LMFDB - Embedded newform 105.4.d.a.64.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(64,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("105.64");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.d (of order $2$, degree $1$, 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:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.84052224.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 6x^{3} + 36x^{2} - 36x + 18 $ x^6 - 2x^5 + 2x^4 + 6x^3 + 36x^2 - 36*x + 18
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			64.6
Root			$-1.55322 + 1.55322i$ of defining polynomial
Character	$\chi$	$=$	105.64
Dual form			105.4.d.a.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.10645i q^{2} +3.00000i q^{3} -8.86293 q^{4} +(-6.58150 + 9.03792i) q^{5} -12.3193 q^{6} -7.00000i q^{7} -3.54358i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+4.10645i q^{2} +3.00000i q^{3} -8.86293 q^{4} +(-6.58150 + 9.03792i) q^{5} -12.3193 q^{6} -7.00000i q^{7} -3.54358i q^{8} -9.00000 q^{9} +(-37.1137 - 27.0266i) q^{10} -8.17432 q^{11} -26.5888i q^{12} -19.2242i q^{13} +28.7451 q^{14} +(-27.1137 - 19.7445i) q^{15} -56.3519 q^{16} +18.8982i q^{17} -36.9580i q^{18} +76.5016 q^{19} +(58.3313 - 80.1024i) q^{20} +21.0000 q^{21} -33.5675i q^{22} +142.692i q^{23} +10.6307 q^{24} +(-38.3678 - 118.966i) q^{25} +78.9433 q^{26} -27.0000i q^{27} +62.0405i q^{28} +96.1582 q^{29} +(81.0798 - 111.341i) q^{30} -270.708 q^{31} -259.755i q^{32} -24.5230i q^{33} -77.6047 q^{34} +(63.2654 + 46.0705i) q^{35} +79.7664 q^{36} +335.614i q^{37} +314.150i q^{38} +57.6727 q^{39} +(32.0266 + 23.3221i) q^{40} -122.965 q^{41} +86.2354i q^{42} +492.574i q^{43} +72.4485 q^{44} +(59.2335 - 81.3412i) q^{45} -585.957 q^{46} +96.9049i q^{47} -169.056i q^{48} -49.0000 q^{49} +(488.528 - 157.556i) q^{50} -56.6947 q^{51} +170.383i q^{52} +388.602i q^{53} +110.874 q^{54} +(53.7993 - 73.8788i) q^{55} -24.8051 q^{56} +229.505i q^{57} +394.869i q^{58} -112.896 q^{59} +(240.307 + 174.994i) q^{60} +347.160 q^{61} -1111.65i q^{62} +63.0000i q^{63} +615.855 q^{64} +(173.747 + 126.524i) q^{65} +100.702 q^{66} -101.653i q^{67} -167.494i q^{68} -428.076 q^{69} +(-189.186 + 259.796i) q^{70} +304.685 q^{71} +31.8922i q^{72} -753.987i q^{73} -1378.18 q^{74} +(356.898 - 115.103i) q^{75} -678.029 q^{76} +57.2203i q^{77} +236.830i q^{78} +1164.38 q^{79} +(370.880 - 509.304i) q^{80} +81.0000 q^{81} -504.949i q^{82} -889.188i q^{83} -186.122 q^{84} +(-170.801 - 124.379i) q^{85} -2022.73 q^{86} +288.475i q^{87} +28.9664i q^{88} +938.829 q^{89} +(334.024 + 243.239i) q^{90} -134.570 q^{91} -1264.67i q^{92} -812.123i q^{93} -397.935 q^{94} +(-503.495 + 691.415i) q^{95} +779.265 q^{96} +1206.06i q^{97} -201.216i q^{98} +73.5689 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 14 q^{5} - 6 q^{6} - 54 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 14 * q^5 - 6 * q^6 - 54 * q^9	$ 6 q - 6 q^{4} - 14 q^{5} - 6 q^{6} - 54 q^{9} - 84 q^{10} - 132 q^{11} + 14 q^{14} - 24 q^{15} - 138 q^{16} + 276 q^{19} + 334 q^{20} + 126 q^{21} + 126 q^{24} + 366 q^{25} - 196 q^{26} - 340 q^{29} - 54 q^{30} - 732 q^{31} + 72 q^{34} + 56 q^{35} + 54 q^{36} + 612 q^{39} + 12 q^{40} - 412 q^{41} + 612 q^{44} + 126 q^{45} - 1344 q^{46} - 294 q^{49} + 1216 q^{50} - 912 q^{51} + 54 q^{54} + 1860 q^{55} - 294 q^{56} + 1760 q^{59} + 624 q^{60} - 1740 q^{61} + 1626 q^{64} - 16 q^{65} - 1116 q^{66} - 1080 q^{69} + 126 q^{70} - 2036 q^{71} - 1960 q^{74} + 936 q^{75} - 900 q^{76} + 3240 q^{79} + 3794 q^{80} + 486 q^{81} - 126 q^{84} + 432 q^{85} - 5864 q^{86} + 3876 q^{89} + 756 q^{90} - 1428 q^{91} - 4224 q^{94} - 828 q^{95} + 906 q^{96} + 1188 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 - 14 * q^5 - 6 * q^6 - 54 * q^9 - 84 * q^10 - 132 * q^11 + 14 * q^14 - 24 * q^15 - 138 * q^16 + 276 * q^19 + 334 * q^20 + 126 * q^21 + 126 * q^24 + 366 * q^25 - 196 * q^26 - 340 * q^29 - 54 * q^30 - 732 * q^31 + 72 * q^34 + 56 * q^35 + 54 * q^36 + 612 * q^39 + 12 * q^40 - 412 * q^41 + 612 * q^44 + 126 * q^45 - 1344 * q^46 - 294 * q^49 + 1216 * q^50 - 912 * q^51 + 54 * q^54 + 1860 * q^55 - 294 * q^56 + 1760 * q^59 + 624 * q^60 - 1740 * q^61 + 1626 * q^64 - 16 * q^65 - 1116 * q^66 - 1080 * q^69 + 126 * q^70 - 2036 * q^71 - 1960 * q^74 + 936 * q^75 - 900 * q^76 + 3240 * q^79 + 3794 * q^80 + 486 * q^81 - 126 * q^84 + 432 * q^85 - 5864 * q^86 + 3876 * q^89 + 756 * q^90 - 1428 * q^91 - 4224 * q^94 - 828 * q^95 + 906 * q^96 + 1188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$			4.10645i			1.45185i	0.687774	+	0.725925i	$0.258588\pi$
$2$			4.10645i			1.45185i	−0.687774	+	0.725925i	$0.741412\pi$
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	−8.86293			−1.10787
$5$	−6.58150	+	9.03792i	−0.588667	+	0.808376i
$5$	−6.58150	+	9.03792i	−0.588667	+	0.808376i
$6$	−12.3193			−0.838226
$7$		−	7.00000i		−	0.377964i
$7$		−	7.00000i		−	0.377964i
$8$		−	3.54358i		−	0.156606i
$9$	−9.00000			−0.333333
$10$	−37.1137	−	27.0266i	−1.17364	−	0.854656i
$11$	−8.17432			−0.224059			−0.112030	−	0.993705i	$-0.535735\pi$
$11$	−8.17432			−0.224059			−0.112030	+	0.993705i	$0.535735\pi$
$12$		−	26.5888i		−	0.639627i
$13$		−	19.2242i		−	0.410142i	−0.978747	−	0.205071i	$-0.934258\pi$
$13$		−	19.2242i		−	0.410142i	0.978747	−	0.205071i	$-0.0657425\pi$
$14$	28.7451			0.548747
$15$	−27.1137	−	19.7445i	−0.466716	−	0.339867i
$16$	−56.3519			−0.880499
$17$			18.8982i			0.269618i	0.990872	+	0.134809i	$0.0430420\pi$
$17$			18.8982i			0.269618i	−0.990872	+	0.134809i	$0.956958\pi$
$18$		−	36.9580i		−	0.483950i
$19$	76.5016			0.923720			0.461860	−	0.886953i	$-0.347182\pi$
$19$	76.5016			0.923720			0.461860	+	0.886953i	$0.347182\pi$
$20$	58.3313	−	80.1024i	0.652164	−	0.895572i
$21$	21.0000			0.218218
$22$		−	33.5675i		−	0.325300i
$23$			142.692i			1.29362i	0.762650	+	0.646811i	$0.223898\pi$
$23$			142.692i			1.29362i	−0.762650	+	0.646811i	$0.776102\pi$
$24$	10.6307			0.0904163
$25$	−38.3678	−	118.966i	−0.306943	−	0.951728i
$26$	78.9433			0.595464
$27$		−	27.0000i		−	0.192450i
$28$			62.0405i			0.418734i
$29$	96.1582			0.615728			0.307864	−	0.951430i	$-0.400386\pi$
$29$	96.1582			0.615728			0.307864	+	0.951430i	$0.400386\pi$
$30$	81.0798	−	111.341i	0.493436	−	0.677601i
$31$	−270.708			−1.56840			−0.784202	−	0.620505i	$-0.786928\pi$
$31$	−270.708			−1.56840			−0.784202	+	0.620505i	$0.786928\pi$
$32$		−	259.755i		−	1.43496i
$33$		−	24.5230i		−	0.129361i
$34$	−77.6047			−0.391444
$35$	63.2654	+	46.0705i	0.305537	+	0.222495i
$36$	79.7664			0.369289
$37$			335.614i			1.49120i	0.666391	+	0.745602i	$0.267838\pi$
$37$			335.614i			1.49120i	−0.666391	+	0.745602i	$0.732162\pi$
$38$			314.150i			1.34110i
$39$	57.6727			0.236795
$40$	32.0266	+	23.3221i	0.126596	+	0.0921886i
$41$	−122.965			−0.468387			−0.234194	−	0.972190i	$-0.575245\pi$
$41$	−122.965			−0.468387			−0.234194	+	0.972190i	$0.575245\pi$
$42$			86.2354i			0.316819i
$43$			492.574i			1.74690i	0.486910	+	0.873452i	$0.338124\pi$
$43$			492.574i			1.74690i	−0.486910	+	0.873452i	$0.661876\pi$
$44$	72.4485			0.248228
$45$	59.2335	−	81.3412i	0.196222	−	0.269459i
$46$	−585.957			−1.87814
$47$			96.9049i			0.300745i	0.988629	+	0.150373i	$0.0480473\pi$
$47$			96.9049i			0.300745i	−0.988629	+	0.150373i	$0.951953\pi$
