LMFDB - Embedded newform 17.4.d.a.15.3

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			15.3
Root			$-2.49971i$ of defining polynomial
Character	$\chi$	$=$	17.15
Dual form			17.4.d.a.8.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.47467 + 2.47467i) q^{2} +(-1.08123 - 2.61032i) q^{3} +4.24796i q^{4} +(-8.05561 + 3.33674i) q^{5} +(3.78400 - 9.13537i) q^{6} +(-6.33320 - 2.62330i) q^{7} +(9.28506 - 9.28506i) q^{8} +(13.4472 - 13.4472i) q^{9} +O(q^{10})$	\(q+(2.47467 + 2.47467i) q^{2} +(-1.08123 - 2.61032i) q^{3} +4.24796i q^{4} +(-8.05561 + 3.33674i) q^{5} +(3.78400 - 9.13537i) q^{6} +(-6.33320 - 2.62330i) q^{7} +(9.28506 - 9.28506i) q^{8} +(13.4472 - 13.4472i) q^{9} +(-28.1923 - 11.6776i) q^{10} +(-23.6471 + 57.0891i) q^{11} +(11.0885 - 4.59303i) q^{12} +5.37363i q^{13} +(-9.18078 - 22.1644i) q^{14} +(17.4200 + 17.4200i) q^{15} +79.9385 q^{16} +(44.2970 + 54.3210i) q^{17} +66.5545 q^{18} +(-68.4392 - 68.4392i) q^{19} +(-14.1743 - 34.2199i) q^{20} +19.3681i q^{21} +(-199.795 + 82.7579i) q^{22} +(44.5923 - 107.655i) q^{23} +(-34.2763 - 14.1977i) q^{24} +(-34.6294 + 34.6294i) q^{25} +(-13.2979 + 13.2979i) q^{26} +(-120.120 - 49.7552i) q^{27} +(11.1437 - 26.9032i) q^{28} +(182.351 - 75.5321i) q^{29} +86.2172i q^{30} +(-52.8371 - 127.560i) q^{31} +(123.541 + 123.541i) q^{32} +174.589 q^{33} +(-24.8060 + 244.047i) q^{34} +59.7710 q^{35} +(57.1229 + 57.1229i) q^{36} +(42.6416 + 102.946i) q^{37} -338.729i q^{38} +(14.0269 - 5.81013i) q^{39} +(-43.8149 + 105.779i) q^{40} +(-153.814 - 63.7117i) q^{41} +(-47.9296 + 47.9296i) q^{42} +(-117.300 + 117.300i) q^{43} +(-242.512 - 100.452i) q^{44} +(-63.4553 + 153.195i) q^{45} +(376.762 - 156.060i) q^{46} +130.994i q^{47} +(-86.4320 - 208.665i) q^{48} +(-209.310 - 209.310i) q^{49} -171.392 q^{50} +(93.9001 - 174.363i) q^{51} -22.8269 q^{52} +(505.038 + 505.038i) q^{53} +(-174.129 - 420.384i) q^{54} -538.792i q^{55} +(-83.1616 + 34.4467i) q^{56} +(-104.650 + 252.647i) q^{57} +(638.174 + 264.340i) q^{58} +(-598.365 + 598.365i) q^{59} +(-73.9992 + 73.9992i) q^{60} +(4.61209 + 1.91039i) q^{61} +(184.915 - 446.423i) q^{62} +(-120.439 + 49.8876i) q^{63} -28.0634i q^{64} +(-17.9304 - 43.2878i) q^{65} +(432.050 + 432.050i) q^{66} +314.069 q^{67} +(-230.753 + 188.172i) q^{68} -329.230 q^{69} +(147.913 + 147.913i) q^{70} +(-45.3357 - 109.450i) q^{71} -249.715i q^{72} +(601.028 - 248.954i) q^{73} +(-149.233 + 360.280i) q^{74} +(127.836 + 52.9515i) q^{75} +(290.727 - 290.727i) q^{76} +(299.524 - 299.524i) q^{77} +(49.0901 + 20.3338i) q^{78} +(-79.7533 + 192.542i) q^{79} +(-643.953 + 266.734i) q^{80} -146.115i q^{81} +(-222.972 - 538.303i) q^{82} +(-524.977 - 524.977i) q^{83} -82.2749 q^{84} +(-538.095 - 289.781i) q^{85} -580.555 q^{86} +(-394.326 - 394.326i) q^{87} +(310.511 + 749.640i) q^{88} +215.527i q^{89} +(-536.137 + 222.075i) q^{90} +(14.0966 - 34.0323i) q^{91} +(457.315 + 189.426i) q^{92} +(-275.844 + 275.844i) q^{93} +(-324.167 + 324.167i) q^{94} +(779.683 + 322.955i) q^{95} +(188.905 - 456.058i) q^{96} +(651.973 - 270.056i) q^{97} -1035.94i q^{98} +(449.700 + 1085.67i) 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 $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	2.47467	+	2.47467i	0.874927	+	0.874927i	0.993004	−	0.118077i	$-0.0376731\pi$
$2$	2.47467	+	2.47467i	0.874927	+	0.874927i	−0.118077	+	0.993004i	$0.537673\pi$
$3$	−1.08123	−	2.61032i	−0.208083	−	0.502357i	0.785038	−	0.619447i	$-0.212643\pi$
$3$	−1.08123	−	2.61032i	−0.208083	−	0.502357i	−0.993121	+	0.117090i	$0.962643\pi$
$4$			4.24796i			0.530995i
$5$	−8.05561	+	3.33674i	−0.720515	+	0.298447i	−0.712648	−	0.701522i	$-0.752504\pi$
$5$	−8.05561	+	3.33674i	−0.720515	+	0.298447i	−0.00786742	+	0.999969i	$0.502504\pi$
$6$	3.78400	−	9.13537i	0.257468	−	0.621583i
$7$	−6.33320	−	2.62330i	−0.341961	−	0.141645i	0.205093	−	0.978743i	$-0.434250\pi$
$7$	−6.33320	−	2.62330i	−0.341961	−	0.141645i	−0.547053	+	0.837098i	$0.684250\pi$
$8$	9.28506	−	9.28506i	0.410345	−	0.410345i
$9$	13.4472	−	13.4472i	0.498043	−	0.498043i
$10$	−28.1923	−	11.6776i	−0.891518	−	0.369279i
$11$	−23.6471	+	57.0891i	−0.648170	+	1.56482i	0.167227	+	0.985918i	$0.446519\pi$
$11$	−23.6471	+	57.0891i	−0.648170	+	1.56482i	−0.815397	+	0.578902i	$0.803481\pi$
$12$	11.0885	−	4.59303i	0.266749	−	0.110491i
$13$			5.37363i			0.114644i	0.998356	+	0.0573221i	$0.0182562\pi$
$13$			5.37363i			0.114644i	−0.998356	+	0.0573221i	$0.981744\pi$
$14$	−9.18078	−	22.1644i	−0.175262	−	0.423120i
$15$	17.4200	+	17.4200i	0.299854	+	0.299854i
$16$	79.9385			1.24904
$17$	44.2970	+	54.3210i	0.631977	+	0.774987i
$17$	44.2970	+	54.3210i	0.631977	+	0.774987i
$18$	66.5545			0.871502
$19$	−68.4392	−	68.4392i	−0.826370	−	0.826370i	0.160643	−	0.987013i	$-0.448643\pi$
$19$	−68.4392	−	68.4392i	−0.826370	−	0.826370i	−0.987013	+	0.160643i	$0.948643\pi$
$20$	−14.1743	−	34.2199i	−0.158474	−	0.382590i
$21$			19.3681i			0.201260i
$22$	−199.795	+	82.7579i	−1.93620	+	0.802002i
$23$	44.5923	−	107.655i	0.404267	−	0.975986i	−0.582351	−	0.812937i	$-0.697867\pi$
$23$	44.5923	−	107.655i	0.404267	−	0.975986i	0.986618	−	0.163049i	$-0.0521328\pi$
$24$	−34.2763	−	14.1977i	−0.291526	−	0.120754i
$25$	−34.6294	+	34.6294i	−0.277035	+	0.277035i
$26$	−13.2979	+	13.2979i	−0.100305	+	0.100305i
$27$	−120.120	−	49.7552i	−0.856187	−	0.354644i
$28$	11.1437	−	26.9032i	0.0752126	−	0.181579i
$29$	182.351	−	75.5321i	1.16764	−	0.483653i	0.287230	−	0.957862i	$-0.407266\pi$
$29$	182.351	−	75.5321i	1.16764	−	0.483653i	0.880413	+	0.474208i	$0.157266\pi$
$30$			86.2172i			0.524701i
$31$	−52.8371	−	127.560i	−0.306123	−	0.739047i	−0.999824	−	0.0187835i	$-0.994021\pi$
$31$	−52.8371	−	127.560i	−0.306123	−	0.739047i	0.693700	−	0.720264i	$-0.255979\pi$
$32$	123.541	+	123.541i	0.682473	+	0.682473i
$33$	174.589			0.920972
$34$	−24.8060	+	244.047i	−0.125123	+	1.23099i
$35$	59.7710			0.288661
$36$	57.1229	+	57.1229i	0.264458	+	0.264458i
$37$	42.6416	+	102.946i	0.189466	+	0.457411i	0.989857	−	0.142067i	$-0.0453749\pi$
$37$	42.6416	+	102.946i	0.189466	+	0.457411i	−0.800391	+	0.599478i	$0.795375\pi$
$38$		−	338.729i		−	1.44603i
$39$	14.0269	−	5.81013i	0.0575924	−	0.0238555i
$40$	−43.8149	+	105.779i	−0.173194	+	0.418127i
$41$	−153.814	−	63.7117i	−0.585894	−	0.242685i	0.0699888	−	0.997548i	$-0.477704\pi$
$41$	−153.814	−	63.7117i	−0.585894	−	0.242685i	−0.655883	+	0.754862i	$0.727704\pi$
$42$	−47.9296	+	47.9296i	−0.176088	+	0.176088i
$43$	−117.300	+	117.300i	−0.416000	+	0.416000i	−0.883823	−	0.467822i	$-0.845039\pi$
$43$	−117.300	+	117.300i	−0.416000	+	0.416000i	0.467822	+	0.883823i	$0.345039\pi$
$44$	−242.512	−	100.452i	−0.830911	−	0.344175i
$45$	−63.4553	+	153.195i	−0.210208	+	0.507487i
$46$	376.762	−	156.060i	1.20762	−	0.500213i
$47$			130.994i			0.406541i	0.979123	+	0.203271i	$0.0651571\pi$
$47$			130.994i			0.406541i	−0.979123	+	0.203271i	$0.934843\pi$
$48$	−86.4320	−	208.665i	−0.259904	−	0.627464i
$49$	−209.310	−	209.310i	−0.610233	−	0.610233i
$50$	−171.392			−0.484771
$51$	93.9001	−	174.363i	0.257816	−	0.478740i
$52$	−22.8269			−0.0608755
$53$	505.038	+	505.038i	1.30891	+	1.30891i	0.922201	+	0.386711i	$0.126389\pi$
$53$	505.038	+	505.038i	1.30891	+	1.30891i	0.386711	+	0.922201i	$0.373611\pi$
$54$	−174.129	−	420.384i	−0.438813	−	1.05939i
$55$		−	538.792i		−	1.32092i
$56$	−83.1616	+	34.4467i	−0.198445	+	0.0821987i
$57$	−104.650	+	252.647i	−0.243179	+	0.587087i
$58$	638.174	+	264.340i	1.44476	+	0.598441i
$59$	−598.365	+	598.365i	−1.32035	+	1.32035i	−0.406855	+	0.913493i	$0.633375\pi$
$59$	−598.365	+	598.365i	−1.32035	+	1.32035i	−0.913493	+	0.406855i	$0.866625\pi$
$60$	−73.9992	+	73.9992i	−0.159221	+	0.159221i
$61$	4.61209	+	1.91039i	0.00968061	+	0.00400984i	0.387518	−	0.921862i	$-0.373332\pi$
$61$	4.61209	+	1.91039i	0.00968061	+	0.00400984i	−0.377838	+	0.925872i	$0.623332\pi$
$62$	184.915	−	446.423i	0.378777	−	0.914448i
$63$	−120.439	+	49.8876i	−0.240856	+	0.0997659i
$64$		−	28.0634i		−	0.0548113i
$65$	−17.9304	−	43.2878i	−0.0342153	−	0.0826030i
$66$	432.050	+	432.050i	0.805783	+	0.805783i
$67$	314.069			0.572681			0.286341	−	0.958128i	$-0.407561\pi$
$67$	314.069			0.572681			0.286341	+	0.958128i	$0.407561\pi$
$68$	−230.753	+	188.172i	−0.411514	+	0.335576i
$69$	−329.230			−0.574415
$70$	147.913	+	147.913i	0.252558	+	0.252558i
$71$	−45.3357	−	109.450i	−0.0757796	−	0.182948i	0.881450	−	0.472277i	$-0.156568\pi$
$71$	−45.3357	−	109.450i	−0.0757796	−	0.182948i	−0.957230	+	0.289329i	$0.906568\pi$
$72$		−	249.715i		−	0.408739i
$73$	601.028	−	248.954i	0.963630	−	0.399149i	0.155293	−	0.987868i	$-0.450368\pi$
$73$	601.028	−	248.954i	0.963630	−	0.399149i	0.808337	+	0.588720i	$0.200368\pi$
$74$	−149.233	+	360.280i	−0.234432	+	0.565969i
