LMFDB - Embedded newform 23.3.d.a.14.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,3,Mod(5,23)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("23.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	23.d (of order $22$, degree $10$, 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:	$0.626704608029$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			14.1
Character	$\chi$	$=$	23.14
Dual form			23.3.d.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.10125 + 0.910608i) q^{2} +(-3.16934 - 3.65762i) q^{3} +(5.42352 - 3.48548i) q^{4} +(-5.40865 + 0.777647i) q^{5} +(13.1596 + 8.45714i) q^{6} +(-0.889564 - 0.406250i) q^{7} +(-5.17926 + 5.97719i) q^{8} +(-2.05259 + 14.2761i) q^{9} +O(q^{10})$	\(q+(-3.10125 + 0.910608i) q^{2} +(-3.16934 - 3.65762i) q^{3} +(5.42352 - 3.48548i) q^{4} +(-5.40865 + 0.777647i) q^{5} +(13.1596 + 8.45714i) q^{6} +(-0.889564 - 0.406250i) q^{7} +(-5.17926 + 5.97719i) q^{8} +(-2.05259 + 14.2761i) q^{9} +(16.0654 - 7.33684i) q^{10} +(3.66991 - 12.4986i) q^{11} +(-29.9375 - 8.79045i) q^{12} +(-5.85520 - 12.8211i) q^{13} +(3.12869 + 0.449838i) q^{14} +(19.9862 + 17.3181i) q^{15} +(-0.0933341 + 0.204373i) q^{16} +(-7.74290 + 12.0482i) q^{17} +(-6.63433 - 46.1428i) q^{18} +(-3.48690 - 5.42572i) q^{19} +(-26.6234 + 23.0693i) q^{20} +(1.33343 + 4.54123i) q^{21} +42.1030i q^{22} +(14.0512 - 18.2089i) q^{23} +38.2771 q^{24} +(4.66147 - 1.36873i) q^{25} +(29.8334 + 34.4296i) q^{26} +(22.0789 - 14.1893i) q^{27} +(-6.24054 + 0.897254i) q^{28} +(-2.47928 - 1.59333i) q^{29} +(-77.7522 - 35.5083i) q^{30} +(5.65792 - 6.52959i) q^{31} +(4.60559 - 32.0326i) q^{32} +(-57.3462 + 26.1891i) q^{33} +(13.0415 - 44.4152i) q^{34} +(5.12726 + 1.50550i) q^{35} +(38.6268 + 84.5809i) q^{36} +(30.2033 + 4.34258i) q^{37} +(15.7544 + 13.6513i) q^{38} +(-28.3375 + 62.0505i) q^{39} +(23.3647 - 36.3562i) q^{40} +(-4.02842 - 28.0183i) q^{41} +(-8.27056 - 12.8692i) q^{42} +(-25.3186 + 21.9387i) q^{43} +(-23.6597 - 80.5777i) q^{44} -78.8106i q^{45} +(-26.9951 + 69.2654i) q^{46} +28.3043 q^{47} +(1.04333 - 0.306348i) q^{48} +(-31.4619 - 36.3090i) q^{49} +(-13.2100 + 8.48954i) q^{50} +(68.6075 - 9.86427i) q^{51} +(-76.4435 - 49.1272i) q^{52} +(74.4829 + 34.0152i) q^{53} +(-55.5514 + 64.1097i) q^{54} +(-10.1298 + 70.4544i) q^{55} +(7.03552 - 3.21301i) q^{56} +(-8.79403 + 29.9497i) q^{57} +(9.13975 + 2.68367i) q^{58} +(-37.0343 - 81.0938i) q^{59} +(168.758 + 24.2637i) q^{60} +(13.9664 + 12.1020i) q^{61} +(-11.6007 + 25.4020i) q^{62} +(7.62557 - 11.8656i) q^{63} +(14.7582 + 102.645i) q^{64} +(41.6390 + 64.7916i) q^{65} +(153.997 - 133.439i) q^{66} +(-23.0835 - 78.6152i) q^{67} +92.3312i q^{68} +(-111.134 + 6.31624i) q^{69} -17.2718 q^{70} +(-70.4488 + 20.6856i) q^{71} +(-74.6999 - 86.2083i) q^{72} +(-62.8153 + 40.3690i) q^{73} +(-97.6223 + 14.0360i) q^{74} +(-19.7801 - 12.7119i) q^{75} +(-37.8225 - 17.2730i) q^{76} +(-8.34217 + 9.62738i) q^{77} +(31.3780 - 218.239i) q^{78} +(109.498 - 50.0059i) q^{79} +(0.345882 - 1.17796i) q^{80} +(2.67333 + 0.784960i) q^{81} +(38.0068 + 83.2233i) q^{82} +(-119.345 - 17.1592i) q^{83} +(23.0602 + 19.9818i) q^{84} +(32.5094 - 71.1857i) q^{85} +(58.5417 - 91.0926i) q^{86} +(2.02987 + 14.1181i) q^{87} +(55.6989 + 86.6692i) q^{88} +(-25.2210 + 21.8541i) q^{89} +(71.7656 + 244.411i) q^{90} +13.7839i q^{91} +(12.7402 - 147.731i) q^{92} -41.8146 q^{93} +(-87.7787 + 25.7741i) q^{94} +(23.0787 + 26.6343i) q^{95} +(-131.760 + 84.6768i) q^{96} +(118.310 - 17.0104i) q^{97} +(130.634 + 83.9536i) q^{98} +(170.898 + 78.0465i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9}+O(q^{10}) $ 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9	\( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9} - 11 q^{10} - 11 q^{11} - 14 q^{12} - 11 q^{13} - 11 q^{14} + 66 q^{15} + 73 q^{16} + 44 q^{17} + 126 q^{18} + 22 q^{19} + 77 q^{20} + 22 q^{21} + 36 q^{23} - 22 q^{24} - 152 q^{25} - 186 q^{26} - 62 q^{27} - 275 q^{28} - 88 q^{29} - 363 q^{30} - 110 q^{31} - 147 q^{32} - 132 q^{33} + 231 q^{34} + 209 q^{35} + 229 q^{36} + 341 q^{37} + 374 q^{38} + 295 q^{39} + 429 q^{40} + 77 q^{41} + 319 q^{42} + 77 q^{43} + 110 q^{44} - 99 q^{46} - 110 q^{47} - 550 q^{48} - 422 q^{49} - 396 q^{50} - 275 q^{51} - 472 q^{52} - 187 q^{53} - 198 q^{54} - 165 q^{55} + 176 q^{56} - 176 q^{57} - 13 q^{58} - q^{59} + 539 q^{60} + 297 q^{61} + 82 q^{62} + 264 q^{63} + 386 q^{64} + 220 q^{65} + 264 q^{66} + 11 q^{67} - 66 q^{69} - 198 q^{70} - 176 q^{71} - 605 q^{72} - 121 q^{73} - 352 q^{74} + 154 q^{75} + 110 q^{76} + 110 q^{77} + 360 q^{78} + 33 q^{79} - 242 q^{80} + 494 q^{81} + 96 q^{82} - 154 q^{83} + 11 q^{84} + 275 q^{85} + 143 q^{86} + 271 q^{87} + 429 q^{88} + 121 q^{89} + 242 q^{90} + 166 q^{92} + 260 q^{93} - 295 q^{94} - 154 q^{95} - 419 q^{96} + 154 q^{97} + 77 q^{98} - 242 q^{99}+O(q^{100}) \) 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9 - 11 * q^10 - 11 * q^11 - 14 * q^12 - 11 * q^13 - 11 * q^14 + 66 * q^15 + 73 * q^16 + 44 * q^17 + 126 * q^18 + 22 * q^19 + 77 * q^20 + 22 * q^21 + 36 * q^23 - 22 * q^24 - 152 * q^25 - 186 * q^26 - 62 * q^27 - 275 * q^28 - 88 * q^29 - 363 * q^30 - 110 * q^31 - 147 * q^32 - 132 * q^33 + 231 * q^34 + 209 * q^35 + 229 * q^36 + 341 * q^37 + 374 * q^38 + 295 * q^39 + 429 * q^40 + 77 * q^41 + 319 * q^42 + 77 * q^43 + 110 * q^44 - 99 * q^46 - 110 * q^47 - 550 * q^48 - 422 * q^49 - 396 * q^50 - 275 * q^51 - 472 * q^52 - 187 * q^53 - 198 * q^54 - 165 * q^55 + 176 * q^56 - 176 * q^57 - 13 * q^58 - q^59 + 539 * q^60 + 297 * q^61 + 82 * q^62 + 264 * q^63 + 386 * q^64 + 220 * q^65 + 264 * q^66 + 11 * q^67 - 66 * q^69 - 198 * q^70 - 176 * q^71 - 605 * q^72 - 121 * q^73 - 352 * q^74 + 154 * q^75 + 110 * q^76 + 110 * q^77 + 360 * q^78 + 33 * q^79 - 242 * q^80 + 494 * q^81 + 96 * q^82 - 154 * q^83 + 11 * q^84 + 275 * q^85 + 143 * q^86 + 271 * q^87 + 429 * q^88 + 121 * q^89 + 242 * q^90 + 166 * q^92 + 260 * q^93 - 295 * q^94 - 154 * q^95 - 419 * q^96 + 154 * q^97 + 77 * q^98 - 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{21}{22}\right)$

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 $

$2$	−3.10125	+	0.910608i	−1.55062	+	0.455304i	−0.941287	−	0.337607i	$-0.890382\pi$
$2$	−3.10125	+	0.910608i	−1.55062	+	0.455304i	−0.609337	+	0.792912i	$0.708564\pi$
$3$	−3.16934	−	3.65762i	−1.05645	−	1.21921i	−0.974925	−	0.222534i	$-0.928567\pi$
$3$	−3.16934	−	3.65762i	−1.05645	−	1.21921i	−0.0815227	−	0.996671i	$-0.525978\pi$
$4$	5.42352	−	3.48548i	1.35588	−	0.871370i
$5$	−5.40865	+	0.777647i	−1.08173	+	0.155529i	−0.660055	−	0.751217i	$-0.729467\pi$
$5$	−5.40865	+	0.777647i	−1.08173	+	0.155529i	−0.421676	+	0.906747i	$0.638558\pi$
$6$	13.1596	+	8.45714i	2.19326	+	1.40952i
$7$	−0.889564	−	0.406250i	−0.127081	−	0.0580357i	0.350860	−	0.936428i	$-0.385889\pi$
$7$	−0.889564	−	0.406250i	−0.127081	−	0.0580357i	−0.477941	+	0.878392i	$0.658617\pi$
$8$	−5.17926	+	5.97719i	−0.647408	+	0.747148i
$9$	−2.05259	+	14.2761i	−0.228066	+	1.58623i
$10$	16.0654	−	7.33684i	1.60654	−	0.733684i
$11$	3.66991	−	12.4986i	0.333629	−	1.13623i	−0.606406	−	0.795155i	$-0.707389\pi$
$11$	3.66991	−	12.4986i	0.333629	−	1.13623i	0.940035	−	0.341079i	$-0.110792\pi$
$12$	−29.9375	−	8.79045i	−2.49479	−	0.732538i
$13$	−5.85520	−	12.8211i	−0.450400	−	0.986239i	−0.989571	−	0.144043i	$-0.953990\pi$
$13$	−5.85520	−	12.8211i	−0.450400	−	0.986239i	0.539171	−	0.842196i	$-0.318737\pi$
$14$	3.12869	+	0.449838i	0.223478	+	0.0321313i
$15$	19.9862	+	17.3181i	1.33241	+	1.15454i
$16$	−0.0933341	+	0.204373i	−0.00583338	+	0.0127733i
$17$	−7.74290	+	12.0482i	−0.455465	+	0.708717i	−0.990712	−	0.135979i	$-0.956582\pi$
$17$	−7.74290	+	12.0482i	−0.455465	+	0.708717i	0.535247	+	0.844695i	$0.320218\pi$
$18$	−6.63433	−	46.1428i	−0.368574	−	2.56349i
$19$	−3.48690	−	5.42572i	−0.183521	−	0.285564i	0.737288	−	0.675579i	$-0.236106\pi$
$19$	−3.48690	−	5.42572i	−0.183521	−	0.285564i	−0.920809	+	0.390015i	$0.872470\pi$
$20$	−26.6234	+	23.0693i	−1.33117	+	1.15347i
$21$	1.33343	+	4.54123i	0.0634964	+	0.216249i
$22$			42.1030i			1.91377i
$23$	14.0512	−	18.2089i	0.610922	−	0.791691i
$23$	14.0512	−	18.2089i	0.610922	−	0.791691i
$24$	38.2771			1.59488
$25$	4.66147	−	1.36873i	0.186459	−	0.0547492i
$26$	29.8334	+	34.4296i	1.14744	+	1.32422i
$27$	22.0789	−	14.1893i	0.817739	−	0.525529i
$28$	−6.24054	+	0.897254i	−0.222876	+	0.0320448i
$29$	−2.47928	−	1.59333i	−0.0854922	−	0.0549425i	0.497196	−	0.867638i	$-0.334363\pi$
$29$	−2.47928	−	1.59333i	−0.0854922	−	0.0549425i	−0.582689	+	0.812696i	$0.697999\pi$
$30$	−77.7522	−	35.5083i	−2.59174	−	1.18361i
$31$	5.65792	−	6.52959i	0.182514	−	0.210632i	−0.657119	−	0.753787i	$-0.728225\pi$
$31$	5.65792	−	6.52959i	0.182514	−	0.210632i	0.839632	+	0.543155i	$0.182770\pi$
$32$	4.60559	−	32.0326i	0.143925	−	1.00102i
$33$	−57.3462	+	26.1891i	−1.73776	+	0.793610i
$34$	13.0415	−	44.4152i	0.383573	−	1.30633i
$35$	5.12726	+	1.50550i	0.146493	+	0.0430143i
$36$	38.6268	+	84.5809i	1.07297	+	2.34947i
$37$	30.2033	+	4.34258i	0.816305	+	0.117367i	0.537805	−	0.843069i	$-0.319254\pi$
$37$	30.2033	+	4.34258i	0.816305	+	0.117367i	0.278500	+	0.960436i	$0.410163\pi$
$38$	15.7544	+	13.6513i	0.414591	+	0.359245i
$39$	−28.3375	+	62.0505i	−0.726603	+	1.59104i
$40$	23.3647	−	36.3562i	0.584117	−	0.908904i
$41$	−4.02842	−	28.0183i	−0.0982541	−	0.683372i	−0.978103	−	0.208120i	$-0.933266\pi$
$41$	−4.02842	−	28.0183i	−0.0982541	−	0.683372i	0.879849	−	0.475253i	$-0.157643\pi$
$42$	−8.27056	−	12.8692i	−0.196918	−	0.306411i
$43$	−25.3186	+	21.9387i	−0.588805	+	0.510202i	−0.897532	−	0.440948i	$-0.854642\pi$
$43$	−25.3186	+	21.9387i	−0.588805	+	0.510202i	0.308728	+	0.951150i	$0.400097\pi$
$44$	−23.6597	−	80.5777i	−0.537721	−	1.83131i
$45$		−	78.8106i		−	1.75135i
$46$	−26.9951	+	69.2654i	−0.586851	+	1.50577i
