LMFDB - Embedded newform 17.4.d.a.8.3

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			8.3
Root			$2.49971i$ of defining polynomial
Character	$\chi$	$=$	17.8
Dual form			17.4.d.a.15.3

$q$-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 $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{8}\right)$

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	−0.118077	−	0.993004i	$-0.537673\pi$
$2$	2.47467	−	2.47467i	0.874927	−	0.874927i	0.993004	+	0.118077i	$0.0376731\pi$
$3$	−1.08123	+	2.61032i	−0.208083	+	0.502357i	−0.993121	−	0.117090i	$-0.962643\pi$
$3$	−1.08123	+	2.61032i	−0.208083	+	0.502357i	0.785038	+	0.619447i	$0.212643\pi$
$4$		−	4.24796i		−	0.530995i
$5$	−8.05561	−	3.33674i	−0.720515	−	0.298447i	−0.00786742	−	0.999969i	$-0.502504\pi$
$5$	−8.05561	−	3.33674i	−0.720515	−	0.298447i	−0.712648	+	0.701522i	$0.752504\pi$
$6$	3.78400	+	9.13537i	0.257468	+	0.621583i
$7$	−6.33320	+	2.62330i	−0.341961	+	0.141645i	−0.547053	−	0.837098i	$-0.684250\pi$
$7$	−6.33320	+	2.62330i	−0.341961	+	0.141645i	0.205093	+	0.978743i	$0.434250\pi$
$8$	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	−0.815397	−	0.578902i	$-0.803481\pi$
$11$	−23.6471	−	57.0891i	−0.648170	−	1.56482i	0.167227	−	0.985918i	$-0.446519\pi$
$12$	11.0885	+	4.59303i	0.266749	+	0.110491i
$13$		−	5.37363i		−	0.114644i	−0.998356	−	0.0573221i	$-0.981744\pi$
$13$		−	5.37363i		−	0.114644i	0.998356	−	0.0573221i	$-0.0182562\pi$
$14$	−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	−0.987013	−	0.160643i	$-0.948643\pi$
$19$	−68.4392	+	68.4392i	−0.826370	+	0.826370i	0.160643	+	0.987013i	$0.448643\pi$
$20$	−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	0.986618	+	0.163049i	$0.0521328\pi$
$23$	44.5923	+	107.655i	0.404267	+	0.975986i	−0.582351	+	0.812937i	$0.697867\pi$
$24$	−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	0.880413	−	0.474208i	$-0.157266\pi$
$29$	182.351	+	75.5321i	1.16764	+	0.483653i	0.287230	+	0.957862i	$0.407266\pi$
$30$		−	86.2172i		−	0.524701i
$31$	−52.8371	+	127.560i	−0.306123	+	0.739047i	0.693700	+	0.720264i	$0.255979\pi$
$31$	−52.8371	+	127.560i	−0.306123	+	0.739047i	−0.999824	+	0.0187835i	$0.994021\pi$
$32$	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	−0.800391	−	0.599478i	$-0.795375\pi$
$37$	42.6416	−	102.946i	0.189466	−	0.457411i	0.989857	+	0.142067i	$0.0453749\pi$
$38$			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	−0.655883	−	0.754862i	$-0.727704\pi$
$41$	−153.814	+	63.7117i	−0.585894	+	0.242685i	0.0699888	+	0.997548i	$0.477704\pi$
$42$	−47.9296	−	47.9296i	−0.176088	−	0.176088i
$43$	−117.300	−	117.300i	−0.416000	−	0.416000i	0.467822	−	0.883823i	$-0.345039\pi$
$43$	−117.300	−	117.300i	−0.416000	−	0.416000i	−0.883823	+	0.467822i	$0.845039\pi$
$44$	−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	$-0.934843\pi$
$47$		−	130.994i		−	0.406541i	0.979123	−	0.203271i	$-0.0651571\pi$
$48$	−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	0.386711	−	0.922201i	$-0.373611\pi$
$53$	505.038	−	505.038i	1.30891	−	1.30891i	0.922201	−	0.386711i	$-0.126389\pi$
$54$	−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	−0.913493	−	0.406855i	$-0.866625\pi$
$59$	−598.365	−	598.365i	−1.32035	−	1.32035i	−0.406855	−	0.913493i	$-0.633375\pi$
$60$	−73.9992	−	73.9992i	−0.159221	−	0.159221i
$61$	4.61209	−	1.91039i	0.00968061	−	0.00400984i	−0.377838	−	0.925872i	$-0.623332\pi$
$61$	4.61209	−	1.91039i	0.00968061	−	0.00400984i	0.387518	+	0.921862i	$0.373332\pi$
$62$	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	−0.957230	−	0.289329i	$-0.906568\pi$
