LMFDB - Embedded newform 363.3.b.h.122.2

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			122.2
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	363.122
Dual form			363.3.b.h.122.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.792287i q^{2} +(0.186141 - 2.99422i) q^{3} +3.37228 q^{4} +2.52434i q^{5} +(-2.37228 - 0.147477i) q^{6} +4.74456 q^{7} -5.84096i q^{8} +(-8.93070 - 1.11469i) q^{9} +O(q^{10})$	\(q-0.792287i q^{2} +(0.186141 - 2.99422i) q^{3} +3.37228 q^{4} +2.52434i q^{5} +(-2.37228 - 0.147477i) q^{6} +4.74456 q^{7} -5.84096i q^{8} +(-8.93070 - 1.11469i) q^{9} +2.00000 q^{10} +(0.627719 - 10.0974i) q^{12} +13.4891 q^{13} -3.75906i q^{14} +(7.55842 + 0.469882i) q^{15} +8.86141 q^{16} -22.6641i q^{17} +(-0.883156 + 7.07568i) q^{18} -8.23369 q^{19} +8.51278i q^{20} +(0.883156 - 14.2063i) q^{21} -30.2372i q^{23} +(-17.4891 - 1.08724i) q^{24} +18.6277 q^{25} -10.6873i q^{26} +(-5.00000 + 26.5330i) q^{27} +16.0000 q^{28} +53.6559i q^{29} +(0.372281 - 5.98844i) q^{30} +25.8614 q^{31} -30.3846i q^{32} -17.9565 q^{34} +11.9769i q^{35} +(-30.1168 - 3.75906i) q^{36} -42.6060 q^{37} +6.52344i q^{38} +(2.51087 - 40.3894i) q^{39} +14.7446 q^{40} -30.8820i q^{41} +(-11.2554 - 0.699713i) q^{42} -35.4891 q^{43} +(2.81386 - 22.5441i) q^{45} -23.9565 q^{46} -31.2867i q^{47} +(1.64947 - 26.5330i) q^{48} -26.4891 q^{49} -14.7585i q^{50} +(-67.8614 - 4.21872i) q^{51} +45.4891 q^{52} +9.91220i q^{53} +(21.0217 + 3.96143i) q^{54} -27.7128i q^{56} +(-1.53262 + 24.6535i) q^{57} +42.5109 q^{58} +61.5239i q^{59} +(25.4891 + 1.58457i) q^{60} -51.4456 q^{61} -20.4897i q^{62} +(-42.3723 - 5.28873i) q^{63} +11.3723 q^{64} +34.0511i q^{65} +34.3288 q^{67} -76.4298i q^{68} +(-90.5367 - 5.62836i) q^{69} +9.48913 q^{70} +14.5012i q^{71} +(-6.51087 + 52.1639i) q^{72} +88.2337 q^{73} +33.7562i q^{74} +(3.46738 - 55.7755i) q^{75} -27.7663 q^{76} +(-32.0000 - 1.98933i) q^{78} +93.6793 q^{79} +22.3692i q^{80} +(78.5149 + 19.9100i) q^{81} -24.4674 q^{82} +34.1609i q^{83} +(2.97825 - 47.9075i) q^{84} +57.2119 q^{85} +28.1176i q^{86} +(160.658 + 9.98755i) q^{87} +143.482i q^{89} +(-17.8614 - 2.22938i) q^{90} +64.0000 q^{91} -101.968i q^{92} +(4.81386 - 77.4347i) q^{93} -24.7881 q^{94} -20.7846i q^{95} +(-90.9783 - 5.65581i) q^{96} -40.2853 q^{97} +20.9870i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	0.792287i		−	0.396143i	−0.980188	−	0.198072i	$-0.936532\pi$
$2$		−	0.792287i		−	0.396143i	0.980188	−	0.198072i	$-0.0634679\pi$
$3$	0.186141	−	2.99422i	0.0620469	−	0.998073i
$3$	0.186141	−	2.99422i	0.0620469	−	0.998073i
$4$	3.37228			0.843070
$5$			2.52434i			0.504868i	0.967614	+	0.252434i	$0.0812310\pi$
$5$			2.52434i			0.504868i	−0.967614	+	0.252434i	$0.918769\pi$
$6$	−2.37228	−	0.147477i	−0.395380	−	0.0245795i
$7$	4.74456			0.677795			0.338897	−	0.940823i	$-0.389946\pi$
$7$	4.74456			0.677795			0.338897	+	0.940823i	$0.389946\pi$
$8$		−	5.84096i		−	0.730120i
$9$	−8.93070	−	1.11469i	−0.992300	−	0.123855i
$10$	2.00000			0.200000
$11$		0			0
$11$		0			0
$12$	0.627719	−	10.0974i	0.0523099	−	0.841446i
$13$	13.4891			1.03763			0.518813	−	0.854888i	$-0.326374\pi$
$13$	13.4891			1.03763			0.518813	+	0.854888i	$0.326374\pi$
$14$		−	3.75906i		−	0.268504i
$15$	7.55842	+	0.469882i	0.503895	+	0.0313255i
$16$	8.86141			0.553838
$17$		−	22.6641i		−	1.33318i	−0.745423	−	0.666592i	$-0.767752\pi$
$17$		−	22.6641i		−	1.33318i	0.745423	−	0.666592i	$-0.232248\pi$
$18$	−0.883156	+	7.07568i	−0.0490642	+	0.393093i
$19$	−8.23369			−0.433352			−0.216676	−	0.976244i	$-0.569522\pi$
$19$	−8.23369			−0.433352			−0.216676	+	0.976244i	$0.569522\pi$
$20$			8.51278i			0.425639i
$21$	0.883156	−	14.2063i	0.0420550	−	0.676489i
$22$		0			0
$23$		−	30.2372i		−	1.31466i	−0.753603	−	0.657329i	$-0.771686\pi$
$23$		−	30.2372i		−	1.31466i	0.753603	−	0.657329i	$-0.228314\pi$
$24$	−17.4891	−	1.08724i	−0.728714	−	0.0453017i
$25$	18.6277			0.745109
$26$		−	10.6873i		−	0.411048i
$27$	−5.00000	+	26.5330i	−0.185185	+	0.982704i
$28$	16.0000			0.571429
$29$			53.6559i			1.85020i	0.379719	+	0.925102i	$0.376021\pi$
$29$			53.6559i			1.85020i	−0.379719	+	0.925102i	$0.623979\pi$
$30$	0.372281	−	5.98844i	0.0124094	−	0.199615i
$31$	25.8614			0.834239			0.417119	−	0.908852i	$-0.363040\pi$
$31$	25.8614			0.834239			0.417119	+	0.908852i	$0.363040\pi$
$32$		−	30.3846i		−	0.949520i
$33$		0			0
$34$	−17.9565			−0.528132
$35$			11.9769i			0.342197i
$36$	−30.1168	−	3.75906i	−0.836579	−	0.104418i
$37$	−42.6060			−1.15151			−0.575756	−	0.817621i	$-0.695292\pi$
$37$	−42.6060			−1.15151			−0.575756	+	0.817621i	$0.695292\pi$
$38$			6.52344i			0.171670i
$39$	2.51087	−	40.3894i	0.0643814	−	1.03563i
$40$	14.7446			0.368614
$41$		−	30.8820i		−	0.753219i	−0.926372	−	0.376609i	$-0.877090\pi$
$41$		−	30.8820i		−	0.753219i	0.926372	−	0.376609i	$-0.122910\pi$
$42$	−11.2554	−	0.699713i	−0.267987	−	0.0166598i
$43$	−35.4891			−0.825328			−0.412664	−	0.910883i	$-0.635402\pi$
$43$	−35.4891			−0.825328			−0.412664	+	0.910883i	$0.635402\pi$
$44$		0			0
$45$	2.81386	−	22.5441i	0.0625302	−	0.500980i
$46$	−23.9565			−0.520794
$47$		−	31.2867i		−	0.665675i	−0.942984	−	0.332837i	$-0.891994\pi$
$47$		−	31.2867i		−	0.665675i	0.942984	−	0.332837i	$-0.108006\pi$
$48$	1.64947	−	26.5330i	0.0343639	−	0.552771i
$49$	−26.4891			−0.540594
$50$		−	14.7585i		−	0.295170i
$51$	−67.8614	−	4.21872i	−1.33062	−	0.0827200i
$52$	45.4891			0.874791
$53$			9.91220i			0.187023i	0.995618	+	0.0935114i	$0.0298091\pi$
$53$			9.91220i			0.187023i	−0.995618	+	0.0935114i	$0.970191\pi$
$54$	21.0217	+	3.96143i	0.389292	+	0.0733599i
$55$		0			0
$56$		−	27.7128i		−	0.494872i
$57$	−1.53262	+	24.6535i	−0.0268881	+	0.432517i
$58$	42.5109			0.732946
$59$			61.5239i			1.04278i	0.853319	+	0.521389i	$0.174586\pi$
$59$			61.5239i			1.04278i	−0.853319	+	0.521389i	$0.825414\pi$
$60$	25.4891	+	1.58457i	0.424819	+	0.0264096i
$61$	−51.4456			−0.843371			−0.421685	−	0.906742i	$-0.638561\pi$
$61$	−51.4456			−0.843371			−0.421685	+	0.906742i	$0.638561\pi$
$62$		−	20.4897i		−	0.330478i
$63$	−42.3723	−	5.28873i	−0.672576	−	0.0839480i
$64$	11.3723			0.177692
$65$			34.0511i			0.523863i
$66$		0			0
$67$	34.3288			0.512370			0.256185	−	0.966628i	$-0.417534\pi$
$67$	34.3288			0.512370			0.256185	+	0.966628i	$0.417534\pi$
$68$		−	76.4298i		−	1.12397i
$69$	−90.5367	−	5.62836i	−1.31213	−	0.0815705i
$70$	9.48913			0.135559
$71$			14.5012i			0.204242i	0.994772	+	0.102121i	$0.0325630\pi$
$71$			14.5012i			0.204242i	−0.994772	+	0.102121i	$0.967437\pi$
$72$	−6.51087	+	52.1639i	−0.0904288	+	0.724499i
$73$	88.2337			1.20868			0.604340	−	0.796726i	$-0.293437\pi$
$73$	88.2337			1.20868			0.604340	+	0.796726i	$0.293437\pi$
$74$			33.7562i			0.456164i
$75$	3.46738	−	55.7755i	0.0462317	−	0.743673i
$76$	−27.7663			−0.365346
$77$		0			0
$78$	−32.0000	−	1.98933i	−0.410256	−	0.0255043i
$79$	93.6793			1.18581			0.592907	−	0.805271i	$-0.297980\pi$
$79$	93.6793			1.18581			0.592907	+	0.805271i	$0.297980\pi$
$80$			22.3692i			0.279615i
$81$	78.5149	+	19.9100i	0.969320	+	0.245802i
