LMFDB - Embedded newform 105.3.c.a.71.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(71,105)]

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([1, 0, 0]))

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

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

chi := DirichletCharacter("105.71");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.c (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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 46x^{14} + 823x^{12} + 7252x^{10} + 32831x^{8} + 71486x^{6} + 60809x^{4} + 15680x^{2} + 576 $ x^16 + 46x^14 + 823x^12 + 7252x^10 + 32831x^8 + 71486x^6 + 60809x^4 + 15680*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.9
Root			$0.209282i$ of defining polynomial
Character	$\chi$	$=$	105.71
Dual form			105.3.c.a.71.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.209282i q^{2} +(1.91543 - 2.30892i) q^{3} +3.95620 q^{4} -2.23607i q^{5} +(0.483215 + 0.400865i) q^{6} -2.64575 q^{7} +1.66509i q^{8} +(-1.66223 - 8.84517i) q^{9} +O(q^{10})$	\(q+0.209282i q^{2} +(1.91543 - 2.30892i) q^{3} +3.95620 q^{4} -2.23607i q^{5} +(0.483215 + 0.400865i) q^{6} -2.64575 q^{7} +1.66509i q^{8} +(-1.66223 - 8.84517i) q^{9} +0.467968 q^{10} +9.19797i q^{11} +(7.57784 - 9.13456i) q^{12} -7.18410 q^{13} -0.553707i q^{14} +(-5.16290 - 4.28304i) q^{15} +15.4763 q^{16} -4.35298i q^{17} +(1.85113 - 0.347875i) q^{18} +20.7496 q^{19} -8.84633i q^{20} +(-5.06776 + 6.10883i) q^{21} -1.92497 q^{22} +26.5430i q^{23} +(3.84455 + 3.18936i) q^{24} -5.00000 q^{25} -1.50350i q^{26} +(-23.6067 - 13.1044i) q^{27} -10.4671 q^{28} +27.3836i q^{29} +(0.896361 - 1.08050i) q^{30} -33.2578 q^{31} +9.89926i q^{32} +(21.2374 + 17.6181i) q^{33} +0.910998 q^{34} +5.91608i q^{35} +(-6.57612 - 34.9933i) q^{36} -58.4402 q^{37} +4.34251i q^{38} +(-13.7607 + 16.5875i) q^{39} +3.72325 q^{40} +39.8731i q^{41} +(-1.27847 - 1.06059i) q^{42} +23.7965 q^{43} +36.3890i q^{44} +(-19.7784 + 3.71686i) q^{45} -5.55497 q^{46} -85.1268i q^{47} +(29.6439 - 35.7336i) q^{48} +7.00000 q^{49} -1.04641i q^{50} +(-10.0507 - 8.33784i) q^{51} -28.4218 q^{52} +20.7258i q^{53} +(2.74250 - 4.94045i) q^{54} +20.5673 q^{55} -4.40541i q^{56} +(39.7444 - 47.9091i) q^{57} -5.73089 q^{58} +72.4687i q^{59} +(-20.4255 - 16.9446i) q^{60} +86.5222 q^{61} -6.96024i q^{62} +(4.39785 + 23.4021i) q^{63} +59.8336 q^{64} +16.0641i q^{65} +(-3.68714 + 4.44459i) q^{66} -38.8274 q^{67} -17.2213i q^{68} +(61.2858 + 50.8414i) q^{69} -1.23813 q^{70} -91.4233i q^{71} +(14.7280 - 2.76776i) q^{72} +11.4771 q^{73} -12.2305i q^{74} +(-9.57717 + 11.5446i) q^{75} +82.0895 q^{76} -24.3355i q^{77} +(-3.47146 - 2.87986i) q^{78} -41.5002 q^{79} -34.6061i q^{80} +(-75.4740 + 29.4054i) q^{81} -8.34470 q^{82} -154.585i q^{83} +(-20.0491 + 24.1678i) q^{84} -9.73355 q^{85} +4.98017i q^{86} +(63.2266 + 52.4515i) q^{87} -15.3154 q^{88} -135.478i q^{89} +(-0.777871 - 4.13926i) q^{90} +19.0073 q^{91} +105.010i q^{92} +(-63.7030 + 76.7895i) q^{93} +17.8155 q^{94} -46.3975i q^{95} +(22.8566 + 18.9614i) q^{96} -48.0704 q^{97} +1.46497i q^{98} +(81.3575 - 15.2892i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9	$ 16 q + 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9} - 20 q^{10} + 12 q^{12} + 10 q^{15} + 92 q^{16} - 52 q^{18} - 16 q^{19} - 14 q^{21} + 16 q^{22} + 128 q^{24} - 80 q^{25} - 148 q^{27} + 112 q^{28} + 80 q^{30} - 72 q^{31} - 4 q^{33} - 176 q^{34} - 76 q^{36} - 40 q^{37} + 90 q^{39} - 60 q^{40} + 280 q^{43} + 40 q^{45} + 72 q^{46} - 172 q^{48} + 112 q^{49} + 38 q^{51} - 88 q^{52} + 208 q^{54} + 80 q^{55} - 36 q^{57} - 24 q^{58} - 80 q^{60} - 56 q^{61} - 56 q^{63} - 44 q^{64} - 260 q^{66} - 120 q^{67} + 60 q^{69} + 376 q^{72} - 208 q^{73} - 40 q^{75} + 144 q^{76} - 228 q^{78} - 204 q^{79} + 458 q^{81} - 384 q^{82} - 84 q^{84} + 100 q^{85} - 324 q^{87} + 168 q^{88} - 160 q^{90} - 28 q^{91} + 108 q^{93} + 984 q^{94} + 40 q^{96} + 728 q^{97} - 166 q^{99}+O(q^{100}) $ 16 * q + 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9 - 20 * q^10 + 12 * q^12 + 10 * q^15 + 92 * q^16 - 52 * q^18 - 16 * q^19 - 14 * q^21 + 16 * q^22 + 128 * q^24 - 80 * q^25 - 148 * q^27 + 112 * q^28 + 80 * q^30 - 72 * q^31 - 4 * q^33 - 176 * q^34 - 76 * q^36 - 40 * q^37 + 90 * q^39 - 60 * q^40 + 280 * q^43 + 40 * q^45 + 72 * q^46 - 172 * q^48 + 112 * q^49 + 38 * q^51 - 88 * q^52 + 208 * q^54 + 80 * q^55 - 36 * q^57 - 24 * q^58 - 80 * q^60 - 56 * q^61 - 56 * q^63 - 44 * q^64 - 260 * q^66 - 120 * q^67 + 60 * q^69 + 376 * q^72 - 208 * q^73 - 40 * q^75 + 144 * q^76 - 228 * q^78 - 204 * q^79 + 458 * q^81 - 384 * q^82 - 84 * q^84 + 100 * q^85 - 324 * q^87 + 168 * q^88 - 160 * q^90 - 28 * q^91 + 108 * q^93 + 984 * q^94 + 40 * q^96 + 728 * q^97 - 166 * 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 $

$2$			0.209282i			0.104641i	0.998630	+	0.0523204i	$0.0166617\pi$
$2$			0.209282i			0.104641i	−0.998630	+	0.0523204i	$0.983338\pi$
$3$	1.91543	−	2.30892i	0.638478	−	0.769640i
$3$	1.91543	−	2.30892i	0.638478	−	0.769640i
$4$	3.95620			0.989050
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$	0.483215	+	0.400865i	0.0805358	+	0.0668108i
$7$	−2.64575			−0.377964
$7$	−2.64575			−0.377964
$8$			1.66509i			0.208136i
$9$	−1.66223	−	8.84517i	−0.184692	−	0.982796i
$10$	0.467968			0.0467968
$11$			9.19797i			0.836179i	0.908406	+	0.418089i	$0.137300\pi$
$11$			9.19797i			0.836179i	−0.908406	+	0.418089i	$0.862700\pi$
$12$	7.57784	−	9.13456i	0.631487	−	0.761213i
$13$	−7.18410			−0.552623			−0.276312	−	0.961068i	$-0.589112\pi$
$13$	−7.18410			−0.552623			−0.276312	+	0.961068i	$0.589112\pi$
$14$		−	0.553707i		−	0.0395505i
$15$	−5.16290	−	4.28304i	−0.344194	−	0.285536i
$16$	15.4763			0.967271
$17$		−	4.35298i		−	0.256057i	−0.991770	−	0.128029i	$-0.959135\pi$
$17$		−	4.35298i		−	0.256057i	0.991770	−	0.128029i	$-0.0408650\pi$
$18$	1.85113	−	0.347875i	0.102841	−	0.0193264i
$19$	20.7496			1.09208			0.546041	−	0.837758i	$-0.316134\pi$
$19$	20.7496			1.09208			0.546041	+	0.837758i	$0.316134\pi$
$20$		−	8.84633i		−	0.442317i
$21$	−5.06776	+	6.10883i	−0.241322	+	0.290897i
$22$	−1.92497			−0.0874984
$23$			26.5430i			1.15405i	0.816728	+	0.577023i	$0.195786\pi$
$23$			26.5430i			1.15405i	−0.816728	+	0.577023i	$0.804214\pi$
$24$	3.84455	+	3.18936i	0.160190	+	0.132890i
$25$	−5.00000			−0.200000
$26$		−	1.50350i		−	0.0578270i
$27$	−23.6067	−	13.1044i	−0.874322	−	0.485347i
$28$	−10.4671			−0.373826
$29$			27.3836i			0.944263i	0.881528	+	0.472131i	$0.156515\pi$
$29$			27.3836i			0.944263i	−0.881528	+	0.472131i	$0.843485\pi$
$30$	0.896361	−	1.08050i	0.0298787	−	0.0360167i
$31$	−33.2578			−1.07283			−0.536416	−	0.843954i	$-0.680222\pi$
$31$	−33.2578			−1.07283			−0.536416	+	0.843954i	$0.680222\pi$
$32$			9.89926i			0.309352i
$33$	21.2374	+	17.6181i	0.643557	+	0.533881i
$34$	0.910998			0.0267941
$35$			5.91608i			0.169031i
$36$	−6.57612	−	34.9933i	−0.182670	−	0.972035i
$37$	−58.4402			−1.57947			−0.789733	−	0.613451i	$-0.789781\pi$
$37$	−58.4402			−1.57947			−0.789733	+	0.613451i	$0.789781\pi$
$38$			4.34251i			0.114276i
$39$	−13.7607	+	16.5875i	−0.352838	+	0.425321i
$40$	3.72325			0.0930812
$41$			39.8731i			0.972514i	0.873816	+	0.486257i	$0.161638\pi$
$41$			39.8731i			0.972514i	−0.873816	+	0.486257i	$0.838362\pi$
$42$	−1.27847	−	1.06059i	−0.0304397	−	0.0252521i
$43$	23.7965			0.553407			0.276704	−	0.960955i	$-0.410758\pi$
$43$	23.7965			0.553407			0.276704	+	0.960955i	$0.410758\pi$
$44$			36.3890i			0.827023i
$45$	−19.7784	+	3.71686i	−0.439520	+	0.0825970i
$46$	−5.55497			−0.120760
$47$		−	85.1268i		−	1.81121i	−0.424124	−	0.905604i	$-0.639418\pi$
$47$		−	85.1268i		−	1.81121i	0.424124	−	0.905604i	$-0.360582\pi$
$48$	29.6439	−	35.7336i	0.617581	−	0.744451i