$47$	28.3043			0.602219			0.301110	−	0.953590i	$-0.402643\pi$
$47$	28.3043			0.602219			0.301110	+	0.953590i	$0.402643\pi$
$48$	1.04333	−	0.306348i	0.0217360	−	0.00638226i
$49$	−31.4619	−	36.3090i	−0.642079	−	0.740999i
$50$	−13.2100	+	8.48954i	−0.264200	+	0.169791i
$51$	68.6075	−	9.86427i	1.34525	−	0.193417i
$52$	−76.4435	−	49.1272i	−1.47007	−	0.944755i
$53$	74.4829	+	34.0152i	1.40534	+	0.641796i	0.966476	−	0.256758i	$-0.0826543\pi$
$53$	74.4829	+	34.0152i	1.40534	+	0.641796i	0.438862	+	0.898554i	$0.355382\pi$
$54$	−55.5514	+	64.1097i	−1.02873	+	1.18722i
$55$	−10.1298	+	70.4544i	−0.184178	+	1.28099i
$56$	7.03552	−	3.21301i	0.125634	−	0.0573752i
$57$	−8.79403	+	29.9497i	−0.154281	+	0.525434i
$58$	9.13975	+	2.68367i	0.157582	+	0.0462702i
$59$	−37.0343	−	81.0938i	−0.627700	−	1.37447i	−0.909784	−	0.415081i	$-0.863753\pi$
$59$	−37.0343	−	81.0938i	−0.627700	−	1.37447i	0.282084	−	0.959390i	$-0.408974\pi$
$60$	168.758	+	24.2637i	2.81263	+	0.404395i
$61$	13.9664	+	12.1020i	0.228958	+	0.198393i	0.761783	−	0.647832i	$-0.224324\pi$
$61$	13.9664	+	12.1020i	0.228958	+	0.198393i	−0.532825	+	0.846225i	$0.678870\pi$
$62$	−11.6007	+	25.4020i	−0.187108	+	0.409710i
$63$	7.62557	−	11.8656i	0.121041	−	0.188343i
$64$	14.7582	+	102.645i	0.230597	+	1.60383i
$65$	41.6390	+	64.7916i	0.640601	+	0.996794i
$66$	153.997	−	133.439i	2.33328	−	2.02180i
$67$	−23.0835	−	78.6152i	−0.344530	−	1.17336i	−0.931497	−	0.363750i	$-0.881496\pi$
$67$	−23.0835	−	78.6152i	−0.344530	−	1.17336i	0.586967	−	0.809611i	$-0.300322\pi$
$68$			92.3312i			1.35781i
$69$	−111.134	+	6.31624i	−1.61064	+	0.0915397i
$70$	−17.2718			−0.246740
$71$	−70.4488	+	20.6856i	−0.992237	+	0.291347i	−0.737267	−	0.675602i	$-0.763884\pi$
$71$	−70.4488	+	20.6856i	−0.992237	+	0.291347i	−0.254970	+	0.966949i	$0.582066\pi$
$72$	−74.6999	−	86.2083i	−1.03750	−	1.19734i
$73$	−62.8153	+	40.3690i	−0.860484	+	0.552999i	−0.894828	−	0.446411i	$-0.852702\pi$
$73$	−62.8153	+	40.3690i	−0.860484	+	0.552999i	0.0343443	+	0.999410i	$0.489066\pi$
$74$	−97.6223	+	14.0360i	−1.31922	+	0.189675i
$75$	−19.7801	−	12.7119i	−0.263734	−	0.169492i
$76$	−37.8225	−	17.2730i	−0.497665	−	0.227276i
$77$	−8.34217	+	9.62738i	−0.108340	+	0.125031i
$78$	31.3780	−	218.239i	0.402282	−	2.79793i
$79$	109.498	−	50.0059i	1.38605	−	0.632986i	0.423947	−	0.905687i	$-0.360644\pi$
$79$	109.498	−	50.0059i	1.38605	−	0.632986i	0.962099	+	0.272702i	$0.0879171\pi$
$80$	0.345882	−	1.17796i	0.00432352	−	0.0147246i
$81$	2.67333	+	0.784960i	0.0330040	+	0.00969086i
$82$	38.0068	+	83.2233i	0.463498	+	1.01492i
$83$	−119.345	−	17.1592i	−1.43789	−	0.206738i	−0.621127	−	0.783710i	$-0.713325\pi$
$83$	−119.345	−	17.1592i	−1.43789	−	0.206738i	−0.816764	+	0.576972i	$0.804234\pi$
$84$	23.0602	+	19.9818i	0.274526	+	0.237879i
$85$	32.5094	−	71.1857i	0.382464	−	0.837479i
$86$	58.5417	−	91.0926i	0.680717	−	1.05922i
$87$	2.02987	+	14.1181i	0.0233318	+	0.162277i
$88$	55.6989	+	86.6692i	0.632942	+	0.984877i
$89$	−25.2210	+	21.8541i	−0.283382	+	0.245552i	−0.784939	−	0.619572i	$-0.787306\pi$
$89$	−25.2210	+	21.8541i	−0.283382	+	0.245552i	0.501558	+	0.865124i	$0.332761\pi$
$90$	71.7656	+	244.411i	0.797396	+	2.71568i
$91$			13.7839i			0.151471i
$92$	12.7402	−	147.731i	0.138481	−	1.60578i
$93$	−41.8146			−0.449620
$94$	−87.7787	+	25.7741i	−0.933816	+	0.274193i
$95$	23.0787	+	26.6343i	0.242934	+	0.280361i
$96$	−131.760	+	84.6768i	−1.37250	+	0.882050i
$97$	118.310	−	17.0104i	1.21969	−	0.175365i	0.497751	−	0.867320i	$-0.334159\pi$
$97$	118.310	−	17.0104i	1.21969	−	0.175365i	0.721941	+	0.691955i	$0.243250\pi$
$98$	130.634	+	83.9536i	1.33300	+	0.856669i
$99$	170.898	+	78.0465i	1.72624	+	0.788348i
$100$	20.5109	−	23.6708i	0.205109	−	0.236708i
$101$	−5.57360	+	38.7653i	−0.0551842	+	0.383815i	0.943448	+	0.331522i	$0.107562\pi$
$101$	−5.57360	+	38.7653i	−0.0551842	+	0.383815i	−0.998632	+	0.0522928i	$0.983347\pi$
$102$	−203.786	+	93.0662i	−1.99791	+	0.912413i
$103$	15.5668	−	53.0155i	0.151134	−	0.514714i	−0.848768	−	0.528766i	$-0.822655\pi$
$103$	15.5668	−	53.0155i	0.151134	−	0.514714i	0.999901	+	0.0140523i	$0.00447312\pi$
$104$	106.960	+	31.4062i	1.02846	+	0.301983i
$105$	−10.7435	−	23.5250i	−0.102319	−	0.224048i
$106$	−261.965	−	37.6648i	−2.47136	−	0.355328i
$107$	28.5114	+	24.7053i	0.266462	+	0.230890i	0.777835	−	0.628468i	$-0.216318\pi$
$107$	28.5114	+	24.7053i	0.266462	+	0.230890i	−0.511374	+	0.859358i	$0.670863\pi$
$108$	70.2890	−	153.911i	0.650824	−	1.42511i
$109$	67.9227	−	105.690i	0.623144	−	0.969631i	−0.375932	−	0.926647i	$-0.622677\pi$
$109$	67.9227	−	105.690i	0.623144	−	0.969631i	0.999076	−	0.0429835i	$-0.0136863\pi$
$110$	−32.7413	−	227.721i	−0.297648	−	2.07019i
$111$	−79.8411	−	124.235i	−0.719289	−	1.11924i
$112$	0.166053	−	0.143886i	0.00148262	−	0.00128470i
$113$	56.6517	+	192.938i	0.501343	+	1.70742i	0.688631	+	0.725112i	$0.258212\pi$
$113$	56.6517	+	192.938i	0.501343	+	1.70742i	−0.187289	+	0.982305i	$0.559970\pi$
$114$		−	100.889i		−	0.884995i
$115$	−61.8381	+	109.412i	−0.537722	+	0.951412i
$116$	−18.9999			−0.163792
$117$	195.054	−	57.2729i	1.66712	−	0.489512i
$118$	188.697	+	217.768i	1.59913	+	1.84549i
$119$	11.7824	−	7.57207i	0.0990116	−	0.0636309i
$120$	−207.028	+	29.7661i	−1.72523	+	0.248051i
$121$	−40.9545	−	26.3199i	−0.338467	−	0.217520i
$122$	−54.3336	−	24.8133i	−0.445357	−	0.203388i
$123$	−89.7127	+	103.534i	−0.729371	+	0.841739i
$124$	7.92706	−	55.1339i	0.0639279	−	0.444628i
$125$	100.114	−	45.7205i	0.800912	−	0.365764i
$126$	−12.8439	+	43.7422i	−0.101935	+	0.347160i
$127$	−74.4291	−	21.8544i	−0.586056	−	0.172082i	−0.0247555	−	0.999694i	$-0.507881\pi$
$127$	−74.4291	−	21.8544i	−0.586056	−	0.172082i	−0.561301	+	0.827612i	$0.689699\pi$
$128$	−85.4639	−	187.140i	−0.667686	−	1.46203i
$129$	160.487	+	23.0745i	1.24408	+	0.178872i
$130$	−188.133	−	163.018i	−1.44718	−	1.25398i
$131$	−8.75733	+	19.1759i	−0.0668499	+	0.146381i	−0.940108	−	0.340878i	$-0.889276\pi$
$131$	−8.75733	+	19.1759i	−0.0668499	+	0.146381i	0.873258	+	0.487259i	$0.162003\pi$
$132$	−219.736	+	341.916i	−1.66467	+	2.59028i
$133$	0.897619	+	6.24308i	0.00674902	+	0.0469404i
$134$	143.175	+	222.785i	1.06847	+	1.66258i
$135$	−108.383	+	93.9145i	−0.802838	+	0.695663i
$136$	−31.9118	−	108.681i	−0.234645	−	0.799128i
$137$		−	169.870i		−	1.23993i	−0.784630	−	0.619965i	$-0.787147\pi$
$137$		−	169.870i		−	1.23993i	0.784630	−	0.619965i	$-0.212853\pi$
$138$	338.903	−	120.788i	2.45582	−	0.875275i
$139$	−31.2547			−0.224854			−0.112427	−	0.993660i	$-0.535862\pi$
$139$	−31.2547			−0.224854			−0.112427	+	0.993660i	$0.535862\pi$
$140$	33.0552	−	9.70587i	0.236108	−	0.0693277i
$141$	−89.7061	−	103.526i	−0.636213	−	0.734229i
$142$	199.643	−	128.303i	1.40594	−	0.903540i
$143$	−181.734	+	26.1294i	−1.27086	+	0.182723i
$144$	−2.72607	−	1.75194i	−0.0189311	−	0.0121663i
$145$	14.6486	+	6.68979i	0.101025	+	0.0461365i
$146$	158.046	−	182.394i	1.08250	−	1.24928i
$147$	−33.0907	+	230.151i	−0.225107	+	1.56565i
$148$	178.944	−	81.7210i	1.20908	−	0.552169i
$149$	−40.7866	+	138.906i	−0.273735	+	0.932257i	0.701792	+	0.712381i	$0.252383\pi$
$149$	−40.7866	+	138.906i	−0.273735	+	0.932257i	−0.975528	+	0.219876i	$0.929435\pi$
$150$	72.9185	+	21.4108i	0.486123	+	0.142739i
$151$	40.3370	+	88.3258i	0.267133	+	0.584939i	0.994898	−	0.100888i	$-0.0321682\pi$
$151$	40.3370	+	88.3258i	0.267133	+	0.584939i	−0.727765	+	0.685826i	$0.759441\pi$
$152$	50.4901	+	7.25938i	0.332172	+	0.0477591i
$153$	−156.108	−	135.268i	−1.02031	−	0.884107i
$154$	17.1044	−	37.4533i	0.111067	−	0.243204i
$155$	−25.5240	+	39.7162i	−0.164671	+	0.256233i
$156$	62.5870	+	435.302i	0.401199	+	2.79040i
$157$	−84.1467	−	130.935i	−0.535966	−	0.833980i	0.462651	−	0.886540i	$-0.346898\pi$
$157$	−84.1467	−	130.935i	−0.535966	−	0.833980i	−0.998618	+	0.0525603i	$0.983262\pi$
$158$	−294.043	+	254.790i	−1.86103	+	1.61260i
$159$	−111.647	−	380.236i	−0.702184	−	2.39142i
$160$			176.835i			1.10522i
$161$	−19.8968	+	10.4897i	−0.123583	+	0.0651531i
$162$	−9.00544			−0.0555891
$163$	31.2644	−	9.18007i	0.191806	−	0.0563194i	−0.184419	−	0.982848i	$-0.559040\pi$
$163$	31.2644	−	9.18007i	0.191806	−	0.0563194i	0.376225	+	0.926528i	$0.377222\pi$
$164$	−119.505	−	137.917i	−0.728691	−	0.840955i
$165$	289.800	−	186.243i	1.75636	−	1.12875i
$166$	385.744	−	55.4616i	2.32376	−	0.334106i
$167$	118.325	+	76.0431i	0.708536	+	0.455348i	0.844632	−	0.535347i	$-0.179819\pi$
$167$	118.325	+	76.0431i	0.708536	+	0.455348i	−0.136096	+	0.990696i	$0.543456\pi$
$168$	−34.0499	−	15.5501i	−0.202678	−	0.0925600i
$169$	−19.4258	+	22.4186i	−0.114946	+	0.132654i
$170$	−35.9975	+	250.368i	−0.211750	+	1.47275i
$171$	84.6153	−	38.6425i	0.494826	−	0.225980i
$172$	−60.8489	+	207.232i	−0.353773	+	1.20484i
$173$	−81.9298	−	24.0568i	−0.473583	−	0.139056i	0.0362271	−	0.999344i	$-0.488466\pi$
$173$	−81.9298	−	24.0568i	−0.473583	−	0.139056i	−0.509810	+	0.860287i	$0.670284\pi$
$174$	−19.1512	−	41.9352i	−0.110064	−	0.241007i
$175$	−4.70272	−	0.676149i	−0.0268727	−	0.00386371i
$176$	2.21185	+	1.91658i	0.0125673	+	0.0108896i
$177$	−179.236	+	392.471i	−1.01263	+	2.21735i
$178$	58.3160	−	90.7414i	0.327618	−	0.509783i
$179$	3.26607	+	22.7160i	0.0182462	+	0.126905i	0.996909	−	0.0785695i	$-0.0250353\pi$
$179$	3.26607	+	22.7160i	0.0182462	+	0.126905i	−0.978662	+	0.205475i	$0.934126\pi$
$180$	−274.693	−	427.431i	−1.52607	−	2.37461i
$181$	125.528	−	108.771i	0.693526	−	0.600943i	−0.235096	−	0.971972i	$-0.575540\pi$
$181$	125.528	−	108.771i	0.693526	−	0.600943i	0.928621	+	0.371029i	$0.120995\pi$
$182$	−12.5517	−	42.7472i	−0.0689654	−	0.234875i
$183$		−	89.4393i		−	0.488739i
$184$	36.0630	+	178.295i	0.195994	+	0.968996i
$185$	−166.736			−0.901277
$186$	129.678	−	38.0768i	0.697191	−	0.204714i
$187$	122.169	+	140.991i	0.653312	+	0.753963i
$188$	153.509	−	98.6542i	0.816536	−	0.524756i
$189$	−25.4050	+	3.65269i	−0.134418	+	0.0193264i
