LMFDB - Embedded newform 51.3.f.a.38.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,3,Mod(38,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.38"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	51.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.38964934824$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 62 x^{18} + 1545 x^{16} + 20120 x^{14} + 149608 x^{12} + 655792 x^{10} + 1690896 x^{8} + \cdots + 36864 $ x^20 + 62x^18 + 1545x^16 + 20120x^14 + 149608x^12 + 655792x^10 + 1690896x^8 + 2476352x^6 + 1880640x^4 + 593152*x^2 + 36864
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			38.6
Root			$-0.791600i$ of defining polynomial
Character	$\chi$	$=$	51.38
Dual form			51.3.f.a.47.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.208400 q^{2} +(-0.709732 + 2.91484i) q^{3} -3.95657 q^{4} +(5.25648 + 5.25648i) q^{5} +(-0.147908 + 0.607451i) q^{6} +(2.40158 + 2.40158i) q^{7} -1.65815 q^{8} +(-7.99256 - 4.13751i) q^{9} +(1.09545 + 1.09545i) q^{10} +(11.4695 - 11.4695i) q^{11} +(2.80810 - 11.5328i) q^{12} -8.12160 q^{13} +(0.500488 + 0.500488i) q^{14} +(-19.0525 + 11.5911i) q^{15} +15.4807 q^{16} +(13.5788 + 10.2282i) q^{17} +(-1.66565 - 0.862255i) q^{18} -24.0029i q^{19} +(-20.7976 - 20.7976i) q^{20} +(-8.70468 + 5.29573i) q^{21} +(2.39024 - 2.39024i) q^{22} +(-5.74247 + 5.74247i) q^{23} +(1.17684 - 4.83323i) q^{24} +30.2612i q^{25} -1.69254 q^{26} +(17.7327 - 20.3605i) q^{27} +(-9.50201 - 9.50201i) q^{28} +(11.7489 + 11.7489i) q^{29} +(-3.97053 + 2.41558i) q^{30} +(5.33493 - 5.33493i) q^{31} +9.85876 q^{32} +(25.2915 + 41.5720i) q^{33} +(2.82983 + 2.13154i) q^{34} +25.2477i q^{35} +(31.6231 + 16.3703i) q^{36} +(-42.7533 + 42.7533i) q^{37} -5.00220i q^{38} +(5.76415 - 23.6731i) q^{39} +(-8.71602 - 8.71602i) q^{40} +(8.11856 - 8.11856i) q^{41} +(-1.81405 + 1.10363i) q^{42} +2.45499i q^{43} +(-45.3799 + 45.3799i) q^{44} +(-20.2640 - 63.7615i) q^{45} +(-1.19673 + 1.19673i) q^{46} -64.4496i q^{47} +(-10.9872 + 45.1238i) q^{48} -37.4649i q^{49} +6.30643i q^{50} +(-39.4507 + 32.3209i) q^{51} +32.1337 q^{52} -9.84366 q^{53} +(3.69550 - 4.24312i) q^{54} +120.578 q^{55} +(-3.98217 - 3.98217i) q^{56} +(69.9646 + 17.0356i) q^{57} +(2.44846 + 2.44846i) q^{58} -73.8881 q^{59} +(75.3825 - 45.8610i) q^{60} +(-55.3702 - 55.3702i) q^{61} +(1.11180 - 1.11180i) q^{62} +(-9.25821 - 29.1313i) q^{63} -59.8683 q^{64} +(-42.6910 - 42.6910i) q^{65} +(5.27074 + 8.66359i) q^{66} +27.1997 q^{67} +(-53.7256 - 40.4684i) q^{68} +(-12.6628 - 20.8140i) q^{69} +5.26161i q^{70} +(6.71855 + 6.71855i) q^{71} +(13.2528 + 6.86059i) q^{72} +(-1.60189 + 1.60189i) q^{73} +(-8.90977 + 8.90977i) q^{74} +(-88.2065 - 21.4773i) q^{75} +94.9692i q^{76} +55.0898 q^{77} +(1.20125 - 4.93347i) q^{78} +(-64.8910 - 64.8910i) q^{79} +(81.3741 + 81.3741i) q^{80} +(46.7621 + 66.1385i) q^{81} +(1.69190 - 1.69190i) q^{82} +64.2751 q^{83} +(34.4407 - 20.9529i) q^{84} +(17.6128 + 125.141i) q^{85} +0.511620i q^{86} +(-42.5846 + 25.9075i) q^{87} +(-19.0181 + 19.0181i) q^{88} +142.221i q^{89} +(-4.22302 - 13.2879i) q^{90} +(-19.5046 - 19.5046i) q^{91} +(22.7205 - 22.7205i) q^{92} +(11.7641 + 19.3368i) q^{93} -13.4313i q^{94} +(126.171 - 126.171i) q^{95} +(-6.99708 + 28.7367i) q^{96} +(48.5370 - 48.5370i) q^{97} -7.80767i q^{98} +(-139.126 + 44.2156i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{3} + 24 q^{4} - 2 q^{6} - 4 q^{7} - 16 q^{10} - 42 q^{12} - 12 q^{13} - 64 q^{16} - 4 q^{18} + 88 q^{21} - 40 q^{22} - 82 q^{24} + 54 q^{27} - 160 q^{28} + 48 q^{31} + 264 q^{33} + 152 q^{34}+ \cdots - 864 q^{99}+O(q^{100}) $ 20 * q - 6 * q^3 + 24 * q^4 - 2 * q^6 - 4 * q^7 - 16 * q^10 - 42 * q^12 - 12 * q^13 - 64 * q^16 - 4 * q^18 + 88 * q^21 - 40 * q^22 - 82 * q^24 + 54 * q^27 - 160 * q^28 + 48 * q^31 + 264 * q^33 + 152 * q^34 + 32 * q^37 + 56 * q^39 + 52 * q^40 + 64 * q^45 + 388 * q^46 - 230 * q^48 - 298 * q^51 + 64 * q^52 - 254 * q^54 - 204 * q^55 - 24 * q^57 + 396 * q^58 - 336 * q^61 - 400 * q^63 - 480 * q^64 - 408 * q^67 - 132 * q^69 + 276 * q^72 - 88 * q^73 - 358 * q^75 + 380 * q^78 - 172 * q^79 + 388 * q^81 + 372 * q^82 + 1320 * q^84 + 648 * q^85 - 156 * q^88 + 672 * q^90 - 124 * q^91 + 194 * q^96 + 688 * q^97 - 864 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.208400			0.104200			0.0520999	−	0.998642i	$-0.483409\pi$
$2$	0.208400			0.104200			0.0520999	+	0.998642i	$0.483409\pi$
$3$	−0.709732	+	2.91484i	−0.236577	+	0.971613i
$3$	−0.709732	+	2.91484i	−0.236577	+	0.971613i
$4$	−3.95657			−0.989142
$5$	5.25648	+	5.25648i	1.05130	+	1.05130i	0.998611	+	0.0526852i	$0.0167780\pi$
$5$	5.25648	+	5.25648i	1.05130	+	1.05130i	0.0526852	+	0.998611i	$0.483222\pi$
$6$	−0.147908	+	0.607451i	−0.0246513	+	0.101242i
$7$	2.40158	+	2.40158i	0.343082	+	0.343082i	0.857525	−	0.514442i	$-0.172001\pi$
$7$	2.40158	+	2.40158i	0.343082	+	0.343082i	−0.514442	+	0.857525i	$0.672001\pi$
$8$	−1.65815			−0.207268
$9$	−7.99256	−	4.13751i	−0.888062	−	0.459723i
$10$	1.09545	+	1.09545i	0.109545	+	0.109545i
$11$	11.4695	−	11.4695i	1.04268	−	1.04268i	0.0436344	−	0.999048i	$-0.486106\pi$
$11$	11.4695	−	11.4695i	1.04268	−	1.04268i	0.999048	−	0.0436344i	$-0.0138937\pi$
$12$	2.80810	−	11.5328i	0.234009	−	0.961063i
$13$	−8.12160			−0.624738			−0.312369	−	0.949961i	$-0.601123\pi$
$13$	−8.12160			−0.624738			−0.312369	+	0.949961i	$0.601123\pi$
$14$	0.500488	+	0.500488i	0.0357491	+	0.0357491i
$15$	−19.0525	+	11.5911i	−1.27017	+	0.772740i
$16$	15.4807			0.967545
$17$	13.5788	+	10.2282i	0.798755	+	0.601656i
$17$	13.5788	+	10.2282i	0.798755	+	0.601656i
$18$	−1.66565	−	0.862255i	−0.0925360	−	0.0479031i
$19$		−	24.0029i		−	1.26331i	−0.775249	−	0.631656i	$-0.782376\pi$
$19$		−	24.0029i		−	1.26331i	0.775249	−	0.631656i	$-0.217624\pi$
$20$	−20.7976	−	20.7976i	−1.03988	−	1.03988i
$21$	−8.70468	+	5.29573i	−0.414509	+	0.252178i
$22$	2.39024	−	2.39024i	0.108647	−	0.108647i
$23$	−5.74247	+	5.74247i	−0.249673	+	0.249673i	−0.820836	−	0.571164i	$-0.806492\pi$
$23$	−5.74247	+	5.74247i	−0.249673	+	0.249673i	0.571164	+	0.820836i	$0.306492\pi$
$24$	1.17684	−	4.83323i	0.0490350	−	0.201385i
$25$			30.2612i			1.21045i
$26$	−1.69254			−0.0650976
$27$	17.7327	−	20.3605i	0.656768	−	0.754093i
$28$	−9.50201	−	9.50201i	−0.339357	−	0.339357i
$29$	11.7489	+	11.7489i	0.405133	+	0.405133i	0.880037	−	0.474904i	$-0.157517\pi$
$29$	11.7489	+	11.7489i	0.405133	+	0.405133i	−0.474904	+	0.880037i	$0.657517\pi$
$30$	−3.97053	+	2.41558i	−0.132351	+	0.0805194i
$31$	5.33493	−	5.33493i	0.172094	−	0.172094i	−0.615805	−	0.787899i	$-0.711169\pi$
$31$	5.33493	−	5.33493i	0.172094	−	0.172094i	0.787899	+	0.615805i	$0.211169\pi$
$32$	9.85876			0.308086
$33$	25.2915	+	41.5720i	0.766408	+	1.25976i
$34$	2.82983	+	2.13154i	0.0832302	+	0.0626925i
$35$			25.2477i			0.721363i
$36$	31.6231	+	16.3703i	0.878420	+	0.454731i
$37$	−42.7533	+	42.7533i	−1.15549	+	1.15549i	−0.170060	+	0.985434i	$0.554396\pi$
$37$	−42.7533	+	42.7533i	−1.15549	+	1.15549i	−0.985434	+	0.170060i	$0.945604\pi$
$38$		−	5.00220i		−	0.131637i
$39$	5.76415	−	23.6731i	0.147799	−	0.607004i
$40$	−8.71602	−	8.71602i	−0.217900	−	0.217900i
$41$	8.11856	−	8.11856i	0.198014	−	0.198014i	−0.601134	−	0.799148i	$-0.705284\pi$
$41$	8.11856	−	8.11856i	0.198014	−	0.198014i	0.799148	+	0.601134i	$0.205284\pi$
$42$	−1.81405	+	1.10363i	−0.0431917	+	0.0262769i
$43$			2.45499i			0.0570929i	0.999592	+	0.0285464i	$0.00908785\pi$
$43$			2.45499i			0.0570929i	−0.999592	+	0.0285464i	$0.990912\pi$
$44$	−45.3799	+	45.3799i	−1.03136	+	1.03136i
$45$	−20.2640	−	63.7615i	−0.450312	−	1.41692i
$46$	−1.19673	+	1.19673i	−0.0260158	+	0.0260158i
$47$		−	64.4496i		−	1.37127i	−0.727947	−	0.685634i	$-0.759525\pi$
$47$		−	64.4496i		−	1.37127i	0.727947	−	0.685634i	$-0.240475\pi$
$48$	−10.9872	+	45.1238i	−0.228899	+	0.940079i
$49$		−	37.4649i		−	0.764589i
$50$			6.30643i			0.126129i
$51$	−39.4507	+	32.3209i	−0.773544	+	0.633743i
$52$	32.1337			0.617955
$53$	−9.84366			−0.185729			−0.0928647	−	0.995679i	$-0.529602\pi$
$53$	−9.84366			−0.185729			−0.0928647	+	0.995679i	$0.529602\pi$
$54$	3.69550	−	4.24312i	0.0684351	−	0.0785764i
$55$	120.578			2.19234
$56$	−3.98217	−	3.98217i	−0.0711101	−	0.0711101i
$57$	69.9646	+	17.0356i	1.22745	+	0.298871i
$58$	2.44846	+	2.44846i	0.0422148	+	0.0422148i
$59$	−73.8881			−1.25234			−0.626170	−	0.779686i	$-0.715378\pi$
$59$	−73.8881			−1.25234			−0.626170	+	0.779686i	$0.715378\pi$
$60$	75.3825	−	45.8610i	1.25637	−	0.764350i
$61$	−55.3702	−	55.3702i	−0.907709	−	0.907709i	0.0883785	−	0.996087i	$-0.471832\pi$
$61$	−55.3702	−	55.3702i	−0.907709	−	0.907709i	−0.996087	+	0.0883785i	$0.971832\pi$
