LMFDB - Embedded newform 210.3.h.a.139.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(139,210)]

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([0, 1, 1]))

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

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

chi := DirichletCharacter("210.139");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.h (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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 96 x^{14} - 532 x^{13} + 3236 x^{12} - 12864 x^{11} + 49526 x^{10} - 141436 x^{9} + \cdots + 33750 $ x^16 - 8x^15 + 96x^14 - 532x^13 + 3236x^12 - 12864x^11 + 49526x^10 - 141436x^9 + 362298x^8 - 722060x^7 + 1208164x^6 - 1570812x^5 + 1591101x^4 - 1183860x^3 + 619650x^2 - 202500*x + 33750
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.10
Root			$0.500000 - 3.55177i$ of defining polynomial
Character	$\chi$	$=$	210.139
Dual form			210.3.h.a.139.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +(1.38028 - 4.80571i) q^{5} -2.44949i q^{6} +(-5.24961 + 4.63050i) q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +(1.38028 - 4.80571i) q^{5} -2.44949i q^{6} +(-5.24961 + 4.63050i) q^{7} -2.82843i q^{8} +3.00000 q^{9} +(6.79630 + 1.95201i) q^{10} +11.7671 q^{11} +3.46410 q^{12} +24.8280 q^{13} +(-6.54852 - 7.42407i) q^{14} +(-2.39072 + 8.32373i) q^{15} +4.00000 q^{16} +7.26100 q^{17} +4.24264i q^{18} -23.0050i q^{19} +(-2.76057 + 9.61141i) q^{20} +(9.09260 - 8.02027i) q^{21} +16.6412i q^{22} +26.4223i q^{23} +4.89898i q^{24} +(-21.1896 - 13.2665i) q^{25} +35.1122i q^{26} -5.19615 q^{27} +(10.4992 - 9.26101i) q^{28} +57.0861 q^{29} +(-11.7715 - 3.38099i) q^{30} +10.2222i q^{31} +5.65685i q^{32} -20.3812 q^{33} +10.2686i q^{34} +(15.0069 + 31.6195i) q^{35} -6.00000 q^{36} +14.2196i q^{37} +32.5340 q^{38} -43.0034 q^{39} +(-13.5926 - 3.90403i) q^{40} +16.2271i q^{41} +(11.3424 + 12.8589i) q^{42} -82.3114i q^{43} -23.5342 q^{44} +(4.14085 - 14.4171i) q^{45} -37.3668 q^{46} -51.6631 q^{47} -6.92820 q^{48} +(6.11686 - 48.6167i) q^{49} +(18.7616 - 29.9667i) q^{50} -12.5764 q^{51} -49.6561 q^{52} -64.8273i q^{53} -7.34847i q^{54} +(16.2419 - 56.5491i) q^{55} +(13.0970 + 14.8481i) q^{56} +39.8459i q^{57} +80.7320i q^{58} +81.7685i q^{59} +(4.78144 - 16.6475i) q^{60} -13.1240i q^{61} -14.4564 q^{62} +(-15.7488 + 13.8915i) q^{63} -8.00000 q^{64} +(34.2697 - 119.316i) q^{65} -28.8233i q^{66} +22.4035i q^{67} -14.5220 q^{68} -45.7648i q^{69} +(-44.7167 + 21.2230i) q^{70} +91.5022 q^{71} -8.48528i q^{72} -71.9256 q^{73} -20.1096 q^{74} +(36.7015 + 22.9782i) q^{75} +46.0100i q^{76} +(-61.7726 + 54.4875i) q^{77} -60.8160i q^{78} +45.2802 q^{79} +(5.52113 - 19.2228i) q^{80} +9.00000 q^{81} -22.9486 q^{82} +17.7328 q^{83} +(-18.1852 + 16.0405i) q^{84} +(10.0222 - 34.8943i) q^{85} +116.406 q^{86} -98.8761 q^{87} -33.2823i q^{88} +77.5800i q^{89} +(20.3889 + 5.85604i) q^{90} +(-130.338 + 114.966i) q^{91} -52.8446i q^{92} -17.7054i q^{93} -73.0627i q^{94} +(-110.555 - 31.7534i) q^{95} -9.79796i q^{96} -6.15741 q^{97} +(68.7544 + 8.65055i) q^{98} +35.3012 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 32 q^{4} + 48 q^{9}+O(q^{10}) $ 16 * q - 32 * q^4 + 48 * q^9	$ 16 q - 32 q^{4} + 48 q^{9} + 96 q^{11} + 16 q^{14} - 24 q^{15} + 64 q^{16} + 24 q^{21} + 24 q^{25} + 64 q^{29} + 24 q^{30} - 8 q^{35} - 96 q^{36} - 144 q^{39} - 192 q^{44} - 176 q^{46} + 224 q^{49} - 96 q^{50} - 48 q^{51} - 32 q^{56} + 48 q^{60} - 128 q^{64} + 368 q^{65} - 56 q^{70} - 384 q^{71} + 224 q^{74} - 608 q^{79} + 144 q^{81} - 48 q^{84} - 440 q^{85} + 416 q^{86} + 224 q^{91} - 560 q^{95} + 288 q^{99}+O(q^{100}) $ 16 * q - 32 * q^4 + 48 * q^9 + 96 * q^11 + 16 * q^14 - 24 * q^15 + 64 * q^16 + 24 * q^21 + 24 * q^25 + 64 * q^29 + 24 * q^30 - 8 * q^35 - 96 * q^36 - 144 * q^39 - 192 * q^44 - 176 * q^46 + 224 * q^49 - 96 * q^50 - 48 * q^51 - 32 * q^56 + 48 * q^60 - 128 * q^64 + 368 * q^65 - 56 * q^70 - 384 * q^71 + 224 * q^74 - 608 * q^79 + 144 * q^81 - 48 * q^84 - 440 * q^85 + 416 * q^86 + 224 * q^91 - 560 * q^95 + 288 * 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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−2.00000			−0.500000
$5$	1.38028	−	4.80571i	0.276057	−	0.961141i
$5$	1.38028	−	4.80571i	0.276057	−	0.961141i
$6$		−	2.44949i		−	0.408248i
$7$	−5.24961	+	4.63050i	−0.749945	+	0.661501i
$7$	−5.24961	+	4.63050i	−0.749945	+	0.661501i
$8$		−	2.82843i		−	0.353553i
$9$	3.00000			0.333333
$10$	6.79630	+	1.95201i	0.679630	+	0.195201i
$11$	11.7671			1.06973			0.534867	−	0.844936i	$-0.320362\pi$
$11$	11.7671			1.06973			0.534867	+	0.844936i	$0.320362\pi$
$12$	3.46410			0.288675
$13$	24.8280			1.90985			0.954925	−	0.296848i	$-0.0959354\pi$
$13$	24.8280			1.90985			0.954925	+	0.296848i	$0.0959354\pi$
$14$	−6.54852	−	7.42407i	−0.467752	−	0.530291i
$15$	−2.39072	+	8.32373i	−0.159381	+	0.554915i
$16$	4.00000			0.250000
$17$	7.26100			0.427118			0.213559	−	0.976930i	$-0.431494\pi$
$17$	7.26100			0.427118			0.213559	+	0.976930i	$0.431494\pi$
$18$			4.24264i			0.235702i
$19$		−	23.0050i		−	1.21079i	−0.795925	−	0.605395i	$-0.793015\pi$
$19$		−	23.0050i		−	1.21079i	0.795925	−	0.605395i	$-0.206985\pi$
$20$	−2.76057	+	9.61141i	−0.138028	+	0.480571i
$21$	9.09260	−	8.02027i	0.432981	−	0.381918i
$22$			16.6412i			0.756417i
$23$			26.4223i			1.14880i	0.818576	+	0.574398i	$0.194764\pi$
$23$			26.4223i			1.14880i	−0.818576	+	0.574398i	$0.805236\pi$
$24$			4.89898i			0.204124i
$25$	−21.1896	−	13.2665i	−0.847586	−	0.530659i
$26$			35.1122i			1.35047i
$27$	−5.19615			−0.192450
$28$	10.4992	−	9.26101i	0.374972	−	0.330750i
$29$	57.0861			1.96849			0.984243	−	0.176819i	$-0.0565806\pi$
$29$	57.0861			1.96849			0.984243	+	0.176819i	$0.0565806\pi$
$30$	−11.7715	−	3.38099i	−0.392384	−	0.112700i
$31$			10.2222i			0.329749i	0.986315	+	0.164874i	$0.0527219\pi$
$31$			10.2222i			0.329749i	−0.986315	+	0.164874i	$0.947278\pi$
$32$			5.65685i			0.176777i
$33$	−20.3812			−0.617612
$34$			10.2686i			0.302018i
$35$	15.0069	+	31.6195i	0.428768	+	0.903414i
$36$	−6.00000			−0.166667
$37$			14.2196i			0.384314i	0.981364	+	0.192157i	$0.0615482\pi$
$37$			14.2196i			0.384314i	−0.981364	+	0.192157i	$0.938452\pi$
$38$	32.5340			0.856158
$39$	−43.0034			−1.10265
$40$	−13.5926	−	3.90403i	−0.339815	−	0.0976007i
$41$			16.2271i			0.395782i	0.980224	+	0.197891i	$0.0634093\pi$
$41$			16.2271i			0.395782i	−0.980224	+	0.197891i	$0.936591\pi$
$42$	11.3424	+	12.8589i	0.270056	+	0.306164i
$43$		−	82.3114i		−	1.91422i	−0.289725	−	0.957110i	$-0.593564\pi$
$43$		−	82.3114i		−	1.91422i	0.289725	−	0.957110i	$-0.406436\pi$
$44$	−23.5342			−0.534867
$45$	4.14085	−	14.4171i	0.0920188	−	0.320380i
$46$	−37.3668			−0.812321
$47$	−51.6631			−1.09922			−0.549608	−	0.835423i	$-0.685223\pi$
$47$	−51.6631			−1.09922			−0.549608	+	0.835423i	$0.685223\pi$
$48$	−6.92820			−0.144338
$49$	6.11686	−	48.6167i	0.124834	−	0.992178i
$50$	18.7616	−	29.9667i	0.375232	−	0.599333i
$51$	−12.5764			−0.246597
$52$	−49.6561			−0.954925
$53$		−	64.8273i		−	1.22316i	−0.791184	−	0.611579i	$-0.790535\pi$
$53$		−	64.8273i		−	1.22316i	0.791184	−	0.611579i	$-0.209465\pi$
$54$		−	7.34847i		−	0.136083i
$55$	16.2419	−	56.5491i	0.295307	−	1.02817i
$56$	13.0970	+	14.8481i	0.233876	+	0.265145i
$57$			39.8459i			0.699050i
$58$			80.7320i			1.39193i
$59$			81.7685i			1.38591i	0.720982	+	0.692953i	$0.243691\pi$
$59$			81.7685i			1.38591i	−0.720982	+	0.692953i	$0.756309\pi$
$60$	4.78144	−	16.6475i	0.0796907	−	0.277458i
