LMFDB - Embedded newform 17.4.d.a.9.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,4,Mod(2,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("17.2");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	17.d (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.00303247010$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 54x^{10} + 1085x^{8} + 9836x^{6} + 38276x^{4} + 49664x^{2} + 16384 $ x^12 + 54x^10 + 1085x^8 + 9836x^6 + 38276x^4 + 49664*x^2 + 16384
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			9.3
Root			$-4.15292i$ of defining polynomial
Character	$\chi$	$=$	17.9
Dual form			17.4.d.a.2.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.22945 - 2.22945i) q^{2} +(-1.83980 - 0.762069i) q^{3} -1.94089i q^{4} +(-1.91633 + 4.62643i) q^{5} +(-5.80073 + 2.40274i) q^{6} +(1.06584 + 2.57316i) q^{7} +(13.5085 + 13.5085i) q^{8} +(-16.2878 - 16.2878i) q^{9} +O(q^{10})$	\(q+(2.22945 - 2.22945i) q^{2} +(-1.83980 - 0.762069i) q^{3} -1.94089i q^{4} +(-1.91633 + 4.62643i) q^{5} +(-5.80073 + 2.40274i) q^{6} +(1.06584 + 2.57316i) q^{7} +(13.5085 + 13.5085i) q^{8} +(-16.2878 - 16.2878i) q^{9} +(6.04203 + 14.5867i) q^{10} +(-25.1714 + 10.4263i) q^{11} +(-1.47909 + 3.57084i) q^{12} -59.7352i q^{13} +(8.11295 + 3.36049i) q^{14} +(7.05131 - 7.05131i) q^{15} +75.7601 q^{16} +(70.0883 - 0.790881i) q^{17} -72.6256 q^{18} +(23.5187 - 23.5187i) q^{19} +(8.97939 + 3.71938i) q^{20} -5.54633i q^{21} +(-32.8734 + 79.3634i) q^{22} +(-194.831 + 80.7017i) q^{23} +(-14.5585 - 35.1473i) q^{24} +(70.6568 + 70.6568i) q^{25} +(-133.177 - 133.177i) q^{26} +(38.1297 + 92.0531i) q^{27} +(4.99421 - 2.06867i) q^{28} +(7.67362 - 18.5258i) q^{29} -31.4411i q^{30} +(123.485 + 51.1492i) q^{31} +(60.8354 - 60.8354i) q^{32} +54.2559 q^{33} +(154.495 - 158.022i) q^{34} -13.9470 q^{35} +(-31.6128 + 31.6128i) q^{36} +(141.143 + 58.4634i) q^{37} -104.868i q^{38} +(-45.5223 + 109.901i) q^{39} +(-88.3827 + 36.6093i) q^{40} +(-100.202 - 241.908i) q^{41} +(-12.3653 - 12.3653i) q^{42} +(-224.025 - 224.025i) q^{43} +(20.2364 + 48.8550i) q^{44} +(106.567 - 44.1415i) q^{45} +(-254.446 + 614.286i) q^{46} +329.443i q^{47} +(-139.383 - 57.7344i) q^{48} +(237.052 - 237.052i) q^{49} +315.052 q^{50} +(-129.551 - 51.9571i) q^{51} -115.939 q^{52} +(-219.585 + 219.585i) q^{53} +(290.236 + 120.220i) q^{54} -136.434i q^{55} +(-20.3616 + 49.1573i) q^{56} +(-61.1926 + 25.3468i) q^{57} +(-24.1943 - 58.4102i) q^{58} +(38.7062 + 38.7062i) q^{59} +(-13.6858 - 13.6858i) q^{60} +(-313.322 - 756.427i) q^{61} +(389.338 - 161.269i) q^{62} +(24.5509 - 59.2711i) q^{63} +334.822i q^{64} +(276.360 + 114.472i) q^{65} +(120.961 - 120.961i) q^{66} -731.181 q^{67} +(-1.53501 - 136.034i) q^{68} +419.950 q^{69} +(-31.0942 + 31.0942i) q^{70} +(581.286 + 240.777i) q^{71} -440.046i q^{72} +(-189.995 + 458.689i) q^{73} +(445.012 - 184.330i) q^{74} +(-76.1489 - 183.840i) q^{75} +(-45.6473 - 45.6473i) q^{76} +(-53.6572 - 53.6572i) q^{77} +(143.528 + 346.507i) q^{78} +(83.1733 - 34.4515i) q^{79} +(-145.181 + 350.498i) q^{80} +423.512i q^{81} +(-762.717 - 315.928i) q^{82} +(-257.404 + 257.404i) q^{83} -10.7648 q^{84} +(-130.653 + 325.774i) q^{85} -998.907 q^{86} +(-28.2358 + 28.2358i) q^{87} +(-480.872 - 199.184i) q^{88} +192.079i q^{89} +(139.174 - 335.997i) q^{90} +(153.708 - 63.6679i) q^{91} +(156.633 + 378.146i) q^{92} +(-188.208 - 188.208i) q^{93} +(734.476 + 734.476i) q^{94} +(63.7380 + 153.877i) q^{95} +(-158.286 + 65.5640i) q^{96} +(516.698 - 1247.42i) q^{97} -1056.99i q^{98} +(579.808 + 240.165i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 4 q^{3} - 20 q^{5} + 20 q^{6} - 4 q^{7} + 28 q^{8} - 64 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 - 4 * q^3 - 20 * q^5 + 20 * q^6 - 4 * q^7 + 28 * q^8 - 64 * q^9	\( 12 q - 4 q^{2} - 4 q^{3} - 20 q^{5} + 20 q^{6} - 4 q^{7} + 28 q^{8} - 64 q^{9} - 116 q^{10} + 40 q^{11} + 56 q^{12} - 132 q^{14} + 244 q^{15} + 184 q^{16} + 52 q^{17} - 12 q^{19} + 572 q^{20} - 620 q^{22} - 276 q^{23} - 184 q^{24} - 464 q^{25} - 708 q^{26} - 664 q^{27} + 452 q^{28} + 632 q^{29} + 188 q^{31} + 700 q^{32} + 1400 q^{33} + 764 q^{34} - 632 q^{35} + 524 q^{36} + 940 q^{37} - 1112 q^{39} - 1864 q^{40} + 176 q^{41} + 48 q^{42} - 1360 q^{43} - 1364 q^{44} - 32 q^{45} + 452 q^{46} - 540 q^{48} + 1044 q^{49} + 2856 q^{50} + 340 q^{51} + 792 q^{52} - 360 q^{53} - 244 q^{54} - 1788 q^{56} - 148 q^{57} - 360 q^{58} - 584 q^{59} - 1792 q^{60} - 1052 q^{61} - 380 q^{62} + 1752 q^{63} + 404 q^{65} + 1372 q^{66} + 1080 q^{67} + 2532 q^{68} - 344 q^{69} + 2072 q^{70} + 28 q^{71} + 824 q^{73} - 2292 q^{74} + 400 q^{75} + 1328 q^{76} - 1252 q^{77} + 1128 q^{78} - 196 q^{79} - 904 q^{80} - 1528 q^{82} - 1008 q^{83} - 4768 q^{84} - 2824 q^{85} - 1200 q^{86} - 2516 q^{87} - 56 q^{88} - 860 q^{90} + 2456 q^{91} + 396 q^{92} - 836 q^{93} + 6360 q^{94} + 2172 q^{95} + 1668 q^{96} - 904 q^{97} + 3280 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 4 * q^3 - 20 * q^5 + 20 * q^6 - 4 * q^7 + 28 * q^8 - 64 * q^9 - 116 * q^10 + 40 * q^11 + 56 * q^12 - 132 * q^14 + 244 * q^15 + 184 * q^16 + 52 * q^17 - 12 * q^19 + 572 * q^20 - 620 * q^22 - 276 * q^23 - 184 * q^24 - 464 * q^25 - 708 * q^26 - 664 * q^27 + 452 * q^28 + 632 * q^29 + 188 * q^31 + 700 * q^32 + 1400 * q^33 + 764 * q^34 - 632 * q^35 + 524 * q^36 + 940 * q^37 - 1112 * q^39 - 1864 * q^40 + 176 * q^41 + 48 * q^42 - 1360 * q^43 - 1364 * q^44 - 32 * q^45 + 452 * q^46 - 540 * q^48 + 1044 * q^49 + 2856 * q^50 + 340 * q^51 + 792 * q^52 - 360 * q^53 - 244 * q^54 - 1788 * q^56 - 148 * q^57 - 360 * q^58 - 584 * q^59 - 1792 * q^60 - 1052 * q^61 - 380 * q^62 + 1752 * q^63 + 404 * q^65 + 1372 * q^66 + 1080 * q^67 + 2532 * q^68 - 344 * q^69 + 2072 * q^70 + 28 * q^71 + 824 * q^73 - 2292 * q^74 + 400 * q^75 + 1328 * q^76 - 1252 * q^77 + 1128 * q^78 - 196 * q^79 - 904 * q^80 - 1528 * q^82 - 1008 * q^83 - 4768 * q^84 - 2824 * q^85 - 1200 * q^86 - 2516 * q^87 - 56 * q^88 - 860 * q^90 + 2456 * q^91 + 396 * q^92 - 836 * q^93 + 6360 * q^94 + 2172 * q^95 + 1668 * q^96 - 904 * q^97 + 3280 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$	2.22945	−	2.22945i	0.788229	−	0.788229i	−0.192974	−	0.981204i	$-0.561813\pi$
$2$	2.22945	−	2.22945i	0.788229	−	0.788229i	0.981204	+	0.192974i	$0.0618134\pi$
$3$	−1.83980	−	0.762069i	−0.354069	−	0.146660i	0.198557	−	0.980089i	$-0.436374\pi$
$3$	−1.83980	−	0.762069i	−0.354069	−	0.146660i	−0.552626	+	0.833429i	$0.686374\pi$
$4$		−	1.94089i		−	0.242611i
$5$	−1.91633	+	4.62643i	−0.171402	+	0.413800i	−0.986115	−	0.166064i	$-0.946894\pi$
$5$	−1.91633	+	4.62643i	−0.171402	+	0.413800i	0.814713	+	0.579864i	$0.196894\pi$
$6$	−5.80073	+	2.40274i	−0.394690	+	0.163486i
$7$	1.06584	+	2.57316i	0.0575498	+	0.138937i	0.950039	−	0.312131i	$-0.101043\pi$
$7$	1.06584	+	2.57316i	0.0575498	+	0.138937i	−0.892489	+	0.451069i	$0.851043\pi$
$8$	13.5085	+	13.5085i	0.596996	+	0.596996i
$9$	−16.2878	−	16.2878i	−0.603251	−	0.603251i
$10$	6.04203	+	14.5867i	0.191066	+	0.461273i
$11$	−25.1714	+	10.4263i	−0.689952	+	0.285787i	−0.699980	−	0.714162i	$-0.746808\pi$
$11$	−25.1714	+	10.4263i	−0.689952	+	0.285787i	0.0100284	+	0.999950i	$0.496808\pi$
$12$	−1.47909	+	3.57084i	−0.0355814	+	0.0859011i
$13$		−	59.7352i		−	1.27443i	−0.770687	−	0.637214i	$-0.780087\pi$
$13$		−	59.7352i		−	1.27443i	0.770687	−	0.637214i	$-0.219913\pi$
$14$	8.11295	+	3.36049i	0.154877	+	0.0641521i
$15$	7.05131	−	7.05131i	0.121376	−	0.121376i
$16$	75.7601			1.18375
$17$	70.0883	−	0.790881i	0.999936	−	0.0112833i
$17$	70.0883	−	0.790881i	0.999936	−	0.0112833i
$18$	−72.6256			−0.951000
$19$	23.5187	−	23.5187i	0.283977	−	0.283977i	−0.550716	−	0.834693i	$-0.685645\pi$
$19$	23.5187	−	23.5187i	0.283977	−	0.283977i	0.834693	+	0.550716i	$0.185645\pi$
$20$	8.97939	+	3.71938i	0.100393	+	0.0415840i
$21$		−	5.54633i		−	0.0576337i
$22$	−32.8734	+	79.3634i	−0.318574	+	0.769106i
$23$	−194.831	+	80.7017i	−1.76631	+	0.731629i	−0.770787	+	0.637093i	$0.780137\pi$
$23$	−194.831	+	80.7017i	−1.76631	+	0.731629i	−0.995522	+	0.0945353i	$0.969863\pi$
$24$	−14.5585	−	35.1473i	−0.123822	−	0.298933i
$25$	70.6568	+	70.6568i	0.565255	+	0.565255i
$26$	−133.177	−	133.177i	−1.00454	−	1.00454i
$27$	38.1297	+	92.0531i	0.271780	+	0.656135i
$28$	4.99421	−	2.06867i	0.0337078	−	0.0139622i
$29$	7.67362	−	18.5258i	0.0491364	−	0.118626i	−0.897405	−	0.441207i	$-0.854551\pi$
$29$	7.67362	−	18.5258i	0.0491364	−	0.118626i	0.946542	+	0.322581i	$0.104551\pi$
$30$		−	31.4411i		−	0.191344i
$31$	123.485	+	51.1492i	0.715438	+	0.296344i	0.710553	−	0.703644i	$-0.248445\pi$
$31$	123.485	+	51.1492i	0.715438	+	0.296344i	0.00488535	+	0.999988i	$0.498445\pi$
$32$	60.8354	−	60.8354i	0.336071	−	0.336071i
$33$	54.2559			0.286204
$34$	154.495	−	158.022i	0.779285	−	0.797073i
$35$	−13.9470			−0.0673565
$36$	−31.6128	+	31.6128i	−0.146355	+	0.146355i
$37$	141.143	+	58.4634i	0.627129	+	0.259765i	0.673533	−	0.739157i	$-0.264776\pi$
$37$	141.143	+	58.4634i	0.627129	+	0.259765i	−0.0464037	+	0.998923i	$0.514776\pi$
$38$		−	104.868i		−	0.447678i
$39$	−45.5223	+	109.901i	−0.186908	+	0.451235i
$40$	−88.3827	+	36.6093i	−0.349363	+	0.144711i
$41$	−100.202	−	241.908i	−0.381680	−	0.921456i	−0.991641	−	0.129025i	$-0.958815\pi$
$41$	−100.202	−	241.908i	−0.381680	−	0.921456i	0.609962	−	0.792431i	$-0.291185\pi$
$42$	−12.3653	−	12.3653i	−0.0454286	−	0.0454286i
$43$	−224.025	−	224.025i	−0.794501	−	0.794501i	0.187721	−	0.982222i	$-0.439890\pi$