$49$	7.00000			0.142857
$50$		−	1.04641i		−	0.0209282i
$51$	−10.0507	−	8.33784i	−0.197072	−	0.163487i
$52$	−28.4218			−0.546572
$53$			20.7258i			0.391053i	0.980698	+	0.195527i	$0.0626416\pi$
$53$			20.7258i			0.391053i	−0.980698	+	0.195527i	$0.937358\pi$
$54$	2.74250	−	4.94045i	0.0507871	−	0.0914898i
$55$	20.5673			0.373950
$56$		−	4.40541i		−	0.0786680i
$57$	39.7444	−	47.9091i	0.697270	−	0.840511i
$58$	−5.73089			−0.0988084
$59$			72.4687i			1.22828i	0.789196	+	0.614141i	$0.210498\pi$
$59$			72.4687i			1.22828i	−0.789196	+	0.614141i	$0.789502\pi$
$60$	−20.4255	−	16.9446i	−0.340425	−	0.282409i
$61$	86.5222			1.41840			0.709198	−	0.705009i	$-0.249057\pi$
$61$	86.5222			1.41840			0.709198	+	0.705009i	$0.249057\pi$
$62$		−	6.96024i		−	0.112262i
$63$	4.39785	+	23.4021i	0.0698072	+	0.371462i
$64$	59.8336			0.934900
$65$			16.0641i			0.247141i
$66$	−3.68714	+	4.44459i	−0.0558658	+	0.0673423i
$67$	−38.8274			−0.579513			−0.289756	−	0.957100i	$-0.593574\pi$
$67$	−38.8274			−0.579513			−0.289756	+	0.957100i	$0.593574\pi$
$68$		−	17.2213i		−	0.253254i
$69$	61.2858	+	50.8414i	0.888200	+	0.736832i
$70$	−1.23813			−0.0176875
$71$		−	91.4233i		−	1.28765i	−0.765172	−	0.643826i	$-0.777346\pi$
$71$		−	91.4233i		−	1.28765i	0.765172	−	0.643826i	$-0.222654\pi$
$72$	14.7280	−	2.76776i	0.204555	−	0.0384411i
$73$	11.4771			0.157220			0.0786100	−	0.996905i	$-0.474952\pi$
$73$	11.4771			0.157220			0.0786100	+	0.996905i	$0.474952\pi$
$74$		−	12.2305i		−	0.165277i
$75$	−9.57717	+	11.5446i	−0.127696	+	0.153928i
$76$	82.0895			1.08012
$77$		−	24.3355i		−	0.316046i
$78$	−3.47146	−	2.87986i	−0.0445060	−	0.0369212i
$79$	−41.5002			−0.525319			−0.262660	−	0.964889i	$-0.584600\pi$
$79$	−41.5002			−0.525319			−0.262660	+	0.964889i	$0.584600\pi$
$80$		−	34.6061i		−	0.432577i
$81$	−75.4740	+	29.4054i	−0.931777	+	0.363030i
$82$	−8.34470			−0.101765
$83$		−	154.585i		−	1.86247i	−0.364416	−	0.931236i	$-0.618731\pi$
$83$		−	154.585i		−	1.86247i	0.364416	−	0.931236i	$-0.381269\pi$
$84$	−20.0491	+	24.1678i	−0.238679	+	0.287711i
$85$	−9.73355			−0.114512
$86$			4.98017i			0.0579090i
$87$	63.2266	+	52.4515i	0.726743	+	0.602891i
$88$	−15.3154			−0.174039
$89$		−	135.478i		−	1.52223i	−0.648618	−	0.761114i	$-0.724653\pi$
$89$		−	135.478i		−	1.52223i	0.648618	−	0.761114i	$-0.275347\pi$
$90$	−0.777871	−	4.13926i	−0.00864301	−	0.0459917i
$91$	19.0073			0.208872
$92$			105.010i			1.14141i
$93$	−63.7030	+	76.7895i	−0.684979	+	0.825694i
$94$	17.8155			0.189526
$95$		−	46.3975i		−	0.488394i
$96$	22.8566	+	18.9614i	0.238090	+	0.197514i
$97$	−48.0704			−0.495571			−0.247786	−	0.968815i	$-0.579703\pi$
$97$	−48.0704			−0.495571			−0.247786	+	0.968815i	$0.579703\pi$
$98$			1.46497i			0.0149487i
$99$	81.3575	−	15.2892i	0.821793	−	0.154436i
$100$	−19.7810			−0.197810
$101$			13.5771i			0.134427i	0.997739	+	0.0672135i	$0.0214109\pi$
$101$			13.5771i			0.134427i	−0.997739	+	0.0672135i	$0.978589\pi$
$102$	1.74496	−	2.10342i	0.0171074	−	0.0206218i
$103$	70.1536			0.681103			0.340552	−	0.940226i	$-0.389386\pi$
$103$	70.1536			0.681103			0.340552	+	0.940226i	$0.389386\pi$
$104$		−	11.9622i		−	0.115021i
$105$	13.6598	+	11.3319i	0.130093	+	0.107922i
$106$	−4.33753			−0.0409201
$107$		−	103.093i		−	0.963486i	−0.876313	−	0.481743i	$-0.840004\pi$
$107$		−	103.093i		−	0.963486i	0.876313	−	0.481743i	$-0.159996\pi$
$108$	−93.3928	−	51.8435i	−0.864748	−	0.480032i
$109$	−153.757			−1.41062			−0.705309	−	0.708900i	$-0.749192\pi$
$109$	−153.757			−1.41062			−0.705309	+	0.708900i	$0.749192\pi$
$110$			4.30435i			0.0391305i
$111$	−111.938	+	134.934i	−1.00845	+	1.21562i
$112$	−40.9465			−0.365594
$113$			131.466i			1.16342i	0.813397	+	0.581709i	$0.197616\pi$
$113$			131.466i			1.16342i	−0.813397	+	0.581709i	$0.802384\pi$
$114$	10.0265	+	8.31778i	0.0879518	+	0.0729630i
$115$	59.3521			0.516105
$116$			108.335i			0.933923i
$117$	11.9416	+	63.5446i	0.102065	+	0.543116i
$118$	−15.1664			−0.128529
$119$			11.5169i			0.0967806i
$120$	7.13163	−	8.59668i	0.0594303	−	0.0716390i
$121$	36.3974			0.300805
$122$			18.1075i			0.148422i
$123$	92.0638	+	76.3742i	0.748486	+	0.620928i
$124$	−131.574			−1.06108
$125$			11.1803i			0.0894427i
$126$	−4.89763	+	0.920390i	−0.0388701	+	0.00730468i
$127$	66.5987			0.524399			0.262200	−	0.965014i	$-0.415552\pi$
$127$	66.5987			0.524399			0.262200	+	0.965014i	$0.415552\pi$
$128$			52.1191i			0.407181i
$129$	45.5806	−	54.9443i	0.353338	−	0.425925i
$130$	−3.36193			−0.0258610
$131$		−	101.191i		−	0.772448i	−0.922405	−	0.386224i	$-0.873779\pi$
$131$		−	101.191i		−	0.772448i	0.922405	−	0.386224i	$-0.126221\pi$
$132$	84.0193	+	69.7007i	0.636510	+	0.528036i
$133$	−54.8982			−0.412768
$134$		−	8.12585i		−	0.0606407i
$135$	−29.3023	+	52.7862i	−0.217054	+	0.391009i
$136$	7.24808			0.0532947
$137$			146.705i			1.07084i	0.844586	+	0.535420i	$0.179846\pi$
$137$			146.705i			1.07084i	−0.844586	+	0.535420i	$0.820154\pi$
$138$	−10.6402	+	12.8260i	−0.0771027	+	0.0929420i
$139$	−35.5337			−0.255638			−0.127819	−	0.991797i	$-0.540798\pi$
$139$	−35.5337			−0.255638			−0.127819	+	0.991797i	$0.540798\pi$
$140$			23.4052i			0.167180i
$141$	−196.551	−	163.055i	−1.39398	−	1.15642i
$142$	19.1332			0.134741
$143$		−	66.0791i		−	0.462092i
$144$	−25.7253	−	136.891i	−0.178648	−	0.950630i
$145$	61.2316			0.422287
$146$			2.40194i			0.0164516i
$147$	13.4080	−	16.1624i	0.0912111	−	0.109949i
$148$	−231.201			−1.56217
$149$		−	256.471i		−	1.72128i	−0.509214	−	0.860640i	$-0.670064\pi$
$149$		−	256.471i		−	1.72128i	0.509214	−	0.860640i	$-0.329936\pi$
$150$	−2.41607	−	2.00433i	−0.0161072	−	0.0133622i
$151$	212.094			1.40460			0.702298	−	0.711883i	$-0.252157\pi$
$151$	212.094			1.40460			0.702298	+	0.711883i	$0.252157\pi$
$152$			34.5498i			0.227302i
$153$	−38.5028	+	7.23566i	−0.251652	+	0.0472919i
$154$	5.09298			0.0330713
$155$			74.3666i			0.479785i
$156$	−54.4400	+	65.6236i	−0.348974	+	0.420664i
$157$	−102.498			−0.652856			−0.326428	−	0.945222i	$-0.605845\pi$
$157$	−102.498			−0.652856			−0.326428	+	0.945222i	$0.605845\pi$
$158$		−	8.68523i		−	0.0549698i
$159$	47.8543	+	39.6989i	0.300970	+	0.249679i
$160$	22.1354			0.138346
$161$		−	70.2263i		−	0.436188i
$162$	−6.15402	−	15.7953i	−0.0379878	−	0.0975020i
$163$	203.812			1.25038			0.625189	−	0.780473i	$-0.285022\pi$
$163$	203.812			1.25038			0.625189	+	0.780473i	$0.285022\pi$
$164$			157.746i			0.961865i
$165$	39.3952	−	47.4882i	0.238759	−	0.287807i
$166$	32.3519			0.194891
$167$			29.1149i			0.174341i	0.996193	+	0.0871704i	$0.0277825\pi$
$167$			29.1149i			0.174341i	−0.996193	+	0.0871704i	$0.972218\pi$
$168$	−10.1717	−	8.43826i	−0.0605460	−	0.0502277i
$169$	−117.389			−0.694608
$170$		−	2.03705i		−	0.0119827i
$171$	−34.4906	−	183.533i	−0.201699	−	1.07329i
$172$	94.1438			0.547348
$173$			198.774i			1.14898i	0.818510	+	0.574492i	$0.194800\pi$
$173$			198.774i			1.14898i	−0.818510	+	0.574492i	$0.805200\pi$
$174$	−10.9771	+	13.2322i	−0.0630870	+	0.0760470i
$175$	13.2288			0.0755929
$176$			142.351i			0.808811i
$177$	167.324	+	138.809i	0.945336	+	0.784231i
$178$	28.3531			0.159287
$179$		−	201.033i		−	1.12309i	−0.827446	−	0.561545i	$-0.810207\pi$
$179$		−	201.033i		−	1.12309i	0.827446	−	0.561545i	$-0.189793\pi$
$180$	−78.2473	+	14.7047i	−0.434707	+	0.0816925i
$181$	−116.878			−0.645735			−0.322867	−	0.946444i	$-0.604647\pi$
$181$	−116.878			−0.645735			−0.322867	+	0.946444i	$0.604647\pi$
$182$			3.97789i			0.0218565i
$183$	165.727	−	199.773i	0.905614	−	1.09165i
$184$	−44.1965			−0.240198
$185$			130.676i			0.706358i
$186$	−16.0706	−	13.3319i	−0.0864013	−	0.0716767i
$187$	40.0385			0.214110
$188$		−	336.779i		−	1.79138i
$189$	62.4574	+	34.6709i	0.330463	+	0.183444i
$190$	9.71014			0.0511060
