LMFDB - Embedded newform 33.4.d.b.32.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,4,Mod(32,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("33.32");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	33.d (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:	$1.94706303019$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 35x^{6} + 10x^{5} + 2614x^{4} + 16258x^{3} + 120841x^{2} + 205270x + 821047 $ x^8 - 2x^7 - 35x^6 + 10x^5 + 2614x^4 + 16258x^3 + 120841x^2 + 205270*x + 821047
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			32.6
Root			$-0.459178 - 3.22272i$ of defining polynomial
Character	$\chi$	$=$	33.32
Dual form			33.4.d.b.32.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.61686 q^{2} +(4.07603 + 3.22272i) q^{3} -1.15207 q^{4} +5.53456i q^{5} +(10.6664 + 8.43340i) q^{6} -31.3500i q^{7} -23.9496 q^{8} +(6.22810 + 26.2719i) q^{9} +O(q^{10})$	\(q+2.61686 q^{2} +(4.07603 + 3.22272i) q^{3} -1.15207 q^{4} +5.53456i q^{5} +(10.6664 + 8.43340i) q^{6} -31.3500i q^{7} -23.9496 q^{8} +(6.22810 + 26.2719i) q^{9} +14.4832i q^{10} +(18.7159 - 31.3164i) q^{11} +(-4.69587 - 3.71280i) q^{12} +31.3500i q^{13} -82.0383i q^{14} +(-17.8364 + 22.5591i) q^{15} -53.4562 q^{16} -85.3311 q^{17} +(16.2980 + 68.7497i) q^{18} +67.4672i q^{19} -6.37619i q^{20} +(101.032 - 127.783i) q^{21} +(48.9769 - 81.9504i) q^{22} +31.3164i q^{23} +(-97.6195 - 77.1831i) q^{24} +94.3686 q^{25} +82.0383i q^{26} +(-59.2810 + 127.156i) q^{27} +36.1173i q^{28} +100.236 q^{29} +(-46.6752 + 59.0338i) q^{30} +122.456 q^{31} +51.7099 q^{32} +(177.211 - 67.3303i) q^{33} -223.299 q^{34} +173.508 q^{35} +(-7.17519 - 30.2670i) q^{36} +55.8017 q^{37} +176.552i q^{38} +(-101.032 + 127.783i) q^{39} -132.551i q^{40} -311.177 q^{41} +(264.387 - 334.391i) q^{42} -72.2345i q^{43} +(-21.5620 + 36.0785i) q^{44} +(-145.403 + 34.4698i) q^{45} +81.9504i q^{46} +80.3551i q^{47} +(-217.889 - 172.275i) q^{48} -639.820 q^{49} +246.949 q^{50} +(-347.813 - 274.999i) q^{51} -36.1173i q^{52} -614.624i q^{53} +(-155.130 + 332.750i) q^{54} +(173.322 + 103.584i) q^{55} +750.820i q^{56} +(-217.428 + 274.999i) q^{57} +262.304 q^{58} -163.235i q^{59} +(20.5487 - 25.9896i) q^{60} -98.8172i q^{61} +320.450 q^{62} +(823.622 - 195.251i) q^{63} +562.967 q^{64} -173.508 q^{65} +(463.735 - 176.194i) q^{66} -158.106 q^{67} +98.3072 q^{68} +(-100.924 + 127.647i) q^{69} +454.046 q^{70} +654.415i q^{71} +(-149.161 - 629.202i) q^{72} +1089.74i q^{73} +146.025 q^{74} +(384.650 + 304.124i) q^{75} -77.7268i q^{76} +(-981.766 - 586.744i) q^{77} +(-264.387 + 334.391i) q^{78} -986.151i q^{79} -295.857i q^{80} +(-651.422 + 327.248i) q^{81} -814.304 q^{82} +329.265 q^{83} +(-116.396 + 147.215i) q^{84} -472.271i q^{85} -189.027i q^{86} +(408.567 + 323.034i) q^{87} +(-448.240 + 750.015i) q^{88} -1197.30i q^{89} +(-380.499 + 90.2025i) q^{90} +982.820 q^{91} -36.0785i q^{92} +(499.136 + 394.643i) q^{93} +210.278i q^{94} -373.402 q^{95} +(210.771 + 166.647i) q^{96} -1177.97 q^{97} -1674.32 q^{98} +(939.304 + 296.661i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} + 44 q^{4} - 30 q^{9}+O(q^{10}) $ 8 * q + 6 * q^3 + 44 * q^4 - 30 * q^9	$ 8 q + 6 q^{3} + 44 q^{4} - 30 q^{9} - 144 q^{12} + 150 q^{15} - 268 q^{16} - 300 q^{22} + 276 q^{25} + 324 q^{27} + 820 q^{31} + 834 q^{33} + 768 q^{34} - 696 q^{36} - 884 q^{37} - 120 q^{42} - 1722 q^{45} - 732 q^{48} - 2032 q^{49} - 476 q^{55} + 1992 q^{58} + 2772 q^{60} - 1084 q^{64} + 2076 q^{66} + 172 q^{67} - 834 q^{69} + 5016 q^{70} + 1800 q^{75} + 120 q^{78} - 4014 q^{81} - 6408 q^{82} - 3852 q^{88} + 4776 q^{91} + 1146 q^{93} - 3836 q^{97} + 1074 q^{99}+O(q^{100}) $ 8 * q + 6 * q^3 + 44 * q^4 - 30 * q^9 - 144 * q^12 + 150 * q^15 - 268 * q^16 - 300 * q^22 + 276 * q^25 + 324 * q^27 + 820 * q^31 + 834 * q^33 + 768 * q^34 - 696 * q^36 - 884 * q^37 - 120 * q^42 - 1722 * q^45 - 732 * q^48 - 2032 * q^49 - 476 * q^55 + 1992 * q^58 + 2772 * q^60 - 1084 * q^64 + 2076 * q^66 + 172 * q^67 - 834 * q^69 + 5016 * q^70 + 1800 * q^75 + 120 * q^78 - 4014 * q^81 - 6408 * q^82 - 3852 * q^88 + 4776 * q^91 + 1146 * q^93 - 3836 * q^97 + 1074 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	2.61686			0.925198			0.462599	−	0.886568i	$-0.346917\pi$
$2$	2.61686			0.925198			0.462599	+	0.886568i	$0.346917\pi$
$3$	4.07603	+	3.22272i	0.784433	+	0.620214i
$3$	4.07603	+	3.22272i	0.784433	+	0.620214i
$4$	−1.15207			−0.144008
$5$			5.53456i			0.495026i	0.968885	+	0.247513i	$0.0796134\pi$
$5$			5.53456i			0.495026i	−0.968885	+	0.247513i	$0.920387\pi$
$6$	10.6664	+	8.43340i	0.725756	+	0.573820i
$7$		−	31.3500i		−	1.69274i	−0.532596	−	0.846369i	$-0.678784\pi$
$7$		−	31.3500i		−	1.69274i	0.532596	−	0.846369i	$-0.321216\pi$
$8$	−23.9496			−1.05843
$9$	6.22810	+	26.2719i	0.230670	+	0.973032i
$10$			14.4832i			0.457998i
$11$	18.7159	−	31.3164i	0.513006	−	0.858385i
$11$	18.7159	−	31.3164i	0.513006	−	0.858385i
$12$	−4.69587	−	3.71280i	−0.112965	−	0.0893160i
$13$			31.3500i			0.668840i	0.942424	+	0.334420i	$0.108540\pi$
$13$			31.3500i			0.668840i	−0.942424	+	0.334420i	$0.891460\pi$
$14$		−	82.0383i		−	1.56612i
$15$	−17.8364	+	22.5591i	−0.307022	+	0.388315i
$16$	−53.4562			−0.835253
$17$	−85.3311			−1.21740			−0.608701	−	0.793400i	$-0.708309\pi$
$17$	−85.3311			−1.21740			−0.608701	+	0.793400i	$0.708309\pi$
$18$	16.2980	+	68.7497i	0.213416	+	0.900247i
$19$			67.4672i			0.814634i	0.913287	+	0.407317i	$0.133536\pi$
$19$			67.4672i			0.814634i	−0.913287	+	0.407317i	$0.866464\pi$
$20$		−	6.37619i		−	0.0712880i
$21$	101.032	−	127.783i	1.04986	−	1.32784i
$22$	48.9769	−	81.9504i	0.474632	−	0.794176i
$23$			31.3164i			0.283909i	0.989873	+	0.141955i	$0.0453387\pi$
$23$			31.3164i			0.283909i	−0.989873	+	0.141955i	$0.954661\pi$
$24$	−97.6195	−	77.1831i	−0.830271	−	0.656455i
$25$	94.3686			0.754949
$26$			82.0383i			0.618809i
$27$	−59.2810	+	127.156i	−0.422542	+	0.906343i
$28$			36.1173i			0.243769i
$29$	100.236			0.641842			0.320921	−	0.947106i	$-0.396008\pi$
$29$	100.236			0.641842			0.320921	+	0.947106i	$0.396008\pi$
$30$	−46.6752	+	59.0338i	−0.284056	+	0.359268i
$31$	122.456			0.709477			0.354738	−	0.934966i	$-0.384570\pi$
$31$	122.456			0.709477			0.354738	+	0.934966i	$0.384570\pi$
$32$	51.7099			0.285660
$33$	177.211	−	67.3303i	0.934801	−	0.355173i
$34$	−223.299			−1.12634
$35$	173.508			0.837950
$36$	−7.17519	−	30.2670i	−0.0332185	−	0.140125i
$37$	55.8017			0.247939			0.123969	−	0.992286i	$-0.460438\pi$
$37$	55.8017			0.247939			0.123969	+	0.992286i	$0.460438\pi$
$38$			176.552i			0.753698i
$39$	−101.032	+	127.783i	−0.414823	+	0.524660i
$40$		−	132.551i		−	0.523953i
$41$	−311.177			−1.18531			−0.592654	−	0.805457i	$-0.701920\pi$
$41$	−311.177			−1.18531			−0.592654	+	0.805457i	$0.701920\pi$
$42$	264.387	−	334.391i	0.971328	−	1.22852i
$43$		−	72.2345i		−	0.256178i	−0.991763	−	0.128089i	$-0.959116\pi$
$43$		−	72.2345i		−	0.256178i	0.991763	−	0.128089i	$-0.0408843\pi$
$44$	−21.5620	+	36.0785i	−0.0738772	+	0.123615i
$45$	−145.403	+	34.4698i	−0.481677	+	0.114188i
$46$			81.9504i			0.262672i
$47$			80.3551i			0.249383i	0.992196	+	0.124691i	$0.0397941\pi$
$47$			80.3551i			0.249383i	−0.992196	+	0.124691i	$0.960206\pi$
$48$	−217.889	−	172.275i	−0.655200	−	0.518035i
$49$	−639.820			−1.86536
$50$	246.949			0.698477
$51$	−347.813	−	274.999i	−0.954971	−	0.755049i
$52$		−	36.1173i		−	0.0963185i
$53$		−	614.624i		−	1.59293i	−0.604687	−	0.796463i	$-0.706702\pi$
$53$		−	614.624i		−	1.59293i	0.604687	−	0.796463i	$-0.293298\pi$
$54$	−155.130	+	332.750i	−0.390935	+	0.838547i
$55$	173.322	+	103.584i	0.424923	+	0.253951i
$56$			750.820i			1.79165i
$57$	−217.428	+	274.999i	−0.505247	+	0.639026i
