LMFDB - Embedded newform 287.3.b.a.83.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,3,Mod(83,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("287.83");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	287.b (of order $2$, degree $1$, 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:	$7.82018358714$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			83.20
Character	$\chi$	$=$	287.83
Dual form			287.3.b.a.83.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.34917 q^{2} +3.09036i q^{3} -2.17974 q^{4} +2.40453i q^{5} -4.16942i q^{6} +(6.89193 - 1.22527i) q^{7} +8.33752 q^{8} -0.550339 q^{9} +O(q^{10})$	\(q-1.34917 q^{2} +3.09036i q^{3} -2.17974 q^{4} +2.40453i q^{5} -4.16942i q^{6} +(6.89193 - 1.22527i) q^{7} +8.33752 q^{8} -0.550339 q^{9} -3.24412i q^{10} +13.0835 q^{11} -6.73620i q^{12} -1.53461i q^{13} +(-9.29838 + 1.65309i) q^{14} -7.43088 q^{15} -2.52973 q^{16} -3.56602i q^{17} +0.742499 q^{18} +34.0047i q^{19} -5.24127i q^{20} +(3.78652 + 21.2986i) q^{21} -17.6519 q^{22} -18.4523 q^{23} +25.7659i q^{24} +19.2182 q^{25} +2.07044i q^{26} +26.1125i q^{27} +(-15.0227 + 2.67077i) q^{28} -17.4477 q^{29} +10.0255 q^{30} -32.4561i q^{31} -29.9370 q^{32} +40.4329i q^{33} +4.81116i q^{34} +(2.94620 + 16.5719i) q^{35} +1.19960 q^{36} -31.3471 q^{37} -45.8781i q^{38} +4.74249 q^{39} +20.0478i q^{40} +6.40312i q^{41} +(-5.10865 - 28.7353i) q^{42} +33.4616 q^{43} -28.5188 q^{44} -1.32331i q^{45} +24.8953 q^{46} +73.5530i q^{47} -7.81779i q^{48} +(45.9974 - 16.8889i) q^{49} -25.9286 q^{50} +11.0203 q^{51} +3.34505i q^{52} +37.8282 q^{53} -35.2302i q^{54} +31.4598i q^{55} +(57.4616 - 10.2157i) q^{56} -105.087 q^{57} +23.5399 q^{58} +31.8902i q^{59} +16.1974 q^{60} -35.7022i q^{61} +43.7888i q^{62} +(-3.79290 + 0.674312i) q^{63} +50.5090 q^{64} +3.69001 q^{65} -54.5508i q^{66} +31.8146 q^{67} +7.77301i q^{68} -57.0243i q^{69} +(-3.97491 - 22.3582i) q^{70} -23.1104 q^{71} -4.58846 q^{72} +28.9903i q^{73} +42.2926 q^{74} +59.3913i q^{75} -74.1216i q^{76} +(90.1709 - 16.0308i) q^{77} -6.39842 q^{78} -117.129 q^{79} -6.08282i q^{80} -85.6502 q^{81} -8.63889i q^{82} -9.07575i q^{83} +(-8.25365 - 46.4254i) q^{84} +8.57461 q^{85} -45.1453 q^{86} -53.9197i q^{87} +109.084 q^{88} +170.937i q^{89} +1.78536i q^{90} +(-1.88030 - 10.5764i) q^{91} +40.2213 q^{92} +100.301 q^{93} -99.2354i q^{94} -81.7654 q^{95} -92.5163i q^{96} -145.475i q^{97} +(-62.0583 + 22.7860i) q^{98} -7.20038 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 2 q^{2} + 90 q^{4} + 12 q^{7} - 2 q^{8} - 140 q^{9}+O(q^{10}) $ 52 * q + 2 * q^2 + 90 * q^4 + 12 * q^7 - 2 * q^8 - 140 * q^9	$ 52 q + 2 q^{2} + 90 q^{4} + 12 q^{7} - 2 q^{8} - 140 q^{9} + 24 q^{11} - 14 q^{14} + 44 q^{15} + 194 q^{16} + 70 q^{18} - 16 q^{21} - 48 q^{22} - 80 q^{23} - 304 q^{25} + 64 q^{28} - 12 q^{29} + 64 q^{30} - 166 q^{32} + 30 q^{35} - 70 q^{36} + 36 q^{37} - 68 q^{39} + 164 q^{42} - 172 q^{43} + 72 q^{44} + 68 q^{46} - 172 q^{49} - 234 q^{50} + 156 q^{51} + 64 q^{53} - 234 q^{56} + 140 q^{57} - 556 q^{58} + 152 q^{60} - 130 q^{63} + 334 q^{64} - 76 q^{65} + 160 q^{67} + 202 q^{70} - 408 q^{71} - 40 q^{72} + 398 q^{74} - 248 q^{77} + 390 q^{78} + 264 q^{79} - 116 q^{81} - 418 q^{84} + 232 q^{85} + 368 q^{86} - 220 q^{88} + 32 q^{91} - 74 q^{92} + 240 q^{93} - 44 q^{95} + 838 q^{98} - 24 q^{99}+O(q^{100}) $ 52 * q + 2 * q^2 + 90 * q^4 + 12 * q^7 - 2 * q^8 - 140 * q^9 + 24 * q^11 - 14 * q^14 + 44 * q^15 + 194 * q^16 + 70 * q^18 - 16 * q^21 - 48 * q^22 - 80 * q^23 - 304 * q^25 + 64 * q^28 - 12 * q^29 + 64 * q^30 - 166 * q^32 + 30 * q^35 - 70 * q^36 + 36 * q^37 - 68 * q^39 + 164 * q^42 - 172 * q^43 + 72 * q^44 + 68 * q^46 - 172 * q^49 - 234 * q^50 + 156 * q^51 + 64 * q^53 - 234 * q^56 + 140 * q^57 - 556 * q^58 + 152 * q^60 - 130 * q^63 + 334 * q^64 - 76 * q^65 + 160 * q^67 + 202 * q^70 - 408 * q^71 - 40 * q^72 + 398 * q^74 - 248 * q^77 + 390 * q^78 + 264 * q^79 - 116 * q^81 - 418 * q^84 + 232 * q^85 + 368 * q^86 - 220 * q^88 + 32 * q^91 - 74 * q^92 + 240 * q^93 - 44 * q^95 + 838 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.34917			−0.674584			−0.337292	−	0.941400i	$-0.609511\pi$
$2$	−1.34917			−0.674584			−0.337292	+	0.941400i	$0.609511\pi$
$3$			3.09036i			1.03012i	0.857154	+	0.515060i	$0.172231\pi$
$3$			3.09036i			1.03012i	−0.857154	+	0.515060i	$0.827769\pi$
$4$	−2.17974			−0.544936
$5$			2.40453i			0.480907i	0.970661	+	0.240453i	$0.0772961\pi$
$5$			2.40453i			0.480907i	−0.970661	+	0.240453i	$0.922704\pi$
$6$		−	4.16942i		−	0.694903i
$7$	6.89193	−	1.22527i	0.984562	−	0.175038i
$7$	6.89193	−	1.22527i	0.984562	−	0.175038i
$8$	8.33752			1.04219
$9$	−0.550339			−0.0611487
$10$		−	3.24412i		−	0.324412i
$11$	13.0835			1.18941			0.594707	−	0.803943i	$-0.297268\pi$
$11$	13.0835			1.18941			0.594707	+	0.803943i	$0.297268\pi$
$12$		−	6.73620i		−	0.561350i
$13$		−	1.53461i		−	0.118047i	−0.998257	−	0.0590233i	$-0.981201\pi$
$13$		−	1.53461i		−	0.118047i	0.998257	−	0.0590233i	$-0.0187986\pi$
$14$	−9.29838	+	1.65309i	−0.664170	+	0.118078i
$15$	−7.43088			−0.495392
$16$	−2.52973			−0.158108
$17$		−	3.56602i		−	0.209766i	−0.994485	−	0.104883i	$-0.966553\pi$
$17$		−	3.56602i		−	0.209766i	0.994485	−	0.104883i	$-0.0334468\pi$
$18$	0.742499			0.0412500
$19$			34.0047i			1.78972i	0.446345	+	0.894861i	$0.352725\pi$
$19$			34.0047i			1.78972i	−0.446345	+	0.894861i	$0.647275\pi$
$20$		−	5.24127i		−	0.262063i
$21$	3.78652	+	21.2986i	0.180311	+	1.01422i
$22$	−17.6519			−0.802359
$23$	−18.4523			−0.802274			−0.401137	−	0.916018i	$-0.631385\pi$
$23$	−18.4523			−0.802274			−0.401137	+	0.916018i	$0.631385\pi$
$24$			25.7659i			1.07358i
$25$	19.2182			0.768729
$26$			2.07044i			0.0796324i
$27$			26.1125i			0.967130i
$28$	−15.0227	+	2.67077i	−0.536523	+	0.0953847i
$29$	−17.4477			−0.601645			−0.300822	−	0.953680i	$-0.597261\pi$
$29$	−17.4477			−0.601645			−0.300822	+	0.953680i	$0.597261\pi$
$30$	10.0255			0.334183
$31$		−	32.4561i		−	1.04697i	−0.852034	−	0.523486i	$-0.824631\pi$
$31$		−	32.4561i		−	1.04697i	0.852034	−	0.523486i	$-0.175369\pi$
$32$	−29.9370			−0.935532
$33$			40.4329i			1.22524i
$34$			4.81116i			0.141505i
$35$	2.94620	+	16.5719i	0.0841770	+	0.473482i
$36$	1.19960			0.0333222
$37$	−31.3471			−0.847220			−0.423610	−	0.905845i	$-0.639237\pi$
$37$	−31.3471			−0.847220			−0.423610	+	0.905845i	$0.639237\pi$
$38$		−	45.8781i		−	1.20732i
$39$	4.74249			0.121602
$40$			20.0478i			0.501196i
$41$			6.40312i			0.156174i
$41$			6.40312i			0.156174i
$42$	−5.10865	−	28.7353i	−0.121635	−	0.684175i
$43$	33.4616			0.778177			0.389088	−	0.921200i	$-0.372790\pi$
$43$	33.4616			0.778177			0.389088	+	0.921200i	$0.372790\pi$
$44$	−28.5188			−0.648155
$45$		−	1.32331i		−	0.0294068i
$46$	24.8953			0.541201
$47$			73.5530i			1.56496i	0.622677	+	0.782479i	$0.286045\pi$
$47$			73.5530i			1.56496i	−0.622677	+	0.782479i	$0.713955\pi$
$48$		−	7.81779i		−	0.162871i
$49$	45.9974	−	16.8889i	0.938723	−	0.344672i
$50$	−25.9286			−0.518572
$51$	11.0203			0.216084
$52$			3.34505i			0.0643279i