$61$		−	13.1240i		−	0.215148i	−0.994197	−	0.107574i	$-0.965692\pi$
$61$		−	13.1240i		−	0.215148i	0.994197	−	0.107574i	$-0.0343083\pi$
$62$	−14.4564			−0.233168
$63$	−15.7488	+	13.8915i	−0.249982	+	0.220500i
$64$	−8.00000			−0.125000
$65$	34.2697	−	119.316i	0.527226	−	1.83564i
$66$		−	28.8233i		−	0.436717i
$67$			22.4035i			0.334381i	0.985925	+	0.167190i	$0.0534695\pi$
$67$			22.4035i			0.334381i	−0.985925	+	0.167190i	$0.946531\pi$
$68$	−14.5220			−0.213559
$69$		−	45.7648i		−	0.663257i
$70$	−44.7167	+	21.2230i	−0.638810	+	0.303185i
$71$	91.5022			1.28876			0.644382	−	0.764704i	$-0.277115\pi$
$71$	91.5022			1.28876			0.644382	+	0.764704i	$0.277115\pi$
$72$		−	8.48528i		−	0.117851i
$73$	−71.9256			−0.985282			−0.492641	−	0.870233i	$-0.663968\pi$
$73$	−71.9256			−0.985282			−0.492641	+	0.870233i	$0.663968\pi$
$74$	−20.1096			−0.271751
$75$	36.7015	+	22.9782i	0.489354	+	0.306376i
$76$			46.0100i			0.605395i
$77$	−61.7726	+	54.4875i	−0.802242	+	0.707630i
$78$		−	60.8160i		−	0.779693i
$79$	45.2802			0.573167			0.286584	−	0.958055i	$-0.407480\pi$
$79$	45.2802			0.573167			0.286584	+	0.958055i	$0.407480\pi$
$80$	5.52113	−	19.2228i	0.0690141	−	0.240285i
$81$	9.00000			0.111111
$82$	−22.9486			−0.279860
$83$	17.7328			0.213648			0.106824	−	0.994278i	$-0.465932\pi$
$83$	17.7328			0.213648			0.106824	+	0.994278i	$0.465932\pi$
$84$	−18.1852	+	16.0405i	−0.216490	+	0.190959i
$85$	10.0222	−	34.8943i	0.117909	−	0.410521i
$86$	116.406			1.35356
$87$	−98.8761			−1.13651
$88$		−	33.2823i		−	0.378208i
$89$			77.5800i			0.871686i	0.900023	+	0.435843i	$0.143550\pi$
$89$			77.5800i			0.871686i	−0.900023	+	0.435843i	$0.856450\pi$
$90$	20.3889	+	5.85604i	0.226543	+	0.0650672i
$91$	−130.338	+	114.966i	−1.43228	+	1.26337i
$92$		−	52.8446i		−	0.574398i
$93$		−	17.7054i		−	0.190381i
$94$		−	73.0627i		−	0.777263i
$95$	−110.555	−	31.7534i	−1.16374	−	0.334247i
$96$		−	9.79796i		−	0.102062i
$97$	−6.15741			−0.0634785			−0.0317392	−	0.999496i	$-0.510105\pi$
$97$	−6.15741			−0.0634785			−0.0317392	+	0.999496i	$0.510105\pi$
$98$	68.7544	+	8.65055i	0.701576	+	0.0882709i
$99$	35.3012			0.356578
$100$	42.3793	+	26.5329i	0.423793	+	0.265329i
$101$		−	142.983i		−	1.41568i	−0.706374	−	0.707839i	$-0.749670\pi$
$101$		−	142.983i		−	1.41568i	0.706374	−	0.707839i	$-0.250330\pi$
$102$		−	17.7858i		−	0.174370i
$103$	14.5292			0.141060			0.0705302	−	0.997510i	$-0.477531\pi$
$103$	14.5292			0.141060			0.0705302	+	0.997510i	$0.477531\pi$
$104$		−	70.2243i		−	0.675234i
$105$	−25.9927	−	54.7666i	−0.247550	−	0.521587i
$106$	91.6797			0.864903
$107$			78.4228i			0.732923i	0.930433	+	0.366462i	$0.119431\pi$
$107$			78.4228i			0.732923i	−0.930433	+	0.366462i	$0.880569\pi$
$108$	10.3923			0.0962250
$109$	−74.7424			−0.685710			−0.342855	−	0.939388i	$-0.611394\pi$
$109$	−74.7424			−0.685710			−0.342855	+	0.939388i	$0.611394\pi$
$110$	79.9726	+	22.9695i	0.727023	+	0.208814i
$111$		−	24.6291i		−	0.221884i
$112$	−20.9985	+	18.5220i	−0.187486	+	0.165375i
$113$			85.2417i			0.754351i	0.926142	+	0.377175i	$0.123105\pi$
$113$			85.2417i			0.754351i	−0.926142	+	0.377175i	$0.876895\pi$
$114$	−56.3506			−0.494303
$115$	126.978	+	36.4702i	1.10415	+	0.317132i
$116$	−114.172			−0.984243
$117$	74.4841			0.636617
$118$	−115.638			−0.979984
$119$	−38.1175	+	33.6221i	−0.320315	+	0.282539i
$120$	23.5431	+	6.76198i	0.196192	+	0.0563498i
$121$	17.4642			0.144332
$122$	18.5602			0.152133
$123$		−	28.1061i		−	0.228505i
$124$		−	20.4444i		−	0.164874i
$125$	−93.0025	+	83.5197i	−0.744020	+	0.668158i
$126$	−19.6456	−	22.2722i	−0.155917	−	0.176764i
$127$			66.7734i			0.525775i	0.964827	+	0.262887i	$0.0846747\pi$
$127$			66.7734i			0.525775i	−0.964827	+	0.262887i	$0.915325\pi$
$128$		−	11.3137i		−	0.0883883i
$129$			142.568i			1.10518i
$130$	168.739	+	48.4647i	1.29799	+	0.372805i
$131$			28.8330i			0.220099i	0.993926	+	0.110049i	$0.0351009\pi$
$131$			28.8330i			0.220099i	−0.993926	+	0.110049i	$0.964899\pi$
$132$	40.7624			0.308806
$133$	106.525	+	120.767i	0.800939	+	0.908026i
$134$	−31.6834			−0.236443
$135$	−7.17216	+	24.9712i	−0.0531271	+	0.184972i
$136$		−	20.5372i		−	0.151009i
$137$			119.450i			0.871897i	0.899972	+	0.435948i	$0.143587\pi$
$137$			119.450i			0.871897i	−0.899972	+	0.435948i	$0.856413\pi$
$138$	64.7211			0.468994
$139$			200.948i			1.44567i	0.691021	+	0.722834i	$0.257161\pi$
$139$			200.948i			1.44567i	−0.691021	+	0.722834i	$0.742839\pi$
$140$	−30.0138	−	63.2390i	−0.214384	−	0.451707i
$141$	89.4832			0.634633
$142$			129.404i			0.911293i
$143$	292.154			2.04303
$144$	12.0000			0.0833333
$145$	78.7950	−	274.339i	0.543414	−	1.89199i
$146$		−	101.718i		−	0.696700i
$147$	−10.5947	+	84.2066i	−0.0720729	+	0.572834i
$148$		−	28.4392i		−	0.192157i
$149$	−5.70484			−0.0382875			−0.0191438	−	0.999817i	$-0.506094\pi$
$149$	−5.70484			−0.0382875			−0.0191438	+	0.999817i	$0.506094\pi$
$150$	−32.4961	+	51.9038i	−0.216641	+	0.346025i
$151$	−216.490			−1.43371			−0.716854	−	0.697223i	$-0.754419\pi$
$151$	−216.490			−1.43371			−0.716854	+	0.697223i	$0.754419\pi$
$152$	−65.0680			−0.428079
$153$	21.7830			0.142373
$154$	−77.0570	−	87.3597i	−0.500370	−	0.567271i
$155$	49.1250	+	14.1095i	0.316935	+	0.0910293i
$156$	86.0069			0.551326
$157$	−108.287			−0.689726			−0.344863	−	0.938653i	$-0.612075\pi$
$157$	−108.287			−0.689726			−0.344863	+	0.938653i	$0.612075\pi$
$158$			64.0359i			0.405290i
$159$			112.284i			0.706190i
$160$	27.1852	+	7.80806i	0.169907	+	0.0488004i
$161$	−122.349	−	138.707i	−0.759929	−	0.861533i
$162$			12.7279i			0.0785674i
$163$		−	234.395i		−	1.43800i	−0.695008	−	0.719002i	$-0.744599\pi$
$163$		−	234.395i		−	1.43800i	0.695008	−	0.719002i	$-0.255401\pi$
$164$		−	32.4542i		−	0.197891i
$165$	−28.1318	+	97.9460i	−0.170496	+	0.593612i
$166$			25.0779i			0.151072i
$167$	41.8830			0.250796			0.125398	−	0.992106i	$-0.459979\pi$
$167$	41.8830			0.250796			0.125398	+	0.992106i	$0.459979\pi$
$168$	−22.6847	−	25.7177i	−0.135028	−	0.153082i
$169$	447.432			2.64753
$170$	49.3479	+	14.1736i	0.290282	+	0.0833740i
$171$		−	69.0151i		−	0.403597i
$172$			164.623i			0.957110i
$173$	13.0301			0.0753183			0.0376592	−	0.999291i	$-0.488010\pi$
$173$	13.0301			0.0753183			0.0376592	+	0.999291i	$0.488010\pi$
$174$		−	139.832i		−	0.803631i
$175$	172.668	−	28.4749i	0.986673	−	0.162714i
$176$	47.0683			0.267434
$177$		−	141.627i		−	0.800154i
$178$	−109.715			−0.616375
$179$	−24.1573			−0.134957			−0.0674786	−	0.997721i	$-0.521495\pi$
$179$	−24.1573			−0.134957			−0.0674786	+	0.997721i	$0.521495\pi$
$180$	−8.28170	+	28.8342i	−0.0460094	+	0.160190i
$181$			43.5107i			0.240390i	0.992750	+	0.120195i	$0.0383521\pi$
$181$			43.5107i			0.240390i	−0.992750	+	0.120195i	$0.961648\pi$
$182$	−162.587	−	184.325i	−0.893335	−	1.01278i
$183$			22.7315i			0.124216i
$184$	74.7335			0.406160
$185$	68.3353	+	19.6271i	0.369380	+	0.106092i
$186$	25.0392			0.134619
$187$	85.4408			0.456903
$188$	103.326			0.549608
$189$	27.2778	−	24.0608i	0.144327	−	0.127306i
$190$	44.9061	−	156.349i	0.236348	−	0.822889i
$191$	−246.572			−1.29095			−0.645477	−	0.763780i	$-0.723341\pi$
$191$	−246.572			−1.29095			−0.645477	+	0.763780i	$0.723341\pi$
$192$	13.8564			0.0721688
$193$		−	161.875i		−	0.838733i	−0.907817	−	0.419366i	$-0.862252\pi$
$193$		−	161.875i		−	0.838733i	0.907817	−	0.419366i	$-0.137748\pi$
$194$		−	8.70789i		−	0.0448860i
$195$	−59.3569	+	206.662i	−0.304394	+	1.05980i
$196$	−12.2337	+	97.2334i	−0.0624170	+	0.496089i
$197$		−	44.8380i		−	0.227604i	−0.993503	−	0.113802i	$-0.963697\pi$
