260 - 46.9259i) q^{98} +(6.79552 + 6.79552i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} - 12 q^{8} - 56 q^{10} + 32 q^{11} - 24 q^{12} - 44 q^{14} + 32 q^{16} + 12 q^{18} - 32 q^{19} + 80 q^{20} + 32 q^{22} - 128 q^{23} + 36 q^{24} - 100 q^{26} - 120 q^{28} + 32 q^{29} + 72 q^{30}+ \cdots + 96 q^{99}+O(q^{100}) $ 16 * q + 12 * q^4 - 12 * q^8 - 56 * q^10 + 32 * q^11 - 24 * q^12 - 44 * q^14 + 32 * q^16 + 12 * q^18 - 32 * q^19 + 80 * q^20 + 32 * q^22 - 128 * q^23 + 36 * q^24 - 100 * q^26 - 120 * q^28 + 32 * q^29 + 72 * q^30 + 160 * q^32 + 96 * q^34 + 96 * q^35 + 12 * q^36 - 96 * q^37 + 168 * q^38 + 48 * q^40 - 60 * q^42 + 160 * q^43 + 88 * q^44 + 136 * q^46 - 144 * q^48 + 112 * q^49 - 236 * q^50 - 96 * q^51 - 48 * q^52 - 160 * q^53 - 36 * q^54 - 256 * q^55 - 224 * q^56 + 144 * q^58 - 128 * q^59 - 72 * q^60 - 32 * q^61 - 276 * q^62 - 408 * q^64 - 32 * q^65 + 72 * q^66 + 320 * q^67 - 448 * q^68 + 96 * q^69 - 384 * q^70 + 512 * q^71 + 60 * q^72 + 348 * q^74 + 192 * q^75 + 72 * q^76 + 224 * q^77 + 396 * q^78 + 552 * q^80 - 144 * q^81 - 40 * q^82 - 160 * q^83 + 72 * q^84 + 160 * q^85 + 528 * q^86 + 480 * q^88 - 24 * q^90 - 480 * q^91 + 496 * q^92 + 312 * q^94 - 480 * q^96 - 440 * q^98 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.78012	−	0.911682i	−0.890061	−	0.455841i
$2$	−1.78012	−	0.911682i	−0.890061	−	0.455841i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$4$	2.33767	+	3.24581i	0.584418	+	0.811453i
$5$	1.00772	+	1.00772i	0.201544	+	0.201544i	0.800661	−	0.599117i	$-0.204482\pi$
$5$	1.00772	+	1.00772i	0.201544	+	0.201544i	−0.599117	+	0.800661i	$0.704482\pi$
$6$	−1.06362	−	3.29677i	−0.177270	−	0.549462i
$7$	10.0236			1.43194			0.715969	−	0.698133i	$-0.245985\pi$
$7$	10.0236			1.43194			0.715969	+	0.698133i	$0.245985\pi$
$8$	−1.20220	−	7.90915i	−0.150274	−	0.988644i
$9$			3.00000i			0.333333i
$10$	−0.875146	−	2.71259i	−0.0875146	−	0.271259i
$11$	2.26517	−	2.26517i	0.205925	−	0.205925i	−0.596608	−	0.802533i	$-0.703485\pi$
$11$	2.26517	−	2.26517i	0.205925	−	0.205925i	0.802533	+	0.596608i	$0.203485\pi$
$12$	−1.11224	+	6.83834i	−0.0926865	+	0.569862i
$13$	−6.88229	+	6.88229i	−0.529407	+	0.529407i	−0.920395	−	0.390989i	$-0.872133\pi$
$13$	−6.88229	+	6.88229i	−0.529407	+	0.529407i	0.390989	+	0.920395i	$0.372133\pi$
$14$	−17.8432	−	9.13830i	−1.27451	−	0.652736i
$15$			2.46840i			0.164560i
$16$	−5.07058	+	15.1753i	−0.316911	+	0.948455i
$17$	−22.3801			−1.31648			−0.658240	−	0.752809i	$-0.728699\pi$
$17$	−22.3801			−1.31648			−0.658240	+	0.752809i	$0.728699\pi$
$18$	2.73505	−	5.34037i	0.151947	−	0.296687i
$19$	−16.8918	−	16.8918i	−0.889041	−	0.889041i	0.105390	−	0.994431i	$-0.466391\pi$
$19$	−16.8918	−	16.8918i	−0.889041	−	0.889041i	−0.994431	+	0.105390i	$0.966391\pi$
$20$	−0.915151	+	5.62660i	−0.0457575	+	0.281330i
$21$	12.2763	+	12.2763i	0.584586	+	0.584586i
$22$	−6.09740	+	1.96717i	−0.277155	+	0.0894167i
$23$	33.2007			1.44351			0.721755	−	0.692149i	$-0.243336\pi$
$23$	33.2007			1.44351			0.721755	+	0.692149i	$0.243336\pi$
$24$	8.21431	−	11.1591i	0.342263	−	0.464962i
$25$		−	22.9690i		−	0.918760i
$26$	18.5258	−	5.97686i	0.712530	−	0.229879i
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	23.4318	+	32.5346i	0.836850	+	1.16195i
$29$	−24.6412	+	24.6412i	−0.849696	+	0.849696i	−0.990095	−	0.140399i	$-0.955161\pi$
$29$	−24.6412	+	24.6412i	−0.849696	+	0.849696i	0.140399	+	0.990095i	$0.455161\pi$
$30$	2.25040	−	4.39406i	0.0750133	−	0.146469i
$31$		−	41.3761i		−	1.33471i	−0.744738	−	0.667357i	$-0.767426\pi$
$31$		−	41.3761i		−	1.33471i	0.744738	−	0.667357i	$-0.232574\pi$
$32$	22.8613	−	22.3911i	0.714415	−	0.699722i
$33$	5.54852			0.168137
$34$	39.8394	+	20.4036i	1.17175	+	0.600105i
$35$	10.1010	+	10.1010i	0.288599	+	0.288599i
$36$	−9.73743	+	7.01302i	−0.270484	+	0.194806i
$37$	−6.60031	−	6.60031i	−0.178387	−	0.178387i	0.612266	−	0.790652i	$-0.290258\pi$
$37$	−6.60031	−	6.60031i	−0.178387	−	0.178387i	−0.790652	+	0.612266i	$0.790258\pi$
$38$	14.6695	+	45.4693i	0.386039	+	1.19656i
$39$	−16.8581			−0.432259
$40$	6.75875	−	9.18170i	0.168969	−	0.229543i
$41$		−	47.1477i		−	1.14994i	−0.818173	−	0.574972i	$-0.805013\pi$
$41$		−	47.1477i		−	1.14994i	0.818173	−	0.574972i	$-0.194987\pi$
$42$	−10.6612	−	33.0454i	−0.253839	−	0.786795i
$43$	−48.8218	+	48.8218i	−1.13539	+	1.13539i	−0.146124	+	0.989266i	$0.546680\pi$
$43$	−48.8218	+	48.8218i	−1.13539	+	1.13539i	−0.989266	+	0.146124i	$0.953320\pi$
$44$	12.6475	+	2.05709i	0.287444	+	0.0467521i
$45$	−3.02316	+	3.02316i	−0.0671814	+	0.0671814i
$46$	−59.1013	−	30.2685i	−1.28481	−	0.658011i
$47$			45.6048i			0.970315i	0.874427	+	0.485157i	$0.161238\pi$
$47$			45.6048i			0.970315i	−0.874427	+	0.485157i	$0.838762\pi$
$48$	−24.7960	+	12.3757i	−0.516584	+	0.257827i
$49$	51.4717			1.05044
$50$	−20.9404	+	40.8876i	−0.418808	+	0.817752i
$51$	−27.4100	−	27.4100i	−0.537450	−	0.537450i
$52$	−38.4271	−	6.25007i	−0.738983	−	0.120194i
$53$	25.1401	+	25.1401i	0.474341	+	0.474341i	0.903316	−	0.428975i	$-0.141125\pi$
$53$	25.1401	+	25.1401i	0.474341	+	0.474341i	−0.428975	+	0.903316i	$0.641125\pi$
$54$	9.89032	−	3.19085i	0.183154	−	0.0590899i
$55$	4.56532			0.0830059
$56$	−12.0503	−	79.2779i	−0.215184	−	1.41568i
$57$		−	41.3762i		−	0.725899i
$58$	66.3292	−	21.3994i	1.14361	−	0.368955i
$59$	6.23974	−	6.23974i	0.105758	−	0.105758i	−0.652248	−	0.758006i	$-0.726174\pi$
$59$	6.23974	−	6.23974i	0.105758	−	0.105758i	0.758006	+	0.652248i	$0.226174\pi$
$60$	−8.01197	+	5.77032i	−0.133533	+	0.0961720i
$61$	35.9513	−	35.9513i	0.589366	−	0.589366i	−0.348093	−	0.937460i	$-0.613171\pi$
$61$	35.9513	−	35.9513i	0.589366	−	0.589366i	0.937460	+	0.348093i	$0.113171\pi$
$62$	−37.7219	+	73.6546i	−0.608417	+	1.18798i
$63$			30.0707i			0.477312i
$64$	−61.1095	+	19.0167i	−0.954835	+	0.297136i
$65$	−13.8709			−0.213398
$66$	−9.87704	−	5.05848i	−0.149652	−	0.0766437i
$67$	10.2045	+	10.2045i	0.152307	+	0.152307i	0.779147	−	0.626841i	$-0.215652\pi$
$67$	10.2045	+	10.2045i	0.152307	+	0.152307i	−0.626841	+	0.779147i	$0.715652\pi$
$68$	−52.3174	−	72.6417i	−0.769374	−	1.06826i
$69$	40.6624	+	40.6624i	0.589310	+	0.589310i
$70$	−8.77208	−	27.1898i	−0.125315	−	0.388426i
$71$	11.9529			0.168350			0.0841752	−	0.996451i	$-0.473174\pi$
$71$	11.9529			0.168350			0.0841752	+	0.996451i	$0.473174\pi$
$72$	23.7275	−	3.60659i	0.329548	−	0.0500915i
$73$			111.332i			1.52510i	0.646929	+	0.762550i	$0.276053\pi$
$73$			111.332i			1.52510i	−0.646929	+	0.762550i	$0.723947\pi$
$74$	5.73197	+	17.7667i	0.0774591	+	0.240091i
$75$	28.1312	−	28.1312i	0.375082	−	0.375082i
$76$	15.3401	−	94.3149i	0.201843	−	1.24099i
$77$	22.7051	−	22.7051i	0.294871	−	0.294871i
$78$	30.0095	+	15.3692i	0.384737	+	0.197041i
$79$			4.46031i			0.0564596i	0.999601	+	0.0282298i	$0.00898702\pi$
$79$			4.46031i			0.0564596i	−0.999601	+	0.0282298i	$0.991013\pi$
$80$	−20.4022	+	10.1827i	−0.255027	+	0.127284i
$81$	−9.00000			−0.111111
$82$	−42.9837	+	83.9287i	−0.524192	+	1.02352i
$83$	10.1751	+	10.1751i	0.122592	+	0.122592i	0.765741	−	0.643149i	$-0.222373\pi$
$83$	10.1751	+	10.1751i	0.122592	+	0.122592i	−0.643149	+	0.765741i	$0.722373\pi$
$84$	−11.1486	+	68.5445i	−0.132721	+	0.816006i
$85$	−22.5530	−	22.5530i	−0.265329	−	0.265329i
$86$	131.419	−	42.3988i	1.52812	−	0.493010i
$87$	−60.3583			−0.693774
$88$	−20.6388	−	15.1924i	−0.234532	−	0.172641i
$89$		−	21.9364i		−	0.246476i	−0.992377	−	0.123238i	$-0.960672\pi$
$89$		−	21.9364i		−	0.246476i	0.992377	−	0.123238i	$-0.0393279\pi$
$90$	8.13777	−	2.62544i	0.0904196	−	0.0291715i
$91$	−68.9850	+	68.9850i	−0.758077	+	0.758077i
$92$	77.6124	+	107.763i	0.843613	+	1.17134i
$93$	50.6752	−	50.6752i	0.544895	−	0.544895i
$94$	41.5771	−	81.1821i	0.442309	−	0.863640i
$95$		−	34.0444i		−	0.358362i
$96$	55.4226	+	0.575837i	0.577319	+	0.00599830i
$97$	107.309			1.10628			0.553140	−	0.833088i	$-0.313429\pi$
$97$	107.309			1.10628			0.553140	+	0.833088i	$0.313429\pi$
$98$	−91.6260	−	46.9259i	−0.934959	−	0.478835i
$99$	6.79552	+	6.79552i	0.0686416	+	0.0686416i
$100$	74.5530	−	53.6940i	0.745530	−	0.536940i
$101$	−100.780	−	100.780i	−0.997824	−	0.997824i	0.00217389	−	0.999998i	$-0.499308\pi$
$101$	−100.780	−	100.780i	−0.997824	−	0.997824i	−0.999998	+	0.00217389i	$0.999308\pi$
$102$	23.8039	+	73.7823i	0.233372	+	0.723356i
$103$	58.0562			0.563653			0.281826	−	0.959465i	$-0.409060\pi$
$103$	58.0562			0.563653			0.281826	+	0.959465i	$0.409060\pi$
$104$	62.7069	+	46.1592i	0.602951	+	0.443839i
$105$			24.7422i			0.235640i
$106$	−21.8327	−	67.6722i	−0.205968	−	0.638417i
