LMFDB - Embedded newform 210.3.c.a.29.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(29,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, 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("210.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.c (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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.16
Character	$\chi$	$=$	210.29
Dual form			210.3.c.a.29.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +(-2.70965 + 1.28756i) q^{3} +2.00000 q^{4} +(3.71627 - 3.34505i) q^{5} +(-3.83202 + 1.82088i) q^{6} -2.64575i q^{7} +2.82843 q^{8} +(5.68438 - 6.97766i) q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +(-2.70965 + 1.28756i) q^{3} +2.00000 q^{4} +(3.71627 - 3.34505i) q^{5} +(-3.83202 + 1.82088i) q^{6} -2.64575i q^{7} +2.82843 q^{8} +(5.68438 - 6.97766i) q^{9} +(5.25560 - 4.73061i) q^{10} -10.4698i q^{11} +(-5.41930 + 2.57512i) q^{12} +11.9937i q^{13} -3.74166i q^{14} +(-5.76283 + 13.8488i) q^{15} +4.00000 q^{16} +29.1133 q^{17} +(8.03893 - 9.86791i) q^{18} +20.3176 q^{19} +(7.43254 - 6.69010i) q^{20} +(3.40656 + 7.16905i) q^{21} -14.8066i q^{22} -7.71572 q^{23} +(-7.66404 + 3.64177i) q^{24} +(2.62131 - 24.8622i) q^{25} +16.9617i q^{26} +(-6.41851 + 26.2260i) q^{27} -5.29150i q^{28} -47.4046i q^{29} +(-8.14988 + 19.5852i) q^{30} -35.5084 q^{31} +5.65685 q^{32} +(13.4805 + 28.3695i) q^{33} +41.1724 q^{34} +(-8.85016 - 9.83232i) q^{35} +(11.3688 - 13.9553i) q^{36} +58.0907i q^{37} +28.7334 q^{38} +(-15.4426 - 32.4988i) q^{39} +(10.5112 - 9.46122i) q^{40} +52.5850i q^{41} +(4.81761 + 10.1386i) q^{42} -15.7629i q^{43} -20.9396i q^{44} +(-2.21593 - 44.9454i) q^{45} -10.9117 q^{46} -85.2023 q^{47} +(-10.8386 + 5.15024i) q^{48} -7.00000 q^{49} +(3.70710 - 35.1605i) q^{50} +(-78.8867 + 37.4850i) q^{51} +23.9875i q^{52} -42.7649 q^{53} +(-9.07715 + 37.0892i) q^{54} +(-35.0221 - 38.9087i) q^{55} -7.48331i q^{56} +(-55.0535 + 26.1601i) q^{57} -67.0403i q^{58} +37.9769i q^{59} +(-11.5257 + 27.6976i) q^{60} +53.5108 q^{61} -50.2165 q^{62} +(-18.4612 - 15.0395i) q^{63} +8.00000 q^{64} +(40.1196 + 44.5719i) q^{65} +(19.0643 + 40.1206i) q^{66} -27.6366i q^{67} +58.2265 q^{68} +(20.9069 - 9.93444i) q^{69} +(-12.5160 - 13.9050i) q^{70} +58.0688i q^{71} +(16.0779 - 19.7358i) q^{72} -67.8080i q^{73} +82.1526i q^{74} +(24.9087 + 70.7429i) q^{75} +40.6352 q^{76} -27.7005 q^{77} +(-21.8392 - 45.9602i) q^{78} +19.2994 q^{79} +(14.8651 - 13.3802i) q^{80} +(-16.3756 - 79.3274i) q^{81} +74.3664i q^{82} -33.6998 q^{83} +(6.81312 + 14.3381i) q^{84} +(108.193 - 97.3852i) q^{85} -22.2920i q^{86} +(61.0363 + 128.450i) q^{87} -29.6131i q^{88} +46.8325i q^{89} +(-3.13380 - 63.5624i) q^{90} +31.7324 q^{91} -15.4314 q^{92} +(96.2153 - 45.7192i) q^{93} -120.494 q^{94} +(75.5056 - 67.9633i) q^{95} +(-15.3281 + 7.28354i) q^{96} -65.1337i q^{97} -9.89949 q^{98} +(-73.0549 - 59.5145i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 48 q^{4} + 44 q^{9}+O(q^{10}) $ 24 * q + 48 * q^4 + 44 * q^9	$ 24 q + 48 q^{4} + 44 q^{9} + 16 q^{10} + 4 q^{15} + 96 q^{16} - 80 q^{19} - 28 q^{21} + 48 q^{25} - 56 q^{30} + 224 q^{31} + 128 q^{34} + 88 q^{36} - 92 q^{39} + 32 q^{40} - 72 q^{45} - 144 q^{46} - 168 q^{49} - 284 q^{51} - 144 q^{54} - 320 q^{55} + 8 q^{60} + 192 q^{64} + 224 q^{66} - 152 q^{69} - 56 q^{70} + 48 q^{75} - 160 q^{76} - 72 q^{79} - 212 q^{81} - 56 q^{84} - 64 q^{85} - 240 q^{90} + 168 q^{91} - 128 q^{94} - 876 q^{99}+O(q^{100}) $ 24 * q + 48 * q^4 + 44 * q^9 + 16 * q^10 + 4 * q^15 + 96 * q^16 - 80 * q^19 - 28 * q^21 + 48 * q^25 - 56 * q^30 + 224 * q^31 + 128 * q^34 + 88 * q^36 - 92 * q^39 + 32 * q^40 - 72 * q^45 - 144 * q^46 - 168 * q^49 - 284 * q^51 - 144 * q^54 - 320 * q^55 + 8 * q^60 + 192 * q^64 + 224 * q^66 - 152 * q^69 - 56 * q^70 + 48 * q^75 - 160 * q^76 - 72 * q^79 - 212 * q^81 - 56 * q^84 - 64 * q^85 - 240 * q^90 + 168 * q^91 - 128 * q^94 - 876 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$1$	$-1$	$-1$

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
$3$	−2.70965	+	1.28756i	−0.903216	+	0.429186i
$3$	−2.70965	+	1.28756i	−0.903216	+	0.429186i
$4$	2.00000			0.500000
$5$	3.71627	−	3.34505i	0.743254	−	0.669010i
$5$	3.71627	−	3.34505i	0.743254	−	0.669010i
$6$	−3.83202	+	1.82088i	−0.638670	+	0.303481i
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	2.82843			0.353553
$9$	5.68438	−	6.97766i	0.631598	−	0.775296i
$10$	5.25560	−	4.73061i	0.525560	−	0.473061i
$11$		−	10.4698i		−	0.951802i	−0.879499	−	0.475901i	$-0.842122\pi$
$11$		−	10.4698i		−	0.951802i	0.879499	−	0.475901i	$-0.157878\pi$
$12$	−5.41930	+	2.57512i	−0.451608	+	0.214593i
$13$			11.9937i			0.922595i	0.887246	+	0.461297i	$0.152616\pi$
$13$			11.9937i			0.922595i	−0.887246	+	0.461297i	$0.847384\pi$
$14$		−	3.74166i		−	0.267261i
$15$	−5.76283	+	13.8488i	−0.384189	+	0.923255i
$16$	4.00000			0.250000
$17$	29.1133			1.71254			0.856272	−	0.516525i	$-0.172775\pi$
$17$	29.1133			1.71254			0.856272	+	0.516525i	$0.172775\pi$
$18$	8.03893	−	9.86791i	0.446607	−	0.548217i
$19$	20.3176			1.06935			0.534673	−	0.845059i	$-0.320435\pi$
$19$	20.3176			1.06935			0.534673	+	0.845059i	$0.320435\pi$
$20$	7.43254	−	6.69010i	0.371627	−	0.334505i
$21$	3.40656	+	7.16905i	0.162217	+	0.341384i
$22$		−	14.8066i		−	0.673026i
$23$	−7.71572			−0.335466			−0.167733	−	0.985832i	$-0.553645\pi$
$23$	−7.71572			−0.335466			−0.167733	+	0.985832i	$0.553645\pi$
$24$	−7.66404	+	3.64177i	−0.319335	+	0.151740i
$25$	2.62131	−	24.8622i	0.104853	−	0.994488i
$26$			16.9617i			0.652373i
$27$	−6.41851	+	26.2260i	−0.237723	+	0.971333i
$28$		−	5.29150i		−	0.188982i
$29$		−	47.4046i		−	1.63464i	−0.576182	−	0.817321i	$-0.695458\pi$
$29$		−	47.4046i		−	1.63464i	0.576182	−	0.817321i	$-0.304542\pi$
$30$	−8.14988	+	19.5852i	−0.271663	+	0.652840i
$31$	−35.5084			−1.14543			−0.572717	−	0.819753i	$-0.694110\pi$
$31$	−35.5084			−1.14543			−0.572717	+	0.819753i	$0.694110\pi$
$32$	5.65685			0.176777
$33$	13.4805	+	28.3695i	0.408501	+	0.859683i
$34$	41.1724			1.21095
$35$	−8.85016	−	9.83232i	−0.252862	−	0.280924i
$36$	11.3688	−	13.9553i	0.315799	−	0.387648i
$37$			58.0907i			1.57002i	0.619485	+	0.785009i	$0.287342\pi$
$37$			58.0907i			1.57002i	−0.619485	+	0.785009i	$0.712658\pi$
$38$	28.7334			0.756142
$39$	−15.4426	−	32.4988i	−0.395965	−	0.833302i
$40$	10.5112	−	9.46122i	0.262780	−	0.236531i
$41$			52.5850i			1.28256i	0.767307	+	0.641280i	$0.221596\pi$
$41$			52.5850i			1.28256i	−0.767307	+	0.641280i	$0.778404\pi$
$42$	4.81761	+	10.1386i	0.114705	+	0.241395i
$43$		−	15.7629i		−	0.366578i	−0.983059	−	0.183289i	$-0.941326\pi$
$43$		−	15.7629i		−	0.366578i	0.983059	−	0.183289i	$-0.0586744\pi$
$44$		−	20.9396i		−	0.475901i
$45$	−2.21593	−	44.9454i	−0.0492429	−	0.998787i
$46$	−10.9117			−0.237210
$47$	−85.2023			−1.81281			−0.906407	−	0.422405i	$-0.861186\pi$
$47$	−85.2023			−1.81281			−0.906407	+	0.422405i	$0.861186\pi$
$48$	−10.8386	+	5.15024i	−0.225804	+	0.107297i
$49$	−7.00000			−0.142857
$50$	3.70710	−	35.1605i	0.0741419	−	0.703209i
$51$	−78.8867	+	37.4850i	−1.54680	+	0.735001i
$52$			23.9875i			0.461297i
$53$	−42.7649			−0.806885			−0.403443	−	0.915005i	$-0.632187\pi$
$53$	−42.7649			−0.806885			−0.403443	+	0.915005i	$0.632187\pi$
$54$	−9.07715	+	37.0892i	−0.168095	+	0.686836i
$55$	−35.0221	−	38.9087i	−0.636765	−	0.707431i
$56$		−	7.48331i		−	0.133631i
$57$	−55.0535	+	26.1601i	−0.965850	+	0.458949i
$58$		−	67.0403i		−	1.15587i
$59$			37.9769i			0.643676i	0.946795	+	0.321838i	$0.104301\pi$
$59$			37.9769i			0.643676i	−0.946795	+	0.321838i	$0.895699\pi$
$60$	−11.5257	+	27.6976i	−0.192094	+	0.461627i
$61$	53.5108			0.877226			0.438613	−	0.898676i	$-0.355470\pi$
$61$	53.5108			0.877226			0.438613	+	0.898676i	$0.355470\pi$
$62$	−50.2165			−0.809944
$63$	−18.4612	−	15.0395i	−0.293034	−	0.238722i
