LMFDB - Embedded newform 333.3.r.a.38.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [333,3,Mod(38,333)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(333, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("333.38");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 333 = 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	333.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.07359280320$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			38.16
Character	$\chi$	$=$	333.38
Dual form			333.3.r.a.149.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.28078 - 1.31681i) q^{2} +(2.69783 - 1.31214i) q^{3} +(1.46798 + 2.54262i) q^{4} +(-3.77668 + 2.18047i) q^{5} +(-7.88101 - 0.559825i) q^{6} +(0.802344 - 1.38970i) q^{7} +2.80227i q^{8} +(5.55658 - 7.07986i) q^{9} +O(q^{10})$	\(q+(-2.28078 - 1.31681i) q^{2} +(2.69783 - 1.31214i) q^{3} +(1.46798 + 2.54262i) q^{4} +(-3.77668 + 2.18047i) q^{5} +(-7.88101 - 0.559825i) q^{6} +(0.802344 - 1.38970i) q^{7} +2.80227i q^{8} +(5.55658 - 7.07986i) q^{9} +11.4851 q^{10} +(-9.47059 - 5.46785i) q^{11} +(7.29663 + 4.93335i) q^{12} +(-2.51680 - 4.35923i) q^{13} +(-3.65994 + 2.11307i) q^{14} +(-7.32777 + 10.8381i) q^{15} +(9.56199 - 16.5618i) q^{16} +25.3452i q^{17} +(-21.9962 + 8.83067i) q^{18} -21.9108 q^{19} +(-11.0882 - 6.40177i) q^{20} +(0.341106 - 4.80196i) q^{21} +(14.4002 + 24.9419i) q^{22} +(-27.4576 + 15.8527i) q^{23} +(3.67698 + 7.56006i) q^{24} +(-2.99111 + 5.18075i) q^{25} +13.2566i q^{26} +(5.70093 - 26.3913i) q^{27} +4.71130 q^{28} +(-0.673810 - 0.389024i) q^{29} +(30.9847 - 15.0700i) q^{30} +(-2.43926 - 4.22492i) q^{31} +(-33.9103 + 19.5781i) q^{32} +(-32.7246 - 2.32459i) q^{33} +(33.3748 - 57.8069i) q^{34} +6.99794i q^{35} +(26.1583 + 3.73515i) q^{36} +6.08276 q^{37} +(49.9738 + 28.8524i) q^{38} +(-12.5098 - 8.45806i) q^{39} +(-6.11027 - 10.5833i) q^{40} +(1.45288 - 0.838822i) q^{41} +(-7.10127 + 10.5031i) q^{42} +(-18.1610 + 31.4558i) q^{43} -32.1068i q^{44} +(-5.54801 + 38.8543i) q^{45} +83.4999 q^{46} +(-15.7819 - 9.11166i) q^{47} +(4.06516 - 57.2277i) q^{48} +(23.2125 + 40.2052i) q^{49} +(13.6441 - 7.87745i) q^{50} +(33.2564 + 68.3770i) q^{51} +(7.38923 - 12.7985i) q^{52} +32.7854i q^{53} +(-47.7549 + 52.6857i) q^{54} +47.6899 q^{55} +(3.89432 + 2.24839i) q^{56} +(-59.1117 + 28.7501i) q^{57} +(1.02454 + 1.77456i) q^{58} +(-60.6591 + 35.0216i) q^{59} +(-38.3141 - 2.72163i) q^{60} +(22.6715 - 39.2683i) q^{61} +12.8482i q^{62} +(-5.38060 - 13.4025i) q^{63} +26.6267 q^{64} +(19.0103 + 10.9756i) q^{65} +(71.5767 + 48.3940i) q^{66} +(13.5293 + 23.4335i) q^{67} +(-64.4431 + 37.2062i) q^{68} +(-53.2751 + 78.7961i) q^{69} +(9.21497 - 15.9608i) q^{70} +99.0942i q^{71} +(19.8397 + 15.5711i) q^{72} +13.1960 q^{73} +(-13.8735 - 8.00985i) q^{74} +(-1.27163 + 17.9015i) q^{75} +(-32.1647 - 55.7108i) q^{76} +(-15.1973 + 8.77419i) q^{77} +(17.3945 + 35.7641i) q^{78} +(8.24464 - 14.2801i) q^{79} +83.3985i q^{80} +(-19.2489 - 78.6796i) q^{81} -4.41828 q^{82} +(-84.8523 - 48.9895i) q^{83} +(12.7103 - 6.18189i) q^{84} +(-55.2644 - 95.7207i) q^{85} +(82.8426 - 47.8292i) q^{86} +(-2.32828 - 0.165389i) q^{87} +(15.3224 - 26.5392i) q^{88} -162.760i q^{89} +(63.8176 - 81.3126i) q^{90} -8.07736 q^{91} +(-80.6146 - 46.5429i) q^{92} +(-12.1244 - 8.19747i) q^{93} +(23.9967 + 41.5635i) q^{94} +(82.7502 - 47.7759i) q^{95} +(-65.7950 + 97.3134i) q^{96} +(26.4561 - 45.8233i) q^{97} -122.266i q^{98} +(-91.3357 + 36.6679i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 4 q^{3} + 144 q^{4} - 30 q^{6} + 4 q^{9}+O(q^{10}) $ 144 * q + 4 * q^3 + 144 * q^4 - 30 * q^6 + 4 * q^9	$ 144 q + 4 q^{3} + 144 q^{4} - 30 q^{6} + 4 q^{9} - 12 q^{12} + 72 q^{14} - 18 q^{15} - 288 q^{16} - 90 q^{18} - 24 q^{19} + 32 q^{21} - 24 q^{22} + 144 q^{23} - 48 q^{24} + 360 q^{25} - 50 q^{27} - 216 q^{29} + 28 q^{30} + 36 q^{32} - 110 q^{33} + 60 q^{34} - 10 q^{36} + 36 q^{38} + 88 q^{39} - 60 q^{40} + 108 q^{41} + 278 q^{42} - 60 q^{43} + 64 q^{45} - 216 q^{46} + 90 q^{47} - 238 q^{48} - 552 q^{49} - 522 q^{50} + 90 q^{51} - 18 q^{52} + 216 q^{54} + 48 q^{55} + 432 q^{56} - 264 q^{57} + 138 q^{58} - 270 q^{59} - 458 q^{60} + 96 q^{61} + 148 q^{63} - 636 q^{64} - 54 q^{65} - 224 q^{66} + 84 q^{67} - 72 q^{68} + 410 q^{69} - 216 q^{70} - 636 q^{72} - 72 q^{73} + 344 q^{75} + 84 q^{76} + 432 q^{77} - 384 q^{78} + 108 q^{79} + 556 q^{81} - 204 q^{82} - 180 q^{83} - 308 q^{84} + 60 q^{85} + 72 q^{86} + 126 q^{87} + 168 q^{88} - 206 q^{90} + 168 q^{91} - 36 q^{92} + 70 q^{93} - 186 q^{94} - 864 q^{95} + 932 q^{96} - 180 q^{97} + 128 q^{99}+O(q^{100}) $ 144 * q + 4 * q^3 + 144 * q^4 - 30 * q^6 + 4 * q^9 - 12 * q^12 + 72 * q^14 - 18 * q^15 - 288 * q^16 - 90 * q^18 - 24 * q^19 + 32 * q^21 - 24 * q^22 + 144 * q^23 - 48 * q^24 + 360 * q^25 - 50 * q^27 - 216 * q^29 + 28 * q^30 + 36 * q^32 - 110 * q^33 + 60 * q^34 - 10 * q^36 + 36 * q^38 + 88 * q^39 - 60 * q^40 + 108 * q^41 + 278 * q^42 - 60 * q^43 + 64 * q^45 - 216 * q^46 + 90 * q^47 - 238 * q^48 - 552 * q^49 - 522 * q^50 + 90 * q^51 - 18 * q^52 + 216 * q^54 + 48 * q^55 + 432 * q^56 - 264 * q^57 + 138 * q^58 - 270 * q^59 - 458 * q^60 + 96 * q^61 + 148 * q^63 - 636 * q^64 - 54 * q^65 - 224 * q^66 + 84 * q^67 - 72 * q^68 + 410 * q^69 - 216 * q^70 - 636 * q^72 - 72 * q^73 + 344 * q^75 + 84 * q^76 + 432 * q^77 - 384 * q^78 + 108 * q^79 + 556 * q^81 - 204 * q^82 - 180 * q^83 - 308 * q^84 + 60 * q^85 + 72 * q^86 + 126 * q^87 + 168 * q^88 - 206 * q^90 + 168 * q^91 - 36 * q^92 + 70 * q^93 - 186 * q^94 - 864 * q^95 + 932 * q^96 - 180 * q^97 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/333\mathbb{Z}\right)^\times$.

$n$	$38$	$298$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−2.28078	−	1.31681i	−1.14039	−	0.658405i	−0.193864	−	0.981028i	$-0.562102\pi$
$2$	−2.28078	−	1.31681i	−1.14039	−	0.658405i	−0.946528	+	0.322623i	$0.895435\pi$
$3$	2.69783	−	1.31214i	0.899277	−	0.437380i
$3$	2.69783	−	1.31214i	0.899277	−	0.437380i
$4$	1.46798	+	2.54262i	0.366995	+	0.635654i
$5$	−3.77668	+	2.18047i	−0.755337	+	0.436094i	−0.827619	−	0.561290i	$-0.810305\pi$
$5$	−3.77668	+	2.18047i	−0.755337	+	0.436094i	0.0722822	+	0.997384i	$0.476972\pi$
$6$	−7.88101	−	0.559825i	−1.31350	−	0.0933042i
$7$	0.802344	−	1.38970i	0.114621	−	0.198529i	−0.803007	−	0.595969i	$-0.796768\pi$
$7$	0.802344	−	1.38970i	0.114621	−	0.198529i	0.917628	+	0.397440i	$0.130101\pi$
$8$			2.80227i			0.350284i
$9$	5.55658	−	7.07986i	0.617398	−	0.786651i
$10$	11.4851			1.14851
$11$	−9.47059	−	5.46785i	−0.860963	−	0.497077i	0.00337194	−	0.999994i	$-0.498927\pi$
$11$	−9.47059	−	5.46785i	−0.860963	−	0.497077i	−0.864335	+	0.502917i	$0.832260\pi$
$12$	7.29663	+	4.93335i	0.608053	+	0.411113i
$13$	−2.51680	−	4.35923i	−0.193600	−	0.335325i	0.752841	−	0.658203i	$-0.228683\pi$
$13$	−2.51680	−	4.35923i	−0.193600	−	0.335325i	−0.946441	+	0.322878i	$0.895350\pi$
$14$	−3.65994	+	2.11307i	−0.261425	+	0.150934i
$15$	−7.32777	+	10.8381i	−0.488518	+	0.722538i
$16$	9.56199	−	16.5618i	0.597624	−	1.03512i
$17$			25.3452i			1.49089i	0.666565	+	0.745447i	$0.267764\pi$
$17$			25.3452i			1.49089i	−0.666565	+	0.745447i	$0.732236\pi$
$18$	−21.9962	+	8.83067i	−1.22201	+	0.490593i
$19$	−21.9108			−1.15320			−0.576601	−	0.817026i	$-0.695621\pi$
$19$	−21.9108			−1.15320			−0.576601	+	0.817026i	$0.695621\pi$
$20$	−11.0882	−	6.40177i	−0.554410	−	0.320089i
$21$	0.341106	−	4.80196i	0.0162432	−	0.228665i
$22$	14.4002	+	24.9419i	0.654556	+	1.13372i
$23$	−27.4576	+	15.8527i	−1.19381	+	0.689247i	−0.959169	−	0.282835i	$-0.908725\pi$
$23$	−27.4576	+	15.8527i	−1.19381	+	0.689247i	−0.234642	+	0.972082i	$0.575392\pi$
$24$	3.67698	+	7.56006i	0.153207	+	0.315003i
$25$	−2.99111	+	5.18075i	−0.119644	+	0.207230i
$26$			13.2566i			0.509870i
$27$	5.70093	−	26.3913i	0.211146	−	0.977455i
$28$	4.71130			0.168261
$29$	−0.673810	−	0.389024i	−0.0232348	−	0.0134146i	0.488338	−	0.872655i	$-0.337603\pi$
$29$	−0.673810	−	0.389024i	−0.0232348	−	0.0134146i	−0.511572	+	0.859240i	$0.670937\pi$
$30$	30.9847	−	15.0700i	1.03282	−	0.502334i
$31$	−2.43926	−	4.22492i	−0.0786858	−	0.136288i	0.823997	−	0.566594i	$-0.191739\pi$
$31$	−2.43926	−	4.22492i	−0.0786858	−	0.136288i	−0.902683	+	0.430306i	$0.858406\pi$
$32$	−33.9103	+	19.5781i	−1.05970	+	0.611816i
$33$	−32.7246	−	2.32459i	−0.991655	−	0.0704420i
$34$	33.3748	−	57.8069i	0.981612	−	1.70020i
$35$			6.99794i			0.199941i
$36$	26.1583	+	3.73515i	0.726620	+	0.103754i
$37$	6.08276			0.164399
$37$	6.08276			0.164399
$38$	49.9738	+	28.8524i	1.31510	+	0.759274i
$39$	−12.5098	−	8.45806i	−0.320765	−	0.216873i
$40$	−6.11027	−	10.5833i	−0.152757	−	0.264583i
$41$	1.45288	−	0.838822i	0.0354362	−	0.0204591i	−0.482177	−	0.876074i	$-0.660154\pi$
$41$	1.45288	−	0.838822i	0.0354362	−	0.0204591i	0.517613	+	0.855615i	$0.326821\pi$
$42$	−7.10127	+	10.5031i	−0.169078	+	0.250073i
$43$	−18.1610	+	31.4558i	−0.422349	+	0.731530i	−0.996169	−	0.0874518i	$-0.972128\pi$
$43$	−18.1610	+	31.4558i	−0.422349	+	0.731530i	0.573820	+	0.818982i	$0.305461\pi$
$44$		−	32.1068i		−	0.729699i
$45$	−5.54801	+	38.8543i	−0.123289	+	0.863430i
$46$	83.4999			1.81522
$47$	−15.7819	−	9.11166i	−0.335784	−	0.193865i	0.322622	−	0.946528i	$-0.395436\pi$