$48$		−	169.056i		−	0.508356i
$49$	−49.0000			−0.142857
$50$	488.528	−	157.556i	1.38177	−	0.445634i
$51$	−56.6947			−0.155664
$52$			170.383i			0.454382i
$53$			388.602i			1.00714i	0.863953	+	0.503572i	$0.167981\pi$
$53$			388.602i			1.00714i	−0.863953	+	0.503572i	$0.832019\pi$
$54$	110.874			0.279409
$55$	53.7993	−	73.8788i	0.131896	−	0.181124i
$56$	−24.8051			−0.0591914
$57$			229.505i			0.533310i
$58$			394.869i			0.893945i
$59$	−112.896			−0.249116			−0.124558	−	0.992212i	$-0.539751\pi$
$59$	−112.896			−0.249116			−0.124558	+	0.992212i	$0.539751\pi$
$60$	240.307	+	174.994i	0.517059	+	0.376527i
$61$	347.160			0.728676			0.364338	−	0.931267i	$-0.381295\pi$
$61$	347.160			0.728676			0.364338	+	0.931267i	$0.381295\pi$
$62$		−	1111.65i		−	2.27709i
$63$			63.0000i			0.125988i
$64$	615.855			1.20284
$65$	173.747	+	126.524i	0.331549	+	0.241437i
$66$	100.702			0.187812
$67$		−	101.653i		−	0.185356i	−0.995696	−	0.0926781i	$-0.970457\pi$
$67$		−	101.653i		−	0.185356i	0.995696	−	0.0926781i	$-0.0295427\pi$
$68$		−	167.494i		−	0.298700i
$69$	−428.076			−0.746873
$70$	−189.186	+	259.796i	−0.323029	+	0.443594i
$71$	304.685			0.509287			0.254644	−	0.967035i	$-0.418042\pi$
$71$	304.685			0.509287			0.254644	+	0.967035i	$0.418042\pi$
$72$			31.8922i			0.0522019i
$73$		−	753.987i		−	1.20887i	−0.796655	−	0.604435i	$-0.793399\pi$
$73$		−	753.987i		−	1.20887i	0.796655	−	0.604435i	$-0.206601\pi$
$74$	−1378.18			−2.16500
$75$	356.898	−	115.103i	0.549480	−	0.177213i
$76$	−678.029			−1.02336
$77$			57.2203i			0.0846864i
$78$			236.830i			0.343791i
$79$	1164.38			1.65827			0.829135	−	0.559049i	$-0.188834\pi$
$79$	1164.38			1.65827			0.829135	+	0.559049i	$0.188834\pi$
$80$	370.880	−	509.304i	0.518320	−	0.711774i
$81$	81.0000			0.111111
$82$		−	504.949i		−	0.680027i
$83$		−	889.188i		−	1.17592i	−0.808891	−	0.587958i	$-0.799932\pi$
$83$		−	889.188i		−	1.17592i	0.808891	−	0.587958i	$-0.200068\pi$
$84$	−186.122			−0.241756
$85$	−170.801	−	124.379i	−0.217952	−	0.158715i
$86$	−2022.73			−2.53624
$87$			288.475i			0.355491i
$88$			28.9664i			0.0350889i
$89$	938.829			1.11815			0.559077	−	0.829116i	$-0.311156\pi$
$89$	938.829			1.11815			0.559077	+	0.829116i	$0.311156\pi$
$90$	334.024	+	243.239i	0.391213	+	0.284885i
$91$	−134.570			−0.155019
$92$		−	1264.67i		−	1.43316i
$93$		−	812.123i		−	0.905519i
$94$	−397.935			−0.436637
$95$	−503.495	+	691.415i	−0.543763	+	0.746713i
$96$	779.265			0.828473
$97$			1206.06i			1.26244i	0.775605	+	0.631218i	$0.217445\pi$
$97$			1206.06i			1.26244i	−0.775605	+	0.631218i	$0.782555\pi$
$98$		−	201.216i		−	0.207407i
$99$	73.5689			0.0746864
$100$	340.051	+	1054.39i	0.340051	+	1.05439i
$101$	436.407			0.429942			0.214971	−	0.976620i	$-0.431034\pi$
$101$	436.407			0.429942			0.214971	+	0.976620i	$0.431034\pi$
$102$		−	232.814i		−	0.226000i
$103$		−	1765.48i		−	1.68891i	−0.535629	−	0.844454i	$-0.679925\pi$
$103$		−	1765.48i		−	1.68891i	0.535629	−	0.844454i	$-0.320075\pi$
$104$	−68.1226			−0.0642305
$105$	−138.211	+	189.796i	−0.128458	+	0.176402i
$106$	−1595.78			−1.46222
$107$			304.599i			0.275203i	0.990488	+	0.137601i	$0.0439393\pi$
$107$			304.599i			0.275203i	−0.990488	+	0.137601i	$0.956061\pi$
$108$			239.299i			0.213209i
$109$	1037.76			0.911918			0.455959	−	0.890001i	$-0.349296\pi$
$109$	1037.76			0.911918			0.455959	+	0.890001i	$0.349296\pi$
$110$	303.380	+	220.924i	0.262965	+	0.191493i
$111$	−1006.84			−0.860947
$112$			394.463i			0.332797i
$113$			1479.63i			1.23178i	0.787830	+	0.615892i	$0.211204\pi$
$113$			1479.63i			1.23178i	−0.787830	+	0.615892i	$0.788796\pi$
$114$	−942.450			−0.774286
$115$	−1289.64	−	939.126i	−1.04573	−	0.761513i
$116$	−852.243			−0.682145
$117$			173.018i			0.136714i
$118$		−	463.604i		−	0.361679i
$119$	132.288			0.101906
$120$	−69.9662	+	96.0798i	−0.0532251	+	0.0730903i
$121$	−1264.18			−0.949797
$122$			1425.59i			1.05793i
$123$		−	368.894i		−	0.270423i
$124$	2399.26			1.73758
$125$	1327.72	+	436.209i	0.950041	+	0.312126i
$126$	−258.706			−0.182916
$127$		−	1633.52i		−	1.14135i	−0.821175	−	0.570676i	$-0.806681\pi$
$127$		−	1633.52i		−	1.14135i	0.821175	−	0.570676i	$-0.193319\pi$
$128$			450.940i			0.311389i
$129$	−1477.72			−1.00858
$130$	−519.565	+	713.483i	−0.350530	+	0.481359i
$131$	−359.287			−0.239627			−0.119813	−	0.992796i	$-0.538230\pi$
$131$	−359.287			−0.239627			−0.119813	+	0.992796i	$0.538230\pi$
$132$			217.345i			0.143314i
$133$		−	535.511i		−	0.349133i
$134$	417.432			0.269109
$135$	244.024	+	177.700i	0.155572	+	0.113289i
$136$	66.9675			0.0422236
$137$			2573.71i			1.60501i	0.596643	+	0.802507i	$0.296501\pi$
$137$			2573.71i			1.60501i	−0.596643	+	0.802507i	$0.703499\pi$
$138$		−	1757.87i		−	1.08435i
$139$	2267.12			1.38341			0.691706	−	0.722179i	$-0.256859\pi$
$139$	2267.12			1.38341			0.691706	+	0.722179i	$0.256859\pi$
$140$	−560.717	−	408.319i	−0.338494	−	0.246495i
$141$	−290.715			−0.173635
$142$			1251.17i			0.739409i
$143$			157.145i			0.0918960i
$144$	507.167			0.293500
$145$	−632.865	+	869.069i	−0.362459	+	0.497740i
$146$	3096.21			1.75510
$147$		−	147.000i		−	0.0824786i
$148$		−	2974.52i		−	1.65206i
$149$	−457.166			−0.251359			−0.125680	−	0.992071i	$-0.540111\pi$
$149$	−457.166			−0.251359			−0.125680	+	0.992071i	$0.540111\pi$
$150$	472.667	+	1465.58i	0.257287	+	0.797763i
$151$	2260.38			1.21819			0.609096	−	0.793097i	$-0.291532\pi$
$151$	2260.38			1.21819			0.609096	+	0.793097i	$0.291532\pi$
$152$		−	271.090i		−	0.144660i
$153$		−	170.084i		−	0.0898725i
$154$	−234.972			−0.122952
$155$	1781.66	−	2446.63i	0.923268	−	1.26786i
$156$	−511.149			−0.262338
$157$			643.877i			0.327305i	0.986518	+	0.163653i	$0.0523276\pi$
$157$			643.877i			0.327305i	−0.986518	+	0.163653i	$0.947672\pi$
$158$			4781.48i			2.40756i
$159$	−1165.81			−0.581475
$160$	2347.64	+	1709.58i	1.15998	+	0.844712i
$161$	998.843			0.488943
$162$			332.622i			0.161317i
$163$		−	3089.66i		−	1.48467i	−0.670030	−	0.742334i	$-0.733719\pi$
$163$		−	3089.66i		−	1.48467i	0.670030	−	0.742334i	$-0.266281\pi$
$164$	1089.83			0.518910
$165$	221.637	+	161.398i	0.104572	+	0.0761503i
$166$	3651.41			1.70725
$167$			2726.84i			1.26353i	0.775161	+	0.631764i	$0.217669\pi$
$167$			2726.84i			1.26353i	−0.775161	+	0.631764i	$0.782331\pi$
$168$		−	74.4152i		−	0.0341742i
$169$	1827.43			0.831784
$170$	510.755	−	701.385i	0.230430	−	0.316434i
$171$	−688.515			−0.307907
$172$		−	4365.65i		−	1.93534i
$173$		−	901.915i		−	0.396366i	−0.980165	−	0.198183i	$-0.936496\pi$
$173$		−	901.915i		−	0.396366i	0.980165	−	0.198183i	$-0.0635040\pi$
$174$	−1184.61			−0.516119
$175$	−832.762	+	268.575i	−0.359719	+	0.116013i
$176$	460.639			0.197284
$177$		−	338.689i		−	0.143827i
$178$			3855.25i			1.62339i
$179$	−4547.62			−1.89891			−0.949455	−	0.313903i	$-0.898363\pi$
$179$	−4547.62			−1.89891			−0.949455	+	0.313903i	$0.898363\pi$
$180$	−524.982	+	720.922i	−0.217388	+	0.298524i
$181$	−402.003			−0.165086			−0.0825432	−	0.996587i	$-0.526304\pi$
$181$	−402.003			−0.165086			−0.0825432	+	0.996587i	$0.526304\pi$
$182$		−	552.603i		−	0.225064i
$183$			1041.48i			0.420701i
$184$	505.640			0.202589
$185$	−3033.25	−	2208.84i	−1.20545	−	0.877823i
$186$	3334.94			1.31468
$187$		−	154.480i		−	0.0604103i
$188$		−	858.861i		−	0.333186i
$189$	−189.000			−0.0727393
