LMFDB - Embedded newform 33.4.d.b.32.4

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			32.4
Root			$-5.69289 - 3.22272i$ of defining polynomial
Character	$\chi$	$=$	33.32
Dual form			33.4.d.b.32.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61686 q^{2} +(4.07603 + 3.22272i) q^{3} -1.15207 q^{4} +5.53456i q^{5} +(-10.6664 - 8.43340i) q^{6} +31.3500i q^{7} +23.9496 q^{8} +(6.22810 + 26.2719i) q^{9} +O(q^{10})$	\(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} +(24.6372 - 187.963i) 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} +(-64.4720 + 491.871i) 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} +(706.174 - 686.744i) 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	$-0.653083\pi$
$2$	−2.61686			−0.925198			−0.462599	+	0.886568i	$0.653083\pi$
$3$	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	$0.321216\pi$
$7$			31.3500i			1.69274i	−0.532596	+	0.846369i	$0.678784\pi$
$8$	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	$-0.891460\pi$
$13$		−	31.3500i		−	0.668840i	0.942424	−	0.334420i	$-0.108540\pi$
$14$		−	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	$-0.291691\pi$
$17$	85.3311			1.21740			0.608701	+	0.793400i	$0.291691\pi$
$18$	−16.2980	−	68.7497i	−0.213416	−	0.900247i
$19$		−	67.4672i		−	0.814634i	−0.913287	−	0.407317i	$-0.866464\pi$
$19$		−	67.4672i		−	0.814634i	0.913287	−	0.407317i	$-0.133536\pi$
$20$		−	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	$-0.603992\pi$
$29$	−100.236			−0.641842			−0.320921	+	0.947106i	$0.603992\pi$
$30$	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
$33$	24.6372	−	187.963i	0.129963	−	0.991519i
$34$	−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	$-0.298080\pi$
$41$	311.177			1.18531			0.592654	+	0.805457i	$0.298080\pi$
$42$	264.387	−	334.391i	0.971328	−	1.22852i
$43$			72.2345i			0.256178i	0.991763	+	0.128089i	$0.0408843\pi$
$43$			72.2345i			0.256178i	−0.991763	+	0.128089i	$0.959116\pi$
$44$	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	$0.0330704\pi$
$61$			98.8172i			0.207414i	−0.994608	+	0.103707i	$0.966930\pi$
$62$	−320.450			−0.656407
$63$	−823.622	+	195.251i	−1.64709	+	0.390465i
$64$	562.967			1.09955
$65$	173.508			0.331093
$66$	−64.4720	+	491.871i	−0.120242	+	0.917351i
$67$	−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	$-0.661787\pi$
$73$		−	1089.74i		−	1.74718i	0.486666	−	0.873588i	$-0.338213\pi$
$74$	−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	$0.247807\pi$
$79$			986.151i			1.40444i	−0.711961	+	0.702219i	$0.752193\pi$
$80$		−	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	$-0.569862\pi$
$83$	−329.265			−0.435441			−0.217720	+	0.976011i	$0.569862\pi$
$84$	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
$99$	706.174	−	686.744i	0.716901	−	0.697175i
$100$	−108.719			−0.108719
$101$	−1433.46			−1.41222			−0.706111	−	0.708102i	$-0.749552\pi$
$101$	−1433.46			−1.41222			−0.706111	+	0.708102i	$0.749552\pi$
$102$	−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	$-0.420498\pi$
$107$	547.152			0.494348			0.247174	+	0.968971i	$0.420498\pi$
$108$	68.2957	−	146.493i	0.0608496	−	0.130521i
$109$		−	186.079i		−	0.163515i	−0.996652	−	0.0817573i	$-0.973947\pi$
$109$		−	186.079i		−	0.163515i	0.996652	−	0.0817573i	$-0.0260532\pi$
$110$	−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	$0.0827835\pi$
$127$			736.076i			0.514301i	−0.966371	+	0.257150i	$0.917216\pi$
$128$	−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	$-0.742956\pi$
