LMFDB - Embedded newform 161.4.e.a.93.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,4,Mod(93,161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("161.93");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.e (of order $3$, 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:	$9.49930751092$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			93.18
Character	$\chi$	$=$	161.93
Dual form			161.4.e.a.116.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.81191 - 3.13831i) q^{2} +(-0.112864 - 0.195487i) q^{3} +(-2.56601 - 4.44446i) q^{4} +(-1.55669 + 2.69626i) q^{5} -0.818000 q^{6} +(-8.28058 - 16.5660i) q^{7} +10.3930 q^{8} +(13.4745 - 23.3386i) q^{9} +(5.64114 + 9.77074i) q^{10} +(-13.6603 - 23.6604i) q^{11} +(-0.579223 + 1.00324i) q^{12} -46.9064 q^{13} +(-66.9929 - 4.02897i) q^{14} +0.702778 q^{15} +(39.3593 - 68.1722i) q^{16} +(-30.3738 - 52.6090i) q^{17} +(-48.8292 - 84.5746i) q^{18} +(-0.916584 + 1.58757i) q^{19} +15.9779 q^{20} +(-2.30385 + 3.48846i) q^{21} -99.0050 q^{22} +(11.5000 - 19.9186i) q^{23} +(-1.17300 - 2.03170i) q^{24} +(57.6535 + 99.8587i) q^{25} +(-84.9901 + 147.207i) q^{26} -12.1779 q^{27} +(-52.3788 + 79.3112i) q^{28} +115.694 q^{29} +(1.27337 - 2.20554i) q^{30} +(32.9474 + 57.0666i) q^{31} +(-101.059 - 175.039i) q^{32} +(-3.08353 + 5.34084i) q^{33} -220.138 q^{34} +(57.5565 + 3.46146i) q^{35} -138.303 q^{36} +(-4.26505 + 7.38728i) q^{37} +(3.32153 + 5.75306i) q^{38} +(5.29407 + 9.16960i) q^{39} +(-16.1787 + 28.0223i) q^{40} +129.654 q^{41} +(6.77351 + 13.5510i) q^{42} +200.276 q^{43} +(-70.1052 + 121.426i) q^{44} +(41.9512 + 72.6616i) q^{45} +(-41.6739 - 72.1812i) q^{46} +(38.8781 - 67.3388i) q^{47} -17.7691 q^{48} +(-205.864 + 274.352i) q^{49} +417.851 q^{50} +(-6.85625 + 11.8754i) q^{51} +(120.362 + 208.474i) q^{52} +(14.2548 + 24.6901i) q^{53} +(-22.0651 + 38.2180i) q^{54} +85.0594 q^{55} +(-86.0602 - 172.171i) q^{56} +0.413799 q^{57} +(209.627 - 363.084i) q^{58} +(-25.6223 - 44.3792i) q^{59} +(-1.80334 - 3.12347i) q^{60} +(30.5548 - 52.9225i) q^{61} +238.791 q^{62} +(-498.203 - 29.9621i) q^{63} -102.686 q^{64} +(73.0186 - 126.472i) q^{65} +(11.1742 + 19.3542i) q^{66} +(8.64942 + 14.9812i) q^{67} +(-155.879 + 269.990i) q^{68} -5.19177 q^{69} +(115.150 - 174.358i) q^{70} +366.502 q^{71} +(140.041 - 242.558i) q^{72} +(455.230 + 788.481i) q^{73} +(15.4557 + 26.7701i) q^{74} +(13.0141 - 22.5410i) q^{75} +9.40786 q^{76} +(-278.842 + 422.219i) q^{77} +38.3694 q^{78} +(611.129 - 1058.51i) q^{79} +(122.540 + 212.246i) q^{80} +(-362.438 - 627.760i) q^{81} +(234.921 - 406.895i) q^{82} +825.101 q^{83} +(21.4160 + 1.28797i) q^{84} +189.130 q^{85} +(362.881 - 628.529i) q^{86} +(-13.0577 - 22.6167i) q^{87} +(-141.972 - 245.903i) q^{88} +(-348.966 + 604.426i) q^{89} +304.047 q^{90} +(388.412 + 777.051i) q^{91} -118.036 q^{92} +(7.43719 - 12.8816i) q^{93} +(-140.887 - 244.023i) q^{94} +(-2.85367 - 4.94270i) q^{95} +(-22.8118 + 39.5113i) q^{96} -658.577 q^{97} +(487.996 + 1143.17i) q^{98} -736.266 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 6 q^{3} - 88 q^{4} - 20 q^{5} + 24 q^{6} - 12 q^{7} + 42 q^{8} - 238 q^{9} - 182 q^{10} + 28 q^{11} - 127 q^{12} + 440 q^{13} + 16 q^{14} + 40 q^{15} - 436 q^{16} - 294 q^{17} + 155 q^{18} - 252 q^{19}+ \cdots - 5764 q^{99}+O(q^{100}) $ 44 * q - 6 * q^3 - 88 * q^4 - 20 * q^5 + 24 * q^6 - 12 * q^7 + 42 * q^8 - 238 * q^9 - 182 * q^10 + 28 * q^11 - 127 * q^12 + 440 * q^13 + 16 * q^14 + 40 * q^15 - 436 * q^16 - 294 * q^17 + 155 * q^18 - 252 * q^19 + 708 * q^20 + 110 * q^21 + 28 * q^22 + 506 * q^23 - 458 * q^24 - 684 * q^25 - 396 * q^26 + 972 * q^27 - 354 * q^28 + 628 * q^29 + 905 * q^30 - 172 * q^31 + 127 * q^32 - 1524 * q^33 + 800 * q^34 - 1588 * q^35 + 2644 * q^36 + 710 * q^37 + 323 * q^38 + 136 * q^39 - 1808 * q^40 + 784 * q^41 - 2775 * q^42 + 504 * q^43 + 1106 * q^44 - 658 * q^45 - 448 * q^47 + 2730 * q^48 - 570 * q^49 + 738 * q^50 + 896 * q^51 - 1224 * q^52 - 308 * q^53 - 945 * q^54 + 4324 * q^55 - 481 * q^56 - 124 * q^57 + 1153 * q^58 + 282 * q^59 - 4442 * q^60 - 3076 * q^61 + 3500 * q^62 - 732 * q^63 - 4354 * q^64 + 1024 * q^65 + 549 * q^66 - 1056 * q^67 - 2478 * q^68 - 276 * q^69 + 2071 * q^70 - 96 * q^71 + 1922 * q^72 - 4430 * q^73 - 3322 * q^74 - 2540 * q^75 + 15026 * q^76 - 1116 * q^77 - 3990 * q^78 + 530 * q^79 - 296 * q^80 - 3446 * q^81 - 1570 * q^82 + 3572 * q^83 - 4571 * q^84 - 2624 * q^85 + 397 * q^86 + 1724 * q^87 - 5375 * q^88 - 658 * q^89 + 13620 * q^90 - 1098 * q^91 - 4048 * q^92 + 1722 * q^93 + 1944 * q^94 - 1742 * q^95 - 1142 * q^96 + 21364 * q^97 + 2001 * q^98 - 5764 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/161\mathbb{Z}\right)^\times$.

$n$	$24$	$120$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.81191	−	3.13831i	0.640606	−	1.10956i	−0.344692	−	0.938716i	$-0.612017\pi$
$2$	1.81191	−	3.13831i	0.640606	−	1.10956i	0.985298	−	0.170846i	$-0.0546500\pi$
$3$	−0.112864	−	0.195487i	−0.0217208	−	0.0376215i	0.854961	−	0.518693i	$-0.173581\pi$
$3$	−0.112864	−	0.195487i	−0.0217208	−	0.0376215i	−0.876681	+	0.481071i	$0.840248\pi$
$4$	−2.56601	−	4.44446i	−0.320751	−	0.555558i
$5$	−1.55669	+	2.69626i	−0.139234	+	0.241161i	−0.927207	−	0.374549i	$-0.877797\pi$
$5$	−1.55669	+	2.69626i	−0.139234	+	0.241161i	0.787973	+	0.615710i	$0.211131\pi$
$6$	−0.818000			−0.0556578
$7$	−8.28058	−	16.5660i	−0.447109	−	0.894479i
$7$	−8.28058	−	16.5660i	−0.447109	−	0.894479i
$8$	10.3930			0.459311
$9$	13.4745	−	23.3386i	0.499056	−	0.864391i
$10$	5.64114	+	9.77074i	0.178388	+	0.308978i
$11$	−13.6603	−	23.6604i	−0.374432	−	0.648534i	0.615810	−	0.787895i	$-0.288829\pi$
$11$	−13.6603	−	23.6604i	−0.374432	−	0.648534i	−0.990242	+	0.139360i	$0.955495\pi$
$12$	−0.579223	+	1.00324i	−0.0139339	+	0.0241343i
$13$	−46.9064			−1.00073			−0.500365	−	0.865814i	$-0.666801\pi$
$13$	−46.9064			−1.00073			−0.500365	+	0.865814i	$0.666801\pi$
$14$	−66.9929	−	4.02897i	−1.27890	−	0.0769135i
$15$	0.702778			0.0120971
$16$	39.3593	−	68.1722i	0.614988	−	1.06519i
$17$	−30.3738	−	52.6090i	−0.433337	−	0.750562i	0.563821	−	0.825897i	$-0.309331\pi$
$17$	−30.3738	−	52.6090i	−0.433337	−	0.750562i	−0.997158	+	0.0753349i	$0.975997\pi$
$18$	−48.8292	−	84.5746i	−0.639397	−	1.10747i
$19$	−0.916584	+	1.58757i	−0.0110673	+	0.0191691i	−0.871506	−	0.490385i	$-0.836856\pi$
$19$	−0.916584	+	1.58757i	−0.0110673	+	0.0191691i	0.860439	+	0.509554i	$0.170190\pi$
$20$	15.9779			0.178638
$21$	−2.30385	+	3.48846i	−0.0239401	+	0.0362497i
$22$	−99.0050			−0.959452
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$24$	−1.17300	−	2.03170i	−0.00997659	−	0.0172800i
$25$	57.6535	+	99.8587i	0.461228	+	0.798870i
$26$	−84.9901	+	147.207i	−0.641074	+	1.11037i
$27$	−12.1779			−0.0868011
$28$	−52.3788	+	79.3112i	−0.353524	+	0.535300i
$29$	115.694			0.740822			0.370411	−	0.928868i	$-0.379217\pi$
$29$	115.694			0.740822			0.370411	+	0.928868i	$0.379217\pi$
$30$	1.27337	−	2.20554i	0.00774947	−	0.0134225i
$31$	32.9474	+	57.0666i	0.190888	+	0.330628i	0.945545	−	0.325492i	$-0.105530\pi$
$31$	32.9474	+	57.0666i	0.190888	+	0.330628i	−0.754657	+	0.656120i	$0.772197\pi$
$32$	−101.059	−	175.039i	−0.558275	−	0.966960i
$33$	−3.08353	+	5.34084i	−0.0162659	+	0.0281733i
$34$	−220.138			−1.11039
$35$	57.5565	+	3.46146i	0.277966	+	0.0167170i
$36$	−138.303			−0.640292
$37$	−4.26505	+	7.38728i	−0.0189505	+	0.0328233i	−0.875345	−	0.483499i	$-0.839366\pi$
$37$	−4.26505	+	7.38728i	−0.0189505	+	0.0328233i	0.856395	+	0.516322i	$0.172699\pi$
$38$	3.32153	+	5.75306i	0.0141796	+	0.0245597i
$39$	5.29407	+	9.16960i	0.0217367	+	0.0376490i
$40$	−16.1787	+	28.0223i	−0.0639518	+	0.110768i
$41$	129.654			0.493867			0.246933	−	0.969032i	$-0.420577\pi$
$41$	129.654			0.493867			0.246933	+	0.969032i	$0.420577\pi$
$42$	6.77351	+	13.5510i	0.0248851	+	0.0497848i
$43$	200.276			0.710274			0.355137	−	0.934814i	$-0.384434\pi$
$43$	200.276			0.710274			0.355137	+	0.934814i	$0.384434\pi$
$44$	−70.1052	+	121.426i	−0.240199	+	0.416037i
$45$	41.9512	+	72.6616i	0.138971	+	0.240706i
$46$	−41.6739	−	72.1812i	−0.133576	−	0.231360i
$47$	38.8781	−	67.3388i	0.120658	−	0.208987i	−0.799369	−	0.600840i	$-0.794833\pi$
$47$	38.8781	−	67.3388i	0.120658	−	0.208987i	0.920028	+	0.391854i	$0.128166\pi$
$48$	−17.7691			−0.0534321
$49$	−205.864	+	274.352i	−0.600187	+	0.799860i
$50$	417.851			1.18186
$51$	−6.85625	+	11.8754i	−0.0188248	+	0.0326056i
$52$	120.362	+	208.474i	0.320986	+	0.555964i
$53$	14.2548	+	24.6901i	0.0369444	+	0.0639895i	0.883906	−	0.467664i	$-0.154904\pi$
$53$	14.2548	+	24.6901i	0.0369444	+	0.0639895i	−0.846962	+	0.531653i	$0.821571\pi$
$54$	−22.0651	+	38.2180i	−0.0556053	+	0.0963112i
$55$	85.0594			0.208535
$56$	−86.0602	−	172.171i	−0.205362	−	0.410844i
$57$	0.413799			0.000961562
$58$	209.627	−	363.084i	0.474575	−	0.821988i
$59$	−25.6223	−	44.3792i	−0.0565380	−	0.0979267i	0.836371	−	0.548164i	$-0.184673\pi$