$53$	37.8282			0.713740			0.356870	−	0.934154i	$-0.383844\pi$
$53$	37.8282			0.713740			0.356870	+	0.934154i	$0.383844\pi$
$54$		−	35.2302i		−	0.652411i
$55$			31.4598i			0.571997i
$56$	57.4616	−	10.2157i	1.02610	−	0.182423i
$57$	−105.087			−1.84363
$58$	23.5399			0.405860
$59$			31.8902i			0.540512i	0.962789	+	0.270256i	$0.0871083\pi$
$59$			31.8902i			0.540512i	−0.962789	+	0.270256i	$0.912892\pi$
$60$	16.1974			0.269957
$61$		−	35.7022i		−	0.585282i	−0.956222	−	0.292641i	$-0.905466\pi$
$61$		−	35.7022i		−	0.585282i	0.956222	−	0.292641i	$-0.0945341\pi$
$62$			43.7888i			0.706271i
$63$	−3.79290	+	0.674312i	−0.0602047	+	0.0107034i
$64$	50.5090			0.789203
$65$	3.69001			0.0567694
$66$		−	54.5508i		−	0.826527i
$67$	31.8146			0.474844			0.237422	−	0.971407i	$-0.423698\pi$
$67$	31.8146			0.474844			0.237422	+	0.971407i	$0.423698\pi$
$68$			7.77301i			0.114309i
$69$		−	57.0243i		−	0.826439i
$70$	−3.97491	−	22.3582i	−0.0567845	−	0.319404i
$71$	−23.1104			−0.325499			−0.162749	−	0.986667i	$-0.552036\pi$
$71$	−23.1104			−0.325499			−0.162749	+	0.986667i	$0.552036\pi$
$72$	−4.58846			−0.0637286
$73$			28.9903i			0.397128i	0.980088	+	0.198564i	$0.0636278\pi$
$73$			28.9903i			0.397128i	−0.980088	+	0.198564i	$0.936372\pi$
$74$	42.2926			0.571521
$75$			59.3913i			0.791884i
$76$		−	74.1216i		−	0.975284i
$77$	90.1709	−	16.0308i	1.17105	−	0.208193i
$78$	−6.39842			−0.0820310
$79$	−117.129			−1.48265			−0.741323	−	0.671149i	$-0.765801\pi$
$79$	−117.129			−1.48265			−0.741323	+	0.671149i	$0.765801\pi$
$80$		−	6.08282i		−	0.0760353i
$81$	−85.6502			−1.05741
$82$		−	8.63889i		−	0.105352i
$83$		−	9.07575i		−	0.109346i	−0.998504	−	0.0546732i	$-0.982588\pi$
$83$		−	9.07575i		−	0.109346i	0.998504	−	0.0546732i	$-0.0174117\pi$
$84$	−8.25365	−	46.4254i	−0.0982577	−	0.552684i
$85$	8.57461			0.100878
$86$	−45.1453			−0.524946
$87$		−	53.9197i		−	0.619767i
$88$	109.084			1.23959
$89$			170.937i			1.92064i	0.278902	+	0.960320i	$0.410030\pi$
$89$			170.937i			1.92064i	−0.278902	+	0.960320i	$0.589970\pi$
$90$			1.78536i			0.0198374i
$91$	−1.88030	−	10.5764i	−0.0206627	−	0.116224i
$92$	40.2213			0.437188
$93$	100.301			1.07851
$94$		−	99.2354i		−	1.05570i
$95$	−81.7654			−0.860689
$96$		−	92.5163i		−	0.963711i
$97$		−	145.475i		−	1.49974i	−0.661584	−	0.749871i	$-0.730116\pi$
$97$		−	145.475i		−	1.49974i	0.661584	−	0.749871i	$-0.269884\pi$
$98$	−62.0583	+	22.7860i	−0.633248	+	0.232510i
$99$	−7.20038			−0.0727311
$100$	−41.8908			−0.418908
$101$		−	108.022i		−	1.06953i	−0.845001	−	0.534764i	$-0.820400\pi$
$101$		−	108.022i		−	1.06953i	0.845001	−	0.534764i	$-0.179600\pi$
$102$	−14.8682			−0.145767
$103$		−	109.923i		−	1.06721i	−0.845732	−	0.533607i	$-0.820836\pi$
$103$		−	109.923i		−	1.06721i	0.845732	−	0.533607i	$-0.179164\pi$
$104$		−	12.7948i		−	0.123027i
$105$	−51.2131	+	9.10481i	−0.487744	+	0.0867125i
$106$	−51.0367			−0.481478
$107$	173.344			1.62004			0.810018	−	0.586405i	$-0.199457\pi$
$107$	173.344			1.62004			0.810018	+	0.586405i	$0.199457\pi$
$108$		−	56.9186i		−	0.527024i
$109$	−70.8686			−0.650171			−0.325085	−	0.945685i	$-0.605393\pi$
$109$	−70.8686			−0.650171			−0.325085	+	0.945685i	$0.605393\pi$
$110$		−	42.4446i		−	0.385860i
$111$		−	96.8740i		−	0.872739i
$112$	−17.4347	+	3.09960i	−0.155667	+	0.0276750i
$113$	21.6710			0.191779			0.0958893	−	0.995392i	$-0.469431\pi$
$113$	21.6710			0.191779			0.0958893	+	0.995392i	$0.469431\pi$
$114$	141.780			1.24368
$115$		−	44.3692i		−	0.385819i
$116$	38.0315			0.327858
$117$			0.844553i			0.00721841i
$118$		−	43.0252i		−	0.364621i
$119$	−4.36933	−	24.5767i	−0.0367170	−	0.206527i
$120$	−61.9551			−0.516292
$121$	50.1792			0.414704
$122$			48.1683i			0.394822i
$123$	−19.7880			−0.160878
$124$			70.7461i			0.570533i
$125$			106.324i			0.850593i
$126$	5.11725	−	0.909760i	0.0406131	−	0.00722032i
$127$	−43.5342			−0.342789			−0.171395	−	0.985202i	$-0.554827\pi$
$127$	−43.5342			−0.342789			−0.171395	+	0.985202i	$0.554827\pi$
$128$	51.6029			0.403148
$129$			103.408i			0.801616i
$130$	−4.97845			−0.0382958
$131$			69.2841i			0.528886i	0.964401	+	0.264443i	$0.0851881\pi$
$131$			69.2841i			0.528886i	−0.964401	+	0.264443i	$0.914812\pi$
$132$		−	88.1334i		−	0.667677i
$133$	41.6649	+	234.358i	0.313270	+	1.76209i
$134$	−42.9232			−0.320322
$135$	−62.7884			−0.465099
$136$		−	29.7317i		−	0.218616i
$137$	−158.316			−1.15559			−0.577797	−	0.816180i	$-0.696088\pi$
$137$	−158.316			−1.15559			−0.577797	+	0.816180i	$0.696088\pi$
$138$			76.9354i			0.557503i
$139$		−	194.557i		−	1.39969i	−0.714295	−	0.699845i	$-0.753253\pi$
$139$		−	194.557i		−	1.39969i	0.714295	−	0.699845i	$-0.246747\pi$
$140$	−6.42196	−	36.1225i	−0.0458711	−	0.258018i
$141$	−227.305			−1.61209
$142$	31.1798			0.219576
$143$		−	20.0781i		−	0.140406i
$144$	1.39221			0.00966812
$145$		−	41.9535i		−	0.289335i
$146$		−	39.1128i		−	0.267896i
$147$	52.1929	+	142.149i	0.355054	+	0.966998i
$148$	68.3287			0.461681
$149$	−135.590			−0.910002			−0.455001	−	0.890491i	$-0.650361\pi$
$149$	−135.590			−0.910002			−0.455001	+	0.890491i	$0.650361\pi$
$150$		−	80.1288i		−	0.534192i
$151$	153.433			1.01612			0.508058	−	0.861323i	$-0.330364\pi$
$151$	153.433			1.01612			0.508058	+	0.861323i	$0.330364\pi$
$152$			283.515i			1.86523i
$153$			1.96252i			0.0128269i
$154$	−121.656	+	21.6283i	−0.789972	+	0.140444i
$155$	78.0419			0.503496
$156$	−10.3374			−0.0662655
$157$		−	24.6422i		−	0.156957i	−0.996916	−	0.0784783i	$-0.974994\pi$
$157$		−	24.6422i		−	0.156957i	0.996916	−	0.0784783i	$-0.0250061\pi$
$158$	158.027			1.00017
$159$			116.903i			0.735239i
$160$		−	71.9846i		−	0.449904i
$161$	−127.172	+	22.6090i	−0.789888	+	0.140429i
$162$	115.556			0.713312
$163$	194.719			1.19460			0.597299	−	0.802019i	$-0.296241\pi$
$163$	194.719			1.19460			0.597299	+	0.802019i	$0.296241\pi$
$164$		−	13.9572i		−	0.0851047i
$165$	−97.2222			−0.589226
$166$			12.2447i			0.0737633i
$167$		−	125.204i		−	0.749723i	−0.927081	−	0.374862i	$-0.877690\pi$
$167$		−	125.204i		−	0.749723i	0.927081	−	0.374862i	$-0.122310\pi$
$168$	31.5702	+	177.577i	0.187918	+	1.05701i
$169$	166.645			0.986065
$170$	−11.5686			−0.0680505
$171$		−	18.7141i		−	0.109439i
$172$	−72.9378			−0.424057
$173$			314.487i			1.81784i	0.416965	+	0.908922i	$0.363094\pi$
$173$			314.487i			1.81784i	−0.416965	+	0.908922i	$0.636906\pi$
$174$			72.7467i			0.418085i
$175$	132.451	−	23.5475i	0.756861	−	0.134557i
$176$	−33.0979			−0.188056
$177$	−98.5523			−0.556793
$178$		−	230.623i		−	1.29563i
$179$	−24.5775			−0.137305			−0.0686523	−	0.997641i	$-0.521870\pi$
$179$	−24.5775			−0.137305			−0.0686523	+	0.997641i	$0.521870\pi$
$180$			2.88447i			0.0160248i
$181$			307.419i			1.69845i	0.528034	+	0.849223i	$0.322929\pi$
$181$			307.419i			1.69845i	−0.528034	+	0.849223i	$0.677071\pi$
$182$	2.53685	+	14.2694i	0.0139387	+	0.0784030i
$183$	110.333			0.602911
$184$	−153.846			−0.836121
$185$		−	75.3752i		−	0.407433i
$186$	−135.323			−0.727544
$187$		−	46.6562i		−	0.249498i
$188$		−	160.327i		−	0.852802i
$189$	31.9948	+	179.966i	0.169285	+	0.952199i