$82$	−24.4674			−0.298383
$83$			34.1609i			0.411577i	0.978596	+	0.205789i	$0.0659759\pi$
$83$			34.1609i			0.411577i	−0.978596	+	0.205789i	$0.934024\pi$
$84$	2.97825	−	47.9075i	0.0354554	−	0.570328i
$85$	57.2119			0.673082
$86$			28.1176i			0.326949i
$87$	160.658	+	9.98755i	1.84664	+	0.114799i
$88$		0			0
$89$			143.482i			1.61216i	0.591805	+	0.806081i	$0.298416\pi$
$89$			143.482i			1.61216i	−0.591805	+	0.806081i	$0.701584\pi$
$90$	−17.8614	−	2.22938i	−0.198460	−	0.0247709i
$91$	64.0000			0.703297
$92$		−	101.968i		−	1.10835i
$93$	4.81386	−	77.4347i	0.0517619	−	0.832632i
$94$	−24.7881			−0.263703
$95$		−	20.7846i		−	0.218785i
$96$	−90.9783	−	5.65581i	−0.947690	−	0.0589147i
$97$	−40.2853			−0.415312			−0.207656	−	0.978202i	$-0.566583\pi$
$97$	−40.2853			−0.415312			−0.207656	+	0.978202i	$0.566583\pi$
$98$			20.9870i			0.214153i
$99$		0			0
$100$	62.8179			0.628179
$101$			92.7557i			0.918373i	0.888340	+	0.459187i	$0.151859\pi$
$101$			92.7557i			0.918373i	−0.888340	+	0.459187i	$0.848141\pi$
$102$	−3.34244	+	53.7657i	−0.0327690	+	0.527115i
$103$	−19.5761			−0.190059			−0.0950297	−	0.995474i	$-0.530295\pi$
$103$	−19.5761			−0.190059			−0.0950297	+	0.995474i	$0.530295\pi$
$104$		−	78.7895i		−	0.757591i
$105$	35.8614	+	2.22938i	0.341537	+	0.0212322i
$106$	7.85331			0.0740878
$107$			84.4281i			0.789047i	0.918886	+	0.394524i	$0.129090\pi$
$107$			84.4281i			0.789047i	−0.918886	+	0.394524i	$0.870910\pi$
$108$	−16.8614	+	89.4767i	−0.156124	+	0.828488i
$109$	−167.723			−1.53874			−0.769371	−	0.638803i	$-0.779430\pi$
$109$	−167.723			−1.53874			−0.769371	+	0.638803i	$0.779430\pi$
$110$		0			0
$111$	−7.93070	+	127.572i	−0.0714478	+	1.14929i
$112$	42.0435			0.375388
$113$			123.507i			1.09299i	0.837464	+	0.546493i	$0.184037\pi$
$113$			123.507i			1.09299i	−0.837464	+	0.546493i	$0.815963\pi$
$114$	19.5326	+	1.21428i	0.171339	+	0.0106516i
$115$	76.3288			0.663729
$116$			180.943i			1.55985i
$117$	−120.467	−	15.0362i	−1.02964	−	0.128515i
$118$	48.7446			0.413090
$119$		−	107.531i		−	0.903625i
$120$	2.74456	−	44.1485i	0.0228714	−	0.367904i
$121$		0			0
$122$			40.7597i			0.334096i
$123$	−92.4674	−	5.74839i	−0.751767	−	0.0467349i
$124$	87.2119			0.703322
$125$			110.131i			0.881049i
$126$	−4.19019	+	33.5710i	−0.0332555	+	0.266437i
$127$	128.848			1.01455			0.507275	−	0.861784i	$-0.330653\pi$
$127$	128.848			1.01455			0.507275	+	0.861784i	$0.330653\pi$
$128$		−	130.549i		−	1.01991i
$129$	−6.60597	+	106.262i	−0.0512091	+	0.823738i
$130$	26.9783			0.207525
$131$			125.997i			0.961811i	0.876772	+	0.480906i	$0.159692\pi$
$131$			125.997i			0.961811i	−0.876772	+	0.480906i	$0.840308\pi$
$132$		0			0
$133$	−39.0652			−0.293724
$134$		−	27.1982i		−	0.202972i
$135$	−66.9783	−	12.6217i	−0.496135	−	0.0934940i
$136$	−132.380			−0.973385
$137$		−	59.3149i		−	0.432956i	−0.976288	−	0.216478i	$-0.930543\pi$
$137$		−	59.3149i		−	0.432956i	0.976288	−	0.216478i	$-0.0694569\pi$
$138$	−4.45928	+	71.7310i	−0.0323136	+	0.519790i
$139$	130.935			0.941977			0.470988	−	0.882139i	$-0.343897\pi$
$139$	130.935			0.941977			0.470988	+	0.882139i	$0.343897\pi$
$140$			40.3894i			0.288496i
$141$	−93.6793	−	5.82373i	−0.664392	−	0.0413031i
$142$	11.4891			0.0809093
$143$		0			0
$144$	−79.1386	−	9.87774i	−0.549574	−	0.0685954i
$145$	−135.446			−0.934108
$146$		−	69.9064i		−	0.478811i
$147$	−4.93070	+	79.3143i	−0.0335422	+	0.539553i
$148$	−143.679			−0.970806
$149$		−	74.3307i		−	0.498864i	−0.968392	−	0.249432i	$-0.919756\pi$
$149$		−	74.3307i		−	0.498864i	0.968392	−	0.249432i	$-0.0802439\pi$
$150$	−44.1902	−	2.74716i	−0.294601	−	0.0183144i
$151$	6.23369			0.0412827			0.0206414	−	0.999787i	$-0.493429\pi$
$151$	6.23369			0.0412827			0.0206414	+	0.999787i	$0.493429\pi$
$152$			48.0927i			0.316399i
$153$	−25.2635	+	202.407i	−0.165121	+	1.32292i
$154$		0			0
$155$			65.2829i			0.421180i
$156$	8.46738	−	136.204i	0.0542781	−	0.873105i
$157$	98.7962			0.629275			0.314637	−	0.949212i	$-0.398117\pi$
$157$	98.7962			0.629275			0.314637	+	0.949212i	$0.398117\pi$
$158$		−	74.2209i		−	0.469753i
$159$	29.6793	+	1.84506i	0.186662	+	0.0116042i
$160$	76.7011			0.479382
$161$		−	143.462i		−	0.891069i
$162$	15.7744	−	62.2064i	0.0973729	−	0.383990i
$163$	207.870			1.27527			0.637637	−	0.770337i	$-0.279912\pi$
$163$	207.870			1.27527			0.637637	+	0.770337i	$0.279912\pi$
$164$		−	104.143i		−	0.635016i
$165$		0			0
$166$	27.0652			0.163044
$167$			63.1633i			0.378224i	0.981956	+	0.189112i	$0.0605609\pi$
$167$			63.1633i			0.378224i	−0.981956	+	0.189112i	$0.939439\pi$
$168$	−82.9783	−	5.15848i	−0.493918	−	0.0307052i
$169$	12.9565			0.0766657
$170$		−	45.3283i		−	0.266637i
$171$	73.5326	+	9.17803i	0.430015	+	0.0536727i
$172$	−119.679			−0.695810
$173$		−	193.359i		−	1.11768i	−0.829275	−	0.558841i	$-0.811246\pi$
$173$		−	193.359i		−	1.11768i	0.829275	−	0.558841i	$-0.188754\pi$
$174$	7.91300	−	127.287i	0.0454770	−	0.731534i
$175$	88.3804			0.505031
$176$		0			0
$177$	184.216	+	11.4521i	1.04077	+	0.0647011i
$178$	113.679			0.638648
$179$		−	31.0122i		−	0.173253i	−0.996241	−	0.0866263i	$-0.972391\pi$
$179$		−	31.0122i		−	0.173253i	0.996241	−	0.0866263i	$-0.0276086\pi$
$180$	9.48913	−	76.0251i	0.0527174	−	0.422362i
$181$	102.139			0.564302			0.282151	−	0.959370i	$-0.408952\pi$
$181$	102.139			0.564302			0.282151	+	0.959370i	$0.408952\pi$
$182$		−	50.7064i		−	0.278606i
$183$	−9.57612	+	154.040i	−0.0523285	+	0.841746i
$184$	−176.614			−0.959859
$185$		−	107.552i		−	0.581361i
$186$	−61.3505	−	3.81396i	−0.329842	−	0.0205052i
$187$		0			0
$188$		−	105.508i		−	0.561211i
$189$	−23.7228	+	125.887i	−0.125518	+	0.666071i
$190$	−16.4674			−0.0866704
$191$			69.4876i			0.363810i	0.983316	+	0.181905i	$0.0582263\pi$
$191$			69.4876i			0.363810i	−0.983316	+	0.181905i	$0.941774\pi$
$192$	2.11684	−	34.0511i	0.0110252	−	0.177350i
$193$	−271.505			−1.40676			−0.703382	−	0.710812i	$-0.748327\pi$
$193$	−271.505			−1.40676			−0.703382	+	0.710812i	$0.748327\pi$
$194$			31.9175i			0.164523i
$195$	101.957	+	6.33830i	0.522854	+	0.0325041i
$196$	−89.3288			−0.455759
$197$		−	106.612i		−	0.541178i	−0.962695	−	0.270589i	$-0.912782\pi$
$197$		−	106.612i		−	0.541178i	0.962695	−	0.270589i	$-0.0872185\pi$
$198$		0			0
$199$	−289.272			−1.45363			−0.726813	−	0.686835i	$-0.758999\pi$
$199$	−289.272			−1.45363			−0.726813	+	0.686835i	$0.758999\pi$
$200$		−	108.804i		−	0.544019i
$201$	6.38998	−	102.788i	0.0317910	−	0.511383i
$202$	73.4891			0.363808
$203$			254.574i			1.25406i
$204$	−228.848	−	14.2267i	−1.12180	−	0.0697387i
$205$	77.9565			0.380276
$206$			15.5099i			0.0752908i
$207$	−33.7051	+	270.039i	−0.162827	+	1.30454i
$208$	119.533			0.574676
$209$		0			0
$210$	1.76631	−	28.4125i	0.00841101	−	0.135298i
$211$	187.212			0.887260			0.443630	−	0.896210i	$-0.353690\pi$
$211$	187.212			0.887260			0.443630	+	0.896210i	$0.353690\pi$
$212$			33.4267i			0.157673i
$213$	43.4198	+	2.69927i	0.203849	+	0.0126726i
$214$	66.8913			0.312576
$215$		−	89.5865i		−	0.416682i
$216$	154.978	+	29.2048i	0.717492	+	0.135207i
$217$	122.701			0.565443