$59$	−25.6223	−	44.3792i	−0.0565380	−	0.0979267i	−0.892909	+	0.450237i	$0.851340\pi$
$60$	−1.80334	−	3.12347i	−0.00388016	−	0.00672064i
$61$	30.5548	−	52.9225i	0.0641336	−	0.111083i	−0.832176	−	0.554512i	$-0.812905\pi$
$61$	30.5548	−	52.9225i	0.0641336	−	0.111083i	0.896309	+	0.443429i	$0.146238\pi$
$62$	238.791			0.489136
$63$	−498.203	−	29.9621i	−0.996313	−	0.0599185i
$64$	−102.686			−0.200559
$65$	73.0186	−	126.472i	0.139336	−	0.241337i
$66$	11.1742	+	19.3542i	0.0208400	+	0.0360960i
$67$	8.64942	+	14.9812i	0.0157716	+	0.0273171i	0.873803	−	0.486279i	$-0.161646\pi$
$67$	8.64942	+	14.9812i	0.0157716	+	0.0273171i	−0.858032	+	0.513596i	$0.828313\pi$
$68$	−155.879	+	269.990i	−0.277987	+	0.481488i
$69$	−5.19177			−0.00905819
$70$	115.150	−	174.358i	0.196615	−	0.297712i
$71$	366.502			0.612616			0.306308	−	0.951932i	$-0.400906\pi$
$71$	366.502			0.612616			0.306308	+	0.951932i	$0.400906\pi$
$72$	140.041	−	242.558i	0.229222	−	0.397024i
$73$	455.230	+	788.481i	0.729872	+	1.26418i	0.956937	+	0.290295i	$0.0937536\pi$
$73$	455.230	+	788.481i	0.729872	+	1.26418i	−0.227065	+	0.973880i	$0.572913\pi$
$74$	15.4557	+	26.7701i	0.0242796	+	0.0420535i
$75$	13.0141	−	22.5410i	0.0200364	−	0.0347041i
$76$	9.40786			0.0141994
$77$	−278.842	+	422.219i	−0.412689	+	0.624887i
$78$	38.3694			0.0556985
$79$	611.129	−	1058.51i	0.870347	−	1.50749i	0.00870893	−	0.999962i	$-0.497228\pi$
$79$	611.129	−	1058.51i	0.870347	−	1.50749i	0.861638	−	0.507523i	$-0.169439\pi$
$80$	122.540	+	212.246i	0.171255	+	0.296622i
$81$	−362.438	−	627.760i	−0.497171	−	0.861125i
$82$	234.921	−	406.895i	0.316374	−	0.547976i
$83$	825.101			1.09116			0.545582	−	0.838057i	$-0.316309\pi$
$83$	825.101			1.09116			0.545582	+	0.838057i	$0.316309\pi$
$84$	21.4160	+	1.28797i	0.0278176	+	0.00167296i
$85$	189.130			0.241341
$86$	362.881	−	628.529i	0.455006	−	0.788093i
$87$	−13.0577	−	22.6167i	−0.0160912	−	0.0278708i
$88$	−141.972	−	245.903i	−0.171980	−	0.297879i
$89$	−348.966	+	604.426i	−0.415621	+	0.719877i	−0.995493	−	0.0948303i	$-0.969769\pi$
$89$	−348.966	+	604.426i	−0.415621	+	0.719877i	0.579872	+	0.814707i	$0.303102\pi$
$90$	304.047			0.356104
$91$	388.412	+	777.051i	0.447436	+	0.895133i
$92$	−118.036			−0.133763
$93$	7.43719	−	12.8816i	0.00829248	−	0.0143630i
$94$	−140.887	−	244.023i	−0.154589	−	0.267756i
$95$	−2.85367	−	4.94270i	−0.00308190	−	0.00533800i
$96$	−22.8118	+	39.5113i	−0.0242523	+	0.0420063i
$97$	−658.577			−0.689365			−0.344682	−	0.938719i	$-0.612013\pi$
$97$	−658.577			−0.689365			−0.344682	+	0.938719i	$0.612013\pi$
$98$	487.996	+	1143.17i	0.503011	+	1.17834i
$99$	−736.266			−0.747450
$100$	295.879	−	512.477i	0.295879	−	0.512477i
$101$	863.494	+	1495.61i	0.850701	+	1.47346i	0.880577	+	0.473904i	$0.157156\pi$
$101$	863.494	+	1495.61i	0.850701	+	1.47346i	−0.0298754	+	0.999554i	$0.509511\pi$
$102$	24.8458	+	43.0341i	0.0241186	+	0.0417746i
$103$	287.951	−	498.747i	0.275463	−	0.477116i	−0.694789	−	0.719214i	$-0.744502\pi$
$103$	287.951	−	498.747i	0.275463	−	0.477116i	0.970252	+	0.242098i	$0.0778355\pi$
$104$	−487.499			−0.459647
$105$	−5.81941	−	11.6422i	−0.00540873	−	0.0108206i
$106$	103.314			0.0946671
$107$	−833.211	+	1443.16i	−0.752800	+	1.30389i	0.193661	+	0.981069i	$0.437964\pi$
$107$	−833.211	+	1443.16i	−0.752800	+	1.30389i	−0.946461	+	0.322819i	$0.895369\pi$
$108$	31.2485	+	54.1240i	0.0278416	+	0.0482230i
$109$	−205.579	−	356.073i	−0.180650	−	0.312895i	0.761452	−	0.648221i	$-0.224487\pi$
$109$	−205.579	−	356.073i	−0.180650	−	0.312895i	−0.942102	+	0.335326i	$0.891154\pi$
$110$	154.120	−	266.943i	0.133589	−	0.231382i
$111$	1.92549			0.00164648
$112$	−1455.26	−	87.5196i	−1.22776	−	0.0738378i
$113$	868.120			0.722706			0.361353	−	0.932429i	$-0.382315\pi$
$113$	868.120			0.722706			0.361353	+	0.932429i	$0.382315\pi$
$114$	0.749766	−	1.29863i	0.000615982	−	0.00106691i
$115$	35.8038	+	62.0140i	0.0290323	+	0.0502855i
$116$	−296.872	−	514.198i	−0.237620	−	0.411569i
$117$	−632.042	+	1094.73i	−0.499421	+	0.865023i
$118$	−185.701			−0.144874
$119$	−620.007	+	938.805i	−0.477613	+	0.723194i
$120$	7.30399			0.00555633
$121$	292.290	−	506.262i	0.219602	−	0.380362i
$122$	−110.725	−	191.781i	−0.0821686	−	0.142320i
$123$	−14.6333	−	25.3457i	−0.0107272	−	0.0185800i
$124$	169.087	−	292.867i	0.122455	−	0.212099i
$125$	−748.165			−0.535343
$126$	−996.728	+	1509.23i	−0.704727	+	1.06709i
$127$	−2092.70			−1.46218			−0.731090	−	0.682281i	$-0.760988\pi$
$127$	−2092.70			−1.46218			−0.731090	+	0.682281i	$0.760988\pi$
$128$	622.410	−	1078.05i	0.429795	−	0.744428i
$129$	−22.6040	−	39.1513i	−0.0154277	−	0.0267216i
$130$	−264.606	−	458.310i	−0.178519	−	0.309204i
$131$	−574.154	+	994.463i	−0.382932	+	0.663257i	−0.991480	−	0.130260i	$-0.958419\pi$
$131$	−574.154	+	994.463i	−0.382932	+	0.663257i	0.608548	+	0.793517i	$0.291752\pi$
$132$	31.6495			0.0208692
$133$	33.8895	+	2.03813i	0.0220947	+	0.00132878i
$134$	62.6878			0.0404134
$135$	18.9571	−	32.8347i	0.0120857	−	0.0209330i
$136$	−315.676	−	546.766i	−0.199036	−	0.344741i
$137$	75.7532	+	131.208i	0.0472411	+	0.0818241i	0.888679	−	0.458530i	$-0.151624\pi$
$137$	75.7532	+	131.208i	0.0472411	+	0.0818241i	−0.841438	+	0.540354i	$0.818290\pi$
$138$	−9.40700	+	16.2934i	−0.00580273	+	0.0100506i
$139$	1883.12			1.14910			0.574548	−	0.818471i	$-0.305178\pi$
$139$	1883.12			1.14910			0.574548	+	0.818471i	$0.305178\pi$
$140$	−132.306	−	264.690i	−0.0798708	−	0.159788i
$141$	−17.5518			−0.0104832
$142$	664.067	−	1150.20i	0.392445	−	0.679735i
$143$	640.758	+	1109.82i	0.374705	+	0.649008i
$144$	−1060.69	−	1837.18i	−0.613828	−	1.06318i
$145$	−180.099	+	311.941i	−0.103148	+	0.178657i
$146$	3299.34			1.87024
$147$	76.8670	+	9.27917i	0.0431284	+	0.00520634i
$148$	43.7766			0.0243136
$149$	202.297	−	350.389i	0.111227	−	0.192651i	−0.805038	−	0.593223i	$-0.797855\pi$
$149$	202.297	−	350.389i	0.111227	−	0.192651i	0.916265	+	0.400572i	$0.131189\pi$
$150$	−47.1605	−	81.6844i	−0.0256709	−	0.0444633i
$151$	−1116.66	−	1934.12i	−0.601807	−	1.04236i	−0.992547	−	0.121860i	$-0.961114\pi$
$151$	−1116.66	−	1934.12i	−0.601807	−	1.04236i	0.390740	−	0.920501i	$-0.372219\pi$
$152$	−9.52608	+	16.4996i	−0.00508333	+	0.00880459i
$153$	−1637.09			−0.865039
$154$	819.819	+	1640.12i	0.428980	+	0.858210i
$155$	−205.155			−0.106313
$156$	27.1693	−	47.0586i	0.0139441	−	0.0241519i
$157$	−1782.17	−	3086.80i	−0.905939	−	1.56913i	−0.819652	−	0.572862i	$-0.805833\pi$
$157$	−1782.17	−	3086.80i	−0.905939	−	1.56913i	−0.0862873	−	0.996270i	$-0.527500\pi$
$158$	−2214.62	−	3835.83i	−1.11510	−	1.93141i
$159$	3.21773	−	5.57327i	0.00160492	−	0.00277980i
$160$	629.266			0.310924
$161$	−425.198	−	25.5715i	−0.208138	−	0.0125175i
$162$	−2626.81			−1.27396
$163$	−718.105	+	1243.79i	−0.345070	+	0.597678i	−0.985366	−	0.170449i	$-0.945478\pi$
$163$	−718.105	+	1243.79i	−0.345070	+	0.597678i	0.640297	+	0.768128i	$0.278811\pi$
$164$	−332.693	−	576.242i	−0.158408	−	0.274371i
$165$	−9.60019	−	16.6280i	−0.00452954	−	0.00784539i
$166$	1495.01	−	2589.43i	0.699006	−	1.21071i
$167$	124.915			0.0578815			0.0289407	−	0.999581i	$-0.490787\pi$
$167$	124.915			0.0578815			0.0289407	+	0.999581i	$0.490787\pi$
$168$	−23.9440	+	36.2556i	−0.0109959	+	0.0166499i
$169$	3.21270			0.00146231
$170$	342.686	−	593.549i	0.154605	−	0.267783i
$171$	24.7011	+	42.7835i	0.0110464	+	0.0191330i
$172$	−513.910	−	890.118i	−0.227821	−	0.394598i
$173$	−324.114	+	561.383i	−0.142439	+	0.246712i	−0.928415	−	0.371546i	$-0.878828\pi$
$173$	−324.114	+	561.383i	−0.142439	+	0.246712i	0.785976	+	0.618258i	$0.212161\pi$
$174$	−94.6377			−0.0412325
$175$	1176.85	−	1781.97i	0.508353	−	0.769741i
$176$	−2150.64			−0.921084
$177$	−5.78370	+	10.0177i	−0.00245610	+	0.00425409i
$178$	1264.59	+	2190.33i	0.532499	+	0.922315i
$179$	1188.84	+	2059.13i	0.496414	+	0.859814i	0.999991	−	0.00413569i	$-0.00131643\pi$
$179$	1188.84	+	2059.13i	0.496414	+	0.859814i	−0.503577	+	0.863950i	$0.667983\pi$
$180$	215.294	−	372.901i	0.0891506	−	0.154413i
$181$	930.543			0.382137			0.191068	−	0.981577i	$-0.438805\pi$
$181$	930.543			0.382137			0.191068	+	0.981577i	$0.438805\pi$
$182$	3142.40	+	188.985i	1.27984	+	0.0769697i
$183$	−13.7942			−0.00557212
$184$	119.520	−	207.014i	0.0478865	−	0.0829418i
$185$	−13.2787	−	22.9993i	−0.00527712	−	0.00914024i
$186$	−26.9510	−	46.6805i	−0.0106244	−	0.0184020i
$187$	−829.833	+	1437.31i	−0.324510	+	0.562068i
$188$	−399.046			−0.154806
$189$	100.840	+	201.738i	0.0388096	+	0.0776418i
$190$	−20.6823			−0.00789712
$191$	80.8877	−	140.102i	0.0306431	−	0.0530753i	−0.850297	−	0.526303i	$-0.823578\pi$
$191$	80.8877	−	140.102i	0.0306431	−	0.0530753i	0.880940	+	0.473228i	$0.156911\pi$
$192$	11.5896	+	20.0738i	0.00435630	+	0.00754534i
$193$	393.217	+	681.071i	0.146655	+	0.254013i	0.929989	−	0.367587i	$-0.119816\pi$
$193$	393.217	+	681.071i	0.146655	+	0.254013i	−0.783334	+	0.621601i	$0.786483\pi$