$107$	112.747	−	112.747i	1.05371	−	1.05371i	0.0552381	−	0.998473i	$-0.482408\pi$
$107$	112.747	−	112.747i	1.05371	−	1.05371i	0.998473	−	0.0552381i	$-0.0175918\pi$
$108$	−20.5150	−	3.33671i	−0.189954	−	0.0308955i
$109$	−81.1384	+	81.1384i	−0.744389	+	0.744389i	−0.973419	−	0.229030i	$-0.926445\pi$
$109$	−81.1384	+	81.1384i	−0.744389	+	0.744389i	0.229030	+	0.973419i	$0.426445\pi$
$110$	−8.12684	−	4.16212i	−0.0738803	−	0.0378375i
$111$		−	16.1674i		−	0.145652i
$112$	−50.8252	+	152.110i	−0.453797	+	1.35813i
$113$	−171.844			−1.52074			−0.760371	−	0.649489i	$-0.774983\pi$
$113$	−171.844			−1.52074			−0.760371	+	0.649489i	$0.774983\pi$
$114$	−37.7219	+	73.6547i	−0.330894	+	0.646094i
$115$	33.4571	+	33.4571i	0.290931	+	0.290931i
$116$	−137.584	−	22.3776i	−1.18607	−	0.192910i
$117$	−20.6469	−	20.6469i	−0.176469	−	0.176469i
$118$	−16.7962	+	5.41884i	−0.142340	+	0.0459224i
$119$	−224.329			−1.88512
$120$	19.5230	−	2.96750i	0.162692	−	0.0247292i
$121$			110.738i			0.915190i
$122$	−96.7740	+	31.2216i	−0.793230	+	0.255915i
$123$	57.7439	−	57.7439i	0.469463	−	0.469463i
$124$	134.299	−	96.7238i	1.08306	−	0.780031i
$125$	48.3394	−	48.3394i	0.386715	−	0.386715i
$126$	27.4149	−	53.5295i	0.217579	−	0.424837i
$127$		−	36.8333i		−	0.290026i	−0.989430	−	0.145013i	$-0.953678\pi$
$127$		−	36.8333i		−	0.290026i	0.989430	−	0.145013i	$-0.0463224\pi$
$128$	126.119	+	21.8603i	0.985309	+	0.170784i
$129$	−119.588			−0.927042
$130$	24.6918	+	12.6458i	0.189937	+	0.0972754i
$131$	−12.3686	−	12.3686i	−0.0944170	−	0.0944170i	0.658321	−	0.752738i	$-0.271267\pi$
$131$	−12.3686	−	12.3686i	−0.0944170	−	0.0944170i	−0.752738	+	0.658321i	$0.771267\pi$
$132$	12.9706	+	18.0094i	0.0982622	+	0.136435i
$133$	−169.316	−	169.316i	−1.27305	−	1.27305i
$134$	−8.86204	−	27.4686i	−0.0661347	−	0.204990i
$135$	−7.40521			−0.0548534
$136$	26.9053	+	177.008i	0.197833	+	1.30153i
$137$			145.679i			1.06335i	0.846949	+	0.531674i	$0.178437\pi$
$137$			145.679i			1.06335i	−0.846949	+	0.531674i	$0.821563\pi$
$138$	−35.3129	−	109.455i	−0.255890	−	0.793154i
$139$	82.5709	−	82.5709i	0.594035	−	0.594035i	−0.344684	−	0.938719i	$-0.612014\pi$
$139$	82.5709	−	82.5709i	0.594035	−	0.594035i	0.938719	+	0.344684i	$0.112014\pi$
$140$	−9.17307	+	56.3985i	−0.0655219	+	0.402847i
$141$	−55.8542	+	55.8542i	−0.396129	+	0.396129i
$142$	−21.2776	−	10.8972i	−0.149842	−	0.0767410i
$143$			31.1791i			0.218036i
$144$	−45.5259	−	15.2117i	−0.316152	−	0.105637i
$145$	−49.6629			−0.342503
$146$	101.500	−	198.185i	0.695203	−	1.35743i
$147$	63.0398	+	63.0398i	0.428842	+	0.428842i
$148$	5.99399	−	36.8527i	0.0405000	−	0.249005i
$149$	196.248	+	196.248i	1.31710	+	1.31710i	0.916059	+	0.401043i	$0.131352\pi$
$149$	196.248	+	196.248i	1.31710	+	1.31710i	0.401043	+	0.916059i	$0.368648\pi$
$150$	−75.7236	+	24.4302i	−0.504824	+	0.162868i
$151$	64.5007			0.427157			0.213578	−	0.976926i	$-0.431488\pi$
$151$	64.5007			0.427157			0.213578	+	0.976926i	$0.431488\pi$
$152$	−113.292	+	153.907i	−0.745345	+	1.01254i
$153$		−	67.1404i		−	0.438826i
$154$	−61.1177	+	19.7180i	−0.396868	+	0.128039i
$155$	41.6956	−	41.6956i	0.269004	−	0.269004i
$156$	−39.4087	−	54.7182i	−0.252620	−	0.350758i
$157$	54.4202	−	54.4202i	0.346625	−	0.346625i	−0.512226	−	0.858851i	$-0.671179\pi$
$157$	54.4202	−	54.4202i	0.346625	−	0.346625i	0.858851	+	0.512226i	$0.171179\pi$
$158$	4.06638	−	7.93990i	0.0257366	−	0.0502525i
$159$			61.5803i			0.387298i
$160$	45.6018	+	0.473799i	0.285011	+	0.00296124i
$161$	332.789			2.06701
$162$	16.0211	+	8.20514i	0.0988957	+	0.0506490i
$163$	104.803	+	104.803i	0.642961	+	0.642961i	0.951282	−	0.308321i	$-0.0997671\pi$
$163$	104.803	+	104.803i	0.642961	+	0.642961i	−0.308321	+	0.951282i	$0.599767\pi$
$164$	153.033	−	110.216i	0.933126	−	0.672048i
$165$	5.59136	+	5.59136i	0.0338870	+	0.0338870i
$166$	−8.83647	−	27.3894i	−0.0532317	−	0.164996i
$167$	53.3110			0.319228			0.159614	−	0.987180i	$-0.448975\pi$
$167$	53.3110			0.319228			0.159614	+	0.987180i	$0.448975\pi$
$168$	82.3367	−	111.854i	0.490099	−	0.665796i
$169$			74.2683i			0.439457i
$170$	19.5859	+	60.7081i	0.115211	+	0.357107i
$171$	50.6753	−	50.6753i	0.296347	−	0.296347i
$172$	−272.596	−	44.3370i	−1.58486	−	0.257773i
$173$	−41.5780	+	41.5780i	−0.240335	+	0.240335i	−0.816989	−	0.576654i	$-0.804358\pi$
$173$	−41.5780	+	41.5780i	−0.240335	+	0.240335i	0.576654	+	0.816989i	$0.304358\pi$
$174$	107.445	+	55.0276i	0.617501	+	0.316251i
$175$		−	230.231i		−	1.31561i
$176$	22.8889	+	45.8604i	0.130051	+	0.260570i
$177$	15.2842			0.0863513
$178$	−19.9990	+	39.0495i	−0.112354	+	0.219379i
$179$	53.0709	+	53.0709i	0.296486	+	0.296486i	0.839636	−	0.543150i	$-0.182769\pi$
$179$	53.0709	+	53.0709i	0.296486	+	0.296486i	−0.543150	+	0.839636i	$0.682769\pi$
$180$	−16.8798	−	2.74545i	−0.0937766	−	0.0152525i
$181$	−66.6042	−	66.6042i	−0.367979	−	0.367979i	0.498761	−	0.866740i	$-0.333789\pi$
$181$	−66.6042	−	66.6042i	−0.367979	−	0.367979i	−0.866740	+	0.498761i	$0.833789\pi$
$182$	185.694	−	59.9094i	1.02030	−	0.329172i
$183$	88.0625			0.481216
$184$	−39.9138	−	262.590i	−0.216923	−	1.42712i
$185$		−	13.3025i		−	0.0719056i
$186$	−136.408	+	44.0084i	−0.733375	+	0.236604i
$187$	−50.6949	+	50.6949i	−0.271096	+	0.271096i
$188$	−148.025	+	106.609i	−0.787365	+	0.567070i
$189$	−36.8289	+	36.8289i	−0.194862	+	0.194862i
$190$	−31.0377	+	60.6032i	−0.163356	+	0.318964i
$191$			113.753i			0.595567i	0.954633	+	0.297784i	$0.0962474\pi$
$191$			113.753i			0.595567i	−0.954633	+	0.297784i	$0.903753\pi$
$192$	−98.1341	−	51.5529i	−0.511115	−	0.268505i
$193$	−26.5596			−0.137615			−0.0688073	−	0.997630i	$-0.521919\pi$
$193$	−26.5596			−0.137615			−0.0688073	+	0.997630i	$0.521919\pi$
$194$	−191.023	−	97.8318i	−0.984657	−	0.504288i
$195$	−16.9883	−	16.9883i	−0.0871193	−	0.0871193i
$196$	120.324	+	167.068i	0.613898	+	0.852386i
$197$	51.8935	+	51.8935i	0.263419	+	0.263419i	0.826442	−	0.563023i	$-0.190362\pi$
$197$	51.8935	+	51.8935i	0.263419	+	0.263419i	−0.563023	+	0.826442i	$0.690362\pi$
$198$	−5.90150	−	18.2922i	−0.0298056	−	0.0923848i
$199$	−136.741			−0.687140			−0.343570	−	0.939127i	$-0.611636\pi$
$199$	−136.741			−0.687140			−0.343570	+	0.939127i	$0.611636\pi$
$200$	−181.665	+	27.6132i	−0.908327	+	0.138066i
$201$			24.9959i			0.124358i
$202$	87.5216	+	271.281i	0.433275	+	1.34297i
$203$	−246.992	+	246.992i	−1.21671	+	1.21671i
$204$	24.8921	−	153.043i	0.122020	−	0.750211i
$205$	47.5118	−	47.5118i	0.231765	−	0.231765i
$206$	−103.347	−	52.9288i	−0.501686	−	0.256936i
$207$			99.6022i			0.481170i
$208$	−69.5435	−	139.338i	−0.334344	−	0.669893i
$209$	−76.5255			−0.366151
$210$	22.5570	−	44.0441i	0.107414	−	0.209734i
$211$	−141.171	−	141.171i	−0.669057	−	0.669057i	0.288441	−	0.957498i	$-0.406863\pi$
$211$	−141.171	−	141.171i	−0.669057	−	0.669057i	−0.957498	+	0.288441i	$0.906863\pi$
$212$	−22.8307	+	140.369i	−0.107692	+	0.662119i
$213$	14.6392	+	14.6392i	0.0687288	+	0.0687288i
$214$	−303.493	+	97.9142i	−1.41819	+	0.457543i
$215$	−98.3975			−0.457663
$216$	33.4772	+	24.6429i	0.154987	+	0.114088i
$217$		−	414.736i		−	1.91123i
$218$	218.409	−	70.4639i	1.00188	−	0.323229i
$219$	−136.354	+	136.354i	−0.622620	+	0.622620i
$220$	10.6722	+	14.8182i	0.0485101	+	0.0673554i
$221$	154.027	−	154.027i	0.696953	−	0.696953i
$222$	−14.7395	+	28.7799i	−0.0663942	+	0.129639i
$223$			122.607i			0.549806i	0.961472	+	0.274903i	$0.0886457\pi$
$223$			122.607i			0.549806i	−0.961472	+	0.274903i	$0.911354\pi$
$224$	229.151	−	224.439i	1.02300	−	1.00196i
$225$	68.9070			0.306253
$226$	305.903	+	156.667i	1.35355	+	0.693216i
$227$	−295.844	−	295.844i	−1.30328	−	1.30328i	−0.926168	−	0.377112i	$-0.876917\pi$
$227$	−295.844	−	295.844i	−1.30328	−	1.30328i	−0.377112	−	0.926168i	$-0.623083\pi$
$228$	134.299	−	96.7240i	0.589032	−	0.424228i
$229$	73.3817	+	73.3817i	0.320444	+	0.320444i	0.848937	−	0.528493i	$-0.177243\pi$
$229$	73.3817	+	73.3817i	0.320444	+	0.320444i	−0.528493	+	0.848937i	$0.677243\pi$
$230$	−29.0555	−	90.0599i	−0.126328	−	0.391565i
$231$	55.6159			0.240761
$232$	224.514	+	165.267i	0.967735	+	0.712359i
$233$		−	156.229i		−	0.670509i	−0.942128	−	0.335255i	$-0.891178\pi$
$233$		−	156.229i		−	0.670509i	0.942128	−	0.335255i	$-0.108822\pi$
$234$	17.9306	+	55.5773i	0.0766264	+	0.237510i
$235$	−45.9569	+	45.9569i	−0.195561	+	0.195561i
$236$	34.8395	+	5.66655i	0.147625	+	0.0240108i
$237$	−5.46274	+	5.46274i	−0.0230495	+	0.0230495i
$238$	399.333	+	204.516i	1.67787	+	0.859313i
$239$			13.1716i			0.0551113i	0.999620	+	0.0275557i	$0.00877235\pi$