$190$	−95.8262	−	61.5838i	−0.504349	−	0.324125i
$191$	−55.2883	−	25.2493i	−0.289467	−	0.132195i	0.265389	−	0.964141i	$-0.414500\pi$
$191$	−55.2883	−	25.2493i	−0.289467	−	0.132195i	−0.554856	+	0.831946i	$0.687227\pi$
$192$	328.664	−	379.298i	1.71179	−	1.97551i
$193$	0.790541	−	5.49834i	0.00409607	−	0.0284888i	−0.987671	−	0.156544i	$-0.949965\pi$
$193$	0.790541	−	5.49834i	0.00409607	−	0.0284888i	0.991767	+	0.128056i	$0.0408736\pi$
$194$	−351.419	+	160.488i	−1.81144	+	0.827257i
$195$	105.014	−	357.646i	0.538536	−	1.83408i
$196$	−297.188	−	87.2624i	−1.51627	−	0.445216i
$197$	−59.0035	−	129.200i	−0.299510	−	0.655836i	0.698714	−	0.715401i	$-0.253756\pi$
$197$	−59.0035	−	129.200i	−0.299510	−	0.655836i	−0.998224	+	0.0595649i	$0.981029\pi$
$198$	−601.067	−	86.4204i	−3.03569	−	0.436466i
$199$	5.89878	+	5.11132i	0.0296421	+	0.0256850i	0.669556	−	0.742762i	$-0.266484\pi$
$199$	5.89878	+	5.11132i	0.0296421	+	0.0256850i	−0.639914	+	0.768447i	$0.721030\pi$
$200$	−15.9618	+	34.9515i	−0.0798090	+	0.174757i
$201$	−214.385	+	333.589i	−1.06659	+	1.65965i
$202$	−18.0149	−	125.296i	−0.0891825	−	0.620278i
$203$	1.55818	+	2.42458i	0.00767577	+	0.0119437i
$204$	337.712	−	292.629i	1.65545	−	1.43446i
$205$	43.5766	+	148.408i	0.212569	+	0.723944i
$206$			178.589i			0.866939i
$207$	231.110	+	237.972i	1.11647	+	1.14962i
$208$	3.16678			0.0152249
$209$	−80.6104	+	23.6694i	−0.385696	+	0.113251i
$210$	54.7403	+	63.1737i	0.260668	+	0.300827i
$211$	−293.762	+	188.789i	−1.39224	+	0.894736i	−0.999688	−	0.0249949i	$-0.992043\pi$
$211$	−293.762	+	188.789i	−1.39224	+	0.894736i	−0.392549	+	0.919731i	$0.628407\pi$
$212$	522.519	−	75.1268i	2.46471	−	0.354372i
$213$	298.937	+	192.115i	1.40346	+	0.901948i
$214$	−110.918	−	50.6544i	−0.518307	−	0.236703i
$215$	119.879	−	138.348i	0.557576	−	0.643478i
$216$	−29.5407	+	205.460i	−0.136762	+	0.951203i
$217$	−7.68573	+	3.50996i	−0.0354181	+	0.0161749i
$218$	−114.403	+	389.621i	−0.524785	+	1.78725i
$219$	346.737	+	101.811i	1.58328	+	0.464892i
$220$	190.628	+	417.418i	0.866492	+	1.89735i
$221$	199.807	+	28.7279i	0.904105	+	0.129991i
$222$	360.737	+	312.580i	1.62494	+	1.40802i
$223$	159.619	−	349.517i	0.715780	−	1.56734i	−0.103946	−	0.994583i	$-0.533147\pi$
$223$	159.619	−	349.517i	0.715780	−	1.56734i	0.819726	−	0.572757i	$-0.194126\pi$
$224$	−17.1102	+	26.6240i	−0.0763849	+	0.118857i
$225$	9.97203	+	69.3570i	0.0443201	+	0.308253i
$226$	−351.382	−	546.761i	−1.55479	−	2.41930i
$227$	190.299	−	164.895i	0.838322	−	0.726410i	−0.125747	−	0.992062i	$-0.540133\pi$
$227$	190.299	−	164.895i	0.838322	−	0.726410i	0.964069	+	0.265652i	$0.0855873\pi$
$228$	56.6946	+	193.084i	0.248661	+	0.846860i
$229$			201.638i			0.880514i	0.897872	+	0.440257i	$0.145113\pi$
$229$			201.638i			0.880514i	−0.897872	+	0.440257i	$0.854887\pi$
$230$	92.1433	−	395.625i	0.400623	−	1.72011i
$231$	61.6525			0.266894
$232$	22.3645	−	6.56680i	0.0963986	−	0.0283052i
$233$	−217.430	−	250.927i	−0.933174	−	1.07694i	−0.996877	−	0.0789712i	$-0.974836\pi$
$233$	−217.430	−	250.927i	−0.933174	−	1.07694i	0.0637030	−	0.997969i	$-0.479709\pi$
$234$	−552.756	+	355.235i	−2.36221	+	1.51810i
$235$	−153.088	+	22.0108i	−0.651439	+	0.0936628i
$236$	−483.507	−	310.731i	−2.04876	−	1.31666i
$237$	−529.938	−	242.014i	−2.23602	−	1.02116i
$238$	−29.6449	+	34.2120i	−0.124558	+	0.143748i
$239$	38.1832	−	265.570i	0.159762	−	1.11117i	−0.739308	−	0.673368i	$-0.764847\pi$
$239$	38.1832	−	265.570i	0.159762	−	1.11117i	0.899070	−	0.437804i	$-0.144244\pi$
$240$	−5.40476	+	2.46827i	−0.0225198	+	0.0102845i
$241$	−14.2327	+	48.4723i	−0.0590570	+	0.201130i	−0.983737	−	0.179616i	$-0.942514\pi$
$241$	−14.2327	+	48.4723i	−0.0590570	+	0.201130i	0.924680	+	0.380746i	$0.124333\pi$
$242$	150.977	+	44.3309i	0.623873	+	0.183186i
$243$	−103.726	−	227.128i	−0.426855	−	0.934682i
$244$	117.928	+	16.9556i	0.483314	+	0.0694900i
$245$	198.402	+	171.916i	0.809804	+	0.701699i
$246$	183.942	−	402.777i	0.747733	−	1.63731i
$247$	−49.1472	+	76.4746i	−0.198977	+	0.309614i
$248$	9.72472	+	67.6369i	0.0392126	+	0.272730i
$249$	315.483	+	490.902i	1.26700	+	1.97149i
$250$	−268.845	+	232.955i	−1.07538	+	0.931822i
$251$	−7.46870	−	25.4361i	−0.0297558	−	0.101339i	0.943276	−	0.332009i	$-0.107726\pi$
$251$	−7.46870	−	25.4361i	−0.0297558	−	0.101339i	−0.973032	+	0.230670i	$0.925908\pi$
$252$		−	90.9322i		−	0.360842i
$253$	−176.018	−	242.445i	−0.695725	−	0.958282i
$254$	250.724			0.987102
$255$	−363.403	+	106.705i	−1.42511	+	0.418451i
$256$	163.817	+	189.055i	0.639910	+	0.738496i
$257$	350.507	−	225.257i	1.36384	−	0.876486i	0.365320	−	0.930882i	$-0.380960\pi$
$257$	350.507	−	225.257i	1.36384	−	0.876486i	0.998519	+	0.0543958i	$0.0173233\pi$
$258$	−518.721	+	74.5808i	−2.01054	+	0.289073i
$259$	−25.1036	−	16.1331i	−0.0969251	−	0.0622899i
$260$	451.660	+	206.266i	1.73715	+	0.793332i
$261$	27.8355	−	32.1239i	0.106649	−	0.123080i
$262$	9.69694	−	67.4437i	0.0370112	−	0.257419i
$263$	146.205	−	66.7697i	0.555913	−	0.253877i	−0.117589	−	0.993062i	$-0.537517\pi$
$263$	146.205	−	66.7697i	0.555913	−	0.253877i	0.673502	+	0.739185i	$0.264789\pi$
$264$	140.474	−	478.410i	0.532097	−	1.81216i
$265$	−429.304	−	126.055i	−1.62002	−	0.475679i
$266$	−8.46874	−	18.5440i	−0.0318374	−	0.0697141i
$267$	159.868	+	22.9855i	0.598756	+	0.0860881i
$268$	−399.205	−	345.914i	−1.48957	−	1.29072i
$269$	−18.6398	+	40.8155i	−0.0692929	+	0.151730i	−0.941109	−	0.338103i	$-0.890215\pi$
$269$	−18.6398	+	40.8155i	−0.0692929	+	0.151730i	0.871816	+	0.489833i	$0.162942\pi$
$270$	250.603	−	389.947i	0.928161	−	1.44425i
$271$	56.2390	+	391.151i	0.207524	+	1.44336i	0.781201	+	0.624280i	$0.214607\pi$
$271$	56.2390	+	391.151i	0.207524	+	1.44336i	−0.573677	+	0.819082i	$0.694484\pi$
$272$	−1.73965	−	2.70695i	−0.00639577	−	0.00995201i
$273$	50.4161	−	43.6858i	0.184674	−	0.160021i
$274$	154.685	+	526.810i	0.564545	+	1.92266i
$275$		−	63.2848i		−	0.230127i
$276$	−580.723	+	421.613i	−2.10407	+	1.52758i
$277$	−343.340			−1.23949			−0.619747	−	0.784801i	$-0.712765\pi$
$277$	−343.340			−1.23949			−0.619747	+	0.784801i	$0.712765\pi$
$278$	96.9284	−	28.4608i	0.348663	−	0.102377i
$279$	81.6036	+	94.1756i	0.292486	+	0.337547i
$280$	−35.5541	+	22.8492i	−0.126979	+	0.0816044i
$281$	90.3158	−	12.9855i	0.321409	−	0.0462116i	0.0202777	−	0.999794i	$-0.493545\pi$
$281$	90.3158	−	12.9855i	0.321409	−	0.0462116i	0.301131	+	0.953583i	$0.402636\pi$
$282$	372.473	+	239.374i	1.32083	+	0.848843i
$283$	389.627	+	177.937i	1.37677	+	0.628751i	0.959933	−	0.280228i	$-0.0904102\pi$
$283$	389.627	+	177.937i	1.37677	+	0.628751i	0.416840	+	0.908980i	$0.363137\pi$
$284$	−309.981	+	357.737i	−1.09148	+	1.25964i
$285$	24.2736	−	168.826i	0.0851704	−	0.592373i
$286$	539.807	−	246.522i	1.88744	−	0.861964i
$287$	−7.79889	+	26.5606i	−0.0271738	+	0.0925456i
$288$	447.847	+	131.500i	1.55502	+	0.456596i
$289$	34.8487	+	76.3079i	0.120584	+	0.264041i
$290$	−51.5207	−	7.40756i	−0.177658	−	0.0255433i
$291$	−437.183	−	378.821i	−1.50235	−	1.30179i
$292$	−199.975	+	437.883i	−0.684845	+	1.49960i
$293$	−146.965	+	228.682i	−0.501588	+	0.780485i	−0.996058	−	0.0887092i	$-0.971726\pi$
$293$	−146.965	+	228.682i	−0.501588	+	0.780485i	0.494470	+	0.869195i	$0.335362\pi$
$294$	−106.955	−	743.888i	−0.363792	−	2.53023i
$295$	263.368	+	409.809i	0.892773	+	1.38918i
$296$	−182.387	+	158.039i	−0.616173	+	0.533917i
$297$	−96.3179	−	328.029i	−0.324303	−	1.10447i
$298$		−	467.924i		−	1.57021i
$299$	−315.731	−	73.5354i	−1.05596	−	0.245938i
$300$	−151.585			−0.505282
$301$	31.4351	−	9.23018i	0.104436	−	0.0306650i
$302$	−205.525	−	237.189i	−0.680547	−	0.785393i
$303$	159.453	−	102.474i	0.526248	−	0.338199i
$304$	1.43432	−	0.206224i	0.00471815	−	0.000678368i
$305$	−84.9507	−	54.5945i	−0.278527	−	0.178998i
$306$	607.306	+	277.347i	1.98466	+	0.906364i
$307$	−176.795	+	204.032i	−0.575878	+	0.664599i	−0.966713	−	0.255862i	$-0.917641\pi$
$307$	−176.795	+	204.032i	−0.575878	+	0.664599i	0.390835	+	0.920461i	$0.372186\pi$
$308$	−11.6878	+	81.2907i	−0.0379475	+	0.263931i
$309$	−243.247	+	111.087i	−0.787206	+	0.359505i
$310$	42.9905	−	146.412i	0.138679	−	0.472297i
$311$	284.965	+	83.6733i	0.916287	+	0.269046i	0.705685	−	0.708526i	$-0.250639\pi$
$311$	284.965	+	83.6733i	0.916287	+	0.269046i	0.210602	+	0.977572i	$0.432458\pi$
$312$	−224.120	−	490.755i	−0.718334	−	1.57293i
$313$	411.987	+	59.2348i	1.31625	+	0.189249i	0.764427	−	0.644710i	$-0.223022\pi$
$313$	411.987	+	59.2348i	1.31625	+	0.189249i	0.551827	+	0.833959i	$0.313931\pi$
$314$	380.190	+	329.437i	1.21080	+	1.04916i
$315$	−32.0168	+	70.1071i	−0.101641	+	0.222562i
$316$	419.567	−	652.859i	1.32774	−	2.06601i
$317$	−1.41146	−	9.81691i	−0.00445255	−	0.0309682i	0.987474	−	0.157782i	$-0.0504342\pi$
$317$	−1.41146	−	9.81691i	−0.00445255	−	0.0309682i	−0.991927	+	0.126813i	$0.959525\pi$
$318$	692.492	+	1077.54i	2.17765	+	3.38849i
$319$	−29.0131	+	25.1400i	−0.0909503	+	0.0788088i
$320$	−159.644	−	543.697i	−0.498887	−	1.69905i
$321$		−	182.583i		−	0.568795i
$322$	52.1530	−	50.6492i	0.161966	−	0.157296i
$323$	92.3688			0.285972
$324$	17.2348	−	5.06059i	0.0531938	−	0.0156191i
$325$	−44.8425	−	51.7510i	−0.137977	−	0.159234i
$326$	−88.5993	+	56.9393i	−0.271777	+	0.174661i
$327$	−601.843	+	86.5319i	−1.84050	+	0.264624i
$328$	188.335	+	121.035i	0.574191	+	0.369010i
$329$	−25.1785	−	11.4986i	−0.0765304	−	0.0349502i
$330$	−729.147	+	841.480i	−2.20954	+	2.54994i
$331$	−1.55056	+	10.7844i	−0.00468449	+	0.0325813i	−0.992030	−	0.126005i	$-0.959784\pi$
$331$	−1.55056	+	10.7844i	−0.00468449	+	0.0325813i	0.987345	+	0.158586i	$0.0506936\pi$
$332$	−707.078	+	322.911i	−2.12975	+	0.972625i
$333$	−123.990	+	422.271i	−0.372343	+	1.26808i
$334$	−436.202	−	128.080i	−1.30599	−	0.383474i
$335$	185.985	+	407.251i	0.555181	+	1.21568i
$336$	−1.05256	−	0.151335i	−0.00313262	−	0.000450402i