$194$	−1193.28	+	2066.82i	−0.441611	+	0.764892i
$195$	−32.9648			−0.0121059
$196$	1747.60	+	210.965i	0.636879	+	0.0768822i
$197$	−2877.57			−1.04070			−0.520352	−	0.853952i	$-0.674199\pi$
$197$	−2877.57			−1.04070			−0.520352	+	0.853952i	$0.674199\pi$
$198$	−1334.05	+	2310.63i	−0.478821	+	0.829342i
$199$	−2412.93	−	4179.32i	−0.859539	−	1.48876i	−0.872370	−	0.488847i	$-0.837418\pi$
$199$	−2412.93	−	4179.32i	−0.859539	−	1.48876i	0.0128311	−	0.999918i	$-0.495916\pi$
$200$	599.193	+	1037.83i	0.211847	+	0.366930i
$201$	1.95242	−	3.38170i	0.000685141	−	0.00118670i
$202$	6258.28			2.17986
$203$	−958.013	−	1916.59i	−0.331228	−	0.662650i
$204$	70.3728			0.0241524
$205$	−201.830	+	349.581i	−0.0687632	+	0.119101i
$206$	−1043.48	−	1807.36i	−0.352926	−	0.611287i
$207$	−309.914	−	536.787i	−0.104060	−	0.180238i
$208$	−1846.20	+	3197.72i	−0.615438	+	1.06597i
$209$	50.0834			0.0165758
$210$	−47.0812	−	2.83147i	−0.0154710	−	0.000930430i
$211$	4350.18			1.41933			0.709665	−	0.704539i	$-0.248846\pi$
$211$	4350.18			1.41933			0.709665	+	0.704539i	$0.248846\pi$
$212$	73.1561	−	126.710i	0.0236999	−	0.0410495i
$213$	−41.3650	−	71.6463i	−0.0133065	−	0.0230475i
$214$	3019.40	+	5229.76i	0.964496	+	1.67056i
$215$	−311.767	+	539.996i	−0.0988944	+	0.171290i
$216$	−126.565			−0.0398687
$217$	672.541	−	1018.35i	0.210392	−	0.318572i
$218$	−1489.96			−0.462902
$219$	102.759	−	177.983i	0.0317068	−	0.0549177i
$220$	−218.263	−	378.043i	−0.0668878	−	0.115853i
$221$	1424.73	+	2467.70i	0.433654	+	0.751111i
$222$	3.48881	−	6.04279i	0.00105474	−	0.00182687i
$223$	6359.82			1.90980			0.954899	−	0.296931i	$-0.0959630\pi$
$223$	6359.82			1.90980			0.954899	+	0.296931i	$0.0959630\pi$
$224$	−2062.86	+	3123.56i	−0.615316	+	0.931702i
$225$	3107.41			0.920715
$226$	1572.95	−	2724.43i	0.462970	−	0.801887i
$227$	−1518.85	−	2630.73i	−0.444096	−	0.769197i	0.553893	−	0.832588i	$-0.313142\pi$
$227$	−1518.85	−	2630.73i	−0.444096	−	0.769197i	−0.997989	+	0.0633910i	$0.979808\pi$
$228$	−1.06181	−	1.83911i	−0.000308422	−	0.000534203i
$229$	−3099.52	+	5368.53i	−0.894420	+	1.54918i	−0.0598983	+	0.998204i	$0.519078\pi$
$229$	−3099.52	+	5368.53i	−0.894420	+	1.54918i	−0.834521	+	0.550976i	$0.814256\pi$
$230$	259.492			0.0743931
$231$	114.010	+	6.85658i	0.0324731	+	0.00195294i
$232$	1202.41			0.340268
$233$	−1890.68	+	3274.75i	−0.531599	+	0.920756i	0.467721	+	0.883876i	$0.345075\pi$
$233$	−1890.68	+	3274.75i	−0.531599	+	0.920756i	−0.999320	+	0.0368800i	$0.988258\pi$
$234$	2290.40	+	3967.09i	0.639864	+	1.10828i
$235$	121.042	+	209.651i	0.0335996	+	0.0581962i
$236$	−131.494	+	227.755i	−0.0362693	+	0.0628202i
$237$	−275.899			−0.0756185
$238$	1822.87	+	3646.80i	0.496467	+	0.993224i
$239$	4051.01			1.09639			0.548197	−	0.836349i	$-0.315314\pi$
$239$	4051.01			1.09639			0.548197	+	0.836349i	$0.315314\pi$
$240$	27.6608	−	47.9100i	0.00743958	−	0.0128857i
$241$	−2657.65	−	4603.18i	−0.710350	−	1.23036i	−0.964726	−	0.263256i	$-0.915203\pi$
$241$	−2657.65	−	4603.18i	−0.710350	−	1.23036i	0.254376	−	0.967105i	$-0.418130\pi$
$242$	−1059.21	−	1834.60i	−0.281357	−	0.487324i
$243$	−246.214	+	426.455i	−0.0649985	+	0.112581i
$244$	−313.616			−0.0822837
$245$	−419.258	−	982.143i	−0.109328	−	0.256109i
$246$	−106.057			−0.0274876
$247$	42.9937	−	74.4673i	0.0110754	−	0.0191832i
$248$	342.423	+	593.094i	0.0876770	+	0.151861i
$249$	−93.1246	−	161.297i	−0.0237009	−	0.0410512i
$250$	−1355.60	+	2347.98i	−0.342944	+	0.593996i
$251$	6690.02			1.68235			0.841176	−	0.540762i	$-0.181864\pi$
$251$	6690.02			1.68235			0.841176	+	0.540762i	$0.181864\pi$
$252$	1145.23	+	2291.13i	0.286280	+	0.572728i
$253$	−628.376			−0.156149
$254$	−3791.77	+	6567.54i	−0.936680	+	1.62238i
$255$	−21.3461	−	36.9724i	−0.00524212	−	0.00907963i
$256$	−2666.24	−	4618.07i	−0.650938	−	1.12746i
$257$	−911.975	+	1579.59i	−0.221352	+	0.383393i	−0.955219	−	0.295901i	$-0.904380\pi$
$257$	−911.975	+	1579.59i	−0.221352	+	0.383393i	0.733867	+	0.679293i	$0.237714\pi$
$258$	−163.826			−0.0395323
$259$	157.695	+	9.48380i	0.0378327	+	0.00227527i
$260$	−749.466			−0.178769
$261$	1558.92	−	2700.13i	0.369712	−	0.640360i
$262$	2080.63	+	3603.75i	0.490616	+	0.849772i
$263$	1313.64	+	2275.30i	0.307995	+	0.533463i	0.977924	−	0.208962i	$-0.0670086\pi$
$263$	1313.64	+	2275.30i	0.307995	+	0.533463i	−0.669929	+	0.742426i	$0.733675\pi$
$264$	−32.0472	+	55.5074i	−0.00747110	+	0.0129403i
$265$	−88.7612			−0.0205757
$266$	67.8009	−	102.663i	0.0156284	−	0.0236642i
$267$	157.543			0.0361105
$268$	44.3890	−	76.8840i	0.0101175	−	0.0175240i
$269$	−798.856	−	1383.66i	−0.181067	−	0.313618i	0.761177	−	0.648544i	$-0.224622\pi$
$269$	−798.856	−	1383.66i	−0.181067	−	0.313618i	−0.942244	+	0.334927i	$0.891288\pi$
$270$	−68.6970	−	118.987i	−0.0154843	−	0.0268196i
$271$	980.342	−	1698.00i	0.219747	−	0.380613i	−0.734983	−	0.678085i	$-0.762810\pi$
$271$	980.342	−	1698.00i	0.219747	−	0.380613i	0.954731	+	0.297472i	$0.0961434\pi$
$272$	−4781.96			−1.06599
$273$	108.066	−	163.631i	0.0239576	−	0.0362762i
$274$	549.031			0.121052
$275$	1575.13	−	2728.21i	0.345396	−	0.598244i
$276$	13.3221	+	23.0746i	0.00290543	+	0.00503235i
$277$	44.3567	+	76.8280i	0.00962142	+	0.0166648i	0.870796	−	0.491644i	$-0.163604\pi$
$277$	44.3567	+	76.8280i	0.00962142	+	0.0166648i	−0.861175	+	0.508309i	$0.830271\pi$
$278$	3412.04	−	5909.83i	0.736118	−	1.27499i
$279$	1775.80			0.381056
$280$	598.185	+	35.9750i	0.127673	+	0.00767828i
$281$	2149.45			0.456318			0.228159	−	0.973624i	$-0.426729\pi$
$281$	2149.45			0.456318			0.228159	+	0.973624i	$0.426729\pi$
$282$	−31.8022	+	55.0831i	−0.00671559	+	0.0116317i
$283$	−730.294	−	1264.91i	−0.153397	−	0.265692i	0.779077	−	0.626928i	$-0.215688\pi$
$283$	−730.294	−	1264.91i	−0.153397	−	0.265692i	−0.932474	+	0.361236i	$0.882355\pi$
$284$	−940.447	−	1628.90i	−0.196497	−	0.340344i
$285$	−0.644155	+	1.11571i	−0.000133882	+	0.000231891i
$286$	4643.97			0.960153
$287$	−1073.61	−	2147.85i	−0.220812	−	0.441754i
$288$	−5446.86			−1.11444
$289$	611.363	−	1058.91i	0.124438	−	0.215533i
$290$	652.646	+	1130.42i	0.132154	+	0.228898i
$291$	74.3300	+	128.743i	0.0149735	+	0.0259349i
$292$	2336.25	−	4046.50i	0.468215	−	0.810972i
$293$	−5241.67			−1.04513			−0.522563	−	0.852601i	$-0.675024\pi$
$293$	−5241.67			−1.04513			−0.522563	+	0.852601i	$0.675024\pi$
$294$	168.397	−	224.420i	0.0334051	−	0.0445185i
$295$	159.544			0.0314881
$296$	−44.3267	+	76.7761i	−0.00870418	+	0.0150761i
$297$	166.354	+	288.133i	0.0325011	+	0.0562935i
$298$	−733.088	−	1269.75i	−0.142506	−	0.246827i
$299$	−539.424	+	934.310i	−0.104333	+	0.180711i
$300$	−133.577			−0.0257069
$301$	−1658.40	−	3317.77i	−0.317570	−	0.635325i
$302$	−8093.17			−1.54208
$303$	194.915	−	337.604i	0.0369558	−	0.0640093i
$304$	72.1522	+	124.971i	0.0136125	+	0.0235776i
$305$	95.1286	+	164.768i	0.0178592	+	0.0309330i
$306$	−2966.26	+	5137.70i	−0.554149	+	0.959814i
$307$	9095.08			1.69083			0.845413	−	0.534113i	$-0.179354\pi$
$307$	9095.08			1.69083			0.845413	+	0.534113i	$0.179354\pi$
$308$	2592.05	+	155.887i	0.479531	+	0.0288391i
$309$	−129.998			−0.0239331
$310$	−371.722	+	643.841i	−0.0681045	+	0.117960i
$311$	−5269.73	−	9127.44i	−0.960833	−	1.66421i	−0.720417	−	0.693541i	$-0.756050\pi$
$311$	−5269.73	−	9127.44i	−0.960833	−	1.66421i	−0.240415	−	0.970670i	$-0.577284\pi$
$312$	55.0214	+	95.2998i	0.00998388	+	0.0172926i
$313$	2193.13	−	3798.61i	0.396048	−	0.685975i	−0.597186	−	0.802102i	$-0.703715\pi$
$313$	2193.13	−	3798.61i	0.396048	−	0.685975i	0.993234	+	0.116127i	$0.0370481\pi$
$314$	−12916.5			−2.32140
$315$	856.331	−	1296.64i	0.153171	−	0.231929i
$316$	−6272.66			−1.11666
$317$	−1539.46	+	2666.42i	−0.272759	+	0.472432i	−0.969567	−	0.244825i	$-0.921269\pi$
$317$	−1539.46	+	2666.42i	−0.272759	+	0.472432i	0.696808	+	0.717257i	$0.254603\pi$
$318$	−11.6604	−	20.1965i	−0.00205624	−	0.00356152i
$319$	−1580.42	−	2737.37i	−0.277387	−	0.480449i
$320$	159.850	−	276.869i	0.0279247	−	0.0483670i
$321$	376.160			0.0654056
$322$	−850.670	+	1288.07i	−0.147224	+	0.222924i
$323$	111.361			0.0191835
$324$	−1860.04	+	3221.68i	−0.318937	+	0.552414i
$325$	−2704.32	−	4684.02i	−0.461565	−	0.799454i
$326$	2602.28	+	4507.28i	0.442107	+	0.765752i
$327$	−46.4051	+	80.3759i	−0.00784773	+	0.0135927i
$328$	1347.50			0.226838
$329$	−1437.47	−	86.4497i	−0.240882	−	0.0144867i
$330$	−69.5786			−0.0116066
$331$	3021.40	−	5233.22i	0.501726	−	0.869014i	−0.498272	−	0.867021i	$-0.666032\pi$
$331$	3021.40	−	5233.22i	0.501726	−	0.869014i	0.999998	−	0.00199383i	$-0.000634656\pi$
$332$	−2117.22	−	3667.13i	−0.349992	−	0.606205i
$333$	114.939	+	199.080i	0.0189148	+	0.0327613i
$334$	226.334	−	392.022i	0.0370792	−	0.0642231i
$335$	−53.8577			−0.00878376
$336$	147.138	+	294.362i	0.0238900	+	0.0477939i
$337$	−7200.61			−1.16392			−0.581962	−	0.813216i	$-0.697715\pi$
$337$	−7200.61			−1.16392			−0.581962	+	0.813216i	$0.697715\pi$
$338$	5.82111	−	10.0825i	0.000936764	−	0.00162252i
