LMFDB - Embedded newform 62.3.b.a.61.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [62,3,Mod(61,62)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(62, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("62.61");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	62.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:	$1.68937763903$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.48128.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 14x^{2} + 47 $ x^4 + 14*x^2 + 47
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			61.4
Root			$2.36343i$ of defining polynomial
Character	$\chi$	$=$	62.61
Dual form			62.3.b.a.61.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +3.34239i q^{3} +2.00000 q^{4} -0.171573 q^{5} +4.72685i q^{6} -1.58579 q^{7} +2.82843 q^{8} -2.17157 q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +3.34239i q^{3} +2.00000 q^{4} -0.171573 q^{5} +4.72685i q^{6} -1.58579 q^{7} +2.82843 q^{8} -2.17157 q^{9} -0.242641 q^{10} -2.76893i q^{11} +6.68478i q^{12} -14.7540i q^{13} -2.24264 q^{14} -0.573464i q^{15} +4.00000 q^{16} -17.5230i q^{17} -3.07107 q^{18} -12.2132 q^{19} -0.343146 q^{20} -5.30032i q^{21} -3.91585i q^{22} +22.2498i q^{23} +9.45371i q^{24} -24.9706 q^{25} -20.8653i q^{26} +22.8233i q^{27} -3.17157 q^{28} +14.7540i q^{29} -0.811000i q^{30} +(21.5858 - 22.2498i) q^{31} +5.65685 q^{32} +9.25483 q^{33} -24.7812i q^{34} +0.272078 q^{35} -4.34315 q^{36} -8.30678i q^{37} -17.2721 q^{38} +49.3137 q^{39} -0.485281 q^{40} +5.34315 q^{41} -7.49578i q^{42} +60.0646i q^{43} -5.53785i q^{44} +0.372583 q^{45} +31.4660i q^{46} +39.7401 q^{47} +13.3696i q^{48} -46.4853 q^{49} -35.3137 q^{50} +58.5685 q^{51} -29.5080i q^{52} +92.9151i q^{53} +32.2770i q^{54} +0.475073i q^{55} -4.48528 q^{56} -40.8213i q^{57} +20.8653i q^{58} +13.7868 q^{59} -1.14693i q^{60} -69.8543i q^{61} +(30.5269 - 31.4660i) q^{62} +3.44365 q^{63} +8.00000 q^{64} +2.53139i q^{65} +13.0883 q^{66} -109.054 q^{67} -35.0459i q^{68} -74.3675 q^{69} +0.384776 q^{70} +2.75736 q^{71} -6.14214 q^{72} -74.0077i q^{73} -11.7476i q^{74} -83.4614i q^{75} -24.4264 q^{76} +4.39093i q^{77} +69.7401 q^{78} -102.942i q^{79} -0.686292 q^{80} -95.8284 q^{81} +7.55635 q^{82} +110.872i q^{83} -10.6006i q^{84} +3.00646i q^{85} +84.9442i q^{86} -49.3137 q^{87} -7.83171i q^{88} -50.4718i q^{89} +0.526912 q^{90} +23.3967i q^{91} +44.4996i q^{92} +(74.3675 + 72.1481i) q^{93} +56.2010 q^{94} +2.09545 q^{95} +18.9074i q^{96} -113.711 q^{97} -65.7401 q^{98} +6.01293i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{4} - 12 q^{5} - 12 q^{7} - 20 q^{9}+O(q^{10}) $ 4 * q + 8 * q^4 - 12 * q^5 - 12 * q^7 - 20 * q^9	$ 4 q + 8 q^{4} - 12 q^{5} - 12 q^{7} - 20 q^{9} + 16 q^{10} + 8 q^{14} + 16 q^{16} + 16 q^{18} + 36 q^{19} - 24 q^{20} - 32 q^{25} - 24 q^{28} + 92 q^{31} - 144 q^{33} + 52 q^{35} - 40 q^{36} - 120 q^{38} + 152 q^{39} + 32 q^{40} + 44 q^{41} + 92 q^{45} - 56 q^{47} - 152 q^{49} - 96 q^{50} + 8 q^{51} + 16 q^{56} + 140 q^{59} - 8 q^{62} + 76 q^{63} + 32 q^{64} + 256 q^{66} - 176 q^{67} + 8 q^{69} - 72 q^{70} + 28 q^{71} + 32 q^{72} + 72 q^{76} + 64 q^{78} - 48 q^{80} - 372 q^{81} - 32 q^{82} - 152 q^{87} - 128 q^{90} - 8 q^{93} + 304 q^{94} - 348 q^{95} - 172 q^{97} - 48 q^{98}+O(q^{100}) $ 4 * q + 8 * q^4 - 12 * q^5 - 12 * q^7 - 20 * q^9 + 16 * q^10 + 8 * q^14 + 16 * q^16 + 16 * q^18 + 36 * q^19 - 24 * q^20 - 32 * q^25 - 24 * q^28 + 92 * q^31 - 144 * q^33 + 52 * q^35 - 40 * q^36 - 120 * q^38 + 152 * q^39 + 32 * q^40 + 44 * q^41 + 92 * q^45 - 56 * q^47 - 152 * q^49 - 96 * q^50 + 8 * q^51 + 16 * q^56 + 140 * q^59 - 8 * q^62 + 76 * q^63 + 32 * q^64 + 256 * q^66 - 176 * q^67 + 8 * q^69 - 72 * q^70 + 28 * q^71 + 32 * q^72 + 72 * q^76 + 64 * q^78 - 48 * q^80 - 372 * q^81 - 32 * q^82 - 152 * q^87 - 128 * q^90 - 8 * q^93 + 304 * q^94 - 348 * q^95 - 172 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

Coefficient data

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

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

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

$2$	1.41421			0.707107
$2$	1.41421			0.707107
$3$			3.34239i			1.11413i	0.830469	+	0.557065i	$0.188073\pi$
$3$			3.34239i			1.11413i	−0.830469	+	0.557065i	$0.811927\pi$
$4$	2.00000			0.500000
$5$	−0.171573			−0.0343146			−0.0171573	−	0.999853i	$-0.505462\pi$
$5$	−0.171573			−0.0343146			−0.0171573	+	0.999853i	$0.505462\pi$
$6$			4.72685i			0.787809i
$7$	−1.58579			−0.226541			−0.113270	−	0.993564i	$-0.536133\pi$
$7$	−1.58579			−0.226541			−0.113270	+	0.993564i	$0.536133\pi$
$8$	2.82843			0.353553
$9$	−2.17157			−0.241286
$10$	−0.242641			−0.0242641
$11$		−	2.76893i		−	0.251721i	−0.992048	−	0.125860i	$-0.959831\pi$
$11$		−	2.76893i		−	0.251721i	0.992048	−	0.125860i	$-0.0401691\pi$
$12$			6.68478i			0.557065i
$13$		−	14.7540i		−	1.13492i	−0.823399	−	0.567462i	$-0.807925\pi$
$13$		−	14.7540i		−	1.13492i	0.823399	−	0.567462i	$-0.192075\pi$
$14$	−2.24264			−0.160189
$15$		−	0.573464i		−	0.0382309i
$16$	4.00000			0.250000
$17$		−	17.5230i		−	1.03076i	−0.856961	−	0.515381i	$-0.827650\pi$
$17$		−	17.5230i		−	1.03076i	0.856961	−	0.515381i	$-0.172350\pi$
$18$	−3.07107			−0.170615
$19$	−12.2132			−0.642800			−0.321400	−	0.946943i	$-0.604153\pi$
$19$	−12.2132			−0.642800			−0.321400	+	0.946943i	$0.604153\pi$
$20$	−0.343146			−0.0171573
$21$		−	5.30032i		−	0.252396i
$22$		−	3.91585i		−	0.177993i
$23$			22.2498i			0.967383i	0.875239	+	0.483691i	$0.160704\pi$
$23$			22.2498i			0.967383i	−0.875239	+	0.483691i	$0.839296\pi$
$24$			9.45371i			0.393904i
$25$	−24.9706			−0.998823
$26$		−	20.8653i		−	0.802513i
$27$			22.8233i			0.845306i
$28$	−3.17157			−0.113270
$29$			14.7540i			0.508759i	0.967104	+	0.254380i	$0.0818713\pi$
$29$			14.7540i			0.508759i	−0.967104	+	0.254380i	$0.918129\pi$
$30$		−	0.811000i		−	0.0270333i
$31$	21.5858	−	22.2498i	0.696316	−	0.717736i
$31$	21.5858	−	22.2498i	0.696316	−	0.717736i
$32$	5.65685			0.176777
$33$	9.25483			0.280450
$34$		−	24.7812i		−	0.728859i
$35$	0.272078			0.00777366
$36$	−4.34315			−0.120643
$37$		−	8.30678i		−	0.224508i	−0.993680	−	0.112254i	$-0.964193\pi$
$37$		−	8.30678i		−	0.224508i	0.993680	−	0.112254i	$-0.0358070\pi$
$38$	−17.2721			−0.454528
$39$	49.3137			1.26445
$40$	−0.485281			−0.0121320
$41$	5.34315			0.130321			0.0651603	−	0.997875i	$-0.479244\pi$
$41$	5.34315			0.130321			0.0651603	+	0.997875i	$0.479244\pi$
$42$		−	7.49578i		−	0.178471i
$43$			60.0646i			1.39685i	0.715682	+	0.698426i	$0.246116\pi$
$43$			60.0646i			1.39685i	−0.715682	+	0.698426i	$0.753884\pi$
$44$		−	5.53785i		−	0.125860i
$45$	0.372583			0.00827962
$46$			31.4660i			0.684043i
$47$	39.7401			0.845534			0.422767	−	0.906238i	$-0.361059\pi$
$47$	39.7401			0.845534			0.422767	+	0.906238i	$0.361059\pi$
$48$			13.3696i			0.278533i
$49$	−46.4853			−0.948679