$337$	−266.757	−	231.146i	−0.791564	−	0.685894i	0.162098	−	0.986775i	$-0.448174\pi$
$337$	−266.757	−	231.146i	−0.791564	−	0.685894i	−0.953662	+	0.300881i	$0.902719\pi$
$338$	39.8297	−	87.2149i	0.117839	−	0.258032i
$339$	526.145	−	818.697i	1.55205	−	2.41504i
$340$	−71.8011	−	499.388i	−0.211180	−	1.46879i
$341$	−60.8465	−	94.6790i	−0.178436	−	0.277651i
$342$	−227.225	+	196.891i	−0.664400	+	0.575706i
$343$	26.7372	+	91.0584i	0.0779509	+	0.265476i
$344$		−	264.960i		−	0.770233i
$345$	596.175	−	120.586i	1.72804	−	0.349523i
$346$	275.991			0.797661
$347$	−164.645	+	48.3442i	−0.474482	+	0.139321i	−0.510226	−	0.860040i	$-0.670438\pi$
$347$	−164.645	+	48.3442i	−0.474482	+	0.139321i	0.0357436	+	0.999361i	$0.488620\pi$
$348$	60.2173	+	69.4944i	0.173038	+	0.199697i
$349$	−79.2149	+	50.9083i	−0.226977	+	0.145869i	−0.649187	−	0.760629i	$-0.724891\pi$
$349$	−79.2149	+	50.9083i	−0.226977	+	0.145869i	0.422210	+	0.906498i	$0.361254\pi$
$350$	15.2000	−	2.18543i	0.0434286	−	0.00624409i
$351$	−311.199	−	199.995i	−0.886606	−	0.569787i
$352$	−383.460	−	175.120i	−1.08937	−	0.497501i
$353$	−38.6544	+	44.6096i	−0.109503	+	0.126373i	−0.807855	−	0.589382i	$-0.799371\pi$
$353$	−38.6544	+	44.6096i	−0.109503	+	0.126373i	0.698352	+	0.715754i	$0.253917\pi$
$354$	198.466	−	1380.36i	0.560640	−	3.89933i
$355$	364.947	−	166.666i	1.02802	−	0.469481i
$356$	−60.6143	+	206.433i	−0.170265	+	0.579869i
$357$	−65.0381	−	19.0969i	−0.182180	−	0.0534928i
$358$	−30.8143	−	67.4739i	−0.0860735	−	0.188475i
$359$	−231.145	−	33.2337i	−0.643859	−	0.0925729i	−0.187352	−	0.982293i	$-0.559990\pi$
$359$	−231.145	−	33.2337i	−0.643859	−	0.0925729i	−0.456507	+	0.889720i	$0.650900\pi$
$360$	471.066	+	408.181i	1.30852	+	1.13384i
$361$	132.685	−	290.539i	0.367548	−	0.804818i
$362$	−290.246	+	451.632i	−0.801785	+	1.24760i
$363$	33.5309	+	233.213i	0.0923717	+	0.642459i
$364$	48.0434	+	74.7570i	0.131987	+	0.205376i
$365$	308.354	−	267.190i	0.844804	−	0.732027i
$366$	81.4441	+	277.373i	0.222525	+	0.757851i
$367$			466.001i			1.26976i	0.772612	+	0.634879i	$0.218950\pi$
$367$			466.001i			1.26976i	−0.772612	+	0.634879i	$0.781050\pi$
$368$	2.40995	+	4.57120i	0.00654878	+	0.0124217i
$369$	408.260			1.10640
$370$	517.090	−	151.831i	1.39754	−	0.410355i
$371$	−52.4386	−	60.5174i	−0.141344	−	0.163120i
$372$	−226.782	+	145.744i	−0.609630	+	0.391785i
$373$	−426.128	+	61.2680i	−1.14244	+	0.164257i	−0.687443	−	0.726238i	$-0.741267\pi$
$373$	−426.128	+	61.2680i	−1.14244	+	0.164257i	−0.454992	+	0.890496i	$0.650358\pi$
$374$	−507.265	−	326.000i	−1.35632	−	0.871657i
$375$	−484.524	−	221.275i	−1.29206	−	0.590066i
$376$	−146.595	+	169.180i	−0.389881	+	0.449947i
$377$	−5.91164	+	41.1163i	−0.0156807	+	0.109062i
$378$	75.4611	−	34.4619i	0.199633	−	0.0911691i
$379$	54.7723	−	186.537i	0.144518	−	0.492183i	−0.855138	−	0.518400i	$-0.826528\pi$
$379$	54.7723	−	186.537i	0.144518	−	0.492183i	0.999656	+	0.0262168i	$0.00834604\pi$
$380$	218.001	+	64.0109i	0.573687	+	0.168450i
$381$	155.957	+	341.497i	0.409335	+	0.896318i
$382$	194.455	+	27.9584i	0.509044	+	0.0731895i
$383$	−31.8478	−	27.5963i	−0.0831536	−	0.0720530i	0.612292	−	0.790632i	$-0.290248\pi$
$383$	−31.8478	−	27.5963i	−0.0831536	−	0.0720530i	−0.695446	+	0.718579i	$0.744793\pi$
$384$	−413.621	+	905.704i	−1.07714	+	2.35860i
$385$	37.6332	−	58.5584i	0.0977486	−	0.152100i
$386$	2.55517	+	17.7716i	0.00661960	+	0.0460403i
$387$	−261.230	−	406.482i	−0.675013	−	1.05034i
$388$	582.367	−	504.624i	1.50095	−	1.30058i
$389$	86.1483	+	293.394i	0.221461	+	0.754226i	0.993007	+	0.118053i	$0.0376654\pi$
$389$	86.1483	+	293.394i	0.221461	+	0.754226i	−0.771546	+	0.636173i	$0.780516\pi$
$390$			1204.78i			3.08917i
$391$	110.587	+	310.281i	0.282831	+	0.793558i
$392$	379.975			0.969324
$393$	97.8930	−	28.7440i	0.249092	−	0.0731399i
$394$	300.635	+	346.951i	0.763033	+	0.880587i
$395$	−553.347	+	355.615i	−1.40088	+	0.900291i
$396$	1198.90	−	172.375i	3.02752	−	0.435292i
$397$	111.820	+	71.8621i	0.281662	+	0.181013i	0.673842	−	0.738875i	$-0.264643\pi$
$397$	111.820	+	71.8621i	0.281662	+	0.181013i	−0.392181	+	0.919888i	$0.628279\pi$
$398$	−22.9480	−	10.4800i	−0.0576582	−	0.0263316i
$399$	19.9899	−	23.0696i	0.0501001	−	0.0578186i
$400$	−0.155342	+	1.08043i	−0.000388355	+	0.00270107i
$401$	−434.725	+	198.532i	−1.08410	+	0.495093i	−0.875653	−	0.482940i	$-0.839569\pi$
$401$	−434.725	+	198.532i	−1.08410	+	0.495093i	−0.208449	+	0.978033i	$0.566842\pi$
$402$	361.091	−	1229.76i	0.898236	−	3.05911i
$403$	−116.845	−	34.3087i	−0.289938	−	0.0851333i
$404$	104.887	+	229.671i	0.259622	+	0.568492i
$405$	−15.0695	−	2.16667i	−0.0372087	−	0.00534980i
$406$	−7.04015	−	6.10032i	−0.0173403	−	0.0150254i
$407$	165.120	−	361.561i	0.405699	−	0.888357i
$408$	−296.376	+	461.170i	−0.726411	+	1.13032i
$409$	−50.8160	−	353.433i	−0.124244	−	0.864139i	−0.952663	−	0.304029i	$-0.901668\pi$
$409$	−50.8160	−	353.433i	−0.124244	−	0.864139i	0.828418	−	0.560110i	$-0.189241\pi$
$410$	−270.284	−	420.570i	−0.659229	−	1.02578i
$411$	−621.320	+	538.377i	−1.51173	+	1.30992i
$412$	−100.358	−	341.788i	−0.243587	−	0.829583i
$413$			87.1833i			0.211098i
$414$	−933.429	−	527.558i	−2.25466	−	1.27430i
$415$	658.839			1.58756
$416$	−437.660	+	128.509i	−1.05207	+	0.308915i
$417$	99.0567	+	114.318i	0.237546	+	0.274143i
$418$	228.439	−	146.809i	0.546506	−	0.351218i
$419$	666.662	−	95.8515i	1.59108	−	0.228763i	0.710861	−	0.703333i	$-0.248306\pi$
$419$	666.662	−	95.8515i	1.59108	−	0.228763i	0.880218	+	0.474570i	$0.157396\pi$
$420$	−140.264	−	90.1419i	−0.333961	−	0.214624i
$421$	432.269	+	197.411i	1.02677	+	0.468909i	0.856314	−	0.516456i	$-0.172749\pi$
$421$	432.269	+	197.411i	1.02677	+	0.468909i	0.170455	+	0.985366i	$0.445476\pi$
$422$	739.115	−	852.985i	1.75146	−	2.02129i
$423$	−58.0972	+	404.075i	−0.137346	+	0.955260i
$424$	−589.082	+	269.025i	−1.38934	+	0.634492i
$425$	−19.6026	+	66.7602i	−0.0461237	+	0.157083i
$426$	−1102.02	−	323.582i	−2.58690	−	0.759582i
$427$	−7.50761	−	16.4394i	−0.0175822	−	0.0384997i
$428$	240.742	+	34.6134i	0.562481	+	0.0808725i
$429$	671.547	+	581.899i	1.56538	+	1.35641i
$430$	−245.794	+	538.213i	−0.571613	+	1.25166i
$431$	419.135	−	652.186i	0.972470	−	1.51319i	0.118445	−	0.992961i	$-0.462209\pi$
$431$	419.135	−	652.186i	0.972470	−	1.51319i	0.854025	−	0.520232i	$-0.174155\pi$
$432$	0.839189	+	5.83669i	0.00194257	+	0.0135108i
$433$	−284.450	−	442.613i	−0.656928	−	1.02220i	−0.996659	−	0.0816775i	$-0.973972\pi$
$433$	−284.450	−	442.613i	−0.656928	−	1.02220i	0.339731	−	0.940523i	$-0.389664\pi$
$434$	20.6392	−	17.8839i	0.0475557	−	0.0412072i
$435$	−21.9577	−	74.7812i	−0.0504775	−	0.171911i
$436$		−	809.953i		−	1.85769i
$437$	−147.791	−	12.7454i	−0.338196	−	0.0291657i
$438$	−1168.03			−2.66673
$439$	−406.664	+	119.407i	−0.926341	+	0.271998i	−0.709904	−	0.704298i	$-0.751262\pi$
$439$	−406.664	+	119.407i	−0.926341	+	0.271998i	−0.216437	+	0.976297i	$0.569444\pi$
$440$	−368.654	−	425.449i	−0.837850	−	0.966931i
$441$	582.928	−	374.625i	1.32183	−	0.849490i
$442$	−645.812	+	92.8537i	−1.46111	+	0.210076i
$443$	48.8393	+	31.3871i	0.110247	+	0.0708512i	0.594602	−	0.804020i	$-0.297310\pi$
$443$	48.8393	+	31.3871i	0.110247	+	0.0708512i	−0.484356	+	0.874871i	$0.660946\pi$
$444$	−866.039	−	395.507i	−1.95054	−	0.890781i
$445$	119.417	−	137.814i	0.268352	−	0.309695i
$446$	−176.745	+	1229.29i	−0.396289	+	2.75625i
$447$	637.333	−	291.060i	1.42580	−	0.651141i
$448$	28.5714	−	97.3051i	0.0637754	−	0.217199i
$449$	480.449	+	141.072i	1.07004	+	0.314193i	0.768888	−	0.639383i	$-0.220810\pi$
$449$	480.449	+	141.072i	1.07004	+	0.314193i	0.301153	+	0.953576i	$0.402628\pi$
$450$	−94.0828	−	206.013i	−0.209073	−	0.457806i
$451$	−364.973	−	52.4751i	−0.809252	−	0.116353i
$452$	979.734	+	848.944i	2.16755	+	1.87819i
$453$	195.220	−	427.472i	0.430949	−	0.943647i
$454$	−440.010	+	684.668i	−0.969184	+	1.50808i
$455$	−10.7190	−	74.5521i	−0.0235582	−	0.163851i
$456$	−133.468	−	207.681i	−0.292694	−	0.455441i
$457$	−117.286	+	101.629i	−0.256643	+	0.222383i	−0.773673	−	0.633585i	$-0.781583\pi$
$457$	−117.286	+	101.629i	−0.256643	+	0.222383i	0.517030	+	0.855967i	$0.327037\pi$
$458$	−183.613	−	625.329i	−0.400902	−	1.36535i
$459$			375.877i			0.818905i
$460$	45.9753	+	808.935i	0.0999463	+	1.75856i
$461$	−37.1200			−0.0805207			−0.0402603	−	0.999189i	$-0.512819\pi$
$461$	−37.1200			−0.0805207			−0.0402603	+	0.999189i	$0.512819\pi$
$462$	−191.200	+	56.1413i	−0.413852	+	0.121518i
$463$	−369.627	−	426.572i	−0.798331	−	0.921323i	0.199958	−	0.979804i	$-0.435919\pi$
$463$	−369.627	−	426.572i	−0.798331	−	0.921323i	−0.998288	+	0.0584819i	$0.981374\pi$
$464$	0.557036	−	0.357985i	0.00120051	−	0.000771519i
$465$	226.161	−	32.5170i	0.486367	−	0.0699291i
$466$	902.799	+	580.194i	1.93734	+	1.24505i
$467$	−307.154	−	140.273i	−0.657718	−	0.300370i	0.0584577	−	0.998290i	$-0.481382\pi$
$467$	−307.154	−	140.273i	−0.657718	−	0.300370i	−0.716175	+	0.697920i	$0.754109\pi$
$468$	858.252	−	990.476i	1.83387	−	2.11640i
$469$	−11.4032	+	79.3109i	−0.0243138	+	0.169106i
$470$	454.721	−	207.664i	0.967492	−	0.441839i
$471$	−212.220	+	722.754i	−0.450573	+	1.53451i
$472$	676.523	+	198.645i	1.43331	+	0.420858i
$473$	181.285	+	396.960i	0.383267	+	0.839238i
$474$	1863.85	+	267.981i	3.93217	+	0.565361i
$475$	−23.6804	−	20.5192i	−0.0498535	−	0.0431983i
$476$	37.5096	−	82.1345i	0.0788016	−	0.172552i
$477$	−638.487	+	993.505i	−1.33855	+	2.08282i
$478$	123.415	+	858.369i	0.258190	+	1.79575i
$479$	−110.203	−	171.480i	−0.230070	−	0.357995i	0.706955	−	0.707258i	$-0.250068\pi$
$479$	−110.203	−	171.480i	−0.230070	−	0.357995i	−0.937025	+	0.349263i	$0.886432\pi$
$480$	646.794	−	560.450i	1.34749	−	1.16760i
$481$	−121.170	−	412.666i	−0.251912	−	0.857934i
$482$		−	163.285i		−	0.338765i
$483$	101.427	+	39.5296i	0.209994	+	0.0818418i
$484$	−313.855			−0.648461