$218$			132.885i			0.609562i
$219$	16.4239	−	264.191i	0.0749949	−	1.20635i
$220$		0			0
$221$		−	305.719i		−	1.38335i
$222$	101.073	+	6.28339i	0.455285	+	0.0283036i
$223$	−227.731			−1.02121			−0.510607	−	0.859814i	$-0.670579\pi$
$223$	−227.731			−1.02121			−0.510607	+	0.859814i	$0.670579\pi$
$224$		−	144.162i		−	0.643579i
$225$	−166.359	−	20.7642i	−0.739372	−	0.0922852i
$226$	97.8533			0.432979
$227$			426.339i			1.87814i	0.343721	+	0.939072i	$0.388312\pi$
$227$			426.339i			1.87814i	−0.343721	+	0.939072i	$0.611688\pi$
$228$	−5.16844	+	83.1384i	−0.0226686	+	0.364642i
$229$	−101.584			−0.443599			−0.221800	−	0.975092i	$-0.571193\pi$
$229$	−101.584			−0.443599			−0.221800	+	0.975092i	$0.571193\pi$
$230$		−	60.4743i		−	0.262932i
$231$		0			0
$232$	313.402			1.35087
$233$			173.205i			0.743369i	0.928359	+	0.371685i	$0.121220\pi$
$233$			173.205i			0.743369i	−0.928359	+	0.371685i	$0.878780\pi$
$234$	−11.9130	+	95.4447i	−0.0509103	+	0.407883i
$235$	78.9783			0.336078
$236$			207.476i			0.879135i
$237$	17.4375	−	280.496i	0.0735761	−	1.18353i
$238$	−85.1957			−0.357965
$239$			161.297i			0.674883i	0.941346	+	0.337442i	$0.109562\pi$
$239$			161.297i			0.674883i	−0.941346	+	0.337442i	$0.890438\pi$
$240$	66.9783	+	4.16381i	0.279076	+	0.0173492i
$241$	56.7011			0.235274			0.117637	−	0.993057i	$-0.462468\pi$
$241$	56.7011			0.235274			0.117637	+	0.993057i	$0.462468\pi$
$242$		0			0
$243$	74.2296	−	231.385i	0.305472	−	0.952201i
$244$	−173.489			−0.711021
$245$		−	66.8675i		−	0.272929i
$246$	−4.55437	+	73.2607i	−0.0185137	+	0.297808i
$247$	−111.065			−0.449657
$248$		−	151.056i		−	0.609095i
$249$	102.285	+	6.35874i	0.410784	+	0.0255371i
$250$	87.2554			0.349022
$251$		−	67.4919i		−	0.268892i	−0.990921	−	0.134446i	$-0.957075\pi$
$251$		−	67.4919i		−	0.268892i	0.990921	−	0.134446i	$-0.0429255\pi$
$252$	−142.891	−	17.8351i	−0.567029	−	0.0707741i
$253$		0			0
$254$		−	102.084i		−	0.401907i
$255$	10.6495	−	171.305i	0.0417626	−	0.671785i
$256$	−57.9428			−0.226339
$257$		−	146.672i		−	0.570708i	−0.958422	−	0.285354i	$-0.907889\pi$
$257$		−	146.672i		−	0.570708i	0.958422	−	0.285354i	$-0.0921112\pi$
$258$	84.1902	+	5.23382i	0.326319	+	0.0202861i
$259$	−202.147			−0.780489
$260$			114.830i			0.441654i
$261$	59.8098	−	479.185i	0.229156	−	1.83596i
$262$	99.8260			0.381015
$263$		−	146.192i		−	0.555863i	−0.960601	−	0.277932i	$-0.910351\pi$
$263$		−	146.192i		−	0.555863i	0.960601	−	0.277932i	$-0.0896488\pi$
$264$		0			0
$265$	−25.0217			−0.0944217
$266$			30.9509i			0.116357i
$267$	429.618	+	26.7079i	1.60906	+	0.100030i
$268$	115.766			0.431964
$269$		−	57.0102i		−	0.211934i	−0.994370	−	0.105967i	$-0.966206\pi$
$269$		−	57.0102i		−	0.211934i	0.994370	−	0.105967i	$-0.0337938\pi$
$270$	−10.0000	+	53.0660i	−0.0370370	+	0.196541i
$271$	−128.380			−0.473728			−0.236864	−	0.971543i	$-0.576120\pi$
$271$	−128.380			−0.473728			−0.236864	+	0.971543i	$0.576120\pi$
$272$		−	200.836i		−	0.738368i
$273$	11.9130	−	191.630i	0.0436374	−	0.701942i
$274$	−46.9944			−0.171513
$275$		0			0
$276$	−305.315	−	18.9804i	−1.10621	−	0.0687697i
$277$	−236.277			−0.852986			−0.426493	−	0.904491i	$-0.640251\pi$
$277$	−236.277			−0.852986			−0.426493	+	0.904491i	$0.640251\pi$
$278$		−	103.738i		−	0.373158i
$279$	−230.961	−	28.8275i	−0.827816	−	0.103324i
$280$	69.9565			0.249845
$281$		−	203.977i		−	0.725898i	−0.931809	−	0.362949i	$-0.881770\pi$
$281$		−	203.977i		−	0.725898i	0.931809	−	0.362949i	$-0.118230\pi$
$282$	−4.61407	+	74.2209i	−0.0163619	+	0.263195i
$283$	−479.212			−1.69333			−0.846664	−	0.532128i	$-0.821393\pi$
$283$	−479.212			−1.69333			−0.846664	+	0.532128i	$0.821393\pi$
$284$			48.9022i			0.172191i
$285$	−62.2337	−	3.86886i	−0.218364	−	0.0135750i
$286$		0			0
$287$		−	146.521i		−	0.510528i
$288$	−33.8695	+	271.356i	−0.117602	+	0.942209i
$289$	−224.663			−0.777381
$290$			107.312i			0.370041i
$291$	−7.49873	+	120.623i	−0.0257688	+	0.414512i
$292$	297.549			1.01900
$293$			9.35676i			0.0319343i	0.999873	+	0.0159672i	$0.00508272\pi$
$293$			9.35676i			0.0319343i	−0.999873	+	0.0159672i	$0.994917\pi$
$294$	62.8397	+	3.90653i	0.213740	+	0.0132875i
$295$	−155.307			−0.526465
$296$			248.860i			0.840743i
$297$		0			0
$298$	−58.8913			−0.197622
$299$		−	407.873i		−	1.36412i
$300$	11.6930	−	188.091i	0.0389766	−	0.626969i
$301$	−168.380			−0.559403
$302$		−	4.93887i		−	0.0163539i
$303$	277.731	+	17.2656i	0.916604	+	0.0569822i
$304$	−72.9621			−0.240007
$305$		−	129.866i		−	0.425791i
$306$	160.364	+	20.0160i	0.524066	+	0.0654117i
$307$	−72.5271			−0.236245			−0.118122	−	0.992999i	$-0.537687\pi$
$307$	−72.5271			−0.236245			−0.118122	+	0.992999i	$0.537687\pi$
$308$		0			0
$309$	−3.64391	+	58.6152i	−0.0117926	+	0.189693i
$310$	51.7228			0.166848
$311$		−	380.646i		−	1.22394i	−0.790880	−	0.611972i	$-0.790377\pi$
$311$		−	380.646i		−	1.22394i	0.790880	−	0.611972i	$-0.209623\pi$
$312$	−235.913	−	14.6659i	−0.756131	−	0.0470062i
$313$	53.1007			0.169651			0.0848253	−	0.996396i	$-0.472967\pi$
$313$	53.1007			0.169651			0.0848253	+	0.996396i	$0.472967\pi$
$314$		−	78.2749i		−	0.249283i
$315$	13.3505	−	106.962i	0.0423826	−	0.339562i
$316$	315.913			0.999725
$317$			73.2467i			0.231062i	0.993304	+	0.115531i	$0.0368570\pi$
$317$			73.2467i			0.231062i	−0.993304	+	0.115531i	$0.963143\pi$
$318$	1.46182	−	23.5145i	0.00459692	−	0.0739451i
$319$		0			0
$320$			28.7075i			0.0897109i
$321$	252.796	+	15.7155i	0.787527	+	0.0489579i
$322$	−113.663			−0.352991
$323$			186.609i			0.577738i
$324$	264.774	+	67.1420i	0.817205	+	0.207228i
$325$	251.272			0.773143
$326$		−	164.692i		−	0.505191i
$327$	−31.2200	+	502.199i	−0.0954741	+	1.53578i
$328$	−180.380			−0.549940
$329$		−	148.442i		−	0.451191i
$330$		0			0
$331$	−167.351			−0.505591			−0.252795	−	0.967520i	$-0.581350\pi$
$331$	−167.351			−0.505591			−0.252795	+	0.967520i	$0.581350\pi$
$332$			115.200i			0.346989i
$333$	380.501	+	47.4925i	1.14265	+	0.142620i
$334$	50.0435			0.149831
$335$			86.6574i			0.258679i
$336$	7.82600	−	125.887i	0.0232917	−	0.374665i
$337$	−429.272			−1.27380			−0.636902	−	0.770945i	$-0.719784\pi$
$337$	−429.272			−1.27380			−0.636902	+	0.770945i	$0.719784\pi$
$338$		−	10.2653i		−	0.0303706i
$339$	369.808	+	22.9897i	1.09088	+	0.0678164i
$340$	192.935			0.567455
$341$		0			0
$342$	7.27163	−	58.2589i	0.0212621	−	0.170348i
$343$	−358.163			−1.04421
$344$			207.291i			0.602589i
$345$	14.2079	−	228.545i	0.0411823	−	0.662450i
$346$	−153.196			−0.442762
$347$			515.335i			1.48512i	0.669782	+	0.742558i	$0.266388\pi$
$347$			515.335i			1.48512i	−0.669782	+	0.742558i	$0.733612\pi$
$348$	541.783	+	33.6808i	1.55685	+	0.0967839i
$349$	−280.016			−0.802339			−0.401169	−	0.916004i	$-0.631396\pi$
$349$	−280.016			−0.802339			−0.401169	+	0.916004i	$0.631396\pi$
$350$		−	70.0226i		−	0.200065i
$351$	−67.4456	+	357.907i	−0.192153	+	1.01968i
$352$		0			0
$353$			373.911i			1.05924i	0.848236	+	0.529619i	$0.177665\pi$
$353$			373.911i			1.05924i	−0.848236	+	0.529619i	$0.822335\pi$
$354$	9.07335	−	145.952i	0.0256309	−	0.412294i
