LMFDB - Embedded newform 210.3.c.a.29.9

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			29.9
Character	$\chi$	$=$	210.29
Dual form			210.3.c.a.29.10

$q$-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} +(-14.3767 - 4.27898i) 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} +(20.3318 + 6.05140i) 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} +(-44.4653 + 6.91635i) 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} +(-28.7535 - 8.55797i) 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} +(39.1144 + 63.9927i) 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} +(62.8834 - 9.78120i) 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	$-0.847384\pi$
$13$		−	11.9937i		−	0.922595i	0.887246	−	0.461297i	$-0.152616\pi$
$14$		−	3.74166i		−	0.267261i
$15$	−14.3767	−	4.27898i	−0.958449	−	0.285266i
$16$	4.00000			0.250000
$17$	−29.1133			−1.71254			−0.856272	−	0.516525i	$-0.827225\pi$
$17$	−29.1133			−1.71254			−0.856272	+	0.516525i	$0.827225\pi$
$18$	−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	$-0.446355\pi$
$23$	7.71572			0.335466			0.167733	+	0.985832i	$0.446355\pi$
$24$	−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	$-0.304542\pi$
$30$	20.3318	+	6.05140i	0.677725	+	0.201713i
$31$	−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	$-0.712658\pi$
$37$		−	58.0907i		−	1.57002i	0.619485	−	0.785009i	$-0.287342\pi$
$38$	−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	$0.0586744\pi$
$43$			15.7629i			0.366578i	−0.983059	+	0.183289i	$0.941326\pi$
$44$		−	20.9396i		−	0.475901i
$45$	−44.4653	+	6.91635i	−0.988118	+	0.153697i
$46$	−10.9117			−0.237210
$47$	85.2023			1.81281			0.906407	−	0.422405i	$-0.138814\pi$
$47$	85.2023			1.81281			0.906407	+	0.422405i	$0.138814\pi$
$48$	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	$-0.367813\pi$
$53$	42.7649			0.806885			0.403443	+	0.915005i	$0.367813\pi$
$54$	−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	$0.895699\pi$
$60$	−28.7535	−	8.55797i	−0.479224	−	0.142633i
$61$	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	$0.0661238\pi$
$67$			27.6366i			0.412487i	−0.978501	+	0.206243i	$0.933876\pi$
$68$	−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	$0.153744\pi$
$73$			67.8080i			0.928877i	−0.885605	+	0.464438i	$0.846256\pi$
$74$			82.1526i			1.11017i
$75$	39.1144	+	63.9927i	0.521525	+	0.853236i
$76$	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	$-0.434927\pi$
$83$	33.6998			0.406021			0.203011	+	0.979177i	$0.434927\pi$
$84$	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	$0.915254\pi$
$90$	62.8834	−	9.78120i	0.698705	−	0.108680i
$91$	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	$0.108987\pi$
$97$			65.1337i			0.671482i	−0.941954	+	0.335741i	$0.891013\pi$
$98$	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	$-0.782858\pi$
$103$		−	129.879i		−	1.26096i	0.776205	−	0.630481i	$-0.217142\pi$
$104$			33.9234i			0.326186i
$105$	11.3211	−	38.0372i	0.107820	−	0.362259i
$106$	−60.4787			−0.570554
$107$	−29.1627			−0.272549			−0.136274	−	0.990671i	$-0.543513\pi$
$107$	−29.1627			−0.272549			−0.136274	+	0.990671i	$0.543513\pi$
$108$	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	$-0.459671\pi$
$113$	28.5568			0.252715			0.126358	+	0.991985i	$0.459671\pi$
$114$	−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
$120$	40.6635	+	12.1028i	0.338863	+	0.100857i
$121$	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	$-0.779658\pi$
$127$		−	162.116i		−	1.27650i	0.769828	−	0.638252i	$-0.220342\pi$