$191$		−	160.165i		−	0.838560i	−0.907857	−	0.419280i	$-0.862283\pi$
$191$		−	160.165i		−	0.838560i	0.907857	−	0.419280i	$-0.137717\pi$
$192$	114.607	−	138.151i	0.596913	−	0.719537i
$193$	224.486			1.16314			0.581570	−	0.813496i	$-0.302439\pi$
$193$	224.486			1.16314			0.581570	+	0.813496i	$0.302439\pi$
$194$		−	10.0603i		−	0.0518570i
$195$	37.0908	+	30.7698i	0.190209	+	0.157794i
$196$	27.6934			0.141293
$197$			7.98264i			0.0405210i	0.999795	+	0.0202605i	$0.00644956\pi$
$197$			7.98264i			0.0405210i	−0.999795	+	0.0202605i	$0.993550\pi$
$198$	3.19974	+	17.0266i	0.0161603	+	0.0859932i
$199$	35.0150			0.175955			0.0879775	−	0.996122i	$-0.471960\pi$
$199$	35.0150			0.175955			0.0879775	+	0.996122i	$0.471960\pi$
$200$		−	8.32544i		−	0.0416272i
$201$	−74.3712	+	89.6493i	−0.370006	+	0.446016i
$202$	−2.84144			−0.0140665
$203$		−	72.4502i		−	0.356898i
$204$	−39.7625	−	32.9862i	−0.194914	−	0.161697i
$205$	89.1589			0.434921
$206$			14.6819i			0.0712712i
$207$	234.778	−	44.1207i	1.13419	−	0.213143i
$208$	−111.184			−0.534536
$209$			190.854i			0.913176i
$210$	−2.37155	+	2.85874i	−0.0112931	+	0.0136130i
$211$	311.027			1.47406			0.737031	−	0.675859i	$-0.236227\pi$
$211$	311.027			1.47406			0.737031	+	0.675859i	$0.236227\pi$
$212$			81.9955i			0.386771i
$213$	−211.089	−	175.115i	−0.991029	−	0.822137i
$214$	21.5755			0.100820
$215$		−	53.2106i		−	0.247491i
$216$	21.8199	−	39.3072i	0.101018	−	0.181978i
$217$	87.9918			0.405492
$218$		−	32.1786i		−	0.147608i
$219$	21.9835	−	26.4996i	0.100381	−	0.121003i
$220$	81.3683			0.369856
$221$			31.2722i			0.141503i
$222$	−28.2392	−	23.4266i	−0.127204	−	0.105525i
$223$	−283.260			−1.27022			−0.635111	−	0.772421i	$-0.719046\pi$
$223$	−283.260			−1.27022			−0.635111	+	0.772421i	$0.719046\pi$
$224$		−	26.1910i		−	0.116924i
$225$	8.31116	+	44.2258i	0.0369385	+	0.196559i
$226$	−27.5135			−0.121741
$227$			218.272i			0.961550i	0.876844	+	0.480775i	$0.159645\pi$
$227$			218.272i			0.961550i	−0.876844	+	0.480775i	$0.840355\pi$
$228$	157.237	−	189.538i	0.689636	−	0.831308i
$229$	−380.158			−1.66008			−0.830039	−	0.557705i	$-0.811682\pi$
$229$	−380.158			−1.66008			−0.830039	+	0.557705i	$0.811682\pi$
$230$			12.4213i			0.0540056i
$231$	−56.1888	−	46.6131i	−0.243242	−	0.201788i
$232$	−45.5961			−0.196535
$233$		−	113.624i		−	0.487656i	−0.969819	−	0.243828i	$-0.921597\pi$
$233$		−	113.624i		−	0.487656i	0.969819	−	0.243828i	$-0.0784032\pi$
$234$	−13.2987	+	2.49917i	−0.0568321	+	0.0106802i
$235$	−190.349			−0.809997
$236$			286.701i			1.21483i
$237$	−79.4909	+	95.8207i	−0.335405	+	0.404307i
$238$	−2.41027			−0.0101272
$239$			430.545i			1.80144i	0.434399	+	0.900721i	$0.356961\pi$
$239$			430.545i			1.80144i	−0.434399	+	0.900721i	$0.643039\pi$
$240$	−79.9028	−	66.2857i	−0.332928	−	0.276191i
$241$	−155.332			−0.644532			−0.322266	−	0.946649i	$-0.604445\pi$
$241$	−155.332			−0.644532			−0.322266	+	0.946649i	$0.604445\pi$
$242$			7.61731i			0.0314765i
$243$	−76.6705	+	230.588i	−0.315517	+	0.948920i
$244$	342.299			1.40287
$245$		−	15.6525i		−	0.0638877i
$246$	−15.9837	+	19.2673i	−0.0649745	+	0.0783222i
$247$	−149.067			−0.603510
$248$		−	55.3771i		−	0.223295i
$249$	−356.925	−	296.098i	−1.43343	−	1.18915i
$250$	−2.33984			−0.00935936
$251$		−	243.402i		−	0.969730i	−0.874589	−	0.484865i	$-0.838869\pi$
$251$		−	243.402i		−	0.969730i	0.874589	−	0.484865i	$-0.161131\pi$
$252$	17.3988	+	92.5835i	0.0690428	+	0.367395i
$253$	−244.142			−0.964988
$254$			13.9379i			0.0548736i
$255$	−18.6440	+	22.4740i	−0.0731136	+	0.0881333i
$256$	228.427			0.892292
$257$			114.619i			0.445989i	0.974820	+	0.222994i	$0.0715832\pi$
$257$			114.619i			0.445989i	−0.974820	+	0.222994i	$0.928417\pi$
$258$	11.4988	+	9.53919i	0.0445691	+	0.0369736i
$259$	154.618			0.596982
$260$			63.5530i			0.244434i
$261$	242.213	−	45.5179i	0.928018	−	0.174398i
$262$	21.1774			0.0808296
$263$			487.208i			1.85250i	0.376906	+	0.926251i	$0.376988\pi$
$263$			487.208i			1.85250i	−0.376906	+	0.926251i	$0.623012\pi$
$264$	−29.3357	+	35.3621i	−0.111120	+	0.133947i
$265$	46.3443			0.174884
$266$		−	11.4892i		−	0.0431924i
$267$	−312.809	−	259.500i	−1.17157	−	0.971909i
$268$	−153.609			−0.573167
$269$			28.8106i			0.107103i	0.998565	+	0.0535513i	$0.0170541\pi$
$269$			28.8106i			0.107103i	−0.998565	+	0.0535513i	$0.982946\pi$
$270$	−11.0472	−	6.13242i	−0.0409155	−	0.0227127i
$271$	−427.071			−1.57591			−0.787954	−	0.615734i	$-0.788860\pi$
$271$	−427.071			−1.57591			−0.787954	+	0.615734i	$0.788860\pi$
$272$		−	67.3681i		−	0.247677i
$273$	36.4073	−	43.8865i	0.133360	−	0.160756i
$274$	−30.7027			−0.112053
$275$		−	45.9898i		−	0.167236i
$276$	242.459	+	201.139i	0.878474	+	0.728764i
$277$	−234.608			−0.846960			−0.423480	−	0.905905i	$-0.639192\pi$
$277$	−234.608			−0.846960			−0.423480	+	0.905905i	$0.639192\pi$
$278$		−	7.43656i		−	0.0267502i
$279$	55.2821	+	294.170i	0.198144	+	1.05437i
$280$	−9.85079			−0.0351814
$281$			345.791i			1.23057i	0.788304	+	0.615286i	$0.210959\pi$
$281$			345.791i			1.23057i	−0.788304	+	0.615286i	$0.789041\pi$
$282$	34.1244	−	41.1345i	0.121008	−	0.145867i
$283$	233.611			0.825481			0.412740	−	0.910849i	$-0.364572\pi$
$283$	233.611			0.825481			0.412740	+	0.910849i	$0.364572\pi$
$284$		−	361.689i		−	1.27355i
$285$	−107.128	−	88.8712i	−0.375888	−	0.311829i
$286$	13.8291			0.0483537
$287$		−	105.494i		−	0.367576i
$288$	87.5606	−	16.4549i	0.304030	−	0.0571349i
$289$	270.052			0.934435
$290$			12.8147i			0.0441885i
$291$	−92.0757	+	110.991i	−0.316411	+	0.381412i
$292$	45.4055			0.155498
$293$			442.552i			1.51042i	0.655485	+	0.755208i	$0.272464\pi$
$293$			442.552i			1.51042i	−0.655485	+	0.755208i	$0.727536\pi$
$294$	3.38250	+	2.80606i	0.0115051	+	0.00954441i
$295$	162.045			0.549305
$296$		−	97.3081i		−	0.328743i
$297$	120.534	−	217.133i	0.405837	−	0.731089i
$298$	53.6746			0.180116
$299$		−	190.688i		−	0.637752i
$300$	−37.8892	+	45.6728i	−0.126297	+	0.152243i
$301$	−62.9597			−0.209168
$302$			44.3874i			0.146978i
$303$	31.3485	+	26.0061i	0.103460	+	0.0858286i
$304$	321.127			1.05634
$305$		−	193.469i		−	0.634326i
$306$	−1.51429	−	8.05793i	−0.00494866	−	0.0263331i
$307$	−40.6283			−0.132340			−0.0661699	−	0.997808i	$-0.521078\pi$
$307$	−40.6283			−0.132340			−0.0661699	+	0.997808i	$0.521078\pi$
$308$		−	96.2763i		−	0.312585i
$309$	134.375	−	161.979i	0.434869	−	0.524205i
$310$	−15.5636			−0.0502051
$311$		−	31.7633i		−	0.102133i	−0.998695	−	0.0510664i	$-0.983738\pi$
$311$		−	31.7633i		−	0.102133i	0.998695	−	0.0510664i	$-0.0162620\pi$
$312$	−27.6197	−	22.9127i	−0.0885246	−	0.0734382i
$313$	199.579			0.637634			0.318817	−	0.947816i	$-0.396714\pi$
$313$	199.579			0.637634			0.318817	+	0.947816i	$0.396714\pi$
$314$		−	21.4510i		−	0.0683154i
$315$	52.3287	−	9.83390i	0.166123	−	0.0312187i
$316$	−164.183			−0.519567
$317$			37.7963i			0.119231i	0.998221	+	0.0596156i	$0.0189875\pi$
$317$			37.7963i			0.119231i	−0.998221	+	0.0596156i	$0.981012\pi$
$318$	−8.30826	+	10.0150i	−0.0261266	+	0.0314938i
$319$	−251.874			−0.789572
$320$		−	133.792i		−	0.418100i
$321$	−238.034	−	197.468i	−0.741537	−	0.615164i
$322$	14.6971			0.0456431
$323$		−	90.3224i		−	0.279636i
$324$	−298.590	+	116.334i	−0.921575	+	0.359055i
$325$	35.9205			0.110525
$326$			42.6541i			0.130841i
$327$	−294.512	+	355.013i	−0.900648	+	1.08567i
$328$	−66.3921			−0.202415
$329$			225.224i			0.684572i
$330$	9.93841	+	8.24470i	0.0301164	+	0.0249839i
$331$	94.5031			0.285508			0.142754	−	0.989758i	$-0.454404\pi$
$331$	94.5031			0.285508			0.142754	+	0.989758i	$0.454404\pi$
$332$		−	611.570i		−	1.84208i
$333$	97.1412	+	516.914i	0.291715	+	1.55229i
$334$	−6.09322			−0.0182432
$335$			86.8206i			0.259166i