$355$	−36.6060			−0.103115
$356$			483.863i			1.35917i
$357$	−321.973	−	20.0160i	−0.901884	−	0.0560671i
$358$	−24.5706			−0.0686329
$359$		−	108.862i		−	0.303237i	−0.988439	−	0.151618i	$-0.951552\pi$
$359$		−	108.862i		−	0.303237i	0.988439	−	0.151618i	$-0.0484484\pi$
$360$	−131.679	−	16.4356i	−0.365776	−	0.0456546i
$361$	−293.206			−0.812206
$362$		−	80.9231i		−	0.223544i
$363$		0			0
$364$	215.826			0.592929
$365$			222.732i			0.610224i
$366$	122.043	+	7.58704i	0.333452	+	0.0207296i
$367$	477.965			1.30236			0.651178	−	0.758925i	$-0.274275\pi$
$367$	477.965			1.30236			0.651178	+	0.758925i	$0.274275\pi$
$368$		−	267.944i		−	0.728108i
$369$	−34.4239	+	275.798i	−0.0932896	+	0.747419i
$370$	−85.2119			−0.230303
$371$			47.0291i			0.126763i
$372$	16.2337	−	261.132i	0.0436389	−	0.701967i
$373$	207.081			0.555178			0.277589	−	0.960700i	$-0.410465\pi$
$373$	207.081			0.555178			0.277589	+	0.960700i	$0.410465\pi$
$374$		0			0
$375$	329.757	+	20.4999i	0.879351	+	0.0546663i
$376$	−182.745			−0.486023
$377$			723.771i			1.91982i
$378$	99.7390	+	18.7953i	0.263860	+	0.0497230i
$379$	310.606			0.819541			0.409770	−	0.912189i	$-0.365609\pi$
$379$	310.606			0.819541			0.409770	+	0.912189i	$0.365609\pi$
$380$		−	70.0916i		−	0.184451i
$381$	23.9838	−	385.798i	0.0629496	−	1.01259i
$382$	55.0541			0.144121
$383$			359.869i			0.939607i	0.882771	+	0.469803i	$0.155675\pi$
$383$			359.869i			0.939607i	−0.882771	+	0.469803i	$0.844325\pi$
$384$	−390.891	−	24.3004i	−1.01795	−	0.0632823i
$385$		0			0
$386$			215.110i			0.557280i
$387$	316.943	+	39.5594i	0.818974	+	0.102221i
$388$	−135.853			−0.350137
$389$		−	624.541i		−	1.60550i	−0.596314	−	0.802751i	$-0.703369\pi$
$389$		−	624.541i		−	1.60550i	0.596314	−	0.802751i	$-0.296631\pi$
$390$	5.02175	−	80.7788i	0.0128763	−	0.207125i
$391$	−685.299			−1.75268
$392$			154.722i			0.394699i
$393$	377.264	+	23.4532i	0.959958	+	0.0596774i
$394$	−84.4674			−0.214384
$395$			236.478i			0.598679i
$396$		0			0
$397$	−78.7284			−0.198308			−0.0991541	−	0.995072i	$-0.531614\pi$
$397$	−78.7284			−0.198308			−0.0991541	+	0.995072i	$0.531614\pi$
$398$			229.186i			0.575845i
$399$	−7.27163	+	116.970i	−0.0182246	+	0.293158i
$400$	165.068			0.412669
$401$		−	790.104i		−	1.97033i	−0.171600	−	0.985167i	$-0.554894\pi$
$401$		−	790.104i		−	1.97033i	0.171600	−	0.985167i	$-0.445106\pi$
$402$	−81.4375	−	5.06270i	−0.202581	−	0.0125938i
$403$	348.848			0.865627
$404$			312.798i			0.774253i
$405$	−50.2595	+	198.198i	−0.124097	+	0.489378i
$406$	201.696			0.496787
$407$		0			0
$408$	−24.6414	+	396.376i	−0.0603955	+	0.971510i
$409$	507.696			1.24131			0.620655	−	0.784084i	$-0.286867\pi$
$409$	507.696			1.24131			0.620655	+	0.784084i	$0.286867\pi$
$410$		−	61.7639i		−	0.150644i
$411$	−177.602	−	11.0409i	−0.432121	−	0.0268636i
$412$	−66.0162			−0.160233
$413$			291.904i			0.706789i
$414$	213.948	+	26.7041i	0.516784	+	0.0645027i
$415$	−86.2337			−0.207792
$416$		−	409.862i		−	0.985245i
$417$	24.3723	−	392.047i	0.0584467	−	0.940162i
$418$		0			0
$419$			334.392i			0.798073i	0.916935	+	0.399036i	$0.130655\pi$
$419$			334.392i			0.798073i	−0.916935	+	0.399036i	$0.869345\pi$
$420$	120.935	+	7.51811i	0.287940	+	0.0179003i
$421$	−443.315			−1.05301			−0.526503	−	0.850174i	$-0.676497\pi$
$421$	−443.315			−1.05301			−0.526503	+	0.850174i	$0.676497\pi$
$422$		−	148.326i		−	0.351482i
$423$	−34.8751	+	279.412i	−0.0824469	+	0.660549i
$424$	57.8968			0.136549
$425$		−	422.181i		−	0.993367i
$426$	2.13859	−	34.4010i	0.00502017	−	0.0807534i
$427$	−244.087			−0.571632
$428$			284.715i			0.665222i
$429$		0			0
$430$	−70.9783			−0.165066
$431$		−	795.303i		−	1.84525i	−0.385697	−	0.922625i	$-0.626039\pi$
$431$		−	795.303i		−	1.84525i	0.385697	−	0.922625i	$-0.373961\pi$
$432$	−44.3070	+	235.120i	−0.102563	+	0.544259i
$433$	−18.6222			−0.0430073			−0.0215037	−	0.999769i	$-0.506845\pi$
$433$	−18.6222			−0.0430073			−0.0215037	+	0.999769i	$0.506845\pi$
$434$		−	97.2145i		−	0.223996i
$435$	−25.2119	+	405.554i	−0.0579585	+	0.932308i
$436$	−565.609			−1.29727
$437$			248.963i			0.569710i
$438$	−209.315	−	13.0124i	−0.477888	−	0.0297087i
$439$	254.891			0.580618			0.290309	−	0.956933i	$-0.406242\pi$
$439$	254.891			0.580618			0.290309	+	0.956933i	$0.406242\pi$
$440$		0			0
$441$	236.567	+	29.5272i	0.536432	+	0.0669551i
$442$	−242.217			−0.548003
$443$		−	61.5519i		−	0.138943i	−0.997584	−	0.0694717i	$-0.977869\pi$
$443$		−	61.5519i		−	0.138943i	0.997584	−	0.0694717i	$-0.0221314\pi$
$444$	−26.7446	+	430.207i	−0.0602355	+	0.968936i
$445$	−362.198			−0.813929
$446$			180.428i			0.404548i
$447$	−222.562	−	13.8360i	−0.497903	−	0.0309529i
$448$	53.9565			0.120439
$449$			137.433i			0.306086i	0.988220	+	0.153043i	$0.0489073\pi$
$449$			137.433i			0.306086i	−0.988220	+	0.153043i	$0.951093\pi$
$450$	−16.4512	+	131.804i	−0.0365582	+	0.292897i
$451$		0			0
$452$			416.502i			0.921464i
$453$	1.16034	−	18.6650i	0.00256146	−	0.0412032i
$454$	337.783			0.744014
$455$			161.558i			0.355072i
$456$	144.000	+	8.95200i	0.315789	+	0.0196316i
$457$	307.592			0.673069			0.336534	−	0.941671i	$-0.390745\pi$
$457$	307.592			0.673069			0.336534	+	0.941671i	$0.390745\pi$
$458$			80.4839i			0.175729i
$459$	601.348	+	113.321i	1.31013	+	0.246886i
$460$	257.402			0.559570
$461$			528.162i			1.14569i	0.819664	+	0.572844i	$0.194160\pi$
$461$			528.162i			1.14569i	−0.819664	+	0.572844i	$0.805840\pi$
$462$		0			0
$463$	−45.9484			−0.0992406			−0.0496203	−	0.998768i	$-0.515801\pi$
$463$	−45.9484			−0.0992406			−0.0496203	+	0.998768i	$0.515801\pi$
$464$			475.467i			1.02471i
$465$	195.471	+	12.1518i	0.420369	+	0.0261329i
$466$	137.228			0.294481
$467$			359.066i			0.768879i	0.923150	+	0.384439i	$0.125605\pi$
$467$			359.066i			0.768879i	−0.923150	+	0.384439i	$0.874395\pi$
$468$	−406.250	−	50.7064i	−0.868055	−	0.108347i
$469$	162.875			0.347282
$470$		−	62.5734i		−	0.133135i
$471$	18.3900	−	295.817i	0.0390445	−	0.628062i
$472$	359.359			0.761353
$473$		0			0
$474$	−222.234	−	13.8155i	−0.468847	−	0.0291467i
$475$	−153.375			−0.322894
$476$		−	362.626i		−	0.761820i
$477$	11.0491	−	88.5229i	0.0231636	−	0.185583i
$478$	127.794			0.267351
$479$			577.400i			1.20543i	0.797957	+	0.602715i	$0.205914\pi$
$479$			577.400i			1.20543i	−0.797957	+	0.602715i	$0.794086\pi$
$480$	14.2772	−	229.660i	0.0297441	−	0.478458i
$481$	−574.717			−1.19484
$482$		−	44.9235i		−	0.0932023i
$483$	−429.557	−	26.7041i	−0.889352	−	0.0552880i
$484$		0			0
$485$		−	101.694i		−	0.209678i
$486$	−183.323	−	58.8112i	−0.377208	−	0.121011i
$487$	−606.899			−1.24620			−0.623100	−	0.782142i	$-0.714127\pi$
$487$	−606.899			−1.24620			−0.623100	+	0.782142i	$0.714127\pi$
$488$			300.492i			0.615762i
$489$	38.6930	−	622.407i	0.0791267	−	1.27282i
$490$	−52.9783			−0.108119
$491$		−	768.867i		−	1.56592i	−0.622072	−	0.782960i	$-0.713709\pi$
$491$		−	768.867i		−	1.56592i	0.622072	−	0.782960i	$-0.286291\pi$
$492$	−311.826	−	19.3852i	−0.633793	−	0.0394008i
$493$	1216.06			2.46666
$494$			87.9956i			0.178129i
$495$		0			0
$496$	229.168			0.462033