$43$	−224.025	−	224.025i	−0.794501	−	0.794501i	−0.982222	+	0.187721i	$0.939890\pi$
$44$	20.2364	+	48.8550i	0.0693352	+	0.167390i
$45$	106.567	−	44.1415i	0.353024	−	0.146227i
$46$	−254.446	+	614.286i	−0.815565	+	1.96895i
$47$			329.443i			1.02243i	0.859453	+	0.511215i	$0.170804\pi$
$47$			329.443i			1.02243i	−0.859453	+	0.511215i	$0.829196\pi$
$48$	−139.383	−	57.7344i	−0.419130	−	0.173609i
$49$	237.052	−	237.052i	0.691115	−	0.691115i
$50$	315.052			0.891101
$51$	−129.551	−	51.9571i	−0.355701	−	0.142656i
$52$	−115.939			−0.309190
$53$	−219.585	+	219.585i	−0.569100	+	0.569100i	−0.931876	−	0.362776i	$-0.881829\pi$
$53$	−219.585	+	219.585i	−0.569100	+	0.569100i	0.362776	+	0.931876i	$0.381829\pi$
$54$	290.236	+	120.220i	0.731409	+	0.302960i
$55$		−	136.434i		−	0.334487i
$56$	−20.3616	+	49.1573i	−0.0485881	+	0.117302i
$57$	−61.1926	+	25.3468i	−0.142196	+	0.0588994i
$58$	−24.1943	−	58.4102i	−0.0547735	−	0.132235i
$59$	38.7062	+	38.7062i	0.0854087	+	0.0854087i	0.748520	−	0.663112i	$-0.230765\pi$
$59$	38.7062	+	38.7062i	0.0854087	+	0.0854087i	−0.663112	+	0.748520i	$0.730765\pi$
$60$	−13.6858	−	13.6858i	−0.0294472	−	0.0294472i
$61$	−313.322	−	756.427i	−0.657653	−	1.58771i	−0.801419	−	0.598103i	$-0.795921\pi$
$61$	−313.322	−	756.427i	−0.657653	−	1.58771i	0.143767	−	0.989612i	$-0.454079\pi$
$62$	389.338	−	161.269i	0.797517	−	0.330342i
$63$	24.5509	−	59.2711i	0.0490972	−	0.118531i
$64$			334.822i			0.653948i
$65$	276.360	+	114.472i	0.527358	+	0.218439i
$66$	120.961	−	120.961i	0.225595	−	0.225595i
$67$	−731.181			−1.33325			−0.666627	−	0.745392i	$-0.732262\pi$
$67$	−731.181			−1.33325			−0.666627	+	0.745392i	$0.732262\pi$
$68$	−1.53501	−	136.034i	−0.00273747	−	0.242596i
$69$	419.950			0.732696
$70$	−31.0942	+	31.0942i	−0.0530923	+	0.0530923i
$71$	581.286	+	240.777i	0.971633	+	0.402464i	0.811320	−	0.584603i	$-0.198750\pi$
$71$	581.286	+	240.777i	0.971633	+	0.402464i	0.160313	+	0.987066i	$0.448750\pi$
$72$		−	440.046i		−	0.720277i
$73$	−189.995	+	458.689i	−0.304620	+	0.735417i	0.695242	+	0.718776i	$0.255297\pi$
$73$	−189.995	+	458.689i	−0.304620	+	0.735417i	−0.999862	+	0.0166414i	$0.994703\pi$
$74$	445.012	−	184.330i	0.699076	−	0.289567i
$75$	−76.1489	−	183.840i	−0.117239	−	0.283040i
$76$	−45.6473	−	45.6473i	−0.0688960	−	0.0688960i
$77$	−53.6572	−	53.6572i	−0.0794131	−	0.0794131i
$78$	143.528	+	346.507i	0.208351	+	0.503003i
$79$	83.1733	−	34.4515i	0.118452	−	0.0490646i	−0.322670	−	0.946511i	$-0.604580\pi$
$79$	83.1733	−	34.4515i	0.118452	−	0.0490646i	0.441122	+	0.897447i	$0.354580\pi$
$80$	−145.181	+	350.498i	−0.202897	+	0.489836i
$81$			423.512i			0.580950i
$82$	−762.717	−	315.928i	−1.02717	−	0.425468i
$83$	−257.404	+	257.404i	−0.340407	+	0.340407i	−0.856520	−	0.516113i	$-0.827378\pi$
$83$	−257.404	+	257.404i	−0.340407	+	0.340407i	0.516113	+	0.856520i	$0.327378\pi$
$84$	−10.7648			−0.0139826
$85$	−130.653	+	325.774i	−0.166722	+	0.415708i
$86$	−998.907			−1.25250
$87$	−28.2358	+	28.2358i	−0.0347954	+	0.0347954i
$88$	−480.872	−	199.184i	−0.582512	−	0.241285i
$89$			192.079i			0.228767i	0.993437	+	0.114384i	$0.0364893\pi$
$89$			192.079i			0.228767i	−0.993437	+	0.114384i	$0.963511\pi$
$90$	139.174	−	335.997i	0.163003	−	0.393524i
$91$	153.708	−	63.6679i	0.177066	−	0.0733430i
$92$	156.633	+	378.146i	0.177501	+	0.428526i
$93$	−188.208	−	188.208i	−0.209853	−	0.209853i
$94$	734.476	+	734.476i	0.805909	+	0.805909i
$95$	63.7380	+	153.877i	0.0688356	+	0.166184i
$96$	−158.286	+	65.5640i	−0.168281	+	0.0697042i
$97$	516.698	−	1247.42i	0.540853	−	1.30574i	−0.383268	−	0.923637i	$-0.625202\pi$
$97$	516.698	−	1247.42i	0.540853	−	1.30574i	0.924122	−	0.382098i	$-0.124798\pi$
$98$		−	1056.99i		−	1.08951i
$99$	579.808	+	240.165i	0.588616	+	0.243813i
$100$	137.137	−	137.137i	0.137137	−	0.137137i
$101$	304.020			0.299516			0.149758	−	0.988723i	$-0.452150\pi$
$101$	304.020			0.299516			0.149758	+	0.988723i	$0.452150\pi$
$102$	−404.663	+	172.992i	−0.392820	+	0.167929i
$103$	988.515			0.945643			0.472822	−	0.881158i	$-0.343236\pi$
$103$	988.515			0.945643			0.472822	+	0.881158i	$0.343236\pi$
$104$	806.931	−	806.931i	0.760828	−	0.760828i
$105$	25.6597	+	10.6286i	0.0238488	+	0.00987851i
$106$			979.107i			0.897163i
$107$	449.658	−	1085.57i	0.406263	−	0.980805i	−0.579849	−	0.814724i	$-0.696889\pi$
$107$	449.658	−	1085.57i	0.406263	−	0.980805i	0.986112	−	0.166081i	$-0.0531114\pi$
$108$	178.665	−	74.0055i	0.159186	−	0.0659368i
$109$	321.020	+	775.010i	0.282093	+	0.681032i	0.999884	−	0.0152262i	$-0.00484683\pi$
$109$	321.020	+	775.010i	0.282093	+	0.681032i	−0.717791	+	0.696258i	$0.754847\pi$
$110$	−304.173	−	304.173i	−0.263652	−	0.263652i
$111$	−215.121	−	215.121i	−0.183950	−	0.183950i
$112$	80.7478	+	194.943i	0.0681246	+	0.164467i
$113$	−1872.53	+	775.626i	−1.55887	+	0.645706i	−0.984893	−	0.173164i	$-0.944601\pi$
$113$	−1872.53	+	775.626i	−1.55887	+	0.645706i	−0.573979	+	0.818870i	$0.694601\pi$
$114$	−79.9163	+	192.935i	−0.0656566	+	0.158509i
$115$		−	1056.02i		−	0.856301i
$116$	−35.9564	−	14.8936i	−0.0287799	−	0.0119210i
$117$	−972.953	+	972.953i	−0.768800	+	0.768800i
$118$	172.587			0.134643
$119$	76.7378	+	179.505i	0.0591138	+	0.138279i
$120$	190.505			0.144922
$121$	−416.267	+	416.267i	−0.312748	+	0.312748i
$122$	−2384.95	−	987.880i	−1.76986	−	0.733102i
$123$			521.423i			0.382237i
$124$	99.2750	−	239.671i	0.0718964	−	0.173573i
$125$	−1040.59	+	431.028i	−0.744588	+	0.308419i
$126$	−77.4070	−	186.877i	−0.0547299	−	0.132130i
$127$	1131.58	+	1131.58i	0.790645	+	0.790645i	0.981599	−	0.190954i	$-0.0611582\pi$
$127$	1131.58	+	1131.58i	0.790645	+	0.790645i	−0.190954	+	0.981599i	$0.561158\pi$
$128$	1233.15	+	1233.15i	0.851533	+	0.851533i
$129$	241.438	+	582.884i	0.164787	+	0.397830i
$130$	871.342	−	360.921i	0.587859	−	0.243499i
$131$	1000.75	−	2416.01i	0.667447	−	1.61136i	−0.118420	−	0.992964i	$-0.537783\pi$
$131$	1000.75	−	2416.01i	0.667447	−	1.61136i	0.785867	−	0.618396i	$-0.212217\pi$
$132$		−	105.305i		−	0.0694364i
$133$	85.5845	+	35.4502i	0.0557979	+	0.0231122i
$134$	−1630.13	+	1630.13i	−1.05091	+	1.05091i
$135$	−498.946			−0.318092
$136$	957.470	+	936.103i	0.603694	+	0.590222i
$137$	745.711			0.465039			0.232520	−	0.972592i	$-0.425303\pi$
$137$	745.711			0.465039			0.232520	+	0.972592i	$0.425303\pi$
$138$	936.257	−	936.257i	0.577533	−	0.577533i
$139$	−2339.68	−	969.128i	−1.42769	−	0.591369i	−0.470912	−	0.882180i	$-0.656075\pi$
$139$	−2339.68	−	969.128i	−1.42769	−	0.591369i	−0.956781	+	0.290811i	$0.906075\pi$
$140$			27.0696i			0.0163414i
$141$	251.058	−	606.108i	0.149950	−	0.362011i
$142$	1832.75	−	759.149i	1.08310	−	0.448636i
$143$	622.819	+	1503.62i	0.364215	+	0.879293i
$144$	−1233.96	−	1233.96i	−0.714099	−	0.714099i
$145$	71.0029	+	71.0029i	0.0406653	+	0.0406653i
$146$	599.039	+	1446.21i	0.339567	+	0.819788i
$147$	−616.779	+	255.478i	−0.346062	+	0.143343i
$148$	113.471	−	273.943i	0.0630220	−	0.152149i
$149$		−	1816.70i		−	0.998858i	−0.866355	−	0.499429i	$-0.833543\pi$
$149$		−	1816.70i		−	0.998858i	0.866355	−	0.499429i	$-0.166457\pi$
$150$	−579.631	−	240.091i	−0.315511	−	0.130689i
$151$	1499.42	−	1499.42i	0.808085	−	0.808085i	−0.176259	−	0.984344i	$-0.556400\pi$
$151$	1499.42	−	1499.42i	0.808085	−	0.808085i	0.984344	+	0.176259i	$0.0563996\pi$
$152$	635.404			0.339066
$153$	−1154.46	−	1128.70i	−0.610019	−	0.596406i
$154$	−239.252			−0.125191
$155$	−473.276	+	473.276i	−0.245255	+	0.245255i
$156$	213.305	+	88.3538i	0.109475	+	0.0453459i
$157$			1607.82i			0.817314i	0.912688	+	0.408657i	$0.134003\pi$
$157$			1607.82i			0.817314i	−0.912688	+	0.408657i	$0.865997\pi$
$158$	108.623	−	262.239i	0.0546935	−	0.132042i
$159$	571.330	−	236.653i	0.284965	−	0.118036i
$160$	164.870	+	398.031i	0.0814632	+	0.196670i
$161$	−415.316	−	415.316i	−0.203301	−	0.203301i
$162$	944.199	+	944.199i	0.457922	+	0.457922i
$163$	−871.753	−	2104.60i	−0.418902	−	1.01132i	−0.982666	−	0.185383i	$-0.940647\pi$
$163$	−871.753	−	2104.60i	−0.418902	−	1.01132i	0.563765	−	0.825936i	$-0.309353\pi$
$164$	−469.517	+	194.480i	−0.223556	+	0.0925998i
$165$	−103.972	+	251.011i	−0.0490559	+	0.118431i
$166$			1147.74i			0.536638i
$167$	1526.36	+	632.239i	0.707265	+	0.292959i	0.707172	−	0.707041i	$-0.249971\pi$
$167$	1526.36	+	632.239i	0.707265	+	0.292959i	9.26752e−5		1.00000i	$0.499971\pi$
$168$	74.9224	−	74.9224i	0.0344071	−	0.0344071i
$169$	−1371.29			−0.624165
$170$	435.012	+	1017.58i	0.196258	+	0.459088i
$171$	−766.135			−0.342619
$172$	−434.809	+	434.809i	−0.192755	+	0.192755i
$173$	2042.54	+	846.046i	0.897637	+	0.371813i	0.783311	−	0.621630i	$-0.213529\pi$
$173$	2042.54	+	846.046i	0.897637	+	0.371813i	0.114326	+	0.993443i	$0.463529\pi$
$174$			125.901i			0.0548534i
$175$	−106.502	+	257.120i	−0.0460048	+	0.111065i
$176$	−1906.99	+	789.900i	−0.816731	+	0.338301i
$177$	−41.7147	−	100.708i	−0.0177145	−	0.0427667i
$178$	428.230	+	428.230i	0.180321	+	0.180321i
$179$	14.6759	+	14.6759i	0.00612807	+	0.00612807i	0.710164	−	0.704036i	$-0.248621\pi$
$179$	14.6759	+	14.6759i	0.00612807	+	0.00612807i	−0.704036	+	0.710164i	$0.748621\pi$
$180$	−85.6738	−	206.835i	−0.0354764	−	0.0856475i
$181$	403.272	−	167.041i	0.165608	−	0.0685969i	−0.298340	−	0.954460i	$-0.596433\pi$
$181$	403.272	−	167.041i	0.165608	−	0.0685969i	0.463947	+	0.885863i	$0.346433\pi$
$182$	200.740	−	484.629i	0.0817572	−	0.197379i
$183$			1630.45i			0.658612i
$184$	−3722.03	−	1541.71i	−1.49126	−	0.617700i
