LMFDB - Embedded newform 74.4.c.b.63.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,4,Mod(47,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("74.47");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	74.c (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:	$4.36614134042$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 84 x^{8} - 140 x^{7} + 6309 x^{6} - 5214 x^{5} + 67648 x^{4} + 164178 x^{3} + 511389 x^{2} + \cdots + 443556 $ x^10 + 84x^8 - 140x^7 + 6309x^6 - 5214x^5 + 67648x^4 + 164178x^3 + 511389x^2 + 497502x + 443556
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			63.5
Root			$3.92323 - 6.79524i$ of defining polynomial
Character	$\chi$	$=$	74.63
Dual form			74.4.c.b.47.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(3.42323 - 5.92921i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.94299 - 5.09740i) q^{5} -13.6929 q^{6} +(8.40192 - 14.5526i) q^{7} +8.00000 q^{8} +(-9.93705 - 17.2115i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(3.42323 - 5.92921i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.94299 - 5.09740i) q^{5} -13.6929 q^{6} +(8.40192 - 14.5526i) q^{7} +8.00000 q^{8} +(-9.93705 - 17.2115i) q^{9} -11.7719 q^{10} -26.2337 q^{11} +(13.6929 + 23.7169i) q^{12} +(-19.5419 + 33.8476i) q^{13} -33.6077 q^{14} +(-20.1491 - 34.8992i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-11.4147 - 19.7709i) q^{17} +(-19.8741 + 34.4229i) q^{18} +(38.0743 - 65.9466i) q^{19} +(11.7719 + 20.3896i) q^{20} +(-57.5235 - 99.6335i) q^{21} +(26.2337 + 45.4381i) q^{22} -40.7683 q^{23} +(27.3859 - 47.4337i) q^{24} +(45.1777 + 78.2500i) q^{25} +78.1678 q^{26} +48.7873 q^{27} +(33.6077 + 58.2102i) q^{28} +145.866 q^{29} +(-40.2981 + 69.7984i) q^{30} +242.321 q^{31} +(-16.0000 + 27.7128i) q^{32} +(-89.8040 + 155.545i) q^{33} +(-22.8295 + 39.5418i) q^{34} +(-49.4535 - 85.6559i) q^{35} +79.4964 q^{36} +(-131.380 + 182.735i) q^{37} -152.297 q^{38} +(133.793 + 231.737i) q^{39} +(23.5439 - 40.7792i) q^{40} +(108.622 - 188.140i) q^{41} +(-115.047 + 199.267i) q^{42} +372.125 q^{43} +(52.4674 - 90.8762i) q^{44} -116.978 q^{45} +(40.7683 + 70.6127i) q^{46} -83.4851 q^{47} -109.543 q^{48} +(30.3155 + 52.5080i) q^{49} +(90.3553 - 156.500i) q^{50} -156.301 q^{51} +(-78.1678 - 135.391i) q^{52} +(-197.444 - 341.984i) q^{53} +(-48.7873 - 84.5021i) q^{54} +(-77.2054 + 133.724i) q^{55} +(67.2154 - 116.420i) q^{56} +(-260.674 - 451.501i) q^{57} +(-145.866 - 252.647i) q^{58} +(-72.7869 - 126.071i) q^{59} +161.192 q^{60} +(-28.8064 + 49.8942i) q^{61} +(-242.321 - 419.712i) q^{62} -333.961 q^{63} +64.0000 q^{64} +(115.023 + 199.226i) q^{65} +359.216 q^{66} +(-402.457 + 697.076i) q^{67} +91.3180 q^{68} +(-139.559 + 241.724i) q^{69} +(-98.9069 + 171.312i) q^{70} +(91.1160 - 157.818i) q^{71} +(-79.4964 - 137.692i) q^{72} -751.633 q^{73} +(447.887 + 44.8217i) q^{74} +618.615 q^{75} +(152.297 + 263.786i) q^{76} +(-220.413 + 381.767i) q^{77} +(267.587 - 463.474i) q^{78} +(-371.812 + 643.998i) q^{79} -94.1755 q^{80} +(435.310 - 753.980i) q^{81} -434.490 q^{82} +(512.353 + 887.422i) q^{83} +460.188 q^{84} -134.374 q^{85} +(-372.125 - 644.540i) q^{86} +(499.333 - 864.870i) q^{87} -209.870 q^{88} +(-376.495 - 652.109i) q^{89} +(116.978 + 202.612i) q^{90} +(328.380 + 568.770i) q^{91} +(81.5366 - 141.225i) q^{92} +(829.521 - 1436.77i) q^{93} +(83.4851 + 144.600i) q^{94} +(-224.104 - 388.160i) q^{95} +(109.543 + 189.735i) q^{96} -980.396 q^{97} +(60.6310 - 105.016i) q^{98} +(260.685 + 451.520i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} - 5 q^{3} - 20 q^{4} - q^{5} + 20 q^{6} - q^{7} + 80 q^{8} - 38 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 - 5 * q^3 - 20 * q^4 - q^5 + 20 * q^6 - q^7 + 80 * q^8 - 38 * q^9	\( 10 q - 10 q^{2} - 5 q^{3} - 20 q^{4} - q^{5} + 20 q^{6} - q^{7} + 80 q^{8} - 38 q^{9} + 4 q^{10} - 80 q^{11} - 20 q^{12} + 73 q^{13} + 4 q^{14} + 113 q^{15} - 80 q^{16} + 69 q^{17} - 76 q^{18} + 33 q^{19} - 4 q^{20} - 109 q^{21} + 80 q^{22} - 524 q^{23} - 40 q^{24} + 132 q^{25} - 292 q^{26} + 898 q^{27} - 4 q^{28} + 296 q^{29} + 226 q^{30} - 784 q^{31} - 160 q^{32} + 124 q^{33} + 138 q^{34} - 263 q^{35} + 304 q^{36} + 24 q^{37} - 132 q^{38} + 679 q^{39} - 8 q^{40} + 345 q^{41} - 218 q^{42} - 492 q^{43} + 160 q^{44} - 1816 q^{45} + 524 q^{46} - 32 q^{47} + 160 q^{48} + 150 q^{49} + 264 q^{50} + 342 q^{51} + 292 q^{52} - 19 q^{53} - 898 q^{54} + 340 q^{55} - 8 q^{56} + 207 q^{57} - 296 q^{58} - 105 q^{59} - 904 q^{60} + 219 q^{61} + 784 q^{62} - 304 q^{63} + 640 q^{64} + 1191 q^{65} - 496 q^{66} + 773 q^{67} - 552 q^{68} + 604 q^{69} - 526 q^{70} + 555 q^{71} - 304 q^{72} + 348 q^{73} + 102 q^{74} - 2952 q^{75} + 132 q^{76} + 884 q^{77} + 1358 q^{78} - 727 q^{79} + 32 q^{80} - 2609 q^{81} - 1380 q^{82} + 2229 q^{83} + 872 q^{84} - 3042 q^{85} + 492 q^{86} + 2660 q^{87} - 640 q^{88} + 901 q^{89} + 1816 q^{90} - 1405 q^{91} + 1048 q^{92} + 3236 q^{93} + 32 q^{94} - 3337 q^{95} - 160 q^{96} - 4596 q^{97} + 300 q^{98} + 6784 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 5 * q^3 - 20 * q^4 - q^5 + 20 * q^6 - q^7 + 80 * q^8 - 38 * q^9 + 4 * q^10 - 80 * q^11 - 20 * q^12 + 73 * q^13 + 4 * q^14 + 113 * q^15 - 80 * q^16 + 69 * q^17 - 76 * q^18 + 33 * q^19 - 4 * q^20 - 109 * q^21 + 80 * q^22 - 524 * q^23 - 40 * q^24 + 132 * q^25 - 292 * q^26 + 898 * q^27 - 4 * q^28 + 296 * q^29 + 226 * q^30 - 784 * q^31 - 160 * q^32 + 124 * q^33 + 138 * q^34 - 263 * q^35 + 304 * q^36 + 24 * q^37 - 132 * q^38 + 679 * q^39 - 8 * q^40 + 345 * q^41 - 218 * q^42 - 492 * q^43 + 160 * q^44 - 1816 * q^45 + 524 * q^46 - 32 * q^47 + 160 * q^48 + 150 * q^49 + 264 * q^50 + 342 * q^51 + 292 * q^52 - 19 * q^53 - 898 * q^54 + 340 * q^55 - 8 * q^56 + 207 * q^57 - 296 * q^58 - 105 * q^59 - 904 * q^60 + 219 * q^61 + 784 * q^62 - 304 * q^63 + 640 * q^64 + 1191 * q^65 - 496 * q^66 + 773 * q^67 - 552 * q^68 + 604 * q^69 - 526 * q^70 + 555 * q^71 - 304 * q^72 + 348 * q^73 + 102 * q^74 - 2952 * q^75 + 132 * q^76 + 884 * q^77 + 1358 * q^78 - 727 * q^79 + 32 * q^80 - 2609 * q^81 - 1380 * q^82 + 2229 * q^83 + 872 * q^84 - 3042 * q^85 + 492 * q^86 + 2660 * q^87 - 640 * q^88 + 901 * q^89 + 1816 * q^90 - 1405 * q^91 + 1048 * q^92 + 3236 * q^93 + 32 * q^94 - 3337 * q^95 - 160 * q^96 - 4596 * q^97 + 300 * q^98 + 6784 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$3$	3.42323	−	5.92921i	0.658801	−	1.14108i	−0.322125	−	0.946697i	$-0.604397\pi$
$3$	3.42323	−	5.92921i	0.658801	−	1.14108i	0.980926	−	0.194380i	$-0.0622696\pi$
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	2.94299	−	5.09740i	0.263229	−	0.455925i	−0.703869	−	0.710329i	$-0.748546\pi$
$5$	2.94299	−	5.09740i	0.263229	−	0.455925i	0.967098	+	0.254404i	$0.0818793\pi$
$6$	−13.6929			−0.931686
$7$	8.40192	−	14.5526i	0.453661	−	0.785764i	−0.544949	−	0.838469i	$-0.683451\pi$
$7$	8.40192	−	14.5526i	0.453661	−	0.785764i	0.998610	+	0.0527052i	$0.0167844\pi$
$8$	8.00000			0.353553
$9$	−9.93705	−	17.2115i	−0.368039	−	0.637462i
$10$	−11.7719			−0.372262
$11$	−26.2337			−0.719069			−0.359534	−	0.933132i	$-0.617064\pi$
$11$	−26.2337			−0.719069			−0.359534	+	0.933132i	$0.617064\pi$
$12$	13.6929	+	23.7169i	0.329401	+	0.570539i
$13$	−19.5419	+	33.8476i	−0.416920	+	0.722127i	−0.995628	−	0.0934082i	$-0.970224\pi$
$13$	−19.5419	+	33.8476i	−0.416920	+	0.722127i	0.578708	+	0.815535i	$0.303557\pi$
$14$	−33.6077			−0.641574
$15$	−20.1491	−	34.8992i	−0.346831	−	0.600729i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−11.4147	−	19.7709i	−0.162852	−	0.282068i	0.773038	−	0.634359i	$-0.218736\pi$
$17$	−11.4147	−	19.7709i	−0.162852	−	0.282068i	−0.935890	+	0.352291i	$0.885403\pi$
$18$	−19.8741	+	34.4229i	−0.260243	+	0.450754i
$19$	38.0743	−	65.9466i	0.459728	−	0.796273i	−0.539218	−	0.842166i	$-0.681280\pi$
$19$	38.0743	−	65.9466i	0.459728	−	0.796273i	0.998946	+	0.0458936i	$0.0146135\pi$
$20$	11.7719	+	20.3896i	0.131614	+	0.227963i
$21$	−57.5235	−	99.6335i	−0.597745	−	1.03532i
$22$	26.2337	+	45.4381i	0.254229	+	0.440338i
$23$	−40.7683			−0.369599			−0.184799	−	0.982776i	$-0.559164\pi$
$23$	−40.7683			−0.369599			−0.184799	+	0.982776i	$0.559164\pi$
$24$	27.3859	−	47.4337i	0.232921	−	0.403432i
$25$	45.1777	+	78.2500i	0.361421	+	0.626000i
$26$	78.1678			0.589614
$27$	48.7873			0.347745
$28$	33.6077	+	58.2102i	0.226830	+	0.392882i
$29$	145.866			0.934022			0.467011	−	0.884252i	$-0.345331\pi$
$29$	145.866			0.934022			0.467011	+	0.884252i	$0.345331\pi$
$30$	−40.2981	+	69.7984i	−0.245246	+	0.424779i
$31$	242.321			1.40394			0.701969	−	0.712207i	$-0.252304\pi$
$31$	242.321			1.40394			0.701969	+	0.712207i	$0.252304\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$	−89.8040	+	155.545i	−0.473723	+	0.820513i
$34$	−22.8295	+	39.5418i	−0.115154	+	0.199452i
$35$	−49.4535	−	85.6559i	−0.238833	−	0.413671i
$36$	79.4964			0.368039
$37$	−131.380	+	182.735i	−0.583751	+	0.811933i
$37$	−131.380	+	182.735i	−0.583751	+	0.811933i
$38$	−152.297			−0.650154
$39$	133.793	+	231.737i	0.549335	+	0.951476i
$40$	23.5439	−	40.7792i	0.0930654	−	0.161194i
