LMFDB - Embedded newform 690.3.b.a.599.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(599,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("690.599");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.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:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			599.8
Character	$\chi$	$=$	690.599
Dual form			690.3.b.a.599.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +(-2.76001 + 1.17574i) q^{3} +2.00000 q^{4} +(-2.52270 + 4.31694i) q^{5} +(3.90324 - 1.66274i) q^{6} +6.80400i q^{7} -2.82843 q^{8} +(6.23528 - 6.49009i) q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +(-2.76001 + 1.17574i) q^{3} +2.00000 q^{4} +(-2.52270 + 4.31694i) q^{5} +(3.90324 - 1.66274i) q^{6} +6.80400i q^{7} -2.82843 q^{8} +(6.23528 - 6.49009i) q^{9} +(3.56764 - 6.10507i) q^{10} -9.88220i q^{11} +(-5.52002 + 2.35147i) q^{12} +4.88365i q^{13} -9.62230i q^{14} +(1.88710 - 14.8808i) q^{15} +4.00000 q^{16} +23.8286 q^{17} +(-8.81802 + 9.17837i) q^{18} +36.4177 q^{19} +(-5.04541 + 8.63388i) q^{20} +(-7.99971 - 18.7791i) q^{21} +13.9755i q^{22} +4.79583 q^{23} +(7.80648 - 3.32549i) q^{24} +(-12.2719 - 21.7807i) q^{25} -6.90652i q^{26} +(-9.57879 + 25.2437i) q^{27} +13.6080i q^{28} -11.1656i q^{29} +(-2.66876 + 21.0447i) q^{30} +10.5765 q^{31} -5.65685 q^{32} +(11.6189 + 27.2749i) q^{33} -33.6988 q^{34} +(-29.3724 - 17.1645i) q^{35} +(12.4706 - 12.9802i) q^{36} -41.3514i q^{37} -51.5024 q^{38} +(-5.74188 - 13.4789i) q^{39} +(7.13528 - 12.2101i) q^{40} +34.4083i q^{41} +(11.3133 + 26.5576i) q^{42} -33.3830i q^{43} -19.7644i q^{44} +(12.2875 + 43.2899i) q^{45} -6.78233 q^{46} -13.0445 q^{47} +(-11.0400 + 4.70295i) q^{48} +2.70565 q^{49} +(17.3551 + 30.8026i) q^{50} +(-65.7672 + 28.0162i) q^{51} +9.76729i q^{52} +42.5227 q^{53} +(13.5465 - 35.7000i) q^{54} +(42.6608 + 24.9299i) q^{55} -19.2446i q^{56} +(-100.513 + 42.8177i) q^{57} +15.7905i q^{58} +94.4998i q^{59} +(3.77419 - 29.7616i) q^{60} +10.7373 q^{61} -14.9574 q^{62} +(44.1585 + 42.4248i) q^{63} +8.00000 q^{64} +(-21.0824 - 12.3200i) q^{65} +(-16.4316 - 38.5726i) q^{66} +17.6081i q^{67} +47.6573 q^{68} +(-13.2365 + 5.63864i) q^{69} +(41.5389 + 24.2742i) q^{70} +83.8565i q^{71} +(-17.6360 + 18.3567i) q^{72} +70.2097i q^{73} +58.4797i q^{74} +(59.4790 + 45.6864i) q^{75} +72.8355 q^{76} +67.2384 q^{77} +(8.12025 + 19.0620i) q^{78} -1.50786 q^{79} +(-10.0908 + 17.2678i) q^{80} +(-3.24248 - 80.9351i) q^{81} -48.6607i q^{82} +99.1421 q^{83} +(-15.9994 - 37.5582i) q^{84} +(-60.1126 + 102.867i) q^{85} +47.2107i q^{86} +(13.1278 + 30.8171i) q^{87} +27.9511i q^{88} -25.8390i q^{89} +(-17.3772 - 61.2212i) q^{90} -33.2283 q^{91} +9.59166 q^{92} +(-29.1912 + 12.4352i) q^{93} +18.4477 q^{94} +(-91.8711 + 157.213i) q^{95} +(15.6130 - 6.65097i) q^{96} -39.5735i q^{97} -3.82636 q^{98} +(-64.1363 - 61.6183i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 176 q^{4} + 8 q^{9}+O(q^{10}) $ 88 * q + 176 * q^4 + 8 * q^9	$ 88 q + 176 q^{4} + 8 q^{9} + 32 q^{10} - 12 q^{15} + 352 q^{16} - 16 q^{19} - 176 q^{21} + 72 q^{25} - 72 q^{30} + 32 q^{31} + 160 q^{34} + 16 q^{36} + 144 q^{39} + 64 q^{40} + 92 q^{45} - 360 q^{49} + 48 q^{51} - 144 q^{54} + 16 q^{55} - 24 q^{60} + 208 q^{61} + 704 q^{64} + 512 q^{66} + 304 q^{70} + 536 q^{75} - 32 q^{76} + 448 q^{79} - 24 q^{81} - 352 q^{84} - 96 q^{85} + 32 q^{90} - 64 q^{91} + 160 q^{94} + 296 q^{99}+O(q^{100}) $ 88 * q + 176 * q^4 + 8 * q^9 + 32 * q^10 - 12 * q^15 + 352 * q^16 - 16 * q^19 - 176 * q^21 + 72 * q^25 - 72 * q^30 + 32 * q^31 + 160 * q^34 + 16 * q^36 + 144 * q^39 + 64 * q^40 + 92 * q^45 - 360 * q^49 + 48 * q^51 - 144 * q^54 + 16 * q^55 - 24 * q^60 + 208 * q^61 + 704 * q^64 + 512 * q^66 + 304 * q^70 + 536 * q^75 - 32 * q^76 + 448 * q^79 - 24 * q^81 - 352 * q^84 - 96 * q^85 + 32 * q^90 - 64 * q^91 + 160 * q^94 + 296 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$	−2.76001	+	1.17574i	−0.920003	+	0.391912i
$3$	−2.76001	+	1.17574i	−0.920003	+	0.391912i
$4$	2.00000			0.500000
$5$	−2.52270	+	4.31694i	−0.504541	+	0.863388i
$5$	−2.52270	+	4.31694i	−0.504541	+	0.863388i
$6$	3.90324	−	1.66274i	0.650540	−	0.277124i
$7$			6.80400i			0.971999i	0.873959	+	0.486000i	$0.161544\pi$
$7$			6.80400i			0.971999i	−0.873959	+	0.486000i	$0.838456\pi$
$8$	−2.82843			−0.353553
$9$	6.23528	−	6.49009i	0.692809	−	0.721121i
$10$	3.56764	−	6.10507i	0.356764	−	0.610507i
$11$		−	9.88220i		−	0.898382i	−0.893436	−	0.449191i	$-0.851712\pi$
$11$		−	9.88220i		−	0.898382i	0.893436	−	0.449191i	$-0.148288\pi$
$12$	−5.52002	+	2.35147i	−0.460001	+	0.195956i
$13$			4.88365i			0.375665i	0.982201	+	0.187833i	$0.0601462\pi$
$13$			4.88365i			0.375665i	−0.982201	+	0.187833i	$0.939854\pi$
$14$		−	9.62230i		−	0.687307i
$15$	1.88710	−	14.8808i	0.125806	−	0.992055i
$16$	4.00000			0.250000
$17$	23.8286			1.40168			0.700842	−	0.713316i	$-0.252808\pi$
$17$	23.8286			1.40168			0.700842	+	0.713316i	$0.252808\pi$
$18$	−8.81802	+	9.17837i	−0.489890	+	0.509909i
$19$	36.4177			1.91672			0.958361	−	0.285559i	$-0.0921792\pi$
$19$	36.4177			1.91672			0.958361	+	0.285559i	$0.0921792\pi$
$20$	−5.04541	+	8.63388i	−0.252270	+	0.431694i
$21$	−7.99971	−	18.7791i	−0.380939	−	0.894242i
$22$			13.9755i			0.635252i
$23$	4.79583			0.208514
$23$	4.79583			0.208514
$24$	7.80648	−	3.32549i	0.325270	−	0.138562i
$25$	−12.2719	−	21.7807i	−0.490877	−	0.871229i
$26$		−	6.90652i		−	0.265635i
$27$	−9.57879	+	25.2437i	−0.354770	+	0.934954i
$28$			13.6080i			0.486000i
$29$		−	11.1656i		−	0.385021i	−0.981295	−	0.192510i	$-0.938337\pi$
$29$		−	11.1656i		−	0.385021i	0.981295	−	0.192510i	$-0.0616629\pi$
$30$	−2.66876	+	21.0447i	−0.0889585	+	0.701489i
$31$	10.5765			0.341177			0.170588	−	0.985342i	$-0.445433\pi$
$31$	10.5765			0.341177			0.170588	+	0.985342i	$0.445433\pi$
$32$	−5.65685			−0.176777
$33$	11.6189	+	27.2749i	0.352087	+	0.826513i
$34$	−33.6988			−0.991140
$35$	−29.3724	−	17.1645i	−0.839212	−	0.490413i
$36$	12.4706	−	12.9802i	0.346405	−	0.360560i
$37$		−	41.3514i		−	1.11761i	−0.829301	−	0.558803i	$-0.811261\pi$
$37$		−	41.3514i		−	1.11761i	0.829301	−	0.558803i	$-0.188739\pi$
$38$	−51.5024			−1.35533
$39$	−5.74188	−	13.4789i	−0.147228	−	0.345613i
$40$	7.13528	−	12.2101i	0.178382	−	0.305254i
$41$			34.4083i			0.839227i	0.907703	+	0.419614i	$0.137834\pi$
$41$			34.4083i			0.839227i	−0.907703	+	0.419614i	$0.862166\pi$
$42$	11.3133	+	26.5576i	0.269364	+	0.632324i
$43$		−	33.3830i		−	0.776350i	−0.921586	−	0.388175i	$-0.873106\pi$
$43$		−	33.3830i		−	0.776350i	0.921586	−	0.388175i	$-0.126894\pi$
$44$		−	19.7644i		−	0.449191i
$45$	12.2875	+	43.2899i	0.273056	+	0.961998i
$46$	−6.78233			−0.147442
$47$	−13.0445			−0.277542			−0.138771	−	0.990324i	$-0.544315\pi$
$47$	−13.0445			−0.277542			−0.138771	+	0.990324i	$0.544315\pi$
$48$	−11.0400	+	4.70295i	−0.230001	+	0.0979781i
$49$	2.70565			0.0552173
$50$	17.3551	+	30.8026i	0.347103	+	0.616052i
$51$	−65.7672	+	28.0162i	−1.28955	+	0.549337i
$52$			9.76729i			0.187833i
$53$	42.5227			0.802315			0.401157	−	0.916009i	$-0.368608\pi$
$53$	42.5227			0.802315			0.401157	+	0.916009i	$0.368608\pi$
$54$	13.5465	−	35.7000i	0.250860	−	0.661112i
$55$	42.6608	+	24.9299i	0.775652	+	0.453270i
$56$		−	19.2446i		−	0.343654i
$57$	−100.513	+	42.8177i	−1.76339	+	0.751187i
$58$			15.7905i			0.272251i
$59$			94.4998i			1.60169i	0.598871	+	0.800846i	$0.295616\pi$
$59$			94.4998i			1.60169i	−0.598871	+	0.800846i	$0.704384\pi$
$60$	3.77419	−	29.7616i	0.0629032	−	0.496027i
$61$	10.7373			0.176021			0.0880104	−	0.996120i	$-0.471949\pi$
$61$	10.7373			0.176021			0.0880104	+	0.996120i	$0.471949\pi$
$62$	−14.9574			−0.241248
$63$	44.1585	+	42.4248i	0.700929	+	0.673410i
$64$	8.00000			0.125000
$65$	−21.0824	−	12.3200i	−0.324345	−	0.189538i