$64$	8.00000			0.125000
$65$	40.1196	+	44.5719i	0.617225	+	0.685722i
$66$	19.0643	+	40.1206i	0.288854	+	0.607888i
$67$		−	27.6366i		−	0.412487i	−0.978501	−	0.206243i	$-0.933876\pi$
$67$		−	27.6366i		−	0.412487i	0.978501	−	0.206243i	$-0.0661238\pi$
$68$	58.2265			0.856272
$69$	20.9069	−	9.93444i	0.302998	−	0.143977i
$70$	−12.5160	−	13.9050i	−0.178800	−	0.198643i
$71$			58.0688i			0.817871i	0.912563	+	0.408935i	$0.134100\pi$
$71$			58.0688i			0.817871i	−0.912563	+	0.408935i	$0.865900\pi$
$72$	16.0779	−	19.7358i	0.223304	−	0.274109i
$73$		−	67.8080i		−	0.928877i	−0.885605	−	0.464438i	$-0.846256\pi$
$73$		−	67.8080i		−	0.928877i	0.885605	−	0.464438i	$-0.153744\pi$
$74$			82.1526i			1.11017i
$75$	24.9087	+	70.7429i	0.332116	+	0.943238i
$76$	40.6352			0.534673
$77$	−27.7005			−0.359747
$78$	−21.8392	−	45.9602i	−0.279990	−	0.589234i
$79$	19.2994			0.244296			0.122148	−	0.992512i	$-0.461022\pi$
$79$	19.2994			0.244296			0.122148	+	0.992512i	$0.461022\pi$
$80$	14.8651	−	13.3802i	0.185813	−	0.167252i
$81$	−16.3756	−	79.3274i	−0.202168	−	0.979351i
$82$			74.3664i			0.906907i
$83$	−33.6998			−0.406021			−0.203011	−	0.979177i	$-0.565073\pi$
$83$	−33.6998			−0.406021			−0.203011	+	0.979177i	$0.565073\pi$
$84$	6.81312	+	14.3381i	0.0811086	+	0.170692i
$85$	108.193	−	97.3852i	1.27286	−	1.14571i
$86$		−	22.2920i		−	0.259210i
$87$	61.0363	+	128.450i	0.701566	+	1.47643i
$88$		−	29.6131i		−	0.336513i
$89$			46.8325i			0.526208i	0.964768	+	0.263104i	$0.0847462\pi$
$89$			46.8325i			0.526208i	−0.964768	+	0.263104i	$0.915254\pi$
$90$	−3.13380	−	63.5624i	−0.0348200	−	0.706249i
$91$	31.7324			0.348708
$92$	−15.4314			−0.167733
$93$	96.2153	−	45.7192i	1.03457	−	0.491604i
$94$	−120.494			−1.28185
$95$	75.5056	−	67.9633i	0.794796	−	0.715403i
$96$	−15.3281	+	7.28354i	−0.159668	+	0.0758702i
$97$		−	65.1337i		−	0.671482i	−0.941954	−	0.335741i	$-0.891013\pi$
$97$		−	65.1337i		−	0.671482i	0.941954	−	0.335741i	$-0.108987\pi$
$98$	−9.89949			−0.101015
$99$	−73.0549	−	59.5145i	−0.737928	−	0.601156i
$100$	5.24263	−	49.7244i	0.0524263	−	0.497244i
$101$			171.169i			1.69474i	0.531000	+	0.847372i	$0.321816\pi$
$101$			171.169i			1.69474i	−0.531000	+	0.847372i	$0.678184\pi$
$102$	−111.563	+	53.0119i	−1.09375	+	0.519724i
$103$			129.879i			1.26096i	0.776205	+	0.630481i	$0.217142\pi$
$103$			129.879i			1.26096i	−0.776205	+	0.630481i	$0.782858\pi$
$104$			33.9234i			0.326186i
$105$	36.6405	+	15.2470i	0.348957	+	0.145210i
$106$	−60.4787			−0.570554
$107$	29.1627			0.272549			0.136274	−	0.990671i	$-0.456487\pi$
$107$	29.1627			0.272549			0.136274	+	0.990671i	$0.456487\pi$
$108$	−12.8370	+	52.4520i	−0.118861	+	0.485667i
$109$	19.3296			0.177336			0.0886680	−	0.996061i	$-0.471739\pi$
$109$	19.3296			0.177336			0.0886680	+	0.996061i	$0.471739\pi$
$110$	−49.5287	−	55.0252i	−0.450261	−	0.500229i
$111$	−74.7952	−	157.405i	−0.673830	−	1.41807i
$112$		−	10.5830i		−	0.0944911i
$113$	−28.5568			−0.252715			−0.126358	−	0.991985i	$-0.540329\pi$
$113$	−28.5568			−0.252715			−0.126358	+	0.991985i	$0.540329\pi$
$114$	−77.8574	+	36.9959i	−0.682959	+	0.324526i
$115$	−28.6737	+	25.8094i	−0.249336	+	0.224430i
$116$		−	94.8092i		−	0.817321i
$117$	83.6882	+	68.1769i	0.715284	+	0.582709i
$118$			53.7074i			0.455148i
$119$		−	77.0264i		−	0.647281i
$120$	−16.2998	+	39.1704i	−0.135831	+	0.326420i
$121$	11.3828			0.0940727
$122$	75.6757			0.620292
$123$	−67.7063	−	142.487i	−0.550457	−	1.15843i
$124$	−71.0169			−0.572717
$125$	−73.4237	−	101.163i	−0.587390	−	0.809304i
$126$	−26.1080	−	21.2690i	−0.207207	−	0.168802i
$127$			162.116i			1.27650i	0.769828	+	0.638252i	$0.220342\pi$
$127$			162.116i			1.27650i	−0.769828	+	0.638252i	$0.779658\pi$
$128$	11.3137			0.0883883
$129$	20.2956	+	42.7118i	0.157330	+	0.331099i
$130$	56.7377	+	63.0342i	0.436444	+	0.484879i
$131$		−	49.5756i		−	0.378440i	−0.981935	−	0.189220i	$-0.939404\pi$
$131$		−	49.5756i		−	0.378440i	0.981935	−	0.189220i	$-0.0605959\pi$
$132$	26.9610	+	56.7391i	0.204250	+	0.429841i
$133$		−	53.7553i		−	0.404175i
$134$		−	39.0840i		−	0.291672i
$135$	63.8743	+	118.933i	0.473143	+	0.880986i
$136$	82.3447			0.605476
$137$	−212.721			−1.55271			−0.776354	−	0.630297i	$-0.782933\pi$
$137$	−212.721			−1.55271			−0.776354	+	0.630297i	$0.782933\pi$
$138$	29.5668	−	14.0494i	0.214252	−	0.101807i
$139$	74.1650			0.533561			0.266780	−	0.963757i	$-0.414040\pi$
$139$	74.1650			0.533561			0.266780	+	0.963757i	$0.414040\pi$
$140$	−17.7003	−	19.6646i	−0.126431	−	0.140462i
$141$	230.868	−	109.703i	1.63736	−	0.778036i
$142$			82.1217i			0.578322i
$143$	125.572			0.878128
$144$	22.7375	−	27.9107i	0.157899	−	0.193824i
$145$	−158.571	−	176.168i	−1.09359	−	1.21495i
$146$		−	95.8950i		−	0.656815i
$147$	18.9675	−	9.01292i	0.129031	−	0.0613124i
$148$			116.181i			0.785009i
$149$			23.1598i			0.155435i	0.996975	+	0.0777176i	$0.0247632\pi$
$149$			23.1598i			0.155435i	−0.996975	+	0.0777176i	$0.975237\pi$
$150$	35.2262	+	100.046i	0.234842	+	0.666970i
$151$	75.1469			0.497661			0.248831	−	0.968547i	$-0.419954\pi$
$151$	75.1469			0.497661			0.248831	+	0.968547i	$0.419954\pi$
$152$	57.4668			0.378071
$153$	165.491	−	203.143i	1.08164	−	1.32773i
$154$	−39.1745			−0.254380
$155$	−131.959	+	118.777i	−0.851348	+	0.766306i
$156$	−30.8853	−	64.9976i	−0.197983	−	0.416651i
$157$			66.6968i			0.424820i	0.977181	+	0.212410i	$0.0681313\pi$
$157$			66.6968i			0.424820i	−0.977181	+	0.212410i	$0.931869\pi$
$158$	27.2934			0.172743
$159$	115.878	−	55.0624i	0.728792	−	0.346304i
$160$	21.0224	−	18.9224i	0.131390	−	0.118265i
$161$			20.4139i			0.126794i
$162$	−23.1586	−	112.186i	−0.142954	−	0.692506i
$163$			248.817i			1.52648i	0.646114	+	0.763241i	$0.276393\pi$
$163$			248.817i			1.52648i	−0.646114	+	0.763241i	$0.723607\pi$
$164$			105.170i			0.641280i
$165$	144.995	+	60.3358i	0.878756	+	0.365672i
$166$	−47.6587			−0.287100
$167$	92.0222			0.551031			0.275516	−	0.961297i	$-0.411151\pi$
$167$	92.0222			0.551031			0.275516	+	0.961297i	$0.411151\pi$
$168$	9.63521	+	20.2771i	0.0573525	+	0.120697i
$169$	25.1504			0.148819
$170$	153.008	−	137.724i	0.900045	−	0.810138i
$171$	115.493	−	141.769i	0.675397	−	0.829060i
$172$		−	31.5257i		−	0.183289i
$173$	233.473			1.34956			0.674778	−	0.738021i	$-0.264239\pi$
$173$	233.473			1.34956			0.674778	+	0.738021i	$0.264239\pi$
$174$	86.3183	+	181.655i	0.496082	+	1.04400i
$175$	−65.7792	−	6.93534i	−0.375881	−	0.0396305i
$176$		−	41.8793i		−	0.237951i
$177$	−48.8975	−	102.904i	−0.276257	−	0.581379i
$178$			66.2311i			0.372085i
$179$		−	185.252i		−	1.03493i	−0.855705	−	0.517465i	$-0.826876\pi$
$179$		−	185.252i		−	1.03493i	0.855705	−	0.517465i	$-0.173124\pi$
$180$	−4.43186	−	89.8908i	−0.0246214	−	0.499393i
$181$	−146.372			−0.808684			−0.404342	−	0.914608i	$-0.632499\pi$
$181$	−146.372			−0.808684			−0.404342	+	0.914608i	$0.632499\pi$
$182$	44.8764			0.246574
$183$	−144.995	+	68.8983i	−0.792324	+	0.376493i
$184$	−21.8233			−0.118605
$185$	194.316	+	215.881i	1.05036	+	1.16692i
$186$	136.069	−	64.6567i	0.731554	−	0.347617i
$187$		−	304.811i		−	1.63000i
$188$	−170.405			−0.906407
$189$	69.3875	+	16.9818i	0.367129	+	0.0898507i
$190$	106.781	−	96.1146i	0.562005	−	0.505866i
$191$			83.4780i			0.437057i	0.975831	+	0.218529i	$0.0701257\pi$
$191$			83.4780i			0.437057i	−0.975831	+	0.218529i	$0.929874\pi$
$192$	−21.6772	+	10.3005i	−0.112902	+	0.0536483i
$193$		−	88.5046i		−	0.458573i	−0.973359	−	0.229287i	$-0.926361\pi$
$193$		−	88.5046i		−	0.458573i	0.973359	−	0.229287i	$-0.0736393\pi$
$194$		−	92.1130i		−	0.474809i
$195$	−166.099	−	69.1179i	−0.851790	−	0.354451i
$196$	−14.0000			−0.0714286
$197$	36.9343			0.187484			0.0937419	−	0.995597i	$-0.470117\pi$
$197$	36.9343			0.187484			0.0937419	+	0.995597i	$0.470117\pi$
$198$	−103.315	−	84.1662i	−0.521794	−	0.425082i
$199$	−205.101			−1.03066			−0.515330	−	0.856992i	$-0.672331\pi$