$239$			13.1716i			0.0551113i	−0.999620	+	0.0275557i	$0.991228\pi$
$240$	−37.4587	−	12.5162i	−0.156078	−	0.0521510i
$241$	−189.519			−0.786386			−0.393193	−	0.919456i	$-0.628630\pi$
$241$	−189.519			−0.786386			−0.393193	+	0.919456i	$0.628630\pi$
$242$	100.958	−	197.127i	0.417181	−	0.814575i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$	200.734	+	32.6488i	0.822679	+	0.133807i
$245$	51.8692	+	51.8692i	0.211711	+	0.211711i
$246$	−155.435	+	50.1472i	−0.631851	+	0.203850i
$247$	232.508			0.941328
$248$	−327.250	+	49.7422i	−1.31956	+	0.200573i
$249$			24.9238i			0.100096i
$250$	−130.120	+	41.9799i	−0.520481	+	0.167920i
$251$	−27.4434	+	27.4434i	−0.109336	+	0.109336i	−0.759658	−	0.650322i	$-0.774634\pi$
$251$	−27.4434	+	27.4434i	−0.109336	+	0.109336i	0.650322	+	0.759658i	$0.274634\pi$
$252$	−97.6037	+	70.2954i	−0.387316	+	0.278950i
$253$	75.2053	−	75.2053i	0.297254	−	0.297254i
$254$	−33.5802	+	65.5678i	−0.132206	+	0.258141i
$255$		−	55.2432i		−	0.216640i
$256$	−204.578	−	153.895i	−0.799135	−	0.601152i
$257$	135.375			0.526752			0.263376	−	0.964693i	$-0.415164\pi$
$257$	135.375			0.526752			0.263376	+	0.964693i	$0.415164\pi$
$258$	212.882	+	109.027i	0.825125	+	0.422584i
$259$	−66.1586	−	66.1586i	−0.255438	−	0.255438i
$260$	−32.4255	−	45.0222i	−0.124714	−	0.173162i
$261$	−73.9236	−	73.9236i	−0.283232	−	0.283232i
$262$	10.7414	+	33.2939i	0.0409978	+	0.127076i
$263$	31.6123			0.120199			0.0600994	−	0.998192i	$-0.480858\pi$
$263$	31.6123			0.120199			0.0600994	+	0.998192i	$0.480858\pi$
$264$	−6.67040	−	43.8841i	−0.0252667	−	0.166228i
$265$			50.6684i			0.191201i
$266$	147.041	+	455.765i	0.552784	+	1.71340i
$267$	26.8665	−	26.8665i	0.100624	−	0.100624i
$268$	−9.26715	+	56.9769i	−0.0345789	+	0.212600i
$269$	−194.213	+	194.213i	−0.721981	+	0.721981i	−0.969008	−	0.247028i	$-0.920546\pi$
$269$	−194.213	+	194.213i	−0.721981	+	0.721981i	0.247028	+	0.969008i	$0.420546\pi$
$270$	13.1822	+	6.75120i	0.0488229	+	0.0250044i
$271$			291.647i			1.07619i	0.842884	+	0.538095i	$0.180856\pi$
$271$			291.647i			1.07619i	−0.842884	+	0.538095i	$0.819144\pi$
$272$	113.480	−	339.625i	0.417207	−	1.24862i
$273$	−168.978			−0.618967
$274$	132.813	−	259.326i	0.484717	−	0.946444i
$275$	−52.0287	−	52.0287i	−0.189195	−	0.189195i
$276$	−36.9271	+	227.038i	−0.133794	+	0.822601i
$277$	305.166	+	305.166i	1.10168	+	1.10168i	0.994208	+	0.107475i	$0.0342765\pi$
$277$	305.166	+	305.166i	1.10168	+	1.10168i	0.107475	+	0.994208i	$0.465723\pi$
$278$	−222.265	+	71.7079i	−0.799513	+	0.257942i
$279$	124.128			0.444905
$280$	67.7467	−	92.0333i	0.241952	−	0.328691i
$281$		−	211.861i		−	0.753955i	−0.926222	−	0.376978i	$-0.876963\pi$
$281$		−	211.861i		−	0.753955i	0.926222	−	0.376978i	$-0.123037\pi$
$282$	150.349	−	48.5061i	0.533151	−	0.172007i
$283$	105.325	−	105.325i	0.372175	−	0.372175i	−0.496094	−	0.868269i	$-0.665233\pi$
$283$	105.325	−	105.325i	0.372175	−	0.372175i	0.868269	+	0.496094i	$0.165233\pi$
$284$	27.9419	+	38.7968i	0.0983870	+	0.136608i
$285$	41.6957	−	41.6957i	0.146301	−	0.146301i
$286$	28.4254	−	55.5027i	0.0993897	−	0.194065i
$287$		−	472.588i		−	1.64665i
$288$	67.1733	+	68.5838i	0.233241	+	0.238138i
$289$	211.871			0.733117
$290$	88.4060	+	45.2768i	0.304848	+	0.156127i
$291$	131.426	+	131.426i	0.451637	+	0.451637i
$292$	−361.364	+	260.258i	−1.23755	+	0.891296i
$293$	−171.289	−	171.289i	−0.584603	−	0.584603i	0.351562	−	0.936165i	$-0.385651\pi$
$293$	−171.289	−	171.289i	−0.584603	−	0.584603i	−0.936165	+	0.351562i	$0.885651\pi$
$294$	−54.7463	−	169.691i	−0.186212	−	0.577179i
$295$	12.5758			0.0426300
$296$	−44.2680	+	60.1377i	−0.149554	+	0.203168i
$297$			16.6455i			0.0560456i
$298$	−170.430	−	528.262i	−0.571912	−	1.77269i
$299$	−228.497	+	228.497i	−0.764204	+	0.764204i
$300$	157.070	+	25.5470i	0.523566	+	0.0851566i
$301$	−489.368	+	489.368i	−1.62581	+	1.62581i
$302$	−114.819	−	58.8041i	−0.380196	−	0.194716i
$303$		−	246.860i		−	0.814720i
$304$	341.988	−	170.686i	1.12496	−	0.561468i
$305$	72.4579			0.237567
$306$	−61.2107	+	119.518i	−0.200035	+	0.390582i
$307$	−27.1124	−	27.1124i	−0.0883140	−	0.0883140i	0.661570	−	0.749884i	$-0.269891\pi$
$307$	−27.1124	−	27.1124i	−0.0883140	−	0.0883140i	−0.749884	+	0.661570i	$0.769891\pi$
$308$	126.773	+	20.6194i	0.411602	+	0.0669460i
$309$	71.1041	+	71.1041i	0.230110	+	0.230110i
$310$	−112.236	+	36.2102i	−0.362053	+	0.116807i
$311$	371.124			1.19333			0.596663	−	0.802492i	$-0.296493\pi$
$311$	371.124			1.19333			0.596663	+	0.802492i	$0.296493\pi$
$312$	20.2667	+	133.333i	0.0649575	+	0.427350i
$313$		−	374.501i		−	1.19649i	−0.801313	−	0.598245i	$-0.795865\pi$
$313$		−	374.501i		−	1.19649i	0.801313	−	0.598245i	$-0.204135\pi$
$314$	−146.488	+	47.2607i	−0.466524	+	0.150512i
$315$	−30.3029	+	30.3029i	−0.0961996	+	0.0961996i
$316$	−14.4773	+	10.4267i	−0.0458143	+	0.0329960i
$317$	−48.5840	+	48.5840i	−0.153262	+	0.153262i	−0.779573	−	0.626311i	$-0.784564\pi$
$317$	−48.5840	+	48.5840i	−0.153262	+	0.153262i	0.626311	+	0.779573i	$0.284564\pi$
$318$	56.1417	−	109.621i	0.176546	−	0.344719i
$319$			111.633i			0.349947i
$320$	−80.7448	−	42.4178i	−0.252328	−	0.132555i
$321$	276.173			0.860352
$322$	−592.406	−	303.398i	−1.83977	−	0.942230i
$323$	378.040	+	378.040i	1.17040	+	1.17040i
$324$	−21.0391	−	29.2123i	−0.0649353	−	0.0901614i
$325$	158.079	+	158.079i	0.486398	+	0.486398i
$326$	−91.0149	−	282.108i	−0.279187	−	0.865363i
$327$	−198.748			−0.607791
$328$	−372.899	+	56.6808i	−1.13689	+	0.172807i
$329$			457.122i			1.38943i
$330$	−4.85576	−	15.0508i	−0.0147144	−	0.0456086i
$331$	−1.88883	+	1.88883i	−0.00570644	+	0.00570644i	−0.709954	−	0.704248i	$-0.751284\pi$
$331$	−1.88883	+	1.88883i	−0.00570644	+	0.00570644i	0.704248	+	0.709954i	$0.251284\pi$
$332$	−9.24040	+	56.8125i	−0.0278325	+	0.171122i
$333$	19.8009	−	19.8009i	0.0594622	−	0.0594622i
$334$	−94.9001	−	48.6027i	−0.284132	−	0.145517i
$335$			20.5667i			0.0613931i
$336$	−248.544	+	124.048i	−0.739715	+	0.369192i
$337$	−386.980			−1.14831			−0.574154	−	0.818747i	$-0.694669\pi$
$337$	−386.980			−1.14831			−0.574154	+	0.818747i	$0.694669\pi$
$338$	67.7090	−	132.207i	0.200323	−	0.391144i
$339$	−210.465	−	210.465i	−0.620840	−	0.620840i
$340$	20.4812	−	125.924i	0.0602388	−	0.370365i
$341$	−93.7240	−	93.7240i	−0.274851	−	0.274851i
$342$	−136.408	+	44.0085i	−0.398854	+	0.128680i
$343$	24.7757			0.0722325
$344$	444.832	+	327.446i	1.29312	+	0.951877i
$345$			81.9528i			0.237544i
$346$	111.920	−	36.1080i	0.323468	−	0.104358i
$347$	441.887	−	441.887i	1.27345	−	1.27345i	0.329183	−	0.944266i	$-0.393227\pi$
$347$	441.887	−	441.887i	1.27345	−	1.27345i	0.944266	−	0.329183i	$-0.106773\pi$
$348$	−141.098	−	195.912i	−0.405454	−	0.562965i
$349$	119.382	−	119.382i	0.342068	−	0.342068i	−0.515076	−	0.857144i	$-0.672236\pi$
$349$	119.382	−	119.382i	0.342068	−	0.342068i	0.857144	+	0.515076i	$0.172236\pi$
$350$	−209.898	+	409.840i	−0.599707	+	1.17097i
$351$		−	50.5743i		−	0.144086i
$352$	1.06501	−	102.504i	0.00302560	−	0.291206i
$353$	−515.642			−1.46074			−0.730371	−	0.683050i	$-0.760653\pi$
$353$	−515.642			−1.46074			−0.730371	+	0.683050i	$0.760653\pi$
$354$	−27.2077	−	13.9343i	−0.0768580	−	0.0393625i
$355$	12.0452	+	12.0452i	0.0339301	+	0.0339301i
$356$	71.2014	−	51.2801i	0.200004	−	0.144045i
$357$	−274.745	−	274.745i	−0.769595	−	0.769595i
$358$	−46.0890	−	142.857i	−0.128740	−	0.399041i
$359$	428.264			1.19294			0.596468	−	0.802637i	$-0.296570\pi$
$359$	428.264			1.19294			0.596468	+	0.802637i	$0.296570\pi$
$360$	27.5451	+	20.2762i	0.0765142	+	0.0563229i
$361$			209.664i			0.580786i
$362$	57.8418	+	179.286i	0.159784	+	0.495264i
$363$	−135.626	+	135.626i	−0.373625	+	0.373625i
$364$	−385.177	−	62.6480i	−1.05818	−	0.172110i
$365$	−112.192	+	112.192i	−0.307375	+	0.307375i
$366$	−156.762	−	80.2850i	−0.428311	−	0.219358i
$367$			219.482i			0.598043i	0.954246	+	0.299021i	$0.0966602\pi$
$367$			219.482i			0.598043i	−0.954246	+	0.299021i	$0.903340\pi$
$368$	−168.347	+	503.830i	−0.457464	+	1.36910i
$369$	141.443			0.383315
$370$	−12.1277	+	23.6802i	−0.0327775	+	0.0640004i
$371$	251.993	+	251.993i	0.679226	+	0.679226i
$372$	282.944	+	46.0201i	0.760602	+	0.123710i
$373$	425.005	+	425.005i	1.13942	+	1.13942i	0.988554	+	0.150870i	$0.0482075\pi$
$373$	425.005	+	425.005i	1.13942	+	1.13942i	0.150870	+	0.988554i	$0.451793\pi$
$374$	136.461	−	44.0255i	0.364868	−	0.117715i
$375$	118.407			0.315752
$376$	360.695	−	54.8259i	0.959296	−	0.145814i
$377$		−	339.175i		−	0.899669i