$66$	−16.4316	−	38.5726i	−0.248963	−	0.584433i
$67$			17.6081i			0.262808i	0.991329	+	0.131404i	$0.0419485\pi$
$67$			17.6081i			0.262808i	−0.991329	+	0.131404i	$0.958051\pi$
$68$	47.6573			0.700842
$69$	−13.2365	+	5.63864i	−0.191834	+	0.0817194i
$70$	41.5389	+	24.2742i	0.593413	+	0.346775i
$71$			83.8565i			1.18108i	0.807009	+	0.590539i	$0.201085\pi$
$71$			83.8565i			1.18108i	−0.807009	+	0.590539i	$0.798915\pi$
$72$	−17.6360	+	18.3567i	−0.244945	+	0.254955i
$73$			70.2097i			0.961777i	0.876782	+	0.480888i	$0.159686\pi$
$73$			70.2097i			0.961777i	−0.876782	+	0.480888i	$0.840314\pi$
$74$			58.4797i			0.790266i
$75$	59.4790	+	45.6864i	0.793054	+	0.609152i
$76$	72.8355			0.958361
$77$	67.2384			0.873226
$78$	8.12025	+	19.0620i	0.104106	+	0.244385i
$79$	−1.50786			−0.0190868			−0.00954341	−	0.999954i	$-0.503038\pi$
$79$	−1.50786			−0.0190868			−0.00954341	+	0.999954i	$0.503038\pi$
$80$	−10.0908	+	17.2678i	−0.126135	+	0.215847i
$81$	−3.24248	−	80.9351i	−0.0400306	−	0.999198i
$82$		−	48.6607i		−	0.593423i
$83$	99.1421			1.19448			0.597242	−	0.802061i	$-0.296263\pi$
$83$	99.1421			1.19448			0.597242	+	0.802061i	$0.296263\pi$
$84$	−15.9994	−	37.5582i	−0.190469	−	0.447121i
$85$	−60.1126	+	102.867i	−0.707207	+	1.21020i
$86$			47.2107i			0.548962i
$87$	13.1278	+	30.8171i	0.150894	+	0.354220i
$88$			27.9511i			0.317626i
$89$		−	25.8390i		−	0.290326i	−0.989408	−	0.145163i	$-0.953629\pi$
$89$		−	25.8390i		−	0.290326i	0.989408	−	0.145163i	$-0.0463706\pi$
$90$	−17.3772	−	61.2212i	−0.193080	−	0.680235i
$91$	−33.2283			−0.365146
$92$	9.59166			0.104257
$93$	−29.1912	+	12.4352i	−0.313883	+	0.133711i
$94$	18.4477			0.196252
$95$	−91.8711	+	157.213i	−0.967065	+	1.65487i
$96$	15.6130	−	6.65097i	0.162635	−	0.0692810i
$97$		−	39.5735i		−	0.407974i	−0.978974	−	0.203987i	$-0.934610\pi$
$97$		−	39.5735i		−	0.407974i	0.978974	−	0.203987i	$-0.0653901\pi$
$98$	−3.82636			−0.0390445
$99$	−64.1363	−	61.6183i	−0.647842	−	0.622407i
$100$	−24.5439	−	43.5614i	−0.245439	−	0.435614i
$101$		−	73.2651i		−	0.725397i	−0.931907	−	0.362698i	$-0.881856\pi$
$101$		−	73.2651i		−	0.725397i	0.931907	−	0.362698i	$-0.118144\pi$
$102$	93.0089	−	39.6209i	0.911852	−	0.388440i
$103$			78.9282i			0.766293i	0.923688	+	0.383146i	$0.125160\pi$
$103$			78.9282i			0.766293i	−0.923688	+	0.383146i	$0.874840\pi$
$104$		−	13.8130i		−	0.132818i
$105$	101.249	+	12.8398i	0.964277	+	0.122284i
$106$	−60.1362			−0.567322
$107$	28.9236			0.270314			0.135157	−	0.990824i	$-0.456846\pi$
$107$	28.9236			0.270314			0.135157	+	0.990824i	$0.456846\pi$
$108$	−19.1576	+	50.4875i	−0.177385	+	0.467477i
$109$	−176.410			−1.61844			−0.809222	−	0.587503i	$-0.800111\pi$
$109$	−176.410			−1.61844			−0.809222	+	0.587503i	$0.800111\pi$
$110$	−60.3315	−	35.2561i	−0.548469	−	0.320510i
$111$	48.6184	+	114.130i	0.438003	+	1.02820i
$112$			27.2160i			0.243000i
$113$	−26.1909			−0.231778			−0.115889	−	0.993262i	$-0.536972\pi$
$113$	−26.1909			−0.231778			−0.115889	+	0.993262i	$0.536972\pi$
$114$	142.147	−	60.5533i	1.24690	−	0.531170i
$115$	−12.0985	+	20.7033i	−0.105204	+	0.180029i
$116$		−	22.3312i		−	0.192510i
$117$	31.6953	+	30.4509i	0.270900	+	0.260264i
$118$		−	133.643i		−	1.13257i
$119$			162.130i			1.36244i
$120$	−5.33751	+	42.0893i	−0.0444793	+	0.350744i
$121$	23.3422			0.192911
$122$	−15.1848			−0.124466
$123$	−40.4551	−	94.9672i	−0.328904	−	0.772091i
$124$	21.1530			0.170588
$125$	124.984	+	1.96913i	0.999876	+	0.0157530i
$126$	−62.4496	−	59.9978i	−0.495632	−	0.476173i
$127$			183.850i			1.44764i	0.689990	+	0.723819i	$0.257615\pi$
$127$			183.850i			1.44764i	−0.689990	+	0.723819i	$0.742385\pi$
$128$	−11.3137			−0.0883883
$129$	39.2497	+	92.1374i	0.304261	+	0.714244i
$130$	29.8150	+	17.4231i	0.229346	+	0.134024i
$131$			15.3027i			0.116815i	0.998293	+	0.0584073i	$0.0186022\pi$
$131$			15.3027i			0.116815i	−0.998293	+	0.0584073i	$0.981398\pi$
$132$	23.2377	+	54.5499i	0.176043	+	0.413257i
$133$			247.786i			1.86305i
$134$		−	24.9017i		−	0.185833i
$135$	−84.8113	−	105.034i	−0.628232	−	0.778026i
$136$	−67.3975			−0.495570
$137$	17.9160			0.130774			0.0653870	−	0.997860i	$-0.479172\pi$
$137$	17.9160			0.130774			0.0653870	+	0.997860i	$0.479172\pi$
$138$	18.7193	−	7.97424i	0.135647	−	0.0577843i
$139$	21.9531			0.157936			0.0789679	−	0.996877i	$-0.474838\pi$
$139$	21.9531			0.157936			0.0789679	+	0.996877i	$0.474838\pi$
$140$	−58.7449	−	34.3289i	−0.419606	−	0.245207i
$141$	36.0029	−	15.3369i	0.255340	−	0.108772i
$142$		−	118.591i		−	0.835148i
$143$	48.2611			0.337491
$144$	24.9411	−	25.9604i	0.173202	−	0.180280i
$145$	48.2012	+	28.1675i	0.332422	+	0.194259i
$146$		−	99.2915i		−	0.680079i
$147$	−7.46761	+	3.18113i	−0.0508001	+	0.0216404i
$148$		−	82.7028i		−	0.558803i
$149$			156.433i			1.04989i	0.851138	+	0.524943i	$0.175913\pi$
$149$			156.433i			1.04989i	−0.851138	+	0.524943i	$0.824087\pi$
$150$	−84.1160	−	64.6103i	−0.560774	−	0.430735i
$151$	−217.732			−1.44193			−0.720966	−	0.692970i	$-0.756302\pi$
$151$	−217.732			−1.44193			−0.720966	+	0.692970i	$0.756302\pi$
$152$	−103.005			−0.677664
$153$	148.578	−	154.650i	0.971100	−	1.01078i
$154$	−95.0895			−0.617464
$155$	−26.6813	+	45.6580i	−0.172138	+	0.294568i
$156$	−11.4838	−	26.9578i	−0.0736139	−	0.172806i
$157$		−	274.821i		−	1.75045i	−0.483714	−	0.875226i	$-0.660712\pi$
$157$		−	274.821i		−	1.75045i	0.483714	−	0.875226i	$-0.339288\pi$
$158$	2.13243			0.0134964
$159$	−117.363	+	49.9955i	−0.738132	+	0.314437i
$160$	14.2706	−	24.4203i	0.0891911	−	0.152627i
$161$			32.6308i			0.202676i
$162$	4.58556	+	114.459i	0.0283059	+	0.706540i
$163$		−	181.322i		−	1.11240i	−0.831048	−	0.556201i	$-0.812258\pi$
$163$		−	181.322i		−	1.11240i	0.831048	−	0.556201i	$-0.187742\pi$
$164$			68.8166i			0.419614i
$165$	−147.055	−	18.6486i	−0.891244	−	0.113022i
$166$	−140.208			−0.844627
$167$	−186.672			−1.11780			−0.558898	−	0.829237i	$-0.688775\pi$
$167$	−186.672			−1.11780			−0.558898	+	0.829237i	$0.688775\pi$
$168$	22.6266	+	53.1153i	0.134682	+	0.316162i
$169$	145.150			0.858876
$170$	85.0120	−	145.476i	0.500071	−	0.855739i
$171$	227.075	−	236.354i	1.32792	−	1.38219i
$172$		−	66.7661i		−	0.388175i
$173$	315.255			1.82228			0.911141	−	0.412095i	$-0.135203\pi$
$173$	315.255			1.82228			0.911141	+	0.412095i	$0.135203\pi$
$174$	−18.5655	−	43.5820i	−0.106698	−	0.250471i
$175$	148.196	−	83.4982i	0.846834	−	0.477132i
$176$		−	39.5288i		−	0.224595i
$177$	−111.107	−	260.820i	−0.627723	−	1.47356i
$178$			36.5419i			0.205291i
$179$			74.2072i			0.414565i	0.978281	+	0.207283i	$0.0664620\pi$
$179$			74.2072i			0.414565i	−0.978281	+	0.207283i	$0.933538\pi$
$180$	24.5751	+	86.5798i	0.136528	+	0.480999i
$181$	277.209			1.53154			0.765771	−	0.643113i	$-0.222358\pi$
$181$	277.209			1.53154			0.765771	+	0.643113i	$0.222358\pi$
$182$	46.9919			0.258197
$183$	−29.6349	+	12.6242i	−0.161940	+	0.0689847i
$184$	−13.5647			−0.0737210
$185$	178.511	+	104.317i	0.964927	+	0.563877i
$186$	41.2825	−	17.5860i	0.221949	−	0.0945482i
$187$		−	235.479i		−	1.25925i
$188$	−26.0890			−0.138771
$189$	−171.758	−	65.1741i	−0.908774	−	0.344836i
$190$	129.925	−	222.333i	0.683818	−	1.17017i
$191$			36.5558i			0.191391i	0.995411	+	0.0956957i	$0.0305076\pi$
$191$			36.5558i			0.191391i	−0.995411	+	0.0956957i	$0.969492\pi$
$192$	−22.0801	+	9.40590i	−0.115000	+	0.0489891i
$193$		−	132.274i		−	0.685357i	−0.939453	−	0.342678i	$-0.888666\pi$
$193$		−	132.274i		−	0.685357i	0.939453	−	0.342678i	$-0.111334\pi$
$194$			55.9654i			0.288481i
$195$	72.6727	+	9.21590i	0.372680	+	0.0472610i
$196$	5.41130			0.0276087
$197$	−271.150			−1.37639			−0.688197	−	0.725523i	$-0.741598\pi$
$197$	−271.150			−1.37639			−0.688197	+	0.725523i	$0.741598\pi$
$198$	90.7025	+	87.1414i	0.458093	+	0.440108i
$199$	−178.921			−0.899100			−0.449550	−	0.893255i	$-0.648416\pi$