$190$	−2839.26	−	2067.58i	−1.08411	−	0.789462i
$191$	−4399.62			−1.66673			−0.833365	−	0.552723i	$-0.813589\pi$
$191$	−4399.62			−1.66673			−0.833365	+	0.552723i	$0.813589\pi$
$192$			1847.57i			0.694461i
$193$			301.958i			0.112619i	0.998413	+	0.0563094i	$0.0179333\pi$
$193$			301.958i			0.112619i	−0.998413	+	0.0563094i	$0.982067\pi$
$194$	−4952.61			−1.83287
$195$	−379.573	+	521.241i	−0.139394	+	0.191420i
$196$	434.284			0.158267
$197$			952.950i			0.344644i	0.985041	+	0.172322i	$0.0551270\pi$
$197$			952.950i			0.344644i	−0.985041	+	0.172322i	$0.944873\pi$
$198$			302.107i			0.108433i
$199$	−4124.90			−1.46938			−0.734690	−	0.678403i	$-0.762672\pi$
$199$	−4124.90			−1.46938			−0.734690	+	0.678403i	$0.762672\pi$
$200$	−421.566	+	135.959i	−0.149046	+	0.0480689i
$201$	304.958			0.107015
$202$			1792.08i			0.624210i
$203$		−	673.107i		−	0.232723i
$204$	502.482			0.172455
$205$	809.292	−	1111.35i	0.275724	−	0.378633i
$206$	7249.83			2.45204
$207$		−	1284.23i		−	0.431207i
$208$			1083.32i			0.361129i
$209$	−625.349			−0.206968
$210$	−779.389	−	567.558i	−0.256109	−	0.186501i
$211$	−1014.74			−0.331079			−0.165540	−	0.986203i	$-0.552937\pi$
$211$	−1014.74			−0.331079			−0.165540	+	0.986203i	$0.552937\pi$
$212$		−	3444.15i		−	1.11578i
$213$			914.054i			0.294037i
$214$	−1250.82			−0.399553
$215$	−4451.85	−	3241.88i	−1.41215	−	1.02834i
$216$	−95.6767			−0.0301388
$217$			1894.95i			0.592801i
$218$			4261.50i			1.32397i
$219$	2261.96			0.697941
$220$	−476.819	+	654.783i	−0.146123	+	0.200661i
$221$	363.304			0.110581
$222$		−	4134.54i		−	1.24997i
$223$			5042.95i			1.51435i	0.653210	+	0.757177i	$0.273422\pi$
$223$			5042.95i			1.51435i	−0.653210	+	0.757177i	$0.726578\pi$
$224$	−1818.28			−0.542363
$225$	345.310	+	1070.69i	0.102314	+	0.317243i
$226$	−6076.02			−1.78837
$227$		−	5831.62i		−	1.70510i	−0.522643	−	0.852552i	$-0.675054\pi$
$227$		−	5831.62i		−	1.70510i	0.522643	−	0.852552i	$-0.324946\pi$
$228$		−	2034.09i		−	0.590836i
$229$	−18.5657			−0.00535744			−0.00267872	−	0.999996i	$-0.500853\pi$
$229$	−18.5657			−0.00535744			−0.00267872	+	0.999996i	$0.500853\pi$
$230$	3856.47	−	5295.83i	1.10560	−	1.51825i
$231$	−171.661			−0.0488937
$232$		−	340.744i		−	0.0964265i
$233$			1732.62i			0.487158i	0.969881	+	0.243579i	$0.0783216\pi$
$233$			1732.62i			0.487158i	−0.969881	+	0.243579i	$0.921678\pi$
$234$	−710.490			−0.198488
$235$	−875.818	−	637.779i	−0.243115	−	0.177039i
$236$	1000.59			0.275988
$237$			3493.15i			0.957402i
$238$			543.233i			0.147952i
$239$	1937.54			0.524389			0.262195	−	0.965015i	$-0.415554\pi$
$239$	1937.54			0.524389			0.262195	+	0.965015i	$0.415554\pi$
$240$	1527.91	+	1112.64i	0.410943	+	0.299252i
$241$	5613.02			1.50027			0.750137	−	0.661282i	$-0.229987\pi$
$241$	5613.02			1.50027			0.750137	+	0.661282i	$0.229987\pi$
$242$		−	5191.29i		−	1.37896i
$243$			243.000i			0.0641500i
$244$	−3076.85			−0.807275
$245$	322.493	−	442.858i	0.0840953	−	0.115482i
$246$	1514.85			0.392614
$247$		−	1470.69i		−	0.378856i
$248$			959.275i			0.245621i
$249$	2667.56			0.678916
$250$	−1791.27	+	5452.23i	−0.453160	+	1.37932i
$251$	−5132.49			−1.29068			−0.645338	−	0.763897i	$-0.723284\pi$
$251$	−5132.49			−1.29068			−0.645338	+	0.763897i	$0.723284\pi$
$252$		−	558.365i		−	0.139578i
$253$		−	1166.41i		−	0.289848i
$254$	6707.98			1.65707
$255$	373.136	−	512.402i	0.0916341	−	0.125835i
$256$	3075.08			0.750752
$257$		−	4689.21i		−	1.13815i	−0.822285	−	0.569075i	$-0.807301\pi$
$257$		−	4689.21i		−	1.13815i	0.822285	−	0.569075i	$-0.192699\pi$
$258$		−	6068.20i		−	1.46430i
$259$	2349.30			0.563622
$260$	−1539.91	−	1121.38i	−0.367312	−	0.267480i
$261$	−865.424			−0.205243
$262$		−	1475.40i		−	0.347902i
$263$			1767.86i			0.414491i	0.978289	+	0.207246i	$0.0664499\pi$
$263$			1767.86i			0.414491i	−0.978289	+	0.207246i	$0.933550\pi$
$264$	−86.8991			−0.0202586
$265$	−3512.15	−	2557.58i	−0.814151	−	0.592872i
$266$	2199.05			0.506889
$267$			2816.49i			0.645566i
$268$			900.941i			0.205350i
$269$	7869.14			1.78361			0.891803	−	0.452425i	$-0.149441\pi$
$269$	7869.14			1.78361			0.891803	+	0.452425i	$0.149441\pi$
$270$	−729.718	+	1002.07i	−0.164479	+	0.225867i
$271$	4820.52			1.08054			0.540268	−	0.841493i	$-0.318323\pi$
$271$	4820.52			1.08054			0.540268	+	0.841493i	$0.318323\pi$
$272$		−	1064.95i		−	0.237398i
$273$		−	403.709i		−	0.0895003i
$274$	−10568.8			−2.33024
$275$	313.631	+	972.467i	0.0687733	+	0.213243i
$276$	3794.00			0.827436
$277$			1783.66i			0.386895i	0.981111	+	0.193448i	$0.0619670\pi$
$277$			1783.66i			0.386895i	−0.981111	+	0.193448i	$0.938033\pi$
$278$			9309.80i			2.00851i
$279$	2436.37			0.522802
$280$	163.254	−	224.186i	0.0348440	−	0.0478489i
$281$	1779.27			0.377730			0.188865	−	0.982003i	$-0.439519\pi$
$281$	1779.27			0.377730			0.188865	+	0.982003i	$0.439519\pi$
$282$		−	1193.80i		−	0.252092i
$283$		−	7374.55i		−	1.54902i	−0.632564	−	0.774508i	$-0.717998\pi$
$283$		−	7374.55i		−	1.54902i	0.632564	−	0.774508i	$-0.282002\pi$
$284$	−2700.40			−0.564222
$285$	−2074.25	−	1510.49i	−0.431115	−	0.313942i
$286$	−645.308			−0.133419
$287$			860.753i			0.177034i
$288$			2337.79i			0.478319i
$289$	4555.86			0.927306
$290$	−3568.79	−	2598.83i	−0.722643	−	0.526236i
$291$	−3618.17			−0.728868
$292$			6682.53i			1.33927i
$293$			934.020i			0.186232i	0.995655	+	0.0931161i	$0.0296828\pi$
$293$			934.020i			0.186232i	−0.995655	+	0.0931161i	$0.970317\pi$
$294$	603.648			0.119747
$295$	743.028	−	1020.35i	0.146647	−	0.201380i
$296$	1189.27			0.233531
$297$			220.707i			0.0431202i
$298$		−	1877.33i		−	0.364936i
$299$	2743.14			0.530568
$300$	−3163.16	+	1020.15i	−0.608751	+	0.196329i
$301$	3448.02			0.660268
$302$			9282.13i			1.76863i
$303$			1309.22i			0.248227i
$304$	−4311.01			−0.813334
$305$	−2284.83	+	3137.60i	−0.428947	+	0.589044i
$306$	698.442			0.130481
$307$		−	1929.10i		−	0.358630i	−0.983792	−	0.179315i	$-0.942612\pi$
$307$		−	1929.10i		−	0.358630i	0.983792	−	0.179315i	$-0.0573882\pi$
$308$		−	507.139i		−	0.0938212i
$309$	5296.43			0.975091
$310$	10047.0	+	7316.31i	1.84074	+	1.34045i
$311$	−4465.18			−0.814138			−0.407069	−	0.913397i	$-0.633449\pi$
$311$	−4465.18			−0.814138			−0.407069	+	0.913397i	$0.633449\pi$
$312$		−	204.368i		−	0.0370835i
$313$			7457.31i			1.34668i	0.739332	+	0.673342i	$0.235142\pi$
$313$			7457.31i			1.34668i	−0.739332	+	0.673342i	$0.764858\pi$
$314$	−2644.05			−0.475198
$315$	−569.389	−	414.634i	−0.101846	−	0.0741651i
$316$	−10319.8			−1.83714
$317$		−	2024.84i		−	0.358758i	−0.983780	−	0.179379i	$-0.942591\pi$
$317$		−	2024.84i		−	0.358758i	0.983780	−	0.179379i	$-0.0574089\pi$
$318$		−	4787.33i		−	0.844214i
$319$	−786.028			−0.137960
$320$	−4053.25	+	5566.05i	−0.708074	+	0.972349i
$321$	−913.797			−0.158888
$322$			4101.70i			0.709872i
$323$			1445.75i			0.249051i
$324$	−717.897			−0.123096
$325$	−2287.03	+	737.592i	−0.390343	+	0.125890i
$326$	12687.5			2.15551
$327$			3113.27i			0.526496i
$328$			435.736i			0.0733521i
$329$	678.334			0.113671
$330$	−662.772	+	910.139i	−0.110559	+	0.151823i
$331$	3153.56			0.523671			0.261836	−	0.965112i	$-0.415672\pi$
$331$	3153.56			0.523671			0.261836	+	0.965112i	$0.415672\pi$
$332$			7880.81i			1.30276i
$333$		−	3020.52i		−	0.497068i
$334$	−11197.6			−1.83445
$335$	918.729	+	669.027i	0.149837	+	0.109113i
