LMFDB - Embedded newform 105.3.c.a.71.2

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			71.2
Root			$-3.57278i$ of defining polynomial
Character	$\chi$	$=$	105.71
Dual form			105.3.c.a.71.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.57278i q^{2} +(-2.99481 + 0.176471i) q^{3} -8.76473 q^{4} -2.23607i q^{5} +(0.630492 + 10.6998i) q^{6} -2.64575 q^{7} +17.0233i q^{8} +(8.93772 - 1.05699i) q^{9} +O(q^{10})$	\(q-3.57278i q^{2} +(-2.99481 + 0.176471i) q^{3} -8.76473 q^{4} -2.23607i q^{5} +(0.630492 + 10.6998i) q^{6} -2.64575 q^{7} +17.0233i q^{8} +(8.93772 - 1.05699i) q^{9} -7.98897 q^{10} +12.0685i q^{11} +(26.2487 - 1.54672i) q^{12} -12.7142 q^{13} +9.45268i q^{14} +(0.394601 + 6.69659i) q^{15} +25.7616 q^{16} -22.2556i q^{17} +(-3.77640 - 31.9325i) q^{18} -28.9289 q^{19} +19.5985i q^{20} +(7.92351 - 0.466899i) q^{21} +43.1180 q^{22} -21.9101i q^{23} +(-3.00412 - 50.9815i) q^{24} -5.00000 q^{25} +45.4249i q^{26} +(-26.5802 + 4.74274i) q^{27} +23.1893 q^{28} +11.4122i q^{29} +(23.9254 - 1.40982i) q^{30} -4.93977 q^{31} -23.9470i q^{32} +(-2.12974 - 36.1428i) q^{33} -79.5144 q^{34} +5.91608i q^{35} +(-78.3367 + 9.26426i) q^{36} -36.7045 q^{37} +103.356i q^{38} +(38.0765 - 2.24369i) q^{39} +38.0653 q^{40} -57.6874i q^{41} +(-1.66812 - 28.3089i) q^{42} +57.7493 q^{43} -105.777i q^{44} +(-2.36351 - 19.9853i) q^{45} -78.2798 q^{46} +15.6773i q^{47} +(-77.1508 + 4.54617i) q^{48} +7.00000 q^{49} +17.8639i q^{50} +(3.92747 + 66.6513i) q^{51} +111.436 q^{52} -91.2304i q^{53} +(16.9447 + 94.9651i) q^{54} +26.9860 q^{55} -45.0394i q^{56} +(86.6363 - 5.10511i) q^{57} +40.7733 q^{58} +34.3101i q^{59} +(-3.45857 - 58.6938i) q^{60} +71.1225 q^{61} +17.6487i q^{62} +(-23.6470 + 2.79654i) q^{63} +17.4888 q^{64} +28.4298i q^{65} +(-129.130 + 7.60909i) q^{66} +20.1716 q^{67} +195.065i q^{68} +(3.86649 + 65.6164i) q^{69} +21.1368 q^{70} -69.7718i q^{71} +(17.9935 + 152.150i) q^{72} -96.8693 q^{73} +131.137i q^{74} +(14.9740 - 0.882355i) q^{75} +253.554 q^{76} -31.9302i q^{77} +(-8.01619 - 136.039i) q^{78} -84.2348 q^{79} -57.6046i q^{80} +(78.7655 - 18.8942i) q^{81} -206.104 q^{82} -20.4474i q^{83} +(-69.4474 + 4.09224i) q^{84} -49.7651 q^{85} -206.325i q^{86} +(-2.01393 - 34.1774i) q^{87} -205.446 q^{88} -1.65255i q^{89} +(-71.4031 + 8.44428i) q^{90} +33.6386 q^{91} +192.036i q^{92} +(14.7936 - 0.871726i) q^{93} +56.0116 q^{94} +64.6869i q^{95} +(4.22596 + 71.7167i) q^{96} +29.7125 q^{97} -25.0094i q^{98} +(12.7563 + 107.865i) 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 $

$2$		−	3.57278i		−	1.78639i	−0.449671	−	0.893194i	$-0.648459\pi$
$2$		−	3.57278i		−	1.78639i	0.449671	−	0.893194i	$-0.351541\pi$
$3$	−2.99481	+	0.176471i	−0.998268	+	0.0588237i
$3$	−2.99481	+	0.176471i	−0.998268	+	0.0588237i
$4$	−8.76473			−2.19118
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$	0.630492	+	10.6998i	0.105082	+	1.78329i
$7$	−2.64575			−0.377964
$7$	−2.64575			−0.377964
$8$			17.0233i			2.12791i
$9$	8.93772	−	1.05699i	0.993080	−	0.117444i
$10$	−7.98897			−0.798897
$11$			12.0685i			1.09714i	0.836106	+	0.548568i	$0.184827\pi$
$11$			12.0685i			1.09714i	−0.836106	+	0.548568i	$0.815173\pi$
$12$	26.2487	−	1.54672i	2.18739	−	0.128893i
$13$	−12.7142			−0.978014			−0.489007	−	0.872280i	$-0.662641\pi$
$13$	−12.7142			−0.978014			−0.489007	+	0.872280i	$0.662641\pi$
$14$			9.45268i			0.675191i
$15$	0.394601	+	6.69659i	0.0263068	+	0.446439i
$16$	25.7616			1.61010
$17$		−	22.2556i		−	1.30915i	−0.755995	−	0.654577i	$-0.772847\pi$
$17$		−	22.2556i		−	1.30915i	0.755995	−	0.654577i	$-0.227153\pi$
$18$	−3.77640	−	31.9325i	−0.209800	−	1.77403i
$19$	−28.9289			−1.52257			−0.761286	−	0.648417i	$-0.775432\pi$
$19$	−28.9289			−1.52257			−0.761286	+	0.648417i	$0.775432\pi$
$20$			19.5985i			0.979926i
$21$	7.92351	−	0.466899i	0.377310	−	0.0222333i
$22$	43.1180			1.95991
$23$		−	21.9101i		−	0.952612i	−0.879280	−	0.476306i	$-0.841975\pi$
$23$		−	21.9101i		−	0.952612i	0.879280	−	0.476306i	$-0.158025\pi$
$24$	−3.00412	−	50.9815i	−0.125172	−	2.12423i
$25$	−5.00000			−0.200000
$26$			45.4249i			1.74711i
$27$	−26.5802	+	4.74274i	−0.984451	+	0.175657i
$28$	23.1893			0.828189
$29$			11.4122i			0.393525i	0.980451	+	0.196763i	$0.0630428\pi$
$29$			11.4122i			0.393525i	−0.980451	+	0.196763i	$0.936957\pi$
$30$	23.9254	−	1.40982i	0.797514	−	0.0469941i
$31$	−4.93977			−0.159347			−0.0796737	−	0.996821i	$-0.525388\pi$
$31$	−4.93977			−0.159347			−0.0796737	+	0.996821i	$0.525388\pi$
$32$		−	23.9470i		−	0.748345i
$33$	−2.12974	−	36.1428i	−0.0645376	−	1.09524i
$34$	−79.5144			−2.33866
$35$			5.91608i			0.169031i
$36$	−78.3367	+	9.26426i	−2.17602	+	0.257340i
$37$	−36.7045			−0.992014			−0.496007	−	0.868319i	$-0.665201\pi$
$37$	−36.7045			−0.992014			−0.496007	+	0.868319i	$0.665201\pi$
$38$			103.356i			2.71990i
$39$	38.0765	−	2.24369i	0.976321	−	0.0575304i
$40$	38.0653			0.951632
$41$		−	57.6874i		−	1.40701i	−0.710691	−	0.703504i	$-0.751618\pi$
$41$		−	57.6874i		−	1.40701i	0.710691	−	0.703504i	$-0.248382\pi$
$42$	−1.66812	−	28.3089i	−0.0397172	−	0.674022i
$43$	57.7493			1.34301			0.671503	−	0.741002i	$-0.265649\pi$
$43$	57.7493			1.34301			0.671503	+	0.741002i	$0.265649\pi$
$44$		−	105.777i		−	2.40403i
$45$	−2.36351	−	19.9853i	−0.0525224	−	0.444119i
$46$	−78.2798			−1.70173
$47$			15.6773i			0.333561i	0.985994	+	0.166780i	$0.0533370\pi$
$47$			15.6773i			0.333561i	−0.985994	+	0.166780i	$0.946663\pi$
$48$	−77.1508	+	4.54617i	−1.60731	+	0.0947119i
$49$	7.00000			0.142857
$50$			17.8639i			0.357278i
$51$	3.92747	+	66.6513i	0.0770093	+	1.30689i
$52$	111.436			2.14301
$53$		−	91.2304i		−	1.72133i	−0.509173	−	0.860664i	$-0.670049\pi$
$53$		−	91.2304i		−	1.72133i	0.509173	−	0.860664i	$-0.329951\pi$
$54$	16.9447	+	94.9651i	0.313791	+	1.75861i
$55$	26.9860			0.490654
$56$		−	45.0394i		−	0.804276i
$57$	86.6363	−	5.10511i	1.51993	−	0.0895633i
$58$	40.7733			0.702989
$59$			34.3101i			0.581527i	0.956795	+	0.290763i	$0.0939093\pi$
$59$			34.3101i			0.581527i	−0.956795	+	0.290763i	$0.906091\pi$
$60$	−3.45857	−	58.6938i	−0.0576429	−	0.978230i
$61$	71.1225			1.16594			0.582971	−	0.812493i	$-0.301890\pi$
$61$	71.1225			1.16594			0.582971	+	0.812493i	$0.301890\pi$
$62$			17.6487i			0.284656i
$63$	−23.6470	+	2.79654i	−0.375349	+	0.0443895i
$64$	17.4888			0.273263
$65$			28.4298i			0.437381i
$66$	−129.130	+	7.60909i	−1.95652	+	0.115289i
$67$	20.1716			0.301069			0.150534	−	0.988605i	$-0.451901\pi$
$67$	20.1716			0.301069			0.150534	+	0.988605i	$0.451901\pi$
$68$			195.065i			2.86860i
$69$	3.86649	+	65.6164i	0.0560362	+	0.950963i
$70$	21.1368			0.301955
$71$		−	69.7718i		−	0.982702i	−0.870962	−	0.491351i	$-0.836503\pi$
$71$		−	69.7718i		−	0.982702i	0.870962	−	0.491351i	$-0.163497\pi$
$72$	17.9935	+	152.150i	0.249910	+	2.11319i
$73$	−96.8693			−1.32698			−0.663489	−	0.748186i	$-0.730925\pi$
$73$	−96.8693			−1.32698			−0.663489	+	0.748186i	$0.730925\pi$
$74$			131.137i			1.77212i
$75$	14.9740	−	0.882355i	0.199654	−	0.0117647i
$76$	253.554			3.33623
$77$		−	31.9302i		−	0.414679i
$78$	−8.01619	−	136.039i	−0.102772	−	1.74409i
$79$	−84.2348			−1.06626			−0.533132	−	0.846032i	$-0.678985\pi$
$79$	−84.2348			−1.06626			−0.533132	+	0.846032i	$0.678985\pi$
