LMFDB - Embedded newform 63.4.o.a.20.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(20,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("63.20");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.o (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:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			20.16
Character	$\chi$	$=$	63.20
Dual form			63.4.o.a.41.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.93743 + 1.11857i) q^{2} +(5.00204 + 1.40697i) q^{3} +(-1.49759 - 2.59390i) q^{4} +(2.75758 + 4.77627i) q^{5} +(8.11730 + 8.32104i) q^{6} +(13.1049 + 13.0867i) q^{7} -24.5978i q^{8} +(23.0409 + 14.0754i) q^{9} +O(q^{10})$	\(q+(1.93743 + 1.11857i) q^{2} +(5.00204 + 1.40697i) q^{3} +(-1.49759 - 2.59390i) q^{4} +(2.75758 + 4.77627i) q^{5} +(8.11730 + 8.32104i) q^{6} +(13.1049 + 13.0867i) q^{7} -24.5978i q^{8} +(23.0409 + 14.0754i) q^{9} +12.3382i q^{10} +(-30.2441 - 17.4614i) q^{11} +(-3.84148 - 15.0818i) q^{12} +(-23.1532 + 13.3675i) q^{13} +(10.7514 + 40.0133i) q^{14} +(7.07349 + 27.7709i) q^{15} +(15.5338 - 26.9053i) q^{16} -35.9093 q^{17} +(28.8957 + 53.0430i) q^{18} -78.0198i q^{19} +(8.25943 - 14.3058i) q^{20} +(47.1389 + 83.8983i) q^{21} +(-39.0638 - 67.6605i) q^{22} +(-50.1284 + 28.9416i) q^{23} +(34.6083 - 123.039i) q^{24} +(47.2915 - 81.9113i) q^{25} -59.8102 q^{26} +(95.4480 + 102.824i) q^{27} +(14.3198 - 53.5913i) q^{28} +(-192.066 - 110.889i) q^{29} +(-17.3594 + 61.7163i) q^{30} +(-126.002 + 72.7471i) q^{31} +(-110.228 + 63.6400i) q^{32} +(-126.715 - 129.895i) q^{33} +(-69.5717 - 40.1672i) q^{34} +(-26.3676 + 98.6801i) q^{35} +(2.00440 - 80.8449i) q^{36} +290.956 q^{37} +(87.2708 - 151.158i) q^{38} +(-134.621 + 34.2892i) q^{39} +(117.486 - 67.8304i) q^{40} +(54.0606 + 93.6357i) q^{41} +(-2.51838 + 215.275i) q^{42} +(174.061 - 301.482i) q^{43} +104.600i q^{44} +(-3.69080 + 148.863i) q^{45} -129.493 q^{46} +(-125.545 + 217.450i) q^{47} +(115.555 - 112.726i) q^{48} +(0.477554 + 343.000i) q^{49} +(183.248 - 105.798i) q^{50} +(-179.620 - 50.5232i) q^{51} +(69.3480 + 40.0381i) q^{52} +160.173i q^{53} +(69.9077 + 305.979i) q^{54} -192.605i q^{55} +(321.904 - 322.352i) q^{56} +(109.771 - 390.258i) q^{57} +(-248.076 - 429.680i) q^{58} +(367.425 + 636.398i) q^{59} +(61.4417 - 59.9373i) q^{60} +(581.350 + 335.643i) q^{61} -325.492 q^{62} +(117.749 + 485.986i) q^{63} -533.284 q^{64} +(-127.694 - 73.7240i) q^{65} +(-100.203 - 393.402i) q^{66} +(344.364 + 596.455i) q^{67} +(53.7774 + 93.1452i) q^{68} +(-291.464 + 74.2385i) q^{69} +(-161.466 + 161.691i) q^{70} -577.396i q^{71} +(346.224 - 566.756i) q^{72} +37.4543i q^{73} +(563.705 + 325.455i) q^{74} +(351.801 - 343.187i) q^{75} +(-202.375 + 116.841i) q^{76} +(-167.834 - 624.626i) q^{77} +(-299.173 - 84.1509i) q^{78} +(-428.000 + 741.317i) q^{79} +171.342 q^{80} +(332.766 + 648.620i) q^{81} +241.883i q^{82} +(616.129 - 1067.17i) q^{83} +(147.029 - 247.918i) q^{84} +(-99.0228 - 171.513i) q^{85} +(674.460 - 389.400i) q^{86} +(-804.705 - 824.903i) q^{87} +(-429.513 + 743.939i) q^{88} -1505.64 q^{89} +(-173.665 + 284.284i) q^{90} +(-478.358 - 127.819i) q^{91} +(150.143 + 86.6853i) q^{92} +(-732.619 + 186.604i) q^{93} +(-486.467 + 280.862i) q^{94} +(372.643 - 215.146i) q^{95} +(-640.903 + 163.243i) q^{96} +(-1002.35 - 578.705i) q^{97} +(-382.745 + 665.071i) q^{98} +(-451.074 - 828.025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) $ 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7	$ 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7} - 18 q^{11} + 204 q^{14} + 66 q^{15} - 242 q^{16} - 210 q^{18} - 57 q^{21} - 34 q^{22} - 102 q^{23} - 352 q^{25} + 300 q^{28} + 246 q^{29} - 144 q^{30} + 1068 q^{32} - 1818 q^{36} + 328 q^{37} - 798 q^{39} - 1158 q^{42} - 170 q^{43} + 968 q^{46} - 79 q^{49} + 288 q^{50} - 204 q^{51} + 1212 q^{56} + 324 q^{57} - 538 q^{58} + 5316 q^{60} + 783 q^{63} - 808 q^{64} + 4350 q^{65} - 590 q^{67} + 384 q^{70} + 4284 q^{72} - 5304 q^{74} - 2787 q^{77} + 612 q^{78} - 302 q^{79} - 3720 q^{81} + 7050 q^{84} - 612 q^{85} - 13692 q^{86} + 1294 q^{88} + 210 q^{91} - 10194 q^{92} - 4266 q^{93} + 6336 q^{95} + 1014 q^{99}+O(q^{100}) $ 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7 - 18 * q^11 + 204 * q^14 + 66 * q^15 - 242 * q^16 - 210 * q^18 - 57 * q^21 - 34 * q^22 - 102 * q^23 - 352 * q^25 + 300 * q^28 + 246 * q^29 - 144 * q^30 + 1068 * q^32 - 1818 * q^36 + 328 * q^37 - 798 * q^39 - 1158 * q^42 - 170 * q^43 + 968 * q^46 - 79 * q^49 + 288 * q^50 - 204 * q^51 + 1212 * q^56 + 324 * q^57 - 538 * q^58 + 5316 * q^60 + 783 * q^63 - 808 * q^64 + 4350 * q^65 - 590 * q^67 + 384 * q^70 + 4284 * q^72 - 5304 * q^74 - 2787 * q^77 + 612 * q^78 - 302 * q^79 - 3720 * q^81 + 7050 * q^84 - 612 * q^85 - 13692 * q^86 + 1294 * q^88 + 210 * q^91 - 10194 * q^92 - 4266 * q^93 + 6336 * q^95 + 1014 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.93743	+	1.11857i	0.684983	+	0.395475i	0.801730	−	0.597686i	$-0.203913\pi$
$2$	1.93743	+	1.11857i	0.684983	+	0.395475i	−0.116747	+	0.993162i	$0.537247\pi$
$3$	5.00204	+	1.40697i	0.962644	+	0.270771i
$3$	5.00204	+	1.40697i	0.962644	+	0.270771i
$4$	−1.49759	−	2.59390i	−0.187198	−	0.324237i
$5$	2.75758	+	4.77627i	0.246645	+	0.427202i	0.962593	−	0.270952i	$-0.0873384\pi$
$5$	2.75758	+	4.77627i	0.246645	+	0.427202i	−0.715948	+	0.698154i	$0.754005\pi$
$6$	8.11730	+	8.32104i	0.552312	+	0.566175i
$7$	13.1049	+	13.0867i	0.707599	+	0.706614i
$7$	13.1049	+	13.0867i	0.707599	+	0.706614i
$8$		−	24.5978i		−	1.08708i
$9$	23.0409	+	14.0754i	0.853367	+	0.521311i
$10$			12.3382i			0.390169i
$11$	−30.2441	−	17.4614i	−0.828995	−	0.478620i	0.0245137	−	0.999699i	$-0.492196\pi$
$11$	−30.2441	−	17.4614i	−0.828995	−	0.478620i	−0.853508	+	0.521079i	$0.825530\pi$
$12$	−3.84148	−	15.0818i	−0.0924115	−	0.362813i
$13$	−23.1532	+	13.3675i	−0.493965	+	0.285191i	−0.726218	−	0.687464i	$-0.758724\pi$
$13$	−23.1532	+	13.3675i	−0.493965	+	0.285191i	0.232253	+	0.972656i	$0.425390\pi$
$14$	10.7514	+	40.0133i	0.205245	+	0.763857i
$15$	7.07349	+	27.7709i	0.121758	+	0.478028i
$16$	15.5338	−	26.9053i	0.242715	−	0.420395i
$17$	−35.9093			−0.512311			−0.256156	−	0.966636i	$-0.582456\pi$
$17$	−35.9093			−0.512311			−0.256156	+	0.966636i	$0.582456\pi$
$18$	28.8957	+	53.0430i	0.378376	+	0.694575i
$19$		−	78.0198i		−	0.942051i	−0.882120	−	0.471025i	$-0.843884\pi$
$19$		−	78.0198i		−	0.942051i	0.882120	−	0.471025i	$-0.156116\pi$
$20$	8.25943	−	14.3058i	0.0923432	−	0.159943i
$21$	47.1389	+	83.8983i	0.489835	+	0.871815i
$22$	−39.0638	−	67.6605i	−0.378565	−	0.655694i
$23$	−50.1284	+	28.9416i	−0.454456	+	0.262380i	−0.709710	−	0.704494i	$-0.751174\pi$
$23$	−50.1284	+	28.9416i	−0.454456	+	0.262380i	0.255254	+	0.966874i	$0.417841\pi$
$24$	34.6083	−	123.039i	0.294349	−	1.04647i
$25$	47.2915	−	81.9113i	0.378332	−	0.655291i
$26$	−59.8102			−0.451144
$27$	95.4480	+	102.824i	0.680332	+	0.732904i
$28$	14.3198	−	53.5913i	0.0966493	−	0.361707i
$29$	−192.066	−	110.889i	−1.22985	−	0.710056i	−0.262854	−	0.964836i	$-0.584664\pi$
$29$	−192.066	−	110.889i	−1.22985	−	0.710056i	−0.966999	+	0.254779i	$0.917997\pi$
$30$	−17.3594	+	61.7163i	−0.105646	+	0.375593i
$31$	−126.002	+	72.7471i	−0.730018	+	0.421476i	−0.818429	−	0.574608i	$-0.805155\pi$
$31$	−126.002	+	72.7471i	−0.730018	+	0.421476i	0.0884105	+	0.996084i	$0.471821\pi$
$32$	−110.228	+	63.6400i	−0.608928	+	0.351564i
$33$	−126.715	−	129.895i	−0.668430	−	0.685208i
$34$	−69.5717	−	40.1672i	−0.350925	−	0.202607i
$35$	−26.3676	+	98.6801i	−0.127341	+	0.476571i
$36$	2.00440	−	80.8449i	0.00927964	−	0.374282i
$37$	290.956			1.29278			0.646390	−	0.763008i	$-0.276278\pi$
$37$	290.956			1.29278			0.646390	+	0.763008i	$0.276278\pi$
$38$	87.2708	−	151.158i	0.372558	−	0.645289i
$39$	−134.621	+	34.2892i	−0.552734	+	0.140786i
$40$	117.486	−	67.8304i	0.464403	−	0.268123i
$41$	54.0606	+	93.6357i	0.205923	+	0.356669i	0.950426	−	0.310949i	$-0.100647\pi$
$41$	54.0606	+	93.6357i	0.205923	+	0.356669i	−0.744503	+	0.667619i	$0.767314\pi$
$42$	−2.51838	+	215.275i	−0.00925226	+	0.790897i
$43$	174.061	−	301.482i	0.617303	−	1.06920i	−0.372673	−	0.927963i	$-0.621559\pi$
$43$	174.061	−	301.482i	0.617303	−	1.06920i	0.989976	−	0.141238i	$-0.0451082\pi$
$44$			104.600i			0.358388i
$45$	−3.69080	+	148.863i	−0.0122265	+	0.493139i
$46$	−129.493			−0.415060
$47$	−125.545	+	217.450i	−0.389630	+	0.674858i	−0.992400	−	0.123057i	$-0.960730\pi$
$47$	−125.545	+	217.450i	−0.389630	+	0.674858i	0.602770	+	0.797915i	$0.294064\pi$
$48$	115.555	−	112.726i	0.347479	−	0.338970i
$49$	0.477554	+	343.000i	0.00139229	+	0.999999i
$50$	183.248	−	105.798i	0.518303	−	0.299242i
$51$	−179.620	−	50.5232i	−0.493173	−	0.138719i
$52$	69.3480	+	40.0381i	0.184939	+	0.106775i
$53$			160.173i			0.415122i	0.978222	+	0.207561i	$0.0665525\pi$
$53$			160.173i			0.415122i	−0.978222	+	0.207561i	$0.933448\pi$
$54$	69.9077	+	305.979i	0.176171	+	0.771082i
$55$		−	192.605i		−	0.472198i
$56$	321.904	−	322.352i	0.768147	−	0.769217i
$57$	109.771	−	390.258i	0.255080	−	0.906859i
$58$	−248.076	−	429.680i	−0.561620	−	0.972754i
$59$	367.425	+	636.398i	0.810756	+	1.40427i	0.912336	+	0.409443i	$0.134277\pi$
$59$	367.425	+	636.398i	0.810756	+	1.40427i	−0.101580	+	0.994827i	$0.532390\pi$