$336$	−1183.39			−0.192141
$337$			5058.35i			0.817644i	0.912614	+	0.408822i	$0.134060\pi$
$337$			5058.35i			0.817644i	−0.912614	+	0.408822i	$0.865940\pi$
$338$			7504.25i			1.20762i
$339$	−4438.88			−0.711171
$340$	1513.80	+	1102.36i	0.241462	+	0.175835i
$341$	2212.85			0.351416
$342$		−	2827.35i		−	0.447034i
$343$			343.000i			0.0539949i
$344$	1745.48			0.273575
$345$	2817.38	−	3868.91i	0.439659	−	0.603754i
$346$	3703.67			0.575464
$347$		−	7950.25i		−	1.22995i	−0.788548	−	0.614973i	$-0.789167\pi$
$347$		−	7950.25i		−	1.22995i	0.788548	−	0.614973i	$-0.210833\pi$
$348$		−	2556.73i		−	0.393837i
$349$	−4711.92			−0.722702			−0.361351	−	0.932430i	$-0.617684\pi$
$349$	−4711.92			−0.722702			−0.361351	+	0.932430i	$0.617684\pi$
$350$	−1102.89	−	3419.70i	−0.168434	−	0.522258i
$351$	−519.054			−0.0789318
$352$			2123.32i			0.321515i
$353$		−	308.497i		−	0.0465146i	−0.999730	−	0.0232573i	$-0.992596\pi$
$353$		−	308.497i		−	0.0465146i	0.999730	−	0.0232573i	$-0.00740370\pi$
$354$	1390.81			0.208816
$355$	−2005.28	+	2753.71i	−0.299801	+	0.411696i
$356$	−8320.77			−1.23876
$357$			396.863i			0.0588354i
$358$		−	18674.6i		−	2.75693i
$359$	7598.91			1.11715			0.558573	−	0.829456i	$-0.311349\pi$
$359$	7598.91			1.11715			0.558573	+	0.829456i	$0.311349\pi$
$360$	−288.239	−	209.899i	−0.0421987	−	0.0307295i
$361$	−1006.50			−0.146742
$362$		−	1650.80i		−	0.239681i
$363$		−	3792.54i		−	0.548366i
$364$	1192.68			0.171740
$365$	6814.47	+	4962.36i	0.977221	+	0.711621i
$366$	−4276.78			−0.610795
$367$			2057.48i			0.292642i	0.989237	+	0.146321i	$0.0467432\pi$
$367$			2057.48i			0.292642i	−0.989237	+	0.146321i	$0.953257\pi$
$368$		−	8040.96i		−	1.13903i
$369$	1106.68			0.156129
$370$	9070.49	−	12455.9i	1.27447	−	1.75014i
$371$	2720.22			0.380665
$372$			7197.79i			1.00319i
$373$		−	5661.44i		−	0.785893i	−0.919561	−	0.392947i	$-0.871456\pi$
$373$		−	5661.44i		−	0.785893i	0.919561	−	0.392947i	$-0.128544\pi$
$374$	634.366			0.0877066
$375$	−1308.63	+	3983.17i	−0.180206	+	0.548506i
$376$	343.390			0.0470984
$377$		−	1848.57i		−	0.252536i
$378$		−	776.119i		−	0.105606i
$379$	1822.92			0.247063			0.123532	−	0.992341i	$-0.460578\pi$
$379$	1822.92			0.247063			0.123532	+	0.992341i	$0.460578\pi$
$380$	4462.44	−	6127.97i	0.602417	−	0.827258i
$381$	4900.57			0.658960
$382$		−	18066.8i		−	2.41984i
$383$			1886.34i			0.251664i	0.992052	+	0.125832i	$0.0401600\pi$
$383$			1886.34i			0.251664i	−0.992052	+	0.125832i	$0.959840\pi$
$384$	−1352.82			−0.179781
$385$	−517.152	−	376.595i	−0.0684584	−	0.0498521i
$386$	−1239.98			−0.163505
$387$		−	4433.17i		−	0.582301i
$388$		−	10689.2i		−	1.39861i
$389$	9079.55			1.18342			0.591711	−	0.806150i	$-0.298453\pi$
$389$	9079.55			1.18342			0.591711	+	0.806150i	$0.298453\pi$
$390$	−2140.45	−	1558.70i	−0.277913	−	0.202379i
$391$	−2696.63			−0.348783
$392$			173.635i			0.0223722i
$393$		−	1077.86i		−	0.138348i
$394$	−3913.24			−0.500371
$395$	−7663.38	+	10523.6i	−0.976168	+	1.34050i
$396$	−652.036			−0.0827426
$397$			2620.95i			0.331339i	0.986181	+	0.165669i	$0.0529785\pi$
$397$			2620.95i			0.331339i	−0.986181	+	0.165669i	$0.947022\pi$
$398$		−	16938.7i		−	2.13332i
$399$	1606.53			0.201572
$400$	2162.10	+	6703.96i	0.270262	+	0.837995i
$401$	−10752.1			−1.33899			−0.669493	−	0.742818i	$-0.733489\pi$
$401$	−10752.1			−1.33899			−0.669493	+	0.742818i	$0.733489\pi$
$402$			1252.30i			0.155370i
$403$			5204.15i			0.643268i
$404$	−3867.84			−0.476318
$405$	−533.101	+	732.071i	−0.0654074	+	0.0898195i
$406$	2764.08			0.337879
$407$		−	2743.42i		−	0.334118i
$408$			200.902i			0.0243778i
$409$	−13382.0			−1.61785			−0.808923	−	0.587914i	$-0.799949\pi$
$409$	−13382.0			−1.61785			−0.808923	+	0.587914i	$0.799949\pi$
$410$	4563.68	+	3323.32i	0.549718	+	0.400310i
$411$	−7721.13			−0.926655
$412$			15647.3i			1.87108i
$413$			790.275i			0.0941571i
$414$	5273.61			0.626048
$415$	8036.41	+	5852.19i	0.950583	+	0.692223i
$416$	−4993.59			−0.588536
$417$			6801.35i			0.798714i
$418$		−	2567.96i		−	0.300486i
$419$	−2335.91			−0.272354			−0.136177	−	0.990684i	$-0.543482\pi$
$419$	−2335.91			−0.272354			−0.136177	+	0.990684i	$0.543482\pi$
$420$	1224.96	−	1682.15i	0.142314	−	0.195430i
$421$	4262.71			0.493472			0.246736	−	0.969083i	$-0.420642\pi$
$421$	4262.71			0.493472			0.246736	+	0.969083i	$0.420642\pi$
$422$		−	4166.99i		−	0.480677i
$423$		−	872.144i		−	0.100248i
$424$	1377.04			0.157724
$425$	2248.25	−	725.085i	0.256603	−	0.0827571i
$426$	−3753.52			−0.426898
$427$		−	2430.12i		−	0.275414i
$428$		−	2699.64i		−	0.304888i
$429$	−471.435			−0.0530562
$430$	13312.6	−	18281.3i	1.49300	−	2.05024i
$431$	5233.78			0.584924			0.292462	−	0.956277i	$-0.405526\pi$
$431$	5233.78			0.584924			0.292462	+	0.956277i	$0.405526\pi$
$432$			1521.50i			0.169452i
$433$			14627.5i			1.62345i	0.584039	+	0.811726i	$0.301472\pi$
$433$			14627.5i			1.62345i	−0.584039	+	0.811726i	$0.698528\pi$
$434$	−7781.54			−0.860658
$435$	−2607.21	−	1898.59i	−0.287370	−	0.209266i
$436$	−9197.57			−1.01028
$437$			10916.2i			1.19494i
$438$			9288.62i			1.01331i
$439$	−35.2964			−0.00383737			−0.00191868	−	0.999998i	$-0.500611\pi$
$439$	−35.2964			−0.00383737			−0.00191868	+	0.999998i	$0.500611\pi$
$440$	−261.796	−	190.642i	−0.0283650	−	0.0206557i
$441$	441.000			0.0476190
$442$			1491.89i			0.160548i
$443$			2805.40i			0.300877i	0.988619	+	0.150439i	$0.0480686\pi$
$443$			2805.40i			0.300877i	−0.988619	+	0.150439i	$0.951931\pi$
$444$	8923.56			0.953815
$445$	−6178.90	+	8485.05i	−0.658220	+	0.903888i
$446$	−20708.6			−2.19861
$447$		−	1371.50i		−	0.145122i
$448$		−	4310.99i		−	0.454632i
$449$	−14903.0			−1.56641			−0.783203	−	0.621766i	$-0.786415\pi$
$449$	−14903.0			−1.56641			−0.783203	+	0.621766i	$0.786415\pi$
$450$	−4396.75	+	1418.00i	−0.460589	+	0.148545i
$451$	1005.15			0.104946
$452$		−	13113.8i		−	1.36465i
$453$			6781.14i			0.703323i
$454$	23947.3			2.47555
$455$	885.669	−	1216.23i	0.0912546	−	0.125314i
$456$	813.269			0.0835193
$457$		−	2633.85i		−	0.269598i	−0.990873	−	0.134799i	$-0.956961\pi$
$457$		−	2633.85i		−	0.269598i	0.990873	−	0.134799i	$-0.0430388\pi$
$458$		−	76.2390i		−	0.00777820i
$459$	510.253			0.0518879
$460$	11430.0	+	8323.41i	1.15853	+	0.843654i
$461$	−18415.2			−1.86048			−0.930239	−	0.366955i	$-0.880400\pi$
$461$	−18415.2			−1.86048			−0.930239	+	0.366955i	$0.880400\pi$
$462$		−	704.916i		−	0.0709863i
$463$		−	14811.0i		−	1.48666i	−0.668923	−	0.743332i	$-0.733244\pi$
$463$		−	14811.0i		−	1.48666i	0.668923	−	0.743332i	$-0.266756\pi$
$464$	−5418.70			−0.542148
$465$	7339.90	+	5344.99i	0.732000	+	0.533049i
$466$	−7114.93			−0.707280
$467$		−	14407.1i		−	1.42758i	−0.700360	−	0.713790i	$-0.746977\pi$
$467$		−	14407.1i		−	1.42758i	0.700360	−	0.713790i	$-0.253023\pi$
$468$		−	1533.45i		−	0.151461i
$469$	−711.569			−0.0700580
$470$	2619.01	−	3596.50i	0.257034	−	0.352967i
$471$	−1931.63			−0.188970
$472$			400.058i			0.0390130i
$473$		−	4026.46i		−	0.391410i
$474$	−14344.4			−1.39000
$475$	−2935.20	−	9101.09i	−0.283529	−	0.879130i
$476$	−1172.46			−0.112898
$477$		−	3497.42i		−	0.335715i
$478$			7956.41i			0.761334i
$479$	6629.16			0.632347			0.316174	−	0.948701i	$-0.397602\pi$
$479$	6629.16			0.632347			0.316174	+	0.948701i	$0.397602\pi$
$480$	−5128.73	+	7042.93i	−0.487694	+	0.669717i