$80$		−	57.6046i		−	0.720057i
$81$	78.7655	−	18.8942i	0.972414	−	0.233262i
$82$	−206.104			−2.51346
$83$		−	20.4474i		−	0.246354i	−0.992385	−	0.123177i	$-0.960692\pi$
$83$		−	20.4474i		−	0.246354i	0.992385	−	0.123177i	$-0.0393083\pi$
$84$	−69.4474	+	4.09224i	−0.826755	+	0.0487171i
$85$	−49.7651			−0.585472
$86$		−	206.325i		−	2.39913i
$87$	−2.01393	−	34.1774i	−0.0231486	−	0.392844i
$88$	−205.446			−2.33461
$89$		−	1.65255i		−	0.0185680i	−0.999957	−	0.00928398i	$-0.997045\pi$
$89$		−	1.65255i		−	0.0185680i	0.999957	−	0.00928398i	$-0.00295523\pi$
$90$	−71.4031	+	8.44428i	−0.793368	+	0.0938254i
$91$	33.6386			0.369655
$92$			192.036i			2.08735i
$93$	14.7936	−	0.871726i	0.159071	−	0.00937340i
$94$	56.0116			0.595869
$95$			64.6869i			0.680915i
$96$	4.22596	+	71.7167i	0.0440204	+	0.747049i
$97$	29.7125			0.306314			0.153157	−	0.988202i	$-0.451056\pi$
$97$	29.7125			0.306314			0.153157	+	0.988202i	$0.451056\pi$
$98$		−	25.0094i		−	0.255198i
$99$	12.7563	+	107.865i	0.128852	+	1.08954i
$100$	43.8236			0.438236
$101$		−	33.7684i		−	0.334341i	−0.985928	−	0.167170i	$-0.946537\pi$
$101$		−	33.7684i		−	0.334341i	0.985928	−	0.167170i	$-0.0534630\pi$
$102$	238.130	−	14.0320i	2.33461	−	0.137569i
$103$	−120.360			−1.16855			−0.584274	−	0.811557i	$-0.698621\pi$
$103$	−120.360			−1.16855			−0.584274	+	0.811557i	$0.698621\pi$
$104$		−	216.438i		−	2.08113i
$105$	−1.04402	−	17.7175i	−0.00994302	−	0.168738i
$106$	−325.946			−3.07496
$107$			174.545i			1.63126i	0.578570	+	0.815632i	$0.303611\pi$
$107$			174.545i			1.63126i	−0.578570	+	0.815632i	$0.696389\pi$
$108$	232.968	−	41.5688i	2.15711	−	0.384896i
$109$	25.2313			0.231480			0.115740	−	0.993280i	$-0.463076\pi$
$109$	25.2313			0.231480			0.115740	+	0.993280i	$0.463076\pi$
$110$		−	96.4149i		−	0.876499i
$111$	109.923	−	6.47728i	0.990296	−	0.0583539i
$112$	−68.1587			−0.608560
$113$			126.424i			1.11880i	0.828898	+	0.559400i	$0.188969\pi$
$113$			126.424i			1.11880i	−0.828898	+	0.559400i	$0.811031\pi$
$114$	−18.2394	−	309.532i	−0.159995	−	2.71519i
$115$	−48.9924			−0.426021
$116$		−	100.025i		−	0.862285i
$117$	−113.636	+	13.4388i	−0.971246	+	0.114862i
$118$	122.582			1.03883
$119$			58.8829i			0.494814i
$120$	−113.998	+	6.71742i	−0.949984	+	0.0559785i
$121$	−24.6487			−0.203708
$122$		−	254.105i		−	2.08283i
$123$	10.1801	+	172.762i	0.0827654	+	1.40457i
$124$	43.2957			0.349159
$125$			11.1803i			0.0894427i
$126$	9.99141	+	84.4853i	0.0792969	+	0.670519i
$127$	−7.33093			−0.0577238			−0.0288619	−	0.999583i	$-0.509188\pi$
$127$	−7.33093			−0.0577238			−0.0288619	+	0.999583i	$0.509188\pi$
$128$		−	158.272i		−	1.23650i
$129$	−172.948	+	10.1911i	−1.34068	+	0.0790006i
$130$	101.573			0.781333
$131$		−	96.8346i		−	0.739195i	−0.929192	−	0.369598i	$-0.879495\pi$
$131$		−	96.8346i		−	0.739195i	0.929192	−	0.369598i	$-0.120505\pi$
$132$	18.6666	+	316.782i	0.141414	+	2.39986i
$133$	76.5386			0.575478
$134$		−	72.0687i		−	0.537826i
$135$	10.6051	+	59.4351i	0.0785561	+	0.440260i
$136$	378.865			2.78577
$137$		−	228.866i		−	1.67055i	−0.549830	−	0.835277i	$-0.685307\pi$
$137$		−	228.866i		−	1.67055i	0.549830	−	0.835277i	$-0.314693\pi$
$138$	234.433	−	13.8141i	1.69879	−	0.100102i
$139$	162.799			1.17121			0.585606	−	0.810596i	$-0.300856\pi$
$139$	162.799			1.17121			0.585606	+	0.810596i	$0.300856\pi$
$140$		−	51.8528i		−	0.370377i
$141$	−2.76660	−	46.9506i	−0.0196213	−	0.332983i
$142$	−249.279			−1.75549
$143$		−	153.441i		−	1.07301i
$144$	230.249	−	27.2298i	1.59895	−	0.189096i
$145$	25.5185			0.175990
$146$			346.092i			2.37050i
$147$	−20.9636	+	1.23530i	−0.142610	+	0.00840338i
$148$	321.705			2.17368
$149$			1.91716i			0.0128668i	0.999979	+	0.00643341i	$0.00204783\pi$
$149$			1.91716i			0.0128668i	−0.999979	+	0.00643341i	$0.997952\pi$
$150$	−3.15246	−	53.4988i	−0.0210164	−	0.356659i
$151$	3.34803			0.0221724			0.0110862	−	0.999939i	$-0.496471\pi$
$151$	3.34803			0.0221724			0.0110862	+	0.999939i	$0.496471\pi$
$152$		−	492.465i		−	3.23990i
$153$	−23.5240	−	198.915i	−0.153752	−	1.30009i
$154$	−114.080			−0.740777
$155$			11.0457i			0.0712623i
$156$	−333.730	+	19.6653i	−2.13930	+	0.126060i
$157$	3.98288			0.0253687			0.0126843	−	0.999920i	$-0.495962\pi$
$157$	3.98288			0.0253687			0.0126843	+	0.999920i	$0.495962\pi$
$158$			300.952i			1.90476i
$159$	16.0995	+	273.217i	0.101255	+	1.71835i
$160$	−53.5472			−0.334670
$161$			57.9686i			0.360054i
$162$	−67.5048	−	281.412i	−0.416696	−	1.73711i
$163$	−238.081			−1.46062			−0.730310	−	0.683116i	$-0.760624\pi$
$163$	−238.081			−1.46062			−0.730310	+	0.683116i	$0.760624\pi$
$164$			505.614i			3.08301i
$165$	−80.8178	+	4.76225i	−0.489805	+	0.0288621i
$166$	−73.0540			−0.440084
$167$			93.0174i			0.556990i	0.960438	+	0.278495i	$0.0898356\pi$
$167$			93.0174i			0.556990i	−0.960438	+	0.278495i	$0.910164\pi$
$168$	7.94816	+	134.884i	0.0473105	+	0.802883i
$169$	−7.34951			−0.0434882
$170$			177.800i			1.04588i
$171$	−258.558	+	30.5776i	−1.51203	+	0.178816i
$172$	−506.157			−2.94277
$173$		−	20.2396i		−	0.116992i	−0.998288	−	0.0584959i	$-0.981370\pi$
$173$		−	20.2396i		−	0.116992i	0.998288	−	0.0584959i	$-0.0186305\pi$
$174$	−122.108	+	7.19531i	−0.701771	+	0.0413524i
$175$	13.2288			0.0755929
$176$			310.903i			1.76650i
$177$	−6.05474	−	102.752i	−0.0342076	−	0.580520i
$178$	−5.90419			−0.0331696
$179$		−	115.119i		−	0.643122i	−0.946889	−	0.321561i	$-0.895793\pi$
$179$		−	115.119i		−	0.643122i	0.946889	−	0.321561i	$-0.104207\pi$
$180$	20.7155	+	175.166i	0.115086	+	0.973145i
$181$	−35.1309			−0.194093			−0.0970467	−	0.995280i	$-0.530940\pi$
$181$	−35.1309			−0.194093			−0.0970467	+	0.995280i	$0.530940\pi$
$182$		−	120.183i		−	0.660347i
$183$	−212.998	+	12.5511i	−1.16392	+	0.0685850i
$184$	372.982			2.02708
$185$			82.0738i			0.443642i
$186$	−3.11448	−	52.8544i	−0.0167445	−	0.284163i
$187$	268.592			1.43632
$188$		−	137.408i		−	0.730892i
$189$	70.3246	−	12.5481i	0.372088	−	0.0663921i
$190$	231.112			1.21638
$191$			128.664i			0.673631i	0.941571	+	0.336816i	$0.109350\pi$
$191$			128.664i			0.673631i	−0.941571	+	0.336816i	$0.890650\pi$
$192$	−52.3756	+	3.08627i	−0.272790	+	0.0160743i
$193$	149.261			0.773373			0.386686	−	0.922211i	$-0.373620\pi$
$193$	149.261			0.773373			0.386686	+	0.922211i	$0.373620\pi$
$194$		−	106.156i		−	0.547196i
$195$	−5.01703	−	85.1417i	−0.0257284	−	0.436624i
$196$	−61.3531			−0.313026
$197$			304.740i			1.54691i	0.633854	+	0.773453i	$0.281472\pi$
$197$			304.740i			1.54691i	−0.633854	+	0.773453i	$0.718528\pi$
$198$	385.377	−	45.5755i	1.94635	−	0.230179i
$199$	−98.5989			−0.495472			−0.247736	−	0.968828i	$-0.579687\pi$
$199$	−98.5989			−0.495472			−0.247736	+	0.968828i	$0.579687\pi$
$200$		−	85.1165i		−	0.425583i
$201$	−60.4101	+	3.55971i	−0.300548	+	0.0177100i
$202$	−120.647			−0.597263
$203$		−	30.1939i		−	0.148739i
$204$	−34.4233	−	584.180i	−0.168741	−	2.86363i
$205$	−128.993			−0.629233
$206$			430.021i			2.08748i
$207$	−23.1588	−	195.826i	−0.111878	−	0.946020i
$208$	−327.537			−1.57470
$209$		−	349.128i		−	1.67047i
$210$	−63.3007	+	3.73004i	−0.301432	+	0.0177621i
$211$	255.428			1.21056			0.605280	−	0.796013i	$-0.293061\pi$
$211$	255.428			1.21056			0.605280	+	0.796013i	$0.293061\pi$