$60$	61.4417	−	59.9373i	0.132202	−	0.128964i
$61$	581.350	+	335.643i	1.22023	+	0.704502i	0.964968	−	0.262368i	$-0.0845035\pi$
$61$	581.350	+	335.643i	1.22023	+	0.704502i	0.255266	+	0.966871i	$0.417837\pi$
$62$	−325.492			−0.666734
$63$	117.749	+	485.986i	0.235475	+	0.971880i
$64$	−533.284			−1.04157
$65$	−127.694	−	73.7240i	−0.243669	−	0.140682i
$66$	−100.203	−	393.402i	−0.186881	−	0.733704i
$67$	344.364	+	596.455i	0.627921	+	1.08759i	0.987968	+	0.154657i	$0.0494273\pi$
$67$	344.364	+	596.455i	0.627921	+	1.08759i	−0.360047	+	0.932934i	$0.617239\pi$
$68$	53.7774	+	93.1452i	0.0959039	+	0.166110i
$69$	−291.464	+	74.2385i	−0.508524	+	0.129526i
$70$	−161.466	+	161.691i	−0.275699	+	0.276083i
$71$		−	577.396i		−	0.965130i	−0.875860	−	0.482565i	$-0.839705\pi$
$71$		−	577.396i		−	0.965130i	0.875860	−	0.482565i	$-0.160295\pi$
$72$	346.224	−	566.756i	0.566707	−	0.927678i
$73$			37.4543i			0.0600506i	0.999549	+	0.0300253i	$0.00955879\pi$
$73$			37.4543i			0.0600506i	−0.999549	+	0.0300253i	$0.990441\pi$
$74$	563.705	+	325.455i	0.885532	+	0.511262i
$75$	351.801	−	343.187i	0.541633	−	0.528370i
$76$	−202.375	+	116.841i	−0.305448	+	0.176350i
$77$	−167.834	−	624.626i	−0.248396	−	0.924451i
$78$	−299.173	−	84.1509i	−0.434291	−	0.122157i
$79$	−428.000	+	741.317i	−0.609541	+	1.05576i	0.381775	+	0.924255i	$0.375313\pi$
$79$	−428.000	+	741.317i	−0.609541	+	1.05576i	−0.991316	+	0.131501i	$0.958020\pi$
$80$	171.342			0.239458
$81$	332.766	+	648.620i	0.456469	+	0.889739i
$82$			241.883i			0.325750i
$83$	616.129	−	1067.17i	0.814806	−	1.41129i	−0.0946603	−	0.995510i	$-0.530176\pi$
$83$	616.129	−	1067.17i	0.814806	−	1.41129i	0.909467	−	0.415777i	$-0.136490\pi$
$84$	147.029	−	247.918i	0.190978	−	0.322025i
$85$	−99.0228	−	171.513i	−0.126359	−	0.218861i
$86$	674.460	−	389.400i	0.845685	−	0.488256i
$87$	−804.705	−	824.903i	−0.991649	−	1.01654i
$88$	−429.513	+	743.939i	−0.520299	+	0.901184i
$89$	−1505.64			−1.79323			−0.896615	−	0.442811i	$-0.853981\pi$
$89$	−1505.64			−1.79323			−0.896615	+	0.442811i	$0.853981\pi$
$90$	−173.665	+	284.284i	−0.203399	+	0.332957i
$91$	−478.358	−	127.819i	−0.551050	−	0.147242i
$92$	150.143	+	86.6853i	0.170147	+	0.0982344i
$93$	−732.619	+	186.604i	−0.816871	+	0.208064i
$94$	−486.467	+	280.862i	−0.533780	+	0.308178i
$95$	372.643	−	215.146i	0.402446	−	0.232352i
$96$	−640.903	+	163.243i	−0.681374	+	0.173552i
$97$	−1002.35	−	578.705i	−1.04921	−	0.605759i	−0.126778	−	0.991931i	$-0.540464\pi$
$97$	−1002.35	−	578.705i	−1.04921	−	0.605759i	−0.922427	+	0.386172i	$0.873797\pi$
$98$	−382.745	+	665.071i	−0.394521	+	0.685533i
$99$	−451.074	−	828.025i	−0.457926	−	0.840603i
$100$	−283.293			−0.283293
$101$	−77.7834	+	134.725i	−0.0766311	+	0.132729i	−0.901794	−	0.432165i	$-0.857750\pi$
$101$	−77.7834	+	134.725i	−0.0766311	+	0.132729i	0.825163	+	0.564894i	$0.191083\pi$
$102$	−291.487	−	298.803i	−0.282956	−	0.290058i
$103$	1640.73	−	947.276i	1.56957	−	0.906193i	0.573354	−	0.819307i	$-0.305642\pi$
$103$	1640.73	−	947.276i	1.56957	−	0.906193i	0.996218	−	0.0868857i	$-0.0276915\pi$
$104$	328.812	+	569.519i	0.310026	+	0.536980i
$105$	−270.732	+	456.504i	−0.251626	+	0.424288i
$106$	−179.165	+	310.323i	−0.164170	+	0.284351i
$107$		−	507.467i		−	0.458492i	−0.973369	−	0.229246i	$-0.926374\pi$
$107$		−	507.467i		−	0.458492i	0.973369	−	0.229246i	$-0.0736260\pi$
$108$	123.772	−	401.570i	0.110278	−	0.357787i
$109$	298.426			0.262239			0.131119	−	0.991367i	$-0.458143\pi$
$109$	298.426			0.262239			0.131119	+	0.991367i	$0.458143\pi$
$110$	215.443	−	373.158i	0.186743	−	0.323448i
$111$	1455.37	+	409.365i	1.24449	+	0.350047i
$112$	555.669	−	149.306i	0.468802	−	0.125965i
$113$	216.173	−	124.808i	0.179964	−	0.103902i	−0.407312	−	0.913289i	$-0.633534\pi$
$113$	216.173	−	124.808i	0.179964	−	0.103902i	0.587276	+	0.809387i	$0.300200\pi$
$114$	649.206	−	633.310i	0.533366	−	0.520306i
$115$	−276.466	−	159.618i	−0.224179	−	0.129430i
$116$			664.266i			0.531686i
$117$	−721.625	−	17.8914i	−0.570207	−	0.0141373i
$118$			1643.97i			1.28254i
$119$	−470.589	−	469.934i	−0.362511	−	0.362007i
$120$	683.104	−	173.992i	0.519655	−	0.132360i
$121$	−55.6960	−	96.4683i	−0.0418452	−	0.0724781i
$122$	750.882	+	1300.57i	0.557227	+	0.965145i
$123$	138.671	+	544.431i	0.101655	+	0.399103i
$124$	377.397	+	217.890i	0.273317	+	0.157799i
$125$	1211.03			0.866546
$126$	−315.482	+	1073.27i	−0.223058	+	0.758847i
$127$	1942.24			1.35706			0.678528	−	0.734574i	$-0.262618\pi$
$127$	1942.24			1.35706			0.678528	+	0.734574i	$0.262618\pi$
$128$	−151.377	−	87.3976i	−0.104531	−	0.0603510i
$129$	1294.84	−	1263.13i	0.883751	−	0.862112i
$130$	−164.931	−	285.670i	−0.111273	−	0.192730i
$131$	13.2642	+	22.9743i	0.00884655	+	0.0153227i	0.870415	−	0.492319i	$-0.163851\pi$
$131$	13.2642	+	22.9743i	0.00884655	+	0.0153227i	−0.861568	+	0.507642i	$0.830517\pi$
$132$	−147.169	+	523.215i	−0.0970409	+	0.345000i
$133$	1021.02	−	1022.44i	0.665667	−	0.666594i
$134$			1540.78i			0.993309i
$135$	−227.907	+	739.429i	−0.145297	+	0.471407i
$136$			883.291i			0.556924i
$137$	−230.946	−	133.337i	−0.144023	−	0.0831515i	0.426257	−	0.904602i	$-0.359832\pi$
$137$	−230.946	−	133.337i	−0.144023	−	0.0831515i	−0.570280	+	0.821451i	$0.693165\pi$
$138$	−647.732	−	182.193i	−0.399555	−	0.112386i
$139$	−444.807	+	256.810i	−0.271425	+	0.156707i	−0.629535	−	0.776972i	$-0.716755\pi$
$139$	−444.807	+	256.810i	−0.271425	+	0.156707i	0.358110	+	0.933679i	$0.383421\pi$
$140$	295.454	−	79.3871i	0.178360	−	0.0479245i
$141$	−933.925	+	911.057i	−0.557806	+	0.544148i
$142$	645.859	−	1118.66i	0.381685	−	0.661098i
$143$	933.665			0.545993
$144$	736.614	−	401.277i	0.426281	−	0.232221i
$145$		−	1223.14i		−	0.700528i
$146$	−41.8954	+	72.5650i	−0.0237486	+	0.0411337i
$147$	−480.200	+	1716.37i	−0.269430	+	0.963020i
$148$	−435.732	−	754.709i	−0.242006	−	0.419167i
$149$	−1835.58	+	1059.77i	−1.00924	+	0.582683i	−0.910968	−	0.412477i	$-0.864664\pi$
$149$	−1835.58	+	1059.77i	−1.00924	+	0.582683i	−0.0982688	+	0.995160i	$0.531331\pi$
$150$	1065.47	−	271.384i	0.579967	−	0.147723i
$151$	1141.85	−	1977.74i	0.615380	−	1.06587i	−0.374937	−	0.927050i	$-0.622336\pi$
$151$	1141.85	−	1977.74i	0.615380	−	1.06587i	0.990318	−	0.138820i	$-0.0443309\pi$
$152$	−1919.12			−1.02408
$153$	−827.383	−	505.439i	−0.437189	−	0.267074i
$154$	373.524	−	1397.90i	0.195451	−	0.731468i
$155$	−694.919	−	401.212i	−0.360111	−	0.207910i
$156$	290.549	+	297.842i	0.149119	+	0.152862i
$157$	−3179.20	+	1835.51i	−1.61610	+	0.933057i	−0.628186	+	0.778063i	$0.716202\pi$
$157$	−3179.20	+	1835.51i	−1.61610	+	0.933057i	−0.987916	+	0.154993i	$0.950464\pi$
$158$	−1658.44	+	957.498i	−0.835051	+	0.482117i
$159$	−225.358	+	801.192i	−0.112403	+	0.399614i
$160$	−607.923	−	350.984i	−0.300378	−	0.173423i
$161$	−1035.68	−	276.737i	−0.506974	−	0.135465i
$162$	−80.8198	+	1628.88i	−0.0391963	+	0.789979i
$163$	169.826			0.0816063			0.0408032	−	0.999167i	$-0.487008\pi$
$163$	169.826			0.0816063			0.0408032	+	0.999167i	$0.487008\pi$
$164$	161.921	−	280.455i	0.0770970	−	0.133536i
$165$	270.989	−	963.420i	0.127857	−	0.454558i
$166$	2387.41	−	1378.37i	1.11626	−	0.644472i
$167$	−218.313	−	378.129i	−0.101159	−	0.175213i	0.811003	−	0.585041i	$-0.198922\pi$
$167$	−218.313	−	378.129i	−0.101159	−	0.175213i	−0.912162	+	0.409829i	$0.865588\pi$
$168$	2063.72	−	1159.51i	0.947733	−	0.532490i
$169$	−741.119	+	1283.66i	−0.337332	+	0.584276i
$170$		−	443.057i		−	0.199888i
$171$	1098.16	−	1797.65i	0.491102	−	0.803915i
$172$	−1042.69			−0.462233
$173$	−827.732	+	1433.67i	−0.363765	+	0.630059i	−0.988577	−	0.150716i	$-0.951842\pi$
$173$	−827.732	+	1433.67i	−0.363765	+	0.630059i	0.624812	+	0.780775i	$0.285175\pi$
$174$	−636.341	−	2498.31i	−0.277247	−	1.08849i
$175$	1691.70	−	454.552i	0.730745	−	0.196348i
$176$	−939.610	+	542.484i	−0.402419	+	0.232337i
$177$	942.484	+	3700.24i	0.400234	+	1.57134i
$178$	−2917.07	−	1684.17i	−1.22833	−	0.709178i
$179$		−	4545.28i		−	1.89793i	−0.315376	−	0.948967i	$-0.602131\pi$
$179$		−	4545.28i		−	1.89793i	0.315376	−	0.948967i	$-0.397869\pi$
$180$	391.664	−	213.363i	0.162183	−	0.0883506i
$181$		−	69.4780i		−	0.0285318i	−0.999898	−	0.0142659i	$-0.995459\pi$
$181$		−	69.4780i		−	0.0285318i	0.999898	−	0.0142659i	$-0.00454113\pi$
$182$	−783.808	−	782.717i	−0.319229	−	0.318785i
$183$	2435.70	+	2496.84i	0.983892	+	1.00859i
$184$	711.901	+	1233.05i	0.285229	+	0.494030i
$185$	802.333	+	1389.68i	0.318858	+	0.552278i
$186$	−1628.12	−	457.956i	−0.641827	−	0.180532i
$187$	1086.05	+	627.029i	0.424703	+	0.245203i
$188$	752.057			0.291752
$189$	−94.7814	+	2596.59i	−0.0364779	+	0.999334i
$190$	962.625			0.367559
$191$	1216.59	+	702.396i	0.460885	+	0.266092i	0.712416	−	0.701757i	$-0.247601\pi$
$191$	1216.59	+	702.396i	0.460885	+	0.266092i	−0.251531	+	0.967849i	$0.580934\pi$
$192$	−2667.51	−	750.312i	−1.00266	−	0.282027i
$193$	−1156.04	−	2002.32i	−0.431158	−	0.746787i	0.565815	−	0.824532i	$-0.308561\pi$
$193$	−1156.04	−	2002.32i	−0.431158	−	0.746787i	−0.996973	+	0.0777446i	$0.975228\pi$
$194$	−1294.65	−	2242.40i	−0.479125	−	0.829870i
$195$	−535.002	−	548.431i	−0.196473	−	0.201405i
$196$	888.991	−	514.911i	0.323976	−	0.187650i
$197$			1556.72i			0.563005i	0.959561	+	0.281502i	$0.0908327\pi$