$50$	−35.3137			−0.706274
$51$	58.5685			1.14840
$52$		−	29.5080i		−	0.567462i
$53$			92.9151i			1.75311i	0.481298	+	0.876557i	$0.340166\pi$
$53$			92.9151i			1.75311i	−0.481298	+	0.876557i	$0.659834\pi$
$54$			32.2770i			0.597722i
$55$			0.475073i			0.00863769i
$56$	−4.48528			−0.0800943
$57$		−	40.8213i		−	0.716163i
$58$			20.8653i			0.359747i
$59$	13.7868			0.233675			0.116837	−	0.993151i	$-0.462724\pi$
$59$	13.7868			0.233675			0.116837	+	0.993151i	$0.462724\pi$
$60$		−	1.14693i		−	0.0191155i
$61$		−	69.8543i		−	1.14515i	−0.819852	−	0.572576i	$-0.805944\pi$
$61$		−	69.8543i		−	1.14515i	0.819852	−	0.572576i	$-0.194056\pi$
$62$	30.5269	−	31.4660i	0.492370	−	0.507516i
$63$	3.44365			0.0546611
$64$	8.00000			0.125000
$65$			2.53139i			0.0389445i
$66$	13.0883			0.198308
$67$	−109.054			−1.62767			−0.813835	−	0.581097i	$-0.802624\pi$
$67$	−109.054			−1.62767			−0.813835	+	0.581097i	$0.802624\pi$
$68$		−	35.0459i		−	0.515381i
$69$	−74.3675			−1.07779
$70$	0.384776			0.00549680
$71$	2.75736			0.0388360			0.0194180	−	0.999811i	$-0.493819\pi$
$71$	2.75736			0.0388360			0.0194180	+	0.999811i	$0.493819\pi$
$72$	−6.14214			−0.0853074
$73$		−	74.0077i		−	1.01380i	−0.862004	−	0.506902i	$-0.830791\pi$
$73$		−	74.0077i		−	1.01380i	0.862004	−	0.506902i	$-0.169209\pi$
$74$		−	11.7476i		−	0.158751i
$75$		−	83.4614i		−	1.11282i
$76$	−24.4264			−0.321400
$77$			4.39093i			0.0570250i
$78$	69.7401			0.894104
$79$		−	102.942i		−	1.30307i	−0.758620	−	0.651533i	$-0.774126\pi$
$79$		−	102.942i		−	1.30307i	0.758620	−	0.651533i	$-0.225874\pi$
$80$	−0.686292			−0.00857864
$81$	−95.8284			−1.18307
$82$	7.55635			0.0921506
$83$			110.872i			1.33581i	0.744246	+	0.667906i	$0.232809\pi$
$83$			110.872i			1.33581i	−0.744246	+	0.667906i	$0.767191\pi$
$84$		−	10.6006i		−	0.126198i
$85$			3.00646i			0.0353702i
$86$			84.9442i			0.987723i
$87$	−49.3137			−0.566824
$88$		−	7.83171i		−	0.0889967i
$89$		−	50.4718i		−	0.567099i	−0.958958	−	0.283549i	$-0.908488\pi$
$89$		−	50.4718i		−	0.567099i	0.958958	−	0.283549i	$-0.0915120\pi$
$90$	0.526912			0.00585458
$91$			23.3967i			0.257107i
$92$			44.4996i			0.483691i
$93$	74.3675	+	72.1481i	0.799651	+	0.775786i
$94$	56.2010			0.597883
$95$	2.09545			0.0220574
$96$			18.9074i			0.196952i
$97$	−113.711			−1.17228			−0.586138	−	0.810212i	$-0.699352\pi$
$97$	−113.711			−1.17228			−0.586138	+	0.810212i	$0.699352\pi$
$98$	−65.7401			−0.670818
$99$			6.01293i			0.0607366i
$100$	−49.9411			−0.499411
$101$	172.255			1.70549			0.852747	−	0.522325i	$-0.174935\pi$
$101$	172.255			1.70549			0.852747	+	0.522325i	$0.174935\pi$
$102$	82.8284			0.812043
$103$	−3.75231			−0.0364302			−0.0182151	−	0.999834i	$-0.505798\pi$
$103$	−3.75231			−0.0364302			−0.0182151	+	0.999834i	$0.505798\pi$
$104$		−	41.7307i		−	0.401257i
$105$			0.909391i			0.00866086i
$106$			131.402i			1.23964i
$107$	4.81623			0.0450115			0.0225058	−	0.999747i	$-0.492836\pi$
$107$	4.81623			0.0450115			0.0225058	+	0.999747i	$0.492836\pi$
$108$			45.6465i			0.422653i
$109$	80.6812			0.740195			0.370097	−	0.928993i	$-0.379324\pi$
$109$	80.6812			0.740195			0.370097	+	0.928993i	$0.379324\pi$
$110$			0.671854i			0.00610777i
$111$	27.7645			0.250131
$112$	−6.34315			−0.0566352
$113$	175.853			1.55622			0.778110	−	0.628128i	$-0.216179\pi$
$113$	175.853			1.55622			0.778110	+	0.628128i	$0.216179\pi$
$114$		−	57.7300i		−	0.506404i
$115$		−	3.81746i		−	0.0331953i
$116$			29.5080i			0.254380i
$117$			32.0394i			0.273841i
$118$	19.4975			0.165233
$119$			27.7877i			0.233510i
$120$		−	1.62200i		−	0.0135167i
$121$	113.333			0.936637
$122$		−	98.7889i		−	0.809745i
$123$			17.8589i			0.145194i
$124$	43.1716	−	44.4996i	0.348158	−	0.358868i
$125$	8.57359			0.0685887
$126$	4.87006			0.0386513
$127$			105.810i			0.833146i	0.909102	+	0.416573i	$0.136769\pi$
$127$			105.810i			0.833146i	−0.909102	+	0.416573i	$0.863231\pi$
$128$	11.3137			0.0883883
$129$	−200.759			−1.55627
$130$			3.57993i			0.0275379i
$131$	−169.848			−1.29655			−0.648274	−	0.761407i	$-0.724509\pi$
$131$	−169.848			−1.29655			−0.648274	+	0.761407i	$0.724509\pi$
$132$	18.5097			0.140225
$133$	19.3675			0.145621
$134$	−154.225			−1.15094
$135$		−	3.91585i		−	0.0290063i
$136$		−	49.5624i		−	0.364429i
$137$			1.85954i			0.0135733i	0.999977	+	0.00678663i	$0.00216027\pi$
$137$			1.85954i			0.0135733i	−0.999977	+	0.00678663i	$0.997840\pi$
$138$	−105.172			−0.762113
$139$		−	24.4453i		−	0.175865i	−0.996126	−	0.0879326i	$-0.971974\pi$
$139$		−	24.4453i		−	0.175865i	0.996126	−	0.0879326i	$-0.0280260\pi$
$140$	0.544156			0.00388683
$141$			132.827i			0.942035i
$142$	3.89949			0.0274612
$143$	−40.8528			−0.285684
$144$	−8.68629			−0.0603215
$145$		−	2.53139i		−	0.0174579i
$146$		−	104.663i		−	0.716867i
$147$		−	155.372i		−	1.05695i
$148$		−	16.6136i		−	0.112254i
$149$	−62.0244			−0.416271			−0.208136	−	0.978100i	$-0.566740\pi$
$149$	−62.0244			−0.416271			−0.208136	+	0.978100i	$0.566740\pi$
$150$		−	118.032i		−	0.786881i
$151$		−	28.2627i		−	0.187170i	−0.995611	−	0.0935852i	$-0.970167\pi$
$151$		−	28.2627i		−	0.187170i	0.995611	−	0.0935852i	$-0.0298328\pi$
$152$	−34.5442			−0.227264
$153$			38.0524i			0.248708i
$154$			6.20971i			0.0403228i
$155$	−3.70354	+	3.81746i	−0.0238938	+	0.0246288i
$156$	98.6274			0.632227
$157$	179.569			1.14375			0.571874	−	0.820341i	$-0.306216\pi$
$157$	179.569			1.14375			0.571874	+	0.820341i	$0.306216\pi$
$158$		−	145.582i		−	0.921407i
$159$	−310.558			−1.95320
$160$	−0.970563			−0.00606602
$161$		−	35.2834i		−	0.219152i
$162$	−135.522			−0.836555
$163$	263.718			1.61790			0.808950	−	0.587877i	$-0.200036\pi$
$163$	263.718			1.61790			0.808950	+	0.587877i	$0.200036\pi$
$164$	10.6863			0.0651603
$165$	−1.58788			−0.00962351
$166$			156.797i			0.944561i
$167$		−	125.192i		−	0.749653i	−0.927095	−	0.374826i	$-0.877702\pi$
$167$		−	125.192i		−	0.749653i	0.927095	−	0.374826i	$-0.122298\pi$
$168$		−	14.9916i		−	0.0892355i
$169$	−48.6812			−0.288055
$170$			4.25178i			0.0250105i
$171$	26.5219			0.155099
$172$			120.129i			0.698426i
$173$	134.711			0.778674			0.389337	−	0.921095i	$-0.372704\pi$
$173$	134.711			0.778674			0.389337	+	0.921095i	$0.372704\pi$
$174$	−69.7401			−0.400805
$175$	39.5980			0.226274
$176$		−	11.0757i		−	0.0629302i
$177$			46.0809i			0.260344i
$178$		−	71.3779i		−	0.400999i
$179$		−	316.183i		−	1.76639i	−0.469008	−	0.883194i	$-0.655389\pi$
$179$		−	316.183i		−	1.76639i	0.469008	−	0.883194i	$-0.344611\pi$
$180$	0.745166			0.00413981
$181$			329.217i			1.81888i	0.415837	+	0.909439i	$0.363489\pi$
$181$			329.217i			1.81888i	−0.415837	+	0.909439i	$0.636511\pi$
$182$			33.0880i			0.181802i
$183$	233.480			1.27585
$184$			62.9320i			0.342021i
$185$			1.42522i			0.00770388i
$186$	105.172	+	102.033i	0.565439	+	0.548564i
$187$	−48.5198			−0.259464
$188$	79.4802			0.422767
$189$		−	36.1928i		−	0.191496i