$212$			799.610i			3.77175i
$213$	12.3127	+	208.953i	0.0578061	+	0.981000i
$214$	623.611			2.91407
$215$		−	129.131i		−	0.600611i
$216$	−80.7371	−	452.483i	−0.373783	−	2.09483i
$217$	13.0694			0.0602276
$218$		−	90.1459i		−	0.413514i
$219$	290.105	−	17.0946i	1.32468	−	0.0780577i
$220$	−236.525			−1.07511
$221$			282.962i			1.28037i
$222$	−23.1419	−	392.730i	−0.104243	−	1.76905i
$223$	−30.8285			−0.138244			−0.0691222	−	0.997608i	$-0.522020\pi$
$223$	−30.8285			−0.138244			−0.0691222	+	0.997608i	$0.522020\pi$
$224$			63.3579i			0.282848i
$225$	−44.6886	+	5.28496i	−0.198616	+	0.0234887i
$226$	451.686			1.99861
$227$		−	123.793i		−	0.545343i	−0.962107	−	0.272672i	$-0.912093\pi$
$227$		−	123.793i		−	0.545343i	0.962107	−	0.272672i	$-0.0879072\pi$
$228$	−759.344	+	44.7449i	−3.33045	+	0.196249i
$229$	−38.8512			−0.169656			−0.0848279	−	0.996396i	$-0.527034\pi$
$229$	−38.8512			−0.169656			−0.0848279	+	0.996396i	$0.527034\pi$
$230$			175.039i			0.761039i
$231$	5.63476	+	95.6249i	0.0243929	+	0.413960i
$232$	−194.274			−0.837388
$233$		−	194.201i		−	0.833479i	−0.909026	−	0.416740i	$-0.863173\pi$
$233$		−	194.201i		−	0.833479i	0.909026	−	0.416740i	$-0.136827\pi$
$234$	48.0138	+	405.995i	0.205187	+	1.73502i
$235$	35.0556			0.149173
$236$		−	300.719i		−	1.27423i
$237$	252.267	−	14.8650i	1.06442	−	0.0627215i
$238$	210.375			0.883930
$239$		−	228.989i		−	0.958115i	−0.877784	−	0.479057i	$-0.840979\pi$
$239$		−	228.989i		−	0.958115i	0.877784	−	0.479057i	$-0.159021\pi$
$240$	10.1655	+	172.515i	0.0423564	+	0.718811i
$241$	407.123			1.68931			0.844654	−	0.535313i	$-0.179806\pi$
$241$	407.123			1.68931			0.844654	+	0.535313i	$0.179806\pi$
$242$			88.0642i			0.363902i
$243$	−232.553	+	70.4843i	−0.957009	+	0.290059i
$244$	−623.369			−2.55479
$245$		−	15.6525i		−	0.0638877i
$246$	617.241	−	36.3714i	2.50911	−	0.147851i
$247$	367.807			1.48910
$248$		−	84.0912i		−	0.339077i
$249$	3.60838	+	61.2360i	0.0144915	+	0.245928i
$250$	39.9449			0.159779
$251$			164.458i			0.655211i	0.944815	+	0.327605i	$0.106242\pi$
$251$			164.458i			0.655211i	−0.944815	+	0.327605i	$0.893758\pi$
$252$	207.259	−	24.5109i	0.822458	−	0.0972655i
$253$	264.422			1.04515
$254$			26.1918i			0.103117i
$255$	149.037	−	8.78210i	0.584458	−	0.0344396i
$256$	−495.514			−1.93560
$257$			384.159i			1.49478i	0.664385	+	0.747390i	$0.268693\pi$
$257$			384.159i			1.49478i	−0.664385	+	0.747390i	$0.731307\pi$
$258$	36.4104	+	617.904i	0.141126	+	2.39498i
$259$	97.1110			0.374946
$260$		−	249.179i		−	0.958382i
$261$	12.0626	+	101.999i	0.0462170	+	0.390802i
$262$	−345.968			−1.32049
$263$		−	198.192i		−	0.753582i	−0.926298	−	0.376791i	$-0.877028\pi$
$263$		−	198.192i		−	0.753582i	0.926298	−	0.376791i	$-0.122972\pi$
$264$	615.270	−	36.2552i	2.33057	−	0.137330i
$265$	−203.997			−0.769802
$266$		−	273.455i		−	1.02803i
$267$	0.291627	+	4.94906i	0.00109224	+	0.0185358i
$268$	−176.799			−0.659697
$269$		−	14.3502i		−	0.0533465i	−0.999644	−	0.0266732i	$-0.991509\pi$
$269$		−	14.3502i		−	0.0533465i	0.999644	−	0.0266732i	$-0.00849136\pi$
$270$	212.348	−	37.8896i	0.786475	−	0.140332i
$271$	−26.2455			−0.0968468			−0.0484234	−	0.998827i	$-0.515420\pi$
$271$	−26.2455			−0.0968468			−0.0484234	+	0.998827i	$0.515420\pi$
$272$		−	573.340i		−	2.10787i
$273$	−100.741	+	5.93623i	−0.369015	+	0.0217444i
$274$	−817.686			−2.98426
$275$		−	60.3425i		−	0.219427i
$276$	−33.8888	−	575.110i	−0.122785	−	2.08373i
$277$	21.2740			0.0768014			0.0384007	−	0.999262i	$-0.487774\pi$
$277$	21.2740			0.0768014			0.0384007	+	0.999262i	$0.487774\pi$
$278$		−	581.643i		−	2.09224i
$279$	−44.1503	+	5.22130i	−0.158245	+	0.0187143i
$280$	−100.711			−0.359683
$281$		−	322.063i		−	1.14613i	−0.819509	−	0.573066i	$-0.805754\pi$
$281$		−	322.063i		−	1.14613i	0.819509	−	0.573066i	$-0.194246\pi$
$282$	−167.744	+	9.88443i	−0.594837	+	0.0350512i
$283$	−259.309			−0.916288			−0.458144	−	0.888878i	$-0.651486\pi$
$283$	−259.309			−0.916288			−0.458144	+	0.888878i	$0.651486\pi$
$284$			611.531i			2.15328i
$285$	−11.4154	−	193.725i	−0.0400539	−	0.679736i
$286$	−548.211			−1.91682
$287$			152.626i			0.531799i
$288$	−25.3119	−	214.032i	−0.0878884	−	0.743166i
$289$	−206.313			−0.713886
$290$		−	91.1720i		−	0.314386i
$291$	−88.9830	+	5.24339i	−0.305784	+	0.0180185i
$292$	849.034			2.90765
$293$		−	301.196i		−	1.02797i	−0.857798	−	0.513986i	$-0.828168\pi$
$293$		−	301.196i		−	1.02797i	0.857798	−	0.513986i	$-0.171832\pi$
$294$	4.41344	+	74.8984i	0.0150117	+	0.254756i
$295$	76.7197			0.260067
$296$		−	624.832i		−	2.11092i
$297$	−57.2377	−	320.783i	−0.192720	−	1.08008i
$298$	6.84957			0.0229851
$299$			278.569i			0.931668i
$300$	−131.243	+	7.73361i	−0.437478	+	0.0257787i
$301$	−152.790			−0.507609
$302$		−	11.9618i		−	0.0396084i
$303$	5.95915	+	101.130i	0.0196672	+	0.333762i
$304$	−745.252			−2.45149
$305$		−	159.035i		−	0.521425i
$306$	−710.677	+	84.0461i	−2.32247	+	0.274661i
$307$	−262.697			−0.855690			−0.427845	−	0.903852i	$-0.640727\pi$
$307$	−262.697			−0.855690			−0.427845	+	0.903852i	$0.640727\pi$
$308$			279.860i			0.908636i
$309$	360.456	−	21.2401i	1.16652	−	0.0687383i
$310$	39.4637			0.127302
$311$		−	248.536i		−	0.799151i	−0.916700	−	0.399575i	$-0.869158\pi$
$311$		−	248.536i		−	0.799151i	0.916700	−	0.399575i	$-0.130842\pi$
$312$	38.1950	+	648.188i	0.122420	+	2.07753i
$313$	426.733			1.36336			0.681682	−	0.731648i	$-0.261249\pi$
$313$	426.733			1.36336			0.681682	+	0.731648i	$0.261249\pi$
$314$		−	14.2299i		−	0.0453183i
$315$	6.25325	+	52.8762i	0.0198516	+	0.167861i
$316$	738.295			2.33638
$317$			107.379i			0.338735i	0.985553	+	0.169367i	$0.0541725\pi$
$317$			107.379i			0.338735i	−0.985553	+	0.169367i	$0.945828\pi$
$318$	976.144	−	57.5200i	3.06964	−	0.180881i
$319$	−137.728			−0.431751
$320$		−	39.1062i		−	0.122207i
$321$	−30.8022	−	522.729i	−0.0959570	−	1.62844i
$322$	207.109			0.643195
$323$			643.830i			1.99328i
$324$	−690.359	+	165.603i	−2.13074	+	0.511119i
$325$	63.5709			0.195603
$326$			850.610i			2.60923i
$327$	−75.5630	+	4.45260i	−0.231079	+	0.0136165i
$328$	982.030			2.99399
$329$		−	41.4784i		−	0.126074i
$330$	17.0144	+	288.744i	0.0515589	+	0.874981i
$331$	−451.938			−1.36537			−0.682687	−	0.730711i	$-0.739189\pi$
$331$	−451.938			−1.36537			−0.682687	+	0.730711i	$0.739189\pi$
$332$			179.216i			0.539807i
$333$	−328.054	+	38.7964i	−0.985148	+	0.116506i
$334$	332.330			0.995001
$335$		−	45.1051i		−	0.134642i
$336$	204.122	−	12.0280i	0.607506	−	0.0357977i
$337$	−638.072			−1.89339			−0.946695	−	0.322133i	$-0.895600\pi$
$337$	−638.072			−1.89339			−0.946695	+	0.322133i	$0.895600\pi$
$338$			26.2582i			0.0776869i
$339$	−22.3103	−	378.617i	−0.0658120	−	1.11686i
$340$	436.178			1.28288
$341$		−	59.6156i		−	0.174826i
$342$	109.247	+	923.770i	0.319435	+	2.70108i
$343$	−18.5203			−0.0539949
$344$			983.084i			2.85780i
$345$	146.723	−	8.64575i	0.425283	−	0.0250601i
$346$	−72.3115			−0.208993
$347$			129.949i			0.374493i	0.982313	+	0.187246i	$0.0599563\pi$
$347$			129.949i			0.374493i	−0.982313	+	0.187246i	$0.940044\pi$
$348$	17.6515	+	299.556i	0.0507228	+	0.860792i
$349$	−15.1067			−0.0432856			−0.0216428	−	0.999766i	$-0.506890\pi$
$349$	−15.1067			−0.0432856			−0.0216428	+	0.999766i	$0.506890\pi$