$199$	−205.101			−1.03066			−0.515330	+	0.856992i	$0.672331\pi$
$200$	7.41419	−	70.3209i	0.0370710	−	0.351605i
$201$	35.5838	+	74.8854i	0.177034	+	0.372564i
$202$			242.070i			1.19836i
$203$	−125.421			−0.617837
$204$	−157.773	+	74.9701i	−0.773399	+	0.367500i
$205$	175.899	+	195.420i	0.858045	+	0.953268i
$206$			183.677i			0.891634i
$207$	−43.8591	+	53.8377i	−0.211880	+	0.260085i
$208$			47.9749i			0.230649i
$209$		−	212.721i		−	1.01781i
$210$	51.8175	+	21.5625i	0.246750	+	0.102679i
$211$	49.4829			0.234516			0.117258	−	0.993101i	$-0.462590\pi$
$211$	49.4829			0.234516			0.117258	+	0.993101i	$0.462590\pi$
$212$	−85.5298			−0.403443
$213$	−74.7670	−	157.346i	−0.351019	−	0.738714i
$214$	41.2423			0.192721
$215$	−52.7275	−	58.5790i	−0.245244	−	0.272461i
$216$	−18.1543	+	74.1783i	−0.0840477	+	0.343418i
$217$			93.9465i			0.432933i
$218$	27.3362			0.125395
$219$	87.3069	+	183.736i	0.398661	+	0.838976i
$220$	−70.0441	−	77.8174i	−0.318382	−	0.353715i
$221$			349.177i			1.57998i
$222$	−105.776	−	222.605i	−0.476470	−	1.00272i
$223$			1.69928i			0.00762011i	0.999993	+	0.00381005i	$0.00121278\pi$
$223$			1.69928i			0.00762011i	−0.999993	+	0.00381005i	$0.998787\pi$
$224$		−	14.9666i		−	0.0668153i
$225$	−158.580	−	159.617i	−0.704798	−	0.709408i
$226$	−40.3855			−0.178697
$227$	206.970			0.911762			0.455881	−	0.890041i	$-0.349324\pi$
$227$	206.970			0.911762			0.455881	+	0.890041i	$0.349324\pi$
$228$	−110.107	+	52.3202i	−0.482925	+	0.229474i
$229$	−7.02543			−0.0306787			−0.0153394	−	0.999882i	$-0.504883\pi$
$229$	−7.02543			−0.0306787			−0.0153394	+	0.999882i	$0.504883\pi$
$230$	−40.5507	+	36.5001i	−0.176307	+	0.158696i
$231$	75.0587	−	35.6661i	0.324930	−	0.154399i
$232$		−	134.081i		−	0.577933i
$233$	−116.672			−0.500738			−0.250369	−	0.968151i	$-0.580552\pi$
$233$	−116.672			−0.500738			−0.250369	+	0.968151i	$0.580552\pi$
$234$	118.353	+	96.4168i	0.505782	+	0.412037i
$235$	−316.635	+	285.006i	−1.34738	+	1.21279i
$236$			75.9538i			0.321838i
$237$	−52.2945	+	24.8491i	−0.220652	+	0.104848i
$238$		−	108.932i		−	0.457697i
$239$		−	157.119i		−	0.657400i	−0.944434	−	0.328700i	$-0.893389\pi$
$239$		−	157.119i		−	0.657400i	0.944434	−	0.328700i	$-0.106611\pi$
$240$	−23.0513	+	55.3953i	−0.0960472	+	0.230814i
$241$	−287.032			−1.19101			−0.595503	−	0.803353i	$-0.703047\pi$
$241$	−287.032			−1.19101			−0.595503	+	0.803353i	$0.703047\pi$
$242$	16.0977			0.0665194
$243$	146.511	+	193.865i	0.602926	+	0.797797i
$244$	107.022			0.438613
$245$	−26.0139	+	23.4153i	−0.106179	+	0.0955728i
$246$	−95.7511	−	201.507i	−0.389232	−	0.819133i
$247$			243.684i			0.986573i
$248$	−100.433			−0.404972
$249$	91.3145	−	43.3905i	0.366725	−	0.174259i
$250$	−103.837	−	143.066i	−0.415347	−	0.572264i
$251$		−	161.056i		−	0.641658i	−0.947137	−	0.320829i	$-0.896039\pi$
$251$		−	161.056i		−	0.641658i	0.947137	−	0.320829i	$-0.103961\pi$
$252$	−36.9223	−	30.0789i	−0.146517	−	0.119361i
$253$			80.7822i			0.319297i
$254$			229.267i			0.902625i
$255$	−167.775	+	403.184i	−0.657941	+	1.58111i
$256$	16.0000			0.0625000
$257$	−356.900			−1.38871			−0.694357	−	0.719630i	$-0.744311\pi$
$257$	−356.900			−1.38871			−0.694357	+	0.719630i	$0.744311\pi$
$258$	28.7023	+	60.4036i	0.111249	+	0.234122i
$259$	153.693			0.593411
$260$	80.2392	+	89.1439i	0.308612	+	0.342861i
$261$	−330.774	−	269.466i	−1.26733	−	1.03244i
$262$		−	70.1105i		−	0.267597i
$263$	−126.259			−0.480071			−0.240036	−	0.970764i	$-0.577159\pi$
$263$	−126.259			−0.480071			−0.240036	+	0.970764i	$0.577159\pi$
$264$	38.1287	+	80.2412i	0.144427	+	0.303944i
$265$	−158.926	+	143.051i	−0.599721	+	0.539814i
$266$		−	76.0214i		−	0.285795i
$267$	−60.2996	−	126.900i	−0.225841	−	0.475279i
$268$		−	55.2732i		−	0.206243i
$269$		−	356.319i		−	1.32461i	−0.749236	−	0.662304i	$-0.769579\pi$
$269$		−	356.319i		−	1.32461i	0.749236	−	0.662304i	$-0.230421\pi$
$270$	90.3319	+	168.197i	0.334562	+	0.622951i
$271$	−422.588			−1.55937			−0.779683	−	0.626175i	$-0.784620\pi$
$271$	−422.588			−1.55937			−0.779683	+	0.626175i	$0.784620\pi$
$272$	116.453			0.428136
$273$	−85.9837	+	40.8574i	−0.314959	+	0.149661i
$274$	−300.833			−1.09793
$275$	−260.303	−	27.4447i	−0.946556	−	0.0997989i
$276$	41.8137	−	19.8689i	0.151499	−	0.0719887i
$277$		−	267.379i		−	0.965266i	−0.875823	−	0.482633i	$-0.839680\pi$
$277$		−	267.379i		−	0.965266i	0.875823	−	0.482633i	$-0.160320\pi$
$278$	104.885			0.377284
$279$	−201.843	+	247.766i	−0.723453	+	0.888050i
$280$	−25.0320	−	27.8100i	−0.0894002	−	0.0993215i
$281$			417.470i			1.48566i	0.669480	+	0.742830i	$0.266517\pi$
$281$			417.470i			1.48566i	−0.669480	+	0.742830i	$0.733483\pi$
$282$	326.497	−	155.143i	1.15779	−	0.550154i
$283$			56.1781i			0.198509i	0.995062	+	0.0992546i	$0.0316458\pi$
$283$			56.1781i			0.198509i	−0.995062	+	0.0992546i	$0.968354\pi$
$284$			116.138i			0.408935i
$285$	−117.087	+	281.374i	−0.410831	+	0.987279i
$286$	177.586			0.620930
$287$	139.127			0.484762
$288$	32.1557	−	39.4716i	0.111652	−	0.137054i
$289$	558.582			1.93281
$290$	−224.253	−	249.140i	−0.773286	−	0.859102i
$291$	83.8635	+	176.489i	0.288191	+	0.606493i
$292$		−	135.616i		−	0.464438i
$293$	−35.8668			−0.122412			−0.0612062	−	0.998125i	$-0.519495\pi$
$293$	−35.8668			−0.122412			−0.0612062	+	0.998125i	$0.519495\pi$
$294$	26.8241	−	12.7462i	0.0912386	−	0.0433544i
$295$	127.035	+	141.132i	0.430625	+	0.478415i
$296$			164.305i			0.555085i
$297$	274.582	+	67.2007i	0.924517	+	0.226265i
$298$			32.7530i			0.109909i
$299$		−	92.5402i		−	0.309499i
$300$	49.8174	+	141.486i	0.166058	+	0.471619i
$301$	−41.7046			−0.138553
$302$	106.274			0.351900
$303$	−220.390	−	463.808i	−0.727361	−	1.53072i
$304$	81.2703			0.267337
$305$	198.860	−	178.996i	0.652001	−	0.586872i
$306$	234.039	−	287.287i	0.764835	−	0.938846i
$307$		−	496.572i		−	1.61750i	−0.588154	−	0.808749i	$-0.700145\pi$
$307$		−	496.572i		−	1.61750i	0.588154	−	0.808749i	$-0.299855\pi$
$308$	−55.4011			−0.179874
$309$	−167.227	−	351.926i	−0.541188	−	1.13892i
$310$	−186.618	+	167.977i	−0.601994	+	0.541860i
$311$		−	49.5016i		−	0.159169i	−0.996828	−	0.0795846i	$-0.974641\pi$
$311$		−	49.5016i		−	0.159169i	0.996828	−	0.0795846i	$-0.0253594\pi$
$312$	−43.6784	−	91.9204i	−0.139995	−	0.294617i
$313$			219.172i			0.700229i	0.936707	+	0.350114i	$0.113857\pi$
$313$			219.172i			0.700229i	−0.936707	+	0.350114i	$0.886143\pi$
$314$			94.3235i			0.300393i
$315$	−118.914	+	5.86280i	−0.377506	+	0.0186121i
$316$	38.5987			0.122148
$317$	−96.3016			−0.303791			−0.151895	−	0.988397i	$-0.548538\pi$
$317$	−96.3016			−0.303791			−0.151895	+	0.988397i	$0.548538\pi$
$318$	163.876	−	77.8700i	0.515333	−	0.244874i
$319$	−496.318			−1.55586
$320$	29.7302	−	26.7604i	0.0929067	−	0.0836262i
$321$	−79.0206	+	37.5487i	−0.246170	+	0.116974i
$322$			28.8696i			0.0896570i
$323$	591.511			1.83130
$324$	−32.7512	−	158.655i	−0.101084	−	0.489675i
$325$	298.190	+	31.4393i	0.917509	+	0.0967364i
$326$			351.880i			1.07939i
$327$	−52.3764	+	24.8880i	−0.160173	+	0.0761102i
$328$			148.733i			0.453453i
$329$			225.424i			0.685180i
$330$	205.053	+	85.3278i	0.621374	+	0.258569i
$331$	538.706			1.62751			0.813755	−	0.581208i	$-0.197420\pi$
$331$	538.706			1.62751			0.813755	+	0.581208i	$0.197420\pi$
$332$	−67.3995			−0.203011
$333$	405.337	+	330.209i	1.21723	+	0.991620i
$334$	130.139			0.389638
$335$	−92.4457	−	102.705i	−0.275957	−	0.306582i
$336$	13.6262	+	28.6762i	0.0405543	+	0.0853459i
$337$		−	202.735i		−	0.601589i	−0.953689	−	0.300794i	$-0.902748\pi$
$337$		−	202.735i		−	0.601589i	0.953689	−	0.300794i	$-0.0972518\pi$
$338$	35.5681			0.105231
$339$	77.3790	−	36.7686i	0.228257	−	0.108462i
$340$	216.385	−	194.770i	0.636428	−	0.572854i
$341$			371.767i			1.09023i
$342$	163.332	−	200.492i	0.477578	−	0.586234i
$343$			18.5203i			0.0539949i
$344$		−	44.5841i		−	0.129605i