$47$	−15.7819	−	9.11166i	−0.335784	−	0.193865i	−0.658406	+	0.752663i	$0.728769\pi$
$48$	4.06516	−	57.2277i	0.0846908	−	1.19224i
$49$	23.2125	+	40.2052i	0.473724	+	0.820514i
$50$	13.6441	−	7.87745i	0.272883	−	0.157549i
$51$	33.2564	+	68.3770i	0.652087	+	1.34073i
$52$	7.38923	−	12.7985i	0.142101	−	0.246126i
$53$			32.7854i			0.618592i	0.950966	+	0.309296i	$0.100093\pi$
$53$			32.7854i			0.618592i	−0.950966	+	0.309296i	$0.899907\pi$
$54$	−47.7549	+	52.6857i	−0.884350	+	0.975661i
$55$	47.6899			0.867089
$56$	3.89432	+	2.24839i	0.0695414	+	0.0401498i
$57$	−59.1117	+	28.7501i	−1.03705	+	0.504387i
$58$	1.02454	+	1.77456i	0.0176645	+	0.0305959i
$59$	−60.6591	+	35.0216i	−1.02812	+	0.593586i	−0.916446	−	0.400159i	$-0.868955\pi$
$59$	−60.6591	+	35.0216i	−1.02812	+	0.593586i	−0.111675	+	0.993745i	$0.535622\pi$
$60$	−38.3141	−	2.72163i	−0.638568	−	0.0453606i
$61$	22.6715	−	39.2683i	0.371665	−	0.643742i	−0.618157	−	0.786055i	$-0.712120\pi$
$61$	22.6715	−	39.2683i	0.371665	−	0.643742i	0.989822	+	0.142312i	$0.0454538\pi$
$62$			12.8482i			0.207229i
$63$	−5.38060	−	13.4025i	−0.0854064	−	0.212737i
$64$	26.6267			0.416043
$65$	19.0103	+	10.9756i	0.292467	+	0.168856i
$66$	71.5767	+	48.3940i	1.08450	+	0.733243i
$67$	13.5293	+	23.4335i	0.201930	+	0.349754i	0.949150	−	0.314823i	$-0.101945\pi$
$67$	13.5293	+	23.4335i	0.201930	+	0.349754i	−0.747220	+	0.664577i	$0.768612\pi$
$68$	−64.4431	+	37.2062i	−0.947693	+	0.547151i
$69$	−53.2751	+	78.7961i	−0.772103	+	1.14197i
$70$	9.21497	−	15.9608i	0.131642	−	0.228011i
$71$			99.0942i			1.39569i	0.716247	+	0.697847i	$0.245858\pi$
$71$			99.0942i			1.39569i	−0.716247	+	0.697847i	$0.754142\pi$
$72$	19.8397	+	15.5711i	0.275552	+	0.216265i
$73$	13.1960			0.180767			0.0903833	−	0.995907i	$-0.471191\pi$
$73$	13.1960			0.180767			0.0903833	+	0.995907i	$0.471191\pi$
$74$	−13.8735	−	8.00985i	−0.187479	−	0.108241i
$75$	−1.27163	+	17.9015i	−0.0169551	+	0.238687i
$76$	−32.1647	−	55.7108i	−0.423219	−	0.733037i
$77$	−15.1973	+	8.77419i	−0.197368	+	0.113950i
$78$	17.3945	+	35.7641i	0.223007	+	0.458514i
$79$	8.24464	−	14.2801i	0.104363	−	0.180761i	−0.809115	−	0.587650i	$-0.800053\pi$
$79$	8.24464	−	14.2801i	0.104363	−	0.180761i	0.913478	+	0.406889i	$0.133386\pi$
$80$			83.3985i			1.04248i
$81$	−19.2489	−	78.6796i	−0.237641	−	0.971353i
$82$	−4.41828			−0.0538815
$83$	−84.8523	−	48.9895i	−1.02232	−	0.590235i	−0.107543	−	0.994200i	$-0.534298\pi$
$83$	−84.8523	−	48.9895i	−1.02232	−	0.590235i	−0.914774	+	0.403965i	$0.867632\pi$
$84$	12.7103	−	6.18189i	0.151313	−	0.0735939i
$85$	−55.2644	−	95.7207i	−0.650169	−	1.12613i
$86$	82.8426	−	47.8292i	0.963286	−	0.556154i
$87$	−2.32828	−	0.165389i	−0.0267618	−	0.00190102i
$88$	15.3224	−	26.5392i	0.174118	−	0.301582i
$89$		−	162.760i		−	1.82876i	−0.404858	−	0.914379i	$-0.632679\pi$
$89$		−	162.760i		−	1.82876i	0.404858	−	0.914379i	$-0.367321\pi$
$90$	63.8176	−	81.3126i	0.709085	−	0.903474i
$91$	−8.07736			−0.0887622
$92$	−80.6146	−	46.5429i	−0.876246	−	0.505901i
$93$	−12.1244	−	8.19747i	−0.130370	−	0.0881449i
$94$	23.9967	+	41.5635i	0.255284	+	0.442164i
$95$	82.7502	−	47.7759i	0.871055	−	0.502904i
$96$	−65.7950	+	97.3134i	−0.685364	+	1.01368i
$97$	26.4561	−	45.8233i	0.272743	−	0.472405i	−0.696820	−	0.717246i	$-0.745402\pi$
$97$	26.4561	−	45.8233i	0.272743	−	0.472405i	0.969563	+	0.244841i	$0.0787357\pi$
$98$		−	122.266i		−	1.24761i
$99$	−91.3357	+	36.6679i	−0.922582	+	0.370383i
$100$	−17.5636			−0.175636
$101$	−90.0562	−	51.9939i	−0.891645	−	0.514792i	−0.0171648	−	0.999853i	$-0.505464\pi$
$101$	−90.0562	−	51.9939i	−0.891645	−	0.514792i	−0.874480	+	0.485061i	$0.838797\pi$
$102$	14.1889	−	199.746i	0.139107	−	1.95829i
$103$	60.0936	+	104.085i	0.583433	+	1.01053i	0.995069	+	0.0991867i	$0.0316241\pi$
$103$	60.0936	+	104.085i	0.583433	+	1.01053i	−0.411636	+	0.911348i	$0.635043\pi$
$104$	12.2158	−	7.05277i	0.117459	−	0.0678151i
$105$	9.18228	+	18.8793i	0.0874503	+	0.179803i
$106$	43.1721	−	74.7763i	0.407284	−	0.705437i
$107$		−	175.454i		−	1.63976i	−0.572537	−	0.819879i	$-0.694041\pi$
$107$		−	175.454i		−	1.63976i	0.572537	−	0.819879i	$-0.305959\pi$
$108$	75.4718	−	24.2466i	0.698813	−	0.224505i
$109$	−175.447			−1.60961			−0.804805	−	0.593540i	$-0.797730\pi$
$109$	−175.447			−1.60961			−0.804805	+	0.593540i	$0.797730\pi$
$110$	−108.770	−	62.7986i	−0.988821	−	0.570896i
$111$	16.4103	−	7.98144i	0.147840	−	0.0719048i
$112$	−15.3440	−	26.5766i	−0.137000	−	0.237291i
$113$	116.756	−	67.4093i	1.03324	−	0.596542i	0.115330	−	0.993327i	$-0.463207\pi$
$113$	116.756	−	67.4093i	1.03324	−	0.596542i	0.917912	+	0.396785i	$0.129874\pi$
$114$	172.679	+	12.2662i	1.51473	+	0.107599i
$115$	69.1326	−	119.741i	0.601153	−	1.04123i
$116$		−	2.28432i		−	0.0196924i
$117$	−44.8475	−	6.40378i	−0.383312	−	0.0547332i
$118$	184.467			1.56328
$119$	35.2222	+	20.3356i	0.295985	+	0.170887i
$120$	−30.3713	−	20.5344i	−0.253094	−	0.171120i
$121$	−0.705306	−	1.22163i	−0.00582897	−	0.0100961i
$122$	−103.418	+	59.7083i	−0.847687	+	0.489412i
$123$	2.81898	−	4.16939i	0.0229185	−	0.0338974i
$124$	7.16157	−	12.4042i	0.0577546	−	0.100034i
$125$		−	135.112i		−	1.08089i
$126$	−5.37652	+	37.6533i	−0.0426708	+	0.298836i
$127$	−197.684			−1.55657			−0.778284	−	0.627912i	$-0.783910\pi$
$127$	−197.684			−1.55657			−0.778284	+	0.627912i	$0.783910\pi$
$128$	74.9113	+	43.2501i	0.585244	+	0.337891i
$129$	−7.72092	+	108.692i	−0.0598521	+	0.842575i
$130$	−28.9056	−	50.0660i	−0.222351	−	0.385123i
$131$	−27.7991	+	16.0498i	−0.212207	+	0.122518i	−0.602336	−	0.798242i	$-0.705763\pi$
$131$	−27.7991	+	16.0498i	−0.212207	+	0.122518i	0.390130	+	0.920760i	$0.372430\pi$
$132$	−42.1286	−	86.6186i	−0.319156	−	0.656202i
$133$	−17.5800	+	30.4495i	−0.132181	+	0.228943i
$134$		−	71.2623i		−	0.531808i
$135$	36.0147	+	112.102i	0.266776	+	0.830387i
$136$	−71.0242			−0.522236
$137$	−2.26769	−	1.30925i	−0.0165525	−	0.00955657i	0.491701	−	0.870764i	$-0.336375\pi$
$137$	−2.26769	−	1.30925i	−0.0165525	−	0.00955657i	−0.508253	+	0.861208i	$0.669709\pi$
$138$	225.269	−	109.564i	1.63238	−	0.793939i
$139$	53.1162	+	91.9999i	0.382131	+	0.661870i	0.991367	−	0.131119i	$-0.0418571\pi$
$139$	53.1162	+	91.9999i	0.382131	+	0.661870i	−0.609236	+	0.792989i	$0.708524\pi$
$140$	−17.7931	+	10.2728i	−0.127094	+	0.0733775i
$141$	−54.5326	−	3.87371i	−0.386756	−	0.0274731i
$142$	130.488	−	226.012i	0.918932	−	1.59164i
$143$			55.0460i			0.384937i
$144$	−64.1237	−	159.725i	−0.445303	−	1.10920i
$145$	3.39302			0.0234002
$146$	−30.0971	−	17.3766i	−0.206145	−	0.119018i
$147$	115.378	+	78.0088i	0.784886	+	0.530672i
$148$	8.92938	+	15.4661i	0.0603336	+	0.104501i
$149$	10.5399	−	6.08523i	0.0707378	−	0.0408405i	−0.464214	−	0.885723i	$-0.653663\pi$
$149$	10.5399	−	6.08523i	0.0707378	−	0.0408405i	0.534952	+	0.844883i	$0.320330\pi$
$150$	26.4733	−	39.1550i	0.176488	−	0.261034i
$151$	−88.9014	+	153.982i	−0.588751	+	1.01975i	0.405645	+	0.914031i	$0.367047\pi$
$151$	−88.9014	+	153.982i	−0.588751	+	1.01975i	−0.994396	+	0.105716i	$0.966287\pi$
$152$		−	61.4001i		−	0.403948i
$153$	179.440	+	140.832i	1.17281	+	0.920474i
$154$	46.2158			0.300102
$155$	18.4246	+	10.6375i	0.118869	+	0.0686288i
$156$	3.14144	−	44.2240i	0.0201374	−	0.283487i
$157$	−89.8712	−	155.662i	−0.572428	−	0.991475i	−0.996316	−	0.0857598i	$-0.972668\pi$
$157$	−89.8712	−	155.662i	−0.572428	−	0.991475i	0.423888	−	0.905715i	$-0.360665\pi$
$158$	−37.6085	+	21.7133i	−0.238028	+	0.137426i
$159$	43.0190	+	88.4493i	0.270560	+	0.556285i
$160$	85.3789	−	147.881i	0.533618	−	0.924254i
$161$			50.8772i			0.316007i
$162$	−59.7036	+	204.798i	−0.368541	+	1.26419i
$163$	57.5333			0.352965			0.176483	−	0.984304i	$-0.443528\pi$
$163$	57.5333			0.352965			0.176483	+	0.984304i	$0.443528\pi$
$164$	4.26561	+	2.46275i	0.0260098	+	0.0150168i
$165$	128.659	−	62.5758i	0.779753	−	0.379247i
$166$	129.020	+	223.469i	0.777228	+	1.34620i
$167$	−198.062	+	114.351i	−1.18600	+	0.684737i	−0.957395	−	0.288782i	$-0.906750\pi$
$167$	−198.062	+	114.351i	−1.18600	+	0.684737i	−0.228604	+	0.973519i	$0.573416\pi$
$168$	13.4564	+	0.955873i	0.0800977	+	0.00568972i
$169$	71.8314	−	124.416i	0.425038	−	0.736187i
$170$			291.091i			1.71230i
$171$	−121.749	+	155.126i	−0.711984	+	0.907167i
$172$	−106.640			−0.620000
$173$	161.107	+	93.0154i	0.931256	+	0.537661i	0.887209	−	0.461368i	$-0.152641\pi$
$173$	161.107	+	93.0154i	0.931256	+	0.537661i	0.0440476	+	0.999029i	$0.485975\pi$
$174$	5.09251	+	3.44312i	0.0292673	+	0.0197880i
$175$	4.79979	+	8.31349i	0.0274274	+	0.0475056i
$176$	−181.115	+	104.567i	−1.02906	+	0.594130i
$177$	−117.695	+	174.076i	−0.664943	+	0.983478i
$178$	−214.324	+	371.219i	−1.20406	+	2.08550i
$179$		−	214.457i		−	1.19808i	−0.800717	−	0.599042i	$-0.795548\pi$
$179$		−	214.457i		−	1.19808i	0.800717	−	0.599042i	$-0.204452\pi$
$180$	−106.936	+	42.9310i	−0.594089	+	0.238505i
$181$	−125.633			−0.694103			−0.347052	−	0.937846i	$-0.612817\pi$
$181$	−125.633			−0.694103			−0.347052	+	0.937846i	$0.612817\pi$
$182$	18.4227	+	10.6364i	0.101224	+	0.0584415i
$183$	9.63852	−	135.687i	0.0526695	−	0.741461i
$184$	−44.4236	−	76.9438i	−0.241432	−	0.418173i
$185$	−22.9727	+	13.2633i	−0.124177	+	0.0716934i
$186$	16.8586	+	34.6622i	0.0906376	+	0.186356i
$187$	138.584	−	240.034i	0.741089	−	1.28360i
$188$		−	53.5030i		−	0.284590i