$339$	−97.9799	−	169.706i	−0.0156977	−	0.0271893i
$340$	−485.309	−	840.581i	−0.0774106	−	0.134079i
$341$	900.146	−	1559.10i	0.142949	−	0.247595i
$342$	179.024			0.0283056
$343$	6249.58	+	1138.55i	0.983807	+	0.179230i
$344$	2081.47			0.326237
$345$	8.08195	−	13.9983i	0.00126121	−	0.00218448i
$346$	1174.53	+	2034.35i	0.182495	+	0.316090i
$347$	−3105.70	−	5379.22i	−0.480468	−	0.832195i	0.519281	−	0.854604i	$-0.326200\pi$
$347$	−3105.70	−	5379.22i	−0.480468	−	0.832195i	−0.999749	+	0.0224085i	$0.992867\pi$
$348$	−67.0126	+	116.069i	−0.0103226	+	0.0178792i
$349$	3356.94			0.514879			0.257439	−	0.966294i	$-0.417121\pi$
$349$	3356.94			0.514879			0.257439	+	0.966294i	$0.417121\pi$
$350$	−3460.05	−	6922.11i	−0.528421	−	1.05715i
$351$	571.220			0.0868646
$352$	−2760.99	+	4782.17i	−0.418071	+	0.724121i
$353$	−4070.61	−	7050.51i	−0.613759	−	1.06306i	−0.990601	−	0.136784i	$-0.956323\pi$
$353$	−4070.61	−	7050.51i	−0.613759	−	1.06306i	0.376842	−	0.926277i	$-0.377010\pi$
$354$	20.9590	+	36.3021i	0.00314678	+	0.00545038i
$355$	−570.528	+	988.183i	−0.0852971	+	0.147739i
$356$	3581.80			0.533244
$357$	253.501	+	15.2456i	0.0375818	+	0.00226018i
$358$	8616.27			1.27202
$359$	495.602	−	858.407i	0.0728603	−	0.126198i	−0.827293	−	0.561770i	$-0.810121\pi$
$359$	495.602	−	858.407i	0.0728603	−	0.126198i	0.900154	+	0.435572i	$0.143454\pi$
$360$	436.000	+	755.173i	0.0638311	+	0.110559i
$361$	3427.82	+	5937.16i	0.499755	+	0.865601i
$362$	1686.06	−	2920.34i	0.244799	−	0.424004i
$363$	−131.957			−0.0190797
$364$	2456.90	−	3720.21i	0.353782	−	0.535692i
$365$	−2834.60			−0.406492
$366$	−24.9938	+	43.2906i	−0.00356953	+	0.00618261i
$367$	1093.36	+	1893.75i	0.155512	+	0.269355i	0.933245	−	0.359240i	$-0.116964\pi$
$367$	1093.36	+	1893.75i	0.155512	+	0.269355i	−0.777733	+	0.628594i	$0.783631\pi$
$368$	−905.263	−	1567.96i	−0.128234	−	0.222108i
$369$	1747.02	−	3025.94i	0.246467	−	0.426894i
$370$	−96.2389			−0.0135222
$371$	290.978	−	440.594i	0.0407191	−	0.0616563i
$372$	−76.3356			−0.0106393
$373$	−2941.56	+	5094.94i	−0.408333	+	0.707254i	−0.994703	−	0.102789i	$-0.967223\pi$
$373$	−2941.56	+	5094.94i	−0.408333	+	0.707254i	0.586370	+	0.810043i	$0.300557\pi$
$374$	3007.16	+	5208.55i	0.415766	+	0.720128i
$375$	84.4412	+	146.256i	0.0116281	+	0.0201404i
$376$	404.060	−	699.853i	0.0554198	−	0.0959898i
$377$	−5426.79			−0.741364
$378$	815.830	+	49.0643i	0.111010	+	0.00667617i
$379$	−7571.91			−1.02623			−0.513117	−	0.858318i	$-0.671509\pi$
$379$	−7571.91			−1.02623			−0.513117	+	0.858318i	$0.671509\pi$
$380$	−14.6451	+	25.3660i	−0.00197704	+	0.00342434i
$381$	236.191	+	409.095i	0.0317597	+	0.0550094i
$382$	−293.122	−	507.702i	−0.0392602	−	0.0680007i
$383$	−2977.45	+	5157.10i	−0.397234	+	0.688030i	−0.993384	−	0.114844i	$-0.963363\pi$
$383$	−2977.45	+	5157.10i	−0.397234	+	0.688030i	0.596149	+	0.802874i	$0.296697\pi$
$384$	−280.992			−0.0373420
$385$	−704.341	−	1409.09i	−0.0932378	−	0.186530i
$386$	2849.89			0.375791
$387$	2698.62	−	4674.15i	0.354467	−	0.613955i
$388$	1689.92	+	2927.02i	0.221115	+	0.382982i
$389$	4741.04	+	8211.72i	0.617944	+	1.07031i	0.989860	+	0.142044i	$0.0453674\pi$
$389$	4741.04	+	8211.72i	0.617944	+	1.07031i	−0.371917	+	0.928266i	$0.621299\pi$
$390$	−59.7292	+	103.454i	−0.00775514	+	0.0134323i
$391$	−1397.20			−0.180714
$392$	−2139.55	+	2851.34i	−0.275672	+	0.367384i
$393$	259.206			0.0332703
$394$	−5213.90	+	9030.73i	−0.666681	+	1.15473i
$395$	1902.67	+	3295.53i	0.242364	+	0.419787i
$396$	1889.27	+	3272.31i	0.239746	+	0.415251i
$397$	−7361.53	+	12750.5i	−0.930641	+	1.61192i	−0.148413	+	0.988926i	$0.547416\pi$
$397$	−7361.53	+	12750.5i	−0.930641	+	1.61192i	−0.782228	+	0.622992i	$0.785917\pi$
$398$	−17488.0			−2.20250
$399$	−3.42650	−	6.85499i	−0.000429923	−	0.000860098i
$400$	9076.79			1.13460
$401$	−5139.90	+	8902.56i	−0.640085	+	1.10866i	0.345328	+	0.938482i	$0.387768\pi$
$401$	−5139.90	+	8902.56i	−0.640085	+	1.10866i	−0.985413	+	0.170178i	$0.945566\pi$
$402$	−7.07522	−	12.2546i	−0.000877811	−	0.00152041i
$403$	−1545.45	−	2676.79i	−0.191028	−	0.330870i
$404$	4431.47	−	7675.53i	0.545727	−	0.945227i
$405$	2256.81			0.276893
$406$	−7750.68	−	466.128i	−0.947438	−	0.0569792i
$407$	233.048			0.0283827
$408$	−71.2571	+	123.421i	−0.00864645	+	0.0149761i
$409$	5985.36	+	10366.9i	0.723611	+	1.25333i	0.959543	+	0.281561i	$0.0908523\pi$
$409$	5985.36	+	10366.9i	0.723611	+	1.25333i	−0.235932	+	0.971769i	$0.575814\pi$
$410$	731.396	+	1266.81i	0.0881001	+	0.152594i
$411$	17.0997	−	29.6175i	0.00205223	−	0.00355456i
$412$	−2955.55			−0.353421
$413$	−523.017	+	791.944i	−0.0623147	+	0.0943560i
$414$	−2246.14			−0.266647
$415$	−1284.42	+	2224.69i	−0.151927	+	0.263146i
$416$	4740.30	+	8210.43i	0.558683	+	0.967667i
$417$	−212.538	−	368.126i	−0.0249593	−	0.0432307i
$418$	90.7465	−	157.177i	0.0106186	−	0.0183919i
$419$	−7014.83			−0.817892			−0.408946	−	0.912559i	$-0.634104\pi$
$419$	−7014.83			−0.817892			−0.408946	+	0.912559i	$0.634104\pi$
$420$	−36.8107	+	55.7382i	−0.00427662	+	0.00647558i
$421$	2278.39			0.263758			0.131879	−	0.991266i	$-0.457899\pi$
$421$	2278.39			0.263758			0.131879	+	0.991266i	$0.457899\pi$
$422$	7882.12	−	13652.2i	0.909231	−	1.57483i
$423$	−1047.73	−	1814.72i	−0.120431	−	0.208592i
$424$	148.151	+	256.605i	0.0169690	+	0.0293911i
$425$	3502.31	−	6066.18i	0.399734	−	0.692360i
$426$	−299.798			−0.0340969
$427$	−1129.73	−	67.9420i	−0.128036	−	0.00770011i
$428$	8552.12			0.965846
$429$	144.638	−	250.520i	0.0162778	−	0.0281939i
$430$	1129.78	+	1956.84i	0.126705	+	0.219459i
$431$	5180.13	+	8972.25i	0.578928	+	1.00273i	0.995603	+	0.0936771i	$0.0298621\pi$
$431$	5180.13	+	8972.25i	0.578928	+	1.00273i	−0.416675	+	0.909056i	$0.636805\pi$
$432$	−479.312	+	830.192i	−0.0533817	+	0.0924598i
$433$	−4684.42			−0.519905			−0.259952	−	0.965621i	$-0.583707\pi$
$433$	−4684.42			−0.519905			−0.259952	+	0.965621i	$0.583707\pi$
$434$	−1977.32	−	3955.80i	−0.218697	−	0.437522i
$435$	81.3072			0.00896180
$436$	−1055.03	+	1827.37i	−0.115888	+	0.200723i
$437$	21.0814	+	36.5141i	0.00230769	+	0.00399704i
$438$	−372.378	−	644.978i	−0.0406231	−	0.0703612i
$439$	3416.18	−	5917.01i	0.371402	−	0.643288i	−0.618379	−	0.785880i	$-0.712210\pi$
$439$	3416.18	−	5917.01i	0.371402	−	0.643288i	0.989782	+	0.142592i	$0.0455437\pi$
$440$	884.024			0.0957823
$441$	3629.06	+	8501.33i	0.391865	+	0.917971i
$442$	10325.9			1.11120
$443$	−598.076	+	1035.90i	−0.0641432	+	0.111099i	−0.896314	−	0.443421i	$-0.853765\pi$
$443$	−598.076	+	1035.90i	−0.0641432	+	0.111099i	0.832170	+	0.554520i	$0.187098\pi$
$444$	−4.94083	−	8.55776i	−0.000528111	−	0.000914715i
$445$	−1086.46	−	1881.80i	−0.115737	−	0.200463i
$446$	11523.4	−	19959.1i	1.22343	−	2.11904i
$447$	−91.3288			−0.00966376
$448$	850.302	+	1701.10i	0.0896719	+	0.179396i
$449$	11508.1			1.20958			0.604791	−	0.796384i	$-0.293257\pi$
$449$	11508.1			1.20958			0.604791	+	0.796384i	$0.293257\pi$
$450$	5630.34	−	9752.03i	0.589815	−	1.02159i
$451$	−1771.12	−	3067.66i	−0.184919	−	0.320290i
$452$	−2227.60	−	3858.32i	−0.231809	−	0.401505i
$453$	−252.064	+	436.587i	−0.0261434	+	0.0452818i
$454$	−11008.1			−1.13796
$455$	−2699.77	−	162.365i	−0.278169	−	0.0167292i
$456$	4.30062			0.000441656
$457$	−671.527	+	1163.12i	−0.0687368	+	0.119056i	−0.898345	−	0.439290i	$-0.855230\pi$
$457$	−671.527	+	1163.12i	−0.0687368	+	0.119056i	0.829609	+	0.558345i	$0.188564\pi$
$458$	11232.1	+	19454.5i	1.14594	+	1.98483i
$459$	369.888	+	640.665i	0.0376142	+	0.0651496i
$460$	183.746	−	318.257i	0.0186243	−	0.0322583i
$461$	−6399.46			−0.646535			−0.323267	−	0.946308i	$-0.604781\pi$
$461$	−6399.46			−0.646535			−0.323267	+	0.946308i	$0.604781\pi$
$462$	228.093	−	345.375i	0.0229694	−	0.0347799i
$463$	−4694.74			−0.471238			−0.235619	−	0.971845i	$-0.575712\pi$
$463$	−4694.74			−0.471238			−0.235619	+	0.971845i	$0.575712\pi$
$464$	4553.63	−	7887.12i	0.455597	−	0.789117i
$465$	23.1547	+	40.1052i	0.00230919	+	0.00399964i
$466$	6851.47	+	11867.1i	0.681091	+	1.17968i
$467$	4687.30	−	8118.63i	0.464459	−	0.804466i	−0.534718	−	0.845030i	$-0.679582\pi$
$467$	4687.30	−	8118.63i	0.464459	−	0.804466i	0.999177	+	0.0405645i	$0.0129156\pi$
$468$	6487.30			0.640760
$469$	176.557	−	267.339i	0.0173830	−	0.0263211i
$470$	877.266			0.0860963
$471$	−402.287	+	696.781i	−0.0393554	+	0.0681656i
$472$	−266.293	−	461.233i	−0.0259685	−	0.0449788i
$473$	−2735.84	−	4738.61i	−0.265949	−	0.460637i
$474$	−499.903	+	865.858i	−0.0484416	+	0.0839033i
$475$	−211.377			−0.0204182
$476$	5763.43	+	346.614i	0.554971	+	0.0333761i
$477$	768.308			0.0737493
$478$	7340.06	−	12713.4i	0.702356	−	1.21652i
$479$	8265.72	+	14316.6i	0.788456	+	1.36565i	0.926913	+	0.375277i	$0.122452\pi$
$479$	8265.72	+	14316.6i	0.788456	+	1.36565i	−0.138457	+	0.990368i	$0.544214\pi$
$480$	−71.0217	−	123.013i	−0.00675351	−	0.0116974i
$481$	200.058	−	346.511i	0.0189644	−	0.0328473i
$482$	−19261.7			−1.82022