$345$	44.4644	−	106.854i	0.128882	−	0.309720i
$346$	330.181			0.954280
$347$	139.011			0.400607			0.200304	−	0.979734i	$-0.435807\pi$
$347$	139.011			0.400607			0.200304	+	0.979734i	$0.435807\pi$
$348$	122.073	+	256.900i	0.350783	+	0.738217i
$349$	452.984			1.29795			0.648974	−	0.760811i	$-0.275199\pi$
$349$	452.984			1.29795			0.648974	+	0.760811i	$0.275199\pi$
$350$	−93.0258	−	9.80806i	−0.265788	−	0.0280230i
$351$	−314.547	−	76.9819i	−0.896147	−	0.219322i
$352$		−	59.2263i		−	0.168256i
$353$	−453.499			−1.28470			−0.642349	−	0.766412i	$-0.722040\pi$
$353$	−453.499			−1.28470			−0.642349	+	0.766412i	$0.722040\pi$
$354$	−69.1515	−	145.528i	−0.195343	−	0.411097i
$355$	194.243	+	215.799i	0.547163	+	0.607885i
$356$			93.6650i			0.263104i
$357$	99.1761	+	208.715i	0.277804	+	0.584635i
$358$		−	261.986i		−	0.731806i
$359$		−	150.308i		−	0.418686i	−0.977842	−	0.209343i	$-0.932868\pi$
$359$		−	150.308i		−	0.418686i	0.977842	−	0.209343i	$-0.0671324\pi$
$360$	−6.26759	−	127.125i	−0.0174100	−	0.353124i
$361$	51.8039			0.143501
$362$	−207.001			−0.571826
$363$	−30.8434	+	14.6560i	−0.0849680	+	0.0403747i
$364$	63.4649			0.174354
$365$	−226.821	−	251.993i	−0.621428	−	0.690391i
$366$	−205.054	+	97.4369i	−0.560258	+	0.266221i
$367$		−	382.992i		−	1.04357i	−0.853076	−	0.521787i	$-0.825265\pi$
$367$		−	382.992i		−	1.04357i	0.853076	−	0.521787i	$-0.174735\pi$
$368$	−30.8629			−0.0838665
$369$	366.920	+	298.913i	0.994364	+	0.810062i
$370$	274.804	+	305.301i	0.742714	+	0.825138i
$371$			113.145i			0.304974i
$372$	192.431	−	91.4384i	0.517287	−	0.245802i
$373$			80.3409i			0.215391i	0.994184	+	0.107696i	$0.0343472\pi$
$373$			80.3409i			0.215391i	−0.994184	+	0.107696i	$0.965653\pi$
$374$		−	431.067i		−	1.15259i
$375$	329.206	+	179.579i	0.877882	+	0.478877i
$376$	−240.988			−0.640927
$377$	568.558			1.50811
$378$	98.1287	+	24.0159i	0.259600	+	0.0635341i
$379$	−636.088			−1.67833			−0.839166	−	0.543875i	$-0.816956\pi$
$379$	−636.088			−1.67833			−0.839166	+	0.543875i	$0.816956\pi$
$380$	151.011	−	135.927i	0.397398	−	0.357701i
$381$	−208.734	−	439.277i	−0.547858	−	1.15296i
$382$			118.056i			0.309046i
$383$	−343.675			−0.897323			−0.448661	−	0.893702i	$-0.648099\pi$
$383$	−343.675			−0.897323			−0.448661	+	0.893702i	$0.648099\pi$
$384$	−30.6562	+	14.5671i	−0.0798338	+	0.0379351i
$385$	−102.943	+	92.6597i	−0.267384	+	0.240674i
$386$		−	125.164i		−	0.324260i
$387$	−109.988	−	89.6021i	−0.284207	−	0.231530i
$388$		−	130.267i		−	0.335741i
$389$		−	520.410i		−	1.33782i	−0.743345	−	0.668908i	$-0.766762\pi$
$389$		−	520.410i		−	1.33782i	0.743345	−	0.668908i	$-0.233238\pi$
$390$	−234.899	−	97.7474i	−0.602306	−	0.250634i
$391$	−224.630			−0.574500
$392$	−19.7990			−0.0505076
$393$	63.8316	+	134.333i	0.162421	+	0.341813i
$394$	52.2330			0.132571
$395$	71.7216	−	64.5573i	0.181574	−	0.163436i
$396$	−146.110	−	119.029i	−0.368964	−	0.300578i
$397$		−	184.320i		−	0.464281i	−0.972682	−	0.232140i	$-0.925427\pi$
$397$		−	184.320i		−	0.464281i	0.972682	−	0.232140i	$-0.0745729\pi$
$398$	−290.057			−0.728787
$399$	69.2131	+	145.658i	0.173466	+	0.365057i
$400$	10.4853	−	99.4488i	0.0262131	−	0.248622i
$401$			10.1322i			0.0252674i	0.999920	+	0.0126337i	$0.00402154\pi$
$401$			10.1322i			0.0252674i	−0.999920	+	0.0126337i	$0.995978\pi$
$402$	50.3230	+	105.904i	0.125182	+	0.263443i
$403$		−	425.879i		−	1.05677i
$404$			342.338i			0.847372i
$405$	−326.210	−	240.025i	−0.805457	−	0.592654i
$406$	−177.372			−0.436876
$407$	608.199			1.49435
$408$	−223.125	+	106.024i	−0.546876	+	0.259862i
$409$	−802.483			−1.96206			−0.981031	−	0.193853i	$-0.937901\pi$
$409$	−802.483			−1.96206			−0.981031	+	0.193853i	$0.937901\pi$
$410$	248.759	+	276.365i	0.606729	+	0.674062i
$411$	576.399	−	273.891i	1.40243	−	0.666402i
$412$			259.758i			0.630481i
$413$	100.477			0.243287
$414$	−62.0261	+	76.1380i	−0.149822	+	0.183908i
$415$	−125.237	+	112.727i	−0.301777	+	0.271632i
$416$			67.8468i			0.163093i
$417$	−200.961	+	95.4918i	−0.481921	+	0.228997i
$418$		−	300.834i		−	0.719697i
$419$			27.2524i			0.0650414i	0.999471	+	0.0325207i	$0.0103535\pi$
$419$			27.2524i			0.0650414i	−0.999471	+	0.0325207i	$0.989647\pi$
$420$	73.2811	+	30.4940i	0.174479	+	0.0726049i
$421$	792.513			1.88245			0.941227	−	0.337775i	$-0.109674\pi$
$421$	792.513			1.88245			0.941227	+	0.337775i	$0.109674\pi$
$422$	69.9793			0.165828
$423$	−484.322	+	594.513i	−1.14497	+	1.40547i
$424$	−120.957			−0.285277
$425$	76.3150	−	723.819i	0.179565	−	1.70310i
$426$	−105.737	−	222.521i	−0.248208	−	0.522349i
$427$		−	141.576i		−	0.331560i
$428$	58.3254			0.136274
$429$	−340.257	+	161.682i	−0.793139	+	0.376880i
$430$	−74.5680	−	82.8433i	−0.173414	−	0.192659i
$431$		−	483.889i		−	1.12271i	−0.827574	−	0.561357i	$-0.810280\pi$
$431$		−	483.889i		−	1.12271i	0.827574	−	0.561357i	$-0.189720\pi$
$432$	−25.6741	+	104.904i	−0.0594307	+	0.242833i
$433$			567.937i			1.31163i	0.754920	+	0.655816i	$0.227675\pi$
$433$			567.937i			1.31163i	−0.754920	+	0.655816i	$0.772325\pi$
$434$			132.860i			0.306130i
$435$	656.498	+	273.185i	1.50919	+	0.628011i
$436$	38.6592			0.0886680
$437$	−156.765			−0.358729
$438$	123.471	+	259.842i	0.281896	+	0.593246i
$439$	834.645			1.90124			0.950621	−	0.310355i	$-0.100448\pi$
$439$	834.645			1.90124			0.950621	+	0.310355i	$0.100448\pi$
$440$	−99.0573	−	110.050i	−0.225130	−	0.250114i
$441$	−39.7907	+	48.8437i	−0.0902283	+	0.110757i
$442$			493.810i			1.11722i
$443$	543.969			1.22792			0.613960	−	0.789337i	$-0.289576\pi$
$443$	543.969			1.22792			0.613960	+	0.789337i	$0.289576\pi$
$444$	−149.590	−	314.810i	−0.336915	−	0.709033i
$445$	156.657	+	174.042i	0.352038	+	0.391106i
$446$			2.40315i			0.00538823i
$447$	−29.8197	−	62.7550i	−0.0667107	−	0.140392i
$448$		−	21.1660i		−	0.0472456i
$449$			308.306i			0.686649i	0.939217	+	0.343325i	$0.111553\pi$
$449$			308.306i			0.686649i	−0.939217	+	0.343325i	$0.888447\pi$
$450$	−224.265	−	225.732i	−0.498367	−	0.501627i
$451$	550.555			1.22074
$452$	−57.1137			−0.126358
$453$	−203.622	+	96.7560i	−0.449496	+	0.213589i
$454$	292.700			0.644713
$455$	117.926	−	106.146i	0.259179	−	0.233289i
$456$	−155.715	+	73.9919i	−0.341480	+	0.162263i
$457$		−	475.765i		−	1.04106i	−0.853843	−	0.520530i	$-0.825734\pi$
$457$		−	475.765i		−	1.04106i	0.853843	−	0.520530i	$-0.174266\pi$
$458$	−9.93545			−0.0216931
$459$	−186.864	+	763.524i	−0.407111	+	1.66345i
$460$	−57.3474	+	51.6189i	−0.124668	+	0.112215i
$461$			764.494i			1.65834i	0.558998	+	0.829169i	$0.311186\pi$
$461$			764.494i			1.65834i	−0.558998	+	0.829169i	$0.688814\pi$
$462$	106.149	−	50.4395i	0.229760	−	0.109176i
$463$			558.506i			1.20628i	0.797637	+	0.603138i	$0.206083\pi$
$463$			558.506i			1.20628i	−0.797637	+	0.603138i	$0.793917\pi$
$464$		−	189.618i		−	0.408661i
$465$	204.629	−	491.750i	0.440063	−	1.05753i
$466$	−164.999			−0.354075
$467$	251.321			0.538160			0.269080	−	0.963118i	$-0.413280\pi$
$467$	251.321			0.538160			0.269080	+	0.963118i	$0.413280\pi$
$468$	167.376	+	136.354i	0.357642	+	0.291354i
$469$	−73.1196			−0.155905
$470$	−447.789	+	403.059i	−0.952743	+	0.857572i
$471$	−85.8761	−	180.725i	−0.182327	−	0.383705i
$472$			107.415i			0.227574i
$473$	−165.034			−0.348910
$474$	−73.9556	+	35.1419i	−0.156024	+	0.0741391i
$475$	53.2587	−	505.140i	0.112124	−	1.06345i
$476$		−	154.053i		−	0.323641i
$477$	−243.092	+	298.399i	−0.509627	+	0.625575i
$478$		−	222.199i		−	0.464852i
$479$			343.617i			0.717363i	0.933460	+	0.358681i	$0.116774\pi$
$479$			343.617i			0.717363i	−0.933460	+	0.358681i	$0.883226\pi$
$480$	−32.5995	+	78.3407i	−0.0679156	+	0.163210i
$481$	−696.724			−1.44849
$482$	−405.925			−0.842169
$483$	−26.2841	−	55.3144i	−0.0544184	−	0.114523i
$484$	22.7656			0.0470363
$485$	−217.875	−	242.054i	−0.449228	−	0.499081i
$486$	207.198	+	274.166i	0.426333	+	0.564128i