$497$			68.8019i			0.138434i
$498$	5.03794	−	81.0393i	0.0101164	−	0.162730i
$499$	−498.032			−0.998061			−0.499030	−	0.866584i	$-0.666310\pi$
$499$	−498.032			−0.998061			−0.499030	+	0.866584i	$0.666310\pi$
$500$			371.393i			0.742786i
$501$	189.125	+	11.7573i	0.377495	+	0.0234676i
$502$	−53.4729			−0.106520
$503$			170.516i			0.338998i	0.985530	+	0.169499i	$0.0542150\pi$
$503$			170.516i			0.338998i	−0.985530	+	0.169499i	$0.945785\pi$
$504$	−30.8913	+	247.495i	−0.0612922	+	0.491061i
$505$	−234.147			−0.463657
$506$		0			0
$507$	2.41173	−	38.7946i	0.00475687	−	0.0765180i
$508$	434.511			0.855336
$509$			412.798i			0.810997i	0.914096	+	0.405499i	$0.132902\pi$
$509$			412.798i			0.810997i	−0.914096	+	0.405499i	$0.867098\pi$
$510$	−135.723	−	8.43744i	−0.266123	−	0.0165440i
$511$	418.630			0.819237
$512$		−	476.287i		−	0.930248i
$513$	41.1684	−	218.464i	0.0802504	−	0.425857i
$514$	−116.206			−0.226082
$515$		−	49.4167i		−	0.0959548i
$516$	−22.2772	+	358.346i	−0.0431728	+	0.694469i
$517$		0			0
$518$			160.158i			0.309186i
$519$	−578.959	−	35.9920i	−1.11553	−	0.0693487i
$520$	198.891			0.382483
$521$			111.270i			0.213570i	0.994282	+	0.106785i	$0.0340557\pi$
$521$			111.270i			0.213570i	−0.994282	+	0.106785i	$0.965944\pi$
$522$	−379.652	−	47.3865i	−0.727303	−	0.0907788i
$523$	305.842			0.584784			0.292392	−	0.956299i	$-0.405549\pi$
$523$	305.842			0.584784			0.292392	+	0.956299i	$0.405549\pi$
$524$			424.898i			0.810875i
$525$	16.4512	−	264.630i	0.0313356	−	0.504058i
$526$	−115.826			−0.220202
$527$		−	586.126i		−	1.11219i
$528$		0			0
$529$	−385.285			−0.728328
$530$			19.8244i			0.0374045i
$531$	68.5802	−	549.451i	0.129153	−	1.03475i
$532$	−131.739			−0.247630
$533$		−	416.571i		−	0.781558i
$534$	21.1603	−	340.381i	0.0396261	−	0.637417i
$535$	−213.125			−0.398364
$536$		−	200.513i		−	0.374092i
$537$	−92.8574	−	5.77263i	−0.172919	−	0.0107498i
$538$	−45.1684			−0.0839562
$539$		0			0
$540$	−225.870	−	42.5639i	−0.418277	−	0.0788220i
$541$	−311.794			−0.576328			−0.288164	−	0.957581i	$-0.593045\pi$
$541$	−311.794			−0.576328			−0.288164	+	0.957581i	$0.593045\pi$
$542$			101.714i			0.187664i
$543$	19.0121	−	305.825i	0.0350132	−	0.563214i
$544$	−688.641			−1.26588
$545$		−	423.389i		−	0.776861i
$546$	−151.826	−	9.43852i	−0.278070	−	0.0172867i
$547$	882.983			1.61423			0.807115	−	0.590395i	$-0.201028\pi$
$547$	882.983			1.61423			0.807115	+	0.590395i	$0.201028\pi$
$548$		−	200.027i		−	0.365012i
$549$	459.446	+	57.3460i	0.836877	+	0.104455i
$550$		0			0
$551$		−	441.786i		−	0.801789i
$552$	−32.8751	+	528.821i	−0.0595563	+	0.958010i
$553$	444.467			0.803738
$554$			187.199i			0.337905i
$555$	−322.034	−	20.0198i	−0.580241	−	0.0360717i
$556$	441.549			0.794153
$557$			323.897i			0.581502i	0.956799	+	0.290751i	$0.0939052\pi$
$557$			323.897i			0.581502i	−0.956799	+	0.290751i	$0.906095\pi$
$558$	−22.8397	+	182.987i	−0.0409313	+	0.327934i
$559$	−478.717			−0.856381
$560$			106.132i			0.189521i
$561$		0			0
$562$	−161.609			−0.287560
$563$		−	495.222i		−	0.879613i	−0.898092	−	0.439807i	$-0.855047\pi$
$563$		−	495.222i		−	0.879613i	0.898092	−	0.439807i	$-0.144953\pi$
$564$	−315.913	−	19.6393i	−0.560129	−	0.0348214i
$565$	−311.774			−0.551813
$566$			379.673i			0.670801i
$567$	372.519	+	94.4641i	0.657000	+	0.166603i
$568$	84.7011			0.149122
$569$		−	544.447i		−	0.956850i	−0.878129	−	0.478425i	$-0.841208\pi$
$569$		−	544.447i		−	0.956850i	0.878129	−	0.478425i	$-0.158792\pi$
$570$	−3.06525	+	49.3069i	−0.00537763	+	0.0865034i
$571$	−779.886			−1.36582			−0.682912	−	0.730500i	$-0.739287\pi$
$571$	−779.886			−1.36582			−0.682912	+	0.730500i	$0.739287\pi$
$572$		0			0
$573$	208.061	+	12.9345i	0.363109	+	0.0225732i
$574$	−116.087			−0.202242
$575$		−	563.249i		−	0.979564i
$576$	−101.562	−	12.6766i	−0.176324	−	0.0220080i
$577$	1135.30			1.96758			0.983792	−	0.179314i	$-0.0573877\pi$
$577$	1135.30			1.96758			0.983792	+	0.179314i	$0.0573877\pi$
$578$			177.998i			0.307954i
$579$	−50.5382	+	812.947i	−0.0872853	+	1.40405i
$580$	−456.761			−0.787519
$581$			162.079i			0.278965i
$582$	95.5680	+	5.94115i	0.164206	+	0.0102082i
$583$		0			0
$584$		−	515.370i		−	0.882482i
$585$	37.9565	−	304.100i	0.0648829	−	0.519830i
$586$	7.41324			0.0126506
$587$		−	627.504i		−	1.06900i	−0.845168	−	0.534501i	$-0.820500\pi$
$587$		−	627.504i		−	1.06900i	0.845168	−	0.534501i	$-0.179500\pi$
$588$	−16.6277	+	267.470i	−0.0282784	+	0.454881i
$589$	−212.935			−0.361519
$590$			123.048i			0.208555i
$591$	−319.220	−	19.8448i	−0.540135	−	0.0335784i
$592$	−377.549			−0.637751
$593$		−	961.677i		−	1.62171i	−0.585244	−	0.810857i	$-0.699001\pi$
$593$		−	961.677i		−	1.62171i	0.585244	−	0.810857i	$-0.300999\pi$
$594$		0			0
$595$	271.446			0.456211
$596$		−	250.664i		−	0.420577i
$597$	−53.8452	+	866.143i	−0.0901930	+	1.45083i
$598$	−323.152			−0.540388
$599$			982.427i			1.64011i	0.572283	+	0.820056i	$0.306058\pi$
$599$			982.427i			1.64011i	−0.572283	+	0.820056i	$0.693942\pi$
$600$	−325.783	−	20.2528i	−0.542971	−	0.0337547i
$601$	321.239			0.534508			0.267254	−	0.963626i	$-0.413884\pi$
$601$	321.239			0.534508			0.267254	+	0.963626i	$0.413884\pi$
$602$			133.406i			0.221604i
$603$	−306.580	−	38.2660i	−0.508425	−	0.0634594i
$604$	21.0217			0.0348042
$605$		0			0
$606$	13.6793	−	220.043i	0.0225731	−	0.363107i
$607$	501.560			0.826293			0.413147	−	0.910665i	$-0.364430\pi$
$607$	501.560			0.826293			0.413147	+	0.910665i	$0.364430\pi$
$608$			250.178i			0.411476i
$609$	762.250	+	47.3865i	1.25164	+	0.0778104i
$610$	−102.891			−0.168674
$611$		−	422.030i		−	0.690721i
$612$	−85.1957	+	682.572i	−0.139209	+	1.11531i
$613$	369.750			0.603181			0.301591	−	0.953438i	$-0.402482\pi$
$613$	369.750			0.603181			0.301591	+	0.953438i	$0.402482\pi$
$614$			57.4623i			0.0935867i
$615$	14.5109	−	233.419i	0.0235949	−	0.379543i
$616$		0			0
$617$		−	560.582i		−	0.908560i	−0.890859	−	0.454280i	$-0.849897\pi$
$617$		−	560.582i		−	0.908560i	0.890859	−	0.454280i	$-0.150103\pi$
$618$	46.4401	+	2.88702i	0.0751457	+	0.00467156i
$619$	413.410			0.667868			0.333934	−	0.942596i	$-0.391624\pi$
$619$	413.410			0.667868			0.333934	+	0.942596i	$0.391624\pi$
$620$			220.152i			0.355085i
$621$	802.282	+	151.186i	1.29192	+	0.243455i
$622$	−301.581			−0.484857
$623$			680.762i			1.09272i
$624$	22.2499	−	357.907i	0.0356569	−	0.573569i
$625$	187.685			0.300296
$626$		−	42.0710i		−	0.0672060i
$627$		0			0
$628$	333.168			0.530523
$629$			965.628i			1.53518i
$630$	−84.7446	−	10.5775i	−0.134515	−	0.0167896i
$631$	1095.50			1.73614			0.868068	−	0.496445i	$-0.165361\pi$
$631$	1095.50			1.73614			0.868068	+	0.496445i	$0.165361\pi$
$632$		−	547.177i		−	0.865787i
$633$	34.8478	−	560.554i	0.0550517	−	0.885551i
$634$	58.0324			0.0915337
$635$			325.255i			0.512213i
$636$	100.087	+	6.22208i	0.157369	+	0.00978314i
$637$	−357.315			−0.560934
$638$		0			0
$639$	16.1644	−	129.506i	0.0252964	−	0.202670i
$640$	329.549			0.514920
$641$		−	987.942i		−	1.54125i	−0.637288	−	0.770625i	$-0.719944\pi$
$641$		−	987.942i		−	1.54125i	0.637288	−	0.770625i	$-0.280056\pi$
