LMFDB - Embedded newform 363.3.b.h.122.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,3,Mod(122,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("363.122");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			122.4
Root			$-1.18614 - 1.26217i$ of defining polynomial
Character	$\chi$	$=$	363.122
Dual form			363.3.b.h.122.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.52434i q^{2} +(-2.68614 - 1.33591i) q^{3} -2.37228 q^{4} -0.792287i q^{5} +(3.37228 - 6.78073i) q^{6} -6.74456 q^{7} +4.10891i q^{8} +(5.43070 + 7.17687i) q^{9} +O(q^{10})$	\(q+2.52434i q^{2} +(-2.68614 - 1.33591i) q^{3} -2.37228 q^{4} -0.792287i q^{5} +(3.37228 - 6.78073i) q^{6} -6.74456 q^{7} +4.10891i q^{8} +(5.43070 + 7.17687i) q^{9} +2.00000 q^{10} +(6.37228 + 3.16915i) q^{12} -9.48913 q^{13} -17.0256i q^{14} +(-1.05842 + 2.12819i) q^{15} -19.8614 q^{16} -29.2974i q^{17} +(-18.1168 + 13.7089i) q^{18} +26.2337 q^{19} +1.87953i q^{20} +(18.1168 + 9.01011i) q^{21} -26.9205i q^{23} +(5.48913 - 11.0371i) q^{24} +24.3723 q^{25} -23.9538i q^{26} +(-5.00000 - 26.5330i) q^{27} +16.0000 q^{28} -25.9431i q^{29} +(-5.37228 - 2.67181i) q^{30} -2.86141 q^{31} -33.7013i q^{32} +73.9565 q^{34} +5.34363i q^{35} +(-12.8832 - 17.0256i) q^{36} -2.39403 q^{37} +66.2227i q^{38} +(25.4891 + 12.6766i) q^{39} +3.25544 q^{40} -17.6155i q^{41} +(-22.7446 + 45.7330i) q^{42} -12.5109 q^{43} +(5.68614 - 4.30268i) q^{45} +67.9565 q^{46} +41.6790i q^{47} +(53.3505 + 26.5330i) q^{48} -3.51087 q^{49} +61.5239i q^{50} +(-39.1386 + 78.6969i) q^{51} +22.5109 q^{52} -89.5865i q^{53} +(66.9783 - 12.6217i) q^{54} -27.7128i q^{56} +(-70.4674 - 35.0458i) q^{57} +65.4891 q^{58} -14.7585i q^{59} +(2.51087 - 5.04868i) q^{60} +63.4456 q^{61} -7.22316i q^{62} +(-36.6277 - 48.4048i) q^{63} +5.62772 q^{64} +7.51811i q^{65} -63.3288 q^{67} +69.5016i q^{68} +(-35.9633 + 72.3123i) q^{69} -13.4891 q^{70} +4.55134i q^{71} +(-29.4891 + 22.3143i) q^{72} +53.7663 q^{73} -6.04334i q^{74} +(-65.4674 - 32.5591i) q^{75} -62.2337 q^{76} +(-32.0000 + 64.3432i) q^{78} -55.6793 q^{79} +15.7359i q^{80} +(-22.0149 + 77.9509i) q^{81} +44.4674 q^{82} -65.3378i q^{83} +(-42.9783 - 21.3745i) q^{84} -23.2119 q^{85} -31.5817i q^{86} +(-34.6576 + 69.6868i) q^{87} +14.1341i q^{89} +(10.8614 + 14.3537i) q^{90} +64.0000 q^{91} +63.8631i q^{92} +(7.68614 + 3.82257i) q^{93} -105.212 q^{94} -20.7846i q^{95} +(-45.0217 + 90.5263i) q^{96} +149.285 q^{97} -8.86263i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} - 7 q^{9}+O(q^{10}) $ 4 * q - 5 * q^3 + 2 * q^4 + 2 * q^6 - 4 * q^7 - 7 * q^9	$ 4 q - 5 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} - 7 q^{9} + 8 q^{10} + 14 q^{12} + 8 q^{13} + 13 q^{15} - 22 q^{16} - 38 q^{18} + 36 q^{19} + 38 q^{21} - 24 q^{24} + 86 q^{25} - 20 q^{27} + 64 q^{28} - 10 q^{30} + 46 q^{31} + 112 q^{34} - 86 q^{36} - 90 q^{37} + 56 q^{39} + 36 q^{40} - 68 q^{42} - 96 q^{43} + 17 q^{45} + 88 q^{46} + 110 q^{48} - 60 q^{49} - 214 q^{51} + 136 q^{52} + 176 q^{54} - 144 q^{57} + 216 q^{58} + 56 q^{60} + 24 q^{61} - 158 q^{63} + 34 q^{64} - 58 q^{67} - 253 q^{69} - 8 q^{70} - 72 q^{72} + 284 q^{73} - 124 q^{75} - 180 q^{76} - 128 q^{78} + 76 q^{79} + 113 q^{81} + 40 q^{82} - 80 q^{84} + 68 q^{85} + 252 q^{87} - 14 q^{90} + 256 q^{91} + 25 q^{93} - 260 q^{94} - 272 q^{96} + 218 q^{97}+O(q^{100}) $ 4 * q - 5 * q^3 + 2 * q^4 + 2 * q^6 - 4 * q^7 - 7 * q^9 + 8 * q^10 + 14 * q^12 + 8 * q^13 + 13 * q^15 - 22 * q^16 - 38 * q^18 + 36 * q^19 + 38 * q^21 - 24 * q^24 + 86 * q^25 - 20 * q^27 + 64 * q^28 - 10 * q^30 + 46 * q^31 + 112 * q^34 - 86 * q^36 - 90 * q^37 + 56 * q^39 + 36 * q^40 - 68 * q^42 - 96 * q^43 + 17 * q^45 + 88 * q^46 + 110 * q^48 - 60 * q^49 - 214 * q^51 + 136 * q^52 + 176 * q^54 - 144 * q^57 + 216 * q^58 + 56 * q^60 + 24 * q^61 - 158 * q^63 + 34 * q^64 - 58 * q^67 - 253 * q^69 - 8 * q^70 - 72 * q^72 + 284 * q^73 - 124 * q^75 - 180 * q^76 - 128 * q^78 + 76 * q^79 + 113 * q^81 + 40 * q^82 - 80 * q^84 + 68 * q^85 + 252 * q^87 - 14 * q^90 + 256 * q^91 + 25 * q^93 - 260 * q^94 - 272 * q^96 + 218 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$			2.52434i			1.26217i	0.775714	+	0.631084i	$0.217390\pi$
$2$			2.52434i			1.26217i	−0.775714	+	0.631084i	$0.782610\pi$
$3$	−2.68614	−	1.33591i	−0.895380	−	0.445302i
$3$	−2.68614	−	1.33591i	−0.895380	−	0.445302i
$4$	−2.37228			−0.593070
$5$		−	0.792287i		−	0.158457i	−0.996856	−	0.0792287i	$-0.974754\pi$
$5$		−	0.792287i		−	0.158457i	0.996856	−	0.0792287i	$-0.0252457\pi$
$6$	3.37228	−	6.78073i	0.562047	−	1.13012i
$7$	−6.74456			−0.963509			−0.481754	−	0.876306i	$-0.660000\pi$
$7$	−6.74456			−0.963509			−0.481754	+	0.876306i	$0.660000\pi$
$8$			4.10891i			0.513614i
$9$	5.43070	+	7.17687i	0.603411	+	0.797430i
$10$	2.00000			0.200000
$11$		0			0
$11$		0			0
$12$	6.37228	+	3.16915i	0.531023	+	0.264096i
$13$	−9.48913			−0.729933			−0.364966	−	0.931021i	$-0.618920\pi$
$13$	−9.48913			−0.729933			−0.364966	+	0.931021i	$0.618920\pi$
$14$		−	17.0256i		−	1.21611i
$15$	−1.05842	+	2.12819i	−0.0705615	+	0.141880i
$16$	−19.8614			−1.24134
$17$		−	29.2974i		−	1.72338i	−0.507439	−	0.861688i	$-0.669408\pi$
$17$		−	29.2974i		−	1.72338i	0.507439	−	0.861688i	$-0.330592\pi$
$18$	−18.1168	+	13.7089i	−1.00649	+	0.761607i
$19$	26.2337			1.38072			0.690360	−	0.723466i	$-0.257452\pi$
$19$	26.2337			1.38072			0.690360	+	0.723466i	$0.257452\pi$
$20$			1.87953i			0.0939764i
$21$	18.1168	+	9.01011i	0.862707	+	0.429053i
$22$		0			0
$23$		−	26.9205i		−	1.17046i	−0.810868	−	0.585229i	$-0.801005\pi$
$23$		−	26.9205i		−	1.17046i	0.810868	−	0.585229i	$-0.198995\pi$
$24$	5.48913	−	11.0371i	0.228714	−	0.459880i
$25$	24.3723			0.974891
$26$		−	23.9538i		−	0.921298i
$27$	−5.00000	−	26.5330i	−0.185185	−	0.982704i
$28$	16.0000			0.571429
$29$		−	25.9431i		−	0.894589i	−0.894387	−	0.447295i	$-0.852388\pi$
$29$		−	25.9431i		−	0.894589i	0.894387	−	0.447295i	$-0.147612\pi$
$30$	−5.37228	−	2.67181i	−0.179076	−	0.0890605i
$31$	−2.86141			−0.0923034			−0.0461517	−	0.998934i	$-0.514696\pi$
$31$	−2.86141			−0.0923034			−0.0461517	+	0.998934i	$0.514696\pi$
$32$		−	33.7013i		−	1.05316i
$33$		0			0
$34$	73.9565			2.17519
$35$			5.34363i			0.152675i
$36$	−12.8832	−	17.0256i	−0.357865	−	0.472932i
$37$	−2.39403			−0.0647035			−0.0323518	−	0.999477i	$-0.510300\pi$
$37$	−2.39403			−0.0647035			−0.0323518	+	0.999477i	$0.510300\pi$
$38$			66.2227i			1.74270i
$39$	25.4891	+	12.6766i	0.653567	+	0.325041i
$40$	3.25544			0.0813859
$41$		−	17.6155i		−	0.429645i	−0.976653	−	0.214823i	$-0.931083\pi$
$41$		−	17.6155i		−	0.429645i	0.976653	−	0.214823i	$-0.0689174\pi$
$42$	−22.7446	+	45.7330i	−0.541537	+	1.08888i
$43$	−12.5109			−0.290951			−0.145475	−	0.989362i	$-0.546471\pi$
$43$	−12.5109			−0.290951			−0.145475	+	0.989362i	$0.546471\pi$
$44$		0			0
$45$	5.68614	−	4.30268i	0.126359	−	0.0956150i
$46$	67.9565			1.47732
$47$			41.6790i			0.886788i	0.896327	+	0.443394i	$0.146226\pi$
$47$			41.6790i			0.886788i	−0.896327	+	0.443394i	$0.853774\pi$
$48$	53.3505	+	26.5330i	1.11147	+	0.552771i
$49$	−3.51087			−0.0716505
$50$			61.5239i			1.23048i
$51$	−39.1386	+	78.6969i	−0.767423	+	1.54308i
$52$	22.5109			0.432901
$53$		−	89.5865i		−	1.69031i	−0.534520	−	0.845156i	$-0.679507\pi$
$53$		−	89.5865i		−	1.69031i	0.534520	−	0.845156i	$-0.320493\pi$
$54$	66.9783	−	12.6217i	1.24034	−	0.233735i
$55$		0			0
$56$		−	27.7128i		−	0.494872i
$57$	−70.4674	−	35.0458i	−1.23627	−	0.614838i
$58$	65.4891			1.12912