$128$	−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
$135$	−111.580	+	75.9926i	−0.826519	+	0.562908i
$136$	82.3447			0.605476
$137$	212.721			1.55271			0.776354	−	0.630297i	$-0.217067\pi$
$137$	212.721			1.55271			0.776354	+	0.630297i	$0.217067\pi$
$138$	−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	$0.975237\pi$
$150$	−55.3161	−	90.4993i	−0.368774	−	0.603329i
$151$	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	$-0.931869\pi$
$157$		−	66.6968i		−	0.424820i	0.977181	−	0.212410i	$-0.0681313\pi$
$158$	−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	$-0.723607\pi$
$163$		−	248.817i		−	1.52648i	0.646114	−	0.763241i	$-0.276393\pi$
$164$			105.170i			0.641280i
$165$	−44.8002	+	150.522i	−0.271516	+	0.912253i
$166$	−47.6587			−0.287100
$167$	−92.0222			−0.551031			−0.275516	−	0.961297i	$-0.588849\pi$
$167$	−92.0222			−0.551031			−0.275516	+	0.961297i	$0.588849\pi$
$168$	−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	$-0.735761\pi$
$173$	−233.473			−1.34956			−0.674778	+	0.738021i	$0.735761\pi$
$174$	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	$-0.173124\pi$
$180$	−88.9306	+	13.8327i	−0.494059	+	0.0768484i
$181$	−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	$0.0736393\pi$
$193$			88.5046i			0.458573i	−0.973359	+	0.229287i	$0.926361\pi$
$194$		−	92.1130i		−	0.474809i
$195$	−51.3210	+	172.431i	−0.263184	+	0.884259i
$196$	−14.0000			−0.0714286
$197$	−36.9343			−0.187484			−0.0937419	−	0.995597i	$-0.529883\pi$
$197$	−36.9343			−0.187484			−0.0937419	+	0.995597i	$0.529883\pi$
$198$	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
$210$	−16.0105	+	53.7928i	−0.0762404	+	0.256156i
$211$	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	$-0.998787\pi$
$223$		−	1.69928i		−	0.00762011i	0.999993	−	0.00381005i	$-0.00121278\pi$
$224$		−	14.9666i		−	0.0668153i
$225$	188.381	+	123.036i	0.837247	+	0.546825i
$226$	−40.3855			−0.178697
$227$	−206.970			−0.911762			−0.455881	−	0.890041i	$-0.650676\pi$
$227$	−206.970			−0.911762			−0.455881	+	0.890041i	$0.650676\pi$
$228$	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	$-0.419448\pi$
$233$	116.672			0.500738			0.250369	+	0.968151i	$0.419448\pi$
$234$	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	$-0.106611\pi$
$240$	−57.5069	−	17.1159i	−0.239612	−	0.0713164i
$241$	−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
$255$	418.553	+	124.575i	1.64139	+	0.488530i
$256$	16.0000			0.0625000
$257$	356.900			1.38871			0.694357	−	0.719630i	$-0.255689\pi$
$257$	356.900			1.38871			0.694357	+	0.719630i	$0.255689\pi$
$258$	−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	$-0.422841\pi$
$263$	126.259			0.480071			0.240036	+	0.970764i	$0.422841\pi$
$264$	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	$-0.230421\pi$
$270$	157.798	−	107.470i	0.584437	−	0.398036i
$271$	−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	$0.160320\pi$
$277$			267.379i			0.965266i	−0.875823	+	0.482633i	$0.839680\pi$
$278$	−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	$-0.968354\pi$
$283$		−	56.1781i		−	0.198509i	0.995062	−	0.0992546i	$-0.0316458\pi$
$284$			116.138i			0.408935i
$285$	−292.100	−	86.9386i	−1.02491	−	0.305048i
$286$	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	$-0.480505\pi$
$293$	35.8668			0.122412			0.0612062	+	0.998125i	$0.480505\pi$
$294$	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
$300$	78.2288	+	127.985i	0.260763	+	0.426618i
$301$	−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	$0.299855\pi$