$199$	−178.921			−0.899100			−0.449550	+	0.893255i	$0.648416\pi$
$200$	34.7103	+	61.6052i	0.173551	+	0.308026i
$201$	−20.7025	−	48.5986i	−0.102998	−	0.241784i
$202$			103.612i			0.512933i
$203$	75.9707			0.374240
$204$	−131.534	+	56.0324i	−0.644776	+	0.274669i
$205$	−148.539	−	86.8020i	−0.724579	−	0.423424i
$206$		−	111.621i		−	0.541851i
$207$	29.9034	−	31.1254i	0.144461	−	0.150364i
$208$			19.5346i			0.0939163i
$209$		−	359.887i		−	1.72195i
$210$	−143.188	−	18.1582i	−0.681847	−	0.0864676i
$211$	259.891			1.23171			0.615856	−	0.787859i	$-0.288810\pi$
$211$	259.891			1.23171			0.615856	+	0.787859i	$0.288810\pi$
$212$	85.0454			0.401157
$213$	−98.5932	−	231.444i	−0.462879	−	1.08659i
$214$	−40.9041			−0.191141
$215$	144.113	+	84.2155i	0.670291	+	0.391700i
$216$	27.0929	−	71.4001i	0.125430	−	0.330556i
$217$			71.9623i			0.331623i
$218$	249.482			1.14441
$219$	−82.5482	−	193.779i	−0.376932	−	0.884837i
$220$	85.3217	+	49.8597i	0.387826	+	0.226635i
$221$			116.371i			0.526564i
$222$	−68.7568	−	161.404i	−0.309715	−	0.727047i
$223$			308.191i			1.38202i	0.722843	+	0.691012i	$0.242835\pi$
$223$			308.191i			1.38202i	−0.722843	+	0.691012i	$0.757165\pi$
$224$		−	38.4892i		−	0.171827i
$225$	−217.878	−	56.1631i	−0.968346	−	0.249614i
$226$	37.0396			0.163892
$227$	125.303			0.551997			0.275998	−	0.961158i	$-0.410992\pi$
$227$	125.303			0.551997			0.275998	+	0.961158i	$0.410992\pi$
$228$	−201.026	+	85.6354i	−0.881695	+	0.375594i
$229$	−338.928			−1.48003			−0.740017	−	0.672588i	$-0.765183\pi$
$229$	−338.928			−1.48003			−0.740017	+	0.672588i	$0.765183\pi$
$230$	17.1098	−	29.2789i	0.0743905	−	0.127300i
$231$	−185.579	+	79.0547i	−0.803370	+	0.342228i
$232$			31.5811i			0.136125i
$233$	160.840			0.690301			0.345151	−	0.938547i	$-0.387828\pi$
$233$	160.840			0.690301			0.345151	+	0.938547i	$0.387828\pi$
$234$	−44.8239	−	43.0641i	−0.191555	−	0.184035i
$235$	32.9074	−	56.3123i	0.140031	−	0.239627i
$236$			189.000i			0.800846i
$237$	4.16170	−	1.77285i	0.0175599	−	0.00748036i
$238$		−	229.286i		−	0.963388i
$239$		−	279.640i		−	1.17004i	−0.811019	−	0.585020i	$-0.801087\pi$
$239$		−	279.640i		−	1.17004i	0.811019	−	0.585020i	$-0.198913\pi$
$240$	7.54838	−	59.5233i	0.0314516	−	0.248014i
$241$	−370.691			−1.53814			−0.769069	−	0.639166i	$-0.779280\pi$
$241$	−370.691			−1.53814			−0.769069	+	0.639166i	$0.779280\pi$
$242$	−33.0108			−0.136408
$243$	104.108	+	219.569i	0.428427	+	0.903577i
$244$	21.4745			0.0880104
$245$	−6.82555	+	11.6801i	−0.0278594	+	0.0476740i
$246$	57.2122	+	134.304i	0.232570	+	0.545951i
$247$			177.851i			0.720046i
$248$	−29.9148			−0.120624
$249$	−273.633	+	116.565i	−1.09893	+	0.468133i
$250$	−176.755	−	2.78477i	−0.707019	−	0.0111391i
$251$			343.840i			1.36988i	0.728600	+	0.684939i	$0.240171\pi$
$251$			343.840i			1.36988i	−0.728600	+	0.684939i	$0.759829\pi$
$252$	88.3171	+	84.8497i	0.350464	+	0.336705i
$253$		−	47.3934i		−	0.187326i
$254$		−	260.003i		−	1.02363i
$255$	44.9669	−	354.590i	0.176341	−	1.39055i
$256$	16.0000			0.0625000
$257$	−226.994			−0.883247			−0.441624	−	0.897200i	$-0.645597\pi$
$257$	−226.994			−0.883247			−0.441624	+	0.897200i	$0.645597\pi$
$258$	−55.5074	−	130.302i	−0.215145	−	0.505046i
$259$	281.355			1.08631
$260$	−42.1648	−	24.6400i	−0.162172	−	0.0947692i
$261$	−72.4657	−	69.6207i	−0.277646	−	0.266746i
$262$		−	21.6413i		−	0.0826003i
$263$	270.805			1.02968			0.514838	−	0.857288i	$-0.327852\pi$
$263$	270.805			1.02968			0.514838	+	0.857288i	$0.327852\pi$
$264$	−32.8631	−	77.1452i	−0.124482	−	0.292217i
$265$	−107.272	+	183.568i	−0.404801	+	0.692709i
$266$		−	350.422i		−	1.31738i
$267$	30.3799	+	71.3158i	0.113782	+	0.267101i
$268$			35.2163i			0.131404i
$269$		−	86.0153i		−	0.319760i	−0.987136	−	0.159880i	$-0.948889\pi$
$269$		−	86.0153i		−	0.319760i	0.987136	−	0.159880i	$-0.0511107\pi$
$270$	119.941	+	148.540i	0.444227	+	0.550148i
$271$	20.6816			0.0763158			0.0381579	−	0.999272i	$-0.487851\pi$
$271$	20.6816			0.0763158			0.0381579	+	0.999272i	$0.487851\pi$
$272$	95.3145			0.350421
$273$	91.7104	−	39.0678i	0.335935	−	0.143105i
$274$	−25.3371			−0.0924712
$275$	−215.241	+	121.274i	−0.782696	+	0.440995i
$276$	−26.4731	+	11.2773i	−0.0959169	+	0.0408597i
$277$		−	341.121i		−	1.23148i	−0.787948	−	0.615741i	$-0.788857\pi$
$277$		−	341.121i		−	1.23148i	0.787948	−	0.615741i	$-0.211143\pi$
$278$	−31.0463			−0.111677
$279$	65.9473	−	68.6423i	0.236370	−	0.246030i
$280$	83.0778	+	48.5484i	0.296706	+	0.173387i
$281$		−	351.167i		−	1.24971i	−0.780743	−	0.624853i	$-0.785159\pi$
$281$		−	351.167i		−	1.24971i	0.780743	−	0.624853i	$-0.214841\pi$
$282$	−50.9158	+	21.6897i	−0.180552	+	0.0769137i
$283$			165.167i			0.583629i	0.956475	+	0.291815i	$0.0942591\pi$
$283$			165.167i			0.583629i	−0.956475	+	0.291815i	$0.905741\pi$
$284$			167.713i			0.590539i
$285$	68.7237	−	541.926i	0.241136	−	1.90149i
$286$	−68.2516			−0.238642
$287$	−234.114			−0.815728
$288$	−35.2721	+	36.7135i	−0.122473	+	0.127477i
$289$	278.804			0.964718
$290$	−68.1668	−	39.8349i	−0.235058	−	0.137362i
$291$	46.5281	+	109.223i	0.159890	+	0.375338i
$292$			140.419i			0.480888i
$293$	−42.7560			−0.145925			−0.0729624	−	0.997335i	$-0.523245\pi$
$293$	−42.7560			−0.145925			−0.0729624	+	0.997335i	$0.523245\pi$
$294$	10.5608	−	4.49880i	0.0359211	−	0.0153020i
$295$	−407.950	−	238.395i	−1.38288	−	0.808119i
$296$			116.959i			0.395133i
$297$	249.464	+	94.6595i	0.839945	+	0.318719i
$298$		−	221.230i		−	0.742381i
$299$			23.4211i			0.0783316i
$300$	118.958	+	91.3728i	0.396527	+	0.304576i
$301$	227.138			0.754611
$302$	307.919			1.01960
$303$	86.1405	+	202.212i	0.284292	+	0.667367i
$304$	145.671			0.479181
$305$	−27.0870	+	46.3521i	−0.0888097	+	0.151974i
$306$	−210.121	+	218.708i	−0.686671	+	0.714732i
$307$		−	381.120i		−	1.24143i	−0.784035	−	0.620717i	$-0.786842\pi$
$307$		−	381.120i		−	1.24143i	0.784035	−	0.620717i	$-0.213158\pi$
$308$	134.477			0.436613
$309$	−92.7988	−	217.842i	−0.300320	−	0.704991i
$310$	37.7331	−	64.5702i	0.121720	−	0.208291i
$311$			426.669i			1.37193i	0.727636	+	0.685963i	$0.240619\pi$
$311$			426.669i			1.37193i	−0.727636	+	0.685963i	$0.759381\pi$
$312$	16.2405	+	38.1241i	0.0520529	+	0.122193i
$313$			383.577i			1.22548i	0.790283	+	0.612742i	$0.209934\pi$
$313$			383.577i			1.22548i	−0.790283	+	0.612742i	$0.790066\pi$
$314$			388.656i			1.23776i
$315$	−294.544	+	83.6044i	−0.935061	+	0.265411i
$316$	−3.01572			−0.00954341
$317$	−93.7258			−0.295665			−0.147832	−	0.989012i	$-0.547230\pi$
$317$	−93.7258			−0.295665			−0.147832	+	0.989012i	$0.547230\pi$
$318$	165.976	−	70.7043i	0.521938	−	0.222341i
$319$	−110.341			−0.345895
$320$	−20.1816	+	34.5355i	−0.0630676	+	0.107923i
$321$	−79.8292	+	34.0065i	−0.248689	+	0.105939i
$322$		−	46.1469i		−	0.143313i
$323$	867.784			2.68664
$324$	−6.48495	−	161.870i	−0.0200153	−	0.499599i
$325$	106.369	−	59.9318i	0.327290	−	0.184405i
$326$			256.427i			0.786587i
$327$	486.894	−	207.412i	1.48897	−	0.634288i
$328$		−	97.3214i		−	0.296712i
$329$		−	88.7547i		−	0.269771i
$330$	207.967	+	26.3732i	0.630205	+	0.0799187i
$331$	236.616			0.714851			0.357425	−	0.933942i	$-0.383655\pi$
$331$	236.616			0.714851			0.357425	+	0.933942i	$0.383655\pi$
$332$	198.284			0.597242
$333$	−268.374	−	257.838i	−0.805929	−	0.774287i
$334$	263.994			0.790400
$335$	−76.0132	−	44.4201i	−0.226905	−	0.132597i
$336$	−31.9988	−	75.1163i	−0.0952347	−	0.223560i
$337$		−	185.435i		−	0.550251i	−0.961408	−	0.275125i	$-0.911281\pi$
$337$		−	185.435i		−	0.550251i	0.961408	−	0.275125i	$-0.0887194\pi$
$338$	−205.273			−0.607317
$339$	72.2872	−	30.7937i	0.213236	−	0.0908367i
$340$	−120.225	+	205.733i	−0.353603	+	0.605099i
$341$		−	104.519i		−	0.306507i
$342$	−321.132	+	334.255i	−0.938983	+	0.977355i
$343$			351.805i			1.02567i
$344$			94.4215i			0.274481i