$185$	−540.953	+	540.953i	−0.214982	+	0.214982i
$186$	−839.202			−0.330824
$187$	−1755.98	+	750.673i	−0.686683	+	0.293554i
$188$	639.412			0.248053
$189$	−196.227	+	196.227i	−0.0755208	+	0.0755208i
$190$	485.162	+	200.961i	0.185249	+	0.0767328i
$191$		−	787.808i		−	0.298449i	−0.988803	−	0.149225i	$-0.952322\pi$
$191$		−	787.808i		−	0.298449i	0.988803	−	0.149225i	$-0.0476777\pi$
$192$	255.157	−	616.004i	0.0959082	−	0.231543i
$193$	3443.17	−	1426.21i	1.28417	−	0.531921i	0.366928	−	0.930249i	$-0.380410\pi$
$193$	3443.17	−	1426.21i	1.28417	−	0.531921i	0.917243	+	0.398329i	$0.130410\pi$
$194$	−1629.11	−	3933.01i	−0.602903	−	1.45554i
$195$	−421.211	−	421.211i	−0.154685	−	0.154685i
$196$	−460.093	−	460.093i	−0.167672	−	0.167672i
$197$	172.929	+	417.488i	0.0625415	+	0.150989i	0.952061	−	0.305909i	$-0.0989605\pi$
$197$	172.929	+	417.488i	0.0625415	+	0.150989i	−0.889519	+	0.456898i	$0.848960\pi$
$198$	1828.09	−	757.219i	0.656144	−	0.271784i
$199$	−1331.80	+	3215.25i	−0.474416	+	1.14534i	0.487775	+	0.872969i	$0.337809\pi$
$199$	−1331.80	+	3215.25i	−0.474416	+	1.14534i	−0.962192	+	0.272373i	$0.912191\pi$
$200$			1908.93i			0.674910i
$201$	1345.22	+	557.210i	0.472064	+	0.195535i
$202$	677.798	−	677.798i	0.236088	−	0.236088i
$203$	55.8485			0.0193093
$204$	−100.843	+	251.444i	−0.0346099	+	0.0862972i
$205$	1311.19			0.446719
$206$	2203.84	−	2203.84i	0.745384	−	0.745384i
$207$	4487.82	+	1858.91i	1.50688	+	0.624171i
$208$		−	4525.54i		−	1.50860i
$209$	−346.785	+	837.214i	−0.114773	+	0.277088i
$210$	80.9029	−	33.5111i	0.0265849	−	0.0110118i
$211$	695.912	+	1680.08i	0.227055	+	0.548159i	0.995816	−	0.0913768i	$-0.0291268\pi$
$211$	695.912	+	1680.08i	0.227055	+	0.548159i	−0.768762	+	0.639535i	$0.779127\pi$
$212$	426.190	+	426.190i	0.138070	+	0.138070i
$213$	−885.960	−	885.960i	−0.285000	−	0.285000i
$214$	−1417.74	−	3422.72i	−0.452871	−	1.09333i
$215$	1465.74	−	607.131i	0.464944	−	0.192586i
$216$	−728.424	+	1758.57i	−0.229458	+	0.553961i
$217$			372.263i			0.116456i
$218$	2443.54	+	1012.15i	0.759163	+	0.314456i
$219$	699.105	−	699.105i	0.215713	−	0.215713i
$220$	−264.803			−0.0811502
$221$	−47.2434	−	4186.74i	−0.0143798	−	1.27435i
$222$	−959.205			−0.289989
$223$	−4601.73	+	4601.73i	−1.38186	+	1.38186i	−0.540546	+	0.841315i	$0.681782\pi$
$223$	−4601.73	+	4601.73i	−1.38186	+	1.38186i	−0.841315	+	0.540546i	$0.818218\pi$
$224$	221.380	+	91.6984i	0.0660337	+	0.0273521i
$225$		−	2301.69i		−	0.681981i
$226$	−2445.48	+	5903.92i	−0.719784	+	1.73771i
$227$	−2242.41	+	928.835i	−0.655655	+	0.271581i	−0.685609	−	0.727970i	$-0.740464\pi$
$227$	−2242.41	+	928.835i	−0.655655	+	0.271581i	0.0299538	+	0.999551i	$0.490464\pi$
$228$	49.1953	+	118.768i	0.0142897	+	0.0344983i
$229$	−463.654	−	463.654i	−0.133795	−	0.133795i	0.637037	−	0.770833i	$-0.280160\pi$
$229$	−463.654	−	463.654i	−0.133795	−	0.133795i	−0.770833	+	0.637037i	$0.780160\pi$
$230$	−2354.35	−	2354.35i	−0.674962	−	0.674962i
$231$	57.8279	+	139.609i	0.0164710	+	0.0397645i
$232$	353.914	−	146.596i	0.100153	−	0.0414849i
$233$	−448.391	+	1082.51i	−0.126073	+	0.304368i	−0.974296	−	0.225272i	$-0.927673\pi$
$233$	−448.391	+	1082.51i	−0.126073	+	0.304368i	0.848223	+	0.529640i	$0.177673\pi$
$234$			4338.30i			1.21198i
$235$	−1524.14	−	631.321i	−0.423081	−	0.175246i
$236$	75.1244	−	75.1244i	0.0207211	−	0.0207211i
$237$	−179.277			−0.0491361
$238$	571.281	+	229.115i	0.155591	+	0.0624005i
$239$	−5281.06			−1.42930			−0.714651	−	0.699481i	$-0.753415\pi$
$239$	−5281.06			−1.42930			−0.714651	+	0.699481i	$0.753415\pi$
$240$	534.208	−	534.208i	0.143679	−	0.143679i
$241$	1226.76	+	508.143i	0.327896	+	0.135819i	0.540558	−	0.841307i	$-0.318213\pi$
$241$	1226.76	+	508.143i	0.327896	+	0.135819i	−0.212662	+	0.977126i	$0.568213\pi$
$242$			1856.09i			0.493034i
$243$	1352.25	−	3264.61i	0.356982	−	0.861831i
$244$	−1468.14	+	608.124i	−0.385197	+	0.159554i
$245$	642.436	+	1550.98i	0.167525	+	0.404442i
$246$	1162.49	+	1162.49i	0.301290	+	0.301290i
$247$	−1404.89	−	1404.89i	−0.361908	−	0.361908i
$248$	977.148	+	2359.04i	0.250197	+	0.604030i
$249$	669.732	−	277.412i	0.170452	−	0.0706035i
$250$	−1359.00	+	3280.91i	−0.343802	+	0.830011i
$251$		−	4280.39i		−	1.07640i	−0.842818	−	0.538198i	$-0.819105\pi$
$251$		−	4280.39i		−	1.07640i	0.842818	−	0.538198i	$-0.180895\pi$
$252$	−115.039	−	47.6506i	−0.0287570	−	0.0119115i
$253$	4062.75	−	4062.75i	1.00958	−	1.00958i
$254$	5045.62			1.24642
$255$	488.638	−	499.791i	0.119999	−	0.122738i
$256$	2819.92			0.688458
$257$	171.749	−	171.749i	0.0416865	−	0.0416865i	−0.685956	−	0.727643i	$-0.740616\pi$
$257$	171.749	−	171.749i	0.0416865	−	0.0416865i	0.727643	+	0.685956i	$0.240616\pi$
$258$	1837.79	+	761.236i	0.443471	+	0.183692i
$259$			425.496i			0.102081i
$260$	222.178	−	536.385i	0.0529957	−	0.127943i
$261$	−426.730	+	176.757i	−0.101203	+	0.0419195i
$262$	−3155.27	−	7617.49i	−0.744020	−	1.79622i
$263$	2229.86	+	2229.86i	0.522809	+	0.522809i	0.918419	−	0.395609i	$-0.129467\pi$
$263$	2229.86	+	2229.86i	0.522809	+	0.522809i	−0.395609	+	0.918419i	$0.629467\pi$
$264$	732.915	+	732.915i	0.170863	+	0.170863i
$265$	−595.097	−	1436.69i	−0.137949	−	0.333038i
$266$	269.841	−	111.772i	0.0621993	−	0.0257638i
$267$	146.377	−	353.386i	0.0335511	−	0.0809995i
$268$			1419.14i			0.323462i
$269$	−194.844	−	80.7072i	−0.0441631	−	0.0182930i	0.360493	−	0.932762i	$-0.382609\pi$
$269$	−194.844	−	80.7072i	−0.0441631	−	0.0182930i	−0.404656	+	0.914469i	$0.632609\pi$
$270$	−1112.38	+	1112.38i	−0.250730	+	0.250730i
$271$	1627.36			0.364780			0.182390	−	0.983226i	$-0.441617\pi$
$271$	1627.36			0.364780			0.182390	+	0.983226i	$0.441617\pi$
$272$	5309.90	−	59.9172i	1.18368	−	0.0133567i
$273$	−331.311			−0.0734500
$274$	1662.52	−	1662.52i	0.366558	−	0.366558i
$275$	−2515.23	−	1041.84i	−0.551541	−	0.228456i
$276$		−	815.076i		−	0.177760i
$277$	−1770.63	+	4274.69i	−0.384069	+	0.927224i	0.607101	+	0.794625i	$0.292332\pi$
$277$	−1770.63	+	4274.69i	−0.384069	+	0.927224i	−0.991170	+	0.132599i	$0.957668\pi$
$278$	−7376.82	+	3055.58i	−1.59148	+	0.659214i
$279$	−1178.19	−	2844.41i	−0.252819	−	0.610359i
$280$	−188.403	−	188.403i	−0.0402115	−	0.0402115i
$281$	−3589.47	−	3589.47i	−0.762029	−	0.762029i	0.214660	−	0.976689i	$-0.431136\pi$
$281$	−3589.47	−	3589.47i	−0.762029	−	0.762029i	−0.976689	+	0.214660i	$0.931136\pi$
$282$	−791.566	−	1911.01i	−0.167153	−	0.403542i
$283$	−2251.53	+	932.616i	−0.472932	+	0.195895i	−0.606402	−	0.795158i	$-0.707388\pi$
$283$	−2251.53	+	932.616i	−0.472932	+	0.195895i	0.133470	+	0.991053i	$0.457388\pi$
$284$	467.321	−	1128.21i	0.0976422	−	0.235729i
$285$		−	331.676i		−	0.0689360i
$286$	4740.79	+	1963.70i	0.980170	+	0.406000i
$287$	515.669	−	515.669i	0.106059	−	0.106059i
$288$	−1981.75			−0.405471
$289$	4911.75	−	110.863i	0.999745	−	0.0225653i
$290$	316.595			0.0641072
$291$	−1901.24	+	1901.24i	−0.382999	+	0.382999i
$292$	890.265	+	368.760i	0.178421	+	0.0739042i
$293$			3300.30i			0.658041i	0.944323	+	0.329020i	$0.106718\pi$
$293$			3300.30i			0.658041i	−0.944323	+	0.329020i	$0.893282\pi$
$294$	−805.502	+	1944.65i	−0.159788	+	0.385763i
$295$	−253.245	+	104.898i	−0.0499814	+	0.0207030i
$296$	1116.88	+	2696.38i	0.219315	+	0.529472i
$297$	−1919.56	−	1919.56i	−0.375030	−	0.375030i
$298$	−4050.24	−	4050.24i	−0.787329	−	0.787329i
$299$	4820.73	+	11638.3i	0.932408	+	2.25103i
$300$	−356.812	+	147.797i	−0.0686686	+	0.0284435i
$301$	337.678	−	815.227i	0.0646626	−	0.156109i
$302$		−	6685.75i		−	1.27391i
$303$	−559.336	−	231.684i	−0.106049	−	0.0439271i
$304$	1781.78	−	1781.78i	0.336158	−	0.336158i
$305$	4099.98			0.769719
$306$	−5090.20	+	57.4382i	−0.950940	+	0.0107305i
$307$	−1186.40			−0.220558			−0.110279	−	0.993901i	$-0.535174\pi$
$307$	−1186.40			−0.220558			−0.110279	+	0.993901i	$0.535174\pi$
$308$	−104.143	+	104.143i	−0.0192665	+	0.0192665i
$309$	−1818.67	−	753.316i	−0.334823	−	0.138688i
$310$			2110.29i			0.386634i
$311$	251.604	−	607.425i	0.0458751	−	0.110752i	−0.899281	−	0.437371i	$-0.855909\pi$
$311$	251.604	−	607.425i	0.0458751	−	0.110752i	0.945156	+	0.326619i	$0.105909\pi$
$312$	−2099.53	+	869.653i	−0.380969	+	0.157803i
$313$	2324.29	+	5611.33i	0.419733	+	1.01333i	0.982425	+	0.186659i	$0.0597659\pi$
$313$	2324.29	+	5611.33i	0.419733	+	1.01333i	−0.562691	+	0.826667i	$0.690234\pi$
$314$	3584.56	+	3584.56i	0.644231	+	0.644231i
$315$	227.166	+	227.166i	0.0406329	+	0.0406329i
$316$	−66.8666	−	161.430i	−0.0119036	−	0.0287379i
$317$	−5315.32	+	2201.68i	−0.941761	+	0.390090i	−0.800128	−	0.599829i	$-0.795235\pi$
$317$	−5315.32	+	2201.68i	−0.941761	+	0.390090i	−0.141633	+	0.989919i	$0.545235\pi$
$318$	746.147	−	1801.36i	0.131578	−	0.317658i
$319$			546.327i			0.0958886i
$320$	−1549.03	−	641.628i	−0.270604	−	0.112088i
$321$	−1654.56	+	1654.56i	−0.287690	+	0.287690i
$322$	−1851.85			−0.320496
$323$	1629.79	−	1666.99i	0.280755	−	0.287163i
$324$	821.991			0.140945
$325$	4220.70	−	4220.70i	0.720376	−	0.720376i
$326$	−6635.63	−	2748.57i	−1.12734	−	0.466960i
$327$		−	1670.50i		−	0.282504i
$328$	1914.24	−	4621.38i	0.322245	−	0.777967i
$329$	−847.708	+	351.132i	−0.142054	+	0.0588406i
$330$	327.816	+	791.417i	0.0546838	+	0.132018i
$331$	63.5284	+	63.5284i	0.0105493	+	0.0105493i	0.712362	−	0.701812i	$-0.247626\pi$
$331$	63.5284	+	63.5284i	0.0105493	+	0.0105493i	−0.701812	+	0.712362i	$0.747626\pi$
$332$	499.594	+	499.594i	0.0825866	+	0.0825866i
$333$	−1346.67	−	3251.15i	−0.221613	−	0.535020i
$334$	4812.49	−	1993.40i	0.788406	−	0.326568i