$197$			1556.72i			0.563005i	−0.959561	+	0.281502i	$0.909167\pi$
$198$	52.2838	−	2108.80i	0.0187659	−	0.756898i
$199$			1187.87i			0.423146i	0.977362	+	0.211573i	$0.0678585\pi$
$199$			1187.87i			0.423146i	−0.977362	+	0.211573i	$0.932141\pi$
$200$	−2014.84	−	1163.27i	−0.712353	−	0.411277i
$201$	883.330	+	3468.00i	0.309977	+	1.21699i
$202$	−301.399	+	174.013i	−0.104982	+	0.0606114i
$203$	−1065.83	−	3966.70i	−0.368507	−	1.37147i
$204$	137.945	+	541.579i	0.0473435	+	0.185873i
$205$	−298.153	+	516.416i	−0.101580	+	0.175942i
$206$	4238.39			1.43351
$207$	−1562.37	−	38.7361i	−0.524600	−	0.0130065i
$208$			830.592i			0.276881i
$209$	−1362.34	+	2359.64i	−0.450885	+	0.780955i
$210$	−1035.16	+	581.609i	−0.340155	+	0.191118i
$211$	−122.996	−	213.035i	−0.0401298	−	0.0695069i	0.845263	−	0.534351i	$-0.179444\pi$
$211$	−122.996	−	213.035i	−0.0401298	−	0.0695069i	−0.885393	+	0.464844i	$0.846110\pi$
$212$	415.472	−	239.873i	0.134598	−	0.0777101i
$213$	812.376	−	2888.16i	0.261329	−	0.929077i
$214$	567.639	−	983.179i	0.181322	−	0.314059i
$215$	1919.95			0.609020
$216$	2529.24	−	2347.81i	0.796725	−	0.739576i
$217$	−2603.26	−	695.599i	−0.814381	−	0.217605i
$218$	578.178	+	333.811i	0.179629	+	0.103709i
$219$	−52.6969	+	187.348i	−0.0162600	+	0.0578074i
$220$	−499.598	+	288.443i	−0.153104	+	0.0883947i
$221$	831.417	−	480.019i	0.253064	−	0.146107i
$222$	2361.77	+	2421.06i	0.714018	+	0.731940i
$223$	951.393	+	549.287i	0.285695	+	0.164946i	0.635999	−	0.771690i	$-0.280588\pi$
$223$	951.393	+	549.287i	0.285695	+	0.164946i	−0.350304	+	0.936636i	$0.613922\pi$
$224$	−2277.36	−	608.518i	−0.679297	−	0.181510i
$225$	2242.57	−	1221.66i	0.664466	−	0.361974i
$226$	558.427			0.164363
$227$	−2151.95	+	3727.29i	−0.629208	+	1.08982i	0.358503	+	0.933528i	$0.383287\pi$
$227$	−2151.95	+	3727.29i	−0.629208	+	1.08982i	−0.987711	+	0.156291i	$0.950046\pi$
$228$	−1176.68	+	299.711i	−0.341788	+	0.0870564i
$229$	−2476.51	+	1429.81i	−0.714639	+	0.412597i	−0.812776	−	0.582576i	$-0.802045\pi$
$229$	−2476.51	+	1429.81i	−0.714639	+	0.412597i	0.0981371	+	0.995173i	$0.468712\pi$
$230$	−357.088	−	618.495i	−0.102373	−	0.177315i
$231$	39.3131	−	3360.54i	0.0111975	−	0.957175i
$232$	−2727.64	+	4724.40i	−0.771888	+	1.33695i
$233$			2256.65i			0.634497i	0.948342	+	0.317249i	$0.102759\pi$
$233$			2256.65i			0.634497i	−0.948342	+	0.317249i	$0.897241\pi$
$234$	−1378.08	−	841.853i	−0.384991	−	0.235187i
$235$	−1384.80			−0.384401
$236$	1100.50	−	1906.12i	0.303545	−	0.525755i
$237$	−3183.88	+	3105.92i	−0.872639	+	0.851271i
$238$	−386.075	−	1436.85i	−0.105149	−	0.391333i
$239$	1367.09	−	789.292i	0.370000	−	0.213620i	−0.303458	−	0.952845i	$-0.598141\pi$
$239$	1367.09	−	789.292i	0.370000	−	0.213620i	0.673458	+	0.739225i	$0.264808\pi$
$240$	857.062	+	241.073i	0.230513	+	0.0648382i
$241$	1248.30	+	720.708i	0.333652	+	0.192634i	0.657461	−	0.753488i	$-0.271630\pi$
$241$	1248.30	+	720.708i	0.333652	+	0.192634i	−0.323809	+	0.946122i	$0.604964\pi$
$242$		−	249.200i		−	0.0661951i
$243$	751.924	+	3712.62i	0.198502	+	0.980101i
$244$		−	2010.62i		−	0.527527i
$245$	−1636.94	+	948.129i	−0.426858	+	0.247240i
$246$	−340.321	+	1209.91i	−0.0882035	+	0.313581i
$247$	1042.93	+	1806.41i	0.268664	+	0.465341i
$248$	1789.42	+	3099.37i	0.458179	+	0.793589i
$249$	4583.37	−	4471.14i	1.16650	−	1.13794i
$250$	2346.29	+	1354.63i	0.593570	+	0.342698i
$251$	2935.90			0.738296			0.369148	−	0.929371i	$-0.379650\pi$
$251$	2935.90			0.738296			0.369148	+	0.929371i	$0.379650\pi$
$252$	1084.26	−	1033.23i	0.271039	−	0.258284i
$253$	2021.45			0.502322
$254$	3762.95	+	2172.54i	0.929562	+	0.536683i
$255$	−254.004	−	997.235i	−0.0623779	−	0.244899i
$256$	1937.62	+	3356.05i	0.473051	+	0.819348i
$257$	−3638.04	−	6301.27i	−0.883015	−	1.52943i	−0.847973	−	0.530040i	$-0.822177\pi$
$257$	−3638.04	−	6301.27i	−0.883015	−	1.52943i	−0.0350420	−	0.999386i	$-0.511157\pi$
$258$	3921.55	−	998.853i	0.946299	−	0.241030i
$259$	3812.95	+	3807.65i	0.914769	+	0.913496i
$260$			441.632i			0.105342i
$261$	−2864.56	−	5258.40i	−0.679355	−	1.24707i
$262$			59.3479i			0.0139944i
$263$	5830.68	+	3366.35i	1.36705	+	0.789269i	0.990551	−	0.137146i	$-0.0437930\pi$
$263$	5830.68	+	3366.35i	1.36705	+	0.789269i	0.376503	+	0.926415i	$0.377126\pi$
$264$	−3195.14	+	3116.91i	−0.744876	+	0.726637i
$265$	−765.029	+	441.689i	−0.177341	+	0.102388i
$266$	3121.83	−	838.821i	0.719592	−	0.193351i
$267$	−7531.28	−	2118.38i	−1.72624	−	0.485554i
$268$	1031.43	−	1786.49i	0.235092	−	0.407191i
$269$	7501.34			1.70024			0.850121	−	0.526588i	$-0.176529\pi$
$269$	7501.34			1.70024			0.850121	+	0.526588i	$0.176529\pi$
$270$	−1268.66	+	1177.66i	−0.285956	+	0.265444i
$271$		−	4621.90i		−	1.03602i	−0.855376	−	0.518008i	$-0.826674\pi$
$271$		−	4621.90i		−	1.03602i	0.855376	−	0.518008i	$-0.173326\pi$
$272$	−557.807	+	966.150i	−0.124346	+	0.215373i
$273$	−2212.93	−	1312.39i	−0.490596	−	0.290950i
$274$	−298.294	−	516.661i	−0.0657687	−	0.113915i
$275$	−2860.58	+	1651.56i	−0.627271	+	0.362155i
$276$	629.060	+	644.850i	0.137192	+	0.140636i
$277$	982.366	−	1701.51i	0.213085	−	0.369075i	−0.739593	−	0.673054i	$-0.764982\pi$
$277$	982.366	−	1701.51i	0.213085	−	0.369075i	0.952679	+	0.303980i	$0.0983154\pi$
$278$	−1149.04			−0.247895
$279$	−3927.14	−	97.3663i	−0.842694	−	0.0208931i
$280$	2427.32	+	648.586i	0.518071	+	0.138430i
$281$	1702.23	+	982.785i	0.361376	+	0.208641i	0.669684	−	0.742646i	$-0.266429\pi$
$281$	1702.23	+	982.785i	0.361376	+	0.208641i	−0.308308	+	0.951287i	$0.599763\pi$
$282$	−2828.50	+	720.442i	−0.597285	+	0.152134i
$283$	−4621.27	+	2668.09i	−0.970692	+	0.560429i	−0.899447	−	0.437030i	$-0.856030\pi$
$283$	−4621.27	+	2668.09i	−0.970692	+	0.560429i	−0.0712447	+	0.997459i	$0.522697\pi$
$284$	−1497.71	+	864.701i	−0.312931	+	0.180671i
$285$	2166.68	−	551.872i	0.450327	−	0.114702i
$286$	1808.91	+	1044.37i	0.373996	+	0.215927i
$287$	−516.921	+	1934.56i	−0.106317	+	0.397887i
$288$	−3435.50	−	85.1771i	−0.702913	−	0.0174275i
$289$	−3623.52			−0.737537
$290$	1368.18	−	2369.75i	0.277042	−	0.479850i
$291$	−4199.57	−	4304.98i	−0.845989	−	0.867224i
$292$	97.1527	−	56.0911i	0.0194707	−	0.0112414i
$293$	1032.50	+	1788.34i	0.205867	+	0.356572i	0.950409	−	0.311004i	$-0.100665\pi$
$293$	1032.50	+	1788.34i	0.205867	+	0.356572i	−0.744542	+	0.667576i	$0.767332\pi$
$294$	−2850.24	+	2788.20i	−0.565406	+	0.553100i
$295$	−2026.40	+	3509.83i	−0.399938	+	0.692713i
$296$		−	7156.88i		−	1.40535i
$297$	−1091.29	−	4776.47i	−0.213209	−	0.933194i
$298$	−4741.73			−0.921748
$299$	773.756	−	1340.18i	0.149657	−	0.259214i
$300$	−1417.04	−	398.583i	−0.272710	−	0.0767074i
$301$	6226.46	−	1673.02i	1.19232	−	0.320370i
$302$	4424.50	−	2554.49i	0.843051	−	0.486736i
$303$	−578.629	+	564.461i	−0.109708	+	0.107021i
$304$	−2099.14	−	1211.94i	−0.396033	−	0.228650i
$305$			3702.24i			0.695049i
$306$	−1037.62	−	1904.74i	−0.193846	−	0.355839i
$307$		−	395.602i		−	0.0735446i	−0.999324	−	0.0367723i	$-0.988292\pi$
$307$		−	395.602i		−	0.0735446i	0.999324	−	0.0367723i	$-0.0117076\pi$
$308$	−1368.87	+	1370.78i	−0.253242	+	0.253595i
$309$	9539.79	−	2429.87i	1.75631	−	0.447347i
$310$	−897.569	−	1554.64i	−0.164447	−	0.284830i
$311$	−3155.13	−	5464.85i	−0.575277	−	0.996409i	−0.996011	−	0.0892250i	$-0.971561\pi$
$311$	−3155.13	−	5464.85i	−0.575277	−	0.996409i	0.420735	−	0.907184i	$-0.361772\pi$
$312$	843.438	+	3311.39i	0.153046	+	0.600866i
$313$	−8787.97	−	5073.73i	−1.58698	−	0.916244i	−0.993801	−	0.111175i	$-0.964539\pi$
$313$	−8787.97	−	5073.73i	−1.58698	−	0.916244i	−0.593180	−	0.805070i	$-0.702128\pi$
$314$	−8212.62			−1.47600
$315$	−1996.50	+	1902.54i	−0.357111	+	0.340305i
$316$	2563.87			0.456421
$317$	1537.07	+	887.426i	0.272335	+	0.157233i	0.629948	−	0.776637i	$-0.283076\pi$
$317$	1537.07	+	887.426i	0.272335	+	0.157233i	−0.357613	+	0.933870i	$0.616409\pi$
$318$	−1332.81	+	1300.17i	−0.235032	+	0.229277i
$319$	3872.58	+	6707.50i	0.679695	+	1.17727i
$320$	−1470.57	−	2547.11i	−0.256898	−	0.444961i
$321$	713.988	−	2538.37i	0.124146	−	0.441365i
$322$	−1697.00	−	1694.64i	−0.293696	−	0.293287i
$323$			2801.64i			0.482623i
$324$	1184.11	−	1834.53i	0.203036	−	0.314562i
$325$			2528.68i			0.431588i
$326$	329.026	+	189.963i	0.0558990	+	0.0322733i
$327$	1492.74	+	419.875i	0.252443	+	0.0710065i
$328$	2303.23	−	1329.77i	0.387728	−	0.223855i
$329$	−4490.95	+	1206.70i	−0.752566	+	0.202211i
$330$	1602.68	−	1563.43i	0.267347	−	0.260801i
$331$	−2397.72	+	4152.98i	−0.398160	+	0.689633i	−0.993499	−	0.113842i	$-0.963684\pi$
$331$	−2397.72	+	4152.98i	−0.398160	+	0.689633i	0.595339	+	0.803474i	$0.297018\pi$
$332$	−3690.83			−0.610122
$333$	6703.88	+	4095.32i	1.10321	+	0.673940i
$334$		−	976.796i		−	0.160024i
$335$	−1899.22	+	3289.54i	−0.309748	+	0.536498i
$336$	2989.55	+	34.9731i	0.485397	+	0.00567839i
$337$	−3694.91	−	6399.77i	−0.597253	−	1.03447i	−0.993225	−	0.116210i	$-0.962925\pi$
$337$	−3694.91	−	6399.77i	−0.597253	−	1.03447i	0.395971	−	0.918263i	$-0.370408\pi$
$338$	−2871.72	+	1657.99i	−0.462134	+	0.266813i
$339$	1256.91	−	320.146i	0.201374	−	0.0512918i
$340$	−296.591	+	513.710i	−0.0473085	+	0.0819407i
$341$	5081.08			0.806908
$342$	4138.40	−	2254.43i	0.654325	−	0.356450i
$343$	−4482.47	+	4501.23i	−0.705628	+	0.708582i