$485$	−626.670	+	184.007i	−1.29210	+	0.379396i
$486$	528.504	+	609.926i	1.08746	+	1.25499i
$487$	106.619	−	68.5200i	0.218931	−	0.140698i	−0.426579	−	0.904450i	$-0.640281\pi$
$487$	106.619	−	68.5200i	0.218931	−	0.140698i	0.645510	+	0.763752i	$0.276645\pi$
$488$	−144.672	+	20.8007i	−0.296458	+	0.0426243i
$489$	−132.665	−	85.2586i	−0.271298	−	0.174353i
$490$	−771.842	−	352.489i	−1.57519	−	0.719364i
$491$	−100.797	+	116.326i	−0.205289	+	0.236916i	−0.849053	−	0.528308i	$-0.822827\pi$
$491$	−100.797	+	116.326i	−0.205289	+	0.236916i	0.643764	+	0.765224i	$0.277372\pi$
$492$	−125.692	+	874.210i	−0.255472	+	1.77685i
$493$	38.3936	−	17.5337i	0.0778774	−	0.0355654i
$494$	82.7793	−	281.921i	0.167570	−	0.570689i
$495$	−985.021	−	289.228i	−1.98994	−	0.584299i
$496$	0.806396	+	1.76576i	0.00162580	+	0.00356000i
$497$	71.0723	+	10.2187i	0.143003	+	0.0205607i
$498$	−1425.41	−	1235.13i	−2.86227	−	2.48017i
$499$	112.222	−	245.732i	0.224894	−	0.492448i	−0.763227	−	0.646131i	$-0.776386\pi$
$499$	112.222	−	245.732i	0.224894	−	0.492448i	0.988120	+	0.153683i	$0.0491133\pi$
$500$	383.612	−	596.912i	0.767224	−	1.19382i
$501$	−96.8772	−	673.796i	−0.193368	−	1.34490i
$502$	46.3246	+	72.0825i	0.0922801	+	0.143591i
$503$	−147.693	+	127.977i	−0.293625	+	0.254427i	−0.789198	−	0.614139i	$-0.789504\pi$
$503$	−147.693	+	127.977i	−0.293625	+	0.254427i	0.495573	+	0.868566i	$0.334958\pi$
$504$	31.4282	+	107.035i	0.0623576	+	0.212370i
$505$		−	214.002i		−	0.423767i
$506$	766.649	+	591.599i	1.51512	+	1.16917i
$507$	143.566			0.283167
$508$	−479.841	+	140.894i	−0.944568	+	0.277350i
$509$	−464.703	−	536.296i	−0.912973	−	1.05363i	−0.998358	−	0.0572788i	$-0.981758\pi$
$509$	−464.703	−	536.296i	−0.912973	−	1.05363i	0.0853854	−	0.996348i	$-0.472788\pi$
$510$	1029.84	−	661.837i	2.01929	−	1.29772i
$511$	72.2781	−	10.3920i	0.141444	−	0.0203366i
$512$	12.0962	+	7.77378i	0.0236255	+	0.0151832i
$513$	−153.974	−	70.3176i	−0.300144	−	0.137071i
$514$	−881.887	+	1017.75i	−1.71573	+	1.98006i
$515$	−42.9678	+	298.848i	−0.0834327	+	0.580287i
$516$	950.827	−	434.228i	1.84269	−	0.841528i
$517$	103.874	−	353.764i	0.200918	−	0.684262i
$518$	92.5434	+	27.1732i	0.178655	+	0.0524579i
$519$	171.673	+	375.912i	0.330777	+	0.724300i
$520$	−602.931	−	86.6884i	−1.15948	−	0.166708i
$521$	−58.3153	−	50.5305i	−0.111929	−	0.0969875i	0.597098	−	0.802168i	$-0.296320\pi$
$521$	−58.3153	−	50.5305i	−0.111929	−	0.0969875i	−0.709027	+	0.705181i	$0.750866\pi$
$522$	−57.0725	+	124.971i	−0.109334	+	0.239409i
$523$	−388.831	+	605.032i	−0.743462	+	1.15685i	0.239115	+	0.970991i	$0.423143\pi$
$523$	−388.831	+	605.032i	−0.743462	+	1.15685i	−0.982577	+	0.185858i	$0.940494\pi$
$524$	19.3417	+	134.524i	0.0369116	+	0.256726i
$525$	12.4314	+	19.3437i	0.0236789	+	0.0368451i
$526$	−392.617	+	340.205i	−0.746421	+	0.646777i
$527$	34.8610	+	118.726i	0.0661499	+	0.225286i
$528$		−	14.1644i		−	0.0268265i
$529$	−134.127	−	511.714i	−0.253548	−	0.967323i
$530$	1446.17			2.72861
$531$	1233.72	−	362.252i	2.32339	−	0.682208i
$532$	26.6284	+	30.7308i	0.0500534	+	0.0577647i
$533$	−335.638	+	215.701i	−0.629715	+	0.404693i
$534$	−516.721	+	74.2932i	−0.967642	+	0.139126i
$535$	−173.420	−	111.450i	−0.324150	−	0.208319i
$536$	589.453	+	269.194i	1.09973	+	0.502228i
$537$	72.7352	−	83.9409i	0.135447	−	0.156315i
$538$	20.6397	−	143.552i	0.0383638	−	0.266826i
$539$	−569.273	+	259.978i	−1.05616	+	0.482334i
$540$	−260.480	+	887.114i	−0.482371	+	1.64280i
$541$	846.574	+	248.577i	1.56483	+	0.459476i	0.945492	−	0.325646i	$-0.105582\pi$
$541$	846.574	+	248.577i	1.56483	+	0.459476i	0.619341	+	0.785122i	$0.287400\pi$
$542$	−530.596	−	1161.84i	−0.978960	−	2.14362i
$543$	−795.683	−	114.402i	−1.46535	−	0.210685i
$544$	350.274	+	303.514i	0.643886	+	0.557931i
$545$	−285.181	+	624.459i	−0.523268	+	1.14580i
$546$	−116.572	+	181.390i	−0.213502	+	0.332216i
$547$	−5.41018	−	37.6286i	−0.00989064	−	0.0687909i	0.984278	−	0.176624i	$-0.0565178\pi$
$547$	−5.41018	−	37.6286i	−0.00989064	−	0.0687909i	−0.994169	+	0.107833i	$0.965609\pi$
$548$	−592.080	−	921.294i	−1.08044	−	1.68119i
$549$	−201.437	+	174.546i	−0.366915	+	0.317934i
$550$	57.6277	+	196.262i	0.104778	+	0.356840i
$551$			19.0077i			0.0344966i
$552$	537.840	−	696.984i	0.974348	−	1.26265i
$553$	−117.720			−0.212875
$554$	1064.78	−	312.648i	1.92199	−	0.564347i
$555$	528.444	+	609.857i	0.952152	+	1.09884i
$556$	−169.510	+	108.938i	−0.304874	+	0.195931i
$557$	95.3735	−	13.7126i	0.171227	−	0.0246187i	−0.0561680	−	0.998421i	$-0.517888\pi$
$557$	95.3735	−	13.7126i	0.171227	−	0.0246187i	0.227395	+	0.973803i	$0.426979\pi$
$558$	−338.830	−	217.753i	−0.607222	−	0.390238i
$559$	429.524	+	196.157i	0.768379	+	0.350907i
$560$	−0.786232	+	0.907360i	−0.00140399	+	0.00162029i
$561$	128.494	−	893.698i	0.229045	−	1.59304i
$562$	−268.267	+	122.513i	−0.477344	+	0.217996i
$563$	−167.219	+	569.496i	−0.297015	+	1.01154i	0.666860	+	0.745183i	$0.267638\pi$
$563$	−167.219	+	569.496i	−0.297015	+	1.01154i	−0.963875	+	0.266356i	$0.914180\pi$
$564$	−847.361	−	248.808i	−1.50241	−	0.441148i
$565$	−456.447	−	999.480i	−0.807871	−	1.76899i
$566$	−1370.36	−	197.028i	−2.42113	−	0.348106i
$567$	−2.05920	−	1.78431i	−0.00363175	−	0.00314693i
$568$	241.231	−	528.222i	0.424703	−	0.929969i
$569$	315.775	−	491.356i	0.554966	−	0.863543i	−0.444515	−	0.895771i	$-0.646624\pi$
$569$	315.775	−	491.356i	0.554966	−	0.863543i	0.999481	+	0.0322281i	$0.0102603\pi$
$570$	78.4563	+	545.676i	0.137643	+	0.957326i
$571$	86.1621	+	134.071i	0.150897	+	0.234800i	0.908470	−	0.417950i	$-0.137251\pi$
$571$	86.1621	+	134.071i	0.150897	+	0.234800i	−0.757573	+	0.652750i	$0.773615\pi$
$572$	−894.562	+	775.142i	−1.56392	+	1.35514i
$573$	82.8752	+	282.247i	0.144634	+	0.492578i
$574$		−	89.4727i		−	0.155876i
$575$	40.5762	−	104.112i	0.0705674	−	0.181065i
$576$	−1495.67			−2.59664
$577$	946.244	−	277.842i	1.63994	−	0.481529i	0.673662	−	0.739040i	$-0.264720\pi$
$577$	946.244	−	277.842i	1.63994	−	0.481529i	0.966275	+	0.257511i	$0.0829022\pi$
$578$	−177.561	−	204.916i	−0.307199	−	0.354526i
$579$	−22.6163	+	14.5346i	−0.0390610	+	0.0251030i
$580$	102.764	−	14.7752i	0.177179	−	0.0254745i
$581$	99.1940	+	63.7481i	0.170730	+	0.109721i
$582$	1700.77	+	776.716i	2.92229	+	1.33456i
$583$	698.488	−	806.098i	1.19809	−	1.38267i
$584$	84.0442	−	584.540i	0.143911	−	1.00093i
$585$	−1010.44	+	461.452i	−1.72725	+	0.788807i
$586$	247.535	−	843.028i	0.422415	−	1.43861i
$587$	−410.642	−	120.575i	−0.699561	−	0.205410i	−0.0874353	−	0.996170i	$-0.527867\pi$
$587$	−410.642	−	120.575i	−0.699561	−	0.205410i	−0.612126	+	0.790761i	$0.709685\pi$
$588$	622.719	+	1363.57i	1.05905	+	2.31899i
$589$	−55.1564	−	7.93029i	−0.0936441	−	0.0134640i
$590$	−1189.94	−	1031.09i	−2.01686	−	1.74761i
$591$	−285.561	+	625.290i	−0.483182	+	1.05802i
$592$	−3.70651	+	5.76743i	−0.00626099	+	0.00974229i
$593$	57.8337	+	402.242i	0.0975273	+	0.678317i	0.978666	+	0.205459i	$0.0658687\pi$
$593$	57.8337	+	402.242i	0.0975273	+	0.678317i	−0.881138	+	0.472858i	$0.843222\pi$
$594$	597.412	+	929.591i	1.00574	+	1.56497i
$595$	−57.8384	+	50.1173i	−0.0972074	+	0.0842307i
$596$	262.949	+	895.522i	0.441189	+	1.50255i
$597$		−	37.7750i		−	0.0632747i
$598$	1046.12	−	59.4556i	1.74937	−	0.0994241i
$599$	194.807			0.325220			0.162610	−	0.986690i	$-0.448009\pi$
$599$	194.807			0.325220			0.162610	+	0.986690i	$0.448009\pi$
$600$	178.428	−	52.3911i	0.297379	−	0.0873184i
$601$	654.528	+	755.365i	1.08906	+	1.25685i	0.964343	+	0.264656i	$0.0852583\pi$
$601$	654.528	+	755.365i	1.08906	+	1.25685i	0.124721	+	0.992192i	$0.460196\pi$
$602$	−89.0829	+	57.2501i	−0.147978	+	0.0950999i
$603$	1169.70	−	168.177i	1.93980	−	0.278901i
$604$	526.626	+	338.442i	0.871898	+	0.560335i
$605$	241.976	+	110.507i	0.399961	+	0.182656i
$606$	−401.190	+	462.998i	−0.662029	+	0.764023i
$607$	152.687	−	1061.96i	0.251544	−	1.74953i	−0.337409	−	0.941358i	$-0.609550\pi$
$607$	152.687	−	1061.96i	0.251544	−	1.74953i	0.588953	−	0.808168i	$-0.299540\pi$
$608$	−189.859	+	86.7058i	−0.312268	+	0.142608i
$609$	3.92976	−	13.3835i	0.00645281	−	0.0219763i
$610$	313.167	+	91.9543i	0.513389	+	0.150745i
$611$	−165.727	−	362.892i	−0.271240	−	0.593932i
$612$	−1318.13	−	189.518i	−2.15381	−	0.309671i
$613$	636.423	+	551.464i	1.03821	+	0.899615i	0.995042	−	0.0994527i	$-0.0317092\pi$
$613$	636.423	+	551.464i	1.03821	+	0.899615i	0.0431688	+	0.999068i	$0.486255\pi$
$614$	362.491	−	793.744i	0.590376	−	1.29274i
$615$	404.712	−	629.744i	0.658068	−	1.02397i
$616$	−14.3384	−	99.7254i	−0.0232765	−	0.161892i
$617$	628.913	+	978.608i	1.01931	+	1.58607i	0.790366	+	0.612635i	$0.209890\pi$
$617$	628.913	+	978.608i	1.01931	+	1.58607i	0.228943	+	0.973440i	$0.426473\pi$
$618$	653.212	−	566.011i	1.05698	−	0.915876i
$619$	−48.1634	−	164.030i	−0.0778084	−	0.264991i	0.911397	−	0.411529i	$-0.135005\pi$
$619$	−48.1634	−	164.030i	−0.0778084	−	0.264991i	−0.989205	+	0.146538i	$0.953187\pi$
$620$			304.365i			0.490911i
$621$	51.8651	−	601.409i	0.0835187	−	0.968453i
$622$	−959.941			−1.54331
$623$	31.3139	−	9.19459i	0.0502631	−	0.0147586i
$624$	−10.0366	−	11.5829i	−0.0160843	−	0.0185623i
$625$	−608.103	+	390.804i	−0.972965	+	0.625287i
$626$	−1331.61	+	191.457i	−2.12718	+	0.305842i
$627$	342.056	+	219.826i	0.545543	+	0.350599i
$628$	−912.742	−	416.835i	−1.45341	−	0.663751i
$629$	−286.181	+	330.271i	−0.454978	+	0.525073i
$630$	35.4520	−	246.574i	0.0562730	−	0.391388i
$631$	−554.063	+	253.032i	−0.878071	+	0.401002i	−0.802861	−	0.596166i	$-0.796690\pi$
$631$	−554.063	+	253.032i	−0.878071	+	0.401002i	−0.0752099	+	0.997168i	$0.523963\pi$
$632$	−268.222	+	913.481i	−0.424402	+	1.44538i
$633$	1621.55	+	476.130i	2.56169	+	0.752181i
$634$	13.3166	+	29.1594i	0.0210042	+	0.0459927i
$635$	419.556	+	60.3231i	0.660719	+	0.0949970i
$636$	−1930.83	−	1673.07i	−3.03589	−	2.63061i
$637$	−281.305	+	615.972i	−0.441609	+	0.966990i