$75$	127.836	+	52.9515i	0.196817	+	0.0815242i
$76$	290.727	−	290.727i	0.438798	−	0.438798i
$77$	299.524	−	299.524i	0.443297	−	0.443297i
$78$	49.0901	+	20.3338i	0.0712610	+	0.0295173i
$79$	−79.7533	+	192.542i	−0.113582	+	0.274210i	−0.970440	−	0.241341i	$-0.922413\pi$
$79$	−79.7533	+	192.542i	−0.113582	+	0.274210i	0.856859	+	0.515551i	$0.172413\pi$
$80$	−643.953	+	266.734i	−0.899952	+	0.372772i
$81$		−	146.115i		−	0.200432i
$82$	−222.972	−	538.303i	−0.300283	−	0.724947i
$83$	−524.977	−	524.977i	−0.694262	−	0.694262i	0.268905	−	0.963167i	$-0.413338\pi$
$83$	−524.977	−	524.977i	−0.694262	−	0.694262i	−0.963167	+	0.268905i	$0.913338\pi$
$84$	−82.2749			−0.106868
$85$	−538.095	−	289.781i	−0.686642	−	0.369778i
$86$	−580.555			−0.727940
$87$	−394.326	−	394.326i	−0.485933	−	0.485933i
$88$	310.511	+	749.640i	0.376143	+	0.908090i
$89$			215.527i			0.256695i	0.991729	+	0.128348i	$0.0409673\pi$
$89$			215.527i			0.256695i	−0.991729	+	0.128348i	$0.959033\pi$
$90$	−536.137	+	222.075i	−0.627931	+	0.260097i
$91$	14.0966	−	34.0323i	0.0162388	−	0.0392038i
$92$	457.315	+	189.426i	0.518244	+	0.214663i
$93$	−275.844	+	275.844i	−0.307567	+	0.307567i
$94$	−324.167	+	324.167i	−0.355694	+	0.355694i
$95$	779.683	+	322.955i	0.842040	+	0.348784i
$96$	188.905	−	456.058i	0.200834	−	0.484856i
$97$	651.973	−	270.056i	0.682452	−	0.282681i	−0.0143996	−	0.999896i	$-0.504584\pi$
$97$	651.973	−	270.056i	0.682452	−	0.282681i	0.696851	+	0.717216i	$0.254584\pi$
$98$		−	1035.94i		−	1.06782i
$99$	449.700	+	1085.67i	0.456531	+	1.10216i
$100$	−147.104	−	147.104i	−0.147104	−	0.147104i
$101$	546.988			0.538884			0.269442	−	0.963017i	$-0.413161\pi$
$101$	546.988			0.538884			0.269442	+	0.963017i	$0.413161\pi$
$102$	663.862	−	199.120i	0.644433	−	0.193292i
$103$	1550.96			1.48369			0.741846	−	0.670570i	$-0.233950\pi$
$103$	1550.96			1.48369			0.741846	+	0.670570i	$0.233950\pi$
$104$	49.8944	+	49.8944i	0.0470438	+	0.0470438i
$105$	−64.6263	−	156.022i	−0.0600656	−	0.145011i
$106$			2499.60i			2.29041i
$107$	227.070	−	94.0554i	0.205156	−	0.0849783i	−0.277739	−	0.960656i	$-0.589585\pi$
$107$	227.070	−	94.0554i	0.205156	−	0.0849783i	0.482895	+	0.875678i	$0.339585\pi$
$108$	211.358	−	510.263i	0.188314	−	0.454631i
$109$	−1841.65	−	762.836i	−1.61833	−	0.670334i	−0.624477	−	0.781043i	$-0.714688\pi$
$109$	−1841.65	−	762.836i	−1.61833	−	0.670334i	−0.993853	+	0.110708i	$0.964688\pi$
$110$	1333.33	−	1333.33i	1.15571	−	1.15571i
$111$	222.617	−	222.617i	0.190359	−	0.190359i
$112$	−506.267	−	209.703i	−0.427122	−	0.176920i
$113$	−414.351	+	1000.33i	−0.344946	+	0.832773i	0.652255	+	0.758000i	$0.273823\pi$
$113$	−414.351	+	1000.33i	−0.344946	+	0.832773i	−0.997201	+	0.0747730i	$0.976177\pi$
$114$	−884.191	+	366.244i	−0.726422	+	0.300894i
$115$			1016.02i			0.823865i
$116$	320.857	+	774.617i	0.256817	+	0.620012i
$117$	72.2600	+	72.2600i	0.0570977	+	0.0570977i
$118$	−2961.51			−2.31042
$119$	−138.042	−	460.230i	−0.106338	−	0.354531i
$120$	323.491			0.246088
$121$	−1758.83	−	1758.83i	−1.32143	−	1.32143i
$122$	6.68580	+	16.1410i	0.00496151	+	0.0119781i
$123$			470.391i			0.344827i
$124$	541.870	−	224.450i	0.392430	−	0.162550i
$125$	580.504	−	1401.46i	0.415375	−	1.00280i
$126$	−421.503	−	174.592i	−0.298019	−	0.123444i
$127$	718.468	−	718.468i	0.501998	−	0.501998i	−0.410061	−	0.912058i	$-0.634492\pi$
$127$	718.468	−	718.468i	0.501998	−	0.501998i	0.912058	+	0.410061i	$0.134492\pi$
$128$	1057.77	−	1057.77i	0.730429	−	0.730429i
$129$	433.018	+	179.362i	0.295543	+	0.122418i
$130$	62.7512	−	151.495i	0.0423357	−	0.102207i
$131$	−1024.45	+	424.340i	−0.683255	+	0.283014i	−0.697187	−	0.716889i	$-0.745565\pi$
$131$	−1024.45	+	424.340i	−0.683255	+	0.283014i	0.0139317	+	0.999903i	$0.495565\pi$
$132$			741.647i			0.489031i
$133$	253.903	+	612.976i	0.165535	+	0.399637i
$134$	777.217	+	777.217i	0.501054	+	0.501054i
$135$	1133.66			0.722738
$136$	915.674	+	93.0731i	0.577341	+	0.0586835i
$137$	−1975.27			−1.23182			−0.615909	−	0.787818i	$-0.711211\pi$
$137$	−1975.27			−1.23182			−0.615909	+	0.787818i	$0.711211\pi$
$138$	−814.734	−	814.734i	−0.502571	−	0.502571i
$139$	397.418	+	959.451i	0.242507	+	0.585465i	0.997531	−	0.0702334i	$-0.0223744\pi$
$139$	397.418	+	959.451i	0.242507	+	0.585465i	−0.755023	+	0.655698i	$0.772374\pi$
$140$			253.905i			0.153278i
$141$	341.937	−	141.635i	0.204229	−	0.0845944i
$142$	158.662	−	383.043i	0.0937647	−	0.226368i
$143$	−306.776	−	127.071i	−0.179398	−	0.0743090i
$144$	1074.95	−	1074.95i	0.622075	−	0.622075i
$145$	−1216.91	+	1216.91i	−0.696960	+	0.696960i
$146$	2103.42	+	871.266i	1.19233	+	0.493880i
$147$	−320.054	+	772.679i	−0.179576	+	0.433534i
$148$	−437.310	+	181.140i	−0.242883	+	0.100605i
$149$		−	119.562i		−	0.0657377i	−0.999460	−	0.0328689i	$-0.989536\pi$
$149$		−	119.562i		−	0.0657377i	0.999460	−	0.0328689i	$-0.0104644\pi$
$150$	185.315	+	447.390i	0.100873	+	0.243528i
$151$	−1108.64	−	1108.64i	−0.597481	−	0.597481i	0.342160	−	0.939642i	$-0.388841\pi$
$151$	−1108.64	−	1108.64i	−0.597481	−	0.597481i	−0.939642	+	0.342160i	$0.888841\pi$
$152$	−1270.92			−0.678194
$153$	1326.13	+	134.794i	0.700728	+	0.0712251i
$154$	1482.44			0.775705
$155$	851.270	+	851.270i	0.441133	+	0.441133i
$156$	24.6812	+	59.5857i	0.0126672	+	0.0305812i
$157$			2121.62i			1.07850i	0.842147	+	0.539248i	$0.181291\pi$
$157$			2121.62i			1.07850i	−0.842147	+	0.539248i	$0.818709\pi$
$158$	−673.839	+	279.113i	−0.339290	+	0.140538i
$159$	772.250	−	1864.38i	0.385179	−	0.929904i
$160$	−1407.42	−	582.972i	−0.695414	−	0.288050i
$161$	−564.824	+	564.824i	−0.276487	+	0.276487i
$162$	361.586	−	361.586i	0.175363	−	0.175363i
$163$	409.544	+	169.639i	0.196797	+	0.0815160i	0.478905	−	0.877867i	$-0.341034\pi$
$163$	409.544	+	169.639i	0.196797	+	0.0815160i	−0.282108	+	0.959383i	$0.591034\pi$
$164$	270.645	−	653.394i	0.128865	−	0.311107i
$165$	−1406.42	+	582.559i	−0.663574	+	0.274861i
$166$		−	2598.29i		−	1.21486i
$167$	900.241	+	2173.37i	0.417142	+	1.00707i	0.983171	+	0.182685i	$0.0584790\pi$
$167$	900.241	+	2173.37i	0.417142	+	1.00707i	−0.566029	+	0.824385i	$0.691521\pi$
$168$	179.834	+	179.834i	0.0825862	+	0.0825862i
$169$	2168.12			0.986857
$170$	−614.494	−	2048.72i	−0.277233	−	0.924291i
$171$	−1840.63			−0.823135
$172$	−498.284	−	498.284i	−0.220894	−	0.220894i
$173$	−727.203	−	1755.62i	−0.319585	−	0.771547i	−0.999276	−	0.0380481i	$-0.987886\pi$
$173$	−727.203	−	1755.62i	−0.319585	−	0.771547i	0.679691	−	0.733499i	$-0.262114\pi$
$174$		−	1951.65i		−	0.850313i
$175$	310.158	−	128.472i	0.133976	−	0.0554945i
$176$	−1890.31	+	4563.62i	−0.809590	+	1.95452i
$177$	2208.90	+	914.956i	0.938028	+	0.388544i
$178$	−533.359	+	533.359i	−0.224589	+	0.224589i
$179$	−70.5199	+	70.5199i	−0.0294464	+	0.0294464i	−0.721677	−	0.692230i	$-0.756628\pi$
$179$	−70.5199	+	70.5199i	−0.0294464	+	0.0294464i	0.692230	+	0.721677i	$0.256628\pi$
$180$	−650.764	−	269.555i	−0.269473	−	0.111619i
$181$	1484.36	−	3583.56i	0.609567	−	1.47162i	−0.253906	−	0.967229i	$-0.581715\pi$
$181$	1484.36	−	3583.56i	0.609567	−	1.47162i	0.863473	−	0.504395i	$-0.168285\pi$
$182$	119.103	−	49.3341i	0.0485082	−	0.0200928i
$183$		−	14.1046i		−	0.00569750i
$184$	−585.544	−	1413.63i	−0.234602	−	0.566380i
$185$	−687.007	−	687.007i	−0.273026	−	0.273026i
$186$	−1365.24			−0.538197
$187$	−4148.64	+	1244.35i	−1.62234	+	0.486607i
$188$	−556.457			−0.215871
$189$	630.219	+	630.219i	0.242549	+	0.242549i
$190$	1130.25	+	2728.66i	0.431563	+	1.04188i
$191$		−	2326.90i		−	0.881511i	−0.897627	−	0.440756i	$-0.854711\pi$
$191$		−	2326.90i		−	0.881511i	0.897627	−	0.440756i	$-0.145289\pi$
$192$	−73.2545	+	30.3430i	−0.0275348	+	0.0114053i
$193$	−534.412	+	1290.18i	−0.199315	+	0.481189i	−0.991660	−	0.128885i	$-0.958860\pi$
$193$	−534.412	+	1290.18i	−0.199315	+	0.481189i	0.792345	+	0.610074i	$0.208860\pi$
$194$	2281.72	+	945.117i	0.844421	+	0.349770i
$195$	−93.6083	+	93.6083i	−0.0343766	+	0.0343766i
$196$	889.140	−	889.140i	0.324030	−	0.324030i
$197$	−1869.77	−	774.486i	−0.676223	−	0.280101i	0.0180240	−	0.999838i	$-0.494262\pi$
$197$	−1869.77	−	774.486i	−0.676223	−	0.280101i	−0.694247	+	0.719737i	$0.744262\pi$
$198$	−1573.82	+	3799.54i	−0.564881	+	1.36374i
$199$	3827.94	−	1585.59i	1.36360	−	0.564820i	0.423552	−	0.905872i	$-0.360783\pi$
$199$	3827.94	−	1585.59i	1.36360	−	0.564820i	0.940045	+	0.341052i	$0.110783\pi$
$200$			643.072i			0.227360i
$201$	−339.581	−	819.822i	−0.119165	−	0.287691i
$202$	1353.61	+	1353.61i	0.471484	+	0.471484i
$203$	−1353.01			−0.467795
$204$	740.688	+	398.884i	0.254208	+	0.136899i
$205$	1451.65			0.494575
$206$	3838.10	+	3838.10i	1.29812	+	1.29812i
$207$	−848.018	−	2047.30i	−0.284741	−	0.687425i
$208$			429.560i			0.143195i
$209$	5525.52	−	2288.75i	1.82875	−	0.757493i