$189$	−32.1019	−	29.0975i	−0.169851	−	0.153955i
$190$	−251.647			−1.32446
$191$	154.259	+	89.0617i	0.807641	+	0.466292i	0.846136	−	0.532967i	$-0.178923\pi$
$191$	154.259	+	89.0617i	0.807641	+	0.466292i	−0.0384949	+	0.999259i	$0.512256\pi$
$192$	71.8344	−	34.9380i	0.374138	−	0.181969i
$193$	17.4720	+	30.2624i	0.0905287	+	0.156800i	0.907734	−	0.419547i	$-0.137811\pi$
$193$	17.4720	+	30.2624i	0.0905287	+	0.156800i	−0.817205	+	0.576347i	$0.804478\pi$
$194$	−120.681	+	69.6753i	−0.622068	+	0.359151i
$195$	65.6882	+	4.66615i	0.336863	+	0.0239290i
$196$	−68.1510	+	118.041i	−0.347709	+	0.602250i
$197$		−	274.427i		−	1.39303i	−0.717541	−	0.696516i	$-0.754733\pi$
$197$		−	274.427i		−	1.39303i	0.717541	−	0.696516i	$-0.245267\pi$
$198$	256.602	+	36.6401i	1.29597	+	0.185051i
$199$	−219.424			−1.10263			−0.551317	−	0.834296i	$-0.685875\pi$
$199$	−219.424			−1.10263			−0.551317	+	0.834296i	$0.685875\pi$
$200$	−14.5179	−	8.38190i	−0.0725894	−	0.0419095i
$201$	67.2478	+	45.4672i	0.334566	+	0.226205i
$202$	136.932	+	237.174i	0.677883	+	1.17413i
$203$	−1.08125	+	0.624262i	−0.00532638	+	0.00307518i
$204$	−125.037	+	184.935i	−0.612925	+	0.906542i
$205$	−3.65805	+	6.33593i	−0.0178442	+	0.0309070i
$206$		−	316.527i		−	1.53654i
$207$	−40.3358	+	282.483i	−0.194859	+	1.36465i
$208$	−96.2625			−0.462801
$209$	207.508	+	119.805i	0.992863	+	0.573230i
$210$	3.91763	−	55.1508i	0.0186554	−	0.262623i
$211$	−8.39689	−	14.5438i	−0.0397957	−	0.0689281i	0.845442	−	0.534068i	$-0.179337\pi$
$211$	−8.39689	−	14.5438i	−0.0397957	−	0.0689281i	−0.885237	+	0.465140i	$0.846004\pi$
$212$	−83.3606	+	48.1283i	−0.393210	+	0.227020i
$213$	130.026	+	267.339i	0.610448	+	1.25511i
$214$	−231.040	+	400.173i	−1.07963	+	1.86997i
$215$		−	158.398i		−	0.736735i
$216$	73.9556	+	15.9756i	0.342387	+	0.0739610i
$217$	−7.82850			−0.0360760
$218$	400.157	+	231.031i	1.83558	+	1.05978i
$219$	35.6005	−	17.3149i	0.162559	−	0.0790637i
$220$	70.0078	+	121.257i	0.318217	+	0.551169i
$221$	110.485	−	63.7888i	0.499934	−	0.288637i
$222$	−47.9383	−	3.40528i	−0.215938	−	0.0153391i
$223$	108.531	−	187.981i	0.486685	−	0.842963i	−0.513198	−	0.858270i	$-0.671539\pi$
$223$	108.531	−	187.981i	0.486685	−	0.842963i	0.999883	+	0.0153072i	$0.00487263\pi$
$224$			62.8335i			0.280507i
$225$	20.0587	+	49.9639i	0.0891497	+	0.222062i
$226$	−355.061			−1.57107
$227$	−12.0483	−	6.95610i	−0.0530763	−	0.0306436i	0.473227	−	0.880941i	$-0.343089\pi$
$227$	−12.0483	−	6.95610i	−0.0530763	−	0.0306436i	−0.526303	+	0.850297i	$0.676422\pi$
$228$	−159.875	−	108.094i	−0.701207	−	0.474096i
$229$	147.802	+	256.001i	0.645424	+	1.11791i	0.984203	+	0.177042i	$0.0566528\pi$
$229$	147.802	+	256.001i	0.645424	+	1.11791i	−0.338779	+	0.940866i	$0.610014\pi$
$230$	−315.353	+	182.069i	−1.37110	+	0.791604i
$231$	−29.4869	+	43.6123i	−0.127649	+	0.188798i
$232$	1.09015	−	1.88820i	0.00469893	−	0.00813879i
$233$		−	104.172i		−	0.447091i	−0.974693	−	0.223546i	$-0.928237\pi$
$233$		−	104.172i		−	0.447091i	0.974693	−	0.223546i	$-0.0717631\pi$
$234$	93.8550	+	73.6614i	0.401090	+	0.314792i
$235$	79.4708			0.338174
$236$	−178.093	−	102.822i	−0.754631	−	0.435686i
$237$	3.50510	−	49.3435i	0.0147895	−	0.208200i
$238$	−53.5561	−	92.7620i	−0.225026	−	0.389756i
$239$	27.0614	−	15.6239i	0.113228	−	0.0653719i	−0.442317	−	0.896859i	$-0.645843\pi$
$239$	27.0614	−	15.6239i	0.113228	−	0.0653719i	0.555544	+	0.831487i	$0.312510\pi$
$240$	109.430	+	224.995i	0.455960	+	0.937479i
$241$	76.5345	−	132.562i	0.317571	−	0.550049i	−0.662410	−	0.749142i	$-0.730466\pi$
$241$	76.5345	−	132.562i	0.317571	−	0.550049i	0.979981	+	0.199093i	$0.0637996\pi$
$242$			3.71502i			0.0153513i
$243$	−155.169	−	187.007i	−0.638555	−	0.769576i
$244$	133.126			0.545597
$245$	−175.332	−	101.228i	−0.715643	−	0.413176i
$246$	−11.9198	+	5.79740i	−0.0484543	+	0.0235667i
$247$	55.1452	+	95.5143i	0.223260	+	0.386698i
$248$	11.8394	−	6.83547i	0.0477395	−	0.0275624i
$249$	−293.198	−	20.8273i	−1.17750	−	0.0836437i
$250$	−177.916	+	308.160i	−0.711665	+	1.23264i
$251$			279.830i			1.11486i	0.830224	+	0.557430i	$0.188212\pi$
$251$			279.830i			1.11486i	−0.830224	+	0.557430i	$0.811788\pi$
$252$	26.1787	−	33.3554i	0.103884	−	0.132363i
$253$	346.720			1.37043
$254$	450.875	+	260.313i	1.77510	+	1.02485i
$255$	−274.693	−	185.724i	−1.07723	−	0.728328i
$256$	−167.158	−	289.526i	−0.652960	−	1.13096i
$257$	289.508	−	167.148i	1.12649	−	0.650380i	0.183441	−	0.983031i	$-0.441276\pi$
$257$	289.508	−	167.148i	1.12649	−	0.650380i	0.943050	+	0.332651i	$0.107943\pi$
$258$	160.737	−	237.736i	0.623011	−	0.921458i
$259$	4.88047	−	8.45322i	0.0188435	−	0.0326379i
$260$			64.4480i			0.247877i
$261$	−6.49831	+	2.60884i	−0.0248978	+	0.00999554i
$262$	84.5382			0.322665
$263$	245.749	+	141.883i	0.934408	+	0.539481i	0.888203	−	0.459451i	$-0.151954\pi$
$263$	245.749	+	141.883i	0.934408	+	0.539481i	0.0462051	+	0.998932i	$0.485287\pi$
$264$	6.51413	−	91.7034i	0.0246747	−	0.347361i
$265$	−71.4875	−	123.820i	−0.269764	−	0.467245i
$266$	80.1924	−	46.2991i	0.301475	−	0.174057i
$267$	−213.563	−	439.098i	−0.799863	−	1.64456i
$268$	−39.7216	+	68.7998i	−0.148215	+	0.256716i
$269$			359.960i			1.33814i	0.743198	+	0.669071i	$0.233308\pi$
$269$			359.960i			1.33814i	−0.743198	+	0.669071i	$0.766692\pi$
$270$	65.4756	−	303.105i	0.242502	−	1.12261i
$271$	−276.798			−1.02140			−0.510698	−	0.859760i	$-0.670613\pi$
$271$	−276.798			−1.02140			−0.510698	+	0.859760i	$0.670613\pi$
$272$	419.763	+	242.350i	1.54325	+	0.890994i
$273$	−21.7914	+	10.5986i	−0.0798218	+	0.0388228i
$274$	3.44807	+	5.97223i	0.0125842	+	0.0217965i
$275$	56.6551	−	32.7098i	0.206019	−	0.118945i
$276$	−278.555	−	19.7871i	−1.00926	−	0.0716924i
$277$	−131.982	+	228.599i	−0.476469	+	0.825268i	−0.999636	−	0.0269617i	$-0.991417\pi$
$277$	−131.982	+	228.599i	−0.476469	+	0.825268i	0.523168	+	0.852230i	$0.324750\pi$
$278$		−	279.776i		−	1.00639i
$279$	−43.4658	−	6.20648i	−0.155791	−	0.0222455i
$280$	−19.6102			−0.0700363
$281$	−127.760	−	73.7622i	−0.454661	−	0.262499i	0.255136	−	0.966905i	$-0.417880\pi$
$281$	−127.760	−	73.7622i	−0.454661	−	0.262499i	−0.709797	+	0.704406i	$0.751213\pi$
$282$	119.276	+	80.6442i	0.422965	+	0.285972i
$283$	115.840	+	200.641i	0.409329	+	0.708978i	0.994815	−	0.101704i	$-0.0324296\pi$
$283$	115.840	+	200.641i	0.409329	+	0.708978i	−0.585486	+	0.810683i	$0.699096\pi$
$284$	−251.959	+	145.468i	−0.887179	+	0.512213i
$285$	160.557	−	237.471i	0.563360	−	0.833232i
$286$	72.4851	−	125.548i	0.253444	−	0.438979i
$287$		−	2.69209i		−	0.00938012i
$288$	−49.8148	+	348.867i	−0.172968	+	1.21134i
$289$	−353.378			−1.22276
$290$	−7.73875	−	4.46797i	−0.0266853	−	0.0154068i
$291$	11.2475	−	158.338i	0.0386511	−	0.544115i
$292$	19.3714	+	33.5523i	0.0663404	+	0.114905i
$293$	307.361	−	177.455i	1.04901	−	0.605648i	0.126640	−	0.991949i	$-0.459581\pi$
$293$	307.361	−	177.455i	1.04901	−	0.605648i	0.922373	+	0.386301i	$0.126247\pi$
$294$	−160.430	−	329.852i	−0.545680	−	1.12195i
$295$	152.727	−	264.531i	0.517718	−	0.896714i
$296$			17.0456i			0.0575864i
$297$	−198.295	+	218.769i	−0.667659	+	0.736596i
$298$	−32.0524			−0.107558
$299$	138.211	+	79.7961i	0.462244	+	0.266877i
$300$	−47.3835	+	23.0458i	−0.157945	+	0.0768195i
$301$	29.1427	+	50.4767i	0.0968197	+	0.167697i
$302$	405.530	−	234.133i	1.34281	−	0.775274i
$303$	−311.180	−	22.1046i	−1.02700	−	0.0729524i
$304$	−209.511	+	362.884i	−0.689181	+	1.19370i
$305$			197.738i			0.648323i
$306$	−223.815	−	557.497i	−0.731421	−	1.82189i
$307$	242.801			0.790881			0.395441	−	0.918492i	$-0.370592\pi$
$307$	242.801			0.790881			0.395441	+	0.918492i	$0.370592\pi$
$308$	−44.6188	−	25.7607i	−0.144866	−	0.0836385i
$309$	298.696	+	201.953i	0.966655	+	0.653569i
$310$	−28.0150	−	48.5235i	−0.0903711	−	0.156527i
$311$	−34.6821	+	20.0237i	−0.111518	+	0.0643849i	−0.554722	−	0.832036i	$-0.687175\pi$
$311$	−34.6821	+	20.0237i	−0.111518	+	0.0643849i	0.443204	+	0.896421i	$0.353842\pi$
$312$	23.7018	−	35.0560i	0.0759674	−	0.112359i
$313$	50.6672	−	87.7582i	0.161876	−	0.280378i	−0.773665	−	0.633594i	$-0.781579\pi$
$313$	50.6672	−	87.7582i	0.161876	−	0.280378i	0.935542	+	0.353217i	$0.114912\pi$
$314$			473.373i			1.50756i
$315$	49.5445	+	38.8846i	0.157284	+	0.123443i
$316$	48.4119			0.153202
$317$	−448.553	−	258.972i	−1.41499	−	0.816946i	−0.419140	−	0.907922i	$-0.637668\pi$
$317$	−448.553	−	258.972i	−1.41499	−	0.816946i	−0.995853	+	0.0909754i	$0.971002\pi$
$318$	18.3541	−	258.382i	0.0577172	−	0.812521i
$319$	4.25425	+	7.36858i	0.0133362	+	0.0230990i
$320$	−100.561	+	58.0588i	−0.314252	+	0.181434i
$321$	−230.220	−	473.345i	−0.717197	−	1.47460i
$322$	66.9956	−	116.040i	0.208061	−	0.360372i
$323$		−	555.334i		−	1.71930i
$324$	171.795	−	164.443i	0.530232	−	0.507539i
$325$	30.1121			0.0926526
$326$	−131.221	−	75.7605i	−0.402518	−	0.232394i
$327$	−473.327	+	230.212i	−1.44748	+	0.704011i
$328$	2.35061	+	4.07138i	0.00716649	+	0.0124127i
$329$	−25.3250	+	14.6214i	−0.0769756	+	0.0444419i
$330$	−375.844	−	26.6980i	−1.13892	−	0.0809031i
$331$	253.455	−	438.996i	0.765724	−	1.32627i	−0.174139	−	0.984721i	$-0.555714\pi$
$331$	253.455	−	438.996i	0.765724	−	1.32627i	0.939863	−	0.341552i	$-0.110953\pi$
$332$		−	287.663i		−	0.866454i
$333$	33.7993	−	43.0651i	0.101500	−	0.129325i