$62$	1.11180	−	1.11180i	0.0179322	−	0.0179322i
$63$	−9.25821	−	29.1313i	−0.146956	−	0.462401i
$64$	−59.8683			−0.935442
$65$	−42.6910	−	42.6910i	−0.656785	−	0.656785i
$66$	5.27074	+	8.66359i	0.0798596	+	0.131267i
$67$	27.1997			0.405965			0.202983	−	0.979182i	$-0.434937\pi$
$67$	27.1997			0.405965			0.202983	+	0.979182i	$0.434937\pi$
$68$	−53.7256	−	40.4684i	−0.790083	−	0.595124i
$69$	−12.6628	−	20.8140i	−0.183518	−	0.301652i
$70$			5.26161i			0.0751659i
$71$	6.71855	+	6.71855i	0.0946275	+	0.0946275i	0.752836	−	0.658208i	$-0.228685\pi$
$71$	6.71855	+	6.71855i	0.0946275	+	0.0946275i	−0.658208	+	0.752836i	$0.728685\pi$
$72$	13.2528	+	6.86059i	0.184067	+	0.0952860i
$73$	−1.60189	+	1.60189i	−0.0219437	+	0.0219437i	−0.717993	−	0.696050i	$-0.754939\pi$
$73$	−1.60189	+	1.60189i	−0.0219437	+	0.0219437i	0.696050	+	0.717993i	$0.254939\pi$
$74$	−8.90977	+	8.90977i	−0.120402	+	0.120402i
$75$	−88.2065	−	21.4773i	−1.17609	−	0.286364i
$76$			94.9692i			1.24959i
$77$	55.0898			0.715452
$78$	1.20125	−	4.93347i	0.0154006	−	0.0632497i
$79$	−64.8910	−	64.8910i	−0.821405	−	0.821405i	0.164904	−	0.986310i	$-0.447268\pi$
$79$	−64.8910	−	64.8910i	−0.821405	−	0.821405i	−0.986310	+	0.164904i	$0.947268\pi$
$80$	81.3741	+	81.3741i	1.01718	+	1.01718i
$81$	46.7621	+	66.1385i	0.577310	+	0.816525i
$82$	1.69190	−	1.69190i	0.0206330	−	0.0206330i
$83$	64.2751			0.774399			0.387200	−	0.921996i	$-0.373442\pi$
$83$	64.2751			0.774399			0.387200	+	0.921996i	$0.373442\pi$
$84$	34.4407	−	20.9529i	0.410008	−	0.249440i
$85$	17.6128	+	125.141i	0.207210	+	1.47225i
$86$			0.511620i			0.00594907i
$87$	−42.5846	+	25.9075i	−0.489478	+	0.297787i
$88$	−19.0181	+	19.0181i	−0.216115	+	0.216115i
$89$			142.221i			1.59799i	0.601337	+	0.798996i	$0.294635\pi$
$89$			142.221i			1.59799i	−0.601337	+	0.798996i	$0.705365\pi$
$90$	−4.22302	−	13.2879i	−0.0469224	−	0.147643i
$91$	−19.5046	−	19.5046i	−0.214337	−	0.214337i
$92$	22.7205	−	22.7205i	0.246962	−	0.246962i
$93$	11.7641	+	19.3368i	0.126495	+	0.207923i
$94$		−	13.4313i		−	0.142886i
$95$	126.171	−	126.171i	1.32811	−	1.32811i
$96$	−6.99708	+	28.7367i	−0.0728862	+	0.299341i
$97$	48.5370	−	48.5370i	0.500381	−	0.500381i	−0.411175	−	0.911556i	$-0.634881\pi$
$97$	48.5370	−	48.5370i	0.500381	−	0.500381i	0.911556	+	0.411175i	$0.134881\pi$
$98$		−	7.80767i		−	0.0796701i
$99$	−139.126	+	44.2156i	−1.40531	+	0.446622i
$100$		−	119.731i		−	1.19731i
$101$			41.2075i			0.407995i	0.978971	+	0.203997i	$0.0653934\pi$
$101$			41.2075i			0.407995i	−0.978971	+	0.203997i	$0.934607\pi$
$102$	−8.22152	+	6.73566i	−0.0806032	+	0.0660359i
$103$	−42.8144			−0.415674			−0.207837	−	0.978163i	$-0.566642\pi$
$103$	−42.8144			−0.415674			−0.207837	+	0.978163i	$0.566642\pi$
$104$	13.4668			0.129488
$105$	−73.5929	−	17.9191i	−0.700885	−	0.170658i
$106$	−2.05141			−0.0193530
$107$	49.4125	+	49.4125i	0.461799	+	0.461799i	0.899245	−	0.437446i	$-0.144117\pi$
$107$	49.4125	+	49.4125i	0.461799	+	0.461799i	−0.437446	+	0.899245i	$0.644117\pi$
$108$	−70.1608	+	80.5578i	−0.649637	+	0.745905i
$109$	99.6210	+	99.6210i	0.913954	+	0.913954i	0.996581	−	0.0826264i	$-0.0263308\pi$
$109$	99.6210	+	99.6210i	0.913954	+	0.913954i	−0.0826264	+	0.996581i	$0.526331\pi$
$110$	25.1285			0.228441
$111$	−94.2755	−	154.962i	−0.849329	−	1.39606i
$112$	37.1781	+	37.1781i	0.331948	+	0.331948i
$113$	42.2935	−	42.2935i	0.374279	−	0.374279i	−0.494754	−	0.869033i	$-0.664742\pi$
$113$	42.2935	−	42.2935i	0.374279	−	0.374279i	0.869033	+	0.494754i	$0.164742\pi$
$114$	14.5806	+	3.55022i	0.127900	+	0.0311423i
$115$	−60.3704			−0.524960
$116$	−46.4852	−	46.4852i	−0.400734	−	0.400734i
$117$	64.9124	+	33.6032i	0.554806	+	0.287206i
$118$	−15.3983			−0.130494
$119$	8.04693	+	57.1743i	0.0676212	+	0.480456i
$120$	31.5918	−	19.2197i	0.263265	−	0.160165i
$121$		−	142.099i		−	1.17437i
$122$	−11.5391	−	11.5391i	−0.0945831	−	0.0945831i
$123$	17.9023	+	29.4263i	0.145547	+	0.239238i
$124$	−21.1080	+	21.1080i	−0.170226	+	0.170226i
$125$	−27.6554	+	27.6554i	−0.221243	+	0.221243i
$126$	−1.92941	−	6.07095i	−0.0153128	−	0.0481822i
$127$			73.4454i			0.578310i	0.957282	+	0.289155i	$0.0933743\pi$
$127$			73.4454i			0.578310i	−0.957282	+	0.289155i	$0.906626\pi$
$128$	−51.9116			−0.405559
$129$	−7.15591	−	1.74239i	−0.0554722	−	0.0135069i
$130$	−8.89680	−	8.89680i	−0.0684369	−	0.0684369i
$131$	−135.680	−	135.680i	−1.03573	−	1.03573i	−0.999338	−	0.0363881i	$-0.988415\pi$
$131$	−135.680	−	135.680i	−1.03573	−	1.03573i	−0.0363881	−	0.999338i	$-0.511585\pi$
$132$	−100.067	−	164.483i	−0.758087	−	1.24608i
$133$	57.6448	−	57.6448i	0.433420	−	0.433420i
$134$	5.66840			0.0423015
$135$	200.236	−	13.8128i	1.48323	−	0.102317i
$136$	−22.5157	−	16.9598i	−0.165557	−	0.124704i
$137$		−	187.183i		−	1.36630i	−0.730279	−	0.683149i	$-0.760610\pi$
$137$		−	187.183i		−	1.36630i	0.730279	−	0.683149i	$-0.239390\pi$
$138$	−2.63891	−	4.33763i	−0.0191226	−	0.0314321i
$139$	−10.4696	+	10.4696i	−0.0753212	+	0.0753212i	−0.743764	−	0.668443i	$-0.766961\pi$
$139$	−10.4696	+	10.4696i	−0.0753212	+	0.0753212i	0.668443	+	0.743764i	$0.266961\pi$
$140$		−	99.8942i		−	0.713530i
$141$	187.860	+	45.7419i	1.33234	+	0.324411i
$142$	1.40014	+	1.40014i	0.00986017	+	0.00986017i
$143$	−93.1507	+	93.1507i	−0.651403	+	0.651403i
$144$	−123.731	−	64.0516i	−0.859240	−	0.444803i
$145$			123.515i			0.851830i
$146$	−0.333833	+	0.333833i	−0.00228653	+	0.00228653i
$147$	109.204	+	26.5900i	0.742884	+	0.180884i
$148$	169.156	−	169.156i	1.14295	−	1.14295i
$149$			235.010i			1.57725i	0.614875	+	0.788624i	$0.289206\pi$
$149$			235.010i			1.57725i	−0.614875	+	0.788624i	$0.710794\pi$
$150$	−18.3822	−	4.47587i	−0.122548	−	0.0298391i
$151$			158.973i			1.05280i	0.850236	+	0.526402i	$0.176459\pi$
$151$			158.973i			1.05280i	−0.850236	+	0.526402i	$0.823541\pi$
$152$			39.8004i			0.261844i
$153$	−66.2107	−	137.932i	−0.432749	−	0.901514i
$154$	11.4807			0.0745500
$155$	56.0859			0.361844
$156$	−22.8063	+	93.6644i	−0.146194	+	0.600413i
$157$	−96.4573			−0.614377			−0.307189	−	0.951649i	$-0.599388\pi$
$157$	−96.4573			−0.614377			−0.307189	+	0.951649i	$0.599388\pi$
$158$	−13.5233	−	13.5233i	−0.0855903	−	0.0855903i
$159$	6.98635	−	28.6927i	0.0439393	−	0.180457i
$160$	51.8224	+	51.8224i	0.323890	+	0.323890i
$161$	−27.5820			−0.171317
$162$	9.74521	+	13.7833i	0.0601556	+	0.0850818i
$163$	−146.948	−	146.948i	−0.901524	−	0.901524i	0.0940437	−	0.995568i	$-0.470021\pi$
$163$	−146.948	−	146.948i	−0.901524	−	0.901524i	−0.995568	+	0.0940437i	$0.970021\pi$
$164$	−32.1216	+	32.1216i	−0.195864	+	0.195864i
$165$	−85.5783	+	351.467i	−0.518657	+	2.13010i
$166$	13.3949			0.0806923
$167$	180.063	+	180.063i	1.07822	+	1.07822i	0.996669	+	0.0815525i	$0.0259878\pi$
$167$	180.063	+	180.063i	1.07822	+	1.07822i	0.0815525	+	0.996669i	$0.474012\pi$
$168$	14.4336	−	8.78110i	0.0859145	−	0.0522685i
$169$	−103.040			−0.609702
$170$	3.67051	+	26.0794i	0.0215912	+	0.153408i
$171$	−99.3122	+	191.845i	−0.580773	+	1.12190i
$172$		−	9.71336i		−	0.0564730i
$173$	−58.9172	−	58.9172i	−0.340562	−	0.340562i	0.516017	−	0.856579i	$-0.327414\pi$
$173$	−58.9172	−	58.9172i	−0.340562	−	0.340562i	−0.856579	+	0.516017i	$0.827414\pi$
$174$	−8.87461	+	5.39911i	−0.0510035	+	0.0310294i
$175$	−72.6746	+	72.6746i	−0.415283	+	0.415283i
$176$	177.556	−	177.556i	1.00884	−	1.00884i
$177$	52.4407	−	215.372i	0.296275	−	1.21679i
$178$			29.6389i			0.166511i
$179$	98.2385			0.548819			0.274409	−	0.961613i	$-0.411518\pi$
$179$	98.2385			0.548819			0.274409	+	0.961613i	$0.411518\pi$
$180$	80.1760	+	252.277i	0.445422	+	1.40154i
$181$	−36.6158	−	36.6158i	−0.202297	−	0.202297i	0.598686	−	0.800984i	$-0.295690\pi$
$181$	−36.6158	−	36.6158i	−0.202297	−	0.202297i	−0.800984	+	0.598686i	$0.795690\pi$
$182$	−4.06476	−	4.06476i	−0.0223338	−	0.0223338i
$183$	200.693	−	122.097i	1.09668	−	0.667198i
$184$	9.52186	−	9.52186i	0.0517492	−	0.0517492i
$185$	−449.463			−2.42953
$186$	2.45163	+	4.02979i	0.0131808	+	0.0216655i
$187$	273.054	−	38.4307i	1.46018	−	0.205512i
$188$			254.999i			1.35638i
$189$	91.4838	−	6.31079i	0.484041	−	0.0333904i
$190$	26.2940	−	26.2940i	0.138389	−	0.138389i
$191$		−	162.394i		−	0.850228i	−0.905140	−	0.425114i	$-0.860234\pi$
$191$		−	162.394i		−	0.850228i	0.905140	−	0.425114i	$-0.139766\pi$
$192$	42.4904	−	174.506i	0.221304	−	0.908888i
$193$	−30.4810	−	30.4810i	−0.157933	−	0.157933i	0.623717	−	0.781650i	$-0.285622\pi$
$193$	−30.4810	−	30.4810i	−0.157933	−	0.157933i	−0.781650	+	0.623717i	$0.785622\pi$
$194$	10.1151	−	10.1151i	0.0521397	−	0.0521397i
$195$	154.737	−	94.1382i	0.793521	−	0.482760i
$196$			148.232i			0.756287i
$197$	−91.4122	+	91.4122i	−0.464021	+	0.464021i	−0.899971	−	0.435950i	$-0.856412\pi$