$481$	6451.92			0.611605
$482$			23049.6i			2.17817i
$483$			2996.53i			0.282292i
$484$	11204.3			1.05225
$485$	−10900.2	−	7937.65i	−1.02052	−	0.743155i
$486$	−997.867			−0.0931362
$487$		−	3890.46i		−	0.361999i	−0.983483	−	0.180999i	$-0.942067\pi$
$487$		−	3890.46i		−	0.361999i	0.983483	−	0.180999i	$-0.0579332\pi$
$488$		−	1230.19i		−	0.114115i
$489$	9268.98			0.857173
$490$	1818.57	+	1324.30i	0.167663	+	0.122094i
$491$	−12804.1			−1.17687			−0.588433	−	0.808546i	$-0.700255\pi$
$491$	−12804.1			−1.17687			−0.588433	+	0.808546i	$0.700255\pi$
$492$			3269.48i			0.299593i
$493$			1817.22i			0.166011i
$494$	6039.29			0.550042
$495$	−484.194	+	664.910i	−0.0439654	+	0.0603747i
$496$	15254.9			1.38098
$497$		−	2132.79i		−	0.192493i
$498$			10954.2i			0.985684i
$499$	5842.56			0.524146			0.262073	−	0.965048i	$-0.415594\pi$
$499$	5842.56			0.524146			0.262073	+	0.965048i	$0.415594\pi$
$500$	−11767.5	−	3866.09i	−1.05252	−	0.345794i
$501$	−8180.51			−0.729498
$502$		−	21076.3i		−	1.87387i
$503$			18045.9i			1.59966i	0.600227	+	0.799830i	$0.295077\pi$
$503$			18045.9i			1.59966i	−0.600227	+	0.799830i	$0.704923\pi$
$504$	223.246			0.0197305
$505$	−2872.21	+	3944.21i	−0.253092	+	0.347554i
$506$	4789.80			0.420816
$507$			5482.29i			0.480231i
$508$			14477.8i			1.26447i
$509$	21723.0			1.89166			0.945831	−	0.324659i	$-0.105250\pi$
$509$	21723.0			1.89166			0.945831	+	0.324659i	$0.105250\pi$
$510$	2104.15	+	1532.27i	0.182693	+	0.133039i
$511$	−5277.91			−0.456910
$512$			16235.2i			1.40137i
$513$		−	2065.54i		−	0.177770i
$514$	19256.0			1.65242
$515$	15956.2	+	11619.5i	1.36527	+	0.994204i
$516$	13097.0			1.11737
$517$		−	792.132i		−	0.0673847i
$518$			9647.27i			0.818295i
$519$	2705.74			0.228842
$520$	448.349	−	615.686i	0.0378104	−	0.0519224i
$521$	17101.2			1.43804			0.719018	−	0.694992i	$-0.244592\pi$
$521$	17101.2			1.43804			0.719018	+	0.694992i	$0.244592\pi$
$522$		−	3553.82i		−	0.297982i
$523$			4938.15i			0.412869i	0.978460	+	0.206434i	$0.0661860\pi$
$523$			4938.15i			0.412869i	−0.978460	+	0.206434i	$0.933814\pi$
$524$	3184.34			0.265474
$525$	−805.724	−	2498.29i	−0.0669804	−	0.207684i
$526$	−7259.64			−0.601779
$527$		−	5115.90i		−	0.422869i
$528$			1381.92i			0.113902i
$529$	−8193.97			−0.673458
$530$	10502.6	−	14422.5i	0.860761	−	1.18202i
$531$	1016.07			0.0830388
$532$			4746.20i			0.386793i
$533$			2363.90i			0.192105i
$534$	−11565.8			−0.937265
$535$	−2752.94	−	2004.72i	−0.222467	−	0.162003i
$536$	−360.215			−0.0290278
$537$		−	13642.9i		−	1.09634i
$538$			32314.2i			2.58953i
$539$	400.542			0.0320085
$540$	−2162.77	−	1574.95i	−0.172353	−	0.125509i
$541$	11481.7			0.912451			0.456226	−	0.889864i	$-0.349201\pi$
$541$	11481.7			0.912451			0.456226	+	0.889864i	$0.349201\pi$
$542$			19795.2i			1.56878i
$543$		−	1206.01i		−	0.0953127i
$544$	4908.91			0.386890
$545$	−6829.99	+	9379.16i	−0.536816	+	0.737173i
$546$	1657.81			0.129941
$547$		−	18561.2i		−	1.45086i	−0.688298	−	0.725428i	$-0.741642\pi$
$547$		−	18561.2i		−	1.45086i	0.688298	−	0.725428i	$-0.258358\pi$
$548$		−	22810.6i		−	1.77814i
$549$	−3124.44			−0.242892
$550$	−3993.39	+	1287.91i	−0.309597	+	0.0998485i
$551$	7356.26			0.568761
$552$			1516.92i			0.116965i
$553$		−	8150.68i		−	0.626767i
$554$	−7324.53			−0.561714
$555$	6626.52	−	9099.75i	0.506811	−	0.695969i
$556$	−20093.3			−1.53264
$557$		−	17604.9i		−	1.33922i	−0.742714	−	0.669608i	$-0.766462\pi$
$557$		−	17604.9i		−	1.33922i	0.742714	−	0.669608i	$-0.233538\pi$
$558$			10004.8i			0.759029i
$559$	9469.36			0.716478
$560$	−3565.13	−	2596.16i	−0.269025	−	0.195907i
$561$	463.441			0.0348779
$562$			7306.47i			0.548407i
$563$		−	3586.87i		−	0.268505i	−0.990947	−	0.134253i	$-0.957137\pi$
$563$		−	3586.87i		−	0.268505i	0.990947	−	0.134253i	$-0.0428634\pi$
$564$	2576.58			0.192365
$565$	−13372.8	−	9738.17i	−0.995745	−	0.725111i
$566$	30283.2			2.24894
$567$		−	567.000i		−	0.0419961i
$568$		−	1079.67i		−	0.0797573i
$569$	3213.58			0.236767			0.118383	−	0.992968i	$-0.462229\pi$
$569$	3213.58			0.236767			0.118383	+	0.992968i	$0.462229\pi$
$570$	6202.73	−	8517.79i	0.455796	−	0.625914i
$571$	−14706.3			−1.07783			−0.538913	−	0.842361i	$-0.681165\pi$
$571$	−14706.3			−1.07783			−0.538913	+	0.842361i	$0.681165\pi$
$572$		−	1392.77i		−	0.101809i
$573$		−	13198.9i		−	0.962287i
$574$	−3534.64			−0.257026
$575$	16975.5	−	5474.78i	1.23118	−	0.397068i
$576$	−5542.70			−0.400947
$577$			3632.05i			0.262052i	0.991379	+	0.131026i	$0.0418272\pi$
$577$			3632.05i			0.262052i	−0.991379	+	0.131026i	$0.958173\pi$
$578$			18708.4i			1.34631i
$579$	−905.874			−0.0650205
$580$	5609.04	−	7702.50i	0.401556	−	0.551429i
$581$	−6224.32			−0.444455
$582$		−	14857.8i		−	1.05821i
$583$		−	3176.56i		−	0.225660i
$584$	−2671.81			−0.189316
$585$	−1563.72	−	1138.72i	−0.110516	−	0.0804790i
$586$	−3835.51			−0.270381
$587$			15671.9i			1.10196i	0.834520	+	0.550978i	$0.185745\pi$
$587$			15671.9i			1.10196i	−0.834520	+	0.550978i	$0.814255\pi$
$588$			1302.85i			0.0913753i
$589$	−20709.6			−1.44877
$590$	4190.01	+	3051.21i	0.292373	+	0.212909i
$591$	−2858.85			−0.198980
$592$		−	18912.5i		−	1.31300i
$593$		−	6007.59i		−	0.416024i	−0.978126	−	0.208012i	$-0.933301\pi$
$593$		−	6007.59i		−	0.416024i	0.978126	−	0.208012i	$-0.0666992\pi$
$594$	−906.321			−0.0626041
$595$	−870.651	+	1195.61i	−0.0599886	+	0.0823782i
$596$	4051.83			0.278472
$597$		−	12374.7i		−	0.848347i
$598$			11264.6i			0.770305i
$599$	−10787.4			−0.735832			−0.367916	−	0.929859i	$-0.619929\pi$
$599$	−10787.4			−0.735832			−0.367916	+	0.929859i	$0.619929\pi$
$600$	−407.878	−	1264.70i	−0.0277526	−	0.0860517i
$601$	−9839.14			−0.667798			−0.333899	−	0.942609i	$-0.608364\pi$
$601$	−9839.14			−0.667798			−0.333899	+	0.942609i	$0.608364\pi$
$602$			14159.1i			0.958609i
$603$			914.875i			0.0617854i
$604$	−20033.6			−1.34959
$605$	8320.20	−	11425.6i	0.559114	−	0.767793i
$606$	−5376.25			−0.360388
$607$			5572.23i			0.372603i	0.982493	+	0.186301i	$0.0596501\pi$
$607$			5572.23i			0.372603i	−0.982493	+	0.186301i	$0.940350\pi$
$608$		−	19871.7i		−	1.32550i
$609$	2019.32			0.134363
$610$	−12884.4	−	9382.54i	−0.855203	−	0.622767i
$611$	1862.92			0.123348
$612$			1507.44i			0.0995667i
$613$			27431.5i			1.80742i	0.428147	+	0.903709i	$0.359167\pi$
$613$			27431.5i			1.80742i	−0.428147	+	0.903709i	$0.640833\pi$
$614$	7921.75			0.520677
$615$	3334.04	+	2427.88i	0.218604	+	0.159189i
$616$	202.765			0.0132624
$617$		−	6390.91i		−	0.416999i	−0.978022	−	0.208499i	$-0.933142\pi$
$617$		−	6390.91i		−	0.416999i	0.978022	−	0.208499i	$-0.0668580\pi$
$618$			21749.5i			1.41569i
$619$	−5725.64			−0.371782			−0.185891	−	0.982570i	$-0.559517\pi$
$619$	−5725.64			−0.371782			−0.185891	+	0.982570i	$0.559517\pi$
$620$	−15790.7	+	21684.3i	−1.02286	+	1.40462i
$621$	3852.68			0.248958
$622$		−	18336.0i		−	1.18201i
$623$		−	6571.80i		−	0.422622i
$624$	−3249.97			−0.208498
$625$	−12680.8	+	9128.93i	−0.811573	+	0.584252i
$626$	−30623.1			−1.95518
$627$		−	1876.05i		−	0.119493i
$628$		−	5706.63i		−	0.362611i
$629$	−6342.51			−0.402055
$630$	1702.67	−	2338.17i	0.107676	−	0.147865i
$631$	16835.6			1.06215			0.531074	−	0.847326i	$-0.321789\pi$
$631$	16835.6			1.06215			0.531074	+	0.847326i	$0.321789\pi$
$632$		−	4126.08i		−	0.259694i