$483$	42.9908	+	86.0067i	0.00405000	+	0.00810237i
$484$	−3000.08			−0.281751
$485$	1025.20	−	1775.69i	0.0959831	−	0.166248i
$486$	892.233	+	1545.39i	0.0832768	+	0.144240i
$487$	−3310.41	−	5733.79i	−0.308026	−	0.533517i	0.669904	−	0.742448i	$-0.266335\pi$
$487$	−3310.41	−	5733.79i	−0.308026	−	0.533517i	−0.977931	+	0.208930i	$0.933002\pi$
$488$	317.557	−	550.025i	0.0294572	−	0.0510214i
$489$	324.194			0.0299807
$490$	−3841.93	−	463.787i	−0.354205	−	0.0427587i
$491$	19288.8			1.77290			0.886449	−	0.462826i	$-0.153164\pi$
$491$	19288.8			1.77290			0.886449	+	0.462826i	$0.153164\pi$
$492$	−75.0985	+	130.074i	−0.00688151	+	0.0119191i
$493$	−3514.07	−	6086.55i	−0.321026	−	0.556033i
$494$	−155.801	−	269.855i	−0.0141899	−	0.0245777i
$495$	1146.14	−	1985.16i	0.104071	−	0.180256i
$496$	5187.15			0.469576
$497$	−3034.84	−	6071.46i	−0.273906	−	0.547972i
$498$	−674.933			−0.0607318
$499$	−4144.06	+	7177.72i	−0.371770	+	0.643925i	−0.989838	−	0.142200i	$-0.954582\pi$
$499$	−4144.06	+	7177.72i	−0.371770	+	0.643925i	0.618068	+	0.786125i	$0.287916\pi$
$500$	1919.80	+	3325.19i	0.171712	+	0.297414i
$501$	−14.0985	−	24.4192i	−0.00125723	−	0.00217759i
$502$	12121.7	−	20995.4i	1.07772	−	1.86667i
$503$	−7588.41			−0.672665			−0.336332	−	0.941743i	$-0.609187\pi$
$503$	−7588.41			−0.672665			−0.336332	+	0.941743i	$0.609187\pi$
$504$	−5177.83	−	311.396i	−0.457617	−	0.0275212i
$505$	−5376.75			−0.473787
$506$	−1138.56	+	1972.04i	−0.100030	+	0.173257i
$507$	−0.362599	−	0.628040i	−3.17625e−5	−	5.50143e-5i
$508$	5369.88	+	9300.91i	0.468996	+	0.812325i
$509$	−6463.47	+	11195.1i	−0.562846	+	0.974877i	0.434401	+	0.900720i	$0.356960\pi$
$509$	−6463.47	+	11195.1i	−0.562846	+	0.974877i	−0.997247	+	0.0741575i	$0.976373\pi$
$510$	−154.708			−0.0134325
$511$	9292.41	−	14070.4i	0.804446	−	1.21808i
$512$	−9365.38			−0.808389
$513$	11.1620	−	19.3332i	0.000960655	−	0.00166390i
$514$	3304.83	+	5724.13i	0.283598	+	0.491207i
$515$	896.500	+	1552.78i	0.0767078	+	0.132862i
$516$	−116.004	+	200.925i	−0.00989691	+	0.0171420i
$517$	−2124.35			−0.180713
$518$	315.491	−	477.711i	0.0267604	−	0.0405202i
$519$	146.324			0.0123755
$520$	758.883	−	1314.42i	0.0639985	−	0.110849i
$521$	7221.77	+	12508.5i	0.607277	+	1.05184i	0.991687	+	0.128673i	$0.0410717\pi$
$521$	7221.77	+	12508.5i	0.607277	+	1.05184i	−0.384410	+	0.923163i	$0.625595\pi$
$522$	−5649.24	−	9784.77i	−0.473679	−	0.820437i
$523$	−7955.50	+	13779.3i	−0.665143	+	1.15206i	0.314104	+	0.949389i	$0.398296\pi$
$523$	−7955.50	+	13779.3i	−0.665143	+	1.15206i	−0.979247	+	0.202672i	$0.935037\pi$
$524$	5893.14			0.491303
$525$	−481.178	−	28.9382i	−0.0400006	−	0.00240565i
$526$	9520.80			0.789214
$527$	2001.48	−	3466.66i	0.165438	−	0.286547i
$528$	242.731	+	420.423i	0.0200067	+	0.0346526i
$529$	−264.500	−	458.127i	−0.0217391	−	0.0376533i
$530$	−160.827	+	278.560i	−0.0131809	+	0.0228300i
$531$	−1380.99			−0.112863
$532$	−77.9025	−	155.851i	−0.00634869	−	0.0127011i
$533$	−6081.60			−0.494228
$534$	285.454	−	494.420i	0.0231326	−	0.0400668i
$535$	−2594.10	−	4493.11i	−0.209631	−	0.363092i
$536$	89.8936	+	155.700i	0.00724405	+	0.0125471i
$537$	268.356	−	464.806i	0.0215650	−	0.0373517i
$538$	−5789.81			−0.463971
$539$	9303.45	+	1123.09i	0.743466	+	0.0897491i
$540$	−194.577			−0.0155060
$541$	4165.21	−	7214.35i	0.331010	−	0.573326i	−0.651700	−	0.758477i	$-0.725944\pi$
$541$	4165.21	−	7214.35i	0.331010	−	0.573326i	0.982710	+	0.185151i	$0.0592773\pi$
$542$	−3552.57	−	6153.24i	−0.281543	−	0.487646i
$543$	−105.025	−	181.909i	−0.00830030	−	0.0143765i
$544$	−6139.07	+	10633.2i	−0.483843	+	0.838040i
$545$	1280.09			0.100611
$546$	−317.721	−	635.628i	−0.0249033	−	0.0498212i
$547$	9377.15			0.732976			0.366488	−	0.930423i	$-0.380560\pi$
$547$	9377.15			0.732976			0.366488	+	0.930423i	$0.380560\pi$
$548$	388.767	−	673.365i	0.0303053	−	0.0524903i
$549$	−823.424	−	1426.21i	−0.0640125	−	0.110873i
$550$	−5707.98	−	9886.52i	−0.442526	−	0.766477i
$551$	−106.043	+	183.672i	−0.00819891	+	0.0142009i
$552$	−53.9581			−0.00416053
$553$	−22595.7	−	1358.91i	−1.73755	−	0.104497i
$554$	321.481			0.0246542
$555$	−2.99738	+	5.19162i	−0.000229246	+	0.000397066i
$556$	−4832.11	−	8369.47i	−0.368574	−	0.638389i
$557$	8948.09	+	15498.5i	0.680687	+	1.17898i	0.974772	+	0.223205i	$0.0716519\pi$
$557$	8948.09	+	15498.5i	0.680687	+	1.17898i	−0.294085	+	0.955779i	$0.595015\pi$
$558$	3217.59	−	5573.03i	0.244107	−	0.422805i
$559$	−9394.22			−0.710793
$560$	2501.36	−	3787.51i	0.188753	−	0.285806i
$561$	374.635			0.0281945
$562$	3894.60	−	6745.65i	0.292320	−	0.506313i
$563$	9438.37	+	16347.7i	0.706536	+	1.22376i	0.966134	+	0.258040i	$0.0830765\pi$
$563$	9438.37	+	16347.7i	0.706536	+	1.22376i	−0.259598	+	0.965717i	$0.583590\pi$
$564$	45.0381	+	78.0083i	0.00336250	+	0.00582401i
$565$	−1351.39	+	2340.68i	−0.100625	+	0.174288i
$566$	−5292.90			−0.393069
$567$	−7398.28	+	11202.4i	−0.547969	+	0.829726i
$568$	3809.06			0.281381
$569$	−13181.5	+	22831.1i	−0.971174	+	1.68212i	−0.279150	+	0.960248i	$0.590053\pi$
$569$	−13181.5	+	22831.1i	−0.971174	+	1.68212i	−0.692024	+	0.721874i	$0.743281\pi$
$570$	2.33430	+	4.04312i	0.000171532	+	0.000297101i
$571$	7420.20	+	12852.2i	0.543828	+	0.941938i	0.998680	+	0.0513705i	$0.0163590\pi$
$571$	7420.20	+	12852.2i	0.543828	+	0.941938i	−0.454852	+	0.890567i	$0.650308\pi$
$572$	3288.38	−	5695.65i	0.240374	−	0.416341i
$573$	−36.5174			−0.00266237
$574$	−8685.89	−	522.372i	−0.631607	−	0.0379850i
$575$	2652.06			0.192345
$576$	−1383.65	+	2396.55i	−0.100090	+	0.173362i
$577$	−10893.4	−	18867.9i	−0.785956	−	1.36132i	−0.928426	−	0.371517i	$-0.878838\pi$
$577$	−10893.4	−	18867.9i	−0.785956	−	1.36132i	0.142470	−	0.989799i	$-0.454496\pi$
$578$	−2215.46	−	3837.30i	−0.159431	−	0.276143i
$579$	88.7604	−	153.737i	0.00637091	−	0.0110347i
$580$	1848.55			0.132339
$581$	−6832.32	−	13668.6i	−0.487870	−	0.976024i
$582$	538.716			0.0383685
$583$	389.452	−	674.550i	0.0276663	−	0.0479194i
$584$	4731.21	+	8194.70i	0.335238	+	0.580649i
$585$	−1967.78	−	3408.30i	−0.139073	−	0.240882i
$586$	−9497.42	+	16450.0i	−0.669513	+	1.15963i
$587$	6790.87			0.477494			0.238747	−	0.971082i	$-0.423263\pi$
$587$	6790.87			0.477494			0.238747	+	0.971082i	$0.423263\pi$
$588$	−156.001	−	365.443i	−0.0109411	−	0.0256303i
$589$	−120.796			−0.00845047
$590$	289.078	−	500.698i	0.0201714	−	0.0349380i
$591$	324.776	+	562.528i	0.0226049	+	0.0391528i
$592$	335.738	+	581.516i	0.0233087	+	0.0403719i
$593$	−2480.33	+	4296.06i	−0.171762	+	0.297501i	−0.939036	−	0.343819i	$-0.888279\pi$
$593$	−2480.33	+	4296.06i	−0.171762	+	0.297501i	0.767274	+	0.641320i	$0.221613\pi$
$594$	1205.67			0.0832815
$595$	−1566.11	−	3133.12i	−0.107906	−	0.215875i
$596$	−2076.39			−0.142705
$597$	−544.669	+	943.394i	−0.0373397	+	0.0646743i
$598$	1954.77	+	3385.76i	0.133673	+	0.231529i
$599$	7501.85	+	12993.6i	0.511715	+	0.886316i	0.999908	+	0.0135803i	$0.00432288\pi$
$599$	7501.85	+	12993.6i	0.511715	+	0.886316i	−0.488193	+	0.872736i	$0.662344\pi$
$600$	135.255	−	234.269i	0.00920296	−	0.0159400i
$601$	−14385.8			−0.976387			−0.488193	−	0.872735i	$-0.662344\pi$
$601$	−14385.8			−0.976387			−0.488193	+	0.872735i	$0.662344\pi$
$602$	−13417.1	−	806.906i	−0.908370	−	0.0546296i
$603$	466.187			0.0314836
$604$	−5730.75	+	9925.95i	−0.386061	+	0.668677i
$605$	910.008	+	1576.18i	0.0611522	+	0.105919i
$606$	−706.337	−	1223.41i	−0.0473482	−	0.0820094i
$607$	1116.64	−	1934.07i	0.0746671	−	0.129327i	−0.826274	−	0.563268i	$-0.809544\pi$
$607$	1116.64	−	1934.07i	0.0746671	−	0.129327i	0.900941	+	0.433941i	$0.142877\pi$
$608$	370.515			0.0247144
$609$	−266.542	+	403.594i	−0.0177354	+	0.0268546i
$610$	689.456			0.0457627
$611$	−1823.63	+	3158.62i	−0.120747	+	0.209139i
$612$	4200.79	+	7275.99i	0.277462	+	0.480579i
$613$	1003.41	+	1737.95i	0.0661130	+	0.114511i	0.897187	−	0.441650i	$-0.145607\pi$
$613$	1003.41	+	1737.95i	0.0661130	+	0.114511i	−0.831074	+	0.556162i	$0.812274\pi$
$614$	16479.4	−	28543.2i	1.08315	−	1.87608i
$615$	91.1179			0.00597436
$616$	−2898.01	+	4388.13i	−0.189553	+	0.287017i
$617$	16288.8			1.06282			0.531412	−	0.847113i	$-0.321661\pi$
$617$	16288.8			1.06282			0.531412	+	0.847113i	$0.321661\pi$
$618$	−235.544	+	407.974i	−0.0153317	+	0.0265552i
$619$	−9711.18	−	16820.3i	−0.630574	−	1.09219i	−0.987434	−	0.158029i	$-0.949486\pi$
$619$	−9711.18	−	16820.3i	−0.630574	−	1.09219i	0.356860	−	0.934158i	$-0.383847\pi$
$620$	526.430	+	911.804i	0.0340999	+	0.0590628i
$621$	−140.045	+	242.566i	−0.00904964	+	0.0156744i
$622$	−38193.0			−2.46206
$623$	12902.6	+	775.964i	0.829743	+	0.0499010i
$624$	833.483			0.0534712
$625$	−6042.02	+	10465.1i	−0.386690	+	0.669766i
$626$	−7947.49	−	13765.5i	−0.507421	−	0.878879i
$627$	−5.65264	−	9.79066i	−0.000360039	−	0.000623606i
$628$	−9146.12	+	15841.5i	−0.581162	+	1.00660i
$629$	518.183			0.0328479
$630$	−2517.68	−	5036.83i	−0.159217	−	0.318527i