$58$	262.304			0.593831
$59$		−	163.235i		−	0.360193i	−0.983649	−	0.180096i	$-0.942359\pi$
$59$		−	163.235i		−	0.360193i	0.983649	−	0.180096i	$-0.0576410\pi$
$60$	20.5487	−	25.9896i	0.0442138	−	0.0559206i
$61$		−	98.8172i		−	0.207414i	−0.994608	−	0.103707i	$-0.966930\pi$
$61$		−	98.8172i		−	0.207414i	0.994608	−	0.103707i	$-0.0330704\pi$
$62$	320.450			0.656407
$63$	823.622	−	195.251i	1.64709	−	0.390465i
$64$	562.967			1.09955
$65$	−173.508			−0.331093
$66$	463.735	−	176.194i	0.864876	−	0.328605i
$67$	−158.106			−0.288294			−0.144147	−	0.989556i	$-0.546044\pi$
$67$	−158.106			−0.288294			−0.144147	+	0.989556i	$0.546044\pi$
$68$	98.3072			0.175316
$69$	−100.924	+	127.647i	−0.176084	+	0.222708i
$70$	454.046			0.775270
$71$			654.415i			1.09387i	0.837175	+	0.546935i	$0.184206\pi$
$71$			654.415i			1.09387i	−0.837175	+	0.546935i	$0.815794\pi$
$72$	−149.161	−	629.202i	−0.244150	−	1.02989i
$73$			1089.74i			1.74718i	0.486666	+	0.873588i	$0.338213\pi$
$73$			1089.74i			1.74718i	−0.486666	+	0.873588i	$0.661787\pi$
$74$	146.025			0.229393
$75$	384.650	+	304.124i	0.592207	+	0.468229i
$76$		−	77.7268i		−	0.117314i
$77$	−981.766	−	586.744i	−1.45302	−	0.868385i
$78$	−264.387	+	334.391i	−0.383794	+	0.485414i
$79$		−	986.151i		−	1.40444i	−0.711961	−	0.702219i	$-0.752193\pi$
$79$		−	986.151i		−	1.40444i	0.711961	−	0.702219i	$-0.247807\pi$
$80$		−	295.857i		−	0.413472i
$81$	−651.422	+	327.248i	−0.893582	+	0.448899i
$82$	−814.304			−1.09664
$83$	329.265			0.435441			0.217720	−	0.976011i	$-0.430138\pi$
$83$	329.265			0.435441			0.217720	+	0.976011i	$0.430138\pi$
$84$	−116.396	+	147.215i	−0.151189	+	0.191220i
$85$		−	472.271i		−	0.602646i
$86$		−	189.027i		−	0.237016i
$87$	408.567	+	323.034i	0.503482	+	0.398079i
$88$	−448.240	+	750.015i	−0.542983	+	0.908544i
$89$		−	1197.30i		−	1.42599i	−0.701168	−	0.712996i	$-0.747338\pi$
$89$		−	1197.30i		−	1.42599i	0.701168	−	0.712996i	$-0.252662\pi$
$90$	−380.499	+	90.2025i	−0.445646	+	0.105646i
$91$	982.820			1.13217
$92$		−	36.0785i		−	0.0408853i
$93$	499.136	+	394.643i	0.556537	+	0.440027i
$94$			210.278i			0.230728i
$95$	−373.402			−0.403265
$96$	210.771	+	166.647i	0.224081	+	0.177170i
$97$	−1177.97			−1.23304			−0.616518	−	0.787341i	$-0.711457\pi$
$97$	−1177.97			−1.23304			−0.616518	+	0.787341i	$0.711457\pi$
$98$	−1674.32			−1.72583
$99$	939.304	+	296.661i	0.953571	+	0.301167i
$100$	−108.719			−0.108719
$101$	1433.46			1.41222			0.706111	−	0.708102i	$-0.250448\pi$
$101$	1433.46			1.41222			0.706111	+	0.708102i	$0.250448\pi$
$102$	−910.175	−	719.632i	−0.883537	−	0.698570i
$103$	561.051			0.536719			0.268359	−	0.963319i	$-0.413519\pi$
$103$	561.051			0.536719			0.268359	+	0.963319i	$0.413519\pi$
$104$		−	750.820i		−	0.707923i
$105$	707.226	+	559.169i	0.657316	+	0.519708i
$106$		−	1608.38i		−	1.47377i
$107$	−547.152			−0.494348			−0.247174	−	0.968971i	$-0.579502\pi$
$107$	−547.152			−0.494348			−0.247174	+	0.968971i	$0.579502\pi$
$108$	68.2957	−	146.493i	0.0608496	−	0.130521i
$109$			186.079i			0.163515i	0.996652	+	0.0817573i	$0.0260532\pi$
$109$			186.079i			0.163515i	−0.996652	+	0.0817573i	$0.973947\pi$
$110$	453.560	+	271.066i	0.393138	+	0.234955i
$111$	227.450	+	179.833i	0.194491	+	0.153775i
$112$			1675.85i			1.41387i
$113$		−	438.994i		−	0.365461i	−0.983163	−	0.182730i	$-0.941506\pi$
$113$		−	438.994i		−	0.365461i	0.983163	−	0.182730i	$-0.0584935\pi$
$114$	−568.978	+	719.632i	−0.467453	+	0.591225i
$115$	−173.322			−0.140543
$116$	−115.479			−0.0924307
$117$	−823.622	+	195.251i	−0.650802	+	0.154281i
$118$		−	427.162i		−	0.333250i
$119$			2675.13i			2.06074i
$120$	427.175	−	540.281i	0.324963	−	0.411006i
$121$	−630.428	−	1172.23i	−0.473650	−	0.880713i
$122$		−	258.590i		−	0.191899i
$123$	−1268.37	−	1002.84i	−0.929795	−	0.735144i
$124$	−141.078			−0.102171
$125$			1214.11i			0.868746i
$126$	2155.30	−	510.943i	1.52388	−	0.361257i
$127$		−	736.076i		−	0.514301i	−0.966371	−	0.257150i	$-0.917216\pi$
$127$		−	736.076i		−	0.514301i	0.966371	−	0.257150i	$-0.0827835\pi$
$128$	1059.52			0.731637
$129$	232.792	−	294.430i	0.158885	−	0.200955i
$130$	−454.046			−0.306327
$131$	2072.98			1.38257			0.691287	−	0.722580i	$-0.257044\pi$
$131$	2072.98			1.38257			0.691287	+	0.722580i	$0.257044\pi$
$132$	−204.159	+	77.5690i	−0.134619	+	0.0511478i
$133$	2115.09			1.37896
$134$	−413.740			−0.266729
$135$	−703.755	−	328.095i	−0.448664	−	0.209169i
$136$	2043.65			1.28854
$137$		−	340.203i		−	0.212157i	−0.994358	−	0.106078i	$-0.966171\pi$
$137$		−	340.203i		−	0.212157i	0.994358	−	0.106078i	$-0.0338294\pi$
$138$	−264.103	+	334.032i	−0.162913	+	0.206049i
$139$			192.867i			0.117689i	0.998267	+	0.0588445i	$0.0187416\pi$
$139$			192.867i			0.117689i	−0.998267	+	0.0588445i	$0.981258\pi$
$140$	−199.893			−0.120672
$141$	−258.962	+	327.530i	−0.154671	+	0.195624i
$142$			1712.51i			1.01205i
$143$	981.766	+	586.744i	0.574122	+	0.343119i
$144$	−332.931	−	1404.39i	−0.192668	−	0.812728i
$145$			554.765i			0.317729i
$146$			2851.68i			1.61648i
$147$	−2607.93	−	2061.96i	−1.46325	−	1.15692i
$148$	−64.2873			−0.0357053
$149$	−2241.72			−1.23254			−0.616270	−	0.787535i	$-0.711357\pi$
$149$	−2241.72			−1.23254			−0.616270	+	0.787535i	$0.711357\pi$
$150$	1006.57	+	795.848i	0.547909	+	0.433205i
$151$			3102.92i			1.67227i	0.548527	+	0.836133i	$0.315189\pi$
$151$			3102.92i			1.67227i	−0.548527	+	0.836133i	$0.684811\pi$
$152$		−	1615.82i		−	0.862236i
$153$	−531.451	−	2241.81i	−0.280819	−	1.18457i
$154$	−2569.14	−	1535.42i	−1.34433	−	0.803428i
$155$			677.742i			0.351210i
$156$	116.396	−	147.215i	0.0597381	−	0.0755554i
$157$	863.055			0.438721			0.219361	−	0.975644i	$-0.429603\pi$
$157$	863.055			0.438721			0.219361	+	0.975644i	$0.429603\pi$
$158$		−	2580.61i		−	1.29938i
$159$	1980.76	−	2505.23i	0.987955	−	1.24954i
$160$			286.192i			0.141409i
$161$	981.766			0.480584
$162$	−1704.68	+	856.360i	−0.826741	+	0.415321i
$163$	−3746.03			−1.80007			−0.900035	−	0.435817i	$-0.856459\pi$
$163$	−3746.03			−1.80007			−0.900035	+	0.435817i	$0.856459\pi$
$164$	358.496			0.170694
$165$	372.644	+	980.784i	0.175820	+	0.462751i
$166$	861.640			0.402869
$167$	−440.549			−0.204136			−0.102068	−	0.994777i	$-0.532546\pi$
$167$	−440.549			−0.204136			−0.102068	+	0.994777i	$0.532546\pi$
$168$	−2419.69	+	3060.37i	−1.11121	+	1.40543i
$169$	1214.18			0.552654
$170$		−	1235.86i		−	0.557567i
$171$	−1772.49	+	420.193i	−0.792665	+	0.187912i
$172$			83.2190i			0.0368918i
$173$	−1336.07			−0.587164			−0.293582	−	0.955934i	$-0.594847\pi$
$173$	−1336.07			−0.587164			−0.293582	+	0.955934i	$0.594847\pi$
$174$	1069.16	+	845.334i	0.465821	+	0.368302i
$175$		−	2958.45i		−	1.27793i
$176$	−1000.48	+	1674.05i	−0.428490	+	0.716969i
$177$	526.061	−	665.351i	0.223397	−	0.282547i
$178$		−	3133.16i		−	1.31933i
$179$		−	1488.74i		−	0.621640i	−0.950469	−	0.310820i	$-0.899396\pi$
$179$		−	1488.74i		−	0.621640i	0.950469	−	0.310820i	$-0.100604\pi$
$180$	167.514	−	39.7116i	0.0693655	−	0.0164440i
$181$	740.437			0.304068			0.152034	−	0.988375i	$-0.451418\pi$
$181$	740.437			0.304068			0.152034	+	0.988375i	$0.451418\pi$
$182$	2571.90			1.04748
$183$	318.460	−	402.782i	0.128641	−	0.162702i
$184$		−	750.015i		−	0.300499i
$185$			308.838i			0.122736i
$186$	1306.17	+	1032.72i	0.514907	+	0.407112i
$187$	−1597.05	+	2672.26i	−0.624534	+	1.04500i
$188$		−	92.5744i		−	0.0359132i
$189$	3986.35	+	1858.46i	1.53420	+	0.715253i
$190$	−977.138			−0.373100
$191$			1153.54i			0.437000i	0.975837	+	0.218500i	$0.0701164\pi$
$191$			1153.54i			0.437000i	−0.975837	+	0.218500i	$0.929884\pi$
$192$	2294.67	+	1814.29i	0.862519	+	0.681953i
$193$			2194.50i			0.818463i	0.912431	+	0.409231i	$0.134203\pi$