$210$	226.173	−	546.031i	0.0743212	−	0.179427i
$211$	2171.62	+	899.516i	0.708535	+	0.293485i	0.707698	−	0.706515i	$-0.249734\pi$
$211$	2171.62	+	899.516i	0.708535	+	0.293485i	0.000836499		1.00000i	$0.499734\pi$
$212$	−2145.38	+	2145.38i	−0.695025	+	0.695025i
$213$	−236.681	+	236.681i	−0.0761368	+	0.0761368i
$214$	794.678	+	329.166i	0.253846	+	0.105147i
$215$	553.521	−	1336.32i	0.175581	−	0.423889i
$216$	−1577.30	+	653.338i	−0.496859	+	0.205806i
$217$			946.471i			0.296086i
$218$	−2669.70	−	6445.24i	−0.829427	−	2.00241i
$219$	−1299.70	−	1299.70i	−0.401030	−	0.401030i
$220$	2288.77			0.701402
$221$	−291.901	+	238.036i	−0.0888478	+	0.0724526i
$222$	1101.80			0.333100
$223$	−291.603	−	291.603i	−0.0875657	−	0.0875657i	0.661967	−	0.749533i	$-0.269722\pi$
$223$	−291.603	−	291.603i	−0.0875657	−	0.0875657i	−0.749533	+	0.661967i	$0.769722\pi$
$224$	−458.324	−	1106.49i	−0.136710	−	0.330048i
$225$			931.333i			0.275951i
$226$	−3500.87	+	1450.11i	−1.03042	+	0.426813i
$227$	−733.181	+	1770.05i	−0.214374	+	0.517545i	−0.994086	−	0.108593i	$-0.965365\pi$
$227$	−733.181	+	1770.05i	−0.214374	+	0.517545i	0.779712	+	0.626138i	$0.215365\pi$
$228$	−1073.23	−	444.548i	−0.311740	−	0.129127i
$229$	−3439.04	+	3439.04i	−0.992394	+	0.992394i	−0.999971	−	0.00757695i	$-0.997588\pi$
$229$	−3439.04	+	3439.04i	−0.992394	+	0.992394i	0.00757695	+	0.999971i	$0.497588\pi$
$230$	−2514.32	+	2514.32i	−0.720822	+	0.720822i
$231$	−1105.71	−	457.999i	−0.314936	−	0.130451i
$232$	991.815	−	2394.45i	0.280672	−	0.677602i
$233$	513.374	−	212.646i	0.144344	−	0.0597894i	−0.309342	−	0.950951i	$-0.600109\pi$
$233$	513.374	−	212.646i	0.144344	−	0.0597894i	0.453686	+	0.891162i	$0.350109\pi$
$234$			357.639i			0.0999127i
$235$	−437.093	−	1055.24i	−0.121331	−	0.292919i
$236$	−2541.83	−	2541.83i	−0.701098	−	0.701098i
$237$	588.828			0.161386
$238$	797.309	−	1480.52i	0.217151	−	0.403228i
$239$	−3205.56			−0.867575			−0.433787	−	0.901015i	$-0.642823\pi$
$239$	−3205.56			−0.867575			−0.433787	+	0.901015i	$0.642823\pi$
$240$	1392.53	+	1392.53i	0.374530	+	0.374530i
$241$	−341.888	−	825.391i	−0.0913815	−	0.220614i	0.871580	−	0.490253i	$-0.163096\pi$
$241$	−341.888	−	825.391i	−0.0913815	−	0.220614i	−0.962962	+	0.269639i	$0.913096\pi$
$242$		−	8705.02i		−	2.31231i
$243$	−3624.64	+	1501.37i	−0.956875	+	0.396351i
$244$	−8.11525	+	19.5920i	−0.00212920	+	0.00514035i
$245$	2384.53	+	987.705i	0.621805	+	0.257560i
$246$	−1164.06	+	1164.06i	−0.301698	+	0.301698i
$247$	367.767	−	367.767i	0.0947386	−	0.0947386i
$248$	−1675.00	−	693.807i	−0.428881	−	0.177648i
$249$	−802.738	+	1937.98i	−0.204303	+	0.493231i
$250$	4904.70	−	2031.60i	1.24080	−	0.513957i
$251$			2431.39i			0.611427i	0.952124	+	0.305713i	$0.0988949\pi$
$251$			2431.39i			0.611427i	−0.952124	+	0.305713i	$0.901105\pi$
$252$	−211.921	−	511.622i	−0.0529752	−	0.127893i
$253$	5091.47	+	5091.47i	1.26521	+	1.26521i
$254$	3555.94			0.878422
$255$	−174.617	+	1717.92i	−0.0428821	+	0.421884i
$256$	5010.77			1.22333
$257$	2273.66	+	2273.66i	0.551856	+	0.551856i	0.926976	−	0.375120i	$-0.122399\pi$
$257$	2273.66	+	2273.66i	0.551856	+	0.551856i	−0.375120	+	0.926976i	$0.622399\pi$
$258$	627.714	+	1515.44i	0.151472	+	0.365686i
$259$		−	763.838i		−	0.183253i
$260$	183.885	−	76.1676i	0.0438617	−	0.0181681i
$261$	1436.40	−	3467.79i	0.340656	−	0.822416i
$262$	−3585.27	−	1485.07i	−0.845415	−	0.350182i
$263$	1880.31	−	1880.31i	0.440856	−	0.440856i	−0.451444	−	0.892300i	$-0.649091\pi$
$263$	1880.31	−	1880.31i	0.440856	−	0.440856i	0.892300	+	0.451444i	$0.149091\pi$
$264$	1621.07	−	1621.07i	0.377917	−	0.377917i
$265$	−5753.57	−	2383.21i	−1.33373	−	0.552450i
$266$	−888.586	+	2145.24i	−0.204822	+	0.494484i
$267$	562.596	−	233.035i	0.128953	−	0.0534139i
$268$			1334.15i			0.304091i
$269$	2186.04	+	5277.57i	0.495484	+	1.19620i	0.951892	+	0.306434i	$0.0991359\pi$
$269$	2186.04	+	5277.57i	0.495484	+	1.19620i	−0.456408	+	0.889771i	$0.650864\pi$
$270$	2805.42	+	2805.42i	0.632343	+	0.632343i
$271$	250.885			0.0562369			0.0281185	−	0.999605i	$-0.491048\pi$
$271$	250.885			0.0562369			0.0281185	+	0.999605i	$0.491048\pi$
$272$	3541.04	+	4342.34i	0.789364	+	0.967989i
$273$	−104.077			−0.0230733
$274$	−4888.14	−	4888.14i	−1.07775	−	1.07775i
$275$	−1158.08	−	2795.85i	−0.253944	−	0.613076i
$276$		−	1398.55i		−	0.305011i
$277$	−3407.52	+	1411.44i	−0.739126	+	0.306156i	−0.720296	−	0.693667i	$-0.755994\pi$
$277$	−3407.52	+	1411.44i	−0.739126	+	0.306156i	−0.0188299	+	0.999823i	$0.505994\pi$
$278$	−1390.85	+	3357.80i	−0.300063	+	0.724415i
$279$	−2425.83	−	1004.81i	−0.520540	−	0.215615i
$280$	554.978	−	554.978i	0.118451	−	0.118451i
$281$	−2497.50	+	2497.50i	−0.530208	+	0.530208i	−0.920634	−	0.390426i	$-0.872328\pi$
$281$	−2497.50	+	2497.50i	−0.530208	+	0.530208i	0.390426	+	0.920634i	$0.372328\pi$
$282$	1196.68	+	495.681i	0.252699	+	0.104671i
$283$	−301.639	+	728.220i	−0.0633589	+	0.152962i	−0.952388	−	0.304889i	$-0.901381\pi$
$283$	−301.639	+	728.220i	−0.0633589	+	0.152962i	0.889029	+	0.457851i	$0.151381\pi$
$284$	464.939	−	192.584i	0.0971445	−	0.0402386i
$285$		−	2384.42i		−	0.495581i
$286$	−444.710	−	1073.63i	−0.0919450	−	0.221975i
$287$	806.998	+	806.998i	0.165978	+	0.165978i
$288$	3322.54			0.679801
$289$	−988.544	+	4812.52i	−0.201210	+	0.979548i
$290$	−6022.91			−1.21958
$291$	−1409.87	−	1409.87i	−0.284013	−	0.284013i
$292$	1057.55	+	2553.14i	0.211946	+	0.511683i
$293$		−	1413.82i		−	0.281899i	−0.990017	−	0.140949i	$-0.954985\pi$
$293$		−	1413.82i		−	0.281899i	0.990017	−	0.140949i	$-0.0450154\pi$
$294$	−2704.15	+	1120.10i	−0.536426	+	0.222195i
$295$	2823.61	−	6816.79i	0.557277	−	1.34539i
$296$	1351.79	+	559.929i	0.265443	+	0.109950i
$297$	5680.96	−	5680.96i	1.10991	−	1.10991i
$298$	295.877	−	295.877i	0.0575157	−	0.0575157i
$299$	578.499	+	239.622i	0.111891	+	0.0463469i
$300$	−224.936	+	543.043i	−0.0432889	+	0.104509i
$301$	1050.59	−	435.170i	0.201180	−	0.0833315i
$302$		−	5487.02i		−	1.04551i
$303$	−591.420	−	1427.81i	−0.112133	−	0.270712i
$304$	−5470.93	−	5470.93i	−1.03217	−	1.03217i
$305$	−43.5276			−0.00817175
$306$	2948.17	+	3615.31i	0.550769	+	0.675403i
$307$	4499.58			0.836498			0.418249	−	0.908333i	$-0.362644\pi$
$307$	4499.58			0.836498			0.418249	+	0.908333i	$0.362644\pi$
$308$	1272.36	+	1272.36i	0.235388	+	0.235388i
$309$	−1676.94	−	4048.50i	−0.308731	−	0.745343i
$310$			4213.22i			0.771919i
$311$	−4357.74	+	1805.04i	−0.794550	+	0.329113i	−0.742771	−	0.669545i	$-0.766489\pi$
$311$	−4357.74	+	1805.04i	−0.794550	+	0.329113i	−0.0517785	+	0.998659i	$0.516489\pi$
$312$	76.2932	−	184.188i	0.0138438	−	0.0334218i
$313$	−5701.55	−	2361.66i	−1.02962	−	0.426482i	−0.197044	−	0.980395i	$-0.563134\pi$
$313$	−5701.55	−	2361.66i	−1.02962	−	0.426482i	−0.832575	+	0.553913i	$0.813134\pi$
$314$	−5250.30	+	5250.30i	−0.943605	+	0.943605i
$315$	803.750	−	803.750i	0.143766	−	0.143766i
$316$	−817.908	−	338.789i	−0.145604	−	0.0603113i
$317$	454.194	−	1096.52i	0.0804735	−	0.194280i	−0.878522	−	0.477702i	$-0.841470\pi$
$317$	454.194	−	1096.52i	0.0804735	−	0.194280i	0.958995	+	0.283422i	$0.0914698\pi$
$318$	6524.77	−	2702.65i	1.15060	−	0.476595i
$319$			12196.3i			2.14064i
$320$	93.6403	+	226.068i	0.0163583	+	0.0394924i
$321$	−491.030	−	491.030i	−0.0853789	−	0.0853789i
$322$	−2795.50			−0.483811
$323$	686.033	−	6749.34i	0.118179	−	1.16267i
$324$	620.690			0.106428
$325$	−186.085	−	186.085i	−0.0317605	−	0.0317605i
$326$	593.685	+	1433.28i	0.100863	+	0.243504i
$327$			5632.10i			0.952465i
$328$	−2019.74	+	836.602i	−0.340004	+	0.140834i
$329$	343.636	−	829.611i	0.0575844	−	0.139021i
$330$	−4922.06	−	2038.79i	−0.821063	−	0.340095i
$331$	2170.88	−	2170.88i	0.360491	−	0.360491i	−0.503503	−	0.863994i	$-0.667956\pi$
$331$	2170.88	−	2170.88i	0.360491	−	0.360491i	0.863994	+	0.503503i	$0.167956\pi$
$332$	2230.08	−	2230.08i	0.368649	−	0.368649i
$333$	1957.74	+	810.921i	0.322172	+	0.133448i
$334$	−3150.58	+	7606.18i	−0.516144	+	1.24608i
$335$	−2530.02	+	1047.97i	−0.412626	+	0.170915i
$336$			1548.26i			0.251382i
$337$	−1698.14	−	4099.67i	−0.274491	−	0.662681i	0.725173	−	0.688566i	$-0.241760\pi$
$337$	−1698.14	−	4099.67i	−0.274491	−	0.662681i	−0.999665	+	0.0258852i	$0.991760\pi$
$338$	5365.39	+	5365.39i	0.863428	+	0.863428i
$339$	3059.20			0.490127
$340$	1230.98	−	2285.80i	0.196350	−	0.364603i
$341$	8531.74			1.35490
$342$	−4554.94	−	4554.94i	−0.720183	−	0.720183i
$343$	1676.31	+	4046.97i	0.263884	+	0.637073i
$344$			2178.27i			0.341408i
$345$	2652.15	−	1098.55i	0.413875	−	0.171432i
$346$	2545.00	−	6144.17i	0.395434	−	0.954661i
$347$	8050.88	+	3334.79i	1.24552	+	0.515910i	0.905434	−	0.424486i	$-0.139545\pi$
$347$	8050.88	+	3334.79i	1.24552	+	0.515910i	0.340082	+	0.940396i	$0.389545\pi$