$59$		−	14.7585i		−	0.250144i	−0.992148	−	0.125072i	$-0.960084\pi$
$59$		−	14.7585i		−	0.250144i	0.992148	−	0.125072i	$-0.0399162\pi$
$60$	2.51087	−	5.04868i	0.0418479	−	0.0841446i
$61$	63.4456			1.04009			0.520046	−	0.854138i	$-0.325915\pi$
$61$	63.4456			1.04009			0.520046	+	0.854138i	$0.325915\pi$
$62$		−	7.22316i		−	0.116503i
$63$	−36.6277	−	48.4048i	−0.581392	−	0.768331i
$64$	5.62772			0.0879331
$65$			7.51811i			0.115663i
$66$		0			0
$67$	−63.3288			−0.945206			−0.472603	−	0.881276i	$-0.656685\pi$
$67$	−63.3288			−0.945206			−0.472603	+	0.881276i	$0.656685\pi$
$68$			69.5016i			1.02208i
$69$	−35.9633	+	72.3123i	−0.521208	+	1.04800i
$70$	−13.4891			−0.192702
$71$			4.55134i			0.0641034i	0.999486	+	0.0320517i	$0.0102041\pi$
$71$			4.55134i			0.0641034i	−0.999486	+	0.0320517i	$0.989796\pi$
$72$	−29.4891	+	22.3143i	−0.409571	+	0.309921i
$73$	53.7663			0.736525			0.368262	−	0.929722i	$-0.379953\pi$
$73$	53.7663			0.736525			0.368262	+	0.929722i	$0.379953\pi$
$74$		−	6.04334i		−	0.0816668i
$75$	−65.4674	−	32.5591i	−0.872898	−	0.434121i
$76$	−62.2337			−0.818864
$77$		0			0
$78$	−32.0000	+	64.3432i	−0.410256	+	0.824912i
$79$	−55.6793			−0.704801			−0.352401	−	0.935849i	$-0.614635\pi$
$79$	−55.6793			−0.704801			−0.352401	+	0.935849i	$0.614635\pi$
$80$			15.7359i			0.196699i
$81$	−22.0149	+	77.9509i	−0.271789	+	0.962357i
$82$	44.4674			0.542285
$83$		−	65.3378i		−	0.787203i	−0.919281	−	0.393601i	$-0.871229\pi$
$83$		−	65.3378i		−	0.787203i	0.919281	−	0.393601i	$-0.128771\pi$
$84$	−42.9783	−	21.3745i	−0.511646	−	0.254459i
$85$	−23.2119			−0.273082
$86$		−	31.5817i		−	0.367229i
$87$	−34.6576	+	69.6868i	−0.398363	+	0.800998i
$88$		0			0
$89$			14.1341i			0.158810i	0.996842	+	0.0794052i	$0.0253021\pi$
$89$			14.1341i			0.158810i	−0.996842	+	0.0794052i	$0.974698\pi$
$90$	10.8614	+	14.3537i	0.120682	+	0.159486i
$91$	64.0000			0.703297
$92$			63.8631i			0.694164i
$93$	7.68614	+	3.82257i	0.0826467	+	0.0411029i
$94$	−105.212			−1.11928
$95$		−	20.7846i		−	0.218785i
$96$	−45.0217	+	90.5263i	−0.468977	+	0.942982i
$97$	149.285			1.53902			0.769512	−	0.638633i	$-0.220500\pi$
$97$	149.285			1.53902			0.769512	+	0.638633i	$0.220500\pi$
$98$		−	8.86263i		−	0.0904350i
$99$		0			0
$100$	−57.8179			−0.578179
$101$		−	20.0096i		−	0.198114i	−0.995082	−	0.0990572i	$-0.968417\pi$
$101$		−	20.0096i		−	0.198114i	0.995082	−	0.0990572i	$-0.0315827\pi$
$102$	−198.658	−	98.7990i	−1.94762	−	0.968618i
$103$	−180.424			−1.75169			−0.875844	−	0.482594i	$-0.839695\pi$
$103$	−180.424			−1.75169			−0.875844	+	0.482594i	$0.839695\pi$
$104$		−	38.9900i		−	0.374904i
$105$	7.13859	−	14.3537i	0.0679866	−	0.136702i
$106$	226.147			2.13346
$107$			64.5283i			0.603068i	0.953455	+	0.301534i	$0.0974987\pi$
$107$			64.5283i			0.603068i	−0.953455	+	0.301534i	$0.902501\pi$
$108$	11.8614	+	62.9437i	0.109828	+	0.582812i
$109$	−110.277			−1.01172			−0.505859	−	0.862616i	$-0.668824\pi$
$109$	−110.277			−1.01172			−0.505859	+	0.862616i	$0.668824\pi$
$110$		0			0
$111$	6.43070	+	3.19820i	0.0579343	+	0.0288126i
$112$	133.957			1.19604
$113$		−	125.239i		−	1.10831i	−0.832412	−	0.554157i	$-0.813041\pi$
$113$		−	125.239i		−	1.10831i	0.832412	−	0.554157i	$-0.186959\pi$
$114$	88.4674	−	177.883i	0.776030	−	1.56038i
$115$	−21.3288			−0.185468
$116$			61.5443i			0.530554i
$117$	−51.5326	−	68.1022i	−0.440450	−	0.582070i
$118$	37.2554			0.315724
$119$			197.598i			1.66049i
$120$	−8.74456	−	4.34896i	−0.0728714	−	0.0362414i
$121$		0			0
$122$			160.158i			1.31277i
$123$	−23.5326	+	47.3176i	−0.191322	+	0.384696i
$124$	6.78806			0.0547424
$125$		−	39.1170i		−	0.312936i
$126$	122.190	−	92.4607i	0.969763	−	0.733815i
$127$	−192.848			−1.51849			−0.759243	−	0.650807i	$-0.774431\pi$
$127$	−192.848			−1.51849			−0.759243	+	0.650807i	$0.774431\pi$
$128$		−	120.599i		−	0.942178i
$129$	33.6060	+	16.7134i	0.260511	+	0.129561i
$130$	−18.9783			−0.145987
$131$			106.098i			0.809905i	0.914338	+	0.404952i	$0.132712\pi$
$131$			106.098i			0.809905i	−0.914338	+	0.404952i	$0.867288\pi$
$132$		0			0
$133$	−176.935			−1.33034
$134$		−	159.863i		−	1.19301i
$135$	−21.0217	+	3.96143i	−0.155717	+	0.0293440i
$136$	120.380			0.885150
$137$		−	195.297i		−	1.42552i	−0.701407	−	0.712761i	$-0.747444\pi$
$137$		−	195.297i		−	1.42552i	0.701407	−	0.712761i	$-0.252556\pi$
$138$	−182.541	−	90.7836i	−1.32276	−	0.657852i
$139$	−6.93475			−0.0498903			−0.0249452	−	0.999689i	$-0.507941\pi$
$139$	−6.93475			−0.0498903			−0.0249452	+	0.999689i	$0.507941\pi$
$140$		−	12.6766i		−	0.0905471i
$141$	55.6793	−	111.956i	0.394889	−	0.794012i
$142$	−11.4891			−0.0809093
$143$		0			0
$144$	−107.861	−	142.543i	−0.749038	−	0.989880i
$145$	−20.5544			−0.141754
$146$			135.724i			0.929619i
$147$	9.43070	+	4.69020i	0.0641544	+	0.0319061i
$148$	5.67931			0.0383737
$149$		−	67.6975i		−	0.454345i	−0.973854	−	0.227173i	$-0.927052\pi$
$149$		−	67.6975i		−	0.454345i	0.973854	−	0.227173i	$-0.0729482\pi$
$150$	82.1902	−	165.262i	0.547935	−	1.10175i
$151$	−28.2337			−0.186978			−0.0934890	−	0.995620i	$-0.529802\pi$
$151$	−28.2337			−0.186978			−0.0934890	+	0.995620i	$0.529802\pi$
$152$			107.792i			0.709157i
$153$	210.264	−	159.105i	1.37427	−	1.03990i
$154$		0			0
$155$			2.26706i			0.0146262i
$156$	−60.4674	−	30.0724i	−0.387611	−	0.192772i
$157$	−67.7962			−0.431823			−0.215911	−	0.976413i	$-0.569272\pi$
$157$	−67.7962			−0.431823			−0.215911	+	0.976413i	$0.569272\pi$
$158$		−	140.553i		−	0.889578i
$159$	−119.679	+	240.642i	−0.752700	+	1.51347i
$160$	−26.7011			−0.166882
$161$			181.567i			1.12775i
$162$	−196.774	−	55.5731i	−1.21466	−	0.343044i
$163$	−67.8695			−0.416377			−0.208189	−	0.978089i	$-0.566757\pi$
$163$	−67.8695			−0.416377			−0.208189	+	0.978089i	$0.566757\pi$
$164$			41.7888i			0.254810i
$165$		0			0
$166$	164.935			0.993583
$167$		−	56.2351i		−	0.336737i	−0.985724	−	0.168369i	$-0.946150\pi$
$167$		−	56.2351i		−	0.336737i	0.985724	−	0.168369i	$-0.0538499\pi$
$168$	−37.0217	+	74.4405i	−0.220368	+	0.443098i
$169$	−78.9565			−0.467198
$170$		−	58.5948i		−	0.344675i
$171$	142.467	+	188.276i	0.833143	+	1.10103i
$172$	29.6793			0.172554
$173$			224.536i			1.29789i	0.760833	+	0.648947i	$0.224791\pi$
$173$			224.536i			1.29789i	−0.760833	+	0.648947i	$0.775209\pi$
$174$	−175.913	−	87.4874i	−1.01099	−	0.502801i
$175$	−164.380			−0.939316
$176$		0			0
$177$	−19.7160	+	39.6434i	−0.111390	+	0.223974i
$178$	−35.6793			−0.200446
$179$		−	140.461i		−	0.784697i	−0.919817	−	0.392349i	$-0.871663\pi$
$179$		−	140.461i		−	0.784697i	0.919817	−	0.392349i	$-0.128337\pi$
$180$	−13.4891	+	10.2072i	−0.0749396	+	0.0567064i
$181$	130.861			0.722991			0.361496	−	0.932374i	$-0.382266\pi$
$181$	130.861			0.722991			0.361496	+	0.932374i	$0.382266\pi$
$182$			161.558i			0.887679i
$183$	−170.424	−	84.7575i	−0.931278	−	0.463156i
$184$	110.614			0.601163
$185$			1.89676i			0.0102528i
$186$	−9.64947	+	19.4024i	−0.0518789	+	0.104314i
$187$		0			0
$188$		−	98.8744i		−	0.525928i
$189$	33.7228	+	178.953i	0.178428	+	0.946844i
$190$	52.4674			0.276144
$191$			351.401i			1.83979i	0.392160	+	0.919897i	$0.371728\pi$
$191$			351.401i			1.83979i	−0.392160	+	0.919897i	$0.628272\pi$
$192$	−15.1168	−	7.51811i	−0.0787336	−	0.0391568i
$193$	245.505			1.27205			0.636024	−	0.771669i	$-0.280578\pi$
$193$	245.505			1.27205			0.636024	+	0.771669i	$0.280578\pi$
$194$			376.846i			1.94251i
$195$	10.0435	−	20.1947i	0.0515051	−	0.103563i
$196$	8.32878			0.0424938