$307$			496.572i			1.61750i	−0.588154	+	0.808749i	$0.700145\pi$
$308$	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	$-0.886143\pi$
$313$		−	219.172i		−	0.700229i	0.936707	−	0.350114i	$-0.113857\pi$
$314$			94.3235i			0.300393i
$315$	−18.2990	−	117.644i	−0.0580919	−	0.373474i
$316$	38.5987			0.122148
$317$	96.3016			0.303791			0.151895	−	0.988397i	$-0.451462\pi$
$317$	96.3016			0.303791			0.151895	+	0.988397i	$0.451462\pi$
$318$	−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
$330$	63.3570	−	212.870i	0.191991	−	0.645061i
$331$	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	$0.0972518\pi$
$337$			202.735i			0.601589i	−0.953689	+	0.300794i	$0.902748\pi$
$338$	−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
$345$	−110.927	−	33.0154i	−0.321527	−	0.0956969i
$346$	330.181			0.954280
$347$	−139.011			−0.400607			−0.200304	−	0.979734i	$-0.564193\pi$
$347$	−139.011			−0.400607			−0.200304	+	0.979734i	$0.564193\pi$
$348$	−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	$-0.277960\pi$
$353$	453.499			1.28470			0.642349	+	0.766412i	$0.277960\pi$
$354$	−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	$-0.0671324\pi$
$360$	125.767	−	19.5624i	0.349352	−	0.0543400i
$361$	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	$0.174735\pi$
$367$			382.992i			1.04357i	−0.853076	+	0.521787i	$0.825265\pi$
$368$	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	$-0.965653\pi$
$373$		−	80.3409i		−	0.215391i	0.994184	−	0.107696i	$-0.0343472\pi$
$374$		−	431.067i		−	1.15259i
$375$	68.6990	−	368.654i	0.183197	−	0.983076i
$376$	−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	$-0.351901\pi$
$383$	343.675			0.897323			0.448661	+	0.893702i	$0.351901\pi$
$384$	−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	$-0.233238\pi$
$390$	72.5788	−	243.854i	0.186100	−	0.625266i
$391$	−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	$0.0745729\pi$
$397$			184.320i			0.464281i	−0.972682	+	0.232140i	$0.925427\pi$
$398$	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
$405$	−204.498	+	349.579i	−0.504933	+	0.863159i
$406$	−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	$0.989647\pi$
$420$	22.6423	−	76.0745i	0.0539101	−	0.181130i
$421$	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	$-0.772325\pi$
$433$		−	567.937i		−	1.31163i	0.754920	−	0.655816i	$-0.227675\pi$
$434$			132.860i			0.306130i
$435$	−202.844	+	681.523i	−0.466307	+	1.56672i
$436$	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	$-0.710424\pi$
$443$	−543.969			−1.22792			−0.613960	+	0.789337i	$0.710424\pi$
$444$	−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	$0.888447\pi$
$450$	−266.410	−	173.999i	−0.592023	−	0.386663i
$451$	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	$0.174266\pi$
$457$			475.765i			1.04106i	−0.853843	+	0.520530i	$0.825734\pi$
$458$	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	$-0.793917\pi$
$463$		−	558.506i		−	1.20628i	0.797637	−	0.603138i	$-0.206083\pi$
$464$		−	189.618i		−	0.408661i
$465$	510.495	+	151.940i	1.09784	+	0.326753i
$466$	−164.999			−0.354075
$467$	−251.321			−0.538160			−0.269080	−	0.963118i	$-0.586720\pi$
$467$	−251.321			−0.538160			−0.269080	+	0.963118i	$0.586720\pi$
$468$	−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	$0.883226\pi$
$480$	81.3271	+	24.2056i	0.169431	+	0.0504283i
$481$	−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	$0.383837\pi$
$487$			909.858i			1.86829i	−0.356892	+	0.934146i	$0.616163\pi$