$131$	−2072.98			−1.38257			−0.691287	+	0.722580i	$0.742956\pi$
$132$	−28.3837	+	216.546i	−0.0187158	+	0.142787i
$133$	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	$-0.981258\pi$
$139$		−	192.867i		−	0.117689i	0.998267	−	0.0588445i	$-0.0187416\pi$
$140$	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	$-0.288643\pi$
$149$	2241.72			1.23254			0.616270	+	0.787535i	$0.288643\pi$
$150$	−1006.57	−	795.848i	−0.547909	−	0.433205i
$151$		−	3102.92i		−	1.67227i	−0.548527	−	0.836133i	$-0.684811\pi$
$151$		−	3102.92i		−	1.67227i	0.548527	−	0.836133i	$-0.315189\pi$
$152$		−	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
$165$	1040.29	+	136.356i	0.490828	+	0.0643353i
$166$	861.640			0.402869
$167$	440.549			0.204136			0.102068	−	0.994777i	$-0.467454\pi$
$167$	440.549			0.204136			0.102068	+	0.994777i	$0.467454\pi$
$168$	−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	$-0.405153\pi$
$173$	1336.07			0.587164			0.293582	+	0.955934i	$0.405153\pi$
$174$	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	$-0.865797\pi$
$193$		−	2194.50i		−	0.818463i	0.912431	−	0.409231i	$-0.134203\pi$
$194$	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	$-0.565232\pi$
$197$	−1125.37			−0.407001			−0.203501	+	0.979075i	$0.565232\pi$
$198$	−1847.96	+	1797.11i	−0.663275	+	0.645025i
$199$	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	$-0.879125\pi$
$211$		−	2272.22i		−	0.741357i	0.928761	−	0.370679i	$-0.120875\pi$
$212$			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	$-0.422741\pi$
$227$	1643.96			0.480677			0.240339	+	0.970689i	$0.422741\pi$
$228$	−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
$231$	5892.63	+	772.376i	1.67838	+	0.219994i
$232$	−2400.63			−0.679348
$233$	5355.07			1.50568			0.752838	−	0.658206i	$-0.228684\pi$
$233$	5355.07			1.50568			0.752838	+	0.658206i	$0.228684\pi$
$234$	−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	$-0.705593\pi$
$239$	−4447.93			−1.20382			−0.601909	+	0.798565i	$0.705593\pi$
$240$	953.465	−	1205.92i	0.256441	−	0.324341i
$241$		−	3378.85i		−	0.903117i	−0.892242	−	0.451558i	$-0.850868\pi$
$241$		−	3378.85i		−	0.903117i	0.892242	−	0.451558i	$-0.149132\pi$
$242$	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	$-0.429354\pi$
$263$	1877.72			0.440247			0.220124	+	0.975472i	$0.429354\pi$
$264$	590.052	−	4501.64i	0.137558	−	1.04946i
$265$	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	$0.0643309\pi$
$271$			1790.99i			0.401457i	−0.979647	+	0.200729i	$0.935669\pi$
$272$	−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	$0.162403\pi$
$277$			4502.84i			0.976712i	−0.872644	+	0.488356i	$0.837597\pi$
$278$			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	$-0.583681\pi$
$281$	−2448.22			−0.519745			−0.259873	+	0.965643i	$0.583681\pi$
$282$	677.667	−	857.098i	0.143101	−	0.180991i
$283$			5366.18i			1.12716i	0.826061	+	0.563580i	$0.190576\pi$
$283$			5366.18i			1.12716i	−0.826061	+	0.563580i	$0.809424\pi$
$284$		−	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	$-0.505724\pi$
$293$	−180.359			−0.0359615			−0.0179807	+	0.999838i	$0.505724\pi$
$294$	6824.57	+	5395.86i	1.35380	+	1.07038i
$295$	903.434			0.178305
$296$	1336.43			0.262427
$297$	5091.58	−	523.386i	0.994758	−	0.102256i
$298$	−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	$-0.899939\pi$
$307$		−	3326.41i		−	0.618399i	0.950997	−	0.309199i	$-0.100061\pi$