$336$	−78.4303	+	94.5423i	−0.233424	+	0.281376i
$337$	−29.9297			−0.0888121			−0.0444060	−	0.999014i	$-0.514140\pi$
$337$	−29.9297			−0.0888121			−0.0444060	+	0.999014i	$0.514140\pi$
$338$		−	24.5673i		−	0.0726843i
$339$	303.545	+	251.815i	0.895413	+	0.742816i
$340$	−38.5079			−0.113258
$341$		−	305.904i		−	0.897079i
$342$	38.4102	−	7.21825i	0.112310	−	0.0211060i
$343$	−18.5203			−0.0539949
$344$			39.6233i			0.115184i
$345$	113.685	−	137.039i	0.329521	−	0.397215i
$346$	−41.5998			−0.120231
$347$		−	631.822i		−	1.82081i	−0.413716	−	0.910406i	$-0.635769\pi$
$347$		−	631.822i		−	1.82081i	0.413716	−	0.910406i	$-0.364231\pi$
$348$	250.137	+	207.509i	0.718785	+	0.596289i
$349$	126.280			0.361834			0.180917	−	0.983498i	$-0.442093\pi$
$349$	126.280			0.361834			0.180917	+	0.983498i	$0.442093\pi$
$350$			2.76854i			0.00791010i
$351$	169.593	+	94.1431i	0.483170	+	0.268214i
$352$	−91.0531			−0.258673
$353$		−	133.830i		−	0.379123i	−0.981869	−	0.189561i	$-0.939293\pi$
$353$		−	133.830i		−	0.379123i	0.981869	−	0.189561i	$-0.0607066\pi$
$354$	−29.0502	+	35.0179i	−0.0820626	+	0.0989207i
$355$	−204.429			−0.575855
$356$		−	535.980i		−	1.50556i
$357$	26.5916	+	22.0598i	0.0744863	+	0.0617923i
$358$	42.0725			0.117521
$359$		−	52.7942i		−	0.147059i	−0.997293	−	0.0735295i	$-0.976574\pi$
$359$		−	52.7942i		−	0.147059i	0.997293	−	0.0735295i	$-0.0234263\pi$
$360$	−6.18890	−	32.9328i	−0.0171914	−	0.0914799i
$361$	69.5447			0.192645
$362$		−	24.4604i		−	0.0675702i
$363$	69.7168	−	84.0388i	0.192057	−	0.231512i
$364$	75.1969			0.206585
$365$		−	25.6635i		−	0.0703109i
$366$	41.8088	+	34.6837i	0.114232	+	0.0947642i
$367$	−452.241			−1.23227			−0.616133	−	0.787642i	$-0.711301\pi$
$367$	−452.241			−1.23227			−0.616133	+	0.787642i	$0.711301\pi$
$368$			410.789i			1.11627i
$369$	352.684	−	66.2783i	0.955783	−	0.179616i
$370$	−27.3482			−0.0739139
$371$		−	54.8354i		−	0.147804i
$372$	−252.022	+	303.795i	−0.677478	+	0.816653i
$373$	592.754			1.58915			0.794576	−	0.607165i	$-0.207693\pi$
$373$	592.754			1.58915			0.794576	+	0.607165i	$0.207693\pi$
$374$			8.37933i			0.0224046i
$375$	25.8145	+	21.4152i	0.0688387	+	0.0571072i
$376$	141.744			0.376977
$377$		−	196.727i		−	0.521821i
$378$	−7.25598	+	13.0712i	−0.0191957	+	0.0345799i
$379$	336.370			0.887520			0.443760	−	0.896146i	$-0.353644\pi$
$379$	336.370			0.887520			0.443760	+	0.896146i	$0.353644\pi$
$380$		−	183.558i		−	0.483046i
$381$	127.565	−	153.771i	0.334817	−	0.403599i
$382$	33.5196			0.0877476
$383$		−	285.846i		−	0.746335i	−0.927764	−	0.373168i	$-0.878272\pi$
$383$		−	285.846i		−	0.746335i	0.927764	−	0.373168i	$-0.121728\pi$
$384$	120.339	+	99.8307i	0.313383	+	0.259976i
$385$	−54.4159			−0.141340
$386$			46.9808i			0.121712i
$387$	−39.5553	−	210.484i	−0.102210	−	0.543887i
$388$	−190.176			−0.490145
$389$		−	189.971i		−	0.488357i	−0.969730	−	0.244179i	$-0.921482\pi$
$389$		−	189.971i		−	0.488357i	0.969730	−	0.244179i	$-0.0785184\pi$
$390$	−6.43955	+	7.76243i	−0.0165117	+	0.0199037i
$391$	115.541			0.295502
$392$			11.6556i			0.0297337i
$393$	−233.641	−	193.824i	−0.594507	−	0.493191i
$394$	−1.67062			−0.00424015
$395$			92.7973i			0.234930i
$396$	321.867	−	60.4870i	0.812795	−	0.152745i
$397$	736.620			1.85547			0.927733	−	0.373245i	$-0.121755\pi$
$397$	736.620			1.85547			0.927733	+	0.373245i	$0.121755\pi$
$398$			7.32800i			0.0184121i
$399$	−105.154	+	126.756i	−0.263543	+	0.317683i
$400$	−77.3817			−0.193454
$401$			742.336i			1.85121i	0.378488	+	0.925606i	$0.376444\pi$
$401$			742.336i			1.85121i	−0.378488	+	0.925606i	$0.623556\pi$
$402$	−18.7620	−	15.5645i	−0.0466715	−	0.0387177i
$403$	238.927			0.592871
$404$			53.7138i			0.132955i
$405$	65.7526	+	168.765i	0.162352	+	0.416704i
$406$	15.1625			0.0373461
$407$		−	537.531i		−	1.32072i
$408$	13.8832	−	16.7353i	0.0340275	−	0.0410178i
$409$	129.708			0.317135			0.158568	−	0.987348i	$-0.449312\pi$
$409$	129.708			0.317135			0.158568	+	0.987348i	$0.449312\pi$
$410$			18.6593i			0.0455105i
$411$	338.730	+	281.004i	0.824161	+	0.683707i
$412$	277.542			0.673645
$413$		−	191.734i		−	0.464247i
$414$	9.23365	+	49.1347i	0.0223035	+	0.118683i
$415$	−345.663			−0.832923
$416$		−	71.1173i		−	0.170955i
$417$	−68.0625	+	82.0446i	−0.163219	+	0.196750i
$418$	−39.9422			−0.0955555
$419$			731.075i			1.74481i	0.488784	+	0.872405i	$0.337440\pi$
$419$			731.075i			1.74481i	−0.488784	+	0.872405i	$0.662560\pi$
$420$	54.0408	+	44.8311i	0.128668	+	0.106741i
$421$	−196.390			−0.466486			−0.233243	−	0.972419i	$-0.574934\pi$
$421$	−196.390			−0.466486			−0.233243	+	0.972419i	$0.574934\pi$
$422$			65.0923i			0.154247i
$423$	−752.961	+	141.500i	−1.78005	+	0.334516i
$424$	−34.5103			−0.0813922
$425$			21.7649i			0.0512115i
$426$	36.6484	−	44.1771i	0.0860291	−	0.103702i
$427$	−228.916			−0.536103
$428$		−	407.857i		−	0.952936i
$429$	−152.571	−	126.570i	−0.355644	−	0.295035i
$430$	11.1360			0.0258977
$431$			168.477i			0.390899i	0.980714	+	0.195449i	$0.0626165\pi$
$431$			168.477i			0.390899i	−0.980714	+	0.195449i	$0.937383\pi$
$432$	−365.345	−	202.808i	−0.845706	−	0.469462i
$433$	−374.758			−0.865492			−0.432746	−	0.901516i	$-0.642455\pi$
$433$	−374.758			−0.865492			−0.432746	+	0.901516i	$0.642455\pi$
$434$			18.4151i			0.0424310i
$435$	117.285	−	141.379i	0.269621	−	0.325009i
$436$	−608.295			−1.39517
$437$			550.757i			1.26031i
$438$	5.54588	+	4.60075i	0.0126618	+	0.0105040i
$439$	−350.834			−0.799167			−0.399583	−	0.916697i	$-0.630845\pi$
$439$	−350.834			−0.799167			−0.399583	+	0.916697i	$0.630845\pi$
$440$			34.2463i			0.0778325i
$441$	−11.6356	−	61.9162i	−0.0263846	−	0.140399i
$442$	−6.54470			−0.0148070
$443$		−	110.346i		−	0.249089i	−0.992214	−	0.124544i	$-0.960253\pi$
$443$		−	110.346i		−	0.249089i	0.992214	−	0.124544i	$-0.0397469\pi$
$444$	−442.851	+	533.825i	−0.997411	+	1.20231i
$445$	−302.939			−0.680761
$446$		−	59.2811i		−	0.132917i
$447$	−592.171	−	491.252i	−1.32477	−	1.09900i
$448$	−158.305			−0.353359
$449$		−	23.0858i		−	0.0514160i	−0.999669	−	0.0257080i	$-0.991816\pi$
$449$		−	23.0858i		−	0.0514160i	0.999669	−	0.0257080i	$-0.00818401\pi$
$450$	−9.25566	+	1.73937i	−0.0205681	+	0.00386527i
$451$	−366.751			−0.813195
$452$			520.107i			1.15068i
$453$	406.252	−	489.708i	0.896804	−	1.08103i
$454$	−45.6803			−0.100617
$455$		−	42.5017i		−	0.0934104i
$456$	79.7729	+	66.1779i	0.174940	+	0.145127i
$457$	−31.5292			−0.0689917			−0.0344959	−	0.999405i	$-0.510983\pi$
$457$	−31.5292			−0.0689917			−0.0344959	+	0.999405i	$0.510983\pi$
$458$		−	79.5601i		−	0.173712i
$459$	−57.0430	+	102.759i	−0.124277	+	0.223877i
$460$	234.809			0.510454
$461$		−	44.1707i		−	0.0958149i	−0.998852	−	0.0479074i	$-0.984745\pi$
$461$		−	44.1707i		−	0.0958149i	0.998852	−	0.0479074i	$-0.0152552\pi$
$462$	9.75526	−	11.7593i	0.0211153	−	0.0254530i
$463$	67.6473			0.146107			0.0730533	−	0.997328i	$-0.476726\pi$
$463$	67.6473			0.146107			0.0730533	+	0.997328i	$0.476726\pi$
$464$			423.798i			0.913358i
$465$	171.707	+	142.444i	0.369262	+	0.306332i
$466$	23.7794			0.0510287
$467$		−	117.700i		−	0.252034i	−0.992028	−	0.126017i	$-0.959781\pi$
$467$		−	117.700i		−	0.252034i	0.992028	−	0.126017i	$-0.0402193\pi$
$468$	47.2435	+	251.395i	0.100948	+	0.537169i
$469$	102.728			0.219035
$470$		−	39.8366i		−	0.0847588i
$471$	−196.329	+	236.661i	−0.416834	+	0.502464i
$472$	−120.667			−0.255650
$473$			218.880i			0.462747i
$474$	−20.0535	−	16.6360i	−0.0423070	−	0.0350970i
$475$	−103.748			−0.218417
$476$			45.5631i			0.0957209i
$477$	183.323	−	34.4511i	0.384326	−	0.0722246i
$478$	−90.1051			−0.188504
$479$			329.804i			0.688527i	0.938873	+	0.344263i	$0.111871\pi$
$479$			329.804i			0.688527i	−0.938873	+	0.344263i	$0.888129\pi$
$480$	42.3989	−	51.1089i	0.0883311	−	0.106477i
