LMFDB - Embedded newform 45.5.i.a.11.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,5,Mod(11,45)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("45.11"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	45.i (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.65164833877$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.7
Character	$\chi$	$=$	45.11
Dual form			45.5.i.a.41.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.15054 - 1.24161i) q^{2} +(-6.81039 - 5.88376i) q^{3} +(-4.91680 - 8.51614i) q^{4} +(9.68246 - 5.59017i) q^{5} +(7.34064 + 21.1091i) q^{6} +(-15.7848 + 27.3401i) q^{7} +64.1506i q^{8} +(11.7628 + 80.1414i) q^{9} -27.7633 q^{10} +(-182.954 - 105.629i) q^{11} +(-16.6216 + 86.9275i) q^{12} +(143.587 + 248.700i) q^{13} +(67.8916 - 39.1972i) q^{14} +(-98.8325 - 18.8980i) q^{15} +(0.981458 - 1.69994i) q^{16} -195.177i q^{17} +(74.2081 - 186.952i) q^{18} -139.924 q^{19} +(-95.2134 - 54.9715i) q^{20} +(268.363 - 93.3227i) q^{21} +(262.300 + 454.317i) q^{22} +(-409.868 + 236.637i) q^{23} +(377.447 - 436.891i) q^{24} +(62.5000 - 108.253i) q^{25} -713.117i q^{26} +(391.423 - 615.003i) q^{27} +310.443 q^{28} +(-1009.98 - 583.111i) q^{29} +(189.079 + 163.352i) q^{30} +(-160.474 - 277.950i) q^{31} +(884.676 - 510.768i) q^{32} +(624.497 + 1795.83i) q^{33} +(-242.335 + 419.736i) q^{34} +352.959i q^{35} +(624.660 - 494.213i) q^{36} -2151.28 q^{37} +(300.912 + 173.731i) q^{38} +(485.406 - 2538.57i) q^{39} +(358.613 + 621.136i) q^{40} +(-520.096 + 300.278i) q^{41} +(-692.995 - 132.509i) q^{42} +(-1386.35 + 2401.24i) q^{43} +2077.42i q^{44} +(561.897 + 710.209i) q^{45} +1175.25 q^{46} +(-692.571 - 399.856i) q^{47} +(-16.6861 + 5.80256i) q^{48} +(702.180 + 1216.21i) q^{49} +(-268.817 + 155.202i) q^{50} +(-1148.38 + 1329.23i) q^{51} +(1411.98 - 2445.61i) q^{52} -78.0197i q^{53} +(-1605.36 + 836.592i) q^{54} -2361.93 q^{55} +(-1753.88 - 1012.61i) q^{56} +(952.937 + 823.279i) q^{57} +(1448.00 + 2508.00i) q^{58} +(893.450 - 515.833i) q^{59} +(325.001 + 934.589i) q^{60} +(2581.52 - 4471.33i) q^{61} +796.988i q^{62} +(-2376.75 - 943.419i) q^{63} -2568.11 q^{64} +(2780.55 + 1605.35i) q^{65} +(886.725 - 4637.39i) q^{66} +(-2033.11 - 3521.44i) q^{67} +(-1662.16 + 959.648i) q^{68} +(4183.68 + 799.970i) q^{69} +(438.238 - 759.051i) q^{70} -2637.50i q^{71} +(-5141.12 + 754.592i) q^{72} +5276.42 q^{73} +(4626.41 + 2671.06i) q^{74} +(-1062.58 + 369.512i) q^{75} +(687.978 + 1191.61i) q^{76} +(5775.80 - 3334.66i) q^{77} +(-4195.81 + 4856.61i) q^{78} +(2454.21 - 4250.81i) q^{79} -21.9461i q^{80} +(-6284.27 + 1885.38i) q^{81} +1491.31 q^{82} +(-3130.65 - 1807.48i) q^{83} +(-2114.24 - 1826.57i) q^{84} +(-1091.08 - 1889.80i) q^{85} +(5962.81 - 3442.63i) q^{86} +(3447.46 + 9913.67i) q^{87} +(6776.15 - 11736.6i) q^{88} +8334.74i q^{89} +(-326.575 - 2224.99i) q^{90} -9065.96 q^{91} +(4030.47 + 2327.00i) q^{92} +(-542.496 + 2837.14i) q^{93} +(992.933 + 1719.81i) q^{94} +(-1354.81 + 782.199i) q^{95} +(-9030.22 - 1726.69i) q^{96} +(-319.918 + 554.115i) q^{97} -3487.34i q^{98} +(6313.17 - 15904.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{3} + 128 q^{4} + 98 q^{6} - 26 q^{7} - 220 q^{9} - 738 q^{11} - 214 q^{12} + 10 q^{13} + 1998 q^{14} - 50 q^{15} - 1024 q^{16} - 2504 q^{18} + 508 q^{19} - 1620 q^{21} + 672 q^{22} + 1998 q^{23}+ \cdots + 53512 q^{99}+O(q^{100}) $ 32 * q - 8 * q^3 + 128 * q^4 + 98 * q^6 - 26 * q^7 - 220 * q^9 - 738 * q^11 - 214 * q^12 + 10 * q^13 + 1998 * q^14 - 50 * q^15 - 1024 * q^16 - 2504 * q^18 + 508 * q^19 - 1620 * q^21 + 672 * q^22 + 1998 * q^23 + 4164 * q^24 + 2000 * q^25 + 2158 * q^27 - 1664 * q^28 - 270 * q^29 + 2000 * q^30 - 1472 * q^31 - 6048 * q^32 - 1354 * q^33 - 594 * q^34 + 4498 * q^36 + 2068 * q^37 - 7164 * q^38 - 4616 * q^39 + 1650 * q^40 - 13428 * q^41 - 10230 * q^42 + 568 * q^43 - 100 * q^45 + 5724 * q^46 + 12528 * q^47 + 25844 * q^48 - 1674 * q^49 + 1454 * q^51 + 1534 * q^52 + 8456 * q^54 + 21294 * q^56 - 12512 * q^57 - 8190 * q^58 - 4374 * q^59 - 5050 * q^60 - 4478 * q^61 + 5604 * q^63 - 37216 * q^64 - 8550 * q^65 - 19472 * q^66 + 12838 * q^67 + 65736 * q^68 + 8706 * q^69 + 2400 * q^70 - 36372 * q^72 + 29236 * q^73 - 20628 * q^74 + 1000 * q^75 + 6190 * q^76 - 31806 * q^77 - 42430 * q^78 - 3512 * q^79 - 3088 * q^81 + 34692 * q^82 - 43074 * q^83 - 19350 * q^84 - 4350 * q^85 - 10746 * q^86 + 69622 * q^87 - 16128 * q^88 - 26750 * q^90 - 48904 * q^91 + 27036 * q^92 + 27030 * q^93 + 5118 * q^94 + 6300 * q^95 + 53566 * q^96 + 23266 * q^97 + 53512 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.15054	−	1.24161i	−0.537634	−	0.310403i	0.206486	−	0.978450i	$-0.433797\pi$
$2$	−2.15054	−	1.24161i	−0.537634	−	0.310403i	−0.744119	+	0.668047i	$0.767131\pi$
$3$	−6.81039	−	5.88376i	−0.756710	−	0.653751i
$3$	−6.81039	−	5.88376i	−0.756710	−	0.653751i
$4$	−4.91680	−	8.51614i	−0.307300	−	0.532259i
$5$	9.68246	−	5.59017i	0.387298	−	0.223607i
$5$	9.68246	−	5.59017i	0.387298	−	0.223607i
$6$	7.34064	+	21.1091i	0.203907	+	0.586364i
$7$	−15.7848	+	27.3401i	−0.322139	+	0.557961i	−0.980929	−	0.194366i	$-0.937735\pi$
$7$	−15.7848	+	27.3401i	−0.322139	+	0.557961i	0.658790	+	0.752327i	$0.271068\pi$
$8$			64.1506i			1.00235i
$9$	11.7628	+	80.1414i	0.145220	+	0.989399i
$10$	−27.7633			−0.277633
$11$	−182.954	−	105.629i	−1.51202	−	0.872965i	−0.999901	−	0.0140505i	$-0.995527\pi$
$11$	−182.954	−	105.629i	−1.51202	−	0.872965i	−0.512119	−	0.858915i	$-0.671139\pi$
$12$	−16.6216	+	86.9275i	−0.115428	+	0.603663i
$13$	143.587	+	248.700i	0.849627	+	1.47160i	0.881542	+	0.472106i	$0.156506\pi$
$13$	143.587	+	248.700i	0.849627	+	1.47160i	−0.0319153	+	0.999491i	$0.510161\pi$
$14$	67.8916	−	39.1972i	0.346386	−	0.199986i
$15$	−98.8325	−	18.8980i	−0.439256	−	0.0839911i
$16$	0.981458	−	1.69994i	0.00383382	−	0.00664037i
$17$		−	195.177i		−	0.675355i	−0.941262	−	0.337677i	$-0.890359\pi$
$17$		−	195.177i		−	0.675355i	0.941262	−	0.337677i	$-0.109641\pi$
$18$	74.2081	−	186.952i	0.229037	−	0.577011i
$19$	−139.924			−0.387601			−0.193801	−	0.981041i	$-0.562081\pi$
$19$	−139.924			−0.387601			−0.193801	+	0.981041i	$0.562081\pi$
$20$	−95.2134	−	54.9715i	−0.238033	−	0.137429i
$21$	268.363	−	93.3227i	0.608533	−	0.211616i
$22$	262.300	+	454.317i	0.541942	+	0.938671i
$23$	−409.868	+	236.637i	−0.774797	+	0.447330i	−0.834583	−	0.550882i	$-0.814292\pi$
$23$	−409.868	+	236.637i	−0.774797	+	0.447330i	0.0597859	+	0.998211i	$0.480958\pi$
$24$	377.447	−	436.891i	0.655289	−	0.758491i
$25$	62.5000	−	108.253i	0.100000	−	0.173205i
$26$		−	713.117i		−	1.05491i
$27$	391.423	−	615.003i	0.536931	−	0.843626i
$28$	310.443			0.395973
$29$	−1009.98	−	583.111i	−1.20092	−	0.693354i	−0.240164	−	0.970732i	$-0.577201\pi$
$29$	−1009.98	−	583.111i	−1.20092	−	0.693354i	−0.960761	+	0.277378i	$0.910534\pi$
$30$	189.079	+	163.352i	0.210088	+	0.181503i
$31$	−160.474	−	277.950i	−0.166987	−	0.289230i	0.770372	−	0.637594i	$-0.220070\pi$
$31$	−160.474	−	277.950i	−0.166987	−	0.289230i	−0.937359	+	0.348365i	$0.886737\pi$
$32$	884.676	−	510.768i	0.863941	−	0.498797i
$33$	624.497	+	1795.83i	0.573459	+	1.64907i
$34$	−242.335	+	419.736i	−0.209632	+	0.363094i
$35$			352.959i			0.288130i
$36$	624.660	−	494.213i	0.481991	−	0.381337i
$37$	−2151.28			−1.57143			−0.785713	−	0.618591i	$-0.787704\pi$
$37$	−2151.28			−1.57143			−0.785713	+	0.618591i	$0.787704\pi$
$38$	300.912	+	173.731i	0.208388	+	0.120313i
$39$	485.406	−	2538.57i	0.319136	−	1.66902i
$40$	358.613	+	621.136i	0.224133	+	0.388210i
$41$	−520.096	+	300.278i	−0.309397	+	0.178630i	−0.646657	−	0.762781i	$-0.723833\pi$
$41$	−520.096	+	300.278i	−0.309397	+	0.178630i	0.337260	+	0.941412i	$0.390500\pi$
$42$	−692.995	−	132.509i	−0.392854	−	0.0751186i
$43$	−1386.35	+	2401.24i	−0.749786	+	1.29867i	0.198139	+	0.980174i	$0.436510\pi$
$43$	−1386.35	+	2401.24i	−0.749786	+	1.29867i	−0.947925	+	0.318493i	$0.896823\pi$
$44$			2077.42i			1.07305i
$45$	561.897	+	710.209i	0.277480	+	0.350721i
$46$	1175.25			0.555410
$47$	−692.571	−	399.856i	−0.313522	−	0.181012i	0.334979	−	0.942226i	$-0.391271\pi$
$47$	−692.571	−	399.856i	−0.313522	−	0.181012i	−0.648502	+	0.761213i	$0.724604\pi$
$48$	−16.6861	+	5.80256i	−0.00724224	+	0.00251847i
$49$	702.180	+	1216.21i	0.292453	+	0.506544i
$50$	−268.817	+	155.202i	−0.107527	+	0.0620806i
$51$	−1148.38	+	1329.23i	−0.441514	+	0.511048i
$52$	1411.98	−	2445.61i	0.522180	−	0.904443i
$53$		−	78.0197i		−	0.0277749i	−0.999904	−	0.0138875i	$-0.995579\pi$
$53$		−	78.0197i		−	0.0277749i	0.999904	−	0.0138875i	$-0.00442066\pi$
$54$	−1605.36	+	836.592i	−0.550537	+	0.286897i
$55$	−2361.93			−0.780804
$56$	−1753.88	−	1012.61i	−0.559274	−	0.322897i
$57$	952.937	+	823.279i	0.293302	+	0.253394i
$58$	1448.00	+	2508.00i	0.430438	+	0.745541i
$59$	893.450	−	515.833i	0.256665	−	0.148185i	−0.366147	−	0.930557i	$-0.619323\pi$
$59$	893.450	−	515.833i	0.256665	−	0.148185i	0.622812	+	0.782371i	$0.285990\pi$
$60$	325.001	+	934.589i	0.0902782	+	0.259608i
$61$	2581.52	−	4471.33i	0.693771	−	1.20165i	−0.276822	−	0.960921i	$-0.589281\pi$