$190$	2.96342			0.0155969
$191$	−250.213			−1.31002			−0.655008	−	0.755622i	$-0.727335\pi$
$191$	−250.213			−1.31002			−0.655008	+	0.755622i	$0.727335\pi$
$192$			26.7391i			0.139266i
$193$	−70.3970			−0.364751			−0.182376	−	0.983229i	$-0.558379\pi$
$193$	−70.3970			−0.364751			−0.182376	+	0.983229i	$0.558379\pi$
$194$	−160.811			−0.828924
$195$	−8.46089			−0.0433892
$196$	−92.9706			−0.474340
$197$			321.623i			1.63260i	0.577626	+	0.816302i	$0.303979\pi$
$197$			321.623i			1.63260i	−0.577626	+	0.816302i	$0.696021\pi$
$198$			8.50356i			0.0429473i
$199$			107.235i			0.538868i	0.963019	+	0.269434i	$0.0868366\pi$
$199$			107.235i			0.538868i	−0.963019	+	0.269434i	$0.913163\pi$
$200$	−70.6274			−0.353137
$201$		−	364.500i		−	1.81344i
$202$	243.605			1.20597
$203$		−	23.3967i		−	0.115255i
$204$	117.137			0.574201
$205$	−0.916739			−0.00447190
$206$	−5.30657			−0.0257600
$207$		−	48.3171i		−	0.233416i
$208$		−	59.0161i		−	0.283731i
$209$			33.8175i			0.161806i
$210$			1.28607i			0.00612416i
$211$	−55.0172			−0.260745			−0.130373	−	0.991465i	$-0.541617\pi$
$211$	−55.0172			−0.260745			−0.130373	+	0.991465i	$0.541617\pi$
$212$			185.830i			0.876557i
$213$			9.21617i			0.0432684i
$214$	6.81118			0.0318280
$215$		−	10.3055i		−	0.0479324i
$216$			64.5540i			0.298861i
$217$	−34.2304	+	35.2834i	−0.157744	+	0.162596i
$218$	114.101			0.523397
$219$	247.362			1.12951
$220$			0.950145i			0.00431884i
$221$	−258.534			−1.16984
$222$	39.2649			0.176869
$223$			209.522i			0.939561i	0.882783	+	0.469780i	$0.155667\pi$
$223$			209.522i			0.939561i	−0.882783	+	0.469780i	$0.844333\pi$
$224$	−8.97056			−0.0400472
$225$	54.2254			0.241002
$226$	248.693			1.10041
$227$	−173.515			−0.764382			−0.382191	−	0.924083i	$-0.624830\pi$
$227$	−173.515			−0.764382			−0.382191	+	0.924083i	$0.624830\pi$
$228$		−	81.6426i		−	0.358082i
$229$			38.4867i			0.168064i	0.996463	+	0.0840321i	$0.0267798\pi$
$229$			38.4867i			0.168064i	−0.996463	+	0.0840321i	$0.973220\pi$
$230$		−	5.39871i		−	0.0234726i
$231$	−14.6762			−0.0635333
$232$			41.7307i			0.179874i
$233$	136.019			0.583774			0.291887	−	0.956453i	$-0.405717\pi$
$233$	136.019			0.583774			0.291887	+	0.956453i	$0.405717\pi$
$234$			45.3106i			0.193635i
$235$	−6.81833			−0.0290142
$236$	27.5736			0.116837
$237$	344.073			1.45179
$238$			39.2977i			0.165116i
$239$		−	396.876i		−	1.66057i	−0.557340	−	0.830284i	$-0.688178\pi$
$239$		−	396.876i		−	1.66057i	0.557340	−	0.830284i	$-0.311822\pi$
$240$		−	2.29385i		−	0.00955773i
$241$		−	152.406i		−	0.632391i	−0.948694	−	0.316196i	$-0.897594\pi$
$241$		−	152.406i		−	0.632391i	0.948694	−	0.316196i	$-0.102406\pi$
$242$	160.277			0.662302
$243$		−	114.887i		−	0.472784i
$244$		−	139.709i		−	0.572576i
$245$	7.97561			0.0325535
$246$			25.2563i			0.102668i
$247$			180.194i			0.729530i
$248$	61.0538	−	62.9320i	0.246185	−	0.253758i
$249$	−370.579			−1.48827
$250$	12.1249			0.0484996
$251$			148.589i			0.591987i	0.955190	+	0.295994i	$0.0956507\pi$
$251$			148.589i			0.591987i	−0.955190	+	0.295994i	$0.904349\pi$
$252$	6.88730			0.0273306
$253$	61.6081			0.243510
$254$			149.637i			0.589123i
$255$	−10.0488			−0.0394070
$256$	16.0000			0.0625000
$257$	−383.818			−1.49346			−0.746728	−	0.665129i	$-0.768376\pi$
$257$	−383.818			−1.49346			−0.746728	+	0.665129i	$0.768376\pi$
$258$	−283.917			−1.10045
$259$			13.1728i			0.0508602i
$260$			5.06278i			0.0194722i
$261$		−	32.0394i		−	0.122756i
$262$	−240.201			−0.916798
$263$			194.710i			0.740344i	0.928963	+	0.370172i	$0.120701\pi$
$263$			194.710i			0.740344i	−0.928963	+	0.370172i	$0.879299\pi$
$264$	26.1766			0.0991539
$265$		−	15.9417i		−	0.0601574i
$266$	27.3898			0.102969
$267$	168.696			0.631822
$268$	−218.108			−0.813835
$269$		−	180.686i		−	0.671695i	−0.941916	−	0.335847i	$-0.890977\pi$
$269$		−	180.686i		−	0.671695i	0.941916	−	0.335847i	$-0.109023\pi$
$270$		−	5.53785i		−	0.0205106i
$271$		−	48.9889i		−	0.180771i	−0.995907	−	0.0903855i	$-0.971190\pi$
$271$		−	48.9889i		−	0.180771i	0.995907	−	0.0903855i	$-0.0288099\pi$
$272$		−	70.0918i		−	0.257690i
$273$	−78.2010			−0.286451
$274$			2.62978i			0.00959774i
$275$			69.1417i			0.251424i
$276$	−148.735			−0.538895
$277$		−	359.397i		−	1.29746i	−0.761018	−	0.648731i	$-0.775300\pi$
$277$		−	359.397i		−	1.29746i	0.761018	−	0.648731i	$-0.224700\pi$
$278$		−	34.5708i		−	0.124356i
$279$	−46.8751	+	48.3171i	−0.168011	+	0.173179i
$280$	0.769553			0.00274840
$281$	203.333			0.723605			0.361803	−	0.932255i	$-0.382161\pi$
$281$	203.333			0.723605			0.361803	+	0.932255i	$0.382161\pi$
$282$			187.846i			0.666120i
$283$	−347.789			−1.22894			−0.614468	−	0.788942i	$-0.710629\pi$
$283$	−347.789			−1.22894			−0.614468	+	0.788942i	$0.710629\pi$
$284$	5.51472			0.0194180
$285$			7.00383i			0.0245748i
$286$	−57.7746			−0.202009
$287$	−8.47309			−0.0295230
$288$	−12.2843			−0.0426537
$289$	−18.0538			−0.0624700
$290$		−	3.57993i		−	0.0123446i
$291$		−	380.065i		−	1.30607i
$292$		−	148.015i		−	0.506902i
$293$	73.4071			0.250536			0.125268	−	0.992123i	$-0.460021\pi$
$293$	73.4071			0.250536			0.125268	+	0.992123i	$0.460021\pi$
$294$		−	219.729i		−	0.747378i
$295$	−2.36544			−0.00801844
$296$		−	23.4951i		−	0.0793754i
$297$	63.1960			0.212781
$298$	−87.7157			−0.294348
$299$	328.274			1.09791
$300$		−	166.923i		−	0.556409i
$301$		−	95.2497i		−	0.316444i
$302$		−	39.9695i		−	0.132349i
$303$			575.743i			1.90014i
$304$	−48.8528			−0.160700
$305$			11.9851i			0.0392954i
$306$			53.8142i			0.175863i
$307$	340.532			1.10922			0.554612	−	0.832109i	$-0.312867\pi$
$307$	340.532			1.10922			0.554612	+	0.832109i	$0.312867\pi$
$308$			8.78185i			0.0285125i
$309$		−	12.5417i		−	0.0405880i
$310$	−5.23759	+	5.39871i	−0.0168955	+	0.0174152i
$311$	−318.252			−1.02332			−0.511659	−	0.859189i	$-0.670969\pi$
$311$	−318.252			−1.02332			−0.511659	+	0.859189i	$0.670969\pi$
$312$	139.480			0.447052
$313$		−	380.123i		−	1.21445i	−0.794530	−	0.607225i	$-0.792282\pi$
$313$		−	380.123i		−	1.21445i	0.794530	−	0.607225i	$-0.207718\pi$
$314$	253.948			0.808752
$315$	−0.590837			−0.00187567
$316$		−	205.884i		−	0.651533i
$317$	384.470			1.21284			0.606420	−	0.795145i	$-0.292605\pi$
$317$	384.470			1.21284			0.606420	+	0.795145i	$0.292605\pi$
$318$	−439.196			−1.38112
$319$	40.8528			0.128065
$320$	−1.37258			−0.00428932
$321$			16.0977i			0.0501487i
$322$		−	49.8983i		−	0.154964i
$323$			214.011i			0.662574i
$324$	−191.657			−0.591534
$325$			368.416i			1.13359i
$326$	372.953			1.14403
$327$			269.668i			0.824673i
$328$	15.1127			0.0460753
$329$	−63.0193			−0.191548
$330$	−2.24560			−0.00680485
$331$			409.000i			1.23565i	0.786316	+	0.617825i	$0.211986\pi$
$331$			409.000i			1.23565i	−0.786316	+	0.617825i	$0.788014\pi$
$332$			221.745i			0.667906i
$333$			18.0388i			0.0541705i
$334$		−	177.048i		−	0.530085i