$348$	1675.08	−	1675.08i	0.258028	−	0.258028i
$349$	71.3677	−	71.3677i	0.0109462	−	0.0109462i	−0.701612	−	0.712559i	$-0.747536\pi$
$349$	71.3677	−	71.3677i	0.0109462	−	0.0109462i	0.712559	+	0.701612i	$0.247536\pi$
$350$	1085.46	+	449.613i	0.165773	+	0.0686653i
$351$	267.366	−	645.478i	0.0406579	−	0.0981569i
$352$	−9974.22	+	4131.46i	−1.51031	+	0.625589i
$353$		−	8688.88i		−	1.31009i	−0.755589	−	0.655046i	$-0.772649\pi$
$353$		−	8688.88i		−	1.31009i	0.755589	−	0.655046i	$-0.227351\pi$
$354$	3202.08	+	7730.50i	0.480759	+	1.16065i
$355$	730.412	+	730.412i	0.109201	+	0.109201i
$356$	−915.551			−0.136304
$357$	−1052.09	+	857.949i	−0.155974	+	0.127192i
$358$	−349.026			−0.0515269
$359$	−1705.20	−	1705.20i	−0.250688	−	0.250688i	0.570565	−	0.821253i	$-0.306724\pi$
$359$	−1705.20	−	1705.20i	−0.250688	−	0.250688i	−0.821253	+	0.570565i	$0.806724\pi$
$360$	833.235	+	2011.61i	0.121987	+	0.294503i
$361$			2508.85i			0.365775i
$362$	12541.4	−	5194.82i	1.82089	−	0.754237i
$363$	−2689.41	+	6492.80i	−0.388863	+	0.938798i
$364$	144.568	+	59.8818i	0.0208170	+	0.00862270i
$365$	−4010.95	+	4010.95i	−0.575186	+	0.575186i
$366$	34.9042	−	34.9042i	0.00498490	−	0.00498490i
$367$	−2101.09	−	870.300i	−0.298845	−	0.123786i	0.228223	−	0.973609i	$-0.426709\pi$
$367$	−2101.09	−	870.300i	−0.298845	−	0.123786i	−0.527068	+	0.849823i	$0.676709\pi$
$368$	3564.64	−	8605.81i	0.504945	−	1.21905i
$369$	−2925.10	+	1211.62i	−0.412668	+	0.170933i
$370$		−	3400.23i		−	0.477755i
$371$	−1873.64	−	4523.37i	−0.262196	−	0.632997i
$372$	−1171.77	−	1171.77i	−0.163316	−	0.163316i
$373$	−9493.93			−1.31790			−0.658951	−	0.752186i	$-0.728999\pi$
$373$	−9493.93			−1.31790			−0.658951	+	0.752186i	$0.728999\pi$
$374$	−13345.8	−	7187.15i	−1.84518	−	0.993687i
$375$	−4285.93			−0.590198
$376$	1216.29	+	1216.29i	0.166822	+	0.166822i
$377$	405.881	+	979.883i	0.0554481	+	0.133864i
$378$			3119.17i			0.424425i
$379$	4931.39	−	2042.65i	0.668360	−	0.276844i	−0.0225917	−	0.999745i	$-0.507192\pi$
$379$	4931.39	−	2042.65i	0.668360	−	0.276844i	0.690952	+	0.722901i	$0.257192\pi$
$380$	−1371.90	+	3312.06i	−0.185203	+	0.447119i
$381$	−2652.26	−	1098.60i	−0.356639	−	0.147725i
$382$	5758.31	−	5758.31i	0.771258	−	0.771258i
$383$	551.137	−	551.137i	0.0735295	−	0.0735295i	−0.669386	−	0.742915i	$-0.733443\pi$
$383$	551.137	−	551.137i	0.0735295	−	0.0735295i	0.742915	+	0.669386i	$0.233443\pi$
$384$	−3904.83	−	1617.43i	−0.518926	−	0.214946i
$385$	−1413.41	+	3412.28i	−0.187102	+	0.451703i
$386$	−4515.27	+	1870.28i	−0.595391	+	0.246619i
$387$			3154.69i			0.414372i
$388$	1147.19	+	2769.55i	0.150102	+	0.362378i
$389$	−7655.19	−	7655.19i	−0.997772	−	0.997772i	0.00222529	−	0.999998i	$-0.499292\pi$
$389$	−7655.19	−	7655.19i	−0.997772	−	0.997772i	−0.999998	+	0.00222529i	$0.999292\pi$
$390$	−463.299			−0.0601540
$391$	7823.25	−	2346.51i	1.01186	−	0.303499i
$392$	−3886.91			−0.500813
$393$	2215.33	+	2215.33i	0.284348	+	0.284348i
$394$	−2710.48	−	6543.67i	−0.346578	−	0.836714i
$395$		−	1817.16i		−	0.231471i
$396$	−4611.89	+	1910.31i	−0.585243	+	0.242416i
$397$	−2337.00	+	5642.01i	−0.295442	+	0.713260i	0.704551	+	0.709653i	$0.251148\pi$
$397$	−2337.00	+	5642.01i	−0.295442	+	0.713260i	−0.999993	+	0.00360730i	$0.998852\pi$
$398$	13396.7	+	5549.09i	1.68722	+	0.698871i
$399$	1325.54	−	1325.54i	0.166315	−	0.166315i
$400$	−2768.22	+	2768.22i	−0.346028	+	0.346028i
$401$	10579.9	+	4382.32i	1.31754	+	0.545743i	0.927075	−	0.374875i	$-0.122314\pi$
$401$	10579.9	+	4382.32i	1.31754	+	0.545743i	0.390464	+	0.920618i	$0.372314\pi$
$402$	1188.44	−	2869.14i	0.147447	−	0.355969i
$403$	685.460	−	283.927i	0.0847276	−	0.0350953i
$404$			2323.58i			0.286145i
$405$	487.548	+	1177.04i	0.0598184	+	0.144414i
$406$	−3348.24	−	3348.24i	−0.409286	−	0.409286i
$407$	−6885.44			−0.838571
$408$	−747.105	−	2490.84i	−0.0906549	−	0.302243i
$409$	−7597.11			−0.918466			−0.459233	−	0.888316i	$-0.651876\pi$
$409$	−7597.11			−0.918466			−0.459233	+	0.888316i	$0.651876\pi$
$410$	3592.36	+	3592.36i	0.432717	+	0.432717i
$411$	2135.73	+	5156.10i	0.256320	+	0.618812i
$412$			6588.40i			0.787833i
$413$	5359.26	−	2219.88i	0.638527	−	0.264487i
$414$	2967.82	−	7164.94i	0.352319	−	0.850574i
$415$	5980.72	+	2477.30i	0.707427	+	0.293026i
$416$	−663.862	+	663.862i	−0.0782416	+	0.0782416i
$417$	2074.78	−	2074.78i	0.243651	−	0.243651i
$418$	19337.7	+	8009.95i	2.26277	+	0.937271i
$419$	2635.75	−	6363.26i	0.307315	−	0.741923i	−0.692476	−	0.721441i	$-0.743480\pi$
$419$	2635.75	−	6363.26i	0.307315	−	0.741923i	0.999790	−	0.0204818i	$-0.00652001\pi$
$420$	662.774	−	274.530i	0.0770001	−	0.0318945i
$421$		−	13586.7i		−	1.57286i	−0.617678	−	0.786431i	$-0.711927\pi$
$421$		−	13586.7i		−	1.57286i	0.617678	−	0.786431i	$-0.288073\pi$
$422$	3148.04	+	7600.05i	0.363138	+	0.876694i
$423$	1761.50	+	1761.50i	0.202475	+	0.202475i
$424$	9378.62			1.07421
$425$	−3415.08	−	347.124i	−0.389778	−	0.0396188i
$426$	−1171.42			−0.133228
$427$	−24.1978	−	24.1978i	−0.00274242	−	0.00274242i
$428$	399.543	+	964.583i	0.0451230	+	0.108937i
$429$			938.177i			0.105584i
$430$	4676.72	−	1937.16i	0.524492	−	0.217252i
$431$	−6434.61	+	15534.5i	−0.719128	+	1.73613i	−0.0433099	+	0.999062i	$0.513790\pi$
$431$	−6434.61	+	15534.5i	−0.719128	+	1.73613i	−0.675819	+	0.737068i	$0.736210\pi$
$432$	−9602.19	−	3977.36i	−1.06941	−	0.442964i
$433$	−175.945	+	175.945i	−0.0195274	+	0.0195274i	−0.716803	−	0.697276i	$-0.754395\pi$
$433$	−175.945	+	175.945i	−0.0195274	+	0.0195274i	0.697276	+	0.716803i	$0.254395\pi$
$434$	−2342.20	+	2342.20i	−0.259054	+	0.259054i
$435$	4492.30	+	1860.77i	0.495148	+	0.205097i
$436$	3240.50	−	7823.25i	0.355944	−	0.859325i
$437$	−10419.7	+	4315.98i	−1.14060	+	0.472452i
$438$		−	6432.66i		−	0.701745i
$439$	3777.10	+	9118.74i	0.410641	+	0.991375i	0.984966	+	0.172748i	$0.0552645\pi$
$439$	3777.10	+	9118.74i	0.410641	+	0.991375i	−0.574325	+	0.818627i	$0.694735\pi$
$440$	−5002.71	−	5002.71i	−0.542034	−	0.542034i
$441$	−5629.24			−0.607844
$442$	−1311.42	−	133.298i	−0.141126	−	0.0143447i
$443$	−10000.3			−1.07253			−0.536264	−	0.844051i	$-0.680165\pi$
$443$	−10000.3			−1.07253			−0.536264	+	0.844051i	$0.680165\pi$
$444$	945.666	+	945.666i	0.101080	+	0.101080i
$445$	−719.159	−	1736.20i	−0.0766099	−	0.184953i
$446$		−	1443.24i		−	0.153227i
$447$	−312.096	+	129.274i	−0.0330238	+	0.0136789i
$448$	−73.6186	+	177.731i	−0.00776373	+	0.0187433i
$449$	−7927.24	−	3283.57i	−0.833206	−	0.345125i	−0.0750349	−	0.997181i	$-0.523907\pi$
$449$	−7927.24	−	3283.57i	−0.833206	−	0.345125i	−0.758171	+	0.652056i	$0.773907\pi$
$450$	−2304.74	+	2304.74i	−0.241437	+	0.241437i
$451$	7274.50	−	7274.50i	0.759518	−	0.759518i
$452$	−4249.37	−	1760.15i	−0.442198	−	0.183164i
$453$	−1695.21	+	4092.60i	−0.175823	+	0.424475i
$454$	−6194.67	+	2565.92i	−0.640375	+	0.265252i
$455$			321.187i			0.0330934i
$456$	1374.16	+	3317.52i	0.141121	+	0.340696i
$457$	5901.41	+	5901.41i	0.604062	+	0.604062i	0.941388	−	0.337326i	$-0.109522\pi$
$457$	5901.41	+	5901.41i	0.604062	+	0.604062i	−0.337326	+	0.941388i	$0.609522\pi$
$458$	−17021.0			−1.73655
$459$	−2618.19	−	8729.03i	−0.266246	−	0.887661i
$460$	−4316.02			−0.437468
$461$	6081.73	+	6081.73i	0.614435	+	0.614435i	0.944099	−	0.329663i	$-0.106935\pi$
$461$	6081.73	+	6081.73i	0.614435	+	0.614435i	−0.329663	+	0.944099i	$0.606935\pi$
$462$	−1602.86	−	3869.66i	−0.161411	−	0.389681i
$463$		−	15888.5i		−	1.59482i	−0.603440	−	0.797408i	$-0.706204\pi$
$463$		−	15888.5i		−	1.59482i	0.603440	−	0.797408i	$-0.293796\pi$
$464$	14576.8	−	6037.92i	1.45843	−	0.604102i
$465$	1301.67	−	3142.51i	0.129814	−	0.313399i
$466$	1796.66	+	744.200i	0.178602	+	0.0739794i
$467$	−4201.42	+	4201.42i	−0.416314	+	0.416314i	−0.883931	−	0.467617i	$-0.845113\pi$
$467$	−4201.42	+	4201.42i	−0.416314	+	0.416314i	0.467617	+	0.883931i	$0.345113\pi$
$468$	−306.957	+	306.957i	−0.0303186	+	0.0303186i
$469$	−1989.06	−	823.897i	−0.195835	−	0.0811173i
$470$	1529.70	−	3693.02i	0.150127	−	0.362439i
$471$	5538.12	−	2293.96i	0.541790	−	0.224417i
$472$			11111.7i			1.08360i
$473$	−3922.74	−	9470.33i	−0.381327	−	0.920605i
$474$	1457.15	+	1457.15i	0.141201	+	0.141201i
$475$	4740.02			0.457867
$476$	1955.04	−	586.396i	0.188254	−	0.0564652i
$477$	13582.7			1.30379
$478$	−7932.69	−	7932.69i	−0.759064	−	0.759064i
$479$	5707.77	+	13779.8i	0.544456	+	1.31443i	0.921551	+	0.388258i	$0.126923\pi$
$479$	5707.77	+	13779.8i	0.544456	+	1.31443i	−0.377094	+	0.926175i	$0.623077\pi$
$480$			4304.15i			0.409285i
$481$	−553.192	+	229.140i	−0.0524395	+	0.0217212i
$482$	1196.51	−	2888.63i	0.113069	−	0.272974i
$483$	2085.08	+	863.668i	0.196427	+	0.0813628i
$484$	7471.42	−	7471.42i	0.701673	−	0.701673i
$485$	−4350.93	+	4350.93i	−0.407352	+	0.407352i