$193$			2194.50i			0.818463i	−0.912431	+	0.409231i	$0.865797\pi$
$194$	−3082.57			−1.14080
$195$	−707.226	−	559.169i	−0.259720	−	0.205349i
$196$	737.116			0.268628
$197$	1125.37			0.407001			0.203501	−	0.979075i	$-0.434768\pi$
$197$	1125.37			0.407001			0.203501	+	0.979075i	$0.434768\pi$
$198$	2458.02	+	776.319i	0.882242	+	0.278639i
$199$	764.813			0.272443			0.136221	−	0.990678i	$-0.456504\pi$
$199$	764.813			0.272443			0.136221	+	0.990678i	$0.456504\pi$
$200$	−2260.09			−0.799064
$201$	−644.445	−	509.531i	−0.226147	−	0.178804i
$202$	3751.15			1.30658
$203$		−	3142.41i		−	1.08647i
$204$	400.703	+	316.817i	0.137524	+	0.108733i
$205$		−	1722.23i		−	0.586759i
$206$	1468.19			0.496571
$207$	−822.739	+	195.041i	−0.276253	+	0.0654894i
$208$		−	1675.85i		−	0.558650i
$209$	2112.83	+	1262.71i	0.699270	+	0.417912i
$210$	1850.71	+	1463.27i	0.608147	+	0.480833i
$211$			2272.22i			0.741357i	0.928761	+	0.370679i	$0.120875\pi$
$211$			2272.22i			0.741357i	−0.928761	+	0.370679i	$0.879125\pi$
$212$			708.088i			0.229395i
$213$	−2109.00	+	2667.42i	−0.678433	+	0.858068i
$214$	−1431.82			−0.457369
$215$	399.787			0.126815
$216$	1419.76	−	3045.35i	0.447233	−	0.959305i
$217$		−	3839.00i		−	1.20096i
$218$			486.941i			0.151283i
$219$	−3511.92	+	4441.80i	−1.08362	+	1.37054i
$220$	−199.679	−	119.336i	−0.0611925	−	0.0365711i
$221$		−	2675.13i		−	0.814247i
$222$	595.203	+	470.598i	0.179943	+	0.142272i
$223$	4328.25			1.29974			0.649868	−	0.760047i	$-0.274824\pi$
$223$	4328.25			1.29974			0.649868	+	0.760047i	$0.274824\pi$
$224$		−	1621.10i		−	0.483547i
$225$	587.737	+	2479.24i	0.174144	+	0.734589i
$226$		−	1148.78i		−	0.338123i
$227$	−1643.96			−0.480677			−0.240339	−	0.970689i	$-0.577259\pi$
$227$	−1643.96			−0.480677			−0.240339	+	0.970689i	$0.577259\pi$
$228$	250.492	−	316.817i	0.0727598	−	0.0920251i
$229$	−4275.60			−1.23380			−0.616899	−	0.787042i	$-0.711611\pi$
$229$	−4275.60			−1.23380			−0.616899	+	0.787042i	$0.711611\pi$
$230$	−453.560			−0.130030
$231$	−2110.80	−	5555.55i	−0.601214	−	1.58237i
$232$	−2400.63			−0.679348
$233$	−5355.07			−1.50568			−0.752838	−	0.658206i	$-0.771316\pi$
$233$	−5355.07			−1.50568			−0.752838	+	0.658206i	$0.771316\pi$
$234$	−2155.30	+	510.943i	−0.602121	+	0.142741i
$235$	−444.730			−0.123451
$236$			188.058i			0.0518708i
$237$	3178.09	−	4019.58i	0.871052	−	1.10169i
$238$			7000.42i			1.90660i
$239$	4447.93			1.20382			0.601909	−	0.798565i	$-0.294407\pi$
$239$	4447.93			1.20382			0.601909	+	0.798565i	$0.294407\pi$
$240$	953.465	−	1205.92i	0.256441	−	0.324341i
$241$			3378.85i			0.903117i	0.892242	+	0.451558i	$0.149132\pi$
$241$			3378.85i			0.903117i	−0.892242	+	0.451558i	$0.850868\pi$
$242$	−1649.74	−	3067.55i	−0.438220	−	0.814834i
$243$	−3709.84	−	765.479i	−0.979369	−	0.202080i
$244$			113.844i			0.0298693i
$245$		−	3541.12i		−	0.923405i
$246$	−3319.13	−	2624.28i	−0.860244	−	0.680154i
$247$	−2115.09			−0.544859
$248$	−2932.78			−0.750935
$249$	1342.10	+	1061.13i	0.341574	+	0.270066i
$250$			3177.15i			0.803762i
$251$			2992.78i			0.752599i	0.926498	+	0.376300i	$0.122804\pi$
$251$			2992.78i			0.752599i	−0.926498	+	0.376300i	$0.877196\pi$
$252$	−948.868	+	224.942i	−0.237195	+	0.0562302i
$253$	980.714	+	586.115i	0.243703	+	0.145647i
$254$		−	1926.20i		−	0.475830i
$255$	1522.00	−	1924.99i	0.373769	−	0.472736i
$256$	−1731.12			−0.422636
$257$			4528.01i			1.09902i	0.835486	+	0.549512i	$0.185186\pi$
$257$			4528.01i			1.09902i	−0.835486	+	0.549512i	$0.814814\pi$
$258$	609.183	−	770.482i	0.147000	−	0.185923i
$259$		−	1749.38i		−	0.419696i
$260$	199.893			0.0476802
$261$	624.282	+	2633.40i	0.148054	+	0.624533i
$262$	5424.70			1.27916
$263$	−1877.72			−0.440247			−0.220124	−	0.975472i	$-0.570646\pi$
$263$	−1877.72			−0.440247			−0.220124	+	0.975472i	$0.570646\pi$
$264$	−4244.13	+	1612.54i	−0.989425	+	0.375927i
$265$	3401.68			0.788541
$266$	5534.90			1.27581
$267$	3858.56	−	4880.23i	0.884420	−	1.11860i
$268$	182.149			0.0415168
$269$			5266.95i			1.19380i	0.802317	+	0.596899i	$0.203601\pi$
$269$			5266.95i			1.19380i	−0.802317	+	0.596899i	$0.796399\pi$
$270$	−1841.63	−	858.576i	−0.415103	−	0.193523i
$271$		−	1790.99i		−	0.401457i	−0.979647	−	0.200729i	$-0.935669\pi$
$271$		−	1790.99i		−	0.401457i	0.979647	−	0.200729i	$-0.0643309\pi$
$272$	4561.48			1.01684
$273$	4006.01	+	3167.36i	0.888112	+	0.702187i
$274$		−	890.261i		−	0.196287i
$275$	1766.20	−	2955.28i	0.387293	−	0.648037i
$276$	116.271	−	147.057i	0.0253576	−	0.0320718i
$277$		−	4502.84i		−	0.976712i	−0.872644	−	0.488356i	$-0.837597\pi$
$277$		−	4502.84i		−	0.976712i	0.872644	−	0.488356i	$-0.162403\pi$
$278$			504.705i			0.108886i
$279$	762.670	+	3217.15i	0.163655	+	0.690344i
$280$	−4155.46			−0.886916
$281$	2448.22			0.519745			0.259873	−	0.965643i	$-0.416319\pi$
$281$	2448.22			0.519745			0.259873	+	0.965643i	$0.416319\pi$
$282$	−677.667	+	857.098i	−0.143101	+	0.180991i
$283$		−	5366.18i		−	1.12716i	−0.826061	−	0.563580i	$-0.809424\pi$
$283$		−	5366.18i		−	1.12716i	0.826061	−	0.563580i	$-0.190576\pi$
$284$		−	753.931i		−	0.157527i
$285$	−1522.00	−	1203.37i	−0.316335	−	0.250111i
$286$	2569.14	+	1535.42i	0.531177	+	0.317453i
$287$			9755.37i			2.00642i
$288$	322.055	+	1358.52i	0.0658933	+	0.277956i
$289$	2368.40			0.482068
$290$			1451.74i			0.293962i
$291$	−4801.43	−	3796.26i	−0.967234	−	0.764745i
$292$		−	1255.45i		−	0.251608i
$293$	180.359			0.0359615			0.0179807	−	0.999838i	$-0.494276\pi$
$293$	180.359			0.0359615			0.0179807	+	0.999838i	$0.494276\pi$
$294$	−6824.57	−	5395.86i	−1.35380	−	1.07038i
$295$	903.434			0.178305
$296$	−1336.43			−0.262427
$297$	2872.58	+	4236.32i	0.561225	+	0.827663i
$298$	−5866.25			−1.14034
$299$	−981.766			−0.189890
$300$	−443.142	−	350.371i	−0.0852828	−	0.0674290i
$301$	−2264.55			−0.433643
$302$			8119.90i			1.54718i
$303$	5842.82	+	4619.64i	1.10779	+	0.875879i
$304$		−	3606.54i		−	0.680425i
$305$	546.910			0.102675
$306$	−1390.73	−	5866.49i	−0.259813	−	1.09596i
$307$			3326.41i			0.618399i	0.950997	+	0.309199i	$0.100061\pi$
$307$			3326.41i			0.618399i	−0.950997	+	0.309199i	$0.899939\pi$
$308$	1131.06	+	675.968i	0.209247	+	0.125055i
$309$	2286.86	+	1808.11i	0.421020	+	0.332880i
$310$			1773.55i			0.324939i
$311$			768.857i			0.140186i	0.997540	+	0.0700931i	$0.0223296\pi$
$311$			768.857i			0.140186i	−0.997540	+	0.0700931i	$0.977670\pi$
$312$	2419.69	−	3060.37i	0.439063	−	0.555318i
$313$	−2791.25			−0.504061			−0.252030	−	0.967719i	$-0.581098\pi$
$313$	−2791.25			−0.504061			−0.252030	+	0.967719i	$0.581098\pi$
$314$	2258.49			0.405904
$315$	1080.63	+	4558.39i	0.193290	+	0.815352i
$316$			1136.11i			0.202251i
$317$		−	8283.66i		−	1.46769i	−0.679318	−	0.733844i	$-0.737724\pi$
$317$		−	8283.66i		−	1.46769i	0.679318	−	0.733844i	$-0.262276\pi$
$318$	5183.37	−	6555.82i	0.914054	−	1.15608i
$319$	1876.02	−	3139.04i	0.329269	−	0.550948i
$320$			3115.78i			0.544304i
$321$	−2230.21	−	1763.32i	−0.387783	−	0.306601i
$322$	2569.14			0.444635
$323$		−	5757.05i		−	0.991737i
$324$	750.481	−	377.011i	0.128683	−	0.0646453i
$325$			2958.45i			0.504940i
$326$	−9802.81			−1.66542
$327$	−599.680	+	758.463i	−0.101414	+	0.128266i
$328$	7452.57			1.25457
$329$	2519.13			0.422140
$330$	975.154	+	2566.57i	0.162668	+	0.428136i
$331$	−5679.76			−0.943166			−0.471583	−	0.881822i	$-0.656317\pi$
$331$	−5679.76			−0.943166			−0.471583	+	0.881822i	$0.656317\pi$
$332$	−379.336			−0.0627071
$333$	347.539	+	1466.01i	0.0571922	+	0.241252i
$334$	−1152.85			−0.188866
$335$		−	875.047i		−	0.142713i
$336$	−5400.80	+	6830.82i	−0.876898	+	1.10908i
$337$		−	4983.76i		−	0.805587i	−0.915291	−	0.402794i	$-0.868039\pi$
$337$		−	4983.76i		−	0.805587i	0.915291	−	0.402794i	$-0.131961\pi$