$334$	602.315			1.80334
$335$	−102.192	−	59.0006i	−0.305051	−	0.176121i
$336$	−76.2677	−	51.5657i	−0.226987	−	0.153469i
$337$	320.890	+	555.798i	0.952195	+	1.64925i	0.740659	+	0.671881i	$0.234513\pi$
$337$	320.890	+	555.798i	0.952195	+	1.64925i	0.211536	+	0.977370i	$0.432153\pi$
$338$	−327.664	+	189.177i	−0.969419	+	0.559695i
$339$	226.538	−	335.059i	0.668254	−	0.988376i
$340$	162.254	−	281.032i	0.477218	−	0.826566i
$341$			53.3500i			0.156452i
$342$	481.955	−	193.487i	1.40922	−	0.565752i
$343$	153.127			0.446435
$344$	−88.1477	−	50.8921i	−0.256243	−	0.147942i
$345$	29.3908	−	413.753i	0.0851908	−	1.19928i
$346$	−244.967	−	424.296i	−0.707998	−	1.22629i
$347$	−336.651	+	194.366i	−0.970177	+	0.560132i	−0.899290	−	0.437352i	$-0.855916\pi$
$347$	−336.651	+	194.366i	−0.970177	+	0.560132i	−0.0708868	+	0.997484i	$0.522583\pi$
$348$	−2.99735	−	6.16271i	−0.00861307	−	0.0177089i
$349$	−69.1180	+	119.716i	−0.198046	+	0.343026i	−0.947895	−	0.318584i	$-0.896793\pi$
$349$	−69.1180	+	119.716i	−0.198046	+	0.343026i	0.749849	+	0.661609i	$0.230126\pi$
$350$		−	25.2817i		−	0.0722334i
$351$	−129.394	+	41.5699i	−0.368643	+	0.118433i
$352$	428.200			1.21648
$353$	244.249	+	141.017i	0.691923	+	0.399482i	0.804332	−	0.594180i	$-0.202523\pi$
$353$	244.249	+	141.017i	0.691923	+	0.399482i	−0.112409	+	0.993662i	$0.535857\pi$
$354$	497.661	−	242.047i	1.40582	−	0.683748i
$355$	−216.072	−	374.248i	−0.608653	−	1.05422i
$356$	413.835	−	238.928i	1.16246	−	0.671146i
$357$	121.707	+	8.64540i	0.340915	+	0.0242168i
$358$	−282.400	+	489.130i	−0.788826	+	1.36629i
$359$		−	50.0982i		−	0.139549i	−0.997563	−	0.0697747i	$-0.977772\pi$
$359$		−	50.0982i		−	0.139549i	0.997563	−	0.0697747i	$-0.0222280\pi$
$360$	−108.881	−	15.5471i	−0.302446	−	0.0431863i
$361$	119.084			0.329873
$362$	286.541	+	165.434i	0.791549	+	0.457001i
$363$	−3.50574	−	2.37028i	−0.00965768	−	0.00652969i
$364$	−11.8574	−	20.5376i	−0.0325753	−	0.0564221i
$365$	−49.8370	+	28.7734i	−0.136540	+	0.0788312i
$366$	−200.658	+	296.781i	−0.548246	+	0.810878i
$367$	−161.878	+	280.381i	−0.441084	+	0.763980i	−0.997770	−	0.0667430i	$-0.978739\pi$
$367$	−161.878	+	280.381i	−0.441084	+	0.763980i	0.556686	+	0.830723i	$0.312073\pi$
$368$			606.332i			1.64764i
$369$	2.13431	−	14.9472i	0.00578404	−	0.0405073i
$370$	69.8609			0.188813
$371$	45.5618	+	26.3051i	0.122808	+	0.0709033i
$372$	3.04465	−	42.8614i	0.00818455	−	0.115219i
$373$	342.952	+	594.011i	0.919443	+	1.59252i	0.800263	+	0.599649i	$0.204693\pi$
$373$	342.952	+	594.011i	0.919443	+	1.59252i	0.119180	+	0.992873i	$0.461974\pi$
$374$	−632.158	+	364.977i	−1.69026	+	0.975873i
$375$	−177.285	−	364.508i	−0.472761	−	0.972021i
$376$	25.5334	−	44.2251i	0.0679079	−	0.117620i
$377$			3.91639i			0.0103883i
$378$	34.9015	+	108.637i	0.0923320	+	0.287400i
$379$	−369.533			−0.975021			−0.487511	−	0.873117i	$-0.662095\pi$
$379$	−369.533			−0.975021			−0.487511	+	0.873117i	$0.662095\pi$
$380$	242.952	+	140.268i	0.639346	+	0.369127i
$381$	−533.319	+	259.389i	−1.39979	+	0.680812i
$382$	−234.555	−	406.261i	−0.614018	−	1.06351i
$383$	−293.110	+	169.227i	−0.765301	+	0.441847i	−0.831196	−	0.555980i	$-0.812343\pi$
$383$	−293.110	+	169.227i	−0.765301	+	0.441847i	0.0658947	+	0.997827i	$0.479010\pi$
$384$	258.848	+	18.3872i	0.674083	+	0.0478834i
$385$	38.2637	−	66.2746i	0.0993862	−	0.172142i
$386$		−	92.0294i		−	0.238418i
$387$	121.790	+	303.364i	0.314702	+	0.783886i
$388$	155.348			0.400382
$389$	149.289	+	86.1919i	0.383775	+	0.221573i	0.679460	−	0.733713i	$-0.262214\pi$
$389$	149.289	+	86.1919i	0.383775	+	0.221573i	−0.295684	+	0.955286i	$0.595548\pi$
$390$	−143.676	−	97.1414i	−0.368400	−	0.249080i
$391$	−401.789	−	695.919i	−1.02759	−	1.77984i
$392$	−112.666	+	65.0478i	−0.287413	+	0.165938i
$393$	−53.9376	+	79.7759i	−0.137246	+	0.202992i
$394$	−361.369	+	625.909i	−0.917179	+	1.58860i
$395$			71.9087i			0.182047i
$396$	−227.312	−	178.404i	−0.574019	−	0.450515i
$397$	−192.868			−0.485812			−0.242906	−	0.970050i	$-0.578101\pi$
$397$	−192.868			−0.485812			−0.242906	+	0.970050i	$0.578101\pi$
$398$	500.459	+	288.940i	1.25743	+	0.725980i
$399$	−7.47392	+	105.215i	−0.0187316	+	0.263697i
$400$	57.2019	+	99.0765i	0.143005	+	0.247691i
$401$	−346.328	+	199.953i	−0.863661	+	0.498635i	−0.865237	−	0.501364i	$-0.832832\pi$
$401$	−346.328	+	199.953i	−0.863661	+	0.498635i	0.00157525	+	0.999999i	$0.499499\pi$
$402$	−93.5061	−	192.253i	−0.232602	−	0.478243i
$403$	−12.2783	+	21.2666i	−0.0304672	+	0.0527707i
$404$		−	305.304i		−	0.755704i
$405$	244.255	+	255.176i	0.603100	+	0.630065i
$406$	3.28814			0.00809887
$407$	−57.6073	−	33.2596i	−0.141541	−	0.0817190i
$408$	−191.611	+	93.1936i	−0.469635	+	0.228416i
$409$	157.733	+	273.201i	0.385655	+	0.667974i	0.991860	−	0.127335i	$-0.0406423\pi$
$409$	157.733	+	273.201i	0.385655	+	0.667974i	−0.606205	+	0.795308i	$0.707309\pi$
$410$	16.6864	−	9.63392i	0.0406986	−	0.0234974i
$411$	−7.83575	−	0.556611i	−0.0190651	−	0.00135428i
$412$	−176.432	+	305.590i	−0.428234	+	0.741723i
$413$			112.397i			0.272149i
$414$	463.974	−	591.168i	1.12071	−	1.42794i
$415$	427.281			1.02959
$416$	170.691	+	98.5485i	0.410315	+	0.236895i
$417$	264.015	+	178.504i	0.633130	+	0.428068i
$418$	−315.521	−	546.499i	−0.754835	−	1.30741i
$419$	608.862	−	351.527i	1.45313	−	0.838966i	0.454473	−	0.890760i	$-0.349827\pi$
$419$	608.862	−	351.527i	1.45313	−	0.838966i	0.998658	+	0.0517946i	$0.0164941\pi$
$420$	−34.5233	+	51.0614i	−0.0821984	+	0.121575i
$421$	141.582	−	245.227i	0.336299	−	0.582487i	−0.647434	−	0.762121i	$-0.724158\pi$
$421$	141.582	−	245.227i	0.336299	−	0.582487i	0.983734	+	0.179634i	$0.0574913\pi$
$422$			44.2285i			0.104807i
$423$	−152.202	+	61.1038i	−0.359817	+	0.144453i
$424$	−91.8736			−0.216683
$425$	−131.307	−	75.8102i	−0.308958	−	0.178377i
$426$	55.4755	−	780.962i	0.130224	−	1.83324i
$427$	−36.3808	−	63.0133i	−0.0852008	−	0.147572i
$428$	446.113	−	257.563i	1.04232	−	0.601783i
$429$	72.2280	+	148.505i	0.168364	+	0.346165i
$430$	−208.580	+	361.272i	−0.485070	+	0.840166i
$431$			242.617i			0.562917i	0.959573	+	0.281458i	$0.0908181\pi$
$431$			242.617i			0.562917i	−0.959573	+	0.281458i	$0.909182\pi$
$432$	−382.576	−	346.771i	−0.885593	−	0.802711i
$433$	747.663			1.72670			0.863352	−	0.504602i	$-0.168361\pi$
$433$	747.663			1.72670			0.863352	+	0.504602i	$0.168361\pi$
$434$	17.8551	+	10.3087i	0.0411408	+	0.0237527i
$435$	9.15380	−	4.45212i	0.0210432	−	0.0102348i
$436$	−257.553	−	446.096i	−0.590719	−	1.02316i
$437$	601.620	−	347.345i	1.37670	−	0.794840i
$438$	−103.997	−	7.38743i	−0.237437	−	0.0168663i
$439$	−132.545	+	229.574i	−0.301924	+	0.522947i	−0.976572	−	0.215192i	$-0.930962\pi$
$439$	−132.545	+	229.574i	−0.301924	+	0.522947i	0.674648	+	0.738140i	$0.264295\pi$
$440$			133.640i			0.303728i
$441$	413.629	+	59.0622i	0.937935	+	0.133928i
$442$	−335.991			−0.760161
$443$	95.9303	+	55.3854i	0.216547	+	0.125023i	0.604350	−	0.796719i	$-0.293433\pi$
$443$	95.9303	+	55.3854i	0.216547	+	0.125023i	−0.387803	+	0.921742i	$0.626766\pi$
$444$	44.3837	+	30.0084i	0.0999633	+	0.0675865i
$445$	354.892	+	614.691i	0.797511	+	1.38133i
$446$	−495.070	+	285.829i	−1.11002	+	0.640872i
$447$	20.4503	−	30.2468i	0.0457501	−	0.0676662i
$448$	21.3638	−	37.0032i	0.0476871	−	0.0825964i
$449$			344.848i			0.768036i	0.923326	+	0.384018i	$0.125460\pi$
$449$			344.848i			0.768036i	−0.923326	+	0.384018i	$0.874540\pi$
$450$	20.0435	−	140.370i	0.0445410	−	0.311934i
$451$	−18.3462			−0.0406789
$452$	342.792	+	197.911i	0.758389	+	0.437856i
$453$	−37.7953	+	532.068i	−0.0834333	+	1.17454i
$454$	18.3197	+	31.7307i	0.0403519	+	0.0698915i
$455$	30.5056	−	17.6124i	0.0670454	−	0.0387087i
$456$	−80.5656	−	165.647i	−0.176679	−	0.363261i
$457$	−221.146	+	383.037i	−0.483909	+	0.838155i	−0.999829	−	0.0184816i	$-0.994117\pi$
$457$	−221.146	+	383.037i	−0.483909	+	0.838155i	0.515920	+	0.856637i	$0.327450\pi$
$458$		−	778.510i		−	1.69980i
$459$	668.892	+	144.491i	1.45728	+	0.314796i
$460$	405.941			0.882481
$461$	111.105	+	64.1464i	0.241008	+	0.139146i	0.615640	−	0.788027i	$-0.288898\pi$
$461$	111.105	+	64.1464i	0.241008	+	0.139146i	−0.374632	+	0.927174i	$0.622231\pi$
$462$	124.682	−	60.6416i	0.269875	−	0.131259i
$463$	−332.732	−	576.309i	−0.718644	−	1.24473i	−0.961537	−	0.274675i	$-0.911430\pi$
$463$	−332.732	−	576.309i	−0.718644	−	1.24473i	0.242894	−	0.970053i	$-0.421903\pi$
$464$	−12.8859	+	7.43969i	−0.0277714	+	0.0160338i
$465$	63.6643	+	4.52238i	0.136913	+	0.00972555i
$466$	−137.175	+	237.594i	−0.294367	+	0.509859i
$467$		−	456.611i		−	0.977753i	−0.872353	−	0.488877i	$-0.837407\pi$
$467$		−	456.611i		−	0.977753i	0.872353	−	0.488877i	$-0.162593\pi$
$468$	−49.5530	−	123.431i	−0.105882	−	0.263741i
$469$	43.4207			0.0925814
$470$	−181.256	−	104.648i	−0.385650	−	0.222655i
$471$	−446.707	−	302.025i	−0.948422	−	0.641241i
$472$	−98.1400	−	169.984i	−0.207924	−	0.360135i
$473$	343.991	−	198.603i	0.727253	−	0.419880i
$474$	−72.9704	+	107.926i	−0.153946	+	0.227693i
$475$	65.5376	−	113.515i	0.137974	−	0.238978i
$476$			119.409i			0.250859i
$477$	232.116	+	182.174i	0.486616	+	0.381917i
$478$	−82.2949			−0.172165
$479$	−607.052	−	350.481i	−1.26733	−	0.731694i	−0.292849	−	0.956159i	$-0.594603\pi$
$479$	−607.052	−	350.481i	−1.26733	−	0.731694i	−0.974482	+	0.224465i	$0.927937\pi$