$481$	419.840			0.872849
$482$		−	32.5082i		−	0.0674444i
$483$	−162.147	−	134.514i	−0.335708	−	0.278496i
$484$	143.996			0.297511
$485$			107.489i			0.221626i
$486$	−48.2578	−	16.0457i	−0.0992958	−	0.0330159i
$487$	203.861			0.418606			0.209303	−	0.977851i	$-0.432881\pi$
$487$	203.861			0.418606			0.209303	+	0.977851i	$0.432881\pi$
$488$			144.067i			0.295219i
$489$	390.388	−	470.585i	0.798339	−	0.962342i
$490$	3.27578			0.00668526
$491$		−	77.4330i		−	0.157705i	−0.996886	−	0.0788524i	$-0.974874\pi$
$491$		−	77.4330i		−	0.157705i	0.996886	−	0.0788524i	$-0.0251256\pi$
$492$	364.223	+	302.152i	0.740290	+	0.614129i
$493$	119.200			0.241785
$494$		−	31.1970i		−	0.0631518i
$495$	−34.1876	−	181.921i	−0.0690658	−	0.367517i
$496$	−514.708			−1.03772
$497$			241.883i			0.486687i
$498$	61.9678	−	74.6979i	0.124433	−	0.149996i
$499$	−418.996			−0.839670			−0.419835	−	0.907600i	$-0.637912\pi$
$499$	−418.996			−0.839670			−0.419835	+	0.907600i	$0.637912\pi$
$500$			44.2317i			0.0884633i
$501$	67.2241	+	55.7677i	0.134180	+	0.111313i
$502$	50.9396			0.101473
$503$		−	117.318i		−	0.233237i	−0.993177	−	0.116618i	$-0.962795\pi$
$503$		−	117.318i		−	0.233237i	0.993177	−	0.116618i	$-0.0372054\pi$
$504$	−38.9666	+	7.32281i	−0.0773146	+	0.0145294i
$505$	30.3594			0.0601176
$506$		−	51.0945i		−	0.100977i
$507$	−224.850	+	271.041i	−0.443491	+	0.534598i
$508$	263.478			0.518657
$509$		−	473.850i		−	0.930944i	−0.885063	−	0.465472i	$-0.845885\pi$
$509$		−	473.850i		−	0.930944i	0.885063	−	0.465472i	$-0.154115\pi$
$510$	−4.70340	−	3.90184i	−0.00922235	−	0.00765067i
$511$	−30.3654			−0.0594236
$512$			256.282i			0.500551i
$513$	−489.829	−	271.910i	−0.954832	−	0.530039i
$514$	−23.9877			−0.0466686
$515$		−	156.868i		−	0.304599i
$516$	180.326	−	217.371i	0.349469	−	0.421261i
$517$	782.993			1.51449
$518$			32.3588i			0.0624687i
$519$	458.954	+	380.739i	0.884304	+	0.733601i
$520$	−26.7482			−0.0514388
$521$		−	446.140i		−	0.856315i	−0.903704	−	0.428157i	$-0.859163\pi$
$521$		−	446.140i		−	0.856315i	0.903704	−	0.428157i	$-0.140837\pi$
$522$	9.52607	+	50.6907i	0.0182492	+	0.0971086i
$523$	406.509			0.777265			0.388632	−	0.921393i	$-0.372948\pi$
$523$	406.509			0.777265			0.388632	+	0.921393i	$0.372948\pi$
$524$		−	400.331i		−	0.763990i
$525$	25.3388	−	30.5442i	0.0482644	−	0.0581793i
$526$	−101.964			−0.193847
$527$			144.770i			0.274706i
$528$	328.677	+	272.663i	0.622494	+	0.516408i
$529$	−175.533			−0.331821
$530$			9.69902i			0.0183000i
$531$	640.998	−	120.460i	1.20715	−	0.226855i
$532$	−217.188			−0.408249
$533$		−	286.452i		−	0.537434i
$534$	54.3085	−	65.4652i	0.101701	−	0.122594i
$535$	−230.523			−0.430884
$536$		−	64.6509i		−	0.120617i
$537$	−464.169	−	385.065i	−0.864375	−	0.717067i
$538$	−6.02953			−0.0112073
$539$			64.3858i			0.119454i
$540$	−115.926	+	208.833i	−0.214677	+	0.386727i
$541$	181.081			0.334716			0.167358	−	0.985896i	$-0.446476\pi$
$541$	181.081			0.334716			0.167358	+	0.985896i	$0.446476\pi$
$542$		−	89.3781i		−	0.164904i
$543$	−223.872	+	269.862i	−0.412287	+	0.496983i
$544$	43.0912			0.0792119
$545$			343.812i			0.630847i
$546$	9.18463	+	7.61938i	0.0168217	+	0.0139549i
$547$	969.937			1.77319			0.886597	−	0.462544i	$-0.153063\pi$
$547$	969.937			1.77319			0.886597	+	0.462544i	$0.153063\pi$
$548$			580.394i			1.05911i
$549$	−143.820	−	765.303i	−0.261967	−	1.39399i
$550$	9.62483			0.0174997
$551$			568.198i			1.03121i
$552$	−84.6554	+	102.046i	−0.153361	+	0.184866i
$553$	109.799			0.198552
$554$		−	49.0991i		−	0.0886266i
$555$	301.721	+	250.302i	0.543642	+	0.450994i
$556$	−140.579			−0.252839
$557$			566.982i			1.01792i	0.860790	+	0.508961i	$0.169970\pi$
$557$			566.982i			1.01792i	−0.860790	+	0.508961i	$0.830030\pi$
$558$	−61.5645	+	11.5695i	−0.110331	+	0.0207339i
$559$	−170.957			−0.305826
$560$			91.5592i			0.163499i
$561$	76.6911	−	92.4458i	0.136704	−	0.164788i
$562$	−72.3676			−0.128768
$563$			63.2382i			0.112324i	0.998422	+	0.0561619i	$0.0178863\pi$
$563$			63.2382i			0.112324i	−0.998422	+	0.0561619i	$0.982114\pi$
$564$	−777.595	−	645.077i	−1.37872	−	1.14375i
$565$	293.967			0.520296
$566$			48.8905i			0.0863790i
$567$	199.685	−	77.7995i	0.352179	−	0.137212i
$568$	152.228			0.268007
$569$		−	758.525i		−	1.33308i	−0.745468	−	0.666542i	$-0.767774\pi$
$569$		−	758.525i		−	1.33308i	0.745468	−	0.666542i	$-0.232226\pi$
$570$	18.5991	−	22.4199i	0.0326300	−	0.0393332i
$571$	−607.400			−1.06375			−0.531874	−	0.846824i	$-0.678512\pi$
$571$	−607.400			−1.06375			−0.531874	+	0.846824i	$0.678512\pi$
$572$		−	261.422i		−	0.457032i
$573$	−369.808	−	306.785i	−0.645390	−	0.535402i
$574$	22.0780			0.0384634
$575$		−	132.715i		−	0.230809i
$576$	−99.4573	−	529.238i	−0.172669	−	0.918816i
$577$	684.584			1.18645			0.593227	−	0.805035i	$-0.297854\pi$
$577$	684.584			1.18645			0.593227	+	0.805035i	$0.297854\pi$
$578$			56.5168i			0.0977800i
$579$	429.988	−	518.320i	0.742639	−	0.895199i
$580$	242.245			0.417663
$581$			408.994i			0.703948i
$582$	−23.2283	−	19.2698i	−0.0399112	−	0.0331095i
$583$	−190.635			−0.326990
$584$			19.1103i			0.0327231i
$585$	142.090	−	26.7023i	0.242889	−	0.0456450i
$586$	−92.6180			−0.158051
$587$		−	100.694i		−	0.171540i	−0.996315	−	0.0857700i	$-0.972665\pi$
$587$		−	100.694i		−	0.171540i	0.996315	−	0.0857700i	$-0.0273350\pi$
$588$	53.0449	−	63.9419i	0.0902124	−	0.108745i
$589$	−690.084			−1.17162
$590$			33.9130i			0.0574797i
$591$	18.4313	+	15.2902i	0.0311866	+	0.0258718i
$592$	−904.440			−1.52777
$593$			273.169i			0.460657i	0.973113	+	0.230328i	$0.0739800\pi$
$593$			273.169i			0.460657i	−0.973113	+	0.230328i	$0.926020\pi$
$594$	45.4421	+	25.2255i	0.0765018	+	0.0424671i
$595$	25.7526			0.0432816
$596$		−	1014.65i		−	1.70243i
$597$	67.0689	−	80.8469i	0.112343	−	0.135422i
$598$	39.9075			0.0667349
$599$		−	639.385i		−	1.06742i	−0.845667	−	0.533710i	$-0.820797\pi$
$599$		−	639.385i		−	1.06742i	0.845667	−	0.533710i	$-0.179203\pi$
$600$	−19.2228	−	15.9468i	−0.0320380	−	0.0265780i
$601$	22.3501			0.0371882			0.0185941	−	0.999827i	$-0.494081\pi$
$601$	22.3501			0.0371882			0.0185941	+	0.999827i	$0.494081\pi$
$602$		−	13.1763i		−	0.0218875i
$603$	64.5401	+	343.434i	0.107032	+	0.569543i
$604$	839.087			1.38922
$605$		−	81.3871i		−	0.134524i
$606$	−5.44259	+	6.56067i	−0.00898118	+	0.0108262i
$607$	928.820			1.53018			0.765091	−	0.643923i	$-0.222694\pi$
$607$	928.820			1.53018			0.765091	+	0.643923i	$0.222694\pi$
$608$			205.405i			0.337838i
$609$	−167.282	−	138.774i	−0.274683	−	0.227871i
$610$	40.4896			0.0663764
$611$			611.560i			1.00092i
$612$	−152.325	+	28.6257i	−0.248897	+	0.0467740i
$613$	−168.131			−0.274275			−0.137138	−	0.990552i	$-0.543790\pi$
$613$	−168.131			−0.274275			−0.137138	+	0.990552i	$0.543790\pi$
$614$		−	8.50276i		−	0.0138481i
$615$	170.778	−	205.861i	0.277688	−	0.334733i
$616$	40.5208			0.0657805
$617$			414.177i			0.671276i	0.941991	+	0.335638i	$0.108952\pi$
$617$			414.177i			0.671276i	−0.941991	+	0.335638i	$0.891048\pi$
$618$	33.8993	+	28.1221i	0.0548532	+	0.0455051i
$619$	768.889			1.24215			0.621074	−	0.783752i	$-0.286697\pi$
$619$	768.889			1.24215			0.621074	+	0.783752i	$0.286697\pi$
$620$			294.209i			0.474531i
$621$	347.830	−	626.593i	0.560112	−	1.00901i
$622$	6.64747			0.0106873
$623$			358.442i			0.575348i
$624$	−212.965	+	256.714i	−0.341289	+	0.411401i
$625$	25.0000			0.0400000
$626$			41.7683i			0.0667226i
$627$	440.666	+	365.568i	0.702817	+	0.583043i
$628$	−405.504			−0.645707
$629$			254.389i			0.404434i
$630$	2.05805	+	10.9514i	0.00326675	+	0.0173832i
$631$	−458.473			−0.726582			−0.363291	−	0.931676i	$-0.618347\pi$
$631$	−458.473			−0.726582			−0.363291	+	0.931676i	$0.618347\pi$
$632$		−	69.1015i		−	0.109338i