$190$	110.315			0.580607
$191$	14.4980			0.0759059			0.0379530	−	0.999280i	$-0.487916\pi$
$191$	14.4980			0.0759059			0.0379530	+	0.999280i	$0.487916\pi$
$192$			156.091i			0.812975i
$193$	−41.5464			−0.215266			−0.107633	−	0.994191i	$-0.534327\pi$
$193$	−41.5464			−0.215266			−0.107633	+	0.994191i	$0.534327\pi$
$194$			196.270i			1.01170i
$195$			11.4035i			0.0584794i
$196$	−100.263	+	36.8135i	−0.511544	+	0.187824i
$197$	208.222			1.05696			0.528481	−	0.848945i	$-0.322762\pi$
$197$	208.222			1.05696			0.528481	+	0.848945i	$0.322762\pi$
$198$	9.71453			0.0490633
$199$		−	52.1700i		−	0.262161i	−0.991372	−	0.131080i	$-0.958155\pi$
$199$		−	52.1700i		−	0.262161i	0.991372	−	0.131080i	$-0.0418446\pi$
$200$	160.232			0.801161
$201$			98.3185i			0.489147i
$202$			145.740i			0.721487i
$203$	−120.248	+	21.3781i	−0.592356	+	0.105311i
$204$	−24.0214			−0.117752
$205$	−15.3965			−0.0751050
$206$			148.305i			0.719926i
$207$	10.1550			0.0490580
$208$			3.88214i			0.0186642i
$209$			444.902i			2.12872i
$210$	69.0951	−	12.2839i	0.329024	−	0.0584949i
$211$	196.997			0.933636			0.466818	−	0.884353i	$-0.345400\pi$
$211$	196.997			0.933636			0.466818	+	0.884353i	$0.345400\pi$
$212$	−82.4559			−0.388943
$213$		−	71.4195i		−	0.335303i
$214$	−233.870			−1.09285
$215$			80.4595i			0.374230i
$216$			217.714i			1.00793i
$217$	−39.7675	−	223.686i	−0.183260	−	1.03081i
$218$	95.6137			0.438595
$219$	−89.5906			−0.409090
$220$		−	68.5744i		−	0.311702i
$221$	−5.47244			−0.0247622
$222$			130.699i			0.588736i
$223$		−	44.6683i		−	0.200306i	−0.994972	−	0.100153i	$-0.968067\pi$
$223$		−	44.6683i		−	0.200306i	0.994972	−	0.100153i	$-0.0319333\pi$
$224$	−206.324	+	36.6809i	−0.921089	+	0.163754i
$225$	−10.5765			−0.0470068
$226$	−29.2378			−0.129371
$227$		−	274.484i		−	1.20918i	−0.796537	−	0.604590i	$-0.793337\pi$
$227$		−	274.484i		−	1.20918i	0.796537	−	0.604590i	$-0.206663\pi$
$228$	229.063			1.00466
$229$		−	346.846i		−	1.51461i	−0.653060	−	0.757306i	$-0.726515\pi$
$229$		−	346.846i		−	1.51461i	0.653060	−	0.757306i	$-0.273485\pi$
$230$			59.8615i			0.260267i
$231$	49.5411	+	278.661i	0.214464	+	1.20632i
$232$	−145.470			−0.627028
$233$	−239.399			−1.02746			−0.513731	−	0.857951i	$-0.671737\pi$
$233$	−239.399			−1.02746			−0.513731	+	0.857951i	$0.671737\pi$
$234$		−	1.13944i		−	0.00486942i
$235$	−176.861			−0.752598
$236$		−	69.5125i		−	0.294545i
$237$		−	361.971i		−	1.52730i
$238$	5.89496	+	33.1582i	0.0247687	+	0.139320i
$239$	265.665			1.11157			0.555785	−	0.831326i	$-0.312418\pi$
$239$	265.665			1.11157			0.555785	+	0.831326i	$0.312418\pi$
$240$	18.7981			0.0783255
$241$		−	244.030i		−	1.01257i	−0.862366	−	0.506285i	$-0.831018\pi$
$241$		−	244.030i		−	1.01257i	0.862366	−	0.506285i	$-0.168982\pi$
$242$	−67.7002			−0.279753
$243$		−	29.6774i		−	0.122129i
$244$			77.8217i			0.318942i
$245$	40.6100	+	110.602i	0.165755	+	0.451438i
$246$	26.6973			0.108526
$247$	52.1839			0.211271
$248$		−	270.604i		−	1.09114i
$249$	28.0474			0.112640
$250$		−	143.449i		−	0.573797i
$251$		−	283.586i		−	1.12982i	−0.825151	−	0.564912i	$-0.808910\pi$
$251$		−	283.586i		−	1.12982i	0.825151	−	0.564912i	$-0.191090\pi$
$252$	8.26755	−	1.46983i	0.0328077	−	0.00583265i
$253$	−241.422			−0.954235
$254$	58.7350			0.231240
$255$			26.4986i			0.103916i
$256$	−271.657			−1.06116
$257$		−	181.465i		−	0.706090i	−0.935606	−	0.353045i	$-0.885146\pi$
$257$		−	181.465i		−	0.706090i	0.935606	−	0.353045i	$-0.114854\pi$
$258$		−	139.515i		−	0.540757i
$259$	−216.042	+	38.4086i	−0.834140	+	0.148296i
$260$	−8.04329			−0.0309357
$261$	9.60214			0.0367898
$262$		−	93.4759i		−	0.356778i
$263$	−225.545			−0.857587			−0.428793	−	0.903403i	$-0.641061\pi$
$263$	−225.545			−0.857587			−0.428793	+	0.903403i	$0.641061\pi$
$264$			337.110i			1.27693i
$265$			90.9592i			0.343242i
$266$	−56.2129	−	316.189i	−0.211327	−	1.18868i
$267$	−528.257			−1.97849
$268$	−69.3476			−0.258760
$269$			207.825i			0.772583i	0.922377	+	0.386291i	$0.126244\pi$
$269$			207.825i			0.772583i	−0.922377	+	0.386291i	$0.873756\pi$
$270$	84.7121			0.313749
$271$		−	426.199i		−	1.57269i	−0.617788	−	0.786345i	$-0.711971\pi$
$271$		−	426.199i		−	1.57269i	0.617788	−	0.786345i	$-0.288029\pi$
$272$			9.02107i			0.0331657i
$273$	32.6849	−	5.81082i	0.119725	−	0.0212851i
$274$	213.596			0.779546
$275$	251.443			0.914337
$276$			124.298i			0.450357i
$277$	200.258			0.722953			0.361477	−	0.932381i	$-0.382273\pi$
$277$	200.258			0.722953			0.361477	+	0.932381i	$0.382273\pi$
$278$			262.490i			0.944208i
$279$			17.8619i			0.0640210i
$280$	24.5640	+	138.168i	0.0877284	+	0.493458i
$281$	−86.0107			−0.306088			−0.153044	−	0.988219i	$-0.548908\pi$
$281$	−86.0107			−0.306088			−0.153044	+	0.988219i	$0.548908\pi$
$282$	306.673			1.08749
$283$		−	234.992i		−	0.830361i	−0.909739	−	0.415181i	$-0.863718\pi$
$283$		−	234.992i		−	0.830361i	0.909739	−	0.415181i	$-0.136282\pi$
$284$	50.3748			0.177376
$285$		−	252.685i		−	0.886613i
$286$			27.0887i			0.0947159i
$287$	7.84554	+	44.1299i	0.0273364	+	0.153763i
$288$	16.4755			0.0572066
$289$	276.284			0.955998
$290$			56.6024i			0.195181i
$291$	449.570			1.54491
$292$		−	63.1915i		−	0.216409i
$293$			189.910i			0.648158i	0.946030	+	0.324079i	$0.105054\pi$
$293$			189.910i			0.648158i	−0.946030	+	0.324079i	$0.894946\pi$
$294$	−70.4170	−	191.783i	−0.239514	−	0.652322i
$295$	−76.6810			−0.259936
$296$	−261.357			−0.882963
$297$			341.644i			1.15032i
$298$	182.934			0.613873
$299$			28.3170i			0.0947058i
$300$		−	129.458i		−	0.431526i
$301$	230.615	−	40.9994i	0.766163	−	0.136211i
$302$	−207.007			−0.685455
$303$	333.828			1.10174
$304$		−	86.0228i		−	0.282970i
$305$	85.8471			0.281466
$306$		−	2.64777i		−	0.00865283i
$307$		−	523.084i		−	1.70386i	−0.523659	−	0.851928i	$-0.675433\pi$
$307$		−	523.084i		−	1.70386i	0.523659	−	0.851928i	$-0.324567\pi$
$308$	−196.550	+	34.9432i	−0.638148	+	0.113452i
$309$	339.702			1.09936
$310$	−105.292			−0.339650
$311$			271.664i			0.873517i	0.899579	+	0.436759i	$0.143874\pi$
$311$			271.664i			0.873517i	−0.899579	+	0.436759i	$0.856126\pi$
$312$	39.5406			0.126733
$313$		−	247.424i		−	0.790490i	−0.918576	−	0.395245i	$-0.870660\pi$
$313$		−	247.424i		−	0.790490i	0.918576	−	0.395245i	$-0.129340\pi$
$314$			33.2465i			0.105880i
$315$	−1.62141	−	9.12014i	−0.00514732	−	0.0289528i
$316$	255.311			0.807947
$317$	−612.850			−1.93328			−0.966641	−	0.256136i	$-0.917550\pi$
$317$	−612.850			−1.93328			−0.966641	+	0.256136i	$0.917550\pi$
$318$		−	157.722i		−	0.495980i
$319$	−228.278			−0.715604
$320$			121.451i			0.379533i
$321$			535.695i			1.66883i
$322$	171.576	−	30.5034i	0.532846	−	0.0947309i
$323$	121.261			0.375422
$324$	186.696			0.576221
$325$		−	29.4924i		−	0.0907459i
$326$	−262.709			−0.805857
$327$		−	219.010i		−	0.669755i
$328$			53.3862i			0.162763i
$329$	90.1221	+	506.922i	0.273927	+	1.54080i
$330$	131.169			0.397482
$331$	82.3773			0.248874			0.124437	−	0.992228i	$-0.460288\pi$
$331$	82.3773			0.248874			0.124437	+	0.992228i	$0.460288\pi$
$332$			19.7828i			0.0595868i
$333$	17.2515			0.0518064