$345$	9.05019	−	71.3659i	0.0262324	−	0.206858i
$346$	−445.837			−1.28855
$347$	−556.885			−1.60486			−0.802429	−	0.596748i	$-0.796459\pi$
$347$	−556.885			−1.60486			−0.802429	+	0.596748i	$0.796459\pi$
$348$	26.2556	+	61.6343i	0.0754472	+	0.177110i
$349$	−226.627			−0.649360			−0.324680	−	0.945824i	$-0.605257\pi$
$349$	−226.627			−0.649360			−0.324680	+	0.945824i	$0.605257\pi$
$350$	−209.581	+	118.084i	−0.598802	+	0.337383i
$351$	−123.282	−	46.7794i	−0.351229	−	0.133275i
$352$			55.9022i			0.158813i
$353$	214.562			0.607823			0.303912	−	0.952700i	$-0.401707\pi$
$353$	214.562			0.607823			0.303912	+	0.952700i	$0.401707\pi$
$354$	157.129	+	368.855i	0.443867	+	1.04196i
$355$	−362.003	−	211.545i	−1.01973	−	0.595902i
$356$		−	51.6780i		−	0.145163i
$357$	−190.622	−	447.480i	−0.533956	−	1.25344i
$358$		−	104.945i		−	0.293142i
$359$			496.982i			1.38435i	0.721730	+	0.692175i	$0.243347\pi$
$359$			496.982i			1.38435i	−0.721730	+	0.692175i	$0.756653\pi$
$360$	−34.7544	−	122.442i	−0.0965400	−	0.340118i
$361$	965.251			2.67382
$362$	−392.033			−1.08296
$363$	−64.4246	+	27.4443i	−0.177478	+	0.0756040i
$364$	−66.4566			−0.182573
$365$	−303.091	−	177.118i	−0.830387	−	0.485256i
$366$	41.9101	−	17.8533i	0.114509	−	0.0487796i
$367$			504.879i			1.37569i	0.725857	+	0.687846i	$0.241443\pi$
$367$			504.879i			1.37569i	−0.725857	+	0.687846i	$0.758557\pi$
$368$	19.1833			0.0521286
$369$	223.313	+	214.546i	0.605184	+	0.581425i
$370$	−252.453	−	147.527i	−0.682306	−	0.398722i
$371$			289.324i			0.779849i
$372$	−58.3823	+	24.8703i	−0.156942	+	0.0668557i
$373$			316.318i			0.848038i	0.905653	+	0.424019i	$0.139381\pi$
$373$			316.318i			0.848038i	−0.905653	+	0.424019i	$0.860619\pi$
$374$			333.018i			0.890422i
$375$	−347.273	+	141.514i	−0.926062	+	0.377371i
$376$	36.8954			0.0981261
$377$	54.5288			0.144639
$378$	242.903	+	92.1700i	0.642600	+	0.243836i
$379$	88.0235			0.232252			0.116126	−	0.993234i	$-0.462952\pi$
$379$	88.0235			0.232252			0.116126	+	0.993234i	$0.462952\pi$
$380$	−183.742	+	314.426i	−0.483532	+	0.827437i
$381$	−216.159	−	507.427i	−0.567347	−	1.33183i
$382$		−	51.6977i		−	0.135334i
$383$	399.427			1.04289			0.521446	−	0.853285i	$-0.325393\pi$
$383$	399.427			1.04289			0.521446	+	0.853285i	$0.325393\pi$
$384$	31.2259	−	13.3019i	0.0813175	−	0.0346405i
$385$	−169.623	+	290.264i	−0.440578	+	0.753933i
$386$			187.064i			0.484620i
$387$	−216.659	−	208.153i	−0.559842	−	0.537862i
$388$		−	79.1470i		−	0.203987i
$389$		−	403.418i		−	1.03706i	−0.855058	−	0.518532i	$-0.826479\pi$
$389$		−	403.418i		−	1.03706i	0.855058	−	0.518532i	$-0.173521\pi$
$390$	−102.775	−	13.0333i	−0.263525	−	0.0334186i
$391$	114.278			0.292271
$392$	−7.65273			−0.0195223
$393$	−17.9920	−	42.2356i	−0.0457811	−	0.107470i
$394$	383.464			0.973258
$395$	3.80388	−	6.50933i	0.00963008	−	0.0164793i
$396$	−128.273	−	123.237i	−0.323921	−	0.311204i
$397$			554.412i			1.39650i	0.715852	+	0.698252i	$0.246039\pi$
$397$			554.412i			1.39650i	−0.715852	+	0.698252i	$0.753961\pi$
$398$	253.032			0.635760
$399$	−291.331	−	683.891i	−0.730154	−	1.71401i
$400$	−49.0877	−	87.1229i	−0.122719	−	0.217807i
$401$			427.924i			1.06714i	0.845755	+	0.533572i	$0.179150\pi$
$401$			427.924i			1.06714i	−0.845755	+	0.533572i	$0.820850\pi$
$402$	29.2778	+	68.7288i	0.0728304	+	0.170967i
$403$			51.6518i			0.128168i
$404$		−	146.530i		−	0.362698i
$405$	357.572	+	190.178i	0.882893	+	0.469574i
$406$	−107.439			−0.264627
$407$	−408.643			−1.00404
$408$	186.018	−	79.2418i	0.455926	−	0.194220i
$409$	717.855			1.75515			0.877573	−	0.479442i	$-0.159161\pi$
$409$	717.855			1.75515			0.877573	+	0.479442i	$0.159161\pi$
$410$	210.065	+	122.757i	0.512355	+	0.299406i
$411$	−49.4484	+	21.0646i	−0.120312	+	0.0512520i
$412$			157.856i			0.383146i
$413$	−642.976			−1.55684
$414$	−42.2898	+	44.0179i	−0.102149	+	0.106323i
$415$	−250.106	+	427.990i	−0.602665	+	1.03130i
$416$		−	27.6261i		−	0.0664088i
$417$	−60.5906	+	25.8110i	−0.145301	+	0.0618970i
$418$			508.957i			1.21760i
$419$			7.70955i			0.0183999i	0.999958	+	0.00919994i	$0.00292847\pi$
$419$			7.70955i			0.0183999i	−0.999958	+	0.00919994i	$0.997072\pi$
$420$	202.498	+	25.6796i	0.482138	+	0.0611418i
$421$	641.178			1.52299			0.761494	−	0.648171i	$-0.224466\pi$
$421$	641.178			1.52299			0.761494	+	0.648171i	$0.224466\pi$
$422$	−367.541			−0.870951
$423$	−81.3361	+	84.6599i	−0.192284	+	0.200142i
$424$	−120.272			−0.283661
$425$	−292.423	−	519.005i	−0.688055	−	1.22119i
$426$	139.432	+	327.312i	0.327305	+	0.768338i
$427$			73.0563i			0.171092i
$428$	57.8471			0.135157
$429$	−133.201	+	56.7424i	−0.310492	+	0.132267i
$430$	−203.806	−	119.099i	−0.473967	−	0.276974i
$431$			731.842i			1.69801i	0.528385	+	0.849005i	$0.322798\pi$
$431$			731.842i			1.69801i	−0.528385	+	0.849005i	$0.677202\pi$
$432$	−38.3152	+	100.975i	−0.0886925	+	0.233738i
$433$		−	68.2321i		−	0.157580i	−0.996891	−	0.0787900i	$-0.974894\pi$
$433$		−	68.2321i		−	0.157580i	0.996891	−	0.0787900i	$-0.0251057\pi$
$434$		−	101.770i		−	0.234493i
$435$	−166.153	−	21.0705i	−0.381962	−	0.0484380i
$436$	−352.821			−0.809222
$437$	174.653			0.399664
$438$	116.741	+	274.045i	0.266531	+	0.625674i
$439$	472.232			1.07570			0.537850	−	0.843041i	$-0.319237\pi$
$439$	472.232			1.07570			0.537850	+	0.843041i	$0.319237\pi$
$440$	−120.663	−	70.5123i	−0.274234	−	0.160255i
$441$	16.8705	−	17.5599i	0.0382551	−	0.0398184i
$442$		−	164.573i		−	0.372337i
$443$	633.039			1.42898			0.714491	−	0.699644i	$-0.246658\pi$
$443$	633.039			1.42898			0.714491	+	0.699644i	$0.246658\pi$
$444$	97.2368	+	228.260i	0.219002	+	0.514100i
$445$	111.545	+	65.1841i	0.250664	+	0.146481i
$446$		−	435.849i		−	0.977239i
$447$	−183.924	−	431.756i	−0.411463	−	0.965897i
$448$			54.4320i			0.121500i
$449$		−	664.528i		−	1.48002i	−0.672597	−	0.740009i	$-0.734821\pi$
$449$		−	664.528i		−	1.48002i	0.672597	−	0.740009i	$-0.265179\pi$
$450$	308.126	+	79.4266i	0.684724	+	0.176503i
$451$	340.030			0.753946
$452$	−52.3819			−0.115889
$453$	600.942	−	255.995i	1.32658	−	0.565111i
$454$	−177.206			−0.390321
$455$	83.8252	−	143.445i	0.184231	−	0.315263i
$456$	284.294	−	121.107i	0.623452	−	0.265585i
$457$			464.273i			1.01591i	0.861382	+	0.507957i	$0.169599\pi$
$457$			464.273i			1.01591i	−0.861382	+	0.507957i	$0.830401\pi$
$458$	479.316			1.04654
$459$	−228.249	+	601.524i	−0.497276	+	1.31051i
$460$	−24.1969	+	41.4066i	−0.0526020	+	0.0900144i
$461$		−	176.434i		−	0.382721i	−0.981520	−	0.191361i	$-0.938710\pi$
$461$		−	176.434i		−	0.382721i	0.981520	−	0.191361i	$-0.0612900\pi$
$462$	262.448	−	111.800i	0.568069	−	0.241992i
$463$			120.561i			0.260392i	0.991488	+	0.130196i	$0.0415606\pi$
$463$			120.561i			0.260392i	−0.991488	+	0.130196i	$0.958439\pi$
$464$		−	44.6624i		−	0.0962551i
$465$	19.9588	−	157.387i	0.0429222	−	0.338466i
$466$	−227.462			−0.488117
$467$	−366.952			−0.785765			−0.392882	−	0.919589i	$-0.628522\pi$
$467$	−366.952			−0.785765			−0.392882	+	0.919589i	$0.628522\pi$
$468$	63.3906	+	60.9018i	0.135450	+	0.130132i
$469$	−119.806			−0.255449
$470$	−46.5381	+	79.6376i	−0.0990172	+	0.169442i
$471$	323.117	+	758.508i	0.686024	+	1.61042i
$472$		−	267.286i		−	0.566283i
$473$	−329.898			−0.697458
$474$	−5.88553	+	2.50718i	−0.0124167	+	0.00528941i
$475$	−446.916	−	793.204i	−0.940875	−	1.66990i
$476$			324.260i			0.681218i
$477$	265.141	−	275.976i	0.555851	−	0.578566i
$478$			395.470i			0.827343i
$479$		−	790.473i		−	1.65026i	−0.564945	−	0.825129i	$-0.691103\pi$
$479$		−	790.473i		−	1.65026i	0.564945	−	0.825129i	$-0.308897\pi$
$480$	−10.6750	+	84.1786i	−0.0222396	+	0.175372i
$481$	201.946			0.419845
$482$	524.236			1.08763
$483$	−38.3653	−	90.0613i	−0.0794312	−	0.186462i
$484$	46.6843			0.0964553
$485$	170.836	+	99.8323i	0.352240	+	0.205840i