$197$	−91.4122	+	91.4122i	−0.464021	+	0.464021i	0.435950	+	0.899971i	$0.356412\pi$
$198$	−28.9938	+	9.21451i	−0.146433	+	0.0465379i
$199$	−33.8948	+	33.8948i	−0.170326	+	0.170326i	−0.787122	−	0.616797i	$-0.788430\pi$
$199$	−33.8948	+	33.8948i	−0.170326	+	0.170326i	0.616797	+	0.787122i	$0.288430\pi$
$200$		−	50.1775i		−	0.250888i
$201$	−19.3045	+	79.2826i	−0.0960421	+	0.394441i
$202$			8.58763i			0.0425130i
$203$			56.4316i			0.277988i
$204$	156.090	−	127.880i	0.765145	−	0.626862i
$205$	85.3501			0.416342
$206$	−8.92251			−0.0433132
$207$	69.6565	−	22.1375i	0.336505	−	0.106945i
$208$	−125.728			−0.604462
$209$	−275.301	−	275.301i	−1.31723	−	1.31723i
$210$	−15.3367	−	3.73433i	−0.0730321	−	0.0177825i
$211$	46.7481	+	46.7481i	0.221555	+	0.221555i	0.809153	−	0.587598i	$-0.199926\pi$
$211$	46.7481	+	46.7481i	0.221555	+	0.221555i	−0.587598	+	0.809153i	$0.699926\pi$
$212$	38.9471			0.183713
$213$	−24.3519	+	14.8151i	−0.114328	+	0.0695545i
$214$	10.2975	+	10.2975i	0.0481194	+	0.0481194i
$215$	−12.9046	+	12.9046i	−0.0600216	+	0.0600216i
$216$	−29.4035	+	33.7607i	−0.136127	+	0.156300i
$217$	25.6245			0.118085
$218$	20.7610	+	20.7610i	0.0952339	+	0.0952339i
$219$	−3.53233	−	5.80615i	−0.0161294	−	0.0265121i
$220$	−477.077			−2.16853
$221$	−110.282	−	83.0689i	−0.499013	−	0.375878i
$222$	−19.6470	−	32.2941i	−0.0884999	−	0.145469i
$223$			174.588i			0.782907i	0.920198	+	0.391454i	$0.128028\pi$
$223$			174.588i			0.782907i	−0.920198	+	0.391454i	$0.871972\pi$
$224$	23.6766	+	23.6766i	0.105699	+	0.105699i
$225$	125.206	−	241.865i	0.556471	−	1.07495i
$226$	8.81395	−	8.81395i	0.0389998	−	0.0389998i
$227$	−134.151	+	134.151i	−0.590974	+	0.590974i	−0.937895	−	0.346921i	$-0.887227\pi$
$227$	−134.151	+	134.151i	−0.590974	+	0.590974i	0.346921	+	0.937895i	$0.387227\pi$
$228$	−276.820	−	67.4027i	−1.21412	−	0.295626i
$229$		−	304.733i		−	1.33071i	−0.746527	−	0.665355i	$-0.768280\pi$
$229$		−	304.733i		−	1.33071i	0.746527	−	0.665355i	$-0.231720\pi$
$230$	−12.5812			−0.0547007
$231$	−39.0990	+	160.578i	−0.169260	+	0.695142i
$232$	−19.4813	−	19.4813i	−0.0839713	−	0.0839713i
$233$	−33.4180	−	33.4180i	−0.143425	−	0.143425i	0.631749	−	0.775173i	$-0.282338\pi$
$233$	−33.4180	−	33.4180i	−0.143425	−	0.143425i	−0.775173	+	0.631749i	$0.782338\pi$
$234$	13.5277	+	7.00289i	0.0578108	+	0.0299269i
$235$	338.778	−	338.778i	1.44161	−	1.44161i
$236$	292.343			1.23874
$237$	235.202	−	143.092i	0.992414	−	0.603762i
$238$	1.67698	+	11.9151i	0.00704612	+	0.0500635i
$239$		−	107.386i		−	0.449314i	−0.974438	−	0.224657i	$-0.927874\pi$
$239$		−	107.386i		−	0.449314i	0.974438	−	0.224657i	$-0.0721262\pi$
$240$	−294.946	+	179.439i	−1.22894	+	0.747661i
$241$	311.851	−	311.851i	1.29399	−	1.29399i	0.361691	−	0.932298i	$-0.382200\pi$
$241$	311.851	−	311.851i	1.29399	−	1.29399i	0.932298	−	0.361691i	$-0.117800\pi$
$242$		−	29.6134i		−	0.122369i
$243$	−225.972	+	89.3633i	−0.929925	+	0.367750i
$244$	219.076	+	219.076i	0.897853	+	0.897853i
$245$	196.933	−	196.933i	0.803810	−	0.803810i
$246$	3.73083	+	6.13243i	0.0151660	+	0.0249286i
$247$			194.942i			0.789239i
$248$	−8.84609	+	8.84609i	−0.0356697	+	0.0356697i
$249$	−45.6181	+	187.352i	−0.183205	+	0.752416i
$250$	−5.76338	+	5.76338i	−0.0230535	+	0.0230535i
$251$		−	68.1607i		−	0.271557i	−0.990739	−	0.135778i	$-0.956646\pi$
$251$		−	68.1607i		−	0.271557i	0.990739	−	0.135778i	$-0.0433535\pi$
$252$	36.6308	+	115.260i	0.145360	+	0.457381i
$253$			131.727i			0.520658i
$254$			15.3060i			0.0602598i
$255$	−377.266	−	37.4780i	−1.47948	−	0.146973i
$256$	228.655			0.893183
$257$	96.8926			0.377014			0.188507	−	0.982072i	$-0.439635\pi$
$257$	96.8926			0.377014			0.188507	+	0.982072i	$0.439635\pi$
$258$	−1.49129	−	0.363113i	−0.00578019	−	0.00140741i
$259$	−205.350			−0.792859
$260$	168.910	+	168.910i	0.649654	+	0.649654i
$261$	−45.2925	−	142.514i	−0.173535	−	0.546033i
$262$	−28.2757	−	28.2757i	−0.107922	−	0.107922i
$263$	313.842			1.19332			0.596658	−	0.802496i	$-0.296495\pi$
$263$	313.842			1.19332			0.596658	+	0.802496i	$0.296495\pi$
$264$	−41.9370	−	68.9325i	−0.158852	−	0.261108i
$265$	−51.7430	−	51.7430i	−0.195257	−	0.195257i
$266$	12.0132	−	12.0132i	0.0451623	−	0.0451623i
$267$	−414.552	−	100.939i	−1.55263	−	0.378048i
$268$	−107.617			−0.401557
$269$	77.5856	+	77.5856i	0.288422	+	0.288422i	0.836456	−	0.548034i	$-0.184623\pi$
$269$	77.5856	+	77.5856i	0.288422	+	0.288422i	−0.548034	+	0.836456i	$0.684623\pi$
$270$	41.7292	−	2.87859i	0.154553	−	0.0106614i
$271$	−428.668			−1.58180			−0.790900	−	0.611946i	$-0.790387\pi$
$271$	−428.668			−1.58180			−0.790900	+	0.611946i	$0.790387\pi$
$272$	210.210	+	158.339i	0.772832	+	0.582129i
$273$	70.6959	−	43.0098i	0.258959	−	0.157545i
$274$		−	39.0089i		−	0.142368i
$275$	347.081	+	347.081i	1.26211	+	1.26211i
$276$	50.1011	+	82.3520i	0.181526	+	0.298377i
$277$	−253.924	+	253.924i	−0.916694	+	0.916694i	−0.996787	−	0.0800938i	$-0.974478\pi$
$277$	−253.924	+	253.924i	−0.916694	+	0.916694i	0.0800938	+	0.996787i	$0.474478\pi$
$278$	−2.18187	+	2.18187i	−0.00784846	+	0.00784846i
$279$	−64.7130	+	20.5664i	−0.231946	+	0.0737148i
$280$		−	41.8644i		−	0.149516i
$281$	−291.576			−1.03764			−0.518818	−	0.854885i	$-0.673628\pi$
$281$	−291.576			−1.03764			−0.518818	+	0.854885i	$0.673628\pi$
$282$	39.1500	+	9.53260i	0.138830	+	0.0338035i
$283$	317.214	+	317.214i	1.12090	+	1.12090i	0.991607	+	0.129291i	$0.0412702\pi$
$283$	317.214	+	317.214i	1.12090	+	1.12090i	0.129291	+	0.991607i	$0.458730\pi$
$284$	−26.5824	−	26.5824i	−0.0936000	−	0.0936000i
$285$	278.220	+	457.315i	0.976211	+	1.60461i
$286$	−19.4126	+	19.4126i	−0.0678761	+	0.0678761i
$287$	38.9947			0.135870
$288$	−78.7968	−	40.7907i	−0.273600	−	0.141634i
$289$	79.7697	+	277.773i	0.276020	+	0.961152i
$290$			25.7406i			0.0887606i
$291$	107.029	+	175.926i	0.367798	+	0.604556i
$292$	6.33798	−	6.33798i	0.0217054	−	0.0217054i
$293$			322.630i			1.10113i	0.834794	+	0.550563i	$0.185587\pi$
$293$			322.630i			1.10113i	−0.834794	+	0.550563i	$0.814413\pi$
$294$	22.7581	+	5.54135i	0.0774084	+	0.0188481i
$295$	−388.391	−	388.391i	−1.31658	−	1.31658i
$296$	70.8912	−	70.8912i	0.239497	−	0.239497i
$297$	−30.1392	−	436.910i	−0.101479	−	1.47108i
$298$			48.9760i			0.164349i
$299$	46.6380	−	46.6380i	0.155980	−	0.155980i
$300$	348.995	+	84.9766i	1.16332	+	0.283255i
$301$	−5.89586	+	5.89586i	−0.0195876	+	0.0195876i
$302$			33.1300i			0.109702i
$303$	−120.113	−	29.2463i	−0.396413	−	0.0965223i
$304$		−	371.582i		−	1.22231i
$305$		−	582.105i		−	1.90854i
$306$	−13.7983	−	28.7449i	−0.0450924	−	0.0939377i
$307$	−274.964			−0.895649			−0.447825	−	0.894121i	$-0.647801\pi$
$307$	−274.964			−0.895649			−0.447825	+	0.894121i	$0.647801\pi$
$308$	−217.967			−0.707684
$309$	30.3868	−	124.797i	0.0983390	−	0.403874i
$310$	11.6883			0.0377041
$311$	192.999	+	192.999i	0.620576	+	0.620576i	0.945679	−	0.325103i	$-0.105399\pi$
$311$	192.999	+	192.999i	0.620576	+	0.620576i	−0.325103	+	0.945679i	$0.605399\pi$
$312$	−9.55781	+	39.2535i	−0.0306340	+	0.125813i
$313$	187.331	+	187.331i	0.598501	+	0.598501i	0.939913	−	0.341413i	$-0.110905\pi$
$313$	187.331	+	187.331i	0.598501	+	0.598501i	−0.341413	+	0.939913i	$0.610905\pi$
$314$	−20.1017			−0.0640180
$315$	104.462	−	201.794i	0.331627	−	0.640615i
$316$	256.746	+	256.746i	0.812487	+	0.812487i
$317$	−304.768	+	304.768i	−0.961412	+	0.961412i	−0.999283	−	0.0378706i	$-0.987943\pi$
$317$	−304.768	+	304.768i	−0.961412	+	0.961412i	0.0378706	+	0.999283i	$0.487943\pi$
$318$	1.45595	−	5.97954i	0.00457847	−	0.0188036i
$319$	269.507			0.844850
$320$	−314.697	−	314.697i	−0.983427	−	0.983427i
$321$	−179.099	+	108.960i	−0.557940	+	0.339438i
$322$	−5.74807			−0.0178512
$323$	245.506	−	325.932i	0.760079	−	1.00908i
$324$	−185.017	−	261.682i	−0.571042	−	0.807660i
$325$		−	245.769i		−	0.756213i
$326$	−30.6240	−	30.6240i	−0.0939387	−	0.0939387i
$327$	−361.083	+	219.675i	−1.10423	+	0.671789i
$328$	−13.4618	+	13.4618i	−0.0410419	+	0.0410419i
$329$	154.781	−	154.781i	0.470458	−	0.470458i
$330$	−17.8345	+	73.2455i	−0.0540439	+	0.221956i
$331$			311.214i			0.940223i	0.882607	+	0.470111i	$0.155786\pi$
$331$			311.214i			0.940223i	−0.882607	+	0.470111i	$0.844214\pi$
$332$	−254.309			−0.765991
$333$	518.600	−	164.816i	1.55736	−	0.494944i
$334$	37.5251	+	37.5251i	0.112351	+	0.112351i
$335$	142.975	+	142.975i	0.426790	+	0.426790i
$336$	−134.755	+	81.9818i	−0.401056	+	0.243993i
$337$	213.957	−	213.957i	0.634887	−	0.634887i	−0.314402	−	0.949290i	$-0.601804\pi$
$337$	213.957	−	213.957i	0.634887	−	0.634887i	0.949290	+	0.314402i	$0.101804\pi$
$338$	−21.4734			−0.0635309