$334$			168.921i			0.505751i
$335$			76.4991i			0.228356i
$336$	−9.57888	−	53.8797i	−0.0285086	−	0.160356i
$337$	298.719			0.886408			0.443204	−	0.896421i	$-0.353842\pi$
$337$	298.719			0.886408			0.443204	+	0.896421i	$0.353842\pi$
$338$	−224.832			−0.665184
$339$			66.9712i			0.197555i
$340$	−18.6905			−0.0549719
$341$		−	424.642i		−	1.24528i
$342$			25.2485i			0.0738260i
$343$	296.318	−	172.756i	0.863900	−	0.503663i
$344$	278.987			0.811008
$345$	137.117			0.397440
$346$		−	424.296i		−	1.22629i
$347$	627.485			1.80831			0.904157	−	0.427201i	$-0.140500\pi$
$347$	627.485			1.80831			0.904157	+	0.427201i	$0.140500\pi$
$348$			117.531i			0.337733i
$349$			152.859i			0.437991i	0.975726	+	0.218995i	$0.0702780\pi$
$349$			152.859i			0.437991i	−0.975726	+	0.218995i	$0.929722\pi$
$350$	−178.698	+	31.7695i	−0.510566	+	0.0907700i
$351$	40.0724			0.114167
$352$	−391.683			−1.11273
$353$		−	563.117i		−	1.59523i	−0.603165	−	0.797616i	$-0.706094\pi$
$353$		−	563.117i		−	1.59523i	0.603165	−	0.797616i	$-0.293906\pi$
$354$	132.964			0.375603
$355$		−	55.5697i		−	0.156534i
$356$		−	372.599i		−	1.04663i
$357$	75.9511	−	13.5028i	0.212748	−	0.0378230i
$358$	33.1592			0.0926235
$359$	−92.6055			−0.257954			−0.128977	−	0.991648i	$-0.541169\pi$
$359$	−92.6055			−0.257954			−0.128977	+	0.991648i	$0.541169\pi$
$360$		−	11.0331i		−	0.0306475i
$361$	−795.321			−2.20310
$362$		−	414.760i		−	1.14575i
$363$			155.072i			0.427196i
$364$	4.09858	+	23.0539i	0.0112598	+	0.0633348i
$365$	−69.7082			−0.190981
$366$	−148.857			−0.406714
$367$		−	52.5421i		−	0.143166i	−0.997435	−	0.0715832i	$-0.977195\pi$
$367$		−	52.5421i		−	0.143166i	0.997435	−	0.0715832i	$-0.0228052\pi$
$368$	46.6794			0.126846
$369$		−	3.52389i		−	0.00954983i
$370$			101.694i			0.274848i
$371$	260.710	−	46.3497i	0.702721	−	0.124932i
$372$	−218.631			−0.587718
$373$	545.226			1.46173			0.730867	−	0.682520i	$-0.239116\pi$
$373$	545.226			1.46173			0.730867	+	0.682520i	$0.239116\pi$
$374$			62.9470i			0.168308i
$375$	−328.580			−0.876214
$376$			613.249i			1.63098i
$377$			26.7754i			0.0710221i
$378$	−43.1664	−	242.804i	−0.114197	−	0.642339i
$379$	−397.991			−1.05011			−0.525054	−	0.851069i	$-0.675955\pi$
$379$	−397.991			−1.05011			−0.525054	+	0.851069i	$0.675955\pi$
$380$	178.228			0.469021
$381$		−	134.536i		−	0.353114i
$382$	−19.5603			−0.0512049
$383$		−	337.086i		−	0.880120i	−0.897968	−	0.440060i	$-0.854957\pi$
$383$		−	337.086i		−	0.880120i	0.897968	−	0.440060i	$-0.145043\pi$
$384$			159.472i			0.415291i
$385$	38.5467	+	216.819i	0.100121	+	0.563166i
$386$	56.0531			0.145215
$387$	−18.4152			−0.0475845
$388$			317.098i			0.817264i
$389$	−365.549			−0.939714			−0.469857	−	0.882743i	$-0.655695\pi$
$389$	−365.549			−0.939714			−0.469857	+	0.882743i	$0.655695\pi$
$390$		−	15.3852i		−	0.0394492i
$391$			65.8012i			0.168290i
$392$	383.504	−	140.812i	0.978327	−	0.359213i
$393$	−214.113			−0.544817
$394$	−280.926			−0.713010
$395$		−	281.641i		−	0.713014i
$396$	15.6950			0.0396338
$397$			33.1806i			0.0835783i	0.999126	+	0.0417892i	$0.0133058\pi$
$397$			33.1806i			0.0835783i	−0.999126	+	0.0417892i	$0.986694\pi$
$398$			70.3861i			0.176850i
$399$	−724.252	+	128.760i	−1.81517	+	0.322706i
$400$	−48.6170			−0.121542
$401$	34.6961			0.0865239			0.0432620	−	0.999064i	$-0.486225\pi$
$401$	34.6961			0.0865239			0.0432620	+	0.999064i	$0.486225\pi$
$402$		−	132.648i		−	0.329971i
$403$	−49.8074			−0.123592
$404$			235.461i			0.582825i
$405$		−	205.949i		−	0.508515i
$406$	162.235	−	28.8426i	0.399594	−	0.0710410i
$407$	−410.132			−1.00769
$408$	91.8818			0.225201
$409$			548.706i			1.34158i	0.741647	+	0.670790i	$0.234045\pi$
$409$			548.706i			1.34158i	−0.741647	+	0.670790i	$0.765955\pi$
$410$	20.7725			0.0506646
$411$		−	489.255i		−	1.19040i
$412$			239.604i			0.581564i
$413$	39.0740	+	219.785i	0.0946103	+	0.532167i
$414$	−13.7008			−0.0330938
$415$	21.8229			0.0525854
$416$			45.9416i			0.110436i
$417$	601.251			1.44185
$418$		−	600.248i		−	1.43600i
$419$		−	53.5633i		−	0.127836i	−0.997955	−	0.0639180i	$-0.979640\pi$
$419$		−	53.5633i		−	0.127836i	0.997955	−	0.0639180i	$-0.0203596\pi$
$420$	111.631	−	19.8462i	0.265789	−	0.0472528i
$421$	−247.910			−0.588860			−0.294430	−	0.955673i	$-0.595130\pi$
$421$	−247.910			−0.588860			−0.294430	+	0.955673i	$0.595130\pi$
$422$	−265.782			−0.629816
$423$		−	40.4790i		−	0.0956952i
$424$	315.394			0.743853
$425$		−	68.5325i		−	0.161253i
$426$			96.3569i			0.226190i
$427$	−43.7448	−	246.057i	−0.102447	−	0.576246i
$428$	−377.845			−0.882816
$429$	62.0486			0.144635
$430$		−	108.553i		−	0.252450i
$431$	−596.642			−1.38432			−0.692160	−	0.721744i	$-0.743341\pi$
$431$	−596.642			−1.38432			−0.692160	+	0.721744i	$0.743341\pi$
$432$		−	66.0577i		−	0.152911i
$433$		−	267.788i		−	0.618449i	−0.950989	−	0.309224i	$-0.899931\pi$
$433$		−	267.788i		−	0.618449i	0.950989	−	0.309224i	$-0.100069\pi$
$434$	53.6530	+	301.789i	0.123624	+	0.695367i
$435$	129.652			0.298050
$436$	154.476			0.354302
$437$		−	627.465i		−	1.43585i
$438$	120.873			0.275965
$439$			624.468i			1.42248i	0.702950	+	0.711239i	$0.251866\pi$
$439$			624.468i			1.42248i	−0.702950	+	0.711239i	$0.748134\pi$
$440$			262.297i			0.596129i
$441$	−25.3142	+	9.29463i	−0.0574017	+	0.0210762i
$442$	7.38324			0.0167042
$443$	520.599			1.17517			0.587583	−	0.809164i	$-0.300080\pi$
$443$	520.599			1.17517			0.587583	+	0.809164i	$0.300080\pi$
$444$			211.161i			0.475587i
$445$	−411.023			−0.923648
$446$			60.2651i			0.135124i
$447$		−	419.023i		−	0.937412i
$448$	348.105	−	61.8871i	0.777019	−	0.138141i
$449$	284.340			0.633274			0.316637	−	0.948547i	$-0.397446\pi$
$449$	284.340			0.633274			0.316637	+	0.948547i	$0.397446\pi$
$450$	14.2695			0.0317100
$451$			83.7756i			0.185755i
$452$	−47.2372			−0.104507
$453$			474.165i			1.04672i
$454$			370.325i			0.815693i
$455$	25.4313	−	4.52125i	0.0558930	−	0.00993682i
$456$	−876.164			−1.92141
$457$	13.4848			0.0295072			0.0147536	−	0.999891i	$-0.495304\pi$
$457$	13.4848			0.0295072			0.0147536	+	0.999891i	$0.495304\pi$
$458$			467.954i			1.02173i
$459$	93.1177			0.202871
$460$			96.7134i			0.210247i
$461$		−	683.135i		−	1.48186i	−0.671585	−	0.740928i	$-0.734386\pi$
$461$		−	683.135i		−	1.48186i	0.671585	−	0.740928i	$-0.265614\pi$
$462$	−66.8393	−	375.960i	−0.144674	−	0.813767i
$463$	−602.288			−1.30084			−0.650419	−	0.759576i	$-0.725407\pi$
$463$	−602.288			−1.30084			−0.650419	+	0.759576i	$0.725407\pi$
$464$	44.1380			0.0951250
$465$			241.178i			0.518662i
$466$	322.989			0.693110
$467$		−	102.311i		−	0.219080i	−0.993982	−	0.109540i	$-0.965062\pi$
$467$		−	102.311i		−	0.219080i	0.993982	−	0.109540i	$-0.0349379\pi$
$468$		−	1.84091i		−	0.00393357i
$469$	219.264	−	38.9814i	0.467513	−	0.0831159i
$470$	238.615			0.507691
$471$	76.1533			0.161684
$472$			265.885i			0.563316i
$473$	437.796			0.925574
$474$			488.360i			1.03030i
$475$			653.510i			1.37581i
$476$	9.52402	+	53.5710i	0.0200084	+	0.112544i
$477$	−20.8183			−0.0436443
$478$	−358.427			−0.749847
$479$		−	381.664i		−	0.796793i	−0.917213	−	0.398397i	$-0.869567\pi$