$480$	36.2978	−	510.986i	0.0756204	−	1.06455i
$481$	−15.3091	−	26.5162i	−0.0318277	−	0.0551271i
$482$	−349.117	+	201.563i	−0.724310	+	0.418180i
$483$	66.7580	+	137.258i	0.138215	+	0.284178i
$484$	2.07075	−	3.58664i	0.00427841	−	0.00741042i
$485$			230.747i			0.475767i
$486$	107.654	+	630.850i	0.221510	+	1.29805i
$487$	−5.64386			−0.0115890			−0.00579451	−	0.999983i	$-0.501844\pi$
$487$	−5.64386			−0.0115890			−0.00579451	+	0.999983i	$0.501844\pi$
$488$	110.040	+	63.5319i	0.225493	+	0.130188i
$489$	155.215	−	75.4917i	0.317413	−	0.154380i
$490$	266.597	+	461.759i	0.544075	+	0.942366i
$491$	75.6645	−	43.6849i	0.154103	−	0.0889713i	−0.420966	−	0.907077i	$-0.638309\pi$
$491$	75.6645	−	43.6849i	0.154103	−	0.0889713i	0.575068	+	0.818105i	$0.304975\pi$
$492$	14.7394	+	1.04701i	0.0299580	+	0.00212806i
$493$	9.85989	−	17.0778i	0.0199998	−	0.0346406i
$494$		−	290.463i		−	0.587982i
$495$	264.993	−	337.638i	0.535338	−	0.682097i
$496$	−93.2967			−0.188098
$497$	137.711	+	79.5076i	0.277085	+	0.159975i
$498$	641.296	+	433.589i	1.28774	+	0.870661i
$499$	−157.815	−	273.344i	−0.316263	−	0.547784i	0.663442	−	0.748228i	$-0.269095\pi$
$499$	−157.815	−	273.344i	−0.316263	−	0.547784i	−0.979705	+	0.200444i	$0.935762\pi$
$500$	343.537	−	198.341i	0.687074	−	0.396682i
$501$	−384.293	+	568.385i	−0.767051	+	1.13450i
$502$	368.483	−	638.231i	0.734030	−	1.27138i
$503$			442.306i			0.879335i	0.898161	+	0.439668i	$0.144904\pi$
$503$			442.306i			0.879335i	−0.898161	+	0.439668i	$0.855096\pi$
$504$	37.5574	−	15.0779i	0.0745186	−	0.0299165i
$505$	453.485			0.897990
$506$	−790.793	−	456.565i	−1.56283	−	0.902302i
$507$	30.5382	−	429.905i	0.0602332	−	0.847939i
$508$	−290.197	−	502.635i	−0.571253	−	0.989440i
$509$	−512.688	+	296.001i	−1.00725	+	0.581534i	−0.910384	−	0.413764i	$-0.864214\pi$
$509$	−512.688	+	296.001i	−1.00725	+	0.581534i	−0.0968621	+	0.995298i	$0.530881\pi$
$510$	381.952	+	785.314i	0.748926	+	1.53983i
$511$	10.5877	−	18.3384i	0.0207196	−	0.0358873i
$512$			534.460i			1.04387i
$513$	−124.912	+	578.255i	−0.243493	+	1.12720i
$514$	−880.407			−1.71285
$515$	−453.909	−	262.064i	−0.881376	−	0.508863i
$516$	−287.697	+	139.927i	−0.557552	+	0.271176i
$517$	99.6424	+	172.586i	0.192732	+	0.333821i
$518$	−22.2626	+	12.8533i	−0.0429779	+	0.0248133i
$519$	556.689	+	39.5443i	1.07262	+	0.0761933i
$520$	−30.7567	+	53.2722i	−0.0591475	+	0.102446i
$521$		−	603.293i		−	1.15795i	−0.815345	−	0.578976i	$-0.803453\pi$
$521$		−	603.293i		−	1.15795i	0.815345	−	0.578976i	$-0.196547\pi$
$522$	18.2566	+	2.60686i	0.0349743	+	0.00499398i
$523$	861.919			1.64803			0.824015	−	0.566569i	$-0.191729\pi$
$523$	861.919			1.64803			0.824015	+	0.566569i	$0.191729\pi$
$524$	−81.6170	−	47.1216i	−0.155758	−	0.0899267i
$525$	23.8575	+	16.1304i	0.0454428	+	0.0307245i
$526$	−373.667	−	647.211i	−0.710394	−	1.23044i
$527$	107.081	−	61.8235i	0.203191	−	0.117312i
$528$	−351.412	+	519.753i	−0.665553	+	0.984380i
$529$	238.115	−	412.427i	0.450122	−	0.779635i
$530$			376.542i			0.710456i
$531$	−89.1093	+	624.058i	−0.167814	+	1.17525i
$532$	−103.228			−0.194039
$533$	−7.31324	−	4.22230i	−0.0137209	−	0.00792176i
$534$	−91.1169	+	1282.71i	−0.170631	+	2.40208i
$535$	382.572	+	662.635i	0.715088	+	1.23857i
$536$	−65.6671	+	37.9129i	−0.122513	+	0.0707330i
$537$	−281.398	−	578.569i	−0.524018	−	1.07741i
$538$	474.000	−	820.992i	0.881040	−	1.52601i
$539$		−	507.689i		−	0.941910i
$540$	−232.164	+	256.136i	−0.429933	+	0.474325i
$541$	−326.044			−0.602670			−0.301335	−	0.953518i	$-0.597432\pi$
$541$	−326.044			−0.602670			−0.301335	+	0.953518i	$0.597432\pi$
$542$	631.317	+	364.491i	1.16479	+	0.672493i
$543$	−338.936	+	164.848i	−0.624191	+	0.303587i
$544$	−496.211	−	859.462i	−0.912152	−	1.57989i
$545$	662.609	−	382.558i	1.21580	−	0.701941i
$546$	63.6577	+	4.52191i	0.116589	+	0.00828189i
$547$	−215.873	+	373.903i	−0.394649	+	0.683551i	−0.993056	−	0.117640i	$-0.962467\pi$
$547$	−215.873	+	373.903i	−0.394649	+	0.683551i	0.598408	+	0.801192i	$0.295800\pi$
$548$		−	7.68781i		−	0.0140289i
$549$	−152.038	−	378.709i	−0.276936	−	0.689815i
$550$	−172.291			−0.313256
$551$	14.7637	+	8.52384i	0.0267944	+	0.0154698i
$552$	−220.808	−	149.292i	−0.400015	−	0.270456i
$553$	−13.2301	−	22.9152i	−0.0239242	−	0.0414379i
$554$	602.044	−	347.590i	1.08672	−	0.627419i
$555$	−44.5731	+	65.9254i	−0.0803119	+	0.118785i
$556$	−155.947	+	270.108i	−0.280480	+	0.485806i
$557$		−	827.057i		−	1.48484i	−0.669934	−	0.742421i	$-0.733678\pi$
$557$		−	827.057i		−	1.48484i	0.669934	−	0.742421i	$-0.266322\pi$
$558$	90.9633	+	71.3919i	0.163017	+	0.127942i
$559$	182.831			0.327067
$560$	115.899	+	66.9143i	0.206962	+	0.119490i
$561$	58.9171	−	829.412i	0.105021	−	1.47845i
$562$	194.262	+	336.471i	0.345661	+	0.598703i
$563$	−939.301	+	542.306i	−1.66839	+	0.963243i	−0.699878	+	0.714263i	$0.746762\pi$
$563$	−939.301	+	542.306i	−1.66839	+	0.963243i	−0.968508	+	0.248981i	$0.919904\pi$
$564$	−70.2034	−	144.342i	−0.124474	−	0.255926i
$565$	−293.968	+	509.167i	−0.520297	+	0.901180i
$566$		−	610.158i		−	1.07802i
$567$	−124.785	−	36.3779i	−0.220080	−	0.0641586i
$568$	−277.689			−0.488889
$569$	−532.771	−	307.596i	−0.936329	−	0.540590i	−0.0475212	−	0.998870i	$-0.515132\pi$
$569$	−532.771	−	307.596i	−0.936329	−	0.540590i	−0.888808	+	0.458281i	$0.848466\pi$
$570$	−678.901	+	330.196i	−1.19105	+	0.579292i
$571$	−157.972	−	273.616i	−0.276659	−	0.479187i	0.693893	−	0.720078i	$-0.255894\pi$
$571$	−157.972	−	273.616i	−0.276659	−	0.479187i	−0.970552	+	0.240891i	$0.922561\pi$
$572$	−139.961	+	80.8064i	−0.244687	+	0.141270i
$573$	533.027	+	37.8635i	0.930240	+	0.0660794i
$574$	−3.54498	+	6.14008i	−0.00617592	+	0.0106970i
$575$		−	189.668i		−	0.329858i
$576$	147.954	−	188.514i	0.256864	−	0.327281i
$577$	124.885			0.216438			0.108219	−	0.994127i	$-0.465485\pi$
$577$	124.885			0.216438			0.108219	+	0.994127i	$0.465485\pi$
$578$	805.979	+	465.332i	1.39443	+	0.805073i
$579$	86.8451	+	58.7172i	0.149992	+	0.101411i
$580$	4.98089	+	8.62716i	0.00858774	+	0.0148744i
$581$	−136.161	+	78.6129i	−0.234357	+	0.135306i
$582$	−234.154	+	346.323i	−0.402326	+	0.595056i
$583$	179.265	−	310.497i	0.307488	−	0.532584i
$584$			36.9787i			0.0633197i
$585$	183.338	−	73.6036i	0.313399	−	0.125818i
$586$	−934.698			−1.59505
$587$	−867.336	−	500.757i	−1.47757	−	0.853078i	−0.477896	−	0.878417i	$-0.658600\pi$
$587$	−867.336	−	500.757i	−1.47757	−	0.853078i	−0.999679	+	0.0253383i	$0.991934\pi$
$588$	−28.9735	+	407.878i	−0.0492747	+	0.693670i
$589$	53.4462	+	92.5715i	0.0907406	+	0.157167i
$590$	−696.674	+	402.225i	−1.18080	+	0.681737i
$591$	−360.087	−	740.358i	−0.609284	−	1.25272i
$592$	58.1633	−	100.742i	0.0982488	−	0.170172i
$593$			3.47723i			0.00586379i	0.999996	+	0.00293189i	$0.000933252\pi$
$593$			3.47723i			0.00586379i	−0.999996	+	0.00293189i	$0.999067\pi$
$594$	740.344	−	237.848i	1.24637	−	0.400418i
$595$	−177.364			−0.298091
$596$	30.9448	+	17.8660i	0.0519209	+	0.0299765i
$597$	−591.969	+	287.915i	−0.991573	+	0.482270i
$598$	−210.153	−	363.995i	−0.351426	−	0.608688i
$599$	−371.872	+	214.700i	−0.620821	+	0.358431i	−0.777188	−	0.629268i	$-0.783355\pi$
$599$	−371.872	+	214.700i	−0.620821	+	0.358431i	0.156368	+	0.987699i	$0.450021\pi$
$600$	−50.1650	−	3.56346i	−0.0836084	−	0.00593910i
$601$	−491.660	+	851.580i	−0.818070	+	1.41694i	0.0890326	+	0.996029i	$0.471622\pi$
$601$	−491.660	+	851.580i	−0.818070	+	1.41694i	−0.907102	+	0.420910i	$0.861711\pi$
$602$		−	153.502i		−	0.254987i
$603$	241.083	+	34.4242i	0.399805	+	0.0570882i
$604$	−522.022			−0.864275
$605$	5.32743	+	3.07579i	0.00880567	+	0.00508396i
$606$	680.626	+	460.180i	1.12314	+	0.759373i
$607$	422.778	+	732.273i	0.696504	+	1.20638i	0.969671	+	0.244414i	$0.0785955\pi$
$607$	422.778	+	732.273i	0.696504	+	1.20638i	−0.273167	+	0.961967i	$0.588071\pi$
$608$	743.002	−	428.972i	1.22204	−	0.705547i
$609$	−2.09792	+	3.10291i	−0.00344486	+	0.00509509i
$610$	260.384	−	450.999i	0.426859	−	0.739342i
$611$			91.7290i			0.150129i
$612$	−94.6680	+	662.988i	−0.154686	+	1.08331i
$613$	−483.081			−0.788061			−0.394030	−	0.919097i	$-0.628920\pi$
$613$	−483.081			−0.788061			−0.394030	+	0.919097i	$0.628920\pi$
$614$	−553.775	−	319.722i	−0.901914	−	0.520720i
$615$	−1.55517	+	21.8931i	−0.00252874	+	0.0355986i
$616$	−24.5877	−	42.5871i	−0.0399151	−	0.0691349i
$617$	930.131	−	537.011i	1.50750	−	0.870358i	0.507543	−	0.861626i	$-0.330554\pi$
$617$	930.131	−	537.011i	1.50750	−	0.870358i	0.999962	−	0.00873199i	$-0.00277951\pi$
$618$	−415.328	−	853.937i	−0.672052	−	1.38178i
$619$	−411.081	+	712.012i	−0.664104	+	1.15026i	0.315423	+	0.948951i	$0.397854\pi$
$619$	−411.081	+	712.012i	−0.664104	+	1.15026i	−0.979527	+	0.201311i	$0.935480\pi$
$620$			62.4624i			0.100746i
$621$	261.838	+	815.017i	0.421640	+	1.31243i
$622$	105.470			0.169565
$623$	−226.187	−	130.589i	−0.363061	−	0.209613i
$624$	−259.700	+	126.310i	−0.416186	+	0.202420i
$625$	219.829	+	380.755i	0.351726	+	0.609208i
$626$	−231.122	+	133.438i	−0.369204	+	0.213160i
$627$	717.023	+	50.9336i	1.14358	+	0.0812338i
$628$	263.858	−	457.016i	0.420157	−	0.727733i
$629$			154.169i			0.245101i
$630$	−61.7965	−	153.928i	−0.0980897	−	0.244330i
$631$	74.8306			0.118591			0.0592953	−	0.998240i	$-0.481115\pi$