$631$	−11350.4			−0.716087			−0.358044	−	0.933705i	$-0.616556\pi$
$631$	−11350.4			−0.716087			−0.358044	+	0.933705i	$0.616556\pi$
$632$	6351.48	−	11001.1i	0.399760	−	0.692404i
$633$	−490.981	−	850.403i	−0.0308290	−	0.0533973i
$634$	5578.71	+	9662.61i	0.349462	+	0.605286i
$635$	3257.67	−	5642.45i	0.203585	−	0.352620i
$636$	−33.0269			−0.00205912
$637$	9656.35	−	12868.9i	0.600625	−	0.800444i
$638$	−11454.3			−0.710783
$639$	4938.43	−	8553.62i	0.305730	−	0.529540i
$640$	1937.79	+	3356.36i	0.119684	+	0.207300i
$641$	6336.68	+	10975.5i	0.390459	+	0.676294i	0.992510	−	0.122163i	$-0.0389831\pi$
$641$	6336.68	+	10975.5i	0.390459	+	0.676294i	−0.602051	+	0.798457i	$0.705650\pi$
$642$	681.567	−	1180.51i	0.0418992	−	0.0725715i
$643$	9799.06			0.600991			0.300496	−	0.953783i	$-0.402848\pi$
$643$	9799.06			0.600991			0.300496	+	0.953783i	$0.402848\pi$
$644$	977.410	+	1955.39i	0.0598065	+	0.119648i
$645$	140.749			0.00859226
$646$	201.775	−	349.485i	0.0122891	−	0.0212853i
$647$	−1726.43	−	2990.27i	−0.104904	−	0.181700i	0.808795	−	0.588091i	$-0.200120\pi$
$647$	−1726.43	−	2990.27i	−0.104904	−	0.181700i	−0.913699	+	0.406391i	$0.866787\pi$
$648$	−3766.82	−	6524.33i	−0.228356	−	0.395524i
$649$	−700.019	+	1212.47i	−0.0423392	+	0.0733337i
$650$	−19599.9			−1.18272
$651$	−274.980	−	16.5374i	−0.0165550	−	0.000995625i
$652$	7370.66			0.442726
$653$	−339.381	+	587.825i	−0.0203385	+	0.0352272i	−0.876015	−	0.482283i	$-0.839808\pi$
$653$	−339.381	+	587.825i	−0.0203385	+	0.0352272i	0.855677	+	0.517510i	$0.173141\pi$
$654$	168.163	+	291.267i	0.0100546	+	0.0174151i
$655$	−1787.55	−	3096.13i	−0.106634	−	0.184696i
$656$	5103.08	−	8838.80i	0.303722	−	0.526063i
$657$	24536.0			1.45699
$658$	−2875.86	+	4354.58i	−0.170384	+	0.257993i
$659$	−7398.18			−0.437317			−0.218659	−	0.975801i	$-0.570168\pi$
$659$	−7398.18			−0.437317			−0.218659	+	0.975801i	$0.570168\pi$
$660$	−49.2684	+	85.3353i	−0.00290571	+	0.00503284i
$661$	−10574.9	−	18316.3i	−0.622264	−	1.07779i	−0.989063	−	0.147492i	$-0.952880\pi$
$661$	−10574.9	−	18316.3i	−0.622264	−	1.07779i	0.366800	−	0.930300i	$-0.380454\pi$
$662$	−10949.0	−	18964.2i	−0.642817	−	1.11339i
$663$	321.602	−	557.031i	0.0188386	−	0.0326294i
$664$	8575.29			0.501184
$665$	−58.2507	+	88.2022i	−0.00339679	+	0.00514336i
$666$	833.034			0.0484676
$667$	1330.48	−	2304.46i	0.0772361	−	0.133777i
$668$	−320.533	−	555.179i	−0.0185656	−	0.0321565i
$669$	−717.798	−	1243.26i	−0.0414823	−	0.0718495i
$670$	−97.5851	+	169.022i	−0.00562693	+	0.00974613i
$671$	−1669.56			−0.0960545
$672$	843.438	+	50.7246i	0.0484172	+	0.00291182i
$673$	−7170.68			−0.410712			−0.205356	−	0.978687i	$-0.565835\pi$
$673$	−7170.68			−0.410712			−0.205356	+	0.978687i	$0.565835\pi$
$674$	−13046.8	+	22597.8i	−0.745616	+	1.29145i
$675$	−702.096	−	1216.07i	−0.0400351	−	0.0693428i
$676$	−8.24381	−	14.2787i	−0.000469038	−	0.000812398i
$677$	−251.763	+	436.065i	−0.0142925	+	0.0247553i	−0.873083	−	0.487571i	$-0.837883\pi$
$677$	−251.763	+	436.065i	−0.0142925	+	0.0247553i	0.858791	+	0.512327i	$0.171216\pi$
$678$	−710.121			−0.0402243
$679$	5453.40	+	10910.0i	0.308221	+	0.616622i
$680$	1965.63			0.110851
$681$	−342.849	+	593.832i	−0.0192922	+	0.0334151i
$682$	−3261.96	−	5649.88i	−0.183148	−	0.317222i
$683$	10911.1	+	18898.5i	0.611274	+	1.05876i	0.991026	+	0.133669i	$0.0426759\pi$
$683$	10911.1	+	18898.5i	0.611274	+	1.05876i	−0.379752	+	0.925088i	$0.623991\pi$
$684$	126.766	−	219.566i	0.00708631	−	0.0122738i
$685$	−471.696			−0.0263103
$686$	14896.8	−	17550.2i	0.829099	−	0.976779i
$687$	1399.30			0.0777100
$688$	7882.71	−	13653.3i	0.436810	−	0.756578i
$689$	−668.643	−	1158.12i	−0.0369714	−	0.0640363i
$690$	−29.2875	−	50.7274i	−0.00161588	−	0.00279878i
$691$	−9969.22	+	17267.2i	−0.548838	+	0.950615i	0.449517	+	0.893272i	$0.351596\pi$
$691$	−9969.22	+	17267.2i	−0.548838	+	0.950615i	−0.998355	+	0.0573433i	$0.981737\pi$
$692$	3326.72			0.182750
$693$	6096.71	+	12197.0i	0.334192	+	0.668579i
$694$	−22508.9			−1.23116
$695$	−2931.43	+	5077.39i	−0.159994	+	0.277117i
$696$	−135.709	−	235.056i	−0.00739088	−	0.0128014i
$697$	−3938.08	−	6820.96i	−0.214011	−	0.370678i
$698$	6082.45	−	10535.1i	0.329834	−	0.571290i
$699$	853.562			0.0461870
$700$	−10939.7	−	657.919i	−0.590690	−	0.0355243i
$701$	27263.6			1.46894			0.734472	−	0.678639i	$-0.237430\pi$
$701$	27263.6			1.46894			0.734472	+	0.678639i	$0.237430\pi$
$702$	1035.00	−	1792.67i	0.0556459	−	0.0963816i
$703$	−7.81855	−	13.5421i	−0.000419463	−	0.000726530i
$704$	1402.73	+	2429.60i	0.0750957	+	0.130070i
$705$	27.3227	−	47.3242i	0.00145962	−	0.00252813i
$706$	−29502.3			−1.57271
$707$	17626.1	−	26689.2i	0.937621	−	1.41973i
$708$	59.3641			0.00315119
$709$	9285.96	−	16083.8i	0.491878	−	0.851958i	−0.508078	−	0.861311i	$-0.669644\pi$
$709$	9285.96	−	16083.8i	0.491878	−	0.851958i	0.999956	+	0.00935314i	$0.00297724\pi$
$710$	2067.49	+	3580.99i	0.109284	+	0.189285i
$711$	−16469.4	−	28525.8i	−0.868705	−	1.50464i
$712$	−3626.81	+	6281.81i	−0.190899	+	0.330647i
$713$	1515.58			0.0796059
$714$	507.166	−	767.942i	0.0265829	−	0.0402514i
$715$	−3989.83			−0.208687
$716$	6101.16	−	10567.5i	0.318451	−	0.551573i
$717$	−457.215	−	791.920i	−0.0238145	−	0.0412480i
$718$	−1795.97	−	3110.71i	−0.0933495	−	0.161686i
$719$	8530.13	−	14774.6i	0.442448	−	0.766342i	−0.555423	−	0.831568i	$-0.687444\pi$
$719$	8530.13	−	14774.6i	0.442448	−	0.766342i	0.997871	+	0.0652261i	$0.0207769\pi$
$720$	6604.67			0.341863
$721$	−10646.6	−	640.292i	−0.549933	−	0.0330731i
$722$	24843.6			1.28058
$723$	−599.909	+	1039.07i	−0.0308587	+	0.0534488i
$724$	−2387.78	−	4135.76i	−0.122571	−	0.212299i
$725$	6670.16	+	11553.1i	0.341688	+	0.591820i
$726$	−239.093	+	414.122i	−0.0122226	+	0.0211701i
$727$	24057.0			1.22727			0.613636	−	0.789589i	$-0.289706\pi$
$727$	24057.0			1.22727			0.613636	+	0.789589i	$0.289706\pi$
$728$	4036.78	+	8075.91i	0.205512	+	0.411144i
$729$	−19460.5			−0.988695
$730$	−5136.03	+	8895.87i	−0.260401	+	0.451028i
$731$	−6083.14	−	10536.3i	−0.307788	−	0.533105i
$732$	35.3961	+	61.3079i	0.00178727	+	0.00309564i
$733$	6432.17	−	11140.8i	0.324117	−	0.561387i	−0.657216	−	0.753702i	$-0.728266\pi$
$733$	6432.17	−	11140.8i	0.324117	−	0.561387i	0.981333	+	0.192315i	$0.0615996\pi$
$734$	7924.26			0.398487
$735$	−144.677	+	192.809i	−0.00726052	+	0.00967599i
$736$	−4648.69			−0.232817
$737$	236.308	−	409.297i	0.0118107	−	0.0204568i
$738$	−6330.89	−	10965.4i	−0.315777	−	0.546942i
$739$	12335.3	+	21365.4i	0.614022	+	1.06352i	0.990555	+	0.137114i	$0.0437826\pi$
$739$	12335.3	+	21365.4i	0.614022	+	1.06352i	−0.376534	+	0.926403i	$0.622884\pi$
$740$	−68.1464	+	118.033i	−0.00338529	+	0.00586349i
$741$	−19.4098			−0.000962265
$742$	−855.497	−	1711.49i	−0.0423265	−	0.0846778i
$743$	−34449.1			−1.70096			−0.850482	−	0.526004i	$-0.823690\pi$
$743$	−34449.1			−1.70096			−0.850482	+	0.526004i	$0.823690\pi$
$744$	77.2948	−	133.879i	0.00380883	−	0.00659708i
$745$	629.827	+	1090.89i	0.0309733	+	0.0536473i
$746$	10659.7	+	18463.1i	0.523161	+	0.906142i
$747$	11117.8	−	19256.7i	0.544553	−	0.943193i
$748$	8517.44			0.416348
$749$	30806.9	+	1852.74i	1.50288	+	0.0903839i
$750$	611.998			0.0297960
$751$	−11144.8	+	19303.3i	−0.541516	+	0.937933i	0.457301	+	0.889312i	$0.348816\pi$
$751$	−11144.8	+	19303.3i	−0.541516	+	0.937933i	−0.998817	+	0.0486213i	$0.984517\pi$
$752$	−3060.42	−	5300.81i	−0.148407	−	0.257049i
$753$	−755.065	−	1307.81i	−0.0365420	−	0.0632926i
$754$	−9832.84	+	17031.0i	−0.474922	+	0.822589i
$755$	6953.18			0.335169
$756$	637.862	−	965.841i	0.0306863	−	0.0464647i
$757$	−26620.9			−1.27814			−0.639070	−	0.769148i	$-0.720681\pi$
$757$	−26620.9			−1.27814			−0.639070	+	0.769148i	$0.720681\pi$
$758$	−13719.6	+	23763.0i	−0.657412	+	1.13867i
$759$	70.9213	+	122.839i	0.00339167	+	0.00587455i
$760$	−29.6582	−	51.3695i	−0.00141555	−	0.00245180i
$761$	−7786.46	+	13486.6i	−0.370906	+	0.642427i	−0.989705	−	0.143122i	$-0.954286\pi$
$761$	−7786.46	+	13486.6i	−0.370906	+	0.642427i	0.618800	+	0.785549i	$0.287619\pi$
$762$	1711.82			0.0813817
$763$	−4196.39	+	6354.10i	−0.199108	+	0.301486i
$764$	−830.234			−0.0393152
$765$	2548.44	−	4414.02i	0.120443	−	0.208613i
$766$	10789.7	+	18688.4i	0.508941	+	0.881512i
$767$	1201.85	+	2081.67i	0.0565793	+	0.0979982i
$768$	−601.848	+	1042.43i	−0.0282778	+	0.0489786i
$769$	25603.0			1.20061			0.600305	−	0.799771i	$-0.295046\pi$
$769$	25603.0			1.20061			0.600305	+	0.799771i	$0.295046\pi$
$770$	−5698.38	−	342.702i	−0.266695	−	0.0160391i
$771$	411.718			0.0192317
$772$	2018.00	−	3495.27i	0.0940793	−	0.162950i
$773$	−12861.0	−	22276.0i	−0.598421	−	1.03650i	−0.993054	−	0.117657i	$-0.962462\pi$
$773$	−12861.0	−	22276.0i	−0.598421	−	1.03650i	0.394633	−	0.918839i	$-0.370872\pi$
$774$	−9779.30	−	16938.2i	−0.454147	−	0.786606i
$775$	−3799.07	+	6580.18i	−0.176086	+	0.304990i
$776$	−6844.60			−0.316633
$777$	−15.9442	−	31.8976i	−0.000736156	−	0.00147274i