$479$		−	381.664i		−	0.796793i	0.917213	−	0.398397i	$-0.130433\pi$
$480$	222.458			0.463455
$481$			48.1055i			0.100011i
$482$			329.237i			0.683064i
$483$	−69.8700	−	393.007i	−0.144658	−	0.813680i
$484$	−109.378			−0.225987
$485$	349.799			0.721236
$486$			40.0399i			0.0823865i
$487$	767.974			1.57695			0.788475	−	0.615067i	$-0.210871\pi$
$487$	767.974			1.57695			0.788475	+	0.615067i	$0.210871\pi$
$488$		−	297.668i		−	0.609975i
$489$			601.754i			1.23058i
$490$	−54.7897	−	149.221i	−0.111816	−	0.304533i
$491$	−68.7532			−0.140027			−0.0700134	−	0.997546i	$-0.522304\pi$
$491$	−68.7532			−0.140027			−0.0700134	+	0.997546i	$0.522304\pi$
$492$	43.1327			0.0876682
$493$			62.2188i			0.126204i
$494$	−70.4048			−0.142520
$495$		−	17.3136i		−	0.0349769i
$496$			82.1054i			0.165535i
$497$	−159.275	+	28.3164i	−0.320473	+	0.0569747i
$498$	−37.8406			−0.0759851
$499$	−327.096			−0.655503			−0.327751	−	0.944764i	$-0.606291\pi$
$499$	−327.096			−0.655503			−0.327751	+	0.944764i	$0.606291\pi$
$500$		−	231.760i		−	0.463519i
$501$	386.925			0.772305
$502$			382.605i			0.762162i
$503$		−	336.505i		−	0.668996i	−0.942396	−	0.334498i	$-0.891433\pi$
$503$		−	336.505i		−	0.668996i	0.942396	−	0.334498i	$-0.108567\pi$
$504$	−31.6233	+	5.62209i	−0.0627447	+	0.0111549i
$505$	259.743			0.514343
$506$	325.718			0.643712
$507$			514.993i			1.01577i
$508$	94.8935			0.186798
$509$			103.209i			0.202768i	0.994847	+	0.101384i	$0.0323271\pi$
$509$			103.209i			0.202768i	−0.994847	+	0.101384i	$0.967673\pi$
$510$		−	35.7511i		−	0.0701002i
$511$	35.5209	+	199.799i	0.0695126	+	0.390997i
$512$	160.099			0.312694
$513$	−887.949			−1.73089
$514$			244.827i			0.476317i
$515$	264.314			0.513230
$516$		−	225.404i		−	0.436830i
$517$			962.334i			1.86138i
$518$	291.477	−	51.8197i	0.562698	−	0.100038i
$519$	−971.879			−1.87260
$520$	30.7655			0.0591645
$521$			573.438i			1.10065i	0.834951	+	0.550324i	$0.185496\pi$
$521$			573.438i			1.10065i	−0.834951	+	0.550324i	$0.814504\pi$
$522$	−12.9549			−0.0248178
$523$		−	606.183i		−	1.15905i	−0.814955	−	0.579525i	$-0.803238\pi$
$523$		−	606.183i		−	1.15905i	0.814955	−	0.579525i	$-0.196762\pi$
$524$		−	151.022i		−	0.288209i
$525$	72.7702	+	409.321i	0.138610	+	0.779658i
$526$	304.299			0.578514
$527$	−115.739			−0.219619
$528$		−	102.284i		−	0.193720i
$529$	−188.513			−0.356357
$530$		−	122.719i		−	0.231546i
$531$		−	17.5504i		−	0.0330516i
$532$	−90.8188	−	510.841i	−0.170712	−	0.960227i
$533$	9.82628			0.0184358
$534$	712.707			1.33466
$535$			416.811i			0.779086i
$536$	265.254			0.494878
$537$		−	75.9534i		−	0.141440i
$538$		−	280.391i		−	0.521172i
$539$	601.810	−	220.967i	1.11653	−	0.409957i
$540$	136.863			0.253449
$541$	−605.886			−1.11994			−0.559968	−	0.828514i	$-0.689187\pi$
$541$	−605.886			−1.11994			−0.559968	+	0.828514i	$0.689187\pi$
$542$			575.014i			1.06091i
$543$	−950.036			−1.74961
$544$			106.756i			0.196243i
$545$		−	170.406i		−	0.312671i
$546$	−44.0975	+	7.83978i	−0.0807646	+	0.0143586i
$547$	665.261			1.21620			0.608100	−	0.793861i	$-0.291932\pi$
$547$	665.261			1.21620			0.608100	+	0.793861i	$0.291932\pi$
$548$	345.089			0.629725
$549$			19.6483i			0.0357893i
$550$	−339.238			−0.616797
$551$		−	593.304i		−	1.07678i
$552$		−	475.441i		−	0.861306i
$553$	−807.245	+	143.514i	−1.45976	+	0.259520i
$554$	−270.182			−0.487693
$555$	232.937			0.419706
$556$			424.084i			0.762741i
$557$	702.274			1.26081			0.630407	−	0.776264i	$-0.282888\pi$
$557$	702.274			1.26081			0.630407	+	0.776264i	$0.282888\pi$
$558$		−	24.0987i		−	0.0431876i
$559$		−	51.3504i		−	0.0918612i
$560$	−7.45309	−	41.9224i	−0.0133091	−	0.0748614i
$561$	144.184			0.257013
$562$	116.043			0.206482
$563$		−	326.661i		−	0.580215i	−0.956994	−	0.290107i	$-0.906309\pi$
$563$		−	326.661i		−	0.580215i	0.956994	−	0.290107i	$-0.0936910\pi$
$564$	495.468			0.878489
$565$			52.1086i			0.0922276i
$566$			317.044i			0.560149i
$567$	−590.295	+	104.944i	−1.04108	+	0.185087i
$568$	−192.683			−0.339231
$569$	−741.803			−1.30370			−0.651848	−	0.758350i	$-0.726006\pi$
$569$	−741.803			−1.30370			−0.651848	+	0.758350i	$0.726006\pi$
$570$			340.914i			0.598095i
$571$	−227.796			−0.398942			−0.199471	−	0.979904i	$-0.563922\pi$
$571$	−227.796			−0.398942			−0.199471	+	0.979904i	$0.563922\pi$
$572$			43.7651i			0.0765125i
$573$			44.8042i			0.0781923i
$574$	−10.5850	−	59.5387i	−0.0184407	−	0.103726i
$575$	−354.620			−0.616731
$576$	−27.7971			−0.0482588
$577$		−	161.675i		−	0.280199i	−0.990137	−	0.140099i	$-0.955258\pi$
$577$		−	161.675i		−	0.280199i	0.990137	−	0.140099i	$-0.0447422\pi$
$578$	−372.753			−0.644901
$579$		−	128.393i		−	0.221750i
$580$			91.4480i			0.157669i
$581$	−11.1202	−	62.5494i	−0.0191398	−	0.107658i
$582$	−606.546			−1.04218
$583$	494.928			0.848932
$584$			241.707i			0.413883i
$585$	−2.03076			−0.00347138
$586$		−	256.221i		−	0.437237i
$587$			53.7343i			0.0915405i	0.998952	+	0.0457703i	$0.0145742\pi$
$587$			53.7343i			0.0915405i	−0.998952	+	0.0457703i	$0.985426\pi$
$588$	−113.767	−	309.848i	−0.193482	−	0.526952i
$589$	1103.66			1.87379
$590$	103.456			0.175349
$591$			643.480i			1.08880i
$592$	79.2998			0.133952
$593$			578.176i			0.975002i	0.873122	+	0.487501i	$0.162092\pi$
$593$			578.176i			0.975002i	−0.873122	+	0.487501i	$0.837908\pi$
$594$		−	460.936i		−	0.775986i
$595$	59.0956	−	10.5062i	0.0993203	−	0.0176575i
$596$	295.552			0.495893
$597$	161.224			0.270057
$598$		−	38.2044i		−	0.0638870i
$599$	−70.8502			−0.118281			−0.0591404	−	0.998250i	$-0.518836\pi$
$599$	−70.8502			−0.118281			−0.0591404	+	0.998250i	$0.518836\pi$
$600$			495.176i			0.825293i
$601$			354.094i			0.589174i	0.955625	+	0.294587i	$0.0951821\pi$
$601$			354.094i			0.589174i	−0.955625	+	0.294587i	$0.904818\pi$
$602$	−311.139	+	55.3151i	−0.516841	+	0.0918856i
$603$	−17.5088			−0.0290361
$604$	−334.446			−0.553718
$605$			120.658i			0.199434i
$606$	−450.390			−0.743219
$607$		−	921.830i		−	1.51867i	−0.650703	−	0.759333i	$-0.725526\pi$
$607$		−	921.830i		−	1.51867i	0.650703	−	0.759333i	$-0.274474\pi$
$608$		−	1018.00i		−	1.67434i
$609$	−66.0661	−	371.611i	−0.108483	−	0.610198i
$610$	−115.822			−0.189873
$611$	112.875			0.184738
$612$		−	4.27779i		−	0.00698985i
$613$	928.461			1.51462			0.757309	−	0.653056i	$-0.226514\pi$
$613$	928.461			1.51462			0.757309	+	0.653056i	$0.226514\pi$
$614$			705.728i			1.14939i
$615$		−	47.5808i		−	0.0773672i
$616$	751.801	−	133.657i	1.22046	−	0.216976i
$617$	485.724			0.787235			0.393617	−	0.919274i	$-0.371223\pi$
$617$	485.724			0.787235			0.393617	+	0.919274i	$0.371223\pi$
$618$	−458.315			−0.741611
$619$			1198.74i			1.93658i	0.249829	+	0.968290i	$0.419626\pi$
$619$			1198.74i			1.93658i	−0.249829	+	0.968290i	$0.580374\pi$
$620$	−170.111			−0.274373
$621$		−	481.836i		−	0.775903i
$622$		−	366.520i		−	0.589261i
$623$	209.443	+	1178.09i	0.336185	+	1.89099i
$624$	−11.9972			−0.0192263
$625$	224.796			0.359673
$626$			333.816i			0.533252i
$627$	−1374.91			−2.19284
$628$			53.7137i			0.0855314i
$629$			111.784i			0.177718i