$487$		−	909.858i		−	1.86829i	−0.356892	−	0.934146i	$-0.616163\pi$
$487$		−	909.858i		−	1.86829i	0.356892	−	0.934146i	$-0.383837\pi$
$488$	151.351			0.310146
$489$	−320.366	−	674.206i	−0.655146	−	1.37874i
$490$	−36.7892	+	33.1143i	−0.0750800	+	0.0675802i
$491$			584.882i			1.19121i	0.803279	+	0.595603i	$0.203087\pi$
$491$			584.882i			1.19121i	−0.803279	+	0.595603i	$0.796913\pi$
$492$	−135.413	−	284.973i	−0.275229	−	0.579214i
$493$		−	1380.10i		−	2.79940i
$494$			344.621i			0.697612i
$495$	−470.570	+	23.2004i	−0.950647	+	0.0468695i
$496$	−142.034			−0.286358
$497$	153.636			0.309126
$498$	129.138	−	61.3634i	0.259314	−	0.123220i
$499$	903.199			1.81002			0.905009	−	0.425392i	$-0.139864\pi$
$499$	903.199			1.81002			0.905009	+	0.425392i	$0.139864\pi$
$500$	−146.847	−	202.326i	−0.293695	−	0.404652i
$501$	−249.348	+	118.484i	−0.497700	+	0.236495i
$502$		−	227.768i		−	0.453720i
$503$	188.576			0.374903			0.187452	−	0.982274i	$-0.439977\pi$
$503$	188.576			0.374903			0.187452	+	0.982274i	$0.439977\pi$
$504$	−52.2161	−	42.5380i	−0.103603	−	0.0844008i
$505$	572.569	+	636.111i	1.13380	+	1.25962i
$506$			114.243i			0.225777i
$507$	−68.1488	+	32.3827i	−0.134416	+	0.0638711i
$508$			324.232i			0.638252i
$509$			526.061i			1.03352i	0.856131	+	0.516759i	$0.172862\pi$
$509$			526.061i			1.03352i	−0.856131	+	0.516759i	$0.827138\pi$
$510$	−237.269	+	570.189i	−0.465234	+	1.11802i
$511$	−179.403			−0.351083
$512$	22.6274			0.0441942
$513$	−130.409	+	532.849i	−0.254208	+	1.03869i
$514$	−504.732			−0.981970
$515$	434.451	+	482.665i	0.843595	+	0.937214i
$516$	40.5912	+	85.4236i	0.0786652	+	0.165550i
$517$			892.053i			1.72544i
$518$	217.355			0.419605
$519$	−632.630	+	300.611i	−1.21894	+	0.579211i
$520$	113.475	+	126.068i	0.218222	+	0.242439i
$521$		−	636.046i		−	1.22082i	−0.792087	−	0.610408i	$-0.791005\pi$
$521$		−	636.046i		−	1.22082i	0.792087	−	0.610408i	$-0.208995\pi$
$522$	−467.784	−	381.082i	−0.896139	−	0.730043i
$523$		−	662.926i		−	1.26755i	−0.773519	−	0.633773i	$-0.781506\pi$
$523$		−	662.926i		−	1.26755i	0.773519	−	0.633773i	$-0.218494\pi$
$524$		−	99.1513i		−	0.189220i
$525$	187.168	−	65.9023i	0.356511	−	0.125528i
$526$	−178.557			−0.339461
$527$	−1033.77			−1.96161
$528$	53.9221	+	113.478i	0.102125	+	0.214921i
$529$	−469.468			−0.887463
$530$	−224.755	+	202.304i	−0.424066	+	0.381706i
$531$	264.990	+	215.875i	0.499040	+	0.406545i
$532$		−	107.511i		−	0.202087i
$533$	−630.690			−1.18328
$534$	−85.2765	−	179.463i	−0.159694	−	0.336073i
$535$	108.376	−	97.5506i	0.202573	−	0.182338i
$536$		−	78.1681i		−	0.145836i
$537$	238.523	+	501.969i	0.444178	+	0.934765i
$538$		−	503.912i		−	0.936639i
$539$			73.2888i			0.135972i
$540$	127.749	+	237.866i	0.236571	+	0.440493i
$541$	−299.602			−0.553793			−0.276897	−	0.960900i	$-0.589306\pi$
$541$	−299.602			−0.553793			−0.276897	+	0.960900i	$0.589306\pi$
$542$	−597.630			−1.10264
$543$	396.616	−	188.462i	0.730416	−	0.347076i
$544$	164.689			0.302738
$545$	71.8340	−	64.6585i	0.131806	−	0.118639i
$546$	−121.599	+	57.7811i	−0.222709	+	0.105826i
$547$		−	177.699i		−	0.324862i	−0.986720	−	0.162431i	$-0.948067\pi$
$547$		−	177.699i		−	0.324862i	0.986720	−	0.162431i	$-0.0519334\pi$
$548$	−425.442			−0.776354
$549$	304.176	−	373.380i	0.554054	−	0.680110i
$550$	−368.124	−	38.8126i	−0.669316	−	0.0705685i
$551$		−	963.147i		−	1.74800i
$552$	59.1336	−	28.0989i	0.107126	−	0.0509037i
$553$		−	51.0613i		−	0.0923351i
$554$		−	378.131i		−	0.682546i
$555$	−804.487	−	334.767i	−1.44953	−	0.603183i
$556$	148.330			0.266780
$557$	−227.747			−0.408882			−0.204441	−	0.978879i	$-0.565538\pi$
$557$	−227.747			−0.408882			−0.204441	+	0.978879i	$0.565538\pi$
$558$	−285.450	+	350.394i	−0.511559	+	0.627946i
$559$	189.055			0.338203
$560$	−35.4007	−	39.3293i	−0.0632155	−	0.0702309i
$561$	392.462	+	825.930i	0.699575	+	1.47225i
$562$			590.392i			1.05052i
$563$	−271.221			−0.481742			−0.240871	−	0.970557i	$-0.577433\pi$
$563$	−271.221			−0.481742			−0.240871	+	0.970557i	$0.577433\pi$
$564$	461.736	−	219.406i	0.818682	−	0.389018i
$565$	−106.125	+	95.5240i	−0.187832	+	0.169069i
$566$			79.4479i			0.140367i
$567$	−209.881	+	43.3258i	−0.370160	+	0.0764123i
$568$			164.243i			0.289161i
$569$		−	63.1031i		−	0.110902i	−0.998461	−	0.0554509i	$-0.982340\pi$
$569$		−	63.1031i		−	0.110902i	0.998461	−	0.0554509i	$-0.0176596\pi$
$570$	−165.586	+	397.924i	−0.290501	+	0.698111i
$571$	130.175			0.227977			0.113988	−	0.993482i	$-0.463637\pi$
$571$	130.175			0.227977			0.113988	+	0.993482i	$0.463637\pi$
$572$	251.144			0.439064
$573$	−107.483	−	226.196i	−0.187579	−	0.394757i
$574$	196.755			0.342779
$575$	−20.2253	+	191.830i	−0.0351745	+	0.333617i
$576$	45.4751	−	55.8213i	0.0789497	−	0.0969120i
$577$		−	371.832i		−	0.644424i	−0.946668	−	0.322212i	$-0.895574\pi$
$577$		−	371.832i		−	0.644424i	0.946668	−	0.322212i	$-0.104426\pi$
$578$	789.954			1.36670
$579$	113.955	+	239.816i	0.196813	+	0.414190i
$580$	−317.141	−	352.337i	−0.546796	−	0.607477i
$581$			89.1612i			0.153462i
$582$	118.601	+	249.594i	0.203782	+	0.428855i
$583$			447.741i			0.767995i
$584$		−	191.790i		−	0.328408i
$585$	539.063	−	26.5773i	0.921475	−	0.0454312i
$586$	−50.7233			−0.0865586
$587$	824.490			1.40458			0.702291	−	0.711890i	$-0.252160\pi$
$587$	824.490			1.40458			0.702291	+	0.711890i	$0.252160\pi$
$588$	37.9351	−	18.0258i	0.0645154	−	0.0306562i
$589$	−721.445			−1.22486
$590$	179.654	+	199.591i	0.304498	+	0.338290i
$591$	−100.079	+	47.5551i	−0.169338	+	0.0804655i
$592$			232.363i			0.392504i
$593$	−148.957			−0.251192			−0.125596	−	0.992081i	$-0.540084\pi$
$593$	−148.957			−0.251192			−0.125596	+	0.992081i	$0.540084\pi$
$594$	388.317	+	95.0361i	0.653732	+	0.159994i
$595$	−257.657	−	286.251i	−0.433037	−	0.481094i
$596$			46.3197i			0.0777176i
$597$	555.752	−	264.080i	0.930909	−	0.442345i
$598$		−	130.872i		−	0.218849i
$599$			98.6062i			0.164618i	0.996607	+	0.0823090i	$0.0262294\pi$
$599$			98.6062i			0.164618i	−0.996607	+	0.0823090i	$0.973771\pi$
$600$	70.4525	+	200.091i	0.117421	+	0.333485i
$601$	244.192			0.406310			0.203155	−	0.979147i	$-0.434880\pi$
$601$	244.192			0.406310			0.203155	+	0.979147i	$0.434880\pi$
$602$	−58.9792			−0.0979721
$603$	−192.839	−	157.097i	−0.319799	−	0.260526i
$604$	150.294			0.248831
$605$	42.3015	−	38.0760i	0.0699199	−	0.0629355i
$606$	−311.679	−	655.924i	−0.514322	−	1.08238i
$607$			504.707i			0.831478i	0.909484	+	0.415739i	$0.136477\pi$
$607$			504.707i			0.831478i	−0.909484	+	0.415739i	$0.863523\pi$
$608$	114.934			0.189035
$609$	339.846	−	161.487i	0.558040	−	0.265167i
$610$	281.231	−	253.139i	0.461035	−	0.414981i
$611$		−	1021.89i		−	1.67249i
$612$	330.982	−	406.285i	0.540820	−	0.663865i
$613$			416.536i			0.679503i	0.940515	+	0.339752i	$0.110343\pi$
$613$			416.536i			0.679503i	−0.940515	+	0.339752i	$0.889657\pi$
$614$		−	702.259i		−	1.14374i
$615$	−728.240	−	303.038i	−1.18413	−	0.492745i
$616$	−78.3490			−0.127190
$617$	132.241			0.214330			0.107165	−	0.994241i	$-0.465823\pi$
$617$	132.241			0.214330			0.107165	+	0.994241i	$0.465823\pi$
$618$	−236.495	−	497.699i	−0.382677	−	0.805338i
$619$	669.449			1.08150			0.540751	−	0.841183i	$-0.318140\pi$
$619$	669.449			1.08150			0.540751	+	0.841183i	$0.318140\pi$
$620$	−263.918	+	237.555i	−0.425674	+	0.383153i
$621$	49.5234	−	202.352i	0.0797479	−	0.325849i
$622$		−	70.0059i		−	0.112550i
$623$	123.907			0.198888
$624$	−61.7706	−	129.995i	−0.0989913	−	0.208326i
$625$	−611.257	−	130.343i	−0.978012	−	0.208549i
$626$			309.955i			0.495137i
$627$	273.891	+	576.400i	0.436829	+	0.919299i
$628$			133.394i			0.212410i
$629$			1691.21i			2.68873i
$630$	−168.170	+	8.29125i	−0.266937	+	0.0131607i
$631$	590.546			0.935889			0.467944	−	0.883758i	$-0.344995\pi$
$631$	590.546			0.935889			0.467944	+	0.883758i	$0.344995\pi$
$632$	54.5869			0.0863716