$197$		−	44.8380i		−	0.227604i	0.993503	−	0.113802i	$-0.0363029\pi$
$198$			49.9235i			0.252139i
$199$		−	114.767i		−	0.576718i	−0.957522	−	0.288359i	$-0.906890\pi$
$199$		−	114.767i		−	0.576718i	0.957522	−	0.288359i	$-0.0931097\pi$
$200$	−37.5232	+	59.9333i	−0.187616	+	0.299667i
$201$		−	38.8040i		−	0.193055i
$202$	202.209			1.00104
$203$	−299.680	+	264.338i	−1.47626	+	1.30216i
$204$	25.1529			0.123298
$205$	77.9826	+	22.3980i	0.380403	+	0.109258i
$206$			20.5474i			0.0997448i
$207$			79.2669i			0.382932i
$208$	99.3122			0.477462
$209$		−	270.702i		−	1.29522i
$210$	77.4517	−	36.7592i	0.368817	−	0.175044i
$211$	−219.602			−1.04077			−0.520384	−	0.853932i	$-0.674211\pi$
$211$	−219.602			−1.04077			−0.520384	+	0.853932i	$0.674211\pi$
$212$			129.655i			0.611579i
$213$	−158.486			−0.744068
$214$	−110.907			−0.518255
$215$	−395.565	−	113.613i	−1.83984	−	0.528433i
$216$			14.6969i			0.0680414i
$217$	−47.3340	−	53.6626i	−0.218129	−	0.247293i
$218$		−	105.702i		−	0.484870i
$219$	124.579			0.568853
$220$	−32.4838	+	113.098i	−0.147654	+	0.514083i
$221$	180.277			0.815731
$222$	34.8308			0.156895
$223$	−3.57102			−0.0160136			−0.00800678	−	0.999968i	$-0.502549\pi$
$223$	−3.57102			−0.0160136			−0.00800678	+	0.999968i	$0.502549\pi$
$224$	−26.1941	−	29.6963i	−0.116938	−	0.132573i
$225$	−63.5689	−	39.7994i	−0.282529	−	0.176886i
$226$	−120.550			−0.533407
$227$	68.0647			0.299844			0.149922	−	0.988698i	$-0.452098\pi$
$227$	68.0647			0.299844			0.149922	+	0.988698i	$0.452098\pi$
$228$		−	79.6917i		−	0.349525i
$229$			180.019i			0.786109i	0.919515	+	0.393054i	$0.128582\pi$
$229$			180.019i			0.786109i	−0.919515	+	0.393054i	$0.871418\pi$
$230$	−51.5767	+	179.574i	−0.224247	+	0.780755i
$231$	106.993	−	94.3752i	0.463175	−	0.408550i
$232$		−	161.464i		−	0.695965i
$233$		−	115.207i		−	0.494449i	−0.968958	−	0.247225i	$-0.920481\pi$
$233$		−	115.207i		−	0.494449i	0.968958	−	0.247225i	$-0.0795185\pi$
$234$			105.336i			0.450156i
$235$	−71.3097	+	248.278i	−0.303446	+	1.05650i
$236$		−	163.537i		−	0.692953i
$237$	−78.4276			−0.330918
$238$	−47.5488	−	53.9062i	−0.199785	−	0.226497i
$239$	15.6873			0.0656374			0.0328187	−	0.999461i	$-0.489552\pi$
$239$	15.6873			0.0656374			0.0328187	+	0.999461i	$0.489552\pi$
$240$	−9.56288	+	33.2949i	−0.0398453	+	0.138729i
$241$			303.442i			1.25909i	0.776962	+	0.629547i	$0.216760\pi$
$241$			303.442i			1.25909i	−0.776962	+	0.629547i	$0.783240\pi$
$242$			24.6981i			0.102058i
$243$	−15.5885			−0.0641500
$244$			26.2481i			0.107574i
$245$	−225.195	−	96.5007i	−0.919162	−	0.393880i
$246$	39.7481			0.161578
$247$		−	571.170i		−	2.31243i
$248$	28.9128			0.116584
$249$	−30.7141			−0.123350
$250$	−118.115	−	131.525i	−0.472459	−	0.526101i
$251$		−	80.5241i		−	0.320813i	−0.987051	−	0.160407i	$-0.948719\pi$
$251$		−	80.5241i		−	0.320813i	0.987051	−	0.160407i	$-0.0512805\pi$
$252$	31.4977	−	27.7830i	0.124991	−	0.110250i
$253$			310.913i			1.22891i
$254$	−94.4318			−0.371779
$255$	−17.3590	+	60.4386i	−0.0680746	+	0.237014i
$256$	16.0000			0.0625000
$257$	39.1012			0.152145			0.0760723	−	0.997102i	$-0.475762\pi$
$257$	39.1012			0.152145			0.0760723	+	0.997102i	$0.475762\pi$
$258$	−201.621			−0.781477
$259$	−65.8439	−	74.6474i	−0.254224	−	0.288214i
$260$	−68.5394	+	238.633i	−0.263613	+	0.917818i
$261$	171.258			0.656162
$262$	−40.7760			−0.155633
$263$			79.1644i			0.301005i	0.988610	+	0.150503i	$0.0480892\pi$
$263$			79.1644i			0.301005i	−0.988610	+	0.150503i	$0.951911\pi$
$264$			57.6467i			0.218359i
$265$	−311.541	−	89.4801i	−1.17563	−	0.337661i
$266$	−170.791	+	150.649i	−0.642071	+	0.566349i
$267$		−	134.373i		−	0.503268i
$268$		−	44.8070i		−	0.167190i
$269$		−	53.2775i		−	0.198058i	−0.995085	−	0.0990288i	$-0.968426\pi$
$269$		−	53.2775i		−	0.198058i	0.995085	−	0.0990288i	$-0.0315736\pi$
$270$	−35.3146	−	10.1430i	−0.130795	−	0.0375665i
$271$		−	237.638i		−	0.876892i	−0.898757	−	0.438446i	$-0.855529\pi$
$271$		−	237.638i		−	0.876892i	0.898757	−	0.438446i	$-0.144471\pi$
$272$	29.0440			0.106779
$273$	225.751	−	199.128i	0.826928	−	0.729405i
$274$	−168.928			−0.616524
$275$	−249.340	−	156.108i	−0.906692	−	0.567664i
$276$			91.5295i			0.331629i
$277$		−	168.185i		−	0.607167i	−0.952805	−	0.303583i	$-0.901817\pi$
$277$		−	168.185i		−	0.607167i	0.952805	−	0.303583i	$-0.0981831\pi$
$278$	−284.183			−1.02224
$279$			30.6666i			0.109916i
$280$	89.4335	−	42.4459i	0.319405	−	0.151593i
$281$	128.175			0.456140			0.228070	−	0.973645i	$-0.426758\pi$
$281$	128.175			0.456140			0.228070	+	0.973645i	$0.426758\pi$
$282$			126.548i			0.448753i
$283$	72.7293			0.256994			0.128497	−	0.991710i	$-0.458985\pi$
$283$	72.7293			0.256994			0.128497	+	0.991710i	$0.458985\pi$
$284$	−183.004			−0.644382
$285$	191.488	+	54.9986i	0.671886	+	0.192977i
$286$			413.168i			1.44464i
$287$	−75.1396	−	85.1859i	−0.261810	−	0.296815i
$288$			16.9706i			0.0589256i
$289$	−236.278			−0.817570
$290$	387.974	+	111.433i	1.33784	+	0.384252i
$291$	10.6649			0.0366493
$292$	143.851			0.492641
$293$	−273.216			−0.932477			−0.466238	−	0.884659i	$-0.654391\pi$
$293$	−273.216			−0.932477			−0.466238	+	0.884659i	$0.654391\pi$
$294$	−119.086	−	14.9832i	−0.405055	−	0.0509632i
$295$	392.955	+	112.864i	1.33205	+	0.382589i
$296$	40.2191			0.135875
$297$	−61.1436			−0.205871
$298$		−	8.06786i		−	0.0270734i
$299$			656.014i			2.19403i
$300$	−73.4031	−	45.9564i	−0.244677	−	0.153188i
$301$	381.143	+	432.103i	1.26626	+	1.43556i
$302$		−	306.163i		−	1.01379i
$303$			247.655i			0.817342i
$304$		−	92.0201i		−	0.302698i
$305$	−63.0703	−	18.1149i	−0.206788	−	0.0593931i
$306$			30.8058i			0.100673i
$307$	336.086			1.09474			0.547372	−	0.836889i	$-0.315628\pi$
$307$	336.086			1.09474			0.547372	+	0.836889i	$0.315628\pi$
$308$	123.545	−	108.975i	0.401121	−	0.353815i
$309$	−25.1653			−0.0814412
$310$	−19.9539	+	69.4732i	−0.0643674	+	0.224107i
$311$		−	497.276i		−	1.59896i	−0.600693	−	0.799480i	$-0.705109\pi$
$311$		−	497.276i		−	1.59896i	0.600693	−	0.799480i	$-0.294891\pi$
$312$			121.632i			0.389846i
$313$	−252.024			−0.805188			−0.402594	−	0.915379i	$-0.631891\pi$
$313$	−252.024			−0.805188			−0.402594	+	0.915379i	$0.631891\pi$
$314$		−	153.141i		−	0.487710i
$315$	45.0207	+	94.8585i	0.142923	+	0.301138i
$316$	−90.5604			−0.286584
$317$		−	270.203i		−	0.852377i	−0.904634	−	0.426188i	$-0.859856\pi$
$317$		−	270.203i		−	0.852377i	0.904634	−	0.426188i	$-0.140144\pi$
$318$	−158.794			−0.499352
$319$	671.737			2.10576
$320$	−11.0423	+	38.4457i	−0.0345071	+	0.120143i
$321$		−	135.832i		−	0.423153i
$322$	196.161	−	173.027i	0.609196	−	0.537351i
$323$		−	167.040i		−	0.517150i
$324$	−18.0000			−0.0555556
$325$	−526.097	−	329.380i	−1.61876	−	1.01348i
$326$	331.484			1.01682
$327$	129.458			0.395895
$328$	45.8971			0.139930
$329$	271.211	−	239.226i	0.824351	−	0.727132i
$330$	−138.517	−	39.7844i	−0.419747	−	0.120559i
$331$	−306.813			−0.926926			−0.463463	−	0.886116i	$-0.653393\pi$
$331$	−306.813			−0.926926			−0.463463	+	0.886116i	$0.653393\pi$
$332$	−35.4656			−0.106824
$333$			42.6588i			0.128105i
$334$			59.2315i			0.177340i
$335$	107.665	+	30.9232i	0.321387	+	0.0923080i
$336$	36.3704	−	32.0811i	0.108245	−	0.0954794i
$337$			485.903i			1.44185i	0.693014	+	0.720924i	$0.256282\pi$
$337$			485.903i			1.44185i	−0.693014	+	0.720924i	$0.743718\pi$
$338$			632.764i			1.87208i
$339$		−	147.643i		−	0.435525i
$340$	−20.0445	+	69.7885i	−0.0589543	+	0.205260i
$341$			120.286i			0.352744i
$342$	97.6020			0.285386
$343$	193.009	+	283.543i	0.562708	+	0.826656i