$378$	99.1362	−	31.9837i	0.262265	−	0.0846130i
$379$	365.916	−	365.916i	0.965476	−	0.965476i	−0.0339473	−	0.999424i	$-0.510808\pi$
$379$	365.916	−	365.916i	0.965476	−	0.965476i	0.999424	+	0.0339473i	$0.0108078\pi$
$380$	110.502	−	79.5846i	0.290794	−	0.209433i
$381$	45.1114	−	45.1114i	0.118403	−	0.118403i
$382$	103.707	−	202.495i	0.271484	−	0.530091i
$383$			213.276i			0.556857i	0.960457	+	0.278428i	$0.0898135\pi$
$383$			213.276i			0.556857i	−0.960457	+	0.278428i	$0.910187\pi$
$384$	127.691	+	181.238i	0.332528	+	0.471973i
$385$	45.7608			0.118859
$386$	47.2793	+	24.2139i	0.122485	+	0.0627303i
$387$	−146.465	−	146.465i	−0.378464	−	0.378464i
$388$	250.854	+	348.305i	0.646530	+	0.897694i
$389$	−210.798	−	210.798i	−0.541898	−	0.541898i	0.382187	−	0.924085i	$-0.375171\pi$
$389$	−210.798	−	210.798i	−0.541898	−	0.541898i	−0.924085	+	0.382187i	$0.875171\pi$
$390$	14.7533	+	45.7291i	0.0378290	+	0.117254i
$391$	−743.037			−1.90035
$392$	−61.8791	−	407.098i	−0.157855	−	1.03852i
$393$		−	30.2968i		−	0.0770912i
$394$	−45.0665	−	139.687i	−0.114382	−	0.354536i
$395$	−4.49475	+	4.49475i	−0.0113791	+	0.0113791i
$396$	−6.17127	+	37.9426i	−0.0155840	+	0.0958148i
$397$	392.907	−	392.907i	0.989690	−	0.989690i	−0.0102579	−	0.999947i	$-0.503265\pi$
$397$	392.907	−	392.907i	0.989690	−	0.989690i	0.999947	+	0.0102579i	$0.00326524\pi$
$398$	243.415	+	124.664i	0.611597	+	0.313226i
$399$		−	414.737i		−	1.03944i
$400$	348.561	+	116.466i	0.871403	+	0.291165i
$401$	29.3290			0.0731396			0.0365698	−	0.999331i	$-0.488357\pi$
$401$	29.3290			0.0731396			0.0365698	+	0.999331i	$0.488357\pi$
$402$	22.7883	−	44.4958i	0.0566874	−	0.110686i
$403$	284.762	+	284.762i	0.706606	+	0.706606i
$404$	91.5224	−	562.705i	0.226541	−	1.39283i
$405$	−9.06949	−	9.06949i	−0.0223938	−	0.0223938i
$406$	664.855	−	214.498i	1.63757	−	0.528321i
$407$	−29.9017			−0.0734684
$408$	−183.838	+	249.742i	−0.450582	+	0.612112i
$409$			601.115i			1.46972i	0.678219	+	0.734860i	$0.262752\pi$
$409$			601.115i			1.46972i	−0.678219	+	0.734860i	$0.737248\pi$
$410$	−127.892	+	41.2612i	−0.311933	+	0.100637i
$411$	−178.419	+	178.419i	−0.434110	+	0.434110i
$412$	135.716	+	188.440i	0.329409	+	0.457378i
$413$	62.5444	−	62.5444i	0.151439	−	0.151439i
$414$	90.8055	−	177.304i	0.219337	−	0.428271i
$415$			20.5073i			0.0494153i
$416$	−3.23584	+	311.440i	−0.00777845	+	0.748654i
$417$	202.257			0.485028
$418$	136.225	+	69.7669i	0.325897	+	0.166907i
$419$	−518.885	−	518.885i	−1.23839	−	1.23839i	−0.960659	−	0.277729i	$-0.910418\pi$
$419$	−518.885	−	518.885i	−1.23839	−	1.23839i	−0.277729	−	0.960659i	$-0.589582\pi$
$420$	−80.3085	+	57.8391i	−0.191211	+	0.137712i
$421$	−411.213	−	411.213i	−0.976754	−	0.976754i	0.0229817	−	0.999736i	$-0.492684\pi$
$421$	−411.213	−	411.213i	−0.976754	−	0.976754i	−0.999736	+	0.0229817i	$0.992684\pi$
$422$	122.599	+	380.005i	0.290518	+	0.900485i
$423$	−136.814			−0.323438
$424$	168.613	−	229.060i	0.397673	−	0.540236i
$425$			514.049i			1.20953i
$426$	−12.7133	−	39.4059i	−0.0298434	−	0.0925022i
$427$	360.360	−	360.360i	0.843936	−	0.843936i
$428$	629.522	+	102.390i	1.47084	+	0.239229i
$429$	−38.1865	+	38.1865i	−0.0890128	+	0.0890128i
$430$	175.160	+	89.7072i	0.407348	+	0.208622i
$431$			41.1083i			0.0953789i	0.998862	+	0.0476895i	$0.0151858\pi$
$431$			41.1083i			0.0953789i	−0.998862	+	0.0476895i	$0.984814\pi$
$432$	−37.1271	−	74.3880i	−0.0859423	−	0.172195i
$433$	−351.682			−0.812199			−0.406100	−	0.913829i	$-0.633111\pi$
$433$	−351.682			−0.812199			−0.406100	+	0.913829i	$0.633111\pi$
$434$	−378.107	+	738.281i	−0.871215	+	1.70111i
$435$	−60.8244	−	60.8244i	−0.139826	−	0.139826i
$436$	−453.035	−	73.6850i	−1.03907	−	0.169002i
$437$	−560.819	−	560.819i	−1.28334	−	1.28334i
$438$	367.037	−	118.415i	0.837985	−	0.270354i
$439$	−775.613			−1.76677			−0.883386	−	0.468646i	$-0.844742\pi$
$439$	−775.613			−1.76677			−0.883386	+	0.468646i	$0.844742\pi$
$440$	−5.48841	−	36.1079i	−0.0124737	−	0.0820633i
$441$			154.415i			0.350148i
$442$	−414.609	+	133.763i	−0.938030	+	0.302631i
$443$	−241.372	+	241.372i	−0.544858	+	0.544858i	−0.924949	−	0.380091i	$-0.875893\pi$
$443$	−241.372	+	241.372i	−0.544858	+	0.544858i	0.380091	+	0.924949i	$0.375893\pi$
$444$	52.4763	−	37.7940i	0.118190	−	0.0851217i
$445$	22.1058	−	22.1058i	0.0496759	−	0.0496759i
$446$	111.778	−	218.255i	0.250624	−	0.489361i
$447$			480.708i			1.07541i
$448$	−612.534	+	190.615i	−1.36726	+	0.425480i
$449$	266.360			0.593228			0.296614	−	0.954997i	$-0.404142\pi$
$449$	266.360			0.593228			0.296614	+	0.954997i	$0.404142\pi$
$450$	−122.663	−	62.8213i	−0.272584	−	0.139603i
$451$	−106.798	−	106.798i	−0.236802	−	0.236802i
$452$	−401.714	−	557.772i	−0.888749	−	1.23401i
$453$	78.9969	+	78.9969i	0.174386	+	0.174386i
$454$	256.923	+	796.355i	0.565910	+	1.75409i
$455$	−139.035			−0.305572
$456$	−327.251	+	49.7423i	−0.717655	+	0.109084i
$457$		−	515.244i		−	1.12745i	−0.825963	−	0.563725i	$-0.809368\pi$
$457$		−	515.244i		−	1.12745i	0.825963	−	0.563725i	$-0.190632\pi$
$458$	−63.7277	−	197.529i	−0.139143	−	0.431287i
$459$	82.2299	−	82.2299i	0.179150	−	0.179150i
$460$	−30.3837	+	186.807i	−0.0660514	+	0.406102i
$461$	5.67717	−	5.67717i	0.0123149	−	0.0123149i	−0.700923	−	0.713237i	$-0.747228\pi$
$461$	5.67717	−	5.67717i	0.0123149	−	0.0123149i	0.713237	+	0.700923i	$0.247228\pi$
$462$	−99.0031	−	50.7040i	−0.214292	−	0.109749i
$463$		−	464.510i		−	1.00326i	−0.865082	−	0.501631i	$-0.832733\pi$
$463$		−	464.510i		−	1.00326i	0.865082	−	0.501631i	$-0.167267\pi$
$464$	−248.992	−	498.882i	−0.536621	−	1.07518i
$465$	102.133			0.219641
$466$	−142.431	+	278.106i	−0.305646	+	0.596794i
$467$	495.985	+	495.985i	1.06207	+	1.06207i	0.997942	+	0.0641248i	$0.0204256\pi$
$467$	495.985	+	495.985i	1.06207	+	1.06207i	0.0641248	+	0.997942i	$0.479574\pi$
$468$	18.7502	−	115.281i	0.0400646	−	0.246328i
$469$	102.286	+	102.286i	0.218094	+	0.218094i
$470$	123.707	−	39.9109i	0.263207	−	0.0849167i
$471$	133.302			0.283018
$472$	−56.8525	−	41.8497i	−0.120450	−	0.0886646i
$473$			221.180i			0.467610i
$474$	14.7046	−	4.74407i	0.0310224	−	0.0100086i
$475$	−387.987	+	387.987i	−0.816815	+	0.816815i
$476$	−524.407	−	728.129i	−1.10170	−	1.52968i
$477$	−75.4202	+	75.4202i	−0.158114	+	0.158114i
$478$	12.0083	−	23.4471i	0.0251220	−	0.0490525i
$479$		−	378.802i		−	0.790818i	−0.918505	−	0.395409i	$-0.870603\pi$
$479$		−	378.802i		−	0.790818i	0.918505	−	0.395409i	$-0.129397\pi$
$480$	55.2703	+	56.4309i	0.115146	+	0.117564i
$481$	90.8504			0.188878
$482$	337.367	+	172.781i	0.699932	+	0.358467i
$483$	407.582	+	407.582i	0.843855	+	0.843855i
$484$	−359.435	+	258.869i	−0.742633	+	0.534854i
$485$	108.138	+	108.138i	0.222964	+	0.222964i
$486$	9.57256	+	29.6710i	0.0196966	+	0.0610514i
$487$	147.446			0.302764			0.151382	−	0.988475i	$-0.451628\pi$
$487$	147.446			0.302764			0.151382	+	0.988475i	$0.451628\pi$
$488$	−327.565	−	241.124i	−0.671240	−	0.494107i
$489$			256.713i			0.524976i
$490$	−45.0453	−	139.622i	−0.0919292	−	0.284942i
$491$	109.547	−	109.547i	0.223110	−	0.223110i	−0.586697	−	0.809807i	$-0.699572\pi$
$491$	109.547	−	109.547i	0.223110	−	0.223110i	0.809807	+	0.586697i	$0.199572\pi$
$492$	322.412	+	52.4395i	0.655310	+	0.106584i
$493$	551.473	−	551.473i	1.11861	−	1.11861i
$494$	−413.893	−	211.973i	−0.837840	−	0.429096i
$495$			13.6960i			0.0276686i
$496$	627.894	+	209.801i	1.26592	+	0.422985i
$497$	119.810			0.241067
$498$	22.7226	−	44.3674i	0.0456277	−	0.0890912i
$499$	−360.523	−	360.523i	−0.722491	−	0.722491i	0.246621	−	0.969112i	$-0.420680\pi$
$499$	−360.523	−	360.523i	−0.722491	−	0.722491i	−0.969112	+	0.246621i	$0.920680\pi$
$500$	269.902	+	43.8989i	0.539804	+	0.0877977i
$501$	65.2924	+	65.2924i	0.130324	+	0.130324i
$502$	73.8722	−	23.8329i	0.147156	−	0.0474760i
$503$	−927.420			−1.84378			−0.921889	−	0.387454i	$-0.873355\pi$
$503$	−927.420			−1.84378			−0.921889	+	0.387454i	$0.873355\pi$
$504$	237.834	−	36.1508i	0.471892	−	0.0717279i
$505$		−	203.117i		−	0.402211i
$506$	−202.438	+	65.3114i	−0.400075	+	0.129074i
$507$	−90.9597	+	90.9597i	−0.179408	+	0.179408i
$508$	119.554	−	86.1042i	0.235342	−	0.169496i
$509$	677.931	−	677.931i	1.33189	−	1.33189i	0.428208	−	0.903680i	$-0.359145\pi$
$509$	677.931	−	677.931i	1.33189	−	1.33189i	0.903680	−	0.428208i	$-0.140855\pi$
$510$	−50.3642	+	98.3397i	−0.0987534	+	0.192823i
$511$			1115.95i			2.18385i
$512$	223.872	+	460.462i	0.437249	+	0.899340i
$513$	124.129			0.241966
$514$	−240.984	−	123.419i	−0.468841	−	0.240115i
$515$	58.5045	+	58.5045i	0.113601	+	0.113601i