$486$	−147.230	−	310.518i	−0.302943	−	0.638925i
$487$			35.6013i			0.0731033i	0.999332	+	0.0365516i	$0.0116373\pi$
$487$			35.6013i			0.0731033i	−0.999332	+	0.0365516i	$0.988363\pi$
$488$	−30.3696			−0.0622328
$489$	213.187	+	500.449i	0.435964	+	1.02341i
$490$	9.65278	−	16.5182i	0.0196996	−	0.0337106i
$491$		−	822.108i		−	1.67435i	−0.546932	−	0.837177i	$-0.684205\pi$
$491$		−	822.108i		−	1.67435i	0.546932	−	0.837177i	$-0.315795\pi$
$492$	−80.9103	−	189.934i	−0.164452	−	0.386046i
$493$		−	266.061i		−	0.539677i
$494$		−	251.520i		−	0.509149i
$495$	427.799	−	121.428i	0.864241	−	0.245309i
$496$	42.3059			0.0852942
$497$	−570.559			−1.14801
$498$	386.975	−	164.848i	0.777059	−	0.331020i
$499$	101.299			0.203005			0.101502	−	0.994835i	$-0.467635\pi$
$499$	101.299			0.203005			0.101502	+	0.994835i	$0.467635\pi$
$500$	249.969	+	3.93825i	0.499938	+	0.00787651i
$501$	515.215	−	219.477i	1.02837	−	0.438078i
$502$		−	486.263i		−	0.968650i
$503$	−198.216			−0.394067			−0.197033	−	0.980397i	$-0.563131\pi$
$503$	−198.216			−0.394067			−0.197033	+	0.980397i	$0.563131\pi$
$504$	−124.899	−	119.996i	−0.247816	−	0.238086i
$505$	316.281	+	184.826i	0.626299	+	0.365992i
$506$			67.0243i			0.132459i
$507$	−400.615	+	170.658i	−0.790168	+	0.336604i
$508$			367.700i			0.723819i
$509$			249.428i			0.490036i	0.969519	+	0.245018i	$0.0787938\pi$
$509$			249.428i			0.490036i	−0.969519	+	0.245018i	$0.921206\pi$
$510$	−63.5928	+	501.465i	−0.124692	+	0.983266i
$511$	−477.707			−0.934847
$512$	−22.6274			−0.0441942
$513$	−348.838	+	919.320i	−0.679996	+	1.79205i
$514$	321.019			0.624550
$515$	−340.728	−	199.112i	−0.661608	−	0.386626i
$516$	78.4993	+	184.275i	0.152131	+	0.357122i
$517$			128.908i			0.249339i
$518$	−397.896			−0.768138
$519$	−870.105	+	370.657i	−1.67650	+	0.714175i
$520$	59.6300	+	34.8462i	0.114673	+	0.0670119i
$521$		−	451.691i		−	0.866969i	−0.901161	−	0.433484i	$-0.857284\pi$
$521$		−	451.691i		−	0.866969i	0.901161	−	0.433484i	$-0.142716\pi$
$522$	102.482	+	98.4585i	0.196326	+	0.188618i
$523$			250.044i			0.478095i	0.971008	+	0.239047i	$0.0768352\pi$
$523$			250.044i			0.478095i	−0.971008	+	0.239047i	$0.923165\pi$
$524$			30.6054i			0.0584073i
$525$	−310.850	+	404.695i	−0.592095	+	0.770848i
$526$	−382.976			−0.728091
$527$	252.023			0.478222
$528$	46.4755	+	109.100i	0.0880217	+	0.206628i
$529$	23.0000			0.0434783
$530$	151.706	−	259.604i	0.286237	−	0.489819i
$531$	613.312	+	589.233i	1.15501	+	1.10967i
$532$			495.572i			0.931526i
$533$	−168.038			−0.315268
$534$	−42.9636	−	100.856i	−0.0804562	−	0.188869i
$535$	−72.9656	+	124.861i	−0.136384	+	0.233386i
$536$		−	49.8033i		−	0.0929166i
$537$	−87.2482	−	204.812i	−0.162473	−	0.381401i
$538$			121.644i			0.226104i
$539$		−	26.7378i		−	0.0496062i
$540$	−169.623	−	210.067i	−0.314116	−	0.389013i
$541$	−678.246			−1.25369			−0.626845	−	0.779144i	$-0.715654\pi$
$541$	−678.246			−1.25369			−0.626845	+	0.779144i	$0.715654\pi$
$542$	−29.2482			−0.0539634
$543$	−765.099	+	325.925i	−1.40902	+	0.600230i
$544$	−134.795			−0.247785
$545$	445.031	−	761.553i	0.816571	−	1.39735i
$546$	−129.698	+	55.2501i	−0.237542	+	0.101191i
$547$			703.374i			1.28587i	0.765919	+	0.642937i	$0.222284\pi$
$547$			703.374i			1.28587i	−0.765919	+	0.642937i	$0.777716\pi$
$548$	35.8321			0.0653870
$549$	66.9499	−	69.6858i	0.121949	−	0.126932i
$550$	304.397	−	171.507i	0.553450	−	0.311831i
$551$		−	406.626i		−	0.737978i
$552$	37.4386	−	15.9485i	0.0678235	−	0.0288922i
$553$		−	10.2595i		−	0.0185524i
$554$			482.417i			0.870790i
$555$	−615.343	−	78.0340i	−1.10873	−	0.140602i
$556$	43.9061			0.0789679
$557$	611.566			1.09796			0.548982	−	0.835834i	$-0.315016\pi$
$557$	611.566			1.09796			0.548982	+	0.835834i	$0.315016\pi$
$558$	−93.2636	+	97.0748i	−0.167139	+	0.173969i
$559$	163.031			0.291647
$560$	−117.490	−	68.6579i	−0.209803	−	0.122603i
$561$	276.862	+	649.924i	0.493515	+	1.15851i
$562$			496.625i			0.883675i
$563$	775.464			1.37738			0.688689	−	0.725057i	$-0.258187\pi$
$563$	775.464			1.37738			0.688689	+	0.725057i	$0.258187\pi$
$564$	72.0058	−	30.6738i	0.127670	−	0.0543862i
$565$	66.0720	−	113.065i	0.116942	−	0.200114i
$566$		−	233.582i		−	0.412688i
$567$	550.682	−	22.0618i	0.971220	−	0.0389097i
$568$		−	237.182i		−	0.417574i
$569$			993.400i			1.74587i	0.487836	+	0.872935i	$0.337786\pi$
$569$			993.400i			1.74587i	−0.487836	+	0.872935i	$0.662214\pi$
$570$	−97.1900	+	766.399i	−0.170509	+	1.34456i
$571$	524.115			0.917890			0.458945	−	0.888465i	$-0.348228\pi$
$571$	524.115			0.917890			0.458945	+	0.888465i	$0.348228\pi$
$572$	96.5223			0.168745
$573$	−42.9800	−	100.894i	−0.0750087	−	0.176081i
$574$	331.087			0.576807
$575$	−58.8541	−	104.457i	−0.102355	−	0.181664i
$576$	49.8823	−	51.9207i	0.0866012	−	0.0901401i
$577$		−	302.382i		−	0.524059i	−0.965060	−	0.262029i	$-0.915608\pi$
$577$		−	302.382i		−	0.524059i	0.965060	−	0.262029i	$-0.0843918\pi$
$578$	−394.288			−0.682159
$579$	155.519	+	365.077i	0.268600	+	0.630530i
$580$	96.4024	+	56.3350i	0.166211	+	0.0971293i
$581$			674.562i			1.16104i
$582$	−65.8006	−	154.465i	−0.113059	−	0.265404i
$583$		−	420.218i		−	0.720785i
$584$		−	198.583i		−	0.340040i
$585$	−211.413	+	60.0080i	−0.361389	+	0.102578i
$586$	60.4661			0.103184
$587$	−171.830			−0.292725			−0.146363	−	0.989231i	$-0.546757\pi$
$587$	−171.830			−0.292725			−0.146363	+	0.989231i	$0.546757\pi$
$588$	−14.9352	+	6.36226i	−0.0254000	+	0.0108202i
$589$	385.171			0.653941
$590$	576.928	+	337.141i	0.977844	+	0.571426i
$591$	748.376	−	318.801i	1.26629	−	0.539426i
$592$		−	165.406i		−	0.279401i
$593$	−1163.90			−1.96273			−0.981363	−	0.192161i	$-0.938450\pi$
$593$	−1163.90			−1.96273			−0.981363	+	0.192161i	$0.938450\pi$
$594$	−352.795	−	133.869i	−0.593931	−	0.225368i
$595$	−699.905	−	409.006i	−1.17631	−	0.687405i
$596$			312.866i			0.524943i
$597$	493.823	−	210.364i	0.827174	−	0.352368i
$598$		−	33.1225i		−	0.0553888i
$599$			1116.41i			1.86380i	0.362720	+	0.931898i	$0.381848\pi$
$599$			1116.41i			1.86380i	−0.362720	+	0.931898i	$0.618152\pi$
$600$	−168.232	−	129.221i	−0.280387	−	0.215368i
$601$	−164.655			−0.273969			−0.136984	−	0.990573i	$-0.543741\pi$
$601$	−164.655			−0.273969			−0.136984	+	0.990573i	$0.543741\pi$
$602$	−321.222			−0.533591
$603$	114.278	+	109.792i	0.189516	+	0.182076i
$604$	−435.464			−0.720966
$605$	−58.8854	+	100.767i	−0.0973312	+	0.166557i
$606$	−121.821	−	285.971i	−0.201025	−	0.471900i
$607$			997.201i			1.64284i	0.570327	+	0.821418i	$0.306817\pi$
$607$			997.201i			1.64284i	−0.570327	+	0.821418i	$0.693183\pi$
$608$	−206.010			−0.338832
$609$	−209.680	+	89.3216i	−0.344302	+	0.146669i
$610$	38.3067	−	65.5518i	0.0627979	−	0.107462i
$611$		−	63.7047i		−	0.104263i
$612$	297.157	−	309.300i	0.485550	−	0.505392i
$613$		−	368.242i		−	0.600721i	−0.953826	−	0.300361i	$-0.902893\pi$
$613$		−	368.242i		−	0.600721i	0.953826	−	0.300361i	$-0.0971070\pi$
$614$			538.985i			0.877826i
$615$	512.024	+	64.9318i	0.832560	+	0.105580i
$616$	−190.179			−0.308732
$617$	6.35206			0.0102951			0.00514754	−	0.999987i	$-0.498361\pi$
$617$	6.35206			0.0102951			0.00514754	+	0.999987i	$0.498361\pi$
$618$	131.237	+	308.076i	0.212358	+	0.498504i
$619$	601.534			0.971783			0.485892	−	0.874019i	$-0.338495\pi$
$619$	601.534			0.971783			0.485892	+	0.874019i	$0.338495\pi$
$620$	−53.3626	+	91.3160i	−0.0860688	+	0.147284i
$621$	−45.9383	+	121.065i	−0.0739747	+	0.194951i
$622$		−	603.401i		−	0.970098i
$623$	175.808			0.282197
$624$	−22.9675	−	53.9156i	−0.0368069	−	0.0864032i
$625$	−323.799	+	534.583i	−0.518079	+	0.855333i
$626$		−	542.459i		−	0.866548i
$627$	423.133	+	993.291i	0.674853	+	1.58420i
$628$		−	549.642i		−	0.875226i
$629$		−	985.347i		−	1.56653i
$630$	416.549	−	118.234i	0.661188	−	0.187674i
$631$	−837.199			−1.32678			−0.663391	−	0.748273i	$-0.730883\pi$