$344$	−232.812			−0.676779
$345$	−219.932	−	63.1683i	−0.637484	−	0.183097i
$346$			18.4273i			0.0532581i
$347$		−	8.02712i		−	0.0231329i	−0.999933	−	0.0115665i	$-0.996318\pi$
$347$		−	8.02712i		−	0.0231329i	0.999933	−	0.0115665i	$-0.00368180\pi$
$348$	197.752			0.568253
$349$		−	649.899i		−	1.86217i	−0.364798	−	0.931087i	$-0.618862\pi$
$349$		−	649.899i		−	1.86217i	0.364798	−	0.931087i	$-0.381138\pi$
$350$	40.2696	+	244.189i	0.115056	+	0.697683i
$351$	−129.010			−0.367551
$352$			66.5647i			0.189104i
$353$	396.496			1.12322			0.561608	−	0.827403i	$-0.310183\pi$
$353$	396.496			1.12322			0.561608	+	0.827403i	$0.310183\pi$
$354$	200.291			0.565794
$355$	126.299	−	439.733i	0.355772	−	1.23868i
$356$		−	155.160i		−	0.435843i
$357$	66.0214	−	58.2352i	0.184934	−	0.163124i
$358$		−	34.1636i		−	0.0954291i
$359$	398.981			1.11137			0.555684	−	0.831394i	$-0.312457\pi$
$359$	398.981			1.11137			0.555684	+	0.831394i	$0.312457\pi$
$360$	−40.7778	−	11.7121i	−0.113272	−	0.0325336i
$361$	−168.231			−0.466014
$362$	−61.5334			−0.169982
$363$	−30.2489			−0.0833303
$364$	260.675	−	229.933i	0.716141	−	0.631683i
$365$	−99.2777	+	345.653i	−0.271994	+	0.946996i
$366$	−32.1472			−0.0878339
$367$	−506.200			−1.37929			−0.689646	−	0.724147i	$-0.742234\pi$
$367$	−506.200			−1.37929			−0.689646	+	0.724147i	$0.742234\pi$
$368$			105.689i			0.287199i
$369$			48.6812i			0.131927i
$370$	−27.7569	+	96.6406i	−0.0750186	+	0.261191i
$371$	300.183	+	340.318i	0.809119	+	0.917300i
$372$			35.4108i			0.0951903i
$373$			278.751i			0.747322i	0.927565	+	0.373661i	$0.121898\pi$
$373$			278.751i			0.747322i	−0.927565	+	0.373661i	$0.878102\pi$
$374$			120.832i			0.323079i
$375$	161.085	−	144.660i	0.429560	−	0.385761i
$376$			146.125i			0.388631i
$377$	1417.34			3.75951
$378$	34.0271	+	38.5766i	0.0900188	+	0.102055i
$379$	−515.959			−1.36137			−0.680685	−	0.732576i	$-0.738318\pi$
$379$	−515.959			−1.36137			−0.680685	+	0.732576i	$0.738318\pi$
$380$	221.111	+	63.5069i	0.581870	+	0.167123i
$381$		−	115.655i		−	0.303556i
$382$		−	348.706i		−	0.912842i
$383$	−238.715			−0.623276			−0.311638	−	0.950201i	$-0.600878\pi$
$383$	−238.715			−0.623276			−0.311638	+	0.950201i	$0.600878\pi$
$384$			19.5959i			0.0510310i
$385$	176.587	+	372.069i	0.458669	+	0.966414i
$386$	228.926			0.593073
$387$		−	246.934i		−	0.638073i
$388$	12.3148			0.0317392
$389$	−170.748			−0.438941			−0.219471	−	0.975619i	$-0.570433\pi$
$389$	−170.748			−0.438941			−0.219471	+	0.975619i	$0.570433\pi$
$390$	−292.264	−	83.9433i	−0.749395	−	0.215239i
$391$			191.852i			0.490671i
$392$	−137.509	−	17.3011i	−0.350788	−	0.0441355i
$393$		−	49.9402i		−	0.127074i
$394$	63.4105			0.160940
$395$	62.4995	−	217.603i	0.158227	−	0.550895i
$396$	−70.6025			−0.178289
$397$	80.7184			0.203321			0.101660	−	0.994819i	$-0.467584\pi$
$397$	80.7184			0.203321			0.101660	+	0.994819i	$0.467584\pi$
$398$	162.305			0.407801
$399$	−184.506	−	209.175i	−0.462422	−	0.524249i
$400$	−84.7586	−	53.0659i	−0.211896	−	0.132665i
$401$	469.375			1.17051			0.585255	−	0.810849i	$-0.300994\pi$
$401$	469.375			1.17051			0.585255	+	0.810849i	$0.300994\pi$
$402$	54.8772			0.136510
$403$			253.798i			0.629770i
$404$			285.967i			0.707839i
$405$	12.4225	−	43.2514i	0.0306729	−	0.106793i
$406$	−373.830	−	423.812i	−0.920763	−	1.04387i
$407$			167.323i			0.411114i
$408$			35.5715i			0.0871851i
$409$			671.238i			1.64117i	0.571525	+	0.820585i	$0.306352\pi$
$409$			671.238i			1.64117i	−0.571525	+	0.820585i	$0.693648\pi$
$410$	−31.6755	+	110.284i	−0.0772573	+	0.268985i
$411$		−	206.893i		−	0.503390i
$412$	−29.0584			−0.0705302
$413$	−378.629	−	429.253i	−0.916778	−	1.03935i
$414$	−112.100			−0.270774
$415$	24.4763	−	85.2185i	0.0589789	−	0.205346i
$416$			140.449i			0.337617i
$417$		−	348.052i		−	0.834657i
$418$	382.830			0.915862
$419$			16.1628i			0.0385747i	0.999814	+	0.0192874i	$0.00613974\pi$
$419$			16.1628i			0.0385747i	−0.999814	+	0.0192874i	$0.993860\pi$
$420$	51.9854	+	109.533i	0.123775	+	0.260793i
$421$	−463.356			−1.10061			−0.550304	−	0.834964i	$-0.685488\pi$
$421$	−463.356			−1.10061			−0.550304	+	0.834964i	$0.685488\pi$
$422$		−	310.564i		−	0.735934i
$423$	−154.989			−0.366405
$424$	−183.359			−0.432451
$425$	−153.858	−	96.3279i	−0.362019	−	0.226654i
$426$		−	224.134i		−	0.526135i
$427$	60.7709	+	68.8961i	0.142321	+	0.161349i
$428$		−	156.846i		−	0.366462i
$429$	−506.025			−1.17955
$430$	160.673	−	559.413i	0.373658	−	1.30096i
$431$	425.457			0.987140			0.493570	−	0.869706i	$-0.335692\pi$
$431$	425.457			0.987140			0.493570	+	0.869706i	$0.335692\pi$
$432$	−20.7846			−0.0481125
$433$	−480.947			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$433$	−480.947			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$434$	75.8904	−	66.9404i	0.174863	−	0.154240i
$435$	−136.477	+	475.169i	−0.313740	+	1.09234i
$436$	149.485			0.342855
$437$	607.845			1.39095
$438$			176.181i			0.402240i
$439$			73.3796i			0.167152i	0.996501	+	0.0835759i	$0.0266341\pi$
$439$			73.3796i			0.167152i	−0.996501	+	0.0835759i	$0.973366\pi$
$440$	−159.945	−	45.9390i	−0.363512	−	0.104407i
$441$	18.3506	−	145.850i	0.0416113	−	0.330726i
$442$			254.950i			0.576809i
$443$			72.4361i			0.163513i	0.996652	+	0.0817563i	$0.0260529\pi$
$443$			72.4361i			0.163513i	−0.996652	+	0.0817563i	$0.973947\pi$
$444$			49.2582i			0.110942i
$445$	372.827	+	107.082i	0.837813	+	0.240635i
$446$		−	5.05019i		−	0.0113233i
$447$	9.88107			0.0221053
$448$	41.9969	−	37.0440i	0.0937431	−	0.0826876i
$449$	−721.760			−1.60748			−0.803742	−	0.594978i	$-0.797161\pi$
$449$	−721.760			−1.60748			−0.803742	+	0.594978i	$0.797161\pi$
$450$	56.2849	−	89.9000i	0.125077	−	0.199778i
$451$			190.945i			0.423382i
$452$		−	170.483i		−	0.377175i
$453$	374.972			0.827752
$454$			96.2580i			0.212022i
$455$	372.592	+	785.050i	0.818883	+	1.72539i
$456$	112.701			0.247152
$457$			622.396i			1.36192i	0.732322	+	0.680958i	$0.238436\pi$
$457$			622.396i			1.36192i	−0.732322	+	0.680958i	$0.761564\pi$
$458$	−254.585			−0.555863
$459$	−37.7293			−0.0821989
$460$	−253.956	−	72.9405i	−0.552077	−	0.158566i
$461$			600.196i			1.30194i	0.759102	+	0.650971i	$0.225638\pi$
$461$			600.196i			1.30194i	−0.759102	+	0.650971i	$0.774362\pi$
$462$	133.467	+	151.311i	0.288889	+	0.327514i
$463$		−	127.513i		−	0.275406i	−0.990474	−	0.137703i	$-0.956028\pi$
$463$		−	127.513i		−	0.275406i	0.990474	−	0.137703i	$-0.0439720\pi$
$464$	228.344			0.492122
$465$	−85.0869	−	24.4384i	−0.182983	−	0.0525558i
$466$	162.927			0.349628
$467$	11.4438			0.0245048			0.0122524	−	0.999925i	$-0.496100\pi$
$467$	11.4438			0.0245048			0.0122524	+	0.999925i	$0.496100\pi$
$468$	−148.968			−0.318308
$469$	−103.740	−	117.610i	−0.221193	−	0.250767i
$470$	−351.118	−	100.847i	−0.747060	−	0.214569i
$471$	187.559			0.398214
$472$	231.276			0.489992
$473$		−	968.566i		−	2.04771i
$474$		−	110.913i		−	0.233995i
$475$	−305.195	+	487.468i	−0.642517	+	1.02625i
$476$	76.2349	−	67.2442i	0.160157	−	0.141269i
$477$		−	194.482i		−	0.407719i
$478$			22.1853i			0.0464127i
$479$			205.867i			0.429784i	0.976638	+	0.214892i	$0.0689400\pi$
$479$			205.867i			0.429784i	−0.976638	+	0.214892i	$0.931060\pi$
$480$	−47.0861	−	13.5240i	−0.0980961	−	0.0281749i
$481$			353.045i			0.733981i
$482$	−429.131			−0.890314
$483$	211.914	+	240.247i	0.438745	+	0.497406i
$484$	−34.9284			−0.0721662
$485$	−8.49897	+	29.5907i	−0.0175236	+	0.0610118i
$486$		−	22.0454i		−	0.0453609i
$487$		−	603.451i		−	1.23912i	−0.784950	−	0.619559i	$-0.787311\pi$