$642$	12.4512	−	200.287i	0.0193944	−	0.311974i
$643$	−1025.69			−1.59516			−0.797580	−	0.603214i	$-0.793887\pi$
$643$	−1025.69			−1.59516			−0.797580	+	0.603214i	$0.793887\pi$
$644$		−	483.794i		−	0.751234i
$645$	−268.242	−	16.6757i	−0.415879	−	0.0258538i
$646$	147.848			0.228867
$647$			481.010i			0.743446i	0.928344	+	0.371723i	$0.121233\pi$
$647$			481.010i			0.743446i	−0.928344	+	0.371723i	$0.878767\pi$
$648$	116.293	−	458.603i	0.179465	−	0.707720i
$649$		0			0
$650$		−	199.079i		−	0.306276i
$651$	22.8397	−	367.394i	0.0350840	−	0.564353i
$652$	700.994			1.07514
$653$		−	776.192i		−	1.18866i	−0.804223	−	0.594328i	$-0.797418\pi$
$653$		−	776.192i		−	1.18866i	0.804223	−	0.594328i	$-0.202582\pi$
$654$	397.886	+	24.7352i	0.608388	+	0.0378214i
$655$	−318.060			−0.485587
$656$		−	273.658i		−	0.417161i
$657$	−787.989	−	98.3534i	−1.19937	−	0.149701i
$658$	−117.609			−0.178736
$659$		−	52.5987i		−	0.0798160i	−0.999203	−	0.0399080i	$-0.987294\pi$
$659$		−	52.5987i		−	0.0798160i	0.999203	−	0.0399080i	$-0.0127065\pi$
$660$		0			0
$661$	−233.530			−0.353297			−0.176649	−	0.984274i	$-0.556526\pi$
$661$	−233.530			−0.353297			−0.176649	+	0.984274i	$0.556526\pi$
$662$			132.590i			0.200286i
$663$	−915.391	−	56.9068i	−1.38068	−	0.0858323i
$664$	199.533			0.300501
$665$		−	98.6139i		−	0.148292i
$666$	37.6277	−	301.466i	0.0564981	−	0.452652i
$667$	1622.40			2.43239
$668$			213.005i			0.318869i
$669$	−42.3900	+	681.876i	−0.0633632	+	1.01925i
$670$	68.6576			0.102474
$671$		0			0
$672$	−431.652	−	26.8344i	−0.642339	−	0.0399321i
$673$	−236.511			−0.351428			−0.175714	−	0.984441i	$-0.556223\pi$
$673$	−236.511			−0.351428			−0.175714	+	0.984441i	$0.556223\pi$
$674$			340.106i			0.504609i
$675$	−93.1386	+	494.249i	−0.137983	+	0.732221i
$676$	43.6930			0.0646346
$677$		−	295.663i		−	0.436725i	−0.975868	−	0.218363i	$-0.929928\pi$
$677$		−	295.663i		−	0.436725i	0.975868	−	0.218363i	$-0.0700715\pi$
$678$	18.2145	−	292.994i	0.0268650	−	0.432145i
$679$	−191.136			−0.281496
$680$		−	334.173i		−	0.491431i
$681$	1276.55	+	79.3589i	1.87452	+	0.116533i
$682$		0			0
$683$		−	905.661i		−	1.32600i	−0.748617	−	0.663002i	$-0.769282\pi$
$683$		−	905.661i		−	1.32600i	0.748617	−	0.663002i	$-0.230718\pi$
$684$	247.973	+	30.9509i	0.362533	+	0.0452498i
$685$	149.731			0.218585
$686$			283.768i			0.413656i
$687$	−18.9090	+	304.165i	−0.0275240	+	0.442745i
$688$	−314.484			−0.457098
$689$			133.707i			0.194059i
$690$	−181.073	−	11.2567i	−0.262425	−	0.0163141i
$691$	−352.024			−0.509442			−0.254721	−	0.967015i	$-0.581984\pi$
$691$	−352.024			−0.509442			−0.254721	+	0.967015i	$0.581984\pi$
$692$		−	652.061i		−	0.942284i
$693$		0			0
$694$	408.293			0.588319
$695$			330.524i			0.475573i
$696$	58.3369	−	938.395i	0.0838174	−	1.34827i
$697$	−699.913			−1.00418
$698$			221.853i			0.317841i
$699$	518.614	+	32.2405i	0.741937	+	0.0461238i
$700$	298.043			0.425776
$701$		−	1250.36i		−	1.78367i	−0.452357	−	0.891837i	$-0.649417\pi$
$701$		−	1250.36i		−	1.78367i	0.452357	−	0.891837i	$-0.350583\pi$
$702$	283.565	+	53.4363i	0.403939	+	0.0761201i
$703$	350.804			0.499010
$704$		0			0
$705$	14.7011	−	236.478i	0.0208526	−	0.335430i
$706$	296.245			0.419610
$707$			440.085i			0.622468i
$708$	621.228	+	38.6197i	0.877441	+	0.0545476i
$709$	−134.932			−0.190313			−0.0951564	−	0.995462i	$-0.530335\pi$
$709$	−134.932			−0.190313			−0.0951564	+	0.995462i	$0.530335\pi$
$710$			29.0024i			0.0408485i
$711$	−836.622	−	104.424i	−1.17668	−	0.146869i
$712$	838.076			1.17707
$713$		−	781.975i		−	1.09674i
$714$	−15.8584	+	255.095i	−0.0222106	+	0.357276i
$715$		0			0
$716$		−	104.582i		−	0.146064i
$717$	482.959	+	30.0240i	0.673583	+	0.0418744i
$718$	−86.2499			−0.120125
$719$			112.278i			0.156158i	0.996947	+	0.0780790i	$0.0248786\pi$
$719$			112.278i			0.156158i	−0.996947	+	0.0780790i	$0.975121\pi$
$720$	24.9348	−	199.773i	0.0346316	−	0.277462i
$721$	−92.8801			−0.128821
$722$			232.304i			0.321750i
$723$	10.5544	−	169.775i	0.0145980	−	0.234821i
$724$	344.440			0.475746
$725$			999.487i			1.37860i
$726$		0			0
$727$	160.372			0.220595			0.110297	−	0.993899i	$-0.464820\pi$
$727$	160.372			0.220595			0.110297	+	0.993899i	$0.464820\pi$
$728$		−	373.822i		−	0.513491i
$729$	−679.000	−	265.330i	−0.931413	−	0.363964i
$730$	176.467			0.241736
$731$			804.330i			1.10032i
$732$	−32.2934	+	519.465i	−0.0441166	+	0.709651i
$733$	−490.978			−0.669820			−0.334910	−	0.942250i	$-0.608706\pi$
$733$	−490.978			−0.669820			−0.334910	+	0.942250i	$0.608706\pi$
$734$		−	378.685i		−	0.515920i
$735$	−200.216	−	12.4468i	−0.272403	−	0.0169344i
$736$	−918.745			−1.24829
$737$		0			0
$738$	218.511	+	27.2736i	0.296085	+	0.0369561i
$739$	237.359			0.321189			0.160594	−	0.987020i	$-0.448659\pi$
$739$	237.359			0.321189			0.160594	+	0.987020i	$0.448659\pi$
$740$		−	362.695i		−	0.490129i
$741$	−20.6738	+	332.554i	−0.0278998	+	0.448790i
$742$	37.2605			0.0502163
$743$		−	245.204i		−	0.330019i	−0.986292	−	0.165010i	$-0.947235\pi$
$743$		−	245.204i		−	0.330019i	0.986292	−	0.165010i	$-0.0527655\pi$
$744$	−452.293	−	28.1176i	−0.607921	−	0.0377924i
$745$	187.636			0.251860
$746$		−	164.068i		−	0.219930i
$747$	38.0789	−	305.081i	0.0509758	−	0.408408i
$748$		0			0
$749$			400.574i			0.534812i
$750$	16.2418	−	261.262i	0.0216557	−	0.348349i
$751$	740.633			0.986196			0.493098	−	0.869974i	$-0.335864\pi$
$751$	740.633			0.986196			0.493098	+	0.869974i	$0.335864\pi$
$752$		−	277.244i		−	0.368676i
$753$	−202.085	−	12.5630i	−0.268374	−	0.0166839i
$754$	573.435			0.760523
$755$			15.7359i			0.0208423i
$756$	−80.0000	+	424.528i	−0.105820	+	0.561545i
$757$	324.717			0.428953			0.214476	−	0.976729i	$-0.431195\pi$
$757$	324.717			0.428953			0.214476	+	0.976729i	$0.431195\pi$
$758$		−	246.089i		−	0.324656i
$759$		0			0
$760$	−121.402			−0.159740
$761$		−	677.552i		−	0.890344i	−0.895445	−	0.445172i	$-0.853143\pi$
$761$		−	677.552i		−	0.890344i	0.895445	−	0.445172i	$-0.146857\pi$
$762$	−305.663	−	19.0021i	−0.401133	−	0.0249371i
$763$	−795.771			−1.04295
$764$			234.332i			0.306717i
$765$	−510.943	−	63.7737i	−0.667899	−	0.0833643i
$766$	285.120			0.372219
$767$			829.903i			1.08201i
$768$	−10.7855	+	173.494i	−0.0140436	+	0.225903i
$769$	−632.440			−0.822419			−0.411209	−	0.911541i	$-0.634894\pi$
$769$	−632.440			−0.822419			−0.411209	+	0.911541i	$0.634894\pi$
$770$		0			0
$771$	−439.168	−	27.3016i	−0.569609	−	0.0354107i
$772$	−915.592			−1.18600
$773$		−	185.094i		−	0.239449i	−0.992807	−	0.119724i	$-0.961799\pi$
$773$		−	185.094i		−	0.239449i	0.992807	−	0.119724i	$-0.0382011\pi$
$774$	31.3424	−	251.110i	0.0404941	−	0.324431i
$775$	481.739			0.621599
$776$			235.305i			0.303228i
$777$	−37.6277	+	605.272i	−0.0484269	+	0.778985i
$778$	−494.815			−0.636009
$779$			254.272i			0.326409i
$780$	343.826	+	21.3745i	0.440803	+	0.0274032i
$781$		0			0
$782$			542.953i			0.694314i
$783$	−1423.65	−	268.280i	−1.81820	−	0.342630i
$784$	−234.731			−0.299402
$785$			249.395i			0.317700i
$786$	18.5817	−	298.901i	0.0236408	−	0.380281i