$350$		−	47.2634i		−	0.135038i
$351$	337.945	−	60.3000i	0.962807	−	0.171795i
$352$	289.005			0.821036
$353$			688.966i			1.95174i	0.218343	+	0.975872i	$0.429935\pi$
$353$			688.966i			1.95174i	−0.218343	+	0.975872i	$0.570065\pi$
$354$	−367.110	+	21.6322i	−1.03703	+	0.0611080i
$355$	−156.015			−0.439478
$356$			14.4841i			0.0406858i
$357$	−10.3911	−	176.343i	−0.0291068	−	0.493957i
$358$	−411.294			−1.14886
$359$		−	596.806i		−	1.66241i	−0.555965	−	0.831206i	$-0.687651\pi$
$359$		−	596.806i		−	1.66241i	0.555965	−	0.831206i	$-0.312349\pi$
$360$	340.217	−	40.2347i	0.945046	−	0.111763i
$361$	475.879			1.31822
$362$			125.515i			0.346726i
$363$	73.8180	−	4.34978i	0.203355	−	0.0119829i
$364$	−294.833			−0.809981
$365$			216.606i			0.593442i
$366$	44.8421	+	760.994i	0.122519	+	2.07922i
$367$	653.268			1.78002			0.890011	−	0.455939i	$-0.150696\pi$
$367$	653.268			1.78002			0.890011	+	0.455939i	$0.150696\pi$
$368$		−	564.438i		−	1.53380i
$369$	−60.9751	−	515.593i	−0.165244	−	1.39727i
$370$	293.231			0.792517
$371$			241.373i			0.650601i
$372$	−129.662	+	7.64044i	−0.348555	+	0.0205388i
$373$	−106.838			−0.286430			−0.143215	−	0.989692i	$-0.545744\pi$
$373$	−106.838			−0.286430			−0.143215	+	0.989692i	$0.545744\pi$
$374$		−	959.619i		−	2.56583i
$375$	−1.97301	−	33.4829i	−0.00526135	−	0.0892878i
$376$	−266.880			−0.709788
$377$		−	145.097i		−	0.384873i
$378$	−44.8316	−	251.254i	−0.118602	−	0.664693i
$379$	−152.839			−0.403270			−0.201635	−	0.979461i	$-0.564625\pi$
$379$	−152.839			−0.403270			−0.201635	+	0.979461i	$0.564625\pi$
$380$		−	566.963i		−	1.49201i
$381$	21.9547	−	1.29370i	0.0576239	−	0.00339553i
$382$	459.686			1.20337
$383$		−	201.860i		−	0.527050i	−0.964653	−	0.263525i	$-0.915115\pi$
$383$		−	201.860i		−	0.527050i	0.964653	−	0.263525i	$-0.0848851\pi$
$384$	27.9304	+	473.993i	0.0727354	+	1.23436i
$385$	−71.3982			−0.185450
$386$		−	533.276i		−	1.38154i
$387$	516.147	−	61.0406i	1.33371	−	0.157728i
$388$	−260.422			−0.671190
$389$		−	414.977i		−	1.06678i	−0.845870	−	0.533389i	$-0.820918\pi$
$389$		−	414.977i		−	1.06678i	0.845870	−	0.533389i	$-0.179082\pi$
$390$	−304.192	+	17.9247i	−0.779980	+	0.0459609i
$391$	−487.623			−1.24712
$392$			119.163i			0.303988i
$393$	17.0885	+	290.001i	0.0434822	+	0.737915i
$394$	1088.77			2.76337
$395$			188.355i			0.476847i
$396$	−111.806	−	945.406i	−0.282338	−	2.38739i
$397$	−410.015			−1.03278			−0.516391	−	0.856353i	$-0.672725\pi$
$397$	−410.015			−1.03278			−0.516391	+	0.856353i	$0.672725\pi$
$398$			352.272i			0.885105i
$399$	−229.218	+	13.5068i	−0.574481	+	0.0338517i
$400$	−128.808			−0.322019
$401$			347.186i			0.865801i	0.901442	+	0.432901i	$0.142510\pi$
$401$			347.186i			0.865801i	−0.901442	+	0.432901i	$0.857490\pi$
$402$	12.7180	+	215.832i	0.0316369	+	0.536895i
$403$	62.8051			0.155844
$404$			295.971i			0.732602i
$405$	−42.2487	−	176.125i	−0.104318	−	0.434877i
$406$	−107.876			−0.265705
$407$		−	442.968i		−	1.08837i
$408$	−1134.63	+	66.8586i	−2.78094	+	0.163869i
$409$	−103.523			−0.253112			−0.126556	−	0.991959i	$-0.540392\pi$
$409$	−103.523			−0.253112			−0.126556	+	0.991959i	$0.540392\pi$
$410$			460.863i			1.12406i
$411$	40.3882	+	685.409i	0.0982681	+	1.66766i
$412$	1054.93			2.56050
$413$		−	90.7760i		−	0.219797i
$414$	−699.643	+	82.7412i	−1.68996	+	0.199858i
$415$	−45.7218			−0.110173
$416$			304.467i			0.731892i
$417$	−487.550	+	28.7292i	−1.16918	+	0.0688951i
$418$	−1247.36			−2.98411
$419$		−	85.1144i		−	0.203137i	−0.994829	−	0.101569i	$-0.967614\pi$
$419$		−	85.1144i		−	0.203137i	0.994829	−	0.101569i	$-0.0323861\pi$
$420$	9.15052	+	155.289i	0.0217870	+	0.369736i
$421$	−489.724			−1.16324			−0.581620	−	0.813461i	$-0.697581\pi$
$421$	−489.724			−1.16324			−0.581620	+	0.813461i	$0.697581\pi$
$422$		−	912.588i		−	2.16253i
$423$	16.5708	+	140.120i	0.0391746	+	0.331252i
$424$	1553.04			3.66284
$425$			111.278i			0.261831i
$426$	746.542	−	43.9905i	1.75245	−	0.103264i
$427$	−188.172			−0.440685
$428$		−	1529.84i		−	3.57440i
$429$	27.0779	+	459.526i	0.0631187	+	1.07116i
$430$	−461.357			−1.07292
$431$		−	577.191i		−	1.33919i	−0.742727	−	0.669595i	$-0.766468\pi$
$431$		−	577.191i		−	1.33919i	0.742727	−	0.669595i	$-0.233532\pi$
$432$	−684.747	+	122.180i	−1.58506	+	0.282825i
$433$	94.5352			0.218326			0.109163	−	0.994024i	$-0.465183\pi$
$433$	94.5352			0.218326			0.109163	+	0.994024i	$0.465183\pi$
$434$		−	46.6940i		−	0.107590i
$435$	−76.4230	+	4.50328i	−0.175685	+	0.0103524i
$436$	−221.146			−0.507215
$437$			633.834i			1.45042i
$438$	−61.0753	−	1036.48i	−0.139441	−	2.36639i
$439$	159.446			0.363202			0.181601	−	0.983372i	$-0.441872\pi$
$439$	159.446			0.363202			0.181601	+	0.983372i	$0.441872\pi$
$440$			459.391i			1.04407i
$441$	62.5640	−	7.39895i	0.141869	−	0.0167777i
$442$	1010.96			2.28724
$443$			129.501i			0.292326i	0.989261	+	0.146163i	$0.0466924\pi$
$443$			129.501i			0.292326i	−0.989261	+	0.146163i	$0.953308\pi$
$444$	−963.444	+	56.7716i	−2.16992	+	0.127864i
$445$	−3.69521			−0.00830385
$446$			110.143i			0.246958i
$447$	−0.338323	−	5.74151i	−0.000756874	−	0.0128445i
$448$	−46.2711			−0.103284
$449$			306.203i			0.681967i	0.940069	+	0.340984i	$0.110760\pi$
$449$			306.203i			0.681967i	−0.940069	+	0.340984i	$0.889240\pi$
$450$	18.8820	+	159.662i	0.0419600	+	0.354805i
$451$	696.200			1.54368
$452$		−	1108.08i		−	2.45150i
$453$	−10.0267	+	0.590830i	−0.0221340	+	0.00130426i
$454$	−442.284			−0.974195
$455$		−	75.2181i		−	0.165315i
$456$	86.9058	+	1474.84i	0.190583	+	3.23429i
$457$	−143.189			−0.313325			−0.156662	−	0.987652i	$-0.550073\pi$
$457$	−143.189			−0.313325			−0.156662	+	0.987652i	$0.550073\pi$
$458$			138.807i			0.303071i
$459$	105.553	+	591.559i	0.229962	+	1.28880i
$460$	429.405			0.933490
$461$			743.362i			1.61250i	0.591575	+	0.806250i	$0.298506\pi$
$461$			743.362i			1.61250i	−0.591575	+	0.806250i	$0.701494\pi$
$462$	341.646	−	20.1318i	0.739494	−	0.0435752i
$463$	−577.246			−1.24675			−0.623375	−	0.781923i	$-0.714239\pi$
$463$	−577.246			−1.24675			−0.623375	+	0.781923i	$0.714239\pi$
$464$			293.997i			0.633614i
$465$	−1.94924	−	33.0796i	−0.00419191	−	0.0711389i
$466$	−693.835			−1.48892
$467$			338.396i			0.724617i	0.932058	+	0.362308i	$0.118011\pi$
$467$			338.396i			0.724617i	−0.932058	+	0.362308i	$0.881989\pi$
$468$	995.987	−	117.787i	2.12818	−	0.251683i
$469$	−53.3691			−0.113793
$470$		−	125.246i		−	0.266481i
$471$	−11.9280	+	0.702863i	−0.0253247	+	0.00149228i
$472$	−584.071			−1.23744
$473$			696.947i			1.47346i
$474$	−53.1093	−	901.293i	−0.112045	−	1.90146i
$475$	144.644			0.304514
$476$		−	516.092i		−	1.08423i
$477$	−96.4299	−	815.392i	−0.202159	−	1.70942i
$478$	−818.128			−1.71156
$479$		−	239.609i		−	0.500228i	−0.968216	−	0.250114i	$-0.919532\pi$
$479$		−	239.609i		−	0.500228i	0.968216	−	0.250114i	$-0.0804681\pi$
$480$	160.363	−	9.44953i	0.334091	−	0.0196865i
$481$	466.668			0.970203
$482$		−	1454.56i		−	3.01776i
$483$	−10.2298	−	173.605i	−0.0211797	−	0.359430i
$484$	216.039			0.446362
$485$		−	66.4391i		−	0.136988i
$486$	251.825	+	830.860i	0.518158	+	1.70959i
$487$	−95.6658			−0.196439			−0.0982195	−	0.995165i	$-0.531315\pi$
$487$	−95.6658			−0.196439			−0.0982195	+	0.995165i	$0.531315\pi$