$516$	−279.559	−	388.162i	−0.541780	−	0.752251i
$517$	103.303	+	103.303i	0.199812	+	0.199812i
$518$	57.4548	+	178.086i	0.110917	+	0.343795i
$519$	−101.845			−0.196233
$520$	16.6755	+	109.707i	0.0320682	+	0.210974i
$521$		−	143.173i		−	0.274804i	−0.990515	−	0.137402i	$-0.956125\pi$
$521$		−	143.173i		−	0.274804i	0.990515	−	0.137402i	$-0.0438753\pi$
$522$	64.1982	+	198.988i	0.122985	+	0.381203i
$523$	226.187	−	226.187i	0.432481	−	0.432481i	−0.456991	−	0.889471i	$-0.651073\pi$
$523$	226.187	−	226.187i	0.432481	−	0.432481i	0.889471	+	0.456991i	$0.151073\pi$
$524$	11.2324	−	69.0600i	0.0214359	−	0.131794i
$525$	281.974	−	281.974i	0.537094	−	0.537094i
$526$	−56.2738	−	28.8204i	−0.106984	−	0.0547916i
$527$			926.004i			1.75712i
$528$	−28.1342	+	84.2003i	−0.0532844	+	0.159470i
$529$	573.288			1.08372
$530$	46.1934	−	90.1959i	0.0871574	−	0.170181i
$531$	18.7192	+	18.7192i	0.0352528	+	0.0352528i
$532$	153.762	−	945.371i	0.289027	−	1.77701i
$533$	324.484	+	324.484i	0.608788	+	0.608788i
$534$	−72.3193	+	23.3319i	−0.135429	+	0.0436928i
$535$	227.235			0.424739
$536$	68.4415	−	92.9772i	0.127689	−	0.173465i
$537$			129.997i			0.242080i
$538$	522.783	−	168.662i	0.971716	−	0.313499i
$539$	116.592	−	116.592i	0.216312	−	0.216312i
$540$	−17.3110	−	24.0359i	−0.0320573	−	0.0445109i
$541$	−156.708	+	156.708i	−0.289663	+	0.289663i	−0.836947	−	0.547284i	$-0.815662\pi$
$541$	−156.708	+	156.708i	−0.289663	+	0.289663i	0.547284	+	0.836947i	$0.315662\pi$
$542$	265.890	−	519.168i	0.490571	−	0.957875i
$543$		−	163.146i		−	0.300454i
$544$	−511.639	+	501.116i	−0.940512	+	0.921170i
$545$	−163.530			−0.300055
$546$	300.802	+	154.054i	0.550919	+	0.282151i
$547$	247.357	+	247.357i	0.452207	+	0.452207i	0.896086	−	0.443880i	$-0.146398\pi$
$547$	247.357	+	247.357i	0.452207	+	0.452207i	−0.443880	+	0.896086i	$0.646398\pi$
$548$	−472.845	+	340.549i	−0.862856	+	0.621440i
$549$	107.854	+	107.854i	0.196455	+	0.196455i
$550$	45.1839	+	140.051i	0.0821525	+	0.254638i
$551$	832.466			1.51083
$552$	272.721	−	370.489i	0.494060	−	0.671177i
$553$			44.7082i			0.0808466i
$554$	−265.019	−	821.447i	−0.478373	−	1.48276i
$555$	16.2922	−	16.2922i	0.0293553	−	0.0293553i
$556$	461.033	+	74.9858i	0.829196	+	0.134867i
$557$	−661.193	+	661.193i	−1.18706	+	1.18706i	−0.209184	+	0.977876i	$0.567081\pi$
$557$	−661.193	+	661.193i	−1.18706	+	1.18706i	−0.977876	+	0.209184i	$0.932919\pi$
$558$	−220.964	−	113.166i	−0.395992	−	0.202806i
$559$		−	672.011i		−	1.20217i
$560$	−204.503	+	102.067i	−0.365183	+	0.182263i
$561$	−124.177			−0.221349
$562$	−193.150	+	377.139i	−0.343684	+	0.671066i
$563$	246.685	+	246.685i	0.438162	+	0.438162i	0.891393	−	0.453231i	$-0.149729\pi$
$563$	246.685	+	246.685i	0.438162	+	0.438162i	−0.453231	+	0.891393i	$0.649729\pi$
$564$	−311.861	−	50.7234i	−0.552945	−	0.0899351i
$565$	−173.171	−	173.171i	−0.306497	−	0.306497i
$566$	−283.516	+	91.4689i	−0.500911	+	0.161606i
$567$	−90.2120			−0.159104
$568$	−14.3697	−	94.5372i	−0.0252988	−	0.166439i
$569$		−	243.567i		−	0.428061i	−0.976827	−	0.214030i	$-0.931341\pi$
$569$		−	243.567i		−	0.428061i	0.976827	−	0.214030i	$-0.0686592\pi$
$570$	−112.237	+	36.2102i	−0.196906	+	0.0635267i
$571$	59.9229	−	59.9229i	0.104944	−	0.104944i	−0.652685	−	0.757629i	$-0.726358\pi$
$571$	59.9229	−	59.9229i	0.104944	−	0.104944i	0.757629	+	0.652685i	$0.226358\pi$
$572$	−101.202	+	72.8866i	−0.176926	+	0.127424i
$573$	−139.319	+	139.319i	−0.243139	+	0.243139i
$574$	−430.850	+	841.265i	−0.750610	+	1.46562i
$575$		−	762.587i		−	1.32624i
$576$	−57.0501	−	183.328i	−0.0990453	−	0.318278i
$577$	136.609			0.236757			0.118378	−	0.992969i	$-0.462230\pi$
$577$	136.609			0.236757			0.118378	+	0.992969i	$0.462230\pi$
$578$	−377.156	−	193.159i	−0.652519	−	0.334185i
$579$	−32.5287	−	32.5287i	−0.0561809	−	0.0561809i
$580$	−116.096	−	161.196i	−0.200165	−	0.277925i
$581$	101.991	+	101.991i	0.175543	+	0.175543i
$582$	−114.136	−	353.774i	−0.196110	−	0.607859i
$583$	113.893			0.195357
$584$	880.544	−	133.843i	1.50778	−	0.229184i
$585$		−	41.6126i		−	0.0711326i
$586$	148.754	+	461.076i	0.253846	+	0.786818i
$587$	−331.817	+	331.817i	−0.565276	+	0.565276i	−0.930801	−	0.365525i	$-0.880889\pi$
$587$	−331.817	+	331.817i	−0.565276	+	0.565276i	0.365525	+	0.930801i	$0.380889\pi$
$588$	−57.2488	+	351.981i	−0.0973620	+	0.598608i
$589$	−698.916	+	698.916i	−1.18661	+	1.18661i
$590$	−22.3865	−	11.4652i	−0.0379433	−	0.0194325i
$591$			127.113i			0.215081i
$592$	133.629	−	66.6942i	0.225724	−	0.112659i
$593$	131.285			0.221391			0.110695	−	0.993854i	$-0.464692\pi$
$593$	131.285			0.221391			0.110695	+	0.993854i	$0.464692\pi$
$594$	15.1754	−	29.6311i	0.0255479	−	0.0498840i
$595$	−226.061	−	226.061i	−0.379934	−	0.379934i
$596$	−178.221	+	1095.75i	−0.299028	+	1.83850i
$597$	−167.473	−	167.473i	−0.280524	−	0.280524i
$598$	615.069	−	198.436i	1.02854	−	0.331833i
$599$	−136.119			−0.227243			−0.113621	−	0.993524i	$-0.536245\pi$
$599$	−136.119			−0.227243			−0.113621	+	0.993524i	$0.536245\pi$
$600$	−256.313	−	188.675i	−0.427188	−	0.314458i
$601$		−	498.566i		−	0.829561i	−0.909922	−	0.414780i	$-0.863858\pi$
$601$		−	498.566i		−	0.829561i	0.909922	−	0.414780i	$-0.136142\pi$
$602$	1317.28	−	424.987i	2.18818	−	0.705959i
$603$	−30.6136	+	30.6136i	−0.0507689	+	0.0507689i
$604$	150.781	+	209.357i	0.249638	+	0.346617i
$605$	−111.593	+	111.593i	−0.184451	+	0.184451i
$606$	−225.058	+	439.441i	−0.371383	+	0.725150i
$607$		−	568.740i		−	0.936969i	−0.883472	−	0.468484i	$-0.844800\pi$
$607$		−	568.740i		−	0.936969i	0.883472	−	0.468484i	$-0.155200\pi$
$608$	−764.393	−	7.94198i	−1.25723	−	0.0130625i
$609$	−605.005			−0.993441
$610$	−128.984	−	66.0585i	−0.211449	−	0.108293i
$611$	−313.865	−	313.865i	−0.513691	−	0.513691i
$612$	217.925	−	156.952i	0.356087	−	0.256458i
$613$	−168.441	−	168.441i	−0.274782	−	0.274782i	0.556240	−	0.831022i	$-0.312244\pi$
$613$	−168.441	−	168.441i	−0.274782	−	0.274782i	−0.831022	+	0.556240i	$0.812244\pi$
$614$	23.5455	+	72.9813i	0.0383478	+	0.118862i
$615$	116.380			0.189235
$616$	−206.874	−	152.282i	−0.335834	−	0.247211i
$617$			599.157i			0.971081i	0.874214	+	0.485541i	$0.161377\pi$
$617$			599.157i			0.971081i	−0.874214	+	0.485541i	$0.838623\pi$
$618$	−61.7497	−	191.398i	−0.0999186	−	0.309706i
$619$	126.719	−	126.719i	0.204715	−	0.204715i	−0.597301	−	0.802017i	$-0.703760\pi$
$619$	126.719	−	126.719i	0.204715	−	0.204715i	0.802017	+	0.597301i	$0.203760\pi$
$620$	232.807	+	37.8654i	0.375495	+	0.0610732i
$621$	−121.987	+	121.987i	−0.196437	+	0.196437i
$622$	−660.647	−	338.347i	−1.06213	−	0.543967i
$623$		−	219.881i		−	0.352939i
$624$	85.4802	−	255.826i	0.136988	−	0.409978i
$625$	−476.800			−0.762879
$626$	−341.426	+	666.658i	−0.545409	+	1.06495i
$627$	−93.7242	−	93.7242i	−0.149480	−	0.149480i
$628$	303.854	+	49.4210i	0.483844	+	0.0786959i
$629$	147.716	+	147.716i	0.234842	+	0.234842i
$630$	81.5694	−	26.3162i	0.129475	−	0.0417718i
$631$	668.283			1.05909			0.529543	−	0.848283i	$-0.322363\pi$
$631$	668.283			1.05909			0.529543	+	0.848283i	$0.322363\pi$
$632$	35.2773	−	5.36216i	0.0558185	−	0.00848444i
$633$		−	345.797i		−	0.546283i
$634$	130.779	−	42.1923i	0.206275	−	0.0665494i
$635$	37.1177	−	37.1177i	0.0584531	−	0.0584531i
$636$	−199.878	+	143.955i	−0.314274	+	0.226344i
$637$	−354.243	+	354.243i	−0.556112	+	0.556112i
$638$	101.774	−	198.720i	0.159520	−	0.311474i
$639$			35.8586i			0.0561168i
$640$	105.064	+	149.122i	0.164163	+	0.233004i
$641$	484.574			0.755966			0.377983	−	0.925813i	$-0.376618\pi$
$641$	484.574			0.755966			0.377983	+	0.925813i	$0.376618\pi$
$642$	−491.622	−	251.782i	−0.765766	−	0.392184i
$643$	75.2980	+	75.2980i	0.117104	+	0.117104i	0.763230	−	0.646126i	$-0.223612\pi$
$643$	75.2980	+	75.2980i	0.117104	+	0.117104i	−0.646126	+	0.763230i	$0.723612\pi$
$644$	777.952	+	1080.17i	1.20800	+	1.67728i
$645$	−120.512	−	120.512i	−0.186840	−	0.186840i
$646$	−328.306	−	1017.61i	−0.508213	−	1.57525i
$647$	−582.307			−0.900011			−0.450006	−	0.893026i	$-0.648578\pi$
$647$	−582.307			−0.900011			−0.450006	+	0.893026i	$0.648578\pi$
$648$	10.8198	+	71.1824i	0.0166972	+	0.109849i
$649$		−	28.2682i		−	0.0435565i
$650$	−137.282	−	425.518i	−0.211204	−	0.654644i
$651$	507.946	−	507.946i	0.780255	−	0.780255i
$652$	−95.1754	+	585.164i	−0.145974	+	0.897491i
$653$	457.453	−	457.453i	0.700541	−	0.700541i	−0.263986	−	0.964527i	$-0.585037\pi$
$653$	457.453	−	457.453i	0.700541	−	0.700541i	0.964527	+	0.263986i	$0.0850371\pi$
$654$	353.795	+	181.195i	0.540972	+	0.277056i