$61$	2581.52	−	4471.33i	0.693771	−	1.20165i	0.970593	−	0.240726i	$-0.0773854\pi$
$62$			796.988i			0.207333i
$63$	−2376.75	−	943.419i	−0.598827	−	0.237697i
$64$	−2568.11			−0.626980
$65$	2780.55	+	1605.35i	0.658118	+	0.379965i
$66$	886.725	−	4637.39i	0.203564	−	1.06460i
$67$	−2033.11	−	3521.44i	−0.452909	−	0.784461i	0.545657	−	0.838009i	$-0.316280\pi$
$67$	−2033.11	−	3521.44i	−0.452909	−	0.784461i	−0.998565	+	0.0535481i	$0.982947\pi$
$68$	−1662.16	+	959.648i	−0.359463	+	0.207536i
$69$	4183.68	+	799.970i	0.878739	+	0.168026i
$70$	438.238	−	759.051i	0.0894364	−	0.154908i
$71$		−	2637.50i		−	0.523209i	−0.965175	−	0.261604i	$-0.915748\pi$
$71$		−	2637.50i		−	0.523209i	0.965175	−	0.261604i	$-0.0842516\pi$
$72$	−5141.12	+	754.592i	−0.991728	+	0.145562i
$73$	5276.42			0.990133			0.495067	−	0.868855i	$-0.335144\pi$
$73$	5276.42			0.990133			0.495067	+	0.868855i	$0.335144\pi$
$74$	4626.41	+	2671.06i	0.844852	+	0.487775i
$75$	−1062.58	+	369.512i	−0.188904	+	0.0656909i
$76$	687.978	+	1191.61i	0.119110	+	0.206304i
$77$	5775.80	−	3334.66i	0.974161	−	0.562432i
$78$	−4195.81	+	4856.61i	−0.689646	+	0.798259i
$79$	2454.21	−	4250.81i	0.393239	−	0.681110i	−0.599635	−	0.800273i	$-0.704688\pi$
$79$	2454.21	−	4250.81i	0.393239	−	0.681110i	0.992875	+	0.119163i	$0.0380211\pi$
$80$		−	21.9461i		−	0.00342907i
$81$	−6284.27	+	1885.38i	−0.957822	+	0.287361i
$82$	1491.31			0.221790
$83$	−3130.65	−	1807.48i	−0.454441	−	0.262372i	0.255263	−	0.966872i	$-0.417838\pi$
$83$	−3130.65	−	1807.48i	−0.454441	−	0.262372i	−0.709704	+	0.704500i	$0.751171\pi$
$84$	−2114.24	−	1826.57i	−0.299637	−	0.258868i
$85$	−1091.08	−	1889.80i	−0.151014	−	0.261564i
$86$	5962.81	−	3442.63i	0.806221	−	0.465472i
$87$	3447.46	+	9913.67i	0.455471	+	1.30977i
$88$	6776.15	−	11736.6i	0.875020	−	1.51558i
$89$			8334.74i			1.05223i	0.850412	+	0.526117i	$0.176353\pi$
$89$			8334.74i			1.05223i	−0.850412	+	0.526117i	$0.823647\pi$
$90$	−326.575	−	2224.99i	−0.0403179	−	0.274690i
$91$	−9065.96			−1.09479
$92$	4030.47	+	2327.00i	0.476190	+	0.274929i
$93$	−542.496	+	2837.14i	−0.0627235	+	0.328031i
$94$	992.933	+	1719.81i	0.112374	+	0.194637i
$95$	−1354.81	+	782.199i	−0.150117	+	0.0866702i
$96$	−9030.22	−	1726.69i	−0.979842	−	0.187358i
$97$	−319.918	+	554.115i	−0.0340013	+	0.0588920i	−0.882525	−	0.470265i	$-0.844158\pi$
$97$	−319.918	+	554.115i	−0.0340013	+	0.0588920i	0.848524	+	0.529157i	$0.177492\pi$
$98$		−	3487.34i		−	0.363113i
$99$	6313.17	−	15904.7i	0.644136	−	1.62276i
$100$	−1229.20			−0.122920
$101$	1547.97	+	893.722i	0.151747	+	0.0876112i	0.573951	−	0.818890i	$-0.305410\pi$
$101$	1547.97	+	893.722i	0.151747	+	0.0876112i	−0.422204	+	0.906501i	$0.638743\pi$
$102$	4120.02	−	1432.73i	0.396003	−	0.137709i
$103$	3225.83	+	5587.30i	0.304065	+	0.526657i	0.977053	−	0.212997i	$-0.0683225\pi$
$103$	3225.83	+	5587.30i	0.304065	+	0.526657i	−0.672987	+	0.739654i	$0.734989\pi$
$104$	−15954.2	+	9211.19i	−1.47506	+	0.851626i
$105$	2076.72	−	2403.79i	0.188365	−	0.218031i
$106$	−96.8703	+	167.784i	−0.00862142	+	0.0149327i
$107$		−	4943.00i		−	0.431741i	−0.976422	−	0.215870i	$-0.930741\pi$
$107$		−	4943.00i		−	0.431741i	0.976422	−	0.215870i	$-0.0692589\pi$
$108$	−7162.00	−	309.565i	−0.614026	−	0.0265402i
$109$	−19023.5			−1.60117			−0.800586	−	0.599217i	$-0.795479\pi$
$109$	−19023.5			−1.60117			−0.800586	+	0.599217i	$0.795479\pi$
$110$	5079.42	+	2932.60i	0.419787	+	0.242364i
$111$	14651.1	+	12657.6i	1.18911	+	1.02732i
$112$	30.9842	+	53.6663i	0.00247005	+	0.00427824i
$113$	4273.19	−	2467.12i	0.334653	−	0.193212i	−0.323252	−	0.946313i	$-0.604776\pi$
$113$	4273.19	−	2467.12i	0.334653	−	0.193212i	0.657905	+	0.753101i	$0.271443\pi$
$114$	−1027.13	−	2953.67i	−0.0790345	−	0.227275i
$115$	−2645.69	+	4582.46i	−0.200052	+	0.346500i
$116$			11468.1i			0.852270i
$117$	−18242.2	+	14432.7i	−1.33261	+	1.05433i
$118$	−2561.86			−0.183989
$119$	5336.17	+	3080.84i	0.376821	+	0.217558i
$120$	1212.32	−	6340.17i	0.0841887	−	0.440289i
$121$	14994.4	+	25971.0i	1.02414	+	1.77386i
$122$	−11103.3	+	6410.50i	−0.745990	+	0.430697i
$123$	5308.82	+	1015.11i	0.350903	+	0.0670970i
$124$	−1578.04	+	2733.25i	−0.102630	+	0.177761i
$125$		−	1397.54i		−	0.0894427i
$126$	3939.91	+	4979.85i	0.248168	+	0.313672i
$127$	70.4302			0.00436668			0.00218334	−	0.999998i	$-0.499305\pi$
$127$	70.4302			0.00436668			0.00218334	+	0.999998i	$0.499305\pi$
$128$	−8632.00	−	4983.69i	−0.526856	−	0.304180i
$129$	23569.9	−	8196.38i	1.41637	−	0.492541i
$130$	−3986.45	−	6904.73i	−0.235884	−	0.408564i
$131$	−6645.48	+	3836.77i	−0.387243	+	0.223575i	−0.680965	−	0.732316i	$-0.738439\pi$
$131$	−6645.48	+	3836.77i	−0.387243	+	0.223575i	0.293722	+	0.955891i	$0.405106\pi$
$132$	12223.0	−	14148.0i	0.701506	−	0.811986i
$133$	2208.67	−	3825.53i	0.124861	−	0.216266i
$134$			10097.3i			0.562337i
$135$	351.961	−	8142.86i	0.0193120	−	0.446796i
$136$	12520.8			0.676944
$137$	−6850.42	−	3955.09i	−0.364986	−	0.210725i	0.306280	−	0.951942i	$-0.400916\pi$
$137$	−6850.42	−	3955.09i	−0.364986	−	0.210725i	−0.671266	+	0.741217i	$0.734249\pi$
$138$	−8003.89	−	6914.87i	−0.420284	−	0.363100i
$139$	−10678.3	−	18495.3i	−0.552676	−	0.957263i	−0.998080	−	0.0619336i	$-0.980273\pi$
$139$	−10678.3	−	18495.3i	−0.552676	−	0.957263i	0.445404	−	0.895330i	$-0.353060\pi$
$140$	3005.85	−	1735.43i	0.153360	−	0.0885422i
$141$	2364.02	+	6798.10i	0.118909	+	0.341939i
$142$	−3274.75	+	5672.03i	−0.162406	+	0.281295i
$143$		−	60667.6i		−	2.96678i
$144$	147.780	+	58.6593i	0.00712673	+	0.00282886i
$145$	−13038.8			−0.620155
$146$	−11347.1	−	6551.27i	−0.532329	−	0.307340i
$147$	2373.77	−	12414.3i	0.109851	−	0.574498i
$148$	10577.4	+	18320.6i	0.482899	+	0.836405i
$149$	29973.1	−	17305.0i	1.35008	−	0.779468i	0.361818	−	0.932249i	$-0.382156\pi$
$149$	29973.1	−	17305.0i	1.35008	−	0.779468i	0.988260	+	0.152781i	$0.0488230\pi$
$150$	2743.92	+	524.671i	0.121952	+	0.0233187i
$151$	2290.05	−	3966.48i	0.100436	−	0.173961i	−0.811428	−	0.584452i	$-0.801309\pi$
$151$	2290.05	−	3966.48i	0.100436	−	0.173961i	0.911865	+	0.410491i	$0.134643\pi$
$152$		−	8976.21i		−	0.388513i
$153$	15641.8	−	2295.84i	0.668195	−	0.0980750i
$154$	−16561.4			−0.698323
$155$	−3107.57	−	1794.16i	−0.129348	−	0.0746788i
$156$	−24005.5	+	8347.86i	−0.986419	+	0.343025i
$157$	7347.48	+	12726.2i	0.298084	+	0.516297i	0.975698	−	0.219121i	$-0.0703191\pi$
$157$	7347.48	+	12726.2i	0.298084	+	0.516297i	−0.677613	+	0.735418i	$0.736986\pi$
$158$	−10555.7	+	6094.35i	−0.422838	+	0.244125i
$159$	−459.049	+	531.345i	−0.0181579	+	0.0210176i
$160$	5710.56	−	9890.98i	0.223069	−	0.386366i
$161$		−	14941.1i		−	0.576409i
$162$	15855.5	+	3748.06i	0.604156	+	0.142816i
$163$	30100.9			1.13293			0.566466	−	0.824085i	$-0.308310\pi$
$163$	30100.9			1.13293			0.566466	+	0.824085i	$0.308310\pi$
$164$	5114.41	+	2952.81i	0.190155	+	0.109786i
$165$	16085.7	+	13897.0i	0.590842	+	0.510451i
$166$	4488.38	+	7774.10i	0.162882	+	0.282120i
$167$	−18234.6	+	10527.7i	−0.653828	+	0.377487i	−0.789921	−	0.613208i	$-0.789879\pi$
$167$	−18234.6	+	10527.7i	−0.653828	+	0.377487i	0.136094	+	0.990696i	$0.456545\pi$
$168$	5986.71	+	17215.7i	0.212114	+	0.609965i
$169$	−26953.9	+	46685.5i	−0.943731	+	1.63459i
$170$			5418.77i			0.187501i
$171$	−1645.90	−	11213.7i	−0.0562874	−	0.383492i
$172$	27265.7			0.921636
$173$	−25480.2	−	14711.0i	−0.851353	−	0.491529i	0.00975391	−	0.999952i	$-0.496895\pi$
$173$	−25480.2	−	14711.0i	−0.851353	−	0.491529i	−0.861107	+	0.508423i	$0.830229\pi$
$174$	4895.06	−	25600.1i	0.161681	−	0.845558i
$175$	1973.10	+	3417.51i	0.0644278	+	0.111592i
$176$	−359.124	+	207.340i	−0.0115936	+	0.00669358i
$177$	−9119.78	−	1743.81i	−0.291097	−	0.0556613i
$178$	10348.5	−	17924.2i	0.326617	−	0.565717i
$179$			53541.9i			1.67104i	0.549458	+	0.835522i	$0.314834\pi$
$179$			53541.9i			1.67104i	−0.549458	+	0.835522i	$0.685166\pi$
$180$	3285.51	−	8277.15i	0.101405	−	0.255468i
$181$	−4168.77			−0.127248			−0.0636239	−	0.997974i	$-0.520266\pi$
$181$	−4168.77			−0.127248			−0.0636239	+	0.997974i	$0.520266\pi$
$182$	19496.7	+	11256.4i	0.588597	+	0.339827i
$183$	−43889.4	+	15262.4i	−1.31056	+	0.455745i
$184$	−15180.4	−	26293.3i	−0.448382	−	0.776621i
$185$	−20829.7	+	12026.0i	−0.608611	+	0.351381i
$186$	4689.28	−	5427.80i	0.135544	−	0.156891i
$187$	−20616.4	+	35708.6i	−0.589561	+	1.02115i
$188$			7864.05i			0.222500i
$189$	10635.7	+	20409.2i	0.297744	+	0.571351i
$190$	3884.75			0.107611
$191$	−29311.0	−	16922.7i	−0.803460	−	0.463878i	0.0412194	−	0.999150i	$-0.486876\pi$
$191$	−29311.0	−	16922.7i	−0.803460	−	0.463878i	−0.844680	+	0.535272i	$0.820209\pi$
$192$	17489.8	+	15110.1i	0.474442	+	0.409888i
$193$	−13338.4	−	23102.7i	−0.358087	−	0.620224i	0.629554	−	0.776956i	$-0.283237\pi$
$193$	−13338.4	−	23102.7i	−0.358087	−	0.620224i	−0.987641	+	0.156732i	$0.949904\pi$
$194$	1375.99	−	794.429i	0.0365605	−	0.0211082i
$195$	−9491.13	−	27293.1i	−0.249602	−	0.717768i
$196$	6904.95	−	11959.7i	0.179742	−	0.311322i
$197$			7023.20i			0.180968i	0.995898	+	0.0904842i	$0.0288415\pi$