$41$	108.622	−	188.140i	0.413755	−	0.716645i	−0.581542	−	0.813517i	$-0.697550\pi$
$41$	108.622	−	188.140i	0.413755	−	0.716645i	0.995297	+	0.0968713i	$0.0308835\pi$
$42$	−115.047	+	199.267i	−0.422670	+	0.732085i
$43$	372.125			1.31973			0.659867	−	0.751382i	$-0.270612\pi$
$43$	372.125			1.31973			0.659867	+	0.751382i	$0.270612\pi$
$44$	52.4674	−	90.8762i	0.179767	−	0.311366i
$45$	−116.978			−0.387513
$46$	40.7683	+	70.6127i	0.130673	+	0.226332i
$47$	−83.4851			−0.259097			−0.129548	−	0.991573i	$-0.541353\pi$
$47$	−83.4851			−0.259097			−0.129548	+	0.991573i	$0.541353\pi$
$48$	−109.543			−0.329401
$49$	30.3155	+	52.5080i	0.0883834	+	0.153085i
$50$	90.3553	−	156.500i	0.255563	−	0.442649i
$51$	−156.301			−0.429148
$52$	−78.1678	−	135.391i	−0.208460	−	0.361063i
$53$	−197.444	−	341.984i	−0.511718	−	0.886322i	−0.999908	−	0.0135841i	$-0.995676\pi$
$53$	−197.444	−	341.984i	−0.511718	−	0.886322i	0.488190	−	0.872738i	$-0.337657\pi$
$54$	−48.7873	−	84.5021i	−0.122946	−	0.212949i
$55$	−77.2054	+	133.724i	−0.189279	+	0.327842i
$56$	67.2154	−	116.420i	0.160393	−	0.277809i
$57$	−260.674	−	451.501i	−0.605739	−	1.04917i
$58$	−145.866	−	252.647i	−0.330227	−	0.571969i
$59$	−72.7869	−	126.071i	−0.160611	−	0.278186i	0.774477	−	0.632602i	$-0.218013\pi$
$59$	−72.7869	−	126.071i	−0.160611	−	0.278186i	−0.935088	+	0.354416i	$0.884680\pi$
$60$	161.192			0.346831
$61$	−28.8064	+	49.8942i	−0.0604636	+	0.104726i	−0.894673	−	0.446722i	$-0.852591\pi$
$61$	−28.8064	+	49.8942i	−0.0604636	+	0.104726i	0.834209	+	0.551448i	$0.185925\pi$
$62$	−242.321	−	419.712i	−0.496367	−	0.859733i
$63$	−333.961			−0.667859
$64$	64.0000			0.125000
$65$	115.023	+	199.226i	0.219491	+	0.380169i
$66$	359.216			0.669946
$67$	−402.457	+	697.076i	−0.733850	+	1.27107i	0.221376	+	0.975188i	$0.428945\pi$
$67$	−402.457	+	697.076i	−0.733850	+	1.27107i	−0.955226	+	0.295877i	$0.904388\pi$
$68$	91.3180			0.162852
$69$	−139.559	+	241.724i	−0.243492	+	0.421741i
$70$	−98.9069	+	171.312i	−0.168881	+	0.292510i
$71$	91.1160	−	157.818i	0.152303	−	0.263796i	−0.779771	−	0.626065i	$-0.784665\pi$
$71$	91.1160	−	157.818i	0.152303	−	0.263796i	0.932074	+	0.362269i	$0.117998\pi$
$72$	−79.4964	−	137.692i	−0.130121	−	0.225377i
$73$	−751.633			−1.20510			−0.602548	−	0.798083i	$-0.705848\pi$
$73$	−751.633			−1.20510			−0.602548	+	0.798083i	$0.705848\pi$
$74$	447.887	+	44.8217i	0.703592	+	0.0704111i
$75$	618.615			0.952420
$76$	152.297	+	263.786i	0.229864	+	0.398136i
$77$	−220.413	+	381.767i	−0.326213	+	0.565018i
$78$	267.587	−	463.474i	0.388439	−	0.672795i
$79$	−371.812	+	643.998i	−0.529521	+	0.917158i	0.469886	+	0.882727i	$0.344295\pi$
$79$	−371.812	+	643.998i	−0.529521	+	0.917158i	−0.999407	+	0.0344304i	$0.989038\pi$
$80$	−94.1755			−0.131614
$81$	435.310	−	753.980i	0.597134	−	1.03427i
$82$	−434.490			−0.585139
$83$	512.353	+	887.422i	0.677567	+	1.17358i	0.975711	+	0.219060i	$0.0702992\pi$
$83$	512.353	+	887.422i	0.677567	+	1.17358i	−0.298144	+	0.954521i	$0.596368\pi$
$84$	460.188			0.597745
$85$	−134.374			−0.171469
$86$	−372.125	−	644.540i	−0.466597	−	0.808169i
$87$	499.333	−	864.870i	0.615335	−	1.06579i
$88$	−209.870			−0.254229
$89$	−376.495	−	652.109i	−0.448409	−	0.776668i	0.549873	−	0.835248i	$-0.314676\pi$
$89$	−376.495	−	652.109i	−0.448409	−	0.776668i	−0.998283	+	0.0585804i	$0.981343\pi$
$90$	116.978	+	202.612i	0.137007	+	0.237303i
$91$	328.380	+	568.770i	0.378281	+	0.655202i
$92$	81.5366	−	141.225i	0.0923997	−	0.160041i
$93$	829.521	−	1436.77i	0.924917	−	1.60200i
$94$	83.4851	+	144.600i	0.0916046	+	0.158664i
$95$	−224.104	−	388.160i	−0.242027	−	0.419203i
$96$	109.543	+	189.735i	0.116461	+	0.201716i
$97$	−980.396			−1.02623			−0.513114	−	0.858320i	$-0.671508\pi$
$97$	−980.396			−1.02623			−0.513114	+	0.858320i	$0.671508\pi$
$98$	60.6310	−	105.016i	0.0624965	−	0.108247i
$99$	260.685	+	451.520i	0.264645	+	0.458379i
$100$	−361.421			−0.361421
$101$	952.448			0.938337			0.469169	−	0.883109i	$-0.344554\pi$
$101$	952.448			0.938337			0.469169	+	0.883109i	$0.344554\pi$
$102$	156.301	+	270.722i	0.151727	+	0.262799i
$103$	1792.82			1.71507			0.857534	−	0.514427i	$-0.171995\pi$
$103$	1792.82			1.71507			0.857534	+	0.514427i	$0.171995\pi$
$104$	−156.336	+	270.781i	−0.147404	+	0.255310i
$105$	−677.163			−0.629374
$106$	−394.889	+	683.967i	−0.361839	+	0.626724i
$107$	−1039.59	+	1800.62i	−0.939261	+	1.62685i	−0.172407	+	0.985026i	$0.555155\pi$
$107$	−1039.59	+	1800.62i	−0.939261	+	1.62685i	−0.766854	+	0.641822i	$0.778179\pi$
$108$	−97.5746	+	169.004i	−0.0869363	+	0.150578i
$109$	800.575	+	1386.64i	0.703497	+	1.21849i	0.967231	+	0.253897i	$0.0817126\pi$
$109$	800.575	+	1386.64i	0.703497	+	1.21849i	−0.263734	+	0.964595i	$0.584954\pi$
$110$	308.821			0.267682
$111$	633.732	+	1404.53i	0.541903	+	1.20101i
$112$	−268.861			−0.226830
$113$	−805.244	−	1394.72i	−0.670363	−	1.16110i	−0.977801	−	0.209534i	$-0.932805\pi$
$113$	−805.244	−	1394.72i	−0.670363	−	1.16110i	0.307439	−	0.951568i	$-0.400528\pi$
$114$	−521.348	+	903.002i	−0.428322	+	0.741876i
$115$	−119.980	+	207.812i	−0.0972890	+	0.168510i
$116$	−291.732	+	505.295i	−0.233505	+	0.404443i
$117$	776.757			0.613771
$118$	−145.574	+	252.141i	−0.113569	+	0.196707i
$119$	−383.623			−0.295518
$120$	−161.192	−	279.193i	−0.122623	−	0.212390i
$121$	−642.794			−0.482940
$122$	115.226			0.0855085
$123$	−743.680	−	1288.09i	−0.545165	−	0.944254i
$124$	−484.642	+	839.424i	−0.350985	+	0.607923i
$125$	1267.58			0.907003
$126$	333.961	+	578.437i	0.236124	+	0.408979i
$127$	563.899	+	976.701i	0.393999	+	0.682427i	0.992973	−	0.118342i	$-0.0377579\pi$
$127$	563.899	+	976.701i	0.393999	+	0.682427i	−0.598974	+	0.800769i	$0.704425\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$	1273.87	−	2206.41i	0.869443	−	1.50592i
$130$	230.047	−	398.453i	0.155203	−	0.268820i
$131$	−207.371	−	359.178i	−0.138306	−	0.239553i	0.788549	−	0.614971i	$-0.210832\pi$
$131$	−207.371	−	359.178i	−0.138306	−	0.239553i	−0.926856	+	0.375418i	$0.877499\pi$
$132$	−359.216	−	622.181i	−0.236862	−	0.410257i
$133$	−639.794	−	1108.16i	−0.417121	−	0.722476i
$134$	1609.83			1.03782
$135$	143.580	−	248.688i	0.0915365	−	0.158546i
$136$	−91.3180	−	158.167i	−0.0575768	−	0.0997260i
$137$	−1612.25			−1.00543			−0.502714	−	0.864453i	$-0.667665\pi$
$137$	−1612.25			−1.00543			−0.502714	+	0.864453i	$0.667665\pi$
$138$	558.237			0.344350
$139$	−246.781	−	427.437i	−0.150587	−	0.260825i	0.780856	−	0.624711i	$-0.214783\pi$
$139$	−246.781	−	427.437i	−0.150587	−	0.260825i	−0.931444	+	0.363886i	$0.881450\pi$
$140$	395.628			0.238833
$141$	−285.789	+	495.001i	−0.170693	+	0.295650i
$142$	−364.464			−0.215388
$143$	512.657	−	887.949i	0.299794	−	0.519259i
$144$	−158.993	+	275.384i	−0.0920097	+	0.159365i
$145$	429.281	−	743.537i	0.245861	−	0.425844i
$146$	751.633	+	1301.87i	0.426065	+	0.737967i
$147$	415.108			0.232908
$148$	−370.254	−	820.585i	−0.205640	−	0.455755i
$149$	−3005.06			−1.65224			−0.826122	−	0.563492i	$-0.809458\pi$
$149$	−3005.06			−1.65224			−0.826122	+	0.563492i	$0.809458\pi$
$150$	−618.615	−	1071.47i	−0.336731	−	0.583236i
$151$	944.326	−	1635.62i	0.508928	−	0.881490i	−0.491018	−	0.871149i	$-0.663375\pi$
$151$	944.326	−	1635.62i	0.508928	−	0.881490i	0.999947	−	0.0103406i	$-0.00329157\pi$
$152$	304.594	−	527.572i	0.162538	−	0.281525i
$153$	−226.858	+	392.929i	−0.119872	+	0.207624i
$154$	881.653			0.461335
$155$	713.147	−	1235.21i	0.369557	−	0.640091i
$156$	−1070.35			−0.549335
$157$	1001.97	+	1735.46i	0.509336	+	0.882195i	0.999942	+	0.0108136i	$0.00344214\pi$
$157$	1001.97	+	1735.46i	0.509336	+	0.882195i	−0.490606	+	0.871382i	$0.663225\pi$
$158$	1487.25			0.748856
$159$	−2703.59			−1.34848
$160$	94.1755	+	163.117i	0.0465327	+	0.0805970i
$161$	−342.532	+	593.283i	−0.167673	+	0.290417i
$162$	−1741.24			−0.844475
$163$	−1673.53	−	2898.63i	−0.804176	−	1.39287i	−0.916846	−	0.399241i	$-0.869274\pi$
$163$	−1673.53	−	2898.63i	−0.804176	−	1.39287i	0.112671	−	0.993632i	$-0.464059\pi$
$164$	434.490	+	752.558i	0.206878	+	0.358323i
$165$	528.584	+	915.534i	0.249395	+	0.431965i
$166$	1024.71	−	1774.84i	0.479113	−	0.829847i
$167$	733.006	−	1269.60i	0.339651	−	0.588293i	−0.644716	−	0.764422i	$-0.723024\pi$
$167$	733.006	−	1269.60i	0.339651	−	0.588293i	0.984367	+	0.176129i	$0.0563577\pi$
$168$	−460.188	−	797.068i	−0.211335	−	0.366043i
$169$	334.724	+	579.760i	0.152355	+	0.263887i
$170$	134.374	+	232.742i	0.0606235	+	0.105003i
$171$	−1513.38			−0.676791
$172$	−744.251	+	1289.08i	−0.329934	+	0.571462i
$173$	262.987	+	455.508i	0.115576	+	0.200183i	0.918010	−	0.396558i	$-0.129795\pi$
$173$	262.987	+	455.508i	0.115576	+	0.200183i	−0.802434	+	0.596741i	$0.796462\pi$
$174$	−1997.33			−0.870215
$175$	1518.32			0.655851
$176$	209.870	+	363.505i	0.0898836	+	0.155683i
$177$	−996.666			−0.423243
$178$	−752.991	+	1304.22i	−0.317073	+	0.549187i
$179$	−1191.27			−0.497429			−0.248715	−	0.968577i	$-0.580008\pi$
$179$	−1191.27			−0.497429			−0.248715	+	0.968577i	$0.580008\pi$
$180$	233.957	−	405.225i	0.0968783	−	0.167798i
$181$	−1353.01	+	2343.48i	−0.555627	+	0.962375i	0.442227	+	0.896903i	$0.354188\pi$