$197$			6.15315i			0.0312343i	0.999878	+	0.0156171i	$0.00497129\pi$
$197$			6.15315i			0.0312343i	−0.999878	+	0.0156171i	$0.995029\pi$
$198$		0			0
$199$	193.272			0.971214			0.485607	−	0.874177i	$-0.338599\pi$
$199$	193.272			0.971214			0.485607	+	0.874177i	$0.338599\pi$
$200$			100.144i			0.500718i
$201$	170.110	+	84.6014i	0.846318	+	0.420902i
$202$	50.5109			0.250054
$203$			174.975i			0.861945i
$204$	92.8478	−	186.691i	0.455136	−	0.915153i
$205$	−13.9565			−0.0680805
$206$		−	455.451i		−	2.21093i
$207$	193.205	−	146.197i	0.933358	−	0.706268i
$208$	188.467			0.906093
$209$		0			0
$210$	36.2337	+	18.0202i	0.172541	+	0.0858106i
$211$	106.788			0.506105			0.253052	−	0.967453i	$-0.418566\pi$
$211$	106.788			0.506105			0.253052	+	0.967453i	$0.418566\pi$
$212$			212.524i			1.00247i
$213$	6.08017	−	12.2255i	0.0285454	−	0.0573969i
$214$	−162.891			−0.761174
$215$			9.91220i			0.0461033i
$216$	109.022	−	20.5446i	0.504730	−	0.0951137i
$217$	19.2989			0.0889352
$218$		−	278.377i		−	1.27696i
$219$	−144.424	−	71.8268i	−0.659470	−	0.327976i
$220$		0			0
$221$			278.007i			1.25795i
$222$	−8.07335	+	16.2333i	−0.0363664	+	0.0731228i
$223$	76.7309			0.344085			0.172042	−	0.985090i	$-0.444963\pi$
$223$	76.7309			0.344085			0.172042	+	0.985090i	$0.444963\pi$
$224$			227.300i			1.01473i
$225$	132.359	+	174.917i	0.588261	+	0.777408i
$226$	316.147			1.39888
$227$			48.2433i			0.212526i	0.994338	+	0.106263i	$0.0338885\pi$
$227$			48.2433i			0.212526i	−0.994338	+	0.106263i	$0.966111\pi$
$228$	167.168	+	83.1384i	0.733195	+	0.364642i
$229$	−15.4158			−0.0673178			−0.0336589	−	0.999433i	$-0.510716\pi$
$229$	−15.4158			−0.0673178			−0.0336589	+	0.999433i	$0.510716\pi$
$230$		−	53.8411i		−	0.234092i
$231$		0			0
$232$	106.598			0.459474
$233$			173.205i			0.743369i	0.928359	+	0.371685i	$0.121220\pi$
$233$			173.205i			0.743369i	−0.928359	+	0.371685i	$0.878780\pi$
$234$	171.913	−	130.086i	0.734671	−	0.555922i
$235$	33.0217			0.140518
$236$			35.0113i			0.148353i
$237$	149.562	+	74.3824i	0.631065	+	0.313850i
$238$	−498.804			−2.09582
$239$		−	296.397i		−	1.24016i	−0.784540	−	0.620078i	$-0.787101\pi$
$239$		−	296.397i		−	1.24016i	0.784540	−	0.620078i	$-0.212899\pi$
$240$	21.0217	−	42.2689i	0.0875906	−	0.176121i
$241$	−46.7011			−0.193780			−0.0968902	−	0.995295i	$-0.530890\pi$
$241$	−46.7011			−0.193780			−0.0968902	+	0.995295i	$0.530890\pi$
$242$		0			0
$243$	163.270	−	179.977i	0.671894	−	0.740647i
$244$	−150.511			−0.616848
$245$			2.78162i			0.0113536i
$246$	−119.446	−	59.4043i	−0.485551	−	0.241481i
$247$	−248.935			−1.00783
$248$		−	11.7573i		−	0.0474083i
$249$	−87.2853	+	175.507i	−0.350543	+	0.704846i
$250$	98.7446			0.394978
$251$			207.788i			0.827841i	0.910313	+	0.413920i	$0.135841\pi$
$251$			207.788i			0.827841i	−0.910313	+	0.413920i	$0.864159\pi$
$252$	86.8913	+	114.830i	0.344807	+	0.455674i
$253$		0			0
$254$		−	486.813i		−	1.91659i
$255$	62.3505	+	31.0090i	0.244512	+	0.121604i
$256$	326.943			1.27712
$257$		−	199.738i		−	0.777191i	−0.921408	−	0.388595i	$-0.872960\pi$
$257$		−	199.738i		−	0.777191i	0.921408	−	0.388595i	$-0.127040\pi$
$258$	−42.1902	+	84.8328i	−0.163528	+	0.328809i
$259$	16.1467			0.0623424
$260$		−	17.8351i		−	0.0685964i
$261$	186.190	−	140.889i	0.713372	−	0.539805i
$262$	−267.826			−1.02224
$263$		−	99.7592i		−	0.379313i	−0.981851	−	0.189656i	$-0.939263\pi$
$263$		−	99.7592i		−	0.379313i	0.981851	−	0.189656i	$-0.0607374\pi$
$264$		0			0
$265$	−70.9783			−0.267842
$266$		−	446.643i		−	1.67911i
$267$	18.8819	−	37.9663i	0.0707187	−	0.142196i
$268$	150.234			0.560573
$269$		−	50.3770i		−	0.187275i	−0.995606	−	0.0936375i	$-0.970151\pi$
$269$		−	50.3770i		−	0.187275i	0.995606	−	0.0936375i	$-0.0298495\pi$
$270$	−10.0000	−	53.0660i	−0.0370370	−	0.196541i
$271$	124.380			0.458968			0.229484	−	0.973312i	$-0.426296\pi$
$271$	124.380			0.458968			0.229484	+	0.973312i	$0.426296\pi$
$272$			581.887i			2.13929i
$273$	−171.913	−	85.4981i	−0.629718	−	0.313180i
$274$	492.994			1.79925
$275$		0			0
$276$	85.3151	−	171.545i	0.309113	−	0.621540i
$277$	−293.723			−1.06037			−0.530186	−	0.847882i	$-0.677878\pi$
$277$	−293.723			−1.06037			−0.530186	+	0.847882i	$0.677878\pi$
$278$		−	17.5057i		−	0.0629700i
$279$	−15.5395	−	20.5359i	−0.0556970	−	0.0736055i
$280$	−21.9565			−0.0784161
$281$		−	263.676i		−	0.938350i	−0.883105	−	0.469175i	$-0.844551\pi$
$281$		−	263.676i		−	0.938350i	0.883105	−	0.469175i	$-0.155449\pi$
$282$	282.614	+	140.553i	1.00218	+	0.498416i
$283$	−398.788			−1.40915			−0.704573	−	0.709632i	$-0.748861\pi$
$283$	−398.788			−1.40915			−0.704573	+	0.709632i	$0.748861\pi$
$284$		−	10.7971i		−	0.0380178i
$285$	−27.7663	+	55.8304i	−0.0974257	+	0.195896i
$286$		0			0
$287$			118.809i			0.413967i
$288$	241.870	−	183.022i	0.839825	−	0.635491i
$289$	−569.337			−1.97002
$290$		−	51.8862i		−	0.178918i
$291$	−401.001	−	199.431i	−1.37801	−	0.685331i
$292$	−127.549			−0.436811
$293$		−	348.839i		−	1.19058i	−0.803512	−	0.595288i	$-0.797038\pi$
$293$		−	348.839i		−	1.19058i	0.803512	−	0.595288i	$-0.202962\pi$
$294$	−11.8397	+	23.8063i	−0.0402709	+	0.0809737i
$295$	−11.6930			−0.0396372
$296$		−	9.83686i		−	0.0332326i
$297$		0			0
$298$	170.891			0.573461
$299$			255.452i			0.854355i
$300$	155.307	+	77.2394i	0.517690	+	0.257465i
$301$	84.3804			0.280333
$302$		−	71.2714i		−	0.235998i
$303$	−26.7309	+	53.7485i	−0.0882208	+	0.177388i
$304$	−521.038			−1.71394
$305$		−	50.2671i		−	0.164810i
$306$	401.636	+	530.776i	1.31254	+	1.73456i
$307$	398.527			1.29813			0.649067	−	0.760731i	$-0.275160\pi$
$307$	398.527			1.29813			0.649067	+	0.760731i	$0.275160\pi$
$308$		0			0
$309$	484.644	+	241.030i	1.56843	+	0.780031i
$310$	−5.72281			−0.0184607
$311$		−	440.346i		−	1.41590i	−0.706261	−	0.707951i	$-0.749620\pi$
$311$		−	440.346i		−	1.41590i	0.706261	−	0.707951i	$-0.250380\pi$
$312$	−52.0870	+	104.733i	−0.166946	+	0.335681i
$313$	529.899			1.69297			0.846485	−	0.532413i	$-0.178715\pi$
$313$	529.899			1.69297			0.846485	+	0.532413i	$0.178715\pi$
$314$		−	171.140i		−	0.545033i
$315$	−38.3505	+	29.0197i	−0.121748	+	0.0921259i
$316$	132.087			0.417997
$317$			368.426i			1.16223i	0.813822	+	0.581114i	$0.197383\pi$
$317$			368.426i			1.16223i	−0.813822	+	0.581114i	$0.802617\pi$
$318$	−607.462	−	302.111i	−1.91026	−	0.950035i
$319$		0			0
$320$		−	4.45877i		−	0.0139337i
$321$	86.2038	−	173.332i	0.268548	−	0.539975i
$322$	−458.337			−1.42341
$323$		−	768.579i		−	2.37950i
$324$	52.2256	−	184.921i	0.161190	−	0.570745i
$325$	−231.272			−0.711605
$326$		−	171.326i		−	0.525539i
$327$	296.220	+	147.320i	0.905872	+	0.450520i
$328$	72.3804			0.220672
$329$		−	281.107i		−	0.854428i
$330$		0			0
$331$	−115.649			−0.349394			−0.174697	−	0.984622i	$-0.555895\pi$
$331$	−115.649			−0.349394			−0.174697	+	0.984622i	$0.555895\pi$
$332$			155.000i			0.466867i
$333$	−13.0013	−	17.1816i	−0.0390429	−	0.0515965i
$334$	141.957			0.425019
$335$			50.1746i			0.149775i
$336$	−359.826	−	178.953i	−1.07091	−	0.532600i
$337$	53.2716			0.158076			0.0790380	−	0.996872i	$-0.474815\pi$
$337$	53.2716			0.158076			0.0790380	+	0.996872i	$0.474815\pi$
$338$		−	199.313i		−	0.589683i
$339$	−167.308	+	336.411i	−0.493535	+	0.992362i
$340$	55.0652			0.161957
$341$		0			0
$342$	−475.272	+	359.636i	−1.38968	+	1.05157i
$343$	354.163			1.03254
$344$		−	51.4061i		−	0.149436i
$345$	57.2921	+	28.4933i	0.166064	+	0.0825892i
$346$	−566.804			−1.63816
$347$			11.2082i			0.0323004i	0.999870	+	0.0161502i	$0.00514099\pi$