$344$	−7415.81	−	4281.52i	−1.16231	−	0.671058i
$345$	−1158.32	−	1187.39i	−0.180759	−	0.185296i
$346$	−3207.34	+	1851.76i	−0.498346	+	0.287720i
$347$	1565.28	−	903.715i	0.242157	−	0.139810i	−0.374010	−	0.927424i	$-0.622018\pi$
$347$	1565.28	−	903.715i	0.242157	−	0.139810i	0.616168	+	0.787615i	$0.288684\pi$
$348$	−934.599	+	3322.69i	−0.143965	+	0.511824i
$349$	5094.40	+	2941.25i	0.781367	+	0.451122i	0.836914	−	0.547334i	$-0.184357\pi$
$349$	5094.40	+	2941.25i	0.781367	+	0.451122i	−0.0555477	+	0.998456i	$0.517690\pi$
$350$	3785.99	+	1011.63i	0.578199	+	0.154497i
$351$	−3584.43	−	1104.79i	−0.545078	−	0.168004i
$352$	4444.98			0.673064
$353$	1196.54	−	2072.48i	0.180413	−	0.312484i	−0.761609	−	0.648037i	$-0.775590\pi$
$353$	1196.54	−	2072.48i	0.180413	−	0.312484i	0.942021	+	0.335554i	$0.108923\pi$
$354$	−2313.00	+	8223.19i	−0.347273	+	1.23463i
$355$	2757.80	−	1592.21i	0.412306	−	0.238045i
$356$	2254.83	+	3905.48i	0.335690	+	0.581432i
$357$	−1692.73	−	3012.73i	−0.250948	−	0.446641i
$358$	5084.23	−	8806.14i	0.750586	−	1.30005i
$359$		−	10728.4i		−	1.57723i	−0.614887	−	0.788615i	$-0.710798\pi$
$359$		−	10728.4i		−	1.57723i	0.614887	−	0.788615i	$-0.289202\pi$
$360$	3661.72	+	90.7857i	0.536082	+	0.0132912i
$361$	771.915			0.112540
$362$	77.7162	−	134.608i	0.0112836	−	0.0195438i
$363$	−142.866	−	560.901i	−0.0206571	−	0.0811011i
$364$	384.834	+	1432.23i	0.0554142	+	0.206234i
$365$	−178.892	+	103.283i	−0.0256538	+	0.0148112i
$366$	1926.09	+	7561.95i	0.275078	+	1.07997i
$367$	−4743.12	−	2738.44i	−0.674630	−	0.389498i	0.123199	−	0.992382i	$-0.460685\pi$
$367$	−4743.12	−	2738.44i	−0.674630	−	0.389498i	−0.797829	+	0.602884i	$0.794018\pi$
$368$			1798.29i			0.254735i
$369$	−72.3559	+	2918.38i	−0.0102078	+	0.411720i
$370$			3589.87i			0.504402i
$371$	−2096.13	+	2099.05i	−0.293331	+	0.293740i
$372$	1581.19	+	1620.88i	0.220379	+	0.225911i
$373$	−6052.38	−	10483.0i	−0.840162	−	1.45520i	−0.889757	−	0.456434i	$-0.849127\pi$
$373$	−6052.38	−	10483.0i	−0.840162	−	1.45520i	0.0495956	−	0.998769i	$-0.484207\pi$
$374$	1402.76	+	2429.64i	0.193943	+	0.335920i
$375$	6057.65	+	1703.88i	0.834175	+	0.234635i
$376$	5348.80	+	3088.13i	0.733625	+	0.423559i
$377$	5929.26			0.810007
$378$	−3088.11	+	4924.68i	−0.420199	+	0.670101i
$379$	2.33509			0.000316479			0.000158240	−	1.00000i	$-0.499950\pi$
$379$	2.33509			0.000316479			0.000158240		1.00000i	$0.499950\pi$
$380$	−1116.13	−	644.399i	−0.150675	−	0.0869920i
$381$	9715.19	+	2732.67i	1.30636	+	0.367451i
$382$	1571.36	+	2721.68i	0.210466	+	0.364537i
$383$	4098.57	+	7098.93i	0.546807	+	0.947097i	0.998491	+	0.0549191i	$0.0174901\pi$
$383$	4098.57	+	7098.93i	0.546807	+	0.947097i	−0.451684	+	0.892178i	$0.649177\pi$
$384$	−634.230	−	650.149i	−0.0842849	−	0.0864005i
$385$	2520.56	−	2524.07i	0.333662	−	0.334127i
$386$		−	5172.45i		−	0.682049i
$387$	8254.01	−	4496.45i	1.08417	−	0.590613i
$388$			3466.65i			0.453588i
$389$	−4487.63	−	2590.94i	−0.584915	−	0.337701i	0.178169	−	0.984000i	$-0.442983\pi$
$389$	−4487.63	−	2590.94i	−0.584915	−	0.337701i	−0.763084	+	0.646299i	$0.776316\pi$
$390$	−423.067	−	1660.98i	−0.0549303	−	0.215660i
$391$	1800.08	−	1039.28i	0.232823	−	0.134420i
$392$	8437.04	−	11.7468i	1.08708	−	0.00151353i
$393$	34.0241	+	133.580i	0.00436715	+	0.0171457i
$394$	−1741.31	+	3016.04i	−0.222655	+	0.385649i
$395$	−4720.97			−0.601362
$396$	−1472.29	+	2410.08i	−0.186832	+	0.305836i
$397$			6757.41i			0.854269i	0.904188	+	0.427135i	$0.140477\pi$
$397$			6757.41i			0.854269i	−0.904188	+	0.427135i	$0.859523\pi$
$398$	−1328.72	+	2301.41i	−0.167344	+	0.289848i
$399$	6545.73	−	3677.76i	0.821294	−	0.461450i
$400$	−1469.23	−	2544.78i	−0.183654	−	0.318098i
$401$	−7670.47	+	4428.55i	−0.955225	+	0.551499i	−0.894700	−	0.446667i	$-0.852611\pi$
$401$	−7670.47	+	4428.55i	−0.955225	+	0.551499i	−0.0605248	+	0.998167i	$0.519277\pi$
$402$	−2167.83	+	7707.07i	−0.268959	+	0.956203i
$403$	1944.90	−	3368.66i	0.240403	−	0.416389i
$404$	465.950			0.0573809
$405$	−2180.35	+	3378.00i	−0.267513	+	0.414455i
$406$	2372.07	−	8877.40i	0.289960	−	1.08517i
$407$	−8799.70	−	5080.51i	−1.07171	−	0.618750i
$408$	−1242.76	+	4418.26i	−0.150799	+	0.536119i
$409$	9564.59	−	5522.12i	1.15633	−	0.667607i	0.205907	−	0.978571i	$-0.433985\pi$
$409$	9564.59	−	5522.12i	1.15633	−	0.667607i	0.950421	+	0.310965i	$0.100652\pi$
$410$	−1155.30	+	667.011i	−0.139161	+	0.0803447i
$411$	−967.604	−	991.891i	−0.116127	−	0.119042i
$412$	−4914.28	−	2837.26i	−0.587643	−	0.339276i
$413$	−3513.27	+	13148.3i	−0.418588	+	1.56655i
$414$	−2983.64	−	1822.67i	−0.354198	−	0.216375i
$415$	6796.10			0.803873
$416$	1701.42	−	2946.94i	0.200526	−	0.347321i
$417$	−2586.27	+	658.745i	−0.303717	+	0.0773594i
$418$	−5278.86	+	3047.75i	−0.617697	+	0.356628i
$419$	−4827.28	−	8361.09i	−0.562835	−	0.974859i	−0.997247	−	0.0741448i	$-0.976377\pi$
$419$	−4827.28	−	8361.09i	−0.562835	−	0.974859i	0.434412	−	0.900714i	$-0.356956\pi$
$420$	1589.57	+	18.5955i	0.184674	+	0.00216040i
$421$	1311.18	−	2271.02i	0.151788	−	0.262905i	−0.780097	−	0.625659i	$-0.784830\pi$
$421$	1311.18	−	2271.02i	0.151788	−	0.262905i	0.931885	+	0.362754i	$0.118164\pi$
$422$		−	550.320i		−	0.0634814i
$423$	−5953.36	+	3243.15i	−0.684308	+	0.372783i
$424$	3939.91			0.451271
$425$	−1698.21	+	2941.38i	−0.193824	+	0.335713i
$426$	4804.53	−	4686.89i	0.546433	−	0.533053i
$427$	3226.10	+	12006.5i	0.365625	+	1.36074i
$428$	−1316.32	+	759.976i	−0.148660	+	0.0858290i
$429$	4670.23	+	1313.63i	0.525597	+	0.147839i
$430$	3719.75	+	2147.60i	0.417168	+	0.240852i
$431$		−	2142.38i		−	0.239431i	−0.992808	−	0.119716i	$-0.961802\pi$
$431$		−	2142.38i		−	0.239431i	0.992808	−	0.119716i	$-0.0381983\pi$
$432$	4249.16	−	970.817i	0.473236	−	0.108121i
$433$		−	8576.98i		−	0.951925i	−0.879466	−	0.475962i	$-0.842100\pi$
$433$		−	8576.98i		−	0.951925i	0.879466	−	0.475962i	$-0.157900\pi$
$434$	−4265.54	−	4259.61i	−0.471780	−	0.471124i
$435$	1720.92	−	6118.22i	0.189682	−	0.674359i
$436$	−446.919	−	774.086i	−0.0490907	−	0.0850276i
$437$	2258.02	+	3911.01i	0.247176	+	0.428121i
$438$	−311.659	+	304.028i	−0.0339992	+	0.0331667i
$439$	−6408.01	−	3699.67i	−0.696669	−	0.402222i	0.109437	−	0.993994i	$-0.465095\pi$
$439$	−6408.01	−	3699.67i	−0.696669	−	0.402222i	−0.806106	+	0.591772i	$0.798429\pi$
$440$	−4737.67			−0.513317
$441$	−4816.86	+	7909.74i	−0.520123	+	0.854092i
$442$	2147.75			0.231126
$443$	12279.2	+	7089.41i	1.31694	+	0.760334i	0.983235	−	0.182345i	$-0.0583687\pi$
$443$	12279.2	+	7089.41i	1.31694	+	0.760334i	0.333702	+	0.942679i	$0.391702\pi$
$444$	−1117.70	−	4388.15i	−0.119468	−	0.469037i
$445$	−4151.92	−	7191.33i	−0.442292	−	0.766072i
$446$	1228.84	+	2128.41i	0.130464	+	0.225971i
$447$	−10672.7	+	2718.43i	−1.12931	+	0.287645i
$448$	−6988.64	−	6978.92i	−0.737014	−	0.735989i
$449$			6800.58i			0.714787i	0.933954	+	0.357393i	$0.116334\pi$
$449$			6800.58i			0.714787i	−0.933954	+	0.357393i	$0.883666\pi$
$450$	5711.34	+	141.602i	0.598300	+	0.0148338i
$451$		−	3775.90i		−	0.394236i
$452$	−647.477	−	373.821i	−0.0673778	−	0.0389006i
$453$	8494.20	−	8286.21i	0.880998	−	0.859426i
$454$	−8338.50	+	4814.23i	−0.861994	+	0.497672i
$455$	−708.613	−	2637.23i	−0.0730116	−	0.271726i
$456$	−9599.50	−	2700.13i	−0.985829	−	0.277292i
$457$	1885.91	−	3266.49i	0.193040	−	0.334355i	−0.753216	−	0.657773i	$-0.771499\pi$
$457$	1885.91	−	3266.49i	0.193040	−	0.334355i	0.946256	+	0.323418i	$0.104832\pi$
$458$	−6397.41			−0.652688
$459$	−3427.47	−	3692.33i	−0.348542	−	0.375475i
$460$			956.166i			0.0969162i
$461$	7807.12	−	13522.3i	0.788750	−	1.36616i	−0.137983	−	0.990435i	$-0.544062\pi$
$461$	7807.12	−	13522.3i	0.788750	−	1.36616i	0.926733	−	0.375721i	$-0.122605\pi$
$462$	3835.18	−	6466.83i	0.386209	−	0.651221i
$463$	−4055.66	−	7024.62i	−0.407090	−	0.705101i	0.587472	−	0.809244i	$-0.300123\pi$
$463$	−4055.66	−	7024.62i	−0.407090	−	0.705101i	−0.994562	+	0.104144i	$0.966790\pi$
$464$	−5967.01	+	3445.06i	−0.597008	+	0.344683i
$465$	−2911.52	−	2984.61i	−0.290363	−	0.297651i
$466$	−2524.23	+	4372.09i	−0.250928	+	0.434620i
$467$	−6607.80			−0.654759			−0.327380	−	0.944893i	$-0.606166\pi$
$467$	−6607.80			−0.654759			−0.327380	+	0.944893i	$0.606166\pi$
$468$	1034.29	+	1898.61i	0.102158	+	0.187529i
$469$	−3292.76	+	12323.1i	−0.324191	+	1.21328i
$470$	−2682.94	−	1549.00i	−0.263309	−	0.152021i
$471$	−18485.0	+	4708.29i	−1.80837	+	0.460608i
$472$	15654.0	−	9037.84i	1.52655	−	0.881357i
$473$	−10528.6	+	6078.71i	−1.02348	+	0.590908i
$474$	−9642.74	+	2456.09i	−0.934400	+	0.238000i
$475$	−6390.70	−	3689.67i	−0.617317	−	0.356408i
$476$	−514.213	+	1924.43i	−0.0495145	+	0.185307i
$477$	−2254.50	+	3690.53i	−0.216408	+	0.354251i
$478$	3531.53			0.337925
$479$	−4138.13	+	7167.45i	−0.394731	+	0.683694i	−0.993067	−	0.117552i	$-0.962495\pi$
$479$	−4138.13	+	7167.45i	−0.394731	+	0.683694i	0.598336	+	0.801245i	$0.295829\pi$
$480$	−2547.03	−	2610.97i	−0.242199	−	0.248279i
$481$	−6736.57	+	3889.36i	−0.638588	+	0.368689i
$482$	1612.33	+	2792.64i	0.152364	+	0.263903i
$483$	−4791.15	−	2841.41i	−0.451356	−	0.267678i
$484$	−166.819	+	288.940i	−0.0156667	+	0.0271356i
$485$		−	6383.30i		−	0.597630i
$486$	−2696.04	+	8034.00i	−0.251635	+	0.749855i