$335$	18.7107			0.0558528
$336$		−	21.2013i		−	0.0630990i
$337$		−	113.404i		−	0.336510i	−0.985744	−	0.168255i	$-0.946187\pi$
$337$		−	113.404i		−	0.336510i	0.985744	−	0.168255i	$-0.0538131\pi$
$338$	−68.8457			−0.203685
$339$			587.769i			1.73383i
$340$			6.01293i			0.0176851i
$341$	−61.6081	−	59.7695i	−0.180669	−	0.175277i
$342$	37.5076			0.109671
$343$	151.419			0.441456
$344$			169.888i			0.493862i
$345$	12.7595			0.0369839
$346$	190.510			0.550606
$347$		−	143.329i		−	0.413053i	−0.978441	−	0.206526i	$-0.933784\pi$
$347$		−	143.329i		−	0.413053i	0.978441	−	0.206526i	$-0.0662159\pi$
$348$	−98.6274			−0.283412
$349$	52.9361			0.151679			0.0758396	−	0.997120i	$-0.475836\pi$
$349$	52.9361			0.151679			0.0758396	+	0.997120i	$0.475836\pi$
$350$	56.0000			0.160000
$351$	336.735			0.959359
$352$		−	15.6634i		−	0.0444983i
$353$			598.746i			1.69616i	0.529865	+	0.848082i	$0.322243\pi$
$353$			598.746i			1.69616i	−0.529865	+	0.848082i	$0.677757\pi$
$354$			65.1682i			0.184091i
$355$	−0.473088			−0.00133264
$356$		−	100.944i		−	0.283549i
$357$	−92.8772			−0.260160
$358$		−	447.151i		−	1.24902i
$359$	370.806			1.03289			0.516443	−	0.856322i	$-0.327256\pi$
$359$	370.806			1.03289			0.516443	+	0.856322i	$0.327256\pi$
$360$	1.05382			0.00292729
$361$	−211.838			−0.586808
$362$			465.583i			1.28614i
$363$			378.803i			1.04354i
$364$			46.7935i			0.128553i
$365$			12.6977i			0.0347882i
$366$	330.191			0.902161
$367$		−	489.217i		−	1.33302i	−0.745497	−	0.666509i	$-0.767788\pi$
$367$		−	489.217i		−	1.33302i	0.745497	−	0.666509i	$-0.232212\pi$
$368$			88.9992i			0.241846i
$369$	−11.6030			−0.0314445
$370$			2.01556i			0.00544747i
$371$		−	147.343i		−	0.397152i
$372$	148.735	+	144.296i	0.399825	+	0.387893i
$373$	−423.461			−1.13528			−0.567642	−	0.823276i	$-0.692144\pi$
$373$	−423.461			−1.13528			−0.567642	+	0.823276i	$0.692144\pi$
$374$	−68.6173			−0.183469
$375$			28.6563i			0.0764168i
$376$	112.402			0.298942
$377$	217.681			0.577404
$378$		−	51.1844i		−	0.135408i
$379$	208.711			0.550688			0.275344	−	0.961346i	$-0.411208\pi$
$379$	208.711			0.550688			0.275344	+	0.961346i	$0.411208\pi$
$380$	4.19091			0.0110287
$381$	−353.657			−0.928233
$382$	−353.855			−0.926322
$383$		−	716.500i		−	1.87076i	−0.353648	−	0.935379i	$-0.615059\pi$
$383$		−	716.500i		−	1.87076i	0.353648	−	0.935379i	$-0.384941\pi$
$384$			37.8148i			0.0984761i
$385$		−	0.753364i		−	0.00195679i
$386$	−99.5563			−0.257918
$387$		−	130.435i		−	0.337041i
$388$	−227.421			−0.586138
$389$		−	70.1733i		−	0.180394i	−0.995924	−	0.0901971i	$-0.971250\pi$
$389$		−	70.1733i		−	0.180394i	0.995924	−	0.0901971i	$-0.0287497\pi$
$390$	−11.9655			−0.0306808
$391$	389.882			0.997141
$392$	−131.480			−0.335409
$393$		−	567.698i		−	1.44452i
$394$			454.843i			1.15442i
$395$			17.6621i			0.0447142i
$396$			12.0259i			0.0303683i
$397$	−484.696			−1.22090			−0.610448	−	0.792057i	$-0.709010\pi$
$397$	−484.696			−1.22090			−0.610448	+	0.792057i	$0.709010\pi$
$398$			151.653i			0.381037i
$399$			64.7339i			0.162240i
$400$	−99.8823			−0.249706
$401$		−	424.819i		−	1.05940i	−0.848185	−	0.529700i	$-0.822304\pi$
$401$		−	424.819i		−	1.05940i	0.848185	−	0.529700i	$-0.177696\pi$
$402$		−	515.481i		−	1.28229i
$403$	−328.274	−	318.477i	−0.814576	−	0.790266i
$404$	344.510			0.852747
$405$	16.4416			0.0405964
$406$		−	33.0880i		−	0.0814975i
$407$	−23.0009			−0.0565132
$408$	165.657			0.406022
$409$		−	644.352i		−	1.57543i	−0.616038	−	0.787716i	$-0.711263\pi$
$409$		−	644.352i		−	1.57543i	0.616038	−	0.787716i	$-0.288737\pi$
$410$	−1.29646			−0.00316211
$411$	−6.21530			−0.0151224
$412$	−7.50462			−0.0182151
$413$	−21.8629			−0.0529368
$414$		−	68.3307i		−	0.165050i
$415$		−	19.0227i		−	0.0458378i
$416$		−	83.4614i		−	0.200628i
$417$	81.7056			0.195937
$418$			47.8251i			0.114414i
$419$	−522.037			−1.24591			−0.622955	−	0.782257i	$-0.714068\pi$
$419$	−522.037			−1.24591			−0.622955	+	0.782257i	$0.714068\pi$
$420$			1.81878i			0.00433043i
$421$	−584.127			−1.38748			−0.693738	−	0.720228i	$-0.744037\pi$
$421$	−584.127			−1.38748			−0.693738	+	0.720228i	$0.744037\pi$
$422$	−77.8061			−0.184375
$423$	−86.2986			−0.204016
$424$			262.804i			0.619820i
$425$			437.558i			1.02955i
$426$			13.0336i			0.0305954i
$427$			110.774i			0.259424i
$428$	9.63247			0.0225058
$429$		−	136.546i		−	0.318289i
$430$		−	14.5741i		−	0.0338933i
$431$	−401.172			−0.930793			−0.465396	−	0.885102i	$-0.654088\pi$
$431$	−401.172			−0.930793			−0.465396	+	0.885102i	$0.654088\pi$
$432$			91.2931i			0.211327i
$433$			47.5876i			0.109902i	0.998489	+	0.0549510i	$0.0175003\pi$
$433$			47.5876i			0.109902i	−0.998489	+	0.0549510i	$0.982500\pi$
$434$	−48.4092	+	49.8983i	−0.111542	+	0.114973i
$435$	8.46089			0.0194503
$436$	161.362			0.370097
$437$		−	271.741i		−	0.621834i
$438$	349.823			0.798684
$439$	189.434			0.431512			0.215756	−	0.976447i	$-0.430779\pi$
$439$	189.434			0.431512			0.215756	+	0.976447i	$0.430779\pi$
$440$			1.34371i			0.00305388i
$441$	100.946			0.228903
$442$	−365.622			−0.827200
$443$	−145.115			−0.327573			−0.163786	−	0.986496i	$-0.552371\pi$
$443$	−145.115			−0.327573			−0.163786	+	0.986496i	$0.552371\pi$
$444$	55.5290			0.125065
$445$			8.65959i			0.0194597i
$446$			296.309i			0.664370i
$447$		−	207.310i		−	0.463780i
$448$	−12.6863			−0.0283176
$449$			749.924i			1.67021i	0.550091	+	0.835105i	$0.314593\pi$
$449$			749.924i			1.67021i	−0.550091	+	0.835105i	$0.685407\pi$
$450$	76.6863			0.170414
$451$		−	14.7948i		−	0.0328044i
$452$	351.706			0.778110
$453$	94.4651			0.208532
$454$	−245.387			−0.540500
$455$		−	4.01424i		−	0.00882252i
$456$		−	115.460i		−	0.253202i
$457$			689.761i			1.50932i	0.656114	+	0.754662i	$0.272199\pi$
$457$			689.761i			1.50932i	−0.656114	+	0.754662i	$0.727801\pi$
$458$			54.4284i			0.118839i
$459$	399.931			0.871309
$460$		−	7.63493i		−	0.0165977i
$461$		−	193.465i		−	0.419664i	−0.977737	−	0.209832i	$-0.932708\pi$
$461$		−	193.465i		−	0.419664i	0.977737	−	0.209832i	$-0.0672917\pi$
$462$	−20.7553			−0.0449248
$463$		−	174.951i		−	0.377864i	−0.981990	−	0.188932i	$-0.939497\pi$
$463$		−	174.951i		−	0.377864i	0.981990	−	0.188932i	$-0.0605026\pi$
$464$			59.0161i			0.127190i
$465$	−12.7595	−	12.3787i	−0.0274397	−	0.0266208i
$466$	192.360			0.412791
$467$	−778.144			−1.66626			−0.833131	−	0.553076i	$-0.813454\pi$
$467$	−778.144			−1.66626			−0.833131	+	0.553076i	$0.813454\pi$
$468$			64.0789i			0.136921i
$469$	172.936			0.368734
$470$	−9.64257			−0.0205161
$471$			600.188i			1.27428i
$472$	38.9949			0.0826164
$473$	166.315			0.351616
$474$	486.593			1.02657
$475$	304.971			0.642043
$476$			55.5753i			0.116755i
$477$		−	201.772i		−	0.423002i
$478$		−	561.267i		−	1.17420i
$479$	670.335			1.39945			0.699724	−	0.714414i	$-0.253307\pi$
$479$	670.335			1.39945			0.699724	+	0.714414i	$0.253307\pi$
$480$		−	3.24400i		−	0.00675833i