$181$	−1353.01	+	2343.48i	−0.555627	+	0.962375i	−0.997854	+	0.0654715i	$0.979145\pi$
$182$	656.759	−	1137.54i	0.267485	−	0.463297i
$183$	197.222	+	341.599i	0.0796671	+	0.137987i
$184$	−326.146			−0.130673
$185$	544.826	+	1207.49i	0.216521	+	0.479871i
$186$	−3318.08			−1.30803
$187$	299.451	+	518.664i	0.117102	+	0.202826i
$188$	166.970	−	289.201i	0.0647742	−	0.112192i
$189$	409.907	−	709.979i	0.157758	−	0.273246i
$190$	−448.208	+	776.319i	−0.171139	+	0.296422i
$191$	707.424			0.267997			0.133998	−	0.990982i	$-0.457218\pi$
$191$	707.424			0.267997			0.133998	+	0.990982i	$0.457218\pi$
$192$	219.087	−	379.470i	0.0823502	−	0.142635i
$193$	−2035.85			−0.759295			−0.379648	−	0.925131i	$-0.623955\pi$
$193$	−2035.85			−0.759295			−0.379648	+	0.925131i	$0.623955\pi$
$194$	980.396	+	1698.10i	0.362826	+	0.628434i
$195$	1575.01			0.578403
$196$	−242.524			−0.0883834
$197$	2445.41	+	4235.57i	0.884406	+	1.53184i	0.846393	+	0.532559i	$0.178770\pi$
$197$	2445.41	+	4235.57i	0.884406	+	1.53184i	0.0380138	+	0.999277i	$0.487897\pi$
$198$	521.371	−	903.041i	0.187132	−	0.324123i
$199$	4406.40			1.56966			0.784828	−	0.619714i	$-0.212751\pi$
$199$	4406.40			1.56966			0.784828	+	0.619714i	$0.212751\pi$
$200$	361.421	+	626.000i	0.127782	+	0.221324i
$201$	2755.41	+	4772.51i	0.966923	+	1.67476i
$202$	−952.448	−	1649.69i	−0.331752	−	0.574612i
$203$	1225.55	−	2122.72i	0.423729	−	0.733921i
$204$	312.603	−	541.444i	0.107287	−	0.185827i
$205$	−639.348	−	1107.38i	−0.217825	−	0.377283i
$206$	−1792.82	−	3105.26i	−0.606368	−	1.05026i
$207$	405.116	+	701.682i	0.136027	+	0.235605i
$208$	625.342			0.208460
$209$	−998.828	+	1730.02i	−0.330576	+	0.572575i
$210$	677.163	+	1172.88i	0.222517	+	0.385412i
$211$	−3271.92			−1.06753			−0.533763	−	0.845634i	$-0.679223\pi$
$211$	−3271.92			−1.06753			−0.533763	+	0.845634i	$0.679223\pi$
$212$	1579.55			0.511718
$213$	−623.823	−	1080.49i	−0.200674	−	0.347578i
$214$	4158.36			1.32832
$215$	1095.16	−	1896.87i	0.347392	−	0.601701i
$216$	390.298			0.122946
$217$	2035.96	−	3526.39i	0.636912	−	1.10316i
$218$	1601.15	−	2773.27i	0.497448	−	0.861605i
$219$	−2573.01	+	4456.59i	−0.793918	+	1.37511i
$220$	−308.821	−	534.894i	−0.0946397	−	0.163921i
$221$	892.265			0.271585
$222$	1798.98	−	2502.18i	0.543872	−	0.756467i
$223$	−2568.10			−0.771177			−0.385589	−	0.922671i	$-0.626002\pi$
$223$	−2568.10			−0.771177			−0.385589	+	0.922671i	$0.626002\pi$
$224$	268.861	+	465.682i	0.0801967	+	0.138905i
$225$	897.865	−	1555.15i	0.266034	−	0.460785i
$226$	−1610.49	+	2789.45i	−0.474018	+	0.821023i
$227$	−1649.03	+	2856.21i	−0.482159	+	0.835124i	−0.999790	−	0.0204798i	$-0.993481\pi$
$227$	−1649.03	+	2856.21i	−0.482159	+	0.835124i	0.517631	+	0.855604i	$0.326814\pi$
$228$	2085.39			0.605739
$229$	1459.13	−	2527.28i	0.421055	−	0.729289i	−0.574988	−	0.818162i	$-0.694993\pi$
$229$	1459.13	−	2527.28i	0.421055	−	0.729289i	0.996043	+	0.0888727i	$0.0283264\pi$
$230$	479.922			0.137587
$231$	1509.05	+	2613.76i	0.429820	+	0.744470i
$232$	1166.93			0.330227
$233$	−2564.33			−0.721009			−0.360505	−	0.932757i	$-0.617395\pi$
$233$	−2564.33			−0.721009			−0.360505	+	0.932757i	$0.617395\pi$
$234$	−776.757	−	1345.38i	−0.217001	−	0.375856i
$235$	−245.695	+	425.557i	−0.0682017	+	0.118129i
$236$	582.295			0.160611
$237$	2545.60	+	4409.11i	0.697699	+	1.20845i
$238$	383.623	+	664.455i	0.104481	+	0.180967i
$239$	512.925	+	888.412i	0.138821	+	0.240446i	0.927051	−	0.374936i	$-0.122335\pi$
$239$	512.925	+	888.412i	0.138821	+	0.240446i	−0.788229	+	0.615382i	$0.789002\pi$
$240$	−322.385	+	558.387i	−0.0867077	+	0.150182i
$241$	−235.474	+	407.853i	−0.0629387	+	0.109013i	−0.895778	−	0.444502i	$-0.853381\pi$
$241$	−235.474	+	407.853i	−0.0629387	+	0.109013i	0.832839	+	0.553515i	$0.186714\pi$
$242$	642.794	+	1113.35i	0.170745	+	0.295739i
$243$	−2321.71	−	4021.32i	−0.612913	−	1.06160i
$244$	−115.226	−	199.577i	−0.0302318	−	0.0523631i
$245$	356.872			0.0930602
$246$	−1487.36	+	2576.18i	−0.385490	+	0.667688i
$247$	1488.09	+	2577.45i	0.383340	+	0.663964i
$248$	1938.57			0.496367
$249$	7015.62			1.78553
$250$	−1267.58	−	2195.50i	−0.320674	−	0.555424i
$251$	−6333.31			−1.59265			−0.796324	−	0.604870i	$-0.793225\pi$
$251$	−6333.31			−1.59265			−0.796324	+	0.604870i	$0.793225\pi$
$252$	667.922	−	1156.87i	0.166965	−	0.289192i
$253$	1069.50			0.265767
$254$	1127.80	−	1953.40i	0.278600	−	0.482549i
$255$	−459.993	+	796.730i	−0.112964	+	0.195660i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−463.191	−	802.270i	−0.112424	−	0.194725i	0.804323	−	0.594192i	$-0.202528\pi$
$257$	−463.191	−	802.270i	−0.112424	−	0.194725i	−0.916747	+	0.399468i	$0.869195\pi$
$258$	−5095.49			−1.22958
$259$	1555.42	+	3447.25i	0.373163	+	0.827032i
$260$	−920.187			−0.219491
$261$	−1449.48	−	2510.57i	−0.343756	−	0.595403i
$262$	−414.743	+	718.355i	−0.0977973	+	0.169390i
$263$	−525.555	+	910.288i	−0.123221	+	0.213425i	−0.921036	−	0.389477i	$-0.872656\pi$
$263$	−525.555	+	910.288i	−0.123221	+	0.213425i	0.797815	+	0.602902i	$0.205989\pi$
$264$	−718.432	+	1244.36i	−0.167487	+	0.290095i
$265$	−2324.30			−0.538795
$266$	−1279.59	+	2216.31i	−0.294949	+	0.510867i
$267$	−5155.32			−1.18165
$268$	−1609.83	−	2788.30i	−0.366925	−	0.635533i
$269$	−6737.43			−1.52709			−0.763547	−	0.645753i	$-0.776544\pi$
$269$	−6737.43			−1.52709			−0.763547	+	0.645753i	$0.776544\pi$
$270$	−574.321			−0.129452
$271$	−2299.72	−	3983.23i	−0.515491	−	0.892857i	−0.999838	−	0.0179811i	$-0.994276\pi$
$271$	−2299.72	−	3983.23i	−0.515491	−	0.892857i	0.484347	−	0.874876i	$-0.339057\pi$
$272$	−182.636	+	316.335i	−0.0407130	+	0.0705169i
$273$	4496.48			0.996848
$274$	1612.25	+	2792.49i	0.355472	+	0.615696i
$275$	−1185.18	−	2052.79i	−0.259887	−	0.450137i
$276$	−558.237	−	966.895i	−0.121746	−	0.210871i
$277$	1543.22	−	2672.93i	0.334740	−	0.579786i	−0.648695	−	0.761048i	$-0.724685\pi$
$277$	1543.22	−	2672.93i	0.334740	−	0.579786i	0.983435	+	0.181262i	$0.0580183\pi$
$278$	−493.561	+	854.873i	−0.106481	+	0.184431i
$279$	−2407.95	−	4170.70i	−0.516704	−	0.894957i
$280$	−395.628	−	685.247i	−0.0844403	−	0.146255i
$281$	1894.23	+	3280.90i	0.402136	+	0.696520i	0.993983	−	0.109530i	$-0.0349346\pi$
$281$	1894.23	+	3280.90i	0.402136	+	0.696520i	−0.591847	+	0.806050i	$0.701601\pi$
$282$	1143.16			0.241397
$283$	4285.54	−	7422.78i	0.900174	−	1.55915i	0.0729056	−	0.997339i	$-0.476773\pi$
$283$	4285.54	−	7422.78i	0.900174	−	1.55915i	0.827268	−	0.561808i	$-0.189894\pi$
$284$	364.464	+	631.270i	0.0761513	+	0.131898i
$285$	−3068.64			−0.637792
$286$	−2050.63			−0.423973
$287$	−1825.27	−	3161.47i	−0.375409	−	0.650228i
$288$	635.971			0.130121
$289$	2195.91	−	3803.42i	0.446959	−	0.774155i
$290$	−1717.13			−0.347700
$291$	−3356.12	+	5812.98i	−0.676080	+	1.17101i
$292$	1503.27	−	2603.73i	0.301274	−	0.521821i
$293$	−1587.43	+	2749.52i	−0.316515	+	0.548220i	−0.979758	−	0.200184i	$-0.935846\pi$
$293$	−1587.43	+	2749.52i	−0.316515	+	0.548220i	0.663243	+	0.748404i	$0.269179\pi$
$294$	−415.108	−	718.989i	−0.0823456	−	0.142627i
$295$	−856.843			−0.169110
$296$	−1051.04	+	1461.88i	−0.206387	+	0.287062i
$297$	−1279.87			−0.250053
$298$	3005.06	+	5204.92i	0.584156	+	1.01179i
$299$	796.692	−	1379.91i	0.154093	−	0.266897i
$300$	−1237.23	+	2142.94i	−0.238105	+	0.412410i
$301$	3126.57	−	5415.37i	0.598712	−	1.03700i
$302$	−3777.31			−0.719734
$303$	3260.45	−	5647.27i	0.618178	−	1.07072i
$304$	−1218.38			−0.229864
$305$	169.554	+	293.676i	0.0318315	+	0.0551338i
$306$	907.431			0.169524
$307$	5117.68			0.951406			0.475703	−	0.879606i	$-0.342194\pi$
$307$	5117.68			0.951406			0.475703	+	0.879606i	$0.342194\pi$
$308$	−881.653	−	1527.07i	−0.163107	−	0.282509i
$309$	6137.25	−	10630.0i	1.12989	−	1.95703i
$310$	−2852.59			−0.522632
$311$	995.218	+	1723.77i	0.181459	+	0.314295i	0.942377	−	0.334552i	$-0.108585\pi$
$311$	995.218	+	1723.77i	0.181459	+	0.314295i	−0.760919	+	0.648847i	$0.775252\pi$
$312$	1070.35	+	1853.89i	0.194219	+	0.336398i
$313$	417.656	+	723.401i	0.0754227	+	0.130636i	0.901270	−	0.433258i	$-0.142636\pi$
$313$	417.656	+	723.401i	0.0754227	+	0.130636i	−0.825847	+	0.563894i	$0.809303\pi$
$314$	2003.93	−	3470.92i	0.360155	−	0.623806i
$315$	−982.843	+	1702.33i	−0.175800	+	0.304494i
$316$	−1487.25	−	2575.99i	−0.264761	−	0.458579i
$317$	−3849.61	−	6667.73i	−0.682069	−	1.18138i	−0.974348	−	0.225045i	$-0.927747\pi$
$317$	−3849.61	−	6667.73i	−0.682069	−	1.18138i	0.292279	−	0.956333i	$-0.405586\pi$
$318$	2703.59	+	4682.76i	0.476761	+	0.825773i
$319$	−3826.60			−0.671626
$320$	188.351	−	326.234i	0.0329036	−	0.0569907i
$321$	7117.52	+	12327.9i	1.23757	+	2.14354i
$322$	1370.13			0.237125
$323$	−1738.43			−0.299470
$324$	1741.24	+	3015.92i	0.298567	+	0.517133i
$325$	−3531.44			−0.602735
$326$	−3347.05	+	5797.26i	−0.568638	+	0.984910i
$327$	10962.2			1.85386
$328$	868.979	−	1505.12i	0.146285	−	0.253372i
$329$	−701.435	+	1214.92i	−0.117542	+	0.203589i
$330$	1057.17	−	1831.07i	0.176349	−	0.305445i
$331$	−2488.06	−	4309.45i	−0.413161	−	0.715616i	0.582072	−	0.813137i	$-0.302242\pi$