$486$	−12685.2	−	5254.37i	−1.18397	−	0.490418i
$487$	−3146.75	+	7596.92i	−0.292798	+	0.706878i	−1.00000		0.000134144i	$-0.999957\pi$
$487$	−3146.75	+	7596.92i	−0.292798	+	0.706878i	0.707202	+	0.707012i	$0.249957\pi$
$488$	60.5616	−	25.0854i	0.00561781	−	0.00232697i
$489$		−	1252.46i		−	0.115825i
$490$	3456.68	+	8345.16i	0.318688	+	0.769380i
$491$	−1863.67	−	1863.67i	−0.171295	−	0.171295i	0.616253	−	0.787548i	$-0.288650\pi$
$491$	−1863.67	−	1863.67i	−0.171295	−	0.171295i	−0.787548	+	0.616253i	$0.788650\pi$
$492$	−1998.20			−0.183101
$493$	12180.6	+	6559.62i	1.11275	+	0.599250i
$494$	1820.20			0.165779
$495$	−7245.22	−	7245.22i	−0.657875	−	0.657875i
$496$	−4223.72	−	10197.0i	−0.382360	−	0.923099i
$497$			812.097i			0.0732949i
$498$	−6782.37	+	2809.35i	−0.610292	+	0.252791i
$499$	4884.55	−	11792.3i	0.438201	−	1.05791i	−0.538368	−	0.842710i	$-0.680959\pi$
$499$	4884.55	−	11792.3i	0.438201	−	1.05791i	0.976570	−	0.215202i	$-0.0690409\pi$
$500$	5953.35	+	2465.96i	0.532484	+	0.220562i
$501$	4699.84	−	4699.84i	0.419109	−	0.419109i
$502$	−6016.89	+	6016.89i	−0.534954	+	0.534954i
$503$	5915.75	+	2450.38i	0.524394	+	0.217211i	0.629146	−	0.777287i	$-0.283405\pi$
$503$	5915.75	+	2450.38i	0.524394	+	0.217211i	−0.104752	+	0.994498i	$0.533405\pi$
$504$	−655.077	+	1581.50i	−0.0578958	+	0.139773i
$505$	−4406.32	+	1825.16i	−0.388274	+	0.160828i
$506$			25199.4i			2.21393i
$507$	−2344.24	−	5659.51i	−0.205348	−	0.495754i
$508$	3052.02	+	3052.02i	0.266558	+	0.266558i
$509$	7892.36			0.687274			0.343637	−	0.939103i	$-0.388341\pi$
$509$	7892.36			0.687274			0.343637	+	0.939103i	$0.388341\pi$
$510$	−4683.40	+	3819.17i	−0.406637	+	0.331599i
$511$	−4459.51			−0.386061
$512$	3937.80	+	3937.80i	0.339898	+	0.339898i
$513$	4815.69	+	11626.1i	0.414460	+	1.00059i
$514$			11253.1i			0.965667i
$515$	−12493.9	+	5175.14i	−1.06902	+	0.442804i
$516$	−761.922	+	1839.44i	−0.0650034	+	0.156932i
$517$	−7478.33	−	3097.63i	−0.636164	−	0.263508i
$518$	1890.25	−	1890.25i	0.160333	−	0.160333i
$519$	−3796.47	+	3796.47i	−0.321092	+	0.321092i
$520$	−568.415	−	235.445i	−0.0479358	−	0.0198557i
$521$	3255.41	−	7859.25i	0.273747	−	0.660883i	−0.725891	−	0.687810i	$-0.758572\pi$
$521$	3255.41	−	7859.25i	0.273747	−	0.660883i	0.999637	+	0.0269270i	$0.00857216\pi$
$522$	12136.2	−	5027.00i	1.01760	−	0.421505i
$523$		−	18757.8i		−	1.56830i	−0.620571	−	0.784150i	$-0.713099\pi$
$523$		−	18757.8i		−	1.56830i	0.620571	−	0.784150i	$-0.286901\pi$
$524$	−1802.58	−	4351.81i	−0.150279	−	0.362805i
$525$	−670.705	−	670.705i	−0.0557562	−	0.0557562i
$526$	9306.30			0.771433
$527$	4588.67	−	8520.70i	0.379289	−	0.704303i
$528$	13956.4			1.15033
$529$	−997.824	−	997.824i	−0.0820107	−	0.0820107i
$530$	−8340.53	−	20135.8i	−0.683565	−	1.65027i
$531$			16092.6i			1.31518i
$532$	−2603.89	+	1078.57i	−0.212205	+	0.0878983i
$533$	342.363	−	826.537i	0.0278225	−	0.0671694i
$534$	1968.92	+	815.555i	0.159557	+	0.0660908i
$535$	−1515.35	+	1515.35i	−0.122456	+	0.122456i
$536$	2916.15	−	2916.15i	0.234997	−	0.234997i
$537$	260.328	+	107.831i	0.0209199	+	0.00866530i
$538$	−7650.50	+	18470.0i	−0.613079	+	1.48010i
$539$	16898.9	−	6999.75i	1.35044	−	0.559370i
$540$			4815.73i			0.383770i
$541$	−5127.75	−	12379.5i	−0.407503	−	0.983800i	−0.985792	−	0.167968i	$-0.946279\pi$
$541$	−5127.75	−	12379.5i	−0.407503	−	0.983800i	0.578289	−	0.815832i	$-0.303721\pi$
$542$	620.858	+	620.858i	0.0492032	+	0.0492032i
$543$	−10959.2			−0.866121
$544$	−1238.37	+	12183.4i	−0.0976005	+	0.960215i
$545$	17381.0			1.36609
$546$	−257.556	−	257.556i	−0.0201875	−	0.0201875i
$547$	2729.96	+	6590.70i	0.213391	+	0.515170i	0.993940	−	0.109924i	$-0.0350606\pi$
$547$	2729.96	+	6590.70i	0.213391	+	0.515170i	−0.780549	+	0.625094i	$0.785061\pi$
$548$		−	8390.88i		−	0.654089i
$549$	87.7087	−	36.3301i	0.00681843	−	0.00282429i
$550$	4052.93	−	9784.65i	0.314214	−	0.758579i
$551$	−17649.3	−	7310.57i	−1.36458	−	0.565228i
$552$	−3056.92	+	3056.92i	−0.235708	+	0.235708i
$553$	1010.19	−	1010.19i	0.0776809	−	0.0776809i
$554$	−11925.3	−	4939.63i	−0.914546	−	0.378817i
$555$	−1050.50	+	2536.13i	−0.0803444	+	0.193969i
$556$	−4075.71	+	1688.21i	−0.310879	+	0.128770i
$557$		−	5175.60i		−	0.393712i	−0.980432	−	0.196856i	$-0.936927\pi$
$557$		−	5175.60i		−	0.393712i	0.980432	−	0.196856i	$-0.0630731\pi$
$558$	−3516.55	−	8489.70i	−0.266787	−	0.644081i
$559$	−630.324	−	630.324i	−0.0476921	−	0.0476921i
$560$	4778.01			0.360550
$561$	7733.78	+	9483.86i	0.582033	+	0.713741i
$562$	−12361.0			−0.927787
$563$	−3938.10	−	3938.10i	−0.294798	−	0.294798i	0.544174	−	0.838972i	$-0.316843\pi$
$563$	−3938.10	−	3938.10i	−0.294798	−	0.294798i	−0.838972	+	0.544174i	$0.816843\pi$
$564$	601.659	+	1452.53i	0.0449192	+	0.108444i
$565$		−	9440.87i		−	0.702974i
$566$	−2548.56	+	1055.65i	−0.189265	+	0.0783961i
$567$	−383.303	+	925.375i	−0.0283901	+	0.0685398i
$568$	−1437.19	−	595.305i	−0.106168	−	0.0439761i
$569$	−10840.0	+	10840.0i	−0.798660	+	0.798660i	−0.982884	−	0.184224i	$-0.941023\pi$
$569$	−10840.0	+	10840.0i	−0.798660	+	0.798660i	0.184224	+	0.982884i	$0.441023\pi$
$570$	5900.64	−	5900.64i	0.433597	−	0.433597i
$571$	−20588.7	−	8528.10i	−1.50895	−	0.625026i	−0.533606	−	0.845733i	$-0.679164\pi$
$571$	−20588.7	−	8528.10i	−1.50895	−	0.625026i	−0.975340	+	0.220707i	$0.929164\pi$
$572$	539.791	−	1303.17i	0.0394577	−	0.0952592i
$573$	−6073.96	+	2515.92i	−0.442833	+	0.183428i
$574$			3994.11i			0.290437i
$575$	2183.83	+	5272.24i	0.158386	+	0.382378i
$576$	−377.373	−	377.373i	−0.0272984	−	0.0272984i
$577$	19321.1			1.39401			0.697007	−	0.717064i	$-0.254515\pi$
$577$	19321.1			1.39401			0.697007	+	0.717064i	$0.254515\pi$
$578$	−14355.7	+	9463.07i	−1.03308	+	0.680989i
$579$	3945.62			0.283203
$580$	−5169.40	−	5169.40i	−0.370082	−	0.370082i
$581$	1947.61	+	4701.96i	0.139072	+	0.335749i
$582$		−	6977.91i		−	0.496982i
$583$	−40774.9	+	16889.5i	−2.89661	+	1.19981i
$584$	3269.03	−	7892.13i	0.231632	−	0.559210i
$585$	−823.211	−	340.985i	−0.0581805	−	0.0240991i
$586$	3498.74	−	3498.74i	0.246641	−	0.246641i
$587$	16667.4	−	16667.4i	1.17195	−	1.17195i	0.190210	−	0.981743i	$-0.439083\pi$
$587$	16667.4	−	16667.4i	1.17195	−	1.17195i	0.981743	−	0.190210i	$-0.0609169\pi$
$588$	−3282.31	−	1359.58i	−0.230204	−	0.0953537i
$589$	−5113.98	+	12346.2i	−0.357755	+	0.863698i
$590$	23856.8	−	9881.80i	1.66469	−	0.689537i
$591$			5718.12i			0.397990i
$592$	3408.70	+	8229.34i	0.236650	+	0.571324i
$593$	19330.9	+	19330.9i	1.33866	+	1.33866i	0.897359	+	0.441302i	$0.145483\pi$
$593$	19330.9	+	19330.9i	1.33866	+	1.33866i	0.441302	+	0.897359i	$0.354517\pi$
$594$	28117.0			1.94218
$595$	2647.68	+	3246.82i	0.182427	+	0.223709i
$596$	507.895			0.0349064
$597$	−8277.79	−	8277.79i	−0.567483	−	0.567483i
$598$	838.608	+	2024.58i	0.0573465	+	0.138447i
$599$		−	3930.83i		−	0.268129i	−0.990973	−	0.134064i	$-0.957197\pi$
$599$		−	3930.83i		−	0.268129i	0.990973	−	0.134064i	$-0.0428029\pi$
$600$	1678.63	−	695.309i	0.114216	−	0.0473098i
$601$	−8595.04	+	20750.3i	−0.583359	+	1.40835i	0.306391	+	0.951906i	$0.400879\pi$
$601$	−8595.04	+	20750.3i	−0.583359	+	1.40835i	−0.889750	+	0.456448i	$0.849121\pi$
$602$	3676.77	+	1522.97i	0.248927	+	0.103109i
$603$	4223.34	−	4223.34i	0.285220	−	0.285220i
$604$	4709.45	−	4709.45i	0.317259	−	0.317259i
$605$	20037.2	+	8299.66i	1.34649	+	0.557734i
$606$	2069.80	−	4996.94i	0.138746	−	0.334961i
$607$	2057.72	−	852.335i	0.137595	−	0.0569938i	−0.312823	−	0.949811i	$-0.601275\pi$
$607$	2057.72	−	852.335i	0.137595	−	0.0569938i	0.450419	+	0.892818i	$0.351275\pi$
$608$		−	16910.1i		−	1.12795i
$609$	1462.91	+	3531.78i	0.0973402	+	0.235000i
$610$	−107.716	−	107.716i	−0.00714969	−	0.00714969i
$611$	−703.913			−0.0466076
$612$	−572.599	+	5633.35i	−0.0378201	+	0.372083i
$613$	721.642			0.0475479			0.0237739	−	0.999717i	$-0.492432\pi$
$613$	721.642			0.0475479			0.0237739	+	0.999717i	$0.492432\pi$
$614$	11135.0	+	11135.0i	0.731874	+	0.731874i
$615$	−1569.57	−	3789.28i	−0.102913	−	0.248453i
$616$		−	5562.19i		−	0.363810i
$617$	6311.56	−	2614.33i	0.411821	−	0.170582i	−0.167147	−	0.985932i	$-0.553455\pi$
$617$	6311.56	−	2614.33i	0.411821	−	0.170582i	0.578968	+	0.815350i	$0.303455\pi$
$618$	5868.81	−	14168.6i	0.382004	−	0.922239i
$619$	14869.8	+	6159.26i	0.965536	+	0.399938i	0.809048	−	0.587742i	$-0.199983\pi$
$619$	14869.8	+	6159.26i	0.965536	+	0.399938i	0.156487	+	0.987680i	$0.449983\pi$
$620$	−3616.16	+	3616.16i	−0.234240	+	0.234240i
$621$	−10712.8	+	10712.8i	−0.692256	+	0.692256i
$622$	−15250.8	−	6317.10i	−0.983123	−	0.407223i
$623$	565.393	−	1364.98i	0.0363595	−	0.0877796i
$624$	1121.29	−	464.453i	0.0719351	−	0.0297965i
$625$			7104.94i			0.454716i
$626$	−8265.11	−	19953.8i	−0.527700	−	1.27398i
$627$	−11948.7	−	11948.7i	−0.761063	−	0.761063i