$71$	−45.3357	+	109.450i	−0.0757796	+	0.182948i	0.881450	+	0.472277i	$0.156568\pi$
$72$			249.715i			0.408739i
$73$	601.028	+	248.954i	0.963630	+	0.399149i	0.808337	−	0.588720i	$-0.200368\pi$
$73$	601.028	+	248.954i	0.963630	+	0.399149i	0.155293	+	0.987868i	$0.450368\pi$
$74$	−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	0.856859	−	0.515551i	$-0.172413\pi$
$79$	−79.7533	−	192.542i	−0.113582	−	0.274210i	−0.970440	+	0.241341i	$0.922413\pi$
$80$	−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	−0.963167	−	0.268905i	$-0.913338\pi$
$83$	−524.977	+	524.977i	−0.694262	+	0.694262i	0.268905	+	0.963167i	$0.413338\pi$
$84$	−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	$-0.959033\pi$
$89$		−	215.527i		−	0.256695i	0.991729	−	0.128348i	$-0.0409673\pi$
$90$	−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	0.696851	−	0.717216i	$-0.254584\pi$
$97$	651.973	+	270.056i	0.682452	+	0.282681i	−0.0143996	+	0.999896i	$0.504584\pi$
$98$			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	0.482895	−	0.875678i	$-0.339585\pi$
$107$	227.070	+	94.0554i	0.205156	+	0.0849783i	−0.277739	+	0.960656i	$0.589585\pi$
$108$	211.358	+	510.263i	0.188314	+	0.454631i
$109$	−1841.65	+	762.836i	−1.61833	+	0.670334i	−0.993853	−	0.110708i	$-0.964688\pi$
$109$	−1841.65	+	762.836i	−1.61833	+	0.670334i	−0.624477	+	0.781043i	$0.714688\pi$
$110$	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	−0.997201	−	0.0747730i	$-0.976177\pi$
$113$	−414.351	−	1000.33i	−0.344946	−	0.832773i	0.652255	−	0.758000i	$-0.273823\pi$
$114$	−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	0.912058	−	0.410061i	$-0.134492\pi$
$127$	718.468	+	718.468i	0.501998	+	0.501998i	−0.410061	+	0.912058i	$0.634492\pi$
$128$	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	0.0139317	−	0.999903i	$-0.495565\pi$
$131$	−1024.45	−	424.340i	−0.683255	−	0.283014i	−0.697187	+	0.716889i	$0.745565\pi$
$132$		−	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	−0.755023	−	0.655698i	$-0.772374\pi$
$139$	397.418	−	959.451i	0.242507	−	0.585465i	0.997531	+	0.0702334i	$0.0223744\pi$
$140$		−	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	$0.0104644\pi$
$149$			119.562i			0.0657377i	−0.999460	+	0.0328689i	$0.989536\pi$
$150$	185.315	−	447.390i	0.100873	−	0.243528i
$151$	−1108.64	+	1108.64i	−0.597481	+	0.597481i	−0.939642	−	0.342160i	$-0.888841\pi$
$151$	−1108.64	+	1108.64i	−0.597481	+	0.597481i	0.342160	+	0.939642i	$0.388841\pi$
$152$	−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	$-0.818709\pi$
$157$		−	2121.62i		−	1.07850i	0.842147	−	0.539248i	$-0.181291\pi$
$158$	−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	−0.282108	−	0.959383i	$-0.591034\pi$
$163$	409.544	−	169.639i	0.196797	−	0.0815160i	0.478905	+	0.877867i	$0.341034\pi$
$164$	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	−0.566029	−	0.824385i	$-0.691521\pi$
$167$	900.241	−	2173.37i	0.417142	−	1.00707i	0.983171	−	0.182685i	$-0.0584790\pi$
$168$	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	0.679691	+	0.733499i	$0.262114\pi$
$173$	−727.203	+	1755.62i	−0.319585	+	0.771547i	−0.999276	+	0.0380481i	$0.987886\pi$
$174$			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	0.692230	−	0.721677i	$-0.256628\pi$
$179$	−70.5199	−	70.5199i	−0.0294464	−	0.0294464i	−0.721677	+	0.692230i	$0.756628\pi$
$180$	−650.764	+	269.555i	−0.269473	+	0.111619i
$181$	1484.36	+	3583.56i	0.609567	+	1.47162i	0.863473	+	0.504395i	$0.168285\pi$
$181$	1484.36	+	3583.56i	0.609567	+	1.47162i	−0.253906	+	0.967229i	$0.581715\pi$