$197$			7023.20i			0.180968i	−0.995898	+	0.0904842i	$0.971159\pi$
$198$	−33324.2	+	26365.1i	−0.850020	+	0.672511i
$199$	25748.9			0.650208			0.325104	−	0.945678i	$-0.394601\pi$
$199$	25748.9			0.650208			0.325104	+	0.945678i	$0.394601\pi$
$200$	6944.51	+	4009.41i	0.173613	+	0.100235i
$201$	−6873.07	+	35944.7i	−0.170121	+	0.889699i
$202$	−2219.31	−	3843.96i	−0.0543896	−	0.0942055i
$203$	31884.6	−	18408.6i	0.773729	−	0.446713i
$204$	16966.3	+	3244.16i	0.407687	+	0.0779547i
$205$	−3357.21	+	5814.85i	−0.0798859	+	0.138366i
$206$		−	16020.9i		−	0.377531i
$207$	−23785.6	−	30063.8i	−0.555104	−	0.701623i
$208$	563.698			0.0130293
$209$	25599.7	+	14780.0i	0.586061	+	0.338362i
$210$	−7450.64	+	2590.95i	−0.168949	+	0.0587516i
$211$	−26855.6	−	46515.3i	−0.603212	−	1.04479i	−0.992331	−	0.123607i	$-0.960554\pi$
$211$	−26855.6	−	46515.3i	−0.603212	−	1.04479i	0.389119	−	0.921187i	$-0.372779\pi$
$212$	−664.427	+	383.607i	−0.0147834	+	0.00853523i
$213$	−15518.4	+	17962.4i	−0.342048	+	0.395917i
$214$	−6137.29	+	10630.1i	−0.134014	+	0.232118i
$215$			30999.8i			0.670629i
$216$	39452.9	+	25110.0i	0.845612	+	0.538195i
$217$	10132.2			0.215172
$218$	40910.8	+	23619.9i	0.860845	+	0.497009i
$219$	−35934.5	−	31045.2i	−0.749244	−	0.647300i
$220$	11613.1	+	20114.5i	0.239941	+	0.415590i
$221$	48540.6	−	28024.9i	0.993849	−	0.573799i
$222$	−15791.8	−	45411.6i	−0.320424	−	0.921427i
$223$	−27686.8	+	47955.0i	−0.556754	+	0.964326i	0.441011	+	0.897502i	$0.354620\pi$
$223$	−27686.8	+	47955.0i	−0.556754	+	0.964326i	−0.997765	+	0.0668241i	$0.978713\pi$
$224$			32249.5i			0.642727i
$225$	9410.73	+	3735.47i	0.185891	+	0.0737871i
$226$	−12252.9			−0.239894
$227$	10260.8	+	5924.06i	0.199126	+	0.114966i	0.596248	−	0.802800i	$-0.296658\pi$
$227$	10260.8	+	5924.06i	0.199126	+	0.114966i	−0.397122	+	0.917766i	$0.629991\pi$
$228$	2325.76	−	12163.2i	0.0447399	−	0.233980i
$229$	−45945.2	−	79579.5i	−0.876132	−	1.51751i	−0.855552	−	0.517717i	$-0.826782\pi$
$229$	−45945.2	−	79579.5i	−0.876132	−	1.51751i	−0.0205804	−	0.999788i	$-0.506551\pi$
$230$	11379.3	−	6569.83i	0.215109	−	0.124193i
$231$	−58955.8	−	11273.1i	−1.10485	−	0.211260i
$232$	37406.9	−	64790.7i	0.694986	−	1.20375i
$233$			87547.4i			1.61262i	0.591495	+	0.806309i	$0.298538\pi$
$233$			87547.4i			1.61262i	−0.591495	+	0.806309i	$0.701462\pi$
$234$	57150.2	−	8388.27i	1.04372	−	0.153194i
$235$	−8941.06			−0.161902
$236$	−8785.82	−	5072.50i	−0.157746	−	0.0910747i
$237$	−41724.8	+	14509.7i	−0.742845	+	0.258323i
$238$	−7650.41	−	13250.9i	−0.135061	−	0.233933i
$239$	42484.7	−	24528.6i	0.743768	−	0.429414i	−0.0796700	−	0.996821i	$-0.525387\pi$
$239$	42484.7	−	24528.6i	0.743768	−	0.429414i	0.823438	+	0.567407i	$0.192053\pi$
$240$	−129.125	+	149.461i	−0.00224176	+	0.00259481i
$241$	48298.6	−	83655.6i	0.831573	−	1.44033i	−0.0652181	−	0.997871i	$-0.520774\pi$
$241$	48298.6	−	83655.6i	0.831573	−	1.44033i	0.896791	−	0.442455i	$-0.145892\pi$
$242$		−	74468.8i		−	1.27158i
$243$	53891.4	+	24135.0i	0.912656	+	0.408728i
$244$	−50771.3			−0.852783
$245$	13597.7	+	7850.61i	0.226533	+	0.130789i
$246$	−10156.4	−	8774.52i	−0.167830	−	0.144995i
$247$	−20091.3	−	34799.1i	−0.329316	−	0.570392i
$248$	17830.7	−	10294.5i	0.289911	−	0.167380i
$249$	10686.2	+	30729.6i	0.172355	+	0.495631i
$250$	−1735.21	+	3005.47i	−0.0277633	+	0.0480874i
$251$			52332.9i			0.830668i	0.909669	+	0.415334i	$0.136335\pi$
$251$			52332.9i			0.830668i	−0.909669	+	0.415334i	$0.863665\pi$
$252$	3651.68	+	24879.3i	0.0575032	+	0.391775i
$253$	99982.8			1.56201
$254$	−151.463	−	87.4470i	−0.00234768	−	0.00135543i
$255$	−3688.46	+	19289.9i	−0.0567237	+	0.296653i
$256$	32920.5	+	57020.0i	0.502327	+	0.870056i
$257$	−57891.8	+	33423.8i	−0.876498	+	0.506046i	−0.869502	−	0.493929i	$-0.835560\pi$
$257$	−57891.8	+	33423.8i	−0.876498	+	0.506046i	−0.00699554	+	0.999976i	$0.502227\pi$
$258$	−60864.6	−	11638.1i	−0.914378	−	0.174840i
$259$	33957.6	−	58816.2i	0.506217	−	0.876794i
$260$		−	31572.7i		−	0.467052i
$261$	34851.1	−	87800.0i	0.511606	−	1.28888i
$262$	19055.1			0.277593
$263$	−68358.3	−	39466.7i	−0.988280	−	0.570583i	−0.0835200	−	0.996506i	$-0.526616\pi$
$263$	−68358.3	−	39466.7i	−0.988280	−	0.570583i	−0.904760	+	0.425923i	$0.859950\pi$
$264$	−115204.	+	40061.9i	−1.65295	+	0.574809i
$265$	−436.144	−	755.423i	−0.00621066	−	0.0107572i
$266$	−9499.66	+	5484.63i	−0.134259	+	0.0775147i
$267$	49039.6	−	56762.8i	0.687898	−	0.796236i
$268$	−19992.7	+	34628.5i	−0.278357	+	0.482129i
$269$		−	52284.6i		−	0.722553i	−0.932459	−	0.361276i	$-0.882341\pi$
$269$		−	52284.6i		−	0.722553i	0.932459	−	0.361276i	$-0.117659\pi$
$270$	−10867.2	+	17074.5i	−0.149070	+	0.234218i
$271$	34857.3			0.474631			0.237315	−	0.971433i	$-0.423733\pi$
$271$	34857.3			0.474631			0.237315	+	0.971433i	$0.423733\pi$
$272$	−331.789	−	191.559i	−0.00448461	−	0.00258919i
$273$	61742.8	+	53341.9i	0.828439	+	0.715720i
$274$	9821.38	+	17011.1i	0.130819	+	0.226585i
$275$	−22869.3	+	13203.6i	−0.302404	+	0.174593i
$276$	−13757.6	−	39562.1i	−0.180603	−	0.519351i
$277$	−52291.8	+	90572.1i	−0.681513	+	1.18042i	0.293006	+	0.956111i	$0.405344\pi$
$277$	−52291.8	+	90572.1i	−0.681513	+	1.18042i	−0.974519	+	0.224305i	$0.927989\pi$
$278$			53033.0i			0.686210i
$279$	20387.6	−	16130.1i	0.261914	−	0.207219i
$280$	−22642.5			−0.288808
$281$	114872.	+	66321.5i	1.45480	+	0.839927i	0.998748	−	0.0500271i	$-0.0159308\pi$
$281$	114872.	+	66321.5i	1.45480	+	0.839927i	0.456049	+	0.889955i	$0.349264\pi$
$282$	3356.68	−	17554.8i	0.0422097	−	0.220748i
$283$	13435.8	+	23271.6i	0.167761	+	0.290571i	0.937632	−	0.347628i	$-0.113013\pi$
$283$	13435.8	+	23271.6i	0.167761	+	0.290571i	−0.769871	+	0.638199i	$0.779680\pi$
$284$	−22461.3	+	12968.0i	−0.278483	+	0.160782i
$285$	13829.0	+	2644.28i	0.170256	+	0.0325550i
$286$	−75325.7	+	130468.i	−0.920897	+	1.59504i
$287$		−	18959.3i		−	0.230175i
$288$	51339.9	+	64891.0i	0.618971	+	0.782348i
$289$	45426.8			0.543896
$290$	28040.3	+	16189.1i	0.333416	+	0.192498i
$291$	5439.04	−	1891.42i	0.0642298	−	0.0223358i
$292$	−25943.1	−	44934.7i	−0.304268	−	0.527007i
$293$	−2431.70	+	1403.94i	−0.0283253	+	0.0163536i	−0.514096	−	0.857733i	$-0.671872\pi$
$293$	−2431.70	+	1403.94i	−0.0283253	+	0.0163536i	0.485770	+	0.874086i	$0.338539\pi$
$294$	−20518.7	+	23750.2i	−0.237386	+	0.274772i
$295$	5767.19	−	9989.07i	0.0662705	−	0.114784i
$296$		−	138006.i		−	1.57512i
$297$	−136575.	+	71172.1i	−1.54831	+	0.806857i
$298$	−85944.2			−0.967797
$299$	−117703.	−	67956.0i	−1.31658	−	0.760126i
$300$	8371.33	+	7232.31i	0.0930147	+	0.0803590i
$301$	−43766.7	−	75806.1i	−0.483070	−	0.836702i
$302$	−9849.67	+	5686.71i	−0.107996	+	0.0623515i
$303$	−5283.85	−	15194.5i	−0.0575526	−	0.165501i
$304$	−137.330	+	237.862i	−0.00148599	+	0.00257382i
$305$		−	57724.6i		−	0.620528i
$306$	−36488.8	−	14483.8i	−0.389687	−	0.154681i
$307$	168172.			1.78434			0.892170	−	0.451700i	$-0.149182\pi$
$307$	168172.			1.78434			0.892170	+	0.451700i	$0.149182\pi$
$308$	−56796.9	−	32791.7i	−0.598719	−	0.345671i
$309$	10905.2	−	57031.7i	0.114213	−	0.597310i
$310$	4455.30	+	7716.80i	0.0463611	+	0.0802997i
$311$	−104382.	+	60265.0i	−1.07921	+	0.623081i	−0.930683	−	0.365827i	$-0.880786\pi$
$311$	−104382.	+	60265.0i	−1.07921	+	0.623081i	−0.148526	+	0.988909i	$0.547453\pi$
$312$	162851.	+	31139.1i	1.67294	+	0.319887i
$313$	−34485.9	+	59731.4i	−0.352009	+	0.609697i	−0.986601	−	0.163150i	$-0.947835\pi$
$313$	−34485.9	+	59731.4i	−0.352009	+	0.609697i	0.634593	+	0.772847i	$0.281168\pi$
$314$		−	36490.9i		−	0.370105i
$315$	−28286.6	+	4151.79i	−0.285075	+	0.0418422i
$316$	−48267.3			−0.483369
$317$	80407.1	+	46423.0i	0.800158	+	0.461971i	0.843526	−	0.537088i	$-0.180476\pi$
$317$	80407.1	+	46423.0i	0.800158	+	0.461971i	−0.0433684	+	0.999059i	$0.513809\pi$
$318$	1646.93	−	572.715i	0.0162862	−	0.00566349i
$319$	123187.	+	213365.i	1.21055	+	2.09673i
$320$	−24865.6	+	14356.2i	−0.242828	+	0.140197i
$321$	−29083.4	+	33663.8i	−0.282251	+	0.326702i
$322$	−18551.0	+	32131.4i	−0.178919	+	0.309897i
$323$			27310.0i			0.261768i
$324$	46954.6	+	44247.7i	0.447289	+	0.421503i
$325$	35896.7			0.339851
$326$	−64733.0	−	37373.6i	−0.609103	−	0.351666i
$327$	129558.	+	111930.i	1.21162	+	1.04677i
$328$	−19263.0	−	33364.5i	−0.179051	−	0.310125i
$329$	21864.2	−	12623.3i	0.201996	−	0.116622i
$330$	−17338.1	−	49858.2i	−0.159211	−	0.457835i
$331$	−1604.13	+	2778.43i	−0.0146414	+	0.0253596i	−0.873253	−	0.487267i	$-0.837994\pi$
$331$	−1604.13	+	2778.43i	−0.0146414	+	0.0253596i	0.858612	+	0.512626i	$0.171327\pi$
$332$			35548.0i			0.322507i
$333$	−25305.1	−	172407.i	−0.228202	−	1.55477i
$334$	52285.5			0.468693
$335$	−39370.9	−	22730.8i	−0.350821	−	0.202547i
$336$	104.745	−	547.792i	0.000927797	−	0.00485218i
$337$	−55672.9	−	96428.2i	−0.490212	−	0.849072i	0.509725	−	0.860337i	$-0.329747\pi$
$337$	−55672.9	−	96428.2i	−0.490212	−	0.849072i	−0.999937	+	0.0112659i	$0.996414\pi$
$338$	115931.	−	66932.6i	1.01476	−	0.585874i
$339$	−43618.0	−	8340.30i	−0.379548	−	0.0725742i
$340$	−10729.2	+	18583.5i	−0.0928131	+	0.160757i
$341$			67802.9i			0.583095i