$638$	67.0842	−	104.385i	0.105148	−	0.163613i
$639$	−150.707	−	1048.19i	−0.235849	−	1.64036i
$640$	607.773	+	945.713i	0.949645	+	1.47768i
$641$	48.5119	−	42.0358i	0.0756816	−	0.0655785i	−0.616199	−	0.787591i	$-0.711328\pi$
$641$	48.5119	−	42.0358i	0.0756816	−	0.0655785i	0.691880	+	0.722012i	$0.256783\pi$
$642$	166.262	+	566.236i	0.258975	+	0.881987i
$643$			761.478i			1.18426i	0.805843	+	0.592129i	$0.201712\pi$
$643$			761.478i			1.18426i	−0.805843	+	0.592129i	$0.798288\pi$
$644$	−71.3492	+	126.241i	−0.110791	+	0.196026i
$645$	−885.960			−1.37358
$646$	−286.459	+	84.1118i	−0.443434	+	0.130204i
$647$	409.930	+	473.085i	0.633586	+	0.731197i	0.978227	−	0.207537i	$-0.0665448\pi$
$647$	409.930	+	473.085i	0.633586	+	0.731197i	−0.344641	+	0.938735i	$0.611999\pi$
$648$	−18.5377	+	11.9135i	−0.0286076	+	0.0183850i
$649$	−1149.47	+	165.269i	−1.77114	+	0.254651i
$650$	186.192	+	119.659i	0.286450	+	0.184090i
$651$	37.1968	+	16.9872i	0.0571379	+	0.0260940i
$652$	137.566	−	158.760i	0.210991	−	0.243497i
$653$	−18.2619	+	127.014i	−0.0279661	+	0.194509i	−0.999015	−	0.0443719i	$-0.985871\pi$
$653$	−18.2619	+	127.014i	−0.0279661	+	0.194509i	0.971049	+	0.238881i	$0.0767804\pi$
$654$	1787.67	−	816.400i	2.73344	−	1.24832i
$655$	32.4533	−	110.526i	0.0495470	−	0.168742i
$656$	6.10217	+	1.79176i	0.00930209	+	0.00273134i
$657$	−447.377	−	979.618i	−0.680939	−	1.49105i
$658$	88.5555	+	12.7324i	0.134583	+	0.0193501i
$659$	−14.9685	−	12.9703i	−0.0227140	−	0.0196818i	0.643430	−	0.765505i	$-0.277511\pi$
$659$	−14.9685	−	12.9703i	−0.0227140	−	0.0196818i	−0.666144	+	0.745823i	$0.732056\pi$
$660$	922.587	−	2020.18i	1.39786	−	3.06089i
$661$	−210.035	+	326.820i	−0.317753	+	0.494433i	−0.962986	−	0.269553i	$-0.913124\pi$
$661$	−210.035	+	326.820i	−0.317753	+	0.494433i	0.645233	+	0.763986i	$0.276760\pi$
$662$	−5.01169	−	34.8571i	−0.00757053	−	0.0526542i
$663$	−528.182	−	821.867i	−0.796654	−	1.23962i
$664$	720.683	−	624.475i	1.08537	−	0.940475i
$665$	−9.70982	−	33.0686i	−0.0146012	−	0.0497272i
$666$		−	1422.47i		−	2.13585i
$667$	−63.8496	+	22.7566i	−0.0957266	+	0.0341178i
$668$	906.787			1.35747
$669$	−1784.29	+	523.913i	−2.66709	+	0.783129i
$670$	−947.634	−	1093.63i	−1.41438	−	1.63228i
$671$	202.513	−	130.147i	0.301808	−	0.193960i
$672$	151.609	−	21.7980i	0.225608	−	0.0324375i
$673$	−1033.54	−	664.218i	−1.53573	−	0.986951i	−0.988712	−	0.149827i	$-0.952128\pi$
$673$	−1033.54	−	664.218i	−1.53573	−	0.986951i	−0.547013	−	0.837124i	$-0.684235\pi$
$674$	1037.76	+	473.930i	1.53971	+	0.703161i
$675$	83.4990	−	96.3630i	0.123702	−	0.142760i
$676$	−27.2166	+	189.296i	−0.0402613	+	0.280023i
$677$	541.466	−	247.279i	0.799802	−	0.365257i	0.0267838	−	0.999641i	$-0.491473\pi$
$677$	541.466	−	247.279i	0.799802	−	0.365257i	0.773018	+	0.634384i	$0.218746\pi$
$678$	−886.193	+	3018.09i	−1.30707	+	4.45147i
$679$	−112.155	−	32.9316i	−0.165177	−	0.0485002i
$680$	257.115	+	563.004i	0.378111	+	0.827947i
$681$	−1206.25	−	173.432i	−1.77129	−	0.254672i
$682$	274.916	+	238.216i	0.403102	+	0.349290i
$683$	384.043	−	840.938i	0.562289	−	1.23124i	−0.388514	−	0.921443i	$-0.627011\pi$
$683$	384.043	−	840.938i	0.562289	−	1.23124i	0.950802	−	0.309798i	$-0.100261\pi$
$684$	324.224	−	504.503i	0.474012	−	0.737578i
$685$	132.099	+	918.769i	0.192845	+	1.34127i
$686$	−165.837	−	258.048i	−0.241745	−	0.376163i
$687$	737.514	−	639.059i	1.07353	−	0.930217i
$688$	−2.12059	−	7.22207i	−0.00308225	−	0.0104972i
$689$		−	1154.12i		−	1.67506i
$690$	−1739.08	+	916.847i	−2.52040	+	1.32876i
$691$	−304.936			−0.441296			−0.220648	−	0.975353i	$-0.570817\pi$
$691$	−304.936			−0.441296			−0.220648	+	0.975353i	$0.570817\pi$
$692$	−528.197	+	155.093i	−0.763290	+	0.224122i
$693$	−120.318	−	138.855i	−0.173619	−	0.200367i
$694$	466.583	−	299.855i	0.672310	−	0.432068i
$695$	169.046	−	24.3051i	0.243231	−	0.0349713i
$696$	−94.8995	−	60.9882i	−0.136350	−	0.0876267i
$697$	368.761	+	168.407i	0.529069	+	0.241618i
$698$	199.307	−	230.013i	0.285541	−	0.329532i
$699$	−228.686	+	1590.55i	−0.327162	+	2.27546i
$700$	−27.8620	+	12.7241i	−0.0398028	+	0.0181773i
$701$	281.867	−	959.952i	0.402093	−	1.36940i	−0.471122	−	0.882068i	$-0.656151\pi$
$701$	281.867	−	959.952i	0.402093	−	1.36940i	0.873215	−	0.487335i	$-0.162031\pi$
$702$	1147.22	+	336.855i	1.63422	+	0.479850i
$703$	−81.7543	−	179.017i	−0.116293	−	0.254647i
$704$	1337.08	+	192.243i	1.89926	+	0.273073i
$705$	565.696	+	490.178i	0.802405	+	0.695288i
$706$	79.2550	−	173.544i	0.112259	−	0.245814i
$707$	20.7065	−	32.2199i	0.0292878	−	0.0455727i
$708$	395.864	+	2753.30i	0.559130	+	3.88884i
$709$	244.971	+	381.182i	0.345516	+	0.537634i	0.969906	−	0.243479i	$-0.0782888\pi$
$709$	244.971	+	381.182i	0.345516	+	0.537634i	−0.624390	+	0.781113i	$0.714652\pi$
$710$	−980.024	+	849.196i	−1.38032	+	1.19605i
$711$	489.134	+	1665.84i	0.687953	+	2.34295i
$712$		−	263.939i		−	0.370700i
$713$	−39.3959	−	194.773i	−0.0552537	−	0.273174i
$714$	219.089			0.306848
$715$	962.615	−	282.649i	1.34631	−	0.395314i
$716$	96.8899	+	111.817i	0.135321	+	0.156169i
$717$	−1092.37	+	702.023i	−1.52353	+	0.979112i
$718$	747.102	−	107.417i	1.04053	−	0.149606i
$719$	127.002	+	81.6191i	0.176637	+	0.113518i	0.625972	−	0.779846i	$-0.284703\pi$
$719$	127.002	+	81.6191i	0.176637	+	0.113518i	−0.449335	+	0.893363i	$0.648339\pi$
$720$	16.1068	+	7.35572i	0.0223705	+	0.0102163i
$721$	−35.3852	+	40.8367i	−0.0490779	+	0.0566389i
$722$	−146.921	+	1021.86i	−0.203492	+	1.41532i
$723$	222.401	−	101.567i	0.307609	−	0.140480i
$724$	301.685	−	1027.45i	0.416692	−	1.41912i
$725$	−13.7379	−	4.03381i	−0.0189488	−	0.00556388i
$726$	−316.353	−	692.717i	−0.435748	−	0.954155i
$727$	652.318	+	93.7892i	0.897274	+	0.129009i	0.575494	−	0.817806i	$-0.304810\pi$
$727$	652.318	+	93.7892i	0.897274	+	0.129009i	0.321780	+	0.946814i	$0.395719\pi$
$728$	−82.3887	−	71.3902i	−0.113171	−	0.0980635i
$729$	−491.587	+	1076.43i	−0.674331	+	1.47658i
$730$	−712.975	+	1109.41i	−0.976679	+	1.51974i
$731$	−68.2821	−	474.912i	−0.0934091	−	0.649675i
$732$	−311.739	−	485.075i	−0.425873	−	0.662671i
$733$	1047.40	−	907.578i	1.42892	−	1.23817i	0.500975	−	0.865462i	$-0.332975\pi$
$733$	1047.40	−	907.578i	1.42892	−	1.23817i	0.927949	−	0.372707i	$-0.121570\pi$
$734$	−424.345	−	1445.18i	−0.578126	−	1.96892i
$735$		−	1270.54i		−	1.72863i
$736$	−518.564	−	533.960i	−0.704570	−	0.725489i
$737$	−1067.29			−1.44816
$738$	−1266.12	+	371.765i	−1.71560	+	0.503747i
$739$	−679.026	−	783.638i	−0.918845	−	1.06040i	−0.997979	−	0.0635395i	$-0.979761\pi$
$739$	−679.026	−	783.638i	−0.918845	−	1.06040i	0.0791345	−	0.996864i	$-0.474784\pi$
$740$	−904.296	+	581.156i	−1.22202	+	0.785346i
$741$	435.479	−	62.6124i	0.587691	−	0.0844972i
$742$	217.733	+	139.928i	0.293440	+	0.188583i
$743$	207.514	+	94.7685i	0.279292	+	0.127548i	0.550137	−	0.835075i	$-0.314576\pi$
$743$	207.514	+	94.7685i	0.279292	+	0.127548i	−0.270844	+	0.962623i	$0.587303\pi$
$744$	216.569	−	249.934i	0.291087	−	0.335933i
$745$	112.580	−	783.014i	0.151115	−	1.05103i
$746$	1265.74	−	578.043i	1.69670	−	0.774857i
$747$	489.933	−	1668.56i	0.655868	−	2.23368i
$748$	1154.01	+	338.848i	1.54279	+	0.453005i
$749$	−15.3262	−	33.5597i	−0.0204622	−	0.0448060i
$750$	1704.12	+	245.016i	2.27216	+	0.326688i
$751$	−96.3917	−	83.5239i	−0.128351	−	0.111217i	0.588320	−	0.808628i	$-0.299790\pi$
$751$	−96.3917	−	83.5239i	−0.128351	−	0.111217i	−0.716671	+	0.697411i	$0.754335\pi$
$752$	−2.64176	+	5.78464i	−0.00351298	+	0.00769234i
$753$	−69.3645	+	107.933i	−0.0921175	+	0.143338i
$754$	−19.1074	−	132.895i	−0.0253414	−	0.176253i
$755$	−286.855	−	446.355i	−0.379941	−	0.591199i
$756$	−125.053	+	108.359i	−0.165414	+	0.143332i
$757$	319.858	+	1089.34i	0.422534	+	1.43902i	0.846037	+	0.533124i	$0.178982\pi$
$757$	319.858	+	1089.34i	0.422534	+	1.43902i	−0.423504	+	0.905894i	$0.639200\pi$
$758$			628.375i			0.828991i
$759$	−328.909	+	1412.20i	−0.433345	+	1.86061i
$760$	−278.729			−0.366748
$761$	1454.43	−	427.059i	1.91121	−	0.561181i	0.930264	−	0.366890i	$-0.119577\pi$
$761$	1454.43	−	427.059i	1.91121	−	0.561181i	0.980944	−	0.194291i	$-0.0622407\pi$
$762$	−794.630	−	917.052i	−1.04282	−	1.20348i
$763$	−103.358	+	66.4242i	−0.135463	+	0.0870566i
$764$	−387.863	+	55.7662i	−0.507674	+	0.0729925i
$765$	949.525	+	610.222i	1.24121	+	0.797676i
$766$	123.898	+	56.5821i	0.161746	+	0.0738670i
$767$	−822.868	+	949.641i	−1.07284	+	1.23812i
$768$	172.298	−	1198.36i	0.224347	−	1.56036i
$769$	−1027.18	+	469.099i	−1.33574	+	0.610012i	−0.949900	−	0.312554i	$-0.898816\pi$
$769$	−1027.18	+	469.099i	−1.33574	+	0.610012i	−0.385840	+	0.922566i	$0.626088\pi$
$770$	−63.3861	+	215.873i	−0.0823196	+	0.280355i
$771$	−1934.78	−	568.103i	−2.50944	−	0.736839i
$772$	−14.8768	−	32.5757i	−0.0192705	−	0.0421965i
$773$	−850.070	−	122.222i	−1.09970	−	0.158113i	−0.431514	−	0.902106i	$-0.642021\pi$
$773$	−850.070	−	122.222i	−1.09970	−	0.158113i	−0.668188	+	0.743993i	$0.732930\pi$
$774$	1180.28	+	1022.72i	1.52492	+	1.32135i
$775$	17.4370	−	38.1817i	0.0224993	−	0.0492666i
$776$	−511.085	+	795.263i	−0.658614	+	1.02482i
$777$	20.5532	+	142.951i	0.0264520	+	0.183978i
$778$	−534.334	−	831.440i	−0.686805	−	1.06869i
$779$	−137.973	+	119.554i	−0.177115	+	0.153471i
$780$	−677.023	−	2305.73i	−0.867978	−	2.95606i
$781$			956.425i			1.22462i
$782$	−625.502	−	861.557i	−0.799875	−	1.10174i
$783$	−77.3480			−0.0987842
$784$	10.3570	−	3.04110i	0.0132105	−	0.00387896i
$785$	556.942	+	642.745i	0.709480	+	0.818783i
$786$	−277.416	+	178.284i	−0.352947	+	0.226825i
$787$	287.889	−	41.3921i	0.365805	−	0.0525948i	0.0430384	−	0.999073i	$-0.486296\pi$
$787$	287.889	−	41.3921i	0.365805	−	0.0525948i	0.322767	+	0.946479i	$0.395387\pi$
$788$	−770.330	−	495.061i	−0.977576	−	0.628250i
$789$	−707.592	−	323.146i	−0.896821	−	0.409565i
$790$	1392.24	−	1606.73i	1.76233	−	2.03384i