$787$	−929.723			−1.18135			−0.590675	−	0.806909i	$-0.701139\pi$
$787$	−929.723			−1.18135			−0.590675	+	0.806909i	$0.701139\pi$
$788$		−	359.526i		−	0.456251i
$789$	−437.731	−	27.2123i	−0.554792	−	0.0344896i
$790$	187.359			0.237163
$791$			585.989i			0.740820i
$792$		0			0
$793$	−693.957			−0.875103
$794$			62.3755i			0.0785585i
$795$	−4.65756	+	74.9206i	−0.00585857	+	0.0942398i
$796$	−975.505			−1.22551
$797$		−	902.739i		−	1.13267i	−0.824175	−	0.566335i	$-0.808361\pi$
$797$		−	902.739i		−	1.13267i	0.824175	−	0.566335i	$-0.191639\pi$
$798$	92.6738	+	5.76122i	0.116133	+	0.00721957i
$799$	−709.087			−0.887467
$800$		−	565.996i		−	0.707495i
$801$	159.939	−	1281.40i	0.199674	−	1.59975i
$802$	−625.989			−0.780535
$803$		0			0
$804$	21.5488	−	346.630i	0.0268020	−	0.431132i
$805$	362.147			0.449872
$806$		−	276.388i		−	0.342913i
$807$	−170.701	−	10.6119i	−0.211525	−	0.0131498i
$808$	541.783			0.670523
$809$		−	306.667i		−	0.379069i	−0.981874	−	0.189534i	$-0.939302\pi$
$809$		−	306.667i		−	0.379069i	0.981874	−	0.189534i	$-0.0606979\pi$
$810$	157.030	+	39.8199i	0.193864	+	0.0491604i
$811$	1303.87			1.60773			0.803865	−	0.594811i	$-0.202773\pi$
$811$	1303.87			1.60773			0.803865	+	0.594811i	$0.202773\pi$
$812$			858.494i			1.05726i
$813$	−23.8968	+	384.399i	−0.0293934	+	0.472816i
$814$		0			0
$815$			524.733i			0.643844i
$816$	−601.348	−	37.3838i	−0.736945	−	0.0458134i
$817$	292.206			0.357658
$818$		−	402.241i		−	0.491737i
$819$	−571.565	−	71.3403i	−0.697882	−	0.0871066i
$820$	262.891			0.320599
$821$		−	1363.05i		−	1.66023i	−0.557595	−	0.830113i	$-0.688276\pi$
$821$		−	1363.05i		−	1.66023i	0.557595	−	0.830113i	$-0.311724\pi$
$822$	−8.74758	+	140.712i	−0.0106418	+	0.171182i
$823$	268.301			0.326004			0.163002	−	0.986626i	$-0.447882\pi$
$823$	268.301			0.326004			0.163002	+	0.986626i	$0.447882\pi$
$824$			114.343i			0.138766i
$825$		0			0
$826$	231.272			0.279990
$827$			637.024i			0.770283i	0.922857	+	0.385142i	$0.125847\pi$
$827$			637.024i			0.770283i	−0.922857	+	0.385142i	$0.874153\pi$
$828$	−113.663	+	910.648i	−0.137274	+	1.09982i
$829$	27.1927			0.0328018			0.0164009	−	0.999865i	$-0.494779\pi$
$829$	27.1927			0.0328018			0.0164009	+	0.999865i	$0.494779\pi$
$830$			68.3218i			0.0823155i
$831$	−43.9808	+	707.466i	−0.0529251	+	0.851343i
$832$	153.402			0.184378
$833$			600.353i			0.720712i
$834$	−310.614	−	19.3098i	−0.372439	−	0.0231533i
$835$	−159.446			−0.190953
$836$		0			0
$837$	−129.307	+	686.181i	−0.154489	+	0.819810i
$838$	264.935			0.316151
$839$			1013.92i			1.20849i	0.796800	+	0.604243i	$0.206524\pi$
$839$			1013.92i			1.20849i	−0.796800	+	0.604243i	$0.793476\pi$
$840$	13.0217	−	209.465i	0.0155021	−	0.249363i
$841$	−2037.96			−2.42325
$842$			351.233i			0.417141i
$843$	−610.753	−	37.9685i	−0.724499	−	0.0450397i
$844$	631.331			0.748023
$845$			32.7066i			0.0387060i
$846$	221.375	+	27.6311i	0.261672	+	0.0326608i
$847$		0			0
$848$			87.8361i			0.103580i
$849$	−89.2008	+	1434.87i	−0.105066	+	1.69007i
$850$	−334.489			−0.393516
$851$			1288.28i			1.51385i
$852$	146.424	+	9.10268i	0.171859	+	0.0106839i
$853$	1290.35			1.51272			0.756362	−	0.654154i	$-0.226975\pi$
$853$	1290.35			1.51272			0.756362	+	0.654154i	$0.226975\pi$
$854$			193.387i			0.226448i
$855$	−23.1684	+	185.621i	−0.0270976	+	0.217101i
$856$	493.141			0.576099
$857$		−	618.449i		−	0.721644i	−0.932635	−	0.360822i	$-0.882496\pi$
$857$		−	618.449i		−	0.721644i	0.932635	−	0.360822i	$-0.117504\pi$
$858$		0			0
$859$	1207.23			1.40538			0.702692	−	0.711494i	$-0.251981\pi$
$859$	1207.23			1.40538			0.702692	+	0.711494i	$0.251981\pi$
$860$		−	302.111i		−	0.351292i
$861$	−438.717	−	27.2736i	−0.509544	−	0.0316766i
$862$	−630.108			−0.730984
$863$		−	1105.28i		−	1.28075i	−0.768064	−	0.640373i	$-0.778780\pi$
$863$		−	1105.28i		−	1.28075i	0.768064	−	0.640373i	$-0.221220\pi$
$864$	806.195	+	151.923i	0.933096	+	0.175837i
$865$	488.103			0.564281
$866$			14.7541i			0.0170371i
$867$	−41.8189	+	672.691i	−0.0482341	+	0.775883i
$868$	413.783			0.476708
$869$		0			0
$870$	321.315	+	19.9751i	0.369328	+	0.0229599i
$871$	463.065			0.531648
$872$			979.663i			1.12347i
$873$	359.776	+	44.9057i	0.412114	+	0.0514384i
$874$	197.250			0.225687
$875$			522.524i			0.597170i
$876$	55.3859	−	890.927i	0.0632260	−	1.01704i
$877$	−1332.36			−1.51922			−0.759611	−	0.650377i	$-0.774611\pi$
$877$	−1332.36			−1.51922			−0.759611	+	0.650377i	$0.774611\pi$
$878$		−	201.947i		−	0.230008i
$879$	28.0162	+	1.74167i	0.0318728	+	0.00198143i
$880$		0			0
$881$			1171.98i			1.33029i	0.746715	+	0.665145i	$0.231630\pi$
$881$			1171.98i			1.33029i	−0.746715	+	0.665145i	$0.768370\pi$
$882$	23.3940	−	187.429i	0.0265238	−	0.212504i
$883$	728.195			0.824683			0.412342	−	0.911029i	$-0.364711\pi$
$883$	728.195			0.824683			0.412342	+	0.911029i	$0.364711\pi$
$884$		−	1030.97i		−	1.16626i
$885$	−28.9090	+	465.023i	−0.0326655	+	0.525450i
$886$	−48.7668			−0.0550415
$887$			979.772i			1.10459i	0.833648	+	0.552296i	$0.186248\pi$
$887$			979.772i			1.10459i	−0.833648	+	0.552296i	$0.813752\pi$
$888$	745.141	+	46.3229i	0.839123	+	0.0521655i
$889$	611.326			0.687656
$890$			286.965i			0.322433i
$891$		0			0
$892$	−767.973			−0.860956
$893$			257.605i			0.288472i
$894$	−10.9621	+	176.333i	−0.0122618	+	0.197241i
$895$	78.2853			0.0874696
$896$		−	619.396i		−	0.691290i
$897$	−1221.26	−	75.9217i	−1.36149	−	0.0846396i
$898$	108.886			0.121254
$899$			1387.62i			1.54351i
$900$	−561.008	−	70.0226i	−0.623342	−	0.0778029i
$901$	224.652			0.249336
$902$		0			0
$903$	−31.3424	+	504.168i	−0.0347092	+	0.558325i
$904$	721.402			0.798011
$905$			257.832i			0.284898i
$906$	−14.7881	−	0.919325i	−0.0163224	−	0.00101471i
$907$	1102.71			1.21577			0.607887	−	0.794024i	$-0.292018\pi$
$907$	1102.71			1.21577			0.607887	+	0.794024i	$0.292018\pi$
$908$			1437.73i			1.58341i
$909$	103.394	−	828.374i	0.113745	−	0.911302i
$910$	128.000			0.140659
$911$		−	463.277i		−	0.508536i	−0.967134	−	0.254268i	$-0.918165\pi$
$911$		−	463.277i		−	0.508536i	0.967134	−	0.254268i	$-0.0818346\pi$
$912$	−13.5812	+	218.464i	−0.0148917	+	0.239544i
$913$		0			0
$914$		−	243.701i		−	0.266632i
$915$	−388.848	−	24.1734i	−0.424970	−	0.0264190i
$916$	−342.571			−0.373985
$917$			597.802i			0.651911i
$918$	89.7825	−	476.440i	0.0978023	−	0.518998i
$919$	−195.929			−0.213198			−0.106599	−	0.994302i	$-0.533996\pi$
$919$	−195.929			−0.213198			−0.106599	+	0.994302i	$0.533996\pi$
$920$		−	445.834i		−	0.484602i
$921$	−13.5002	+	217.162i	−0.0146582	+	0.235789i
$922$	418.456			0.453857
$923$			195.609i			0.211927i
$924$		0			0
$925$	−793.652			−0.858002
$926$			36.4043i			0.0393135i
$927$	174.829	+	21.8213i	0.188596	+	0.0235398i
$928$	1630.31			1.75680
$929$			121.526i			0.130813i	0.997859	+	0.0654067i	$0.0208345\pi$
$929$			121.526i			0.130813i	−0.997859	+	0.0654067i	$0.979166\pi$
$930$	9.62772	−	154.869i	0.0103524	−	0.166526i
$931$	218.103			0.234268
$932$			584.096i			0.626713i
$933$	−1139.74	−	70.8538i	−1.22159	−	0.0759419i
$934$	284.484			0.304586
$935$		0			0