$481$	−122.558			−0.254799
$482$		−	215.535i		−	0.447168i
$483$	117.931			0.244164
$484$	226.666			0.468318
$485$	19.5097			0.0402261
$486$		−	162.474i		−	0.334309i
$487$		−	570.402i		−	1.17126i	−0.810580	−	0.585628i	$-0.800848\pi$
$487$		−	570.402i		−	1.17126i	0.810580	−	0.585628i	$-0.199152\pi$
$488$		−	197.578i		−	0.404872i
$489$			881.448i			1.80255i
$490$	11.2792			0.0230188
$491$		−	410.147i		−	0.835330i	−0.908601	−	0.417665i	$-0.862849\pi$
$491$		−	410.147i		−	0.835330i	0.908601	−	0.417665i	$-0.137151\pi$
$492$			35.7178i			0.0725971i
$493$	258.534			0.524410
$494$			254.833i			0.515856i
$495$		−	1.03166i		−	0.00208415i
$496$	86.3431	−	88.9992i	0.174079	−	0.179434i
$497$	−4.37258			−0.00879795
$498$	−524.077			−1.05236
$499$			204.181i			0.409180i	0.978848	+	0.204590i	$0.0655862\pi$
$499$			204.181i			0.409180i	−0.978848	+	0.204590i	$0.934414\pi$
$500$	17.1472			0.0342944
$501$	418.441			0.835211
$502$			210.136i			0.418598i
$503$	391.101			0.777536			0.388768	−	0.921336i	$-0.372901\pi$
$503$	391.101			0.777536			0.388768	+	0.921336i	$0.372901\pi$
$504$	9.74012			0.0193256
$505$	−29.5543			−0.0585233
$506$	87.1270			0.172188
$507$		−	162.712i		−	0.320930i
$508$			211.619i			0.416573i
$509$			218.066i			0.428421i	0.976788	+	0.214211i	$0.0687179\pi$
$509$			218.066i			0.428421i	−0.976788	+	0.214211i	$0.931282\pi$
$510$	−14.2111			−0.0278649
$511$			117.360i			0.229668i
$512$	22.6274			0.0441942
$513$		−	278.745i		−	0.543363i
$514$	−542.801			−1.05603
$515$	0.643794			0.00125009
$516$	−401.519			−0.778137
$517$		−	110.037i		−	0.212838i
$518$			18.6291i			0.0359636i
$519$			450.256i			0.867545i
$520$			7.15985i			0.0137689i
$521$	64.7006			0.124185			0.0620927	−	0.998070i	$-0.480223\pi$
$521$	64.7006			0.124185			0.0620927	+	0.998070i	$0.480223\pi$
$522$		−	45.3106i		−	0.0868019i
$523$			949.222i			1.81496i	0.420100	+	0.907478i	$0.361995\pi$
$523$			949.222i			1.81496i	−0.420100	+	0.907478i	$0.638005\pi$
$524$	−339.696			−0.648274
$525$			132.352i			0.252099i
$526$			275.362i			0.523502i
$527$	−389.882	−	378.247i	−0.739815	−	0.717736i
$528$	37.0193			0.0701124
$529$	33.9462			0.0641705
$530$		−	22.5450i		−	0.0425377i
$531$	−29.9390			−0.0563824
$532$	38.7351			0.0728103
$533$		−	78.8329i		−	0.147904i
$534$	238.573			0.446765
$535$	−0.826335			−0.00154455
$536$	−308.451			−0.575468
$537$	1056.81			1.96799
$538$		−	255.528i		−	0.474960i
$539$			128.714i			0.238802i
$540$		−	7.83171i		−	0.0145032i
$541$	655.337			1.21134			0.605672	−	0.795714i	$-0.292904\pi$
$541$	655.337			1.21134			0.605672	+	0.795714i	$0.292904\pi$
$542$		−	69.2808i		−	0.127824i
$543$	−1100.37			−2.02647
$544$		−	99.1248i		−	0.182215i
$545$	−13.8427			−0.0253995
$546$	−110.593			−0.202551
$547$	−661.947			−1.21014			−0.605071	−	0.796172i	$-0.706855\pi$
$547$	−661.947			−1.21014			−0.605071	+	0.796172i	$0.706855\pi$
$548$			3.71907i			0.00678663i
$549$			151.694i			0.276309i
$550$			97.7811i			0.177784i
$551$		−	180.194i		−	0.327031i
$552$	−210.343			−0.381056
$553$			163.244i			0.295198i
$554$		−	508.264i		−	0.917444i
$555$	−4.76364			−0.00858313
$556$		−	48.8905i		−	0.0879326i
$557$			46.9902i			0.0843631i	0.999110	+	0.0421815i	$0.0134308\pi$
$557$			46.9902i			0.0843631i	−0.999110	+	0.0421815i	$0.986569\pi$
$558$	−66.2914	+	68.3307i	−0.118802	+	0.122456i
$559$	886.195			1.58532
$560$	1.08831			0.00194341
$561$		−	162.172i		−	0.289077i
$562$	287.556			0.511666
$563$	−486.556			−0.864221			−0.432110	−	0.901821i	$-0.642231\pi$
$563$	−486.556			−0.864221			−0.432110	+	0.901821i	$0.642231\pi$
$564$			265.654i			0.471018i
$565$	−30.1716			−0.0534010
$566$	−491.848			−0.868989
$567$	151.963			0.268013
$568$	7.79899			0.0137306
$569$			435.542i			0.765452i	0.923862	+	0.382726i	$0.125015\pi$
$569$			435.542i			0.765452i	−0.923862	+	0.382726i	$0.874985\pi$
$570$			9.90491i			0.0173770i
$571$		−	19.8744i		−	0.0348064i	−0.999849	−	0.0174032i	$-0.994460\pi$
$571$		−	19.8744i		−	0.0348064i	0.999849	−	0.0174032i	$-0.00553989\pi$
$572$	−81.7056			−0.142842
$573$		−	836.310i		−	1.45953i
$574$	−11.9828			−0.0208759
$575$		−	555.590i		−	0.966244i
$576$	−17.3726			−0.0301607
$577$	193.622			0.335567			0.167784	−	0.985824i	$-0.446339\pi$
$577$	193.622			0.335567			0.167784	+	0.985824i	$0.446339\pi$
$578$	−25.5320			−0.0441729
$579$		−	235.294i		−	0.406380i
$580$		−	5.06278i		−	0.00872893i
$581$		−	175.820i		−	0.302616i
$582$		−	537.494i		−	0.923529i
$583$	257.275			0.441295
$584$		−	209.325i		−	0.358434i
$585$		−	5.49710i		−	0.00939675i
$586$	103.813			0.177156
$587$			212.488i			0.361989i	0.983484	+	0.180995i	$0.0579317\pi$
$587$			212.488i			0.361989i	−0.983484	+	0.180995i	$0.942068\pi$
$588$		−	310.744i		−	0.528476i
$589$	−263.632	+	271.741i	−0.447592	+	0.461361i
$590$	−3.34524			−0.00566989
$591$	−1074.99			−1.81893
$592$		−	33.2271i		−	0.0561269i
$593$	1018.91			1.71822			0.859112	−	0.511788i	$-0.171017\pi$
$593$	1018.91			1.71822			0.859112	+	0.511788i	$0.171017\pi$
$594$	89.3726			0.150459
$595$		−	4.76761i		−	0.00801279i
$596$	−124.049			−0.208136
$597$	−358.420			−0.600369
$598$	464.250			0.776337
$599$	177.090			0.295643			0.147822	−	0.989014i	$-0.452774\pi$
$599$	177.090			0.295643			0.147822	+	0.989014i	$0.452774\pi$
$600$		−	236.064i		−	0.393441i
$601$			640.354i			1.06548i	0.846278	+	0.532741i	$0.178838\pi$
$601$			640.354i			1.06548i	−0.846278	+	0.532741i	$0.821162\pi$
$602$		−	134.703i		−	0.223760i
$603$	236.818			0.392734
$604$		−	56.5255i		−	0.0935852i
$605$	−19.4449			−0.0321403
$606$			814.223i			1.34360i
$607$	−870.583			−1.43424			−0.717119	−	0.696950i	$-0.754540\pi$
$607$	−870.583			−1.43424			−0.717119	+	0.696950i	$0.754540\pi$
$608$	−69.0883			−0.113632
$609$	78.2010			0.128409
$610$			16.9495i			0.0277860i
$611$		−	586.327i		−	0.959618i
$612$			76.1047i			0.124354i
$613$		−	812.069i		−	1.32475i	−0.749175	−	0.662373i	$-0.769550\pi$
$613$		−	812.069i		−	1.32475i	0.749175	−	0.662373i	$-0.230450\pi$
$614$	481.585			0.784340
$615$		−	3.06410i		−	0.00498228i
$616$			12.4194i			0.0201614i
$617$	−674.975			−1.09396			−0.546981	−	0.837145i	$-0.684223\pi$
$617$	−674.975			−1.09396			−0.546981	+	0.837145i	$0.684223\pi$
$618$		−	17.7366i		−	0.0287000i
$619$			145.820i			0.235573i	0.993039	+	0.117787i	$0.0375799\pi$
$619$			145.820i			0.235573i	−0.993039	+	0.117787i	$0.962420\pi$
$620$	−7.40707	+	7.63493i	−0.0119469	+	0.0123144i
$621$	−507.813			−0.817735
$622$	−450.076			−0.723595
$623$			80.0375i			0.128471i
$624$	197.255			0.316114
$625$	622.793			0.996469
$626$		−	537.575i		−	0.858746i
$627$	−113.031			−0.180273
$628$	359.137			0.571874
$629$	−145.559			−0.231414
$630$	−0.835570			−0.00132630
$631$			688.302i			1.09081i	0.838172	+	0.545406i	$0.183624\pi$
$631$			688.302i			1.09081i	−0.838172	+	0.545406i	$0.816376\pi$
$632$		−	291.165i		−	0.460704i