$347$			11.2082i			0.0323004i	−0.999870	+	0.0161502i	$0.994859\pi$
$348$	82.2175	−	165.317i	0.236257	−	0.475048i
$349$	214.016			0.613227			0.306613	−	0.951834i	$-0.400804\pi$
$349$	214.016			0.613227			0.306613	+	0.951834i	$0.400804\pi$
$350$		−	414.952i		−	1.18558i
$351$	47.4456	+	251.775i	0.135173	+	0.717308i
$352$		0			0
$353$		−	531.528i		−	1.50574i	−0.658167	−	0.752872i	$-0.728668\pi$
$353$		−	531.528i		−	1.50574i	0.658167	−	0.752872i	$-0.271332\pi$
$354$	−100.073	−	49.7698i	−0.282693	−	0.140593i
$355$	3.60597			0.0101577
$356$		−	33.5301i		−	0.0941858i
$357$	263.973	−	530.776i	0.739419	−	1.48677i
$358$	354.571			0.990421
$359$		−	175.194i		−	0.488007i	−0.969774	−	0.244003i	$-0.921539\pi$
$359$		−	175.194i		−	0.488007i	0.969774	−	0.244003i	$-0.0784608\pi$
$360$	17.6793	+	23.3639i	0.0491092	+	0.0648996i
$361$	327.206			0.906389
$362$			330.338i			0.912537i
$363$		0			0
$364$	−151.826			−0.417104
$365$		−	42.5983i		−	0.116708i
$366$	213.957	−	430.207i	0.584581	−	1.17543i
$367$	139.035			0.378843			0.189422	−	0.981896i	$-0.439339\pi$
$367$	139.035			0.378843			0.189422	+	0.981896i	$0.439339\pi$
$368$			534.680i			1.45293i
$369$	126.424	−	95.6643i	0.342612	−	0.259253i
$370$	−4.78806			−0.0129407
$371$			604.222i			1.62863i
$372$	−18.2337	−	9.06822i	−0.0490153	−	0.0243769i
$373$	−149.081			−0.399682			−0.199841	−	0.979828i	$-0.564043\pi$
$373$	−149.081			−0.399682			−0.199841	+	0.979828i	$0.564043\pi$
$374$		0			0
$375$	−52.2567	+	105.074i	−0.139351	+	0.280197i
$376$	−171.255			−0.455467
$377$			246.177i			0.652990i
$378$	−451.739	+	85.1278i	−1.19508	+	0.225206i
$379$	270.394			0.713441			0.356720	−	0.934211i	$-0.383895\pi$
$379$	270.394			0.713441			0.356720	+	0.934211i	$0.383895\pi$
$380$			49.3069i			0.129755i
$381$	518.016	+	257.627i	1.35962	+	0.676186i
$382$	−887.054			−2.32213
$383$		−	631.801i		−	1.64961i	−0.565416	−	0.824806i	$-0.691284\pi$
$383$		−	631.801i		−	1.64961i	0.565416	−	0.824806i	$-0.308716\pi$
$384$	−161.109	+	323.945i	−0.419554	+	0.843607i
$385$		0			0
$386$			619.738i			1.60554i
$387$	−67.9428	−	89.7889i	−0.175563	−	0.232013i
$388$	−354.147			−0.912749
$389$			459.996i			1.18251i	0.806485	+	0.591254i	$0.201367\pi$
$389$			459.996i			1.18251i	−0.806485	+	0.591254i	$0.798633\pi$
$390$	50.9783	+	25.3532i	0.130713	+	0.0650082i
$391$	−788.701			−2.01714
$392$		−	14.4259i		−	0.0368007i
$393$	141.736	−	284.993i	0.360653	−	0.725173i
$394$	−15.5326			−0.0394229
$395$			44.1140i			0.111681i
$396$		0			0
$397$	−561.272			−1.41378			−0.706891	−	0.707322i	$-0.749903\pi$
$397$	−561.272			−1.41378			−0.706891	+	0.707322i	$0.749903\pi$
$398$			487.883i			1.22584i
$399$	475.272	+	236.368i	1.19116	+	0.592402i
$400$	−484.068			−1.21017
$401$		−	179.845i		−	0.448491i	−0.974533	−	0.224245i	$-0.928008\pi$
$401$		−	179.845i		−	0.448491i	0.974533	−	0.224245i	$-0.0719917\pi$
$402$	−213.562	+	429.415i	−0.531250	+	1.06820i
$403$	27.1522			0.0673753
$404$			47.4683i			0.117496i
$405$	61.7595	+	17.4421i	0.152493	+	0.0430670i
$406$	−441.696			−1.08792
$407$		0			0
$408$	−323.359	−	160.817i	−0.792546	−	0.394159i
$409$	−135.696			−0.331774			−0.165887	−	0.986145i	$-0.553049\pi$
$409$	−135.696			−0.331774			−0.165887	+	0.986145i	$0.553049\pi$
$410$		−	35.2309i		−	0.0859291i
$411$	−260.898	+	524.594i	−0.634789	+	1.27638i
$412$	428.016			1.03887
$413$			99.5396i			0.241016i
$414$	369.052	+	487.715i	0.891429	+	1.17806i
$415$	−51.7663			−0.124738
$416$			319.795i			0.768739i
$417$	18.6277	+	9.26419i	0.0446708	+	0.0222163i
$418$		0			0
$419$		−	50.3361i		−	0.120134i	−0.998194	−	0.0600669i	$-0.980869\pi$
$419$		−	50.3361i		−	0.120134i	0.998194	−	0.0600669i	$-0.0191314\pi$
$420$	−16.9348	+	34.0511i	−0.0403208	+	0.0810741i
$421$	−52.6849			−0.125142			−0.0625711	−	0.998041i	$-0.519930\pi$
$421$	−52.6849			−0.125142			−0.0625711	+	0.998041i	$0.519930\pi$
$422$			269.569i			0.638789i
$423$	−299.125	+	226.346i	−0.707151	+	0.535098i
$424$	368.103			0.868168
$425$		−	714.044i		−	1.68010i
$426$	30.8614	+	15.3484i	0.0724446	+	0.0360291i
$427$	−427.913			−1.00214
$428$		−	153.079i		−	0.357662i
$429$		0			0
$430$	−25.0217			−0.0581901
$431$		−	496.807i		−	1.15268i	−0.817209	−	0.576342i	$-0.804480\pi$
$431$		−	496.807i		−	1.15268i	0.817209	−	0.576342i	$-0.195520\pi$
$432$	99.3070	+	526.983i	0.229877	+	1.21987i
$433$	515.622			1.19081			0.595407	−	0.803424i	$-0.296991\pi$
$433$	515.622			1.19081			0.595407	+	0.803424i	$0.296991\pi$
$434$			48.7170i			0.112251i
$435$	55.2119	+	27.4587i	0.126924	+	0.0631235i
$436$	261.609			0.600020
$437$		−	706.225i		−	1.61607i
$438$	181.315	−	364.575i	0.413961	−	0.832362i
$439$	25.1087			0.0571953			0.0285977	−	0.999591i	$-0.490896\pi$
$439$	25.1087			0.0571953			0.0285977	+	0.999591i	$0.490896\pi$
$440$		0			0
$441$	−19.0665	−	25.1971i	−0.0432347	−	0.0571363i
$442$	−701.783			−1.58774
$443$			870.420i			1.96483i	0.186711	+	0.982415i	$0.440217\pi$
$443$			870.420i			1.96483i	−0.186711	+	0.982415i	$0.559783\pi$
$444$	−15.2554	−	7.58704i	−0.0343591	−	0.0170879i
$445$	11.1983			0.0251647
$446$			193.695i			0.434293i
$447$	−90.4375	+	181.845i	−0.202321	+	0.406812i
$448$	−37.9565			−0.0847243
$449$		−	575.642i		−	1.28205i	−0.767519	−	0.641026i	$-0.778509\pi$
$449$		−	575.642i		−	1.28205i	0.767519	−	0.641026i	$-0.221491\pi$
$450$	−441.549	+	334.118i	−0.981220	+	0.742484i
$451$		0			0
$452$			297.103i			0.657308i
$453$	75.8397	+	37.7176i	0.167416	+	0.0832618i
$454$	−121.783			−0.268243
$455$		−	50.7064i		−	0.111443i
$456$	144.000	−	289.544i	0.315789	−	0.634965i
$457$	−25.5923			−0.0560007			−0.0280003	−	0.999608i	$-0.508914\pi$
$457$	−25.5923			−0.0560007			−0.0280003	+	0.999608i	$0.508914\pi$
$458$		−	38.9146i		−	0.0849665i
$459$	−777.348	+	146.487i	−1.69357	+	0.319144i
$460$	50.5979			0.109995
$461$			289.365i			0.627691i	0.949474	+	0.313845i	$0.101617\pi$
$461$			289.365i			0.627691i	−0.949474	+	0.313845i	$0.898383\pi$
$462$		0			0
$463$	−201.052			−0.434237			−0.217118	−	0.976145i	$-0.569666\pi$
$463$	−201.052			−0.434237			−0.217118	+	0.976145i	$0.569666\pi$
$464$			515.266i			1.11049i
$465$	3.02858	−	6.08963i	0.00651307	−	0.0130960i
$466$	−437.228			−0.938258
$467$			110.319i			0.236230i	0.993000	+	0.118115i	$0.0376852\pi$
$467$			110.319i			0.236230i	−0.993000	+	0.118115i	$0.962315\pi$
$468$	122.250	+	161.558i	0.261218	+	0.345209i
$469$	427.125			0.910714
$470$			83.3581i			0.177358i
$471$	182.110	+	90.5694i	0.386645	+	0.192292i
$472$	60.6414			0.128477
$473$		0			0
$474$	−187.766	+	377.546i	−0.396131	+	0.796511i
$475$	639.375			1.34605
$476$		−	468.758i		−	0.984786i
$477$	642.951	−	486.518i	1.34791	−	1.01995i
$478$	748.206			1.56529
$479$			683.532i			1.42700i	0.700656	+	0.713499i	$0.252891\pi$
$479$			683.532i			1.42700i	−0.700656	+	0.713499i	$0.747109\pi$
$480$	71.7228	+	35.6701i	0.149423	+	0.0743128i
$481$	22.7173			0.0472292
$482$		−	117.889i		−	0.244584i
$483$	242.557	−	487.715i	0.502188	−	1.00976i
$484$		0			0
$485$		−	118.277i		−	0.243870i
$486$	454.323	+	412.150i	0.934821	+	0.848044i
$487$	−130.101			−0.267147			−0.133574	−	0.991039i	$-0.542645\pi$
$487$	−130.101			−0.267147			−0.133574	+	0.991039i	$0.542645\pi$
$488$			260.692i			0.534206i
$489$	182.307	+	90.6674i	0.372816	+	0.185414i
$490$	−7.02175			−0.0143301
$491$			796.580i			1.62236i	0.584795	+	0.811181i	$0.301175\pi$
$491$			796.580i			1.62236i	−0.584795	+	0.811181i	$0.698825\pi$
$492$	55.8260	−	112.251i	0.113467	−	0.228152i