$487$	229.243			0.0213306			0.0106653	−	0.999943i	$-0.496605\pi$
$487$	229.243			0.0213306			0.0106653	+	0.999943i	$0.496605\pi$
$488$	8256.08	−	14299.9i	0.765851	−	1.32649i
$489$	849.479	+	238.940i	0.0785578	+	0.0220966i
$490$	−4232.00	+	5.89216i	−0.390168	+	0.000543226i
$491$	17923.6	−	10348.2i	1.64742	−	0.951138i	0.669326	−	0.742969i	$-0.266583\pi$
$491$	17923.6	−	10348.2i	1.64742	−	0.951138i	0.978093	−	0.208169i	$-0.0667505\pi$
$492$	1204.53	−	1175.03i	0.110375	−	0.107672i
$493$	6896.96	+	3981.96i	0.630068	+	0.363770i
$494$			4666.38i			0.425001i
$495$	2711.00	−	4437.80i	0.246162	−	0.402958i
$496$			4520.14i			0.409195i
$497$	7556.19	−	7566.72i	0.681975	−	0.682925i
$498$	13881.2	−	3535.67i	1.24906	−	0.318147i
$499$	6552.36	+	11349.0i	0.587824	+	1.01814i	0.994517	+	0.104576i	$0.0333485\pi$
$499$	6552.36	+	11349.0i	0.587824	+	1.01814i	−0.406693	+	0.913565i	$0.633318\pi$
$500$	−1813.63	−	3141.30i	−0.162216	−	0.280966i
$501$	−559.997	−	2198.58i	−0.0499377	−	0.196058i
$502$	5688.08	+	3284.02i	0.505720	+	0.291978i
$503$	7415.97			0.657379			0.328690	−	0.944438i	$-0.393393\pi$
$503$	7415.97			0.657379			0.328690	+	0.944438i	$0.393393\pi$
$504$	11954.2	−	2896.36i	1.05651	−	0.255980i
$505$	−857.975			−0.0756028
$506$	3916.41	+	2261.14i	0.344082	+	0.198656i
$507$	−5513.17	+	5378.17i	−0.482936	+	0.471110i
$508$	−2908.68	−	5037.98i	−0.254039	−	0.440008i
$509$	10536.9	+	18250.5i	0.917565	+	1.58927i	0.803103	+	0.595841i	$0.203181\pi$
$509$	10536.9	+	18250.5i	0.917565	+	1.58927i	0.114462	+	0.993428i	$0.463486\pi$
$510$	623.366	−	2216.19i	0.0541237	−	0.192421i
$511$	−490.153	+	490.836i	−0.0424327	+	0.0424918i
$512$			10067.8i			0.869021i
$513$	8022.27	−	7446.83i	0.690433	−	0.640908i
$514$		−	16277.7i		−	1.39684i
$515$	9048.89	+	5224.38i	0.774255	+	0.447017i
$516$	−5215.56	−	1467.02i	−0.444966	−	0.125159i
$517$	7593.98	−	4384.39i	0.646002	−	0.372969i
$518$	3128.18	+	11642.1i	0.265336	+	0.987499i
$519$	−6157.48	+	6006.71i	−0.520777	+	0.508026i
$520$	−1813.45	+	3140.99i	−0.152933	+	0.264887i
$521$	−19991.7			−1.68110			−0.840548	−	0.541736i	$-0.817767\pi$
$521$	−19991.7			−1.68110			−0.840548	+	0.541736i	$0.817767\pi$
$522$	332.030	−	13392.0i	0.0278401	−	1.12289i
$523$			3604.15i			0.301336i	0.988584	+	0.150668i	$0.0481424\pi$
$523$			3604.15i			0.301336i	−0.988584	+	0.150668i	$0.951858\pi$
$524$	39.7286	−	68.8119i	0.00331212	−	0.00573676i
$525$	9101.49	+	106.473i	0.756613	+	0.00885119i
$526$	7531.01	+	13044.1i	0.624273	+	1.08127i
$527$	4524.64	−	2612.30i	0.373997	−	0.215927i
$528$	−5463.22	+	1391.53i	−0.450296	+	0.114694i
$529$	−4408.26	+	7635.34i	−0.362313	+	0.627545i
$530$	−1976.25			−0.161967
$531$	−491.769	+	19834.8i	−0.0401901	+	1.62101i
$532$	−4181.18	−	1117.22i	−0.340746	−	0.0910485i
$533$	−2503.35	−	1445.31i	−0.203438	−	0.117455i
$534$	−12221.7	−	12528.5i	−0.990423	−	1.01528i
$535$	2423.80	−	1399.38i	0.195869	−	0.113085i
$536$	14671.5	−	8470.59i	1.18230	−	0.682601i
$537$	6395.05	−	22735.7i	0.513905	−	1.82703i
$538$	14533.3	+	8390.80i	1.16464	+	0.672404i
$539$	5974.83	−	10382.1i	0.477466	−	0.829660i
$540$	2259.31	−	516.191i	0.180047	−	0.0411358i
$541$	−13211.0			−1.04988			−0.524939	−	0.851140i	$-0.675912\pi$
$541$	−13211.0			−1.04988			−0.524939	+	0.851140i	$0.675912\pi$
$542$	5169.93	−	8954.58i	0.409719	−	0.709654i
$543$	97.7531	−	347.532i	0.00772557	−	0.0274660i
$544$	3958.20	−	2285.27i	0.311961	−	0.180111i
$545$	822.933	+	1425.36i	0.0646799	+	0.112029i
$546$	−2819.39	−	5017.98i	−0.220986	−	0.393314i
$547$	−8858.54	+	15343.4i	−0.692439	+	1.19934i	0.278598	+	0.960408i	$0.410130\pi$
$547$	−8858.54	+	15343.4i	−0.692439	+	1.19934i	−0.971037	+	0.238931i	$0.923203\pi$
$548$			798.735i			0.0622633i
$549$	8670.52	+	15916.3i	0.674042	+	1.23732i
$550$	−7389.55			−0.572893
$551$	−8651.56	+	14984.9i	−0.668909	+	1.15858i
$552$	1826.10	+	7169.39i	0.140805	+	0.552807i
$553$	−15310.3	+	4113.80i	−1.17732	+	0.316341i
$554$	3806.52	−	2197.70i	0.291920	−	0.168540i
$555$	2058.07	+	8080.11i	0.157406	+	0.617984i
$556$	1332.28	+	769.190i	0.101621	+	0.0586707i
$557$		−	13013.3i		−	0.989933i	−0.868912	−	0.494966i	$-0.835180\pi$
$557$		−	13013.3i		−	0.989933i	0.868912	−	0.494966i	$-0.164820\pi$
$558$	−7499.62	−	4581.43i	−0.568968	−	0.347576i
$559$			9307.05i			0.704198i
$560$	2245.43	+	2242.30i	0.169440	+	0.169205i
$561$	4550.24	+	4664.46i	0.342445	+	0.351040i
$562$	2198.63	+	3808.14i	0.165024	+	0.285831i
$563$	−7866.96	−	13626.0i	−0.588904	−	1.02001i	−0.994376	−	0.105904i	$-0.966226\pi$
$563$	−7866.96	−	13626.0i	−0.588904	−	1.02001i	0.405473	−	0.914107i	$-0.367107\pi$
$564$	3761.82	+	1058.12i	0.280854	+	0.0789979i
$565$	1192.23	+	688.335i	0.0887744	+	0.0512539i
$566$	−11937.8			−0.886544
$567$	−4127.41	+	12854.9i	−0.305706	+	0.952126i
$568$	−14202.7			−1.04917
$569$	5395.51	+	3115.10i	0.397524	+	0.229511i	0.685415	−	0.728152i	$-0.259621\pi$
$569$	5395.51	+	3115.10i	0.397524	+	0.229511i	−0.287891	+	0.957663i	$0.592954\pi$
$570$	4815.09	+	1354.38i	0.353828	+	0.0995241i
$571$	1182.19	+	2047.62i	0.0866432	+	0.150070i	0.906090	−	0.423084i	$-0.139053\pi$
$571$	1182.19	+	2047.62i	0.0866432	+	0.150070i	−0.819447	+	0.573155i	$0.805719\pi$
$572$	−1398.25	−	2421.83i	−0.102209	−	0.177031i
$573$	5097.17	+	5225.11i	0.371618	+	0.380946i
$574$	−3165.45	+	3169.86i	−0.230180	+	0.230500i
$575$			5474.78i			0.397068i
$576$	−12287.3	−	7506.19i	−0.888841	−	0.542983i
$577$			4194.43i			0.302628i	0.988486	+	0.151314i	$0.0483505\pi$
$577$			4194.43i			0.302628i	−0.988486	+	0.151314i	$0.951650\pi$
$578$	−7020.30	−	4053.17i	−0.505201	−	0.291678i
$579$	−2965.36	−	11642.2i	−0.212843	−	0.835635i
$580$	−3172.71	+	1831.77i	−0.227137	+	0.131138i
$581$	22040.0	−	5922.04i	1.57379	−	0.422871i
$582$	−3320.91	−	13038.1i	−0.236523	−	0.928602i
$583$	2796.85	−	4844.29i	0.198686	−	0.344134i
$584$	921.295			0.0652799
$585$	−1904.48	−	3496.01i	−0.134599	−	0.247081i
$586$			4619.69i			0.325662i
$587$	6703.36	−	11610.6i	0.471341	−	0.816387i	−0.528121	−	0.849169i	$-0.677103\pi$
$587$	6703.36	−	11610.6i	0.471341	−	0.816387i	0.999463	+	0.0327817i	$0.0104366\pi$
$588$	5171.23	−	1324.83i	0.362684	−	0.0929166i
$589$	5675.71	+	9830.62i	0.397052	+	0.687714i
$590$	−7852.01	+	4533.36i	−0.547902	+	0.316332i
$591$	−2190.26	+	7786.80i	−0.152445	+	0.541973i
$592$	4519.64	−	7828.24i	0.313777	−	0.543478i
$593$	4672.62			0.323577			0.161789	−	0.986825i	$-0.448274\pi$
$593$	4672.62			0.323577			0.161789	+	0.986825i	$0.448274\pi$
$594$	3228.53	−	10474.7i	0.223010	−	0.723542i
$595$	946.845	−	3543.54i	0.0652384	−	0.244153i
$596$	5497.87	+	3174.20i	0.377855	+	0.218155i
$597$	−1671.29	+	5941.79i	−0.114575	+	0.407339i
$598$	2998.19	−	1731.01i	0.205025	−	0.118371i
$599$	5611.71	−	3239.92i	0.382785	−	0.221001i	−0.296244	−	0.955112i	$-0.595734\pi$
$599$	5611.71	−	3239.92i	0.382785	−	0.221001i	0.679029	+	0.734111i	$0.262401\pi$
$600$	−8441.64	−	8653.53i	−0.574381	−	0.588798i
$601$	−2243.61	−	1295.35i	−0.152277	−	0.0879174i	0.421925	−	0.906631i	$-0.361354\pi$
$601$	−2243.61	−	1295.35i	−0.152277	−	0.0879174i	−0.574203	+	0.818713i	$0.694688\pi$
$602$	13934.7	+	3723.39i	0.943415	+	0.252083i
$603$	−460.904	+	18589.9i	−0.0311268	+	1.25546i
$604$	−6840.08			−0.460793
$605$	307.172	−	532.038i	0.0206419	−	0.0357528i
$606$	−1752.44	+	446.362i	−0.117472	+	0.0299211i
$607$	−1869.60	+	1079.41i	−0.125016	+	0.0721781i	−0.561204	−	0.827678i	$-0.689662\pi$
$607$	−1869.60	+	1079.41i	−0.125016	+	0.0721781i	0.436188	+	0.899856i	$0.356328\pi$
$608$	4965.18	+	8599.94i	0.331192	+	0.573641i
$609$	249.659	−	21341.2i	0.0166120	−	1.42002i
$610$	−4141.23	+	7172.82i	−0.274875	+	0.476097i
$611$		−	6712.89i		−	0.444476i
$612$	−71.9768	+	2903.09i	−0.00475407	+	0.191749i
$613$	6333.20			0.417285			0.208642	−	0.977992i	$-0.433096\pi$
$613$	6333.20			0.417285			0.208642	+	0.977992i	$0.433096\pi$
$614$	442.510	−	766.449i	0.0290851	−	0.0503768i
$615$	−2217.95	+	2163.64i	−0.145425	+	0.141864i
$616$	−15364.4	+	4128.35i	−1.00495	+	0.270026i
$617$	1802.84	−	1040.87i	0.117633	−	0.0679157i	−0.440029	−	0.897984i	$-0.645032\pi$
$617$	1802.84	−	1040.87i	0.117633	−	0.0679157i	0.557662	+	0.830068i	$0.311698\pi$
$618$	21200.6	+	5963.27i	1.37996	+	0.388152i
$619$	20384.1	+	11768.8i	1.32360	+	0.764179i	0.984301	−	0.176501i	$-0.0564778\pi$
$619$	20384.1	+	11768.8i	1.32360	+	0.764179i	0.339296	+	0.940680i	$0.389811\pi$
$620$			2403.40i			0.155682i
$621$	−7760.54	−	2391.96i	−0.501481	−	0.154567i
$622$		−	14117.0i		−	0.910031i
$623$	−19731.3	−	19703.8i	−1.26889	−	1.26712i
$624$	−1168.61	+	4154.66i	−0.0749711	+	0.266537i
$625$	−2571.92	−	4454.69i	−0.164603	−	0.285100i
$626$	−11350.7	−	19660.0i	−0.724704	−	1.25522i
$627$	−10134.4	+	9886.25i	−0.645501	+	0.629695i
$628$	9522.27	+	5497.68i	0.605063	+	0.349333i
$629$	−10448.0			−0.662306
$630$	−5996.20	+	1452.81i	−0.379197	+	0.0918750i
$631$	13465.2			0.849510			0.424755	−	0.905308i	$-0.360360\pi$
$631$	13465.2			0.849510			0.424755	+	0.905308i	$0.360360\pi$
$632$	18234.8	+	10527.9i	1.14769	+	0.662620i
$633$	−315.498	−	1238.66i	−0.0198103	−	0.0777763i
$634$	1985.30	+	3438.64i	0.124363	+	0.215404i
$635$	5355.89	+	9276.67i	0.334712	+	0.579738i
$636$	2415.70	−	615.300i	0.150611	−	0.0383620i