$488$			1210.74i			2.48102i
$489$	713.007	−	42.0144i	1.45809	−	0.0859191i
$490$	−55.9228			−0.114128
$491$		−	352.470i		−	0.717861i	−0.933364	−	0.358930i	$-0.883142\pi$
$491$		−	352.470i		−	0.717861i	0.933364	−	0.358930i	$-0.116858\pi$
$492$	−89.2263	−	1514.22i	−0.181354	−	3.07767i
$493$	253.986			0.515185
$494$		−	1314.09i		−	2.66010i
$495$	241.193	−	28.5240i	0.487259	−	0.0576242i
$496$	−127.256			−0.256565
$497$			184.599i			0.371426i
$498$	218.783	−	12.8919i	0.439322	−	0.0258874i
$499$	−317.440			−0.636152			−0.318076	−	0.948065i	$-0.603037\pi$
$499$	−317.440			−0.636152			−0.318076	+	0.948065i	$0.603037\pi$
$500$		−	97.9926i		−	0.195985i
$501$	−16.4149	−	278.569i	−0.0327642	−	0.556026i
$502$	587.571			1.17046
$503$		−	244.292i		−	0.485670i	−0.970068	−	0.242835i	$-0.921923\pi$
$503$		−	244.292i		−	0.485670i	0.970068	−	0.242835i	$-0.0780773\pi$
$504$	−47.6064	−	402.550i	−0.0944571	−	0.798710i
$505$	−75.5085			−0.149522
$506$		−	944.720i		−	1.86704i
$507$	22.0104	−	1.29698i	0.0434129	−	0.00255814i
$508$	64.2536			0.126483
$509$		−	4.58079i		−	0.00899959i	−0.999990	−	0.00449979i	$-0.998568\pi$
$509$		−	4.58079i		−	0.00899959i	0.999990	−	0.00449979i	$-0.00143233\pi$
$510$	−31.3765	−	532.475i	−0.0615225	−	1.04407i
$511$	256.292			0.501550
$512$			1137.27i			2.22124i
$513$	768.935	−	137.202i	1.49890	−	0.267450i
$514$	1372.51			2.67026
$515$			269.134i			0.522590i
$516$	1515.84	−	89.3220i	2.93768	−	0.173105i
$517$	−189.202			−0.365961
$518$		−	346.956i		−	0.669799i
$519$	3.57170	+	60.6136i	0.00688189	+	0.116789i
$520$	−483.969			−0.930710
$521$			813.583i			1.56158i	0.624794	+	0.780789i	$0.285183\pi$
$521$			813.583i			1.56158i	−0.624794	+	0.780789i	$0.714817\pi$
$522$	364.421	−	43.0971i	0.698124	−	0.0825616i
$523$	−6.71882			−0.0128467			−0.00642335	−	0.999979i	$-0.502045\pi$
$523$	−6.71882			−0.0128467			−0.00642335	+	0.999979i	$0.502045\pi$
$524$			848.729i			1.61971i
$525$	−39.6175	+	2.33449i	−0.0754620	+	0.00444665i
$526$	−708.096			−1.34619
$527$			109.938i			0.208610i
$528$	−54.8654	−	931.095i	−0.103912	−	1.76344i
$529$	48.9484			0.0925301
$530$			728.837i			1.37516i
$531$	36.2655	+	306.654i	0.0682966	+	0.577502i
$532$	−670.840			−1.26098
$533$			733.448i			1.37607i
$534$	17.6819	−	1.04192i	0.0331122	−	0.00195116i
$535$	390.295			0.729524
$536$			343.388i			0.640649i
$537$	20.3151	+	344.758i	0.0378308	+	0.642008i
$538$	−51.2701			−0.0952975
$539$			84.4795i			0.156734i
$540$	−92.9507	−	520.933i	−0.172131	−	0.964690i
$541$	18.1305			0.0335129			0.0167565	−	0.999860i	$-0.494666\pi$
$541$	18.1305			0.0335129			0.0167565	+	0.999860i	$0.494666\pi$
$542$			93.7692i			0.173006i
$543$	105.210	−	6.19959i	0.193757	−	0.0114173i
$544$	−532.957			−0.979699
$545$		−	56.4190i		−	0.103521i
$546$	21.2088	+	359.925i	0.0388440	+	0.659203i
$547$	111.345			0.203556			0.101778	−	0.994807i	$-0.467547\pi$
$547$	111.345			0.203556			0.101778	+	0.994807i	$0.467547\pi$
$548$			2005.95i			3.66049i
$549$	635.673	−	75.1760i	1.15787	−	0.136933i
$550$	−215.590			−0.391982
$551$		−	330.143i		−	0.599170i
$552$	−1117.01	+	65.8205i	−2.02357	+	0.119240i
$553$	222.864			0.403010
$554$		−	76.0072i		−	0.137197i
$555$	−14.4836	−	245.795i	−0.0260967	−	0.442874i
$556$	−1426.89			−2.56634
$557$		−	100.916i		−	0.181177i	−0.995888	−	0.0905885i	$-0.971125\pi$
$557$		−	100.916i		−	0.181177i	0.995888	−	0.0905885i	$-0.0288748\pi$
$558$	18.6545	+	157.739i	0.0334311	+	0.282686i
$559$	−734.235			−1.31348
$560$			152.407i			0.272156i
$561$	−804.381	+	47.3987i	−1.43383	+	0.0844897i
$562$	−1150.66			−2.04744
$563$		−	942.043i		−	1.67326i	−0.547772	−	0.836628i	$-0.684524\pi$
$563$		−	942.043i		−	1.67326i	0.547772	−	0.836628i	$-0.315476\pi$
$564$	24.2485	+	411.509i	0.0429938	+	0.729626i
$565$	282.694			0.500343
$566$			926.455i			1.63685i
$567$	−208.394	+	49.9894i	−0.367538	+	0.0881647i
$568$	1187.75			2.09110
$569$			1113.81i			1.95749i	0.205086	+	0.978744i	$0.434253\pi$
$569$			1113.81i			1.95749i	−0.205086	+	0.978744i	$0.565747\pi$
$570$	−692.135	+	40.7845i	−1.21427	+	0.0715518i
$571$	−489.370			−0.857041			−0.428520	−	0.903532i	$-0.640965\pi$
$571$	−489.370			−0.857041			−0.428520	+	0.903532i	$0.640965\pi$
$572$			1344.87i			2.35117i
$573$	−22.7054	−	385.322i	−0.0396255	−	0.672465i
$574$	545.300			0.950000
$575$			109.550i			0.190522i
$576$	156.310	−	18.4856i	0.271372	−	0.0320930i
$577$	176.145			0.305277			0.152638	−	0.988282i	$-0.451223\pi$
$577$	176.145			0.305277			0.152638	+	0.988282i	$0.451223\pi$
$578$			737.111i			1.27528i
$579$	−447.008	+	26.3402i	−0.772034	+	0.0454926i
$580$	−223.663			−0.385626
$581$			54.0988i			0.0931132i
$582$	18.7335	+	317.916i	0.0321881	+	0.546248i
$583$	1101.01			1.88853
$584$		−	1649.04i		−	2.82369i
$585$	30.0501	+	254.097i	0.0513677	+	0.434354i
$586$	−1076.11			−1.83636
$587$		−	120.248i		−	0.204852i	−0.994741	−	0.102426i	$-0.967340\pi$
$587$		−	120.248i		−	0.204852i	0.994741	−	0.102426i	$-0.0326604\pi$
$588$	183.741	−	10.8270i	0.312484	−	0.0184133i
$589$	142.902			0.242618
$590$		−	274.102i		−	0.464580i
$591$	−53.7779	−	912.638i	−0.0909947	−	1.54423i
$592$	−945.565			−1.59724
$593$		−	808.407i		−	1.36325i	−0.731702	−	0.681625i	$-0.761274\pi$
$593$		−	808.407i		−	1.36325i	0.731702	−	0.681625i	$-0.238726\pi$
$594$	−1146.09	+	204.498i	−1.92944	+	0.344272i
$595$	131.666			0.221288
$596$		−	16.8034i		−	0.0281936i
$597$	295.285	−	17.3999i	0.494614	−	0.0291455i
$598$	995.264			1.66432
$599$		−	679.382i		−	1.13419i	−0.823651	−	0.567097i	$-0.808066\pi$
$599$		−	679.382i		−	1.13419i	0.823651	−	0.567097i	$-0.191934\pi$
$600$	15.0206	+	254.907i	0.0250343	+	0.424846i
$601$	349.965			0.582305			0.291153	−	0.956677i	$-0.405961\pi$
$601$	349.965			0.582305			0.291153	+	0.956677i	$0.405961\pi$
$602$			545.885i			0.906786i
$603$	180.288	−	21.3213i	0.298985	−	0.0353586i
$604$	−29.3446			−0.0485837
$605$			55.1161i			0.0911011i
$606$	361.314	−	21.2907i	0.596228	−	0.0351332i
$607$	463.847			0.764163			0.382082	−	0.924129i	$-0.375207\pi$
$607$	463.847			0.764163			0.382082	+	0.924129i	$0.375207\pi$
$608$			692.761i			1.13941i
$609$	5.32835	+	90.4249i	0.00874935	+	0.148481i
$610$	−568.195			−0.931468
$611$		−	199.325i		−	0.326227i
$612$	206.182	+	1743.43i	0.336898	+	2.84874i
$613$	−137.987			−0.225102			−0.112551	−	0.993646i	$-0.535902\pi$
$613$	−137.987			−0.225102			−0.112551	+	0.993646i	$0.535902\pi$
$614$			938.557i			1.52859i
$615$	386.308	−	22.7635i	0.628144	−	0.0370138i
$616$	543.559			0.882400
$617$			90.3121i			0.146373i	0.997318	+	0.0731864i	$0.0233168\pi$
$617$			90.3121i			0.146373i	−0.997318	+	0.0731864i	$0.976683\pi$
$618$	−75.8862	−	1287.83i	−0.122793	−	2.08387i
$619$	−558.874			−0.902866			−0.451433	−	0.892305i	$-0.649087\pi$
$619$	−558.874			−0.902866			−0.451433	+	0.892305i	$0.649087\pi$
$620$		−	96.8122i		−	0.156149i
$621$	103.914	+	582.374i	0.167333	+	0.937800i
$622$	−887.963			−1.42759
$623$			4.37223i			0.00701803i
$624$	980.910	−	57.8008i	1.57197	−	0.0926295i
$625$	25.0000			0.0400000
$626$		−	1524.62i		−	2.43550i
$627$	61.6110	+	1045.57i	0.0982631	+	1.66758i
$628$	−34.9089			−0.0555874
$629$			816.882i			1.29870i
$630$	188.915	−	22.3415i	0.299865	−	0.0354627i