$342$	−10383.5	+	26159.0i	−0.0887752	+	0.223650i
$343$	−120134.			−1.02112
$344$	−154041.	−	88935.5i	−1.30172	−	0.751550i
$345$	44980.2	−	15641.8i	0.377906	−	0.131416i
$346$	36530.7	+	63273.0i	0.305144	+	0.528525i
$347$	−49539.3	+	28601.5i	−0.411425	+	0.237536i	−0.691402	−	0.722470i	$-0.743007\pi$
$347$	−49539.3	+	28601.5i	−0.411425	+	0.237536i	0.279977	+	0.960007i	$0.409673\pi$
$348$	67475.8	−	78102.6i	0.557172	−	0.644921i
$349$	−8250.82	+	14290.8i	−0.0677402	+	0.117329i	−0.897906	−	0.440187i	$-0.854912\pi$
$349$	−8250.82	+	14290.8i	−0.0677402	+	0.117329i	0.830166	+	0.557516i	$0.188246\pi$
$350$		−	9799.30i		−	0.0799943i
$351$	209154.	+	9040.33i	1.69767	+	0.0733787i
$352$	−215807.			−1.74173
$353$	121089.	+	69910.9i	0.971754	+	0.561043i	0.899771	−	0.436363i	$-0.143734\pi$
$353$	121089.	+	69910.9i	0.971754	+	0.561043i	0.0719836	+	0.997406i	$0.477067\pi$
$354$	17447.3	+	15073.4i	0.139226	+	0.120283i
$355$	−14744.1	−	25537.4i	−0.116993	−	0.202638i
$356$	70979.9	−	40980.2i	0.560061	−	0.323351i
$357$	−18214.5	−	52378.4i	−0.142916	−	0.410976i
$358$	66478.3	−	115144.i	0.518697	−	0.898410i
$359$			122208.i			0.948222i	0.880465	+	0.474111i	$0.157230\pi$
$359$			122208.i			0.948222i	−0.880465	+	0.474111i	$0.842770\pi$
$360$	−45560.4	+	36046.0i	−0.351546	+	0.278133i
$361$	−110742.			−0.849765
$362$	8965.08	+	5175.99i	0.0684128	+	0.0394981i
$363$	50689.6	−	265096.i	0.384686	−	2.01182i
$364$	44575.5	+	77207.0i	0.336429	+	0.582712i
$365$	51088.7	−	29496.1i	0.383477	−	0.221401i
$366$	113336.	+	21671.2i	0.846067	+	0.161778i
$367$	−24156.9	+	41841.0i	−0.179353	+	0.310649i	−0.941659	−	0.336568i	$-0.890734\pi$
$367$	−24156.9	+	41841.0i	−0.179353	+	0.310649i	0.762306	+	0.647217i	$0.224067\pi$
$368$			928.998i			0.00685992i
$369$	−30182.4	−	38149.1i	−0.221667	−	0.280176i
$370$	59726.7			0.436280
$371$	2133.07	+	1231.53i	0.0154973	+	0.00894738i
$372$	26828.8	−	9329.67i	0.193872	−	0.0674187i
$373$	−33857.4	−	58642.8i	−0.243353	−	0.421500i	0.718314	−	0.695719i	$-0.244914\pi$
$373$	−33857.4	−	58642.8i	−0.243353	−	0.421500i	−0.961667	+	0.274219i	$0.911581\pi$
$374$	88672.4	−	51195.1i	0.633936	−	0.366003i
$375$	−8222.80	+	9517.81i	−0.0584732	+	0.0676822i
$376$	25651.0	−	44428.9i	0.181438	−	0.314260i
$377$		−	334908.i		−	2.35637i
$378$	2467.88	−	57096.2i	0.0172719	−	0.399599i
$379$	241316.			1.67999			0.839997	−	0.542591i	$-0.182557\pi$
$379$	241316.			1.67999			0.839997	+	0.542591i	$0.182557\pi$
$380$	13322.6	+	7691.83i	0.0922620	+	0.0532675i
$381$	−479.657	−	414.394i	−0.00330431	−	0.00285472i
$382$	42023.0	+	72785.9i	0.287978	+	0.498793i
$383$	−190220.	+	109824.i	−1.29676	+	0.748683i	−0.979843	−	0.199771i	$-0.935980\pi$
$383$	−190220.	+	109824.i	−1.29676	+	0.748683i	−0.316915	+	0.948454i	$0.602647\pi$
$384$	29464.5	+	84729.5i	0.199819	+	0.574608i
$385$	37282.6	−	64575.4i	0.251527	−	0.435658i
$386$			66244.4i			0.444605i
$387$	−208746.	−	82859.0i	−1.39378	−	0.553245i
$388$	6291.89			0.0417944
$389$	−110095.	−	63563.5i	−0.727561	−	0.420057i	0.0899684	−	0.995945i	$-0.471323\pi$
$389$	−110095.	−	63563.5i	−0.727561	−	0.420057i	−0.817529	+	0.575887i	$0.804657\pi$
$390$	−13476.5	+	70479.2i	−0.0886028	+	0.463374i
$391$	46186.3	+	79997.0i	0.302106	+	0.523263i
$392$	−78020.7	+	45045.3i	−0.507736	+	0.293141i
$393$	67832.9	+	12970.5i	0.439193	+	0.0839790i
$394$	8720.10	−	15103.6i	0.0561732	−	0.0972948i
$395$		−	54877.7i		−	0.351724i
$396$	−166487.	+	24436.3i	−1.06167	+	0.155828i
$397$	−110607.			−0.701783			−0.350891	−	0.936416i	$-0.614121\pi$
$397$	−110607.			−0.701783			−0.350891	+	0.936416i	$0.614121\pi$
$398$	−55373.9	−	31970.1i	−0.349574	−	0.201827i
$399$	−37550.4	+	13058.1i	−0.235868	+	0.0820226i
$400$	−122.682	−	212.492i	−0.000766764	−	0.00132807i
$401$	−183374.	+	105871.i	−1.14038	+	0.658397i	−0.946524	−	0.322633i	$-0.895432\pi$
$401$	−183374.	+	105871.i	−1.14038	+	0.658397i	−0.193854	+	0.981030i	$0.562099\pi$
$402$	59410.2	−	68766.7i	0.367628	−	0.425526i
$403$	46084.0	−	79819.9i	0.283753	−	0.491475i
$404$		−	17577.0i		−	0.107692i
$405$	−50307.6	+	53385.2i	−0.306707	+	0.325470i
$406$	−91425.3			−0.554644
$407$	393587.	+	227237.i	2.37603	+	1.37180i
$408$	−85271.2	−	73669.1i	−0.512250	−	0.442553i
$409$	−64782.8	−	112207.i	−0.387270	−	0.670771i	0.604812	−	0.796369i	$-0.293248\pi$
$409$	−64782.8	−	112207.i	−0.387270	−	0.670771i	−0.992081	+	0.125598i	$0.959915\pi$
$410$	14439.6	−	8336.70i	0.0858987	−	0.0495937i
$411$	23383.2	+	67241.9i	0.138427	+	0.398067i
$412$	31721.5	−	54943.3i	0.186879	−	0.323683i
$413$			32569.3i			0.190945i
$414$	13824.2	+	94185.9i	0.0806566	+	0.549522i
$415$	−40416.5			−0.234673
$416$	254056.	+	146679.i	1.46805	+	0.847582i
$417$	−36098.7	+	188788.i	−0.207596	+	1.08568i
$418$	−36702.1	−	63569.8i	−0.210057	−	0.363830i
$419$	133439.	−	77040.9i	0.760071	−	0.438827i	−0.0692504	−	0.997599i	$-0.522061\pi$
$419$	133439.	−	77040.9i	0.760071	−	0.438827i	0.829321	+	0.558772i	$0.188727\pi$
$420$	−30681.8	−	5866.74i	−0.173933	−	0.0332582i
$421$	7866.44	−	13625.1i	0.0443827	−	0.0768732i	−0.842981	−	0.537944i	$-0.819201\pi$
$421$	7866.44	−	13625.1i	0.0443827	−	0.0768732i	0.887363	+	0.461071i	$0.152535\pi$
$422$			133377.i			0.748956i
$423$	23898.4	−	60207.0i	0.133564	−	0.336486i
$424$	5005.01			0.0278403
$425$	−21128.6	−	12198.6i	−0.116975	−	0.0675355i
$426$	55675.2	−	19360.9i	0.306791	−	0.106686i
$427$	81497.6	+	141158.i	0.446981	+	0.774194i
$428$	−42095.3	+	24303.7i	−0.229798	+	0.132674i
$429$	−356954.	+	413170.i	−1.93953	+	2.24499i
$430$	38489.8	−	66666.2i	0.208165	−	0.360553i
$431$			285514.i			1.53699i	0.639853	+	0.768497i	$0.278995\pi$
$431$			285514.i			1.53699i	−0.639853	+	0.768497i	$0.721005\pi$
$432$	−661.301	−	1268.99i	−0.00354349	−	0.00679973i
$433$	−266643.			−1.42218			−0.711090	−	0.703101i	$-0.751798\pi$
$433$	−266643.			−1.42218			−0.711090	+	0.703101i	$0.751798\pi$
$434$	−21789.7	−	12580.3i	−0.115684	−	0.0667900i
$435$	88799.0	+	76716.8i	0.469277	+	0.405427i
$436$	93534.9	+	162007.i	0.492040	+	0.852239i
$437$	57350.3	−	33111.2i	0.300312	−	0.173385i
$438$	38732.3	+	111380.i	0.201895	+	0.580578i
$439$	−9719.98	+	16835.5i	−0.0504355	+	0.0873569i	−0.890141	−	0.455685i	$-0.849394\pi$
$439$	−9719.98	+	16835.5i	−0.0504355	+	0.0873569i	0.839705	+	0.543042i	$0.182728\pi$
$440$		−	151519.i		−	0.782641i
$441$	−89209.2	+	70579.7i	−0.458704	+	0.362913i
$442$	−139184.			−0.712436
$443$	−26639.2	−	15380.1i	−0.135742	−	0.0783705i	0.430591	−	0.902547i	$-0.358305\pi$
$443$	−26639.2	−	15380.1i	−0.135742	−	0.0783705i	−0.566333	+	0.824177i	$0.691638\pi$
$444$	35757.8	−	187006.i	0.181386	−	0.948612i
$445$	46592.6	+	80700.8i	0.235287	+	0.407528i
$446$	119083.	−	68752.6i	0.598659	−	0.345636i
$447$	−305946.	−	58500.7i	−1.53119	−	0.292783i
$448$	40537.1	−	70212.3i	0.201975	−	0.349830i
$449$		−	67901.9i		−	0.336813i	−0.985718	−	0.168407i	$-0.946138\pi$
$449$		−	67901.9i		−	0.336813i	0.985718	−	0.168407i	$-0.0538622\pi$
$450$	−15600.1	−	19717.7i	−0.0770376	−	0.0973716i
$451$	126872.			0.623752
$452$	−42020.8	−	24260.7i	−0.205678	−	0.118748i
$453$	−38934.0	+	13539.2i	−0.189728	+	0.0659776i
$454$	−14710.8	−	25479.8i	−0.0713713	−	0.123619i
$455$	−87780.8	+	50680.3i	−0.424011	+	0.244803i
$456$	−52813.8	+	61131.5i	−0.253991	+	0.293992i
$457$	171806.	−	297578.i	0.822635	−	1.42485i	−0.0810784	−	0.996708i	$-0.525836\pi$
$457$	171806.	−	297578.i	0.822635	−	1.42485i	0.903713	−	0.428138i	$-0.140830\pi$
$458$			228185.i			1.08782i
$459$	−120035.	−	76396.9i	−0.569747	−	0.362619i
$460$	52033.2			0.245904
$461$	−231373.	−	133583.i	−1.08871	−	0.628565i	−0.155474	−	0.987840i	$-0.549691\pi$
$461$	−231373.	−	133583.i	−1.08871	−	0.628565i	−0.933232	+	0.359275i	$0.883024\pi$
$462$	112790.	+	97443.4i	0.528428	+	0.456529i
$463$	33096.5	+	57324.8i	0.154390	+	0.267412i	0.932837	−	0.360299i	$-0.117325\pi$
$463$	33096.5	+	57324.8i	0.154390	+	0.267412i	−0.778447	+	0.627711i	$0.783992\pi$
$464$	−1982.50	+	1144.60i	−0.00920826	+	0.00531639i
$465$	10607.4	+	30503.1i	0.0490572	+	0.141071i
$466$	108700.	−	188274.i	0.500561	−	0.866998i
$467$		−	65412.7i		−	0.299936i	−0.988691	−	0.149968i	$-0.952083\pi$
$467$		−	65412.7i		−	0.299936i	0.988691	−	0.149968i	$-0.0479171\pi$
$468$	212604.	+	84390.3i	0.970686	+	0.385302i
$469$	128369.			0.583598
$470$	19228.1	+	11101.3i	0.0870442	+	0.0502550i
$471$	24838.7	−	129901.i	0.111966	−	0.585560i
$472$	33091.0	+	57315.4i	0.148534	+	0.257269i
$473$	507279.	−	292878.i	2.26738	−	1.30907i
$474$	107746.	+	20602.4i	0.479563	+	0.0916983i
$475$	−8745.25	+	15147.2i	−0.0387601	+	0.0671345i
$476$		−	60591.4i		−	0.267422i
$477$	6252.61	−	917.732i	0.0274805	−	0.00403347i
$478$	−121820.			−0.533166
$479$	−280298.	−	161830.i	−1.22166	−	0.705323i	−0.256385	−	0.966575i	$-0.582532\pi$
$479$	−280298.	−	161830.i	−1.22166	−	0.705323i	−0.965271	+	0.261251i	$0.915865\pi$
$480$	−97087.2	+	33761.9i	−0.421385	+	0.146536i
$481$	−308896.	−	535023.i	−1.33513	−	2.31250i
$482$	−207736.	+	119936.i	−0.894163	+	0.516245i
$483$	−87909.8	+	101755.i	−0.376828	+	0.436174i