$637$	−4596.11	−	7935.17i	−0.285879	−	0.493568i
$638$			17327.0i			1.07521i
$639$	8127.08	−	13303.7i	0.503133	−	0.823610i
$640$		−	964.023i		−	0.0595412i
$641$	−2697.97	−	1557.67i	−0.166246	−	0.0959819i	0.414569	−	0.910018i	$-0.363932\pi$
$641$	−2697.97	−	1557.67i	−0.166246	−	0.0959819i	−0.580814	+	0.814036i	$0.697266\pi$
$642$	4222.65	−	4119.26i	0.259587	−	0.253231i
$643$	138.508	−	79.9675i	0.00849489	−	0.00490452i	−0.495747	−	0.868467i	$-0.665106\pi$
$643$	138.508	−	79.9675i	0.00849489	−	0.00490452i	0.504241	+	0.863563i	$0.331772\pi$
$644$	833.192	+	3100.88i	0.0509820	+	0.189739i
$645$	9603.66	+	2701.30i	0.586269	+	0.164905i
$646$	−3133.84	+	5427.97i	−0.190866	+	0.330589i
$647$	−11705.0			−0.711239			−0.355619	−	0.934631i	$-0.615730\pi$
$647$	−11705.0			−0.711239			−0.355619	+	0.934631i	$0.615730\pi$
$648$	15954.6	−	8185.31i	0.967218	−	0.496218i
$649$		−	25663.1i		−	1.55218i
$650$	−2828.52	+	4899.13i	−0.170682	+	0.295631i
$651$	−12042.9	−	7142.11i	−0.725038	−	0.429987i
$652$	−254.330	−	440.512i	−0.0152766	−	0.0264598i
$653$	−23280.1	+	13440.8i	−1.39513	+	0.805479i	−0.993878	−	0.110487i	$-0.964759\pi$
$653$	−23280.1	+	13440.8i	−1.39513	+	0.805479i	−0.401254	+	0.915967i	$0.631425\pi$
$654$	2422.41	+	2483.22i	0.144838	+	0.148473i
$655$	−73.1541	+	126.707i	−0.00436392	+	0.00755853i
$656$	3359.06			0.199923
$657$	−527.185	+	862.981i	−0.0313051	+	0.0512452i
$658$	−10050.7	−	2685.57i	−0.595465	−	0.159110i
$659$	−7188.85	−	4150.48i	−0.424943	−	0.245341i	0.272247	−	0.962227i	$-0.412233\pi$
$659$	−7188.85	−	4150.48i	−0.424943	−	0.245341i	−0.697190	+	0.716886i	$0.745567\pi$
$660$	−2904.84	+	739.888i	−0.171319	+	0.0436365i
$661$	1248.35	−	720.734i	0.0734571	−	0.0424105i	−0.462822	−	0.886451i	$-0.653163\pi$
$661$	1248.35	−	720.734i	0.0734571	−	0.0424105i	0.536279	+	0.844041i	$0.319830\pi$
$662$	−9290.83	+	5364.06i	−0.545466	+	0.314925i
$663$	4834.16	−	1231.30i	0.283172	−	0.0721264i
$664$	−26250.0	−	15155.4i	−1.53418	−	0.885760i
$665$	7699.00	+	2057.20i	0.448954	+	0.119962i
$666$	8407.36	+	15433.2i	0.489157	+	0.897932i
$667$	12837.3			0.745219
$668$	−653.886	+	1132.56i	−0.0378736	+	0.0655991i
$669$	3986.08	+	4086.13i	0.230360	+	0.236142i
$670$	−7359.19	+	4248.83i	−0.424344	+	0.244995i
$671$	−11721.6	−	20302.4i	−0.674378	−	1.16806i
$672$	−10535.3	−	6248.00i	−0.604773	−	0.358663i
$673$	8012.16	−	13877.5i	0.458909	−	0.794854i	−0.539994	−	0.841669i	$-0.681574\pi$
$673$	8012.16	−	13877.5i	0.458909	−	0.794854i	0.998904	+	0.0468146i	$0.0149070\pi$
$674$		−	16532.1i		−	0.944796i
$675$	12936.3	−	2955.59i	0.737657	−	0.168534i
$676$	4439.56			0.252592
$677$	−13755.2	+	23824.7i	−0.780880	+	1.35252i	0.150549	+	0.988602i	$0.451896\pi$
$677$	−13755.2	+	23824.7i	−0.780880	+	1.35252i	−0.931430	+	0.363922i	$0.881438\pi$
$678$	2793.28	+	785.687i	0.158223	+	0.0445046i
$679$	−5562.34	−	20701.3i	−0.314378	−	1.17002i
$680$	−4218.83	+	2435.75i	−0.237919	+	0.137363i
$681$	−16008.3	+	15616.4i	−0.900794	+	0.878737i
$682$	9844.21	+	5683.56i	0.552719	+	0.319112i
$683$			2208.68i			0.123738i	0.998084	+	0.0618688i	$0.0197060\pi$
$683$			2208.68i			0.123738i	−0.998084	+	0.0618688i	$0.980294\pi$
$684$	−6307.50	−	156.383i	−0.352592	−	0.00874190i
$685$		−	1470.75i		−	0.0820357i
$686$	−13719.4	+	3706.83i	−0.763571	+	0.206308i
$687$	−14399.3	+	3667.63i	−0.799662	+	0.203681i
$688$	−5407.64	−	9366.31i	−0.299658	−	0.519022i
$689$	−2141.12	−	3708.52i	−0.118389	−	0.205056i
$690$	−915.970	−	3596.15i	−0.0505368	−	0.198410i
$691$	−20410.4	−	11784.0i	−1.12366	−	0.648746i	−0.181328	−	0.983423i	$-0.558040\pi$
$691$	−20410.4	−	11784.0i	−1.12366	−	0.648746i	−0.942333	+	0.334676i	$0.891373\pi$
$692$	4958.40			0.272385
$693$	4924.81	−	16754.3i	0.269954	−	0.918387i
$694$	4043.48			0.221165
$695$	−2453.18	−	1416.35i	−0.133891	−	0.0773022i
$696$	−20290.8	+	19794.0i	−1.10506	+	1.07800i
$697$	−1941.28	−	3362.40i	−0.105497	−	0.182726i
$698$	6580.02	+	11396.9i	0.356816	+	0.618023i
$699$	−3175.03	+	11287.9i	−0.171803	+	0.610795i
$700$	−3712.53	−	3707.36i	−0.200458	−	0.200179i
$701$			18383.9i			0.990516i	0.868746	+	0.495258i	$0.164926\pi$
$701$			18383.9i			0.990516i	−0.868746	+	0.495258i	$0.835074\pi$
$702$	−5708.77	−	6149.90i	−0.306928	−	0.330645i
$703$		−	22700.3i		−	1.21786i
$704$	16128.7	+	9311.91i	0.863456	+	0.498517i
$705$	−6926.82	−	1948.36i	−0.370042	−	0.104085i
$706$	4636.43	−	2676.85i	0.247159	−	0.142697i
$707$	−2782.45	+	747.630i	−0.148012	+	0.0397702i
$708$	8186.60	−	7986.15i	0.434564	−	0.423923i
$709$	11608.4	−	20106.3i	0.614895	−	1.06503i	−0.375508	−	0.926819i	$-0.622532\pi$
$709$	11608.4	−	20106.3i	0.614895	−	1.06503i	0.990403	−	0.138211i	$-0.0441351\pi$
$710$	7124.03			0.376564
$711$	−20295.8	+	11056.3i	−1.07054	+	0.583186i
$712$			37035.5i			1.94939i
$713$	4210.84	−	7293.39i	0.221174	−	0.383085i
$714$	90.4335	−	7730.38i	0.00474004	−	0.405185i
$715$	2574.65	+	4459.43i	0.134667	+	0.233249i
$716$	−11790.0	+	6806.95i	−0.615381	+	0.355290i
$717$	7948.77	−	2024.62i	0.414020	−	0.105454i
$718$	12000.6	−	20785.6i	0.623756	−	1.08038i
$719$	24589.3			1.27542			0.637709	−	0.770278i	$-0.279882\pi$
$719$	24589.3			1.27542			0.637709	+	0.770278i	$0.279882\pi$
$720$	3947.88	+	2411.71i	0.204346	+	0.124832i
$721$	33898.3	+	9057.74i	1.75096	+	0.467861i
$722$	1495.53	+	863.443i	0.0770883	+	0.0445070i
$723$	5230.05	+	5361.33i	0.269029	+	0.275781i
$724$	−180.219	+	104.049i	−0.00925107	+	0.00534111i
$725$	−18166.2	+	10488.3i	−0.930586	+	0.537274i
$726$	350.616	−	1246.51i	0.0179237	−	0.0637223i
$727$	14219.3	+	8209.54i	0.725400	+	0.418810i	0.816737	−	0.577010i	$-0.195781\pi$
$727$	14219.3	+	8209.54i	0.725400	+	0.418810i	−0.0913367	+	0.995820i	$0.529114\pi$
$728$	−3144.06	+	11766.6i	−0.160064	+	0.599035i
$729$	−1462.36	+	19628.6i	−0.0742958	+	0.997236i
$730$	−462.119			−0.0234299
$731$	−6250.41	+	10826.0i	−0.316252	+	0.547764i
$732$	2828.87	−	10057.2i	0.142839	−	0.507821i
$733$	1654.43	−	955.186i	0.0833667	−	0.0481318i	−0.457737	−	0.889088i	$-0.651340\pi$
$733$	1654.43	−	955.186i	0.0833667	−	0.0481318i	0.541104	+	0.840956i	$0.318007\pi$
$734$	−6126.30	−	10611.1i	−0.308073	−	0.533599i
$735$	−9522.03	+	2439.47i	−0.477858	+	0.122423i
$736$	3683.69	−	6380.34i	0.184487	−	0.319541i
$737$		−	24052.3i		−	1.20214i
$738$	−3404.60	+	5573.20i	−0.169817	+	0.277984i
$739$	10538.9			0.524601			0.262300	−	0.964986i	$-0.415519\pi$
$739$	10538.9			0.524601			0.262300	+	0.964986i	$0.415519\pi$
$740$	2403.13	−	4162.34i	0.119379	−	0.206771i
$741$	2675.23	+	10503.1i	0.132628	+	0.520704i
$742$	−6409.05	+	1722.08i	−0.317094	+	0.0852016i
$743$	−9283.92	+	5360.07i	−0.458404	+	0.264660i	−0.711373	−	0.702815i	$-0.751926\pi$
$743$	−9283.92	+	5360.07i	−0.458404	+	0.264660i	0.252969	+	0.967474i	$0.418593\pi$
$744$	4590.06	+	18020.8i	0.226182	+	0.888004i
$745$	−10123.5	−	5844.80i	−0.497847	−	0.287432i
$746$		−	27080.1i		−	1.32905i
$747$	29217.0	−	15916.2i	1.43105	−	0.779577i
$748$		−	3756.12i		−	0.183606i
$749$	6641.05	−	6650.31i	0.323977	−	0.324428i
$750$	9830.33	+	10077.1i	0.478604	+	0.490617i
$751$	16974.5	+	29400.7i	0.824779	+	1.42856i	0.902088	+	0.431552i	$0.142034\pi$
$751$	16974.5	+	29400.7i	0.824779	+	1.42856i	−0.0773094	+	0.997007i	$0.524633\pi$
$752$	3900.37	+	6755.63i	0.189138	+	0.327597i
$753$	14685.5	+	4130.71i	0.710716	+	0.199909i
$754$	11487.5	+	6632.32i	0.554841	+	0.320338i
$755$	12595.0			0.607123
$756$	6877.24	−	3642.77i	0.330850	−	0.175246i
$757$	−4201.14			−0.201708			−0.100854	−	0.994901i	$-0.532158\pi$
$757$	−4201.14			−0.201708			−0.100854	+	0.994901i	$0.532158\pi$
$758$	4.52407	+	2.61197i	0.000216783	+	0.000125160i
$759$	10111.4	+	2844.11i	0.483557	+	0.136014i
$760$	−5292.11	−	9166.21i	−0.252586	−	0.437491i
$761$	1844.61	+	3194.96i	0.0878674	+	0.152191i	0.906609	−	0.421971i	$-0.138661\pi$
$761$	1844.61	+	3194.96i	0.0878674	+	0.152191i	−0.818742	+	0.574161i	$0.805328\pi$
$762$	15765.8	+	16161.5i	0.749519	+	0.768332i
$763$	3910.85	+	3905.41i	0.185560	+	0.185302i
$764$		−	4207.60i		−	0.199248i
$765$	132.534	−	5345.59i	0.00626377	−	0.252641i
$766$			18338.2i			0.864994i
$767$	−17014.1	−	9823.11i	−0.800971	−	0.462441i
$768$	4970.19	+	19513.3i	0.233524	+	0.916828i
$769$	2527.18	−	1459.07i	0.118508	−	0.0684204i	−0.439574	−	0.898206i	$-0.644871\pi$
$769$	2527.18	−	1459.07i	0.118508	−	0.0684204i	0.558082	+	0.829786i	$0.311537\pi$
$770$	7706.77	−	2070.77i	0.360692	−	0.0969162i
$771$	−9331.97	−	36637.8i	−0.435905	−	1.71139i
$772$	−3462.54	+	5997.29i	−0.161424	+	0.279595i
$773$	−6902.85			−0.321188			−0.160594	−	0.987021i	$-0.551341\pi$
$773$	−6902.85			−0.321188			−0.160594	+	0.987021i	$0.551341\pi$
$774$	21021.1	+	521.181i	0.976213	+	0.0242034i
$775$			13761.3i			0.637832i
$776$	−14234.9	+	24655.5i	−0.658509	+	1.14057i
$777$	13715.3	+	24410.7i	0.633249	+	1.12706i
$778$	−5796.31	−	10039.5i	−0.267105	−	0.462639i
$779$	7305.44	−	4217.80i	0.336001	−	0.193990i
$780$	−621.362	+	2209.07i	−0.0285235	+	0.101407i
$781$	−10082.2	+	17462.8i	−0.461931	+	0.800088i
$782$	4650.02			0.212640
$783$	−6930.27	−	30333.1i	−0.316306	−	1.38444i
$784$	9235.92	+	5315.23i	0.420732	+	0.242130i
$785$	−17533.8	−	10123.1i	−0.797208	−	0.460268i
$786$	−83.5004	+	296.861i	−0.00378926	+	0.0134716i