$335$	1401.18	−	3382.75i	0.228522	−	0.551700i
$336$		−	420.190i		−	0.0682240i
$337$	782.810	+	324.251i	0.126535	+	0.0524126i	0.445053	−	0.895504i	$-0.353185\pi$
$337$	782.810	+	324.251i	0.126535	+	0.0524126i	−0.318517	+	0.947917i	$0.603185\pi$
$338$	−3057.22	+	3057.22i	−0.491985	+	0.491985i
$339$	4036.15			0.646648
$340$	632.292	+	253.584i	0.100855	+	0.0404486i
$341$	−3641.60			−0.578309
$342$	−1708.06	+	1708.06i	−0.270062	+	0.270062i
$343$	1745.23	+	722.896i	0.274733	+	0.113798i
$344$		−	6052.48i		−	0.948628i
$345$	−804.762	+	1942.87i	−0.125585	+	0.303190i
$346$	6439.95	−	2667.51i	1.00062	−	0.414469i
$347$	−225.906	−	545.386i	−0.0349490	−	0.0843742i	0.905441	−	0.424471i	$-0.139540\pi$
$347$	−225.906	−	545.386i	−0.0349490	−	0.0843742i	−0.940390	+	0.340097i	$0.889540\pi$
$348$	54.8026	+	54.8026i	0.00844174	+	0.00844174i
$349$	6638.10	+	6638.10i	1.01813	+	1.01813i	0.999832	+	0.0183025i	$0.00582618\pi$
$349$	6638.10	+	6638.10i	1.01813	+	1.01813i	0.0183025	+	0.999832i	$0.494174\pi$
$350$	335.794	+	810.677i	0.0512826	+	0.123807i
$351$	5498.81	−	2277.68i	0.836196	−	0.346364i
$352$	−897.023	+	2165.60i	−0.135828	+	0.327918i
$353$		−	6176.09i		−	0.931218i	−0.884990	−	0.465609i	$-0.845835\pi$
$353$		−	6176.09i		−	0.931218i	0.884990	−	0.465609i	$-0.154165\pi$
$354$	−317.525	−	131.523i	−0.0476731	−	0.0197468i
$355$	−2227.87	+	2227.87i	−0.333079	+	0.333079i
$356$	372.804			0.0555015
$357$	−4.38649	−	388.733i	−0.000650301	−	0.0576300i
$358$	65.4382			0.00966066
$359$	5056.62	−	5056.62i	0.743393	−	0.743393i	−0.229836	−	0.973229i	$-0.573819\pi$
$359$	5056.62	−	5056.62i	0.743393	−	0.743393i	0.973229	+	0.229836i	$0.0738191\pi$
$360$	2035.84	+	843.273i	0.298051	+	0.123457i
$361$			5752.74i			0.838714i
$362$	526.666	−	1271.48i	0.0764667	−	0.184607i
$363$	1083.07	−	448.623i	0.156602	−	0.0648667i
$364$	−123.572	−	298.330i	−0.0177938	−	0.0429581i
$365$	−1758.00	−	1758.00i	−0.252104	−	0.252104i
$366$	3635.00	+	3635.00i	0.519137	+	0.519137i
$367$	−1285.07	−	3102.43i	−0.182780	−	0.441269i	0.805758	−	0.592245i	$-0.201758\pi$
$367$	−1285.07	−	3102.43i	−0.182780	−	0.441269i	−0.988537	+	0.150976i	$0.951758\pi$
$368$	−14760.4	+	6113.96i	−2.09087	+	0.866066i
$369$	−2308.08	+	5572.21i	−0.325621	+	0.786118i
$370$			2412.05i			0.338910i
$371$	−799.068	−	330.985i	−0.111821	−	0.0463177i
$372$	−365.292	+	365.292i	−0.0509126	+	0.0509126i
$373$	−8379.14			−1.16315			−0.581576	−	0.813492i	$-0.697564\pi$
$373$	−8379.14			−1.16315			−0.581576	+	0.813492i	$0.697564\pi$
$374$	−2241.27	+	5588.45i	−0.309876	+	0.772652i
$375$	2242.95			0.308868
$376$	−4450.27	+	4450.27i	−0.610386	+	0.610386i
$377$	−1106.64	−	458.385i	−0.151180	−	0.0626207i
$378$			874.957i			0.119055i
$379$	2447.53	−	5908.86i	0.331718	−	0.800839i	−0.666738	−	0.745292i	$-0.732310\pi$
$379$	2447.53	−	5908.86i	0.331718	−	0.800839i	0.998456	−	0.0555463i	$-0.0176901\pi$
$380$	298.659	−	123.709i	0.0403181	−	0.0167003i
$381$	−1219.54	−	2944.23i	−0.163987	−	0.395899i
$382$	−1756.38	−	1756.38i	−0.235246	−	0.235246i
$383$	−144.736	−	144.736i	−0.0193098	−	0.0193098i	0.697386	−	0.716696i	$-0.254346\pi$
$383$	−144.736	−	144.736i	−0.0193098	−	0.0193098i	−0.716696	+	0.697386i	$0.754346\pi$
$384$	−1329.00	−	3208.49i	−0.176615	−	0.426387i
$385$	351.066	−	145.416i	0.0464727	−	0.0192496i
$386$	4496.72	−	10856.0i	0.592945	−	1.43150i
$387$			7297.75i			0.958567i
$388$	−2421.11	−	1002.85i	−0.316786	−	0.131217i
$389$	−4080.40	+	4080.40i	−0.531837	+	0.531837i	−0.921119	−	0.389282i	$-0.872723\pi$
$389$	−4080.40	+	4080.40i	−0.531837	+	0.531837i	0.389282	+	0.921119i	$0.372723\pi$
$390$	−1878.14			−0.243854
$391$	−13591.6	+	5810.33i	−1.75794	+	0.751512i
$392$	6404.44			0.825186
$393$	−3682.34	+	3682.34i	−0.472645	+	0.472645i
$394$	1316.30	+	545.231i	0.168311	+	0.0697166i
$395$			450.816i			0.0574253i
$396$	466.133	−	1125.34i	0.0591517	−	0.142805i
$397$	6600.54	−	2734.03i	0.834437	−	0.345635i	0.0757795	−	0.997125i	$-0.475855\pi$
$397$	6600.54	−	2734.03i	0.834437	−	0.345635i	0.758658	+	0.651489i	$0.225855\pi$
$398$	4199.06	+	10137.4i	0.528844	+	1.27674i
$399$	−130.443	−	130.443i	−0.0163667	−	0.0163667i
$400$	5352.97	+	5352.97i	0.669121	+	0.669121i
$401$	−2435.60	−	5880.05i	−0.303312	−	0.732259i	−0.999891	−	0.0147789i	$-0.995296\pi$
$401$	−2435.60	−	5880.05i	−0.303312	−	0.732259i	0.696579	−	0.717480i	$-0.254704\pi$
$402$	4241.38	−	1756.84i	0.526221	−	0.217968i
$403$	3055.41	−	7376.40i	0.377669	−	0.911774i
$404$		−	590.070i		−	0.0726660i
$405$	−1959.35	−	811.589i	−0.240397	−	0.0995757i
$406$	124.511	−	124.511i	0.0152202	−	0.0152202i
$407$	−4162.33			−0.506926
$408$	−1048.18	−	2451.90i	−0.127187	−	0.297517i
$409$	2997.87			0.362433			0.181217	−	0.983443i	$-0.441997\pi$
$409$	2997.87			0.362433			0.181217	+	0.983443i	$0.441997\pi$
$410$	2923.23	−	2923.23i	0.352117	−	0.352117i
$411$	−1371.96	−	568.283i	−0.164656	−	0.0682028i
$412$		−	1918.60i		−	0.229424i
$413$	−58.3426	+	140.852i	−0.00695122	+	0.0167817i
$414$	14149.7	−	5861.00i	1.67976	−	0.695779i
$415$	−697.591	−	1684.13i	−0.0825142	−	0.199207i
$416$	−3634.01	−	3634.01i	−0.428298	−	0.428298i
$417$	3566.00	+	3566.00i	0.418771	+	0.418771i
$418$	1093.39	+	2639.67i	0.127941	+	0.308876i
$419$	10853.1	−	4495.49i	1.26541	−	0.524150i	0.353844	−	0.935304i	$-0.384874\pi$
$419$	10853.1	−	4495.49i	1.26541	−	0.524150i	0.911566	+	0.411154i	$0.134874\pi$
$420$	20.6289	−	49.8026i	0.00239664	−	0.00578600i
$421$			8842.15i			1.02361i	0.859102	+	0.511805i	$0.171023\pi$
$421$			8842.15i			1.02361i	−0.859102	+	0.511805i	$0.828977\pi$
$422$	5297.15	+	2194.15i	0.611046	+	0.253103i
$423$	5365.89	−	5365.89i	0.616782	−	0.616782i
$424$	−5932.52			−0.679501
$425$	5008.10	+	4896.34i	0.571597	+	0.558841i
$426$	−3950.41			−0.449291
$427$	1612.46	−	1612.46i	0.182745	−	0.182745i
$428$	−2106.97	−	872.737i	−0.237954	−	0.0985639i
$429$		−	3240.98i		−	0.364746i
$430$	1914.23	−	4621.37i	0.214680	−	0.518284i
$431$	2863.45	−	1186.08i	0.320018	−	0.132556i	−0.216891	−	0.976196i	$-0.569592\pi$
$431$	2863.45	−	1186.08i	0.320018	−	0.132556i	0.536909	+	0.843640i	$0.319592\pi$
$432$	2888.71	+	6973.95i	0.321720	+	0.776700i
$433$	−7122.55	−	7122.55i	−0.790503	−	0.790503i	0.191073	−	0.981576i	$-0.438803\pi$
$433$	−7122.55	−	7122.55i	−0.790503	−	0.790503i	−0.981576	+	0.191073i	$0.938803\pi$
$434$	829.942	+	829.942i	0.0917938	+	0.0917938i
$435$	−76.5218	−	184.740i	−0.00843434	−	0.0203623i
$436$	1504.21	−	623.064i	0.165226	−	0.0684389i
$437$	−2684.18	+	6480.18i	−0.293825	+	0.709357i
$438$		−	3117.24i		−	0.340063i
$439$	−16036.6	−	6642.57i	−1.74347	−	0.722170i	−0.998481	−	0.0550975i	$-0.982453\pi$
$439$	−16036.6	−	6642.57i	−1.74347	−	0.722170i	−0.744992	−	0.667073i	$-0.767547\pi$
$440$	1843.02	−	1843.02i	0.199687	−	0.199687i
$441$	−7722.12			−0.833832
$442$	−9439.45	−	9228.79i	−1.01581	−	0.993143i
$443$	6979.90			0.748589			0.374295	−	0.927310i	$-0.377885\pi$
$443$	6979.90			0.748589			0.374295	+	0.927310i	$0.377885\pi$
$444$	−417.527	+	417.527i	−0.0446283	+	0.0446283i
$445$	−888.638	−	368.086i	−0.0946640	−	0.0392111i
$446$			20518.7i			2.17845i
$447$	−1384.45	+	3342.36i	−0.146493	+	0.353665i
$448$	−861.549	+	356.865i	−0.0908579	+	0.0376346i
$449$	−3532.36	−	8527.87i	−0.371275	−	0.896336i	−0.993535	−	0.113526i	$-0.963785\pi$
$449$	−3532.36	−	8527.87i	−0.371275	−	0.896336i	0.622260	−	0.782810i	$-0.286215\pi$
$450$	−5131.49	−	5131.49i	−0.537557	−	0.537557i
$451$	5044.44	+	5044.44i	0.526681	+	0.526681i
$452$	1505.40	+	3634.37i	0.156655	+	0.378200i
$453$	−3901.28	+	1615.96i	−0.404632	+	0.167604i
$454$	−2928.54	+	7070.12i	−0.302738	+	0.730875i
$455$			833.127i			0.0858409i
$456$	−1169.02	−	484.222i	−0.120053	−	0.0497276i
$457$	−8662.49	+	8662.49i	−0.886683	+	0.886683i	−0.994203	−	0.107520i	$-0.965709\pi$
$457$	−8662.49	+	8662.49i	−0.886683	+	0.886683i	0.107520	+	0.994203i	$0.465709\pi$
$458$	−2067.39			−0.210923
$459$	2745.25	+	6421.69i	0.279166	+	0.653026i
$460$	−2049.62			−0.207748
$461$	4426.14	−	4426.14i	0.447171	−	0.447171i	−0.447242	−	0.894413i	$-0.647594\pi$
$461$	4426.14	−	4426.14i	0.447171	−	0.447171i	0.894413	+	0.447242i	$0.147594\pi$
$462$	440.175	+	182.327i	0.0443264	+	0.0183606i
$463$		−	10195.0i		−	1.02333i	−0.859185	−	0.511665i	$-0.829029\pi$
$463$		−	10195.0i		−	1.02333i	0.859185	−	0.511665i	$-0.170971\pi$
$464$	581.354	−	1403.51i	0.0581652	−	0.140423i
$465$	1231.40	−	510.063i	0.122806	−	0.0508680i
$466$	1413.74	+	3413.07i	0.140537	+	0.339286i
$467$	10453.2	+	10453.2i	1.03579	+	1.03579i	0.999335	+	0.0364587i	$0.0116077\pi$
$467$	10453.2	+	10453.2i	1.03579	+	1.03579i	0.0364587	+	0.999335i	$0.488392\pi$
$468$	1888.40	+	1888.40i	0.186519	+	0.186519i
$469$	−779.319	−	1881.44i	−0.0767284	−	0.185239i
$470$	−4805.50	+	1990.50i	−0.471619	+	0.195351i
$471$	1225.27	−	2958.07i	0.119867	−	0.289386i
$472$			1045.72i			0.101977i
$473$	7974.80	+	3303.27i	0.775226	+	0.321109i
$474$	−399.688	+	399.688i	−0.0387305	+	0.0387305i
$475$	3323.52			0.321039
$476$	348.400	−	148.940i	0.0335481	−	0.0143417i
$477$	7153.10			0.686620
$478$	−11773.9	+	11773.9i	−1.12662	+	1.12662i
$479$	−15123.9	−	6264.54i	−1.44265	−	0.597566i	−0.482212	−	0.876054i	$-0.660167\pi$
$479$	−15123.9	−	6264.54i	−1.44265	−	0.597566i	−0.960440	+	0.278488i	$0.910167\pi$
$480$		−	857.939i		−	0.0815820i
$481$	3492.32	−	8431.20i	0.331052	−	0.799230i
$482$	3867.89	−	1602.13i	0.365513	−	0.151401i
$483$	447.598	+	1080.60i	0.0421665	+	0.101799i