$630$	2.18755	+	12.3046i	0.00347230	+	0.0195311i
$631$	353.959			0.560950			0.280475	−	0.959861i	$-0.409508\pi$
$631$	353.959			0.560950			0.280475	+	0.959861i	$0.409508\pi$
$632$	−976.565			−1.54520
$633$			608.793i			0.961758i
$634$	826.838			1.30416
$635$		−	104.679i		−	0.164849i
$636$		−	254.819i		−	0.400658i
$637$	−25.9179	−	70.5880i	−0.0406874	−	0.110813i
$638$	307.985			0.482735
$639$	12.7185			0.0199038
$640$			124.081i			0.193877i
$641$	940.400			1.46708			0.733541	−	0.679645i	$-0.237866\pi$
$641$	940.400			1.46708			0.733541	+	0.679645i	$0.237866\pi$
$642$		−	722.743i		−	1.12577i
$643$			56.2634i			0.0875014i	0.999042	+	0.0437507i	$0.0139307\pi$
$643$			56.2634i			0.0875014i	−0.999042	+	0.0437507i	$0.986069\pi$
$644$	277.202	−	49.2819i	0.430439	−	0.0765246i
$645$	−248.649			−0.385502
$646$	−163.602			−0.253254
$647$		−	215.727i		−	0.333426i	−0.986005	−	0.166713i	$-0.946685\pi$
$647$		−	215.727i		−	0.333426i	0.986005	−	0.166713i	$-0.0533153\pi$
$648$	−714.110			−1.10202
$649$			417.237i			0.642892i
$650$			39.7902i			0.0612157i
$651$	691.269	−	122.896i	1.06186	−	0.188780i
$652$	−424.439			−0.650980
$653$	−722.459			−1.10637			−0.553184	−	0.833059i	$-0.686587\pi$
$653$	−722.459			−1.10637			−0.553184	+	0.833059i	$0.686587\pi$
$654$			295.481i			0.451806i
$655$	−166.596			−0.254345
$656$		−	16.1982i		−	0.0246924i
$657$		−	15.9545i		−	0.0242839i
$658$	−121.590	−	683.923i	−0.184787	−	1.03940i
$659$	−488.531			−0.741321			−0.370661	−	0.928768i	$-0.620869\pi$
$659$	−488.531			−0.741321			−0.370661	+	0.928768i	$0.620869\pi$
$660$	211.920			0.321090
$661$			483.351i			0.731242i	0.930764	+	0.365621i	$0.119143\pi$
$661$			483.351i			0.731242i	−0.930764	+	0.365621i	$0.880857\pi$
$662$	−111.141			−0.167887
$663$		−	16.9118i		−	0.0255080i
$664$		−	75.6692i		−	0.113960i
$665$	−563.522	+	100.185i	−0.847401	+	0.150653i
$666$	−23.2752			−0.0349478
$667$	321.950			0.482684
$668$			272.912i			0.408551i
$669$	138.041			0.206340
$670$		−	103.210i		−	0.154045i
$671$		−	467.112i		−	0.696143i
$672$	−113.357	−	637.616i	−0.168686	−	0.948833i
$673$	−675.889			−1.00429			−0.502147	−	0.864782i	$-0.667456\pi$
$673$	−675.889			−1.00429			−0.502147	+	0.864782i	$0.667456\pi$
$674$	−403.023			−0.597957
$675$			501.836i			0.743461i
$676$	−363.244			−0.537343
$677$		−	443.716i		−	0.655414i	−0.944779	−	0.327707i	$-0.893724\pi$
$677$		−	443.716i		−	0.655414i	0.944779	−	0.327707i	$-0.106276\pi$
$678$		−	90.3554i		−	0.133268i
$679$	−178.246	−	1002.60i	−0.262512	−	1.47659i
$680$	71.4909			0.105134
$681$	848.254			1.24560
$682$			572.913i			0.840048i
$683$	−363.421			−0.532096			−0.266048	−	0.963960i	$-0.585718\pi$
$683$	−363.421			−0.532096			−0.266048	+	0.963960i	$0.585718\pi$
$684$			40.7920i			0.0596374i
$685$		−	380.677i		−	0.555733i
$686$	−399.782	+	233.078i	−0.582773	+	0.339763i
$687$	1071.88			1.56023
$688$	−84.6489			−0.123036
$689$		−	58.0515i		−	0.0842547i
$690$	−184.994			−0.268107
$691$		−	517.562i		−	0.749005i	−0.927226	−	0.374502i	$-0.877814\pi$
$691$		−	517.562i		−	0.749005i	0.927226	−	0.374502i	$-0.122186\pi$
$692$		−	685.502i		−	0.990609i
$693$	−49.6245	+	8.82239i	−0.0716083	+	0.0127307i
$694$	−846.582			−1.21986
$695$	467.818			0.673120
$696$		−	449.556i		−	0.645914i
$697$	22.8337			0.0327599
$698$		−	206.232i		−	0.295462i
$699$		−	739.829i		−	1.05841i
$700$	−288.709	+	51.3275i	−0.412441	+	0.0733250i
$701$	962.239			1.37267			0.686333	−	0.727287i	$-0.259219\pi$
$701$	962.239			1.37267			0.686333	+	0.727287i	$0.259219\pi$
$702$	−54.0645			−0.0770149
$703$		−	1065.95i		−	1.51629i
$704$	660.837			0.938689
$705$		−	546.563i		−	0.775267i
$706$			759.740i			1.07612i
$707$	−132.356	−	744.483i	−0.187208	−	1.05302i
$708$	214.819			0.303416
$709$	−942.231			−1.32896			−0.664479	−	0.747307i	$-0.731346\pi$
$709$	−942.231			−1.32896			−0.664479	+	0.747307i	$0.731346\pi$
$710$			74.9729i			0.105596i
$711$	64.4606			0.0906619
$712$			1425.19i			2.00167i
$713$			598.891i			0.839959i
$714$	−102.471	+	18.2175i	−0.143516	+	0.0255148i
$715$	48.2785			0.0675223
$716$	53.5727			0.0748222
$717$			821.001i			1.14505i
$718$	124.940			0.174012
$719$			240.490i			0.334479i	0.985916	+	0.167239i	$0.0534852\pi$
$719$			240.490i			0.334479i	−0.985916	+	0.167239i	$0.946515\pi$
$720$			3.34761i			0.00464946i
$721$	−134.685	−	757.582i	−0.186803	−	1.05074i
$722$	1073.02			1.48618
$723$	754.140			1.04307
$724$		−	670.095i		−	0.925545i
$725$	−335.314			−0.462502
$726$		−	209.218i		−	0.288179i
$727$			216.947i			0.298414i	0.988806	+	0.149207i	$0.0476721\pi$
$727$			216.947i			0.298414i	−0.988806	+	0.149207i	$0.952328\pi$
$728$	−15.6771	−	88.1810i	−0.0215344	−	0.121128i
$729$	−679.138			−0.931602
$730$	94.0481			0.128833
$731$		−	119.325i		−	0.163235i
$732$	−240.497			−0.328548
$733$		−	381.819i		−	0.520899i	−0.965488	−	0.260449i	$-0.916129\pi$
$733$		−	381.819i		−	0.520899i	0.965488	−	0.260449i	$-0.0838707\pi$
$734$			70.8881i			0.0965778i
$735$	−341.801	+	125.499i	−0.465036	+	0.170748i
$736$	552.407			0.750553
$737$	416.247			0.564786
$738$			4.75432i			0.00644216i
$739$	4.99753			0.00676256			0.00338128	−	0.999994i	$-0.498924\pi$
$739$	4.99753			0.00676256			0.00338128	+	0.999994i	$0.498924\pi$
$740$			164.299i			0.222025i
$741$			161.267i			0.217634i
$742$	−351.741	+	62.5336i	−0.474045	+	0.0842770i
$743$	−524.544			−0.705982			−0.352991	−	0.935627i	$-0.614835\pi$
$743$	−524.544			−0.705982			−0.352991	+	0.935627i	$0.614835\pi$
$744$	836.263			1.12401
$745$		−	326.031i		−	0.437626i
$746$	−735.602			−0.986062
$747$			4.99474i			0.00668639i
$748$			101.699i			0.135961i
$749$	1194.67	−	212.393i	1.59502	−	0.283568i
$750$	443.310			0.591080
$751$	−615.493			−0.819564			−0.409782	−	0.912183i	$-0.634395\pi$
$751$	−615.493			−0.819564			−0.409782	+	0.912183i	$0.634395\pi$
$752$		−	186.069i		−	0.247433i
$753$	876.383			1.16386
$754$		−	36.1245i		−	0.0479104i
$755$			368.936i			0.488656i
$756$	−69.7405	−	392.279i	−0.0922494	−	0.518888i
$757$	729.556			0.963747			0.481873	−	0.876241i	$-0.339956\pi$
$757$	729.556			0.963747			0.481873	+	0.876241i	$0.339956\pi$
$758$	536.957			0.708386
$759$		−	746.080i		−	0.982978i
$760$	−681.721			−0.897001
$761$		−	502.495i		−	0.660309i	−0.943927	−	0.330154i	$-0.892899\pi$
$761$		−	502.495i		−	0.660309i	0.943927	−	0.330154i	$-0.107101\pi$
$762$			181.512i			0.238205i
$763$	−488.422	+	86.8330i	−0.640133	+	0.113805i
$764$	−31.6020			−0.0413639
$765$	−4.71894			−0.00616854
$766$			454.786i			0.593715i
$767$	48.9389			0.0638056
$768$		−	839.519i		−	1.09312i
$769$			683.025i			0.888199i	0.895977	+	0.444099i	$0.146476\pi$
$769$			683.025i			0.888199i	−0.895977	+	0.444099i	$0.853524\pi$
$770$	−52.0060	−	292.525i	−0.0675402	−	0.379903i
$771$	560.793			0.727358
$772$	90.5605			0.117306
$773$			795.345i			1.02891i	0.857518	+	0.514453i	$0.172005\pi$
$773$			795.345i			1.02891i	−0.857518	+	0.514453i	$0.827995\pi$
$774$	24.8452			0.0320998
$775$		−	623.749i		−	0.804838i
$776$		−	1212.90i		−	1.56301i
$777$	−118.697	−	667.649i	−0.152763	−	0.859265i