$631$	74.8306			0.118591			0.0592953	+	0.998240i	$0.481115\pi$
$632$	40.0169	+	23.1037i	0.0633178	+	0.0365566i
$633$	−41.7369	−	28.2189i	−0.0659351	−	0.0445796i
$634$	682.034	+	1181.32i	1.07576	+	1.86328i
$635$	746.591	−	431.044i	1.17573	−	0.678810i
$636$	−161.742	+	239.223i	−0.254311	+	0.376136i
$637$	116.842	−	202.377i	0.183426	−	0.317703i
$638$		−	22.4082i		−	0.0351225i
$639$	701.574	+	550.625i	1.09792	+	0.861698i
$640$	−377.222			−0.589409
$641$	103.379	+	59.6861i	0.161278	+	0.0931140i	0.578467	−	0.815706i	$-0.303651\pi$
$641$	103.379	+	59.6861i	0.161278	+	0.0931140i	−0.417189	+	0.908820i	$0.636985\pi$
$642$	−98.2236	+	1382.75i	−0.152996	+	2.15382i
$643$	−633.828	−	1097.82i	−0.985735	−	1.70734i	−0.638622	−	0.769520i	$-0.720495\pi$
$643$	−633.828	−	1097.82i	−0.985735	−	1.70734i	−0.347113	−	0.937823i	$-0.612838\pi$
$644$	−129.361	+	74.6867i	−0.200871	+	0.115973i
$645$	−207.840	−	427.331i	−0.322233	−	0.662529i
$646$	−731.270	+	1266.60i	−1.13200	+	1.96067i
$647$			1062.35i			1.64196i	0.570957	+	0.820980i	$0.306572\pi$
$647$			1062.35i			1.64196i	−0.570957	+	0.820980i	$0.693428\pi$
$648$	220.482	−	53.9407i	0.340250	−	0.0832418i
$649$	765.970			1.18023
$650$	−68.6792	−	39.6519i	−0.105660	−	0.0610030i
$651$	−21.1200	+	10.2721i	−0.0324423	+	0.0157789i
$652$	84.4578	+	146.285i	0.129536	+	0.224364i
$653$	65.8191	−	38.0007i	0.100795	−	0.0581940i	−0.448755	−	0.893655i	$-0.648132\pi$
$653$	65.8191	−	38.0007i	0.100795	−	0.0581940i	0.549550	+	0.835461i	$0.314799\pi$
$654$	1382.70	+	98.2199i	2.11422	+	0.150183i
$655$	69.9922	−	121.230i	0.106858	−	0.185084i
$656$		−	32.0832i		−	0.0489074i
$657$	73.3244	−	93.4255i	0.111605	−	0.142200i
$658$	77.0143			0.117043
$659$	−264.495	−	152.706i	−0.401358	−	0.231724i	0.285712	−	0.958316i	$-0.407770\pi$
$659$	−264.495	−	152.706i	−0.401358	−	0.231724i	−0.687070	+	0.726591i	$0.741103\pi$
$660$	347.976	+	235.271i	0.527236	+	0.356471i
$661$	362.047	+	627.083i	0.547726	+	0.948689i	0.998430	+	0.0560156i	$0.0178397\pi$
$661$	362.047	+	627.083i	0.547726	+	0.948689i	−0.450704	+	0.892673i	$0.648827\pi$
$662$	−1156.15	+	667.504i	−1.74645	+	1.00831i
$663$	214.371	−	317.064i	0.323335	−	0.478226i
$664$	137.282	−	237.779i	0.206750	−	0.358102i
$665$		−	153.331i		−	0.230573i
$666$	−133.798	+	53.7149i	−0.200897	+	0.0806529i
$667$	24.6683			0.0369840
$668$	−581.502	−	335.730i	−0.870512	−	0.502590i
$669$	46.1405	−	649.548i	0.0689693	−	0.970923i
$670$	155.385	+	269.135i	0.231918	+	0.401694i
$671$	−429.426	+	247.929i	−0.639979	+	0.369492i
$672$	82.4463	+	169.514i	0.122688	+	0.252253i
$673$	−310.416	+	537.656i	−0.461242	+	0.798894i	−0.999023	−	0.0441902i	$-0.985929\pi$
$673$	−310.416	+	537.656i	−0.461242	+	0.798894i	0.537781	+	0.843084i	$0.319263\pi$
$674$		−	1690.20i		−	2.50772i
$675$	119.674	+	108.474i	0.177296	+	0.160703i
$676$	421.789			0.623948
$677$	−108.879	−	62.8616i	−0.160826	−	0.0928531i	0.417427	−	0.908711i	$-0.362932\pi$
$677$	−108.879	−	62.8616i	−0.160826	−	0.0928531i	−0.578253	+	0.815857i	$0.696265\pi$
$678$	−957.894	+	465.890i	−1.41282	+	0.687153i
$679$	−42.4538	−	73.5321i	−0.0625240	−	0.108295i
$680$	268.236	−	154.866i	0.394464	−	0.227744i
$681$	−41.6317	−	2.95730i	−0.0611332	−	0.00434258i
$682$	70.2518	−	121.680i	0.103009	−	0.178416i
$683$			885.537i			1.29654i	0.761410	+	0.648270i	$0.224507\pi$
$683$			885.537i			1.29654i	−0.761410	+	0.648270i	$0.775493\pi$
$684$	−573.151	−	81.8402i	−0.837939	−	0.119649i
$685$	11.4191			0.0166702
$686$	−349.250	−	201.640i	−0.509111	−	0.293935i
$687$	734.654	+	496.710i	1.06937	+	0.723013i
$688$	347.311	+	601.560i	0.504812	+	0.874360i
$689$	142.919	−	82.5143i	0.207429	−	0.119759i
$690$	−611.868	+	904.978i	−0.886765	+	1.31156i
$691$	−117.012	+	202.670i	−0.169337	+	0.293300i	−0.938187	−	0.346129i	$-0.887496\pi$
$691$	−117.012	+	202.670i	−0.169337	+	0.293300i	0.768850	+	0.639429i	$0.220829\pi$
$692$			546.179i			0.789276i
$693$	−22.3251	+	156.349i	−0.0322152	+	0.225613i
$694$	1023.77			1.47518
$695$	−401.206	−	231.636i	−0.577275	−	0.333290i
$696$	0.463465	−	6.52448i	0.000665897	−	0.00937425i
$697$	21.2601	+	36.8236i	0.0305023	+	0.0528315i
$698$	315.286	−	182.031i	0.451700	−	0.260789i
$699$	−136.689	−	281.039i	−0.195549	−	0.402059i
$700$	−14.0920	+	24.4081i	−0.0201314	+	0.0348687i
$701$			327.469i			0.467146i	0.972339	+	0.233573i	$0.0750417\pi$
$701$			327.469i			0.467146i	−0.972339	+	0.233573i	$0.924958\pi$
$702$	349.859	+	75.5751i	0.498374	+	0.107657i
$703$	−133.278			−0.189585
$704$	−252.171	−	145.591i	−0.358197	−	0.206805i
$705$	214.399	−	104.277i	0.304112	−	0.147910i
$706$	−371.386	−	643.259i	−0.526042	−	0.911132i
$707$	−144.512	+	83.4340i	−0.204402	+	0.118011i
$708$	−615.381	−	43.7135i	−0.869183	−	0.0617422i
$709$	207.481	−	359.367i	0.292638	−	0.506865i	−0.681794	−	0.731544i	$-0.738800\pi$
$709$	207.481	−	359.367i	0.292638	−	0.506865i	0.974433	+	0.224679i	$0.0721335\pi$
$710$			1138.10i			1.60296i
$711$	−55.2894	−	137.720i	−0.0777629	−	0.193698i
$712$	456.097			0.640585
$713$	133.953	+	77.3376i	0.187872	+	0.108468i
$714$	−266.202	−	179.983i	−0.372832	−	0.252077i
$715$	−120.026	−	207.891i	−0.167869	−	0.290757i
$716$	545.283	−	314.819i	0.761568	−	0.439691i
$717$	52.5063	−	77.6589i	0.0732305	−	0.108311i
$718$	−65.9699	+	114.263i	−0.0918801	+	0.159141i
$719$			867.108i			1.20599i	0.797744	+	0.602996i	$0.206026\pi$
$719$			867.108i			1.20599i	−0.797744	+	0.602996i	$0.793974\pi$
$720$	590.450	+	463.410i	0.820069	+	0.643625i
$721$	192.863			0.267493
$722$	−271.605	−	156.811i	−0.376184	−	0.217190i
$723$	32.5377	−	458.053i	0.0450037	−	0.633545i
$724$	−184.426	−	319.436i	−0.254733	−	0.441210i
$725$	4.03088	−	2.32723i	0.00555983	−	0.00320997i
$726$	4.87462	+	10.0225i	0.00671435	+	0.0138051i
$727$	395.423	−	684.892i	0.543910	−	0.942080i	−0.454765	−	0.890612i	$-0.650277\pi$
$727$	395.423	−	684.892i	0.543910	−	0.942080i	0.998675	−	0.0514682i	$-0.0163901\pi$
$728$		−	22.6350i		−	0.0310920i
$729$	−663.999	−	300.910i	−0.910835	−	0.412771i
$730$	151.556			0.207611
$731$	−797.253	−	460.294i	−1.09063	−	0.629677i
$732$	359.150	−	174.679i	0.490642	−	0.238633i
$733$	225.413	+	390.427i	0.307521	+	0.532643i	0.977820	−	0.209449i	$-0.0671671\pi$
$733$	225.413	+	390.427i	0.307521	+	0.532643i	−0.670298	+	0.742092i	$0.733834\pi$
$734$	738.416	−	426.325i	1.00602	−	0.580824i
$735$	−605.843	−	43.0359i	−0.824276	−	0.0585522i
$736$	620.731	−	1075.14i	0.843384	−	1.46078i
$737$		−	295.905i		−	0.401500i
$738$	−24.5505	+	31.2808i	−0.0332663	+	0.0423859i
$739$	618.509			0.836955			0.418477	−	0.908227i	$-0.362564\pi$
$739$	618.509			0.836955			0.418477	+	0.908227i	$0.362564\pi$
$740$	−67.4469	−	38.9405i	−0.0911444	−	0.0526223i
$741$	274.101	+	185.323i	0.369906	+	0.250099i
$742$	−69.2777	−	119.993i	−0.0933662	−	0.161715i
$743$	−136.211	+	78.6415i	−0.183326	+	0.105843i	−0.588854	−	0.808239i	$-0.700421\pi$
$743$	−136.211	+	78.6415i	−0.183326	+	0.105843i	0.405529	+	0.914082i	$0.367087\pi$
$744$	22.9716	−	33.9759i	0.0308758	−	0.0456665i
$745$	−26.5373	+	45.9640i	−0.0356206	+	0.0616966i
$746$		−	1806.41i		−	2.42146i
$747$	−818.328	+	328.529i	−1.09549	+	0.439797i
$748$	813.752			1.08790
$749$	−243.829	−	140.774i	−0.325539	−	0.187950i
$750$	−75.6389	+	1064.81i	−0.100852	+	1.41975i
$751$	−68.3140	−	118.323i	−0.0909641	−	0.157554i	0.816953	−	0.576704i	$-0.195662\pi$
$751$	−68.3140	−	118.323i	−0.0909641	−	0.157554i	−0.907917	+	0.419150i	$0.862328\pi$
$752$	−301.812	+	174.251i	−0.401346	+	0.231717i
$753$	367.176	+	754.933i	0.487617	+	1.00257i
$754$	5.15714	−	8.93243i	0.00683971	−	0.0118467i
$755$		−	775.387i		−	1.02700i
$756$	26.8588	−	124.337i	0.0355275	−	0.164467i
$757$	−1116.35			−1.47470			−0.737349	−	0.675512i	$-0.763923\pi$
$757$	−1116.35			−1.47470			−0.737349	+	0.675512i	$0.763923\pi$
$758$	842.825	+	486.605i	1.11191	+	0.641959i
$759$	935.392	−	454.945i	1.23240	−	0.599401i
$760$	133.881	+	231.889i	0.176159	+	0.305117i
$761$	−1148.42	+	663.039i	−1.50909	+	0.871274i	−0.509147	+	0.860680i	$0.670039\pi$
$761$	−1148.42	+	663.039i	−1.50909	+	0.871274i	−0.999944	+	0.0105939i	$0.996628\pi$
$762$	1557.95	+	110.669i	2.04455	+	0.145234i
$763$	−140.769	+	243.819i	−0.184494	+	0.319553i
$764$			522.964i			0.684508i
$765$	−984.771	−	140.615i	−1.28728	−	0.183811i
$766$	891.361			1.16366
$767$	305.334	+	176.285i	0.398089	+	0.229837i
$768$	−830.861	−	561.757i	−1.08185	−	0.731454i
$769$	−7.65712	−	13.2625i	−0.00995725	−	0.0172465i	0.861004	−	0.508598i	$-0.169836\pi$
$769$	−7.65712	−	13.2625i	−0.00995725	−	0.0172465i	−0.870961	+	0.491352i	$0.836503\pi$
$770$	−174.542	+	100.772i	−0.226678	+	0.130873i
$771$	561.723	−	830.811i	0.728564	−	1.07758i
$772$	−51.2972	+	88.8494i	−0.0664472	+	0.115090i
$773$			1414.40i			1.82975i	0.403737	+	0.914875i	$0.367711\pi$
$773$			1414.40i			1.82975i	−0.403737	+	0.914875i	$0.632289\pi$
$774$	121.697	−	852.281i	0.157232	−	1.10114i
$775$	29.1844			0.0376572
$776$	128.409	+	74.1372i	0.165476	+	0.0955377i
$777$	2.07487	−	29.2092i	0.00267036	−	0.0375923i
$778$	−226.997	−	393.170i	−0.291770	−	0.505360i
$779$	−31.8339	+	18.3793i	−0.0408650	+	0.0235934i
$780$	84.5648	+	173.870i	0.108416	+	0.222910i
$781$	541.832	−	938.481i	0.693767	−	1.20164i
$782$			2116.32i			2.70629i
$783$	−14.1082	+	15.5649i	−0.0180181	+	0.0198785i