$338$	3177.33			0.511314
$339$	1414.76	−	1789.35i	0.226664	−	0.286679i
$340$			544.087i			0.0867861i
$341$	2291.88	−	3834.88i	0.363966	−	0.609004i
$342$	−4638.35	+	1099.58i	−0.733372	+	0.173856i
$343$			9305.29i			1.46484i
$344$			1729.99i			0.271148i
$345$	−706.468	−	558.570i	−0.110246	−	0.0871664i
$346$	−3496.29			−0.543243
$347$	−6193.96			−0.958240			−0.479120	−	0.877749i	$-0.659044\pi$
$347$	−6193.96			−0.958240			−0.479120	+	0.877749i	$0.659044\pi$
$348$	−470.697	−	372.157i	−0.0725057	−	0.0573268i
$349$			7398.44i			1.13475i	0.823458	+	0.567377i	$0.192042\pi$
$349$			7398.44i			1.13475i	−0.823458	+	0.567377i	$0.807958\pi$
$350$		−	7741.84i		−	1.18234i
$351$	−3986.35	−	1858.46i	−0.606198	−	0.282613i
$352$	967.800	−	1619.37i	0.146545	−	0.245206i
$353$		−	10982.6i		−	1.65593i	−0.560782	−	0.827964i	$-0.689499\pi$
$353$		−	10982.6i		−	1.65593i	0.560782	−	0.827964i	$-0.310501\pi$
$354$	1376.63	−	1741.13i	0.206686	−	0.261412i
$355$	−3621.90			−0.541495
$356$			1379.37i			0.205355i
$357$	−8621.20	+	10903.9i	−1.27810	+	1.61652i
$358$		−	3895.81i		−	0.575140i
$359$	8901.12			1.30859			0.654294	−	0.756240i	$-0.272966\pi$
$359$	8901.12			1.30859			0.654294	+	0.756240i	$0.272966\pi$
$360$	3482.36	−	825.540i	0.509823	−	0.120860i
$361$	2307.17			0.336372
$362$	1937.62			0.281323
$363$	1208.12	−	6809.74i	0.174683	−	0.984625i
$364$	−1132.27			−0.163042
$365$	−6031.21			−0.864898
$366$	833.365	−	1054.02i	0.119018	−	0.150532i
$367$	−2464.65			−0.350554			−0.175277	−	0.984519i	$-0.556082\pi$
$367$	−2464.65			−0.350554			−0.175277	+	0.984519i	$0.556082\pi$
$368$		−	1674.05i		−	0.237136i
$369$	−1938.04	−	8175.19i	−0.273415	−	1.15334i
$370$			808.184i			0.113555i
$371$	−19268.4			−2.69641
$372$	−575.038	−	454.655i	−0.0801460	−	0.0633676i
$373$			3752.61i			0.520920i	0.965485	+	0.260460i	$0.0838741\pi$
$373$			3752.61i			0.520920i	−0.965485	+	0.260460i	$0.916126\pi$
$374$	−4179.25	+	6992.92i	−0.577818	+	0.966832i
$375$	−3912.74	+	4948.75i	−0.538808	+	0.681473i
$376$		−	1924.47i		−	0.263955i
$377$			3142.41i			0.429290i
$378$	10431.7	+	4863.31i	1.41944	+	0.661751i
$379$	10155.4			1.37638			0.688191	−	0.725529i	$-0.258405\pi$
$379$	10155.4			1.37638			0.688191	+	0.725529i	$0.258405\pi$
$380$	430.184			0.0580736
$381$	2372.17	−	3000.27i	0.318976	−	0.403434i
$382$			3018.64i			0.404312i
$383$			2719.27i			0.362789i	0.983410	+	0.181395i	$0.0580611\pi$
$383$			2719.27i			0.362789i	−0.983410	+	0.181395i	$0.941939\pi$
$384$	4318.66	+	3414.55i	0.573920	+	0.453771i
$385$	3247.37	−	5433.65i	0.429873	−	0.719284i
$386$			5742.68i			0.757240i
$387$	1897.74	−	449.884i	0.249270	−	0.0590927i
$388$	1357.10			0.177567
$389$		−	6595.32i		−	0.859630i	−0.902917	−	0.429815i	$-0.858579\pi$
$389$		−	6595.32i		−	0.859630i	0.902917	−	0.429815i	$-0.141421\pi$
$390$	−1850.71	−	1463.27i	−0.240293	−	0.189988i
$391$		−	2672.26i		−	0.345632i
$392$	15323.5			1.97437
$393$	8449.55	+	6680.65i	1.08454	+	0.857492i
$394$	2944.93			0.376557
$395$	5457.91			0.695234
$396$	−1082.14	−	341.773i	−0.137322	−	0.0433706i
$397$	4542.34			0.574241			0.287121	−	0.957894i	$-0.407302\pi$
$397$	4542.34			0.574241			0.287121	+	0.957894i	$0.407302\pi$
$398$	2001.40			0.252064
$399$	8621.20	+	6816.37i	1.08170	+	0.855251i
$400$	−5044.59			−0.630573
$401$		−	1755.50i		−	0.218617i	−0.994008	−	0.109308i	$-0.965136\pi$
$401$		−	1755.50i		−	0.218617i	0.994008	−	0.109308i	$-0.0348636\pi$
$402$	−1686.42	−	1333.37i	−0.209231	−	0.165429i
$403$			3839.00i			0.474526i
$404$	−1651.44			−0.203372
$405$	−1811.17	−	3605.33i	−0.222217	−	0.442347i
$406$		−	8223.22i		−	1.00520i
$407$	1044.38	−	1747.51i	0.127194	−	0.212827i
$408$	8329.98	+	6586.12i	1.01077	+	0.799170i
$409$		−	5484.95i		−	0.663113i	−0.943435	−	0.331556i	$-0.892426\pi$
$409$		−	5484.95i		−	0.663113i	0.943435	−	0.331556i	$-0.107574\pi$
$410$		−	4506.82i		−	0.542868i
$411$	1096.38	−	1386.68i	0.131582	−	0.166423i
$412$	−646.369			−0.0772920
$413$	−5117.41			−0.609713
$414$	−2152.99	+	510.395i	−0.255588	+	0.0605907i
$415$			1822.34i			0.215555i
$416$			1621.10i			0.191061i
$417$	−621.557	+	786.133i	−0.0729923	+	0.0923191i
$418$	5528.96	+	3304.33i	0.646963	+	0.386651i
$419$			1727.12i			0.201374i	0.994918	+	0.100687i	$0.0321040\pi$
$419$			1727.12i			0.201374i	−0.994918	+	0.100687i	$0.967896\pi$
$420$	−814.772	−	644.201i	−0.0946590	−	0.0748423i
$421$	−12472.2			−1.44384			−0.721921	−	0.691976i	$-0.756741\pi$
$421$	−12472.2			−1.44384			−0.721921	+	0.691976i	$0.756741\pi$
$422$			5946.08i			0.685902i
$423$	−2111.08	+	500.459i	−0.242657	+	0.0575252i
$424$			14720.0i			1.68601i
$425$	−8052.58			−0.919076
$426$	−5518.95	+	6980.25i	−0.627685	+	0.793883i
$427$	−3097.91			−0.351097
$428$	630.356			0.0711902
$429$	2110.80	+	5555.55i	0.237553	+	0.625232i
$430$	1046.18			0.117329
$431$	10753.1			1.20176			0.600881	−	0.799338i	$-0.294816\pi$
$431$	10753.1			1.20176			0.600881	+	0.799338i	$0.294816\pi$
$432$	3168.94	−	6797.30i	0.352930	−	0.757026i
$433$	−5234.91			−0.581002			−0.290501	−	0.956875i	$-0.593822\pi$
$433$	−5234.91			−0.581002			−0.290501	+	0.956875i	$0.593822\pi$
$434$		−	10046.1i		−	1.11112i
$435$	−1787.85	+	2261.24i	−0.197060	+	0.249237i
$436$		−	214.375i		−	0.0235475i
$437$	−2112.83			−0.231282
$438$	−9190.18	+	11623.5i	−1.00257	+	1.26802i
$439$		−	15674.4i		−	1.70410i	−0.523463	−	0.852049i	$-0.675360\pi$
$439$		−	15674.4i		−	1.70410i	0.523463	−	0.852049i	$-0.324640\pi$
$440$	−4151.01	−	2480.81i	−0.449753	−	0.268791i
$441$	−3984.86	−	16809.3i	−0.430284	−	1.81506i
$442$		−	7000.42i		−	0.753340i
$443$		−	8387.86i		−	0.899592i	−0.893131	−	0.449796i	$-0.851497\pi$
$443$		−	8387.86i		−	0.899592i	0.893131	−	0.449796i	$-0.148503\pi$
$444$	−262.037	−	207.180i	−0.0280084	−	0.0221449i
$445$	6626.52			0.705904
$446$	11326.4			1.20251
$447$	−9137.31	−	7224.43i	−0.966845	−	0.764438i
$448$		−	17649.0i		−	1.86124i
$449$			11504.8i			1.20923i	0.796517	+	0.604616i	$0.206673\pi$
$449$			11504.8i			1.20923i	−0.796517	+	0.604616i	$0.793327\pi$
$450$	1538.02	+	6487.81i	0.161118	+	0.679641i
$451$	−5823.96	+	9744.92i	−0.608070	+	1.01745i
$452$			505.750i			0.0526294i
$453$	−9999.86	+	12647.6i	−1.03716	+	1.31178i
$454$	−4302.02			−0.444722
$455$			5439.48i			0.560454i
$456$	5207.33	−	6586.12i	0.534771	−	0.676367i
$457$			6605.46i			0.676128i	0.941123	+	0.338064i	$0.109772\pi$
$457$			6605.46i			0.676128i	−0.941123	+	0.338064i	$0.890228\pi$
$458$	−11188.6			−1.14151
$459$	5058.52	−	10850.4i	0.514404	−	1.10338i
$460$	199.679			0.0202393
$461$	−9031.60			−0.912458			−0.456229	−	0.889862i	$-0.650800\pi$
$461$	−9031.60			−0.912458			−0.456229	+	0.889862i	$0.650800\pi$
$462$	−5523.66	−	14538.1i	−0.556242	−	1.46401i
$463$	6282.62			0.630622			0.315311	−	0.948988i	$-0.397891\pi$
$463$	6282.62			0.630622			0.315311	+	0.948988i	$0.397891\pi$
$464$	−5358.26			−0.536101
$465$	−2184.17	+	2762.50i	−0.217825	+	0.275501i
$466$	−14013.5			−1.39305
$467$			8744.66i			0.866498i	0.901274	+	0.433249i	$0.142633\pi$
$467$			8744.66i			0.866498i	−0.901274	+	0.433249i	$0.857367\pi$
$468$	948.868	−	224.942i	0.0937210	−	0.0222178i
$469$			4956.61i			0.488006i
$470$	−1163.79			−0.114217
$471$	3517.84	+	2781.39i	0.344148	+	0.272101i
$472$			3909.42i			0.381241i
$473$	−2262.12	−	1351.94i	−0.219900	−	0.131421i
$474$	8316.61	−	10518.7i	0.805895	−	1.01928i
$475$			6366.79i			0.615007i
$476$		−	3081.93i		−	0.296764i
$477$	16147.3	−	3827.94i	1.54997	−	0.367441i
$478$	11639.6			1.11377
$479$	9062.52			0.864462			0.432231	−	0.901763i	$-0.357727\pi$
$479$	9062.52			0.864462			0.432231	+	0.901763i	$0.357727\pi$
$480$	−922.318	+	1166.53i	−0.0877039	+	0.110926i
$481$			1749.38i			0.165831i
$482$			8841.97i			0.835562i