$488$	−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
$495$	72.4130	+	465.544i	0.146289	+	0.940493i
$496$	−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	$-0.560023\pi$
$503$	−188.576			−0.374903			−0.187452	+	0.982274i	$0.560023\pi$
$504$	−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	$0.827138\pi$
$510$	−591.924	−	176.176i	−1.16064	−	0.345443i
$511$	−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	$0.218494\pi$
$523$			662.926i			1.26755i	−0.773519	+	0.633773i	$0.781506\pi$
$524$		−	99.1513i		−	0.189220i
$525$	−169.309	+	103.487i	−0.322493	+	0.197118i
$526$	−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
$540$	−223.160	+	151.985i	−0.413260	+	0.281454i
$541$	−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	$0.0519334\pi$
$547$			177.699i			0.324862i	−0.986720	+	0.162431i	$0.948067\pi$
$548$	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
$555$	−248.569	+	835.154i	−0.447872	+	1.50478i
$556$	148.330			0.266780
$557$	227.747			0.408882			0.204441	−	0.978879i	$-0.434462\pi$
$557$	227.747			0.408882			0.204441	+	0.978879i	$0.434462\pi$
$558$	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	$-0.422567\pi$
$563$	271.221			0.481742			0.240871	+	0.970557i	$0.422567\pi$
$564$	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	$-0.0176596\pi$
$570$	413.092	+	122.950i	0.724723	+	0.215701i
$571$	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	$0.104426\pi$
$577$			371.832i			0.644424i	−0.946668	+	0.322212i	$0.895574\pi$
$578$	−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
$585$	82.9529	+	533.305i	0.141800	+	0.911632i
$586$	−50.7233			−0.0865586
$587$	−824.490			−1.40458			−0.702291	−	0.711890i	$-0.747840\pi$
$587$	−824.490			−1.40458			−0.702291	+	0.711890i	$0.747840\pi$
$588$	−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	$-0.459916\pi$
$593$	148.957			0.251192			0.125596	+	0.992081i	$0.459916\pi$
$594$	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	$0.973771\pi$
$600$	−110.632	−	180.999i	−0.184387	−	0.301664i
$601$	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	$-0.863523\pi$
$607$		−	504.707i		−	0.831478i	0.909484	−	0.415739i	$-0.136477\pi$
$608$	−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	$-0.889657\pi$
$613$		−	416.536i		−	0.679503i	0.940515	−	0.339752i	$-0.110343\pi$
$614$		−	702.259i		−	1.14374i
$615$	225.010	−	756.000i	0.365870	−	1.22927i
$616$	−78.3490			−0.127190
$617$	−132.241			−0.214330			−0.107165	−	0.994241i	$-0.534177\pi$
$617$	−132.241			−0.214330			−0.107165	+	0.994241i	$0.534177\pi$
$618$	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
$630$	25.8786	+	166.374i	0.0410772	+	0.264086i
$631$	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	$0.139582\pi$
$643$			546.024i			0.849181i	−0.905385	+	0.424591i	$0.860418\pi$
$644$			40.8277i			0.0633971i
$645$	67.4490	−	226.618i	0.104572	−	0.351346i
$646$	836.523			1.29493
$647$	801.011			1.23804			0.619020	−	0.785376i	$-0.287530\pi$
$647$	801.011			1.23804			0.619020	+	0.785376i	$0.287530\pi$
$648$	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	$-0.867104\pi$
$653$	−1193.82			−1.82821			−0.914103	+	0.405482i	$0.867104\pi$
$654$	−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	$-0.386325\pi$
$660$	−89.6004	+	301.044i	−0.135758	+	0.456127i
$661$	−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	$0.0893067\pi$
$673$			372.706i			0.553798i	−0.960899	+	0.276899i	$0.910693\pi$
$674$		−	286.711i		−	0.425387i
$675$	668.861	+	90.8318i	0.990905	+	0.134566i