$182$	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	$0.145289\pi$
$191$			2326.90i			0.881511i	−0.897627	+	0.440756i	$0.854711\pi$
$192$	−73.2545	−	30.3430i	−0.0275348	−	0.0114053i
$193$	−534.412	−	1290.18i	−0.199315	−	0.481189i	0.792345	−	0.610074i	$-0.208860\pi$
$193$	−534.412	−	1290.18i	−0.199315	−	0.481189i	−0.991660	+	0.128885i	$0.958860\pi$
$194$	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	−0.694247	−	0.719737i	$-0.744262\pi$
$197$	−1869.77	+	774.486i	−0.676223	+	0.280101i	0.0180240	+	0.999838i	$0.494262\pi$
$198$	−1573.82	−	3799.54i	−0.564881	−	1.36374i
$199$	3827.94	+	1585.59i	1.36360	+	0.564820i	0.940045	−	0.341052i	$-0.110783\pi$
$199$	3827.94	+	1585.59i	1.36360	+	0.564820i	0.423552	+	0.905872i	$0.360783\pi$
$200$		−	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	0.000836499	−	1.00000i	$-0.499734\pi$
$211$	2171.62	−	899.516i	0.708535	−	0.293485i	0.707698	+	0.706515i	$0.249734\pi$
$212$	−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	−0.749533	−	0.661967i	$-0.769722\pi$
$223$	−291.603	+	291.603i	−0.0875657	+	0.0875657i	0.661967	+	0.749533i	$0.269722\pi$
$224$	−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	0.779712	−	0.626138i	$-0.215365\pi$
$227$	−733.181	−	1770.05i	−0.214374	−	0.517545i	−0.994086	+	0.108593i	$0.965365\pi$
$228$	−1073.23	+	444.548i	−0.311740	+	0.129127i
$229$	−3439.04	−	3439.04i	−0.992394	−	0.992394i	0.00757695	−	0.999971i	$-0.497588\pi$
$229$	−3439.04	−	3439.04i	−0.992394	−	0.992394i	−0.999971	+	0.00757695i	$0.997588\pi$
$230$	−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	0.453686	−	0.891162i	$-0.350109\pi$
$233$	513.374	+	212.646i	0.144344	+	0.0597894i	−0.309342	+	0.950951i	$0.600109\pi$
$234$		−	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	−0.962962	−	0.269639i	$-0.913096\pi$
$241$	−341.888	+	825.391i	−0.0913815	+	0.220614i	0.871580	+	0.490253i	$0.163096\pi$
$242$			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	$-0.901105\pi$
$251$		−	2431.39i		−	0.611427i	0.952124	−	0.305713i	$-0.0988949\pi$
$252$	−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	−0.375120	−	0.926976i	$-0.622399\pi$
$257$	2273.66	−	2273.66i	0.551856	−	0.551856i	0.926976	+	0.375120i	$0.122399\pi$
$258$	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	0.892300	−	0.451444i	$-0.149091\pi$
$263$	1880.31	+	1880.31i	0.440856	+	0.440856i	−0.451444	+	0.892300i	$0.649091\pi$
$264$	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	−0.456408	−	0.889771i	$-0.650864\pi$
$269$	2186.04	−	5277.57i	0.495484	−	1.19620i	0.951892	−	0.306434i	$-0.0991359\pi$
$270$	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	−0.0188299	−	0.999823i	$-0.505994\pi$
$277$	−3407.52	−	1411.44i	−0.739126	−	0.306156i	−0.720296	+	0.693667i	$0.755994\pi$
$278$	−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	0.390426	−	0.920634i	$-0.372328\pi$
$281$	−2497.50	−	2497.50i	−0.530208	−	0.530208i	−0.920634	+	0.390426i	$0.872328\pi$
$282$	1196.68	−	495.681i	0.252699	−	0.104671i
$283$	−301.639	−	728.220i	−0.0633589	−	0.152962i	0.889029	−	0.457851i	$-0.151381\pi$
$283$	−301.639	−	728.220i	−0.0633589	−	0.152962i	−0.952388	+	0.304889i	$0.901381\pi$
$284$	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	$0.0450154\pi$
$293$			1413.82i			0.281899i	−0.990017	+	0.140949i	$0.954985\pi$
$294$	−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	−0.0517785	−	0.998659i	$-0.516489\pi$
$311$	−4357.74	−	1805.04i	−0.794550	−	0.329113i	−0.742771	+	0.669545i	$0.766489\pi$
$312$	76.2932	+	184.188i	0.0138438	+	0.0334218i