$483$	4001.71	+	3163.96i	0.376986	+	0.298065i
$484$	726.296	+	1350.49i	0.0682096	+	0.126830i
$485$		−	6519.53i		−	0.610385i
$486$	−9708.13	−	2003.15i	−0.906110	−	0.186964i
$487$	−1312.74			−0.122148			−0.0610741	−	0.998133i	$-0.519453\pi$
$487$	−1312.74			−0.122148			−0.0610741	+	0.998133i	$0.519453\pi$
$488$			2366.64i			0.219534i
$489$	−15268.9	−	12072.4i	−1.41203	−	1.11643i
$490$		−	9266.61i		−	0.854332i
$491$	18634.5			1.71276			0.856379	−	0.516348i	$-0.172709\pi$
$491$	18634.5			1.71276			0.856379	+	0.516348i	$0.172709\pi$
$492$	1461.24	+	1155.33i	0.133898	+	0.105867i
$493$	−8553.28			−0.781380
$494$	−5534.90			−0.504103
$495$	−1641.89	+	5198.64i	−0.149086	+	0.472043i
$496$	−6546.04			−0.592593
$497$	20515.9			1.85164
$498$	3512.07	+	2776.83i	0.316024	+	0.249865i
$499$	1647.41			0.147792			0.0738959	−	0.997266i	$-0.476457\pi$
$499$	1647.41			0.147792			0.0738959	+	0.997266i	$0.476457\pi$
$500$		−	1398.74i		−	0.125107i
$501$	−1795.69	−	1419.77i	−0.160131	−	0.126608i
$502$			7831.66i			0.696303i
$503$	13771.7			1.22078			0.610389	−	0.792102i	$-0.291013\pi$
$503$	13771.7			1.22078			0.610389	+	0.792102i	$0.291013\pi$
$504$	−19725.4	+	4676.18i	−1.74334	+	0.413281i
$505$			7933.56i			0.699087i
$506$	2566.39	+	1533.78i	0.225474	+	0.134752i
$507$	4949.04	+	3912.97i	0.433520	+	0.342763i
$508$			848.009i			0.0740636i
$509$			18543.7i			1.61480i	0.590001	+	0.807402i	$0.299127\pi$
$509$			18543.7i			1.61480i	−0.590001	+	0.807402i	$0.700873\pi$
$510$	3982.85	−	5037.42i	0.345811	−	0.437374i
$511$	34163.2			2.95751
$512$	−13006.3			−1.12266
$513$	−8578.89	−	3999.53i	−0.738338	−	0.344217i
$514$			11849.1i			1.01682i
$515$			3105.17i			0.265690i
$516$	−268.192	+	339.204i	−0.0228808	+	0.0289392i
$517$	2516.43	+	1503.92i	0.214066	+	0.127935i
$518$		−	4577.88i		−	0.388302i
$519$	−5445.85	−	4305.78i	−0.460590	−	0.364167i
$520$	4155.46			0.350440
$521$			7299.58i			0.613821i	0.951738	+	0.306910i	$0.0992951\pi$
$521$			7299.58i			0.613821i	−0.951738	+	0.306910i	$0.900705\pi$
$522$	1633.66	+	6891.22i	0.136979	+	0.577817i
$523$		−	20549.8i		−	1.71813i	−0.511868	−	0.859064i	$-0.671046\pi$
$523$		−	20549.8i		−	1.71813i	0.511868	−	0.859064i	$-0.328954\pi$
$524$	−2388.22			−0.199102
$525$	9534.27	−	12058.7i	0.792590	−	1.00245i
$526$	−4913.72			−0.407316
$527$	−10449.3			−0.863719
$528$	−9473.01	+	3599.22i	−0.780795	+	0.296659i
$529$	11186.3			0.919396
$530$	8901.70			0.729556
$531$	4288.49	−	1016.64i	0.350479	−	0.0830859i
$532$	−2436.73			−0.198582
$533$		−	9755.37i		−	0.792781i
$534$	10097.3	−	12770.8i	0.818264	−	1.03492i
$535$		−	3028.25i		−	0.244715i
$536$	3786.58			0.305140
$537$	4797.79	−	6068.15i	0.385550	−	0.487635i
$538$			13782.8i			1.10450i
$539$	−11974.8	+	20036.8i	−0.956943	+	1.60120i
$540$	810.774	+	377.987i	0.0646114	+	0.0301222i
$541$		−	16253.8i		−	1.29170i	−0.763466	−	0.645848i	$-0.776504\pi$
$541$		−	16253.8i		−	1.29170i	0.763466	−	0.645848i	$-0.223496\pi$
$542$		−	4686.76i		−	0.371427i
$543$	3018.04	+	2386.22i	0.238521	+	0.188587i
$544$	−4412.47			−0.347763
$545$	−1029.86			−0.0809441
$546$	10483.1	+	8288.52i	0.821680	+	0.649663i
$547$		−	3989.38i		−	0.311834i	−0.987770	−	0.155917i	$-0.950167\pi$
$547$		−	3989.38i		−	0.311834i	0.987770	−	0.155917i	$-0.0498333\pi$
$548$			391.936i			0.0305523i
$549$	2596.11	−	615.443i	0.201820	−	0.0478442i
$550$	4621.88	−	7733.54i	0.358323	−	0.599562i
$551$			6762.67i			0.522867i
$552$	2417.09	−	3057.09i	0.186374	−	0.235722i
$553$	−30915.8			−2.37735
$554$		−	11783.3i		−	0.903652i
$555$	−995.300	+	1258.83i	−0.0761227	+	0.0962784i
$556$		−	222.196i		−	0.0169482i
$557$	5131.88			0.390386			0.195193	−	0.980765i	$-0.437467\pi$
$557$	5131.88			0.390386			0.195193	+	0.980765i	$0.437467\pi$
$558$	1995.80	+	8418.82i	0.151414	+	0.638705i
$559$	2264.55			0.171342
$560$	−9275.10			−0.699901
$561$	−15121.6	+	5745.37i	−1.13803	+	0.432388i
$562$	6406.63			0.480867
$563$	−12818.7			−0.959579			−0.479789	−	0.877384i	$-0.659287\pi$
$563$	−12818.7			−0.959579			−0.479789	+	0.877384i	$0.659287\pi$
$564$	298.342	−	377.337i	0.0222739	−	0.0281715i
$565$	2429.64			0.180913
$566$		−	14042.5i		−	1.04285i
$567$	10259.2	+	20422.0i	0.759869	+	1.51260i
$568$		−	15673.0i		−	1.15779i
$569$	−12934.1			−0.952942			−0.476471	−	0.879190i	$-0.658084\pi$
$569$	−12934.1			−0.952942			−0.476471	+	0.879190i	$0.658084\pi$
$570$	−3982.85	−	3149.05i	−0.292672	−	0.231402i
$571$			13100.2i			0.960119i	0.877236	+	0.480060i	$0.159385\pi$
$571$			13100.2i			0.960119i	−0.877236	+	0.480060i	$0.840615\pi$
$572$	−1131.06	−	675.968i	−0.0826784	−	0.0494120i
$573$	−3717.53	+	4701.86i	−0.271034	+	0.342798i
$574$			25528.4i			1.85633i
$575$			2955.28i			0.214337i
$576$	3506.22	+	14790.2i	0.253633	+	1.06989i
$577$	1908.15			0.137673			0.0688366	−	0.997628i	$-0.478071\pi$
$577$	1908.15			0.137673			0.0688366	+	0.997628i	$0.478071\pi$
$578$	6197.76			0.446009
$579$	−7072.26	+	8944.84i	−0.507622	+	0.642029i
$580$		−	639.126i		−	0.0457556i
$581$		−	10322.5i		−	0.737087i
$582$	−12564.7	−	9934.27i	−0.894883	−	0.707541i
$583$	−19247.8	−	11503.3i	−1.36734	−	0.817181i
$584$		−	26098.8i		−	1.84927i
$585$	−1080.63	−	4558.39i	−0.0763734	−	0.322164i
$586$	471.975			0.0332715
$587$		−	20278.3i		−	1.42585i	−0.701240	−	0.712925i	$-0.747370\pi$
$587$		−	20278.3i		−	1.42585i	0.701240	−	0.712925i	$-0.252630\pi$
$588$	3004.51	+	2375.52i	0.210721	+	0.166607i
$589$			8261.78i			0.577964i
$590$	2364.16			0.164967
$591$	4587.04	+	3626.75i	0.319265	+	0.252428i
$592$	−2982.95			−0.207092
$593$	16590.4			1.14888			0.574441	−	0.818546i	$-0.305220\pi$
$593$	16590.4			1.14888			0.574441	+	0.818546i	$0.305220\pi$
$594$	7517.12	+	11085.8i	0.519244	+	0.765752i
$595$	−14805.7			−1.02012
$596$	2582.61			0.177496
$597$	3117.40	+	2464.78i	0.213713	+	0.168973i
$598$	−2569.14			−0.175686
$599$		−	16785.3i		−	1.14496i	−0.819919	−	0.572479i	$-0.805982\pi$
$599$		−	16785.3i		−	1.14496i	0.819919	−	0.572479i	$-0.194018\pi$
$600$	−9212.22	−	7283.66i	−0.626812	−	0.495590i
$601$			12434.4i			0.843942i	0.906609	+	0.421971i	$0.138662\pi$
$601$			12434.4i			0.843942i	−0.906609	+	0.421971i	$0.861338\pi$
$602$	−5926.00			−0.401205
$603$	−984.699	−	4153.73i	−0.0665009	−	0.280519i
$604$		−	3574.77i		−	0.240820i
$605$	6487.78	−	3489.14i	0.435976	−	0.234469i
$606$	15289.8	+	12088.9i	1.02493	+	0.810361i
$607$		−	9097.24i		−	0.608313i	−0.952622	−	0.304156i	$-0.901625\pi$
$607$		−	9097.24i		−	0.608313i	0.952622	−	0.304156i	$-0.0983745\pi$
$608$			3488.73i			0.232708i
$609$	10127.1	−	12808.6i	0.673844	−	0.852264i
$610$	1431.18			0.0949950
$611$	−2519.13			−0.166797
$612$	612.267	+	2582.71i	0.0404403	+	0.170588i
$613$		−	12870.2i		−	0.847999i	−0.905662	−	0.424000i	$-0.860626\pi$
$613$		−	12870.2i		−	0.847999i	0.905662	−	0.424000i	$-0.139374\pi$
$614$			8704.74i			0.572141i
$615$	5550.26	−	7019.85i	0.363916	−	0.460273i
$616$	23513.0	+	14052.3i	1.53793	+	0.919128i
$617$			9969.27i			0.650482i	0.945631	+	0.325241i	$0.105445\pi$
$617$			9969.27i			0.650482i	−0.945631	+	0.325241i	$0.894555\pi$
$618$	5984.39	+	4731.57i	0.389527	+	0.307980i
$619$	3113.79			0.202187			0.101094	−	0.994877i	$-0.467766\pi$
$619$	3113.79			0.202187			0.101094	+	0.994877i	$0.467766\pi$
$620$		−	780.804i		−	0.0505772i
$621$	−3982.08	−	1856.47i	−0.257319	−	0.119964i
$622$			2011.99i			0.129700i
$623$	−37535.2			−2.41383
$624$	5400.80	−	6830.82i	0.346482	−	0.438224i
$625$	5076.51			0.324897
$626$	−7304.31			−0.466356
$627$	4542.59	+	11955.9i	0.289336	+	0.761520i
$628$	−994.297			−0.0631796
$629$	−4761.62			−0.301841
$630$	2827.85	+	11928.6i	0.178832	+	0.754363i
$631$	−12998.4			−0.820058			−0.410029	−	0.912072i	$-0.634481\pi$