$339$	93.2616	+	153.296i	0.275108	+	0.452200i
$340$	−69.6863	−	495.129i	−0.204960	−	1.45626i
$341$		−	122.378i		−	0.358879i
$342$	−20.6966	+	39.9804i	−0.0605165	+	0.116902i
$343$	207.652	−	207.652i	0.605399	−	0.605399i
$344$		−	4.07074i		−	0.0118336i
$345$	42.8468	−	175.970i	0.124194	−	0.510058i
$346$	−12.2783	−	12.2783i	−0.0354865	−	0.0354865i
$347$	−435.384	+	435.384i	−1.25471	+	1.25471i	−0.301124	+	0.953585i	$0.597362\pi$
$347$	−435.384	+	435.384i	−1.25471	+	1.25471i	−0.953585	+	0.301124i	$0.902638\pi$
$348$	168.489	−	102.505i	0.484163	−	0.294554i
$349$			120.847i			0.346267i	0.984898	+	0.173133i	$0.0553892\pi$
$349$			120.847i			0.346267i	−0.984898	+	0.173133i	$0.944611\pi$
$350$	−15.1454	+	15.1454i	−0.0432725	+	0.0432725i
$351$	−144.018	+	165.360i	−0.410308	+	0.471111i
$352$	113.075	−	113.075i	0.321236	−	0.321236i
$353$		−	25.6098i		−	0.0725491i	−0.999342	−	0.0362745i	$-0.988451\pi$
$353$		−	25.6098i		−	0.0725491i	0.999342	−	0.0362745i	$-0.0115491\pi$
$354$	10.9286	−	44.8834i	0.0308718	−	0.126789i
$355$			70.6319i			0.198963i
$356$		−	562.708i		−	1.58064i
$357$	−172.365	−	17.1229i	−0.482815	−	0.0479634i
$358$	20.4729			0.0571868
$359$	−326.176			−0.908568			−0.454284	−	0.890857i	$-0.650105\pi$
$359$	−326.176			−0.908568			−0.454284	+	0.890857i	$0.650105\pi$
$360$	33.6007	+	105.726i	0.0933354	+	0.293683i
$361$	−215.140			−0.595955
$362$	−7.63072	−	7.63072i	−0.0210793	−	0.0210793i
$363$	414.195	+	100.852i	1.14103	+	0.277829i
$364$	77.1714	+	77.1714i	0.212009	+	0.212009i
$365$	−16.8406			−0.0461386
$366$	41.8244	−	25.4450i	0.114274	−	0.0695219i
$367$	−291.432	−	291.432i	−0.794092	−	0.794092i	0.188065	−	0.982157i	$-0.439778\pi$
$367$	−291.432	−	291.432i	−0.794092	−	0.794092i	−0.982157	+	0.188065i	$0.939778\pi$
$368$	−88.8976	+	88.8976i	−0.241569	+	0.241569i
$369$	−98.4786	+	31.2975i	−0.266880	+	0.0848170i
$370$	−93.6681			−0.253157
$371$	−23.6403	−	23.6403i	−0.0637205	−	0.0637205i
$372$	−46.5454	−	76.5074i	−0.125122	−	0.205665i
$373$	−151.514			−0.406204			−0.203102	−	0.979158i	$-0.565102\pi$
$373$	−151.514			−0.406204			−0.203102	+	0.979158i	$0.565102\pi$
$374$	56.9044	−	8.00894i	0.152151	−	0.0214143i
$375$	−60.9831	−	100.239i	−0.162622	−	0.267304i
$376$			106.867i			0.284220i
$377$	−95.4195	−	95.4195i	−0.253102	−	0.253102i
$378$	19.0652	−	1.31517i	0.0504370	−	0.00347928i
$379$	19.0727	−	19.0727i	0.0503238	−	0.0503238i	−0.681497	−	0.731821i	$-0.738671\pi$
$379$	19.0727	−	19.0727i	0.0503238	−	0.0503238i	0.731821	+	0.681497i	$0.238671\pi$
$380$	−499.204	+	499.204i	−1.31369	+	1.31369i
$381$	−214.081	−	52.1265i	−0.561893	−	0.136815i
$382$		−	33.8428i		−	0.0885937i
$383$	375.569			0.980597			0.490299	−	0.871555i	$-0.336888\pi$
$383$	375.569			0.980597			0.490299	+	0.871555i	$0.336888\pi$
$384$	36.8433	−	151.314i	0.0959461	−	0.394047i
$385$	289.578	+	289.578i	0.752152	+	0.752152i
$386$	−6.35223	−	6.35223i	−0.0164565	−	0.0164565i
$387$	10.1576	−	19.6217i	0.0262469	−	0.0507021i
$388$	−192.040	+	192.040i	−0.494949	+	0.494949i
$389$	699.064			1.79708			0.898540	−	0.438891i	$-0.144629\pi$
$389$	699.064			1.79708			0.898540	+	0.438891i	$0.144629\pi$
$390$	32.2471	−	19.6184i	0.0826848	−	0.0503035i
$391$	−136.711	+	19.2412i	−0.349644	+	0.0492103i
$392$			62.1222i			0.158475i
$393$	491.782	−	299.189i	1.25135	−	0.761295i
$394$	−19.0503	+	19.0503i	−0.0483509	+	0.0483509i
$395$		−	682.197i		−	1.72708i
$396$	550.461	−	174.942i	1.39005	−	0.441773i
$397$	77.1209	+	77.1209i	0.194259	+	0.194259i	0.797534	−	0.603274i	$-0.206138\pi$
$397$	77.1209	+	77.1209i	0.194259	+	0.194259i	−0.603274	+	0.797534i	$0.706138\pi$
$398$	−7.06367	+	7.06367i	−0.0177479	+	0.0177479i
$399$	127.113	+	208.938i	0.318579	+	0.523654i
$400$			468.465i			1.17116i
$401$	−414.092	+	414.092i	−1.03265	+	1.03265i	−0.0332009	+	0.999449i	$0.510570\pi$
$401$	−414.092	+	414.092i	−1.03265	+	1.03265i	−0.999449	+	0.0332009i	$0.989430\pi$
$402$	−4.02304	+	16.5225i	−0.0100076	+	0.0411007i
$403$	−43.3281	+	43.3281i	−0.107514	+	0.107514i
$404$		−	163.040i		−	0.403565i
$405$	−101.852	+	593.460i	−0.251486	+	1.46533i
$406$			11.7603i			0.0289663i
$407$			980.717i			2.40962i
$408$	65.4151	−	53.5927i	0.160331	−	0.131355i
$409$	−187.440			−0.458289			−0.229144	−	0.973392i	$-0.573593\pi$
$409$	−187.440			−0.458289			−0.229144	+	0.973392i	$0.573593\pi$
$410$	17.7869			0.0433828
$411$	545.608	+	132.850i	1.32751	+	0.323235i
$412$	169.398			0.411161
$413$	−177.448	−	177.448i	−0.429656	−	0.429656i
$414$	14.5164	−	4.61346i	0.0350638	−	0.0111436i
$415$	337.861	+	337.861i	0.814123	+	0.814123i
$416$	−80.0689			−0.192473
$417$	−23.0867	−	37.9480i	−0.0553638	−	0.0910023i
$418$	−57.3727	−	57.3727i	−0.137255	−	0.137255i
$419$	136.575	−	136.575i	0.325955	−	0.325955i	−0.525091	−	0.851046i	$-0.675969\pi$
$419$	136.575	−	136.575i	0.325955	−	0.325955i	0.851046	+	0.525091i	$0.175969\pi$
$420$	291.176	+	70.8981i	0.693275	+	0.168805i
$421$	−43.5185			−0.103369			−0.0516846	−	0.998663i	$-0.516459\pi$
$421$	−43.5185			−0.103369			−0.0516846	+	0.998663i	$0.516459\pi$
$422$	9.74228	+	9.74228i	0.0230860	+	0.0230860i
$423$	−266.660	+	515.117i	−0.630403	+	1.21777i
$424$	16.3222			0.0384958
$425$	−309.516	+	410.912i	−0.728273	+	0.966852i
$426$	−5.07492	+	3.08747i	−0.0119130	+	0.00724757i
$427$		−	265.952i		−	0.622838i
$428$	−195.504	−	195.504i	−0.456785	−	0.456785i
$429$	−205.407	−	337.631i	−0.478804	−	0.787019i
$430$	−2.68932	+	2.68932i	−0.00625424	+	0.00625424i
$431$	383.047	−	383.047i	0.888741	−	0.888741i	−0.105661	−	0.994402i	$-0.533696\pi$
$431$	383.047	−	383.047i	0.888741	−	0.888741i	0.994402	+	0.105661i	$0.0336959\pi$
$432$	274.516	−	315.195i	0.635453	−	0.729619i
$433$		−	546.173i		−	1.26137i	−0.776039	−	0.630685i	$-0.782774\pi$
$433$		−	546.173i		−	1.26137i	0.776039	−	0.630685i	$-0.217226\pi$
$434$	5.34013			0.0123045
$435$	−360.027	−	87.6628i	−0.827649	−	0.201524i
$436$	−394.157	−	394.157i	−0.904031	−	0.904031i
$437$	137.836	+	137.836i	0.315414	+	0.315414i
$438$	−0.736137	−	1.21000i	−0.00168068	−	0.00276256i
$439$	176.803	−	176.803i	0.402740	−	0.402740i	−0.476458	−	0.879197i	$-0.658079\pi$
$439$	176.803	−	176.803i	0.402740	−	0.402740i	0.879197	+	0.476458i	$0.158079\pi$
$440$	−199.937			−0.454402
$441$	−155.011	+	299.440i	−0.351499	+	0.679003i
$442$	−22.9827	−	17.3115i	−0.0519971	−	0.0391664i
$443$			44.3558i			0.100126i	0.998746	+	0.0500630i	$0.0159422\pi$
$443$			44.3558i			0.100126i	−0.998746	+	0.0500630i	$0.984058\pi$
$444$	373.008	+	613.119i	0.840107	+	1.38090i
$445$	−747.583	+	747.583i	−1.67996	+	1.67996i
$446$			36.3842i			0.0815788i
$447$	−685.016	−	166.794i	−1.53247	−	0.373141i
$448$	−143.778	−	143.778i	−0.320934	−	0.320934i
$449$	104.094	−	104.094i	0.231835	−	0.231835i	−0.581623	−	0.813458i	$-0.697582\pi$
$449$	104.094	−	104.094i	0.231835	−	0.231835i	0.813458	+	0.581623i	$0.197582\pi$
$450$	26.0929	−	50.4045i	0.0579842	−	0.112010i
$451$		−	186.232i		−	0.412930i
$452$	−167.337	+	167.337i	−0.370215	+	0.370215i
$453$	−463.382	−	112.828i	−1.02292	−	0.249069i
$454$	−27.9570	+	27.9570i	−0.0615794	+	0.0615794i
$455$		−	205.052i		−	0.450663i
$456$	−116.012	−	28.2476i	−0.254411	−	0.0619464i
$457$		−	52.3160i		−	0.114477i	−0.998361	−	0.0572385i	$-0.981770\pi$
$457$		−	52.3160i		−	0.114477i	0.998361	−	0.0572385i	$-0.0182295\pi$
$458$		−	63.5062i		−	0.138660i
$459$	449.040	−	95.0989i	0.978301	−	0.207187i
$460$	238.860			0.519260
$461$	291.344			0.631983			0.315991	−	0.948762i	$-0.397663\pi$
$461$	291.344			0.631983			0.315991	+	0.948762i	$0.397663\pi$
$462$	−8.14821	+	33.4644i	−0.0176368	+	0.0724337i
$463$	711.561			1.53685			0.768425	−	0.639940i	$-0.221041\pi$
$463$	711.561			1.53685			0.768425	+	0.639940i	$0.221041\pi$
$464$	181.881	+	181.881i	0.391985	+	0.391985i
$465$	−39.8059	+	163.481i	−0.0856041	+	0.351573i
$466$	−6.96430	−	6.96430i	−0.0149449	−	0.0149449i
$467$	−378.114			−0.809666			−0.404833	−	0.914391i	$-0.632670\pi$
$467$	−378.114			−0.809666			−0.404833	+	0.914391i	$0.632670\pi$
$468$	−256.830	−	132.953i	−0.548783	−	0.284088i
$469$	65.3221	+	65.3221i	0.139279	+	0.139279i
$470$	70.6012	−	70.6012i	0.150215	−	0.150215i
$471$	68.4588	−	281.157i	0.145348	−	0.596937i
$472$	122.517			0.259571
$473$	28.1576	+	28.1576i	0.0595297	+	0.0595297i
$474$	49.0160	−	29.8202i	0.103409	−	0.0629119i
$475$	726.357			1.52917
$476$	−31.8382	−	226.214i	−0.0668870	−	0.475240i
$477$	78.6760	+	40.7282i	0.164939	+	0.0853840i
$478$		−	22.3792i		−	0.0468185i
$479$	−152.051	−	152.051i	−0.317434	−	0.317434i	0.530347	−	0.847781i	$-0.322062\pi$
$479$	−152.051	−	152.051i	−0.317434	−	0.317434i	−0.847781	+	0.530347i	$0.822062\pi$
$480$	−187.834	+	114.274i	−0.391321	+	0.238071i