$791$	27.9858	−	194.645i	0.0353803	−	0.246075i
$792$	−1351.62	+	617.266i	−1.70660	+	0.779376i
$793$	73.3845	−	249.925i	0.0925404	−	0.315164i
$794$	−412.219	−	121.038i	−0.519167	−	0.152441i
$795$	899.551	+	1969.74i	1.13151	+	2.47766i
$796$	49.8075	+	7.16124i	0.0625722	+	0.00899653i
$797$	−693.547	−	600.962i	−0.870197	−	0.754030i	0.100348	−	0.994952i	$-0.468004\pi$
$797$	−693.547	−	600.962i	−0.870197	−	0.754030i	−0.970544	+	0.240923i	$0.922550\pi$
$798$	−40.9863	+	89.7475i	−0.0513613	+	0.112466i
$799$	−219.157	+	341.016i	−0.274290	+	0.426803i
$800$	−22.3752	−	155.623i	−0.0279690	−	0.194528i
$801$	−260.223	−	404.915i	−0.324872	−	0.505511i
$802$	1167.40	−	1011.56i	1.45562	−	1.26130i
$803$	274.028	+	933.253i	0.341255	+	1.16221i
$804$			2556.46i			3.17968i
$805$	99.4577	−	72.2076i	0.123550	−	0.0896989i
$806$	393.607			0.488346
$807$	208.363	−	61.1810i	0.258195	−	0.0758128i
$808$	−202.840	−	234.090i	−0.251040	−	0.289715i
$809$	749.248	−	481.513i	0.926141	−	0.595195i	0.0117080	−	0.999931i	$-0.496273\pi$
$809$	749.248	−	481.513i	0.926141	−	0.595195i	0.914433	+	0.404737i	$0.132637\pi$
$810$	48.7073	−	7.00305i	0.0601325	−	0.00864574i
$811$	−1223.15	−	786.069i	−1.50820	−	0.969259i	−0.993737	−	0.111745i	$-0.964356\pi$
$811$	−1223.15	−	786.069i	−1.50820	−	0.969259i	−0.514460	−	0.857514i	$-0.672008\pi$
$812$	16.9016	+	7.71872i	0.0208148	+	0.00950581i
$813$	1252.44	−	1445.39i	1.54052	−	1.77785i
$814$	−182.836	+	1271.65i	−0.224614	+	1.56222i
$815$	−161.960	+	73.9645i	−0.198724	+	0.0907540i
$816$	−4.38743	+	14.9422i	−0.00537675	+	0.0183115i
$817$	207.317	+	60.8736i	0.253753	+	0.0745087i
$818$	479.432	+	1049.81i	0.586103	+	1.28339i
$819$	−196.780	−	28.2926i	−0.240268	−	0.0345454i
$820$	753.613	+	653.010i	0.919041	+	0.796353i
$821$	125.587	−	274.997i	0.152968	−	0.334954i	−0.817597	−	0.575790i	$-0.804694\pi$
$821$	125.587	−	274.997i	0.152968	−	0.334954i	0.970566	+	0.240836i	$0.0774217\pi$
$822$	1436.62	−	2235.42i	1.74771	−	2.71949i
$823$	65.2056	+	453.515i	0.0792292	+	0.551051i	0.990315	+	0.138835i	$0.0443359\pi$
$823$	65.2056	+	453.515i	0.0792292	+	0.551051i	−0.911086	+	0.412216i	$0.864755\pi$
$824$	236.259	+	367.627i	0.286722	+	0.446149i
$825$	−231.472	+	200.571i	−0.280572	+	0.243117i
$826$	−79.3898	−	270.377i	−0.0961136	−	0.327333i
$827$		−	217.299i		−	0.262756i	−0.991332	−	0.131378i	$-0.958060\pi$
$827$		−	217.299i		−	0.262756i	0.991332	−	0.131378i	$-0.0419402\pi$
$828$	2082.88	+	485.113i	2.51555	+	0.585885i
$829$	1359.45			1.63987			0.819935	−	0.572456i	$-0.194009\pi$
$829$	1359.45			1.63987			0.819935	+	0.572456i	$0.194009\pi$
$830$	−2043.22	+	599.945i	−2.46172	+	0.722825i
$831$	1088.16	+	1255.81i	1.30946	+	1.51120i
$832$	1229.61	−	790.225i	1.47790	−	0.949790i
$833$	681.063	−	97.9221i	0.817603	−	0.117554i
$834$	−411.298	−	264.325i	−0.493163	−	0.316937i
$835$	−699.116	−	319.276i	−0.837265	−	0.382366i
$836$	−354.693	+	409.337i	−0.424274	+	0.489638i
$837$	32.2708	−	224.448i	0.0385553	−	0.268158i
$838$	−1980.20	+	904.327i	−2.36301	+	1.07915i
$839$	−315.093	+	1073.11i	−0.375558	+	1.27903i	0.527515	+	0.849545i	$0.323124\pi$
$839$	−315.093	+	1073.11i	−0.375558	+	1.27903i	−0.903073	+	0.429487i	$0.858694\pi$
$840$	196.257	+	57.6262i	0.233639	+	0.0686026i
$841$	−345.756	−	757.100i	−0.411125	−	0.900238i
$842$	−1520.34	−	218.592i	−1.80563	−	0.259610i
$843$	−333.738	−	289.185i	−0.395893	−	0.343043i
$844$	−935.201	+	2047.80i	−1.10806	+	2.42631i
$845$	87.6337	−	136.361i	0.103709	−	0.161374i
$846$	−187.780	−	1306.04i	−0.221962	−	1.54378i
$847$	25.7392	+	40.0510i	0.0303887	+	0.0472857i
$848$	−13.9036	+	12.0475i	−0.0163957	+	0.0142070i
$849$	−584.037	−	1989.05i	−0.687912	−	2.34281i
$850$		−	224.890i		−	0.264577i
$851$	503.467	−	488.950i	0.591618	−	0.574559i
$852$	2290.90			2.68885
$853$	179.937	−	52.8341i	0.210945	−	0.0619392i	−0.174552	−	0.984648i	$-0.555848\pi$
$853$	179.937	−	52.8341i	0.210945	−	0.0619392i	0.385498	+	0.922709i	$0.374030\pi$
$854$	38.2528	+	44.1460i	0.0447925	+	0.0516933i
$855$	−427.604	+	274.805i	−0.500122	+	0.321409i
$856$	−295.336	+	42.4629i	−0.345019	+	0.0496062i
$857$	299.616	+	192.551i	0.349610	+	0.224681i	0.703645	−	0.710551i	$-0.251554\pi$
$857$	299.616	+	192.551i	0.349610	+	0.224681i	−0.354036	+	0.935232i	$0.615191\pi$
$858$	−2612.52	−	1193.10i	−3.04489	−	1.39056i
$859$	−677.411	+	781.774i	−0.788604	+	0.910098i	−0.997699	−	0.0677973i	$-0.978403\pi$
$859$	−677.411	+	781.774i	−0.788604	+	0.910098i	0.209095	+	0.977895i	$0.432948\pi$
$860$	167.957	−	1168.17i	0.195299	−	1.35833i
$861$	121.866	−	55.6542i	0.141540	−	0.0646391i
$862$	−705.954	+	2404.26i	−0.818972	+	2.78916i
$863$	−1107.41	−	325.164i	−1.28321	−	0.376784i	−0.432124	−	0.901814i	$-0.642236\pi$
$863$	−1107.41	−	325.164i	−1.28321	−	0.376784i	−0.851083	+	0.525031i	$0.824054\pi$
$864$	−352.833	−	772.596i	−0.408371	−	0.894208i
$865$	461.837	+	66.4022i	0.533916	+	0.0767656i
$866$	1285.20	+	1113.63i	1.48406	+	1.28595i
$867$	168.658	−	369.309i	0.194530	−	0.425962i
$868$	−29.4498	+	45.8248i	−0.0339283	+	0.0527935i
$869$	−223.156	−	1552.08i	−0.256796	−	1.78605i
$870$	136.193	+	211.920i	0.156543	+	0.243586i
$871$	−872.775	+	756.264i	−1.00204	+	0.868270i
$872$	279.938	+	953.382i	0.321030	+	1.09333i
$873$			1723.92i			1.97471i
$874$	469.944	−	95.0535i	0.537694	−	0.108757i
$875$	−107.632			−0.123008
$876$	2235.40	−	656.372i	2.55182	−	0.749283i
$877$	451.316	+	520.847i	0.514614	+	0.593896i	0.952274	−	0.305244i	$-0.0987382\pi$
$877$	451.316	+	520.847i	0.514614	+	0.593896i	−0.437660	+	0.899140i	$0.644193\pi$
$878$	1152.43	−	740.623i	1.31256	−	0.843534i
$879$	1302.21	−	187.230i	1.48147	−	0.213004i
$880$	−13.4535	−	8.64606i	−0.0152881	−	0.00982507i
$881$	166.371	+	75.9791i	0.188843	+	0.0862419i	0.507593	−	0.861597i	$-0.330536\pi$
$881$	166.371	+	75.9791i	0.188843	+	0.0862419i	−0.318749	+	0.947839i	$0.603263\pi$
$882$	−1466.67	+	1692.63i	−1.66289	+	1.91908i
$883$	113.499	−	789.400i	0.128537	−	0.893997i	−0.818873	−	0.573975i	$-0.805401\pi$
$883$	113.499	−	789.400i	0.128537	−	0.893997i	0.947410	−	0.320022i	$-0.103690\pi$
$884$	1183.79	−	540.618i	1.33913	−	0.611559i
$885$	664.219	−	2262.12i	0.750530	−	2.55607i
$886$	−180.044	−	52.8657i	−0.203210	−	0.0596678i
$887$	585.620	+	1282.33i	0.660226	+	1.44569i	0.882311	+	0.470666i	$0.155986\pi$
$887$	585.620	+	1282.33i	0.660226	+	1.44569i	−0.222085	+	0.975027i	$0.571286\pi$
$888$	1156.10	+	166.221i	1.30191	+	0.187186i
$889$	57.3311	+	49.6777i	0.0644895	+	0.0558804i
$890$	−244.846	+	536.138i	−0.275108	+	0.602402i
$891$	19.6218	−	30.5321i	0.0220222	−	0.0342672i
$892$	−352.538	−	2451.96i	−0.395222	−	2.74883i
$893$	−98.6943	−	153.571i	−0.110520	−	0.171972i
$894$	−1711.48	+	1483.01i	−1.91441	+	1.65885i
$895$	−35.3301	−	120.323i	−0.0394750	−	0.134439i
$896$			201.192i			0.224545i
$897$	731.694	+	1387.88i	0.815713	+	1.54725i
$898$	−1618.45			−1.80229
$899$	−24.4314	+	7.17370i	−0.0271762	+	0.00797964i
$900$	295.826	+	341.401i	0.328695	+	0.379335i
$901$	−986.535	+	634.008i	−1.09493	+	0.703671i
$902$	1179.65	−	169.609i	1.30782	−	0.188036i
$903$	−133.389	−	85.7239i	−0.147718	−	0.0949324i
$904$	−1446.64	−	660.659i	−1.60027	−	0.730817i
$905$	−594.353	+	685.920i	−0.656744	+	0.757922i
$906$	−216.166	+	1503.47i	−0.238593	+	1.65945i
$907$	1180.19	−	538.976i	1.30121	−	0.594241i	0.360277	−	0.932845i	$-0.382682\pi$
$907$	1180.19	−	538.976i	1.30121	−	0.594241i	0.940929	+	0.338604i	$0.109955\pi$
$908$	457.351	−	1557.59i	0.503691	−	1.71541i
$909$	−541.976	−	159.139i	−0.596233	−	0.175070i
$910$	101.130	+	221.444i	0.111132	+	0.243345i
$911$	−705.378	−	101.418i	−0.774290	−	0.111326i	−0.256167	−	0.966632i	$-0.582460\pi$
$911$	−705.378	−	101.418i	−0.774290	−	0.111326i	−0.518123	+	0.855306i	$0.673369\pi$
$912$	−5.30014	−	4.59259i	−0.00581155	−	0.00503574i
$913$	−652.452	+	1428.67i	−0.714624	+	1.56481i
$914$	271.189	−	421.978i	0.296705	−	0.461682i
$915$	69.5522	+	483.746i	0.0760133	+	0.528684i
$916$	702.805	+	1093.59i	0.767254	+	1.19387i
$917$	15.5804	−	13.5005i	0.0169906	−	0.0147225i
$918$	−342.277	−	1165.69i	−0.372851	−	1.26981i
$919$		−	1453.27i		−	1.58136i	−0.612229	−	0.790680i	$-0.709727\pi$
$919$		−	1453.27i		−	1.58136i	0.612229	−	0.790680i	$-0.290273\pi$
$920$	−333.703	−	936.293i	−0.362721	−	1.01771i
$921$	1306.59			1.41867
$922$	115.118	−	33.8018i	0.124857	−	0.0366614i
$923$	677.705	+	782.113i	0.734242	+	0.847360i
$924$	334.373	−	214.889i	0.361876	−	0.232563i
$925$	146.736	−	21.0974i	0.158633	−	0.0228080i
$926$	1534.75	+	986.321i	1.65739	+	1.06514i
$927$	724.902	+	331.052i	0.781987	+	0.357121i
$928$	−62.4572	+	72.0794i	−0.0673030	+	0.0776718i
$929$	−32.1369	+	223.517i	−0.0345930	+	0.240600i	−0.999780	−	0.0209599i	$-0.993328\pi$
$929$	−32.1369	+	223.517i	−0.0345930	+	0.240600i	0.965187	+	0.261560i	$0.0842369\pi$
$930$	−671.771	+	306.787i	−0.722334	+	0.329879i
$931$	−87.2978	+	297.309i	−0.0937678	+	0.319344i
$932$	−2053.83	−	603.060i	−2.20368	−	0.647060i
$933$	−597.107	−	1307.48i	−0.639986	−	1.40137i
$934$	1080.29	+	155.323i	1.15663	+	0.166299i
$935$	−770.413	−	667.567i	−0.823971	−	0.713975i
$936$	−667.903	+	1462.50i	−0.713571	+	1.56250i
$937$	−78.0792	+	121.494i	−0.0833289	+	0.129662i	−0.880416	−	0.474202i	$-0.842737\pi$
$937$	−78.0792	+	121.494i	−0.0833289	+	0.129662i	0.797087	+	0.603864i	$0.206373\pi$
$938$	−36.8571	−	256.347i	−0.0392932	−	0.273291i
$939$	−1089.07	−	1694.63i	−1.15982	−	1.80471i
$940$	−753.558	+	652.962i	−0.801658	+	0.694640i
$941$	−135.597	−	461.802i	−0.144099	−	0.490757i	0.855537	−	0.517742i	$-0.173227\pi$
$941$	−135.597	−	461.802i	−0.144099	−	0.490757i	−0.999636	+	0.0269856i	$0.991409\pi$
$942$		−	2434.69i		−	2.58459i
$943$	−566.786	−	320.338i	−0.601045	−	0.339701i
$944$	20.0300			0.0212182
$945$	134.566	−	39.5123i	0.142398	−	0.0418119i
$946$	−923.686	−	1065.99i	−0.976412	−	1.12684i