$631$	−837.199			−1.32678			−0.663391	+	0.748273i	$0.730883\pi$
$632$	4.26487			0.00674821
$633$	−717.301	+	305.564i	−1.13318	+	0.482723i
$634$	132.548			0.209067
$635$	−793.669	−	463.799i	−1.24987	−	0.730392i
$636$	−234.726	+	99.9910i	−0.369066	+	0.157219i
$637$			13.2134i			0.0207432i
$638$	156.045			0.244585
$639$	544.236	+	522.869i	0.851699	+	0.818261i
$640$	28.5411	−	48.8406i	0.0445955	−	0.0763134i
$641$		−	1023.80i		−	1.59720i	−0.601864	−	0.798599i	$-0.705575\pi$
$641$		−	1023.80i		−	1.59720i	0.601864	−	0.798599i	$-0.294425\pi$
$642$	112.896	−	48.0925i	0.175850	−	0.0749104i
$643$			567.219i			0.882144i	0.897472	+	0.441072i	$0.145402\pi$
$643$			567.219i			0.882144i	−0.897472	+	0.441072i	$0.854598\pi$
$644$			65.2616i			0.101338i
$645$	−496.767	−	62.9970i	−0.770181	−	0.0976697i
$646$	−1227.23			−1.89974
$647$	−161.598			−0.249765			−0.124882	−	0.992172i	$-0.539855\pi$
$647$	−161.598			−0.249765			−0.124882	+	0.992172i	$0.539855\pi$
$648$	9.17111	+	228.919i	0.0141529	+	0.353270i
$649$	933.866			1.43893
$650$	−150.429	+	84.7563i	−0.231429	+	0.130394i
$651$	−84.6088	−	198.616i	−0.129967	−	0.305094i
$652$		−	362.643i		−	0.556201i
$653$	61.5410			0.0942435			0.0471218	−	0.998889i	$-0.484995\pi$
$653$	61.5410			0.0942435			0.0471218	+	0.998889i	$0.484995\pi$
$654$	−688.572	+	293.325i	−1.05286	+	0.448510i
$655$	−66.0608	−	38.6042i	−0.100856	−	0.0589377i
$656$			137.633i			0.209807i
$657$	455.667	+	437.778i	0.693557	+	0.666328i
$658$			125.518i			0.190757i
$659$		−	451.630i		−	0.685326i	−0.939458	−	0.342663i	$-0.888671\pi$
$659$		−	451.630i		−	0.685326i	0.939458	−	0.342663i	$-0.111329\pi$
$660$	−294.110	−	37.2973i	−0.445622	−	0.0565111i
$661$	−11.7356			−0.0177543			−0.00887717	−	0.999961i	$-0.502826\pi$
$661$	−11.7356			−0.0177543			−0.00887717	+	0.999961i	$0.502826\pi$
$662$	−334.625			−0.505476
$663$	−136.821	−	321.184i	−0.206367	−	0.484440i
$664$	−280.416			−0.422314
$665$	−1069.68	−	625.091i	−1.60854	−	0.939986i
$666$	379.538	+	364.638i	0.569878	+	0.547504i
$667$		−	53.5483i		−	0.0802823i
$668$	−373.344			−0.558898
$669$	−362.352	−	850.611i	−0.541633	−	1.27147i
$670$	107.499	+	62.8195i	0.160446	+	0.0937605i
$671$		−	106.108i		−	0.158134i
$672$	45.2532	+	106.231i	0.0673411	+	0.158081i
$673$			312.344i			0.464107i	0.972703	+	0.232053i	$0.0745444\pi$
$673$			312.344i			0.464107i	−0.972703	+	0.232053i	$0.925456\pi$
$674$			262.244i			0.389086i
$675$	667.377	−	101.157i	0.988707	−	0.149862i
$676$	290.300			0.429438
$677$	−1009.66			−1.49137			−0.745686	−	0.666298i	$-0.767878\pi$
$677$	−1009.66			−1.49137			−0.745686	+	0.666298i	$0.767878\pi$
$678$	−102.229	+	43.5488i	−0.150781	+	0.0642313i
$679$	269.258			0.396551
$680$	170.024	−	290.951i	0.250035	−	0.427869i
$681$	−345.838	+	147.324i	−0.507838	+	0.216334i
$682$			147.812i			0.216733i
$683$	−1040.36			−1.52323			−0.761613	−	0.648033i	$-0.775592\pi$
$683$	−1040.36			−1.52323			−0.761613	+	0.648033i	$0.775592\pi$
$684$	454.150	−	472.708i	0.663962	−	0.691094i
$685$	−45.1969	+	77.3425i	−0.0659808	+	0.112909i
$686$		−	497.527i		−	0.725259i
$687$	935.443	−	398.490i	1.36163	−	0.580044i
$688$		−	133.532i		−	0.194087i
$689$			207.666i			0.301402i
$690$	−12.7989	+	100.927i	−0.0185491	+	0.146271i
$691$	−974.664			−1.41051			−0.705256	−	0.708953i	$-0.749168\pi$
$691$	−974.664			−1.41051			−0.705256	+	0.708953i	$0.749168\pi$
$692$	630.509			0.911141
$693$	419.251	−	436.383i	0.604979	−	0.629702i
$694$	787.555			1.13481
$695$	−55.3811	+	94.7701i	−0.0796850	+	0.136360i
$696$	−37.1311	−	87.1640i	−0.0533492	−	0.125236i
$697$			819.903i			1.17633i
$698$	320.498			0.459167
$699$	−443.920	+	189.106i	−0.635079	+	0.270538i
$700$	296.392	−	166.996i	0.423417	−	0.238566i
$701$		−	954.417i		−	1.36151i	−0.732512	−	0.680754i	$-0.761652\pi$
$701$		−	954.417i		−	1.36151i	0.732512	−	0.680754i	$-0.238348\pi$
$702$	174.346	+	66.1561i	0.248357	+	0.0942394i
$703$		−	1505.92i		−	2.14214i
$704$		−	79.0576i		−	0.112298i
$705$	−24.6162	+	194.113i	−0.0349166	+	0.275337i
$706$	−303.436			−0.429796
$707$	498.495			0.705085
$708$	−222.214	−	521.640i	−0.313861	−	0.736780i
$709$	833.880			1.17614			0.588068	−	0.808812i	$-0.299889\pi$
$709$	833.880			1.17614			0.588068	+	0.808812i	$0.299889\pi$
$710$	511.950	+	299.170i	0.721056	+	0.421366i
$711$	−9.40192	+	9.78613i	−0.0132235	+	0.0137639i
$712$			73.0837i			0.102646i
$713$	50.7230			0.0711402
$714$	269.580	+	632.832i	0.377564	+	0.886319i
$715$	−121.749	+	208.340i	−0.170278	+	0.291385i
$716$			148.414i			0.207283i
$717$	328.783	+	771.807i	0.458553	+	1.07644i
$718$		−	702.838i		−	0.978883i
$719$		−	118.872i		−	0.165330i	−0.996577	−	0.0826651i	$-0.973657\pi$
$719$		−	118.872i		−	0.165330i	0.996577	−	0.0826651i	$-0.0263432\pi$
$720$	49.1502	+	173.160i	0.0682641	+	0.240500i
$721$	−537.027			−0.744836
$722$	−1365.07			−1.89068
$723$	1023.11	−	435.835i	1.41509	−	0.602815i
$724$	554.418			0.765771
$725$	−243.195	+	137.023i	−0.335441	+	0.188998i
$726$	91.1101	−	38.8121i	0.125496	−	0.0534601i
$727$		−	1270.03i		−	1.74694i	−0.486878	−	0.873470i	$-0.661864\pi$
$727$		−	1270.03i		−	1.74694i	0.486878	−	0.873470i	$-0.338136\pi$
$728$	93.9838			0.129099
$729$	−545.494	−	483.609i	−0.748276	−	0.663387i
$730$	428.636	+	250.483i	0.587172	+	0.343128i
$731$		−	795.472i		−	1.08820i
$732$	−59.2699	+	25.2484i	−0.0809698	+	0.0344924i
$733$		−	814.568i		−	1.11128i	−0.831423	−	0.555640i	$-0.812473\pi$
$733$		−	814.568i		−	1.11128i	0.831423	−	0.555640i	$-0.187527\pi$
$734$		−	714.006i		−	0.972761i
$735$	5.10582	−	40.2623i	0.00694669	−	0.0547786i
$736$	−27.1293			−0.0368605
$737$	174.007			0.236102
$738$	−315.812	−	303.413i	−0.427930	−	0.411129i
$739$	62.6723			0.0848069			0.0424035	−	0.999101i	$-0.486499\pi$
$739$	62.6723			0.0848069			0.0424035	+	0.999101i	$0.486499\pi$
$740$	357.023	+	208.635i	0.482463	+	0.281939i
$741$	−209.106	−	490.871i	−0.282195	−	0.662444i
$742$		−	409.166i		−	0.551437i
$743$	867.681			1.16781			0.583904	−	0.811823i	$-0.301525\pi$
$743$	867.681			1.16781			0.583904	+	0.811823i	$0.301525\pi$
$744$	82.5651	−	35.1719i	0.110975	−	0.0472741i
$745$	−675.311	−	394.634i	−0.906458	−	0.529710i
$746$		−	447.341i		−	0.599653i
$747$	618.179	−	643.441i	0.827549	−	0.861367i
$748$		−	470.958i		−	0.629624i
$749$			196.796i			0.262745i
$750$	491.119	−	200.131i	0.654825	−	0.266842i
$751$	−437.191			−0.582145			−0.291073	−	0.956701i	$-0.594012\pi$
$751$	−437.191			−0.582145			−0.291073	+	0.956701i	$0.594012\pi$
$752$	−52.1780			−0.0693856
$753$	−404.265	−	949.000i	−0.536872	−	1.26029i
$754$	−77.1154			−0.102275
$755$	549.273	−	939.935i	0.727514	−	1.24495i
$756$	−343.517	−	130.348i	−0.454387	−	0.172418i
$757$			447.984i			0.591789i	0.955221	+	0.295894i	$0.0956177\pi$
$757$			447.984i			0.591789i	−0.955221	+	0.295894i	$0.904382\pi$
$758$	−124.484			−0.164227
$759$	55.7221	+	130.806i	0.0734152	+	0.172340i
$760$	259.851	−	444.666i	0.341909	−	0.585087i
$761$			178.177i			0.234135i	0.993124	+	0.117067i	$0.0373494\pi$
$761$			178.177i			0.234135i	−0.993124	+	0.117067i	$0.962651\pi$
$762$	305.695	+	717.611i	0.401175	+	0.941746i
$763$		−	1200.30i		−	1.57313i
$764$			73.1115i			0.0956957i
$765$	292.795	+	1031.54i	0.382739	+	1.34842i
$766$	−564.876			−0.737435
$767$	−461.503			−0.601699
$768$	−44.1601	+	18.8118i	−0.0575002	+	0.0244945i
$769$	5.08745			0.00661567			0.00330784	−	0.999995i	$-0.498947\pi$
$769$	5.08745			0.00661567			0.00330784	+	0.999995i	$0.498947\pi$
$770$	239.883	−	410.496i	0.311536	−	0.533111i
$771$	626.507	−	266.886i	0.812590	−	0.346156i
$772$		−	264.548i		−	0.342678i
$773$	144.982			0.187558			0.0937791	−	0.995593i	$-0.470105\pi$
$773$	144.982			0.187558			0.0937791	+	0.995593i	$0.470105\pi$
$774$	306.402	+	294.372i	0.395868	+	0.380326i
$775$	−129.794	−	230.363i	−0.167476	−	0.297243i