$308$	−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
$330$	−2722.29	−	356.825i	−0.454113	−	0.0595229i
$331$	−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	$0.131961\pi$
$337$			4983.76i			0.805587i	−0.915291	+	0.402794i	$0.868039\pi$
$338$	−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	$-0.340956\pi$
$347$	6193.96			0.958240			0.479120	+	0.877749i	$0.340956\pi$
$348$	470.697	+	372.157i	0.0725057	+	0.0573268i
$349$		−	7398.44i		−	1.13475i	−0.823458	−	0.567377i	$-0.807958\pi$
$349$		−	7398.44i		−	1.13475i	0.823458	−	0.567377i	$-0.192042\pi$
$350$		−	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	$-0.727034\pi$
$359$	−8901.12			−1.30859			−0.654294	+	0.756240i	$0.727034\pi$
$360$	−3482.36	+	825.540i	−0.509823	+	0.120860i
$361$	2307.17			0.336372
$362$	−1937.62			−0.281323
$363$	−6347.42	+	2746.35i	−0.917777	+	0.397096i
$364$	−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	$-0.916126\pi$
$373$		−	3752.61i		−	0.520920i	0.965485	−	0.260460i	$-0.0838741\pi$
$374$	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
$396$	−813.560	+	791.175i	−0.103240	+	0.100399i
$397$	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	$0.107574\pi$
$409$			5484.95i			0.663113i	−0.943435	+	0.331556i	$0.892426\pi$
$410$		−	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
$429$	−5892.63	−	772.376i	−0.663167	−	0.0869246i
$430$	1046.18			0.117329
$431$	−10753.1			−1.20176			−0.600881	−	0.799338i	$-0.705184\pi$
$431$	−10753.1			−1.20176			−0.600881	+	0.799338i	$0.705184\pi$
$432$	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	$0.324640\pi$
$439$			15674.4i			1.70410i	−0.523463	+	0.852049i	$0.675360\pi$
$440$	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	$-0.890228\pi$
$457$		−	6605.46i		−	0.676128i	0.941123	−	0.338064i	$-0.109772\pi$
$458$	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	$-0.349200\pi$
$461$	9031.60			0.912458			0.456229	+	0.889862i	$0.349200\pi$
$462$	−15420.1	−	2021.20i	−1.55284	−	0.203538i
$463$	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	$-0.642273\pi$
$479$	−9062.52			−0.864462			−0.432231	+	0.901763i	$0.642273\pi$
$480$	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	$-0.827291\pi$
$491$	−18634.5			−1.71276			−0.856379	+	0.516348i	$0.827291\pi$
$492$	−1461.24	−	1155.33i	−0.133898	−	0.105867i
$493$	−8553.28			−0.781380
$494$	5534.90			0.504103
$495$	3800.83	+	3908.37i	0.345120	+	0.354885i
$496$	−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	$-0.708987\pi$
$503$	−13771.7			−1.22078			−0.610389	+	0.792102i	$0.708987\pi$
$504$	−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	$0.328954\pi$
$523$			20549.8i			1.71813i	−0.511868	+	0.859064i	$0.671046\pi$
$524$	2388.22			0.199102
$525$	−9534.27	+	12058.7i	−0.792590	+	1.00245i
$526$	−4913.72			−0.407316
$527$	10449.3			0.863719
$528$	−1317.01	+	10047.8i	−0.108552	+	0.828169i
$529$	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	$0.223496\pi$
$541$			16253.8i			1.29170i	−0.763466	+	0.645848i	$0.776504\pi$
$542$		−	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	$0.0498333\pi$
$547$			3989.38i			0.311834i	−0.987770	+	0.155917i	$0.950167\pi$
$548$			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	$-0.562533\pi$
$557$	−5131.88			−0.390386			−0.195193	+	0.980765i	$0.562533\pi$
$558$	−1995.80	−	8418.82i	−0.151414	−	0.638705i
$559$	2264.55			0.171342
$560$	9275.10			0.699901
$561$	2102.32	−	16039.1i	0.158218	−	1.20708i
$562$	6406.63			0.480867