$633$	−134.081	+	63.7121i	−0.211819	+	0.100651i
$634$	−136.191			−0.214812
$635$	542.286	+	602.467i	0.853993	+	0.948766i
$636$	231.756	−	110.125i	0.364396	−	0.173152i
$637$		−	83.9561i		−	0.131799i
$638$	−701.900			−1.10016
$639$	405.185	+	330.085i	0.634092	+	0.516565i
$640$	42.0448	−	37.8449i	0.0656950	−	0.0591326i
$641$			542.271i			0.845977i	0.906135	+	0.422989i	$0.139019\pi$
$641$			542.271i			0.845977i	−0.906135	+	0.422989i	$0.860981\pi$
$642$	−111.752	+	53.1019i	−0.174069	+	0.0827132i
$643$		−	546.024i		−	0.849181i	−0.905385	−	0.424591i	$-0.860418\pi$
$643$		−	546.024i		−	0.849181i	0.905385	−	0.424591i	$-0.139582\pi$
$644$			40.8277i			0.0633971i
$645$	218.297	+	90.8387i	0.338445	+	0.140835i
$646$	836.523			1.29493
$647$	−801.011			−1.23804			−0.619020	−	0.785376i	$-0.712470\pi$
$647$	−801.011			−1.23804			−0.619020	+	0.785376i	$0.712470\pi$
$648$	−46.3172	−	224.372i	−0.0714772	−	0.346253i
$649$	397.611			0.612652
$650$	421.705	+	44.4619i	0.648777	+	0.0684030i
$651$	−120.962	−	254.562i	−0.185809	−	0.391032i
$652$			497.633i			0.763241i
$653$	1193.82			1.82821			0.914103	−	0.405482i	$-0.132896\pi$
$653$	1193.82			1.82821			0.914103	+	0.405482i	$0.132896\pi$
$654$	−74.0715	+	35.1970i	−0.113259	+	0.0538180i
$655$	−165.833	−	184.236i	−0.253180	−	0.281277i
$656$			210.340i			0.320640i
$657$	−473.142	−	385.447i	−0.720155	−	0.586677i
$658$			318.798i			0.484495i
$659$		−	1234.84i		−	1.87381i	−0.349579	−	0.936907i	$-0.613675\pi$
$659$		−	1234.84i		−	1.87381i	0.349579	−	0.936907i	$-0.386325\pi$
$660$	289.989	+	120.672i	0.439378	+	0.182836i
$661$	−660.309			−0.998954			−0.499477	−	0.866327i	$-0.666475\pi$
$661$	−660.309			−0.998954			−0.499477	+	0.866327i	$0.666475\pi$
$662$	761.845			1.15082
$663$	−449.586	−	946.146i	−0.678108	−	1.42707i
$664$	−95.3174			−0.143550
$665$	−179.814	−	199.769i	−0.270397	−	0.300405i
$666$	573.233	+	466.987i	0.860711	+	0.701181i
$667$			365.761i			0.548367i
$668$	184.044			0.275516
$669$	−2.18793	−	4.60446i	−0.00327045	−	0.00688260i
$670$	−130.738	−	145.247i	−0.195131	−	0.216786i
$671$		−	560.248i		−	0.834945i
$672$	19.2704	+	40.5543i	0.0286762	+	0.0603487i
$673$		−	372.706i		−	0.553798i	−0.960899	−	0.276899i	$-0.910693\pi$
$673$		−	372.706i		−	0.553798i	0.960899	−	0.276899i	$-0.0893067\pi$
$674$		−	286.711i		−	0.425387i
$675$	635.211	+	228.325i	0.941053	+	0.338259i
$676$	50.3009			0.0744096
$677$	−762.928			−1.12693			−0.563463	−	0.826142i	$-0.690531\pi$
$677$	−762.928			−1.12693			−0.563463	+	0.826142i	$0.690531\pi$
$678$	109.430	−	51.9987i	0.161402	−	0.0766942i
$679$	−172.328			−0.253796
$680$	306.015	−	275.447i	0.450022	−	0.405069i
$681$	−560.816	+	266.486i	−0.823518	+	0.391316i
$682$			525.758i			0.770906i
$683$	−28.2779			−0.0414024			−0.0207012	−	0.999786i	$-0.506590\pi$
$683$	−28.2779			−0.0414024			−0.0207012	+	0.999786i	$0.506590\pi$
$684$	230.986	−	283.538i	0.337698	−	0.414530i
$685$	−790.529	+	711.562i	−1.15406	+	1.03878i
$686$			26.1916i			0.0381802i
$687$	19.0364	−	9.04565i	0.0277095	−	0.0131669i
$688$		−	63.0514i		−	0.0916445i
$689$		−	512.911i		−	0.744428i
$690$	62.8821	−	151.114i	0.0911335	−	0.219005i
$691$	−587.034			−0.849543			−0.424771	−	0.905301i	$-0.639645\pi$
$691$	−587.034			−0.849543			−0.424771	+	0.905301i	$0.639645\pi$
$692$	466.946			0.674778
$693$	−157.460	+	193.285i	−0.227216	+	0.278911i
$694$	196.591			0.283272
$695$	275.617	−	248.085i	0.396571	−	0.356957i
$696$	172.637	+	363.311i	0.248041	+	0.521999i
$697$			1530.92i			2.19644i
$698$	640.616			0.917787
$699$	316.140	−	150.222i	0.452274	−	0.214910i
$700$	−131.558	−	13.8707i	−0.187941	−	0.0198153i
$701$		−	221.461i		−	0.315922i	−0.987445	−	0.157961i	$-0.949508\pi$
$701$		−	221.461i		−	0.315922i	0.987445	−	0.157961i	$-0.0504920\pi$
$702$	−444.837	−	108.869i	−0.633671	−	0.155084i
$703$			1180.26i			1.67889i
$704$		−	83.7586i		−	0.118975i
$705$	491.007	−	1179.95i	0.696463	−	1.67369i
$706$	−641.344			−0.908419
$707$	452.871			0.640553
$708$	−97.7950	−	205.808i	−0.138129	−	0.290689i
$709$	−1187.65			−1.67511			−0.837553	−	0.546356i	$-0.816014\pi$
$709$	−1187.65			−1.67511			−0.837553	+	0.546356i	$0.816014\pi$
$710$	274.701	+	305.186i	0.386903	+	0.429840i
$711$	109.705	−	134.665i	0.154297	−	0.189402i
$712$			132.462i			0.186043i
$713$	273.973			0.384254
$714$	140.256	+	295.167i	0.196437	+	0.413399i
$715$	466.660	−	420.045i	0.652672	−	0.587476i
$716$		−	370.505i		−	0.517465i
$717$	202.300	+	425.736i	0.282147	+	0.593774i
$718$		−	212.568i		−	0.296055i
$719$			611.937i			0.851095i	0.904936	+	0.425547i	$0.139918\pi$
$719$			611.937i			0.851095i	−0.904936	+	0.425547i	$0.860082\pi$
$720$	−8.86372	−	179.782i	−0.0123107	−	0.249697i
$721$	343.628			0.476599
$722$	73.2618			0.101471
$723$	777.757	−	369.571i	1.07574	−	0.511164i
$724$	−292.744			−0.404342
$725$	−1178.58	−	124.262i	−1.62563	−	0.171396i
$726$	−43.6191	+	20.7268i	−0.0600814	+	0.0285492i
$727$			1136.33i			1.56304i	0.623881	+	0.781520i	$0.285555\pi$
$727$			1136.33i			1.56304i	−0.623881	+	0.781520i	$0.714445\pi$
$728$	89.7529			0.123287
$729$	−646.605	−	336.664i	−0.886976	−	0.461816i
$730$	−320.773	−	356.372i	−0.439416	−	0.488180i
$731$		−	458.908i		−	0.627781i
$732$	−289.991	+	137.797i	−0.396162	+	0.188247i
$733$		−	401.450i		−	0.547681i	−0.961775	−	0.273840i	$-0.911706\pi$
$733$		−	401.450i		−	0.547681i	0.961775	−	0.273840i	$-0.0882940\pi$
$734$		−	541.632i		−	0.737919i
$735$	40.3398	−	96.9417i	0.0548841	−	0.131894i
$736$	−43.6467			−0.0593026
$737$	−289.350			−0.392606
$738$	518.904	+	422.727i	0.703121	+	0.572801i
$739$	−75.9398			−0.102760			−0.0513801	−	0.998679i	$-0.516362\pi$
$739$	−75.9398			−0.102760			−0.0513801	+	0.998679i	$0.516362\pi$
$740$	388.632	+	431.761i	0.525178	+	0.583461i
$741$	−313.757	−	660.297i	−0.423424	−	0.891088i
$742$			160.012i			0.215649i
$743$	308.906			0.415755			0.207877	−	0.978155i	$-0.433345\pi$
$743$	308.906			0.415755			0.207877	+	0.978155i	$0.433345\pi$
$744$	272.138	−	129.313i	0.365777	−	0.173808i
$745$	77.4708	+	86.0682i	0.103988	+	0.115528i
$746$			113.619i			0.152305i
$747$	−191.562	+	235.146i	−0.256442	+	0.314787i
$748$		−	609.621i		−	0.815002i
$749$		−	77.1572i		−	0.103014i
$750$	465.567	+	253.963i	0.620756	+	0.338617i
$751$	629.294			0.837941			0.418971	−	0.908000i	$-0.362391\pi$
$751$	629.294			0.837941			0.418971	+	0.908000i	$0.362391\pi$
$752$	−340.809			−0.453204
$753$	207.369	+	436.405i	0.275391	+	0.579555i
$754$	804.063			1.06640
$755$	279.266	−	251.370i	0.369889	−	0.332940i
$756$	138.775	+	33.9636i	0.183565	+	0.0449254i
$757$			526.381i			0.695351i	0.937615	+	0.347676i	$0.113029\pi$
$757$			526.381i			0.695351i	−0.937615	+	0.347676i	$0.886971\pi$
$758$	−899.564			−1.18676
$759$	−104.012	−	218.891i	−0.137038	−	0.288394i
$760$	213.562	−	192.229i	0.281003	−	0.252933i
$761$		−	955.908i		−	1.25612i	−0.778164	−	0.628061i	$-0.783849\pi$
$761$		−	955.908i		−	1.25612i	0.778164	−	0.628061i	$-0.216151\pi$
$762$	−295.194	−	621.232i	−0.387394	−	0.815265i
$763$		−	51.1414i		−	0.0670267i
$764$			166.956i			0.218529i
$765$	−64.5129	−	1308.51i	−0.0843306	−	1.71047i
$766$	−486.029			−0.634503
$767$	−455.485			−0.593852
$768$	−43.3544	+	20.6010i	−0.0564510	+	0.0268242i
$769$	1062.16			1.38123			0.690613	−	0.723225i	$-0.257341\pi$
$769$	1062.16			1.38123			0.690613	+	0.723225i	$0.257341\pi$
$770$	−145.583	+	131.041i	−0.189069	+	0.170183i
$771$	967.072	−	459.530i	1.25431	−	0.596018i
$772$		−	177.009i		−	0.229287i
$773$	548.202			0.709188			0.354594	−	0.935020i	$-0.384619\pi$
$773$	548.202			0.709188			0.354594	+	0.935020i	$0.384619\pi$
$774$	−155.546	−	126.717i	−0.200964	−	0.163716i
$775$	−93.0787	+	882.818i	−0.120102	+	1.13912i
$776$		−	184.226i		−	0.237405i
$777$	−416.455	+	197.889i	−0.535978	+	0.254684i
$778$		−	735.971i		−	0.945979i
$779$			1068.40i			1.37150i
$780$	−332.198	−	138.236i	−0.425895	−	0.177225i