$778$	493.187			0.633916
$779$	−217.736			−0.279508
$780$		−	24.8567i		−	0.0318675i
$781$	−302.366			−0.387152
$782$		−	88.7769i		−	0.113525i
$783$		−	455.603i		−	0.581869i
$784$	−116.361	+	42.7245i	−0.148420	+	0.0544955i
$785$	59.2530			0.0754815
$786$	288.874			0.367525
$787$			586.173i			0.744820i	0.928068	+	0.372410i	$0.121468\pi$
$787$			586.173i			0.744820i	−0.928068	+	0.372410i	$0.878532\pi$
$788$	−453.870			−0.575977
$789$		−	697.017i		−	0.883418i
$790$			379.980i			0.480988i
$791$	149.355	−	26.5527i	0.188818	−	0.0335686i
$792$	−60.0333			−0.0757996
$793$	−54.7889			−0.0690906
$794$		−	44.7662i		−	0.0563806i
$795$	−281.097			−0.353581
$796$			113.717i			0.142861i
$797$		−	905.186i		−	1.13574i	−0.823118	−	0.567871i	$-0.807767\pi$
$797$		−	905.186i		−	1.13574i	0.823118	−	0.567871i	$-0.192233\pi$
$798$	977.137	−	173.718i	1.22448	−	0.217692i
$799$	262.291			0.328274
$800$	−575.336			−0.719171
$801$		−	94.0732i		−	0.117445i
$802$	−46.8109			−0.0583677
$803$			379.296i			0.472349i
$804$		−	214.309i		−	0.266554i
$805$	−54.3641	−	305.789i	−0.0675330	−	0.379862i
$806$	67.1986			0.0833730
$807$	−642.254			−0.795854
$808$		−	900.638i		−	1.11465i
$809$	−973.844			−1.20376			−0.601881	−	0.798586i	$-0.705582\pi$
$809$	−973.844			−1.20376			−0.601881	+	0.798586i	$0.705582\pi$
$810$			277.859i			0.343036i
$811$			835.800i			1.03058i	0.857016	+	0.515289i	$0.172316\pi$
$811$			835.800i			1.03058i	−0.857016	+	0.515289i	$0.827684\pi$
$812$	262.111	−	46.5988i	0.322796	−	0.0573877i
$813$	1317.11			1.62006
$814$	553.337			0.679775
$815$			468.209i			0.574490i
$816$	−27.8784			−0.0341647
$817$			1137.85i			1.39272i
$818$		−	740.297i		−	0.905009i
$819$	1.03480	+	5.82060i	0.00126350	+	0.00710696i
$820$	33.5605			0.0409274
$821$	−254.360			−0.309818			−0.154909	−	0.987929i	$-0.549508\pi$
$821$	−254.360			−0.309818			−0.154909	+	0.987929i	$0.549508\pi$
$822$			660.088i			0.803026i
$823$	1545.82			1.87828			0.939138	−	0.343540i	$-0.111626\pi$
$823$	1545.82			1.87828			0.939138	+	0.343540i	$0.111626\pi$
$824$		−	916.486i		−	1.11224i
$825$			777.049i			0.941877i
$826$	−52.7174	−	296.527i	−0.0638226	−	0.358992i
$827$	841.481			1.01751			0.508755	−	0.860911i	$-0.330106\pi$
$827$	841.481			1.01751			0.508755	+	0.860911i	$0.330106\pi$
$828$	−22.1353			−0.0267335
$829$		−	1588.28i		−	1.91590i	−0.286942	−	0.957948i	$-0.592639\pi$
$829$		−	1588.28i		−	1.91590i	0.286942	−	0.957948i	$-0.407361\pi$
$830$	−29.4428			−0.0354733
$831$			618.870i			0.744729i
$832$		−	77.5115i		−	0.0931629i
$833$	−60.2262	−	164.028i	−0.0723004	−	0.196912i
$834$	−811.189			−0.972649
$835$	301.057			0.360547
$836$		−	969.774i		−	1.16002i
$837$	847.512			1.01256
$838$			72.2658i			0.0862361i
$839$			897.223i			1.06940i	0.845043	+	0.534698i	$0.179575\pi$
$839$			897.223i			1.06940i	−0.845043	+	0.534698i	$0.820425\pi$
$840$	−426.990	+	75.9115i	−0.508321	+	0.0903709i
$841$	−536.578			−0.638024
$842$	334.472			0.397236
$843$		−	265.804i		−	0.315307i
$844$	−429.404			−0.508772
$845$			400.703i			0.474205i
$846$			54.6130i			0.0645544i
$847$	345.832	−	61.4830i	0.408302	−	0.0725891i
$848$	−95.6953			−0.112848
$849$	726.211			0.855372
$850$			92.4619i			0.108779i
$851$	578.427			0.679702
$852$			155.676i			0.182719i
$853$		−	151.161i		−	0.177211i	−0.996067	−	0.0886057i	$-0.971759\pi$
$853$		−	151.161i		−	0.177211i	0.996067	−	0.0886057i	$-0.0282411\pi$
$854$	59.0191	+	331.973i	0.0691090	+	0.388727i
$855$	44.9987			0.0526300
$856$	1445.26			1.68838
$857$			1092.20i			1.27445i	0.770680	+	0.637223i	$0.219917\pi$
$857$			1092.20i			1.27445i	−0.770680	+	0.637223i	$0.780083\pi$
$858$	−83.7140			−0.0975688
$859$		−	468.084i		−	0.544917i	−0.962168	−	0.272458i	$-0.912163\pi$
$859$		−	468.084i		−	0.544917i	0.962168	−	0.272458i	$-0.0878367\pi$
$860$		−	175.381i		−	0.203932i
$861$	−136.377	+	24.2456i	−0.158394	+	0.0281598i
$862$	804.970			0.933840
$863$	−16.1995			−0.0187711			−0.00938555	−	0.999956i	$-0.502988\pi$
$863$	−16.1995			−0.0187711			−0.00938555	+	0.999956i	$0.502988\pi$
$864$		−	781.731i		−	0.904781i
$865$	−756.195			−0.874213
$866$			361.291i			0.417196i
$867$			853.816i			0.984794i
$868$	86.6829	+	487.577i	0.0998651	+	0.561725i
$869$	−1532.46			−1.76348
$870$	−174.922			−0.201060
$871$		−	48.8228i		−	0.0560538i
$872$	−590.868			−0.677601
$873$			80.0605i			0.0917073i
$874$			846.556i			0.968600i
$875$	130.276	+	732.779i	0.148886	+	0.837462i
$876$	195.285			0.222928
$877$	−1714.50			−1.95496			−0.977479	−	0.211033i	$-0.932317\pi$
$877$	−1714.50			−1.95496			−0.977479	+	0.211033i	$0.932317\pi$
$878$		−	842.512i		−	0.959581i
$879$	−586.891			−0.667681
$880$		−	79.5849i		−	0.0904374i
$881$		−	537.148i		−	0.609702i	−0.952400	−	0.304851i	$-0.901393\pi$
$881$		−	537.148i		−	0.609702i	0.952400	−	0.304851i	$-0.0986067\pi$
$882$	34.1531	−	12.5400i	0.0387223	−	0.0142177i
$883$	−1073.87			−1.21616			−0.608082	−	0.793875i	$-0.708061\pi$
$883$	−1073.87			−1.21616			−0.608082	+	0.793875i	$0.708061\pi$
$884$	11.9285			0.0134938
$885$		−	236.972i		−	0.267765i
$886$	−702.375			−0.792748
$887$			467.411i			0.526957i	0.964665	+	0.263479i	$0.0848698\pi$
$887$			467.411i			0.526957i	−0.964665	+	0.263479i	$0.915130\pi$
$888$		−	807.688i		−	0.909559i
$889$	−300.035	+	53.3411i	−0.337497	+	0.0600012i
$890$	554.540			0.623078
$891$	−1120.61			−1.25770
$892$			97.3656i			0.109154i
$893$	−2501.15			−2.80084
$894$			565.333i			0.632363i
$895$		−	59.0974i		−	0.0660307i
$896$	355.644	−	63.2274i	0.396924	−	0.0705663i
$897$	−87.5099			−0.0975584
$898$	−383.622			−0.427196
$899$			566.285i			0.629905i
$900$	23.0541			0.0256157
$901$		−	134.896i		−	0.149718i
$902$		−	113.027i		−	0.125307i
$903$	126.703	+	712.684i	0.140313	+	0.789240i
$904$	180.682			0.199870
$905$	−739.199			−0.816794
$906$		−	639.728i		−	0.706102i
$907$	820.821			0.904985			0.452493	−	0.891768i	$-0.350535\pi$
$907$	820.821			0.904985			0.452493	+	0.891768i	$0.350535\pi$
$908$			598.305i			0.658926i
$909$			59.4489i			0.0654003i
$910$	−34.3111	+	6.09993i	−0.0377045	+	0.00670322i
$911$	−523.800			−0.574973			−0.287486	−	0.957785i	$-0.592820\pi$
$911$	−523.800			−0.574973			−0.287486	+	0.957785i	$0.592820\pi$
$912$	265.842			0.291493
$913$		−	118.743i		−	0.130058i
$914$	−18.1932			−0.0199051
$915$			265.299i			0.289944i
$916$			756.036i			0.825367i
$917$	84.8916	+	477.501i	0.0925753	+	0.520721i
$918$	−125.631			−0.136853
$919$	616.337			0.670660			0.335330	−	0.942101i	$-0.391152\pi$
$919$	616.337			0.670660			0.335330	+	0.942101i	$0.391152\pi$
$920$		−	369.929i		−	0.402096i
$921$	1616.52			1.75518
$922$			921.665i			0.999636i
$923$			35.4654i			0.0384240i
$924$	−107.987	−	607.409i	−0.116869	−	0.657370i
$925$	−602.436			−0.651282
$926$	812.588			0.877524
$927$			60.4949i			0.0652588i
$928$	522.332			0.562858
$929$			1189.58i			1.28050i	0.768167	+	0.640250i	$0.221169\pi$
$929$			1189.58i			1.28050i	−0.768167	+	0.640250i	$0.778831\pi$
$930$		−	325.389i		−	0.349881i
$931$	574.303	+	1564.13i	0.616867	+	1.68005i
$932$	521.828			0.559902
$933$	−839.540			−0.899828