$676$	50.3009			0.0744096
$677$	762.928			1.12693			0.563463	−	0.826142i	$-0.309469\pi$
$677$	762.928			1.12693			0.563463	+	0.826142i	$0.309469\pi$
$678$	−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	$-0.493410\pi$
$683$	28.2779			0.0414024			0.0207012	+	0.999786i	$0.493410\pi$
$684$	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
$690$	156.874	+	46.6909i	0.227354	+	0.0676679i
$691$	−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
$705$	−1224.93	−	364.579i	−1.73749	−	0.517134i
$706$	−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	$0.860082\pi$
$720$	−177.861	+	27.6654i	−0.247030	+	0.0384242i
$721$	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	$-0.714445\pi$
$727$		−	1136.33i		−	1.56304i	0.623881	−	0.781520i	$-0.285555\pi$
$728$	−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	$0.0882940\pi$
$733$			401.450i			0.547681i	−0.961775	+	0.273840i	$0.911706\pi$
$734$		−	541.632i		−	0.737919i
$735$	100.637	+	29.9529i	0.136921	+	0.0407522i
$736$	−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	$-0.566655\pi$
$743$	−308.906			−0.415755			−0.207877	+	0.978155i	$0.566655\pi$
$744$	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
$750$	−97.1551	+	521.355i	−0.129540	+	0.695140i
$751$	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	$-0.886971\pi$
$757$		−	526.381i		−	0.695351i	0.937615	−	0.347676i	$-0.113029\pi$
$758$	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
$765$	1294.53	−	201.358i	1.69220	−	0.263213i
$766$	−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	$-0.615381\pi$
$773$	−548.202			−0.709188			−0.354594	+	0.935020i	$0.615381\pi$
$774$	−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
$780$	−102.642	+	344.861i	−0.131592	+	0.442130i
$781$	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	$-0.877572\pi$
$787$		−	590.574i		−	0.750412i	0.926942	−	0.375206i	$-0.122428\pi$
$788$	−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
$795$	−614.820	−	182.990i	−0.773358	−	0.230177i
$796$	−410.203			−0.515330
$797$	913.353			1.14599			0.572994	−	0.819560i	$-0.305782\pi$
$797$	913.353			1.14599			0.572994	+	0.819560i	$0.305782\pi$
$798$	−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	$-0.0568609\pi$
$810$	289.204	−	494.380i	0.357041	−	0.610345i
$811$	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	$-0.986765\pi$
$823$		−	68.4196i		−	0.0831344i	0.999136	−	0.0415672i	$-0.0132351\pi$
$824$			367.353i			0.445817i
$825$	669.992	−	409.521i	0.812112	−	0.496389i
$826$	142.097			0.172030
$827$	1072.36			1.29668			0.648342	−	0.761349i	$-0.275463\pi$
$827$	1072.36			1.29668			0.648342	+	0.761349i	$0.275463\pi$
$828$	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	$0.801432\pi$
$840$	−32.0210	+	107.586i	−0.0381202	+	0.128078i
$841$	−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	$-0.993507\pi$
$853$		−	34.7970i		−	0.0407936i	0.999792	−	0.0203968i	$-0.00649296\pi$
$854$		−	200.219i		−	0.234448i
$855$	−903.427	+	140.524i	−1.05664	+	0.164355i
$856$	82.4845			0.0963605
$857$	−79.5168			−0.0927851			−0.0463926	−	0.998923i	$-0.514773\pi$
$857$	−79.5168			−0.0927851			−0.0463926	+	0.998923i	$0.514773\pi$
$858$	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	$-0.526795\pi$
$863$	−145.121			−0.168159			−0.0840796	+	0.996459i	$0.526795\pi$
$864$	−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
$870$	286.864	−	963.820i	0.329729	−	1.10784i
$871$	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	$0.110198\pi$