$787$	29189.2	−	16852.4i	1.32209	−	0.763308i	0.338026	−	0.941137i	$-0.390241\pi$
$787$	29189.2	−	16852.4i	1.32209	−	0.763308i	0.984061	+	0.177829i	$0.0569073\pi$
$788$	4037.98	−	2331.33i	0.182547	−	0.105394i
$789$	24429.0	+	25042.2i	1.10228	+	1.12994i
$790$	−9146.53	−	5280.75i	−0.411923	−	0.237824i
$791$	4466.25	+	1193.40i	0.200761	+	0.0536439i
$792$	−20367.6	+	11095.4i	−0.913803	+	0.497802i
$793$	−17946.8			−0.803671
$794$	−7558.66	+	13092.0i	−0.337842	+	0.585160i
$795$	−4448.15	+	1132.98i	−0.198440	+	0.0505443i
$796$	3081.22	−	1778.94i	0.137200	−	0.0792122i
$797$	2571.40	+	4453.80i	0.114283	+	0.197944i	0.917493	−	0.397752i	$-0.130210\pi$
$797$	2571.40	+	4453.80i	0.114283	+	0.197944i	−0.803210	+	0.595696i	$0.796876\pi$
$798$	16795.7	+	196.484i	0.745065	+	0.00871610i
$799$	4508.23	−	7808.49i	0.199612	−	0.345738i
$800$			12038.5i			0.532033i
$801$	−34691.3	−	21192.5i	−1.53028	−	0.934831i
$802$	−19814.6			−0.872418
$803$	654.007	−	1132.77i	0.0287415	−	0.0497817i
$804$	7672.78	−	7484.91i	0.336565	−	0.328324i
$805$	−1534.20	−	5709.80i	−0.0671718	−	0.249992i
$806$	7536.19	−	4351.02i	0.329344	−	0.190147i
$807$	37522.1	+	10554.1i	1.63673	+	0.460375i
$808$	3313.94	+	1913.30i	0.144287	+	0.0833041i
$809$			4644.84i			0.201859i	0.994894	+	0.100930i	$0.0321817\pi$
$809$			4644.84i			0.201859i	−0.994894	+	0.100930i	$0.967818\pi$
$810$	−8002.81	+	4105.74i	−0.347148	+	0.178100i
$811$			8124.92i			0.351794i	0.984409	+	0.175897i	$0.0562825\pi$
$811$			8124.92i			0.351794i	−0.984409	+	0.175897i	$0.943717\pi$
$812$	−8693.04	+	8705.15i	−0.375697	+	0.376220i
$813$	6502.85	−	23118.9i	0.280523	−	0.997314i
$814$	−11365.8	−	19686.2i	−0.489401	−	0.847668i
$815$	468.310	+	811.136i	0.0201278	+	0.0348624i
$816$	−4149.52	+	4047.91i	−0.178017	+	0.173658i
$817$	−23521.6	−	13580.2i	−1.00724	−	0.581531i
$818$	24707.6			1.05609
$819$	−9222.69	−	9678.14i	−0.393488	−	0.412920i
$820$	1786.04			0.0760624
$821$	2253.56	+	1301.09i	0.0957976	+	0.0553088i	0.547133	−	0.837045i	$-0.315719\pi$
$821$	2253.56	+	1301.09i	0.0957976	+	0.0553088i	−0.451336	+	0.892354i	$0.649052\pi$
$822$	−765.158	−	3004.05i	−0.0324671	−	0.127468i
$823$	−9500.29	−	16455.0i	−0.402381	−	0.696944i	0.591632	−	0.806208i	$-0.298484\pi$
$823$	−9500.29	−	16455.0i	−0.402381	−	0.696944i	−0.994013	+	0.109264i	$0.965150\pi$
$824$	−23300.9	−	40358.4i	−0.985105	−	1.70625i
$825$	−16632.4	+	4236.42i	−0.701899	+	0.178780i
$826$	−21514.0	+	21544.0i	−0.906258	+	0.907521i
$827$		−	20997.3i		−	0.882886i	−0.897289	−	0.441443i	$-0.854467\pi$
$827$		−	20997.3i		−	0.882886i	0.897289	−	0.441443i	$-0.145533\pi$
$828$	2239.31	+	4110.63i	0.0939870	+	0.172529i
$829$		−	5441.05i		−	0.227956i	−0.993483	−	0.113978i	$-0.963641\pi$
$829$		−	5441.05i		−	0.227956i	0.993483	−	0.113978i	$-0.0363594\pi$
$830$	13166.9	+	7601.93i	0.550640	+	0.317912i
$831$	7307.80	−	7128.86i	0.305060	−	0.297590i
$832$	12347.2	−	7128.69i	0.514500	−	0.297047i
$833$	−17.1486	−	12316.9i	−0.000713284	−	0.512311i
$834$	−5747.56	−	1616.66i	−0.238635	−	0.0671228i
$835$	1204.03	−	2085.44i	0.0499008	−	0.0864307i
$836$	8160.88			0.337620
$837$	−19506.7	−	6012.38i	−0.805557	−	0.248289i
$838$		−	21598.6i		−	0.890350i
$839$	−15441.7	+	26745.7i	−0.635406	+	1.10055i	0.351024	+	0.936367i	$0.385834\pi$
$839$	−15441.7	+	26745.7i	−0.635406	+	1.10055i	−0.986429	+	0.164188i	$0.947500\pi$
$840$	11229.0	+	6659.41i	0.461235	+	0.273537i
$841$	12398.4	+	21474.6i	0.508360	+	0.880505i
$842$	5080.61	−	2933.29i	0.207945	−	0.120057i
$843$	7131.90	+	7310.91i	0.291383	+	0.298697i
$844$	−368.394	+	638.078i	−0.0150245	+	0.0260232i
$845$	−8174.77			−0.332805
$846$	−15161.9	−	375.912i	−0.616166	−	0.0152767i
$847$	532.559	−	1993.09i	0.0216044	−	0.0808539i
$848$	4309.50	+	2488.09i	0.174515	+	0.100756i
$849$	−26869.7	+	6843.94i	−1.08618	+	0.276659i
$850$	−6580.30	+	3799.14i	−0.265532	+	0.153305i
$851$	−14585.1	+	8420.74i	−0.587511	+	0.339200i
$852$	−8708.19	+	2218.05i	−0.350162	+	0.0891892i
$853$	6988.53	+	4034.83i	0.280519	+	0.161958i	0.633658	−	0.773613i	$-0.281552\pi$
$853$	6988.53	+	4034.83i	0.280519	+	0.161958i	−0.353139	+	0.935571i	$0.614886\pi$
$854$	−7179.85	+	26870.4i	−0.287692	+	1.07668i
$855$	11614.3	+	287.955i	0.464562	+	0.0115180i
$856$	−12482.6			−0.498418
$857$	14248.6	−	24679.3i	0.567938	−	0.983697i	−0.428832	−	0.903384i	$-0.641075\pi$
$857$	14248.6	−	24679.3i	0.567938	−	0.983697i	0.996770	−	0.0803127i	$-0.0255919\pi$
$858$	7578.84	+	7769.07i	0.301558	+	0.309128i
$859$	−31536.5	+	18207.6i	−1.25263	+	0.723208i	−0.971632	−	0.236500i	$-0.924000\pi$
$859$	−31536.5	+	18207.6i	−1.25263	+	0.723208i	−0.281001	+	0.959707i	$0.590666\pi$
$860$	−2875.29	−	4980.14i	−0.114008	−	0.197467i
$861$	−5307.52	+	8949.47i	−0.210081	+	0.354236i
$862$	2396.41	−	4150.71i	0.0946892	−	0.164006i
$863$			784.791i			0.0309555i	0.999880	+	0.0154778i	$0.00492692\pi$
$863$			784.791i			0.0309555i	−0.999880	+	0.0154778i	$0.995073\pi$
$864$	−17064.7	−	5259.69i	−0.671936	−	0.207105i
$865$	−9130.14			−0.358883
$866$	9593.98	−	16617.3i	0.376463	−	0.652053i
$867$	−18125.0	−	5098.17i	−0.709985	−	0.199703i
$868$	2094.30	+	7794.31i	0.0818952	+	0.304788i
$869$	25888.9	−	14947.0i	1.01061	−	0.583477i
$870$	10177.8	−	9928.62i	0.396622	−	0.386910i
$871$	−15946.3	−	9206.58i	−0.620343	−	0.358155i
$872$		−	7340.63i		−	0.285075i
$873$	−14949.5	−	27442.3i	−0.579568	−	1.06390i
$874$			10103.0i			0.391008i
$875$	15870.5	+	15848.4i	0.613167	+	0.612314i
$876$	564.880	−	143.880i	0.0217871	−	0.00554937i
$877$	7678.68	+	13299.9i	0.295656	+	0.512092i	0.975137	−	0.221601i	$-0.0711284\pi$
$877$	7678.68	+	13299.9i	0.295656	+	0.512092i	−0.679481	+	0.733693i	$0.737795\pi$
$878$	−8276.70	−	14335.7i	−0.318138	−	0.551031i
$879$	2648.47	+	10398.0i	0.101627	+	0.398995i
$880$	−5182.09	−	2991.88i	−0.198509	−	0.114610i
$881$	−40911.2			−1.56451			−0.782254	−	0.622959i	$-0.785930\pi$
$881$	−40911.2			−1.56451			−0.782254	+	0.622959i	$0.785930\pi$
$882$	−18179.9	+	9936.53i	−0.694048	+	0.379343i
$883$	−33904.8			−1.29217			−0.646086	−	0.763265i	$-0.723595\pi$
$883$	−33904.8			−1.29217			−0.646086	+	0.763265i	$0.723595\pi$
$884$	−2490.24	−	1437.74i	−0.0947464	−	0.0547019i
$885$	−15074.4	+	14705.3i	−0.572565	+	0.558545i
$886$	15860.0	+	27470.4i	0.601387	+	1.04163i
$887$	−8641.25	−	14967.1i	−0.327108	−	0.566568i	0.654829	−	0.755777i	$-0.272741\pi$
$887$	−8641.25	−	14967.1i	−0.327108	−	0.566568i	−0.981937	+	0.189210i	$0.939407\pi$
$888$	10069.5	−	35799.0i	0.380529	−	1.35286i
$889$	25452.9	+	25417.5i	0.960252	+	0.958916i
$890$		−	18576.9i		−	0.699662i
$891$	1261.63	−	25427.5i	0.0474369	−	0.956064i
$892$		−	3290.42i		−	0.123511i
$893$	16965.4	+	9794.98i	0.635751	+	0.367051i
$894$	−23718.3	−	6671.44i	−0.887315	−	0.249582i
$895$	21709.5	−	12534.0i	0.810801	−	0.468116i
$896$	−840.039	−	3126.36i	−0.0313211	−	0.116567i
$897$	5755.96	−	5615.02i	0.214254	−	0.209008i
$898$	−7606.95	+	13175.6i	−0.282681	+	0.489617i
$899$	32267.5			1.19709
$900$	−6527.32	−	3987.46i	−0.241753	−	0.147684i
$901$		−	5751.71i		−	0.212672i
$902$	4223.63	−	7315.53i	0.155911	−	0.270045i
$903$	33498.9	+	391.885i	1.23452	+	0.0144420i
$904$	−3070.00	−	5317.40i	−0.112950	−	0.195635i
$905$	331.845	−	191.591i	0.0121888	−	0.00703723i
$906$	25725.6	−	6552.53i	0.943351	−	0.240280i
$907$	−23198.5	+	40181.0i	−0.849276	+	1.47099i	0.0325796	+	0.999469i	$0.489628\pi$
$907$	−23198.5	+	40181.0i	−0.849276	+	1.47099i	−0.881855	+	0.471520i	$0.843706\pi$
$908$	12891.0			0.471147
$909$	−3688.51	+	2009.35i	−0.134587	+	0.0733178i
$910$	1577.05	−	5902.08i	0.0574493	−	0.215002i
$911$	−6266.99	−	3618.25i	−0.227919	−	0.131589i	0.381692	−	0.924289i	$-0.375341\pi$
$911$	−6266.99	−	3618.25i	−0.227919	−	0.131589i	−0.609612	+	0.792700i	$0.708675\pi$
$912$	−8794.85	−	9015.60i	−0.319327	−	0.327343i
$913$	−37268.5	+	21517.0i	−1.35094	+	0.779966i
$914$	7307.62	−	4219.06i	0.264458	−	0.152685i
$915$	−5208.93	+	18518.8i	−0.188199	+	0.669085i
$916$	7417.58	+	4282.54i	0.267559	+	0.154475i
$917$	−126.831	+	474.660i	−0.00456741	+	0.0170934i
$918$	−2510.34	−	10987.5i	−0.0902544	−	0.395034i
$919$	4016.19			0.144159			0.0720793	−	0.997399i	$-0.477037\pi$
$919$	4016.19			0.144159			0.0720793	+	0.997399i	$0.477037\pi$
$920$	−3926.25	+	6800.46i	−0.140701	+	0.243701i
$921$	556.598	−	1978.82i	0.0199137	−	0.0707973i
$922$	30251.4	−	17465.7i	1.08056	−	0.623863i
$923$	7718.35	+	13368.6i	0.275247	+	0.476741i
$924$	−8775.78	+	4930.73i	−0.312448	+	0.175551i
$925$	13759.7	−	23832.6i	0.489100	−	0.847146i
$926$		−	18146.2i		−	0.643976i
$927$	51137.2	+	1267.85i	1.81183	+	0.0449210i
$928$	28228.0			0.998522
$929$	6595.59	−	11423.9i	0.232932	−	0.403451i	−0.725737	−	0.687972i	$-0.758501\pi$
$929$	6595.59	−	11423.9i	0.232932	−	0.403451i	0.958670	+	0.284521i	$0.0918345\pi$
$930$	−2302.36	−	9039.20i	−0.0811801	−	0.318717i
$931$	26760.8	−	37.2586i	0.942050	−	0.00131160i
$932$	5853.51	−	3379.53i	0.205728	−	0.118777i
$933$	−8093.26	−	31774.6i	−0.283989	−	1.11495i
$934$	−12802.1	−	7391.31i	−0.448499	−	0.258941i
$935$			6916.33i			0.241912i
$936$	−440.089	+	17750.4i	−0.0153683	+	0.619861i
$937$			35573.0i			1.24025i	0.784502	+	0.620127i	$0.212919\pi$
$937$			35573.0i			1.24025i	−0.784502	+	0.620127i	$0.787081\pi$