$484$	147449.	−	255389.i	0.629434	−	1.09021i
$485$			7153.59i			0.0304117i
$486$	−85929.2	−	118815.i	−0.363805	−	0.503037i
$487$	15920.9			0.0671287			0.0335644	−	0.999437i	$-0.489314\pi$
$487$	15920.9			0.0671287			0.0335644	+	0.999437i	$0.489314\pi$
$488$	286838.	+	165606.i	1.20447	+	0.695404i
$489$	−204999.	−	177106.i	−0.857302	−	0.740656i
$490$	−19494.8	−	33766.0i	−0.0811946	−	0.140633i
$491$	160887.	−	92887.9i	0.667355	−	0.385298i	−0.127719	−	0.991810i	$-0.540765\pi$
$491$	160887.	−	92887.9i	0.667355	−	0.385298i	0.795074	+	0.606513i	$0.207432\pi$
$492$	−17457.5	−	50201.7i	−0.0721195	−	0.207390i
$493$	−113810.	+	197125.i	−0.468260	+	0.811050i
$494$			99782.2i			0.408883i
$495$	−27783.0	−	189288.i	−0.113388	−	0.772527i
$496$	−629.996			−0.00256079
$497$	72109.4	+	41632.4i	0.291930	+	0.168546i
$498$	15173.3	−	79353.2i	0.0611817	−	0.319967i
$499$	168233.	+	291388.i	0.675633	+	1.17023i	0.976284	+	0.216496i	$0.0694628\pi$
$499$	168233.	+	291388.i	0.675633	+	1.17023i	−0.300651	+	0.953734i	$0.597204\pi$
$500$	−11901.7	+	6871.43i	−0.0476067	+	0.0274857i
$501$	186127.	+	35589.8i	0.741541	+	0.141792i
$502$	64977.2	−	112544.i	0.257842	−	0.446595i
$503$			248667.i			0.982838i	0.870923	+	0.491419i	$0.163522\pi$
$503$			248667.i			0.982838i	−0.870923	+	0.491419i	$0.836478\pi$
$504$	60520.9	−	152470.i	0.238256	−	0.600237i
$505$	19984.2			0.0783619
$506$	−215017.	−	124140.i	−0.839791	−	0.484853i
$507$	458253.	−	159356.i	1.78274	−	0.619946i
$508$	−346.291	−	599.794i	−0.00134188	−	0.00232421i
$509$	44574.6	−	25735.2i	0.172049	−	0.0993325i	−0.411503	−	0.911409i	$-0.634996\pi$
$509$	44574.6	−	25735.2i	0.172049	−	0.0993325i	0.583552	+	0.812076i	$0.301663\pi$
$510$	31882.7	−	36903.9i	0.122579	−	0.141884i
$511$	−83287.3	+	144258.i	−0.318960	+	0.552456i
$512$		−	4019.95i		−	0.0153349i
$513$	−54769.4	+	86053.7i	−0.208115	+	0.326990i
$514$	165998.			0.628313
$515$	62467.9	+	36065.9i	0.235528	+	0.135982i
$516$	−185690.	−	160425.i	−0.697411	−	0.602520i
$517$	84472.6	+	146311.i	0.316035	+	0.547388i
$518$	−146054.	+	84324.3i	−0.544319	+	0.314263i
$519$	86974.0	+	250106.i	0.322890	+	0.928518i
$520$	−102984.	+	178374.i	−0.380859	+	0.659667i
$521$			58808.5i			0.216653i	0.994115	+	0.108326i	$0.0345492\pi$
$521$			58808.5i			0.216653i	−0.994115	+	0.108326i	$0.965451\pi$
$522$	−183962.	+	145545.i	−0.675130	+	0.534143i
$523$	79752.3			0.291568			0.145784	−	0.989316i	$-0.453430\pi$
$523$	79752.3			0.291568			0.145784	+	0.989316i	$0.453430\pi$
$524$	65348.9	+	37729.2i	0.237999	+	0.137409i
$525$	6670.21	−	34883.8i	0.0242003	−	0.126563i
$526$	98004.7	+	169749.i	0.354222	+	0.613530i
$527$	−54249.5	+	31321.0i	−0.195333	+	0.112775i
$528$	3665.72	+	700.930i	0.0131489	+	0.00251424i
$529$	−27926.1	+	48369.4i	−0.0997926	+	0.172846i
$530$			2166.08i			0.00771123i
$531$	51849.1	+	65534.6i	0.183887	+	0.232424i
$532$	−43438.4			−0.153480
$533$	−149358.	−	86231.8i	−0.525743	−	0.303538i
$534$	−175939.	+	61182.4i	−0.616992	+	0.214558i
$535$	−27632.2	−	47860.4i	−0.0965401	−	0.167212i
$536$	225903.	−	130425.i	0.786307	−	0.453975i
$537$	315027.	−	364641.i	1.09245	−	1.26450i
$538$	−64917.3	+	112440.i	−0.224283	+	0.388469i
$539$		−	296682.i		−	1.02121i
$540$	−71076.3	+	37039.5i	−0.243746	+	0.127021i
$541$	−164771.			−0.562970			−0.281485	−	0.959566i	$-0.590827\pi$
$541$	−164771.			−0.562970			−0.281485	+	0.959566i	$0.590827\pi$
$542$	−74962.0	−	43279.3i	−0.255178	−	0.147327i
$543$	28390.9	+	24528.0i	0.0962897	+	0.0831884i
$544$	−99690.4	−	172669.i	−0.336865	−	0.583467i
$545$	−184195.	+	106345.i	−0.620132	+	0.358033i
$546$	−66550.0	−	191374.i	−0.223235	−	0.641946i
$547$	−111877.	+	193777.i	−0.373909	+	0.647630i	−0.990163	−	0.139918i	$-0.955316\pi$
$547$	−111877.	+	193777.i	−0.373909	+	0.647630i	0.616254	+	0.787547i	$0.288649\pi$
$548$			77785.5i			0.259023i
$549$	388704.	+	154291.i	1.28966	+	0.511914i
$550$	65575.0			0.216777
$551$	141320.	+	81591.2i	0.465480	+	0.268745i
$552$	−51318.6	+	268385.i	−0.168421	+	0.880807i
$553$	77478.3	+	134196.i	0.253355	+	0.438824i
$554$	224911.	−	129852.i	0.732809	−	0.423087i
$555$	212617.	+	40654.9i	0.690258	+	0.131986i
$556$	−105006.	+	181875.i	−0.339675	+	0.588334i
$557$		−	435479.i		−	1.40364i	−0.712352	−	0.701822i	$-0.752370\pi$
$557$		−	435479.i		−	1.40364i	0.712352	−	0.701822i	$-0.247630\pi$
$558$	−63871.7	+	9374.83i	−0.205135	+	0.0301089i
$559$	−796249.			−2.54815
$560$	600.007	+	346.414i	0.00191329	+	0.00110464i
$561$	350506.	−	121888.i	1.11370	−	0.387288i
$562$	−164691.	−	285254.i	−0.521432	−	0.903147i
$563$	−391849.	+	226234.i	−1.23624	+	0.713742i	−0.968323	−	0.249701i	$-0.919668\pi$
$563$	−391849.	+	226234.i	−1.23624	+	0.713742i	−0.267914	+	0.963443i	$0.586334\pi$
$564$	46270.1	−	53557.2i	0.145460	−	0.168368i
$565$	27583.3	−	47775.7i	0.0864071	−	0.149661i
$566$		−	66728.4i		−	0.208295i
$567$	47649.6	−	201573.i	0.148215	−	0.626998i
$568$	169197.			0.524440
$569$	191606.	+	110624.i	0.591813	+	0.341683i	0.765814	−	0.643062i	$-0.222336\pi$
$569$	191606.	+	110624.i	0.591813	+	0.341683i	−0.174001	+	0.984745i	$0.555670\pi$
$570$	−26456.7	−	22856.9i	−0.0814302	−	0.0703507i
$571$	−99024.8	−	171516.i	−0.303719	−	0.526057i	0.673256	−	0.739409i	$-0.264895\pi$
$571$	−99024.8	−	171516.i	−0.303719	−	0.526057i	−0.976975	+	0.213353i	$0.931562\pi$
$572$	−516654.	+	298290.i	−1.57909	+	0.911690i
$573$	100050.	+	287709.i	0.304726	+	0.876284i
$574$	−23540.1	+	40772.6i	−0.0714471	+	0.123750i
$575$			59159.3i			0.178932i
$576$	−30208.2	−	205812.i	−0.0910500	−	0.620333i
$577$	148915.			0.447288			0.223644	−	0.974671i	$-0.428205\pi$
$577$	148915.			0.447288			0.223644	+	0.974671i	$0.428205\pi$
$578$	−97691.9	−	56402.4i	−0.292417	−	0.168827i
$579$	−45091.4	+	235818.i	−0.134504	+	0.703429i
$580$	64108.9	+	111040.i	0.190573	+	0.330083i
$581$	98833.3	−	57061.4i	0.292787	−	0.169040i
$582$	−14045.3	−	2685.63i	−0.0414652	−	0.00792866i
$583$	−8241.13	+	14274.1i	−0.0242465	+	0.0419962i
$584$			338486.i			0.992463i
$585$	−95947.8	+	241720.i	−0.280365	+	0.706320i
$586$	6972.60			0.0203048
$587$	−360376.	−	208063.i	−1.04587	−	0.603836i	−0.124383	−	0.992234i	$-0.539695\pi$
$587$	−360376.	−	208063.i	−1.04587	−	0.603836i	−0.921492	+	0.388398i	$0.873028\pi$
$588$	−117394.	+	40823.4i	−0.339539	+	0.118074i
$589$	22454.2	+	38891.9i	0.0647243	+	0.112106i
$590$	−24805.1	+	14321.2i	−0.0712586	+	0.0411412i
$591$	41322.8	−	47830.7i	0.118308	−	0.136941i
$592$	−2111.39	+	3657.04i	−0.00602456	+	0.0104349i
$593$		−	140902.i		−	0.400690i	−0.979725	−	0.200345i	$-0.935794\pi$
$593$		−	140902.i		−	0.400690i	0.979725	−	0.200345i	$-0.0642062\pi$
$594$	382077.	+	16514.6i	1.08287	+	0.0468053i
$595$	68889.6			0.194590
$596$	−294743.	−	170170.i	−0.829757	−	0.479061i
$597$	−175360.	−	151500.i	−0.492019	−	0.425074i
$598$	168750.	+	292284.i	0.471891	+	0.817339i
$599$	179590.	−	103687.i	0.500529	−	0.288981i	−0.228403	−	0.973567i	$-0.573350\pi$
$599$	179590.	−	103687.i	0.500529	−	0.288981i	0.728932	+	0.684586i	$0.240017\pi$
$600$	−23704.4	−	68165.5i	−0.0658455	−	0.189349i
$601$	−185356.	+	321046.i	−0.513167	+	0.888831i	0.486717	+	0.873560i	$0.338194\pi$
$601$	−185356.	+	321046.i	−0.513167	+	0.888831i	−0.999883	+	0.0152707i	$0.995139\pi$
$602$			217365.i			0.599786i
$603$	258298.	−	204358.i	0.710374	−	0.562027i
$604$	−45038.9			−0.123456
$605$	290365.	+	167642.i	0.793293	+	0.458008i
$606$	−7502.55	+	39236.8i	−0.0204298	+	0.106844i
$607$	205086.	+	355219.i	0.556619	+	0.964093i	0.997776	+	0.0666627i	$0.0212351\pi$
$607$	205086.	+	355219.i	0.556619	+	0.964093i	−0.441156	+	0.897430i	$0.645432\pi$
$608$	−123787.	+	71468.7i	−0.334865	+	0.193334i
$609$	−325458.	−	62231.6i	−0.877527	−	0.167794i
$610$	−71671.6	+	124139.i	−0.192614	+	0.333617i
$611$		−	229656.i		−	0.615171i
$612$	−96459.2	−	121920.i	−0.257538	−	0.325515i
$613$	207476.			0.552138			0.276069	−	0.961138i	$-0.410968\pi$
$613$	207476.			0.552138			0.276069	+	0.961138i	$0.410968\pi$
$614$	−361660.	−	208805.i	−0.959322	−	0.553865i
$615$	57077.0	−	19848.4i	0.150908	−	0.0524778i
$616$	213920.	+	370521.i	0.563756	+	0.976454i
$617$	149818.	−	86497.6i	0.393545	−	0.227213i	−0.290150	−	0.956981i	$-0.593705\pi$
$617$	149818.	−	86497.6i	0.393545	−	0.227213i	0.683695	+	0.729768i	$0.260372\pi$
$618$	−94263.2	+	109109.i	−0.246811	+	0.285682i
$619$	−26068.6	+	45152.2i	−0.0680357	+	0.117841i	−0.898037	−	0.439921i	$-0.855006\pi$
$619$	−26068.6	+	45152.2i	−0.0680357	+	0.117841i	0.830001	+	0.557762i	$0.188340\pi$
$620$			35286.1i			0.0917951i
$621$	−14898.9	+	344695.i	−0.0386340	+	0.893824i
$622$	299303.			0.773626
$623$	−227873.	−	131562.i	−0.587105	−	0.338965i
$624$	−3839.00	−	3316.66i	−0.00985937	−	0.00851789i
$625$	−7812.50	−	13531.6i	−0.0200000	−	0.0346410i
$626$	148327.	−	85636.4i	0.378504	−	0.218529i
$627$	−87382.1	−	251280.i	−0.222273	−	0.639180i
$628$	72252.1	−	125144.i	0.183202	−	0.317316i
$629$			419882.i			1.06127i
$630$	65986.3	+	26192.4i	0.166254	+	0.0659925i
$631$	629939.			1.58212			0.791061	−	0.611737i	$-0.209529\pi$