$631$	−12998.4			−0.820058			−0.410029	+	0.912072i	$0.634481\pi$
$632$			23618.0i			1.48651i
$633$	−7322.75	+	9261.66i	−0.459800	+	0.581545i
$634$		−	21677.2i		−	1.35790i
$635$	4073.86			0.254592
$636$	−2281.97	+	2886.19i	−0.142274	+	0.179945i
$637$		−	20058.3i		−	1.24763i
$638$	4909.26	−	8214.41i	0.304639	−	0.509736i
$639$	−17192.7	+	4075.77i	−1.06437	+	0.252324i
$640$			5864.00i			0.362180i
$641$			27451.6i			1.69153i	0.533552	+	0.845767i	$0.320857\pi$
$641$			27451.6i			1.69153i	−0.533552	+	0.845767i	$0.679143\pi$
$642$	−5836.14	−	4614.35i	−0.358776	−	0.283667i
$643$	1820.94			0.111681			0.0558406	−	0.998440i	$-0.482216\pi$
$643$	1820.94			0.111681			0.0558406	+	0.998440i	$0.482216\pi$
$644$	−1131.06			−0.0692082
$645$	1629.54	+	1288.40i	0.0994779	+	0.0786524i
$646$		−	15065.4i		−	0.917553i
$647$		−	27260.5i		−	1.65645i	−0.560397	−	0.828224i	$-0.689351\pi$
$647$		−	27260.5i		−	1.65645i	0.560397	−	0.828224i	$-0.310649\pi$
$648$	15601.3	−	7837.46i	0.945798	−	0.475131i
$649$	−5111.93	−	3055.09i	−0.309184	−	0.184781i
$650$			7741.84i			0.467169i
$651$	12372.0	−	15647.9i	0.744851	−	0.942072i
$652$	4315.67			0.259225
$653$		−	4373.46i		−	0.262093i	−0.991376	−	0.131046i	$-0.958166\pi$
$653$		−	4373.46i		−	0.262093i	0.991376	−	0.131046i	$-0.0418337\pi$
$654$	−1569.28	+	1984.79i	−0.0938280	+	0.118672i
$655$			11473.1i			0.684411i
$656$	16634.3			0.990032
$657$	−28629.4	+	6786.98i	−1.70006	+	0.403022i
$658$	6592.19			0.390563
$659$	21764.1			1.28651			0.643255	−	0.765652i	$-0.277584\pi$
$659$	21764.1			1.28651			0.643255	+	0.765652i	$0.277584\pi$
$660$	−429.310	−	1129.93i	−0.0253195	−	0.0666401i
$661$	18703.1			1.10055			0.550276	−	0.834983i	$-0.314522\pi$
$661$	18703.1			1.10055			0.550276	+	0.834983i	$0.314522\pi$
$662$	−14863.1			−0.872616
$663$	8621.20	−	10903.9i	0.505007	−	0.638722i
$664$	−7885.79			−0.460885
$665$			11706.1i			0.682623i
$666$	909.458	+	3836.35i	0.0529141	+	0.223206i
$667$			3139.04i			0.182225i
$668$	507.542			0.0293973
$669$	17642.1	+	13948.8i	1.01956	+	0.806113i
$670$		−	2289.87i		−	0.132038i
$671$	−3094.59	−	1849.46i	−0.178041	−	0.106405i
$672$	5224.37	−	6607.68i	0.299903	−	0.379311i
$673$			24662.4i			1.41258i	0.707923	+	0.706290i	$0.249633\pi$
$673$			24662.4i			1.41258i	−0.707923	+	0.706290i	$0.750367\pi$
$674$		−	13041.8i		−	0.745328i
$675$	−5594.27	+	11999.6i	−0.318998	+	0.684243i
$676$	−1398.82			−0.0795868
$677$	15997.9			0.908199			0.454099	−	0.890951i	$-0.349961\pi$
$677$	15997.9			0.908199			0.454099	+	0.890951i	$0.349961\pi$
$678$	3702.21	−	4682.48i	0.209709	−	0.265235i
$679$			36929.2i			2.08721i
$680$			11310.7i			0.637862i
$681$	−6700.86	−	5298.04i	−0.377059	−	0.298123i
$682$	5997.52	−	10035.3i	0.336740	−	0.563450i
$683$			7106.38i			0.398123i	0.979987	+	0.199061i	$0.0637893\pi$
$683$			7106.38i			0.398123i	−0.979987	+	0.199061i	$0.936211\pi$
$684$	2042.03	−	484.090i	0.114150	−	0.0270609i
$685$	1882.87			0.105023
$686$			24350.6i			1.35526i
$687$	−17427.5	−	13779.1i	−0.967832	−	0.765219i
$688$			3861.38i			0.213974i
$689$	19268.4			1.06541
$690$	−1848.72	−	1461.70i	−0.102000	−	0.0806462i
$691$	17320.5			0.953552			0.476776	−	0.879025i	$-0.341805\pi$
$691$	17320.5			0.953552			0.476776	+	0.879025i	$0.341805\pi$
$692$	1539.24			0.0845565
$693$	9300.30	−	29447.1i	0.509797	−	1.61415i
$694$	−16208.7			−0.886562
$695$	−1067.43			−0.0582592
$696$	−9785.03	−	7736.55i	−0.532903	−	0.421341i
$697$	26553.0			1.44300
$698$			19360.6i			1.04987i
$699$	−21827.5	−	17257.9i	−1.18110	−	0.933841i
$700$			3408.34i			0.184033i
$701$	3497.72			0.188455			0.0942275	−	0.995551i	$-0.469962\pi$
$701$	3497.72			0.188455			0.0942275	+	0.995551i	$0.469962\pi$
$702$	−10431.7	−	4863.31i	−0.560853	−	0.261473i
$703$			3764.78i			0.201979i
$704$	10536.5	−	17630.1i	0.564073	−	0.943833i
$705$	−1812.74	−	1433.24i	−0.0968391	−	0.0765660i
$706$		−	28739.8i		−	1.53206i
$707$		−	44938.8i		−	2.39052i
$708$	−606.058	+	766.530i	−0.0321710	+	0.0406892i
$709$	−10075.2			−0.533682			−0.266841	−	0.963741i	$-0.585980\pi$
$709$	−10075.2			−0.533682			−0.266841	+	0.963741i	$0.585980\pi$
$710$	−9478.00			−0.500990
$711$	25908.0	−	6141.85i	1.36656	−	0.323962i
$712$			28674.9i			1.50932i
$713$			3834.88i			0.201427i
$714$	−22560.4	+	28534.0i	−1.18250	+	1.49560i
$715$	−3247.37	+	5433.65i	−0.169853	+	0.284206i
$716$			1715.13i			0.0895214i
$717$	18129.9	+	14334.4i	0.944315	+	0.746624i
$718$	23292.9			1.21070
$719$			19298.2i			1.00098i	0.865744	+	0.500488i	$0.166846\pi$
$719$			19298.2i			1.00098i	−0.865744	+	0.500488i	$0.833154\pi$
$720$	7772.71	−	1842.63i	0.402322	−	0.0953758i
$721$		−	17588.9i		−	0.908524i
$722$	6037.54			0.311211
$723$	−10889.1	+	13772.3i	−0.560125	+	0.708434i
$724$	−853.033			−0.0437883
$725$	9459.17			0.484558
$726$	3161.49	−	17820.1i	0.161617	−	0.910973i
$727$	−30373.0			−1.54948			−0.774741	−	0.632279i	$-0.782120\pi$
$727$	−30373.0			−1.54948			−0.774741	+	0.632279i	$0.782120\pi$
$728$	−23538.2			−1.19833
$729$	−12654.5	−	15075.9i	−0.642916	−	0.765936i
$730$	−15782.8			−0.800202
$731$			6163.85i			0.311872i
$732$	−366.888	+	464.032i	−0.0185254	+	0.0234305i
$733$			10930.3i			0.550775i	0.961333	+	0.275388i	$0.0888062\pi$
$733$			10930.3i			0.550775i	−0.961333	+	0.275388i	$0.911194\pi$
$734$	−6449.62			−0.324332
$735$	11412.1	−	14433.7i	0.572708	−	0.724349i
$736$			1619.37i			0.0811014i
$737$	−2959.10	+	4951.30i	−0.147897	+	0.247467i
$738$	−5071.57	−	21393.3i	−0.252963	−	1.06707i
$739$		−	17039.4i		−	0.848177i	−0.905621	−	0.424088i	$-0.860595\pi$
$739$		−	17039.4i		−	0.848177i	0.905621	−	0.424088i	$-0.139405\pi$
$740$		−	355.802i		−	0.0176751i
$741$	−8621.20	−	6816.37i	−0.427406	−	0.337929i
$742$	−50422.7			−2.49471
$743$	−40039.8			−1.97701			−0.988506	−	0.151183i	$-0.951692\pi$
$743$	−40039.8			−1.97701			−0.988506	+	0.151183i	$0.951692\pi$
$744$	−11954.1	−	9451.55i	−0.589058	−	0.465740i
$745$		−	12406.9i		−	0.610140i
$746$			9820.05i			0.481954i
$747$	2050.70	+	8650.41i	0.100443	+	0.423698i
$748$	1839.91	−	3078.62i	0.0899382	−	0.150489i
$749$			17153.2i			0.836801i
$750$	−10239.1	+	12950.2i	−0.498504	+	0.630498i
$751$	−10979.1			−0.533465			−0.266732	−	0.963771i	$-0.585944\pi$
$751$	−10979.1			−0.533465			−0.266732	+	0.963771i	$0.585944\pi$
$752$		−	4295.48i		−	0.208298i
$753$	−9644.89	+	12198.7i	−0.466772	+	0.590364i
$754$			8223.22i			0.397178i
$755$	−17173.3			−0.827816
$756$	−4592.54	−	2141.07i	−0.220938	−	0.103002i
$757$	−10139.7			−0.486836			−0.243418	−	0.969922i	$-0.578269\pi$
$757$	−10139.7			−0.486836			−0.243418	+	0.969922i	$0.578269\pi$
$758$	26575.3			1.27343
$759$	2108.54	+	5549.59i	0.100837	+	0.265399i
$760$	8942.83			0.426830
$761$	6431.57			0.306365			0.153183	−	0.988198i	$-0.451048\pi$
$761$	6431.57			0.306365			0.153183	+	0.988198i	$0.451048\pi$
$762$	6207.62	−	7851.27i	0.295116	−	0.373257i
$763$	5833.56			0.276788
$764$		−	1328.95i		−	0.0629317i
$765$	12407.4	−	2941.35i	0.586394	−	0.139013i
$766$			7115.94i			0.335652i
$767$	5117.41			0.240911
$768$	−7056.09	−	5578.91i	−0.331529	−	0.262124i
$769$		−	25916.3i		−	1.21530i	−0.794205	−	0.607650i	$-0.792112\pi$
$769$		−	25916.3i		−	1.21530i	0.794205	−	0.607650i	$-0.207888\pi$
$770$	8497.90	−	14219.1i	0.397718	−	0.665480i
$771$	−14592.5	+	18456.3i	−0.681630	+	0.862111i
$772$		−	2528.21i		−	0.117866i
$773$			10562.0i			0.491446i	0.969340	+	0.245723i	$0.0790253\pi$
$773$			10562.0i			0.491446i	−0.969340	+	0.245723i	$0.920975\pi$
$774$	4966.10	−	1177.28i	0.230624	−	0.0546725i
$775$	11556.0			0.535619
$776$	28211.9			1.30509
$777$	5637.77	−	7130.53i	0.260301	−	0.329223i
$778$		−	17259.0i		−	0.795328i
$779$		−	20994.2i		−	0.965592i