$781$	607.970			0.778451
$782$	−317.674			−0.406233
$783$	1243.23	+	304.267i	1.58778	+	0.388592i
$784$	−28.0000			−0.0357143
$785$	223.104	+	247.863i	0.284209	+	0.315749i
$786$	90.2715	+	189.975i	0.114849	+	0.241698i
$787$			590.574i			0.750412i	0.926942	+	0.375206i	$0.122428\pi$
$787$			590.574i			0.750412i	−0.926942	+	0.375206i	$0.877572\pi$
$788$	73.8686			0.0937419
$789$	342.117	−	162.566i	0.433608	−	0.206040i
$790$	101.430	−	91.2978i	0.128392	−	0.115567i
$791$			75.5543i			0.0955174i
$792$	−206.631	−	168.332i	−0.260897	−	0.212541i
$793$			641.794i			0.809324i
$794$		−	260.667i		−	0.328296i
$795$	246.447	−	592.244i	0.309996	−	0.744960i
$796$	−410.203			−0.515330
$797$	−913.353			−1.14599			−0.572994	−	0.819560i	$-0.694218\pi$
$797$	−913.353			−1.14599			−0.572994	+	0.819560i	$0.694218\pi$
$798$	97.8821	+	205.991i	0.122659	+	0.258134i
$799$	−2480.52			−3.10453
$800$	14.8284	−	140.642i	0.0185355	−	0.175802i
$801$	326.781	+	266.214i	0.407967	+	0.332352i
$802$			14.3292i			0.0178668i
$803$	−709.938			−0.884107
$804$	71.1675	+	149.771i	0.0885168	+	0.186282i
$805$	68.2854	+	75.8634i	0.0848265	+	0.0942403i
$806$		−	602.283i		−	0.747250i
$807$	458.782	+	965.500i	0.568504	+	1.19641i
$808$			484.139i			0.599182i
$809$		−	287.495i		−	0.355370i	−0.984087	−	0.177685i	$-0.943139\pi$
$809$		−	287.495i		−	0.355370i	0.984087	−	0.177685i	$-0.0568609\pi$
$810$	−461.331	−	339.446i	−0.569544	−	0.419070i
$811$	319.747			0.394262			0.197131	−	0.980377i	$-0.436838\pi$
$811$	319.747			0.394262			0.197131	+	0.980377i	$0.436838\pi$
$812$	−250.842			−0.308918
$813$	1145.06	−	544.107i	1.40844	−	0.669258i
$814$	860.123			1.05666
$815$	832.304	+	924.670i	1.02123	+	1.13456i
$816$	−315.547	+	149.940i	−0.386699	+	0.183750i
$817$		−	320.263i		−	0.391999i
$818$	−1134.88			−1.38739
$819$	180.379	−	221.418i	0.220243	−	0.270352i
$820$	351.798	+	390.840i	0.429022	+	0.476634i
$821$			1361.35i			1.65816i	0.559130	+	0.829080i	$0.311135\pi$
$821$			1361.35i			1.65816i	−0.559130	+	0.829080i	$0.688865\pi$
$822$	815.152	−	387.340i	0.991669	−	0.471217i
$823$			68.4196i			0.0831344i	0.999136	+	0.0415672i	$0.0132351\pi$
$823$			68.4196i			0.0831344i	−0.999136	+	0.0415672i	$0.986765\pi$
$824$			367.353i			0.445817i
$825$	740.666	−	260.790i	0.897776	−	0.316109i
$826$	142.097			0.172030
$827$	−1072.36			−1.29668			−0.648342	−	0.761349i	$-0.724537\pi$
$827$	−1072.36			−1.29668			−0.648342	+	0.761349i	$0.724537\pi$
$828$	−87.7182	+	107.675i	−0.105940	+	0.130043i
$829$	−970.657			−1.17088			−0.585438	−	0.810717i	$-0.699078\pi$
$829$	−970.657			−1.17088			−0.585438	+	0.810717i	$0.699078\pi$
$830$	−177.112	+	159.421i	−0.213389	+	0.192073i
$831$	344.266	+	724.502i	0.414279	+	0.871844i
$832$			95.9498i			0.115324i
$833$	−203.793			−0.244649
$834$	−284.202	+	135.046i	−0.340769	+	0.161925i
$835$	341.979	−	307.819i	0.409556	−	0.368645i
$836$		−	425.443i		−	0.508903i
$837$	227.911	−	931.244i	0.272296	−	1.11260i
$838$			38.5407i			0.0459912i
$839$			980.187i			1.16828i	0.811653	+	0.584140i	$0.198568\pi$
$839$			980.187i			1.16828i	−0.811653	+	0.584140i	$0.801432\pi$
$840$	103.635	+	43.1251i	0.123375	+	0.0513394i
$841$	−1406.20			−1.67206
$842$	1120.78			1.33110
$843$	−537.518	−	1131.20i	−0.637625	−	1.34187i
$844$	98.9657			0.117258
$845$	93.4658	−	84.1294i	0.110610	−	0.0995614i
$846$	−684.935	+	840.768i	−0.809616	+	0.993816i
$847$		−	30.1160i		−	0.0355561i
$848$	−171.060			−0.201721
$849$	−72.3327	−	152.223i	−0.0851975	−	0.179297i
$850$	107.926	−	1023.64i	0.126971	−	1.20428i
$851$		−	448.211i		−	0.526688i
$852$	−149.534	−	314.692i	−0.175509	−	0.369357i
$853$			34.7970i			0.0407936i	0.999792	+	0.0203968i	$0.00649296\pi$
$853$			34.7970i			0.0407936i	−0.999792	+	0.0203968i	$0.993507\pi$
$854$		−	200.219i		−	0.234448i
$855$	−45.0223	−	913.182i	−0.0526577	−	1.06805i
$856$	82.4845			0.0963605
$857$	79.5168			0.0927851			0.0463926	−	0.998923i	$-0.485227\pi$
$857$	79.5168			0.0927851			0.0463926	+	0.998923i	$0.485227\pi$
$858$	−481.195	+	228.652i	−0.560834	+	0.266495i
$859$	−311.130			−0.362200			−0.181100	−	0.983465i	$-0.557966\pi$
$859$	−311.130			−0.362200			−0.181100	+	0.983465i	$0.557966\pi$
$860$	−105.455	−	117.158i	−0.122622	−	0.136230i
$861$	−376.984	+	179.134i	−0.437845	+	0.208053i
$862$		−	684.323i		−	0.793878i
$863$	145.121			0.168159			0.0840796	−	0.996459i	$-0.473205\pi$
$863$	145.121			0.168159			0.0840796	+	0.996459i	$0.473205\pi$
$864$	−36.3086	+	148.357i	−0.0420238	+	0.171709i
$865$	867.649	−	780.979i	1.00306	−	0.902866i
$866$			803.184i			0.927465i
$867$	−1513.56	+	719.207i	−1.74574	+	0.829535i
$868$			187.893i			0.216467i
$869$		−	202.061i		−	0.232521i
$870$	928.428	+	386.342i	1.06716	+	0.444071i
$871$	331.466			0.380558
$872$	54.6724			0.0626977
$873$	−454.481	−	370.245i	−0.520597	−	0.424106i
$874$	−221.699			−0.253660
$875$	−267.652	+	194.261i	−0.305888	+	0.222012i
$876$	174.614	+	367.472i	0.199331	+	0.419488i
$877$		−	595.173i		−	0.678647i	−0.940670	−	0.339324i	$-0.889802\pi$
$877$		−	595.173i		−	0.678647i	0.940670	−	0.339324i	$-0.110198\pi$
$878$	1180.37			1.34438
$879$	97.1865	−	46.1807i	0.110565	−	0.0525377i
$880$	−140.088	−	155.635i	−0.159191	−	0.176858i
$881$			321.893i			0.365372i	0.983171	+	0.182686i	$0.0584792\pi$
$881$			321.893i			0.365372i	−0.983171	+	0.182686i	$0.941521\pi$
$882$	−56.2725	+	69.0754i	−0.0638010	+	0.0783167i
$883$		−	944.347i		−	1.06948i	−0.845018	−	0.534738i	$-0.820410\pi$
$883$		−	944.347i		−	1.06948i	0.845018	−	0.534738i	$-0.179590\pi$
$884$			698.353i			0.789992i
$885$	−525.935	−	218.854i	−0.594277	−	0.247293i
$886$	769.288			0.868271
$887$	1184.20			1.33506			0.667528	−	0.744584i	$-0.267352\pi$
$887$	1184.20			1.33506			0.667528	+	0.744584i	$0.267352\pi$
$888$	−211.553	−	445.209i	−0.238235	−	0.501362i
$889$	428.919			0.482473
$890$	221.546	+	246.133i	0.248928	+	0.276554i
$891$	−830.544	+	171.450i	−0.932148	+	0.192424i
$892$			3.39857i			0.00381005i
$893$	−1731.10			−1.93853
$894$	−42.1714	−	88.7490i	−0.0471716	−	0.0992718i
$895$	−619.678	−	688.448i	−0.692378	−	0.769215i
$896$		−	29.9333i		−	0.0334077i
$897$	119.151	+	250.751i	0.132833	+	0.279545i
$898$			436.010i			0.485534i
$899$			1683.26i			1.87237i
$900$	−317.159	−	319.234i	−0.352399	−	0.354704i
$901$	−1245.03			−1.38183
$902$	778.603			0.863196
$903$	113.005	−	53.6972i	0.125144	−	0.0594653i
$904$	−80.7709			−0.0893484
$905$	−543.957	+	489.621i	−0.601058	+	0.541017i
$906$	−287.964	+	136.834i	−0.317841	+	0.151031i
$907$		−	291.663i		−	0.321569i	−0.986990	−	0.160785i	$-0.948598\pi$
$907$		−	291.663i		−	0.321569i	0.986990	−	0.160785i	$-0.0514025\pi$
$908$	413.940			0.455881
$909$	1194.36	+	972.991i	1.31393	+	1.07040i
$910$	166.773	−	150.114i	0.183267	−	0.164960i
$911$		−	1318.03i		−	1.44679i	−0.690434	−	0.723395i	$-0.742580\pi$
$911$		−	1318.03i		−	1.44679i	0.690434	−	0.723395i	$-0.257420\pi$
$912$	−220.214	+	104.640i	−0.241463	+	0.114737i
$913$			352.831i			0.386452i
$914$		−	672.833i		−	0.736141i
$915$	−308.374	+	741.061i	−0.337020	+	0.809903i
$916$	−14.0509			−0.0153394
$917$	−131.165			−0.143037
$918$	−264.265	+	1079.79i	−0.287871	+	1.17624i
$919$	−569.882			−0.620111			−0.310056	−	0.950718i	$-0.600348\pi$
$919$	−569.882			−0.620111			−0.310056	+	0.950718i	$0.600348\pi$
$920$	−81.1014	+	73.0001i	−0.0881537	+	0.0793480i
$921$	639.366	+	1345.53i	0.694208	+	1.46095i
$922$			1081.16i			1.17262i
$923$	−696.462			−0.754563
$924$	150.117	−	71.3322i	0.162465	−	0.0771994i
$925$	1444.26	+	152.274i	1.56136	+	0.164620i
$926$			789.847i			0.852966i
$927$	906.252	+	738.282i	0.977618	+	0.796421i
$928$		−	268.161i		−	0.288967i
$929$		−	198.562i		−	0.213737i	−0.994273	−	0.106869i	$-0.965918\pi$
$929$		−	198.562i		−	0.213737i	0.994273	−	0.106869i	$-0.0340824\pi$
$930$	289.389	−	695.439i	0.311171	−	0.747784i