$487$		−	603.451i		−	1.23912i	0.784950	−	0.619559i	$-0.212689\pi$
$488$	−37.1204			−0.0760664
$489$			405.983i			0.830232i
$490$	136.473	−	318.473i	0.278515	−	0.649946i
$491$	−522.576			−1.06431			−0.532154	−	0.846647i	$-0.678617\pi$
$491$	−522.576			−1.06431			−0.532154	+	0.846647i	$0.678617\pi$
$492$			56.2123i			0.114253i
$493$	414.503			0.840776
$494$	807.756			1.63513
$495$	48.7257	−	169.647i	0.0984358	−	0.342722i
$496$			40.8888i			0.0824372i
$497$	−480.351	+	423.701i	−0.966501	+	0.852518i
$498$		−	43.4363i		−	0.0872214i
$499$	124.569			0.249636			0.124818	−	0.992180i	$-0.460165\pi$
$499$	124.569			0.249636			0.124818	+	0.992180i	$0.460165\pi$
$500$	186.005	−	167.039i	0.372010	−	0.334079i
$501$	−72.5435			−0.144797
$502$	113.878			0.226849
$503$	−33.8355			−0.0672673			−0.0336337	−	0.999434i	$-0.510708\pi$
$503$	−33.8355			−0.0672673			−0.0336337	+	0.999434i	$0.510708\pi$
$504$	39.2911	+	44.5444i	0.0779586	+	0.0883818i
$505$	−687.137	−	197.358i	−1.36067	−	0.390807i
$506$	−439.698			−0.868968
$507$	−774.975			−1.52855
$508$		−	133.547i		−	0.262887i
$509$			630.938i			1.23956i	0.784774	+	0.619782i	$0.212779\pi$
$509$			630.938i			1.23956i	−0.784774	+	0.619782i	$0.787221\pi$
$510$	−85.4731	−	24.5494i	−0.167594	−	0.0481360i
$511$	377.582	−	333.052i	0.738907	−	0.651765i
$512$			22.6274i			0.0441942i
$513$			119.538i			0.233017i
$514$			55.2974i			0.107582i
$515$	20.0544	−	69.8232i	0.0389406	−	0.135579i
$516$		−	285.135i		−	0.552588i
$517$	−607.924			−1.17587
$518$	105.567	−	93.1174i	0.203798	−	0.179763i
$519$	−22.5687			−0.0434850
$520$	−337.477	−	96.9294i	−0.648995	−	0.186403i
$521$			492.821i			0.945914i	0.881086	+	0.472957i	$0.156813\pi$
$521$			492.821i			0.945914i	−0.881086	+	0.472957i	$0.843187\pi$
$522$			242.196i			0.463977i
$523$	−331.944			−0.634692			−0.317346	−	0.948310i	$-0.602792\pi$
$523$	−331.944			−0.634692			−0.317346	+	0.948310i	$0.602792\pi$
$524$		−	57.6659i		−	0.110049i
$525$	−299.069	+	49.3200i	−0.569656	+	0.0939428i
$526$	−111.955			−0.212843
$527$			74.2235i			0.140842i
$528$	−81.5247			−0.154403
$529$	−169.138			−0.319731
$530$	126.544	−	440.586i	0.238762	−	0.831294i
$531$			245.306i			0.461969i
$532$	−213.050	−	241.535i	−0.400469	−	0.454013i
$533$			402.887i			0.755885i
$534$	190.031			0.355864
$535$	376.877	+	108.246i	0.704443	+	0.202328i
$536$	63.3667			0.118221
$537$	41.8417			0.0779175
$538$	75.3457			0.140048
$539$	71.9776	−	572.077i	0.133539	−	1.06137i
$540$	14.3443	−	49.9424i	0.0265636	−	0.0924859i
$541$	−96.8104			−0.178947			−0.0894735	−	0.995989i	$-0.528518\pi$
$541$	−96.8104			−0.178947			−0.0894735	+	0.995989i	$0.528518\pi$
$542$	336.071			0.620057
$543$		−	75.3627i		−	0.138789i
$544$			41.0744i			0.0755045i
$545$	−103.166	+	359.190i	−0.189295	+	0.659065i
$546$	281.609	+	319.261i	0.515767	+	0.584726i
$547$		−	772.034i		−	1.41140i	−0.708512	−	0.705699i	$-0.750633\pi$
$547$		−	772.034i		−	1.41140i	0.708512	−	0.705699i	$-0.249367\pi$
$548$		−	238.900i		−	0.435948i
$549$		−	39.3721i		−	0.0717161i
$550$	220.770	−	352.620i	0.401399	−	0.641128i
$551$		−	1313.27i		−	2.38343i
$552$	−129.442			−0.234497
$553$	−237.704	+	209.670i	−0.429844	+	0.379150i
$554$	237.850			0.429332
$555$	−118.360	−	33.9951i	−0.213261	−	0.0612524i
$556$		−	401.896i		−	0.722834i
$557$		−	42.3682i		−	0.0760650i	−0.999277	−	0.0380325i	$-0.987891\pi$
$557$		−	42.3682i		−	0.0760650i	0.999277	−	0.0380325i	$-0.0121090\pi$
$558$	−43.3692			−0.0777225
$559$		−	2043.63i		−	3.65587i
$560$	60.0276	+	126.478i	0.107192	+	0.225854i
$561$	−147.988			−0.263793
$562$			181.267i			0.322540i
$563$	370.393			0.657891			0.328946	−	0.944349i	$-0.393307\pi$
$563$	370.393			0.657891			0.328946	+	0.944349i	$0.393307\pi$
$564$	−178.966			−0.317316
$565$	409.646	+	117.658i	0.725038	+	0.208244i
$566$			102.855i			0.181722i
$567$	−47.2465	+	41.6745i	−0.0833272	+	0.0735001i
$568$		−	258.807i		−	0.455647i
$569$	−419.012			−0.736401			−0.368201	−	0.929746i	$-0.620026\pi$
$569$	−419.012			−0.736401			−0.368201	+	0.929746i	$0.620026\pi$
$570$	−77.7797	+	270.804i	−0.136456	+	0.475095i
$571$	−113.210			−0.198266			−0.0991329	−	0.995074i	$-0.531607\pi$
$571$	−113.210			−0.198266			−0.0991329	+	0.995074i	$0.531607\pi$
$572$	−584.307			−1.02152
$573$	427.075			0.745332
$574$	120.471	−	106.263i	0.209880	−	0.185128i
$575$	350.531	−	559.879i	0.609618	−	0.973702i
$576$	−24.0000			−0.0416667
$577$	−604.749			−1.04809			−0.524046	−	0.851690i	$-0.675578\pi$
$577$	−604.749			−1.04809			−0.524046	+	0.851690i	$0.675578\pi$
$578$		−	334.147i		−	0.578109i
$579$			280.376i			0.484242i
$580$	−157.590	+	548.678i	−0.271707	+	0.945997i
$581$	−93.0902	+	82.1117i	−0.160224	+	0.141328i
$582$			15.0825i			0.0259150i
$583$		−	762.829i		−	1.30845i
$584$			203.436i			0.348350i
$585$	102.809	−	357.949i	0.175742	−	0.611878i
$586$		−	386.385i		−	0.659360i
$587$	−458.151			−0.780496			−0.390248	−	0.920710i	$-0.627611\pi$
$587$	−458.151			−0.780496			−0.390248	+	0.920710i	$0.627611\pi$
$588$	21.1894	−	168.413i	0.0360365	−	0.286417i
$589$	235.162			0.399257
$590$	−159.613	+	555.723i	−0.270531	+	0.941903i
$591$			77.6616i			0.131407i
$592$			56.8784i			0.0960784i
$593$	−780.457			−1.31612			−0.658059	−	0.752967i	$-0.728622\pi$
$593$	−780.457			−1.31612			−0.658059	+	0.752967i	$0.728622\pi$
$594$		−	86.4700i		−	0.145572i
$595$	108.965	+	229.589i	0.183135	+	0.385864i
$596$	11.4097			0.0191438
$597$			198.782i			0.332968i
$598$	−927.744			−1.55141
$599$	−11.7391			−0.0195977			−0.00979887	−	0.999952i	$-0.503119\pi$
$599$	−11.7391			−0.0195977			−0.00979887	+	0.999952i	$0.503119\pi$
$600$	64.9922	−	103.808i	0.108320	−	0.173013i
$601$			182.878i			0.304290i	0.988358	+	0.152145i	$0.0486181\pi$
$601$			182.878i			0.304290i	−0.988358	+	0.152145i	$0.951382\pi$
$602$	−611.086	+	539.018i	−1.01509	+	0.895379i
$603$			67.2106i			0.111460i
$604$	432.980			0.716854
$605$	24.1056	−	83.9279i	0.0398439	−	0.138724i
$606$	−350.236			−0.577948
$607$	777.171			1.28035			0.640174	−	0.768230i	$-0.278862\pi$
$607$	777.171			1.28035			0.640174	+	0.768230i	$0.278862\pi$
$608$	130.136			0.214040
$609$	519.061	−	457.846i	0.852317	−	0.751800i
$610$	25.6183	−	89.1949i	0.0419973	−	0.146221i
$611$	−1282.69			−2.09934
$612$	−43.5660			−0.0711863
$613$			106.169i			0.173196i	0.996243	+	0.0865978i	$0.0275995\pi$
$613$			106.169i			0.173196i	−0.996243	+	0.0865978i	$0.972400\pi$
$614$			475.298i			0.774101i
$615$	−135.070	−	38.7944i	−0.219626	−	0.0630803i
$616$	154.114	+	174.719i	0.250185	+	0.283635i
$617$			680.569i			1.10303i	0.834165	+	0.551515i	$0.185950\pi$
$617$			680.569i			1.10303i	−0.834165	+	0.551515i	$0.814050\pi$
$618$		−	35.5892i		−	0.0575877i
$619$			861.054i			1.39104i	0.718507	+	0.695520i	$0.244826\pi$
$619$			861.054i			1.39104i	−0.718507	+	0.695520i	$0.755174\pi$
$620$	−98.2499	−	28.2191i	−0.158468	−	0.0455147i
$621$		−	137.294i		−	0.221086i
$622$	703.255			1.13063
$623$	−359.235	−	407.265i	−0.576621	−	0.653716i
$624$	−172.014			−0.275663
$625$	273.002	+	562.223i	0.436803	+	0.899557i
$626$		−	356.416i		−	0.569354i
$627$			468.870i			0.747798i
$628$	216.574			0.344863
$629$			103.249i			0.164147i
$630$	−134.150	+	63.6689i	−0.212937	+	0.101062i
$631$	−489.247			−0.775352			−0.387676	−	0.921796i	$-0.626722\pi$
$631$	−489.247			−0.775352			−0.387676	+	0.921796i	$0.626722\pi$
$632$		−	128.072i		−	0.202645i
$633$	380.362			0.600888
$634$	382.125			0.602721
$635$	320.893	+	92.1661i	0.505344	+	0.145144i
$636$		−	224.569i		−	0.353095i