$493$	−760.065			−1.54171
$494$		−	628.395i		−	1.27206i
$495$		0			0
$496$	56.8316			0.114580
$497$		−	30.6968i		−	0.0617642i
$498$	−443.038	−	220.338i	−0.889634	−	0.442445i
$499$	490.032			0.982029			0.491014	−	0.871151i	$-0.336626\pi$
$499$	490.032			0.982029			0.491014	+	0.871151i	$0.336626\pi$
$500$			92.7966i			0.185593i
$501$	−75.1249	+	151.056i	−0.149950	+	0.301508i
$502$	−524.527			−1.04487
$503$			283.281i			0.563183i	0.959534	+	0.281592i	$0.0908624\pi$
$503$			283.281i			0.563183i	−0.959534	+	0.281592i	$0.909138\pi$
$504$	198.891	−	150.500i	0.394626	−	0.298611i
$505$	−15.8533			−0.0313927
$506$		0			0
$507$	212.088	+	105.479i	0.418320	+	0.208045i
$508$	457.489			0.900569
$509$			243.650i			0.478683i	0.970935	+	0.239342i	$0.0769316\pi$
$509$			243.650i			0.478683i	−0.970935	+	0.239342i	$0.923068\pi$
$510$	−78.2772	+	157.394i	−0.153485	+	0.308615i
$511$	−362.630			−0.709648
$512$			342.919i			0.669764i
$513$	−131.168	−	696.058i	−0.255689	−	1.35684i
$514$	504.206			0.980946
$515$			142.947i			0.277568i
$516$	−79.7228	−	39.6488i	−0.154502	−	0.0768388i
$517$		0			0
$518$			40.7597i			0.0786867i
$519$	299.959	−	603.135i	0.577956	−	1.16211i
$520$	−30.8913			−0.0594063
$521$		−	376.274i		−	0.722215i	−0.932524	−	0.361107i	$-0.882399\pi$
$521$		−	376.274i		−	0.722215i	0.932524	−	0.361107i	$-0.117601\pi$
$522$	355.652	+	470.007i	0.681326	+	0.900396i
$523$	−555.842			−1.06280			−0.531398	−	0.847122i	$-0.678333\pi$
$523$	−555.842			−1.06280			−0.531398	+	0.847122i	$0.678333\pi$
$524$		−	251.693i		−	0.480331i
$525$	441.549	+	219.597i	0.841045	+	0.418280i
$526$	251.826			0.478757
$527$			83.8317i			0.159074i
$528$		0			0
$529$	−195.715			−0.369971
$530$		−	179.173i		−	0.338062i
$531$	105.920	−	80.1490i	0.199472	−	0.150940i
$532$	419.739			0.788983
$533$			167.155i			0.313612i
$534$	95.8397	+	47.6643i	0.179475	+	0.0892589i
$535$	51.1249			0.0955606
$536$		−	260.212i		−	0.485471i
$537$	−187.643	+	377.298i	−0.349428	+	0.702602i
$538$	127.168			0.236373
$539$		0			0
$540$	49.8695	−	9.39764i	0.0923509	−	0.0174030i
$541$	−932.206			−1.72312			−0.861559	−	0.507658i	$-0.830511\pi$
$541$	−932.206			−1.72312			−0.861559	+	0.507658i	$0.830511\pi$
$542$			313.978i			0.579295i
$543$	−351.512	−	174.819i	−0.647352	−	0.321950i
$544$	−987.359			−1.81500
$545$			87.3712i			0.160314i
$546$	215.826	−	433.966i	0.395286	−	0.794810i
$547$	−736.983			−1.34732			−0.673659	−	0.739042i	$-0.735278\pi$
$547$	−736.983			−1.34732			−0.673659	+	0.739042i	$0.735278\pi$
$548$			463.298i			0.845435i
$549$	344.554	+	455.341i	0.627604	+	0.829401i
$550$		0			0
$551$		−	680.583i		−	1.23518i
$552$	−297.125	−	147.770i	−0.538270	−	0.267700i
$553$	375.533			0.679083
$554$		−	741.456i		−	1.33837i
$555$	2.53389	−	5.09496i	0.00456558	−	0.00918011i
$556$	16.4512			0.0295885
$557$			635.659i			1.14122i	0.821221	+	0.570610i	$0.193293\pi$
$557$			635.659i			1.14122i	−0.821221	+	0.570610i	$0.806707\pi$
$558$	51.8397	−	39.2268i	0.0929026	−	0.0702990i
$559$	118.717			0.212374
$560$		−	106.132i		−	0.189521i
$561$		0			0
$562$	665.609			1.18436
$563$		−	800.352i		−	1.42158i	−0.703402	−	0.710792i	$-0.748337\pi$
$563$		−	800.352i		−	1.42158i	0.703402	−	0.710792i	$-0.251663\pi$
$564$	−132.087	+	265.590i	−0.234197	+	0.470905i
$565$	−99.2256			−0.175621
$566$		−	1006.68i		−	1.77858i
$567$	148.481	−	525.745i	0.261871	−	0.927239i
$568$	−18.7011			−0.0329244
$569$			52.5450i			0.0923463i	0.998933	+	0.0461731i	$0.0147026\pi$
$569$			52.5450i			0.0923463i	−0.998933	+	0.0461731i	$0.985297\pi$
$570$	−140.935	−	70.0916i	−0.247254	−	0.122968i
$571$	−10.1143			−0.0177133			−0.00885666	−	0.999961i	$-0.502819\pi$
$571$	−10.1143			−0.0177133			−0.00885666	+	0.999961i	$0.502819\pi$
$572$		0			0
$573$	469.439	−	943.912i	0.819265	−	1.64732i
$574$	−299.913			−0.522497
$575$		−	656.115i		−	1.14107i
$576$	30.5625	+	40.3894i	0.0530598	+	0.0701205i
$577$	−88.2959			−0.153026			−0.0765129	−	0.997069i	$-0.524379\pi$
$577$	−88.2959			−0.153026			−0.0765129	+	0.997069i	$0.524379\pi$
$578$		−	1437.20i		−	2.48650i
$579$	−659.462	−	327.972i	−1.13897	−	0.566446i
$580$	48.7608			0.0840703
$581$			440.675i			0.758477i
$582$	503.432	−	1012.26i	0.865003	−	1.73928i
$583$		0			0
$584$			220.921i			0.378289i
$585$	−53.9565	+	40.8286i	−0.0922333	+	0.0697925i
$586$	880.587			1.50271
$587$			752.212i			1.28145i	0.767770	+	0.640726i	$0.221366\pi$
$587$			752.212i			1.28145i	−0.767770	+	0.640726i	$0.778634\pi$
$588$	−22.3723	−	11.1265i	−0.0380481	−	0.0189226i
$589$	−75.0652			−0.127445
$590$		−	29.5170i		−	0.0500288i
$591$	8.22004	−	16.5282i	0.0139087	−	0.0279665i
$592$	47.5488			0.0803189
$593$			656.836i			1.10765i	0.832633	+	0.553825i	$0.186832\pi$
$593$			656.836i			1.10765i	−0.832633	+	0.553825i	$0.813168\pi$
$594$		0			0
$595$	156.554			0.263117
$596$			160.597i			0.269459i
$597$	−519.155	−	258.193i	−0.869606	−	0.432484i
$598$	−644.848			−1.07834
$599$		−	403.922i		−	0.674327i	−0.941446	−	0.337164i	$-0.890532\pi$
$599$		−	403.922i		−	0.674327i	0.941446	−	0.337164i	$-0.109468\pi$
$600$	133.783	−	269.000i	0.222971	−	0.448333i
$601$	826.761			1.37564			0.687821	−	0.725880i	$-0.258567\pi$
$601$	826.761			1.37564			0.687821	+	0.725880i	$0.258567\pi$
$602$			213.005i			0.353828i
$603$	−343.920	−	454.502i	−0.570348	−	0.753735i
$604$	66.9783			0.110891
$605$		0			0
$606$	−135.679	−	67.4778i	−0.223893	−	0.111350i
$607$	1156.44			1.90517			0.952587	−	0.304268i	$-0.0984118\pi$
$607$	1156.44			1.90517			0.952587	+	0.304268i	$0.0984118\pi$
$608$		−	884.108i		−	1.45413i
$609$	233.750	−	470.007i	0.383826	−	0.771768i
$610$	126.891			0.208018
$611$		−	395.497i		−	0.647295i
$612$	−498.804	+	377.443i	−0.815040	+	0.616737i
$613$	898.250			1.46533			0.732667	−	0.680587i	$-0.238275\pi$
$613$	898.250			1.46533			0.732667	+	0.680587i	$0.238275\pi$
$614$			1006.02i			1.63846i
$615$	37.4891	+	18.6446i	0.0609579	+	0.0303164i
$616$		0			0
$617$			713.002i			1.15560i	0.816180	+	0.577798i	$0.196088\pi$
$617$			713.002i			1.15560i	−0.816180	+	0.577798i	$0.803912\pi$
$618$	−608.440	+	1223.40i	−0.984531	+	1.97962i
$619$	−40.4102			−0.0652831			−0.0326415	−	0.999467i	$-0.510392\pi$
$619$	−40.4102			−0.0652831			−0.0326415	+	0.999467i	$0.510392\pi$
$620$		−	5.37809i		−	0.00867434i
$621$	−714.282	+	134.603i	−1.15021	+	0.216751i
$622$	1111.58			1.78711
$623$		−	95.3285i		−	0.153015i
$624$	−506.250	−	251.775i	−0.811298	−	0.403485i
$625$	578.315			0.925304
$626$			1337.64i			2.13681i
$627$		0			0
$628$	160.832			0.256101
$629$			70.1388i			0.111508i
$630$	−73.2554	−	96.8097i	−0.116278	−	0.153666i
$631$	−748.502			−1.18622			−0.593108	−	0.805123i	$-0.702099\pi$
$631$	−748.502			−1.18622			−0.593108	+	0.805123i	$0.702099\pi$
$632$		−	228.781i		−	0.361996i
$633$	−286.848	−	142.659i	−0.453156	−	0.225370i
$634$	−930.032			−1.46693
$635$			152.791i			0.240615i
$636$	283.913	−	570.871i	0.446404	−	0.897595i
$637$	33.3151			0.0523000
$638$		0			0
$639$	−32.6644	+	24.7170i	−0.0511180	+	0.0386807i
$640$	−95.5488			−0.149295
$641$		−	122.303i		−	0.190800i	−0.995439	−	0.0954000i	$-0.969587\pi$
$641$		−	122.303i		−	0.190800i	0.995439	−	0.0954000i	$-0.0304130\pi$
$642$	437.549	+	217.608i	0.681540	+	0.338953i
$643$	−629.313			−0.978713			−0.489357	−	0.872084i	$-0.662768\pi$
$643$	−629.313			−0.978713			−0.489357	+	0.872084i	$0.662768\pi$
$644$		−	430.728i		−	0.668833i
$645$	13.2418	−	26.6256i	0.0205299	−	0.0412800i
$646$	1940.15			3.00333