$778$	34361.3			1.58343
$779$	−118.839	+	205.835i	−0.00546578	+	0.00946700i
$780$	84.5881	+	146.511i	0.00388300	+	0.00672555i
$781$	−5006.54	−	8671.58i	−0.229383	−	0.397303i
$782$	−2531.59	+	4384.84i	−0.115766	+	0.200513i
$783$	−1408.91			−0.0643042
$784$	10600.5	+	24832.5i	0.482896	+	1.13122i
$785$	11097.1			0.504551
$786$	469.657	−	813.470i	0.0213131	−	0.0369154i
$787$	780.983	+	1352.70i	0.0353736	+	0.0612689i	0.883170	−	0.469053i	$-0.155405\pi$
$787$	780.983	+	1352.70i	0.0353736	+	0.0612689i	−0.847797	+	0.530322i	$0.822071\pi$
$788$	7383.89	+	12789.3i	0.333807	+	0.578171i
$789$	296.527	−	513.600i	0.0133798	−	0.0231745i
$790$	13789.9			0.621039
$791$	−7188.53	−	14381.3i	−0.323129	−	0.646446i
$792$	−7652.03			−0.343312
$793$	−1433.22	+	2482.41i	−0.0641804	+	0.111164i
$794$	26676.8	+	46205.6i	1.19235	+	2.06521i
$795$	10.0180	+	17.3517i	0.000446920	+	0.000774088i
$796$	−12383.2	+	21448.4i	−0.551396	+	0.955046i
$797$	44762.5			1.98942			0.994710	−	0.102719i	$-0.0327543\pi$
$797$	44762.5			1.98942			0.994710	+	0.102719i	$0.0327543\pi$
$798$	−27.7216	−	1.66719i	−0.00122974	−	7.39571e-5i
$799$	−4723.50			−0.209143
$800$	11652.7	−	20183.2i	0.514984	−	0.891978i
$801$	9404.29	+	16288.7i	0.414837	+	0.718519i
$802$	18626.0	+	32261.2i	0.820084	+	1.42043i
$803$	12437.2	−	21541.8i	0.546574	−	0.946694i
$804$	−20.0398			−0.000879040
$805$	730.847	−	1106.64i	0.0319987	−	0.0484519i
$806$	−11200.8			−0.489494
$807$	−180.325	+	312.332i	−0.00786584	+	0.0136240i
$808$	8974.30	+	15543.9i	0.390736	+	0.676775i
$809$	−10760.3	−	18637.4i	−0.467629	−	0.809957i	0.531687	−	0.846941i	$-0.321558\pi$
$809$	−10760.3	−	18637.4i	−0.467629	−	0.809957i	−0.999316	+	0.0369838i	$0.988225\pi$
$810$	4089.12	−	7082.57i	0.177379	−	0.307230i
$811$	567.298			0.0245629			0.0122814	−	0.999925i	$-0.496091\pi$
$811$	567.298			0.0245629			0.0122814	+	0.999925i	$0.496091\pi$
$812$	−6059.92	+	9175.83i	−0.261898	+	0.396562i
$813$	−442.583			−0.0190923
$814$	422.261	−	731.378i	0.0181821	−	0.0314923i
$815$	−2235.73	−	3872.40i	−0.0960910	−	0.166434i
$816$	539.714	+	934.812i	0.0231541	+	0.0401041i
$817$	−183.570	+	317.952i	−0.00786082	+	0.0136153i
$818$	43379.6			1.85420
$819$	23368.9	+	1405.41i	0.997041	+	0.0599623i
$820$	2071.60			0.0882235
$821$	−23005.2	+	39846.2i	−0.977939	+	1.69384i	−0.308064	+	0.951366i	$0.599681\pi$
$821$	−23005.2	+	39846.2i	−0.977939	+	1.69384i	−0.669875	+	0.742474i	$0.733652\pi$
$822$	−61.9661	−	107.328i	−0.00262934	−	0.00455415i
$823$	−12623.0	−	21863.7i	−0.534643	−	0.926029i	−0.999181	−	0.0404756i	$-0.987113\pi$
$823$	−12623.0	−	21863.7i	−0.534643	−	0.926029i	0.464537	−	0.885554i	$-0.346221\pi$
$824$	2992.68	−	5183.48i	0.126523	−	0.219145i
$825$	−711.106			−0.0300091
$826$	1537.71	+	3076.32i	0.0647746	+	0.129587i
$827$	8676.16			0.364812			0.182406	−	0.983223i	$-0.441611\pi$
$827$	8676.16			0.364812			0.182406	+	0.983223i	$0.441611\pi$
$828$	−1590.49	+	2754.80i	−0.0667551	+	0.115623i
$829$	13778.3	+	23864.7i	0.577250	+	0.999825i	0.995793	+	0.0916288i	$0.0292073\pi$
$829$	13778.3	+	23864.7i	0.577250	+	0.999825i	−0.418544	+	0.908197i	$0.637459\pi$
$830$	4654.51	+	8061.85i	0.194651	+	0.337146i
$831$	10.0126	−	17.3423i	0.000417970	−	0.000723945i
$832$	4816.65			0.200706
$833$	20686.3	+	2497.19i	0.860428	+	0.103868i
$834$	−1540.39			−0.0639562
$835$	−194.453	+	336.803i	−0.00805908	+	0.0139587i
$836$	−128.515	−	222.594i	−0.00531671	−	0.00920881i
$837$	−401.229	−	694.949i	−0.0165693	−	0.0286989i
$838$	−12710.2	+	22014.7i	−0.523946	+	0.907502i
$839$	−34858.0			−1.43436			−0.717182	−	0.696886i	$-0.754569\pi$
$839$	−34858.0			−1.43436			−0.717182	+	0.696886i	$0.754569\pi$
$840$	−60.4812	−	120.998i	−0.00248429	−	0.00497002i
$841$	−11003.9			−0.451182
$842$	4128.24	−	7150.32i	0.168965	−	0.292656i
$843$	−242.597	−	420.190i	−0.00991159	−	0.0171674i
$844$	−11162.6	−	19334.2i	−0.455252	−	0.788520i
$845$	−5.00116	+	8.66226i	−0.000203604	+	0.000352652i
$846$	−7593.53			−0.308595
$847$	−10807.1	−	649.939i	−0.438412	−	0.0263662i
$848$	2244.24			0.0908815
$849$	−164.849	+	285.526i	−0.00666382	+	0.0115421i
$850$	−12691.7	−	21982.7i	−0.512144	−	0.887059i
$851$	98.0961	+	169.907i	0.00395146	+	0.00684412i
$852$	−212.286	+	367.690i	−0.00853615	+	0.0147851i
$853$	43761.4			1.75658			0.878289	−	0.478130i	$-0.158685\pi$
$853$	43761.4			1.75658			0.878289	+	0.478130i	$0.158685\pi$
$854$	−2260.18	+	3422.33i	−0.0905642	+	0.137131i
$855$	−153.807			−0.00615216
$856$	−8659.58	+	14998.8i	−0.345769	+	0.598890i
$857$	−18232.7	−	31580.0i	−0.726741	−	1.25875i	−0.958253	−	0.285920i	$-0.907701\pi$
$857$	−18232.7	−	31580.0i	−0.726741	−	1.25875i	0.231512	−	0.972832i	$-0.425633\pi$
$858$	−524.139	−	907.836i	−0.0208553	−	0.0361224i
$859$	−4238.52	+	7341.33i	−0.168354	+	0.291598i	−0.937841	−	0.347064i	$-0.887179\pi$
$859$	−4238.52	+	7341.33i	−0.168354	+	0.291598i	0.769487	+	0.638662i	$0.220512\pi$
$860$	3199.99			0.126882
$861$	−298.704	+	452.292i	−0.0118232	+	0.0179025i
$862$	37543.6			1.48346
$863$	−10041.2	+	17391.9i	−0.396067	+	0.686009i	−0.993237	−	0.116106i	$-0.962959\pi$
$863$	−10041.2	+	17391.9i	−0.396067	+	0.686009i	0.597169	+	0.802115i	$0.296292\pi$
$864$	1230.68	+	2131.60i	0.0484589	+	0.0839333i
$865$	−1009.09	−	1747.79i	−0.0396648	−	0.0687014i
$866$	−8487.72	+	14701.2i	−0.333054	+	0.576866i
$867$	−276.005			−0.0108115
$868$	−6251.77	−	375.983i	−0.244469	−	0.0147024i
$869$	−33392.9			−1.30354
$870$	147.321	−	255.168i	0.00574098	−	0.00994367i
$871$	−405.713	−	702.716i	−0.0157831	−	0.0273371i
$872$	−2136.58	−	3700.67i	−0.0829746	−	0.143716i
$873$	−8874.01	+	15370.2i	−0.344032	+	0.595881i
$874$	152.790			0.00591329
$875$	6195.24	+	12394.1i	0.239357	+	0.478853i
$876$	−1054.72			−0.0406800
$877$	−10453.8	+	18106.6i	−0.402509	+	0.697167i	−0.994028	−	0.109125i	$-0.965195\pi$
$877$	−10453.8	+	18106.6i	−0.402509	+	0.697167i	0.591519	+	0.806291i	$0.298529\pi$
$878$	−12379.6	−	21442.1i	−0.475845	−	0.824187i
$879$	591.599	+	1024.68i	0.0227009	+	0.0393192i
$880$	3347.88	−	5798.69i	0.128246	−	0.222129i
$881$	−34959.5			−1.33691			−0.668453	−	0.743754i	$-0.733043\pi$
$881$	−34959.5			−1.33691			−0.668453	+	0.743754i	$0.733043\pi$
$882$	33255.4	+	4014.49i	1.26958	+	0.153260i
$883$	−16807.4			−0.640560			−0.320280	−	0.947323i	$-0.603777\pi$
$883$	−16807.4			−0.640560			−0.320280	+	0.947323i	$0.603777\pi$
$884$	7311.73	−	12664.3i	0.278190	−	0.481839i
$885$	−18.0068	−	31.1887i	−0.000683946	−	0.00118463i
$886$	2167.32	+	3753.90i	0.0821810	+	0.142342i
$887$	796.267	−	1379.17i	0.0301421	−	0.0522076i	−0.850561	−	0.525877i	$-0.823737\pi$
$887$	796.267	−	1379.17i	0.0301421	−	0.0522076i	0.880703	+	0.473669i	$0.157071\pi$
$888$	20.0116			0.000756246
$889$	17328.7	+	34667.6i	0.653754	+	1.30789i
$890$	−7874.26			−0.296568
$891$	−9902.04	+	17150.8i	−0.372313	+	0.644865i
$892$	−16319.4	−	28266.0i	−0.612570	−	1.06100i
$893$	71.2701	+	123.443i	0.00267073	+	0.00462584i
$894$	−165.479	+	286.618i	−0.00619066	+	0.0107225i
$895$	−7402.61			−0.276471
$896$	−23012.8	−	1384.00i	−0.858041	−	0.0516028i
$897$	243.527			0.00906481
$898$	20851.7	−	36116.1i	0.774865	−	1.34211i
$899$	3811.82	+	6602.27i	0.141414	+	0.244937i
$900$	−7973.65	−	13810.8i	−0.295320	−	0.511510i
$901$	865.947	−	1499.86i	0.0320187	−	0.0554581i
$902$	−12836.4			−0.473842
$903$	−461.406	+	698.654i	−0.0170040	+	0.0257472i
$904$	9022.38			0.331947
$905$	−1448.56	+	2508.98i	−0.0532065	+	0.0921563i
$906$	913.431	+	1582.11i	0.0334953	+	0.0580155i
$907$	−12186.8	−	21108.2i	−0.446149	−	0.772753i	0.551982	−	0.833856i	$-0.313872\pi$
$907$	−12186.8	−	21108.2i	−0.446149	−	0.772753i	−0.998131	+	0.0611026i	$0.980538\pi$
$908$	−7794.79	+	13501.0i	−0.284889	+	0.493442i
$909$	46540.7			1.69819
$910$	−5401.28	+	8178.53i	−0.196759	+	0.297929i
$911$	−41830.0			−1.52128			−0.760641	−	0.649172i	$-0.775115\pi$
$911$	−41830.0			−1.52128			−0.760641	+	0.649172i	$0.775115\pi$
$912$	16.2868	−	28.2096i	0.000591350	−	0.00102425i
$913$	−11271.2	−	19522.2i	−0.408566	−	0.707658i
$914$	2433.49	+	4214.93i	0.0880664	+	0.152535i
$915$	21.4733	−	37.1928i	0.000775830	−	0.00134378i
$916$	31813.6			1.14755
$917$	21228.6	+	1276.69i	0.764482	+	0.0459762i
$918$	2680.81			0.0963834
$919$	6405.44	−	11094.5i	0.229919	−	0.398232i	−0.727865	−	0.685721i	$-0.759487\pi$
$919$	6405.44	−	11094.5i	0.229919	−	0.398232i	0.957784	+	0.287489i	$0.0928204\pi$
$920$	372.109	+	644.512i	0.0133349	+	0.0230967i
$921$	−1026.51	−	1777.97i	−0.0367261	−	0.0636114i
$922$	−11595.2	+	20083.5i	−0.414174	+	0.717370i
$923$	−17191.3			−0.613064
$924$	−262.076	−	524.306i	−0.00933082	−	0.0186671i
$925$	−983.579			−0.0349620
$926$	−8506.44	+	14733.6i	−0.301878	+	0.522868i
$927$	−7760.02	−	13440.7i	−0.274943	−	0.476216i
$928$	−11691.9	−	20250.9i	−0.413582	−	0.716346i
$929$	4799.62	−	8313.19i	0.169505	−	0.293592i	−0.768741	−	0.639561i	$-0.779116\pi$