$331$	−2488.06	−	4309.45i	−0.413161	−	0.715616i	−0.995233	+	0.0975209i	$0.968909\pi$
$332$	−4098.83			−0.677567
$333$	4450.68	+	445.395i	0.732419	+	0.0732958i
$334$	−2932.02			−0.480339
$335$	2368.85	+	4102.97i	0.386341	+	0.669161i
$336$	−920.375	+	1594.14i	−0.149436	+	0.258831i
$337$	−1551.19	+	2686.74i	−0.250738	+	0.434291i	−0.963729	−	0.266882i	$-0.914007\pi$
$337$	−1551.19	+	2686.74i	−0.250738	+	0.434291i	0.712991	+	0.701173i	$0.247340\pi$
$338$	669.449	−	1159.52i	0.107731	−	0.186596i
$339$	−11026.2			−1.76654
$340$	268.747	−	465.484i	0.0428673	−	0.0742483i
$341$	−6356.97			−1.00953
$342$	1513.38	+	2621.26i	0.239282	+	0.414448i
$343$	6782.55			1.06771
$344$	2977.00			0.466597
$345$	821.442	+	1422.78i	0.128188	+	0.222029i
$346$	525.975	−	911.015i	0.0817242	−	0.141551i
$347$	7263.12			1.12364			0.561822	−	0.827258i	$-0.310101\pi$
$347$	7263.12			1.12364			0.561822	+	0.827258i	$0.310101\pi$
$348$	1997.33	+	3459.48i	0.307667	+	0.532896i
$349$	3575.43	+	6192.83i	0.548391	+	0.949841i	0.998385	+	0.0568094i	$0.0180927\pi$
$349$	3575.43	+	6192.83i	0.548391	+	0.949841i	−0.449994	+	0.893031i	$0.648574\pi$
$350$	−1518.32	−	2629.80i	−0.231878	−	0.401625i
$351$	−953.399	+	1651.33i	−0.144982	+	0.251116i
$352$	419.739	−	727.009i	0.0635573	−	0.110084i
$353$	1284.69	+	2225.16i	0.193704	+	0.335505i	0.946475	−	0.322778i	$-0.104617\pi$
$353$	1284.69	+	2225.16i	0.193704	+	0.335505i	−0.752771	+	0.658282i	$0.771283\pi$
$354$	996.666	+	1726.28i	0.149639	+	0.259182i
$355$	−536.306	−	928.910i	−0.0801808	−	0.138877i
$356$	3011.96			0.448409
$357$	−1313.23	+	2274.58i	−0.194688	+	0.337209i
$358$	1191.27	+	2063.34i	0.175868	+	0.304612i
$359$	2236.25			0.328759			0.164380	−	0.986397i	$-0.447438\pi$
$359$	2236.25			0.328759			0.164380	+	0.986397i	$0.447438\pi$
$360$	−935.827			−0.137007
$361$	530.201	+	918.335i	0.0773001	+	0.133888i
$362$	5412.04			0.785775
$363$	−2200.43	+	3811.26i	−0.318162	+	0.551072i
$364$	−2627.04			−0.378281
$365$	−2212.04	+	3831.37i	−0.317216	+	0.549433i
$366$	394.444	−	683.197i	0.0563331	−	0.0975718i
$367$	−3177.18	+	5503.04i	−0.451901	+	0.782715i	−0.998504	−	0.0546767i	$-0.982587\pi$
$367$	−3177.18	+	5503.04i	−0.451901	+	0.782715i	0.546603	+	0.837392i	$0.315921\pi$
$368$	326.146	+	564.902i	0.0461999	+	0.0800205i
$369$	−4317.54			−0.609112
$370$	1546.60	−	2151.15i	0.217308	−	0.302251i
$371$	−6635.64			−0.928586
$372$	3318.08	+	5747.09i	0.462458	+	0.801002i
$373$	3061.21	−	5302.16i	0.424942	−	0.736020i	−0.571473	−	0.820621i	$-0.693628\pi$
$373$	3061.21	−	5302.16i	0.424942	−	0.736020i	0.996415	+	0.0846002i	$0.0269613\pi$
$374$	598.902	−	1037.33i	0.0828034	−	0.143420i
$375$	4339.21	−	7515.72i	0.597535	−	1.03496i
$376$	−667.881			−0.0916046
$377$	−2850.51	+	4937.22i	−0.389412	+	0.674482i
$378$	−1639.63			−0.223104
$379$	−409.738	−	709.687i	−0.0555325	−	0.0961852i	0.836923	−	0.547321i	$-0.184352\pi$
$379$	−409.738	−	709.687i	−0.0555325	−	0.0961852i	−0.892455	+	0.451136i	$0.851019\pi$
$380$	1792.83			0.242027
$381$	7721.42			1.03827
$382$	−707.424	−	1225.29i	−0.0947512	−	0.164114i
$383$	6945.74	−	12030.4i	0.926660	−	1.60502i	0.137790	−	0.990461i	$-0.456000\pi$
$383$	6945.74	−	12030.4i	0.926660	−	1.60502i	0.788870	−	0.614561i	$-0.210667\pi$
$384$	−876.348			−0.116461
$385$	1297.35	+	2247.07i	0.171737	+	0.297458i
$386$	2035.85	+	3526.20i	0.268451	+	0.464971i
$387$	−3697.83	−	6404.83i	−0.485714	−	0.841281i
$388$	1960.79	−	3396.19i	0.256557	−	0.444370i
$389$	−4472.54	+	7746.66i	−0.582948	+	1.00969i	0.412180	+	0.911102i	$0.364767\pi$
$389$	−4472.54	+	7746.66i	−0.582948	+	1.00969i	−0.995128	+	0.0985926i	$0.968566\pi$
$390$	−1575.01	−	2727.99i	−0.204496	−	0.354198i
$391$	465.360	+	806.026i	0.0601899	+	0.104252i
$392$	242.524	+	420.064i	0.0312483	+	0.0541236i
$393$	−2839.52			−0.364465
$394$	4890.81	−	8471.14i	0.625370	−	1.08317i
$395$	2188.48	+	3790.55i	0.278770	+	0.482844i
$396$	−2085.48			−0.264645
$397$	−14667.3			−1.85424			−0.927118	−	0.374770i	$-0.877722\pi$
$397$	−14667.3			−1.85424			−0.927118	+	0.374770i	$0.877722\pi$
$398$	−4406.40	−	7632.11i	−0.554957	−	0.961214i
$399$	−8760.65			−1.09920
$400$	722.843	−	1252.00i	0.0903553	−	0.156500i
$401$	14861.1			1.85069			0.925347	−	0.379121i	$-0.123773\pi$
$401$	14861.1			1.85069			0.925347	+	0.379121i	$0.123773\pi$
$402$	5510.81	−	9545.01i	0.683718	−	1.18423i
$403$	−4735.42	+	8201.99i	−0.585330	+	1.01382i
$404$	−1904.90	+	3299.38i	−0.234584	+	0.406312i
$405$	−2562.22	−	4437.90i	−0.314365	−	0.544497i
$406$	−4902.22			−0.599244
$407$	3446.59	−	4793.82i	0.419757	−	0.583836i
$408$	−1250.41			−0.151727
$409$	−179.840	−	311.493i	−0.0217422	−	0.0376585i	0.854950	−	0.518711i	$-0.173588\pi$
$409$	−179.840	−	311.493i	−0.0217422	−	0.0376585i	−0.876692	+	0.481053i	$0.840255\pi$
$410$	−1278.70	+	2214.77i	−0.154025	+	0.266780i
$411$	−5519.10	+	9559.36i	−0.662377	+	1.14727i
$412$	−3585.64	+	6210.52i	−0.428767	+	0.742646i
$413$	−2446.20			−0.291452
$414$	810.233	−	1403.36i	0.0961854	−	0.166598i
$415$	6031.40			0.713421
$416$	−625.342	−	1083.12i	−0.0737018	−	0.127655i
$417$	−3379.15			−0.396829
$418$	3995.31			0.467505
$419$	4940.53	+	8557.25i	0.576040	+	0.997730i	0.995928	+	0.0901544i	$0.0287361\pi$
$419$	4940.53	+	8557.25i	0.576040	+	0.997730i	−0.419888	+	0.907576i	$0.637931\pi$
$420$	1354.33	−	2345.76i	0.157344	−	0.272527i
$421$	7189.80			0.832327			0.416163	−	0.909290i	$-0.363374\pi$
$421$	7189.80			0.832327			0.416163	+	0.909290i	$0.363374\pi$
$422$	3271.92	+	5667.13i	0.377427	+	0.653724i
$423$	829.595	+	1436.90i	0.0953577	+	0.165164i
$424$	−1579.55	−	2735.87i	−0.180920	−	0.313362i
$425$	1031.38	−	1786.41i	0.117716	−	0.203891i
$426$	−1247.65	+	2160.98i	−0.141898	+	0.245775i
$427$	484.058	+	838.413i	0.0548600	+	0.0950203i
$428$	−4158.36	−	7202.49i	−0.469631	−	0.813424i
$429$	−3509.89	−	6079.31i	−0.395010	−	0.684177i
$430$	−4380.64			−0.491286
$431$	4567.70	−	7911.49i	0.510483	−	0.884183i	−0.489443	−	0.872035i	$-0.662800\pi$
$431$	4567.70	−	7911.49i	0.510483	−	0.884183i	0.999926	−	0.0121477i	$-0.00386684\pi$
$432$	−390.298	−	676.016i	−0.0434681	−	0.0752890i
$433$	7278.81			0.807846			0.403923	−	0.914793i	$-0.367646\pi$
$433$	7278.81			0.807846			0.403923	+	0.914793i	$0.367646\pi$
$434$	−8143.84			−0.900730
$435$	−2939.06	−	5090.60i	−0.323948	−	0.561094i
$436$	−6404.60			−0.703497
$437$	−1552.22	+	2688.53i	−0.169915	+	0.294301i
$438$	10292.1			1.12277
$439$	2051.45	−	3553.21i	0.223030	−	0.386299i	−0.732697	−	0.680555i	$-0.761739\pi$
$439$	2051.45	−	3553.21i	0.223030	−	0.386299i	0.955727	+	0.294256i	$0.0950719\pi$
$440$	−617.643	+	1069.79i	−0.0669204	+	0.115910i
$441$	602.493	−	1043.55i	0.0650570	−	0.112682i
$442$	−892.265	−	1545.45i	−0.0960198	−	0.166311i
$443$	4791.19			0.513852			0.256926	−	0.966431i	$-0.417290\pi$
$443$	4791.19			0.513852			0.256926	+	0.966431i	$0.417290\pi$
$444$	−6132.89	−	613.741i	−0.655527	−	0.0656010i
$445$	−4432.08			−0.472137
$446$	2568.10	+	4448.07i	0.272652	+	0.472248i
$447$	−10287.0	+	17817.7i	−1.08850	+	1.88534i
$448$	537.723	−	931.363i	0.0567076	−	0.0982205i
$449$	1751.89	−	3034.37i	0.184136	−	0.318932i	−0.759149	−	0.650917i	$-0.774385\pi$
$449$	1751.89	−	3034.37i	0.184136	−	0.318932i	0.943285	+	0.331984i	$0.107718\pi$
$450$	−3591.46			−0.376229
$451$	−2849.57	+	4935.59i	−0.297519	+	0.515317i
$452$	6441.95			0.670363
$453$	−6465.30	−	11198.2i	−0.670566	−	1.16145i
$454$	6596.13			0.681876
$455$	3865.67			0.398297
$456$	−2085.39	−	3612.01i	−0.214161	−	0.370938i
$457$	−421.086	+	729.342i	−0.0431019	+	0.0746546i	−0.886772	−	0.462208i	$-0.847057\pi$
$457$	−421.086	+	729.342i	−0.0431019	+	0.0746546i	0.843670	+	0.536863i	$0.180391\pi$
$458$	−5836.50			−0.595462
$459$	−556.894	−	964.569i	−0.0566309	−	0.0980877i
$460$	−479.922	−	831.249i	−0.0486445	−	0.0842548i
$461$	1716.49	+	2973.05i	0.173416	+	0.300366i	0.939612	−	0.342241i	$-0.111186\pi$
$461$	1716.49	+	2973.05i	0.173416	+	0.300366i	−0.766196	+	0.642607i	$0.777853\pi$
$462$	3018.10	−	5227.51i	0.303928	−	0.526419i
$463$	5818.54	−	10078.0i	0.584040	−	1.01159i	−0.410955	−	0.911656i	$-0.634805\pi$
$463$	5818.54	−	10078.0i	0.584040	−	1.01159i	0.994994	−	0.0999307i	$-0.0318621\pi$
$464$	−1166.93	−	2021.18i	−0.116753	−	0.202222i
$465$	−4882.53	−	8456.80i	−0.486929	−	0.843386i
$466$	2564.33	+	4441.56i	0.254915	+	0.441526i
$467$	−15006.8			−1.48701			−0.743505	−	0.668731i	$-0.766838\pi$
$467$	−15006.8			−1.48701			−0.743505	+	0.668731i	$0.766838\pi$
$468$	−1553.51	+	2690.77i	−0.153443	+	0.265771i
$469$	6762.82	+	11713.5i	0.665838	+	1.15327i
$470$	982.782			0.0964518
$471$	13719.9			1.34220
$472$	−582.295	−	1008.56i	−0.0567846	−	0.0983537i
$473$	−9762.22			−0.948980
$474$	5091.20	−	8818.22i	0.493347	−	0.854503i
$475$	6880.43			0.664622
$476$	767.246	−	1328.91i	0.0738796	−	0.127963i
$477$	−3924.03	+	6796.61i	−0.376664	+	0.652401i
$478$	1025.85	−	1776.82i	0.0981616	−	0.170021i
$479$	−712.976	−	1234.91i	−0.0680098	−	0.117797i	0.830015	−	0.557741i	$-0.188332\pi$
$479$	−712.976	−	1234.91i	−0.0680098	−	0.117797i	−0.898025	+	0.439944i	$0.854998\pi$
$480$	1289.54			0.122623