$647$			185.830i			0.287218i	0.989635	+	0.143609i	$0.0458707\pi$
$647$			185.830i			0.287218i	−0.989635	+	0.143609i	$0.954129\pi$
$648$	−320.293	−	90.4574i	−0.494280	−	0.139595i
$649$		0			0
$650$		−	583.808i		−	0.898166i
$651$	−51.8397	−	25.7816i	−0.0796308	−	0.0396031i
$652$	161.006			0.246941
$653$		−	202.416i		−	0.309979i	−0.987916	−	0.154990i	$-0.950466\pi$
$653$		−	202.416i		−	0.309979i	0.987916	−	0.154990i	$-0.0495344\pi$
$654$	−371.886	+	747.759i	−0.568633	+	1.14336i
$655$	84.0597			0.128335
$656$			349.868i			0.533335i
$657$	291.989	+	385.874i	0.444428	+	0.587327i
$658$	709.609			1.07843
$659$		−	1094.02i		−	1.66012i	−0.557674	−	0.830060i	$-0.688306\pi$
$659$		−	1094.02i		−	1.66012i	0.557674	−	0.830060i	$-0.311694\pi$
$660$		0			0
$661$	1024.53			1.54997			0.774985	−	0.631980i	$-0.217758\pi$
$661$	1024.53			1.54997			0.774985	+	0.631980i	$0.217758\pi$
$662$		−	291.938i		−	0.440994i
$663$	371.391	−	746.765i	0.560167	−	1.12634i
$664$	268.467			0.404318
$665$			140.183i			0.210802i
$666$	43.3723	−	32.8196i	0.0651235	−	0.0492787i
$667$	−698.402			−1.04708
$668$			133.406i			0.199709i
$669$	−206.110	−	102.505i	−0.308087	−	0.153222i
$670$	−126.658			−0.189041
$671$		0			0
$672$	303.652	−	610.560i	0.451863	−	0.908572i
$673$	−259.489			−0.385571			−0.192785	−	0.981241i	$-0.561752\pi$
$673$	−259.489			−0.385571			−0.192785	+	0.981241i	$0.561752\pi$
$674$			134.476i			0.199519i
$675$	−121.861	−	646.670i	−0.180535	−	0.958029i
$676$	187.307			0.277081
$677$		−	116.565i		−	0.172179i	−0.996287	−	0.0860895i	$-0.972563\pi$
$677$		−	116.565i		−	0.172179i	0.996287	−	0.0860895i	$-0.0274371\pi$
$678$	−849.214	−	422.343i	−1.25253	−	0.622924i
$679$	−1006.86			−1.48286
$680$		−	95.3758i		−	0.140259i
$681$	64.4486	−	129.588i	0.0946382	−	0.190291i
$682$		0			0
$683$			739.385i			1.08255i	0.840844	+	0.541277i	$0.182059\pi$
$683$			739.385i			1.08255i	−0.840844	+	0.541277i	$0.817941\pi$
$684$	−337.973	−	446.643i	−0.494112	−	0.652987i
$685$	−154.731			−0.225885
$686$			894.027i			1.30325i
$687$	41.4090	+	20.5941i	0.0602750	+	0.0299768i
$688$	248.484			0.361168
$689$			850.098i			1.23381i
$690$	−71.9267	+	144.625i	−0.104242	+	0.209601i
$691$	389.024			0.562987			0.281494	−	0.959563i	$-0.409170\pi$
$691$	389.024			0.562987			0.281494	+	0.959563i	$0.409170\pi$
$692$		−	532.662i		−	0.769743i
$693$		0			0
$694$	−28.2934			−0.0407686
$695$			5.49431i			0.00790549i
$696$	−286.337	−	142.405i	−0.411404	−	0.204605i
$697$	−516.087			−0.740440
$698$			540.249i			0.773996i
$699$	231.386	−	465.253i	0.331024	−	0.665598i
$700$	389.957			0.557081
$701$		−	1164.12i		−	1.66066i	−0.557271	−	0.830330i	$-0.688152\pi$
$701$		−	1164.12i		−	1.66066i	0.557271	−	0.830330i	$-0.311848\pi$
$702$	−635.565	+	119.769i	−0.905363	+	0.170611i
$703$	−62.8043			−0.0893375
$704$		0			0
$705$	−88.7011	−	44.1140i	−0.125817	−	0.0625730i
$706$	1341.76			1.90050
$707$			134.956i			0.190885i
$708$	46.7719	−	94.0453i	0.0660620	−	0.132832i
$709$	1329.93			1.87579			0.937893	−	0.346926i	$-0.112774\pi$
$709$	1329.93			1.87579			0.937893	+	0.346926i	$0.112774\pi$
$710$			9.10268i			0.0128207i
$711$	−302.378	−	399.603i	−0.425285	−	0.562030i
$712$	−58.0759			−0.0815673
$713$			77.0306i			0.108037i
$714$	1339.86	+	666.356i	1.87655	+	0.933272i
$715$		0			0
$716$			333.213i			0.465381i
$717$	−395.959	+	796.164i	−0.552244	+	1.11041i
$718$	442.250			0.615947
$719$			838.618i			1.16637i	0.812340	+	0.583184i	$0.198193\pi$
$719$			838.618i			1.16637i	−0.812340	+	0.583184i	$0.801807\pi$
$720$	−112.935	+	85.4572i	−0.156854	+	0.118691i
$721$	1216.88			1.68777
$722$			825.979i			1.14402i
$723$	125.446	+	62.3883i	0.173507	+	0.0862909i
$724$	−310.440			−0.428785
$725$		−	632.292i		−	0.872127i
$726$		0			0
$727$	154.628			0.212693			0.106346	−	0.994329i	$-0.466085\pi$
$727$	154.628			0.212693			0.106346	+	0.994329i	$0.466085\pi$
$728$			262.970i			0.361223i
$729$	−679.000	+	265.330i	−0.931413	+	0.363964i
$730$	107.533			0.147305
$731$			366.536i			0.501417i
$732$	404.293	+	201.069i	0.552313	+	0.274684i
$733$	−445.022			−0.607124			−0.303562	−	0.952812i	$-0.598176\pi$
$733$	−445.022			−0.607124			−0.303562	+	0.952812i	$0.598176\pi$
$734$			350.972i			0.478164i
$735$	3.71599	−	7.47182i	0.00505576	−	0.0101657i
$736$	−907.255			−1.23268
$737$		0			0
$738$	241.489	+	319.137i	0.327221	+	0.432434i
$739$	−61.3586			−0.0830293			−0.0415146	−	0.999138i	$-0.513218\pi$
$739$	−61.3586			−0.0830293			−0.0415146	+	0.999138i	$0.513218\pi$
$740$		−	4.49965i		−	0.00608060i
$741$	668.674	+	332.554i	0.902394	+	0.448790i
$742$	−1525.26			−2.05561
$743$			723.250i			0.973419i	0.873564	+	0.486709i	$0.161803\pi$
$743$			723.250i			0.973419i	−0.873564	+	0.486709i	$0.838197\pi$
$744$	−15.7066	+	31.5817i	−0.0211110	+	0.0424485i
$745$	−53.6358			−0.0719944
$746$		−	376.332i		−	0.504466i
$747$	468.921	−	354.830i	0.627739	−	0.475007i
$748$		0			0
$749$		−	435.215i		−	0.581062i
$750$	−265.242	−	131.914i	−0.353656	−	0.175885i
$751$	1286.37			1.71287			0.856436	−	0.516253i	$-0.172674\pi$
$751$	1286.37			1.71287			0.856436	+	0.516253i	$0.172674\pi$
$752$		−	827.804i		−	1.10080i
$753$	277.585	−	558.148i	0.368639	−	0.741232i
$754$	−621.435			−0.824184
$755$			22.3692i			0.0296281i
$756$	−80.0000	−	424.528i	−0.105820	−	0.561545i
$757$	−272.717			−0.360261			−0.180130	−	0.983643i	$-0.557652\pi$
$757$	−272.717			−0.360261			−0.180130	+	0.983643i	$0.557652\pi$
$758$			682.566i			0.900483i
$759$		0			0
$760$	85.4021			0.112371
$761$			476.634i			0.626326i	0.949699	+	0.313163i	$0.101389\pi$
$761$			476.634i			0.626326i	−0.949699	+	0.313163i	$0.898611\pi$
$762$	−650.337	+	1307.65i	−0.853460	+	1.71607i
$763$	743.771			0.974799
$764$		−	833.621i		−	1.09113i
$765$	−126.057	−	166.589i	−0.164781	−	0.217763i
$766$	1594.88			2.08209
$767$			140.045i			0.182588i
$768$	−878.214	−	436.765i	−1.14351	−	0.568705i
$769$	22.4401			0.0291808			0.0145904	−	0.999894i	$-0.495356\pi$
$769$	22.4401			0.0291808			0.0145904	+	0.999894i	$0.495356\pi$
$770$		0			0
$771$	−266.832	+	536.525i	−0.346085	+	0.695881i
$772$	−582.408			−0.754414
$773$			1227.79i			1.58834i	0.607694	+	0.794171i	$0.292095\pi$
$773$			1227.79i			1.58834i	−0.607694	+	0.794171i	$0.707905\pi$
$774$	226.658	−	171.511i	0.292839	−	0.221590i
$775$	−69.7390			−0.0899858
$776$			613.400i			0.790464i
$777$	−43.3723	−	21.5705i	−0.0558202	−	0.0277612i
$778$	−1161.18			−1.49253
$779$		−	462.119i		−	0.593220i
$780$	−23.8260	+	47.9075i	−0.0305462	+	0.0614199i
$781$		0			0
$782$		−	1990.95i		−	2.54597i
$783$	−688.348	+	129.715i	−0.879116	+	0.165665i
$784$	69.7309			0.0889425
$785$			53.7140i			0.0684255i
$786$	719.418	+	357.791i	0.915290	+	0.455204i
$787$	−872.277			−1.10836			−0.554179	−	0.832398i	$-0.686968\pi$
$787$	−872.277			−1.10836			−0.554179	+	0.832398i	$0.686968\pi$
$788$		−	14.5970i		−	0.0185241i
$789$	−133.269	+	267.967i	−0.168909	+	0.339629i
$790$	−111.359			−0.140960
$791$			844.685i			1.06787i
$792$		0			0
$793$	−602.043			−0.759197
$794$		−	1416.84i		−	1.78443i
$795$	190.658	+	94.8204i	0.239821	+	0.119271i
$796$	−458.495			−0.575998
$797$			55.7659i			0.0699697i	0.999388	+	0.0349849i	$0.0111383\pi$
$797$			55.7659i			0.0699697i	−0.999388	+	0.0349849i	$0.988862\pi$
$798$	−596.674	+	1199.75i	−0.747711	+	1.50344i
$799$	1221.09			1.52827
$800$		−	821.376i		−	1.02672i
$801$	−101.439	+	76.7583i	−0.126640	+	0.0958280i
$802$	453.989			0.566071
$803$		0			0
$804$	−403.549	−	200.698i	−0.501926	−	0.249625i
$805$	143.853			0.178700