$934$			138.034i			0.147788i
$935$	112.186			0.119985
$936$			7.04148i			0.00752295i
$937$			1714.56i			1.82984i	0.403641	+	0.914918i	$0.367745\pi$
$937$			1714.56i			1.82984i	−0.403641	+	0.914918i	$0.632255\pi$
$938$	−295.824	+	52.5924i	−0.315377	+	0.0560687i
$939$	764.628			0.814301
$940$	385.511			0.410118
$941$			1220.01i			1.29651i	0.761424	+	0.648254i	$0.224500\pi$
$941$			1220.01i			1.29651i	−0.761424	+	0.648254i	$0.775500\pi$
$942$	−102.744			−0.109070
$943$		−	118.152i		−	0.125294i
$944$		−	80.6737i		−	0.0854594i
$945$	−432.733	+	76.9326i	−0.457919	+	0.0814101i
$946$	−590.661			−0.624377
$947$	536.061			0.566062			0.283031	−	0.959111i	$-0.408660\pi$
$947$	536.061			0.566062			0.283031	+	0.959111i	$0.408660\pi$
$948$			789.005i			0.832283i
$949$	44.4888			0.0468796
$950$		−	881.695i		−	0.928100i
$951$		−	1893.93i		−	1.99151i
$952$	−36.4293	−	204.909i	−0.0382661	−	0.215241i
$953$	−445.294			−0.467255			−0.233628	−	0.972326i	$-0.575060\pi$
$953$	−445.294			−0.467255			−0.233628	+	0.972326i	$0.575060\pi$
$954$	28.0874			0.0294418
$955$			34.8610i			0.0365036i
$956$	−579.082			−0.605734
$957$		−	705.461i		−	0.737159i
$958$			514.929i			0.537504i
$959$	−1091.11	+	193.980i	−1.13775	+	0.202273i
$960$	−375.326			−0.390965
$961$	−92.4015			−0.0961514
$962$		−	64.9024i		−	0.0674662i
$963$	−95.3978			−0.0990631
$964$			531.922i			0.551787i
$965$		−	99.8996i		−	0.103523i
$966$	94.2664	+	530.233i	0.0975843	+	0.548896i
$967$	−1115.34			−1.15341			−0.576704	−	0.816953i	$-0.695661\pi$
$967$	−1115.34			−1.15341			−0.576704	+	0.816953i	$0.695661\pi$
$968$	418.370			0.432201
$969$			374.742i			0.386730i
$970$	−471.938			−0.486534
$971$		−	464.288i		−	0.478154i	−0.971001	−	0.239077i	$-0.923155\pi$
$971$		−	464.288i		−	0.478154i	0.971001	−	0.239077i	$-0.0768448\pi$
$972$			64.6892i			0.0665527i
$973$	−238.384	−	1340.87i	−0.244999	−	1.37808i
$974$	−1036.13			−1.06378
$975$	91.1423			0.0934792
$976$			90.3171i			0.0925380i
$977$	358.464			0.366902			0.183451	−	0.983029i	$-0.441273\pi$
$977$	358.464			0.366902			0.183451	+	0.983029i	$0.441273\pi$
$978$		−	811.867i		−	0.830130i
$979$			2236.46i			2.28443i
$980$	−88.5194	−	241.085i	−0.0903259	−	0.246005i
$981$	39.0017			0.0397571
$982$	92.7596			0.0944599
$983$			392.990i			0.399786i	0.979818	+	0.199893i	$0.0640595\pi$
$983$			392.990i			0.399786i	−0.979818	+	0.199893i	$0.935940\pi$
$984$	−164.983			−0.167665
$985$			500.676i			0.508300i
$986$		−	83.9436i		−	0.0851355i
$987$	−1566.57	+	278.510i	−1.58721	+	0.282178i
$988$	−113.748			−0.115129
$989$	−617.443			−0.624311
$990$			23.3589i			0.0235948i
$991$	−398.689			−0.402310			−0.201155	−	0.979559i	$-0.564469\pi$
$991$	−398.689			−0.402310			−0.201155	+	0.979559i	$0.564469\pi$
$992$			971.641i			0.979476i
$993$			254.576i			0.256370i
$994$	214.889	−	38.2036i	0.216186	−	0.0384342i
$995$	125.444			0.126075
$996$	−61.1361			−0.0613816
$997$			22.5994i			0.0226674i	0.999936	+	0.0113337i	$0.00360771\pi$
$997$			22.5994i			0.0226674i	−0.999936	+	0.0113337i	$0.996392\pi$
$998$	441.307			0.442192
$999$		−	818.552i		−	0.819372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.b.a.83.20	yes	52
7.6	odd	2	inner	287.3.b.a.83.19	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.b.a.83.19	✓	52	7.6	odd	2	inner
287.3.b.a.83.20	yes	52	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.34917 q^{2} +3.09036i q^{3} -2.17974 q^{4} +2.40453i q^{5} -4.16942i q^{6} +(6.89193 - 1.22527i) q^{7} +8.33752 q^{8} -0.550339 q^{9} +O(q^{10})\)	\(q-1.34917 q^{2} +3.09036i q^{3} -2.17974 q^{4} +2.40453i q^{5} -4.16942i q^{6} +(6.89193 - 1.22527i) q^{7} +8.33752 q^{8} -0.550339 q^{9} -3.24412i q^{10} +13.0835 q^{11} -6.73620i q^{12} -1.53461i q^{13} +(-9.29838 + 1.65309i) q^{14} -7.43088 q^{15} -2.52973 q^{16} -3.56602i q^{17} +0.742499 q^{18} +34.0047i q^{19} -5.24127i q^{20} +(3.78652 + 21.2986i) q^{21} -17.6519 q^{22} -18.4523 q^{23} +25.7659i q^{24} +19.2182 q^{25} +2.07044i q^{26} +26.1125i q^{27} +(-15.0227 + 2.67077i) q^{28} -17.4477 q^{29} +10.0255 q^{30} -32.4561i q^{31} -29.9370 q^{32} +40.4329i q^{33} +4.81116i q^{34} +(2.94620 + 16.5719i) q^{35} +1.19960 q^{36} -31.3471 q^{37} -45.8781i q^{38} +4.74249 q^{39} +20.0478i q^{40} +6.40312i q^{41} +(-5.10865 - 28.7353i) q^{42} +33.4616 q^{43} -28.5188 q^{44} -1.32331i q^{45} +24.8953 q^{46} +73.5530i q^{47} -7.81779i q^{48} +(45.9974 - 16.8889i) q^{49} -25.9286 q^{50} +11.0203 q^{51} +3.34505i q^{52} +37.8282 q^{53} -35.2302i q^{54} +31.4598i q^{55} +(57.4616 - 10.2157i) q^{56} -105.087 q^{57} +23.5399 q^{58} +31.8902i q^{59} +16.1974 q^{60} -35.7022i q^{61} +43.7888i q^{62} +(-3.79290 + 0.674312i) q^{63} +50.5090 q^{64} +3.69001 q^{65} -54.5508i q^{66} +31.8146 q^{67} +7.77301i q^{68} -57.0243i q^{69} +(-3.97491 - 22.3582i) q^{70} -23.1104 q^{71} -4.58846 q^{72} +28.9903i q^{73} +42.2926 q^{74} +59.3913i q^{75} -74.1216i q^{76} +(90.1709 - 16.0308i) q^{77} -6.39842 q^{78} -117.129 q^{79} -6.08282i q^{80} -85.6502 q^{81} -8.63889i q^{82} -9.07575i q^{83} +(-8.25365 - 46.4254i) q^{84} +8.57461 q^{85} -45.1453 q^{86} -53.9197i q^{87} +109.084 q^{88} +170.937i q^{89} +1.78536i q^{90} +(-1.88030 - 10.5764i) q^{91} +40.2213 q^{92} +100.301 q^{93} -99.2354i q^{94} -81.7654 q^{95} -92.5163i q^{96} -145.475i q^{97} +(-62.0583 + 22.7860i) q^{98} -7.20038 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 2 q^{2} + 90 q^{4} + 12 q^{7} - 2 q^{8} - 140 q^{9}+O(q^{10}) \) 52 * q + 2 * q^2 + 90 * q^4 + 12 * q^7 - 2 * q^8 - 140 * q^9	\( 52 q + 2 q^{2} + 90 q^{4} + 12 q^{7} - 2 q^{8} - 140 q^{9} + 24 q^{11} - 14 q^{14} + 44 q^{15} + 194 q^{16} + 70 q^{18} - 16 q^{21} - 48 q^{22} - 80 q^{23} - 304 q^{25} + 64 q^{28} - 12 q^{29} + 64 q^{30} - 166 q^{32} + 30 q^{35} - 70 q^{36} + 36 q^{37} - 68 q^{39} + 164 q^{42} - 172 q^{43} + 72 q^{44} + 68 q^{46} - 172 q^{49} - 234 q^{50} + 156 q^{51} + 64 q^{53} - 234 q^{56} + 140 q^{57} - 556 q^{58} + 152 q^{60} - 130 q^{63} + 334 q^{64} - 76 q^{65} + 160 q^{67} + 202 q^{70} - 408 q^{71} - 40 q^{72} + 398 q^{74} - 248 q^{77} + 390 q^{78} + 264 q^{79} - 116 q^{81} - 418 q^{84} + 232 q^{85} + 368 q^{86} - 220 q^{88} + 32 q^{91} - 74 q^{92} + 240 q^{93} - 44 q^{95} + 838 q^{98} - 24 q^{99}+O(q^{100}) \) 52 * q + 2 * q^2 + 90 * q^4 + 12 * q^7 - 2 * q^8 - 140 * q^9 + 24 * q^11 - 14 * q^14 + 44 * q^15 + 194 * q^16 + 70 * q^18 - 16 * q^21 - 48 * q^22 - 80 * q^23 - 304 * q^25 + 64 * q^28 - 12 * q^29 + 64 * q^30 - 166 * q^32 + 30 * q^35 - 70 * q^36 + 36 * q^37 - 68 * q^39 + 164 * q^42 - 172 * q^43 + 72 * q^44 + 68 * q^46 - 172 * q^49 - 234 * q^50 + 156 * q^51 + 64 * q^53 - 234 * q^56 + 140 * q^57 - 556 * q^58 + 152 * q^60 - 130 * q^63 + 334 * q^64 - 76 * q^65 + 160 * q^67 + 202 * q^70 - 408 * q^71 - 40 * q^72 + 398 * q^74 - 248 * q^77 + 390 * q^78 + 264 * q^79 - 116 * q^81 - 418 * q^84 + 232 * q^85 + 368 * q^86 - 220 * q^88 + 32 * q^91 - 74 * q^92 + 240 * q^93 - 44 * q^95 + 838 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

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