$633$		−	3044.23i		−	0.191149i
$634$	8314.91			0.520863
$635$	14763.6	+	10751.0i	0.922641	+	0.671876i
$636$	10332.5			0.644196
$637$			941.987i			0.0585917i
$638$		−	3227.78i		−	0.200297i
$639$	−2742.16			−0.169762
$640$	−4075.55	−	2967.86i	−0.251719	−	0.183304i
$641$	12957.8			0.798446			0.399223	−	0.916854i	$-0.369280\pi$
$641$	12957.8			0.798446			0.399223	+	0.916854i	$0.369280\pi$
$642$		−	3752.46i		−	0.230682i
$643$		−	5665.07i		−	0.347447i	−0.984794	−	0.173724i	$-0.944420\pi$
$643$		−	5665.07i		−	0.347447i	0.984794	−	0.173724i	$-0.0555800\pi$
$644$	−8852.68			−0.541684
$645$	9725.63	−	13355.5i	0.593715	−	0.815308i
$646$	−5936.89			−0.361585
$647$			11556.3i			0.702201i	0.936338	+	0.351101i	$0.114192\pi$
$647$			11556.3i			0.702201i	−0.936338	+	0.351101i	$0.885808\pi$
$648$		−	287.030i		−	0.0174006i
$649$	922.852			0.0558168
$650$	−3028.88	−	9391.57i	−0.182773	−	0.566720i
$651$	−5684.86			−0.342254
$652$			27383.4i			1.64481i
$653$			21891.6i			1.31192i	0.754795	+	0.655961i	$0.227736\pi$
$653$			21891.6i			1.31192i	−0.754795	+	0.655961i	$0.772264\pi$
$654$	−12784.5			−0.764393
$655$	2364.65	−	3247.21i	0.141060	−	0.193708i
$656$	6929.30			0.412414
$657$			6785.88i			0.402956i
$658$			2785.54i			0.165033i
$659$	−12118.3			−0.716332			−0.358166	−	0.933658i	$-0.616598\pi$
$659$	−12118.3			−0.716332			−0.358166	+	0.933658i	$0.616598\pi$
$660$	−1964.35	−	1430.46i	−0.115852	−	0.0843644i
$661$	739.495			0.0435144			0.0217572	−	0.999763i	$-0.493074\pi$
$661$	739.495			0.0435144			0.0217572	+	0.999763i	$0.493074\pi$
$662$			12949.9i			0.760292i
$663$			1089.91i			0.0638442i
$664$	−3150.91			−0.184155
$665$	4839.91	+	3524.47i	0.282231	+	0.205523i
$666$	12403.6			0.721668
$667$			13721.0i			0.796520i
$668$		−	24167.8i		−	1.39982i
$669$	−15128.8			−0.874312
$670$	−2747.33	+	3772.71i	−0.158416	+	0.217541i
$671$	−2837.79			−0.163267
$672$		−	5454.85i		−	0.313133i
$673$		−	21080.0i		−	1.20739i	−0.797215	−	0.603695i	$-0.793694\pi$
$673$		−	21080.0i		−	1.20739i	0.797215	−	0.603695i	$-0.206306\pi$
$674$	−20771.9			−1.18710
$675$	−3212.08	+	1035.93i	−0.183160	+	0.0590711i
$676$	−16196.4			−0.921505
$677$		−	9588.70i		−	0.544348i	−0.962248	−	0.272174i	$-0.912257\pi$
$677$		−	9588.70i		−	0.544348i	0.962248	−	0.272174i	$-0.0877427\pi$
$678$		−	18228.1i		−	1.03251i
$679$	8442.39			0.477156
$680$	−440.746	+	605.246i	−0.0248557	+	0.0341326i
$681$	17494.9			0.984442
$682$			9086.97i			0.510202i
$683$		−	33084.2i		−	1.85348i	−0.375698	−	0.926742i	$-0.622597\pi$
$683$		−	33084.2i		−	1.85348i	0.375698	−	0.926742i	$-0.377403\pi$
$684$	6102.26			0.341119
$685$	−23261.0	−	16938.9i	−1.29745	−	0.944818i
$686$	−1408.51			−0.0783925
$687$		−	55.6970i		−	0.00309312i
$688$		−	27757.5i		−	1.53815i
$689$	7470.58			0.413072
$690$	15887.5	+	11569.4i	0.876560	+	0.638319i
$691$	−6292.90			−0.346445			−0.173222	−	0.984883i	$-0.555418\pi$
$691$	−6292.90			−0.346445			−0.173222	+	0.984883i	$0.555418\pi$
$692$			7993.61i			0.439120i
$693$		−	514.982i		−	0.0282288i
$694$	32647.3			1.78570
$695$	−14921.0	+	20490.0i	−0.814369	+	1.11832i
$696$	1022.23			0.0556719
$697$		−	2323.82i		−	0.126285i
$698$		−	19349.2i		−	1.04925i
$699$	−5197.87			−0.281261
$700$	7380.71	−	2380.36i	0.398521	−	0.128527i
$701$	23822.6			1.28355			0.641775	−	0.766893i	$-0.278198\pi$
$701$	23822.6			1.28355			0.641775	+	0.766893i	$0.278198\pi$
$702$		−	2131.47i		−	0.114597i
$703$			25675.0i			1.37746i
$704$	−5034.20			−0.269508
$705$	1913.34	−	2627.45i	0.102213	−	0.140363i
$706$	1266.83			0.0675322
$707$		−	3054.85i		−	0.162503i
$708$			3001.78i			0.159342i
$709$	−10562.0			−0.559471			−0.279736	−	0.960077i	$-0.590247\pi$
$709$	−10562.0			−0.559471			−0.279736	+	0.960077i	$0.590247\pi$
$710$	−11308.0	−	8234.58i	−0.597720	−	0.435265i
$711$	−10479.4			−0.552756
$712$		−	3326.82i		−	0.175109i
$713$		−	38627.8i		−	2.02892i
$714$	−1629.70			−0.0854201
$715$	−1420.26	−	1034.25i	−0.0742865	−	0.0540962i
$716$	40305.2			2.10374
$717$			5812.62i			0.302756i
$718$			31204.5i			1.62193i
$719$	3538.42			0.183534			0.0917670	−	0.995781i	$-0.470749\pi$
$719$	3538.42			0.183534			0.0917670	+	0.995781i	$0.470749\pi$
$720$	−3337.92	+	4583.73i	−0.172773	+	0.237258i
$721$	−12358.3			−0.638347
$722$		−	4133.14i		−	0.213047i
$723$			16839.0i			0.866184i
$724$	3562.92			0.182894
$725$	−3689.38	−	11439.6i	−0.188993	−	0.586006i
$726$	15573.9			0.796145
$727$		−	14066.6i		−	0.717608i	−0.933413	−	0.358804i	$-0.883185\pi$
$727$		−	14066.6i		−	0.717608i	0.933413	−	0.358804i	$-0.116815\pi$
$728$			476.858i			0.0242768i
$729$	−729.000			−0.0370370
$730$	−20377.7	+	27983.3i	−1.03317	+	1.41878i
$731$	−9308.79			−0.470996
$732$		−	9230.55i		−	0.466081i
$733$		−	34204.1i		−	1.72354i	−0.507298	−	0.861771i	$-0.669356\pi$
$733$		−	34204.1i		−	1.72354i	0.507298	−	0.861771i	$-0.330644\pi$
$734$	−8448.94			−0.424872
$735$	1328.57	+	967.480i	0.0666737	+	0.0485524i
$736$	37064.9			1.85629
$737$			830.943i			0.0415308i
$738$			4544.54i			0.226676i
$739$	24949.9			1.24195			0.620973	−	0.783832i	$-0.286738\pi$
$739$	24949.9			1.24195			0.620973	+	0.783832i	$0.286738\pi$
$740$	26883.5	+	19576.8i	1.33548	+	0.972510i
$741$	4412.06			0.218733
$742$			11170.4i			0.552668i
$743$			16171.5i			0.798487i	0.916845	+	0.399244i	$0.130727\pi$
$743$			16171.5i			0.798487i	−0.916845	+	0.399244i	$0.869273\pi$
$744$	−2877.82			−0.141809
$745$	3008.84	−	4131.83i	0.147967	−	0.203193i
$746$	23248.4			1.14100
$747$			8002.69i			0.391972i
$748$			1369.15i			0.0669265i
$749$	2132.19			0.104017
$750$	−16356.7	−	5373.81i	−0.796348	−	0.261632i
$751$	18661.4			0.906744			0.453372	−	0.891321i	$-0.350221\pi$
$751$	18661.4			0.906744			0.453372	+	0.891321i	$0.350221\pi$
$752$		−	5460.77i		−	0.264806i
$753$		−	15397.5i		−	0.745172i
$754$	7591.05			0.366644
$755$	−14876.7	+	20429.1i	−0.717109	+	0.984757i
$756$	1675.09			0.0805854
$757$			23051.3i			1.10675i	0.832931	+	0.553377i	$0.186661\pi$
$757$			23051.3i			1.10675i	−0.832931	+	0.553377i	$0.813339\pi$
$758$			7485.71i			0.358698i
$759$	3499.23			0.167344
$760$	2450.09	+	1784.18i	0.116939	+	0.0851564i
$761$	−18693.9			−0.890478			−0.445239	−	0.895412i	$-0.646881\pi$
$761$	−18693.9			−0.890478			−0.445239	+	0.895412i	$0.646881\pi$
$762$			20123.9i			0.956711i
$763$		−	7264.30i		−	0.344673i
$764$	38993.5			1.84651
$765$	1537.21	+	1119.41i	0.0726508	+	0.0529050i
$766$	−7746.14			−0.365378
$767$			2170.35i			0.102173i
$768$			9225.25i			0.433447i
$769$	−6553.93			−0.307335			−0.153668	−	0.988123i	$-0.549109\pi$
$769$	−6553.93			−0.307335			−0.153668	+	0.988123i	$0.549109\pi$
$770$	1546.47	−	2123.66i	0.0723777	−	0.0993913i
$771$	14067.6			0.657112
$772$		−	2676.23i		−	0.124767i
$773$		−	10818.2i		−	0.503368i	−0.967809	−	0.251684i	$-0.919016\pi$
$773$		−	10818.2i		−	0.503368i	0.967809	−	0.251684i	$-0.0809844\pi$
$774$	18204.6			0.845414
$775$	10386.5	+	32205.0i	0.481410	+	1.49269i
$776$	4273.75			0.197705
$777$			7047.89i			0.325407i
$778$			37284.7i			1.71815i
$779$	−9407.01			−0.432658
$780$	3364.13	−	4619.72i	0.154430	−	0.212067i
$781$	−2490.59			−0.114111
$782$		−	11073.6i		−	0.506381i
$783$		−	2596.27i		−	0.118497i
$784$	2761.24			0.125786
$785$	−5819.30	−	4237.67i	−0.264586	−	0.192674i
$786$	4426.19			0.200861