$484$	807.929	+	807.929i	0.0758761	+	0.0758761i
$485$	4780.93	+	4780.93i	0.447610	+	0.447610i
$486$	−4263.52	−	10293.1i	−0.397937	−	0.960704i
$487$	3793.74	−	1571.42i	0.352999	−	0.146217i	−0.199135	−	0.979972i	$-0.563813\pi$
$487$	3793.74	−	1571.42i	0.352999	−	0.146217i	0.552135	+	0.833755i	$0.313813\pi$
$488$	5985.67	−	14450.7i	0.555243	−	1.34048i
$489$			4536.37i			0.419513i
$490$	4890.10	+	2025.55i	0.450841	+	0.186745i
$491$	620.841	−	620.841i	0.0570634	−	0.0570634i	−0.677999	−	0.735063i	$-0.737153\pi$
$491$	620.841	−	620.841i	0.0570634	−	0.0570634i	0.735063	+	0.677999i	$0.237153\pi$
$492$	1012.02			0.0927349
$493$	523.179	−	1304.51i	0.0477948	−	0.119173i
$494$	−6264.28			−0.570533
$495$	−2222.21	+	2222.21i	−0.201779	+	0.201779i
$496$	9355.24	+	3875.07i	0.846901	+	0.350798i
$497$			1752.37i			0.158158i
$498$	874.657	−	2111.61i	0.0787034	−	0.190007i
$499$	−12767.7	+	5288.55i	−1.14541	+	0.474445i	−0.872992	−	0.487734i	$-0.837824\pi$
$499$	−12767.7	+	5288.55i	−1.14541	+	0.474445i	−0.272419	+	0.962179i	$0.587824\pi$
$500$	836.578	+	2019.68i	0.0748258	+	0.180646i
$501$	−2326.38	−	2326.38i	−0.207455	−	0.207455i
$502$	−9542.91	−	9542.91i	−0.848448	−	0.848448i
$503$	1806.81	+	4362.03i	0.160163	+	0.386667i	0.983506	−	0.180877i	$-0.0578937\pi$
$503$	1806.81	+	4362.03i	0.160163	+	0.386667i	−0.823343	+	0.567544i	$0.807894\pi$
$504$	1132.31	−	469.017i	0.100073	−	0.0414518i
$505$	−582.603	+	1406.53i	−0.0513376	+	0.123940i
$506$		−	18115.4i		−	1.59156i
$507$	2522.90	+	1045.02i	0.220997	+	0.0915401i
$508$	2196.28	−	2196.28i	0.191819	−	0.191819i
$509$	16554.3			1.44156			0.720782	−	0.693161i	$-0.243783\pi$
$509$	16554.3			1.44156			0.720782	+	0.693161i	$0.243783\pi$
$510$	−24.8662	−	2203.65i	−0.00215900	−	0.191332i
$511$	−1382.78			−0.119708
$512$	−3578.33	+	3578.33i	−0.308870	+	0.308870i
$513$	3061.73	+	1268.21i	0.263506	+	0.109148i
$514$		−	765.813i		−	0.0657171i
$515$	−1894.32	+	4573.29i	−0.162085	+	0.391307i
$516$	1131.31	−	468.606i	0.0965180	−	0.0399791i
$517$	−3434.88	−	8292.54i	−0.292197	−	0.705427i
$518$	948.621	+	948.621i	0.0804633	+	0.0804633i
$519$	−3113.11	−	3113.11i	−0.263295	−	0.263295i
$520$	2186.86	+	5279.55i	0.184424	+	0.445238i
$521$	−13632.3	+	5646.69i	−1.14634	+	0.474829i	−0.873304	−	0.487175i	$-0.838027\pi$
$521$	−13632.3	+	5646.69i	−1.14634	+	0.474829i	−0.273035	+	0.962004i	$0.588027\pi$
$522$	−557.301	+	1345.44i	−0.0467287	+	0.112813i
$523$			7800.86i			0.652214i	0.945333	+	0.326107i	$0.105737\pi$
$523$			7800.86i			0.652214i	−0.945333	+	0.326107i	$0.894263\pi$
$524$	−4689.22	−	1942.34i	−0.390934	−	0.161930i
$525$	391.886	−	391.886i	0.0325777	−	0.0325777i
$526$	9942.71			0.824188
$527$	8695.32	+	3487.30i	0.718736	+	0.288253i
$528$	4110.43			0.338795
$529$	22843.0	−	22843.0i	1.87746	−	1.87746i
$530$	−4529.77	−	1876.29i	−0.371246	−	0.153775i
$531$		−	1260.88i		−	0.103046i
$532$	68.8050	−	166.110i	0.00560729	−	0.0135372i
$533$	−14450.4	+	5985.56i	−1.17433	+	0.486423i
$534$	−461.515	−	1114.20i	−0.0374002	−	0.0902921i
$535$	4160.62	+	4160.62i	0.336223	+	0.336223i
$536$	−9877.14	−	9877.14i	−0.795947	−	0.795947i
$537$	−15.8166	−	38.1846i	−0.00127102	−	0.00306851i
$538$	−614.329	+	254.463i	−0.0492297	+	0.0203916i
$539$	−3495.36	+	8438.54i	−0.279324	+	0.674348i
$540$			968.399i			0.0771727i
$541$	21275.5	+	8812.61i	1.69077	+	0.700339i	0.999747	−	0.0224947i	$-0.00716090\pi$
$541$	21275.5	+	8812.61i	1.69077	+	0.700339i	0.691022	+	0.722834i	$0.257161\pi$
$542$	3628.13	−	3628.13i	0.287530	−	0.287530i
$543$	−869.235			−0.0686970
$544$	4215.74	−	4311.97i	0.332258	−	0.339842i
$545$	−4200.71			−0.330162
$546$	−738.641	+	738.641i	−0.0578954	+	0.0578954i
$547$	−2440.68	−	1010.96i	−0.190779	−	0.0790232i	0.285249	−	0.958454i	$-0.407924\pi$
$547$	−2440.68	−	1010.96i	−0.190779	−	0.0790232i	−0.476028	+	0.879430i	$0.657924\pi$
$548$		−	1447.34i		−	0.112824i
$549$	−7217.19	+	17423.8i	−0.561061	+	1.35452i
$550$	−7930.30	+	3284.84i	−0.614816	+	0.254665i
$551$	−255.228	−	616.176i	−0.0197334	−	0.0476406i
$552$	5672.88	+	5672.88i	0.437417	+	0.437417i
$553$	177.298	+	177.298i	0.0136338	+	0.0136338i
$554$	5582.66	+	13477.7i	0.428131	+	1.03360i
$555$	1407.49	−	583.000i	0.107648	−	0.0445892i
$556$	−1880.97	+	4541.06i	−0.143473	+	0.346374i
$557$		−	19800.8i		−	1.50626i	−0.657873	−	0.753129i	$-0.728544\pi$
$557$		−	19800.8i		−	1.50626i	0.657873	−	0.753129i	$-0.271456\pi$
$558$	−8968.18	−	3714.74i	−0.680382	−	0.281823i
$559$	−13382.2	+	13382.2i	−1.01253	+	1.01253i
$560$	−1056.63			−0.0797333
$561$	3802.71	−	42.9100i	0.286186	−	0.00322934i
$562$	−16005.1			−1.20131
$563$	−6882.93	+	6882.93i	−0.515241	+	0.515241i	−0.916128	−	0.400886i	$-0.868702\pi$
$563$	−6882.93	+	6882.93i	−0.515241	+	0.515241i	0.400886	+	0.916128i	$0.368702\pi$
$564$	−1176.39	−	487.276i	−0.0878279	−	0.0363795i
$565$		−	10149.5i		−	0.755736i
$566$	−2940.46	+	7098.90i	−0.218369	+	0.527189i
$567$	−1089.76	+	451.395i	−0.0807156	+	0.0334335i
$568$	4599.76	+	11104.8i	0.339792	+	0.820330i
$569$	−4483.53	−	4483.53i	−0.330333	−	0.330333i	0.522380	−	0.852713i	$-0.325044\pi$
$569$	−4483.53	−	4483.53i	−0.330333	−	0.330333i	−0.852713	+	0.522380i	$0.825044\pi$
$570$	−739.454	−	739.454i	−0.0543374	−	0.0543374i
$571$	4736.75	+	11435.5i	0.347157	+	0.838112i	0.996953	+	0.0780032i	$0.0248544\pi$
$571$	4736.75	+	11435.5i	0.347157	+	0.838112i	−0.649796	+	0.760109i	$0.725146\pi$
$572$	2918.36	−	1208.82i	0.213326	−	0.0883627i
$573$	−600.364	+	1449.41i	−0.0437706	+	0.105672i
$574$		−	2299.32i		−	0.167198i
$575$	−19468.3	−	8064.02i	−1.41197	−	0.584857i
$576$	5453.50	−	5453.50i	0.394495	−	0.394495i
$577$	36.6040			0.00264098			0.00132049	−	0.999999i	$-0.499580\pi$
$577$	36.6040			0.00264098			0.00132049	+	0.999999i	$0.499580\pi$
$578$	10703.3	−	11197.7i	0.770242	−	0.805815i
$579$	−7421.61			−0.532697
$580$	137.809	−	137.809i	0.00986586	−	0.00986586i
$581$	−936.693	−	387.991i	−0.0668857	−	0.0277049i
$582$			8477.44i			0.603782i
$583$	3237.80	−	7816.73i	0.230010	−	0.555293i
$584$	−8762.74	+	3629.64i	−0.620898	+	0.257184i
$585$	−2636.80	−	6365.80i	−0.186356	−	0.449903i
$586$	7357.86	+	7357.86i	0.518687	+	0.518687i
$587$	−14389.9	−	14389.9i	−1.01182	−	1.01182i	−0.999929	−	0.0118873i	$-0.996216\pi$
$587$	−14389.9	−	14389.9i	−1.01182	−	1.01182i	−0.0118873	−	0.999929i	$-0.503784\pi$
$588$	495.855	+	1197.10i	0.0347767	+	0.0839584i
$589$	4107.18	−	1701.25i	0.287323	−	0.119013i
$590$	−330.733	+	798.461i	−0.0230781	+	0.0557155i
$591$		−	899.876i		−	0.0626328i
$592$	10693.0	+	4429.19i	0.742365	+	0.307498i
$593$	14416.1	−	14416.1i	0.998308	−	0.998308i	−0.00169056	−	0.999999i	$-0.500538\pi$
$593$	14416.1	−	14416.1i	0.998308	−	0.998308i	0.999999	+	0.00169056i	$0.000538123\pi$
$594$	−8559.10			−0.591219
$595$	−977.523	+	11.0304i	−0.0673522	+	0.000760006i
$596$	−3526.02			−0.242334
$597$	4900.49	−	4900.49i	0.335952	−	0.335952i
$598$	36694.5	+	15199.4i	2.50928	+	1.03938i
$599$		−	316.417i		−	0.0215834i	−0.999942	−	0.0107917i	$-0.996565\pi$
$599$		−	316.417i		−	0.0215834i	0.999942	−	0.0107917i	$-0.00343517\pi$
$600$	1454.74	−	3512.05i	0.0989824	−	0.238965i
$601$	1230.47	−	509.678i	0.0835141	−	0.0345927i	−0.340535	−	0.940232i	$-0.610608\pi$
$601$	1230.47	−	509.678i	0.0835141	−	0.0345927i	0.424049	+	0.905639i	$0.360608\pi$
$602$	−1064.67	−	2570.34i	−0.0720810	−	0.174019i
$603$	11909.3	+	11909.3i	0.804286	+	0.804286i
$604$	−2910.20	−	2910.20i	−0.196050	−	0.196050i
$605$	−1128.13	−	2723.54i	−0.0758096	−	0.183021i
$606$	−1763.54	+	730.482i	−0.118216	+	0.0489667i
$607$	5309.03	−	12817.1i	0.355003	−	0.857053i	−0.640984	−	0.767554i	$-0.721473\pi$
$607$	5309.03	−	12817.1i	0.355003	−	0.857053i	0.995987	−	0.0894989i	$-0.0285266\pi$
$608$		−	2861.54i		−	0.190873i
$609$	−102.750	−	42.5604i	−0.00683684	−	0.00283191i
$610$	9140.71	−	9140.71i	0.606715	−	0.606715i
$611$	19679.3			1.30301
$612$	−2190.69	+	2240.69i	−0.144695	+	0.147998i
$613$	15297.0			1.00790			0.503948	−	0.863734i	$-0.331880\pi$
$613$	15297.0			1.00790			0.503948	+	0.863734i	$0.331880\pi$
$614$	−2645.01	+	2645.01i	−0.173850	+	0.173850i
$615$	−2412.32	−	999.217i	−0.158170	−	0.0655160i
$616$		−	1449.66i		−	0.0948186i
$617$	−5784.96	+	13966.1i	−0.377461	+	0.911272i	0.614979	+	0.788544i	$0.289165\pi$
$617$	−5784.96	+	13966.1i	−0.377461	+	0.911272i	−0.992440	+	0.122729i	$0.960835\pi$
$618$	−5734.11	+	2375.14i	−0.373236	+	0.154599i
$619$	−8576.73	−	20706.0i	−0.556911	−	1.34450i	−0.912200	−	0.409745i	$-0.865618\pi$
$619$	−8576.73	−	20706.0i	−0.556911	−	1.34450i	0.355289	−	0.934756i	$-0.384382\pi$
$620$	918.577	+	918.577i	0.0595015	+	0.0595015i
$621$	−14857.7	−	14857.7i	−0.960094	−	0.960094i
$622$	−793.286	−	1915.16i	−0.0511381	−	0.123458i
$623$	−494.249	+	204.724i	−0.0317844	+	0.0131655i
$624$	−3448.77	+	8326.08i	−0.221252	+	0.534150i
$625$			6850.26i			0.438417i
$626$	17692.1	+	7328.29i	1.12958	+	0.467887i
$627$	1276.03	−	1276.03i	0.0812754	−	0.0812754i
$628$	3120.61			0.198290
$629$	9938.72	+	3985.97i	0.630020	+	0.252673i
$630$	1012.91			0.0640560
$631$	−3415.99	+	3415.99i	−0.215513	+	0.215513i	−0.806604	−	0.591092i	$-0.798697\pi$
$631$	−3415.99	+	3415.99i	−0.215513	+	0.215513i	0.591092	+	0.806604i	$0.298697\pi$
$632$	1588.93	+	658.158i	0.100007	+	0.0414242i
$633$		−	3621.34i		−	0.227386i
$634$	−6941.71	+	16758.8i	−0.434843	+	1.04980i
$635$	−7403.68	+	3066.70i	−0.462687	+	0.191651i
$636$	−459.317	−	1108.89i	−0.0286370	−	0.0691357i