$481$	347.225	−	347.225i	0.721881	−	0.721881i
$482$	64.9897	−	64.9897i	0.134833	−	0.134833i
$483$	19.5758	−	80.3970i	0.0405296	−	0.166453i
$484$			562.224i			1.16162i
$485$	510.268			1.05210
$486$	−47.0924	+	18.6233i	−0.0968980	+	0.0383195i
$487$	−329.746	−	329.746i	−0.677097	−	0.677097i	0.282245	−	0.959342i	$-0.408921\pi$
$487$	−329.746	−	329.746i	−0.677097	−	0.677097i	−0.959342	+	0.282245i	$0.908921\pi$
$488$	91.8120	+	91.8120i	0.188139	+	0.188139i
$489$	532.625	−	324.037i	1.08921	−	0.662652i
$490$	41.0409	−	41.0409i	0.0837568	−	0.0837568i
$491$	−432.522			−0.880900			−0.440450	−	0.897777i	$-0.645181\pi$
$491$	−432.522			−0.880900			−0.440450	+	0.897777i	$0.645181\pi$
$492$	−70.8316	−	116.427i	−0.143967	−	0.236640i
$493$	39.3667	+	279.705i	0.0798514	+	0.567353i
$494$			40.6259i			0.0822386i
$495$	−963.731	−	498.894i	−1.94693	−	1.00787i
$496$	82.5885	−	82.5885i	0.166509	−	0.166509i
$497$			32.2702i			0.0649300i
$498$	−9.50680	+	39.0440i	−0.0190900	+	0.0784016i
$499$	29.1588	+	29.1588i	0.0584344	+	0.0584344i	0.735720	−	0.677286i	$-0.236844\pi$
$499$	29.1588	+	29.1588i	0.0584344	+	0.0584344i	−0.677286	+	0.735720i	$0.736844\pi$
$500$	109.421	−	109.421i	0.218841	−	0.218841i
$501$	−652.651	+	397.058i	−1.30270	+	0.792531i
$502$		−	14.2047i		−	0.0282962i
$503$	537.457	−	537.457i	1.06850	−	1.06850i	0.0710294	−	0.997474i	$-0.477372\pi$
$503$	537.457	−	537.457i	1.06850	−	1.06850i	0.997474	−	0.0710294i	$-0.0226284\pi$
$504$	15.3515	+	48.3040i	0.0304593	+	0.0958412i
$505$	−216.606	+	216.606i	−0.428924	+	0.428924i
$506$			27.4518i			0.0542525i
$507$	73.1305	−	300.344i	0.144242	−	0.592394i
$508$		−	290.592i		−	0.572031i
$509$		−	56.9404i		−	0.111867i	−0.998434	−	0.0559336i	$-0.982186\pi$
$509$		−	56.9404i		−	0.111867i	0.998434	−	0.0559336i	$-0.0178135\pi$
$510$	−78.6222	−	7.81041i	−0.154161	−	0.0153145i
$511$	−7.69411			−0.0150570
$512$	255.298			0.498629
$513$	−488.711	−	425.637i	−0.952654	−	0.829702i
$514$	20.1924			0.0392848
$515$	−225.053	−	225.053i	−0.436997	−	0.436997i
$516$	28.3129	+	6.89388i	0.0548699	+	0.0133602i
$517$	−739.204	−	739.204i	−1.42980	−	1.42980i
$518$	−42.7950			−0.0826158
$519$	213.550	−	129.919i	0.411463	−	0.250325i
$520$	70.7880	+	70.7880i	0.136131	+	0.136131i
$521$	526.193	−	526.193i	1.00997	−	1.00997i	0.0100166	−	0.999950i	$-0.496812\pi$
$521$	526.193	−	526.193i	1.00997	−	1.00997i	0.999950	−	0.0100166i	$-0.00318845\pi$
$522$	−9.43895	−	29.7000i	−0.0180823	−	0.0568965i
$523$	−917.253			−1.75383			−0.876915	−	0.480645i	$-0.840403\pi$
$523$	−917.253			−1.75383			−0.876915	+	0.480645i	$0.840403\pi$
$524$	536.828	+	536.828i	1.02448	+	1.02448i
$525$	−160.255	−	263.414i	−0.305248	−	0.501741i
$526$	65.4046			0.124343
$527$	127.009	−	17.8757i	0.241003	−	0.0339197i
$528$	391.530	+	643.565i	0.741534	+	1.21887i
$529$			463.048i			0.875327i
$530$	−10.7832	−	10.7832i	−0.0203457	−	0.0203457i
$531$	590.555	+	305.712i	1.11216	+	0.575730i
$532$	−228.076	+	228.076i	−0.428714	+	0.428714i
$533$	−65.9356	+	65.9356i	−0.123707	+	0.123707i
$534$	−86.3925	−	21.0356i	−0.161784	−	0.0393926i
$535$			519.471i			0.970974i
$536$	−45.1010			−0.0841437
$537$	−69.7230	+	286.349i	−0.129838	+	0.533239i
$538$	16.1688	+	16.1688i	0.0300536	+	0.0300536i
$539$	−429.703	−	429.703i	−0.797223	−	0.797223i
$540$	−792.249	+	54.6514i	−1.46713	+	0.101206i
$541$	118.414	−	118.414i	0.218879	−	0.218879i	−0.589147	−	0.808026i	$-0.700536\pi$
$541$	118.414	−	118.414i	0.218879	−	0.218879i	0.808026	+	0.589147i	$0.200536\pi$
$542$	−89.3342			−0.164823
$543$	132.716	−	80.7417i	0.244413	−	0.148696i
$544$	133.871	+	100.837i	0.246086	+	0.185362i
$545$			1047.31i			1.92167i
$546$	14.7330	−	8.96323i	0.0269835	−	0.0164162i
$547$	50.1729	−	50.1729i	0.0917238	−	0.0917238i	−0.659756	−	0.751480i	$-0.729340\pi$
$547$	50.1729	−	50.1729i	0.0917238	−	0.0917238i	0.751480	+	0.659756i	$0.229340\pi$
$548$			740.602i			1.35146i
$549$	213.455	+	671.645i	0.388807	+	1.22340i
$550$	72.3316	+	72.3316i	0.131512	+	0.131512i
$551$	282.007	−	282.007i	0.511809	−	0.511809i
$552$	20.9967	+	34.5126i	0.0380375	+	0.0625229i
$553$		−	311.682i		−	0.563619i
$554$	−52.9177	+	52.9177i	−0.0955193	+	0.0955193i
$555$	318.998	−	1310.11i	0.574772	−	2.36056i
$556$	41.4239	−	41.4239i	0.0745034	−	0.0745034i
$557$			423.368i			0.760085i	0.924969	+	0.380043i	$0.124091\pi$
$557$			423.368i			0.760085i	−0.924969	+	0.380043i	$0.875909\pi$
$558$	−13.4862	+	4.28604i	−0.0241688	+	0.00768107i
$559$		−	19.9385i		−	0.0356681i
$560$			390.852i			0.697951i
$561$	−81.7761	+	823.185i	−0.145768	+	1.46735i
$562$	−60.7643			−0.108121
$563$	−48.4445			−0.0860471			−0.0430236	−	0.999074i	$-0.513699\pi$
$563$	−48.4445			−0.0860471			−0.0430236	+	0.999074i	$0.513699\pi$
$564$	−743.281	−	180.981i	−1.31787	−	0.320888i
$565$	444.630			0.786955
$566$	66.1073	+	66.1073i	0.116797	+	0.116797i
$567$	−46.5340	+	271.140i	−0.0820706	+	0.478200i
$568$	−11.1403	−	11.1403i	−0.0196133	−	0.0196133i
$569$	732.102			1.28665			0.643323	−	0.765595i	$-0.277555\pi$
$569$	732.102			1.28665			0.643323	+	0.765595i	$0.277555\pi$
$570$	57.9810	+	95.3043i	0.101721	+	0.167201i
$571$	309.245	+	309.245i	0.541584	+	0.541584i	0.923993	−	0.382409i	$-0.124905\pi$
$571$	309.245	+	309.245i	0.541584	+	0.541584i	−0.382409	+	0.923993i	$0.624905\pi$
$572$	368.557	−	368.557i	0.644330	−	0.644330i
$573$	473.351	+	115.256i	0.826093	+	0.201145i
$574$	8.12648			0.0141576
$575$	−173.774	−	173.774i	−0.302216	−	0.302216i
$576$	478.501	+	247.706i	0.830731	+	0.430044i
$577$	791.867			1.37239			0.686193	−	0.727419i	$-0.259281\pi$
$577$	791.867			1.37239			0.686193	+	0.727419i	$0.259281\pi$
$578$	16.6240	+	57.8878i	0.0287612	+	0.100152i
$579$	110.480	−	67.2138i	0.190813	−	0.116086i
$580$		−	488.697i		−	0.842581i
$581$	154.362	+	154.362i	0.265683	+	0.265683i
$582$	22.3049	+	36.6629i	0.0383245	+	0.0629946i
$583$	−112.902	+	112.902i	−0.193657	+	0.193657i
$584$	2.65616	−	2.65616i	0.00454823	−	0.00454823i
$585$	164.576	+	517.845i	0.281327	+	0.885205i
$586$			67.2360i			0.114737i
$587$	−914.776			−1.55839			−0.779196	−	0.626780i	$-0.784372\pi$
$587$	−914.776			−1.55839			−0.779196	+	0.626780i	$0.784372\pi$
$588$	−432.073	−	105.205i	−0.734818	−	0.178920i
$589$	−128.054	−	128.054i	−0.217409	−	0.217409i
$590$	−80.9406	−	80.9406i	−0.137188	−	0.137188i
$591$	−201.574	−	331.330i	−0.341072	−	0.560626i
$592$	−661.851	+	661.851i	−1.11799	+	1.11799i
$593$	−476.612			−0.803730			−0.401865	−	0.915699i	$-0.631638\pi$
$593$	−476.612			−0.803730			−0.401865	+	0.915699i	$0.631638\pi$
$594$	−6.28100	−	91.0520i	−0.0105741	−	0.153286i
$595$	−258.237	+	342.834i	−0.434012	+	0.576192i
$596$		−	929.833i		−	1.56012i
$597$	−74.7417	−	122.854i	−0.125195	−	0.205786i
$598$	9.71935	−	9.71935i	0.0162531	−	0.0162531i
$599$			338.504i			0.565116i	0.959250	+	0.282558i	$0.0911829\pi$
$599$			338.504i			0.565116i	−0.959250	+	0.282558i	$0.908817\pi$
$600$	146.259	+	35.6126i	0.243766	+	0.0593543i
$601$	−475.300	−	475.300i	−0.790848	−	0.790848i	0.190784	−	0.981632i	$-0.438897\pi$
$601$	−475.300	−	475.300i	−0.790848	−	0.790848i	−0.981632	+	0.190784i	$0.938897\pi$
$602$	−1.22870	+	1.22870i	−0.00204102	+	0.00204102i
$603$	−217.395	−	112.539i	−0.360522	−	0.186631i
$604$		−	628.989i		−	1.04137i
$605$	746.940	−	746.940i	1.23461	−	1.23461i
$606$	−25.0315	−	6.09491i	−0.0413062	−	0.0100576i
$607$	39.2266	−	39.2266i	0.0646237	−	0.0646237i	−0.674056	−	0.738680i	$-0.735449\pi$
$607$	39.2266	−	39.2266i	0.0646237	−	0.0646237i	0.738680	+	0.674056i	$0.235449\pi$
$608$		−	236.639i		−	0.389209i
$609$	−164.489	−	40.0513i	−0.270097	−	0.0657657i
$610$		−	121.311i		−	0.198870i
$611$			523.433i			0.856683i
$612$	261.967	+	545.736i	0.428051	+	0.891726i
$613$	610.766			0.996355			0.498178	−	0.867075i	$-0.334003\pi$
$613$	610.766			0.996355			0.498178	+	0.867075i	$0.334003\pi$
$614$	−57.3025			−0.0933265
$615$	−60.5757	+	248.782i	−0.0984970	+	0.404523i
$616$	−91.3469			−0.148290
$617$	489.618	+	489.618i	0.793546	+	0.793546i	0.982069	−	0.188523i	$-0.0603699\pi$
$617$	489.618	+	489.618i	0.793546	+	0.793546i	−0.188523	+	0.982069i	$0.560370\pi$
$618$	6.33259	−	26.0077i	0.0102469	−	0.0420836i
$619$	−144.357	−	144.357i	−0.233209	−	0.233209i	0.580822	−	0.814031i	$-0.302731\pi$
$619$	−144.357	−	144.357i	−0.233209	−	0.233209i	−0.814031	+	0.580822i	$0.802731\pi$
$620$	−221.908			−0.357916
$621$	15.0899	+	218.749i	0.0242993	+	0.352253i
$622$	40.2210	+	40.2210i	0.0646639	+	0.0646639i
$623$	−341.555	+	341.555i	−0.548243	+	0.548243i
$624$	89.2333	−	366.477i	0.143002	−	0.587303i
$625$	465.790			0.745264
$626$	39.0397	+	39.0397i	0.0623637	+	0.0623637i