$655$		−	24.9283i		−	0.0380584i
$656$	715.480	+	239.066i	1.09067	+	0.364430i
$657$	−333.997			−0.508367
$658$	416.750	−	813.734i	0.633359	−	1.23668i
$659$	−430.079	−	430.079i	−0.652623	−	0.652623i	0.301001	−	0.953624i	$-0.402679\pi$
$659$	−430.079	−	430.079i	−0.652623	−	0.652623i	−0.953624	+	0.301001i	$0.902679\pi$
$660$	−5.07773	+	31.2193i	−0.00769353	+	0.0473019i
$661$	−513.622	−	513.622i	−0.777038	−	0.777038i	0.202288	−	0.979326i	$-0.435162\pi$
$661$	−513.622	−	513.622i	−0.777038	−	0.777038i	−0.979326	+	0.202288i	$0.935162\pi$
$662$	5.08436	−	1.64034i	0.00768031	−	0.00247785i
$663$	377.287			0.569060
$664$	68.2440	−	92.7089i	0.102777	−	0.139622i
$665$		−	341.246i		−	0.513152i
$666$	−53.3002	+	17.1959i	−0.0800303	+	0.0258197i
$667$	−818.105	+	818.105i	−1.22654	+	1.22654i
$668$	124.624	+	173.037i	0.186562	+	0.259038i
$669$	−150.162	+	150.162i	−0.224457	+	0.224457i
$670$	18.7503	−	36.6112i	0.0279855	−	0.0546436i
$671$		−	162.872i		−	0.242730i
$672$	555.532	+	5.77193i	0.826685	+	0.00858919i
$673$	−1112.68			−1.65332			−0.826659	−	0.562703i	$-0.809761\pi$
$673$	−1112.68			−1.65332			−0.826659	+	0.562703i	$0.809761\pi$
$674$	688.871	+	352.802i	1.02206	+	0.523446i
$675$	84.3935	+	84.3935i	0.125027	+	0.125027i
$676$	−241.061	+	173.615i	−0.356599	+	0.256827i
$677$	633.271	+	633.271i	0.935408	+	0.935408i	0.998037	−	0.0626291i	$-0.0199485\pi$
$677$	633.271	+	633.271i	0.935408	+	0.935408i	−0.0626291	+	0.998037i	$0.519949\pi$
$678$	182.776	+	566.530i	0.269581	+	0.835590i
$679$	1075.62			1.58412
$680$	−151.262	+	205.488i	−0.222444	+	0.302188i
$681$		−	724.668i		−	1.06412i
$682$	81.3937	+	252.287i	0.119346	+	0.369922i
$683$	−429.651	+	429.651i	−0.629065	+	0.629065i	−0.947833	−	0.318768i	$-0.896731\pi$
$683$	−429.651	+	429.651i	−0.629065	+	0.629065i	0.318768	+	0.947833i	$0.396731\pi$
$684$	282.945	+	46.0202i	0.413662	+	0.0672810i
$685$	−146.803	+	146.803i	−0.214312	+	0.214312i
$686$	−44.1038	−	22.5876i	−0.0642913	−	0.0329265i
$687$			179.748i			0.261642i
$688$	−493.330	−	988.439i	−0.717049	−	1.43668i
$689$	−346.042			−0.502239
$690$	74.7148	−	145.886i	0.108282	−	0.211429i
$691$	−151.617	−	151.617i	−0.219417	−	0.219417i	0.588836	−	0.808253i	$-0.299586\pi$
$691$	−151.617	−	151.617i	−0.219417	−	0.219417i	−0.808253	+	0.588836i	$0.799586\pi$
$692$	−232.150	−	37.7586i	−0.335477	−	0.0545644i
$693$	68.1153	+	68.1153i	0.0982904	+	0.0982904i
$694$	−1189.47	+	383.753i	−1.71394	+	0.552958i
$695$	166.417			0.239449
$696$	72.5625	+	477.383i	0.104257	+	0.685896i
$697$			1055.17i			1.51388i
$698$	−321.353	+	103.676i	−0.460391	+	0.148533i
$699$	191.340	−	191.340i	0.273734	−	0.273734i
$700$	747.287	−	538.205i	1.06755	−	0.768864i
$701$	−920.704	+	920.704i	−1.31341	+	1.31341i	−0.394533	+	0.918882i	$0.629094\pi$
$701$	−920.704	+	920.704i	−1.31341	+	1.31341i	−0.918882	+	0.394533i	$0.870906\pi$
$702$	−46.1076	+	90.0284i	−0.0656804	+	0.128246i
$703$			222.982i			0.317186i
$704$	−95.3473	+	181.500i	−0.135437	+	0.257812i
$705$	−112.571			−0.159675
$706$	917.906	+	470.102i	1.30015	+	0.665866i
$707$	−1010.18	−	1010.18i	−1.42882	−	1.42882i
$708$	35.7294	+	49.6096i	0.0504653	+	0.0700700i
$709$	405.348	+	405.348i	0.571718	+	0.571718i	0.932608	−	0.360890i	$-0.117527\pi$
$709$	405.348	+	405.348i	0.571718	+	0.571718i	−0.360890	+	0.932608i	$0.617527\pi$
$710$	−10.4605	−	32.4233i	−0.0147331	−	0.0456666i
$711$	−13.3809			−0.0188199
$712$	−173.498	+	26.3718i	−0.243677	+	0.0370391i
$713$		−	1373.72i		−	1.92667i
$714$	238.600	+	739.561i	0.334174	+	1.03580i
$715$	−31.4199	+	31.4199i	−0.0439439	+	0.0439439i
$716$	−48.1958	+	296.321i	−0.0673125	+	0.413856i
$717$	−16.1319	+	16.1319i	−0.0224991	+	0.0224991i
$718$	−762.363	−	390.441i	−1.06179	−	0.543789i
$719$			880.704i			1.22490i	0.790509	+	0.612450i	$0.209816\pi$
$719$			880.704i			1.22490i	−0.790509	+	0.612450i	$0.790184\pi$
$720$	−30.5482	−	61.2066i	−0.0424280	−	0.0850091i
$721$	581.930			0.807115
$722$	191.147	−	373.227i	0.264746	−	0.516935i
$723$	−232.112	−	232.112i	−0.321041	−	0.321041i
$724$	60.4859	−	371.884i	0.0835440	−	0.513651i
$725$	565.983	+	565.983i	0.780667	+	0.780667i
$726$	365.078	−	117.783i	0.502862	−	0.162235i
$727$	1000.46			1.37615			0.688077	−	0.725637i	$-0.258455\pi$
$727$	1000.46			1.37615			0.688077	+	0.725637i	$0.258455\pi$
$728$	628.547	+	462.680i	0.863388	+	0.635549i
$729$		−	27.0000i		−	0.0370370i
$730$	301.999	−	97.4320i	0.413697	−	0.133469i
$731$	1092.64	−	1092.64i	1.49472	−	1.49472i
$732$	205.861	+	285.834i	0.281231	+	0.390484i
$733$	540.306	−	540.306i	0.737116	−	0.737116i	−0.234903	−	0.972019i	$-0.575477\pi$
$733$	540.306	−	540.306i	0.737116	−	0.737116i	0.972019	+	0.234903i	$0.0754772\pi$
$734$	200.097	−	390.704i	0.272612	−	0.532295i
$735$			127.053i			0.172861i
$736$	759.011	−	743.401i	1.03126	−	1.01006i
$737$	46.2301			0.0627274
$738$	−251.786	−	128.951i	−0.341174	−	0.174731i
$739$	893.726	+	893.726i	1.20937	+	1.20937i	0.971230	+	0.238142i	$0.0765384\pi$
$739$	893.726	+	893.726i	1.20937	+	1.20937i	0.238142	+	0.971230i	$0.423462\pi$
$740$	43.1775	−	31.0970i	0.0583480	−	0.0420229i
$741$	284.763	+	284.763i	0.384296	+	0.384296i
$742$	−218.841	−	678.316i	−0.294934	−	0.914172i
$743$	1295.75			1.74394			0.871969	−	0.489561i	$-0.162843\pi$
$743$	1295.75			1.74394			0.871969	+	0.489561i	$0.162843\pi$
$744$	−461.719	−	339.876i	−0.620591	−	0.456823i
$745$			395.527i			0.530909i
$746$	−369.092	−	1144.03i	−0.494761	−	1.53355i
$747$	−30.5253	+	30.5253i	−0.0408639	+	0.0408639i
$748$	−283.054	−	46.0380i	−0.378414	−	0.0615481i
$749$	1130.13	−	1130.13i	1.50885	−	1.50885i
$750$	−210.779	−	107.949i	−0.281038	−	0.143932i
$751$		−	229.818i		−	0.306016i	−0.988225	−	0.153008i	$-0.951104\pi$
$751$		−	229.818i		−	0.306016i	0.988225	−	0.153008i	$-0.0488961\pi$
$752$	−692.066	−	231.243i	−0.920300	−	0.307504i
$753$	−67.2223			−0.0892726
$754$	−309.220	+	603.774i	−0.410106	+	0.800761i
$755$	64.9987	+	64.9987i	0.0860910	+	0.0860910i
$756$	−205.634	−	33.4458i	−0.272002	−	0.0442404i
$757$	−373.678	−	373.678i	−0.493630	−	0.493630i	0.415818	−	0.909448i	$-0.363495\pi$
$757$	−373.678	−	373.678i	−0.493630	−	0.493630i	−0.909448	+	0.415818i	$0.863495\pi$
$758$	−984.973	+	317.776i	−1.29944	+	0.419229i
$759$	184.215			0.242707
$760$	−269.262	+	40.9280i	−0.354293	+	0.0538527i
$761$			384.012i			0.504615i	0.967647	+	0.252307i	$0.0811894\pi$
$761$			384.012i			0.504615i	−0.967647	+	0.252307i	$0.918811\pi$
$762$	−121.431	+	39.1766i	−0.159358	+	0.0514128i
$763$	−813.296	+	813.296i	−1.06592	+	1.06592i
$764$	−369.222	+	265.918i	−0.483275	+	0.348060i
$765$	67.6589	−	67.6589i	0.0884429	−	0.0884429i
$766$	194.440	−	379.658i	0.253838	−	0.495637i
$767$			85.8874i			0.111978i
$768$	−62.0745	−	439.038i	−0.0808261	−	0.571665i
$769$	865.026			1.12487			0.562436	−	0.826841i	$-0.309864\pi$
$769$	865.026			1.12487			0.562436	+	0.826841i	$0.309864\pi$
$770$	−81.4598	−	41.7193i	−0.105792	−	0.0541809i
$771$	165.800	+	165.800i	0.215045	+	0.215045i
$772$	−62.0876	−	86.2074i	−0.0804244	−	0.111668i
$773$	−1.78859	−	1.78859i	−0.00231383	−	0.00231383i	0.705949	−	0.708263i	$-0.250521\pi$
$773$	−1.78859	−	1.78859i	−0.00231383	−	0.00231383i	−0.708263	+	0.705949i	$0.750521\pi$
$774$	127.196	+	394.256i	0.164337	+	0.509375i
$775$	−950.368			−1.22628
$776$	−129.007	−	848.725i	−0.166246	−	1.09372i
$777$		−	162.055i		−	0.208565i
$778$	183.066	+	567.428i	0.235303	+	0.729341i
$779$	−796.409	+	796.409i	−1.02235	+	1.02235i
$780$	15.4277	−	94.8537i	0.0197791	−	0.121607i
$781$	27.0753	−	27.0753i	0.0346675	−	0.0346675i
$782$	1322.70	+	677.413i	1.69143	+	0.866257i
$783$		−	181.075i		−	0.231258i
$784$	−260.991	+	781.098i	−0.332897	+	0.996299i
$785$	109.681			0.139721
$786$	−27.6211	+	53.9321i	−0.0351413	+	0.0686159i
$787$	143.702	+	143.702i	0.182595	+	0.182595i	0.792485	−	0.609891i	$-0.208787\pi$
$787$	143.702	+	143.702i	0.182595	+	0.182595i	−0.609891	+	0.792485i	$0.708787\pi$
$788$	−47.1265	+	289.747i	−0.0598052	+	0.367699i
$789$	38.7170	+	38.7170i	0.0490710	+	0.0490710i
$790$	12.0990	−	3.90342i	0.0153152	−	0.00494104i
$791$	−1722.49			−2.17761
$792$	45.5772	−	61.9163i	0.0575470	−	0.0781772i
$793$			494.855i			0.624029i
$794$	−1057.63	+	341.216i	−1.33203	+	0.429743i
$795$	−62.0558	+	62.0558i	−0.0780577	+	0.0780577i
$796$	−319.655	−	443.835i	−0.401577	−	0.557582i
$797$	−477.929	+	477.929i	−0.599660	+	0.599660i	−0.940222	−	0.340562i	$-0.889383\pi$
$797$	−477.929	+	477.929i	−0.599660	+	0.599660i	0.340562	+	0.940222i	$0.389383\pi$
$798$	−378.108	+	738.283i	−0.473820	+	0.925166i