$637$	−14160.4	−	14160.4i	−0.880776	−	0.880776i
$638$	1218.01	+	1218.01i	0.0755822	+	0.0755822i
$639$	−5546.14	−	13389.6i	−0.343352	−	0.828925i
$640$	−8068.21	+	3341.96i	−0.498319	+	0.206410i
$641$	−8804.50	+	21255.9i	−0.542522	+	1.30976i	0.380416	+	0.924816i	$0.375781\pi$
$641$	−8804.50	+	21255.9i	−0.542522	+	1.30976i	−0.922938	+	0.384949i	$0.874219\pi$
$642$			7377.52i			0.453532i
$643$	−5256.78	−	2177.43i	−0.322406	−	0.133545i	0.215610	−	0.976480i	$-0.430826\pi$
$643$	−5256.78	−	2177.43i	−0.322406	−	0.133545i	−0.538016	+	0.842935i	$0.680826\pi$
$644$	−806.083	+	806.083i	−0.0493232	+	0.0493232i
$645$	−3159.35			−0.192867
$646$	−82.9378	−	7350.00i	−0.00505131	−	0.447650i
$647$	−15949.0			−0.969122			−0.484561	−	0.874758i	$-0.661021\pi$
$647$	−15949.0			−0.969122			−0.484561	+	0.874758i	$0.661021\pi$
$648$	−5721.01	+	5721.01i	−0.346825	+	0.346825i
$649$	−1377.85	−	570.726i	−0.0833366	−	0.0345192i
$650$		−	18819.7i		−	1.13564i
$651$	283.690	−	684.889i	0.0170794	−	0.0412334i
$652$	−4084.79	+	1691.98i	−0.245357	+	0.101630i
$653$	4119.43	+	9945.18i	0.246869	+	0.595995i	0.997935	−	0.0642322i	$-0.0204598\pi$
$653$	4119.43	+	9945.18i	0.246869	+	0.595995i	−0.751066	+	0.660228i	$0.770460\pi$
$654$	−3724.30	−	3724.30i	−0.222678	−	0.222678i
$655$	9259.75	+	9259.75i	0.552379	+	0.552379i
$656$	−7591.28	−	18327.0i	−0.451814	−	1.09078i
$657$	10565.6	−	4376.42i	0.627404	−	0.259879i
$658$	−1107.09	+	2672.75i	−0.0655910	+	0.158351i
$659$			25208.2i			1.49010i	0.667011	+	0.745048i	$0.267573\pi$
$659$			25208.2i			1.49010i	−0.667011	+	0.745048i	$0.732427\pi$
$660$	487.185	+	201.798i	0.0287328	+	0.0119015i
$661$	−10196.1	+	10196.1i	−0.599975	+	0.599975i	−0.940306	−	0.340331i	$-0.889461\pi$
$661$	−10196.1	+	10196.1i	−0.599975	+	0.599975i	0.340331	+	0.940306i	$0.389461\pi$
$662$	283.267			0.0166306
$663$	−3103.66	+	7738.75i	−0.181804	+	0.453316i
$664$	−6954.28			−0.406444
$665$	−328.016	+	328.016i	−0.0191277	+	0.0191277i
$666$	−10250.6	−	4245.93i	−0.596400	−	0.247037i
$667$			4228.67i			0.245479i
$668$	1227.11	−	2962.50i	0.0710751	−	0.171590i
$669$	11973.1	−	4959.42i	0.691938	−	0.286610i
$670$	−4417.81	−	10665.5i	−0.254739	−	0.614994i
$671$	15773.5	+	15773.5i	0.907497	+	0.907497i
$672$	−337.413	−	337.413i	−0.0193690	−	0.0193690i
$673$	−807.706	−	1949.97i	−0.0462627	−	0.111688i	0.899059	−	0.437828i	$-0.144252\pi$
$673$	−807.706	−	1949.97i	−0.0462627	−	0.111688i	−0.945322	+	0.326140i	$0.894252\pi$
$674$	2468.14	−	1022.34i	0.141052	−	0.0584256i
$675$	−3810.06	+	9198.30i	−0.217258	+	0.524508i
$676$			2661.52i			0.151429i
$677$	−11035.3	−	4570.96i	−0.626470	−	0.259493i	0.0467822	−	0.998905i	$-0.485103\pi$
$677$	−11035.3	−	4570.96i	−0.626470	−	0.259493i	−0.673253	+	0.739413i	$0.735103\pi$
$678$	8998.39	−	8998.39i	0.509707	−	0.509707i
$679$	3760.52			0.212541
$680$	−6165.64	+	2635.79i	−0.347708	+	0.148644i
$681$	4833.41			0.271977
$682$	−8118.75	+	8118.75i	−0.455840	+	0.455840i
$683$	17633.0	+	7303.83i	0.987859	+	0.409185i	0.817331	−	0.576168i	$-0.195453\pi$
$683$	17633.0	+	7303.83i	0.987859	+	0.409185i	0.170528	+	0.985353i	$0.445453\pi$
$684$			1486.98i			0.0831232i
$685$	−1429.03	+	3449.98i	−0.0797085	+	0.192433i
$686$	5502.55	−	2279.23i	0.306251	−	0.126853i
$687$	499.693	+	1206.37i	0.0277503	+	0.0669953i
$688$	−16972.2	−	16972.2i	−0.940492	−	0.940492i
$689$	13116.9	+	13116.9i	0.725277	+	0.725277i
$690$	2537.35	+	6125.70i	0.139993	+	0.337973i
$691$	26161.3	−	10836.4i	1.44026	−	0.596577i	0.480402	−	0.877048i	$-0.340491\pi$
$691$	26161.3	−	10836.4i	1.44026	−	0.596577i	0.959862	+	0.280471i	$0.0904908\pi$
$692$	1642.08	−	3964.34i	0.0902061	−	0.217777i
$693$			1747.91i			0.0958121i
$694$	−1719.56	−	712.264i	−0.0940540	−	0.0389585i
$695$	8967.20	−	8967.20i	0.489418	−	0.489418i
$696$	−762.846			−0.0415454
$697$	−7214.29	−	16875.7i	−0.392053	−	0.917091i
$698$	29598.6			1.60505
$699$	1649.90	−	1649.90i	0.0892773	−	0.0892773i
$700$	499.041	+	206.710i	0.0269457	+	0.0111613i
$701$			5916.75i			0.318791i	0.987215	+	0.159396i	$0.0509545\pi$
$701$			5916.75i			0.318791i	−0.987215	+	0.159396i	$0.949045\pi$
$702$	7181.34	−	17337.3i	0.386100	−	0.932128i
$703$	4694.49	−	1944.52i	0.251858	−	0.104323i
$704$	−3490.97	−	8427.94i	−0.186890	−	0.451193i
$705$	2323.00	+	2323.00i	0.124098	+	0.124098i
$706$	−13769.3	−	13769.3i	−0.734014	−	0.734014i
$707$	324.036	+	782.292i	0.0172371	+	0.0416140i
$708$	−195.464	+	80.9637i	−0.0103757	+	0.00429774i
$709$	−7079.57	+	17091.6i	−0.375005	+	0.905343i	0.617880	+	0.786272i	$0.287992\pi$
$709$	−7079.57	+	17091.6i	−0.375005	+	0.905343i	−0.992886	+	0.119071i	$0.962008\pi$
$710$			9933.85i			0.525085i
$711$	−1915.85	−	793.570i	−0.101055	−	0.0418582i
$712$	−2594.69	+	2594.69i	−0.136573	+	0.136573i
$713$	−28186.6			−1.48050
$714$	−876.440	−	856.881i	−0.0459383	−	0.0449131i
$715$	−8149.91			−0.426279
$716$	28.4842	−	28.4842i	0.00148674	−	0.00148674i
$717$	9716.08	+	4024.53i	0.506072	+	0.209622i
$718$		−	22546.9i		−	1.17193i
$719$	8498.05	−	20516.1i	0.440784	−	1.06415i	−0.534890	−	0.844922i	$-0.679647\pi$
$719$	8498.05	−	20516.1i	0.440784	−	1.06415i	0.975674	−	0.219226i	$-0.0703531\pi$
$720$	8073.52	−	3344.16i	0.417892	−	0.173097i
$721$	1053.60	+	2543.60i	0.0544215	+	0.131385i
$722$	12825.4	+	12825.4i	0.661099	+	0.661099i
$723$	−1869.76	−	1869.76i	−0.0961785	−	0.0961785i
$724$	−324.208	−	782.706i	−0.0166424	−	0.0401783i
$725$	1851.16	−	766.778i	0.0948283	−	0.0392792i
$726$	1414.47	−	3414.84i	0.0723085	−	0.174568i
$727$			3777.02i			0.192685i	0.995348	+	0.0963424i	$0.0307144\pi$
$727$			3777.02i			0.192685i	−0.995348	+	0.0963424i	$0.969286\pi$
$728$	2936.42	+	1216.30i	0.149493	+	0.0619220i
$729$	3109.93	−	3109.93i	0.158001	−	0.158001i
$730$	−7838.73			−0.397431
$731$	−15878.7	−	15524.4i	−0.803415	−	0.785486i
$732$	3164.52			0.159787
$733$	−14111.3	+	14111.3i	−0.711068	+	0.711068i	−0.966759	−	0.255690i	$-0.917697\pi$
$733$	−14111.3	+	14111.3i	−0.711068	+	0.711068i	0.255690	+	0.966759i	$0.417697\pi$
$734$	−9781.72	−	4051.72i	−0.491894	−	0.203749i
$735$		−	3343.06i		−	0.167770i
$736$	−6943.11	+	16762.1i	−0.347726	+	0.839485i
$737$	18404.9	−	7623.54i	0.919880	−	0.381027i
$738$	7277.20	+	17568.7i	0.362978	+	0.876306i
$739$	−16453.2	−	16453.2i	−0.819001	−	0.819001i	0.166962	−	0.985963i	$-0.446604\pi$
$739$	−16453.2	−	16453.2i	−0.819001	−	0.819001i	−0.985963	+	0.166962i	$0.946604\pi$
$740$	1049.93	+	1049.93i	0.0521570	+	0.0521570i
$741$	1514.09	+	3655.35i	0.0750630	+	0.181218i
$742$	−2519.40	+	1043.57i	−0.124649	+	0.0516315i
$743$	4816.87	−	11629.0i	0.237838	−	0.574193i	−0.759220	−	0.650834i	$-0.774420\pi$
$743$	4816.87	−	11629.0i	0.237838	−	0.574193i	0.997059	+	0.0766410i	$0.0244195\pi$
$744$		−	5084.82i		−	0.250562i
$745$	8404.83	+	3481.39i	0.413328	+	0.171206i
$746$	−18680.9	+	18680.9i	−0.916830	+	0.916830i
$747$	8385.09			0.410702
$748$	1456.97	+	3408.16i	0.0712195	+	0.166597i
$749$	3272.61			0.159651
$750$	5000.55	−	5000.55i	0.243459	−	0.243459i
$751$	2460.10	+	1019.01i	0.119534	+	0.0495127i	0.441649	−	0.897188i	$-0.354394\pi$
$751$	2460.10	+	1019.01i	0.119534	+	0.0495127i	−0.322115	+	0.946701i	$0.604394\pi$
$752$			24958.6i			1.21030i
$753$	−3261.95	+	7875.04i	−0.157865	+	0.381119i
$754$	−3489.14	+	1445.25i	−0.168524	+	0.0698049i
$755$	4063.57	+	9810.32i	0.195879	+	0.472893i
$756$	380.855	+	380.855i	0.0183222	+	0.0183222i
$757$	18689.0	+	18689.0i	0.897308	+	0.897308i	0.995197	−	0.0978891i	$-0.0312090\pi$
$757$	18689.0	+	18689.0i	0.897308	+	0.897308i	−0.0978891	+	0.995197i	$0.531209\pi$
$758$	−7716.86	−	18630.2i	−0.369775	−	0.892715i
$759$	−10570.7	+	4378.54i	−0.505525	+	0.209395i
$760$	−1217.64	+	2939.65i	−0.0581166	+	0.140306i
$761$		−	8469.75i		−	0.403454i	−0.979442	−	0.201727i	$-0.935345\pi$
$761$		−	8469.75i		−	0.403454i	0.979442	−	0.201727i	$-0.0646553\pi$
$762$	−9282.92	−	3845.11i	−0.441318	−	0.182800i
$763$	−1652.07	+	1652.07i	−0.0783865	+	0.0783865i
$764$	−1529.05			−0.0724071
$765$	7434.19	−	3178.08i	0.351351	−	0.150201i
$766$	−645.361			−0.0304410
$767$	2312.12	−	2312.12i	0.108847	−	0.108847i
$768$	−5188.09	−	2148.98i	−0.243762	−	0.100969i
$769$			8452.54i			0.396367i	0.980165	+	0.198184i	$0.0635043\pi$
$769$			8452.54i			0.396367i	−0.980165	+	0.198184i	$0.936496\pi$
$770$	458.486	−	1106.88i	0.0214580	−	0.0518043i
$771$	−446.869	+	185.099i	−0.0208737	+	0.00864615i
$772$	−2768.11	−	6682.82i	−0.129050	−	0.311554i
$773$	−23996.5	−	23996.5i	−1.11655	−	1.11655i	−0.992244	−	0.124307i	$-0.960329\pi$
$773$	−23996.5	−	23996.5i	−1.11655	−	1.11655i	−0.124307	−	0.992244i	$-0.539671\pi$
$774$	16270.0	+	16270.0i	0.755571	+	0.755571i
$775$	5111.03	+	12339.1i	0.236895	+	0.571915i
$776$	23830.6	−	9870.94i	1.10241	−	0.456632i
$777$	324.257	−	782.826i	0.0149712	−	0.0361438i
$778$			18194.1i			0.838419i
$779$	−8045.99	−	3332.76i	−0.370061	−	0.153284i
$780$	−817.525	+	817.525i	−0.0375283	+	0.0375283i
$781$	−17142.2			−0.785399
$782$	−17347.8	+	43255.5i	−0.793296	+	1.97802i
$783$	1997.95			0.0911887
$784$	17959.1	−	17959.1i	0.818108	−	0.818108i
$785$	−7438.48	−	3081.12i	−0.338205	−	0.140089i
$786$			16419.2i			0.745105i
$787$	13156.3	−	31762.1i	0.595898	−	1.43863i	−0.281829	−	0.959465i	$-0.590941\pi$
$787$	13156.3	−	31762.1i	0.595898	−	1.43863i	0.877727	−	0.479161i	$-0.159059\pi$
$788$	810.297	−	335.636i	0.0366315	−	0.0151733i
$789$	−2403.18	−	5801.79i	−0.108435	−	0.261786i
$790$	1005.07	+	1005.07i	0.0452643	+	0.0452643i
$791$	−3991.61	−	3991.61i	−0.179425	−	0.179425i