$627$	997.849	−	607.069i	1.59147	−	0.968212i
$628$	381.640			0.607707
$629$	−1017.83	+	143.253i	−1.61817	+	0.227747i
$630$	21.7699	−	42.0538i	0.0345555	−	0.0667520i
$631$			138.795i			0.219960i	0.993934	+	0.109980i	$0.0350787\pi$
$631$			138.795i			0.219960i	−0.993934	+	0.109980i	$0.964921\pi$
$632$	107.599	+	107.599i	0.170251	+	0.170251i
$633$	−169.442	+	103.084i	−0.267680	+	0.162851i
$634$	−63.5135	+	63.5135i	−0.100179	+	0.100179i
$635$	−386.064	+	386.064i	−0.607975	+	0.607975i
$636$	−27.6420	+	113.525i	−0.0434623	+	0.178498i
$637$			304.274i			0.477668i
$638$	56.1652			0.0880333
$639$	−25.9004	−	81.4965i	−0.0405327	−	0.127538i
$640$	−272.872	−	272.872i	−0.426363	−	0.426363i
$641$	−222.717	−	222.717i	−0.347453	−	0.347453i	0.511707	−	0.859160i	$-0.329013\pi$
$641$	−222.717	−	222.717i	−0.347453	−	0.347453i	−0.859160	+	0.511707i	$0.829013\pi$
$642$	−37.3242	+	22.7072i	−0.0581373	+	0.0353694i
$643$	−417.674	+	417.674i	−0.649570	+	0.649570i	−0.952889	−	0.303319i	$-0.901905\pi$
$643$	−417.674	+	417.674i	−0.649570	+	0.649570i	0.303319	+	0.952889i	$0.401905\pi$
$644$	109.130			0.169456
$645$	−28.4561	−	46.7737i	−0.0441180	−	0.0725174i
$646$	51.1633	−	67.9241i	0.0792001	−	0.105146i
$647$		−	790.271i		−	1.22144i	−0.791847	−	0.610720i	$-0.790880\pi$
$647$		−	790.271i		−	1.22144i	0.791847	−	0.610720i	$-0.209120\pi$
$648$	−77.5384	−	109.667i	−0.119658	−	0.169240i
$649$	−847.459	+	847.459i	−1.30579	+	1.30579i
$650$		−	51.2182i		−	0.0787973i
$651$	−18.1865	+	74.6912i	−0.0279362	+	0.114733i
$652$	581.412	+	581.412i	0.891736	+	0.891736i
$653$	263.332	−	263.332i	0.403265	−	0.403265i	−0.476117	−	0.879382i	$-0.657956\pi$
$653$	263.332	−	263.332i	0.403265	−	0.403265i	0.879382	+	0.476117i	$0.157956\pi$
$654$	−75.2497	+	45.7802i	−0.115061	+	0.0700003i
$655$		−	1426.40i		−	2.17771i
$656$	125.681	−	125.681i	0.191587	−	0.191587i
$657$	19.4310	−	6.17537i	0.0295753	−	0.00939934i
$658$	32.2562	−	32.2562i	0.0490216	−	0.0490216i
$659$			237.290i			0.360076i	0.983660	+	0.180038i	$0.0576221\pi$
$659$			237.290i			0.360076i	−0.983660	+	0.180038i	$0.942378\pi$
$660$	338.597	−	1390.60i	0.513025	−	2.10697i
$661$			808.638i			1.22336i	0.791107	+	0.611678i	$0.209505\pi$
$661$			808.638i			1.22336i	−0.791107	+	0.611678i	$0.790495\pi$
$662$			64.8568i			0.0979711i
$663$	320.403	−	262.497i	0.483262	−	0.395923i
$664$	−106.578			−0.160508
$665$	606.018			0.911305
$666$	108.076	−	34.3476i	0.162276	−	0.0515730i
$667$	−134.935			−0.202301
$668$	−712.432	−	712.432i	−1.06651	−	1.06651i
$669$	−508.897	−	123.911i	−0.760683	−	0.185218i
$670$	29.7958	+	29.7958i	0.0444714	+	0.0444714i
$671$	−1270.14			−1.89290
$672$	−85.8174	+	52.2094i	−0.127704	+	0.0776925i
$673$	−761.037	−	761.037i	−1.13081	−	1.13081i	−0.990042	−	0.140771i	$-0.955042\pi$
$673$	−761.037	−	761.037i	−1.13081	−	1.13081i	−0.140771	−	0.990042i	$-0.544958\pi$
$674$	44.5886	−	44.5886i	0.0661552	−	0.0661552i
$675$	616.133	+	536.614i	0.912790	+	0.794983i
$676$	407.684			0.603082
$677$	−674.888	−	674.888i	−0.996880	−	0.996880i	0.00311505	−	0.999995i	$-0.499008\pi$
$677$	−674.888	−	674.888i	−0.996880	−	0.996880i	−0.999995	+	0.00311505i	$0.999008\pi$
$678$	19.4357	+	31.9468i	0.0286662	+	0.0471191i
$679$	233.131			0.343344
$680$	−29.2046	−	207.502i	−0.0429480	−	0.305150i
$681$	−295.817	−	486.240i	−0.434387	−	0.714009i
$682$		−	25.5035i		−	0.0373952i
$683$	−281.976	−	281.976i	−0.412849	−	0.412849i	0.469881	−	0.882730i	$-0.344297\pi$
$683$	−281.976	−	281.976i	−0.412849	−	0.412849i	−0.882730	+	0.469881i	$0.844297\pi$
$684$	392.936	−	759.047i	0.574467	−	1.10972i
$685$	983.923	−	983.923i	1.43638	−	1.43638i
$686$	43.2746	−	43.2746i	0.0630825	−	0.0630825i
$687$	888.247	+	216.279i	1.29294	+	0.314816i
$688$			38.0051i			0.0552400i
$689$	79.9462			0.116032
$690$	8.92925	−	36.6721i	0.0129409	−	0.0531479i
$691$	−83.8802	−	83.8802i	−0.121390	−	0.121390i	0.643802	−	0.765192i	$-0.277356\pi$
$691$	−83.8802	−	83.8802i	−0.121390	−	0.121390i	−0.765192	+	0.643802i	$0.777356\pi$
$692$	233.110	+	233.110i	0.336864	+	0.336864i
$693$	−440.308	−	227.934i	−0.635366	−	0.328909i
$694$	−90.7339	+	90.7339i	−0.130740	+	0.130740i
$695$	−110.067			−0.158370
$696$	70.6115	−	42.9584i	0.101453	−	0.0617219i
$697$	193.278	−	27.2027i	0.277300	−	0.0390283i
$698$			25.1845i			0.0360810i
$699$	121.126	−	73.6902i	0.173284	−	0.105422i
$700$	287.542	−	287.542i	0.410774	−	0.410774i
$701$			439.507i			0.626972i	0.949593	+	0.313486i	$0.101497\pi$
$701$			439.507i			0.626972i	−0.949593	+	0.313486i	$0.898503\pi$
$702$	−30.0133	+	34.4609i	−0.0427540	+	0.0490896i
$703$	1026.20	+	1026.20i	1.45975	+	1.45975i
$704$	−686.660	+	686.660i	−0.975369	+	0.975369i
$705$	747.041	+	1227.92i	1.05963	+	1.74174i
$706$		−	5.33708i		−	0.00755960i
$707$	−98.9629	+	98.9629i	−0.139976	+	0.139976i
$708$	−207.485	+	852.133i	−0.293058	+	1.20358i
$709$	542.109	−	542.109i	0.764611	−	0.764611i	−0.212541	−	0.977152i	$-0.568174\pi$
$709$	542.109	−	542.109i	0.764611	−	0.764611i	0.977152	+	0.212541i	$0.0681740\pi$
$710$			14.7197i			0.0207319i
$711$	250.158	+	787.132i	0.351840	+	1.10708i
$712$		−	235.824i		−	0.331213i
$713$			61.2713i			0.0859345i
$714$	−35.9208	−	3.56842i	−0.0503093	−	0.00499778i
$715$	−979.289			−1.36964
$716$	−388.688			−0.542860
$717$	313.013	+	76.2153i	0.436559	+	0.106298i
$718$	−67.9750			−0.0946726
$719$	93.0554	+	93.0554i	0.129423	+	0.129423i	0.768851	−	0.639428i	$-0.220829\pi$
$719$	93.0554	+	93.0554i	0.129423	+	0.129423i	−0.639428	+	0.768851i	$0.720829\pi$
$720$	−313.702	−	987.074i	−0.435697	−	1.37094i
$721$	−102.822	−	102.822i	−0.142610	−	0.142610i
$722$	−44.8351			−0.0620985
$723$	687.665	+	1130.33i	0.951128	+	1.56338i
$724$	144.873	+	144.873i	0.200101	+	0.200101i
$725$	−355.535	+	355.535i	−0.490393	+	0.490393i
$726$	86.3182	+	21.0176i	0.118896	+	0.0289498i
$727$	−331.684			−0.456236			−0.228118	−	0.973634i	$-0.573257\pi$
$727$	−331.684			−0.456236			−0.228118	+	0.973634i	$0.573257\pi$
$728$	32.3415	+	32.3415i	0.0444252	+	0.0444252i
$729$	−100.100	−	722.095i	−0.137312	−	0.990528i
$730$	−3.50957			−0.00480763
$731$	−25.1101	+	33.3360i	−0.0343503	+	0.0456033i
$732$	−794.057	+	483.086i	−1.08478	+	0.659954i
$733$			288.501i			0.393589i	0.980445	+	0.196795i	$0.0630533\pi$
$733$			288.501i			0.393589i	−0.980445	+	0.196795i	$0.936947\pi$
$734$	−60.7343	−	60.7343i	−0.0827442	−	0.0827442i
$735$	434.259	+	713.799i	0.590829	+	0.971155i
$736$	−56.6137	+	56.6137i	−0.0769207	+	0.0769207i
$737$	311.967	−	311.967i	0.423292	−	0.423292i
$738$	−20.5229	+	6.52239i	−0.0278088	+	0.00883792i
$739$		−	778.144i		−	1.05297i	−0.850185	−	0.526484i	$-0.823510\pi$
$739$		−	778.144i		−	1.05297i	0.850185	−	0.526484i	$-0.176490\pi$
$740$	1778.33			2.40315
$741$	−568.224	−	138.356i	−0.766834	−	0.186716i
$742$	−4.92663	−	4.92663i	−0.00663966	−	0.00663966i
$743$	757.612	+	757.612i	1.01967	+	1.01967i	0.999803	+	0.0198633i	$0.00632311\pi$
$743$	757.612	+	757.612i	1.01967	+	1.01967i	0.0198633	+	0.999803i	$0.493677\pi$
$744$	−19.5066	−	32.0633i	−0.0262185	−	0.0430958i
$745$	−1235.33	+	1235.33i	−1.65816	+	1.65816i
$746$	−31.5755			−0.0423264
$747$	−513.723	−	265.939i	−0.687715	−	0.356009i
$748$	−1080.36	+	152.054i	−1.44433	+	0.203280i
$749$			237.336i			0.316870i
$750$	−12.7089	−	20.8898i	−0.0169452	−	0.0278530i
$751$	421.711	−	421.711i	0.561533	−	0.561533i	−0.368210	−	0.929743i	$-0.620029\pi$
$751$	421.711	−	421.711i	0.561533	−	0.561533i	0.929743	+	0.368210i	$0.120029\pi$
$752$		−	997.726i		−	1.32676i
$753$	198.678	+	48.3758i	0.263848	+	0.0642441i
$754$	−19.8854	−	19.8854i	−0.0263732	−	0.0263732i
$755$	−835.641	+	835.641i	−1.10681	+	1.10681i
$756$	−361.962	+	24.9691i	−0.478786	+	0.0330279i
$757$			797.793i			1.05389i	0.849900	+	0.526944i	$0.176662\pi$
$757$			797.793i			1.05389i	−0.849900	+	0.526944i	$0.823338\pi$
$758$	3.97475	−	3.97475i	0.00524374	−	0.00524374i
$759$	−383.962	−	93.4905i	−0.505878	−	0.123176i
$760$	−209.210	+	209.210i	−0.275276	+	0.275276i
$761$		−	81.3949i		−	0.106958i	−0.998569	−	0.0534789i	$-0.982969\pi$
$761$		−	81.3949i		−	0.106958i	0.998569	−	0.0534789i	$-0.0170310\pi$
$762$	−44.6145	−	10.8632i	−0.0585492	−	0.0142561i
$763$			478.495i			0.627123i
$764$			642.522i			0.840997i
$765$	377.000	−	1073.07i	0.492811	−	1.40271i
$766$	78.2684			0.102178
$767$	600.089			0.782385
$768$	−162.284	+	666.492i	−0.211307	+	0.867828i
$769$	−412.662			−0.536621			−0.268310	−	0.963332i	$-0.586465\pi$
$769$	−412.662			−0.536621			−0.268310	+	0.963332i	$0.586465\pi$
$770$	60.3481	+	60.3481i	0.0783741	+	0.0783741i
$771$	−68.7678	+	282.426i	−0.0891929	+	0.366312i
$772$	120.600	+	120.600i	0.156218	+	0.156218i