$780$	814.772	+	644.201i	0.0374019	+	0.0295719i
$781$	20493.9	+	12248.0i	0.938962	+	0.561162i
$782$		−	6992.92i		−	0.319778i
$783$	−5942.11	+	12745.7i	−0.271205	+	0.581730i
$784$	34202.3			1.55805
$785$			4776.63i			0.217179i
$786$	22111.2	+	17482.3i	1.00341	+	0.793350i
$787$			16056.7i			0.727266i	0.931542	+	0.363633i	$0.118464\pi$
$787$			16056.7i			0.727266i	−0.931542	+	0.363633i	$0.881536\pi$
$788$	−1296.50			−0.0586116
$789$	−7653.64	−	6051.37i	−0.345344	−	0.273047i
$790$	14282.6			0.643229
$791$	−13762.4			−0.618629
$792$	−22496.0	−	7104.92i	−1.00929	−	0.318766i
$793$	3097.91			0.138727
$794$	11886.7			0.531287
$795$	13865.3	+	10962.7i	0.618557	+	0.489064i
$796$	−881.116			−0.0392341
$797$			14633.0i			0.650349i	0.945654	+	0.325174i	$0.105423\pi$
$797$			14633.0i			0.650349i	−0.945654	+	0.325174i	$0.894577\pi$
$798$	22560.4	+	17837.4i	1.00079	+	0.791277i
$799$		−	6856.79i		−	0.303599i
$800$	4879.80			0.215659
$801$	31455.2	−	7456.89i	1.38754	−	0.328934i
$802$		−	4593.88i		−	0.202264i
$803$	34126.5	+	20395.4i	1.49975	+	0.896311i
$804$	742.444	+	587.014i	0.0325671	+	0.0257493i
$805$			5433.65i			0.237902i
$806$			10046.1i			0.439031i
$807$	−16973.9	+	21468.3i	−0.740409	+	0.936454i
$808$	−34330.8			−1.49474
$809$	3761.86			0.163486			0.0817429	−	0.996653i	$-0.473951\pi$
$809$	3761.86			0.163486			0.0817429	+	0.996653i	$0.473951\pi$
$810$	−4739.58	−	9434.64i	−0.205595	−	0.409258i
$811$		−	23288.0i		−	1.00833i	−0.863609	−	0.504163i	$-0.831801\pi$
$811$		−	23288.0i		−	1.00833i	0.863609	−	0.504163i	$-0.168199\pi$
$812$			3620.26i			0.156461i
$813$	5771.87	−	7300.14i	0.248989	−	0.314916i
$814$	2732.99	−	4572.97i	0.117680	−	0.196907i
$815$		−	20732.6i		−	0.891082i
$816$	18592.7	+	14700.4i	0.797642	+	0.630657i
$817$	4873.46			0.208691
$818$		−	14353.3i		−	0.613511i
$819$	6121.10	+	25820.5i	0.261158	+	1.10164i
$820$			1984.12i			0.0844982i
$821$	−36822.5			−1.56531			−0.782653	−	0.622459i	$-0.786134\pi$
$821$	−36822.5			−1.56531			−0.782653	+	0.622459i	$0.786134\pi$
$822$	2869.06	−	3628.73i	0.121740	−	0.153974i
$823$	9995.11			0.423338			0.211669	−	0.977341i	$-0.432110\pi$
$823$	9995.11			0.423338			0.211669	+	0.977341i	$0.432110\pi$
$824$	−13437.0			−0.568081
$825$	16723.1	−	6353.86i	0.705727	−	0.268137i
$826$	−13391.5			−0.564105
$827$	−18209.1			−0.765650			−0.382825	−	0.923821i	$-0.625049\pi$
$827$	−18209.1			−0.765650			−0.382825	+	0.923821i	$0.625049\pi$
$828$	947.851	−	224.701i	0.0397827	−	0.00943103i
$829$	20799.4			0.871402			0.435701	−	0.900091i	$-0.356501\pi$
$829$	20799.4			0.871402			0.435701	+	0.900091i	$0.356501\pi$
$830$			4768.80i			0.199431i
$831$	14511.4	−	18353.7i	0.605770	−	0.766165i
$832$			17649.0i			0.735419i
$833$	54596.6			2.27090
$834$	−1626.53	+	2057.20i	−0.0675323	+	0.0854135i
$835$		−	2438.24i		−	0.101053i
$836$	−2434.12	−	1454.73i	−0.100701	−	0.0601828i
$837$	−7259.33	+	15571.1i	−0.299784	+	0.643030i
$838$			4519.63i			0.186310i
$839$		−	19324.4i		−	0.795175i	−0.917564	−	0.397588i	$-0.869847\pi$
$839$		−	19324.4i		−	0.795175i	0.917564	−	0.397588i	$-0.130153\pi$
$840$	−16937.8	−	13391.9i	−0.695726	−	0.550077i
$841$	−14341.7			−0.588038
$842$	−32637.9			−1.33584
$843$	9979.02	+	7889.93i	0.407705	+	0.322353i
$844$		−	2617.75i		−	0.106762i
$845$			6719.96i			0.273578i
$846$	−5524.38	+	1309.63i	−0.224506	+	0.0532222i
$847$	−36749.3	+	19763.9i	−1.49082	+	0.801766i
$848$			32855.5i			1.33050i
$849$	17293.7	−	21872.7i	0.699080	−	0.884182i
$850$	−21072.4			−0.850328
$851$			1747.51i			0.0703921i
$852$	2429.71	−	3073.05i	0.0977001	−	0.123569i
$853$		−	5283.23i		−	0.212068i	−0.994362	−	0.106034i	$-0.966185\pi$
$853$		−	5283.23i		−	0.212068i	0.994362	−	0.106034i	$-0.0338153\pi$
$854$	−8106.79			−0.324835
$855$	−2325.58	−	9809.96i	−0.0930214	−	0.392390i
$856$	13104.1			0.523234
$857$	−36468.1			−1.45359			−0.726795	−	0.686855i	$-0.758991\pi$
$857$	−36468.1			−1.45359			−0.726795	+	0.686855i	$0.758991\pi$
$858$	5523.66	+	14538.1i	0.219784	+	0.578463i
$859$	20435.1			0.811685			0.405843	−	0.913943i	$-0.366978\pi$
$859$	20435.1			0.811685			0.405843	+	0.913943i	$0.366978\pi$
$860$	−460.581			−0.0182624
$861$	−31438.9	+	39763.2i	−1.24441	+	1.57390i
$862$	28139.4			1.11187
$863$		−	31825.3i		−	1.25532i	−0.778486	−	0.627662i	$-0.784012\pi$
$863$		−	31825.3i		−	1.25532i	0.778486	−	0.627662i	$-0.215988\pi$
$864$	−3065.42	+	6575.25i	−0.120703	+	0.258906i
$865$		−	7394.55i		−	0.290661i
$866$	−13699.0			−0.537542
$867$	9653.68	+	7632.70i	0.378150	+	0.298985i
$868$			4422.78i			0.172948i
$869$	−30882.6	−	18456.7i	−1.20555	−	0.720485i
$870$	−4678.55	+	5917.34i	−0.182319	+	0.230594i
$871$		−	4956.61i		−	0.192822i
$872$		−	4456.51i		−	0.173070i
$873$	−7336.50	−	30947.4i	−0.284425	−	1.19978i
$874$	−5528.96			−0.213982
$875$	38062.3			1.47056
$876$	4045.96	−	5117.25i	0.156051	−	0.197370i
$877$			3908.07i			0.150474i	0.997166	+	0.0752372i	$0.0239714\pi$
$877$			3908.07i			0.150474i	−0.997166	+	0.0752372i	$0.976029\pi$
$878$		−	41017.7i		−	1.57663i
$879$	735.151	+	581.249i	0.0282094	+	0.0223038i
$880$	−9265.15	−	5537.23i	−0.354919	−	0.212114i
$881$			7116.54i			0.272148i	0.990699	+	0.136074i	$0.0434485\pi$
$881$			7116.54i			0.272148i	−0.990699	+	0.136074i	$0.956551\pi$
$882$	−10427.8	−	43987.4i	−0.398098	−	1.67929i
$883$	36035.3			1.37337			0.686685	−	0.726955i	$-0.259065\pi$
$883$	36035.3			1.37337			0.686685	+	0.726955i	$0.259065\pi$
$884$			3081.93i			0.117258i
$885$	3682.43	+	2911.52i	0.139868	+	0.110587i
$886$		−	21949.8i		−	0.832301i
$887$	−3302.10			−0.124999			−0.0624993	−	0.998045i	$-0.519907\pi$
$887$	−3302.10			−0.124999			−0.0624993	+	0.998045i	$0.519907\pi$
$888$	−5447.33	−	4306.95i	−0.205856	−	0.162761i
$889$	−23075.9			−0.870576
$890$	17340.7			0.653101
$891$	−1943.75	+	26524.9i	−0.0730844	+	0.997326i
$892$	−4986.43			−0.187173
$893$	−5421.33			−0.203156
$894$	−23911.0	−	18905.3i	−0.894523	−	0.707257i
$895$	8239.52			0.307728
$896$		−	33216.0i		−	1.23847i
$897$	−4001.71	−	3163.96i	−0.148956	−	0.117772i
$898$			30106.4i			1.11878i
$899$	12274.6			0.455372
$900$	−677.113	−	2856.25i	−0.0250783	−	0.105787i
$901$			52446.6i			1.93923i
$902$	−15240.5	+	25501.0i	−0.562585	+	0.941343i
$903$	−9230.38	−	7298.02i	−0.340164	−	0.268951i
$904$			10513.7i			0.386816i
$905$			4097.99i			0.150521i
$906$	−26168.2	+	33097.0i	−0.959580	+	1.21366i
$907$	−4973.95			−0.182092			−0.0910459	−	0.995847i	$-0.529021\pi$
$907$	−4973.95			−0.182092			−0.0910459	+	0.995847i	$0.529021\pi$
$908$	1893.96			0.0692216
$909$	8927.72	+	37659.6i	0.325758	+	1.37414i
$910$			14234.3i			0.518531i
$911$		−	37535.8i		−	1.36511i	−0.730833	−	0.682556i	$-0.760868\pi$
$911$		−	37535.8i		−	1.36511i	0.730833	−	0.682556i	$-0.239132\pi$
$912$	11622.9	−	14700.4i	0.422009	−	0.533748i
$913$	6162.51	−	10311.4i	0.223384	−	0.373776i
$914$			17285.5i			0.625552i
$915$	2229.22	+	1762.54i	0.0805419	+	0.0636806i
$916$	4925.78			0.177677
$917$		−	64987.9i		−	2.34034i
$918$	13237.4	−	28393.9i	0.475925	−	1.02085i
$919$			7301.84i			0.262095i	0.991376	+	0.131048i	$0.0418341\pi$
$919$			7301.84i			0.262095i	−0.991376	+	0.131048i	$0.958166\pi$
$920$	4151.01			0.148755
$921$	−10720.1	+	13558.6i	−0.383539	+	0.485092i
$922$	−23634.4			−0.844205
$923$	−20515.9			−0.731624
$924$	2431.78	+	6400.37i	0.0865799	+	0.227875i
$925$	5265.93			0.187181
$926$	16440.7			0.583451
$927$	3494.28	+	14739.9i	0.123805	+	0.522244i
$928$	5183.22			0.183349
$929$			35469.4i			1.25265i	0.779562	+	0.626325i	$0.215442\pi$
$929$			35469.4i			1.25265i	−0.779562	+	0.626325i	$0.784558\pi$
$930$	−5715.67	+	7229.06i	−0.201531	+	0.254893i
$931$		−	43166.9i		−	1.51959i
$932$	6169.40			0.216830
$933$	−2477.81	+	3133.89i	−0.0869453	+	0.109967i