$631$	−699.239			−1.10814			−0.554072	−	0.832469i	$-0.686927\pi$
$631$	−699.239			−1.10814			−0.554072	+	0.832469i	$0.686927\pi$
$632$		−	1433.95i		−	2.26892i
$633$	−764.958	+	45.0757i	−1.20846	+	0.0712096i
$634$	383.641			0.605112
$635$			16.3925i			0.0258149i
$636$	−141.108	−	2394.68i	−0.221868	−	3.76521i
$637$	−88.9993			−0.139716
$638$			492.073i			0.771274i
$639$	−73.7483	−	623.601i	−0.115412	−	0.975901i
$640$	−353.907			−0.552979
$641$		−	773.823i		−	1.20721i	−0.797283	−	0.603606i	$-0.793730\pi$
$641$		−	773.823i		−	1.20721i	0.797283	−	0.603606i	$-0.206270\pi$
$642$	−1867.59	+	110.049i	−2.90903	+	0.171416i
$643$	93.1342			0.144843			0.0724216	−	0.997374i	$-0.476927\pi$
$643$	93.1342			0.144843			0.0724216	+	0.997374i	$0.476927\pi$
$644$		−	508.079i		−	0.788943i
$645$	22.7879	+	386.723i	0.0353301	+	0.599571i
$646$	2300.26			3.56077
$647$		−	1130.06i		−	1.74662i	−0.487164	−	0.873311i	$-0.661969\pi$
$647$		−	1130.06i		−	1.74662i	0.487164	−	0.873311i	$-0.338031\pi$
$648$	321.642	+	1340.85i	0.496361	+	2.06921i
$649$	−414.071			−0.638014
$650$		−	227.125i		−	0.349423i
$651$	−39.1403	+	2.30637i	−0.0601234	+	0.00354281i
$652$	2086.72			3.20049
$653$		−	482.760i		−	0.739296i	−0.929172	−	0.369648i	$-0.879478\pi$
$653$		−	482.760i		−	0.739296i	0.929172	−	0.369648i	$-0.120522\pi$
$654$	15.9082	+	269.970i	0.0243244	+	0.412797i
$655$	−216.529			−0.330578
$656$		−	1486.12i		−	2.26542i
$657$	−865.791	+	102.390i	−1.31779	+	0.155845i
$658$	−148.193			−0.225217
$659$			39.2039i			0.0594901i	0.999558	+	0.0297450i	$0.00946953\pi$
$659$			39.2039i			0.0594901i	−0.999558	+	0.0297450i	$0.990530\pi$
$660$	708.346	−	41.7398i	1.07325	−	0.0632421i
$661$	−638.260			−0.965598			−0.482799	−	0.875731i	$-0.660380\pi$
$661$	−638.260			−0.965598			−0.482799	+	0.875731i	$0.660380\pi$
$662$			1614.67i			2.43909i
$663$	−49.9346	−	847.417i	−0.0753162	−	1.27815i
$664$	348.083			0.524221
$665$		−	171.145i		−	0.257362i
$666$	138.611	+	1172.06i	0.208124	+	1.75986i
$667$	250.043			0.374877
$668$		−	815.272i		−	1.22047i
$669$	92.3253	−	5.44033i	0.138005	−	0.00813204i
$670$	−161.150			−0.240523
$671$			858.342i			1.27920i
$672$	−11.1808	−	189.745i	−0.0166382	−	0.282358i
$673$	233.289			0.346641			0.173320	−	0.984866i	$-0.444550\pi$
$673$	233.289			0.346641			0.173320	+	0.984866i	$0.444550\pi$
$674$			2279.69i			3.38233i
$675$	132.901	−	23.7137i	0.196890	−	0.0351314i
$676$	64.4165			0.0952906
$677$		−	550.920i		−	0.813766i	−0.913480	−	0.406883i	$-0.866616\pi$
$677$		−	550.920i		−	0.813766i	0.913480	−	0.406883i	$-0.133384\pi$
$678$	−1352.71	+	79.7096i	−1.99515	+	0.117566i
$679$	−78.6118			−0.115776
$680$		−	847.167i		−	1.24583i
$681$	21.8459	+	370.736i	0.0320791	+	0.544399i
$682$	−212.993			−0.312307
$683$		−	117.573i		−	0.172142i	−0.996289	−	0.0860712i	$-0.972569\pi$
$683$		−	117.573i		−	0.172142i	0.996289	−	0.0860712i	$-0.0274313\pi$
$684$	2266.19	−	268.004i	3.31314	−	0.391819i
$685$	−511.760			−0.747094
$686$			66.1687i			0.0964559i
$687$	116.352	−	6.85611i	0.169362	−	0.00997978i
$688$	1487.71			2.16237
$689$			1159.92i			1.68348i
$690$	−30.8893	−	524.208i	−0.0447671	−	0.759721i
$691$	831.462			1.20327			0.601637	−	0.798770i	$-0.294515\pi$
$691$	831.462			1.20327			0.601637	+	0.798770i	$0.294515\pi$
$692$			177.394i			0.256350i
$693$	−33.7500	−	285.383i	−0.0487014	−	0.411809i
$694$	464.278			0.668989
$695$		−	364.029i		−	0.523782i
$696$	581.813	−	34.2837i	0.835938	−	0.0492582i
$697$	−1283.87			−1.84199
$698$			53.9727i			0.0773248i
$699$	34.2708	+	581.593i	0.0490283	+	0.832036i
$700$	−115.946			−0.165638
$701$		−	1265.38i		−	1.80510i	−0.430583	−	0.902551i	$-0.641692\pi$
$701$		−	1265.38i		−	1.80510i	0.430583	−	0.902551i	$-0.358308\pi$
$702$	−215.438	−	1207.40i	−0.306892	−	1.71995i
$703$	1061.82			1.51041
$704$			211.064i			0.299807i
$705$	−104.985	+	6.18630i	−0.148914	+	0.00877489i
$706$	2461.52			3.48657
$707$			89.3429i			0.126369i
$708$	53.0681	+	900.594i	0.0749550	+	1.27202i
$709$	404.244			0.570161			0.285080	−	0.958504i	$-0.407980\pi$
$709$	404.244			0.570161			0.285080	+	0.958504i	$0.407980\pi$
$710$			557.405i			0.785078i
$711$	−752.867	+	89.0356i	−1.05888	+	0.125226i
$712$	28.1319			0.0395110
$713$			108.231i			0.151796i
$714$	−630.033	+	37.1252i	−0.882399	+	0.0519960i
$715$	−343.105			−0.479867
$716$			1008.98i			1.40920i
$717$	40.4100	+	685.779i	0.0563598	+	0.956456i
$718$	−2132.25			−2.96971
$719$		−	790.437i		−	1.09936i	−0.835377	−	0.549678i	$-0.814750\pi$
$719$		−	790.437i		−	1.09936i	0.835377	−	0.549678i	$-0.185250\pi$
$720$	−60.8876	−	514.854i	−0.0845662	−	0.715074i
$721$	318.444			0.441670
$722$		−	1700.21i		−	2.35486i
$723$	−1219.25	+	71.8454i	−1.68638	+	0.0993713i
$724$	307.913			0.425294
$725$		−	57.0611i		−	0.0787050i
$726$	−15.5408	−	263.735i	−0.0214060	−	0.363272i
$727$	951.432			1.30871			0.654355	−	0.756188i	$-0.272940\pi$
$727$	951.432			1.30871			0.654355	+	0.756188i	$0.272940\pi$
$728$			572.640i			0.786593i
$729$	684.013	−	252.126i	0.938289	−	0.345851i
$730$	773.886			1.06012
$731$		−	1285.25i		−	1.75820i
$732$	1866.87	−	110.007i	2.55037	−	0.150282i
$733$	920.746			1.25613			0.628067	−	0.778159i	$-0.283846\pi$
$733$	920.746			1.25613			0.628067	+	0.778159i	$0.283846\pi$
$734$		−	2333.98i		−	3.17981i
$735$	2.76221	+	46.8761i	0.00375811	+	0.0637770i
$736$	−524.682			−0.712883
$737$			243.441i			0.330314i
$738$	−1842.10	+	217.850i	−2.49607	+	0.295190i
$739$	−312.768			−0.423231			−0.211615	−	0.977353i	$-0.567872\pi$
$739$	−312.768			−0.423231			−0.211615	+	0.977353i	$0.567872\pi$
$740$		−	719.354i		−	0.972100i
$741$	−1101.51	+	64.9073i	−1.48652	+	0.0875941i
$742$	862.372			1.16223
$743$			1116.08i			1.50212i	0.660234	+	0.751060i	$0.270457\pi$
$743$			1116.08i			1.50212i	−0.660234	+	0.751060i	$0.729543\pi$
$744$	14.8397	+	251.837i	0.0199458	+	0.338490i
$745$	4.28689			0.00575422
$746$			381.710i			0.511676i
$747$	−21.6128	−	182.753i	−0.0289328	−	0.244649i
$748$	−2354.14			−3.14724
$749$		−	461.804i		−	0.616560i
$750$	−119.627	+	7.04911i	−0.159503	+	0.00939881i
$751$	−1419.71			−1.89043			−0.945215	−	0.326448i	$-0.894148\pi$
$751$	−1419.71			−1.89043			−0.945215	+	0.326448i	$0.894148\pi$
$752$			403.873i			0.537065i
$753$	−29.0221	−	492.519i	−0.0385419	−	0.654076i
$754$	−518.400			−0.687533
$755$		−	7.48642i		−	0.00991578i
$756$	−616.376	+	109.981i	−0.815312	+	0.145477i
$757$	822.074			1.08596			0.542981	−	0.839745i	$-0.317295\pi$
$757$	822.074			1.08596			0.542981	+	0.839745i	$0.317295\pi$
$758$			546.060i			0.720396i
$759$	−791.892	+	46.6628i	−1.04334	+	0.0614793i
$760$	−1101.19			−1.44893
$761$			1366.47i			1.79562i	0.440380	+	0.897812i	$0.354844\pi$
$761$			1366.47i			1.79562i	−0.440380	+	0.897812i	$0.645156\pi$
$762$	−4.62209	−	78.4392i	−0.00606573	−	0.102939i
$763$	−66.7559			−0.0874913
$764$		−	1127.70i		−	1.47605i
$765$	−444.786	+	52.6014i	−0.581420	+	0.0687600i
$766$	−721.201			−0.941516
$767$		−	436.225i		−	0.568742i
$768$	1483.97	−	87.4440i	1.93225	−	0.113859i
$769$	117.440			0.152718			0.0763591	−	0.997080i	$-0.475670\pi$
$769$	117.440			0.152718			0.0763591	+	0.997080i	$0.475670\pi$
$770$			255.090i			0.331285i
$771$	−67.7929	−	1150.48i	−0.0879285	−	1.49219i
$772$	−1308.23			−1.69460