$637$	151.870	−	1207.06i	0.238414	−	1.89491i
$638$			949.980i			1.48900i
$639$	274.507			0.429588
$640$	−54.3704	−	15.6161i	−0.0849537	−	0.0244002i
$641$	962.813			1.50205			0.751024	−	0.660275i	$-0.229560\pi$
$641$	962.813			1.50205			0.751024	+	0.660275i	$0.229560\pi$
$642$	192.096			0.299215
$643$	581.069			0.903684			0.451842	−	0.892098i	$-0.350767\pi$
$643$	581.069			0.903684			0.451842	+	0.892098i	$0.350767\pi$
$644$	244.697	+	277.414i	0.379964	+	0.430766i
$645$	685.138	+	196.784i	1.06223	+	0.305091i
$646$	236.230			0.365681
$647$	339.036			0.524012			0.262006	−	0.965066i	$-0.415616\pi$
$647$	339.036			0.524012			0.262006	+	0.965066i	$0.415616\pi$
$648$		−	25.4558i		−	0.0392837i
$649$			962.177i			1.48255i
$650$	465.814	−	744.014i	0.716637	−	1.14464i
$651$	81.9849	+	92.9464i	0.125937	+	0.142775i
$652$			468.789i			0.719002i
$653$		−	289.383i		−	0.443159i	−0.975142	−	0.221580i	$-0.928879\pi$
$653$		−	289.383i		−	0.443159i	0.975142	−	0.221580i	$-0.0711213\pi$
$654$			183.081i			0.279940i
$655$	138.563	+	39.7976i	0.211546	+	0.0607598i
$656$			64.9083i			0.0989456i
$657$	−215.777			−0.328427
$658$	338.317	+	383.551i	0.514160	+	0.582904i
$659$	62.6627			0.0950875			0.0475438	−	0.998869i	$-0.484861\pi$
$659$	62.6627			0.0950875			0.0475438	+	0.998869i	$0.484861\pi$
$660$	56.2636	−	195.892i	0.0852479	−	0.296806i
$661$			148.826i			0.225153i	0.993643	+	0.112577i	$0.0359104\pi$
$661$			148.826i			0.225153i	−0.993643	+	0.112577i	$0.964090\pi$
$662$		−	433.899i		−	0.655436i
$663$	−312.248			−0.470962
$664$		−	50.1559i		−	0.0755360i
$665$	727.407	−	345.234i	1.09385	−	0.519149i
$666$	−60.3287			−0.0905836
$667$			1508.35i			2.26139i
$668$	−83.7660			−0.125398
$669$	6.18519			0.00924543
$670$	−43.7320	+	152.261i	−0.0652716	+	0.227255i
$671$		−	154.432i		−	0.230152i
$672$	45.3695	+	51.4355i	0.0675141	+	0.0765409i
$673$			833.049i			1.23781i	0.785464	+	0.618907i	$0.212424\pi$
$673$			833.049i			1.23781i	−0.785464	+	0.618907i	$0.787576\pi$
$674$	−687.170			−1.01954
$675$	110.105	+	68.9346i	0.163118	+	0.102125i
$676$	−894.864			−1.32376
$677$	−391.042			−0.577611			−0.288805	−	0.957388i	$-0.593258\pi$
$677$	−391.042			−0.577611			−0.288805	+	0.957388i	$0.593258\pi$
$678$	208.799			0.307962
$679$	32.3240	−	28.5119i	0.0476053	−	0.0419910i
$680$	−98.6959	−	28.3472i	−0.145141	−	0.0416870i
$681$	−117.891			−0.173115
$682$	−170.110			−0.249427
$683$			992.775i			1.45355i	0.686875	+	0.726775i	$0.258982\pi$
$683$			992.775i			1.45355i	−0.686875	+	0.726775i	$0.741018\pi$
$684$			138.030i			0.201798i
$685$	574.041	+	164.875i	0.838016	+	0.240693i
$686$	−400.990	+	272.956i	−0.584534	+	0.397894i
$687$		−	311.802i		−	0.453860i
$688$		−	329.246i		−	0.478555i
$689$		−	1609.54i		−	2.33605i
$690$	89.3335	−	311.031i	0.129469	−	0.450769i
$691$		−	697.871i		−	1.00994i	−0.863136	−	0.504972i	$-0.831503\pi$
$691$		−	697.871i		−	1.00994i	0.863136	−	0.504972i	$-0.168497\pi$
$692$	−26.0601			−0.0376592
$693$	−185.318	+	163.463i	−0.267414	+	0.235877i
$694$	11.3521			0.0163574
$695$	965.697	+	277.365i	1.38949	+	0.399086i
$696$			279.664i			0.401816i
$697$			117.825i			0.169046i
$698$	919.095			1.31676
$699$			199.544i			0.285470i
$700$	−345.336	+	56.9498i	−0.493337	+	0.0813568i
$701$	−222.920			−0.318003			−0.159002	−	0.987278i	$-0.550828\pi$
$701$	−222.920			−0.318003			−0.159002	+	0.987278i	$0.550828\pi$
$702$		−	182.448i		−	0.259898i
$703$	327.122			0.465323
$704$	−94.1367			−0.133717
$705$	123.512	−	430.030i	0.175194	−	0.609972i
$706$			560.729i			0.794234i
$707$	662.085	+	750.608i	0.936472	+	1.06168i
$708$			283.254i			0.400077i
$709$	−267.679			−0.377544			−0.188772	−	0.982021i	$-0.560451\pi$
$709$	−267.679			−0.377544			−0.188772	+	0.982021i	$0.560451\pi$
$710$	621.876	+	178.614i	0.875882	+	0.251568i
$711$	135.841			0.191056
$712$	219.429			0.308187
$713$	−270.094			−0.378814
$714$	82.3570	+	93.3683i	0.115346	+	0.130768i
$715$	403.255	−	1404.00i	0.563992	−	1.96364i
$716$	48.3147			0.0674786
$717$	−27.1713			−0.0378958
$718$			564.244i			0.785856i
$719$		−	217.258i		−	0.302167i	−0.988521	−	0.151083i	$-0.951724\pi$
$719$		−	217.258i		−	0.302167i	0.988521	−	0.151083i	$-0.0482762\pi$
$720$	16.5634	−	57.6685i	0.0230047	−	0.0800951i
$721$	−76.2728	+	67.2776i	−0.105787	+	0.0933115i
$722$		−	237.915i		−	0.329522i
$723$		−	525.577i		−	0.726939i
$724$		−	87.0213i		−	0.120195i
$725$	−1209.63	−	757.331i	−1.66846	−	1.04459i
$726$		−	42.7784i		−	0.0589235i
$727$	−771.678			−1.06146			−0.530728	−	0.847543i	$-0.678081\pi$
$727$	−771.678			−1.06146			−0.530728	+	0.847543i	$0.678081\pi$
$728$	325.174	+	368.650i	0.446668	+	0.506388i
$729$	27.0000			0.0370370
$730$	−488.828	−	140.400i	−0.669627	−	0.192329i
$731$		−	597.664i		−	0.817598i
$732$		−	45.4630i		−	0.0621080i
$733$	1103.98			1.50611			0.753053	−	0.657960i	$-0.228580\pi$
$733$	1103.98			1.50611			0.753053	+	0.657960i	$0.228580\pi$
$734$		−	715.875i		−	0.975306i
$735$	390.049	+	167.144i	0.530678	+	0.227407i
$736$	−149.467			−0.203080
$737$			263.624i			0.357699i
$738$	−68.8457			−0.0932868
$739$	264.136			0.357423			0.178712	−	0.983901i	$-0.442807\pi$
$739$	264.136			0.357423			0.178712	+	0.983901i	$0.442807\pi$
$740$	−136.671	−	39.2541i	−0.184690	−	0.0530461i
$741$			989.295i			1.33508i
$742$	−481.283	+	424.523i	−0.648629	+	0.572134i
$743$		−	1069.03i		−	1.43880i	−0.694595	−	0.719401i	$-0.744417\pi$
$743$		−	1069.03i		−	1.43880i	0.694595	−	0.719401i	$-0.255583\pi$
$744$	−50.0784			−0.0673097
$745$	−7.87429	+	27.4158i	−0.0105695	+	0.0367997i
$746$	−394.213			−0.528436
$747$	53.1983			0.0712160
$748$	−170.882			−0.228451
$749$	−363.137	−	411.689i	−0.484829	−	0.549652i
$750$	204.581	+	227.809i	0.272774	+	0.303745i
$751$	987.190			1.31450			0.657250	−	0.753673i	$-0.271720\pi$
$751$	987.190			1.31450			0.657250	+	0.753673i	$0.271720\pi$
$752$	−206.653			−0.274804
$753$			139.472i			0.185222i
$754$			2004.42i			2.65838i
$755$	−298.817	+	1040.39i	−0.395785	+	1.37800i
$756$	−54.5556	+	48.1216i	−0.0721635	+	0.0636529i
$757$			1173.09i			1.54966i	0.632169	+	0.774830i	$0.282165\pi$
$757$			1173.09i			1.54966i	−0.632169	+	0.774830i	$0.717835\pi$
$758$		−	729.677i		−	0.962634i
$759$		−	538.518i		−	0.709509i
$760$	−89.8123	+	312.698i	−0.118174	+	0.411445i
$761$			271.712i			0.357045i	0.983936	+	0.178523i	$0.0571318\pi$
$761$			271.712i			0.357045i	−0.983936	+	0.178523i	$0.942868\pi$
$762$	163.561			0.214647
$763$	392.369	−	346.095i	0.514245	−	0.453598i
$764$	493.144			0.645477
$765$	30.0667	−	104.683i	0.0393029	−	0.136840i
$766$		−	337.594i		−	0.440723i
$767$			2030.15i			2.64687i
$768$	−27.7128			−0.0360844
$769$		−	1031.82i		−	1.34177i	−0.741563	−	0.670883i	$-0.765915\pi$
$769$		−	1031.82i		−	1.34177i	0.741563	−	0.670883i	$-0.234085\pi$
$770$	−526.185	+	249.732i	−0.683358	+	0.324328i
$771$	−67.7252			−0.0878407
$772$			323.751i			0.419366i
$773$	877.988			1.13582			0.567910	−	0.823091i	$-0.307752\pi$
$773$	877.988			1.13582			0.567910	+	0.823091i	$0.307752\pi$
$774$	349.218			0.451186
$775$	135.613	−	216.605i	0.174984	−	0.279490i
$776$			17.4158i			0.0224430i
$777$	114.045	+	129.293i	0.146776	+	0.166400i
$778$		−	241.474i		−	0.310378i
$779$	373.304			0.479210
$780$	118.714	−	413.324i	0.152197	−	0.529902i
$781$	1076.71			1.37863
$782$	−271.320			−0.346957
$783$	−296.628			−0.378835
$784$	24.4675	−	194.467i	0.0312085	−	0.248044i
$785$	−149.467	+	520.396i	−0.190403	+	0.662924i
$786$	70.6260			0.0898550
$787$	−142.727			−0.181356			−0.0906780	−	0.995880i	$-0.528903\pi$