$633$	595.752	−	718.137i	0.941156	−	1.13450i
$634$	−7.91007			−0.0124765
$635$		−	148.919i		−	0.234519i
$636$	189.321	+	157.057i	0.297675	+	0.246945i
$637$	−50.2887			−0.0789462
$638$		−	52.7125i		−	0.0826215i
$639$	−808.654	+	151.967i	−1.26550	+	0.237820i
$640$	116.542			0.182097
$641$		−	60.0906i		−	0.0937450i	−0.998901	−	0.0468725i	$-0.985075\pi$
$641$		−	60.0906i		−	0.0937450i	0.998901	−	0.0468725i	$-0.0149255\pi$
$642$	41.3264	−	49.8161i	0.0643713	−	0.0775951i
$643$	210.726			0.327723			0.163862	−	0.986483i	$-0.447605\pi$
$643$	210.726			0.327723			0.163862	+	0.986483i	$0.447605\pi$
$644$		−	277.829i		−	0.431412i
$645$	−122.859	−	101.921i	−0.190479	−	0.158018i
$646$	18.9028			0.0292613
$647$			514.260i			0.794838i	0.917637	+	0.397419i	$0.130094\pi$
$647$			514.260i			0.794838i	−0.917637	+	0.397419i	$0.869906\pi$
$648$	−48.9626	−	125.671i	−0.0755596	−	0.193936i
$649$	−666.565			−1.02706
$650$			7.51750i			0.0115654i
$651$	168.542	−	203.166i	0.258898	−	0.312083i
$652$	806.320			1.23669
$653$		−	392.202i		−	0.600616i	−0.953842	−	0.300308i	$-0.902911\pi$
$653$		−	392.202i		−	0.600616i	0.953842	−	0.300308i	$-0.0970894\pi$
$654$	−74.2978	−	61.6359i	−0.113605	−	0.0942445i
$655$	−226.269			−0.345449
$656$			617.089i			0.940684i
$657$	−19.0775	−	101.516i	−0.0290373	−	0.154515i
$658$	−47.1353			−0.0716342
$659$		−	403.030i		−	0.611578i	−0.952099	−	0.305789i	$-0.901080\pi$
$659$		−	403.030i		−	0.611578i	0.952099	−	0.305789i	$-0.0989203\pi$
$660$	155.856	−	187.873i	0.236145	−	0.284656i
$661$	339.854			0.514152			0.257076	−	0.966391i	$-0.417241\pi$
$661$	339.854			0.514152			0.257076	+	0.966391i	$0.417241\pi$
$662$			19.7778i			0.0298758i
$663$	72.2051	+	59.8999i	0.108907	+	0.0903467i
$664$	257.398			0.387647
$665$			122.756i			0.184596i
$666$	−108.181	+	20.3299i	−0.162433	+	0.0305253i
$667$	−726.845			−1.08972
$668$			115.184i			0.172432i
$669$	−542.565	+	654.024i	−0.811009	+	0.977615i
$670$	−18.1700			−0.0271193
$671$			795.828i			1.18603i
$672$	−60.4729	−	50.1671i	−0.0899894	−	0.0746534i
$673$	−474.937			−0.705701			−0.352850	−	0.935680i	$-0.614788\pi$
$673$	−474.937			−0.705701			−0.352850	+	0.935680i	$0.614788\pi$
$674$		−	6.26373i		−	0.00929337i
$675$	118.033	+	65.5218i	0.174864	+	0.0970694i
$676$	−464.413			−0.687002
$677$			725.415i			1.07151i	0.844372	+	0.535757i	$0.179974\pi$
$677$			725.415i			1.07151i	−0.844372	+	0.535757i	$0.820026\pi$
$678$	−52.7002	+	63.5264i	−0.0777289	+	0.0936968i
$679$	127.182			0.187308
$680$		−	16.2072i		−	0.0238341i
$681$	503.973	+	418.085i	0.740048	+	0.613929i
$682$	64.0201			0.0938710
$683$		−	679.610i		−	0.995037i	−0.867453	−	0.497518i	$-0.834245\pi$
$683$		−	679.610i		−	0.995037i	0.867453	−	0.497518i	$-0.165755\pi$
$684$	−136.452	−	726.095i	−0.199491	−	1.06154i
$685$	328.042			0.478894
$686$		−	3.87595i		−	0.00565007i
$687$	−728.167	+	877.754i	−1.05992	+	1.27766i
$688$	368.283			0.535295
$689$		−	148.896i		−	0.216105i
$690$	28.6798	+	23.7922i	0.0415649	+	0.0344814i
$691$	−710.948			−1.02887			−0.514434	−	0.857530i	$-0.671998\pi$
$691$	−710.948			−1.02887			−0.514434	+	0.857530i	$0.671998\pi$
$692$			786.391i			1.13640i
$693$	−215.252	+	40.4513i	−0.310609	+	0.0583713i
$694$	132.229			0.190531
$695$			79.4559i			0.114325i
$696$	−87.3363	+	105.278i	−0.125483	+	0.151261i
$697$	173.567			0.249019
$698$			26.4281i			0.0378626i
$699$	−262.348	−	217.639i	−0.375319	−	0.311357i
$700$	52.3356			0.0747652
$701$		−	591.726i		−	0.844117i	−0.906569	−	0.422059i	$-0.861308\pi$
$701$		−	591.726i		−	0.844117i	0.906569	−	0.422059i	$-0.138692\pi$
$702$	−19.7024	+	35.4927i	−0.0280661	+	0.0505594i
$703$	−1212.61			−1.72491
$704$			550.347i			0.781743i
$705$	−364.601	+	439.502i	−0.517165	+	0.623406i
$706$	28.0082			0.0396717
$707$		−	35.9217i		−	0.0508086i
$708$	661.969	+	549.156i	0.934985	+	0.775644i
$709$	−406.642			−0.573543			−0.286772	−	0.957999i	$-0.592582\pi$
$709$	−406.642			−0.573543			−0.286772	+	0.957999i	$0.592582\pi$
$710$		−	42.7832i		−	0.0602580i
$711$	68.9830	+	367.076i	0.0970224	+	0.516282i
$712$	225.583			0.316830
$713$		−	882.762i		−	1.23810i
$714$	−4.61672	+	5.56513i	−0.00646599	+	0.00779430i
$715$	−147.757			−0.206654
$716$		−	795.327i		−	1.11079i
$717$	994.093	+	824.679i	1.38646	+	1.15018i
$718$	11.0489			0.0153884
$719$			656.359i			0.912877i	0.889755	+	0.456439i	$0.150875\pi$
$719$			656.359i			0.912877i	−0.889755	+	0.456439i	$0.849125\pi$
$720$	−306.097	+	57.5234i	−0.425135	+	0.0798936i
$721$	−185.609			−0.257433
$722$			14.5544i			0.0201585i
$723$	−297.528	+	358.650i	−0.411519	+	0.496058i
$724$	−462.393			−0.638664
$725$		−	136.918i		−	0.188853i
$726$	17.5878	+	14.5905i	0.0242256	+	0.0200970i
$727$	−770.295			−1.05955			−0.529776	−	0.848137i	$-0.677724\pi$
$727$	−770.295			−1.05955			−0.529776	+	0.848137i	$0.677724\pi$
$728$			31.6489i			0.0434737i
$729$	385.551	+	618.701i	0.528877	+	0.848699i
$730$	5.37090			0.00735739
$731$		−	103.586i		−	0.141704i
$732$	655.651	−	790.342i	0.895698	−	1.07970i
$733$	−1035.49			−1.41267			−0.706335	−	0.707878i	$-0.749653\pi$
$733$	−1035.49			−1.41267			−0.706335	+	0.707878i	$0.749653\pi$
$734$		−	94.6458i		−	0.128945i
$735$	−36.1403	−	29.9813i	−0.0491705	−	0.0407908i
$736$	−262.757			−0.357006
$737$		−	357.133i		−	0.484576i
$738$	13.8708	+	73.8103i	0.0187952	+	0.100014i
$739$	1413.25			1.91238			0.956188	−	0.292752i	$-0.0945710\pi$
$739$	1413.25			1.91238			0.956188	+	0.292752i	$0.0945710\pi$
$740$			516.982i			0.698624i
$741$	−285.528	+	344.184i	−0.385328	+	0.464486i
$742$	11.4760			0.0154664
$743$		−	248.893i		−	0.334983i	−0.985873	−	0.167492i	$-0.946433\pi$
$743$		−	248.893i		−	0.334983i	0.985873	−	0.167492i	$-0.0535667\pi$
$744$	−127.861	−	106.071i	−0.171857	−	0.142569i
$745$	−573.486			−0.769780
$746$			124.053i			0.166290i
$747$	−1367.33	+	256.956i	−1.83043	+	0.343985i
$748$	158.400			0.211765
$749$			272.758i			0.364163i
$750$	−4.48181	+	5.40251i	−0.00597574	+	0.00720334i
$751$	865.135			1.15198			0.575988	−	0.817458i	$-0.304617\pi$
$751$	865.135			1.15198			0.575988	+	0.817458i	$0.304617\pi$
$752$		−	1317.45i		−	1.75193i
$753$	−561.996	−	466.221i	−0.746343	−	0.619151i
$754$	41.1713			0.0546038
$755$		−	474.257i		−	0.628155i
$756$	247.094	+	137.165i	0.326844	+	0.181435i
$757$	−293.625			−0.387880			−0.193940	−	0.981013i	$-0.562127\pi$
$757$	−293.625			−0.387880			−0.193940	+	0.981013i	$0.562127\pi$
$758$			70.3961i			0.0928708i
$759$	−467.638	+	563.705i	−0.616124	+	0.742694i
$760$	77.2558			0.101652
$761$		−	317.097i		−	0.416685i	−0.978056	−	0.208342i	$-0.933193\pi$
$761$		−	317.097i		−	0.416685i	0.978056	−	0.208342i	$-0.0668068\pi$
$762$	32.1815	+	26.6971i	0.0422329	+	0.0350356i
$763$	406.804			0.533163
$764$		−	633.645i		−	0.829378i
$765$	16.1794	+	86.0949i	0.0211496	+	0.112542i
$766$	59.8224			0.0780972
$767$		−	520.622i		−	0.678778i
$768$	437.536	−	527.419i	0.569709	−	0.686744i
$769$	−1243.98			−1.61766			−0.808831	−	0.588042i	$-0.799899\pi$
$769$	−1243.98			−1.61766			−0.808831	+	0.588042i	$0.799899\pi$
$770$		−	11.3883i		−	0.0147899i
$771$	264.646	+	219.545i	0.343251	+	0.284754i
$772$	888.112			1.15040
$773$		−	676.877i		−	0.875649i	−0.899060	−	0.437825i	$-0.855749\pi$
$773$		−	676.877i		−	0.875649i	0.899060	−	0.437825i	$-0.144251\pi$
$774$	44.0505	−	8.27820i	0.0569128	−	0.0106954i
$775$	166.289			0.214566
$776$		−	80.0414i		−	0.103146i
$777$	296.161	−	357.001i	0.381160	−	0.459461i
$778$	39.7575			0.0511021
$779$			827.349i			1.06207i
$780$	146.739	+	121.731i	0.188127	+	0.156066i
$781$	840.908			1.07671
$782$			24.1807i			0.0309216i
$783$	358.845	−	646.436i	0.458295	−	0.825589i
$784$	108.334			0.138182
$785$			229.193i			0.291966i
$786$	40.5638	−	48.8968i	0.0516079	−	0.0622097i