$628$	−9012.55			−0.572675
$629$	−3703.23	+	6876.53i	−0.234749	+	0.435906i
$630$	3978.03			0.251569
$631$	19184.5	+	19184.5i	1.21034	+	1.21034i	0.970916	+	0.239421i	$0.0769578\pi$
$631$	19184.5	+	19184.5i	1.21034	+	1.21034i	0.239421	+	0.970916i	$0.423042\pi$
$632$	1047.25	+	2528.27i	0.0659132	+	0.159129i
$633$		−	6641.23i		−	0.417007i
$634$	3837.51	−	1589.55i	0.240389	−	0.0995725i
$635$	−3390.35	+	8185.03i	−0.211877	+	0.511517i
$636$	7919.79	+	3280.49i	0.493774	+	0.204528i
$637$	1124.75	−	1124.75i	0.0699597	−	0.0699597i
$638$	−30181.9	+	30181.9i	−1.87290	+	1.87290i
$639$	−2081.43	−	862.155i	−0.128857	−	0.0533745i
$640$	−4991.49	+	12050.5i	−0.308291	+	0.744280i
$641$	−12843.5	+	5319.95i	−0.791400	+	0.327809i	−0.741506	−	0.670946i	$-0.765888\pi$
$641$	−12843.5	+	5319.95i	−0.791400	+	0.327809i	−0.0498939	+	0.998755i	$0.515888\pi$
$642$		−	2430.27i		−	0.149401i
$643$	−3378.07	−	8155.37i	−0.207182	−	0.500181i	0.785795	−	0.618487i	$-0.212254\pi$
$643$	−3378.07	−	8155.37i	−0.207182	−	0.500181i	−0.992977	+	0.118305i	$0.962254\pi$
$644$	−2399.35	−	2399.35i	−0.146813	−	0.146813i
$645$	−4086.71			−0.249479
$646$	18400.1	−	15004.7i	1.12065	−	0.913856i
$647$	−14695.4			−0.892946			−0.446473	−	0.894797i	$-0.647320\pi$
$647$	−14695.4			−0.892946			−0.446473	+	0.894797i	$0.647320\pi$
$648$	−1356.68	−	1356.68i	−0.0822463	−	0.0822463i
$649$	−20010.6	−	48309.8i	−1.21030	−	2.92192i
$650$		−	920.999i		−	0.0555762i
$651$	2470.60	−	1023.35i	0.148741	−	0.0616105i
$652$	−720.617	+	1739.72i	−0.0432846	+	0.104498i
$653$	6413.85	+	2656.70i	0.384370	+	0.159211i	0.566497	−	0.824064i	$-0.308298\pi$
$653$	6413.85	+	2656.70i	0.384370	+	0.159211i	−0.182127	+	0.983275i	$0.558298\pi$
$654$	−13937.6	+	13937.6i	−0.833337	+	0.833337i
$655$	6836.64	−	6836.64i	0.407831	−	0.407831i
$656$	−12295.6	−	5093.02i	−0.731805	−	0.303124i
$657$	4734.39	−	11429.8i	0.281136	−	0.678722i
$658$	2903.40	−	1202.63i	0.172016	−	0.0712512i
$659$			11804.8i			0.697800i	0.937160	+	0.348900i	$0.113445\pi$
$659$			11804.8i			0.697800i	−0.937160	+	0.348900i	$0.886555\pi$
$660$	−2474.69	−	5974.42i	−0.145950	−	0.352354i
$661$	2731.80	+	2731.80i	0.160748	+	0.160748i	0.782898	−	0.622150i	$-0.213741\pi$
$661$	2731.80	+	2731.80i	0.160748	+	0.160748i	−0.622150	+	0.782898i	$0.713741\pi$
$662$	10744.4			0.630806
$663$	936.963	+	504.584i	0.0548848	+	0.0295572i
$664$	−9748.88			−0.569774
$665$	−4090.68	−	4090.68i	−0.238541	−	0.238541i
$666$	2837.99	+	6851.50i	0.165120	+	0.398634i
$667$		−	22999.1i		−	1.33513i
$668$	−9232.40	+	3824.19i	−0.534749	+	0.221500i
$669$	−445.887	+	1076.47i	−0.0257683	+	0.0622102i
$670$	−8854.32	−	3667.58i	−0.510556	−	0.211479i
$671$	−218.125	+	218.125i	−0.0125494	+	0.0125494i
$672$	−2392.75	+	2392.75i	−0.137355	+	0.137355i
$673$	809.824	+	335.440i	0.0463840	+	0.0192129i	0.405755	−	0.913982i	$-0.367009\pi$
$673$	809.824	+	335.440i	0.0463840	+	0.0192129i	−0.359371	+	0.933195i	$0.617009\pi$
$674$	5943.00	−	14347.7i	0.339638	−	0.819958i
$675$	5882.66	−	2436.68i	0.335443	−	0.138945i
$676$			9210.10i			0.524016i
$677$	−7784.19	−	18792.7i	−0.441906	−	1.06686i	−0.975279	−	0.220976i	$-0.929076\pi$
$677$	−7784.19	−	18792.7i	−0.441906	−	1.06686i	0.533373	−	0.845880i	$-0.320924\pi$
$678$	7570.50	+	7570.50i	0.428825	+	0.428825i
$679$	−4837.51			−0.273412
$680$	−7686.87	+	2305.61i	−0.433497	+	0.130024i
$681$	5413.15			0.304600
$682$	21113.2	+	21113.2i	1.18544	+	1.18544i
$683$	11493.8	+	27748.5i	0.643922	+	1.55456i	0.821346	+	0.570430i	$0.193223\pi$
$683$	11493.8	+	27748.5i	0.643922	+	1.55456i	−0.177425	+	0.984134i	$0.556777\pi$
$684$		−	7818.90i		−	0.437080i
$685$	15912.0	−	6590.98i	0.887543	−	0.367633i
$686$	−5866.60	+	14163.2i	−0.326513	+	0.788272i
$687$	12695.4	+	5258.61i	0.705037	+	0.292036i
$688$	−9376.76	+	9376.76i	−0.519601	+	0.519601i
$689$	−2713.89	+	2713.89i	−0.150059	+	0.150059i
$690$	9281.74	+	3844.62i	0.512101	+	0.212119i
$691$	4132.11	−	9975.80i	0.227486	−	0.549200i	−0.768384	−	0.639989i	$-0.778939\pi$
$691$	4132.11	−	9975.80i	0.227486	−	0.549200i	0.995870	+	0.0907888i	$0.0289388\pi$
$692$	7457.82	−	3089.13i	0.409687	−	0.169698i
$693$		−	8055.48i		−	0.441562i
$694$	11670.8	+	28175.7i	0.638352	+	1.54112i
$695$	−6402.88	−	6402.88i	−0.349461	−	0.349461i
$696$	−7322.68			−0.398801
$697$	−3352.61	−	11177.6i	−0.182194	−	0.607432i
$698$	353.223			0.0191543
$699$	−1110.15	−	1110.15i	−0.0600713	−	0.0600713i
$700$	545.742	+	1317.54i	0.0294673	+	0.0711404i
$701$		−	328.897i		−	0.0177208i	−0.999961	−	0.00886039i	$-0.997180\pi$
$701$		−	328.897i		−	0.0177208i	0.999961	−	0.00886039i	$-0.00282039\pi$
$702$	2258.98	−	935.702i	0.121453	−	0.0503074i
$703$	4127.18	−	9963.88i	0.221422	−	0.534559i
$704$	1602.11	+	663.618i	0.0857698	+	0.0355270i
$705$	−2281.91	+	2281.91i	−0.121903	+	0.121903i
$706$	21502.1	−	21502.1i	1.14624	−	1.14624i
$707$	−3464.18	−	1434.91i	−0.184277	−	0.0763301i
$708$	−3886.69	+	9383.31i	−0.206315	+	0.498088i
$709$	4480.97	−	1856.08i	0.237357	−	0.0983167i	−0.260834	−	0.965384i	$-0.583998\pi$
$709$	4480.97	−	1856.08i	0.237357	−	0.0983167i	0.498192	+	0.867067i	$0.333998\pi$
$710$			3615.06i			0.191085i
$711$	1516.68	+	3661.59i	0.0800000	+	0.193137i
$712$	2001.18	+	2001.18i	0.105334	+	0.105334i
$713$	−16088.7			−0.845056
$714$	−4726.72	−	480.445i	−0.247750	−	0.0251824i
$715$	2895.27			0.151436
$716$	−299.565	−	299.565i	−0.0156359	−	0.0156359i
$717$	3465.95	+	8367.55i	0.180528	+	0.435832i
$718$		−	8439.60i		−	0.438667i
$719$	30379.9	−	12583.8i	1.57577	−	0.652705i	0.588034	−	0.808836i	$-0.299902\pi$
$719$	30379.9	−	12583.8i	1.57577	−	0.652705i	0.987736	+	0.156131i	$0.0499021\pi$
$720$	−5072.52	+	12246.2i	−0.262558	+	0.633871i
$721$	−9822.52	−	4068.62i	−0.507365	−	0.210157i
$722$	−6208.57	+	6208.57i	−0.320026	+	0.320026i
$723$	−1784.88	+	1784.88i	−0.0918123	+	0.0918123i
$724$	15222.8	+	6305.50i	0.781425	+	0.323677i
$725$	−3699.06	+	8930.31i	−0.189489	+	0.457467i
$726$	−22722.9	+	9412.14i	−1.16161	+	0.481153i
$727$			16213.2i			0.827116i	0.910478	+	0.413558i	$0.135714\pi$
$727$			16213.2i			0.827116i	−0.910478	+	0.413558i	$0.864286\pi$
$728$	−185.103	−	446.879i	−0.00942361	−	0.0227506i
$729$	5048.54	+	5048.54i	0.256492	+	0.256492i
$730$	−19851.5			−1.00649
$731$	−11567.9	−	1175.81i	−0.585298	−	0.0594922i
$732$	59.9158			0.00302534
$733$	17579.4	+	17579.4i	0.885826	+	0.885826i	0.994119	−	0.108293i	$-0.0345384\pi$
$733$	17579.4	+	17579.4i	0.885826	+	0.885826i	−0.108293	+	0.994119i	$0.534538\pi$
$734$	−3045.80	−	7353.20i	−0.153164	−	0.369771i
$735$		−	7292.34i		−	0.365962i
$736$	18808.8	−	7790.86i	0.941985	−	0.390183i
$737$	−7426.82	+	17929.9i	−0.371195	+	0.896143i
$738$	−10237.0	−	4240.30i	−0.510608	−	0.211501i
$739$	724.084	−	724.084i	0.0360431	−	0.0360431i	−0.688856	−	0.724899i	$-0.741887\pi$
$739$	724.084	−	724.084i	0.0360431	−	0.0360431i	0.724899	+	0.688856i	$0.241887\pi$
$740$	2918.38	−	2918.38i	0.144975	−	0.144975i
$741$	−1357.63	−	562.349i	−0.0673061	−	0.0278791i
$742$	6557.20	−	15830.5i	0.324424	−	0.783229i
$743$	6347.67	−	2629.29i	0.313423	−	0.129824i	−0.220426	−	0.975404i	$-0.570745\pi$
$743$	6347.67	−	2629.29i	0.313423	−	0.129824i	0.533849	+	0.845580i	$0.320745\pi$
$744$			5122.45i			0.252417i
$745$	398.948	+	963.146i	0.0196192	+	0.0473650i
$746$	−23494.3	−	23494.3i	−1.15307	−	1.15307i
$747$	−14118.9			−0.691544
$748$	−5285.93	−	17623.2i	−0.258386	−	0.861456i
$749$	−1684.81			−0.0821919
$750$	−10606.2	−	10606.2i	−0.516380	−	0.516380i
$751$	4656.89	+	11242.7i	0.226275	+	0.546275i	0.995718	−	0.0924395i	$-0.0294665\pi$
$751$	4656.89	+	11242.7i	0.226275	+	0.546275i	−0.769444	+	0.638715i	$0.779466\pi$
$752$			10471.5i			0.507786i
$753$	6346.72	−	2628.90i	0.307155	−	0.127228i
$754$	−1420.46	+	3429.31i	−0.0686078	+	0.165634i
$755$	12630.0	+	5231.51i	0.608811	+	0.252178i
$756$	−2677.14	+	2677.14i	−0.128792	+	0.128792i
$757$	−19971.1	+	19971.1i	−0.958866	+	0.958866i	−0.999187	−	0.0403208i	$-0.987162\pi$
$757$	−19971.1	+	19971.1i	−0.958866	+	0.958866i	0.0403208	+	0.999187i	$0.487162\pi$
$758$	17258.4	+	7148.67i	0.826984	+	0.342548i
$759$	7785.33	−	18795.4i	0.372318	−	0.898856i
$760$	10238.1	−	4240.74i	0.488649	−	0.202405i
$761$		−	30505.2i		−	1.45310i	−0.687112	−	0.726552i	$-0.741122\pi$
$761$		−	30505.2i		−	1.45310i	0.687112	−	0.726552i	$-0.258878\pi$
$762$	−3844.79	−	9282.15i	−0.182785	−	0.441282i
$763$	9662.39	+	9662.39i	0.458456	+	0.458456i
$764$	9884.58			0.468078
$765$	−11132.6	+	3339.11i	−0.526142	+	0.157812i
$766$	2727.76			0.128666
$767$	−3215.39	−	3215.39i	−0.151370	−	0.151370i
$768$	−5417.80	−	13079.7i	−0.254555	−	0.614550i
$769$			20404.5i			0.956834i	0.878133	+	0.478417i	$0.158789\pi$
$769$			20404.5i			0.956834i	−0.878133	+	0.478417i	$0.841211\pi$