$931$	−142.223			−0.152764
$932$	−233.344			−0.250369
$933$	63.7363	+	134.132i	0.0683133	+	0.143764i
$934$	355.421			0.380537
$935$	−1019.61	−	1132.76i	−1.09049	−	1.21151i
$936$	236.706	+	192.834i	0.252891	+	0.206019i
$937$		−	1307.73i		−	1.39566i	−0.716266	−	0.697828i	$-0.754150\pi$
$937$		−	1307.73i		−	1.39566i	0.716266	−	0.697828i	$-0.245850\pi$
$938$	−103.407			−0.110242
$939$	−282.196	−	593.878i	−0.300529	−	0.632458i
$940$	−633.269	+	570.011i	−0.673691	+	0.606395i
$941$			1542.60i			1.63932i	0.572853	+	0.819658i	$0.305837\pi$
$941$			1542.60i			1.63932i	−0.572853	+	0.819658i	$0.694163\pi$
$942$	−121.447	−	255.584i	−0.128925	−	0.271320i
$943$		−	405.731i		−	0.430255i
$944$			151.908i			0.160919i
$945$	314.667	−	168.995i	0.332981	−	0.178831i
$946$	−233.394			−0.246716
$947$	−377.167			−0.398276			−0.199138	−	0.979971i	$-0.563814\pi$
$947$	−377.167			−0.398276			−0.199138	+	0.979971i	$0.563814\pi$
$948$	−104.589	+	49.6982i	−0.110326	+	0.0524242i
$949$	813.271			0.856977
$950$	75.3192	−	714.375i	0.0792834	−	0.751974i
$951$	260.943	−	123.994i	0.274388	−	0.130383i
$952$		−	217.864i		−	0.228848i
$953$	−673.763			−0.706991			−0.353496	−	0.935436i	$-0.615007\pi$
$953$	−673.763			−0.706991			−0.353496	+	0.935436i	$0.615007\pi$
$954$	−343.784	+	422.000i	−0.360361	+	0.442348i
$955$	279.238	+	310.227i	0.292396	+	0.324845i
$956$		−	314.237i		−	0.328700i
$957$	1344.85	−	639.039i	1.40527	−	0.667752i
$958$			485.947i			0.507252i
$959$			562.807i			0.586869i
$960$	−46.1027	+	110.791i	−0.0480236	+	0.115407i
$961$	299.849			0.312017
$962$	−985.316			−1.02424
$963$	165.772	−	203.487i	0.172141	−	0.211306i
$964$	−574.065			−0.595503
$965$	−296.052	−	328.907i	−0.306790	−	0.340836i
$966$	−37.1713	−	78.2264i	−0.0384796	−	0.0809797i
$967$		−	1121.04i		−	1.15929i	−0.814867	−	0.579647i	$-0.803190\pi$
$967$		−	1121.04i		−	1.15929i	0.814867	−	0.579647i	$-0.196810\pi$
$968$	32.1954			0.0332597
$969$	−1602.79	+	761.605i	−1.65406	+	0.785970i
$970$	−308.122	−	342.317i	−0.317652	−	0.352904i
$971$			1490.39i			1.53490i	0.641108	+	0.767451i	$0.278475\pi$
$971$			1490.39i			1.53490i	−0.641108	+	0.767451i	$0.721525\pi$
$972$	293.022	+	387.730i	0.301463	+	0.398899i
$973$		−	196.222i		−	0.201667i
$974$		−	1286.73i		−	1.32108i
$975$	−848.471	+	298.748i	−0.870227	+	0.306409i
$976$	214.043			0.219306
$977$	1171.66			1.19924			0.599621	−	0.800284i	$-0.295318\pi$
$977$	1171.66			1.19924			0.599621	+	0.800284i	$0.295318\pi$
$978$	−453.066	−	953.471i	−0.463258	−	0.974919i
$979$	490.328			0.500846
$980$	−52.0278	+	46.8307i	−0.0530896	+	0.0477864i
$981$	109.877	−	134.876i	0.112005	−	0.137488i
$982$			827.148i			0.842309i
$983$	1018.78			1.03639			0.518197	−	0.855261i	$-0.326603\pi$
$983$	1018.78			1.03639			0.518197	+	0.855261i	$0.326603\pi$
$984$	−191.502	−	403.013i	−0.194616	−	0.409566i
$985$	137.258	−	123.547i	0.139348	−	0.125428i
$986$		−	1951.76i		−	1.97947i
$987$	−290.247	−	610.820i	−0.294070	−	0.618865i
$988$			487.367i			0.493287i
$989$			121.622i			0.122974i
$990$	−665.487	+	32.8103i	−0.672209	+	0.0331417i
$991$	−240.455			−0.242639			−0.121320	−	0.992613i	$-0.538713\pi$
$991$	−240.455			−0.242639			−0.121320	+	0.992613i	$0.538713\pi$
$992$	−200.866			−0.202486
$993$	−1459.70	+	693.615i	−1.46999	+	0.698505i
$994$	217.274			0.218585
$995$	−762.212	+	686.074i	−0.766042	+	0.689521i
$996$	182.629	−	86.7809i	0.183362	−	0.0871294i
$997$		−	723.800i		−	0.725978i	−0.931793	−	0.362989i	$-0.881756\pi$
$997$		−	723.800i		−	0.725978i	0.931793	−	0.362989i	$-0.118244\pi$
$998$	1277.32			1.27988
$999$	−1523.49	−	372.856i	−1.52501	−	0.373229i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.c.a.29.16	yes	24
3.2	odd	2	inner	210.3.c.a.29.10	yes	24
5.2	odd	4		1050.3.e.e.701.4		24
5.3	odd	4		1050.3.e.e.701.1		24
5.4	even	2	inner	210.3.c.a.29.9	✓	24
15.2	even	4		1050.3.e.e.701.2		24
15.8	even	4		1050.3.e.e.701.3		24
15.14	odd	2	inner	210.3.c.a.29.15	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.c.a.29.9	✓	24	5.4	even	2	inner
210.3.c.a.29.10	yes	24	3.2	odd	2	inner
210.3.c.a.29.15	yes	24	15.14	odd	2	inner
210.3.c.a.29.16	yes	24	1.1	even	1	trivial
1050.3.e.e.701.1		24	5.3	odd	4
1050.3.e.e.701.2		24	15.2	even	4
1050.3.e.e.701.3		24	15.8	even	4
1050.3.e.e.701.4		24	5.2	odd	4

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +(-2.70965 + 1.28756i) q^{3} +2.00000 q^{4} +(3.71627 - 3.34505i) q^{5} +(-3.83202 + 1.82088i) q^{6} -2.64575i q^{7} +2.82843 q^{8} +(5.68438 - 6.97766i) q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +(-2.70965 + 1.28756i) q^{3} +2.00000 q^{4} +(3.71627 - 3.34505i) q^{5} +(-3.83202 + 1.82088i) q^{6} -2.64575i q^{7} +2.82843 q^{8} +(5.68438 - 6.97766i) q^{9} +(5.25560 - 4.73061i) q^{10} -10.4698i q^{11} +(-5.41930 + 2.57512i) q^{12} +11.9937i q^{13} -3.74166i q^{14} +(-5.76283 + 13.8488i) q^{15} +4.00000 q^{16} +29.1133 q^{17} +(8.03893 - 9.86791i) q^{18} +20.3176 q^{19} +(7.43254 - 6.69010i) q^{20} +(3.40656 + 7.16905i) q^{21} -14.8066i q^{22} -7.71572 q^{23} +(-7.66404 + 3.64177i) q^{24} +(2.62131 - 24.8622i) q^{25} +16.9617i q^{26} +(-6.41851 + 26.2260i) q^{27} -5.29150i q^{28} -47.4046i q^{29} +(-8.14988 + 19.5852i) q^{30} -35.5084 q^{31} +5.65685 q^{32} +(13.4805 + 28.3695i) q^{33} +41.1724 q^{34} +(-8.85016 - 9.83232i) q^{35} +(11.3688 - 13.9553i) q^{36} +58.0907i q^{37} +28.7334 q^{38} +(-15.4426 - 32.4988i) q^{39} +(10.5112 - 9.46122i) q^{40} +52.5850i q^{41} +(4.81761 + 10.1386i) q^{42} -15.7629i q^{43} -20.9396i q^{44} +(-2.21593 - 44.9454i) q^{45} -10.9117 q^{46} -85.2023 q^{47} +(-10.8386 + 5.15024i) q^{48} -7.00000 q^{49} +(3.70710 - 35.1605i) q^{50} +(-78.8867 + 37.4850i) q^{51} +23.9875i q^{52} -42.7649 q^{53} +(-9.07715 + 37.0892i) q^{54} +(-35.0221 - 38.9087i) q^{55} -7.48331i q^{56} +(-55.0535 + 26.1601i) q^{57} -67.0403i q^{58} +37.9769i q^{59} +(-11.5257 + 27.6976i) q^{60} +53.5108 q^{61} -50.2165 q^{62} +(-18.4612 - 15.0395i) q^{63} +8.00000 q^{64} +(40.1196 + 44.5719i) q^{65} +(19.0643 + 40.1206i) q^{66} -27.6366i q^{67} +58.2265 q^{68} +(20.9069 - 9.93444i) q^{69} +(-12.5160 - 13.9050i) q^{70} +58.0688i q^{71} +(16.0779 - 19.7358i) q^{72} -67.8080i q^{73} +82.1526i q^{74} +(24.9087 + 70.7429i) q^{75} +40.6352 q^{76} -27.7005 q^{77} +(-21.8392 - 45.9602i) q^{78} +19.2994 q^{79} +(14.8651 - 13.3802i) q^{80} +(-16.3756 - 79.3274i) q^{81} +74.3664i q^{82} -33.6998 q^{83} +(6.81312 + 14.3381i) q^{84} +(108.193 - 97.3852i) q^{85} -22.2920i q^{86} +(61.0363 + 128.450i) q^{87} -29.6131i q^{88} +46.8325i q^{89} +(-3.13380 - 63.5624i) q^{90} +31.7324 q^{91} -15.4314 q^{92} +(96.2153 - 45.7192i) q^{93} -120.494 q^{94} +(75.5056 - 67.9633i) q^{95} +(-15.3281 + 7.28354i) q^{96} -65.1337i q^{97} -9.89949 q^{98} +(-73.0549 - 59.5145i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 48 q^{4} + 44 q^{9}+O(q^{10}) \) 24 * q + 48 * q^4 + 44 * q^9	\( 24 q + 48 q^{4} + 44 q^{9} + 16 q^{10} + 4 q^{15} + 96 q^{16} - 80 q^{19} - 28 q^{21} + 48 q^{25} - 56 q^{30} + 224 q^{31} + 128 q^{34} + 88 q^{36} - 92 q^{39} + 32 q^{40} - 72 q^{45} - 144 q^{46} - 168 q^{49} - 284 q^{51} - 144 q^{54} - 320 q^{55} + 8 q^{60} + 192 q^{64} + 224 q^{66} - 152 q^{69} - 56 q^{70} + 48 q^{75} - 160 q^{76} - 72 q^{79} - 212 q^{81} - 56 q^{84} - 64 q^{85} - 240 q^{90} + 168 q^{91} - 128 q^{94} - 876 q^{99}+O(q^{100}) \) 24 * q + 48 * q^4 + 44 * q^9 + 16 * q^10 + 4 * q^15 + 96 * q^16 - 80 * q^19 - 28 * q^21 + 48 * q^25 - 56 * q^30 + 224 * q^31 + 128 * q^34 + 88 * q^36 - 92 * q^39 + 32 * q^40 - 72 * q^45 - 144 * q^46 - 168 * q^49 - 284 * q^51 - 144 * q^54 - 320 * q^55 + 8 * q^60 + 192 * q^64 + 224 * q^66 - 152 * q^69 - 56 * q^70 + 48 * q^75 - 160 * q^76 - 72 * q^79 - 212 * q^81 - 56 * q^84 - 64 * q^85 - 240 * q^90 + 168 * q^91 - 128 * q^94 - 876 * q^99

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