$784$	887.830			1.13244
$785$	678.830	+	391.923i	0.864752	+	0.499265i
$786$	228.070	−	110.926i	0.290165	−	0.141127i
$787$	−102.173	−	176.969i	−0.129826	−	0.224866i	0.793783	−	0.608201i	$-0.208109\pi$
$787$	−102.173	−	176.969i	−0.129826	−	0.224866i	−0.923609	+	0.383336i	$0.874775\pi$
$788$	697.763	−	402.854i	0.885487	−	0.511236i
$789$	849.161	+	60.3199i	1.07625	+	0.0764511i
$790$	94.6902	−	164.008i	0.119861	−	0.207605i
$791$		−	216.342i		−	0.273504i
$792$	−102.754	−	255.948i	−0.129739	−	0.323166i
$793$	−228.239			−0.287817
$794$	439.889	+	253.970i	0.554016	+	0.319862i
$795$	−355.330	−	240.244i	−0.446956	−	0.302193i
$796$	−322.111	−	557.912i	−0.404662	−	0.700894i
$797$	976.376	−	563.711i	1.22506	−	0.707291i	0.259071	−	0.965858i	$-0.416584\pi$
$797$	976.376	−	563.711i	1.22506	−	0.707291i	0.965993	+	0.258567i	$0.0832503\pi$
$798$	155.595	−	230.131i	0.194981	−	0.288384i
$799$	230.937	−	399.994i	0.289032	−	0.500619i
$800$		−	234.241i		−	0.292801i
$801$	−1152.32	−	904.386i	−1.43860	−	1.12907i
$802$	1053.20			1.31322
$803$	−124.973	−	72.1535i	−0.155633	−	0.0898549i
$804$	−16.8871	+	237.731i	−0.0210039	+	0.295685i
$805$	−110.936	−	192.147i	−0.137809	−	0.238692i
$806$	56.0081	−	32.3363i	0.0694890	−	0.0401195i
$807$	472.318	+	971.112i	0.585277	+	1.20336i
$808$	145.701	−	252.362i	0.180323	−	0.312329i
$809$		−	1320.50i		−	1.63226i	−0.577866	−	0.816131i	$-0.696115\pi$
$809$		−	1320.50i		−	1.63226i	0.577866	−	0.816131i	$-0.303885\pi$
$810$	−221.075	−	903.640i	−0.272932	−	1.11561i
$811$	−427.318			−0.526902			−0.263451	−	0.964673i	$-0.584861\pi$
$811$	−427.318			−0.526902			−0.263451	+	0.964673i	$0.584861\pi$
$812$	−3.17452	−	1.83281i	−0.00390951	−	0.00225716i
$813$	−746.755	+	363.198i	−0.918518	+	0.446738i
$814$	87.5932	+	151.716i	0.107608	+	0.186383i
$815$	−217.285	+	125.450i	−0.266607	+	0.153926i
$816$	1450.45	+	103.032i	1.77751	+	0.126265i
$817$	397.923	−	689.222i	0.487053	−	0.843601i
$818$		−	830.817i		−	1.01567i
$819$	−44.8825	+	57.1866i	−0.0548016	+	0.0698249i
$820$	−21.4798			−0.0261949
$821$	−14.2879	−	8.24911i	−0.0174030	−	0.0100476i	0.491273	−	0.871006i	$-0.336532\pi$
$821$	−14.2879	−	8.24911i	−0.0174030	−	0.0100476i	−0.508676	+	0.860958i	$0.669865\pi$
$822$	17.1387	+	11.5877i	0.0208500	+	0.0140970i
$823$	5.87543	+	10.1765i	0.00713904	+	0.0123652i	0.869573	−	0.493805i	$-0.164394\pi$
$823$	5.87543	+	10.1765i	0.00713904	+	0.0123652i	−0.862434	+	0.506170i	$0.831061\pi$
$824$	−291.675	+	168.399i	−0.353974	+	0.204367i
$825$	109.926	−	162.585i	0.133244	−	0.197073i
$826$	148.006	−	256.354i	0.179184	−	0.310356i
$827$			209.184i			0.252944i	0.991970	+	0.126472i	$0.0403653\pi$
$827$			209.184i			0.252944i	−0.991970	+	0.126472i	$0.959635\pi$
$828$	−777.458	+	312.121i	−0.938959	+	0.376958i
$829$	157.800			0.190350			0.0951748	−	0.995461i	$-0.469659\pi$
$829$	157.800			0.190350			0.0951748	+	0.995461i	$0.469659\pi$
$830$	−974.534	−	562.648i	−1.17414	−	0.677889i
$831$	−56.1104	+	789.901i	−0.0675216	+	0.950542i
$832$	−67.0142	−	116.072i	−0.0805460	−	0.139510i
$833$	−1019.01	+	588.325i	−1.22330	+	0.706272i
$834$	−367.105	−	754.787i	−0.440174	−	0.905021i
$835$	498.678	−	863.736i	0.597219	−	1.03441i
$836$			703.486i			0.841490i
$837$	−125.407	+	40.2892i	−0.149829	+	0.0481352i
$838$	−1851.58			−2.20952
$839$	−1296.34	−	748.444i	−1.54510	−	0.892066i	−0.998504	−	0.0546726i	$-0.982588\pi$
$839$	−1296.34	−	748.444i	−1.54510	−	0.892066i	−0.546600	−	0.837394i	$-0.684078\pi$
$840$	−52.9049	+	25.7313i	−0.0629820	+	0.0306325i
$841$	−420.197	−	727.803i	−0.499640	−	0.865402i
$842$	−645.836	+	372.873i	−0.767026	+	0.442843i
$843$	−441.461	−	31.3591i	−0.523678	−	0.0371993i
$844$	24.6529	−	42.7001i	0.0292096	−	0.0505926i
$845$			626.505i			0.741426i
$846$	427.603	+	61.0574i	0.505441	+	0.0721719i
$847$	−2.26359			−0.00267248
$848$	542.986	+	313.493i	0.640314	+	0.369685i
$849$	575.786	+	389.297i	0.678193	+	0.458536i
$850$	199.655	+	345.813i	0.234889	+	0.406839i
$851$	−167.018	+	96.4281i	−0.196261	+	0.113311i
$852$	−488.867	+	723.054i	−0.573788	+	0.848655i
$853$	244.134	−	422.852i	0.286206	−	0.495723i	−0.686695	−	0.726946i	$-0.740939\pi$
$853$	244.134	−	422.852i	0.286206	−	0.495723i	0.972901	+	0.231222i	$0.0742725\pi$
$854$			191.626i			0.224387i
$855$	121.562	−	851.331i	0.142177	−	0.995708i
$856$	491.670			0.574381
$857$	−1069.75	−	617.620i	−1.24825	−	0.720677i	−0.277489	−	0.960729i	$-0.589502\pi$
$857$	−1069.75	−	617.620i	−1.24825	−	0.720677i	−0.970760	+	0.240052i	$0.922836\pi$
$858$	30.8161	−	433.817i	0.0359162	−	0.505615i
$859$	−204.136	−	353.573i	−0.237643	−	0.411610i	0.722394	−	0.691481i	$-0.243042\pi$
$859$	−204.136	−	353.573i	−0.237643	−	0.411610i	−0.960038	+	0.279871i	$0.909708\pi$
$860$	402.746	−	232.525i	0.468309	−	0.270378i
$861$	−3.53241	−	7.26282i	−0.00410268	−	0.00843533i
$862$	319.481	−	553.357i	0.370627	−	0.641945i
$863$		−	843.606i		−	0.977527i	−0.872416	−	0.488764i	$-0.837448\pi$
$863$		−	843.606i		−	0.977527i	0.872416	−	0.488764i	$-0.162552\pi$
$864$	323.371	+	1006.55i	0.374272	+	1.16499i
$865$	−811.269			−0.937883
$866$	−1705.26	−	984.531i	−1.96912	−	1.13687i
$867$	−953.355	+	463.682i	−1.09960	+	0.534812i
$868$	−11.4921	−	19.9049i	−0.0132397	−	0.0229319i
$869$	−156.163	+	90.1609i	−0.179704	+	0.103752i
$870$	−26.7404	−	1.89950i	−0.0307361	−	0.00218333i
$871$	68.1013	−	117.955i	0.0781875	−	0.135425i
$872$		−	491.652i		−	0.563821i
$873$	−177.417	−	441.926i	−0.203227	−	0.506216i
$874$	−1829.55			−2.09331
$875$	−187.765	−	108.406i	−0.214588	−	0.123892i
$876$	96.2861	+	65.1003i	0.109916	+	0.0743154i
$877$	388.785	+	673.396i	0.443313	+	0.767840i	0.997933	−	0.0642635i	$-0.0204698\pi$
$877$	388.785	+	673.396i	0.443313	+	0.767840i	−0.554620	+	0.832104i	$0.687136\pi$
$878$	604.611	−	349.072i	0.688623	−	0.397576i
$879$	596.362	−	882.044i	0.678455	−	1.00346i
$880$	456.010	−	789.833i	0.518193	−	0.897537i
$881$			289.506i			0.328611i	0.986409	+	0.164306i	$0.0525383\pi$
$881$			289.506i			0.328611i	−0.986409	+	0.164306i	$0.947462\pi$
$882$	−865.625	−	679.379i	−0.981434	−	0.770272i
$883$	583.079			0.660339			0.330169	−	0.943922i	$-0.392894\pi$
$883$	583.079			0.660339			0.330169	+	0.943922i	$0.392894\pi$
$884$	324.381	+	187.282i	0.366947	+	0.211857i
$885$	64.9299	−	914.058i	0.0733671	−	1.03283i
$886$	−145.864	−	252.644i	−0.164632	−	0.285151i
$887$	−1332.80	+	769.495i	−1.50260	+	0.867525i	−0.502602	+	0.864518i	$0.667624\pi$
$887$	−1332.80	+	769.495i	−1.50260	+	0.867525i	−0.999995	+	0.00300711i	$0.999043\pi$
$888$	22.3662	+	45.9861i	0.0251871	+	0.0517861i
$889$	−158.611	+	274.722i	−0.178415	+	0.309023i
$890$		−	1869.30i		−	2.10034i
$891$	−247.910	+	850.392i	−0.278238	+	0.954424i
$892$	637.284			0.714444
$893$	345.794	+	199.644i	0.387227	+	0.223566i
$894$	−86.4719	+	42.0572i	−0.0967248	+	0.0470439i
$895$	467.617	+	809.937i	0.522477	+	0.904958i
$896$	120.209	−	69.4028i	0.134162	−	0.0774585i
$897$	477.573	+	33.9243i	0.532412	+	0.0378197i
$898$	454.100	−	786.523i	0.505679	−	0.875861i
$899$			3.79572i			0.00422216i
$900$	−97.5933	+	124.348i	−0.108437	+	0.138164i
$901$	−830.951			−0.922254
$902$	41.8437	+	24.1585i	0.0463899	+	0.0267832i
$903$	144.855	+	97.9382i	0.160415	+	0.108459i
$904$	188.899	+	327.183i	0.208959	+	0.361928i
$905$	474.475	−	273.938i	0.524282	−	0.302694i
$906$	786.835	−	1163.76i	0.868472	−	1.28451i
$907$	717.224	−	1242.27i	0.790766	−	1.36965i	−0.134728	−	0.990883i	$-0.543016\pi$
$907$	717.224	−	1242.27i	0.790766	−	1.36965i	0.925494	−	0.378763i	$-0.123651\pi$
$908$		−	40.8457i		−	0.0449843i
$909$	−868.514	+	348.677i	−0.955461	+	0.383583i
$910$	−92.7690			−0.101944
$911$	1135.12	+	655.360i	1.24601	+	0.719385i	0.970312	−	0.241858i	$-0.0777569\pi$
$911$	1135.12	+	655.360i	1.24601	+	0.719385i	0.275700	+	0.961244i	$0.411090\pi$
$912$	−89.0710	+	1253.91i	−0.0976655	+	1.37490i
$913$	535.734	+	927.919i	0.586785	+	1.01634i
$914$	1008.77	−	582.416i	1.10369	−	0.637217i
$915$	259.461	+	533.465i	0.283563	+	0.583022i
$916$	−433.942	+	751.609i	−0.473735	+	0.820534i
$917$			51.5098i			0.0561721i
$918$	−1335.33	−	1210.36i	−1.45461	−	1.31847i
$919$	−794.225			−0.864228			−0.432114	−	0.901819i	$-0.642232\pi$
$919$	−794.225			−0.864228			−0.432114	+	0.901819i	$0.642232\pi$
$920$	335.547	+	193.728i	0.364725	+	0.210574i
$921$	655.035	−	318.588i	0.711221	−	0.345916i
$922$	−168.937	−	292.608i	−0.183229	−	0.317362i
$923$	431.975	−	249.401i	0.468011	−	0.270207i
$924$	−154.176	−	10.9518i	−0.166857	−	0.0118526i
$925$	−18.1942	+	31.5133i	−0.0196694	+	0.0340684i
$926$			1752.58i			1.89264i
$927$	1070.82	+	152.903i	1.15515	+	0.164944i
$928$	30.4654			0.0328291
$929$	1415.62	+	817.310i	1.52381	+	0.879774i	0.999603	+	0.0281862i	$0.00897314\pi$
$929$	1415.62	+	817.310i	1.52381	+	0.879774i	0.524211	+	0.851588i	$0.324360\pi$
$930$	−139.249	−	94.1485i	−0.149731	−	0.101235i
$931$	−508.605	−	880.929i	−0.546299	−	0.946218i
$932$	264.870	−	152.923i	0.284195	−	0.164080i
$933$	−67.2925	+	99.5283i	−0.0721248	+	0.106676i
$934$	−601.270	+	1041.43i	−0.643758	+	1.11502i
$935$			1208.71i			1.29274i
$936$	17.9452	−	125.675i	0.0191722	−	0.134268i
$937$	858.395			0.916110			0.458055	−	0.888924i	$-0.348546\pi$
$937$	858.395			0.916110			0.458055	+	0.888924i	$0.348546\pi$