$770$	−11942.0	+	4946.53i	−0.558908	+	0.231507i
$771$	3476.64	−	8393.34i	0.162397	−	0.392061i
$772$	−5480.65	−	2270.16i	−0.255509	−	0.105835i
$773$	21642.1	−	21642.1i	1.00700	−	1.00700i	0.00702854	−	0.999975i	$-0.497763\pi$
$773$	21642.1	−	21642.1i	1.00700	−	1.00700i	0.999975	−	0.00702854i	$-0.00223727\pi$
$774$	−7806.81	+	7806.81i	−0.362545	+	0.362545i
$775$	6247.05	+	2587.61i	0.289549	+	0.119935i
$776$	3546.12	−	8561.09i	0.164044	−	0.396038i
$777$	−1993.86	+	825.886i	−0.0920586	+	0.0381319i
$778$		−	37888.1i		−	1.74596i
$779$	6166.51	+	14887.3i	0.283618	+	0.684713i
$780$	−397.644	−	397.644i	−0.0182538	−	0.0182538i
$781$	7320.46			0.335399
$782$	25166.8	+	13553.1i	1.15085	+	0.619767i
$783$	−25662.0			−1.17124
$784$	−16731.9	−	16731.9i	−0.762205	−	0.762205i
$785$	−7079.30	−	17090.9i	−0.321874	−	0.777072i
$786$			10964.4i			0.497567i
$787$	−33344.2	+	13811.6i	−1.51028	+	0.625580i	−0.975617	−	0.219482i	$-0.929563\pi$
$787$	−33344.2	+	13811.6i	−1.51028	+	0.625580i	−0.534668	+	0.845062i	$0.679563\pi$
$788$	3289.98	−	7942.73i	0.148732	−	0.359071i
$789$	−6941.28	−	2875.17i	−0.313202	−	0.129732i
$790$	4496.86	−	4496.86i	0.202520	−	0.202520i
$791$	5248.34	−	5248.34i	0.235916	−	0.235916i
$792$	14256.0	+	5905.04i	0.639603	+	0.264932i
$793$	−10.2657	+	24.7836i	−0.000459705	+	0.00110983i
$794$	−19745.4	+	8178.81i	−0.882541	+	0.365560i
$795$			17595.5i			0.784966i
$796$	6735.50	+	16260.9i	0.299917	+	0.724063i
$797$	−15101.8	−	15101.8i	−0.671185	−	0.671185i	0.286804	−	0.957989i	$-0.407407\pi$
$797$	−15101.8	−	15101.8i	−0.671185	−	0.671185i	−0.957989	+	0.286804i	$0.907407\pi$
$798$	6560.53			0.291028
$799$	−7115.72	+	5802.65i	−0.315064	+	0.256925i
$800$	−8556.28			−0.378138
$801$	2898.23	+	2898.23i	0.127845	+	0.127845i
$802$	15336.9	+	37026.5i	0.675266	+	1.63024i
$803$			40199.2i			1.76662i
$804$	3482.57	−	1442.53i	0.152762	−	0.0632762i
$805$	2665.33	−	6434.67i	0.116696	−	0.281730i
$806$	2398.91	+	993.661i	0.104836	+	0.0434246i
$807$	11412.5	−	11412.5i	0.497820	−	0.497820i
$808$	5078.81	−	5078.81i	0.221129	−	0.221129i
$809$	−24176.9	−	10014.4i	−1.05070	−	0.435213i	−0.210556	−	0.977582i	$-0.567527\pi$
$809$	−24176.9	−	10014.4i	−1.05070	−	0.435213i	−0.840140	+	0.542369i	$0.817527\pi$
$810$	−1706.27	+	4119.31i	−0.0740153	+	0.178689i
$811$	−18503.7	+	7664.48i	−0.801174	+	0.331857i	−0.745427	−	0.666588i	$-0.767754\pi$
$811$	−18503.7	+	7664.48i	−0.801174	+	0.331857i	−0.0557475	+	0.998445i	$0.517754\pi$
$812$		−	5747.51i		−	0.248397i
$813$	−271.265	−	654.892i	−0.0117019	−	0.0282510i
$814$	−17039.2	−	17039.2i	−0.733689	−	0.733689i
$815$	−3865.16			−0.166124
$816$	7506.23	−	13938.3i	0.322023	−	0.597965i
$817$	16055.8			0.687541
$818$	−18800.3	−	18800.3i	−0.803591	−	0.803591i
$819$	−268.077	−	647.196i	−0.0114376	−	0.0276128i
$820$			6166.56i			0.262617i
$821$	1997.50	−	827.392i	0.0849126	−	0.0351719i	−0.339823	−	0.940489i	$-0.610367\pi$
$821$	1997.50	−	827.392i	0.0849126	−	0.0351719i	0.424735	+	0.905318i	$0.360367\pi$
$822$	−7474.42	+	18044.9i	−0.317154	+	0.765677i
$823$	36378.3	+	15068.4i	1.54079	+	0.638214i	0.981621	−	0.190842i	$-0.0611218\pi$
$823$	36378.3	+	15068.4i	1.54079	+	0.638214i	0.559165	+	0.829056i	$0.311122\pi$
$824$	14400.7	−	14400.7i	0.608826	−	0.608826i
$825$	−6045.91	+	6045.91i	−0.255141	+	0.255141i
$826$	18755.8	+	7768.92i	0.790072	+	0.327258i
$827$	−8644.75	+	20870.3i	−0.363492	+	0.877546i	0.631293	+	0.775545i	$0.282525\pi$
$827$	−8644.75	+	20870.3i	−0.363492	+	0.877546i	−0.994784	+	0.102002i	$0.967475\pi$
$828$	8696.83	−	3602.35i	0.365019	−	0.151196i
$829$			10977.3i			0.459898i	0.973203	+	0.229949i	$0.0738560\pi$
$829$			10977.3i			0.459898i	−0.973203	+	0.229949i	$0.926144\pi$
$830$	8669.81	+	20930.8i	0.362571	+	0.875323i
$831$	7368.63	+	7368.63i	0.307599	+	0.307599i
$832$	150.802			0.00628380
$833$	2098.12	−	20641.7i	0.0872694	−	0.858576i
$834$	10268.8			0.426353
$835$	−14504.0	−	14504.0i	−0.601115	−	0.601115i
$836$	9722.50	+	23472.2i	0.402225	+	0.971056i
$837$			17951.4i			0.741327i
$838$	22269.6	−	9224.36i	0.918006	−	0.380251i
$839$	17065.4	−	41199.4i	0.702219	−	1.69531i	−0.0163657	−	0.999866i	$-0.505210\pi$
$839$	17065.4	−	41199.4i	0.702219	−	1.69531i	0.718584	−	0.695440i	$-0.244790\pi$
$840$	−2048.73	−	848.612i	−0.0841523	−	0.0348570i
$841$	10301.0	−	10301.0i	0.422362	−	0.422362i
$842$	33622.5	−	33622.5i	1.37614	−	1.37614i
$843$	9219.67	+	3818.91i	0.376681	+	0.156026i
$844$	−3821.11	+	9224.97i	−0.155839	+	0.376228i
$845$	−17465.6	+	7234.47i	−0.711045	+	0.294525i
$846$			8718.23i			0.354301i
$847$	6525.07	+	15752.9i	0.264704	+	0.639052i
$848$	40372.0	+	40372.0i	1.63488	+	1.63488i
$849$	2227.03			0.0900254
$850$	−7592.18	−	9310.21i	−0.306364	−	0.375691i
$851$	12984.1			0.523021
$852$	−1005.41	−	1005.41i	−0.0404283	−	0.0404283i
$853$	−14188.3	−	34253.7i	−0.569519	−	1.37494i	−0.901961	−	0.431817i	$-0.857873\pi$
$853$	−14188.3	−	34253.7i	−0.569519	−	1.37494i	0.332443	−	0.943123i	$-0.392127\pi$
$854$		−	119.763i		−	0.00479883i
$855$	14827.4	−	6141.69i	0.593082	−	0.245662i
$856$	1235.05	−	2981.67i	0.0493143	−	0.119055i
$857$	−42102.6	−	17439.5i	−1.67818	−	0.695123i	−0.678940	−	0.734194i	$-0.737560\pi$
$857$	−42102.6	−	17439.5i	−1.67818	−	0.695123i	−0.999236	+	0.0390702i	$0.987560\pi$
$858$	−2321.68	+	2321.68i	−0.0923784	+	0.0923784i
$859$	−48.4609	+	48.4609i	−0.00192487	+	0.00192487i	−0.708069	−	0.706144i	$-0.750433\pi$
$859$	−48.4609	+	48.4609i	−0.00192487	+	0.00192487i	0.706144	+	0.708069i	$0.250433\pi$
$860$	5676.62	+	2351.33i	0.225083	+	0.0932324i
$861$	1233.98	−	2979.08i	0.0488429	−	0.117917i
$862$	−54366.3	+	22519.3i	−2.14817	+	0.889802i
$863$			5064.23i			0.199755i	0.995000	+	0.0998774i	$0.0318451\pi$
$863$			5064.23i			0.199755i	−0.995000	+	0.0998774i	$0.968155\pi$
$864$	−8692.88	−	20986.5i	−0.342289	−	0.826359i
$865$	11716.1	+	11716.1i	0.460532	+	0.460532i
$866$	−870.810			−0.0341701
$867$	13631.1	−	2623.03i	0.533951	−	0.102748i
$868$	−4020.57			−0.157220
$869$	−9106.10	−	9106.10i	−0.355470	−	0.355470i
$870$	6512.16	+	15721.7i	0.253773	+	0.612663i
$871$			1687.69i			0.0656546i
$872$	−24182.8	+	10016.8i	−0.939143	+	0.389006i
$873$	5135.70	−	12398.7i	0.199103	−	0.480677i
$874$	−36465.9	−	15104.7i	−1.41130	−	0.584581i
$875$	−7352.90	+	7352.90i	−0.284084	+	0.284084i
$876$	5521.08	−	5521.08i	0.212945	−	0.212945i
$877$	−3535.56	−	1464.48i	−0.136131	−	0.0563875i	0.313578	−	0.949563i	$-0.398472\pi$
$877$	−3535.56	−	1464.48i	−0.136131	−	0.0563875i	−0.449709	+	0.893175i	$0.648472\pi$
$878$	−13218.8	+	31912.9i	−0.508100	+	1.22666i
$879$	−3690.53	+	1528.67i	−0.141614	+	0.0586583i
$880$		−	43070.2i		−	1.64988i
$881$	15695.8	+	37893.0i	0.600232	+	1.44909i	0.873343	+	0.487105i	$0.161947\pi$
$881$	15695.8	+	37893.0i	0.600232	+	1.44909i	−0.273112	+	0.961982i	$0.588053\pi$
$882$	−13930.5	−	13930.5i	−0.531819	−	0.531819i
$883$	−7085.32			−0.270034			−0.135017	−	0.990843i	$-0.543109\pi$
$883$	−7085.32			−0.270034			−0.135017	+	0.990843i	$0.543109\pi$
$884$	−1011.17	−	1239.98i	−0.0384719	−	0.0471777i
$885$	−20847.0			−0.791824
$886$	−24747.5	−	24747.5i	−0.938383	−	0.938383i
$887$	−6602.86	−	15940.7i	−0.249946	−	0.603424i	0.748253	−	0.663414i	$-0.230893\pi$
$887$	−6602.86	−	15940.7i	−0.249946	−	0.603424i	−0.998199	+	0.0599902i	$0.980893\pi$
$888$		−	4134.01i		−	0.156226i
$889$	−6434.95	+	2665.45i	−0.242769	+	0.100558i
$890$	2516.85	−	6076.21i	0.0947921	−	0.228848i
$891$	8341.57	+	3455.19i	0.313640	+	0.129914i
$892$	1238.72	−	1238.72i	0.0464969	−	0.0464969i
$893$	8965.12	−	8965.12i	0.335953	−	0.335953i
$894$	−1092.25	−	452.423i	−0.0408615	−	0.0169254i
$895$	332.774	−	803.387i	0.0124284	−	0.0300048i
$896$	−9473.95	+	3924.24i	−0.353239	+	0.146317i
$897$		−	1769.16i		−	0.0658534i
$898$	−11491.5	−	27743.0i	−0.427035	−	1.03095i
$899$	−19269.8	−	19269.8i	−0.714886	−	0.714886i
$900$	−3956.26			−0.146528
$901$	−5062.49	+	49805.9i	−0.187188	+	1.84159i
$902$	36003.9			1.32905
$903$	−2271.87	−	2271.87i	−0.0837244	−	0.0837244i
$904$	5440.87	+	13135.4i	0.200178	+	0.483271i
$905$			33820.7i			1.24225i
$906$	−14322.9	+	5932.74i	−0.525217	+	0.217552i
$907$	6929.04	−	16728.2i	0.253666	−	0.612404i	−0.744828	−	0.667256i	$-0.767469\pi$
$907$	6929.04	−	16728.2i	0.253666	−	0.612404i	0.998494	+	0.0548519i	$0.0174687\pi$
$908$	−7519.12	−	3114.52i	−0.274813	−	0.113831i
$909$	7355.43	−	7355.43i	0.268387	−	0.268387i
$910$	−794.832	+	794.832i	−0.0289543	+	0.0289543i
$911$	−17702.1	−	7332.47i	−0.643796	−	0.266669i	0.0368060	−	0.999322i	$-0.488282\pi$
$911$	−17702.1	−	7332.47i	−0.643796	−	0.266669i	−0.680602	+	0.732653i	$0.738282\pi$
$912$	−8365.56	+	20196.2i	−0.303740	+	0.733294i
$913$	42384.7	−	17556.3i	1.53639	−	0.636395i
$914$			29208.1i			1.05702i