$631$	629939.			1.58212			0.791061	+	0.611737i	$0.209529\pi$
$632$	272692.	+	157439.i	0.682713	+	0.394165i
$633$	−90787.4	+	474799.i	−0.226578	+	1.18496i
$634$	−115279.	−	199669.i	−0.286795	−	0.496743i
$635$	681.938	−	393.717i	0.00169121	−	0.000976420i
$636$	6782.06	+	1296.81i	0.0167667	+	0.00320600i
$637$	−201648.	+	349264.i	−0.496952	+	0.860746i
$638$		−	611800.i		−	1.50303i
$639$	211373.	−	31024.4i	0.517663	−	0.0759804i
$640$	−111439.			−0.272067
$641$	−63105.0	−	36433.7i	−0.153585	−	0.0886721i	0.421238	−	0.906950i	$-0.361596\pi$
$641$	−63105.0	−	36433.7i	−0.153585	−	0.0886721i	−0.574823	+	0.818278i	$0.694929\pi$
$642$	104342.	−	36284.8i	0.253157	−	0.0880348i
$643$	−249169.	−	431573.i	−0.602659	−	1.04384i	−0.992417	−	0.122919i	$-0.960775\pi$
$643$	−249169.	−	431573.i	−0.602659	−	1.04384i	0.389758	−	0.920917i	$-0.372559\pi$
$644$	−127240.	+	73462.3i	−0.306799	+	0.177130i
$645$	182395.	−	211121.i	0.438424	−	0.507472i
$646$	33908.4	−	58731.2i	0.0812537	−	0.140735i
$647$		−	720075.i		−	1.72016i	−0.510158	−	0.860081i	$-0.670413\pi$
$647$		−	720075.i		−	1.72016i	0.510158	−	0.860081i	$-0.329587\pi$
$648$	−120948.	−	403140.i	−0.288038	−	0.960077i
$649$	−217947.			−0.517443
$650$	−77197.2	−	44569.8i	−0.182715	−	0.105491i
$651$	−69004.4	−	59615.6i	−0.162823	−	0.140669i
$652$	−148000.	−	256343.i	−0.348150	−	0.603014i
$653$	554425.	−	320097.i	1.30022	−	0.750681i	0.319777	−	0.947493i	$-0.396392\pi$
$653$	554425.	−	320097.i	1.30022	−	0.750681i	0.980441	+	0.196811i	$0.0630586\pi$
$654$	−139645.	−	401570.i	−0.326490	−	0.938870i
$655$	−42896.4	+	74298.7i	−0.0999857	+	0.173180i
$656$			1178.84i			0.00273935i
$657$	62065.6	+	422859.i	0.143787	+	0.979637i
$658$	−62693.0			−0.144800
$659$	152861.	+	88254.6i	0.351988	+	0.203220i	0.665560	−	0.746344i	$-0.268193\pi$
$659$	152861.	+	88254.6i	0.351988	+	0.203220i	−0.313573	+	0.949564i	$0.601526\pi$
$660$	39259.1	−	205317.i	0.0901265	−	0.471342i
$661$	−385461.	−	667638.i	−0.882221	−	1.52805i	−0.848866	−	0.528608i	$-0.822714\pi$
$661$	−385461.	−	667638.i	−0.882221	−	1.52805i	−0.0333548	−	0.999444i	$-0.510619\pi$
$662$	6899.46	−	3983.40i	0.0157434	−	0.00908947i
$663$	−495472.	−	94740.4i	−1.12718	−	0.215530i
$664$	115951.	−	200833.i	0.262989	−	0.455511i
$665$		−	49387.4i		−	0.111679i
$666$	−159643.	+	402186.i	−0.359915	+	0.906731i
$667$	551943.			1.24063
$668$	179312.	+	103526.i	0.401842	+	0.232004i
$669$	470713.	−	163690.i	1.05173	−	0.365737i
$670$	56445.7	+	97766.9i	0.125742	+	0.217792i
$671$	−944602.	+	545366.i	−2.09799	+	1.21128i
$672$	189748.	−	219632.i	0.420183	−	0.486358i
$673$	−113266.	+	196183.i	−0.250075	+	0.433143i	−0.963546	−	0.267542i	$-0.913789\pi$
$673$	−113266.	+	196183.i	−0.250075	+	0.433143i	0.713471	+	0.700685i	$0.247122\pi$
$674$			276496.i			0.608653i
$675$	−42112.1	−	80810.5i	−0.0924272	−	0.177362i
$676$	530107.			1.16003
$677$	282598.	+	163158.i	0.616584	+	0.355985i	0.775538	−	0.631301i	$-0.217479\pi$
$677$	282598.	+	163158.i	0.616584	+	0.355985i	−0.158954	+	0.987286i	$0.550812\pi$
$678$	83446.7	+	72092.8i	0.181531	+	0.156831i
$679$	−10099.7	−	17493.2i	−0.0219063	−	0.0379428i
$680$	121232.	−	69993.2i	0.262179	−	0.151369i
$681$	−35024.1	−	100717.i	−0.0755220	−	0.217174i
$682$	84184.9	−	145812.i	0.180994	−	0.313492i
$683$		−	358820.i		−	0.769194i	−0.923085	−	0.384597i	$-0.874340\pi$
$683$		−	358820.i		−	0.769194i	0.923085	−	0.384597i	$-0.125660\pi$
$684$	−87404.9	+	69152.2i	−0.186820	+	0.147807i
$685$	−88438.5			−0.188478
$686$	258352.	+	149160.i	0.548989	+	0.316959i
$687$	−155321.	+	812298.i	−0.329092	+	1.72108i
$688$	2721.30	+	4713.42i	0.00574909	+	0.00995771i
$689$	19403.5	−	11202.6i	0.0408735	−	0.0235983i
$690$	−116153.	−	22209.8i	−0.243967	−	0.0466495i
$691$	263097.	−	455697.i	0.551011	−	0.954378i	−0.447191	−	0.894438i	$-0.647576\pi$
$691$	263097.	−	455697.i	0.551011	−	0.954378i	0.998202	−	0.0599399i	$-0.0190909\pi$
$692$			289323.i			0.604187i
$693$	335184.	+	423655.i	0.697938	+	0.882158i
$694$	142048.			0.294928
$695$	−206784.	−	119387.i	−0.428101	−	0.247164i
$696$	−635968.	+	221157.i	−1.31286	+	0.456543i
$697$	58607.4	+	101511.i	0.120639	+	0.208953i
$698$	35487.4	−	20488.7i	0.0728389	−	0.0420535i
$699$	515108.	−	596232.i	1.05425	−	1.22028i
$700$	19402.7	−	33606.4i	0.0395973	−	0.0685845i
$701$		−	270484.i		−	0.550434i	−0.961382	−	0.275217i	$-0.911250\pi$
$701$		−	270484.i		−	0.550434i	0.961382	−	0.275217i	$-0.0887497\pi$
$702$	−438569.	−	279130.i	−0.889947	−	0.566412i
$703$	301016.			0.609086
$704$	469847.	+	271266.i	0.948006	+	0.547332i
$705$	60892.1	+	52607.0i	0.122513	+	0.105844i
$706$	−173605.	−	300692.i	−0.348299	−	0.603271i
$707$	−48868.9	+	28214.5i	−0.0977673	+	0.0564460i
$708$	29989.5	+	86239.3i	0.0598278	+	0.172044i
$709$	−22544.9	+	39048.8i	−0.0448492	+	0.0776812i	−0.887579	−	0.460656i	$-0.847614\pi$
$709$	−22544.9	+	39048.8i	−0.0448492	+	0.0776812i	0.842729	+	0.538337i	$0.180947\pi$
$710$			73225.6i			0.145260i
$711$	369534.	+	146682.i	0.730997	+	0.290160i
$712$	−534679.			−1.05471
$713$	131547.	+	75948.5i	0.258762	+	0.149396i
$714$	−25862.8	+	135257.i	−0.0507317	+	0.265316i
$715$	−339142.	−	587412.i	−0.663392	−	1.14903i
$716$	455970.	−	263255.i	0.889428	−	0.513511i
$717$	−433658.	−	82920.7i	−0.843546	−	0.161296i
$718$	151735.	−	262812.i	0.294331	−	0.509796i
$719$			782866.i			1.51436i	0.653206	+	0.757181i	$0.273424\pi$
$719$			782866.i			1.51436i	−0.653206	+	0.757181i	$0.726576\pi$
$720$	1758.79	−	258.148i	0.00339272	−	0.000497970i
$721$	−203676.			−0.391805
$722$	238155.	+	137499.i	0.456863	+	0.263770i
$723$	−821141.	+	285550.i	−1.57087	+	0.546268i
$724$	20497.0	+	35501.8i	0.0391032	+	0.0677288i
$725$	−126247.	+	72888.8i	−0.240185	+	0.138671i
$726$	−438156.	+	507162.i	−0.831297	+	0.962218i
$727$	130962.	−	226834.i	0.247787	−	0.429179i	−0.715125	−	0.698997i	$-0.753630\pi$
$727$	130962.	−	226834.i	0.247787	−	0.429179i	0.962911	+	0.269818i	$0.0869635\pi$
$728$		−	581587.i		−	1.09737i
$729$	−225017.	−	481453.i	−0.423410	−	0.905938i
$730$	−146491.			−0.274894
$731$	468667.	+	270585.i	0.877061	+	0.506371i
$732$	345772.	+	298726.i	0.645309	+	0.557507i
$733$	−160183.	−	277446.i	−0.298133	−	0.516381i	0.677576	−	0.735453i	$-0.263031\pi$
$733$	−160183.	−	277446.i	−0.298133	−	0.516381i	−0.975709	+	0.219072i	$0.929697\pi$
$734$	103901.	−	59987.1i	0.192853	−	0.111344i
$735$	−46414.3	−	133471.i	−0.0859165	−	0.247066i
$736$	−241733.	+	418695.i	−0.446253	+	0.772933i
$737$			859018.i			1.58149i
$738$	17542.1	+	119516.i	0.0322083	+	0.219439i
$739$	−796278.			−1.45806			−0.729031	−	0.684481i	$-0.760029\pi$
$739$	−796278.			−1.45806			−0.729031	+	0.684481i	$0.760029\pi$
$740$	204831.	+	118259.i	0.374052	+	0.215959i
$741$	−67920.0	+	355207.i	−0.123698	+	0.646912i
$742$	−3058.16	−	5296.88i	−0.00555459	−	0.00962083i
$743$	−36868.7	+	21286.2i	−0.0667852	+	0.0385585i	−0.533021	−	0.846102i	$-0.678943\pi$
$743$	−36868.7	+	21286.2i	−0.0667852	+	0.0385585i	0.466236	+	0.884661i	$0.345610\pi$
$744$	−182004.	−	34801.4i	−0.328803	−	0.0628711i
$745$	193475.	−	335109.i	0.348589	−	0.603773i
$746$			168151.i			0.302150i
$747$	108029.	−	272155.i	0.193597	−	0.487726i
$748$	405466.			0.724688
$749$	135142.	+	78024.3i	0.240894	+	0.139080i
$750$	29500.9	−	10258.9i	0.0524460	−	0.0182380i
$751$	476957.	+	826113.i	0.845666	+	1.46474i	0.885041	+	0.465512i	$0.154130\pi$
$751$	476957.	+	826113.i	0.845666	+	1.46474i	−0.0393753	+	0.999224i	$0.512537\pi$
$752$	−1359.46	+	784.884i	−0.00240398	+	0.00138794i
$753$	307914.	−	356407.i	0.543049	−	0.628574i
$754$	−415826.	+	720232.i	−0.731424	+	1.26686i
$755$		−	51207.1i		−	0.0898331i
$756$	121514.	−	190923.i	0.212610	−	0.334053i
$757$	−854962.			−1.49195			−0.745976	−	0.665973i	$-0.768017\pi$
$757$	−854962.			−1.49195			−0.745976	+	0.665973i	$0.768017\pi$
$758$	−518959.	−	299621.i	−0.903222	−	0.521475i
$759$	−680922.	−	588275.i	−1.18199	−	1.02117i
$760$	−50178.5	−	86911.8i	−0.0868742	−	0.150471i
$761$	−473095.	+	273142.i	−0.816919	+	0.471649i	−0.849353	−	0.527825i	$-0.823008\pi$
$761$	−473095.	+	273142.i	−0.816919	+	0.471649i	0.0324337	+	0.999474i	$0.489674\pi$
$762$	517.003	+	1486.72i	0.000890396	+	0.00256046i
$763$	300283.	−	520105.i	0.515800	−	0.893392i
$764$			332823.i			0.570199i
$765$	138617.	−	109670.i	0.236861	−	0.187397i
$766$	545433.			0.929574
$767$	256575.	+	148134.i	0.436138	+	0.251805i
$768$	111290.	−	582024.i	0.188684	−	0.986776i
$769$	−409892.	−	709955.i	−0.693134	−	1.20054i	−0.970806	−	0.239867i	$-0.922896\pi$
$769$	−409892.	−	709955.i	−0.693134	−	1.20054i	0.277672	−	0.960676i	$-0.410437\pi$
$770$	−160355.	+	92581.1i	−0.270459	+	0.156150i
$771$	590923.	+	112992.i	0.994082	+	0.190081i
$772$	−131164.	+	227183.i	−0.220080	+	0.381190i
$773$			793360.i			1.32773i	0.747851	+	0.663867i	$0.231086\pi$
$773$			793360.i			1.32773i	−0.747851	+	0.663867i	$0.768914\pi$
$774$	346036.	+	437372.i	0.577617	+	0.730078i
$775$	−40118.6			−0.0667948
$776$	−35546.8	−	20523.0i	−0.0590306	−	0.0340813i
$777$	−577325.	+	200763.i	−0.956264	+	0.332539i
$778$	157842.	+	273391.i	0.260774	+	0.451674i