$947$	874.786	−	562.191i	0.923745	−	0.593655i	0.0100027	−	0.999950i	$-0.496816\pi$
$947$	874.786	−	562.191i	0.923745	−	0.593655i	0.913742	+	0.406295i	$0.133180\pi$
$948$	−3717.66	+	534.519i	−3.92158	+	0.563839i
$949$	885.371	+	568.993i	0.932951	+	0.599571i
$950$	92.1238	+	42.0715i	0.0969724	+	0.0442858i
$951$	−31.4331	+	36.2757i	−0.0330527	+	0.0381448i
$952$	−15.7643	+	109.643i	−0.0165592	+	0.115171i
$953$	137.184	−	62.6496i	0.143949	−	0.0657394i	−0.342138	−	0.939650i	$-0.611151\pi$
$953$	137.184	−	62.6496i	0.143949	−	0.0657394i	0.486087	+	0.873910i	$0.338424\pi$
$954$	1075.41	−	3662.52i	1.12727	−	3.83912i
$955$	318.670	+	93.5700i	0.333686	+	0.0979790i
$956$	−718.552	−	1573.41i	−0.751624	−	1.64583i
$957$	183.905	+	26.4416i	0.192168	+	0.0276296i
$958$	497.919	+	431.449i	0.519748	+	0.450364i
$959$	−69.0098	+	151.110i	−0.0719602	+	0.157571i
$960$	−1482.67	+	2307.08i	−1.54445	+	2.40320i
$961$	126.141	+	877.331i	0.131260	+	0.912935i
$962$	751.555	+	1169.44i	0.781242	+	1.21564i
$963$	−411.217	+	356.322i	−0.427017	+	0.370012i
$964$	91.7577	+	312.498i	0.0951843	+	0.324168i
$965$			30.3533i			0.0314542i
$966$	−350.546	−	30.2308i	−0.362884	−	0.0312949i
$967$	−858.605			−0.887905			−0.443953	−	0.896050i	$-0.646424\pi$
$967$	−858.605			−0.887905			−0.443953	+	0.896050i	$0.646424\pi$
$968$	369.433	−	108.475i	0.381646	−	0.112061i
$969$	−292.748	−	337.850i	−0.302114	−	0.348658i
$970$	1775.90	−	1141.30i	1.83083	−	1.17660i
$971$	−471.201	+	67.7485i	−0.485274	+	0.0697719i	−0.380610	−	0.924736i	$-0.624286\pi$
$971$	−471.201	+	67.7485i	−0.485274	+	0.0697719i	−0.104664	+	0.994508i	$0.533377\pi$
$972$	−1354.21	−	870.297i	−1.39322	−	0.895367i
$973$	27.8030	+	12.6972i	0.0285745	+	0.0130495i
$974$	−268.258	+	309.586i	−0.275419	+	0.317850i
$975$	−47.1640	+	328.033i	−0.0483734	+	0.336444i
$976$	−3.77687	+	1.72484i	−0.00386974	+	0.00176725i
$977$	−406.072	+	1382.95i	−0.415631	+	1.41551i	0.440035	+	0.897981i	$0.354966\pi$
$977$	−406.072	+	1382.95i	−0.415631	+	1.41551i	−0.855666	+	0.517529i	$0.826852\pi$
$978$	489.064	+	143.602i	0.500065	+	0.146832i
$979$	180.586	+	395.429i	0.184460	+	0.403911i
$980$	1675.25	+	240.864i	1.70944	+	0.245780i
$981$	1369.42	+	1186.61i	1.39594	+	1.20959i
$982$	206.669	−	452.541i	0.210457	−	0.460836i
$983$	213.637	−	332.426i	0.217332	−	0.338175i	−0.715419	−	0.698695i	$-0.753764\pi$
$983$	213.637	−	332.426i	0.217332	−	0.338175i	0.932752	+	0.360520i	$0.117401\pi$
$984$	−154.196	−	1072.46i	−0.156704	−	1.08990i
$985$	419.601	+	652.912i	0.425991	+	0.662855i
$986$	−103.102	+	89.3380i	−0.104565	+	0.0906065i
$987$	37.7417	+	128.536i	0.0382388	+	0.130229i
$988$			586.063i			0.593181i
$989$	43.7220	+	769.288i	0.0442083	+	0.777845i
$990$	3318.17			3.35168
$991$	−471.222	+	138.363i	−0.475502	+	0.139620i	−0.510697	−	0.859761i	$-0.670613\pi$
$991$	−471.222	+	138.363i	−0.475502	+	0.139620i	0.0351956	+	0.999380i	$0.488795\pi$
$992$	−183.102	−	211.311i	−0.184578	−	0.213015i
$993$	44.3595	−	28.5081i	0.0446722	−	0.0287091i
$994$	−229.718	+	33.0285i	−0.231105	+	0.0332278i
$995$	−35.8792	−	23.0582i	−0.0360595	−	0.0231741i
$996$	3422.06	+	1562.80i	3.43580	+	1.56908i
$997$	504.917	−	582.706i	0.506437	−	0.584459i	−0.443746	−	0.896153i	$-0.646351\pi$
$997$	504.917	−	582.706i	0.506437	−	0.584459i	0.950183	+	0.311693i	$0.100896\pi$
$998$	−124.263	+	864.265i	−0.124512	+	0.865997i
$999$	728.475	−	332.683i	0.729204	−	0.333016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.3.d.a.14.1	yes	30
3.2	odd	2		207.3.j.a.37.3		30
4.3	odd	2		368.3.p.a.129.3		30
23.5	odd	22	inner	23.3.d.a.5.1	✓	30
23.8	even	11		529.3.b.b.528.30		30
23.15	odd	22		529.3.b.b.528.29		30
69.5	even	22		207.3.j.a.28.3		30
92.51	even	22		368.3.p.a.97.3		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.3.d.a.5.1	✓	30	23.5	odd	22	inner
23.3.d.a.14.1	yes	30	1.1	even	1	trivial
207.3.j.a.28.3		30	69.5	even	22
207.3.j.a.37.3		30	3.2	odd	2
368.3.p.a.97.3		30	92.51	even	22
368.3.p.a.129.3		30	4.3	odd	2
529.3.b.b.528.29		30	23.15	odd	22
529.3.b.b.528.30		30	23.8	even	11

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:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	23.d (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.10125 + 0.910608i) q^{2} +(-3.16934 - 3.65762i) q^{3} +(5.42352 - 3.48548i) q^{4} +(-5.40865 + 0.777647i) q^{5} +(13.1596 + 8.45714i) q^{6} +(-0.889564 - 0.406250i) q^{7} +(-5.17926 + 5.97719i) q^{8} +(-2.05259 + 14.2761i) q^{9} +O(q^{10})\)	\(q+(-3.10125 + 0.910608i) q^{2} +(-3.16934 - 3.65762i) q^{3} +(5.42352 - 3.48548i) q^{4} +(-5.40865 + 0.777647i) q^{5} +(13.1596 + 8.45714i) q^{6} +(-0.889564 - 0.406250i) q^{7} +(-5.17926 + 5.97719i) q^{8} +(-2.05259 + 14.2761i) q^{9} +(16.0654 - 7.33684i) q^{10} +(3.66991 - 12.4986i) q^{11} +(-29.9375 - 8.79045i) q^{12} +(-5.85520 - 12.8211i) q^{13} +(3.12869 + 0.449838i) q^{14} +(19.9862 + 17.3181i) q^{15} +(-0.0933341 + 0.204373i) q^{16} +(-7.74290 + 12.0482i) q^{17} +(-6.63433 - 46.1428i) q^{18} +(-3.48690 - 5.42572i) q^{19} +(-26.6234 + 23.0693i) q^{20} +(1.33343 + 4.54123i) q^{21} +42.1030i q^{22} +(14.0512 - 18.2089i) q^{23} +38.2771 q^{24} +(4.66147 - 1.36873i) q^{25} +(29.8334 + 34.4296i) q^{26} +(22.0789 - 14.1893i) q^{27} +(-6.24054 + 0.897254i) q^{28} +(-2.47928 - 1.59333i) q^{29} +(-77.7522 - 35.5083i) q^{30} +(5.65792 - 6.52959i) q^{31} +(4.60559 - 32.0326i) q^{32} +(-57.3462 + 26.1891i) q^{33} +(13.0415 - 44.4152i) q^{34} +(5.12726 + 1.50550i) q^{35} +(38.6268 + 84.5809i) q^{36} +(30.2033 + 4.34258i) q^{37} +(15.7544 + 13.6513i) q^{38} +(-28.3375 + 62.0505i) q^{39} +(23.3647 - 36.3562i) q^{40} +(-4.02842 - 28.0183i) q^{41} +(-8.27056 - 12.8692i) q^{42} +(-25.3186 + 21.9387i) q^{43} +(-23.6597 - 80.5777i) q^{44} -78.8106i q^{45} +(-26.9951 + 69.2654i) q^{46} +28.3043 q^{47} +(1.04333 - 0.306348i) q^{48} +(-31.4619 - 36.3090i) q^{49} +(-13.2100 + 8.48954i) q^{50} +(68.6075 - 9.86427i) q^{51} +(-76.4435 - 49.1272i) q^{52} +(74.4829 + 34.0152i) q^{53} +(-55.5514 + 64.1097i) q^{54} +(-10.1298 + 70.4544i) q^{55} +(7.03552 - 3.21301i) q^{56} +(-8.79403 + 29.9497i) q^{57} +(9.13975 + 2.68367i) q^{58} +(-37.0343 - 81.0938i) q^{59} +(168.758 + 24.2637i) q^{60} +(13.9664 + 12.1020i) q^{61} +(-11.6007 + 25.4020i) q^{62} +(7.62557 - 11.8656i) q^{63} +(14.7582 + 102.645i) q^{64} +(41.6390 + 64.7916i) q^{65} +(153.997 - 133.439i) q^{66} +(-23.0835 - 78.6152i) q^{67} +92.3312i q^{68} +(-111.134 + 6.31624i) q^{69} -17.2718 q^{70} +(-70.4488 + 20.6856i) q^{71} +(-74.6999 - 86.2083i) q^{72} +(-62.8153 + 40.3690i) q^{73} +(-97.6223 + 14.0360i) q^{74} +(-19.7801 - 12.7119i) q^{75} +(-37.8225 - 17.2730i) q^{76} +(-8.34217 + 9.62738i) q^{77} +(31.3780 - 218.239i) q^{78} +(109.498 - 50.0059i) q^{79} +(0.345882 - 1.17796i) q^{80} +(2.67333 + 0.784960i) q^{81} +(38.0068 + 83.2233i) q^{82} +(-119.345 - 17.1592i) q^{83} +(23.0602 + 19.9818i) q^{84} +(32.5094 - 71.1857i) q^{85} +(58.5417 - 91.0926i) q^{86} +(2.02987 + 14.1181i) q^{87} +(55.6989 + 86.6692i) q^{88} +(-25.2210 + 21.8541i) q^{89} +(71.7656 + 244.411i) q^{90} +13.7839i q^{91} +(12.7402 - 147.731i) q^{92} -41.8146 q^{93} +(-87.7787 + 25.7741i) q^{94} +(23.0787 + 26.6343i) q^{95} +(-131.760 + 84.6768i) q^{96} +(118.310 - 17.0104i) q^{97} +(130.634 + 83.9536i) q^{98} +(170.898 + 78.0465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9}+O(q^{10}) \) 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9	\( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9} - 11 q^{10} - 11 q^{11} - 14 q^{12} - 11 q^{13} - 11 q^{14} + 66 q^{15} + 73 q^{16} + 44 q^{17} + 126 q^{18} + 22 q^{19} + 77 q^{20} + 22 q^{21} + 36 q^{23} - 22 q^{24} - 152 q^{25} - 186 q^{26} - 62 q^{27} - 275 q^{28} - 88 q^{29} - 363 q^{30} - 110 q^{31} - 147 q^{32} - 132 q^{33} + 231 q^{34} + 209 q^{35} + 229 q^{36} + 341 q^{37} + 374 q^{38} + 295 q^{39} + 429 q^{40} + 77 q^{41} + 319 q^{42} + 77 q^{43} + 110 q^{44} - 99 q^{46} - 110 q^{47} - 550 q^{48} - 422 q^{49} - 396 q^{50} - 275 q^{51} - 472 q^{52} - 187 q^{53} - 198 q^{54} - 165 q^{55} + 176 q^{56} - 176 q^{57} - 13 q^{58} - q^{59} + 539 q^{60} + 297 q^{61} + 82 q^{62} + 264 q^{63} + 386 q^{64} + 220 q^{65} + 264 q^{66} + 11 q^{67} - 66 q^{69} - 198 q^{70} - 176 q^{71} - 605 q^{72} - 121 q^{73} - 352 q^{74} + 154 q^{75} + 110 q^{76} + 110 q^{77} + 360 q^{78} + 33 q^{79} - 242 q^{80} + 494 q^{81} + 96 q^{82} - 154 q^{83} + 11 q^{84} + 275 q^{85} + 143 q^{86} + 271 q^{87} + 429 q^{88} + 121 q^{89} + 242 q^{90} + 166 q^{92} + 260 q^{93} - 295 q^{94} - 154 q^{95} - 419 q^{96} + 154 q^{97} + 77 q^{98} - 242 q^{99}+O(q^{100}) \) 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9 - 11 * q^10 - 11 * q^11 - 14 * q^12 - 11 * q^13 - 11 * q^14 + 66 * q^15 + 73 * q^16 + 44 * q^17 + 126 * q^18 + 22 * q^19 + 77 * q^20 + 22 * q^21 + 36 * q^23 - 22 * q^24 - 152 * q^25 - 186 * q^26 - 62 * q^27 - 275 * q^28 - 88 * q^29 - 363 * q^30 - 110 * q^31 - 147 * q^32 - 132 * q^33 + 231 * q^34 + 209 * q^35 + 229 * q^36 + 341 * q^37 + 374 * q^38 + 295 * q^39 + 429 * q^40 + 77 * q^41 + 319 * q^42 + 77 * q^43 + 110 * q^44 - 99 * q^46 - 110 * q^47 - 550 * q^48 - 422 * q^49 - 396 * q^50 - 275 * q^51 - 472 * q^52 - 187 * q^53 - 198 * q^54 - 165 * q^55 + 176 * q^56 - 176 * q^57 - 13 * q^58 - q^59 + 539 * q^60 + 297 * q^61 + 82 * q^62 + 264 * q^63 + 386 * q^64 + 220 * q^65 + 264 * q^66 + 11 * q^67 - 66 * q^69 - 198 * q^70 - 176 * q^71 - 605 * q^72 - 121 * q^73 - 352 * q^74 + 154 * q^75 + 110 * q^76 + 110 * q^77 + 360 * q^78 + 33 * q^79 - 242 * q^80 + 494 * q^81 + 96 * q^82 - 154 * q^83 + 11 * q^84 + 275 * q^85 + 143 * q^86 + 271 * q^87 + 429 * q^88 + 121 * q^89 + 242 * q^90 + 166 * q^92 + 260 * q^93 - 295 * q^94 - 154 * q^95 - 419 * q^96 + 154 * q^97 + 77 * q^98 - 242 * q^99

Introduction

L-functions

Modular forms

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