$936$	−87.8260	+	703.645i	−0.0938312	+	0.751758i
$937$	−330.419			−0.352635			−0.176317	−	0.984333i	$-0.556419\pi$
$937$	−330.419			−0.352635			−0.176317	+	0.984333i	$0.556419\pi$
$938$		−	129.044i		−	0.137573i
$939$	9.88419	−	158.995i	0.0105263	−	0.169324i
$940$	266.337			0.283337
$941$			895.084i			0.951205i	0.879660	+	0.475603i	$0.157770\pi$
$941$			895.084i			0.951205i	−0.879660	+	0.475603i	$0.842230\pi$
$942$	−234.372	−	14.5701i	−0.248803	−	0.0154672i
$943$	−933.783			−0.990225
$944$			545.188i			0.577530i
$945$	−317.783	−	59.8844i	−0.336278	−	0.0633697i
$946$		0			0
$947$			1308.11i			1.38132i	0.723181	+	0.690659i	$0.242679\pi$
$947$			1308.11i			1.38132i	−0.723181	+	0.690659i	$0.757321\pi$
$948$	58.8043	−	945.913i	0.0620298	−	0.997798i
$949$	1190.20			1.25416
$950$			121.517i			0.127913i
$951$	219.317	+	13.6342i	0.230617	+	0.0143367i
$952$	−628.087			−0.659755
$953$		−	2.03021i		−	0.00213034i	−0.999999	−	0.00106517i	$-0.999661\pi$
$953$		−	2.03021i		−	0.00213034i	0.999999	−	0.00106517i	$-0.000339054\pi$
$954$	−70.1356	−	8.75402i	−0.0735174	−	0.00917612i
$955$	−175.410			−0.183676
$956$			543.939i			0.568974i
$957$		0			0
$958$	457.467			0.477523
$959$		−	281.423i		−	0.293455i
$960$	85.9565	+	5.34363i	0.0895380	+	0.00556628i
$961$	−292.188			−0.304045
$962$			455.341i			0.473327i
$963$	94.1113	−	754.002i	0.0977272	−	0.782972i
$964$	191.212			0.198353
$965$		−	685.371i		−	0.710229i
$966$	−21.1573	+	340.332i	−0.0219020	+	0.352311i
$967$	520.674			0.538442			0.269221	−	0.963078i	$-0.413234\pi$
$967$	520.674			0.538442			0.269221	+	0.963078i	$0.413234\pi$
$968$		0			0
$969$	558.750	+	34.7356i	0.576625	+	0.0358469i
$970$	−80.5706			−0.0830624
$971$		−	1812.06i		−	1.86617i	−0.359650	−	0.933087i	$-0.617104\pi$
$971$		−	1812.06i		−	1.86617i	0.359650	−	0.933087i	$-0.382896\pi$
$972$	250.323	−	780.295i	0.257534	−	0.802773i
$973$	621.228			0.638467
$974$			480.838i			0.493674i
$975$	46.7719	−	752.362i	0.0479711	−	0.771654i
$976$	−455.881			−0.467091
$977$		−	427.388i		−	0.437449i	−0.975787	−	0.218725i	$-0.929810\pi$
$977$		−	427.388i		−	0.437449i	0.975787	−	0.218725i	$-0.0701897\pi$
$978$	−493.125	−	30.6559i	−0.504218	−	0.0313455i
$979$		0			0
$980$		−	225.496i		−	0.230098i
$981$	1497.88	+	186.959i	1.52689	+	0.190580i
$982$	−609.163			−0.620329
$983$			1003.52i			1.02088i	0.859915	+	0.510438i	$0.170517\pi$
$983$			1003.52i			1.02088i	−0.859915	+	0.510438i	$0.829483\pi$
$984$	−33.5761	+	540.098i	−0.0341221	+	0.548881i
$985$	269.125			0.273223
$986$		−	963.472i		−	0.977152i
$987$	−444.467	−	27.6311i	−0.450322	−	0.0279950i
$988$	−374.543			−0.379092
$989$			1073.09i			1.08503i
$990$		0			0
$991$	862.380			0.870212			0.435106	−	0.900379i	$-0.356711\pi$
$991$	862.380			0.870212			0.435106	+	0.900379i	$0.356711\pi$
$992$		−	785.789i		−	0.792126i
$993$	−31.1507	+	501.084i	−0.0313703	+	0.504617i
$994$	54.5109			0.0548399
$995$		−	730.219i		−	0.733889i
$996$	344.935	+	21.4434i	0.346320	+	0.0215296i
$997$	285.277			0.286135			0.143068	−	0.989713i	$-0.454303\pi$
$997$	285.277			0.286135			0.143068	+	0.989713i	$0.454303\pi$
$998$			394.585i			0.395375i
$999$	213.030	−	1130.46i	0.213243	−	1.13160i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.b.h.122.2		4
3.2	odd	2	inner	363.3.b.h.122.3		4
11.2	odd	10		363.3.h.m.323.3		16
11.3	even	5		363.3.h.l.251.2		16
11.4	even	5		363.3.h.l.269.3		16
11.5	even	5		363.3.h.l.245.3		16
11.6	odd	10		363.3.h.m.245.2		16
11.7	odd	10		363.3.h.m.269.2		16
11.8	odd	10		363.3.h.m.251.3		16
11.9	even	5		363.3.h.l.323.2		16
11.10	odd	2		33.3.b.b.23.3	yes	4
33.2	even	10		363.3.h.m.323.2		16
33.5	odd	10		363.3.h.l.245.2		16
33.8	even	10		363.3.h.m.251.2		16
33.14	odd	10		363.3.h.l.251.3		16
33.17	even	10		363.3.h.m.245.3		16
33.20	odd	10		363.3.h.l.323.3		16
33.26	odd	10		363.3.h.l.269.2		16
33.29	even	10		363.3.h.m.269.3		16
33.32	even	2		33.3.b.b.23.2	✓	4
44.43	even	2		528.3.i.d.353.2		4
132.131	odd	2		528.3.i.d.353.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.b.b.23.2	✓	4	33.32	even	2
33.3.b.b.23.3	yes	4	11.10	odd	2
363.3.b.h.122.2		4	1.1	even	1	trivial
363.3.b.h.122.3		4	3.2	odd	2	inner
363.3.h.l.245.2		16	33.5	odd	10
363.3.h.l.245.3		16	11.5	even	5
363.3.h.l.251.2		16	11.3	even	5
363.3.h.l.251.3		16	33.14	odd	10
363.3.h.l.269.2		16	33.26	odd	10
363.3.h.l.269.3		16	11.4	even	5
363.3.h.l.323.2		16	11.9	even	5
363.3.h.l.323.3		16	33.20	odd	10
363.3.h.m.245.2		16	11.6	odd	10
363.3.h.m.245.3		16	33.17	even	10
363.3.h.m.251.2		16	33.8	even	10
363.3.h.m.251.3		16	11.8	odd	10
363.3.h.m.269.2		16	11.7	odd	10
363.3.h.m.269.3		16	33.29	even	10
363.3.h.m.323.2		16	33.2	even	10
363.3.h.m.323.3		16	11.2	odd	10
528.3.i.d.353.1		4	132.131	odd	2
528.3.i.d.353.2		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)

\(f(q)\)	\(=\)	\(q-0.792287i q^{2} +(0.186141 - 2.99422i) q^{3} +3.37228 q^{4} +2.52434i q^{5} +(-2.37228 - 0.147477i) q^{6} +4.74456 q^{7} -5.84096i q^{8} +(-8.93070 - 1.11469i) q^{9} +O(q^{10})\)	\(q-0.792287i q^{2} +(0.186141 - 2.99422i) q^{3} +3.37228 q^{4} +2.52434i q^{5} +(-2.37228 - 0.147477i) q^{6} +4.74456 q^{7} -5.84096i q^{8} +(-8.93070 - 1.11469i) q^{9} +2.00000 q^{10} +(0.627719 - 10.0974i) q^{12} +13.4891 q^{13} -3.75906i q^{14} +(7.55842 + 0.469882i) q^{15} +8.86141 q^{16} -22.6641i q^{17} +(-0.883156 + 7.07568i) q^{18} -8.23369 q^{19} +8.51278i q^{20} +(0.883156 - 14.2063i) q^{21} -30.2372i q^{23} +(-17.4891 - 1.08724i) q^{24} +18.6277 q^{25} -10.6873i q^{26} +(-5.00000 + 26.5330i) q^{27} +16.0000 q^{28} +53.6559i q^{29} +(0.372281 - 5.98844i) q^{30} +25.8614 q^{31} -30.3846i q^{32} -17.9565 q^{34} +11.9769i q^{35} +(-30.1168 - 3.75906i) q^{36} -42.6060 q^{37} +6.52344i q^{38} +(2.51087 - 40.3894i) q^{39} +14.7446 q^{40} -30.8820i q^{41} +(-11.2554 - 0.699713i) q^{42} -35.4891 q^{43} +(2.81386 - 22.5441i) q^{45} -23.9565 q^{46} -31.2867i q^{47} +(1.64947 - 26.5330i) q^{48} -26.4891 q^{49} -14.7585i q^{50} +(-67.8614 - 4.21872i) q^{51} +45.4891 q^{52} +9.91220i q^{53} +(21.0217 + 3.96143i) q^{54} -27.7128i q^{56} +(-1.53262 + 24.6535i) q^{57} +42.5109 q^{58} +61.5239i q^{59} +(25.4891 + 1.58457i) q^{60} -51.4456 q^{61} -20.4897i q^{62} +(-42.3723 - 5.28873i) q^{63} +11.3723 q^{64} +34.0511i q^{65} +34.3288 q^{67} -76.4298i q^{68} +(-90.5367 - 5.62836i) q^{69} +9.48913 q^{70} +14.5012i q^{71} +(-6.51087 + 52.1639i) q^{72} +88.2337 q^{73} +33.7562i q^{74} +(3.46738 - 55.7755i) q^{75} -27.7663 q^{76} +(-32.0000 - 1.98933i) q^{78} +93.6793 q^{79} +22.3692i q^{80} +(78.5149 + 19.9100i) q^{81} -24.4674 q^{82} +34.1609i q^{83} +(2.97825 - 47.9075i) q^{84} +57.2119 q^{85} +28.1176i q^{86} +(160.658 + 9.98755i) q^{87} +143.482i q^{89} +(-17.8614 - 2.22938i) q^{90} +64.0000 q^{91} -101.968i q^{92} +(4.81386 - 77.4347i) q^{93} -24.7881 q^{94} -20.7846i q^{95} +(-90.9783 - 5.65581i) q^{96} -40.2853 q^{97} +20.9870i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} - 7 q^{9}+O(q^{10}) \) 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

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