$563$	12818.7			0.959579			0.479789	−	0.877384i	$-0.340713\pi$
$563$	12818.7			0.959579			0.479789	+	0.877384i	$0.340713\pi$
$564$	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	$-0.341916\pi$
$569$	12934.1			0.952942			0.476471	+	0.879190i	$0.341916\pi$
$570$	−3982.85	−	3149.05i	−0.292672	−	0.231402i
$571$		−	13100.2i		−	0.960119i	−0.877236	−	0.480060i	$-0.840615\pi$
$571$		−	13100.2i		−	0.960119i	0.877236	−	0.480060i	$-0.159385\pi$
$572$	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	$-0.694780\pi$
$593$	−16590.4			−1.14888			−0.574441	+	0.818546i	$0.694780\pi$
$594$	−13323.9	+	1369.62i	−0.920348	+	0.0946067i
$595$	−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	$-0.861338\pi$
$601$		−	12434.4i		−	0.843942i	0.906609	−	0.421971i	$-0.138662\pi$
$602$	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	$0.0983745\pi$
$607$			9097.24i			0.608313i	−0.952622	+	0.304156i	$0.901625\pi$
$608$			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	$0.139374\pi$
$613$			12870.2i			0.847999i	−0.905662	+	0.424000i	$0.860626\pi$
$614$			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
$627$	−12681.3	−	1662.20i	−0.807725	−	0.105873i
$628$	−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	$-0.722416\pi$
$659$	−21764.1			−1.28651			−0.643255	+	0.765652i	$0.722416\pi$
$660$	−1198.49	−	157.092i	−0.0706834	−	0.00926482i
$661$	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	$-0.750367\pi$
$673$		−	24662.4i		−	1.41258i	0.707923	−	0.706290i	$-0.249633\pi$
$674$		−	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	$-0.650039\pi$
$677$	−15997.9			−0.908199			−0.454099	+	0.890951i	$0.650039\pi$
$678$	−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
$693$	21529.4	+	22138.5i	1.18014	+	1.21353i
$694$	−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	$-0.530038\pi$
$701$	−3497.72			−0.188455			−0.0942275	+	0.995551i	$0.530038\pi$
$702$	−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
$726$	16610.3	−	7186.80i	0.849125	−	0.367393i
$727$	−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	$-0.911194\pi$
$733$		−	10930.3i		−	0.550775i	0.961333	−	0.275388i	$-0.0888062\pi$
$734$	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	$0.139405\pi$
$739$			17039.4i			0.848177i	−0.905621	+	0.424088i	$0.860595\pi$
$740$		−	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	$-0.0483084\pi$
$743$	40039.8			1.97701			0.988506	+	0.151183i	$0.0483084\pi$
$744$	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
$759$	5886.31	+	771.548i	0.281501	+	0.0368978i
$760$	8942.83			0.426830
$761$	−6431.57			−0.306365			−0.153183	−	0.988198i	$-0.548952\pi$
$761$	−6431.57			−0.306365			−0.153183	+	0.988198i	$0.548952\pi$
$762$	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	$0.207888\pi$
$769$			25916.3i			1.21530i	−0.794205	+	0.607650i	$0.792112\pi$
$770$	−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	$-0.881536\pi$
$787$		−	16056.7i		−	0.727266i	0.931542	−	0.363633i	$-0.118464\pi$
$788$	1296.50			0.0586116
$789$	7653.64	+	6051.37i	0.345344	+	0.273047i
$790$	14282.6			0.643229
$791$	13762.4			0.618629
$792$	16912.6	−	16447.3i	0.758793	−	0.737914i
$793$	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	$-0.526049\pi$
$809$	−3761.86			−0.163486			−0.0817429	+	0.996653i	$0.526049\pi$
$810$	4739.58	+	9434.64i	0.205595	+	0.409258i
$811$			23288.0i			1.00833i	0.863609	+	0.504163i	$0.168199\pi$