$776$			111.931i			0.144241i
$777$	−776.541	+	330.799i	−0.999409	+	0.425739i
$778$			570.519i			0.733315i
$779$			1253.07i			1.60857i
$780$	145.345	+	18.4318i	0.186340	+	0.0236305i
$781$	828.686			1.06106
$782$	−161.614			−0.206667
$783$	281.862	+	106.953i	0.359976	+	0.136594i
$784$	10.8226			0.0138043
$785$	1186.39	+	693.292i	1.51132	+	0.883175i
$786$	25.4445	+	59.7301i	0.0323721	+	0.0759925i
$787$		−	1314.58i		−	1.67037i	−0.549968	−	0.835186i	$-0.685360\pi$
$787$		−	1314.58i		−	1.67037i	0.549968	−	0.835186i	$-0.314640\pi$
$788$	−542.300			−0.688197
$789$	−747.423	+	318.395i	−0.947304	+	0.403543i
$790$	−5.37950	+	9.20559i	−0.00680949	+	0.0116526i
$791$		−	178.203i		−	0.225288i
$792$	181.405	+	174.283i	0.229047	+	0.220054i
$793$			52.4370i			0.0661249i
$794$		−	784.058i		−	0.987478i
$795$	80.2444	−	632.772i	0.100936	−	0.795940i
$796$	−357.842			−0.449550
$797$	1331.60			1.67077			0.835385	−	0.549665i	$-0.185245\pi$
$797$	1331.60			1.67077			0.835385	+	0.549665i	$0.185245\pi$
$798$	412.005	+	967.168i	0.516297	+	1.21199i
$799$	−310.832			−0.389027
$800$	69.4205	+	123.210i	0.0867757	+	0.154013i
$801$	−167.697	−	161.113i	−0.209360	−	0.201140i
$802$		−	605.176i		−	0.754584i
$803$	693.826			0.864043
$804$	−41.4051	−	97.1972i	−0.0514989	−	0.120892i
$805$	−140.865	−	82.3179i	−0.174988	−	0.102258i
$806$		−	73.0466i		−	0.0906286i
$807$	101.131	+	237.403i	0.125318	+	0.294180i
$808$			207.225i			0.256466i
$809$		−	1283.74i		−	1.58682i	−0.608686	−	0.793411i	$-0.708303\pi$
$809$		−	1283.74i		−	1.58682i	0.608686	−	0.793411i	$-0.291697\pi$
$810$	−505.683	−	268.952i	−0.624300	−	0.332039i
$811$	−1327.85			−1.63730			−0.818648	−	0.574295i	$-0.805276\pi$
$811$	−1327.85			−1.63730			−0.818648	+	0.574295i	$0.805276\pi$
$812$	151.941			0.187120
$813$	−57.0813	+	24.3161i	−0.0702107	+	0.0299091i
$814$	577.908			0.709961
$815$	782.754	+	457.421i	0.960435	+	0.561252i
$816$	−263.069	+	112.065i	−0.322388	+	0.137334i
$817$		−	1215.73i		−	1.48805i
$818$	−1015.20			−1.24108
$819$	−207.188	+	215.655i	−0.252977	+	0.263315i
$820$	−297.077	−	173.604i	−0.362289	−	0.211712i
$821$			147.862i			0.180100i	0.995937	+	0.0900499i	$0.0287027\pi$
$821$			147.862i			0.180100i	−0.995937	+	0.0900499i	$0.971297\pi$
$822$	69.9306	−	29.7898i	0.0850737	−	0.0362406i
$823$		−	109.172i		−	0.132651i	−0.997798	−	0.0663256i	$-0.978872\pi$
$823$		−	109.172i		−	0.132651i	0.997798	−	0.0663256i	$-0.0211276\pi$
$824$		−	223.243i		−	0.270925i
$825$	451.482	−	587.783i	0.547251	−	0.712465i
$826$	909.306			1.10085
$827$	524.450			0.634160			0.317080	−	0.948399i	$-0.397298\pi$
$827$	524.450			0.634160			0.317080	+	0.948399i	$0.397298\pi$
$828$	59.8067	−	62.2507i	0.0722304	−	0.0751820i
$829$	−589.662			−0.711293			−0.355647	−	0.934620i	$-0.615739\pi$
$829$	−589.662			−0.711293			−0.355647	+	0.934620i	$0.615739\pi$
$830$	353.704	−	605.270i	0.426149	−	0.729241i
$831$	401.068	+	941.496i	0.482633	+	1.13297i
$832$			39.0692i			0.0469581i
$833$	64.4719			0.0773972
$834$	85.6881	−	36.5023i	0.102744	−	0.0437678i
$835$	470.918	−	805.851i	0.563973	−	0.965091i
$836$		−	719.774i		−	0.860974i
$837$	−101.310	+	266.990i	−0.121039	+	0.318984i
$838$		−	10.9030i		−	0.0130107i
$839$			260.576i			0.310579i	0.987869	+	0.155290i	$0.0496311\pi$
$839$			260.576i			0.310579i	−0.987869	+	0.155290i	$0.950369\pi$
$840$	−286.376	−	36.3164i	−0.340923	−	0.0432338i
$841$	716.329			0.851759
$842$	−906.763			−1.07692
$843$	412.880	+	969.224i	0.489775	+	1.14973i
$844$	519.782			0.615856
$845$	−366.170	+	626.604i	−0.433338	+	0.741543i
$846$	115.027	−	119.727i	0.135965	−	0.141522i
$847$			158.820i			0.187509i
$848$	170.091			0.200579
$849$	−194.193	−	455.863i	−0.228732	−	0.536941i
$850$	413.549	+	733.983i	0.486528	+	0.863510i
$851$		−	198.314i		−	0.233037i
$852$	−197.186	−	462.889i	−0.231439	−	0.543297i
$853$		−	1258.29i		−	1.47513i	−0.675275	−	0.737566i	$-0.735975\pi$
$853$		−	1258.29i		−	1.47513i	0.675275	−	0.737566i	$-0.264025\pi$
$854$		−	103.317i		−	0.120980i
$855$	447.484	+	1576.52i	0.523373	+	1.84388i
$856$	−81.8082			−0.0955703
$857$	−495.628			−0.578329			−0.289164	−	0.957279i	$-0.593377\pi$
$857$	−495.628			−0.578329			−0.289164	+	0.957279i	$0.593377\pi$
$858$	188.375	−	80.2459i	0.219551	−	0.0935267i
$859$	462.818			0.538787			0.269394	−	0.963030i	$-0.413177\pi$
$859$	462.818			0.538787			0.269394	+	0.963030i	$0.413177\pi$
$860$	288.225	+	168.431i	0.335145	+	0.195850i
$861$	646.157	−	275.257i	0.750472	−	0.319694i
$862$		−	1034.98i		−	1.20067i
$863$	137.901			0.159792			0.0798960	−	0.996803i	$-0.474541\pi$
$863$	137.901			0.159792			0.0798960	+	0.996803i	$0.474541\pi$
$864$	54.1858	−	142.800i	0.0627151	−	0.165278i
$865$	−795.294	+	1360.94i	−0.919415	+	1.57334i
$866$			96.4948i			0.111426i
$867$	−769.500	+	327.800i	−0.887543	+	0.378085i
$868$			143.925i			0.165812i
$869$			14.9010i			0.0171472i
$870$	234.976	+	29.7983i	0.270088	+	0.0342509i
$871$	−85.9919			−0.0987278
$872$	498.964			0.572206
$873$	−256.836	−	246.752i	−0.294199	−	0.282648i
$874$	−246.997			−0.282605
$875$	−13.3979	+	850.394i	−0.0153119	+	0.971879i
$876$	−165.096	−	387.559i	−0.188466	−	0.442419i
$877$			960.769i			1.09552i	0.836636	+	0.547759i	$0.184519\pi$
$877$			960.769i			1.09552i	−0.836636	+	0.547759i	$0.815481\pi$
$878$	−667.837			−0.760635
$879$	118.007	−	50.2698i	0.134251	−	0.0571898i
$880$	170.643	+	99.7194i	0.193913	+	0.113318i
$881$			1584.47i			1.79849i	0.437443	+	0.899246i	$0.355884\pi$
$881$			1584.47i			1.79849i	−0.437443	+	0.899246i	$0.644116\pi$
$882$	−23.8585	+	24.8334i	−0.0270504	+	0.0281558i
$883$			386.919i			0.438186i	0.975704	+	0.219093i	$0.0703099\pi$
$883$			386.919i			0.438186i	−0.975704	+	0.219093i	$0.929690\pi$
$884$			232.741i			0.263282i
$885$	1406.23	+	178.330i	1.58897	+	0.201503i
$886$	−895.253			−1.01044
$887$	−373.291			−0.420847			−0.210424	−	0.977610i	$-0.567484\pi$
$887$	−373.291			−0.420847			−0.210424	+	0.977610i	$0.567484\pi$
$888$	−137.514	−	322.809i	−0.154858	−	0.363524i
$889$	−1250.91			−1.40710
$890$	−157.749	−	92.1843i	−0.177246	−	0.103578i
$891$	−799.816	+	32.0428i	−0.897661	+	0.0359627i
$892$			616.383i			0.691012i
$893$	−475.051			−0.531972
$894$	260.108	+	610.595i	0.290948	+	0.682993i
$895$	−320.348	−	187.203i	−0.357931	−	0.209165i
$896$		−	76.9784i		−	0.0859134i
$897$	−27.5371	−	64.6425i	−0.0306991	−	0.0720652i
$898$			939.784i			1.04653i
$899$		−	118.093i		−	0.131360i
$900$	−435.755	−	112.326i	−0.484173	−	0.124807i
$901$	1013.26			1.12459
$902$	−480.875			−0.533121
$903$	−626.903	+	267.055i	−0.694244	+	0.295742i
$904$	74.0791			0.0819459
$905$	−699.316	+	1196.69i	−0.772725	+	1.32231i
$906$	−849.860	+	362.032i	−0.938035	+	0.399594i
$907$		−	1427.03i		−	1.57335i	−0.617367	−	0.786676i	$-0.711800\pi$
$907$		−	1427.03i		−	1.57335i	0.617367	−	0.786676i	$-0.288200\pi$
$908$	250.606			0.275998
$909$	−475.497	−	456.828i	−0.523099	−	0.502562i
$910$	−118.547	+	202.861i	−0.130271	+	0.222924i
$911$			156.788i			0.172105i	0.996291	+	0.0860527i	$0.0274253\pi$
$911$			156.788i			0.172105i	−0.996291	+	0.0860527i	$0.972575\pi$
$912$	−402.053	+	171.271i	−0.440847	+	0.187797i
$913$		−	979.742i		−	1.07310i
$914$		−	656.581i		−	0.718360i
$915$	20.2623	−	159.779i	0.0221445	−	0.174622i
$916$	−677.855			−0.740017
$917$	−104.120			−0.113544
$918$	322.794	−	850.683i	0.351627	−	0.926670i
$919$	−929.004			−1.01089			−0.505443	−	0.862860i	$-0.668671\pi$
$919$	−929.004			−1.01089			−0.505443	+	0.862860i	$0.668671\pi$
$920$	34.2196	−	58.5578i	0.0371952	−	0.0636498i
$921$	448.097	+	1051.89i	0.486533	+	1.14212i
$922$			249.516i			0.270625i
$923$	−409.525			−0.443689
$924$	−371.157	+	158.109i	−0.401685	+	0.171114i
$925$	−900.663	+	507.461i	−0.973690	+	0.548607i
$926$		−	170.500i		−	0.184125i