$633$		−	183.889i		−	0.290504i
$634$	543.723			0.857607
$635$		−	18.1541i		−	0.0285891i
$636$	−621.117			−0.976599
$637$			685.845i			1.07668i
$638$	57.7746			0.0905558
$639$	−5.98781			−0.00937059
$640$	−1.94113			−0.00303301
$641$			315.020i			0.491450i	0.969340	+	0.245725i	$0.0790260\pi$
$641$			315.020i			0.491450i	−0.969340	+	0.245725i	$0.920974\pi$
$642$			22.7656i			0.0354605i
$643$		−	1101.41i		−	1.71293i	−0.516204	−	0.856465i	$-0.672656\pi$
$643$		−	1101.41i		−	1.71293i	0.516204	−	0.856465i	$-0.327344\pi$
$644$		−	70.5669i		−	0.109576i
$645$	34.4449			0.0534029
$646$			302.658i			0.468510i
$647$			42.7961i			0.0661454i	0.999453	+	0.0330727i	$0.0105293\pi$
$647$			42.7961i			0.0661454i	−0.999453	+	0.0330727i	$0.989471\pi$
$648$	−271.044			−0.418277
$649$		−	38.1746i		−	0.0588207i
$650$			521.019i			0.801568i
$651$	−117.931	−	114.412i	−0.181154	−	0.175747i
$652$	527.436			0.808950
$653$	−1084.35			−1.66056			−0.830281	−	0.557345i	$-0.811820\pi$
$653$	−1084.35			−1.66056			−0.830281	+	0.557345i	$0.811820\pi$
$654$			381.368i			0.583132i
$655$	29.1413			0.0444905
$656$	21.3726			0.0325802
$657$			160.713i			0.244616i
$658$	−89.1228			−0.135445
$659$	56.4445			0.0856518			0.0428259	−	0.999083i	$-0.486364\pi$
$659$	56.4445			0.0856518			0.0428259	+	0.999083i	$0.486364\pi$
$660$	−3.17576			−0.00481175
$661$	594.200			0.898941			0.449471	−	0.893295i	$-0.351613\pi$
$661$	594.200			0.898941			0.449471	+	0.893295i	$0.351613\pi$
$662$			578.413i			0.873736i
$663$		−	864.122i		−	1.30335i
$664$			313.594i			0.472281i
$665$	−3.32294			−0.00499691
$666$			25.5107i			0.0383043i
$667$	−328.274			−0.492165
$668$		−	250.384i		−	0.374826i
$669$	−700.304			−1.04679
$670$	26.4609			0.0394939
$671$	−193.421			−0.288258
$672$		−	29.9831i		−	0.0446177i
$673$			420.707i			0.625122i	0.949898	+	0.312561i	$0.101187\pi$
$673$			420.707i			0.625122i	−0.949898	+	0.312561i	$0.898813\pi$
$674$		−	160.377i		−	0.237948i
$675$		−	569.910i		−	0.844311i
$676$	−97.3625			−0.144027
$677$			895.449i			1.32267i	0.750090	+	0.661336i	$0.230010\pi$
$677$			895.449i			1.32267i	−0.750090	+	0.661336i	$0.769990\pi$
$678$			831.231i			1.22600i
$679$	180.321			0.265568
$680$			8.50356i			0.0125052i
$681$		−	579.954i		−	0.851621i
$682$	−87.1270	−	84.5268i	−0.127752	−	0.123940i
$683$	518.934			0.759786			0.379893	−	0.925030i	$-0.375961\pi$
$683$	518.934			0.759786			0.379893	+	0.925030i	$0.375961\pi$
$684$	53.0437			0.0775493
$685$		−	0.319046i		−	0.000465761i
$686$	214.139			0.312156
$687$	−128.638			−0.187245
$688$			240.259i			0.349213i
$689$	1370.87			1.98965
$690$	18.0446			0.0261516
$691$	677.247			0.980097			0.490048	−	0.871695i	$-0.336979\pi$
$691$	677.247			0.980097			0.490048	+	0.871695i	$0.336979\pi$
$692$	269.421			0.389337
$693$		−	9.53522i		−	0.0137593i
$694$		−	202.698i		−	0.292072i
$695$			4.19414i			0.00603474i
$696$	−139.480			−0.200403
$697$		−	93.6277i		−	0.134330i
$698$	74.8629			0.107253
$699$			454.630i			0.650400i
$700$	79.1960			0.113137
$701$	−333.382			−0.475580			−0.237790	−	0.971317i	$-0.576423\pi$
$701$	−333.382			−0.475580			−0.237790	+	0.971317i	$0.576423\pi$
$702$	476.215			0.678369
$703$			101.452i			0.144314i
$704$		−	22.1514i		−	0.0314651i
$705$		−	22.7895i		−	0.0323255i
$706$			846.755i			1.19937i
$707$	−273.159			−0.386364
$708$			92.1617i			0.130172i
$709$		−	1028.87i		−	1.45115i	−0.688143	−	0.725575i	$-0.741574\pi$
$709$		−	1028.87i		−	1.45115i	0.688143	−	0.725575i	$-0.258426\pi$
$710$	−0.669048			−0.000942321
$711$			223.547i			0.314412i
$712$		−	142.756i		−	0.200500i
$713$	495.054	+	480.280i	0.694325	+	0.673604i
$714$	−131.348			−0.183961
$715$	7.00923			0.00980313
$716$		−	632.367i		−	0.883194i
$717$	1326.51			1.85009
$718$	524.399			0.730361
$719$		−	59.1145i		−	0.0822176i	−0.999155	−	0.0411088i	$-0.986911\pi$
$719$		−	59.1145i		−	0.0822176i	0.999155	−	0.0411088i	$-0.0130890\pi$
$720$	1.49033			0.00206991
$721$	5.95036			0.00825293
$722$	−299.584			−0.414936
$723$	509.401			0.704566
$724$			658.434i			0.909439i
$725$		−	368.416i		−	0.508160i
$726$			535.709i			0.737891i
$727$	622.217			0.855870			0.427935	−	0.903810i	$-0.359241\pi$
$727$	622.217			0.855870			0.427935	+	0.903810i	$0.359241\pi$
$728$			66.1760i			0.0909010i
$729$	−478.460			−0.656324
$730$			17.9573i			0.0245990i
$731$	1052.51			1.43982
$732$	466.960			0.637924
$733$	−995.965			−1.35875			−0.679376	−	0.733791i	$-0.737749\pi$
$733$	−995.965			−1.35875			−0.679376	+	0.733791i	$0.737749\pi$
$734$		−	691.858i		−	0.942586i
$735$			26.6576i			0.0362689i
$736$			125.864i			0.171011i
$737$			301.962i			0.409718i
$738$	−16.4092			−0.0222346
$739$			217.418i			0.294206i	0.989121	+	0.147103i	$0.0469949\pi$
$739$			217.418i			0.294206i	−0.989121	+	0.147103i	$0.953005\pi$
$740$			2.85044i			0.00385194i
$741$	−602.278			−0.812791
$742$		−	208.375i		−	0.280829i
$743$			1045.54i			1.40719i	0.710600	+	0.703596i	$0.248424\pi$
$743$			1045.54i			1.40719i	−0.710600	+	0.703596i	$0.751576\pi$
$744$	210.343	+	204.066i	0.282719	+	0.274282i
$745$	10.6417			0.0142842
$746$	−598.864			−0.802767
$747$		−	240.767i		−	0.322312i
$748$	−97.0395			−0.129732
$749$	−7.63752			−0.0101970
$750$			40.5261i			0.0540348i
$751$	−617.458			−0.822181			−0.411091	−	0.911595i	$-0.634852\pi$
$751$	−617.458			−0.822181			−0.411091	+	0.911595i	$0.634852\pi$
$752$	158.960			0.211384
$753$	−496.642			−0.659551
$754$	307.848			0.408286
$755$			4.84912i			0.00642267i
$756$		−	72.3857i		−	0.0957482i
$757$			703.565i			0.929412i	0.885465	+	0.464706i	$0.153840\pi$
$757$			703.565i			0.929412i	−0.885465	+	0.464706i	$0.846160\pi$
$758$	295.161			0.389395
$759$			205.918i			0.271302i
$760$	5.92684			0.00779847
$761$			702.343i			0.922922i	0.887161	+	0.461461i	$0.152674\pi$
$761$			702.343i			0.922922i	−0.887161	+	0.461461i	$0.847326\pi$
$762$	−500.146			−0.656360
$763$	−127.943			−0.167684
$764$	−500.426			−0.655008
$765$		−	6.52875i		−	0.00853432i
$766$		−	1013.28i		−	1.32283i
$767$		−	203.411i		−	0.265203i
$768$			53.4782i			0.0696331i
$769$	−686.734			−0.893022			−0.446511	−	0.894778i	$-0.647334\pi$
$769$	−686.734			−0.893022			−0.446511	+	0.894778i	$0.647334\pi$
$770$		−	1.06542i		−	0.00138366i
$771$		−	1282.87i		−	1.66390i
$772$	−140.794			−0.182376
$773$		−	850.908i		−	1.10079i	−0.834905	−	0.550393i	$-0.814478\pi$
$773$		−	850.908i		−	1.10079i	0.834905	−	0.550393i	$-0.185522\pi$
$774$		−	184.463i		−	0.238324i
$775$	−539.009	+	555.590i	−0.695496	+	0.716891i
$776$	−321.622			−0.414462
$777$	−44.0286			−0.0566648
$778$		−	99.2401i		−	0.127558i
$779$	−65.2569			−0.0837701
$780$	−16.9218			−0.0216946
$781$		−	7.63493i		−	0.00977583i
$782$	551.377			0.705085
$783$	−336.735			−0.430058
$784$	−185.941			−0.237170
$785$	−30.8091			−0.0392472
$786$		−	802.846i		−	1.02143i