$773$			306.116i			0.396011i	0.980201	+	0.198005i	$0.0634464\pi$
$773$			306.116i			0.396011i	−0.980201	+	0.198005i	$0.936554\pi$
$774$	−218.084	−	1844.08i	−0.281763	−	2.38253i
$775$	24.6988			0.0318695
$776$			505.804i			0.651810i
$777$	−290.828	+	17.1373i	−0.374297	+	0.0220557i
$778$	−1482.62			−1.90568
$779$			1668.83i			2.14227i
$780$	43.9729	+	746.244i	0.0563756	+	0.956722i
$781$	842.041			1.07816
$782$			1742.17i			2.22783i
$783$	−54.1252	−	303.339i	−0.0691254	−	0.387406i
$784$	180.331			0.230014
$785$		−	8.90599i		−	0.0113452i
$786$	1036.11	−	61.0534i	1.31820	−	0.0776761i
$787$	−279.568			−0.355232			−0.177616	−	0.984100i	$-0.556839\pi$
$787$	−279.568			−0.355232			−0.177616	+	0.984100i	$0.556839\pi$
$788$		−	2670.97i		−	3.38955i
$789$	34.9752	+	593.546i	0.0443285	+	0.752277i
$790$	672.949			0.851834
$791$		−	334.488i		−	0.422867i
$792$	−1836.22	+	217.155i	−2.31845	+	0.274185i
$793$	−904.264			−1.14031
$794$			1464.89i			1.84495i
$795$	610.933	−	35.9996i	0.768469	−	0.0452826i
$796$	864.193			1.08567
$797$		−	327.577i		−	0.411013i	−0.978656	−	0.205507i	$-0.934116\pi$
$797$		−	327.577i		−	0.411013i	0.978656	−	0.205507i	$-0.0658842\pi$
$798$	48.2569	+	818.945i	0.0604723	+	1.02625i
$799$	348.909			0.436682
$800$			119.735i			0.149669i
$801$	−1.74673	−	14.7700i	−0.00218069	−	0.0184395i
$802$	1240.42			1.54666
$803$		−	1169.07i		−	1.45588i
$804$	529.478	−	31.1999i	0.658555	−	0.0388058i
$805$	129.622			0.161021
$806$		−	224.389i		−	0.278398i
$807$	2.53240	+	42.9761i	0.00313804	+	0.0532541i
$808$	574.851			0.711449
$809$			219.021i			0.270731i	0.990796	+	0.135365i	$0.0432208\pi$
$809$			219.021i			0.270731i	−0.990796	+	0.135365i	$0.956779\pi$
$810$	−629.255	+	150.945i	−0.776859	+	0.186352i
$811$	57.9161			0.0714132			0.0357066	−	0.999362i	$-0.488632\pi$
$811$	57.9161			0.0714132			0.0357066	+	0.999362i	$0.488632\pi$
$812$			264.642i			0.325913i
$813$	78.6001	−	4.63157i	0.0966791	−	0.00569688i
$814$	−1582.63			−1.94426
$815$			532.366i			0.653209i
$816$	101.178	+	1717.04i	0.123992	+	2.10422i
$817$	−1670.62			−2.04482
$818$			369.863i			0.452156i
$819$	300.652	−	35.5557i	0.367096	−	0.0434136i
$820$	1130.59			1.37877
$821$		−	1385.60i		−	1.68770i	−0.536577	−	0.843851i	$-0.680283\pi$
$821$		−	1385.60i		−	1.68770i	0.536577	−	0.843851i	$-0.319717\pi$
$822$	2448.81	−	144.298i	2.97909	−	0.175545i
$823$	1414.41			1.71861			0.859303	−	0.511468i	$-0.170898\pi$
$823$	1414.41			1.71861			0.859303	+	0.511468i	$0.170898\pi$
$824$		−	2048.93i		−	2.48657i
$825$	10.6487	+	180.714i	0.0129075	+	0.219047i
$826$	−324.322			−0.392642
$827$		−	305.144i		−	0.368977i	−0.982835	−	0.184488i	$-0.940937\pi$
$827$		−	305.144i		−	0.368977i	0.982835	−	0.184488i	$-0.0590628\pi$
$828$	202.981	+	1716.36i	0.245146	+	2.07290i
$829$	517.903			0.624732			0.312366	−	0.949962i	$-0.398878\pi$
$829$	517.903			0.624732			0.312366	+	0.949962i	$0.398878\pi$
$830$			163.354i			0.196812i
$831$	−63.7114	+	3.75424i	−0.0766684	+	0.00451774i
$832$	−222.356			−0.267255
$833$		−	155.789i		−	0.187022i
$834$	102.643	+	1741.91i	0.123073	+	2.08862i
$835$	207.993			0.249094
$836$			3060.01i			3.66030i
$837$	131.300	−	23.4280i	0.156870	−	0.0279905i
$838$	−304.095			−0.362882
$839$		−	3.40272i		−	0.00405569i	−0.999998	−	0.00202784i	$-0.999355\pi$
$839$		−	3.40272i		−	0.00405569i	0.999998	−	0.00202784i	$-0.000645483\pi$
$840$	301.611	−	17.7726i	0.359060	−	0.0211579i
$841$	710.761			0.845138
$842$			1749.67i			2.07800i
$843$	56.8349	+	964.517i	0.0674198	+	1.14415i
$844$	−2238.76			−2.65256
$845$			16.4340i			0.0194485i
$846$	500.616	−	59.2039i	0.591745	−	0.0699810i
$847$	65.2143			0.0769944
$848$		−	2350.24i		−	2.77151i
$849$	776.581	−	45.7606i	0.914701	−	0.0538994i
$850$	397.572			0.467732
$851$			804.199i			0.945004i
$852$	−107.918	−	1831.42i	−0.126664	−	2.14955i
$853$	639.114			0.749255			0.374627	−	0.927175i	$-0.377771\pi$
$853$	639.114			0.749255			0.374627	+	0.927175i	$0.377771\pi$
$854$			672.298i			0.787234i
$855$	68.3736	+	578.153i	0.0799691	+	0.676202i
$856$	−2971.34			−3.47119
$857$			724.119i			0.844946i	0.906375	+	0.422473i	$0.138838\pi$
$857$			724.119i			0.844946i	−0.906375	+	0.422473i	$0.861162\pi$
$858$	1641.78	−	96.7433i	1.91350	−	0.112754i
$859$	−952.638			−1.10901			−0.554504	−	0.832181i	$-0.687092\pi$
$859$	−952.638			−1.10901			−0.554504	+	0.832181i	$0.687092\pi$
$860$			1131.80i			1.31605i
$861$	−26.9341	−	457.086i	−0.0312824	−	0.530878i
$862$	−2062.17			−2.39231
$863$		−	1609.84i		−	1.86540i	−0.360659	−	0.932698i	$-0.617448\pi$
$863$		−	1609.84i		−	1.86540i	0.360659	−	0.932698i	$-0.382552\pi$
$864$	113.574	+	636.517i	0.131452	+	0.736709i
$865$	−45.2571			−0.0523203
$866$		−	337.753i		−	0.390015i
$867$	617.868	−	36.4083i	0.712650	−	0.0419934i
$868$	−114.550			−0.131970
$869$		−	1016.59i		−	1.16984i
$870$	16.0892	+	273.042i	0.0184933	+	0.313842i
$871$	−256.466			−0.294450
$872$			429.521i			0.492570i
$873$	265.562	−	31.4059i	0.304194	−	0.0359746i
$874$	2264.55			2.59101
$875$		−	29.5804i		−	0.0338062i
$876$	−2542.69	+	149.830i	−2.90261	+	0.171039i
$877$	740.088			0.843886			0.421943	−	0.906622i	$-0.361348\pi$
$877$	740.088			0.843886			0.421943	+	0.906622i	$0.361348\pi$
$878$		−	569.664i		−	0.648820i
$879$	53.1524	+	902.023i	0.0604691	+	1.02619i
$880$	695.201			0.790001
$881$			81.0232i			0.0919673i	0.998942	+	0.0459836i	$0.0146422\pi$
$881$			81.0232i			0.0919673i	−0.998942	+	0.0459836i	$0.985358\pi$
$882$	−26.4348	−	223.527i	−0.0299714	−	0.253432i
$883$	783.824			0.887682			0.443841	−	0.896105i	$-0.353615\pi$
$883$	783.824			0.887682			0.443841	+	0.896105i	$0.353615\pi$
$884$		−	2480.09i		−	2.80553i
$885$	−229.761	+	13.5388i	−0.259616	+	0.0152981i
$886$	462.676			0.522208
$887$		−	1320.12i		−	1.48830i	−0.668012	−	0.744150i	$-0.732855\pi$
$887$		−	1320.12i		−	1.48830i	0.668012	−	0.744150i	$-0.267145\pi$
$888$	110.265	+	1871.25i	0.124172	+	2.10726i
$889$	19.3958			0.0218176
$890$			13.2022i			0.0148339i
$891$	228.025	+	950.582i	0.255920	+	1.06687i
$892$	270.203			0.302918
$893$		−	453.528i		−	0.507870i
$894$	−20.5131	+	1.20875i	−0.0229453	+	0.00135207i
$895$	−257.413			−0.287613
$896$			418.748i			0.467352i
$897$	−49.1593	−	834.259i	−0.0548042	−	0.930055i
$898$	1094.00			1.21826
$899$		−	56.3738i		−	0.0627072i
$900$	391.683	−	46.3213i	0.435204	−	0.0514681i
$901$	−2030.39			−2.25349
$902$		−	2487.37i		−	2.75761i
$903$	457.577	−	26.9631i	0.506730	−	0.0298594i
$904$	−2152.16			−2.38071
$905$			78.5551i			0.0868012i
$906$	2.11090	+	35.8231i	0.00232991	+	0.0395399i
$907$	1149.97			1.26788			0.633942	−	0.773381i	$-0.281436\pi$
$907$	1149.97			1.26788			0.633942	+	0.773381i	$0.281436\pi$
$908$			1085.01i			1.19495i
$909$	−35.6930	−	301.813i	−0.0392662	−	0.332027i
$910$	−268.738			−0.295316
$911$			1275.15i			1.39972i	0.714280	+	0.699860i	$0.246754\pi$
$911$			1275.15i			1.39972i	−0.714280	+	0.699860i	$0.753246\pi$
$912$	2231.89	−	131.515i	2.44724	−	0.144206i
$913$	246.770			0.270284
$914$			511.584i			0.559720i
$915$	28.0650	+	476.278i	0.0306722	+	0.520522i
$916$	340.520			0.371747
$917$			256.200i			0.279390i
$918$	2113.51	−	377.116i	2.30230	−	0.410801i
$919$	−228.393			−0.248523			−0.124262	−	0.992249i	$-0.539656\pi$