$792$	4588.07	+	11076.6i	0.205846	+	0.496956i
$793$	−45185.3	+	18716.4i	−2.02343	+	0.838131i
$794$	8620.18	−	20811.0i	0.385288	−	0.930168i
$795$			3096.72i			0.138150i
$796$	6240.45	+	2584.88i	0.277873	+	0.115099i
$797$	2354.14	−	2354.14i	0.104627	−	0.104627i	−0.652855	−	0.757483i	$-0.726429\pi$
$797$	2354.14	−	2354.14i	0.104627	−	0.104627i	0.757483	+	0.652855i	$0.226429\pi$
$798$	−581.630			−0.0258014
$799$	260.550	+	23090.1i	0.0115364	+	1.02236i
$800$	8596.87			0.379932
$801$	3128.54	−	3128.54i	0.138004	−	0.138004i
$802$	−18539.3	−	7679.24i	−0.816267	−	0.338109i
$803$		−	13526.8i		−	0.594459i
$804$	1081.48	−	2610.93i	0.0474390	−	0.114528i
$805$	2717.31	−	1125.55i	0.118972	−	0.0492799i
$806$	−9633.45	−	23257.2i	−0.420997	−	1.01638i
$807$	296.970	+	296.970i	0.0129539	+	0.0129539i
$808$	4106.85	+	4106.85i	0.178810	+	0.178810i
$809$	−2762.07	−	6668.23i	−0.120036	−	0.289793i	0.852428	−	0.522844i	$-0.175129\pi$
$809$	−2762.07	−	6668.23i	−0.120036	−	0.289793i	−0.972464	+	0.233051i	$0.925129\pi$
$810$	−6177.66	+	2558.87i	−0.267977	+	0.111000i
$811$	13992.5	−	33780.9i	0.605848	−	1.46265i	−0.261628	−	0.965169i	$-0.584259\pi$
$811$	13992.5	−	33780.9i	0.605848	−	1.46265i	0.867476	−	0.497478i	$-0.165741\pi$
$812$		−	108.396i		−	0.00468466i
$813$	−2994.02	−	1240.16i	−0.129157	−	0.0534987i
$814$	−9279.70	+	9279.70i	−0.399574	+	0.399574i
$815$	11407.3			0.490284
$816$	−9814.79	−	3936.27i	−0.421062	−	0.168869i
$817$	−10537.6			−0.451240
$818$	6683.60	−	6683.60i	0.285680	−	0.285680i
$819$	−3540.57	−	1466.55i	−0.151059	−	0.0625708i
$820$		−	2544.88i		−	0.108379i
$821$	−8855.50	+	21379.1i	−0.376442	+	0.908812i	0.616185	+	0.787602i	$0.288677\pi$
$821$	−8855.50	+	21379.1i	−0.376442	+	0.908812i	−0.992627	+	0.121210i	$0.961323\pi$
$822$	−4325.67	+	1791.75i	−0.183546	+	0.0760273i
$823$	15800.2	+	38145.0i	0.669210	+	1.61562i	0.782935	+	0.622103i	$0.213722\pi$
$823$	15800.2	+	38145.0i	0.669210	+	1.61562i	−0.113725	+	0.993512i	$0.536278\pi$
$824$	13353.3	+	13353.3i	0.564545	+	0.564545i
$825$	3833.55	+	3833.55i	0.161778	+	0.161778i
$826$	183.949	+	444.093i	0.00774869	+	0.0187070i
$827$	9246.14	−	3829.88i	0.388779	−	0.161037i	−0.179727	−	0.983716i	$-0.557522\pi$
$827$	9246.14	−	3829.88i	0.388779	−	0.161037i	0.568506	+	0.822679i	$0.307522\pi$
$828$	3607.95	−	8710.36i	0.151431	−	0.365587i
$829$		−	44643.6i		−	1.87037i	−0.354159	−	0.935185i	$-0.615233\pi$
$829$		−	44643.6i		−	1.87037i	0.354159	−	0.935185i	$-0.384767\pi$
$830$	−5309.94	−	2199.45i	−0.222061	−	0.0919806i
$831$	6515.21	−	6515.21i	0.271974	−	0.271974i
$832$	20000.6			0.833410
$833$	16427.1	−	16802.1i	0.683273	−	0.698869i
$834$	15900.4			0.660176
$835$	−5850.01	+	5850.01i	−0.242453	+	0.242453i
$836$	1624.94	+	673.072i	0.0672246	+	0.0278453i
$837$			13317.5i			0.549964i
$838$	14173.9	−	34218.8i	0.584283	−	1.41058i
$839$	13151.7	−	5447.61i	0.541176	−	0.224163i	−0.0953141	−	0.995447i	$-0.530386\pi$
$839$	13151.7	−	5447.61i	0.541176	−	0.224163i	0.636490	+	0.771285i	$0.280386\pi$
$840$	203.047	+	490.199i	0.00834023	+	0.0201351i
$841$	16961.3	+	16961.3i	0.695449	+	0.695449i
$842$	19713.1	+	19713.1i	0.806840	+	0.806840i
$843$	3868.48	+	9339.33i	0.158052	+	0.381570i
$844$	3260.85	−	1350.69i	0.132989	−	0.0550860i
$845$	2627.84	−	6344.17i	0.106983	−	0.258280i
$846$		−	23926.0i		−	0.972331i
$847$	−1514.79	−	627.448i	−0.0614509	−	0.0254538i
$848$	−16635.8	+	16635.8i	−0.673673	+	0.673673i
$849$	4853.08			0.196181
$850$	22081.4	−	249.168i	0.891044	−	0.0100546i
$851$	−32217.1			−1.29775
$852$	−1719.55	+	1719.55i	−0.0691442	+	0.0691442i
$853$	−25618.2	−	10611.4i	−1.02831	−	0.425942i	−0.196211	−	0.980562i	$-0.562864\pi$
$853$	−25618.2	−	10611.4i	−1.02831	−	0.425942i	−0.832104	+	0.554620i	$0.812864\pi$
$854$		−	7189.78i		−	0.288090i
$855$	1468.17	−	3544.47i	0.0587255	−	0.141776i
$856$	20738.6	−	8590.22i	0.828074	−	0.342999i
$857$	11970.6	+	28899.6i	0.477138	+	1.15191i	0.960945	+	0.276739i	$0.0892538\pi$
$857$	11970.6	+	28899.6i	0.477138	+	1.15191i	−0.483807	+	0.875175i	$0.660746\pi$
$858$	−7225.61	−	7225.61i	−0.287504	−	0.287504i
$859$	−39.0952	−	39.0952i	−0.00155287	−	0.00155287i	0.706330	−	0.707883i	$-0.250350\pi$
$859$	−39.0952	−	39.0952i	−0.00155287	−	0.00155287i	−0.707883	+	0.706330i	$0.750350\pi$
$860$	−1178.37	−	2844.85i	−0.0467235	−	0.112801i
$861$	−1341.70	+	555.751i	−0.0531070	+	0.0219976i
$862$	3739.62	−	9028.23i	0.147763	−	0.356732i
$863$		−	22900.4i		−	0.903291i	−0.892197	−	0.451646i	$-0.850837\pi$
$863$		−	22900.4i		−	0.903291i	0.892197	−	0.451646i	$-0.149163\pi$
$864$	7919.72	+	3280.46i	0.311845	+	0.129171i
$865$	−7828.34	+	7828.34i	−0.307713	+	0.307713i
$866$	−31758.7			−1.24620
$867$	−9121.11	−	3539.13i	−0.357288	−	0.138633i
$868$	722.522			0.0282535
$869$	−1734.39	+	1734.39i	−0.0677043	+	0.0677043i
$870$	−582.470	−	241.267i	−0.0226984	−	0.00940197i
$871$			43677.2i			1.69913i
$872$	−6132.72	+	14805.7i	−0.238165	+	0.574982i
$873$	−28733.6	+	11901.8i	−1.11396	+	0.461416i
$874$	8462.99	+	20431.5i	0.327534	+	0.790738i
$875$	−2218.21	−	2218.21i	−0.0857018	−	0.0857018i
$876$	−1356.89	−	1356.89i	−0.0523344	−	0.0523344i
$877$	−682.134	−	1646.82i	−0.0262646	−	0.0634083i	0.910203	−	0.414162i	$-0.135925\pi$
$877$	−682.134	−	1646.82i	−0.0262646	−	0.0634083i	−0.936468	+	0.350754i	$0.885925\pi$
$878$	−50562.1	+	20943.5i	−1.94349	+	0.805021i
$879$	2515.06	−	6071.89i	0.0965084	−	0.232992i
$880$		−	10336.3i		−	0.395949i
$881$	15920.8	+	6594.62i	0.608838	+	0.252189i	0.665731	−	0.746191i	$-0.268120\pi$
$881$	15920.8	+	6594.62i	0.608838	+	0.252189i	−0.0568939	+	0.998380i	$0.518120\pi$
$882$	−17216.1	+	17216.1i	−0.657251	+	0.657251i
$883$	−10188.2			−0.388291			−0.194145	−	0.980973i	$-0.562193\pi$
$883$	−10188.2			−0.388291			−0.194145	+	0.980973i	$0.562193\pi$
$884$	−8126.00	+	91.6943i	−0.309171	+	0.00348870i
$885$	545.859			0.0207332
$886$	15561.3	−	15561.3i	0.590060	−	0.590060i
$887$	−14478.7	−	5997.28i	−0.548081	−	0.227022i	0.0914208	−	0.995812i	$-0.470859\pi$
$887$	−14478.7	−	5997.28i	−0.548081	−	0.227022i	−0.639501	+	0.768790i	$0.720859\pi$
$888$		−	5811.93i		−	0.219635i
$889$	−1705.66	+	4117.83i	−0.0643487	+	0.155352i
$890$	−2801.80	+	1160.54i	−0.105524	+	0.0437096i
$891$	−4415.68	−	10660.4i	−0.166028	−	0.400827i
$892$	8931.46	+	8931.46i	0.335255	+	0.335255i
$893$	7748.07	+	7748.07i	0.290347	+	0.290347i
$894$	4365.06	+	10538.2i	0.163299	+	0.394239i
$895$	−96.0206	+	39.7730i	−0.00358616	+	0.00148544i
$896$	−1858.75	+	4487.43i	−0.0693042	+	0.167315i
$897$		−	25085.8i		−	0.933768i
$898$	−26887.7	−	11137.2i	−0.999168	−	0.413869i
$899$	1895.16	−	1895.16i	0.0703081	−	0.0703081i
$900$	−4467.32			−0.165456
$901$	−15216.7	+	15564.0i	−0.562643	+	0.575485i
$902$	22492.6			0.830291
$903$	−1242.52	+	1242.52i	−0.0457900	+	0.0457900i
$904$	−35772.5	−	14817.5i	−1.31612	−	0.545156i
$905$			2185.81i			0.0802861i
$906$	−5095.00	+	12300.4i	−0.186832	+	0.451053i
$907$	15621.3	−	6470.54i	0.571881	−	0.236881i	−0.0779531	−	0.996957i	$-0.524838\pi$
$907$	15621.3	−	6470.54i	0.571881	−	0.236881i	0.649834	+	0.760076i	$0.274838\pi$
$908$	1802.77	+	4352.26i	0.0658887	+	0.159069i
$909$	−4951.82	−	4951.82i	−0.180684	−	0.180684i
$910$	1857.42	+	1857.42i	0.0676623	+	0.0676623i
$911$	13815.1	+	33352.6i	0.502431	+	1.21298i	0.948156	+	0.317806i	$0.102946\pi$
$911$	13815.1	+	33352.6i	0.502431	+	1.21298i	−0.445724	+	0.895170i	$0.647054\pi$
$912$	−4635.95	+	1920.27i	−0.168324	+	0.0697222i
$913$	3795.45	−	9163.02i	0.137580	−	0.332149i
$914$			38625.1i			1.39782i
$915$	−7543.14	−	3124.47i	−0.272534	−	0.112887i
$916$	−899.902	+	899.902i	−0.0324603	+	0.0324603i
$917$	7283.41			0.262290
$918$	20437.2	+	8196.45i	0.734781	+	0.294688i
$919$	20016.2			0.718470			0.359235	−	0.933247i	$-0.383038\pi$
$919$	20016.2			0.718470			0.359235	+	0.933247i	$0.383038\pi$
$920$	14265.3	−	14265.3i	0.511208	−	0.511208i
$921$	2182.73	+	904.116i	0.0780927	+	0.0323470i
$922$		−	19735.7i		−	0.704947i
$923$	14382.8	−	34723.2i	0.512911	−	1.23828i
$924$	270.966	−	112.238i	0.00964731	−	0.00399605i
$925$	5841.88	+	14103.6i	0.207654	+	0.501321i
$926$	−22729.2	−	22729.2i	−0.806618	−	0.806618i
$927$	−16100.7	−	16100.7i	−0.570460	−	0.570460i
$928$	−660.194	−	1593.85i	−0.0233534	−	0.0563800i
$929$	28298.7	−	11721.7i	0.999407	−	0.413968i	0.177828	−	0.984062i	$-0.443093\pi$
$929$	28298.7	−	11721.7i	0.999407	−	0.413968i	0.821580	+	0.570094i	$0.193093\pi$
$930$	1608.19	−	3882.51i	0.0567038	−	0.136895i
$931$		−	11150.3i		−	0.392522i
$932$	2101.04	+	870.278i	0.0738431	+	0.0305868i
$933$	−925.800	+	925.800i	−0.0324859	+	0.0324859i
$934$	46609.7			1.63289
$935$	−107.903	−	9562.43i	−0.00377413	−	0.334465i
$936$	−26286.2			−0.917941
$937$	2746.18	−	2746.18i	0.0957458	−	0.0957458i	−0.657611	−	0.753357i	$-0.728433\pi$
$937$	2746.18	−	2746.18i	0.0957458	−	0.0957458i	0.753357	+	0.657611i	$0.228433\pi$
$938$	−5932.03	−	2457.13i	−0.206490	−	0.0855310i
$939$		−	12095.0i		−	0.420346i
$940$	−1225.32	+	2958.19i	−0.0425167	+	0.102644i
$941$	20044.5	−	8302.68i	0.694400	−	0.287630i	−0.00743202	−	0.999972i	$-0.502366\pi$
$941$	20044.5	−	8302.68i	0.694400	−	0.287630i	0.701832	+	0.712342i	$0.252366\pi$
$942$	−3863.18	−	9326.55i	−0.133619	−	0.322585i
$943$	39044.8	+	39044.8i	1.34833	+	1.34833i
$944$	2932.38	+	2932.38i	0.101103	+	0.101103i
$945$	−531.795	−	1283.87i	−0.0183061	−	0.0441949i
$946$	25143.9	−	10414.9i	0.864163	−	0.357948i