$313$	−5701.55	+	2361.66i	−1.02962	+	0.426482i	−0.832575	−	0.553913i	$-0.813134\pi$
$313$	−5701.55	+	2361.66i	−1.02962	+	0.426482i	−0.197044	+	0.980395i	$0.563134\pi$
$314$	−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	0.958995	−	0.283422i	$-0.0914698\pi$
$317$	454.194	+	1096.52i	0.0804735	+	0.194280i	−0.878522	+	0.477702i	$0.841470\pi$
$318$	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	0.863994	−	0.503503i	$-0.167956\pi$
$331$	2170.88	+	2170.88i	0.360491	+	0.360491i	−0.503503	+	0.863994i	$0.667956\pi$
$332$	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	−0.999665	−	0.0258852i	$-0.991760\pi$
$337$	−1698.14	+	4099.67i	−0.274491	+	0.662681i	0.725173	+	0.688566i	$0.241760\pi$
$338$	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	0.340082	−	0.940396i	$-0.389545\pi$
$347$	8050.88	−	3334.79i	1.24552	−	0.515910i	0.905434	+	0.424486i	$0.139545\pi$
$348$	1675.08	+	1675.08i	0.258028	+	0.258028i
$349$	71.3677	+	71.3677i	0.0109462	+	0.0109462i	0.712559	−	0.701612i	$-0.247536\pi$
$349$	71.3677	+	71.3677i	0.0109462	+	0.0109462i	−0.701612	+	0.712559i	$0.747536\pi$
$350$	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	$0.227351\pi$
$353$			8688.88i			1.31009i	−0.755589	+	0.655046i	$0.772649\pi$
$354$	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	−0.821253	−	0.570565i	$-0.806724\pi$
$359$	−1705.20	+	1705.20i	−0.250688	+	0.250688i	0.570565	+	0.821253i	$0.306724\pi$
$360$	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	−0.527068	−	0.849823i	$-0.676709\pi$
$367$	−2101.09	+	870.300i	−0.298845	+	0.123786i	0.228223	+	0.973609i	$0.426709\pi$
$368$	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	0.690952	−	0.722901i	$-0.257192\pi$
$379$	4931.39	+	2042.65i	0.668360	+	0.276844i	−0.0225917	+	0.999745i	$0.507192\pi$
$380$	−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	0.742915	−	0.669386i	$-0.233443\pi$
$383$	551.137	+	551.137i	0.0735295	+	0.0735295i	−0.669386	+	0.742915i	$0.733443\pi$
$384$	−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	−0.999998	−	0.00222529i	$-0.999292\pi$
$389$	−7655.19	+	7655.19i	−0.997772	+	0.997772i	0.00222529	+	0.999998i	$0.499292\pi$
$390$	−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	−0.999993	−	0.00360730i	$-0.998852\pi$
$397$	−2337.00	−	5642.01i	−0.295442	−	0.713260i	0.704551	−	0.709653i	$-0.251148\pi$
$398$	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	0.390464	−	0.920618i	$-0.372314\pi$
$401$	10579.9	−	4382.32i	1.31754	−	0.545743i	0.927075	+	0.374875i	$0.122314\pi$
$402$	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	0.999790	+	0.0204818i	$0.00652001\pi$
$419$	2635.75	+	6363.26i	0.307315	+	0.741923i	−0.692476	+	0.721441i	$0.743480\pi$
$420$	662.774	+	274.530i	0.0770001	+	0.0318945i
$421$			13586.7i			1.57286i	0.617678	+	0.786431i	$0.288073\pi$
$421$			13586.7i			1.57286i	−0.617678	+	0.786431i	$0.711927\pi$
$422$	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	−0.675819	−	0.737068i	$-0.736210\pi$
$431$	−6434.61	−	15534.5i	−0.719128	−	1.73613i	−0.0433099	−	0.999062i	$-0.513790\pi$
$432$	−9602.19	+	3977.36i	−1.06941	+	0.442964i
$433$	−175.945	−	175.945i	−0.0195274	−	0.0195274i	0.697276	−	0.716803i	$-0.254395\pi$
$433$	−175.945	−	175.945i	−0.0195274	−	0.0195274i	−0.716803	+	0.697276i	$0.754395\pi$
$434$	−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	−0.574325	−	0.818627i	$-0.694735\pi$
$439$	3777.10	−	9118.74i	0.410641	−	0.991375i	0.984966	−	0.172748i	$-0.0552645\pi$
$440$	−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	−0.758171	−	0.652056i	$-0.773907\pi$