$927$	512.251	+	492.140i	0.552590	+	0.530895i
$928$			63.1622i			0.0680627i
$929$		−	1129.08i		−	1.21537i	−0.794179	−	0.607683i	$-0.792099\pi$
$929$		−	1129.08i		−	1.21537i	0.794179	−	0.607683i	$-0.207901\pi$
$930$	−28.2260	+	222.578i	−0.0303506	+	0.239332i
$931$	98.5336			0.105836
$932$	321.680			0.345151
$933$	−501.651	−	1177.61i	−0.537675	−	1.26218i
$934$	518.949			0.555620
$935$	1016.55	+	594.044i	1.08722	+	0.635342i
$936$	−89.6478	−	86.1282i	−0.0957776	−	0.0920173i
$937$			449.455i			0.479675i	0.970813	+	0.239837i	$0.0770941\pi$
$937$			449.455i			0.479675i	−0.970813	+	0.239837i	$0.922906\pi$
$938$	169.431			0.180630
$939$	−450.985	−	1058.67i	−0.480283	−	1.12745i
$940$	65.8148	−	112.625i	0.0700157	−	0.119813i
$941$			1348.78i			1.43335i	0.697409	+	0.716673i	$0.254336\pi$
$941$			1348.78i			1.43335i	−0.697409	+	0.716673i	$0.745664\pi$
$942$	−456.957	−	1072.69i	−0.485092	−	1.13874i
$943$			165.017i			0.174991i
$944$			377.999i			0.400423i
$945$	714.648	−	577.055i	0.756241	−	0.610641i
$946$	466.546			0.493177
$947$	1405.60			1.48427			0.742133	−	0.670253i	$-0.233814\pi$
$947$	1405.60			1.48427			0.742133	+	0.670253i	$0.233814\pi$
$948$	8.32340	−	3.54569i	0.00877996	−	0.00374018i
$949$	−342.879			−0.361306
$950$	632.034	+	1121.76i	0.665299	+	1.18080i
$951$	258.684	−	110.197i	0.272012	−	0.115875i
$952$		−	458.573i		−	0.481694i
$953$	−1194.99			−1.25392			−0.626961	−	0.779051i	$-0.715701\pi$
$953$	−1194.99			−1.25392			−0.626961	+	0.779051i	$0.715701\pi$
$954$	−374.966	+	390.289i	−0.393046	+	0.409108i
$955$	−157.809	−	92.2194i	−0.165245	−	0.0965648i
$956$		−	559.279i		−	0.585020i
$957$	304.541	−	129.732i	0.318225	−	0.135561i
$958$			1117.90i			1.16691i
$959$			121.901i			0.127112i
$960$	15.0968	−	119.047i	0.0157258	−	0.124007i
$961$	−849.138			−0.883598
$962$	−285.594			−0.296875
$963$	180.347	−	187.716i	0.187276	−	0.194929i
$964$	−741.382			−0.769069
$965$	571.018	+	333.688i	0.591729	+	0.345790i
$966$	54.2567	+	127.366i	0.0561663	+	0.131849i
$967$		−	778.291i		−	0.804852i	−0.915453	−	0.402426i	$-0.868167\pi$
$967$		−	778.291i		−	0.804852i	0.915453	−	0.402426i	$-0.131833\pi$
$968$	−66.0216			−0.0682042
$969$	−2395.09	+	1020.29i	−2.47171	+	1.05293i
$970$	−241.599	−	141.184i	−0.249071	−	0.145551i
$971$		−	315.297i		−	0.324713i	−0.986732	−	0.162357i	$-0.948090\pi$
$971$		−	315.297i		−	0.324713i	0.986732	−	0.162357i	$-0.0519095\pi$
$972$	208.215	+	439.138i	0.214213	+	0.451788i
$973$			149.369i			0.153513i
$974$		−	50.3478i		−	0.0516918i
$975$	−223.116	+	290.474i	−0.228837	+	0.297923i
$976$	42.9491			0.0440052
$977$	556.468			0.569568			0.284784	−	0.958592i	$-0.408078\pi$
$977$	556.468			0.569568			0.284784	+	0.958592i	$0.408078\pi$
$978$	−301.491	−	707.742i	−0.308273	−	0.723662i
$979$	−255.346			−0.260823
$980$	−13.6511	+	23.3602i	−0.0139297	+	0.0238370i
$981$	−1099.97	+	1144.92i	−1.12127	+	1.16709i
$982$			1162.64i			1.18395i
$983$	−829.558			−0.843904			−0.421952	−	0.906618i	$-0.638655\pi$
$983$	−829.558			−0.843904			−0.421952	+	0.906618i	$0.638655\pi$
$984$	114.424	+	268.608i	0.116285	+	0.272975i
$985$	684.031	−	1170.54i	0.694447	−	1.18836i
$986$			376.267i			0.381609i
$987$	104.352	+	244.964i	0.105727	+	0.248190i
$988$			355.703i			0.360023i
$989$		−	160.099i		−	0.161880i
$990$	−605.000	+	171.725i	−0.611111	+	0.173460i
$991$	−894.794			−0.902921			−0.451460	−	0.892291i	$-0.649097\pi$
$991$	−894.794			−0.902921			−0.451460	+	0.892291i	$0.649097\pi$
$992$	−59.8296			−0.0603121
$993$	−653.061	+	278.198i	−0.657664	+	0.280159i
$994$	806.892			0.811763
$995$	451.364	−	772.390i	0.453633	−	0.776272i
$996$	−547.266	+	233.130i	−0.549464	+	0.234066i
$997$			1621.92i			1.62680i	0.581703	+	0.813401i	$0.302387\pi$
$997$			1621.92i			1.62680i	−0.581703	+	0.813401i	$0.697613\pi$
$998$	−143.259			−0.143546
$999$	1043.86	+	396.096i	1.04491	+	0.396493i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.b.a.599.8	yes	88
3.2	odd	2	inner	690.3.b.a.599.82	yes	88
5.4	even	2	inner	690.3.b.a.599.81	yes	88
15.14	odd	2	inner	690.3.b.a.599.7	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.b.a.599.7	✓	88	15.14	odd	2	inner
690.3.b.a.599.8	yes	88	1.1	even	1	trivial
690.3.b.a.599.81	yes	88	5.4	even	2	inner
690.3.b.a.599.82	yes	88	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +(-2.76001 + 1.17574i) q^{3} +2.00000 q^{4} +(-2.52270 + 4.31694i) q^{5} +(3.90324 - 1.66274i) q^{6} +6.80400i q^{7} -2.82843 q^{8} +(6.23528 - 6.49009i) q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +(-2.76001 + 1.17574i) q^{3} +2.00000 q^{4} +(-2.52270 + 4.31694i) q^{5} +(3.90324 - 1.66274i) q^{6} +6.80400i q^{7} -2.82843 q^{8} +(6.23528 - 6.49009i) q^{9} +(3.56764 - 6.10507i) q^{10} -9.88220i q^{11} +(-5.52002 + 2.35147i) q^{12} +4.88365i q^{13} -9.62230i q^{14} +(1.88710 - 14.8808i) q^{15} +4.00000 q^{16} +23.8286 q^{17} +(-8.81802 + 9.17837i) q^{18} +36.4177 q^{19} +(-5.04541 + 8.63388i) q^{20} +(-7.99971 - 18.7791i) q^{21} +13.9755i q^{22} +4.79583 q^{23} +(7.80648 - 3.32549i) q^{24} +(-12.2719 - 21.7807i) q^{25} -6.90652i q^{26} +(-9.57879 + 25.2437i) q^{27} +13.6080i q^{28} -11.1656i q^{29} +(-2.66876 + 21.0447i) q^{30} +10.5765 q^{31} -5.65685 q^{32} +(11.6189 + 27.2749i) q^{33} -33.6988 q^{34} +(-29.3724 - 17.1645i) q^{35} +(12.4706 - 12.9802i) q^{36} -41.3514i q^{37} -51.5024 q^{38} +(-5.74188 - 13.4789i) q^{39} +(7.13528 - 12.2101i) q^{40} +34.4083i q^{41} +(11.3133 + 26.5576i) q^{42} -33.3830i q^{43} -19.7644i q^{44} +(12.2875 + 43.2899i) q^{45} -6.78233 q^{46} -13.0445 q^{47} +(-11.0400 + 4.70295i) q^{48} +2.70565 q^{49} +(17.3551 + 30.8026i) q^{50} +(-65.7672 + 28.0162i) q^{51} +9.76729i q^{52} +42.5227 q^{53} +(13.5465 - 35.7000i) q^{54} +(42.6608 + 24.9299i) q^{55} -19.2446i q^{56} +(-100.513 + 42.8177i) q^{57} +15.7905i q^{58} +94.4998i q^{59} +(3.77419 - 29.7616i) q^{60} +10.7373 q^{61} -14.9574 q^{62} +(44.1585 + 42.4248i) q^{63} +8.00000 q^{64} +(-21.0824 - 12.3200i) q^{65} +(-16.4316 - 38.5726i) q^{66} +17.6081i q^{67} +47.6573 q^{68} +(-13.2365 + 5.63864i) q^{69} +(41.5389 + 24.2742i) q^{70} +83.8565i q^{71} +(-17.6360 + 18.3567i) q^{72} +70.2097i q^{73} +58.4797i q^{74} +(59.4790 + 45.6864i) q^{75} +72.8355 q^{76} +67.2384 q^{77} +(8.12025 + 19.0620i) q^{78} -1.50786 q^{79} +(-10.0908 + 17.2678i) q^{80} +(-3.24248 - 80.9351i) q^{81} -48.6607i q^{82} +99.1421 q^{83} +(-15.9994 - 37.5582i) q^{84} +(-60.1126 + 102.867i) q^{85} +47.2107i q^{86} +(13.1278 + 30.8171i) q^{87} +27.9511i q^{88} -25.8390i q^{89} +(-17.3772 - 61.2212i) q^{90} -33.2283 q^{91} +9.59166 q^{92} +(-29.1912 + 12.4352i) q^{93} +18.4477 q^{94} +(-91.8711 + 157.213i) q^{95} +(15.6130 - 6.65097i) q^{96} -39.5735i q^{97} -3.82636 q^{98} +(-64.1363 - 61.6183i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 176 q^{4} + 8 q^{9}+O(q^{10}) \) 88 * q + 176 * q^4 + 8 * q^9	\( 88 q + 176 q^{4} + 8 q^{9} + 32 q^{10} - 12 q^{15} + 352 q^{16} - 16 q^{19} - 176 q^{21} + 72 q^{25} - 72 q^{30} + 32 q^{31} + 160 q^{34} + 16 q^{36} + 144 q^{39} + 64 q^{40} + 92 q^{45} - 360 q^{49} + 48 q^{51} - 144 q^{54} + 16 q^{55} - 24 q^{60} + 208 q^{61} + 704 q^{64} + 512 q^{66} + 304 q^{70} + 536 q^{75} - 32 q^{76} + 448 q^{79} - 24 q^{81} - 352 q^{84} - 96 q^{85} + 32 q^{90} - 64 q^{91} + 160 q^{94} + 296 q^{99}+O(q^{100}) \) 88 * q + 176 * q^4 + 8 * q^9 + 32 * q^10 - 12 * q^15 + 352 * q^16 - 16 * q^19 - 176 * q^21 + 72 * q^25 - 72 * q^30 + 32 * q^31 + 160 * q^34 + 16 * q^36 + 144 * q^39 + 64 * q^40 + 92 * q^45 - 360 * q^49 + 48 * q^51 - 144 * q^54 + 16 * q^55 - 24 * q^60 + 208 * q^61 + 704 * q^64 + 512 * q^66 + 304 * q^70 + 536 * q^75 - 32 * q^76 + 448 * q^79 - 24 * q^81 - 352 * q^84 - 96 * q^85 + 32 * q^90 - 64 * q^91 + 160 * q^94 + 296 * q^99

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