$787$	−307.442			−0.390651			−0.195325	−	0.980738i	$-0.562576\pi$
$787$	−307.442			−0.390651			−0.195325	+	0.980738i	$0.562576\pi$
$788$			31.5809i			0.0400773i
$789$	1124.93	+	933.215i	1.42576	+	1.18278i
$790$	−19.4208			−0.0245833
$791$		−	347.827i		−	0.439730i
$792$	25.4578	+	135.467i	0.0321436	+	0.171045i
$793$	−621.584			−0.783839
$794$			154.161i			0.194157i
$795$	88.7695	−	107.005i	0.111660	−	0.134598i
$796$	138.526			0.174028
$797$			336.565i			0.422290i	0.977455	+	0.211145i	$0.0677193\pi$
$797$			336.565i			0.422290i	−0.977455	+	0.211145i	$0.932281\pi$
$798$	−26.5276	−	22.0068i	−0.0332426	−	0.0275774i
$799$	−370.555			−0.463773
$800$		−	49.4963i		−	0.0618704i
$801$	−1198.33	+	225.196i	−1.49604	+	0.281144i
$802$	−155.357			−0.193712
$803$			105.566i			0.131464i
$804$	−294.227	+	354.671i	−0.365955	+	0.441133i
$805$	−157.031			−0.195069
$806$			50.0031i			0.0620385i
$807$	66.5214	+	55.1848i	0.0824305	+	0.0683826i
$808$	−22.6071			−0.0279791
$809$			323.811i			0.400261i	0.979769	+	0.200130i	$0.0641366\pi$
$809$			323.811i			0.400261i	−0.979769	+	0.200130i	$0.935863\pi$
$810$	−35.3194	+	13.7608i	−0.0436042	+	0.0169886i
$811$	685.432			0.845169			0.422585	−	0.906323i	$-0.361123\pi$
$811$	685.432			0.845169			0.422585	+	0.906323i	$0.361123\pi$
$812$		−	286.628i		−	0.352990i
$813$	−818.026	+	986.073i	−1.00618	+	1.21288i
$814$	112.495			0.138201
$815$		−	455.737i		−	0.559186i
$816$	−155.548	−	129.039i	−0.190622	−	0.158136i
$817$	493.768			0.604367
$818$			27.1456i			0.0331853i
$819$	−31.5946	−	168.123i	−0.0385771	−	0.205279i
$820$	352.730			0.430159
$821$		−	1032.60i		−	1.25774i	−0.777511	−	0.628869i	$-0.783518\pi$
$821$		−	1032.60i		−	1.25774i	0.777511	−	0.628869i	$-0.216482\pi$
$822$	−58.8089	+	70.8900i	−0.0715437	+	0.0862409i
$823$	1387.10			1.68542			0.842712	−	0.538364i	$-0.180957\pi$
$823$	1387.10			1.68542			0.842712	+	0.538364i	$0.180957\pi$
$824$			116.812i			0.141762i
$825$	−106.187	−	88.0904i	−0.128711	−	0.106776i
$826$	40.1264			0.0485792
$827$		−	892.129i		−	1.07875i	−0.842065	−	0.539376i	$-0.818660\pi$
$827$		−	892.129i		−	1.07875i	0.842065	−	0.539376i	$-0.181340\pi$
$828$	928.828	−	174.550i	1.12177	−	0.210810i
$829$	866.124			1.04478			0.522391	−	0.852706i	$-0.325040\pi$
$829$	866.124			1.04478			0.522391	+	0.852706i	$0.325040\pi$
$830$		−	72.3409i		−	0.0871578i
$831$	−449.376	+	541.691i	−0.540765	+	0.651855i
$832$	−429.851			−0.516647
$833$		−	30.4708i		−	0.0365796i
$834$	−17.1704	−	14.2442i	−0.0205880	−	0.0170794i
$835$	65.1029			0.0779676
$836$			755.056i			0.903177i
$837$	785.106	+	435.822i	0.937999	+	0.520695i
$838$	−153.001			−0.182578
$839$		−	841.348i		−	1.00280i	−0.865216	−	0.501399i	$-0.832819\pi$
$839$		−	841.348i		−	1.00280i	0.865216	−	0.501399i	$-0.167181\pi$
$840$	−18.8685	+	22.7447i	−0.0224625	+	0.0270770i
$841$	91.1375			0.108368
$842$		−	41.1009i		−	0.0488134i
$843$	798.403	+	662.339i	0.947097	+	0.785693i
$844$	1230.49			1.45792
$845$			262.489i			0.310638i
$846$	−29.6135	−	157.581i	−0.0350041	−	0.186266i
$847$	−96.2985			−0.113694
$848$			320.760i			0.378254i
$849$	447.466	−	539.390i	0.527051	−	0.635323i
$850$	−4.55499			−0.00535881
$851$		−	1551.18i		−	1.82277i
$852$	−835.111	−	692.791i	−0.980177	−	0.813135i
$853$	799.326			0.937076			0.468538	−	0.883443i	$-0.344781\pi$
$853$	799.326			0.937076			0.468538	+	0.883443i	$0.344781\pi$
$854$		−	47.9080i		−	0.0560983i
$855$	−410.393	+	77.1233i	−0.479992	+	0.0902027i
$856$	171.659			0.200536
$857$			30.1221i			0.0351483i	0.999846	+	0.0175742i	$0.00559432\pi$
$857$			30.1221i			0.0351483i	−0.999846	+	0.0175742i	$0.994406\pi$
$858$	26.4888	−	31.9304i	0.0308727	−	0.0372149i
$859$	−1211.44			−1.41029			−0.705146	−	0.709062i	$-0.749119\pi$
$859$	−1211.44			−1.41029			−0.705146	+	0.709062i	$0.749119\pi$
$860$		−	210.512i		−	0.244781i
$861$	−243.578	−	202.067i	−0.282901	−	0.234689i
$862$	−35.2592			−0.0409040
$863$			1114.29i			1.29118i	0.763682	+	0.645592i	$0.223389\pi$
$863$			1114.29i			1.29118i	−0.763682	+	0.645592i	$0.776611\pi$
$864$	129.724	−	233.689i	0.150143	−	0.270473i
$865$	444.473			0.513841
$866$		−	78.4300i		−	0.0905658i
$867$	517.266	−	623.528i	0.596616	−	0.719179i
$868$	348.113			0.401052
$869$		−	381.717i		−	0.439261i
$870$	29.5880	+	24.5456i	0.0340092	+	0.0282134i
$871$	278.940			0.320252
$872$		−	256.019i		−	0.293600i
$873$	79.9042	+	425.191i	0.0915283	+	0.487046i
$874$	−115.263			−0.131880
$875$		−	29.5804i		−	0.0338062i
$876$	86.9713	−	104.838i	0.0992823	−	0.119678i
$877$	−981.524			−1.11918			−0.559592	−	0.828768i	$-0.689042\pi$
$877$	−981.524			−1.11918			−0.559592	+	0.828768i	$0.689042\pi$
$878$		−	73.4232i		−	0.0836255i
$879$	1021.82	+	847.679i	1.16248	+	0.964367i
$880$	318.306			0.361711
$881$			1712.80i			1.94416i	0.234657	+	0.972078i	$0.424603\pi$
$881$			1712.80i			1.94416i	−0.234657	+	0.972078i	$0.575397\pi$
$882$	12.9579	−	2.43512i	0.0146915	−	0.00276091i
$883$	361.433			0.409324			0.204662	−	0.978833i	$-0.434391\pi$
$883$	361.433			0.409324			0.204662	+	0.978833i	$0.434391\pi$
$884$			123.719i			0.139954i
$885$	310.386	−	374.149i	0.350719	−	0.422767i
$886$	23.0935			0.0260649
$887$			1.67263i			0.00188571i	1.00000		0.000942857i	$0.000300121\pi$
$887$			1.67263i			0.00188571i	−1.00000		0.000942857i	$0.999700\pi$
$888$	−224.677	−	186.387i	−0.253014	−	0.209895i
$889$	−176.204			−0.198204
$890$		−	63.3995i		−	0.0712354i
$891$	−270.470	−	694.207i	−0.303558	−	0.779132i
$892$	−1120.63			−1.25631
$893$		−	1766.34i		−	1.97799i
$894$	102.810	−	123.930i	0.115000	−	0.138625i
$895$	−449.523			−0.502261
$896$		−	137.894i		−	0.153900i
$897$	−440.283	−	365.250i	−0.490840	−	0.407191i
$898$	4.83143			0.00538021
$899$		−	910.718i		−	1.01303i
$900$	32.8806	+	174.966i	0.0365340	+	0.194407i
$901$	90.2190			0.100132
$902$		−	76.7543i		−	0.0850934i
$903$	−120.595	+	145.369i	−0.133549	+	0.160984i
$904$	−218.903			−0.242149
$905$			261.347i			0.288781i
$906$	102.487	+	85.0211i	0.113120	+	0.0938423i
$907$	−682.079			−0.752016			−0.376008	−	0.926616i	$-0.622704\pi$
$907$	−682.079			−0.752016			−0.376008	+	0.926616i	$0.622704\pi$
$908$			863.528i			0.951022i
$909$	120.092	−	22.5683i	0.132114	−	0.0248276i
$910$	8.89483			0.00977454
$911$			274.638i			0.301468i	0.988574	+	0.150734i	$0.0481638\pi$
$911$			274.638i			0.301468i	−0.988574	+	0.150734i	$0.951836\pi$
$912$	615.098	−	741.457i	0.674449	−	0.813002i
$913$	1421.87			1.55736
$914$		−	6.59849i		−	0.00721935i
$915$	−446.706	−	370.578i	−0.488203	−	0.405003i
$916$	−1503.98			−1.64190
$917$			267.725i			0.291958i
$918$	−21.5056	−	11.9381i	−0.0234266	−	0.0130044i
$919$	1318.82			1.43505			0.717527	−	0.696530i	$-0.245274\pi$
$919$	1318.82			1.43505			0.717527	+	0.696530i	$0.245274\pi$
$920$			98.8263i			0.107420i
$921$	−77.8208	+	93.8075i	−0.0844960	+	0.101854i
$922$	9.24411			0.0100261
$923$			656.794i			0.711586i
$924$	−222.294	−	184.411i	−0.240578	−	0.199579i
$925$	292.201			0.315893
$926$			14.1573i			0.0152887i
$927$	−116.612	−	620.521i	−0.125795	−	0.669386i
$928$	−271.078			−0.292109
$929$			1136.96i			1.22385i	0.790916	+	0.611925i	$0.209605\pi$
$929$			1136.96i			1.22385i	−0.790916	+	0.611925i	$0.790395\pi$
$930$	−29.8110	+	35.9351i	−0.0320548	+	0.0386398i
$931$	145.247			0.156012
$932$		−	449.518i		−	0.482316i
$933$	−73.3389	−	60.8405i	−0.0786055	−	0.0652095i
$934$	24.6324			0.0263730
$935$		−	89.5289i		−	0.0957528i
$936$	−105.807	+	19.8839i	−0.113042	+	0.0212435i
$937$	13.8469			0.0147779			0.00738895	−	0.999973i	$-0.497648\pi$
$937$	13.8469			0.0147779			0.00738895	+	0.999973i	$0.497648\pi$
$938$			21.4990i			0.0229200i
$939$	382.281	−	460.813i	0.407115	−	0.490749i
$940$	−753.060			−0.801128
$941$		−	592.052i		−	0.629173i	−0.949229	−	0.314586i	$-0.898134\pi$