$779$	72773.9	−	42016.0i	0.119923	−	0.0692373i
$780$	−185766.	+	215023.i	−0.305336	+	0.353423i
$781$	−278596.	+	482542.i	−0.456743	+	0.791102i
$782$		−	229382.i		−	0.375099i
$783$	−753943.	+	392897.i	−1.22975	+	0.640848i
$784$	2756.64			0.00448485
$785$	142283.	+	82147.3i	0.230895	+	0.133307i
$786$	−129773.	−	112116.i	−0.210058	−	0.181477i
$787$	156894.	+	271748.i	0.253313	+	0.438750i	0.964436	−	0.264317i	$-0.0851466\pi$
$787$	156894.	+	271748.i	0.253313	+	0.438750i	−0.711123	+	0.703067i	$0.751813\pi$
$788$	59810.6	−	34531.7i	0.0963220	−	0.0556116i
$789$	233334.	+	670987.i	0.374822	+	1.07785i
$790$	−68136.9	+	118017.i	−0.109176	+	0.189099i
$791$			155772.i			0.248964i
$792$	1.02030e6	+	404994.i	1.62658	+	0.645652i
$793$	1.48269e6			2.35779
$794$	237865.	+	137331.i	0.377302	+	0.217836i
$795$	−1474.42	+	7710.89i	−0.00233284	+	0.0122003i
$796$	−126602.	−	219281.i	−0.199809	−	0.346079i
$797$	878698.	−	507316.i	1.38332	−	0.798660i	0.390769	−	0.920489i	$-0.372209\pi$
$797$	878698.	−	507316.i	1.38332	−	0.798660i	0.992551	+	0.121828i	$0.0388757\pi$
$798$	96966.6	+	18541.2i	0.152271	+	0.0291160i
$799$	−78042.9	+	135174.i	−0.122247	+	0.211739i
$800$		−	127692.i		−	0.199519i
$801$	−667958.	+	98040.1i	−1.04108	+	0.152805i
$802$	525803.			0.817474
$803$	−965344.	−	557342.i	−1.49710	−	0.864352i
$804$	339904.	−	118201.i	0.525828	−	0.182856i
$805$	−83523.3	−	144667.i	−0.128889	−	0.223242i
$806$	−198211.	+	114437.i	−0.305111	+	0.176156i
$807$	−307630.	+	356079.i	−0.472369	+	0.546763i
$808$	−57332.8	+	99303.4i	−0.0878174	+	0.152104i
$809$		−	581506.i		−	0.888500i	−0.895903	−	0.444250i	$-0.853470\pi$
$809$		−	581506.i		−	0.888500i	0.895903	−	0.444250i	$-0.146530\pi$
$810$	174472.	−	52344.3i	0.265923	−	0.0797809i
$811$	−470704.			−0.715660			−0.357830	−	0.933787i	$-0.616483\pi$
$811$	−470704.			−0.715660			−0.357830	+	0.933787i	$0.616483\pi$
$812$	−313540.	−	181022.i	−0.475533	−	0.274549i
$813$	−237392.	−	205092.i	−0.359158	−	0.310290i
$814$	−564281.	−	977364.i	−0.851622	−	1.47505i
$815$	291451.	−	168269.i	0.438783	−	0.253331i
$816$	1132.53	+	3256.75i	0.00170086	+	0.00489108i
$817$	193984.	−	335990.i	0.290618	−	0.503365i
$818$			321741.i			0.480839i
$819$	−106641.	−	726559.i	−0.158986	−	1.08319i
$820$	66026.8			0.0981957
$821$	−806901.	−	465864.i	−1.19711	−	0.691151i	−0.237200	−	0.971461i	$-0.576230\pi$
$821$	−806901.	−	465864.i	−1.19711	−	0.691151i	−0.959910	+	0.280310i	$0.909563\pi$
$822$	33201.9	−	173639.i	0.0491382	−	0.256983i
$823$	242529.	+	420073.i	0.358067	+	0.620190i	0.987638	−	0.156753i	$-0.0501026\pi$
$823$	242529.	+	420073.i	0.358067	+	0.620190i	−0.629571	+	0.776943i	$0.716769\pi$
$824$	−358429.	+	206939.i	−0.527896	+	0.304781i
$825$	233436.	+	44635.8i	0.342972	+	0.0655805i
$826$	40438.5	−	70041.5i	0.0592700	−	0.102659i
$827$			73886.9i			0.108033i	0.998540	+	0.0540165i	$0.0172024\pi$
$827$			73886.9i			0.108033i	−0.998540	+	0.0540165i	$0.982798\pi$
$828$	−139079.	+	350380.i	−0.202862	+	0.511067i
$829$	1.14364e6			1.66410			0.832050	−	0.554701i	$-0.187167\pi$
$829$	1.14364e6			1.66410			0.832050	+	0.554701i	$0.187167\pi$
$830$	86917.1	+	50181.6i	0.126168	+	0.0728431i
$831$	889032.	−	309159.i	1.28740	−	0.447692i
$832$	−368747.	−	638688.i	−0.532699	−	0.922661i
$833$	237377.	−	137050.i	0.342097	−	0.197510i
$834$	312033.	−	361176.i	0.448610	−	0.519262i
$835$	−117704.	+	203869.i	−0.168818	+	0.292401i
$836$		−	290681.i		−	0.415915i
$837$	−233753.	−	10103.6i	−0.333662	−	0.0144220i
$838$	−382620.			−0.544853
$839$	212770.	+	122843.i	0.302264	+	0.174512i	0.643460	−	0.765480i	$-0.277498\pi$
$839$	212770.	+	122843.i	0.302264	+	0.174512i	−0.341195	+	0.939992i	$0.610832\pi$
$840$	154205.	+	133223.i	0.218544	+	0.188808i
$841$	326396.	+	565334.i	0.461480	+	0.799306i
$842$	−33834.1	+	19534.1i	−0.0477233	+	0.0275531i
$843$	−392105.	−	1.12756e6i	−0.551756	−	1.58666i
$844$	−264087.	+	457412.i	−0.370734	+	0.642130i
$845$			602707.i			0.844098i
$846$	−126148.	+	99804.8i	−0.176255	+	0.139447i
$847$	−946733.			−1.31966
$848$	−132.628	−	76.5731i	−0.000184436	−	0.000106484i
$849$	45420.9	−	237542.i	0.0630145	−	0.329552i
$850$	30291.8	+	52467.0i	0.0419264	+	0.0726187i
$851$	881741.	−	509074.i	1.21754	−	0.702945i
$852$	229271.	+	43839.4i	0.315842	+	0.0603928i
$853$	−82969.0	+	143706.i	−0.114030	+	0.197505i	−0.917391	−	0.397986i	$-0.869709\pi$
$853$	−82969.0	+	143706.i	−0.114030	+	0.197505i	0.803362	+	0.595491i	$0.203043\pi$
$854$		−	404754.i		−	0.554977i
$855$	−78622.8	−	99375.3i	−0.107552	−	0.135940i
$856$	317096.			0.432757
$857$	−591000.	−	341214.i	−0.804685	−	0.464585i	0.0404215	−	0.999183i	$-0.487130\pi$
$857$	−591000.	−	341214.i	−0.804685	−	0.464585i	−0.845107	+	0.534597i	$0.820463\pi$
$858$	1.28064e6	−	445339.i	1.73961	−	0.604946i
$859$	497906.	+	862399.i	0.674779	+	1.16875i	0.976534	+	0.215365i	$0.0690942\pi$
$859$	497906.	+	862399.i	0.674779	+	1.16875i	−0.301755	+	0.953385i	$0.597572\pi$
$860$	263999.	−	152420.i	0.356948	−	0.206084i
$861$	−111552.	+	129120.i	−0.150477	+	0.174176i
$862$	354497.	−	614007.i	0.477088	−	0.826340i
$863$		−	935842.i		−	1.25655i	−0.777990	−	0.628277i	$-0.783760\pi$
$863$		−	935842.i		−	1.25655i	0.777990	−	0.628277i	$-0.216240\pi$
$864$	32158.3	−	744005.i	0.0430790	−	0.996663i
$865$	−328947.			−0.439637
$866$	573425.	+	331067.i	0.764612	+	0.441449i
$867$	−309374.	−	267280.i	−0.411572	−	0.355573i
$868$	−49818.1	−	86287.5i	−0.0661223	−	0.114527i
$869$	−898016.	+	518470.i	−1.18917	+	0.686568i
$870$	−95712.8	−	275236.i	−0.126454	−	0.363636i
$871$	583855.	−	1.01127e6i	0.769606	−	1.33300i
$872$		−	1.22037e6i		−	1.60494i
$873$	−48170.6	−	19120.7i	−0.0632054	−	0.0250886i
$874$	−164445.			−0.215277
$875$	38208.9	+	22059.9i	0.0499055	+	0.0288130i
$876$	−87702.5	+	458666.i	−0.114289	+	0.597707i
$877$	170730.	+	295713.i	0.221979	+	0.384478i	0.955409	−	0.295287i	$-0.0954151\pi$
$877$	170730.	+	295713.i	0.221979	+	0.384478i	−0.733430	+	0.679765i	$0.762082\pi$
$878$	41806.3	−	24136.9i	0.0542317	−	0.0313107i
$879$	24821.3	+	4746.13i	0.0321252	+	0.00614273i
$880$	−2318.14	+	4015.13i	−0.00299346	+	0.00518483i
$881$		−	96624.3i		−	0.124490i	−0.998061	−	0.0622450i	$-0.980174\pi$
$881$		−	96624.3i		−	0.124490i	0.998061	−	0.0622450i	$-0.0198260\pi$
$882$	279480.	−	41021.0i	0.359264	−	0.0527313i
$883$	−1.17097e6			−1.50184			−0.750921	−	0.660392i	$-0.770390\pi$
$883$	−1.17097e6			−1.50184			−0.750921	+	0.660392i	$0.770390\pi$
$884$	−477329.	−	275586.i	−0.610819	−	0.352657i
$885$	−98050.1	+	34096.7i	−0.125188	+	0.0435337i
$886$	38192.3	+	66151.1i	0.0486529	+	0.0842693i
$887$	−641980.	+	370647.i	−0.815970	+	0.471100i	−0.849025	−	0.528353i	$-0.822810\pi$
$887$	−641980.	+	370647.i	−0.815970	+	0.471100i	0.0330550	+	0.999454i	$0.489476\pi$
$888$	−811994.	+	939875.i	−1.02974	+	1.19191i
$889$	−1111.73	+	1925.57i	−0.00140668	+	0.00243644i
$890$		−	231400.i		−	0.292135i
$891$	1.34889e6	+	318862.i	1.69910	+	0.401650i
$892$	544522.			0.684361
$893$	96907.3	+	55949.5i	0.121522	+	0.0701606i
$894$	585314.	+	505675.i	0.732341	+	0.632698i
$895$	299308.	+	518417.i	0.373657	+	0.647192i
$896$	272509.	−	157333.i	0.339441	−	0.195977i
$897$	401769.	+	1.15534e6i	0.499334	+	1.43591i
$898$	−84307.9	+	146025.i	−0.104548	+	0.181082i
$899$			374297.i			0.463124i
$900$	−14458.9	−	98509.7i	−0.0178504	−	0.121617i
$901$	−15227.7			−0.0187579
$902$	−272842.	−	157526.i	−0.335350	−	0.193615i
$903$	−147956.	+	773781.i	−0.181451	+	0.948949i
$904$	158268.	+	274127.i	0.193667	+	0.335441i
$905$	−40363.9	+	23304.1i	−0.0492829	+	0.0284535i
$906$	100539.	+	19224.4i	0.122484	+	0.0234205i
$907$	−283255.	+	490611.i	−0.344320	+	0.596380i	−0.985230	−	0.171236i	$-0.945224\pi$
$907$	−283255.	+	490611.i	−0.344320	+	0.596380i	0.640910	+	0.767616i	$0.278557\pi$
$908$		−	116510.i		−	0.141316i
$909$	−53415.6	+	134569.i	−0.0646458	+	0.162861i
$910$	251701.			0.303950
$911$	−848066.	−	489631.i	−1.02186	−	0.589973i	−0.107220	−	0.994235i	$-0.534195\pi$
$911$	−848066.	−	489631.i	−1.02186	−	0.589973i	−0.914643	+	0.404262i	$0.867528\pi$
$912$	2334.79	−	811.918i	0.00280710	−	0.000976163i
$913$	381844.	+	661373.i	0.458083	+	0.793423i
$914$	−738952.	+	426634.i	−0.884553	+	0.510697i
$915$	−339637.	+	393127.i	−0.405670	+	0.469560i
$916$	−451807.	+	782553.i	−0.538471	+	0.932658i
$917$		−	242250.i		−	0.288089i
$918$	163284.	+	313331.i	0.193757	+	0.371807i
$919$	440425.			0.521483			0.260742	−	0.965409i	$-0.416033\pi$
$919$	440425.			0.521483			0.260742	+	0.965409i	$0.416033\pi$
$920$	−293968.	−	169722.i	−0.347315	−	0.200523i
$921$	−1.14532e6	−	989485.i	−1.35023	−	1.16651i
$922$	331717.	+	574551.i	0.390217	+	0.675875i
$923$	655945.	−	378710.i	0.769952	−	0.444532i
$924$	193871.	+	557503.i	0.227074	+	0.652985i
$925$	−134455.	+	232883.i	−0.157143	+	0.272179i
$926$		−	164372.i		−	0.191693i
$927$	−409829.	+	324245.i	−0.476918	+	0.377323i
$928$	−1.19134e6			−1.38337
$929$	175177.	+	101139.i	0.202977	+	0.117189i	0.598043	−	0.801464i	$-0.295945\pi$
$929$	175177.	+	101139.i	0.202977	+	0.117189i	−0.395067	+	0.918653i	$0.629278\pi$