$787$			28571.9i			1.29413i	0.762436	+	0.647064i	$0.224003\pi$
$787$			28571.9i			1.29413i	−0.762436	+	0.647064i	$0.775997\pi$
$788$		−	8445.93i		−	0.381819i
$789$	−5303.59			−0.239307
$790$	−43214.6	−	31469.3i	−1.94621	−	1.41725i
$791$	10357.4			0.465571
$792$		−	260.697i		−	0.0116963i
$793$		−	6673.88i		−	0.298860i
$794$	−10762.8			−0.481054
$795$	7672.75	−	10536.5i	0.342295	−	0.470050i
$796$	36558.7			1.62788
$797$			531.831i			0.0236367i	0.999930	+	0.0118183i	$0.00376198\pi$
$797$			531.831i			0.0236367i	−0.999930	+	0.0118183i	$0.996238\pi$
$798$			6597.15i			0.292652i
$799$	−1831.33			−0.0810862
$800$	−30902.0	+	9966.23i	−1.36569	+	0.440449i
$801$	−8449.46			−0.372718
$802$		−	44152.9i		−	1.94401i
$803$			6163.33i			0.270858i
$804$	−2702.82			−0.118559
$805$	−6573.88	+	9027.46i	−0.287825	+	0.395250i
$806$	−21370.6			−0.933929
$807$			23607.4i			1.02976i
$808$		−	1546.44i		−	0.0673313i
$809$	−44326.9			−1.92639			−0.963196	−	0.268801i	$-0.913373\pi$
$809$	−44326.9			−1.92639			−0.963196	+	0.268801i	$0.913373\pi$
$810$	−3006.21	−	2189.15i	−0.130404	−	0.0949617i
$811$	9509.56			0.411746			0.205873	−	0.978579i	$-0.433997\pi$
$811$	9509.56			0.411746			0.205873	+	0.978579i	$0.433997\pi$
$812$			5965.70i			0.257827i
$813$			14461.5i			0.623848i
$814$	11265.7			0.485089
$815$	27924.1	+	20334.6i	1.20017	+	0.873974i
$816$	3194.86			0.137062
$817$			37682.7i			1.61365i
$818$		−	54952.7i		−	2.34887i
$819$	1211.13			0.0516730
$820$	−7172.70	+	9849.78i	−0.305465	+	0.419474i
$821$	45600.8			1.93846			0.969232	−	0.246148i	$-0.0791650\pi$
$821$	45600.8			1.93846			0.969232	+	0.246148i	$0.0791650\pi$
$822$		−	31706.4i		−	1.34536i
$823$			14111.4i			0.597681i	0.954303	+	0.298841i	$0.0965999\pi$
$823$			14111.4i			0.597681i	−0.954303	+	0.298841i	$0.903400\pi$
$824$	−6256.10			−0.264492
$825$	−2917.40	+	940.893i	−0.123116	+	0.0397063i
$826$	−3245.23			−0.136702
$827$		−	10907.3i		−	0.458628i	−0.973352	−	0.229314i	$-0.926352\pi$
$827$		−	10907.3i		−	0.458628i	0.973352	−	0.229314i	$-0.0736483\pi$
$828$			11382.0i			0.477720i
$829$	6653.10			0.278736			0.139368	−	0.990241i	$-0.455493\pi$
$829$	6653.10			0.278736			0.139368	+	0.990241i	$0.455493\pi$
$830$	−24031.7	+	33001.1i	−1.00500	+	1.38010i
$831$	−5350.99			−0.223374
$832$		−	11839.3i		−	0.493336i
$833$		−	926.014i		−	0.0385168i
$834$	−27929.4			−1.15961
$835$	−24644.9	−	17946.7i	−1.02140	−	0.743797i
$836$	5542.43			0.229293
$837$			7309.11i			0.301840i
$838$		−	9592.28i		−	0.395418i
$839$	4960.81			0.204131			0.102066	−	0.994778i	$-0.467455\pi$
$839$	4960.81			0.204131			0.102066	+	0.994778i	$0.467455\pi$
$840$	672.558	+	489.763i	0.0276256	+	0.0201172i
$841$	−15142.6			−0.620878
$842$			17504.6i			0.716447i
$843$			5337.80i			0.218083i
$844$	8993.59			0.366791
$845$	−12027.2	+	16516.1i	−0.489644	+	0.672394i
$846$	3581.41			0.145546
$847$			8849.26i			0.358990i
$848$		−	21898.5i		−	0.886789i
$849$	22123.7			0.894325
$850$	2977.52	+	9232.32i	0.120151	+	0.372548i
$851$	−47889.4			−1.92906
$852$		−	8101.19i		−	0.325754i
$853$			26053.2i			1.04577i	0.852402	+	0.522887i	$0.175145\pi$
$853$			26053.2i			1.04577i	−0.852402	+	0.522887i	$0.824855\pi$
$854$	9979.15			0.399859
$855$	4531.46	−	6222.74i	0.181254	−	0.248904i
$856$	1079.37			0.0430983
$857$		−	42983.0i		−	1.71327i	−0.515924	−	0.856635i	$-0.672551\pi$
$857$		−	42983.0i		−	1.71327i	0.515924	−	0.856635i	$-0.327449\pi$
$858$		−	1935.93i		−	0.0770296i
$859$	31824.0			1.26405			0.632027	−	0.774946i	$-0.282223\pi$
$859$	31824.0			1.26405			0.632027	+	0.774946i	$0.282223\pi$
$860$	39456.4	+	28732.5i	1.56448	+	1.13927i
$861$	−2582.26			−0.102210
$862$			21492.2i			0.849221i
$863$			20388.4i			0.804207i	0.915594	+	0.402103i	$0.131721\pi$
$863$			20388.4i			0.804207i	−0.915594	+	0.402103i	$0.868279\pi$
$864$	−7013.38			−0.276158
$865$	8151.43	+	5935.95i	0.320413	+	0.233327i
$866$	−60067.2			−2.35701
$867$			13667.6i			0.535381i
$868$		−	16794.8i		−	0.656745i
$869$	−9518.04			−0.371551
$870$	7796.48	−	10706.4i	0.303822	−	0.417218i
$871$	−1954.20			−0.0760223
$872$		−	3677.38i		−	0.142812i
$873$		−	10854.5i		−	0.420812i
$874$	−44826.7			−1.73488
$875$	3053.46	−	9294.06i	0.117972	−	0.359082i
$876$	−20047.6			−0.773225
$877$		−	15298.2i		−	0.589034i	−0.955646	−	0.294517i	$-0.904841\pi$
$877$		−	15298.2i		−	0.589034i	0.955646	−	0.294517i	$-0.0951588\pi$
$878$		−	144.943i		−	0.00557128i
$879$	−2802.06			−0.107521
$880$	−3031.69	+	4163.21i	−0.116134	+	0.159479i
$881$	22994.9			0.879361			0.439681	−	0.898154i	$-0.355092\pi$
$881$	22994.9			0.879361			0.439681	+	0.898154i	$0.355092\pi$
$882$			1810.94i			0.0691357i
$883$		−	799.661i		−	0.0304765i	−0.999884	−	0.0152382i	$-0.995149\pi$
$883$		−	799.661i		−	0.0304765i	0.999884	−	0.0152382i	$-0.00485067\pi$
$884$	−3219.94			−0.122509
$885$	3061.05	+	2229.08i	0.116267	+	0.0846664i
$886$	−11520.2			−0.436828
$887$			6611.21i			0.250262i	0.992140	+	0.125131i	$0.0399352\pi$
$887$			6611.21i			0.250262i	−0.992140	+	0.125131i	$0.960065\pi$
$888$			3567.82i			0.134829i
$889$	−11434.7			−0.431391
$890$	−34843.4	−	25373.3i	−1.31231	−	0.955636i
$891$	−662.120			−0.0248955
$892$		−	44695.3i		−	1.67770i
$893$			7413.38i			0.277804i
$894$	5631.99			0.210696
$895$	29930.1	−	41101.0i	1.11783	−	1.53503i
$896$	3156.58			0.117694
$897$			8229.42i			0.306324i
$898$		−	61198.4i		−	2.27418i
$899$	−26030.8			−0.965712
$900$	−3060.46	−	9489.49i	−0.113350	−	0.351462i
$901$	−7343.90			−0.271544
$902$			4127.61i			0.152366i
$903$			10344.1i			0.381206i
$904$	5243.18			0.192904
$905$	2645.78	−	3633.27i	0.0971809	−	0.133452i
$906$	−27846.4			−1.02112
$907$			11367.9i			0.416169i	0.978111	+	0.208084i	$0.0667228\pi$
$907$			11367.9i			0.416169i	−0.978111	+	0.208084i	$0.933277\pi$
$908$			51685.3i			1.88903i
$909$	−3927.66			−0.143314
$910$	4994.38	+	3636.96i	0.181936	+	0.132488i
$911$	−18431.4			−0.670318			−0.335159	−	0.942162i	$-0.608790\pi$
$911$	−18431.4			−0.670318			−0.335159	+	0.942162i	$0.608790\pi$
$912$		−	12933.0i		−	0.469579i
$913$			7268.51i			0.263475i
$914$	10815.8			0.391415
$915$	−9412.80	−	6854.49i	−0.340085	−	0.247653i
$916$	164.546			0.00593533
$917$			2515.01i			0.0905703i
$918$			2095.33i			0.0753334i
$919$	16263.1			0.583755			0.291877	−	0.956456i	$-0.405720\pi$
$919$	16263.1			0.583755			0.291877	+	0.956456i	$0.405720\pi$
$920$	−3327.87	+	4569.93i	−0.119257	+	0.163768i
$921$	5787.30			0.207055
$922$		−	75621.0i		−	2.70113i
$923$		−	5857.33i		−	0.208880i
$924$	1521.42			0.0541677
$925$	39926.6	−	12876.8i	1.41922	−	0.457714i
$926$	60820.6			2.15841
$927$			15889.3i			0.562969i
$928$		−	24977.6i		−	0.883544i
$929$	3972.84			0.140306			0.0701532	−	0.997536i	$-0.477651\pi$
$929$	3972.84			0.140306			0.0701532	+	0.997536i	$0.477651\pi$
$930$	−21948.9	+	30140.9i	−0.773907	+	1.06275i
$931$	−3748.58			−0.131960
$932$		−	15356.1i		−	0.539706i
$933$		−	13395.5i		−	0.470043i
$934$	59161.9			2.07263
$935$	1396.18	+	1016.71i	0.0488342	+	0.0355615i
$936$	613.104			0.0214102
$937$			144.199i			0.00502750i	0.999997	+	0.00251375i	$0.000800152\pi$
$937$			144.199i			0.00502750i	−0.999997	+	0.00251375i	$0.999200\pi$
$938$		−	2922.02i		−	0.101714i
$939$	−22371.9			−0.777508
$940$	7762.31	+	5652.59i	0.269339	+	0.196135i
$941$	48589.1			1.68327			0.841637	−	0.540044i	$-0.181593\pi$