$941$		−	592.052i		−	0.629173i	0.949229	−	0.314586i	$-0.101866\pi$
$942$	−49.5287	−	41.0880i	−0.0525783	−	0.0436178i
$943$	−1058.35			−1.12233
$944$			1121.55i			1.18808i
$945$	77.5265	−	139.659i	0.0820386	−	0.147787i
$946$	−45.8075			−0.0484223
$947$		−	1541.53i		−	1.62780i	−0.581002	−	0.813902i	$-0.697339\pi$
$947$		−	1541.53i		−	1.62780i	0.581002	−	0.813902i	$-0.302661\pi$
$948$	−314.482	+	379.086i	−0.331732	+	0.399880i
$949$	−82.4523			−0.0868834
$950$		−	21.7125i		−	0.0228553i
$951$	87.2687	+	72.3963i	0.0917652	+	0.0761265i
$952$	−19.1766			−0.0201435
$953$			1653.61i			1.73517i	0.497293	+	0.867583i	$0.334327\pi$
$953$			1653.61i			1.73517i	−0.497293	+	0.867583i	$0.665673\pi$
$954$	7.20999	+	38.3662i	0.00755764	+	0.0402162i
$955$	−358.140			−0.375015
$956$			1703.32i			1.78172i
$957$	−482.447	+	581.556i	−0.504124	+	0.607687i
$958$	−69.0220			−0.0720480
$959$		−	388.145i		−	0.404739i
$960$	−308.915	−	256.270i	−0.321787	−	0.266948i
$961$	145.079			0.150966
$962$			87.8649i			0.0913357i
$963$	−911.875	+	171.364i	−0.946910	+	0.177949i
$964$	−614.525			−0.637475
$965$		−	501.966i		−	0.520172i
$966$	28.1513	−	33.9344i	0.0291421	−	0.0351288i
$967$	−846.585			−0.875475			−0.437738	−	0.899103i	$-0.644220\pi$
$967$	−846.585			−0.875475			−0.437738	+	0.899103i	$0.644220\pi$
$968$			60.6049i			0.0626083i
$969$	−208.547	−	173.007i	−0.215219	−	0.178541i
$970$	−22.4954			−0.0231912
$971$		−	601.310i		−	0.619269i	−0.950856	−	0.309634i	$-0.899793\pi$
$971$		−	601.310i		−	0.619269i	0.950856	−	0.309634i	$-0.100207\pi$
$972$	−303.324	+	912.251i	−0.312062	+	0.938530i
$973$	94.0134			0.0966222
$974$			42.6644i			0.0438033i
$975$	68.8033	−	82.9376i	0.0705675	−	0.0850642i
$976$	1339.05			1.37197
$977$		−	107.574i		−	0.110106i	−0.998483	−	0.0550532i	$-0.982467\pi$
$977$		−	107.574i		−	0.110106i	0.998483	−	0.0550532i	$-0.0175328\pi$
$978$	98.4848	+	81.7010i	0.100700	+	0.0835388i
$979$	1246.13			1.27286
$980$		−	61.9243i		−	0.0631881i
$981$	255.580	+	1360.01i	0.260530	+	1.38635i
$982$	16.2053			0.0165024
$983$			963.935i			0.980606i	0.871552	+	0.490303i	$0.163114\pi$
$983$			963.935i			0.980606i	−0.871552	+	0.490303i	$0.836886\pi$
$984$	−127.170	+	153.294i	−0.129237	+	0.155787i
$985$	17.8497			0.0181215
$986$			24.9464i			0.0253006i
$987$	520.025	+	431.402i	0.526875	+	0.437084i
$988$	−589.739			−0.596902
$989$			631.632i			0.638657i
$990$	38.0727	−	7.15483i	0.0384573	−	0.00722710i
$991$	−119.179			−0.120261			−0.0601306	−	0.998191i	$-0.519152\pi$
$991$	−119.179			−0.120261			−0.0601306	+	0.998191i	$0.519152\pi$
$992$		−	329.227i		−	0.331882i
$993$	181.014	−	218.200i	0.182290	−	0.219738i
$994$	−50.6217			−0.0509273
$995$		−	78.2960i		−	0.0786894i
$996$	−1412.07	−	1171.42i	−1.41774	−	1.17613i
$997$	122.639			0.123008			0.0615039	−	0.998107i	$-0.480410\pi$
$997$	122.639			0.123008			0.0615039	+	0.998107i	$0.480410\pi$
$998$		−	87.6881i		−	0.0878638i
$999$	1379.58	+	765.822i	1.38096	+	0.766589i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.c.a.71.9	yes	16
3.2	odd	2	inner	105.3.c.a.71.8	✓	16
4.3	odd	2		1680.3.l.a.1121.6		16
5.2	odd	4		525.3.f.b.449.15		32
5.3	odd	4		525.3.f.b.449.17		32
5.4	even	2		525.3.c.b.176.8		16
12.11	even	2		1680.3.l.a.1121.5		16
15.2	even	4		525.3.f.b.449.18		32
15.8	even	4		525.3.f.b.449.16		32
15.14	odd	2		525.3.c.b.176.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.c.a.71.8	✓	16	3.2	odd	2	inner
105.3.c.a.71.9	yes	16	1.1	even	1	trivial
525.3.c.b.176.8		16	5.4	even	2
525.3.c.b.176.9		16	15.14	odd	2
525.3.f.b.449.15		32	5.2	odd	4
525.3.f.b.449.16		32	15.8	even	4
525.3.f.b.449.17		32	5.3	odd	4
525.3.f.b.449.18		32	15.2	even	4
1680.3.l.a.1121.5		16	12.11	even	2
1680.3.l.a.1121.6		16	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.209282i q^{2} +(1.91543 - 2.30892i) q^{3} +3.95620 q^{4} -2.23607i q^{5} +(0.483215 + 0.400865i) q^{6} -2.64575 q^{7} +1.66509i q^{8} +(-1.66223 - 8.84517i) q^{9} +O(q^{10})\)	\(q+0.209282i q^{2} +(1.91543 - 2.30892i) q^{3} +3.95620 q^{4} -2.23607i q^{5} +(0.483215 + 0.400865i) q^{6} -2.64575 q^{7} +1.66509i q^{8} +(-1.66223 - 8.84517i) q^{9} +0.467968 q^{10} +9.19797i q^{11} +(7.57784 - 9.13456i) q^{12} -7.18410 q^{13} -0.553707i q^{14} +(-5.16290 - 4.28304i) q^{15} +15.4763 q^{16} -4.35298i q^{17} +(1.85113 - 0.347875i) q^{18} +20.7496 q^{19} -8.84633i q^{20} +(-5.06776 + 6.10883i) q^{21} -1.92497 q^{22} +26.5430i q^{23} +(3.84455 + 3.18936i) q^{24} -5.00000 q^{25} -1.50350i q^{26} +(-23.6067 - 13.1044i) q^{27} -10.4671 q^{28} +27.3836i q^{29} +(0.896361 - 1.08050i) q^{30} -33.2578 q^{31} +9.89926i q^{32} +(21.2374 + 17.6181i) q^{33} +0.910998 q^{34} +5.91608i q^{35} +(-6.57612 - 34.9933i) q^{36} -58.4402 q^{37} +4.34251i q^{38} +(-13.7607 + 16.5875i) q^{39} +3.72325 q^{40} +39.8731i q^{41} +(-1.27847 - 1.06059i) q^{42} +23.7965 q^{43} +36.3890i q^{44} +(-19.7784 + 3.71686i) q^{45} -5.55497 q^{46} -85.1268i q^{47} +(29.6439 - 35.7336i) q^{48} +7.00000 q^{49} -1.04641i q^{50} +(-10.0507 - 8.33784i) q^{51} -28.4218 q^{52} +20.7258i q^{53} +(2.74250 - 4.94045i) q^{54} +20.5673 q^{55} -4.40541i q^{56} +(39.7444 - 47.9091i) q^{57} -5.73089 q^{58} +72.4687i q^{59} +(-20.4255 - 16.9446i) q^{60} +86.5222 q^{61} -6.96024i q^{62} +(4.39785 + 23.4021i) q^{63} +59.8336 q^{64} +16.0641i q^{65} +(-3.68714 + 4.44459i) q^{66} -38.8274 q^{67} -17.2213i q^{68} +(61.2858 + 50.8414i) q^{69} -1.23813 q^{70} -91.4233i q^{71} +(14.7280 - 2.76776i) q^{72} +11.4771 q^{73} -12.2305i q^{74} +(-9.57717 + 11.5446i) q^{75} +82.0895 q^{76} -24.3355i q^{77} +(-3.47146 - 2.87986i) q^{78} -41.5002 q^{79} -34.6061i q^{80} +(-75.4740 + 29.4054i) q^{81} -8.34470 q^{82} -154.585i q^{83} +(-20.0491 + 24.1678i) q^{84} -9.73355 q^{85} +4.98017i q^{86} +(63.2266 + 52.4515i) q^{87} -15.3154 q^{88} -135.478i q^{89} +(-0.777871 - 4.13926i) q^{90} +19.0073 q^{91} +105.010i q^{92} +(-63.7030 + 76.7895i) q^{93} +17.8155 q^{94} -46.3975i q^{95} +(22.8566 + 18.9614i) q^{96} -48.0704 q^{97} +1.46497i q^{98} +(81.3575 - 15.2892i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9	\( 16 q + 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9} - 20 q^{10} + 12 q^{12} + 10 q^{15} + 92 q^{16} - 52 q^{18} - 16 q^{19} - 14 q^{21} + 16 q^{22} + 128 q^{24} - 80 q^{25} - 148 q^{27} + 112 q^{28} + 80 q^{30} - 72 q^{31} - 4 q^{33} - 176 q^{34} - 76 q^{36} - 40 q^{37} + 90 q^{39} - 60 q^{40} + 280 q^{43} + 40 q^{45} + 72 q^{46} - 172 q^{48} + 112 q^{49} + 38 q^{51} - 88 q^{52} + 208 q^{54} + 80 q^{55} - 36 q^{57} - 24 q^{58} - 80 q^{60} - 56 q^{61} - 56 q^{63} - 44 q^{64} - 260 q^{66} - 120 q^{67} + 60 q^{69} + 376 q^{72} - 208 q^{73} - 40 q^{75} + 144 q^{76} - 228 q^{78} - 204 q^{79} + 458 q^{81} - 384 q^{82} - 84 q^{84} + 100 q^{85} - 324 q^{87} + 168 q^{88} - 160 q^{90} - 28 q^{91} + 108 q^{93} + 984 q^{94} + 40 q^{96} + 728 q^{97} - 166 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9 - 20 * q^10 + 12 * q^12 + 10 * q^15 + 92 * q^16 - 52 * q^18 - 16 * q^19 - 14 * q^21 + 16 * q^22 + 128 * q^24 - 80 * q^25 - 148 * q^27 + 112 * q^28 + 80 * q^30 - 72 * q^31 - 4 * q^33 - 176 * q^34 - 76 * q^36 - 40 * q^37 + 90 * q^39 - 60 * q^40 + 280 * q^43 + 40 * q^45 + 72 * q^46 - 172 * q^48 + 112 * q^49 + 38 * q^51 - 88 * q^52 + 208 * q^54 + 80 * q^55 - 36 * q^57 - 24 * q^58 - 80 * q^60 - 56 * q^61 - 56 * q^63 - 44 * q^64 - 260 * q^66 - 120 * q^67 + 60 * q^69 + 376 * q^72 - 208 * q^73 - 40 * q^75 + 144 * q^76 - 228 * q^78 - 204 * q^79 + 458 * q^81 - 384 * q^82 - 84 * q^84 + 100 * q^85 - 324 * q^87 + 168 * q^88 - 160 * q^90 - 28 * q^91 + 108 * q^93 + 984 * q^94 + 40 * q^96 + 728 * q^97 - 166 * q^99

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