$806$			68.5414i			0.0850390i
$807$	−67.2989	+	135.320i	−0.0833940	+	0.167682i
$808$	82.2175			0.101754
$809$			1325.11i			1.63796i	0.573819	+	0.818982i	$0.305461\pi$
$809$			1325.11i			1.63796i	−0.573819	+	0.818982i	$0.694539\pi$
$810$	−44.0298	+	155.902i	−0.0543578	+	0.192471i
$811$	1028.13			1.26773			0.633866	−	0.773443i	$-0.281467\pi$
$811$	1028.13			1.26773			0.633866	+	0.773443i	$0.281467\pi$
$812$		−	415.089i		−	0.511194i
$813$	−334.103	−	166.161i	−0.410951	−	0.204380i
$814$		0			0
$815$			53.7721i			0.0659781i
$816$	777.348	−	1563.03i	0.952632	−	1.91548i
$817$	−328.206			−0.401721
$818$		−	342.541i		−	0.418755i
$819$	347.565	+	459.320i	0.424377	+	0.560830i
$820$	33.1087			0.0403765
$821$		−	892.085i		−	1.08658i	−0.839544	−	0.543292i	$-0.817178\pi$
$821$		−	892.085i		−	1.08658i	0.839544	−	0.543292i	$-0.182822\pi$
$822$	−1324.25	−	658.595i	−1.61101	−	0.801210i
$823$	−415.301			−0.504619			−0.252310	−	0.967647i	$-0.581190\pi$
$823$	−415.301			−0.504619			−0.252310	+	0.967647i	$0.581190\pi$
$824$		−	741.346i		−	0.899691i
$825$		0			0
$826$	−251.272			−0.304203
$827$			464.560i			0.561741i	0.959746	+	0.280871i	$0.0906232\pi$
$827$			464.560i			0.561741i	−0.959746	+	0.280871i	$0.909377\pi$
$828$	−458.337	+	346.821i	−0.553547	+	0.418866i
$829$	−886.193			−1.06899			−0.534495	−	0.845172i	$-0.679498\pi$
$829$	−886.193			−1.06899			−0.534495	+	0.845172i	$0.679498\pi$
$830$		−	130.676i		−	0.157441i
$831$	788.981	+	392.386i	0.949435	+	0.472186i
$832$	−53.4021			−0.0641852
$833$			102.859i			0.123481i
$834$	−23.3859	+	47.0227i	−0.0280407	+	0.0563821i
$835$	−44.5544			−0.0533585
$836$		0			0
$837$	14.3070	+	75.9217i	0.0170932	+	0.0907069i
$838$	127.065			0.151629
$839$		−	163.482i		−	0.194854i	−0.995243	−	0.0974270i	$-0.968939\pi$
$839$		−	163.482i		−	0.194854i	0.995243	−	0.0974270i	$-0.0310612\pi$
$840$	58.9783	+	29.3319i	0.0702122	+	0.0349189i
$841$	167.956			0.199710
$842$		−	132.994i		−	0.157951i
$843$	−352.247	+	708.272i	−0.417850	+	0.840180i
$844$	−253.331			−0.300156
$845$			62.5562i			0.0740310i
$846$	−571.375	−	755.092i	−0.675384	−	0.892544i
$847$		0			0
$848$			1779.31i			2.09825i
$849$	1071.20	+	532.744i	1.26172	+	0.627496i
$850$	1802.49			2.12057
$851$			64.4486i			0.0757327i
$852$	−14.4239	+	29.0024i	−0.0169294	+	0.0340404i
$853$	451.647			0.529481			0.264740	−	0.964320i	$-0.414714\pi$
$853$	451.647			0.529481			0.264740	+	0.964320i	$0.414714\pi$
$854$		−	1080.20i		−	1.26487i
$855$	149.168	−	112.875i	0.174466	−	0.132018i
$856$	−265.141			−0.309744
$857$		−	233.720i		−	0.272719i	−0.990659	−	0.136360i	$-0.956460\pi$
$857$		−	233.720i		−	0.272719i	0.990659	−	0.136360i	$-0.0435402\pi$
$858$		0			0
$859$	−694.225			−0.808178			−0.404089	−	0.914720i	$-0.632411\pi$
$859$	−694.225			−0.808178			−0.404089	+	0.914720i	$0.632411\pi$
$860$		−	23.5145i		−	0.0273425i
$861$	158.717	−	319.137i	0.184341	−	0.370658i
$862$	1254.11			1.45488
$863$			1143.39i			1.32490i	0.749106	+	0.662450i	$0.230483\pi$
$863$			1143.39i			1.32490i	−0.749106	+	0.662450i	$0.769517\pi$
$864$	−894.195	+	168.506i	−1.03495	+	0.195030i
$865$	177.897			0.205661
$866$			1301.60i			1.50301i
$867$	1529.32	+	760.581i	1.76392	+	0.877256i
$868$	−45.7825			−0.0527448
$869$		0			0
$870$	−69.3151	+	139.374i	−0.0796726	+	0.160200i
$871$	600.935			0.689937
$872$		−	453.119i		−	0.519632i
$873$	810.724	+	1071.40i	0.928664	+	1.22726i
$874$	1782.75			2.03976
$875$			263.827i			0.301517i
$876$	342.614	+	170.393i	0.391112	+	0.194513i
$877$	1080.36			1.23188			0.615940	−	0.787793i	$-0.288777\pi$
$877$	1080.36			1.23188			0.615940	+	0.787793i	$0.288777\pi$
$878$			63.3830i			0.0721902i
$879$	−466.016	+	937.030i	−0.530166	+	1.06602i
$880$		0			0
$881$			638.008i			0.724186i	0.932142	+	0.362093i	$0.117938\pi$
$881$			638.008i			0.724186i	−0.932142	+	0.362093i	$0.882062\pi$
$882$	63.6060	−	48.1303i	0.0721156	−	0.0545695i
$883$	−972.195			−1.10101			−0.550507	−	0.834831i	$-0.685566\pi$
$883$	−972.195			−1.10101			−0.550507	+	0.834831i	$0.685566\pi$
$884$		−	659.510i		−	0.746052i
$885$	31.4090	+	15.6207i	0.0354903	+	0.0176505i
$886$	−2197.23			−2.47995
$887$		−	525.975i		−	0.592982i	−0.955036	−	0.296491i	$-0.904183\pi$
$887$		−	525.975i		−	0.592982i	0.955036	−	0.296491i	$-0.0958165\pi$
$888$	−13.1411	+	26.4232i	−0.0147986	+	0.0297558i
$889$	1300.67			1.46308
$890$			28.2683i			0.0317621i
$891$		0			0
$892$	−182.027			−0.204066
$893$			1093.39i			1.22441i
$894$	−459.038	−	228.295i	−0.513465	−	0.255363i
$895$	−111.285			−0.124341
$896$			813.386i			0.907797i
$897$	341.261	−	686.181i	0.380447	−	0.764973i
$898$	1453.11			1.61817
$899$			74.2337i			0.0825737i
$900$	−313.992	−	414.952i	−0.348880	−	0.461057i
$901$	−2624.65			−2.91304
$902$		0			0
$903$	−226.658	−	112.724i	−0.251005	−	0.124833i
$904$	514.598			0.569245
$905$		−	103.680i		−	0.114563i
$906$	−95.2119	+	191.445i	−0.105090	+	0.211308i
$907$	−574.706			−0.633634			−0.316817	−	0.948487i	$-0.602614\pi$
$907$	−574.706			−0.633634			−0.316817	+	0.948487i	$0.602614\pi$
$908$		−	114.447i		−	0.126043i
$909$	143.606	−	108.666i	0.157982	−	0.119545i
$910$	128.000			0.140659
$911$		−	1279.17i		−	1.40413i	−0.712111	−	0.702067i	$-0.752261\pi$
$911$		−	1279.17i		−	1.40413i	0.712111	−	0.702067i	$-0.247739\pi$
$912$	1399.58	+	696.058i	1.53463	+	0.763222i
$913$		0			0
$914$		−	64.6037i		−	0.0706823i
$915$	−67.1522	+	135.025i	−0.0733904	+	0.147568i
$916$	36.5706			0.0399242
$917$		−	715.581i		−	0.780351i
$918$	−369.783	−	1962.29i	−0.402813	−	2.13757i
$919$	481.929			0.524406			0.262203	−	0.965013i	$-0.415551\pi$
$919$	481.929			0.524406			0.262203	+	0.965013i	$0.415551\pi$
$920$		−	87.6381i		−	0.0952588i
$921$	−1070.50	−	532.395i	−1.16232	−	0.578062i
$922$	−730.456			−0.792252
$923$		−	43.1883i		−	0.0467912i
$924$		0			0
$925$	−58.3480			−0.0630789
$926$		−	507.522i		−	0.548080i
$927$	−979.829	−	1294.88i	−1.05699	−	1.39685i
$928$	−874.315			−0.942149
$929$		−	1112.26i		−	1.19726i	−0.801024	−	0.598632i	$-0.795711\pi$
$929$		−	1112.26i		−	1.19726i	0.801024	−	0.598632i	$-0.204289\pi$
$930$	15.3723	+	7.64515i	0.0165293	+	0.00822059i
$931$	−92.1032			−0.0989293
$932$		−	410.891i		−	0.440870i
$933$	−588.261	+	1182.83i	−0.630505	+	1.26777i
$934$	−278.484			−0.298162
$935$		0			0
$936$	279.826	−	211.743i	0.298959	−	0.226221i
$937$	−1743.58			−1.86081			−0.930406	−	0.366530i	$-0.880546\pi$
$937$	−1743.58			−1.86081			−0.930406	+	0.366530i	$0.880546\pi$
$938$			1078.21i			1.14948i
$939$	−1423.38	−	707.896i	−1.51585	−	0.753883i
$940$	−78.3369			−0.0833371
$941$		−	836.194i		−	0.888623i	−0.895872	−	0.444311i	$-0.853448\pi$
$941$		−	836.194i		−	0.888623i	0.895872	−	0.444311i	$-0.146552\pi$
$942$	−228.628	+	459.707i	−0.242705	+	0.488012i
$943$	−474.217			−0.502882
$944$			293.125i			0.310513i
$945$	141.783	−	26.7181i	0.150034	−	0.0282732i
$946$		0			0
$947$		−	114.725i		−	0.121145i	−0.998164	−	0.0605726i	$-0.980707\pi$
$947$		−	114.725i		−	0.121145i	0.998164	−	0.0605726i	$-0.0192927\pi$
$948$	−354.804	−	176.456i	−0.374266	−	0.186135i
$949$	−510.195			−0.537614
$950$			1614.00i			1.69895i
$951$	492.183	−	989.645i	0.517543	−	1.04064i
$952$	−811.913			−0.852850
$953$		−	327.059i		−	0.343189i	−0.985168	−	0.171595i	$-0.945108\pi$
$953$		−	327.059i		−	0.343189i	0.985168	−	0.171595i	$-0.0548919\pi$
$954$	1228.14	+	1623.03i	1.28735	+	1.70128i
$955$	278.410			0.291529
$956$			703.137i			0.735499i
$957$		0			0
$958$	−1725.47			−1.80111