$481$	−3617.74	−	8017.92i	−0.342941	−	0.760053i
$482$	941.896			0.0890087
$483$	2345.13	+	4061.89i	0.220926	+	0.382655i
$484$	1285.59	−	2226.70i	0.120735	−	0.209119i
$485$	−2885.29	+	4997.47i	−0.270133	+	0.467883i
$486$	−4643.42	+	8042.64i	−0.433395	+	0.750662i
$487$	−16529.6			−1.53804			−0.769020	−	0.639225i	$-0.779255\pi$
$487$	−16529.6			−1.53804			−0.769020	+	0.639225i	$0.779255\pi$
$488$	−230.451	+	399.153i	−0.0213771	+	0.0370263i
$489$	−22915.5			−2.11917
$490$	−356.872	−	618.121i	−0.0329017	−	0.0569875i
$491$	17883.4			1.64372			0.821858	−	0.569692i	$-0.192938\pi$
$491$	17883.4			1.64372			0.821858	+	0.569692i	$0.192938\pi$
$492$	5949.44			0.545165
$493$	−1665.02	−	2883.90i	−0.152107	−	0.263457i
$494$	2976.18	−	5154.90i	0.271062	−	0.469493i
$495$	3068.77			0.278649
$496$	−1938.57	−	3357.70i	−0.175492	−	0.303962i
$497$	−1531.10	−	2651.94i	−0.138187	−	0.239348i
$498$	−7015.62	−	12151.4i	−0.631280	−	1.09341i
$499$	6277.26	−	10872.5i	0.563144	−	0.975394i	−0.434076	−	0.900876i	$-0.642925\pi$
$499$	6277.26	−	10872.5i	0.563144	−	0.975394i	0.997220	−	0.0745175i	$-0.0237417\pi$
$500$	−2535.15	+	4391.01i	−0.226751	+	0.392744i
$501$	−5018.50	−	8692.30i	−0.447525	−	0.775136i
$502$	6333.31	+	10969.6i	0.563086	+	0.975294i
$503$	5555.85	+	9623.02i	0.492492	+	0.853020i	0.999963	−	0.00864843i	$-0.00275291\pi$
$503$	5555.85	+	9623.02i	0.492492	+	0.853020i	−0.507471	+	0.861669i	$0.669420\pi$
$504$	−2671.69			−0.236124
$505$	2803.04	−	4855.01i	0.246997	−	0.427812i
$506$	−1069.50	−	1852.43i	−0.0939628	−	0.162748i
$507$	4583.36			0.401487
$508$	−4511.19			−0.393999
$509$	1640.08	+	2840.70i	0.142820	+	0.247371i	0.928557	−	0.371189i	$-0.121050\pi$
$509$	1640.08	+	2840.70i	0.142820	+	0.247371i	−0.785738	+	0.618560i	$0.787716\pi$
$510$	1839.97			0.159755
$511$	−6315.16	+	10938.2i	−0.546705	+	0.946920i
$512$	512.000			0.0441942
$513$	1857.54	−	3217.35i	0.159868	−	0.276900i
$514$	−926.382	+	1604.54i	−0.0794960	+	0.137691i
$515$	5276.25	−	9138.73i	0.451455	−	0.781943i
$516$	5095.49	+	8825.64i	0.434722	+	0.752960i
$517$	2190.12			0.186308
$518$	4415.38	−	6141.31i	0.374519	−	0.520915i
$519$	3601.07			0.304565
$520$	920.187	+	1593.81i	0.0776017	+	0.134410i
$521$	6014.47	−	10417.4i	0.505756	−	0.875995i	−0.494222	−	0.869336i	$-0.664547\pi$
$521$	6014.47	−	10417.4i	0.505756	−	0.875995i	0.999978	−	0.00665888i	$-0.00211960\pi$
$522$	−2898.95	+	5021.14i	−0.243072	+	0.421014i
$523$	−7907.08	+	13695.5i	−0.661095	+	1.14505i	0.319234	+	0.947676i	$0.396574\pi$
$523$	−7907.08	+	13695.5i	−0.661095	+	1.14505i	−0.980328	+	0.197373i	$0.936759\pi$
$524$	1658.97			0.138306
$525$	5197.55	−	9002.42i	0.432076	−	0.748377i
$526$	2102.22			0.174261
$527$	−2766.03	−	4790.90i	−0.228634	−	0.396006i
$528$	2873.73			0.236862
$529$	−10504.9			−0.863397
$530$	2324.30	+	4025.81i	0.190493	+	0.329943i
$531$	−1446.57	+	2505.54i	−0.118222	+	0.204767i
$532$	5118.35			0.417121
$533$	4245.39	+	7353.23i	0.345006	+	0.597568i
$534$	5155.32	+	8929.28i	0.417777	+	0.723610i
$535$	6119.00	+	10598.4i	0.494481	+	0.856466i
$536$	−3219.66	+	5576.61i	−0.259455	+	0.449389i
$537$	−4078.00	+	7063.30i	−0.327707	+	0.567605i
$538$	6737.43	+	11669.6i	0.539909	+	0.935150i
$539$	−795.288	−	1377.48i	−0.0635537	−	0.110078i
$540$	574.321	+	994.753i	0.0457682	+	0.0792729i
$541$	−2296.95			−0.182539			−0.0912694	−	0.995826i	$-0.529092\pi$
$541$	−2296.95			−0.182539			−0.0912694	+	0.995826i	$0.529092\pi$
$542$	−4599.44	+	7966.47i	−0.364507	+	0.631345i
$543$	9263.34	+	16044.6i	0.732096	+	1.26803i
$544$	730.544			0.0575768
$545$	9424.33			0.740722
$546$	−4496.48	−	7788.13i	−0.352439	−	0.610442i
$547$	−22622.7			−1.76833			−0.884165	−	0.467174i	$-0.845272\pi$
$547$	−22622.7			−1.76833			−0.884165	+	0.467174i	$0.845272\pi$
$548$	3224.49	−	5584.99i	0.251357	−	0.435363i
$549$	1145.00			0.0890119
$550$	−2370.35	+	4105.57i	−0.183768	+	0.318295i
$551$	5553.74	−	9619.36i	0.429396	−	0.743736i
$552$	−1116.47	+	1933.79i	−0.0860875	+	0.149108i
$553$	6247.88	+	10821.6i	0.480446	+	0.832157i
$554$	−6172.86			−0.473393
$555$	9024.50	+	903.115i	0.690214	+	0.0690722i
$556$	1974.24			0.150587
$557$	5274.20	+	9135.19i	0.401212	+	0.694920i	0.993872	−	0.110533i	$-0.0352557\pi$
$557$	5274.20	+	9135.19i	0.401212	+	0.694920i	−0.592660	+	0.805453i	$0.701922\pi$
$558$	−4815.91	+	8341.39i	−0.365365	+	0.632830i
$559$	−7272.06	+	12595.6i	−0.550224	+	0.953016i
$560$	−791.255	+	1370.49i	−0.0597083	+	0.103418i
$561$	4100.36			0.308587
$562$	3788.46	−	6561.80i	0.284353	−	0.492514i
$563$	−6356.73			−0.475851			−0.237926	−	0.971283i	$-0.576467\pi$
$563$	−6356.73			−0.475851			−0.237926	+	0.971283i	$0.576467\pi$
$564$	−1143.16	−	1980.00i	−0.0853467	−	0.147825i
$565$	−9479.29			−0.705835
$566$	−17142.2			−1.27304
$567$	−7314.89	−	12669.8i	−0.541793	−	0.938412i
$568$	728.928	−	1262.54i	0.0538471	−	0.0932659i
$569$	24087.3			1.77468			0.887341	−	0.461114i	$-0.152550\pi$
$569$	24087.3			1.77468			0.887341	+	0.461114i	$0.152550\pi$
$570$	3068.64	+	5315.04i	0.225493	+	0.390566i
$571$	2273.44	+	3937.72i	0.166621	+	0.288596i	0.937230	−	0.348712i	$-0.113381\pi$
$571$	2273.44	+	3937.72i	0.166621	+	0.288596i	−0.770609	+	0.637309i	$0.780048\pi$
$572$	2050.63	+	3551.79i	0.149897	+	0.259629i
$573$	2421.68	−	4194.47i	0.176557	−	0.305805i
$574$	−3650.55	+	6322.93i	−0.265455	+	0.459781i
$575$	−1841.82	−	3190.12i	−0.133581	−	0.231369i
$576$	−635.971	−	1101.53i	−0.0460048	−	0.0796827i
$577$	−6234.66	−	10798.7i	−0.449831	−	0.779130i	0.548544	−	0.836122i	$-0.315182\pi$
$577$	−6234.66	−	10798.7i	−0.449831	−	0.779130i	−0.998375	+	0.0569922i	$0.981849\pi$
$578$	−8783.63			−0.632095
$579$	−6969.20	+	12071.0i	−0.500225	+	0.866415i
$580$	1717.13	+	2974.15i	0.122931	+	0.212922i
$581$	17219.0			1.22954
$582$	13424.5			0.956122
$583$	5179.69	+	8971.49i	0.367960	+	0.637326i
$584$	−6013.06			−0.426065
$585$	2285.98	−	3959.44i	0.161562	−	0.279834i
$586$	6349.73			0.447620
$587$	8167.35	−	14146.3i	0.574280	−	0.994682i	−0.421839	−	0.906671i	$-0.638615\pi$
$587$	8167.35	−	14146.3i	0.574280	−	0.994682i	0.996119	−	0.0880117i	$-0.0280513\pi$
$588$	−830.216	+	1437.98i	−0.0582271	+	0.100852i
$589$	9226.19	−	15980.2i	0.645430	−	1.11792i
$590$	856.843	+	1484.10i	0.0597893	+	0.103558i
$591$	33484.8			2.33059
$592$	3583.10	+	358.574i	0.248757	+	0.0248941i
$593$	−19655.6			−1.36115			−0.680573	−	0.732680i	$-0.738269\pi$
$593$	−19655.6			−1.36115			−0.680573	+	0.732680i	$0.738269\pi$
$594$	1279.87	+	2216.80i	0.0884069	+	0.153125i
$595$	−1129.00	+	1955.48i	−0.0777889	+	0.134734i
$596$	6010.12	−	10409.8i	0.413061	−	0.715442i
$597$	15084.1	−	26126.5i	1.03409	−	1.79110i
$598$	−3186.77			−0.217921
$599$	5619.52	−	9733.29i	0.383317	−	0.663925i	−0.608217	−	0.793771i	$-0.708115\pi$
$599$	5619.52	−	9733.29i	0.383317	−	0.663925i	0.991534	+	0.129846i	$0.0414482\pi$
$600$	4948.92			0.336731
$601$	−3662.02	−	6342.80i	−0.248547	−	0.430496i	0.714576	−	0.699558i	$-0.246620\pi$
$601$	−3662.02	−	6342.80i	−0.248547	−	0.430496i	−0.963123	+	0.269062i	$0.913286\pi$
$602$	−12506.3			−0.846707
$603$	15996.9			1.08034
$604$	3777.31	+	6542.49i	0.254464	+	0.440745i
$605$	−1891.73	+	3276.58i	−0.127124	+	0.220185i
$606$	−13041.8			−0.874236
$607$	854.838	+	1480.62i	0.0571612	+	0.0990060i	0.893190	−	0.449679i	$-0.148462\pi$
$607$	854.838	+	1480.62i	0.0571612	+	0.0990060i	−0.836029	+	0.548685i	$0.815128\pi$
$608$	1218.38	+	2110.29i	0.0812692	+	0.140762i
$609$	−8390.71	−	14533.1i	−0.558307	−	0.967016i
$610$	339.107	−	587.351i	0.0225083	−	0.0389855i
$611$	1631.46	−	2825.77i	0.108023	−	0.187101i
$612$	−907.431	−	1571.72i	−0.0599358	−	0.103812i
$613$	−1112.68	−	1927.21i	−0.0733125	−	0.126981i	0.827039	−	0.562145i	$-0.190024\pi$
$613$	−1112.68	−	1927.21i	−0.0733125	−	0.126981i	−0.900351	+	0.435164i	$0.856690\pi$
$614$	−5117.68	−	8864.08i	−0.336373	−	0.582615i
$615$	−8754.55			−0.574013
$616$	−1763.31	+	3054.14i	−0.115334	+	0.199764i
$617$	−13334.7	−	23096.3i	−0.870071	−	1.50701i	−0.861922	−	0.507041i	$-0.830739\pi$
$617$	−13334.7	−	23096.3i	−0.870071	−	1.50701i	−0.00814934	−	0.999967i	$-0.502594\pi$
$618$	−24549.0			−1.59791
$619$	6909.24			0.448636			0.224318	−	0.974516i	$-0.427985\pi$
$619$	6909.24			0.448636			0.224318	+	0.974516i	$0.427985\pi$
$620$	2852.59	+	4940.83i	0.184778	+	0.320046i
$621$	−1988.97			−0.128526
$622$	1990.44	−	3447.54i	0.128311	−	0.222240i
$623$	−12653.1			−0.813703
$624$	2140.69	−	3707.79i	0.137334	−	0.237869i
$625$	−1916.75	+	3319.91i	−0.122672	+	0.212474i
$626$	835.311	−	1446.80i	0.0533319	−	0.0923735i
$627$	6838.44	+	11844.5i	0.435568	+	0.754426i
$628$	−8015.74			−0.509336
$629$	5112.52	+	511.628i	0.324085	+	0.0324324i
$630$	3931.37			0.248618
$631$	237.854	+	411.975i	0.0150061	+	0.0259912i	0.873431	−	0.486948i	$-0.161890\pi$
$631$	237.854	+	411.975i	0.0150061	+	0.0259912i	−0.858425	+	0.512939i	$0.828557\pi$
$632$	−2974.50	+	5151.98i	−0.187214	+	0.324264i
$633$	−11200.5	+	19399.9i	−0.703288	+	1.21813i
$634$	−7699.23	+	13335.5i	−0.482296	+	0.835360i
$635$	6638.18			0.414848
$636$	5407.18	−	9365.51i	0.337121	−	0.583910i
$637$	−2369.70			−0.147395