$811$			23288.0i			1.00833i	−0.863609	+	0.504163i	$0.831801\pi$
$812$			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	$-0.213866\pi$
$821$	36822.5			1.56531			0.782653	+	0.622459i	$0.213866\pi$
$822$	−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
$825$	2324.98	−	17737.8i	0.0981157	−	0.748546i
$826$	−13391.5			−0.564105
$827$	18209.1			0.765650			0.382825	−	0.923821i	$-0.374951\pi$
$827$	18209.1			0.765650			0.382825	+	0.923821i	$0.374951\pi$
$828$	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	$0.0338153\pi$
$853$			5283.23i			0.212068i	−0.994362	+	0.106034i	$0.966185\pi$
$854$	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	$-0.241009\pi$
$857$	36468.1			1.45359			0.726795	+	0.686855i	$0.241009\pi$
$858$	15420.1	+	2021.20i	0.613561	+	0.0804225i
$859$	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	$-0.976029\pi$
$877$		−	3908.07i		−	0.150474i	0.997166	−	0.0752372i	$-0.0239714\pi$
$878$		−	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	$-0.480093\pi$
$887$	3302.10			0.124999			0.0624993	+	0.998045i	$0.480093\pi$
$888$	5447.33	+	4306.95i	0.205856	+	0.162761i
$889$	−23075.9			−0.870576
$890$	−17340.7			−0.653101
$891$	22440.2	+	14275.4i	0.843741	+	0.536750i
$892$	−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	$-0.958166\pi$
$919$		−	7301.84i		−	0.262095i	0.991376	−	0.131048i	$-0.0418341\pi$
$920$	−4151.01			−0.148755
$921$	10720.1	−	13558.6i	0.383539	−	0.485092i
$922$	−23634.4			−0.844205
$923$	20515.9			0.731624
$924$	−6788.70	−	889.829i	−0.241701	−	0.0316810i
$925$	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	$-0.828111\pi$
$937$		−	29493.1i		−	1.02828i	0.857706	−	0.514140i	$-0.171889\pi$
$938$			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	$-0.428373\pi$
$941$	12881.6			0.446257			0.223128	+	0.974789i	$0.428373\pi$
$942$	−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	$-0.761821\pi$
$953$	−43121.9			−1.46575			−0.732873	+	0.680365i	$0.761821\pi$
$954$	−42255.2	+	10017.2i	−1.43403	+	0.339956i
$955$	−6384.33			−0.216327
$956$	5124.31			0.173360
$957$	−2469.55	+	18840.7i	−0.0834160	+	0.636399i
$958$	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	$-0.887096\pi$
$967$		−	20887.4i		−	0.694617i	0.937751	−	0.347308i	$-0.112904\pi$
$968$	−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
$990$	−9946.21	−	10227.6i	−0.319304	−	0.328339i
$991$	−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	$0.432121\pi$
$997$			61535.0i			1.95470i	−0.211636	+	0.977349i	$0.567879\pi$
$998$	−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.32.4	yes	8
3.2	odd	2	inner	33.4.d.b.32.5	yes	8
4.3	odd	2		528.4.b.e.65.1		8
11.10	odd	2	inner	33.4.d.b.32.6	yes	8
12.11	even	2		528.4.b.e.65.3		8
33.32	even	2	inner	33.4.d.b.32.3	✓	8
44.43	even	2		528.4.b.e.65.2		8
132.131	odd	2		528.4.b.e.65.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.d.b.32.3	✓	8	33.32	even	2	inner
33.4.d.b.32.4	yes	8	1.1	even	1	trivial
33.4.d.b.32.5	yes	8	3.2	odd	2	inner
33.4.d.b.32.6	yes	8	11.10	odd	2	inner
528.4.b.e.65.1		8	4.3	odd	2
528.4.b.e.65.2		8	44.43	even	2
528.4.b.e.65.3		8	12.11	even	2
528.4.b.e.65.4		8	132.131	odd	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} +(24.6372 - 187.963i) 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} +(-64.4720 + 491.871i) 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} +(706.174 - 686.744i) 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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