$941$	48589.1			1.68327			0.841637	+	0.540044i	$0.181593\pi$
$942$		−	7932.14i		−	0.274356i
$943$		−	17546.1i		−	0.605916i
$944$	6361.93			0.219347
$945$	1243.90	−	1708.17i	0.0428192	−	0.0588007i
$946$	16534.5			0.568268
$947$		−	11977.2i		−	0.410989i	−0.978658	−	0.205494i	$-0.934120\pi$
$947$		−	11977.2i		−	0.410989i	0.978658	−	0.205494i	$-0.0658802\pi$
$948$		−	30959.5i		−	1.06067i
$949$	−14494.8			−0.495808
$950$	37373.2	−	12053.3i	1.27636	−	0.411641i
$951$	6074.52			0.207129
$952$		−	468.772i		−	0.0159590i
$953$			45863.7i			1.55894i	0.626439	+	0.779471i	$0.284512\pi$
$953$			45863.7i			1.55894i	−0.626439	+	0.779471i	$0.715488\pi$
$954$	14362.0			0.487407
$955$	28956.1	−	39763.4i	0.981149	−	1.34734i
$956$	−17172.3			−0.580953
$957$		−	2358.08i		−	0.0796510i
$958$			27222.3i			0.918073i
$959$	18016.0			0.606638
$960$	−16698.1	−	12159.7i	−0.561386	−	0.408806i
$961$	43491.7			1.45989
$962$			26494.5i			0.887959i
$963$		−	2741.39i		−	0.0917342i
$964$	−49747.8			−1.66210
$965$	−2729.07	−	1987.34i	−0.0910383	−	0.0662949i
$966$	−12305.1			−0.409845
$967$			19843.3i			0.659894i	0.944000	+	0.329947i	$0.107031\pi$
$967$			19843.3i			0.659894i	−0.944000	+	0.329947i	$0.892969\pi$
$968$			4479.73i			0.148744i
$969$	−4337.24			−0.143790
$970$	32595.6	−	44761.2i	1.07895	−	1.48165i
$971$	−45035.7			−1.48843			−0.744214	−	0.667941i	$-0.767176\pi$
$971$	−45035.7			−1.48843			−0.744214	+	0.667941i	$0.767176\pi$
$972$		−	2153.69i		−	0.0710697i
$973$		−	15869.8i		−	0.522881i
$974$	15976.0			0.525568
$975$	−2212.78	−	6861.09i	−0.0726826	−	0.225365i
$976$	−19563.1			−0.641598
$977$		−	25098.2i		−	0.821865i	−0.911666	−	0.410932i	$-0.865203\pi$
$977$		−	25098.2i		−	0.821865i	0.911666	−	0.410932i	$-0.134797\pi$
$978$			38062.6i			1.24449i
$979$	−7674.29			−0.250533
$980$	−2858.24	+	3925.02i	−0.0931663	+	0.127939i
$981$	−9339.81			−0.303973
$982$		−	52579.4i		−	1.70863i
$983$			388.045i			0.0125908i	0.999980	+	0.00629538i	$0.00200389\pi$
$983$			388.045i			0.0125908i	−0.999980	+	0.00629538i	$0.997996\pi$
$984$	−1307.21			−0.0423498
$985$	−8612.68	−	6271.84i	−0.278602	−	0.202881i
$986$	−7462.33			−0.241023
$987$			2035.00i			0.0656280i
$988$			13034.6i			0.419722i
$989$	−70286.4			−2.25983
$990$	−2730.42	−	1988.32i	−0.0876549	−	0.0638312i
$991$	53520.8			1.71558			0.857792	−	0.513997i	$-0.171836\pi$
$991$	53520.8			1.71558			0.857792	+	0.513997i	$0.171836\pi$
$992$			70317.7i			2.25059i
$993$			9460.68i			0.302342i
$994$	8758.20			0.279470
$995$	27148.0	−	37280.5i	0.864975	−	1.18781i
$996$	−23642.4			−0.752148
$997$		−	5968.90i		−	0.189606i	−0.995496	−	0.0948028i	$-0.969778\pi$
$997$		−	5968.90i		−	0.189606i	0.995496	−	0.0948028i	$-0.0302221\pi$
$998$			23992.2i			0.760981i
$999$	9061.57			0.286982

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.d.a.64.6	yes	6
3.2	odd	2		315.4.d.a.64.1		6
5.2	odd	4		525.4.a.q.1.1		3
5.3	odd	4		525.4.a.r.1.3		3
5.4	even	2	inner	105.4.d.a.64.1	✓	6
15.2	even	4		1575.4.a.bd.1.3		3
15.8	even	4		1575.4.a.bc.1.1		3
15.14	odd	2		315.4.d.a.64.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.d.a.64.1	✓	6	5.4	even	2	inner
105.4.d.a.64.6	yes	6	1.1	even	1	trivial
315.4.d.a.64.1		6	3.2	odd	2
315.4.d.a.64.6		6	15.14	odd	2
525.4.a.q.1.1		3	5.2	odd	4
525.4.a.r.1.3		3	5.3	odd	4
1575.4.a.bc.1.1		3	15.8	even	4
1575.4.a.bd.1.3		3	15.2	even	4

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4.10645i q^{2} +3.00000i q^{3} -8.86293 q^{4} +(-6.58150 + 9.03792i) q^{5} -12.3193 q^{6} -7.00000i q^{7} -3.54358i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+4.10645i q^{2} +3.00000i q^{3} -8.86293 q^{4} +(-6.58150 + 9.03792i) q^{5} -12.3193 q^{6} -7.00000i q^{7} -3.54358i q^{8} -9.00000 q^{9} +(-37.1137 - 27.0266i) q^{10} -8.17432 q^{11} -26.5888i q^{12} -19.2242i q^{13} +28.7451 q^{14} +(-27.1137 - 19.7445i) q^{15} -56.3519 q^{16} +18.8982i q^{17} -36.9580i q^{18} +76.5016 q^{19} +(58.3313 - 80.1024i) q^{20} +21.0000 q^{21} -33.5675i q^{22} +142.692i q^{23} +10.6307 q^{24} +(-38.3678 - 118.966i) q^{25} +78.9433 q^{26} -27.0000i q^{27} +62.0405i q^{28} +96.1582 q^{29} +(81.0798 - 111.341i) q^{30} -270.708 q^{31} -259.755i q^{32} -24.5230i q^{33} -77.6047 q^{34} +(63.2654 + 46.0705i) q^{35} +79.7664 q^{36} +335.614i q^{37} +314.150i q^{38} +57.6727 q^{39} +(32.0266 + 23.3221i) q^{40} -122.965 q^{41} +86.2354i q^{42} +492.574i q^{43} +72.4485 q^{44} +(59.2335 - 81.3412i) q^{45} -585.957 q^{46} +96.9049i q^{47} -169.056i q^{48} -49.0000 q^{49} +(488.528 - 157.556i) q^{50} -56.6947 q^{51} +170.383i q^{52} +388.602i q^{53} +110.874 q^{54} +(53.7993 - 73.8788i) q^{55} -24.8051 q^{56} +229.505i q^{57} +394.869i q^{58} -112.896 q^{59} +(240.307 + 174.994i) q^{60} +347.160 q^{61} -1111.65i q^{62} +63.0000i q^{63} +615.855 q^{64} +(173.747 + 126.524i) q^{65} +100.702 q^{66} -101.653i q^{67} -167.494i q^{68} -428.076 q^{69} +(-189.186 + 259.796i) q^{70} +304.685 q^{71} +31.8922i q^{72} -753.987i q^{73} -1378.18 q^{74} +(356.898 - 115.103i) q^{75} -678.029 q^{76} +57.2203i q^{77} +236.830i q^{78} +1164.38 q^{79} +(370.880 - 509.304i) q^{80} +81.0000 q^{81} -504.949i q^{82} -889.188i q^{83} -186.122 q^{84} +(-170.801 - 124.379i) q^{85} -2022.73 q^{86} +288.475i q^{87} +28.9664i q^{88} +938.829 q^{89} +(334.024 + 243.239i) q^{90} -134.570 q^{91} -1264.67i q^{92} -812.123i q^{93} -397.935 q^{94} +(-503.495 + 691.415i) q^{95} +779.265 q^{96} +1206.06i q^{97} -201.216i q^{98} +73.5689 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 14 q^{5} - 6 q^{6} - 54 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 14 * q^5 - 6 * q^6 - 54 * q^9	\( 6 q - 6 q^{4} - 14 q^{5} - 6 q^{6} - 54 q^{9} - 84 q^{10} - 132 q^{11} + 14 q^{14} - 24 q^{15} - 138 q^{16} + 276 q^{19} + 334 q^{20} + 126 q^{21} + 126 q^{24} + 366 q^{25} - 196 q^{26} - 340 q^{29} - 54 q^{30} - 732 q^{31} + 72 q^{34} + 56 q^{35} + 54 q^{36} + 612 q^{39} + 12 q^{40} - 412 q^{41} + 612 q^{44} + 126 q^{45} - 1344 q^{46} - 294 q^{49} + 1216 q^{50} - 912 q^{51} + 54 q^{54} + 1860 q^{55} - 294 q^{56} + 1760 q^{59} + 624 q^{60} - 1740 q^{61} + 1626 q^{64} - 16 q^{65} - 1116 q^{66} - 1080 q^{69} + 126 q^{70} - 2036 q^{71} - 1960 q^{74} + 936 q^{75} - 900 q^{76} + 3240 q^{79} + 3794 q^{80} + 486 q^{81} - 126 q^{84} + 432 q^{85} - 5864 q^{86} + 3876 q^{89} + 756 q^{90} - 1428 q^{91} - 4224 q^{94} - 828 q^{95} + 906 q^{96} + 1188 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 - 14 * q^5 - 6 * q^6 - 54 * q^9 - 84 * q^10 - 132 * q^11 + 14 * q^14 - 24 * q^15 - 138 * q^16 + 276 * q^19 + 334 * q^20 + 126 * q^21 + 126 * q^24 + 366 * q^25 - 196 * q^26 - 340 * q^29 - 54 * q^30 - 732 * q^31 + 72 * q^34 + 56 * q^35 + 54 * q^36 + 612 * q^39 + 12 * q^40 - 412 * q^41 + 612 * q^44 + 126 * q^45 - 1344 * q^46 - 294 * q^49 + 1216 * q^50 - 912 * q^51 + 54 * q^54 + 1860 * q^55 - 294 * q^56 + 1760 * q^59 + 624 * q^60 - 1740 * q^61 + 1626 * q^64 - 16 * q^65 - 1116 * q^66 - 1080 * q^69 + 126 * q^70 - 2036 * q^71 - 1960 * q^74 + 936 * q^75 - 900 * q^76 + 3240 * q^79 + 3794 * q^80 + 486 * q^81 - 126 * q^84 + 432 * q^85 - 5864 * q^86 + 3876 * q^89 + 756 * q^90 - 1428 * q^91 - 4224 * q^94 - 828 * q^95 + 906 * q^96 + 1188 * q^99

Introduction

L-functions

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