$638$	3826.60	+	6627.87i	0.237456	+	0.411285i
$639$	−3621.70			−0.224213
$640$	−753.404			−0.0465327
$641$	−12327.9	−	21352.6i	−0.759633	−	1.31572i	−0.943038	−	0.332685i	$-0.892045\pi$
$641$	−12327.9	−	21352.6i	−0.759633	−	1.31572i	0.183405	−	0.983037i	$-0.441288\pi$
$642$	14235.0	−	24655.8i	0.875096	−	1.51571i
$643$	−25870.5			−1.58668			−0.793339	−	0.608781i	$-0.791659\pi$
$643$	−25870.5			−1.58668			−0.793339	+	0.608781i	$0.791659\pi$
$644$	−1370.13	−	2373.13i	−0.0838363	−	0.145209i
$645$	−7497.97	−	12986.9i	−0.457725	−	0.792802i
$646$	1738.43	+	3011.05i	0.105879	+	0.183387i
$647$	−8969.62	+	15535.8i	−0.545027	+	0.944014i	0.453579	+	0.891216i	$0.350147\pi$
$647$	−8969.62	+	15535.8i	−0.545027	+	0.944014i	−0.998605	+	0.0527974i	$0.983186\pi$
$648$	3482.48	−	6031.84i	0.211119	−	0.365668i
$649$	1909.47	+	3307.30i	0.115490	+	0.200035i
$650$	3531.44	+	6116.63i	0.213099	+	0.369099i
$651$	−13939.1	−	24143.3i	−0.839197	−	1.45353i
$652$	13388.2			0.804176
$653$	−3703.75	+	6415.08i	−0.221958	+	0.384443i	−0.955403	−	0.295307i	$-0.904578\pi$
$653$	−3703.75	+	6415.08i	−0.221958	+	0.384443i	0.733444	+	0.679750i	$0.237912\pi$
$654$	−10962.2	−	18987.1i	−0.655438	−	1.13525i
$655$	−2441.16			−0.145625
$656$	−3475.92			−0.206878
$657$	7469.01	+	12936.7i	0.443522	+	0.768202i
$658$	2805.74			0.166230
$659$	−8633.78	+	14954.1i	−0.510356	+	0.883962i	0.489572	+	0.871963i	$0.337153\pi$
$659$	−8633.78	+	14954.1i	−0.510356	+	0.883962i	−0.999928	+	0.0119991i	$0.996180\pi$
$660$	−4228.67			−0.249395
$661$	−1516.93	+	2627.41i	−0.0892615	+	0.154605i	−0.907199	−	0.420701i	$-0.861784\pi$
$661$	−1516.93	+	2627.41i	−0.0892615	+	0.154605i	0.817938	+	0.575307i	$0.195117\pi$
$662$	−4976.13	+	8618.91i	−0.292149	+	0.506017i
$663$	3054.43	−	5290.43i	0.178921	−	0.309899i
$664$	4098.83	+	7099.38i	0.239556	+	0.414924i
$665$	−7531.62			−0.439193
$666$	−3679.23	−	8154.19i	−0.214065	−	0.474427i
$667$	−5946.70			−0.345213
$668$	2932.02	+	5078.42i	0.169826	+	0.294146i
$669$	−8791.19	+	15226.8i	−0.508053	+	0.879973i
$670$	4737.70	−	8205.94i	0.273184	−	0.473169i
$671$	755.698	−	1308.91i	0.0434775	−	0.0753053i
$672$	3681.50			0.211335
$673$	−5200.68	+	9007.84i	−0.297877	+	0.515939i	−0.975650	−	0.219333i	$-0.929612\pi$
$673$	−5200.68	+	9007.84i	−0.297877	+	0.515939i	0.677773	+	0.735271i	$0.262945\pi$
$674$	6204.75			0.354597
$675$	2204.10	+	3817.61i	0.125682	+	0.217688i
$676$	−2677.80			−0.152355
$677$	−24301.1			−1.37957			−0.689784	−	0.724015i	$-0.742294\pi$
$677$	−24301.1			−1.37957			−0.689784	+	0.724015i	$0.742294\pi$
$678$	11026.2	+	19097.9i	0.624568	+	1.08178i
$679$	−8237.21	+	14267.3i	−0.465560	+	0.806373i
$680$	−1074.99			−0.0606235
$681$	11290.0	+	19554.9i	0.635294	+	1.10036i
$682$	6356.97	+	11010.6i	0.356922	+	0.618207i
$683$	−5669.23	−	9819.39i	−0.317609	−	0.550115i	0.662380	−	0.749168i	$-0.269547\pi$
$683$	−5669.23	−	9819.39i	−0.317609	−	0.550115i	−0.979989	+	0.199053i	$0.936213\pi$
$684$	3026.77	−	5242.51i	0.169198	−	0.293059i
$685$	−4744.82	+	8218.27i	−0.264657	+	0.458400i
$686$	−6782.55	−	11747.7i	−0.377491	−	0.653834i
$687$	−9989.85	−	17302.9i	−0.554784	−	0.960914i
$688$	−2977.00	−	5156.32i	−0.164967	−	0.285731i
$689$	15433.8			0.853382
$690$	1642.88	−	2845.56i	0.0906428	−	0.156998i
$691$	4088.21	+	7080.98i	0.225069	+	0.389831i	0.956340	−	0.292256i	$-0.0944059\pi$
$691$	4088.21	+	7080.98i	0.225069	+	0.389831i	−0.731271	+	0.682087i	$0.761073\pi$
$692$	−2103.90			−0.115576
$693$	8761.03			0.480237
$694$	−7263.12	−	12580.1i	−0.397268	−	0.688089i
$695$	−2905.09			−0.158556
$696$	3994.67	−	6918.96i	0.217554	−	0.376814i
$697$	−4959.59			−0.269523
$698$	7150.86	−	12385.7i	0.387771	−	0.671639i
$699$	−8778.31	+	15204.5i	−0.475002	+	0.822727i
$700$	−3036.63	+	5259.60i	−0.163963	+	0.283992i
$701$	6604.33	+	11439.0i	0.355837	+	0.616328i	0.987261	−	0.159110i	$-0.0508624\pi$
$701$	6604.33	+	11439.0i	0.355837	+	0.616328i	−0.631424	+	0.775438i	$0.717529\pi$
$702$	3813.59			0.205035
$703$	7048.57	+	15621.6i	0.378153	+	0.838093i
$704$	−1678.96			−0.0898836
$705$	1682.15	+	2913.56i	0.0898628	+	0.155647i
$706$	2569.39	−	4450.31i	0.136969	−	0.237238i
$707$	8002.39	−	13860.5i	0.425687	−	0.737312i
$708$	1993.33	−	3452.55i	0.105811	−	0.183270i
$709$	2726.39			0.144417			0.0722085	−	0.997390i	$-0.476995\pi$
$709$	2726.39			0.144417			0.0722085	+	0.997390i	$0.476995\pi$
$710$	−1072.61	+	1857.82i	−0.0566964	+	0.0982010i
$711$	14778.9			0.779537
$712$	−3011.96	−	5216.87i	−0.158537	−	0.274593i
$713$	−9879.00			−0.518894
$714$	5252.92			0.275330
$715$	−3017.49	−	5226.44i	−0.157829	−	0.273368i
$716$	2382.54	−	4126.69i	0.124357	−	0.215393i
$717$	7023.44			0.365823
$718$	−2236.25	−	3873.29i	−0.116234	−	0.201323i
$719$	−6572.31	−	11383.6i	−0.340898	−	0.590453i	0.643702	−	0.765277i	$-0.277398\pi$
$719$	−6572.31	−	11383.6i	−0.340898	−	0.590453i	−0.984600	+	0.174824i	$0.944064\pi$
$720$	935.827	+	1620.90i	0.0484392	+	0.0838991i
$721$	15063.1	−	26090.1i	0.778060	−	1.34764i
$722$	1060.40	−	1836.67i	0.0546594	−	0.0946729i
$723$	1612.16	+	2792.35i	0.0829282	+	0.143636i
$724$	−5412.04	−	9373.94i	−0.277814	−	0.481187i
$725$	6589.88	+	11414.0i	0.337575	+	0.584698i
$726$	8801.73			0.449949
$727$	2518.23	−	4361.70i	0.128468	−	0.222512i	−0.794615	−	0.607113i	$-0.792328\pi$
$727$	2518.23	−	4361.70i	0.128468	−	0.222512i	0.923083	+	0.384601i	$0.125661\pi$
$728$	2627.04	+	4550.16i	0.133742	+	0.231649i
$729$	−8284.25			−0.420883
$730$	8848.18			0.448611
$731$	−4247.72	−	7357.26i	−0.214921	−	0.372255i
$732$	−1577.78			−0.0796671
$733$	−3717.38	+	6438.69i	−0.187319	+	0.324445i	−0.944355	−	0.328927i	$-0.893313\pi$
$733$	−3717.38	+	6438.69i	−0.187319	+	0.324445i	0.757037	+	0.653372i	$0.226646\pi$
$734$	12708.7			0.639084
$735$	1221.66	−	2115.97i	0.0613082	−	0.106189i
$736$	652.293	−	1129.80i	0.0326682	−	0.0565830i
$737$	10557.9	−	18286.9i	0.527688	−	0.913983i
$738$	4317.54	+	7478.21i	0.215354	+	0.373003i
$739$	9747.19			0.485191			0.242596	−	0.970128i	$-0.422001\pi$
$739$	9747.19			0.485191			0.242596	+	0.970128i	$0.422001\pi$
$740$	−5272.50	−	527.639i	−0.261920	−	0.0262113i
$741$	20376.3			1.01018
$742$	6635.64	+	11493.3i	0.328305	+	0.568641i
$743$	16580.6	−	28718.5i	0.818686	−	1.41801i	−0.0879639	−	0.996124i	$-0.528036\pi$
$743$	16580.6	−	28718.5i	0.818686	−	1.41801i	0.906650	−	0.421883i	$-0.138631\pi$
$744$	6636.16	−	11494.2i	0.327008	−	0.566394i
$745$	−8843.85	+	15318.0i	−0.434918	+	0.753300i
$746$	−12244.8			−0.600958
$747$	10182.6	−	17636.7i	0.498742	−	0.863847i
$748$	−2395.61			−0.117102
$749$	17469.1	+	30257.4i	0.852212	+	1.47607i
$750$	−17356.8			−0.845042
$751$	−4151.01			−0.201694			−0.100847	−	0.994902i	$-0.532155\pi$
$751$	−4151.01			−0.201694			−0.100847	+	0.994902i	$0.532155\pi$
$752$	667.881	+	1156.80i	0.0323871	+	0.0560961i
$753$	−21680.4	+	37551.5i	−1.04924	+	1.81734i
$754$	11402.0			0.550712
$755$	−5558.28	−	9627.22i	−0.267929	−	0.464067i
$756$	1639.63	+	2839.92i	0.0788792	+	0.136623i
$757$	11392.0	+	19731.4i	0.546959	+	0.947360i	0.998481	+	0.0551004i	$0.0175479\pi$
$757$	11392.0	+	19731.4i	0.546959	+	0.947360i	−0.451522	+	0.892260i	$0.649119\pi$
$758$	−819.476	+	1419.37i	−0.0392674	+	0.0680132i
$759$	3661.16	−	6341.31i	0.175088	−	0.303261i
$760$	−1792.83	−	3105.28i	−0.0855695	−	0.148211i
$761$	−2927.77	−	5071.05i	−0.139463	−	0.241558i	0.787830	−	0.615892i	$-0.211204\pi$
$761$	−2927.77	−	5071.05i	−0.139463	−	0.241558i	−0.927294	+	0.374335i	$0.877871\pi$
$762$	−7721.42	−	13373.9i	−0.367084	−	0.635807i
$763$	26905.5			1.27660
$764$	−1414.85	+	2450.59i	−0.0669992	+	0.116046i
$765$	1335.28	+	2312.77i	0.0631073	+	0.109305i
$766$	−27783.0			−1.31050
$767$	5689.59			0.267848
$768$	876.348	+	1517.88i	0.0411751	+	0.0713174i
$769$	25053.5			1.17484			0.587420	−	0.809282i	$-0.300144\pi$
$769$	25053.5			1.17484			0.587420	+	0.809282i	$0.300144\pi$
$770$	2594.69	−	4494.14i	0.121437	−	0.210335i
$771$	−6342.44			−0.296261
$772$	4071.71	−	7052.40i	0.189824	−	0.328784i
$773$	−12320.0	+	21338.8i	−0.573245	+	0.992889i	0.422985	+	0.906137i	$0.360982\pi$
$773$	−12320.0	+	21338.8i	−0.573245	+	0.992889i	−0.996230	+	0.0867525i	$0.972351\pi$
$774$	−7395.66	+	12809.7i	−0.343451	+	0.594875i
$775$	10947.5	+	18961.6i	0.507413	+	0.878866i
$776$	−7843.17			−0.362826
$777$	25764.0	+	2578.30i	1.18955	+	0.119042i
$778$	17890.1			0.824412
$779$	−8271.44	−	14326.5i	−0.380430	−	0.658924i
$780$	−3150.01	+	5455.98i	−0.144601	+	0.250456i
$781$	−2390.31	+	4140.14i	−0.109516	+	0.189687i
$782$	930.719	−	1612.05i	0.0425607	−	0.0737172i
$783$	7116.40			0.324801
$784$	485.048	−	840.128i	0.0220959	−	0.0382711i
$785$	11795.1			0.536287
$786$	2839.52	+	4918.19i	0.128858	+	0.223189i
$787$	−5002.81			−0.226596			−0.113298	−	0.993561i	$-0.536141\pi$
$787$	−5002.81			−0.226596			−0.113298	+	0.993561i	$0.536141\pi$
$788$	−19563.3			−0.884406
$789$	3598.19	+	6232.25i	0.162356	+	0.281209i
$790$	4376.95	−	7581.11i	0.197120	−	0.341422i
$791$	−27062.4			−1.21647
$792$	2085.48	+	3612.16i	0.0935662	+	0.162061i
$793$	−1125.87	−	1950.06i	−0.0504170	−	0.0873248i