$919$	−228.393			−0.248523			−0.124262	+	0.992249i	$0.539656\pi$
$920$		−	834.013i		−	0.906536i
$921$	786.726	−	46.3584i	0.854209	−	0.0503349i
$922$	2655.87			2.88055
$923$			887.092i			0.961096i
$924$	−49.3872	−	838.126i	−0.0534493	−	0.907063i
$925$	183.523			0.198403
$926$			2062.37i			2.22718i
$927$	−1075.75	+	127.220i	−1.16046	+	0.137239i
$928$	273.289			0.294493
$929$		−	71.5997i		−	0.0770718i	−0.999257	−	0.0385359i	$-0.987731\pi$
$929$		−	71.5997i		−	0.0770718i	0.999257	−	0.0385359i	$-0.0122694\pi$
$930$	−118.186	+	6.96419i	−0.127082	+	0.00748838i
$931$	−202.502			−0.217510
$932$			1702.12i			1.82630i
$933$	43.8594	+	744.317i	0.0470090	+	0.797767i
$934$	1209.01			1.29445
$935$		−	600.590i		−	0.642342i
$936$	−228.773	−	1934.46i	−0.244415	−	2.06673i
$937$	606.742			0.647536			0.323768	−	0.946136i	$-0.395050\pi$
$937$	606.742			0.647536			0.323768	+	0.946136i	$0.395050\pi$
$938$			190.676i			0.203279i
$939$	−1277.98	+	75.3060i	−1.36100	+	0.0801981i
$940$	−307.253			−0.326865
$941$		−	1043.93i		−	1.10938i	−0.832056	−	0.554692i	$-0.812836\pi$
$941$		−	1043.93i		−	1.10938i	0.832056	−	0.554692i	$-0.187164\pi$
$942$	2.51117	+	42.6159i	0.00266579	+	0.0452398i
$943$	−1263.93			−1.34033
$944$			883.881i			0.936315i
$945$	−28.0584	−	157.251i	−0.0296914	−	0.166403i
$946$	2490.04			2.63217
$947$		−	1057.69i		−	1.11688i	−0.829545	−	0.558440i	$-0.811400\pi$
$947$		−	1057.69i		−	1.11688i	0.829545	−	0.558440i	$-0.188600\pi$
$948$	−2211.05	+	130.288i	−2.33233	+	0.137434i
$949$	1231.61			1.29780
$950$		−	516.782i		−	0.543981i
$951$	−18.9493	−	321.579i	−0.0199256	−	0.338148i
$952$	−1002.38			−1.05292
$953$		−	278.572i		−	0.292311i	−0.989262	−	0.146155i	$-0.953310\pi$
$953$		−	278.572i		−	0.292311i	0.989262	−	0.146155i	$-0.0466900\pi$
$954$	−2913.21	+	344.523i	−3.05368	+	0.361135i
$955$	287.700			0.301257
$956$			2007.03i			2.09940i
$957$	412.470	−	24.3051i	0.431003	−	0.0253972i
$958$	−856.070			−0.893601
$959$			605.522i			0.631410i
$960$	6.90111	+	117.115i	0.00718866	+	0.121995i
$961$	−936.599			−0.974608
$962$		−	1667.30i		−	1.73316i
$963$	184.493	+	1560.04i	0.191582	+	1.61998i
$964$	−3568.32			−3.70158
$965$		−	333.758i		−	0.345863i
$966$	−620.251	+	36.5487i	−0.642082	+	0.0378351i
$967$	717.616			0.742105			0.371053	−	0.928612i	$-0.378997\pi$
$967$	717.616			0.742105			0.371053	+	0.928612i	$0.378997\pi$
$968$		−	419.602i		−	0.433473i
$969$	−113.617	−	1928.15i	−0.117252	−	1.98983i
$970$	−237.372			−0.244713
$971$			1566.83i			1.61363i	0.590806	+	0.806814i	$0.298810\pi$
$971$			1566.83i			1.61363i	−0.590806	+	0.806814i	$0.701190\pi$
$972$	2038.27	−	617.776i	2.09698	−	0.635572i
$973$	−430.725			−0.442677
$974$			341.792i			0.350916i
$975$	−190.383	+	11.2184i	−0.195264	+	0.0115061i
$976$	1832.23			1.87728
$977$		−	727.568i		−	0.744696i	−0.928093	−	0.372348i	$-0.878553\pi$
$977$		−	727.568i		−	0.744696i	0.928093	−	0.372348i	$-0.121447\pi$
$978$	−150.108	−	2547.41i	−0.153485	−	2.60472i
$979$	19.9438			0.0203716
$980$			137.190i			0.139989i
$981$	225.511	−	26.6694i	0.229878	−	0.0271859i
$982$	−1259.30			−1.28238
$983$			686.673i			0.698549i	0.937021	+	0.349274i	$0.113572\pi$
$983$			686.673i			0.698549i	−0.937021	+	0.349274i	$0.886428\pi$
$984$	−2940.99	+	173.300i	−2.98881	+	0.176118i
$985$	681.420			0.691797
$986$		−	907.436i		−	0.920321i
$987$	7.31973	+	124.220i	0.00741614	+	0.125856i
$988$	−3223.73			−3.26288
$989$		−	1265.29i		−	1.27936i
$990$	−101.910	−	861.729i	−0.102939	−	0.870433i
$991$	468.764			0.473022			0.236511	−	0.971629i	$-0.423996\pi$
$991$	468.764			0.473022			0.236511	+	0.971629i	$0.423996\pi$
$992$			118.293i			0.119247i
$993$	1353.47	−	79.7541i	1.36301	−	0.0803163i
$994$	659.531			0.663512
$995$			220.474i			0.221582i
$996$	−31.6264	−	536.717i	−0.0317535	−	0.538873i
$997$	−1860.83			−1.86643			−0.933213	−	0.359323i	$-0.883008\pi$
$997$	−1860.83			−1.86643			−0.933213	+	0.359323i	$0.883008\pi$
$998$			1134.14i			1.13641i
$999$	975.613	−	174.080i	0.976589	−	0.174254i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.c.a.71.2	✓	16
3.2	odd	2	inner	105.3.c.a.71.15	yes	16
4.3	odd	2		1680.3.l.a.1121.15		16
5.2	odd	4		525.3.f.b.449.30		32
5.3	odd	4		525.3.f.b.449.4		32
5.4	even	2		525.3.c.b.176.15		16
12.11	even	2		1680.3.l.a.1121.16		16
15.2	even	4		525.3.f.b.449.3		32
15.8	even	4		525.3.f.b.449.29		32
15.14	odd	2		525.3.c.b.176.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.c.a.71.2	✓	16	1.1	even	1	trivial
105.3.c.a.71.15	yes	16	3.2	odd	2	inner
525.3.c.b.176.2		16	15.14	odd	2
525.3.c.b.176.15		16	5.4	even	2
525.3.f.b.449.3		32	15.2	even	4
525.3.f.b.449.4		32	5.3	odd	4
525.3.f.b.449.29		32	15.8	even	4
525.3.f.b.449.30		32	5.2	odd	4
1680.3.l.a.1121.15		16	4.3	odd	2
1680.3.l.a.1121.16		16	12.11	even	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)

\(f(q)\)	\(=\)	\(q-3.57278i q^{2} +(-2.99481 + 0.176471i) q^{3} -8.76473 q^{4} -2.23607i q^{5} +(0.630492 + 10.6998i) q^{6} -2.64575 q^{7} +17.0233i q^{8} +(8.93772 - 1.05699i) q^{9} +O(q^{10})\)	\(q-3.57278i q^{2} +(-2.99481 + 0.176471i) q^{3} -8.76473 q^{4} -2.23607i q^{5} +(0.630492 + 10.6998i) q^{6} -2.64575 q^{7} +17.0233i q^{8} +(8.93772 - 1.05699i) q^{9} -7.98897 q^{10} +12.0685i q^{11} +(26.2487 - 1.54672i) q^{12} -12.7142 q^{13} +9.45268i q^{14} +(0.394601 + 6.69659i) q^{15} +25.7616 q^{16} -22.2556i q^{17} +(-3.77640 - 31.9325i) q^{18} -28.9289 q^{19} +19.5985i q^{20} +(7.92351 - 0.466899i) q^{21} +43.1180 q^{22} -21.9101i q^{23} +(-3.00412 - 50.9815i) q^{24} -5.00000 q^{25} +45.4249i q^{26} +(-26.5802 + 4.74274i) q^{27} +23.1893 q^{28} +11.4122i q^{29} +(23.9254 - 1.40982i) q^{30} -4.93977 q^{31} -23.9470i q^{32} +(-2.12974 - 36.1428i) q^{33} -79.5144 q^{34} +5.91608i q^{35} +(-78.3367 + 9.26426i) q^{36} -36.7045 q^{37} +103.356i q^{38} +(38.0765 - 2.24369i) q^{39} +38.0653 q^{40} -57.6874i q^{41} +(-1.66812 - 28.3089i) q^{42} +57.7493 q^{43} -105.777i q^{44} +(-2.36351 - 19.9853i) q^{45} -78.2798 q^{46} +15.6773i q^{47} +(-77.1508 + 4.54617i) q^{48} +7.00000 q^{49} +17.8639i q^{50} +(3.92747 + 66.6513i) q^{51} +111.436 q^{52} -91.2304i q^{53} +(16.9447 + 94.9651i) q^{54} +26.9860 q^{55} -45.0394i q^{56} +(86.6363 - 5.10511i) q^{57} +40.7733 q^{58} +34.3101i q^{59} +(-3.45857 - 58.6938i) q^{60} +71.1225 q^{61} +17.6487i q^{62} +(-23.6470 + 2.79654i) q^{63} +17.4888 q^{64} +28.4298i q^{65} +(-129.130 + 7.60909i) q^{66} +20.1716 q^{67} +195.065i q^{68} +(3.86649 + 65.6164i) q^{69} +21.1368 q^{70} -69.7718i q^{71} +(17.9935 + 152.150i) q^{72} -96.8693 q^{73} +131.137i q^{74} +(14.9740 - 0.882355i) q^{75} +253.554 q^{76} -31.9302i q^{77} +(-8.01619 - 136.039i) q^{78} -84.2348 q^{79} -57.6046i q^{80} +(78.7655 - 18.8942i) q^{81} -206.104 q^{82} -20.4474i q^{83} +(-69.4474 + 4.09224i) q^{84} -49.7651 q^{85} -206.325i q^{86} +(-2.01393 - 34.1774i) q^{87} -205.446 q^{88} -1.65255i q^{89} +(-71.4031 + 8.44428i) q^{90} +33.6386 q^{91} +192.036i q^{92} +(14.7936 - 0.871726i) q^{93} +56.0116 q^{94} +64.6869i q^{95} +(4.22596 + 71.7167i) q^{96} +29.7125 q^{97} -25.0094i q^{98} +(12.7563 + 107.865i) 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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