$773$	915.455			1.18429			0.592144	−	0.805832i	$-0.298282\pi$
$773$	915.455			1.18429			0.592144	+	0.805832i	$0.298282\pi$
$774$	2.11683	−	4.08916i	0.00273492	−	0.00528315i
$775$	161.441	+	161.441i	0.208311	+	0.208311i
$776$	−80.4815	+	80.4815i	−0.103713	+	0.103713i
$777$	145.744	−	598.563i	0.187572	−	0.770352i
$778$	145.685			0.187256
$779$	−194.869	−	194.869i	−0.250153	−	0.250153i
$780$	−612.226	+	372.465i	−0.784905	+	0.477519i
$781$	154.117			0.197333
$782$	−28.4905	+	4.00986i	−0.0364329	+	0.00512770i
$783$	447.552	−	30.8733i	0.571586	−	0.0394295i
$784$		−	579.983i		−	0.739774i
$785$	−507.026	−	507.026i	−0.645893	−	0.645893i
$786$	102.487	−	62.3509i	0.130391	−	0.0793268i
$787$	603.765	−	603.765i	0.767172	−	0.767172i	−0.210435	−	0.977608i	$-0.567488\pi$
$787$	603.765	−	603.765i	0.767172	−	0.767172i	0.977608	+	0.210435i	$0.0674881\pi$
$788$	361.679	−	361.679i	0.458983	−	0.458983i
$789$	−222.744	+	914.798i	−0.282311	+	1.15944i
$790$		−	142.170i		−	0.179962i
$791$	203.142			0.256817
$792$	230.691	−	73.3159i	0.291277	−	0.0925706i
$793$	449.695	+	449.695i	0.567080	+	0.567080i
$794$	16.0720	+	16.0720i	0.0202418	+	0.0202418i
$795$	187.546	−	114.099i	0.235907	−	0.143521i
$796$	134.107	−	134.107i	0.168476	−	0.168476i
$797$	1418.96			1.78037			0.890187	−	0.455595i	$-0.150573\pi$
$797$	1418.96			1.78037			0.890187	+	0.455595i	$0.150573\pi$
$798$	26.4903	+	43.5426i	0.0331959	+	0.0545646i
$799$	659.200	−	875.150i	0.825031	−	1.09531i
$800$			298.338i			0.372923i
$801$	588.441	−	1136.71i	0.734633	−	1.41912i
$802$	−86.2968	+	86.2968i	−0.107602	+	0.107602i
$803$			36.7457i			0.0457605i
$804$	76.3794	−	313.687i	0.0949993	−	0.390158i
$805$	−144.984	−	144.984i	−0.180104	−	0.180104i
$806$	−9.02957	+	9.02957i	−0.0112029	+	0.0112029i
$807$	−281.215	+	171.085i	−0.348469	+	0.212001i
$808$		−	68.3281i		−	0.0845644i
$809$	−831.666	+	831.666i	−1.02802	+	1.02802i	−0.0284212	+	0.999596i	$0.509048\pi$
$809$	−831.666	+	831.666i	−1.02802	+	1.02802i	−0.999596	+	0.0284212i	$0.990952\pi$
$810$	−21.2259	+	123.677i	−0.0262048	+	0.152688i
$811$	−987.345	+	987.345i	−1.21744	+	1.21744i	−0.248916	+	0.968525i	$0.580074\pi$
$811$	−987.345	+	987.345i	−1.21744	+	1.21744i	−0.968525	+	0.248916i	$0.919926\pi$
$812$		−	223.276i		−	0.274970i
$813$	304.239	−	1249.50i	0.374218	−	1.53690i
$814$			204.381i			0.251083i
$815$		−	1544.86i		−	1.89554i
$816$	−610.726	+	500.350i	−0.748439	+	0.613174i
$817$	58.9270			0.0721261
$818$	−39.0625			−0.0477536
$819$	75.1915	+	236.593i	0.0918089	+	0.288880i
$820$	−337.694			−0.411821
$821$	382.463	+	382.463i	0.465850	+	0.465850i	0.900567	−	0.434717i	$-0.143152\pi$
$821$	382.463	+	382.463i	0.465850	+	0.465850i	−0.434717	+	0.900567i	$0.643152\pi$
$822$	113.704	+	27.6858i	0.138327	+	0.0336810i
$823$	−423.539	−	423.539i	−0.514629	−	0.514629i	0.401313	−	0.915941i	$-0.368554\pi$
$823$	−423.539	−	423.539i	−0.514629	−	0.514629i	−0.915941	+	0.401313i	$0.868554\pi$
$824$	70.9926			0.0861561
$825$	−1258.02	+	765.350i	−1.52487	+	0.927697i
$826$	−36.9801	−	36.9801i	−0.0447701	−	0.0447701i
$827$	−200.991	+	200.991i	−0.243036	+	0.243036i	−0.818105	−	0.575069i	$-0.804975\pi$
$827$	−200.991	+	200.991i	−0.243036	+	0.243036i	0.575069	+	0.818105i	$0.304975\pi$
$828$	−275.601	+	87.5887i	−0.332851	+	0.105783i
$829$	11.6848			0.0140950			0.00704751	−	0.999975i	$-0.497757\pi$
$829$	11.6848			0.0140950			0.00704751	+	0.999975i	$0.497757\pi$
$830$	70.4102	+	70.4102i	0.0848315	+	0.0848315i
$831$	−559.930	−	920.366i	−0.673802	−	1.10754i
$832$	486.226			0.584407
$833$	383.196	−	508.729i	0.460020	−	0.610719i
$834$	−4.81126	−	7.90835i	−0.00576890	−	0.00948243i
$835$			1893.00i			2.26706i
$836$	1089.25	+	1089.25i	1.30293	+	1.30293i
$837$	−14.0190	−	203.225i	−0.0167491	−	0.242801i
$838$	28.4622	−	28.4622i	0.0339645	−	0.0339645i
$839$	153.284	−	153.284i	0.182699	−	0.182699i	−0.609832	−	0.792531i	$-0.708763\pi$
$839$	153.284	−	153.284i	0.182699	−	0.182699i	0.792531	+	0.609832i	$0.208763\pi$
$840$	122.028	+	29.7125i	0.145271	+	0.0353720i
$841$		−	564.928i		−	0.671734i
$842$	−9.06923			−0.0107711
$843$	206.940	−	849.896i	0.245481	−	1.00818i
$844$	−184.962	−	184.962i	−0.219149	−	0.219149i
$845$	−541.626	−	541.626i	−0.640978	−	0.640978i
$846$	−55.5719	+	107.350i	−0.0656879	+	0.126892i
$847$	341.261	−	341.261i	0.402906	−	0.402906i
$848$	−152.387			−0.179702
$849$	−1149.76	+	699.491i	−1.35426	+	0.823900i
$850$	−64.5031	+	85.6339i	−0.0758860	+	0.100746i
$851$		−	491.019i		−	0.576990i
$852$	96.3498	−	58.6170i	0.113087	−	0.0687994i
$853$	311.919	−	311.919i	0.365673	−	0.365673i	−0.500223	−	0.865896i	$-0.666749\pi$
$853$	311.919	−	311.919i	0.365673	−	0.365673i	0.865896	+	0.500223i	$0.166749\pi$
$854$		−	55.4242i		−	0.0648996i
$855$	−1530.46	+	486.396i	−1.79001	+	0.568884i
$856$	−81.9331	−	81.9331i	−0.0957162	−	0.0957162i
$857$	803.544	−	803.544i	0.937625	−	0.937625i	−0.0605412	−	0.998166i	$-0.519283\pi$
$857$	803.544	−	803.544i	0.937625	−	0.937625i	0.998166	+	0.0605412i	$0.0192826\pi$
$858$	−42.8068	−	70.3622i	−0.0498914	−	0.0820072i
$859$		−	1489.02i		−	1.73344i	−0.498796	−	0.866720i	$-0.666224\pi$
$859$		−	1489.02i		−	1.73344i	0.498796	−	0.866720i	$-0.333776\pi$
$860$	51.0581	−	51.0581i	0.0593699	−	0.0593699i
$861$	−27.6758	+	113.663i	−0.0321437	+	0.132013i
$862$	79.8270	−	79.8270i	0.0926067	−	0.0926067i
$863$			340.663i			0.394743i	0.980329	+	0.197372i	$0.0632406\pi$
$863$			340.663i			0.394743i	−0.980329	+	0.197372i	$0.936759\pi$
$864$	174.823	−	200.729i	0.202341	−	0.232326i
$865$		−	619.394i		−	0.716063i
$866$		−	113.822i		−	0.131435i
$867$	−866.278	+	35.3716i	−0.999167	+	0.0407977i
$868$	−101.385			−0.116803
$869$	−1488.54			−1.71293
$870$	−75.0296	−	18.2689i	−0.0862409	−	0.0209987i
$871$	−220.905			−0.253622
$872$	−165.186	−	165.186i	−0.189434	−	0.189434i
$873$	−588.757	+	187.113i	−0.674407	+	0.214333i
$874$	28.7250	+	28.7250i	0.0328661	+	0.0328661i
$875$	−132.833			−0.151809
$876$	13.9759	+	22.9724i	0.0159542	+	0.0262243i
$877$	586.686	+	586.686i	0.668969	+	0.668969i	0.957477	−	0.288508i	$-0.0931593\pi$
$877$	586.686	+	586.686i	0.668969	+	0.668969i	−0.288508	+	0.957477i	$0.593159\pi$
$878$	36.8456	−	36.8456i	0.0419654	−	0.0419654i
$879$	−940.414	−	228.981i	−1.06987	−	0.260501i
$880$	1866.64			2.12118
$881$	552.994	+	552.994i	0.627689	+	0.627689i	0.947486	−	0.319797i	$-0.103615\pi$
$881$	552.994	+	552.994i	0.627689	+	0.627689i	−0.319797	+	0.947486i	$0.603615\pi$
$882$	−32.3043	+	62.4032i	−0.0366261	+	0.0707520i
$883$	61.7667			0.0699510			0.0349755	−	0.999388i	$-0.488865\pi$
$883$	61.7667			0.0699510			0.0349755	+	0.999388i	$0.488865\pi$
$884$	436.338	+	328.668i	0.493595	+	0.371796i
$885$	1407.75	−	856.444i	1.59068	−	0.967734i
$886$			9.24374i			0.0104331i
$887$	−278.018	−	278.018i	−0.313436	−	0.313436i	0.532803	−	0.846239i	$-0.321139\pi$
$887$	−278.018	−	278.018i	−0.313436	−	0.313436i	−0.846239	+	0.532803i	$0.821139\pi$
$888$	156.323	+	256.950i	0.176039	+	0.289358i
$889$	−176.385	+	176.385i	−0.198408	+	0.198408i
$890$	−155.796	+	155.796i	−0.175052	+	0.175052i
$891$	1294.91	+	222.238i	1.45333	+	0.249426i
$892$		−	690.771i		−	0.774407i
$893$	−1546.98			−1.73234
$894$	−142.757	−	34.7598i	−0.159684	−	0.0388812i
$895$	516.389	+	516.389i	0.576971	+	0.576971i
$896$	−124.670	−	124.670i	−0.139140	−	0.139140i
$897$	102.842	+	169.043i	0.114651	+	0.188453i
$898$	21.6931	−	21.6931i	0.0241571	−	0.0241571i
$899$	125.359			0.139442
$900$	−495.386	+	956.954i	−0.550429	+	1.06328i
$901$	−133.665	−	100.682i	−0.148352	−	0.111745i
$902$		−	38.8106i		−	0.0430273i
$903$	−13.0010	−	21.3699i	−0.0143976	−	0.0236655i
$904$	−70.1288	+	70.1288i	−0.0775761	+	0.0775761i
$905$		−	384.940i		−	0.425349i
$906$	−96.5686	−	23.5134i	−0.106588	−	0.0259530i
$907$	−134.894	−	134.894i	−0.148726	−	0.148726i	0.628823	−	0.777549i	$-0.283537\pi$
$907$	−134.894	−	134.894i	−0.148726	−	0.148726i	−0.777549	+	0.628823i	$0.783537\pi$
$908$	530.778	−	530.778i	0.584557	−	0.584557i
$909$	170.496	−	329.353i	0.187565	−	0.362325i
$910$		−	42.7327i		−	0.0469590i
$911$	−529.607	+	529.607i	−0.581347	+	0.581347i	−0.935273	−	0.353926i	$-0.884846\pi$
$911$	−529.607	+	529.607i	−0.581347	+	0.581347i	0.353926	+	0.935273i	$0.384846\pi$
$912$	1083.10	+	263.724i	1.18761	+	0.289171i
$913$	737.204	−	737.204i	0.807452	−	0.807452i
$914$		−	10.9026i		−	0.0119285i
$915$	1696.74	+	413.138i	1.85436	+	0.451517i
$916$			1205.70i			1.31626i
$917$		−	651.692i		−	0.710679i
$918$	93.5799	−	19.8186i	0.101939	−	0.0215889i
$919$	−427.922			−0.465639			−0.232820	−	0.972520i	$-0.574795\pi$
$919$	−427.922			−0.465639			−0.232820	+	0.972520i	$0.574795\pi$
$920$	100.103			0.108808