$938$	−20163.7	+	20191.8i	−0.701887	+	0.702865i
$939$	−36819.2	−	37743.4i	−1.27961	−	1.31172i
$940$	2073.86	+	3592.03i	0.0719593	+	0.124637i
$941$	13592.7	+	23543.3i	0.470893	+	0.815610i	0.999446	−	0.0332901i	$-0.0105985\pi$
$941$	13592.7	+	23543.3i	0.470893	+	0.815610i	−0.528553	+	0.848900i	$0.677265\pi$
$942$	−41079.9	−	11554.9i	−1.42087	−	0.399658i
$943$	−5419.94	−	3129.20i	−0.187166	−	0.108060i
$944$	22829.9			0.787131
$945$	−12663.4	+	6707.60i	−0.435915	+	0.230898i
$946$	−27197.9			−0.934758
$947$	47661.0	+	27517.1i	1.63545	+	0.944229i	0.982371	+	0.186940i	$0.0598570\pi$
$947$	47661.0	+	27517.1i	1.63545	+	0.944229i	0.653081	+	0.757288i	$0.273476\pi$
$948$	12824.6	+	3607.27i	0.439370	+	0.123585i
$949$	−500.672	−	867.189i	−0.0171259	−	0.0296629i
$950$	−8254.34	−	14296.9i	−0.281901	−	0.488267i
$951$	6439.90	+	6601.55i	0.219588	+	0.225100i
$952$	−11559.4	+	11575.5i	−0.393530	+	0.394079i
$953$			29456.0i			1.00123i	0.865670	+	0.500615i	$0.166893\pi$
$953$			29456.0i			1.00123i	−0.865670	+	0.500615i	$0.833107\pi$
$954$	−8496.05	+	4628.30i	−0.288333	+	0.157072i
$955$			7747.65i			0.262521i
$956$	−4094.69	−	2364.07i	−0.138527	−	0.0799785i
$957$	9933.58	+	38999.8i	0.335535	+	1.31733i
$958$	−16034.6	+	9257.61i	−0.540768	+	0.312213i
$959$	−1281.59	−	4769.69i	−0.0431542	−	0.160606i
$960$	−3772.18	−	14809.8i	−0.126819	−	0.497900i
$961$	−4311.22	+	7467.25i	−0.144715	+	0.250655i
$962$	−17402.1			−0.583230
$963$	7142.80	−	11692.5i	0.239017	−	0.391262i
$964$		−	4317.29i		−	0.144243i
$965$	6375.73	−	11043.1i	0.212686	−	0.368383i
$966$	−6104.17	−	10864.3i	−0.203311	−	0.361855i
$967$	−13886.7	−	24052.5i	−0.461806	−	0.799872i	0.537245	−	0.843426i	$-0.319465\pi$
$967$	−13886.7	−	24052.5i	−0.461806	−	0.799872i	−0.999051	+	0.0435547i	$0.986132\pi$
$968$	−2372.91	+	1370.00i	−0.0787895	+	0.0454891i
$969$	−3941.81	+	14013.9i	−0.130680	+	0.464594i
$970$	7140.19	−	12367.2i	0.236348	−	0.409367i
$971$	−13906.7			−0.459615			−0.229807	−	0.973236i	$-0.573810\pi$
$971$	−13906.7			−0.459615			−0.229807	+	0.973236i	$0.573810\pi$
$972$	8504.07	−	7510.38i	0.280626	−	0.247835i
$973$	−9189.95	−	2455.58i	−0.302792	−	0.0809069i
$974$	444.142	+	256.425i	0.0146111	+	0.00843573i
$975$	−3557.77	+	12648.6i	−0.116861	+	0.415465i
$976$	18061.1	−	10427.6i	0.592338	−	0.341987i
$977$	7241.30	−	4180.76i	0.237123	−	0.136903i	−0.376730	−	0.926323i	$-0.622952\pi$
$977$	7241.30	−	4180.76i	0.237123	−	0.136903i	0.613854	+	0.789420i	$0.289618\pi$
$978$	1378.53	+	1413.13i	0.0450722	+	0.0462035i
$979$	45536.7	+	26290.6i	1.48658	+	0.858276i
$980$	4910.81	+	2826.15i	0.160072	+	0.0921205i
$981$	6876.00	+	4200.47i	0.223786	+	0.136708i
$982$	46301.0			1.50461
$983$	4846.51	−	8394.40i	0.157253	−	0.272370i	−0.776624	−	0.629964i	$-0.783070\pi$
$983$	4846.51	−	8394.40i	0.157253	−	0.272370i	0.933877	+	0.357594i	$0.116403\pi$
$984$	13391.8	−	3411.01i	0.433857	−	0.110507i
$985$	−7435.32	+	4292.79i	−0.240517	+	0.138862i
$986$	8908.23	+	15429.5i	0.287724	+	0.498353i
$987$	−24161.7	−	282.655i	−0.779206	−	0.00911550i
$988$	3123.76	−	5410.51i	0.100587	−	0.174222i
$989$			20150.4i			0.647873i
$990$	10216.4	−	5565.45i	0.327977	−	0.178668i
$991$	31419.3			1.00713			0.503566	−	0.863957i	$-0.332021\pi$
$991$	31419.3			1.00713			0.503566	+	0.863957i	$0.332021\pi$
$992$	9259.25	−	16037.5i	0.296352	−	0.513297i
$993$	−17836.6	+	17399.9i	−0.570018	+	0.556061i
$994$	23103.5	−	6207.80i	0.737222	−	0.198088i
$995$	−5673.59	+	3275.65i	−0.180769	+	0.104367i
$996$	−18461.7	−	5192.87i	−0.587330	−	0.165203i
$997$	−11388.3	−	6575.05i	−0.361757	−	0.208860i	0.308094	−	0.951356i	$-0.400309\pi$
$997$	−11388.3	−	6575.05i	−0.361757	−	0.208860i	−0.669851	+	0.742495i	$0.733642\pi$
$998$			29317.2i			0.929880i
$999$	27771.1	+	29917.1i	0.879520	+	0.947483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.o.a.20.16	yes	44
3.2	odd	2		189.4.o.a.62.7		44
7.6	odd	2	inner	63.4.o.a.20.15	✓	44
9.2	odd	6		567.4.c.c.566.16		44
9.4	even	3		189.4.o.a.125.8		44
9.5	odd	6	inner	63.4.o.a.41.15	yes	44
9.7	even	3		567.4.c.c.566.29		44
21.20	even	2		189.4.o.a.62.8		44
63.13	odd	6		189.4.o.a.125.7		44
63.20	even	6		567.4.c.c.566.30		44
63.34	odd	6		567.4.c.c.566.15		44
63.41	even	6	inner	63.4.o.a.41.16	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.o.a.20.15	✓	44	7.6	odd	2	inner
63.4.o.a.20.16	yes	44	1.1	even	1	trivial
63.4.o.a.41.15	yes	44	9.5	odd	6	inner
63.4.o.a.41.16	yes	44	63.41	even	6	inner
189.4.o.a.62.7		44	3.2	odd	2
189.4.o.a.62.8		44	21.20	even	2
189.4.o.a.125.7		44	63.13	odd	6
189.4.o.a.125.8		44	9.4	even	3
567.4.c.c.566.15		44	63.34	odd	6
567.4.c.c.566.16		44	9.2	odd	6
567.4.c.c.566.29		44	9.7	even	3
567.4.c.c.566.30		44	63.20	even	6

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.93743 + 1.11857i) q^{2} +(5.00204 + 1.40697i) q^{3} +(-1.49759 - 2.59390i) q^{4} +(2.75758 + 4.77627i) q^{5} +(8.11730 + 8.32104i) q^{6} +(13.1049 + 13.0867i) q^{7} -24.5978i q^{8} +(23.0409 + 14.0754i) q^{9} +O(q^{10})\)	\(q+(1.93743 + 1.11857i) q^{2} +(5.00204 + 1.40697i) q^{3} +(-1.49759 - 2.59390i) q^{4} +(2.75758 + 4.77627i) q^{5} +(8.11730 + 8.32104i) q^{6} +(13.1049 + 13.0867i) q^{7} -24.5978i q^{8} +(23.0409 + 14.0754i) q^{9} +12.3382i q^{10} +(-30.2441 - 17.4614i) q^{11} +(-3.84148 - 15.0818i) q^{12} +(-23.1532 + 13.3675i) q^{13} +(10.7514 + 40.0133i) q^{14} +(7.07349 + 27.7709i) q^{15} +(15.5338 - 26.9053i) q^{16} -35.9093 q^{17} +(28.8957 + 53.0430i) q^{18} -78.0198i q^{19} +(8.25943 - 14.3058i) q^{20} +(47.1389 + 83.8983i) q^{21} +(-39.0638 - 67.6605i) q^{22} +(-50.1284 + 28.9416i) q^{23} +(34.6083 - 123.039i) q^{24} +(47.2915 - 81.9113i) q^{25} -59.8102 q^{26} +(95.4480 + 102.824i) q^{27} +(14.3198 - 53.5913i) q^{28} +(-192.066 - 110.889i) q^{29} +(-17.3594 + 61.7163i) q^{30} +(-126.002 + 72.7471i) q^{31} +(-110.228 + 63.6400i) q^{32} +(-126.715 - 129.895i) q^{33} +(-69.5717 - 40.1672i) q^{34} +(-26.3676 + 98.6801i) q^{35} +(2.00440 - 80.8449i) q^{36} +290.956 q^{37} +(87.2708 - 151.158i) q^{38} +(-134.621 + 34.2892i) q^{39} +(117.486 - 67.8304i) q^{40} +(54.0606 + 93.6357i) q^{41} +(-2.51838 + 215.275i) q^{42} +(174.061 - 301.482i) q^{43} +104.600i q^{44} +(-3.69080 + 148.863i) q^{45} -129.493 q^{46} +(-125.545 + 217.450i) q^{47} +(115.555 - 112.726i) q^{48} +(0.477554 + 343.000i) q^{49} +(183.248 - 105.798i) q^{50} +(-179.620 - 50.5232i) q^{51} +(69.3480 + 40.0381i) q^{52} +160.173i q^{53} +(69.9077 + 305.979i) q^{54} -192.605i q^{55} +(321.904 - 322.352i) q^{56} +(109.771 - 390.258i) q^{57} +(-248.076 - 429.680i) q^{58} +(367.425 + 636.398i) q^{59} +(61.4417 - 59.9373i) q^{60} +(581.350 + 335.643i) q^{61} -325.492 q^{62} +(117.749 + 485.986i) q^{63} -533.284 q^{64} +(-127.694 - 73.7240i) q^{65} +(-100.203 - 393.402i) q^{66} +(344.364 + 596.455i) q^{67} +(53.7774 + 93.1452i) q^{68} +(-291.464 + 74.2385i) q^{69} +(-161.466 + 161.691i) q^{70} -577.396i q^{71} +(346.224 - 566.756i) q^{72} +37.4543i q^{73} +(563.705 + 325.455i) q^{74} +(351.801 - 343.187i) q^{75} +(-202.375 + 116.841i) q^{76} +(-167.834 - 624.626i) q^{77} +(-299.173 - 84.1509i) q^{78} +(-428.000 + 741.317i) q^{79} +171.342 q^{80} +(332.766 + 648.620i) q^{81} +241.883i q^{82} +(616.129 - 1067.17i) q^{83} +(147.029 - 247.918i) q^{84} +(-99.0228 - 171.513i) q^{85} +(674.460 - 389.400i) q^{86} +(-804.705 - 824.903i) q^{87} +(-429.513 + 743.939i) q^{88} -1505.64 q^{89} +(-173.665 + 284.284i) q^{90} +(-478.358 - 127.819i) q^{91} +(150.143 + 86.6853i) q^{92} +(-732.619 + 186.604i) q^{93} +(-486.467 + 280.862i) q^{94} +(372.643 - 215.146i) q^{95} +(-640.903 + 163.243i) q^{96} +(-1002.35 - 578.705i) q^{97} +(-382.745 + 665.071i) q^{98} +(-451.074 - 828.025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) \) 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7	\( 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7} - 18 q^{11} + 204 q^{14} + 66 q^{15} - 242 q^{16} - 210 q^{18} - 57 q^{21} - 34 q^{22} - 102 q^{23} - 352 q^{25} + 300 q^{28} + 246 q^{29} - 144 q^{30} + 1068 q^{32} - 1818 q^{36} + 328 q^{37} - 798 q^{39} - 1158 q^{42} - 170 q^{43} + 968 q^{46} - 79 q^{49} + 288 q^{50} - 204 q^{51} + 1212 q^{56} + 324 q^{57} - 538 q^{58} + 5316 q^{60} + 783 q^{63} - 808 q^{64} + 4350 q^{65} - 590 q^{67} + 384 q^{70} + 4284 q^{72} - 5304 q^{74} - 2787 q^{77} + 612 q^{78} - 302 q^{79} - 3720 q^{81} + 7050 q^{84} - 612 q^{85} - 13692 q^{86} + 1294 q^{88} + 210 q^{91} - 10194 q^{92} - 4266 q^{93} + 6336 q^{95} + 1014 q^{99}+O(q^{100}) \) 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7 - 18 * q^11 + 204 * q^14 + 66 * q^15 - 242 * q^16 - 210 * q^18 - 57 * q^21 - 34 * q^22 - 102 * q^23 - 352 * q^25 + 300 * q^28 + 246 * q^29 - 144 * q^30 + 1068 * q^32 - 1818 * q^36 + 328 * q^37 - 798 * q^39 - 1158 * q^42 - 170 * q^43 + 968 * q^46 - 79 * q^49 + 288 * q^50 - 204 * q^51 + 1212 * q^56 + 324 * q^57 - 538 * q^58 + 5316 * q^60 + 783 * q^63 - 808 * q^64 + 4350 * q^65 - 590 * q^67 + 384 * q^70 + 4284 * q^72 - 5304 * q^74 - 2787 * q^77 + 612 * q^78 - 302 * q^79 - 3720 * q^81 + 7050 * q^84 - 612 * q^85 - 13692 * q^86 + 1294 * q^88 + 210 * q^91 - 10194 * q^92 - 4266 * q^93 + 6336 * q^95 + 1014 * q^99

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