$938$	−99.0332	−	57.1768i	−0.105579	−	0.0609561i
$939$	21.5405	−	303.239i	0.0229399	−	0.322938i
$940$	116.662	+	202.064i	0.124108	+	0.214962i
$941$	−177.302	+	102.365i	−0.188418	+	0.108783i	−0.591242	−	0.806494i	$-0.701362\pi$
$941$	−177.302	+	102.365i	−0.188418	+	0.108783i	0.402824	+	0.915278i	$0.368029\pi$
$942$	621.132	+	1277.08i	0.659376	+	1.35571i
$943$	−26.5952	+	46.0642i	−0.0282027	+	0.0488485i
$944$			1339.50i			1.41897i
$945$	184.685	+	39.8948i	0.195434	+	0.0422167i
$946$	−1046.09			−1.10580
$947$	638.722	+	368.766i	0.674468	+	0.389405i	0.797768	−	0.602965i	$-0.206014\pi$
$947$	638.722	+	368.766i	0.674468	+	0.389405i	−0.123299	+	0.992370i	$0.539347\pi$
$948$	130.607	−	63.5232i	0.137771	−	0.0670076i
$949$	−33.2116	−	57.5242i	−0.0349964	−	0.0606156i
$950$	−298.954	+	172.601i	−0.314689	+	0.181686i
$951$	−1549.93	−	110.099i	−1.62979	−	0.115771i
$952$	−56.9858	+	98.7023i	−0.0598590	+	0.103679i
$953$			1295.08i			1.35895i	0.733698	+	0.679475i	$0.237793\pi$
$953$			1295.08i			1.35895i	−0.733698	+	0.679475i	$0.762207\pi$
$954$	−289.517	−	721.153i	−0.303477	−	0.755925i
$955$	−776.786			−0.813388
$956$	79.4512	+	45.8712i	0.0831079	+	0.0479824i
$957$	21.1458	+	14.2970i	0.0220960	+	0.0149394i
$958$	923.036	+	1598.74i	0.963503	+	1.66884i
$959$	−3.63893	+	2.10094i	−0.00379450	+	0.00219076i
$960$	−195.115	+	288.583i	−0.203244	+	0.300607i
$961$	468.600	−	811.639i	0.487617	−	0.844578i
$962$			80.6368i			0.0838220i
$963$	−1242.19	−	974.924i	−1.28992	−	1.01238i
$964$	449.405			0.466188
$965$	−131.973	−	76.1945i	−0.136759	−	0.0789580i
$966$	28.4823	−	400.963i	0.0294848	−	0.415076i
$967$	126.305	+	218.768i	0.130616	+	0.226233i	0.923914	−	0.382600i	$-0.124971\pi$
$967$	126.305	+	218.768i	0.130616	+	0.226233i	−0.793298	+	0.608833i	$0.791638\pi$
$968$	3.42333	−	1.97646i	0.00353650	−	0.00204180i
$969$	−728.676	−	1498.20i	−0.751987	−	1.54613i
$970$	303.850	−	526.283i	0.313247	−	0.542560i
$971$			224.888i			0.231605i	0.993272	+	0.115802i	$0.0369440\pi$
$971$			224.888i			0.231605i	−0.993272	+	0.115802i	$0.963056\pi$
$972$	247.702	−	669.058i	0.254838	−	0.688331i
$973$	170.470			0.175200
$974$	12.8724	+	7.43189i	0.0132160	+	0.00763028i
$975$	81.2374	−	39.5113i	0.0833204	−	0.0405244i
$976$	−433.570	−	750.966i	−0.444232	−	0.769432i
$977$	388.418	−	224.253i	0.397562	−	0.229533i	−0.287869	−	0.957670i	$-0.592947\pi$
$977$	388.418	−	224.253i	0.397562	−	0.229533i	0.685432	+	0.728137i	$0.259614\pi$
$978$	−453.420	−	32.2086i	−0.463620	−	0.0329331i
$979$	−889.944	+	1541.43i	−0.909034	+	1.57449i
$980$		−	594.404i		−	0.606535i
$981$	−974.887	+	1242.14i	−0.993769	+	1.26620i
$982$	−230.099			−0.234317
$983$	38.6706	+	22.3265i	0.0393393	+	0.0227126i	0.519541	−	0.854446i	$-0.326103\pi$
$983$	38.6706	+	22.3265i	0.0393393	+	0.0227126i	−0.480201	+	0.877158i	$0.659436\pi$
$984$	11.6838	+	7.89955i	0.0118737	+	0.00802800i
$985$	598.380	+	1036.42i	0.607493	+	1.05221i
$986$	−44.9765	+	25.9672i	−0.0456152	+	0.0263359i
$987$	−49.1372	+	72.6759i	−0.0497844	+	0.0736331i
$988$	−161.904	+	280.426i	−0.163871	+	0.283832i
$989$		−	1151.60i		−	1.16441i
$990$	−1049.00	+	421.134i	−1.05959	+	0.425387i
$991$	569.525			0.574698			0.287349	−	0.957826i	$-0.407226\pi$
$991$	569.525			0.574698			0.287349	+	0.957826i	$0.407226\pi$
$992$	165.432	+	95.5122i	0.166766	+	0.0962824i
$993$	107.753	−	1516.91i	0.108513	−	1.52760i
$994$	−209.393	−	362.679i	−0.210657	−	0.364869i
$995$	828.696	−	478.448i	0.832860	−	0.480852i
$996$	−377.454	−	776.065i	−0.378970	−	0.779182i
$997$	571.370	−	989.643i	0.573090	−	0.992620i	−0.423157	−	0.906057i	$-0.639078\pi$
$997$	571.370	−	989.643i	0.573090	−	0.992620i	0.996246	−	0.0865639i	$-0.0275887\pi$
$998$			831.252i			0.832918i
$999$	34.6774	−	160.532i	0.0347121	−	0.160693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	333.3.r.a.38.16	✓	144
9.5	odd	6	inner	333.3.r.a.149.16	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
333.3.r.a.38.16	✓	144	1.1	even	1	trivial
333.3.r.a.149.16	yes	144	9.5	odd	6	inner

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:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	333.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.28078 - 1.31681i) q^{2} +(2.69783 - 1.31214i) q^{3} +(1.46798 + 2.54262i) q^{4} +(-3.77668 + 2.18047i) q^{5} +(-7.88101 - 0.559825i) q^{6} +(0.802344 - 1.38970i) q^{7} +2.80227i q^{8} +(5.55658 - 7.07986i) q^{9} +O(q^{10})\)	\(q+(-2.28078 - 1.31681i) q^{2} +(2.69783 - 1.31214i) q^{3} +(1.46798 + 2.54262i) q^{4} +(-3.77668 + 2.18047i) q^{5} +(-7.88101 - 0.559825i) q^{6} +(0.802344 - 1.38970i) q^{7} +2.80227i q^{8} +(5.55658 - 7.07986i) q^{9} +11.4851 q^{10} +(-9.47059 - 5.46785i) q^{11} +(7.29663 + 4.93335i) q^{12} +(-2.51680 - 4.35923i) q^{13} +(-3.65994 + 2.11307i) q^{14} +(-7.32777 + 10.8381i) q^{15} +(9.56199 - 16.5618i) q^{16} +25.3452i q^{17} +(-21.9962 + 8.83067i) q^{18} -21.9108 q^{19} +(-11.0882 - 6.40177i) q^{20} +(0.341106 - 4.80196i) q^{21} +(14.4002 + 24.9419i) q^{22} +(-27.4576 + 15.8527i) q^{23} +(3.67698 + 7.56006i) q^{24} +(-2.99111 + 5.18075i) q^{25} +13.2566i q^{26} +(5.70093 - 26.3913i) q^{27} +4.71130 q^{28} +(-0.673810 - 0.389024i) q^{29} +(30.9847 - 15.0700i) q^{30} +(-2.43926 - 4.22492i) q^{31} +(-33.9103 + 19.5781i) q^{32} +(-32.7246 - 2.32459i) q^{33} +(33.3748 - 57.8069i) q^{34} +6.99794i q^{35} +(26.1583 + 3.73515i) q^{36} +6.08276 q^{37} +(49.9738 + 28.8524i) q^{38} +(-12.5098 - 8.45806i) q^{39} +(-6.11027 - 10.5833i) q^{40} +(1.45288 - 0.838822i) q^{41} +(-7.10127 + 10.5031i) q^{42} +(-18.1610 + 31.4558i) q^{43} -32.1068i q^{44} +(-5.54801 + 38.8543i) q^{45} +83.4999 q^{46} +(-15.7819 - 9.11166i) q^{47} +(4.06516 - 57.2277i) q^{48} +(23.2125 + 40.2052i) q^{49} +(13.6441 - 7.87745i) q^{50} +(33.2564 + 68.3770i) q^{51} +(7.38923 - 12.7985i) q^{52} +32.7854i q^{53} +(-47.7549 + 52.6857i) q^{54} +47.6899 q^{55} +(3.89432 + 2.24839i) q^{56} +(-59.1117 + 28.7501i) q^{57} +(1.02454 + 1.77456i) q^{58} +(-60.6591 + 35.0216i) q^{59} +(-38.3141 - 2.72163i) q^{60} +(22.6715 - 39.2683i) q^{61} +12.8482i q^{62} +(-5.38060 - 13.4025i) q^{63} +26.6267 q^{64} +(19.0103 + 10.9756i) q^{65} +(71.5767 + 48.3940i) q^{66} +(13.5293 + 23.4335i) q^{67} +(-64.4431 + 37.2062i) q^{68} +(-53.2751 + 78.7961i) q^{69} +(9.21497 - 15.9608i) q^{70} +99.0942i q^{71} +(19.8397 + 15.5711i) q^{72} +13.1960 q^{73} +(-13.8735 - 8.00985i) q^{74} +(-1.27163 + 17.9015i) q^{75} +(-32.1647 - 55.7108i) q^{76} +(-15.1973 + 8.77419i) q^{77} +(17.3945 + 35.7641i) q^{78} +(8.24464 - 14.2801i) q^{79} +83.3985i q^{80} +(-19.2489 - 78.6796i) q^{81} -4.41828 q^{82} +(-84.8523 - 48.9895i) q^{83} +(12.7103 - 6.18189i) q^{84} +(-55.2644 - 95.7207i) q^{85} +(82.8426 - 47.8292i) q^{86} +(-2.32828 - 0.165389i) q^{87} +(15.3224 - 26.5392i) q^{88} -162.760i q^{89} +(63.8176 - 81.3126i) q^{90} -8.07736 q^{91} +(-80.6146 - 46.5429i) q^{92} +(-12.1244 - 8.19747i) q^{93} +(23.9967 + 41.5635i) q^{94} +(82.7502 - 47.7759i) q^{95} +(-65.7950 + 97.3134i) q^{96} +(26.4561 - 45.8233i) q^{97} -122.266i q^{98} +(-91.3357 + 36.6679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 4 q^{3} + 144 q^{4} - 30 q^{6} + 4 q^{9}+O(q^{10}) \) 144 * q + 4 * q^3 + 144 * q^4 - 30 * q^6 + 4 * q^9	\( 144 q + 4 q^{3} + 144 q^{4} - 30 q^{6} + 4 q^{9} - 12 q^{12} + 72 q^{14} - 18 q^{15} - 288 q^{16} - 90 q^{18} - 24 q^{19} + 32 q^{21} - 24 q^{22} + 144 q^{23} - 48 q^{24} + 360 q^{25} - 50 q^{27} - 216 q^{29} + 28 q^{30} + 36 q^{32} - 110 q^{33} + 60 q^{34} - 10 q^{36} + 36 q^{38} + 88 q^{39} - 60 q^{40} + 108 q^{41} + 278 q^{42} - 60 q^{43} + 64 q^{45} - 216 q^{46} + 90 q^{47} - 238 q^{48} - 552 q^{49} - 522 q^{50} + 90 q^{51} - 18 q^{52} + 216 q^{54} + 48 q^{55} + 432 q^{56} - 264 q^{57} + 138 q^{58} - 270 q^{59} - 458 q^{60} + 96 q^{61} + 148 q^{63} - 636 q^{64} - 54 q^{65} - 224 q^{66} + 84 q^{67} - 72 q^{68} + 410 q^{69} - 216 q^{70} - 636 q^{72} - 72 q^{73} + 344 q^{75} + 84 q^{76} + 432 q^{77} - 384 q^{78} + 108 q^{79} + 556 q^{81} - 204 q^{82} - 180 q^{83} - 308 q^{84} + 60 q^{85} + 72 q^{86} + 126 q^{87} + 168 q^{88} - 206 q^{90} + 168 q^{91} - 36 q^{92} + 70 q^{93} - 186 q^{94} - 864 q^{95} + 932 q^{96} - 180 q^{97} + 128 q^{99}+O(q^{100}) \) 144 * q + 4 * q^3 + 144 * q^4 - 30 * q^6 + 4 * q^9 - 12 * q^12 + 72 * q^14 - 18 * q^15 - 288 * q^16 - 90 * q^18 - 24 * q^19 + 32 * q^21 - 24 * q^22 + 144 * q^23 - 48 * q^24 + 360 * q^25 - 50 * q^27 - 216 * q^29 + 28 * q^30 + 36 * q^32 - 110 * q^33 + 60 * q^34 - 10 * q^36 + 36 * q^38 + 88 * q^39 - 60 * q^40 + 108 * q^41 + 278 * q^42 - 60 * q^43 + 64 * q^45 - 216 * q^46 + 90 * q^47 - 238 * q^48 - 552 * q^49 - 522 * q^50 + 90 * q^51 - 18 * q^52 + 216 * q^54 + 48 * q^55 + 432 * q^56 - 264 * q^57 + 138 * q^58 - 270 * q^59 - 458 * q^60 + 96 * q^61 + 148 * q^63 - 636 * q^64 - 54 * q^65 - 224 * q^66 + 84 * q^67 - 72 * q^68 + 410 * q^69 - 216 * q^70 - 636 * q^72 - 72 * q^73 + 344 * q^75 + 84 * q^76 + 432 * q^77 - 384 * q^78 + 108 * q^79 + 556 * q^81 - 204 * q^82 - 180 * q^83 - 308 * q^84 + 60 * q^85 + 72 * q^86 + 126 * q^87 + 168 * q^88 - 206 * q^90 + 168 * q^91 - 36 * q^92 + 70 * q^93 - 186 * q^94 - 864 * q^95 + 932 * q^96 - 180 * q^97 + 128 * q^99

Introduction

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