$794$	14667.3	+	25404.5i	0.655571	+	1.13548i
$795$	−7956.63	+	13781.3i	−0.354959	+	0.614807i
$796$	−8812.80	+	15264.2i	−0.392414	+	0.679681i
$797$	16398.8	+	28403.5i	0.728827	+	1.26237i	0.957379	+	0.288834i	$0.0932675\pi$
$797$	16398.8	+	28403.5i	0.728827	+	1.26237i	−0.228552	+	0.973532i	$0.573399\pi$
$798$	8760.65	+	15173.9i	0.388626	+	0.673120i
$799$	952.961	+	1650.58i	0.0421944	+	0.0730829i
$800$	−2891.37			−0.127782
$801$	−7482.50	+	12960.1i	−0.330064	+	0.571688i
$802$	−14861.1	−	25740.2i	−0.654319	−	1.13331i
$803$	19718.1			0.866546
$804$	−22043.3			−0.966923
$805$	2016.13	+	3492.04i	0.0882725	+	0.152892i
$806$	18941.7			0.827782
$807$	−23063.8	+	39947.6i	−1.00605	+	1.74253i
$808$	7619.58			0.331752
$809$	−17485.4	+	30285.6i	−0.759894	+	1.31617i	0.183010	+	0.983111i	$0.441416\pi$
$809$	−17485.4	+	30285.6i	−0.759894	+	1.31617i	−0.942904	+	0.333064i	$0.891918\pi$
$810$	−5124.45	+	8875.81i	−0.222290	+	0.385017i
$811$	6833.30	−	11835.6i	0.295869	−	0.512460i	−0.679318	−	0.733844i	$-0.737724\pi$
$811$	6833.30	−	11835.6i	0.295869	−	0.512460i	0.975187	+	0.221384i	$0.0710576\pi$
$812$	4902.22	+	8490.89i	0.211865	+	0.366960i
$813$	−31489.9			−1.35843
$814$	−11749.7	−	1175.84i	−0.505931	−	0.0506304i
$815$	−19700.6			−0.846728
$816$	1250.41	+	2165.77i	0.0536435	+	0.0929133i
$817$	14168.4	−	24540.4i	0.606719	−	1.05087i
$818$	−359.681	+	622.986i	−0.0153740	+	0.0266286i
$819$	6526.25	−	11303.8i	0.278444	−	0.482279i
$820$	5114.79			0.217825
$821$	18628.9	−	32266.2i	0.791903	−	1.37162i	−0.132884	−	0.991132i	$-0.542424\pi$
$821$	18628.9	−	32266.2i	0.791903	−	1.37162i	0.924787	−	0.380485i	$-0.124243\pi$
$822$	22076.4			0.936743
$823$	−21010.8	−	36391.8i	−0.889903	−	1.54136i	−0.839989	−	0.542604i	$-0.817438\pi$
$823$	−21010.8	−	36391.8i	−0.889903	−	1.54136i	−0.0499144	−	0.998754i	$-0.515895\pi$
$824$	14342.6			0.606368
$825$	−16228.5			−0.684855
$826$	2446.20	+	4236.94i	0.103044	+	0.178477i
$827$	−19433.2	+	33659.3i	−0.817122	+	1.41530i	0.0906725	+	0.995881i	$0.471098\pi$
$827$	−19433.2	+	33659.3i	−0.817122	+	1.41530i	−0.907794	+	0.419416i	$0.862235\pi$
$828$	−3240.93			−0.136027
$829$	−3205.15	−	5551.49i	−0.134282	−	0.232583i	0.791041	−	0.611763i	$-0.209539\pi$
$829$	−3205.15	−	5551.49i	−0.134282	−	0.232583i	−0.925323	+	0.379180i	$0.876206\pi$
$830$	−6031.40	−	10446.7i	−0.252232	−	0.436879i
$831$	−10565.6	−	18300.1i	−0.441054	−	0.763928i
$832$	−1250.68	+	2166.25i	−0.0521150	+	0.0902659i
$833$	692.088	−	1198.73i	0.0287868	−	0.0498602i
$834$	3379.15	+	5852.86i	0.140300	+	0.243007i
$835$	−4314.45	−	7472.85i	−0.178812	−	0.309711i
$836$	−3995.31	−	6920.09i	−0.165288	−	0.286287i
$837$	11822.2			0.488213
$838$	9881.06	−	17114.5i	0.407322	−	0.705502i
$839$	−68.2232	−	118.166i	−0.00280730	−	0.00486239i	0.864618	−	0.502429i	$-0.167560\pi$
$839$	−68.2232	−	118.166i	−0.00280730	−	0.00486239i	−0.867426	+	0.497567i	$0.834227\pi$
$840$	−5417.30			−0.222517
$841$	−3112.12			−0.127603
$842$	−7189.80	−	12453.1i	−0.294272	−	0.509694i
$843$	25937.5			1.05971
$844$	6543.83	−	11334.3i	0.266882	−	0.462252i
$845$	3940.36			0.160417
$846$	1659.19	−	2873.80i	0.0674281	−	0.116789i
$847$	−5400.70	+	9354.29i	−0.219091	+	0.379477i
$848$	−3159.11	+	5471.74i	−0.127930	+	0.221580i
$849$	−29340.8	−	50819.8i	−1.18607	−	2.05434i
$850$	−4125.53			−0.166476
$851$	5356.14	−	7449.81i	0.215754	−	0.300090i
$852$	4990.58			0.200674
$853$	−21039.8	−	36441.9i	−0.844534	−	1.46278i	−0.886025	−	0.463637i	$-0.846544\pi$
$853$	−21039.8	−	36441.9i	−0.844534	−	1.46278i	0.0414915	−	0.999139i	$-0.486789\pi$
$854$	968.116	−	1676.83i	0.0387919	−	0.0671895i
$855$	−4453.86	+	7714.32i	−0.178151	+	0.308566i
$856$	−8316.72	+	14405.0i	−0.332079	+	0.575178i
$857$	35641.7			1.42065			0.710325	−	0.703874i	$-0.248548\pi$
$857$	35641.7			1.42065			0.710325	+	0.703874i	$0.248548\pi$
$858$	−7019.78	+	12158.6i	−0.279314	+	0.483786i
$859$	−18133.9			−0.720281			−0.360141	−	0.932898i	$-0.617271\pi$
$859$	−18133.9			−0.720281			−0.360141	+	0.932898i	$0.617271\pi$
$860$	4380.64	+	7587.49i	0.173696	+	0.300850i
$861$	−24993.3			−0.989281
$862$	−18270.8			−0.721932
$863$	−14680.0	−	25426.5i	−0.579043	−	1.00293i	−0.995589	−	0.0938170i	$-0.970093\pi$
$863$	−14680.0	−	25426.5i	−0.579043	−	1.00293i	0.416547	−	0.909114i	$-0.363240\pi$
$864$	−780.597	+	1352.03i	−0.0307366	+	0.0532374i
$865$	3095.87			0.121691
$866$	−7278.81	−	12607.3i	−0.285617	−	0.494702i
$867$	−15034.2	−	26040.0i	−0.588914	−	1.02003i
$868$	8143.84	+	14105.5i	0.318456	+	0.551582i
$869$	9754.01	−	16894.4i	0.380762	−	0.659499i
$870$	−5878.12	+	10181.2i	−0.229065	+	0.396753i
$871$	−15729.6	−	27244.4i	−0.611913	−	1.05987i
$872$	6404.60	+	11093.1i	0.248724	+	0.430802i
$873$	9742.24	+	16874.1i	0.377692	+	0.654181i
$874$	6208.89			0.240296
$875$	10650.1	−	18446.5i	0.411472	−	0.712690i
$876$	−10292.1	−	17826.4i	−0.396959	−	0.687553i
$877$	41953.8			1.61537			0.807686	−	0.589614i	$-0.200720\pi$
$877$	41953.8			1.61537			0.807686	+	0.589614i	$0.200720\pi$
$878$	−8205.79			−0.315412
$879$	10868.3	+	18824.5i	0.417041	+	0.722336i
$880$	2470.57			0.0946397
$881$	−14044.6	+	24325.9i	−0.537087	+	0.930262i	0.461972	+	0.886894i	$0.347142\pi$
$881$	−14044.6	+	24325.9i	−0.537087	+	0.930262i	−0.999059	+	0.0433677i	$0.986191\pi$
$882$	−2409.97			−0.0920046
$883$	−8620.02	+	14930.3i	−0.328524	+	0.569020i	−0.982219	−	0.187738i	$-0.939884\pi$
$883$	−8620.02	+	14930.3i	−0.328524	+	0.569020i	0.653695	+	0.756758i	$0.273218\pi$
$884$	−1784.53	+	3090.90i	−0.0678962	+	0.117600i
$885$	−2933.17	+	5080.41i	−0.111410	+	0.192967i
$886$	−4791.19	−	8298.59i	−0.181674	−	0.314669i
$887$	19258.6			0.729018			0.364509	−	0.931200i	$-0.381237\pi$
$887$	19258.6			0.729018			0.364509	+	0.931200i	$0.381237\pi$
$888$	5069.86	+	11236.2i	0.191592	+	0.424620i
$889$	18951.3			0.714968
$890$	4432.08	+	7676.59i	0.166925	+	0.289123i
$891$	−11419.8	+	19779.7i	−0.429380	+	0.743708i
$892$	5136.19	−	8896.15i	0.192794	−	0.333929i
$893$	−3178.63	+	5505.56i	−0.119114	+	0.206312i
$894$	41148.1			1.53937
$895$	−3505.90	+	6072.39i	−0.130938	+	0.226791i
$896$	−2150.89			−0.0801967
$897$	−5454.52	−	9447.51i	−0.203034	−	0.351665i
$898$	−7007.57			−0.260407
$899$	35346.4			1.31131
$900$	3591.46	+	6220.59i	0.133017	+	0.230392i
$901$	−4507.55	+	7807.31i	−0.166669	+	0.288678i
$902$	11398.3			0.420755
$903$	−21405.9	−	37076.2i	−0.788865	−	1.36635i
$904$	−6441.95	−	11157.8i	−0.237009	−	0.410512i
$905$	7963.78	+	13793.7i	0.292514	+	0.506649i
$906$	−12930.6	+	22396.5i	−0.474162	+	0.821272i
$907$	14741.7	−	25533.4i	0.539680	−	0.934754i	−0.459241	−	0.888312i	$-0.651878\pi$
$907$	14741.7	−	25533.4i	0.539680	−	0.934754i	0.998921	−	0.0464419i	$-0.0147882\pi$
$908$	−6596.13	−	11424.8i	−0.241080	−	0.417562i
$909$	−9464.52	−	16393.0i	−0.345345	−	0.598154i
$910$	−3865.67	−	6695.53i	−0.140819	−	0.243906i
$911$	−18242.0			−0.663429			−0.331715	−	0.943380i	$-0.607627\pi$
$911$	−18242.0			−0.663429			−0.331715	+	0.943380i	$0.607627\pi$
$912$	−4170.79	+	7224.01i	−0.151435	+	0.262293i
$913$	−13440.9	−	23280.4i	−0.487218	−	0.843885i
$914$	1684.34			0.0609553
$915$	2321.69			0.0838826
$916$	5836.50	+	10109.1i	0.210528	+	0.364645i
$917$	−6969.27			−0.250977
$918$	−1113.79	+	1929.14i	−0.0400441	+	0.0693585i
$919$	9446.60			0.339080			0.169540	−	0.985523i	$-0.445772\pi$
$919$	9446.60			0.339080			0.169540	+	0.985523i	$0.445772\pi$
$920$	−959.844	+	1662.50i	−0.0343969	+	0.0595771i
$921$	17519.0	−	30343.8i	0.626787	−	1.08563i
$922$	3432.98	−	5946.10i	0.122624	−	0.212391i
$923$	3561.17	+	6168.12i	0.126996	+	0.219963i
$924$	−12072.4			−0.429820
$925$	−20234.5	−	2024.94i	−0.719250	−	0.0719780i
$926$	−23274.2			−0.825957
$927$	−17815.4	−	30857.1i	−0.631212	−	1.09329i
$928$	−2333.86	+	4042.36i	−0.0825566	+	0.142992i
$929$	−6231.13	+	10792.6i	−0.220061	+	0.381157i	−0.954826	−	0.297164i	$-0.903959\pi$
$929$	−6231.13	+	10792.6i	−0.220061	+	0.381157i	0.734765	+	0.678322i	$0.237292\pi$
$930$	−9765.07	+	16913.6i	−0.344311	+	0.596364i
$931$	4616.96			0.162529
$932$	5128.67	−	8883.11i	0.180252	−	0.312206i
$933$	13627.4			0.478181
$934$	15006.8	+	25992.6i	0.525737	+	0.910604i
$935$	3525.12			0.123298
$936$	6214.06			0.217001
$937$	−8823.69	−	15283.1i	−0.307639	−	0.532846i	0.670207	−	0.742174i	$-0.266205\pi$
$937$	−8823.69	−	15283.1i	−0.307639	−	0.532846i	−0.977845	+	0.209329i	$0.932872\pi$
$938$	13525.6	−	23427.1i	0.470819	−	0.815482i
$939$	5718.93			0.198754
$940$	−982.782	−	1702.23i	−0.0341009	−	0.0590644i
$941$	7384.30	+	12790.0i	0.255814	+	0.443083i	0.965116	−	0.261821i	$-0.0843231\pi$
$941$	7384.30	+	12790.0i	0.255814	+	0.443083i	−0.709302	+	0.704905i	$0.750990\pi$
$942$	−13719.9	−	23763.5i	−0.474541	−	0.821929i
$943$	−4428.35	+	7670.13i	−0.152924	+	0.264871i
$944$	−1164.59	+	2017.13i	−0.0401527	+	0.0695466i
$945$	−2412.70	−	4178.92i	−0.0830530	−	0.143852i
$946$	9762.22	+	16908.7i	0.335515	+	0.581129i
$947$	143.370	+	248.324i	0.00491964	+	0.00852107i	0.868475	−	0.495733i	$-0.165101\pi$
$947$	143.370	+	248.324i	0.00491964	+	0.00852107i	−0.863555	+	0.504254i	$0.831767\pi$
$948$	−20364.8			−0.697699