$877$			595.173i			0.678647i	−0.940670	+	0.339324i	$0.889802\pi$
$878$	−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	$0.179590\pi$
$883$			944.347i			1.06948i	−0.845018	+	0.534738i	$0.820410\pi$
$884$			698.353i			0.789992i
$885$	162.502	−	545.983i	0.183619	−	0.616930i
$886$	769.288			0.868271
$887$	−1184.20			−1.33506			−0.667528	−	0.744584i	$-0.732648\pi$
$887$	−1184.20			−1.33506			−0.667528	+	0.744584i	$0.732648\pi$
$888$	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
$900$	376.761	+	246.071i	0.418624	+	0.273412i
$901$	−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	$0.0514025\pi$
$907$			291.663i			0.321569i	−0.986990	+	0.160785i	$0.948598\pi$
$908$	−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
$915$	−769.310	−	228.972i	−0.840776	−	0.250242i
$916$	−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	$-0.0340824\pi$
$930$	−721.949	−	214.876i	−0.776289	−	0.231049i
$931$	−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	$0.245850\pi$
$937$			1307.73i			1.39566i	−0.716266	+	0.697828i	$0.754150\pi$
$938$	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
$945$	−201.058	−	295.213i	−0.212759	−	0.312395i
$946$	−233.394			−0.246716
$947$	377.167			0.398276			0.199138	−	0.979971i	$-0.436186\pi$
$947$	377.167			0.398276			0.199138	+	0.979971i	$0.436186\pi$
$948$	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	$-0.384993\pi$
$953$	673.763			0.706991			0.353496	+	0.935436i	$0.384993\pi$
$954$	−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
$960$	−115.014	−	34.2319i	−0.119806	−	0.0356582i
$961$	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	$0.196810\pi$
$967$			1121.04i			1.15929i	−0.814867	+	0.579647i	$0.803190\pi$
$968$	−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
$975$	767.511	−	469.127i	0.787191	−	0.481156i
$976$	214.043			0.219306
$977$	−1171.66			−1.19924			−0.599621	−	0.800284i	$-0.704682\pi$
$977$	−1171.66			−1.19924			−0.599621	+	0.800284i	$0.704682\pi$
$978$	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	$-0.673397\pi$
$983$	−1018.78			−1.03639			−0.518197	+	0.855261i	$0.673397\pi$
$984$	−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
$990$	−102.407	−	658.379i	−0.103442	−	0.665029i
$991$	−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	$0.118244\pi$
$997$			723.800i			0.725978i	−0.931793	+	0.362989i	$0.881756\pi$
$998$	−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.29.9	✓	24
3.2	odd	2	inner	210.3.c.a.29.15	yes	24
5.2	odd	4		1050.3.e.e.701.1		24
5.3	odd	4		1050.3.e.e.701.4		24
5.4	even	2	inner	210.3.c.a.29.16	yes	24
15.2	even	4		1050.3.e.e.701.3		24
15.8	even	4		1050.3.e.e.701.2		24
15.14	odd	2	inner	210.3.c.a.29.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.c.a.29.9	✓	24	1.1	even	1	trivial
210.3.c.a.29.10	yes	24	15.14	odd	2	inner
210.3.c.a.29.15	yes	24	3.2	odd	2	inner
210.3.c.a.29.16	yes	24	5.4	even	2	inner
1050.3.e.e.701.1		24	5.2	odd	4
1050.3.e.e.701.2		24	15.8	even	4
1050.3.e.e.701.3		24	15.2	even	4
1050.3.e.e.701.4		24	5.3	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} +(-14.3767 - 4.27898i) 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} +(20.3318 + 6.05140i) 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} +(-44.4653 + 6.91635i) 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} +(-28.7535 - 8.55797i) 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} +(39.1144 + 63.9927i) 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} +(62.8834 - 9.78120i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more