$449$	−7927.24	+	3283.57i	−0.833206	+	0.345125i	−0.0750349	+	0.997181i	$0.523907\pi$
$450$	−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	−0.337326	−	0.941388i	$-0.609522\pi$
$457$	5901.41	−	5901.41i	0.604062	−	0.604062i	0.941388	+	0.337326i	$0.109522\pi$
$458$	−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	−0.329663	−	0.944099i	$-0.606935\pi$
$461$	6081.73	−	6081.73i	0.614435	−	0.614435i	0.944099	+	0.329663i	$0.106935\pi$
$462$	−1602.86	+	3869.66i	−0.161411	+	0.389681i
$463$			15888.5i			1.59482i	0.603440	+	0.797408i	$0.293796\pi$
$463$			15888.5i			1.59482i	−0.603440	+	0.797408i	$0.706204\pi$
$464$	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	0.467617	−	0.883931i	$-0.345113\pi$
$467$	−4201.42	−	4201.42i	−0.416314	−	0.416314i	−0.883931	+	0.467617i	$0.845113\pi$
$468$	−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	−0.377094	−	0.926175i	$-0.623077\pi$
$479$	5707.77	−	13779.8i	0.544456	−	1.31443i	0.921551	−	0.388258i	$-0.126923\pi$
$480$		−	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	0.707202	−	0.707012i	$-0.249957\pi$
$487$	−3146.75	−	7596.92i	−0.292798	−	0.706878i	−1.00000		0.000134144i	$0.999957\pi$
$488$	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	−0.787548	−	0.616253i	$-0.788650\pi$
$491$	−1863.67	+	1863.67i	−0.171295	+	0.171295i	0.616253	+	0.787548i	$0.288650\pi$
$492$	−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	0.976570	+	0.215202i	$0.0690409\pi$
$499$	4884.55	+	11792.3i	0.438201	+	1.05791i	−0.538368	+	0.842710i	$0.680959\pi$
$500$	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	−0.104752	−	0.994498i	$-0.533405\pi$
$503$	5915.75	−	2450.38i	0.524394	−	0.217211i	0.629146	+	0.777287i	$0.283405\pi$
$504$	−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	0.999637	−	0.0269270i	$-0.00857216\pi$
$521$	3255.41	+	7859.25i	0.273747	+	0.660883i	−0.725891	+	0.687810i	$0.758572\pi$
$522$	12136.2	+	5027.00i	1.01760	+	0.421505i
$523$			18757.8i			1.56830i	0.620571	+	0.784150i	$0.286901\pi$
$523$			18757.8i			1.56830i	−0.620571	+	0.784150i	$0.713099\pi$
$524$	−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	0.578289	+	0.815832i	$0.303721\pi$
$541$	−5127.75	+	12379.5i	−0.407503	+	0.983800i	−0.985792	+	0.167968i	$0.946279\pi$
$542$	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	−0.780549	−	0.625094i	$-0.785061\pi$
$547$	2729.96	−	6590.70i	0.213391	−	0.515170i	0.993940	+	0.109924i	$0.0350606\pi$
$548$			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	$0.0630731\pi$
$557$			5175.60i			0.393712i	−0.980432	+	0.196856i	$0.936927\pi$
$558$	−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	−0.838972	−	0.544174i	$-0.816843\pi$
$563$	−3938.10	+	3938.10i	−0.294798	+	0.294798i	0.544174	+	0.838972i	$0.316843\pi$
$564$	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	0.184224	−	0.982884i	$-0.441023\pi$
$569$	−10840.0	−	10840.0i	−0.798660	−	0.798660i	−0.982884	+	0.184224i	$0.941023\pi$
$570$	5900.64	+	5900.64i	0.433597	+	0.433597i
$571$	−20588.7	+	8528.10i	−1.50895	+	0.625026i	−0.975340	−	0.220707i	$-0.929164\pi$
$571$	−20588.7	+	8528.10i	−1.50895	+	0.625026i	−0.533606	+	0.845733i	$0.679164\pi$
$572$	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	0.981743	+	0.190210i	$0.0609169\pi$
$587$	16667.4	+	16667.4i	1.17195	+	1.17195i	0.190210	+	0.981743i	$0.439083\pi$
$588$	−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	0.441302	−	0.897359i	$-0.354517\pi$
$593$	19330.9	−	19330.9i	1.33866	−	1.33866i	0.897359	−	0.441302i	$-0.145483\pi$
$594$	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	$0.0428029\pi$