$959$			1317.19i			1.37350i
$960$	−5.95650	+	11.9769i	−0.00620469	+	0.0124759i
$961$	−952.812			−0.991480
$962$			57.3460i			0.0596113i
$963$	−463.111	+	350.434i	−0.480905	+	0.363898i
$964$	110.788			0.114925
$965$		−	194.511i		−	0.201565i
$966$	1231.16	+	612.296i	1.27449	+	0.633846i
$967$	−168.674			−0.174430			−0.0872150	−	0.996190i	$-0.527797\pi$
$967$	−168.674			−0.174430			−0.0872150	+	0.996190i	$0.527797\pi$
$968$		0			0
$969$	−1026.75	+	2064.51i	−1.05960	+	2.13056i
$970$	298.571			0.307805
$971$			81.7370i			0.0841782i	0.999114	+	0.0420891i	$0.0134013\pi$
$971$			81.7370i			0.0841782i	−0.999114	+	0.0420891i	$0.986599\pi$
$972$	−387.323	+	426.957i	−0.398481	+	0.439256i
$973$	46.7719			0.0480698
$974$		−	328.418i		−	0.337185i
$975$	621.228	+	308.957i	0.637157	+	0.316879i
$976$	−1260.12			−1.29111
$977$			20.3562i			0.0208354i	0.999946	+	0.0104177i	$0.00331612\pi$
$977$			20.3562i			0.0208354i	−0.999946	+	0.0104177i	$0.996684\pi$
$978$	−228.875	+	460.205i	−0.234024	+	0.470557i
$979$		0			0
$980$		−	6.59879i		−	0.00673346i
$981$	−598.883	−	791.445i	−0.610482	−	0.806774i
$982$	−2010.84			−2.04770
$983$		−	797.407i		−	0.811197i	−0.914051	−	0.405598i	$-0.867063\pi$
$983$		−	797.407i		−	0.811197i	0.914051	−	0.405598i	$-0.132937\pi$
$984$	−194.424	−	96.6935i	−0.197585	−	0.0982657i
$985$	4.87506			0.00494930
$986$		−	1918.66i		−	1.94590i
$987$	−375.533	+	755.092i	−0.380479	+	0.765038i
$988$	590.543			0.597716
$989$			336.799i			0.340545i
$990$		0			0
$991$	609.620			0.615156			0.307578	−	0.951523i	$-0.400481\pi$
$991$	609.620			0.615156			0.307578	+	0.951523i	$0.400481\pi$
$992$			96.4330i			0.0972107i
$993$	310.651	+	154.497i	0.312841	+	0.155586i
$994$	77.4891			0.0779569
$995$		−	153.127i		−	0.153896i
$996$	207.065	−	416.351i	0.207897	−	0.418023i
$997$	−1771.28			−1.77661			−0.888303	−	0.459257i	$-0.848116\pi$
$997$	−1771.28			−1.77661			−0.888303	+	0.459257i	$0.848116\pi$
$998$			1237.01i			1.23949i
$999$	11.9702	+	63.5208i	0.0119821	+	0.0635844i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.b.h.122.4		4
3.2	odd	2	inner	363.3.b.h.122.1		4
11.2	odd	10		363.3.h.m.323.1		16
11.3	even	5		363.3.h.l.251.4		16
11.4	even	5		363.3.h.l.269.1		16
11.5	even	5		363.3.h.l.245.1		16
11.6	odd	10		363.3.h.m.245.4		16
11.7	odd	10		363.3.h.m.269.4		16
11.8	odd	10		363.3.h.m.251.1		16
11.9	even	5		363.3.h.l.323.4		16
11.10	odd	2		33.3.b.b.23.1	✓	4
33.2	even	10		363.3.h.m.323.4		16
33.5	odd	10		363.3.h.l.245.4		16
33.8	even	10		363.3.h.m.251.4		16
33.14	odd	10		363.3.h.l.251.1		16
33.17	even	10		363.3.h.m.245.1		16
33.20	odd	10		363.3.h.l.323.1		16
33.26	odd	10		363.3.h.l.269.4		16
33.29	even	10		363.3.h.m.269.1		16
33.32	even	2		33.3.b.b.23.4	yes	4
44.43	even	2		528.3.i.d.353.4		4
132.131	odd	2		528.3.i.d.353.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.b.b.23.1	✓	4	11.10	odd	2
33.3.b.b.23.4	yes	4	33.32	even	2
363.3.b.h.122.1		4	3.2	odd	2	inner
363.3.b.h.122.4		4	1.1	even	1	trivial
363.3.h.l.245.1		16	11.5	even	5
363.3.h.l.245.4		16	33.5	odd	10
363.3.h.l.251.1		16	33.14	odd	10
363.3.h.l.251.4		16	11.3	even	5
363.3.h.l.269.1		16	11.4	even	5
363.3.h.l.269.4		16	33.26	odd	10
363.3.h.l.323.1		16	33.20	odd	10
363.3.h.l.323.4		16	11.9	even	5
363.3.h.m.245.1		16	33.17	even	10
363.3.h.m.245.4		16	11.6	odd	10
363.3.h.m.251.1		16	11.8	odd	10
363.3.h.m.251.4		16	33.8	even	10
363.3.h.m.269.1		16	33.29	even	10
363.3.h.m.269.4		16	11.7	odd	10
363.3.h.m.323.1		16	11.2	odd	10
363.3.h.m.323.4		16	33.2	even	10
528.3.i.d.353.3		4	132.131	odd	2
528.3.i.d.353.4		4	44.43	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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.52434i q^{2} +(-2.68614 - 1.33591i) q^{3} -2.37228 q^{4} -0.792287i q^{5} +(3.37228 - 6.78073i) q^{6} -6.74456 q^{7} +4.10891i q^{8} +(5.43070 + 7.17687i) q^{9} +O(q^{10})\)	\(q+2.52434i q^{2} +(-2.68614 - 1.33591i) q^{3} -2.37228 q^{4} -0.792287i q^{5} +(3.37228 - 6.78073i) q^{6} -6.74456 q^{7} +4.10891i q^{8} +(5.43070 + 7.17687i) q^{9} +2.00000 q^{10} +(6.37228 + 3.16915i) q^{12} -9.48913 q^{13} -17.0256i q^{14} +(-1.05842 + 2.12819i) q^{15} -19.8614 q^{16} -29.2974i q^{17} +(-18.1168 + 13.7089i) q^{18} +26.2337 q^{19} +1.87953i q^{20} +(18.1168 + 9.01011i) q^{21} -26.9205i q^{23} +(5.48913 - 11.0371i) q^{24} +24.3723 q^{25} -23.9538i q^{26} +(-5.00000 - 26.5330i) q^{27} +16.0000 q^{28} -25.9431i q^{29} +(-5.37228 - 2.67181i) q^{30} -2.86141 q^{31} -33.7013i q^{32} +73.9565 q^{34} +5.34363i q^{35} +(-12.8832 - 17.0256i) q^{36} -2.39403 q^{37} +66.2227i q^{38} +(25.4891 + 12.6766i) q^{39} +3.25544 q^{40} -17.6155i q^{41} +(-22.7446 + 45.7330i) q^{42} -12.5109 q^{43} +(5.68614 - 4.30268i) q^{45} +67.9565 q^{46} +41.6790i q^{47} +(53.3505 + 26.5330i) q^{48} -3.51087 q^{49} +61.5239i q^{50} +(-39.1386 + 78.6969i) q^{51} +22.5109 q^{52} -89.5865i q^{53} +(66.9783 - 12.6217i) q^{54} -27.7128i q^{56} +(-70.4674 - 35.0458i) q^{57} +65.4891 q^{58} -14.7585i q^{59} +(2.51087 - 5.04868i) q^{60} +63.4456 q^{61} -7.22316i q^{62} +(-36.6277 - 48.4048i) q^{63} +5.62772 q^{64} +7.51811i q^{65} -63.3288 q^{67} +69.5016i q^{68} +(-35.9633 + 72.3123i) q^{69} -13.4891 q^{70} +4.55134i q^{71} +(-29.4891 + 22.3143i) q^{72} +53.7663 q^{73} -6.04334i q^{74} +(-65.4674 - 32.5591i) q^{75} -62.2337 q^{76} +(-32.0000 + 64.3432i) q^{78} -55.6793 q^{79} +15.7359i q^{80} +(-22.0149 + 77.9509i) q^{81} +44.4674 q^{82} -65.3378i q^{83} +(-42.9783 - 21.3745i) q^{84} -23.2119 q^{85} -31.5817i q^{86} +(-34.6576 + 69.6868i) q^{87} +14.1341i q^{89} +(10.8614 + 14.3537i) q^{90} +64.0000 q^{91} +63.8631i q^{92} +(7.68614 + 3.82257i) q^{93} -105.212 q^{94} -20.7846i q^{95} +(-45.0217 + 90.5263i) q^{96} +149.285 q^{97} -8.86263i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} - 7 q^{9}+O(q^{10}) \) 4 * q - 5 * q^3 + 2 * q^4 + 2 * q^6 - 4 * q^7 - 7 * q^9	\( 4 q - 5 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} - 7 q^{9} + 8 q^{10} + 14 q^{12} + 8 q^{13} + 13 q^{15} - 22 q^{16} - 38 q^{18} + 36 q^{19} + 38 q^{21} - 24 q^{24} + 86 q^{25} - 20 q^{27} + 64 q^{28} - 10 q^{30} + 46 q^{31} + 112 q^{34} - 86 q^{36} - 90 q^{37} + 56 q^{39} + 36 q^{40} - 68 q^{42} - 96 q^{43} + 17 q^{45} + 88 q^{46} + 110 q^{48} - 60 q^{49} - 214 q^{51} + 136 q^{52} + 176 q^{54} - 144 q^{57} + 216 q^{58} + 56 q^{60} + 24 q^{61} - 158 q^{63} + 34 q^{64} - 58 q^{67} - 253 q^{69} - 8 q^{70} - 72 q^{72} + 284 q^{73} - 124 q^{75} - 180 q^{76} - 128 q^{78} + 76 q^{79} + 113 q^{81} + 40 q^{82} - 80 q^{84} + 68 q^{85} + 252 q^{87} - 14 q^{90} + 256 q^{91} + 25 q^{93} - 260 q^{94} - 272 q^{96} + 218 q^{97}+O(q^{100}) \) 4 * q - 5 * q^3 + 2 * q^4 + 2 * q^6 - 4 * q^7 - 7 * q^9 + 8 * q^10 + 14 * q^12 + 8 * q^13 + 13 * q^15 - 22 * q^16 - 38 * q^18 + 36 * q^19 + 38 * q^21 - 24 * q^24 + 86 * q^25 - 20 * q^27 + 64 * q^28 - 10 * q^30 + 46 * q^31 + 112 * q^34 - 86 * q^36 - 90 * q^37 + 56 * q^39 + 36 * q^40 - 68 * q^42 - 96 * q^43 + 17 * q^45 + 88 * q^46 + 110 * q^48 - 60 * q^49 - 214 * q^51 + 136 * q^52 + 176 * q^54 - 144 * q^57 + 216 * q^58 + 56 * q^60 + 24 * q^61 - 158 * q^63 + 34 * q^64 - 58 * q^67 - 253 * q^69 - 8 * q^70 - 72 * q^72 + 284 * q^73 - 124 * q^75 - 180 * q^76 - 128 * q^78 + 76 * q^79 + 113 * q^81 + 40 * q^82 - 80 * q^84 + 68 * q^85 + 252 * q^87 - 14 * q^90 + 256 * q^91 + 25 * q^93 - 260 * q^94 - 272 * q^96 + 218 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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