$787$			303.486i			0.385623i	0.981236	+	0.192812i	$0.0617607\pi$
$787$			303.486i			0.385623i	−0.981236	+	0.192812i	$0.938239\pi$
$788$			643.246i			0.816302i
$789$	−650.798			−0.824839
$790$			24.9780i			0.0316177i
$791$	−278.865			−0.352547
$792$			17.0071i			0.0214736i
$793$	−1030.63			−1.29966
$794$	−685.463			−0.863304
$795$	53.2834			0.0670232
$796$			214.470i			0.269434i
$797$		−	728.804i		−	0.914434i	−0.889355	−	0.457217i	$-0.848846\pi$
$797$		−	728.804i		−	0.914434i	0.889355	−	0.457217i	$-0.151154\pi$
$798$			91.5475i			0.114721i
$799$		−	696.364i		−	0.871545i
$800$	−141.255			−0.176569
$801$			109.603i			0.136833i
$802$		−	600.785i		−	0.749109i
$803$	−204.922			−0.255195
$804$		−	729.001i		−	0.906718i
$805$			6.05368i			0.00752010i
$806$	−464.250	−	450.395i	−0.575992	−	0.558802i
$807$	603.923			0.748355
$808$	487.210			0.602983
$809$			698.264i			0.863120i	0.902084	+	0.431560i	$0.142037\pi$
$809$			698.264i			0.863120i	−0.902084	+	0.431560i	$0.857963\pi$
$810$	23.2519			0.0287060
$811$	796.317			0.981895			0.490948	−	0.871189i	$-0.336651\pi$
$811$	796.317			0.981895			0.490948	+	0.871189i	$0.336651\pi$
$812$		−	46.7935i		−	0.0576274i
$813$	163.740			0.201402
$814$	−32.5281			−0.0399609
$815$	−45.2468			−0.0555176
$816$	234.274			0.287101
$817$		−	733.582i		−	0.897897i
$818$		−	911.251i		−	1.11400i
$819$		−	50.8077i		−	0.0620363i
$820$	−1.83348			−0.00223595
$821$		−	1071.39i		−	1.30498i	−0.757796	−	0.652491i	$-0.773724\pi$
$821$		−	1071.39i		−	1.30498i	0.757796	−	0.652491i	$-0.226276\pi$
$822$	−8.78976			−0.0106931
$823$		−	671.508i		−	0.815928i	−0.912998	−	0.407964i	$-0.866239\pi$
$823$		−	671.508i		−	0.815928i	0.912998	−	0.407964i	$-0.133761\pi$
$824$	−10.6131			−0.0128800
$825$	−231.098			−0.280119
$826$	−30.9188			−0.0374320
$827$			1029.64i			1.24503i	0.782610	+	0.622513i	$0.213888\pi$
$827$			1029.64i			1.24503i	−0.782610	+	0.622513i	$0.786112\pi$
$828$		−	96.6341i		−	0.116708i
$829$		−	633.432i		−	0.764092i	−0.924143	−	0.382046i	$-0.875220\pi$
$829$		−	633.432i		−	0.764092i	0.924143	−	0.382046i	$-0.124780\pi$
$830$		−	26.9021i		−	0.0324122i
$831$	1201.24			1.44554
$832$		−	118.032i		−	0.141866i
$833$			814.559i			0.977862i
$834$	115.549			0.138548
$835$			21.4796i			0.0257240i
$836$			67.6349i			0.0809030i
$837$	507.813	+	492.658i	0.606706	+	0.588600i
$838$	−738.271			−0.880992
$839$	−491.720			−0.586079			−0.293039	−	0.956100i	$-0.594667\pi$
$839$	−491.720			−0.586079			−0.293039	+	0.956100i	$0.594667\pi$
$840$			2.57215i			0.00306208i
$841$	623.319			0.741164
$842$	−826.080			−0.981093
$843$			679.618i			0.806190i
$844$	−110.034			−0.130373
$845$	8.35238			0.00988447
$846$	−122.045			−0.144261
$847$	−179.722			−0.212187
$848$			371.660i			0.438279i
$849$		−	1162.45i		−	1.36919i
$850$			618.800i			0.728000i
$851$	184.824			0.217185
$852$			18.4323i			0.0216342i
$853$	663.523			0.777870			0.388935	−	0.921265i	$-0.372843\pi$
$853$	663.523			0.777870			0.388935	+	0.921265i	$0.372843\pi$
$854$			156.658i			0.183440i
$855$	−4.55043			−0.00532214
$856$	13.6224			0.0159140
$857$	852.250			0.994457			0.497229	−	0.867620i	$-0.334351\pi$
$857$	852.250			0.994457			0.497229	+	0.867620i	$0.334351\pi$
$858$		−	193.105i		−	0.225064i
$859$		−	168.429i		−	0.196076i	−0.995183	−	0.0980381i	$-0.968743\pi$
$859$		−	168.429i		−	0.196076i	0.995183	−	0.0980381i	$-0.0312567\pi$
$860$		−	20.6109i		−	0.0239662i
$861$		−	28.3204i		−	0.0328924i
$862$	−567.342			−0.658170
$863$			905.754i			1.04954i	0.851244	+	0.524771i	$0.175849\pi$
$863$			905.754i			1.04954i	−0.851244	+	0.524771i	$0.824151\pi$
$864$			129.108i			0.149430i
$865$	−23.1127			−0.0267199
$866$			67.2990i			0.0777125i
$867$		−	60.3429i		−	0.0695997i
$868$	−68.4609	+	70.5669i	−0.0788720	+	0.0812982i
$869$	−285.040			−0.328009
$870$	11.9655			0.0137535
$871$			1608.98i			1.84728i
$872$	228.201			0.261698
$873$	246.931			0.282853
$874$		−	384.300i		−	0.439703i
$875$	−13.5959			−0.0155382
$876$	494.725			0.564755
$877$	−839.258			−0.956965			−0.478482	−	0.878097i	$-0.658813\pi$
$877$	−839.258			−0.956965			−0.478482	+	0.878097i	$0.658813\pi$
$878$	267.899			0.305125
$879$			245.355i			0.279130i
$880$			1.90029i			0.00215942i
$881$		−	1139.46i		−	1.29337i	−0.762757	−	0.646686i	$-0.776155\pi$
$881$		−	1139.46i		−	1.29337i	0.762757	−	0.646686i	$-0.223845\pi$
$882$	142.759			0.161859
$883$			342.234i			0.387581i	0.981043	+	0.193790i	$0.0620782\pi$
$883$			342.234i			0.387581i	−0.981043	+	0.193790i	$0.937922\pi$
$884$	−517.068			−0.584919
$885$		−	7.90622i		−	0.00893359i
$886$	−205.223			−0.231629
$887$	1128.08			1.27179			0.635896	−	0.771775i	$-0.280631\pi$
$887$	1128.08			1.27179			0.635896	+	0.771775i	$0.280631\pi$
$888$	78.5299			0.0884345
$889$		−	167.791i		−	0.188742i
$890$			12.2465i			0.0137601i
$891$			265.342i			0.297802i
$892$			419.044i			0.469780i
$893$	−485.354			−0.543510
$894$		−	293.180i		−	0.327942i
$895$			54.2485i			0.0606128i
$896$	−17.9411			−0.0200236
$897$			1097.22i			1.22321i
$898$			1060.55i			1.18102i
$899$	328.274	+	318.477i	0.365155	+	0.354257i
$900$	108.451			0.120501
$901$	1628.15			1.80704
$902$		−	20.9230i		−	0.0231962i
$903$	318.362			0.352560
$904$	497.387			0.550207
$905$		−	56.4847i		−	0.0624140i
$906$	133.594			0.147455
$907$	−508.301			−0.560420			−0.280210	−	0.959939i	$-0.590404\pi$
$907$	−508.301			−0.560420			−0.280210	+	0.959939i	$0.590404\pi$
$908$	−347.029			−0.382191
$909$	−374.064			−0.411511
$910$		−	5.67700i		−	0.00623846i
$911$			752.710i			0.826246i	0.910675	+	0.413123i	$0.135562\pi$
$911$			752.710i			0.826246i	−0.910675	+	0.413123i	$0.864438\pi$
$912$		−	163.285i		−	0.179041i
$913$	306.997			0.336251
$914$			975.469i			1.06725i
$915$	−40.0589			−0.0437802
$916$			76.9734i			0.0840321i
$917$	269.342			0.293721
$918$	565.588			0.616109
$919$	−910.396			−0.990638			−0.495319	−	0.868711i	$-0.664949\pi$
$919$	−910.396			−0.990638			−0.495319	+	0.868711i	$0.664949\pi$
$920$		−	10.7974i		−	0.0117363i
$921$			1138.19i			1.23582i
$922$		−	273.601i		−	0.296747i
$923$		−	40.6821i		−	0.0440760i
$924$	−29.3524			−0.0317666
$925$			207.425i			0.224243i
$926$		−	247.418i		−	0.267190i
$927$	8.14841			0.00879009
$928$			83.4614i			0.0899368i
$929$		−	961.821i		−	1.03533i	−0.855583	−	0.517665i	$-0.826801\pi$
$929$		−	961.821i		−	1.03533i	0.855583	−	0.517665i	$-0.173199\pi$
$930$	−18.0446	−	17.5061i	−0.0194028	−	0.0188237i
$931$	567.734			0.609811
$932$	272.039			0.291887
$933$		−	1063.72i		−	1.14011i
$934$	−1100.46			−1.17822
$935$	8.32468			0.00890340
$936$			90.6212i			0.0968175i
$937$	−515.024			−0.549652			−0.274826	−	0.961494i	$-0.588620\pi$
$937$	−515.024			−0.549652			−0.274826	+	0.961494i	$0.588620\pi$
$938$	244.569			0.260734
$939$	1270.52			1.35306
$940$	−13.6367			−0.0145071
$941$			736.670i			0.782858i	0.920208	+	0.391429i	$0.128019\pi$