$930$	15061.5	−	78768.3i	0.0174141	−	0.0910722i
$931$	−98251.8	−	170177.i	−0.113355	−	0.196337i
$932$	745566.	−	430453.i	0.858330	−	0.495557i
$933$	1.06547e6	+	203731.i	1.22399	+	0.234041i
$934$	−81217.3	+	140672.i	−0.0931011	+	0.161256i
$935$			460996.i			0.527319i
$936$	−925864.	−	1.17025e6i	−1.05681	−	1.33575i
$937$	567578.			0.646468			0.323234	−	0.946319i	$-0.395230\pi$
$937$	567578.			0.646468			0.323234	+	0.946319i	$0.395230\pi$
$938$	−276062.	−	159384.i	−0.313762	−	0.181151i
$939$	586308.	−	203887.i	0.664958	−	0.231238i
$940$	43961.4	+	76143.3i	0.0497526	+	0.0861739i
$941$	−682887.	+	394265.i	−0.771204	+	0.445255i	−0.833304	−	0.552815i	$-0.813554\pi$
$941$	−682887.	+	394265.i	−0.771204	+	0.445255i	0.0620997	+	0.998070i	$0.480220\pi$
$942$	−214703.	+	248517.i	−0.241956	+	0.280062i
$943$	142114.	−	246148.i	0.159813	−	0.276805i
$944$		−	2025.08i		−	0.00227247i
$945$	217071.	+	138156.i	0.243074	+	0.154706i
$946$	−1.45456e6			−1.62536
$947$	394343.	+	227674.i	0.439718	+	0.253871i	0.703478	−	0.710717i	$-0.251629\pi$
$947$	394343.	+	227674.i	0.439718	+	0.253871i	−0.263760	+	0.964588i	$0.584963\pi$
$948$	328719.	+	283993.i	0.365771	+	0.316003i
$949$	757625.	+	1.31224e6i	0.841244	+	1.45708i
$950$	37613.9	−	21716.4i	0.0416775	−	0.0240625i
$951$	−274462.	−	789255.i	−0.303473	−	0.872682i
$952$	−197638.	+	342319.i	−0.218070	+	0.377708i
$953$			1.71277e6i			1.88587i	0.332971	+	0.942937i	$0.391949\pi$
$953$			1.71277e6i			1.88587i	−0.332971	+	0.942937i	$0.608051\pi$
$954$	−14585.9	−	5789.70i	−0.0160264	−	0.00636149i
$955$	−378404.			−0.414905
$956$	−417778.	−	241204.i	−0.457119	−	0.263918i
$957$	416441.	−	2.17790e6i	0.454705	−	2.37801i
$958$	401861.	+	696043.i	0.437869	+	0.758412i
$959$	216265.	−	124861.i	0.235152	−	0.135765i
$960$	253813.	+	48532.1i	0.275404	+	0.0526607i
$961$	410256.	−	710585.i	0.444231	−	0.769430i
$962$			1.53412e6i			1.65771i
$963$	396139.	−	58143.6i	0.427164	−	0.0626974i
$964$	−949897.			−1.02217
$965$	−258296.	−	149128.i	−0.277373	−	0.160141i
$966$	315393.	−	109677.i	0.337985	−	0.117534i
$967$	−394899.	−	683985.i	−0.422312	−	0.731465i	0.573853	−	0.818958i	$-0.305448\pi$
$967$	−394899.	−	683985.i	−0.422312	−	0.731465i	−0.996165	+	0.0874926i	$0.972115\pi$
$968$	−1.66606e6	+	961899.i	−1.77803	+	1.02655i
$969$	160685.	−	185992.i	0.171131	−	0.198083i
$970$	8881.98	−	15384.0i	0.00943988	−	0.0163504i
$971$		−	34673.8i		−	0.0367759i	−0.999831	−	0.0183880i	$-0.994147\pi$
$971$		−	34673.8i		−	0.0367759i	0.999831	−	0.0183880i	$-0.00585340\pi$
$972$	−59436.4	−	577614.i	−0.0629100	−	0.611371i
$973$	674217.			0.712154
$974$	−34238.4	−	19767.5i	−0.0360907	−	0.0208370i
$975$	−244471.	−	211208.i	−0.257168	−	0.222178i
$976$	−5067.31	−	8776.84i	−0.00531959	−	0.00921380i
$977$	−165976.	+	95826.1i	−0.173882	+	0.100391i	−0.584415	−	0.811455i	$-0.698676\pi$
$977$	−165976.	+	95826.1i	−0.173882	+	0.100391i	0.410533	+	0.911846i	$0.365343\pi$
$978$	220960.	+	635402.i	0.231013	+	0.664311i
$979$	880389.	−	1.52488e6i	0.918563	−	1.59100i
$980$		−	154399.i		−	0.160766i
$981$	−223770.	−	1.52457e6i	−0.232522	−	1.58420i
$982$	−461323.			−0.478390
$983$	774879.	+	447376.i	0.801912	+	0.462984i	0.844139	−	0.536124i	$-0.180112\pi$
$983$	774879.	+	447376.i	0.801912	+	0.462984i	−0.0422273	+	0.999108i	$0.513445\pi$
$984$	−65120.0	+	340564.i	−0.0672549	+	0.351729i
$985$	39260.9	+	68001.9i	0.0404658	+	0.0700888i
$986$	489505.	−	282616.i	0.503505	−	0.290699i
$987$	−223176.	−	42674.0i	−0.229094	−	0.0438056i
$988$	−197569.	+	342200.i	−0.202398	+	0.350563i
$989$		−	1.31225e6i		−	1.34161i
$990$	−175275.	+	441567.i	−0.178833	+	0.450533i
$991$	−619450.			−0.630752			−0.315376	−	0.948967i	$-0.602131\pi$
$991$	−619450.			−0.630752			−0.315376	+	0.948967i	$0.602131\pi$
$992$	−283936.	−	163930.i	−0.288534	−	0.166585i
$993$	27272.3	−	9483.89i	0.0276582	−	0.00961807i
$994$	−103383.	−	179064.i	−0.104634	−	0.181232i
$995$	249313.	−	143941.i	0.251824	−	0.145391i
$996$	209156.	−	242096.i	0.210839	−	0.244045i
$997$	−184606.	+	319746.i	−0.185718	+	0.321674i	−0.943818	−	0.330465i	$-0.892795\pi$
$997$	−184606.	+	319746.i	−0.185718	+	0.321674i	0.758100	+	0.652138i	$0.226128\pi$
$998$		−	835522.i		−	0.838874i
$999$	−842061.	+	1.32305e6i	−0.843747	+	1.32570i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.i.a.11.7	✓	32
3.2	odd	2		135.5.i.a.116.10		32
9.2	odd	6		405.5.c.b.161.13		32
9.4	even	3		135.5.i.a.71.10		32
9.5	odd	6	inner	45.5.i.a.41.7	yes	32
9.7	even	3		405.5.c.b.161.20		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.i.a.11.7	✓	32	1.1	even	1	trivial
45.5.i.a.41.7	yes	32	9.5	odd	6	inner
135.5.i.a.71.10		32	9.4	even	3
135.5.i.a.116.10		32	3.2	odd	2
405.5.c.b.161.13		32	9.2	odd	6
405.5.c.b.161.20		32	9.7	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	45.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.15054 - 1.24161i) q^{2} +(-6.81039 - 5.88376i) q^{3} +(-4.91680 - 8.51614i) q^{4} +(9.68246 - 5.59017i) q^{5} +(7.34064 + 21.1091i) q^{6} +(-15.7848 + 27.3401i) q^{7} +64.1506i q^{8} +(11.7628 + 80.1414i) q^{9} -27.7633 q^{10} +(-182.954 - 105.629i) q^{11} +(-16.6216 + 86.9275i) q^{12} +(143.587 + 248.700i) q^{13} +(67.8916 - 39.1972i) q^{14} +(-98.8325 - 18.8980i) q^{15} +(0.981458 - 1.69994i) q^{16} -195.177i q^{17} +(74.2081 - 186.952i) q^{18} -139.924 q^{19} +(-95.2134 - 54.9715i) q^{20} +(268.363 - 93.3227i) q^{21} +(262.300 + 454.317i) q^{22} +(-409.868 + 236.637i) q^{23} +(377.447 - 436.891i) q^{24} +(62.5000 - 108.253i) q^{25} -713.117i q^{26} +(391.423 - 615.003i) q^{27} +310.443 q^{28} +(-1009.98 - 583.111i) q^{29} +(189.079 + 163.352i) q^{30} +(-160.474 - 277.950i) q^{31} +(884.676 - 510.768i) q^{32} +(624.497 + 1795.83i) q^{33} +(-242.335 + 419.736i) q^{34} +352.959i q^{35} +(624.660 - 494.213i) q^{36} -2151.28 q^{37} +(300.912 + 173.731i) q^{38} +(485.406 - 2538.57i) q^{39} +(358.613 + 621.136i) q^{40} +(-520.096 + 300.278i) q^{41} +(-692.995 - 132.509i) q^{42} +(-1386.35 + 2401.24i) q^{43} +2077.42i q^{44} +(561.897 + 710.209i) q^{45} +1175.25 q^{46} +(-692.571 - 399.856i) q^{47} +(-16.6861 + 5.80256i) q^{48} +(702.180 + 1216.21i) q^{49} +(-268.817 + 155.202i) q^{50} +(-1148.38 + 1329.23i) q^{51} +(1411.98 - 2445.61i) q^{52} -78.0197i q^{53} +(-1605.36 + 836.592i) q^{54} -2361.93 q^{55} +(-1753.88 - 1012.61i) q^{56} +(952.937 + 823.279i) q^{57} +(1448.00 + 2508.00i) q^{58} +(893.450 - 515.833i) q^{59} +(325.001 + 934.589i) q^{60} +(2581.52 - 4471.33i) q^{61} +796.988i q^{62} +(-2376.75 - 943.419i) q^{63} -2568.11 q^{64} +(2780.55 + 1605.35i) q^{65} +(886.725 - 4637.39i) q^{66} +(-2033.11 - 3521.44i) q^{67} +(-1662.16 + 959.648i) q^{68} +(4183.68 + 799.970i) q^{69} +(438.238 - 759.051i) q^{70} -2637.50i q^{71} +(-5141.12 + 754.592i) q^{72} +5276.42 q^{73} +(4626.41 + 2671.06i) q^{74} +(-1062.58 + 369.512i) q^{75} +(687.978 + 1191.61i) q^{76} +(5775.80 - 3334.66i) q^{77} +(-4195.81 + 4856.61i) q^{78} +(2454.21 - 4250.81i) q^{79} -21.9461i q^{80} +(-6284.27 + 1885.38i) q^{81} +1491.31 q^{82} +(-3130.65 - 1807.48i) q^{83} +(-2114.24 - 1826.57i) q^{84} +(-1091.08 - 1889.80i) q^{85} +(5962.81 - 3442.63i) q^{86} +(3447.46 + 9913.67i) q^{87} +(6776.15 - 11736.6i) q^{88} +8334.74i q^{89} +(-326.575 - 2224.99i) q^{90} -9065.96 q^{91} +(4030.47 + 2327.00i) q^{92} +(-542.496 + 2837.14i) q^{93} +(992.933 + 1719.81i) q^{94} +(-1354.81 + 782.199i) q^{95} +(-9030.22 - 1726.69i) q^{96} +(-319.918 + 554.115i) q^{97} -3487.34i q^{98} +(6313.17 - 15904.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{3} + 128 q^{4} + 98 q^{6} - 26 q^{7} - 220 q^{9} - 738 q^{11} - 214 q^{12} + 10 q^{13} + 1998 q^{14} - 50 q^{15} - 1024 q^{16} - 2504 q^{18} + 508 q^{19} - 1620 q^{21} + 672 q^{22} + 1998 q^{23}+ \cdots + 53512 q^{99}+O(q^{100}) \) 32 * q - 8 * q^3 + 128 * q^4 + 98 * q^6 - 26 * q^7 - 220 * q^9 - 738 * q^11 - 214 * q^12 + 10 * q^13 + 1998 * q^14 - 50 * q^15 - 1024 * q^16 - 2504 * q^18 + 508 * q^19 - 1620 * q^21 + 672 * q^22 + 1998 * q^23 + 4164 * q^24 + 2000 * q^25 + 2158 * q^27 - 1664 * q^28 - 270 * q^29 + 2000 * q^30 - 1472 * q^31 - 6048 * q^32 - 1354 * q^33 - 594 * q^34 + 4498 * q^36 + 2068 * q^37 - 7164 * q^38 - 4616 * q^39 + 1650 * q^40 - 13428 * q^41 - 10230 * q^42 + 568 * q^43 - 100 * q^45 + 5724 * q^46 + 12528 * q^47 + 25844 * q^48 - 1674 * q^49 + 1454 * q^51 + 1534 * q^52 + 8456 * q^54 + 21294 * q^56 - 12512 * q^57 - 8190 * q^58 - 4374 * q^59 - 5050 * q^60 - 4478 * q^61 + 5604 * q^63 - 37216 * q^64 - 8550 * q^65 - 19472 * q^66 + 12838 * q^67 + 65736 * q^68 + 8706 * q^69 + 2400 * q^70 - 36372 * q^72 + 29236 * q^73 - 20628 * q^74 + 1000 * q^75 + 6190 * q^76 - 31806 * q^77 - 42430 * q^78 - 3512 * q^79 - 3088 * q^81 + 34692 * q^82 - 43074 * q^83 - 19350 * q^84 - 4350 * q^85 - 10746 * q^86 + 69622 * q^87 - 16128 * q^88 - 26750 * q^90 - 48904 * q^91 + 27036 * q^92 + 27030 * q^93 + 5118 * q^94 + 6300 * q^95 + 53566 * q^96 + 23266 * q^97 + 53512 * q^99

Introduction

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