$799$		−	1020.64i		−	1.27740i
$800$	−514.301	−	525.101i	−0.642877	−	0.656376i
$801$	65.8092			0.0821588
$802$	−52.2091	−	26.7387i	−0.0650987	−	0.0333400i
$803$	252.187	+	252.187i	0.314056	+	0.314056i
$804$	−81.1321	+	58.4323i	−0.100911	+	0.0726770i
$805$	335.359	+	335.359i	0.416595	+	0.416595i
$806$	−247.299	−	766.524i	−0.306823	−	0.951023i
$807$	−475.722			−0.589495
$808$	−675.929	+	918.244i	−0.836545	+	1.13644i
$809$		−	1524.96i		−	1.88500i	−0.334212	−	0.942498i	$-0.608470\pi$
$809$		−	1524.96i		−	1.88500i	0.334212	−	0.942498i	$-0.391530\pi$
$810$	7.87632	+	24.4133i	0.00972385	+	0.0301399i
$811$	−576.427	+	576.427i	−0.710761	+	0.710761i	−0.966694	−	0.255933i	$-0.917617\pi$
$811$	−576.427	+	576.427i	−0.710761	+	0.710761i	0.255933	+	0.966694i	$0.417617\pi$
$812$	−1379.08	−	224.303i	−1.69837	−	0.276236i
$813$	−357.194	+	357.194i	−0.439353	+	0.439353i
$814$	53.2286	+	27.2608i	0.0653914	+	0.0334899i
$815$			211.224i			0.259170i
$816$	554.938	−	276.970i	0.680072	−	0.339424i
$817$	1649.37			2.01882
$818$	548.026	−	1070.06i	0.669958	−	1.30814i
$819$	−206.955	−	206.955i	−0.252692	−	0.252692i
$820$	265.281	+	43.1473i	0.323514	+	0.0526186i
$821$	−386.324	−	386.324i	−0.470552	−	0.470552i	0.431541	−	0.902093i	$-0.357970\pi$
$821$	−386.324	−	386.324i	−0.470552	−	0.470552i	−0.902093	+	0.431541i	$0.857970\pi$
$822$	480.269	−	154.946i	0.584269	−	0.188499i
$823$	377.870			0.459138			0.229569	−	0.973292i	$-0.426268\pi$
$823$	377.870			0.459138			0.229569	+	0.973292i	$0.426268\pi$
$824$	−69.7950	−	459.176i	−0.0847026	−	0.557252i
$825$		−	127.444i		−	0.154477i
$826$	−168.357	+	54.3161i	−0.203822	+	0.0657580i
$827$	140.900	−	140.900i	0.170375	−	0.170375i	−0.616769	−	0.787144i	$-0.711559\pi$
$827$	140.900	−	140.900i	0.170375	−	0.170375i	0.787144	+	0.616769i	$0.211559\pi$
$828$	−323.290	+	232.837i	−0.390447	+	0.281204i
$829$	−522.203	+	522.203i	−0.629919	+	0.629919i	−0.948048	−	0.318128i	$-0.896946\pi$
$829$	−522.203	+	522.203i	−0.629919	+	0.629919i	0.318128	+	0.948048i	$0.396946\pi$
$830$	18.6962	−	36.5056i	0.0225255	−	0.0439826i
$831$			747.501i			0.899520i
$832$	289.694	−	551.451i	0.348190	−	0.662802i
$833$	−1151.95			−1.38289
$834$	−360.041	−	184.394i	−0.431704	−	0.221095i
$835$	53.7226	+	53.7226i	0.0643385	+	0.0643385i
$836$	−178.892	−	248.387i	−0.213985	−	0.297114i
$837$	152.026	+	152.026i	0.181632	+	0.181632i
$838$	450.621	+	1396.74i	0.537734	+	1.66675i
$839$	−442.133			−0.526976			−0.263488	−	0.964663i	$-0.584873\pi$
$839$	−442.133			−0.526976			−0.263488	+	0.964663i	$0.584873\pi$
$840$	195.690	−	29.7450i	0.232964	−	0.0354107i
$841$		−	373.376i		−	0.443967i
$842$	357.114	+	1106.91i	0.424126	+	1.31462i
$843$	259.476	−	259.476i	0.307801	−	0.307801i
$844$	128.203	−	788.226i	0.151899	−	0.933917i
$845$	−74.8417	+	74.8417i	−0.0885701	+	0.0885701i
$846$	243.546	+	124.731i	0.287880	+	0.147436i
$847$			1109.99i			1.31049i
$848$	−508.982	+	254.033i	−0.600215	+	0.299567i
$849$	257.994			0.303879
$850$	468.650	−	915.071i	0.551352	−	1.07655i
$851$	−219.135	−	219.135i	−0.257503	−	0.257503i
$852$	−13.2945	+	81.7379i	−0.0156038	+	0.0959365i
$853$	−494.617	−	494.617i	−0.579856	−	0.579856i	0.355007	−	0.934863i	$-0.384478\pi$
$853$	−494.617	−	494.617i	−0.579856	−	0.579856i	−0.934863	+	0.355007i	$0.884478\pi$
$854$	−970.020	+	312.952i	−1.13585	+	0.366454i
$855$	102.133			0.119454
$856$	−1027.28	−	756.190i	−1.20009	−	0.883400i
$857$			1676.75i			1.95654i	0.207340	+	0.978269i	$0.433519\pi$
$857$			1676.75i			1.95654i	−0.207340	+	0.978269i	$0.566481\pi$
$858$	102.791	−	33.1627i	0.119802	−	0.0386511i
$859$	228.948	−	228.948i	0.266529	−	0.266529i	−0.561171	−	0.827700i	$-0.689649\pi$
$859$	228.948	−	228.948i	0.266529	−	0.266529i	0.827700	+	0.561171i	$0.189649\pi$
$860$	−230.021	−	319.380i	−0.267466	−	0.371372i
$861$	578.800	−	578.800i	0.672241	−	0.672241i
$862$	37.4777	−	73.1778i	0.0434776	−	0.0848931i
$863$		−	1603.23i		−	1.85774i	−0.370401	−	0.928872i	$-0.620780\pi$
$863$		−	1603.23i		−	1.85774i	0.370401	−	0.928872i	$-0.379220\pi$
$864$	−1.72751	+	166.268i	−0.00199943	+	0.192440i
$865$	−83.7981			−0.0968764
$866$	626.038	+	320.622i	0.722907	+	0.370234i
$867$	259.488	+	259.488i	0.299294	+	0.299294i
$868$	1346.15	−	969.517i	1.55087	−	1.11695i
$869$	10.1034	+	10.1034i	0.0116264	+	0.0116264i
$870$	52.8224	+	163.727i	0.0607154	+	0.188192i
$871$	−140.461			−0.161264
$872$	739.281	+	544.192i	0.847799	+	0.624074i
$873$			321.927i			0.368760i
$874$	487.038	+	1509.61i	0.557252	+	1.72725i
$875$	484.533	−	484.533i	0.553752	−	0.553752i
$876$	−761.328	−	123.828i	−0.869096	−	0.141356i
$877$	289.017	−	289.017i	0.329552	−	0.329552i	−0.522864	−	0.852416i	$-0.675136\pi$
$877$	289.017	−	289.017i	0.329552	−	0.329552i	0.852416	+	0.522864i	$0.175136\pi$
$878$	1380.69	+	707.113i	1.57254	+	0.805367i
$879$		−	419.570i		−	0.477326i
$880$	−23.1488	+	69.2801i	−0.0263055	+	0.0787274i
$881$	937.450			1.06408			0.532038	−	0.846721i	$-0.321426\pi$
$881$	937.450			1.06408			0.532038	+	0.846721i	$0.321426\pi$
$882$	140.778	−	274.878i	0.159612	−	0.311653i
$883$	−485.966	−	485.966i	−0.550357	−	0.550357i	0.376187	−	0.926544i	$-0.377235\pi$
$883$	−485.966	−	485.966i	−0.550357	−	0.550357i	−0.926544	+	0.376187i	$0.877235\pi$
$884$	860.005	+	139.877i	0.972856	+	0.158232i
$885$	15.4022	+	15.4022i	0.0174036	+	0.0174036i
$886$	649.726	−	209.617i	0.733326	−	0.236588i
$887$	−534.193			−0.602247			−0.301123	−	0.953585i	$-0.597362\pi$
$887$	−534.193			−0.602247			−0.301123	+	0.953585i	$0.597362\pi$
$888$	−127.870	+	19.4364i	−0.143998	+	0.0218878i
$889$		−	369.201i		−	0.415299i
$890$	−59.5044	+	19.1976i	−0.0668589	+	0.0215703i
$891$	−20.3865	+	20.3865i	−0.0228805	+	0.0228805i
$892$	−397.958	+	286.614i	−0.446142	+	0.321316i
$893$	770.346	−	770.346i	0.862649	−	0.862649i
$894$	438.253	−	855.719i	0.490216	−	0.957180i
$895$			106.961i			0.119510i
$896$	1264.17	+	219.118i	1.41090	+	0.244552i
$897$	−559.701			−0.623970
$898$	−474.153	−	242.835i	−0.528010	−	0.270418i
$899$	1019.56	+	1019.56i	1.13410	+	1.13410i
$900$	161.082	+	223.659i	0.178980	+	0.248510i
$901$	−562.638	−	562.638i	−0.624460	−	0.624460i
$902$	92.7475	+	287.479i	0.102824	+	0.318712i
$903$	−1198.70			−1.32747
$904$	206.590	+	1359.14i	0.228529	+	1.50347i
$905$		−	134.237i		−	0.148328i
$906$	−68.6041	−	212.644i	−0.0757219	−	0.234706i
$907$	368.669	−	368.669i	0.406471	−	0.406471i	−0.474035	−	0.880506i	$-0.657203\pi$
$907$	368.669	−	368.669i	0.406471	−	0.406471i	0.880506	+	0.474035i	$0.157203\pi$
$908$	268.668	−	1651.84i	0.295890	−	1.81921i
$909$	302.341	−	302.341i	0.332608	−	0.332608i
$910$	247.500	+	126.756i	0.271978	+	0.139292i
$911$			1592.43i			1.74800i	0.485927	+	0.873999i	$0.338482\pi$
$911$			1592.43i			1.74800i	−0.485927	+	0.873999i	$0.661518\pi$
$912$	627.896	+	209.801i	0.688482	+	0.230045i
$913$	46.0967			0.0504893
$914$	−469.739	+	917.198i	−0.513938	+	1.00350i
$915$	88.7424	+	88.7424i	0.0969863	+	0.0969863i
$916$	−66.6408	+	409.726i	−0.0727519	+	0.447299i
$917$	−123.978	−	123.978i	−0.135199	−	0.135199i
$918$	−221.347	+	71.4118i	−0.241119	+	0.0777906i
$919$	−403.500			−0.439064			−0.219532	−	0.975605i	$-0.570453\pi$
$919$	−403.500			−0.439064			−0.219532	+	0.975605i	$0.570453\pi$
$920$	224.395	−	304.839i	0.243908	−	0.331347i
$921$		−	66.4116i		−	0.0721081i
$922$	−15.2818	+	4.93029i	−0.0165747	+	0.00534738i
$923$	−82.2632	+	82.2632i	−0.0891258	+	0.0891258i
$924$	130.012	+	180.519i	0.140705	+	0.195366i
$925$	−151.602	+	151.602i	−0.163894	+	0.163894i
$926$	−423.486	+	826.886i	−0.457328	+	0.892965i
$927$			174.169i			0.187884i
$928$	−11.5855	+	1115.07i	−0.0124844	+	1.20159i
$929$	348.546			0.375184			0.187592	−	0.982247i	$-0.439932\pi$
$929$	348.546			0.375184			0.187592	+	0.982247i	$0.439932\pi$
$930$	−181.809	−	93.1128i	−0.195494	−	0.100121i
$931$	−869.449	−	869.449i	−0.933887	−	0.933887i
$932$	507.089	−	365.211i	0.544087	−	0.391858i
$933$	454.533	+	454.533i	0.487173	+	0.487173i
$934$	−430.734	−	1335.10i	−0.461171	−	1.42944i
$935$	−102.173			−0.109276
$936$	−138.478	+	188.121i	−0.147946	+	0.200984i
$937$		−	248.875i		−	0.265609i	−0.991142	−	0.132804i	$-0.957602\pi$
$937$		−	248.875i		−	0.265609i	0.991142	−	0.132804i	$-0.0423982\pi$
$938$	−88.8292	−	275.334i	−0.0947007	−	0.293533i
$939$	458.669	−	458.669i	0.488465	−	0.488465i
$940$	−256.600	−	41.7353i	−0.272978	−	0.0443992i
$941$	884.188	−	884.188i	0.939626	−	0.939626i	−0.0586528	−	0.998278i	$-0.518681\pi$
$941$	884.188	−	884.188i	0.939626	−	0.939626i	0.998278	+	0.0586528i	$0.0186805\pi$