$599$			3930.83i			0.268129i	−0.990973	+	0.134064i	$0.957197\pi$
$600$	1678.63	+	695.309i	0.114216	+	0.0473098i
$601$	−8595.04	−	20750.3i	−0.583359	−	1.40835i	−0.889750	−	0.456448i	$-0.849121\pi$
$601$	−8595.04	−	20750.3i	−0.583359	−	1.40835i	0.306391	−	0.951906i	$-0.400879\pi$
$602$	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	0.450419	−	0.892818i	$-0.351275\pi$
$607$	2057.72	+	852.335i	0.137595	+	0.0569938i	−0.312823	+	0.949811i	$0.601275\pi$
$608$			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	0.578968	−	0.815350i	$-0.303455\pi$
$617$	6311.56	+	2614.33i	0.411821	+	0.170582i	−0.167147	+	0.985932i	$0.553455\pi$
$618$	5868.81	+	14168.6i	0.382004	+	0.922239i
$619$	14869.8	−	6159.26i	0.965536	−	0.399938i	0.156487	−	0.987680i	$-0.449983\pi$
$619$	14869.8	−	6159.26i	0.965536	−	0.399938i	0.809048	+	0.587742i	$0.199983\pi$
$620$	−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	0.239421	−	0.970916i	$-0.423042\pi$
$631$	19184.5	−	19184.5i	1.21034	−	1.21034i	0.970916	−	0.239421i	$-0.0769578\pi$
$632$	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	−0.0498939	−	0.998755i	$-0.515888\pi$
$641$	−12843.5	−	5319.95i	−0.791400	−	0.327809i	−0.741506	+	0.670946i	$0.765888\pi$
$642$			2430.27i			0.149401i
$643$	−3378.07	+	8155.37i	−0.207182	+	0.500181i	−0.992977	−	0.118305i	$-0.962254\pi$
$643$	−3378.07	+	8155.37i	−0.207182	+	0.500181i	0.785795	+	0.618487i	$0.212254\pi$
$644$	−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	−0.182127	−	0.983275i	$-0.558298\pi$
$653$	6413.85	−	2656.70i	0.384370	−	0.159211i	0.566497	+	0.824064i	$0.308298\pi$
$654$	−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	$-0.886555\pi$
$659$		−	11804.8i		−	0.697800i	0.937160	−	0.348900i	$-0.113445\pi$
$660$	−2474.69	+	5974.42i	−0.145950	+	0.352354i
$661$	2731.80	−	2731.80i	0.160748	−	0.160748i	−0.622150	−	0.782898i	$-0.713741\pi$
$661$	2731.80	−	2731.80i	0.160748	−	0.160748i	0.782898	+	0.622150i	$0.213741\pi$
$662$	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	−0.359371	−	0.933195i	$-0.617009\pi$
$673$	809.824	−	335.440i	0.0463840	−	0.0192129i	0.405755	+	0.913982i	$0.367009\pi$
$674$	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	0.533373	+	0.845880i	$0.320924\pi$
$677$	−7784.19	+	18792.7i	−0.441906	+	1.06686i	−0.975279	+	0.220976i	$0.929076\pi$
$678$	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	−0.177425	−	0.984134i	$-0.556777\pi$
$683$	11493.8	−	27748.5i	0.643922	−	1.55456i	0.821346	−	0.570430i	$-0.193223\pi$
$684$			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	0.995870	−	0.0907888i	$-0.0289388\pi$
$691$	4132.11	+	9975.80i	0.227486	+	0.549200i	−0.768384	+	0.639989i	$0.778939\pi$
$692$	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	$0.00282039\pi$
$701$			328.897i			0.0177208i	−0.999961	+	0.00886039i	$0.997180\pi$
$702$	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	0.498192	−	0.867067i	$-0.333998\pi$
$709$	4480.97	+	1856.08i	0.237357	+	0.0983167i	−0.260834	+	0.965384i	$0.583998\pi$
$710$		−	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	0.987736	−	0.156131i	$-0.0499021\pi$
$719$	30379.9	+	12583.8i	1.57577	+	0.652705i	0.588034	+	0.808836i	$0.299902\pi$
$720$	−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	$-0.864286\pi$
$727$		−	16213.2i		−	0.827116i	0.910478	−	0.413558i	$-0.135714\pi$
$728$	−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	−0.108293	−	0.994119i	$-0.534538\pi$
$733$	17579.4	−	17579.4i	0.885826	−	0.885826i	0.994119	+	0.108293i	$0.0345384\pi$