$949$	14688.4	−	25441.0i	0.502428	−	0.870231i
$950$	−6880.43	−	11917.2i	−0.234979	−	0.406996i
$951$	−52712.5			−1.79739
$952$	−3068.98			−0.104481
$953$	18245.9	+	31602.9i	0.620193	+	1.07421i	0.989449	+	0.144878i	$0.0462791\pi$
$953$	18245.9	+	31602.9i	0.620193	+	1.07421i	−0.369256	+	0.929328i	$0.620388\pi$
$954$	15696.1			0.532684
$955$	2081.94	−	3606.02i	0.0705445	−	0.122187i
$956$	−4103.40			−0.138821
$957$	−13099.4	+	22688.7i	−0.442468	+	0.766377i
$958$	−1425.95	+	2469.82i	−0.0480902	+	0.0832947i
$959$	−13546.0	+	23462.3i	−0.456123	+	0.790029i
$960$	−1289.54	−	2233.55i	−0.0433539	−	0.0750911i
$961$	28928.4			0.971044
$962$	−10269.7	+	14284.0i	−0.344188	+	0.478727i
$963$	41321.8			1.38274
$964$	−941.896	−	1631.41i	−0.0314693	−	0.0545065i
$965$	−5991.49	+	10377.6i	−0.199868	+	0.346182i
$966$	4690.26	−	8123.78i	0.156218	−	0.270578i
$967$	−3767.58	+	6525.63i	−0.125292	+	0.217012i	−0.921847	−	0.387554i	$-0.873320\pi$
$967$	−3767.58	+	6525.63i	−0.125292	+	0.217012i	0.796555	+	0.604566i	$0.206653\pi$
$968$	−5142.35			−0.170745
$969$	−5951.06	+	10307.5i	−0.197292	+	0.341719i
$970$	11541.2			0.382025
$971$	−4504.56	−	7802.13i	−0.148876	−	0.257860i	0.781937	−	0.623358i	$-0.214232\pi$
$971$	−4504.56	−	7802.13i	−0.148876	−	0.257860i	−0.930812	+	0.365498i	$0.880899\pi$
$972$	18573.7			0.612913
$973$	−8293.72			−0.273263
$974$	16529.6	+	28630.0i	0.543779	+	0.941853i
$975$	−12088.9	+	20938.7i	−0.397083	+	0.687768i
$976$	921.805			0.0302318
$977$	12083.2	+	20928.6i	0.395675	+	0.685329i	0.993187	−	0.116531i	$-0.0371774\pi$
$977$	12083.2	+	20928.6i	0.395675	+	0.685329i	−0.597512	+	0.801860i	$0.703844\pi$
$978$	22915.5	+	39690.8i	0.749239	+	1.29772i
$979$	9876.86	+	17107.2i	0.322437	+	0.558477i
$980$	−713.745	+	1236.24i	−0.0232650	+	0.0402962i
$981$	15910.7	−	27558.1i	0.517828	−	0.896905i
$982$	−17883.4	−	30974.9i	−0.581141	−	1.00657i
$983$	22465.4	+	38911.2i	0.728927	+	1.26254i	0.957337	+	0.288973i	$0.0933139\pi$
$983$	22465.4	+	38911.2i	0.728927	+	1.26254i	−0.228410	+	0.973565i	$0.573353\pi$
$984$	−5949.44	−	10304.7i	−0.192745	−	0.333844i
$985$	28787.2			0.931204
$986$	−3330.05	+	5767.81i	−0.107556	+	0.186293i
$987$	4802.35	+	8317.92i	0.154874	+	0.268249i
$988$	−11904.7			−0.383340
$989$	−15170.9			−0.487773
$990$	−3068.77	−	5315.27i	−0.0985172	−	0.170637i
$991$	33530.9			1.07482			0.537409	−	0.843321i	$-0.319403\pi$
$991$	33530.9			1.07482			0.537409	+	0.843321i	$0.319403\pi$
$992$	−3877.13	+	6715.39i	−0.124092	+	0.214933i
$993$	−34068.9			−1.08876
$994$	−3062.20	+	5303.88i	−0.0977133	+	0.169244i
$995$	12968.0	−	22461.2i	0.413178	−	0.715646i
$996$	−14031.2	+	24302.8i	−0.446382	+	0.773157i
$997$	−14216.7	−	24624.0i	−0.451602	−	0.782198i	0.546884	−	0.837209i	$-0.315814\pi$
$997$	−14216.7	−	24624.0i	−0.451602	−	0.782198i	−0.998486	+	0.0550110i	$0.982481\pi$
$998$	−25109.0			−0.796406
$999$	−6409.68	+	8915.17i	−0.202996	+	0.282346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.4.c.b.63.5	yes	10
3.2	odd	2		666.4.f.d.433.2		10
37.10	even	3	inner	74.4.c.b.47.5	✓	10
111.47	odd	6		666.4.f.d.343.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.4.c.b.47.5	✓	10	37.10	even	3	inner
74.4.c.b.63.5	yes	10	1.1	even	1	trivial
666.4.f.d.343.2		10	111.47	odd	6
666.4.f.d.433.2		10	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	74.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(3.42323 - 5.92921i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.94299 - 5.09740i) q^{5} -13.6929 q^{6} +(8.40192 - 14.5526i) q^{7} +8.00000 q^{8} +(-9.93705 - 17.2115i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(3.42323 - 5.92921i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.94299 - 5.09740i) q^{5} -13.6929 q^{6} +(8.40192 - 14.5526i) q^{7} +8.00000 q^{8} +(-9.93705 - 17.2115i) q^{9} -11.7719 q^{10} -26.2337 q^{11} +(13.6929 + 23.7169i) q^{12} +(-19.5419 + 33.8476i) q^{13} -33.6077 q^{14} +(-20.1491 - 34.8992i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-11.4147 - 19.7709i) q^{17} +(-19.8741 + 34.4229i) q^{18} +(38.0743 - 65.9466i) q^{19} +(11.7719 + 20.3896i) q^{20} +(-57.5235 - 99.6335i) q^{21} +(26.2337 + 45.4381i) q^{22} -40.7683 q^{23} +(27.3859 - 47.4337i) q^{24} +(45.1777 + 78.2500i) q^{25} +78.1678 q^{26} +48.7873 q^{27} +(33.6077 + 58.2102i) q^{28} +145.866 q^{29} +(-40.2981 + 69.7984i) q^{30} +242.321 q^{31} +(-16.0000 + 27.7128i) q^{32} +(-89.8040 + 155.545i) q^{33} +(-22.8295 + 39.5418i) q^{34} +(-49.4535 - 85.6559i) q^{35} +79.4964 q^{36} +(-131.380 + 182.735i) q^{37} -152.297 q^{38} +(133.793 + 231.737i) q^{39} +(23.5439 - 40.7792i) q^{40} +(108.622 - 188.140i) q^{41} +(-115.047 + 199.267i) q^{42} +372.125 q^{43} +(52.4674 - 90.8762i) q^{44} -116.978 q^{45} +(40.7683 + 70.6127i) q^{46} -83.4851 q^{47} -109.543 q^{48} +(30.3155 + 52.5080i) q^{49} +(90.3553 - 156.500i) q^{50} -156.301 q^{51} +(-78.1678 - 135.391i) q^{52} +(-197.444 - 341.984i) q^{53} +(-48.7873 - 84.5021i) q^{54} +(-77.2054 + 133.724i) q^{55} +(67.2154 - 116.420i) q^{56} +(-260.674 - 451.501i) q^{57} +(-145.866 - 252.647i) q^{58} +(-72.7869 - 126.071i) q^{59} +161.192 q^{60} +(-28.8064 + 49.8942i) q^{61} +(-242.321 - 419.712i) q^{62} -333.961 q^{63} +64.0000 q^{64} +(115.023 + 199.226i) q^{65} +359.216 q^{66} +(-402.457 + 697.076i) q^{67} +91.3180 q^{68} +(-139.559 + 241.724i) q^{69} +(-98.9069 + 171.312i) q^{70} +(91.1160 - 157.818i) q^{71} +(-79.4964 - 137.692i) q^{72} -751.633 q^{73} +(447.887 + 44.8217i) q^{74} +618.615 q^{75} +(152.297 + 263.786i) q^{76} +(-220.413 + 381.767i) q^{77} +(267.587 - 463.474i) q^{78} +(-371.812 + 643.998i) q^{79} -94.1755 q^{80} +(435.310 - 753.980i) q^{81} -434.490 q^{82} +(512.353 + 887.422i) q^{83} +460.188 q^{84} -134.374 q^{85} +(-372.125 - 644.540i) q^{86} +(499.333 - 864.870i) q^{87} -209.870 q^{88} +(-376.495 - 652.109i) q^{89} +(116.978 + 202.612i) q^{90} +(328.380 + 568.770i) q^{91} +(81.5366 - 141.225i) q^{92} +(829.521 - 1436.77i) q^{93} +(83.4851 + 144.600i) q^{94} +(-224.104 - 388.160i) q^{95} +(109.543 + 189.735i) q^{96} -980.396 q^{97} +(60.6310 - 105.016i) q^{98} +(260.685 + 451.520i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - 5 q^{3} - 20 q^{4} - q^{5} + 20 q^{6} - q^{7} + 80 q^{8} - 38 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 - 5 * q^3 - 20 * q^4 - q^5 + 20 * q^6 - q^7 + 80 * q^8 - 38 * q^9	\( 10 q - 10 q^{2} - 5 q^{3} - 20 q^{4} - q^{5} + 20 q^{6} - q^{7} + 80 q^{8} - 38 q^{9} + 4 q^{10} - 80 q^{11} - 20 q^{12} + 73 q^{13} + 4 q^{14} + 113 q^{15} - 80 q^{16} + 69 q^{17} - 76 q^{18} + 33 q^{19} - 4 q^{20} - 109 q^{21} + 80 q^{22} - 524 q^{23} - 40 q^{24} + 132 q^{25} - 292 q^{26} + 898 q^{27} - 4 q^{28} + 296 q^{29} + 226 q^{30} - 784 q^{31} - 160 q^{32} + 124 q^{33} + 138 q^{34} - 263 q^{35} + 304 q^{36} + 24 q^{37} - 132 q^{38} + 679 q^{39} - 8 q^{40} + 345 q^{41} - 218 q^{42} - 492 q^{43} + 160 q^{44} - 1816 q^{45} + 524 q^{46} - 32 q^{47} + 160 q^{48} + 150 q^{49} + 264 q^{50} + 342 q^{51} + 292 q^{52} - 19 q^{53} - 898 q^{54} + 340 q^{55} - 8 q^{56} + 207 q^{57} - 296 q^{58} - 105 q^{59} - 904 q^{60} + 219 q^{61} + 784 q^{62} - 304 q^{63} + 640 q^{64} + 1191 q^{65} - 496 q^{66} + 773 q^{67} - 552 q^{68} + 604 q^{69} - 526 q^{70} + 555 q^{71} - 304 q^{72} + 348 q^{73} + 102 q^{74} - 2952 q^{75} + 132 q^{76} + 884 q^{77} + 1358 q^{78} - 727 q^{79} + 32 q^{80} - 2609 q^{81} - 1380 q^{82} + 2229 q^{83} + 872 q^{84} - 3042 q^{85} + 492 q^{86} + 2660 q^{87} - 640 q^{88} + 901 q^{89} + 1816 q^{90} - 1405 q^{91} + 1048 q^{92} + 3236 q^{93} + 32 q^{94} - 3337 q^{95} - 160 q^{96} - 4596 q^{97} + 300 q^{98} + 6784 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 5 * q^3 - 20 * q^4 - q^5 + 20 * q^6 - q^7 + 80 * q^8 - 38 * q^9 + 4 * q^10 - 80 * q^11 - 20 * q^12 + 73 * q^13 + 4 * q^14 + 113 * q^15 - 80 * q^16 + 69 * q^17 - 76 * q^18 + 33 * q^19 - 4 * q^20 - 109 * q^21 + 80 * q^22 - 524 * q^23 - 40 * q^24 + 132 * q^25 - 292 * q^26 + 898 * q^27 - 4 * q^28 + 296 * q^29 + 226 * q^30 - 784 * q^31 - 160 * q^32 + 124 * q^33 + 138 * q^34 - 263 * q^35 + 304 * q^36 + 24 * q^37 - 132 * q^38 + 679 * q^39 - 8 * q^40 + 345 * q^41 - 218 * q^42 - 492 * q^43 + 160 * q^44 - 1816 * q^45 + 524 * q^46 - 32 * q^47 + 160 * q^48 + 150 * q^49 + 264 * q^50 + 342 * q^51 + 292 * q^52 - 19 * q^53 - 898 * q^54 + 340 * q^55 - 8 * q^56 + 207 * q^57 - 296 * q^58 - 105 * q^59 - 904 * q^60 + 219 * q^61 + 784 * q^62 - 304 * q^63 + 640 * q^64 + 1191 * q^65 - 496 * q^66 + 773 * q^67 - 552 * q^68 + 604 * q^69 - 526 * q^70 + 555 * q^71 - 304 * q^72 + 348 * q^73 + 102 * q^74 - 2952 * q^75 + 132 * q^76 + 884 * q^77 + 1358 * q^78 - 727 * q^79 + 32 * q^80 - 2609 * q^81 - 1380 * q^82 + 2229 * q^83 + 872 * q^84 - 3042 * q^85 + 492 * q^86 + 2660 * q^87 - 640 * q^88 + 901 * q^89 + 1816 * q^90 - 1405 * q^91 + 1048 * q^92 + 3236 * q^93 + 32 * q^94 - 3337 * q^95 - 160 * q^96 - 4596 * q^97 + 300 * q^98 + 6784 * q^99

Introduction

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Modular forms

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