$934$			22883.5i			0.801683i
$935$	−14789.8	−	8838.98i	−0.517303	−	0.309161i
$936$	19725.4	−	4676.18i	0.688832	−	0.163297i
$937$			29493.1i			1.02828i	0.857706	+	0.514140i	$0.171889\pi$
$937$			29493.1i			1.02828i	−0.857706	+	0.514140i	$0.828111\pi$
$938$			12970.7i			0.451503i
$939$	−11377.2	−	8995.44i	−0.395402	−	0.312625i
$940$	512.359			0.0177780
$941$	−12881.6			−0.446257			−0.223128	−	0.974789i	$-0.571627\pi$
$941$	−12881.6			−0.446257			−0.223128	+	0.974789i	$0.571627\pi$
$942$	9205.68	+	7278.49i	0.318405	+	0.251747i
$943$		−	9744.92i		−	0.336520i
$944$			8725.92i			0.300852i
$945$	−10285.7	+	22062.7i	−0.354069	+	0.759471i
$946$	−5919.65	−	3537.82i	−0.203451	−	0.121590i
$947$		−	23796.5i		−	0.816560i	−0.912857	−	0.408280i	$-0.866129\pi$
$947$		−	23796.5i		−	0.816560i	0.912857	−	0.408280i	$-0.133871\pi$
$948$	−3661.38	+	4630.83i	−0.125439	+	0.158652i
$949$	−34163.2			−1.16858
$950$			16661.0i			0.569003i
$951$	26696.0	−	33764.5i	0.910280	−	1.15130i
$952$		−	64068.3i		−	2.18116i
$953$	43121.9			1.46575			0.732873	−	0.680365i	$-0.238179\pi$
$953$	43121.9			1.46575			0.732873	+	0.680365i	$0.238179\pi$
$954$	42255.2	−	10017.2i	1.43403	−	0.339956i
$955$	−6384.33			−0.216327
$956$	−5124.31			−0.173360
$957$	17763.0	−	6748.94i	0.599995	−	0.227965i
$958$	23715.3			0.799798
$959$	−10665.3			−0.359126
$960$	−10041.3	+	12700.0i	−0.337585	+	0.426970i
$961$	−14795.5			−0.496643
$962$			4577.88i			0.153427i
$963$	−3407.72	−	14374.7i	−0.114031	−	0.481016i
$964$		−	3892.67i		−	0.130056i
$965$	−12145.6			−0.405161
$966$	10471.9	+	8279.63i	0.348787	+	0.275769i
$967$			20887.4i			0.694617i	0.937751	+	0.347308i	$0.112904\pi$
$967$			20887.4i			0.694617i	−0.937751	+	0.347308i	$0.887096\pi$
$968$	15098.5	+	28074.5i	0.501327	+	0.932177i
$969$	18553.4	−	23465.9i	0.615089	−	0.777951i
$970$		−	17060.7i		−	0.564727i
$971$			26197.7i			0.865835i	0.901434	+	0.432917i	$0.142516\pi$
$971$			26197.7i			0.865835i	−0.901434	+	0.432917i	$0.857484\pi$
$972$	4273.99	+	881.884i	0.141037	+	0.0291013i
$973$	6046.37			0.199217
$974$	−3435.26			−0.113011
$975$	−9534.27	+	12058.7i	−0.313170	+	0.396091i
$976$			5282.39i			0.173243i
$977$			51436.7i			1.68435i	0.539207	+	0.842173i	$0.318724\pi$
$977$			51436.7i			1.68435i	−0.539207	+	0.842173i	$0.681276\pi$
$978$	−39956.6	−	31591.8i	−1.30641	−	1.03292i
$979$	−37495.0	−	22408.5i	−1.22405	−	0.731543i
$980$			4079.61i			0.132978i
$981$	−4888.63	+	1158.92i	−0.159105	+	0.0377180i
$982$	48763.8			1.58464
$983$			50475.0i			1.63774i	0.573977	+	0.818871i	$0.305400\pi$
$983$			50475.0i			1.63774i	−0.573977	+	0.818871i	$0.694600\pi$
$984$	30376.9	+	24017.6i	0.984127	+	0.778102i
$985$			6228.43i			0.201476i
$986$	−22382.7			−0.722932
$987$	10268.0	+	8118.45i	0.331140	+	0.261817i
$988$	2436.73			0.0784643
$989$	2262.12			0.0727313
$990$	−4296.58	+	13604.1i	−0.137934	+	0.436733i
$991$	−22152.1			−0.710076			−0.355038	−	0.934852i	$-0.615532\pi$
$991$	−22152.1			−0.710076			−0.355038	+	0.934852i	$0.615532\pi$
$992$	6332.20			0.202669
$993$	−23150.9	−	18304.3i	−0.739851	−	0.584964i
$994$	53687.1			1.71313
$995$			4232.91i			0.134866i
$996$	−1546.19	−	1222.49i	−0.0491895	−	0.0388918i
$997$		−	61535.0i		−	1.95470i	−0.211636	−	0.977349i	$-0.567879\pi$
$997$		−	61535.0i		−	1.95470i	0.211636	−	0.977349i	$-0.432121\pi$
$998$	4311.03			0.136737
$999$	−3307.98	+	7095.54i	−0.104765	+	0.224718i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.4.d.b.32.6	yes	8
3.2	odd	2	inner	33.4.d.b.32.3	✓	8
4.3	odd	2		528.4.b.e.65.2		8
11.10	odd	2	inner	33.4.d.b.32.4	yes	8
12.11	even	2		528.4.b.e.65.4		8
33.32	even	2	inner	33.4.d.b.32.5	yes	8
44.43	even	2		528.4.b.e.65.1		8
132.131	odd	2		528.4.b.e.65.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.d.b.32.3	✓	8	3.2	odd	2	inner
33.4.d.b.32.4	yes	8	11.10	odd	2	inner
33.4.d.b.32.5	yes	8	33.32	even	2	inner
33.4.d.b.32.6	yes	8	1.1	even	1	trivial
528.4.b.e.65.1		8	44.43	even	2
528.4.b.e.65.2		8	4.3	odd	2
528.4.b.e.65.3		8	132.131	odd	2
528.4.b.e.65.4		8	12.11	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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	33.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.61686 q^{2} +(4.07603 + 3.22272i) q^{3} -1.15207 q^{4} +5.53456i q^{5} +(10.6664 + 8.43340i) q^{6} -31.3500i q^{7} -23.9496 q^{8} +(6.22810 + 26.2719i) q^{9} +O(q^{10})\)	\(q+2.61686 q^{2} +(4.07603 + 3.22272i) q^{3} -1.15207 q^{4} +5.53456i q^{5} +(10.6664 + 8.43340i) q^{6} -31.3500i q^{7} -23.9496 q^{8} +(6.22810 + 26.2719i) q^{9} +14.4832i q^{10} +(18.7159 - 31.3164i) q^{11} +(-4.69587 - 3.71280i) q^{12} +31.3500i q^{13} -82.0383i q^{14} +(-17.8364 + 22.5591i) q^{15} -53.4562 q^{16} -85.3311 q^{17} +(16.2980 + 68.7497i) q^{18} +67.4672i q^{19} -6.37619i q^{20} +(101.032 - 127.783i) q^{21} +(48.9769 - 81.9504i) q^{22} +31.3164i q^{23} +(-97.6195 - 77.1831i) q^{24} +94.3686 q^{25} +82.0383i q^{26} +(-59.2810 + 127.156i) q^{27} +36.1173i q^{28} +100.236 q^{29} +(-46.6752 + 59.0338i) q^{30} +122.456 q^{31} +51.7099 q^{32} +(177.211 - 67.3303i) q^{33} -223.299 q^{34} +173.508 q^{35} +(-7.17519 - 30.2670i) q^{36} +55.8017 q^{37} +176.552i q^{38} +(-101.032 + 127.783i) q^{39} -132.551i q^{40} -311.177 q^{41} +(264.387 - 334.391i) q^{42} -72.2345i q^{43} +(-21.5620 + 36.0785i) q^{44} +(-145.403 + 34.4698i) q^{45} +81.9504i q^{46} +80.3551i q^{47} +(-217.889 - 172.275i) q^{48} -639.820 q^{49} +246.949 q^{50} +(-347.813 - 274.999i) q^{51} -36.1173i q^{52} -614.624i q^{53} +(-155.130 + 332.750i) q^{54} +(173.322 + 103.584i) q^{55} +750.820i q^{56} +(-217.428 + 274.999i) q^{57} +262.304 q^{58} -163.235i q^{59} +(20.5487 - 25.9896i) q^{60} -98.8172i q^{61} +320.450 q^{62} +(823.622 - 195.251i) q^{63} +562.967 q^{64} -173.508 q^{65} +(463.735 - 176.194i) q^{66} -158.106 q^{67} +98.3072 q^{68} +(-100.924 + 127.647i) q^{69} +454.046 q^{70} +654.415i q^{71} +(-149.161 - 629.202i) q^{72} +1089.74i q^{73} +146.025 q^{74} +(384.650 + 304.124i) q^{75} -77.7268i q^{76} +(-981.766 - 586.744i) q^{77} +(-264.387 + 334.391i) q^{78} -986.151i q^{79} -295.857i q^{80} +(-651.422 + 327.248i) q^{81} -814.304 q^{82} +329.265 q^{83} +(-116.396 + 147.215i) q^{84} -472.271i q^{85} -189.027i q^{86} +(408.567 + 323.034i) q^{87} +(-448.240 + 750.015i) q^{88} -1197.30i q^{89} +(-380.499 + 90.2025i) q^{90} +982.820 q^{91} -36.0785i q^{92} +(499.136 + 394.643i) q^{93} +210.278i q^{94} -373.402 q^{95} +(210.771 + 166.647i) q^{96} -1177.97 q^{97} -1674.32 q^{98} +(939.304 + 296.661i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} + 44 q^{4} - 30 q^{9}+O(q^{10}) \) 8 * q + 6 * q^3 + 44 * q^4 - 30 * q^9	\( 8 q + 6 q^{3} + 44 q^{4} - 30 q^{9} - 144 q^{12} + 150 q^{15} - 268 q^{16} - 300 q^{22} + 276 q^{25} + 324 q^{27} + 820 q^{31} + 834 q^{33} + 768 q^{34} - 696 q^{36} - 884 q^{37} - 120 q^{42} - 1722 q^{45} - 732 q^{48} - 2032 q^{49} - 476 q^{55} + 1992 q^{58} + 2772 q^{60} - 1084 q^{64} + 2076 q^{66} + 172 q^{67} - 834 q^{69} + 5016 q^{70} + 1800 q^{75} + 120 q^{78} - 4014 q^{81} - 6408 q^{82} - 3852 q^{88} + 4776 q^{91} + 1146 q^{93} - 3836 q^{97} + 1074 q^{99}+O(q^{100}) \) 8 * q + 6 * q^3 + 44 * q^4 - 30 * q^9 - 144 * q^12 + 150 * q^15 - 268 * q^16 - 300 * q^22 + 276 * q^25 + 324 * q^27 + 820 * q^31 + 834 * q^33 + 768 * q^34 - 696 * q^36 - 884 * q^37 - 120 * q^42 - 1722 * q^45 - 732 * q^48 - 2032 * q^49 - 476 * q^55 + 1992 * q^58 + 2772 * q^60 - 1084 * q^64 + 2076 * q^66 + 172 * q^67 - 834 * q^69 + 5016 * q^70 + 1800 * q^75 + 120 * q^78 - 4014 * q^81 - 6408 * q^82 - 3852 * q^88 + 4776 * q^91 + 1146 * q^93 - 3836 * q^97 + 1074 * q^99

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