$915$	47.0635	+	113.621i	0.00170040	+	0.00410514i
$916$	−14608.9	−	14608.9i	−0.526956	−	0.526956i
$917$	7601.21			0.273734
$918$	15122.3	−	28080.6i	0.543693	−	1.00958i
$919$	−13214.6			−0.474329			−0.237165	−	0.971469i	$-0.576218\pi$
$919$	−13214.6			−0.474329			−0.237165	+	0.971469i	$0.576218\pi$
$920$	9433.82	+	9433.82i	0.338069	+	0.338069i
$921$	−4865.09	−	11745.4i	−0.174061	−	0.420220i
$922$			30100.5i			1.07517i
$923$	588.143	−	243.617i	0.0209740	−	0.00868770i
$924$	1945.56	−	4697.00i	0.0692687	−	0.167229i
$925$	−5041.60	−	2088.30i	−0.179207	−	0.0742301i
$926$	39318.7	−	39318.7i	1.39535	−	1.39535i
$927$	20856.0	−	20856.0i	0.738942	−	0.738942i
$928$	31859.0	+	13196.4i	1.12696	+	0.466804i
$929$	−3109.06	+	7505.93i	−0.109801	+	0.265082i	−0.969223	−	0.246184i	$-0.920823\pi$
$929$	−3109.06	+	7505.93i	−0.109801	+	0.265082i	0.859422	+	0.511266i	$0.170823\pi$
$930$	10997.9	−	4555.47i	0.387779	−	0.160623i
$931$			28650.0i			1.00856i
$932$	903.313	+	2180.79i	0.0317479	+	0.0766461i
$933$	9423.46	+	9423.46i	0.330665	+	0.330665i
$934$	−20794.2			−0.728489
$935$	29267.7	−	23866.9i	1.02370	−	0.834792i
$936$	1341.88			0.0468596
$937$	8214.97	+	8214.97i	0.286415	+	0.286415i	0.835661	−	0.549246i	$-0.185085\pi$
$937$	8214.97	+	8214.97i	0.286415	+	0.286415i	−0.549246	+	0.835661i	$0.685085\pi$
$938$	−2883.40	−	6961.14i	−0.100369	−	0.242313i
$939$			17436.4i			0.605980i
$940$	4482.60	−	1856.75i	0.155539	−	0.0644262i
$941$	4902.44	−	11835.5i	0.169835	−	0.410019i	−0.815929	−	0.578152i	$-0.803774\pi$
$941$	4902.44	−	11835.5i	0.169835	−	0.410019i	0.985764	+	0.168133i	$0.0537740\pi$
$942$	19381.8	+	8028.20i	0.670375	+	0.277678i
$943$	−13717.8	+	13717.8i	−0.473715	+	0.473715i
$944$	−47832.4	+	47832.4i	−1.64917	+	1.64917i
$945$	−7179.68	−	2973.92i	−0.247148	−	0.102372i
$946$	13728.4	−	33143.4i	0.471829	−	1.13910i
$947$	19835.0	−	8215.93i	0.680624	−	0.281924i	−0.0154635	−	0.999880i	$-0.504922\pi$
$947$	19835.0	−	8215.93i	0.680624	−	0.281924i	0.696088	+	0.717957i	$0.254922\pi$
$948$			2501.31i			0.0856951i
$949$	1337.79	+	3229.70i	0.0457601	+	0.110475i
$950$	11730.0	+	11730.0i	0.400600	+	0.400600i
$951$	−3353.37			−0.114343
$952$	−5554.99	−	2991.54i	−0.189116	−	0.101845i
$953$	15897.5			0.540369			0.270184	−	0.962809i	$-0.412915\pi$
$953$	15897.5			0.540369			0.270184	+	0.962809i	$0.412915\pi$
$954$	33612.6	+	33612.6i	1.14072	+	1.14072i
$955$	7764.27	+	18744.6i	0.263085	+	0.635142i
$956$		−	13617.1i		−	0.460678i
$957$	31836.4	−	13187.1i	1.07537	−	0.445431i
$958$	−19975.5	+	48225.2i	−0.673674	+	1.62639i
$959$	12509.8	+	5181.73i	0.421233	+	0.174480i
$960$	488.863	−	488.863i	0.0164354	−	0.0164354i
$961$	7585.60	−	7585.60i	0.254627	−	0.254627i
$962$	−1936.01	−	801.922i	−0.0648852	−	0.0268763i
$963$	1788.67	−	4318.22i	0.0598535	−	0.144499i
$964$	3506.22	−	1452.33i	0.117145	−	0.0485231i
$965$		−	12176.4i		−	0.406189i
$966$	3022.59	+	7297.17i	0.100673	+	0.243046i
$967$	−23469.7	−	23469.7i	−0.780492	−	0.780492i	0.199421	−	0.979914i	$-0.436094\pi$
$967$	−23469.7	−	23469.7i	−0.780492	−	0.780492i	−0.979914	+	0.199421i	$0.936094\pi$
$968$	−32661.6			−1.08449
$969$	−18359.7	+	5506.83i	−0.608668	+	0.182564i
$970$	−21534.2			−0.712806
$971$	−22510.4	−	22510.4i	−0.743968	−	0.743968i	0.229371	−	0.973339i	$-0.426333\pi$
$971$	−22510.4	−	22510.4i	−0.743968	−	0.743968i	−0.973339	+	0.229371i	$0.926333\pi$
$972$	−6377.77	−	15397.3i	−0.210460	−	0.508096i
$973$		−	7118.94i		−	0.234556i
$974$	−26587.0	+	11012.7i	−0.874644	+	0.362289i
$975$	−284.542	+	686.944i	−0.00934628	+	0.0225639i
$976$	368.683	+	152.714i	0.0120915	+	0.00500845i
$977$	−10216.1	+	10216.1i	−0.334536	+	0.334536i	−0.854306	−	0.519770i	$-0.826018\pi$
$977$	−10216.1	+	10216.1i	−0.334536	+	0.334536i	0.519770	+	0.854306i	$0.326018\pi$
$978$	3099.42	−	3099.42i	0.101338	−	0.101338i
$979$	−12304.3	−	5096.60i	−0.401682	−	0.166382i
$980$	−4195.73	+	10129.4i	−0.136763	+	0.330175i
$981$	−35022.9	+	14507.0i	−1.13985	+	0.472143i
$982$		−	9223.90i		−	0.299742i
$983$	2996.76	+	7234.81i	0.0972347	+	0.234745i	0.965011	−	0.262210i	$-0.0844513\pi$
$983$	2996.76	+	7234.81i	0.0972347	+	0.234745i	−0.867776	+	0.496955i	$0.834451\pi$
$984$	4367.61	+	4367.61i	0.141498	+	0.141498i
$985$	17646.4			0.570824
$986$	13910.0	+	46375.7i	0.449274	+	1.49787i
$987$	−2537.10			−0.0818206
$988$	1562.26	+	1562.26i	0.0503057	+	0.0503057i
$989$	7397.27	+	17858.6i	0.237836	+	0.574186i
$990$		−	35859.0i		−	1.15119i
$991$	13532.7	−	5605.45i	0.433786	−	0.179680i	−0.155095	−	0.987899i	$-0.549569\pi$
$991$	13532.7	−	5605.45i	0.433786	−	0.179680i	0.588881	+	0.808219i	$0.299569\pi$
$992$	9231.34	−	22286.4i	0.295459	−	0.713301i
$993$	−8013.93	−	3319.48i	−0.256107	−	0.106083i
$994$	−2009.67	+	2009.67i	−0.0641277	+	0.0641277i
$995$	−25545.7	+	25545.7i	−0.813923	+	0.813923i
$996$	−8232.47	−	3410.00i	−0.261903	−	0.108484i
$997$	18818.3	−	45431.4i	0.597775	−	1.44316i	−0.278068	−	0.960561i	$-0.589694\pi$
$997$	18818.3	−	45431.4i	0.597775	−	1.44316i	0.875843	−	0.482596i	$-0.160306\pi$
$998$	41269.8	−	17094.5i	1.30899	−	0.542201i
$999$		−	14487.5i		−	0.458822i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.4.d.a.15.3	yes	12
3.2	odd	2		153.4.l.a.100.1		12
17.3	odd	16		289.4.b.e.288.9		12
17.5	odd	16		289.4.a.g.1.4		12
17.8	even	8	inner	17.4.d.a.8.3	✓	12
17.12	odd	16		289.4.a.g.1.3		12
17.14	odd	16		289.4.b.e.288.10		12
51.8	odd	8		153.4.l.a.127.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.d.a.8.3	✓	12	17.8	even	8	inner
17.4.d.a.15.3	yes	12	1.1	even	1	trivial
153.4.l.a.100.1		12	3.2	odd	2
153.4.l.a.127.1		12	51.8	odd	8
289.4.a.g.1.3		12	17.12	odd	16
289.4.a.g.1.4		12	17.5	odd	16
289.4.b.e.288.9		12	17.3	odd	16
289.4.b.e.288.10		12	17.14	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)

\(f(q)\)	\(=\)	\(q+(2.47467 + 2.47467i) q^{2} +(-1.08123 - 2.61032i) q^{3} +4.24796i q^{4} +(-8.05561 + 3.33674i) q^{5} +(3.78400 - 9.13537i) q^{6} +(-6.33320 - 2.62330i) q^{7} +(9.28506 - 9.28506i) q^{8} +(13.4472 - 13.4472i) q^{9} +O(q^{10})\)	\(q+(2.47467 + 2.47467i) q^{2} +(-1.08123 - 2.61032i) q^{3} +4.24796i q^{4} +(-8.05561 + 3.33674i) q^{5} +(3.78400 - 9.13537i) q^{6} +(-6.33320 - 2.62330i) q^{7} +(9.28506 - 9.28506i) q^{8} +(13.4472 - 13.4472i) q^{9} +(-28.1923 - 11.6776i) q^{10} +(-23.6471 + 57.0891i) q^{11} +(11.0885 - 4.59303i) q^{12} +5.37363i q^{13} +(-9.18078 - 22.1644i) q^{14} +(17.4200 + 17.4200i) q^{15} +79.9385 q^{16} +(44.2970 + 54.3210i) q^{17} +66.5545 q^{18} +(-68.4392 - 68.4392i) q^{19} +(-14.1743 - 34.2199i) q^{20} +19.3681i q^{21} +(-199.795 + 82.7579i) q^{22} +(44.5923 - 107.655i) q^{23} +(-34.2763 - 14.1977i) q^{24} +(-34.6294 + 34.6294i) q^{25} +(-13.2979 + 13.2979i) q^{26} +(-120.120 - 49.7552i) q^{27} +(11.1437 - 26.9032i) q^{28} +(182.351 - 75.5321i) q^{29} +86.2172i q^{30} +(-52.8371 - 127.560i) q^{31} +(123.541 + 123.541i) q^{32} +174.589 q^{33} +(-24.8060 + 244.047i) q^{34} +59.7710 q^{35} +(57.1229 + 57.1229i) q^{36} +(42.6416 + 102.946i) q^{37} -338.729i q^{38} +(14.0269 - 5.81013i) q^{39} +(-43.8149 + 105.779i) q^{40} +(-153.814 - 63.7117i) q^{41} +(-47.9296 + 47.9296i) q^{42} +(-117.300 + 117.300i) q^{43} +(-242.512 - 100.452i) q^{44} +(-63.4553 + 153.195i) q^{45} +(376.762 - 156.060i) q^{46} +130.994i q^{47} +(-86.4320 - 208.665i) q^{48} +(-209.310 - 209.310i) q^{49} -171.392 q^{50} +(93.9001 - 174.363i) q^{51} -22.8269 q^{52} +(505.038 + 505.038i) q^{53} +(-174.129 - 420.384i) q^{54} -538.792i q^{55} +(-83.1616 + 34.4467i) q^{56} +(-104.650 + 252.647i) q^{57} +(638.174 + 264.340i) q^{58} +(-598.365 + 598.365i) q^{59} +(-73.9992 + 73.9992i) q^{60} +(4.61209 + 1.91039i) q^{61} +(184.915 - 446.423i) q^{62} +(-120.439 + 49.8876i) q^{63} -28.0634i q^{64} +(-17.9304 - 43.2878i) q^{65} +(432.050 + 432.050i) q^{66} +314.069 q^{67} +(-230.753 + 188.172i) q^{68} -329.230 q^{69} +(147.913 + 147.913i) q^{70} +(-45.3357 - 109.450i) q^{71} -249.715i q^{72} +(601.028 - 248.954i) q^{73} +(-149.233 + 360.280i) q^{74} +(127.836 + 52.9515i) q^{75} +(290.727 - 290.727i) q^{76} +(299.524 - 299.524i) q^{77} +(49.0901 + 20.3338i) q^{78} +(-79.7533 + 192.542i) q^{79} +(-643.953 + 266.734i) q^{80} -146.115i q^{81} +(-222.972 - 538.303i) q^{82} +(-524.977 - 524.977i) q^{83} -82.2749 q^{84} +(-538.095 - 289.781i) q^{85} -580.555 q^{86} +(-394.326 - 394.326i) q^{87} +(310.511 + 749.640i) q^{88} +215.527i q^{89} +(-536.137 + 222.075i) q^{90} +(14.0966 - 34.0323i) q^{91} +(457.315 + 189.426i) q^{92} +(-275.844 + 275.844i) q^{93} +(-324.167 + 324.167i) q^{94} +(779.683 + 322.955i) q^{95} +(188.905 - 456.058i) q^{96} +(651.973 - 270.056i) q^{97} -1035.94i q^{98} +(449.700 + 1085.67i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more