$787$	−142.727			−0.181356			−0.0906780	+	0.995880i	$0.528903\pi$
$788$			89.6759i			0.113802i
$789$		−	137.117i		−	0.173786i
$790$	307.738	+	88.3876i	0.389541	+	0.111883i
$791$	−394.712	−	447.486i	−0.499004	−	0.565721i
$792$		−	99.8470i		−	0.126069i
$793$		−	325.844i		−	0.410901i
$794$			114.153i			0.143770i
$795$	539.605	+	154.984i	0.678749	+	0.194948i
$796$			229.534i			0.288359i
$797$	−317.415			−0.398262			−0.199131	−	0.979973i	$-0.563812\pi$
$797$	−317.415			−0.398262			−0.199131	+	0.979973i	$0.563812\pi$
$798$	295.819	−	260.932i	0.370700	−	0.326982i
$799$	−375.126			−0.469495
$800$	75.0465	−	119.867i	0.0938081	−	0.149833i
$801$			232.740i			0.290562i
$802$			663.796i			0.827676i
$803$	−846.354			−1.05399
$804$			77.6081i			0.0965274i
$805$	−835.460	+	396.517i	−1.03784	+	0.492567i
$806$	−358.924			−0.445315
$807$			92.2793i			0.114349i
$808$	−404.418			−0.500518
$809$	−1392.39			−1.72112			−0.860560	−	0.509350i	$-0.829886\pi$
$809$	−1392.39			−1.72112			−0.860560	+	0.509350i	$0.829886\pi$
$810$	61.1667	+	17.5681i	0.0755144	+	0.0216891i
$811$		−	1087.46i		−	1.34089i	−0.741958	−	0.670447i	$-0.766102\pi$
$811$		−	1087.46i		−	1.34089i	0.741958	−	0.670447i	$-0.233898\pi$
$812$	599.360	−	528.675i	0.738128	−	0.651078i
$813$			411.601i			0.506274i
$814$	−236.631			−0.290701
$815$	−1126.43	−	323.531i	−1.38212	−	0.396970i
$816$	−50.3057			−0.0616492
$817$	−1893.58			−2.31772
$818$	−949.274			−1.16048
$819$	−391.013	+	344.899i	−0.477427	+	0.421122i
$820$	−155.965	−	44.7959i	−0.190201	−	0.0546292i
$821$	172.333			0.209906			0.104953	−	0.994477i	$-0.466531\pi$
$821$	172.333			0.209906			0.104953	+	0.994477i	$0.466531\pi$
$822$	292.591			0.355950
$823$		−	215.439i		−	0.261773i	−0.991397	−	0.130886i	$-0.958218\pi$
$823$		−	215.439i		−	0.261773i	0.991397	−	0.130886i	$-0.0417823\pi$
$824$		−	41.0948i		−	0.0498724i
$825$	431.870	+	270.386i	0.523479	+	0.327741i
$826$	607.055	−	535.463i	0.734934	−	0.648260i
$827$		−	797.435i		−	0.964250i	−0.876102	−	0.482125i	$-0.839865\pi$
$827$		−	797.435i		−	0.964250i	0.876102	−	0.482125i	$-0.160135\pi$
$828$		−	158.534i		−	0.191466i
$829$		−	389.170i		−	0.469445i	−0.972062	−	0.234723i	$-0.924582\pi$
$829$		−	389.170i		−	0.469445i	0.972062	−	0.234723i	$-0.0754182\pi$
$830$	120.517	+	34.6146i	0.145201	+	0.0417044i
$831$			291.305i			0.350548i
$832$	−198.624			−0.238731
$833$	44.4146	−	353.006i	0.0533188	−	0.423777i
$834$	492.220			0.590192
$835$	57.8104	−	201.277i	0.0692340	−	0.241051i
$836$			541.404i			0.647612i
$837$		−	53.1162i		−	0.0634602i
$838$	−22.8577			−0.0272764
$839$		−	280.262i		−	0.334043i	−0.985953	−	0.167021i	$-0.946585\pi$
$839$		−	280.262i		−	0.334043i	0.985953	−	0.167021i	$-0.0534149\pi$
$840$	−154.903	+	73.5185i	−0.184409	+	0.0875220i
$841$	2417.83			2.87494
$842$		−	655.285i		−	0.778248i
$843$	−222.006			−0.263353
$844$	439.204			0.520384
$845$	617.582	−	2150.23i	0.730867	−	2.54465i
$846$		−	219.188i		−	0.259088i
$847$	−91.6804	+	80.8681i	−0.108241	+	0.0954760i
$848$		−	259.309i		−	0.305789i
$849$	−125.971			−0.148376
$850$	136.228	−	217.588i	0.160268	−	0.255986i
$851$	−375.715			−0.441498
$852$	316.973			0.372034
$853$	245.874			0.288246			0.144123	−	0.989560i	$-0.453964\pi$
$853$	245.874			0.288246			0.144123	+	0.989560i	$0.453964\pi$
$854$	−97.4339	+	85.9431i	−0.114091	+	0.100636i
$855$	−331.666	−	95.2603i	−0.387914	−	0.111416i
$856$	221.813			0.259127
$857$	−798.850			−0.932147			−0.466074	−	0.884746i	$-0.654332\pi$
$857$	−798.850			−0.932147			−0.466074	+	0.884746i	$0.654332\pi$
$858$		−	715.627i		−	0.834064i
$859$			1274.93i			1.48420i	0.670287	+	0.742102i	$0.266171\pi$
$859$			1274.93i			1.48420i	−0.670287	+	0.742102i	$0.733829\pi$
$860$	791.129	+	227.226i	0.919918	+	0.264216i
$861$	130.146	+	147.546i	0.151156	+	0.171366i
$862$			601.688i			0.698013i
$863$			736.114i			0.852971i	0.904494	+	0.426486i	$0.140249\pi$
$863$			736.114i			0.852971i	−0.904494	+	0.426486i	$0.859751\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	17.9852	−	62.6187i	0.0207921	−	0.0723915i
$866$		−	680.162i		−	0.785407i
$867$	409.245			0.472024
$868$	94.6680	+	107.325i	0.109064	+	0.123647i
$869$	532.816			0.613137
$870$	−671.991	−	193.008i	−0.772403	−	0.221848i
$871$			556.236i			0.638617i
$872$			211.404i			0.242435i
$873$	−18.4722			−0.0211595
$874$			859.623i			0.983551i
$875$	101.488	−	869.094i	0.115987	−	0.993251i
$876$	−249.158			−0.284426
$877$		−	1103.15i		−	1.25787i	−0.777457	−	0.628936i	$-0.783491\pi$
$877$		−	1103.15i		−	1.25787i	0.777457	−	0.628936i	$-0.216509\pi$
$878$	−103.774			−0.118194
$879$	473.223			0.538366
$880$	64.9676	−	226.197i	0.0738268	−	0.257042i
$881$			269.425i			0.305817i	0.988240	+	0.152909i	$0.0488640\pi$
$881$			269.425i			0.305817i	−0.988240	+	0.152909i	$0.951136\pi$
$882$	206.263	+	25.9517i	0.233859	+	0.0294236i
$883$		−	1077.49i		−	1.22026i	−0.792302	−	0.610129i	$-0.791118\pi$
$883$		−	1077.49i		−	1.22026i	0.792302	−	0.610129i	$-0.208882\pi$
$884$	−360.553			−0.407865
$885$	−680.619	−	195.486i	−0.769061	−	0.220888i
$886$	−102.440			−0.115621
$887$	500.908			0.564721			0.282361	−	0.959308i	$-0.408883\pi$
$887$	500.908			0.564721			0.282361	+	0.959308i	$0.408883\pi$
$888$	−69.6615			−0.0784477
$889$	−309.194	−	350.534i	−0.347800	−	0.394302i
$890$	−151.437	+	527.257i	−0.170154	+	0.592423i
$891$	105.904			0.118859
$892$	7.14204			0.00800678
$893$			1188.51i			1.33092i
$894$			13.9739i			0.0156308i
$895$	−33.3439	+	116.093i	−0.0372558	+	0.129713i
$896$	52.3882	+	59.3926i	0.0584689	+	0.0662864i
$897$		−	1136.25i		−	1.26672i
$898$		−	1020.72i		−	1.13666i
$899$			583.546i			0.649106i
$900$	127.138	+	79.5988i	0.141264	+	0.0884431i
$901$		−	470.712i		−	0.522433i
$902$	−270.038			−0.299376
$903$	−660.160	−	748.425i	−0.731074	−	0.828820i
$904$	241.100			0.266703
$905$	209.100	+	60.0570i	0.231049	+	0.0663614i
$906$			530.290i			0.585309i
$907$		−	789.727i		−	0.870702i	−0.900261	−	0.435351i	$-0.856624\pi$
$907$		−	789.727i		−	0.870702i	0.900261	−	0.435351i	$-0.143376\pi$
$908$	−136.129			−0.149922
$909$		−	428.950i		−	0.471893i
$910$	−1110.23	+	526.924i	−1.22003	+	0.579038i
$911$	885.912			0.972461			0.486231	−	0.873830i	$-0.338371\pi$
$911$	885.912			0.972461			0.486231	+	0.873830i	$0.338371\pi$
$912$			159.383i			0.174763i
$913$	208.663			0.228547
$914$	−880.200			−0.963020
$915$	109.241	+	31.3759i	0.119389	+	0.0342906i
$916$		−	360.038i		−	0.393054i
$917$	−133.511	−	151.362i	−0.145596	−	0.165062i
$918$		−	53.3573i		−	0.0581234i
$919$	−1411.37			−1.53577			−0.767883	−	0.640590i	$-0.778690\pi$
$919$	−1411.37			−1.53577			−0.767883	+	0.640590i	$0.778690\pi$
$920$	103.153	−	359.147i	0.112123	−	0.390378i
$921$	−582.119			−0.632051
$922$	−848.805			−0.920613
$923$	2271.82			2.46134
$924$	−213.987	+	188.750i	−0.231587	+	0.204275i
$925$	188.644	−	301.308i	0.203939	−	0.325739i
$926$	180.331			0.194742
$927$	43.5877			0.0470201
$928$			322.928i			0.347983i
$929$			1394.66i			1.50125i	0.660727	+	0.750627i	$0.270248\pi$
$929$			1394.66i			1.50125i	−0.660727	+	0.750627i	$0.729752\pi$
$930$	34.5612	−	120.331i	0.0371626	−	0.129388i
$931$	−1118.43	−	140.719i	−1.20132	−	0.151148i
$932$			230.413i			0.247225i
$933$			861.308i			0.923160i
$934$			16.1839i			0.0173275i
$935$	117.933	−	410.604i	0.126131	−	0.439148i
$936$		−	210.673i		−	0.225078i
$937$	448.660			0.478826			0.239413	−	0.970918i	$-0.423045\pi$
$937$	448.660			0.478826			0.239413	+	0.970918i	$0.423045\pi$
$938$	166.325	−	146.710i	0.177319	−	0.156407i
$939$	436.518			0.464876