$734$	−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	0.724899	−	0.688856i	$-0.241887\pi$
$739$	724.084	+	724.084i	0.0360431	+	0.0360431i	−0.688856	+	0.724899i	$0.741887\pi$
$740$	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	0.533849	−	0.845580i	$-0.320745\pi$
$743$	6347.67	+	2629.29i	0.313423	+	0.129824i	−0.220426	+	0.975404i	$0.570745\pi$
$744$		−	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	−0.769444	−	0.638715i	$-0.779466\pi$
$751$	4656.89	−	11242.7i	0.226275	−	0.546275i	0.995718	+	0.0924395i	$0.0294665\pi$
$752$		−	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	0.0403208	−	0.999187i	$-0.487162\pi$
$757$	−19971.1	−	19971.1i	−0.958866	−	0.958866i	−0.999187	+	0.0403208i	$0.987162\pi$
$758$	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	$0.258878\pi$
$761$			30505.2i			1.45310i	−0.687112	+	0.726552i	$0.741122\pi$
$762$	−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	$-0.841211\pi$
$769$		−	20404.5i		−	0.956834i	0.878133	−	0.478417i	$-0.158789\pi$
$770$	−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	0.999975	+	0.00702854i	$0.00223727\pi$
$773$	21642.1	+	21642.1i	1.00700	+	1.00700i	0.00702854	+	0.999975i	$0.497763\pi$
$774$	−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	−0.534668	−	0.845062i	$-0.679563\pi$
$787$	−33344.2	−	13811.6i	−1.51028	−	0.625580i	−0.975617	+	0.219482i	$0.929563\pi$
$788$	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	−0.957989	−	0.286804i	$-0.907407\pi$
$797$	−15101.8	+	15101.8i	−0.671185	+	0.671185i	0.286804	+	0.957989i	$0.407407\pi$
$798$	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	−0.840140	−	0.542369i	$-0.817527\pi$
$809$	−24176.9	+	10014.4i	−1.05070	+	0.435213i	−0.210556	+	0.977582i	$0.567527\pi$
$810$	−1706.27	−	4119.31i	−0.0740153	−	0.178689i
$811$	−18503.7	−	7664.48i	−0.801174	−	0.331857i	−0.0557475	−	0.998445i	$-0.517754\pi$
$811$	−18503.7	−	7664.48i	−0.801174	−	0.331857i	−0.745427	+	0.666588i	$0.767754\pi$
$812$			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	0.424735	−	0.905318i	$-0.360367\pi$
$821$	1997.50	+	827.392i	0.0849126	+	0.0351719i	−0.339823	+	0.940489i	$0.610367\pi$
$822$	−7474.42	−	18044.9i	−0.317154	−	0.765677i
$823$	36378.3	−	15068.4i	1.54079	−	0.638214i	0.559165	−	0.829056i	$-0.311122\pi$
$823$	36378.3	−	15068.4i	1.54079	−	0.638214i	0.981621	+	0.190842i	$0.0611218\pi$
$824$	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	−0.994784	−	0.102002i	$-0.967475\pi$
$827$	−8644.75	−	20870.3i	−0.363492	−	0.877546i	0.631293	−	0.775545i	$-0.282525\pi$
$828$	8696.83	+	3602.35i	0.365019	+	0.151196i
$829$		−	10977.3i		−	0.459898i	−0.973203	−	0.229949i	$-0.926144\pi$
$829$		−	10977.3i		−	0.459898i	0.973203	−	0.229949i	$-0.0738560\pi$
$830$	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	0.718584	+	0.695440i	$0.244790\pi$
$839$	17065.4	+	41199.4i	0.702219	+	1.69531i	−0.0163657	+	0.999866i	$0.505210\pi$
$840$	−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	0.332443	+	0.943123i	$0.392127\pi$
$853$	−14188.3	+	34253.7i	−0.569519	+	1.37494i	−0.901961	+	0.431817i	$0.857873\pi$
$854$			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	−0.999236	−	0.0390702i	$-0.987560\pi$
$857$	−42102.6	+	17439.5i	−1.67818	+	0.695123i	−0.678940	+	0.734194i	$0.737560\pi$
$858$	−2321.68	−	2321.68i	−0.0923784	−	0.0923784i
$859$	−48.4609	−	48.4609i	−0.00192487	−	0.00192487i	0.706144	−	0.708069i	$-0.250433\pi$
$859$	−48.4609	−	48.4609i	−0.00192487	−	0.00192487i	−0.708069	+	0.706144i	$0.750433\pi$
$860$	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	$-0.968155\pi$