$929$	4799.62	−	8313.19i	0.169505	−	0.293592i	0.938246	+	0.345969i	$0.112450\pi$
$930$	167.817			0.00591713
$931$	−246.861	−	578.290i	−0.00869017	−	0.0203574i
$932$	19406.0			0.682044
$933$	−1189.53	+	2060.33i	−0.0417401	+	0.0722959i
$934$	−16985.9	−	29420.4i	−0.595070	−	1.03069i
$935$	−2583.58	−	4474.89i	−0.0903659	−	0.156518i
$936$	−6568.82	+	11377.5i	−0.229390	+	0.397314i
$937$	11704.8			0.408088			0.204044	−	0.978962i	$-0.434591\pi$
$937$	11704.8			0.408088			0.204044	+	0.978962i	$0.434591\pi$
$938$	−519.091	−	1038.48i	−0.0180692	−	0.0361490i
$939$	−990.106			−0.0344099
$940$	621.190	−	1075.93i	0.0215542	−	0.0373330i
$941$	−16659.2	−	28854.6i	−0.577126	−	0.999611i	−0.995807	−	0.0914778i	$-0.970841\pi$
$941$	−16659.2	−	28854.6i	−0.577126	−	0.999611i	0.418681	−	0.908133i	$-0.362492\pi$
$942$	1457.81	+	2525.00i	0.0504226	+	0.0873345i
$943$	1491.02	−	2582.52i	0.0514892	−	0.0891819i
$944$	−4033.90			−0.139081
$945$	−700.915	−	42.1532i	−0.0241278	−	0.00145105i
$946$	−19828.3			−0.681474
$947$	−2875.16	+	4979.93i	−0.0986591	+	0.170883i	−0.911130	−	0.412119i	$-0.864789\pi$
$947$	−2875.16	+	4979.93i	−0.0986591	+	0.170883i	0.812471	+	0.583002i	$0.198122\pi$
$948$	707.960	+	1226.22i	0.0242547	+	0.0420104i
$949$	−21353.2	−	36984.8i	−0.730405	−	1.26510i
$950$	−382.995	+	663.368i	−0.0130800	+	0.0226552i
$951$	695.000			0.0236981
$952$	−6443.75	+	9757.02i	−0.219373	+	0.332171i
$953$	−2522.27			−0.0857339			−0.0428669	−	0.999081i	$-0.513649\pi$
$953$	−2522.27			−0.0857339			−0.0428669	+	0.999081i	$0.513649\pi$
$954$	1392.10	−	2411.19i	0.0472442	−	0.0818294i
$955$	251.833	+	436.188i	0.00853313	+	0.0147798i
$956$	−10394.9	−	18004.6i	−0.351670	−	0.609110i
$957$	−356.747	+	617.903i	−0.0120501	+	0.0208714i
$958$	59906.8			2.02036
$959$	1546.32	−	2341.41i	0.0520680	−	0.0788405i
$960$	−72.1657			−0.00242619
$961$	12724.4	−	22039.4i	0.427123	−	0.739799i
$962$	−724.973	−	1255.69i	−0.0242974	−	0.0420843i
$963$	22454.3	+	38891.9i	0.751379	+	1.30143i
$964$	−13639.1	+	23623.6i	−0.455691	+	0.789280i
$965$	−2448.46			−0.0816774
$966$	347.812	+	20.9175i	0.0115845	+	0.000696697i
$967$	−25074.8			−0.833868			−0.416934	−	0.908937i	$-0.636895\pi$
$967$	−25074.8			−0.833868			−0.416934	+	0.908937i	$0.636895\pi$
$968$	3037.78	−	5261.59i	0.100866	−	0.174704i
$969$	−12.5687	−	21.7696i	−0.000416681	−	0.000721712i
$970$	−3715.12	−	6434.78i	−0.122975	−	0.212998i
$971$	20734.4	−	35913.1i	0.685272	−	1.18693i	−0.288080	−	0.957606i	$-0.593017\pi$
$971$	20734.4	−	35913.1i	0.685272	−	1.18693i	0.973351	−	0.229319i	$-0.0736499\pi$
$972$	2527.15			0.0833934
$973$	−15593.3	−	31195.8i	−0.513772	−	1.02784i
$974$	−23992.6			−0.789294
$975$	−610.443	+	1057.32i	−0.0200511	+	0.0347295i
$976$	−2405.23	−	4165.98i	−0.0788828	−	0.136629i
$977$	−1264.42	−	2190.04i	−0.0414048	−	0.0717152i	0.844580	−	0.535429i	$-0.179850\pi$
$977$	−1264.42	−	2190.04i	−0.0414048	−	0.0717152i	−0.885985	+	0.463714i	$0.846517\pi$
$978$	587.410	−	1017.42i	0.0192058	−	0.0332655i
$979$	19068.0			0.622487
$980$	−3289.27	+	4383.57i	−0.107216	+	0.142886i
$981$	−11080.3			−0.360619
$982$	34949.6	−	60534.4i	1.13573	−	1.96714i
$983$	−12037.3	−	20849.2i	−0.390569	−	0.676485i	0.601956	−	0.798529i	$-0.294388\pi$
$983$	−12037.3	−	20849.2i	−0.390569	−	0.676485i	−0.992525	+	0.122044i	$0.961055\pi$
$984$	−152.084	−	263.418i	−0.00492711	−	0.00853400i
$985$	4479.48	−	7758.69i	0.144902	−	0.250977i
$986$	−25468.7			−0.822604
$987$	145.339	+	290.763i	0.00468713	+	0.00937699i
$988$	−441.289			−0.0142098
$989$	2303.17	−	3989.21i	0.0740512	−	0.128260i
$990$	−4153.38	−	7193.86i	−0.133336	−	0.230945i
$991$	−17078.9	−	29581.6i	−0.547458	−	0.948225i	−0.998448	−	0.0556957i	$-0.982262\pi$
$991$	−17078.9	−	29581.6i	−0.547458	−	0.948225i	0.450990	−	0.892529i	$-0.351071\pi$
$992$	6659.24	−	11534.1i	0.213136	−	0.369163i
$993$	−1364.04			−0.0435915
$994$	−24553.0	−	1476.63i	−0.783475	−	0.0471184i
$995$	15024.7			0.478709
$996$	−477.918	+	827.778i	−0.0152042	+	0.0263345i
$997$	−22516.2	−	38999.2i	−0.715241	−	1.23883i	−0.962867	−	0.269977i	$-0.912984\pi$
$997$	−22516.2	−	38999.2i	−0.715241	−	1.23883i	0.247626	−	0.968856i	$-0.420350\pi$
$998$	15017.3	+	26010.7i	0.476317	+	0.825005i
$999$	51.9391	−	89.9612i	0.00164493	−	0.00284910i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.e.a.93.18	✓	44
7.2	even	3		1127.4.a.l.1.5		22
7.4	even	3	inner	161.4.e.a.116.18	yes	44
7.5	odd	6		1127.4.a.k.1.5		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.e.a.93.18	✓	44	1.1	even	1	trivial
161.4.e.a.116.18	yes	44	7.4	even	3	inner
1127.4.a.k.1.5		22	7.5	odd	6
1127.4.a.l.1.5		22	7.2	even	3

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:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.81191 - 3.13831i) q^{2} +(-0.112864 - 0.195487i) q^{3} +(-2.56601 - 4.44446i) q^{4} +(-1.55669 + 2.69626i) q^{5} -0.818000 q^{6} +(-8.28058 - 16.5660i) q^{7} +10.3930 q^{8} +(13.4745 - 23.3386i) q^{9} +(5.64114 + 9.77074i) q^{10} +(-13.6603 - 23.6604i) q^{11} +(-0.579223 + 1.00324i) q^{12} -46.9064 q^{13} +(-66.9929 - 4.02897i) q^{14} +0.702778 q^{15} +(39.3593 - 68.1722i) q^{16} +(-30.3738 - 52.6090i) q^{17} +(-48.8292 - 84.5746i) q^{18} +(-0.916584 + 1.58757i) q^{19} +15.9779 q^{20} +(-2.30385 + 3.48846i) q^{21} -99.0050 q^{22} +(11.5000 - 19.9186i) q^{23} +(-1.17300 - 2.03170i) q^{24} +(57.6535 + 99.8587i) q^{25} +(-84.9901 + 147.207i) q^{26} -12.1779 q^{27} +(-52.3788 + 79.3112i) q^{28} +115.694 q^{29} +(1.27337 - 2.20554i) q^{30} +(32.9474 + 57.0666i) q^{31} +(-101.059 - 175.039i) q^{32} +(-3.08353 + 5.34084i) q^{33} -220.138 q^{34} +(57.5565 + 3.46146i) q^{35} -138.303 q^{36} +(-4.26505 + 7.38728i) q^{37} +(3.32153 + 5.75306i) q^{38} +(5.29407 + 9.16960i) q^{39} +(-16.1787 + 28.0223i) q^{40} +129.654 q^{41} +(6.77351 + 13.5510i) q^{42} +200.276 q^{43} +(-70.1052 + 121.426i) q^{44} +(41.9512 + 72.6616i) q^{45} +(-41.6739 - 72.1812i) q^{46} +(38.8781 - 67.3388i) q^{47} -17.7691 q^{48} +(-205.864 + 274.352i) q^{49} +417.851 q^{50} +(-6.85625 + 11.8754i) q^{51} +(120.362 + 208.474i) q^{52} +(14.2548 + 24.6901i) q^{53} +(-22.0651 + 38.2180i) q^{54} +85.0594 q^{55} +(-86.0602 - 172.171i) q^{56} +0.413799 q^{57} +(209.627 - 363.084i) q^{58} +(-25.6223 - 44.3792i) q^{59} +(-1.80334 - 3.12347i) q^{60} +(30.5548 - 52.9225i) q^{61} +238.791 q^{62} +(-498.203 - 29.9621i) q^{63} -102.686 q^{64} +(73.0186 - 126.472i) q^{65} +(11.1742 + 19.3542i) q^{66} +(8.64942 + 14.9812i) q^{67} +(-155.879 + 269.990i) q^{68} -5.19177 q^{69} +(115.150 - 174.358i) q^{70} +366.502 q^{71} +(140.041 - 242.558i) q^{72} +(455.230 + 788.481i) q^{73} +(15.4557 + 26.7701i) q^{74} +(13.0141 - 22.5410i) q^{75} +9.40786 q^{76} +(-278.842 + 422.219i) q^{77} +38.3694 q^{78} +(611.129 - 1058.51i) q^{79} +(122.540 + 212.246i) q^{80} +(-362.438 - 627.760i) q^{81} +(234.921 - 406.895i) q^{82} +825.101 q^{83} +(21.4160 + 1.28797i) q^{84} +189.130 q^{85} +(362.881 - 628.529i) q^{86} +(-13.0577 - 22.6167i) q^{87} +(-141.972 - 245.903i) q^{88} +(-348.966 + 604.426i) q^{89} +304.047 q^{90} +(388.412 + 777.051i) q^{91} -118.036 q^{92} +(7.43719 - 12.8816i) q^{93} +(-140.887 - 244.023i) q^{94} +(-2.85367 - 4.94270i) q^{95} +(-22.8118 + 39.5113i) q^{96} -658.577 q^{97} +(487.996 + 1143.17i) q^{98} -736.266 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 6 q^{3} - 88 q^{4} - 20 q^{5} + 24 q^{6} - 12 q^{7} + 42 q^{8} - 238 q^{9} - 182 q^{10} + 28 q^{11} - 127 q^{12} + 440 q^{13} + 16 q^{14} + 40 q^{15} - 436 q^{16} - 294 q^{17} + 155 q^{18} - 252 q^{19}+ \cdots - 5764 q^{99}+O(q^{100}) \) 44 * q - 6 * q^3 - 88 * q^4 - 20 * q^5 + 24 * q^6 - 12 * q^7 + 42 * q^8 - 238 * q^9 - 182 * q^10 + 28 * q^11 - 127 * q^12 + 440 * q^13 + 16 * q^14 + 40 * q^15 - 436 * q^16 - 294 * q^17 + 155 * q^18 - 252 * q^19 + 708 * q^20 + 110 * q^21 + 28 * q^22 + 506 * q^23 - 458 * q^24 - 684 * q^25 - 396 * q^26 + 972 * q^27 - 354 * q^28 + 628 * q^29 + 905 * q^30 - 172 * q^31 + 127 * q^32 - 1524 * q^33 + 800 * q^34 - 1588 * q^35 + 2644 * q^36 + 710 * q^37 + 323 * q^38 + 136 * q^39 - 1808 * q^40 + 784 * q^41 - 2775 * q^42 + 504 * q^43 + 1106 * q^44 - 658 * q^45 - 448 * q^47 + 2730 * q^48 - 570 * q^49 + 738 * q^50 + 896 * q^51 - 1224 * q^52 - 308 * q^53 - 945 * q^54 + 4324 * q^55 - 481 * q^56 - 124 * q^57 + 1153 * q^58 + 282 * q^59 - 4442 * q^60 - 3076 * q^61 + 3500 * q^62 - 732 * q^63 - 4354 * q^64 + 1024 * q^65 + 549 * q^66 - 1056 * q^67 - 2478 * q^68 - 276 * q^69 + 2071 * q^70 - 96 * q^71 + 1922 * q^72 - 4430 * q^73 - 3322 * q^74 - 2540 * q^75 + 15026 * q^76 - 1116 * q^77 - 3990 * q^78 + 530 * q^79 - 296 * q^80 - 3446 * q^81 - 1570 * q^82 + 3572 * q^83 - 4571 * q^84 - 2624 * q^85 + 397 * q^86 + 1724 * q^87 - 5375 * q^88 - 658 * q^89 + 13620 * q^90 - 1098 * q^91 - 4048 * q^92 + 1722 * q^93 + 1944 * q^94 - 1742 * q^95 - 1142 * q^96 + 21364 * q^97 + 2001 * q^98 - 5764 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more