$942$	−237.293	−	121.529i	−0.251904	−	0.129011i
$943$		−	1565.34i		−	1.65996i
$944$	63.0508	+	126.329i	0.0667911	+	0.133823i
$945$	−74.2266			−0.0785466
$946$	201.645	−	393.727i	0.213156	−	0.416202i
$947$	462.279	+	462.279i	0.488151	+	0.488151i	0.907722	−	0.419571i	$-0.137820\pi$
$947$	462.279	+	462.279i	0.488151	+	0.488151i	−0.419571	+	0.907722i	$0.637820\pi$
$948$	−30.5011	−	4.96093i	−0.0321742	−	0.00523304i
$949$	−766.221	−	766.221i	−0.807398	−	0.807398i
$950$	1044.39	−	336.944i	1.09935	−	0.354678i
$951$	−119.006			−0.125138
$952$	269.687	+	1774.25i	0.283285	+	1.86371i
$953$			707.656i			0.742556i	0.928522	+	0.371278i	$0.121080\pi$
$953$			707.656i			0.742556i	−0.928522	+	0.371278i	$0.878920\pi$
$954$	203.016	−	65.4980i	0.212806	−	0.0686562i
$955$	−114.632	+	114.632i	−0.120033	+	0.120033i
$956$	−42.7525	+	30.7909i	−0.0447202	+	0.0322081i
$957$	−136.722	+	136.722i	−0.142865	+	0.142865i
$958$	−345.347	+	674.314i	−0.360487	+	0.703877i
$959$			1460.22i			1.52265i
$960$	−46.9409	−	150.843i	−0.0488968	−	0.157128i
$961$	−750.983			−0.781460
$962$	−161.725	−	82.8267i	−0.168113	−	0.0860984i
$963$	338.241	+	338.241i	0.351237	+	0.351237i
$964$	−443.033	−	615.143i	−0.459578	−	0.638115i
$965$	−26.7647	−	26.7647i	−0.0277354	−	0.0277354i
$966$	−353.961	−	1097.13i	−0.366419	−	1.13575i
$967$	−841.240			−0.869949			−0.434974	−	0.900443i	$-0.643243\pi$
$967$	−841.240			−0.869949			−0.434974	+	0.900443i	$0.643243\pi$
$968$	875.844	−	133.129i	0.904797	−	0.137530i
$969$			926.006i			0.955630i
$970$	−93.9112	−	291.086i	−0.0968157	−	0.300088i
$971$	308.415	−	308.415i	0.317626	−	0.317626i	−0.530229	−	0.847855i	$-0.677894\pi$
$971$	308.415	−	308.415i	0.317626	−	0.317626i	0.847855	+	0.530229i	$0.177894\pi$
$972$	10.0101	−	61.5451i	0.0102985	−	0.0633180i
$973$	827.654	−	827.654i	0.850621	−	0.850621i
$974$	−262.472	−	134.424i	−0.269478	−	0.138012i
$975$			387.213i			0.397142i
$976$	363.278	+	727.866i	0.372211	+	0.745764i
$977$	−1316.85			−1.34786			−0.673928	−	0.738797i	$-0.735394\pi$
$977$	−1316.85			−1.34786			−0.673928	+	0.738797i	$0.735394\pi$
$978$	234.041	−	456.981i	0.239305	−	0.467260i
$979$	−49.6897	−	49.6897i	−0.0507556	−	0.0507556i
$980$	−47.1044	+	289.611i	−0.0480657	+	0.295521i
$981$	−243.415	−	243.415i	−0.248130	−	0.248130i
$982$	−294.880	+	95.1352i	−0.300285	+	0.0968791i
$983$	504.538			0.513263			0.256632	−	0.966509i	$-0.417387\pi$
$983$	504.538			0.513263			0.256632	+	0.966509i	$0.417387\pi$
$984$	−526.125	−	387.286i	−0.534680	−	0.393584i
$985$			104.588i			0.106181i
$986$	−1484.46	+	478.922i	−1.50554	+	0.485722i
$987$	−559.858	+	559.858i	−0.567232	+	0.567232i
$988$	543.528	+	754.677i	0.550129	+	0.763843i
$989$	−1620.92	+	1620.92i	−1.63895	+	1.63895i
$990$	12.4864	−	24.3805i	0.0126125	−	0.0246268i
$991$		−	436.650i		−	0.440616i	−0.975430	−	0.220308i	$-0.929294\pi$
$991$		−	436.650i		−	0.440616i	0.975430	−	0.220308i	$-0.0707062\pi$
$992$	−926.457	−	945.911i	−0.933929	−	0.953539i
$993$	−4.62667			−0.00465929
$994$	−213.277	−	109.229i	−0.214565	−	0.109888i
$995$	−137.797	−	137.797i	−0.138489	−	0.138489i
$996$	−80.8979	+	58.2637i	−0.0812228	+	0.0584977i
$997$	−383.801	−	383.801i	−0.384956	−	0.384956i	0.487928	−	0.872884i	$-0.337753\pi$
$997$	−383.801	−	383.801i	−0.384956	−	0.384956i	−0.872884	+	0.487928i	$0.837753\pi$
$998$	313.093	+	970.458i	0.313720	+	0.972403i
$999$	48.5021			0.0485507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.3.l.a.43.3	yes	16
3.2	odd	2		144.3.m.c.91.6		16
4.3	odd	2		192.3.l.a.79.3		16
8.3	odd	2		384.3.l.b.31.6		16
8.5	even	2		384.3.l.a.31.2		16
12.11	even	2		576.3.m.c.271.4		16
16.3	odd	4	inner	48.3.l.a.19.3	✓	16
16.5	even	4		384.3.l.b.223.6		16
16.11	odd	4		384.3.l.a.223.2		16
16.13	even	4		192.3.l.a.175.3		16
24.5	odd	2		1152.3.m.f.415.5		16
24.11	even	2		1152.3.m.c.415.5		16
48.5	odd	4		1152.3.m.c.991.5		16
48.11	even	4		1152.3.m.f.991.5		16
48.29	odd	4		576.3.m.c.559.4		16
48.35	even	4		144.3.m.c.19.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.l.a.19.3	✓	16	16.3	odd	4	inner
48.3.l.a.43.3	yes	16	1.1	even	1	trivial
144.3.m.c.19.6		16	48.35	even	4
144.3.m.c.91.6		16	3.2	odd	2
192.3.l.a.79.3		16	4.3	odd	2
192.3.l.a.175.3		16	16.13	even	4
384.3.l.a.31.2		16	8.5	even	2
384.3.l.a.223.2		16	16.11	odd	4
384.3.l.b.31.6		16	8.3	odd	2
384.3.l.b.223.6		16	16.5	even	4
576.3.m.c.271.4		16	12.11	even	2
576.3.m.c.559.4		16	48.29	odd	4
1152.3.m.c.415.5		16	24.11	even	2
1152.3.m.c.991.5		16	48.5	odd	4
1152.3.m.f.415.5		16	24.5	odd	2
1152.3.m.f.991.5		16	48.11	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.78012 - 0.911682i) q^{2} +(1.22474 + 1.22474i) q^{3} +(2.33767 + 3.24581i) q^{4} +(1.00772 + 1.00772i) q^{5} +(-1.06362 - 3.29677i) q^{6} +10.0236 q^{7} +(-1.20220 - 7.90915i) q^{8} +3.00000i q^{9} +(-0.875146 - 2.71259i) q^{10} +(2.26517 - 2.26517i) q^{11} +(-1.11224 + 6.83834i) q^{12} +(-6.88229 + 6.88229i) q^{13} +(-17.8432 - 9.13830i) q^{14} +2.46840i q^{15} +(-5.07058 + 15.1753i) q^{16} -22.3801 q^{17} +(2.73505 - 5.34037i) q^{18} +(-16.8918 - 16.8918i) q^{19} +(-0.915151 + 5.62660i) q^{20} +(12.2763 + 12.2763i) q^{21} +(-6.09740 + 1.96717i) q^{22} +33.2007 q^{23} +(8.21431 - 11.1591i) q^{24} -22.9690i q^{25} +(18.5258 - 5.97686i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(23.4318 + 32.5346i) q^{28} +(-24.6412 + 24.6412i) q^{29} +(2.25040 - 4.39406i) q^{30} -41.3761i q^{31} +(22.8613 - 22.3911i) q^{32} +5.54852 q^{33} +(39.8394 + 20.4036i) q^{34} +(10.1010 + 10.1010i) q^{35} +(-9.73743 + 7.01302i) q^{36} +(-6.60031 - 6.60031i) q^{37} +(14.6695 + 45.4693i) q^{38} -16.8581 q^{39} +(6.75875 - 9.18170i) q^{40} -47.1477i q^{41} +(-10.6612 - 33.0454i) q^{42} +(-48.8218 + 48.8218i) q^{43} +(12.6475 + 2.05709i) q^{44} +(-3.02316 + 3.02316i) q^{45} +(-59.1013 - 30.2685i) q^{46} +45.6048i q^{47} +(-24.7960 + 12.3757i) q^{48} +51.4717 q^{49} +(-20.9404 + 40.8876i) q^{50} +(-27.4100 - 27.4100i) q^{51} +(-38.4271 - 6.25007i) q^{52} +(25.1401 + 25.1401i) q^{53} +(9.89032 - 3.19085i) q^{54} +4.56532 q^{55} +(-12.0503 - 79.2779i) q^{56} -41.3762i q^{57} +(66.3292 - 21.3994i) q^{58} +(6.23974 - 6.23974i) q^{59} +(-8.01197 + 5.77032i) q^{60} +(35.9513 - 35.9513i) q^{61} +(-37.7219 + 73.6546i) q^{62} +30.0707i q^{63} +(-61.1095 + 19.0167i) q^{64} -13.8709 q^{65} +(-9.87704 - 5.05848i) q^{66} +(10.2045 + 10.2045i) q^{67} +(-52.3174 - 72.6417i) q^{68} +(40.6624 + 40.6624i) q^{69} +(-8.77208 - 27.1898i) q^{70} +11.9529 q^{71} +(23.7275 - 3.60659i) q^{72} +111.332i q^{73} +(5.73197 + 17.7667i) q^{74} +(28.1312 - 28.1312i) q^{75} +(15.3401 - 94.3149i) q^{76} +(22.7051 - 22.7051i) q^{77} +(30.0095 + 15.3692i) q^{78} +4.46031i q^{79} +(-20.4022 + 10.1827i) q^{80} -9.00000 q^{81} +(-42.9837 + 83.9287i) q^{82} +(10.1751 + 10.1751i) q^{83} +(-11.1486 + 68.5445i) q^{84} +(-22.5530 - 22.5530i) q^{85} +(131.419 - 42.3988i) q^{86} -60.3583 q^{87} +(-20.6388 - 15.1924i) q^{88} -21.9364i q^{89} +(8.13777 - 2.62544i) q^{90} +(-68.9850 + 68.9850i) q^{91} +(77.6124 + 107.763i) q^{92} +(50.6752 - 50.6752i) q^{93} +(41.5771 - 81.1821i) q^{94} -34.0444i q^{95} +(55.4226 + 0.575837i) q^{96} +107.309 q^{97} +(-91.6260 - 46.9259i) q^{98} +(6.79552 + 6.79552i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} - 12 q^{8} - 56 q^{10} + 32 q^{11} - 24 q^{12} - 44 q^{14} + 32 q^{16} + 12 q^{18} - 32 q^{19} + 80 q^{20} + 32 q^{22} - 128 q^{23} + 36 q^{24} - 100 q^{26} - 120 q^{28} + 32 q^{29} + 72 q^{30}+ \cdots + 96 q^{99}+O(q^{100}) \) 16 * q + 12 * q^4 - 12 * q^8 - 56 * q^10 + 32 * q^11 - 24 * q^12 - 44 * q^14 + 32 * q^16 + 12 * q^18 - 32 * q^19 + 80 * q^20 + 32 * q^22 - 128 * q^23 + 36 * q^24 - 100 * q^26 - 120 * q^28 + 32 * q^29 + 72 * q^30 + 160 * q^32 + 96 * q^34 + 96 * q^35 + 12 * q^36 - 96 * q^37 + 168 * q^38 + 48 * q^40 - 60 * q^42 + 160 * q^43 + 88 * q^44 + 136 * q^46 - 144 * q^48 + 112 * q^49 - 236 * q^50 - 96 * q^51 - 48 * q^52 - 160 * q^53 - 36 * q^54 - 256 * q^55 - 224 * q^56 + 144 * q^58 - 128 * q^59 - 72 * q^60 - 32 * q^61 - 276 * q^62 - 408 * q^64 - 32 * q^65 + 72 * q^66 + 320 * q^67 - 448 * q^68 + 96 * q^69 - 384 * q^70 + 512 * q^71 + 60 * q^72 + 348 * q^74 + 192 * q^75 + 72 * q^76 + 224 * q^77 + 396 * q^78 + 552 * q^80 - 144 * q^81 - 40 * q^82 - 160 * q^83 + 72 * q^84 + 160 * q^85 + 528 * q^86 + 480 * q^88 - 24 * q^90 - 480 * q^91 + 496 * q^92 + 312 * q^94 - 480 * q^96 - 440 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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