$863$		−	5064.23i		−	0.199755i	0.995000	−	0.0998774i	$-0.0318451\pi$
$864$	−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	−0.449709	−	0.893175i	$-0.648472\pi$
$877$	−3535.56	+	1464.48i	−0.136131	+	0.0563875i	0.313578	+	0.949563i	$0.398472\pi$
$878$	−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	−0.273112	−	0.961982i	$-0.588053\pi$
$881$	15695.8	−	37893.0i	0.600232	−	1.44909i	0.873343	−	0.487105i	$-0.161947\pi$
$882$	−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	−0.998199	−	0.0599902i	$-0.980893\pi$
$887$	−6602.86	+	15940.7i	−0.249946	+	0.603424i	0.748253	+	0.663414i	$0.230893\pi$
$888$			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	0.998494	−	0.0548519i	$-0.0174687\pi$
$907$	6929.04	+	16728.2i	0.253666	+	0.612404i	−0.744828	+	0.667256i	$0.767469\pi$
$908$	−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	−0.680602	−	0.732653i	$-0.738282\pi$
$911$	−17702.1	+	7332.47i	−0.643796	+	0.266669i	0.0368060	+	0.999322i	$0.488282\pi$
$912$	−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	0.859422	−	0.511266i	$-0.170823\pi$
$929$	−3109.06	−	7505.93i	−0.109801	−	0.265082i	−0.969223	+	0.246184i	$0.920823\pi$
$930$	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	−0.549246	−	0.835661i	$-0.685085\pi$
$937$	8214.97	−	8214.97i	0.286415	−	0.286415i	0.835661	+	0.549246i	$0.185085\pi$
$938$	−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	0.985764	−	0.168133i	$-0.0537740\pi$
$941$	4902.44	+	11835.5i	0.169835	+	0.410019i	−0.815929	+	0.578152i	$0.803774\pi$
$942$	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	0.696088	−	0.717957i	$-0.254922\pi$
$947$	19835.0	+	8215.93i	0.680624	+	0.281924i	−0.0154635	+	0.999880i	$0.504922\pi$
$948$		−	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	−0.979914	−	0.199421i	$-0.936094\pi$
$967$	−23469.7	+	23469.7i	−0.780492	+	0.780492i	0.199421	+	0.979914i	$0.436094\pi$
$968$	−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	−0.973339	−	0.229371i	$-0.926333\pi$
$971$	−22510.4	+	22510.4i	−0.743968	+	0.743968i	0.229371	+	0.973339i	$0.426333\pi$
$972$	−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	0.519770	−	0.854306i	$-0.326018\pi$
$977$	−10216.1	−	10216.1i	−0.334536	−	0.334536i	−0.854306	+	0.519770i	$0.826018\pi$
$978$	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	−0.867776	−	0.496955i	$-0.834451\pi$
$983$	2996.76	−	7234.81i	0.0972347	−	0.234745i	0.965011	+	0.262210i	$0.0844513\pi$
$984$	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	0.588881	−	0.808219i	$-0.299569\pi$
$991$	13532.7	+	5605.45i	0.433786	+	0.179680i	−0.155095	+	0.987899i	$0.549569\pi$
$992$	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	0.875843	+	0.482596i	$0.160306\pi$
$997$	18818.3	+	45431.4i	0.597775	+	1.44316i	−0.278068	+	0.960561i	$0.589694\pi$
$998$	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.8.3	✓	12
3.2	odd	2		153.4.l.a.127.1		12
17.6	odd	16		289.4.b.e.288.10		12
17.7	odd	16		289.4.a.g.1.4		12
17.10	odd	16		289.4.a.g.1.3		12
17.11	odd	16		289.4.b.e.288.9		12
17.15	even	8	inner	17.4.d.a.15.3	yes	12
51.32	odd	8		153.4.l.a.100.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.d.a.8.3	✓	12	1.1	even	1	trivial
17.4.d.a.15.3	yes	12	17.15	even	8	inner
153.4.l.a.100.1		12	51.32	odd	8
153.4.l.a.127.1		12	3.2	odd	2
289.4.a.g.1.3		12	17.10	odd	16
289.4.a.g.1.4		12	17.7	odd	16
289.4.b.e.288.9		12	17.11	odd	16
289.4.b.e.288.10		12	17.6	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

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