$940$	142.619	−	496.556i	0.151723	−	0.528251i
$941$			1061.98i			1.12856i	0.825583	+	0.564281i	$0.190847\pi$
$941$			1061.98i			1.12856i	−0.825583	+	0.564281i	$0.809153\pi$
$942$			265.248i			0.281580i
$943$	−428.757			−0.454673
$944$			327.074i			0.346477i
$945$	−77.9781	−	164.300i	−0.0825165	−	0.173862i
$946$	1369.76			1.44795
$947$		−	470.708i		−	0.497051i	−0.968625	−	0.248526i	$-0.920054\pi$
$947$		−	470.708i		−	0.497051i	0.968625	−	0.248526i	$-0.0799460\pi$
$948$	156.855			0.165459
$949$	−1785.77			−1.88174
$950$	−689.384	−	431.611i	−0.725667	−	0.454328i
$951$			468.006i			0.492120i
$952$	95.0977	+	107.812i	0.0998925	+	0.113248i
$953$		−	625.282i		−	0.656119i	−0.944657	−	0.328060i	$-0.893605\pi$
$953$		−	625.282i		−	0.656119i	0.944657	−	0.328060i	$-0.106395\pi$
$954$	275.039			0.288301
$955$	−340.339	+	1184.95i	−0.356376	+	1.24079i
$956$	−31.3747			−0.0328187
$957$	−1163.48			−1.21576
$958$	−291.139			−0.303903
$959$	−553.113	−	627.065i	−0.576760	−	0.653874i
$960$	19.1258	−	66.5898i	0.0199227	−	0.0693644i
$961$	856.506			0.891266
$962$	−499.281			−0.519003
$963$			235.268i			0.244308i
$964$		−	606.884i		−	0.629547i
$965$	−777.926	−	223.434i	−0.806141	−	0.231538i
$966$	−339.761	+	299.691i	−0.351719	+	0.310240i
$967$			593.257i			0.613503i	0.951790	+	0.306751i	$0.0992420\pi$
$967$			593.257i			0.613503i	−0.951790	+	0.306751i	$0.900758\pi$
$968$		−	49.3963i		−	0.0510292i
$969$			289.321i			0.298577i
$970$	−41.8476	−	12.0194i	−0.0431418	−	0.0123911i
$971$			1633.10i			1.68187i	0.541133	+	0.840937i	$0.317996\pi$
$971$			1633.10i			1.68187i	−0.541133	+	0.840937i	$0.682004\pi$
$972$	31.1769			0.0320750
$973$	−930.490	−	1054.90i	−0.956311	−	1.08417i
$974$	853.408			0.876189
$975$	911.227	+	570.504i	0.934592	+	0.585132i
$976$		−	52.4962i		−	0.0537871i
$977$		−	1137.81i		−	1.16459i	−0.812977	−	0.582296i	$-0.802154\pi$
$977$		−	1137.81i		−	1.16459i	0.812977	−	0.582296i	$-0.197846\pi$
$978$	−574.147			−0.587062
$979$			912.891i			0.932472i
$980$	450.389	+	193.001i	0.459581	+	0.196940i
$981$	−224.227			−0.228570
$982$		−	739.034i		−	0.752580i
$983$	−746.446			−0.759355			−0.379677	−	0.925119i	$-0.623965\pi$
$983$	−746.446			−0.759355			−0.379677	+	0.925119i	$0.623965\pi$
$984$	−79.4961			−0.0807888
$985$	−215.478	−	61.8891i	−0.218760	−	0.0628315i
$986$			586.195i			0.594518i
$987$	−469.752	+	414.352i	−0.475939	+	0.419810i
$988$			1142.34i			1.15621i
$989$	2174.86			2.19905
$990$	239.918	+	68.9085i	0.242341	+	0.0696046i
$991$	−765.218			−0.772168			−0.386084	−	0.922464i	$-0.626172\pi$
$991$	−765.218			−0.772168			−0.386084	+	0.922464i	$0.626172\pi$
$992$	−57.8256			−0.0582919
$993$	531.415			0.535161
$994$	−599.204	−	679.319i	−0.602821	−	0.683420i
$995$	−551.536	−	158.411i	−0.554308	−	0.159207i
$996$	61.4282			0.0616749
$997$	1799.05			1.80446			0.902230	−	0.431255i	$-0.141929\pi$
$997$	1799.05			1.80446			0.902230	+	0.431255i	$0.141929\pi$
$998$			176.167i			0.176520i
$999$		−	73.8872i		−	0.0739612i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.h.a.139.10	yes	16
3.2	odd	2		630.3.h.e.559.4		16
4.3	odd	2		1680.3.bd.a.769.11		16
5.2	odd	4		1050.3.f.e.601.5		16
5.3	odd	4		1050.3.f.e.601.12		16
5.4	even	2	inner	210.3.h.a.139.7	yes	16
7.6	odd	2	inner	210.3.h.a.139.15	yes	16
15.14	odd	2		630.3.h.e.559.13		16
20.19	odd	2		1680.3.bd.a.769.5		16
21.20	even	2		630.3.h.e.559.5		16
28.27	even	2		1680.3.bd.a.769.6		16
35.13	even	4		1050.3.f.e.601.16		16
35.27	even	4		1050.3.f.e.601.1		16
35.34	odd	2	inner	210.3.h.a.139.2	✓	16
105.104	even	2		630.3.h.e.559.12		16
140.139	even	2		1680.3.bd.a.769.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.h.a.139.2	✓	16	35.34	odd	2	inner
210.3.h.a.139.7	yes	16	5.4	even	2	inner
210.3.h.a.139.10	yes	16	1.1	even	1	trivial
210.3.h.a.139.15	yes	16	7.6	odd	2	inner
630.3.h.e.559.4		16	3.2	odd	2
630.3.h.e.559.5		16	21.20	even	2
630.3.h.e.559.12		16	105.104	even	2
630.3.h.e.559.13		16	15.14	odd	2
1050.3.f.e.601.1		16	35.27	even	4
1050.3.f.e.601.5		16	5.2	odd	4
1050.3.f.e.601.12		16	5.3	odd	4
1050.3.f.e.601.16		16	35.13	even	4
1680.3.bd.a.769.5		16	20.19	odd	2
1680.3.bd.a.769.6		16	28.27	even	2
1680.3.bd.a.769.11		16	4.3	odd	2
1680.3.bd.a.769.12		16	140.139	even	2

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.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +(1.38028 - 4.80571i) q^{5} -2.44949i q^{6} +(-5.24961 + 4.63050i) q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +(1.38028 - 4.80571i) q^{5} -2.44949i q^{6} +(-5.24961 + 4.63050i) q^{7} -2.82843i q^{8} +3.00000 q^{9} +(6.79630 + 1.95201i) q^{10} +11.7671 q^{11} +3.46410 q^{12} +24.8280 q^{13} +(-6.54852 - 7.42407i) q^{14} +(-2.39072 + 8.32373i) q^{15} +4.00000 q^{16} +7.26100 q^{17} +4.24264i q^{18} -23.0050i q^{19} +(-2.76057 + 9.61141i) q^{20} +(9.09260 - 8.02027i) q^{21} +16.6412i q^{22} +26.4223i q^{23} +4.89898i q^{24} +(-21.1896 - 13.2665i) q^{25} +35.1122i q^{26} -5.19615 q^{27} +(10.4992 - 9.26101i) q^{28} +57.0861 q^{29} +(-11.7715 - 3.38099i) q^{30} +10.2222i q^{31} +5.65685i q^{32} -20.3812 q^{33} +10.2686i q^{34} +(15.0069 + 31.6195i) q^{35} -6.00000 q^{36} +14.2196i q^{37} +32.5340 q^{38} -43.0034 q^{39} +(-13.5926 - 3.90403i) q^{40} +16.2271i q^{41} +(11.3424 + 12.8589i) q^{42} -82.3114i q^{43} -23.5342 q^{44} +(4.14085 - 14.4171i) q^{45} -37.3668 q^{46} -51.6631 q^{47} -6.92820 q^{48} +(6.11686 - 48.6167i) q^{49} +(18.7616 - 29.9667i) q^{50} -12.5764 q^{51} -49.6561 q^{52} -64.8273i q^{53} -7.34847i q^{54} +(16.2419 - 56.5491i) q^{55} +(13.0970 + 14.8481i) q^{56} +39.8459i q^{57} +80.7320i q^{58} +81.7685i q^{59} +(4.78144 - 16.6475i) q^{60} -13.1240i q^{61} -14.4564 q^{62} +(-15.7488 + 13.8915i) q^{63} -8.00000 q^{64} +(34.2697 - 119.316i) q^{65} -28.8233i q^{66} +22.4035i q^{67} -14.5220 q^{68} -45.7648i q^{69} +(-44.7167 + 21.2230i) q^{70} +91.5022 q^{71} -8.48528i q^{72} -71.9256 q^{73} -20.1096 q^{74} +(36.7015 + 22.9782i) q^{75} +46.0100i q^{76} +(-61.7726 + 54.4875i) q^{77} -60.8160i q^{78} +45.2802 q^{79} +(5.52113 - 19.2228i) q^{80} +9.00000 q^{81} -22.9486 q^{82} +17.7328 q^{83} +(-18.1852 + 16.0405i) q^{84} +(10.0222 - 34.8943i) q^{85} +116.406 q^{86} -98.8761 q^{87} -33.2823i q^{88} +77.5800i q^{89} +(20.3889 + 5.85604i) q^{90} +(-130.338 + 114.966i) q^{91} -52.8446i q^{92} -17.7054i q^{93} -73.0627i q^{94} +(-110.555 - 31.7534i) q^{95} -9.79796i q^{96} -6.15741 q^{97} +(68.7544 + 8.65055i) q^{98} +35.3012 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{4} + 48 q^{9}+O(q^{10}) \) 16 * q - 32 * q^4 + 48 * q^9	\( 16 q - 32 q^{4} + 48 q^{9} + 96 q^{11} + 16 q^{14} - 24 q^{15} + 64 q^{16} + 24 q^{21} + 24 q^{25} + 64 q^{29} + 24 q^{30} - 8 q^{35} - 96 q^{36} - 144 q^{39} - 192 q^{44} - 176 q^{46} + 224 q^{49} - 96 q^{50} - 48 q^{51} - 32 q^{56} + 48 q^{60} - 128 q^{64} + 368 q^{65} - 56 q^{70} - 384 q^{71} + 224 q^{74} - 608 q^{79} + 144 q^{81} - 48 q^{84} - 440 q^{85} + 416 q^{86} + 224 q^{91} - 560 q^{95} + 288 q^{99}+O(q^{100}) \) 16 * q - 32 * q^4 + 48 * q^9 + 96 * q^11 + 16 * q^14 - 24 * q^15 + 64 * q^16 + 24 * q^21 + 24 * q^25 + 64 * q^29 + 24 * q^30 - 8 * q^35 - 96 * q^36 - 144 * q^39 - 192 * q^44 - 176 * q^46 + 224 * q^49 - 96 * q^50 - 48 * q^51 - 32 * q^56 + 48 * q^60 - 128 * q^64 + 368 * q^65 - 56 * q^70 - 384 * q^71 + 224 * q^74 - 608 * q^79 + 144 * q^81 - 48 * q^84 - 440 * q^85 + 416 * q^86 + 224 * q^91 - 560 * q^95 + 288 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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