$921$	195.151	−	801.477i	0.211890	−	0.870224i
$922$	60.7160			0.0658525
$923$	−54.5654	−	54.5654i	−0.0591174	−	0.0591174i
$924$	154.698	−	635.337i	0.167422	−	0.687594i
$925$	−1293.77	−	1293.77i	−1.39866	−	1.39866i
$926$	148.289			0.160139
$927$	342.197	+	177.145i	0.369144	+	0.191095i
$928$	115.829	+	115.829i	0.124816	+	0.124816i
$929$	872.431	−	872.431i	0.939107	−	0.939107i	−0.0591421	−	0.998250i	$-0.518837\pi$
$929$	872.431	−	872.431i	0.939107	−	0.939107i	0.998250	+	0.0591421i	$0.0188365\pi$
$930$	−8.29554	+	34.0694i	−0.00891994	+	0.0366338i
$931$	−899.266			−0.965914
$932$	132.221	+	132.221i	0.141868	+	0.141868i
$933$	−699.539	+	425.584i	−0.749774	+	0.456145i
$934$	−78.7989			−0.0843671
$935$	1637.32	+	1233.29i	1.75114	+	1.31903i
$936$	−107.634	−	55.7190i	−0.114994	−	0.0595288i
$937$			855.452i			0.912969i	0.889731	+	0.456485i	$0.150892\pi$
$937$			855.452i			0.912969i	−0.889731	+	0.456485i	$0.849108\pi$
$938$	13.6131	+	13.6131i	0.0145129	+	0.0145129i
$939$	−678.993	+	413.084i	−0.723102	+	0.439919i
$940$	−1340.40	+	1340.40i	−1.42596	+	1.42596i
$941$	−701.925	+	701.925i	−0.745936	+	0.745936i	−0.973713	−	0.227778i	$-0.926854\pi$
$941$	−701.925	+	701.925i	−0.745936	+	0.745936i	0.227778	+	0.973713i	$0.426854\pi$
$942$	14.2668	−	58.5931i	0.0151452	−	0.0622007i
$943$			93.2411i			0.0988771i
$944$	−1143.84			−1.21170
$945$	514.056	+	447.711i	0.543974	+	0.473768i
$946$	5.86803	+	5.86803i	0.00620299	+	0.00620299i
$947$	392.939	+	392.939i	0.414930	+	0.414930i	0.883452	−	0.468522i	$-0.155213\pi$
$947$	392.939	+	392.939i	0.414930	+	0.414930i	−0.468522	+	0.883452i	$0.655213\pi$
$948$	−930.593	+	566.152i	−0.981638	+	0.597207i
$949$	13.0099	−	13.0099i	0.0137090	−	0.0137090i
$950$	151.373			0.159340
$951$	−672.045	−	1104.65i	−0.706672	−	1.16157i
$952$	−13.3430	−	94.8034i	−0.0140157	−	0.0995834i
$953$			1366.13i			1.43350i	0.697328	+	0.716752i	$0.254372\pi$
$953$			1366.13i			1.43350i	−0.697328	+	0.716752i	$0.745628\pi$
$954$	16.3961	+	8.48774i	0.0171866	+	0.00889700i
$955$	853.619	−	853.619i	0.893842	−	0.893842i
$956$			424.881i			0.444436i
$957$	−191.278	+	785.570i	−0.199872	+	0.820867i
$958$	−31.6874	−	31.6874i	−0.0330766	−	0.0330766i
$959$	449.534	−	449.534i	0.468753	−	0.468753i
$960$	1140.64	−	693.940i	1.18817	−	0.722854i
$961$			904.077i			0.940767i
$962$	72.3615	−	72.3615i	0.0752199	−	0.0752199i
$963$	−190.488	−	599.376i	−0.197807	−	0.622405i
$964$	−1233.86	+	1233.86i	−1.27994	+	1.27994i
$965$		−	320.445i		−	0.332068i
$966$	4.07959	−	16.7547i	0.00422318	−	0.0173444i
$967$			332.446i			0.343791i	0.985115	+	0.171896i	$0.0549892\pi$
$967$			332.446i			0.343791i	−0.985115	+	0.171896i	$0.945011\pi$
$968$			235.621i			0.243410i
$969$	775.795	+	946.933i	0.800614	+	0.977227i
$970$	106.340			0.109629
$971$	−284.514			−0.293011			−0.146506	−	0.989210i	$-0.546803\pi$
$971$	−284.514			−0.293011			−0.146506	+	0.989210i	$0.546803\pi$
$972$	894.073	−	353.572i	0.919828	−	0.363757i
$973$	−50.2873			−0.0516828
$974$	−68.7190	−	68.7190i	−0.0705534	−	0.0705534i
$975$	716.378	+	174.430i	0.734746	+	0.178903i
$976$	−857.171	−	857.171i	−0.878249	−	0.878249i
$977$	843.372			0.863226			0.431613	−	0.902059i	$-0.357945\pi$
$977$	843.372			0.863226			0.431613	+	0.902059i	$0.357945\pi$
$978$	110.999	−	67.5292i	0.113496	−	0.0690483i
$979$	1631.21	+	1631.21i	1.66620	+	1.66620i
$980$	−779.180	+	779.180i	−0.795082	+	0.795082i
$981$	−384.045	−	1208.41i	−0.391483	−	1.23181i
$982$	−90.1374			−0.0917896
$983$	−84.6921	−	84.6921i	−0.0861568	−	0.0861568i	0.662715	−	0.748872i	$-0.269404\pi$
$983$	−84.6921	−	84.6921i	−0.0861568	−	0.0861568i	−0.748872	+	0.662715i	$0.769404\pi$
$984$	−29.6846	−	48.7931i	−0.0301673	−	0.0495865i
$985$	−961.013			−0.975647
$986$	8.20402	+	58.2905i	0.00832050	+	0.0591181i
$987$	341.308	+	561.013i	0.345803	+	0.568402i
$988$		−	771.301i		−	0.780670i
$989$	−14.0977	−	14.0977i	−0.0142545	−	0.0142545i
$990$	−200.841	−	103.969i	−0.202870	−	0.105020i
$991$	581.980	−	581.980i	0.587265	−	0.587265i	−0.349625	−	0.936890i	$-0.613691\pi$
$991$	581.980	−	581.980i	0.587265	−	0.587265i	0.936890	+	0.349625i	$0.113691\pi$
$992$	52.5958	−	52.5958i	0.0530199	−	0.0530199i
$993$	−907.137	−	220.878i	−0.913532	−	0.222435i
$994$			6.72511i			0.00676570i
$995$	−356.335			−0.358126
$996$	180.491	−	741.270i	0.181216	−	0.744247i
$997$	829.581	+	829.581i	0.832078	+	0.832078i	0.987801	−	0.155723i	$-0.0497707\pi$
$997$	829.581	+	829.581i	0.832078	+	0.832078i	−0.155723	+	0.987801i	$0.549771\pi$
$998$	6.07668	+	6.07668i	0.00608885	+	0.00608885i
$999$	112.346	+	1628.61i	0.112458	+	1.63024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.3.f.a.38.6	yes	20
3.2	odd	2	inner	51.3.f.a.38.5	✓	20
17.13	even	4	inner	51.3.f.a.47.5	yes	20
51.47	odd	4	inner	51.3.f.a.47.6	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.3.f.a.38.5	✓	20	3.2	odd	2	inner
51.3.f.a.38.6	yes	20	1.1	even	1	trivial
51.3.f.a.47.5	yes	20	17.13	even	4	inner
51.3.f.a.47.6	yes	20	51.47	odd	4	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	51.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.208400 q^{2} +(-0.709732 + 2.91484i) q^{3} -3.95657 q^{4} +(5.25648 + 5.25648i) q^{5} +(-0.147908 + 0.607451i) q^{6} +(2.40158 + 2.40158i) q^{7} -1.65815 q^{8} +(-7.99256 - 4.13751i) q^{9} +(1.09545 + 1.09545i) q^{10} +(11.4695 - 11.4695i) q^{11} +(2.80810 - 11.5328i) q^{12} -8.12160 q^{13} +(0.500488 + 0.500488i) q^{14} +(-19.0525 + 11.5911i) q^{15} +15.4807 q^{16} +(13.5788 + 10.2282i) q^{17} +(-1.66565 - 0.862255i) q^{18} -24.0029i q^{19} +(-20.7976 - 20.7976i) q^{20} +(-8.70468 + 5.29573i) q^{21} +(2.39024 - 2.39024i) q^{22} +(-5.74247 + 5.74247i) q^{23} +(1.17684 - 4.83323i) q^{24} +30.2612i q^{25} -1.69254 q^{26} +(17.7327 - 20.3605i) q^{27} +(-9.50201 - 9.50201i) q^{28} +(11.7489 + 11.7489i) q^{29} +(-3.97053 + 2.41558i) q^{30} +(5.33493 - 5.33493i) q^{31} +9.85876 q^{32} +(25.2915 + 41.5720i) q^{33} +(2.82983 + 2.13154i) q^{34} +25.2477i q^{35} +(31.6231 + 16.3703i) q^{36} +(-42.7533 + 42.7533i) q^{37} -5.00220i q^{38} +(5.76415 - 23.6731i) q^{39} +(-8.71602 - 8.71602i) q^{40} +(8.11856 - 8.11856i) q^{41} +(-1.81405 + 1.10363i) q^{42} +2.45499i q^{43} +(-45.3799 + 45.3799i) q^{44} +(-20.2640 - 63.7615i) q^{45} +(-1.19673 + 1.19673i) q^{46} -64.4496i q^{47} +(-10.9872 + 45.1238i) q^{48} -37.4649i q^{49} +6.30643i q^{50} +(-39.4507 + 32.3209i) q^{51} +32.1337 q^{52} -9.84366 q^{53} +(3.69550 - 4.24312i) q^{54} +120.578 q^{55} +(-3.98217 - 3.98217i) q^{56} +(69.9646 + 17.0356i) q^{57} +(2.44846 + 2.44846i) q^{58} -73.8881 q^{59} +(75.3825 - 45.8610i) q^{60} +(-55.3702 - 55.3702i) q^{61} +(1.11180 - 1.11180i) q^{62} +(-9.25821 - 29.1313i) q^{63} -59.8683 q^{64} +(-42.6910 - 42.6910i) q^{65} +(5.27074 + 8.66359i) q^{66} +27.1997 q^{67} +(-53.7256 - 40.4684i) q^{68} +(-12.6628 - 20.8140i) q^{69} +5.26161i q^{70} +(6.71855 + 6.71855i) q^{71} +(13.2528 + 6.86059i) q^{72} +(-1.60189 + 1.60189i) q^{73} +(-8.90977 + 8.90977i) q^{74} +(-88.2065 - 21.4773i) q^{75} +94.9692i q^{76} +55.0898 q^{77} +(1.20125 - 4.93347i) q^{78} +(-64.8910 - 64.8910i) q^{79} +(81.3741 + 81.3741i) q^{80} +(46.7621 + 66.1385i) q^{81} +(1.69190 - 1.69190i) q^{82} +64.2751 q^{83} +(34.4407 - 20.9529i) q^{84} +(17.6128 + 125.141i) q^{85} +0.511620i q^{86} +(-42.5846 + 25.9075i) q^{87} +(-19.0181 + 19.0181i) q^{88} +142.221i q^{89} +(-4.22302 - 13.2879i) q^{90} +(-19.5046 - 19.5046i) q^{91} +(22.7205 - 22.7205i) q^{92} +(11.7641 + 19.3368i) q^{93} -13.4313i q^{94} +(126.171 - 126.171i) q^{95} +(-6.99708 + 28.7367i) q^{96} +(48.5370 - 48.5370i) q^{97} -7.80767i q^{98} +(-139.126 + 44.2156i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3} + 24 q^{4} - 2 q^{6} - 4 q^{7} - 16 q^{10} - 42 q^{12} - 12 q^{13} - 64 q^{16} - 4 q^{18} + 88 q^{21} - 40 q^{22} - 82 q^{24} + 54 q^{27} - 160 q^{28} + 48 q^{31} + 264 q^{33} + 152 q^{34}+ \cdots - 864 q^{99}+O(q^{100}) \) 20 * q - 6 * q^3 + 24 * q^4 - 2 * q^6 - 4 * q^7 - 16 * q^10 - 42 * q^12 - 12 * q^13 - 64 * q^16 - 4 * q^18 + 88 * q^21 - 40 * q^22 - 82 * q^24 + 54 * q^27 - 160 * q^28 + 48 * q^31 + 264 * q^33 + 152 * q^34 + 32 * q^37 + 56 * q^39 + 52 * q^40 + 64 * q^45 + 388 * q^46 - 230 * q^48 - 298 * q^51 + 64 * q^52 - 254 * q^54 - 204 * q^55 - 24 * q^57 + 396 * q^58 - 336 * q^61 - 400 * q^63 - 480 * q^64 - 408 * q^67 - 132 * q^69 + 276 * q^72 - 88 * q^73 - 358 * q^75 + 380 * q^78 - 172 * q^79 + 388 * q^81 + 372 * q^82 + 1320 * q^84 + 648 * q^85 - 156 * q^88 + 672 * q^90 - 124 * q^91 + 194 * q^96 + 688 * q^97 - 864 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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