$947$	−6086.52	+	14694.2i	−0.208855	+	0.504220i	−0.993243	−	0.116050i	$-0.962977\pi$
$947$	−6086.52	+	14694.2i	−0.208855	+	0.504220i	0.784389	+	0.620269i	$0.212977\pi$
$948$			347.956i			0.0119210i
$949$	27399.9	+	11349.4i	0.937236	+	0.388216i
$950$	7409.61	−	7409.61i	0.253052	−	0.253052i
$951$	11456.9			0.390659
$952$	−1388.23	+	3461.45i	−0.0472615	+	0.117843i
$953$	−81.8493			−0.00278212			−0.00139106	−	0.999999i	$-0.500443\pi$
$953$	−81.8493			−0.00278212			−0.00139106	+	0.999999i	$0.500443\pi$
$954$	15947.5	−	15947.5i	0.541214	−	0.541214i
$955$	3644.74	+	1509.70i	0.123498	+	0.0511547i
$956$			10250.0i			0.346765i
$957$	416.339	−	1005.13i	0.0140630	−	0.0339512i
$958$	−47684.5	+	19751.6i	−1.60816	+	0.666122i
$959$	794.806	+	1918.83i	0.0267629	+	0.0646113i
$960$	2360.93	+	2360.93i	0.0793737	+	0.0793737i
$961$	−8433.08	−	8433.08i	−0.283075	−	0.283075i
$962$	−11011.0	−	26582.9i	−0.369032	−	0.890922i
$963$	−25005.5	+	10357.6i	−0.836750	+	0.346593i
$964$	986.249	−	2381.02i	0.0329512	−	0.0795512i
$965$			18662.7i			0.622562i
$966$	3407.03	+	1411.24i	0.113478	+	0.0470040i
$967$	13632.8	−	13632.8i	0.453363	−	0.453363i	−0.443106	−	0.896469i	$-0.646124\pi$
$967$	13632.8	−	13632.8i	0.453363	−	0.453363i	0.896469	+	0.443106i	$0.146124\pi$
$968$	−11246.3			−0.373419
$969$	−4268.84	+	1824.91i	−0.141522	+	0.0605001i
$970$	21317.7			0.705639
$971$	−38025.6	+	38025.6i	−1.25674	+	1.25674i	−0.304107	+	0.952638i	$0.598358\pi$
$971$	−38025.6	+	38025.6i	−1.25674	+	1.25674i	−0.952638	+	0.304107i	$0.901642\pi$
$972$	−6336.25	−	2624.56i	−0.209090	−	0.0866079i
$973$		−	7053.30i		−	0.232393i
$974$	4954.55	−	11961.3i	0.162992	−	0.393497i
$975$	−10981.7	+	4548.76i	−0.360713	+	0.149412i
$976$	−23737.3	−	57307.0i	−0.778497	−	1.87946i
$977$	−38705.7	−	38705.7i	−1.26746	−	1.26746i	−0.947397	−	0.320061i	$-0.896297\pi$
$977$	−38705.7	−	38705.7i	−1.26746	−	1.26746i	−0.320061	−	0.947397i	$-0.603703\pi$
$978$	10113.6	+	10113.6i	0.330672	+	0.330672i
$979$	−2002.68	−	4834.89i	−0.0653788	−	0.157838i
$980$	3010.27	−	1246.90i	0.0981221	−	0.0406435i
$981$	7394.49	−	17851.9i	0.240661	−	0.581006i
$982$		−	2768.27i		−	0.0899581i
$983$	−3146.11	−	1303.16i	−0.102081	−	0.0422832i	0.331059	−	0.943610i	$-0.392594\pi$
$983$	−3146.11	−	1303.16i	−0.102081	−	0.0422832i	−0.433139	+	0.901327i	$0.642594\pi$
$984$	−7043.63	+	7043.63i	−0.228194	+	0.228194i
$985$	−2262.86			−0.0731988
$986$	−1741.93	−	4074.74i	−0.0562621	−	0.131609i
$987$	1827.20			0.0589264
$988$	−2726.75	+	2726.75i	−0.0878030	+	0.0878030i
$989$	61726.3	+	25567.9i	1.98461	+	0.822054i
$990$			9908.60i			0.318097i
$991$	−11452.1	+	27647.8i	−0.367091	+	0.886237i	0.627133	+	0.778912i	$0.284228\pi$
$991$	−11452.1	+	27647.8i	−0.367091	+	0.886237i	−0.994224	+	0.107324i	$0.965772\pi$
$992$	10624.0	−	4400.58i	0.340031	−	0.140845i
$993$	−68.4663	−	165.292i	−0.00218803	−	0.00528237i
$994$	3906.82	+	3906.82i	0.124665	+	0.124665i
$995$	−12323.0	−	12323.0i	−0.392627	−	0.392627i
$996$	−538.426	−	1299.88i	−0.0171292	−	0.0413535i
$997$	−30224.2	+	12519.3i	−0.960092	+	0.397683i	−0.807015	−	0.590531i	$-0.798918\pi$
$997$	−30224.2	+	12519.3i	−0.960092	+	0.397683i	−0.153077	+	0.988214i	$0.548918\pi$
$998$	−16674.4	+	40255.5i	−0.528875	+	1.27682i
$999$			15221.8i			0.482080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.4.d.a.9.3	yes	12
3.2	odd	2		153.4.l.a.145.1		12
17.2	even	8	inner	17.4.d.a.2.3	✓	12
17.6	odd	16		289.4.a.g.1.11		12
17.7	odd	16		289.4.b.e.288.2		12
17.10	odd	16		289.4.b.e.288.1		12
17.11	odd	16		289.4.a.g.1.12		12
51.2	odd	8		153.4.l.a.19.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.d.a.2.3	✓	12	17.2	even	8	inner
17.4.d.a.9.3	yes	12	1.1	even	1	trivial
153.4.l.a.19.1		12	51.2	odd	8
153.4.l.a.145.1		12	3.2	odd	2
289.4.a.g.1.11		12	17.6	odd	16
289.4.a.g.1.12		12	17.11	odd	16
289.4.b.e.288.1		12	17.10	odd	16
289.4.b.e.288.2		12	17.7	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	17.d (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.22945 - 2.22945i) q^{2} +(-1.83980 - 0.762069i) q^{3} -1.94089i q^{4} +(-1.91633 + 4.62643i) q^{5} +(-5.80073 + 2.40274i) q^{6} +(1.06584 + 2.57316i) q^{7} +(13.5085 + 13.5085i) q^{8} +(-16.2878 - 16.2878i) q^{9} +O(q^{10})\)	\(q+(2.22945 - 2.22945i) q^{2} +(-1.83980 - 0.762069i) q^{3} -1.94089i q^{4} +(-1.91633 + 4.62643i) q^{5} +(-5.80073 + 2.40274i) q^{6} +(1.06584 + 2.57316i) q^{7} +(13.5085 + 13.5085i) q^{8} +(-16.2878 - 16.2878i) q^{9} +(6.04203 + 14.5867i) q^{10} +(-25.1714 + 10.4263i) q^{11} +(-1.47909 + 3.57084i) q^{12} -59.7352i q^{13} +(8.11295 + 3.36049i) q^{14} +(7.05131 - 7.05131i) q^{15} +75.7601 q^{16} +(70.0883 - 0.790881i) q^{17} -72.6256 q^{18} +(23.5187 - 23.5187i) q^{19} +(8.97939 + 3.71938i) q^{20} -5.54633i q^{21} +(-32.8734 + 79.3634i) q^{22} +(-194.831 + 80.7017i) q^{23} +(-14.5585 - 35.1473i) q^{24} +(70.6568 + 70.6568i) q^{25} +(-133.177 - 133.177i) q^{26} +(38.1297 + 92.0531i) q^{27} +(4.99421 - 2.06867i) q^{28} +(7.67362 - 18.5258i) q^{29} -31.4411i q^{30} +(123.485 + 51.1492i) q^{31} +(60.8354 - 60.8354i) q^{32} +54.2559 q^{33} +(154.495 - 158.022i) q^{34} -13.9470 q^{35} +(-31.6128 + 31.6128i) q^{36} +(141.143 + 58.4634i) q^{37} -104.868i q^{38} +(-45.5223 + 109.901i) q^{39} +(-88.3827 + 36.6093i) q^{40} +(-100.202 - 241.908i) q^{41} +(-12.3653 - 12.3653i) q^{42} +(-224.025 - 224.025i) q^{43} +(20.2364 + 48.8550i) q^{44} +(106.567 - 44.1415i) q^{45} +(-254.446 + 614.286i) q^{46} +329.443i q^{47} +(-139.383 - 57.7344i) q^{48} +(237.052 - 237.052i) q^{49} +315.052 q^{50} +(-129.551 - 51.9571i) q^{51} -115.939 q^{52} +(-219.585 + 219.585i) q^{53} +(290.236 + 120.220i) q^{54} -136.434i q^{55} +(-20.3616 + 49.1573i) q^{56} +(-61.1926 + 25.3468i) q^{57} +(-24.1943 - 58.4102i) q^{58} +(38.7062 + 38.7062i) q^{59} +(-13.6858 - 13.6858i) q^{60} +(-313.322 - 756.427i) q^{61} +(389.338 - 161.269i) q^{62} +(24.5509 - 59.2711i) q^{63} +334.822i q^{64} +(276.360 + 114.472i) q^{65} +(120.961 - 120.961i) q^{66} -731.181 q^{67} +(-1.53501 - 136.034i) q^{68} +419.950 q^{69} +(-31.0942 + 31.0942i) q^{70} +(581.286 + 240.777i) q^{71} -440.046i q^{72} +(-189.995 + 458.689i) q^{73} +(445.012 - 184.330i) q^{74} +(-76.1489 - 183.840i) q^{75} +(-45.6473 - 45.6473i) q^{76} +(-53.6572 - 53.6572i) q^{77} +(143.528 + 346.507i) q^{78} +(83.1733 - 34.4515i) q^{79} +(-145.181 + 350.498i) q^{80} +423.512i q^{81} +(-762.717 - 315.928i) q^{82} +(-257.404 + 257.404i) q^{83} -10.7648 q^{84} +(-130.653 + 325.774i) q^{85} -998.907 q^{86} +(-28.2358 + 28.2358i) q^{87} +(-480.872 - 199.184i) q^{88} +192.079i q^{89} +(139.174 - 335.997i) q^{90} +(153.708 - 63.6679i) q^{91} +(156.633 + 378.146i) q^{92} +(-188.208 - 188.208i) q^{93} +(734.476 + 734.476i) q^{94} +(63.7380 + 153.877i) q^{95} +(-158.286 + 65.5640i) q^{96} +(516.698 - 1247.42i) q^{97} -1056.99i q^{98} +(579.808 + 240.165i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 4 q^{3} - 20 q^{5} + 20 q^{6} - 4 q^{7} + 28 q^{8} - 64 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 - 4 * q^3 - 20 * q^5 + 20 * q^6 - 4 * q^7 + 28 * q^8 - 64 * q^9	\( 12 q - 4 q^{2} - 4 q^{3} - 20 q^{5} + 20 q^{6} - 4 q^{7} + 28 q^{8} - 64 q^{9} - 116 q^{10} + 40 q^{11} + 56 q^{12} - 132 q^{14} + 244 q^{15} + 184 q^{16} + 52 q^{17} - 12 q^{19} + 572 q^{20} - 620 q^{22} - 276 q^{23} - 184 q^{24} - 464 q^{25} - 708 q^{26} - 664 q^{27} + 452 q^{28} + 632 q^{29} + 188 q^{31} + 700 q^{32} + 1400 q^{33} + 764 q^{34} - 632 q^{35} + 524 q^{36} + 940 q^{37} - 1112 q^{39} - 1864 q^{40} + 176 q^{41} + 48 q^{42} - 1360 q^{43} - 1364 q^{44} - 32 q^{45} + 452 q^{46} - 540 q^{48} + 1044 q^{49} + 2856 q^{50} + 340 q^{51} + 792 q^{52} - 360 q^{53} - 244 q^{54} - 1788 q^{56} - 148 q^{57} - 360 q^{58} - 584 q^{59} - 1792 q^{60} - 1052 q^{61} - 380 q^{62} + 1752 q^{63} + 404 q^{65} + 1372 q^{66} + 1080 q^{67} + 2532 q^{68} - 344 q^{69} + 2072 q^{70} + 28 q^{71} + 824 q^{73} - 2292 q^{74} + 400 q^{75} + 1328 q^{76} - 1252 q^{77} + 1128 q^{78} - 196 q^{79} - 904 q^{80} - 1528 q^{82} - 1008 q^{83} - 4768 q^{84} - 2824 q^{85} - 1200 q^{86} - 2516 q^{87} - 56 q^{88} - 860 q^{90} + 2456 q^{91} + 396 q^{92} - 836 q^{93} + 6360 q^{94} + 2172 q^{95} + 1668 q^{96} - 904 q^{97} + 3280 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 4 * q^3 - 20 * q^5 + 20 * q^6 - 4 * q^7 + 28 * q^8 - 64 * q^9 - 116 * q^10 + 40 * q^11 + 56 * q^12 - 132 * q^14 + 244 * q^15 + 184 * q^16 + 52 * q^17 - 12 * q^19 + 572 * q^20 - 620 * q^22 - 276 * q^23 - 184 * q^24 - 464 * q^25 - 708 * q^26 - 664 * q^27 + 452 * q^28 + 632 * q^29 + 188 * q^31 + 700 * q^32 + 1400 * q^33 + 764 * q^34 - 632 * q^35 + 524 * q^36 + 940 * q^37 - 1112 * q^39 - 1864 * q^40 + 176 * q^41 + 48 * q^42 - 1360 * q^43 - 1364 * q^44 - 32 * q^45 + 452 * q^46 - 540 * q^48 + 1044 * q^49 + 2856 * q^50 + 340 * q^51 + 792 * q^52 - 360 * q^53 - 244 * q^54 - 1788 * q^56 - 148 * q^57 - 360 * q^58 - 584 * q^59 - 1792 * q^60 - 1052 * q^61 - 380 * q^62 + 1752 * q^63 + 404 * q^65 + 1372 * q^66 + 1080 * q^67 + 2532 * q^68 - 344 * q^69 + 2072 * q^70 + 28 * q^71 + 824 * q^73 - 2292 * q^74 + 400 * q^75 + 1328 * q^76 - 1252 * q^77 + 1128 * q^78 - 196 * q^79 - 904 * q^80 - 1528 * q^82 - 1008 * q^83 - 4768 * q^84 - 2824 * q^85 - 1200 * q^86 - 2516 * q^87 - 56 * q^88 - 860 * q^90 + 2456 * q^91 + 396 * q^92 - 836 * q^93 + 6360 * q^94 + 2172 * q^95 + 1668 * q^96 - 904 * q^97 + 3280 * q^99

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