$941$			736.670i			0.782858i	−0.920208	+	0.391429i	$0.871981\pi$
$942$			848.794i			0.901055i
$943$			118.884i			0.126070i
$944$	55.1472			0.0584186
$945$			6.20971i			0.00657112i
$946$	235.204			0.248630
$947$		−	348.443i		−	0.367945i	−0.982931	−	0.183972i	$-0.941104\pi$
$947$		−	348.443i		−	0.367945i	0.982931	−	0.183972i	$-0.0588957\pi$
$948$	688.146			0.725893
$949$	−1091.91			−1.15059
$950$	431.294			0.453993
$951$			1285.05i			1.35126i
$952$			78.5954i			0.0825582i
$953$		−	617.497i		−	0.647951i	−0.946065	−	0.323976i	$-0.894980\pi$
$953$		−	617.497i		−	0.647951i	0.946065	−	0.323976i	$-0.105020\pi$
$954$		−	285.348i		−	0.299107i
$955$	42.9298			0.0449527
$956$		−	793.752i		−	0.830284i
$957$			136.546i			0.142681i
$958$	947.997			0.989558
$959$		−	2.94883i		−	0.00307490i
$960$		−	4.58771i		−	0.00477886i
$961$	−29.1076	−	960.559i	−0.0302889	−	0.999541i
$962$	−173.324			−0.180170
$963$	−10.4588			−0.0108606
$964$		−	304.812i		−	0.316196i
$965$	12.0782			0.0125163
$966$	166.780			0.172650
$967$		−	1058.96i		−	1.09510i	−0.836772	−	0.547551i	$-0.815560\pi$
$967$		−	1058.96i		−	1.09510i	0.836772	−	0.547551i	$-0.184440\pi$
$968$	320.554			0.331151
$969$	−715.310			−0.738194
$970$	27.5908			0.0284442
$971$	−1112.85			−1.14609			−0.573043	−	0.819526i	$-0.694237\pi$
$971$	−1112.85			−1.14609			−0.573043	+	0.819526i	$0.694237\pi$
$972$		−	229.773i		−	0.236392i
$973$			38.7650i			0.0398407i
$974$		−	806.670i		−	0.828203i
$975$	−1231.39			−1.26297
$976$		−	279.417i		−	0.286288i
$977$	1859.00			1.90277			0.951384	−	0.308008i	$-0.0996622\pi$
$977$	1859.00			1.90277			0.951384	+	0.308008i	$0.0996622\pi$
$978$			1246.56i			1.27460i
$979$	−139.753			−0.142750
$980$	15.9512			0.0162768
$981$	−175.205			−0.178599
$982$		−	580.035i		−	0.590667i
$983$			922.826i			0.938785i	0.882990	+	0.469393i	$0.155527\pi$
$983$			922.826i			0.938785i	−0.882990	+	0.469393i	$0.844473\pi$
$984$			50.5125i			0.0513339i
$985$		−	55.1818i		−	0.0560221i
$986$	365.622			0.370814
$987$		−	210.635i		−	0.213410i
$988$			360.388i			0.364765i
$989$	−1336.43			−1.35129
$990$		−	1.45898i		−	0.00147372i
$991$		−	1536.86i		−	1.55082i	−0.631461	−	0.775408i	$-0.717544\pi$
$991$		−	1536.86i		−	1.55082i	0.631461	−	0.775408i	$-0.282456\pi$
$992$	122.108	−	125.864i	0.123092	−	0.126879i
$993$	−1367.04			−1.37667
$994$	−6.18377			−0.00622109
$995$		−	18.3986i		−	0.0184910i
$996$	−741.157			−0.744134
$997$	1334.88			1.33890			0.669449	−	0.742858i	$-0.266530\pi$
$997$	1334.88			1.33890			0.669449	+	0.742858i	$0.266530\pi$
$998$			288.756i			0.289334i
$999$	189.588			0.189778

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.3.b.a.61.4	yes	4
3.2	odd	2		558.3.d.a.433.2		4
4.3	odd	2		496.3.e.d.433.2		4
5.2	odd	4		1550.3.d.a.1549.7		8
5.3	odd	4		1550.3.d.a.1549.2		8
5.4	even	2		1550.3.c.a.1301.1		4
31.30	odd	2	inner	62.3.b.a.61.3	✓	4
93.92	even	2		558.3.d.a.433.1		4
124.123	even	2		496.3.e.d.433.3		4
155.92	even	4		1550.3.d.a.1549.6		8
155.123	even	4		1550.3.d.a.1549.3		8
155.154	odd	2		1550.3.c.a.1301.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.3.b.a.61.3	✓	4	31.30	odd	2	inner
62.3.b.a.61.4	yes	4	1.1	even	1	trivial
496.3.e.d.433.2		4	4.3	odd	2
496.3.e.d.433.3		4	124.123	even	2
558.3.d.a.433.1		4	93.92	even	2
558.3.d.a.433.2		4	3.2	odd	2
1550.3.c.a.1301.1		4	5.4	even	2
1550.3.c.a.1301.2		4	155.154	odd	2
1550.3.d.a.1549.2		8	5.3	odd	4
1550.3.d.a.1549.3		8	155.123	even	4
1550.3.d.a.1549.6		8	155.92	even	4
1550.3.d.a.1549.7		8	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	62.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +3.34239i q^{3} +2.00000 q^{4} -0.171573 q^{5} +4.72685i q^{6} -1.58579 q^{7} +2.82843 q^{8} -2.17157 q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +3.34239i q^{3} +2.00000 q^{4} -0.171573 q^{5} +4.72685i q^{6} -1.58579 q^{7} +2.82843 q^{8} -2.17157 q^{9} -0.242641 q^{10} -2.76893i q^{11} +6.68478i q^{12} -14.7540i q^{13} -2.24264 q^{14} -0.573464i q^{15} +4.00000 q^{16} -17.5230i q^{17} -3.07107 q^{18} -12.2132 q^{19} -0.343146 q^{20} -5.30032i q^{21} -3.91585i q^{22} +22.2498i q^{23} +9.45371i q^{24} -24.9706 q^{25} -20.8653i q^{26} +22.8233i q^{27} -3.17157 q^{28} +14.7540i q^{29} -0.811000i q^{30} +(21.5858 - 22.2498i) q^{31} +5.65685 q^{32} +9.25483 q^{33} -24.7812i q^{34} +0.272078 q^{35} -4.34315 q^{36} -8.30678i q^{37} -17.2721 q^{38} +49.3137 q^{39} -0.485281 q^{40} +5.34315 q^{41} -7.49578i q^{42} +60.0646i q^{43} -5.53785i q^{44} +0.372583 q^{45} +31.4660i q^{46} +39.7401 q^{47} +13.3696i q^{48} -46.4853 q^{49} -35.3137 q^{50} +58.5685 q^{51} -29.5080i q^{52} +92.9151i q^{53} +32.2770i q^{54} +0.475073i q^{55} -4.48528 q^{56} -40.8213i q^{57} +20.8653i q^{58} +13.7868 q^{59} -1.14693i q^{60} -69.8543i q^{61} +(30.5269 - 31.4660i) q^{62} +3.44365 q^{63} +8.00000 q^{64} +2.53139i q^{65} +13.0883 q^{66} -109.054 q^{67} -35.0459i q^{68} -74.3675 q^{69} +0.384776 q^{70} +2.75736 q^{71} -6.14214 q^{72} -74.0077i q^{73} -11.7476i q^{74} -83.4614i q^{75} -24.4264 q^{76} +4.39093i q^{77} +69.7401 q^{78} -102.942i q^{79} -0.686292 q^{80} -95.8284 q^{81} +7.55635 q^{82} +110.872i q^{83} -10.6006i q^{84} +3.00646i q^{85} +84.9442i q^{86} -49.3137 q^{87} -7.83171i q^{88} -50.4718i q^{89} +0.526912 q^{90} +23.3967i q^{91} +44.4996i q^{92} +(74.3675 + 72.1481i) q^{93} +56.2010 q^{94} +2.09545 q^{95} +18.9074i q^{96} -113.711 q^{97} -65.7401 q^{98} +6.01293i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4} - 12 q^{5} - 12 q^{7} - 20 q^{9}+O(q^{10}) \) 4 * q + 8 * q^4 - 12 * q^5 - 12 * q^7 - 20 * q^9	\( 4 q + 8 q^{4} - 12 q^{5} - 12 q^{7} - 20 q^{9} + 16 q^{10} + 8 q^{14} + 16 q^{16} + 16 q^{18} + 36 q^{19} - 24 q^{20} - 32 q^{25} - 24 q^{28} + 92 q^{31} - 144 q^{33} + 52 q^{35} - 40 q^{36} - 120 q^{38} + 152 q^{39} + 32 q^{40} + 44 q^{41} + 92 q^{45} - 56 q^{47} - 152 q^{49} - 96 q^{50} + 8 q^{51} + 16 q^{56} + 140 q^{59} - 8 q^{62} + 76 q^{63} + 32 q^{64} + 256 q^{66} - 176 q^{67} + 8 q^{69} - 72 q^{70} + 28 q^{71} + 32 q^{72} + 72 q^{76} + 64 q^{78} - 48 q^{80} - 372 q^{81} - 32 q^{82} - 152 q^{87} - 128 q^{90} - 8 q^{93} + 304 q^{94} - 348 q^{95} - 172 q^{97} - 48 q^{98}+O(q^{100}) \) 4 * q + 8 * q^4 - 12 * q^5 - 12 * q^7 - 20 * q^9 + 16 * q^10 + 8 * q^14 + 16 * q^16 + 16 * q^18 + 36 * q^19 - 24 * q^20 - 32 * q^25 - 24 * q^28 + 92 * q^31 - 144 * q^33 + 52 * q^35 - 40 * q^36 - 120 * q^38 + 152 * q^39 + 32 * q^40 + 44 * q^41 + 92 * q^45 - 56 * q^47 - 152 * q^49 - 96 * q^50 + 8 * q^51 + 16 * q^56 + 140 * q^59 - 8 * q^62 + 76 * q^63 + 32 * q^64 + 256 * q^66 - 176 * q^67 + 8 * q^69 - 72 * q^70 + 28 * q^71 + 32 * q^72 + 72 * q^76 + 64 * q^78 - 48 * q^80 - 372 * q^81 - 32 * q^82 - 152 * q^87 - 128 * q^90 - 8 * q^93 + 304 * q^94 - 348 * q^95 - 172 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

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